LMFDB - Embedded newform 567.2.u.a.550.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(100,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16, 6]))

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

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

chi := DirichletCharacter("567.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.u (of order $9$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			550.22
Character	$\chi$	$=$	567.550
Dual form			567.2.u.a.100.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.467294 + 2.65016i) q^{2} +(-4.92558 + 1.79277i) q^{4} +(-2.75387 + 1.00233i) q^{5} +(-0.609446 - 2.57460i) q^{7} +(-4.36176 - 7.55480i) q^{8} +O(q^{10})$	\(q+(0.467294 + 2.65016i) q^{2} +(-4.92558 + 1.79277i) q^{4} +(-2.75387 + 1.00233i) q^{5} +(-0.609446 - 2.57460i) q^{7} +(-4.36176 - 7.55480i) q^{8} +(-3.94319 - 6.82980i) q^{10} +(2.20625 + 0.803010i) q^{11} +(-1.68408 + 0.612957i) q^{13} +(6.53831 - 2.81822i) q^{14} +(9.95243 - 8.35108i) q^{16} +(0.185180 + 0.320741i) q^{17} +(-0.496899 + 0.860655i) q^{19} +(11.7675 - 9.87408i) q^{20} +(-1.09713 + 6.22215i) q^{22} +(1.14680 - 6.50383i) q^{23} +(2.74891 - 2.30661i) q^{25} +(-2.41139 - 4.17666i) q^{26} +(7.61753 + 11.5888i) q^{28} +(-6.76911 - 2.46375i) q^{29} +(-3.45754 + 1.25844i) q^{31} +(13.4172 + 11.2583i) q^{32} +(-0.763481 + 0.640637i) q^{34} +(4.25893 + 6.47925i) q^{35} -1.65927 q^{37} +(-2.51307 - 0.914682i) q^{38} +(19.5841 + 16.4330i) q^{40} +(-8.90071 + 3.23959i) q^{41} +(-1.36359 - 7.73328i) q^{43} -12.3067 q^{44} +17.7721 q^{46} +(0.234461 + 0.0853368i) q^{47} +(-6.25715 + 3.13816i) q^{49} +(7.39743 + 6.20718i) q^{50} +(7.19621 - 6.03834i) q^{52} +(4.11638 - 7.12978i) q^{53} -6.88060 q^{55} +(-16.7923 + 15.8341i) q^{56} +(3.36617 - 19.0905i) q^{58} +(-3.89379 - 3.26728i) q^{59} +(0.813935 + 0.296248i) q^{61} +(-4.95075 - 8.57495i) q^{62} +(-10.5746 + 18.3158i) q^{64} +(4.02336 - 3.37600i) q^{65} +(0.371283 - 2.10565i) q^{67} +(-1.48713 - 1.24785i) q^{68} +(-15.1809 + 14.3145i) q^{70} +(-0.743006 + 1.28692i) q^{71} -9.96945 q^{73} +(-0.775366 - 4.39732i) q^{74} +(0.904566 - 5.13005i) q^{76} +(0.722839 - 6.16961i) q^{77} +(1.60454 + 9.09978i) q^{79} +(-19.0372 + 32.9734i) q^{80} +(-12.7447 - 22.0744i) q^{82} +(6.30367 + 2.29435i) q^{83} +(-0.831449 - 0.697669i) q^{85} +(19.8572 - 7.22743i) q^{86} +(-3.55657 - 20.1703i) q^{88} +(-6.39738 + 11.0806i) q^{89} +(2.60448 + 3.96228i) q^{91} +(6.01118 + 34.0911i) q^{92} +(-0.116594 + 0.661236i) q^{94} +(0.505738 - 2.86819i) q^{95} +(2.55575 + 14.4944i) q^{97} +(-11.2406 - 15.1160i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 + 3 * q^10 + 15 * q^11 - 12 * q^13 + 30 * q^14 + 9 * q^16 - 27 * q^17 + 3 * q^19 + 18 * q^20 - 12 * q^22 + 36 * q^23 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 + 75 * q^32 - 18 * q^34 - 15 * q^35 - 6 * q^37 - 69 * q^38 + 51 * q^40 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 21 * q^47 - 42 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 111 * q^56 - 3 * q^58 - 27 * q^59 - 21 * q^61 - 75 * q^62 - 30 * q^64 + 90 * q^65 - 3 * q^67 + 30 * q^68 + 39 * q^70 + 18 * q^71 - 42 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 + 93 * q^86 - 51 * q^88 - 75 * q^89 - 21 * q^91 + 66 * q^92 + 33 * q^94 - 15 * q^95 - 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.467294	+	2.65016i	0.330427	+	1.87394i	0.468413	+	0.883510i	$0.344826\pi$
$2$	0.467294	+	2.65016i	0.330427	+	1.87394i	−0.137986	+	0.990434i	$0.544063\pi$
$3$		0			0
$3$		0			0
$4$	−4.92558	+	1.79277i	−2.46279	+	0.896383i
$5$	−2.75387	+	1.00233i	−1.23157	+	0.448254i	−0.874134	−	0.485685i	$-0.838570\pi$
$5$	−2.75387	+	1.00233i	−1.23157	+	0.448254i	−0.357433	+	0.933939i	$0.616348\pi$
$6$		0			0
$7$	−0.609446	−	2.57460i	−0.230349	−	0.973108i
$7$	−0.609446	−	2.57460i	−0.230349	−	0.973108i
$8$	−4.36176	−	7.55480i	−1.54212	−	2.67102i
$9$		0			0
$10$	−3.94319	−	6.82980i	−1.24695	−	2.15977i
$11$	2.20625	+	0.803010i	0.665210	+	0.242117i	0.652484	−	0.757802i	$-0.273727\pi$
$11$	2.20625	+	0.803010i	0.665210	+	0.242117i	0.0127258	+	0.999919i	$0.495949\pi$
$12$		0			0
$13$	−1.68408	+	0.612957i	−0.467081	+	0.170004i	−0.564830	−	0.825208i	$-0.691058\pi$
$13$	−1.68408	+	0.612957i	−0.467081	+	0.170004i	0.0977486	+	0.995211i	$0.468836\pi$
$14$	6.53831	−	2.81822i	1.74744	−	0.753202i
$15$		0			0
$16$	9.95243	−	8.35108i	2.48811	−	2.08777i
$17$	0.185180	+	0.320741i	0.0449128	+	0.0777912i	0.887608	−	0.460600i	$-0.152366\pi$
$17$	0.185180	+	0.320741i	0.0449128	+	0.0777912i	−0.842695	+	0.538391i	$0.819032\pi$
$18$		0			0
$19$	−0.496899	+	0.860655i	−0.113997	+	0.197448i	−0.917378	−	0.398017i	$-0.869699\pi$
$19$	−0.496899	+	0.860655i	−0.113997	+	0.197448i	0.803382	+	0.595464i	$0.203032\pi$
$20$	11.7675	−	9.87408i	2.63129	−	2.20791i
$21$		0			0
$22$	−1.09713	+	6.22215i	−0.233910	+	1.32657i
$23$	1.14680	−	6.50383i	0.239124	−	1.35614i	−0.594627	−	0.804002i	$-0.702700\pi$
$23$	1.14680	−	6.50383i	0.239124	−	1.35614i	0.833751	−	0.552140i	$-0.186189\pi$
$24$		0			0
$25$	2.74891	−	2.30661i	0.549782	−	0.461322i
$26$	−2.41139	−	4.17666i	−0.472913	−	0.819110i
$27$		0			0
$28$	7.61753	+	11.5888i	1.43958	+	2.19008i
$29$	−6.76911	−	2.46375i	−1.25699	−	0.457507i	−0.374233	−	0.927335i	$-0.622094\pi$
$29$	−6.76911	−	2.46375i	−1.25699	−	0.457507i	−0.882758	+	0.469827i	$0.844316\pi$
$30$		0			0
$31$	−3.45754	+	1.25844i	−0.620992	+	0.226023i	−0.633306	−	0.773902i	$-0.718302\pi$
$31$	−3.45754	+	1.25844i	−0.620992	+	0.226023i	0.0123140	+	0.999924i	$0.496080\pi$
$32$	13.4172	+	11.2583i	2.37184	+	1.99021i
$33$		0			0
$34$	−0.763481	+	0.640637i	−0.130936	+	0.109868i
$35$	4.25893	+	6.47925i	0.719890	+	1.09519i
$36$		0			0
$37$	−1.65927			−0.272782			−0.136391	−	0.990655i	$-0.543550\pi$
$37$	−1.65927			−0.272782			−0.136391	+	0.990655i	$0.543550\pi$
$38$	−2.51307	−	0.914682i	−0.407674	−	0.148381i
$39$		0			0
$40$	19.5841	+	16.4330i	3.09652	+	2.59829i
$41$	−8.90071	+	3.23959i	−1.39006	+	0.505939i	−0.925211	−	0.379453i	$-0.876112\pi$
$41$	−8.90071	+	3.23959i	−1.39006	+	0.505939i	−0.464845	+	0.885392i	$0.653890\pi$
$42$		0			0
$43$	−1.36359	−	7.73328i	−0.207945	−	1.17931i	−0.892738	−	0.450577i	$-0.851218\pi$
$43$	−1.36359	−	7.73328i	−0.207945	−	1.17931i	0.684793	−	0.728738i	$-0.259893\pi$
$44$	−12.3067			−1.85530
$45$		0			0
$46$	17.7721			2.62035
$47$	0.234461	+	0.0853368i	0.0341996	+	0.0124477i	0.359063	−	0.933313i	$-0.383096\pi$
$47$	0.234461	+	0.0853368i	0.0341996	+	0.0124477i	−0.324864	+	0.945761i	$0.605318\pi$
$48$		0			0
$49$	−6.25715	+	3.13816i	−0.893879	+	0.448309i
$50$	7.39743	+	6.20718i	1.04615	+	0.877828i
$51$		0			0
$52$	7.19621	−	6.03834i	0.997935	−	0.837367i
$53$	4.11638	−	7.12978i	0.565429	−	0.979351i	−0.431581	−	0.902074i	$-0.642044\pi$
$53$	4.11638	−	7.12978i	0.565429	−	0.979351i	0.997010	−	0.0772769i	$-0.0246225\pi$
$54$		0			0
$55$	−6.88060			−0.927781
$56$	−16.7923	+	15.8341i	−2.24397	+	2.11591i
$57$		0			0
$58$	3.36617	−	19.0905i	0.442000	−	2.50670i
$59$	−3.89379	−	3.26728i	−0.506928	−	0.425363i	0.353119	−	0.935579i	$-0.385121\pi$
$59$	−3.89379	−	3.26728i	−0.506928	−	0.425363i	−0.860047	+	0.510215i	$0.829566\pi$
$60$		0			0
$61$	0.813935	+	0.296248i	0.104214	+	0.0379307i	0.393601	−	0.919281i	$-0.371229\pi$
$61$	0.813935	+	0.296248i	0.104214	+	0.0379307i	−0.289387	+	0.957212i	$0.593451\pi$
$62$	−4.95075	−	8.57495i	−0.628746	−	1.08902i
$63$		0			0
$64$	−10.5746	+	18.3158i	−1.32183	+	2.28947i
$65$	4.02336	−	3.37600i	0.499037	−	0.418742i
$66$		0			0
$67$	0.371283	−	2.10565i	0.0453595	−	0.257246i	−0.953692	−	0.300784i	$-0.902752\pi$
$67$	0.371283	−	2.10565i	0.0453595	−	0.257246i	0.999052	+	0.0435375i	$0.0138628\pi$
