LMFDB - Embedded newform 135.2.m.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(8,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.m (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			8.3
Root			$1.60599 + 0.430324i$ of defining polynomial
Character	$\chi$	$=$	135.8
Dual form			135.2.m.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60599 - 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(1.24906 - 1.85468i) q^{5} +(0.465559 + 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +O(q^{10})$	\(q+(1.60599 - 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(1.24906 - 1.85468i) q^{5} +(0.465559 + 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +(1.20786 - 3.51610i) q^{10} +(-3.12636 - 1.80501i) q^{11} +(0.342574 - 1.27850i) q^{13} +(1.49537 + 2.59005i) q^{14} +(-2.47224 + 4.28205i) q^{16} +(0.277007 + 0.277007i) q^{17} +6.25273i q^{19} +(0.118000 - 1.70513i) q^{20} +(-5.79765 - 1.55348i) q^{22} +(-2.16347 - 0.579699i) q^{23} +(-1.87971 - 4.63322i) q^{25} -2.20068i q^{26} +(0.972242 + 0.972242i) q^{28} +(-1.56832 + 2.71642i) q^{29} +(-2.42605 - 4.20205i) q^{31} +(-1.06430 + 3.97202i) q^{32} +(0.564074 + 0.325668i) q^{34} +(3.80401 + 1.30676i) q^{35} +(5.55242 - 5.55242i) q^{37} +(2.69070 + 10.0418i) q^{38} +(0.879778 + 4.50872i) q^{40} +(-1.29036 + 0.744991i) q^{41} +(4.10976 - 1.10121i) q^{43} -2.75943 q^{44} -3.72396 q^{46} +(3.82042 - 1.02368i) q^{47} +(3.26005 - 1.88219i) q^{49} +(-5.01258 - 6.63202i) q^{50} +(-0.261857 - 0.977265i) q^{52} +(7.48222 - 7.48222i) q^{53} +(-7.25273 + 3.54386i) q^{55} +(-3.20031 - 1.84770i) q^{56} +(-1.34977 + 5.03742i) q^{58} +(0.279377 + 0.483896i) q^{59} +(-2.96237 + 5.13097i) q^{61} +(-5.70446 - 5.70446i) q^{62} -3.05196i q^{64} +(-1.94332 - 2.23229i) q^{65} +(10.8351 + 2.90325i) q^{67} +(0.289242 + 0.0775020i) q^{68} +(6.67153 + 0.461690i) q^{70} +8.01611i q^{71} +(-1.29315 - 1.29315i) q^{73} +(6.52779 - 11.3065i) q^{74} +(2.38974 + 4.13915i) q^{76} +(1.68068 - 6.27237i) q^{77} +(-6.96917 - 4.02365i) q^{79} +(4.85388 + 9.93376i) q^{80} +(-1.75172 + 1.75172i) q^{82} +(0.150243 + 0.560714i) q^{83} +(0.859759 - 0.167763i) q^{85} +(6.12636 - 3.53706i) q^{86} +(7.16367 - 1.91950i) q^{88} -16.4343 q^{89} +2.38087 q^{91} +(-1.65372 + 0.443112i) q^{92} +(5.69504 - 3.28804i) q^{94} +(11.5968 + 7.81002i) q^{95} +(-1.37786 - 5.14224i) q^{97} +(4.42566 - 4.42566i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7	$ 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7} - 8 q^{10} - 2 q^{13} - 8 q^{16} - 18 q^{20} - 10 q^{22} - 18 q^{23} + 4 q^{25} - 16 q^{28} - 4 q^{31} - 30 q^{32} + 4 q^{37} + 30 q^{38} + 6 q^{40} + 24 q^{41} - 2 q^{43} + 32 q^{46} + 12 q^{47} + 54 q^{50} - 14 q^{52} - 16 q^{55} - 36 q^{56} - 6 q^{58} + 8 q^{61} - 66 q^{65} + 4 q^{67} - 42 q^{68} + 18 q^{70} - 8 q^{73} + 24 q^{76} + 6 q^{77} + 32 q^{82} + 66 q^{83} + 22 q^{85} + 48 q^{86} + 18 q^{88} - 40 q^{91} + 60 q^{92} + 36 q^{95} + 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7 - 8 * q^10 - 2 * q^13 - 8 * q^16 - 18 * q^20 - 10 * q^22 - 18 * q^23 + 4 * q^25 - 16 * q^28 - 4 * q^31 - 30 * q^32 + 4 * q^37 + 30 * q^38 + 6 * q^40 + 24 * q^41 - 2 * q^43 + 32 * q^46 + 12 * q^47 + 54 * q^50 - 14 * q^52 - 16 * q^55 - 36 * q^56 - 6 * q^58 + 8 * q^61 - 66 * q^65 + 4 * q^67 - 42 * q^68 + 18 * q^70 - 8 * q^73 + 24 * q^76 + 6 * q^77 + 32 * q^82 + 66 * q^83 + 22 * q^85 + 48 * q^86 + 18 * q^88 - 40 * q^91 + 60 * q^92 + 36 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.60599	−	0.430324i	1.13561	−	0.304285i	0.358423	−	0.933559i	$-0.383314\pi$
$2$	1.60599	−	0.430324i	1.13561	−	0.304285i	0.777183	+	0.629274i	$0.216648\pi$
$3$		0			0
$3$		0			0
$4$	0.661975	−	0.382191i	0.330987	−	0.191096i
$5$	1.24906	−	1.85468i	0.558596	−	0.829440i
$5$	1.24906	−	1.85468i	0.558596	−	0.829440i
$6$		0			0
$7$	0.465559	+	1.73749i	0.175965	+	0.656710i	0.996385	+	0.0849489i	$0.0270727\pi$
$7$	0.465559	+	1.73749i	0.175965	+	0.656710i	−0.820421	+	0.571761i	$0.806261\pi$
$8$	−1.45267	+	1.45267i	−0.513598	+	0.513598i
$9$		0			0
$10$	1.20786	−	3.51610i	0.381959	−	1.11189i
$11$	−3.12636	−	1.80501i	−0.942634	−	0.544230i	−0.0518493	−	0.998655i	$-0.516512\pi$
$11$	−3.12636	−	1.80501i	−0.942634	−	0.544230i	−0.890785	+	0.454425i	$0.849845\pi$
$12$		0			0
$13$	0.342574	−	1.27850i	0.0950128	−	0.354593i	−0.902009	−	0.431718i	$-0.857908\pi$
$13$	0.342574	−	1.27850i	0.0950128	−	0.354593i	0.997021	+	0.0771255i	$0.0245742\pi$
$14$	1.49537	+	2.59005i	0.399654	+	0.692220i
$15$		0			0
$16$	−2.47224	+	4.28205i	−0.618061	+	1.07051i
$17$	0.277007	+	0.277007i	0.0671841	+	0.0671841i	0.739900	−	0.672716i	$-0.234873\pi$
$17$	0.277007	+	0.277007i	0.0671841	+	0.0671841i	−0.672716	+	0.739900i	$0.734873\pi$
$18$		0			0
$19$			6.25273i			1.43447i	0.696829	+	0.717237i	$0.254594\pi$
$19$			6.25273i			1.43447i	−0.696829	+	0.717237i	$0.745406\pi$
$20$	0.118000	−	1.70513i	0.0263857	−	0.381280i
$21$		0			0
$22$	−5.79765	−	1.55348i	−1.23606	−	0.331202i
$23$	−2.16347	−	0.579699i	−0.451114	−	0.120876i	0.0261067	−	0.999659i	$-0.491689\pi$
$23$	−2.16347	−	0.579699i	−0.451114	−	0.120876i	−0.477221	+	0.878784i	$0.658356\pi$
$24$		0			0
$25$	−1.87971	−	4.63322i	−0.375942	−	0.926643i
$26$		−	2.20068i		−	0.431589i
$27$		0			0
$28$	0.972242	+	0.972242i	0.183737	+	0.183737i
$29$	−1.56832	+	2.71642i	−0.291230	+	0.504426i	−0.974101	−	0.226114i	$-0.927398\pi$
$29$	−1.56832	+	2.71642i	−0.291230	+	0.504426i	0.682871	+	0.730539i	$0.260731\pi$
$30$		0			0
$31$	−2.42605	−	4.20205i	−0.435732	−	0.754710i	0.561623	−	0.827393i	$-0.310177\pi$
$31$	−2.42605	−	4.20205i	−0.435732	−	0.754710i	−0.997355	+	0.0726832i	$0.976844\pi$
$32$	−1.06430	+	3.97202i	−0.188143	+	0.702160i
$33$		0			0
$34$	0.564074	+	0.325668i	0.0967378	+	0.0558516i
$35$	3.80401	+	1.30676i	0.642994	+	0.220883i
$36$		0			0
$37$	5.55242	−	5.55242i	0.912812	−	0.912812i	−0.0836807	−	0.996493i	$-0.526668\pi$
$37$	5.55242	−	5.55242i	0.912812	−	0.912812i	0.996493	+	0.0836807i	$0.0266676\pi$
$38$	2.69070	+	10.0418i	0.436489	+	1.62900i
$39$		0			0
$40$	0.879778	+	4.50872i	0.139105	+	0.712892i
$41$	−1.29036	+	0.744991i	−0.201521	+	0.116348i	−0.597365	−	0.801970i	$-0.703785\pi$
$41$	−1.29036	+	0.744991i	−0.201521	+	0.116348i	0.395844	+	0.918318i	$0.370452\pi$
$42$		0			0
$43$	4.10976	−	1.10121i	0.626733	−	0.167933i	0.0685463	−	0.997648i	$-0.478164\pi$
$43$	4.10976	−	1.10121i	0.626733	−	0.167933i	0.558187	+	0.829715i	$0.311497\pi$
$44$	−2.75943			−0.416000
$45$		0			0
$46$	−3.72396			−0.549069
$47$	3.82042	−	1.02368i	0.557266	−	0.149319i	0.0308158	−	0.999525i	$-0.490189\pi$
$47$	3.82042	−	1.02368i	0.557266	−	0.149319i	0.526450	+	0.850206i	$0.323523\pi$
$48$		0			0
$49$	3.26005	−	1.88219i	0.465722	−	0.268884i
$50$	−5.01258	−	6.63202i	−0.708886	−	0.937909i
$51$		0			0
$52$	−0.261857	−	0.977265i	−0.0363131	−	0.135522i
$53$	7.48222	−	7.48222i	1.02776	−	1.02776i	0.0281581	−	0.999603i	$-0.491036\pi$
$53$	7.48222	−	7.48222i	1.02776	−	1.02776i	0.999603	−	0.0281581i	$-0.00896420\pi$
$54$		0			0
$55$	−7.25273	+	3.54386i	−0.977958	+	0.477854i
$56$	−3.20031	−	1.84770i	−0.427660	−	0.246909i
$57$		0			0
$58$	−1.34977	+	5.03742i	−0.177234	+	0.661446i
$59$	0.279377	+	0.483896i	0.0363718	+	0.0629978i	0.883638	−	0.468170i	$-0.155087\pi$
$59$	0.279377	+	0.483896i	0.0363718	+	0.0629978i	−0.847266	+	0.531168i	$0.821753\pi$
$60$		0			0
$61$	−2.96237	+	5.13097i	−0.379292	+	0.656953i	−0.990959	−	0.134162i	$-0.957166\pi$
$61$	−2.96237	+	5.13097i	−0.379292	+	0.656953i	0.611667	+	0.791115i	$0.290499\pi$
$62$	−5.70446	−	5.70446i	−0.724467	−	0.724467i
$63$		0			0
$64$		−	3.05196i		−	0.381495i
$65$	−1.94332	−	2.23229i	−0.241040	−	0.276881i
$66$		0			0
$67$	10.8351	+	2.90325i	1.32371	+	0.354688i	0.850368	−	0.526188i	$-0.176379\pi$
$67$	10.8351	+	2.90325i	1.32371	+	0.354688i	0.473346	+	0.880876i	$0.343046\pi$
