LMFDB - Embedded newform 504.2.cj.c.37.2

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			37.2
Root			$-0.981777 - 1.01790i$ of defining polynomial
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.c.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.804171 - 1.16332i) q^{2} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(1.47779 - 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +O(q^{10})$	\(q+(-0.804171 - 1.16332i) q^{2} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(1.47779 - 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +(-0.371724 - 4.56521i) q^{10} +(-2.08913 + 1.20616i) q^{11} +3.09491i q^{13} +(-3.74138 + 0.0456667i) q^{14} +(-3.00138 - 2.64419i) q^{16} +(1.97779 + 3.42563i) q^{17} +(2.33831 + 1.35002i) q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +(1.37241 - 2.37709i) q^{23} +(2.74483 + 4.75418i) q^{25} +(3.60037 - 2.48884i) q^{26} +(3.06183 + 4.31569i) q^{28} -2.01745i q^{29} +(1.10538 + 1.91457i) q^{31} +(-0.662411 + 5.61794i) q^{32} +(2.39462 - 5.05560i) q^{34} +(7.69885 - 3.76234i) q^{35} +(4.30285 + 2.48425i) q^{37} +(-0.309892 - 3.80584i) q^{38} +(8.80423 + 2.53036i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(-0.780522 - 4.76109i) q^{44} +(-3.86897 + 0.315032i) q^{46} +(-3.31613 + 5.74371i) q^{47} +(-2.63227 - 6.48623i) q^{49} +(3.32331 - 7.01628i) q^{50} +(-5.79062 - 2.18693i) q^{52} +(-2.23998 + 1.29325i) q^{53} -7.81297 q^{55} +(2.55829 - 7.03244i) q^{56} +(-2.34694 + 1.62238i) q^{58} +(10.6283 - 6.13625i) q^{59} +(-7.54801 - 4.35784i) q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} +(-5.01186 + 8.68080i) q^{65} +(5.01858 - 2.89748i) q^{67} +(-7.80695 + 1.27985i) q^{68} +(-10.5680 - 5.93065i) q^{70} -6.64663 q^{71} +(4.77890 + 8.27729i) q^{73} +(-0.570250 - 7.00335i) q^{74} +(-4.17820 + 3.42105i) q^{76} +(-0.440297 + 6.36720i) q^{77} +(-0.838343 + 1.45205i) q^{79} +(-4.13648 - 12.2770i) q^{80} +(-1.69886 - 2.45758i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(-13.4828 + 9.32027i) q^{86} +(-4.91099 + 4.73673i) q^{88} +(6.98965 - 12.1064i) q^{89} +(6.79200 + 4.57363i) q^{91} +(3.47779 + 4.24750i) q^{92} +(9.34850 - 0.761205i) q^{94} +(4.37241 + 7.57324i) q^{95} -1.37709 q^{97} +(-5.42876 + 8.27820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.804171	−	1.16332i	−0.568635	−	0.822590i
$2$	−0.804171	−	1.16332i	−0.568635	−	0.822590i
$3$		0			0
$3$		0			0
$4$	−0.706619	+	1.87101i	−0.353310	+	0.935506i
$5$	2.80486	+	1.61939i	1.25437	+	0.724212i	0.971975	−	0.235086i	$-0.0755372\pi$
$5$	2.80486	+	1.61939i	1.25437	+	0.724212i	0.282397	+	0.959298i	$0.408870\pi$
$6$		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
$10$	−0.371724	−	4.56521i	−0.117549	−	1.44365i
$11$	−2.08913	+	1.20616i	−0.629897	+	0.363671i	−0.780712	−	0.624891i	$-0.785144\pi$
$11$	−2.08913	+	1.20616i	−0.629897	+	0.363671i	0.150815	+	0.988562i	$0.451810\pi$
$12$		0			0
$13$			3.09491i			0.858375i	0.903216	+	0.429187i	$0.141200\pi$
$13$			3.09491i			0.858375i	−0.903216	+	0.429187i	$0.858800\pi$
$14$	−3.74138	+	0.0456667i	−0.999926	+	0.0122049i
$15$		0			0
$16$	−3.00138	−	2.64419i	−0.750345	−	0.661047i
$17$	1.97779	+	3.42563i	0.479685	+	0.830838i	0.999728	−	0.0233012i	$-0.00741769\pi$
$17$	1.97779	+	3.42563i	0.479685	+	0.830838i	−0.520044	+	0.854140i	$0.674084\pi$
$18$		0			0
$19$	2.33831	+	1.35002i	0.536444	+	0.309716i	0.743637	−	0.668584i	$-0.233099\pi$
$19$	2.33831	+	1.35002i	0.536444	+	0.309716i	−0.207192	+	0.978300i	$0.566433\pi$
$20$	−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	−0.686724	−	0.726918i	$-0.740952\pi$
$23$	1.37241	−	2.37709i	0.286168	−	0.495657i	0.972892	+	0.231261i	$0.0742852\pi$
$24$		0			0
$25$	2.74483	+	4.75418i	0.548965	+	0.950836i
$26$	3.60037	−	2.48884i	0.706091	−	0.488101i
$27$		0			0
$28$	3.06183	+	4.31569i	0.578632	+	0.815589i
$29$		−	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	0.948053	−	0.318114i	$-0.103049\pi$
$31$	1.10538	+	1.91457i	0.198532	+	0.343867i	−0.749521	+	0.661981i	$0.769716\pi$
$32$	−0.662411	+	5.61794i	−0.117099	+	0.993120i
$33$		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	$-0.199417\pi$
$37$	4.30285	+	2.48425i	0.707385	+	0.408409i	−0.102707	+	0.994712i	$0.532751\pi$
$38$	−0.309892	−	3.80584i	−0.0502711	−	0.617389i
$39$		0			0
$40$	8.80423	+	2.53036i	1.39207	+	0.400086i
$41$	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	$-0.344971\pi$
$44$	−0.780522	−	4.76109i	−0.117668	−	0.717762i
$45$		0			0
$46$	−3.86897	+	0.315032i	−0.570448	+	0.0464489i
$47$	−3.31613	+	5.74371i	−0.483708	+	0.837807i	−0.999825	−	0.0187115i	$-0.994044\pi$
$47$	−3.31613	+	5.74371i	−0.483708	+	0.837807i	0.516117	+	0.856518i	$0.327377\pi$
$48$		0			0
$49$	−2.63227	−	6.48623i	−0.376038	−	0.926604i
$50$	3.32331	−	7.01628i	0.469988	−	0.992251i
$51$		0			0
$52$	−5.79062	−	2.18693i	−0.803015	−	0.303272i
$53$	−2.23998	+	1.29325i	−0.307684	+	0.177642i	−0.645890	−	0.763431i	$-0.723513\pi$
$53$	−2.23998	+	1.29325i	−0.307684	+	0.177642i	0.338205	+	0.941072i	$0.390180\pi$
$54$		0			0
$55$	−7.81297			−1.05350
$56$	2.55829	−	7.03244i	0.341865	−	0.939749i
$57$		0			0
$58$	−2.34694	+	1.62238i	−0.308168	+	0.213028i
$59$	10.6283	−	6.13625i	1.38369	−	0.798872i	0.391093	−	0.920351i	$-0.372097\pi$
$59$	10.6283	−	6.13625i	1.38369	−	0.798872i	0.992594	+	0.121479i	$0.0387638\pi$
$60$		0			0
$61$	−7.54801	−	4.35784i	−0.966424	−	0.557965i	−0.0682795	−	0.997666i	$-0.521751\pi$
$61$	−7.54801	−	4.35784i	−0.966424	−	0.557965i	−0.898144	+	0.439701i	$0.855084\pi$
$62$	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	$-0.551494\pi$
$67$	5.01858	−	2.89748i	0.613117	−	0.353983i	0.774184	+	0.632960i	$0.218160\pi$
$68$	−7.80695	+	1.27985i	−0.946732	+	0.155205i
$69$		0			0