$68$	−1.48713	−	1.24785i	−0.180341	−	0.151324i
$69$		0			0
$70$	−15.1809	+	14.3145i	−1.81446	+	1.71091i
$71$	−0.743006	+	1.28692i	−0.0881786	+	0.152730i	−0.906741	−	0.421687i	$-0.861438\pi$
$71$	−0.743006	+	1.28692i	−0.0881786	+	0.152730i	0.818563	+	0.574417i	$0.194771\pi$
$72$		0			0
$73$	−9.96945			−1.16684			−0.583418	−	0.812172i	$-0.698285\pi$
$73$	−9.96945			−1.16684			−0.583418	+	0.812172i	$0.698285\pi$
$74$	−0.775366	−	4.39732i	−0.0901345	−	0.511178i
$75$		0			0
$76$	0.904566	−	5.13005i	0.103761	−	0.588457i
$77$	0.722839	−	6.16961i	0.0823752	−	0.703092i
$78$		0			0
$79$	1.60454	+	9.09978i	0.180525	+	1.02381i	0.931572	+	0.363557i	$0.118438\pi$
$79$	1.60454	+	9.09978i	0.180525	+	1.02381i	−0.751047	+	0.660248i	$0.770451\pi$
$80$	−19.0372	+	32.9734i	−2.12842	+	3.68653i
$81$		0			0
$82$	−12.7447	−	22.0744i	−1.40741	−	2.43771i
$83$	6.30367	+	2.29435i	0.691918	+	0.251838i	0.663956	−	0.747771i	$-0.268876\pi$
$83$	6.30367	+	2.29435i	0.691918	+	0.251838i	0.0279619	+	0.999609i	$0.491098\pi$
$84$		0			0
$85$	−0.831449	−	0.697669i	−0.0901833	−	0.0756728i
$86$	19.8572	−	7.22743i	2.14126	−	0.779354i
$87$		0			0
$88$	−3.55657	−	20.1703i	−0.379132	−	2.15016i
$89$	−6.39738	+	11.0806i	−0.678121	+	1.17454i	0.297425	+	0.954745i	$0.403872\pi$
$89$	−6.39738	+	11.0806i	−0.678121	+	1.17454i	−0.975546	+	0.219795i	$0.929461\pi$
$90$		0			0
$91$	2.60448	+	3.96228i	0.273024	+	0.415360i
$92$	6.01118	+	34.0911i	0.626708	+	3.55424i
$93$		0			0
$94$	−0.116594	+	0.661236i	−0.0120257	+	0.0682012i
$95$	0.505738	−	2.86819i	0.0518877	−	0.294270i
$96$		0			0
$97$	2.55575	+	14.4944i	0.259497	+	1.47168i	0.784261	+	0.620431i	$0.213042\pi$
$97$	2.55575	+	14.4944i	0.259497	+	1.47168i	−0.524764	+	0.851248i	$0.675847\pi$
$98$	−11.2406	−	15.1160i	−1.13547	−	1.52695i
$99$		0			0
$100$	−9.40478	+	16.2896i	−0.940478	+	1.62896i
$101$	−1.48438	−	8.41831i	−0.147701	−	0.837653i	−0.965159	−	0.261665i	$-0.915728\pi$
$101$	−1.48438	−	8.41831i	−0.147701	−	0.837653i	0.817458	−	0.575988i	$-0.195383\pi$
$102$		0			0
$103$	−7.98496	+	2.90629i	−0.786782	+	0.286365i	−0.703998	−	0.710202i	$-0.748603\pi$
$103$	−7.98496	+	2.90629i	−0.786782	+	0.286365i	−0.0827842	+	0.996567i	$0.526381\pi$
$104$	11.9763	+	10.0493i	1.17438	+	0.985419i
$105$		0			0
$106$	20.8186	+	7.57735i	2.02208	+	0.735978i
$107$	7.94622	+	13.7633i	0.768190	+	1.33054i	0.938543	+	0.345161i	$0.112176\pi$
$107$	7.94622	+	13.7633i	0.768190	+	1.33054i	−0.170353	+	0.985383i	$0.554491\pi$
$108$		0			0
$109$	2.43123	−	4.21101i	0.232869	−	0.403341i	−0.725782	−	0.687925i	$-0.758522\pi$
$109$	2.43123	−	4.21101i	0.232869	−	0.403341i	0.958651	+	0.284583i	$0.0918552\pi$
$110$	−3.21527	−	18.2347i	−0.306564	−	1.73861i
$111$		0			0
$112$	−27.5662	−	20.5340i	−2.60476	−	1.94028i
$113$	−1.58605	+	8.99494i	−0.149203	+	0.846173i	0.814693	+	0.579893i	$0.196906\pi$
$113$	−1.58605	+	8.99494i	−0.149203	+	0.846173i	−0.963896	+	0.266280i	$0.914206\pi$
$114$		0			0
$115$	3.36082	+	19.0602i	0.313398	+	1.77737i
$116$	37.7587			3.50581
$117$		0			0
$118$	6.83925	−	11.8459i	0.629604	−	1.09051i
$119$	0.712924	−	0.672240i	0.0653536	−	0.0616241i
$120$		0			0
$121$	−4.20377	−	3.52738i	−0.382161	−	0.320671i
$122$	−0.404757	+	2.29549i	−0.0366450	+	0.207824i
$123$		0			0
$124$	14.7743	−	12.3971i	1.32677	−	1.11329i
$125$	2.06835	−	3.58249i	0.184999	−	0.320427i
$126$		0			0
$127$	−6.07362	−	10.5198i	−0.538947	−	0.933483i	−0.998961	−	0.0455717i	$-0.985489\pi$
$127$	−6.07362	−	10.5198i	−0.538947	−	0.933483i	0.460014	−	0.887911i	$-0.347844\pi$
$128$	−20.5640	−	7.48467i	−1.81761	−	0.661558i
$129$		0			0
$130$	10.8270	+	9.08496i	0.949594	+	0.796804i
$131$	2.39787	−	13.5990i	0.209502	−	1.18815i	−0.680693	−	0.732569i	$-0.738321\pi$
$131$	2.39787	−	13.5990i	0.209502	−	1.18815i	0.890195	−	0.455579i	$-0.150568\pi$
$132$		0			0
$133$	2.51868	+	0.754795i	0.218397	+	0.0654490i
$134$	5.75381			0.497053
$135$		0			0
$136$	1.61542	−	2.79800i	0.138521	−	0.239926i
$137$	−8.80875	+	7.39142i	−0.752582	+	0.631492i	−0.936184	−	0.351509i	$-0.885669\pi$
$137$	−8.80875	+	7.39142i	−0.752582	+	0.631492i	0.183602	+	0.983001i	$0.441224\pi$
$138$		0			0
$139$	−7.48876	−	6.28381i	−0.635188	−	0.532986i	0.267348	−	0.963600i	$-0.413853\pi$
$139$	−7.48876	−	6.28381i	−0.635188	−	0.532986i	−0.902536	+	0.430614i	$0.858297\pi$
$140$	−32.5935	−	24.2788i	−2.75465	−	2.05194i
$141$		0			0
$142$	−3.75775	−	1.36771i	−0.315344	−	0.114776i
$143$	−4.20772			−0.351868
$144$		0			0
$145$	21.1107			1.75315
$146$	−4.65866	−	26.4206i	−0.385554	−	2.18658i
$147$		0			0
$148$	8.17286	−	2.97468i	0.671805	−	0.244517i
$149$	1.42758	+	1.19789i	0.116952	+	0.0981346i	0.699388	−	0.714742i	$-0.253456\pi$
$149$	1.42758	+	1.19789i	0.116952	+	0.0981346i	−0.582436	+	0.812877i	$0.697900\pi$
$150$		0			0
$151$	−15.4952	−	5.63979i	−1.26098	−	0.458960i	−0.376883	−	0.926261i	$-0.623004\pi$
$151$	−15.4952	−	5.63979i	−1.26098	−	0.458960i	−0.884098	+	0.467301i	$0.845226\pi$
$152$	8.66943			0.703184
$153$		0			0
$154$	16.6882	−	0.967386i	1.34477	−	0.0779542i
$155$	8.26023	−	6.93116i	0.663478	−	0.556724i
$156$		0			0
$157$	−0.979587	−	0.821971i	−0.0781796	−	0.0656005i	0.602860	−	0.797847i	$-0.294028\pi$
$157$	−0.979587	−	0.821971i	−0.0781796	−	0.0656005i	−0.681040	+	0.732246i	$0.738472\pi$
$158$	−23.3661	+	8.50455i	−1.85890	+	0.676586i
$159$		0			0
$160$	−48.2336	−	17.5556i	−3.81320	−	1.38789i
$161$	−17.4437	+	1.01118i	−1.37475	+	0.0796921i
$162$		0			0
$163$	0.824782	+	1.42856i	0.0646019	+	0.111894i	0.896517	−	0.443009i	$-0.146089\pi$
$163$	0.824782	+	1.42856i	0.0646019	+	0.111894i	−0.831915	+	0.554902i	$0.812756\pi$
$164$	38.0333	−	31.9137i	2.96990	−	2.49205i
$165$		0			0
$166$	−3.13472	+	17.7779i	−0.243301	+	1.37983i
$167$	−2.59321	+	14.7068i	−0.200669	+	1.13805i	0.703443	+	0.710752i	$0.251645\pi$
$167$	−2.59321	+	14.7068i	−0.200669	+	1.13805i	−0.904111	+	0.427297i	$0.859466\pi$
$168$		0			0
$169$	−7.49815	+	6.29170i	−0.576781	+	0.483977i
$170$	1.46040	−	2.52949i	0.112008	−	0.194003i
$171$		0			0
$172$	20.5804	+	35.6463i	1.56924	+	2.71801i
$173$	5.87313	−	4.92815i	0.446526	−	0.374680i	−0.391619	−	0.920128i	$-0.628085\pi$
$173$	5.87313	−	4.92815i	0.446526	−	0.374680i	0.838145	+	0.545448i	$0.183640\pi$
$174$		0			0
$175$	−7.61392	−	5.67160i	−0.575558	−	0.428733i
$176$	28.6636	−	10.4327i	2.16060	−	0.786393i
$177$		0			0
$178$	−32.3548	−	11.7762i	−2.42509	−	0.882661i
$179$	11.4119	+	19.7659i	0.852963	+	1.47737i	0.878522	+	0.477701i	$0.158530\pi$
$179$	11.4119	+	19.7659i	0.852963	+	1.47737i	−0.0255596	+	0.999673i	$0.508137\pi$
$180$		0			0
$181$	−6.10213	−	10.5692i	−0.453567	−	0.785602i	0.545037	−	0.838412i	$-0.316516\pi$
$181$	−6.10213	−	10.5692i	−0.453567	−	0.785602i	−0.998605	+	0.0528100i	$0.983182\pi$
$182$	−9.28361	+	8.75383i	−0.688147	+	0.648877i
$183$		0			0
$184$	−54.1372	+	19.7043i	−3.99104	+	1.45262i
$185$	4.56940	−	1.66313i	0.335949	−	0.122276i
$186$		0			0
$187$	0.150995	+	0.856338i	0.0110419	+	0.0626216i
$188$	−1.30785			−0.0953844
$189$		0			0
$190$	7.83747			0.568590
$191$	1.26078	+	7.15023i	0.0912267	+	0.517372i	0.995838	+	0.0911358i	$0.0290497\pi$
$191$	1.26078	+	7.15023i	0.0912267	+	0.517372i	−0.904612	+	0.426236i	$0.859839\pi$
$192$		0			0
$193$	23.0279	−	8.38149i	1.65759	−	0.603313i	0.667607	−	0.744514i	$-0.267319\pi$
$193$	23.0279	−	8.38149i	1.65759	−	0.603313i	0.989981	+	0.141202i	$0.0450966\pi$
$194$	−37.2180	+	13.5463i	−2.67210	+	0.972564i
$195$		0			0
$196$	25.1941	−	26.6749i	1.79958	−	1.90535i
$197$	−0.145635	−	0.252248i	−0.0103761	−	0.0179719i	0.860791	−	0.508959i	$-0.169970\pi$
$197$	−0.145635	−	0.252248i	−0.0103761	−	0.0179719i	−0.871167	+	0.490987i	$0.836636\pi$
$198$		0			0
