LMFDB - Embedded newform 378.2.u.c.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	378.169
Dual form			378.2.u.c.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.0350640 - 1.73170i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.00462235 - 0.0262146i) q^{5} +(-0.625224 - 1.61527i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99754 + 0.121440i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.0350640 - 1.73170i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.00462235 - 0.0262146i) q^{5} +(-0.625224 - 1.61527i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99754 + 0.121440i) q^{9} +(-0.0133095 - 0.0230528i) q^{10} +(0.928690 - 5.26686i) q^{11} +(-1.13997 - 1.30402i) q^{12} +(-2.00735 - 0.730617i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(-0.0452337 + 0.00892369i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.97681 + 6.88804i) q^{17} +(-2.77523 + 1.13934i) q^{18} +(1.24288 - 2.15274i) q^{19} +(-0.0203914 - 0.0171104i) q^{20} +(-1.08625 + 1.34909i) q^{21} +(-0.928690 - 5.26686i) q^{22} +(0.588710 - 0.493987i) q^{23} +(-1.51722 - 0.835482i) q^{24} +(4.69780 - 1.70986i) q^{25} -2.13618 q^{26} +(0.315404 + 5.18657i) q^{27} -1.00000 q^{28} +(-5.00127 + 1.82031i) q^{29} +(-0.0394537 + 0.0238563i) q^{30} +(-1.09812 + 0.921435i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-9.15316 - 1.42353i) q^{33} +(6.09283 + 5.11249i) q^{34} +(-0.0133095 + 0.0230528i) q^{35} +(-2.21819 + 2.01981i) q^{36} +(-2.77985 - 4.81485i) q^{37} +(0.431649 - 2.44800i) q^{38} +(-1.19482 + 3.50174i) q^{39} +(-0.0250137 - 0.00910424i) q^{40} +(9.08987 + 3.30844i) q^{41} +(-0.559325 + 1.63925i) q^{42} +(-0.277141 + 1.57175i) q^{43} +(-2.67406 - 4.63160i) q^{44} +(0.0170392 + 0.0780181i) q^{45} +(0.384253 - 0.665547i) q^{46} +(5.11612 + 4.29293i) q^{47} +(-1.71148 - 0.266175i) q^{48} +(0.173648 + 0.984808i) q^{49} +(3.82968 - 3.21348i) q^{50} +(11.7886 - 7.12815i) q^{51} +(-2.00735 + 0.730617i) q^{52} +6.91611 q^{53} +(2.07029 + 4.76591i) q^{54} -0.142361 q^{55} +(-0.939693 + 0.342020i) q^{56} +(-3.77147 - 2.07681i) q^{57} +(-4.07707 + 3.42107i) q^{58} +(1.56166 + 8.85661i) q^{59} +(-0.0289150 + 0.0359116i) q^{60} +(-3.41996 - 2.86969i) q^{61} +(-0.716749 + 1.24145i) q^{62} +(2.37431 + 1.83375i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.00987417 + 0.0559992i) q^{65} +(-9.08804 + 1.79289i) q^{66} +(0.133891 + 0.0487322i) q^{67} +(7.47396 + 2.72030i) q^{68} +(-0.876077 - 1.00215i) q^{69} +(-0.00462235 + 0.0262146i) q^{70} +(2.49128 + 4.31503i) q^{71} +(-1.39360 + 2.65667i) q^{72} +(-4.79657 + 8.30791i) q^{73} +(-4.25898 - 3.57371i) q^{74} +(-3.12568 - 8.07520i) q^{75} +(-0.431649 - 2.44800i) q^{76} +(-4.09689 + 3.43770i) q^{77} +(0.0749030 + 3.69922i) q^{78} +(15.9224 - 5.79528i) q^{79} -0.0266190 q^{80} +(8.97050 - 0.728045i) q^{81} +9.67324 q^{82} +(6.84689 - 2.49206i) q^{83} +(0.0350640 + 1.73170i) q^{84} +(0.162185 - 0.136090i) q^{85} +(0.277141 + 1.57175i) q^{86} +(3.32759 + 8.59685i) q^{87} +(-4.09689 - 3.43770i) q^{88} +(-5.05312 + 8.75226i) q^{89} +(0.0426953 + 0.0674853i) q^{90} +(1.06809 + 1.84999i) q^{91} +(0.133450 - 0.756832i) q^{92} +(1.63415 + 1.86931i) q^{93} +(6.27585 + 2.28422i) q^{94} +(-0.0621783 - 0.0226310i) q^{95} +(-1.69930 + 0.335237i) q^{96} +(-0.308063 + 1.74711i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-2.14418 + 15.9004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−0.0350640	−	1.73170i	−0.0202442	−	0.999795i
$3$	−0.0350640	−	1.73170i	−0.0202442	−	0.999795i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.00462235	−	0.0262146i	−0.00206718	−	0.0117235i	0.983757	−	0.179507i	$-0.0574502\pi$
$5$	−0.00462235	−	0.0262146i	−0.00206718	−	0.0117235i	−0.985824	+	0.167783i	$0.946339\pi$
$6$	−0.625224	−	1.61527i	−0.255247	−	0.659431i
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.99754	+	0.121440i	−0.999180	+	0.0404801i
$10$	−0.0133095	−	0.0230528i	−0.00420884	−	0.00728992i
$11$	0.928690	−	5.26686i	0.280010	−	1.58802i	−0.442572	−	0.896733i	$-0.645934\pi$
$11$	0.928690	−	5.26686i	0.280010	−	1.58802i	0.722582	−	0.691285i	$-0.242955\pi$
$12$	−1.13997	−	1.30402i	−0.329082	−	0.376437i
$13$	−2.00735	−	0.730617i	−0.556740	−	0.202637i	0.0482987	−	0.998833i	$-0.484620\pi$
$13$	−2.00735	−	0.730617i	−0.556740	−	0.202637i	−0.605038	+	0.796196i	$0.706842\pi$
$14$	−0.939693	−	0.342020i	−0.251143	−	0.0914087i
$15$	−0.0452337	+	0.00892369i	−0.0116793	+	0.00230409i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	3.97681	+	6.88804i	0.964519	+	1.67060i	0.710902	+	0.703291i	$0.248287\pi$
$17$	3.97681	+	6.88804i	0.964519	+	1.67060i	0.253617	+	0.967305i	$0.418380\pi$
$18$	−2.77523	+	1.13934i	−0.654128	+	0.268544i
$19$	1.24288	−	2.15274i	0.285137	−	0.493872i	−0.687505	−	0.726179i	$-0.741294\pi$
$19$	1.24288	−	2.15274i	0.285137	−	0.493872i	0.972642	+	0.232307i	$0.0746275\pi$
$20$	−0.0203914	−	0.0171104i	−0.00455965	−	0.00382600i
$21$	−1.08625	+	1.34909i	−0.237040	+	0.294397i
$22$	−0.928690	−	5.26686i	−0.197997	−	1.12290i
$23$	0.588710	−	0.493987i	0.122755	−	0.103003i	−0.579344	−	0.815083i	$-0.696691\pi$
$23$	0.588710	−	0.493987i	0.122755	−	0.103003i	0.702098	+	0.712080i	$0.252247\pi$
$24$	−1.51722	−	0.835482i	−0.309702	−	0.170542i
$25$	4.69780	−	1.70986i	0.939559	−	0.341972i
$26$	−2.13618			−0.418940
$27$	0.315404	+	5.18657i	0.0606994	+	0.998156i
$28$	−1.00000			−0.188982
$29$	−5.00127	+	1.82031i	−0.928713	+	0.338024i	−0.761699	−	0.647931i	$-0.775635\pi$
$29$	−5.00127	+	1.82031i	−0.928713	+	0.338024i	−0.167013	+	0.985955i	$0.553412\pi$
$30$	−0.0394537	+	0.0238563i	−0.00720322	+	0.00435555i
$31$	−1.09812	+	0.921435i	−0.197229	+	0.165495i	−0.736054	−	0.676923i	$-0.763313\pi$
$31$	−1.09812	+	0.921435i	−0.197229	+	0.165495i	0.538825	+	0.842418i	$0.318868\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−9.15316	−	1.42353i	−1.59336	−	0.247805i
$34$	6.09283	+	5.11249i	1.04491	+	0.876785i
$35$	−0.0133095	+	0.0230528i	−0.00224972	+	0.00389663i
$36$	−2.21819	+	2.01981i	−0.369698	+	0.336635i
$37$	−2.77985	−	4.81485i	−0.457005	−	0.791556i	0.541796	−	0.840510i	$-0.317745\pi$
$37$	−2.77985	−	4.81485i	−0.457005	−	0.791556i	−0.998801	+	0.0489538i	$0.984411\pi$
$38$	0.431649	−	2.44800i	0.0700227	−	0.397119i
$39$	−1.19482	+	3.50174i	−0.191324	+	0.560728i
$40$	−0.0250137	−	0.00910424i	−0.00395501	−	0.00143951i
$41$	9.08987	+	3.30844i	1.41960	+	0.516692i	0.933932	−	0.357452i	$-0.116354\pi$
$41$	9.08987	+	3.30844i	1.41960	+	0.516692i	0.485668	+	0.874144i	$0.338577\pi$
$42$	−0.559325	+	1.63925i	−0.0863058	+	0.252942i
$43$	−0.277141	+	1.57175i	−0.0422636	+	0.239689i	−0.998620	−	0.0525131i	$-0.983277\pi$
$43$	−0.277141	+	1.57175i	−0.0422636	+	0.239689i	0.956357	+	0.292202i	$0.0943880\pi$
$44$	−2.67406	−	4.63160i	−0.403129	−	0.698240i
$45$	0.0170392	+	0.0780181i	0.00254005	+	0.0116302i
$46$	0.384253	−	0.665547i	0.0566551	−	0.0981295i
$47$	5.11612	+	4.29293i	0.746263	+	0.626189i	0.934512	−	0.355933i	$-0.115837\pi$
$47$	5.11612	+	4.29293i	0.746263	+	0.626189i	−0.188249	+	0.982121i	$0.560281\pi$
$48$	−1.71148	−	0.266175i	−0.247030	−	0.0384190i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	3.82968	−	3.21348i	0.541598	−	0.454455i
$51$	11.7886	−	7.12815i	1.65073	−	0.998141i
$52$	−2.00735	+	0.730617i	−0.278370	+	0.101318i
$53$	6.91611			0.950000			0.475000	−	0.879986i	$-0.342448\pi$
$53$	6.91611			0.950000			0.475000	+	0.879986i	$0.342448\pi$
$54$	2.07029	+	4.76591i	0.281731	+	0.648558i
$55$	−0.142361			−0.0191960
$56$	−0.939693	+	0.342020i	−0.125572	+	0.0457044i
$57$	−3.77147	−	2.07681i	−0.499543	−	0.275081i
$58$	−4.07707	+	3.42107i	−0.535346	+	0.449209i
$59$	1.56166	+	8.85661i	0.203311	+	1.15303i	0.900076	+	0.435733i	$0.143511\pi$
$59$	1.56166	+	8.85661i	0.203311	+	1.15303i	−0.696765	+	0.717299i	$0.745378\pi$
$60$	−0.0289150	+	0.0359116i	−0.00373291	+	0.00463617i
$61$	−3.41996	−	2.86969i	−0.437881	−	0.367426i	0.397035	−	0.917804i	$-0.370039\pi$
$61$	−3.41996	−	2.86969i	−0.437881	−	0.367426i	−0.834916	+	0.550378i	$0.814484\pi$
$62$	−0.716749	+	1.24145i	−0.0910272	+	0.157664i
$63$	2.37431	+	1.83375i	0.299135	+	0.231031i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.00987417	+	0.0559992i	−0.00122474	+	0.00694584i
$66$	−9.08804	+	1.79289i	−1.11866	+	0.220689i
$67$	0.133891	+	0.0487322i	0.0163573	+	0.00595358i	0.350186	−	0.936680i	$-0.386118\pi$
$67$	0.133891	+	0.0487322i	0.0163573	+	0.00595358i	−0.333829	+	0.942634i	$0.608341\pi$
$68$	7.47396	+	2.72030i	0.906351	+	0.329885i
$69$	−0.876077	−	1.00215i	−0.105467	−	0.120644i
$70$	−0.00462235	+	0.0262146i	−0.000552476	+	0.00313325i
$71$	2.49128	+	4.31503i	0.295661	+	0.512100i	0.975138	−	0.221596i	$-0.0711267\pi$
$71$	2.49128	+	4.31503i	0.295661	+	0.512100i	−0.679477	+	0.733696i	$0.737793\pi$
$72$	−1.39360	+	2.65667i	−0.164237	+	0.313091i
$73$	−4.79657	+	8.30791i	−0.561397	+	0.972367i	0.435978	+	0.899957i	$0.356402\pi$
$73$	−4.79657	+	8.30791i	−0.561397	+	0.972367i	−0.997375	+	0.0724103i	$0.976931\pi$
$74$	−4.25898	−	3.57371i	−0.495097	−	0.415436i
$75$	−3.12568	−	8.07520i	−0.360922	−	0.932444i
$76$	−0.431649	−	2.44800i	−0.0495136	−	0.280805i
$77$	−4.09689	+	3.43770i	−0.466884	+	0.391762i
$78$	0.0749030	+	3.69922i	0.00848110	+	0.418854i
$79$	15.9224	−	5.79528i	1.79141	−	0.652020i	0.792287	−	0.610149i	$-0.208890\pi$
