LMFDB - Embedded newform 864.2.bn.a.611.27

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			611.27
Character	$\chi$	$=$	864.611
Dual form			864.2.bn.a.683.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.370153 - 1.36491i) q^{2} +(-1.72597 - 1.01045i) q^{4} +(0.155947 - 1.18454i) q^{5} +(-1.23982 + 4.62708i) q^{7} +(-2.01805 + 1.98178i) q^{8} +O(q^{10})$	\(q+(0.370153 - 1.36491i) q^{2} +(-1.72597 - 1.01045i) q^{4} +(0.155947 - 1.18454i) q^{5} +(-1.23982 + 4.62708i) q^{7} +(-2.01805 + 1.98178i) q^{8} +(-1.55907 - 0.651315i) q^{10} +(-0.714959 - 0.548608i) q^{11} +(1.55287 + 2.02374i) q^{13} +(5.85664 + 3.40497i) q^{14} +(1.95797 + 3.48803i) q^{16} +5.41926 q^{17} +(3.09852 + 1.28345i) q^{19} +(-1.46608 + 1.88691i) q^{20} +(-1.01345 + 0.772789i) q^{22} +(-4.48426 + 1.20155i) q^{23} +(3.45082 + 0.924644i) q^{25} +(3.33703 - 1.37044i) q^{26} +(6.81534 - 6.73344i) q^{28} +(3.97708 - 0.523593i) q^{29} +(-1.91957 - 1.10826i) q^{31} +(5.48560 - 1.38136i) q^{32} +(2.00595 - 7.39682i) q^{34} +(5.28761 + 2.19020i) q^{35} +(0.235657 + 0.568926i) q^{37} +(2.89872 - 3.75414i) q^{38} +(2.03279 + 2.69952i) q^{40} +(2.92522 + 10.9171i) q^{41} +(0.771590 - 1.00556i) q^{43} +(0.679660 + 1.66931i) q^{44} +(-0.0198440 + 6.56538i) q^{46} +(-4.59259 + 2.65153i) q^{47} +(-13.8105 - 7.97351i) q^{49} +(2.53939 - 4.36781i) q^{50} +(-0.635323 - 5.06203i) q^{52} +(2.55243 + 6.16210i) q^{53} +(-0.761343 + 0.761343i) q^{55} +(-6.66784 - 11.7947i) q^{56} +(0.757468 - 5.62218i) q^{58} +(-5.22783 - 0.688257i) q^{59} +(-1.75112 - 13.3011i) q^{61} +(-2.22322 + 2.20982i) q^{62} +(0.145072 - 7.99868i) q^{64} +(2.63937 - 1.52384i) q^{65} +(4.89236 + 6.37585i) q^{67} +(-9.35351 - 5.47591i) q^{68} +(4.94665 - 6.40642i) q^{70} +(-6.14705 + 6.14705i) q^{71} +(8.86496 + 8.86496i) q^{73} +(0.863764 - 0.111062i) q^{74} +(-4.05111 - 5.34611i) q^{76} +(3.42487 - 2.62800i) q^{77} +(2.86568 + 4.96351i) q^{79} +(4.43705 - 1.77535i) q^{80} +(15.9836 + 0.0483107i) q^{82} +(4.89778 - 0.644805i) q^{83} +(0.845120 - 6.41933i) q^{85} +(-1.08689 - 1.42536i) q^{86} +(2.53005 - 0.309775i) q^{88} +(-3.18445 - 3.18445i) q^{89} +(-11.2893 + 4.67619i) q^{91} +(8.95383 + 2.45728i) q^{92} +(1.91915 + 7.24996i) q^{94} +(2.00350 - 3.47017i) q^{95} +(-6.48269 - 11.2284i) q^{97} +(-15.9951 + 15.8987i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.370153	−	1.36491i	0.261737	−	0.965139i
$2$	0.370153	−	1.36491i	0.261737	−	0.965139i
$3$		0			0
$3$		0			0
$4$	−1.72597	−	1.01045i	−0.862987	−	0.505226i
$5$	0.155947	−	1.18454i	0.0697418	−	0.529742i	−0.920538	−	0.390653i	$-0.872249\pi$
$5$	0.155947	−	1.18454i	0.0697418	−	0.529742i	0.990280	−	0.139089i	$-0.0444174\pi$
$6$		0			0
$7$	−1.23982	+	4.62708i	−0.468609	+	1.74887i	0.176031	+	0.984385i	$0.443674\pi$
$7$	−1.23982	+	4.62708i	−0.468609	+	1.74887i	−0.644639	+	0.764487i	$0.722992\pi$
$8$	−2.01805	+	1.98178i	−0.713489	+	0.700666i
$9$		0			0
$10$	−1.55907	−	0.651315i	−0.493021	−	0.205964i
$11$	−0.714959	−	0.548608i	−0.215568	−	0.165411i	0.495333	−	0.868703i	$-0.335046\pi$
$11$	−0.714959	−	0.548608i	−0.215568	−	0.165411i	−0.710901	+	0.703292i	$0.751713\pi$
$12$		0			0
$13$	1.55287	+	2.02374i	0.430690	+	0.561286i	0.957402	−	0.288758i	$-0.0932422\pi$
$13$	1.55287	+	2.02374i	0.430690	+	0.561286i	−0.526713	+	0.850043i	$0.676576\pi$
$14$	5.85664	+	3.40497i	1.56525	+	0.910018i
$15$		0			0
$16$	1.95797	+	3.48803i	0.489493	+	0.872007i
$17$	5.41926			1.31436			0.657182	−	0.753732i	$-0.271748\pi$
$17$	5.41926			1.31436			0.657182	+	0.753732i	$0.271748\pi$
$18$		0			0
$19$	3.09852	+	1.28345i	0.710850	+	0.294444i	0.708656	−	0.705554i	$-0.249302\pi$
$19$	3.09852	+	1.28345i	0.710850	+	0.294444i	0.00219377	+	0.999998i	$0.499302\pi$
$20$	−1.46608	+	1.88691i	−0.327826	+	0.421925i
$21$		0			0
$22$	−1.01345	+	0.772789i	−0.216067	+	0.164759i
$23$	−4.48426	+	1.20155i	−0.935033	+	0.250541i	−0.693999	−	0.719976i	$-0.744153\pi$
$23$	−4.48426	+	1.20155i	−0.935033	+	0.250541i	−0.241033	+	0.970517i	$0.577486\pi$
$24$		0			0
$25$	3.45082	+	0.924644i	0.690163	+	0.184929i
$26$	3.33703	−	1.37044i	0.654446	−	0.268766i
$27$		0			0
$28$	6.81534	−	6.73344i	1.28798	−	1.27250i
$29$	3.97708	−	0.523593i	0.738526	−	0.0972287i	0.248128	−	0.968727i	$-0.420185\pi$
$29$	3.97708	−	0.523593i	0.738526	−	0.0972287i	0.490398	+	0.871499i	$0.336851\pi$
$30$		0			0
$31$	−1.91957	−	1.10826i	−0.344765	−	0.199050i	0.317612	−	0.948221i	$-0.397119\pi$
$31$	−1.91957	−	1.10826i	−0.344765	−	0.199050i	−0.662377	+	0.749171i	$0.730452\pi$
$32$	5.48560	−	1.38136i	0.969727	−	0.244192i
$33$		0			0
$34$	2.00595	−	7.39682i	0.344018	−	1.26854i
$35$	5.28761	+	2.19020i	0.893769	+	0.370211i
$36$		0			0
$37$	0.235657	+	0.568926i	0.0387418	+	0.0935309i	0.942066	−	0.335427i	$-0.108881\pi$
$37$	0.235657	+	0.568926i	0.0387418	+	0.0935309i	−0.903324	+	0.428958i	$0.858881\pi$
$38$	2.89872	−	3.75414i	0.470235	−	0.609002i
$39$		0			0
$40$	2.03279	+	2.69952i	0.321412	+	0.426831i
$41$	2.92522	+	10.9171i	0.456842	+	1.70496i	0.682615	+	0.730778i	$0.260843\pi$
$41$	2.92522	+	10.9171i	0.456842	+	1.70496i	−0.225773	+	0.974180i	$0.572491\pi$
$42$		0			0
$43$	0.771590	−	1.00556i	0.117666	−	0.153346i	−0.730806	−	0.682585i	$-0.760856\pi$
$43$	0.771590	−	1.00556i	0.117666	−	0.153346i	0.848473	+	0.529239i	$0.177522\pi$
$44$	0.679660	+	1.66931i	0.102463	+	0.251659i
$45$		0			0
$46$	−0.0198440	+	6.56538i	−0.00292584	+	0.968013i
$47$	−4.59259	+	2.65153i	−0.669898	+	0.386766i	−0.796038	−	0.605246i	$-0.793075\pi$
$47$	−4.59259	+	2.65153i	−0.669898	+	0.386766i	0.126140	+	0.992012i	$0.459741\pi$
$48$		0			0
$49$	−13.8105	−	7.97351i	−1.97293	−	1.13907i
$50$	2.53939	−	4.36781i	0.359123	−	0.617701i
$51$		0			0
$52$	−0.635323	−	5.06203i	−0.0881035	−	0.701978i
$53$	2.55243	+	6.16210i	0.350603	+	0.846430i	0.996546	+	0.0830445i	$0.0264644\pi$
$53$	2.55243	+	6.16210i	0.350603	+	0.846430i	−0.645943	+	0.763386i	$0.723536\pi$
$54$		0			0
$55$	−0.761343	+	0.761343i	−0.102659	+	0.102659i
$56$	−6.66784	−	11.7947i	−0.891028	−	1.57614i
$57$		0			0
$58$	0.757468	−	5.62218i	0.0994605	−	0.738228i
$59$	−5.22783	−	0.688257i	−0.680606	−	0.0896035i	−0.217707	−	0.976014i	$-0.569858\pi$
$59$	−5.22783	−	0.688257i	−0.680606	−	0.0896035i	−0.462899	+	0.886411i	$0.653191\pi$
$60$		0			0
$61$	−1.75112	−	13.3011i	−0.224208	−	1.70303i	−0.619929	−	0.784658i	$-0.712839\pi$
$61$	−1.75112	−	13.3011i	−0.224208	−	1.70303i	0.395721	−	0.918371i	$-0.370495\pi$
$62$	−2.22322	+	2.20982i	−0.282349	+	0.280647i
$63$		0			0
$64$	0.145072	−	7.99868i	0.0181341	−	0.999836i
$65$	2.63937	−	1.52384i	0.327374	−	0.189009i
$66$		0			0
$67$	4.89236	+	6.37585i	0.597697	+	0.778934i	0.990025	−	0.140891i	$-0.0449968\pi$
$67$	4.89236	+	6.37585i	0.597697	+	0.778934i	−0.392328	+	0.919825i	$0.628330\pi$
$68$	−9.35351	−	5.47591i	−1.13428	−	0.664051i
$69$		0			0
$70$	4.94665	−	6.40642i	0.591238	−	0.765713i
$71$	−6.14705	+	6.14705i	−0.729521	+	0.729521i	−0.970524	−	0.241003i	$-0.922524\pi$
$71$	−6.14705	+	6.14705i	−0.729521	+	0.729521i	0.241003	+	0.970524i	$0.422524\pi$
$72$		0			0
$73$	8.86496	+	8.86496i	1.03756	+	1.03756i	0.999266	+	0.0382983i	$0.0121937\pi$
$73$	8.86496	+	8.86496i	1.03756	+	1.03756i	0.0382983	+	0.999266i	$0.487806\pi$
$74$	0.863764	−	0.111062i	0.100411	−	0.0129107i
$75$		0			0
$76$	−4.05111	−	5.34611i	−0.464694	−	0.613241i
$77$	3.42487	−	2.62800i	0.390301	−	0.299488i
$78$		0			0
$79$	2.86568	+	4.96351i	0.322414	+	0.558438i	0.980986	−	0.194080i	$-0.0621722\pi$
$79$	2.86568	+	4.96351i	0.322414	+	0.558438i	−0.658571	+	0.752518i	$0.728839\pi$
$80$	4.43705	−	1.77535i	0.496077	−	0.198490i
$81$		0			0
$82$	15.9836	+	0.0483107i	1.76509	+	0.00533503i