$199$	−0.581824	−	1.00775i	−0.0412444	−	0.0714374i	0.844666	−	0.535293i	$-0.179799\pi$
$199$	−0.581824	−	1.00775i	−0.0412444	−	0.0714374i	−0.885911	+	0.463856i	$0.846466\pi$
$200$	−29.4161	−	10.7066i	−2.08003	−	0.757070i
$201$		0			0
$202$	21.6162	−	7.86766i	1.52091	−	0.553566i
$203$	−2.21778	+	18.9293i	−0.155657	+	1.32857i
$204$		0			0
$205$	21.2642	−	17.8428i	1.48516	−	1.24620i
$206$	−11.4334	−	19.8033i	−0.796606	−	1.37976i
$207$		0			0
$208$	−11.6419	+	20.1643i	−0.807219	+	1.39814i
$209$	−1.78740	+	1.49981i	−0.123637	+	0.103744i
$210$		0			0
$211$	0.497448	−	2.82117i	0.0342458	−	0.194217i	−0.962885	−	0.269911i	$-0.913006\pi$
$211$	0.497448	−	2.82117i	0.0342458	−	0.194217i	0.997131	+	0.0756932i	$0.0241170\pi$
$212$	−7.49355	+	42.4980i	−0.514659	+	2.91878i
$213$		0			0
$214$	−32.7616	+	27.4902i	−2.23953	+	1.87919i
$215$	11.5064	+	19.9297i	0.784730	+	1.35919i
$216$		0			0
$217$	5.34716	+	8.13483i	0.362989	+	0.552228i
$218$	12.2959	+	4.47535i	0.832785	+	0.303109i
$219$		0			0
$220$	33.8910	−	12.3353i	2.28493	−	0.831646i
$221$	−0.508459	−	0.426648i	−0.0342027	−	0.0286995i
$222$		0			0
$223$	−1.16906	+	0.980960i	−0.0782862	+	0.0656899i	−0.681091	−	0.732199i	$-0.738494\pi$
$223$	−1.16906	+	0.980960i	−0.0782862	+	0.0656899i	0.602805	+	0.797889i	$0.294050\pi$
$224$	20.8087	−	41.4052i	1.39034	−	2.76650i
$225$		0			0
$226$	−24.5791			−1.63498
$227$	−16.2298	−	5.90717i	−1.07721	−	0.392073i	−0.258342	−	0.966053i	$-0.583176\pi$
$227$	−16.2298	−	5.90717i	−1.07721	−	0.392073i	−0.818869	+	0.573980i	$0.805399\pi$
$228$		0			0
$229$	−6.89707	−	5.78733i	−0.455771	−	0.382438i	0.385801	−	0.922582i	$-0.373925\pi$
$229$	−6.89707	−	5.78733i	−0.455771	−	0.382438i	−0.841572	+	0.540144i	$0.818370\pi$
$230$	−48.9419	+	17.8134i	−3.22713	+	1.17458i
$231$		0			0
$232$	10.9121	+	61.8855i	0.716414	+	4.06298i
$233$	−3.91280			−0.256336			−0.128168	−	0.991752i	$-0.540910\pi$
$233$	−3.91280			−0.256336			−0.128168	+	0.991752i	$0.540910\pi$
$234$		0			0
$235$	−0.731210			−0.0476989
$236$	25.0366	+	9.11259i	1.62975	+	0.593179i
$237$		0			0
$238$	2.11469	+	1.57523i	0.137075	+	0.102107i
$239$	−9.32029	−	7.82065i	−0.602879	−	0.505876i	0.289490	−	0.957181i	$-0.406514\pi$
$239$	−9.32029	−	7.82065i	−0.602879	−	0.505876i	−0.892370	+	0.451305i	$0.850959\pi$
$240$		0			0
$241$	21.1617	−	17.7568i	1.36315	−	1.14381i	0.388149	−	0.921597i	$-0.373115\pi$
$241$	21.1617	−	17.7568i	1.36315	−	1.14381i	0.974997	−	0.222218i	$-0.0713297\pi$
$242$	7.38371	−	12.7890i	0.474643	−	0.822106i
$243$		0			0
$244$	−4.54021			−0.290657
$245$	14.0859	−	14.9138i	0.899916	−	0.952807i
$246$		0			0
$247$	0.309276	−	1.75399i	0.0196788	−	0.111604i
$248$	24.5882	+	20.6320i	1.56135	+	1.31013i
$249$		0			0
$250$	10.4607	+	3.80737i	0.661591	+	0.240799i
$251$	−3.00566	−	5.20596i	−0.189716	−	0.328597i	0.755440	−	0.655218i	$-0.227423\pi$
$251$	−3.00566	−	5.20596i	−0.189716	−	0.328597i	−0.945155	+	0.326621i	$0.894090\pi$
$252$		0			0
$253$	7.75277	−	13.4282i	0.487412	−	0.844223i
$254$	25.0410	−	21.0119i	1.57121	−	1.31840i
$255$		0			0
$256$	2.88108	−	16.3394i	0.180067	−	1.02121i
$257$	2.55476	+	2.14370i	0.159361	+	0.133720i	0.718982	−	0.695029i	$-0.244609\pi$
$257$	2.55476	+	2.14370i	0.159361	+	0.133720i	−0.559620	+	0.828749i	$0.689053\pi$
$258$		0			0
$259$	1.01123	+	4.27195i	0.0628350	+	0.265446i
$260$	−13.7650	+	23.8417i	−0.853671	+	1.47860i
$261$		0			0
$262$	37.1599			2.29575
$263$	2.14434	+	12.1611i	0.132225	+	0.749888i	0.976752	+	0.214374i	$0.0687710\pi$
$263$	2.14434	+	12.1611i	0.132225	+	0.749888i	−0.844526	+	0.535514i	$0.820118\pi$
$264$		0			0
$265$	−4.18961	+	23.7604i	−0.257366	+	1.45959i
$266$	−0.823362	+	7.02760i	−0.0504836	+	0.430890i
$267$		0			0
$268$	1.94615	+	11.0372i	0.118880	+	0.674204i
$269$	1.34615	−	2.33159i	0.0820760	−	0.142160i	−0.822066	−	0.569393i	$-0.807178\pi$
$269$	1.34615	−	2.33159i	0.0820760	−	0.142160i	0.904141	+	0.427233i	$0.140512\pi$
$270$		0			0
$271$	11.0044	+	19.0602i	0.668469	+	1.15782i	0.978332	+	0.207041i	$0.0663833\pi$
$271$	11.0044	+	19.0602i	0.668469	+	1.15782i	−0.309864	+	0.950781i	$0.600283\pi$
$272$	4.52153	+	1.64570i	0.274158	+	0.0997853i
$273$		0			0
$274$	−23.7047	−	19.8906i	−1.43205	−	1.20164i
$275$	7.91702	−	2.88156i	0.477414	−	0.173765i
$276$		0			0
$277$	1.69737	+	9.62627i	0.101985	+	0.578387i	0.992382	+	0.123201i	$0.0393160\pi$
$277$	1.69737	+	9.62627i	0.101985	+	0.578387i	−0.890397	+	0.455186i	$0.849573\pi$
$278$	13.1536	−	22.7828i	0.788903	−	1.36642i
$279$		0			0
$280$	30.3730	−	60.4363i	1.81513	−	3.61176i
$281$	−1.22691	−	6.95814i	−0.0731912	−	0.415088i	−0.999285	−	0.0377956i	$-0.987966\pi$
$281$	−1.22691	−	6.95814i	−0.0731912	−	0.415088i	0.926094	−	0.377292i	$-0.123145\pi$
$282$		0			0
$283$	−1.58826	+	9.00744i	−0.0944120	+	0.535437i	0.900514	+	0.434827i	$0.143190\pi$
$283$	−1.58826	+	9.00744i	−0.0944120	+	0.535437i	−0.994926	+	0.100610i	$0.967921\pi$
$284$	1.35258	−	7.67088i	0.0802611	−	0.455183i
$285$		0			0
$286$	−1.96624	−	11.1511i	−0.116266	−	0.659380i
$287$	13.7652	+	20.9414i	0.812532	+	1.23613i
$288$		0			0
$289$	8.43142	−	14.6036i	0.495966	−	0.859038i
$290$	9.86491	+	55.9467i	0.579288	+	3.28530i
$291$		0			0
$292$	49.1053	−	17.8729i	2.87367	−	1.04593i
$293$	15.1908	+	12.7466i	0.887455	+	0.744663i	0.967698	−	0.252112i	$-0.0811253\pi$
$293$	15.1908	+	12.7466i	0.887455	+	0.744663i	−0.0802432	+	0.996775i	$0.525570\pi$
$294$		0			0
$295$	13.9979	+	5.09480i	0.814987	+	0.296631i
$296$	7.23733	+	12.5354i	0.420662	+	0.728607i
$297$		0			0
$298$	−2.50748	+	4.34309i	−0.145255	+	0.251588i
$299$	2.05526	+	11.6559i	0.118858	+	0.674080i
$300$		0			0
$301$	−19.0791	+	8.22371i	−1.09970	+	0.474007i
$302$	7.70551	−	43.7001i	0.443403	−	2.51466i
$303$		0			0
$304$	2.24204	+	12.7153i	0.128590	+	0.729270i
$305$	−2.53841			−0.145349
$306$		0			0
$307$	−12.8118	+	22.1907i	−0.731210	+	1.26649i	0.225157	+	0.974323i	$0.427711\pi$
$307$	−12.8118	+	22.1907i	−0.731210	+	1.26649i	−0.956366	+	0.292170i	$0.905623\pi$
$308$	7.50026	+	31.6848i	0.427367	+	1.80541i
$309$		0			0
$310$	22.2286	+	18.6520i	1.26250	+	1.05936i
$311$	5.62406	−	31.8956i	0.318911	−	1.80863i	−0.230489	−	0.973075i	$-0.574032\pi$
$311$	5.62406	−	31.8956i	0.318911	−	1.80863i	0.549400	−	0.835560i	$-0.314856\pi$
$312$		0			0
$313$	−1.51083	+	1.26774i	−0.0853971	+	0.0716567i	−0.684487	−	0.729025i	$-0.739974\pi$
$313$	−1.51083	+	1.26774i	−0.0853971	+	0.0716567i	0.599090	+	0.800682i	$0.295529\pi$
$314$	1.72060	−	2.98016i	0.0970989	−	0.168180i
$315$		0			0
$316$	−24.2170	−	41.9452i	−1.36232	−	2.35960i
$317$	−2.19415	−	0.798604i	−0.123236	−	0.0448541i	0.279666	−	0.960097i	$-0.409776\pi$
$317$	−2.19415	−	0.798604i	−0.123236	−	0.0448541i	−0.402902	+	0.915243i	$0.631998\pi$
$318$		0			0
$319$	−12.9559	−	10.8713i	−0.725393	−	0.608677i
$320$	10.7627	−	61.0384i	0.601655	−	3.41215i
$321$		0			0
$322$	−10.8311	−	45.7560i	−0.603594	−	2.54988i
$323$	−0.368063			−0.0204796
$324$		0			0
$325$	−3.21555	+	5.56949i	−0.178366	+	0.308940i
$326$	−3.40050	+	2.85336i	−0.188336	+	0.158033i
$327$		0			0
$328$	63.2972	+	53.1127i	3.49501	+	2.93266i
$329$	0.0768170	−	0.655652i	0.00423506	−	0.0361472i
$330$		0			0
$331$	5.76896	+	2.09973i	0.317091	+	0.115412i	0.495662	−	0.868515i	$-0.334925\pi$
$331$	5.76896	+	2.09973i	0.317091	+	0.115412i	−0.178571	+	0.983927i	$0.557148\pi$
$332$	−35.1625			−1.92979
$333$		0			0
$334$	−40.1872			−2.19895
$335$	1.08809	+	6.17084i	0.0594485	+	0.337149i
$336$		0			0
$337$	−18.6292	+	6.78048i	−1.01480	+	0.369356i	−0.795273	−	0.606251i	$-0.792673\pi$
$337$	−18.6292	+	6.78048i	−1.01480	+	0.369356i	−0.219524	+	0.975607i	$0.570450\pi$
$338$	−20.1778	−	16.9312i	−1.09753	−	0.920936i
$339$		0			0
$340$	5.34613	+	1.94583i	0.289934	+	0.105528i
