LMFDB - Embedded newform 540.2.y.a.127.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [540,2,Mod(127,540)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(540, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 3]))

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

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

chi := DirichletCharacter("540.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.y (of order $12$, degree $4$, 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			127.11
Character	$\chi$	$=$	540.127
Dual form			540.2.y.a.523.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.641238 - 1.26048i) q^{2} +(-1.17763 + 1.61654i) q^{4} +(-0.993469 - 2.00325i) q^{5} +(-0.596237 - 2.22519i) q^{7} +(2.79276 + 0.447791i) q^{8} +O(q^{10})$	\(q+(-0.641238 - 1.26048i) q^{2} +(-1.17763 + 1.61654i) q^{4} +(-0.993469 - 2.00325i) q^{5} +(-0.596237 - 2.22519i) q^{7} +(2.79276 + 0.447791i) q^{8} +(-1.88801 + 2.53681i) q^{10} +(2.26837 + 1.30964i) q^{11} +(-3.71970 - 0.996690i) q^{13} +(-2.42248 + 2.17842i) q^{14} +(-1.22639 - 3.80736i) q^{16} +(-3.98193 - 3.98193i) q^{17} +1.39099 q^{19} +(4.40827 + 0.753104i) q^{20} +(0.196216 - 3.69903i) q^{22} +(-1.42137 + 5.30461i) q^{23} +(-3.02604 + 3.98034i) q^{25} +(1.12890 + 5.32773i) q^{26} +(4.29924 + 1.65660i) q^{28} +(-1.10134 - 0.635861i) q^{29} +(-5.32145 + 3.07234i) q^{31} +(-4.01270 + 3.98726i) q^{32} +(-2.46578 + 7.57251i) q^{34} +(-3.86527 + 3.40507i) q^{35} +(-6.77959 - 6.77959i) q^{37} +(-0.891954 - 1.75331i) q^{38} +(-1.87748 - 6.03946i) q^{40} +(-0.436639 - 0.756282i) q^{41} +(-1.09847 + 0.294335i) q^{43} +(-4.78838 + 2.12463i) q^{44} +(7.59779 - 1.60991i) q^{46} +(-1.24724 - 4.65477i) q^{47} +(1.46622 - 0.846521i) q^{49} +(6.95755 + 1.26192i) q^{50} +(5.99160 - 4.83930i) q^{52} +(-5.13321 + 5.13321i) q^{53} +(0.369993 - 5.84520i) q^{55} +(-0.668726 - 6.48139i) q^{56} +(-0.0952674 + 1.79596i) q^{58} +(1.28669 + 2.22860i) q^{59} +(-4.99920 + 8.65887i) q^{61} +(7.28495 + 4.73749i) q^{62} +(7.59897 + 2.50114i) q^{64} +(1.69878 + 8.44167i) q^{65} +(4.08982 + 1.09586i) q^{67} +(11.1262 - 1.74771i) q^{68} +(6.77058 + 2.68864i) q^{70} -16.0712i q^{71} +(3.33894 - 3.33894i) q^{73} +(-4.19822 + 12.8929i) q^{74} +(-1.63806 + 2.24858i) q^{76} +(1.56171 - 5.82840i) q^{77} +(-6.00816 + 10.4064i) q^{79} +(-6.40872 + 6.23926i) q^{80} +(-0.673289 + 1.03533i) q^{82} +(14.6085 - 3.91434i) q^{83} +(-4.02089 + 11.9327i) q^{85} +(1.07539 + 1.19587i) q^{86} +(5.74855 + 4.67326i) q^{88} -11.6676i q^{89} +8.87129i q^{91} +(-6.90126 - 8.54454i) q^{92} +(-5.06748 + 4.55695i) q^{94} +(-1.38190 - 2.78650i) q^{95} +(10.5041 - 2.81456i) q^{97} +(-2.00722 - 1.30532i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.641238	−	1.26048i	−0.453424	−	0.891295i
$2$	−0.641238	−	1.26048i	−0.453424	−	0.891295i
$3$		0			0
$3$		0			0
$4$	−1.17763	+	1.61654i	−0.588813	+	0.808269i
$5$	−0.993469	−	2.00325i	−0.444293	−	0.895882i
$5$	−0.993469	−	2.00325i	−0.444293	−	0.895882i
$6$		0			0
$7$	−0.596237	−	2.22519i	−0.225356	−	0.841042i	−0.982261	−	0.187517i	$-0.939956\pi$
$7$	−0.596237	−	2.22519i	−0.225356	−	0.841042i	0.756905	−	0.653525i	$-0.226711\pi$
$8$	2.79276	+	0.447791i	0.987388	+	0.158318i
$9$		0			0
$10$	−1.88801	+	2.53681i	−0.597042	+	0.802210i
$11$	2.26837	+	1.30964i	0.683938	+	0.394872i	0.801337	−	0.598213i	$-0.204122\pi$
$11$	2.26837	+	1.30964i	0.683938	+	0.394872i	−0.117399	+	0.993085i	$0.537456\pi$
$12$		0			0
$13$	−3.71970	−	0.996690i	−1.03166	−	0.276432i	−0.297006	−	0.954876i	$-0.595988\pi$
$13$	−3.71970	−	0.996690i	−1.03166	−	0.276432i	−0.734653	+	0.678443i	$0.762655\pi$
$14$	−2.42248	+	2.17842i	−0.647434	+	0.582208i