$83$	4.89778	−	0.644805i	0.537601	−	0.0707765i	0.143163	−	0.989699i	$-0.454273\pi$
$83$	4.89778	−	0.644805i	0.537601	−	0.0707765i	0.394438	+	0.918923i	$0.370939\pi$
$84$		0			0
$85$	0.845120	−	6.41933i	0.0916662	−	0.696274i
$86$	−1.08689	−	1.42536i	−0.117202	−	0.153701i
$87$		0			0
$88$	2.53005	−	0.309775i	0.269704	−	0.0330222i
$89$	−3.18445	−	3.18445i	−0.337551	−	0.337551i	0.517894	−	0.855445i	$-0.326716\pi$
$89$	−3.18445	−	3.18445i	−0.337551	−	0.337551i	−0.855445	+	0.517894i	$0.826716\pi$
$90$		0			0
$91$	−11.2893	+	4.67619i	−1.18344	+	0.490198i
$92$	8.95383	+	2.45728i	0.933501	+	0.256189i
$93$		0			0
$94$	1.91915	+	7.24996i	0.197946	+	0.747776i
$95$	2.00350	−	3.47017i	0.205555	−	0.356032i
$96$		0			0
$97$	−6.48269	−	11.2284i	−0.658218	−	1.14007i	−0.981077	−	0.193619i	$-0.937977\pi$
$97$	−6.48269	−	11.2284i	−0.658218	−	1.14007i	0.322859	−	0.946447i	$-0.395356\pi$
$98$	−15.9951	+	15.8987i	−1.61575	+	1.60602i
$99$		0			0
$100$	−5.02171	−	5.08280i	−0.502171	−	0.508280i
$101$	−0.0256902	−	0.0197128i	−0.00255627	−	0.00196150i	0.607483	−	0.794333i	$-0.292179\pi$
$101$	−0.0256902	−	0.0197128i	−0.00255627	−	0.00196150i	−0.610039	+	0.792372i	$0.708846\pi$
$102$		0			0
$103$	9.94130	−	2.66376i	0.979546	−	0.262469i	0.266692	−	0.963782i	$-0.414069\pi$
$103$	9.94130	−	2.66376i	0.979546	−	0.262469i	0.712853	+	0.701313i	$0.247403\pi$
$104$	−7.14440	−	1.00656i	−0.700566	−	0.0987017i
$105$		0			0
$106$	9.35552	−	1.20292i	0.908689	−	0.116838i
$107$	17.9077	−	7.41761i	1.73120	−	0.717087i	0.731836	−	0.681481i	$-0.238664\pi$
$107$	17.9077	−	7.41761i	1.73120	−	0.717087i	0.999366	−	0.0356059i	$-0.0113361\pi$
$108$		0			0
$109$	−6.92091	+	16.7085i	−0.662903	+	1.60039i	0.130331	+	0.991471i	$0.458396\pi$
$109$	−6.92091	+	16.7085i	−0.662903	+	1.60039i	−0.793233	+	0.608918i	$0.791604\pi$
$110$	0.757354	+	1.32098i	0.0722109	+	0.125950i
$111$		0			0
$112$	−18.5669	+	4.73517i	−1.75441	+	0.447431i
$113$	−2.29212	+	3.97008i	−0.215625	+	0.373473i	−0.953466	−	0.301501i	$-0.902512\pi$
$113$	−2.29212	+	3.97008i	−0.215625	+	0.373473i	0.737841	+	0.674975i	$0.235846\pi$
$114$		0			0
$115$	0.723978	+	5.49916i	0.0675113	+	0.512799i
$116$	−7.39341	−	3.11494i	−0.686460	−	0.289215i
$117$		0			0
$118$	−2.87451	+	6.88078i	−0.264620	+	0.633427i
$119$	−6.71892	+	25.0754i	−0.615923	+	2.29865i
$120$		0			0
$121$	−2.63681	−	9.84072i	−0.239710	−	0.894611i
$122$	−18.8030	−	2.53330i	−1.70234	−	0.229354i
$123$		0			0
$124$	2.19328	+	3.85246i	0.196962	+	0.345961i
$125$	3.91950	−	9.46250i	0.350570	−	0.846352i
$126$		0			0
$127$			8.57442i			0.760856i	0.924810	+	0.380428i	$0.124223\pi$
$127$			8.57442i			0.760856i	−0.924810	+	0.380428i	$0.875777\pi$
$128$	−10.8638	−	3.15874i	−0.960234	−	0.279196i
$129$		0			0
$130$	−1.10294	−	4.16656i	−0.0967343	−	0.365432i
$131$	−7.78707	+	5.97523i	−0.680360	+	0.522058i	−0.890138	−	0.455691i	$-0.849392\pi$
$131$	−7.78707	+	5.97523i	−0.680360	+	0.522058i	0.209779	+	0.977749i	$0.432726\pi$
$132$		0			0
$133$	−9.78025	+	12.7459i	−0.848055	+	1.10521i
$134$	10.5134	−	4.31761i	0.908220	−	0.372985i
$135$		0			0
$136$	−10.9364	+	10.7398i	−0.937785	+	0.920931i
$137$	−14.6659	−	3.92972i	−1.25299	−	0.335739i	−0.429502	−	0.903066i	$-0.641311\pi$
$137$	−14.6659	−	3.92972i	−1.25299	−	0.335739i	−0.823492	+	0.567327i	$0.807977\pi$
$138$		0			0
$139$	9.71957	+	1.27961i	0.824403	+	0.108535i	0.530912	−	0.847427i	$-0.321849\pi$
$139$	9.71957	+	1.27961i	0.824403	+	0.108535i	0.293491	+	0.955962i	$0.405183\pi$
$140$	−6.91318	−	9.12310i	−0.584271	−	0.771043i
$141$		0			0
$142$	6.11484	+	10.6655i	0.513146	+	0.895032i
$143$		−	2.29881i		−	0.192236i
$144$		0			0
$145$		−	4.79266i		−	0.398009i
$146$	15.3813	−	8.81851i	1.27296	−	0.729825i
$147$		0			0
$148$	0.168135	−	1.22007i	0.0138206	−	0.100289i
$149$	21.0056	+	2.76544i	1.72085	+	0.226554i	0.925273	−	0.379301i	$-0.123835\pi$
$149$	21.0056	+	2.76544i	1.72085	+	0.226554i	0.795575	+	0.605855i	$0.207169\pi$
$150$		0			0
$151$	−1.43347	−	0.384097i	−0.116654	−	0.0312574i	0.200020	−	0.979792i	$-0.435899\pi$
$151$	−1.43347	−	0.384097i	−0.116654	−	0.0312574i	−0.316674	+	0.948535i	$0.602566\pi$
$152$	−8.79650	+	3.55053i	−0.713491	+	0.287986i
$153$		0			0
$154$	−2.31926	−	5.64741i	−0.186891	−	0.455082i
$155$	−1.61213	+	2.10097i	−0.129490	+	0.168754i
$156$		0			0
$157$	−17.8346	+	13.6850i	−1.42336	+	1.09218i	−0.442651	+	0.896694i	$0.645962\pi$
$157$	−17.8346	+	13.6850i	−1.42336	+	1.09218i	−0.980706	+	0.195486i	$0.937372\pi$
$158$	7.83549	−	2.07415i	0.623358	−	0.165011i
$159$		0			0
$160$	−0.780810	−	6.71333i	−0.0617284	−	0.530735i
$161$		−	22.2387i		−	1.75266i
$162$		0			0
$163$	0.408455	−	0.986098i	0.0319927	−	0.0772371i	−0.907076	−	0.420968i	$-0.861691\pi$
$163$	0.408455	−	0.986098i	0.0319927	−	0.0772371i	0.939068	+	0.343730i	$0.111691\pi$
$164$	5.98231	−	21.7984i	0.467140	−	1.70217i
$165$		0			0
$166$	0.932823	−	6.92372i	0.0724011	−	0.537385i
$167$	0.711220	+	2.65431i	0.0550358	+	0.205397i	0.987969	−	0.154654i	$-0.0494262\pi$
$167$	0.711220	+	2.65431i	0.0550358	+	0.205397i	−0.932933	+	0.360050i	$0.882760\pi$
$168$		0			0
$169$	1.68052	−	6.27180i	0.129271	−	0.482446i
$170$	−8.44900	−	3.52965i	−0.648009	−	0.270712i
$171$		0			0
$172$	−2.34781	+	0.955909i	−0.179019	+	0.0728874i
$173$	−0.957041	−	7.26945i	−0.0727625	−	0.552686i	−0.988535	−	0.150990i	$-0.951754\pi$
$173$	−0.957041	−	7.26945i	−0.0727625	−	0.552686i	0.915773	−	0.401697i	$-0.131579\pi$
$174$		0			0
$175$	−8.55680	+	14.8208i	−0.646833	+	1.12035i
$176$	0.513687	−	3.56796i	0.0387206	−	0.268945i
$177$		0			0
$178$	−5.52522	+	3.16776i	−0.414133	+	0.237434i
$179$	2.79531	−	6.74848i	0.208932	−	0.504405i	−0.784324	−	0.620351i	$-0.786990\pi$
$179$	2.79531	−	6.74848i	0.208932	−	0.504405i	0.993256	+	0.115946i	$0.0369900\pi$
$180$		0			0
$181$	−2.78704	+	1.15443i	−0.207159	+	0.0858081i	−0.483850	−	0.875151i	$-0.660762\pi$
$181$	−2.78704	+	1.15443i	−0.207159	+	0.0858081i	0.276691	+	0.960959i	$0.410762\pi$
$182$	2.20382	+	17.1398i	0.163358	+	1.27049i
$183$		0			0
$184$	6.66825	−	11.3116i	0.491590	−	0.833904i
$185$	0.710666	−	0.190422i	0.0522492	−	0.0140001i
$186$		0			0
$187$	−3.87455	−	2.97305i	−0.283335	−	0.217411i
$188$	10.6059	+	0.0641139i	0.773518	+	0.00467599i
$189$		0			0
$190$	−3.99488	−	4.01910i	−0.289819	−	0.291576i
$191$	−8.13119	−	14.0836i	−0.588352	−	1.01906i	−0.994448	−	0.105226i	$-0.966443\pi$
$191$	−8.13119	−	14.0836i	−0.588352	−	1.01906i	0.406096	−	0.913830i	$-0.366890\pi$
$192$		0			0
$193$	8.29625	−	14.3695i	0.597177	−	1.03434i	−0.396058	−	0.918225i	$-0.629622\pi$
$193$	8.29625	−	14.3695i	0.597177	−	1.03434i	0.993236	−	0.116116i	$-0.0370445\pi$
$194$	−17.7253	+	4.69211i	−1.27260	+	0.336874i
$195$		0			0
$196$	15.7798	+	27.7169i	1.12713	+	1.97978i
$197$	−13.0237	+	5.39459i	−0.927899	+	0.384348i	−0.794881	−	0.606765i	$-0.792467\pi$
$197$	−13.0237	+	5.39459i	−0.927899	+	0.384348i	−0.133018	+	0.991114i	$0.542467\pi$
$198$		0			0
$199$	−18.8458	−	18.8458i	−1.33594	−	1.33594i	−0.899953	−	0.435987i	$-0.856399\pi$
$199$	−18.8458	−	18.8458i	−1.33594	−	1.33594i	−0.435987	−	0.899953i	$-0.643601\pi$
$200$	−8.79637	+	4.97279i	−0.621997	+	0.351629i
$201$		0			0
$202$	−0.0364156	+	0.0277682i	−0.00256219	+	0.00195376i
$203$	−2.50817	+	19.0514i	−0.176039	+	1.33715i
$204$		0			0
$205$	13.3879	−	1.76255i	0.935049	−	0.123101i
$206$	0.0439928	−	14.5550i	0.00306512	−	1.01410i
$207$		0			0
$208$	−4.01839	+	9.37890i	−0.278625	+	0.650310i
$209$	−1.51121	−	2.61749i	−0.104532	−	0.181055i
$210$		0			0
$211$	−16.8643	+	12.9404i	−1.16098	+	0.890855i	−0.995444	−	0.0953480i	$-0.969604\pi$
$211$	−16.8643	+	12.9404i	−1.16098	+	0.890855i	−0.165541	+	0.986203i	$0.552937\pi$
