LMFDB - Embedded newform 675.2.r.a.316.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			316.17
Character	$\chi$	$=$	675.316
Dual form			675.2.r.a.361.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.808045 - 0.359765i) q^{2} +(-0.814755 + 0.904878i) q^{4} +(-1.09577 - 1.94918i) q^{5} +(-0.458035 + 0.793340i) q^{7} +(-0.879476 + 2.70675i) q^{8} +O(q^{10})$	\(q+(0.808045 - 0.359765i) q^{2} +(-0.814755 + 0.904878i) q^{4} +(-1.09577 - 1.94918i) q^{5} +(-0.458035 + 0.793340i) q^{7} +(-0.879476 + 2.70675i) q^{8} +(-1.58668 - 1.18080i) q^{10} +(-1.33506 + 0.594408i) q^{11} +(-1.67311 - 0.744918i) q^{13} +(-0.0846971 + 0.805839i) q^{14} +(0.00858220 + 0.0816542i) q^{16} +(-1.50326 + 4.62656i) q^{17} +(-2.04373 + 6.28996i) q^{19} +(2.65655 + 0.596562i) q^{20} +(-0.864943 + 0.960617i) q^{22} +(0.0683526 - 0.650331i) q^{23} +(-2.59857 + 4.27170i) q^{25} -1.61995 q^{26} +(-0.344689 - 1.06084i) q^{28} +(-6.29829 - 1.33874i) q^{29} +(2.87587 - 0.611285i) q^{31} +(-2.80973 - 4.86660i) q^{32} +(0.449771 + 4.27929i) q^{34} +(2.04826 + 0.0234710i) q^{35} +(-4.86137 + 3.53200i) q^{37} +(0.611478 + 5.81783i) q^{38} +(6.23963 - 1.25173i) q^{40} +(-2.26096 - 1.00664i) q^{41} +(2.01308 - 3.48676i) q^{43} +(0.549883 - 1.69237i) q^{44} +(-0.178734 - 0.550087i) q^{46} +(-5.26308 - 1.11870i) q^{47} +(3.08041 + 5.33542i) q^{49} +(-0.562952 + 4.38660i) q^{50} +(2.03724 - 0.907036i) q^{52} +(3.46201 + 10.6550i) q^{53} +(2.62153 + 1.95093i) q^{55} +(-1.74454 - 1.93751i) q^{56} +(-5.57093 + 1.18414i) q^{58} +(-1.82813 - 0.813937i) q^{59} +(11.5472 - 5.14113i) q^{61} +(2.10391 - 1.52858i) q^{62} +(-4.15407 - 3.01811i) q^{64} +(0.381374 + 4.07745i) q^{65} +(8.34092 - 1.77292i) q^{67} +(-2.96168 - 5.12978i) q^{68} +(1.66353 - 0.717926i) q^{70} +(-5.09668 - 15.6860i) q^{71} +(-2.01962 - 1.46734i) q^{73} +(-2.65752 + 4.60296i) q^{74} +(-4.02650 - 6.97410i) q^{76} +(0.139938 - 1.33142i) q^{77} +(-6.05809 - 1.28769i) q^{79} +(0.149754 - 0.106203i) q^{80} -2.18911 q^{82} +(-2.67975 - 2.97617i) q^{83} +(10.6652 - 2.13954i) q^{85} +(0.372247 - 3.54169i) q^{86} +(-0.434758 - 4.13645i) q^{88} +(11.4149 + 8.29340i) q^{89} +(1.35732 - 0.986149i) q^{91} +(0.532779 + 0.591712i) q^{92} +(-4.65527 + 0.989508i) q^{94} +(14.4997 - 2.90877i) q^{95} +(-5.89193 - 1.25237i) q^{97} +(4.40860 + 3.20304i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.808045	−	0.359765i	0.571374	−	0.254392i	−0.100649	−	0.994922i	$-0.532092\pi$
$2$	0.808045	−	0.359765i	0.571374	−	0.254392i	0.672023	+	0.740530i	$0.265425\pi$
$3$		0			0
$3$		0			0
$4$	−0.814755	+	0.904878i	−0.407378	+	0.452439i
$5$	−1.09577	−	1.94918i	−0.490044	−	0.871698i
$5$	−1.09577	−	1.94918i	−0.490044	−	0.871698i
$6$		0			0
$7$	−0.458035	+	0.793340i	−0.173121	+	0.299854i	−0.939509	−	0.342523i	$-0.888718\pi$
$7$	−0.458035	+	0.793340i	−0.173121	+	0.299854i	0.766388	+	0.642377i	$0.222052\pi$
$8$	−0.879476	+	2.70675i	−0.310942	+	0.956981i
$9$		0			0
$10$	−1.58668	−	1.18080i	−0.501751	−	0.373402i
$11$	−1.33506	+	0.594408i	−0.402536	+	0.179221i	−0.598011	−	0.801488i	$-0.704042\pi$
$11$	−1.33506	+	0.594408i	−0.402536	+	0.179221i	0.195474	+	0.980709i	$0.437375\pi$
$12$		0			0
$13$	−1.67311	−	0.744918i	−0.464038	−	0.206603i	0.161381	−	0.986892i	$-0.448405\pi$
$13$	−1.67311	−	0.744918i	−0.464038	−	0.206603i	−0.625419	+	0.780289i	$0.715072\pi$
$14$	−0.0846971	+	0.805839i	−0.0226362	+	0.215370i
$15$		0			0
$16$	0.00858220	+	0.0816542i	0.00214555	+	0.0204135i
$17$	−1.50326	+	4.62656i	−0.364594	+	1.12211i	0.585641	+	0.810571i	$0.300843\pi$
$17$	−1.50326	+	4.62656i	−0.364594	+	1.12211i	−0.950235	+	0.311535i	$0.899157\pi$
$18$		0			0
$19$	−2.04373	+	6.28996i	−0.468864	+	1.44301i	0.385193	+	0.922836i	$0.374135\pi$
$19$	−2.04373	+	6.28996i	−0.468864	+	1.44301i	−0.854057	+	0.520179i	$0.825865\pi$
$20$	2.65655	+	0.596562i	0.594023	+	0.133395i
$21$		0			0
$22$	−0.864943	+	0.960617i	−0.184406	+	0.204804i
$23$	0.0683526	−	0.650331i	0.0142525	−	0.135603i	−0.985082	−	0.172087i	$-0.944949\pi$
$23$	0.0683526	−	0.650331i	0.0142525	−	0.135603i	0.999334	+	0.0364836i	$0.0116157\pi$
$24$		0			0
$25$	−2.59857	+	4.27170i	−0.519714	+	0.854341i
$26$	−1.61995			−0.317697
$27$		0			0
$28$	−0.344689	−	1.06084i	−0.0651401	−	0.200481i
$29$	−6.29829	−	1.33874i	−1.16956	−	0.248598i	−0.418117	−	0.908393i	$-0.637310\pi$
$29$	−6.29829	−	1.33874i	−1.16956	−	0.248598i	−0.751446	+	0.659795i	$0.770643\pi$
$30$		0			0
$31$	2.87587	−	0.611285i	0.516521	−	0.109790i	0.0577267	−	0.998332i	$-0.481615\pi$
$31$	2.87587	−	0.611285i	0.516521	−	0.109790i	0.458794	+	0.888542i	$0.348281\pi$
$32$	−2.80973	−	4.86660i	−0.496695	−	0.860302i
$33$		0			0
$34$	0.449771	+	4.27929i	0.0771351	+	0.733892i
$35$	2.04826	+	0.0234710i	0.346219	+	0.00396732i
$36$		0			0
$37$	−4.86137	+	3.53200i	−0.799205	+	0.580656i	−0.910681	−	0.413111i	$-0.864442\pi$
$37$	−4.86137	+	3.53200i	−0.799205	+	0.580656i	0.111476	+	0.993767i	$0.464442\pi$
$38$	0.611478	+	5.81783i	0.0991949	+	0.943776i
$39$		0			0
$40$	6.23963	−	1.25173i	0.986573	−	0.197915i
$41$	−2.26096	−	1.00664i	−0.353103	−	0.157212i	0.222517	−	0.974929i	$-0.428573\pi$
$41$	−2.26096	−	1.00664i	−0.353103	−	0.157212i	−0.575620	+	0.817717i	$0.695239\pi$
$42$		0			0
$43$	2.01308	−	3.48676i	0.306992	−	0.531725i	−0.670711	−	0.741719i	$-0.734011\pi$
$43$	2.01308	−	3.48676i	0.306992	−	0.531725i	0.977703	+	0.209993i	$0.0673443\pi$
$44$	0.549883	−	1.69237i	0.0828980	−	0.255134i
$45$		0			0
$46$	−0.178734	−	0.550087i	−0.0263529	−	0.0811060i
$47$	−5.26308	−	1.11870i	−0.767699	−	0.163179i	−0.192615	−	0.981274i	$-0.561697\pi$
$47$	−5.26308	−	1.11870i	−0.767699	−	0.163179i	−0.575083	+	0.818095i	$0.695030\pi$
$48$		0			0
$49$	3.08041	+	5.33542i	0.440058	+	0.762203i
$50$	−0.562952	+	4.38660i	−0.0796134	+	0.620359i
$51$		0			0
$52$	2.03724	−	0.907036i	0.282514	−	0.125783i
$53$	3.46201	+	10.6550i	0.475543	+	1.46357i	0.845223	+	0.534413i	$0.179467\pi$
$53$	3.46201	+	10.6550i	0.475543	+	1.46357i	−0.369680	+	0.929159i	$0.620533\pi$
$54$		0			0
$55$	2.62153	+	1.95093i	0.353487	+	0.263064i
$56$	−1.74454	−	1.93751i	−0.233124	−	0.258911i
$57$		0			0
$58$	−5.57093	+	1.18414i	−0.731499	+	0.155485i
$59$	−1.82813	−	0.813937i	−0.238003	−	0.105966i	0.284270	−	0.958744i	$-0.408249\pi$
$59$	−1.82813	−	0.813937i	−0.238003	−	0.105966i	−0.522272	+	0.852779i	$0.674916\pi$
$60$		0			0
$61$	11.5472	−	5.14113i	1.47846	−	0.658254i	0.500255	−	0.865878i	$-0.333240\pi$
$61$	11.5472	−	5.14113i	1.47846	−	0.658254i	0.978209	+	0.207624i	$0.0665730\pi$
$62$	2.10391	−	1.52858i	0.267197	−	0.194130i
$63$		0			0
$64$	−4.15407	−	3.01811i	−0.519259	−	0.377264i
$65$	0.381374	+	4.07745i	0.0473037	+	0.505745i
$66$		0			0
$67$	8.34092	−	1.77292i	1.01901	−	0.216596i	0.332024	−	0.943271i	$-0.392269\pi$
$67$	8.34092	−	1.77292i	1.01901	−	0.216596i	0.686982	+	0.726675i	$0.258935\pi$
$68$	−2.96168	−	5.12978i	−0.359156	−	0.622077i
$69$		0			0
$70$	1.66353	−	0.717926i	0.198830	−	0.0858086i
$71$	−5.09668	−	15.6860i	−0.604865	−	1.86158i	−0.497717	−	0.867340i	$-0.665828\pi$
$71$	−5.09668	−	15.6860i	−0.604865	−	1.86158i	−0.107148	−	0.994243i	$-0.534172\pi$
$72$		0			0
$73$	−2.01962	−	1.46734i	−0.236378	−	0.171739i	0.463290	−	0.886207i	$-0.346669\pi$
$73$	−2.01962	−	1.46734i	−0.236378	−	0.171739i	−0.699668	+	0.714468i	$0.746669\pi$
$74$	−2.65752	+	4.60296i	−0.308931	+	0.535083i
$75$		0			0
$76$	−4.02650	−	6.97410i	−0.461871	−	0.799984i
$77$	0.139938	−	1.33142i	0.0159474	−	0.151729i
$78$		0			0
$79$	−6.05809	−	1.28769i	−0.681589	−	0.144876i	−0.145910	−	0.989298i	$-0.546611\pi$
$79$	−6.05809	−	1.28769i	−0.681589	−	0.144876i	−0.535679	+	0.844422i	$0.679944\pi$