$341$	−8.63873			−0.467814
$342$		0			0
$343$	11.8929	+	14.1971i	0.642157	+	0.766573i
$344$	−52.4757	+	44.0324i	−2.82930	+	2.37407i
$345$		0			0
$346$	15.8048	+	13.2618i	0.849673	+	0.712961i
$347$	−19.1981	+	6.98752i	−1.03061	+	0.375110i	−0.801312	−	0.598247i	$-0.795864\pi$
$347$	−19.1981	+	6.98752i	−1.03061	+	0.375110i	−0.229294	+	0.973357i	$0.573642\pi$
$348$		0			0
$349$	33.7947	+	12.3003i	1.80899	+	0.658418i	0.997226	+	0.0744315i	$0.0237142\pi$
$349$	33.7947	+	12.3003i	1.80899	+	0.658418i	0.811763	+	0.583987i	$0.198508\pi$
$350$	11.4727	−	22.8284i	0.613241	−	1.22023i
$351$		0			0
$352$	20.5611	+	35.6128i	1.09591	+	1.89817i
$353$	−2.22254	+	1.86493i	−0.118294	+	0.0992602i	−0.700016	−	0.714128i	$-0.746824\pi$
$353$	−2.22254	+	1.86493i	−0.118294	+	0.0992602i	0.581722	+	0.813388i	$0.302379\pi$
$354$		0			0
$355$	0.756223	−	4.28875i	0.0401361	−	0.227623i
$356$	11.6459	−	66.0474i	0.617233	−	3.50050i
$357$		0			0
$358$	−47.0501	+	39.4797i	−2.48668	+	2.08657i
$359$	−5.64377	+	9.77530i	−0.297867	+	0.515921i	−0.975648	−	0.219343i	$-0.929609\pi$
$359$	−5.64377	+	9.77530i	−0.297867	+	0.515921i	0.677781	+	0.735264i	$0.262942\pi$
$360$		0			0
$361$	9.00618	+	15.5992i	0.474010	+	0.821009i
$362$	25.1585	−	21.1105i	1.32230	−	1.10954i
$363$		0			0
$364$	−19.9320	−	14.8473i	−1.04472	−	0.778212i
$365$	27.4545	−	9.99264i	1.43704	−	0.523039i
$366$		0			0
$367$	−23.9923	−	8.73249i	−1.25239	−	0.455832i	−0.371181	−	0.928561i	$-0.621047\pi$
$367$	−23.9923	−	8.73249i	−1.25239	−	0.455832i	−0.881208	+	0.472729i	$0.843269\pi$
$368$	−42.9005	−	74.3059i	−2.23634	−	3.87346i
$369$		0			0
$370$	6.54280	+	11.3325i	0.340144	+	0.589147i
$371$	−20.8651	−	6.25283i	−1.08326	−	0.324631i
$372$		0			0
$373$	25.7924	−	9.38767i	1.33548	−	0.486075i	0.427094	−	0.904207i	$-0.359537\pi$
$373$	25.7924	−	9.38767i	1.33548	−	0.486075i	0.908386	+	0.418132i	$0.137315\pi$
$374$	−2.19887	+	0.800323i	−0.113701	+	0.0413837i
$375$		0			0
$376$	−0.377961	−	2.14352i	−0.0194919	−	0.110544i
$377$	12.9099			0.664895
$378$		0			0
$379$	12.8185			0.658443			0.329221	−	0.944253i	$-0.393214\pi$
$379$	12.8185			0.658443			0.329221	+	0.944253i	$0.393214\pi$
$380$	2.65093	+	15.0342i	0.135990	+	0.771236i
$381$		0			0
$382$	−18.3601	+	6.68252i	−0.939383	+	0.341907i
$383$	17.8169	−	6.48482i	0.910401	−	0.331359i	0.155988	−	0.987759i	$-0.450144\pi$
$383$	17.8169	−	6.48482i	0.910401	−	0.331359i	0.754413	+	0.656400i	$0.227922\pi$
$384$		0			0
$385$	4.19336	+	17.7148i	0.213713	+	0.902831i
$386$	32.9731	+	57.1110i	1.67829	+	2.90688i
$387$		0			0
$388$	−38.5735	−	66.8113i	−1.95827	−	3.39183i
$389$	−18.5894	−	6.76599i	−0.942520	−	0.343049i	−0.175360	−	0.984504i	$-0.556109\pi$
$389$	−18.5894	−	6.76599i	−0.942520	−	0.343049i	−0.767161	+	0.641455i	$0.778331\pi$
$390$		0			0
$391$	2.29841	−	0.836553i	0.116236	−	0.0423063i
$392$	51.0004	+	33.5836i	2.57591	+	1.69623i
$393$		0			0
$394$	0.600442	−	0.503830i	0.0302498	−	0.0253826i
$395$	−13.5396	−	23.4513i	−0.681253	−	1.17996i
$396$		0			0
$397$	3.21569	−	5.56973i	0.161391	−	0.279537i	−0.773977	−	0.633214i	$-0.781735\pi$
$397$	3.21569	−	5.56973i	0.161391	−	0.279537i	0.935368	+	0.353677i	$0.115069\pi$
$398$	2.39881	−	2.01284i	0.120241	−	0.100895i
$399$		0			0
$400$	8.09566	−	45.9128i	0.404783	−	2.29564i
$401$	2.94198	−	16.6848i	0.146916	−	0.833199i	−0.818894	−	0.573945i	$-0.805412\pi$
$401$	2.94198	−	16.6848i	0.146916	−	0.833199i	0.965809	−	0.259254i	$-0.0834767\pi$
$402$		0			0
$403$	5.05141	−	4.23864i	0.251629	−	0.211142i
$404$	22.4035	+	38.8040i	1.11461	+	1.93057i
$405$		0			0
$406$	−51.2019	+	2.96808i	−2.54111	+	0.147303i
$407$	−3.66076	−	1.33241i	−0.181457	−	0.0660450i
$408$		0			0
$409$	−20.2490	+	7.37004i	−1.00125	+	0.364425i	−0.790066	−	0.613022i	$-0.789954\pi$
$409$	−20.2490	+	7.37004i	−1.00125	+	0.364425i	−0.211183	+	0.977447i	$0.567732\pi$
$410$	57.2229	+	48.0157i	2.82604	+	2.37133i
$411$		0			0
$412$	34.1203	−	28.6303i	1.68099	−	1.41051i
$413$	−6.03888	+	12.0162i	−0.297154	+	0.591278i
$414$		0			0
$415$	−19.6592			−0.965031
$416$	−29.4965	−	10.7358i	−1.44618	−	0.526368i
$417$		0			0
$418$	−4.80996	−	4.03604i	−0.235263	−	0.197409i
$419$	−12.2407	+	4.45526i	−0.597998	+	0.217654i	−0.623244	−	0.782028i	$-0.714186\pi$
$419$	−12.2407	+	4.45526i	−0.597998	+	0.217654i	0.0252454	+	0.999681i	$0.491963\pi$
$420$		0			0
$421$	−3.24633	−	18.4109i	−0.158216	−	0.897290i	−0.955786	−	0.294063i	$-0.904992\pi$
$421$	−3.24633	−	18.4109i	−0.158216	−	0.897290i	0.797569	−	0.603227i	$-0.206119\pi$
$422$	7.70900			0.375268
$423$		0			0
$424$	−71.8188			−3.48783
$425$	1.24887	+	0.454551i	0.0605791	+	0.0220490i
$426$		0			0
$427$	0.266671	−	2.27611i	0.0129051	−	0.110149i
$428$	−63.8140	−	53.5463i	−3.08457	−	2.58826i
$429$		0			0
$430$	−47.4399	+	39.8068i	−2.28776	+	1.91965i
$431$	−0.578897	+	1.00268i	−0.0278845	+	0.0482974i	−0.879631	−	0.475657i	$-0.842210\pi$
$431$	−0.578897	+	1.00268i	−0.0278845	+	0.0482974i	0.851746	+	0.523954i	$0.175544\pi$
$432$		0			0
$433$	16.9175			0.813004			0.406502	−	0.913650i	$-0.366748\pi$
$433$	16.9175			0.813004			0.406502	+	0.913650i	$0.366748\pi$
$434$	−19.0599	+	17.9722i	−0.914903	+	0.862692i
$435$		0			0
$436$	−4.42586	+	25.1003i	−0.211960	+	1.20209i
$437$	5.02771	+	4.21875i	0.240508	+	0.201810i
$438$		0			0
$439$	−14.8184	−	5.39346i	−0.707244	−	0.257416i	−0.0367432	−	0.999325i	$-0.511698\pi$
$439$	−14.8184	−	5.39346i	−0.707244	−	0.257416i	−0.670500	+	0.741909i	$0.733921\pi$
$440$	30.0116	+	51.9816i	1.43075	+	2.47812i
$441$		0			0
$442$	0.893084	−	1.54687i	0.0424797	−	0.0735770i
$443$	−30.3711	+	25.4843i	−1.44297	+	1.21080i	−0.505458	+	0.862851i	$0.668676\pi$
$443$	−30.3711	+	25.4843i	−1.44297	+	1.21080i	−0.937514	+	0.347946i	$0.886879\pi$
$444$		0			0
$445$	6.51118	−	36.9268i	0.308660	−	1.75050i
$446$	−3.14599	−	2.63980i	−0.148967	−	0.124998i
$447$		0			0
$448$	53.6005	+	16.0629i	2.53238	+	0.758903i
$449$	17.1715	−	29.7420i	0.810375	−	1.40361i	−0.102226	−	0.994761i	$-0.532597\pi$
$449$	17.1715	−	29.7420i	0.810375	−	1.40361i	0.912602	−	0.408850i	$-0.134070\pi$
$450$		0			0
$451$	−22.2386			−1.04718
$452$	−8.31359	−	47.1487i	−0.391038	−	2.21769i
$453$		0			0
$454$	8.07083	−	45.7720i	0.378783	−	2.14819i
$455$	−11.1439	−	8.30107i	−0.522434	−	0.389160i
$456$		0			0
$457$	−6.31205	−	35.7974i	−0.295265	−	1.67453i	−0.666122	−	0.745842i	$-0.732047\pi$
$457$	−6.31205	−	35.7974i	−0.295265	−	1.67453i	0.370857	−	0.928690i	$-0.379064\pi$
$458$	12.1144	−	20.9827i	0.566067	−	0.980457i
$459$		0			0
$460$	−50.7244	−	87.8572i	−2.36504	−	4.09636i
$461$	−23.0683	−	8.39618i	−1.07440	−	0.391049i	−0.256578	−	0.966523i	$-0.582595\pi$
$461$	−23.0683	−	8.39618i	−1.07440	−	0.391049i	−0.817820	+	0.575474i	$0.804817\pi$
$462$		0			0
$463$	7.47936	+	6.27593i	0.347595	+	0.291667i	0.799824	−	0.600235i	$-0.204926\pi$
$463$	7.47936	+	6.27593i	0.347595	+	0.291667i	−0.452228	+	0.891902i	$0.649371\pi$
$464$	−87.9440	+	32.0090i	−4.08270	+	1.48598i
$465$		0			0
$466$	−1.82843	−	10.3695i	−0.0847004	−	0.480360i
$467$	13.6607	−	23.6610i	0.632140	−	1.09490i	−0.354973	−	0.934876i	$-0.615510\pi$
$467$	13.6607	−	23.6610i	0.632140	−	1.09490i	0.987113	−	0.160022i	$-0.0511567\pi$
$468$		0			0
$469$	−5.64750	+	0.327375i	−0.260777	+	0.0151168i
$470$	−0.341690	−	1.93782i	−0.0157610	−	0.0893850i
$471$		0			0
$472$	−7.69983	+	43.6679i	−0.354413	+	2.00998i
$473$	3.20149	−	18.1565i	0.147205	−	0.834838i
$474$		0			0
$475$	0.619263	+	3.51202i	0.0284138	+	0.161142i
$476$	−2.30640	+	4.58928i	−0.105714	+	0.210349i
$477$		0			0
$478$	16.3706	−	28.3548i	0.748775	−	1.29692i
$479$	−1.47080	−	8.34133i	−0.0672027	−	0.381125i	−0.999796	−	0.0201965i	$-0.993571\pi$
