LMFDB - Embedded newform 261.2.k.a.190.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(82,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.1
Root			$-0.623490 - 0.781831i$ of defining polynomial
Character	$\chi$	$=$	261.190
Dual form			261.2.k.a.136.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.400969 - 0.193096i) q^{2} +(-1.12349 - 1.40881i) q^{4} +(0.623490 + 0.300257i) q^{5} +(0.222521 - 0.279032i) q^{7} +(0.376510 + 1.64960i) q^{8} +(-0.192021 - 0.240787i) q^{10} +(1.09903 - 4.81517i) q^{11} +(1.25786 - 5.51107i) q^{13} +(-0.143104 + 0.0689153i) q^{14} +(-0.634375 + 2.77938i) q^{16} -4.49396 q^{17} +(-1.46950 - 1.84270i) q^{19} +(-0.277479 - 1.21572i) q^{20} +(-1.37047 + 1.71851i) q^{22} +(2.06853 - 0.996152i) q^{23} +(-2.81886 - 3.53474i) q^{25} +(-1.56853 + 1.96688i) q^{26} -0.643104 q^{28} +(5.09783 + 1.73553i) q^{29} +(6.02930 + 2.90356i) q^{31} +(2.90097 - 3.63770i) q^{32} +(1.80194 + 0.867767i) q^{34} +(0.222521 - 0.107160i) q^{35} +(1.09903 + 4.81517i) q^{37} +(0.233406 + 1.02262i) q^{38} +(-0.260553 + 1.14156i) q^{40} -3.10992 q^{41} +(3.06853 - 1.47773i) q^{43} +(-8.01842 + 3.86147i) q^{44} -1.02177 q^{46} +(-1.43416 + 6.28345i) q^{47} +(1.52930 + 6.70031i) q^{49} +(0.447730 + 1.96163i) q^{50} +(-9.17725 + 4.41953i) q^{52} +(-4.22737 - 2.03579i) q^{53} +(2.13102 - 2.67222i) q^{55} +(0.544073 + 0.262012i) q^{56} +(-1.70895 - 1.68027i) q^{58} +12.4940 q^{59} +(-1.02446 + 1.28463i) q^{61} +(-1.85690 - 2.32847i) q^{62} +(3.27144 - 1.57544i) q^{64} +(2.43900 - 3.05841i) q^{65} +(0.516926 + 2.26480i) q^{67} +(5.04892 + 6.33114i) q^{68} -0.109916 q^{70} +(-1.63222 + 7.15122i) q^{71} +(-5.06853 + 2.44088i) q^{73} +(0.489115 - 2.14295i) q^{74} +(-0.945042 + 4.14050i) q^{76} +(-1.09903 - 1.37814i) q^{77} +(1.03803 + 4.54792i) q^{79} +(-1.23005 + 1.54244i) q^{80} +(1.24698 + 0.600514i) q^{82} +(-2.77748 - 3.48285i) q^{83} +(-2.80194 - 1.34934i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-5.11745 - 2.46443i) q^{89} +(-1.25786 - 1.57731i) q^{91} +(-3.72737 - 1.79500i) q^{92} +(1.78836 - 2.24254i) q^{94} +(-0.362937 - 1.59013i) q^{95} +(-0.112605 - 0.141202i) q^{97} +(0.680604 - 2.98192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 7 q^{8} + 9 q^{10} + 11 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} - 8 q^{17} + q^{19} - 2 q^{20} + 6 q^{22} + 7 q^{23} - 24 q^{25} - 4 q^{26} - 12 q^{28} - 6 q^{29}+ \cdots - 19 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 - q^5 + q^7 + 7 * q^8 + 9 * q^10 + 11 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 - 8 * q^17 + q^19 - 2 * q^20 + 6 * q^22 + 7 * q^23 - 24 * q^25 - 4 * q^26 - 12 * q^28 - 6 * q^29 + 5 * q^31 + 13 * q^32 + 2 * q^34 + q^35 + 11 * q^37 - 2 * q^38 + 14 * q^40 - 20 * q^41 + 13 * q^43 - 20 * q^44 - 11 * q^47 - 22 * q^49 - q^50 - 10 * q^52 - 3 * q^53 - 17 * q^55 + 7 * q^56 - 16 * q^58 + 56 * q^59 + 3 * q^61 - 3 * q^62 + q^64 - 5 * q^65 + 19 * q^67 + 12 * q^68 - 2 * q^70 - 21 * q^71 - 25 * q^73 + 6 * q^74 - 5 * q^76 - 11 * q^77 - 9 * q^79 + 18 * q^80 - 2 * q^82 - 17 * q^83 - 8 * q^85 + 16 * q^86 + 42 * q^88 - 7 * q^89 + 5 * q^91 + 8 * q^94 - 13 * q^95 + q^97 - 19 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.400969	−	0.193096i	−0.283528	−	0.136540i	0.286715	−	0.958016i	$-0.407437\pi$
$2$	−0.400969	−	0.193096i	−0.283528	−	0.136540i	−0.570243	+	0.821476i	$0.693151\pi$
$3$		0			0
$3$		0			0
$4$	−1.12349	−	1.40881i	−0.561745	−	0.704406i
$5$	0.623490	+	0.300257i	0.278833	+	0.134279i	0.568074	−	0.822977i	$-0.307689\pi$
$5$	0.623490	+	0.300257i	0.278833	+	0.134279i	−0.289241	+	0.957256i	$0.593403\pi$
$6$		0			0
$7$	0.222521	−	0.279032i	0.0841050	−	0.105464i	−0.737999	−	0.674802i	$-0.764229\pi$
$7$	0.222521	−	0.279032i	0.0841050	−	0.105464i	0.822104	+	0.569338i	$0.192800\pi$
$8$	0.376510	+	1.64960i	0.133116	+	0.583221i
$9$		0			0
$10$	−0.192021	−	0.240787i	−0.0607225	−	0.0761436i
$11$	1.09903	−	4.81517i	0.331370	−	1.45183i	−0.485109	−	0.874454i	$-0.661220\pi$
$11$	1.09903	−	4.81517i	0.331370	−	1.45183i	0.816479	−	0.577375i	$-0.195923\pi$
$12$		0			0
$13$	1.25786	−	5.51107i	0.348869	−	1.52849i	−0.430884	−	0.902407i	$-0.641798\pi$
$13$	1.25786	−	5.51107i	0.348869	−	1.52849i	0.779753	−	0.626087i	$-0.215345\pi$
$14$	−0.143104	+	0.0689153i	−0.0382462	+	0.0184184i
$15$		0			0
$16$	−0.634375	+	2.77938i	−0.158594	+	0.694845i
$17$	−4.49396			−1.08995			−0.544973	−	0.838454i	$-0.683460\pi$
$17$	−4.49396			−1.08995			−0.544973	+	0.838454i	$0.683460\pi$
$18$		0			0
$19$	−1.46950	−	1.84270i	−0.337127	−	0.422743i	0.584153	−	0.811643i	$-0.301427\pi$
$19$	−1.46950	−	1.84270i	−0.337127	−	0.422743i	−0.921280	+	0.388900i	$0.872855\pi$
$20$	−0.277479	−	1.21572i	−0.0620462	−	0.271842i
$21$		0			0
$22$	−1.37047	+	1.71851i	−0.292185	+	0.366388i
$23$	2.06853	−	0.996152i	0.431319	−	0.207712i	−0.205611	−	0.978634i	$-0.565918\pi$
$23$	2.06853	−	0.996152i	0.431319	−	0.207712i	0.636930	+	0.770922i	$0.280204\pi$
$24$		0			0
$25$	−2.81886	−	3.53474i	−0.563773	−	0.706949i
$26$	−1.56853	+	1.96688i	−0.307614	+	0.385736i
$27$		0			0
$28$	−0.643104			−0.121535
$29$	5.09783	+	1.73553i	0.946644	+	0.322281i
$29$	5.09783	+	1.73553i	0.946644	+	0.322281i
$30$		0			0
$31$	6.02930	+	2.90356i	1.08289	+	0.521495i	0.888241	−	0.459377i	$-0.151927\pi$
$31$	6.02930	+	2.90356i	1.08289	+	0.521495i	0.194654	+	0.980872i	$0.437642\pi$
$32$	2.90097	−	3.63770i	0.512824	−	0.643061i
$33$		0			0
$34$	1.80194	+	0.867767i	0.309030	+	0.148821i
$35$	0.222521	−	0.107160i	0.0376129	−	0.0181134i
$36$		0			0
$37$	1.09903	+	4.81517i	0.180680	+	0.791609i	0.981307	+	0.192447i	$0.0616424\pi$
$37$	1.09903	+	4.81517i	0.180680	+	0.791609i	−0.800628	+	0.599162i	$0.795501\pi$
$38$	0.233406	+	1.02262i	0.0378635	+	0.165891i
$39$		0			0
$40$	−0.260553	+	1.14156i	−0.0411971	+	0.180496i
$41$	−3.10992			−0.485687			−0.242844	−	0.970065i	$-0.578080\pi$
$41$	−3.10992			−0.485687			−0.242844	+	0.970065i	$0.578080\pi$
$42$		0			0
$43$	3.06853	−	1.47773i	0.467947	−	0.225351i	−0.185025	−	0.982734i	$-0.559236\pi$
$43$	3.06853	−	1.47773i	0.467947	−	0.225351i	0.652971	+	0.757383i	$0.273522\pi$
$44$	−8.01842	+	3.86147i	−1.20882	+	0.582138i
$45$		0			0
$46$	−1.02177			−0.150652
$47$	−1.43416	+	6.28345i	−0.209193	+	0.916536i	0.755912	+	0.654673i	$0.227194\pi$
$47$	−1.43416	+	6.28345i	−0.209193	+	0.916536i	−0.965105	+	0.261862i	$0.915663\pi$
$48$		0			0
$49$	1.52930	+	6.70031i	0.218472	+	0.957188i
$50$	0.447730	+	1.96163i	0.0633186	+	0.277417i
$51$		0			0
$52$	−9.17725	+	4.41953i	−1.27266	+	0.612879i
$53$	−4.22737	−	2.03579i	−0.580673	−	0.279638i	0.120401	−	0.992725i	$-0.461582\pi$
$53$	−4.22737	−	2.03579i	−0.580673	−	0.279638i	−0.701075	+	0.713088i	$0.747296\pi$
$54$		0			0
$55$	2.13102	−	2.67222i	0.287347	−	0.360322i
$56$	0.544073	+	0.262012i	0.0727048	+	0.0350128i
$57$		0			0
$58$	−1.70895	−	1.68027i	−0.224396	−	0.220630i
$59$	12.4940			1.62657			0.813287	−	0.581862i	$-0.197676\pi$
$59$	12.4940			1.62657			0.813287	+	0.581862i	$0.197676\pi$
$60$		0			0
$61$	−1.02446	+	1.28463i	−0.131168	+	0.164480i	−0.843078	−	0.537791i	$-0.819259\pi$
$61$	−1.02446	+	1.28463i	−0.131168	+	0.164480i	0.711910	+	0.702271i	$0.247830\pi$
$62$	−1.85690	−	2.32847i	−0.235826	−	0.295716i
$63$		0			0
$64$	3.27144	−	1.57544i	0.408930	−	0.196930i
$65$	2.43900	−	3.05841i	0.302521	−	0.379349i
$66$		0			0
$67$	0.516926	+	2.26480i	0.0631526	+	0.276689i	0.996639	−	0.0819245i	$-0.0261066\pi$
$67$	0.516926	+	2.26480i	0.0631526	+	0.276689i	−0.933486	+	0.358614i	$0.883249\pi$
$68$	5.04892	+	6.33114i	0.612271	+	0.767764i
$69$		0			0
$70$	−0.109916			−0.0131375
$71$	−1.63222	+	7.15122i	−0.193709	+	0.848694i	0.780878	+	0.624683i	$0.214772\pi$
$71$	−1.63222	+	7.15122i	−0.193709	+	0.848694i	−0.974587	+	0.224010i	$0.928085\pi$
$72$		0			0
$73$	−5.06853	+	2.44088i	−0.593227	+	0.285683i	−0.706310	−	0.707903i	$-0.749642\pi$
$73$	−5.06853	+	2.44088i	−0.593227	+	0.285683i	0.113083	+	0.993586i	$0.463927\pi$
