LMFDB - Embedded newform 504.2.cj.c.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.6
Root			$-0.390636 + 1.35919i$ of defining polynomial
Character	$\chi$	$=$	504.109
Dual form			504.2.cj.c.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40955 - 0.114773i) q^{2} +(1.97365 - 0.323556i) q^{4} +(-2.80486 + 1.61939i) q^{5} +(1.47779 + 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +O(q^{10})$	\(q+(1.40955 - 0.114773i) q^{2} +(1.97365 - 0.323556i) q^{4} +(-2.80486 + 1.61939i) q^{5} +(1.47779 + 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +(-3.76772 + 2.60453i) q^{10} +(2.08913 + 1.20616i) q^{11} +3.09491i q^{13} +(2.33490 + 2.92374i) q^{14} +(3.79062 - 1.27718i) q^{16} +(1.97779 - 3.42563i) q^{17} +(-2.33831 + 1.35002i) q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +(1.37241 + 2.37709i) q^{23} +(2.74483 - 4.75418i) q^{25} +(0.355213 + 4.36243i) q^{26} +(3.62672 + 3.85317i) q^{28} -2.01745i q^{29} +(1.10538 - 1.91457i) q^{31} +(5.19648 - 2.23530i) q^{32} +(2.39462 - 5.05560i) q^{34} +(-7.69885 - 3.76234i) q^{35} +(-4.30285 + 2.48425i) q^{37} +(-3.14101 + 2.17130i) q^{38} +(-6.59347 + 6.35951i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(4.51349 + 1.70459i) q^{44} +(2.20731 + 3.19311i) q^{46} +(-3.31613 - 5.74371i) q^{47} +(-2.63227 + 6.48623i) q^{49} +(3.32331 - 7.01628i) q^{50} +(1.00138 + 6.10829i) q^{52} +(2.23998 + 1.29325i) q^{53} -7.81297 q^{55} +(5.55427 + 5.01498i) q^{56} +(-0.231549 - 2.84370i) q^{58} +(-10.6283 - 6.13625i) q^{59} +(7.54801 - 4.35784i) q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} +(-5.01186 - 8.68080i) q^{65} +(-5.01858 - 2.89748i) q^{67} +(2.79509 - 7.40094i) q^{68} +(-11.2837 - 4.41959i) q^{70} -6.64663 q^{71} +(4.77890 - 8.27729i) q^{73} +(-5.77995 + 3.99553i) q^{74} +(-4.17820 + 3.42105i) q^{76} +(0.440297 + 6.36720i) q^{77} +(-0.838343 - 1.45205i) q^{79} +(-8.56392 + 9.72078i) q^{80} +(2.97775 - 0.242465i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(-1.33021 - 16.3365i) q^{86} +(6.55762 + 1.88468i) q^{88} +(6.98965 + 12.1064i) q^{89} +(-6.79200 + 4.57363i) q^{91} +(3.47779 + 4.24750i) q^{92} +(-5.33347 - 7.71544i) q^{94} +(4.37241 - 7.57324i) q^{95} -1.37709 q^{97} +(-2.96587 + 9.44477i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40} + 8 q^{41} + 30 q^{44} - 4 q^{46} - 30 q^{47} - 12 q^{49} + 16 q^{50} - 32 q^{52} + 4 q^{55} + 40 q^{56} - 22 q^{58} + 28 q^{62} + 24 q^{64} - 8 q^{65} - 4 q^{68} - 48 q^{70} - 32 q^{71} - 10 q^{73} - 18 q^{74} + 52 q^{76} - 22 q^{79} - 36 q^{80} - 26 q^{82} - 40 q^{86} - 14 q^{88} + 10 q^{89} + 20 q^{92} + 42 q^{94} + 34 q^{95} + 40 q^{97} - 52 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	1.40955	−	0.114773i	0.996701	−	0.0811568i
$2$	1.40955	−	0.114773i	0.996701	−	0.0811568i
$3$		0			0
$3$		0			0
$4$	1.97365	−	0.323556i	0.986827	−	0.161778i
$5$	−2.80486	+	1.61939i	−1.25437	+	0.724212i	−0.971975	−	0.235086i	$-0.924463\pi$
$5$	−2.80486	+	1.61939i	−1.25437	+	0.724212i	−0.282397	+	0.959298i	$0.591130\pi$
$6$		0			0
$7$	1.47779	+	2.19457i	0.558552	+	0.829469i
$7$	1.47779	+	2.19457i	0.558552	+	0.829469i
$8$	2.74483	−	0.682591i	0.970443	−	0.241332i
$9$		0			0
$10$	−3.76772	+	2.60453i	−1.19146	+	0.823624i
$11$	2.08913	+	1.20616i	0.629897	+	0.363671i	0.780712	−	0.624891i	$-0.214856\pi$
$11$	2.08913	+	1.20616i	0.629897	+	0.363671i	−0.150815	+	0.988562i	$0.548190\pi$
$12$		0			0
$13$			3.09491i			0.858375i	0.903216	+	0.429187i	$0.141200\pi$
$13$			3.09491i			0.858375i	−0.903216	+	0.429187i	$0.858800\pi$
$14$	2.33490	+	2.92374i	0.624027	+	0.781403i
$15$		0			0
$16$	3.79062	−	1.27718i	0.947656	−	0.319294i
$17$	1.97779	−	3.42563i	0.479685	−	0.830838i	−0.520044	−	0.854140i	$-0.674084\pi$
$17$	1.97779	−	3.42563i	0.479685	−	0.830838i	0.999728	+	0.0233012i	$0.00741769\pi$
$18$		0			0
$19$	−2.33831	+	1.35002i	−0.536444	+	0.309716i	−0.743637	−	0.668584i	$-0.766901\pi$
$19$	−2.33831	+	1.35002i	−0.536444	+	0.309716i	0.207192	+	0.978300i	$0.433567\pi$
$20$	−5.01186	+	4.10364i	−1.12069	+	0.917602i
$21$		0			0
$22$	3.08317	+	1.46037i	0.657334	+	0.311351i
$23$	1.37241	+	2.37709i	0.286168	+	0.495657i	0.972892	−	0.231261i	$-0.0742852\pi$
$23$	1.37241	+	2.37709i	0.286168	+	0.495657i	−0.686724	+	0.726918i	$0.740952\pi$
$24$		0			0
$25$	2.74483	−	4.75418i	0.548965	−	0.950836i
$26$	0.355213	+	4.36243i	0.0696629	+	0.855543i
$27$		0			0
$28$	3.62672	+	3.85317i	0.685385	+	0.728181i
$29$		−	2.01745i		−	0.374631i	−0.982300	−	0.187316i	$-0.940021\pi$
$29$		−	2.01745i		−	0.374631i	0.982300	−	0.187316i	$-0.0599787\pi$
$30$		0			0
$31$	1.10538	−	1.91457i	0.198532	−	0.343867i	−0.749521	−	0.661981i	$-0.769716\pi$
$31$	1.10538	−	1.91457i	0.198532	−	0.343867i	0.948053	+	0.318114i	$0.103049\pi$
$32$	5.19648	−	2.23530i	0.918617	−	0.395150i
$33$		0			0
$34$	2.39462	−	5.05560i	0.410674	−	0.867027i
$35$	−7.69885	−	3.76234i	−1.30134	−	0.635952i
$36$		0			0
$37$	−4.30285	+	2.48425i	−0.707385	+	0.408409i	−0.810092	−	0.586303i	$-0.800583\pi$
$37$	−4.30285	+	2.48425i	−0.707385	+	0.408409i	0.102707	+	0.994712i	$0.467249\pi$
$38$	−3.14101	+	2.17130i	−0.509539	+	0.352231i
$39$		0			0
$40$	−6.59347	+	6.35951i	−1.04252	+	1.00553i
$41$	2.11256			0.329926			0.164963	−	0.986300i	$-0.447249\pi$
$41$	2.11256			0.329926			0.164963	+	0.986300i	$0.447249\pi$
$42$		0			0
$43$		−	11.5899i		−	1.76745i	−0.468011	−	0.883723i	$-0.655029\pi$
$43$		−	11.5899i		−	1.76745i	0.468011	−	0.883723i	$-0.344971\pi$
$44$	4.51349	+	1.70459i	0.680434	+	0.256977i
$45$		0			0
$46$	2.20731	+	3.19311i	0.325450	+	0.470798i
$47$	−3.31613	−	5.74371i	−0.483708	−	0.837807i	0.516117	−	0.856518i	$-0.327377\pi$
$47$	−3.31613	−	5.74371i	−0.483708	−	0.837807i	−0.999825	+	0.0187115i	$0.994044\pi$
$48$		0			0
$49$	−2.63227	+	6.48623i	−0.376038	+	0.926604i
$50$	3.32331	−	7.01628i	0.469988	−	0.992251i
$51$		0			0
$52$	1.00138	+	6.10829i	0.138866	+	0.847067i
$53$	2.23998	+	1.29325i	0.307684	+	0.177642i	0.645890	−	0.763431i	$-0.276487\pi$
$53$	2.23998	+	1.29325i	0.307684	+	0.177642i	−0.338205	+	0.941072i	$0.609820\pi$
$54$		0			0
$55$	−7.81297			−1.05350
$56$	5.55427	+	5.01498i	0.742221	+	0.670156i
$57$		0			0
$58$	−0.231549	−	2.84370i	−0.0304039	−	0.373396i
$59$	−10.6283	−	6.13625i	−1.38369	−	0.798872i	−0.391093	−	0.920351i	$-0.627903\pi$
$59$	−10.6283	−	6.13625i	−1.38369	−	0.798872i	−0.992594	+	0.121479i	$0.961236\pi$
$60$		0			0
$61$	7.54801	−	4.35784i	0.966424	−	0.557965i	0.0682795	−	0.997666i	$-0.478249\pi$
$61$	7.54801	−	4.35784i	0.966424	−	0.557965i	0.898144	+	0.439701i	$0.144916\pi$
$62$	1.33834	−	2.82555i	0.169970	−	0.358845i
$63$		0			0
$64$	7.06814	−	3.74718i	0.883518	−	0.468398i
$65$	−5.01186	−	8.68080i	−0.621645	−	1.07672i
$66$		0			0
$67$	−5.01858	−	2.89748i	−0.613117	−	0.353983i	0.161067	−	0.986943i	$-0.448506\pi$
$67$	−5.01858	−	2.89748i	−0.613117	−	0.353983i	−0.774184	+	0.632960i	$0.781840\pi$
$68$	2.79509	−	7.40094i	0.338954	−	0.897496i
$69$		0			0
$70$	−11.2837	−	4.41959i	−1.34866	−	0.528242i
$71$	−6.64663			−0.788810			−0.394405	−	0.918937i	$-0.629049\pi$
$71$	−6.64663			−0.788810			−0.394405	+	0.918937i	$0.629049\pi$
$72$		0			0
$73$	4.77890	−	8.27729i	0.559328	−	0.968784i	−0.438225	−	0.898865i	$-0.644393\pi$
$73$	4.77890	−	8.27729i	0.559328	−	0.968784i	0.997553	−	0.0699184i	$-0.0222739\pi$
$74$	−5.77995	+	3.99553i	−0.671906	+	0.464470i
$75$		0			0
$76$	−4.17820	+	3.42105i	−0.479272	+	0.392421i
$77$	0.440297	+	6.36720i	0.0501765	+	0.725610i
$78$		0			0
$79$	−0.838343	−	1.45205i	−0.0943209	−	0.163369i	0.815004	−	0.579455i	$-0.196735\pi$
$79$	−0.838343	−	1.45205i	−0.0943209	−	0.163369i	−0.909325	+	0.416087i	$0.863401\pi$