$479$	−1.47080	−	8.34133i	−0.0672027	−	0.381125i	0.932593	−	0.360929i	$-0.117540\pi$
$480$		0			0
$481$	2.79435	−	1.01706i	0.127411	−	0.0463739i
$482$	56.9470	+	47.7842i	2.59386	+	2.17651i
$483$		0			0
$484$	27.0298	+	9.83803i	1.22863	+	0.447183i
$485$	−21.5663	−	37.3539i	−0.979273	−	1.69615i
$486$		0			0
$487$	0.130959	−	0.226827i	0.00593430	−	0.0102785i	−0.863043	−	0.505130i	$-0.831444\pi$
$487$	0.130959	−	0.226827i	0.00593430	−	0.0102785i	0.868977	+	0.494852i	$0.164778\pi$
$488$	−1.31210	−	7.44128i	−0.0593959	−	0.336851i
$489$		0			0
$490$	46.1062	+	30.3607i	2.08286	+	1.37156i
$491$	−0.966808	+	5.48304i	−0.0436314	+	0.247446i	−0.998821	−	0.0485493i	$-0.984540\pi$
$491$	−0.966808	+	5.48304i	−0.0436314	+	0.247446i	0.955189	+	0.295995i	$0.0956513\pi$
$492$		0			0
$493$	−0.463276	−	2.62737i	−0.0208649	−	0.118331i
$494$	4.79288			0.215642
$495$		0			0
$496$	−23.9015	+	41.3987i	−1.07321	+	1.85886i
$497$	3.76614	+	1.12863i	0.168934	+	0.0506261i
$498$		0			0
$499$	25.5742	+	21.4593i	1.14486	+	0.960649i	0.999587	−	0.0287425i	$-0.00915027\pi$
$499$	25.5742	+	21.4593i	1.14486	+	0.960649i	0.145271	+	0.989392i	$0.453595\pi$
$500$	−3.76527	+	21.3539i	−0.168388	+	0.954975i
$501$		0			0
$502$	12.3921	−	10.3982i	0.553086	−	0.464094i
$503$	−0.241460	+	0.418221i	−0.0107662	+	0.0186475i	−0.871358	−	0.490647i	$-0.836760\pi$
$503$	−0.241460	+	0.418221i	−0.0107662	+	0.0186475i	0.860592	+	0.509295i	$0.170094\pi$
$504$		0			0
$505$	12.5257	+	21.6951i	0.557385	+	0.965419i
$506$	39.2096	+	14.2711i	1.74308	+	0.634429i
$507$		0			0
$508$	48.7757	+	40.9277i	2.16407	+	1.81587i
$509$	4.08937	−	23.1920i	0.181258	−	1.02797i	−0.749412	−	0.662104i	$-0.769664\pi$
$509$	4.08937	−	23.1920i	0.181258	−	1.02797i	0.930670	−	0.365861i	$-0.119225\pi$
$510$		0			0
$511$	6.07584	+	25.6674i	0.268779	+	1.13546i
$512$	0.880867			0.0389292
$513$		0			0
$514$	−4.48731	+	7.77225i	−0.197927	+	0.342819i
$515$	19.0765	−	16.0071i	0.840611	−	0.705356i
$516$		0			0
$517$	0.448753	+	0.376549i	0.0197362	+	0.0165606i
$518$	−10.8488	+	4.67619i	−0.476669	+	0.205460i
$519$		0			0
$520$	−43.0540	−	15.6704i	−1.88804	−	0.687191i
$521$	12.4066			0.543544			0.271772	−	0.962362i	$-0.412390\pi$
$521$	12.4066			0.543544			0.271772	+	0.962362i	$0.412390\pi$
$522$		0			0
$523$	16.0858			0.703383			0.351692	−	0.936116i	$-0.385607\pi$
$523$	16.0858			0.703383			0.351692	+	0.936116i	$0.385607\pi$
$524$	12.5689	+	71.2817i	0.549074	+	3.11395i
$525$		0			0
$526$	−31.2269	+	11.3657i	−1.36156	+	0.495566i
$527$	−1.04390	−	0.875937i	−0.0454730	−	0.0381564i
$528$		0			0
$529$	−19.3717	−	7.05071i	−0.842247	−	0.306553i
$530$	−64.9267			−2.82023
$531$		0			0
$532$	−13.7591	+	0.797592i	−0.596534	+	0.0345800i
$533$	13.0038	−	10.9115i	0.563258	−	0.472629i
$534$		0			0
$535$	−35.6781	−	29.9375i	−1.54250	−	1.29431i
$536$	−17.5272	+	6.37939i	−0.757061	+	0.275548i
$537$		0			0
$538$	6.80814	+	2.47796i	0.293520	+	0.106832i
$539$	−16.3248	+	1.89902i	−0.703160	+	0.0817967i
$540$		0			0
$541$	−13.1928	−	22.8506i	−0.567204	−	0.982425i	−0.996841	−	0.0794239i	$-0.974692\pi$
$541$	−13.1928	−	22.8506i	−0.567204	−	0.982425i	0.429637	−	0.903002i	$-0.358641\pi$
$542$	−45.3701	+	38.0700i	−1.94881	+	1.63525i
$543$		0			0
$544$	−1.12642	+	6.38826i	−0.0482950	+	0.273894i
$545$	−2.47447	+	14.0334i	−0.105995	+	0.601127i
$546$		0			0
$547$	28.9358	−	24.2800i	1.23721	−	1.03814i	0.239469	−	0.970904i	$-0.423027\pi$
$547$	28.9358	−	24.2800i	1.23721	−	1.03814i	0.997737	−	0.0672347i	$-0.0214176\pi$
$548$	30.1371	−	52.1991i	1.28740	−	2.22983i
$549$		0			0
$550$	11.3362	+	19.6348i	0.483376	+	0.837231i
$551$	5.48400	−	4.60163i	0.233626	−	0.196036i
$552$		0			0
$553$	22.4504	−	9.67687i	0.954690	−	0.411502i
$554$	−24.7180	+	8.99660i	−1.05017	+	0.382229i
$555$		0			0
$556$	48.1519	+	17.5259i	2.04210	+	0.743262i
$557$	5.24806	+	9.08990i	0.222367	+	0.385151i	0.955526	−	0.294906i	$-0.0952883\pi$
$557$	5.24806	+	9.08990i	0.222367	+	0.385151i	−0.733159	+	0.680057i	$0.761955\pi$
$558$		0			0
$559$	7.03656	+	12.1877i	0.297615	+	0.515484i
$560$	96.4954	+	28.9177i	4.07768	+	1.22199i
$561$		0			0
$562$	17.8668	−	6.50299i	0.753667	−	0.274312i
$563$	−4.98131	+	1.81305i	−0.209937	+	0.0764108i	−0.444848	−	0.895606i	$-0.646742\pi$
$563$	−4.98131	+	1.81305i	−0.209937	+	0.0764108i	0.234911	+	0.972017i	$0.424520\pi$
$564$		0			0
$565$	−4.64809	−	26.3606i	−0.195547	−	1.10900i
$566$	−24.6133			−1.03457
$567$		0			0
$568$	12.9633			0.543927
$569$	1.65775	+	9.40156i	0.0694965	+	0.394134i	0.999637	+	0.0269311i	$0.00857346\pi$
$569$	1.65775	+	9.40156i	0.0694965	+	0.394134i	−0.930141	+	0.367203i	$0.880315\pi$
$570$		0			0
$571$	26.6672	−	9.70606i	1.11599	−	0.406186i	0.282801	−	0.959179i	$-0.408737\pi$
$571$	26.6672	−	9.70606i	1.11599	−	0.406186i	0.833186	+	0.552993i	$0.186514\pi$
$572$	20.7255	−	7.54346i	0.866576	−	0.315408i
$573$		0			0
$574$	−49.0657	+	46.2656i	−2.04796	+	1.93109i
$575$	−11.8493	−	20.5237i	−0.494152	−	0.855896i
$576$		0			0
$577$	−14.9454	−	25.8862i	−0.622186	−	1.07766i	−0.989078	−	0.147394i	$-0.952912\pi$
$577$	−14.9454	−	25.8862i	−0.622186	−	1.07766i	0.366892	−	0.930263i	$-0.380422\pi$
$578$	42.6419	+	15.5204i	1.77367	+	0.645563i
$579$		0			0
$580$	−103.983	+	37.8465i	−4.31764	+	1.57149i
$581$	2.06529	−	17.6277i	0.0856825	−	0.731322i
$582$		0			0
$583$	14.8071	−	12.4246i	0.613246	−	0.514574i
$584$	43.4844	+	75.3171i	1.79940	+	3.11665i
$585$		0			0
$586$	−26.6819	+	46.2143i	−1.10222	+	1.90910i
$587$	−23.2180	+	19.4822i	−0.958308	+	0.804116i	−0.980677	−	0.195634i	$-0.937324\pi$
$587$	−23.2180	+	19.4822i	−0.958308	+	0.804116i	0.0223688	+	0.999750i	$0.492879\pi$
$588$		0			0
$589$	0.634965	−	3.60106i	0.0261633	−	0.148379i
$590$	−6.96091	+	39.4773i	−0.286576	+	1.62525i
$591$		0			0
$592$	−16.5137	+	13.8567i	−0.678711	+	0.569506i
$593$	6.88951	+	11.9330i	0.282918	+	0.490029i	0.972102	−	0.234558i	$-0.0753641\pi$
$593$	6.88951	+	11.9330i	0.282918	+	0.490029i	−0.689184	+	0.724586i	$0.742031\pi$
$594$		0			0
$595$	−1.28950	+	2.56584i	−0.0528642	+	0.105189i
$596$	−9.17921	−	3.34096i	−0.375995	−	0.136851i
$597$		0			0
$598$	−29.9296	+	10.8935i	−1.22391	+	0.445468i
$599$	−5.52167	−	4.63323i	−0.225609	−	0.189309i	0.522975	−	0.852348i	$-0.324822\pi$
$599$	−5.52167	−	4.63323i	−0.225609	−	0.189309i	−0.748585	+	0.663039i	$0.769266\pi$
$600$		0			0
$601$	−34.2145	+	28.7093i	−1.39564	+	1.17108i	−0.432640	+	0.901567i	$0.642418\pi$
$601$	−34.2145	+	28.7093i	−1.39564	+	1.17108i	−0.962997	+	0.269512i	$0.913138\pi$
$602$	−30.7097	−	46.7197i	−1.25163	−	1.90415i
$603$		0			0
$604$	86.4337			3.51694
$605$	15.1122	+	5.50039i	0.614399	+	0.223623i
$606$		0			0
$607$	−10.1602	−	8.52543i	−0.412390	−	0.346037i	0.412869	−	0.910790i	$-0.364527\pi$
$607$	−10.1602	−	8.52543i	−0.412390	−	0.346037i	−0.825259	+	0.564754i	$0.808971\pi$
$608$	−16.3565	+	5.95329i	−0.663344	+	0.241438i
$609$		0			0
$610$	−1.18618	−	6.72718i	−0.0480271	−	0.272375i
$611$	−0.447160			−0.0180901
$612$		0			0
$613$	−19.4812			−0.786839			−0.393420	−	0.919359i	$-0.628708\pi$
$613$	−19.4812			−0.786839			−0.393420	+	0.919359i	$0.628708\pi$
$614$	−64.7958	−	23.5838i	−2.61495	−	0.951763i
$615$		0			0
$616$	−49.7630	+	21.4495i	−2.00501	+	0.864224i
$617$	26.8526	+	22.5320i	1.08105	+	0.907105i	0.996007	−	0.0892726i	$-0.0284542\pi$
$617$	26.8526	+	22.5320i	1.08105	+	0.907105i	0.0850385	+	0.996378i	$0.472899\pi$
$618$		0			0
$619$	33.0617	−	27.7420i	1.32886	−	1.11505i	0.344519	−	0.938779i	$-0.388042\pi$
$619$	33.0617	−	27.7420i	1.32886	−	1.11505i	0.984342	−	0.176267i	$-0.0564024\pi$
$620$	−28.2605	+	48.9486i	−1.13497	+	1.96582i
$621$		0			0
$622$	87.1565			3.49466
$623$	32.4270	+	9.71769i	1.29916	+	0.389331i
$624$		0			0
