LMFDB - Embedded newform 378.2.v.b.67.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.9
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(1.40163 + 1.01757i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.289065 + 1.63937i) q^{5} +(1.72779 - 0.121449i) q^{6} +(1.93330 - 1.80620i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.929121 + 2.85250i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(1.40163 + 1.01757i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.289065 + 1.63937i) q^{5} +(1.72779 - 0.121449i) q^{6} +(1.93330 - 1.80620i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.929121 + 2.85250i) q^{9} +(0.832330 + 1.44164i) q^{10} +(0.472059 + 2.67718i) q^{11} +(1.24550 - 1.20364i) q^{12} +(-0.391548 + 2.22058i) q^{13} +(0.319985 - 2.62633i) q^{14} +(-2.07333 + 2.00364i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-3.56351 - 6.17218i) q^{17} +(2.54530 + 1.58791i) q^{18} +(1.76602 - 3.05883i) q^{19} +(1.56427 + 0.569347i) q^{20} +(4.54769 - 0.564370i) q^{21} +(2.08247 + 1.74740i) q^{22} +(-2.00945 - 1.68613i) q^{23} +(0.180424 - 1.72263i) q^{24} +(2.09449 + 0.762331i) q^{25} +(1.12742 + 1.95275i) q^{26} +(-1.60032 + 4.94358i) q^{27} +(-1.44305 - 2.21757i) q^{28} +(1.52100 + 8.62604i) q^{29} +(-0.300344 + 2.86759i) q^{30} +(1.52088 - 8.62534i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.06255 + 4.23276i) q^{33} +(-6.69721 - 2.43759i) q^{34} +(2.40219 + 3.69150i) q^{35} +(2.97050 - 0.419674i) q^{36} -9.89756 q^{37} +(-0.613331 - 3.47837i) q^{38} +(-2.80839 + 2.71400i) q^{39} +(1.56427 - 0.569347i) q^{40} +(0.959980 - 5.44432i) q^{41} +(3.12096 - 3.35553i) q^{42} +(-0.952500 + 0.799242i) q^{43} +2.71848 q^{44} +(-4.94487 + 0.698615i) q^{45} -2.62315 q^{46} +(0.104767 + 0.594161i) q^{47} +(-0.969071 - 1.43558i) q^{48} +(0.475260 - 6.98385i) q^{49} +(2.09449 - 0.762331i) q^{50} +(1.28588 - 12.2772i) q^{51} +(2.11885 + 0.771200i) q^{52} +(-2.22157 + 3.84788i) q^{53} +(1.95175 + 4.81567i) q^{54} -4.52534 q^{55} +(-2.53087 - 0.771181i) q^{56} +(5.58786 - 2.49030i) q^{57} +(6.70987 + 5.63025i) q^{58} +(-10.1977 + 3.71166i) q^{59} +(1.61317 + 2.38976i) q^{60} +(-1.63958 - 9.29853i) q^{61} +(-4.37920 - 7.58500i) q^{62} +(6.94845 + 3.83654i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.52717 - 1.28379i) q^{65} +(1.14076 + 4.56826i) q^{66} +(-0.796600 - 0.668427i) q^{67} +(-6.69721 + 2.43759i) q^{68} +(-1.10075 - 4.40807i) q^{69} +(4.21303 + 1.28375i) q^{70} +(-0.486389 + 0.842451i) q^{71} +(2.00577 - 2.23089i) q^{72} -7.91654 q^{73} +(-7.58197 + 6.36203i) q^{74} +(2.15997 + 3.19978i) q^{75} +(-2.70569 - 2.27035i) q^{76} +(5.74815 + 4.32314i) q^{77} +(-0.406826 + 3.88425i) q^{78} +(0.606801 - 0.509166i) q^{79} +(0.832330 - 1.44164i) q^{80} +(-7.27347 + 5.30063i) q^{81} +(-2.76415 - 4.78765i) q^{82} +(1.53575 + 8.70965i) q^{83} +(0.233902 - 4.57660i) q^{84} +(11.1486 - 4.05775i) q^{85} +(-0.215914 + 1.22451i) q^{86} +(-6.64568 + 13.6382i) q^{87} +(2.08247 - 1.74740i) q^{88} +(3.44098 - 5.95995i) q^{89} +(-3.33893 + 3.71367i) q^{90} +(3.25384 + 5.00025i) q^{91} +(-2.00945 + 1.68613i) q^{92} +(10.9086 - 10.5419i) q^{93} +(0.462175 + 0.387811i) q^{94} +(4.50406 + 3.77936i) q^{95} +(-1.66513 - 0.476814i) q^{96} +(13.0432 - 10.9446i) q^{97} +(-4.12506 - 5.65543i) q^{98} +(-7.19804 + 3.83397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	1.40163	+	1.01757i	0.809230	+	0.587492i
$3$	1.40163	+	1.01757i	0.809230	+	0.587492i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.289065	+	1.63937i	−0.129274	+	0.733149i	0.849403	+	0.527744i	$0.176962\pi$
$5$	−0.289065	+	1.63937i	−0.129274	+	0.733149i	−0.978677	+	0.205404i	$0.934149\pi$
$6$	1.72779	−	0.121449i	0.705366	−	0.0495811i
$7$	1.93330	−	1.80620i	0.730717	−	0.682681i
$7$	1.93330	−	1.80620i	0.730717	−	0.682681i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.929121	+	2.85250i	0.309707	+	0.950832i
$10$	0.832330	+	1.44164i	0.263206	+	0.455886i
$11$	0.472059	+	2.67718i	0.142331	+	0.807199i	0.969471	+	0.245204i	$0.0788550\pi$
$11$	0.472059	+	2.67718i	0.142331	+	0.807199i	−0.827140	+	0.561995i	$0.810034\pi$
$12$	1.24550	−	1.20364i	0.359544	−	0.347460i
$13$	−0.391548	+	2.22058i	−0.108596	+	0.615878i	0.881127	+	0.472880i	$0.156786\pi$
$13$	−0.391548	+	2.22058i	−0.108596	+	0.615878i	−0.989723	+	0.142999i	$0.954326\pi$
$14$	0.319985	−	2.62633i	0.0855196	−	0.701916i
$15$	−2.07333	+	2.00364i	−0.535331	+	0.517339i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−3.56351	−	6.17218i	−0.864279	−	1.49697i	−0.867762	−	0.496980i	$-0.834442\pi$
$17$	−3.56351	−	6.17218i	−0.864279	−	1.49697i	0.00348325	−	0.999994i	$-0.498891\pi$
$18$	2.54530	+	1.58791i	0.599932	+	0.374274i
$19$	1.76602	−	3.05883i	0.405152	−	0.701744i	−0.589187	−	0.807997i	$-0.700552\pi$
$19$	1.76602	−	3.05883i	0.405152	−	0.701744i	0.994339	+	0.106253i	$0.0338853\pi$
$20$	1.56427	+	0.569347i	0.349781	+	0.127310i
$21$	4.54769	−	0.564370i	0.992387	−	0.123156i
$22$	2.08247	+	1.74740i	0.443985	+	0.372548i
$23$	−2.00945	−	1.68613i	−0.418999	−	0.351582i	0.408783	−	0.912632i	$-0.365953\pi$
$23$	−2.00945	−	1.68613i	−0.418999	−	0.351582i	−0.827782	+	0.561049i	$0.810398\pi$
$24$	0.180424	−	1.72263i	0.0368288	−	0.351630i
$25$	2.09449	+	0.762331i	0.418897	+	0.152466i
$26$	1.12742	+	1.95275i	0.221105	+	0.382965i
$27$	−1.60032	+	4.94358i	−0.307982	+	0.951392i
$28$	−1.44305	−	2.21757i	−0.272711	−	0.419081i
$29$	1.52100	+	8.62604i	0.282443	+	1.60182i	0.714278	+	0.699862i	$0.246755\pi$
$29$	1.52100	+	8.62604i	0.282443	+	1.60182i	−0.431835	+	0.901953i	$0.642134\pi$
$30$	−0.300344	+	2.86759i	−0.0548351	+	0.523548i
$31$	1.52088	−	8.62534i	0.273158	−	1.54916i	−0.471594	−	0.881816i	$-0.656321\pi$
$31$	1.52088	−	8.62534i	0.273158	−	1.54916i	0.744752	−	0.667341i	$-0.232568\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−2.06255	+	4.23276i	−0.359044	+	0.736828i
$34$	−6.69721	−	2.43759i	−1.14856	−	0.418042i
$35$	2.40219	+	3.69150i	0.406044	+	0.623977i
$36$	2.97050	−	0.419674i	0.495083	−	0.0699457i
$37$	−9.89756			−1.62715			−0.813575	−	0.581460i	$-0.802482\pi$
$37$	−9.89756			−1.62715			−0.813575	+	0.581460i	$0.802482\pi$
$38$	−0.613331	−	3.47837i	−0.0994954	−	0.564267i
$39$	−2.80839	+	2.71400i	−0.449703	+	0.434588i
$40$	1.56427	−	0.569347i	0.247333	−	0.0900217i
$41$	0.959980	−	5.44432i	0.149924	−	0.850260i	−0.813357	−	0.581765i	$-0.802363\pi$
$41$	0.959980	−	5.44432i	0.149924	−	0.850260i	0.963281	−	0.268495i	$-0.0865264\pi$
$42$	3.12096	−	3.35553i	0.481575	−	0.517770i
$43$	−0.952500	+	0.799242i	−0.145255	+	0.121883i	−0.712520	−	0.701652i	$-0.752446\pi$
$43$	−0.952500	+	0.799242i	−0.145255	+	0.121883i	0.567265	+	0.823535i	$0.308002\pi$
$44$	2.71848			0.409826
$45$	−4.94487	+	0.698615i	−0.737138	+	0.104143i
$46$	−2.62315			−0.386762
$47$	0.104767	+	0.594161i	0.0152818	+	0.0866672i	0.991495	−	0.130146i	$-0.0415447\pi$
$47$	0.104767	+	0.594161i	0.0152818	+	0.0866672i	−0.976213	+	0.216814i	$0.930434\pi$
$48$	−0.969071	−	1.43558i	−0.139873	−	0.207209i
$49$	0.475260	−	6.98385i	0.0678942	−	0.997693i
$50$	2.09449	−	0.762331i	0.296205	−	0.107810i
$51$	1.28588	−	12.2772i	0.180060	−	1.71915i
$52$	2.11885	+	0.771200i	0.293832	+	0.106946i
$53$	−2.22157	+	3.84788i	−0.305157	+	0.528547i	−0.977296	−	0.211878i	$-0.932042\pi$