$68$	0.289242	+	0.0775020i	0.0350757	+	0.00939850i
$69$		0			0
$70$	6.67153	+	0.461690i	0.797400	+	0.0551825i
$71$			8.01611i			0.951338i	0.879624	+	0.475669i	$0.157794\pi$
$71$			8.01611i			0.951338i	−0.879624	+	0.475669i	$0.842206\pi$
$72$		0			0
$73$	−1.29315	−	1.29315i	−0.151352	−	0.151352i	0.627370	−	0.778721i	$-0.284131\pi$
$73$	−1.29315	−	1.29315i	−0.151352	−	0.151352i	−0.778721	+	0.627370i	$0.784131\pi$
$74$	6.52779	−	11.3065i	0.758840	−	1.31435i
$75$		0			0
$76$	2.38974	+	4.13915i	0.274122	+	0.474793i
$77$	1.68068	−	6.27237i	0.191531	−	0.714802i
$78$		0			0
$79$	−6.96917	−	4.02365i	−0.784093	−	0.452696i	0.0537859	−	0.998552i	$-0.482871\pi$
$79$	−6.96917	−	4.02365i	−0.784093	−	0.452696i	−0.837879	+	0.545856i	$0.816204\pi$
$80$	4.85388	+	9.93376i	0.542680	+	1.11063i
$81$		0			0
$82$	−1.75172	+	1.75172i	−0.193445	+	0.193445i
$83$	0.150243	+	0.560714i	0.0164913	+	0.0615463i	0.973681	−	0.227914i	$-0.0731907\pi$
$83$	0.150243	+	0.560714i	0.0164913	+	0.0615463i	−0.957190	+	0.289461i	$0.906524\pi$
$84$		0			0
$85$	0.859759	−	0.167763i	0.0932539	−	0.0181965i
$86$	6.12636	−	3.53706i	0.660623	−	0.381411i
$87$		0			0
$88$	7.16367	−	1.91950i	0.763650	−	0.204619i
$89$	−16.4343			−1.74203			−0.871016	−	0.491255i	$-0.836538\pi$
$89$	−16.4343			−1.74203			−0.871016	+	0.491255i	$0.836538\pi$
$90$		0			0
$91$	2.38087			0.249583
$92$	−1.65372	+	0.443112i	−0.172412	+	0.0461976i
$93$		0			0
$94$	5.69504	−	3.28804i	0.587399	−	0.339135i
$95$	11.5968	+	7.81002i	1.18981	+	0.801291i
$96$		0			0
$97$	−1.37786	−	5.14224i	−0.139900	−	0.522116i	−0.999930	−	0.0118706i	$-0.996221\pi$
$97$	−1.37786	−	5.14224i	−0.139900	−	0.522116i	0.860029	−	0.510245i	$-0.170445\pi$
$98$	4.42566	−	4.42566i	0.447059	−	0.447059i
$99$		0			0
$100$	−3.01510	−	2.34866i	−0.301510	−	0.234866i
$101$	4.73008	+	2.73092i	0.470661	+	0.271736i	0.716516	−	0.697570i	$-0.245735\pi$
$101$	4.73008	+	2.73092i	0.470661	+	0.271736i	−0.245855	+	0.969307i	$0.579069\pi$
$102$		0			0
$103$	−1.34888	+	5.03410i	−0.132909	+	0.496024i	−0.999998	−	0.00212995i	$-0.999322\pi$
$103$	−1.34888	+	5.03410i	−0.132909	+	0.496024i	0.867088	+	0.498154i	$0.165989\pi$
$104$	1.35960	+	2.35489i	0.133320	+	0.230916i
$105$		0			0
$106$	8.79659	−	15.2361i	0.854401	−	1.47987i
$107$	4.07498	+	4.07498i	0.393944	+	0.393944i	0.876090	−	0.482147i	$-0.160143\pi$
$107$	4.07498	+	4.07498i	0.393944	+	0.393944i	−0.482147	+	0.876090i	$0.660143\pi$
$108$		0			0
$109$			1.10747i			0.106077i	0.998592	+	0.0530384i	$0.0168906\pi$
$109$			1.10747i			0.106077i	−0.998592	+	0.0530384i	$0.983109\pi$
$110$	−10.1228	+	8.81243i	−0.965171	+	0.840232i
$111$		0			0
$112$	−8.59099	−	2.30195i	−0.811773	−	0.217514i
$113$	−8.06067	−	2.15985i	−0.758284	−	0.203182i	−0.141095	−	0.989996i	$-0.545062\pi$
$113$	−8.06067	−	2.15985i	−0.758284	−	0.203182i	−0.617190	+	0.786815i	$0.711729\pi$
$114$		0			0
$115$	−3.77745	+	3.28847i	−0.352249	+	0.306651i
$116$			2.39760i			0.222611i
$117$		0			0
$118$	0.656909	+	0.656909i	0.0604734	+	0.0604734i
$119$	−0.352334	+	0.610260i	−0.0322984	+	0.0559425i
$120$		0			0
$121$	1.01610	+	1.75994i	0.0923731	+	0.159995i
$122$	−2.54955	+	9.51507i	−0.230826	+	0.861454i
$123$		0			0
$124$	−3.21197	−	1.85443i	−0.288444	−	0.166533i
$125$	−10.9410	−	2.30088i	−0.978595	−	0.205797i
$126$		0			0
$127$	−11.5887	+	11.5887i	−1.02833	+	1.02833i	−0.0287470	+	0.999587i	$0.509152\pi$
$127$	−11.5887	+	11.5887i	−1.02833	+	1.02833i	−0.999587	+	0.0287470i	$0.990848\pi$
$128$	−3.44193	−	12.8454i	−0.304226	−	1.13539i
$129$		0			0
$130$	−4.08157	−	2.74878i	−0.357977	−	0.241084i
$131$	−4.34401	+	2.50802i	−0.379538	+	0.219126i	−0.677617	−	0.735415i	$-0.736987\pi$
$131$	−4.34401	+	2.50802i	−0.379538	+	0.219126i	0.298079	+	0.954541i	$0.403654\pi$
$132$		0			0
$133$	−10.8641	+	2.91101i	−0.942033	+	0.252417i
$134$	18.6504			1.61115
$135$		0			0
$136$	−0.804802			−0.0690112
$137$	0.440837	−	0.118122i	0.0376632	−	0.0100918i	−0.239938	−	0.970788i	$-0.577127\pi$
$137$	0.440837	−	0.118122i	0.0376632	−	0.0100918i	0.277601	+	0.960696i	$0.410461\pi$
$138$		0			0
$139$	−13.8860	+	8.01711i	−1.17780	+	0.680003i	−0.955504	−	0.294977i	$-0.904688\pi$
$139$	−13.8860	+	8.01711i	−1.17780	+	0.680003i	−0.222295	+	0.974980i	$0.571355\pi$
$140$	3.01759	−	0.588816i	0.255033	−	0.0497640i
$141$		0			0
$142$	3.44952	+	12.8738i	0.289478	+	1.08035i
$143$	−3.37872	+	3.37872i	−0.282542	+	0.282542i
$144$		0			0
$145$	3.07917	+	6.30170i	0.255711	+	0.523328i
$146$	−2.63326	−	1.52031i	−0.217930	−	0.125822i
$147$		0			0
$148$	1.55348	−	5.79765i	0.127695	−	0.476564i
$149$	3.44153	+	5.96090i	0.281941	+	0.488336i	0.971863	−	0.235548i	$-0.0756885\pi$
$149$	3.44153	+	5.96090i	0.281941	+	0.488336i	−0.689922	+	0.723884i	$0.742355\pi$
$150$		0			0
$151$	4.30647	−	7.45902i	0.350455	−	0.607006i	−0.635874	−	0.771793i	$-0.719360\pi$
$151$	4.30647	−	7.45902i	0.350455	−	0.607006i	0.986329	+	0.164787i	$0.0526935\pi$
$152$	−9.08317	−	9.08317i	−0.736743	−	0.736743i
$153$		0			0
$154$		−	10.7966i		−	0.870014i
$155$	−10.8238	−	0.749036i	−0.869385	−	0.0601640i
$156$		0			0
$157$	−1.60930	−	0.431209i	−0.128436	−	0.0344142i	0.194029	−	0.980996i	$-0.437845\pi$
$157$	−1.60930	−	0.431209i	−0.128436	−	0.0344142i	−0.322464	+	0.946582i	$0.604511\pi$
$158$	−12.9239	−	3.46295i	−1.02817	−	0.275497i
$159$		0			0
$160$	6.03747	+	6.93521i	0.477304	+	0.548277i
$161$		−	4.02889i		−	0.317521i
$162$		0			0
$163$	−10.5120	−	10.5120i	−0.823363	−	0.823363i	0.163225	−	0.986589i	$-0.447810\pi$
$163$	−10.5120	−	10.5120i	−0.823363	−	0.823363i	−0.986589	+	0.163225i	$0.947810\pi$
$164$	−0.569458	+	0.986331i	−0.0444672	+	0.0770195i
$165$		0			0
$166$	0.482577	+	0.835848i	0.0374552	+	0.0648744i
$167$	−2.51657	+	9.39195i	−0.194738	+	0.726771i	0.797597	+	0.603191i	$0.206104\pi$
$167$	−2.51657	+	9.39195i	−0.194738	+	0.726771i	−0.992335	+	0.123580i	$0.960562\pi$
$168$		0			0
$169$	9.74112	+	5.62404i	0.749317	+	0.432618i
$170$	1.30857	−	0.639400i	0.100363	−	0.0490398i
$171$		0			0
$172$	2.29969	−	2.29969i	0.175350	−	0.175350i
$173$	3.88335	+	14.4929i	0.295246	+	1.10187i	0.941022	+	0.338346i	$0.109867\pi$
$173$	3.88335	+	14.4929i	0.295246	+	1.10187i	−0.645776	+	0.763527i	$0.723466\pi$
$174$		0			0
$175$	7.17505	−	5.42301i	0.542383	−	0.409941i
$176$	15.4583	−	8.92483i	1.16521	−	0.672735i
$177$		0			0
$178$	−26.3933	+	7.07207i	−1.97826	+	0.530074i
$179$	4.21995			0.315414			0.157707	−	0.987486i	$-0.449590\pi$
$179$	4.21995			0.315414			0.157707	+	0.987486i	$0.449590\pi$
$180$		0			0
$181$	23.7930			1.76852			0.884261	−	0.466993i	$-0.154663\pi$
$181$	23.7930			1.76852			0.884261	+	0.466993i	$0.154663\pi$
$182$	3.82366	−	1.02455i	0.283428	−	0.0759444i
$183$		0			0
$184$	3.98492	−	2.30070i	0.293772	−	0.169610i
$185$	−3.36269	−	17.2333i	−0.247230	−	1.26702i
$186$		0			0
$187$	−0.366025	−	1.36603i	−0.0267664	−	0.0998937i
$188$	2.13778	−	2.13778i	0.155914	−	0.155914i
$189$		0			0
$190$	21.9852	+	7.55242i	1.59498	+	0.547910i
$191$	20.1545	+	11.6362i	1.45833	+	0.841965i	0.998929	−	0.0462661i	$-0.0147322\pi$
$191$	20.1545	+	11.6362i	1.45833	+	0.841965i	0.459397	+	0.888231i	$0.348066\pi$
$192$		0			0
$193$	5.36663	−	20.0285i	0.386299	−	1.44169i	−0.449811	−	0.893124i	$-0.648509\pi$
$193$	5.36663	−	20.0285i	0.386299	−	1.44169i	0.836110	−	0.548562i	$-0.184825\pi$
$194$	−4.42566	−	7.66547i	−0.317744	−	0.550348i
$195$		0			0
$196$	1.43871	−	2.49193i	0.102765	−	0.177995i
$197$	6.52613	+	6.52613i	0.464968	+	0.464968i	0.900280	−	0.435312i	$-0.143362\pi$
$197$	6.52613	+	6.52613i	0.464968	+	0.464968i	−0.435312	+	0.900280i	$0.643362\pi$
$198$		0			0
$199$		−	4.03778i		−	0.286231i	−0.989706	−	0.143115i	$-0.954288\pi$
$199$		−	4.03778i		−	0.286231i	0.989706	−	0.143115i	$-0.0457120\pi$
$200$	9.46116	+	3.99995i	0.669005	+	0.282839i
$201$		0			0
$202$	8.77165	+	2.35036i	0.617171	+	0.165370i