$80$	0.149754	−	0.106203i	0.0167430	−	0.0118738i
$81$		0			0
$82$	−2.18911			−0.241747
$83$	−2.67975	−	2.97617i	−0.294141	−	0.326677i	0.577902	−	0.816106i	$-0.303872\pi$
$83$	−2.67975	−	2.97617i	−0.294141	−	0.326677i	−0.872043	+	0.489430i	$0.837205\pi$
$84$		0			0
$85$	10.6652	−	2.13954i	1.15680	−	0.232065i
$86$	0.372247	−	3.54169i	0.0401404	−	0.381910i
$87$		0			0
$88$	−0.434758	−	4.13645i	−0.0463454	−	0.440947i
$89$	11.4149	+	8.29340i	1.20998	+	0.879098i	0.995229	−	0.0975715i	$-0.0311075\pi$
$89$	11.4149	+	8.29340i	1.20998	+	0.879098i	0.214746	+	0.976670i	$0.431107\pi$
$90$		0			0
$91$	1.35732	−	0.986149i	0.142285	−	0.103376i
$92$	0.532779	+	0.591712i	0.0555461	+	0.0616902i
$93$		0			0
$94$	−4.65527	+	0.989508i	−0.480155	+	0.102060i
$95$	14.4997	−	2.90877i	1.48764	−	0.298433i
$96$		0			0
$97$	−5.89193	−	1.25237i	−0.598235	−	0.127159i	−0.101166	−	0.994870i	$-0.532257\pi$
$97$	−5.89193	−	1.25237i	−0.598235	−	0.127159i	−0.497069	+	0.867711i	$0.665591\pi$
$98$	4.40860	+	3.20304i	0.445336	+	0.323556i
$99$		0			0
$100$	−1.74817	−	5.83178i	−0.174817	−	0.583178i
$101$	1.94183	−	3.36335i	0.193219	−	0.334666i	−0.753096	−	0.657911i	$-0.771440\pi$
$101$	1.94183	−	3.36335i	0.193219	−	0.334666i	0.946315	+	0.323245i	$0.104774\pi$
$102$		0			0
$103$	−8.86425	+	9.84474i	−0.873420	+	0.970031i	−0.999759	−	0.0219558i	$-0.993011\pi$
$103$	−8.86425	+	9.84474i	−0.873420	+	0.970031i	0.126339	+	0.991987i	$0.459677\pi$
$104$	3.48777	−	3.87356i	0.342004	−	0.379834i
$105$		0			0
$106$	6.63074	+	7.36418i	0.644034	+	0.715273i
$107$	−0.575014			−0.0555887			−0.0277944	−	0.999614i	$-0.508848\pi$
$107$	−0.575014			−0.0555887			−0.0277944	+	0.999614i	$0.508848\pi$
$108$		0			0
$109$	10.4238	−	7.57330i	0.998415	−	0.725391i	0.0366673	−	0.999328i	$-0.488326\pi$
$109$	10.4238	−	7.57330i	0.998415	−	0.725391i	0.961748	+	0.273936i	$0.0883258\pi$
$110$	2.82019	+	0.633309i	0.268895	+	0.0603836i
$111$		0			0
$112$	−0.0687104	−	0.0305919i	−0.00649253	−	0.00289066i
$113$	−6.68184	−	2.97495i	−0.628575	−	0.279859i	0.0676216	−	0.997711i	$-0.478459\pi$
$113$	−6.68184	−	2.97495i	−0.628575	−	0.279859i	−0.696196	+	0.717852i	$0.745126\pi$
$114$		0			0
$115$	−1.34251	+	0.579383i	−0.125190	+	0.0540278i
$116$	6.34297	−	4.60843i	0.588930	−	0.427882i
$117$		0			0
$118$	−1.77004			−0.162945
$119$	−2.98189	−	3.31172i	−0.273349	−	0.303585i
$120$		0			0
$121$	−5.93137	+	6.58745i	−0.539215	+	0.598859i
$122$	7.48103	−	8.30853i	0.677301	−	0.752219i
$123$		0			0
$124$	−1.78999	+	3.10036i	−0.160746	+	0.278420i
$125$	11.1737	+	0.384254i	0.999409	+	0.0343687i
$126$		0			0
$127$	8.89523	+	6.46276i	0.789324	+	0.573477i	0.907763	−	0.419484i	$-0.137789\pi$
$127$	8.89523	+	6.46276i	0.789324	+	0.573477i	−0.118439	+	0.992961i	$0.537789\pi$
$128$	6.55086	+	1.39243i	0.579019	+	0.123074i
$129$		0			0
$130$	1.77509	+	3.15756i	0.155686	+	0.276936i
$131$	9.44760	−	2.00815i	0.825441	−	0.175453i	0.224223	−	0.974538i	$-0.428016\pi$
$131$	9.44760	−	2.00815i	0.825441	−	0.175453i	0.601218	+	0.799085i	$0.294682\pi$
$132$		0			0
$133$	−4.05397	−	4.50239i	−0.351524	−	0.390407i
$134$	6.10200	−	4.43336i	0.527133	−	0.382984i
$135$		0			0
$136$	−11.2009	−	8.13790i	−0.960465	−	0.697819i
$137$	2.04237	+	19.4319i	0.174492	+	1.66018i	0.634992	+	0.772518i	$0.281003\pi$
$137$	2.04237	+	19.4319i	0.174492	+	1.66018i	−0.460501	+	0.887659i	$0.652330\pi$
$138$		0			0
$139$	−1.68243	+	16.0073i	−0.142702	+	1.35772i	0.655438	+	0.755249i	$0.272484\pi$
$139$	−1.68243	+	16.0073i	−0.142702	+	1.35772i	−0.798140	+	0.602472i	$0.794183\pi$
$140$	−1.69007	+	1.83430i	−0.142837	+	0.155027i
$141$		0			0
$142$	−9.76161	−	10.8414i	−0.819176	−	0.909787i
$143$	2.67649			0.223820
$144$		0			0
$145$	4.29204	+	13.7434i	0.356435	+	1.14133i
$146$	−2.15984	−	0.459087i	−0.178749	−	0.0379943i
$147$		0			0
$148$	0.764808	−	7.27666i	0.0628668	−	0.598138i
$149$	5.73913	+	9.94047i	0.470168	+	0.814355i	0.999418	−	0.0341109i	$-0.0108599\pi$
$149$	5.73913	+	9.94047i	0.470168	+	0.814355i	−0.529250	+	0.848466i	$0.677527\pi$
$150$		0			0
$151$	7.22503	−	12.5141i	0.587964	−	1.01838i	−0.406534	−	0.913636i	$-0.633263\pi$
$151$	7.22503	−	12.5141i	0.587964	−	1.01838i	0.994499	−	0.104749i	$-0.0334038\pi$
$152$	−15.2279	−	11.0637i	−1.23515	−	0.897387i
$153$		0			0
$154$	−0.365921	−	1.12619i	−0.0294868	−	0.0907510i
$155$	−4.34280	−	4.93574i	−0.348822	−	0.396448i
$156$		0			0
$157$	−11.2855	−	19.5471i	−0.900683	−	1.56003i	−0.826610	−	0.562776i	$-0.809733\pi$
$157$	−11.2855	−	19.5471i	−0.900683	−	1.56003i	−0.0740732	−	0.997253i	$-0.523600\pi$
$158$	−5.35848	+	1.13898i	−0.426298	+	0.0906123i
$159$		0			0
$160$	−6.40703	+	10.8093i	−0.506520	+	0.854554i
$161$	0.484626	+	0.352101i	0.0381939	+	0.0277495i
$162$		0			0
$163$	13.3225	−	9.67938i	1.04350	−	0.758148i	0.0725352	−	0.997366i	$-0.476891\pi$
$163$	13.3225	−	9.67938i	1.04350	−	0.758148i	0.970966	+	0.239218i	$0.0768910\pi$
$164$	2.75302	−	1.22572i	0.214975	−	0.0957130i
$165$		0			0
$166$	−3.23608	−	1.44080i	−0.251168	−	0.111827i
$167$	−20.1378	+	4.28042i	−1.55831	+	0.331229i	−0.904850	−	0.425731i	$-0.860017\pi$
$167$	−20.1378	+	4.28042i	−1.55831	+	0.331229i	−0.653461	+	0.756960i	$0.726684\pi$
$168$		0			0
$169$	−6.45429	−	7.16822i	−0.496484	−	0.551402i
$170$	7.84823	−	5.56580i	0.601932	−	0.426878i
$171$		0			0
$172$	1.51492	+	4.66244i	0.115512	+	0.355508i
$173$	−20.0490	+	8.92638i	−1.52430	+	0.678660i	−0.986402	−	0.164352i	$-0.947447\pi$
$173$	−20.0490	+	8.92638i	−1.52430	+	0.678660i	−0.537894	+	0.843012i	$0.680780\pi$
$174$		0			0
$175$	−2.19868	−	4.01814i	−0.166204	−	0.303743i
$176$	−0.0599937	−	0.103912i	−0.00452219	−	0.00783267i
$177$		0			0
$178$	12.2074	+	2.59476i	0.914984	+	0.194486i
$179$	3.58817	+	11.0432i	0.268192	+	0.825410i	0.990941	+	0.134299i	$0.0428784\pi$
$179$	3.58817	+	11.0432i	0.268192	+	0.825410i	−0.722749	+	0.691111i	$0.757122\pi$
$180$		0			0
$181$	4.13289	−	12.7197i	0.307196	−	0.945451i	−0.671653	−	0.740866i	$-0.734415\pi$
$181$	4.13289	−	12.7197i	0.307196	−	0.945451i	0.978849	−	0.204585i	$-0.0655845\pi$
$182$	0.741991	−	1.28517i	0.0550001	−	0.0952629i
$183$		0			0
$184$	1.70017	+	0.756964i	0.125338	+	0.0558041i
$185$	12.2114	+	5.60541i	0.897803	+	0.412118i
$186$		0			0
$187$	−0.743118	−	7.07029i	−0.0543422	−	0.517031i
$188$	5.30041	−	3.85097i	0.386572	−	0.280861i
$189$		0			0
$190$	10.6699	−	7.56689i	0.774078	−	0.548960i
$191$	0.737405	+	7.01594i	0.0533568	+	0.507656i	0.988263	+	0.152761i	$0.0488166\pi$
$191$	0.737405	+	7.01594i	0.0533568	+	0.507656i	−0.934906	+	0.354895i	$0.884517\pi$
$192$		0			0
$193$	−2.80358	−	4.85594i	−0.201806	−	0.349538i	0.747304	−	0.664482i	$-0.231348\pi$
$193$	−2.80358	−	4.85594i	−0.201806	−	0.349538i	−0.949110	+	0.314944i	$0.898014\pi$
$194$	−5.21151	+	1.10774i	−0.374164	+	0.0795311i
$195$		0			0
$196$	−7.33768	−	1.55967i	−0.524120	−	0.111405i
$197$	−0.644829	−	1.98458i	−0.0459422	−	0.141395i	0.925454	−	0.378860i	$-0.123684\pi$
$197$	−0.644829	−	1.98458i	−0.0459422	−	0.141395i	−0.971396	+	0.237464i	$0.923684\pi$
$198$		0			0
$199$	3.06579			0.217328			0.108664	−	0.994079i	$-0.465343\pi$
$199$	3.06579			0.217328			0.108664	+	0.994079i	$0.465343\pi$
$200$	−9.27705	−	10.7905i	−0.655987	−	0.763006i
$201$		0			0
$202$	0.359072	−	3.41634i	0.0252642	−	0.240373i
$203$	3.94692	−	4.38349i	0.277019	−	0.307661i
$204$		0			0
$205$	0.515371	+	5.51006i	0.0359950	+	0.384840i
$206$	−3.62092	+	11.1440i	−0.252281	+	0.776442i
$207$		0			0
$208$	0.0464667	−	0.143010i	0.00322188	−	0.00991594i
$209$	−1.01029	−	9.61229i	−0.0698834	−	0.664896i
$210$		0			0
$211$	0.214854	−	2.04420i	0.0147911	−	0.140728i	−0.984634	−	0.174631i	$-0.944127\pi$
