LMFDB - Embedded newform 162.2.g.b.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	162.103
Dual form			162.2.g.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686242 - 0.727374i) q^{2} +(-1.70169 + 0.322861i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(0.269488 - 0.0314987i) q^{5} +(1.40261 + 1.01621i) q^{6} +(1.70173 + 0.854643i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.79152 - 1.09882i) q^{9} +O(q^{10})$	\(q+(-0.686242 - 0.727374i) q^{2} +(-1.70169 + 0.322861i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(0.269488 - 0.0314987i) q^{5} +(1.40261 + 1.01621i) q^{6} +(1.70173 + 0.854643i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.79152 - 1.09882i) q^{9} +(-0.207845 - 0.174403i) q^{10} +(0.493535 + 1.14414i) q^{11} +(-0.223370 - 1.71759i) q^{12} +(6.47151 + 1.53378i) q^{13} +(-0.546156 - 1.82429i) q^{14} +(-0.448417 + 0.140608i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(0.874267 - 4.95822i) q^{17} +(-2.71491 - 1.27642i) q^{18} +(0.683318 + 3.87529i) q^{19} +(0.0157760 + 0.270864i) q^{20} +(-3.17176 - 0.904918i) q^{21} +(0.493535 - 1.14414i) q^{22} +(1.82524 - 0.916669i) q^{23} +(-1.09604 + 1.34115i) q^{24} +(-4.79359 + 1.13610i) q^{25} +(-3.32539 - 5.75975i) q^{26} +(-4.39555 + 2.77113i) q^{27} +(-0.952145 + 1.64916i) q^{28} +(-1.75411 + 5.85915i) q^{29} +(0.409997 + 0.229675i) q^{30} +(-1.57574 - 1.03638i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-1.20924 - 1.78764i) q^{33} +(-4.20643 + 2.76662i) q^{34} +(0.485518 + 0.176714i) q^{35} +(0.934648 + 2.85069i) q^{36} +(7.10876 - 2.58738i) q^{37} +(2.34986 - 3.15641i) q^{38} +(-11.5077 - 0.520621i) q^{39} +(0.186193 - 0.197353i) q^{40} +(-0.0646786 + 0.0685554i) q^{41} +(1.51838 + 2.92805i) q^{42} +(0.298821 - 0.401387i) q^{43} +(-1.17090 + 0.426174i) q^{44} +(0.717671 - 0.384048i) q^{45} +(-1.91932 - 0.698574i) q^{46} +(-8.22043 + 5.40667i) q^{47} +(1.72767 - 0.123123i) q^{48} +(-2.01462 - 2.70611i) q^{49} +(4.11593 + 2.70709i) q^{50} +(0.113078 + 8.71963i) q^{51} +(-1.90747 + 6.37138i) q^{52} +(5.41495 - 9.37896i) q^{53} +(5.03205 + 1.29554i) q^{54} +(0.169041 + 0.292787i) q^{55} +(1.85296 - 0.439159i) q^{56} +(-2.41398 - 6.37394i) q^{57} +(5.46554 - 2.74490i) q^{58} +(-0.219677 + 0.509269i) q^{59} +(-0.114297 - 0.455834i) q^{60} +(-0.127382 - 2.18707i) q^{61} +(0.327503 + 1.85736i) q^{62} +(5.68953 + 0.515856i) q^{63} +(0.173648 - 0.984808i) q^{64} +(1.79231 + 0.209491i) q^{65} +(-0.470447 + 2.10632i) q^{66} +(-3.40189 - 11.3631i) q^{67} +(4.89899 + 1.16108i) q^{68} +(-2.81004 + 2.14919i) q^{69} +(-0.204645 - 0.474421i) q^{70} +(3.56320 + 2.98988i) q^{71} +(1.43212 - 2.63610i) q^{72} +(0.592380 - 0.497066i) q^{73} +(-6.76031 - 3.39516i) q^{74} +(7.79042 - 3.48096i) q^{75} +(-3.90846 + 0.456834i) q^{76} +(-0.137968 + 2.36882i) q^{77} +(7.51839 + 8.72768i) q^{78} +(-9.82654 - 10.4155i) q^{79} -0.271323 q^{80} +(6.58519 - 6.13476i) q^{81} +0.0942505 q^{82} +(5.24496 + 5.55933i) q^{83} +(1.08781 - 3.11378i) q^{84} +(0.0794276 - 1.36372i) q^{85} +(-0.497022 + 0.0580935i) q^{86} +(1.09328 - 10.5368i) q^{87} +(1.11351 + 0.559226i) q^{88} +(-8.83168 + 7.41066i) q^{89} +(-0.771842 - 0.258465i) q^{90} +(9.70196 + 8.14091i) q^{91} +(0.808990 + 1.87545i) q^{92} +(3.01604 + 1.25486i) q^{93} +(9.57387 + 2.26905i) q^{94} +(0.306212 + 1.02282i) q^{95} +(-1.27515 - 1.17217i) q^{96} +(3.13232 + 0.366116i) q^{97} +(-0.585834 + 3.32243i) q^{98} +(2.63492 + 2.65159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$3$	−1.70169	+	0.322861i	−0.982473	+	0.186404i
$3$	−1.70169	+	0.322861i	−0.982473	+	0.186404i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	0.269488	−	0.0314987i	0.120519	−	0.0140866i	−0.0556197	−	0.998452i	$-0.517713\pi$
$5$	0.269488	−	0.0314987i	0.120519	−	0.0140866i	0.176138	+	0.984365i	$0.443639\pi$
$6$	1.40261	+	1.01621i	0.572614	+	0.414865i
$7$	1.70173	+	0.854643i	0.643195	+	0.323025i	0.740327	−	0.672247i	$-0.234671\pi$
$7$	1.70173	+	0.854643i	0.643195	+	0.323025i	−0.0971319	+	0.995272i	$0.530967\pi$
$8$	0.766044	−	0.642788i	0.270838	−	0.227260i
$9$	2.79152	−	1.09882i	0.930507	−	0.366273i
$10$	−0.207845	−	0.174403i	−0.0657265	−	0.0551510i
$11$	0.493535	+	1.14414i	0.148806	+	0.344972i	0.976273	−	0.216543i	$-0.0694781\pi$
$11$	0.493535	+	1.14414i	0.148806	+	0.344972i	−0.827467	+	0.561515i	$0.810219\pi$
$12$	−0.223370	−	1.71759i	−0.0644813	−	0.495825i
$13$	6.47151	+	1.53378i	1.79487	+	0.425393i	0.986565	−	0.163367i	$-0.0522354\pi$
$13$	6.47151	+	1.53378i	1.79487	+	0.425393i	0.808308	+	0.588760i	$0.200384\pi$
$14$	−0.546156	−	1.82429i	−0.145966	−	0.487562i
$15$	−0.448417	+	0.140608i	−0.115781	+	0.0363049i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	0.874267	−	4.95822i	0.212041	−	1.20254i	−0.673927	−	0.738798i	$-0.735394\pi$
$17$	0.874267	−	4.95822i	0.212041	−	1.20254i	0.885968	−	0.463746i	$-0.153495\pi$
$18$	−2.71491	−	1.27642i	−0.639911	−	0.300856i
$19$	0.683318	+	3.87529i	0.156764	+	0.889052i	0.957155	+	0.289575i	$0.0935138\pi$
$19$	0.683318	+	3.87529i	0.156764	+	0.889052i	−0.800392	+	0.599477i	$0.795375\pi$
$20$	0.0157760	+	0.270864i	0.00352762	+	0.0605670i
$21$	−3.17176	−	0.904918i	−0.692135	−	0.197469i
$22$	0.493535	−	1.14414i	0.105222	−	0.243932i
$23$	1.82524	−	0.916669i	0.380588	−	0.191139i	−0.248211	−	0.968706i	$-0.579843\pi$
$23$	1.82524	−	0.916669i	0.380588	−	0.191139i	0.628800	+	0.777567i	$0.283546\pi$
$24$	−1.09604	+	1.34115i	−0.223729	+	0.273762i
$25$	−4.79359	+	1.13610i	−0.958719	+	0.227220i
$26$	−3.32539	−	5.75975i	−0.652163	−	1.12958i
$27$	−4.39555	+	2.77113i	−0.845924	+	0.533304i
$28$	−0.952145	+	1.64916i	−0.179938	+	0.311662i
$29$	−1.75411	+	5.85915i	−0.325731	+	1.08802i	0.625677	+	0.780082i	$0.284823\pi$
$29$	−1.75411	+	5.85915i	−0.325731	+	1.08802i	−0.951408	+	0.307934i	$0.900362\pi$
$30$	0.409997	+	0.229675i	0.0748548	+	0.0419328i
$31$	−1.57574	−	1.03638i	−0.283012	−	0.186140i	0.400064	−	0.916487i	$-0.368988\pi$
$31$	−1.57574	−	1.03638i	−0.283012	−	0.186140i	−0.683076	+	0.730347i	$0.739358\pi$
$32$	0.597159	+	0.802123i	0.105564	+	0.141797i
$33$	−1.20924	−	1.78764i	−0.210502	−	0.311188i
$34$	−4.20643	+	2.76662i	−0.721398	+	0.474471i
$35$	0.485518	+	0.176714i	0.0820674	+	0.0298701i
$36$	0.934648	+	2.85069i	0.155775	+	0.475115i
$37$	7.10876	−	2.58738i	1.16867	−	0.425362i	0.316485	−	0.948598i	$-0.397497\pi$
$37$	7.10876	−	2.58738i	1.16867	−	0.425362i	0.852188	+	0.523236i	$0.175275\pi$
$38$	2.34986	−	3.15641i	0.381198	−	0.512038i
$39$	−11.5077	−	0.520621i	−1.84271	−	0.0833661i
$40$	0.186193	−	0.197353i	0.0294397	−	0.0312043i
$41$	−0.0646786	+	0.0685554i	−0.0101011	+	0.0107065i	−0.732404	−	0.680870i	$-0.761602\pi$
$41$	−0.0646786	+	0.0685554i	−0.0101011	+	0.0107065i	0.722303	+	0.691576i	$0.243083\pi$
$42$	1.51838	+	2.92805i	0.234291	+	0.451808i
$43$	0.298821	−	0.401387i	0.0455698	−	0.0612109i	−0.778754	−	0.627329i	$-0.784148\pi$
$43$	0.298821	−	0.401387i	0.0455698	−	0.0612109i	0.824324	+	0.566118i	$0.191555\pi$
$44$	−1.17090	+	0.426174i	−0.176520	+	0.0642482i
$45$	0.717671	−	0.384048i	0.106984	−	0.0572505i
$46$	−1.91932	−	0.698574i	−0.282988	−	0.102999i
$47$	−8.22043	+	5.40667i	−1.19907	+	0.788643i	−0.982252	−	0.187568i	$-0.939940\pi$
$47$	−8.22043	+	5.40667i	−1.19907	+	0.788643i	−0.216822	+	0.976211i	$0.569569\pi$
$48$	1.72767	−	0.123123i	0.249368	−	0.0177713i
$49$	−2.01462	−	2.70611i	−0.287803	−	0.386587i
$50$	4.11593	+	2.70709i	0.582081	+	0.382841i
$51$	0.113078	+	8.71963i	0.0158340	+	1.22099i