$625$	−5.22078	+	29.6085i	−0.208831	+	1.18434i
$626$	−4.06570	−	3.41153i	−0.162498	−	0.136352i
$627$		0			0
$628$	6.29864	+	2.29252i	0.251343	+	0.0914814i
$629$	−0.307263	−	0.532196i	−0.0122514	−	0.0212200i
$630$		0			0
$631$	−20.3466	+	35.2413i	−0.809984	+	1.40293i	0.102890	+	0.994693i	$0.467191\pi$
$631$	−20.3466	+	35.2413i	−0.809984	+	1.40293i	−0.912874	+	0.408241i	$0.866142\pi$
$632$	61.7484	−	51.8131i	2.45622	−	2.06101i
$633$		0			0
$634$	1.09111	−	6.18802i	0.0433337	−	0.245758i
$635$	27.2702	+	22.8825i	1.08219	+	0.908063i
$636$		0			0
$637$	8.61401	−	9.12029i	0.341300	−	0.361359i
$638$	22.7565	−	39.4154i	0.900937	−	1.56047i
$639$		0			0
$640$	64.1325			2.53506
$641$	−5.24855	−	29.7660i	−0.207305	−	1.17569i	−0.893771	−	0.448524i	$-0.851950\pi$
$641$	−5.24855	−	29.7660i	−0.207305	−	1.17569i	0.686466	−	0.727162i	$-0.259161\pi$
$642$		0			0
$643$	−2.81411	+	15.9596i	−0.110978	+	0.629387i	0.877685	+	0.479237i	$0.159087\pi$
$643$	−2.81411	+	15.9596i	−0.110978	+	0.629387i	−0.988663	+	0.150150i	$0.952024\pi$
$644$	84.1075	−	36.2531i	3.31430	−	1.42857i
$645$		0			0
$646$	−0.171994	−	0.975426i	−0.00676701	−	0.0383776i
$647$	−3.51357	+	6.08568i	−0.138133	+	0.239253i	−0.926790	−	0.375581i	$-0.877443\pi$
$647$	−3.51357	+	6.08568i	−0.138133	+	0.239253i	0.788657	+	0.614833i	$0.210777\pi$
$648$		0			0
$649$	−5.96702	−	10.3352i	−0.234226	−	0.405692i
$650$	−16.2626	−	5.91911i	−0.637873	−	0.232167i
$651$		0			0
$652$	−6.62361	−	5.55787i	−0.259401	−	0.217663i
$653$	14.4000	−	5.24117i	0.563515	−	0.205103i	−0.0445260	−	0.999008i	$-0.514178\pi$
$653$	14.4000	−	5.24117i	0.563515	−	0.205103i	0.608041	+	0.793905i	$0.291956\pi$
$654$		0			0
$655$	7.02720	+	39.8532i	0.274575	+	1.55719i
$656$	−61.5296	+	106.572i	−2.40233	+	4.16095i
$657$		0			0
$658$	1.77348	−	0.102805i	0.0691373	−	0.00400777i
$659$	0.359040	+	2.03622i	0.0139862	+	0.0793198i	0.991002	−	0.133847i	$-0.0427332\pi$
$659$	0.359040	+	2.03622i	0.0139862	+	0.0793198i	−0.977016	+	0.213167i	$0.931622\pi$
$660$		0			0
$661$	0.870163	−	4.93494i	0.0338454	−	0.191947i	−0.963197	−	0.268795i	$-0.913375\pi$
$661$	0.870163	−	4.93494i	0.0338454	−	0.191947i	0.997043	+	0.0768482i	$0.0244857\pi$
$662$	−2.86881	+	16.2698i	−0.111500	+	0.632346i
$663$		0			0
$664$	−10.1618	−	57.6304i	−0.394354	−	2.23649i
$665$	−7.69266	+	0.445930i	−0.298308	+	0.0172924i
$666$		0			0
$667$	−23.7866	+	41.1997i	−0.921022	+	1.59526i
$668$	−13.5928	−	77.0887i	−0.525922	−	2.98265i
$669$		0			0
$670$	−15.8452	+	5.76719i	−0.612155	+	0.222806i
$671$	1.55786	+	1.30720i	0.0601403	+	0.0504637i
$672$		0			0
$673$	−31.9524	−	11.6297i	−1.23168	−	0.448293i	−0.357504	−	0.933911i	$-0.616372\pi$
$673$	−31.9524	−	11.6297i	−1.23168	−	0.448293i	−0.874171	+	0.485618i	$0.838595\pi$
$674$	−26.6746	−	46.2018i	−1.02747	−	1.77963i
$675$		0			0
$676$	25.6532	−	44.4327i	0.986663	−	1.70895i
$677$	−5.99400	−	33.9936i	−0.230368	−	1.30648i	−0.852153	−	0.523293i	$-0.824703\pi$
$677$	−5.99400	−	33.9936i	−0.230368	−	1.30648i	0.621785	−	0.783188i	$-0.286408\pi$
$678$		0			0
$679$	35.7596	−	15.4136i	1.37233	−	0.591518i
$680$	−1.64416	+	9.32450i	−0.0630507	+	0.357578i
$681$		0			0
$682$	−4.03683	−	22.8940i	−0.154578	−	0.876657i
$683$	−40.3067			−1.54229			−0.771147	−	0.636657i	$-0.780317\pi$
$683$	−40.3067			−1.54229			−0.771147	+	0.636657i	$0.780317\pi$
$684$		0			0
$685$	16.8495	−	29.1842i	0.643787	−	1.11507i
$686$	−32.0671	+	38.1523i	−1.22433	+	1.45666i
$687$		0			0
$688$	−78.1522	−	65.5775i	−2.97953	−	2.50012i
$689$	−2.56209	+	14.5303i	−0.0976078	+	0.553561i
$690$		0			0
$691$	−0.421451	+	0.353639i	−0.0160327	+	0.0134531i	−0.650769	−	0.759276i	$-0.725553\pi$
$691$	−0.421451	+	0.353639i	−0.0160327	+	0.0134531i	0.634736	+	0.772729i	$0.281109\pi$
$692$	−20.0936	+	34.8031i	−0.763844	+	1.32302i
$693$		0			0
$694$	−27.4892	−	47.6126i	−1.04347	−	1.80735i
$695$	26.9215	+	9.79862i	1.02119	+	0.371683i
$696$		0			0
$697$	−2.68730	−	2.25492i	−0.101789	−	0.0854110i
$698$	−16.8056	+	95.3091i	−0.636100	+	3.60750i
$699$		0			0
$700$	47.6708	+	14.2860i	1.80179	+	0.539958i
$701$	−27.6199			−1.04319			−0.521594	−	0.853194i	$-0.674662\pi$
$701$	−27.6199			−1.04319			−0.521594	+	0.853194i	$0.674662\pi$
$702$		0			0
$703$	0.824489	−	1.42806i	0.0310962	−	0.0538602i
$704$	−38.0380	+	31.9177i	−1.43361	+	1.20294i
$705$		0			0
$706$	−5.98093	−	5.01860i	−0.225095	−	0.188877i
$707$	−20.7692	+	8.95219i	−0.781105	+	0.336682i
$708$		0			0
$709$	−30.1781	−	10.9839i	−1.13336	−	0.412511i	−0.293852	−	0.955851i	$-0.594937\pi$
$709$	−30.1781	−	10.9839i	−1.13336	−	0.412511i	−0.839513	+	0.543340i	$0.817159\pi$
$710$	11.7192			0.439816
$711$		0			0
$712$	111.615			4.18297
$713$	4.21957	+	23.9304i	0.158024	+	0.896200i
$714$		0			0
$715$	11.5875	−	4.21751i	0.433349	−	0.157726i
$716$	−91.6457	−	76.8999i	−3.42496	−	2.87388i
$717$		0			0
$718$	−28.5434	−	10.3889i	−1.06523	−	0.387712i
$719$	15.6211			0.582570			0.291285	−	0.956636i	$-0.405917\pi$
$719$	15.6211			0.582570			0.291285	+	0.956636i	$0.405917\pi$
$720$		0			0
$721$	12.3489	+	18.7869i	0.459899	+	0.699660i
$722$	−37.1317	+	31.1572i	−1.38190	+	1.15955i
$723$		0			0
$724$	49.0046	+	41.1197i	1.82124	+	1.52820i
$725$	−24.2906	+	8.84105i	−0.902130	+	0.328348i
$726$		0			0
$727$	−11.7457	−	4.27508i	−0.435623	−	0.158554i	0.114894	−	0.993378i	$-0.463347\pi$
$727$	−11.7457	−	4.27508i	−0.435623	−	0.158554i	−0.550517	+	0.834824i	$0.685569\pi$
$728$	18.5741	−	36.9589i	0.688403	−	1.36979i
$729$		0			0
$730$	39.3114	+	68.0893i	1.45498	+	2.52010i
$731$	2.22787	−	1.86941i	0.0824009	−	0.0691426i
$732$		0			0
$733$	−6.38353	+	36.2028i	−0.235781	+	1.33718i	0.605182	+	0.796087i	$0.293100\pi$
$733$	−6.38353	+	36.2028i	−0.235781	+	1.33718i	−0.840963	+	0.541093i	$0.818011\pi$
$734$	11.9310	−	67.6640i	0.440381	−	2.49753i
$735$		0			0
$736$	88.6091	−	74.3518i	3.26617	−	2.74064i
$737$	2.51001	−	4.34746i	0.0924572	−	0.160141i
$738$		0			0
$739$	−15.6210	−	27.0564i	−0.574628	−	0.995286i	−0.996082	−	0.0884356i	$-0.971813\pi$
$739$	−15.6210	−	27.0564i	−0.574628	−	0.995286i	0.421454	−	0.906850i	$-0.361520\pi$
$740$	−19.5254	+	16.3837i	−0.717767	+	0.602278i
$741$		0			0
$742$	6.82085	−	58.2176i	0.250401	−	2.13724i
$743$	9.31561	−	3.39060i	0.341757	−	0.124389i	−0.165439	−	0.986220i	$-0.552904\pi$
$743$	9.31561	−	3.39060i	0.341757	−	0.124389i	0.507196	+	0.861831i	$0.330682\pi$
$744$		0			0
$745$	−5.13205	−	1.86791i	−0.188024	−	0.0684351i
$746$	36.9314	+	63.9671i	1.35216	+	2.34200i
$747$		0			0
$748$	−2.27895	−	3.94726i	−0.0833268	−	0.144326i
$749$	30.5921	−	28.8463i	1.11781	−	1.05402i
$750$		0			0
$751$	−9.33186	+	3.39652i	−0.340524	+	0.123941i	−0.506621	−	0.862169i	$-0.669106\pi$
$751$	−9.33186	+	3.39652i	−0.340524	+	0.123941i	0.166097	+	0.986109i	$0.446884\pi$
$752$	3.04611	−	1.10869i	0.111080	−	0.0404299i
$753$		0			0
$754$	6.03273	+	34.2133i	0.219699	+	1.24598i
$755$	48.3247			1.75871
$756$		0			0
$757$	−27.0978			−0.984888			−0.492444	−	0.870344i	$-0.663896\pi$
$757$	−27.0978			−0.984888			−0.492444	+	0.870344i	$0.663896\pi$
$758$	5.99001	+	33.9711i	0.217567	+	1.23388i
$759$		0			0
$760$	−23.8745	+	8.68960i	−0.866018	+	0.315205i
$761$	−37.5494	+	13.6669i	−1.36117	+	0.495424i	−0.916415	−	0.400230i	$-0.868930\pi$
$761$	−37.5494	+	13.6669i	−1.36117	+	0.495424i	−0.444751	+	0.895654i	$0.646708\pi$
$762$		0			0
$763$	−12.3234	−	3.69306i	−0.446136	−	0.133698i
$764$	−19.0287	−	32.9587i	−0.688436	−	1.19241i
$765$		0			0
$766$	25.5115	+	44.1873i	0.921769	+	1.59655i
$767$	8.56017	+	3.11565i	0.309090	+	0.112499i
$768$		0			0
$769$	0.304754	−	0.110921i	0.0109897	−	0.00399993i	−0.336519	−	0.941677i	$-0.609250\pi$
$769$	0.304754	−	0.110921i	0.0109897	−	0.00399993i	0.347509	+	0.937677i	$0.387028\pi$