$203$	−5.44989	−	1.46029i	−0.382507	−	0.102493i
$204$		0			0
$205$	−0.230013	+	3.32375i	−0.0160648	+	0.232141i
$206$			8.66517i			0.603731i
$207$		0			0
$208$	4.62768	+	4.62768i	0.320872	+	0.320872i
$209$	11.2862	−	19.5483i	0.780684	−	1.35219i
$210$		0			0
$211$	0.653114	+	1.13123i	0.0449623	+	0.0778769i	0.887631	−	0.460556i	$-0.152350\pi$
$211$	0.653114	+	1.13123i	0.0449623	+	0.0778769i	−0.842668	+	0.538433i	$0.819017\pi$
$212$	2.09340	−	7.81268i	0.143775	−	0.536577i
$213$		0			0
$214$	8.29795	+	4.79082i	0.567236	+	0.327494i
$215$	3.09094	−	8.99779i	0.210800	−	0.613644i
$216$		0			0
$217$	6.17155	−	6.17155i	0.418952	−	0.418952i
$218$	0.476572	+	1.77859i	0.0322776	+	0.120461i
$219$		0			0
$220$	−3.44669	+	5.11788i	−0.232376	+	0.345047i
$221$	0.449050	−	0.259259i	0.0302063	−	0.0174396i
$222$		0			0
$223$	8.01142	−	2.14665i	0.536485	−	0.143751i	0.0196035	−	0.999808i	$-0.493760\pi$
$223$	8.01142	−	2.14665i	0.536485	−	0.143751i	0.516881	+	0.856057i	$0.327093\pi$
$224$	−7.39683			−0.494222
$225$		0			0
$226$	−13.8748			−0.922937
$227$	−8.90739	+	2.38673i	−0.591204	+	0.158413i	−0.542003	−	0.840376i	$-0.682334\pi$
$227$	−8.90739	+	2.38673i	−0.591204	+	0.158413i	−0.0492007	+	0.998789i	$0.515667\pi$
$228$		0			0
$229$	−17.2032	+	9.93228i	−1.13682	+	0.656344i	−0.945641	−	0.325211i	$-0.894565\pi$
$229$	−17.2032	+	9.93228i	−1.13682	+	0.656344i	−0.191179	+	0.981555i	$0.561231\pi$
$230$	−4.65145	+	6.90678i	−0.306707	+	0.455419i
$231$		0			0
$232$	−1.66780	−	6.22433i	−0.109497	−	0.408647i
$233$	5.45304	−	5.45304i	0.357241	−	0.357241i	−0.505554	−	0.862795i	$-0.668712\pi$
$233$	5.45304	−	5.45304i	0.357241	−	0.357241i	0.862795	+	0.505554i	$0.168712\pi$
$234$		0			0
$235$	2.87332	−	8.36431i	0.187435	−	0.545627i
$236$	0.369882	+	0.213551i	0.0240772	+	0.0139010i
$237$		0			0
$238$	−0.303235	+	1.13169i	−0.0196558	+	0.0733566i
$239$	−3.48185	−	6.03074i	−0.225222	−	0.390096i	0.731164	−	0.682202i	$-0.238977\pi$
$239$	−3.48185	−	6.03074i	−0.225222	−	0.390096i	−0.956386	+	0.292106i	$0.905644\pi$
$240$		0			0
$241$	−11.7660	+	20.3794i	−0.757918	+	1.31275i	0.185993	+	0.982551i	$0.440450\pi$
$241$	−11.7660	+	20.3794i	−0.757918	+	1.31275i	−0.943911	+	0.330201i	$0.892883\pi$
$242$	2.38920	+	2.38920i	0.153584	+	0.153584i
$243$		0			0
$244$			4.52877i			0.289925i
$245$	0.581120	−	8.39733i	0.0371264	−	0.536486i
$246$		0			0
$247$	7.99413	+	2.14202i	0.508654	+	0.136293i
$248$	9.62847	+	2.57994i	0.611408	+	0.163826i
$249$		0			0
$250$	−18.5613	+	1.01298i	−1.17392	+	0.0640667i
$251$		−	20.7941i		−	1.31251i	−0.754537	−	0.656257i	$-0.772139\pi$
$251$		−	20.7941i		−	1.31251i	0.754537	−	0.656257i	$-0.227861\pi$
$252$		0			0
$253$	5.71742	+	5.71742i	0.359451	+	0.359451i
$254$	−13.6245	+	23.5983i	−0.854876	+	1.48069i
$255$		0			0
$256$	−8.00344	−	13.8624i	−0.500215	−	0.866398i
$257$	−2.72001	+	10.1512i	−0.169670	+	0.633216i	0.827729	+	0.561129i	$0.189633\pi$
$257$	−2.72001	+	10.1512i	−0.169670	+	0.633216i	−0.997398	+	0.0720873i	$0.977034\pi$
$258$		0			0
$259$	12.2323	+	7.06229i	0.760075	+	0.438830i
$260$	−2.13959	−	0.734997i	−0.132692	−	0.0455826i
$261$		0			0
$262$	−5.89718	+	5.89718i	−0.364329	+	0.364329i
$263$	−3.86662	−	14.4304i	−0.238426	−	0.889818i	−0.976574	−	0.215180i	$-0.930966\pi$
$263$	−3.86662	−	14.4304i	−0.238426	−	0.889818i	0.738148	−	0.674638i	$-0.235700\pi$
$264$		0			0
$265$	−4.53143	−	23.2229i	−0.278364	−	1.42657i
$266$	−16.1949	+	9.35012i	−0.992972	+	0.573293i
$267$		0			0
$268$	8.28214	−	2.21919i	0.505912	−	0.135559i
$269$	−0.781994			−0.0476790			−0.0238395	−	0.999716i	$-0.507589\pi$
$269$	−0.781994			−0.0476790			−0.0238395	+	0.999716i	$0.507589\pi$
$270$		0			0
$271$	−12.4677			−0.757357			−0.378679	−	0.925528i	$-0.623621\pi$
$271$	−12.4677			−0.757357			−0.378679	+	0.925528i	$0.623621\pi$
$272$	−1.87099	+	0.501329i	−0.113445	+	0.0303976i
$273$		0			0
$274$	0.657149	−	0.379405i	0.0396998	−	0.0229207i
$275$	−2.48633	+	17.8780i	−0.149931	+	1.07808i
$276$		0			0
$277$	−2.43120	−	9.07336i	−0.146077	−	0.545165i	−0.999705	−	0.0242830i	$-0.992270\pi$
$277$	−2.43120	−	9.07336i	−0.146077	−	0.545165i	0.853629	−	0.520882i	$-0.174397\pi$
$278$	−18.8509	+	18.8509i	−1.13060	+	1.13060i
$279$		0			0
$280$	−7.42428	+	3.62768i	−0.443685	+	0.216796i
$281$	−26.6024	−	15.3589i	−1.58697	−	0.916237i	−0.993803	−	0.111156i	$-0.964545\pi$
$281$	−26.6024	−	15.3589i	−1.58697	−	0.916237i	−0.593165	−	0.805081i	$-0.702122\pi$
$282$		0			0
$283$	−4.86835	+	18.1689i	−0.289393	+	1.08003i	0.656175	+	0.754609i	$0.272173\pi$
$283$	−4.86835	+	18.1689i	−0.289393	+	1.08003i	−0.945569	+	0.325423i	$0.894493\pi$
$284$	3.06369	+	5.30647i	0.181797	+	0.314881i
$285$		0			0
$286$	−3.97224	+	6.88013i	−0.234884	+	0.406830i
$287$	−1.89515	−	1.89515i	−0.111867	−	0.111867i
$288$		0			0
$289$		−	16.8465i		−	0.990973i
$290$	7.65689	+	8.79544i	0.449628	+	0.516486i
$291$		0			0
$292$	−1.35026	−	0.361802i	−0.0790181	−	0.0211728i
$293$	32.6486	+	8.74817i	1.90735	+	0.511074i	0.994765	+	0.102194i	$0.0325861\pi$
$293$	32.6486	+	8.74817i	1.90735	+	0.511074i	0.912588	+	0.408880i	$0.134081\pi$
$294$		0			0
$295$	1.24643	+	0.0862568i	0.0725701	+	0.00502207i
$296$			16.1317i			0.937636i
$297$		0			0
$298$	8.09218	+	8.09218i	0.468767	+	0.468767i
$299$	−1.48229	+	2.56741i	−0.0857232	+	0.148477i
$300$		0			0
$301$	3.82668	+	6.62800i	0.220566	+	0.382031i
$302$	3.70635	−	13.8323i	0.213276	−	0.795959i
$303$		0			0
$304$	−26.7745	−	15.4583i	−1.53562	−	0.886592i
$305$	5.81616	+	11.9031i	0.333033	+	0.681572i
$306$		0			0
$307$	−2.26728	+	2.26728i	−0.129400	+	0.129400i	−0.768841	−	0.639440i	$-0.779166\pi$
$307$	−2.26728	+	2.26728i	−0.129400	+	0.129400i	0.639440	+	0.768841i	$0.279166\pi$
$308$	−1.28468	−	4.79449i	−0.0732014	−	0.273191i
$309$		0			0
$310$	−17.7052	+	3.45477i	−1.00559	+	0.196218i
$311$	1.86689	−	1.07785i	0.105862	−	0.0611193i	−0.446134	−	0.894966i	$-0.647200\pi$
$311$	1.86689	−	1.07785i	0.105862	−	0.0611193i	0.551996	+	0.833847i	$0.313866\pi$
$312$		0			0
$313$	20.9905	−	5.62439i	1.18645	−	0.317909i	0.388971	−	0.921250i	$-0.372831\pi$
$313$	20.9905	−	5.62439i	1.18645	−	0.317909i	0.797483	+	0.603341i	$0.206164\pi$
$314$	−2.77007			−0.156324
$315$		0			0
$316$	−6.15122			−0.346033
$317$	−4.47853	+	1.20002i	−0.251539	+	0.0673997i	−0.382385	−	0.924003i	$-0.624897\pi$
$317$	−4.47853	+	1.20002i	−0.251539	+	0.0673997i	0.130846	+	0.991403i	$0.458231\pi$
$318$		0			0
$319$	9.80630	−	5.66167i	0.549047	−	0.316993i
$320$	−5.66042	−	3.81207i	−0.316427	−	0.213101i
$321$		0			0
$322$	−1.73373	−	6.47035i	−0.0966167	−	0.360579i
$323$	−1.73205	+	1.73205i	−0.0963739	+	0.0963739i
$324$		0			0
$325$	−6.56751	+	0.815995i	−0.364300	+	0.0452633i
$326$	−21.4057	−	12.3586i	−1.18555	−	0.684480i
$327$		0			0
$328$	0.792246	−	2.95670i	0.0437445	−	0.163257i
$329$	3.55726	+	6.16136i	0.196118	+	0.339687i
$330$		0			0
$331$	14.5549	−	25.2097i	0.800007	−	1.38565i	−0.119604	−	0.992822i	$-0.538162\pi$
$331$	14.5549	−	25.2097i	0.800007	−	1.38565i	0.919611	−	0.392831i	$-0.128504\pi$
$332$	0.313757	+	0.313757i	0.0172197	+	0.0172197i
$333$		0			0
$334$			16.1663i			0.884582i
$335$	18.9182	−	16.4693i	1.03361	−	0.899815i
$336$		0			0
$337$	−24.1823	−	6.47963i	−1.31729	−	0.352968i	−0.469330	−	0.883023i	$-0.655505\pi$
$337$	−24.1823	−	6.47963i	−1.31729	−	0.352968i	−0.847963	+	0.530055i	$0.822171\pi$
$338$	18.0643	+	4.84031i	0.982568	+	0.263278i
$339$		0			0
$340$	0.505021	−	0.439647i	0.0273886	−	0.0238432i
$341$			17.5162i			0.948554i
$342$		0			0
$343$	13.6916	+	13.6916i	0.739274	+	0.739274i
$344$	−4.37045	+	7.56984i	−0.235639	+	0.408138i
$345$		0			0
$346$	12.4733	+	21.6043i	0.670566	+	1.16145i
$347$	9.05260	−	33.7848i	0.485969	−	1.81366i	−0.0896885	−	0.995970i	$-0.528587\pi$
$347$	9.05260	−	33.7848i	0.485969	−	1.81366i	0.575657	−	0.817691i	$-0.304746\pi$
$348$		0			0