$52$	−1.90747	+	6.37138i	−0.264518	+	0.883551i
$53$	5.41495	−	9.37896i	0.743800	−	1.28830i	−0.206953	−	0.978351i	$-0.566355\pi$
$53$	5.41495	−	9.37896i	0.743800	−	1.28830i	0.950753	−	0.309948i	$-0.100312\pi$
$54$	5.03205	+	1.29554i	0.684776	+	0.176301i
$55$	0.169041	+	0.292787i	0.0227935	+	0.0394794i
$56$	1.85296	−	0.439159i	0.247612	−	0.0586851i
$57$	−2.41398	−	6.37394i	−0.319739	−	0.844248i
$58$	5.46554	−	2.74490i	0.717660	−	0.360422i
$59$	−0.219677	+	0.509269i	−0.0285995	+	0.0663011i	−0.931917	−	0.362671i	$-0.881865\pi$
$59$	−0.219677	+	0.509269i	−0.0285995	+	0.0663011i	0.903318	+	0.428972i	$0.141124\pi$
$60$	−0.114297	−	0.455834i	−0.0147557	−	0.0588479i
$61$	−0.127382	−	2.18707i	−0.0163096	−	0.280025i	−0.996596	−	0.0824426i	$-0.973728\pi$
$61$	−0.127382	−	2.18707i	−0.0163096	−	0.280025i	0.980286	−	0.197583i	$-0.0633092\pi$
$62$	0.327503	+	1.85736i	0.0415930	+	0.235885i
$63$	5.68953	+	0.515856i	0.716813	+	0.0649918i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	1.79231	+	0.209491i	0.222308	+	0.0259841i
$66$	−0.470447	+	2.10632i	−0.0579080	+	0.259270i
$67$	−3.40189	−	11.3631i	−0.415607	−	1.38823i	−0.868070	−	0.496442i	$-0.834639\pi$
$67$	−3.40189	−	11.3631i	−0.415607	−	1.38823i	0.452462	−	0.891784i	$-0.350546\pi$
$68$	4.89899	+	1.16108i	0.594090	+	0.140802i
$69$	−2.81004	+	2.14919i	−0.338289	+	0.258732i
$70$	−0.204645	−	0.474421i	−0.0244598	−	0.0567042i
$71$	3.56320	+	2.98988i	0.422874	+	0.354833i	0.829255	−	0.558870i	$-0.188765\pi$
$71$	3.56320	+	2.98988i	0.422874	+	0.354833i	−0.406381	+	0.913704i	$0.633209\pi$
$72$	1.43212	−	2.63610i	0.168777	−	0.310667i
$73$	0.592380	−	0.497066i	0.0693329	−	0.0581772i	−0.607463	−	0.794348i	$-0.707813\pi$
$73$	0.592380	−	0.497066i	0.0693329	−	0.0581772i	0.676796	+	0.736171i	$0.263368\pi$
$74$	−6.76031	−	3.39516i	−0.785871	−	0.394679i
$75$	7.79042	−	3.48096i	0.899561	−	0.401947i
$76$	−3.90846	+	0.456834i	−0.448331	+	0.0524024i
$77$	−0.137968	+	2.36882i	−0.0157229	+	0.269953i
$78$	7.51839	+	8.72768i	0.851290	+	0.988216i
$79$	−9.82654	−	10.4155i	−1.10557	−	1.17184i	−0.983798	−	0.179280i	$-0.942623\pi$
$79$	−9.82654	−	10.4155i	−1.10557	−	1.17184i	−0.121774	−	0.992558i	$-0.538858\pi$
$80$	−0.271323			−0.0303348
$81$	6.58519	−	6.13476i	0.731688	−	0.681640i
$82$	0.0942505			0.0104082
$83$	5.24496	+	5.55933i	0.575709	+	0.610216i	0.948144	−	0.317843i	$-0.102958\pi$
$83$	5.24496	+	5.55933i	0.575709	+	0.610216i	−0.372434	+	0.928059i	$0.621477\pi$
$84$	1.08781	−	3.11378i	0.118690	−	0.339741i
$85$	0.0794276	−	1.36372i	0.00861513	−	0.147916i
$86$	−0.497022	+	0.0580935i	−0.0535952	+	0.00626439i
$87$	1.09328	−	10.5368i	0.117212	−	1.12966i
$88$	1.11351	+	0.559226i	0.118701	+	0.0596137i
$89$	−8.83168	+	7.41066i	−0.936156	+	0.785528i	−0.976912	−	0.213641i	$-0.931468\pi$
$89$	−8.83168	+	7.41066i	−0.936156	+	0.785528i	0.0407561	+	0.999169i	$0.487023\pi$
$90$	−0.771842	−	0.258465i	−0.0813593	−	0.0272446i
$91$	9.70196	+	8.14091i	1.01704	+	0.853399i
$92$	0.808990	+	1.87545i	0.0843430	+	0.195529i
$93$	3.01604	+	1.25486i	0.312749	+	0.130123i
$94$	9.57387	+	2.26905i	0.987469	+	0.234035i
$95$	0.306212	+	1.02282i	0.0314167	+	0.104939i
$96$	−1.27515	−	1.17217i	−0.130145	−	0.119634i
$97$	3.13232	+	0.366116i	0.318039	+	0.0371734i	0.273615	−	0.961839i	$-0.411781\pi$
$97$	3.13232	+	0.366116i	0.318039	+	0.0371734i	0.0444240	+	0.999013i	$0.485855\pi$
$98$	−0.585834	+	3.32243i	−0.0591782	+	0.335616i
$99$	2.63492	+	2.65159i	0.264819	+	0.266495i
$100$	−0.855458	−	4.85154i	−0.0855458	−	0.485154i
$101$	0.656706	+	11.2752i	0.0653447	+	1.12192i	0.858469	+	0.512865i	$0.171416\pi$
$101$	0.656706	+	11.2752i	0.0653447	+	1.12192i	−0.793125	+	0.609059i	$0.791547\pi$
$102$	6.26483	−	6.06602i	0.620311	−	0.600626i
$103$	1.26506	−	2.93275i	0.124651	−	0.288972i	−0.844452	−	0.535632i	$-0.820074\pi$
$103$	1.26506	−	2.93275i	0.124651	−	0.288972i	0.969102	+	0.246659i	$0.0793328\pi$
$104$	5.94335	−	2.98487i	0.582794	−	0.292690i
$105$	−0.883256	−	0.143958i	−0.0861970	−	0.0140489i
$106$	−10.5380	+	2.49754i	−1.02354	+	0.242583i
$107$	−3.58922	−	6.21670i	−0.346983	−	0.600992i	0.638729	−	0.769432i	$-0.279460\pi$
$107$	−3.58922	−	6.21670i	−0.346983	−	0.600992i	−0.985712	+	0.168440i	$0.946127\pi$
$108$	−2.51086	−	4.54924i	−0.241608	−	0.437751i
$109$	−8.59470	+	14.8865i	−0.823223	+	1.42586i	0.0800470	+	0.996791i	$0.474493\pi$
$109$	−8.59470	+	14.8865i	−0.823223	+	1.42586i	−0.903270	+	0.429073i	$0.858840\pi$
$110$	0.0969629	−	0.323879i	0.00924505	−	0.0308806i
$111$	−11.2616	+	6.69806i	−1.06890	+	0.635752i
$112$	−1.59101	−	1.04642i	−0.150336	−	0.0988778i
$113$	−4.23354	−	5.68664i	−0.398258	−	0.534954i	0.557084	−	0.830456i	$-0.311920\pi$
$113$	−4.23354	−	5.68664i	−0.398258	−	0.534954i	−0.955342	+	0.295503i	$0.904513\pi$
$114$	−2.97966	+	6.12992i	−0.279071	+	0.574120i
$115$	0.463006	−	0.304524i	0.0431756	−	0.0283970i
$116$	−5.74724	−	2.09183i	−0.533618	−	0.194221i
$117$	19.7507	−	2.82945i	1.82595	−	0.261583i
$118$	0.521180	−	0.189694i	0.0479785	−	0.0174628i
$119$	5.72528	−	7.69038i	0.524835	−	0.704976i
$120$	−0.253126	+	0.395949i	−0.0231071	+	0.0361450i
$121$	6.48317	−	6.87176i	0.589379	−	0.624706i
$122$	−1.50340	+	1.59351i	−0.136112	+	0.144270i
$123$	0.0879294	−	0.137542i	0.00792833	−	0.0124018i
$124$	1.12625	−	1.51282i	0.101140	−	0.135855i
$125$	−2.53083	+	0.921147i	−0.226364	+	0.0823899i
$126$	−3.52917	−	4.49242i	−0.314404	−	0.400216i
$127$	0.353223	+	0.128563i	0.0313435	+	0.0114081i	0.357644	−	0.933858i	$-0.383580\pi$
$127$	0.353223	+	0.128563i	0.0313435	+	0.0114081i	−0.326301	+	0.945266i	$0.605802\pi$
$128$	−0.835488	+	0.549509i	−0.0738474	+	0.0485702i
$129$	−0.378910	+	0.779515i	−0.0333612	+	0.0686325i
$130$	−1.07758	−	1.44744i	−0.0945098	−	0.126949i
$131$	15.7818	+	10.3799i	1.37886	+	0.906893i	0.999829	−	0.0184896i	$-0.00588575\pi$
$131$	15.7818	+	10.3799i	1.37886	+	0.906893i	0.379035	+	0.925382i	$0.376256\pi$
$132$	1.85492	−	1.10326i	0.161450	−	0.0960261i
$133$	−2.14916	+	7.17871i	−0.186356	+	0.622473i
$134$	−5.93071	+	10.2723i	−0.512335	+	0.887391i
$135$	−1.09726	+	0.885240i	−0.0944373	+	0.0761893i
$136$	−2.51735	−	4.36018i	−0.215861	−	0.373883i
$137$	−21.2886	+	5.04549i	−1.81881	+	0.431066i	−0.991437	−	0.130588i	$-0.958314\pi$
$137$	−21.2886	+	5.04549i	−1.81881	+	0.431066i	−0.827373	+	0.561654i	$0.810165\pi$
$138$	3.49163	+	0.569087i	0.297227	+	0.0484439i
$139$	−16.7788	+	8.42665i	−1.42316	+	0.714739i	−0.983073	−	0.183214i	$-0.941350\pi$
$139$	−16.7788	+	8.42665i	−1.42316	+	0.714739i	−0.440090	+	0.897954i	$0.645053\pi$
$140$	−0.204645	+	0.474421i	−0.0172957	+	0.0400959i
$141$	12.2431	−	11.8545i	1.03105	−	0.998333i
$142$	−0.270456	−	4.64356i	−0.0226962	−	0.389679i
$143$	1.43906	+	8.16130i	0.120340	+	0.682482i
$144$	−2.90021	+	0.767314i	−0.241684	+	0.0639428i
$145$	−0.288158	+	1.63422i	−0.0239302	+	0.135715i
$146$	−0.768069	−	0.0897744i	−0.0635658	−	0.00742978i
$147$	4.30197	+	3.95453i	0.354820	+	0.326164i
$148$	2.16966	+	7.24717i	0.178345	+	0.595714i
$149$	−20.0058	−	4.74145i	−1.63894	−	0.388435i	−0.695117	−	0.718897i	$-0.744647\pi$
$149$	−20.0058	−	4.74145i	−1.63894	−	0.388435i	−0.943819	+	0.330462i	$0.892796\pi$
$150$	−7.87807	−	3.27777i	−0.643242	−	0.267629i
$151$	−8.25827	−	19.1448i	−0.672049	−	1.55798i	−0.822123	−	0.569310i	$-0.807211\pi$
$151$	−8.25827	−	19.1448i	−0.672049	−	1.55798i	0.150074	−	0.988675i	$-0.452049\pi$
$152$	3.01444	+	2.52941i	0.244503	+	0.205163i
$153$	−3.00765	−	14.8016i	−0.243154	−	1.19664i
$154$	1.81770	−	1.52523i	0.146474	−	0.122907i