$211$	0.214854	−	2.04420i	0.0147911	−	0.140728i	0.999425	+	0.0339024i	$0.0107935\pi$
$212$	−12.4621	−	5.54850i	−0.855903	−	0.381072i
$213$		0			0
$214$	−0.464637	+	0.206870i	−0.0317619	+	0.0141413i
$215$	−9.00217	−	0.103156i	−0.613943	−	0.00703517i
$216$		0			0
$217$	−0.832292	+	2.56153i	−0.0564996	+	0.173888i
$218$	5.69826	−	9.86967i	0.385935	−	0.668458i
$219$		0			0
$220$	−3.90126	+	0.782628i	−0.263023	+	0.0527648i
$221$	5.96153	−	6.62095i	0.401016	−	0.445373i
$222$		0			0
$223$	−20.7361	+	9.23232i	−1.38859	+	0.618242i	−0.958643	−	0.284611i	$-0.908136\pi$
$223$	−20.7361	+	9.23232i	−1.38859	+	0.618242i	−0.429950	+	0.902852i	$0.641469\pi$
$224$	5.14783			0.343954
$225$		0			0
$226$	−6.46951			−0.430345
$227$	−6.01094	+	2.67624i	−0.398960	+	0.177628i	−0.596401	−	0.802686i	$-0.703403\pi$
$227$	−6.01094	+	2.67624i	−0.398960	+	0.177628i	0.197442	+	0.980315i	$0.436737\pi$
$228$		0			0
$229$	4.35897	−	4.84112i	0.288049	−	0.319910i	−0.581702	−	0.813402i	$-0.697613\pi$
$229$	4.35897	−	4.84112i	0.288049	−	0.319910i	0.869751	+	0.493492i	$0.164280\pi$
$230$	−0.876365	+	0.951155i	−0.0577858	+	0.0627173i
$231$		0			0
$232$	9.16284	−	15.8705i	0.601570	−	1.04195i
$233$	−1.15048	+	3.54081i	−0.0753703	+	0.231966i	−0.981643	−	0.190727i	$-0.938915\pi$
$233$	−1.15048	+	3.54081i	−0.0753703	+	0.231966i	0.906273	+	0.422694i	$0.138915\pi$
$234$		0			0
$235$	3.58659	+	11.4845i	0.233963	+	0.749166i
$236$	2.22599	−	0.991077i	0.144900	−	0.0645136i
$237$		0			0
$238$	−3.60094	−	1.60324i	−0.233414	−	0.103923i
$239$	−0.596567	+	5.67596i	−0.0385887	+	0.367147i	0.958138	+	0.286306i	$0.0924273\pi$
$239$	−0.596567	+	5.67596i	−0.0385887	+	0.367147i	−0.996727	+	0.0808412i	$0.974239\pi$
$240$		0			0
$241$	3.12340	+	29.7171i	0.201196	+	1.91425i	0.370759	+	0.928729i	$0.379098\pi$
$241$	3.12340	+	29.7171i	0.201196	+	1.91425i	−0.169563	+	0.985519i	$0.554236\pi$
$242$	−2.42288	+	7.45685i	−0.155748	+	0.479345i
$243$		0			0
$244$	−4.75602	+	14.6375i	−0.304473	+	0.937072i
$245$	7.02425	−	11.8507i	0.448763	−	0.757111i
$246$		0			0
$247$	8.10489	−	9.00139i	0.515702	−	0.572745i
$248$	−0.874663	+	8.32186i	−0.0555412	+	0.528439i
$249$		0			0
$250$	9.16712	−	3.70942i	0.579780	−	0.234604i
$251$	4.00907			0.253050			0.126525	−	0.991963i	$-0.459618\pi$
$251$	4.00907			0.253050			0.126525	+	0.991963i	$0.459618\pi$
$252$		0			0
$253$	0.295307	+	0.908862i	0.0185658	+	0.0571397i
$254$	9.51282	+	2.02201i	0.596887	+	0.126872i
$255$		0			0
$256$	15.8393	−	3.36676i	0.989959	−	0.210422i
$257$	5.23224	+	9.06250i	0.326378	+	0.565303i	0.981790	−	0.189968i	$-0.0608384\pi$
$257$	5.23224	+	9.06250i	0.326378	+	0.565303i	−0.655412	+	0.755271i	$0.727505\pi$
$258$		0			0
$259$	−0.575393	−	5.47450i	−0.0357532	−	0.340169i
$260$	−4.00032	−	2.97703i	−0.248089	−	0.184627i
$261$		0			0
$262$	6.91162	−	5.02159i	0.427001	−	0.310235i
$263$	−1.04740	−	9.96535i	−0.0645855	−	0.614490i	−0.978165	−	0.207830i	$-0.933360\pi$
$263$	−1.04740	−	9.96535i	−0.0645855	−	0.614490i	0.913580	−	0.406660i	$-0.133307\pi$
$264$		0			0
$265$	16.9748	−	18.4235i	1.04276	−	1.13175i
$266$	−4.89559	−	2.17966i	−0.300168	−	0.133643i
$267$		0			0
$268$	−5.19154	+	8.99200i	−0.317124	+	0.549274i
$269$	−6.60992	+	20.3433i	−0.403014	+	1.24035i	0.519528	+	0.854453i	$0.326108\pi$
$269$	−6.60992	+	20.3433i	−0.403014	+	1.24035i	−0.922542	+	0.385896i	$0.873892\pi$
$270$		0			0
$271$	2.51483	+	7.73984i	0.152765	+	0.470162i	0.997928	−	0.0643473i	$-0.0204965\pi$
$271$	2.51483	+	7.73984i	0.152765	+	0.470162i	−0.845163	+	0.534509i	$0.820497\pi$
$272$	−0.390679	−	0.0830414i	−0.0236884	−	0.00503512i
$273$		0			0
$274$	8.64124	+	14.9671i	0.522036	+	0.904193i
$275$	0.930116	−	7.24760i	0.0560881	−	0.437047i
$276$		0			0
$277$	0.0811277	−	0.0361204i	0.00487449	−	0.00217026i	−0.404298	−	0.914627i	$-0.632484\pi$
$277$	0.0811277	−	0.0361204i	0.00487449	−	0.00217026i	0.409172	+	0.912457i	$0.365817\pi$
$278$	4.39938	+	13.5399i	0.263857	+	0.812069i
$279$		0			0
$280$	−1.86493	+	5.52349i	−0.111451	+	0.330091i
$281$	13.6010	+	15.1054i	0.811365	+	0.901112i	0.996668	−	0.0815694i	$-0.0259932\pi$
$281$	13.6010	+	15.1054i	0.811365	+	0.901112i	−0.185303	+	0.982681i	$0.559327\pi$
$282$		0			0
$283$	−27.2002	+	5.78158i	−1.61688	+	0.343679i	−0.925482	−	0.378791i	$-0.876340\pi$
$283$	−27.2002	+	5.78158i	−1.61688	+	0.343679i	−0.691402	+	0.722471i	$0.743007\pi$
$284$	18.3464	+	8.16836i	1.08866	+	0.484703i
$285$		0			0
$286$	2.16273	−	0.962908i	0.127885	−	0.0569380i
$287$	1.83421	−	1.33263i	0.108270	−	0.0786628i
$288$		0			0
$289$	−5.39197	−	3.91749i	−0.317174	−	0.230441i
$290$	8.41257	+	9.56118i	0.494003	+	0.561452i
$291$		0			0
$292$	2.97325	−	0.631985i	0.173997	−	0.0369841i
$293$	5.17974	+	8.97157i	0.302604	+	0.524125i	0.976725	−	0.214496i	$-0.0688108\pi$
$293$	5.17974	+	8.97157i	0.302604	+	0.524125i	−0.674121	+	0.738621i	$0.735477\pi$
$294$		0			0
$295$	0.416710	+	4.45524i	0.0242618	+	0.259394i
$296$	−5.28476	−	16.2648i	−0.307171	−	0.945374i
$297$		0			0
$298$	8.21371	+	5.96761i	0.475807	+	0.345694i
$299$	−0.598805	+	1.03716i	−0.0346298	+	0.0599805i
$300$		0			0
$301$	1.84412	+	3.19411i	0.106293	+	0.184106i
$302$	1.33601	−	12.7113i	0.0768787	−	0.731452i
$303$		0			0
$304$	−0.531141	−	0.112897i	−0.0304630	−	0.00647511i
$305$	−22.6740	−	16.8739i	−1.29831	−	0.966200i
$306$		0			0
$307$	−26.4065			−1.50710			−0.753550	−	0.657391i	$-0.771660\pi$
$307$	−26.4065			−1.50710			−0.753550	+	0.657391i	$0.771660\pi$
$308$	1.09076	+	1.21141i	0.0621515	+	0.0690263i
$309$		0			0
$310$	−5.28488	−	2.42592i	−0.300161	−	0.137783i
$311$	−0.852094	+	8.10713i	−0.0483178	+	0.459713i	0.943436	+	0.331555i	$0.107573\pi$
$311$	−0.852094	+	8.10713i	−0.0483178	+	0.459713i	−0.991754	+	0.128158i	$0.959093\pi$
$312$		0			0
$313$	3.04832	+	29.0029i	0.172301	+	1.63934i	0.649370	+	0.760472i	$0.275032\pi$
$313$	3.04832	+	29.0029i	0.172301	+	1.63934i	−0.477069	+	0.878866i	$0.658301\pi$
$314$	−16.1516	−	11.7348i	−0.911486	−	0.662233i
$315$		0			0
$316$	6.10107	−	4.43268i	0.343212	−	0.249358i
$317$	7.21022	+	8.00776i	0.404966	+	0.449761i	0.910786	−	0.412878i	$-0.135477\pi$
$317$	7.21022	+	8.00776i	0.404966	+	0.449761i	−0.505820	+	0.862639i	$0.668810\pi$
$318$		0			0
$319$	9.20437	−	1.95645i	0.515346	−	0.109540i
$320$	−1.33091	+	11.4042i	−0.0744001	+	0.637512i
$321$		0			0
$322$	0.518273	+	0.110162i	0.0288822	+	0.00613910i
$323$	−26.0286	−	18.9109i	−1.44827	−	1.05223i
$324$		0			0
$325$	7.52976	−	5.21132i	0.417676	−	0.289072i
$326$	7.28290	−	12.6144i	0.403362	−	0.698644i
$327$		0			0
$328$	4.71320	−	5.23454i	0.260243	−	0.289029i
$329$	3.29818	−	3.66300i	0.181835	−	0.201948i
$330$		0			0
$331$	10.0456	+	11.1567i	0.552154	+	0.613229i	0.953020	−	0.302908i	$-0.0979574\pi$
$331$	10.0456	+	11.1567i	0.552154	+	0.613229i	−0.400866	+	0.916137i	$0.631291\pi$
$332$	4.87641			0.267628
$333$		0			0
$334$	−14.7323	+	10.7036i	−0.806116	+	0.585678i
$335$	−12.5955	−	14.3152i	−0.688164	−	0.782123i
$336$		0			0
$337$	1.21087	+	0.539114i	0.0659603	+	0.0293674i	0.439452	−	0.898266i	$-0.355173\pi$
$337$	1.21087	+	0.539114i	0.0659603	+	0.0293674i	−0.373491	+	0.927634i	$0.621839\pi$
$338$	−7.79423	−	3.47022i	−0.423950	−	0.188755i
$339$		0			0
$340$	−6.75352	+	11.3939i	−0.366261	+	0.617921i
$341$	−3.47611	+	2.52554i	−0.188242	+	0.136766i
$342$		0			0
$343$	−12.0562			−0.650975
$344$	7.66732	+	8.51542i	0.413394	+	0.459121i
$345$		0			0
$346$	−12.9891	+	14.4258i	−0.698297	+	0.775538i
$347$	5.31615	−	5.90418i	0.285386	−	0.316953i	−0.583358	−	0.812215i	$-0.698261\pi$
$347$	5.31615	−	5.90418i	0.285386	−	0.316953i	0.868743	+	0.495262i	$0.164928\pi$
$348$		0			0
$349$	6.48550	−	11.2332i	0.347161	−	0.601300i	−0.638583	−	0.769553i	$-0.720479\pi$
