LMFDB - Embedded newform 864.2.bn.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.1
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41409 - 0.0185843i) q^{2} +(1.99931 + 0.0525599i) q^{4} +(-0.473408 - 0.363259i) q^{5} +(-2.79519 + 0.748968i) q^{7} +(-2.82623 - 0.111480i) q^{8} +O(q^{10})$	\(q+(-1.41409 - 0.0185843i) q^{2} +(1.99931 + 0.0525599i) q^{4} +(-0.473408 - 0.363259i) q^{5} +(-2.79519 + 0.748968i) q^{7} +(-2.82623 - 0.111480i) q^{8} +(0.662692 + 0.522479i) q^{10} +(-0.328859 + 2.49793i) q^{11} +(4.39502 - 0.578615i) q^{13} +(3.96657 - 1.00716i) q^{14} +(3.99447 + 0.210167i) q^{16} +1.23139 q^{17} +(-5.87478 - 2.43342i) q^{19} +(-0.927397 - 0.751149i) q^{20} +(0.511459 - 3.52619i) q^{22} +(-0.401921 + 1.49999i) q^{23} +(-1.20194 - 4.48569i) q^{25} +(-6.22571 + 0.736536i) q^{26} +(-5.62781 + 1.35050i) q^{28} +(-4.79825 - 6.25320i) q^{29} +(2.70334 - 1.56078i) q^{31} +(-5.64465 - 0.371430i) q^{32} +(-1.74130 - 0.0228845i) q^{34} +(1.59533 + 0.660809i) q^{35} +(-0.693729 - 1.67481i) q^{37} +(8.26226 + 3.55025i) q^{38} +(1.29746 + 1.07943i) q^{40} +(-4.75483 - 1.27405i) q^{41} +(-6.22527 - 0.819572i) q^{43} +(-0.788781 + 4.97685i) q^{44} +(0.596230 - 2.11365i) q^{46} +(-4.57892 - 2.64364i) q^{47} +(1.18994 - 0.687014i) q^{49} +(1.61629 + 6.36551i) q^{50} +(8.81741 - 0.925829i) q^{52} +(4.62779 + 11.1725i) q^{53} +(1.06308 - 1.06308i) q^{55} +(7.98334 - 1.80515i) q^{56} +(6.66895 + 8.93177i) q^{58} +(6.31937 - 8.23556i) q^{59} +(-3.02595 + 2.32189i) q^{61} +(-3.85178 + 2.15684i) q^{62} +(7.97514 + 0.630137i) q^{64} +(-2.29083 - 1.32261i) q^{65} +(-11.0744 + 1.45797i) q^{67} +(2.46193 + 0.0647216i) q^{68} +(-2.24367 - 0.964093i) q^{70} +(-1.59136 + 1.59136i) q^{71} +(-9.90510 - 9.90510i) q^{73} +(0.949871 + 2.38123i) q^{74} +(-11.6176 - 5.17393i) q^{76} +(-0.951648 - 7.22849i) q^{77} +(1.21078 - 2.09714i) q^{79} +(-1.81467 - 1.55052i) q^{80} +(6.70009 + 1.88999i) q^{82} +(-6.05141 - 7.88635i) q^{83} +(-0.582950 - 0.447313i) q^{85} +(8.78787 + 1.27464i) q^{86} +(1.20790 - 7.02306i) q^{88} +(-9.32026 - 9.32026i) q^{89} +(-11.8515 + 4.90907i) q^{91} +(-0.882404 + 2.97782i) q^{92} +(6.42588 + 3.82344i) q^{94} +(1.89721 + 3.28607i) q^{95} +(-2.26617 + 3.92513i) q^{97} +(-1.69546 + 0.949387i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.41409	−	0.0185843i	−0.999914	−	0.0131411i
$2$	−1.41409	−	0.0185843i	−0.999914	−	0.0131411i
$3$		0			0
$3$		0			0
$4$	1.99931	+	0.0525599i	0.999655	+	0.0262799i
$5$	−0.473408	−	0.363259i	−0.211715	−	0.162454i	0.497461	−	0.867487i	$-0.334266\pi$
$5$	−0.473408	−	0.363259i	−0.211715	−	0.162454i	−0.709175	+	0.705032i	$0.750933\pi$
$6$		0			0
$7$	−2.79519	+	0.748968i	−1.05648	+	0.283083i	−0.744928	−	0.667145i	$-0.767516\pi$
$7$	−2.79519	+	0.748968i	−1.05648	+	0.283083i	−0.311554	+	0.950228i	$0.600849\pi$
$8$	−2.82623	−	0.111480i	−0.999223	−	0.0394142i
$9$		0			0
$10$	0.662692	+	0.522479i	0.209562	+	0.165222i
$11$	−0.328859	+	2.49793i	−0.0991546	+	0.753154i	0.867566	+	0.497321i	$0.165683\pi$
$11$	−0.328859	+	2.49793i	−0.0991546	+	0.753154i	−0.966721	+	0.255833i	$0.917650\pi$
$12$		0			0
$13$	4.39502	−	0.578615i	1.21896	−	0.160479i	0.506529	−	0.862223i	$-0.330928\pi$
$13$	4.39502	−	0.578615i	1.21896	−	0.160479i	0.712430	+	0.701744i	$0.247595\pi$
$14$	3.96657	−	1.00716i	1.06011	−	0.269176i
$15$		0			0
$16$	3.99447	+	0.210167i	0.998619	+	0.0525417i
$17$	1.23139			0.298656			0.149328	−	0.988788i	$-0.452289\pi$
$17$	1.23139			0.298656			0.149328	+	0.988788i	$0.452289\pi$
$18$		0			0
$19$	−5.87478	−	2.43342i	−1.34777	−	0.558264i	−0.412098	−	0.911140i	$-0.635204\pi$
$19$	−5.87478	−	2.43342i	−1.34777	−	0.558264i	−0.935670	+	0.352876i	$0.885204\pi$
$20$	−0.927397	−	0.751149i	−0.207372	−	0.167962i
$21$		0			0
$22$	0.511459	−	3.52619i	0.109043	−	0.751786i
$23$	−0.401921	+	1.49999i	−0.0838064	+	0.312770i	−0.995085	−	0.0990196i	$-0.968429\pi$
$23$	−0.401921	+	1.49999i	−0.0838064	+	0.312770i	0.911279	+	0.411789i	$0.135096\pi$
$24$		0			0
$25$	−1.20194	−	4.48569i	−0.240387	−	0.897138i
$26$	−6.22571	+	0.736536i	−1.22096	+	0.144447i
$27$		0			0
$28$	−5.62781	+	1.35050i	−1.06356	+	0.255221i
$29$	−4.79825	−	6.25320i	−0.891012	−	1.16119i	−0.986172	−	0.165728i	$-0.947003\pi$
$29$	−4.79825	−	6.25320i	−0.891012	−	1.16119i	0.0951591	−	0.995462i	$-0.469664\pi$
$30$		0			0
$31$	2.70334	−	1.56078i	0.485535	−	0.280324i	−0.237185	−	0.971464i	$-0.576225\pi$
$31$	2.70334	−	1.56078i	0.485535	−	0.280324i	0.722720	+	0.691141i	$0.242892\pi$
$32$	−5.64465	−	0.371430i	−0.997842	−	0.0656601i
$33$		0			0
$34$	−1.74130	−	0.0228845i	−0.298630	−	0.00392466i
$35$	1.59533	+	0.660809i	0.269661	+	0.111697i
$36$		0			0
$37$	−0.693729	−	1.67481i	−0.114048	−	0.275337i	0.856541	−	0.516080i	$-0.172609\pi$
$37$	−0.693729	−	1.67481i	−0.114048	−	0.275337i	−0.970589	+	0.240742i	$0.922609\pi$
$38$	8.26226	+	3.55025i	1.34032	+	0.575927i
$39$		0			0
$40$	1.29746	+	1.07943i	0.205147	+	0.170673i
$41$	−4.75483	−	1.27405i	−0.742580	−	0.198974i	−0.132356	−	0.991202i	$-0.542254\pi$
$41$	−4.75483	−	1.27405i	−0.742580	−	0.198974i	−0.610224	+	0.792229i	$0.708921\pi$
$42$		0			0
$43$	−6.22527	−	0.819572i	−0.949344	−	0.124984i	−0.360078	−	0.932922i	$-0.617250\pi$
$43$	−6.22527	−	0.819572i	−0.949344	−	0.124984i	−0.589267	+	0.807939i	$0.700583\pi$
$44$	−0.788781	+	4.97685i	−0.118913	+	0.750288i
$45$		0			0
$46$	0.596230	−	2.11365i	0.0879093	−	0.311641i
$47$	−4.57892	−	2.64364i	−0.667904	−	0.385614i	0.127378	−	0.991854i	$-0.459344\pi$
$47$	−4.57892	−	2.64364i	−0.667904	−	0.385614i	−0.795282	+	0.606240i	$0.792677\pi$
$48$		0			0
$49$	1.18994	−	0.687014i	0.169992	−	0.0981449i
$50$	1.61629	+	6.36551i	0.228577	+	0.900219i
$51$		0			0
$52$	8.81741	−	0.925829i	1.22276	−	0.128389i
$53$	4.62779	+	11.1725i	0.635675	+	1.53466i	0.832387	+	0.554195i	$0.186974\pi$
$53$	4.62779	+	11.1725i	0.635675	+	1.53466i	−0.196712	+	0.980461i	$0.563026\pi$
$54$		0			0
$55$	1.06308	−	1.06308i	0.143346	−	0.143346i
$56$	7.98334	−	1.80515i	1.06682	−	0.241223i
$57$		0			0
$58$	6.66895	+	8.93177i	0.875676	+	1.17280i
$59$	6.31937	−	8.23556i	0.822712	−	1.07218i	−0.173467	−	0.984840i	$-0.555497\pi$
$59$	6.31937	−	8.23556i	0.822712	−	1.07218i	0.996179	−	0.0873390i	$-0.0278363\pi$
$60$		0			0
$61$	−3.02595	+	2.32189i	−0.387433	+	0.297288i	−0.784052	−	0.620696i	$-0.786850\pi$
$61$	−3.02595	+	2.32189i	−0.387433	+	0.297288i	0.396618	+	0.917984i	$0.370184\pi$
$62$	−3.85178	+	2.15684i	−0.489177	+	0.273919i
$63$		0			0
$64$	7.97514	+	0.630137i	0.996893	+	0.0787672i
$65$	−2.29083	−	1.32261i	−0.284142	−	0.164049i
$66$		0			0
$67$	−11.0744	+	1.45797i	−1.35295	+	0.178120i	−0.771899	−	0.635745i	$-0.780693\pi$
$67$	−11.0744	+	1.45797i	−1.35295	+	0.178120i	−0.581054	+	0.813865i	$0.697359\pi$
$68$	2.46193	+	0.0647216i	0.298552	+	0.00784865i
$69$		0			0
$70$	−2.24367	−	0.964093i	−0.268170	−	0.115231i
$71$	−1.59136	+	1.59136i	−0.188860	+	0.188860i	−0.795203	−	0.606343i	$-0.792636\pi$
$71$	−1.59136	+	1.59136i	−0.188860	+	0.188860i	0.606343	+	0.795203i	$0.292636\pi$
$72$		0			0
$73$	−9.90510	−	9.90510i	−1.15930	−	1.15930i	−0.984625	−	0.174679i	$-0.944111\pi$
$73$	−9.90510	−	9.90510i	−1.15930	−	1.15930i	−0.174679	−	0.984625i	$-0.555889\pi$
$74$	0.949871	+	2.38123i	0.110420	+	0.276812i
$75$		0			0
$76$	−11.6176	−	5.17393i	−1.33263	−	0.593490i
$77$	−0.951648	−	7.22849i	−0.108450	−	0.823763i
$78$		0			0
$79$	1.21078	−	2.09714i	0.136224	−	0.235947i	−0.789840	−	0.613312i	$-0.789837\pi$
$79$	1.21078	−	2.09714i	0.136224	−	0.235947i	0.926064	+	0.377366i	$0.123170\pi$
$80$	−1.81467	−	1.55052i	−0.202887	−	0.173354i
$81$		0			0
$82$	6.70009	+	1.88999i	0.739901	+	0.208715i