$80$	−8.56392	+	9.72078i	−0.957476	+	1.08682i
$81$		0			0
$82$	2.97775	−	0.242465i	0.328838	−	0.0267757i
$83$			6.47755i			0.711003i	0.934676	+	0.355502i	$0.115690\pi$
$83$			6.47755i			0.711003i	−0.934676	+	0.355502i	$0.884310\pi$
$84$		0			0
$85$			12.8112i			1.38957i
$86$	−1.33021	−	16.3365i	−0.143440	−	1.76161i
$87$		0			0
$88$	6.55762	+	1.88468i	0.699045	+	0.200908i
$89$	6.98965	+	12.1064i	0.740902	+	1.28328i	0.952085	+	0.305833i	$0.0989349\pi$
$89$	6.98965	+	12.1064i	0.740902	+	1.28328i	−0.211184	+	0.977446i	$0.567732\pi$
$90$		0			0
$91$	−6.79200	+	4.57363i	−0.711995	+	0.479447i
$92$	3.47779	+	4.24750i	0.362585	+	0.442832i
$93$		0			0
$94$	−5.33347	−	7.71544i	−0.550106	−	0.795787i
$95$	4.37241	−	7.57324i	0.448600	−	0.776998i
$96$		0			0
$97$	−1.37709			−0.139823			−0.0699113	−	0.997553i	$-0.522272\pi$
$97$	−1.37709			−0.139823			−0.0699113	+	0.997553i	$0.522272\pi$
$98$	−2.96587	+	9.44477i	−0.299598	+	0.954066i
$99$		0			0
$100$	3.87909	−	10.2712i	0.387909	−	1.02712i
$101$	0.689470	+	0.398066i	0.0686048	+	0.0396090i	0.533910	−	0.845541i	$-0.320722\pi$
$101$	0.689470	+	0.398066i	0.0686048	+	0.0396090i	−0.465305	+	0.885150i	$0.654055\pi$
$102$		0			0
$103$	1.32799	+	2.30015i	0.130851	+	0.226641i	0.924005	−	0.382381i	$-0.124896\pi$
$103$	1.32799	+	2.30015i	0.130851	+	0.226641i	−0.793154	+	0.609022i	$0.791562\pi$
$104$	2.11256	+	8.49500i	0.207153	+	0.833003i
$105$		0			0
$106$	3.30579	+	1.56581i	0.321086	+	0.152085i
$107$	4.70287	−	2.71520i	0.454643	−	0.262489i	−0.255146	−	0.966903i	$-0.582123\pi$
$107$	4.70287	−	2.71520i	0.454643	−	0.262489i	0.709789	+	0.704414i	$0.248790\pi$
$108$		0			0
$109$	11.9614	+	6.90593i	1.14570	+	0.661468i	0.947835	−	0.318762i	$-0.103267\pi$
$109$	11.9614	+	6.90593i	1.14570	+	0.661468i	0.197862	+	0.980230i	$0.436600\pi$
$110$	−11.0128	+	0.896718i	−1.05003	+	0.0854987i
$111$		0			0
$112$	8.40460	+	6.43138i	0.794160	+	0.607709i
$113$	−4.53407			−0.426529			−0.213265	−	0.976994i	$-0.568410\pi$
$113$	−4.53407			−0.426529			−0.213265	+	0.976994i	$0.568410\pi$
$114$		0			0
$115$	−7.69885	−	4.44493i	−0.717922	−	0.414492i
$116$	−0.652759	−	3.98175i	−0.0606072	−	0.369697i
$117$		0			0
$118$	−15.6854	−	7.42950i	−1.44396	−	0.683941i
$119$	10.4406	−	0.721973i	0.957084	−	0.0661831i
$120$		0			0
$121$	−2.59035	−	4.48662i	−0.235486	−	0.407874i
$122$	10.1391	−	7.00890i	0.917953	−	0.634556i
$123$		0			0
$124$	1.56216	−	4.13635i	0.140286	−	0.371455i
$125$			1.58587i			0.141845i
$126$		0			0
$127$	−15.4897			−1.37448			−0.687242	−	0.726428i	$-0.741179\pi$
$127$	−15.4897			−1.37448			−0.687242	+	0.726428i	$0.741179\pi$
$128$	9.53281	−	6.09307i	0.842589	−	0.538556i
$129$		0			0
$130$	−8.06078	−	11.6608i	−0.706977	−	1.02272i
$131$	14.5574	−	8.40471i	1.27189	−	0.734323i	0.296543	−	0.955020i	$-0.404166\pi$
$131$	14.5574	−	8.40471i	1.27189	−	0.734323i	0.975343	+	0.220696i	$0.0708330\pi$
$132$		0			0
$133$	−6.41824	−	3.13652i	−0.556532	−	0.271971i
$134$	−7.40648	−	3.50814i	−0.639823	−	0.303057i
$135$		0			0
$136$	3.09039	−	10.7528i	0.264998	−	0.922044i
$137$	−0.443721	+	0.768547i	−0.0379096	+	0.0656614i	−0.884358	−	0.466810i	$-0.845403\pi$
$137$	−0.443721	+	0.768547i	−0.0379096	+	0.0656614i	0.846448	+	0.532471i	$0.178737\pi$
$138$		0			0
$139$		−	2.44264i		−	0.207182i	−0.994620	−	0.103591i	$-0.966967\pi$
$139$		−	2.44264i		−	0.207182i	0.994620	−	0.103591i	$-0.0330333\pi$
$140$	−16.4122	−	4.93455i	−1.38708	−	0.417046i
$141$		0			0
$142$	−9.36875	+	0.762854i	−0.786208	+	0.0640172i
$143$	−3.73296	+	6.46568i	−0.312166	+	0.540688i
$144$		0			0
$145$	3.26704	+	5.65867i	0.271312	+	0.469927i
$146$	5.78608	−	12.2157i	0.478859	−	1.01098i
$147$		0			0
$148$	−7.68855	+	6.29527i	−0.631995	+	0.517468i
$149$	−8.16541	+	4.71430i	−0.668936	+	0.386210i	−0.795673	−	0.605726i	$-0.792883\pi$
$149$	−8.16541	+	4.71430i	−0.668936	+	0.386210i	0.126737	+	0.991936i	$0.459549\pi$
$150$		0			0
$151$	3.52689	−	6.10875i	0.287014	−	0.497123i	−0.686081	−	0.727525i	$-0.740671\pi$
$151$	3.52689	−	6.10875i	0.287014	−	0.497123i	0.973096	+	0.230402i	$0.0740040\pi$
$152$	−5.49673	+	5.30168i	−0.445844	+	0.430023i
$153$		0			0
$154$	1.35140	+	8.92434i	0.108899	+	0.719144i
$155$			7.16014i			0.575116i
$156$		0			0
$157$	7.54801	+	4.35784i	0.602397	+	0.347794i	0.769984	−	0.638063i	$-0.220264\pi$
$157$	7.54801	+	4.35784i	0.602397	+	0.347794i	−0.167587	+	0.985857i	$0.553598\pi$
$158$	−1.34834	−	1.95052i	−0.107268	−	0.155175i
$159$		0			0
$160$	−10.9556	+	14.6848i	−0.866115	+	1.16094i
$161$	−3.18855	+	6.52470i	−0.251293	+	0.514218i
$162$		0			0
$163$	17.1711	−	9.91376i	1.34495	−	0.776505i	0.357418	−	0.933945i	$-0.383657\pi$
$163$	17.1711	−	9.91376i	1.34495	−	0.776505i	0.987529	+	0.157439i	$0.0503239\pi$
$164$	4.16946	−	0.683532i	0.325580	−	0.0533748i
$165$		0			0
$166$	0.743448	+	9.13042i	0.0577027	+	0.708658i
$167$	−22.1600			−1.71479			−0.857396	−	0.514657i	$-0.827919\pi$
$167$	−22.1600			−1.71479			−0.857396	+	0.514657i	$0.827919\pi$
$168$		0			0
$169$	3.42151			0.263193
$170$	1.47038	+	18.0581i	0.112773	+	1.38499i
$171$		0			0
$172$	−3.74999	−	22.8745i	−0.285934	−	1.74416i
$173$	18.8200	−	10.8657i	1.43086	−	0.826105i	0.433669	−	0.901072i	$-0.357219\pi$
$173$	18.8200	−	10.8657i	1.43086	−	0.826105i	0.997186	+	0.0749674i	$0.0238853\pi$
$174$		0			0
$175$	14.4897	−	1.00197i	1.09531	−	0.0757419i
$176$	9.45960	+	1.90391i	0.713044	+	0.143513i
$177$		0			0
$178$	11.2417	+	16.2624i	0.842604	+	1.21892i
$179$	−3.27141	−	1.88875i	−0.244517	−	0.141172i	0.372734	−	0.927938i	$-0.378420\pi$
$179$	−3.27141	−	1.88875i	−0.244517	−	0.141172i	−0.617251	+	0.786766i	$0.711754\pi$
$180$		0			0
$181$		−	14.0326i		−	1.04303i	−0.853242	−	0.521516i	$-0.825367\pi$
$181$		−	14.0326i		−	1.04303i	0.853242	−	0.521516i	$-0.174633\pi$
$182$	−9.04873	+	7.22630i	−0.670736	+	0.535649i
$183$		0			0
$184$	5.38961	+	5.58790i	0.397328	+	0.411945i
$185$	8.04593	−	13.9360i	0.591549	−	1.02459i
$186$		0			0
$187$	8.26374	−	4.77107i	0.604304	−	0.348895i
$188$	−8.40332	−	10.2631i	−0.612875	−	0.748517i
$189$		0			0
$190$	5.29392	−	11.1767i	0.384062	−	0.810842i
$191$	3.63945	+	6.30371i	0.263341	+	0.456120i	0.967128	−	0.254291i	$-0.0818422\pi$
$191$	3.63945	+	6.30371i	0.263341	+	0.456120i	−0.703786	+	0.710412i	$0.748509\pi$
$192$		0			0
$193$	−4.76704	+	8.25675i	−0.343139	+	0.594334i	−0.985014	−	0.172476i	$-0.944823\pi$
$193$	−4.76704	+	8.25675i	−0.343139	+	0.594334i	0.641875	+	0.766809i	$0.278157\pi$
$194$	−1.94108	+	0.158053i	−0.139361	+	0.0113476i
$195$		0			0
$196$	−3.09653	+	13.6533i	−0.221180	+	0.975233i
$197$			11.6667i			0.831221i	0.909543	+	0.415611i	$0.136432\pi$
$197$			11.6667i			0.831221i	−0.909543	+	0.415611i	$0.863568\pi$
$198$		0			0
$199$	−9.48247	+	16.4241i	−0.672195	+	1.16428i	0.305086	+	0.952325i	$0.401315\pi$
$199$	−9.48247	+	16.4241i	−0.672195	+	1.16428i	−0.977280	+	0.211950i	$0.932018\pi$
$200$	4.28891	−	14.9230i	0.303272	−	1.05521i
$201$		0			0
$202$	1.01753	+	0.481960i	0.0715930	+	0.0339106i
$203$	4.42744	−	2.98137i	0.310745	−	0.209251i
$204$		0			0
$205$	−5.92543	+	3.42105i	−0.413850	+	0.238936i
$206$	2.13587	+	3.08976i	0.148813	+	0.215274i
$207$		0			0
$208$	3.95275	+	11.7316i	0.274074	+	0.813443i
$209$	−6.51337			−0.450540
$210$		0			0
$211$			16.1268i			1.11022i	0.831778	+	0.555109i	$0.187323\pi$
$211$			16.1268i			1.11022i	−0.831778	+	0.555109i	$0.812677\pi$
$212$	4.83938	+	1.82767i	0.332370	+	0.125525i
$213$		0			0
$214$	6.31729	−	4.36697i	0.431841	−	0.298520i
$215$	18.7685	+	32.5081i	1.28000	+	2.21703i
$216$		0			0
$217$	5.83518	−	0.403507i	0.396118	−	0.0273918i