$155$	−0.457289	−	0.229659i	−0.0367303	−	0.0184467i
$156$	1.18885	−	11.4580i	0.0951845	−	0.917373i
$157$	−18.3959	+	2.15018i	−1.46816	+	0.171603i	−0.812281	−	0.583266i	$-0.801774\pi$
$157$	−18.3959	+	2.15018i	−1.46816	+	0.171603i	−0.655876	+	0.754869i	$0.727700\pi$
$158$	−0.832596	+	14.2951i	−0.0662378	+	1.13726i
$159$	−6.18648	+	17.7084i	−0.490620	+	1.40437i
$160$	0.186193	+	0.197353i	0.0147198	+	0.0156021i
$161$	3.88950			0.306535
$162$	−8.98129	−	0.579967i	−0.705637	−	0.0455665i
$163$	−9.42363			−0.738116			−0.369058	−	0.929406i	$-0.620320\pi$
$163$	−9.42363			−0.738116			−0.369058	+	0.929406i	$0.620320\pi$
$164$	−0.0646786	−	0.0685554i	−0.00505055	−	0.00535327i
$165$	−0.382185	−	0.443658i	−0.0297531	−	0.0345387i
$166$	0.444402	−	7.63009i	0.0344923	−	0.592210i
$167$	7.01514	−	0.819953i	0.542848	−	0.0634498i	0.159750	−	0.987158i	$-0.448931\pi$
$167$	7.01514	−	0.819953i	0.542848	−	0.0634498i	0.383098	+	0.923708i	$0.374857\pi$
$168$	−3.01138	+	1.34556i	−0.232333	+	0.103812i
$169$	27.9107	+	14.0173i	2.14698	+	1.07825i
$170$	−1.04644	+	0.878067i	−0.0802583	+	0.0673447i
$171$	6.16574	+	10.0671i	0.471506	+	0.769851i
$172$	0.383333	+	0.321654i	0.0292288	+	0.0245259i
$173$	−4.95149	−	11.4789i	−0.376455	−	0.872721i	−0.996132	−	0.0878644i	$-0.971996\pi$
$173$	−4.95149	−	11.4789i	−0.376455	−	0.872721i	0.619677	−	0.784857i	$-0.287263\pi$
$174$	−8.41445	+	6.43558i	−0.637898	+	0.487880i
$175$	−9.12839	−	2.16347i	−0.690041	−	0.163543i
$176$	−0.357371	−	1.19370i	−0.0269379	−	0.0899787i
$177$	0.209400	−	0.937544i	0.0157395	−	0.0704701i
$178$	11.4510	+	1.33843i	0.858288	+	0.100319i
$179$	3.97165	−	22.5244i	0.296855	−	1.68355i	−0.362710	−	0.931902i	$-0.618148\pi$
$179$	3.97165	−	22.5244i	0.296855	−	1.68355i	0.659565	−	0.751648i	$-0.270741\pi$
$180$	0.341669	+	0.738787i	0.0254665	+	0.0550659i
$181$	0.424716	+	2.40868i	0.0315689	+	0.179036i	0.996515	−	0.0834113i	$-0.0265815\pi$
$181$	0.424716	+	2.40868i	0.0315689	+	0.179036i	−0.964946	+	0.262447i	$0.915470\pi$
$182$	−0.736405	−	12.6436i	−0.0545860	−	0.937205i
$183$	0.922884	+	3.68059i	0.0682216	+	0.272077i
$184$	0.808990	−	1.87545i	0.0596395	−	0.138260i
$185$	1.83423	−	0.921184i	0.134855	−	0.0677268i
$186$	−1.15698	−	3.05493i	−0.0848339	−	0.223998i
$187$	6.10439	−	1.44677i	0.446397	−	0.105798i
$188$	−4.91954	−	8.52090i	−0.358794	−	0.621450i
$189$	−9.84838	+	0.959096i	−0.716365	+	0.0697640i
$190$	0.533837	−	0.924633i	0.0387286	−	0.0670799i
$191$	1.58267	−	5.28650i	0.114518	−	0.382517i	−0.881444	−	0.472288i	$-0.843428\pi$
$191$	1.58267	−	5.28650i	0.114518	−	0.382517i	0.995962	+	0.0897706i	$0.0286134\pi$
$192$	0.0224596	+	1.73191i	0.00162089	+	0.124989i
$193$	10.3779	+	6.82562i	0.747015	+	0.491319i	0.865047	−	0.501691i	$-0.167288\pi$
$193$	10.3779	+	6.82562i	0.747015	+	0.491319i	−0.118033	+	0.993010i	$0.537659\pi$
$194$	−1.88323	−	2.52961i	−0.135208	−	0.181615i
$195$	−3.11759	+	0.222176i	−0.223256	+	0.0159104i
$196$	2.81867	−	1.85387i	0.201334	−	0.132419i
$197$	14.4936	+	5.27523i	1.03263	+	0.375845i	0.802080	−	0.597217i	$-0.203727\pi$
$197$	14.4936	+	5.27523i	1.03263	+	0.375845i	0.230545	+	0.973062i	$0.425949\pi$
$198$	0.120507	−	3.73621i	0.00856408	−	0.265521i
$199$	13.6122	−	4.95444i	0.964944	−	0.351211i	0.188975	−	0.981982i	$-0.439483\pi$
$199$	13.6122	−	4.95444i	0.964944	−	0.351211i	0.775969	+	0.630771i	$0.217261\pi$
$200$	−2.94183	+	3.95157i	−0.208019	+	0.279418i
$201$	9.45768	+	18.2382i	0.667094	+	1.28642i
$202$	7.75063	−	8.21518i	0.545332	−	0.578018i
$203$	−7.99252	+	8.47158i	−0.560965	+	0.594588i
$204$	−8.71146	−	0.394115i	−0.609924	−	0.0275936i
$205$	−0.0152707	+	0.0205121i	−0.00106655	+	0.00143263i
$206$	−3.00134	+	1.09240i	−0.209114	+	0.0761111i
$207$	4.08794	−	4.56451i	0.284131	−	0.317255i
$208$	−6.24969	−	2.27470i	−0.433338	−	0.157722i
$209$	−4.09664	+	2.69440i	−0.283371	+	0.186376i
$210$	0.501415	+	0.741247i	0.0346010	+	0.0511509i
$211$	2.11061	+	2.83504i	0.145301	+	0.195172i	0.868815	−	0.495137i	$-0.164882\pi$
$211$	2.11061	+	2.83504i	0.145301	+	0.195172i	−0.723515	+	0.690309i	$0.757475\pi$
$212$	9.04824	+	5.95112i	0.621436	+	0.408725i
$213$	−7.02879	−	3.93744i	−0.481605	−	0.269789i
$214$	−2.05880	+	6.87686i	−0.140737	+	0.470093i
$215$	0.0678857	−	0.117581i	0.00462977	−	0.00801899i
$216$	−1.58594	+	4.94821i	−0.107910	+	0.336683i
$217$	−1.79576	−	3.11035i	−0.121904	−	0.211144i
$218$	16.7261	−	3.96415i	1.13283	−	0.268486i
$219$	−0.847567	+	1.03711i	−0.0572733	+	0.0700814i
$220$	−0.302121	+	0.151731i	−0.0203690	+	0.0102297i
$221$	13.2626	−	30.7462i	0.892140	−	2.06821i
$222$	12.6001	+	3.59488i	0.845666	+	0.241272i
$223$	−0.677162	−	11.6264i	−0.0453461	−	0.778562i	−0.941955	−	0.335739i	$-0.891014\pi$
$223$	−0.677162	−	11.6264i	−0.0453461	−	0.778562i	0.896609	−	0.442823i	$-0.146023\pi$
$224$	0.330676	+	1.87536i	0.0220942	+	0.125303i
$225$	−12.1330	+	8.43875i	−0.808870	+	0.562583i
$226$	−1.23108	+	6.98177i	−0.0818899	+	0.464421i
$227$	24.6339	+	2.87929i	1.63501	+	0.191105i	0.883438	−	0.468548i	$-0.155223\pi$
$227$	24.6339	+	2.87929i	1.63501	+	0.191105i	0.751571	+	0.659653i	$0.229297\pi$
$228$	6.50351	−	2.03928i	0.430706	−	0.135055i
$229$	3.07611	+	10.2749i	0.203275	+	0.678987i	0.997455	+	0.0713035i	$0.0227159\pi$
$229$	3.07611	+	10.2749i	0.203275	+	0.678987i	−0.794179	+	0.607683i	$0.792099\pi$
$230$	−0.539237	−	0.127801i	−0.0355562	−	0.00842698i
$231$	−0.530020	−	4.07556i	−0.0348728	−	0.268152i
$232$	2.42246	+	5.61589i	0.159042	+	0.368701i
$233$	14.6151	+	12.2635i	0.957466	+	0.803410i	0.980539	−	0.196324i	$-0.0629005\pi$
$233$	14.6151	+	12.2635i	0.957466	+	0.803410i	−0.0230728	+	0.999734i	$0.507345\pi$
$234$	−15.6118	−	12.4245i	−1.02058	−	0.812212i
$235$	−2.04501	+	1.71596i	−0.133402	+	0.111937i
$236$	−0.495634	−	0.248917i	−0.0322630	−	0.0162031i
$237$	20.0845	+	14.5514i	1.30463	+	0.945216i
$238$	−9.52271	+	1.11304i	−0.617265	+	0.0721480i
$239$	1.00152	−	17.1955i	0.0647831	−	1.11228i	−0.796660	−	0.604428i	$-0.793402\pi$
$239$	1.00152	−	17.1955i	0.0647831	−	1.11228i	0.861443	−	0.507855i	$-0.169561\pi$
$240$	0.461708	−	0.0875994i	0.0298031	−	0.00565452i
$241$	−5.66871	−	6.00848i	−0.365153	−	0.387040i	0.518581	−	0.855028i	$-0.326460\pi$
$241$	−5.66871	−	6.00848i	−0.365153	−	0.387040i	−0.883735	+	0.467988i	$0.844979\pi$
$242$	−9.44736			−0.607299
$243$	−9.22530	+	12.5656i	−0.591804	+	0.806082i
$244$	2.19078			0.140250
$245$	−0.628156	−	0.665807i	−0.0401314	−	0.0425368i
$246$	−0.160386	+	0.0304298i	−0.0102258	+	0.00194013i
$247$	−1.52173	+	26.1270i	−0.0968251	+	1.66242i
$248$	−1.87326	+	0.218953i	−0.118952	+	0.0139035i
$249$	−10.7202	−	7.76689i	−0.679365	−	0.492207i
$250$	2.40678	+	1.20873i	0.152218	+	0.0764468i
$251$	−12.1672	+	10.2095i	−0.767984	+	0.644415i	−0.940192	−	0.340646i	$-0.889354\pi$
$251$	−12.1672	+	10.2095i	−0.767984	+	0.644415i	0.172208	+	0.985061i	$0.444910\pi$
$252$	−0.845800	+	5.64991i	−0.0532804	+	0.355911i
$253$	1.94962	+	1.63592i	0.122572	+	0.102850i
$254$	−0.148883	−	0.345150i	−0.00934177	−	0.0216567i
$255$	0.305130	+	2.34628i	0.0191080	+	0.146930i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	3.75815	+	12.5531i	0.234427	+	0.783041i	0.991545	+	0.129763i	$0.0414216\pi$
$257$	3.75815	+	12.5531i	0.234427	+	0.783041i	−0.757118	+	0.653278i	$0.773393\pi$
$258$	0.827023	−	0.259326i	0.0514882	−	0.0161449i
$259$	14.3085	+	1.67242i	0.889087	+	0.103919i
$260$	−0.313350	+	1.77709i	−0.0194331	+	0.110211i
$261$	1.54150	+	18.2834i	0.0954165	+	1.13171i
$262$	−3.28010	−	18.6024i	−0.202645	−	1.14926i
