LMFDB - Embedded newform 605.2.e.a.362.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 $ x^20 + 67x^16 + 1315x^12 + 9193x^8 + 16040x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.2
Root			$-1.35329 + 1.35329i$ of defining polynomial
Character	$\chi$	$=$	605.362
Dual form			605.2.e.a.483.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35329 + 1.35329i) q^{2} +(0.185315 - 0.185315i) q^{3} -1.66281i q^{4} +(-0.610994 + 2.15097i) q^{5} +0.501571i q^{6} +(-3.24854 + 3.24854i) q^{7} +(-0.456321 - 0.456321i) q^{8} +2.93132i q^{9} +O(q^{10})$	\(q+(-1.35329 + 1.35329i) q^{2} +(0.185315 - 0.185315i) q^{3} -1.66281i q^{4} +(-0.610994 + 2.15097i) q^{5} +0.501571i q^{6} +(-3.24854 + 3.24854i) q^{7} +(-0.456321 - 0.456321i) q^{8} +2.93132i q^{9} +(-2.08404 - 3.73775i) q^{10} +(-0.308143 - 0.308143i) q^{12} +(-1.15905 - 1.15905i) q^{13} -8.79245i q^{14} +(0.285381 + 0.511834i) q^{15} +4.56069 q^{16} +(-1.01881 + 1.01881i) q^{17} +(-3.96693 - 3.96693i) q^{18} +3.61923 q^{19} +(3.57665 + 1.01597i) q^{20} +1.20400i q^{21} +(3.55745 - 3.55745i) q^{23} -0.169126 q^{24} +(-4.25337 - 2.62847i) q^{25} +3.13706 q^{26} +(1.09916 + 1.09916i) q^{27} +(5.40169 + 5.40169i) q^{28} +1.82741 q^{29} +(-1.07887 - 0.306457i) q^{30} -4.67258 q^{31} +(-5.25931 + 5.25931i) q^{32} -2.75750i q^{34} +(-5.00268 - 8.97235i) q^{35} +4.87421 q^{36} +(-7.32115 - 7.32115i) q^{37} +(-4.89788 + 4.89788i) q^{38} -0.429577 q^{39} +(1.26035 - 0.702725i) q^{40} +6.41419i q^{41} +(-1.62937 - 1.62937i) q^{42} +(-4.54091 - 4.54091i) q^{43} +(-6.30518 - 1.79102i) q^{45} +9.62855i q^{46} +(6.18236 + 6.18236i) q^{47} +(0.845163 - 0.845163i) q^{48} -14.1060i q^{49} +(9.31315 - 2.19898i) q^{50} +0.377602i q^{51} +(-1.92727 + 1.92727i) q^{52} +(-2.62937 + 2.62937i) q^{53} -2.97497 q^{54} +2.96475 q^{56} +(0.670697 - 0.670697i) q^{57} +(-2.47303 + 2.47303i) q^{58} +8.20299i q^{59} +(0.851080 - 0.474533i) q^{60} -11.5963i q^{61} +(6.32337 - 6.32337i) q^{62} +(-9.52249 - 9.52249i) q^{63} -5.11339i q^{64} +(3.20125 - 1.78491i) q^{65} +(-1.55745 - 1.55745i) q^{67} +(1.69409 + 1.69409i) q^{68} -1.31850i q^{69} +(18.9123 + 5.37213i) q^{70} -6.33689 q^{71} +(1.33762 - 1.33762i) q^{72} +(5.23876 + 5.23876i) q^{73} +19.8153 q^{74} +(-1.27531 + 0.301119i) q^{75} -6.01808i q^{76} +(0.581344 - 0.581344i) q^{78} +8.93527 q^{79} +(-2.78655 + 9.80992i) q^{80} -8.38657 q^{81} +(-8.68028 - 8.68028i) q^{82} +(4.63804 + 4.63804i) q^{83} +2.00203 q^{84} +(-1.56895 - 2.81393i) q^{85} +12.2904 q^{86} +(0.338647 - 0.338647i) q^{87} -2.44232i q^{89} +(10.9565 - 6.10899i) q^{90} +7.53041 q^{91} +(-5.91535 - 5.91535i) q^{92} +(-0.865898 + 0.865898i) q^{93} -16.7331 q^{94} +(-2.21133 + 7.78487i) q^{95} +1.94925i q^{96} +(-3.73830 - 3.73830i) q^{97} +(19.0895 + 19.0895i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^3 + 4 * q^5	$ 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.35329	+	1.35329i	−0.956923	+	0.956923i	−0.999110	−	0.0421867i	$-0.986568\pi$
$2$	−1.35329	+	1.35329i	−0.956923	+	0.956923i	0.0421867	+	0.999110i	$0.486568\pi$
$3$	0.185315	−	0.185315i	0.106992	−	0.106992i	−0.651585	−	0.758576i	$-0.725895\pi$
$3$	0.185315	−	0.185315i	0.106992	−	0.106992i	0.758576	+	0.651585i	$0.225895\pi$
$4$		−	1.66281i		−	0.831403i
$5$	−0.610994	+	2.15097i	−0.273245	+	0.961944i
$5$	−0.610994	+	2.15097i	−0.273245	+	0.961944i
$6$			0.501571i			0.204765i
$7$	−3.24854	+	3.24854i	−1.22783	+	1.22783i	−0.263049	+	0.964783i	$0.584728\pi$
$7$	−3.24854	+	3.24854i	−1.22783	+	1.22783i	−0.964783	+	0.263049i	$0.915272\pi$
$8$	−0.456321	−	0.456321i	−0.161334	−	0.161334i
$9$			2.93132i			0.977106i
$10$	−2.08404	−	3.73775i	−0.659032	−	1.18198i
$11$		0			0
$11$		0			0
$12$	−0.308143	−	0.308143i	−0.0889531	−	0.0889531i
$13$	−1.15905	−	1.15905i	−0.321462	−	0.321462i	0.527866	−	0.849328i	$-0.322992\pi$
$13$	−1.15905	−	1.15905i	−0.321462	−	0.321462i	−0.849328	+	0.527866i	$0.822992\pi$
$14$		−	8.79245i		−	2.34988i
$15$	0.285381	+	0.511834i	0.0736850	+	0.132155i
$16$	4.56069			1.14017
$17$	−1.01881	+	1.01881i	−0.247098	+	0.247098i	−0.819779	−	0.572680i	$-0.805904\pi$
$17$	−1.01881	+	1.01881i	−0.247098	+	0.247098i	0.572680	+	0.819779i	$0.305904\pi$
$18$	−3.96693	−	3.96693i	−0.935015	−	0.935015i
$19$	3.61923			0.830308			0.415154	−	0.909751i	$-0.363728\pi$
$19$	3.61923			0.830308			0.415154	+	0.909751i	$0.363728\pi$
$20$	3.57665	+	1.01597i	0.799764	+	0.227177i
$21$			1.20400i			0.262735i
$22$		0			0
$23$	3.55745	−	3.55745i	0.741780	−	0.741780i	−0.231141	−	0.972920i	$-0.574246\pi$
$23$	3.55745	−	3.55745i	0.741780	−	0.741780i	0.972920	+	0.231141i	$0.0742458\pi$
$24$	−0.169126			−0.0345228
$25$	−4.25337	−	2.62847i	−0.850674	−	0.525693i
$26$	3.13706			0.615228
$27$	1.09916	+	1.09916i	0.211534	+	0.211534i
$28$	5.40169	+	5.40169i	1.02082	+	1.02082i
$29$	1.82741			0.339342			0.169671	−	0.985501i	$-0.445729\pi$
$29$	1.82741			0.339342			0.169671	+	0.985501i	$0.445729\pi$
$30$	−1.07887	−	0.306457i	−0.196973	−	0.0559511i
$31$	−4.67258			−0.839219			−0.419610	−	0.907705i	$-0.637833\pi$
$31$	−4.67258			−0.839219			−0.419610	+	0.907705i	$0.637833\pi$
$32$	−5.25931	+	5.25931i	−0.929723	+	0.929723i
$33$		0			0
$34$		−	2.75750i		−	0.472908i
$35$	−5.00268	−	8.97235i	−0.845607	−	1.51660i
$36$	4.87421			0.812369
$37$	−7.32115	−	7.32115i	−1.20359	−	1.20359i	−0.973067	−	0.230523i	$-0.925956\pi$
$37$	−7.32115	−	7.32115i	−1.20359	−	1.20359i	−0.230523	−	0.973067i	$-0.574044\pi$
$38$	−4.89788	+	4.89788i	−0.794541	+	0.794541i
$39$	−0.429577			−0.0687874
$40$	1.26035	−	0.702725i	0.199278	−	0.111111i
$41$			6.41419i			1.00173i	0.865526	+	0.500864i	$0.166984\pi$
$41$			6.41419i			1.00173i	−0.865526	+	0.500864i	$0.833016\pi$
$42$	−1.62937	−	1.62937i	−0.251417	−	0.251417i
$43$	−4.54091	−	4.54091i	−0.692482	−	0.692482i	0.270295	−	0.962777i	$-0.412879\pi$
$43$	−4.54091	−	4.54091i	−0.692482	−	0.692482i	−0.962777	+	0.270295i	$0.912879\pi$
$44$		0			0
$45$	−6.30518	−	1.79102i	−0.939921	−	0.266989i
$46$			9.62855i			1.41965i
$47$	6.18236	+	6.18236i	0.901789	+	0.901789i	0.995591	−	0.0938016i	$-0.0299019\pi$
$47$	6.18236	+	6.18236i	0.901789	+	0.901789i	−0.0938016	+	0.995591i	$0.529902\pi$
$48$	0.845163	−	0.845163i	0.121989	−	0.121989i
$49$		−	14.1060i		−	2.01514i
$50$	9.31315	−	2.19898i	1.31708	−	0.310982i
$51$			0.377602i			0.0528749i
$52$	−1.92727	+	1.92727i	−0.267264	+	0.267264i
$53$	−2.62937	+	2.62937i	−0.361172	+	0.361172i	−0.864244	−	0.503072i	$-0.832203\pi$
$53$	−2.62937	+	2.62937i	−0.361172	+	0.361172i	0.503072	+	0.864244i	$0.332203\pi$
$54$	−2.97497			−0.404843
$55$		0			0
$56$	2.96475			0.396182
$57$	0.670697	−	0.670697i	0.0888360	−	0.0888360i
$58$	−2.47303	+	2.47303i	−0.324724	+	0.324724i
$59$			8.20299i			1.06794i	0.845504	+	0.533969i	$0.179300\pi$
$59$			8.20299i			1.06794i	−0.845504	+	0.533969i	$0.820700\pi$
$60$	0.851080	−	0.474533i	0.109874	−	0.0612620i
$61$		−	11.5963i		−	1.48475i	−0.669982	−	0.742377i	$-0.733698\pi$
$61$		−	11.5963i		−	1.48475i	0.669982	−	0.742377i	$-0.266302\pi$
$62$	6.32337	−	6.32337i	0.803068	−	0.803068i
$63$	−9.52249	−	9.52249i	−1.19972	−	1.19972i
$64$		−	5.11339i		−	0.639174i
$65$	3.20125	−	1.78491i	0.397066	−	0.221391i
$66$		0			0
$67$	−1.55745	−	1.55745i	−0.190273	−	0.190273i	0.605541	−	0.795814i	$-0.292957\pi$
$67$	−1.55745	−	1.55745i	−0.190273	−	0.190273i	−0.795814	+	0.605541i	$0.792957\pi$
$68$	1.69409	+	1.69409i	0.205438	+	0.205438i
$69$		−	1.31850i		−	0.158728i
$70$	18.9123	+	5.37213i	2.26045	+	0.642093i
$71$	−6.33689			−0.752050			−0.376025	−	0.926609i	$-0.622709\pi$
$71$	−6.33689			−0.752050			−0.376025	+	0.926609i	$0.622709\pi$
$72$	1.33762	−	1.33762i	0.157640	−	0.157640i
$73$	5.23876	+	5.23876i	0.613151	+	0.613151i	0.943766	−	0.330615i	$-0.107256\pi$
$73$	5.23876	+	5.23876i	0.613151	+	0.613151i	−0.330615	+	0.943766i	$0.607256\pi$
$74$	19.8153			2.30349
$75$	−1.27531	+	0.301119i	−0.147260	+	0.0347703i
$76$		−	6.01808i		−	0.690321i