$15$		0			0
$16$	−1.22639	−	3.80736i	−0.306597	−	0.951839i
$17$	−3.98193	−	3.98193i	−0.965760	−	0.965760i	0.0336733	−	0.999433i	$-0.489279\pi$
$17$	−3.98193	−	3.98193i	−0.965760	−	0.965760i	−0.999433	+	0.0336733i	$0.989279\pi$
$18$		0			0
$19$	1.39099			0.319114			0.159557	−	0.987189i	$-0.448993\pi$
$19$	1.39099			0.319114			0.159557	+	0.987189i	$0.448993\pi$
$20$	4.40827	+	0.753104i	0.985719	+	0.168399i
$21$		0			0
$22$	0.196216	−	3.69903i	0.0418334	−	0.788635i
$23$	−1.42137	+	5.30461i	−0.296375	+	1.10609i	0.643744	+	0.765241i	$0.277380\pi$
$23$	−1.42137	+	5.30461i	−0.296375	+	1.10609i	−0.940119	+	0.340846i	$0.889286\pi$
$24$		0			0
$25$	−3.02604	+	3.98034i	−0.605208	+	0.796067i
$26$	1.12890	+	5.32773i	0.221396	+	1.04485i
$27$		0			0
$28$	4.29924	+	1.65660i	0.812481	+	0.313068i
$29$	−1.10134	−	0.635861i	−0.204514	−	0.118076i	0.394245	−	0.919005i	$-0.371006\pi$
$29$	−1.10134	−	0.635861i	−0.204514	−	0.118076i	−0.598759	+	0.800929i	$0.704339\pi$
$30$		0			0
$31$	−5.32145	+	3.07234i	−0.955761	+	0.551809i	−0.894866	−	0.446335i	$-0.852729\pi$
$31$	−5.32145	+	3.07234i	−0.955761	+	0.551809i	−0.0608954	+	0.998144i	$0.519396\pi$
$32$	−4.01270	+	3.98726i	−0.709351	+	0.704855i
$33$		0			0
$34$	−2.46578	+	7.57251i	−0.422878	+	1.29868i
$35$	−3.86527	+	3.40507i	−0.653350	+	0.575561i
$36$		0			0
$37$	−6.77959	−	6.77959i	−1.11456	−	1.11456i	−0.992526	−	0.122032i	$-0.961059\pi$
$37$	−6.77959	−	6.77959i	−1.11456	−	1.11456i	−0.122032	−	0.992526i	$-0.538941\pi$
$38$	−0.891954	−	1.75331i	−0.144694	−	0.284425i
$39$		0			0
$40$	−1.87748	−	6.03946i	−0.296855	−	0.954923i
$41$	−0.436639	−	0.756282i	−0.0681916	−	0.118111i	0.829914	−	0.557892i	$-0.188390\pi$
$41$	−0.436639	−	0.756282i	−0.0681916	−	0.118111i	−0.898105	+	0.439780i	$0.855056\pi$
$42$		0			0
$43$	−1.09847	+	0.294335i	−0.167516	+	0.0448857i	−0.341602	−	0.939845i	$-0.610969\pi$
$43$	−1.09847	+	0.294335i	−0.167516	+	0.0448857i	0.174086	+	0.984730i	$0.444303\pi$
$44$	−4.78838	+	2.12463i	−0.721875	+	0.320300i
$45$		0			0
$46$	7.59779	−	1.60991i	1.12023	−	0.237369i
$47$	−1.24724	−	4.65477i	−0.181929	−	0.678969i	−0.995267	−	0.0971771i	$-0.969019\pi$
$47$	−1.24724	−	4.65477i	−0.181929	−	0.678969i	0.813338	−	0.581791i	$-0.197648\pi$
$48$		0			0
$49$	1.46622	−	0.846521i	0.209460	−	0.120932i
$50$	6.95755	+	1.26192i	0.983947	+	0.178463i
$51$		0			0
$52$	5.99160	−	4.83930i	0.830886	−	0.671091i
$53$	−5.13321	+	5.13321i	−0.705101	+	0.705101i	−0.965501	−	0.260400i	$-0.916146\pi$
$53$	−5.13321	+	5.13321i	−0.705101	+	0.705101i	0.260400	+	0.965501i	$0.416146\pi$
$54$		0			0
$55$	0.369993	−	5.84520i	0.0498898	−	0.788167i
$56$	−0.668726	−	6.48139i	−0.0893622	−	0.866113i
$57$		0			0
$58$	−0.0952674	+	1.79596i	−0.0125092	+	0.235821i
$59$	1.28669	+	2.22860i	0.167512	+	0.290140i	0.937545	−	0.347865i	$-0.113093\pi$
$59$	1.28669	+	2.22860i	0.167512	+	0.290140i	−0.770032	+	0.638005i	$0.779760\pi$
$60$		0			0
$61$	−4.99920	+	8.65887i	−0.640082	+	1.10865i	0.345332	+	0.938481i	$0.387766\pi$
$61$	−4.99920	+	8.65887i	−0.640082	+	1.10865i	−0.985414	+	0.170174i	$0.945567\pi$
$62$	7.28495	+	4.73749i	0.925190	+	0.601662i
$63$		0			0
$64$	7.59897	+	2.50114i	0.949871	+	0.312643i
$65$	1.69878	+	8.44167i	0.210708	+	1.04706i
$66$		0			0
$67$	4.08982	+	1.09586i	0.499651	+	0.133881i	0.499838	−	0.866119i	$-0.333393\pi$
$67$	4.08982	+	1.09586i	0.499651	+	0.133881i	−0.000187183		1.00000i	$0.500060\pi$
$68$	11.1262	−	1.74771i	1.34925	−	0.211941i
$69$		0			0
$70$	6.77058	+	2.68864i	0.809239	+	0.321354i
$71$		−	16.0712i		−	1.90730i	−0.300913	−	0.953651i	$-0.597292\pi$
$71$		−	16.0712i		−	1.90730i	0.300913	−	0.953651i	$-0.402708\pi$
$72$		0			0