$74$	0.489115	−	2.14295i	0.0568584	−	0.249113i
$75$		0			0
$76$	−0.945042	+	4.14050i	−0.108404	+	0.474948i
$77$	−1.09903	−	1.37814i	−0.125246	−	0.157054i
$78$		0			0
$79$	1.03803	+	4.54792i	0.116788	+	0.511681i	0.999154	+	0.0411178i	$0.0130919\pi$
$79$	1.03803	+	4.54792i	0.116788	+	0.511681i	−0.882367	+	0.470563i	$0.844051\pi$
$80$	−1.23005	+	1.54244i	−0.137524	+	0.172450i
$81$		0			0
$82$	1.24698	+	0.600514i	0.137706	+	0.0663156i
$83$	−2.77748	−	3.48285i	−0.304868	−	0.382292i	0.605671	−	0.795715i	$-0.292905\pi$
$83$	−2.77748	−	3.48285i	−0.304868	−	0.382292i	−0.910539	+	0.413423i	$0.864333\pi$
$84$		0			0
$85$	−2.80194	−	1.34934i	−0.303913	−	0.146357i
$86$	−1.51573			−0.163445
$87$		0			0
$88$	8.35690			0.890848
$89$	−5.11745	−	2.46443i	−0.542449	−	0.261229i	0.142533	−	0.989790i	$-0.454475\pi$
$89$	−5.11745	−	2.46443i	−0.542449	−	0.261229i	−0.684981	+	0.728561i	$0.740190\pi$
$90$		0			0
$91$	−1.25786	−	1.57731i	−0.131860	−	0.165347i
$92$	−3.72737	−	1.79500i	−0.388605	−	0.187142i
$93$		0			0
$94$	1.78836	−	2.24254i	0.184456	−	0.231300i
$95$	−0.362937	−	1.59013i	−0.0372365	−	0.163144i
$96$		0			0
$97$	−0.112605	−	0.141202i	−0.0114333	−	0.0143369i	0.776082	−	0.630632i	$-0.217204\pi$
$97$	−0.112605	−	0.141202i	−0.0114333	−	0.0143369i	−0.787515	+	0.616295i	$0.788633\pi$
$98$	0.680604	−	2.98192i	0.0687514	−	0.301219i
$99$		0			0
$100$	−1.81282	+	7.94250i	−0.181282	+	0.794250i
$101$	2.90970	−	1.40124i	0.289526	−	0.139428i	−0.283484	−	0.958977i	$-0.591490\pi$
$101$	2.90970	−	1.40124i	0.289526	−	0.139428i	0.573009	+	0.819549i	$0.305776\pi$
$102$		0			0
$103$	3.03803	−	13.3105i	0.299346	−	1.31152i	−0.571758	−	0.820423i	$-0.693738\pi$
$103$	3.03803	−	13.3105i	0.299346	−	1.31152i	0.871104	−	0.491099i	$-0.163405\pi$
$104$	9.56465			0.937891
$105$		0			0
$106$	1.30194	+	1.63258i	0.126455	+	0.158570i
$107$	3.61476	+	15.8373i	0.349452	+	1.53105i	0.778428	+	0.627734i	$0.216017\pi$
$107$	3.61476	+	15.8373i	0.349452	+	1.53105i	−0.428976	+	0.903316i	$0.641126\pi$
$108$		0			0
$109$	3.40850	−	4.27413i	0.326475	−	0.409387i	−0.591323	−	0.806435i	$-0.701394\pi$
$109$	3.40850	−	4.27413i	0.326475	−	0.409387i	0.917798	+	0.397048i	$0.129965\pi$
$110$	−1.37047	+	0.659983i	−0.130669	+	0.0629269i
$111$		0			0
$112$	0.634375	+	0.795481i	0.0599428	+	0.0751659i
$113$	6.65548	−	8.34571i	0.626095	−	0.785098i	−0.363093	−	0.931753i	$-0.618279\pi$
$113$	6.65548	−	8.34571i	0.626095	−	0.785098i	0.989188	+	0.146655i	$0.0468506\pi$
$114$		0			0
$115$	1.58881			0.148157
$116$	−3.28232	−	9.13174i	−0.304756	−	0.847861i
$117$		0			0
$118$	−5.00969	−	2.41254i	−0.461179	−	0.222092i
$119$	−1.00000	+	1.25396i	−0.0916698	+	0.114950i
$120$		0			0
$121$	−12.0673	−	5.81132i	−1.09703	−	0.528302i
$122$	0.658834	−	0.317278i	0.0596480	−	0.0287250i
$123$		0			0
$124$	−2.68329	−	11.7563i	−0.240967	−	1.05574i
$125$	−1.46615	−	6.42361i	−0.131136	−	0.574546i
$126$		0			0
$127$	0.230718	−	1.01084i	0.0204729	−	0.0896976i	−0.963659	−	0.267134i	$-0.913923\pi$
$127$	0.230718	−	1.01084i	0.0204729	−	0.0896976i	0.984132	+	0.177437i	$0.0567805\pi$
$128$	−10.9215			−0.965337
$129$		0			0
$130$	−1.56853	+	0.755365i	−0.137569	+	0.0662499i
$131$	7.22737	−	3.48052i	0.631458	−	0.304094i	−0.0906414	−	0.995884i	$-0.528892\pi$
$131$	7.22737	−	3.48052i	0.631458	−	0.304094i	0.722099	+	0.691790i	$0.243177\pi$
$132$		0			0
$133$	−0.841166			−0.0729384
$134$	0.230054	−	1.00793i	0.0198736	−	0.0870720i
$135$		0			0
$136$	−1.69202	−	7.41323i	−0.145090	−	0.635679i
$137$	3.83459	+	16.8005i	0.327611	+	1.43536i	0.823670	+	0.567070i	$0.191923\pi$
$137$	3.83459	+	16.8005i	0.327611	+	1.43536i	−0.496058	+	0.868289i	$0.665220\pi$
$138$		0			0
$139$	15.0172	−	7.23191i	1.27374	−	0.613403i	0.329969	−	0.943992i	$-0.392962\pi$
$139$	15.0172	−	7.23191i	1.27374	−	0.613403i	0.943775	+	0.330589i	$0.107247\pi$
$140$	−0.400969	−	0.193096i	−0.0338881	−	0.0163196i
$141$		0			0
$142$	2.03534	−	2.55224i	0.170802	−	0.214179i
$143$	−25.1543	−	12.1137i	−2.10351	−	1.01300i
$144$		0			0
$145$	2.65734	+	2.61275i	0.220680	+	0.216977i
$146$	2.50365			0.207203
$147$		0			0
$148$	5.54892	−	6.95812i	0.456118	−	0.571954i
$149$	−11.6012	−	14.5474i	−0.950406	−	1.19177i	−0.981346	−	0.192251i	$-0.938421\pi$
$149$	−11.6012	−	14.5474i	−0.950406	−	1.19177i	0.0309396	−	0.999521i	$-0.490150\pi$
$150$		0			0
$151$	6.78232	−	3.26619i	0.551938	−	0.265799i	−0.137060	−	0.990563i	$-0.543765\pi$
$151$	6.78232	−	3.26619i	0.551938	−	0.265799i	0.688998	+	0.724764i	$0.258051\pi$
$152$	2.48643	−	3.11788i	0.201676	−	0.252893i
$153$		0			0
$154$	0.174563	+	0.764811i	0.0140667	+	0.0616302i
$155$	2.88740	+	3.62068i	0.231921	+	0.290820i
$156$		0			0
$157$	−18.2392			−1.45565			−0.727824	−	0.685764i	$-0.759468\pi$
$157$	−18.2392			−1.45565			−0.727824	+	0.685764i	$0.759468\pi$
$158$	0.461968	−	2.02401i	0.0367522	−	0.161022i
$159$		0			0
$160$	2.90097	−	1.39703i	0.229342	−	0.110445i
$161$	0.182333	−	0.798852i	0.0143698	−	0.0629584i
$162$		0			0
$163$	−2.81282	+	12.3238i	−0.220317	+	0.965273i	0.736922	+	0.675977i	$0.236278\pi$
$163$	−2.81282	+	12.3238i	−0.220317	+	0.965273i	−0.957240	+	0.289296i	$0.906579\pi$
$164$	3.49396	+	4.38129i	0.272832	+	0.342121i
$165$		0			0
$166$	0.441157	+	1.93284i	0.0342404	+	0.150017i
$167$	0.496648	−	0.622776i	0.0384317	−	0.0481919i	−0.762244	−	0.647290i	$-0.775902\pi$
$167$	0.496648	−	0.622776i	0.0384317	−	0.0481919i	0.800676	+	0.599098i	$0.204474\pi$
$168$		0			0
$169$	−17.0770	−	8.22386i	−1.31362	−	0.632605i
$170$	0.862937	+	1.08209i	0.0661842	+	0.0829924i
$171$		0			0
$172$	−5.52930	−	2.66277i	−0.421605	−	0.203034i
$173$	9.15346			0.695924			0.347962	−	0.937509i	$-0.386874\pi$
$173$	9.15346			0.695924			0.347962	+	0.937509i	$0.386874\pi$
$174$		0			0
$175$	−1.61356			−0.121974
$176$	12.6860	+	6.10925i	0.956242	+	0.460502i
$177$		0			0
$178$	1.57606	+	1.97632i	0.118131	+	0.148132i
$179$	3.06853	+	1.47773i	0.229353	+	0.110450i	0.545031	−	0.838416i	$-0.316518\pi$
$179$	3.06853	+	1.47773i	0.229353	+	0.110450i	−0.315678	+	0.948866i	$0.602232\pi$
$180$		0			0
$181$	7.90246	−	9.90937i	0.587385	−	0.736558i	−0.395967	−	0.918265i	$-0.629591\pi$
$181$	7.90246	−	9.90937i	0.587385	−	0.736558i	0.983353	+	0.181707i	$0.0581621\pi$
$182$	0.199791	+	0.875342i	0.0148095	+	0.0648847i
$183$		0			0
$184$	2.42208	+	3.03719i	0.178558	+	0.223904i
$185$	−0.760553	+	3.33220i	−0.0559170	+	0.244988i
$186$		0			0
$187$	−4.93900	+	21.6392i	−0.361176	+	1.58241i
$188$	10.4635	−	5.03894i	0.763126	−	0.367502i
$189$		0			0
$190$	−0.161522	+	0.707674i	−0.0117180	+	0.0513401i
$191$	10.6703			0.772072			0.386036	−	0.922484i	$-0.373844\pi$
$191$	10.6703			0.772072			0.386036	+	0.922484i	$0.373844\pi$
$192$		0			0
$193$	14.1712	+	17.7701i	1.02007	+	1.27912i	0.959724	+	0.280945i	$0.0906477\pi$
$193$	14.1712	+	17.7701i	1.02007	+	1.27912i	0.0603421	+	0.998178i	$0.480781\pi$
$194$	0.0178854	+	0.0783611i	0.00128410	+	0.00562600i
$195$		0			0
$196$	7.72132	−	9.68223i	0.551523	−	0.691588i
$197$	−17.6211	+	8.48587i	−1.25545	+	0.604593i	−0.938968	−	0.344005i	$-0.888216\pi$
$197$	−17.6211	+	8.48587i	−1.25545	+	0.604593i	−0.316483	+	0.948598i	$0.602502\pi$
$198$		0			0
$199$	−0.545565	−	0.684117i	−0.0386741	−	0.0484958i	0.762118	−	0.647438i	$-0.224159\pi$
$199$	−0.545565	−	0.684117i	−0.0386741	−	0.0484958i	−0.800792	+	0.598942i	$0.795588\pi$
$200$	4.76958	−	5.98086i	0.337260	−	0.422911i
$201$		0			0
$202$	−1.43727			−0.101126
$203$	1.61865	−	1.03627i	0.113607	−	0.0727318i
$204$		0			0
$205$	−1.93900	−	0.933774i	−0.135426	−	0.0652176i
$206$	−3.78836	+	4.75046i	−0.263948	+	0.330980i
$207$		0			0
$208$	14.5194	+	6.99216i	1.00674	+	0.484819i
$209$	−10.4879	+	5.05072i	−0.725464	+	0.349365i
$210$		0			0
$211$	4.06518	+	17.8107i	0.279858	+	1.22614i	0.897972	+	0.440052i	$0.145040\pi$
$211$	4.06518	+	17.8107i	0.279858	+	1.22614i	−0.618114	+	0.786088i	$0.712103\pi$
$212$	1.88135	+	8.24275i	0.129212	+	0.566115i