$70$	−10.5680	−	5.93065i	−1.26312	−	0.708848i
$71$	−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	0.997553	+	0.0699184i	$0.0222739\pi$
$73$	4.77890	+	8.27729i	0.559328	+	0.968784i	−0.438225	+	0.898865i	$0.644393\pi$
$74$	−0.570250	−	7.00335i	−0.0662903	−	0.814123i
$75$		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	−0.909325	−	0.416087i	$-0.863401\pi$
$79$	−0.838343	+	1.45205i	−0.0943209	+	0.163369i	0.815004	+	0.579455i	$0.196735\pi$
$80$	−4.13648	−	12.2770i	−0.462473	−	1.37261i
$81$		0			0
$82$	−1.69886	−	2.45758i	−0.187607	−	0.271394i
$83$			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
$86$	−13.4828	+	9.32027i	−1.45388	+	1.00503i
$87$		0			0
$88$	−4.91099	+	4.73673i	−0.523513	+	0.504937i
$89$	6.98965	−	12.1064i	0.740902	−	1.28328i	−0.211184	−	0.977446i	$-0.567732\pi$
$89$	6.98965	−	12.1064i	0.740902	−	1.28328i	0.952085	−	0.305833i	$-0.0989349\pi$
$90$		0			0
$91$	6.79200	+	4.57363i	0.711995	+	0.479447i
$92$	3.47779	+	4.24750i	0.362585	+	0.442832i
$93$		0			0
$94$	9.34850	−	0.761205i	0.964224	−	0.0785123i
$95$	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	$0.522272\pi$
$98$	−5.42876	+	8.27820i	−0.548387	+	0.836224i
$99$		0			0
$100$	−10.8347	+	1.77621i	−1.08347	+	0.177621i
$101$	−0.689470	+	0.398066i	−0.0686048	+	0.0396090i	−0.533910	−	0.845541i	$-0.679278\pi$
$101$	−0.689470	+	0.398066i	−0.0686048	+	0.0396090i	0.465305	+	0.885150i	$0.345945\pi$
$102$		0			0
$103$	1.32799	−	2.30015i	0.130851	−	0.226641i	−0.793154	−	0.609022i	$-0.791562\pi$
$103$	1.32799	−	2.30015i	0.130851	−	0.226641i	0.924005	+	0.382381i	$0.124896\pi$
$104$	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	$-0.417877\pi$
$107$	−4.70287	−	2.71520i	−0.454643	−	0.262489i	−0.709789	+	0.704414i	$0.751210\pi$
$108$		0			0
$109$	−11.9614	+	6.90593i	−1.14570	+	0.661468i	−0.947835	−	0.318762i	$-0.896733\pi$
$109$	−11.9614	+	6.90593i	−1.14570	+	0.661468i	−0.197862	+	0.980230i	$0.563400\pi$
$110$	6.28296	+	9.08897i	0.599057	+	0.866599i
$111$		0			0
$112$	−10.2383	+	2.67918i	−0.967425	+	0.253158i
$113$	−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
$116$	3.77468	+	1.42557i	0.350470	+	0.132361i
$117$		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
$122$	1.00033	+	12.2852i	0.0905653	+	1.11225i
$123$		0			0
$124$	−4.36327	+	0.715304i	−0.391833	+	0.0642362i
$125$			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	$0.741179\pi$
$128$	−10.0432	−	5.20912i	−0.887698	−	0.460426i
$129$		0			0
$130$	14.1289	−	1.15045i	1.23919	−	0.100901i
$131$	−14.5574	−	8.40471i	−1.27189	−	0.734323i	−0.296543	−	0.955020i	$-0.595834\pi$
$131$	−14.5574	−	8.40471i	−1.27189	−	0.734323i	−0.975343	+	0.220696i	$0.929167\pi$
$132$		0			0
$133$	6.41824	−	3.13652i	0.556532	−	0.271971i
$134$	−7.40648	−	3.50814i	−0.639823	−	0.303057i
$135$		0			0
$136$	7.76700	+	8.05275i	0.666015	+	0.690518i
$137$	−0.443721	−	0.768547i	−0.0379096	−	0.0656614i	0.846448	−	0.532471i	$-0.178737\pi$
$137$	−0.443721	−	0.768547i	−0.0379096	−	0.0656614i	−0.884358	+	0.466810i	$0.845403\pi$
$138$		0			0
$139$		−	2.44264i		−	0.207182i	−0.994620	−	0.103591i	$-0.966967\pi$
$139$		−	2.44264i		−	0.207182i	0.994620	−	0.103591i	$-0.0330333\pi$
$140$	1.59924	+	17.0632i	0.135160	+	1.44210i
$141$		0			0
$142$	5.34502	+	7.73215i	0.448544	+	0.648867i
$143$	−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	$-0.207117\pi$
$149$	8.16541	+	4.71430i	0.668936	+	0.386210i	−0.126737	+	0.991936i	$0.540451\pi$
$150$		0			0
$151$	3.52689	+	6.10875i	0.287014	+	0.497123i	0.973096	−	0.230402i	$-0.0740040\pi$
$151$	3.52689	+	6.10875i	0.287014	+	0.497123i	−0.686081	+	0.727525i	$0.740671\pi$
$152$	7.33975	+	2.10947i	0.595333	+	0.171100i
$153$		0			0
$154$	7.76116	−	4.60811i	0.625412	−	0.371332i
$155$			7.16014i			0.575116i
$156$		0			0
$157$	−7.54801	+	4.35784i	−0.602397	+	0.347794i	−0.769984	−	0.638063i	$-0.779736\pi$
$157$	−7.54801	+	4.35784i	−0.602397	+	0.347794i	0.167587	+	0.985857i	$0.446402\pi$
$158$	2.36337	−	0.192438i	0.188020	−	0.0153096i
$159$		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	$-0.616343\pi$
$163$	−17.1711	−	9.91376i	−1.34495	−	0.776505i	−0.987529	+	0.157439i	$0.949676\pi$
$164$	−1.49277	+	3.95262i	−0.116566	+	0.308648i
$165$		0			0
$166$	7.53545	−	5.20905i	0.584864	−	0.404301i
$167$	−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
$170$	14.9035	−	10.3024i	1.14305	−	0.790159i
$171$		0			0
$172$	21.6849	+	8.18965i	1.65346	+	0.624455i
$173$	−18.8200	−	10.8657i	−1.43086	−	0.826105i	−0.433669	−	0.901072i	$-0.642781\pi$
$173$	−18.8200	−	10.8657i	−1.43086	−	0.826105i	−0.997186	+	0.0749674i	$0.976115\pi$
$174$		0			0
$175$	14.4897	+	1.00197i	1.09531	+	0.0757419i
$176$	9.45960	+	1.90391i	0.713044	+	0.143513i
$177$		0			0
$178$	−19.7045	+	1.60445i	−1.47692	+	0.120258i
$179$	3.27141	−	1.88875i	0.244517	−	0.141172i	−0.372734	−	0.927938i	$-0.621580\pi$
$179$	3.27141	−	1.88875i	0.244517	−	0.141172i	0.617251	+	0.786766i	$0.288246\pi$
$180$		0			0
$181$		−	14.0326i		−	1.04303i	−0.853242	−	0.521516i	$-0.825367\pi$
$181$		−	14.0326i		−	1.04303i	0.853242	−	0.521516i	$-0.174633\pi$
$182$	−0.141334	−	11.5792i	−0.0104764	−	0.858311i
$183$		0			0
$184$	2.14446	−	7.46149i	0.158091	−	0.550069i
$185$	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	−0.703786	−	0.710412i	$-0.748509\pi$
$191$	3.63945	−	6.30371i	0.263341	−	0.456120i	0.967128	+	0.254291i	$0.0818422\pi$
$192$		0			0
$193$	−4.76704	−	8.25675i	−0.343139	−	0.594334i	0.641875	−	0.766809i	$-0.278157\pi$
$193$	−4.76704	−	8.25675i	−0.343139	−	0.594334i	−0.985014	+	0.172476i	$0.944823\pi$
$194$	1.10742	+	1.60200i	0.0795080	+	0.115017i
$195$		0			0
$196$	13.9958	−	0.341713i	0.999702	−	0.0244080i
$197$			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	−0.977280	−	0.211950i	$-0.932018\pi$