$77$		0			0
$78$	0.581344	−	0.581344i	0.0658242	−	0.0658242i
$79$	8.93527			1.00530			0.502648	−	0.864491i	$-0.332359\pi$
$79$	8.93527			1.00530			0.502648	+	0.864491i	$0.332359\pi$
$80$	−2.78655	+	9.80992i	−0.311546	+	1.09678i
$81$	−8.38657			−0.931841
$82$	−8.68028	−	8.68028i	−0.958576	−	0.958576i
$83$	4.63804	+	4.63804i	0.509091	+	0.509091i	0.914247	−	0.405156i	$-0.132783\pi$
$83$	4.63804	+	4.63804i	0.509091	+	0.509091i	−0.405156	+	0.914247i	$0.632783\pi$
$84$	2.00203			0.218439
$85$	−1.56895	−	2.81393i	−0.170176	−	0.305213i
$86$	12.2904			1.32530
$87$	0.338647	−	0.338647i	0.0363068	−	0.0363068i
$88$		0			0
$89$		−	2.44232i		−	0.258886i	−0.991587	−	0.129443i	$-0.958681\pi$
$89$		−	2.44232i		−	0.258886i	0.991587	−	0.129443i	$-0.0413189\pi$
$90$	10.9565	−	6.10899i	1.15492	−	0.643944i
$91$	7.53041			0.789402
$92$	−5.91535	−	5.91535i	−0.616718	−	0.616718i
$93$	−0.865898	+	0.865898i	−0.0897894	+	0.0897894i
$94$	−16.7331			−1.72589
$95$	−2.21133	+	7.78487i	−0.226878	+	0.798710i
$96$			1.94925i			0.198945i
$97$	−3.73830	−	3.73830i	−0.379567	−	0.379567i	0.491379	−	0.870946i	$-0.336493\pi$
$97$	−3.73830	−	3.73830i	−0.379567	−	0.379567i	−0.870946	+	0.491379i	$0.836493\pi$
$98$	19.0895	+	19.0895i	1.92833	+	1.92833i
$99$		0			0
$100$	−4.37063	+	7.07254i	−0.437063	+	0.707254i
$101$		−	9.27565i		−	0.922962i	−0.887150	−	0.461481i	$-0.847318\pi$
$101$		−	9.27565i		−	0.922962i	0.887150	−	0.461481i	$-0.152682\pi$
$102$	−0.511006	−	0.511006i	−0.0505972	−	0.0505972i
$103$	−7.99380	+	7.99380i	−0.787653	+	0.787653i	−0.981109	−	0.193456i	$-0.938030\pi$
$103$	−7.99380	+	7.99380i	−0.787653	+	0.787653i	0.193456	+	0.981109i	$0.438030\pi$
$104$			1.05780i			0.103725i
$105$	−2.58978	−	0.735639i	−0.252737	−	0.0717911i
$106$		−	7.11662i		−	0.691227i
$107$	−2.67241	+	2.67241i	−0.258352	+	0.258352i	−0.824383	−	0.566032i	$-0.808478\pi$
$107$	−2.67241	+	2.67241i	−0.258352	+	0.258352i	0.566032	+	0.824383i	$0.308478\pi$
$108$	1.82769	−	1.82769i	0.175870	−	0.175870i
$109$	0.637227			0.0610352			0.0305176	−	0.999534i	$-0.490284\pi$
$109$	0.637227			0.0610352			0.0305176	+	0.999534i	$0.490284\pi$
$110$		0			0
$111$	−2.71343			−0.257548
$112$	−14.8156	+	14.8156i	−1.39994	+	1.39994i
$113$	−5.53998	+	5.53998i	−0.521157	+	0.521157i	−0.917921	−	0.396764i	$-0.870133\pi$
$113$	−5.53998	+	5.53998i	−0.521157	+	0.521157i	0.396764	+	0.917921i	$0.370133\pi$
$114$			1.81530i			0.170018i
$115$	5.47840	+	9.82556i	0.510863	+	0.916238i
$116$		−	3.03864i		−	0.282130i
$117$	3.39753	−	3.39753i	0.314102	−	0.314102i
$118$	−11.1010	−	11.1010i	−1.02193	−	1.02193i
$119$		−	6.61930i		−	0.606790i
$120$	0.103335	−	0.363786i	0.00943317	−	0.0332090i
$121$		0			0
$122$	15.6932	+	15.6932i	1.42080	+	1.42080i
$123$	1.18864	+	1.18864i	0.107176	+	0.107176i
$124$			7.76959i			0.697730i
$125$	8.25254	−	7.54291i	0.738130	−	0.674658i
$126$	25.7734			2.29608
$127$	−7.19563	+	7.19563i	−0.638509	+	0.638509i	−0.950188	−	0.311679i	$-0.899109\pi$
$127$	−7.19563	+	7.19563i	−0.638509	+	0.638509i	0.311679	+	0.950188i	$0.399109\pi$
$128$	−3.59869	−	3.59869i	−0.318082	−	0.318082i
$129$	−1.68300			−0.148179
$130$	−1.91673	+	6.74773i	−0.168108	+	0.591815i
$131$			7.05141i			0.616085i	0.951373	+	0.308042i	$0.0996739\pi$
$131$			7.05141i			0.616085i	−0.951373	+	0.308042i	$0.900326\pi$
$132$		0			0
$133$	−11.7572	+	11.7572i	−1.01948	+	1.01948i
$134$	4.21537			0.364153
$135$	−3.03585	+	1.69268i	−0.261284	+	0.145683i
$136$	0.929812			0.0797307
$137$	8.42628	+	8.42628i	0.719906	+	0.719906i	0.968586	−	0.248680i	$-0.0799968\pi$
$137$	8.42628	+	8.42628i	0.719906	+	0.719906i	−0.248680	+	0.968586i	$0.579997\pi$
$138$	1.78431	+	1.78431i	0.151891	+	0.151891i
$139$	−6.85170			−0.581154			−0.290577	−	0.956852i	$-0.593847\pi$
$139$	−6.85170			−0.581154			−0.290577	+	0.956852i	$0.593847\pi$
$140$	−14.9193	+	8.31848i	−1.26091	+	0.703040i
$141$	2.29136			0.192968
$142$	8.57567	−	8.57567i	0.719654	−	0.719654i
$143$		0			0
$144$			13.3688i			1.11407i
$145$	−1.11654	+	3.93072i	−0.0927236	+	0.326428i
$146$	−14.1792			−1.17348
$147$	−2.61405	−	2.61405i	−0.215603	−	0.215603i
$148$	−12.1737	+	12.1737i	−1.00067	+	1.00067i
$149$	−23.6983			−1.94144			−0.970718	−	0.240220i	$-0.922780\pi$
$149$	−23.6983			−1.94144			−0.970718	+	0.240220i	$0.922780\pi$
$150$	1.31836	−	2.13337i	0.107644	−	0.174189i
$151$			19.2953i			1.57023i	0.619353	+	0.785113i	$0.287395\pi$
$151$			19.2953i			1.57023i	−0.619353	+	0.785113i	$0.712605\pi$
$152$	−1.65153	−	1.65153i	−0.133957	−	0.133957i
$153$	−2.98646	−	2.98646i	−0.241441	−	0.241441i
$154$		0			0
$155$	2.85492	−	10.0506i	0.229313	−	0.807283i
$156$			0.714304i			0.0571901i
$157$	−3.91061	−	3.91061i	−0.312101	−	0.312101i	0.533622	−	0.845723i	$-0.320830\pi$
$157$	−3.91061	−	3.91061i	−0.312101	−	0.312101i	−0.845723	+	0.533622i	$0.820830\pi$
$158$	−12.0920	+	12.0920i	−0.961991	+	0.961991i
$159$			0.974523i			0.0772847i
$160$	−8.09922	−	14.5260i	−0.640300	−	1.14838i
$161$			23.1130i			1.82156i
$162$	11.3495	−	11.3495i	0.891700	−	0.891700i
$163$	−7.11217	+	7.11217i	−0.557068	+	0.557068i	−0.928472	−	0.371404i	$-0.878877\pi$
$163$	−7.11217	+	7.11217i	−0.557068	+	0.557068i	0.371404	+	0.928472i	$0.378877\pi$
$164$	10.6656			0.832840
$165$		0			0
$166$	−12.5533			−0.974322
$167$	5.25514	−	5.25514i	0.406655	−	0.406655i	−0.473915	−	0.880570i	$-0.657160\pi$
$167$	5.25514	−	5.25514i	0.406655	−	0.406655i	0.880570	+	0.473915i	$0.157160\pi$
$168$	0.549413	−	0.549413i	0.0423881	−	0.0423881i
$169$		−	10.3132i		−	0.793325i
$170$	5.93132	+	1.68482i	0.454911	+	0.129220i
$171$			10.6091i			0.811299i
$172$	−7.55065	+	7.55065i	−0.575732	+	0.575732i
$173$	10.3279	+	10.3279i	0.785218	+	0.785218i	0.980706	−	0.195488i	$-0.0626290\pi$
$173$	10.3279	+	10.3279i	0.785218	+	0.785218i	−0.195488	+	0.980706i	$0.562629\pi$
$174$			0.916577i			0.0694856i
$175$	22.3559	−	5.27857i	1.68995	−	0.399022i
$176$		0			0
$177$	1.52013	+	1.52013i	0.114260	+	0.114260i
$178$	3.30518	+	3.30518i	0.247734	+	0.247734i
$179$		−	9.47065i		−	0.707870i	−0.935270	−	0.353935i	$-0.884843\pi$
$179$		−	9.47065i		−	0.707870i	0.935270	−	0.353935i	$-0.115157\pi$
$180$	−2.97812	+	10.4843i	−0.221976	+	0.781454i
$181$	−22.2355			−1.65275			−0.826375	−	0.563120i	$-0.809601\pi$
$181$	−22.2355			−1.65275			−0.826375	+	0.563120i	$0.809601\pi$
$182$	−10.1909	+	10.1909i	−0.755396	+	0.755396i
$183$	−2.14897	−	2.14897i	−0.158856	−	0.158856i
$184$	−3.24668			−0.239349
$185$	20.2208	−	11.2744i	1.48666	−	0.828912i
$186$		−	2.34363i		−	0.171843i
$187$		0			0
$188$	10.2801	−	10.2801i	0.749751	−	0.749751i
$189$	−7.14133			−0.519455
$190$	−7.54263	−	13.5278i	−0.547200	−	0.981409i
$191$	12.1711			0.880667			0.440333	−	0.897834i	$-0.354860\pi$
$191$	12.1711			0.880667			0.440333	+	0.897834i	$0.354860\pi$
$192$	−0.947588	−	0.947588i	−0.0683862	−	0.0683862i
$193$	7.03527	+	7.03527i	0.506410	+	0.506410i	0.913422	−	0.407013i	$-0.133430\pi$
$193$	7.03527	+	7.03527i	0.506410	+	0.506410i	−0.407013	+	0.913422i	$0.633430\pi$
$194$	10.1180			0.726433
$195$	0.262469	−	0.924009i	0.0187958	−	0.0661696i
$196$	−23.4555			−1.67539
$197$	−8.97738	+	8.97738i	−0.639612	+	0.639612i	−0.950460	−	0.310848i	$-0.899387\pi$
$197$	−8.97738	+	8.97738i	−0.639612	+	0.639612i	0.310848	+	0.950460i	$0.399387\pi$
$198$		0			0
$199$			12.9491i			0.917935i	0.888453	+	0.458967i	$0.151781\pi$
$199$			12.9491i			0.917935i	−0.888453	+	0.458967i	$0.848219\pi$
$200$	0.741480	+	3.14033i	0.0524305	+	0.222055i
$201$	−0.577237			−0.0407152
$202$	12.5527	+	12.5527i	0.883204	+	0.883204i
$203$	−5.93642	+	5.93642i	−0.416655	+	0.416655i
$204$	0.627879			0.0439603
$205$	−13.7967	−	3.91903i	−0.963606	−	0.273717i
$206$		−	21.6359i		−	1.50745i
$207$	10.4280	+	10.4280i	0.724797	+	0.724797i
$208$	−5.28605	−	5.28605i	−0.366522	−	0.366522i
$209$		0			0
$210$	4.50027	−	2.50920i	0.310548	−	0.173151i
$211$			3.96174i			0.272737i	0.990658	+	0.136369i	$0.0435432\pi$