$73$	3.33894	−	3.33894i	0.390793	−	0.390793i	−0.484177	−	0.874970i	$-0.660881\pi$
$73$	3.33894	−	3.33894i	0.390793	−	0.390793i	0.874970	+	0.484177i	$0.160881\pi$
$74$	−4.19822	+	12.8929i	−0.488033	+	1.49877i
$75$		0			0
$76$	−1.63806	+	2.24858i	−0.187899	+	0.257930i
$77$	1.56171	−	5.82840i	0.177974	−	0.664208i
$78$		0			0
$79$	−6.00816	+	10.4064i	−0.675970	+	1.17082i	0.300214	+	0.953872i	$0.402942\pi$
$79$	−6.00816	+	10.4064i	−0.675970	+	1.17082i	−0.976184	+	0.216943i	$0.930391\pi$
$80$	−6.40872	+	6.23926i	−0.716516	+	0.697570i
$81$		0			0
$82$	−0.673289	+	1.03533i	−0.0743523	+	0.114333i
$83$	14.6085	−	3.91434i	1.60349	−	0.429654i	0.657396	−	0.753545i	$-0.271658\pi$
$83$	14.6085	−	3.91434i	1.60349	−	0.429654i	0.946094	+	0.323891i	$0.104991\pi$
$84$		0			0
$85$	−4.02089	+	11.9327i	−0.436126	+	1.29429i
$86$	1.07539	+	1.19587i	0.115962	+	0.128954i
$87$		0			0
$88$	5.74855	+	4.67326i	0.612797	+	0.498172i
$89$		−	11.6676i		−	1.23676i	−0.785878	−	0.618381i	$-0.787789\pi$
$89$		−	11.6676i		−	1.23676i	0.785878	−	0.618381i	$-0.212211\pi$
$90$		0			0
$91$			8.87129i			0.929964i
$92$	−6.90126	−	8.54454i	−0.719506	−	0.890830i
$93$		0			0
$94$	−5.06748	+	4.55695i	−0.522670	+	0.470013i
$95$	−1.38190	−	2.78650i	−0.141780	−	0.285889i
$96$		0			0
$97$	10.5041	−	2.81456i	1.06653	−	0.285776i	0.317463	−	0.948271i	$-0.397169\pi$
$97$	10.5041	−	2.81456i	1.06653	−	0.285776i	0.749066	+	0.662495i	$0.230502\pi$
$98$	−2.00722	−	1.30532i	−0.202760	−	0.131857i
$99$		0			0
$100$	−2.87082	−	9.57906i	−0.287082	−	0.957906i
$101$	3.65405	−	6.32900i	0.363591	−	0.629759i	−0.624958	−	0.780659i	$-0.714884\pi$
$101$	3.65405	−	6.32900i	0.363591	−	0.629759i	0.988549	+	0.150900i	$0.0482171\pi$
$102$		0			0
$103$	4.55784	−	17.0101i	0.449098	−	1.67606i	−0.255787	−	0.966733i	$-0.582335\pi$
$103$	4.55784	−	17.0101i	0.449098	−	1.67606i	0.704885	−	0.709322i	$-0.250999\pi$
$104$	−9.94190	−	4.44916i	−0.974883	−	0.436276i
$105$		0			0
$106$	9.76193	+	3.17871i	0.948162	+	0.308743i
$107$	6.62822	−	6.62822i	0.640774	−	0.640774i	−0.309972	−	0.950746i	$-0.600320\pi$
$107$	6.62822	−	6.62822i	0.640774	−	0.640774i	0.950746	+	0.309972i	$0.100320\pi$
$108$		0			0
$109$		−	1.25913i		−	0.120603i	−0.998180	−	0.0603015i	$-0.980794\pi$
$109$		−	1.25913i		−	0.120603i	0.998180	−	0.0603015i	$-0.0192062\pi$
$110$	−7.60502	+	3.28180i	−0.725110	+	0.312907i
$111$		0			0
$112$	−7.74086	+	4.99903i	−0.731443	+	0.472364i
$113$	−6.96813	−	1.86711i	−0.655507	−	0.175643i	−0.0842895	−	0.996441i	$-0.526862\pi$
$113$	−6.96813	−	1.86711i	−0.655507	−	0.175643i	−0.571217	+	0.820799i	$0.693529\pi$
$114$		0			0
$115$	12.0386	−	2.42261i	1.12260	−	0.225909i
$116$	2.32487	−	1.03156i	0.215858	−	0.0957776i
$117$		0			0
$118$	1.98404	−	3.05091i	0.182646	−	0.280859i
$119$	−6.48636	+	11.2347i	−0.594604	+	1.02988i
$120$		0			0
$121$	−2.06967	−	3.58478i	−0.188152	−	0.325889i
$122$	14.1200	+	0.749001i	1.27837	+	0.0678114i
$123$		0			0
$124$	1.30013	−	12.2204i	0.116755	−	1.09742i
$125$	10.9799	+	2.10758i	0.982072	+	0.188508i
$126$		0			0
$127$	0.279968	−	0.279968i	0.0248432	−	0.0248432i	−0.694576	−	0.719419i	$-0.744408\pi$
$127$	0.279968	−	0.279968i	0.0248432	−	0.0248432i	0.719419	+	0.694576i	$0.244408\pi$
$128$	−1.72010	−	11.1822i	−0.152037	−	0.988375i
$129$		0			0
$130$	9.55125	−	7.55441i	0.837700	−	0.662565i
$131$	−7.32394	+	4.22848i	−0.639896	+	0.369444i	−0.784574	−	0.620035i	$-0.787118\pi$
$131$	−7.32394	+	4.22848i	−0.639896	+	0.369444i	0.144679	+	0.989479i	$0.453785\pi$
$132$		0			0
$133$	−0.829358	−	3.09521i	−0.0719144	−	0.268388i
$134$	−1.24123	−	5.85785i	−0.107226	−	0.506041i
$135$		0			0
$136$	−9.33748	−	12.9036i	−0.800682	−	1.10648i