$218$	17.6528	+	8.36140i	1.19560	+	0.566305i
$219$		0			0
$220$	−15.4201	+	2.52793i	−1.03962	+	0.170433i
$221$	10.6020	+	6.12109i	0.713170	+	0.411749i
$222$		0			0
$223$	−7.71477			−0.516619			−0.258310	−	0.966062i	$-0.583165\pi$
$223$	−7.71477			−0.516619			−0.258310	+	0.966062i	$0.583165\pi$
$224$	12.5848	+	8.10073i	0.840860	+	0.541253i
$225$		0			0
$226$	−6.39099	+	0.520389i	−0.425122	+	0.0346158i
$227$	−1.83996	−	1.06230i	−0.122122	−	0.0705074i	0.437694	−	0.899124i	$-0.355795\pi$
$227$	−1.83996	−	1.06230i	−0.122122	−	0.0705074i	−0.559817	+	0.828616i	$0.689129\pi$
$228$		0			0
$229$	−8.11289	+	4.68398i	−0.536115	+	0.309526i	−0.743503	−	0.668733i	$-0.766837\pi$
$229$	−8.11289	+	4.68398i	−0.536115	+	0.309526i	0.207388	+	0.978259i	$0.433504\pi$
$230$	−11.3621	−	5.38173i	−0.749192	−	0.354861i
$231$		0			0
$232$	−1.37709	−	5.53756i	−0.0904106	−	0.363558i
$233$	−4.41366	−	7.64469i	−0.289149	−	0.500820i	0.684458	−	0.729052i	$-0.260039\pi$
$233$	−4.41366	−	7.64469i	−0.289149	−	0.500820i	−0.973607	+	0.228232i	$0.926706\pi$
$234$		0			0
$235$	18.6026	+	10.7402i	1.21350	+	0.700614i
$236$	−22.9620	−	8.67199i	−1.49470	−	0.564498i
$237$		0			0
$238$	14.6336	−	2.21595i	0.948556	−	0.143639i
$239$	−5.93489			−0.383896			−0.191948	−	0.981405i	$-0.561480\pi$
$239$	−5.93489			−0.383896			−0.191948	+	0.981405i	$0.561480\pi$
$240$		0			0
$241$	5.34302	−	9.25439i	0.344174	−	0.596128i	−0.641029	−	0.767517i	$-0.721492\pi$
$241$	5.34302	−	9.25439i	0.344174	−	0.596128i	0.985203	+	0.171389i	$0.0548255\pi$
$242$	−4.16617	−	6.02680i	−0.267811	−	0.387418i
$243$		0			0
$244$	13.4872	−	11.0431i	0.863426	−	0.706961i
$245$	−3.12057	−	22.4556i	−0.199366	−	1.43464i
$246$		0			0
$247$	−4.17820	−	7.23685i	−0.265852	−	0.460470i
$248$	1.72720	−	6.00968i	0.109677	−	0.381615i
$249$		0			0
$250$	0.182015	+	2.23536i	0.0115117	+	0.141377i
$251$			3.82402i			0.241370i	0.992691	+	0.120685i	$0.0385091\pi$
$251$			3.82402i			0.241370i	−0.992691	+	0.120685i	$0.961491\pi$
$252$		0			0
$253$			6.62141i			0.416284i
$254$	−21.8334	+	1.77779i	−1.36995	+	0.111549i
$255$		0			0
$256$	12.7376	−	9.68259i	0.796103	−	0.605162i
$257$	6.20291	+	10.7438i	0.386927	+	0.670177i	0.992034	−	0.125967i	$-0.0402033\pi$
$257$	6.20291	+	10.7438i	0.386927	+	0.670177i	−0.605108	+	0.796144i	$0.706870\pi$
$258$		0			0
$259$	−11.8106	−	5.77170i	−0.733874	−	0.358636i
$260$	−12.7004	−	15.5113i	−0.787646	−	0.961968i
$261$		0			0
$262$	19.5547	−	13.5176i	1.20809	−	0.835123i
$263$	−0.672005	+	1.16395i	−0.0414376	+	0.0717720i	−0.886000	−	0.463685i	$-0.846527\pi$
$263$	−0.672005	+	1.16395i	−0.0414376	+	0.0717720i	0.844563	+	0.535457i	$0.179860\pi$
$264$		0			0
$265$	−8.37709			−0.514601
$266$	−9.40681	−	3.68444i	−0.576769	−	0.225908i
$267$		0			0
$268$	−10.8424	−	4.09483i	−0.662307	−	0.250131i
$269$	−1.68912	−	0.975212i	−0.102987	−	0.0594597i	0.447622	−	0.894223i	$-0.352271\pi$
$269$	−1.68912	−	0.975212i	−0.102987	−	0.0594597i	−0.550609	+	0.834763i	$0.685604\pi$
$270$		0			0
$271$	13.0190	+	22.5496i	0.790850	+	1.36979i	0.925441	+	0.378892i	$0.123695\pi$
$271$	13.0190	+	22.5496i	0.790850	+	1.36979i	−0.134590	+	0.990901i	$0.542972\pi$
$272$	3.12192	−	15.5113i	0.189294	−	0.940509i
$273$		0			0
$274$	−0.537238	+	1.13423i	−0.0324557	+	0.0685214i
$275$	11.4686	−	6.62141i	0.691583	−	0.399286i
$276$		0			0
$277$	−13.9578	−	8.05852i	−0.838641	−	0.484189i	0.0181613	−	0.999835i	$-0.494219\pi$
$277$	−13.9578	−	8.05852i	−0.838641	−	0.484189i	−0.856802	+	0.515646i	$0.827552\pi$
$278$	−0.280349	−	3.44302i	−0.0168142	−	0.206499i
$279$		0			0
$280$	−23.7002	−	5.07182i	−1.41635	−	0.303099i
$281$	16.1313			0.962312			0.481156	−	0.876635i	$-0.340217\pi$
$281$	16.1313			0.962312			0.481156	+	0.876635i	$0.340217\pi$
$282$		0			0
$283$	−22.7949	−	13.1606i	−1.35501	−	0.782318i	−0.366068	−	0.930588i	$-0.619296\pi$
$283$	−22.7949	−	13.1606i	−1.35501	−	0.782318i	−0.988947	+	0.148270i	$0.952629\pi$
$284$	−13.1181	+	2.15056i	−0.778419	+	0.127612i
$285$		0			0
$286$	−4.51971	+	9.54214i	−0.267256	+	0.564239i
$287$	3.12192	+	4.63616i	0.184281	+	0.273664i
$288$		0			0
$289$	0.676686	+	1.17205i	0.0398050	+	0.0689444i
$290$	5.25451	+	7.60120i	0.308555	+	0.446358i
$291$		0			0
$292$	6.75372	−	17.8828i	0.395232	−	1.04651i
$293$		−	9.64929i		−	0.563718i	−0.959456	−	0.281859i	$-0.909049\pi$
$293$		−	9.64929i		−	0.563718i	0.959456	−	0.281859i	$-0.0909510\pi$
$294$		0			0
$295$	39.7479			2.31421
$296$	−10.1149	+	9.75593i	−0.587914	+	0.567052i
$297$		0			0
$298$	−10.9685	+	7.58220i	−0.635386	+	0.439225i
$299$	−7.35688	+	4.24750i	−0.425460	+	0.245639i
$300$		0			0
$301$	25.4349	−	17.1275i	1.46604	−	0.987211i
$302$	4.27020	−	9.01537i	0.245723	−	0.518777i
$303$		0			0
$304$	−7.13942	+	8.10385i	−0.409474	+	0.464788i
$305$	−14.1141	+	24.4463i	−0.808169	+	1.39979i
$306$		0			0
$307$			25.2741i			1.44247i	0.692691	+	0.721235i	$0.256425\pi$
$307$			25.2741i			1.44247i	−0.692691	+	0.721235i	$0.743575\pi$
$308$	2.92914	+	12.4242i	0.166903	+	0.707934i
$309$		0			0
$310$	0.821790	+	10.0926i	0.0466746	+	0.573219i
$311$	11.2742	−	19.5275i	0.639302	−	1.10730i	−0.346284	−	0.938130i	$-0.612557\pi$
$311$	11.2742	−	19.5275i	0.639302	−	1.10730i	0.985586	−	0.169174i	$-0.0541100\pi$
$312$		0			0
$313$	12.6901	+	21.9798i	0.717285	+	1.24237i	0.962072	+	0.272797i	$0.0879486\pi$
$313$	12.6901	+	21.9798i	0.717285	+	1.24237i	−0.244787	+	0.969577i	$0.578718\pi$
$314$	11.1394	+	5.27629i	0.628635	+	0.297758i
$315$		0			0
$316$	−2.12442	−	2.59460i	−0.119508	−	0.145958i
$317$	−14.8384	+	8.56693i	−0.833405	+	0.481167i	−0.855017	−	0.518600i	$-0.826453\pi$
$317$	−14.8384	+	8.56693i	−0.833405	+	0.481167i	0.0216120	+	0.999766i	$0.493120\pi$
$318$		0			0
$319$	2.43337	−	4.21473i	0.136243	−	0.235979i
$320$	−13.7570	+	21.9564i	−0.769040	+	1.22740i
$321$		0			0
$322$	−3.74555	+	9.56284i	−0.208731	+	0.532916i
$323$			10.6802i			0.594264i
$324$		0			0
$325$	14.7138	+	8.49500i	0.816173	+	0.471218i
$326$	23.0657	−	15.9447i	1.27749	−	0.883095i
$327$		0			0
$328$	5.79861	−	1.44201i	0.320174	−	0.0796218i
$329$	7.70442	−	15.7655i	0.424758	−	0.869180i
$330$		0			0
$331$	−7.43566	+	4.29298i	−0.408701	+	0.235963i	−0.690231	−	0.723589i	$-0.742491\pi$
$331$	−7.43566	+	4.29298i	−0.408701	+	0.235963i	0.281531	+	0.959552i	$0.409158\pi$
$332$	2.09585	+	12.7844i	0.115025	+	0.701637i
$333$		0			0
$334$	−31.2356	+	2.54337i	−1.70914	+	0.139167i
$335$	18.7685			1.02544
$336$		0			0
$337$	−3.18070			−0.173264			−0.0866319	−	0.996240i	$-0.527610\pi$
$337$	−3.18070			−0.173264			−0.0866319	+	0.996240i	$0.527610\pi$
$338$	4.82279	−	0.392697i	0.262325	−	0.0213599i
$339$		0			0
$340$	4.14515	+	25.2849i	0.224803	+	1.37127i
$341$	4.61856	−	2.66653i	0.250109	−	0.144401i
$342$		0			0
$343$	−18.1244	+	3.80860i	−0.978627	+	0.205645i
$344$	−7.91116	−	31.8123i	−0.426541	−	1.71520i
$345$		0			0
$346$	25.2806	−	17.4758i	1.35909	−	0.939503i
$347$	19.0373	+	10.9912i	1.02198	+	0.590039i	0.914676	−	0.404187i	$-0.132446\pi$
$347$	19.0373	+	10.9912i	1.02198	+	0.590039i	0.107302	+	0.994226i	$0.465779\pi$
$348$		0			0
$349$		−	15.5480i		−	0.832265i	−0.909304	−	0.416132i	$-0.863385\pi$
$349$		−	15.5480i		−	0.832265i	0.909304	−	0.416132i	$-0.136615\pi$
$350$	20.3089	−	3.07535i	1.08555	−	0.164384i
$351$		0			0
$352$	13.5523	+	1.59795i	0.722339	+	0.0851710i
$353$	−13.2804	+	23.0023i	−0.706845	+	1.22429i	0.259177	+	0.965830i	$0.416549\pi$
$353$	−13.2804	+	23.0023i	−0.706845	+	1.22429i	−0.966022	+	0.258461i	$0.916785\pi$
$354$		0			0
$355$	18.6429	−	10.7635i	0.989460	−	0.571265i
$356$	17.7123	+	21.6324i	0.938748	+	1.14651i
$357$		0			0
$358$	−4.82799	−	2.28682i	−0.255167	−	0.120862i