$263$	−1.18342	−	20.3185i	−0.0729728	−	1.25290i	−0.813778	−	0.581176i	$-0.802593\pi$
$263$	−1.18342	−	20.3185i	−0.0729728	−	1.25290i	0.740805	−	0.671720i	$-0.234444\pi$
$264$	−2.07541	−	0.592123i	−0.127732	−	0.0364426i
$265$	1.16384	−	2.69808i	0.0714941	−	0.165742i
$266$	6.69645	−	3.36308i	0.410585	−	0.206204i
$267$	12.6362	−	15.4621i	0.773323	−	0.946263i
$268$	11.5417	−	2.73543i	0.705021	−	0.167093i
$269$	−5.12459	−	8.87605i	−0.312452	−	0.541183i	0.666441	−	0.745558i	$-0.267817\pi$
$269$	−5.12459	−	8.87605i	−0.312452	−	0.541183i	−0.978893	+	0.204376i	$0.934484\pi$
$270$	1.39689	+	0.190631i	0.0850118	+	0.0116014i
$271$	−0.993514	+	1.72082i	−0.0603517	+	0.104532i	−0.894623	−	0.446823i	$-0.852556\pi$
$271$	−0.993514	+	1.72082i	−0.0603517	+	0.104532i	0.834271	+	0.551355i	$0.185889\pi$
$272$	−1.44397	+	4.82319i	−0.0875535	+	0.292449i
$273$	−19.1381	−	10.7210i	−1.15829	−	0.648862i
$274$	18.2791	+	12.0224i	1.10428	+	0.726297i
$275$	−3.66567	−	4.92385i	−0.221048	−	0.296919i
$276$	−1.98216	−	2.93025i	−0.119312	−	0.176380i
$277$	−21.8689	+	14.3834i	−1.31397	+	0.864213i	−0.996462	−	0.0840422i	$-0.973217\pi$
$277$	−21.8689	+	14.3834i	−1.31397	+	0.864213i	−0.317510	+	0.948255i	$0.602847\pi$
$278$	17.6437	+	6.42177i	1.05820	+	0.385152i
$279$	−5.53752	−	1.16163i	−0.331523	−	0.0695448i
$280$	0.485518	−	0.176714i	0.0290152	−	0.0105607i
$281$	11.6555	−	15.6561i	0.695309	−	0.933963i	−0.304519	−	0.952506i	$-0.598496\pi$
$281$	11.6555	−	15.6561i	0.695309	−	0.933963i	0.999828	+	0.0185438i	$0.00590302\pi$
$282$	−17.0244	−	0.770200i	−1.01379	−	0.0458648i
$283$	3.98059	−	4.21918i	0.236621	−	0.250804i	−0.598172	−	0.801368i	$-0.704106\pi$
$283$	3.98059	−	4.21918i	0.236621	−	0.250804i	0.834793	+	0.550564i	$0.185587\pi$
$284$	−3.19200	+	3.38333i	−0.189411	+	0.200763i
$285$	−0.851308	−	1.64166i	−0.0504271	−	0.0972438i
$286$	4.94877	−	6.64736i	0.292627	−	0.393066i
$287$	−0.168656	+	0.0613859i	−0.00995547	+	0.00362349i
$288$	2.54837	+	1.58297i	0.150164	+	0.0932777i
$289$	−7.84480	−	2.85527i	−0.461459	−	0.167957i
$290$	1.38644	−	0.911874i	0.0814144	−	0.0535471i
$291$	−5.44845	+	0.388286i	−0.319394	+	0.0227617i
$292$	0.461781	+	0.620280i	0.0270237	+	0.0362991i
$293$	−22.2542	−	14.6368i	−1.30010	−	0.855092i	−0.304851	−	0.952400i	$-0.598607\pi$
$293$	−22.2542	−	14.6368i	−1.30010	−	0.855092i	−0.995254	+	0.0973078i	$0.968977\pi$
$294$	−0.0757717	−	5.84290i	−0.00441910	−	0.340765i
$295$	−0.0431591	+	0.144161i	−0.00251282	+	0.00839340i
$296$	3.78249	−	6.55147i	0.219853	−	0.380796i
$297$	−5.33992	−	3.66149i	−0.309854	−	0.212461i
$298$	10.2800	+	17.8054i	0.595503	+	1.03144i
$299$	13.2180	−	3.13273i	0.764417	−	0.181170i
$300$	3.02210	+	7.97964i	0.174481	+	0.460705i
$301$	0.851557	−	0.427668i	0.0490829	−	0.0246504i
$302$	−8.25827	+	19.1448i	−0.475210	+	1.10166i
$303$	−4.75783	−	18.9749i	−0.273330	−	1.09008i
$304$	−0.228804	−	3.92841i	−0.0131228	−	0.225310i
$305$	−0.103218	−	0.585377i	−0.00591023	−	0.0335186i
$306$	−8.70234	+	12.3452i	−0.497480	+	0.705727i
$307$	2.64875	−	15.0218i	0.151172	−	0.857338i	−0.811031	−	0.585004i	$-0.801093\pi$
$307$	2.64875	−	15.0218i	0.151172	−	0.857338i	0.962203	−	0.272335i	$-0.0877958\pi$
$308$	−2.35679	−	0.275470i	−0.134291	−	0.0156963i
$309$	−1.20588	+	5.39908i	−0.0686003	+	0.307143i
$310$	0.146763	+	0.490222i	0.00833556	+	0.0278427i
$311$	−7.54747	−	1.78878i	−0.427978	−	0.101433i	0.0109813	−	0.999940i	$-0.496504\pi$
$311$	−7.54747	−	1.78878i	−0.427978	−	0.101433i	−0.438959	+	0.898507i	$0.644653\pi$
$312$	−9.15007	+	6.99820i	−0.518021	+	0.396195i
$313$	3.38888	+	7.85630i	0.191551	+	0.444064i	0.986743	−	0.162293i	$-0.0518891\pi$
$313$	3.38888	+	7.85630i	0.191551	+	0.444064i	−0.795192	+	0.606358i	$0.792630\pi$
$314$	14.1880	+	11.9052i	0.800678	+	0.671849i
$315$	1.54951	−	0.0401954i	0.0873050	−	0.00226475i
$316$	10.9693	−	9.20430i	0.617069	−	0.517783i
$317$	−7.26843	−	3.65034i	−0.408236	−	0.205024i	0.232817	−	0.972521i	$-0.425206\pi$
$317$	−7.26843	−	3.65034i	−0.408236	−	0.205024i	−0.641053	+	0.767497i	$0.721502\pi$
$318$	17.1260	−	7.65235i	0.960380	−	0.429123i
$319$	−7.56942	+	0.884738i	−0.423806	+	0.0495358i
$320$	0.0157760	−	0.270864i	0.000881906	−	0.0151417i
$321$	8.11488	+	9.42011i	0.452928	+	0.525779i
$322$	−2.66913	−	2.82912i	−0.148745	−	0.157661i
$323$	19.8119			1.10236
$324$	5.74148	+	6.93075i	0.318971	+	0.385042i
$325$	−32.7643			−1.81744
$326$	6.46689	+	6.85450i	0.358168	+	0.379636i
$327$	9.81929	−	28.1071i	0.543008	−	1.55432i
$328$	−0.00548018	+	0.0940911i	−0.000302592	+	0.00519531i
$329$	−18.6098	+	2.17517i	−1.02599	+	0.119921i
$330$	−0.0604335	+	0.582448i	−0.00332675	+	0.0320627i
$331$	25.1810	+	12.6464i	1.38408	+	0.695109i	0.975986	−	0.217833i	$-0.0698989\pi$
$331$	25.1810	+	12.6464i	1.38408	+	0.695109i	0.408089	+	0.912942i	$0.366195\pi$
$332$	−5.85489	+	4.91284i	−0.321329	+	0.269627i
$333$	17.0012	−	15.0340i	0.931660	−	0.823856i
$334$	−5.41049	−	4.53994i	−0.296049	−	0.248415i
$335$	−1.27469	−	2.95507i	−0.0696439	−	0.161453i
$336$	3.04526	+	1.26702i	0.166133	+	0.0691215i
$337$	1.19228	+	0.282575i	0.0649475	+	0.0153928i	0.262961	−	0.964806i	$-0.415301\pi$
$337$	1.19228	+	0.282575i	0.0649475	+	0.0153928i	−0.198014	+	0.980199i	$0.563449\pi$
$338$	−8.95769	−	29.9208i	−0.487234	−	1.62748i
$339$	9.04019	+	8.31007i	0.490995	+	0.451341i
$340$	1.35679	+	0.158586i	0.0735825	+	0.00860056i
$341$	0.408085	−	2.31437i	0.0220991	−	0.125330i
$342$	3.09136	−	11.3933i	0.167162	−	0.616077i
$343$	−3.43033	−	19.4544i	−0.185220	−	1.05044i
$344$	−0.0290960	−	0.499559i	−0.00156875	−	0.0269344i
$345$	−0.689576	+	0.667693i	−0.0371255	+	0.0359474i
$346$	−4.95149	+	11.4789i	−0.266194	+	0.617107i
$347$	−30.8028	+	15.4697i	−1.65358	+	0.830458i	−0.656479	+	0.754344i	$0.727955\pi$
$347$	−30.8028	+	15.4697i	−1.65358	+	0.830458i	−0.997099	+	0.0761143i	$0.975749\pi$
$348$	10.4554	+	1.70409i	0.560469	+	0.0913487i
$349$	22.3937	−	5.30741i	1.19871	−	0.284099i	0.417680	−	0.908594i	$-0.362843\pi$
$349$	22.3937	−	5.30741i	1.19871	−	0.284099i	0.781029	+	0.624495i	$0.214695\pi$
$350$	4.69063	+	8.12441i	0.250725	+	0.434268i
$351$	−32.6961	+	11.1916i	−1.74519	+	0.597363i
$352$	−0.623025	+	1.07911i	−0.0332073	+	0.0575168i
$353$	−5.52530	+	18.4558i	−0.294082	+	0.982303i	0.675464	+	0.737393i	$0.263943\pi$
$353$	−5.52530	+	18.4558i	−0.294082	+	0.982303i	−0.969546	+	0.244910i	$0.921242\pi$
$354$	−0.825644	+	0.491070i	−0.0438825	+	0.0261001i
$355$	1.05442	+	0.693501i	0.0559627	+	0.0368072i
$356$	−6.88460	−	9.24763i	−0.364883	−	0.490123i
$357$	−7.25975	+	14.9351i	−0.384227	+	0.790452i
$358$	−19.1091	+	12.5683i	−1.00995	+	0.664254i
$359$	−17.2240	−	6.26901i	−0.909046	−	0.330866i	−0.155174	−	0.987887i	$-0.549594\pi$
$359$	−17.2240	−	6.26901i	−0.909046	−	0.330866i	−0.753872	+	0.657021i	$0.771816\pi$
$360$	0.302906	−	0.755508i	0.0159646	−	0.0398188i
$361$	3.30323	−	1.20228i	0.173854	−	0.0632777i
$362$	1.46055	−	1.96187i	0.0767651	−	0.103113i
$363$	−8.81375	+	13.7868i	−0.462602	+	0.723619i
$364$	−8.69126	+	9.21219i	−0.455546	+	0.482850i
$365$	0.143983	−	0.152613i	0.00753639	−	0.00798811i
$366$	2.04385	−	3.19706i	0.106834	−	0.167113i
$367$	−0.704887	+	0.946827i	−0.0367948	+	0.0494240i	−0.820140	−	0.572163i	$-0.806104\pi$
$367$	−0.704887	+	0.946827i	−0.0367948	+	0.0494240i	0.783345	+	0.621587i	$0.213512\pi$
$368$	−1.91932	+	0.698574i	−0.100051	+	0.0364157i
$369$	−0.105222	+	0.262444i	−0.00547763	+	0.0136623i
$370$	−1.92877	−	0.702014i	−0.100272	−	0.0364960i
$371$	17.2305	−	11.3327i	0.894561	−	0.588362i
$372$	−1.42810	+	2.93797i	−0.0740438	+	0.152327i