$83$	−6.05141	−	7.88635i	−0.664229	−	0.865640i	0.332774	−	0.943007i	$-0.392015\pi$
$83$	−6.05141	−	7.88635i	−0.664229	−	0.865640i	−0.997003	+	0.0773669i	$0.975349\pi$
$84$		0			0
$85$	−0.582950	−	0.447313i	−0.0632298	−	0.0485179i
$86$	8.78787	+	1.27464i	0.947620	+	0.137448i
$87$		0			0
$88$	1.20790	−	7.02306i	0.128763	−	0.748661i
$89$	−9.32026	−	9.32026i	−0.987946	−	0.987946i	0.0119821	−	0.999928i	$-0.496186\pi$
$89$	−9.32026	−	9.32026i	−0.987946	−	0.987946i	−0.999928	+	0.0119821i	$0.996186\pi$
$90$		0			0
$91$	−11.8515	+	4.90907i	−1.24238	+	0.514610i
$92$	−0.882404	+	2.97782i	−0.0919970	+	0.310459i
$93$		0			0
$94$	6.42588	+	3.82344i	0.662779	+	0.394358i
$95$	1.89721	+	3.28607i	0.194650	+	0.337143i
$96$		0			0
$97$	−2.26617	+	3.92513i	−0.230095	+	0.398536i	−0.957836	−	0.287316i	$-0.907237\pi$
$97$	−2.26617	+	3.92513i	−0.230095	+	0.398536i	0.727741	+	0.685852i	$0.240570\pi$
$98$	−1.69546	+	0.949387i	−0.171267	+	0.0959026i
$99$		0			0
$100$	−2.16728	−	9.03145i	−0.216728	−	0.903145i
$101$	1.93126	−	14.6694i	0.192168	−	1.45966i	−0.574968	−	0.818176i	$-0.694986\pi$
$101$	1.93126	−	14.6694i	0.192168	−	1.45966i	0.767136	−	0.641484i	$-0.221681\pi$
$102$		0			0
$103$	−4.02968	+	15.0390i	−0.397057	+	1.48184i	0.421192	+	0.906971i	$0.361612\pi$
$103$	−4.02968	+	15.0390i	−0.397057	+	1.48184i	−0.818249	+	0.574864i	$0.805055\pi$
$104$	−12.4858	+	1.14534i	−1.22434	+	0.112310i
$105$		0			0
$106$	−6.33648	−	15.8849i	−0.615453	−	1.54288i
$107$	0.406872	−	0.168532i	0.0393338	−	0.0162926i	−0.362930	−	0.931816i	$-0.618224\pi$
$107$	0.406872	−	0.168532i	0.0393338	−	0.0162926i	0.402264	+	0.915524i	$0.368224\pi$
$108$		0			0
$109$	5.17893	−	12.5031i	0.496052	−	1.19758i	−0.455541	−	0.890215i	$-0.650554\pi$
$109$	5.17893	−	12.5031i	0.496052	−	1.19758i	0.951593	−	0.307361i	$-0.0994458\pi$
$110$	−1.52305	+	1.48354i	−0.145217	+	0.141450i
$111$		0			0
$112$	−11.3227	+	2.40428i	−1.06990	+	0.227183i
$113$	−2.45227	−	4.24746i	−0.230690	−	0.399568i	0.727321	−	0.686297i	$-0.240765\pi$
$113$	−2.45227	−	4.24746i	−0.230690	−	0.399568i	−0.958011	+	0.286730i	$0.907432\pi$
$114$		0			0
$115$	0.735158	−	0.564107i	0.0685538	−	0.0526032i
$116$	−9.26452	−	12.7543i	−0.860189	−	1.18420i
$117$		0			0
$118$	−9.08922	+	11.5284i	−0.836730	+	1.06127i
$119$	−3.44196	+	0.922271i	−0.315524	+	0.0845445i
$120$		0			0
$121$	4.49368	+	1.20408i	0.408516	+	0.109462i
$122$	4.32212	−	3.22714i	0.391307	−	0.292171i
$123$		0			0
$124$	5.48686	−	2.97839i	0.492734	−	0.267467i
$125$	−2.20223	+	5.31666i	−0.196974	+	0.475536i
$126$		0			0
$127$			16.2567i			1.44255i	0.692650	+	0.721274i	$0.256443\pi$
$127$			16.2567i			1.44255i	−0.692650	+	0.721274i	$0.743557\pi$
$128$	−11.2659	−	1.03928i	−0.995772	−	0.0918606i
$129$		0			0
$130$	3.21486	+	1.91286i	0.281962	+	0.167769i
$131$	0.666924	+	5.06579i	0.0582695	+	0.442600i	0.995566	+	0.0940672i	$0.0299868\pi$
$131$	0.666924	+	5.06579i	0.0582695	+	0.442600i	−0.937296	+	0.348533i	$0.886680\pi$
$132$		0			0
$133$	18.2437	+	2.40183i	1.58193	+	0.208265i
$134$	15.6873	−	1.85590i	1.35518	−	0.160325i
$135$		0			0
$136$	−3.48019	−	0.137276i	−0.298424	−	0.0117713i
$137$	2.73278	+	10.1989i	0.233477	+	0.871348i	0.978829	+	0.204677i	$0.0656145\pi$
$137$	2.73278	+	10.1989i	0.233477	+	0.871348i	−0.745353	+	0.666671i	$0.767719\pi$
$138$		0			0
$139$	9.24985	−	12.0546i	0.784562	−	1.02246i	−0.214393	−	0.976748i	$-0.568777\pi$
$139$	9.24985	−	12.0546i	0.784562	−	1.02246i	0.998955	−	0.0457134i	$-0.0145561\pi$
$140$	3.15484	+	1.40501i	0.266632	+	0.118745i
$141$		0			0
$142$	2.27990	−	2.22076i	0.191325	−	0.186362i
$143$			11.1687i			0.933976i
$144$		0			0
$145$			4.70332i			0.390590i
$146$	13.8226	+	14.1908i	1.14397	+	1.17444i
$147$		0			0
$148$	−1.29895	−	3.38493i	−0.106773	−	0.278239i
$149$	8.04434	−	10.4836i	0.659018	−	0.858849i	−0.337577	−	0.941298i	$-0.609607\pi$
$149$	8.04434	−	10.4836i	0.659018	−	0.858849i	0.996595	+	0.0824487i	$0.0262741\pi$
$150$		0			0
$151$	−1.77740	−	6.63333i	−0.144642	−	0.539813i	−0.999771	−	0.0213971i	$-0.993189\pi$
$151$	−1.77740	−	6.63333i	−0.144642	−	0.539813i	0.855129	−	0.518416i	$-0.173478\pi$
$152$	16.3322	+	7.53231i	1.32472	+	0.610951i
$153$		0			0
$154$	1.21138	+	10.2394i	0.0976159	+	0.825117i
$155$	−1.84675	−	0.243129i	−0.148335	−	0.0195286i
$156$		0			0
$157$	1.85197	+	14.0671i	0.147803	+	1.12268i	0.891130	+	0.453747i	$0.149913\pi$
$157$	1.85197	+	14.0671i	0.147803	+	1.12268i	−0.743327	+	0.668928i	$0.766754\pi$
$158$	−1.75113	+	2.94305i	−0.139313	+	0.234136i
$159$		0			0
$160$	2.53730	+	2.22631i	0.200591	+	0.176005i
$161$		−	4.49378i		−	0.354160i
$162$		0			0
$163$	2.37281	−	5.72848i	0.185853	−	0.448689i	−0.803300	−	0.595574i	$-0.796925\pi$
$163$	2.37281	−	5.72848i	0.185853	−	0.448689i	0.989154	+	0.146885i	$0.0469247\pi$
$164$	−9.43942	−	2.79714i	−0.737095	−	0.218420i
$165$		0			0
$166$	8.41069	+	11.2645i	0.652796	+	0.874294i
$167$	−10.3058	−	2.76142i	−0.797484	−	0.213685i	−0.163005	−	0.986625i	$-0.552119\pi$
$167$	−10.3058	−	2.76142i	−0.797484	−	0.213685i	−0.634479	+	0.772940i	$0.718785\pi$
$168$		0			0
$169$	6.42436	−	1.72140i	0.494182	−	0.132416i
$170$	0.816031	+	0.643375i	0.0625867	+	0.0493446i
$171$		0			0
$172$	−12.4032	−	1.96578i	−0.945732	−	0.149889i
$173$	2.44886	−	1.87908i	0.186183	−	0.142864i	−0.511464	−	0.859305i	$-0.670897\pi$
$173$	2.44886	−	1.87908i	0.186183	−	0.142864i	0.697648	+	0.716441i	$0.254230\pi$
$174$		0			0
$175$	6.71928	+	11.6381i	0.507930	+	0.879760i
$176$	−1.83860	+	9.90880i	−0.138590	+	0.746904i
$177$		0			0
$178$	13.0065	+	13.3529i	0.974878	+	1.00084i
$179$	7.21844	−	17.4268i	0.539531	−	1.30254i	−0.385519	−	0.922700i	$-0.625978\pi$
$179$	7.21844	−	17.4268i	0.539531	−	1.30254i	0.925051	−	0.379844i	$-0.124022\pi$
$180$		0			0
$181$	−10.5972	+	4.38949i	−0.787681	+	0.326268i	−0.740011	−	0.672595i	$-0.765180\pi$
$181$	−10.5972	+	4.38949i	−0.787681	+	0.326268i	−0.0476703	+	0.998863i	$0.515180\pi$
$182$	16.8504	−	6.72162i	1.24903	−	0.498240i
$183$		0			0
$184$	1.30314	−	4.19451i	0.0960688	−	0.309224i
$185$	−0.279973	+	1.04487i	−0.0205840	+	0.0768205i
$186$		0			0
$187$	−0.404953	+	3.07592i	−0.0296131	+	0.224934i
$188$	−9.01572	−	5.52612i	−0.657539	−	0.403034i
$189$		0			0
$190$	−2.62176	−	4.68206i	−0.190203	−	0.339672i
$191$	−7.03189	+	12.1796i	−0.508810	+	0.881284i	0.491138	+	0.871082i	$0.336581\pi$
$191$	−7.03189	+	12.1796i	−0.508810	+	0.881284i	−0.999948	+	0.0102027i	$0.996752\pi$
$192$		0			0
$193$	5.47293	+	9.47939i	0.393950	+	0.682342i	0.992967	−	0.118395i	$-0.0377749\pi$
$193$	5.47293	+	9.47939i	0.393950	+	0.682342i	−0.599016	+	0.800737i	$0.704442\pi$
$194$	3.27752	−	5.50837i	0.235312	−	0.395478i
$195$		0			0
$196$	2.41518	−	1.31101i	0.172513	−	0.0936436i
$197$	23.5031	−	9.73530i	1.67453	−	0.693612i	0.675485	−	0.737374i	$-0.263934\pi$
$197$	23.5031	−	9.73530i	1.67453	−	0.693612i	0.999042	+	0.0437622i	$0.0139344\pi$
$198$		0			0
$199$	6.34951	+	6.34951i	0.450105	+	0.450105i	0.895389	−	0.445284i	$-0.146897\pi$
$199$	6.34951	+	6.34951i	0.450105	+	0.450105i	−0.445284	+	0.895389i	$0.646897\pi$
$200$	2.89688	+	12.8116i	0.204841	+	0.905915i
$201$		0			0
$202$	−3.00360	+	20.7080i	−0.211333	+	1.45701i
$203$	18.0955	+	13.8851i	1.27005	+	0.974545i
$204$		0			0
$205$	1.78817	+	2.33038i	0.124891	+	0.162761i
$206$	5.97783	−	21.1916i	0.416495	−	1.47649i
$207$		0			0
$208$	17.6774	−	1.38758i	1.22571	−	0.0962112i
$209$	8.01047	−	13.8745i	0.554096	−	0.959722i
$210$		0			0
$211$	−0.596276	−	4.52917i	−0.0410494	−	0.311801i	−0.999635	−	0.0269980i	$-0.991405\pi$
$211$	−0.596276	−	4.52917i	−0.0410494	−	0.311801i	0.958586	−	0.284803i	$-0.0919281\pi$