$211$			3.96174i			0.272737i	−0.990658	+	0.136369i	$0.956457\pi$
$212$	4.37213	+	4.37213i	0.300279	+	0.300279i
$213$	−1.17432	+	1.17432i	−0.0804630	+	0.0804630i
$214$		−	7.23311i		−	0.494445i
$215$	12.5418	−	6.99290i	0.855347	−	0.476912i
$216$		−	1.00314i		−	0.0682551i
$217$	15.1790	−	15.1790i	1.03042	−	1.03042i
$218$	−0.862355	+	0.862355i	−0.0584060	+	0.0584060i
$219$	1.94164			0.131204
$220$		0			0
$221$	2.36170			0.158865
$222$	3.67207	−	3.67207i	0.246453	−	0.246453i
$223$	−1.01451	+	1.01451i	−0.0679368	+	0.0679368i	−0.740259	−	0.672322i	$-0.765297\pi$
$223$	−1.01451	+	1.01451i	−0.0679368	+	0.0679368i	0.672322	+	0.740259i	$0.265297\pi$
$224$		−	34.1701i		−	2.28308i
$225$	7.70486	−	12.4680i	0.513658	−	0.831199i
$226$		−	14.9944i		−	0.997415i
$227$	7.99062	−	7.99062i	0.530356	−	0.530356i	−0.390322	−	0.920678i	$-0.627636\pi$
$227$	7.99062	−	7.99062i	0.530356	−	0.530356i	0.920678	+	0.390322i	$0.127636\pi$
$228$	−1.11524	−	1.11524i	−0.0738585	−	0.0738585i
$229$			0.649417i			0.0429147i	0.999770	+	0.0214573i	$0.00683060\pi$
$229$			0.649417i			0.0429147i	−0.999770	+	0.0214573i	$0.993169\pi$
$230$	−20.7107	−	5.88299i	−1.36563	−	0.387913i
$231$		0			0
$232$	−0.833888	−	0.833888i	−0.0547475	−	0.0547475i
$233$	9.49778	+	9.49778i	0.622220	+	0.622220i	0.946099	−	0.323878i	$-0.104987\pi$
$233$	9.49778	+	9.49778i	0.622220	+	0.622220i	−0.323878	+	0.946099i	$0.604987\pi$
$234$			9.19572i			0.601143i
$235$	−17.0755	+	9.52070i	−1.11388	+	0.621062i
$236$	13.6400			0.887887
$237$	1.65584	−	1.65584i	0.107558	−	0.107558i
$238$	8.95785	+	8.95785i	0.580651	+	0.580651i
$239$	−17.5243			−1.13355			−0.566776	−	0.823872i	$-0.691809\pi$
$239$	−17.5243			−1.13355			−0.566776	+	0.823872i	$0.691809\pi$
$240$	1.30153	+	2.33431i	0.0840136	+	0.150679i
$241$		−	9.77939i		−	0.629946i	−0.949101	−	0.314973i	$-0.898005\pi$
$241$		−	9.77939i		−	0.629946i	0.949101	−	0.314973i	$-0.101995\pi$
$242$		0			0
$243$	−4.85164	+	4.85164i	−0.311233	+	0.311233i
$244$	−19.2824			−1.23443
$245$	30.3416	+	8.61867i	1.93845	+	0.550627i
$246$	−3.21717			−0.205119
$247$	−4.19486	−	4.19486i	−0.266912	−	0.266912i
$248$	2.13220	+	2.13220i	0.135395	+	0.135395i
$249$	1.71900			0.108937
$250$	−0.960342	+	21.3759i	−0.0607374	+	1.35193i
$251$	18.2959			1.15483			0.577413	−	0.816452i	$-0.304062\pi$
$251$	18.2959			1.15483			0.577413	+	0.816452i	$0.304062\pi$
$252$	−15.8341	+	15.8341i	−0.997452	+	0.997452i
$253$		0			0
$254$		−	19.4756i		−	1.22201i
$255$	−0.812212	−	0.230713i	−0.0508627	−	0.0144478i
$256$	19.9670			1.24793
$257$	4.58204	+	4.58204i	0.285820	+	0.285820i	0.835425	−	0.549605i	$-0.185222\pi$
$257$	4.58204	+	4.58204i	0.285820	+	0.285820i	−0.549605	+	0.835425i	$0.685222\pi$
$258$	2.27759	−	2.27759i	0.141796	−	0.141796i
$259$	47.5660			2.95561
$260$	−2.96796	−	5.32306i	−0.184065	−	0.330122i
$261$			5.35673i			0.331573i
$262$	−9.54263	−	9.54263i	−0.589546	−	0.589546i
$263$	3.11501	+	3.11501i	0.192080	+	0.192080i	0.796594	−	0.604514i	$-0.206633\pi$
$263$	3.11501	+	3.11501i	0.192080	+	0.192080i	−0.604514	+	0.796594i	$0.706633\pi$
$264$		0			0
$265$	−4.04917	−	7.26224i	−0.248739	−	0.446116i
$266$		−	31.8219i		−	1.95112i
$267$	−0.452599	−	0.452599i	−0.0276986	−	0.0276986i
$268$	−2.58974	+	2.58974i	−0.158193	+	0.158193i
$269$		−	7.92951i		−	0.483471i	−0.970342	−	0.241735i	$-0.922283\pi$
$269$		−	7.92951i		−	0.483471i	0.970342	−	0.241735i	$-0.0777166\pi$
$270$	1.81769	−	6.39909i	0.110621	−	0.389436i
$271$		−	8.92867i		−	0.542378i	−0.962526	−	0.271189i	$-0.912583\pi$
$271$		−	8.92867i		−	0.542378i	0.962526	−	0.271189i	$-0.0874169\pi$
$272$	−4.64648	+	4.64648i	−0.281734	+	0.281734i
$273$	1.39550	−	1.39550i	0.0844593	−	0.0844593i
$274$	−22.8065			−1.37779
$275$		0			0
$276$	−2.19240			−0.131967
$277$	1.89506	−	1.89506i	0.113863	−	0.113863i	−0.647880	−	0.761743i	$-0.724344\pi$
$277$	1.89506	−	1.89506i	0.113863	−	0.113863i	0.761743	+	0.647880i	$0.224344\pi$
$278$	9.27236	−	9.27236i	0.556119	−	0.556119i
$279$		−	13.6968i		−	0.820006i
$280$	−1.81145	+	6.37710i	−0.108255	+	0.381105i
$281$			10.8217i			0.645566i	0.946473	+	0.322783i	$0.104618\pi$
$281$			10.8217i			0.645566i	−0.946473	+	0.322783i	$0.895382\pi$
$282$	−3.10089	+	3.10089i	−0.184655	+	0.184655i
$283$	−6.75224	−	6.75224i	−0.401379	−	0.401379i	0.477340	−	0.878719i	$-0.341601\pi$
$283$	−6.75224	−	6.75224i	−0.401379	−	0.401379i	−0.878719	+	0.477340i	$0.841601\pi$
$284$			10.5370i			0.625257i
$285$	1.03286	+	1.85244i	0.0611813	+	0.109729i
$286$		0			0
$287$	−20.8367	−	20.8367i	−1.22995	−	1.22995i
$288$	−15.4167	−	15.4167i	−0.908437	−	0.908437i
$289$			14.9240i			0.877885i
$290$	−3.80841	−	6.83042i	−0.223638	−	0.401096i
$291$	−1.38552			−0.0812209
$292$	8.71105	−	8.71105i	0.509776	−	0.509776i
$293$	−13.9270	−	13.9270i	−0.813626	−	0.813626i	0.171549	−	0.985176i	$-0.445123\pi$
$293$	−13.9270	−	13.9270i	−0.813626	−	0.813626i	−0.985176	+	0.171549i	$0.945123\pi$
$294$	7.07514			0.412631
$295$	−17.6444	−	5.01198i	−1.02730	−	0.291809i
$296$			6.68160i			0.388360i
$297$		0			0
$298$	32.0707	−	32.0707i	1.85781	−	1.85781i
$299$	−8.24650			−0.476907
$300$	0.500703	+	2.12059i	0.0289081	+	0.122432i
$301$	29.5026			1.70050
$302$	−26.1121	−	26.1121i	−1.50258	−	1.50258i
$303$	−1.71892	−	1.71892i	−0.0987491	−	0.0987491i
$304$	16.5062			0.946694
$305$	24.9433	+	7.08528i	1.42825	+	0.405702i
$306$	8.08312			0.462081
$307$	1.56136	−	1.56136i	0.0891113	−	0.0891113i	−0.661146	−	0.750257i	$-0.729930\pi$
$307$	1.56136	−	1.56136i	0.0891113	−	0.0891113i	0.750257	+	0.661146i	$0.229930\pi$
$308$		0			0
$309$			2.96274i			0.168544i
$310$	9.73785	+	17.4649i	0.553073	+	0.991942i
$311$	−26.4030			−1.49717			−0.748587	−	0.663036i	$-0.769268\pi$
$311$	−26.4030			−1.49717			−0.748587	+	0.663036i	$0.769268\pi$
$312$	0.196025	+	0.196025i	0.0110977	+	0.0110977i
$313$	11.0666	−	11.0666i	0.625519	−	0.625519i	−0.321418	−	0.946937i	$-0.604159\pi$
$313$	11.0666	−	11.0666i	0.625519	−	0.625519i	0.946937	+	0.321418i	$0.104159\pi$
$314$	10.5844			0.597312
$315$	26.3008	−	14.6644i	1.48188	−	0.826247i
$316$		−	14.8576i		−	0.835807i
$317$	−12.3960	−	12.3960i	−0.696229	−	0.696229i	0.267366	−	0.963595i	$-0.413847\pi$
$317$	−12.3960	−	12.3960i	−0.696229	−	0.696229i	−0.963595	+	0.267366i	$0.913847\pi$
$318$	−1.31882	−	1.31882i	−0.0739555	−	0.0739555i
$319$		0			0
$320$	10.9988	+	3.12426i	0.614850	+	0.174651i
$321$			0.990475i			0.0552829i
$322$	−31.2787	−	31.2787i	−1.74309	−	1.74309i
$323$	−3.68732	+	3.68732i	−0.205168	+	0.205168i
$324$			13.9452i			0.774736i
$325$	1.88334	+	7.97637i	0.104469	+	0.442449i
$326$		−	19.2497i		−	1.06614i
$327$	0.118088	−	0.118088i	0.00653026	−	0.00653026i
$328$	2.92693	−	2.92693i	0.161613	−	0.161613i
$329$	−40.1672			−2.21449
$330$		0			0
$331$	9.55722			0.525312			0.262656	−	0.964889i	$-0.415401\pi$
$331$	9.55722			0.525312			0.262656	+	0.964889i	$0.415401\pi$
$332$	7.71217	−	7.71217i	0.423260	−	0.423260i
$333$	21.4606	−	21.4606i	1.17603	−	1.17603i
$334$			14.2235i			0.778275i
$335$	4.30163	−	2.39844i	0.235023	−	0.131041i
$336$			5.49108i			0.299563i
$337$	3.40270	−	3.40270i	0.185357	−	0.185357i	−0.608329	−	0.793685i	$-0.708160\pi$
$337$	3.40270	−	3.40270i	0.185357	−	0.185357i	0.793685	+	0.608329i	$0.208160\pi$
$338$	13.9568	+	13.9568i	0.759151	+	0.759151i
$339$			2.05328i			0.111519i
$340$	−4.67902	+	2.60886i	−0.253755	+	0.141485i
$341$		0			0
$342$	−14.3572	−	14.3572i	−0.776351	−	0.776351i
$343$	23.0840	+	23.0840i	1.24642	+	1.24642i
$344$			4.14423i			0.223442i
$345$	2.83605	+	0.805594i	0.152688	+	0.0433717i
$346$	−27.9535			−1.50279
$347$	0.203586	−	0.203586i	0.0109291	−	0.0109291i	−0.701621	−	0.712550i	$-0.747540\pi$
$347$	0.203586	−	0.203586i	0.0109291	−	0.0109291i	0.712550	+	0.701621i	$0.247540\pi$
$348$	−0.563104	−	0.563104i	−0.0301856	−	0.0301856i
$349$	−3.53891			−0.189433			−0.0947166	−	0.995504i	$-0.530195\pi$
$349$	−3.53891			−0.189433			−0.0947166	+	0.995504i	$0.530195\pi$
$350$	−23.1106	+	37.3975i	−1.23532	+	1.99898i