$373$	1.97074	+	2.64717i	0.102041	+	0.137065i	0.850211	−	0.526442i	$-0.176474\pi$
$373$	1.97074	+	2.64717i	0.102041	+	0.137065i	−0.748170	+	0.663508i	$0.769067\pi$
$374$	−5.24143	−	3.44734i	−0.271028	−	0.178258i
$375$	4.00930	−	2.38462i	0.207039	−	0.123141i
$376$	−2.82188	+	9.42574i	−0.145527	+	0.486095i
$377$	−20.3384	+	35.2271i	−1.04748	+	1.81429i
$378$	7.45599	+	6.50528i	0.383495	+	0.334596i
$379$	0.989661	+	1.71414i	0.0508355	+	0.0880497i	0.890323	−	0.455329i	$-0.150478\pi$
$379$	0.989661	+	1.71414i	0.0508355	+	0.0880497i	−0.839488	+	0.543378i	$0.817145\pi$
$380$	−1.03889	+	0.246223i	−0.0532942	+	0.0126310i
$381$	−0.642585	−	0.104732i	−0.0329206	−	0.00536561i
$382$	−4.93135	+	2.47662i	−0.252310	+	0.126715i
$383$	1.36101	−	3.15517i	0.0695442	−	0.161222i	−0.879899	−	0.475161i	$-0.842390\pi$
$383$	1.36101	−	3.15517i	0.0695442	−	0.161222i	0.949443	+	0.313940i	$0.101649\pi$
$384$	1.24433	−	1.20484i	0.0634994	−	0.0614843i
$385$	0.0374339	+	0.642716i	0.00190781	+	0.0327558i
$386$	−2.15694	−	12.2326i	−0.109785	−	0.622623i
$387$	0.393115	−	1.44883i	0.0199831	−	0.0736482i
$388$	−0.547624	+	3.10573i	−0.0278014	+	0.157670i
$389$	−7.37009	−	0.861440i	−0.373678	−	0.0436767i	−0.0728188	−	0.997345i	$-0.523199\pi$
$389$	−7.37009	−	0.861440i	−0.373678	−	0.0436767i	−0.300860	+	0.953668i	$0.597274\pi$
$390$	2.30103	+	2.11519i	0.116517	+	0.107107i
$391$	−2.94930	−	9.85134i	−0.149152	−	0.498204i
$392$	−3.28275	−	0.778025i	−0.165804	−	0.0392962i
$393$	−30.2071	−	12.5680i	−1.52374	−	0.633973i
$394$	−6.10904	−	14.1623i	−0.307769	−	0.713488i
$395$	−2.97621	−	2.49734i	−0.149749	−	0.125655i
$396$	−2.80031	+	2.47629i	−0.140721	+	0.124438i
$397$	−1.63802	+	1.37446i	−0.0822097	+	0.0689822i	−0.682966	−	0.730450i	$-0.739310\pi$
$397$	−1.63802	+	1.37446i	−0.0822097	+	0.0689822i	0.600757	+	0.799432i	$0.294866\pi$
$398$	−12.9450	−	6.50122i	−0.648874	−	0.325877i
$399$	1.33950	−	12.9098i	0.0670587	−	0.646300i
$400$	4.89307	−	0.571918i	0.244654	−	0.0285959i
$401$	−0.751896	+	12.9096i	−0.0375479	+	0.644672i	0.926064	+	0.377367i	$0.123170\pi$
$401$	−0.751896	+	12.9096i	−0.0375479	+	0.644672i	−0.963612	+	0.267306i	$0.913867\pi$
$402$	6.77573	−	19.3951i	0.337943	−	0.967339i
$403$	−8.60786	−	9.12380i	−0.428788	−	0.454489i
$404$	−11.2943			−0.561913
$405$	1.58139	−	1.86067i	0.0785801	−	0.0924574i
$406$	11.6468			0.578021
$407$	6.46875	+	6.85647i	0.320644	+	0.339863i
$408$	5.69149	+	6.60694i	0.281771	+	0.327092i
$409$	−1.05733	+	18.1537i	−0.0522816	+	0.897641i	0.865588	+	0.500758i	$0.166945\pi$
$409$	−1.05733	+	18.1537i	−0.0522816	+	0.897641i	−0.917869	+	0.396883i	$0.870092\pi$
$410$	0.0253994	−	0.00296876i	0.00125439	−	0.000146617i
$411$	34.5977	−	15.4591i	1.70658	−	0.762543i
$412$	2.85423	+	1.43345i	0.140618	+	0.0706209i
$413$	−0.809075	+	0.678895i	−0.0398120	+	0.0334062i
$414$	−6.12542	+	0.158898i	−0.301048	+	0.00780939i
$415$	1.58857	+	1.33297i	0.0779796	+	0.0654327i
$416$	2.63424	+	6.10685i	0.129154	+	0.299413i
$417$	25.8318	−	19.7568i	1.26499	−	0.967495i
$418$	4.77112	+	1.13078i	0.233363	+	0.0553081i
$419$	8.37066	+	27.9600i	0.408934	+	1.36593i	0.876256	+	0.481846i	$0.160034\pi$
$419$	8.37066	+	27.9600i	0.408934	+	1.36593i	−0.467322	+	0.884087i	$0.654781\pi$
$420$	0.195072	−	0.873391i	0.00951852	−	0.0426171i
$421$	−28.0994	−	3.28435i	−1.36948	−	0.160069i	−0.600645	−	0.799516i	$-0.705090\pi$
$421$	−28.0994	−	3.28435i	−1.36948	−	0.160069i	−0.768836	+	0.639446i	$0.779164\pi$
$422$	0.613746	−	3.48073i	0.0298767	−	0.169439i
$423$	−17.0066	+	24.1256i	−0.826888	+	1.17303i
$424$	−1.88059	−	10.6654i	−0.0913296	−	0.517956i
$425$	1.44216	+	24.7609i	0.0699550	+	1.20108i
$426$	1.95946	+	7.81459i	0.0949360	+	0.378618i
$427$	1.65239	−	3.83068i	0.0799649	−	0.185380i
$428$	6.41488	−	3.22167i	0.310075	−	0.155726i
$429$	−5.08380	−	13.4234i	−0.245448	−	0.648089i
$430$	−0.132112	+	0.0313110i	−0.00637099	+	0.00150995i
$431$	1.11221	+	1.92640i	0.0535731	+	0.0927913i	0.891568	−	0.452886i	$-0.149606\pi$
$431$	1.11221	+	1.92640i	0.0535731	+	0.0927913i	−0.837995	+	0.545678i	$0.816272\pi$
$432$	4.68754	−	2.24210i	0.225529	−	0.107873i
$433$	12.3517	−	21.3937i	0.593584	−	1.02812i	−0.400161	−	0.916445i	$-0.631046\pi$
$433$	12.3517	−	21.3937i	0.593584	−	1.02812i	0.993745	−	0.111673i	$-0.0356209\pi$
$434$	−1.03006	+	3.44064i	−0.0494444	+	0.165156i
$435$	−0.0372703	−	2.87398i	−0.00178697	−	0.137797i
$436$	−14.3615	−	9.44573i	−0.687793	−	0.452368i
$437$	4.79957	+	6.44695i	0.229595	+	0.308399i
$438$	1.33600	−	0.0952107i	0.0638367	−	0.00454934i
$439$	−10.2024	+	6.71023i	−0.486934	+	0.320262i	−0.769127	−	0.639096i	$-0.779309\pi$
$439$	−10.2024	+	6.71023i	−0.486934	+	0.320262i	0.282193	+	0.959358i	$0.408938\pi$
$440$	0.317693	+	0.115631i	0.0151454	+	0.00551248i
$441$	−8.59739	−	5.34046i	−0.409400	−	0.254307i
$442$	−31.4653	+	11.4524i	−1.49665	+	0.544737i
$443$	−6.78996	+	9.12050i	−0.322601	+	0.433328i	−0.933607	−	0.358297i	$-0.883357\pi$
$443$	−6.78996	+	9.12050i	−0.322601	+	0.433328i	0.611007	+	0.791625i	$0.290765\pi$
$444$	−6.03193	−	11.6320i	−0.286263	−	0.552029i
$445$	−2.14661	+	2.27527i	−0.101759	+	0.107858i
$446$	−7.99205	+	8.47108i	−0.378435	+	0.401117i
$447$	35.5745	+	1.60943i	1.68262	+	0.0761233i
$448$	1.13716	−	1.52747i	0.0537259	−	0.0721664i
$449$	23.8642	−	8.68587i	1.12622	−	0.409911i	0.289303	−	0.957238i	$-0.406577\pi$
$449$	23.8642	−	8.68587i	1.12622	−	0.409911i	0.836919	+	0.547326i	$0.184354\pi$
$450$	14.4643	+	3.03424i	0.681855	+	0.143035i
$451$	−0.110358	−	0.0401671i	−0.00519657	−	0.00189140i
$452$	5.92317	−	3.89573i	0.278603	−	0.183240i
$453$	20.2342	+	29.9124i	0.950684	+	1.40541i
$454$	−14.8105	−	19.8939i	−0.695090	−	0.933668i
$455$	2.87099	+	1.88828i	0.134594	+	0.0885240i
$456$	−5.94630	−	3.33104i	−0.278461	−	0.155990i
$457$	0.944041	−	3.15332i	0.0441604	−	0.147506i	−0.933066	−	0.359705i	$-0.882877\pi$
$457$	0.944041	−	3.15332i	0.0441604	−	0.147506i	0.977226	+	0.212199i	$0.0680625\pi$
$458$	5.36276	−	9.28857i	0.250585	−	0.434027i
$459$	9.89696	+	24.2168i	0.461951	+	1.13034i
$460$	0.277087	+	0.479929i	0.0129193	+	0.0223768i
$461$	11.8525	−	2.80910i	0.552028	−	0.130833i	0.0548706	−	0.998493i	$-0.482525\pi$
$461$	11.8525	−	2.80910i	0.552028	−	0.130833i	0.497157	+	0.867660i	$0.334377\pi$
$462$	−2.60073	+	3.18234i	−0.120997	+	0.148056i
$463$	−1.37839	+	0.692252i	−0.0640591	+	0.0321717i	−0.480540	−	0.876973i	$-0.659559\pi$
$463$	−1.37839	+	0.692252i	−0.0640591	+	0.0321717i	0.416481	+	0.909144i	$0.363263\pi$
$464$	2.42246	−	5.61589i	0.112460	−	0.260711i
$465$	0.852313	+	0.243169i	0.0395251	+	0.0112767i
$466$	−1.10932	−	19.0464i	−0.0513885	−	0.882306i
$467$	4.46037	+	25.2960i	0.206402	+	1.17056i	0.895219	+	0.445626i	$0.147019\pi$
$467$	4.46037	+	25.2960i	0.206402	+	1.17056i	−0.688818	+	0.724935i	$0.741870\pi$
$468$	1.67626	+	19.8818i	0.0774853	+	0.919037i
$469$	3.92229	−	22.2444i	0.181115	−	1.02715i
$470$	2.65152	+	0.309918i	0.122305	+	0.0142954i
$471$	30.6101	−	9.59827i	1.41044	−	0.442265i
$472$	0.159069	+	0.531328i	0.00732175	+	0.0244564i
$473$	0.606723	+	0.143796i	0.0278971	+	0.00661174i
$474$	−3.19851	−	24.5947i	−0.146912	−	1.12967i
$475$	−7.67827	−	17.8002i	−0.352303	−	0.816731i
$476$	7.34448	+	6.16275i	0.336634	+	0.282469i
$477$	4.81015	−	32.1316i	0.220242	−	1.47121i
$478$	−13.1948	+	11.0718i	−0.603517	+	0.506411i
$479$	7.75830	+	3.89636i	0.354486	+	0.178029i	0.617126	−	0.786864i	$-0.288297\pi$
$479$	7.75830	+	3.89636i	0.354486	+	0.178029i	−0.262640	+	0.964894i	$0.584593\pi$