$359$	−15.5062	−	26.8575i	−0.818386	−	1.41749i	−0.906871	−	0.421408i	$-0.861536\pi$
$359$	−15.5062	−	26.8575i	−0.818386	−	1.41749i	0.0884855	−	0.996077i	$-0.471797\pi$
$360$		0			0
$361$	−5.85488	+	10.1410i	−0.308152	+	0.533735i
$362$	−1.61056	−	19.7796i	−0.0846491	−	1.03959i
$363$		0			0
$364$	−11.9252	+	11.2244i	−0.625052	+	0.588317i
$365$			30.9555i			1.62029i
$366$		0			0
$367$	6.38677	−	11.0622i	0.333387	−	0.577443i	−0.649787	−	0.760117i	$-0.725142\pi$
$367$	6.38677	−	11.0622i	0.333387	−	0.577443i	0.983174	+	0.182674i	$0.0584751\pi$
$368$	8.23826	+	7.25783i	0.429449	+	0.378341i
$369$		0			0
$370$	9.74166	−	20.5669i	0.506445	−	1.06922i
$371$	0.472088	+	6.82694i	0.0245096	+	0.354437i
$372$		0			0
$373$	−5.73431	+	3.31070i	−0.296911	+	0.171422i	−0.641054	−	0.767495i	$-0.721503\pi$
$373$	−5.73431	+	3.31070i	−0.296911	+	0.171422i	0.344143	+	0.938917i	$0.388169\pi$
$374$	11.1005	−	7.67351i	0.573996	−	0.396788i
$375$		0			0
$376$	−13.0228	−	13.5019i	−0.671600	−	0.696309i
$377$	6.24384			0.321574
$378$		0			0
$379$			18.7804i			0.964683i	0.875983	+	0.482341i	$0.160214\pi$
$379$			18.7804i			0.964683i	−0.875983	+	0.482341i	$0.839786\pi$
$380$	6.17926	−	16.3617i	0.316989	−	0.839337i
$381$		0			0
$382$	5.85347	+	8.46767i	0.299490	+	0.433244i
$383$	−10.2179	−	17.6980i	−0.522112	−	0.904325i	−0.999669	−	0.0257240i	$-0.991811\pi$
$383$	−10.2179	−	17.6980i	−0.522112	−	0.904325i	0.477557	−	0.878601i	$-0.341522\pi$
$384$		0			0
$385$	−11.5459	−	17.1461i	−0.588435	−	0.873846i
$386$	−5.77172	+	12.1854i	−0.293773	+	0.620221i
$387$		0			0
$388$	−2.71791	+	0.445567i	−0.137981	+	0.0226203i
$389$	2.05734	+	1.18781i	0.104311	+	0.0602242i	0.551248	−	0.834341i	$-0.314152\pi$
$389$	2.05734	+	1.18781i	0.104311	+	0.0602242i	−0.446937	+	0.894566i	$0.647485\pi$
$390$		0			0
$391$	10.8574			0.549082
$392$	−2.79768	+	19.6003i	−0.141304	+	0.989966i
$393$		0			0
$394$	1.33903	+	16.4448i	0.0674592	+	0.828479i
$395$	4.70287	+	2.71520i	0.236627	+	0.136617i
$396$		0			0
$397$	−19.1993	+	11.0847i	−0.963583	+	0.556325i	−0.897274	−	0.441474i	$-0.854456\pi$
$397$	−19.1993	+	11.0847i	−0.963583	+	0.556325i	−0.0663091	+	0.997799i	$0.521122\pi$
$398$	−11.4810	+	24.2389i	−0.575488	+	1.21499i
$399$		0			0
$400$	4.33268	−	21.5269i	0.216634	−	1.07635i
$401$	13.1585	+	22.7912i	0.657104	+	1.13814i	0.981362	+	0.192168i	$0.0615519\pi$
$401$	13.1585	+	22.7912i	0.657104	+	1.13814i	−0.324258	+	0.945969i	$0.605115\pi$
$402$		0			0
$403$	5.92543	+	3.42105i	0.295167	+	0.170415i
$404$	1.48957	+	0.562562i	0.0741090	+	0.0279885i
$405$		0			0
$406$	5.89851	−	4.71054i	0.292738	−	0.233780i
$407$	−11.9856			−0.594106
$408$		0			0
$409$	0.331162	−	0.573590i	0.0163749	−	0.0283622i	−0.857722	−	0.514114i	$-0.828121\pi$
$409$	0.331162	−	0.573590i	0.0163749	−	0.0283622i	0.874097	+	0.485752i	$0.161454\pi$
$410$	−7.95954	+	5.50221i	−0.393094	+	0.271735i
$411$		0			0
$412$	3.36523	+	4.11003i	0.165793	+	0.202487i
$413$	−2.23998	−	32.3926i	−0.110222	−	1.59394i
$414$		0			0
$415$	−10.4897	−	18.1686i	−0.514917	−	0.891862i
$416$	6.91807	+	16.0827i	0.339186	+	0.788517i
$417$		0			0
$418$	−9.18092	+	0.747560i	−0.449053	+	0.0365643i
$419$		−	7.55501i		−	0.369086i	−0.982824	−	0.184543i	$-0.940919\pi$
$419$		−	7.55501i		−	0.369086i	0.982824	−	0.184543i	$-0.0590805\pi$
$420$		0			0
$421$		−	12.5905i		−	0.613625i	−0.951770	−	0.306813i	$-0.900737\pi$
$421$		−	12.5905i		−	0.613625i	0.951770	−	0.306813i	$-0.0992625\pi$
$422$	1.85093	+	22.7316i	0.0901017	+	1.10656i
$423$		0			0
$424$	7.03111	+	2.02076i	0.341461	+	0.0981369i
$425$	−10.8574	−	18.8055i	−0.526661	−	0.912203i
$426$		0			0
$427$	20.7180	+	10.1246i	1.00261	+	0.489966i
$428$	8.40332	−	6.88051i	0.406190	−	0.332582i
$429$		0			0
$430$	30.1862	+	43.6676i	1.45571	+	2.10584i
$431$	−6.45241	+	11.1759i	−0.310802	+	0.538325i	−0.978536	−	0.206075i	$-0.933931\pi$
$431$	−6.45241	+	11.1759i	−0.310802	+	0.538325i	0.667734	+	0.744400i	$0.267264\pi$
$432$		0			0
$433$	−40.5815			−1.95022			−0.975112	−	0.221715i	$-0.928835\pi$
$433$	−40.5815			−1.95022			−0.975112	+	0.221715i	$0.928835\pi$
$434$	8.17865	−	1.23848i	0.392588	−	0.0594491i
$435$		0			0
$436$	25.8422	+	9.75973i	1.23762	+	0.467406i
$437$	−6.41824	−	3.70557i	−0.307026	−	0.177262i
$438$		0			0
$439$	−18.2273	−	31.5706i	−0.869941	−	1.50678i	−0.862055	−	0.506814i	$-0.830823\pi$
$439$	−18.2273	−	31.5706i	−0.869941	−	1.50678i	−0.00788596	−	0.999969i	$-0.502510\pi$
$440$	−21.4452	+	5.33306i	−1.02236	+	0.254244i
$441$		0			0
$442$	15.6466	+	7.41115i	0.744234	+	0.352512i
$443$	−28.1274	+	16.2393i	−1.33637	+	0.771555i	−0.986267	−	0.165156i	$-0.947187\pi$
$443$	−28.1274	+	16.2393i	−1.33637	+	0.771555i	−0.350104	+	0.936711i	$0.613854\pi$
$444$		0			0
$445$	−39.2100	−	22.6379i	−1.85873	−	1.07314i
$446$	−10.8743	+	0.885447i	−0.514915	+	0.0419271i
$447$		0			0
$448$	18.6687	+	9.97397i	0.882013	+	0.471226i
$449$	−25.9823			−1.22618			−0.613091	−	0.790012i	$-0.710074\pi$
$449$	−25.9823			−1.22618			−0.613091	+	0.790012i	$0.710074\pi$
$450$		0			0
$451$	4.41342	+	2.54809i	0.207820	+	0.119985i
$452$	−8.94869	+	1.46703i	−0.420911	+	0.0690031i
$453$		0			0
$454$	−2.71544	−	1.28619i	−0.127442	−	0.0603638i
$455$	11.6441	−	23.8273i	0.545885	−	1.11704i
$456$		0			0
$457$	5.73448	+	9.93241i	0.268248	+	0.464618i	0.968409	−	0.249366i	$-0.0802221\pi$
$457$	5.73448	+	9.93241i	0.268248	+	0.464618i	−0.700162	+	0.713984i	$0.746889\pi$
$458$	−10.8979	+	7.53344i	−0.509226	+	0.352014i
$459$		0			0
$460$	−16.6331	−	6.28175i	−0.775520	−	0.292888i
$461$		−	25.1973i		−	1.17355i	−0.809749	−	0.586777i	$-0.800396\pi$
$461$		−	25.1973i		−	1.17355i	0.809749	−	0.586777i	$-0.199604\pi$
$462$		0			0
$463$	−31.8223			−1.47891			−0.739454	−	0.673207i	$-0.764916\pi$
$463$	−31.8223			−1.47891			−0.739454	+	0.673207i	$0.764916\pi$
$464$	−2.57664	−	7.64740i	−0.119618	−	0.355022i
$465$		0			0
$466$	−7.09868	−	10.2690i	−0.328840	−	0.475702i
$467$	−12.3089	+	7.10656i	−0.569589	+	0.328852i	−0.756985	−	0.653432i	$-0.773329\pi$
$467$	−12.3089	+	7.10656i	−0.569589	+	0.328852i	0.187396	+	0.982284i	$0.439995\pi$
$468$		0			0
$469$	−1.05770	−	15.2955i	−0.0488398	−	0.706280i
$470$	27.4539	+	13.0038i	1.26636	+	0.599819i
$471$		0			0
$472$	−33.3614	−	9.58817i	−1.53558	−	0.441331i
$473$	13.9793	−	24.2129i	0.642769	−	1.11331i
$474$		0			0
$475$			14.8223i			0.680094i
$476$	20.3724	−	4.80303i	0.933769	−	0.220147i
$477$		0			0
$478$	−8.36551	+	0.681165i	−0.382630	+	0.0311558i
$479$	−5.77020	+	9.99428i	−0.263647	+	0.456650i	−0.967208	−	0.253984i	$-0.918259\pi$
$479$	−5.77020	+	9.99428i	−0.263647	+	0.456650i	0.703561	+	0.710635i	$0.251592\pi$
$480$		0			0
$481$	−7.68855	−	13.3170i	−0.350568	−	0.607201i
$482$	6.46910	−	13.6577i	0.294659	−	0.622093i
$483$		0			0
$484$	−6.56413	−	8.01691i	−0.298369	−	0.364405i
$485$	3.86255	−	2.23005i	0.175390	−	0.101261i
$486$		0			0
$487$	8.80829	−	15.2564i	0.399142	−	0.691333i	−0.594479	−	0.804111i	$-0.702642\pi$
$487$	8.80829	−	15.2564i	0.399142	−	0.691333i	0.993620	+	0.112778i	$0.0359749\pi$
$488$	17.7433	−	17.1137i	0.803204	−	0.774702i
$489$		0			0
$490$	−6.97590	−	31.2941i	−0.315139	−	1.41372i
$491$		−	26.8502i		−	1.21173i	−0.795567	−	0.605866i	$-0.792827\pi$
$491$		−	26.8502i		−	1.21173i	0.795567	−	0.605866i	$-0.207173\pi$
$492$		0			0
$493$	−6.91105	−	3.99010i	−0.311258	−	0.179705i
$494$	−6.71997	−	9.72115i	−0.302346	−	0.437375i
$495$		0			0
$496$	1.74483	−	8.66918i	0.0783450	−	0.389258i
$497$	−9.82233	−	14.5865i	−0.440592	−	0.654293i
$498$		0			0
$499$	2.21925	−	1.28129i	0.0993474	−	0.0573583i	−0.449503	−	0.893279i	$-0.648399\pi$