$199$	−9.48247	−	16.4241i	−0.672195	−	1.16428i	0.305086	−	0.952325i	$-0.401315\pi$
$200$	10.7792	+	11.1758i	0.762206	+	0.790248i
$201$		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
$206$	−3.74375	+	0.304836i	−0.260839	+	0.0212389i
$207$		0			0
$208$	8.18353	−	9.28901i	0.567426	−	0.644077i
$209$	−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	$0.812677\pi$
$212$	−0.836879	−	5.10486i	−0.0574771	−	0.350603i
$213$		0			0
$214$	0.623264	+	7.65442i	0.0426054	+	0.523245i
$215$	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
$220$	5.52079	−	14.6182i	0.372212	−	0.985556i
$221$	−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	$0.583165\pi$
$224$	11.3500	+	9.75584i	0.758357	+	0.651840i
$225$		0			0
$226$	3.64617	+	5.27457i	0.242539	+	0.350859i
$227$	1.83996	−	1.06230i	0.122122	−	0.0705074i	−0.437694	−	0.899124i	$-0.644205\pi$
$227$	1.83996	−	1.06230i	0.122122	−	0.0705074i	0.559817	+	0.828616i	$0.310871\pi$
$228$		0			0
$229$	8.11289	+	4.68398i	0.536115	+	0.309526i	0.743503	−	0.668733i	$-0.233163\pi$
$229$	8.11289	+	4.68398i	0.536115	+	0.309526i	−0.207388	+	0.978259i	$0.566496\pi$
$230$	−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	−0.973607	−	0.228232i	$-0.926706\pi$
$233$	−4.41366	+	7.64469i	−0.289149	+	0.500820i	0.684458	+	0.729052i	$0.260039\pi$
$234$		0			0
$235$	−18.6026	+	10.7402i	−1.21350	+	0.700614i
$236$	3.97085	+	24.2217i	0.258480	+	1.57670i
$237$		0			0
$238$	−7.55610	−	12.7263i	−0.489789	−	0.824922i
$239$	−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	0.985203	−	0.171389i	$-0.0548255\pi$
$241$	5.34302	+	9.25439i	0.344174	+	0.596128i	−0.641029	+	0.767517i	$0.721492\pi$
$242$	7.30245	−	0.594604i	0.469419	−	0.0382226i
$243$		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
$248$	4.34094	+	4.50064i	0.275650	+	0.285791i
$249$		0			0
$250$	1.84487	−	1.27531i	0.116680	−	0.0806578i
$251$			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
$254$	12.4563	+	18.0194i	0.781579	+	1.13064i
$255$		0			0
$256$	2.01655	+	15.8724i	0.126034	+	0.992026i
$257$	6.20291	−	10.7438i	0.386927	−	0.670177i	−0.605108	−	0.796144i	$-0.706870\pi$
$257$	6.20291	−	10.7438i	0.386927	−	0.670177i	0.992034	+	0.125967i	$0.0402033\pi$
$258$		0			0
$259$	11.8106	−	5.77170i	0.733874	−	0.358636i
$260$	−12.7004	−	15.5113i	−0.787646	−	0.961968i
$261$		0			0
$262$	1.92927	+	23.6937i	0.119191	+	1.46380i
$263$	−0.672005	−	1.16395i	−0.0414376	−	0.0717720i	0.844563	−	0.535457i	$-0.179860\pi$
$263$	−0.672005	−	1.16395i	−0.0414376	−	0.0717720i	−0.886000	+	0.463685i	$0.846527\pi$
$264$		0			0
$265$	−8.37709			−0.514601
$266$	−8.81014	−	4.94416i	−0.540184	−	0.303146i
$267$		0			0
$268$	1.87499	+	11.4372i	0.114534	+	0.698641i
$269$	1.68912	−	0.975212i	0.102987	−	0.0594597i	−0.447622	−	0.894223i	$-0.647729\pi$
$269$	1.68912	−	0.975212i	0.102987	−	0.0594597i	0.550609	+	0.834763i	$0.314396\pi$
$270$		0			0
$271$	13.0190	−	22.5496i	0.790850	−	1.36979i	−0.134590	−	0.990901i	$-0.542972\pi$
$271$	13.0190	−	22.5496i	0.790850	−	1.36979i	0.925441	−	0.378892i	$-0.123695\pi$
$272$	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	$-0.505781\pi$
$277$	13.9578	−	8.05852i	0.838641	−	0.484189i	0.856802	+	0.515646i	$0.172448\pi$
$278$	−2.84157	+	1.96430i	−0.170426	+	0.117811i
$279$		0			0
$280$	18.5639	−	15.5821i	1.10940	−	0.931211i
$281$	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	$-0.380704\pi$
$283$	22.7949	−	13.1606i	1.35501	−	0.782318i	0.988947	+	0.148270i	$0.0473706\pi$
$284$	4.69664	−	12.4359i	0.278694	−	0.737937i
$285$		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
$290$	−9.21009	+	0.749935i	−0.540835	+	0.0440377i
$291$		0			0
$292$	−18.8638	+	3.09248i	−1.10392	+	0.180974i
$293$		−	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
$296$	13.5063	+	3.88176i	0.785038	+	0.225622i
$297$		0			0
$298$	−1.08215	−	13.2901i	−0.0626872	−	0.769873i
$299$	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
$304$	−3.44843	−	10.2348i	−0.197781	−	0.587009i
$305$	−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	$0.743575\pi$
$308$	−11.6020	−	5.32299i	−0.661085	−	0.303305i
$309$		0			0
$310$	8.32952	−	5.75797i	0.473085	−	0.327031i
$311$	11.2742	+	19.5275i	0.639302	+	1.10730i	0.985586	+	0.169174i	$0.0541100\pi$
$311$	11.2742	+	19.5275i	0.639302	+	1.10730i	−0.346284	+	0.938130i	$0.612557\pi$
$312$		0			0
$313$	12.6901	−	21.9798i	0.717285	−	1.24237i	−0.244787	−	0.969577i	$-0.578718\pi$
$313$	12.6901	−	21.9798i	0.717285	−	1.24237i	0.962072	−	0.272797i	$-0.0879486\pi$
$314$	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	$-0.173547\pi$
$317$	14.8384	+	8.56693i	0.833405	+	0.481167i	−0.0216120	+	0.999766i	$0.506880\pi$
$318$		0			0
$319$	2.43337	+	4.21473i	0.136243	+	0.235979i
$320$	25.8933	+	0.935725i	1.44748	+	0.0523086i
$321$		0			0
$322$	−5.02616	+	8.95626i	−0.280097	+	0.499113i
$323$			10.6802i			0.594264i
$324$		0			0
$325$	−14.7138	+	8.49500i	−0.816173	+	0.471218i
$326$	2.27566	+	27.9478i	0.126037	+	1.54789i
$327$		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	$-0.257509\pi$
$331$	7.43566	+	4.29298i	0.408701	+	0.235963i	−0.281531	+	0.959552i	$0.590842\pi$
$332$	−12.1196	−	4.57716i	−0.665148	−	0.251204i
$333$		0			0
$334$	17.8204	+	25.7791i	0.975090	+	1.41057i
$335$	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	$0.527610\pi$
$338$	−2.75148	−	3.98031i	−0.149661	−	0.216500i
$339$		0			0
$340$	−23.9700	−	9.05266i	−1.29995	−	0.490950i
$341$	−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
$346$	2.49418	+	30.6315i	0.134088	+	1.64676i
$347$	−19.0373	+	10.9912i	−1.02198	+	0.590039i	−0.914676	−	0.404187i	$-0.867554\pi$
$347$	−19.0373	+	10.9912i	−1.02198	+	0.590039i	−0.107302	+	0.994226i	$0.534221\pi$
$348$		0			0