$79$	15.9224	−	5.79528i	1.79141	−	0.652020i	0.999123	−	0.0418706i	$-0.0133317\pi$
$80$	−0.0266190			−0.00297610
$81$	8.97050	−	0.728045i	0.996723	−	0.0808939i
$82$	9.67324			1.06823
$83$	6.84689	−	2.49206i	0.751544	−	0.273540i	0.0622886	−	0.998058i	$-0.480160\pi$
$83$	6.84689	−	2.49206i	0.751544	−	0.273540i	0.689255	+	0.724519i	$0.257938\pi$
$84$	0.0350640	+	1.73170i	0.00382580	+	0.188944i
$85$	0.162185	−	0.136090i	0.0175915	−	0.0147610i
$86$	0.277141	+	1.57175i	0.0298849	+	0.169486i
$87$	3.32759	+	8.59685i	0.356756	+	0.921679i
$88$	−4.09689	−	3.43770i	−0.436730	−	0.366460i
$89$	−5.05312	+	8.75226i	−0.535630	+	0.927738i	0.463503	+	0.886095i	$0.346592\pi$
$89$	−5.05312	+	8.75226i	−0.535630	+	0.927738i	−0.999133	+	0.0416426i	$0.986741\pi$
$90$	0.0426953	+	0.0674853i	0.00450048	+	0.00711357i
$91$	1.06809	+	1.84999i	0.111966	+	0.193931i
$92$	0.133450	−	0.756832i	0.0139131	−	0.0789051i
$93$	1.63415	+	1.86931i	0.169453	+	0.193838i
$94$	6.27585	+	2.28422i	0.647304	+	0.235600i
$95$	−0.0621783	−	0.0226310i	−0.00637936	−	0.00232190i
$96$	−1.69930	+	0.335237i	−0.173434	+	0.0342150i
$97$	−0.308063	+	1.74711i	−0.0312791	+	0.177392i	−0.996445	−	0.0842462i	$-0.973152\pi$
$97$	−0.308063	+	1.74711i	−0.0312791	+	0.177392i	0.965166	+	0.261639i	$0.0842629\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	−2.14418	+	15.9004i	−0.215498	+	1.59805i
$100$	2.49965	−	4.32951i	0.249965	−	0.432951i
$101$	−13.9285	−	11.6874i	−1.38594	−	1.16294i	−0.966954	−	0.254952i	$-0.917940\pi$
$101$	−13.9285	−	11.6874i	−1.38594	−	1.16294i	−0.418989	−	0.907992i	$-0.637615\pi$
$102$	8.63964	−	10.7302i	0.855452	−	1.06245i
$103$	−3.36639	−	19.0918i	−0.331700	−	1.88117i	−0.457654	−	0.889130i	$-0.651310\pi$
$103$	−3.36639	−	19.0918i	−0.331700	−	1.88117i	0.125954	−	0.992036i	$-0.459801\pi$
$104$	−1.63641	+	1.37311i	−0.160463	+	0.134645i
$105$	0.0403870	+	0.0222397i	0.00394137	+	0.00217037i
$106$	6.49901	−	2.36545i	0.631240	−	0.229753i
$107$	−1.80055			−0.174066			−0.0870328	−	0.996205i	$-0.527739\pi$
$107$	−1.80055			−0.174066			−0.0870328	+	0.996205i	$0.527739\pi$
$108$	3.57548	+	3.77041i	0.344050	+	0.362808i
$109$	−18.7857			−1.79935			−0.899673	−	0.436565i	$-0.856195\pi$
$109$	−18.7857			−1.79935			−0.899673	+	0.436565i	$0.856195\pi$
$110$	−0.133776	+	0.0486905i	−0.0127550	+	0.00464246i
$111$	−8.24038	+	4.98269i	−0.782142	+	0.472936i
$112$	−0.766044	+	0.642788i	−0.0723844	+	0.0607377i
$113$	2.71817	+	15.4155i	0.255704	+	1.45017i	0.794259	+	0.607579i	$0.207859\pi$
$113$	2.71817	+	15.4155i	0.255704	+	1.45017i	−0.538555	+	0.842590i	$0.681030\pi$
$114$	−4.25433	−	0.661648i	−0.398455	−	0.0619690i
$115$	−0.0156709	−	0.0131494i	−0.00146132	−	0.00122619i
$116$	−2.66112	+	4.60920i	−0.247079	+	0.427953i
$117$	6.10585	+	1.94628i	0.564486	+	0.179934i
$118$	4.49662	+	7.78837i	0.413947	+	0.716978i
$119$	1.38113	−	7.83279i	0.126608	−	0.718031i
$120$	−0.0148887	+	0.0436354i	−0.00135915	+	0.00398334i
$121$	−16.5407	−	6.02034i	−1.50370	−	0.547303i
$122$	−4.19520	−	1.52693i	−0.379816	−	0.138242i
$123$	5.41049	−	15.8569i	0.487847	−	1.42977i
$124$	−0.248924	+	1.41172i	−0.0223541	+	0.126776i
$125$	−0.133086	−	0.230511i	−0.0119035	−	0.0206175i
$126$	2.85830	+	0.911103i	0.254638	+	0.0811675i
$127$	0.950232	−	1.64585i	0.0843194	−	0.146046i	−0.820782	−	0.571242i	$-0.806462\pi$
$127$	0.950232	−	1.64585i	0.0843194	−	0.146046i	0.905101	+	0.425197i	$0.139795\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	2.73150	+	0.424812i	0.240495	+	0.0374027i
$130$	0.00987417	+	0.0559992i	0.000866022	+	0.00491145i
$131$	−12.0324	+	10.0964i	−1.05127	+	0.882123i	−0.993227	−	0.116191i	$-0.962931\pi$
$131$	−12.0324	+	10.0964i	−1.05127	+	0.882123i	−0.0580459	+	0.998314i	$0.518487\pi$
$132$	−7.92676	+	4.79305i	−0.689936	+	0.417182i
$133$	−2.33586	+	0.850183i	−0.202545	+	0.0737202i
$134$	0.142483			0.0123087
$135$	0.134506	−	0.0322423i	0.0115764	−	0.00277498i
$136$	7.95363			0.682018
$137$	16.3315	−	5.94417i	1.39529	−	0.507845i	0.468515	−	0.883456i	$-0.344789\pi$
$137$	16.3315	−	5.94417i	1.39529	−	0.507845i	0.926777	+	0.375611i	$0.122567\pi$
$138$	−1.16600	−	0.642073i	−0.0992563	−	0.0546569i
$139$	−7.30717	+	6.13144i	−0.619786	+	0.520062i	−0.897736	−	0.440533i	$-0.854789\pi$
$139$	−7.30717	+	6.13144i	−0.619786	+	0.520062i	0.277950	+	0.960595i	$0.410345\pi$
$140$	0.00462235	+	0.0262146i	0.000390659	+	0.00221554i
$141$	7.25466	−	9.01009i	0.610953	−	0.758786i
$142$	3.81687	+	3.20273i	0.320305	+	0.268767i
$143$	−5.71227	+	9.89394i	−0.477684	+	0.827372i
$144$	−0.400922	+	2.97309i	−0.0334102	+	0.247757i
$145$	0.0708364	+	0.122692i	0.00588265	+	0.0101890i
$146$	−1.66583	+	9.44741i	−0.137865	+	0.781873i
$147$	1.69930	−	0.335237i	0.140156	−	0.0276499i
$148$	−5.22442	−	1.90153i	−0.429444	−	0.156305i
$149$	−0.103731	−	0.0377550i	−0.00849797	−	0.00309301i	0.337768	−	0.941230i	$-0.390328\pi$
$149$	−0.103731	−	0.0377550i	−0.00849797	−	0.00309301i	−0.346266	+	0.938137i	$0.612550\pi$
$150$	−5.69906	−	6.51916i	−0.465326	−	0.532287i
$151$	−0.858247	+	4.86736i	−0.0698431	+	0.396100i	0.929766	+	0.368151i	$0.120009\pi$
$151$	−0.858247	+	4.86736i	−0.0698431	+	0.396100i	−0.999609	+	0.0279496i	$0.991102\pi$
$152$	−1.24288	−	2.15274i	−0.100811	−	0.174610i
$153$	−12.7571	−	20.1642i	−1.03135	−	1.63018i
$154$	−2.67406	+	4.63160i	−0.215482	+	0.373225i
$155$	0.0292310	+	0.0245277i	0.00234789	+	0.00197011i
$156$	1.33559	+	3.45051i	0.106933	+	0.276262i
$157$	−0.902117	−	5.11616i	−0.0719968	−	0.408314i	−0.999412	−	0.0342812i	$-0.989086\pi$
$157$	−0.902117	−	5.11616i	−0.0719968	−	0.408314i	0.927415	−	0.374033i	$-0.122025\pi$
$158$	12.9801	−	10.8916i	1.03264	−	0.866486i
$159$	−0.242506	−	11.9766i	−0.0192320	−	0.949806i
$160$	−0.0250137	+	0.00910424i	−0.00197751	+	0.000719754i
$161$	−0.768507			−0.0605668
$162$	8.18051	−	3.75223i	0.642722	−	0.294803i
$163$	3.23832			0.253645			0.126823	−	0.991925i	$-0.459522\pi$
$163$	3.23832			0.253645			0.126823	+	0.991925i	$0.459522\pi$
$164$	9.08987	−	3.30844i	0.709800	−	0.258346i
$165$	0.00499176	+	0.246527i	0.000388608	+	0.0191921i
$166$	5.58164	−	4.68355i	0.433219	−	0.363514i
$167$	0.139354	+	0.790316i	0.0107835	+	0.0611565i	0.989725	−	0.142986i	$-0.0456705\pi$
$167$	0.139354	+	0.790316i	0.0107835	+	0.0611565i	−0.978941	+	0.204143i	$0.934559\pi$
$168$	0.625224	+	1.61527i	0.0482371	+	0.124621i
$169$	−6.46291	−	5.42303i	−0.497147	−	0.417156i
$170$	0.105859	−	0.183353i	0.00811901	−	0.0140625i
$171$	−3.46417	+	6.60386i	−0.264911	+	0.505010i
$172$	0.797996	+	1.38217i	0.0608466	+	0.105389i
$173$	2.15915	−	12.2451i	0.164157	−	0.930979i	−0.785773	−	0.618515i	$-0.787734\pi$
$173$	2.15915	−	12.2451i	0.164157	−	0.930979i	0.949930	−	0.312464i	$-0.101154\pi$
$174$	6.06721	+	6.94029i	0.459954	+	0.526142i
$175$	−4.69780	−	1.70986i	−0.355120	−	0.129253i
$176$	−5.02558	−	1.82916i	−0.378817	−	0.137878i
$177$	15.2822	−	3.01487i	1.14868	−	0.226611i
$178$	−1.75493	+	9.95271i	−0.131538	+	0.745987i
$179$	−9.05376	−	15.6816i	−0.676710	−	1.17210i	−0.975966	−	0.217923i	$-0.930072\pi$
$179$	−9.05376	−	15.6816i	−0.676710	−	1.17210i	0.299256	−	0.954173i	$-0.403262\pi$
$180$	0.0632018	+	0.0488127i	0.00471079	+	0.00363829i
$181$	−5.40975	+	9.36997i	−0.402104	+	0.696464i	−0.993980	−	0.109565i	$-0.965054\pi$
$181$	−5.40975	+	9.36997i	−0.402104	+	0.696464i	0.591876	+	0.806029i	$0.298388\pi$
$182$	1.63641	+	1.37311i	0.121299	+	0.101782i
$183$	−4.84951	+	6.02295i	−0.358486	+	0.445229i
$184$	−0.133450	−	0.756832i	−0.00983805	−	0.0557944i
$185$	−0.113370	+	0.0951287i	−0.00833513	+	0.00699400i
$186$	2.17494	+	1.19766i	0.159474	+	0.0878168i
$187$	39.9716	−	14.5485i	2.92301	−	1.06389i
$188$	6.67862			0.487088
$189$	3.09225	−	4.17588i	0.224928	−	0.303751i
$190$	−0.0661687			−0.00480038
$191$	−12.0818	+	4.39743i	−0.874210	+	0.318187i	−0.739871	−	0.672749i	$-0.765113\pi$
$191$	−12.0818	+	4.39743i	−0.874210	+	0.318187i	−0.134339	+	0.990935i	$0.542891\pi$
$192$	−1.48216	+	0.896214i	−0.106966	+	0.0646787i
$193$	−4.90519	+	4.11594i	−0.353083	+	0.296272i	−0.802027	−	0.597288i	$-0.796245\pi$
$193$	−4.90519	+	4.11594i	−0.353083	+	0.296272i	0.448944	+	0.893560i	$0.351800\pi$
$194$	0.308063	+	1.74711i	0.0221176	+	0.125435i
$195$	0.0973198	+	0.0151355i	0.00696921	+	0.00108388i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	−10.7359	+	18.5951i	−0.764899	+	1.32484i	0.175401	+	0.984497i	$0.443878\pi$
$197$	−10.7359	+	18.5951i	−0.764899	+	1.32484i	−0.940300	+	0.340347i	$0.889455\pi$
$198$	3.42339	+	15.6749i	0.243290	+	1.11396i
$199$	−1.44436	−	2.50171i	−0.102388	−	0.177341i	0.810280	−	0.586043i	$-0.199315\pi$
$199$	−1.44436	−	2.50171i	−0.102388	−	0.177341i	−0.912668	+	0.408702i	$0.865982\pi$
$200$	0.868118	−	4.92334i	0.0613852	−	0.348133i
$201$	0.0796946	−	0.233566i	0.00562122	−	0.0164745i
$202$	−17.0859	−	6.21876i	−1.20216	−	0.437550i
$203$	5.00127	+	1.82031i	0.351020	+	0.127761i
$204$	4.44867	−	13.0380i	0.311469	−	0.912844i
$205$	0.0447130	−	0.253580i	0.00312289	−	0.0177108i
$206$	−9.69314	−	16.7890i	−0.675353	−	1.16975i
$207$	−1.70469	+	1.55224i	−0.118484	+	0.107888i
$208$	−1.06809	+	1.84999i	−0.0740588	+	0.128274i
$209$	−10.1839	−	8.54532i	−0.704437	−	0.591092i
$210$	0.0455578	+	0.00708531i	0.00314379	+	0.000488933i
$211$	2.69436	+	15.2805i	0.185488	+	1.05195i	0.925327	+	0.379169i	$0.123790\pi$