$212$	1.82109	−	13.2147i	0.125073	−	0.907592i
$213$		0			0
$214$	−3.49581	−	27.1881i	−0.238969	−	1.85854i
$215$	−1.07079	−	1.07079i	−0.0730274	−	0.0730274i
$216$		0			0
$217$	7.50794	−	7.50794i	0.509672	−	0.509672i
$218$	20.2439	+	15.6311i	1.37109	+	1.05867i
$219$		0			0
$220$	2.08336	−	0.544758i	0.140460	−	0.0367276i
$221$	8.41543	+	10.9672i	0.566083	+	0.737734i
$222$		0			0
$223$	5.94698	−	3.43349i	0.398239	−	0.229924i	−0.287485	−	0.957785i	$-0.592819\pi$
$223$	5.94698	−	3.43349i	0.398239	−	0.229924i	0.685724	+	0.727862i	$0.259486\pi$
$224$	−0.409505	+	27.0950i	−0.0273612	+	1.81036i
$225$		0			0
$226$	4.57037	+	4.59808i	0.304017	+	0.305860i
$227$	1.14165	+	8.67167i	0.0757738	+	0.575559i	0.986647	+	0.162873i	$0.0520761\pi$
$227$	1.14165	+	8.67167i	0.0757738	+	0.575559i	−0.910873	+	0.412686i	$0.864591\pi$
$228$		0			0
$229$	4.26994	+	0.562149i	0.282166	+	0.0371478i	0.270281	−	0.962782i	$-0.412883\pi$
$229$	4.26994	+	0.562149i	0.282166	+	0.0371478i	0.0118850	+	0.999929i	$0.496217\pi$
$230$	7.77385	+	1.04736i	0.512593	+	0.0690609i
$231$		0			0
$232$	−6.98831	+	8.93835i	−0.458805	+	0.586831i
$233$	2.81755	−	2.81755i	0.184584	−	0.184584i	−0.608766	−	0.793350i	$-0.708335\pi$
$233$	2.81755	−	2.81755i	0.184584	−	0.184584i	0.793350	+	0.608766i	$0.208335\pi$
$234$		0			0
$235$	2.42464	+	5.85360i	0.158166	+	0.381847i
$236$	8.32766	+	6.47039i	0.542084	+	0.421187i
$237$		0			0
$238$	31.7387	+	18.4525i	2.05731	+	1.19609i
$239$	5.92010	+	3.41797i	0.382939	+	0.221090i	0.679096	−	0.734049i	$-0.262372\pi$
$239$	5.92010	+	3.41797i	0.382939	+	0.221090i	−0.296157	+	0.955139i	$0.595705\pi$
$240$		0			0
$241$	−4.93993	+	2.85207i	−0.318209	+	0.183718i	−0.650594	−	0.759426i	$-0.725480\pi$
$241$	−4.93993	+	2.85207i	−0.318209	+	0.183718i	0.332385	+	0.943144i	$0.392147\pi$
$242$	−14.4077	−	0.0435477i	−0.926165	−	0.00279935i
$243$		0			0
$244$	−10.4177	+	24.7267i	−0.666926	+	1.58297i
$245$	−11.5986	+	15.1157i	−0.741011	+	0.965704i
$246$		0			0
$247$	2.21424	+	8.26366i	0.140889	+	0.525804i
$248$	6.07013	−	1.56763i	0.385453	−	0.0995448i
$249$		0			0
$250$	−11.4647	−	8.85234i	−0.725090	−	0.559871i
$251$	−4.85496	−	11.7209i	−0.306442	−	0.739817i	−0.999815	−	0.0192376i	$-0.993876\pi$
$251$	−4.85496	−	11.7209i	−0.306442	−	0.739817i	0.693373	−	0.720579i	$-0.256124\pi$
$252$		0			0
$253$	3.86524	+	1.60104i	0.243006	+	0.100656i
$254$	11.7033	+	3.17384i	0.734332	+	0.199145i
$255$		0			0
$256$	−8.33268	+	13.6589i	−0.520792	+	0.853683i
$257$	−13.1251	−	7.57779i	−0.818722	−	0.472689i	0.0312536	−	0.999511i	$-0.490050\pi$
$257$	−13.1251	−	7.57779i	−0.818722	−	0.472689i	−0.849976	+	0.526822i	$0.823383\pi$
$258$		0			0
$259$	−2.92464	+	0.385036i	−0.181728	+	0.0239250i
$260$	−6.09525	−	0.0368464i	−0.378012	−	0.00228511i
$261$		0			0
$262$	5.27326	+	12.8404i	0.325783	+	0.793284i
$263$	−0.678462	−	0.181793i	−0.0418358	−	0.0112099i	0.237840	−	0.971304i	$-0.423560\pi$
$263$	−0.678462	−	0.181793i	−0.0418358	−	0.0112099i	−0.279676	+	0.960094i	$0.590227\pi$
$264$		0			0
$265$	7.69730	−	2.06248i	0.472841	−	0.126697i
$266$	13.7768	+	18.0671i	0.844711	+	1.10776i
$267$		0			0
$268$	−2.00160	−	15.9481i	−0.122267	−	0.974182i
$269$	17.0155	+	7.04803i	1.03745	+	0.429726i	0.835396	−	0.549648i	$-0.185238\pi$
$269$	17.0155	+	7.04803i	1.03745	+	0.429726i	0.202055	+	0.979374i	$0.435238\pi$
$270$		0			0
$271$	−12.5098			−0.759916			−0.379958	−	0.925004i	$-0.624062\pi$
$271$	−12.5098			−0.759916			−0.379958	+	0.925004i	$0.624062\pi$
$272$	10.6108	+	18.9025i	0.643373	+	1.14613i
$273$		0			0
$274$	−10.7924	+	18.5631i	−0.651990	+	1.12144i
$275$	−1.95993	−	2.55423i	−0.118188	−	0.154026i
$276$		0			0
$277$	8.70831	+	6.68212i	0.523231	+	0.401490i	0.836326	−	0.548232i	$-0.184699\pi$
$277$	8.70831	+	6.68212i	0.523231	+	0.401490i	−0.313095	+	0.949722i	$0.601366\pi$
$278$	5.34428	−	12.7927i	0.320528	−	0.767256i
$279$		0			0
$280$	−15.0112	+	6.05895i	−0.897089	+	0.362092i
$281$	1.62128	−	6.05068i	0.0967172	−	0.360954i	−0.900557	−	0.434738i	$-0.856841\pi$
$281$	1.62128	−	6.05068i	0.0967172	−	0.360954i	0.997274	+	0.0737844i	$0.0235077\pi$
$282$		0			0
$283$	1.44419	−	10.9697i	0.0858484	−	0.652083i	−0.893377	−	0.449308i	$-0.851671\pi$
$283$	1.44419	−	10.9697i	0.0858484	−	0.652083i	0.979225	−	0.202775i	$-0.0649961\pi$
$284$	16.8210	−	4.39835i	0.998140	−	0.260994i
$285$		0			0
$286$	−3.13768	−	0.850911i	−0.185535	−	0.0503154i
$287$	−54.1408			−3.19583
$288$		0			0
$289$	12.3684			0.727554
$290$	−6.54156	−	1.77402i	−0.384134	−	0.104174i
$291$		0			0
$292$	−6.34307	−	24.2583i	−0.371200	−	1.41961i
$293$	0.671066	−	5.09726i	0.0392041	−	0.297785i	−0.960599	−	0.277938i	$-0.910349\pi$
$293$	0.671066	−	5.09726i	0.0392041	−	0.297785i	0.999803	−	0.0198465i	$-0.00631776\pi$
$294$		0			0
$295$	−1.63054	+	6.08524i	−0.0949334	+	0.354296i
$296$	−1.60306	−	0.681102i	−0.0931758	−	0.0395883i
$297$		0			0
$298$	11.5499	−	27.6472i	0.669067	−	1.60156i
$299$	−9.39513	−	7.20913i	−0.543334	−	0.416915i
$300$		0			0
$301$	3.69615	+	4.81692i	0.213043	+	0.277643i
$302$	−1.05486	+	1.81439i	−0.0607004	+	0.104406i
$303$		0			0
$304$	1.59012	+	13.3207i	0.0911994	+	0.763995i
$305$	−16.0287			−0.917802
$306$		0			0
$307$	14.4994	+	6.00584i	0.827524	+	0.342772i	0.755922	−	0.654662i	$-0.227189\pi$
$307$	14.4994	+	6.00584i	0.827524	+	0.342772i	0.0716017	+	0.997433i	$0.477189\pi$
$308$	−8.56671	+	1.07519i	−0.488133	+	0.0612644i
$309$		0			0
$310$	2.27091	+	2.97810i	0.128979	+	0.169145i
$311$	16.2242	−	4.34726i	0.919989	−	0.246510i	0.232408	−	0.972618i	$-0.425339\pi$
$311$	16.2242	−	4.34726i	0.919989	−	0.246510i	0.687581	+	0.726108i	$0.258673\pi$
$312$		0			0
$313$	25.1922	+	6.75022i	1.42395	+	0.381545i	0.886882	−	0.461997i	$-0.152867\pi$
$313$	25.1922	+	6.75022i	1.42395	+	0.381545i	0.537063	+	0.843542i	$0.319534\pi$
$314$	12.0773	+	29.4082i	0.681560	+	1.65960i
$315$		0			0
$316$	0.0692919	−	11.4625i	0.00389798	−	0.644817i
$317$	−0.953603	+	0.125544i	−0.0535597	+	0.00705127i	−0.157258	−	0.987557i	$-0.550266\pi$
$317$	−0.953603	+	0.125544i	−0.0535597	+	0.00705127i	0.103699	+	0.994609i	$0.466932\pi$
$318$		0			0
$319$	−3.13070	−	1.80751i	−0.175285	−	0.101201i
$320$	−9.45213	−	1.41922i	−0.528390	−	0.0793367i
$321$		0			0
$322$	−30.3539	−	8.23173i	−1.69156	−	0.458736i
$323$	16.7917	+	6.95536i	0.934316	+	0.387006i
$324$		0			0
$325$	3.48744	+	8.41943i	0.193448	+	0.467026i
$326$	−1.19475	−	0.922512i	−0.0661709	−	0.0510932i
$327$		0			0
$328$	−27.5385	−	16.2341i	−1.52056	−	0.896376i
$329$	−6.57486	−	24.5377i	−0.362484	−	1.35281i
$330$		0			0
$331$	3.03800	−	3.95920i	0.166984	−	0.217617i	−0.702365	−	0.711817i	$-0.747872\pi$
$331$	3.03800	−	3.95920i	0.166984	−	0.217617i	0.869348	+	0.494200i	$0.164539\pi$
$332$	−9.10499	−	3.83605i	−0.499701	−	0.210531i
$333$		0			0
$334$	3.88616	+	0.0117460i	0.212641	+	0.000642712i
$335$	8.31539	−	4.80089i	0.454318	−	0.262301i
$336$		0			0
$337$	−7.62240	−	4.40080i	−0.415219	−	0.239727i	0.277811	−	0.960636i	$-0.410391\pi$
$337$	−7.62240	−	4.40080i	−0.415219	−	0.239727i	−0.693030	+	0.720909i	$0.743724\pi$
$338$	−7.93841	−	4.61529i	−0.431792	−	0.251039i
$339$		0			0
$340$	−7.94508	+	10.2256i	−0.430882	+	0.554563i
$341$	0.764411	+	1.84545i	0.0413952	+	0.0999368i
$342$		0			0
$343$	30.3059	−	30.3059i	1.63636	−	1.63636i
$344$	0.435684	+	3.55839i	0.0234905	+	0.191855i
$345$		0			0
$346$	−10.2764	−	1.38453i	−0.552464	−	0.0744327i
$347$	−2.18082	−	0.287110i	−0.117072	−	0.0154129i	0.0717623	−	0.997422i	$-0.477138\pi$
$347$	−2.18082	−	0.287110i	−0.117072	−	0.0154129i	−0.188835	+	0.982009i	$0.560471\pi$
$348$		0			0
$349$	−2.16918	−	16.4765i	−0.116113	−	0.881968i	−0.946030	−	0.324080i	$-0.894945\pi$