$213$		0			0
$214$	1.60872	−	7.04826i	0.109970	−	0.481809i
$215$	2.35690			0.160739
$216$		0			0
$217$	2.15183	−	1.03627i	0.146076	−	0.0703465i
$218$	−2.19202	+	1.05562i	−0.148462	+	0.0714957i
$219$		0			0
$220$	−6.15883			−0.415228
$221$	−5.65279	+	24.7665i	−0.380248	+	1.66598i
$222$		0			0
$223$	0.404617	+	1.77274i	0.0270951	+	0.118712i	0.986667	−	0.162752i	$-0.0520372\pi$
$223$	0.404617	+	1.77274i	0.0270951	+	0.118712i	−0.959572	+	0.281464i	$0.909180\pi$
$224$	−0.369510	−	1.61893i	−0.0246889	−	0.108169i
$225$		0			0
$226$	−4.28017	+	2.06122i	−0.284713	+	0.137110i
$227$	−12.4840	−	6.01199i	−0.828594	−	0.399030i	−0.0290066	−	0.999579i	$-0.509234\pi$
$227$	−12.4840	−	6.01199i	−0.828594	−	0.399030i	−0.799588	+	0.600549i	$0.794949\pi$
$228$		0			0
$229$	−7.96346	+	9.98586i	−0.526240	+	0.659884i	−0.971921	−	0.235308i	$-0.924390\pi$
$229$	−7.96346	+	9.98586i	−0.526240	+	0.659884i	0.445681	+	0.895192i	$0.352962\pi$
$230$	−0.637063	−	0.306794i	−0.0420067	−	0.0202294i
$231$		0			0
$232$	−0.943550	+	9.06283i	−0.0619471	+	0.595004i
$233$	8.86592			0.580826			0.290413	−	0.956901i	$-0.406207\pi$
$233$	8.86592			0.580826			0.290413	+	0.956901i	$0.406207\pi$
$234$		0			0
$235$	−2.78083	+	3.48705i	−0.181401	+	0.227470i
$236$	−14.0368	−	17.6016i	−0.913720	−	1.14577i
$237$		0			0
$238$	0.643104	−	0.309703i	0.0416862	−	0.0200750i
$239$	15.9393	−	19.9872i	1.03103	−	1.29287i	0.0757593	−	0.997126i	$-0.475862\pi$
$239$	15.9393	−	19.9872i	1.03103	−	1.29287i	0.955268	−	0.295741i	$-0.0955666\pi$
$240$		0			0
$241$	−2.16541	−	9.48727i	−0.139486	−	0.611129i	−0.995548	−	0.0942554i	$-0.969953\pi$
$241$	−2.16541	−	9.48727i	−0.139486	−	0.611129i	0.856062	−	0.516873i	$-0.172904\pi$
$242$	3.71648	+	4.66032i	0.238904	+	0.299577i
$243$		0			0
$244$	2.96077			0.189544
$245$	−1.05831	+	4.63676i	−0.0676130	+	0.296232i
$246$		0			0
$247$	−12.0036	+	5.78065i	−0.763774	+	0.367814i
$248$	−2.51961	+	11.0392i	−0.159996	+	0.700987i
$249$		0			0
$250$	−0.652497	+	2.85878i	−0.0412676	+	0.180805i
$251$	6.08546	+	7.63092i	0.384111	+	0.481660i	0.935871	−	0.352343i	$-0.114615\pi$
$251$	6.08546	+	7.63092i	0.384111	+	0.481660i	−0.551760	+	0.834003i	$0.686044\pi$
$252$		0			0
$253$	−2.52326	−	11.0551i	−0.158636	−	0.695030i
$254$	−0.287700	+	0.360765i	−0.0180519	+	0.0226364i
$255$		0			0
$256$	−2.16368	−	1.04197i	−0.135230	−	0.0651233i
$257$	−10.1984	−	12.7883i	−0.636156	−	0.797714i	0.354360	−	0.935109i	$-0.384699\pi$
$257$	−10.1984	−	12.7883i	−0.636156	−	0.797714i	−0.990516	+	0.137394i	$0.956127\pi$
$258$		0			0
$259$	1.58815	+	0.764811i	0.0986826	+	0.0475230i
$260$	−7.04892			−0.437155
$261$		0			0
$262$	−3.57002			−0.220557
$263$	21.3741	+	10.2932i	1.31798	+	0.634708i	0.954867	−	0.297035i	$-0.0959979\pi$
$263$	21.3741	+	10.2932i	1.31798	+	0.634708i	0.363118	+	0.931743i	$0.381712\pi$
$264$		0			0
$265$	−2.02446	−	2.53859i	−0.124362	−	0.155944i
$266$	0.337282	+	0.162426i	0.0206801	+	0.00995899i
$267$		0			0
$268$	2.60992	−	3.27273i	0.159426	−	0.199914i
$269$	5.64191	+	24.7188i	0.343993	+	1.50713i	0.790561	+	0.612383i	$0.209789\pi$
$269$	5.64191	+	24.7188i	0.343993	+	1.50713i	−0.446568	+	0.894750i	$0.647354\pi$
$270$		0			0
$271$	−0.750332	−	0.940887i	−0.0455794	−	0.0571548i	0.758519	−	0.651651i	$-0.225923\pi$
$271$	−0.750332	−	0.940887i	−0.0455794	−	0.0571548i	−0.804099	+	0.594496i	$0.797352\pi$
$272$	2.85086	−	12.4904i	0.172858	−	0.757342i
$273$		0			0
$274$	1.70655	−	7.47690i	0.103097	−	0.451696i
$275$	−20.1184	+	9.68851i	−1.21319	+	0.584239i
$276$		0			0
$277$	−2.37316	+	10.3975i	−0.142589	+	0.624724i	0.852239	+	0.523153i	$0.175244\pi$
$277$	−2.37316	+	10.3975i	−0.142589	+	0.624724i	−0.994828	+	0.101572i	$0.967613\pi$
$278$	−7.41789			−0.444896
$279$		0			0
$280$	0.260553	+	0.326723i	0.0155710	+	0.0195255i
$281$	−3.62253	−	15.8713i	−0.216102	−	0.946805i	−0.960327	−	0.278876i	$-0.910038\pi$
$281$	−3.62253	−	15.8713i	−0.216102	−	0.946805i	0.744225	−	0.667929i	$-0.232819\pi$
$282$		0			0
$283$	−3.27144	+	4.10225i	−0.194467	+	0.243854i	−0.869499	−	0.493935i	$-0.835558\pi$
$283$	−3.27144	+	4.10225i	−0.194467	+	0.243854i	0.675032	+	0.737788i	$0.264130\pi$
$284$	11.9085	−	5.73483i	0.706640	−	0.340300i
$285$		0			0
$286$	7.74698	+	9.71441i	0.458089	+	0.574425i
$287$	−0.692021	+	0.867767i	−0.0408487	+	0.0512227i
$288$		0			0
$289$	3.19567			0.187981
$290$	−0.560999	−	1.56075i	−0.0329430	−	0.0916506i
$291$		0			0
$292$	9.13318	+	4.39831i	0.534479	+	0.257391i
$293$	−4.21714	+	5.28813i	−0.246368	+	0.308936i	−0.889604	−	0.456732i	$-0.849020\pi$
$293$	−4.21714	+	5.28813i	−0.246368	+	0.308936i	0.643236	+	0.765668i	$0.277591\pi$
$294$		0			0
$295$	7.78986	+	3.75140i	0.453543	+	0.218415i
$296$	−7.52930	+	3.62592i	−0.437632	+	0.210752i
$297$		0			0
$298$	1.84266	+	8.07321i	0.106742	+	0.467669i
$299$	−2.88793	−	12.6528i	−0.167013	−	0.731733i
$300$		0			0
$301$	0.270479	−	1.18505i	0.0155901	−	0.0683049i
$302$	−3.35019			−0.192782
$303$		0			0
$304$	6.05376	−	2.91534i	0.347207	−	0.167206i
$305$	−1.02446	+	0.493353i	−0.0586603	+	0.0282493i
$306$		0			0
$307$	4.51812			0.257863			0.128931	−	0.991654i	$-0.458845\pi$
$307$	4.51812			0.257863			0.128931	+	0.991654i	$0.458845\pi$
$308$	−0.706791	+	3.09666i	−0.0402732	+	0.176448i
$309$		0			0
$310$	−0.458615	−	2.00933i	−0.0260476	−	0.114122i
$311$	−2.80745	−	12.3002i	−0.159196	−	0.697482i	−0.990018	−	0.140944i	$-0.954986\pi$
$311$	−2.80745	−	12.3002i	−0.159196	−	0.697482i	0.830822	−	0.556538i	$-0.187871\pi$
$312$		0			0
$313$	−17.3349	+	8.34804i	−0.979826	+	0.471859i	−0.854045	−	0.520199i	$-0.825858\pi$
$313$	−17.3349	+	8.34804i	−0.979826	+	0.471859i	−0.125781	+	0.992058i	$0.540144\pi$
$314$	7.31336	+	3.52193i	0.412717	+	0.198754i
$315$		0			0
$316$	5.24094	−	6.57193i	0.294826	−	0.369700i
$317$	2.58426	+	1.24451i	0.145147	+	0.0698989i	0.505047	−	0.863092i	$-0.331475\pi$
$317$	2.58426	+	1.24451i	0.145147	+	0.0698989i	−0.359901	+	0.932991i	$0.617189\pi$
$318$		0			0
$319$	13.9596	−	22.6395i	0.781586	−	1.26757i
$320$	2.51275			0.140467
$321$		0			0
$322$	−0.227365	+	0.285107i	−0.0126706	+	0.0158884i
$323$	6.60388	+	8.28100i	0.367449	+	0.460767i
$324$		0			0
$325$	−23.0260	+	11.0887i	−1.27725	+	0.615091i
$326$	3.50753	−	4.39831i	0.194264	−	0.243600i
$327$		0			0
$328$	−1.17092	−	5.13011i	−0.0646530	−	0.283263i
$329$	1.43416	+	1.79838i	0.0790676	+	0.0991477i
$330$		0			0
$331$	3.13408			0.172265			0.0861323	−	0.996284i	$-0.472549\pi$
$331$	3.13408			0.172265			0.0861323	+	0.996284i	$0.472549\pi$
$332$	−1.78621	+	7.82589i	−0.0980309	+	0.429501i
$333$		0			0
$334$	−0.319396	+	0.153813i	−0.0174766	+	0.00841628i
$335$	−0.357724	+	1.56729i	−0.0195445	+	0.0856302i
$336$		0			0
$337$	−1.10872	+	4.85762i	−0.0603958	+	0.264611i	−0.996107	−	0.0881567i	$-0.971902\pi$
$337$	−1.10872	+	4.85762i	−0.0603958	+	0.264611i	0.935711	+	0.352768i	$0.114760\pi$
$338$	5.25936	+	6.59502i	0.286071	+	0.358722i
$339$		0			0
$340$	1.24698	+	5.46337i	0.0676270	+	0.296293i
$341$	20.6075	−	25.8410i	1.11596	−	1.39937i
$342$		0			0
$343$	4.46077	+	2.14819i	0.240859	+	0.115992i
$344$	3.59299	+	4.50547i	0.193721	+	0.242919i
$345$		0			0
$346$	−3.67025	−	1.76750i	−0.197314	−	0.0950214i
$347$	−20.1172			−1.07995			−0.539974	−	0.841682i	$-0.681566\pi$
$347$	−20.1172			−1.07995			−0.539974	+	0.841682i	$0.681566\pi$
$348$		0			0
$349$	20.4892			1.09676			0.548380	−	0.836229i	$-0.315245\pi$
$349$	20.4892			1.09676			0.548380	+	0.836229i	$0.315245\pi$
$350$	0.646989	+	0.311573i	0.0345830	+	0.0166543i
$351$		0			0
$352$	−14.3279	−	17.9666i	−0.763679	−	0.957623i
$353$	16.2153	+	7.80887i	0.863052	+	0.415624i	0.812406	−	0.583092i	$-0.198157\pi$
$353$	16.2153	+	7.80887i	0.863052	+	0.415624i	0.0506467	+	0.998717i	$0.483872\pi$
$354$		0			0
$355$	−3.16487	+	3.96863i	−0.167974	+	0.210633i
$356$	2.27748	+	9.97829i	0.120706	+	0.528848i
$357$		0			0
$358$	−0.945042	−	1.18505i	−0.0499470	−	0.0626316i