$351$		−	2.54796i		−	0.136000i
$352$		0			0
$353$	−13.3455	+	13.3455i	−0.710310	+	0.710310i	−0.966600	−	0.256290i	$-0.917500\pi$
$353$	−13.3455	+	13.3455i	−0.710310	+	0.710310i	0.256290	+	0.966600i	$0.417500\pi$
$354$	−4.11438			−0.218677
$355$	3.87180	−	13.6305i	0.205494	−	0.723431i
$356$	−4.06111			−0.215238
$357$	−1.22665	−	1.22665i	−0.0649214	−	0.0649214i
$358$	12.8166	+	12.8166i	0.677377	+	0.677377i
$359$	−27.1869			−1.43487			−0.717434	−	0.696626i	$-0.754684\pi$
$359$	−27.1869			−1.43487			−0.717434	+	0.696626i	$0.754684\pi$
$360$	2.05991	+	3.69447i	0.108567	+	0.194716i
$361$	−5.90117			−0.310588
$362$	30.0911	−	30.0911i	1.58155	−	1.58155i
$363$		0			0
$364$		−	12.5216i		−	0.656311i
$365$	−14.4693	+	8.06759i	−0.757358	+	0.422277i
$366$	5.81637			0.304026
$367$	−3.80793	−	3.80793i	−0.198772	−	0.198772i	0.600701	−	0.799473i	$-0.294888\pi$
$367$	−3.80793	−	3.80793i	−0.198772	−	0.198772i	−0.799473	+	0.600701i	$0.794888\pi$
$368$	16.2244	−	16.2244i	0.845756	−	0.845756i
$369$	−18.8020			−0.978794
$370$	−12.1071	+	42.6222i	−0.629416	+	2.21582i
$371$		−	17.0832i		−	0.886916i
$372$	1.43982	+	1.43982i	0.0746512	+	0.0746512i
$373$	−11.4181	−	11.4181i	−0.591209	−	0.591209i	0.346749	−	0.937958i	$-0.387286\pi$
$373$	−11.4181	−	11.4181i	−0.591209	−	0.591209i	−0.937958	+	0.346749i	$0.887286\pi$
$374$		0			0
$375$	0.131506	−	2.92713i	0.00679092	−	0.151156i
$376$		−	5.64228i		−	0.290979i
$377$	−2.11806	−	2.11806i	−0.109086	−	0.109086i
$378$	9.66431	−	9.66431i	0.497079	−	0.497079i
$379$			11.7389i			0.602985i	0.953469	+	0.301492i	$0.0974848\pi$
$379$			11.7389i			0.602985i	−0.953469	+	0.301492i	$0.902515\pi$
$380$	12.9447	+	3.67701i	0.664051	+	0.188627i
$381$			2.66691i			0.136630i
$382$	−16.4710	+	16.4710i	−0.842730	+	0.842730i
$383$	−7.21018	+	7.21018i	−0.368423	+	0.368423i	−0.866902	−	0.498479i	$-0.833892\pi$
$383$	−7.21018	+	7.21018i	−0.368423	+	0.368423i	0.498479	+	0.866902i	$0.333892\pi$
$384$	−1.33378			−0.0680642
$385$		0			0
$386$	−19.0416			−0.969190
$387$	13.3108	−	13.3108i	0.676628	−	0.676628i
$388$	−6.21607	+	6.21607i	−0.315573	+	0.315573i
$389$			5.02321i			0.254687i	0.991859	+	0.127343i	$0.0406451\pi$
$389$			5.02321i			0.254687i	−0.991859	+	0.127343i	$0.959355\pi$
$390$	0.895257	+	1.60565i	0.0453331	+	0.0813054i
$391$			7.24875i			0.366585i
$392$	−6.43686	+	6.43686i	−0.325110	+	0.325110i
$393$	1.30673	+	1.30673i	0.0659159	+	0.0659159i
$394$		−	24.2981i		−	1.22412i
$395$	−5.45940	+	19.2195i	−0.274692	+	0.967039i
$396$		0			0
$397$	9.31638	+	9.31638i	0.467576	+	0.467576i	0.901128	−	0.433553i	$-0.142740\pi$
$397$	9.31638	+	9.31638i	0.467576	+	0.467576i	−0.433553	+	0.901128i	$0.642740\pi$
$398$	−17.5239	−	17.5239i	−0.878393	−	0.878393i
$399$			4.35757i			0.218151i
$400$	−19.3983	−	11.9876i	−0.969915	−	0.599380i
$401$	17.6228			0.880043			0.440021	−	0.897987i	$-0.354971\pi$
$401$	17.6228			0.880043			0.440021	+	0.897987i	$0.354971\pi$
$402$	0.781171	−	0.781171i	0.0389613	−	0.0389613i
$403$	5.41573	+	5.41573i	0.269777	+	0.269777i
$404$	−15.4236			−0.767354
$405$	5.12415	−	18.0393i	0.254621	−	0.896379i
$406$		−	16.0674i		−	0.797414i
$407$		0			0
$408$	0.172308	−	0.172308i	0.00853051	−	0.00853051i
$409$	−35.3545			−1.74817			−0.874083	−	0.485776i	$-0.838537\pi$
$409$	−35.3545			−1.74817			−0.874083	+	0.485776i	$0.838537\pi$
$410$	23.9746	−	13.3674i	1.18402	−	0.660171i
$411$	3.12303			0.154048
$412$	13.2922	+	13.2922i	0.654857	+	0.654857i
$413$	−26.6477	−	26.6477i	−1.31125	−	1.31125i
$414$	−28.2243			−1.38715
$415$	−12.8101	+	7.14249i	−0.628824	+	0.350611i
$416$	12.1916			0.597741
$417$	−1.26972	+	1.26972i	−0.0621785	+	0.0621785i
$418$		0			0
$419$			26.7217i			1.30544i	0.757600	+	0.652719i	$0.226372\pi$
$419$			26.7217i			1.30544i	−0.757600	+	0.652719i	$0.773628\pi$
$420$	−1.22323	+	4.30630i	−0.0596873	+	0.210126i
$421$	−22.8259			−1.11247			−0.556234	−	0.831026i	$-0.687754\pi$
$421$	−22.8259			−1.11247			−0.556234	+	0.831026i	$0.687754\pi$
$422$	−5.36140	−	5.36140i	−0.260989	−	0.260989i
$423$	−18.1224	+	18.1224i	−0.881143	+	0.881143i
$424$	2.39968			0.116539
$425$	7.01130	−	1.65547i	0.340098	−	0.0803023i
$426$		−	3.17840i		−	0.153994i
$427$	37.6710	+	37.6710i	1.82303	+	1.82303i
$428$	4.44370	+	4.44370i	0.214795	+	0.214795i
$429$		0			0
$430$	−7.50935	+	26.4362i	−0.362133	+	1.27487i
$431$			38.3713i			1.84828i	0.382052	+	0.924141i	$0.375218\pi$
$431$			38.3713i			1.84828i	−0.382052	+	0.924141i	$0.624782\pi$
$432$	5.01293	+	5.01293i	0.241185	+	0.241185i
$433$	26.0799	−	26.0799i	1.25332	−	1.25332i	0.299094	−	0.954224i	$-0.403316\pi$
$433$	26.0799	−	26.0799i	1.25332	−	1.25332i	0.954224	−	0.299094i	$-0.0966845\pi$
$434$			41.0834i			1.97206i
$435$	0.521509	+	0.935332i	0.0250045	+	0.0448457i
$436$		−	1.05958i		−	0.0507449i
$437$	12.8752	−	12.8752i	0.615906	−	0.615906i
$438$	−2.62761	+	2.62761i	−0.125552	+	0.125552i
$439$	23.4271			1.11812			0.559058	−	0.829128i	$-0.311163\pi$
$439$	23.4271			1.11812			0.559058	+	0.829128i	$0.311163\pi$
$440$		0			0
$441$	41.3491			1.96900
$442$	−3.19608	+	3.19608i	−0.152022	+	0.152022i
$443$	6.47833	−	6.47833i	0.307795	−	0.307795i	−0.536259	−	0.844054i	$-0.680163\pi$
$443$	6.47833	−	6.47833i	0.307795	−	0.307795i	0.844054	+	0.536259i	$0.180163\pi$
$444$			4.51192i			0.214126i
$445$	5.25337	+	1.49225i	0.249034	+	0.0707392i
$446$		−	2.74587i		−	0.130020i
$447$	−4.39164	+	4.39164i	−0.207717	+	0.207717i
$448$	16.6110	+	16.6110i	0.784798	+	0.784798i
$449$		−	6.57306i		−	0.310202i	−0.987899	−	0.155101i	$-0.950430\pi$
$449$		−	6.57306i		−	0.310202i	0.987899	−	0.155101i	$-0.0495703\pi$
$450$	6.44589	+	27.2998i	0.303862	+	1.28692i
$451$		0			0
$452$	9.21191	+	9.21191i	0.433292	+	0.433292i
$453$	3.57570	+	3.57570i	0.168001	+	0.168001i
$454$			21.6273i			1.01502i
$455$	−4.60104	+	16.1977i	−0.215700	+	0.759360i
$456$	−0.612107			−0.0286645
$457$	−7.30639	+	7.30639i	−0.341779	+	0.341779i	−0.857036	−	0.515257i	$-0.827696\pi$
$457$	−7.30639	+	7.30639i	−0.341779	+	0.341779i	0.515257	+	0.857036i	$0.327696\pi$
$458$	−0.878851	−	0.878851i	−0.0410660	−	0.0410660i
$459$	−2.23968			−0.104539
$460$	16.3380	−	9.10952i	0.761764	−	0.424733i
$461$		−	8.34786i		−	0.388799i	−0.980922	−	0.194399i	$-0.937724\pi$
$461$		−	8.34786i		−	0.388799i	0.980922	−	0.194399i	$-0.0622758\pi$
$462$		0			0
$463$	22.9521	−	22.9521i	1.06668	−	1.06668i	0.0690646	−	0.997612i	$-0.477999\pi$
$463$	22.9521	−	22.9521i	1.06668	−	1.06668i	0.997612	−	0.0690646i	$-0.0220015\pi$
$464$	8.33427			0.386909
$465$	−1.33346	−	2.39158i	−0.0618379	−	0.110907i
$466$	−25.7066			−1.19083
$467$	29.7048	+	29.7048i	1.37457	+	1.37457i	0.853528	+	0.521047i	$0.174458\pi$
$467$	29.7048	+	29.7048i	1.37457	+	1.37457i	0.521047	+	0.853528i	$0.325542\pi$
$468$	−5.64944	−	5.64944i	−0.261146	−	0.261146i
$469$	10.1189			0.467246
$470$	10.2238	−	35.9924i	0.471590	−	1.66021i
$471$	−1.44939			−0.0667842
$472$	3.74320	−	3.74320i	0.172295	−	0.172295i
$473$		0			0
$474$			4.48167i			0.205850i
$475$	−15.3939	−	9.51302i	−0.706322	−	0.436487i
$476$	−11.0066			−0.504487
$477$	−7.70752	−	7.70752i	−0.352903	−	0.352903i
$478$	23.7155	−	23.7155i	1.08472	−	1.08472i
$479$	7.45917			0.340818			0.170409	−	0.985373i	$-0.445491\pi$
$479$	7.45917			0.340818			0.170409	+	0.985373i	$0.445491\pi$
$480$	−4.19279	−	1.19098i	−0.191374	−	0.0543607i
$481$			16.9711i			0.773816i
$482$	13.2344	+	13.2344i	0.602810	+	0.602810i
$483$	4.28318	+	4.28318i	0.194892	+	0.194892i
$484$		0			0
$485$	10.3251	−	5.75690i	0.468837	−	0.261408i
$486$		−	13.1314i		−	0.595652i
$487$	5.83970	+	5.83970i	0.264622	+	0.264622i	0.826929	−	0.562307i	$-0.190086\pi$
$487$	5.83970	+	5.83970i	0.264622	+	0.264622i	−0.562307	+	0.826929i	$0.690086\pi$
$488$	−5.29164	+	5.29164i	−0.239541	+	0.239541i
$489$			2.63598i			0.119203i
$490$	−52.7246	+	29.3975i	−2.38186	+	1.32804i
$491$			6.69275i			0.302039i	0.988531	+	0.151020i	$0.0482557\pi$