$349$	−2.16918	−	16.4765i	−0.116113	−	0.881968i	0.829916	−	0.557888i	$-0.188388\pi$
$350$	17.0618	+	17.1652i	0.911991	+	0.917521i
$351$		0			0
$352$	−4.67981	−	2.02183i	−0.249435	−	0.107764i
$353$	26.2447	−	15.1524i	1.39686	−	0.806479i	0.402800	−	0.915288i	$-0.368037\pi$
$353$	26.2447	−	15.1524i	1.39686	−	0.806479i	0.994063	+	0.108809i	$0.0347037\pi$
$354$		0			0
$355$	6.32280	+	8.24004i	0.335580	+	0.437336i
$356$	2.27854	+	8.71400i	0.120763	+	0.461841i
$357$		0			0
$358$	−8.17640	−	6.31333i	−0.432136	−	0.333670i
$359$	18.7891	−	18.7891i	0.991652	−	0.991652i	−0.00831352	−	0.999965i	$-0.502646\pi$
$359$	18.7891	−	18.7891i	0.991652	−	0.991652i	0.999965	+	0.00831352i	$0.00264630\pi$
$360$		0			0
$361$	−5.48143	−	5.48143i	−0.288496	−	0.288496i
$362$	0.544066	+	4.23138i	0.0285955	+	0.222396i
$363$		0			0
$364$	24.2101	+	3.33633i	1.26896	+	0.174871i
$365$	11.8834	−	9.11842i	0.622003	−	0.477280i
$366$		0			0
$367$	−12.7357	−	22.0589i	−0.664800	−	1.15147i	−0.979340	−	0.202223i	$-0.935184\pi$
$367$	−12.7357	−	22.0589i	−0.664800	−	1.15147i	0.314540	−	0.949244i	$-0.398150\pi$
$368$	−12.9711	−	13.2886i	−0.676166	−	0.692717i
$369$		0			0
$370$	0.00314487	−	1.04048i	0.000163494	−	0.0540921i
$371$	−31.6771	+	4.17037i	−1.64459	+	0.216515i
$372$		0			0
$373$	1.50213	−	11.4098i	0.0777773	−	0.590777i	−0.907530	−	0.419987i	$-0.862035\pi$
$373$	1.50213	−	11.4098i	0.0777773	−	0.590777i	0.985307	−	0.170790i	$-0.0546320\pi$
$374$	−5.49213	+	4.18795i	−0.283991	+	0.216553i
$375$		0			0
$376$	4.01333	−	14.4525i	0.206972	−	0.745329i
$377$	7.23552	+	7.23552i	0.372648	+	0.372648i
$378$		0			0
$379$	17.9995	−	7.45564i	0.924572	−	0.382970i	0.130955	−	0.991388i	$-0.458196\pi$
$379$	17.9995	−	7.45564i	0.924572	−	0.382970i	0.793617	+	0.608418i	$0.208196\pi$
$380$	−6.96444	+	3.96498i	−0.357268	+	0.203399i
$381$		0			0
$382$	−22.2327	+	5.88527i	−1.13753	+	0.301117i
$383$	−4.89477	+	8.47800i	−0.250111	+	0.433205i	−0.963556	−	0.267506i	$-0.913801\pi$
$383$	−4.89477	+	8.47800i	−0.250111	+	0.433205i	0.713445	+	0.700711i	$0.247134\pi$
$384$		0			0
$385$	−2.57886	−	4.46672i	−0.131431	−	0.227645i
$386$	−16.5423	−	16.6426i	−0.841980	−	0.847085i
$387$		0			0
$388$	−0.156751	+	25.9303i	−0.00795783	+	1.31641i
$389$	−24.1751	−	18.5502i	−1.22573	−	0.940535i	−0.226291	−	0.974060i	$-0.572660\pi$
$389$	−24.1751	−	18.5502i	−1.22573	−	0.940535i	−0.999438	+	0.0335252i	$0.989327\pi$
$390$		0			0
$391$	−24.3014	+	6.51154i	−1.22897	+	0.329303i
$392$	43.6721	−	11.2785i	2.20578	−	0.569650i
$393$		0			0
$394$	2.54239	+	19.7730i	0.128084	+	0.996150i
$395$	6.32636	−	2.62046i	0.318314	−	0.131850i
$396$		0			0
$397$	11.3447	−	27.3885i	0.569373	−	1.37459i	−0.332711	−	0.943029i	$-0.607963\pi$
$397$	11.3447	−	27.3885i	0.569373	−	1.37459i	0.902084	−	0.431560i	$-0.142037\pi$
$398$	−32.6986	+	18.7470i	−1.63903	+	0.939703i
$399$		0			0
$400$	3.53143	+	13.8470i	0.176571	+	0.692349i
$401$	−6.43639	+	11.1481i	−0.321418	+	0.556712i	−0.980781	−	0.195113i	$-0.937493\pi$
$401$	−6.43639	+	11.1481i	−0.321418	+	0.556712i	0.659363	+	0.751825i	$0.270826\pi$
$402$		0			0
$403$	−0.738005	−	5.60571i	−0.0367627	−	0.279240i
$404$	0.0244218	+	0.0599826i	0.00121503	+	0.00298424i
$405$		0			0
$406$	25.0751	+	10.4754i	1.24446	+	0.519884i
$407$	0.143632	−	0.536042i	0.00711958	−	0.0265706i
$408$		0			0
$409$	−3.59170	−	13.4044i	−0.177598	−	0.662805i	−0.996094	−	0.0882936i	$-0.971859\pi$
$409$	−3.59170	−	13.4044i	−0.177598	−	0.662805i	0.818496	−	0.574512i	$-0.194808\pi$
$410$	2.54983	−	18.9257i	0.125927	−	0.934672i
$411$		0			0
$412$	−19.8500	−	5.44762i	−0.977941	−	0.268385i
$413$	9.66621	−	23.3363i	0.475643	−	1.14830i
$414$		0			0
$415$		−	5.90217i		−	0.289726i
$416$	11.3140	+	8.95638i	0.554713	+	0.439123i
$417$		0			0
$418$	−4.13202	+	1.09380i	−0.202104	+	0.0534993i
$419$	15.2863	−	11.7296i	0.746786	−	0.573029i	−0.163729	−	0.986505i	$-0.552352\pi$
$419$	15.2863	−	11.7296i	0.746786	−	0.573029i	0.910515	+	0.413476i	$0.135686\pi$
$420$		0			0
$421$	−6.20272	+	8.08354i	−0.302302	+	0.393968i	−0.919661	−	0.392714i	$-0.871536\pi$
$421$	−6.20272	+	8.08354i	−0.302302	+	0.393968i	0.617359	+	0.786682i	$0.288203\pi$
$422$	11.4202	+	27.8082i	0.555926	+	1.35368i
$423$		0			0
$424$	−17.3629	−	7.37709i	−0.843216	−	0.358263i
$425$	18.7009	+	5.01089i	0.907126	+	0.243064i
$426$		0			0
$427$	63.7162	+	8.38840i	3.08344	+	0.405943i
$428$	−38.4033	−	5.29226i	−1.85630	−	0.255811i
$429$		0			0
$430$	−1.85789	+	1.06518i	−0.0895956	+	0.0513676i
$431$			10.2561i			0.494018i	0.969013	+	0.247009i	$0.0794477\pi$
$431$			10.2561i			0.494018i	−0.969013	+	0.247009i	$0.920552\pi$
$432$		0			0
$433$			7.85626i			0.377548i	0.982021	+	0.188774i	$0.0604513\pi$
$433$			7.85626i			0.377548i	−0.982021	+	0.188774i	$0.939549\pi$
$434$	−7.46860	−	13.0268i	−0.358504	−	0.625305i
$435$		0			0
$436$	28.8285	−	21.8453i	1.38063	−	1.04620i
$437$	−15.4367	−	2.03228i	−0.738438	−	0.0972173i
$438$		0			0
$439$	24.0163	+	6.43516i	1.14624	+	0.307133i	0.781456	−	0.623960i	$-0.214477\pi$
$439$	24.0163	+	6.43516i	1.14624	+	0.307133i	0.364781	+	0.931093i	$0.381144\pi$
$440$	0.0276136	−	3.04525i	0.00131643	−	0.145176i
$441$		0			0
$442$	18.0843	−	7.42679i	0.860181	−	0.353256i
$443$	17.3623	−	22.6270i	0.824909	−	1.07504i	−0.171052	−	0.985262i	$-0.554717\pi$
$443$	17.3623	−	22.6270i	0.824909	−	1.07504i	0.995962	−	0.0897807i	$-0.0286166\pi$
$444$		0			0
$445$	−4.26871	+	3.27549i	−0.202356	+	0.155273i
$446$	−2.48513	−	9.38803i	−0.117674	−	0.444536i
$447$		0			0
$448$	36.8307	+	10.5882i	1.74009	+	0.500246i
$449$			13.4706i			0.635717i	0.948138	+	0.317859i	$0.102964\pi$
$449$			13.4706i			0.635717i	−0.948138	+	0.317859i	$0.897036\pi$
$450$		0			0
$451$	3.89777	−	9.41005i	0.183539	−	0.443102i
$452$	7.96772	−	4.53617i	0.374770	−	0.213363i
$453$		0			0
$454$	12.2587	+	1.65159i	0.575327	+	0.0775131i
$455$	3.77858	+	14.1019i	0.177143	+	0.661106i
$456$		0			0
$457$	−1.16978	+	4.36567i	−0.0547199	+	0.204218i	−0.987874	−	0.155260i	$-0.950378\pi$
$457$	−1.16978	+	4.36567i	−0.0547199	+	0.204218i	0.933154	+	0.359478i	$0.117045\pi$
$458$	2.34781	−	5.62002i	0.109706	−	0.262606i
$459$		0			0
$460$	4.30707	−	10.2230i	0.200818	−	0.476648i
$461$	2.24566	+	17.0575i	0.104591	+	0.794447i	0.960688	+	0.277631i	$0.0895494\pi$
$461$	2.24566	+	17.0575i	0.104591	+	0.794447i	−0.856097	+	0.516816i	$0.827117\pi$
$462$		0			0
$463$	−1.87338	+	3.24479i	−0.0870635	+	0.150798i	−0.906269	−	0.422702i	$-0.861082\pi$
$463$	−1.87338	+	3.24479i	−0.0870635	+	0.150798i	0.819205	+	0.573501i	$0.194415\pi$
$464$	9.61333	+	12.8470i	0.446288	+	0.596407i
$465$		0			0
$466$	−2.80279	−	4.88864i	−0.129837	−	0.226462i
$467$	2.81290	−	6.79094i	0.130166	−	0.314247i	−0.845338	−	0.534232i	$-0.820601\pi$
$467$	2.81290	−	6.79094i	0.130166	−	0.314247i	0.975503	+	0.219985i	$0.0706008\pi$
$468$		0			0
$469$	−35.5672	+	14.7324i	−1.64234	+	0.680280i
$470$	8.88715	−	1.14270i	0.409933	−	0.0527088i
$471$		0			0
$472$	11.9140	−	8.97149i	0.548387	−	0.412946i
$473$	−1.10331	+	0.295631i	−0.0507303	+	0.0135931i
$474$		0			0
$475$	9.50570	+	7.29398i	0.436152	+	0.334671i
$476$	36.9341	−	36.4903i	1.69287	−	1.67253i
$477$		0			0
$478$	6.85657	−	6.81525i	0.313612	−	0.311722i
$479$	2.97546	+	5.15366i	0.135952	+	0.235477i	0.925961	−	0.377619i	$-0.123257\pi$
$479$	2.97546	+	5.15366i	0.135952	+	0.235477i	−0.790008	+	0.613096i	$0.789924\pi$
$480$		0			0
$481$	−0.785416	+	1.36038i	−0.0358119	+	0.0620280i
$482$	2.06430	+	7.79827i	0.0940262	+	0.355201i
$483$		0			0
$484$	−5.39250	+	19.6492i	−0.245114	+	0.893146i
$485$	−14.3114	+	5.92797i	−0.649846	+	0.269175i
$486$		0			0