$359$	5.25786	−	23.0362i	0.277499	−	1.21580i	−0.623444	−	0.781868i	$-0.714267\pi$
$359$	5.25786	−	23.0362i	0.277499	−	1.21580i	0.900943	−	0.433937i	$-0.142876\pi$
$360$		0			0
$361$	2.99180	−	13.1079i	0.157463	−	0.689892i
$362$	−5.08211	+	2.44741i	−0.267110	+	0.128633i
$363$		0			0
$364$	−0.808938	+	3.54419i	−0.0423999	+	0.185766i
$365$	−3.89307			−0.203772
$366$		0			0
$367$	−18.4822	−	23.1759i	−0.964762	−	1.20977i	−0.977732	−	0.209857i	$-0.932700\pi$
$367$	−18.4822	−	23.1759i	−0.964762	−	1.20977i	0.0129705	−	0.999916i	$-0.495871\pi$
$368$	1.45646	+	6.38117i	0.0759232	+	0.332641i
$369$		0			0
$370$	0.948394	−	1.18925i	0.0493047	−	0.0618261i
$371$	−1.50873	+	0.726566i	−0.0783293	+	0.0377214i
$372$		0			0
$373$	−15.7044	−	19.6927i	−0.813143	−	1.01965i	−0.999310	−	0.0371310i	$-0.988178\pi$
$373$	−15.7044	−	19.6927i	−0.813143	−	1.01965i	0.186167	−	0.982518i	$-0.440393\pi$
$374$	6.15883	−	7.72293i	0.318466	−	0.399343i
$375$		0			0
$376$	−10.9051			−0.562390
$377$	15.9770	−	25.9114i	0.822859	−	1.33451i
$378$		0			0
$379$	24.2424	+	11.6745i	1.24525	+	0.599681i	0.936234	−	0.351376i	$-0.114286\pi$
$379$	24.2424	+	11.6745i	1.24525	+	0.599681i	0.309016	+	0.951057i	$0.400000\pi$
$380$	−1.83244	+	2.29780i	−0.0940020	+	0.117875i
$381$		0			0
$382$	−4.27844	−	2.06039i	−0.218904	−	0.105419i
$383$	−17.7213	+	8.53414i	−0.905517	+	0.436074i	−0.827879	−	0.560907i	$-0.810452\pi$
$383$	−17.7213	+	8.53414i	−0.905517	+	0.436074i	−0.0776388	+	0.996982i	$0.524738\pi$
$384$		0			0
$385$	−0.271438	−	1.18925i	−0.0138338	−	0.0606097i
$386$	−2.25086	−	9.86168i	−0.114566	−	0.501946i
$387$		0			0
$388$	−0.0724165	+	0.317278i	−0.00367639	+	0.0161073i
$389$	−24.8552			−1.26021			−0.630103	−	0.776511i	$-0.716988\pi$
$389$	−24.8552			−1.26021			−0.630103	+	0.776511i	$0.716988\pi$
$390$		0			0
$391$	−9.29590	+	4.47667i	−0.470114	+	0.226395i
$392$	−10.4770	+	5.04547i	−0.529170	+	0.254835i
$393$		0			0
$394$	8.70410			0.438506
$395$	−0.718341	+	3.14726i	−0.0361436	+	0.158356i
$396$		0			0
$397$	0.888887	+	3.89447i	0.0446120	+	0.195458i	0.992323	−	0.123671i	$-0.0394668\pi$
$397$	0.888887	+	3.89447i	0.0446120	+	0.195458i	−0.947711	+	0.319129i	$0.896610\pi$
$398$	0.0866540	+	0.379656i	0.00434357	+	0.0190304i
$399$		0			0
$400$	11.6126	−	5.59234i	0.580630	−	0.279617i
$401$	−22.4405	−	10.8068i	−1.12062	−	0.539664i	−0.220539	−	0.975378i	$-0.570782\pi$
$401$	−22.4405	−	10.8068i	−1.12062	−	0.539664i	−0.900085	+	0.435714i	$0.856496\pi$
$402$		0			0
$403$	23.5858	−	29.5756i	1.17489	−	1.47327i
$404$	−5.24309	−	2.52494i	−0.260854	−	0.125621i
$405$		0			0
$406$	−0.849126	+	0.102957i	−0.0421414	+	0.00510965i
$407$	24.3937			1.20915
$408$		0			0
$409$	0.176587	−	0.221434i	0.00873169	−	0.0109492i	−0.777446	−	0.628949i	$-0.783485\pi$
$409$	0.176587	−	0.221434i	0.00873169	−	0.0109492i	0.786178	+	0.618000i	$0.212057\pi$
$410$	0.597171	+	0.748828i	0.0294922	+	0.0369820i
$411$		0			0
$412$	−22.1652	+	10.6742i	−1.09200	+	0.525879i
$413$	2.78017	−	3.48622i	0.136803	−	0.171546i
$414$		0			0
$415$	−0.685981	−	3.00548i	−0.0336735	−	0.147533i
$416$	−16.3986	−	20.5632i	−0.804006	−	1.00819i
$417$		0			0
$418$	5.18060			0.253392
$419$	−5.89426	+	25.8245i	−0.287954	+	1.26161i	0.599374	+	0.800469i	$0.295416\pi$
$419$	−5.89426	+	25.8245i	−0.287954	+	1.26161i	−0.887328	+	0.461139i	$0.847441\pi$
$420$		0			0
$421$	15.8409	−	7.62859i	0.772040	−	0.371795i	−0.00602261	−	0.999982i	$-0.501917\pi$
$421$	15.8409	−	7.62859i	0.772040	−	0.371795i	0.778062	+	0.628187i	$0.216203\pi$
$422$	1.80917	−	7.92651i	0.0880693	−	0.385857i
$423$		0			0
$424$	1.76659	−	7.73995i	0.0857934	−	0.375885i
$425$	12.6679	+	15.8850i	0.614481	+	0.770535i
$426$		0			0
$427$	0.130490	+	0.571714i	0.00631486	+	0.0276672i
$428$	18.2506	−	22.8856i	0.882177	−	1.10622i
$429$		0			0
$430$	−0.945042	−	0.455108i	−0.0455740	−	0.0219473i
$431$	17.3300	+	21.7312i	0.834759	+	1.04675i	0.998186	+	0.0601992i	$0.0191736\pi$
$431$	17.3300	+	21.7312i	0.834759	+	1.04675i	−0.163428	+	0.986555i	$0.552255\pi$
$432$		0			0
$433$	−5.29374	−	2.54933i	−0.254401	−	0.122513i	0.302337	−	0.953201i	$-0.402233\pi$
$433$	−5.29374	−	2.54933i	−0.254401	−	0.122513i	−0.556738	+	0.830688i	$0.687947\pi$
$434$	−1.06292			−0.0510217
$435$		0			0
$436$	−9.85086			−0.471770
$437$	−4.87531	−	2.34783i	−0.233218	−	0.112312i
$438$		0			0
$439$	−9.81431	−	12.3068i	−0.468412	−	0.587370i	0.490370	−	0.871515i	$-0.336862\pi$
$439$	−9.81431	−	12.3068i	−0.468412	−	0.587370i	−0.958781	+	0.284145i	$0.908290\pi$
$440$	5.21044	+	2.50922i	0.248398	+	0.119622i
$441$		0			0
$442$	7.04892	−	8.83906i	0.335283	−	0.420431i
$443$	1.49947	+	6.56960i	0.0712419	+	0.312131i	0.997976	−	0.0635859i	$-0.0202537\pi$
$443$	1.49947	+	6.56960i	0.0712419	+	0.312131i	−0.926735	+	0.375717i	$0.877397\pi$
$444$		0			0
$445$	−2.45071	−	3.07310i	−0.116175	−	0.145679i
$446$	0.180071	−	0.788944i	0.00852663	−	0.0373576i
$447$		0			0
$448$	0.288364	−	1.26341i	0.0136239	−	0.0596903i
$449$	11.1000	−	5.34547i	0.523841	−	0.252269i	−0.153224	−	0.988191i	$-0.548966\pi$
$449$	11.1000	−	5.34547i	0.523841	−	0.252269i	0.677065	+	0.735923i	$0.263251\pi$
$450$		0			0
$451$	−3.41789	+	14.9748i	−0.160942	+	0.705135i
$452$	−19.2349			−0.904733
$453$		0			0
$454$	3.84481	+	4.82124i	0.180446	+	0.226272i
$455$	−0.310667	−	1.36112i	−0.0145643	−	0.0638103i
$456$		0			0
$457$	8.51842	−	10.6818i	0.398475	−	0.499672i	−0.541602	−	0.840635i	$-0.682182\pi$
$457$	8.51842	−	10.6818i	0.398475	−	0.499672i	0.940076	+	0.340964i	$0.110753\pi$
$458$	5.12133	−	2.46630i	0.239304	−	0.115243i
$459$		0			0
$460$	−1.78501	−	2.23833i	−0.0832266	−	0.104363i
$461$	−7.23759	+	9.07565i	−0.337088	+	0.422695i	−0.921268	−	0.388929i	$-0.872845\pi$
$461$	−7.23759	+	9.07565i	−0.337088	+	0.422695i	0.584180	+	0.811624i	$0.301416\pi$
$462$		0			0
$463$	−7.24267			−0.336595			−0.168298	−	0.985736i	$-0.553827\pi$
$463$	−7.24267			−0.336595			−0.168298	+	0.985736i	$0.553827\pi$
$464$	−8.05765	+	13.0678i	−0.374067	+	0.606659i
$465$		0			0
$466$	−3.55496	−	1.71198i	−0.164680	−	0.0793058i
$467$	1.28650	−	1.61322i	0.0595323	−	0.0746511i	−0.751174	−	0.660104i	$-0.770512\pi$
$467$	1.28650	−	1.61322i	0.0595323	−	0.0746511i	0.810706	+	0.585453i	$0.199083\pi$
$468$		0			0
$469$	0.746980	+	0.359726i	0.0344923	+	0.0166106i
$470$	1.78836	−	0.861231i	0.0824911	−	0.0397256i
$471$		0			0
$472$	4.70410	+	20.6100i	0.216524	+	0.948653i
$473$	−3.74309	−	16.3996i	−0.172108	−	0.754053i
$474$		0			0
$475$	−2.37113	+	10.3886i	−0.108795	+	0.476662i
$476$	2.89008			0.132467
$477$		0			0
$478$	−10.2506	+	4.93644i	−0.468853	+	0.225788i
$479$	−3.50388	+	1.68738i	−0.160097	+	0.0770985i	−0.512216	−	0.858857i	$-0.671175\pi$
$479$	−3.50388	+	1.68738i	−0.160097	+	0.0770985i	0.352120	+	0.935955i	$0.385461\pi$
$480$		0			0
$481$	27.9191			1.27300
$482$	−0.963697	+	4.22223i	−0.0438952	+	0.192317i
$483$		0			0
$484$	5.37047	+	23.5296i	0.244112	+	1.06953i
$485$	−0.0278111	−	0.121848i	−0.00126284	−	0.00553284i
$486$		0			0
$487$	−8.87047	+	4.27179i	−0.401959	+	0.193573i	−0.623931	−	0.781480i	$-0.714465\pi$
$487$	−8.87047	+	4.27179i	−0.401959	+	0.193573i	0.221971	+	0.975053i	$0.428751\pi$
$488$	−2.50484	−	1.20627i	−0.113389	−	0.0546053i
$489$		0			0
$490$	1.31969	−	1.65484i	0.0596176	−	0.0747581i
$491$	7.01961	+	3.38047i	0.316791	+	0.152558i	0.585521	−	0.810657i	$-0.300890\pi$
$491$	7.01961	+	3.38047i	0.316791	+	0.152558i	−0.268731	+	0.963215i	$0.586604\pi$
$492$		0			0
$493$	−22.9095	−	7.79942i	−1.03179	−	0.351268i
$494$	5.92931			0.266772
$495$		0			0
$496$	−11.8949	+	14.9158i	−0.534098	+	0.669738i
$497$	1.63222	+	2.04674i	0.0732150	+	0.0918087i
$498$		0			0
$499$	18.5286	−	8.92292i	0.829456	−	0.399445i	0.0295448	−	0.999563i	$-0.490594\pi$
$499$	18.5286	−	8.92292i	0.829456	−	0.399445i	0.799911	+	0.600119i	$0.204880\pi$
$500$	−7.40246	+	9.28239i	−0.331048	+	0.415121i
$501$		0			0
$502$	−0.966575	−	4.23484i	−0.0431404	−	0.189010i