$137$	−9.47459	+	2.53871i	−0.809469	+	0.216896i	−0.639737	−	0.768594i	$-0.720957\pi$
$137$	−9.47459	+	2.53871i	−0.809469	+	0.216896i	−0.169732	+	0.985490i	$0.554290\pi$
$138$		0			0
$139$	−1.36131	−	2.35785i	−0.115464	−	0.199990i	0.802501	−	0.596651i	$-0.203502\pi$
$139$	−1.36131	−	2.35785i	−0.115464	−	0.199990i	−0.917965	+	0.396661i	$0.870169\pi$
$140$	−0.952575	−	10.2583i	−0.0805073	−	0.866981i
$141$		0			0
$142$	−20.2575	+	10.3055i	−1.69997	+	0.864817i
$143$	−7.13233	−	7.13233i	−0.596436	−	0.596436i
$144$		0			0
$145$	−0.179640	+	2.83798i	−0.0149183	+	0.235681i
$146$	−6.34972	−	2.06761i	−0.525507	−	0.171117i
$147$		0			0
$148$	18.9433	−	2.97564i	1.55713	−	0.244596i
$149$	5.53558	−	3.19597i	0.453493	−	0.261824i	−0.255811	−	0.966727i	$-0.582343\pi$
$149$	5.53558	−	3.19597i	0.453493	−	0.261824i	0.709304	+	0.704903i	$0.249009\pi$
$150$		0			0
$151$	−5.33255	−	3.07875i	−0.433957	−	0.250545i	0.267074	−	0.963676i	$-0.413943\pi$
$151$	−5.33255	−	3.07875i	−0.433957	−	0.250545i	−0.701031	+	0.713131i	$0.747277\pi$
$152$	3.88469	+	0.622871i	0.315090	+	0.0505215i
$153$		0			0
$154$	−8.34802	+	1.76888i	−0.672703	+	0.142540i
$155$	11.4414	+	7.60794i	0.918993	+	0.611084i
$156$		0			0
$157$	1.89249	−	7.06289i	0.151038	−	0.563680i	−0.848375	−	0.529396i	$-0.822418\pi$
$157$	1.89249	−	7.06289i	0.151038	−	0.563680i	0.999412	−	0.0342834i	$-0.0109149\pi$
$158$	16.9698	+	0.900167i	1.35004	+	0.0716135i
$159$		0			0
$160$	11.9740	+	4.07722i	0.946627	+	0.322333i
$161$	12.6512			0.997056
$162$		0			0
$163$	1.47967	+	1.47967i	0.115897	+	0.115897i	0.762677	−	0.646780i	$-0.223885\pi$
$163$	1.47967	+	1.47967i	0.115897	+	0.115897i	−0.646780	+	0.762677i	$0.723885\pi$
$164$	1.73676	+	0.184774i	0.135618	+	0.0144284i
$165$		0			0
$166$	−14.3015	−	15.9037i	−1.11001	−	1.23437i
$167$	−10.6089	−	2.84264i	−0.820938	−	0.219970i	−0.176182	−	0.984358i	$-0.556375\pi$
$167$	−10.6089	−	2.84264i	−0.820938	−	0.219970i	−0.644757	+	0.764388i	$0.723041\pi$
$168$		0			0
$169$	1.58443	+	0.914773i	0.121879	+	0.0703671i
$170$	17.6193	−	2.58347i	1.35134	−	0.198143i
$171$		0			0
$172$	0.817788	−	2.12234i	0.0623558	−	0.161827i
$173$	−0.393732	−	1.46943i	−0.0299349	−	0.111719i	0.949342	−	0.314245i	$-0.101751\pi$
$173$	−0.393732	−	1.46943i	−0.0299349	−	0.111719i	−0.979277	+	0.202527i	$0.935085\pi$
$174$		0			0
$175$	10.6612	+	4.36028i	0.805913	+	0.329606i
$176$	2.20437	−	10.2426i	0.166161	−	0.772066i
$177$		0			0
$178$	−14.7068	+	7.48171i	−1.10232	+	0.560778i
$179$	−3.08064			−0.230258			−0.115129	−	0.993351i	$-0.536728\pi$
$179$	−3.08064			−0.230258			−0.115129	+	0.993351i	$0.536728\pi$
$180$		0			0
$181$	11.4907			0.854095			0.427047	−	0.904229i	$-0.359554\pi$
$181$	11.4907			0.854095			0.427047	+	0.904229i	$0.359554\pi$
$182$	11.1821	−	5.68861i	0.828872	−	0.421668i
$183$		0			0
$184$	−6.34488	+	14.1780i	−0.467751	+	1.04522i
$185$	−6.84592	+	20.3165i	−0.503322	+	1.49370i
$186$		0			0
$187$	−3.81757	−	14.2474i	−0.279169	−	1.04187i
$188$	8.99340	+	3.46537i	0.655911	+	0.252738i
$189$		0			0
$190$	−2.62620	+	3.52867i	−0.190525	+	0.255997i
$191$	−1.75907	−	1.01560i	−0.127282	−	0.0734863i	0.435007	−	0.900427i	$-0.356746\pi$
$191$	−1.75907	−	1.01560i	−0.127282	−	0.0734863i	−0.562289	+	0.826941i	$0.690079\pi$
$192$		0			0
$193$	−8.78234	−	2.35322i	−0.632167	−	0.169389i	−0.0715141	−	0.997440i	$-0.522783\pi$
$193$	−8.78234	−	2.35322i	−0.632167	−	0.169389i	−0.560653	+	0.828051i	$0.689450\pi$
$194$	−10.2833	−	11.4354i	−0.738300	−	0.821015i
$195$		0			0
$196$	−0.358224	+	3.36708i	−0.0255874	+	0.240506i
$197$	12.1895	+	12.1895i	0.868467	+	0.868467i	0.992303	−	0.123836i	$-0.0395197\pi$