$770$	−44.9875	+	19.3911i	−1.62124	+	0.698806i
$771$		0			0
$772$	−98.4000	+	82.5674i	−3.54149	+	2.97167i
$773$	2.50904	+	4.34578i	0.0902439	+	0.156307i	0.907614	−	0.419806i	$-0.137902\pi$
$773$	2.50904	+	4.34578i	0.0902439	+	0.156307i	−0.817370	+	0.576113i	$0.804569\pi$
$774$		0			0
$775$	−6.60173	+	11.4345i	−0.237141	+	0.410740i
$776$	98.3543	−	82.5291i	3.53072	−	2.96262i
$777$		0			0
$778$	9.24421	−	52.4265i	0.331421	−	1.87958i
$779$	1.63458	−	9.27019i	0.0585650	−	0.332139i
$780$		0			0
$781$	−2.67267	+	2.24264i	−0.0956357	+	0.0802479i
$782$	3.29103	+	5.70023i	0.117687	+	0.203840i
$783$		0			0
$784$	−36.0668	+	83.4863i	−1.28810	+	2.98165i
$785$	3.52154	+	1.28173i	0.125689	+	0.0457471i
$786$		0			0
$787$	1.94701	−	0.708653i	0.0694033	−	0.0252607i	−0.307085	−	0.951682i	$-0.599354\pi$
$787$	1.94701	−	0.708653i	0.0694033	−	0.0252607i	0.376489	+	0.926421i	$0.377131\pi$
$788$	1.16956	+	0.981377i	0.0416638	+	0.0349601i
$789$		0			0
$790$	55.8227	−	46.8408i	1.98608	−	1.66652i
$791$	24.1250	−	1.39848i	0.857786	−	0.0497243i
$792$		0			0
$793$	−1.55232			−0.0551246
$794$	16.2633	+	5.91937i	0.577164	+	0.210071i
$795$		0			0
$796$	4.67248	+	3.92068i	0.165612	+	0.138965i
$797$	40.0366	−	14.5721i	1.41817	−	0.516172i	0.484653	−	0.874706i	$-0.338946\pi$
$797$	40.0366	−	14.5721i	1.41817	−	0.516172i	0.933516	+	0.358535i	$0.116724\pi$
$798$		0			0
$799$	0.0160465	+	0.0910040i	0.000567683	+	0.00321949i
$800$	62.8512			2.22213
$801$		0			0
$802$	45.5921			1.60991
$803$	−21.9951	−	8.00556i	−0.776190	−	0.282510i
$804$		0			0
$805$	47.0241	−	20.2689i	1.65738	−	0.714385i
$806$	13.5936	+	11.4063i	0.478812	+	0.401771i
$807$		0			0
$808$	−57.1242	+	47.9329i	−2.00962	+	1.68627i
$809$	17.2737	−	29.9189i	0.607310	−	1.05189i	−0.384371	−	0.923179i	$-0.625582\pi$
$809$	17.2737	−	29.9189i	0.607310	−	1.05189i	0.991682	−	0.128714i	$-0.0410849\pi$
$810$		0			0
$811$	−48.7022			−1.71017			−0.855083	−	0.518491i	$-0.826494\pi$
$811$	−48.7022			−1.71017			−0.855083	+	0.518491i	$0.826494\pi$
$812$	−23.0119	−	97.2137i	−0.807560	−	3.41153i
$813$		0			0
$814$	1.82044	−	10.3242i	0.0638063	−	0.361864i
$815$	−3.70323	−	3.10738i	−0.129718	−	0.108847i
$816$		0			0
$817$	7.33325	+	2.66908i	0.256558	+	0.0933795i
$818$	−28.9940	−	50.2191i	−1.01375	−	1.75587i
$819$		0			0
$820$	−72.7508	+	126.008i	−2.54057	+	4.40039i
$821$	1.86144	−	1.56193i	0.0649647	−	0.0545118i	−0.609727	−	0.792611i	$-0.708721\pi$
$821$	1.86144	−	1.56193i	0.0649647	−	0.0545118i	0.674692	+	0.738100i	$0.264277\pi$
$822$		0			0
$823$	−2.47662	+	14.0456i	−0.0863297	+	0.489600i	0.910732	+	0.412998i	$0.135518\pi$
$823$	−2.47662	+	14.0456i	−0.0863297	+	0.489600i	−0.997062	+	0.0766022i	$0.975593\pi$
$824$	56.7850	+	47.6482i	1.97820	+	1.65990i
$825$		0			0
$826$	−34.6667	−	10.3889i	−1.20621	−	0.361476i
$827$	20.4016	−	35.3366i	0.709433	−	1.22877i	−0.255634	−	0.966774i	$-0.582284\pi$
$827$	20.4016	−	35.3366i	0.709433	−	1.22877i	0.965068	−	0.262001i	$-0.0843824\pi$
$828$		0			0
$829$	51.3055			1.78191			0.890957	−	0.454088i	$-0.150035\pi$
$829$	51.3055			1.78191			0.890957	+	0.454088i	$0.150035\pi$
$830$	−9.18662	−	52.0999i	−0.318872	−	1.80841i
$831$		0			0
$832$	6.58177	−	37.3271i	0.228182	−	1.29408i
$833$	−2.16524	−	1.42580i	−0.0750211	−	0.0494011i
$834$		0			0
$835$	−7.59968	−	43.0999i	−0.262998	−	1.49153i
$836$	6.11518	−	10.5918i	0.211498	−	0.366325i
$837$		0			0
$838$	−17.5271	−	30.3579i	−0.605465	−	1.04870i
$839$	−52.5210	−	19.1161i	−1.81323	−	0.659960i	−0.996562	−	0.0828447i	$-0.973599\pi$
$839$	−52.5210	−	19.1161i	−1.81323	−	0.659960i	−0.816663	−	0.577115i	$-0.804178\pi$
$840$		0			0
$841$	17.5354	+	14.7140i	0.604670	+	0.507378i
$842$	47.2747	−	17.2066i	1.62919	−	0.592978i
$843$		0			0
$844$	2.60747	+	14.7877i	0.0897529	+	0.509014i
$845$	14.3426	−	24.8421i	0.493400	−	0.854594i
$846$		0			0
$847$	−6.51963	+	12.9728i	−0.224017	+	0.445750i
$848$	−18.5734	−	105.335i	−0.637813	−	3.61722i
$849$		0			0
$850$	−0.621043	+	3.52211i	−0.0213016	+	0.120807i
$851$	−1.90285	+	10.7916i	−0.0652288	+	0.369931i
$852$		0			0
$853$	−7.21789	−	40.9347i	−0.247136	−	1.40158i	−0.815479	−	0.578786i	$-0.803527\pi$
$853$	−7.21789	−	40.9347i	−0.247136	−	1.40158i	0.568344	−	0.822791i	$-0.307584\pi$
$854$	6.15665	−	0.356890i	0.210676	−	0.0122125i
$855$		0			0
$856$	69.3191	−	120.064i	2.36928	−	4.10371i
$857$	−1.06702	−	6.05135i	−0.0364486	−	0.206710i	0.961145	−	0.276044i	$-0.0890236\pi$
$857$	−1.06702	−	6.05135i	−0.0364486	−	0.206710i	−0.997593	+	0.0693342i	$0.977913\pi$
$858$		0			0
$859$	37.2854	−	13.5708i	1.27216	−	0.463029i	0.384329	−	0.923196i	$-0.374433\pi$
$859$	37.2854	−	13.5708i	1.27216	−	0.463029i	0.887832	+	0.460168i	$0.152211\pi$
$860$	−92.4050	−	77.5370i	−3.15098	−	2.64399i
$861$		0			0
$862$	−2.92777	−	1.06562i	−0.0997203	−	0.0362952i
$863$	22.1063	+	38.2892i	0.752506	+	1.30338i	0.946605	+	0.322396i	$0.104488\pi$
$863$	22.1063	+	38.2892i	0.752506	+	1.30338i	−0.194099	+	0.980982i	$0.562178\pi$
$864$		0			0
$865$	−11.2342	+	19.4583i	−0.381975	+	0.661601i
$866$	7.90546	+	44.8341i	0.268639	+	1.52352i
$867$		0			0
$868$	−40.9217	−	30.4825i	−1.38897	−	1.03464i
$869$	−3.76720	+	21.3649i	−0.127794	+	0.724753i
$870$		0			0
$871$	0.665401	+	3.77368i	0.0225463	+	0.127866i
$872$	−42.4178			−1.43645
$873$		0			0
$874$	−8.83092	+	15.2956i	−0.298710	+	0.517381i
$875$	−10.4840	−	3.14184i	−0.354425	−	0.106214i
$876$		0			0
$877$	21.6178	+	18.1395i	0.729983	+	0.612528i	0.930127	−	0.367238i	$-0.119697\pi$
$877$	21.6178	+	18.1395i	0.729983	+	0.612528i	−0.200144	+	0.979766i	$0.564141\pi$
$878$	7.36895	−	41.7914i	0.248690	−	1.41039i
$879$		0			0
$880$	−68.4787	+	57.4605i	−2.30842	+	1.93699i
$881$	−22.6545	+	39.2387i	−0.763249	+	1.32199i	0.177918	+	0.984045i	$0.443064\pi$
$881$	−22.6545	+	39.2387i	−0.763249	+	1.32199i	−0.941167	+	0.337941i	$0.890270\pi$
$882$		0			0
$883$	0.386625	+	0.669653i	0.0130110	+	0.0225356i	0.872458	−	0.488690i	$-0.162525\pi$
$883$	0.386625	+	0.669653i	0.0130110	+	0.0225356i	−0.859447	+	0.511225i	$0.829192\pi$
$884$	3.26934	+	1.18994i	0.109960	+	0.0400221i
$885$		0			0
$886$	−81.7297	−	68.5794i	−2.74576	−	2.30397i
$887$	6.70778	−	38.0417i	0.225225	−	1.27732i	−0.637029	−	0.770840i	$-0.719837\pi$
$887$	6.70778	−	38.0417i	0.225225	−	1.27732i	0.862254	−	0.506476i	$-0.169052\pi$
$888$		0			0
$889$	−23.3828	+	22.0484i	−0.784234	+	0.739480i
$890$	100.904			3.38232
$891$		0			0
$892$	3.99968	−	6.92765i	0.133919	−	0.231955i
$893$	−0.189949	+	0.159386i	−0.00635640	+	0.00533365i
$894$		0			0
$895$	−51.2387	−	42.9944i	−1.71272	−	1.43714i
$896$	−6.73742	+	57.5055i	−0.225081	+	1.92112i
$897$		0			0
$898$	86.8451	+	31.6090i	2.89806	+	1.05481i
$899$	26.5049			0.883988
$900$		0			0
$901$	3.04909			0.101580
$902$	−10.3920	−	58.9358i	−0.346015	−	1.96235i
$903$		0			0
$904$	74.8729	−	27.2515i	2.49024	−	0.906372i
$905$	27.3982	+	22.9898i	0.910748	+	0.764208i
$906$		0			0
$907$	16.5824	+	6.03548i	0.550608	+	0.200405i	0.602317	−	0.798257i	$-0.294244\pi$
$907$	16.5824	+	6.03548i	0.550608	+	0.200405i	−0.0517085	+	0.998662i	$0.516467\pi$
$908$	90.5315			3.00439
$909$		0			0
$910$	16.7917	−	33.4121i	0.556638	−	1.10760i
$911$	−31.9509	+	26.8100i	−1.05858	+	0.888254i	−0.993969	−	0.109657i	$-0.965025\pi$
$911$	−31.9509	+	26.8100i	−1.05858	+	0.888254i	−0.0646099	+	0.997911i	$0.520580\pi$
$912$		0			0
$913$	12.0651	+	10.1238i	0.399297	+	0.335050i
$914$	91.9192	−	33.4558i	3.04042	−	1.10662i
$915$		0			0
$916$	44.3474	+	16.1411i	1.46528	+	0.533318i
$917$	−36.4733	+	2.11429i	−1.20445	+	0.0698201i
$918$		0			0
$919$	3.81069	+	6.60032i	0.125703	+	0.217724i	0.922008	−	0.387172i	$-0.126548\pi$
$919$	3.81069	+	6.60032i	0.125703	+	0.217724i	−0.796304	+	0.604896i	$0.793215\pi$