$212$	8.66515	+	22.5805i	0.595125	+	1.55083i
$213$		0			0
$214$	−0.578486	+	0.230758i	−0.0395445	+	0.0157743i
$215$	2.64938	+	2.64938i	0.180686	+	0.180686i
$216$		0			0
$217$	−6.38738	+	6.38738i	−0.433604	+	0.433604i
$218$	−7.55585	+	17.5842i	−0.511747	+	1.19095i
$219$		0			0
$220$	2.18130	−	2.06955i	0.147063	−	0.139529i
$221$	5.41198	−	0.712500i	0.364049	−	0.0479280i
$222$		0			0
$223$	−9.32956	−	5.38642i	−0.624753	−	0.360701i	0.153964	−	0.988076i	$-0.450796\pi$
$223$	−9.32956	−	5.38642i	−0.624753	−	0.360701i	−0.778717	+	0.627375i	$0.784129\pi$
$224$	16.0560	−	3.18945i	1.07279	−	0.213104i
$225$		0			0
$226$	3.38880	+	6.05187i	0.225420	+	0.402565i
$227$	−14.4752	+	11.1072i	−0.960752	+	0.737211i	−0.964856	−	0.262781i	$-0.915360\pi$
$227$	−14.4752	+	11.1072i	−0.960752	+	0.737211i	0.00410351	+	0.999992i	$0.498694\pi$
$228$		0			0
$229$	5.16403	−	6.72990i	0.341249	−	0.444724i	−0.590930	−	0.806723i	$-0.701239\pi$
$229$	5.16403	−	6.72990i	0.341249	−	0.444724i	0.932178	+	0.361999i	$0.117906\pi$
$230$	−1.05006	+	0.784036i	−0.0692392	+	0.0516978i
$231$		0			0
$232$	12.8638	+	18.2079i	0.844553	+	1.19541i
$233$	−8.24259	+	8.24259i	−0.539990	+	0.539990i	−0.923526	−	0.383536i	$-0.874706\pi$
$233$	−8.24259	+	8.24259i	−0.539990	+	0.539990i	0.383536	+	0.923526i	$0.374706\pi$
$234$		0			0
$235$	1.20737	+	2.91485i	0.0787603	+	0.190144i
$236$	13.0672	−	16.1333i	0.850604	−	1.05019i
$237$		0			0
$238$	4.88439	−	1.24021i	0.316608	−	0.0803908i
$239$	−6.82041	+	3.93776i	−0.441176	+	0.254713i	−0.704096	−	0.710105i	$-0.748648\pi$
$239$	−6.82041	+	3.93776i	−0.441176	+	0.254713i	0.262921	+	0.964817i	$0.415314\pi$
$240$		0			0
$241$	22.2379	+	12.8390i	1.43247	+	0.827036i	0.997309	−	0.0733179i	$-0.0233588\pi$
$241$	22.2379	+	12.8390i	1.43247	+	0.827036i	0.435159	+	0.900354i	$0.356692\pi$
$242$	−6.33210	−	1.78619i	−0.407043	−	0.114821i
$243$		0			0
$244$	−6.17185	+	4.48314i	−0.395112	+	0.287004i
$245$	−0.812894	−	0.107019i	−0.0519339	−	0.00683722i
$246$		0			0
$247$	−27.2278	−	7.29567i	−1.73246	−	0.464212i
$248$	−7.81427	+	4.10974i	−0.496206	+	0.260969i
$249$		0			0
$250$	3.21296	−	7.47731i	0.203206	−	0.472907i
$251$	8.95781	+	21.6261i	0.565412	+	1.36503i	0.905386	+	0.424590i	$0.139582\pi$
$251$	8.95781	+	21.6261i	0.565412	+	1.36503i	−0.339974	+	0.940435i	$0.610418\pi$
$252$		0			0
$253$	−3.61470	−	1.49726i	−0.227254	−	0.0941317i
$254$	0.302119	−	22.9884i	0.0189567	−	1.44242i
$255$		0			0
$256$	15.9117	+	1.67901i	0.994479	+	0.104938i
$257$	3.74788	−	2.16384i	0.233786	−	0.134977i	−0.378531	−	0.925589i	$-0.623571\pi$
$257$	3.74788	−	2.16384i	0.233786	−	0.134977i	0.612318	+	0.790612i	$0.290237\pi$
$258$		0			0
$259$	3.19348	+	4.16183i	0.198433	+	0.258603i
$260$	−4.51055	−	2.76471i	−0.279733	−	0.171460i
$261$		0			0
$262$	−0.848948	−	7.17589i	−0.0524482	−	0.443328i
$263$	4.60833	+	17.1985i	0.284162	+	1.06051i	0.949449	+	0.313920i	$0.101642\pi$
$263$	4.60833	+	17.1985i	0.284162	+	1.06051i	−0.665287	+	0.746587i	$0.731691\pi$
$264$		0			0
$265$	1.86767	−	6.97022i	0.114730	−	0.428177i
$266$	−25.7536	−	3.73545i	−1.57905	−	0.229035i
$267$		0			0
$268$	−22.2178	+	2.33287i	−1.35717	+	0.142503i
$269$	13.0106	+	5.38915i	0.793268	+	0.328582i	0.742257	−	0.670116i	$-0.233756\pi$
$269$	13.0106	+	5.38915i	0.793268	+	0.328582i	0.0510114	+	0.998698i	$0.483756\pi$
$270$		0			0
$271$	27.9658			1.69880			0.849401	−	0.527748i	$-0.176963\pi$
$271$	27.9658			1.69880			0.849401	+	0.527748i	$0.176963\pi$
$272$	4.91875	+	0.258797i	0.298243	+	0.0156919i
$273$		0			0
$274$	−3.67486	−	14.4729i	−0.222006	−	0.874341i
$275$	11.6002	−	1.52720i	0.699519	−	0.0920934i
$276$		0			0
$277$	2.87754	−	21.8570i	0.172894	−	1.31326i	−0.656384	−	0.754427i	$-0.727915\pi$
$277$	2.87754	−	21.8570i	0.172894	−	1.31326i	0.829278	−	0.558836i	$-0.188752\pi$
$278$	−13.3042	+	16.8745i	−0.797930	+	1.01206i
$279$		0			0
$280$	−4.43511	−	2.04545i	−0.265049	−	0.122239i
$281$	−15.5431	+	4.16477i	−0.927226	+	0.248449i	−0.690671	−	0.723169i	$-0.742685\pi$
$281$	−15.5431	+	4.16477i	−0.927226	+	0.248449i	−0.236555	+	0.971618i	$0.576018\pi$
$282$		0			0
$283$	−19.1540	−	14.6974i	−1.13859	−	0.873669i	−0.145306	−	0.989387i	$-0.546417\pi$
$283$	−19.1540	−	14.6974i	−1.13859	−	0.873669i	−0.993282	+	0.115718i	$0.963083\pi$
$284$	−3.26526	+	3.09798i	−0.193758	+	0.183831i
$285$		0			0
$286$	0.207563	−	15.7936i	0.0122735	−	0.933895i
$287$	14.2449			0.840848
$288$		0			0
$289$	−15.4837			−0.910805
$290$	0.0874081	−	6.65093i	0.00513278	−	0.390556i
$291$		0			0
$292$	−19.2828	−	20.3240i	−1.12844	−	1.18937i
$293$	−8.22012	−	6.30752i	−0.480224	−	0.368489i	0.340098	−	0.940390i	$-0.389540\pi$
$293$	−8.22012	−	6.30752i	−0.480224	−	0.368489i	−0.820323	+	0.571901i	$0.806206\pi$
$294$		0			0
$295$	−5.98328	+	1.60322i	−0.348360	+	0.0933428i
$296$	1.77393	+	4.81073i	0.103108	+	0.279618i
$297$		0			0
$298$	−11.5703	+	14.6753i	−0.670247	+	0.850115i
$299$	−0.898534	+	6.82505i	−0.0519636	+	0.394703i
$300$		0			0
$301$	18.0146	−	2.37167i	1.03835	−	0.136701i
$302$	2.39013	+	9.41317i	0.137536	+	0.541667i
$303$		0			0
$304$	−22.9553	−	10.9549i	−1.31657	−	0.628307i
$305$	2.27596			0.130321
$306$		0			0
$307$	27.8097	+	11.5191i	1.58718	+	0.657432i	0.989531	−	0.144324i	$-0.0461006\pi$
$307$	27.8097	+	11.5191i	1.58718	+	0.657432i	0.597652	+	0.801756i	$0.296101\pi$
$308$	−1.52271	−	14.5020i	−0.0867645	−	0.826328i
$309$		0			0
$310$	2.60696	+	0.378128i	0.148065	+	0.0214762i
$311$	−1.64701	+	6.14672i	−0.0933933	+	0.348549i	−0.996771	−	0.0802973i	$-0.974413\pi$
$311$	−1.64701	+	6.14672i	−0.0933933	+	0.348549i	0.903378	+	0.428846i	$0.141080\pi$
$312$		0			0
$313$	−6.67520	−	24.9122i	−0.377305	−	1.40812i	−0.849948	−	0.526866i	$-0.823367\pi$
$313$	−6.67520	−	24.9122i	−0.377305	−	1.40812i	0.472644	−	0.881254i	$-0.343300\pi$
$314$	−2.35742	−	19.9266i	−0.133037	−	1.12452i
$315$		0			0
$316$	2.53096	−	4.12919i	0.142377	−	0.232285i
$317$	14.7730	+	19.2525i	0.829734	+	1.08133i	0.995462	+	0.0951584i	$0.0303358\pi$
$317$	14.7730	+	19.2525i	0.829734	+	1.08133i	−0.165729	+	0.986171i	$0.552998\pi$
$318$		0			0
$319$	17.1980	−	9.92927i	0.962903	−	0.555932i
$320$	−3.54660	−	3.19536i	−0.198261	−	0.178626i
$321$		0			0
$322$	−0.0835139	+	6.35462i	−0.00465405	+	0.354129i
$323$	−7.23414	−	2.99648i	−0.402518	−	0.166729i
$324$		0			0
$325$	−7.87802	−	19.0192i	−0.436994	−	1.05500i
$326$	−3.46184	+	8.05650i	−0.191733	+	0.446208i
$327$		0			0
$328$	13.2962	+	4.13084i	0.734161	+	0.228087i
$329$	14.7789	+	3.96000i	0.814789	+	0.218322i
$330$		0			0
$331$	−18.7417	−	2.46739i	−1.03014	−	0.135620i	−0.403538	−	0.914963i	$-0.632220\pi$
$331$	−18.7417	−	2.46739i	−1.03014	−	0.135620i	−0.626598	+	0.779343i	$0.715553\pi$
$332$	−11.6841	−	16.0853i	−0.641250	−	0.882797i
$333$		0			0
$334$	14.5220	+	4.09643i	0.794607	+	0.224147i
$335$	5.77233	+	3.33266i	0.315376	+	0.182083i
$336$		0			0
$337$	−29.8219	+	17.2177i	−1.62450	+	0.937908i	−0.638810	+	0.769365i	$0.720573\pi$
$337$	−29.8219	+	17.2177i	−1.62450	+	0.937908i	−0.985694	+	0.168543i	$0.946094\pi$
$338$	−9.11662	+	2.31483i	−0.495879	+	0.125910i
$339$		0			0
$340$	−1.14199	−	0.924957i	−0.0619329	−	0.0501628i
$341$	3.00969	+	7.26604i	0.162984	+	0.393478i
$342$		0			0
$343$	11.5120	−	11.5120i	0.621588	−	0.621588i
$344$	17.5027	+	3.01029i	0.943681	+	0.162304i
$345$		0			0
$346$	−3.49784	+	2.61168i	−0.188045	+	0.140405i
$347$	−2.16711	+	2.82424i	−0.116337	+	0.151613i	−0.847892	−	0.530170i	$-0.822128\pi$
$347$	−2.16711	+	2.82424i	−0.116337	+	0.151613i	0.731555	+	0.681782i	$0.238795\pi$
$348$		0			0
$349$	−3.94224	+	3.02499i	−0.211023	+	0.161924i	−0.708865	−	0.705344i	$-0.750793\pi$