$499$	2.21925	−	1.28129i	0.0993474	−	0.0573583i	0.548851	+	0.835921i	$0.315066\pi$
$500$	0.513119	+	3.12996i	0.0229474	+	0.139976i
$501$		0			0
$502$	0.438894	+	5.39014i	0.0195888	+	0.240574i
$503$	14.6941			0.655176			0.327588	−	0.944821i	$-0.393764\pi$
$503$	14.6941			0.655176			0.327588	+	0.944821i	$0.393764\pi$
$504$		0			0
$505$	−2.57849			−0.114741
$506$	0.759959	+	9.33319i	0.0337843	+	0.414911i
$507$		0			0
$508$	−30.5712	+	5.01177i	−1.35638	+	0.222362i
$509$	−11.0283	+	6.36720i	−0.488821	+	0.282221i	−0.724085	−	0.689710i	$-0.757738\pi$
$509$	−11.0283	+	6.36720i	−0.488821	+	0.282221i	0.235264	+	0.971932i	$0.424405\pi$
$510$		0			0
$511$	25.2273	−	1.74449i	1.11599	−	0.0771716i
$512$	16.8430	−	15.1100i	0.744364	−	0.667775i
$513$		0			0
$514$	9.97639	+	14.4319i	0.440040	+	0.636564i
$515$	−7.44968	−	4.30107i	−0.328272	−	0.189528i
$516$		0			0
$517$		−	15.9992i		−	0.703643i
$518$	−17.3100	−	6.77996i	−0.760559	−	0.297894i
$519$		0			0
$520$	−19.6821	−	20.4062i	−0.863118	−	0.894872i
$521$	17.0134	−	29.4680i	0.745369	−	1.29102i	−0.204652	−	0.978835i	$-0.565606\pi$
$521$	17.0134	−	29.4680i	0.745369	−	1.29102i	0.950022	−	0.312183i	$-0.101060\pi$
$522$		0			0
$523$	5.88515	−	3.39779i	0.257340	−	0.148575i	−0.365781	−	0.930701i	$-0.619198\pi$
$523$	5.88515	−	3.39779i	0.257340	−	0.148575i	0.623120	+	0.782126i	$0.285865\pi$
$524$	26.0119	−	21.2981i	1.13633	−	0.930413i
$525$		0			0
$526$	−0.813634	+	1.71777i	−0.0354761	+	0.0748982i
$527$	−4.37241	−	7.57324i	−0.190465	−	0.329896i
$528$		0			0
$529$	7.73296	−	13.3939i	0.336216	−	0.582343i
$530$	−11.8079	+	0.961464i	−0.512903	+	0.0417633i
$531$		0			0
$532$	−13.6822	−	4.11375i	−0.593200	−	0.178354i
$533$			6.53819i			0.283200i
$534$		0			0
$535$	−8.79392	+	15.2315i	−0.380195	+	0.658516i
$536$	−15.7529	−	4.52744i	−0.680422	−	0.195556i
$537$		0			0
$538$	−2.49282	−	1.18074i	−0.107473	−	0.0509055i
$539$	−13.3226	+	10.3757i	−0.573845	+	0.446911i
$540$		0			0
$541$	−21.3952	+	12.3525i	−0.919852	+	0.531077i	−0.883588	−	0.468266i	$-0.844879\pi$
$541$	−21.3952	+	12.3525i	−0.919852	+	0.531077i	−0.0362640	+	0.999342i	$0.511546\pi$
$542$	20.9391	+	30.2906i	0.899410	+	1.30109i
$543$		0			0
$544$	2.62022	−	22.2222i	0.112341	−	0.952769i
$545$	−44.7335			−1.91617
$546$		0			0
$547$		−	27.5793i		−	1.17920i	−0.807694	−	0.589602i	$-0.799284\pi$
$547$		−	27.5793i		−	1.17920i	0.807694	−	0.589602i	$-0.200716\pi$
$548$	−0.627083	+	1.66041i	−0.0267877	+	0.0709294i
$549$		0			0
$550$	15.4056	−	10.6495i	0.656897	−	0.454095i
$551$	2.72360	+	4.71742i	0.116029	+	0.200969i
$552$		0			0
$553$	1.94773	−	3.98563i	0.0828261	−	0.169486i
$554$	−20.5990	−	9.75690i	−0.875169	−	0.414531i
$555$		0			0
$556$	−0.790332	−	4.82093i	−0.0335175	−	0.204453i
$557$	−39.1575	−	22.6076i	−1.65916	−	0.957914i	−0.973106	−	0.230359i	$-0.926010\pi$
$557$	−39.1575	−	22.6076i	−1.65916	−	0.957914i	−0.686050	−	0.727555i	$-0.740657\pi$
$558$		0			0
$559$	35.8698			1.51713
$560$	−33.9886	−	4.42883i	−1.43628	−	0.187152i
$561$		0			0
$562$	22.7378	−	1.85144i	0.959137	−	0.0780981i
$563$	−13.1895	−	7.61497i	−0.555872	−	0.320933i	0.195615	−	0.980681i	$-0.437330\pi$
$563$	−13.1895	−	7.61497i	−0.555872	−	0.320933i	−0.751487	+	0.659748i	$0.770663\pi$
$564$		0			0
$565$	12.7174	−	7.34241i	0.535026	−	0.308898i
$566$	−33.6410	−	15.9343i	−1.41404	−	0.669769i
$567$		0			0
$568$	−18.2438	+	4.53693i	−0.765495	+	0.190365i
$569$	7.04343	+	12.1996i	0.295276	+	0.511433i	0.975049	−	0.221989i	$-0.0712551\pi$
$569$	7.04343	+	12.1996i	0.295276	+	0.511433i	−0.679773	+	0.733423i	$0.737922\pi$
$570$		0			0
$571$	19.2480	+	11.1129i	0.805505	+	0.465058i	0.845392	−	0.534146i	$-0.179367\pi$
$571$	19.2480	+	11.1129i	0.805505	+	0.465058i	−0.0398876	+	0.999204i	$0.512700\pi$
$572$	−5.27557	+	13.9689i	−0.220583	+	0.584067i
$573$		0			0
$574$	4.93260	+	6.17657i	0.205883	+	0.257805i
$575$	15.0681			0.628385
$576$		0			0
$577$	−4.68070	+	8.10721i	−0.194860	+	0.337507i	−0.946855	−	0.321662i	$-0.895759\pi$
$577$	−4.68070	+	8.10721i	−0.194860	+	0.337507i	0.751995	+	0.659169i	$0.229092\pi$
$578$	1.08834	+	1.57440i	0.0452690	+	0.0654865i
$579$		0			0
$580$	8.27890	+	10.1112i	0.343762	+	0.419844i
$581$	−14.2154	+	9.57246i	−0.589755	+	0.397133i
$582$		0			0
$583$	3.11974	+	5.40355i	0.129206	+	0.223792i
$584$	7.46724	−	25.9818i	0.308997	−	1.07513i
$585$		0			0
$586$	−1.10748	−	13.6011i	−0.0457495	−	0.561858i
$587$			13.0157i			0.537217i	0.963249	+	0.268608i	$0.0865637\pi$
$587$			13.0157i			0.537217i	−0.963249	+	0.268608i	$0.913436\pi$
$588$		0			0
$589$			5.96914i			0.245954i
$590$	56.0265	−	4.56198i	2.30658	−	0.187814i
$591$		0			0
$592$	−13.1377	+	14.9124i	−0.539954	+	0.612894i
$593$	−0.698895	−	1.21052i	−0.0287002	−	0.0497101i	0.851319	−	0.524649i	$-0.175803\pi$
$593$	−0.698895	−	1.21052i	−0.0287002	−	0.0497101i	−0.880019	+	0.474939i	$0.842470\pi$
$594$		0			0
$595$	−28.1151	+	18.9323i	−1.15261	+	0.776150i
$596$	−14.5903	+	11.9464i	−0.597644	+	0.489342i
$597$		0			0
$598$	−9.88239	+	6.83143i	−0.404121	+	0.279358i
$599$	−15.9302	+	27.5919i	−0.650891	+	1.12738i	0.332017	+	0.943274i	$0.392271\pi$
$599$	−15.9302	+	27.5919i	−0.650891	+	1.12738i	−0.982907	+	0.184102i	$0.941062\pi$
$600$		0			0
$601$	34.4927			1.40699			0.703493	−	0.710702i	$-0.251623\pi$
$601$	34.4927			1.40699			0.703493	+	0.710702i	$0.251623\pi$
$602$	33.8859	−	27.0612i	1.38109	−	1.10293i
$603$		0			0
$604$	4.98434	−	13.1977i	0.202810	−	0.537007i
$605$	14.5311	+	8.38955i	0.590775	+	0.341084i
$606$		0			0
$607$	4.61573	+	7.99467i	0.187347	+	0.324494i	0.944365	−	0.328900i	$-0.106678\pi$
$607$	4.61573	+	7.99467i	0.187347	+	0.324494i	−0.757018	+	0.653394i	$0.773345\pi$
$608$	−9.13325	+	12.2422i	−0.370402	+	0.496486i
$609$		0			0
$610$	−17.0887	+	36.0781i	−0.691901	+	1.46076i
$611$	17.7763	−	10.2631i	0.719152	−	0.415202i
$612$		0			0
$613$	28.0431	+	16.1907i	1.13265	+	0.653935i	0.944600	−	0.328225i	$-0.106450\pi$
$613$	28.0431	+	16.1907i	1.13265	+	0.653935i	0.188049	+	0.982160i	$0.439784\pi$
$614$	2.90079	+	35.6251i	0.117066	+	1.43771i
$615$		0			0
$616$	5.55473	+	17.1763i	0.223806	+	0.692054i
$617$	10.1600			0.409026			0.204513	−	0.978864i	$-0.434439\pi$
$617$	10.1600			0.409026			0.204513	+	0.978864i	$0.434439\pi$
$618$		0			0
$619$	−32.1866	−	18.5829i	−1.29369	−	0.746911i	−0.314382	−	0.949297i	$-0.601797\pi$
$619$	−32.1866	−	18.5829i	−1.29369	−	0.746911i	−0.979306	+	0.202385i	$0.935131\pi$
$620$	2.31671	+	14.1316i	0.0930412	+	0.567540i
$621$		0			0
$622$	13.6503	−	28.8190i	0.547328	−	1.15553i
$623$	−16.2392	+	33.2301i	−0.650608	+	1.33133i
$624$		0			0
$625$	11.1560	+	19.3227i	0.446240	+	0.772910i
$626$	20.4099	+	29.5252i	0.815746	+	1.18006i
$627$		0			0
$628$	16.3072	+	6.15867i	0.650727	+	0.245758i
$629$			19.6533i			0.783630i
$630$		0			0
$631$	−7.31198			−0.291085			−0.145543	−	0.989352i	$-0.546493\pi$
$631$	−7.31198			−0.291085			−0.145543	+	0.989352i	$0.546493\pi$
$632$	−3.29226	−	3.41339i	−0.130959	−	0.135777i
$633$		0			0
$634$	−19.9321	+	13.7785i	−0.791606	+	0.547216i
$635$	43.4463	−	25.0837i	1.72411	−	0.995418i
$636$		0			0
$637$	−20.0743	−	8.14664i	−0.795373	−	0.322782i
$638$	2.94622	−	6.22015i	0.116642	−	0.246258i
$639$		0			0
$640$	−16.8712	+	32.5275i	−0.666891	+	1.28576i
$641$	6.85337	−	11.8704i	0.270692	−	0.468852i	−0.698347	−	0.715759i	$-0.746081\pi$
$641$	6.85337	−	11.8704i	0.270692	−	0.468852i	0.969039	+	0.246907i	$0.0794142\pi$
$642$		0			0
$643$			30.5812i			1.20600i	0.797740	+	0.603002i	$0.206029\pi$
$643$			30.5812i			1.20600i	−0.797740	+	0.603002i	$0.793971\pi$
$644$	−4.18198	+	13.9092i	−0.164793	+	0.548098i
$645$		0			0
$646$	1.22580	+	15.0543i	0.0482286	+	0.592304i