$349$		−	15.5480i		−	0.832265i	−0.909304	−	0.416132i	$-0.863385\pi$
$349$		−	15.5480i		−	0.832265i	0.909304	−	0.416132i	$-0.136615\pi$
$350$	−10.4865	−	17.6618i	−0.560529	−	0.944065i
$351$		0			0
$352$	−5.39227	−	12.5356i	−0.287409	−	0.668149i
$353$	−13.2804	−	23.0023i	−0.706845	−	1.22429i	−0.966022	−	0.258461i	$-0.916785\pi$
$353$	−13.2804	−	23.0023i	−0.706845	−	1.22429i	0.259177	−	0.965830i	$-0.416549\pi$
$354$		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	0.0884855	+	0.996077i	$0.471797\pi$
$359$	−15.5062	+	26.8575i	−0.818386	+	1.41749i	−0.906871	+	0.421408i	$0.861536\pi$
$360$		0			0
$361$	−5.85488	−	10.1410i	−0.308152	−	0.533735i
$362$	−16.3243	+	11.2846i	−0.857988	+	0.593104i
$363$		0			0
$364$	−13.3567	+	9.47610i	−0.700081	+	0.496683i
$365$			30.9555i			1.62029i
$366$		0			0
$367$	6.38677	+	11.0622i	0.333387	+	0.577443i	0.983174	−	0.182674i	$-0.0584751\pi$
$367$	6.38677	+	11.0622i	0.333387	+	0.577443i	−0.649787	+	0.760117i	$0.725142\pi$
$368$	−10.4046	+	3.50563i	−0.542377	+	0.182743i
$369$		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	$-0.278497\pi$
$373$	5.73431	+	3.31070i	0.296911	+	0.171422i	−0.344143	+	0.938917i	$0.611831\pi$
$374$	1.09518	+	13.4501i	0.0566304	+	0.695489i
$375$		0			0
$376$	−5.18161	+	18.0291i	−0.267221	+	0.929777i
$377$	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	$0.839786\pi$
$380$	−17.2593	+	2.82944i	−0.885382	+	0.145147i
$381$		0			0
$382$	−10.2600	+	0.835421i	−0.524945	+	0.0427438i
$383$	−10.2179	+	17.6980i	−0.522112	+	0.904325i	0.477557	+	0.878601i	$0.341522\pi$
$383$	−10.2179	+	17.6980i	−0.522112	+	0.904325i	−0.999669	+	0.0257240i	$0.991811\pi$
$384$		0			0
$385$	−11.5459	+	17.1461i	−0.588435	+	0.873846i
$386$	−5.77172	+	12.1854i	−0.293773	+	0.620221i
$387$		0			0
$388$	0.973081	−	2.57656i	0.0494007	−	0.130805i
$389$	−2.05734	+	1.18781i	−0.104311	+	0.0602242i	−0.551248	−	0.834341i	$-0.685848\pi$
$389$	−2.05734	+	1.18781i	−0.104311	+	0.0602242i	0.446937	+	0.894566i	$0.352515\pi$
$390$		0			0
$391$	10.8574			0.549082
$392$	−11.6526	−	16.0068i	−0.588543	−	0.808466i
$393$		0			0
$394$	13.5721	−	9.38205i	0.683754	−	0.472661i
$395$	−4.70287	+	2.71520i	−0.236627	+	0.136617i
$396$		0			0
$397$	19.1993	+	11.0847i	0.963583	+	0.556325i	0.897274	−	0.441474i	$-0.145544\pi$
$397$	19.1993	+	11.0847i	0.963583	+	0.556325i	0.0663091	+	0.997799i	$0.478878\pi$
$398$	−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	−0.324258	−	0.945969i	$-0.605115\pi$
$401$	13.1585	−	22.7912i	0.657104	−	1.13814i	0.981362	−	0.192168i	$-0.0615519\pi$
$402$		0			0
$403$	−5.92543	+	3.42105i	−0.295167	+	0.170415i
$404$	−0.257593	−	1.57129i	−0.0128157	−	0.0781745i
$405$		0			0
$406$	0.0921303	+	7.54805i	0.00457235	+	0.374604i
$407$	−11.9856			−0.594106
$408$		0			0
$409$	0.331162	+	0.573590i	0.0163749	+	0.0283622i	0.874097	−	0.485752i	$-0.161454\pi$
$409$	0.331162	+	0.573590i	0.0163749	+	0.0283622i	−0.857722	+	0.514114i	$0.828121\pi$
$410$	−0.785288	−	9.64427i	−0.0387826	−	0.476296i
$411$		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
$416$	−17.3870	−	2.05011i	−0.852469	−	0.100515i
$417$		0			0
$418$	5.23786	+	7.57713i	0.256192	+	0.370609i
$419$		−	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	$-0.0992625\pi$
$422$	18.7606	−	12.9687i	0.913254	−	0.631308i
$423$		0			0
$424$	−5.26559	+	5.07874i	−0.255719	+	0.246645i
$425$	−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
$430$	−52.9104	+	4.30825i	−2.55156	+	0.207762i
$431$	−6.45241	−	11.1759i	−0.310802	−	0.538325i	0.667734	−	0.744400i	$-0.267264\pi$
$431$	−6.45241	−	11.1759i	−0.310802	−	0.538325i	−0.978536	+	0.206075i	$0.933931\pi$
$432$		0			0
$433$	−40.5815			−1.95022			−0.975112	−	0.221715i	$-0.928835\pi$
$433$	−40.5815			−1.95022			−0.975112	+	0.221715i	$0.928835\pi$
$434$	−4.22307	−	7.11266i	−0.202714	−	0.341418i
$435$		0			0
$436$	−4.46891	−	27.2598i	−0.214022	−	1.30551i
$437$	6.41824	−	3.70557i	0.307026	−	0.177262i
$438$		0			0
$439$	−18.2273	+	31.5706i	−0.869941	+	1.50678i	−0.00788596	+	0.999969i	$0.502510\pi$
$439$	−18.2273	+	31.5706i	−0.869941	+	1.50678i	−0.862055	+	0.506814i	$0.830823\pi$
$440$	−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	$-0.0528128\pi$
$443$	28.1274	+	16.2393i	1.33637	+	0.771555i	0.350104	+	0.936711i	$0.386146\pi$
$444$		0			0
$445$	39.2100	−	22.6379i	1.85873	−	1.07314i
$446$	6.20399	+	8.97473i	0.293767	+	0.424966i
$447$		0			0
$448$	2.22178	−	21.0491i	0.104969	−	0.994475i
$449$	−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
$452$	3.20386	−	8.48330i	0.150697	−	0.399021i
$453$		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	−0.700162	−	0.713984i	$-0.746889\pi$
$457$	5.73448	−	9.93241i	0.268248	−	0.464618i	0.968409	+	0.249366i	$0.0802221\pi$
$458$	−1.07519	−	13.2046i	−0.0502403	−	0.617010i
$459$		0			0
$460$	2.87637	+	17.5455i	0.134112	+	0.818064i
$461$		−	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	$0.764916\pi$
$464$	−5.33452	+	6.05514i	−0.247649	+	0.281103i
$465$		0			0
$466$	12.4425	−	1.01314i	0.576390	−	0.0469328i
$467$	12.3089	+	7.10656i	0.569589	+	0.328852i	0.756985	−	0.653432i	$-0.226671\pi$
$467$	12.3089	+	7.10656i	0.569589	+	0.328852i	−0.187396	+	0.982284i	$0.560005\pi$
$468$		0			0
$469$	1.05770	−	15.2955i	0.0488398	−	0.706280i
$470$	27.4539	+	13.0038i	1.26636	+	0.599819i
$471$		0			0
$472$	24.9843	−	24.0977i	1.14999	−	1.10919i
$473$	13.9793	+	24.2129i	0.642769	+	1.11331i
$474$		0			0
$475$			14.8223i			0.680094i
$476$	−8.72832	+	19.0243i	−0.400062	+	0.871975i
$477$		0			0
$478$	4.77266	+	6.90416i	0.218296	+	0.315789i
$479$	−5.77020	−	9.99428i	−0.263647	−	0.456650i	0.703561	−	0.710635i	$-0.251592\pi$
$479$	−5.77020	−	9.99428i	−0.263647	−	0.456650i	−0.967208	+	0.253984i	$0.918259\pi$