$487$	−25.4894	−	25.4894i	−1.15504	−	1.15504i	−0.985529	−	0.169507i	$-0.945783\pi$
$487$	−25.4894	−	25.4894i	−1.15504	−	1.15504i	−0.169507	−	0.985529i	$-0.554217\pi$
$488$	29.8937	+	23.3719i	1.35322	+	1.05800i
$489$		0			0
$490$	16.3383	+	21.4262i	0.738088	+	0.967939i
$491$	4.78779	−	36.3669i	0.216070	−	1.64121i	−0.448352	−	0.893857i	$-0.647989\pi$
$491$	4.78779	−	36.3669i	0.216070	−	1.64121i	0.664422	−	0.747358i	$-0.268678\pi$
$492$		0			0
$493$	21.5529	−	2.83749i	0.970692	−	0.127794i
$494$	12.0988	+	0.0365688i	0.544350	+	0.00164531i
$495$		0			0
$496$	0.107189	−	8.86546i	0.00481292	−	0.398071i
$497$	−20.8216	−	36.0641i	−0.933978	−	1.61770i
$498$		0			0
$499$	7.70331	−	5.91096i	0.344847	−	0.264611i	−0.421786	−	0.906695i	$-0.638597\pi$
$499$	7.70331	−	5.91096i	0.344847	−	0.264611i	0.766634	+	0.642084i	$0.221930\pi$
$500$	−16.3264	+	12.3716i	−0.730137	+	0.553273i
$501$		0			0
$502$	−17.7951	+	2.28807i	−0.794233	+	0.102122i
$503$	23.2112	+	23.2112i	1.03494	+	1.03494i	0.999367	+	0.0355681i	$0.0113241\pi$
$503$	23.2112	+	23.2112i	1.03494	+	1.03494i	0.0355681	+	0.999367i	$0.488676\pi$
$504$		0			0
$505$	−0.0273569	+	0.0273569i	−0.00121737	+	0.00121737i
$506$	3.61601	−	4.68309i	0.160751	−	0.208189i
$507$		0			0
$508$	8.66404	−	14.7992i	0.384404	−	0.656609i
$509$	14.6272	+	19.0625i	0.648338	+	0.844930i	0.995684	−	0.0928066i	$-0.0295838\pi$
$509$	14.6272	+	19.0625i	0.648338	+	0.844930i	−0.347346	+	0.937737i	$0.612917\pi$
$510$		0			0
$511$	−52.0098	+	30.0279i	−2.30078	+	1.32836i
$512$	15.5589	+	16.4293i	0.687612	+	0.726078i
$513$		0			0
$514$	−15.2013	+	15.1097i	−0.670501	+	0.666460i
$515$	−1.60501	−	12.1913i	−0.0707252	−	0.537211i
$516$		0			0
$517$	4.73817	+	0.623792i	0.208384	+	0.0274343i
$518$	−0.557022	+	4.13440i	−0.0244742	+	0.181655i
$519$		0			0
$520$	−2.30647	+	8.30585i	−0.101145	+	0.364236i
$521$	−13.9854	+	13.9854i	−0.612712	+	0.612712i	−0.943652	−	0.330940i	$-0.892634\pi$
$521$	−13.9854	+	13.9854i	−0.612712	+	0.612712i	0.330940	+	0.943652i	$0.392634\pi$
$522$		0			0
$523$	−15.0496	−	36.3331i	−0.658075	−	1.58873i	−0.800773	−	0.598968i	$-0.795578\pi$
$523$	−15.0496	−	36.3331i	−0.658075	−	1.58873i	0.142698	−	0.989766i	$-0.454422\pi$
$524$	19.4780	−	2.44463i	0.850899	−	0.106794i
$525$		0			0
$526$	−0.499267	+	0.858751i	−0.0217691	+	0.0374433i
$527$	−10.4026	−	6.00597i	−0.453146	−	0.261624i
$528$		0			0
$529$	−1.25373	+	0.723840i	−0.0545099	+	0.0314713i
$530$	0.0340625	−	11.2696i	0.00147958	−	0.489519i
$531$		0			0
$532$	29.7595	−	12.1166i	1.29024	−	0.525320i
$533$	−17.5508	+	22.8727i	−0.760211	+	0.990727i
$534$		0			0
$535$	−5.99378	−	22.3691i	−0.259134	−	0.967101i
$536$	−22.5086	−	3.17120i	−0.972223	−	0.136975i
$537$		0			0
$538$	15.9183	−	20.6158i	0.686285	−	0.888809i
$539$	5.49964	+	13.2773i	0.236886	+	0.571894i
$540$		0			0
$541$	11.2440	+	4.65741i	0.483417	+	0.200238i	0.611063	−	0.791582i	$-0.290742\pi$
$541$	11.2440	+	4.65741i	0.483417	+	0.200238i	−0.127646	+	0.991820i	$0.540742\pi$
$542$	−4.63054	+	17.0748i	−0.198899	+	0.733425i
$543$		0			0
$544$	29.7279	−	7.48596i	1.27457	−	0.320958i
$545$	18.7126	+	10.8037i	0.801561	+	0.462781i
$546$		0			0
$547$	4.19878	−	0.552780i	0.179527	−	0.0236352i	−0.0402267	−	0.999191i	$-0.512808\pi$
$547$	4.19878	−	0.552780i	0.179527	−	0.0236352i	0.219754	+	0.975555i	$0.429475\pi$
$548$	21.3422	+	21.6018i	0.911694	+	0.922783i
$549$		0			0
$550$	−4.21177	+	1.72968i	−0.179590	+	0.0737536i
$551$	12.9951	+	3.48202i	0.553609	+	0.148339i
$552$		0			0
$553$	−26.5195	+	7.10587i	−1.12772	+	0.302172i
$554$	12.3439	−	9.41267i	0.524442	−	0.399906i
$555$		0			0
$556$	−15.4828	−	12.0297i	−0.656615	−	0.510174i
$557$	6.71881	+	2.78302i	0.284685	+	0.117921i	0.520457	−	0.853888i	$-0.325762\pi$
$557$	6.71881	+	2.78302i	0.284685	+	0.117921i	−0.235771	+	0.971809i	$0.575762\pi$
$558$		0			0
$559$	3.23317			0.136749
$560$	2.71352	+	22.7317i	0.114667	+	0.960589i
$561$		0			0
$562$	−7.65854	−	4.45258i	−0.323056	−	0.187821i
$563$	10.7050	+	13.9511i	0.451163	+	0.587968i	0.962456	−	0.271439i	$-0.0874996\pi$
$563$	10.7050	+	13.9511i	0.451163	+	0.587968i	−0.511292	+	0.859407i	$0.670833\pi$
$564$		0			0
$565$	4.34526	+	3.33423i	0.182806	+	0.140272i
$566$	−14.4382	−	6.03168i	−0.606881	−	0.253530i
$567$		0			0
$568$	0.222951	−	24.5872i	0.00935482	−	1.03166i
$569$	−1.88166	+	7.02243i	−0.0788831	+	0.294396i	−0.994086	−	0.108598i	$-0.965364\pi$
$569$	−1.88166	+	7.02243i	−0.0788831	+	0.294396i	0.915203	+	0.402994i	$0.132030\pi$
$570$		0			0
$571$	4.57915	−	34.7821i	0.191631	−	1.45558i	−0.577446	−	0.816429i	$-0.695951\pi$
$571$	4.57915	−	34.7821i	0.191631	−	1.45558i	0.769077	−	0.639156i	$-0.220716\pi$
$572$	−2.32284	+	3.96769i	−0.0971228	+	0.165898i
$573$		0			0
$574$	−20.0404	+	73.8975i	−0.836469	+	3.08442i
$575$	−16.5854			−0.691658
$576$		0			0
$577$	−29.9660			−1.24750			−0.623750	−	0.781624i	$-0.714392\pi$
$577$	−29.9660			−1.24750			−0.623750	+	0.781624i	$0.714392\pi$
$578$	4.57820	−	16.8818i	0.190428	−	0.702191i
$579$		0			0
$580$	−4.84275	+	8.27201i	−0.201084	+	0.343476i
$581$	−3.08881	+	23.4619i	−0.128146	+	0.973362i
$582$		0			0
$583$	1.55570	−	5.80594i	0.0644303	−	0.240457i
$584$	−35.4584	−	0.321528i	−1.46728	−	0.0133049i
$585$		0			0
$586$	−6.70891	−	2.80271i	−0.277143	−	0.115779i
$587$	−5.85948	−	4.49614i	−0.241847	−	0.185576i	0.480725	−	0.876871i	$-0.340373\pi$
$587$	−5.85948	−	4.49614i	−0.241847	−	0.185576i	−0.722572	+	0.691296i	$0.757040\pi$
$588$		0			0
$589$	−4.52543	−	5.89765i	−0.186467	−	0.243008i
$590$	7.70228	+	4.47801i	0.317098	+	0.184357i
$591$		0			0
$592$	−1.52302	+	1.93592i	−0.0625958	+	0.0795659i
$593$	−14.5325			−0.596778			−0.298389	−	0.954444i	$-0.596449\pi$
$593$	−14.5325			−0.596778			−0.298389	+	0.954444i	$0.596449\pi$
$594$		0			0
$595$	28.6549	+	11.8693i	1.17474	+	0.486592i
$596$	−33.4608	−	25.9983i	−1.37061	−	1.06493i
$597$		0			0
$598$	−13.3175	+	10.1550i	−0.544592	+	0.415271i
$599$	8.89976	−	2.38468i	0.363634	−	0.0974355i	−0.0723755	−	0.997377i	$-0.523058\pi$
$599$	8.89976	−	2.38468i	0.363634	−	0.0974355i	0.436010	+	0.899942i	$0.356391\pi$
$600$		0			0
$601$	14.9062	+	3.99411i	0.608038	+	0.162923i	0.549684	−	0.835373i	$-0.314748\pi$
$601$	14.9062	+	3.99411i	0.608038	+	0.162923i	0.0583538	+	0.998296i	$0.481415\pi$
$602$	7.94282	−	3.26193i	0.323725	−	0.132946i
$603$		0			0
$604$	2.08602	+	2.11139i	0.0848789	+	0.0859113i
$605$	−12.0679	+	1.58877i	−0.490631	+	0.0645927i
$606$		0			0
$607$	−12.0050	−	6.93106i	−0.487266	−	0.281323i	0.236174	−	0.971711i	$-0.424107\pi$
$607$	−12.0050	−	6.93106i	−0.487266	−	0.281323i	−0.723440	+	0.690388i	$0.757440\pi$
$608$	18.7702	+	2.76032i	0.761231	+	0.111946i
$609$		0			0
$610$	−5.93307	+	21.8778i	−0.240223	+	0.885807i
$611$	−12.4977	−	5.17673i	−0.505605	−	0.209428i
$612$		0			0
$613$	−7.00821	−	16.9193i	−0.283059	−	0.683365i	0.716845	−	0.697233i	$-0.245586\pi$
$613$	−7.00821	−	16.9193i	−0.283059	−	0.683365i	−0.999904	+	0.0138677i	$0.995586\pi$
$614$	13.5644	−	17.5673i	0.547416	−	0.708959i
$615$		0			0
$616$	−1.70345	+	12.0908i	−0.0686341	+	0.487152i
$617$	−3.92674	−	14.6548i	−0.158085	−	0.589980i	−0.998821	−	0.0485361i	$-0.984544\pi$
$617$	−3.92674	−	14.6548i	−0.158085	−	0.589980i	0.840737	−	0.541444i	$-0.182122\pi$
$618$		0			0
$619$	−23.4716	+	30.5888i	−0.943403	+	1.22947i	0.0298087	+	0.999556i	$0.490510\pi$
$619$	−23.4716	+	30.5888i	−0.943403	+	1.22947i	−0.973212	+	0.229911i	$0.926156\pi$
$620$	4.90543	−	1.99724i	0.197007	−	0.0802111i
$621$		0			0
$622$	0.0717961	−	23.7537i	0.00287876	−	0.952438i
$623$	18.6828	−	10.7865i	0.748512	−	0.432154i
$624$		0			0
$625$	4.87212	+	2.81292i	0.194885	+	0.112517i
$626$	18.5384	−	31.8865i	0.740944	−	1.27444i