$349$	17.0932	+	9.86876i	0.914978	+	0.528263i	0.882029	−	0.471194i	$-0.156177\pi$
$349$	17.0932	+	9.86876i	0.914978	+	0.528263i	0.0329483	+	0.999457i	$0.489510\pi$
$350$	9.18941	−	11.7969i	0.491195	−	0.630571i
$351$		0			0
$352$	10.4969	−	10.4969i	0.559487	−	0.559487i
$353$	1.95875	+	7.31017i	0.104254	+	0.389081i	0.998259	−	0.0589749i	$-0.0187832\pi$
$353$	1.95875	+	7.31017i	0.104254	+	0.389081i	−0.894006	+	0.448056i	$0.852117\pi$
$354$		0			0
$355$	14.8674	+	10.0126i	0.789078	+	0.531413i
$356$	−10.8791	+	6.28105i	−0.576591	+	0.332895i
$357$		0			0
$358$	6.77720	−	1.81594i	0.358186	−	0.0959756i
$359$	−8.47760			−0.447430			−0.223715	−	0.974655i	$-0.571819\pi$
$359$	−8.47760			−0.447430			−0.223715	+	0.974655i	$0.571819\pi$
$360$		0			0
$361$	−20.0966			−1.05772
$362$	38.2114	−	10.2387i	2.00835	−	0.538135i
$363$		0			0
$364$	1.57608	−	0.909949i	0.0826089	−	0.0476943i
$365$	−4.01360	+	0.783166i	−0.210081	+	0.0409928i
$366$		0			0
$367$	−2.12506	−	7.93083i	−0.110927	−	0.413986i	0.888023	−	0.459799i	$-0.152079\pi$
$367$	−2.12506	−	7.93083i	−0.110927	−	0.413986i	−0.998950	+	0.0458135i	$0.985412\pi$
$368$	7.83091	−	7.83091i	0.408215	−	0.408215i
$369$		0			0
$370$	−12.8163	−	26.2294i	−0.666290	−	1.36360i
$371$	16.4837	+	9.51686i	0.855791	+	0.494091i
$372$		0			0
$373$	−5.56939	+	20.7853i	−0.288372	+	1.07622i	0.657967	+	0.753046i	$0.271416\pi$
$373$	−5.56939	+	20.7853i	−0.288372	+	1.07622i	−0.946340	+	0.323174i	$0.895250\pi$
$374$	−1.17567	−	2.03631i	−0.0607923	−	0.105295i
$375$		0			0
$376$	−4.06275	+	7.03689i	−0.209520	+	0.362900i
$377$	2.93568	+	2.93568i	0.151195	+	0.151195i
$378$		0			0
$379$		−	11.1614i		−	0.573325i	−0.958032	−	0.286663i	$-0.907454\pi$
$379$		−	11.1614i		−	0.573325i	0.958032	−	0.286663i	$-0.0925458\pi$
$380$	10.6617	+	0.737824i	0.546936	+	0.0378496i
$381$		0			0
$382$	37.3752	+	10.0147i	1.91228	+	0.512394i
$383$	−14.6977	−	3.93824i	−0.751018	−	0.201235i	−0.137049	−	0.990564i	$-0.543762\pi$
$383$	−14.6977	−	3.93824i	−0.751018	−	0.201235i	−0.613970	+	0.789330i	$0.710428\pi$
$384$		0			0
$385$	−9.53400	−	10.9517i	−0.485898	−	0.558149i
$386$		−	34.4750i		−	1.75473i
$387$		0			0
$388$	−2.87743	−	2.87743i	−0.146079	−	0.146079i
$389$	−12.7395	+	22.0655i	−0.645920	+	1.11877i	0.338168	+	0.941086i	$0.390193\pi$
$389$	−12.7395	+	22.0655i	−0.645920	+	1.11877i	−0.984088	+	0.177681i	$0.943140\pi$
$390$		0			0
$391$	−0.438715	−	0.759876i	−0.0221868	−	0.0384286i
$392$	−2.00158	+	7.47000i	−0.101095	+	0.377292i
$393$		0			0
$394$	13.2893	+	7.67255i	0.669503	+	0.386538i
$395$	−16.1675	+	7.89984i	−0.813475	+	0.397484i
$396$		0			0
$397$	−5.96779	+	5.96779i	−0.299515	+	0.299515i	−0.840824	−	0.541309i	$-0.817929\pi$
$397$	−5.96779	+	5.96779i	−0.299515	+	0.299515i	0.541309	+	0.840824i	$0.317929\pi$
$398$	−1.73755	−	6.48464i	−0.0870957	−	0.325046i
$399$		0			0
$400$	24.4868	+	3.40542i	1.22434	+	0.170271i
$401$	−23.6805	+	13.6719i	−1.18255	+	0.682744i	−0.956602	−	0.291396i	$-0.905880\pi$
$401$	−23.6805	+	13.6719i	−1.18255	+	0.682744i	−0.225945	+	0.974140i	$0.572547\pi$
$402$		0			0
$403$	−6.20343	+	1.66220i	−0.309015	+	0.0828003i
$404$	4.17493			0.207711
$405$		0			0
$406$	−9.38087			−0.465565
$407$	−27.3810	+	7.33673i	−1.35723	+	0.363668i
$408$		0			0
$409$	23.5441	−	13.5932i	1.16418	−	0.672140i	0.211878	−	0.977296i	$-0.432042\pi$
$409$	23.5441	−	13.5932i	1.16418	−	0.672140i	0.952302	+	0.305157i	$0.0987088\pi$
$410$	1.06089	+	5.43689i	0.0523936	+	0.268509i
$411$		0			0
$412$	1.03106	+	3.84798i	0.0507968	+	0.189576i
$413$	−0.710697	+	0.710697i	−0.0349711	+	0.0349711i
$414$		0			0
$415$	1.22761	+	0.421711i	0.0602610	+	0.0207010i
$416$	4.71363	+	2.72142i	0.231105	+	0.133428i
$417$		0			0
$418$	9.71346	−	36.2511i	0.475101	−	1.77310i
$419$	−15.7018	−	27.1964i	−0.767084	−	1.32863i	−0.939138	−	0.343541i	$-0.888373\pi$
$419$	−15.7018	−	27.1964i	−0.767084	−	1.32863i	0.172053	−	0.985088i	$-0.444960\pi$
$420$		0			0
$421$	−15.4328	+	26.7304i	−0.752150	+	1.30276i	0.194629	+	0.980877i	$0.437650\pi$
$421$	−15.4328	+	26.7304i	−0.752150	+	1.30276i	−0.946779	+	0.321885i	$0.895683\pi$
$422$	1.53569	+	1.53569i	0.0747562	+	0.0747562i
$423$		0			0
$424$			21.7384i			1.05571i
$425$	0.762741	−	1.80413i	0.0369984	−	0.0875130i
$426$		0			0
$427$	−10.2942	−	2.75831i	−0.498170	−	0.133484i
$428$	4.25496	+	1.14011i	0.205671	+	0.0551095i
$429$		0			0
$430$	1.09206	−	15.7805i	0.0526636	−	0.761002i
$431$		−	32.6869i		−	1.57447i	−0.616652	−	0.787236i	$-0.711511\pi$
$431$		−	32.6869i		−	1.57447i	0.616652	−	0.787236i	$-0.288489\pi$
$432$		0			0
$433$	−7.25927	−	7.25927i	−0.348858	−	0.348858i	0.510826	−	0.859684i	$-0.329340\pi$
$433$	−7.25927	−	7.25927i	−0.348858	−	0.348858i	−0.859684	+	0.510826i	$0.829340\pi$
$434$	7.25568	−	12.5672i	0.348284	−	0.603245i
$435$		0			0
$436$	0.423267	+	0.733120i	0.0202708	+	0.0351101i
$437$	3.62470	−	13.5276i	0.173393	−	0.647111i
$438$		0			0
$439$	−19.4684	−	11.2401i	−0.929175	−	0.536459i	−0.0426241	−	0.999091i	$-0.513572\pi$
$439$	−19.4684	−	11.2401i	−0.929175	−	0.536459i	−0.886550	+	0.462632i	$0.846905\pi$
$440$	5.38777	−	15.6839i	0.256852	−	0.747702i
$441$		0			0
$442$	0.609604	−	0.609604i	0.0289959	−	0.0289959i
$443$	2.00030	+	7.46524i	0.0950373	+	0.354684i	0.997025	−	0.0770774i	$-0.0245589\pi$
$443$	2.00030	+	7.46524i	0.0950373	+	0.354684i	−0.901988	+	0.431762i	$0.857892\pi$
$444$		0			0
$445$	−20.5274	+	30.4804i	−0.973091	+	1.44491i
$446$	11.9425	−	6.89501i	0.565494	−	0.326488i
$447$		0			0
$448$	5.30275	−	1.42087i	0.250531	−	0.0671297i
$449$	38.1502			1.80042			0.900209	−	0.435458i	$-0.143414\pi$
$449$	38.1502			1.80042			0.900209	+	0.435458i	$0.143414\pi$
$450$		0			0
$451$	5.37886			0.253280
$452$	−6.16144	+	1.65095i	−0.289810	+	0.0776543i
$453$		0			0
$454$	−13.2781	+	7.66612i	−0.623173	+	0.359789i
$455$	2.97385	−	4.41577i	0.139416	−	0.207014i
$456$		0			0
$457$	7.20855	+	26.9027i	0.337202	+	1.25845i	0.901463	+	0.432857i	$0.142495\pi$
$457$	7.20855	+	26.9027i	0.337202	+	1.25845i	−0.564261	+	0.825596i	$0.690839\pi$
$458$	−23.3541	+	23.3541i	−1.09127	+	1.09127i
$459$		0			0
$460$	−1.24375	+	3.62060i	−0.0579903	+	0.168811i
$461$	21.2301	+	12.2572i	0.988784	+	0.570874i	0.904910	−	0.425602i	$-0.139938\pi$
$461$	21.2301	+	12.2572i	0.988784	+	0.570874i	0.0838731	+	0.996476i	$0.473271\pi$
$462$		0			0
$463$	−4.62735	+	17.2695i	−0.215051	+	0.802582i	0.771097	+	0.636717i	$0.219708\pi$
$463$	−4.62735	+	17.2695i	−0.215051	+	0.802582i	−0.986149	+	0.165865i	$0.946958\pi$
$464$	−7.75455	−	13.4313i	−0.359996	−	0.623531i
$465$		0			0
$466$	6.41096	−	11.1041i	0.296982	−	0.514388i
$467$	22.2894	+	22.2894i	1.03143	+	1.03143i	0.999490	+	0.0319412i	$0.0101689\pi$
$467$	22.2894	+	22.2894i	1.03143	+	1.03143i	0.0319412	+	0.999490i	$0.489831\pi$
$468$		0			0
$469$			20.1775i			0.931709i
$470$	1.01517	−	14.6695i	0.0468263	−	0.676652i
$471$		0			0
$472$	−1.10879	−	0.297098i	−0.0510360	−	0.0136751i
$473$	−14.8363	−	3.97538i	−0.682174	−	0.182788i
$474$		0			0
$475$	28.9702	−	11.7533i	1.32925	−	0.539279i
$476$			0.538636i			0.0246883i
$477$		0			0
$478$	−8.18699	−	8.18699i	−0.374464	−	0.374464i
$479$	−6.76273	+	11.7134i	−0.308997	+	0.535199i	−0.978143	−	0.207932i	$-0.933327\pi$
$479$	−6.76273	+	11.7134i	−0.308997	+	0.535199i	0.669146	+	0.743131i	$0.266660\pi$
$480$		0			0
$481$	−5.19667	−	9.00089i	−0.236948	−	0.410405i
$482$	−10.1264	+	37.7923i	−0.461246	+	1.72139i
$483$		0			0
$484$	1.34527	+	0.776693i	0.0611487	+	0.0353042i
$485$	−11.2583	−	3.86746i	−0.511211	−	0.175612i
$486$		0			0
$487$	17.7890	−	17.7890i	0.806094	−	0.806094i	−0.177946	−	0.984040i	$-0.556945\pi$
$487$	17.7890	−	17.7890i	0.806094	−	0.806094i	0.984040	+	0.177946i	$0.0569452\pi$
$488$	−3.15027	−	11.7570i	−0.142606	−	0.532213i
$489$		0			0
$490$	−2.68030	−	13.7361i	−0.121084	−	0.620534i
$491$	17.9785	−	10.3799i	0.811359	−	0.468438i	−0.0360688	−	0.999349i	$-0.511484\pi$