$349$	6.48550	−	11.2332i	0.347161	−	0.601300i	0.985744	+	0.168253i	$0.0538124\pi$
$350$	−3.22221	−	2.45583i	−0.172235	−	0.131270i
$351$		0			0
$352$	6.64392	+	4.82709i	0.354122	+	0.257285i
$353$	4.30300	+	0.914630i	0.229025	+	0.0486809i	0.320995	−	0.947081i	$-0.395983\pi$
$353$	4.30300	+	0.914630i	0.229025	+	0.0486809i	−0.0919693	+	0.995762i	$0.529316\pi$
$354$		0			0
$355$	−24.9899	+	27.1226i	−1.32633	+	1.43952i
$356$	−16.8048	+	3.57198i	−0.890655	+	0.189315i
$357$		0			0
$358$	6.87237	+	7.63253i	0.363216	+	0.403392i
$359$	−11.0737	+	8.04552i	−0.584448	+	0.424627i	−0.840325	−	0.542083i	$-0.817636\pi$
$359$	−11.0737	+	8.04552i	−0.584448	+	0.424627i	0.255877	+	0.966709i	$0.417636\pi$
$360$		0			0
$361$	−20.0154	−	14.5420i	−1.05344	−	0.765370i
$362$	−1.23655	−	11.7650i	−0.0649916	−	0.618354i
$363$		0			0
$364$	−0.213538	+	2.03168i	−0.0111924	+	0.106489i
$365$	−0.647059	+	5.54445i	−0.0338686	+	0.290210i
$366$		0			0
$367$	3.50752	+	3.89550i	0.183091	+	0.203343i	0.827703	−	0.561167i	$-0.189648\pi$
$367$	3.50752	+	3.89550i	0.183091	+	0.203343i	−0.644611	+	0.764510i	$0.722981\pi$
$368$	0.0536889			0.00279873
$369$		0			0
$370$	11.8840	+	0.136179i	0.617821	+	0.00707960i
$371$	−10.0387	−	2.13380i	−0.521185	−	0.110781i
$372$		0			0
$373$	−0.885927	+	8.42903i	−0.0458716	+	0.436439i	0.947350	+	0.320201i	$0.103750\pi$
$373$	−0.885927	+	8.42903i	−0.0458716	+	0.436439i	−0.993221	+	0.116238i	$0.962916\pi$
$374$	−3.14411	−	5.44577i	−0.162578	−	0.281594i
$375$		0			0
$376$	7.65680	−	13.2620i	0.394869	−	0.683933i
$377$	9.54050	+	6.93158i	0.491361	+	0.356994i
$378$		0			0
$379$	−7.97105	−	24.5324i	−0.409445	−	1.26014i	−0.917126	−	0.398598i	$-0.869497\pi$
$379$	−7.97105	−	24.5324i	−0.409445	−	1.26014i	0.507680	−	0.861545i	$-0.330503\pi$
$380$	−9.18162	+	15.4904i	−0.471007	+	0.794640i
$381$		0			0
$382$	3.11995	+	5.40390i	0.159630	+	0.276488i
$383$	−7.46117	+	1.58592i	−0.381248	+	0.0810367i	−0.394549	−	0.918875i	$-0.629099\pi$
$383$	−7.46117	+	1.58592i	−0.381248	+	0.0810367i	0.0133014	+	0.999912i	$0.495766\pi$
$384$		0			0
$385$	−2.74851	+	1.18617i	−0.140077	+	0.0604527i
$386$	−4.01241	−	2.91519i	−0.204226	−	0.148379i
$387$		0			0
$388$	5.93373	−	4.31110i	0.301239	−	0.218863i
$389$	32.4386	−	14.4426i	1.64470	−	0.732268i	0.645204	−	0.764011i	$-0.276772\pi$
$389$	32.4386	−	14.4426i	1.64470	−	0.732268i	0.999496	+	0.0317430i	$0.0101058\pi$
$390$		0			0
$391$	2.90604	+	1.29385i	0.146965	+	0.0654330i
$392$	−17.1508	+	3.64552i	−0.866246	+	0.184126i
$393$		0			0
$394$	−1.23503	−	1.37164i	−0.0622200	−	0.0691024i
$395$	4.12836	+	13.2193i	0.207720	+	0.665135i
$396$		0			0
$397$	8.38450	+	25.8048i	0.420806	+	1.29511i	0.906954	+	0.421230i	$0.138402\pi$
$397$	8.38450	+	25.8048i	0.420806	+	1.29511i	−0.486148	+	0.873877i	$0.661598\pi$
$398$	2.47729	−	1.10296i	0.124176	−	0.0552865i
$399$		0			0
$400$	−0.371104	−	0.175523i	−0.0185552	−	0.00877617i
$401$	−11.5052	−	19.9276i	−0.574543	−	0.995138i	−0.996091	−	0.0883319i	$-0.971846\pi$
$401$	−11.5052	−	19.9276i	−0.574543	−	0.995138i	0.421548	−	0.906806i	$-0.361487\pi$
$402$		0			0
$403$	−5.26701	−	1.11954i	−0.262368	−	0.0557681i
$404$	1.46130	+	4.49742i	0.0727025	+	0.223755i
$405$		0			0
$406$	1.61226	−	4.96202i	0.0800150	−	0.246261i
$407$	4.39079	−	7.60507i	0.217643	−	0.376970i
$408$		0			0
$409$	16.5641	+	7.37483i	0.819044	+	0.364662i	0.773101	−	0.634282i	$-0.218704\pi$
$409$	16.5641	+	7.37483i	0.819044	+	0.364662i	0.0459421	+	0.998944i	$0.485371\pi$
$410$	2.39877	+	4.26697i	0.118467	+	0.210730i
$411$		0			0
$412$	−1.68609	−	16.0421i	−0.0830679	−	0.790338i
$413$	1.48308	−	1.07752i	0.0729775	−	0.0530212i
$414$		0			0
$415$	−2.86467	+	8.48451i	−0.140621	+	0.416488i
$416$	1.07578	+	10.2354i	0.0527446	+	0.501831i
$417$		0			0
$418$	−4.27453	−	7.40370i	−0.209074	−	0.362127i
$419$	−3.16469	+	0.672676i	−0.154605	+	0.0328624i	−0.284564	−	0.958657i	$-0.591849\pi$
$419$	−3.16469	+	0.672676i	−0.154605	+	0.0328624i	0.129959	+	0.991519i	$0.458516\pi$
$420$		0			0
$421$	10.1780	+	2.16341i	0.496047	+	0.105438i	0.449140	−	0.893461i	$-0.351730\pi$
$421$	10.1780	+	2.16341i	0.496047	+	0.105438i	0.0469065	+	0.998899i	$0.485064\pi$
$422$	−0.561818	−	1.72910i	−0.0273489	−	0.0841712i
$423$		0			0
$424$	−31.8851			−1.54848
$425$	−15.8570	−	18.4439i	−0.769175	−	0.894661i
$426$		0			0
$427$	−1.21034	+	11.5156i	−0.0585726	+	0.557281i
$428$	0.468496	−	0.520318i	0.0226456	−	0.0251505i
$429$		0			0
$430$	−7.31127	+	3.15531i	−0.352581	+	0.152163i
$431$	−6.18249	+	19.0277i	−0.297800	+	0.916534i	0.684467	+	0.729044i	$0.260035\pi$
$431$	−6.18249	+	19.0277i	−0.297800	+	0.916534i	−0.982267	+	0.187490i	$0.939965\pi$
$432$		0			0
$433$	−1.29700	+	3.99175i	−0.0623297	+	0.191831i	−0.977372	−	0.211526i	$-0.932157\pi$
$433$	−1.29700	+	3.99175i	−0.0623297	+	0.191831i	0.915043	+	0.403357i	$0.132157\pi$
$434$	0.249019	+	2.36926i	0.0119533	+	0.113728i
$435$		0			0
$436$	−1.63990	+	15.6026i	−0.0785370	+	0.747230i
$437$	3.95086	+	1.75904i	0.188995	+	0.0841461i
$438$		0			0
$439$	29.5520	−	13.1574i	1.41044	−	0.627969i	0.446670	−	0.894699i	$-0.352610\pi$
$439$	29.5520	−	13.1574i	1.41044	−	0.627969i	0.963771	+	0.266730i	$0.0859431\pi$
$440$	−7.58626	+	5.38002i	−0.361661	+	0.256482i
$441$		0			0
$442$	2.43520	−	7.49477i	0.115831	−	0.356490i
$443$	0.881739	−	1.52722i	0.0418927	−	0.0725602i	−0.844319	−	0.535841i	$-0.819995\pi$
$443$	0.881739	−	1.52722i	0.0418927	−	0.0725602i	0.886211	+	0.463281i	$0.153328\pi$
$444$		0			0
$445$	3.65718	−	31.3373i	0.173367	−	1.48553i
$446$	−13.4343	+	14.9203i	−0.636130	+	0.706494i
$447$		0			0
$448$	4.29709	−	1.91319i	0.203019	−	0.0903897i
$449$	−4.06171			−0.191684			−0.0958420	−	0.995397i	$-0.530554\pi$
$449$	−4.06171			−0.191684			−0.0958420	+	0.995397i	$0.530554\pi$
$450$		0			0
$451$	3.61688			0.170312
$452$	8.13603	−	3.62239i	0.382687	−	0.170383i
$453$		0			0
$454$	−3.89429	+	4.32504i	−0.182768	+	0.202984i
$455$	−3.40949	−	1.56505i	−0.159839	−	0.0733709i
$456$		0			0
$457$	−17.6151	+	30.5103i	−0.824002	+	1.42721i	0.0786783	+	0.996900i	$0.474930\pi$
$457$	−17.6151	+	30.5103i	−0.824002	+	1.42721i	−0.902680	+	0.430313i	$0.858403\pi$
$458$	1.78057	−	5.48004i	0.0832008	−	0.256066i
$459$		0			0
$460$	0.569545	−	1.68686i	0.0265552	−	0.0786503i
$461$	0.00623691	−	0.00277685i	0.000290482	−	0.000129331i	−0.406591	−	0.913610i	$-0.633283\pi$
$461$	0.00623691	−	0.00277685i	0.000290482	−	0.000129331i	0.406882	+	0.913481i	$0.366616\pi$
$462$		0			0
$463$	26.7037	+	11.8893i	1.24103	+	0.552541i	0.919025	−	0.394198i	$-0.128978\pi$
$463$	26.7037	+	11.8893i	1.24103	+	0.552541i	0.322001	+	0.946739i	$0.395644\pi$
$464$	0.0552608	−	0.525771i	0.00256542	−	0.0244083i
$465$		0			0
$466$	0.344220	+	3.27503i	0.0159457	+	0.151713i
$467$	5.25864	−	16.1844i	0.243341	−	0.748926i	−0.752564	−	0.658519i	$-0.771183\pi$
$467$	5.25864	−	16.1844i	0.243341	−	0.748926i	0.995905	−	0.0904068i	$-0.0288167\pi$
$468$		0			0
$469$	−2.41391	+	7.42924i	−0.111464	+	0.343050i
$470$	7.02984	+	7.98966i	0.324262	+	0.368536i
$471$		0			0
$472$	3.81092	−	4.23246i	0.175412	−	0.194815i
$473$	−0.615031	+	5.85163i	−0.0282791	+	0.269058i
$474$		0			0
$475$	−21.5580	−	25.0751i	−0.989151	−	1.15052i
$476$	5.42621			0.248710
$477$		0			0
$478$	1.55996	+	4.80105i	0.0713507	+	0.219595i
$479$	−38.6010	−	8.20489i	−1.76372	−	0.374891i	−0.791909	−	0.610640i	$-0.790912\pi$
$479$	−38.6010	−	8.20489i	−1.76372	−	0.374891i	−0.971814	+	0.235749i	$0.924246\pi$
$480$		0			0
$481$	10.7647	−	2.28810i	0.490827	−	0.104328i
$482$	13.2150	+	22.8891i	0.601928	+	1.04257i
$483$		0			0
$484$	−1.12822	−	10.7343i	−0.0512828	−	0.487924i
$485$	4.01513	+	12.8567i	0.182318	+	0.583794i