$627$		0			0
$628$	44.6101	−	5.59890i	1.78014	−	0.223421i
$629$	1.27709	+	3.08316i	0.0509208	+	0.122934i
$630$		0			0
$631$	−19.2059	+	19.2059i	−0.764575	+	0.764575i	−0.977146	−	0.212571i	$-0.931816\pi$
$631$	−19.2059	+	19.2059i	−0.764575	+	0.764575i	0.212571	+	0.977146i	$0.431816\pi$
$632$	−15.6197	−	4.33746i	−0.621318	−	0.172535i
$633$		0			0
$634$	−0.181622	+	1.34806i	−0.00721312	+	0.0535381i
$635$	10.1567	+	1.33716i	0.403057	+	0.0530635i
$636$		0			0
$637$	−5.30965	−	40.3308i	−0.210376	−	1.59797i
$638$	−3.62593	+	3.60408i	−0.143552	+	0.142687i
$639$		0			0
$640$	−5.43584	+	12.3760i	−0.214870	+	0.489204i
$641$	32.6527	−	18.8520i	1.28970	−	0.744611i	0.311103	−	0.950376i	$-0.399302\pi$
$641$	32.6527	−	18.8520i	1.28970	−	0.744611i	0.978601	+	0.205766i	$0.0659684\pi$
$642$		0			0
$643$	1.11651	+	1.45506i	0.0440308	+	0.0573821i	0.814850	−	0.579672i	$-0.196819\pi$
$643$	1.11651	+	1.45506i	0.0440308	+	0.0573821i	−0.770819	+	0.637054i	$0.780153\pi$
$644$	−22.4712	+	38.3835i	−0.885488	+	1.51252i
$645$		0			0
$646$	15.7090	−	20.3447i	0.618060	−	0.800451i
$647$	−19.0374	+	19.0374i	−0.748438	+	0.748438i	−0.974186	−	0.225748i	$-0.927517\pi$
$647$	−19.0374	+	19.0374i	−0.748438	+	0.748438i	0.225748	+	0.974186i	$0.427517\pi$
$648$		0			0
$649$	3.36011	+	3.36011i	0.131896	+	0.131896i
$650$	12.7827	−	1.64358i	0.501377	−	0.0644665i
$651$		0			0
$652$	−1.70139	+	1.28926i	−0.0666315	+	0.0504911i
$653$	−2.81412	+	2.15935i	−0.110125	+	0.0845020i	−0.662356	−	0.749189i	$-0.730443\pi$
$653$	−2.81412	+	2.15935i	−0.110125	+	0.0845020i	0.552231	+	0.833691i	$0.313777\pi$
$654$		0			0
$655$	5.86352	+	10.1559i	0.229107	+	0.396824i
$656$	−32.3515	+	31.5786i	−1.26311	+	1.23294i
$657$		0			0
$658$	−35.9256	−	0.108586i	−1.40052	−	0.00423311i
$659$	−23.2164	+	3.05650i	−0.904384	+	0.119064i	−0.568352	−	0.822786i	$-0.692419\pi$
$659$	−23.2164	+	3.05650i	−0.904384	+	0.119064i	−0.336033	+	0.941850i	$0.609085\pi$
$660$		0			0
$661$	−4.20564	+	31.9450i	−0.163580	+	1.24252i	0.690869	+	0.722980i	$0.257228\pi$
$661$	−4.20564	+	31.9450i	−0.163580	+	1.24252i	−0.854449	+	0.519535i	$0.826105\pi$
$662$	−4.27944	−	5.61211i	−0.166325	−	0.218121i
$663$		0			0
$664$	−8.60611	+	11.0076i	−0.333982	+	0.427177i
$665$	13.5728	+	13.5728i	0.526329	+	0.526329i
$666$		0			0
$667$	−17.2051	+	7.12660i	−0.666186	+	0.275943i
$668$	1.45450	−	5.29992i	0.0562764	−	0.205060i
$669$		0			0
$670$	−3.47484	−	13.1269i	−0.134245	−	0.507134i
$671$	−6.04509	+	10.4704i	−0.233368	+	0.404206i
$672$		0			0
$673$	2.85420	+	4.94361i	0.110021	+	0.190562i	0.915779	−	0.401684i	$-0.131575\pi$
$673$	2.85420	+	4.94361i	0.110021	+	0.190562i	−0.805757	+	0.592246i	$0.798241\pi$
$674$	−8.82816	+	8.77495i	−0.340048	+	0.337998i
$675$		0			0
$676$	−9.23789	+	9.12687i	−0.355303	+	0.351034i
$677$	3.08389	+	2.36635i	0.118524	+	0.0909463i	0.666322	−	0.745664i	$-0.267867\pi$
$677$	3.08389	+	2.36635i	0.118524	+	0.0909463i	−0.547799	+	0.836610i	$0.684534\pi$
$678$		0			0
$679$	59.9919	−	16.0748i	2.30228	−	0.616893i
$680$	11.0162	+	14.6294i	0.422453	+	0.561011i
$681$		0			0
$682$	2.80183	−	0.360256i	0.107288	−	0.0137949i
$683$	40.7387	−	16.8745i	1.55882	−	0.645685i	0.573937	−	0.818899i	$-0.305415\pi$
$683$	40.7387	−	16.8745i	1.55882	−	0.645685i	0.984884	+	0.173214i	$0.0554153\pi$
$684$		0			0
$685$	−6.94202	+	16.7595i	−0.265241	+	0.640348i
$686$	−30.1471	−	52.5827i	−1.15102	−	2.00762i
$687$		0			0
$688$	5.01816	+	0.722476i	0.191316	+	0.0275441i
$689$	−8.50693	+	14.7344i	−0.324088	+	0.561337i
$690$		0			0
$691$	5.72504	+	43.4860i	0.217791	+	1.65429i	0.655519	+	0.755179i	$0.272450\pi$
$691$	5.72504	+	43.4860i	0.217791	+	1.65429i	−0.437728	+	0.899108i	$0.644217\pi$
$692$	−5.69360	+	13.5139i	−0.216438	+	0.513722i
$693$		0			0
$694$	−1.19912	+	2.87035i	−0.0455178	+	0.108957i
$695$	3.03149	−	11.3137i	0.114991	−	0.429152i
$696$		0			0
$697$	15.8525	+	59.1624i	0.600457	+	2.24094i
$698$	−23.2920	−	3.13809i	−0.881613	−	0.118779i
$699$		0			0
$700$	29.7445	−	16.9341i	1.12424	−	0.640049i
$701$	5.27727	−	12.7404i	0.199320	−	0.481200i	−0.792341	−	0.610079i	$-0.791138\pi$
$701$	5.27727	−	12.7404i	0.199320	−	0.481200i	0.991660	+	0.128879i	$0.0411378\pi$
$702$		0			0
$703$			2.06529i			0.0778937i
$704$	−4.49186	+	5.63915i	−0.169293	+	0.212533i
$705$		0			0
$706$	−10.9671	−	41.4304i	−0.412753	−	1.55925i
$707$	0.123064	−	0.0944304i	0.00462830	−	0.00355142i
$708$		0			0
$709$	−9.44008	+	12.3025i	−0.354530	+	0.462032i	−0.936239	−	0.351365i	$-0.885718\pi$
$709$	−9.44008	+	12.3025i	−0.354530	+	0.462032i	0.581709	+	0.813397i	$0.302384\pi$
$710$	13.5873	−	5.58001i	0.509924	−	0.209414i
$711$		0			0
$712$	12.7373	+	0.115499i	0.477349	+	0.00432849i
$713$	9.93948	+	2.66328i	0.372236	+	0.0997404i
$714$		0			0
$715$	−2.72303	−	0.358494i	−0.101836	−	0.0134069i
$716$	−11.6437	+	8.82318i	−0.435144	+	0.329738i
$717$		0			0
$718$	−18.6907	−	32.6004i	−0.697530	−	1.21663i
$719$		−	2.23219i		−	0.0832468i	−0.999133	−	0.0416234i	$-0.986747\pi$
$719$		−	2.23219i		−	0.0832468i	0.999133	−	0.0416234i	$-0.0132530\pi$
$720$		0			0
$721$			49.3018i			1.83609i
$722$	−9.51063	+	5.45270i	−0.353949	+	0.202929i
$723$		0			0
$724$	5.97685	+	0.823654i	0.222128	+	0.0306109i
$725$	14.2083	+	1.87056i	0.527684	+	0.0694709i
$726$		0			0
$727$	15.6188	+	4.18503i	0.579268	+	0.155214i	0.536544	−	0.843873i	$-0.319730\pi$
$727$	15.6188	+	4.18503i	0.579268	+	0.155214i	0.0427241	+	0.999087i	$0.486396\pi$
$728$	13.5152	−	31.8098i	0.500908	−	1.17895i
$729$		0			0
$730$	−8.04719	−	19.5949i	−0.297840	−	0.725241i
$731$	4.18145	−	5.44937i	0.154657	−	0.201552i
$732$		0			0
$733$	−0.330246	+	0.253406i	−0.0121979	+	0.00935978i	−0.614842	−	0.788650i	$-0.710780\pi$
$733$	−0.330246	+	0.253406i	−0.0121979	+	0.00935978i	0.602644	+	0.798010i	$0.294114\pi$
$734$	−34.8227	+	9.21799i	−1.28533	+	0.340242i
$735$		0			0
$736$	−22.9391	+	12.7856i	−0.845546	+	0.471285i
$737$		−	7.24246i		−	0.266779i
$738$		0			0
$739$	−8.34979	+	20.1582i	−0.307152	+	0.741530i	0.692643	+	0.721281i	$0.256446\pi$
$739$	−8.34979	+	20.1582i	−0.307152	+	0.741530i	−0.999795	+	0.0202498i	$0.993554\pi$
$740$	−1.41900	−	0.389429i	−0.0521636	−	0.0143157i
$741$		0			0
$742$	−6.03317	+	44.7802i	−0.221485	+	1.64393i
$743$	−8.01409	−	29.9090i	−0.294008	−	1.09725i	−0.942002	−	0.335608i	$-0.891058\pi$
$743$	−8.01409	−	29.9090i	−0.294008	−	1.09725i	0.647993	−	0.761646i	$-0.275608\pi$
$744$		0			0
$745$	6.55155	−	24.4507i	0.240030	−	0.895805i
$746$	−15.0174	−	6.27364i	−0.549825	−	0.229694i
$747$		0			0
$748$	3.68326	+	9.04646i	0.134673	+	0.330771i
$749$	12.1195	+	92.0568i	0.442837	+	3.36368i
$750$		0			0
$751$	7.87620	−	13.6420i	0.287407	−	0.497803i	−0.685783	−	0.727806i	$-0.740540\pi$
$751$	7.87620	−	13.6420i	0.287407	−	0.497803i	0.973190	+	0.230003i	$0.0738736\pi$
$752$	−18.2408	−	10.8275i	−0.665174	−	0.394837i
$753$		0			0
$754$	12.5541	−	7.19761i	0.457194	−	0.262122i
$755$	−0.678523	+	1.63810i	−0.0246940	+	0.0596166i
$756$		0			0
$757$	26.0351	−	10.7841i	0.946261	−	0.391954i	0.144437	−	0.989514i	$-0.453863\pi$
$757$	26.0351	−	10.7841i	0.946261	−	0.391954i	0.801824	+	0.597560i	$0.203863\pi$
$758$	−3.51373	−	27.3275i	−0.127625	−	0.992578i
$759$		0			0
$760$	2.83395	+	10.9735i	0.102798	+	0.398051i
$761$	−41.8566	+	11.2154i	−1.51730	+	0.406560i	−0.918852	−	0.394601i	$-0.870883\pi$
$761$	−41.8566	+	11.2154i	−1.51730	+	0.406560i	−0.598449	+	0.801161i	$0.704216\pi$
$762$		0			0
$763$	−68.7311	−	52.7392i	−2.48823	−	1.90929i
$764$	−0.196612	+	32.5242i	−0.00711316	+	1.17668i
$765$		0			0
$766$	9.75991	+	9.81909i	0.352640	+	0.354778i
$767$	−6.72531	−	11.6486i	−0.242837	−	0.420606i
$768$		0			0