$647$	21.2979	−	36.8891i	0.837308	−	1.45026i	−0.0548287	−	0.998496i	$-0.517461\pi$
$647$	21.2979	−	36.8891i	0.837308	−	1.45026i	0.892137	−	0.451765i	$-0.149205\pi$
$648$		0			0
$649$	−14.8026	−	25.6389i	−0.581054	−	1.00641i
$650$	21.7148	+	10.2854i	0.851723	+	0.403425i
$651$		0			0
$652$	30.6822	−	25.1222i	1.20161	−	0.983859i
$653$	−26.9273	+	15.5465i	−1.05375	+	0.608381i	−0.923696	−	0.383126i	$-0.874848\pi$
$653$	−26.9273	+	15.5465i	−1.05375	+	0.608381i	−0.130051	+	0.991507i	$0.541514\pi$
$654$		0			0
$655$	−27.2210	+	47.1481i	−1.06361	+	1.84223i
$656$	8.00791	−	2.69811i	0.312656	−	0.105343i
$657$		0			0
$658$	9.05030	−	23.1065i	0.352818	−	0.900785i
$659$			35.8472i			1.39641i	0.715899	+	0.698204i	$0.246017\pi$
$659$			35.8472i			1.39641i	−0.715899	+	0.698204i	$0.753983\pi$
$660$		0			0
$661$	23.6297	+	13.6426i	0.919087	+	0.530635i	0.883344	−	0.468726i	$-0.155287\pi$
$661$	23.6297	+	13.6426i	0.919087	+	0.530635i	0.0357432	+	0.999361i	$0.488620\pi$
$662$	−9.98820	+	6.90457i	−0.388202	+	0.268354i
$663$		0			0
$664$	4.42151	+	17.7797i	0.171588	+	0.689988i
$665$	23.0815	−	1.59611i	0.895063	−	0.0618943i
$666$		0			0
$667$	4.79566	−	2.76878i	0.185689	−	0.107208i
$668$	−43.7362	+	7.17001i	−1.69220	+	0.277416i
$669$		0			0
$670$	26.4552	−	2.15412i	1.02205	−	0.0832210i
$671$	21.0251			0.811663
$672$		0			0
$673$	−32.2963			−1.24493			−0.622465	−	0.782648i	$-0.713869\pi$
$673$	−32.2963			−1.24493			−0.622465	+	0.782648i	$0.713869\pi$
$674$	−4.48335	+	0.365058i	−0.172692	+	0.0140615i
$675$		0			0
$676$	6.75288	−	1.10705i	0.259726	−	0.0425789i
$677$	13.5785	−	7.83953i	0.521863	−	0.301298i	−0.215834	−	0.976430i	$-0.569247\pi$
$677$	13.5785	−	7.83953i	0.521863	−	0.301298i	0.737697	+	0.675132i	$0.235914\pi$
$678$		0			0
$679$	−2.03506	−	3.02213i	−0.0780983	−	0.115979i
$680$	8.74483	+	35.1646i	0.335349	+	1.34850i
$681$		0			0
$682$	6.20404	−	4.28869i	0.237565	−	0.164222i
$683$	16.5012	+	9.52698i	0.631401	+	0.364540i	0.781295	−	0.624162i	$-0.214560\pi$
$683$	16.5012	+	9.52698i	0.631401	+	0.364540i	−0.149893	+	0.988702i	$0.547893\pi$
$684$		0			0
$685$		−	2.87422i		−	0.109818i
$686$	−25.1101	+	7.44860i	−0.958709	+	0.284389i
$687$		0			0
$688$	−14.8024	−	43.9330i	−0.564335	−	1.67493i
$689$	−4.00250	+	6.93253i	−0.152483	+	0.264108i
$690$		0			0
$691$	−26.9066	+	15.5345i	−1.02358	+	0.590961i	−0.915138	−	0.403142i	$-0.867918\pi$
$691$	−26.9066	+	15.5345i	−1.02358	+	0.590961i	−0.108438	+	0.994103i	$0.534585\pi$
$692$	33.6284	−	27.5345i	1.27836	−	1.04670i
$693$		0			0
$694$	28.0956	+	13.3077i	1.06649	+	0.505153i
$695$	3.95558	+	6.85127i	0.150044	+	0.259883i
$696$		0			0
$697$	4.17820	−	7.23685i	0.158261	−	0.274115i
$698$	−1.78449	−	21.9156i	−0.0675439	−	0.829519i
$699$		0			0
$700$	28.2734	−	6.66576i	1.06863	−	0.251942i
$701$		−	33.5258i		−	1.26625i	−0.774048	−	0.633127i	$-0.781771\pi$
$701$		−	33.5258i		−	1.26625i	0.774048	−	0.633127i	$-0.218229\pi$
$702$		0			0
$703$	6.70759	−	11.6179i	0.252981	−	0.438177i
$704$	19.2860	+	0.696952i	0.726868	+	0.0262674i
$705$		0			0
$706$	−16.0793	+	33.9472i	−0.605154	+	1.27762i
$707$	0.145310	+	2.10135i	0.00546494	+	0.0790293i
$708$		0			0
$709$	−7.16576	+	4.13715i	−0.269116	+	0.155374i	−0.628486	−	0.777821i	$-0.716325\pi$
$709$	−7.16576	+	4.13715i	−0.269116	+	0.155374i	0.359370	+	0.933195i	$0.382992\pi$
$710$	25.0427	−	17.3113i	0.939834	−	0.649682i
$711$		0			0
$712$	27.4491	+	28.4590i	1.02870	+	1.06655i
$713$	6.06814			0.227254
$714$		0			0
$715$		−	24.1805i		−	0.904298i
$716$	−7.06776	−	2.66926i	−0.264135	−	0.0997548i
$717$		0			0
$718$	−24.9393	−	36.0773i	−0.930725	−	1.34639i
$719$	−1.81462	−	3.14301i	−0.0676739	−	0.117215i	0.830203	−	0.557461i	$-0.188224\pi$
$719$	−1.81462	−	3.14301i	−0.0676739	−	0.117215i	−0.897877	+	0.440246i	$0.854891\pi$
$720$		0			0
$721$	−3.08535	+	6.31352i	−0.114904	+	0.235128i
$722$	−7.08884	+	14.9662i	−0.263819	+	0.556983i
$723$		0			0
$724$	−4.54032	−	27.6954i	−0.168740	−	1.02929i
$725$	−9.59133	−	5.53756i	−0.356213	−	0.205660i
$726$		0			0
$727$	28.1550			1.04421			0.522106	−	0.852881i	$-0.325147\pi$
$727$	28.1550			1.04421			0.522106	+	0.852881i	$0.325147\pi$
$728$	−15.5209	+	17.1900i	−0.575244	+	0.637103i
$729$		0			0
$730$	3.55286	+	43.6333i	0.131497	+	1.61494i
$731$	−39.7028	−	22.9224i	−1.46846	−	0.847816i
$732$		0			0
$733$	25.4264	−	14.6799i	0.939145	−	0.542215i	0.0494525	−	0.998776i	$-0.484252\pi$
$733$	25.4264	−	14.6799i	0.939145	−	0.542215i	0.889692	+	0.456561i	$0.150919\pi$
$734$	7.73282	−	16.3258i	0.285424	−	0.602595i
$735$		0			0
$736$	12.4452	+	9.28474i	0.458737	+	0.342240i
$737$	−6.98965	−	12.1064i	−0.257467	−	0.445946i
$738$		0			0
$739$	−11.2457	−	6.49271i	−0.413680	−	0.238838i	0.278690	−	0.960381i	$-0.410100\pi$
$739$	−11.2457	−	6.49271i	−0.413680	−	0.238838i	−0.692370	+	0.721543i	$0.743433\pi$
$740$	11.3708	−	30.1081i	0.418000	−	1.10680i
$741$		0			0
$742$	1.44898	+	9.56872i	0.0531937	+	0.351279i
$743$	−21.8510			−0.801637			−0.400819	−	0.916157i	$-0.631274\pi$
$743$	−21.8510			−0.801637			−0.400819	+	0.916157i	$0.631274\pi$
$744$		0			0
$745$	15.2685	−	26.4459i	0.559396	−	0.968903i
$746$	−7.70280	+	5.32474i	−0.282020	+	0.194953i
$747$		0			0
$748$	14.7660	−	12.0902i	0.539900	−	0.442062i
$749$	12.9086	+	6.30827i	0.471668	+	0.230499i
$750$		0			0
$751$	−6.03724	−	10.4568i	−0.220302	−	0.381574i	0.734598	−	0.678503i	$-0.237371\pi$
$751$	−6.03724	−	10.4568i	−0.220302	−	0.381574i	−0.954900	+	0.296929i	$0.904038\pi$
$752$	−19.9059	−	17.5370i	−0.725895	−	0.639507i
$753$		0			0
$754$	8.80100	−	0.716624i	0.320513	−	0.0260979i
$755$			22.8456i			0.831436i
$756$		0			0
$757$			27.2309i			0.989725i	0.868971	+	0.494862i	$0.164782\pi$
$757$			27.2309i			0.989725i	−0.868971	+	0.494862i	$0.835218\pi$
$758$	2.15548	+	26.4718i	0.0782905	+	0.961501i
$759$		0			0
$760$	6.83209	−	23.7718i	0.247826	−	0.862294i
$761$	15.2423	+	26.4005i	0.552534	+	0.957017i	0.998091	+	0.0617632i	$0.0196724\pi$
$761$	15.2423	+	26.4005i	0.552534	+	0.957017i	−0.445557	+	0.895254i	$0.646994\pi$
$762$		0			0
$763$	2.52094	+	36.4557i	0.0912642	+	1.31978i
$764$	9.22262	+	11.2638i	0.333663	+	0.407509i
$765$		0			0
$766$	−16.4339	−	23.7734i	−0.593782	−	0.858969i
$767$	18.9912	−	32.8937i	0.685731	−	1.18772i
$768$		0			0
$769$	36.6991			1.32340			0.661701	−	0.749768i	$-0.269835\pi$
$769$	36.6991			1.32340			0.661701	+	0.749768i	$0.269835\pi$
$770$	−18.2425	−	22.8431i	−0.657413	−	0.823208i
$771$		0			0
$772$	−6.73696	+	17.8384i	−0.242468	+	0.642017i
$773$	28.6220	+	16.5249i	1.02946	+	0.594359i	0.916830	−	0.399277i	$-0.130739\pi$
$773$	28.6220	+	16.5249i	1.02946	+	0.594359i	0.112631	+	0.993637i	$0.464072\pi$
$774$		0			0
$775$	−6.06814	−	10.5103i	−0.217974	−	0.377542i
$776$	−3.77988	+	0.939991i	−0.135690	+	0.0337437i
$777$		0			0
$778$	3.03625	+	1.43814i	0.108855	+	0.0515600i
$779$	−4.93981	+	2.85200i	−0.176987	+	0.102183i
$780$		0			0
$781$	−13.8857	−	8.01691i	−0.496869	−	0.286867i
$782$	15.3040	−	1.24613i	0.547270	−	0.0445617i
$783$		0			0
$784$	−1.69387	+	27.9487i	−0.0604955	+	0.998168i
$785$	−28.2281			−1.00751
$786$		0			0
$787$	14.9922	+	8.65572i	0.534413	+	0.308543i	0.742811	−	0.669501i	$-0.233492\pi$
$787$	14.9922	+	8.65572i	0.534413	+	0.308543i	−0.208399	+	0.978044i	$0.566825\pi$
$788$	3.77485	+	23.0261i	0.134473	+	0.820271i
$789$		0			0
$790$	6.94055	+	3.28745i	0.246934	+	0.116962i
$791$	−6.70041	−	9.95033i	−0.238239	−	0.353793i
$792$		0			0
$793$	13.4872	+	23.3604i	0.478943	+	0.829553i
$794$	−25.7901	+	17.8280i	−0.915255	+	0.632691i
$795$		0			0
$796$	−13.4010	+	35.4837i	−0.474986	+	1.25768i