$491$	17.9785	−	10.3799i	0.811359	−	0.468438i	0.847427	+	0.530911i	$0.178150\pi$
$492$		0			0
$493$	−1.18690	+	0.318030i	−0.0534554	+	0.0143233i
$494$	13.7603			0.619103
$495$		0			0
$496$	23.9912			1.07724
$497$	−13.9279	+	3.73197i	−0.624752	+	0.167402i
$498$		0			0
$499$	−8.56156	+	4.94302i	−0.383268	+	0.221280i	−0.679239	−	0.733917i	$-0.737690\pi$
$499$	−8.56156	+	4.94302i	−0.383268	+	0.221280i	0.295971	+	0.955197i	$0.404357\pi$
$500$	−8.12206	+	2.65844i	−0.363230	+	0.118889i
$501$		0			0
$502$	−8.94821	−	33.3952i	−0.399378	−	1.49050i
$503$	−16.8084	+	16.8084i	−0.749450	+	0.749450i	−0.974376	−	0.224926i	$-0.927786\pi$
$503$	−16.8084	+	16.8084i	−0.749450	+	0.749450i	0.224926	+	0.974376i	$0.427786\pi$
$504$		0			0
$505$	10.9731	−	5.36174i	0.488298	−	0.238594i
$506$	11.6425	+	6.72178i	0.517571	+	0.298820i
$507$		0			0
$508$	−3.24234	+	12.1006i	−0.143855	+	0.536876i
$509$	20.1795	+	34.9520i	0.894442	+	1.54922i	0.834494	+	0.551017i	$0.185760\pi$
$509$	20.1795	+	34.9520i	0.894442	+	1.54922i	0.0599475	+	0.998202i	$0.480907\pi$
$510$		0			0
$511$	1.64480	−	2.84887i	0.0727615	−	0.126027i
$512$	−0.0117190	−	0.0117190i	−0.000517913	−	0.000517913i
$513$		0			0
$514$			17.4733i			0.770712i
$515$	7.65183	+	8.78963i	0.337180	+	0.387317i
$516$		0			0
$517$	−13.7918	−	3.69550i	−0.606562	−	0.162528i
$518$	22.6839	+	6.07815i	0.996675	+	0.267058i
$519$		0			0
$520$	6.06580	+	0.419772i	0.266003	+	0.0184082i
$521$			11.5144i			0.504456i	0.967668	+	0.252228i	$0.0811633\pi$
$521$			11.5144i			0.504456i	−0.967668	+	0.252228i	$0.918837\pi$
$522$		0			0
$523$	−29.5457	−	29.5457i	−1.29194	−	1.29194i	−0.933584	−	0.358358i	$-0.883337\pi$
$523$	−29.5457	−	29.5457i	−1.29194	−	1.29194i	−0.358358	−	0.933584i	$-0.616663\pi$
$524$	−1.91708	+	3.32049i	−0.0837482	+	0.145056i
$525$		0			0
$526$	−12.4195	−	21.5112i	−0.541517	−	0.937934i
$527$	0.491963	−	1.83603i	0.0214303	−	0.0799788i
$528$		0			0
$529$	−15.5740	−	8.99168i	−0.677133	−	0.390943i
$530$	−17.2708	−	35.3457i	−0.750195	−	1.53532i
$531$		0			0
$532$	−6.07917	+	6.07917i	−0.263565	+	0.263565i
$533$	0.510428	+	1.90494i	0.0221091	+	0.0825123i
$534$		0			0
$535$	12.6477	−	2.46792i	0.546808	−	0.106697i
$536$	−19.9573	+	11.5223i	−0.862024	+	0.497690i
$537$		0			0
$538$	−1.25587	+	0.336511i	−0.0541446	+	0.0145080i
$539$	−13.5895			−0.585340
$540$		0			0
$541$	6.30670			0.271146			0.135573	−	0.990767i	$-0.456712\pi$
$541$	6.30670			0.271146			0.135573	+	0.990767i	$0.456712\pi$
$542$	−20.0230	+	5.36514i	−0.860060	+	0.230452i
$543$		0			0
$544$	−1.39509	+	0.805458i	−0.0598142	+	0.0345337i
$545$	2.05401	+	1.38330i	0.0879843	+	0.0592540i
$546$		0			0
$547$	7.99863	+	29.8513i	0.341997	+	1.27635i	0.896082	+	0.443889i	$0.146401\pi$
$547$	7.99863	+	29.8513i	0.341997	+	1.27635i	−0.554085	+	0.832460i	$0.686932\pi$
$548$	0.246678	−	0.246678i	0.0105375	−	0.0105375i
$549$		0			0
$550$	3.70031	+	29.7818i	0.157782	+	1.26990i
$551$	−16.9850	−	9.80630i	−0.723586	−	0.417762i
$552$		0			0
$553$	3.74650	−	13.9821i	0.159317	−	0.594580i
$554$	−7.80896	−	13.5255i	−0.331771	−	0.574644i
$555$		0			0
$556$	−6.12814	+	10.6143i	−0.259891	+	0.450145i
$557$	−6.63181	−	6.63181i	−0.280999	−	0.280999i	0.552509	−	0.833507i	$-0.313671\pi$
$557$	−6.63181	−	6.63181i	−0.280999	−	0.280999i	−0.833507	+	0.552509i	$0.813671\pi$
$558$		0			0
$559$		−	5.63159i		−	0.238191i
$560$	−15.0000	+	13.0583i	−0.633867	+	0.551815i
$561$		0			0
$562$	−49.3326	−	13.2186i	−2.08097	−	0.557594i
$563$	18.2031	+	4.87751i	0.767170	+	0.205563i	0.621121	−	0.783715i	$-0.286678\pi$
$563$	18.2031	+	4.87751i	0.767170	+	0.205563i	0.146049	+	0.989277i	$0.453344\pi$
$564$		0			0
$565$	−14.0741	+	12.2522i	−0.592101	+	0.515455i
$566$			31.2741i			1.31455i
$567$		0			0
$568$	−11.6448	−	11.6448i	−0.488605	−	0.488605i
$569$	10.4878	−	18.1654i	0.439670	−	0.761531i	−0.557994	−	0.829845i	$-0.688429\pi$
$569$	10.4878	−	18.1654i	0.439670	−	0.761531i	0.997664	+	0.0683141i	$0.0217620\pi$
$570$		0			0
$571$	−12.2406	−	21.2014i	−0.512254	−	0.887250i	−0.999899	−	0.0142078i	$-0.995477\pi$
$571$	−12.2406	−	21.2014i	−0.512254	−	0.887250i	0.487645	−	0.873042i	$-0.337856\pi$
$572$	−0.945309	+	3.52794i	−0.0395254	+	0.147511i
$573$		0			0
$574$	−3.85913	−	2.22807i	−0.161077	−	0.0929978i
$575$	1.38082	+	11.1135i	0.0575841	+	0.463464i
$576$		0			0
$577$	−12.4198	+	12.4198i	−0.517041	+	0.517041i	−0.916675	−	0.399634i	$-0.869137\pi$
$577$	−12.4198	+	12.4198i	−0.517041	+	0.517041i	0.399634	+	0.916675i	$0.369137\pi$
$578$	−7.24946	−	27.0554i	−0.301538	−	1.12535i
$579$		0			0
$580$	4.44679	+	2.99474i	0.184643	+	0.124350i
$581$	−0.904288	+	0.522091i	−0.0375162	+	0.0216600i
$582$		0			0
$583$	−36.8976	+	9.88668i	−1.52814	+	0.409465i
$584$	3.75705			0.155468
$585$		0			0
$586$	56.1979			2.32151
$587$	−14.6173	+	3.91669i	−0.603320	+	0.161659i	−0.547534	−	0.836784i	$-0.684433\pi$
$587$	−14.6173	+	3.91669i	−0.603320	+	0.161659i	−0.0557861	+	0.998443i	$0.517766\pi$
$588$		0			0
$589$	26.2743	−	15.1695i	1.08261	−	0.625047i
$590$	2.03888	−	0.397842i	0.0839392	−	0.0163789i
$591$		0			0
$592$	10.0488	+	37.5027i	0.413003	+	1.54135i
$593$	12.8270	−	12.8270i	0.526744	−	0.526744i	−0.392856	−	0.919600i	$-0.628513\pi$
$593$	12.8270	−	12.8270i	0.526744	−	0.526744i	0.919600	+	0.392856i	$0.128513\pi$
$594$		0			0
$595$	0.691755	+	1.41572i	0.0283592	+	0.0580388i
$596$	4.55641	+	2.63064i	0.186638	+	0.107755i
$597$		0			0
$598$	−1.27573	+	4.76109i	−0.0521685	+	0.194696i
$599$	3.45057	+	5.97656i	0.140987	+	0.244196i	0.927868	−	0.372908i	$-0.121639\pi$
$599$	3.45057	+	5.97656i	0.140987	+	0.244196i	−0.786882	+	0.617104i	$0.788306\pi$
$600$		0			0
$601$	6.29969	−	10.9114i	0.256970	−	0.445085i	−0.708459	−	0.705752i	$-0.750609\pi$
$601$	6.29969	−	10.9114i	0.256970	−	0.445085i	0.965429	+	0.260667i	$0.0839426\pi$
$602$	8.99779	+	8.99779i	0.366722	+	0.366722i
$603$		0			0
$604$		−	6.58358i		−	0.267882i
$605$	4.53331	+	0.313719i	0.184305	+	0.0127545i
$606$		0			0
$607$	35.9453	+	9.63152i	1.45898	+	0.390931i	0.899136	−	0.437670i	$-0.144196\pi$
$607$	35.9453	+	9.63152i	1.45898	+	0.390931i	0.559839	+	0.828601i	$0.310863\pi$
$608$	−24.8359	−	6.65477i	−1.00723	−	0.269887i
$609$		0			0
$610$	14.4629	+	16.6135i	0.585586	+	0.672660i
$611$		−	5.23510i		−	0.211789i
$612$		0			0
$613$	12.4072	+	12.4072i	0.501121	+	0.501121i	0.911786	−	0.410665i	$-0.134704\pi$
$613$	12.4072	+	12.4072i	0.501121	+	0.501121i	−0.410665	+	0.911786i	$0.634704\pi$
$614$	−2.66556	+	4.61689i	−0.107573	+	0.186322i
$615$		0			0
$616$	6.67023	+	11.5532i	0.268751	+	0.465491i
$617$	2.65843	−	9.92141i	0.107025	−	0.399421i	−0.891542	−	0.452937i	$-0.850376\pi$
$617$	2.65843	−	9.92141i	0.107025	−	0.399421i	0.998567	+	0.0535162i	$0.0170429\pi$
$618$		0			0
$619$	−19.1639	−	11.0643i	−0.770264	−	0.444712i	0.0627048	−	0.998032i	$-0.480027\pi$
$619$	−19.1639	−	11.0643i	−0.770264	−	0.444712i	−0.832969	+	0.553320i	$0.813361\pi$
$620$	−7.45133	+	3.64090i	−0.299253	+	0.146222i
$621$		0			0
$622$	2.53439	−	2.53439i	0.101620	−	0.101620i
$623$	−7.65114	−	28.5544i	−0.306536	−	1.14401i
$624$		0			0
$625$	−17.9334	+	17.4182i	−0.717335	+	0.696728i
$626$	31.2902	−	18.0654i	1.25061	−	0.722040i
$627$		0			0
$628$	−1.23012	+	0.329609i	−0.0490870	+	0.0131528i
$629$	3.07612			0.122653
$630$		0			0
$631$	8.15013			0.324451			0.162226	−	0.986754i	$-0.448133\pi$
$631$	8.15013			0.324451			0.162226	+	0.986754i	$0.448133\pi$
$632$	15.9690	−	4.27888i	0.635212	−	0.170205i
$633$		0			0
$634$	−6.67608	+	3.85443i	−0.265141	+	0.153079i
$635$	7.01845	+	35.9684i	0.278519	+	1.42736i
$636$		0			0
$637$	−1.28958	−	4.81277i	−0.0510949	−	0.190689i
$638$	13.3125	−	13.3125i	0.527046	−	0.527046i
$639$		0			0
$640$	−28.1234	−	9.66101i	−1.11168	−	0.381885i
$641$	2.49058	+	1.43794i	0.0983722	+	0.0567952i	0.548379	−	0.836230i	$-0.315245\pi$