$197$	12.1895	+	12.1895i	0.868467	+	0.868467i	−0.123836	+	0.992303i	$0.539520\pi$
$198$		0			0
$199$	9.96240			0.706216			0.353108	−	0.935583i	$-0.385125\pi$
$199$	9.96240			0.706216			0.353108	+	0.935583i	$0.385125\pi$
$200$	−10.2333	+	9.76107i	−0.723607	+	0.690212i
$201$		0			0
$202$	−10.3207	−	0.547465i	−0.726162	−	0.0385195i
$203$	−0.758248	+	2.82982i	−0.0532186	+	0.198614i
$204$		0			0
$205$	−1.08124	+	1.62604i	−0.0755168	+	0.113568i
$206$	−24.3636	+	5.16245i	−1.69749	+	0.359685i
$207$		0			0
$208$	0.767043	+	15.3846i	0.0531848	+	1.06673i
$209$	3.15527	+	1.82169i	0.218254	+	0.126009i
$210$		0			0
$211$	−4.19968	+	2.42468i	−0.289118	+	0.166922i	−0.637544	−	0.770414i	$-0.720050\pi$
$211$	−4.19968	+	2.42468i	−0.289118	+	0.166922i	0.348426	+	0.937336i	$0.386716\pi$
$212$	−2.25302	−	14.3430i	−0.154738	−	0.985084i
$213$		0			0
$214$	−12.6050	−	4.10448i	−0.861661	−	0.280576i
$215$	1.68093	+	1.90811i	0.114638	+	0.130132i
$216$		0			0
$217$	10.0094	+	10.0094i	0.679481	+	0.679481i
$218$	−1.58711	+	0.807403i	−0.107493	+	0.0546842i
$219$		0			0
$220$	9.01327	+	7.48157i	0.607675	+	0.504407i
$221$	10.8428	+	18.7803i	0.729367	+	1.26330i
$222$		0			0
$223$	5.68524	−	1.52336i	0.380712	−	0.102011i	−0.0633874	−	0.997989i	$-0.520190\pi$
$223$	5.68524	−	1.52336i	0.380712	−	0.102011i	0.444099	+	0.895978i	$0.353524\pi$
$224$	11.2649	+	6.55164i	0.752670	+	0.437750i
$225$		0			0
$226$	2.11478	+	9.98046i	0.140673	+	0.663891i
$227$	3.25056	+	12.1313i	0.215747	+	0.805180i	0.985902	+	0.167323i	$0.0535123\pi$
$227$	3.25056	+	12.1313i	0.215747	+	0.805180i	−0.770155	+	0.637857i	$0.779821\pi$
$228$		0			0
$229$	12.6014	−	7.27545i	0.832727	−	0.480775i	−0.0220585	−	0.999757i	$-0.507022\pi$
$229$	12.6014	−	7.27545i	0.832727	−	0.480775i	0.854785	+	0.518982i	$0.173689\pi$
$230$	−10.7732	−	13.6209i	−0.710366	−	0.898136i
$231$		0			0
$232$	−2.79105	−	2.26898i	−0.183241	−	0.148966i
$233$	−19.5773	+	19.5773i	−1.28255	+	1.28255i	−0.343341	+	0.939211i	$0.611559\pi$
$233$	−19.5773	+	19.5773i	−1.28255	+	1.28255i	−0.939211	+	0.343341i	$0.888441\pi$
$234$		0			0
$235$	−8.08559	+	7.12291i	−0.527446	+	0.464648i
$236$	−5.11786	−	0.544489i	−0.333144	−	0.0354432i
$237$		0			0
$238$	18.3204	+	0.971814i	1.18754	+	0.0629934i
$239$	4.17668	+	7.23423i	0.270167	+	0.467943i	0.968904	−	0.247435i	$-0.0795877\pi$
$239$	4.17668	+	7.23423i	0.270167	+	0.467943i	−0.698737	+	0.715378i	$0.746254\pi$
$240$		0			0
$241$	7.22470	−	12.5135i	0.465384	−	0.806068i	−0.533835	−	0.845589i	$-0.679250\pi$
$241$	7.22470	−	12.5135i	0.465384	−	0.806068i	0.999219	+	0.0395203i	$0.0125830\pi$
$242$	−3.19140	+	4.90749i	−0.205151	+	0.315465i
$243$		0			0
$244$	−8.11020	−	18.2783i	−0.519202	−	1.17015i
$245$	−3.15244	−	2.09621i	−0.201402	−	0.133922i
$246$		0			0
$247$	−5.17405	−	1.38638i	−0.329217	−	0.0882134i
$248$	−16.2373	+	6.19740i	−1.03107	+	0.393535i
$249$		0			0
$250$	−4.38416	−	15.1914i	−0.277279	−	0.960790i
$251$			12.2298i			0.771936i	0.922512	+	0.385968i	$0.126133\pi$
$251$			12.2298i			0.771936i	−0.922512	+	0.385968i	$0.873867\pi$
$252$		0			0
$253$	−10.1713	+	10.1713i	−0.639465	+	0.639465i
$254$	−0.532421	−	0.173368i	−0.0334071	−	0.0108781i
$255$		0			0
$256$	−12.9919	+	9.33860i	−0.811996	+	0.583663i
$257$	6.74379	−	25.1682i	0.420666	−	1.56995i	−0.352544	−	0.935795i	$-0.614683\pi$
$257$	6.74379	−	25.1682i	0.420666	−	1.56995i	0.773209	−	0.634151i	$-0.218650\pi$
$258$		0			0
$259$	−11.0436	+	19.1281i	−0.686217	+	1.18856i
$260$	−15.6468	−	7.19500i	−0.970374	−	0.446215i
$261$		0			0
$262$	10.0263	+	6.52023i	0.619427	+	0.402821i
$263$	−3.90139	+	1.04537i	−0.240570	+	0.0644605i	−0.377089	−	0.926177i	$-0.623075\pi$