$53$	−2.22157	+	3.84788i	−0.305157	+	0.528547i	0.672139	+	0.740425i	$0.265376\pi$
$54$	1.95175	+	4.81567i	0.265600	+	0.655329i
$55$	−4.52534			−0.610197
$56$	−2.53087	−	0.771181i	−0.338201	−	0.103053i
$57$	5.58786	−	2.49030i	0.740130	−	0.329849i
$58$	6.70987	+	5.63025i	0.881049	+	0.739288i
$59$	−10.1977	+	3.71166i	−1.32763	+	0.483217i	−0.905895	−	0.423503i	$-0.860800\pi$
$59$	−10.1977	+	3.71166i	−1.32763	+	0.483217i	−0.421733	+	0.906720i	$0.638578\pi$
$60$	1.61317	+	2.38976i	0.208260	+	0.308517i
$61$	−1.63958	−	9.29853i	−0.209927	−	1.19055i	−0.889496	−	0.456943i	$-0.848944\pi$
$61$	−1.63958	−	9.29853i	−0.209927	−	1.19055i	0.679569	−	0.733612i	$-0.262167\pi$
$62$	−4.37920	−	7.58500i	−0.556159	−	0.963296i
$63$	6.94845	+	3.83654i	0.875423	+	0.483358i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−3.52717	−	1.28379i	−0.437492	−	0.159234i
$66$	1.14076	+	4.56826i	0.140417	+	0.562314i
$67$	−0.796600	−	0.668427i	−0.0973202	−	0.0816613i	0.592829	−	0.805328i	$-0.298011\pi$
$67$	−0.796600	−	0.668427i	−0.0973202	−	0.0816613i	−0.690150	+	0.723667i	$0.742455\pi$
$68$	−6.69721	+	2.43759i	−0.812156	+	0.295601i
$69$	−1.10075	−	4.40807i	−0.132515	−	0.530669i
$70$	4.21303	+	1.28375i	0.503554	+	0.153438i
$71$	−0.486389	+	0.842451i	−0.0577238	+	0.0999805i	−0.893443	−	0.449176i	$-0.851718\pi$
$71$	−0.486389	+	0.842451i	−0.0577238	+	0.0999805i	0.835719	+	0.549157i	$0.185051\pi$
$72$	2.00577	−	2.23089i	0.236383	−	0.262913i
$73$	−7.91654			−0.926561			−0.463281	−	0.886212i	$-0.653328\pi$
$73$	−7.91654			−0.926561			−0.463281	+	0.886212i	$0.653328\pi$
$74$	−7.58197	+	6.36203i	−0.881386	+	0.739571i
$75$	2.15997	+	3.19978i	0.249412	+	0.369479i
$76$	−2.70569	−	2.27035i	−0.310364	−	0.260427i
$77$	5.74815	+	4.32314i	0.655063	+	0.492668i
$78$	−0.406826	+	3.88425i	−0.0460640	+	0.439804i
$79$	0.606801	−	0.509166i	0.0682704	−	0.0572857i	−0.608014	−	0.793926i	$-0.708034\pi$
$79$	0.606801	−	0.509166i	0.0682704	−	0.0572857i	0.676284	+	0.736641i	$0.263589\pi$
$80$	0.832330	−	1.44164i	0.0930573	−	0.161180i
$81$	−7.27347	+	5.30063i	−0.808163	+	0.588958i
$82$	−2.76415	−	4.78765i	−0.305250	−	0.528708i
$83$	1.53575	+	8.70965i	0.168570	+	0.956008i	0.945307	+	0.326183i	$0.105763\pi$
$83$	1.53575	+	8.70965i	0.168570	+	0.956008i	−0.776737	+	0.629826i	$0.783126\pi$
$84$	0.233902	−	4.57660i	0.0255208	−	0.499348i
$85$	11.1486	−	4.05775i	1.20923	−	0.440125i
$86$	−0.215914	+	1.22451i	−0.0232826	+	0.132042i
$87$	−6.64568	+	13.6382i	−0.712492	+	1.46217i
$88$	2.08247	−	1.74740i	0.221992	−	0.186274i
$89$	3.44098	−	5.95995i	0.364743	−	0.631753i	−0.623992	−	0.781431i	$-0.714490\pi$
$89$	3.44098	−	5.95995i	0.364743	−	0.631753i	0.988735	+	0.149678i	$0.0478236\pi$
$90$	−3.33893	+	3.71367i	−0.351954	+	0.391456i
$91$	3.25384	+	5.00025i	0.341095	+	0.524169i
$92$	−2.00945	+	1.68613i	−0.209500	+	0.175791i
$93$	10.9086	−	10.5419i	1.13116	−	1.09315i
$94$	0.462175	+	0.387811i	0.0476697	+	0.0399996i
$95$	4.50406	+	3.77936i	0.462107	+	0.387754i
$96$	−1.66513	−	0.476814i	−0.169946	−	0.0486646i
$97$	13.0432	−	10.9446i	1.32434	−	1.11125i	0.338976	−	0.940795i	$-0.389920\pi$
$97$	13.0432	−	10.9446i	1.32434	−	1.11125i	0.985365	−	0.170458i	$-0.0545248\pi$
$98$	−4.12506	−	5.65543i	−0.416694	−	0.571285i
$99$	−7.19804	+	3.83397i	−0.723430	+	0.385328i
$100$	1.11445	−	1.93029i	0.111445	−	0.193029i
$101$	−3.63473	+	3.04990i	−0.361669	+	0.303476i	−0.805455	−	0.592656i	$-0.798079\pi$
$101$	−3.63473	+	3.04990i	−0.361669	+	0.303476i	0.443787	+	0.896132i	$0.353635\pi$
$102$	−6.90659	−	10.2314i	−0.683855	−	1.01306i
$103$	−2.44199	+	13.8492i	−0.240617	+	1.36460i	0.589840	+	0.807520i	$0.299191\pi$
$103$	−2.44199	+	13.8492i	−0.240617	+	1.36460i	−0.830456	+	0.557084i	$0.811920\pi$
$104$	2.11885	−	0.771200i	0.207771	−	0.0756224i
$105$	−0.389367	+	7.61849i	−0.0379984	+	0.743488i
$106$	0.771545	+	4.37565i	0.0749391	+	0.425001i
$107$	−6.02453	−	10.4348i	−0.582413	−	1.00877i	−0.995193	−	0.0979380i	$-0.968775\pi$
$107$	−6.02453	−	10.4348i	−0.582413	−	1.00877i	0.412779	−	0.910831i	$-0.364558\pi$
$108$	4.59058	+	2.43445i	0.441729	+	0.234255i
$109$	−0.493499	+	0.854765i	−0.0472686	+	0.0818717i	−0.888692	−	0.458505i	$-0.848385\pi$
$109$	−0.493499	+	0.854765i	−0.0472686	+	0.0818717i	0.841423	+	0.540377i	$0.181718\pi$
$110$	−3.46661	+	2.90883i	−0.330529	+	0.277346i
$111$	−13.8727	−	10.0714i	−1.31674	−	0.955937i
$112$	−2.43446	+	1.03605i	−0.230035	+	0.0978975i
$113$	−5.24150	−	4.39814i	−0.493079	−	0.413742i	0.362049	−	0.932159i	$-0.382077\pi$
$113$	−5.24150	−	4.39814i	−0.493079	−	0.413742i	−0.855128	+	0.518417i	$0.826522\pi$
$114$	2.67981	−	5.49949i	0.250987	−	0.515074i
$115$	3.34505	−	2.80683i	0.311928	−	0.261738i
$116$	8.75911			0.813263
$117$	−6.69800	+	0.946298i	−0.619230	+	0.0874852i
$118$	−5.42608	+	9.39825i	−0.499512	+	0.865179i
$119$	−18.0375	−	5.49622i	−1.65350	−	0.503838i
$120$	2.77187	+	0.793733i	0.253036	+	0.0724576i
$121$	3.39218	−	1.23465i	0.308380	−	0.112241i
$122$	−7.23297	−	6.06918i	−0.654843	−	0.549478i
$123$	6.88549	−	6.65407i	0.620844	−	0.599977i
$124$	−8.23021	−	2.99555i	−0.739094	−	0.269008i
$125$	−6.01684	+	10.4215i	−0.538162	+	0.932124i
$126$	7.78890	−	1.52742i	0.693890	−	0.136074i
$127$	4.91915	+	8.52021i	0.436504	+	0.756047i	0.997417	−	0.0718278i	$-0.0228832\pi$
$127$	4.91915	+	8.52021i	0.436504	+	0.756047i	−0.560913	+	0.827875i	$0.689550\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−2.14833	+	0.151009i	−0.189150	+	0.0132956i
$130$	−3.52717	+	1.28379i	−0.309353	+	0.112595i
$131$	16.9367	+	14.2116i	1.47977	+	1.24167i	0.906433	+	0.422351i	$0.138795\pi$
$131$	16.9367	+	14.2116i	1.47977	+	1.24167i	0.573335	+	0.819321i	$0.305650\pi$
$132$	3.81029	+	2.76623i	0.331643	+	0.240769i
$133$	−2.11064	−	9.10341i	−0.183016	−	0.789365i
$134$	−1.03989			−0.0898326
$135$	−7.64176	−	4.05254i	−0.657698	−	0.348787i
$136$	−3.56351	+	6.17218i	−0.305569	+	0.529260i
$137$	4.27703	+	1.55671i	0.365411	+	0.132999i	0.518199	−	0.855260i	$-0.326603\pi$
$137$	4.27703	+	1.55671i	0.365411	+	0.132999i	−0.152787	+	0.988259i	$0.548825\pi$
$138$	−3.67668	−	2.66923i	−0.312980	−	0.227220i
$139$	9.92396	−	3.61203i	0.841739	−	0.306368i	0.115072	−	0.993357i	$-0.463290\pi$
$139$	9.92396	−	3.61203i	0.841739	−	0.306368i	0.726668	+	0.686989i	$0.241068\pi$
$140$	4.05255	−	1.72467i	0.342503	−	0.145761i
$141$	−0.457754	+	0.939399i	−0.0385498	+	0.0791116i
$142$	0.168921	+	0.958000i	0.0141756	+	0.0803936i
$143$	−6.12972			−0.512593
$144$	0.102523	−	2.99825i	0.00854361	−	0.249854i
$145$	−14.5809			−1.21088
$146$	−6.06442	+	5.08865i	−0.501895	+	0.421140i
$147$	7.77266	−	9.30515i	0.641078	−	0.767476i
$148$	−1.71869	+	9.74720i	−0.141276	+	0.801215i
$149$	7.32767	−	2.66706i	0.600307	−	0.218494i	−0.0239500	−	0.999713i	$-0.507624\pi$
$149$	7.32767	−	2.66706i	0.600307	−	0.218494i	0.624256	+	0.781219i	$0.285402\pi$
$150$	3.71141	+	1.06277i	0.303036	+	0.0867751i
$151$	2.91770	+	16.5471i	0.237439	+	1.34658i	0.837416	+	0.546566i	$0.184065\pi$
$151$	2.91770	+	16.5471i	0.237439	+	1.34658i	−0.599977	+	0.800017i	$0.704824\pi$
$152$	−3.53203			−0.286486
$153$	14.2952	−	15.8996i	1.15570	−	1.28541i
$154$	7.18220	−	0.383125i	0.578758	−	0.0308731i
$155$	13.7005	+	4.98657i	1.10045	+	0.400531i
$156$	2.18510	+	3.23701i	0.174948	+	0.259168i
$157$	−9.60323	+	3.49529i	−0.766421	+	0.278954i	−0.695499	−	0.718527i	$-0.744816\pi$