$480$		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	0.993620	−	0.112778i	$-0.0359749\pi$
$487$	8.80829	+	15.2564i	0.399142	+	0.691333i	−0.594479	+	0.804111i	$0.702642\pi$
$488$	−23.6926	−	6.80933i	−1.07251	−	0.308244i
$489$		0			0
$490$	−28.6325	+	14.4279i	−1.29348	+	0.651788i
$491$		−	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
$494$	11.7787	−	0.959089i	0.529951	−	0.0431515i
$495$		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	$-0.351601\pi$
$499$	−2.21925	−	1.28129i	−0.0993474	−	0.0573583i	−0.548851	+	0.835921i	$0.684934\pi$
$500$	−2.96719	−	1.12061i	−0.132697	−	0.0501151i
$501$		0			0
$502$	4.44855	−	3.07516i	0.198548	−	0.137251i
$503$	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
$506$	7.70280	−	5.32474i	0.342431	−	0.236714i
$507$		0			0
$508$	10.9453	−	28.9813i	0.485619	−	1.28584i
$509$	11.0283	+	6.36720i	0.488821	+	0.282221i	0.724085	−	0.689710i	$-0.242262\pi$
$509$	11.0283	+	6.36720i	0.488821	+	0.282221i	−0.235264	+	0.971932i	$0.575595\pi$
$510$		0			0
$511$	25.2273	+	1.74449i	1.11599	+	0.0771716i
$512$	16.8430	−	15.1100i	0.744364	−	0.667775i
$513$		0			0
$514$	−17.4866	+	1.42385i	−0.771301	+	0.0628035i
$515$	7.44968	−	4.30107i	0.328272	−	0.189528i
$516$		0			0
$517$		−	15.9992i		−	0.703643i
$518$	−16.2120	−	9.09803i	−0.712316	−	0.399745i
$519$		0			0
$520$	−7.83126	+	27.2483i	−0.343423	+	1.19492i
$521$	17.0134	+	29.4680i	0.745369	+	1.29102i	0.950022	+	0.312183i	$0.101060\pi$
$521$	17.0134	+	29.4680i	0.745369	+	1.29102i	−0.204652	+	0.978835i	$0.565606\pi$
$522$		0			0
$523$	−5.88515	−	3.39779i	−0.257340	−	0.148575i	0.365781	−	0.930701i	$-0.380802\pi$
$523$	−5.88515	−	3.39779i	−0.257340	−	0.148575i	−0.623120	+	0.782126i	$0.714135\pi$
$524$	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
$530$	6.73661	+	9.74523i	0.292620	+	0.423306i
$531$		0			0
$532$	1.33322	+	14.2249i	0.0578026	+	0.616729i
$533$			6.53819i			0.283200i
$534$		0			0
$535$	−8.79392	−	15.2315i	−0.380195	−	0.658516i
$536$	11.7973	−	11.3787i	0.509567	−	0.491485i
$537$		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	$-0.155121\pi$
$541$	21.3952	+	12.3525i	0.919852	+	0.531077i	0.0362640	+	0.999342i	$0.488454\pi$
$542$	−36.7019	+	2.98847i	−1.57648	+	0.128366i
$543$		0			0
$544$	−20.5551	+	8.84193i	−0.881293	+	0.379094i
$545$	−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	$-0.200716\pi$
$548$	1.75150	−	0.287137i	0.0748205	−	0.0122659i
$549$		0			0
$550$	1.51992	+	18.6664i	0.0648095	+	0.795937i
$551$	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
$556$	4.57021	+	1.72602i	0.193820	+	0.0731995i
$557$	39.1575	−	22.6076i	1.65916	−	0.957914i	0.686050	−	0.727555i	$-0.259343\pi$
$557$	39.1575	−	22.6076i	1.65916	−	0.957914i	0.973106	−	0.230359i	$-0.0739902\pi$
$558$		0			0
$559$	35.8698			1.51713
$560$	−33.0555	−	9.06499i	−1.39685	−	0.383066i
$561$		0			0
$562$	−12.9723	−	18.7658i	−0.547204	−	0.791588i
$563$	13.1895	−	7.61497i	0.555872	−	0.320933i	−0.195615	−	0.980681i	$-0.562670\pi$
$563$	13.1895	−	7.61497i	0.555872	−	0.320933i	0.751487	+	0.659748i	$0.229337\pi$
$564$		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	−0.679773	−	0.733423i	$-0.737922\pi$
$569$	7.04343	−	12.1996i	0.295276	−	0.511433i	0.975049	+	0.221989i	$0.0712551\pi$
$570$		0			0
$571$	−19.2480	+	11.1129i	−0.805505	+	0.465058i	−0.845392	−	0.534146i	$-0.820633\pi$
$571$	−19.2480	+	11.1129i	−0.805505	+	0.465058i	0.0398876	+	0.999204i	$0.487300\pi$
$572$	14.7352	−	2.41565i	0.616108	−	0.101003i
$573$		0			0
$574$	−7.90388	+	0.0964735i	−0.329902	+	0.00402673i
$575$	15.0681			0.628385
$576$		0			0
$577$	−4.68070	−	8.10721i	−0.194860	−	0.337507i	0.751995	−	0.659169i	$-0.229092\pi$
$577$	−4.68070	−	8.10721i	−0.194860	−	0.337507i	−0.946855	+	0.321662i	$0.895759\pi$
$578$	−1.90764	+	0.155331i	−0.0793475	+	0.00646090i
$579$		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
$584$	18.7672	+	19.4577i	0.776594	+	0.805165i
$585$		0			0
$586$	−11.2252	+	7.75968i	−0.463709	+	0.320549i
$587$			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
$590$	−31.9641	−	46.2394i	−1.31594	−	1.90365i
$591$		0			0
$592$	−6.34566	−	18.8337i	−0.260805	−	0.774062i
$593$	−0.698895	+	1.21052i	−0.0287002	+	0.0497101i	−0.880019	−	0.474939i	$-0.842470\pi$
$593$	−0.698895	+	1.21052i	−0.0287002	+	0.0497101i	0.851319	+	0.524649i	$0.175803\pi$
$594$		0			0
$595$	28.1151	+	18.9323i	1.15261	+	0.776150i
$596$	−14.5903	+	11.9464i	−0.597644	+	0.489342i
$597$		0			0
$598$	−0.974997	−	11.9741i	−0.0398706	−	0.489658i
$599$	−15.9302	−	27.5919i	−0.650891	−	1.12738i	−0.982907	−	0.184102i	$-0.941062\pi$
$599$	−15.9302	−	27.5919i	−0.650891	−	1.12738i	0.332017	−	0.943274i	$-0.392271\pi$
$600$		0			0
$601$	34.4927			1.40699			0.703493	−	0.710702i	$-0.251623\pi$
$601$	34.4927			1.40699			0.703493	+	0.710702i	$0.251623\pi$
$602$	0.529273	+	43.3622i	0.0215715	+	1.76731i
$603$		0			0
$604$	−13.9217	+	2.28229i	−0.566467	+	0.0928652i
$605$	−14.5311	+	8.38955i	−0.590775	+	0.341084i
$606$		0			0
$607$	4.61573	−	7.99467i	0.187347	−	0.324494i	−0.757018	−	0.653394i	$-0.773345\pi$
$607$	4.61573	−	7.99467i	0.187347	−	0.324494i	0.944365	+	0.328900i	$0.106678\pi$
$608$	−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	$-0.893550\pi$
$613$	−28.0431	+	16.1907i	−1.13265	+	0.653935i	−0.188049	+	0.982160i	$0.560216\pi$
$614$	29.4018	−	20.3247i	1.18656	−	0.820238i
$615$		0			0
$616$	3.13765	+	17.7774i	0.126420	+	0.716272i
$617$	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	$-0.398203\pi$
$619$	32.1866	−	18.5829i	1.29369	−	0.746911i	0.979306	+	0.202385i	$0.0648694\pi$
$620$	−13.3967	−	5.05949i	−0.538025	−	0.203194i
$621$		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
$626$	−35.7745	+	2.91295i	−1.42984	+	0.116425i