$480$	−0.380561	−	0.275720i	−0.0173702	−	0.0125848i
$481$	49.9728	−	5.84099i	2.27857	−	0.266326i
$482$	−0.480306	+	8.24654i	−0.0218773	+	0.375619i
$483$	−6.61873	+	1.25577i	−0.301163	+	0.0571393i
$484$	6.48317	+	6.87176i	0.294690	+	0.312353i
$485$	0.855655			0.0388533
$486$	15.4707	−	1.91278i	0.701763	−	0.0867654i
$487$	20.3116			0.920406			0.460203	−	0.887814i	$-0.347777\pi$
$487$	20.3116			0.920406			0.460203	+	0.887814i	$0.347777\pi$
$488$	−1.50340	−	1.59351i	−0.0680558	−	0.0721349i
$489$	16.0361	−	3.04252i	0.725179	−	0.137587i
$490$	−0.0532233	+	0.913808i	−0.00240438	+	0.0412817i
$491$	30.1909	−	3.52881i	1.36250	−	0.159253i	0.596767	−	0.802414i	$-0.296452\pi$
$491$	30.1909	−	3.52881i	1.36250	−	0.159253i	0.765731	+	0.643161i	$0.222377\pi$
$492$	0.132197	+	0.0957780i	0.00595990	+	0.00431801i
$493$	27.5174	+	13.8197i	1.23932	+	0.622410i
$494$	20.0484	−	16.8226i	0.902019	−	0.756884i
$495$	0.793602	+	0.631577i	0.0356697	+	0.0283873i
$496$	1.44477	+	1.21231i	0.0648722	+	0.0544342i
$497$	3.50834	+	8.13325i	0.157371	+	0.364826i
$498$	1.70722	+	13.1276i	0.0765023	+	0.588260i
$499$	0.134422	+	0.0318587i	0.00601757	+	0.00142619i	0.233624	−	0.972327i	$-0.424942\pi$
$499$	0.134422	+	0.0318587i	0.00601757	+	0.00142619i	−0.227606	+	0.973753i	$0.573090\pi$
$500$	−0.772434	−	2.58011i	−0.0345443	−	0.115386i
$501$	−11.6729	+	3.66022i	−0.521506	+	0.163527i
$502$	15.7757	+	1.84391i	0.704104	+	0.0822979i
$503$	0.575906	−	3.26613i	0.0256784	−	0.145629i	−0.969273	−	0.245988i	$-0.920888\pi$
$503$	0.575906	−	3.26613i	0.0256784	−	0.145629i	0.994951	+	0.100358i	$0.0319989\pi$
$504$	4.69002	−	3.26199i	0.208910	−	0.145301i
$505$	0.532128	+	3.01785i	0.0236794	+	0.134292i
$506$	−0.147981	−	2.54074i	−0.00657857	−	0.112950i
$507$	−52.0211	−	14.8419i	−2.31034	−	0.659150i
$508$	−0.148883	+	0.345150i	−0.00660563	+	0.0153136i
$509$	10.5474	−	5.29710i	0.467505	−	0.234790i	−0.199421	−	0.979914i	$-0.563906\pi$
$509$	10.5474	−	5.29710i	0.467505	−	0.234790i	0.666926	+	0.745124i	$0.267610\pi$
$510$	1.49723	−	1.83206i	0.0662983	−	0.0811248i
$511$	1.43289	−	0.339601i	0.0633873	−	0.0150231i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	−13.7425	−	15.1405i	−0.606745	−	0.668468i
$514$	6.55179	−	11.3480i	0.288987	−	0.500541i
$515$	0.248542	−	0.830189i	0.0109521	−	0.0365825i
$516$	−0.756164	−	0.423594i	−0.0332883	−	0.0186477i
$517$	−10.2431	−	6.73697i	−0.450490	−	0.296292i
$518$	−8.60261	−	11.5553i	−0.377977	−	0.507711i
$519$	12.1320	+	17.9348i	0.532536	+	0.787253i
$520$	1.50764	−	0.991594i	0.0661146	−	0.0434843i
$521$	−3.72320	−	1.35513i	−0.163116	−	0.0593695i	0.259171	−	0.965831i	$-0.416551\pi$
$521$	−3.72320	−	1.35513i	−0.163116	−	0.0593695i	−0.422288	+	0.906462i	$0.638773\pi$
$522$	12.2410	−	13.6681i	0.535775	−	0.598235i
$523$	−18.6206	+	6.77735i	−0.814223	+	0.296353i	−0.715367	−	0.698749i	$-0.753740\pi$
$523$	−18.6206	+	6.77735i	−0.814223	+	0.296353i	−0.0988557	+	0.995102i	$0.531518\pi$
$524$	−11.2799	+	15.1516i	−0.492766	+	0.661900i
$525$	16.2322	+	0.734362i	0.708432	+	0.0320502i
$526$	−13.9671	+	14.8042i	−0.608993	+	0.645495i
$527$	−6.51623	+	6.90680i	−0.283852	+	0.300865i
$528$	0.993536	+	1.91593i	0.0432381	+	0.0833804i
$529$	−11.2434	+	15.1026i	−0.488845	+	0.656633i
$530$	−2.76119	+	1.00499i	−0.119938	+	0.0436540i
$531$	−0.0536389	+	1.66302i	−0.00232773	+	0.0721689i
$532$	−7.04160	−	2.56293i	−0.305292	−	0.111117i
$533$	−0.523717	+	0.344454i	−0.0226847	+	0.0149200i
$534$	−19.9182	+	1.41948i	−0.861944	+	0.0614268i
$535$	−1.16307	−	1.56227i	−0.0502839	−	0.0675430i
$536$	−9.91007	−	6.51796i	−0.428050	−	0.281533i
$537$	0.513693	+	39.6119i	0.0221675	+	1.70938i
$538$	−2.93950	+	9.81861i	−0.126731	+	0.423310i
$539$	2.10189	−	3.64058i	0.0905347	−	0.156811i
$540$	−0.819942	−	1.14688i	−0.0352847	−	0.0493538i
$541$	−7.31210	−	12.6649i	−0.314372	−	0.544507i	0.664932	−	0.746904i	$-0.268460\pi$
$541$	−7.31210	−	12.6649i	−0.314372	−	0.544507i	−0.979304	+	0.202396i	$0.935127\pi$
$542$	1.93347	−	0.458240i	0.0830495	−	0.0196831i
$543$	−1.50040	−	3.96172i	−0.0643885	−	0.170014i
$544$	4.49918	−	2.25957i	0.192901	−	0.0968783i
$545$	−1.84727	+	4.28245i	−0.0791282	+	0.183440i
$546$	5.33525	+	21.2777i	0.228328	+	0.910603i
$547$	−1.40815	−	24.1770i	−0.0602081	−	1.03373i	−0.884193	−	0.467122i	$-0.845291\pi$
$547$	−1.40815	−	24.1770i	−0.0602081	−	1.03373i	0.823985	−	0.566612i	$-0.191746\pi$
$548$	−3.79914	−	21.5460i	−0.162291	−	0.920398i
$549$	−2.75878	−	5.96528i	−0.117742	−	0.254592i
$550$	−1.06594	+	6.04526i	−0.0454519	+	0.257771i
$551$	−23.9045	−	2.79404i	−1.01837	−	0.119030i
$552$	−0.771144	+	3.45263i	−0.0328221	+	0.146954i
$553$	−7.82060	−	26.1226i	−0.332566	−	1.11085i
$554$	25.4694	+	6.03636i	1.08209	+	0.256460i
$555$	−2.82388	+	2.15977i	−0.119867	+	0.0916772i
$556$	−7.43679	−	17.2404i	−0.315390	−	0.731157i
$557$	10.8786	+	9.12823i	0.460941	+	0.386775i	0.843477	−	0.537165i	$-0.180505\pi$
$557$	10.8786	+	9.12823i	0.460941	+	0.386775i	−0.382536	+	0.923941i	$0.624949\pi$
$558$	2.95514	+	4.82500i	0.125101	+	0.204259i
$559$	2.54946	−	2.13925i	0.107831	−	0.0904808i
$560$	−0.461719	−	0.231884i	−0.0195112	−	0.00979890i
$561$	−9.92070	+	4.43282i	−0.418852	+	0.187154i
$562$	−19.3863	+	2.26593i	−0.817762	+	0.0955827i
$563$	0.693884	−	11.9135i	0.0292437	−	0.502096i	−0.951605	−	0.307324i	$-0.900566\pi$
$563$	0.693884	−	11.9135i	0.0292437	−	0.502096i	0.980849	−	0.194771i	$-0.0623965\pi$
$564$	11.1226	+	12.9116i	0.468347	+	0.543678i
$565$	−1.32001	−	1.39913i	−0.0555333	−	0.0588619i
$566$	−5.80056			−0.243816
$567$	16.4493	−	4.81174i	0.690805	−	0.202074i
$568$	4.65143			0.195170
$569$	−16.2442	−	17.2179i	−0.680993	−	0.721811i	0.291025	−	0.956715i	$-0.406004\pi$
$569$	−16.2442	−	17.2179i	−0.680993	−	0.721811i	−0.972018	+	0.234905i	$0.924522\pi$
$570$	−0.609900	+	1.74580i	−0.0255459	+	0.0731234i
$571$	−0.294103	+	5.04956i	−0.0123078	+	0.211317i	0.986547	+	0.163477i	$0.0522709\pi$
$571$	−0.294103	+	5.04956i	−0.0123078	+	0.211317i	−0.998855	+	0.0478405i	$0.984766\pi$
$572$	−8.23117	+	0.962086i	−0.344162	+	0.0402268i
$573$	−0.986423	+	9.50698i	−0.0412084	+	0.397160i
$574$	0.160389	+	0.0805506i	0.00669452	+	0.00336212i
$575$	−7.70802	+	6.46780i	−0.321447	+	0.269726i
$576$	−0.597383	−	2.93992i	−0.0248910	−	0.122497i
$577$	−19.0340	−	15.9714i	−0.792395	−	0.664899i	0.153942	−	0.988080i	$-0.450803\pi$
$577$	−19.0340	−	15.9714i	−0.792395	−	0.664899i	−0.946337	+	0.323181i	$0.895248\pi$
$578$	3.30658	+	7.66551i	0.137535	+	0.318843i
$579$	−19.8637	−	8.26452i	−0.825505	−	0.343462i
$580$	−1.61470	−	0.382692i	−0.0670469	−	0.0158904i
$581$	4.17428	+	13.9431i	0.173178	+	0.578456i
$582$	4.02138	+	3.69660i	0.166692	+	0.153229i
$583$	13.4033	+	1.56663i	0.555109	+	0.0648830i
$584$	0.134282	−	0.761550i	0.00555662	−	0.0315131i
$585$	5.23346	−	1.38462i	0.216377	−	0.0572472i
$586$	4.62533	+	26.2315i	0.191070	+	1.08361i
$587$	−0.562773	−	9.66244i	−0.0232281	−	0.398812i	−0.989804	−	0.142433i	$-0.954508\pi$
$587$	−0.562773	−	9.66244i	−0.0232281	−	0.398812i	0.966576	−	0.256379i	$-0.0825295\pi$
$588$	−4.19797	+	4.06476i	−0.173122	+	0.167628i
$589$	2.93955	−	6.81464i	0.121122	−	0.280792i
$590$	0.134477	−	0.0675368i	0.00553632	−	0.00278044i
$591$	−26.3668	−	4.29742i	−1.08459	−	0.176772i
$592$	−7.36107	+	1.74460i	−0.302538	+	0.0717028i
$593$	4.42945	+	7.67203i	0.181896	+	0.315052i	0.942526	−	0.334133i	$-0.108443\pi$
$593$	4.42945	+	7.67203i	0.181896	+	0.315052i	−0.760630	+	0.649185i	$0.775110\pi$
$594$	1.00121	+	6.39678i	0.0410800	+	0.262463i