$349$	−3.94224	+	3.02499i	−0.211023	+	0.161924i	0.497842	+	0.867268i	$0.334126\pi$
$350$	−9.28539	−	16.5823i	−0.496325	−	0.886359i
$351$		0			0
$352$	2.78410	−	13.9778i	0.148393	−	0.745018i
$353$	11.1673	+	6.44747i	0.594378	+	0.343164i	0.766827	−	0.641854i	$-0.221835\pi$
$353$	11.1673	+	6.44747i	0.594378	+	0.343164i	−0.172449	+	0.985019i	$0.555168\pi$
$354$		0			0
$355$	1.33144	−	0.175287i	0.0706655	−	0.00930329i
$356$	−18.1442	−	19.1240i	−0.961642	−	1.01357i
$357$		0			0
$358$	−10.5314	+	24.5090i	−0.556601	+	1.29534i
$359$	−20.8993	+	20.8993i	−1.10302	+	1.10302i	−0.108978	+	0.994044i	$0.534758\pi$
$359$	−20.8993	+	20.8993i	−1.10302	+	1.10302i	−0.994044	+	0.108978i	$0.965242\pi$
$360$		0			0
$361$	15.1565	+	15.1565i	0.797713	+	0.797713i
$362$	15.0669	−	6.01020i	0.791901	−	0.315889i
$363$		0			0
$364$	−23.9529	+	9.19183i	−1.25547	+	0.481783i
$365$	1.09104	+	8.28728i	0.0571077	+	0.433776i
$366$		0			0
$367$	−3.02090	+	5.23235i	−0.157690	+	0.273126i	−0.934035	−	0.357181i	$-0.883738\pi$
$367$	−3.02090	+	5.23235i	−0.157690	+	0.273126i	0.776346	+	0.630308i	$0.217071\pi$
$368$	−1.92071	+	5.90721i	−0.100124	+	0.307934i
$369$		0			0
$370$	0.415325	−	1.47234i	0.0215917	−	0.0765434i
$371$	−21.3034	−	27.7631i	−1.10602	−	1.44139i
$372$		0			0
$373$	18.2154	+	13.9772i	0.943158	+	0.723711i	0.961121	−	0.276128i	$-0.0890514\pi$
$373$	18.2154	+	13.9772i	0.943158	+	0.723711i	−0.0179627	+	0.999839i	$0.505718\pi$
$374$	0.629804	−	4.34211i	0.0325664	−	0.224525i
$375$		0			0
$376$	12.6464	+	7.98199i	0.652186	+	0.411640i
$377$	−24.7066	−	24.7066i	−1.27245	−	1.27245i
$378$		0			0
$379$	−9.91785	+	4.10811i	−0.509446	+	0.211019i	−0.622574	−	0.782561i	$-0.713913\pi$
$379$	−9.91785	+	4.10811i	−0.509446	+	0.211019i	0.113128	+	0.993580i	$0.463913\pi$
$380$	3.62040	+	6.66958i	0.185722	+	0.342142i
$381$		0			0
$382$	10.1701	−	17.0924i	0.520347	−	0.874522i
$383$	−9.85743	−	17.0736i	−0.503691	−	0.872419i	−0.999991	−	0.00426763i	$-0.998642\pi$
$383$	−9.85743	−	17.0736i	−0.503691	−	0.872419i	0.496300	−	0.868151i	$-0.334692\pi$
$384$		0			0
$385$	−2.17529	+	3.76772i	−0.110863	+	0.192021i
$386$	−7.56306	−	13.5064i	−0.384949	−	0.687460i
$387$		0			0
$388$	−4.73708	+	7.72843i	−0.240489	+	0.392352i
$389$	−1.84957	+	14.0489i	−0.0937767	+	0.712305i	0.878378	+	0.477966i	$0.158626\pi$
$389$	−1.84957	+	14.0489i	−0.0937767	+	0.712305i	−0.972155	+	0.234339i	$0.924707\pi$
$390$		0			0
$391$	−0.494921	+	1.84707i	−0.0250293	+	0.0934104i
$392$	−3.43964	+	1.80901i	−0.173728	+	0.0913686i
$393$		0			0
$394$	−33.4165	+	13.3298i	−1.68350	+	0.671547i
$395$	−1.33500	+	0.552975i	−0.0671712	+	0.0278232i
$396$		0			0
$397$	3.77882	−	9.12288i	0.189654	−	0.457864i	−0.800239	−	0.599681i	$-0.795294\pi$
$397$	3.77882	−	9.12288i	0.189654	−	0.457864i	0.989893	+	0.141816i	$0.0452943\pi$
$398$	−8.86079	−	9.09679i	−0.444151	−	0.455981i
$399$		0			0
$400$	−3.85836	−	18.1706i	−0.192918	−	0.908529i
$401$	−10.5331	−	18.2439i	−0.525998	−	0.911056i	−0.999541	−	0.0302852i	$-0.990358\pi$
$401$	−10.5331	−	18.2439i	−0.525998	−	0.911056i	0.473543	−	0.880771i	$-0.342975\pi$
$402$		0			0
$403$	10.9782	−	8.42384i	0.546861	−	0.419621i
$404$	4.63221	−	29.2272i	0.230461	−	1.45411i
$405$		0			0
$406$	−25.3306	−	19.9711i	−1.25714	−	0.991151i
$407$	4.41170	−	1.18211i	0.218680	−	0.0585950i
$408$		0			0
$409$	−11.8099	−	3.16446i	−0.583964	−	0.156473i	−0.0452709	−	0.998975i	$-0.514415\pi$
$409$	−11.8099	−	3.16446i	−0.583964	−	0.156473i	−0.538693	+	0.842502i	$0.681082\pi$
$410$	−2.48532	−	3.32861i	−0.122741	−	0.164388i
$411$		0			0
$412$	−8.84703	+	29.8558i	−0.435862	+	1.47089i
$413$	−11.4956	+	27.7529i	−0.565664	+	1.36563i
$414$		0			0
$415$			5.93169i			0.291175i
$416$	−25.0232	+	1.63364i	−1.22687	+	0.0800957i
$417$		0			0
$418$	−11.5854	+	19.4710i	−0.566660	+	0.952358i
$419$	−2.25043	−	17.0937i	−0.109941	−	0.835082i	−0.954205	−	0.299154i	$-0.903295\pi$
$419$	−2.25043	−	17.0937i	−0.109941	−	0.835082i	0.844264	−	0.535927i	$-0.180038\pi$
$420$		0			0
$421$	8.67143	+	1.14162i	0.422620	+	0.0556389i	0.338837	−	0.940845i	$-0.389967\pi$
$421$	8.67143	+	1.14162i	0.422620	+	0.0556389i	0.0837827	+	0.996484i	$0.473300\pi$
$422$	0.759018	+	6.41574i	0.0369484	+	0.312313i
$423$		0			0
$424$	−11.8337	−	32.0919i	−0.574694	−	1.55852i
$425$	−1.48005	−	5.52363i	−0.0717930	−	0.267935i
$426$		0			0
$427$	6.71908	−	8.75647i	0.325159	−	0.423755i
$428$	0.822321	−	0.315562i	0.0397484	−	0.0152533i
$429$		0			0
$430$	−3.69722	−	3.79570i	−0.178296	−	0.183045i
$431$		−	10.5827i		−	0.509751i	−0.966974	−	0.254876i	$-0.917965\pi$
$431$		−	10.5827i		−	0.509751i	0.966974	−	0.254876i	$-0.0820345\pi$
$432$		0			0
$433$			11.1432i			0.535507i	0.963487	+	0.267754i	$0.0862814\pi$
$433$			11.1432i			0.535507i	−0.963487	+	0.267754i	$0.913719\pi$
$434$	9.15105	−	8.91364i	0.439264	−	0.427868i
$435$		0			0
$436$	11.0114	−	24.7253i	0.527353	−	1.18413i
$437$	6.01130	−	7.83408i	0.287560	−	0.374755i
$438$		0			0
$439$	4.31986	+	16.1220i	0.206176	+	0.769459i	0.989088	+	0.147326i	$0.0470668\pi$
$439$	4.31986	+	16.1220i	0.206176	+	0.769459i	−0.782912	+	0.622132i	$0.786267\pi$
$440$	−3.12302	+	2.88599i	−0.148884	+	0.137584i
$441$		0			0
$442$	−7.66627	+	0.906963i	−0.364647	+	0.0431398i
$443$	21.1043	+	2.77843i	1.00269	+	0.132007i	0.613955	−	0.789341i	$-0.289578\pi$
$443$	21.1043	+	2.77843i	1.00269	+	0.132007i	0.388738	+	0.921348i	$0.372911\pi$
$444$		0			0
$445$	1.02662	+	7.79796i	0.0486665	+	0.369659i
$446$	13.0927	+	7.79028i	0.619959	+	0.368880i
$447$		0			0
$448$	−22.7640	+	4.21178i	−1.07550	+	0.198988i
$449$			24.8626i			1.17334i	0.809826	+	0.586670i	$0.199561\pi$
$449$			24.8626i			1.17334i	−0.809826	+	0.586670i	$0.800439\pi$
$450$		0			0
$451$	4.74616	−	11.4583i	0.223488	−	0.539548i
$452$	−4.67961	−	8.62088i	−0.220110	−	0.405492i
$453$		0			0
$454$	20.6757	−	15.4376i	0.970357	−	0.724522i
$455$	7.39388	+	1.98118i	0.346630	+	0.0928794i
$456$		0			0
$457$	−4.00420	+	1.07292i	−0.187308	+	0.0501891i	−0.351254	−	0.936280i	$-0.614245\pi$
$457$	−4.00420	+	1.07292i	−0.187308	+	0.0501891i	0.163945	+	0.986469i	$0.447578\pi$
$458$	−7.42748	+	9.42072i	−0.347063	+	0.440201i
$459$		0			0
$460$	1.49946	−	1.08918i	0.0699126	−	0.0507835i
$461$	−32.1289	+	24.6534i	−1.49639	+	1.14822i	−0.545744	+	0.837952i	$0.683753\pi$
$461$	−32.1289	+	24.6534i	−1.49639	+	1.14822i	−0.950648	+	0.310271i	$0.899580\pi$
$462$		0			0
$463$	−6.09839	−	10.5627i	−0.283416	−	0.490891i	0.688808	−	0.724944i	$-0.258134\pi$
$463$	−6.09839	−	10.5627i	−0.283416	−	0.490891i	−0.972224	+	0.234053i	$0.924801\pi$
$464$	−17.8523	−	25.9867i	−0.828771	−	1.20640i
$465$		0			0
$466$	11.8090	−	11.5026i	0.547039	−	0.532847i
$467$	3.03044	−	7.31614i	0.140232	−	0.338550i	−0.838124	−	0.545480i	$-0.816347\pi$
$467$	3.03044	−	7.31614i	0.140232	−	0.338550i	0.978356	+	0.206930i	$0.0663472\pi$
$468$		0			0
$469$	29.8630	−	12.3697i	1.37895	−	0.571179i
$470$	−1.65316	−	4.14431i	−0.0762548	−	0.191163i
$471$		0			0
$472$	−18.7781	+	22.5711i	−0.864331	+	1.03892i
$473$	4.09447	−	15.2808i	0.188264	−	0.702610i
$474$		0			0
$475$	−3.85443	+	29.2773i	−0.176853	+	1.34333i
$476$	−6.93002	+	1.66300i	−0.317637	+	0.0762233i
$477$		0			0
$478$	9.71786	−	5.44161i	0.444485	−	0.248893i
$479$	5.38815	−	9.33255i	0.246191	−	0.426415i	−0.716275	−	0.697818i	$-0.754154\pi$
$479$	5.38815	−	9.33255i	0.246191	−	0.426415i	0.962466	+	0.271403i	$0.0874877\pi$
$480$		0			0
$481$	−4.01802	−	6.95942i	−0.183206	−	0.317322i
$482$	−31.2078	−	18.5689i	−1.42148	−	0.845788i
$483$		0			0
$484$	8.92097	+	2.64351i	0.405499	+	0.120160i
$485$	2.49866	−	1.03498i	0.113458	−	0.0469960i
$486$		0			0