$491$			6.69275i			0.302039i	−0.988531	+	0.151020i	$0.951744\pi$
$492$	1.97648	−	1.97648i	0.0891068	−	0.0891068i
$493$	−1.86179	+	1.86179i	−0.0838509	+	0.0838509i
$494$	11.3537			0.510829
$495$		0			0
$496$	−21.3102			−0.956854
$497$	20.5856	−	20.5856i	0.923391	−	0.923391i
$498$	−2.32631	+	2.32631i	−0.104244	+	0.104244i
$499$			26.3873i			1.18126i	0.806944	+	0.590628i	$0.201120\pi$
$499$			26.3873i			1.18126i	−0.806944	+	0.590628i	$0.798880\pi$
$500$	−12.5424	−	13.7224i	−0.560913	−	0.613684i
$501$		−	1.94771i		−	0.0870173i
$502$	−24.7597	+	24.7597i	−1.10508	+	1.10508i
$503$	−23.3599	−	23.3599i	−1.04157	−	1.04157i	−0.999098	−	0.0424679i	$-0.986478\pi$
$503$	−23.3599	−	23.3599i	−1.04157	−	1.04157i	−0.0424679	−	0.999098i	$-0.513522\pi$
$504$			8.69063i			0.387111i
$505$	19.9517	+	5.66737i	0.887838	+	0.252195i
$506$		0			0
$507$	−1.91119	−	1.91119i	−0.0848790	−	0.0848790i
$508$	11.9649	+	11.9649i	0.530859	+	0.530859i
$509$		−	26.3558i		−	1.16820i	−0.811682	−	0.584099i	$-0.801448\pi$
$509$		−	26.3558i		−	1.16820i	0.811682	−	0.584099i	$-0.198552\pi$
$510$	1.41138	−	0.786939i	0.0624971	−	0.0348462i
$511$	−34.0366			−1.50569
$512$	−19.8238	+	19.8238i	−0.876095	+	0.876095i
$513$	3.97812	+	3.97812i	0.175638	+	0.175638i
$514$	−12.4017			−0.547015
$515$	−12.3103	−	22.0786i	−0.542456	−	0.972901i
$516$			2.79850i			0.123197i
$517$		0			0
$518$	−64.3708	+	64.3708i	−2.82829	+	2.82829i
$519$	3.82784			0.168023
$520$	−2.27529	−	0.646307i	−0.0997781	−	0.0283425i
$521$	−13.2088			−0.578687			−0.289343	−	0.957225i	$-0.593437\pi$
$521$	−13.2088			−0.578687			−0.289343	+	0.957225i	$0.593437\pi$
$522$	−7.24923	−	7.24923i	−0.317290	−	0.317290i
$523$	−14.9574	−	14.9574i	−0.654043	−	0.654043i	0.299921	−	0.953964i	$-0.403040\pi$
$523$	−14.9574	−	14.9574i	−0.654043	−	0.654043i	−0.953964	+	0.299921i	$0.903040\pi$
$524$	11.7251			0.512215
$525$	3.16468	−	5.12108i	0.138118	−	0.223502i
$526$	−8.43104			−0.367611
$527$	4.76048	−	4.76048i	0.207370	−	0.207370i
$528$		0			0
$529$		−	2.31090i		−	0.100474i
$530$	15.3077	+	4.34821i	0.664922	+	0.188874i
$531$	−24.0456			−1.04349
$532$	19.5499	+	19.5499i	0.847598	+	0.847598i
$533$	7.43434	−	7.43434i	0.322017	−	0.322017i
$534$	1.22500			0.0530108
$535$	−4.11546	−	7.38111i	−0.177927	−	0.319113i
$536$			1.42140i			0.0613949i
$537$	−1.75505	−	1.75505i	−0.0757361	−	0.0757361i
$538$	10.7309	+	10.7309i	0.462644	+	0.462644i
$539$		0			0
$540$	2.81461	+	5.04803i	0.121121	+	0.217232i
$541$		−	11.4552i		−	0.492496i	−0.969207	−	0.246248i	$-0.920802\pi$
$541$		−	11.4552i		−	0.492496i	0.969207	−	0.246248i	$-0.0791978\pi$
$542$	12.0831	+	12.0831i	0.519014	+	0.519014i
$543$	−4.12056	+	4.12056i	−0.176830	+	0.176830i
$544$		−	10.7165i		−	0.459466i
$545$	−0.389342	+	1.37066i	−0.0166776	+	0.0587125i
$546$			3.77703i			0.161642i
$547$	9.94911	−	9.94911i	0.425393	−	0.425393i	−0.461662	−	0.887056i	$-0.652747\pi$
$547$	9.94911	−	9.94911i	0.425393	−	0.425393i	0.887056	+	0.461662i	$0.152747\pi$
$548$	14.0113	−	14.0113i	0.598532	−	0.598532i
$549$	33.9924			1.45076
$550$		0			0
$551$	6.61383			0.281759
$552$	−0.601658	+	0.601658i	−0.0256083	+	0.0256083i
$553$	−29.0266	+	29.0266i	−1.23433	+	1.23433i
$554$			5.12915i			0.217917i
$555$	1.65789	−	5.83653i	0.0703737	−	0.247747i
$556$			11.3931i			0.483173i
$557$	28.3861	−	28.3861i	1.20276	−	1.20276i	0.229436	−	0.973324i	$-0.426312\pi$
$557$	28.3861	−	28.3861i	1.20276	−	1.20276i	0.973324	−	0.229436i	$-0.0736881\pi$
$558$	18.5358	+	18.5358i	0.784683	+	0.784683i
$559$			10.5263i			0.445213i
$560$	−22.8156	−	40.9201i	−0.964137	−	1.72919i
$561$		0			0
$562$	−14.6449	−	14.6449i	−0.617757	−	0.617757i
$563$	−9.19549	−	9.19549i	−0.387544	−	0.387544i	0.486267	−	0.873810i	$-0.338358\pi$
$563$	−9.19549	−	9.19549i	−0.387544	−	0.387544i	−0.873810	+	0.486267i	$0.838358\pi$
$564$		−	3.81010i		−	0.160434i
$565$	−8.53145	−	15.3012i	−0.358921	−	0.643728i
$566$	18.2755			0.768177
$567$	27.2441	−	27.2441i	1.14414	−	1.14414i
$568$	2.89166	+	2.89166i	0.121331	+	0.121331i
$569$	−22.0321			−0.923636			−0.461818	−	0.886975i	$-0.652803\pi$
$569$	−22.0321			−0.923636			−0.461818	+	0.886975i	$0.652803\pi$
$570$	−3.90466	−	1.10914i	−0.163548	−	0.0464567i
$571$			32.3912i			1.35553i	0.735279	+	0.677765i	$0.237051\pi$
$571$			32.3912i			1.35553i	−0.735279	+	0.677765i	$0.762949\pi$
$572$		0			0
$573$	2.25548	−	2.25548i	0.0942239	−	0.0942239i
$574$	56.3964			2.35394
$575$	−24.4818	+	5.78052i	−1.02096	+	0.241064i
$576$	14.9890			0.624541
$577$	−0.0644216	−	0.0644216i	−0.00268191	−	0.00268191i	0.705765	−	0.708446i	$-0.250604\pi$
$577$	−0.0644216	−	0.0644216i	−0.00268191	−	0.00268191i	−0.708446	+	0.705765i	$0.750604\pi$
$578$	−20.1966	−	20.1966i	−0.840068	−	0.840068i
$579$	2.60748			0.108363
$580$	6.53603	+	1.85659i	0.271394	+	0.0770907i
$581$	−30.1337			−1.25016
$582$	1.87502	−	1.87502i	0.0777222	−	0.0777222i
$583$		0			0
$584$		−	4.78112i		−	0.197844i
$585$	5.23213	+	9.38388i	0.216322	+	0.387976i
$586$	37.6947			1.55716
$587$	28.5239	+	28.5239i	1.17731	+	1.17731i	0.980428	+	0.196880i	$0.0630810\pi$
$587$	28.5239	+	28.5239i	1.17731	+	1.17731i	0.196880	+	0.980428i	$0.436919\pi$
$588$	−4.34665	+	4.34665i	−0.179253	+	0.179253i
$589$	−16.9111			−0.696811
$590$	30.6607	−	17.0954i	1.26228	−	0.703806i
$591$			3.32728i			0.136866i
$592$	−33.3895	−	33.3895i	−1.37230	−	1.37230i
$593$	−9.79960	−	9.79960i	−0.402421	−	0.402421i	0.476664	−	0.879086i	$-0.341846\pi$
$593$	−9.79960	−	9.79960i	−0.402421	−	0.402421i	−0.879086	+	0.476664i	$0.841846\pi$
$594$		0			0
$595$	14.2379	+	4.04435i	0.583698	+	0.165802i
$596$			39.4056i			1.61412i
$597$	2.39965	+	2.39965i	0.0982113	+	0.0982113i
$598$	11.1599	−	11.1599i	0.456364	−	0.456364i
$599$		−	7.54664i		−	0.308347i	−0.988044	−	0.154174i	$-0.950728\pi$
$599$		−	7.54664i		−	0.308347i	0.988044	−	0.154174i	$-0.0492715\pi$
$600$	0.719357	+	0.444542i	0.0293676	+	0.0181484i
$601$		−	25.7652i		−	1.05098i	−0.850799	−	0.525492i	$-0.823881\pi$
$601$		−	25.7652i		−	1.05098i	0.850799	−	0.525492i	$-0.176119\pi$
$602$	−39.9257	+	39.9257i	−1.62725	+	1.62725i
$603$	4.56538	−	4.56538i	0.185917	−	0.185917i
$604$	32.0843			1.30549
$605$		0			0
$606$	4.65240			0.188991
$607$	−26.4373	+	26.4373i	−1.07306	+	1.07306i	−0.0759443	+	0.997112i	$0.524197\pi$
$607$	−26.4373	+	26.4373i	−1.07306	+	1.07306i	−0.997112	+	0.0759443i	$0.975803\pi$
$608$	−19.0346	+	19.0346i	−0.771956	+	0.771956i
$609$			2.20021i			0.0891572i
$610$	−43.3441	+	24.1672i	−1.75495	+	0.978502i
$611$		−	14.3313i		−	0.579782i
$612$	−4.96591	+	4.96591i	−0.200735	+	0.200735i
$613$	28.4964	+	28.4964i	1.15096	+	1.15096i	0.986361	+	0.164597i	$0.0526324\pi$
$613$	28.4964	+	28.4964i	1.15096	+	1.15096i	0.164597	+	0.986361i	$0.447368\pi$
$614$			4.22595i			0.170545i
$615$	−3.28300	+	1.83049i	−0.132383	+	0.0738123i
$616$		0			0
$617$	19.0423	+	19.0423i	0.766612	+	0.766612i	0.977508	−	0.210896i	$-0.0676382\pi$
$617$	19.0423	+	19.0423i	0.766612	+	0.766612i	−0.210896	+	0.977508i	$0.567638\pi$
$618$	−4.00946	−	4.00946i	−0.161284	−	0.161284i
$619$			22.9592i			0.922808i	0.887190	+	0.461404i	$0.152654\pi$
$619$			22.9592i			0.922808i	−0.887190	+	0.461404i	$0.847346\pi$
$620$	−16.7122	−	4.74718i	−0.671177	−	0.190651i
$621$	7.82042			0.313823
$622$	35.7310	−	35.7310i	1.43268	−	1.43268i
$623$	7.93397	+	7.93397i	0.317868	+	0.317868i
$624$	−1.95917			−0.0784294
$625$	11.1823	+	22.3597i	0.447294	+	0.894387i
$626$			29.9526i			1.19715i
$627$		0			0
$628$	−6.50259	+	6.50259i	−0.259481	+	0.259481i
$629$	14.9178			0.594810
$630$	−15.7474	+	55.4380i	−0.627393	+	2.20870i
$631$	12.3237			0.490597			0.245299	−	0.969448i	$-0.421114\pi$
$631$	12.3237			0.490597			0.245299	+	0.969448i	$0.421114\pi$
$632$	−4.07736	−	4.07736i	−0.162189	−	0.162189i
$633$	0.734169	+	0.734169i	0.0291806	+	0.0291806i
$634$	33.5509			1.33247
$635$	−11.0811	−	19.8741i	−0.439741	−	0.788680i
$636$	1.62044			0.0642547
$637$	−16.3495	+	16.3495i	−0.647790	+	0.647790i
$638$		0			0