$595$	1.30066	−	2.25281i	0.0533218	−	0.0923560i
$596$	5.89666	−	19.6962i	0.241537	−	0.806789i
$597$	−21.5642	+	12.8258i	−0.882565	+	0.524924i
$598$	−11.3494	−	7.46462i	−0.464112	−	0.305251i
$599$	23.9666	+	32.1927i	0.979249	+	1.31536i	0.948818	+	0.315823i	$0.102280\pi$
$599$	23.9666	+	32.1927i	0.979249	+	1.31536i	0.0304306	+	0.999537i	$0.490312\pi$
$600$	3.73029	−	7.67416i	0.152289	−	0.313296i
$601$	−25.1586	+	16.5471i	−1.02624	+	0.674969i	−0.946784	−	0.321870i	$-0.895689\pi$
$601$	−25.1586	+	16.5471i	−1.02624	+	0.674969i	−0.0794561	+	0.996838i	$0.525318\pi$
$602$	−0.895449	−	0.325917i	−0.0364958	−	0.0132834i
$603$	−21.9825	−	27.9823i	−0.895196	−	1.13953i
$604$	19.5926	−	7.13113i	0.797212	−	0.290162i
$605$	1.53069	−	2.05607i	0.0622313	−	0.0835911i
$606$	−10.5368	+	16.4821i	−0.428029	+	0.669539i
$607$	−18.4472	+	19.5529i	−0.748750	+	0.793628i	−0.983974	−	0.178313i	$-0.942936\pi$
$607$	−18.4472	+	19.5529i	−0.748750	+	0.793628i	0.235224	+	0.971941i	$0.424418\pi$
$608$	−2.70041	+	2.86227i	−0.109516	+	0.116080i
$609$	10.8657	−	16.9965i	0.440300	−	0.688733i
$610$	−0.354955	+	0.476788i	−0.0143717	+	0.0193046i
$611$	−61.4912	+	22.3810i	−2.48767	+	0.905437i
$612$	14.9515	−	2.14192i	0.604377	−	0.0865821i
$613$	11.6813	+	4.25166i	0.471805	+	0.171723i	0.566970	−	0.823739i	$-0.308116\pi$
$613$	11.6813	+	4.25166i	0.471805	+	0.171723i	−0.0951649	+	0.995462i	$0.530338\pi$
$614$	−12.7441	+	8.38195i	−0.514311	+	0.338268i
$615$	0.0193635	−	0.0398357i	0.000780813	−	0.00160633i
$616$	1.41696	+	1.90331i	0.0570910	+	0.0766865i
$617$	7.90407	+	5.19859i	0.318206	+	0.209287i	0.698556	−	0.715555i	$-0.253826\pi$
$617$	7.90407	+	5.19859i	0.318206	+	0.209287i	−0.380350	+	0.924843i	$0.624197\pi$
$618$	4.75468	−	2.82795i	0.191261	−	0.113757i
$619$	−6.89680	+	23.0369i	−0.277206	+	0.925932i	0.700090	+	0.714054i	$0.253143\pi$
$619$	−6.89680	+	23.0369i	−0.277206	+	0.925932i	−0.977296	+	0.211878i	$0.932042\pi$
$620$	0.255860	−	0.443162i	0.0102756	−	0.0177978i
$621$	−5.48272	+	9.08723i	−0.220014	+	0.364658i
$622$	3.87827	+	6.71737i	0.155505	+	0.269342i
$623$	−21.3626	+	5.06304i	−0.855876	+	0.202846i
$624$	11.3695	+	1.85307i	0.455143	+	0.0741820i
$625$	21.3589	−	10.7268i	0.854355	−	0.429073i
$626$	3.38888	−	7.85630i	0.135447	−	0.314001i
$627$	6.10131	−	5.90769i	0.243663	−	0.235931i
$628$	−1.07691	−	18.4898i	−0.0429734	−	0.737825i
$629$	−6.61382	−	37.5088i	−0.263710	−	1.49557i
$630$	−1.09258	−	1.09949i	−0.0435292	−	0.0438047i
$631$	−7.70070	+	43.6728i	−0.306560	+	1.73859i	0.309510	+	0.950896i	$0.399835\pi$
$631$	−7.70070	+	43.6728i	−0.306560	+	1.73859i	−0.616070	+	0.787692i	$0.711276\pi$
$632$	−14.2225	−	1.66238i	−0.565742	−	0.0661257i
$633$	−4.50694	−	4.14294i	−0.179135	−	0.164667i
$634$	2.33274	+	7.79188i	0.0926448	+	0.309455i
$635$	0.0992390	+	0.0235201i	0.00393818	+	0.000933366i
$636$	−17.3187	−	7.20567i	−0.686732	−	0.285723i
$637$	−8.88709	−	20.6026i	−0.352119	−	0.816304i
$638$	5.83799	+	4.89865i	0.231128	+	0.193939i
$639$	13.2321	+	4.43100i	0.523453	+	0.175288i
$640$	−0.207845	+	0.174403i	−0.00821581	+	0.00689388i
$641$	21.5547	+	10.8252i	0.851361	+	0.427570i	0.820290	−	0.571947i	$-0.193812\pi$
$641$	21.5547	+	10.8252i	0.851361	+	0.427570i	0.0310711	+	0.999517i	$0.490108\pi$
$642$	1.28317	−	12.3670i	0.0506429	−	0.488087i
$643$	40.7995	−	4.76878i	1.60897	−	0.188062i	0.736401	−	0.676545i	$-0.236524\pi$
$643$	40.7995	−	4.76878i	1.60897	−	0.188062i	0.872574	+	0.488483i	$0.162449\pi$
$644$	−0.226154	+	3.88292i	−0.00891172	+	0.153008i
$645$	−0.0775582	+	0.222005i	−0.00305385	+	0.00874145i
$646$	−13.5958	−	14.4107i	−0.534918	−	0.566980i
$647$	8.33601			0.327723			0.163861	−	0.986483i	$-0.447605\pi$
$647$	8.33601			0.327723			0.163861	+	0.986483i	$0.447605\pi$
$648$	1.10120	−	8.93238i	0.0432593	−	0.350897i
$649$	−0.691094			−0.0271278
$650$	22.4842	+	23.8319i	0.881904	+	0.934764i
$651$	4.06004	+	4.71308i	0.159126	+	0.184720i
$652$	0.547935	−	9.40769i	0.0214588	−	0.368434i
$653$	8.01744	−	0.937104i	0.313747	−	0.0366717i	0.0422375	−	0.999108i	$-0.486551\pi$
$653$	8.01744	−	0.937104i	0.313747	−	0.0366717i	0.271509	+	0.962436i	$0.412477\pi$
$654$	−27.1828	+	12.1460i	−1.06293	+	0.474944i
$655$	4.57996	+	2.30014i	0.178954	+	0.0898741i
$656$	0.0722001	−	0.0605831i	0.00281894	−	0.00236537i
$657$	1.10746	−	2.03849i	0.0432060	−	0.0795291i
$658$	14.3530	+	12.0436i	0.559537	+	0.469507i
$659$	−19.6755	−	45.6130i	−0.766450	−	1.77683i	−0.615259	−	0.788325i	$-0.710948\pi$
$659$	−19.6755	−	45.6130i	−0.766450	−	1.77683i	−0.151191	−	0.988505i	$-0.548311\pi$
$660$	0.465129	−	0.355742i	0.0181051	−	0.0138472i
$661$	2.96376	+	0.702423i	0.115277	+	0.0273211i	0.287849	−	0.957676i	$-0.407060\pi$
$661$	2.96376	+	0.702423i	0.115277	+	0.0273211i	−0.172573	+	0.984997i	$0.555208\pi$
$662$	−8.08163	−	26.9945i	−0.314101	−	1.04917i
$663$	−12.6422	+	56.6026i	−0.490981	+	2.19826i
$664$	7.59134	+	0.887301i	0.294601	+	0.0344339i
$665$	−0.353055	+	2.00227i	−0.0136909	+	0.0776448i
$666$	−22.6022	−	2.04929i	−0.875819	−	0.0794084i
$667$	2.16922	+	12.3023i	0.0839927	+	0.476346i
$668$	0.410671	+	7.05095i	0.0158893	+	0.272809i
$669$	4.90603	+	19.5660i	0.189678	+	0.756464i
$670$	−1.27469	+	2.95507i	−0.0492457	+	0.114164i
$671$	2.43945	−	1.22514i	0.0941740	−	0.0472960i
$672$	−1.16819	−	3.08452i	−0.0450639	−	0.118988i
$673$	31.9544	−	7.57332i	1.23175	−	0.291930i	0.437331	−	0.899301i	$-0.355924\pi$
$673$	31.9544	−	7.57332i	1.23175	−	0.291930i	0.794419	+	0.607370i	$0.207776\pi$
$674$	−0.612653	−	1.06115i	−0.0235985	−	0.0408738i
$675$	17.9222	−	18.2774i	0.689825	−	0.703499i
$676$	−15.6164	+	27.0485i	−0.600632	+	1.04033i
$677$	2.44012	−	8.15058i	0.0937816	−	0.313252i	−0.898208	−	0.439570i	$-0.855131\pi$
$677$	2.44012	−	8.15058i	0.0937816	−	0.313252i	0.991990	+	0.126318i	$0.0403160\pi$
$678$	−0.159227	−	12.2783i	−0.00611508	−	0.471546i
$679$	5.01748	+	3.30005i	0.192553	+	0.126644i
$680$	−0.815737	−	1.09572i	−0.0312821	−	0.0420191i
$681$	−42.8489	+	3.05365i	−1.64198	+	0.117016i
$682$	−1.96345	+	1.29138i	−0.0751846	+	0.0494497i
$683$	−32.4005	−	11.7928i	−1.23977	−	0.451240i	−0.362838	−	0.931852i	$-0.618192\pi$
$683$	−32.4005	−	11.7928i	−1.23977	−	0.451240i	−0.876933	+	0.480612i	$0.840414\pi$
$684$	−10.4086	+	5.56996i	−0.397982	+	0.212973i
$685$	−5.57810	+	2.03026i	−0.213128	+	0.0775724i
$686$	−11.7966	+	15.8455i	−0.450395	+	0.604985i
$687$	−8.55198	−	16.4916i	−0.326278	−	0.629195i
$688$	−0.343399	+	0.363982i	−0.0130920	+	0.0138767i
$689$	49.4281	−	52.3907i	1.88306	−	1.99593i
$690$	0.958878	+	0.0433806i	0.0365039	+	0.00165147i
$691$	−17.4480	+	23.4368i	−0.663755	+	0.891578i	−0.998716	−	0.0506543i	$-0.983869\pi$
$691$	−17.4480	+	23.4368i	−0.663755	+	0.891578i	0.334961	+	0.942232i	$0.391277\pi$
$692$	11.7473	−	4.27568i	0.446567	−	0.162537i
$693$	2.21777	+	6.76423i	0.0842461	+	0.256952i
$694$	32.3904	+	11.7891i	1.22952	+	0.447510i
$695$	−4.25627	+	2.79939i	−0.161450	+	0.106187i
$696$	−5.93543	−	8.77441i	−0.224982	−	0.332593i
$697$	0.283366	+	0.380626i	0.0107332	+	0.0144173i
$698$	−19.2280	−	12.6464i	−0.727790	−	0.478675i
$699$	−28.8298	−	16.1501i	−1.09044	−	0.610853i
$700$	2.69058	−	8.98715i	0.101694	−	0.339682i
$701$	1.62951	−	2.82240i	0.0615458	−	0.106600i	−0.833611	−	0.552352i	$-0.813730\pi$
$701$	1.62951	−	2.82240i	0.0615458	−	0.106600i	0.895157	+	0.445752i	$0.147064\pi$
$702$	30.5779	+	16.1022i	1.15409	+	0.607737i
$703$	14.8844	+	25.7805i	0.561375	+	0.972329i
$704$	1.21246	−	0.287359i	0.0456964	−	0.0108302i
$705$	2.92596	−	3.58030i	0.110198	−	0.134842i