$641$	2.49058	+	1.43794i	0.0983722	+	0.0567952i	−0.450007	+	0.893025i	$0.648578\pi$
$642$		0			0
$643$	2.54626	−	9.50279i	0.100415	−	0.374753i	−0.897370	−	0.441279i	$-0.854525\pi$
$643$	2.54626	−	9.50279i	0.100415	−	0.374753i	0.997785	+	0.0665259i	$0.0211915\pi$
$644$	−1.53981	−	2.66702i	−0.0606768	−	0.105095i
$645$		0			0
$646$	−2.03631	+	3.52700i	−0.0801177	+	0.138768i
$647$	−14.2662	−	14.2662i	−0.560862	−	0.560862i	0.368691	−	0.929552i	$-0.379806\pi$
$647$	−14.2662	−	14.2662i	−0.560862	−	0.560862i	−0.929552	+	0.368691i	$0.879806\pi$
$648$		0			0
$649$		−	2.01711i		−	0.0791786i
$650$	−10.1962	+	4.13664i	−0.399929	+	0.162252i
$651$		0			0
$652$	−10.9763	−	2.94108i	−0.429864	−	0.115182i
$653$	−38.3580	−	10.2780i	−1.50106	−	0.402209i	−0.587607	−	0.809146i	$-0.699930\pi$
$653$	−38.3580	−	10.2780i	−1.50106	−	0.402209i	−0.913456	+	0.406937i	$0.866597\pi$
$654$		0			0
$655$	−0.774342	+	11.1894i	−0.0302560	+	0.437207i
$656$		−	7.36719i		−	0.287641i
$657$		0			0
$658$	8.36431	+	8.36431i	0.326075	+	0.326075i
$659$	23.3689	−	40.4762i	0.910324	−	1.57673i	0.0967171	−	0.995312i	$-0.469166\pi$
$659$	23.3689	−	40.4762i	0.910324	−	1.57673i	0.813607	−	0.581415i	$-0.197501\pi$
$660$		0			0
$661$	−2.81433	−	4.87455i	−0.109465	−	0.189598i	0.806089	−	0.591794i	$-0.201580\pi$
$661$	−2.81433	−	4.87455i	−0.109465	−	0.189598i	−0.915553	+	0.402196i	$0.868247\pi$
$662$	12.5266	−	46.7499i	0.486860	−	1.81699i
$663$		0			0
$664$	−1.03279	−	0.596280i	−0.0400799	−	0.0231402i
$665$	−8.17082	+	23.7854i	−0.316851	+	0.922359i
$666$		0			0
$667$	4.96772	−	4.96772i	0.192351	−	0.192351i
$668$	1.92362	+	7.17905i	0.0744271	+	0.277766i
$669$		0			0
$670$	23.2954	−	34.5905i	0.899979	−	1.33635i
$671$	18.5229	−	10.6942i	0.715068	−	0.412845i
$672$		0			0
$673$	28.7938	−	7.71528i	1.10992	−	0.297402i	0.343122	−	0.939291i	$-0.388515\pi$
$673$	28.7938	−	7.71528i	1.10992	−	0.297402i	0.766798	+	0.641888i	$0.221849\pi$
$674$	−41.6249			−1.60333
$675$		0			0
$676$	8.59784			0.330686
$677$	48.2839	−	12.9376i	1.85570	−	0.497234i	0.855900	−	0.517141i	$-0.173004\pi$
$677$	48.2839	−	12.9376i	1.85570	−	0.497234i	0.999802	+	0.0199076i	$0.00633719\pi$
$678$		0			0
$679$	8.29312	−	4.78804i	0.318261	−	0.183748i
$680$	−1.00524	+	1.49265i	−0.0385493	+	0.0572407i
$681$		0			0
$682$	7.53763	+	28.1308i	0.288631	+	1.07718i
$683$	−4.38271	+	4.38271i	−0.167700	+	0.167700i	−0.785968	−	0.618268i	$-0.787835\pi$
$683$	−4.38271	+	4.38271i	−0.167700	+	0.167700i	0.618268	+	0.785968i	$0.287835\pi$
$684$		0			0
$685$	0.331552	−	0.965154i	0.0126679	−	0.0368766i
$686$	27.8803	+	16.0967i	1.06447	+	0.614575i
$687$		0			0
$688$	−5.44491	+	20.3207i	−0.207585	+	0.774718i
$689$	−7.00282	−	12.1292i	−0.266786	−	0.462087i
$690$		0			0
$691$	−0.346648	+	0.600412i	−0.0131871	+	0.0228407i	−0.872544	−	0.488536i	$-0.837531\pi$
$691$	−0.346648	+	0.600412i	−0.0131871	+	0.0228407i	0.859357	+	0.511377i	$0.170864\pi$
$692$	8.10973	+	8.10973i	0.308286	+	0.308286i
$693$		0			0
$694$		−	58.1535i		−	2.20748i
$695$	−2.47526	+	35.7681i	−0.0938919	+	1.35676i
$696$		0			0
$697$	−0.563807	−	0.151072i	−0.0213557	−	0.00572225i
$698$	31.6983	+	8.49352i	1.19980	+	0.321485i
$699$		0			0
$700$	2.67708	−	6.33214i	0.101184	−	0.239332i
$701$			8.36037i			0.315767i	0.987458	+	0.157883i	$0.0504670\pi$
$701$			8.36037i			0.315767i	−0.987458	+	0.157883i	$0.949533\pi$
$702$		0			0
$703$	34.7178	+	34.7178i	1.30941	+	1.30941i
$704$	−5.50881	+	9.54154i	−0.207621	+	0.359610i
$705$		0			0
$706$	6.29148	+	10.8972i	0.236783	+	0.410120i
$707$	−2.54281	+	9.48988i	−0.0956320	+	0.356904i
$708$		0			0
$709$	4.59399	+	2.65234i	0.172531	+	0.0996109i	0.583779	−	0.811913i	$-0.301574\pi$
$709$	4.59399	+	2.65234i	0.172531	+	0.0996109i	−0.411248	+	0.911524i	$0.634907\pi$
$710$	28.1855	+	9.68234i	1.05778	+	0.363372i
$711$		0			0
$712$	23.8737	−	23.8737i	0.894704	−	0.894704i
$713$	2.81276	+	10.4974i	0.105339	+	0.393130i
$714$		0			0
$715$	2.04624	+	10.4867i	0.0765251	+	0.392179i
$716$	2.79350	−	1.61283i	0.104398	−	0.0602742i
$717$		0			0
$718$	−13.6149	+	3.64811i	−0.508105	+	0.136146i
$719$	28.3121			1.05586			0.527932	−	0.849286i	$-0.322967\pi$
$719$	28.3121			1.05586			0.527932	+	0.849286i	$0.322967\pi$
$720$		0			0
$721$	−9.37468			−0.349131
$722$	−32.2750	+	8.64806i	−1.20115	+	0.321847i
$723$		0			0
$724$	15.7504	−	9.09349i	0.585359	−	0.337957i
$725$	15.5337	+	2.16031i	0.576908	+	0.0802318i
$726$		0			0
$727$	−11.6483	−	43.4720i	−0.432011	−	1.61229i	−0.748119	−	0.663565i	$-0.769043\pi$
$727$	−11.6483	−	43.4720i	−0.432011	−	1.61229i	0.316108	−	0.948723i	$-0.397624\pi$
$728$	−3.45863	+	3.45863i	−0.128185	+	0.128185i
$729$		0			0
$730$	−6.10879	+	2.98490i	−0.226096	+	0.110476i
$731$	1.44348	+	0.833392i	0.0533889	+	0.0308241i
$732$		0			0
$733$	6.25836	−	23.3565i	0.231158	−	0.862693i	−0.748685	−	0.662926i	$-0.769315\pi$
$733$	6.25836	−	23.3565i	0.231158	−	0.862693i	0.979843	−	0.199768i	$-0.0640187\pi$
$734$	−6.82565	−	11.8224i	−0.251939	−	0.436372i
$735$		0			0
$736$	4.60515	−	7.97635i	0.169748	−	0.294012i
$737$	−28.6340	−	28.6340i	−1.05475	−	1.05475i
$738$		0			0
$739$		−	5.60736i		−	0.206270i	−0.994667	−	0.103135i	$-0.967113\pi$
$739$		−	5.60736i		−	0.206270i	0.994667	−	0.103135i	$-0.0328874\pi$
$740$	−8.81243	−	10.1228i	−0.323951	−	0.372122i
$741$		0			0
$742$	30.5680	+	8.19067i	1.12219	+	0.300689i
$743$	8.24852	+	2.21018i	0.302609	+	0.0810838i	0.406928	−	0.913460i	$-0.366600\pi$
$743$	8.24852	+	2.21018i	0.302609	+	0.0810838i	−0.104320	+	0.994544i	$0.533267\pi$
$744$		0			0
$745$	15.3543	+	1.06256i	0.562536	+	0.0389292i
$746$			35.7776i			1.30991i
$747$		0			0
$748$	−0.764383	−	0.764383i	−0.0279486	−	0.0279486i
$749$	−5.18310	+	8.97739i	−0.189386	+	0.328027i
$750$		0			0
$751$	2.32268	+	4.02301i	0.0847560	+	0.146802i	0.905287	−	0.424800i	$-0.139656\pi$
$751$	2.32268	+	4.02301i	0.0847560	+	0.146802i	−0.820531	+	0.571602i	$0.806322\pi$
$752$	−5.06156	+	18.8900i	−0.184576	+	0.688848i
$753$		0			0
$754$	5.97796	+	3.45138i	0.217704	+	0.125692i
$755$	−8.45510	−	17.3039i	−0.307713	−	0.629753i
$756$		0			0
$757$	−3.09830	+	3.09830i	−0.112609	+	0.112609i	−0.761166	−	0.648557i	$-0.775373\pi$
$757$	−3.09830	+	3.09830i	−0.112609	+	0.112609i	0.648557	+	0.761166i	$0.275373\pi$
$758$	−4.80304	−	17.9252i	−0.174454	−	0.651072i
$759$		0			0
$760$	−28.1918	+	5.50102i	−1.02263	+	0.199543i
$761$	−38.9876	+	22.5095i	−1.41330	+	0.815968i	−0.995698	−	0.0926625i	$-0.970462\pi$
$761$	−38.9876	+	22.5095i	−1.41330	+	0.815968i	−0.417601	+	0.908631i	$0.637129\pi$
$762$		0			0
$763$	−1.92422	+	0.515595i	−0.0696616	+	0.0186658i
$764$	17.7890			0.643584
$765$		0			0
$766$	−25.2991			−0.914094
$767$	0.714369	−	0.191415i	0.0257944	−	0.00691158i
$768$		0			0
$769$	−5.40503	+	3.12060i	−0.194910	+	0.112532i	−0.594279	−	0.804259i	$-0.702563\pi$
$769$	−5.40503	+	3.12060i	−0.194910	+	0.112532i	0.399369	+	0.916790i	$0.369229\pi$
$770$	−20.0243	−	13.4856i	−0.721625	−	0.485986i
$771$		0			0
$772$	−4.10216	−	15.3095i	−0.147640	−	0.551000i
$773$	19.5366	−	19.5366i	0.702681	−	0.702681i	−0.262304	−	0.964985i	$-0.584482\pi$
$773$	19.5366	−	19.5366i	0.702681	−	0.702681i	0.964985	+	0.262304i	$0.0844823\pi$
$774$		0			0
$775$	−14.9087	+	19.1391i	−0.535537	+	0.687495i
$776$	9.47158	+	5.46842i	0.340010	+	0.196305i
$777$		0			0
$778$	−10.9643	+	40.9192i	−0.393088	+	1.46702i
$779$	−4.65823	−	8.06829i	−0.166898	−	0.289076i
$780$		0			0
$781$	14.4691	−	25.0613i	0.517747	−	0.896764i
$782$	−1.03156	−	1.03156i	−0.0368887	−	0.0368887i
$783$		0			0
$784$			18.6129i			0.664748i
$785$	−2.80986	+	2.44613i	−0.100288	+	0.0873061i
$786$		0			0
$787$	−28.3409	−	7.59393i	−1.01024	−	0.270694i	−0.284513	−	0.958672i	$-0.591832\pi$
$787$	−28.3409	−	7.59393i	−1.01024	−	0.270694i	−0.725732	+	0.687978i	$0.758499\pi$
$788$	6.81437	+	1.82590i	0.242752	+	0.0650451i
$789$		0			0
$790$	−22.5654	+	19.6443i	−0.802840	+	0.698914i