$797$			41.7331i			1.47826i	0.673561	+	0.739131i	$0.264764\pi$
$797$			41.7331i			1.47826i	−0.673561	+	0.739131i	$0.735236\pi$
$798$		0			0
$799$	−26.2345			−0.928109
$800$	3.63641	−	30.8405i	0.128566	−	1.09038i
$801$		0			0
$802$	21.1633	+	30.6150i	0.747304	+	1.08105i
$803$	19.9675	−	11.5282i	0.704638	−	0.406823i
$804$		0			0
$805$	−1.62258	−	23.4643i	−0.0571884	−	0.827010i
$806$	8.74483	+	4.14206i	0.308023	+	0.145898i
$807$		0			0
$808$	2.16419	+	0.621995i	0.0761360	+	0.0218817i
$809$	−4.86273	+	8.42250i	−0.170965	+	0.296119i	−0.938757	−	0.344579i	$-0.888022\pi$
$809$	−4.86273	+	8.42250i	−0.170965	+	0.296119i	0.767793	+	0.640698i	$0.221355\pi$
$810$		0			0
$811$		−	55.3405i		−	1.94327i	−0.236492	−	0.971633i	$-0.575998\pi$
$811$		−	55.3405i		−	1.94327i	0.236492	−	0.971633i	$-0.424002\pi$
$812$	7.77359	−	7.31672i	0.272800	−	0.256767i
$813$		0			0
$814$	−16.8943	+	1.37563i	−0.592146	+	0.0482157i
$815$	−32.1084	+	55.6134i	−1.12471	+	1.94805i
$816$		0			0
$817$	15.6466	+	27.1008i	0.547406	+	0.948135i
$818$	0.400957	−	0.846511i	0.0140191	−	0.0295976i
$819$		0			0
$820$	−10.5878	+	8.66918i	−0.369744	+	0.302741i
$821$	36.5157	−	21.0823i	1.27441	−	0.735779i	0.298592	−	0.954381i	$-0.403483\pi$
$821$	36.5157	−	21.0823i	1.27441	−	0.735779i	0.975814	+	0.218602i	$0.0701496\pi$
$822$		0			0
$823$	−7.60689	+	13.1755i	−0.265160	+	0.459270i	−0.967605	−	0.252467i	$-0.918758\pi$
$823$	−7.60689	+	13.1755i	−0.265160	+	0.459270i	0.702446	+	0.711737i	$0.252091\pi$
$824$	5.21518	+	5.40705i	0.181679	+	0.188363i
$825$		0			0
$826$	−6.87516	−	45.4019i	−0.239217	−	1.57973i
$827$			1.24390i			0.0432548i	0.999766	+	0.0216274i	$0.00688475\pi$
$827$			1.24390i			0.0432548i	−0.999766	+	0.0216274i	$0.993115\pi$
$828$		0			0
$829$	18.4517	+	10.6531i	0.640855	+	0.369998i	0.784944	−	0.619567i	$-0.212692\pi$
$829$	18.4517	+	10.6531i	0.640855	+	0.369998i	−0.144089	+	0.989565i	$0.546025\pi$
$830$	−16.8709	−	24.4056i	−0.585599	−	0.847131i
$831$		0			0
$832$	11.5972	+	21.8753i	0.402061	+	0.758389i
$833$	17.0134	+	21.8456i	0.589478	+	0.756905i
$834$		0			0
$835$	62.1557	−	35.8856i	2.15099	−	1.24187i
$836$	−12.8551	+	2.10744i	−0.444605	+	0.0728874i
$837$		0			0
$838$	−0.867111	−	10.6492i	−0.0299539	−	0.367869i
$839$	20.9379			0.722857			0.361429	−	0.932400i	$-0.382289\pi$
$839$	20.9379			0.722857			0.361429	+	0.932400i	$0.382289\pi$
$840$		0			0
$841$	24.9299			0.859651
$842$	−1.44505	−	17.7470i	−0.0497999	−	0.611601i
$843$		0			0
$844$	5.21794	+	31.8288i	0.179609	+	1.09559i
$845$	−9.59686	+	5.54075i	−0.330142	+	0.190608i
$846$		0			0
$847$	6.01820	−	12.3150i	0.206788	−	0.423148i
$848$	10.1426	+	2.04138i	0.348299	+	0.0701013i
$849$		0			0
$850$	−17.4624	−	25.2612i	−0.598955	−	0.866452i
$851$	−11.8106	−	6.81884i	−0.404861	−	0.233747i
$852$		0			0
$853$			17.4758i			0.598361i	0.954197	+	0.299180i	$0.0967133\pi$
$853$			17.4758i			0.598361i	−0.954197	+	0.299180i	$0.903287\pi$
$854$	30.3650	+	11.8933i	1.03907	+	0.406981i
$855$		0			0
$856$	11.0552	−	10.6629i	0.377858	−	0.364450i
$857$	1.75517	−	3.04005i	0.0599556	−	0.103846i	−0.834490	−	0.551024i	$-0.814237\pi$
$857$	1.75517	−	3.04005i	0.0599556	−	0.103846i	0.894445	+	0.447177i	$0.147571\pi$
$858$		0			0
$859$	4.45370	−	2.57134i	0.151958	−	0.0877331i	−0.422093	−	0.906553i	$-0.638704\pi$
$859$	4.45370	−	2.57134i	0.151958	−	0.0877331i	0.574051	+	0.818819i	$0.305371\pi$
$860$	47.5608	+	58.0870i	1.62181	+	1.98075i
$861$		0			0
$862$	−7.81230	+	16.4936i	−0.266088	+	0.561773i
$863$	−20.1410	−	34.8852i	−0.685606	−	1.18750i	−0.973246	−	0.229766i	$-0.926204\pi$
$863$	−20.1410	−	34.8852i	−0.685606	−	1.18750i	0.287640	−	0.957739i	$-0.407129\pi$
$864$		0			0
$865$	−35.1916	+	60.9536i	−1.19655	+	2.07248i
$866$	−57.2016	+	4.65766i	−1.94379	+	0.158274i
$867$		0			0
$868$	11.3861	−	2.68439i	0.386468	−	0.0911142i
$869$		−	4.04471i		−	0.137207i
$870$		0			0
$871$	8.96744	−	15.5321i	0.303850	−	0.526284i
$872$	37.5460	+	10.7908i	1.27147	+	0.365423i
$873$		0			0
$874$	−9.47212	−	4.48655i	−0.320399	−	0.151760i
$875$	−3.48031	+	2.34359i	−0.117656	+	0.0792277i
$876$		0			0
$877$	−36.3471	+	20.9850i	−1.22735	+	0.708613i	−0.966476	−	0.256759i	$-0.917345\pi$
$877$	−36.3471	+	20.9850i	−1.22735	+	0.708613i	−0.260878	+	0.965372i	$0.584012\pi$
$878$	−29.3157	−	42.4083i	−0.989357	−	1.43121i
$879$		0			0
$880$	−29.6160	+	9.97854i	−0.998355	+	0.336376i
$881$	16.5992			0.559241			0.279620	−	0.960111i	$-0.409791\pi$
$881$	16.5992			0.559241			0.279620	+	0.960111i	$0.409791\pi$
$882$		0			0
$883$		−	12.8210i		−	0.431462i	−0.976453	−	0.215731i	$-0.930787\pi$
$883$		−	12.8210i		−	0.431462i	0.976453	−	0.215731i	$-0.0692135\pi$
$884$	22.9053	+	8.65056i	0.770388	+	0.290950i
$885$		0			0
$886$	−37.7831	+	26.1184i	−1.26935	+	0.877465i
$887$	4.14980	+	7.18766i	0.139337	+	0.241338i	0.927246	−	0.374454i	$-0.122170\pi$
$887$	4.14980	+	7.18766i	0.139337	+	0.241338i	−0.787909	+	0.615792i	$0.788836\pi$
$888$		0			0
$889$	−22.8905	−	33.9931i	−0.767722	−	1.14009i
$890$	−57.8666	−	27.4090i	−1.93969	−	0.918751i
$891$		0			0
$892$	−15.2263	+	2.49616i	−0.509814	+	0.0835777i
$893$	15.5083	+	8.95370i	0.518964	+	0.299624i
$894$		0			0
$895$	12.2345			0.408954
$896$	27.4592	+	11.9161i	0.917346	+	0.398090i
$897$		0			0
$898$	−36.6234	+	2.98207i	−1.22214	+	0.0995130i
$899$	−3.86255	−	2.23005i	−0.128823	−	0.0743762i
$900$		0			0
$901$	8.86041	−	5.11556i	0.295183	−	0.170424i
$902$	6.51337	+	3.08511i	0.216872	+	0.102723i
$903$		0			0
$904$	−12.4452	+	3.09491i	−0.413922	+	0.102935i
$905$	22.7241	+	39.3593i	0.755376	+	1.30835i
$906$		0			0
$907$	14.2277	+	8.21434i	0.472422	+	0.272753i	0.717253	−	0.696813i	$-0.245399\pi$
$907$	14.2277	+	8.21434i	0.472422	+	0.272753i	−0.244831	+	0.969566i	$0.578733\pi$
$908$	−3.97516	−	1.50129i	−0.131920	−	0.0498219i
$909$		0			0
$910$	13.6782	−	34.9221i	0.453429	−	1.15766i
$911$	37.1630			1.23127			0.615633	−	0.788033i	$-0.288900\pi$
$911$	37.1630			1.23127			0.615633	+	0.788033i	$0.288900\pi$
$912$		0			0
$913$	−7.81297	+	13.5325i	−0.258571	+	0.447859i
$914$	9.22300	+	13.3420i	0.305070	+	0.441316i
$915$		0			0
$916$	−14.4965	+	11.8695i	−0.478978	+	0.392180i
$917$	39.9575	+	19.5268i	1.31951	+	0.644831i
$918$		0			0
$919$	18.1528	+	31.4416i	0.598806	+	1.03716i	0.992998	+	0.118135i	$0.0376914\pi$
$919$	18.1528	+	31.4416i	0.598806	+	1.03716i	−0.394191	+	0.919028i	$0.628975\pi$
$920$	−24.1661	−	6.94541i	−0.796732	−	0.228983i
$921$		0			0
$922$	−2.89197	−	35.5168i	−0.0952419	−	1.16968i
$923$		−	20.5707i		−	0.677094i
$924$		0			0
$925$			27.2754i			0.896809i
$926$	−44.8551	+	3.65234i	−1.47403	+	0.120023i
$927$		0			0
$928$	−4.50962	−	10.4837i	−0.148035	−	0.344143i
$929$	−10.8263	−	18.7518i	−0.355201	−	0.615226i	0.631952	−	0.775008i	$-0.282254\pi$
$929$	−10.8263	−	18.7518i	−0.355201	−	0.615226i	−0.987152	+	0.159782i	$0.948921\pi$
$930$		0			0
$931$	−2.60150	−	18.7204i	−0.0852608	−	0.613536i
$932$	−11.1845	−	13.6599i	−0.366362	−	0.447445i
$933$		0			0
$934$	−16.5344	+	11.4298i	−0.541022	+	0.373994i
$935$	−15.4524	+	26.7644i	−0.505348	+	0.875288i
$936$		0			0
$937$	−15.8637			−0.518245			−0.259123	−	0.965844i	$-0.583433\pi$
$937$	−15.8637			−0.518245			−0.259123	+	0.965844i	$0.583433\pi$
$938$	−3.24638	−	21.4383i	−0.105998	−	0.699986i
$939$		0			0
$940$	40.1901	+	15.1785i	1.31086	+	0.495067i
$941$	12.7230	+	7.34561i	0.414757	+	0.239460i	0.692832	−	0.721099i	$-0.256363\pi$
$941$	12.7230	+	7.34561i	0.414757	+	0.239460i	−0.278075	+	0.960559i	$0.589696\pi$
$942$		0			0
$943$	2.89930	+	5.02174i	0.0944143	+	0.163530i
$944$	−48.1249	−	9.68600i	−1.56633	−	0.315252i
$945$		0			0