$706$	17.2159	−	8.64617i	0.647931	−	0.325403i
$707$	−8.51874	+	19.7487i	−0.320380	+	0.742725i
$708$	0.923782	+	0.263559i	0.0347179	+	0.00990516i
$709$	0.398378	+	6.83989i	0.0149614	+	0.256878i	0.997492	+	0.0707772i	$0.0225479\pi$
$709$	0.398378	+	6.83989i	0.0149614	+	0.256878i	−0.982531	+	0.186100i	$0.940415\pi$
$710$	−0.219151	−	1.24286i	−0.00822458	−	0.0466439i
$711$	−38.8758	−	18.2776i	−1.45796	−	0.685462i
$712$	−2.00198	+	11.3538i	−0.0750273	+	0.425501i
$713$	−3.82613	−	0.447210i	−0.143290	−	0.0167481i
$714$	15.8454	−	4.96857i	0.592998	−	0.185944i
$715$	0.644879	+	2.15405i	0.0241171	+	0.0805568i
$716$	22.2553	+	5.27461i	0.831720	+	0.197121i
$717$	3.84746	+	29.5848i	0.143686	+	1.10486i
$718$	7.25989	+	16.8303i	0.270937	+	0.628102i
$719$	−32.0452	−	26.8891i	−1.19508	−	1.00279i	−0.999757	−	0.0220555i	$-0.992979\pi$
$719$	−32.0452	−	26.8891i	−1.19508	−	1.00279i	−0.195326	−	0.980738i	$-0.562577\pi$
$720$	−0.757404	+	0.298135i	−0.0282268	+	0.0111108i
$721$	4.65926	−	3.90958i	0.173520	−	0.145600i
$722$	−3.14132	−	1.57763i	−0.116908	−	0.0587133i
$723$	11.5863	+	8.39439i	0.430899	+	0.312191i
$724$	−2.42930	+	0.283945i	−0.0902843	+	0.0105527i
$725$	1.75192	−	30.0792i	0.0650645	−	1.11711i
$726$	16.0765	−	3.05018i	0.596655	−	0.113203i
$727$	−12.2805	−	13.0166i	−0.455459	−	0.482759i	0.458425	−	0.888733i	$-0.348414\pi$
$727$	−12.2805	−	13.0166i	−0.455459	−	0.482759i	−0.913884	+	0.405974i	$0.866932\pi$
$728$	12.6650			0.469396
$729$	11.6417	−	24.3613i	0.431175	−	0.902269i
$730$	−0.209813			−0.00776554
$731$	−1.72891	−	1.83254i	−0.0639461	−	0.0677790i
$732$	−3.72803	+	0.707315i	−0.137792	+	0.0261431i
$733$	2.90117	−	49.8111i	0.107157	−	1.83982i	−0.334221	−	0.942495i	$-0.608473\pi$
$733$	2.90117	−	49.8111i	0.107157	−	1.83982i	0.441378	−	0.897321i	$-0.354490\pi$
$734$	1.17242	−	0.137036i	0.0432748	−	0.00505810i
$735$	1.28389	+	0.930192i	0.0473571	+	0.0343106i
$736$	1.82524	+	0.916669i	0.0672792	+	0.0337889i
$737$	11.3221	−	9.50035i	0.417054	−	0.349950i
$738$	0.263102	−	0.103564i	0.00968493	−	0.00381226i
$739$	15.2533	+	12.7991i	0.561103	+	0.470822i	0.878680	−	0.477411i	$-0.158425\pi$
$739$	15.2533	+	12.7991i	0.561103	+	0.470822i	−0.317577	+	0.948233i	$0.602869\pi$
$740$	0.812974	+	1.88469i	0.0298855	+	0.0692824i
$741$	−5.84587	−	44.9515i	−0.214754	−	1.65133i
$742$	−20.0673	−	4.75605i	−0.736695	−	0.174600i
$743$	9.12533	+	30.4807i	0.334776	+	1.11823i	0.945292	+	0.326225i	$0.105777\pi$
$743$	9.12533	+	30.4807i	0.334776	+	1.11823i	−0.610516	+	0.792004i	$0.709038\pi$
$744$	3.11703	−	0.977394i	0.114276	−	0.0358330i
$745$	−5.54067	−	0.647611i	−0.202994	−	0.0237266i
$746$	0.573074	−	3.25006i	0.0209817	−	0.118993i
$747$	20.7501	+	9.75573i	0.759207	+	0.356944i
$748$	1.08938	+	6.17818i	0.0398317	+	0.225897i
$749$	−0.794829	−	13.6467i	−0.0290424	−	0.498639i
$750$	−4.48585	−	1.27983i	−0.163800	−	0.0467329i
$751$	−3.66595	+	8.49862i	−0.133772	+	0.310119i	−0.971915	−	0.235332i	$-0.924382\pi$
$751$	−3.66595	+	8.49862i	−0.133772	+	0.310119i	0.838143	+	0.545451i	$0.183642\pi$
$752$	8.79253	−	4.41577i	0.320630	−	0.161027i
$753$	17.4085	−	21.3017i	0.634402	−	0.776275i
$754$	39.5803	−	9.38071i	1.44143	−	0.341625i
$755$	−2.82854	−	4.89918i	−0.102941	−	0.178299i
$756$	−0.384841	−	9.88749i	−0.0139965	−	0.359605i
$757$	−6.13904	+	10.6331i	−0.223127	+	0.386468i	−0.955756	−	0.294161i	$-0.904960\pi$
$757$	−6.13904	+	10.6331i	−0.223127	+	0.386468i	0.732629	+	0.680628i	$0.238293\pi$
$758$	0.567676	−	1.89617i	0.0206189	−	0.0688720i
$759$	−3.84583	−	2.15439i	−0.139595	−	0.0781993i
$760$	0.892029	+	0.586697i	0.0323573	+	0.0212817i
$761$	−1.44141	−	1.93615i	−0.0522511	−	0.0701854i	0.775230	−	0.631680i	$-0.217634\pi$
$761$	−1.44141	−	1.93615i	−0.0522511	−	0.0701854i	−0.827481	+	0.561494i	$0.810227\pi$
$762$	0.364789	+	0.539271i	0.0132149	+	0.0195357i
$763$	−27.3485	+	17.9874i	−0.990083	+	0.651188i
$764$	5.18553	+	1.88738i	0.187606	+	0.0682829i
$765$	−1.27676	−	3.89413i	−0.0461613	−	0.140793i
$766$	−3.22897	+	1.17525i	−0.116667	+	0.0424634i
$767$	−2.20275	+

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686242 - 0.727374i) q^{2} +(-1.70169 + 0.322861i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(0.269488 - 0.0314987i) q^{5} +(1.40261 + 1.01621i) q^{6} +(1.70173 + 0.854643i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.79152 - 1.09882i) q^{9} +O(q^{10})\)	\(q+(-0.686242 - 0.727374i) q^{2} +(-1.70169 + 0.322861i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(0.269488 - 0.0314987i) q^{5} +(1.40261 + 1.01621i) q^{6} +(1.70173 + 0.854643i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.79152 - 1.09882i) q^{9} +(-0.207845 - 0.174403i) q^{10} +(0.493535 + 1.14414i) q^{11} +(-0.223370 - 1.71759i) q^{12} +(6.47151 + 1.53378i) q^{13} +(-0.546156 - 1.82429i) q^{14} +(-0.448417 + 0.140608i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(0.874267 - 4.95822i) q^{17} +(-2.71491 - 1.27642i) q^{18} +(0.683318 + 3.87529i) q^{19} +(0.0157760 + 0.270864i) q^{20} +(-3.17176 - 0.904918i) q^{21} +(0.493535 - 1.14414i) q^{22} +(1.82524 - 0.916669i) q^{23} +(-1.09604 + 1.34115i) q^{24} +(-4.79359 + 1.13610i) q^{25} +(-3.32539 - 5.75975i) q^{26} +(-4.39555 + 2.77113i) q^{27} +(-0.952145 + 1.64916i) q^{28} +(-1.75411 + 5.85915i) q^{29} +(0.409997 + 0.229675i) q^{30} +(-1.57574 - 1.03638i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-1.20924 - 1.78764i) q^{33} +(-4.20643 + 2.76662i) q^{34} +(0.485518 + 0.176714i) q^{35} +(0.934648 + 2.85069i) q^{36} +(7.10876 - 2.58738i) q^{37} +(2.34986 - 3.15641i) q^{38} +(-11.5077 - 0.520621i) q^{39} +(0.186193 - 0.197353i) q^{40} +(-0.0646786 + 0.0685554i) q^{41} +(1.51838 + 2.92805i) q^{42} +(0.298821 - 0.401387i) q^{43} +(-1.17090 + 0.426174i) q^{44} +(0.717671 - 0.384048i) q^{45} +(-1.91932 - 0.698574i) q^{46} +(-8.22043 + 5.40667i) q^{47} +(1.72767 - 0.123123i) q^{48} +(-2.01462 - 2.70611i) q^{49} +(4.11593 + 2.70709i) q^{50} +(0.113078 + 8.71963i) q^{51} +(-1.90747 + 6.37138i) q^{52} +(5.41495 - 9.37896i) q^{53} +(5.03205 + 1.29554i) q^{54} +(0.169041 + 0.292787i) q^{55} +(1.85296 - 0.439159i) q^{56} +(-2.41398 - 6.37394i) q^{57} +(5.46554 - 2.74490i) q^{58} +(-0.219677 + 0.509269i) q^{59} +(-0.114297 - 0.455834i) q^{60} +(-0.127382 - 2.18707i) q^{61} +(0.327503 + 1.85736i) q^{62} +(5.68953 + 0.515856i) q^{63} +(0.173648 - 0.984808i) q^{64} +(1.79231 + 0.209491i) q^{65} +(-0.470447 + 2.10632i) q^{66} +(-3.40189 - 11.3631i) q^{67} +(4.89899 + 1.16108i) q^{68} +(-2.81004 + 2.14919i) q^{69} +(-0.204645 - 0.474421i) q^{70} +(3.56320 + 2.98988i) q^{71} +(1.43212 - 2.63610i) q^{72} +(0.592380 - 0.497066i) q^{73} +(-6.76031 - 3.39516i) q^{74} +(7.79042 - 3.48096i) q^{75} +(-3.90846 + 0.456834i) q^{76} +(-0.137968 + 2.36882i) q^{77} +(7.51839 + 8.72768i) q^{78} +(-9.82654 - 10.4155i) q^{79} -0.271323 q^{80} +(6.58519 - 6.13476i) q^{81} +0.0942505 q^{82} +(5.24496 + 5.55933i) q^{83} +(1.08781 - 3.11378i) q^{84} +(0.0794276 - 1.36372i) q^{85} +(-0.497022 + 0.0580935i) q^{86} +(1.09328 - 10.5368i) q^{87} +(1.11351 + 0.559226i) q^{88} +(-8.83168 + 7.41066i) q^{89} +(-0.771842 - 0.258465i) q^{90} +(9.70196 + 8.14091i) q^{91} +(0.808990 + 1.87545i) q^{92} +(3.01604 + 1.25486i) q^{93} +(9.57387 + 2.26905i) q^{94} +(0.306212 + 1.02282i) q^{95} +(-1.27515 - 1.17217i) q^{96} +(3.13232 + 0.366116i) q^{97} +(-0.585834 + 3.32243i) q^{98} +(2.63492 + 2.65159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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