$486$		0			0
$487$	−4.96283	+	3.60570i	−0.224887	+	0.163390i	−0.694524	−	0.719470i	$-0.744385\pi$
$487$	−4.96283	+	3.60570i	−0.224887	+	0.163390i	0.469637	+	0.882860i	$0.344385\pi$
$488$	3.76029	+	35.7768i	0.170220	+	1.61954i
$489$		0			0
$490$	1.41246	−	12.1029i	0.0638084	−	0.546755i
$491$	37.8652	+	16.8587i	1.70883	+	0.760821i	0.998369	+	0.0570848i	$0.0181805\pi$
$491$	37.8652	+	16.8587i	1.70883	+	0.760821i	0.710462	+	0.703736i	$0.248486\pi$
$492$		0			0
$493$	15.6617	−	27.1269i	0.705369	−	1.22174i
$494$	3.31073	−	10.1894i	0.148957	−	0.458442i
$495$		0			0
$496$	0.0745952	+	0.229580i	0.00334942	+	0.0103085i
$497$	14.7788	+	3.14132i	0.662918	+	0.140908i
$498$		0			0
$499$	−21.5077	−	37.2524i	−0.962815	−	1.66765i	−0.715373	−	0.698742i	$-0.753743\pi$
$499$	−21.5077	−	37.2524i	−0.962815	−	1.66765i	−0.247442	−	0.968903i	$-0.579590\pi$
$500$	−9.45156	+	9.79779i	−0.422687	+	0.438170i
$501$		0			0
$502$	3.23951	−	1.44232i	0.144586	−	0.0643740i
$503$	3.68891	+	11.3533i	0.164481	+	0.506219i	0.998998	−	0.0447630i	$-0.0142533\pi$
$503$	3.68891	+	11.3533i	0.164481	+	0.506219i	−0.834517	+	0.550982i	$0.814253\pi$
$504$		0			0
$505$	−8.68356	−	0.0995048i	−0.386413	−	0.00442790i
$506$	0.565598	+	0.628160i	0.0251439	+	0.0279251i
$507$		0			0
$508$	−13.0954	+	2.78352i	−0.581017	+	0.123499i
$509$	−15.8268	−	7.04652i	−0.701509	−	0.312332i	0.0248079	−	0.999692i	$-0.492103\pi$
$509$	−15.8268	−	7.04652i	−0.701509	−	0.312332i	−0.726316	+	0.687361i	$0.758769\pi$
$510$		0			0
$511$	2.08915	−	0.930150i	0.0924186	−	0.0411474i
$512$	0.751353	−	0.545890i	0.0332054	−	0.0241252i
$513$		0			0
$514$	7.48825	+	5.44053i	0.330293	+	0.239972i
$515$	28.9023	+	6.49038i	1.27359	+	0.286000i
$516$		0			0
$517$	7.69150	−	1.63488i	0.338272	−	0.0719019i
$518$	−2.43448	−	4.21663i	−0.106965	−	0.185268i
$519$		0			0
$520$	−11.3720	−	2.55374i	−0.498697	−	0.111989i
$521$	−6.41731	−	19.7505i	−0.281147	−	0.865283i	−0.987527	−	0.157450i	$-0.949673\pi$
$521$	−6.41731	−	19.7505i	−0.281147	−	0.865283i	0.706380	−	0.707833i	$-0.250327\pi$
$522$		0			0
$523$	−13.4985	−	9.80721i	−0.590247	−	0.428839i	0.252157	−	0.967686i	$-0.418860\pi$
$523$	−13.4985	−	9.80721i	−0.590247	−	0.428839i	−0.842404	+	0.538847i	$0.818860\pi$
$524$	−5.88035	+	10.1851i	−0.256884	+	0.444937i
$525$		0			0
$526$	−4.43153	−	7.67563i	−0.193224	−	0.334674i
$527$	−1.49503	+	14.2243i	−0.0651247	+	0.619620i
$528$		0			0
$529$	22.0791	+	4.69307i	0.959962	+	0.204046i
$530$	7.08830	−	20.9939i	0.307896	−	0.911918i
$531$		0			0
$532$	7.37711			0.319838
$533$	3.03298	+	3.36846i	0.131373	+	0.145904i
$534$		0			0
$535$	0.630084	+	1.12080i	0.0272409	+	0.0484566i
$536$	−2.53680	+	24.1360i	−0.109573	+	1.04252i
$537$		0			0
$538$	1.97767	+	18.8163i	0.0852634	+	0.811227i
$539$	−7.28395	−	5.29210i	−0.313742	−	0.227947i
$540$		0			0
$541$	−1.25243	+	0.909945i	−0.0538462	+	0.0391216i	−0.614383	−	0.789008i	$-0.710595\pi$
$541$	−1.25243	+	0.909945i	−0.0538462	+	0.0391216i	0.560537	+	0.828130i	$0.310595\pi$
$542$	4.81661	+	5.34939i	0.206891	+	0.229776i
$543$		0			0
$544$	26.7394	−	5.68363i	1.14644	−	0.243684i
$545$	−26.1838	−	12.0191i	−1.12159	−	0.514843i
$546$		0			0
$547$	−18.4672	−	3.92532i	−0.789599	−	0.167834i	−0.204575	−	0.978851i	$-0.565581\pi$
$547$	−18.4672	−	3.92532i	−0.789599	−	0.167834i	−0.585023	+	0.811016i	$0.698915\pi$
$548$	−19.2475	−	13.9841i	−0.822213	−	0.597373i
$549$		0			0
$550$	−1.85585	−	6.19101i	−0.0791339	−	0.263985i
$551$	21.2926	−	36.8799i	0.907097	−	1.57114i
$552$		0			0
$553$	3.79639	−	4.21632i	0.161439	−	0.179296i
$554$	0.0525600	−	0.0583738i	0.00223306	−	0.00248006i
$555$		0			0
$556$	−13.1139	−	14.5644i	−0.556152	−	0.617669i
$557$	16.8643			0.714561			0.357281	−	0.933997i	$-0.383704\pi$
$557$	16.8643			0.714561			0.357281	+	0.933997i	$0.383704\pi$
$558$		0			0
$559$	−5.96545	+	4.33416i	−0.252312	+	0.183315i
$560$	0.0156621	+	0.167450i	0.000661843	+	0.00707607i
$561$		0			0
$562$	16.4246	+	7.31269i	0.692829	+	0.308467i
$563$	1.64115	+	0.730685i	0.0691660	+	0.0307947i	0.441028	−	0.897493i	$-0.354614\pi$
$563$	1.64115	+	0.730685i	0.0691660	+	0.0307947i	−0.371862	+	0.928288i	$0.621281\pi$
$564$		0			0
$565$	1.52308	+	16.2839i	0.0640764	+	0.685070i
$566$	−19.8990	+	14.4574i	−0.836416	+	0.607692i
$567$		0			0
$568$	46.9404			1.96958
$569$	3.03944	+	3.37564i	0.127420	+	0.141514i	0.803479	−	0.595334i	$-0.202980\pi$
$569$	3.03944	+	3.37564i	0.127420	+	0.141514i	−0.676059	+	0.736848i	$0.736313\pi$
$570$		0			0
$571$	−26.9761	+	29.9600i	−1.12891	+	1.25379i	−0.165370	+	0.986232i	$0.552882\pi$
$571$	−26.9761	+	29.9600i	−1.12891	+	1.25379i	−0.963543	+	0.267554i	$0.913785\pi$
$572$	−2.18069	+	2.42190i	−0.0911792	+	0.101265i
$573$		0			0
$574$	1.00269	−	1.73671i	0.0418515	−	0.0724889i
$575$	2.60040	+	1.98191i	0.108444	+	0.0826514i
$576$		0			0
$577$	−14.4803	−	10.5206i	−0.602824	−	0.437978i	0.244056	−	0.969761i	$-0.421522\pi$
$577$	−14.4803	−	10.5206i	−0.602824	−	0.437978i	−0.846880	+	0.531784i	$0.821522\pi$
$578$	−5.76633	−	1.22567i	−0.239848	−	0.0509812i
$579$		0			0
$580$	−15.9331	−	7.31376i	−0.661586	−	0.303687i
$581$	3.58853	−	0.762766i	0.148877	−	0.0316449i
$582$		0			0
$583$	−10.9554	−	12.1672i	−0.453726	−	0.503914i
$584$	5.74792	−	4.17611i	0.237851	−	0.172809i
$585$		0			0
$586$	7.41312	+	5.38595i	0.306233	+	0.222491i
$587$	−4.04407	−	38.4768i	−0.166917	−	1.58811i	−0.682252	−	0.731117i	$-0.738999\pi$
$587$	−4.04407	−	38.4768i	−0.166917	−	1.58811i	0.515335	−	0.856989i	$-0.327667\pi$
$588$		0			0
$589$	−2.03255	+	19.3384i	−0.0837496	+	0.796824i
$590$	1.93956	+	3.45012i	0.0798504	+	0.142039i
$591$		0			0
$592$	−0.330123	−	0.366639i	−0.0135680	−	0.0150688i
$593$	−0.135281			−0.00555534			−0.00277767	−	0.999996i	$-0.500884\pi$
$593$	−0.135281			−0.00555534			−0.00277767	+	0.999996i	$0.500884\pi$
$594$		0			0
$595$	−3.18766	+	9.44111i	−0.130681	+	0.387048i
$596$	−13.6709	−	2.90584i	−0.559982	−	0.119028i
$597$		0			0
$598$	−0.110727	+	1.05350i	−0.00452798	+	0.0430808i
$599$	0.290350	+	0.502901i	0.0118634	+	0.0205480i	0.871896	−	0.489691i	$-0.162890\pi$
$599$	0.290350	+	0.502901i	0.0118634	+	0.0205480i	−0.860033	+	0.510239i	$0.829557\pi$
$600$		0			0
$601$	11.2892	−	19.5535i	0.460496	−	0.797602i	−0.538490	−	0.842632i	$-0.681005\pi$
$601$	11.2892	−	19.5535i	0.460496	−	0.797602i	0.998986	+	0.0450300i	$0.0143383\pi$
$602$	2.63926	+	1.91754i	0.107568	+	0.0781529i
$603$		0			0
$604$	5.43711	+	16.7337i	0.221233	+	0.680885i
$605$	19.3395	+	4.34293i	0.786263	+	0.176565i
$606$		0			0
$607$	5.42862	+	9.40265i	0.220341	+	0.381642i	0.954912	−	0.296891i	$-0.0959496\pi$
$607$	5.42862	+	9.40265i	0.220341	+	0.381642i	−0.734570	+	0.678532i	$0.762616\pi$
$608$	36.3531	−	7.72708i	1.47431	−	0.313374i
$609$		0			0
$610$	−24.3923	−	5.47759i	−0.987615	−	0.221781i
$611$	7.97238	+	5.79227i	0.322528	+	0.234330i
$612$		0			0
$613$	32.2624	−	23.4400i	1.30307	−	0.946733i	0.303086	−	0.952963i	$-0.401983\pi$
$613$	32.2624	−	23.4400i	1.30307	−	0.946733i	0.999981	+	0.00623024i	$0.00198316\pi$
$614$	−21.3377	+	9.50014i	−0.861118	+	0.383394i
$615$		0			0
$616$	3.48074	+	1.54973i	0.140243	+	0.0624403i
$617$	25.4813	−	5.41621i	1.02584	−	0.218048i	0.335885	−	0.941903i	$-0.390965\pi$
$617$	25.4813	−	5.41621i	1.02584	−	0.218048i	0.689952	+	0.723855i	$0.257631\pi$
$618$		0			0
$619$	−6.20324	−	6.88940i	−0.249329	−	0.276908i	0.605469	−	0.795869i	$-0.292986\pi$
$619$	−6.20324	−	6.88940i	−0.249329	−	0.276908i	−0.854798	+	0.518961i	$0.826319\pi$
$620$	8.00456	+	0.0917241i	0.321471	+	0.00368373i
$621$		0			0
$622$	2.22813	+	6.85748i	0.0893399	+	0.274960i
$623$	−11.8079	+	5.25721i	−0.473073	+	0.210626i
$624$		0			0