$639$		−	18.5754i		−	0.734833i
$640$	9.93946	−	5.54190i	0.392892	−	0.219063i
$641$	38.3865			1.51617			0.758087	−	0.652153i	$-0.226134\pi$
$641$	38.3865			1.51617			0.758087	+	0.652153i	$0.226134\pi$
$642$	−1.34040	−	1.34040i	−0.0529015	−	0.0529015i
$643$	14.4812	−	14.4812i	0.571082	−	0.571082i	−0.361349	−	0.932431i	$-0.617684\pi$
$643$	14.4812	−	14.4812i	0.571082	−	0.571082i	0.932431	+	0.361349i	$0.117684\pi$
$644$	38.4325			1.51445
$645$	1.02830	−	3.62008i	0.0404893	−	0.142540i
$646$		−	9.98004i		−	0.392659i
$647$	−29.4865	−	29.4865i	−1.15924	−	1.15924i	−0.984640	−	0.174595i	$-0.944138\pi$
$647$	−29.4865	−	29.4865i	−1.15924	−	1.15924i	−0.174595	−	0.984640i	$-0.555862\pi$
$648$	3.82697	+	3.82697i	0.150338	+	0.150338i
$649$		0			0
$650$	−13.3431	−	8.24566i	−0.523359	−	0.323421i
$651$		−	5.62580i		−	0.220492i
$652$	11.8262	+	11.8262i	0.463148	+	0.463148i
$653$	2.81677	−	2.81677i	0.110229	−	0.110229i	−0.649841	−	0.760070i	$-0.725165\pi$
$653$	2.81677	−	2.81677i	0.110229	−	0.110229i	0.760070	+	0.649841i	$0.225165\pi$
$654$			0.319614i			0.0124979i
$655$	−15.1674	−	4.30837i	−0.592639	−	0.168342i
$656$			29.2531i			1.14214i
$657$	−15.3565	+	15.3565i	−0.599113	+	0.599113i
$658$	54.3580	−	54.3580i	2.11910	−	2.11910i
$659$	−2.49945			−0.0973648			−0.0486824	−	0.998814i	$-0.515502\pi$
$659$	−2.49945			−0.0973648			−0.0486824	+	0.998814i	$0.515502\pi$
$660$		0			0
$661$	−21.8188			−0.848654			−0.424327	−	0.905509i	$-0.639489\pi$
$661$	−21.8188			−0.848654			−0.424327	+	0.905509i	$0.639489\pi$
$662$	−12.9337	+	12.9337i	−0.502684	+	0.502684i
$663$	0.437658	−	0.437658i	0.0169972	−	0.0169972i
$664$		−	4.23288i		−	0.164267i
$665$	−18.1058	−	32.4730i	−0.702114	−	1.25925i
$666$			58.0850i			2.25075i
$667$	6.50093	−	6.50093i	0.251717	−	0.251717i
$668$	−8.73828	−	8.73828i	−0.338094	−	0.338094i
$669$			0.376008i			0.0145373i
$670$	−2.57557	+	9.06715i	−0.0995029	+	0.350295i
$671$		0			0
$672$	−6.33222	−	6.33222i	−0.244271	−	0.244271i
$673$	−30.5481	−	30.5481i	−1.17754	−	1.17754i	−0.980368	−	0.197176i	$-0.936823\pi$
$673$	−30.5481	−	30.5481i	−1.17754	−	1.17754i	−0.197176	−	0.980368i	$-0.563177\pi$
$674$			9.20970i			0.354744i
$675$	−1.78603	−	7.56425i	−0.0687445	−	0.291148i
$676$	−17.1489			−0.659573
$677$	1.70120	−	1.70120i	0.0653823	−	0.0653823i	−0.673660	−	0.739042i	$-0.735279\pi$
$677$	1.70120	−	1.70120i	0.0653823	−	0.0653823i	0.739042	+	0.673660i	$0.235279\pi$
$678$	−2.77869	−	2.77869i	−0.106715	−	0.106715i
$679$	24.2880			0.932088
$680$	−0.568110	+	2.00000i	−0.0217860	+	0.0766965i
$681$		−	2.96156i		−	0.113487i
$682$		0			0
$683$	−3.00058	+	3.00058i	−0.114814	+	0.114814i	−0.762180	−	0.647366i	$-0.775871\pi$
$683$	−3.00058	+	3.00058i	−0.114814	+	0.114814i	0.647366	+	0.762180i	$0.275871\pi$
$684$	17.6409			0.674517
$685$	−23.2731	+	12.9763i	−0.889220	+	0.495799i
$686$	−62.4789			−2.38545
$687$	0.120347	+	0.120347i	0.00459151	+	0.00459151i
$688$	−20.7097	−	20.7097i	−0.789549	−	0.789549i
$689$	6.09513			0.232206
$690$	−4.92821	+	2.74780i	−0.187614	+	0.104607i
$691$	−20.2736			−0.771245			−0.385623	−	0.922657i	$-0.626013\pi$
$691$	−20.2736			−0.771245			−0.385623	+	0.922657i	$0.626013\pi$
$692$	17.1734	−	17.1734i	0.652833	−	0.652833i
$693$		0			0
$694$			0.551024i			0.0209166i
$695$	4.18635	−	14.7378i	0.158797	−	0.559038i
$696$	−0.309064			−0.0117150
$697$	−6.53485	−	6.53485i	−0.247525	−	0.247525i
$698$	4.78918	−	4.78918i	0.181273	−	0.181273i
$699$	3.52016			0.133145
$700$	−8.77724	−	37.1735i	−0.331748	−	1.40503i
$701$		−	38.2663i		−	1.44530i	−0.691216	−	0.722648i	$-0.742925\pi$
$701$		−	38.2663i		−	1.44530i	0.691216	−	0.722648i	$-0.257075\pi$
$702$	3.44813	+	3.44813i	0.130141	+	0.130141i
$703$	−26.4969	−	26.4969i	−0.999350	−	0.999350i
$704$		0			0
$705$	−1.40001	+	4.92866i	−0.0527275	+	0.185624i
$706$		−	36.1208i		−	1.35942i
$707$	30.1323	+	30.1323i	1.13324	+	1.13324i
$708$	2.52769	−	2.52769i	0.0949964	−	0.0949964i
$709$		−	34.9914i		−	1.31413i	−0.753835	−	0.657064i	$-0.771798\pi$
$709$		−	34.9914i		−	1.31413i	0.753835	−	0.657064i	$-0.228202\pi$
$710$	13.2063	+	23.6857i	0.495625	+	0.888909i
$711$			26.1921i			0.982281i
$712$	−1.11448	+	1.11448i	−0.0417671	+	0.0417671i
$713$	−16.6225	+	16.6225i	−0.622516	+	0.622516i
$714$	3.32004			0.124250
$715$		0			0
$716$	−15.7479			−0.588525
$717$	−3.24751	+	3.24751i	−0.121280	+	0.121280i
$718$	36.7918	−	36.7918i	1.37306	−	1.37306i
$719$			44.2202i			1.64914i	0.565763	+	0.824568i	$0.308582\pi$
$719$			44.2202i			1.64914i	−0.565763	+	0.824568i	$0.691418\pi$
$720$	−28.7560	−	8.16827i	−1.07167	−	0.304414i
$721$		−	51.9363i		−	1.93421i
$722$	7.98602	−	7.98602i	0.297209	−	0.297209i
$723$	−1.81227	−	1.81227i	−0.0673989	−	0.0673989i
$724$			36.9733i			1.37410i
$725$	−7.77267	−	4.80330i	−0.288670	−	0.178390i
$726$		0			0
$727$	17.8123	+	17.8123i	0.660620	+	0.660620i	0.955526	−	0.294906i	$-0.0952883\pi$
$727$	17.8123	+	17.8123i	0.660620	+	0.660620i	−0.294906	+	0.955526i	$0.595288\pi$
$728$	−3.43629	−	3.43629i	−0.127357	−	0.127357i
$729$		−	23.3615i		−	0.865242i
$730$	8.66339	−	30.4990i	0.320647	−	1.12882i
$731$	9.25267			0.342222
$732$	−3.57332	+	3.57332i	−0.132074	+	0.132074i
$733$	5.23876	+	5.23876i	0.193498	+	0.193498i	0.797206	−	0.603708i	$-0.206311\pi$
$733$	5.23876	+	5.23876i	0.193498	+	0.193498i	−0.603708	+	0.797206i	$0.706311\pi$
$734$	10.3065			0.380419
$735$	7.21991	−	4.02557i	0.266310	−	0.148486i
$736$			37.4194i			1.37930i
$737$		0			0
$738$	25.4446	−	25.4446i	0.936630	−	0.936630i
$739$	51.5933			1.89789			0.948945	−	0.315442i	$-0.102153\pi$
$739$	51.5933			1.89789			0.948945	+	0.315442i	$0.102153\pi$
$740$	−18.7472	−	33.6232i	−0.689160	−	1.23602i
$741$	−1.55474			−0.0571147
$742$	23.1186	+	23.1186i	0.848710	+	0.848710i
$743$	13.6160	+	13.6160i	0.499522	+	0.499522i	0.911289	−	0.411767i	$-0.135088\pi$
$743$	13.6160	+	13.6160i	0.499522	+	0.499522i	−0.411767	+	0.911289i	$0.635088\pi$
$744$	0.790255			0.0289722
$745$	14.4795	−	50.9743i	0.530488	−	1.86755i
$746$	30.9042			1.13148
$747$	−13.5956	+	13.5956i	−0.497436	+	0.497436i
$748$		0			0
$749$		−	17.3628i		−	0.634425i
$750$	3.78330	+	4.13923i	0.138147	+	0.151143i
$751$	37.9642			1.38533			0.692667	−	0.721258i	$-0.256436\pi$
$751$	37.9642			1.38533			0.692667	+	0.721258i	$0.256436\pi$
$752$	28.1958	+	28.1958i	1.02819	+	1.02819i
$753$	3.39050	−	3.39050i	0.123557	−	0.123557i
$754$	5.73271			0.208773
$755$	−41.5036	−	11.7893i	−1.51047	−	0.429056i
$756$			11.8746i			0.431877i
$757$	27.6372	+	27.6372i	1.00449	+	1.00449i	0.999990	+	0.00450211i	$0.00143307\pi$
$757$	27.6372	+	27.6372i	1.00449	+	1.00449i	0.00450211	+	0.999990i	$0.498567\pi$
$758$	−15.8861	−	15.8861i	−0.577010	−	0.577010i
$759$		0			0
$760$	4.56148	−	2.54332i	0.165462	−	0.0922561i
$761$			41.9724i			1.52150i	0.649045	+	0.760750i	$0.275169\pi$
$761$			41.9724i			1.52150i	−0.649045	+	0.760750i	$0.724831\pi$
$762$	−3.60912	−	3.60912i	−0.130745	−	0.130745i
$763$	−2.07005	+	2.07005i	−0.0749410	+	0.0749410i
$764$		−	20.2381i		−	0.732189i
$765$	8.24851	−	4.59909i	0.298225	−	0.166280i
$766$		−	19.5150i		−	0.705105i
$767$	9.50765	−	9.50765i	0.343301	−	0.343301i
$768$	3.70017	−	3.70017i	0.133518	−	0.133518i
$769$	22.2634			0.802840			0.401420	−	0.915894i	$-0.368517\pi$
$769$	22.2634			0.802840			0.401420	+	0.915894i	$0.368517\pi$
$770$		0			0
$771$	1.69824			0.0611606
$772$	11.6983	−	11.6983i	0.421031	−	0.421031i
$773$	−25.8022	+	25.8022i	−0.928041	+	0.928041i	−0.997579	−	0.0695381i	$-0.977847\pi$
$773$	−25.8022	+	25.8022i	−0.928041	+	0.928041i	0.0695381	+	0.997579i	$0.477847\pi$
$774$			36.0270i			1.29496i
$775$	19.8742	+	12.2817i	0.713902	+	0.441172i
$776$			3.41173i			0.122474i
$777$	8.81469	−	8.81469i	0.316225	−	0.316225i
$778$	−6.79788	−	6.79788i	−0.243716	−	0.243716i
$779$			23.2144i			0.831743i
$780$	−1.53645	−	0.436436i	−0.0550137	−	0.0156269i
$781$		0			0
$782$	−9.80968	−	9.80968i	−0.350793	−	0.350793i