$157$	−9.60323	+	3.49529i	−0.766421	+	0.278954i	−0.0709223	+	0.997482i	$0.522594\pi$
$158$	0.137551	−	0.780088i	0.0109429	−	0.0620605i
$159$	−7.02929	+	3.13270i	−0.557459	+	0.248439i
$160$	−0.289065	−	1.63937i	−0.0228526	−	0.129604i
$161$	−6.93035	+	0.369691i	−0.546188	+	0.0291357i
$162$	−2.16462	+	8.73581i	−0.170069	+	0.686350i
$163$	9.74051	+	16.8711i	0.762936	+	1.32144i	0.941331	+	0.337485i	$0.109576\pi$
$163$	9.74051	+	16.8711i	0.762936	+	1.32144i	−0.178395	+	0.983959i	$0.557090\pi$
$164$	−5.19491	−	1.89079i	−0.405654	−	0.147646i
$165$	−6.34284	−	4.60483i	−0.493790	−	0.358486i
$166$	6.77491	+	5.68482i	0.525835	+	0.441228i
$167$	13.6941	+	11.4907i	1.05968	+	0.889179i	0.994078	−	0.108667i	$-0.0346583\pi$
$167$	13.6941	+	11.4907i	1.05968	+	0.889179i	0.0656035	+	0.997846i	$0.479103\pi$
$168$	−2.76260	−	3.65623i	−0.213140	−	0.282084i
$169$	7.43833	+	2.70733i	0.572179	+	0.208256i
$170$	5.93204	−	10.2746i	0.454966	−	0.788025i
$171$	10.3661	+	2.19553i	0.792719	+	0.167897i
$172$	0.621700	+	1.07682i	0.0474042	+	0.0821064i
$173$	−1.27575	−	0.464335i	−0.0969935	−	0.0353028i	0.293068	−	0.956092i	$-0.405324\pi$
$173$	−1.27575	−	0.464335i	−0.0969935	−	0.0353028i	−0.390061	+	0.920789i	$0.627546\pi$
$174$	3.67559	+	14.7192i	0.278646	+	1.11586i
$175$	5.42618	−	2.30926i	0.410181	−	0.174564i
$176$	0.472059	−	2.67718i	0.0355828	−	0.201800i
$177$	−18.0702	−	5.17447i	−1.35824	−	0.388937i
$178$	−1.19504	−	6.77740i	−0.0895719	−	0.507988i
$179$	−4.80449	−	8.32162i	−0.359104	−	0.621987i	0.628707	−	0.777642i	$-0.283584\pi$
$179$	−4.80449	−	8.32162i	−0.359104	−	0.621987i	−0.987811	+	0.155655i	$0.950251\pi$
$180$	−0.170667	+	4.99106i	−0.0127207	+	0.372012i
$181$	−2.78085	−	4.81657i	−0.206699	−	0.358013i	0.743974	−	0.668209i	$-0.232939\pi$
$181$	−2.78085	−	4.81657i	−0.206699	−	0.358013i	−0.950673	+	0.310196i	$0.899605\pi$
$182$	5.70669	+	1.73889i	0.423008	+	0.128895i
$183$	7.16378	−	14.7015i	0.529562	−	1.08676i
$184$	−0.455505	+	2.58330i	−0.0335803	+	0.190443i
$185$	2.86104	−	16.2258i	0.210348	−	1.19294i
$186$	1.58022	−	15.0875i	0.115868	−	1.10627i
$187$	14.8418	−	12.4538i	1.08534	−	0.910711i
$188$	0.603326			0.0440021
$189$	5.83522	+	12.4479i	0.424450	+	0.905452i
$190$	5.87964			0.426554
$191$	13.0098	−	10.9165i	0.941358	−	0.789894i	−0.0364627	−	0.999335i	$-0.511609\pi$
$191$	13.0098	−	10.9165i	0.941358	−	0.789894i	0.977821	+	0.209441i	$0.0671646\pi$
$192$	−1.58205	+	0.705062i	−0.114175	+	0.0508835i
$193$	3.86587	−	21.9244i	0.278271	−	1.57816i	−0.450103	−	0.892977i	$-0.648613\pi$
$193$	3.86587	−	21.9244i	0.278271	−	1.57816i	0.728375	−	0.685179i	$-0.240276\pi$
$194$	2.95666	−	16.7681i	0.212276	−	1.20388i
$195$	−3.63745	−	5.38852i	−0.260483	−	0.385880i
$196$	−6.79522	−	1.68077i	−0.485373	−	0.120055i
$197$	−0.401069	−	0.694672i	−0.0285750	−	0.0494934i	0.851384	−	0.524543i	$-0.175764\pi$
$197$	−0.401069	−	0.694672i	−0.0285750	−	0.0494934i	−0.879959	+	0.475049i	$0.842430\pi$
$198$	−3.04959	+	7.56380i	−0.216725	+	0.537536i
$199$	1.19471	+	2.06930i	0.0846908	+	0.146689i	0.905259	−	0.424859i	$-0.139676\pi$
$199$	1.19471	+	2.06930i	0.0846908	+	0.146689i	−0.820569	+	0.571548i	$0.806343\pi$
$200$	−0.387045	−	2.19504i	−0.0273682	−	0.155213i
$201$	−0.436369	−	1.74748i	−0.0307791	−	0.123258i
$202$	−0.823926	+	4.67272i	−0.0579712	+	0.328771i
$203$	18.5209	+	13.9294i	1.29991	+	0.977655i
$204$	−11.8674	−	3.39826i	−0.830884	−	0.237926i
$205$	8.64776	+	3.14753i	0.603986	+	0.219833i
$206$	7.03143	+	12.1788i	0.489903	+	0.848537i
$207$	2.94265	−	7.29857i	0.204529	−	0.507285i
$208$	1.12742	−	1.95275i	0.0781724	−	0.135399i
$209$	9.02269	+	3.28399i	0.624113	+	0.227158i
$210$	4.59880	+	6.08638i	0.317347	+	0.420000i
$211$	7.96237	+	6.68122i	0.548152	+	0.459954i	0.874315	−	0.485360i	$-0.161311\pi$
$211$	7.96237	+	6.68122i	0.548152	+	0.459954i	−0.326163	+	0.945314i	$0.605756\pi$
$212$	3.40365	+	2.85600i	0.233764	+	0.196151i
$213$	−1.53899	+	0.685870i	−0.105450	+	0.0469950i
$214$	−11.3224	−	4.12102i	−0.773984	−	0.281707i
$215$	−1.03492	−	1.79253i	−0.0705809	−	0.122250i
$216$	5.08143	−	1.08587i	0.345747	−	0.0738842i
$217$	−12.6388	−	19.4223i	−0.857978	−	1.31848i
$218$	0.171390	+	0.972003i	0.0116080	+	0.0658324i
$219$	−11.0960	−	8.05560i	−0.749801	−	0.544347i
$220$	−0.785817	+	4.45659i	−0.0529798	+	0.300463i
$221$	15.1011	−	5.49636i	1.01581	−	0.369725i
$222$	−17.1009	+	1.20204i	−1.14774	+	0.0806759i
$223$	−2.39329	−	0.871087i	−0.160267	−	0.0583323i	0.260641	−	0.965436i	$-0.416066\pi$
$223$	−2.39329	−	0.871087i	−0.160267	−	0.0583323i	−0.420908	+	0.907103i	$0.638288\pi$
$224$	−1.19895	+	2.35850i	−0.0801079	+	0.157584i
$225$	−0.228515	+	6.68281i	−0.0152343	+	0.445521i
$226$	−6.84229			−0.455142
$227$	−1.24310	−	7.04998i	−0.0825075	−	0.467923i	−0.997867	−	0.0652850i	$-0.979204\pi$
$227$	−1.24310	−	7.04998i	−0.0825075	−	0.467923i	0.915359	−	0.402638i	$-0.131907\pi$
$228$	−1.48215	−	5.93540i	−0.0981577	−	0.393082i
$229$	−12.2477	+	4.45780i	−0.809351	+	0.294580i	−0.713356	−	0.700802i	$-0.752826\pi$
$229$	−12.2477	+	4.45780i	−0.809351	+	0.294580i	−0.0959950	+	0.995382i	$0.530603\pi$
$230$	0.758262	−	4.30032i	0.0499983	−	0.283554i
$231$	3.65770	+	11.9086i	0.240659	+	0.783526i
$232$	6.70987	−	5.63025i	0.440524	−	0.369644i
$233$	17.5676			1.15089			0.575447	−	0.817839i	$-0.304828\pi$
$233$	17.5676			1.15089			0.575447	+	0.817839i	$0.304828\pi$
$234$	−4.52269	+	5.03029i	−0.295658	+	0.328841i
$235$	−1.00433			−0.0655155
$236$	1.88446	+	10.6873i	0.122668	+	0.695684i
$237$	1.36862	−	0.0962020i	0.0889013	−	0.00624899i
$238$	−17.3505	+	7.38395i	−1.12466	+	0.478631i
$239$	−0.201785	+	0.0734437i	−0.0130524	+	0.00475068i	−0.348538	−	0.937295i	$-0.613322\pi$
$239$	−0.201785	+	0.0734437i	−0.0130524	+	0.00475068i	0.335486	+	0.942045i	$0.391100\pi$
$240$	2.63358	−	1.17369i	0.169997	−	0.0757613i
$241$	6.03653	+	2.19712i	0.388847	+	0.141529i	0.529043	−	0.848595i	$-0.322551\pi$
$241$	6.03653	+	2.19712i	0.388847	+	0.141529i	−0.140196	+	0.990124i	$0.544773\pi$
$242$	1.80494	−	3.12625i	0.116026	−	0.200963i
$243$	−15.5884	+	0.0282727i	−0.999998	+	0.00181369i
$244$	−9.44197			−0.604460
$245$	11.3117	+	2.79791i	0.722680	+	0.178752i
$246$	0.997438	−	9.52322i	0.0635943	−	0.607178i
$247$	6.10090	+	5.11926i	0.388191	+	0.325731i
$248$	−8.23021	+	2.99555i	−0.522619	+	0.190218i
$249$	−6.71010	+	13.7704i	−0.425235	+	0.872664i
$250$	2.08963	+	11.8509i	0.132160	+	0.749514i
$251$	−8.78817	−	15.2216i	−0.554704	−	0.960776i	−0.997926	−	0.0643640i	$-0.979498\pi$
$251$	−8.78817	−	15.2216i	−0.554704	−	0.960776i	0.443222	−	0.896412i	$-0.353835\pi$
$252$	4.98484	−	6.17668i	0.314015	−	0.389094i
$253$	3.56549	−	6.17561i	0.224160	−	0.388257i
$254$	9.24497	+	3.36490i	0.580081	+	0.211132i
$255$	19.7552	+	5.65696i	1.23712	+	0.354252i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	15.4259	−	5.61458i	0.962243	−	0.350228i	0.187331	−	0.982297i	$-0.440016\pi$
$257$	15.4259	−	5.61458i	0.962243	−	0.350228i	0.774912	+	0.632069i	$0.217794\pi$
$258$	−1.54865	+	1.49660i	−0.0964148	+	0.0931743i
$259$	−19.1349	+	17.8770i	−1.18899	+	1.11082i
$260$	−1.87677	+	3.25066i	−0.116392	+	0.201597i
$261$	−23.1925	+	12.3533i	−1.43558	+	0.764649i
$262$	22.1093			1.36592
$263$	−16.1539	+	13.5547i	−0.996089	+	0.835818i	−0.986438	−	0.164135i	$-0.947517\pi$
$263$	−16.1539	+	13.5547i	−0.996089	+	0.835818i	−0.00965134	+	0.999953i	$0.503072\pi$