$503$	−5.13437	−	6.43830i	−0.228930	−	0.287070i	0.654078	−	0.756427i	$-0.273057\pi$
$503$	−5.13437	−	6.43830i	−0.228930	−	0.287070i	−0.883008	+	0.469358i	$0.844486\pi$
$504$		0			0
$505$	2.23490			0.0994517
$506$	−1.12296	+	4.92000i	−0.0499215	+	0.218721i
$507$		0			0
$508$	−1.68329	+	0.810631i	−0.0746840	+	0.0359659i
$509$	1.76151	−	7.71769i	0.0780777	−	0.342081i	−0.920768	−	0.390110i	$-0.872437\pi$
$509$	1.76151	−	7.71769i	0.0780777	−	0.342081i	0.998846	+	0.0480294i	$0.0152941\pi$
$510$		0			0
$511$	−0.446771	+	1.95743i	−0.0197640	+	0.0865916i
$512$	14.2853	+	17.9132i	0.631327	+	0.791659i
$513$		0			0
$514$	1.61984	+	7.09699i	0.0714482	+	0.313035i
$515$	5.89075	−	7.38676i	0.259577	−	0.325500i
$516$		0			0
$517$	28.6797	+	13.8114i	1.26133	+	0.607425i
$518$	−0.489115	−	0.613331i	−0.0214905	−	0.0269482i
$519$		0			0
$520$	5.96346	+	2.87185i	0.261515	+	0.125939i
$521$	3.52542			0.154451			0.0772257	−	0.997014i	$-0.475394\pi$
$521$	3.52542			0.154451			0.0772257	+	0.997014i	$0.475394\pi$
$522$		0			0
$523$	10.0301			0.438587			0.219294	−	0.975659i	$-0.429625\pi$
$523$	10.0301			0.438587			0.219294	+	0.975659i	$0.429625\pi$
$524$	−13.0233	−	6.27167i	−0.568924	−	0.273979i
$525$		0			0
$526$	−6.58277	−	8.25453i	−0.287022	−	0.359915i
$527$	−27.0954	−	13.0485i	−1.18030	−	0.568401i
$528$		0			0
$529$	−11.0538	+	13.8610i	−0.480598	+	0.602651i
$530$	0.321552	+	1.40881i	0.0139673	+	0.0611949i
$531$		0			0
$532$	0.945042	+	1.18505i	0.0409728	+	0.0513782i
$533$	−3.91185	+	17.1390i	−0.169441	+	0.742370i
$534$		0			0
$535$	−2.50149	+	10.9598i	−0.108149	+	0.473831i
$536$	−3.54138	+	1.70544i	−0.152965	+	0.0736638i
$537$		0			0
$538$	2.51089	−	11.0009i	0.108252	−	0.474283i
$539$	33.9439			1.46207
$540$		0			0
$541$	5.12767	+	6.42990i	0.220456	+	0.276443i	0.879744	−	0.475447i	$-0.157714\pi$
$541$	5.12767	+	6.42990i	0.220456	+	0.276443i	−0.659288	+	0.751890i	$0.729142\pi$
$542$	0.119178	+	0.522153i	0.00511913	+	0.0224284i
$543$		0			0
$544$	−13.0368	+	16.3477i	−0.558950	+	0.700901i
$545$	3.40850	−	1.64145i	0.146004	−	0.0703119i
$546$		0			0
$547$	16.1253	+	20.2205i	0.689467	+	0.864564i	0.996188	−	0.0872352i	$-0.0278032\pi$
$547$	16.1253	+	20.2205i	0.689467	+	0.864564i	−0.306721	+	0.951800i	$0.599232\pi$
$548$	19.3605	−	24.2774i	0.827041	−	1.03708i
$549$		0			0
$550$	9.93767			0.423744
$551$	−4.29321	−	11.9441i	−0.182897	−	0.508837i
$552$		0			0
$553$	1.50000	+	0.722362i	0.0637865	+	0.0307180i
$554$	2.95928	−	3.71082i	0.125728	−	0.157658i
$555$		0			0
$556$	−27.0601	−	13.0315i	−1.14760	−	0.552657i
$557$	20.7310	−	9.98353i	0.878401	−	0.423016i	0.0603609	−	0.998177i	$-0.480775\pi$
$557$	20.7310	−	9.98353i	0.878401	−	0.423016i	0.818040	+	0.575161i	$0.195061\pi$
$558$		0			0
$559$	−4.28405	−	18.7697i	−0.181196	−	0.793872i
$560$	0.156678	+	0.686450i	0.00662084	+	0.0290078i
$561$		0			0
$562$	−1.61218	+	7.06341i	−0.0680056	+	0.297952i
$563$	−43.1159			−1.81712			−0.908559	−	0.417757i	$-0.862816\pi$
$563$	−43.1159			−1.81712			−0.908559	+	0.417757i	$0.862816\pi$
$564$		0			0
$565$	6.65548	−	3.20511i	0.279998	−	0.134840i
$566$	2.10388	−	1.01317i	0.0884325	−	0.0425868i
$567$		0			0
$568$	−12.4112			−0.520762
$569$	−5.40999	+	23.7027i	−0.226799	+	0.993670i	0.725433	+	0.688293i	$0.241640\pi$
$569$	−5.40999	+	23.7027i	−0.226799	+	0.993670i	−0.952231	+	0.305377i	$0.901217\pi$
$570$		0			0
$571$	−4.11410	−	18.0250i	−0.172170	−	0.754324i	−0.985103	−	0.171967i	$-0.944988\pi$
$571$	−4.11410	−	18.0250i	−0.172170	−	0.754324i	0.812933	−	0.582357i	$-0.197869\pi$
$572$	11.1947	+	49.0472i	0.468074	+	2.05077i
$573$		0			0
$574$	0.445042	−	0.214321i	0.0185757	−	0.00894558i
$575$	−9.35205	−	4.50371i	−0.390008	−	0.187818i
$576$		0			0
$577$	−23.6042	+	29.5987i	−0.982654	+	1.23221i	−0.0100007	+	0.999950i	$0.503183\pi$
$577$	−23.6042	+	29.5987i	−0.982654	+	1.23221i	−0.972654	+	0.232260i	$0.925388\pi$
$578$	−1.28136	−	0.617072i	−0.0532977	−	0.0256668i
$579$		0			0
$580$	0.695374	−	6.67909i	0.0288738	−	0.277334i
$581$	−1.58987			−0.0659591
$582$		0			0
$583$	−14.4487	+	18.1181i	−0.598404	+	0.750374i
$584$	−5.93482	−	7.44203i	−0.245585	−	0.307953i
$585$		0			0
$586$	2.71206	−	1.30606i	0.112034	−	0.0539529i
$587$	9.00030	−	11.2860i	0.371482	−	0.465824i	−0.560592	−	0.828092i	$-0.689426\pi$
$587$	9.00030	−	11.2860i	0.371482	−	0.465824i	0.932074	+	0.362269i	$0.117998\pi$
$588$		0			0
$589$	−3.50969	−	15.3770i	−0.144614	−	0.633596i
$590$	−2.39911	−	3.00839i	−0.0987697	−	0.123853i
$591$		0			0
$592$	−14.0804			−0.578700
$593$	−2.89320	+	12.6759i	−0.118809	+	0.520538i	0.880140	+	0.474714i	$0.157449\pi$
$593$	−2.89320	+	12.6759i	−0.118809	+	0.520538i	−0.998950	+	0.0458241i	$0.985409\pi$
$594$		0			0
$595$	−1.00000	+	0.481575i	−0.0409960	+	0.0197426i
$596$	−7.46077	+	32.6878i	−0.305605	+	1.33894i
$597$		0			0
$598$	−1.28525	+	5.63104i	−0.0525577	+	0.230270i
$599$	−7.54019	−	9.45510i	−0.308084	−	0.386325i	0.603552	−	0.797323i	$-0.293751\pi$
$599$	−7.54019	−	9.45510i	−0.308084	−	0.386325i	−0.911636	+	0.410999i	$0.865180\pi$
$600$		0			0
$601$	4.97272	+	21.7869i	0.202842	+	0.888707i	0.969196	+	0.246289i	$0.0792113\pi$
$601$	4.97272	+	21.7869i	0.202842	+	0.888707i	−0.766355	+	0.642418i	$0.777932\pi$
$602$	−0.337282	+	0.422938i	−0.0137466	+	0.0172377i
$603$		0			0
$604$	−12.2213	−	5.88548i	−0.497279	−	0.239477i
$605$	−5.77897	−	7.24660i	−0.234949	−	0.294616i
$606$		0			0
$607$	−37.3620	−	17.9926i	−1.51648	−	0.730297i	−0.523886	−	0.851789i	$-0.675518\pi$
$607$	−37.3620	−	17.9926i	−1.51648	−	0.730297i	−0.992593	+	0.121491i	$0.961232\pi$
$608$	−10.9661			−0.444736
$609$		0			0
$610$	0.506041			0.0204890
$611$	32.8245	+	15.8075i	1.32794	+	0.639502i
$612$		0			0
$613$	16.0764	+	20.1591i	0.649318	+	0.814219i	0.992134	−	0.125184i	$-0.0399520\pi$
$613$	16.0764	+	20.1591i	0.649318	+	0.814219i	−0.342816	+	0.939403i	$0.611381\pi$
$614$	−1.81163	−	0.872433i	−0.0731113	−	0.0352085i
$615$		0			0
$616$	1.85958	−	2.33184i	0.0749248	−	0.0939527i
$617$	1.97272	+	8.64306i	0.0794188	+	0.347956i	0.998988	−	0.0449710i	$-0.0143195\pi$
$617$	1.97272	+	8.64306i	0.0794188	+	0.347956i	−0.919570	+	0.392927i	$0.871462\pi$
$618$		0			0
$619$	18.3626	+	23.0259i	0.738054	+	0.925490i	0.999207	−	0.0398069i	$-0.0126743\pi$
$619$	18.3626	+	23.0259i	0.738054	+	0.925490i	−0.261153	+	0.965297i	$0.584103\pi$
$620$	1.85690	−	8.13559i	0.0745747	−	0.326733i
$621$		0			0
$622$	−1.24943	+	5.47412i	−0.0500976	+	0.219492i
$623$	−1.82640	+	0.879546i	−0.0731730	+	0.0352383i
$624$		0			0
$625$	−4.01560	+	17.5935i	−0.160624	+	0.703739i
$626$	8.56273			0.342235
$627$		0			0
$628$	20.4916	+	25.6956i	0.817703	+	1.02537i
$629$	−4.93900	−	21.6392i	−0.196931	−	0.862811i
$630$		0			0
$631$	14.8210	−	18.5850i	0.590015	−	0.739856i	−0.393769	−	0.919209i	$-0.628829\pi$
$631$	14.8210	−	18.5850i	0.590015	−	0.739856i	0.983785	+	0.179353i	$0.0574005\pi$
$632$	−7.11141	+	3.42467i	−0.282877	+	0.136226i
$633$		0			0
$634$	−0.795897	−	0.998023i	−0.0316091	−	0.0396366i
$635$	0.447362	−	0.560974i	0.0177530	−	0.0222616i
$636$		0			0
$637$	38.8495			1.53927
$638$	−9.96897	+	6.38220i	−0.394675	+	0.252674i
$639$		0			0
$640$	−6.80947	−	3.27927i	−0.269168	−	0.129624i
$641$	−17.7479	+	22.2552i	−0.701001	+	0.879028i	−0.997098	−	0.0761300i	$-0.975744\pi$
$641$	−17.7479	+	22.2552i	−0.701001	+	0.879028i	0.296096	+	0.955158i	$0.404315\pi$
$642$		0			0
$643$	17.4308	+	8.39423i	0.687404	+	0.331036i	0.744774	−	0.667317i	$-0.232557\pi$
$643$	17.4308	+	8.39423i	0.687404	+	0.331036i	−0.0573702	+	0.998353i	$0.518272\pi$
$644$	−1.33028	+	0.640630i	−0.0524204	+	0.0252443i
$645$		0			0
$646$	−1.04892	−	4.59561i	−0.0412691	−	0.180812i
$647$	5.05443	+	22.1449i	0.198710	+	0.870605i	0.971706	+	0.236194i	$0.0759002\pi$
$647$	5.05443	+	22.1449i	0.198710	+	0.870605i	−0.772996	+	0.634411i	$0.781243\pi$
$648$		0			0
$649$	13.7313	−	60.1605i	0.538999	−	2.36151i
$650$	11.3739			0.446120
$651$		0			0