$263$	−3.90139	+	1.04537i	−0.240570	+	0.0644605i	0.136520	+	0.990637i	$0.456408\pi$
$264$		0			0
$265$	15.3828	+	5.18343i	0.944958	+	0.318416i
$266$	−3.36963	+	3.03015i	−0.206605	+	0.185791i
$267$		0			0
$268$	−6.58778	+	5.32083i	−0.402413	+	0.325021i
$269$		−	8.07811i		−	0.492531i	−0.969202	−	0.246266i	$-0.920796\pi$
$269$		−	8.07811i		−	0.492531i	0.969202	−	0.246266i	$-0.0792035\pi$
$270$		0			0
$271$		−	16.2617i		−	0.987829i	−0.869510	−	0.493915i	$-0.835566\pi$
$271$		−	16.2617i		−	0.987829i	0.869510	−	0.493915i	$-0.164434\pi$
$272$	−10.2772	+	20.0440i	−0.623149	+	1.21535i
$273$		0			0
$274$	9.27546	+	10.3146i	0.560351	+	0.623129i
$275$	−12.0770	+	5.06583i	−0.728270	+	0.305481i
$276$		0			0
$277$	18.7032	−	5.01151i	1.12377	−	0.301112i	0.351360	−	0.936240i	$-0.385719\pi$
$277$	18.7032	−	5.01151i	1.12377	−	0.301112i	0.772407	+	0.635128i	$0.219053\pi$
$278$	−2.09911	+	3.22785i	−0.125896	+	0.193593i
$279$		0			0
$280$	−12.3195	+	7.77869i	−0.736232	+	0.464865i
$281$	0.0164194	−	0.0284392i	0.000979496	−	0.00169654i	−0.865535	−	0.500848i	$-0.833022\pi$
$281$	0.0164194	−	0.0284392i	0.000979496	−	0.00169654i	0.866515	+	0.499151i	$0.166355\pi$
$282$		0			0
$283$	−8.10461	+	30.2468i	−0.481769	+	1.79799i	0.112420	+	0.993661i	$0.464140\pi$
$283$	−8.10461	+	30.2468i	−0.481769	+	1.79799i	−0.594189	+	0.804325i	$0.702527\pi$
$284$	25.9797	+	18.9259i	1.54161	+	1.12305i
$285$		0			0
$286$	−4.41665	+	13.5637i	−0.261162	+	0.802038i
$287$	−1.42253	+	1.42253i	−0.0839692	+	0.0839692i
$288$		0			0
$289$			14.7115i			0.865383i
$290$	3.69241	−	1.59339i	0.216826	−	0.0935669i
$291$		0			0
$292$	1.46550	+	9.32954i	0.0857616	+	0.545970i
$293$	−2.13272	−	0.571461i	−0.124595	−	0.0333851i	0.195983	−	0.980607i	$-0.437210\pi$
$293$	−2.13272	−	0.571461i	−0.124595	−	0.0333851i	−0.320578	+	0.947222i	$0.603877\pi$
$294$		0			0
$295$	3.18618	−	4.79160i	0.185506	−	0.278978i
$296$	−15.8979	−	21.9696i	−0.924047	−	1.27696i
$297$		0			0
$298$	−7.57809	−	4.92812i	−0.438987	−	0.285478i
$299$	10.5741	−	18.3149i	0.611516	−	1.05918i
$300$		0			0
$301$	1.30990	+	2.26882i	0.0755015	+	0.130772i
$302$	−0.461271	+	8.69579i	−0.0265432	+	0.500387i
$303$		0			0
$304$	−1.70589	−	5.29598i	−0.0978396	−	0.303745i
$305$	22.3124	+	1.41235i	1.27761	+	0.0808707i
$306$		0			0
$307$	−20.6226	+	20.6226i	−1.17700	+	1.17700i	−0.196489	+	0.980506i	$0.562954\pi$
$307$	−20.6226	+	20.6226i	−1.17700	+	1.17700i	−0.980506	+	0.196489i	$0.937046\pi$
$308$	7.58271	+	9.38825i	0.432065	+	0.534945i
$309$		0			0
$310$	2.25302	−	19.3001i	0.127963	−	1.09617i
$311$	−15.6583	+	9.04034i	−0.887902	+	0.512630i	−0.873256	−	0.487262i	$-0.837996\pi$
$311$	−15.6583	+	9.04034i	−0.887902	+	0.512630i	−0.0146463	+	0.999893i	$0.504662\pi$
$312$		0			0
$313$	−8.66978	−	32.3561i	−0.490045	−	1.82887i	−0.556179	−	0.831063i	$-0.687733\pi$
$313$	−8.66978	−	32.3561i	−0.490045	−	1.82887i	0.0661336	−	0.997811i	$-0.478934\pi$
$314$	−10.1162	+	2.14354i	−0.570889	+	0.120967i
$315$		0			0
$316$	−9.74702	−	21.9673i	−0.548313	−	1.23576i
$317$	6.78986	−	1.81934i	0.381356	−	0.102184i	−0.0630478	−	0.998011i	$-0.520082\pi$
$317$	6.78986	−	1.81934i	0.381356	−	0.102184i	0.444404	+	0.895826i	$0.353415\pi$
$318$		0			0
$319$	−1.66550	−	2.88473i	−0.0932501	−	0.161514i
$320$	−2.53892	−	17.7075i	−0.141930	−	0.989877i
$321$		0			0
$322$	−8.11245	−	15.9466i	−0.452089	−	0.888671i
$323$	−5.53881	−	5.53881i	−0.308188	−	0.308188i
$324$		0			0
$325$	15.2231	−	11.7896i	0.844427	−	0.653971i
$326$	0.916277	−	2.81392i	0.0507479	−	0.155849i
$327$		0			0
$328$	−0.880771	−	2.30763i	−0.0486324	−	0.127418i
$329$	−9.61409	+	5.55070i	−0.530042	+	0.306020i
$330$		0			0
$331$	2.78927	+	1.61038i	0.153312	+	0.0885147i	0.574693	−	0.818369i	$-0.305121\pi$