$264$	4.69695	−	0.330155i	0.289077	−	0.0203196i
$265$	−5.66592	−	4.75427i	−0.348055	−	0.292053i
$266$	−7.46840	−	5.61692i	−0.457917	−	0.344396i
$267$	10.8876	−	4.85221i	0.666311	−	0.296950i
$268$	−0.796600	+	0.668427i	−0.0486601	+	0.0408307i
$269$	4.06583	−	7.04222i	0.247898	−	0.429371i	−0.715045	−	0.699079i	$-0.753594\pi$
$269$	4.06583	−	7.04222i	0.247898	−	0.429371i	0.962942	+	0.269707i	$0.0869270\pi$
$270$	−8.45885	+	1.80761i	−0.514789	+	0.110007i
$271$	0.278589	+	0.482530i	0.0169231	+	0.0293116i	0.874363	−	0.485273i	$-0.161280\pi$
$271$	0.278589	+	0.482530i	0.0169231	+	0.0293116i	−0.857440	+	0.514584i	$0.827946\pi$
$272$	1.23759	+	7.01875i	0.0750402	+	0.425574i
$273$	−0.527411	+	10.3195i	−0.0319204	+	0.624564i
$274$	4.27703	−	1.55671i	0.258385	−	0.0940444i
$275$	−1.05217	+	5.96718i	−0.0634485	+	0.359834i
$276$	−4.53225	+	0.318578i	−0.272809	+	0.0191761i
$277$	−22.0507	+	18.5027i	−1.32490	+	1.11172i	−0.339654	+	0.940550i	$0.610310\pi$
$277$	−22.0507	+	18.5027i	−1.32490	+	1.11172i	−0.985242	+	0.171169i	$0.945245\pi$
$278$	5.28043	−	9.14597i	0.316699	−	0.548539i
$279$	26.0168	−	3.67568i	1.55759	−	0.220057i
$280$	1.99584	−	3.92610i	0.119274	−	0.234630i
$281$	−1.88720	+	1.58355i	−0.112581	+	0.0944664i	−0.697340	−	0.716740i	$-0.745633\pi$
$281$	−1.88720	+	1.58355i	−0.112581	+	0.0944664i	0.584760	+	0.811207i	$0.301189\pi$
$282$	0.253174	+	1.01386i	0.0150763	+	0.0603745i
$283$	17.0380	+	14.2966i	1.01280	+	0.849844i	0.988706	−	0.149866i	$-0.0478842\pi$
$283$	17.0380	+	14.2966i	1.01280	+	0.849844i	0.0240978	+	0.999710i	$0.492329\pi$
$284$	0.745192	+	0.625290i	0.0442190	+	0.0371041i
$285$	2.46727	+	9.88043i	0.146149	+	0.585266i
$286$	−4.69564	+	3.94011i	−0.277659	+	0.232984i
$287$	−7.97762	−	12.2594i	−0.470904	−	0.723649i
$288$	−1.84870	−	2.36269i	−0.108936	−	0.139223i
$289$	−16.8972	+	29.2669i	−0.993955	+	1.72158i
$290$	−11.1696	+	9.37245i	−0.655904	+	0.550369i
$291$	29.4186	−	2.06787i	1.72455	−	0.121221i
$292$	−1.37469	+	7.79627i	−0.0804478	+	0.456242i
$293$	−12.9815	+	4.72489i	−0.758389	+	0.276031i	−0.692131	−	0.721772i	$-0.743328\pi$
$293$	−12.9815	+	4.72489i	−0.758389	+	0.276031i	−0.0662575	+	0.997803i	$0.521106\pi$
$294$	−0.0270302	−	12.1243i	−0.00157643	−	0.707105i
$295$	−3.13698	−	17.7907i	−0.182642	−	1.03582i
$296$	4.94878	+	8.57154i	0.287642	+	0.498211i
$297$	−13.9903	−	1.95068i	−0.811799	−	0.113190i
$298$	3.89897	−	6.75322i	0.225862	−	0.391204i
$299$	4.53098	−	3.80195i	0.262033	−	0.219872i
$300$	3.52624	−	1.57152i	0.203588	−	0.0907316i
$301$	−0.397869	+	3.26558i	−0.0229328	+	0.188225i
$302$	12.8713	+	10.8003i	0.740663	+	0.621490i
$303$	−8.19801	+	0.576249i	−0.470963	+	0.0331046i
$304$	−2.70569	+	2.27035i	−0.155182	+	0.130213i
$305$	15.7177			0.899992
$306$	0.730686	−	21.3686i	0.0417706	−	1.22156i
$307$	−2.51120	+	4.34952i	−0.143322	+	0.248240i	−0.928746	−	0.370718i	$-0.879112\pi$
$307$	−2.51120	+	4.34952i	−0.143322	+	0.248240i	0.785424	+	0.618958i	$0.212445\pi$
$308$	5.25562	−	4.91012i	0.299467	−	0.279780i
$309$	−17.5153	+	16.9266i	−0.996408	+	0.962919i
$310$	13.7005	−	4.98657i	0.778136	−	0.283218i
$311$	−14.9273	−	12.5255i	−0.846448	−	0.710254i	0.112556	−	0.993645i	$-0.464096\pi$
$311$	−14.9273	−	12.5255i	−0.846448	−	0.710254i	−0.959004	+	0.283391i	$0.908541\pi$
$312$	3.75459	+	1.07514i	0.212562	+	0.0608677i
$313$	3.40421	+	1.23903i	0.192418	+	0.0700343i	0.436432	−	0.899737i	$-0.356242\pi$
$313$	3.40421	+	1.23903i	0.192418	+	0.0700343i	−0.244014	+	0.969772i	$0.578464\pi$
$314$	−5.10977	+	8.85038i	−0.288361	+	0.499456i
$315$	−8.29806	+	10.2821i	−0.467543	+	0.579329i
$316$	−0.396061	−	0.685998i	−0.0222802	−	0.0385904i
$317$	−5.79125	−	32.8438i	−0.325269	−	1.84469i	−0.507779	−	0.861487i	$-0.669533\pi$
$317$	−5.79125	−	32.8438i	−0.325269	−	1.84469i	0.182510	−	0.983204i	$-0.441578\pi$
$318$	−3.37109	+	6.91813i	−0.189041	+	0.387949i
$319$	−22.3754	+	8.14399i	−1.25278	+	0.455976i
$320$	−1.27520	−	1.07002i	−0.0712861	−	0.0598161i
$321$	2.17394	−	20.7560i	0.121337	−	1.15849i
$322$	−5.07132	+	4.73794i	−0.282614	+	0.264035i
$323$	−25.1729			−1.40066
$324$	3.95707	+	8.08341i	0.219837	+	0.449079i
$325$	−2.51291	+	4.35249i	−0.139391	+	0.241433i
$326$	18.3062	+	6.66290i	1.01389	+	0.369024i
$327$	−1.56148	+	0.695895i	−0.0863501	+	0.0384831i
$328$	−5.19491	+	1.89079i	−0.286841	+	0.104402i
$329$	1.27572	+	0.959458i	0.0703327	+	0.0528966i
$330$	−7.81883	+	0.549596i	−0.430412	+	0.0302543i
$331$	−0.617493	−	3.50198i	−0.0339405	−	0.192486i	0.963123	−	0.269060i	$-0.0867130\pi$
$331$	−0.617493	−	3.50198i	−0.0339405	−	0.192486i	−0.997064	+	0.0765739i	$0.975602\pi$
$332$	8.84401			0.485378
$333$	−9.19603	−	28.2328i	−0.503939	−	1.54715i
$334$	17.8764			0.978152
$335$	1.32607	−	1.11270i	0.0724509	−	0.0607935i
$336$	−4.46646	−	1.02507i	−0.243665	−	0.0559220i
$337$	−6.23333	+	35.3510i	−0.339551	+	1.92569i	0.0370447	+	0.999314i	$0.488206\pi$
$337$	−6.23333	+	35.3510i	−0.339551	+	1.92569i	−0.376596	+	0.926378i	$0.622906\pi$
$338$	7.43833	−	2.70733i	0.404592	−	0.147259i
$339$	−2.87123	−	11.4981i	−0.155944	−	0.624492i
$340$	−2.06017	−	11.6838i	−0.111729	−	0.633645i
$341$	23.8095			1.28936
$342$	9.35219	−	4.98135i	0.505708	−	0.269361i
$343$	−11.6954	−	14.3603i	−0.631494	−	0.775381i
$344$	1.16841	+	0.425268i	0.0629966	+	0.0229289i
$345$	7.54465	−	0.530324i	0.406190	−	0.0285517i
$346$	−1.27575	+	0.464335i	−0.0685848	+	0.0249628i
$347$	−2.67501	+	15.1707i	−0.143602	+	0.814408i	0.824877	+	0.565312i	$0.191244\pi$
$347$	−2.67501	+	15.1707i	−0.143602	+	0.814408i	−0.968479	+	0.249095i	$0.919867\pi$
$348$	12.2770	+	8.91297i	0.658117	+	0.477785i
$349$	−3.89158	−	22.0703i	−0.208312	−	1.18139i	−0.892143	−	0.451753i	$-0.850799\pi$
$349$	−3.89158	−	22.0703i	−0.208312	−	1.18139i	0.683831	−	0.729640i	$-0.260312\pi$
$350$	2.67234	−	5.25688i	0.142842	−	0.280992i
$351$	−10.3510	−	5.48929i	−0.552496	−	0.292997i
$352$	−1.35924	−	2.35427i	−0.0724477	−	0.125483i
$353$	−4.82607	−	1.75655i	−0.256866	−	0.0934915i	0.210378	−	0.977620i	$-0.432531\pi$
$353$	−4.82607	−	1.75655i	−0.256866	−	0.0934915i	−0.467243	+	0.884129i	$0.654753\pi$
$354$	−17.1687	+	7.65146i	−0.912506	+	0.406670i
$355$	−1.24049	−	1.04090i	−0.0658384	−	0.0552450i
$356$	−5.27188	−	4.42363i	−0.279409	−	0.234452i
$357$	−19.6891	−	26.0580i	−1.04206	−	1.37914i
$358$	−9.02949	−	3.28646i	−0.477223	−	0.173695i
$359$	−16.8381	+	29.1644i	−0.888679	+	1.53924i	−0.0472402	+	0.998884i	$0.515043\pi$
$359$	−16.8381	+	29.1644i	−0.888679	+	1.53924i	−0.841438	+	0.540353i	$0.818291\pi$
$360$	3.07746	+	3.93308i	0.162196	+	0.207291i
$361$	3.26237	+	5.65059i	0.171704	+	0.297400i
$362$	−5.22628	−	1.90221i	−0.274687	−	0.0999780i
$363$	6.01091	+	1.72124i	0.315491	+	0.0903418i
$364$	5.48931	−	2.33612i	0.287718	−	0.122446i
$365$	2.28840	−	12.9781i	0.119780	−	0.679307i
$366$	−3.96214	−	15.8668i	−0.207104	−	0.829369i
$367$	−1.24224	−	7.04510i	−0.0648445	−	0.367751i	−0.999912	−	0.0132812i	$-0.995772\pi$
$367$	−1.24224	−	7.04510i	−0.0648445	−	0.367751i	0.935067	−	0.354470i	$-0.115339\pi$
$368$	1.31158	+	2.27172i	0.0683706	+	0.118421i
$369$	16.4218	−	2.32009i	0.854887	−	0.120779i
$370$	−8.23804	−	14.2687i	−0.428275	−	0.741795i
$371$	2.65509	+	11.4517i	0.137846	+	0.594543i
$372$	−8.48752	−	12.5734i	−0.440057	−	0.651901i
$373$	2.66942	−	15.1390i	0.138217	−	0.783869i	−0.834348	−	0.551238i	$-0.814156\pi$