$211$	2.69436	+	15.2805i	0.185488	+	1.05195i	−0.739840	+	0.672783i	$0.765099\pi$
$212$	5.29805	−	4.44559i	0.363871	−	0.305324i
$213$	7.38497	−	4.46545i	0.506010	−	0.305968i
$214$	−1.69196	+	0.615824i	−0.115660	+	0.0420969i
$215$	0.0424838			0.00289737
$216$	4.64940	+	2.32014i	0.316352	+	0.157865i
$217$	1.43350			0.0973122
$218$	−17.6528	+	6.42509i	−1.19560	+	0.435162i
$219$	14.5550	+	8.01490i	0.983533	+	0.541597i
$220$	−0.109055	+	0.0915082i	−0.00735250	+	0.00616948i
$221$	−2.95035	−	16.7323i	−0.198462	−	1.12553i
$222$	−6.03925	+	7.50057i	−0.405328	+	0.503406i
$223$	−1.29879	−	1.08982i	−0.0869737	−	0.0729796i	0.598264	−	0.801299i	$-0.295857\pi$
$223$	−1.29879	−	1.08982i	−0.0869737	−	0.0729796i	−0.685238	+	0.728319i	$0.740302\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−13.8742	+	5.69587i	−0.924946	+	0.379725i
$226$	7.82666	+	13.5562i	0.520622	+	0.901743i
$227$	0.490134	−	2.77969i	0.0325314	−	0.184495i	−0.964212	−	0.265132i	$-0.914584\pi$
$227$	0.490134	−	2.77969i	0.0325314	−	0.184495i	0.996744	+	0.0806374i	$0.0256956\pi$
$228$	−4.22406	+	0.833322i	−0.279745	+	0.0551881i
$229$	11.2527	+	4.09567i	0.743602	+	0.270649i	0.685911	−	0.727685i	$-0.259404\pi$
$229$	11.2527	+	4.09567i	0.743602	+	0.270649i	0.0576913	+	0.998334i	$0.481626\pi$
$230$	−0.0192232	−	0.00699667i	−0.00126754	−	0.000461347i
$231$	6.09670	+	6.97403i	0.401134	+	0.458857i
$232$	−0.924197	+	5.24138i	−0.0606765	+	0.344114i
$233$	−8.55121	−	14.8111i	−0.560208	−	0.970309i	−0.997478	−	0.0709785i	$-0.977388\pi$
$233$	−8.55121	−	14.8111i	−0.560208	−	0.970309i	0.437270	−	0.899330i	$-0.355945\pi$
$234$	6.40329	−	0.259419i	0.418596	−	0.0169587i
$235$	0.0888892	−	0.153961i	0.00579849	−	0.0100433i
$236$	6.88922	+	5.78074i	0.448450	+	0.376294i
$237$	−10.5940	−	27.3695i	−0.688152	−	1.77784i
$238$	−1.38113	−	7.83279i	−0.0895255	−	0.507725i
$239$	7.46646	−	6.26510i	0.482965	−	0.405256i	−0.368532	−	0.929615i	$-0.620140\pi$
$239$	7.46646	−	6.26510i	0.482965	−	0.405256i	0.851497	+	0.524359i	$0.175695\pi$
$240$	0.000933369		0.0460961i	6.02487e−5		0.00297549i
$241$	−11.8880	+	4.32689i	−0.765775	+	0.278719i	−0.695228	−	0.718789i	$-0.744697\pi$
$241$	−11.8880	+	4.32689i	−0.765775	+	0.278719i	−0.0705472	+	0.997508i	$0.522475\pi$
$242$	−17.6023			−1.13152
$243$	−1.57529	−	15.5087i	−0.101055	−	0.994881i
$244$	−4.46444			−0.285806
$245$	0.0250137	−	0.00910424i	0.00159807	−	0.000581649i
$246$	−0.339182	−	16.7511i	−0.0216255	−	1.06801i
$247$	−4.06774	+	3.41324i	−0.258824	+	0.217179i
$248$	0.248924	+	1.41172i	0.0158067	+	0.0896443i
$249$	−4.55558	−	11.7694i	−0.288698	−	0.745852i
$250$	−0.203899	−	0.171092i	−0.0128957	−	0.0108208i
$251$	1.29147	−	2.23689i	0.0815167	−	0.141191i	−0.822385	−	0.568932i	$-0.807357\pi$
$251$	1.29147	−	2.23689i	0.0815167	−	0.141191i	0.903902	+	0.427740i	$0.140690\pi$
$252$	2.99754	−	0.121440i	0.188827	−	0.00765002i
$253$	−2.05503	−	3.55942i	−0.129199	−	0.223779i
$254$	0.330012	−	1.87159i	0.0207068	−	0.117434i
$255$	−0.241353	−	0.276084i	−0.0151141	−	0.0172890i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	6.14102	+	2.23515i	0.383067	+	0.139425i	0.526373	−	0.850253i	$-0.323551\pi$
$257$	6.14102	+	2.23515i	0.383067	+	0.139425i	−0.143307	+	0.989678i	$0.545774\pi$
$258$	2.71207	−	0.535036i	0.168846	−	0.0333099i
$259$	−0.965433	+	5.47524i	−0.0599891	+	0.340215i
$260$	0.0284315	+	0.0492449i	0.00176325	+	0.00305404i
$261$	14.7705	−	6.06382i	0.914268	−	0.375341i
$262$	−7.85357	+	13.6028i	−0.485195	+	0.840383i
$263$	−11.3127	−	9.49246i	−0.697569	−	0.585330i	0.223512	−	0.974701i	$-0.428248\pi$
$263$	−11.3127	−	9.49246i	−0.697569	−	0.585330i	−0.921081	+	0.389371i	$0.872692\pi$
$264$	−5.80940	+	7.21511i	−0.357544	+	0.444059i
$265$	−0.0319686	−	0.181303i	−0.00196382	−	0.0111374i
$266$	−1.90421	+	1.59782i	−0.116755	+	0.0979687i
$267$	15.3334	+	8.44358i	0.938391	+	0.516739i
$268$	0.133891	−	0.0487322i	0.00817867	−	0.00297679i
$269$	7.48952			0.456644			0.228322	−	0.973586i	$-0.426676\pi$
$269$	7.48952			0.456644			0.228322	+	0.973586i	$0.426676\pi$
$270$	0.115367	−	0.0763017i	0.00702100	−	0.00464357i
$271$	−17.8871			−1.08656			−0.543282	−	0.839551i	$-0.682818\pi$
$271$	−17.8871			−1.08656			−0.543282	+	0.839551i	$0.682818\pi$
$272$	7.47396	−	2.72030i	0.453176	−	0.164942i
$273$	3.16616	−	1.91448i	0.191625	−	0.115869i
$274$	13.3135	−	11.1714i	0.804300	−	0.674888i
$275$	−4.64279	−	26.3306i	−0.279971	−	1.58779i
$276$	−1.31528	−	0.204557i	−0.0791706	−	0.0123129i
$277$	8.00335	+	6.71561i	0.480875	+	0.403502i	0.850743	−	0.525583i	$-0.176153\pi$
$277$	8.00335	+	6.71561i	0.480875	+	0.403502i	−0.369868	+	0.929084i	$0.620597\pi$
$278$	−4.76941	+	8.26087i	−0.286050	+	0.495454i
$279$	3.17977	−	2.89540i	0.190368	−	0.173343i
$280$	0.0133095	+	0.0230528i	0.000795395	+	0.00137767i
$281$	3.15309	−	17.8821i	0.188098	−	1.06675i	−0.733813	−	0.679352i	$-0.762261\pi$
$281$	3.15309	−	17.8821i	0.188098	−	1.06675i	0.921910	−	0.387403i	$-0.126628\pi$
$282$	3.73552	−	10.9480i	0.222447	−	0.651941i
$283$	4.95119	+	1.80209i	0.294318	+	0.107123i	0.484959	−	0.874537i	$-0.338834\pi$
$283$	4.95119	+	1.80209i	0.294318	+	0.107123i	−0.190641	+	0.981660i	$0.561057\pi$
$284$	4.68208	+	1.70414i	0.277831	+	0.101122i
$285$	−0.0370099	+	0.108467i	−0.00219227	+	0.00642505i
$286$	−1.98385	+	11.2510i	−0.117307	+	0.665284i
$287$	−4.83662	−	8.37727i	−0.285497	−	0.494495i
$288$	0.640113	+	2.93091i	0.0377190	+	0.172706i
$289$	−23.1301	+	40.0625i	−1.36059	+	2.35662i
$290$	0.108528	+	0.0910656i	0.00637297	+	0.00534755i
$291$	3.03627	+	0.472211i	0.177989	+	0.0276815i
$292$	1.66583	+	9.44741i	0.0974855	+	0.552868i
$293$	−13.5247	+	11.3485i	−0.790119	+	0.662988i	−0.945775	−	0.324823i	$-0.894695\pi$
$293$	−13.5247	+	11.3485i	−0.790119	+	0.662988i	0.155656	+	0.987811i	$0.450251\pi$
$294$	1.48216	−	0.896214i	0.0864414	−	0.0522683i
$295$	0.224954	−	0.0818766i	0.0130973	−	0.00476704i
$296$	−5.55971			−0.323152
$297$	27.6099	+	3.15553i	1.60209	+	0.183102i
$298$	−0.110388			−0.00639461
$299$	−1.54267	+	0.561484i	−0.0892146	+	0.0324715i
$300$	−7.58505	−	4.17682i	−0.437923	−	0.241149i
$301$	1.22260	−	1.02588i	0.0704695	−	0.0591310i
$302$	0.858247	+	4.86736i	0.0493866	+	0.280085i
$303$	−19.7507	+	24.5298i	−1.13465	+	1.40920i
$304$	−1.90421	−	1.59782i	−0.109214	−	0.0916413i
$305$	−0.0594195	+	0.102918i	−0.00340235	+	0.00589305i
$306$	−18.8844	−	14.5850i	−1.07955	−	0.833768i
$307$	14.2571	+	24.6941i	0.813697	+	1.40936i	0.910260	+	0.414038i	$0.135882\pi$
$307$	14.2571	+	24.6941i	0.813697	+	1.40936i	−0.0965627	+	0.995327i	$0.530785\pi$
$308$	−0.928690	+	5.26686i	−0.0529170	+	0.300107i
$309$	−32.9431	+	6.49900i	−1.87407	+	0.369715i
$310$	0.0358571	+	0.0130509i	0.00203655	+	0.000741242i
$311$	5.13243	+	1.86805i	0.291033	+	0.105927i	0.483411	−	0.875393i	$-0.339398\pi$
$311$	5.13243	+	1.86805i	0.291033	+	0.105927i	−0.192378	+	0.981321i	$0.561620\pi$
$312$	2.43519	+	2.78562i	0.137865	+	0.157705i
$313$	3.96637	−	22.4944i	0.224193	−	1.27146i	−0.640030	−	0.768350i	$-0.721078\pi$
$313$	3.96637	−	22.4944i	0.224193	−	1.27146i	0.864223	−	0.503109i	$-0.167811\pi$
$314$	−2.59754	−	4.49908i	−0.146588	−	0.253898i
$315$	0.0370963	−	0.0707179i	0.00209014	−	0.00398450i
$316$	8.47213	−	14.6742i	0.476595	−	0.825486i
$317$	13.0651	+	10.9630i	0.733812	+	0.615741i	0.931168	−	0.364591i	$-0.118791\pi$
$317$	13.0651	+	10.9630i	0.733812	+	0.615741i	−0.197356	+	0.980332i	$0.563235\pi$
$318$	−4.32412	−	11.1714i	−0.242484	−	0.626460i
$319$	4.94271	+	28.0315i	0.276739	+	1.56946i
$320$	−0.0203914	+	0.0171104i	−0.00113991	+	0.000956499i
$321$	0.0631344	+	3.11800i	0.00352382	+	0.174030i
$322$	−0.722160	+	0.262845i	−0.0402444	+	0.0146478i
$323$	19.7709			1.10008
$324$	6.40383	−	6.32384i	0.355768	−	0.351325i
$325$	−10.6794			−0.592386
$326$	3.04303	−	1.10757i	0.168538	−	0.0613427i
$327$	0.658702	+	32.5311i	0.0364263	+	1.79898i
$328$	7.41013	−	6.21784i	0.409156	−	0.343323i
$329$	−1.15973	−	6.57716i	−0.0639380	−	0.362610i
$330$	0.0890079	+	0.229952i	0.00489972	+	0.0126584i
$331$	−19.5374	−	16.3938i	−1.07387	−	0.901087i	−0.0784760	−	0.996916i	$-0.525005\pi$
$331$	−19.5374	−	16.3938i	−1.07387	−	0.901087i	−0.995398	+	0.0958289i	$0.969450\pi$
$332$	3.64315	−	6.31013i	0.199944	−	0.346313i
$333$	8.91744	+	14.0951i	0.488673	+	0.772408i
$334$	0.401254	+	0.694992i	0.0219556	+	0.0380283i
$335$	0.000658607	−	0.00373515i	3.59836e−5	−	0.000204073i
$336$	1.13997	+	1.30402i	0.0621906	+	0.0711400i
$337$	31.5298	+	11.4759i	1.71754	+	0.625133i	0.997622	−	0.0689255i	$-0.0219571\pi$
$337$	31.5298	+	11.4759i	1.71754	+	0.625133i	0.719918	+	0.694059i	$0.244179\pi$
$338$	−7.92793	−	2.88553i	−0.431223	−	0.156952i
$339$	26.5997	−	5.24758i	1.44470	−	0.285009i
$340$	0.0367644	−	0.208501i	0.00199383	−	0.0113076i
$341$	3.83325	+	6.63939i	0.207582	+	0.359543i
$342$	−0.996600	+	7.39041i	−0.0538899	+	0.399628i
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$	1.22260	+	1.02588i	0.0659182	+	0.0553120i
$345$	−0.0222214	+	0.0275983i	−0.00119636	+	0.00148584i
$346$	−2.15915	−	12.2451i	−0.116076	−	0.658302i
$347$	12.7650	−	10.7111i	0.685263	−	0.575004i	−0.232276	−	0.972650i	$-0.574617\pi$
$347$	12.7650	−	10.7111i	0.685263	−	0.575004i	0.917539	+	0.397646i	$0.130173\pi$
$348$	8.07504	+	4.44663i	0.432867	+	0.238365i