$627$		0			0
$628$	−2.82002	−	17.2018i	−0.112531	−	0.686425i
$629$			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	$0.546493\pi$
$632$	−1.30995	+	4.55788i	−0.0521069	+	0.181303i
$633$		0			0
$634$	−1.96650	−	24.1510i	−0.0780999	−	0.959159i
$635$	−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
$640$	−19.7341	−	30.8746i	−0.780058	−	1.22043i
$641$	6.85337	+	11.8704i	0.270692	+	0.468852i	0.969039	−	0.246907i	$-0.0794142\pi$
$641$	6.85337	+	11.8704i	0.270692	+	0.468852i	−0.698347	+	0.715759i	$0.746081\pi$
$642$		0			0
$643$			30.5812i			1.20600i	0.797740	+	0.603002i	$0.206029\pi$
$643$			30.5812i			1.20600i	−0.797740	+	0.603002i	$0.793971\pi$
$644$	14.4609	−	1.35534i	0.569838	−	0.0534077i
$645$		0			0
$646$	12.4245	−	8.58874i	0.488836	−	0.337919i
$647$	21.2979	+	36.8891i	0.837308	+	1.45026i	0.892137	+	0.451765i	$0.149205\pi$
$647$	21.2979	+	36.8891i	0.837308	+	1.45026i	−0.0548287	+	0.998496i	$0.517461\pi$
$648$		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	$-0.125152\pi$
$653$	26.9273	+	15.5465i	1.05375	+	0.608381i	0.130051	+	0.991507i	$0.458486\pi$
$654$		0			0
$655$	−27.2210	−	47.1481i	−1.06361	−	1.84223i
$656$	−6.34059	−	5.58600i	−0.247558	−	0.218097i
$657$		0			0
$658$	12.1446	−	21.6408i	0.473446	−	0.843648i
$659$			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	$-0.844713\pi$
$661$	−23.6297	+	13.6426i	−0.919087	+	0.530635i	−0.0357432	+	0.999361i	$0.511380\pi$
$662$	−0.985436	−	12.1023i	−0.0383001	−	0.470370i
$663$		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
$668$	15.6587	−	41.4617i	0.605853	−	1.60420i
$669$		0			0
$670$	−15.0931	−	21.8338i	−0.583098	−	0.843513i
$671$	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	$0.713869\pi$
$674$	2.55782	+	3.70017i	0.0985237	+	0.142525i
$675$		0			0
$676$	−2.41771	+	6.40169i	−0.0929887	+	0.246219i
$677$	−13.5785	−	7.83953i	−0.521863	−	0.301298i	0.215834	−	0.976430i	$-0.430753\pi$
$677$	−13.5785	−	7.83953i	−0.521863	−	0.301298i	−0.737697	+	0.675132i	$0.764086\pi$
$678$		0			0
$679$	−2.03506	+	3.02213i	−0.0780983	+	0.115979i
$680$	8.74483	+	35.1646i	0.335349	+	1.34850i
$681$		0			0
$682$	0.612091	+	7.51720i	0.0234382	+	0.287849i
$683$	−16.5012	+	9.52698i	−0.631401	+	0.364540i	−0.781295	−	0.624162i	$-0.785440\pi$
$683$	−16.5012	+	9.52698i	−0.631401	+	0.364540i	0.149893	+	0.988702i	$0.452107\pi$
$684$		0			0
$685$		−	2.87422i		−	0.109818i
$686$	10.1445	+	24.1472i	0.387319	+	0.921946i
$687$		0			0
$688$	−30.6459	+	34.7857i	−1.16836	+	1.32619i
$689$	−4.00250	−	6.93253i	−0.152483	−	0.264108i
$690$		0			0
$691$	26.9066	+	15.5345i	1.02358	+	0.590961i	0.915138	−	0.403142i	$-0.132082\pi$
$691$	26.9066	+	15.5345i	1.02358	+	0.590961i	0.108438	+	0.994103i	$0.465415\pi$
$692$	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
$698$	−18.0873	+	12.5032i	−0.684613	+	0.473254i
$699$		0			0
$700$	−12.1134	+	26.4023i	−0.457842	+	0.997914i
$701$		−	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
$704$	−10.2466	+	16.3537i	−0.386182	+	0.616353i
$705$		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	$-0.283675\pi$
$709$	7.16576	+	4.13715i	0.269116	+	0.155374i	−0.359370	+	0.933195i	$0.617008\pi$
$710$	2.47071	+	30.3432i	0.0927241	+	1.13876i
$711$		0			0
$712$	10.9216	−	38.0011i	0.409306	−	1.42415i
$713$	6.06814			0.227254
$714$		0			0
$715$		−	24.1805i		−	0.904298i
$716$	1.22224	+	7.45549i	0.0456771	+	0.278625i
$717$		0			0
$718$	43.7135	−	3.55939i	1.63137	−	0.132835i
$719$	−1.81462	+	3.14301i	−0.0676739	+	0.117215i	−0.897877	−	0.440246i	$-0.854891\pi$
$719$	−1.81462	+	3.14301i	−0.0676739	+	0.117215i	0.830203	+	0.557461i	$0.188224\pi$
$720$		0			0
$721$	−3.08535	−	6.31352i	−0.114904	−	0.235128i
$722$	−7.08884	+	14.9662i	−0.263819	+	0.556983i
$723$		0			0
$724$	26.2551	+	9.91567i	0.975763	+	0.368513i
$725$	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	$0.325147\pi$
$728$	21.7648	+	7.91768i	0.806656	+	0.293449i
$729$		0			0
$730$	36.0111	−	24.8935i	1.33283	−	0.921351i
$731$	39.7028	−	22.9224i	1.46846	−	0.847816i
$732$		0			0
$733$	−25.4264	−	14.6799i	−0.939145	−	0.542215i	−0.0494525	−	0.998776i	$-0.515748\pi$
$733$	−25.4264	−	14.6799i	−0.939145	−	0.542215i	−0.889692	+	0.456561i	$0.849081\pi$
$734$	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	$-0.589900\pi$
$739$	11.2457	−	6.49271i	0.413680	−	0.238838i	0.692370	+	0.721543i	$0.256567\pi$
$740$	−31.7598	+	5.20662i	−1.16751	+	0.191399i
$741$		0			0
$742$	8.32154	−	4.94083i	0.305493	−	0.181384i
$743$	−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
$746$	−0.759959	−	9.33319i	−0.0278241	−	0.341713i
$747$		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	−0.954900	−	0.296929i	$-0.904038\pi$
$751$	−6.03724	+	10.4568i	−0.220302	+	0.381574i	0.734598	+	0.678503i	$0.237371\pi$
$752$	25.1404	−	8.47058i	0.916777	−	0.308890i
$753$		0			0
$754$	−5.02111	−	7.26357i	−0.182858	−	0.264524i
$755$			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	$0.835218\pi$
$758$	21.8475	−	15.1026i	0.793539	−	0.548552i
$759$		0			0
$760$	17.1709	+	17.8027i	0.622855	+	0.645770i
$761$	15.2423	−	26.4005i	0.552534	−	0.957017i	−0.445557	−	0.895254i	$-0.646994\pi$
$761$	15.2423	−	26.4005i	0.552534	−	0.957017i	0.998091	−	0.0617632i	$-0.0196724\pi$
$762$		0			0
$763$	−2.52094	+	36.4557i	−0.0912642	+	1.31978i
$764$	9.22262	+	11.2638i	0.333663	+	0.407509i
$765$		0			0
$766$	28.8054	−	2.34549i	1.04078	−	0.0847459i
$767$	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	$0.269835\pi$
$770$	29.2313	−	0.356792i	1.05342	−	0.0128579i
$771$		0			0
$772$	18.8170	−	3.08481i	0.677237	−	0.111025i
$773$	−28.6220	+	16.5249i	−1.02946	+	0.594359i	−0.916830	−	0.399277i	$-0.869261\pi$
$773$	−28.6220	+	16.5249i	−1.02946	+	0.594359i	−0.112631	+	0.993637i	$0.535928\pi$