$373$	2.66942	−	15.1390i	0.138217	−	0.783869i	0.972565	−	0.232631i	$-0.0747333\pi$
$374$	3.36437	−	19.0803i	0.173968	−	0.986619i
$375$	−19.0379	+	8.48449i	−0.983112	+	0.438137i
$376$	0.462175	−	0.387811i	0.0238348	−	0.0199998i
$377$	−19.7504			−1.01720
$378$	12.4714	+	5.78484i	0.641459	+	0.297540i
$379$	−0.586331			−0.0301178			−0.0150589	−	0.999887i	$-0.504794\pi$
$379$	−0.586331			−0.0301178			−0.0150589	+	0.999887i	$0.504794\pi$
$380$	4.50406	−	3.77936i	0.231054	−	0.193877i
$381$	−1.77506	+	16.9477i	−0.0909392	+	0.868258i
$382$	2.94909	−	16.7251i	0.150889	−	0.855732i
$383$	−1.06538	+	6.04208i	−0.0544385	+	0.308736i	−0.999853	−	0.0171336i	$-0.994546\pi$
$383$	−1.06538	+	6.04208i	−0.0544385	+	0.308736i	0.945415	+	0.325870i	$0.105657\pi$
$384$	−0.758716	+	1.55703i	−0.0387181	+	0.0794570i
$385$	−8.74882	+	8.17369i	−0.445881	+	0.416570i
$386$	−11.1313	−	19.2800i	−0.566570	−	0.981328i
$387$	−3.16482	−	1.97441i	−0.160877	−	0.100365i
$388$	−8.51337	−	14.7456i	−0.432201	−	0.748594i
$389$	−3.91058	−	22.1780i	−0.198274	−	1.12447i	−0.907678	−	0.419667i	$-0.862147\pi$
$389$	−3.91058	−	22.1780i	−0.198274	−	1.12447i	0.709404	−	0.704803i	$-0.248964\pi$
$390$	−6.25012	−	1.78974i	−0.316487	−	0.0906270i
$391$	−3.24640	+	18.4112i	−0.164177	+	0.931096i
$392$	−6.28582	+	3.08034i	−0.317482	+	0.155581i
$393$	9.27774	+	37.1536i	0.468000	+	1.87415i
$394$	−0.753764	−	0.274348i	−0.0379741	−	0.0138214i
$395$	0.659307	+	1.14195i	0.0331733	+	0.0574579i
$396$	2.52579	+	7.75445i	0.126926	+	0.389676i
$397$	−9.42861	+	16.3308i	−0.473209	+	0.819621i	−0.999530	−	0.0306646i	$-0.990238\pi$
$397$	−9.42861	+	16.3308i	−0.473209	+	0.819621i	0.526321	+	0.850286i	$0.323571\pi$
$398$	2.24532	+	0.817231i	0.112548	+	0.0409641i
$399$	6.30498	−	14.9073i	0.315644	−	0.746298i
$400$	−1.70744	−	1.43271i	−0.0853721	−	0.0716357i
$401$	18.3629	+	15.4083i	0.916998	+	0.769453i	0.973437	−	0.228953i	$-0.0735302\pi$
$401$	18.3629	+	15.4083i	0.916998	+	0.769453i	−0.0564391	+	0.998406i	$0.517975\pi$
$402$	−1.45754	−	1.05815i	−0.0726952	−	0.0527759i
$403$	18.5578	+	6.75448i	0.924429	+	0.336464i
$404$	2.37240	+	4.10912i	0.118031	+	0.204436i
$405$	−6.58718	−	13.4561i	−0.327320	−	0.668641i
$406$	23.1415	−	1.23446i	1.14849	−	0.0612650i
$407$	−4.67223	−	26.4975i	−0.231594	−	1.31343i
$408$	−11.2753	+	5.02500i	−0.558211	+	0.248774i
$409$	3.81333	−	21.6265i	0.188557	−	1.06936i	−0.732742	−	0.680506i	$-0.761760\pi$
$409$	3.81333	−	21.6265i	0.188557	−	1.06936i	0.921299	−	0.388854i	$-0.127129\pi$
$410$	8.64776	−	3.14753i	0.427082	−	0.155445i
$411$	4.41075	+	6.53409i	0.217566	+	0.322303i
$412$	13.2148	+	4.80978i	0.651045	+	0.236961i
$413$	−13.0112	+	25.5949i	−0.640237	+	1.25944i
$414$	−2.43722	−	7.48253i	−0.119783	−	0.367746i
$415$	−14.7223			−0.722688
$416$	−0.391548	−	2.22058i	−0.0191972	−	0.108873i
$417$	17.5852	+	5.03556i	0.861150	+	0.246593i
$418$	9.02269	−	3.28399i	0.441314	−	0.160625i
$419$	−1.76140	+	9.98941i	−0.0860501	+	0.488014i	0.911075	+	0.412241i	$0.135254\pi$
$419$	−1.76140	+	9.98941i	−0.0860501	+	0.488014i	−0.997125	+	0.0757736i	$0.975857\pi$
$420$	7.43513	+	1.70639i	0.362797	+	0.0832632i
$421$	−12.2553	+	10.2834i	−0.597289	+	0.501185i	−0.890573	−	0.454841i	$-0.849696\pi$
$421$	−12.2553	+	10.2834i	−0.597289	+	0.501185i	0.293284	+	0.956025i	$0.405252\pi$
$422$	10.3941			0.505978
$423$	−1.59750	+	0.850893i	−0.0776731	+	0.0413718i
$424$	4.44315			0.215778
$425$	−2.75848	−	15.6441i	−0.133806	−	0.758852i
$426$	−0.738063	+	1.51465i	−0.0357593	+	0.0733849i
$427$	−19.9648	−	15.0154i	−0.966166	−	0.726645i
$428$	−11.3224	+	4.12102i	−0.547289	+	0.199197i
$429$	−8.59159	−	6.23740i	−0.414806	−	0.301144i
$430$	−1.94501	−	0.707926i	−0.0937968	−	0.0341392i
$431$	10.1894	−	17.6486i	0.490809	−	0.850105i	−0.509135	−	0.860686i	$-0.670035\pi$
$431$	10.1894	−	17.6486i	0.490809	−	0.850105i	0.999944	+	0.0105811i	$0.00336812\pi$
$432$	3.19461	−	4.09810i	0.153701	−	0.197170i
$433$	9.41053			0.452241			0.226121	−	0.974099i	$-0.427396\pi$
$433$	9.41053			0.452241			0.226121	+	0.974099i	$0.427396\pi$
$434$	−22.1663	−	6.75431i	−1.06402	−	0.324217i
$435$	−20.4371	−	14.8371i	−0.979882	−	0.711383i
$436$	0.756084	+	0.634430i	0.0362099	+	0.0303837i
$437$	−8.70630	+	3.16884i	−0.416479	+	0.151586i
$438$	−13.6781	+	0.961452i	−0.653565	+	0.0459400i
$439$	1.35861	+	7.70504i	0.0648427	+	0.367741i	0.999912	+	0.0132760i	$0.00422601\pi$
$439$	1.35861	+	7.70504i	0.0648427	+	0.367741i	−0.935069	+	0.354465i	$0.884663\pi$
$440$	2.26267	+	3.91906i	0.107869	+	0.186834i
$441$	20.3630	−	5.13316i	0.969665	−	0.244436i
$442$	8.03514	−	13.9173i	0.382193	−	0.661977i
$443$	−16.1126	−	5.86449i	−0.765531	−	0.278630i	−0.0704048	−	0.997519i	$-0.522429\pi$
$443$	−16.1126	−	5.86449i	−0.765531	−	0.278630i	−0.695126	+	0.718888i	$0.744651\pi$
$444$	−12.3274	+	11.9131i	−0.585032	+	0.565369i
$445$	8.77589	+	7.36385i	0.416017	+	0.349080i
$446$	−2.39329	+	0.871087i	−0.113326	+	0.0412472i
$447$	12.9846	+	3.71817i	0.614149	+	0.175863i
$448$	0.597570	+	2.57738i	0.0282325	+	0.121770i
$449$	9.98223	−	17.2897i	0.471091	−	0.815953i	−0.528363	−	0.849019i	$-0.677194\pi$
$449$	9.98223	−	17.2897i	0.471091	−	0.815953i	0.999453	+	0.0330660i	$0.0105272\pi$
$450$	4.12058	+	5.26622i	0.194246	+	0.248252i
$451$	15.0286			0.707668
$452$	−5.24150	+	4.39814i	−0.246539	+	0.206871i
$453$	−12.7482	+	26.1618i	−0.598963	+	1.22919i
$454$	−5.48391	−	4.60154i	−0.257373	−	0.215961i
$455$	−9.13784	+	3.88885i	−0.428389	+	0.182312i
$456$	−4.95060	−	3.59408i	−0.231833	−	0.168308i
$457$	−25.5689	+	21.4548i	−1.19606	+	1.00361i	−0.196327	+	0.980538i	$0.562901\pi$
$457$	−25.5689	+	21.4548i	−1.19606	+	1.00361i	−0.999734	+	0.0230757i	$0.992654\pi$
$458$	−6.51686	+	11.2875i	−0.304513	+	0.527432i
$459$	36.2154	−	7.73903i	1.69039	−	0.361227i
$460$	−2.18333	−	3.78163i	−0.101798	−	0.176320i
$461$	4.49969	+	25.5190i	0.209571	+	1.18854i	0.890082	+	0.455800i	$0.150647\pi$
$461$	4.49969	+	25.5190i	0.209571	+	1.18854i	−0.680511	+	0.732738i	$0.738242\pi$
$462$	10.4566	+	6.77136i	0.486486	+	0.315032i
$463$	4.50746	−	1.64058i	0.209480	−	0.0762443i	−0.235149	−	0.971959i	$-0.575558\pi$
$463$	4.50746	−	1.64058i	0.209480	−	0.0762443i	0.444629	+	0.895715i	$0.353336\pi$
$464$	1.52100	−	8.62604i	0.0706108	−	0.400454i
$465$	14.1288	+	20.9305i	0.655209	+	0.970627i
$466$	13.4576	−	11.2923i	0.623411	−	0.523104i
$467$	−5.01027	+	8.67805i	−0.231848	+	0.401572i	−0.958352	−	0.285590i	$-0.907810\pi$
$467$	−5.01027	+	8.67805i	−0.231848	+	0.401572i	0.726504	+	0.687162i	$0.241144\pi$
$468$	−0.231173	+	6.76056i	−0.0106860	+	0.312507i
$469$	−2.74738	+	0.146555i	−0.126862	+	0.00676730i
$470$	−0.769364	+	0.645573i	−0.0354881	+	0.0297781i
$471$	−17.0168	−	4.87282i	−0.784094	−	0.224528i
$472$	8.31324	+	6.97564i	0.382648	+	0.321080i
$473$	−2.58935	−	2.17272i	−0.119058	−	0.0999018i
$474$	0.986585	−	0.953426i	0.0453154	−	0.0437923i
$475$	6.03074	−	5.06039i	0.276709	−	0.232187i
$476$	−8.54491	+	16.8091i	−0.391655	+	0.770444i
$477$	−13.0402	−	2.76189i	−0.597069	−	0.126458i
$478$	−0.107368	+	0.185966i	−0.00491088	+	0.00850589i
$479$	8.33829	−	6.99666i	0.380986	−	0.319686i	−0.432103	−	0.901824i	$-0.642228\pi$
$479$	8.33829	−	6.99666i	0.380986	−	0.319686i	0.813090	+	0.582139i	$0.197784\pi$
$480$	1.26301	−	2.59193i	0.0576480	−	0.118305i