$791$		−	15.0109i		−	0.533725i
$792$		0			0
$793$	5.54513	+	5.54513i	0.196913	+	0.196913i
$794$	−7.01613	+	12.1523i	−0.248993	+	0.431269i
$795$		0			0
$796$	−1.54321	−	2.67291i	−0.0546975	−	0.0947388i
$797$	−0.454070	+	1.69461i	−0.0160840	+	0.0600263i	−0.973501	−	0.228681i	$-0.926559\pi$
$797$	−0.454070	+	1.69461i	−0.0160840	+	0.0600263i	0.957417	+	0.288707i	$0.0932254\pi$
$798$		0			0
$799$	1.34185	+	0.774718i	0.0474712	+	0.0274075i
$800$	20.4038	−	2.53511i	0.721382	−	0.0896298i
$801$		0			0
$802$	−32.1473	+	32.1473i	−1.13516	+	1.13516i
$803$	1.70871	+	6.37700i	0.0602991	+	0.225039i
$804$		0			0
$805$	−7.47231	−	5.03231i	−0.263364	−	0.177366i
$806$	−9.24736	+	5.33897i	−0.325724	+	0.188057i
$807$		0			0
$808$	−10.8384	+	2.90414i	−0.381294	+	0.102167i
$809$	−27.5870			−0.969908			−0.484954	−	0.874540i	$-0.661164\pi$
$809$	−27.5870			−0.969908			−0.484954	+	0.874540i	$0.661164\pi$
$810$		0			0
$811$	−44.5699			−1.56506			−0.782530	−	0.622613i	$-0.786071\pi$
$811$	−44.5699			−1.56506			−0.782530	+	0.622613i	$0.786071\pi$
$812$	−4.16580	+	1.11622i	−0.146191	+	0.0391718i
$813$		0			0
$814$	−40.8165	+	23.5654i	−1.43062	+	0.825968i
$815$	−32.6265	+	6.36635i	−1.14286	+	0.223004i
$816$		0			0
$817$	6.88556	+	25.6972i	0.240895	+	0.899033i
$818$	31.9621	−	31.9621i	1.11753	−	1.11753i
$819$		0			0
$820$	1.11805	+	2.28815i	0.0390439	+	0.0799056i
$821$	−38.4678	−	22.2094i	−1.34254	−	0.775114i	−0.355357	−	0.934731i	$-0.615641\pi$
$821$	−38.4678	−	22.2094i	−1.34254	−	0.775114i	−0.987179	+	0.159617i	$0.948974\pi$
$822$		0			0
$823$	8.19082	−	30.5686i	0.285514	−	1.06555i	−0.662949	−	0.748665i	$-0.730695\pi$
$823$	8.19082	−	30.5686i	0.285514	−	1.06555i	0.948463	−	0.316888i	$-0.102638\pi$
$824$	−5.35341	−	9.27239i	−0.186495	−	0.323019i
$825$		0			0
$826$	−0.835543	+	1.44720i	−0.0290723	+	0.0503546i
$827$	2.06846	+	2.06846i	0.0719275	+	0.0719275i	0.742155	−	0.670228i	$-0.233804\pi$
$827$	2.06846	+	2.06846i	0.0719275	+	0.0719275i	−0.670228	+	0.742155i	$0.733804\pi$
$828$		0			0
$829$			12.9618i			0.450182i	0.974338	+	0.225091i	$0.0722680\pi$
$829$			12.9618i			0.450182i	−0.974338	+	0.225091i	$0.927732\pi$
$830$	2.15300	+	0.148994i	0.0747317	+	0.00517166i
$831$		0			0
$832$	−3.90193	−	1.04552i	−0.135275	−	0.0362469i
$833$	1.42444	+	0.381677i	0.0493539	+	0.0132243i
$834$		0			0
$835$	14.2758	+	16.3985i	0.494033	+	0.567494i
$836$		−	17.2540i		−	0.596742i
$837$		0			0
$838$	−36.9202	−	36.9202i	−1.27539	−	1.27539i
$839$	−9.19525	+	15.9266i	−0.317455	+	0.549849i	−0.979956	−	0.199212i	$-0.936162\pi$
$839$	−9.19525	+	15.9266i	−0.317455	+	0.549849i	0.662501	+	0.749061i	$0.269495\pi$
$840$		0			0
$841$	9.58072	+	16.5943i	0.330370	+	0.572217i
$842$	−13.2822	+	49.5699i	−0.457736	+	1.70829i
$843$		0			0
$844$	0.864691	+	0.499230i	0.0297639	+	0.0171842i
$845$	22.5980	−	11.0420i	0.777396	−	0.379855i
$846$		0			0
$847$	−2.58483	+	2.58483i	−0.0888158	+	0.0888158i
$848$	13.5414	+	50.5371i	0.465013	+	1.73545i
$849$		0			0
$850$	0.448596	−	3.22564i	0.0153867	−	0.110638i
$851$	−15.2312	+	8.79374i	−0.522119	+	0.301445i
$852$		0			0
$853$	−13.3437	+	3.57544i	−0.456880	+	0.122421i	−0.479917	−	0.877314i	$-0.659333\pi$
$853$	−13.3437	+	3.57544i	−0.456880	+	0.122421i	0.0230366	+	0.999735i	$0.492667\pi$
$854$	−17.7193			−0.606342
$855$		0			0
$856$	−11.8392			−0.404657
$857$	−5.89302	+	1.57903i	−0.201302	+	0.0539387i	−0.358061	−	0.933698i	$-0.616562\pi$
$857$	−5.89302	+	1.57903i	−0.201302	+	0.0539387i	0.156759	+	0.987637i	$0.449895\pi$
$858$		0			0
$859$	−16.1515	+	9.32505i	−0.551081	+	0.318166i	−0.749558	−	0.661939i	$-0.769734\pi$
$859$	−16.1515	+	9.32505i	−0.551081	+	0.318166i	0.198477	+	0.980106i	$0.436400\pi$
$860$	−1.39275	−	7.13764i	−0.0474925	−	0.243392i
$861$		0			0
$862$	−14.0659	−	52.4948i	−0.479088	−	1.78798i
$863$	−9.43441	+	9.43441i	−0.321151	+	0.321151i	−0.849209	−	0.528058i	$-0.822921\pi$
$863$	−9.43441	+	9.43441i	−0.321151	+	0.321151i	0.528058	+	0.849209i	$0.322921\pi$
$864$		0			0
$865$	31.7302	+	10.9000i	1.07886	+	0.370612i
$866$	−14.7822	−	8.53448i	−0.502318	−	0.290013i
$867$		0			0
$868$	1.72670	−	6.44412i	0.0586079	−	0.218728i
$869$	14.5254	+	25.1588i	0.492742	+	0.853454i
$870$		0			0
$871$	7.42362	−	12.8581i	0.251540	−	0.435680i
$872$	−1.60880	−	1.60880i	−0.0544808	−	0.0544808i
$873$		0			0
$874$		−	23.2849i		−	0.787625i
$875$	−1.09593	−	20.0811i	−0.0370491	−	0.678866i
$876$		0			0
$877$	47.4768	+	12.7214i	1.60318	+	0.429570i	0.946000	−	0.324166i	$-0.105084\pi$
$877$	47.4768	+	12.7214i	1.60318	+	0.429570i	0.657177	+	0.753736i	$0.271750\pi$
$878$	−36.1029	−	9.67374i	−1.21841	−	0.326473i
$879$		0			0
$880$	2.75551	−	39.8178i	0.0928883	−	1.34226i
$881$		−	17.7562i		−	0.598222i	−0.954218	−	0.299111i	$-0.903310\pi$
$881$		−	17.7562i		−	0.598222i	0.954218	−	0.299111i	$-0.0966901\pi$
$882$		0			0
$883$	8.09196	+	8.09196i	0.272316	+	0.272316i	0.830032	−	0.557716i	$-0.188322\pi$
$883$	8.09196	+	8.09196i	0.272316	+	0.272316i	−0.557716	+	0.830032i	$0.688322\pi$
$884$	0.198173	−	0.343246i	0.00666528	−	0.0115446i
$885$		0			0
$886$	6.42494	+	11.1283i	0.215850	+	0.373863i
$887$	−2.74978	+	10.2623i	−0.0923287	+	0.344575i	−0.996601	−	0.0823810i	$-0.973748\pi$
$887$	−2.74978	+	10.2623i	−0.0923287	+	0.344575i	0.904272	+	0.426956i	$0.140414\pi$
$888$		0			0
$889$	−25.5305	−	14.7401i	−0.856267	−	0.494366i
$890$	−19.8503	+	57.7847i	−0.665384	+	1.93695i
$891$		0			0
$892$	4.48293	−	4.48293i	0.150100	−	0.150100i
$893$	6.40079	+	23.8881i	0.214194	+	0.799383i
$894$		0			0
$895$	5.27096	−	7.82667i	0.176189	−	0.261617i
$896$	20.7164	−	11.9606i	0.692087	−	0.399577i
$897$		0			0
$898$	61.2688	−	16.4169i	2.04457	−	0.547840i
$899$	15.2193			0.507594
$900$		0			0
$901$	4.14526			0.138098
$902$	8.63839	−	2.31465i	0.287627	−	0.0770694i
$903$		0			0
$904$	14.8471	−	8.57197i	0.493807	−	0.285099i
$905$	29.7189	−	44.1286i	0.987889	−	1.46688i
$906$		0			0
$907$	−2.00855	−	7.49600i	−0.0666927	−	0.248901i	0.924529	−	0.381112i	$-0.124459\pi$
$907$	−2.00855	−	7.49600i	−0.0666927	−	0.248901i	−0.991222	+	0.132212i	$0.957792\pi$
$908$	−4.98428	+	4.98428i	−0.165409	+	0.165409i
$909$		0			0
$910$	2.87576	−	8.37140i	0.0953305	−	0.277509i
$911$	11.1341	+	6.42830i	0.368890	+	0.212979i	0.672974	−	0.739667i	$-0.265017\pi$
$911$	11.1341	+	6.42830i	0.368890	+	0.212979i	−0.304083	+	0.952645i	$0.598350\pi$
$912$		0			0
$913$	0.542379	−	2.02419i	0.0179501	−	0.0669908i
$914$	23.1537	+	40.1034i	0.765857	+	1.32650i
$915$		0			0
$916$	−7.59207	+	13.1498i	−0.250849	+	0.434483i
$917$	−6.38005	−	6.38005i	−0.210688	−	0.210688i
$918$		0			0
$919$			30.7848i			1.01550i	0.861505	+	0.507749i	$0.169522\pi$
$919$			30.7848i			1.01550i	−0.861505	+	0.507749i	$0.830478\pi$
$920$	0.710333	−	10.2645i	0.0234190	−	0.338410i
$921$		0			0
$922$	39.3699	+	10.5491i	1.29658	+	0.347417i
$923$	10.2486	+	2.74611i	0.337337	+	0.0903893i
$924$		0			0
$925$	−36.1625	−	15.2886i	−1.18902	−	0.502687i
$926$			29.7259i			0.976854i
$927$		0			0
$928$	−9.12048	−	9.12048i	−0.299394	−	0.299394i
$929$	12.1446	−	21.0351i	0.398453	−	0.690141i	−0.595082	−	0.803665i	$-0.702881\pi$
$929$	12.1446	−	21.0351i	0.398453	−	0.690141i	0.993535	+	0.113524i	$0.0362139\pi$
$930$		0			0
$931$	11.7688	+	20.3842i	0.385708	+	0.668066i
$932$	1.52567	−	5.69388i	0.0499750	−	0.186509i
$933$		0			0
$934$	45.3882	+	26.2049i	1.48515	+	0.857451i
$935$	−2.99073	−	1.02738i	−0.0978074	−	0.0335990i
$936$		0			0
$937$	−18.4403	+	18.4403i	−0.602420	+	0.602420i	−0.940954	−	0.338534i	$-0.890069\pi$
$937$	−18.4403	+	18.4403i	−0.602420	+	0.602420i	0.338534	+	0.940954i	$0.390069\pi$
$938$	8.68284	+	32.4048i	0.283505	+	1.05805i
$939$		0			0
$940$	−1.29470	−	6.63512i	−0.0422284	−	0.216414i
$941$	34.2802	−	19.7917i	1.11750	−	0.645191i	0.176741	−	0.984257i	$-0.443444\pi$
$941$	34.2802	−	19.7917i	1.11750	−	0.645191i	0.940763	+	0.339066i	$0.110111\pi$