$487$	10.3327	+	10.3327i	0.468219	+	0.468219i	0.901337	−	0.433118i	$-0.142587\pi$
$487$	10.3327	+	10.3327i	0.468219	+	0.468219i	−0.433118	+	0.901337i	$0.642587\pi$
$488$	8.81088	−	6.22487i	0.398850	−	0.281787i
$489$		0			0
$490$	1.14752	+	0.166442i	0.0518395	+	0.00751910i
$491$	−19.3751	−	14.8671i	−0.874388	−	0.670941i	0.0707922	−	0.997491i	$-0.477447\pi$
$491$	−19.3751	−	14.8671i	−0.874388	−	0.670941i	−0.945180	+	0.326550i	$0.894114\pi$
$492$		0			0
$493$	−5.90851	−	7.70012i	−0.266106	−	0.346796i
$494$	38.3670	+	10.8227i	1.72621	+	0.486939i
$495$		0			0
$496$	11.1265	−	5.66633i	0.499593	−	0.254426i
$497$	3.25627	−	5.64003i	0.146064	−	0.252990i
$498$		0			0
$499$	−4.76674	−	36.2070i	−0.213389	−	1.62085i	−0.677812	−	0.735235i	$-0.737072\pi$
$499$	−4.76674	−	36.2070i	−0.213389	−	1.62085i	0.464423	−	0.885613i	$-0.346262\pi$
$500$	−4.68238	+	10.5139i	−0.209403	+	0.470195i
$501$		0			0
$502$	−12.2653	−	30.7477i	−0.547425	−	1.37234i
$503$	−10.8748	−	10.8748i	−0.484882	−	0.484882i	0.421805	−	0.906687i	$-0.361397\pi$
$503$	−10.8748	−	10.8748i	−0.484882	−	0.484882i	−0.906687	+	0.421805i	$0.861397\pi$
$504$		0			0
$505$	−6.24307	+	6.24307i	−0.277813	+	0.277813i
$506$	5.08369	+	2.18443i	0.225997	+	0.0971099i
$507$		0			0
$508$	−0.854449	+	32.5021i	−0.0379100	+	1.44205i
$509$	−10.4299	+	1.37313i	−0.462299	+	0.0608628i	−0.358079	−	0.933691i	$-0.616568\pi$
$509$	−10.4299	+	1.37313i	−0.462299	+	0.0608628i	−0.104220	+	0.994554i	$0.533235\pi$
$510$		0			0
$511$	35.1052	+	20.2680i	1.55296	+	0.896604i
$512$	−22.4693	−	2.66998i	−0.993014	−	0.117998i
$513$		0			0
$514$	−5.34006	+	2.99022i	−0.235540	+	0.131893i
$515$	7.37073	−	5.65576i	0.324793	−	0.249223i
$516$		0			0
$517$	8.10944	−	10.5684i	0.356653	−	0.464799i
$518$	−4.43853	−	5.94455i	−0.195018	−	0.261189i
$519$		0			0
$520$	6.32695	+	3.99338i	0.277455	+	0.175121i
$521$	−2.73925	+	2.73925i	−0.120009	+	0.120009i	−0.764561	−	0.644552i	$-0.777044\pi$
$521$	−2.73925	+	2.73925i	−0.120009	+	0.120009i	0.644552	+	0.764561i	$0.277044\pi$
$522$		0			0
$523$	−3.09935	−	7.48250i	−0.135525	−	0.327187i	0.841518	−	0.540230i	$-0.181663\pi$
$523$	−3.09935	−	7.48250i	−0.135525	−	0.327187i	−0.977043	+	0.213043i	$0.931663\pi$
$524$	1.06713	+	10.1631i	0.0466178	+	0.443979i
$525$		0			0
$526$	−6.19698	−	24.4060i	−0.270201	−	1.06415i
$527$	3.32887	−	1.92192i	0.145008	−	0.0837203i
$528$		0			0
$529$	17.8302	+	10.2942i	0.775224	+	0.447576i
$530$	−2.77059	+	9.82182i	−0.120347	+	0.426633i
$531$		0			0
$532$	36.3485	+	5.76088i	1.57591	+	0.249766i
$533$	−21.6348	−	2.84827i	−0.937106	−	0.123372i
$534$		0			0
$535$	−0.253837	−	0.0680155i	−0.0109743	−	0.00294057i
$536$	31.4613	−	2.88599i	1.35892	−	0.124656i
$537$		0			0
$538$	−18.2980	−	7.86255i	−0.788882	−	0.338978i
$539$	1.32479	+	3.19833i	0.0570628	+	0.137762i
$540$		0			0
$541$	−31.0063	−	12.8432i	−1.33307	−	0.552174i	−0.401537	−	0.915843i	$-0.631524\pi$
$541$	−31.0063	−	12.8432i	−1.33307	−	0.552174i	−0.931528	+	0.363669i	$0.881524\pi$
$542$	−39.5462	−	0.519726i	−1.69866	−	0.0223241i
$543$		0			0
$544$	−6.95075	−	0.457374i	−0.298011	−	0.0196098i
$545$	−6.99360	+	4.03775i	−0.299573	+	0.172958i
$546$		0			0
$547$	−12.4802	−	16.2645i	−0.533613	−	0.695418i	0.446291	−	0.894888i	$-0.352745\pi$
$547$	−12.4802	−	16.2645i	−0.533613	−	0.695418i	−0.979904	+	0.199470i	$0.936078\pi$
$548$	4.92762	+	20.5343i	0.210497	+	0.877183i
$549$		0			0
$550$	−16.4321	+	1.94401i	−0.700668	+	0.0828930i
$551$	12.9720	+	48.4123i	0.552628	+	2.06243i
$552$		0			0
$553$	−1.81368	+	6.76874i	−0.0771254	+	0.287836i
$554$	−4.47530	+	30.8544i	−0.190137	+	1.31088i
$555$		0			0
$556$	19.1269	−	23.6148i	0.811161	−	1.00149i
$557$	21.7102	+	8.99268i	0.919893	+	0.381032i	0.791835	−	0.610735i	$-0.209126\pi$
$557$	21.7102	+	8.99268i	0.919893	+	0.381032i	0.128057	+	0.991767i	$0.459126\pi$
$558$		0			0
$559$	−27.8344			−1.17727
$560$	6.23364	+	2.97487i	0.263420	+	0.125711i
$561$		0			0
$562$	22.0568	−	5.60051i	0.930411	−	0.236243i
$563$	21.9618	−	2.89132i	0.925579	−	0.121855i	0.347356	−	0.937733i	$-0.387080\pi$
$563$	21.9618	−	2.89132i	0.925579	−	0.121855i	0.578223	+	0.815879i	$0.303746\pi$
$564$		0			0
$565$	−0.382002	+	2.90159i	−0.0160710	+	0.122071i
$566$	26.8124	+	21.1394i	1.12701	+	0.888556i
$567$		0			0
$568$	4.67496	−	4.32015i	0.196157	−	0.181269i
$569$	−8.10694	+	2.17225i	−0.339861	+	0.0910654i	−0.424713	−	0.905328i	$-0.639625\pi$
$569$	−8.10694	+	2.17225i	−0.339861	+	0.0910654i	0.0848520	+	0.996394i	$0.472958\pi$
$570$		0			0
$571$	30.8598	+	23.6796i	1.29144	+	0.990960i	0.999403	+	0.0345540i	$0.0110011\pi$
$571$	30.8598	+	23.6796i	1.29144	+	0.990960i	0.292041	+	0.956406i	$0.405666\pi$
$572$	−0.587027	+	22.3297i	−0.0245448	+	0.933653i
$573$		0			0
$574$	−20.1436	−	0.264731i	−0.840776	−	0.0110497i
$575$	7.21158			0.300744
$576$		0			0
$577$	−5.32345			−0.221618			−0.110809	−	0.993842i	$-0.535344\pi$
$577$	−5.32345			−0.221618			−0.110809	+	0.993842i	$0.535344\pi$
$578$	21.8953	+	0.287754i	0.910726	+	0.0119690i
$579$		0			0
$580$	−0.247206	+	9.40340i	−0.0102647	+	0.390455i
$581$	22.8215	+	17.5115i	0.946794	+	0.726500i
$582$		0			0
$583$	−29.4299	+	7.88572i	−1.21886	+	0.326593i
$584$	26.8899	+	29.0983i	1.11271	+	1.20410i
$585$		0			0
$586$	11.5068	+	9.07217i	0.475341	+	0.374768i
$587$	4.44575	−	33.7688i	0.183496	−	1.39379i	−0.613448	−	0.789735i	$-0.710218\pi$
$587$	4.44575	−	33.7688i	0.183496	−	1.39379i	0.796944	−	0.604053i	$-0.206449\pi$
$588$		0			0
$589$	−19.6796	+	2.59087i	−0.810883	+	0.106755i
$590$	8.49070	−	2.15590i	0.349557	−	0.0887569i
$591$		0			0
$592$	−2.41909	−	6.83579i	−0.0994241	−	0.280949i
$593$	−7.50160			−0.308054			−0.154027	−	0.988067i	$-0.549224\pi$
$593$	−7.50160			−0.308054			−0.154027	+	0.988067i	$0.549224\pi$
$594$		0			0
$595$	1.96448	+	0.813713i	0.0805357	+	0.0333590i
$596$	16.6341	−	20.5371i	0.681361	−	0.841234i
$597$		0			0
$598$	1.39745	−	9.63454i	0.0571459	−	0.393986i
$599$	4.34964	−	16.2331i	0.177722	−	0.663266i	−0.818350	−	0.574719i	$-0.805111\pi$
$599$	4.34964	−	16.2331i	0.177722	−	0.663266i	0.996072	−	0.0885464i	$-0.0282222\pi$
$600$		0			0
$601$	−4.75240	−	17.7362i	−0.193855	−	0.723475i	−0.992560	−	0.121753i	$-0.961148\pi$
$601$	−4.75240	−	17.7362i	−0.193855	−	0.723475i	0.798706	−	0.601722i	$-0.205518\pi$
$602$	−25.5184	+	3.01897i	−1.04005	+	0.123044i
$603$		0			0
$604$	−3.20492	−	13.3555i	−0.130406	−	0.543428i
$605$	−1.68995	−	2.20239i	−0.0687064	−	0.0895399i
$606$		0			0
$607$	22.1301	−	12.7768i	0.898232	−	0.518595i	0.0216061	−	0.999767i	$-0.493122\pi$
$607$	22.1301	−	12.7768i	0.898232	−	0.518595i	0.876626	+	0.481172i	$0.159789\pi$
$608$	32.2572	+	15.9178i	1.30820	+	0.645554i
$609$		0			0
$610$	−3.21841	−	0.0422972i	−0.130310	−	0.00171256i
$611$	−21.6541	−	8.96941i	−0.876030	−	0.362864i
$612$		0			0
$613$	14.3756	+	34.7057i	0.580624	+	1.40175i	0.892249	+	0.451545i	$0.149127\pi$
$613$	14.3756	+	34.7057i	0.580624	+	1.40175i	−0.311625	+	0.950205i	$0.600873\pi$
$614$	−39.1114	−	16.8059i	−1.57841	−	0.678233i
$615$		0			0
$616$	1.88374	+	20.5355i	0.0758982	+	0.827397i
$617$	−17.4866	−	4.68552i	−0.703984	−	0.188632i	−0.110969	−	0.993824i	$-0.535396\pi$
$617$	−17.4866	−	4.68552i	−0.703984	−	0.188632i	−0.593014	+	0.805192i	$0.702062\pi$
$618$		0			0
$619$	−0.979352	−	0.128934i	−0.0393635	−	0.00518230i	0.110819	−	0.993841i	$-0.464653\pi$
$619$	−0.979352	−	0.128934i	−0.0393635	−	0.00518230i	−0.150182	+	0.988658i	$0.547986\pi$
$620$	−3.67945	−	0.583156i	−0.147770	−	0.0234201i
$621$		0			0
$622$	2.44325	−	8.66142i	0.0979656	−	0.347291i
$623$	33.0325	+	19.0713i	1.32342	+	0.764076i
$624$		0			0
$625$	−17.1349	+	9.89285i	−0.685397	+	0.395714i