$652$	20.5221	−	9.88291i	0.803706	−	0.387044i
$653$	20.6603	−	9.94949i	0.808501	−	0.389354i	0.0164928	−	0.999864i	$-0.494750\pi$
$653$	20.6603	−	9.94949i	0.808501	−	0.389354i	0.792008	+	0.610510i	$0.209036\pi$
$654$		0			0
$655$	5.55124			0.216905
$656$	1.97285	−	8.64363i	0.0770270	−	0.337477i
$657$		0			0
$658$	−0.227792	−	0.998023i	−0.00888027	−	0.0389070i
$659$	−4.26755	−	18.6974i	−0.166240	−	0.728346i	−0.987478	−	0.157759i	$-0.949573\pi$
$659$	−4.26755	−	18.6974i	−0.166240	−	0.728346i	0.821237	−	0.570587i	$-0.193284\pi$
$660$		0			0
$661$	3.05107	−	1.46932i	0.118673	−	0.0571499i	−0.373605	−	0.927588i	$-0.621879\pi$
$661$	3.05107	−	1.46932i	0.118673	−	0.0571499i	0.492278	+	0.870438i	$0.336164\pi$
$662$	−1.25667	−	0.605180i	−0.0488418	−	0.0235210i
$663$		0			0
$664$	4.69955	−	5.89305i	0.182378	−	0.228695i
$665$	−0.524459	−	0.252566i	−0.0203376	−	0.00979409i
$666$		0			0
$667$	12.2739	−	1.48821i	0.475247	−	0.0576238i
$668$	−1.43535			−0.0555355
$669$		0			0
$670$	0.446074	−	0.559360i	0.0172334	−	0.0216099i
$671$	5.05980	+	6.34479i	0.195332	+	0.244938i
$672$		0			0
$673$	−4.29805	+	2.06983i	−0.165678	+	0.0797862i	−0.514885	−	0.857259i	$-0.672165\pi$
$673$	−4.29805	+	2.06983i	−0.165678	+	0.0797862i	0.349207	+	0.937046i	$0.386451\pi$
$674$	1.38255	−	1.73366i	0.0532539	−	0.0667782i
$675$		0			0
$676$	7.59999	+	33.2977i	0.292307	+	1.28068i
$677$	26.8662	+	33.6892i	1.03255	+	1.29478i	0.954622	+	0.297821i	$0.0962599\pi$
$677$	26.8662	+	33.6892i	1.03255	+	1.29478i	0.0779309	+	0.996959i	$0.475169\pi$
$678$		0			0
$679$	−0.0644568			−0.00247362
$680$	1.17092	−	5.13011i	0.0449025	−	0.196731i
$681$		0			0
$682$	−13.2528	+	6.38220i	−0.507475	+	0.244387i
$683$	5.21432	−	22.8454i	0.199521	−	0.874157i	−0.771702	−	0.635984i	$-0.780594\pi$
$683$	5.21432	−	22.8454i	0.199521	−	0.874157i	0.971223	−	0.238173i	$-0.0765484\pi$
$684$		0			0
$685$	−2.65362	+	11.6263i	−0.101390	+	0.444217i
$686$	−1.37382	−	1.72272i	−0.0524528	−	0.0657737i
$687$		0			0
$688$	2.16056	+	9.46604i	0.0823707	+	0.360890i
$689$	−16.5368	+	20.7365i	−0.630003	+	0.789999i
$690$		0			0
$691$	−38.8657	−	18.7167i	−1.47852	−	0.712018i	−0.491243	−	0.871023i	$-0.663457\pi$
$691$	−38.8657	−	18.7167i	−1.47852	−	0.712018i	−0.987278	+	0.159005i	$0.949171\pi$
$692$	−10.2838	−	12.8955i	−0.390932	−	0.490213i
$693$		0			0
$694$	8.06638	+	3.88456i	0.306195	+	0.147456i
$695$	11.5345			0.437529
$696$		0			0
$697$	13.9758			0.529373
$698$	−8.21552	−	3.95639i	−0.310962	−	0.149751i
$699$		0			0
$700$	1.81282	+	2.27321i	0.0685183	+	0.0859192i
$701$	3.81186	+	1.83570i	0.143972	+	0.0693333i	0.504483	−	0.863422i	$-0.331683\pi$
$701$	3.81186	+	1.83570i	0.143972	+	0.0693333i	−0.360511	+	0.932755i	$0.617398\pi$
$702$		0			0
$703$	7.25786	−	9.10107i	0.273736	−	0.343254i
$704$	−3.99061	−	17.4840i	−0.150402	−	0.658953i
$705$		0			0
$706$	−4.99396	−	6.26223i	−0.187950	−	0.235682i
$707$	0.256478	−	1.12370i	0.00964586	−	0.0422613i
$708$		0			0
$709$	−3.18287	+	13.9450i	−0.119535	+	0.523717i	0.879336	+	0.476203i	$0.157987\pi$
$709$	−3.18287	+	13.9450i	−0.119535	+	0.523717i	−0.998871	+	0.0475144i	$0.984870\pi$
$710$	2.03534	−	0.980170i	0.0763851	−	0.0367851i
$711$		0			0
$712$	2.13856	−	9.36962i	0.0801457	−	0.351141i
$713$	15.3642			0.575393
$714$		0			0
$715$	−12.0462	−	15.1055i	−0.450503	−	0.564913i
$716$	−1.36563	−	5.98319i	−0.0510358	−	0.223602i
$717$		0			0
$718$	−6.55645	+	8.22153i	−0.244685	+	0.306825i
$719$	−21.1194	+	10.1706i	−0.787620	+	0.379298i	−0.784051	−	0.620696i	$-0.786850\pi$
$719$	−21.1194	+	10.1706i	−0.787620	+	0.379298i	−0.00356825	+	0.999994i	$0.501136\pi$
$720$		0			0
$721$	−3.03803	−	3.80957i	−0.113142	−	0.141876i
$722$	−3.73072	+	4.67817i	−0.138843	+	0.174104i
$723$		0			0
$724$	−22.8388			−0.848796
$725$	−8.23543	−	22.9118i	−0.305856	−	0.850922i
$726$		0			0
$727$	−46.8482	−	22.5609i	−1.73750	−	0.836738i	−0.983741	−	0.179592i	$-0.942522\pi$
$727$	−46.8482	−	22.5609i	−1.73750	−	0.836738i	−0.753763	−	0.657146i	$-0.771763\pi$
$728$	2.12833	−	2.66885i	0.0788813	−	0.0989140i
$729$		0			0
$730$	1.56100	+	0.751737i	0.0577752	+	0.0278231i
$731$	−13.7899	+	6.64084i	−0.510036	+	0.245621i
$732$		0			0
$733$	−7.60806	−	33.3331i	−0.281010	−	1.23119i	−0.896501	−	0.443041i	$-0.853899\pi$
$733$	−7.60806	−	33.3331i	−0.281010	−	1.23119i	0.615491	−	0.788144i	$-0.288958\pi$
$734$	2.93559	+	12.8617i	0.108355	+	0.474733i
$735$		0			0
$736$	2.37704	−	10.4145i	0.0876190	−	0.383884i
$737$	11.4735			0.422632
$738$		0			0
$739$	−35.8342	+	17.2569i	−1.31818	+	0.634804i	−0.954915	−	0.296881i	$-0.904054\pi$
$739$	−35.8342	+	17.2569i	−1.31818	+	0.634804i	−0.363269	+	0.931684i	$0.618339\pi$
$740$	5.54892	−	2.67222i	0.203982	−	0.0982327i
$741$		0			0
$742$	0.745251			0.0273590
$743$	1.59730	−	6.99824i	0.0585993	−	0.256740i	−0.937140	−	0.348954i	$-0.886537\pi$
$743$	1.59730	−	6.99824i	0.0585993	−	0.256740i	0.995739	+	0.0922133i	$0.0293942\pi$
$744$		0			0
$745$	−2.86526	−	12.5535i	−0.104975	−	0.459925i
$746$	2.49439	+	10.9286i	0.0913260	+	0.400125i
$747$		0			0
$748$	36.0344	−	17.3533i	1.31755	−	0.634499i
$749$	5.22348	+	2.51550i	0.190862	+	0.0919142i
$750$		0			0
$751$	−16.9393	+	21.2412i	−0.618124	+	0.775103i	−0.988079	−	0.153947i	$-0.950802\pi$
$751$	−16.9393	+	21.2412i	−0.618124	+	0.775103i	0.369955	+	0.929050i	$0.379373\pi$
$752$	−16.5543	−	7.97213i	−0.603673	−	0.290714i
$753$		0			0
$754$	−11.4097	+	7.30457i	−0.415517	+	0.266017i
$755$	5.20941			0.189590
$756$		0			0
$757$	14.7721	−	18.5236i	0.536901	−	0.673253i	−0.437200	−	0.899364i	$-0.644030\pi$
$757$	14.7721	−	18.5236i	0.536901	−	0.673253i	0.974101	+	0.226111i	$0.0726013\pi$
$758$	−7.46615	−	9.36225i	−0.271183	−	0.340052i
$759$		0			0
$760$	2.48643	−	1.19740i	0.0901922	−	0.0434343i
$761$	8.88740	−	11.1444i	0.322168	−	0.403986i	−0.594204	−	0.804315i	$-0.702533\pi$
$761$	8.88740	−	11.1444i	0.322168	−	0.403986i	0.916372	+	0.400329i	$0.131104\pi$
$762$		0			0
$763$	−0.434157	−	1.90216i	−0.0157175	−	0.0688630i
$764$	−11.9879	−	15.0324i	−0.433708	−	0.543852i
$765$		0			0
$766$	8.75361			0.316281
$767$	15.7157	−	68.8550i	0.567461	−	2.48621i
$768$		0			0
$769$	40.2793	−	19.3975i	1.45251	−	0.699491i	0.469479	−	0.882944i	$-0.344442\pi$
$769$	40.2793	−	19.3975i	1.45251	−	0.699491i	0.983029	+	0.183453i	$0.0587275\pi$
$770$	−0.120801	+	0.529265i	−0.00435338	+	0.0190734i
$771$		0			0
$772$	9.11356	−	39.9291i	0.328004	−	1.43708i
$773$	−14.3083	−	17.9420i	−0.514633	−	0.645329i	0.454827	−	0.890580i	$-0.349701\pi$
$773$	−14.3083	−	17.9420i	−0.514633	−	0.645329i	−0.969460	+	0.245251i	$0.921130\pi$
$774$		0			0
$775$	−6.73245	−	29.4968i	−0.241837	−	1.05956i
$776$	0.190530	−	0.238916i	0.00683961	−	0.00857660i
$777$		0			0
$778$	9.96615	+	4.79944i	0.357304	+	0.172068i
$779$	4.57002	+	5.73063i	0.163738	+	0.205321i
$780$		0			0
$781$	32.6405	+	15.7188i	1.16797	+	0.562464i
$782$	4.59179			0.164202
$783$		0			0
$784$	−19.5929			−0.699745
$785$	−11.3720	−	5.47645i	−0.405883	−	0.195463i
$786$		0			0
$787$	8.93631	+	11.2058i	0.318545	+	0.399443i	0.915164	−	0.403082i	$-0.132061\pi$
$787$	8.93631	+	11.2058i	0.318545	+	0.399443i	−0.596619	+	0.802525i	$0.703490\pi$
$788$	31.7521	+	15.2910i	1.13112	+	0.544720i
$789$		0			0
$790$	0.895756	−	1.12324i	0.0318696	−	0.0399632i
$791$	−0.847740	−	3.71419i	−0.0301422	−	0.132061i
$792$		0			0
$793$	5.79105	+	7.26175i	0.205646	+	0.257872i
$794$	0.395592	−	1.73320i	0.0140390	−	0.0615090i
$795$		0			0
$796$	−0.350855	+	1.53720i	−0.0124357	+	0.0544845i
$797$	9.18382	−	4.42270i	0.325308	−	0.156660i	−0.264101	−	0.964495i	$-0.585075\pi$
$797$	9.18382	−	4.42270i	0.325308	−	0.156660i	0.589409	+	0.807835i	$0.299361\pi$
$798$		0			0
$799$	6.44504	−	28.2376i	0.228009	−	0.998974i
$800$	−21.0358			−0.743727
$801$		0			0
$802$	6.91119	+	8.66636i	0.244043	+	0.306020i
$803$	6.18276	+	27.0884i	0.218185	+	0.955930i
$804$		0			0
$805$	0.353543	−	0.443330i	0.0124608	−	0.0156253i
$806$	−15.1681	+	7.30457i	−0.534273	+	0.257292i