$481$	3.87537	−	21.9783i	0.176702	−	1.00213i
$482$	6.03653	−	2.19712i	0.274956	−	0.100076i
$483$	−10.0900	−	6.53392i	−0.459109	−	0.297304i
$484$	−0.626850	−	3.55504i	−0.0284932	−	0.161593i
$485$	14.1719	+	24.5464i	0.643511	+	1.11459i
$486$	−11.9233	+	10.0417i	−0.540850	+	0.455501i
$487$	−6.78837	+	11.7578i	−0.307611	+	0.532797i	−0.977839	−	0.209358i	$-0.932863\pi$
$487$	−6.78837	+	11.7578i	−0.307611	+	0.532797i	0.670229	+	0.742155i	$0.266196\pi$
$488$	−7.23297	+	6.06918i	−0.327421	+	0.274739i
$489$	−3.51484	+	33.5586i	−0.158947	+	1.51757i
$490$	10.4638	−	5.12771i	0.472704	−	0.231647i
$491$	−14.8751	−	12.4817i	−0.671305	−	0.563292i	0.242146	−	0.970240i	$-0.422149\pi$
$491$	−14.8751	−	12.4817i	−0.671305	−	0.563292i	−0.913451	+	0.406948i	$0.866593\pi$
$492$	−5.35732	−	7.93635i	−0.241527	−	0.357798i
$493$	47.8214	−	40.1269i	2.15377	−	1.80722i
$494$	7.96416			0.358324
$495$	−4.20459	−	12.9085i	−0.188982	−	0.580195i
$496$	−4.37920	+	7.58500i	−0.196632	+	0.340576i
$497$	0.581304	+	2.50722i	0.0260750	+	0.112464i
$498$	3.71122	+	14.8619i	0.166304	+	0.665978i
$499$	14.4165	−	5.24717i	0.645371	−	0.234896i	0.00146313	−	0.999999i	$-0.499534\pi$
$499$	14.4165	−	5.24717i	0.645371	−	0.234896i	0.643908	+	0.765103i	$0.277312\pi$
$500$	9.21833	+	7.73510i	0.412256	+	0.345924i
$501$	7.50148	+	30.0404i	0.335141	+	1.34210i
$502$	−16.5164	−	6.01146i	−0.737161	−	0.268305i
$503$	−10.3416	+	17.9122i	−0.461111	+	0.798668i	−0.999017	−	0.0443375i	$-0.985882\pi$
$503$	−10.3416	+	17.9122i	−0.461111	+	0.798668i	0.537906	+	0.843005i	$0.319216\pi$
$504$	−0.151688	−	7.93580i	−0.00675674	−	0.353489i
$505$	−3.94924	−	6.84028i	−0.175739	−	0.304389i
$506$	−1.23828	−	7.02264i	−0.0550483	−	0.312194i
$507$	7.67089	+	11.3637i	0.340676	+	0.504678i
$508$	9.24497	−	3.36490i	0.410179	−	0.149293i
$509$	−2.43730	−	2.04514i	−0.108032	−	0.0906492i	0.587172	−	0.809462i	$-0.300241\pi$
$509$	−2.43730	−	2.04514i	−0.108032	−	0.0906492i	−0.695203	+	0.718813i	$0.744686\pi$
$510$	18.7696	−	8.36491i	0.831131	−	0.370405i
$511$	−15.3050	+	14.2989i	−0.677054	+	0.632545i
$512$	1.00000			0.0441942
$513$	12.2954	+	13.6256i	0.542854	+	0.601583i
$514$	8.20797	−	14.2166i	0.362038	−	0.627068i
$515$	−21.9981	−	8.00666i	−0.969352	−	0.352815i
$516$	−0.224339	+	2.14192i	−0.00987597	+	0.0942926i
$517$	−1.54122	+	0.560957i	−0.0677827	+	0.0246709i
$518$	−3.16707	+	25.9943i	−0.139153	+	1.14212i
$519$	−1.31564	−	1.94899i	−0.0577500	−	0.0855510i
$520$	0.651795	+	3.69651i	0.0285831	+	0.162103i
$521$	−30.1957			−1.32290			−0.661449	−	0.749990i	$-0.730058\pi$
$521$	−30.1957			−1.32290			−0.661449	+	0.749990i	$0.730058\pi$
$522$	−9.82598	+	24.3710i	−0.430072	+	1.06669i
$523$	33.0749			1.44627			0.723133	−	0.690709i	$-0.242701\pi$
$523$	33.0749			1.44627			0.723133	+	0.690709i	$0.242701\pi$
$524$	16.9367	−	14.2116i	0.739884	−	0.620836i
$525$	9.95531	+	2.28478i	0.434485	+	0.0997159i
$526$	−3.66178	+	20.7670i	−0.159661	+	0.905484i
$527$	−58.6569	+	21.3494i	−2.55513	+	0.929992i
$528$	3.38585	−	3.27206i	0.147350	−	0.142398i
$529$	−2.79905	−	15.8742i	−0.121698	−	0.690182i
$530$	−7.39633			−0.321276
$531$	−20.0624	−	25.6403i	−0.870634	−	1.11270i
$532$	−9.33161	+	0.497783i	−0.404577	+	0.0215816i
$533$	11.7137	+	4.26343i	0.507376	+	0.184670i
$534$	5.22145	−	10.7154i	0.225954	−	0.463702i
$535$	18.8480	−	6.86010i	0.814869	−	0.296588i
$536$	−0.180575	+	1.02409i	−0.00779963	+	0.0442339i
$537$	1.73369	−	16.5527i	0.0748142	−	0.714302i
$538$	−1.41205	−	8.00811i	−0.0608776	−	0.345254i
$539$	18.9213	−	2.02443i	0.815000	−	0.0871984i
$540$	−5.31795	+	6.82195i	−0.228848	+	0.293570i
$541$	16.1933	+	28.0475i	0.696202	+	1.20586i	0.969774	+	0.244006i	$0.0784617\pi$
$541$	16.1933	+	28.0475i	0.696202	+	1.20586i	−0.273571	+	0.961852i	$0.588205\pi$
$542$	0.523576	+	0.190566i	0.0224895	+	0.00818551i
$543$	1.00346	−	9.58073i	0.0430627	−	0.411149i
$544$	5.45962	+	4.58116i	0.234079	+	0.196416i
$545$	−1.25862	−	1.05611i	−0.0539135	−	0.0452388i
$546$	6.22922	+	8.24420i	0.266586	+	0.352819i
$547$	−12.8922	−	4.69236i	−0.551229	−	0.200631i	0.0513635	−	0.998680i	$-0.483643\pi$
$547$	−12.8922	−	4.69236i	−0.551229	−	0.200631i	−0.602592	+	0.798049i	$0.705866\pi$
$548$	2.27576	−	3.94173i	0.0972157	−	0.168382i
$549$	25.0007	−	13.3164i	1.06700	−	0.568328i
$550$	3.02961	+	5.24745i	0.129183	+	0.223752i
$551$	29.0717	+	10.5812i	1.23850	+	0.450776i
$552$	−3.26713	+	3.15732i	−0.139058	+	0.134384i
$553$	0.253467	−	2.08037i	0.0107785	−	0.0884665i
$554$	−4.99848	+	28.3478i	−0.212365	+	1.20438i
$555$	20.5209	−	19.8312i	0.871064	−	0.841787i
$556$	−1.83387	−	10.4004i	−0.0777736	−	0.441076i
$557$	−7.54492	−	13.0682i	−0.319689	−	0.553717i	0.660734	−	0.750620i	$-0.270245\pi$
$557$	−7.54492	−	13.0682i	−0.319689	−	0.553717i	−0.980423	+	0.196903i	$0.936912\pi$
$558$	17.5674	−	19.5390i	0.743686	−	0.827153i
$559$	−1.40183	−	2.42804i	−0.0592912	−	0.102695i
$560$	−0.994752	−	4.29047i	−0.0420359	−	0.181305i
$561$	33.4753	−	2.35302i	1.41333	−	0.0993447i
$562$	−0.427793	+	2.42613i	−0.0180453	+	0.102340i
$563$	5.74279	−	32.5690i	0.242030	−	1.37262i	−0.585261	−	0.810845i	$-0.699008\pi$
$563$	5.74279	−	32.5690i	0.242030	−	1.37262i	0.827291	−	0.561774i	$-0.189881\pi$
$564$	0.845639	+	0.613924i	0.0356078	+	0.0258509i
$565$	8.72531	−	7.32141i	0.367077	−	0.308014i
$566$	22.2415			0.934881
$567$	−4.48775	+	23.3850i	−0.188468	+	0.982079i
$568$	0.972779			0.0408169
$569$	17.7559	−	14.8990i	0.744367	−	0.624598i	−0.189639	−	0.981854i	$-0.560732\pi$
$569$	17.7559	−	14.8990i	0.744367	−	0.624598i	0.934007	+	0.357255i	$0.116287\pi$
$570$	8.24106	+	5.98291i	0.345180	+	0.250597i
$571$	−4.32321	+	24.5181i	−0.180921	+	1.02605i	0.750165	+	0.661251i	$0.229974\pi$
$571$	−4.32321	+	24.5181i	−0.180921	+	1.02605i	−0.931086	+	0.364801i	$0.881137\pi$
$572$	−1.06442	+	6.03660i	−0.0445054	+	0.252403i
$573$	29.3432	−	2.06258i	1.22583	−	0.0861653i
$574$	−13.9914	−	4.26333i	−0.583990	−	0.177948i
$575$	−2.92338	−	5.06344i	−0.121913	−	0.211160i
$576$	−2.93489	−	0.621606i	−0.122287	−	0.0259003i
$577$	5.17950	+	8.97115i	0.215625	+	0.373474i	0.953466	−	0.301501i	$-0.0974877\pi$
$577$	5.17950	+	8.97115i	0.215625	+	0.373474i	−0.737841	+	0.674975i	$0.764154\pi$
$578$	5.86835	+	33.2810i	0.244091	+	1.38431i
$579$	27.7281	−	26.7961i	1.15234	−	1.11361i
$580$	−2.53195	+	14.3594i	−0.105134	+	0.596243i
$581$	18.7005	+	14.0645i	0.775825	+	0.583492i
$582$	21.2067	−	20.4940i	0.879048	−	0.849503i
$583$	−11.3502	−	4.13112i	−0.470076	−	0.171094i
$584$	3.95827	+	6.85593i	0.163794	+	0.283700i
$585$	0.384825	−	11.2540i	0.0159106	−	0.465297i
$586$	−6.90733	+	11.9638i	−0.285339	+	0.494222i
$587$	−9.95343	−	3.62275i	−0.410822	−	0.149527i	0.128338	−	0.991731i	$-0.459036\pi$
$587$	−9.95343	−	3.62275i	−0.410822	−	0.149527i	−0.539160	+	0.842203i	$0.681258\pi$
$588$	−7.81407	−	9.27040i	−0.322247	−	0.382305i
$589$	−23.6976	−	19.8846i	−0.976441	−	0.819331i
$590$	−13.8387	−	11.6121i	−0.569731	−	0.478061i
$591$	0.144725	−	1.38179i	0.00595319	−	0.0568391i
$592$	9.30067	+	3.38517i	0.382255	+	0.139129i
$593$	−18.5963	−	32.2097i	−0.763659	−	1.32270i	−0.940953	−	0.338538i	$-0.890068\pi$
$593$	−18.5963	−	32.2097i	−0.763659	−	1.32270i	0.177294	−	0.984158i	$-0.443266\pi$
$594$	−11.9711	+	7.49847i	−0.491178	+	0.307666i
$595$	14.2244	−	27.9814i	0.583142	−	1.14713i
$596$	−1.35410	−	7.67948i	−0.0554661	−	0.314564i