$626$	8.97637	+	35.3522i	0.358768	+	1.41296i
$627$		0			0
$628$	2.96329	+	28.2218i	0.118248	+	1.12617i
$629$	−0.854250	−	2.06234i	−0.0340612	−	0.0822310i
$630$		0			0
$631$	5.46175	−	5.46175i	0.217429	−	0.217429i	−0.589985	−	0.807414i	$-0.700866\pi$
$631$	5.46175	−	5.46175i	0.217429	−	0.217429i	0.807414	+	0.589985i	$0.200866\pi$
$632$	−3.65574	+	5.79202i	−0.145418	+	0.230394i
$633$		0			0
$634$	−20.5326	−	27.4994i	−0.815452	−	1.09214i
$635$	5.90539	−	7.69605i	0.234348	−	0.305408i
$636$		0			0
$637$	4.83231	−	3.70796i	0.191463	−	0.146915i
$638$	−24.5041	+	13.7213i	−0.970125	+	0.543231i
$639$		0			0
$640$	4.95583	+	4.58444i	0.195896	+	0.181216i
$641$	2.81377	+	1.62453i	0.111137	+	0.0641650i	0.554538	−	0.832158i	$-0.312895\pi$
$641$	2.81377	+	1.62453i	0.111137	+	0.0641650i	−0.443401	+	0.896323i	$0.646228\pi$
$642$		0			0
$643$	1.73206	−	0.228030i	0.0683058	−	0.00899264i	−0.0962958	−	0.995353i	$-0.530699\pi$
$643$	1.73206	−	0.228030i	0.0683058	−	0.00899264i	0.164602	+	0.986360i	$0.447366\pi$
$644$	0.236193	−	8.98446i	0.00930729	−	0.354037i
$645$		0			0
$646$	10.1741	+	4.37174i	0.400293	+	0.172004i
$647$	25.6597	−	25.6597i	1.00879	−	1.00879i	0.00882714	−	0.999961i	$-0.497190\pi$
$647$	25.6597	−	25.6597i	1.00879	−	1.00879i	0.999961	−	0.00882714i	$-0.00280980\pi$
$648$		0			0
$649$	18.4937	+	18.4937i	0.725940	+	0.725940i
$650$	10.7868	+	27.0413i	0.423093	+	1.06065i
$651$		0			0
$652$	5.04508	−	11.3283i	0.197580	−	0.443650i
$653$	1.56013	+	11.8503i	0.0610525	+	0.463740i	0.994476	+	0.104963i	$0.0334726\pi$
$653$	1.56013	+	11.8503i	0.0610525	+	0.463740i	−0.933424	+	0.358776i	$0.883194\pi$
$654$		0			0
$655$	1.52447	−	2.64046i	0.0595659	−	0.103171i
$656$	−18.7253	−	6.08848i	−0.731100	−	0.237715i
$657$		0			0
$658$	−20.8252	−	5.87446i	−0.811850	−	0.229010i
$659$	−22.8046	−	29.7196i	−0.888343	−	1.15771i	−0.986699	−	0.162560i	$-0.948025\pi$
$659$	−22.8046	−	29.7196i	−0.888343	−	1.15771i	0.0983559	−	0.995151i	$-0.468642\pi$
$660$		0			0
$661$	−22.3931	−	17.1828i	−0.870990	−	0.668334i	0.0733496	−	0.997306i	$-0.476631\pi$
$661$	−22.3931	−	17.1828i	−0.870990	−	0.668334i	−0.944340	+	0.328972i	$0.893298\pi$
$662$	26.4566	+	3.83741i	1.02826	+	0.149145i
$663$		0			0
$664$	16.2235	+	22.9633i	0.629594	+	0.891147i
$665$	−7.76422	−	7.76422i	−0.301084	−	0.301084i
$666$		0			0
$667$	11.3083	−	4.68403i	0.437858	−	0.181367i
$668$	−20.4593	−	6.06261i	−0.791593	−	0.234569i
$669$		0			0
$670$	−8.10067	−	4.81996i	−0.312956	−	0.186211i
$671$	−4.80482	−	8.32219i	−0.185488	−	0.321274i
$672$		0			0
$673$	−2.75278	+	4.76795i	−0.106112	+	0.183791i	−0.914192	−	0.405282i	$-0.867173\pi$
$673$	−2.75278	+	4.76795i	−0.106112	+	0.183791i	0.808080	+	0.589073i	$0.200507\pi$
$674$	42.4909	−	23.7932i	1.63669	−	0.916479i
$675$		0			0
$676$	12.9348	−	3.10395i	0.497491	−	0.119383i
$677$	5.00632	−	38.0268i	0.192408	−	1.46149i	−0.573853	−	0.818958i	$-0.694552\pi$
$677$	5.00632	−	38.0268i	0.192408	−	1.46149i	0.766261	−	0.642529i	$-0.222115\pi$
$678$		0			0
$679$	3.39458	−	12.6688i	0.130272	−	0.486182i
$680$	1.59768	+	1.32920i	0.0612683	+	0.0509724i
$681$		0			0
$682$	−4.12094	−	10.3308i	−0.157799	−	0.395586i
$683$	−39.4212	+	16.3288i	−1.50841	+	0.624803i	−0.975229	−	0.221198i	$-0.929003\pi$
$683$	−39.4212	+	16.3288i	−1.50841	+	0.624803i	−0.533180	+	0.846002i	$0.679003\pi$
$684$		0			0
$685$	2.41111	−	5.82093i	0.0921238	−	0.222406i
$686$	−16.4929	+	16.0650i	−0.629703	+	0.613366i
$687$		0			0
$688$	−24.6944	−	4.58210i	−0.941466	−	0.174691i
$689$	26.8038	+	46.4255i	1.02114	+	1.76867i
$690$		0			0
$691$	5.96265	−	4.57530i	0.226830	−	0.174053i	−0.489094	−	0.872231i	$-0.662672\pi$
$691$	5.96265	−	4.57530i	0.226830	−	0.174053i	0.715924	+	0.698178i	$0.246006\pi$
$692$	4.99480	−	3.62815i	0.189874	−	0.137921i
$693$		0			0
$694$	3.11698	−	3.95345i	0.118319	−	0.150071i
$695$	−8.75791	+	2.34667i	−0.332206	+	0.0890145i
$696$		0			0
$697$	−5.85505	−	1.56886i	−0.221776	−	0.0594246i
$698$	5.63091	−	4.20435i	0.213133	−	0.159137i
$699$		0			0
$700$	12.8222	+	23.6214i	0.484634	+	0.892805i
$701$	2.90088	−	7.00333i	0.109565	−	0.264512i	−0.859582	−	0.510998i	$-0.829276\pi$
$701$	2.90088	−	7.00333i	0.109565	−	0.264512i	0.969146	+	0.246486i	$0.0792759\pi$
$702$		0			0
$703$			11.5273i			0.434760i
$704$	−4.19673	+	19.7141i	−0.158170	+	0.743004i
$705$		0			0
$706$	−15.6718	−	9.32485i	−0.589817	−	0.350945i
$707$	5.58867	+	42.4502i	0.210184	+	1.59650i
$708$		0			0
$709$	−4.70261	−	0.619111i	−0.176610	−	0.0232512i	0.0417022	−	0.999130i	$-0.486722\pi$
$709$	−4.70261	−	0.619111i	−0.176610	−	0.0232512i	−0.218313	+	0.975879i	$0.570055\pi$
$710$	−1.88603	+	0.223128i	−0.0707816	+	0.00837386i
$711$		0			0
$712$	25.3022	+	27.3802i	0.948239	+	1.02612i
$713$	1.25462	+	4.68230i	0.0469858	+	0.175354i
$714$		0			0
$715$	4.05714	−	5.28737i	0.151728	−	0.197736i
$716$	15.3478	−	34.4623i	0.573576	−	1.28791i
$717$		0			0
$718$	29.9419	−	29.1651i	1.11742	−	1.08843i
$719$			24.1357i			0.900109i	0.893001	+	0.450054i	$0.148595\pi$
$719$			24.1357i			0.900109i	−0.893001	+	0.450054i	$0.851405\pi$
$720$		0			0
$721$		−	45.0549i		−	1.67793i
$722$	−21.1511	−	21.7144i	−0.787161	−	0.808127i
$723$		0			0
$724$	−21.4177	+	8.21896i	−0.795983	+	0.305455i
$725$	−22.2827	+	29.0394i	−0.827559	+	1.07850i
$726$		0			0
$727$	−1.43367	−	5.35052i	−0.0531718	−	0.198440i	0.934230	−	0.356670i	$-0.116088\pi$
$727$	−1.43367	−	5.35052i	−0.0531718	−	0.198440i	−0.987402	+	0.158230i	$0.949421\pi$
$728$	34.0424	−	12.5529i	1.26170	−	0.465243i
$729$		0			0
$730$	−1.38882	−	11.7392i	−0.0514025	−	0.434489i
$731$	−7.66572	−	1.00921i	−0.283527	−	0.0373270i
$732$		0			0
$733$	3.73241	+	28.3505i	0.137860	+	1.04715i	0.910852	+	0.412734i	$0.135426\pi$
$733$	3.73241	+	28.3505i	0.137860	+	1.04715i	−0.772992	+	0.634416i	$0.781241\pi$
$734$	4.36907	−	7.34288i	0.161265	−	0.271031i
$735$		0			0
$736$	2.82585	−	8.31763i	0.104162	−	0.306592i
$737$		−	28.1425i		−	1.03664i
$738$		0			0
$739$	2.25138	−	5.43531i	0.0828183	−	0.199941i	−0.877046	−	0.480407i	$-0.840489\pi$
$739$	2.25138	−	5.43531i	0.0828183	−	0.199941i	0.959864	+	0.280466i	$0.0904890\pi$
$740$	−0.614670	+	2.07431i	−0.0225957	+	0.0762531i
$741$		0			0
$742$	29.6089	+	39.6554i	1.08698	+	1.45580i
$743$	−37.3366	−	10.0043i	−1.36975	−	0.367022i	−0.502360	−	0.864659i	$-0.667535\pi$
$743$	−37.3366	−	10.0043i	−1.36975	−	0.367022i	−0.867386	+	0.497637i	$0.834201\pi$
$744$		0			0
$745$	−7.61652	+	2.04084i	−0.279048	+	0.0747706i
$746$	−25.4985	−	20.1035i	−0.933566	−	0.736042i
$747$		0			0
$748$	−0.971296	+	6.12843i	−0.0355141	+	0.224078i
$749$	−1.01106	+	0.775812i	−0.0369433	+	0.0283476i
$750$		0			0
$751$	3.35967	+	5.81912i	0.122596	+	0.212343i	0.920791	−	0.390057i	$-0.127545\pi$
$751$	3.35967	+	5.81912i	0.122596	+	0.212343i	−0.798195	+	0.602400i	$0.794211\pi$
$752$	−17.7348	−	11.5223i	−0.646720	−	0.420175i
$753$		0			0
$754$	34.4782	+	35.3965i	1.25562	+	1.28907i
$755$	−1.56818	+	3.78593i	−0.0570721	+	0.137784i
$756$		0			0
$757$	25.3912	−	10.5174i	0.922859	−	0.382261i	0.129894	−	0.991528i	$-0.458536\pi$
$757$	25.3912	−	10.5174i	0.922859	−	0.382261i	0.792965	+	0.609267i	$0.208536\pi$
$758$	14.1011	−	5.62493i	0.512175	−	0.204307i
$759$		0			0
$760$	−4.99562	−	9.49868i	−0.181210	−	0.344553i
$761$	−13.6572	+	50.9693i	−0.495073	+	1.84764i	0.0345492	+	0.999403i	$0.489000\pi$
$761$	−13.6572	+	50.9693i	−0.495073	+	1.84764i	−0.529622	+	0.848234i	$0.677666\pi$
$762$		0			0
$763$	−5.11170	+	38.8272i	−0.185056	+	1.40564i
$764$	−14.6991	+	23.9812i	−0.531794	+	0.867609i
$765$		0			0
$766$	13.6220	+	24.3268i	0.492183	+	0.878963i
$767$	23.0085	−	39.8519i	0.830790	−	1.43897i