$331$	2.78927	+	1.61038i	0.153312	+	0.0885147i	−0.421381	+	0.906883i	$0.638455\pi$
$332$	−10.8757	+	28.2248i	−0.596881	+	1.54904i
$333$		0			0
$334$	3.21972	+	15.1951i	0.176175	+	0.831438i
$335$	−1.86781	−	9.28164i	−0.102050	−	0.507110i
$336$		0			0
$337$	−0.0209473	+	0.0781765i	−0.00114107	+	0.00425854i	−0.966494	−	0.256689i	$-0.917368\pi$
$337$	−0.0209473	+	0.0781765i	−0.00114107	+	0.00425854i	0.965353	+	0.260948i	$0.0840350\pi$
$338$	0.137055	−	2.58374i	0.00745482	−	0.140537i
$339$		0			0
$340$	−14.5546	−	20.5522i	−0.789334	−	1.11460i
$341$	−16.0947			−0.871576
$342$		0			0
$343$	−14.1605	−	14.1605i	−0.764597	−	0.764597i
$344$	−3.19957	+	0.330119i	−0.172509	+	0.0177988i
$345$		0			0
$346$	−1.59971	+	1.43855i	−0.0860010	+	0.0773367i
$347$	22.2464	+	5.96090i	1.19425	+	0.319998i	0.800563	−	0.599248i	$-0.204534\pi$
$347$	22.2464	+	5.96090i	1.19425	+	0.319998i	0.393684	+	0.919246i	$0.371200\pi$
$348$		0			0
$349$	4.61857	+	2.66653i	0.247227	+	0.142736i	0.618494	−	0.785790i	$-0.287743\pi$
$349$	4.61857	+	2.66653i	0.247227	+	0.142736i	−0.371267	+	0.928526i	$0.621077\pi$
$350$	−1.34034	−	16.2343i	−0.0716440	−	0.867758i
$351$		0			0
$352$	−14.3242	+	3.78938i	−0.763480	+	0.201975i
$353$	0.375070	+	1.39978i	0.0199629	+	0.0745027i	0.975189	−	0.221375i	$-0.0710545\pi$
$353$	0.375070	+	1.39978i	0.0199629	+	0.0745027i	−0.955226	+	0.295878i	$0.904388\pi$
$354$		0			0
$355$	−32.1947	+	15.9663i	−1.70872	+	0.847401i
$356$	18.8611	+	13.7401i	0.999637	+	0.728223i
$357$		0			0
$358$	1.97542	+	3.88309i	0.104404	+	0.205228i
$359$	0.112966			0.00596213			0.00298106	−	0.999996i	$-0.499051\pi$
$359$	0.112966			0.00596213			0.00298106	+	0.999996i	$0.499051\pi$
$360$		0			0
$361$	−17.0652			−0.898166
$362$	−7.36826	−	14.4838i	−0.387267	−	0.761251i
$363$		0			0
$364$	−14.3408	−	10.4471i	−0.751661	−	0.547575i
$365$	−10.0059	−	3.37160i	−0.523731	−	0.176478i
$366$		0			0
$367$	4.91834	+	18.3555i	0.256735	+	0.958149i	0.967117	+	0.254332i	$0.0818557\pi$
$367$	4.91834	+	18.3555i	0.256735	+	0.958149i	−0.710382	+	0.703817i	$0.751478\pi$
$368$	21.9397	−	1.09387i	1.14369	−	0.0570218i
$369$		0			0
$370$	29.9985	−	4.39859i	1.55955	−	0.228672i
$371$	14.4830	+	8.36174i	0.751918	+	0.434120i
$372$		0			0
$373$	−19.2807	−	5.16624i	−0.998315	−	0.267498i	−0.277575	−	0.960704i	$-0.589531\pi$
$373$	−19.2807	−	5.16624i	−0.998315	−	0.267498i	−0.720739	+	0.693206i	$0.756198\pi$
$374$	−15.5106	+	13.9479i	−0.802033	+	0.721231i
$375$		0			0
$376$	−1.39888	−	13.5581i	−0.0721416	−	0.699208i
$377$	3.46291	+	3.46291i	0.178349	+	0.178349i
$378$		0			0
$379$	32.1760			1.65277			0.826384	−	0.563107i	$-0.190394\pi$
$379$	32.1760			1.65277			0.826384	+	0.563107i	$0.190394\pi$
$380$	6.13184	+	1.04756i	0.314557	+	0.0537386i
$381$		0			0
$382$	−0.152162	+	2.86852i	−0.00778527	+	0.146766i
$383$	0.557000	−	2.07875i	0.0284614	−	0.106219i	−0.950234	−	0.311537i	$-0.899156\pi$
$383$	0.557000	−	2.07875i	0.0284614	−	0.106219i	0.978695	+	0.205318i	$0.0658228\pi$
$384$		0			0
$385$	−13.2273	+	2.66182i	−0.674124	+	0.135659i
$386$	2.66538	+	12.5790i	0.135664	+	0.640252i
$387$		0			0
$388$	−7.82006	+	20.2948i	−0.397003	+	1.03031i
$389$	−3.80532	−	2.19700i	−0.192937	−	0.111392i	0.400420	−	0.916332i	$-0.368864\pi$
$389$	−3.80532	−	2.19700i	−0.192937	−	0.111392i	−0.593357	+	0.804939i	$0.702198\pi$
$390$		0			0
$391$	26.7823	−	15.4628i	1.35444	−	0.781987i
$392$	4.47385	−	1.70757i	0.225964	−	0.0862452i
$393$		0			0
$394$	7.54827	−	23.1810i	0.380276	−	1.16784i
$395$	26.8156	+	1.69739i	1.34924	+	0.0854049i
$396$		0			0
$397$	−3.23398	−	3.23398i	−0.162309	−	0.162309i	0.621280	−	0.783589i	$-0.286613\pi$