$597$	−0.431109	+	4.11609i	−0.0176441	+	0.168460i
$598$	1.02709	−	5.82492i	0.0420008	−	0.238199i
$599$	0.629100	−	0.228973i	0.0257043	−	0.00935560i	−0.329136	−	0.944283i	$-0.606757\pi$
$599$	0.629100	−	0.228973i	0.0257043	−	0.00935560i	0.354840	+	0.934927i	$0.384535\pi$
$600$	1.69111	−	3.47048i	0.0690392	−	0.141682i
$601$	13.9237	+	5.06783i	0.567962	+	0.206721i	0.610009	−	0.792395i	$-0.291166\pi$
$601$	13.9237	+	5.06783i	0.567962	+	0.206721i	−0.0420474	+	0.999116i	$0.513388\pi$
$602$	1.79429	+	2.75732i	0.0731297	+	0.112380i
$603$	1.16655	−	2.89335i	0.0475055	−	0.117826i
$604$	16.8023			0.683678
$605$	1.04349	+	5.91793i	0.0424240	+	0.240598i
$606$	−5.90963	+	5.71101i	−0.240062	+	0.231994i
$607$	−27.3847	+	9.96723i	−1.11151	+	0.404557i	−0.831548	−	0.555453i	$-0.812545\pi$
$607$	−27.3847	+	9.96723i	−1.11151	+	0.404557i	−0.279964	+	0.960010i	$0.590323\pi$
$608$	−0.613331	+	3.47837i	−0.0248739	+	0.141067i
$609$	11.7853	+	38.3701i	0.477566	+	1.55484i
$610$	12.0404	−	10.1031i	0.487503	−	0.409064i
$611$	−1.36040			−0.0550360
$612$	−13.1757	−	16.8390i	−0.532597	−	0.680675i
$613$	42.2199			1.70524			0.852622	−	0.522528i	$-0.175011\pi$
$613$	42.2199			1.70524			0.852622	+	0.522528i	$0.175011\pi$
$614$	0.872130	+	4.94609i	0.0351963	+	0.199608i
$615$	8.91812	+	13.2113i	0.359613	+	0.532732i
$616$	0.869871	−	7.13962i	0.0350481	−	0.287663i
$617$	−18.0926	+	6.58518i	−0.728382	+	0.265109i	−0.679480	−	0.733694i	$-0.737795\pi$
$617$	−18.0926	+	6.58518i	−0.728382	+	0.265109i	−0.0489024	+	0.998804i	$0.515572\pi$
$618$	−2.53728	+	24.2251i	−0.102064	+	0.974476i
$619$	21.9392	+	7.98520i	0.881809	+	0.320952i	0.742940	−	0.669358i	$-0.233431\pi$
$619$	21.9392	+	7.98520i	0.881809	+	0.320952i	0.138870	+	0.990311i	$0.455653\pi$
$620$	7.28988	−	12.6264i	0.292769	−	0.507090i
$621$	11.5513	−	7.23553i	0.463537	−	0.290352i
$622$	−19.4862			−0.781324
$623$	−4.11245	−	17.7374i	−0.164762	−	0.710635i
$624$	3.56727	−	1.58980i	0.142805	−	0.0636430i
$625$	−6.80818	−	5.71274i	−0.272327	−	0.228510i
$626$	3.40421	−	1.23903i	0.136060	−	0.0495217i
$627$	9.30478	+	13.7841i	0.371597	+	0.550485i
$628$	1.77460	+	10.0643i	0.0708144	+	0.401609i
$629$	35.2701	+	61.0896i	1.40631	+	2.43580i
$630$	0.252510	+	13.2104i	0.0100602	+	0.526316i
$631$	22.7548	−	39.4125i	0.905854	−	1.56898i	0.0860870	−	0.996288i	$-0.472564\pi$
$631$	22.7548	−	39.4125i	0.905854	−	1.56898i	0.819767	−	0.572697i	$-0.194103\pi$
$632$	−0.744351	−	0.270922i	−0.0296087	−	0.0107767i
$633$	4.36170	+	17.4668i	0.173362	+	0.694243i
$634$	−25.5479	−	21.4373i	−1.01464	−	0.851383i
$635$	−15.3897	+	5.60141i	−0.610723	+	0.222285i
$636$	1.86448	+	7.46649i	0.0739315	+	0.296066i
$637$	15.3221	+	3.78987i	0.607084	+	0.150160i
$638$	−11.9057	+	20.6213i	−0.471352	+	0.816405i
$639$	−2.85500	−	0.604685i	−0.112942	−	0.0239210i
$640$	−1.66466			−0.0658015
$641$	−17.6023	+	14.7701i	−0.695248	+	0.583382i	−0.920417	−	0.390938i	$-0.872151\pi$
$641$	−17.6023	+	14.7701i	−0.695248	+	0.583382i	0.225170	+	0.974320i	$0.427706\pi$
$642$	−11.6764	−	17.2974i	−0.460831	−	0.682675i
$643$	−18.5835	−	15.5934i	−0.732862	−	0.614944i	0.198048	−	0.980192i	$-0.436540\pi$
$643$	−18.5835	−	15.5934i	−0.732862	−	0.614944i	−0.930910	+	0.365248i	$0.880984\pi$
$644$	−0.839368	+	6.88926i	−0.0330758	+	0.271475i
$645$	0.373448	−	3.56556i	0.0147045	−	0.140394i
$646$	−19.2835	+	16.1808i	−0.758701	+	0.636626i
$647$	−12.9724	+	22.4688i	−0.509996	+	0.883339i	0.489937	+	0.871758i	$0.337020\pi$
$647$	−12.9724	+	22.4688i	−0.509996	+	0.883339i	−0.999933	+	0.0115809i	$0.996314\pi$
$648$	8.22721	+	3.64870i	0.323195	+	0.143334i
$649$	−14.7507	−	25.5489i	−0.579015	−	1.00288i
$650$	0.872725	+	4.94947i	0.0342311	+	0.194134i
$651$	2.04861	−	40.0837i	0.0802913	−	1.57100i
$652$	18.3062	−	6.66290i	0.716925	−	0.260939i
$653$	6.12739	−	34.7501i	0.239783	−	1.35988i	−0.592519	−	0.805556i	$-0.701867\pi$
$653$	6.12739	−	34.7501i	0.239783	−	1.35988i	0.832303	−	0.554322i	$-0.187022\pi$
$654$	−0.748851	+	1.53679i	−0.0292824	+	0.0600931i
$655$	−28.1939	+	23.6575i	−1.10163	+	0.924374i
$656$	−2.76415	+	4.78765i	−0.107922	+	0.186927i
$657$	−7.35542	−	22.5819i	−0.286962	−	0.881004i
$658$	1.59399	−	0.0850291i	0.0621400	−	0.00331478i
$659$	35.1799	−	29.5194i	1.37041	−	1.14991i	0.397803	−	0.917471i	$-0.369773\pi$
$659$	35.1799	−	29.5194i	1.37041	−	1.14991i	0.972610	−	0.232442i	$-0.0746716\pi$
$660$	−5.63630	+	5.44686i	−0.219393	+	0.212019i
$661$	6.53202	+	5.48102i	0.254066	+	0.213187i	0.760921	−	0.648845i	$-0.224747\pi$
$661$	6.53202	+	5.48102i	0.254066	+	0.213187i	−0.506855	+	0.862031i	$0.669192\pi$
$662$	−2.72406	−	2.28575i	−0.105873	−	0.0888383i
$663$	26.7591	+	7.66253i	1.03924	+	0.297588i
$664$	6.77491	−	5.68482i	0.262917	−	0.220614i
$665$	15.5340	−	0.828640i	0.602381	−	0.0321333i
$666$	−25.1922	−	15.7165i	−0.976179	−	0.609000i
$667$	11.4882	−	19.8982i	0.444826	−	0.770461i
$668$	13.6941	−	11.4907i	0.529841	−	0.444589i
$669$	−2.46812	−	3.65627i	−0.0954229	−	0.141360i
$670$	0.300595	−	1.70476i	0.0116130	−	0.0658606i
$671$	24.1198	−	8.77890i	0.931136	−	0.338906i
$672$	−4.08040	+	2.08574i	−0.157405	+	0.0804590i
$673$	7.67594	+	43.5324i	0.295886	+	1.67805i	0.663580	+	0.748105i	$0.269036\pi$
$673$	7.67594	+	43.5324i	0.295886	+	1.67805i	−0.367695	+	0.929947i	$0.619853\pi$
$674$	17.9482	+	31.0871i	0.691338	+	1.19743i
$675$	−7.12049	+	9.13429i	−0.274068	+	0.351579i
$676$	3.95785	−	6.85521i	0.152225	−	0.263662i
$677$	−17.8728	+	14.9970i	−0.686906	+	0.576383i	−0.918015	−	0.396545i	$-0.870209\pi$
$677$	−17.8728	+	14.9970i	−0.686906	+	0.576383i	0.231109	+	0.972928i	$0.425765\pi$
$678$	−9.59034	−	6.96248i	−0.368315	−	0.267392i
$679$	5.44830	−	44.7178i	0.209087	−	1.71611i
$680$	−9.08841	−	7.62608i	−0.348525	−	0.292447i
$681$	5.43145	−	11.1464i	0.208134	−	0.427130i
$682$	18.2391	−	15.3045i	0.698413	−	0.586038i
$683$	−22.9480			−0.878079			−0.439040	−	0.898468i	$-0.644681\pi$
$683$	−22.9480			−0.878079			−0.439040	+	0.898468i	$0.644681\pi$
$684$	3.96224	−	9.82741i	0.151500	−	0.375760i
$685$	−3.78837	+	6.56164i	−0.144746	+	0.250708i
$686$	−18.1898	−	3.48291i	−0.694490	−	0.132978i
$687$	−21.7028	−	6.21466i	−0.828014	−	0.237104i
$688$	1.16841	−	0.425268i	0.0445454	−	0.0162132i
$689$	−7.67468	−	6.43982i	−0.292382	−	0.245338i
$690$	5.43865	−	5.25586i	0.207046	−	0.200087i
$691$	16.1468	+	5.87695i	0.614253	+	0.223570i	0.630363	−	0.776301i	$-0.282906\pi$
$691$	16.1468	+	5.87695i	0.614253	+	0.223570i	−0.0161103	+	0.999870i	$0.505128\pi$
$692$	−0.678813	+	1.17574i	−0.0258046	+	0.0446949i
$693$	−6.99101	+	20.4133i	−0.265567	+	0.775437i
$694$	7.70239	+	13.3409i	0.292379	+	0.506415i
$695$	3.05278	+	17.3132i	0.115798	+	0.656726i
$696$	15.1339	−	1.06378i	0.573648	−	0.0403225i
$697$	−37.0242	+	13.4757i	−1.40239	+	0.510429i
$698$	−17.1676	−	14.4053i	−0.649804	−	0.545250i
$699$	24.6233	+	17.8762i	0.931338	+	0.676141i
$700$	−1.33193	−	5.74475i	−0.0503422	−	0.217131i
$701$	24.0297			0.907588			0.453794	−	0.891107i	$-0.350070\pi$
$701$	24.0297			0.907588			0.453794	+	0.891107i	$0.350070\pi$
$702$	−11.4578	+	2.44846i	−0.432446	+	0.0924113i
$703$	−17.4793	+	30.2750i	−0.659243	+	1.14184i
$704$	−2.55453	−	0.929774i	−0.0962776	−	0.0350422i
$705$	−1.40770	−	1.02198i	−0.0530171	−	0.0384898i
$706$	−4.82607	+	1.75655i	−0.181632	+	0.0661085i
$707$	−1.51826	+	12.4614i	−0.0571002	+	0.468660i