$807$		0			0
$808$	3.40701	+	4.27225i	0.119858	+	0.150297i
$809$	−5.59448	+	7.01526i	−0.196692	+	0.246643i	−0.870390	−	0.492363i	$-0.836133\pi$
$809$	−5.59448	+	7.01526i	−0.196692	+	0.246643i	0.673698	+	0.739006i	$0.264705\pi$
$810$		0			0
$811$	−28.5628			−1.00298			−0.501489	−	0.865164i	$-0.667214\pi$
$811$	−28.5628			−1.00298			−0.501489	+	0.865164i	$0.667214\pi$
$812$	−3.27844	−	1.11613i	−0.115051	−	0.0391685i
$813$		0			0
$814$	−9.78113	−	4.71034i	−0.342828	−	0.165097i
$815$	−5.45407	+	6.83918i	−0.191048	+	0.239566i
$816$		0			0
$817$	−7.23221	−	3.48285i	−0.253023	−	0.121849i
$818$	−0.113564	+	0.0546896i	−0.00397068	+	0.00191218i
$819$		0			0
$820$	0.862937	+	3.78077i	0.0301351	+	0.132030i
$821$	2.52230	+	11.0509i	0.0880290	+	0.385680i	0.999680	−	0.0252844i	$-0.00804914\pi$
$821$	2.52230	+	11.0509i	0.0880290	+	0.385680i	−0.911651	+	0.410965i	$0.865192\pi$
$822$		0			0
$823$	−1.26218	+	5.52996i	−0.0439967	+	0.192762i	−0.992150	−	0.125050i	$-0.960091\pi$
$823$	−1.26218	+	5.52996i	−0.0439967	+	0.192762i	0.948154	+	0.317812i	$0.102948\pi$
$824$	23.1008			0.804755
$825$		0			0
$826$	−1.78794	+	0.861025i	−0.0622103	+	0.0299589i
$827$	−2.61572	+	1.25966i	−0.0909575	+	0.0438028i	−0.478809	−	0.877919i	$-0.658931\pi$
$827$	−2.61572	+	1.25966i	−0.0909575	+	0.0438028i	0.387852	+	0.921722i	$0.373217\pi$
$828$		0			0
$829$	−45.2137			−1.57034			−0.785169	−	0.619282i	$-0.787424\pi$
$829$	−45.2137			−1.57034			−0.785169	+	0.619282i	$0.787424\pi$
$830$	−0.305290	+	1.33756i	−0.0105968	+	0.0464275i
$831$		0			0
$832$	−4.56734	−	20.0108i	−0.158344	−	0.693750i
$833$	−6.87263	−	30.1109i	−0.238122	−	1.04328i
$834$		0			0
$835$	0.496648	−	0.239173i	0.0171872	−	0.00827692i
$836$	18.8986	+	9.10107i	0.653621	+	0.314767i
$837$		0			0
$838$	7.35003	−	9.21664i	0.253902	−	0.318384i
$839$	−41.1073	−	19.7962i	−1.41918	−	0.683442i	−0.442229	−	0.896902i	$-0.645812\pi$
$839$	−41.1073	−	19.7962i	−1.41918	−	0.683442i	−0.976952	+	0.213460i	$0.931527\pi$
$840$		0			0
$841$	22.9758	+	17.6949i	0.792270	+	0.610170i
$842$	−7.82477			−0.269659
$843$		0			0
$844$	20.5248	−	25.7372i	0.706491	−	0.885912i
$845$	−8.17808	−	10.2550i	−0.281334	−	0.352782i
$846$		0			0
$847$	−4.30678	+	2.07404i	−0.147983	+	0.0712648i
$848$	8.33997	−	10.4580i	0.286396	−	0.359129i
$849$		0			0
$850$	−2.01208	−	8.81551i	−0.0690138	−	0.302369i
$851$	7.07002	+	8.86553i	0.242357	+	0.303906i
$852$		0			0
$853$	−36.9288			−1.26442			−0.632210	−	0.774797i	$-0.717852\pi$
$853$	−36.9288			−1.26442			−0.632210	+	0.774797i	$0.717852\pi$
$854$	0.0580735	−	0.254437i	0.00198724	−	0.00870665i
$855$		0			0
$856$	−24.7642	+	11.9258i	−0.846423	+	0.407616i
$857$	7.91066	−	34.6589i	0.270223	−	1.18392i	−0.639527	−	0.768768i	$-0.720870\pi$
$857$	7.91066	−	34.6589i	0.270223	−	1.18392i	0.909750	−	0.415156i	$-0.136273\pi$
$858$		0			0
$859$	−9.43070	+	41.3186i	−0.321771	+	1.40977i	0.512628	+	0.858611i	$0.328672\pi$
$859$	−9.43070	+	41.3186i	−0.321771	+	1.40977i	−0.834399	+	0.551161i	$0.814185\pi$
$860$	−2.64795	−	3.32042i	−0.0902943	−	0.113225i
$861$		0			0
$862$	−2.75259	−	12.0599i	−0.0937537	−	0.410762i
$863$	−31.0371	+	38.9193i	−1.05652	+	1.32483i	−0.112966	+	0.993599i	$0.536035\pi$
$863$	−31.0371	+	38.9193i	−1.05652	+	1.32483i	−0.943550	+	0.331231i	$0.892536\pi$
$864$		0			0
$865$	5.70709	+	2.74839i	0.194047	+	0.0934480i
$866$	1.63036	+	2.04440i	0.0554018	+	0.0694717i
$867$		0			0
$868$	−3.87747	−	1.86729i	−0.131610	−	0.0633800i
$869$	23.0398			0.781572
$870$		0			0
$871$	13.1317			0.444950
$872$	8.33393	+	4.01341i	0.282222	+	0.135911i
$873$		0			0
$874$	1.50149	+	1.88281i	0.0507887	+	0.0636870i
$875$	−2.11865	−	1.02029i	−0.0716233	−	0.0344920i
$876$		0			0
$877$	13.6501	−	17.1167i	0.460931	−	0.577990i	−0.495993	−	0.868326i	$-0.665196\pi$
$877$	13.6501	−	17.1167i	0.460931	−	0.577990i	0.956925	+	0.290337i	$0.0937674\pi$
$878$	1.55884	+	6.82974i	0.0526084	+	0.230492i
$879$		0			0
$880$	6.07524	+	7.61811i	0.204796	+	0.256806i
$881$	−7.46130	+	32.6901i	−0.251378	+	1.10136i	0.678822	+	0.734303i	$0.262491\pi$
$881$	−7.46130	+	32.6901i	−0.251378	+	1.10136i	−0.930199	+	0.367055i	$0.880366\pi$
$882$		0			0
$883$	3.58868	−	15.7230i	0.120769	−	0.529122i	−0.877961	−	0.478732i	$-0.841096\pi$
$883$	3.58868	−	15.7230i	0.120769	−	0.529122i	0.998730	−	0.0503898i	$-0.0160464\pi$
$884$	41.2422	−	19.8612i	1.38713	−	0.668004i
$885$		0			0
$886$	0.667326	−	2.92375i	0.0224192	−	0.0982252i
$887$	−52.7391			−1.77081			−0.885403	−	0.464823i	$-0.846118\pi$
$887$	−52.7391			−1.77081			−0.885403	+	0.464823i	$0.846118\pi$
$888$		0			0
$889$	−0.230718	−	0.289311i	−0.00773802	−	0.00970317i
$890$	0.389256	+	1.70544i	0.0130479	+	0.0571665i
$891$		0			0
$892$	2.04288	−	2.56169i	0.0684006	−	0.0857716i
$893$	13.6860	−	6.59082i	0.457984	−	0.220553i
$894$		0			0
$895$	1.46950	+	1.84270i	0.0491200	+	0.0615945i
$896$	−2.43027	+	3.04746i	−0.0811897	+	0.101809i
$897$		0			0
$898$	−5.48294			−0.182968
$899$	25.6972	+	25.2659i	0.857048	+	0.842666i
$900$		0			0
$901$	18.9976	+	9.14877i	0.632902	+	0.304790i
$902$	4.26205	−	5.34444i	0.141911	−	0.177950i
$903$		0			0
$904$	16.2729	+	7.83663i	0.541230	+	0.260642i
$905$	7.90246	−	3.80562i	0.262687	−	0.126503i
$906$		0			0
$907$	6.64084	+	29.0954i	0.220506	+	0.966098i	0.957099	+	0.289762i	$0.0935761\pi$
$907$	6.64084	+	29.0954i	0.220506	+	0.966098i	−0.736593	+	0.676336i	$0.763567\pi$
$908$	5.55592	+	24.3421i	0.184380	+	0.807820i
$909$		0			0
$910$	−0.138260	+	0.605756i	−0.00458327	+	0.0200806i
$911$	9.34050			0.309465			0.154732	−	0.987956i	$-0.450548\pi$
$911$	9.34050			0.309465			0.154732	+	0.987956i	$0.450548\pi$
$912$		0			0
$913$	−19.8230	+	9.54627i	−0.656047	+	0.315936i
$914$	−5.47823	+	2.63818i	−0.181204	+	0.0872631i
$915$		0			0
$916$	23.0151			0.760439
$917$	0.637063	−	2.79116i	0.0210377	−	0.0921721i
$918$		0			0
$919$	4.09903	+	17.9590i	0.135215	+	0.592414i	0.996448	+	0.0842049i	$0.0268350\pi$
$919$	4.09903	+	17.9590i	0.135215	+	0.592414i	−0.861234	+	0.508209i	$0.830308\pi$
$920$	0.598203	+	2.62090i	0.0197222	+	0.0864085i
$921$		0			0
$922$	4.65452	−	2.24150i	0.153289	−	0.0738199i
$923$	37.3577	+	17.9905i	1.22964	+	0.592166i
$924$		0			0
$925$	13.9224	−	17.4581i	0.457765	−	0.574019i
$926$	2.90408	+	1.39853i	0.0954341	+	0.0459587i
$927$		0			0
$928$	21.1020	−	13.5097i	0.692708	−	0.443476i
$929$	4.84654			0.159010			0.0795050	−	0.996834i	$-0.474666\pi$
$929$	4.84654			0.159010			0.0795050	+	0.996834i	$0.474666\pi$
$930$		0			0
$931$	10.0993	−	12.6642i	0.330992	−	0.415051i
$932$	−9.96077	−	12.4904i	−0.326276	−	0.409137i
$933$		0			0
$934$	−0.827356	+	0.398434i	−0.0270719	+	0.0130371i
$935$	−9.57673	+	12.0088i	−0.313193	+	0.392731i
$936$		0			0
$937$	9.94989	+	43.5933i	0.325049	+	1.42413i	0.828443	+	0.560074i	$0.189227\pi$
$937$	9.94989	+	43.5933i	0.325049	+	1.42413i	−0.503394	+	0.864057i	$0.667916\pi$
$938$	−0.230054	−	0.288478i	−0.00751152	−	0.00941915i
$939$		0			0
$940$	8.03684			0.262133
$941$	3.02297	−	13.2445i	0.0985459	−	0.431758i	−0.901453	−	0.432876i	$-0.857499\pi$
$941$	3.02297	−	13.2445i	0.0985459	−	0.431758i	0.999999	+	0.00111821i	$0.000355936\pi$
$942$		0			0
$943$	−6.43296	+	3.09795i	−0.209486	+	0.100883i
$944$	−7.92585	+	34.7254i	−0.257965	+	1.13022i
$945$		0			0
$946$	−1.66583	+	7.29850i	−0.0541609	+	0.237295i
$947$	−9.35958	−	11.7365i	−0.304146	−	0.381387i	0.606147	−	0.795353i	$-0.292715\pi$
$947$	−9.35958	−	11.7365i	−0.304146	−	0.381387i	−0.910292	+	0.413966i	$0.864143\pi$
$948$		0			0
$949$	7.07630	+	31.0033i	0.229706	+	1.00641i
$950$	2.95675	−	3.70765i	0.0959298	−	0.120292i
$951$		0			0
$952$	−2.44504	−	1.17747i	−0.0792443	−	0.0381620i
$953$	−32.3247	−	40.5339i	−1.04710	−	1.31302i	−0.948114	−	0.317931i	$-0.897012\pi$
$953$	−32.3247	−	40.5339i	−1.04710	−	1.31302i	−0.0989849	−	0.995089i	$-0.531560\pi$
$954$		0			0
$955$	6.65279	+	3.20382i	0.215279	+	0.103673i
$956$	−46.0659			−1.48988