$625$	−11.4949	−	22.2006i	−0.459795	−	0.888025i
$626$	12.8974	+	22.3389i	0.515483	+	0.892843i
$627$		0			0
$628$	26.8827	+	5.71409i	1.07274	+	0.228017i
$629$	−9.03307	−	27.8009i	−0.360172	−	1.10850i
$630$		0			0
$631$	−2.38628	+	7.34421i	−0.0949963	+	0.292368i	−0.987253	−	0.159161i	$-0.949121\pi$
$631$	−2.38628	+	7.34421i	−0.0949963	+	0.292368i	0.892256	+	0.451529i	$0.149121\pi$
$632$	8.81340	−	15.2653i	0.350578	−	0.607219i
$633$		0			0
$634$	8.70709	+	3.87665i	0.345803	+	0.153961i
$635$	2.84992	−	24.4201i	0.113095	−	0.969081i
$636$		0			0
$637$	−1.17942	−	11.2214i	−0.0467303	−	0.444609i
$638$	6.73368	−	4.89231i	0.266589	−	0.193688i
$639$		0			0
$640$	−4.46416	−	14.2945i	−0.176461	−	0.565042i
$641$	3.03061	+	28.8343i	0.119702	+	1.13889i	0.875208	+	0.483746i	$0.160724\pi$
$641$	3.03061	+	28.8343i	0.119702	+	1.13889i	−0.755507	+	0.655141i	$0.772609\pi$
$642$		0			0
$643$	−19.9683	−	34.5861i	−0.787473	−	1.36394i	−0.927511	−	0.373797i	$-0.878056\pi$
$643$	−19.9683	−	34.5861i	−0.787473	−	1.36394i	0.140038	−	0.990146i	$-0.455278\pi$
$644$	−0.713460	+	0.151651i	−0.0281143	+	0.00597587i
$645$		0			0
$646$	−27.8357	−	5.91667i	−1.09518	−	0.232788i
$647$	1.22692	+	3.77608i	0.0482353	+	0.148453i	0.972273	−	0.233848i	$-0.0751318\pi$
$647$	1.22692	+	3.77608i	0.0482353	+	0.148453i	−0.924038	+	0.382301i	$0.875132\pi$
$648$		0			0
$649$	2.92448			0.114796
$650$	4.20954	−	6.91992i	0.165112	−	0.271422i
$651$		0			0
$652$	−2.09595	+	19.9416i	−0.0820836	+	0.780973i
$653$	23.3941	−	25.9818i	0.915483	−	1.01675i	−0.0843104	−	0.996440i	$-0.526869\pi$
$653$	23.3941	−	25.9818i	0.915483	−	1.01675i	0.999794	−	0.0203078i	$-0.00646460\pi$
$654$		0			0
$655$	−14.2666	−	16.2146i	−0.557444	−	0.633555i
$656$	0.0627927	−	0.193256i	0.00245164	−	0.00754538i
$657$		0			0
$658$	1.34726	−	4.14644i	0.0525217	−	0.161645i
$659$	−2.85250	−	27.1397i	−0.111118	−	1.05721i	−0.897965	−	0.440066i	$-0.854955\pi$
$659$	−2.85250	−	27.1397i	−0.111118	−	1.05721i	0.786848	−	0.617147i	$-0.211712\pi$
$660$		0			0
$661$	−3.82476	+	36.3902i	−0.148766	+	1.41541i	0.624348	+	0.781146i	$0.285365\pi$
$661$	−3.82476	+	36.3902i	−0.148766	+	1.41541i	−0.773114	+	0.634267i	$0.781302\pi$
$662$	12.1311	+	5.40109i	0.471487	+	0.209919i
$663$		0			0
$664$	10.4125	−	4.63595i	0.404084	−	0.179910i
$665$	−4.33372	+	12.8355i	−0.168055	+	0.497739i
$666$		0			0
$667$	−1.30113	+	4.00447i	−0.0503800	+	0.155054i
$668$	12.5341	−	21.7098i	0.484960	−	0.839976i
$669$		0			0
$670$	−15.3278	−	7.03592i	−0.592165	−	0.271821i
$671$	−12.3603	+	13.7275i	−0.477163	+	0.529943i
$672$		0			0
$673$	−23.0242	+	10.2510i	−0.887518	+	0.395148i	−0.799285	−	0.600952i	$-0.794788\pi$
$673$	−23.0242	+	10.2510i	−0.887518	+	0.395148i	−0.0882323	+	0.996100i	$0.528122\pi$
$674$	1.17239			0.0451589
$675$		0			0
$676$	11.7450			0.451732
$677$	−10.8854	+	4.84649i	−0.418360	+	0.186266i	−0.605110	−	0.796142i	$-0.706871\pi$
$677$	−10.8854	+	4.84649i	−0.418360	+	0.186266i	0.186751	+	0.982407i	$0.440204\pi$
$678$		0			0
$679$	3.69227	−	4.10068i	0.141696	−	0.157370i
$680$	−3.58861	+	30.7497i	−0.137617	+	1.17920i
$681$		0			0
$682$	−1.90025	+	3.29133i	−0.0727644	+	0.126032i
$683$	10.9564	−	33.7204i	0.419236	−	1.29028i	−0.489171	−	0.872188i	$-0.662701\pi$
$683$	10.9564	−	33.7204i	0.419236	−	1.29028i	0.908407	−	0.418088i	$-0.137299\pi$
$684$		0			0
$685$	35.6382	−	25.2739i	1.36166	−	0.965664i
$686$	−9.74197	+	4.33741i	−0.371950	+	0.165603i
$687$		0			0
$688$	0.301985	+	0.134452i	0.0115131	+	0.00512594i
$689$	2.14474	−	20.4059i	0.0817082	−	0.777402i
$690$		0			0
$691$	−1.82303	−	17.3450i	−0.0693513	−	0.659834i	−0.972881	−	0.231307i	$-0.925700\pi$
$691$	−1.82303	−	17.3450i	−0.0693513	−	0.659834i	0.903529	−	0.428526i	$-0.140967\pi$
$692$	8.25774	−	25.4147i	0.313912	−	0.966122i
$693$		0			0
$694$	2.17157	−	6.68341i	0.0824317	−	0.253699i
$695$	33.0446	−	14.2610i	1.25345	−	0.540950i
$696$		0			0
$697$	8.05612	−	8.94722i	0.305147	−	0.338900i
$698$	1.19926	−	11.4102i	0.0453927	−	0.431882i
$699$		0			0
$700$	5.42731	+	1.28427i	0.205133	+	0.0485407i
$701$	23.1265			0.873476			0.436738	−	0.899589i	$-0.356134\pi$
$701$	23.1265			0.873476			0.436738	+	0.899589i	$0.356134\pi$
$702$		0			0
$703$	−12.2808	−	37.7963i	−0.463177	−	1.42551i
$704$	7.33993	+	1.56015i	0.276634	+	0.0588004i
$705$		0			0
$706$	3.80607	−	0.809004i	0.143243	−	0.0304473i
$707$	1.77885	+	3.08106i	0.0669006	+	0.115875i
$708$		0			0
$709$	−1.08114	−	10.2864i	−0.0406030	−	0.386312i	−0.995886	−	0.0906180i	$-0.971116\pi$
$709$	−1.08114	−	10.2864i	−0.0406030	−	0.386312i	0.955283	−	0.295694i	$-0.0955509\pi$
$710$	−10.4352	+	30.9067i	−0.391627	+	1.15991i
$711$		0			0
$712$	−32.4873	+	23.6034i	−1.21751	+	0.884574i
$713$	−0.200964	−	1.91205i	−0.00752618	−	0.0716068i
$714$		0			0
$715$	−2.93283	−	5.21696i	−0.109682	−	0.195103i
$716$	−12.9163	−	5.75069i	−0.482703	−	0.214913i
$717$		0			0
$718$	−6.05356	+	10.4851i	−0.225917	+	0.391300i
$719$	11.2080	−	34.4945i	0.417986	−	1.28643i	−0.491566	−	0.870840i	$-0.663575\pi$
$719$	11.2080	−	34.4945i	0.417986	−	1.28643i	0.909552	−	0.415589i	$-0.136425\pi$
$720$		0			0
$721$	−3.75009	−	11.5416i	−0.139661	−	0.429832i
$722$	−21.4050	−	4.54978i	−0.796613	−	0.169325i
$723$		0			0
$724$	8.14251	+	14.1032i	0.302614	+	0.524143i
$725$	22.0853	−	23.4256i	0.820226	−	0.870005i
$726$		0			0
$727$	−18.3260	+	8.15926i	−0.679674	+	0.302610i	−0.717383	−	0.696679i	$-0.754660\pi$
$727$	−18.3260	+	8.15926i	−0.679674	+	0.302610i	0.0377098	+	0.999289i	$0.487994\pi$
$728$	1.47553	+	4.54121i	0.0546867	+	0.168309i
$729$		0			0
$730$	1.47185	+	4.71296i	0.0544755	+	0.174434i
$731$	13.1055	+	14.5551i	0.484724	+	0.538341i
$732$		0			0
$733$	28.4700	−	6.05149i	1.05156	−	0.223517i	0.350461	−	0.936577i	$-0.386025\pi$
$733$	28.4700	−	6.05149i	1.05156	−	0.223517i	0.701103	+	0.713060i	$0.252692\pi$
$734$	4.23569	+	1.88585i	0.156342	+	0.0696081i
$735$		0			0
$736$	−3.35696	+	1.49461i	−0.123739	+	0.0550922i
$737$	−10.0818	+	7.32486i	−0.371368	+	0.269815i
$738$		0			0
$739$	−13.5848	−	9.86991i	−0.499724	−	0.363071i	0.309188	−	0.951001i	$-0.399943\pi$
$739$	−13.5848	−	9.86991i	−0.499724	−	0.363071i	−0.808912	+	0.587930i	$0.799943\pi$
$740$	−15.0215	+	6.48282i	−0.552203	+	0.238313i
$741$		0			0
$742$	−8.87941	+	1.88738i	−0.325973	+	0.0692878i
$743$	22.2483	+	38.5352i	0.816211	+	1.41372i	0.908455	+	0.417983i	$0.137263\pi$
$743$	22.2483	+	38.5352i	0.816211	+	1.41372i	−0.0922434	+	0.995736i	$0.529404\pi$
$744$		0			0
$745$	13.0869	−	22.0791i	0.479468	−	0.808914i
$746$	2.31660	+	7.12976i	0.0848168	+	0.261039i
$747$		0			0
$748$	7.00321	+	5.08813i	0.256063	+	0.186040i
$749$	0.263377	−	0.456182i	0.00962357	−	0.0166685i
$750$		0			0
$751$	−18.8265	−	32.6085i	−0.686990	−	1.18990i	−0.972807	−	0.231617i	$-0.925598\pi$
$751$	−18.8265	−	32.6085i	−0.686990	−	1.18990i	0.285817	−	0.958284i	$-0.407735\pi$
$752$	0.0461779	−	0.439353i	0.00168393	−	0.0160216i
$753$		0			0
$754$	10.2029	+	2.16869i	0.371567	+	0.0789790i
$755$	−32.3092	−	0.370231i	−1.17585	−	0.0134741i
$756$		0			0
$757$	23.9415			0.870167			0.435084	−	0.900390i	$-0.356719\pi$
$757$	23.9415			0.870167			0.435084	+	0.900390i	$0.356719\pi$
$758$	−15.2668	−	16.9556i	−0.554517	−	0.615853i
$759$		0			0
$760$	−4.87883	+	41.8052i	−0.176974	+	1.51643i
$761$	2.60057	−	24.7428i	0.0942706	−	0.896924i	−0.840533	−	0.541760i	$-0.817758\pi$
$761$	2.60057	−	24.7428i	0.0942706	−	0.896924i	0.934804	−	0.355164i	$-0.115575\pi$
$762$		0			0
$763$	1.23376	+	11.7384i	0.0446650	+	0.424959i
$764$	−6.94938	−	5.04902i	−0.251420	−	0.182667i
$765$		0			0
$766$	−5.45840	+	3.96576i	−0.197220	+	0.143289i
$767$	2.45236	+	2.72362i	0.0885494	+	0.0983441i