$349$	25.8171	−	9.39666i	1.38196	−	0.502992i	0.459187	−	0.888340i	$-0.348141\pi$
$349$	25.8171	−	9.39666i	1.38196	−	0.502992i	0.922771	+	0.385348i	$0.125919\pi$
$350$	−4.99929			−0.267223
$351$	3.15627	−	10.6417i	0.168469	−	0.568013i
$352$	−5.34811			−0.285055
$353$	−2.06652	+	0.752153i	−0.109990	+	0.0400331i	−0.396429	−	0.918065i	$-0.629751\pi$
$353$	−2.06652	+	0.752153i	−0.109990	+	0.0400331i	0.286439	+	0.958099i	$0.407528\pi$
$354$	13.3294	−	8.05987i	0.708451	−	0.428377i
$355$	0.101601	−	0.0852537i	0.00539244	−	0.00452479i
$356$	1.75493	+	9.95271i	0.0930111	+	0.527492i
$357$	−13.6124	−	2.11705i	−0.720447	−	0.112046i
$358$	−13.8712	−	11.6393i	−0.733114	−	0.615156i
$359$	−2.05136	+	3.55306i	−0.108267	+	0.187523i	−0.915068	−	0.403299i	$-0.867863\pi$
$359$	−2.05136	+	3.55306i	−0.108267	+	0.187523i	0.806801	+	0.590823i	$0.201197\pi$
$360$	0.0760852	+	0.0242527i	0.00401004	+	0.00127823i
$361$	6.41048	+	11.1033i	0.337394	+	0.584383i
$362$	−1.87879	+	10.6551i	−0.0987469	+	0.560021i
$363$	−9.84541	+	28.8546i	−0.516750	+	1.51448i
$364$	2.00735	+	0.730617i	0.105214	+	0.0382947i
$365$	0.239960	+	0.0873384i	0.0125601	+	0.00457150i
$366$	−2.49708	+	7.31835i	−0.130524	+	0.382536i
$367$	−5.41847	+	30.7296i	−0.282842	+	1.60407i	0.430053	+	0.902803i	$0.358495\pi$
$367$	−5.41847	+	30.7296i	−0.282842	+	1.60407i	−0.712895	+	0.701271i	$0.752616\pi$
$368$	−0.384253	−	0.665547i	−0.0200306	−	0.0346940i
$369$	−27.6490	−	8.81331i	−1.43935	−	0.458803i
$370$	−0.0739970	+	0.128167i	−0.00384692	+	0.00666306i
$371$	−5.29805	−	4.44559i	−0.275061	−	0.230803i
$372$	2.45340	+	0.381561i	0.127203	+	0.0197830i
$373$	−2.09436	−	11.8777i	−0.108442	−	0.615005i	−0.989790	−	0.142537i	$-0.954474\pi$
$373$	−2.09436	−	11.8777i	−0.108442	−	0.615005i	0.881347	−	0.472469i	$-0.156637\pi$
$374$	32.5851	−	27.3422i	1.68494	−	1.41383i
$375$	−0.394509	+	0.238547i	−0.0203723	+	0.0123185i
$376$	6.27585	−	2.28422i	0.323652	−	0.117800i
$377$	11.3693			0.585547
$378$	1.47753	−	4.98166i	0.0759959	−	0.256229i
$379$	15.8917			0.816304			0.408152	−	0.912914i	$-0.366173\pi$
$379$	15.8917			0.816304			0.408152	+	0.912914i	$0.366173\pi$
$380$	−0.0621783	+	0.0226310i	−0.00318968	+	0.00116095i
$381$	−2.88343	−	1.58780i	−0.147723	−	0.0813456i
$382$	−9.84920	+	8.26446i	−0.503929	+	0.422846i
$383$	3.92338	+	22.2506i	0.200475	+	1.13695i	0.904403	+	0.426680i	$0.140317\pi$
$383$	3.92338	+	22.2506i	0.200475	+	1.13695i	−0.703927	+	0.710272i	$0.748572\pi$
$384$	−1.08625	+	1.34909i	−0.0554326	+	0.0688457i
$385$	0.109055	+	0.0915082i	0.00555797	+	0.00466369i
$386$	−3.20163	+	5.54539i	−0.162959	+	0.282253i
$387$	0.639869	−	4.74503i	0.0325263	−	0.241203i
$388$	0.887032	+	1.53639i	0.0450322	+	0.0779981i
$389$	−5.07454	+	28.7792i	−0.257290	+	1.45916i	0.532837	+	0.846218i	$0.321126\pi$
$389$	−5.07454	+	28.7792i	−0.257290	+	1.45916i	−0.790126	+	0.612944i	$0.789985\pi$
$390$	0.0966273	−	0.0190626i	0.00489291	−	0.000965273i
$391$	5.74379	+	2.09057i	0.290476	+	0.105725i
$392$	0.939693	+	0.342020i	0.0474616	+	0.0172746i
$393$	17.9057	+	20.4824i	0.903224	+	1.03320i
$394$	−3.72853	+	21.1455i	−0.187841	+	1.06530i
$395$	−0.225520	−	0.390612i	−0.0113471	−	0.0196538i
$396$	8.57805	+	13.5587i	0.431063	+	0.681349i
$397$	8.41941	−	14.5829i	0.422558	−	0.731892i	−0.573631	−	0.819114i	$-0.694466\pi$
$397$	8.41941	−	14.5829i	0.422558	−	0.731892i	0.996189	+	0.0872217i	$0.0277988\pi$
$398$	−2.21289	−	1.85684i	−0.110922	−	0.0930748i
$399$	1.55416	+	4.01519i	0.0778055	+	0.201011i
$400$	−0.868118	−	4.92334i	−0.0434059	−	0.246167i
$401$	−19.0676	+	15.9996i	−0.952192	+	0.798984i	−0.979665	−	0.200639i	$-0.935698\pi$
$401$	−19.0676	+	15.9996i	−0.952192	+	0.798984i	0.0274735	+	0.999623i	$0.491254\pi$
$402$	−0.00499604	−	0.246738i	−0.000249180	−	0.0123062i
$403$	2.87754	−	1.04734i	0.143340	−	0.0521716i
$404$	−18.1824			−0.904610
$405$	−0.0605502	−	0.231793i	−0.00300876	−	0.0115179i
$406$	5.32224			0.264138
$407$	−27.9408	+	10.1696i	−1.38497	+	0.504089i
$408$	−0.278886	−	13.7733i	−0.0138069	−	0.681878i
$409$	−13.9913	+	11.7401i	−0.691827	+	0.580512i	−0.919435	−	0.393241i	$-0.871354\pi$
$409$	−13.9913	+	11.7401i	−0.691827	+	0.580512i	0.227608	+	0.973753i	$0.426909\pi$
$410$	−0.0447130	−	0.253580i	−0.00220822	−	0.0125234i
$411$	−10.8661	−	28.0727i	−0.535987	−	1.38473i
$412$	−14.8507	−	12.4613i	−0.731644	−	0.613922i
$413$	4.49662	−	7.78837i	0.221264	−	0.383241i
$414$	−1.07099	+	2.04167i	−0.0526364	+	0.100342i
$415$	−0.0969772	−	0.167969i	−0.00476042	−	0.00824530i
$416$	−0.370944	+	2.10373i	−0.0181870	+	0.103144i
$417$	10.8740	+	12.4388i	0.532502	+	0.609130i
$418$	−12.4924	−	4.54687i	−0.611025	−	0.222395i
$419$	−6.24224	−	2.27199i	−0.304953	−	0.110994i	0.185011	−	0.982736i	$-0.440768\pi$
$419$	−6.24224	−	2.27199i	−0.304953	−	0.110994i	−0.489964	+	0.871743i	$0.662990\pi$
$420$	0.0452337	−	0.00892369i	0.00220718	−	0.000435431i
$421$	−3.00726	+	17.0550i	−0.146565	+	0.831209i	0.819533	+	0.573032i	$0.194233\pi$
$421$	−3.00726	+	17.0550i	−0.146565	+	0.831209i	−0.966098	+	0.258177i	$0.916878\pi$
$422$	7.75811	+	13.4374i	0.377659	+	0.654124i
$423$	−15.8571	−	12.2469i	−0.770999	−	0.595467i
$424$	3.45805	−	5.98952i	0.167938	−	0.290877i
$425$	30.4598	+	25.5588i	1.47752	+	1.23979i
$426$	5.41233	−	6.72196i	0.262228	−	0.325680i
$427$	0.775242	+	4.39662i	0.0375166	+	0.212767i
$428$	−1.37930	+	1.15737i	−0.0666710	+	0.0559436i
$429$	17.3336	+	9.54499i	0.836873	+	0.460836i
$430$	0.0399217	−	0.0145303i	0.00192519	−	0.000700713i
$431$	−24.9172			−1.20022			−0.600109	−	0.799918i	$-0.704876\pi$
$431$	−24.9172			−1.20022			−0.600109	+	0.799918i	$0.704876\pi$
$432$	5.16254	+	0.590027i	0.248383	+	0.0283877i
$433$	18.2786			0.878415			0.439208	−	0.898386i	$-0.355259\pi$
$433$	18.2786			0.878415			0.439208	+	0.898386i	$0.355259\pi$
$434$	1.34705	−	0.490285i	0.0646604	−	0.0235344i
$435$	0.209982	−	0.126969i	0.0100679	−	0.00608771i
$436$	−14.3907	+	12.0752i	−0.689189	+	0.578298i
$437$	−0.331725	−	1.88131i	−0.0158686	−	0.0899952i
$438$	16.4184	+	2.55345i	0.784504	+	0.122009i
$439$	7.04521	+	5.91163i	0.336250	+	0.282147i	0.795241	−	0.606294i	$-0.207345\pi$
$439$	7.04521	+	5.91163i	0.336250	+	0.282147i	−0.458991	+	0.888441i	$0.651789\pi$
$440$	−0.0711807	+	0.123289i	−0.00339341	+	0.00587756i
$441$	−0.640113	−	2.93091i	−0.0304816	−	0.139567i
$442$	−8.49519	−	14.7141i	−0.404075	−	0.699879i
$443$	2.42609	−	13.7590i	0.115267	−	0.653711i	−0.871351	−	0.490660i	$-0.836756\pi$
$443$	2.42609	−	13.7590i	0.115267	−	0.653711i	0.986618	−	0.163050i	$-0.0521333\pi$
$444$	−3.10969	+	9.11378i	−0.147579	+	0.432521i
$445$	0.252795	+	0.0920097i	0.0119836	+	0.00436168i
$446$	−1.59321	−	0.579880i	−0.0754405	−	0.0274581i
$447$	−0.0617429	+	0.180954i	−0.00292034	+	0.00855884i
$448$	−0.173648	+	0.984808i	−0.00820411	+	0.0465278i
$449$	16.9964	+	29.4386i	0.802110	+	1.38930i	0.918225	+	0.396060i	$0.129623\pi$
$449$	16.9964	+	29.4386i	0.802110	+	1.38930i	−0.116115	+	0.993236i	$0.537044\pi$
$450$	−11.0894	+	10.0976i	−0.522758	+	0.476007i
$451$	25.8668	−	44.8026i	1.21802	−	2.10967i
$452$	11.9911	+	10.0618i	0.564016	+	0.473265i
$453$	8.45888	+	1.31555i	0.397433	+	0.0618101i
$454$	−0.490134	−	2.77969i	−0.0230031	−	0.130457i
$455$	0.0435596	−	0.0365509i	0.00204211	−	0.00171353i
$456$	−3.68431	+	2.22778i	−0.172534	+	0.104325i
$457$	−12.5120	+	4.55399i	−0.585286	+	0.213027i	−0.617655	−	0.786449i	$-0.711917\pi$
$457$	−12.5120	+	4.55399i	−0.585286	+	0.213027i	0.0323688	+	0.999476i	$0.489695\pi$
$458$	11.9749			0.559551
$459$	−34.4710	+	22.7985i	−1.60897	+	1.06414i
$460$	−0.0204569			−0.000953808
$461$	34.8123	−	12.6706i	1.62137	−	0.590130i	0.637727	−	0.770263i	$-0.279875\pi$
$461$	34.8123	−	12.6706i	1.62137	−	0.590130i	0.983642	+	0.180132i	$0.0576526\pi$
$462$	8.11428	+	4.46825i	0.377511	+	0.207882i
$463$	28.4183	−	23.8458i	1.32071	−	1.10821i	0.334557	−	0.942375i	$-0.391413\pi$
$463$	28.4183	−	23.8458i	1.32071	−	1.10821i	0.986154	−	0.165833i	$-0.0530312\pi$
$464$	0.924197	+	5.24138i	0.0429048	+	0.243325i
$465$	0.0414496	−	0.0514792i	0.00192218	−	0.00238729i
$466$	−13.1012	−	10.9932i	−0.606902	−	0.509251i
$467$	0.708607	−	1.22734i	0.0327904	−	0.0567946i	−0.849164	−	0.528128i	$-0.822894\pi$
$467$	0.708607	−	1.22734i	0.0327904	−	0.0567946i	0.881955	+	0.471334i	$0.156227\pi$
$468$	5.92840	−	2.43383i	0.274040	−	0.112504i
$469$	−0.0712417	−	0.123394i	−0.00328963	−	0.00569781i
$470$	0.0308709	−	0.175077i	0.00142397	−	0.00807572i
$471$	−8.82800	+	1.74159i	−0.406773	+	0.0802480i
$472$	8.45088	+	3.07587i	0.388983	+	0.141578i
$473$	8.02079	+	2.91933i	0.368796	+	0.134231i
$474$	−19.3160	−	22.0956i	−0.887213	−	1.01488i
$475$	2.15794	−	12.2383i	0.0990131	−	0.561531i
$476$	−3.97681	−	6.88804i	−0.182277	−	0.315713i
$477$	−20.7313	+	0.839894i	−0.949222	+	0.0384561i
$478$	4.87338	−	8.44095i	0.222903	−	0.386080i
$479$	−15.0623	−	12.6388i	−0.688216	−	0.577482i	0.230178	−	0.973148i	$-0.426069\pi$
$479$	−15.0623	−	12.6388i	−0.688216	−	0.577482i	−0.918394	+	0.395667i	$0.870513\pi$
$480$	0.0166429	+	0.0429969i	0.000759639	+	0.00196253i
$481$	2.06234	+	11.6961i	0.0940346	+	0.533297i
$482$	−9.69121	+	8.13189i	−0.441423	+	0.370398i
$483$	0.0269469	+	1.33082i	0.00122613	+	0.0605544i
$484$	−16.5407	+	6.02034i	−0.751852	+	0.273652i
$485$	0.0472239			0.00214433
$486$	−6.78457	−	14.0346i	−0.307754	−	0.636622i