$783$	2.00862	+	2.00862i	0.0717823	+	0.0717823i
$784$		−	64.3329i		−	2.29760i
$785$	10.8010	−	6.02225i	0.385503	−	0.214943i
$786$	−3.53678			−0.126153
$787$	−7.88776	+	7.88776i	−0.281168	+	0.281168i	−0.833575	−	0.552407i	$-0.813710\pi$
$787$	−7.88776	+	7.88776i	−0.281168	+	0.281168i	0.552407	+	0.833575i	$0.313710\pi$
$788$	14.9277	+	14.9277i	0.531776	+	0.531776i
$789$	1.15451			0.0411018
$790$	−18.6215	−	33.3978i	−0.662523	−	1.18824i
$791$		−	35.9936i		−	1.27979i
$792$		0			0
$793$	−13.4407	+	13.4407i	−0.477292	+	0.477292i
$794$	−25.2156			−0.894868
$795$	−2.09617	−	0.595428i	−0.0743436	−	0.0211176i
$796$	21.5318			0.763174
$797$	29.4824	+	29.4824i	1.04432	+	1.04432i	0.998971	+	0.0453503i	$0.0144404\pi$
$797$	29.4824	+	29.4824i	1.04432	+	1.04432i	0.0453503	+	0.998971i	$0.485560\pi$
$798$	−5.89707	−	5.89707i	−0.208754	−	0.208754i
$799$	−12.5973			−0.445661
$800$	36.1937	−	8.54588i	1.27964	−	0.302142i
$801$	7.15922			0.252959
$802$	−23.8489	+	23.8489i	−0.842133	+	0.842133i
$803$		0			0
$804$			0.959834i			0.0338507i
$805$	−49.7155	−	14.1219i	−1.75224	−	0.497732i
$806$	−14.6582			−0.516312
$807$	−1.46946	−	1.46946i	−0.0517273	−	0.0517273i
$808$	−4.23268	+	4.23268i	−0.148905	+	0.148905i
$809$	−6.24330			−0.219503			−0.109751	−	0.993959i	$-0.535005\pi$
$809$	−6.24330			−0.219503			−0.109751	+	0.993959i	$0.535005\pi$
$810$	17.4780	+	31.3469i	0.614113	+	1.10142i
$811$			19.5621i			0.686919i	0.939167	+	0.343460i	$0.111599\pi$
$811$			19.5621i			0.686919i	−0.939167	+	0.343460i	$0.888401\pi$
$812$	9.87112	+	9.87112i	0.346408	+	0.346408i
$813$	−1.65462	−	1.65462i	−0.0580299	−	0.0580299i
$814$		0			0
$815$	−10.9526	−	19.6436i	−0.383652	−	0.688085i
$816$			1.72212i			0.0602864i
$817$	−16.4346	−	16.4346i	−0.574974	−	0.574974i
$818$	47.8450	−	47.8450i	1.67286	−	1.67286i
$819$			22.0740i			0.771329i
$820$	−6.51659	+	22.9413i	−0.227569	+	0.801146i
$821$			23.7758i			0.829780i	0.909872	+	0.414890i	$0.136180\pi$
$821$			23.7758i			0.829780i	−0.909872	+	0.414890i	$0.863820\pi$
$822$	−4.22637	+	4.22637i	−0.147412	+	0.147412i
$823$	−18.5280	+	18.5280i	−0.645845	+	0.645845i	−0.951986	−	0.306141i	$-0.900962\pi$
$823$	−18.5280	+	18.5280i	−0.645845	+	0.645845i	0.306141	+	0.951986i	$0.400962\pi$
$824$	7.29549			0.254150
$825$		0			0
$826$	72.1243			2.50953
$827$	9.29143	−	9.29143i	0.323095	−	0.323095i	−0.526858	−	0.849953i	$-0.676630\pi$
$827$	9.29143	−	9.29143i	0.323095	−	0.323095i	0.849953	+	0.526858i	$0.176630\pi$
$828$	17.3398	−	17.3398i	0.602599	−	0.602599i
$829$		−	8.82301i		−	0.306436i	−0.988192	−	0.153218i	$-0.951036\pi$
$829$		−	8.82301i		−	0.306436i	0.988192	−	0.153218i	$-0.0489636\pi$
$830$	7.66997	−	27.0017i	0.266229	−	0.937244i
$831$		−	0.702366i		−	0.0243648i
$832$	−5.92666	+	5.92666i	−0.205470	+	0.205470i
$833$	14.3713	+	14.3713i	0.497937	+	0.497937i
$834$		−	3.43661i		−	0.119000i
$835$	8.09280	+	14.5145i	0.280063	+	0.502296i
$836$		0			0
$837$	−5.13591	−	5.13591i	−0.177523	−	0.177523i
$838$	−36.1623	−	36.1623i	−1.24920	−	1.24920i
$839$		−	18.8218i		−	0.649800i	−0.945748	−	0.324900i	$-0.894669\pi$
$839$		−	18.8218i		−	0.649800i	0.945748	−	0.324900i	$-0.105331\pi$
$840$	0.846084	+	1.51746i	0.0291927	+	0.0523573i
$841$	−25.6606			−0.884847
$842$	30.8902	−	30.8902i	1.06455	−	1.06455i
$843$	2.00541	+	2.00541i	0.0690701	+	0.0690701i
$844$	6.58761			0.226755
$845$	22.1835	+	6.30132i	0.763134	+	0.216772i
$846$		−	49.0500i		−	1.68637i
$847$		0			0
$848$	−11.9917	+	11.9917i	−0.411798	+	0.411798i
$849$	−2.50258			−0.0858883
$850$	−7.24800	+	11.7287i	−0.248604	+	0.402291i
$851$	−52.0892			−1.78560
$852$	1.95267	+	1.95267i	0.0668972	+	0.0668972i
$853$	22.5284	+	22.5284i	0.771359	+	0.771359i	0.978344	−	0.206985i	$-0.0663652\pi$
$853$	22.5284	+	22.5284i	0.771359	+	0.771359i	−0.206985	+	0.978344i	$0.566365\pi$
$854$	−101.960			−3.48900
$855$	−22.8199	−	6.48211i	−0.780424	−	0.221683i
$856$	2.43896			0.0833618
$857$	−0.301113	+	0.301113i	−0.0102858	+	0.0102858i	−0.712231	−	0.701945i	$-0.752315\pi$
$857$	−0.301113	+	0.301113i	−0.0102858	+	0.0102858i	0.701945	+	0.712231i	$0.252315\pi$
$858$		0			0
$859$		−	38.1928i		−	1.30312i	−0.758596	−	0.651561i	$-0.774114\pi$
$859$		−	38.1928i		−	1.30312i	0.758596	−	0.651561i	$-0.225886\pi$
$860$	−11.6278	−	20.8547i	−0.396506	−	0.711138i
$861$	−7.72270			−0.263189
$862$	−51.9277	−	51.9277i	−1.76866	−	1.76866i
$863$	−27.1564	+	27.1564i	−0.924416	+	0.924416i	−0.997338	−	0.0729217i	$-0.976768\pi$
$863$	−27.1564	+	27.1564i	−0.924416	+	0.924416i	0.0729217	+	0.997338i	$0.476768\pi$
$864$	−11.5616			−0.393335
$865$	−28.5254	+	15.9048i	−0.969893	+	0.540779i
$866$			70.5874i			2.39866i
$867$	2.76565	+	2.76565i	0.0939263	+	0.0939263i
$868$	−25.2398	−	25.2398i	−0.856694	−	0.856694i
$869$		0			0
$870$	−1.97153	−	0.560024i	−0.0668413	−	0.0189866i
$871$			3.61031i			0.122331i
$872$	−0.290780	−	0.290780i	−0.00984706	−	0.00984706i
$873$	10.9581	−	10.9581i	0.370877	−	0.370877i
$874$			34.8479i			1.17875i
$875$	−2.30527	+	51.3121i	−0.0779323	+	1.73467i
$876$		−	3.22857i		−	0.109083i
$877$	−40.1583	+	40.1583i	−1.35605	+	1.35605i	−0.477319	+	0.878730i	$0.658391\pi$
$877$	−40.1583	+	40.1583i	−1.35605	+	1.35605i	−0.878730	+	0.477319i	$0.841609\pi$
$878$	−31.7038	+	31.7038i	−1.06995	+	1.06995i
$879$	−5.16177			−0.174102
$880$		0			0
$881$	−12.0495			−0.405960			−0.202980	−	0.979183i	$-0.565063\pi$
$881$	−12.0495			−0.405960			−0.202980	+	0.979183i	$0.565063\pi$
$882$	−55.9574	+	55.9574i	−1.88418	+	1.88418i
$883$	6.84927	−	6.84927i	0.230496	−	0.230496i	−0.582404	−	0.812900i	$-0.697888\pi$
$883$	6.84927	−	6.84927i	0.230496	−	0.230496i	0.812900	+	0.582404i	$0.197888\pi$
$884$		−	3.92705i		−	0.132081i
$885$	−4.19856	+	2.34098i	−0.141133	+	0.0786910i
$886$			17.5342i			0.589072i
$887$	−15.4365	+	15.4365i	−0.518308	+	0.518308i	−0.917059	−	0.398752i	$-0.869444\pi$
$887$	−15.4365	+	15.4365i	−0.518308	+	0.518308i	0.398752	+	0.917059i	$0.369444\pi$
$888$	1.23820	+	1.23820i	0.0415512	+	0.0415512i
$889$		−	46.7505i		−	1.56796i
$890$	−9.12880	+	5.08991i	−0.305998	+	0.170614i
$891$		0			0
$892$	1.68694	+	1.68694i	0.0564828	+	0.0564828i
$893$	22.3754	+	22.3754i	0.748763	+	0.748763i
$894$		−	11.8864i		−	0.397539i
$895$	20.3711	+	5.78652i	0.680932	+	0.193422i
$896$	23.3809			0.781102
$897$	−1.52820	+	1.52820i	−0.0510251	+	0.0510251i
$898$	8.89528	+	8.89528i	0.296839	+	0.296839i
$899$	−8.53873			−0.284783
$900$	−20.7318	−	12.8117i	−0.691061	−	0.427057i
$901$		−	5.35767i		−	0.178490i
$902$		0			0
$903$	5.46727	−	5.46727i	0.181939	−	0.181939i
$904$	5.05602			0.168161
$905$	13.5858	−	47.8279i	0.451606	−	1.58985i
$906$	−9.67793			−0.321528
$907$	26.3067	+	26.3067i	0.873500	+	0.873500i	0.992852	−	0.119352i	$-0.0380816\pi$
$907$	26.3067	+	26.3067i	0.873500	+	0.873500i	−0.119352	+	0.992852i	$0.538082\pi$
$908$	−13.2869	−	13.2869i	−0.440940	−	0.440940i
$909$	27.1899			0.901831
$910$	−15.6937	−	28.1468i	−0.520241	−	0.933058i
$911$	−41.2301			−1.36601			−0.683007	−	0.730412i	$-0.739328\pi$
$911$	−41.2301			−1.36601			−0.683007	+	0.730412i	$0.739328\pi$
$912$	3.05884	−	3.05884i	0.101288	−	0.101288i
$913$		0			0
$914$		−	19.7754i		−	0.654111i
$915$	5.93538	−	3.30936i	0.196218	−	0.109404i
$916$	1.07985			0.0356794
$917$	−22.9068	−	22.9068i	−0.756448	−	0.756448i
$918$	3.03094	−	3.03094i	0.100036	−	0.100036i
$919$	19.3961			0.639820			0.319910	−	0.947448i	$-0.396347\pi$
$919$	19.3961			0.639820			0.319910	+	0.947448i	$0.396347\pi$
$920$	1.98370	−	6.98352i	0.0654008	−	0.230240i
$921$		−	0.578685i		−	0.0190683i
$922$	11.2971	+	11.2971i	0.372050	+	0.372050i
$923$	7.34475	+	7.34475i	0.241755	+	0.241755i
$924$		0			0
$925$	11.8962	+	50.3830i	0.391144	+	1.65658i
$926$			62.1220i			2.04146i
$927$	−23.4324	−	23.4324i	−0.769620	−	0.769620i
$928$	−9.61093	+	9.61093i	−0.315494	+	0.315494i
$929$			24.6755i			0.809576i	0.914411	+	0.404788i	$0.132655\pi$
$929$			24.6755i			0.809576i	−0.914411	+	0.404788i	$0.867345\pi$