$769$	0.306129	−	0.530231i	0.0110393	−	0.0191206i	−0.860453	−	0.509530i	$-0.829819\pi$
$769$	0.306129	−	0.530231i	0.0110393	−	0.0191206i	0.871492	+	0.490409i	$0.163153\pi$
$770$	−7.05126	+	1.86656i	−0.254110	+	0.0672660i
$771$		0			0
$772$	−28.8388	+	16.4185i	−1.03793	+	0.590914i
$773$	39.8912	−	16.5235i	1.43479	−	0.594308i	0.476258	−	0.879306i	$-0.341993\pi$
$773$	39.8912	−	16.5235i	1.43479	−	0.594308i	0.958528	+	0.284998i	$0.0919929\pi$
$774$		0			0
$775$	−5.59933	−	5.59933i	−0.201134	−	0.201134i
$776$	35.3346	+	9.81212i	1.26844	+	0.352234i
$777$		0			0
$778$	−34.2680	+	26.1305i	−1.22857	+	0.936826i
$779$	−4.94765	+	37.5811i	−0.177268	+	1.34648i
$780$		0			0
$781$	7.76721	−	1.02257i	0.277933	−	0.0365905i
$782$	−0.107540	+	35.5795i	−0.00384561	+	1.27232i
$783$		0			0
$784$	0.771181	−	63.7834i	0.0275422	−	2.27798i
$785$	13.4291	+	23.2599i	0.479306	+	0.830182i
$786$		0			0
$787$	9.50954	−	7.29693i	0.338979	−	0.260107i	−0.425218	−	0.905091i	$-0.639802\pi$
$787$	9.50954	−	7.29693i	0.338979	−	0.260107i	0.764196	+	0.644984i	$0.223136\pi$
$788$	27.9295	+	3.84889i	0.994947	+	0.137111i
$789$		0			0
$790$	−1.23499	−	9.60490i	−0.0439389	−	0.341727i
$791$	−15.5280	−	15.5280i	−0.552113	−	0.552113i
$792$		0			0
$793$	24.1987	−	24.1987i	0.859321	−	0.859321i
$794$	−33.1836	−	25.6224i	−1.17764	−	0.909306i
$795$		0			0
$796$	13.4846	+	51.5700i	0.477947	+	1.82785i
$797$	−5.13981	−	6.69833i	−0.182061	−	0.237267i	0.693403	−	0.720550i	$-0.256111\pi$
$797$	−5.13981	−	6.69833i	−0.182061	−	0.237267i	−0.875464	+	0.483283i	$0.839444\pi$
$798$		0			0
$799$	−24.8885	+	14.3694i	−0.880491	+	0.508352i
$800$	20.2071	+	0.305404i	0.714428	+	0.0107976i
$801$		0			0
$802$	12.8338	+	12.9116i	0.453177	+	0.455925i
$803$	−1.47470	−	11.2015i	−0.0520411	−	0.395291i
$804$		0			0
$805$	−26.3426	−	3.46808i	−0.928456	−	0.122234i
$806$	−7.92448	−	1.06765i	−0.279128	−	0.0376065i
$807$		0			0
$808$	0.0909108	−	0.0111310i	0.00319823	−	0.000391587i
$809$	−17.1871	+	17.1871i	−0.604266	+	0.604266i	−0.941442	−	0.337176i	$-0.890528\pi$
$809$	−17.1871	+	17.1871i	−0.604266	+	0.604266i	0.337176	+	0.941442i	$0.390528\pi$
$810$		0			0
$811$	0.177117	+	0.427599i	0.00621943	+	0.0150150i	0.926959	−	0.375163i	$-0.122413\pi$
$811$	0.177117	+	0.427599i	0.00621943	+	0.0150150i	−0.920739	+	0.390178i	$0.872413\pi$
$812$	23.5796	−	30.3479i	0.827482	−	1.06500i
$813$		0			0
$814$	−0.678485	−	0.394463i	−0.0237809	−	0.0138259i
$815$	−1.10437	−	0.637610i	−0.0386845	−	0.0223345i
$816$		0			0
$817$	3.68137	−	2.12544i	0.128795	−	0.0743598i
$818$	−19.6253	−	0.0593179i	−0.686184	−	0.00207400i
$819$		0			0
$820$	−24.8881	−	10.4857i	−0.869129	−	0.366176i
$821$	10.1958	−	13.2874i	0.355835	−	0.463733i	−0.580797	−	0.814048i	$-0.697259\pi$
$821$	10.1958	−	13.2874i	0.355835	−	0.463733i	0.936632	+	0.350316i	$0.113926\pi$
$822$		0			0
$823$	7.89285	+	29.4565i	0.275127	+	1.02679i	0.955756	+	0.294161i	$0.0950401\pi$
$823$	7.89285	+	29.4565i	0.275127	+	1.02679i	−0.680628	+	0.732629i	$0.738293\pi$
$824$	−14.7831	+	25.0771i	−0.514993	+	0.873603i
$825$		0			0
$826$	−28.2740	−	21.8315i	−0.983779	−	0.759616i
$827$	−21.6631	−	52.2993i	−0.753299	−	1.81863i	−0.540062	−	0.841625i	$-0.681599\pi$
$827$	−21.6631	−	52.2993i	−0.753299	−	1.81863i	−0.213237	−	0.977000i	$-0.568401\pi$
$828$		0			0
$829$	−21.5086	−	8.90913i	−0.747023	−	0.309427i	−0.0234967	−	0.999724i	$-0.507480\pi$
$829$	−21.5086	−	8.90913i	−0.747023	−	0.309427i	−0.723526	+	0.690297i	$0.757480\pi$
$830$	−8.05594	−	2.18470i	−0.279626	−	0.0758321i
$831$		0			0
$832$	16.4126	−	12.1274i	0.569004	−	0.420440i
$833$	−74.8429	−	43.2106i	−2.59315	−	1.49716i
$834$		0			0
$835$	3.25504	−	0.428535i	0.112645	−	0.0148301i
$836$	−0.0365409	+	6.04472i	−0.00126379	+	0.209061i
$837$		0			0
$838$	−10.3516	−	25.2063i	−0.357591	−	0.870735i
$839$	7.98934	+	2.14074i	0.275823	+	0.0739064i	0.394079	−	0.919077i	$-0.371064\pi$
$839$	7.98934	+	2.14074i	0.275823	+	0.0739064i	−0.118256	+	0.992983i	$0.537730\pi$
$840$		0			0
$841$	−12.4688	+	3.34101i	−0.429959	+	0.115207i
$842$	8.73738	+	11.4583i	0.301110	+	0.394880i
$843$		0			0
$844$	42.1830	−	5.29428i	1.45200	−	0.182237i
$845$	−7.16711	−	2.96872i	−0.246556	−	0.102127i
$846$		0			0
$847$	48.8030			1.67689
$848$	−16.4960	+	20.9682i	−0.566475	+	0.720050i
$849$		0			0
$850$	13.7616	−	23.6703i	0.472019	−	0.811884i
$851$	−1.74034	−	2.26806i	−0.0596582	−	0.0777481i
$852$		0			0
$853$	27.5219	+	21.1183i	0.942333	+	0.723077i	0.960942	−	0.276750i	$-0.0892572\pi$
$853$	27.5219	+	21.1183i	0.942333	+	0.723077i	−0.0186095	+	0.999827i	$0.505924\pi$
$854$	35.0341	−	83.8621i	1.19884	−	2.86970i
$855$		0			0
$856$	−21.4386	+	50.4583i	−0.732755	+	1.72463i
$857$	−10.1959	+	38.0516i	−0.348286	+	1.29982i	0.540441	+	0.841382i	$0.318257\pi$
$857$	−10.1959	+	38.0516i	−0.348286	+	1.29982i	−0.888727	+	0.458437i	$0.848409\pi$
$858$		0			0
$859$	−5.04945	+	38.3544i	−0.172285	+	1.30864i	0.658728	+	0.752382i	$0.271095\pi$
$859$	−5.04945	+	38.3544i	−0.172285	+	1.30864i	−0.831013	+	0.556254i	$0.812238\pi$
$860$	0.766176	+	2.93014i	0.0261264	+	0.0999171i
$861$		0			0
$862$	13.9987	+	3.79631i	0.476796	+	0.129303i
$863$	30.8184			1.04907			0.524535	−	0.851389i	$-0.324239\pi$
$863$	30.8184			1.04907			0.524535	+	0.851389i	$0.324239\pi$
$864$		0			0
$865$	−8.76019			−0.297856
$866$	10.7231	+	2.90801i	0.364386	+	0.0988183i
$867$		0			0
$868$	−20.5449	+	5.37210i	−0.697340	+	0.182341i
$869$	0.674171	−	5.12084i	0.0228697	−	0.173713i
$870$		0			0
$871$	−5.30587	+	19.8018i	−0.179783	+	0.670958i
$872$	−19.1460	−	47.4345i	−0.648364	−	1.60633i
$873$		0			0
$874$	−8.48783	+	20.3175i	−0.287105	+	0.687250i
$875$	38.9243	+	29.8676i	1.31588	+	1.00971i
$876$		0			0
$877$	−3.02912	−	3.94763i	−0.102286	−	0.133302i	0.739406	−	0.673260i	$-0.235107\pi$
$877$	−3.02912	−	3.94763i	−0.102286	−	0.133302i	−0.841692	+	0.539958i	$0.818440\pi$
$878$	17.6731	−	30.3982i	0.596440	−	1.02589i
$879$		0			0
$880$	−4.14628	−	1.16490i	−0.139771	−	0.0392686i
$881$	9.77377			0.329287			0.164643	−	0.986353i	$-0.447353\pi$
$881$	9.77377			0.329287			0.164643	+	0.986353i	$0.447353\pi$
$882$		0			0
$883$	−12.6487	−	5.23927i	−0.425663	−	0.176315i	0.159559	−	0.987188i	$-0.448993\pi$
$883$	−12.6487	−	5.23927i	−0.425663	−	0.176315i	−0.585222	+	0.810873i	$0.698993\pi$
$884$	−3.44298	−	27.4325i	−0.115800	−	0.922655i
$885$		0			0
$886$	−24.4572	−	32.0735i	−0.821656	−	1.07753i
$887$	3.67918	−	0.985834i	0.123535	−	0.0331011i	−0.196522	−	0.980499i	$-0.562965\pi$
$887$	3.67918	−	0.985834i	0.123535	−	0.0331011i	0.320057	+	0.947398i	$0.396298\pi$
$888$		0			0
$889$	−39.6745	−	10.6308i	−1.33064	−	0.356544i
$890$	2.89069	+	7.03885i	0.0968962	+	0.235943i
$891$		0			0
$892$	−13.7337	−	0.0830215i	−0.459839	−	0.00277977i
$893$	−17.6334	+	2.32148i	−0.590078	+	0.0776853i
$894$		0			0
$895$	−7.55792	−	4.36357i	−0.252633	−	0.145858i
$896$	28.0850	−	46.3514i	0.938252	−	1.54849i
$897$		0			0
$898$	18.3862	+	4.98618i	0.613556	+	0.166391i
$899$	−8.21456	−	3.40258i	−0.273971	−	0.113482i
$900$		0			0
$901$	13.8323	+	33.3941i	0.460820	+	1.11252i
$902$	−11.4011	−	8.80327i	−0.379616	−	0.293117i
$903$		0			0
$904$	−3.24220	−	12.5543i	−0.107834	−	0.417550i
$905$	0.932835	+	3.48139i	0.0310085	+	0.115725i
$906$		0			0
$907$	−3.53336	+	4.60477i	−0.117323	+	0.152899i	−0.848323	−	0.529479i	$-0.822387\pi$
$907$	−3.53336	+	4.60477i	−0.117323	+	0.152899i	0.731000	+	0.682378i	$0.239054\pi$
$908$	6.79185	−	16.1207i	0.225396	−	0.534983i
$909$		0			0
$910$	20.6465	+	0.0624043i	0.684424	+	0.00206868i
$911$	−0.966011	+	0.557727i	−0.0320054	+	0.0184783i	−0.515917	−	0.856638i	$-0.672549\pi$
$911$	−0.966011	+	0.557727i	−0.0320054	+	0.0184783i	0.483912	+	0.875117i	$0.339215\pi$