$487$	−22.2228			−1.00701			−0.503505	−	0.863992i	$-0.667956\pi$
$487$	−22.2228			−1.00701			−0.503505	+	0.863992i	$0.667956\pi$
$488$	−4.19520	+	1.52693i	−0.189908	+	0.0691208i
$489$	−0.113549	−	5.60779i	−0.00513484	−	0.253593i
$490$	0.0203914	−	0.0171104i	0.000921188	−	0.000772968i
$491$	−5.56639	−	31.5686i	−0.251208	−	1.42467i	−0.805622	−	0.592429i	$-0.798169\pi$
$491$	−5.56639	−	31.5686i	−0.251208	−	1.42467i	0.554415	−	0.832240i	$-0.312942\pi$
$492$	−6.04794	−	15.6249i	−0.272662	−	0.704424i
$493$	−32.4275	−	27.2099i	−1.46046	−	1.22547i
$494$	−2.65503	+	4.59864i	−0.119455	+	0.206903i
$495$	0.426734	−	0.0172884i	0.0191803	−	0.000777057i
$496$	0.716749	+	1.24145i	0.0321830	+	0.0557426i
$497$	0.865214	−	4.90687i	0.0388102	−	0.220103i
$498$	−8.30620	−	9.50147i	−0.372210	−	0.425771i
$499$	14.5594	+	5.29918i	0.651767	+	0.237224i	0.646678	−	0.762763i	$-0.276158\pi$
$499$	14.5594	+	5.29918i	0.651767	+	0.237224i	0.00508929	+	0.999987i	$0.498380\pi$
$500$	−0.250119	−	0.0910360i	−0.0111857	−	0.00407125i
$501$	1.36370	−	0.269030i	0.0609256	−	0.0120194i
$502$	0.448522	−	2.54370i	0.0200185	−	0.113531i
$503$	−1.72987	−	2.99623i	−0.0771313	−	0.133595i	0.824880	−	0.565308i	$-0.191243\pi$
$503$	−1.72987	−	2.99623i	−0.0771313	−	0.133595i	−0.902011	+	0.431713i	$0.857909\pi$
$504$	2.77523	−	1.13934i	0.123619	−	0.0507501i
$505$	−0.241999	+	0.419155i	−0.0107688	+	0.0186522i
$506$	−3.14849	−	2.64190i	−0.139967	−	0.117447i
$507$	−9.16442	+	11.3819i	−0.407006	+	0.505490i
$508$	−0.330012	−	1.87159i	−0.0146419	−	0.0830384i
$509$	−5.97214	+	5.01122i	−0.264711	+	0.222118i	−0.765476	−	0.643465i	$-0.777496\pi$
$509$	−5.97214	+	5.01122i	−0.264711	+	0.222118i	0.500765	+	0.865583i	$0.333052\pi$
$510$	−0.321223	−	0.176886i	−0.0142240	−	0.00783266i
$511$	9.01461	−	3.28105i	0.398783	−	0.145145i
$512$	−1.00000			−0.0441942
$513$	11.5573	+	5.76733i	0.510269	+	0.254634i
$514$	6.53514			0.288253
$515$	−0.484922	+	0.176497i	−0.0213682	+	0.00777740i
$516$	2.36552	−	1.43035i	0.104136	−	0.0629677i
$517$	27.3616	−	22.9591i	1.20336	−	1.00974i
$518$	0.965433	+	5.47524i	0.0424187	+	0.240568i
$519$	−21.2805	−	3.30962i	−0.934112	−	0.145276i
$520$	0.0435596	+	0.0365509i	0.00191022	+	0.00160286i
$521$	6.12318	−	10.6057i	0.268261	−	0.464642i	−0.700152	−	0.713994i	$-0.746884\pi$
$521$	6.12318	−	10.6057i	0.268261	−	0.464642i	0.968413	+	0.249352i	$0.0802176\pi$
$522$	11.8057	−	10.7499i	0.516723	−	0.470511i
$523$	−11.2522	−	19.4894i	−0.492024	−	0.852210i	0.507934	−	0.861396i	$-0.330409\pi$
$523$	−11.2522	−	19.4894i	−0.492024	−	0.852210i	−0.999958	+	0.00918602i	$0.997076\pi$
$524$	−2.72752	+	15.4685i	−0.119152	+	0.675745i
$525$	−2.79623	+	8.19511i	−0.122038	+	0.357664i
$526$	−13.8770	−	5.05083i	−0.605068	−	0.220227i
$527$	−10.7139	−	3.89955i	−0.466705	−	0.169867i
$528$	−2.99133	+	8.76691i	−0.130181	+	0.381531i
$529$	−3.89135	+	22.0689i	−0.169189	+	0.959519i
$530$	−0.0920500	−	0.159435i	−0.00399840	−	0.00692543i
$531$	−5.75669	−	26.3584i	−0.249819	−	1.14386i
$532$	−1.24288	+	2.15274i	−0.0538859	+	0.0933331i
$533$	−15.8294	−	13.2824i	−0.685647	−	0.575326i
$534$	17.2966	+	2.69002i	0.748497	+	0.116409i
$535$	0.00832276	+	0.0472007i	0.000359824	+	0.00204066i
$536$	0.109149	−	0.0915865i	0.00471450	−	0.00395594i
$537$	−26.8383	+	16.2282i	−1.15816	+	0.700300i
$538$	7.03785	−	2.56157i	0.303423	−	0.110437i
$539$	5.34811			0.230359
$540$	0.0823127	−	0.111158i	0.00354217	−	0.00478347i
$541$	−13.4168			−0.576835			−0.288417	−	0.957505i	$-0.593129\pi$
$541$	−13.4168			−0.576835			−0.288417	+	0.957505i	$0.593129\pi$
$542$	−16.8084	+	6.11774i	−0.721981	+	0.262780i
$543$	16.4156	+	9.03950i	0.704462	+	0.387922i
$544$	6.09283	−	5.11249i	0.261228	−	0.219196i
$545$	0.0868341	+	0.492460i	0.00371956	+	0.0210947i
$546$	2.32043	−	2.88191i	0.0993053	−	0.123334i
$547$	1.56240	+	1.31101i	0.0668032	+	0.0560545i	0.675578	−	0.737289i	$-0.263894\pi$
$547$	1.56240	+	1.31101i	0.0668032	+	0.0560545i	−0.608775	+	0.793343i	$0.708339\pi$
$548$	8.68980	−	15.0512i	0.371210	−	0.642954i
$549$	10.6000	+	8.18668i	0.452395	+	0.349399i
$550$	−13.3684	−	23.1547i	−0.570030	−	0.987320i
$551$	−2.29734	+	13.0289i	−0.0978700	+	0.555048i
$552$	−1.30592	+	0.257632i	−0.0555838	+	0.0109655i
$553$	−15.9224	−	5.79528i	−0.677089	−	0.246440i
$554$	9.81756	+	3.57330i	0.417108	+	0.151815i
$555$	0.168709	+	0.192987i	0.00716131	+	0.00819183i
$556$	−1.65640	+	9.39391i	−0.0702470	+	0.398391i
$557$	14.0821	+	24.3909i	0.596677	+	1.03347i	0.993308	+	0.115496i	$0.0368458\pi$
$557$	14.0821	+	24.3909i	0.596677	+	1.03347i	−0.396631	+	0.917978i	$0.629821\pi$
$558$	1.99772	−	3.80833i	0.0845704	−	0.161219i
$559$	1.70466	−	2.95256i	0.0720996	−	0.124880i
$560$	0.0203914	+	0.0171104i	0.000861692	+	0.000723045i
$561$	−26.5951	−	68.7085i	−1.12285	−	2.90088i
$562$	−3.15309	−	17.8821i	−0.133005	−	0.754310i
$563$	−9.52916	+	7.99592i	−0.401606	+	0.336988i	−0.821114	−	0.570764i	$-0.806647\pi$
$563$	−9.52916	+	7.99592i	−0.401606	+	0.336988i	0.419508	+	0.907752i	$0.362203\pi$
$564$	−0.234179	−	11.5653i	−0.00986072	−	0.486989i
$565$	0.391548	−	0.142512i	0.0164725	−	0.00599551i
$566$	5.26895			0.221470
$567$	−7.33978	−	5.20841i	−0.308242	−	0.218733i
$568$	4.98257			0.209064
$569$	30.6715	−	11.1635i	1.28582	−	0.468000i	0.393466	−	0.919339i	$-0.371276\pi$
$569$	30.6715	−	11.1635i	1.28582	−	0.468000i	0.892352	+	0.451340i	$0.149054\pi$
$570$	0.00232014	+	0.114584i	9.71800e−5	+	0.00479940i
$571$	0.620349	−	0.520535i	0.0259608	−	0.0217837i	−0.629715	−	0.776826i	$-0.716828\pi$
$571$	0.620349	−	0.520535i	0.0259608	−	0.0217837i	0.655676	+	0.755043i	$0.272384\pi$
$572$	1.98385	+	11.2510i	0.0829489	+	0.470427i
$573$	8.03864	+	20.7679i	0.335819	+	0.867590i
$574$	−7.41013	−	6.21784i	−0.309293	−	0.259528i
$575$	1.92100	−	3.32726i	0.0801110	−	0.138756i
$576$	1.60394	+	2.53523i	0.0668309	+	0.105634i
$577$	−12.1186	−	20.9900i	−0.504503	−	0.873825i	−0.999986	−	0.00520772i	$-0.998342\pi$
$577$	−12.1186	−	20.9900i	−0.504503	−	0.873825i	0.495483	−	0.868618i	$-0.334991\pi$
$578$	−8.03300	+	45.5574i	−0.334129	+	1.89494i
$579$	7.29955	+	8.34997i	0.303359	+	0.347013i
$580$	0.133129	+	0.0484550i	0.00552788	+	0.00201198i
$581$	−6.84689	−	2.49206i	−0.284057	−	0.103388i
$582$	3.01467	−	0.594732i	0.124962	−	0.0246524i
$583$	6.42292	−	36.4262i	0.266010	−	1.50862i
$584$	4.79657	+	8.30791i	0.198484	+	0.343784i
$585$	0.0227977	−	0.169059i	0.000942567	−	0.00698973i
$586$	−8.82759	+	15.2898i	−0.364664	+	0.631617i
$587$	13.8765	+	11.6437i	0.572744	+	0.480589i	0.882555	−	0.470209i	$-0.155821\pi$
$587$	13.8765	+	11.6437i	0.572744	+	0.480589i	−0.309811	+	0.950798i	$0.600266\pi$
$588$	1.08625	−	1.34909i	0.0447963	−	0.0556357i
$589$	0.618768	+	3.50921i	0.0254959	+	0.144594i
$590$	0.183384	−	0.153878i	0.00754981	−	0.00633505i
$591$	32.5775	+	17.9392i	1.34006	+	0.737922i
$592$	−5.22442	+	1.90153i	−0.214722	+	0.0781525i
$593$	0.625124			0.0256708			0.0128354	−	0.999918i	$-0.495914\pi$
$593$	0.625124			0.0256708			0.0128354	+	0.999918i	$0.495914\pi$
$594$	27.0240	−	6.47790i	1.10881	−	0.265792i
$595$	−0.211718			−0.00867958
$596$	−0.103731	+	0.0377550i	−0.00424898	+	0.00154650i
$597$	−4.28156	+	2.58892i	−0.175232	+	0.105957i
$598$	−1.25759	+	1.05525i	−0.0514268	+	0.0431522i
$599$	−6.92945	−	39.2989i	−0.283130	−	1.60571i	−0.711891	−	0.702290i	$-0.752161\pi$
$599$	−6.92945	−	39.2989i	−0.283130	−	1.60571i	0.428761	−	0.903418i	$-0.358950\pi$
$600$	−8.55617	−	1.33068i	−0.349304	−	0.0543249i
$601$	−32.8689	−	27.5803i	−1.34075	−	1.12502i	−0.981432	−	0.191809i	$-0.938565\pi$
$601$	−32.8689	−	27.5803i	−1.34075	−	1.12502i	−0.359319	−	0.933215i	$-0.616991\pi$
$602$	0.797996	−	1.38217i	0.0325239	−	0.0563330i
$603$	−0.407260	−	0.129817i	−0.0165849	−	0.00528656i
$604$	2.47122	+	4.28028i	0.100553	+	0.174162i
$605$	−0.0813638	+	0.461437i	−0.00330791	+	0.0187601i
$606$	−10.1699	+	29.8056i	−0.413124	+	1.21077i
$607$	−6.14242	−	2.23566i	−0.249313	−	0.0907426i	0.214341	−	0.976759i	$-0.431240\pi$
$607$	−6.14242	−	2.23566i	−0.249313	−	0.0907426i	−0.463654	+	0.886016i	$0.653462\pi$
$608$	−2.33586	−	0.850183i	−0.0947316	−	0.0344795i
$609$	2.97687	−	8.72451i	0.120629	−	0.353535i
$610$	−0.0206362	+	0.117034i	−0.000835535	+	0.00473855i
$611$	−7.13337	−	12.3554i	−0.288585	−	0.499844i
$612$	−22.7339	−	7.24657i	−0.918962	−	0.292925i
$613$	1.59619	−	2.76468i	0.0644694	−	0.111664i	−0.831989	−	0.554792i	$-0.812798\pi$
$613$	1.59619	−	2.76468i	0.0644694	−	0.111664i	0.896459	+	0.443128i	$0.146131\pi$
$614$	21.8432	+	18.3286i	0.881519	+	0.739682i
$615$	−0.440692	−	0.0685379i	−0.0177704	−	0.00276371i
$616$	0.928690	+	5.26686i	0.0374180	+	0.212208i
$617$	12.9875	−	10.8978i	0.522856	−	0.438728i	−0.342770	−	0.939419i	$-0.611365\pi$
$617$	12.9875	−	10.8978i	0.522856	−	0.438728i	0.865626	+	0.500691i	$0.166921\pi$
$618$	−28.7336	+	17.3743i	−1.15583	+	0.698895i
$619$	13.3509	−	4.85934i	0.536619	−	0.195313i	−0.0594726	−	0.998230i	$-0.518942\pi$
$619$	13.3509	−	4.85934i	0.536619	−	0.195313i	0.596091	+	0.802917i	$0.296720\pi$
$620$	0.0381583			0.00153248
$621$	2.74778	+	2.89758i	0.110265	+	0.116276i
$622$	5.46182			0.218999
$623$	9.49676	−	3.45654i	0.380480	−	0.138483i
$624$	3.24107	+	1.78474i	0.129746	+	0.0714468i
$625$	19.1430	−	16.0629i	0.765719	−	0.642514i
$626$	−3.96637	−	22.4944i	−0.158528	−	0.899057i