$768$		0			0
$769$	−20.7844	+	4.41785i	−0.749503	+	0.159312i	−0.566799	−	0.823856i	$-0.691818\pi$
$769$	−20.7844	+	4.41785i	−0.749503	+	0.159312i	−0.182704	+	0.983168i	$0.558485\pi$
$770$	−1.79418	+	1.94729i	−0.0646576	+	0.0701755i
$771$		0			0
$772$	6.67826	+	1.41951i	0.240356	+	0.0510892i
$773$	4.02099	+	2.92142i	0.144625	+	0.105076i	0.657745	−	0.753241i	$-0.271510\pi$
$773$	4.02099	+	2.92142i	0.144625	+	0.105076i	−0.513120	+	0.858317i	$0.671510\pi$
$774$		0			0
$775$	−4.86191	+	13.8733i	−0.174645	+	0.498344i
$776$	8.57167	−	14.8466i	0.307705	−	0.532961i
$777$		0			0
$778$	21.0159	−	23.3405i	0.753456	−	0.836797i
$779$	10.9525	−	12.1640i	0.392416	−	0.435822i
$780$		0			0
$781$	16.1283	+	17.9122i	0.577114	+	0.640951i
$782$	2.81370			0.100618
$783$		0			0
$784$	−0.409223	+	0.297318i	−0.0146151	+	0.0106185i
$785$	−25.7344	+	43.4166i	−0.918499	+	1.54961i
$786$		0			0
$787$	43.9427	+	19.5646i	1.56639	+	0.697401i	0.992581	−	0.121589i	$-0.0387990\pi$
$787$	43.9427	+	19.5646i	1.56639	+	0.697401i	0.573808	+	0.818990i	$0.305466\pi$
$788$	2.32118	+	1.03346i	0.0826886	+	0.0368153i
$789$		0			0
$790$	8.09174	+	9.19655i	0.287891	+	0.327199i
$791$	5.42066	−	3.93834i	0.192736	−	0.140031i
$792$		0			0
$793$	−23.1494			−0.822060
$794$	16.0587	+	17.8350i	0.569902	+	0.632941i
$795$		0			0
$796$	−2.49787	+	2.77416i	−0.0885346	+	0.0983276i
$797$	−3.58369	+	3.98009i	−0.126941	+	0.140982i	−0.803264	−	0.595623i	$-0.796905\pi$
$797$	−3.58369	+	3.98009i	−0.126941	+	0.140982i	0.676324	+	0.736605i	$0.263572\pi$
$798$		0			0
$799$	13.0875	−	22.6682i	0.463003	−	0.801944i
$800$	28.0900	+	0.643850i	0.993130	+	0.0227635i
$801$		0			0
$802$	−16.4660	−	11.9632i	−0.581434	−	0.422437i
$803$	3.56851	+	0.758510i	0.125930	+	0.0267673i
$804$		0			0
$805$	0.155268	−	1.33044i	0.00547247	−	0.0468920i
$806$	−4.65875	+	0.990247i	−0.164097	+	0.0348800i
$807$		0			0
$808$	7.39595	+	8.21403i	0.260189	+	0.288969i
$809$	−8.50974	+	6.18268i	−0.299186	+	0.217372i	−0.727243	−	0.686380i	$-0.759199\pi$
$809$	−8.50974	+	6.18268i	−0.299186	+	0.217372i	0.428056	+	0.903752i	$0.359199\pi$
$810$		0			0
$811$	14.8190	+	10.7667i	0.520367	+	0.378068i	0.816742	−	0.577003i	$-0.195778\pi$
$811$	14.8190	+	10.7667i	0.520367	+	0.378068i	−0.296375	+	0.955072i	$0.595778\pi$
$812$	0.750754	+	7.14295i	0.0263463	+	0.250668i
$813$		0			0
$814$	0.811919	−	7.72489i	0.0284577	−	0.270757i
$815$	−33.4653	−	15.3615i	−1.17224	−	0.538092i
$816$		0			0
$817$	17.8173	+	19.7882i	0.623350	+	0.692300i
$818$	16.0378			0.560747
$819$		0			0
$820$	−5.40583	−	4.02301i	−0.188780	−	0.140490i
$821$	−47.7890	−	10.1579i	−1.66785	−	0.354512i	−0.725261	−	0.688474i	$-0.758281\pi$
$821$	−47.7890	−	10.1579i	−1.66785	−	0.354512i	−0.942586	+	0.333963i	$0.891614\pi$
$822$		0			0
$823$	1.51205	−	14.3861i	0.0527066	−	0.501470i	−0.936043	−	0.351887i	$-0.885540\pi$
$823$	1.51205	−	14.3861i	0.0527066	−	0.501470i	0.988749	−	0.149583i	$-0.0477931\pi$
$824$	−18.8514	−	32.6515i	−0.656718	−	1.13747i
$825$		0			0
$826$	0.810740	−	1.40424i	0.0282092	−	0.0488598i
$827$	15.1725	+	11.0234i	0.527598	+	0.383322i	0.819458	−	0.573139i	$-0.194274\pi$
$827$	15.1725	+	11.0234i	0.527598	+	0.383322i	−0.291861	+	0.956461i	$0.594274\pi$
$828$		0			0
$829$	1.12241	+	3.45444i	0.0389830	+	0.119977i	0.968654	−	0.248413i	$-0.0799090\pi$
$829$	1.12241	+	3.45444i	0.0389830	+	0.119977i	−0.929671	+	0.368390i	$0.879909\pi$
$830$	0.737642	+	7.88647i	0.0256039	+	0.273743i
$831$		0			0
$832$	4.70198	+	8.14408i	0.163012	+	0.282345i
$833$	−29.3153	+	6.23116i	−1.01572	+	0.215897i
$834$		0			0
$835$	30.4097	+	34.5618i	1.05237	+	1.19606i
$836$	9.52109	+	6.91748i	0.329294	+	0.239246i
$837$		0			0
$838$	−2.31521	+	1.68210i	−0.0799776	+	0.0581071i
$839$	−10.7379	+	4.78083i	−0.370714	+	0.165052i	−0.583633	−	0.812017i	$-0.698369\pi$
$839$	−10.7379	+	4.78083i	−0.370714	+	0.165052i	0.212920	+	0.977070i	$0.431703\pi$
$840$		0			0
$841$	11.3834	+	5.06822i	0.392532	+	0.174766i
$842$	9.00262	−	1.91357i	0.310251	−	0.0659458i
$843$		0			0
$844$	1.67469	+	1.85994i	0.0576454	+	0.0640217i
$845$	−6.89968	+	20.4353i	−0.237356	+	0.702995i
$846$		0			0
$847$	−2.50931	−	7.72287i	−0.0862210	−	0.265361i
$848$	−0.840311	+	0.374130i	−0.0288564	+	0.0128477i
$849$		0			0
$850$	−19.4486	−	9.19873i	−0.667081	−	0.315514i
$851$	1.96468	+	3.40292i	0.0673483	+	0.116651i
$852$		0			0
$853$	44.4770	+	9.45388i	1.52286	+	0.323695i	0.891941	−	0.452151i	$-0.149343\pi$
$853$	44.4770	+	9.45388i	1.52286	+	0.323695i	0.630923	+	0.775846i	$0.282677\pi$
$854$	3.16491	+	9.74060i	0.108301	+	0.333316i
$855$		0			0
$856$	0.505711	−	1.55642i	0.0172849	−	0.0531973i
$857$	−15.6168	+	27.0491i	−0.533460	+	0.923980i	0.465776	+	0.884903i	$0.345775\pi$
$857$	−15.6168	+	27.0491i	−0.533460	+	0.923980i	−0.999236	+	0.0390776i	$0.987558\pi$
$858$		0			0
$859$	−28.5380	−	12.7059i	−0.973704	−	0.433521i	−0.142687	−	0.989768i	$-0.545574\pi$
$859$	−28.5380	−	12.7059i	−0.973704	−	0.433521i	−0.831017	+	0.556247i	$0.812241\pi$
$860$	7.42791	−	8.06182i	0.253290	−	0.274906i
$861$		0			0
$862$	1.84978	+	17.5995i	0.0630038	+	0.599442i
$863$	7.17033	−	5.20955i	0.244081	−	0.177335i	−0.459019	−	0.888427i	$-0.651799\pi$
$863$	7.17033	−	5.20955i	0.244081	−	0.177335i	0.703099	+	0.711092i	$0.251799\pi$
$864$		0			0
$865$	39.3682	+	29.2977i	1.33856	+	0.996152i
$866$	0.388058	+	3.69212i	0.0131867	+	0.125463i
$867$		0			0
$868$	−1.63976	−	2.84014i	−0.0556570	−	0.0964007i
$869$	8.85335	−	1.88184i	0.300329	−	0.0638369i
$870$		0			0
$871$	−15.2760	−	3.24701i	−0.517607	−	0.110021i
$872$	11.3316	+	34.8751i	0.383736	+	1.18102i
$873$		0			0
$874$	3.82531			0.129393
$875$	−5.42280	+	8.68857i	−0.183324	+	0.293727i
$876$		0			0
$877$	−0.186003	+	1.76970i	−0.00628086	+	0.0597584i	−0.997213	−	0.0746021i	$-0.976231\pi$
$877$	−0.186003	+	1.76970i	−0.00628086	+	0.0597584i	0.990933	+	0.134360i	$0.0428980\pi$
$878$	19.1458	−	21.2636i	0.646139	−	0.717610i
$879$		0			0
$880$	−0.136803	+	0.230802i	−0.00461164	+	0.00778034i
$881$	−8.34381	+	25.6796i	−0.281110	+	0.865168i	0.706428	+	0.707785i	$0.250306\pi$
$881$	−8.34381	+	25.6796i	−0.281110	+	0.865168i	−0.987538	+	0.157382i	$0.949694\pi$
$882$		0			0
$883$	−0.231224	+	0.711635i	−0.00778131	+	0.0239484i	−0.954872	−	0.297018i	$-0.904008\pi$
$883$	−0.231224	+	0.711635i	−0.00778131	+	0.0239484i	0.947090	+	0.320967i	$0.104008\pi$
$884$	1.13396	+	10.7889i	0.0381392	+	0.362870i
$885$		0			0
$886$	0.163046	−	1.55128i	0.00547763	−	0.0521162i
$887$	29.8287	+	13.2806i	1.00155	+	0.445919i	0.840957	−	0.541102i	$-0.181993\pi$
$887$	29.8287	+	13.2806i	1.00155	+	0.445919i	0.160593	+	0.987021i	$0.448659\pi$
$888$		0			0
$889$	−9.20149	+	4.09677i	−0.308608	+	0.137401i
$890$	−8.31888	−	26.6376i	−0.278850	−	0.892896i
$891$		0			0
$892$	8.54075	−	26.2857i	0.285966	−	0.880112i
$893$	17.7929	−	30.8182i	0.595416	−	1.03129i
$894$		0			0
$895$	17.5934	−	19.0948i	0.588082	−	0.638270i
$896$	−4.10519	+	4.55927i	−0.137145	+	0.152315i
$897$		0			0
$898$	−3.28204	+	1.46126i	−0.109523	+	0.0487629i
$899$	−18.9314			−0.631398
$900$		0			0
$901$	−54.5001			−1.81566
$902$	2.92260	−	1.30123i	0.0973120	−	0.0433261i
$903$		0			0
$904$	13.9290	−	15.4697i	0.463270	−	0.514514i
$905$	−29.3217	+	5.88220i	−0.974687	+	0.195531i
$906$		0			0
$907$	−9.80283	+	16.9790i	−0.325498	+	0.563778i	−0.981613	−	0.190882i	$-0.938865\pi$
$907$	−9.80283	+	16.9790i	−0.325498	+	0.563778i	0.656115	+	0.754661i	$0.272198\pi$
$908$	2.47577	−	7.61964i	0.0821614	−	0.252867i
$909$		0			0
$910$	−3.31807	−	0.0380217i	−0.109993	−	0.00126041i
$911$	6.69634	−	2.98140i	0.221860	−	0.0987782i	−0.292797	−	0.956175i	$-0.594586\pi$