$912$		0			0
$913$	−3.85546	−	2.22595i	−0.127597	−	0.0736682i
$914$	5.52577	+	3.21261i	0.182776	+	0.106264i
$915$		0			0
$916$	−6.80179	−	5.28483i	−0.224737	−	0.174616i
$917$	−17.9933	−	43.4396i	−0.594191	−	1.43450i
$918$		0			0
$919$	−14.8682	+	14.8682i	−0.490457	+	0.490457i	−0.908450	−	0.417993i	$-0.862734\pi$
$919$	−14.8682	+	14.8682i	−0.490457	+	0.490457i	0.417993	+	0.908450i	$0.362734\pi$
$920$	−12.3592	−	9.66282i	−0.407470	−	0.318574i
$921$		0			0
$922$	24.1132	+	3.24874i	0.794127	+	0.106992i
$923$	−21.9857	−	2.89447i	−0.723667	−	0.0952725i
$924$		0			0
$925$	0.287155	+	2.18116i	0.00944160	+	0.0717161i
$926$	3.73542	+	3.75807i	0.122754	+	0.123498i
$927$		0			0
$928$	21.0934	−	8.36601i	0.692425	−	0.274628i
$929$	−16.7941	+	9.69609i	−0.550997	+	0.318118i	−0.749524	−	0.661977i	$-0.769718\pi$
$929$	−16.7941	+	9.69609i	−0.550997	+	0.318118i	0.198527	+	0.980095i	$0.436384\pi$
$930$		0			0
$931$	−32.5586	−	42.4312i	−1.06707	−	1.39063i
$932$	−7.71002	+	2.01602i	−0.252550	+	0.0660370i
$933$		0			0
$934$	−8.22784	−	6.35305i	−0.269223	−	0.207878i
$935$	−4.12592	+	4.12592i	−0.134932	+	0.134932i
$936$		0			0
$937$	22.5258	+	22.5258i	0.735887	+	0.735887i	0.971779	−	0.235892i	$-0.0758013\pi$
$937$	22.5258	+	22.5258i	0.735887	+	0.735887i	−0.235892	+	0.971779i	$0.575801\pi$
$938$	6.94318	+	53.9994i	0.226703	+	1.76314i
$939$		0			0
$940$	1.72992	−	12.5532i	0.0564236	−	0.409439i
$941$	−28.2164	+	21.6512i	−0.919828	+	0.705809i	−0.955947	−	0.293538i	$-0.905167\pi$
$941$	−28.2164	+	21.6512i	−0.919828	+	0.705809i	0.0361190	+	0.999347i	$0.488500\pi$
$942$		0			0
$943$	−26.2349	−	45.4401i	−0.854325	−	1.47973i
$944$	−7.83530	−	19.5824i	−0.255017	−	0.637354i
$945$		0			0
$946$	−0.00488243	+	1.61535i	−0.000158742	+	0.0525196i
$947$	8.88425	−	1.16963i	0.288699	−	0.0380080i	0.0152143	−	0.999884i	$-0.495157\pi$
$947$	8.88425	−	1.16963i	0.288699	−	0.0380080i	0.273485	+	0.961876i	$0.411824\pi$
$948$		0			0
$949$	−4.17425	+	31.7066i	−0.135502	+	1.02924i
$950$	13.4742	−	10.2746i	0.437161	−	0.333351i
$951$		0			0
$952$	−36.1348	−	63.9188i	−1.17114	−	2.07162i
$953$	24.9238	+	24.9238i	0.807360	+	0.807360i	0.984234	−	0.176874i	$-0.0565984\pi$
$953$	24.9238	+	24.9238i	0.807360	+	0.807360i	−0.176874	+	0.984234i	$0.556598\pi$
$954$		0			0
$955$	−17.9507	+	7.43540i	−0.580870	+	0.240604i
$956$	−6.76424	−	11.8813i	−0.218771	−	0.384269i
$957$		0			0
$958$	8.13567	−	2.15361i	0.262851	−	0.0695800i
$959$	36.3663	−	62.9882i	1.17433	−	2.03400i
$960$		0			0
$961$	−13.0435	−	22.5920i	−0.420758	−	0.728775i
$962$	1.56608	+	1.57557i	0.0504923	+	0.0507985i
$963$		0			0
$964$	11.4081	+	0.0689628i	0.367429	+	0.00222114i
$965$	−15.7275	−	12.0681i	−0.506286	−	0.388487i
$966$		0			0
$967$	18.0621	−	4.83972i	0.580837	−	0.155635i	0.0435748	−	0.999050i	$-0.486125\pi$
$967$	18.0621	−	4.83972i	0.580837	−	0.155635i	0.537262	+	0.843415i	$0.319459\pi$
$968$	24.8234	+	14.6335i	0.797854	+	0.470338i
$969$		0			0
$970$	2.79377	+	21.7280i	0.0897024	+	0.697645i
$971$	−15.9790	+	6.61874i	−0.512792	+	0.212405i	−0.624047	−	0.781386i	$-0.714513\pi$
$971$	−15.9790	+	6.61874i	−0.512792	+	0.212405i	0.111255	+	0.993792i	$0.464513\pi$
$972$		0			0
$973$	−17.9714	+	43.3868i	−0.576136	+	1.39092i
$974$	−44.2258	+	25.3559i	−1.41709	+	0.812454i
$975$		0			0
$976$	42.9659	−	32.1511i	1.37530	−	1.02913i
$977$	28.3312	−	49.0712i	0.906397	−	1.56993i	0.0873657	−	0.996176i	$-0.472155\pi$
$977$	28.3312	−	49.0712i	0.906397	−	1.56993i	0.819031	−	0.573749i	$-0.194512\pi$
$978$		0			0
$979$	0.529738	+	4.02376i	0.0169305	+	0.128600i
$980$	35.2926	−	14.3694i	1.12738	−	0.459012i
$981$		0			0
$982$	−47.8654	−	19.9962i	−1.52745	−	0.638105i
$983$	−4.65479	+	17.3719i	−0.148465	+	0.554078i	0.851112	+	0.524984i	$0.175929\pi$
$983$	−4.65479	+	17.3719i	−0.148465	+	0.554078i	−0.999577	+	0.0290935i	$0.990738\pi$
$984$		0			0
$985$	4.35909	+	16.2683i	0.138892	+	0.518352i
$986$	4.10492	−	30.4681i	0.130727	−	0.970301i
$987$		0			0
$988$	4.52831	−	16.5002i	0.144065	−	0.524943i
$989$	−2.25178	+	5.43628i	−0.0716025	+	0.172864i
$990$		0			0
$991$		−	45.0139i		−	1.42991i	−0.699169	−	0.714956i	$-0.746447\pi$
$991$		−	45.0139i		−	1.42991i	0.699169	−	0.714956i	$-0.253553\pi$
$992$	−12.0609	−	3.42787i	−0.382934	−	0.108835i
$993$		0			0
$994$	−56.9316	+	15.0705i	−1.80576	+	0.478007i
$995$	−25.2625	+	19.3846i	−0.800874	+	0.614532i
$996$		0			0
$997$	−7.88254	+	10.2727i	−0.249643	+	0.325341i	−0.901319	−	0.433157i	$-0.857400\pi$
$997$	−7.88254	+	10.2727i	−0.249643	+	0.325341i	0.651676	+	0.758498i	$0.274066\pi$
$998$	−5.21654	−	12.7023i	−0.165127	−	0.402084i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.611.27		368
3.2	odd	2		288.2.bf.a.131.20	yes	368
9.2	odd	6	inner	864.2.bn.a.35.42		368
9.7	even	3		288.2.bf.a.227.5	yes	368
32.11	odd	8	inner	864.2.bn.a.395.42		368
96.11	even	8		288.2.bf.a.203.5	yes	368
288.11	even	24	inner	864.2.bn.a.683.27		368
288.43	odd	24		288.2.bf.a.11.20	✓	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.20	✓	368	288.43	odd	24
288.2.bf.a.131.20	yes	368	3.2	odd	2
288.2.bf.a.203.5	yes	368	96.11	even	8
288.2.bf.a.227.5	yes	368	9.7	even	3
864.2.bn.a.35.42		368	9.2	odd	6	inner
864.2.bn.a.395.42		368	32.11	odd	8	inner
864.2.bn.a.611.27		368	1.1	even	1	trivial
864.2.bn.a.683.27		368	288.11	even	24	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)

\(f(q)\)	\(=\)	\(q+(0.370153 - 1.36491i) q^{2} +(-1.72597 - 1.01045i) q^{4} +(0.155947 - 1.18454i) q^{5} +(-1.23982 + 4.62708i) q^{7} +(-2.01805 + 1.98178i) q^{8} +O(q^{10})\)	\(q+(0.370153 - 1.36491i) q^{2} +(-1.72597 - 1.01045i) q^{4} +(0.155947 - 1.18454i) q^{5} +(-1.23982 + 4.62708i) q^{7} +(-2.01805 + 1.98178i) q^{8} +(-1.55907 - 0.651315i) q^{10} +(-0.714959 - 0.548608i) q^{11} +(1.55287 + 2.02374i) q^{13} +(5.85664 + 3.40497i) q^{14} +(1.95797 + 3.48803i) q^{16} +5.41926 q^{17} +(3.09852 + 1.28345i) q^{19} +(-1.46608 + 1.88691i) q^{20} +(-1.01345 + 0.772789i) q^{22} +(-4.48426 + 1.20155i) q^{23} +(3.45082 + 0.924644i) q^{25} +(3.33703 - 1.37044i) q^{26} +(6.81534 - 6.73344i) q^{28} +(3.97708 - 0.523593i) q^{29} +(-1.91957 - 1.10826i) q^{31} +(5.48560 - 1.38136i) q^{32} +(2.00595 - 7.39682i) q^{34} +(5.28761 + 2.19020i) q^{35} +(0.235657 + 0.568926i) q^{37} +(2.89872 - 3.75414i) q^{38} +(2.03279 + 2.69952i) q^{40} +(2.92522 + 10.9171i) q^{41} +(0.771590 - 1.00556i) q^{43} +(0.679660 + 1.66931i) q^{44} +(-0.0198440 + 6.56538i) q^{46} +(-4.59259 + 2.65153i) q^{47} +(-13.8105 - 7.97351i) q^{49} +(2.53939 - 4.36781i) q^{50} +(-0.635323 - 5.06203i) q^{52} +(2.55243 + 6.16210i) q^{53} +(-0.761343 + 0.761343i) q^{55} +(-6.66784 - 11.7947i) q^{56} +(0.757468 - 5.62218i) q^{58} +(-5.22783 - 0.688257i) q^{59} +(-1.75112 - 13.3011i) q^{61} +(-2.22322 + 2.20982i) q^{62} +(0.145072 - 7.99868i) q^{64} +(2.63937 - 1.52384i) q^{65} +(4.89236 + 6.37585i) q^{67} +(-9.35351 - 5.47591i) q^{68} +(4.94665 - 6.40642i) q^{70} +(-6.14705 + 6.14705i) q^{71} +(8.86496 + 8.86496i) q^{73} +(0.863764 - 0.111062i) q^{74} +(-4.05111 - 5.34611i) q^{76} +(3.42487 - 2.62800i) q^{77} +(2.86568 + 4.96351i) q^{79} +(4.43705 - 1.77535i) q^{80} +(15.9836 + 0.0483107i) q^{82} +(4.89778 - 0.644805i) q^{83} +(0.845120 - 6.41933i) q^{85} +(-1.08689 - 1.42536i) q^{86} +(2.53005 - 0.309775i) q^{88} +(-3.18445 - 3.18445i) q^{89} +(-11.2893 + 4.67619i) q^{91} +(8.95383 + 2.45728i) q^{92} +(1.91915 + 7.24996i) q^{94} +(2.00350 - 3.47017i) q^{95} +(-6.48269 - 11.2284i) q^{97} +(-15.9951 + 15.8987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 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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