$920$	129.336	−	108.526i	4.26410	−	3.57800i
$921$		0			0
$922$	11.4715	−	65.0581i	0.377794	−	2.14257i
$923$	0.462456	−	2.62272i	0.0152219	−	0.0863278i
$924$		0			0
$925$	−4.56118	+	3.82728i	−0.149971	+	0.125840i
$926$	−13.1371	+	22.7542i	−0.431713	+	0.747749i
$927$		0			0
$928$	−63.0844	−	109.265i	−2.07085	−	3.58681i
$929$	−15.6723	+	13.1507i	−0.514193	+	0.431459i	−0.862602	−	0.505884i	$-0.831166\pi$
$929$	−15.6723	+	13.1507i	−0.514193	+	0.431459i	0.348409	+	0.937343i	$0.386722\pi$
$930$		0			0
$931$	0.408299	−	6.94460i	0.0133814	−	0.227600i
$932$	19.2728	−	7.01474i	0.631303	−	0.229775i
$933$		0			0
$934$	69.0888	+	25.1463i	2.26066	+	0.822811i
$935$	−1.27415	−	2.20689i	−0.0416692	−	0.0721732i
$936$		0			0
$937$	−6.66331	−	11.5412i	−0.217681	−	0.377034i	0.736418	−	0.676527i	$-0.236516\pi$
$937$	−6.66331	−	11.5412i	−0.217681	−	0.377034i	−0.954098	+	0.299493i	$0.903182\pi$
$938$	−3.50664	−	14.8138i	−0.114496	−	0.483687i
$939$		0			0
$940$	3.60163	−	1.31089i	0.117472	−	0.0427564i
$941$	−10.3944	+	3.78324i	−0.338846	+	0.123330i	−0.505838	−	0.862628i	$-0.668817\pi$
$941$	−10.3944	+	3.78324i	−0.338846	+	0.123330i	0.166992	+	0.985958i	$0.446595\pi$
$942$		0			0
$943$	10.8624	+	61.6038i	0.353729	+	2.00610i
$944$	−66.0380			−2.14935
$945$		0			0
$946$	49.6137			1.61308
$947$	5.46656	+	31.0024i	0.177639	+	1.00744i	0.935053	+	0.354508i	$0.115352\pi$
$947$	5.46656	+	31.0024i	0.177639	+	1.00744i	−0.757414	+	0.652935i	$0.773537\pi$
$948$		0			0
$949$	16.7894	−	6.11084i	0.545007	−	0.198366i
$950$	−9.01802	+	3.28229i	−0.292583	+	0.106492i
$951$		0			0
$952$	−8.18824	−	2.45385i	−0.265382	−	0.0795296i
$953$	5.46062	+	9.45807i	0.176887	+	0.306377i	0.940813	−	0.338927i	$-0.110064\pi$
$953$	5.46062	+	9.45807i	0.176887	+	0.306377i	−0.763926	+	0.645304i	$0.776731\pi$
$954$		0			0
$955$	−10.6389	−	18.4271i	−0.344266	−	0.596286i
$956$	59.9284	+	21.8122i	1.93822	+	0.705456i
$957$		0			0
$958$	21.4185	−	7.79571i	0.692002	−	0.251868i
$959$	24.3984	+	18.1744i	0.787866	+	0.586881i
$960$		0			0
$961$	−13.3765	+	11.2242i	−0.431500	+	0.362071i
$962$	4.00115	+	6.93019i	0.129002	+	0.223438i
$963$		0			0
$964$	−72.4000	+	125.400i	−2.33185	+	4.03888i
$965$	−55.0149	+	46.1630i	−1.77099	+	1.48604i
$966$		0			0
$967$	2.20487	−	12.5044i	0.0709038	−	0.402115i	−0.928614	−	0.371048i	$-0.878998\pi$
$967$	2.20487	−	12.5044i	0.0709038	−	0.402115i	0.999517	−	0.0310670i	$-0.00989051\pi$
$968$	−8.31280	+	47.1442i	−0.267183	+	1.51527i
$969$		0			0
$970$	88.9158	−	74.6092i	2.85491	−	2.39556i
$971$	−11.5558	−	20.0153i	−0.370844	−	0.642320i	0.618852	−	0.785508i	$-0.287598\pi$
$971$	−11.5558	−	20.0153i	−0.370844	−	0.642320i	−0.989696	+	0.143188i	$0.954265\pi$
$972$		0			0
$973$	−11.6143	+	23.1102i	−0.372338	+	0.740880i
$974$	0.662323	+	0.241066i	0.0212222	+	0.00772424i
$975$		0			0
$976$	10.5746	−	3.84885i	0.338485	−	0.123199i
$977$	−23.1076	−	19.3895i	−0.739276	−	0.620326i	0.193367	−	0.981126i	$-0.438059\pi$
$977$	−23.1076	−	19.3895i	−0.739276	−	0.620326i	−0.932643	+	0.360800i	$0.882504\pi$
$978$		0			0
$979$	−23.0121	+	19.3094i	−0.735469	+	0.617131i
$980$	−42.6444	+	98.7118i	−1.36222	+	3.15323i
$981$		0			0
$982$	−14.9827			−0.478117
$983$	−10.0260	−	3.64917i	−0.319780	−	0.116390i	0.177143	−	0.984185i	$-0.443315\pi$
$983$	−10.0260	−	3.64917i	−0.319780	−	0.116390i	−0.496923	+	0.867795i	$0.665537\pi$
$984$		0			0
$985$	0.653895	+	0.548683i	0.0208348	+	0.0174825i
$986$	6.74646	−	2.45551i	0.214851	−	0.0781994i
$987$		0			0
$988$	1.62113	+	9.19390i	0.0515751	+	0.292497i
$989$	−51.8597			−1.64904
$990$		0			0
$991$	44.8873			1.42589			0.712946	−	0.701219i	$-0.247361\pi$
$991$	44.8873			1.42589			0.712946	+	0.701219i	$0.247361\pi$
$992$	−60.5583	−	22.0414i	−1.92273	−	0.699815i
$993$		0			0
$994$	−1.23116	+	10.5083i	−0.0390500	+	0.333302i
$995$	2.61236	+	2.19203i	0.0828174	+	0.0694920i
$996$		0			0
$997$	−20.8299	+	17.4783i	−0.659688	+	0.553544i	−0.909993	−	0.414623i	$-0.863914\pi$
$997$	−20.8299	+	17.4783i	−0.659688	+	0.553544i	0.250305	+	0.968167i	$0.419469\pi$
$998$	−44.9198	+	77.8034i	−1.42191	+	2.46282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.u.a.550.22		132
3.2	odd	2		189.2.u.a.4.1	✓	132
7.2	even	3		567.2.w.a.226.22		132
21.2	odd	6		189.2.w.a.58.1	yes	132
27.7	even	9		567.2.w.a.424.22		132
27.20	odd	18		189.2.w.a.88.1	yes	132
189.128	odd	18		189.2.u.a.142.1	yes	132
189.142	even	9	inner	567.2.u.a.100.22		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.1	✓	132	3.2	odd	2
189.2.u.a.142.1	yes	132	189.128	odd	18
189.2.w.a.58.1	yes	132	21.2	odd	6
189.2.w.a.88.1	yes	132	27.20	odd	18
567.2.u.a.100.22		132	189.142	even	9	inner
567.2.u.a.550.22		132	1.1	even	1	trivial
567.2.w.a.226.22		132	7.2	even	3
567.2.w.a.424.22		132	27.7	even	9

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.467294 + 2.65016i) q^{2} +(-4.92558 + 1.79277i) q^{4} +(-2.75387 + 1.00233i) q^{5} +(-0.609446 - 2.57460i) q^{7} +(-4.36176 - 7.55480i) q^{8} +O(q^{10})\)	\(q+(0.467294 + 2.65016i) q^{2} +(-4.92558 + 1.79277i) q^{4} +(-2.75387 + 1.00233i) q^{5} +(-0.609446 - 2.57460i) q^{7} +(-4.36176 - 7.55480i) q^{8} +(-3.94319 - 6.82980i) q^{10} +(2.20625 + 0.803010i) q^{11} +(-1.68408 + 0.612957i) q^{13} +(6.53831 - 2.81822i) q^{14} +(9.95243 - 8.35108i) q^{16} +(0.185180 + 0.320741i) q^{17} +(-0.496899 + 0.860655i) q^{19} +(11.7675 - 9.87408i) q^{20} +(-1.09713 + 6.22215i) q^{22} +(1.14680 - 6.50383i) q^{23} +(2.74891 - 2.30661i) q^{25} +(-2.41139 - 4.17666i) q^{26} +(7.61753 + 11.5888i) q^{28} +(-6.76911 - 2.46375i) q^{29} +(-3.45754 + 1.25844i) q^{31} +(13.4172 + 11.2583i) q^{32} +(-0.763481 + 0.640637i) q^{34} +(4.25893 + 6.47925i) q^{35} -1.65927 q^{37} +(-2.51307 - 0.914682i) q^{38} +(19.5841 + 16.4330i) q^{40} +(-8.90071 + 3.23959i) q^{41} +(-1.36359 - 7.73328i) q^{43} -12.3067 q^{44} +17.7721 q^{46} +(0.234461 + 0.0853368i) q^{47} +(-6.25715 + 3.13816i) q^{49} +(7.39743 + 6.20718i) q^{50} +(7.19621 - 6.03834i) q^{52} +(4.11638 - 7.12978i) q^{53} -6.88060 q^{55} +(-16.7923 + 15.8341i) q^{56} +(3.36617 - 19.0905i) q^{58} +(-3.89379 - 3.26728i) q^{59} +(0.813935 + 0.296248i) q^{61} +(-4.95075 - 8.57495i) q^{62} +(-10.5746 + 18.3158i) q^{64} +(4.02336 - 3.37600i) q^{65} +(0.371283 - 2.10565i) q^{67} +(-1.48713 - 1.24785i) q^{68} +(-15.1809 + 14.3145i) q^{70} +(-0.743006 + 1.28692i) q^{71} -9.96945 q^{73} +(-0.775366 - 4.39732i) q^{74} +(0.904566 - 5.13005i) q^{76} +(0.722839 - 6.16961i) q^{77} +(1.60454 + 9.09978i) q^{79} +(-19.0372 + 32.9734i) q^{80} +(-12.7447 - 22.0744i) q^{82} +(6.30367 + 2.29435i) q^{83} +(-0.831449 - 0.697669i) q^{85} +(19.8572 - 7.22743i) q^{86} +(-3.55657 - 20.1703i) q^{88} +(-6.39738 + 11.0806i) q^{89} +(2.60448 + 3.96228i) q^{91} +(6.01118 + 34.0911i) q^{92} +(-0.116594 + 0.661236i) q^{94} +(0.505738 - 2.86819i) q^{95} +(2.55575 + 14.4944i) q^{97} +(-11.2406 - 15.1160i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 + 3 * q^10 + 15 * q^11 - 12 * q^13 + 30 * q^14 + 9 * q^16 - 27 * q^17 + 3 * q^19 + 18 * q^20 - 12 * q^22 + 36 * q^23 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 + 75 * q^32 - 18 * q^34 - 15 * q^35 - 6 * q^37 - 69 * q^38 + 51 * q^40 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 21 * q^47 - 42 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 111 * q^56 - 3 * q^58 - 27 * q^59 - 21 * q^61 - 75 * q^62 - 30 * q^64 + 90 * q^65 - 3 * q^67 + 30 * q^68 + 39 * q^70 + 18 * q^71 - 42 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 + 93 * q^86 - 51 * q^88 - 75 * q^89 - 21 * q^91 + 66 * q^92 + 33 * q^94 - 15 * q^95 - 12 * q^97 + 36 * q^98

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