$957$		0			0
$958$	1.73078			0.0559188
$959$	5.54115	+	2.66848i	0.178933	+	0.0861696i
$960$		0			0
$961$	8.59365	+	10.7761i	0.277215	+	0.347616i
$962$	−11.1947	−	5.39109i	−0.360932	−	0.173816i
$963$		0			0
$964$	−10.9330	+	13.7095i	−0.352127	+	0.441553i
$965$	3.50000	+	15.3345i	0.112669	+	0.493635i
$966$		0			0
$967$	−25.9527	−	32.5437i	−0.834583	−	1.04653i	−0.998198	−	0.0600094i	$-0.980887\pi$
$967$	−25.9527	−	32.5437i	−0.834583	−	1.04653i	0.163615	−	0.986524i	$-0.447685\pi$
$968$	5.04288	−	22.0943i	0.162084	−	0.710137i
$969$		0			0
$970$	−0.0123771	+	0.0542276i	−0.000397404	+	0.00174114i
$971$	−50.2497	+	24.1990i	−1.61259	+	0.776583i	−0.999906	−	0.0137446i	$-0.995625\pi$
$971$	−50.2497	+	24.1990i	−1.61259	+	0.776583i	−0.612685	+	0.790327i	$0.709911\pi$
$972$		0			0
$973$	1.32371	−	5.79954i	0.0424361	−	0.185925i
$974$	4.38165			0.140397
$975$		0			0
$976$	−2.92058	−	3.66230i	−0.0934856	−	0.117227i
$977$	10.8943	+	47.7309i	0.348538	+	1.52705i	0.780501	+	0.625155i	$0.214964\pi$
$977$	10.8943	+	47.7309i	0.348538	+	1.52705i	−0.431962	+	0.901892i	$0.642179\pi$
$978$		0			0
$979$	−17.4909	+	21.9329i	−0.559012	+	0.700978i
$980$	7.72132	−	3.71839i	0.246649	−	0.118780i
$981$		0			0
$982$	−2.16189	−	2.71092i	−0.0689887	−	0.0865091i
$983$	−3.22550	+	4.04466i	−0.102878	+	0.129004i	−0.830605	−	0.556862i	$-0.812005\pi$
$983$	−3.22550	+	4.04466i	−0.102878	+	0.129004i	0.727727	+	0.685867i	$0.240577\pi$
$984$		0			0
$985$	−13.5345			−0.431246
$986$	7.67994	+	7.55106i	0.244579	+	0.240475i
$987$		0			0
$988$	21.6298	+	10.4164i	0.688136	+	0.331389i
$989$	4.87531	−	6.11345i	0.155026	−	0.194396i
$990$		0			0
$991$	15.1838	+	7.31214i	0.482330	+	0.232278i	0.659216	−	0.751953i	$-0.270888\pi$
$991$	15.1838	+	7.31214i	0.482330	+	0.232278i	−0.176886	+	0.984231i	$0.556602\pi$
$992$	28.0531	−	13.5097i	0.890687	−	0.428932i
$993$		0			0
$994$	−0.259251	−	1.13585i	−0.00822295	−	0.0360271i
$995$	−0.134743	−	0.590349i	−0.00427165	−	0.0187153i
$996$		0			0
$997$	−8.50245	+	37.2517i	−0.269275	+	1.17977i	0.641583	+	0.767054i	$0.278278\pi$
$997$	−8.50245	+	37.2517i	−0.269275	+	1.17977i	−0.910858	+	0.412719i	$0.864579\pi$
$998$	−9.15239			−0.289714
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.a.190.1		6
3.2	odd	2		29.2.d.a.16.1	✓	6
12.11	even	2		464.2.u.f.161.1		6
15.2	even	4		725.2.r.b.74.1		12
15.8	even	4		725.2.r.b.74.2		12
15.14	odd	2		725.2.l.b.451.1		6
29.7	even	7		7569.2.a.r.1.2		3
29.20	even	7	inner	261.2.k.a.136.1		6
29.22	even	14		7569.2.a.p.1.2		3
87.2	even	28		841.2.e.c.267.2		12
87.5	odd	14		841.2.d.c.574.1		6
87.8	even	28		841.2.e.d.270.2		12
87.11	even	28		841.2.e.b.196.2		12
87.14	even	28		841.2.e.b.236.1		12
87.17	even	4		841.2.e.d.651.2		12
87.20	odd	14		29.2.d.a.20.1	yes	6
87.23	odd	14		841.2.d.e.605.1		6
87.26	even	28		841.2.b.c.840.3		6
87.32	even	28		841.2.b.c.840.4		6
87.35	odd	14		841.2.d.a.605.1		6
87.38	odd	14		841.2.d.d.571.1		6
87.41	even	4		841.2.e.d.651.1		12
87.44	even	28		841.2.e.b.236.2		12
87.47	even	28		841.2.e.b.196.1		12
87.50	even	28		841.2.e.d.270.1		12
87.53	odd	14		841.2.d.b.574.1		6
87.56	even	28		841.2.e.c.267.1		12
87.62	odd	14		841.2.d.c.778.1		6
87.65	odd	14		841.2.a.e.1.2		3
87.68	even	28		841.2.e.c.63.2		12
87.71	odd	14		841.2.d.a.645.1		6
87.74	odd	14		841.2.d.e.645.1		6
87.77	even	28		841.2.e.c.63.1		12
87.80	odd	14		841.2.a.f.1.2		3
87.83	odd	14		841.2.d.b.778.1		6
87.86	odd	2		841.2.d.d.190.1		6
348.107	even	14		464.2.u.f.49.1		6
435.107	even	28		725.2.r.b.49.2		12
435.194	odd	14		725.2.l.b.426.1		6
435.368	even	28		725.2.r.b.49.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	3.2	odd	2
29.2.d.a.20.1	yes	6	87.20	odd	14
261.2.k.a.136.1		6	29.20	even	7	inner
261.2.k.a.190.1		6	1.1	even	1	trivial
464.2.u.f.49.1		6	348.107	even	14
464.2.u.f.161.1		6	12.11	even	2
725.2.l.b.426.1		6	435.194	odd	14
725.2.l.b.451.1		6	15.14	odd	2
725.2.r.b.49.1		12	435.368	even	28
725.2.r.b.49.2		12	435.107	even	28
725.2.r.b.74.1		12	15.2	even	4
725.2.r.b.74.2		12	15.8	even	4
841.2.a.e.1.2		3	87.65	odd	14
841.2.a.f.1.2		3	87.80	odd	14
841.2.b.c.840.3		6	87.26	even	28
841.2.b.c.840.4		6	87.32	even	28
841.2.d.a.605.1		6	87.35	odd	14
841.2.d.a.645.1		6	87.71	odd	14
841.2.d.b.574.1		6	87.53	odd	14
841.2.d.b.778.1		6	87.83	odd	14
841.2.d.c.574.1		6	87.5	odd	14
841.2.d.c.778.1		6	87.62	odd	14
841.2.d.d.190.1		6	87.86	odd	2
841.2.d.d.571.1		6	87.38	odd	14
841.2.d.e.605.1		6	87.23	odd	14
841.2.d.e.645.1		6	87.74	odd	14
841.2.e.b.196.1		12	87.47	even	28
841.2.e.b.196.2		12	87.11	even	28
841.2.e.b.236.1		12	87.14	even	28
841.2.e.b.236.2		12	87.44	even	28
841.2.e.c.63.1		12	87.77	even	28
841.2.e.c.63.2		12	87.68	even	28
841.2.e.c.267.1		12	87.56	even	28
841.2.e.c.267.2		12	87.2	even	28
841.2.e.d.270.1		12	87.50	even	28
841.2.e.d.270.2		12	87.8	even	28
841.2.e.d.651.1		12	87.41	even	4
841.2.e.d.651.2		12	87.17	even	4
7569.2.a.p.1.2		3	29.22	even	14
7569.2.a.r.1.2		3	29.7	even	7

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.400969 - 0.193096i) q^{2} +(-1.12349 - 1.40881i) q^{4} +(0.623490 + 0.300257i) q^{5} +(0.222521 - 0.279032i) q^{7} +(0.376510 + 1.64960i) q^{8} +(-0.192021 - 0.240787i) q^{10} +(1.09903 - 4.81517i) q^{11} +(1.25786 - 5.51107i) q^{13} +(-0.143104 + 0.0689153i) q^{14} +(-0.634375 + 2.77938i) q^{16} -4.49396 q^{17} +(-1.46950 - 1.84270i) q^{19} +(-0.277479 - 1.21572i) q^{20} +(-1.37047 + 1.71851i) q^{22} +(2.06853 - 0.996152i) q^{23} +(-2.81886 - 3.53474i) q^{25} +(-1.56853 + 1.96688i) q^{26} -0.643104 q^{28} +(5.09783 + 1.73553i) q^{29} +(6.02930 + 2.90356i) q^{31} +(2.90097 - 3.63770i) q^{32} +(1.80194 + 0.867767i) q^{34} +(0.222521 - 0.107160i) q^{35} +(1.09903 + 4.81517i) q^{37} +(0.233406 + 1.02262i) q^{38} +(-0.260553 + 1.14156i) q^{40} -3.10992 q^{41} +(3.06853 - 1.47773i) q^{43} +(-8.01842 + 3.86147i) q^{44} -1.02177 q^{46} +(-1.43416 + 6.28345i) q^{47} +(1.52930 + 6.70031i) q^{49} +(0.447730 + 1.96163i) q^{50} +(-9.17725 + 4.41953i) q^{52} +(-4.22737 - 2.03579i) q^{53} +(2.13102 - 2.67222i) q^{55} +(0.544073 + 0.262012i) q^{56} +(-1.70895 - 1.68027i) q^{58} +12.4940 q^{59} +(-1.02446 + 1.28463i) q^{61} +(-1.85690 - 2.32847i) q^{62} +(3.27144 - 1.57544i) q^{64} +(2.43900 - 3.05841i) q^{65} +(0.516926 + 2.26480i) q^{67} +(5.04892 + 6.33114i) q^{68} -0.109916 q^{70} +(-1.63222 + 7.15122i) q^{71} +(-5.06853 + 2.44088i) q^{73} +(0.489115 - 2.14295i) q^{74} +(-0.945042 + 4.14050i) q^{76} +(-1.09903 - 1.37814i) q^{77} +(1.03803 + 4.54792i) q^{79} +(-1.23005 + 1.54244i) q^{80} +(1.24698 + 0.600514i) q^{82} +(-2.77748 - 3.48285i) q^{83} +(-2.80194 - 1.34934i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-5.11745 - 2.46443i) q^{89} +(-1.25786 - 1.57731i) q^{91} +(-3.72737 - 1.79500i) q^{92} +(1.78836 - 2.24254i) q^{94} +(-0.362937 - 1.59013i) q^{95} +(-0.112605 - 0.141202i) q^{97} +(0.680604 - 2.98192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 7 q^{8} + 9 q^{10} + 11 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} - 8 q^{17} + q^{19} - 2 q^{20} + 6 q^{22} + 7 q^{23} - 24 q^{25} - 4 q^{26} - 12 q^{28} - 6 q^{29}+ \cdots - 19 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 - q^5 + q^7 + 7 * q^8 + 9 * q^10 + 11 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 - 8 * q^17 + q^19 - 2 * q^20 + 6 * q^22 + 7 * q^23 - 24 * q^25 - 4 * q^26 - 12 * q^28 - 6 * q^29 + 5 * q^31 + 13 * q^32 + 2 * q^34 + q^35 + 11 * q^37 - 2 * q^38 + 14 * q^40 - 20 * q^41 + 13 * q^43 - 20 * q^44 - 11 * q^47 - 22 * q^49 - q^50 - 10 * q^52 - 3 * q^53 - 17 * q^55 + 7 * q^56 - 16 * q^58 + 56 * q^59 + 3 * q^61 - 3 * q^62 + q^64 - 5 * q^65 + 19 * q^67 + 12 * q^68 - 2 * q^70 - 21 * q^71 - 25 * q^73 + 6 * q^74 - 5 * q^76 - 11 * q^77 - 9 * q^79 + 18 * q^80 - 2 * q^82 - 17 * q^83 - 8 * q^85 + 16 * q^86 + 42 * q^88 - 7 * q^89 + 5 * q^91 + 8 * q^94 - 13 * q^95 + q^97 - 19 * q^98

Introduction

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