$627$	−14.4408	+	17.9351i	−0.576711	+	0.716258i
$628$	−3.97967	−	3.33934i	−0.158806	−	0.133254i
$629$	22.1099	−	38.2955i	0.881580	−	1.52694i
$630$	0.0106722	−	0.0791407i	0.000425189	−	0.00315304i
$631$	−16.4948	−	28.5699i	−0.656648	−	1.13735i	−0.981478	−	0.191576i	$-0.938640\pi$
$631$	−16.4948	−	28.5699i	−0.656648	−	1.13735i	0.324830	−	0.945773i	$-0.394693\pi$
$632$	2.94234	−	16.6868i	0.117040	−	0.663767i
$633$	26.3667	−	5.20161i	1.04798	−	0.206746i
$634$	16.0268	+	5.83327i	0.636505	+	0.231669i
$635$	−0.0475376	−	0.0173023i	−0.00188647	−	0.000686620i
$636$	−7.88418	−	9.01872i	−0.312628	−	0.357616i
$637$	0.370944	−	2.10373i	0.0146973	−	0.0833527i
$638$	14.2320	+	24.6505i	0.563449	+	0.975922i
$639$	−7.99175	−	12.6319i	−0.316149	−	0.499712i
$640$	−0.0133095	+	0.0230528i	−0.000526105	+	0.000911240i
$641$	−7.52427	−	6.31361i	−0.297191	−	0.249373i	0.481983	−	0.876180i	$-0.339917\pi$
$641$	−7.52427	−	6.31361i	−0.297191	−	0.249373i	−0.779174	+	0.626808i	$0.784361\pi$
$642$	1.12575	+	2.90837i	0.0444297	+	0.114784i
$643$	−5.01549	−	28.4443i	−0.197792	−	1.12173i	−0.908387	−	0.418131i	$-0.862685\pi$
$643$	−5.01549	−	28.4443i	−0.197792	−	1.12173i	0.710595	−	0.703602i	$-0.248426\pi$
$644$	−0.588710	+	0.493987i	−0.0231984	+	0.0194658i
$645$	−0.00148965	−	0.0735689i	−5.86549e−5	−	0.00289677i
$646$	18.5785	−	6.76204i	0.730963	−	0.266049i
$647$	−6.52841			−0.256658			−0.128329	−	0.991732i	$-0.540961\pi$
$647$	−6.52841			−0.256658			−0.128329	+	0.991732i	$0.540961\pi$
$648$	3.85475	−	8.13271i	0.151429	−	0.319483i
$649$	48.0968			1.88797
$650$	−10.0353	+	3.65257i	−0.393619	+	0.143265i
$651$	−0.0502642	−	2.48238i	−0.00197001	−	0.0972923i
$652$	2.48070	−	2.08155i	0.0971517	−	0.0815199i
$653$	3.06984	+	17.4099i	0.120132	+	0.681304i	0.984081	+	0.177723i	$0.0568732\pi$
$653$	3.06984	+	17.4099i	0.120132	+	0.681304i	−0.863948	+	0.503581i	$0.832016\pi$
$654$	11.7453	+	30.3440i	0.459277	+	1.18654i
$655$	0.320290	+	0.268755i	0.0125148	+	0.0105011i
$656$	4.83662	−	8.37727i	0.188838	−	0.327077i
$657$	13.3690	−	25.4858i	0.521575	−	0.994296i
$658$	−3.33931	−	5.78385i	−0.130180	−	0.225478i
$659$	−5.21623	+	29.5827i	−0.203195	+	1.15238i	0.697059	+	0.717014i	$0.254492\pi$
$659$	−5.21623	+	29.5827i	−0.203195	+	1.15238i	−0.900254	+	0.435365i	$0.856619\pi$
$660$	0.162288	+	0.185642i	0.00631706	+	0.00722610i
$661$	12.1157	+	4.40975i	0.471246	+	0.171520i	0.566717	−	0.823913i	$-0.308213\pi$
$661$	12.1157	+	4.40975i	0.471246	+	0.171520i	−0.0954707	+	0.995432i	$0.530436\pi$
$662$	−23.9662	−	8.72298i	−0.931473	−	0.339028i
$663$	−28.8717	+	5.69581i	−1.12129	+	0.221207i
$664$	1.26525	−	7.17561i	0.0491014	−	0.278468i
$665$	0.0330844	+	0.0573038i	0.00128296	+	0.00222215i
$666$	13.2005	+	10.1951i	0.511508	+	0.395053i
$667$	−2.04509	+	3.54220i	−0.0791862	+	0.137154i
$668$	0.614757	+	0.515842i	0.0237856	+	0.0199585i
$669$	−1.84169	+	2.28733i	−0.0712039	+	0.0884333i
$670$	−0.000658607	−	0.00373515i	−2.54442e−5	−	0.000144301i
$671$	−18.2903	+	15.3474i	−0.706090	+	0.592480i
$672$	1.51722	+	0.835482i	0.0585282	+	0.0322294i
$673$	−11.5544	+	4.20545i	−0.445388	+	0.162108i	−0.554971	−	0.831870i	$-0.687271\pi$
$673$	−11.5544	+	4.20545i	−0.445388	+	0.162108i	0.109583	+	0.993978i	$0.465048\pi$
$674$	33.5534			1.29243
$675$	10.3500	+	23.8262i	0.398372	+	0.917070i
$676$	−8.43673			−0.324490
$677$	−23.4600	+	8.53874i	−0.901641	+	0.328171i	−0.750910	−	0.660404i	$-0.770385\pi$
$677$	−23.4600	+	8.53874i	−0.901641	+	0.328171i	−0.150731	+	0.988575i	$0.548163\pi$
$678$	23.2007	−	14.0287i	0.891019	−	0.538770i
$679$	1.35901	−	1.14035i	0.0521541	−	0.0437625i
$680$	−0.0367644	−	0.208501i	−0.00140985	−	0.00799566i
$681$	−4.83076	−	0.751297i	−0.185115	−	0.0287898i
$682$	5.87288	+	4.92794i	0.224884	+	0.188700i
$683$	−0.286007	+	0.495378i	−0.0109437	+	0.0189551i	−0.871445	−	0.490493i	$-0.836817\pi$
$683$	−0.286007	+	0.495378i	−0.0109437	+	0.0189551i	0.860502	+	0.509448i	$0.170150\pi$
$684$	1.59117	+	7.28557i	0.0608400	+	0.278571i
$685$	−0.231314	−	0.400647i	−0.00883805	−	0.0153080i
$686$	0.173648	−	0.984808i	0.00662992	−	0.0376001i
$687$	6.69788	−	19.6299i	0.255540	−	0.748929i
$688$	1.49974	+	0.545861i	0.0571771	+	0.0208108i
$689$	−13.8831	−	5.05302i	−0.528903	−	0.192505i
$690$	−0.0114421	+	0.0335341i	−0.000435592	+	0.00127662i
$691$	−2.31882	+	13.1507i	−0.0882122	+	0.500276i	0.908405	+	0.418092i	$0.137301\pi$
$691$	−2.31882	+	13.1507i	−0.0882122	+	0.500276i	−0.996617	+	0.0821848i	$0.973810\pi$
$692$	−6.21701	−	10.7682i	−0.236335	−	0.409345i
$693$	11.8631	−	10.8022i	0.450643	−	0.410341i
$694$	8.33179	−	14.4311i	0.316270	−	0.547796i
$695$	0.194510	+	0.163213i	0.00737817	+	0.00619102i
$696$	9.10889	+	1.41665i	0.345272	+	0.0536978i
$697$	13.3600	+	75.7685i	0.506047	+	2.86994i
$698$	21.0463	−	17.6599i	0.796614	−	0.668439i
$699$	−25.3485	+	15.3274i	−0.958769	+	0.579736i
$700$	−4.69780	+	1.70986i	−0.177560	+	0.0646266i
$701$	29.5254			1.11516			0.557579	−	0.830124i	$-0.311730\pi$
$701$	29.5254			1.11516			0.557579	+	0.830124i	$0.311730\pi$
$702$	−0.673759	−	11.0795i	−0.0254294	−	0.418167i
$703$	−13.8201			−0.521237
$704$	−5.02558	+	1.82916i	−0.189409	+	0.0689391i
$705$	−0.269730	−	0.148531i	−0.0101586	−	0.00559398i
$706$	−1.68465	+	1.41359i	−0.0634025	+	0.0532010i
$707$	3.15735	+	17.9062i	0.118744	+	0.673432i
$708$	9.76893	−	12.1327i	0.367139	−	0.455976i
$709$	−3.69783	−	3.10284i	−0.138875	−	0.116530i	0.570704	−	0.821156i	$-0.306670\pi$
$709$	−3.69783	−	3.10284i	−0.138875	−	0.116530i	−0.709579	+	0.704626i	$0.751115\pi$
$710$	0.0663156	−	0.114862i	0.00248878	−	0.00431069i
$711$	−47.0243	+	19.3052i	−1.76355	+	0.724002i
$712$	5.05312	+	8.75226i	0.189374	+	0.328005i
$713$	−0.191300	+	1.08492i	−0.00716424	+	0.0406304i
$714$	−13.5156	+	2.66635i	−0.505808	+	0.0997857i
$715$	0.285770	+	0.104012i	0.0106872	+	0.00388982i
$716$	−17.0155	−	6.19314i	−0.635899	−	0.231448i
$717$	−11.1111	−	12.7099i	−0.414950	−	0.474662i
$718$	−0.712430	+	4.04039i	−0.0265877	+	0.150786i
$719$	−21.2158	−	36.7468i	−0.791215	−	1.37043i	−0.925215	−	0.379444i	$-0.876115\pi$
$719$	−21.2158	−	36.7468i	−0.791215	−	1.37043i	0.133999	−	0.990981i	$-0.457218\pi$
$720$	0.0797916	−	0.00323262i	0.00297366	−	0.000120473i
$721$	−9.69314	+	16.7890i	−0.360991	+	0.625255i
$722$	9.82142	+	8.24115i	0.365515	+	0.306704i
$723$	7.90970	+	20.4347i	0.294165	+	0.759976i
$724$	1.87879	+	10.6551i	0.0698246	+	0.395995i
$725$	−20.3825	+	17.1029i	−0.756986	+	0.635187i
$726$	0.617207	+	30.4818i	0.0229067	+	1.13129i
$727$	2.64128	−	0.961347i	0.0979596	−	0.0356544i	−0.292575	−	0.956242i	$-0.594512\pi$
$727$	2.64128	−	0.961347i	0.0979596	−	0.0356544i	0.390535	+	0.920588i	$0.372290\pi$
$728$	2.13618			0.0791721
$729$	−26.8010	+	3.27173i	−0.992631	+	0.121175i
$730$	0.255360			0.00945131
$731$	−11.9284	+	4.34158i	−0.441187	+	0.160579i
$732$	0.156541	+	7.73105i	0.00578593	+	0.285748i
$733$	−25.8376	+	21.6803i	−0.954334	+	0.800781i	−0.980022	−	0.198889i	$-0.936267\pi$
$733$	−25.8376	+	21.6803i	−0.954334	+	0.800781i	0.0256881	+	0.999670i	$0.491822\pi$
$734$	5.41847	+	30.7296i	0.199999	+	1.13425i
$735$	−0.0166429	−	0.0429969i	−0.000613881	−	0.00158596i
$736$	−0.588710	−	0.493987i	−0.0217002	−	0.0182086i
$737$	0.381008	−	0.659926i	0.0140346	−	0.0243087i
$738$	−28.9959	+	1.17472i	−1.06735	+	0.0432421i
$739$	−20.6804	−	35.8195i	−0.760741	−	1.31764i	−0.942469	−	0.334294i	$-0.891502\pi$
$739$	−20.6804	−	35.8195i	−0.760741	−	1.31764i	0.181728	−	0.983349i	$-0.441831\pi$
$740$	−0.0256989	+	0.145746i	−0.000944710	+	0.00535772i
$741$	6.05332	+	6.92440i	0.222374	+	0.254374i
$742$	−6.49901	−	2.36545i	−0.238586	−	0.0868383i
$743$	45.8894	+	16.7024i	1.68352	+	0.612751i	0.993786	−	0.111311i	$-0.0355049\pi$
$743$	45.8894	+	16.7024i	1.68352	+	0.612751i	0.689735	+	0.724062i	$0.257727\pi$
$744$	2.43594	−	0.480562i	0.0893059	−	0.0176183i
$745$	−0.000510252		0.00289378i	−1.86942e−5		0.000106020i
$746$	−6.03048	−	10.4451i	−0.220792	−	0.382422i
$747$	−20.2212	+	8.30155i	−0.739855	+	0.303738i
$748$	21.2684	−	36.8380i	0.777651	−	1.34693i
$749$	1.37930	+	1.15737i	0.0503985	+	0.0422894i
$750$	−0.289129	+	0.359090i	−0.0105575	+	0.0131121i
$751$	8.05253	+	45.6682i	0.293841	+	1.66645i	0.671876	+	0.740663i	$0.265489\pi$
$751$	8.05253	+	45.6682i	0.293841	+	1.66645i	−0.378035	+	0.925791i	$0.623400\pi$
$752$	5.11612	−	4.29293i	0.186566	−	0.156547i
$753$	−3.91889	−	2.15800i	−0.142812	−	0.0786417i
$754$	10.6836	−	3.88852i	0.389074	−	0.141612i
$755$	0.131563			0.00478807
$756$	−0.315404	−	5.18657i	−0.0114711	−	0.188634i
$757$	22.6977			0.824964			0.412482	−	0.910966i	$-0.364662\pi$
$757$	22.6977			0.824964			0.412482	+	0.910966i	$0.364662\pi$
$758$	14.9334	−	5.43530i	0.542404	−	0.197419i
$759$	−6.09177	+	3.68349i	−0.221117	+	0.133702i
$760$	−0.0506882	+	0.0425324i	−0.00183865	+	0.00154281i
$761$	3.05865	+	17.3465i	0.110876	+	0.628809i	0.988710	+	0.149843i	$0.0478769\pi$
$761$	3.05865	+	17.3465i	0.110876	+	0.628809i	−0.877834	+	0.478965i	$0.841012\pi$
$762$	−3.25260	−	0.505855i	−0.117829	−	0.0183252i
$763$	14.3907	+	12.0752i	0.520978	+	0.437153i
$764$	−6.42861	+	11.1347i	−0.232579	+	0.402838i
$765$	−0.469630	+	0.427630i	−0.0169795	+	0.0154610i
$766$	11.2969	+	19.5668i	0.408174	+	0.706979i
$767$	3.33599	−	18.9193i	0.120456	−	0.683137i
$768$	−0.559325	+	1.63925i	−0.0201829	+	0.0591515i