$942$		0			0
$943$	3.22353	−	0.863741i	0.104972	−	0.0281273i
$944$	−2.76275			−0.0899200
$945$		0			0
$946$	−25.5377			−0.830301
$947$	39.9850	−	10.7139i	1.29934	−	0.348156i	0.458138	−	0.888881i	$-0.348517\pi$
$947$	39.9850	−	10.7139i	1.29934	−	0.348156i	0.841199	+	0.540725i	$0.181850\pi$
$948$		0			0
$949$	−2.09629	+	1.21029i	−0.0680485	+	0.0392878i
$950$	41.4682	−	31.3423i	1.34541	−	1.01688i
$951$		0			0
$952$	−0.374683	−	1.39834i	−0.0121435	−	0.0453203i
$953$	−17.2048	+	17.2048i	−0.557319	+	0.557319i	−0.928543	−	0.371224i	$-0.878938\pi$
$953$	−17.2048	+	17.2048i	−0.557319	+	0.557319i	0.371224	+	0.928543i	$0.378938\pi$
$954$		0			0
$955$	46.7556	−	22.8459i	1.51297	−	0.739276i
$956$	−4.60979	−	2.66147i	−0.149091	−	0.0860780i
$957$		0			0
$958$	−5.82033	+	21.7218i	−0.188046	+	0.701798i
$959$	0.410471	+	0.710957i	0.0132548	+	0.0229580i
$960$		0			0
$961$	3.72853	−	6.45800i	0.120275	−	0.208323i
$962$	−12.2191	−	12.2191i	−0.393959	−	0.393959i
$963$		0			0
$964$			17.9875i			0.579339i
$965$	−30.4434	−	34.9702i	−0.980007	−	1.12573i
$966$		0			0
$967$	−21.3448	−	5.71932i	−0.686402	−	0.183921i	−0.101270	−	0.994859i	$-0.532291\pi$
$967$	−21.3448	−	5.71932i	−0.686402	−	0.183921i	−0.585132	+	0.810938i	$0.698957\pi$
$968$	−4.03269	−	1.08056i	−0.129616	−	0.0347304i
$969$		0			0
$970$	−19.7449	−	1.36641i	−0.633971	−	0.0438727i
$971$			3.58038i			0.114900i	0.998348	+	0.0574499i	$0.0182969\pi$
$971$			3.58038i			0.114900i	−0.998348	+	0.0574499i	$0.981703\pi$
$972$		0			0
$973$	−20.3944	−	20.3944i	−0.653815	−	0.653815i
$974$	20.9139	−	36.2239i	0.670124	−	1.16069i
$975$		0			0
$976$	−14.6474	−	25.3700i	−0.468851	−	0.812074i
$977$	5.33127	−	19.8966i	0.170562	−	0.636548i	−0.826703	−	0.562639i	$-0.809786\pi$
$977$	5.33127	−	19.8966i	0.170562	−	0.636548i	0.997265	−	0.0739084i	$-0.0235473\pi$
$978$		0			0
$979$	51.3796	+	29.6640i	1.64210	+	0.948067i
$980$	−2.82470	−	5.78092i	−0.0902318	−	0.184665i
$981$		0			0
$982$	24.4066	−	24.4066i	0.778846	−	0.778846i
$983$	−7.58120	−	28.2934i	−0.241803	−	0.902420i	−0.974963	−	0.222365i	$-0.928622\pi$
$983$	−7.58120	−	28.2934i	−0.241803	−	0.902420i	0.733161	−	0.680055i	$-0.238044\pi$
$984$		0			0
$985$	20.2554	−	3.95240i	0.645392	−	0.125934i
$986$	−1.76930	+	1.02151i	−0.0563460	+	0.0325314i
$987$		0			0
$988$	6.11057	−	1.63732i	0.194403	−	0.0520902i
$989$	−9.52971			−0.303027
$990$		0			0
$991$	−21.0816			−0.669679			−0.334840	−	0.942275i	$-0.608682\pi$
$991$	−21.0816			−0.669679			−0.334840	+	0.942275i	$0.608682\pi$
$992$	19.2726	−	5.16409i	0.611907	−	0.163960i
$993$		0			0
$994$	−20.7621	+	11.9870i	−0.658535	+	0.380205i
$995$	−7.48881	−	5.04342i	−0.237411	−	0.159887i
$996$		0			0
$997$	−13.3859	−	49.9569i	−0.423936	−	1.58215i	−0.766236	−	0.642559i	$-0.777873\pi$
$997$	−13.3859	−	49.9569i	−0.423936	−	1.58215i	0.342300	−	0.939591i	$-0.388794\pi$
$998$	−11.6227	+	11.6227i	−0.367909	+	0.367909i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.m.a.8.3		16
3.2	odd	2		45.2.l.a.38.2	yes	16
5.2	odd	4	inner	135.2.m.a.62.3		16
5.3	odd	4		675.2.q.a.332.2		16
5.4	even	2		675.2.q.a.143.2		16
9.2	odd	6		405.2.f.a.323.7		16
9.4	even	3		45.2.l.a.23.2	yes	16
9.5	odd	6	inner	135.2.m.a.98.3		16
9.7	even	3		405.2.f.a.323.2		16
12.11	even	2		720.2.cu.c.353.3		16
15.2	even	4		45.2.l.a.2.2	✓	16
15.8	even	4		225.2.p.b.182.3		16
15.14	odd	2		225.2.p.b.218.3		16
36.31	odd	6		720.2.cu.c.113.1		16
45.2	even	12		405.2.f.a.242.2		16
45.4	even	6		225.2.p.b.68.3		16
45.7	odd	12		405.2.f.a.242.7		16
45.13	odd	12		225.2.p.b.32.3		16
45.14	odd	6		675.2.q.a.368.2		16
45.22	odd	12		45.2.l.a.32.2	yes	16
45.23	even	12		675.2.q.a.557.2		16
45.32	even	12	inner	135.2.m.a.17.3		16
60.47	odd	4		720.2.cu.c.497.1		16
180.67	even	12		720.2.cu.c.257.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.2	✓	16	15.2	even	4
45.2.l.a.23.2	yes	16	9.4	even	3
45.2.l.a.32.2	yes	16	45.22	odd	12
45.2.l.a.38.2	yes	16	3.2	odd	2
135.2.m.a.8.3		16	1.1	even	1	trivial
135.2.m.a.17.3		16	45.32	even	12	inner
135.2.m.a.62.3		16	5.2	odd	4	inner
135.2.m.a.98.3		16	9.5	odd	6	inner
225.2.p.b.32.3		16	45.13	odd	12
225.2.p.b.68.3		16	45.4	even	6
225.2.p.b.182.3		16	15.8	even	4
225.2.p.b.218.3		16	15.14	odd	2
405.2.f.a.242.2		16	45.2	even	12
405.2.f.a.242.7		16	45.7	odd	12
405.2.f.a.323.2		16	9.7	even	3
405.2.f.a.323.7		16	9.2	odd	6
675.2.q.a.143.2		16	5.4	even	2
675.2.q.a.332.2		16	5.3	odd	4
675.2.q.a.368.2		16	45.14	odd	6
675.2.q.a.557.2		16	45.23	even	12
720.2.cu.c.113.1		16	36.31	odd	6
720.2.cu.c.257.3		16	180.67	even	12
720.2.cu.c.353.3		16	12.11	even	2
720.2.cu.c.497.1		16	60.47	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.60599 - 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(1.24906 - 1.85468i) q^{5} +(0.465559 + 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +O(q^{10})\)	\(q+(1.60599 - 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(1.24906 - 1.85468i) q^{5} +(0.465559 + 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +(1.20786 - 3.51610i) q^{10} +(-3.12636 - 1.80501i) q^{11} +(0.342574 - 1.27850i) q^{13} +(1.49537 + 2.59005i) q^{14} +(-2.47224 + 4.28205i) q^{16} +(0.277007 + 0.277007i) q^{17} +6.25273i q^{19} +(0.118000 - 1.70513i) q^{20} +(-5.79765 - 1.55348i) q^{22} +(-2.16347 - 0.579699i) q^{23} +(-1.87971 - 4.63322i) q^{25} -2.20068i q^{26} +(0.972242 + 0.972242i) q^{28} +(-1.56832 + 2.71642i) q^{29} +(-2.42605 - 4.20205i) q^{31} +(-1.06430 + 3.97202i) q^{32} +(0.564074 + 0.325668i) q^{34} +(3.80401 + 1.30676i) q^{35} +(5.55242 - 5.55242i) q^{37} +(2.69070 + 10.0418i) q^{38} +(0.879778 + 4.50872i) q^{40} +(-1.29036 + 0.744991i) q^{41} +(4.10976 - 1.10121i) q^{43} -2.75943 q^{44} -3.72396 q^{46} +(3.82042 - 1.02368i) q^{47} +(3.26005 - 1.88219i) q^{49} +(-5.01258 - 6.63202i) q^{50} +(-0.261857 - 0.977265i) q^{52} +(7.48222 - 7.48222i) q^{53} +(-7.25273 + 3.54386i) q^{55} +(-3.20031 - 1.84770i) q^{56} +(-1.34977 + 5.03742i) q^{58} +(0.279377 + 0.483896i) q^{59} +(-2.96237 + 5.13097i) q^{61} +(-5.70446 - 5.70446i) q^{62} -3.05196i q^{64} +(-1.94332 - 2.23229i) q^{65} +(10.8351 + 2.90325i) q^{67} +(0.289242 + 0.0775020i) q^{68} +(6.67153 + 0.461690i) q^{70} +8.01611i q^{71} +(-1.29315 - 1.29315i) q^{73} +(6.52779 - 11.3065i) q^{74} +(2.38974 + 4.13915i) q^{76} +(1.68068 - 6.27237i) q^{77} +(-6.96917 - 4.02365i) q^{79} +(4.85388 + 9.93376i) q^{80} +(-1.75172 + 1.75172i) q^{82} +(0.150243 + 0.560714i) q^{83} +(0.859759 - 0.167763i) q^{85} +(6.12636 - 3.53706i) q^{86} +(7.16367 - 1.91950i) q^{88} -16.4343 q^{89} +2.38087 q^{91} +(-1.65372 + 0.443112i) q^{92} +(5.69504 - 3.28804i) q^{94} +(11.5968 + 7.81002i) q^{95} +(-1.37786 - 5.14224i) q^{97} +(4.42566 - 4.42566i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7	\( 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7} - 8 q^{10} - 2 q^{13} - 8 q^{16} - 18 q^{20} - 10 q^{22} - 18 q^{23} + 4 q^{25} - 16 q^{28} - 4 q^{31} - 30 q^{32} + 4 q^{37} + 30 q^{38} + 6 q^{40} + 24 q^{41} - 2 q^{43} + 32 q^{46} + 12 q^{47} + 54 q^{50} - 14 q^{52} - 16 q^{55} - 36 q^{56} - 6 q^{58} + 8 q^{61} - 66 q^{65} + 4 q^{67} - 42 q^{68} + 18 q^{70} - 8 q^{73} + 24 q^{76} + 6 q^{77} + 32 q^{82} + 66 q^{83} + 22 q^{85} + 48 q^{86} + 18 q^{88} - 40 q^{91} + 60 q^{92} + 36 q^{95} + 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7 - 8 * q^10 - 2 * q^13 - 8 * q^16 - 18 * q^20 - 10 * q^22 - 18 * q^23 + 4 * q^25 - 16 * q^28 - 4 * q^31 - 30 * q^32 + 4 * q^37 + 30 * q^38 + 6 * q^40 + 24 * q^41 - 2 * q^43 + 32 * q^46 + 12 * q^47 + 54 * q^50 - 14 * q^52 - 16 * q^55 - 36 * q^56 - 6 * q^58 + 8 * q^61 - 66 * q^65 + 4 * q^67 - 42 * q^68 + 18 * q^70 - 8 * q^73 + 24 * q^76 + 6 * q^77 + 32 * q^82 + 66 * q^83 + 22 * q^85 + 48 * q^86 + 18 * q^88 - 40 * q^91 + 60 * q^92 + 36 * q^95 + 28 * q^97

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