$930$	5.04108	+	1.43194i	0.165304	+	0.0469553i
$931$		−	51.0528i		−	1.67319i
$932$	15.7930	−	15.7930i	0.517316	−	0.517316i
$933$	−4.89286	+	4.89286i	−0.160185	+	0.160185i
$934$	−80.3987			−2.63072
$935$		0			0
$936$	−3.10073			−0.101351
$937$	4.22625	−	4.22625i	0.138066	−	0.138066i	−0.634696	−	0.772762i	$-0.718875\pi$
$937$	4.22625	−	4.22625i	0.138066	−	0.138066i	0.772762	+	0.634696i	$0.218875\pi$
$938$	−13.6938	+	13.6938i	−0.447118	+	0.447118i
$939$		−	4.10160i		−	0.133851i
$940$	15.8311	+	28.3932i	0.516353	+	0.926084i
$941$			21.3027i			0.694447i	0.937782	+	0.347223i	$0.112875\pi$
$941$			21.3027i			0.694447i	−0.937782	+	0.347223i	$0.887125\pi$
$942$	1.96145	−	1.96145i	0.0639074	−	0.0639074i
$943$	22.8181	+	22.8181i	0.743061	+	0.743061i
$944$			37.4113i			1.21763i
$945$	4.36331	−	15.3608i	0.141939	−	0.499687i
$946$		0			0
$947$	31.9748	+	31.9748i	1.03904	+	1.03904i	0.999206	+	0.0398351i	$0.0126833\pi$
$947$	31.9748	+	31.9748i	1.03904	+	1.03904i	0.0398351	+	0.999206i	$0.487317\pi$
$948$	−2.75334	−	2.75334i	−0.0894243	−	0.0894243i
$949$		−	12.1439i		−	0.394209i
$950$	33.7064	−	7.95860i	1.09358	−	0.258211i
$951$	−4.59433			−0.148981
$952$	−3.02053	+	3.02053i	−0.0978958	+	0.0978958i
$953$	−20.2740	−	20.2740i	−0.656739	−	0.656739i	0.297868	−	0.954607i	$-0.403725\pi$
$953$	−20.2740	−	20.2740i	−0.656739	−	0.656739i	−0.954607	+	0.297868i	$0.903725\pi$
$954$	20.8611			0.675402
$955$	−7.43645	+	26.1796i	−0.240638	+	0.847152i
$956$			29.1395i			0.942439i
$957$		0			0
$958$	−10.0944	+	10.0944i	−0.326137	+	0.326137i
$959$	−54.7461			−1.76785
$960$	2.61721	−	1.45926i	0.0844700	−	0.0470976i
$961$	−9.16703			−0.295711
$962$	−22.9669	−	22.9669i	−0.740482	−	0.740482i
$963$	−7.83368	−	7.83368i	−0.252437	−	0.252437i
$964$	−16.2612			−0.523739
$965$	−19.4312	+	10.8342i	−0.625512	+	0.348764i
$966$	−11.5928			−0.372992
$967$	5.92328	−	5.92328i	0.190480	−	0.190480i	−0.605424	−	0.795903i	$-0.706996\pi$
$967$	5.92328	−	5.92328i	0.190480	−	0.190480i	0.795903	+	0.605424i	$0.206996\pi$
$968$		0			0
$969$			1.36663i			0.0439024i
$970$	−6.18206	+	21.7636i	−0.198494	+	0.698788i
$971$	−10.4838			−0.336441			−0.168220	−	0.985749i	$-0.553802\pi$
$971$	−10.4838			−0.336441			−0.168220	+	0.985749i	$0.553802\pi$
$972$	8.06734	+	8.06734i	0.258760	+	0.258760i
$973$	22.2580	−	22.2580i	0.713559	−	0.713559i
$974$	−15.8057			−0.506446
$975$	1.82715	+	1.12913i	0.0585157	+	0.0361610i
$976$		−	52.8871i		−	1.69288i
$977$	5.93052	+	5.93052i	0.189734	+	0.189734i	0.795581	−	0.605847i	$-0.207166\pi$
$977$	5.93052	+	5.93052i	0.189734	+	0.189734i	−0.605847	+	0.795581i	$0.707166\pi$
$978$	−3.56725	−	3.56725i	−0.114068	−	0.114068i
$979$		0			0
$980$	14.3312	−	50.4522i	0.457793	−	1.61164i
$981$			1.86791i			0.0596379i
$982$	−9.05725	−	9.05725i	−0.289029	−	0.289029i
$983$	36.2491	−	36.2491i	1.15617	−	1.15617i	0.170875	−	0.985293i	$-0.445341\pi$
$983$	36.2491	−	36.2491i	1.15617	−	1.15617i	0.985293	−	0.170875i	$-0.0546594\pi$
$984$		−	1.08481i		−	0.0345824i
$985$	−13.8250	−	24.7952i	−0.440501	−	0.790042i
$986$		−	5.03910i		−	0.160478i
$987$	−7.44358	+	7.44358i	−0.236932	+	0.236932i
$988$	−6.97524	+	6.97524i	−0.221912	+	0.221912i
$989$	−32.3081			−1.02734
$990$		0			0
$991$	−23.6127			−0.750084			−0.375042	−	0.927008i	$-0.622372\pi$
$991$	−23.6127			−0.750084			−0.375042	+	0.927008i	$0.622372\pi$
$992$	24.5745	−	24.5745i	0.780241	−	0.780241i
$993$	1.77109	−	1.77109i	0.0562040	−	0.0562040i
$994$			55.7167i			1.76723i
$995$	−27.8531	−	7.91181i	−0.883002	−	0.250821i
$996$		−	2.85836i		−	0.0905705i
$997$	−33.9047	+	33.9047i	−1.07377	+	1.07377i	−0.0767215	+	0.997053i	$0.524445\pi$
$997$	−33.9047	+	33.9047i	−1.07377	+	1.07377i	−0.997053	+	0.0767215i	$0.975555\pi$
$998$	−35.7097	−	35.7097i	−1.13037	−	1.13037i
$999$		−	16.0942i		−	0.509199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.a.362.2	✓	20
5.3	odd	4	inner	605.2.e.a.483.9	yes	20
11.2	odd	10		605.2.m.f.282.2		80
11.3	even	5		605.2.m.f.112.9		80
11.4	even	5		605.2.m.f.457.2		80
11.5	even	5		605.2.m.f.602.9		80
11.6	odd	10		605.2.m.f.602.2		80
11.7	odd	10		605.2.m.f.457.9		80
11.8	odd	10		605.2.m.f.112.2		80
11.9	even	5		605.2.m.f.282.9		80
11.10	odd	2	inner	605.2.e.a.362.9	yes	20
55.3	odd	20		605.2.m.f.233.9		80
55.8	even	20		605.2.m.f.233.2		80
55.13	even	20		605.2.m.f.403.9		80
55.18	even	20		605.2.m.f.578.9		80
55.28	even	20		605.2.m.f.118.9		80
55.38	odd	20		605.2.m.f.118.2		80
55.43	even	4	inner	605.2.e.a.483.2	yes	20
55.48	odd	20		605.2.m.f.578.2		80
55.53	odd	20		605.2.m.f.403.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.2	✓	20	1.1	even	1	trivial
605.2.e.a.362.9	yes	20	11.10	odd	2	inner
605.2.e.a.483.2	yes	20	55.43	even	4	inner
605.2.e.a.483.9	yes	20	5.3	odd	4	inner
605.2.m.f.112.2		80	11.8	odd	10
605.2.m.f.112.9		80	11.3	even	5
605.2.m.f.118.2		80	55.38	odd	20
605.2.m.f.118.9		80	55.28	even	20
605.2.m.f.233.2		80	55.8	even	20
605.2.m.f.233.9		80	55.3	odd	20
605.2.m.f.282.2		80	11.2	odd	10
605.2.m.f.282.9		80	11.9	even	5
605.2.m.f.403.2		80	55.53	odd	20
605.2.m.f.403.9		80	55.13	even	20
605.2.m.f.457.2		80	11.4	even	5
605.2.m.f.457.9		80	11.7	odd	10
605.2.m.f.578.2		80	55.48	odd	20
605.2.m.f.578.9		80	55.18	even	20
605.2.m.f.602.2		80	11.6	odd	10
605.2.m.f.602.9		80	11.5	even	5

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35329 + 1.35329i) q^{2} +(0.185315 - 0.185315i) q^{3} -1.66281i q^{4} +(-0.610994 + 2.15097i) q^{5} +0.501571i q^{6} +(-3.24854 + 3.24854i) q^{7} +(-0.456321 - 0.456321i) q^{8} +2.93132i q^{9} +O(q^{10})\)	\(q+(-1.35329 + 1.35329i) q^{2} +(0.185315 - 0.185315i) q^{3} -1.66281i q^{4} +(-0.610994 + 2.15097i) q^{5} +0.501571i q^{6} +(-3.24854 + 3.24854i) q^{7} +(-0.456321 - 0.456321i) q^{8} +2.93132i q^{9} +(-2.08404 - 3.73775i) q^{10} +(-0.308143 - 0.308143i) q^{12} +(-1.15905 - 1.15905i) q^{13} -8.79245i q^{14} +(0.285381 + 0.511834i) q^{15} +4.56069 q^{16} +(-1.01881 + 1.01881i) q^{17} +(-3.96693 - 3.96693i) q^{18} +3.61923 q^{19} +(3.57665 + 1.01597i) q^{20} +1.20400i q^{21} +(3.55745 - 3.55745i) q^{23} -0.169126 q^{24} +(-4.25337 - 2.62847i) q^{25} +3.13706 q^{26} +(1.09916 + 1.09916i) q^{27} +(5.40169 + 5.40169i) q^{28} +1.82741 q^{29} +(-1.07887 - 0.306457i) q^{30} -4.67258 q^{31} +(-5.25931 + 5.25931i) q^{32} -2.75750i q^{34} +(-5.00268 - 8.97235i) q^{35} +4.87421 q^{36} +(-7.32115 - 7.32115i) q^{37} +(-4.89788 + 4.89788i) q^{38} -0.429577 q^{39} +(1.26035 - 0.702725i) q^{40} +6.41419i q^{41} +(-1.62937 - 1.62937i) q^{42} +(-4.54091 - 4.54091i) q^{43} +(-6.30518 - 1.79102i) q^{45} +9.62855i q^{46} +(6.18236 + 6.18236i) q^{47} +(0.845163 - 0.845163i) q^{48} -14.1060i q^{49} +(9.31315 - 2.19898i) q^{50} +0.377602i q^{51} +(-1.92727 + 1.92727i) q^{52} +(-2.62937 + 2.62937i) q^{53} -2.97497 q^{54} +2.96475 q^{56} +(0.670697 - 0.670697i) q^{57} +(-2.47303 + 2.47303i) q^{58} +8.20299i q^{59} +(0.851080 - 0.474533i) q^{60} -11.5963i q^{61} +(6.32337 - 6.32337i) q^{62} +(-9.52249 - 9.52249i) q^{63} -5.11339i q^{64} +(3.20125 - 1.78491i) q^{65} +(-1.55745 - 1.55745i) q^{67} +(1.69409 + 1.69409i) q^{68} -1.31850i q^{69} +(18.9123 + 5.37213i) q^{70} -6.33689 q^{71} +(1.33762 - 1.33762i) q^{72} +(5.23876 + 5.23876i) q^{73} +19.8153 q^{74} +(-1.27531 + 0.301119i) q^{75} -6.01808i q^{76} +(0.581344 - 0.581344i) q^{78} +8.93527 q^{79} +(-2.78655 + 9.80992i) q^{80} -8.38657 q^{81} +(-8.68028 - 8.68028i) q^{82} +(4.63804 + 4.63804i) q^{83} +2.00203 q^{84} +(-1.56895 - 2.81393i) q^{85} +12.2904 q^{86} +(0.338647 - 0.338647i) q^{87} -2.44232i q^{89} +(10.9565 - 6.10899i) q^{90} +7.53041 q^{91} +(-5.91535 - 5.91535i) q^{92} +(-0.865898 + 0.865898i) q^{93} -16.7331 q^{94} +(-2.21133 + 7.78487i) q^{95} +1.94925i q^{96} +(-3.73830 - 3.73830i) q^{97} +(19.0895 + 19.0895i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^3 + 4 * q^5	\( 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

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