$769$	−34.9294	−	12.7133i	−1.25959	−	0.458452i	−0.375957	−	0.926637i	$-0.622686\pi$
$769$	−34.9294	−	12.7133i	−1.25959	−	0.458452i	−0.883631	+	0.468185i	$0.844908\pi$
$770$	0.133776	+	0.0486905i	0.00482095	+	0.00175468i
$771$	3.65527	−	10.7128i	0.131641	−	0.385811i
$772$	−1.11192	+	6.30599i	−0.0400187	+	0.226957i
$773$	18.1543	+	31.4442i	0.652966	+	1.13097i	0.982400	+	0.186791i	$0.0598088\pi$
$773$	18.1543	+	31.4442i	0.652966	+	1.13097i	−0.329434	+	0.944179i	$0.606858\pi$
$774$	−1.02162	−	4.67772i	−0.0367212	−	0.168137i
$775$	−3.58324	+	6.20635i	−0.128714	+	0.222939i
$776$	1.35901	+	1.14035i	0.0487857	+	0.0409361i
$777$	9.51531	+	1.47985i	0.341360	+	0.0530894i
$778$	5.07454	+	28.7792i	0.181931	+	1.03178i
$779$	18.4199	−	15.4561i	0.659960	−	0.553772i
$780$	0.0842802	−	0.0509615i	0.00301771	−	0.00182471i
$781$	25.0403	−	9.11393i	0.896013	−	0.326122i
$782$	6.11242			0.218580
$783$	−11.0186	−	25.3653i	−0.393773	−	0.906482i
$784$	1.00000			0.0357143
$785$	−0.129948	+	0.0472973i	−0.00463806	+	0.00168811i
$786$	23.8313	+	13.1230i	0.850033	+	0.468083i
$787$	0.108724	−	0.0912305i	0.00387560	−	0.00325202i	−0.640848	−	0.767668i	$-0.721417\pi$
$787$	0.108724	−	0.0912305i	0.00387560	−	0.00325202i	0.644723	+	0.764416i	$0.276973\pi$
$788$	3.72853	+	21.1455i	0.132823	+	0.753279i
$789$	−16.0414	+	19.9229i	−0.571088	+	0.709276i
$790$	−0.345516	−	0.289923i	−0.0122929	−	0.0103150i
$791$	7.82666	−	13.5562i	0.278284	−	0.482002i
$792$	12.6981	+	9.80712i	0.451206	+	0.348481i
$793$	4.76843	+	8.25916i	0.169332	+	0.293291i
$794$	2.92403	−	16.5830i	0.103770	−	0.588509i
$795$	−0.312841	+	0.0617172i	−0.0110953	+	0.00218888i
$796$	−2.71451	−	0.988002i	−0.0962134	−	0.0350188i
$797$	−17.8206	−	6.48615i	−0.631237	−	0.229751i	0.00653282	−	0.999979i	$-0.497921\pi$
$797$	−17.8206	−	6.48615i	−0.631237	−	0.229751i	−0.637769	+	0.770227i	$0.720143\pi$
$798$	2.83371	+	3.24149i	0.100312	+	0.114747i
$799$	−9.22406	+	52.3122i	−0.326324	+	1.85067i
$800$	−2.49965	−	4.32951i	−0.0883758	−	0.153071i
$801$	14.0841	−	26.8489i	0.497636	−	0.948660i
$802$	−12.4455	+	21.5563i	−0.439466	+	0.761178i
$803$	39.3021	+	32.9784i	1.38694	+	1.16378i
$804$	−0.0890840	−	0.230149i	−0.00314175	−	0.00811673i
$805$	0.00355230	+	0.0201461i	0.000125202	+	0.000710057i
$806$	2.34579	−	1.96835i	0.0826269	−	0.0693322i
$807$	−0.262612	−	12.9696i	−0.00924440	−	0.456550i
$808$	−17.0859	+	6.21876i	−0.601080	+	0.218775i
$809$	30.5528			1.07418			0.537089	−	0.843526i	$-0.319524\pi$
$809$	30.5528			1.07418			0.537089	+	0.843526i	$0.319524\pi$
$810$	−0.136176	−	0.197105i	−0.00478475	−	0.00692556i
$811$	−8.17256			−0.286977			−0.143489	−	0.989652i	$-0.545832\pi$
$811$	−8.17256			−0.286977			−0.143489	+	0.989652i	$0.545832\pi$
$812$	5.00127	−	1.82031i	0.175510	−	0.0638805i
$813$	0.627193	+	30.9750i	0.0219966	+	1.08634i
$814$	−22.7775	+	19.1126i	−0.798352	+	0.669897i
$815$	−0.0149686	−	0.0848914i	−0.000524329	−	0.00297362i
$816$	−4.97280	−	12.8472i	−0.174083	−	0.449744i
$817$	3.03910	+	2.55011i	0.106325	+	0.0892171i
$818$	−9.13220	+	15.8174i	−0.319300	+	0.553043i
$819$	−3.42631	−	5.41570i	−0.119725	−	0.189240i
$820$	−0.128746	−	0.222995i	−0.00449601	−	0.00778731i
$821$	−7.62296	+	43.2319i	−0.266043	+	1.50881i	0.500005	+	0.866022i	$0.333331\pi$
$821$	−7.62296	+	43.2319i	−0.266043	+	1.50881i	−0.766048	+	0.642783i	$0.777780\pi$
$822$	−19.8123	−	22.6633i	−0.691032	−	0.790473i
$823$	−27.1787	−	9.89224i	−0.947390	−	0.344822i	−0.178310	−	0.983974i	$-0.557063\pi$
$823$	−27.1787	−	9.89224i	−0.947390	−	0.344822i	−0.769080	+	0.639152i	$0.779285\pi$
$824$	−18.2171	−	6.63050i	−0.634624	−	0.230984i
$825$	−45.4337	+	8.96316i	−1.58180	+	0.312057i
$826$	1.56166	−	8.85661i	0.0543371	−	0.308161i
$827$	0.440898	+	0.763658i	0.0153315	+	0.0265550i	0.873589	−	0.486664i	$-0.161786\pi$
$827$	0.440898	+	0.763658i	0.0153315	+	0.0265550i	−0.858258	+	0.513219i	$0.828453\pi$
$828$	−0.308111	+	2.28484i	−0.0107076	+	0.0794037i
$829$	23.2421	−	40.2565i	0.807232	−	1.39817i	−0.107542	−	0.994201i	$-0.534298\pi$
$829$	23.2421	−	40.2565i	0.807232	−	1.39817i	0.914774	−	0.403966i	$-0.132369\pi$
$830$	−0.148578	−	0.124672i	−0.00515721	−	0.00432741i
$831$	11.3488	−	14.0948i	0.393684	−	0.488945i
$832$	0.370944	+	2.10373i	0.0128602	+	0.0729336i
$833$	−6.09283	+	5.11249i	−0.211104	+	0.177137i
$834$	14.4725	+	7.96952i	0.501143	+	0.275962i
$835$	0.0200737	−	0.00730623i	0.000694679	−	0.000252842i
$836$	−13.2942			−0.459788
$837$	−5.12544	−	5.40487i	−0.177161	−	0.186820i
$838$	−6.64285			−0.229474
$839$	−49.1919	+	17.9044i	−1.69829	+	0.618128i	−0.995629	−	0.0933935i	$-0.970229\pi$
$839$	−49.1919	+	17.9044i	−1.69829	+	0.618128i	−0.702664	+	0.711522i	$0.748006\pi$
$840$	0.0394537	−	0.0238563i	0.00136128	−	0.000823122i
$841$	−0.516122	+	0.433077i	−0.0177973	+	0.0149337i
$842$	3.00726	+	17.0550i	0.103637	+	0.587754i
$843$	−31.0769	−	4.83318i	−1.07034	−	0.166464i
$844$	11.8861	+	9.97363i	0.409137	+	0.343307i
$845$	−0.112289	+	0.194490i	−0.00386285	+	0.00669065i
$846$	−19.0895	−	6.08491i	−0.656311	−	0.209203i
$847$	8.80114	+	15.2440i	0.302411	+	0.523791i
$848$	1.20097	−	6.81104i	0.0412415	−	0.233892i
$849$	2.94706	−	8.63715i	0.101143	−	0.296426i
$850$	37.3645	+	13.5996i	1.28159	+	0.466462i
$851$	−4.01500	−	1.46134i	−0.137632	−	0.0500941i
$852$	2.78688	−	8.16770i	0.0954769	−	0.279821i
$853$	−5.96448	+	33.8262i	−0.204220	+	1.15819i	0.694443	+	0.719548i	$0.255651\pi$
$853$	−5.96448	+	33.8262i	−0.204220	+	1.15819i	−0.898663	+	0.438640i	$0.855460\pi$
$854$	2.23222	+	3.86632i	0.0763850	+	0.132303i
$855$	0.189130	+	0.0602865i	0.00646812	+	0.00206176i
$856$	−0.900275	+	1.55932i	−0.0307708	+	0.0532965i
$857$	−9.40533	−	7.89201i	−0.321280	−	0.269586i	0.467856	−	0.883805i	$-0.345027\pi$
$857$	−9.40533	−	7.89201i	−0.321280	−	0.269586i	−0.789136	+	0.614219i	$0.789471\pi$
$858$	19.5528	+	3.04092i	0.667522	+	0.103815i
$859$	−8.20864	−	46.5535i	−0.280075	−	1.58839i	−0.722364	−	0.691513i	$-0.756945\pi$
$859$	−8.20864	−	46.5535i	−0.280075	−	1.58839i	0.442289	−	0.896873i	$-0.354167\pi$
$860$	0.0325444	−	0.0273080i	0.00110976	−	0.000931196i
$861$	−14.3373	+	8.66929i	−0.488614	+	0.295449i
$862$	−23.4145	+	8.52218i	−0.797501	+	0.290266i
$863$	−10.1524			−0.345592			−0.172796	−	0.984958i	$-0.555280\pi$
$863$	−10.1524			−0.345592			−0.172796	+	0.984958i	$0.555280\pi$
$864$	5.05301	−	1.21125i	0.171907	−	0.0412076i
$865$	−0.330982			−0.0112537
$866$	17.1763	−	6.25166i	0.583675	−	0.212440i
$867$	70.1871	+	38.6495i	2.38368	+	1.31261i
$868$	1.09812	−	0.921435i	0.0372727	−	0.0312755i
$869$	−15.7360	−	89.2431i	−0.533806	−	3.02736i
$870$	0.153892	−	0.191130i	0.00521744	−	0.00647992i
$871$	−0.233161	−	0.195645i	−0.00790036	−	0.00662919i
$872$	−9.39286	+	16.2689i	−0.318082	+	0.550935i
$873$	0.711262	−	5.27445i	0.0240726	−	0.178513i
$874$	−0.955165	−	1.65439i	−0.0323089	−	0.0559607i
$875$	−0.0462202	+	0.262128i	−0.00156253	+	0.00886153i
$876$	16.3016	−	3.21598i	0.550781	−	0.108658i
$877$	29.2220	+	10.6359i	0.986757	+	0.359150i	0.784464	−	0.620175i	$-0.212938\pi$
$877$	29.2220	+	10.6359i	0.986757	+	0.359150i	0.202293	+	0.979325i	$0.435161\pi$
$878$	8.64223	+	3.14551i	0.291661	+	0.106156i
$879$	20.1264	+	23.0227i	0.678848	+	0.776535i
$880$	−0.0247208	+	0.140199i	−0.000833338	+	0.00472610i
$881$	−2.82126	−	4.88656i	−0.0950506	−	0.164632i	0.814579	−	0.580052i	$-0.196968\pi$
$881$	−2.82126	−	4.88656i	−0.0950506	−	0.164632i	−0.909630	+	0.415420i	$0.863635\pi$
$882$	−1.60394	−	2.53523i	−0.0540075	−	0.0853655i
$883$	17.5346	−	30.3708i	0.590085	−	1.02206i	−0.404135	−	0.914699i	$-0.632427\pi$
$883$	17.5346	−	30.3708i	0.590085	−	1.02206i	0.994220	−	0.107358i	$-0.0342392\pi$
$884$	−13.0154	−	10.9212i	−0.437755	−	0.367320i
$885$	−0.149673	−	0.386681i	−0.00503121	−	0.0129982i
$886$	−2.42609	−	13.7590i	−0.0815060	−	0.462243i
$887$	−34.3105	+	28.7899i	−1.15203	+	0.966671i	−0.999765	−	0.0216683i	$-0.993102\pi$
$887$	−34.3105	+	28.7899i	−1.15203	+	0.966671i	−0.152268	+	0.988339i	$0.548658\pi$
$888$	0.194946	+	9.62772i	0.00654195	+	0.323085i
$889$	−1.78585	+	0.649997i	−0.0598955	+	0.0218002i
$890$	0.269018			0.00901751
$891$	4.49630	−	47.9225i	0.150632	−	1.60547i
$892$	−1.69546			−0.0567680
$893$	15.6003	−	5.67805i	0.522044	−	0.190009i
$894$	0.00387065	+	0.191159i	0.000129454	+	0.00639330i
$895$	−0.369237	+	0.309827i	−0.0123422	+	0.0103564i
$896$	0.173648	+	0.984808i	0.00580118	+	0.0329001i
$897$	1.02641	+	2.65174i	0.0342709	+	0.0885390i
$898$	26.0400	+	21.8502i	0.868966	+	0.729149i
$899$	3.81471	−	6.60727i	0.127228	−	0.220365i
$900$	−6.96701	+	13.2815i	−0.232234	+	0.442715i
$901$	27.5041	+	47.6384i	0.916293	+	1.58707i
$902$	8.98344	−	50.9476i	0.299116	−	1.69637i
$903$	−1.81939	−	2.08120i	−0.0605455	−	0.0692580i
$904$	14.7093	+	5.35375i	0.489224	+	0.178063i
$905$	0.270636	+	0.0985034i	0.00899624	+	0.00327436i
$906$	8.39869	−	1.65689i	0.279028	−	0.0550465i
$907$	−1.10158	+	6.24737i	−0.0365774	+	0.207441i	−0.997619	−	0.0689621i	$-0.978031\pi$
$907$	−1.10158	+	6.24737i	−0.0365774	+	0.207441i	0.961042	+	0.276403i	$0.0891424\pi$
$908$	−1.41129	−	2.44442i	−0.0468352	−	0.0811209i
$909$	43.1707	+	33.3421i	1.43188	+	1.10589i
$910$	0.0284315	−	0.0492449i	0.000942496	−	0.00163245i
$911$	−1.63919	−	1.37545i	−0.0543089	−	0.0455706i	0.615229	−	0.788348i	$-0.289063\pi$