$911$	6.69634	−	2.98140i	0.221860	−	0.0987782i	0.514657	+	0.857396i	$0.327919\pi$
$912$		0			0
$913$	5.34669	+	2.38050i	0.176950	+	0.0787831i
$914$	−3.25729	+	30.9910i	−0.107741	+	1.02509i
$915$		0			0
$916$	0.829132	+	7.88866i	0.0273953	+	0.260649i
$917$	−2.73419	+	8.41496i	−0.0902908	+	0.277886i
$918$		0			0
$919$	−0.919198	+	2.82900i	−0.0303215	+	0.0933201i	−0.965072	−	0.261985i	$-0.915623\pi$
$919$	−0.919198	+	2.82900i	−0.0303215	+	0.0933201i	0.934750	+	0.355305i	$0.115623\pi$
$920$	−0.387542	−	4.14339i	−0.0127769	−	0.136603i
$921$		0			0
$922$	0.00404069	−	0.00448764i	0.000133073	−	0.000147793i
$923$	−3.15744	+	30.0410i	−0.103928	+	0.988812i
$924$		0			0
$925$	−2.45502	−	29.9445i	−0.0807206	−	0.984568i
$926$	25.8551			0.849652
$927$		0			0
$928$	11.1814	+	34.4128i	0.367047	+	1.12966i
$929$	−0.682954	−	0.145166i	−0.0224070	−	0.00476275i	0.196695	−	0.980465i	$-0.436979\pi$
$929$	−0.682954	−	0.145166i	−0.0224070	−	0.00476275i	−0.219102	+	0.975702i	$0.570313\pi$
$930$		0			0
$931$	−39.8551	+	8.47146i	−1.30620	+	0.277641i
$932$	−2.26664	−	3.92593i	−0.0742462	−	0.128598i
$933$		0			0
$934$	−1.57337	−	14.9696i	−0.0514822	−	0.489821i
$935$	−12.9670	+	9.19590i	−0.424065	+	0.300738i
$936$		0			0
$937$	−6.03529	+	4.38490i	−0.197164	+	0.143248i	−0.681987	−	0.731364i	$-0.738884\pi$
$937$	−6.03529	+	4.38490i	−0.197164	+	0.143248i	0.484823	+	0.874612i	$0.338884\pi$
$938$	0.722234	+	6.87160i	0.0235818	+	0.224366i
$939$		0			0
$940$	−13.3143	−	6.11164i	−0.434263	−	0.199340i
$941$	−34.9240	−	15.5492i	−1.13849	−	0.506888i	−0.251124	−	0.967955i	$-0.580800\pi$
$941$	−34.9240	−	15.5492i	−1.13849	−	0.506888i	−0.887366	+	0.461067i	$0.847467\pi$
$942$		0			0
$943$	−0.809195	+	1.40157i	−0.0263510	+	0.0456413i
$944$	0.0507719	−	0.156260i	0.00165249	−	0.00508583i
$945$		0			0
$946$	1.60824	+	4.94964i	0.0522883	+	0.160927i
$947$	−15.0237	−	3.19339i	−0.488206	−	0.103771i	−0.0427694	−	0.999085i	$-0.513618\pi$
$947$	−15.0237	−	3.19339i	−0.488206	−	0.103771i	−0.445436	+	0.895314i	$0.646951\pi$
$948$		0			0
$949$	2.28600	+	3.95947i	0.0742067	+	0.128530i
$950$	−26.4410	−	12.5060i	−0.857859	−	0.405747i
$951$		0			0
$952$	11.5865	−	5.15864i	0.375521	−	0.167193i
$953$	12.6455	+	38.9188i	0.409628	+	1.26070i	0.916969	+	0.398959i	$0.130628\pi$
$953$	12.6455	+	38.9188i	0.409628	+	1.26070i	−0.507341	+	0.861745i	$0.669372\pi$
$954$		0			0
$955$	12.8673	−	9.12521i	0.416375	−	0.295285i
$956$	−4.64999	−	5.16434i	−0.150391	−	0.167027i
$957$		0			0
$958$	−34.1431	+	7.25735i	−1.10311	+	0.234474i
$959$	−16.3516	−	7.28019i	−0.528020	−	0.235089i
$960$		0			0
$961$	−20.4230	+	9.09289i	−0.658805	+	0.293319i
$962$	7.87516	−	5.72164i	0.253905	−	0.184473i
$963$		0			0
$964$	−29.4352	−	21.3859i	−0.948043	−	0.688794i
$965$	−6.39299	+	10.7857i	−0.205798	+	0.347203i
$966$		0			0
$967$	16.3259	−	3.47018i	0.525007	−	0.111594i	0.0622185	−	0.998063i	$-0.480182\pi$
$967$	16.3259	−	3.47018i	0.525007	−	0.111594i	0.462788	+	0.886469i	$0.346849\pi$
$968$	−12.6141	−	21.8482i	−0.405432	−	0.702229i
$969$		0			0
$970$	7.86980	+	8.94431i	0.252684	+	0.287184i
$971$	10.2477	+	31.5391i	0.328863	+	1.01214i	0.969667	+	0.244432i	$0.0786014\pi$
$971$	10.2477	+	31.5391i	0.328863	+	1.01214i	−0.640803	+	0.767705i	$0.721399\pi$
$972$		0			0
$973$	−11.9286	−	8.66664i	−0.382414	−	0.277840i
$974$	−2.71298	+	4.69902i	−0.0869295	+	0.150566i
$975$		0			0
$976$	0.518895	+	0.898752i	0.0166094	+	0.0287684i
$977$	−2.04222	+	19.4304i	−0.0653363	+	0.621633i	0.912036	+	0.410109i	$0.134509\pi$
$977$	−2.04222	+	19.4304i	−0.0653363	+	0.621633i	−0.977373	+	0.211524i	$0.932157\pi$
$978$		0			0
$979$	−20.1692	−	4.28710i	−0.644612	−	0.137016i
$980$	5.00035	+	16.0115i	0.159730	+	0.511468i
$981$		0			0
$982$	36.6619			1.16993
$983$	−22.9263	−	25.4622i	−0.731234	−	0.812117i	0.256782	−	0.966469i	$-0.417338\pi$
$983$	−22.9263	−	25.4622i	−0.731234	−	0.812117i	−0.988016	+	0.154352i	$0.950671\pi$
$984$		0			0
$985$	−3.16171	+	3.43153i	−0.100740	+	0.109338i
$986$	2.89608	−	27.5543i	0.0922298	−	0.877508i
$987$		0			0
$988$	1.54166	+	14.6679i	0.0490466	+	0.466647i
$989$	−2.12995	−	1.54750i	−0.0677284	−	0.0492075i
$990$		0			0
$991$	1.53877	−	1.11799i	0.0488808	−	0.0355140i	−0.563077	−	0.826405i	$-0.690382\pi$
$991$	1.53877	−	1.11799i	0.0488808	−	0.0355140i	0.611957	+	0.790891i	$0.290382\pi$
$992$	−11.0553	−	12.2782i	−0.351006	−	0.389832i
$993$		0			0
$994$	13.0720	−	2.77855i	0.414620	−	0.0881302i
$995$	−3.35940	−	5.97576i	−0.106500	−	0.189444i
$996$		0			0
$997$	−37.4240	−	7.95471i	−1.18523	−	0.251928i	−0.427205	−	0.904155i	$-0.640502\pi$
$997$	−37.4240	−	7.95471i	−1.18523	−	0.251928i	−0.758024	+	0.652226i	$0.773835\pi$
$998$	−30.7812	−	22.3639i	−0.974363	−	0.707916i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.316.17		224
3.2	odd	2		225.2.q.a.16.12	✓	224
9.4	even	3	inner	675.2.r.a.91.12		224
9.5	odd	6		225.2.q.a.166.17	yes	224
25.11	even	5	inner	675.2.r.a.586.12		224
75.11	odd	10		225.2.q.a.61.17	yes	224
225.86	odd	30		225.2.q.a.211.12	yes	224
225.211	even	15	inner	675.2.r.a.361.17		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.12	✓	224	3.2	odd	2
225.2.q.a.61.17	yes	224	75.11	odd	10
225.2.q.a.166.17	yes	224	9.5	odd	6
225.2.q.a.211.12	yes	224	225.86	odd	30
675.2.r.a.91.12		224	9.4	even	3	inner
675.2.r.a.316.17		224	1.1	even	1	trivial
675.2.r.a.361.17		224	225.211	even	15	inner
675.2.r.a.586.12		224	25.11	even	5	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.808045 - 0.359765i) q^{2} +(-0.814755 + 0.904878i) q^{4} +(-1.09577 - 1.94918i) q^{5} +(-0.458035 + 0.793340i) q^{7} +(-0.879476 + 2.70675i) q^{8} +O(q^{10})\)	\(q+(0.808045 - 0.359765i) q^{2} +(-0.814755 + 0.904878i) q^{4} +(-1.09577 - 1.94918i) q^{5} +(-0.458035 + 0.793340i) q^{7} +(-0.879476 + 2.70675i) q^{8} +(-1.58668 - 1.18080i) q^{10} +(-1.33506 + 0.594408i) q^{11} +(-1.67311 - 0.744918i) q^{13} +(-0.0846971 + 0.805839i) q^{14} +(0.00858220 + 0.0816542i) q^{16} +(-1.50326 + 4.62656i) q^{17} +(-2.04373 + 6.28996i) q^{19} +(2.65655 + 0.596562i) q^{20} +(-0.864943 + 0.960617i) q^{22} +(0.0683526 - 0.650331i) q^{23} +(-2.59857 + 4.27170i) q^{25} -1.61995 q^{26} +(-0.344689 - 1.06084i) q^{28} +(-6.29829 - 1.33874i) q^{29} +(2.87587 - 0.611285i) q^{31} +(-2.80973 - 4.86660i) q^{32} +(0.449771 + 4.27929i) q^{34} +(2.04826 + 0.0234710i) q^{35} +(-4.86137 + 3.53200i) q^{37} +(0.611478 + 5.81783i) q^{38} +(6.23963 - 1.25173i) q^{40} +(-2.26096 - 1.00664i) q^{41} +(2.01308 - 3.48676i) q^{43} +(0.549883 - 1.69237i) q^{44} +(-0.178734 - 0.550087i) q^{46} +(-5.26308 - 1.11870i) q^{47} +(3.08041 + 5.33542i) q^{49} +(-0.562952 + 4.38660i) q^{50} +(2.03724 - 0.907036i) q^{52} +(3.46201 + 10.6550i) q^{53} +(2.62153 + 1.95093i) q^{55} +(-1.74454 - 1.93751i) q^{56} +(-5.57093 + 1.18414i) q^{58} +(-1.82813 - 0.813937i) q^{59} +(11.5472 - 5.14113i) q^{61} +(2.10391 - 1.52858i) q^{62} +(-4.15407 - 3.01811i) q^{64} +(0.381374 + 4.07745i) q^{65} +(8.34092 - 1.77292i) q^{67} +(-2.96168 - 5.12978i) q^{68} +(1.66353 - 0.717926i) q^{70} +(-5.09668 - 15.6860i) q^{71} +(-2.01962 - 1.46734i) q^{73} +(-2.65752 + 4.60296i) q^{74} +(-4.02650 - 6.97410i) q^{76} +(0.139938 - 1.33142i) q^{77} +(-6.05809 - 1.28769i) q^{79} +(0.149754 - 0.106203i) q^{80} -2.18911 q^{82} +(-2.67975 - 2.97617i) q^{83} +(10.6652 - 2.13954i) q^{85} +(0.372247 - 3.54169i) q^{86} +(-0.434758 - 4.13645i) q^{88} +(11.4149 + 8.29340i) q^{89} +(1.35732 - 0.986149i) q^{91} +(0.532779 + 0.591712i) q^{92} +(-4.65527 + 0.989508i) q^{94} +(14.4997 - 2.90877i) q^{95} +(-5.89193 - 1.25237i) q^{97} +(4.40860 + 3.20304i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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