$946$	16.9255	−	35.7337i	0.550296	−	1.16180i
$947$	12.0598	−	6.96270i	0.391889	−	0.226257i	−0.291089	−	0.956696i	$-0.594018\pi$
$947$	12.0598	−	6.96270i	0.391889	−	0.226257i	0.682978	+	0.730439i	$0.260684\pi$
$948$		0			0
$949$	25.6175	+	14.7903i	0.831579	+	0.480112i
$950$	1.70120	+	20.8927i	0.0551942	+	0.677850i
$951$		0			0
$952$	28.1647	−	9.10831i	0.912823	−	0.295202i
$953$	−11.2883			−0.365663			−0.182831	−	0.983144i	$-0.558526\pi$
$953$	−11.2883			−0.365663			−0.182831	+	0.983144i	$0.558526\pi$
$954$		0			0
$955$	−20.4163	−	11.7873i	−0.660655	−	0.381430i
$956$	−11.7134	+	1.92027i	−0.378839	+	0.0621060i
$957$		0			0
$958$	−6.98631	+	14.7497i	−0.225717	+	0.476541i
$959$	−2.34236	+	0.161976i	−0.0756386	+	0.00523047i
$960$		0			0
$961$	13.0563	+	22.6141i	0.421170	+	0.729488i
$962$	−12.3658	−	17.8885i	−0.398690	−	0.576747i
$963$		0			0
$964$	7.55097	−	19.9937i	0.243200	−	0.643955i
$965$		−	30.8787i		−	0.994020i
$966$		0			0
$967$	−36.4276			−1.17143			−0.585716	−	0.810517i	$-0.699187\pi$
$967$	−36.4276			−1.17143			−0.585716	+	0.810517i	$0.699187\pi$
$968$	−10.1726	−	10.5468i	−0.326959	−	0.338988i
$969$		0			0
$970$	5.18851	−	3.58668i	0.166593	−	0.115161i
$971$	−5.75503	+	3.32267i	−0.184688	+	0.106629i	−0.589493	−	0.807773i	$-0.700673\pi$
$971$	−5.75503	+	3.32267i	−0.184688	+	0.106629i	0.404806	+	0.914403i	$0.367339\pi$
$972$		0			0
$973$	5.36055	−	3.60971i	0.171851	−	0.115722i
$974$	10.6647	−	22.5156i	0.341719	−	0.721446i
$975$		0			0
$976$	23.0459	−	26.1591i	0.737682	−	0.837332i
$977$	−22.7226	+	39.3567i	−0.726961	+	1.25913i	0.231201	+	0.972906i	$0.425735\pi$
$977$	−22.7226	+	39.3567i	−0.726961	+	1.25913i	−0.958162	+	0.286227i	$0.907599\pi$
$978$		0			0
$979$			33.7226i			1.07778i
$980$	−13.4246	−	43.3100i	−0.428833	−	1.38349i
$981$		0			0
$982$	−3.08168	−	37.8466i	−0.0983402	−	1.20773i
$983$	−9.26538	+	16.0481i	−0.295520	+	0.511855i	−0.975106	−	0.221741i	$-0.928826\pi$
$983$	−9.26538	+	16.0481i	−0.295520	+	0.511855i	0.679586	+	0.733596i	$0.262159\pi$
$984$		0			0
$985$	−18.8930	−	32.7236i	−0.601980	−	1.04266i
$986$	−10.1994	−	4.83104i	−0.324816	−	0.153852i
$987$		0			0
$988$	−10.5878	−	12.9312i	−0.336844	−	0.411395i
$989$	27.5503	−	15.9061i	0.876047	−	0.505786i
$990$		0			0
$991$	18.2392	−	31.5911i	0.579386	−	1.00353i	−0.416164	−	0.909290i	$-0.636626\pi$
$991$	18.2392	−	31.5911i	0.579386	−	1.00353i	0.995550	−	0.0942363i	$-0.0300409\pi$
$992$	1.46443	−	12.4199i	0.0464957	−	0.394332i
$993$		0			0
$994$	−15.5192	−	19.4330i	−0.492239	−	0.616378i
$995$		−	61.4232i		−	1.94724i
$996$		0			0
$997$	13.2738	+	7.66365i	0.420386	+	0.242710i	0.695243	−	0.718775i	$-0.255297\pi$
$997$	13.2738	+	7.66365i	0.420386	+	0.242710i	−0.274856	+	0.961485i	$0.588630\pi$
$998$	2.98109	−	2.06075i	0.0943647	−	0.0652318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.c.109.6		12
3.2	odd	2		56.2.p.a.53.1	yes	12
4.3	odd	2		2016.2.cr.c.1873.1		12
7.2	even	3	inner	504.2.cj.c.37.2		12
8.3	odd	2		2016.2.cr.c.1873.6		12
8.5	even	2	inner	504.2.cj.c.109.2		12
12.11	even	2		224.2.t.a.81.4		12
21.2	odd	6		56.2.p.a.37.5	yes	12
21.5	even	6		392.2.p.g.373.5		12
21.11	odd	6		392.2.b.e.197.3		6
21.17	even	6		392.2.b.f.197.3		6
21.20	even	2		392.2.p.g.165.1		12
24.5	odd	2		56.2.p.a.53.5	yes	12
24.11	even	2		224.2.t.a.81.3		12
28.23	odd	6		2016.2.cr.c.1297.6		12
56.37	even	6	inner	504.2.cj.c.37.6		12
56.51	odd	6		2016.2.cr.c.1297.1		12
84.11	even	6		1568.2.b.f.785.3		6
84.23	even	6		224.2.t.a.177.3		12
84.47	odd	6		1568.2.t.g.177.4		12
84.59	odd	6		1568.2.b.e.785.4		6
84.83	odd	2		1568.2.t.g.753.3		12
168.5	even	6		392.2.p.g.373.1		12
168.11	even	6		1568.2.b.f.785.4		6
168.53	odd	6		392.2.b.e.197.4		6
168.59	odd	6		1568.2.b.e.785.3		6
168.83	odd	2		1568.2.t.g.753.4		12
168.101	even	6		392.2.b.f.197.4		6
168.107	even	6		224.2.t.a.177.4		12
168.125	even	2		392.2.p.g.165.5		12
168.131	odd	6		1568.2.t.g.177.3		12
168.149	odd	6		56.2.p.a.37.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.1	✓	12	168.149	odd	6
56.2.p.a.37.5	yes	12	21.2	odd	6
56.2.p.a.53.1	yes	12	3.2	odd	2
56.2.p.a.53.5	yes	12	24.5	odd	2
224.2.t.a.81.3		12	24.11	even	2
224.2.t.a.81.4		12	12.11	even	2
224.2.t.a.177.3		12	84.23	even	6
224.2.t.a.177.4		12	168.107	even	6
392.2.b.e.197.3		6	21.11	odd	6
392.2.b.e.197.4		6	168.53	odd	6
392.2.b.f.197.3		6	21.17	even	6
392.2.b.f.197.4		6	168.101	even	6
392.2.p.g.165.1		12	21.20	even	2
392.2.p.g.165.5		12	168.125	even	2
392.2.p.g.373.1		12	168.5	even	6
392.2.p.g.373.5		12	21.5	even	6
504.2.cj.c.37.2		12	7.2	even	3	inner
504.2.cj.c.37.6		12	56.37	even	6	inner
504.2.cj.c.109.2		12	8.5	even	2	inner
504.2.cj.c.109.6		12	1.1	even	1	trivial
1568.2.b.e.785.3		6	168.59	odd	6
1568.2.b.e.785.4		6	84.59	odd	6
1568.2.b.f.785.3		6	84.11	even	6
1568.2.b.f.785.4		6	168.11	even	6
1568.2.t.g.177.3		12	168.131	odd	6
1568.2.t.g.177.4		12	84.47	odd	6
1568.2.t.g.753.3		12	84.83	odd	2
1568.2.t.g.753.4		12	168.83	odd	2
2016.2.cr.c.1297.1		12	56.51	odd	6
2016.2.cr.c.1297.6		12	28.23	odd	6
2016.2.cr.c.1873.1		12	4.3	odd	2
2016.2.cr.c.1873.6		12	8.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40955 - 0.114773i) q^{2} +(1.97365 - 0.323556i) q^{4} +(-2.80486 + 1.61939i) q^{5} +(1.47779 + 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +O(q^{10})\)	\(q+(1.40955 - 0.114773i) q^{2} +(1.97365 - 0.323556i) q^{4} +(-2.80486 + 1.61939i) q^{5} +(1.47779 + 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +(-3.76772 + 2.60453i) q^{10} +(2.08913 + 1.20616i) q^{11} +3.09491i q^{13} +(2.33490 + 2.92374i) q^{14} +(3.79062 - 1.27718i) q^{16} +(1.97779 - 3.42563i) q^{17} +(-2.33831 + 1.35002i) q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +(1.37241 + 2.37709i) q^{23} +(2.74483 - 4.75418i) q^{25} +(0.355213 + 4.36243i) q^{26} +(3.62672 + 3.85317i) q^{28} -2.01745i q^{29} +(1.10538 - 1.91457i) q^{31} +(5.19648 - 2.23530i) q^{32} +(2.39462 - 5.05560i) q^{34} +(-7.69885 - 3.76234i) q^{35} +(-4.30285 + 2.48425i) q^{37} +(-3.14101 + 2.17130i) q^{38} +(-6.59347 + 6.35951i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(4.51349 + 1.70459i) q^{44} +(2.20731 + 3.19311i) q^{46} +(-3.31613 - 5.74371i) q^{47} +(-2.63227 + 6.48623i) q^{49} +(3.32331 - 7.01628i) q^{50} +(1.00138 + 6.10829i) q^{52} +(2.23998 + 1.29325i) q^{53} -7.81297 q^{55} +(5.55427 + 5.01498i) q^{56} +(-0.231549 - 2.84370i) q^{58} +(-10.6283 - 6.13625i) q^{59} +(7.54801 - 4.35784i) q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} +(-5.01186 - 8.68080i) q^{65} +(-5.01858 - 2.89748i) q^{67} +(2.79509 - 7.40094i) q^{68} +(-11.2837 - 4.41959i) q^{70} -6.64663 q^{71} +(4.77890 - 8.27729i) q^{73} +(-5.77995 + 3.99553i) q^{74} +(-4.17820 + 3.42105i) q^{76} +(0.440297 + 6.36720i) q^{77} +(-0.838343 - 1.45205i) q^{79} +(-8.56392 + 9.72078i) q^{80} +(2.97775 - 0.242465i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(-1.33021 - 16.3365i) q^{86} +(6.55762 + 1.88468i) q^{88} +(6.98965 + 12.1064i) q^{89} +(-6.79200 + 4.57363i) q^{91} +(3.47779 + 4.24750i) q^{92} +(-5.33347 - 7.71544i) q^{94} +(4.37241 - 7.57324i) q^{95} -1.37709 q^{97} +(-2.96587 + 9.44477i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40} + 8 q^{41} + 30 q^{44} - 4 q^{46} - 30 q^{47} - 12 q^{49} + 16 q^{50} - 32 q^{52} + 4 q^{55} + 40 q^{56} - 22 q^{58} + 28 q^{62} + 24 q^{64} - 8 q^{65} - 4 q^{68} - 48 q^{70} - 32 q^{71} - 10 q^{73} - 18 q^{74} + 52 q^{76} - 22 q^{79} - 36 q^{80} - 26 q^{82} - 40 q^{86} - 14 q^{88} + 10 q^{89} + 20 q^{92} + 42 q^{94} + 34 q^{95} + 40 q^{97} - 52 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

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