$911$	−1.63919	−	1.37545i	−0.0543089	−	0.0455706i	−0.669538	+	0.742778i	$0.733508\pi$
$912$	−2.70017	+	3.35354i	−0.0894116	+	0.111047i
$913$	−6.76672	−	38.3760i	−0.223946	−	1.27006i
$914$	−10.1999	+	8.55870i	−0.337382	+	0.283097i
$915$	0.180306	+	0.0992878i	0.00596072	+	0.00328235i
$916$	11.2527	−	4.09567i	0.371801	−	0.135325i
$917$	15.7071			0.518695
$918$	−24.5946	+	33.2134i	−0.811743	+	1.09621i
$919$	32.0728			1.05798			0.528991	−	0.848627i	$-0.322570\pi$
$919$	32.0728			1.05798			0.528991	+	0.848627i	$0.322570\pi$
$920$	−0.0192232	+	0.00699667i	−0.000633770	+	0.000230673i
$921$	42.2627	−	25.5549i	1.39260	−	0.842062i
$922$	28.3792	−	23.8130i	0.934620	−	0.784239i
$923$	−1.84825	−	10.4820i	−0.0608360	−	0.345018i
$924$	9.15316	+	1.42353i	0.301117	+	0.0468307i
$925$	−21.2919	−	17.8660i	−0.700073	−	0.587431i
$926$	18.5487	−	32.1274i	0.609549	−	1.05577i
$927$	12.4094	+	56.8195i	0.407578	+	1.86620i
$928$	2.66112	+	4.60920i	0.0873556	+	0.151304i
$929$	4.74114	−	26.8883i	0.155552	−	0.882177i	−0.802728	−	0.596345i	$-0.796619\pi$
$929$	4.74114	−	26.8883i	0.155552	−	0.882177i	0.958280	−	0.285832i	$-0.0922699\pi$
$930$	0.0213429	−	0.0625512i	0.000699862	−	0.00205113i
$931$	2.33586	+	0.850183i	0.0765547	+	0.0278636i
$932$	−16.0710	−	5.84937i	−0.526423	−	0.191602i
$933$	3.05493	−	8.95331i	0.100014	−	0.293118i
$934$	0.246097	−	1.39568i	0.00805252	−	0.0456681i
$935$	−0.566145	−	0.980592i	−0.0185149	−	0.0320688i
$936$	4.73845	−	4.31468i	0.154881	−	0.141030i
$937$	−6.35512	+	11.0074i	−0.207613	+	0.359596i	−0.950962	−	0.309308i	$-0.899903\pi$
$937$	−6.35512	+	11.0074i	−0.207613	+	0.359596i	0.743349	+	0.668903i	$0.233236\pi$
$938$	−0.109149	−	0.0915865i	−0.00356383	−	0.00299041i
$939$	−39.0925	−	6.07980i	−1.27574	−	0.198407i
$940$	−0.0308709	−	0.175077i	−0.00100690	−	0.00571040i
$941$	−42.3559	+	35.5408i	−1.38076	+	1.15860i	−0.411833	+	0.911259i	$0.635111\pi$
$941$	−42.3559	+	35.5408i	−1.38076	+	1.15860i	−0.968929	+	0.247338i	$0.920444\pi$
$942$	−7.69995	+	4.65591i	−0.250878	+	0.151698i
$943$	6.98563	−	2.54256i	0.227483	−	0.0827972i
$944$	8.99324			0.292705
$945$	−0.123763	−	0.0617598i	−0.00402600	−	0.00200905i
$946$	8.53554			0.277514
$947$	10.2016	−	3.71310i	0.331509	−	0.120659i	−0.170903	−	0.985288i	$-0.554668\pi$
$947$	10.2016	−	3.71310i	0.331509	−	0.120659i	0.502412	+	0.864628i	$0.332446\pi$
$948$	−25.7082	−	14.1566i	−0.834965	−	0.459786i
$949$	15.6983	−	13.1725i	0.509589	−	0.427596i
$950$	−2.15794	−	12.2383i	−0.0700128	−	0.397062i
$951$	18.5264	−	23.0093i	0.600760	−	0.746127i
$952$	−6.09283	−	5.11249i	−0.197470	−	0.165697i
$953$	14.5363	−	25.1777i	0.470878	−	0.815584i	−0.528567	−	0.848891i	$-0.677271\pi$
$953$	14.5363	−	25.1777i	0.470878	−	0.815584i	0.999445	+	0.0333070i	$0.0106039\pi$
$954$	−19.1938	+	7.87977i	−0.621422	+	0.255117i
$955$	0.171123	+	0.296394i	0.00553742	+	0.00959109i
$956$	1.69251	−	9.59869i	0.0547396	−	0.310444i
$957$	48.3687	−	9.54217i	1.56354	−	0.308454i
$958$	−18.4767	−	6.72497i	−0.596955	−	0.217274i
$959$	−16.3315	−	5.94417i	−0.527371	−	0.191947i
$960$	0.0303450	+	0.0347117i	0.000979380	+	0.00112031i
$961$	−5.02626	+	28.5053i	−0.162137	+	0.919527i
$962$	5.93827	+	10.2854i	0.191458	+	0.331614i
$963$	5.39722	−	0.218659i	0.173923	−	0.00704620i
$964$	−6.32549	+	10.9561i	−0.203730	+	0.352871i
$965$	0.130571	+	0.109562i	0.00420324	+	0.00352694i
$966$	0.480489	+	1.24135i	0.0154595	+	0.0399396i
$967$	7.50578	+	42.5674i	0.241370	+	1.36888i	0.828775	+	0.559582i	$0.189038\pi$
$967$	7.50578	+	42.5674i	0.241370	+	1.36888i	−0.587405	+	0.809293i	$0.699851\pi$
$968$	−13.4841	+	11.3145i	−0.433396	+	0.363663i
$969$	−0.693246	−	34.2371i	−0.0222703	−	1.09986i
$970$	0.0443759	−	0.0161515i	0.00142483	−	0.000518594i
$971$	1.90618			0.0611724			0.0305862	−	0.999532i	$-0.490263\pi$
$971$	1.90618			0.0611724			0.0305862	+	0.999532i	$0.490263\pi$
$972$	−11.1755	−	10.8677i	−0.358455	−	0.348583i
$973$	9.53883			0.305801
$974$	−20.8826	+	7.60063i	−0.669121	+	0.243540i
$975$	0.374462	+	18.4935i	0.0119924	+	0.592265i
$976$	−3.41996	+	2.86969i	−0.109470	+	0.0918564i
$977$	−0.203495	−	1.15408i	−0.00651039	−	0.0369222i	0.981380	−	0.192079i	$-0.0615229\pi$
$977$	−0.203495	−	1.15408i	−0.00651039	−	0.0369222i	−0.987890	+	0.155157i	$0.950412\pi$
$978$	−2.02468	−	5.23076i	−0.0647421	−	0.167261i
$979$	41.4042	+	34.7422i	1.32328	+	1.11037i
$980$	0.0133095	−	0.0230528i	0.000425157	−	0.000736393i
$981$	56.3110	−	2.28134i	1.79787	−	0.0728377i
$982$	−16.0278	−	27.7609i	−0.511467	−	0.885887i
$983$	−2.65877	+	15.0787i	−0.0848017	+	0.480934i	0.912597	+	0.408859i	$0.134073\pi$
$983$	−2.65877	+	15.0787i	−0.0848017	+	0.480934i	−0.997399	+	0.0720753i	$0.977038\pi$
$984$	−11.0272	−	12.6141i	−0.351535	−	0.402122i
$985$	0.537088	+	0.195484i	0.0171130	+	0.00622864i
$986$	−39.7782	−	14.4781i	−1.26680	−	0.461077i
$987$	−11.3490	+	2.23892i	−0.361242	+	0.0712656i
$988$	−0.922081	+	5.22938i	−0.0293353	+	0.166369i
$989$	0.613266	+	1.06221i	0.0195007	+	0.0337762i
$990$	0.395086	−	0.162198i	0.0125567	−	0.00515498i
$991$	19.7972	−	34.2898i	0.628880	−	1.08925i	−0.358897	−	0.933377i	$-0.616847\pi$
$991$	19.7972	−	34.2898i	0.628880	−	1.08925i	0.987777	−	0.155875i	$-0.0498197\pi$
$992$	1.09812	+	0.921435i	0.0348654	+	0.0292556i
$993$	−27.7041	+	34.4077i	−0.879163	+	1.09190i
$994$	−0.865214	−	4.90687i	−0.0274429	−	0.155637i
$995$	−0.0589050	+	0.0494272i	−0.00186741	+	0.00156695i
$996$	−11.0550	−	6.08758i	−0.350290	−	0.192892i
$997$	−37.9539	+	13.8141i	−1.20201	+	0.437497i	−0.863926	−	0.503619i	$-0.832002\pi$
$997$	−37.9539	+	13.8141i	−1.20201	+	0.437497i	−0.338086	+	0.941115i	$0.609779\pi$
$998$	15.4938			0.490447
$999$	24.0958	−	15.9365i	0.762357	−	0.504210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.169.2	yes	24
27.4	even	9	inner	378.2.u.c.85.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.85.2	✓	24	27.4	even	9	inner
378.2.u.c.169.2	yes	24	1.1	even	1	trivial

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.0350640 - 1.73170i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.00462235 - 0.0262146i) q^{5} +(-0.625224 - 1.61527i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99754 + 0.121440i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.0350640 - 1.73170i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.00462235 - 0.0262146i) q^{5} +(-0.625224 - 1.61527i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99754 + 0.121440i) q^{9} +(-0.0133095 - 0.0230528i) q^{10} +(0.928690 - 5.26686i) q^{11} +(-1.13997 - 1.30402i) q^{12} +(-2.00735 - 0.730617i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(-0.0452337 + 0.00892369i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.97681 + 6.88804i) q^{17} +(-2.77523 + 1.13934i) q^{18} +(1.24288 - 2.15274i) q^{19} +(-0.0203914 - 0.0171104i) q^{20} +(-1.08625 + 1.34909i) q^{21} +(-0.928690 - 5.26686i) q^{22} +(0.588710 - 0.493987i) q^{23} +(-1.51722 - 0.835482i) q^{24} +(4.69780 - 1.70986i) q^{25} -2.13618 q^{26} +(0.315404 + 5.18657i) q^{27} -1.00000 q^{28} +(-5.00127 + 1.82031i) q^{29} +(-0.0394537 + 0.0238563i) q^{30} +(-1.09812 + 0.921435i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-9.15316 - 1.42353i) q^{33} +(6.09283 + 5.11249i) q^{34} +(-0.0133095 + 0.0230528i) q^{35} +(-2.21819 + 2.01981i) q^{36} +(-2.77985 - 4.81485i) q^{37} +(0.431649 - 2.44800i) q^{38} +(-1.19482 + 3.50174i) q^{39} +(-0.0250137 - 0.00910424i) q^{40} +(9.08987 + 3.30844i) q^{41} +(-0.559325 + 1.63925i) q^{42} +(-0.277141 + 1.57175i) q^{43} +(-2.67406 - 4.63160i) q^{44} +(0.0170392 + 0.0780181i) q^{45} +(0.384253 - 0.665547i) q^{46} +(5.11612 + 4.29293i) q^{47} +(-1.71148 - 0.266175i) q^{48} +(0.173648 + 0.984808i) q^{49} +(3.82968 - 3.21348i) q^{50} +(11.7886 - 7.12815i) q^{51} +(-2.00735 + 0.730617i) q^{52} +6.91611 q^{53} +(2.07029 + 4.76591i) q^{54} -0.142361 q^{55} +(-0.939693 + 0.342020i) q^{56} +(-3.77147 - 2.07681i) q^{57} +(-4.07707 + 3.42107i) q^{58} +(1.56166 + 8.85661i) q^{59} +(-0.0289150 + 0.0359116i) q^{60} +(-3.41996 - 2.86969i) q^{61} +(-0.716749 + 1.24145i) q^{62} +(2.37431 + 1.83375i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.00987417 + 0.0559992i) q^{65} +(-9.08804 + 1.79289i) q^{66} +(0.133891 + 0.0487322i) q^{67} +(7.47396 + 2.72030i) q^{68} +(-0.876077 - 1.00215i) q^{69} +(-0.00462235 + 0.0262146i) q^{70} +(2.49128 + 4.31503i) q^{71} +(-1.39360 + 2.65667i) q^{72} +(-4.79657 + 8.30791i) q^{73} +(-4.25898 - 3.57371i) q^{74} +(-3.12568 - 8.07520i) q^{75} +(-0.431649 - 2.44800i) q^{76} +(-4.09689 + 3.43770i) q^{77} +(0.0749030 + 3.69922i) q^{78} +(15.9224 - 5.79528i) q^{79} -0.0266190 q^{80} +(8.97050 - 0.728045i) q^{81} +9.67324 q^{82} +(6.84689 - 2.49206i) q^{83} +(0.0350640 + 1.73170i) q^{84} +(0.162185 - 0.136090i) q^{85} +(0.277141 + 1.57175i) q^{86} +(3.32759 + 8.59685i) q^{87} +(-4.09689 - 3.43770i) q^{88} +(-5.05312 + 8.75226i) q^{89} +(0.0426953 + 0.0674853i) q^{90} +(1.06809 + 1.84999i) q^{91} +(0.133450 - 0.756832i) q^{92} +(1.63415 + 1.86931i) q^{93} +(6.27585 + 2.28422i) q^{94} +(-0.0621783 - 0.0226310i) q^{95} +(-1.69930 + 0.335237i) q^{96} +(-0.308063 + 1.74711i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-2.14418 + 15.9004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Introduction

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