$774$		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
$782$	−8.73119	−	12.6306i	−0.312227	−	0.451669i
$783$		0			0
$784$	−9.25037	+	26.4278i	−0.330370	+	0.943851i
$785$	−28.2281			−1.00751
$786$		0			0
$787$	−14.9922	+	8.65572i	−0.534413	+	0.308543i	−0.742811	−	0.669501i	$-0.766508\pi$
$787$	−14.9922	+	8.65572i	−0.534413	+	0.308543i	0.208399	+	0.978044i	$0.433175\pi$
$788$	−21.8286	−	8.24394i	−0.777613	−	0.293678i
$789$		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
$794$	−2.54445	−	31.2488i	−0.0902991	−	1.10898i
$795$		0			0
$796$	37.4302	−	6.13623i	1.32668	−	0.217493i
$797$			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
$800$	−28.5269	+	12.2710i	−1.00858	+	0.433847i
$801$		0			0
$802$	−37.0951	+	3.02048i	−1.30987	+	0.106657i
$803$	−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
$808$	−1.62076	+	1.56325i	−0.0570181	+	0.0549948i
$809$	−4.86273	−	8.42250i	−0.170965	−	0.296119i	0.767793	−	0.640698i	$-0.221355\pi$
$809$	−4.86273	−	8.42250i	−0.170965	−	0.296119i	−0.938757	+	0.344579i	$0.888022\pi$
$810$		0			0
$811$		−	55.3405i		−	1.94327i	−0.236492	−	0.971633i	$-0.575998\pi$
$811$		−	55.3405i		−	1.94327i	0.236492	−	0.971633i	$-0.424002\pi$
$812$	8.70670	−	6.17710i	0.305545	−	0.216774i
$813$		0			0
$814$	9.63850	+	13.9431i	0.337829	+	0.488706i
$815$	−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	$-0.596517\pi$
$821$	−36.5157	−	21.0823i	−1.27441	−	0.735779i	−0.975814	+	0.218602i	$0.929850\pi$
$822$		0			0
$823$	−7.60689	−	13.1755i	−0.265160	−	0.459270i	0.702446	−	0.711737i	$-0.252091\pi$
$823$	−7.60689	−	13.1755i	−0.265160	−	0.459270i	−0.967605	+	0.252467i	$0.918758\pi$
$824$	2.07505	−	7.22000i	0.0722878	−	0.251521i
$825$		0			0
$826$	−39.4843	+	23.4434i	−1.37383	+	0.815700i
$827$			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	$-0.787308\pi$
$829$	−18.4517	+	10.6531i	−0.640855	+	0.369998i	0.144089	+	0.989565i	$0.453975\pi$
$830$	29.5713	−	2.40786i	1.02644	−	0.0835780i
$831$		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
$836$	4.60248	−	12.1866i	0.159180	−	0.421483i
$837$		0			0
$838$	−8.78888	+	6.07552i	−0.303607	+	0.209875i
$839$	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
$842$	−14.6468	+	10.1249i	−0.504762	+	0.348929i
$843$		0			0
$844$	−30.1735	−	11.3955i	−1.03862	−	0.392250i
$845$	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
$850$	30.6080	−	2.49227i	1.04985	−	0.0854841i
$851$	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	$0.903287\pi$
$854$	28.4390	+	15.9597i	0.973161	+	0.546128i
$855$		0			0
$856$	−14.7619	−	4.24262i	−0.504552	−	0.145010i
$857$	1.75517	+	3.04005i	0.0599556	+	0.103846i	0.894445	−	0.447177i	$-0.147571\pi$
$857$	1.75517	+	3.04005i	0.0599556	+	0.103846i	−0.834490	+	0.551024i	$0.814237\pi$
$858$		0			0
$859$	−4.45370	−	2.57134i	−0.151958	−	0.0877331i	0.422093	−	0.906553i	$-0.361296\pi$
$859$	−4.45370	−	2.57134i	−0.151958	−	0.0877331i	−0.574051	+	0.818819i	$0.694629\pi$
$860$	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	0.287640	+	0.957739i	$0.407129\pi$
$863$	−20.1410	+	34.8852i	−0.685606	+	1.18750i	−0.973246	+	0.229766i	$0.926204\pi$
$864$		0			0
$865$	−35.1916	−	60.9536i	−1.19655	−	2.07248i
$866$	32.6345	+	47.2092i	1.10896	+	1.60423i
$867$		0			0
$868$	−4.87821	+	10.6326i	−0.165577	+	0.360893i
$869$		−	4.04471i		−	0.137207i
$870$		0			0
$871$	8.96744	+	15.5321i	0.303850	+	0.526284i
$872$	−28.1181	+	27.1203i	−0.952199	+	0.918410i
$873$		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	$-0.0826546\pi$
$877$	36.3471	+	20.9850i	1.22735	+	0.708613i	0.260878	+	0.965372i	$0.415988\pi$
$878$	51.3845	−	4.18400i	1.73414	−	0.141203i
$879$		0			0
$880$	23.4497	+	20.6589i	0.790488	+	0.696413i
$881$	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	$-0.0692135\pi$
$884$	−3.96104	−	24.1618i	−0.133224	−	0.812651i
$885$		0			0
$886$	−3.72768	−	45.7803i	−0.125234	−	1.53802i
$887$	4.14980	−	7.18766i	0.139337	−	0.241338i	−0.787909	−	0.615792i	$-0.788836\pi$
$887$	4.14980	−	7.18766i	0.139337	−	0.241338i	0.927246	+	0.374454i	$0.122170\pi$
$888$		0			0
$889$	−22.8905	+	33.9931i	−0.767722	+	1.14009i
$890$	−57.8666	−	27.4090i	−1.93969	−	0.918751i
$891$		0			0
$892$	5.45140	−	14.4344i	0.182527	−	0.483301i
$893$	−15.5083	+	8.95370i	−0.518964	+	0.299624i
$894$		0			0
$895$	12.2345			0.408954
$896$	−26.2735	+	14.3424i	−0.877735	+	0.479146i
$897$		0			0
$898$	20.8942	+	30.2257i	0.697249	+	1.00865i
$899$	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	$-0.754601\pi$
$907$	−14.2277	+	8.21434i	−0.472422	+	0.272753i	0.244831	+	0.969566i	$0.421267\pi$
$908$	0.687429	+	4.19323i	0.0228131	+	0.139157i
$909$		0			0
$910$	18.3548	−	32.7070i	0.608457	−	1.08423i
$911$	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
$914$	−16.1661	+	1.31633i	−0.534725	+	0.0435402i
$915$		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	−0.394191	−	0.919028i	$-0.628975\pi$
$919$	18.1528	−	31.4416i	0.598806	−	1.03716i	0.992998	−	0.118135i	$-0.0376914\pi$
$920$	18.0979	−	17.4557i	0.596671	−	0.575499i
$921$		0			0
$922$	−29.3125	+	20.2629i	−0.965354	+	0.667323i
$923$		−	20.5707i		−	0.677094i
$924$		0			0
$925$			27.2754i			0.896809i
$926$	25.5906	+	37.0195i	0.840959	+	1.21654i
$927$		0			0
$928$	11.3339	+	1.33638i	0.372054	+	0.0438689i
$929$	−10.8263	+	18.7518i	−0.355201	+	0.615226i	−0.987152	−	0.159782i	$-0.948921\pi$
$929$	−10.8263	+	18.7518i	−0.355201	+	0.615226i	0.631952	+	0.775008i	$0.282254\pi$
$930$		0			0
$931$	2.60150	−	18.7204i	0.0852608	−	0.613536i
$932$	−11.1845	−	13.6599i	−0.366362	−	0.447445i
$933$		0			0
$934$	−1.63128	−	20.0341i	−0.0533772	−	0.655535i
$935$	−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	$0.583433\pi$
$938$	−18.6441	+	11.0697i	−0.608751	+	0.361440i