$768$		0			0
$769$	−0.934703	−	1.61895i	−0.0337063	−	0.0583809i	0.848680	−	0.528906i	$-0.177398\pi$
$769$	−0.934703	−	1.61895i	−0.0337063	−	0.0583809i	−0.882386	+	0.470525i	$0.844064\pi$
$770$	3.14609	−	5.28748i	0.113377	−	0.190547i
$771$		0			0
$772$	10.4438	+	19.2399i	0.375882	+	0.692459i
$773$	6.72952	−	2.78746i	0.242044	−	0.100258i	−0.258364	−	0.966048i	$-0.583183\pi$
$773$	6.72952	−	2.78746i	0.242044	−	0.100258i	0.500408	+	0.865790i	$0.333183\pi$
$774$		0			0
$775$	−10.2504	−	10.2504i	−0.368206	−	0.368206i
$776$	6.84230	−	10.8407i	0.245624	−	0.389157i
$777$		0			0
$778$	2.87654	−	19.8320i	0.103129	−	0.711011i
$779$	24.8333	+	19.0553i	0.889746	+	0.682726i
$780$		0			0
$781$	−3.45177	−	4.49844i	−0.123514	−	0.160967i
$782$	0.734191	−	2.60273i	0.0262546	−	0.0930735i
$783$		0			0
$784$	4.89759	−	2.49418i	0.174914	−	0.0890777i
$785$	4.23326	−	7.33222i	0.151091	−	0.261698i
$786$		0			0
$787$	−1.31619	−	9.99746i	−0.0469171	−	0.356371i	−0.998760	−	0.0497846i	$-0.984147\pi$
$787$	−1.31619	−	9.99746i	−0.0469171	−	0.356371i	0.951843	−	0.306586i	$-0.0991868\pi$
$788$	47.5017	−	18.2286i	1.69218	−	0.649366i
$789$		0			0
$790$	1.89809	−	0.757148i	0.0675310	−	0.0269381i
$791$	10.0358	+	10.0358i	0.356831	+	0.356831i
$792$		0			0
$793$	−11.9556	+	11.9556i	−0.424557	+	0.424557i
$794$	−5.51314	+	12.8304i	−0.195654	+	0.455332i
$795$		0			0
$796$	12.3609	+	13.0284i	0.438121	+	0.461778i
$797$	23.2116	−	3.05586i	0.822196	−	0.108244i	0.292321	−	0.956320i	$-0.405572\pi$
$797$	23.2116	−	3.05586i	0.822196	−	0.108244i	0.529875	+	0.848076i	$0.322239\pi$
$798$		0			0
$799$	−5.63843	−	3.25535i	−0.199473	−	0.115166i
$800$	5.11839	+	25.7666i	0.180962	+	0.910986i
$801$		0			0
$802$	14.5557	+	25.9943i	0.513981	+	0.917889i
$803$	27.9996	−	21.4849i	0.988085	−	0.758185i
$804$		0			0
$805$	−1.63241	+	2.12739i	−0.0575348	+	0.0749808i
$806$	−15.6807	+	11.7081i	−0.552328	+	0.412399i
$807$		0			0
$808$	−7.09354	+	41.2438i	−0.249550	+	1.45095i
$809$	15.7924	−	15.7924i	0.555233	−	0.555233i	−0.372714	−	0.927946i	$-0.621573\pi$
$809$	15.7924	−	15.7924i	0.555233	−	0.555233i	0.927946	+	0.372714i	$0.121573\pi$
$810$		0			0
$811$	18.7328	+	45.2250i	0.657798	+	1.58806i	0.801198	+	0.598400i	$0.204196\pi$
$811$	18.7328	+	45.2250i	0.657798	+	1.58806i	−0.143400	+	0.989665i	$0.545804\pi$
$812$	35.4486	+	28.7118i	1.24400	+	1.00759i
$813$		0			0
$814$	−6.26051	+	1.58962i	−0.219431	+	0.0557163i
$815$	−3.20423	+	1.84996i	−0.112239	+	0.0648014i
$816$		0			0
$817$	34.5777	+	19.9635i	1.20972	+	0.698433i
$818$	16.6415	+	4.69432i	0.581857	+	0.164133i
$819$		0			0
$820$	3.45261	+	4.75314i	0.120570	+	0.165987i
$821$	−32.4666	−	4.27431i	−1.13309	−	0.149175i	−0.459431	−	0.888214i	$-0.651947\pi$
$821$	−32.4666	−	4.27431i	−1.13309	−	0.149175i	−0.673663	+	0.739039i	$0.735280\pi$
$822$		0			0
$823$	−2.68726	−	0.720048i	−0.0936719	−	0.0250993i	0.211679	−	0.977339i	$-0.432107\pi$
$823$	−2.68726	−	0.720048i	−0.0936719	−	0.0250993i	−0.305351	+	0.952240i	$0.598774\pi$
$824$	13.0654	−	42.0544i	0.455153	−	1.46503i
$825$		0			0
$826$	16.7717	−	39.0316i	0.583561	−	1.35808i
$827$	−2.57660	−	6.22047i	−0.0895973	−	0.216307i	0.872729	−	0.488206i	$-0.162348\pi$
$827$	−2.57660	−	6.22047i	−0.0895973	−	0.216307i	−0.962326	+	0.271899i	$0.912348\pi$
$828$		0			0
$829$	−26.6919	−	11.0562i	−0.927049	−	0.383996i	−0.132491	−	0.991184i	$-0.542298\pi$
$829$	−26.6919	−	11.0562i	−0.927049	−	0.383996i	−0.794558	+	0.607188i	$0.792298\pi$
$830$	0.110237	−	8.38796i	0.00382636	−	0.291150i
$831$		0			0
$832$	35.4155	−	1.84507i	1.22781	−	0.0639664i
$833$	1.46528	−	0.845982i	0.0507691	−	0.0293115i
$834$		0			0
$835$	3.87572	+	5.05094i	0.134125	+	0.174795i
$836$	16.7447	−	27.3185i	0.579126	−	0.944829i
$837$		0			0
$838$	2.86464	+	24.2139i	0.0989572	+	0.836454i
$839$	−4.49723	−	16.7839i	−0.155262	−	0.579445i	−0.999083	−	0.0428201i	$-0.986366\pi$
$839$	−4.49723	−	16.7839i	−0.155262	−	0.579445i	0.843821	−	0.536625i	$-0.180301\pi$
$840$		0			0
$841$	−8.57356	+	31.9970i	−0.295640	+	1.10334i
$842$	−12.2410	−	1.77550i	−0.421852	−	0.0611878i
$843$		0			0
$844$	−0.954088	−	9.08655i	−0.0328411	−	0.312772i
$845$	−3.66666	−	1.51878i	−0.126137	−	0.0522476i
$846$		0			0
$847$	−13.4625			−0.462577
$848$	16.1375	+	45.6007i	0.554164	+	1.56594i
$849$		0			0
$850$	1.99028	+	7.83842i	0.0682659	+	0.268856i
$851$	2.79102	−	0.367445i	0.0956751	−	0.0125959i
$852$		0			0
$853$	−3.24870	+	24.6763i	−0.111233	+	0.844901i	0.841322	+	0.540535i	$0.181778\pi$
$853$	−3.24870	+	24.6763i	−0.111233	+	0.844901i	−0.952555	+	0.304366i	$0.901555\pi$
$854$	−9.66412	+	12.2576i	−0.330699	+	0.419446i
$855$		0			0
$856$	−1.16870	+	0.430952i	−0.0399454	+	0.0147296i
$857$	10.2397	−	2.74371i	0.349780	−	0.0937233i	−0.0796512	−	0.996823i	$-0.525381\pi$
$857$	10.2397	−	2.74371i	0.349780	−	0.0937233i	0.429431	+	0.903099i	$0.358714\pi$
$858$		0			0
$859$	18.1363	+	13.9165i	0.618803	+	0.474824i	0.869960	−	0.493122i	$-0.164145\pi$
$859$	18.1363	+	13.9165i	0.618803	+	0.474824i	−0.251157	+	0.967946i	$0.580811\pi$
$860$	5.15767	+	5.43617i	0.175875	+	0.185372i
$861$		0			0
$862$	−0.196672	+	14.9649i	−0.00669869	+	0.509707i
$863$	51.0142			1.73654			0.868272	−	0.496089i	$-0.165231\pi$
$863$	51.0142			1.73654			0.868272	+	0.496089i	$0.165231\pi$
$864$		0			0
$865$	−1.84190			−0.0626266
$866$	0.207089	−	15.7575i	0.00703716	−	0.535461i
$867$		0			0
$868$	−13.1061	+	12.4346i	−0.444849	+	0.422059i
$869$	4.84033	+	3.71412i	0.164197	+	0.125993i
$870$		0			0
$871$	−47.8286	+	12.8156i	−1.62061	+	0.434241i
$872$	−16.0307	+	34.7591i	−0.542868	+	1.17709i
$873$		0			0
$874$	−8.64612	+	10.9664i	−0.292459	+	0.370944i
$875$	2.17364	−	16.5105i	0.0734825	−	0.558155i
$876$		0			0
$877$	−30.4687	+	4.01128i	−1.02886	+	0.135451i	−0.626009	−	0.779816i	$-0.715313\pi$
$877$	−30.4687	+	4.01128i	−1.02886	+	0.135451i	−0.402847	+	0.915267i	$0.631979\pi$
$878$	−5.80907	−	22.8782i	−0.196047	−	0.772102i
$879$		0			0
$880$	4.46987	−	4.02302i	0.150679	−	0.135616i
$881$	−8.38302			−0.282431			−0.141215	−	0.989979i	$-0.545101\pi$
$881$	−8.38302			−0.282431			−0.141215	+	0.989979i	$0.545101\pi$
$882$		0			0
$883$	−29.6096	−	12.2647i	−0.996442	−	0.412740i	−0.175951	−	0.984399i	$-0.556300\pi$
$883$	−29.6096	−	12.2647i	−0.996442	−	0.412740i	−0.820491	+	0.571659i	$0.806300\pi$
$884$	10.8577	−	1.14006i	0.365183	−	0.0383442i
$885$		0			0
$886$	−29.7917	−	4.32116i	−1.00087	−	0.145172i
$887$	5.47930	−	20.4490i	0.183977	−	0.686611i	−0.810870	−	0.585226i	$-0.801006\pi$
$887$	5.47930	−	20.4490i	0.183977	−	0.686611i	0.994847	−	0.101385i	$-0.0323275\pi$
$888$		0			0
$889$	−12.1757	−	45.4405i	−0.408361	−	1.52403i
$890$	−1.30682	−	11.0461i	−0.0438046	−	0.370266i
$891$		0			0
$892$	−18.3696	−	11.2595i	−0.615058	−	0.376995i
$893$	20.4671	+	26.6732i	0.684905	+	0.892585i
$894$		0			0
$895$	−9.74773	+	5.62785i	−0.325831	+	0.188118i
$896$	32.2686	−	5.53279i	1.07802	−	0.184837i
$897$		0			0
$898$	0.462055	−	35.1580i	0.0154190	−	1.17324i
$899$	−22.7312	−	9.41556i	−0.758127	−	0.314026i
$900$		0			0
$901$	5.69860	+	13.7576i	0.189848	+	0.458334i
$902$	−6.92445	+	16.1148i	−0.230559	+	0.536565i
$903$		0			0
$904$	6.45718	+	12.2777i	0.214763	+	0.408350i
$905$	6.61131	+	1.77149i	0.219767	+	0.0588865i
$906$		0			0
$907$	−32.0867	−	4.22429i	−1.06542	−	0.140265i	−0.422626	−	0.906304i	$-0.638892\pi$
$907$	−32.0867	−	4.22429i	−1.06542	−	0.140265i	−0.642794	+	0.766039i	$0.722225\pi$
$908$	−29.5242	+	21.4459i	−0.979794	+	0.711708i
$909$		0			0
$910$	−10.4188	−	2.93899i	−0.345380	−	0.0974264i
$911$	−33.9301	−	19.5896i	−1.12416	−	0.649031i	−0.181697	−	0.983355i	$-0.558159\pi$