$708$	−8.23372	+	16.8972i	−0.309442	+	0.635035i
$709$	1.35362	+	7.67678i	0.0508364	+	0.288308i	0.999618	−	0.0276239i	$-0.00879409\pi$
$709$	1.35362	+	7.67678i	0.0508364	+	0.288308i	−0.948782	+	0.315932i	$0.897683\pi$
$710$	−1.61935			−0.0607730
$711$	2.01619	+	1.25782i	0.0756129	+	0.0471719i
$712$	−6.88195			−0.257912
$713$	−17.5996	+	14.7678i	−0.659109	+	0.553058i
$714$	−31.8325	−	7.30568i	−1.19130	−	0.273408i
$715$	1.77189	−	10.0489i	0.0662649	−	0.375807i
$716$	−9.02949	+	3.28646i	−0.337448	+	0.122821i
$717$	−0.357561	−	0.102389i	−0.0133534	−	0.00382378i
$718$	5.84780	+	33.1645i	0.218238	+	1.23769i
$719$	−1.05345			−0.0392871			−0.0196436	−	0.999807i	$-0.506253\pi$
$719$	−1.05345			−0.0392871			−0.0196436	+	0.999807i	$0.506253\pi$
$720$	4.88560	+	1.03476i	0.182076	+	0.0385633i
$721$	20.2934	+	31.1854i	0.755766	+	1.16140i
$722$	6.13125	+	2.23159i	0.228182	+	0.0830513i
$723$	6.22526	+	9.22210i	0.231520	+	0.342974i
$724$	−5.22628	+	1.90221i	−0.194233	+	0.0706952i
$725$	−3.39017	+	19.2266i	−0.125908	+	0.714059i
$726$	5.71102	−	2.54519i	0.211956	−	0.0944610i
$727$	3.77605	+	21.4150i	0.140046	+	0.794239i	0.971212	+	0.238216i	$0.0765625\pi$
$727$	3.77605	+	21.4150i	0.140046	+	0.794239i	−0.831166	+	0.556024i	$0.812326\pi$
$728$	2.70343	−	5.31804i	0.100196	−	0.197100i
$729$	−21.8779	−	15.8226i	−0.810294	−	0.586023i
$730$	−6.58918	−	11.4128i	−0.243876	−	0.422406i
$731$	8.32731	+	3.03089i	0.307997	+	0.112102i
$732$	−13.2341	−	9.60783i	−0.489148	−	0.355116i
$733$	−39.0794	−	32.7915i	−1.44343	−	1.21118i	−0.937204	−	0.348783i	$-0.886595\pi$
$733$	−39.0794	−	32.7915i	−1.44343	−	1.21118i	−0.506228	−	0.862400i	$-0.668960\pi$
$734$	−5.48012	−	4.59836i	−0.202275	−	0.169729i
$735$	13.0078	+	15.4321i	0.479799	+	0.569220i
$736$	2.46496	+	0.897170i	0.0908595	+	0.0330701i
$737$	1.41345	−	2.44818i	0.0520653	−	0.0901797i
$738$	11.0885	−	12.3330i	0.408175	−	0.453986i
$739$	−19.2835	−	33.4000i	−0.709355	−	1.22864i	−0.965097	−	0.261894i	$-0.915653\pi$
$739$	−19.2835	−	33.4000i	−0.709355	−	1.22864i	0.255741	−	0.966745i	$-0.417680\pi$
$740$	−15.4825	−	5.63515i	−0.569146	−	0.207152i
$741$	3.34201	+	13.3834i	0.122772	+	0.491650i
$742$	9.39493	+	7.06585i	0.344899	+	0.259396i
$743$	1.59146	−	9.02561i	0.0583849	−	0.331117i	−0.941599	−	0.336735i	$-0.890677\pi$
$743$	1.59146	−	9.02561i	0.0583849	−	0.331117i	0.999984	+	0.00561810i	$0.00178831\pi$
$744$	−14.5839	−	4.17613i	−0.534670	−	0.153104i
$745$	2.25412	+	12.7837i	0.0825844	+	0.468359i
$746$	−7.68628	−	13.3130i	−0.281415	−	0.487425i
$747$	−23.4174	+	12.4730i	−0.856796	+	0.456364i
$748$	−9.68732	−	16.7789i	−0.354204	−	0.613499i
$749$	−30.4945	−	9.29200i	−1.11425	−	0.339522i
$750$	−9.13014	+	18.7368i	−0.333386	+	0.684172i
$751$	0.820318	−	4.65225i	0.0299338	−	0.169763i	−0.966176	−	0.257884i	$-0.916975\pi$
$751$	0.820318	−	4.65225i	0.0299338	−	0.169763i	0.996110	+	0.0881204i	$0.0280860\pi$
$752$	0.104767	−	0.594161i	0.00382044	−	0.0216668i
$753$	3.17119	−	30.2775i	0.115565	−	1.10337i
$754$	−15.1297	+	12.6953i	−0.550990	+	0.462335i
$755$	−27.9702			−1.01794
$756$	13.2721	−	3.58501i	0.482700	−	0.130386i
$757$	−7.23189			−0.262848			−0.131424	−	0.991326i	$-0.541955\pi$
$757$	−7.23189			−0.262848			−0.131424	+	0.991326i	$0.541955\pi$
$758$	−0.449156	+	0.376886i	−0.0163141	+	0.0136891i
$759$	11.2816	−	5.02778i	0.409495	−	0.182497i
$760$	1.02099	−	5.79031i	0.0370351	−	0.210037i
$761$	3.19621	−	18.1266i	0.115863	−	0.657090i	−0.870457	−	0.492245i	$-0.836176\pi$
$761$	3.19621	−	18.1266i	0.115863	−	0.657090i	0.986319	−	0.164845i	$-0.0527124\pi$
$762$	9.53401	+	14.1237i	0.345381	+	0.511648i
$763$	0.589801	+	2.54387i	0.0213522	+	0.0920944i
$764$	−8.49157	−	14.7078i	−0.307214	−	0.532110i
$765$	21.9331	+	28.0311i	0.792993	+	1.01347i
$766$	3.06765	+	5.31332i	0.110839	+	0.191978i
$767$	−4.24915	−	24.0981i	−0.153428	−	0.870133i
$768$	0.419631	+	1.68045i	0.0151421	+	0.0606380i
$769$	−0.489316	+	2.77505i	−0.0176452

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.40163 + 1.01757i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.289065 + 1.63937i) q^{5} +(1.72779 - 0.121449i) q^{6} +(1.93330 - 1.80620i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.929121 + 2.85250i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.40163 + 1.01757i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.289065 + 1.63937i) q^{5} +(1.72779 - 0.121449i) q^{6} +(1.93330 - 1.80620i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.929121 + 2.85250i) q^{9} +(0.832330 + 1.44164i) q^{10} +(0.472059 + 2.67718i) q^{11} +(1.24550 - 1.20364i) q^{12} +(-0.391548 + 2.22058i) q^{13} +(0.319985 - 2.62633i) q^{14} +(-2.07333 + 2.00364i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-3.56351 - 6.17218i) q^{17} +(2.54530 + 1.58791i) q^{18} +(1.76602 - 3.05883i) q^{19} +(1.56427 + 0.569347i) q^{20} +(4.54769 - 0.564370i) q^{21} +(2.08247 + 1.74740i) q^{22} +(-2.00945 - 1.68613i) q^{23} +(0.180424 - 1.72263i) q^{24} +(2.09449 + 0.762331i) q^{25} +(1.12742 + 1.95275i) q^{26} +(-1.60032 + 4.94358i) q^{27} +(-1.44305 - 2.21757i) q^{28} +(1.52100 + 8.62604i) q^{29} +(-0.300344 + 2.86759i) q^{30} +(1.52088 - 8.62534i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.06255 + 4.23276i) q^{33} +(-6.69721 - 2.43759i) q^{34} +(2.40219 + 3.69150i) q^{35} +(2.97050 - 0.419674i) q^{36} -9.89756 q^{37} +(-0.613331 - 3.47837i) q^{38} +(-2.80839 + 2.71400i) q^{39} +(1.56427 - 0.569347i) q^{40} +(0.959980 - 5.44432i) q^{41} +(3.12096 - 3.35553i) q^{42} +(-0.952500 + 0.799242i) q^{43} +2.71848 q^{44} +(-4.94487 + 0.698615i) q^{45} -2.62315 q^{46} +(0.104767 + 0.594161i) q^{47} +(-0.969071 - 1.43558i) q^{48} +(0.475260 - 6.98385i) q^{49} +(2.09449 - 0.762331i) q^{50} +(1.28588 - 12.2772i) q^{51} +(2.11885 + 0.771200i) q^{52} +(-2.22157 + 3.84788i) q^{53} +(1.95175 + 4.81567i) q^{54} -4.52534 q^{55} +(-2.53087 - 0.771181i) q^{56} +(5.58786 - 2.49030i) q^{57} +(6.70987 + 5.63025i) q^{58} +(-10.1977 + 3.71166i) q^{59} +(1.61317 + 2.38976i) q^{60} +(-1.63958 - 9.29853i) q^{61} +(-4.37920 - 7.58500i) q^{62} +(6.94845 + 3.83654i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.52717 - 1.28379i) q^{65} +(1.14076 + 4.56826i) q^{66} +(-0.796600 - 0.668427i) q^{67} +(-6.69721 + 2.43759i) q^{68} +(-1.10075 - 4.40807i) q^{69} +(4.21303 + 1.28375i) q^{70} +(-0.486389 + 0.842451i) q^{71} +(2.00577 - 2.23089i) q^{72} -7.91654 q^{73} +(-7.58197 + 6.36203i) q^{74} +(2.15997 + 3.19978i) q^{75} +(-2.70569 - 2.27035i) q^{76} +(5.74815 + 4.32314i) q^{77} +(-0.406826 + 3.88425i) q^{78} +(0.606801 - 0.509166i) q^{79} +(0.832330 - 1.44164i) q^{80} +(-7.27347 + 5.30063i) q^{81} +(-2.76415 - 4.78765i) q^{82} +(1.53575 + 8.70965i) q^{83} +(0.233902 - 4.57660i) q^{84} +(11.1486 - 4.05775i) q^{85} +(-0.215914 + 1.22451i) q^{86} +(-6.64568 + 13.6382i) q^{87} +(2.08247 - 1.74740i) q^{88} +(3.44098 - 5.95995i) q^{89} +(-3.33893 + 3.71367i) q^{90} +(3.25384 + 5.00025i) q^{91} +(-2.00945 + 1.68613i) q^{92} +(10.9086 - 10.5419i) q^{93} +(0.462175 + 0.387811i) q^{94} +(4.50406 + 3.77936i) q^{95} +(-1.66513 - 0.476814i) q^{96} +(13.0432 - 10.9446i) q^{97} +(-4.12506 - 5.65543i) q^{98} +(-7.19804 + 3.83397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Introduction

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