$939$		0			0
$940$	−6.95012	−	42.3949i	−0.226688	−	1.38277i
$941$	−12.7230	+	7.34561i	−0.414757	+	0.239460i	−0.692832	−	0.721099i	$-0.743637\pi$
$941$	−12.7230	+	7.34561i	−0.414757	+	0.239460i	0.278075	+	0.960559i	$0.410304\pi$
$942$		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	$-0.405982\pi$
$947$	−12.0598	−	6.96270i	−0.391889	−	0.226257i	−0.682978	+	0.730439i	$0.739316\pi$
$948$		0			0
$949$	−25.6175	+	14.7903i	−0.831579	+	0.480112i
$950$	17.2430	−	11.9197i	0.559438	−	0.386725i
$951$		0			0
$952$	29.1503	−	5.14493i	0.944767	−	0.166748i
$953$	−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
$956$	4.19370	−	11.1042i	0.135634	−	0.359137i
$957$		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
$962$	21.6748	−	1.76488i	0.698822	−	0.0569019i
$963$		0			0
$964$	−21.0906	+	3.45754i	−0.679281	+	0.111360i
$965$		−	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	$0.699187\pi$
$968$	−4.04754	+	14.0831i	−0.130093	+	0.452649i
$969$		0			0
$970$	0.511898	+	6.28672i	0.0164361	+	0.201854i
$971$	5.75503	+	3.32267i	0.184688	+	0.106629i	0.589493	−	0.807773i	$-0.299327\pi$
$971$	5.75503	+	3.32267i	0.184688	+	0.106629i	−0.404806	+	0.914403i	$0.632661\pi$
$972$		0			0
$973$	−5.36055	−	3.60971i	−0.171851	−	0.115722i
$974$	10.6647	−	22.5156i	0.341719	−	0.721446i
$975$		0			0
$976$	11.1315	+	33.0379i	0.356310	+	1.05752i
$977$	−22.7226	−	39.3567i	−0.726961	−	1.25913i	−0.958162	−	0.286227i	$-0.907599\pi$
$977$	−22.7226	−	39.3567i	−0.726961	−	1.25913i	0.231201	−	0.972906i	$-0.425735\pi$
$978$		0			0
$979$			33.7226i			1.07778i
$980$	39.8097	+	21.7062i	1.27167	+	0.693379i
$981$		0			0
$982$	−31.2353	+	21.5921i	−0.996759	+	0.689032i
$983$	−9.26538	−	16.0481i	−0.295520	−	0.511855i	0.679586	−	0.733596i	$-0.262159\pi$
$983$	−9.26538	−	16.0481i	−0.295520	−	0.511855i	−0.975106	+	0.221741i	$0.928826\pi$
$984$		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	0.995550	+	0.0942363i	$0.0300409\pi$
$991$	18.2392	+	31.5911i	0.579386	+	1.00353i	−0.416164	+	0.909290i	$0.636626\pi$
$992$	−11.4882	+	4.94171i	−0.364749	+	0.156899i
$993$		0			0
$994$	24.8676	−	0.303529i	0.788751	−	0.00962737i
$995$		−	61.4232i		−	1.94724i
$996$		0			0
$997$	−13.2738	+	7.66365i	−0.420386	+	0.242710i	−0.695243	−	0.718775i	$-0.744703\pi$
$997$	−13.2738	+	7.66365i	−0.420386	+	0.242710i	0.274856	+	0.961485i	$0.411370\pi$
$998$	0.294114	+	3.61207i	0.00931002	+	0.114338i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.1	✓	12	24.5	odd	2
56.2.p.a.37.5	yes	12	3.2	odd	2
56.2.p.a.53.1	yes	12	21.11	odd	6
56.2.p.a.53.5	yes	12	168.53	odd	6
224.2.t.a.81.3		12	168.11	even	6
224.2.t.a.81.4		12	84.11	even	6
224.2.t.a.177.3		12	12.11	even	2
224.2.t.a.177.4		12	24.11	even	2
392.2.b.e.197.3		6	21.2	odd	6
392.2.b.e.197.4		6	168.149	odd	6
392.2.b.f.197.3		6	21.5	even	6
392.2.b.f.197.4		6	168.5	even	6
392.2.p.g.165.1		12	21.17	even	6
392.2.p.g.165.5		12	168.101	even	6
392.2.p.g.373.1		12	168.125	even	2
392.2.p.g.373.5		12	21.20	even	2
504.2.cj.c.37.2		12	1.1	even	1	trivial
504.2.cj.c.37.6		12	8.5	even	2	inner
504.2.cj.c.109.2		12	56.53	even	6	inner
504.2.cj.c.109.6		12	7.4	even	3	inner
1568.2.b.e.785.3		6	168.131	odd	6
1568.2.b.e.785.4		6	84.47	odd	6
1568.2.b.f.785.3		6	84.23	even	6
1568.2.b.f.785.4		6	168.107	even	6
1568.2.t.g.177.3		12	168.83	odd	2
1568.2.t.g.177.4		12	84.83	odd	2
1568.2.t.g.753.3		12	84.59	odd	6
1568.2.t.g.753.4		12	168.59	odd	6
2016.2.cr.c.1297.1		12	8.3	odd	2
2016.2.cr.c.1297.6		12	4.3	odd	2
2016.2.cr.c.1873.1		12	28.11	odd	6
2016.2.cr.c.1873.6		12	56.11	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.804171 - 1.16332i) q^{2} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(1.47779 - 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +O(q^{10})\)	\(q+(-0.804171 - 1.16332i) q^{2} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(1.47779 - 2.19457i) q^{7} +(2.74483 - 0.682591i) q^{8} +(-0.371724 - 4.56521i) q^{10} +(-2.08913 + 1.20616i) q^{11} +3.09491i q^{13} +(-3.74138 + 0.0456667i) q^{14} +(-3.00138 - 2.64419i) q^{16} +(1.97779 + 3.42563i) q^{17} +(2.33831 + 1.35002i) q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +(1.37241 - 2.37709i) q^{23} +(2.74483 + 4.75418i) q^{25} +(3.60037 - 2.48884i) q^{26} +(3.06183 + 4.31569i) q^{28} -2.01745i q^{29} +(1.10538 + 1.91457i) q^{31} +(-0.662411 + 5.61794i) q^{32} +(2.39462 - 5.05560i) q^{34} +(7.69885 - 3.76234i) q^{35} +(4.30285 + 2.48425i) q^{37} +(-0.309892 - 3.80584i) q^{38} +(8.80423 + 2.53036i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(-0.780522 - 4.76109i) q^{44} +(-3.86897 + 0.315032i) q^{46} +(-3.31613 + 5.74371i) q^{47} +(-2.63227 - 6.48623i) q^{49} +(3.32331 - 7.01628i) q^{50} +(-5.79062 - 2.18693i) q^{52} +(-2.23998 + 1.29325i) q^{53} -7.81297 q^{55} +(2.55829 - 7.03244i) q^{56} +(-2.34694 + 1.62238i) q^{58} +(10.6283 - 6.13625i) q^{59} +(-7.54801 - 4.35784i) q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} +(-5.01186 + 8.68080i) q^{65} +(5.01858 - 2.89748i) q^{67} +(-7.80695 + 1.27985i) q^{68} +(-10.5680 - 5.93065i) q^{70} -6.64663 q^{71} +(4.77890 + 8.27729i) q^{73} +(-0.570250 - 7.00335i) q^{74} +(-4.17820 + 3.42105i) q^{76} +(-0.440297 + 6.36720i) q^{77} +(-0.838343 + 1.45205i) q^{79} +(-4.13648 - 12.2770i) q^{80} +(-1.69886 - 2.45758i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(-13.4828 + 9.32027i) q^{86} +(-4.91099 + 4.73673i) q^{88} +(6.98965 - 12.1064i) q^{89} +(6.79200 + 4.57363i) q^{91} +(3.47779 + 4.24750i) q^{92} +(9.34850 - 0.761205i) q^{94} +(4.37241 + 7.57324i) q^{95} -1.37709 q^{97} +(-5.42876 + 8.27820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 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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