$911$	−33.9301	−	19.5896i	−1.12416	−	0.649031i	−0.942458	+	0.334323i	$0.891492\pi$
$912$		0			0
$913$	21.6896	−	12.5225i	0.717821	−	0.414434i
$914$	5.68224	−	1.44279i	0.187952	−	0.0477234i
$915$		0			0
$916$	10.6782	−	13.1837i	0.352818	−	0.435602i
$917$	−5.65830	−	13.6603i	−0.186853	−	0.451104i
$918$		0			0
$919$	36.4909	−	36.4909i	1.20372	−	1.20372i	0.230696	−	0.973026i	$-0.425900\pi$
$919$	36.4909	−	36.4909i	1.20372	−	1.20372i	0.973026	−	0.230696i	$-0.0741004\pi$
$920$	−2.14061	+	1.51234i	−0.0705739	+	0.0498603i
$921$		0			0
$922$	45.8914	−	34.2650i	1.51135	−	1.12846i
$923$	−6.07327	+	7.91485i	−0.199904	+	0.260520i
$924$		0			0
$925$	−6.67886	+	5.12487i	−0.219600	+	0.168505i
$926$	8.42738	+	15.0500i	0.276941	+	0.494573i
$927$		0			0
$928$	24.7618	+	37.0793i	0.812846	+	1.21719i
$929$	37.2048	+	21.4802i	1.22065	+	0.704743i	0.965057	−	0.262041i	$-0.0843956\pi$
$929$	37.2048	+	21.4802i	1.22065	+	0.704743i	0.255594	+	0.966784i	$0.417729\pi$
$930$		0			0
$931$	−8.66246	+	1.14043i	−0.283900	+	0.0373762i
$932$	−16.9127	+	16.0463i	−0.553994	+	0.525613i
$933$		0			0
$934$	−4.42129	+	10.2894i	−0.144669	+	0.336678i
$935$	1.30906	−	1.30906i	0.0428110	−	0.0428110i
$936$		0			0
$937$	−28.8273	−	28.8273i	−0.941746	−	0.941746i	0.0566482	−	0.998394i	$-0.481959\pi$
$937$	−28.8273	−	28.8273i	−0.941746	−	0.941746i	−0.998394	+	0.0566482i	$0.981959\pi$
$938$	−42.4590	+	16.9369i	−1.38633	+	0.553008i
$939$		0			0
$940$	2.26071	+	5.89115i	0.0737361	+	0.192148i
$941$	−7.25827	−	55.1320i	−0.236613	−	1.79725i	−0.537155	−	0.843483i	$-0.680501\pi$
$941$	−7.25827	−	55.1320i	−0.236613	−	1.79725i	0.300542	−	0.953768i	$-0.402832\pi$
$942$		0			0
$943$	3.82214	−	6.62014i	0.124466	−	0.215581i
$944$	26.9734	−	31.5686i	0.877909	−	1.02747i
$945$		0			0
$946$	−6.07393	+	21.5323i	−0.197481	+	0.700075i
$947$	18.9668	+	24.7180i	0.616337	+	0.803226i	0.992359	−	0.123385i	$-0.0393750\pi$
$947$	18.9668	+	24.7180i	0.616337	+	0.803226i	−0.376022	+	0.926611i	$0.622708\pi$
$948$		0			0
$949$	−49.2644	−	37.8019i	−1.59919	−	1.22710i
$950$	5.99461	−	41.3291i	0.194491	−	1.34089i
$951$		0			0
$952$	9.83059	−	2.22284i	0.318611	−	0.0720426i
$953$	−7.33042	−	7.33042i	−0.237456	−	0.237456i	0.578340	−	0.815796i	$-0.303701\pi$
$953$	−7.33042	−	7.33042i	−0.237456	−	0.237456i	−0.815796	+	0.578340i	$0.803701\pi$
$954$		0			0
$955$	7.75330	−	3.21152i	0.250891	−	0.103922i
$956$	−13.8431	+	7.51433i	−0.447717	+	0.243031i
$957$		0			0
$958$	−7.79278	+	13.0969i	−0.251773	+	0.423143i
$959$	−15.2773	−	26.4610i	−0.493328	−	0.854470i
$960$		0			0
$961$	−10.6280	+	18.4082i	−0.342837	+	0.593811i
$962$	5.55252	+	9.91593i	0.179020	+	0.319702i
$963$		0			0
$964$	43.7856	+	26.8380i	1.41024	+	0.864395i
$965$	0.852544	−	6.47571i	0.0274444	−	0.208461i
$966$		0			0
$967$	9.43525	−	35.2129i	0.303417	−	1.13237i	−0.630882	−	0.775879i	$-0.717307\pi$
$967$	9.43525	−	35.2129i	0.303417	−	1.13237i	0.934299	−	0.356490i	$-0.116027\pi$
$968$	−12.5659	−	3.90396i	−0.403885	−	0.125478i
$969$		0			0
$970$	−3.55257	+	1.41712i	−0.114066	+	0.0455010i
$971$	38.8278	−	16.0830i	1.24604	−	0.516128i	0.340446	−	0.940264i	$-0.389422\pi$
$971$	38.8278	−	16.0830i	1.24604	−	0.516128i	0.905599	+	0.424136i	$0.139422\pi$
$972$		0			0
$973$	−16.8265	+	40.6228i	−0.539434	+	1.30231i
$974$	−14.4194	−	14.8034i	−0.462026	−	0.474332i
$975$		0			0
$976$	−12.5751	+	8.63879i	−0.402518	+	0.276521i
$977$	4.04741	+	7.01031i	0.129488	+	0.224280i	0.923478	−	0.383651i	$-0.125333\pi$
$977$	4.04741	+	7.01031i	0.129488	+	0.224280i	−0.793990	+	0.607930i	$0.792000\pi$
$978$		0			0
$979$	26.3464	−	20.2163i	0.842035	−	0.646116i
$980$	−1.61960	−	0.256691i	−0.0517362	−	0.00819968i
$981$		0			0
$982$	27.1219	+	21.3835i	0.865495	+	0.682374i
$983$	−43.0803	+	11.5433i	−1.37405	+	0.368175i	−0.868956	−	0.494889i	$-0.835209\pi$
$983$	−43.0803	+	11.5433i	−1.37405	+	0.368175i	−0.505094	+	0.863065i	$0.668542\pi$
$984$		0			0
$985$	−14.6630	−	3.92894i	−0.467202	−	0.125186i
$986$	8.21207	+	10.9985i	0.261526	+	0.350263i
$987$		0			0
$988$	−54.0533	−	16.0174i	−1.71967	−	0.509581i
$989$	3.73142	−	9.00844i	0.118652	−	0.286452i
$990$		0			0
$991$			26.1500i			0.830682i	0.909666	+	0.415341i	$0.136338\pi$
$991$			26.1500i			0.830682i	−0.909666	+	0.415341i	$0.863662\pi$
$992$	−15.8391	+	7.80593i	−0.502893	+	0.247839i
$993$		0			0
$994$	−4.70948	+	7.91500i	−0.149376	+	0.251049i
$995$	−0.699395	−	5.31243i	−0.0221723	−	0.168415i
$996$		0			0
$997$	−12.0315	−	1.58398i	−0.381042	−	0.0501651i	−0.0624275	−	0.998050i	$-0.519884\pi$
$997$	−12.0315	−	1.58398i	−0.381042	−	0.0501651i	−0.318615	+	0.947884i	$0.603218\pi$
$998$	6.06773	+	51.2886i	0.192071	+	1.62351i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.1		368
3.2	odd	2		288.2.bf.a.227.46	yes	368
9.4	even	3		288.2.bf.a.131.31	yes	368
9.5	odd	6	inner	864.2.bn.a.611.16		368
32.11	odd	8	inner	864.2.bn.a.683.16		368
96.11	even	8		288.2.bf.a.11.31	✓	368
288.139	odd	24		288.2.bf.a.203.46	yes	368
288.203	even	24	inner	864.2.bn.a.395.1		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.31	✓	368	96.11	even	8
288.2.bf.a.131.31	yes	368	9.4	even	3
288.2.bf.a.203.46	yes	368	288.139	odd	24
288.2.bf.a.227.46	yes	368	3.2	odd	2
864.2.bn.a.35.1		368	1.1	even	1	trivial
864.2.bn.a.395.1		368	288.203	even	24	inner
864.2.bn.a.611.16		368	9.5	odd	6	inner
864.2.bn.a.683.16		368	32.11	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41409 - 0.0185843i) q^{2} +(1.99931 + 0.0525599i) q^{4} +(-0.473408 - 0.363259i) q^{5} +(-2.79519 + 0.748968i) q^{7} +(-2.82623 - 0.111480i) q^{8} +O(q^{10})\)	\(q+(-1.41409 - 0.0185843i) q^{2} +(1.99931 + 0.0525599i) q^{4} +(-0.473408 - 0.363259i) q^{5} +(-2.79519 + 0.748968i) q^{7} +(-2.82623 - 0.111480i) q^{8} +(0.662692 + 0.522479i) q^{10} +(-0.328859 + 2.49793i) q^{11} +(4.39502 - 0.578615i) q^{13} +(3.96657 - 1.00716i) q^{14} +(3.99447 + 0.210167i) q^{16} +1.23139 q^{17} +(-5.87478 - 2.43342i) q^{19} +(-0.927397 - 0.751149i) q^{20} +(0.511459 - 3.52619i) q^{22} +(-0.401921 + 1.49999i) q^{23} +(-1.20194 - 4.48569i) q^{25} +(-6.22571 + 0.736536i) q^{26} +(-5.62781 + 1.35050i) q^{28} +(-4.79825 - 6.25320i) q^{29} +(2.70334 - 1.56078i) q^{31} +(-5.64465 - 0.371430i) q^{32} +(-1.74130 - 0.0228845i) q^{34} +(1.59533 + 0.660809i) q^{35} +(-0.693729 - 1.67481i) q^{37} +(8.26226 + 3.55025i) q^{38} +(1.29746 + 1.07943i) q^{40} +(-4.75483 - 1.27405i) q^{41} +(-6.22527 - 0.819572i) q^{43} +(-0.788781 + 4.97685i) q^{44} +(0.596230 - 2.11365i) q^{46} +(-4.57892 - 2.64364i) q^{47} +(1.18994 - 0.687014i) q^{49} +(1.61629 + 6.36551i) q^{50} +(8.81741 - 0.925829i) q^{52} +(4.62779 + 11.1725i) q^{53} +(1.06308 - 1.06308i) q^{55} +(7.98334 - 1.80515i) q^{56} +(6.66895 + 8.93177i) q^{58} +(6.31937 - 8.23556i) q^{59} +(-3.02595 + 2.32189i) q^{61} +(-3.85178 + 2.15684i) q^{62} +(7.97514 + 0.630137i) q^{64} +(-2.29083 - 1.32261i) q^{65} +(-11.0744 + 1.45797i) q^{67} +(2.46193 + 0.0647216i) q^{68} +(-2.24367 - 0.964093i) q^{70} +(-1.59136 + 1.59136i) q^{71} +(-9.90510 - 9.90510i) q^{73} +(0.949871 + 2.38123i) q^{74} +(-11.6176 - 5.17393i) q^{76} +(-0.951648 - 7.22849i) q^{77} +(1.21078 - 2.09714i) q^{79} +(-1.81467 - 1.55052i) q^{80} +(6.70009 + 1.88999i) q^{82} +(-6.05141 - 7.88635i) q^{83} +(-0.582950 - 0.447313i) q^{85} +(8.78787 + 1.27464i) q^{86} +(1.20790 - 7.02306i) q^{88} +(-9.32026 - 9.32026i) q^{89} +(-11.8515 + 4.90907i) q^{91} +(-0.882404 + 2.97782i) q^{92} +(6.42588 + 3.82344i) q^{94} +(1.89721 + 3.28607i) q^{95} +(-2.26617 + 3.92513i) q^{97} +(-1.69546 + 0.949387i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

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