$397$	−3.23398	−	3.23398i	−0.162309	−	0.162309i	−0.783589	+	0.621280i	$0.786613\pi$
$398$	−6.38827	−	12.5574i	−0.320215	−	0.629446i
$399$		0			0
$400$	18.8657	+	6.63977i	0.943283	+	0.331989i
$401$	4.39130	+	7.60595i	0.219291	+	0.379823i	0.954591	−	0.297918i	$-0.0962923\pi$
$401$	4.39130	+	7.60595i	0.219291	+	0.379823i	−0.735300	+	0.677741i	$0.762959\pi$
$402$		0			0
$403$	22.8564	−	6.12435i	1.13856	−	0.305075i
$404$	5.92796	+	13.3601i	0.294927	+	0.664690i
$405$		0			0
$406$	4.05315	−	0.858831i	0.201155	−	0.0426231i
$407$	−6.49976	−	24.2574i	−0.322181	−	1.20240i
$408$		0			0
$409$	24.4994	−	14.1447i	1.21142	−	0.699411i	0.248348	−	0.968671i	$-0.420112\pi$
$409$	24.4994	−	14.1447i	1.21142	−	0.699411i	0.963068	+	0.269260i	$0.0867790\pi$
$410$	2.74292	+	0.320198i	0.135463	+	0.0158134i
$411$		0			0
$412$	22.1300	+	27.3995i	1.09027	+	1.34988i
$413$	4.19189	−	4.19189i	0.206270	−	0.206270i
$414$		0			0
$415$	−22.3545	−	25.3757i	−1.09734	−	1.24565i
$416$	18.9001	−	10.8320i	0.926653	−	0.531083i
$417$		0			0
$418$	0.272934	−	5.14530i	0.0133496	−	0.251665i
$419$	−11.6369	−	20.1557i	−0.568500	−	0.984671i	−0.996715	−	0.0809936i	$-0.974191\pi$
$419$	−11.6369	−	20.1557i	−0.568500	−	0.984671i	0.428215	−	0.903677i	$-0.359143\pi$
$420$		0			0
$421$	−9.25931	+	16.0376i	−0.451271	+	0.781625i	−0.998465	−	0.0553809i	$-0.982363\pi$
$421$	−9.25931	+	16.0376i	−0.451271	+	0.781625i	0.547194	+	0.837006i	$0.315696\pi$
$422$	5.74926	+	3.73881i	0.279870	+	0.182003i
$423$		0			0
$424$	−16.6344	+	12.0372i	−0.807838	+	0.584578i
$425$	27.8989	−	3.79994i	1.35330	−	0.184324i
$426$		0			0
$427$	22.2483	+	5.96142i	1.07667	+	0.288493i
$428$	2.90920	+	18.5203i	0.140621	+	0.895214i
$429$		0			0
$430$	1.32726	−	3.34233i	0.0640061	−	0.161181i
$431$		−	0.639729i		−	0.0308146i	−0.999881	−	0.0154073i	$-0.995096\pi$
$431$		−	0.639729i		−	0.0308146i	0.999881	−	0.0154073i	$-0.00490450\pi$
$432$		0			0
$433$	−14.6836	+	14.6836i	−0.705648	+	0.705648i	−0.965617	−	0.259969i	$-0.916288\pi$
$433$	−14.6836	+	14.6836i	−0.705648	+	0.705648i	0.259969	+	0.965617i	$0.416288\pi$
$434$	6.19824	−	19.0350i	0.297525	−	0.913712i
$435$		0			0
$436$	2.03543	+	1.48279i	0.0974796	+	0.0710126i
$437$	−1.97710	+	7.37864i	−0.0945775	+	0.352968i
$438$		0			0
$439$	12.1175	−	20.9881i	0.578335	−	1.00171i	−0.417335	−	0.908753i	$-0.637036\pi$
$439$	12.1175	−	20.9881i	0.578335	−	1.00171i	0.995670	−	0.0929533i	$-0.0296307\pi$
$440$	3.65073	−	16.1585i	0.174042	−	0.770328i
$441$		0			0
$442$	16.7194	−	25.7098i	0.795261	−	1.22289i
$443$	−11.7411	+	3.14603i	−0.557838	+	0.149472i	−0.526713	−	0.850043i	$-0.676576\pi$
$443$	−11.7411	+	3.14603i	−0.557838	+	0.149472i	−0.0311250	+	0.999515i	$0.509909\pi$
$444$		0			0
$445$	−23.3731	+	11.5914i	−1.10799	+	0.549485i
$446$	−5.56576	−	6.18931i	−0.263546	−	0.293072i
$447$		0			0
$448$	1.03472	−	18.4004i	0.0488861	−	0.869337i
$449$		−	32.4645i		−	1.53210i	−0.642783	−	0.766048i	$-0.722220\pi$
$449$		−	32.4645i		−	1.53210i	0.642783	−	0.766048i	$-0.277780\pi$
$450$		0			0
$451$		−	2.28737i		−	0.107708i
$452$	11.2241	−	9.06550i	0.527938	−	0.426405i
$453$		0			0
$454$	13.2069	−	11.8763i	0.619828	−	0.557383i
$455$	17.7714	−	8.81335i	0.833138	−	0.413176i
$456$		0			0
$457$	−29.4695	+	7.89632i	−1.37852	+	0.369374i	−0.870584	−	0.492019i	$-0.836259\pi$
$457$	−29.4695	+	7.89632i	−1.37852	+	0.369374i	−0.507939	+	0.861393i	$0.669592\pi$
$458$	−17.2511	−	11.2186i	−0.806091	−	0.524210i
$459$		0			0
$460$	−10.2607	+	22.3137i	−0.478407	+	1.04038i
$461$	−2.29124	+	3.96855i	−0.106714	+	0.184834i	−0.914437	−	0.404728i	$-0.867366\pi$
$461$	−2.29124	+	3.96855i	−0.106714	+	0.184834i	0.807723	+	0.589562i	$0.200700\pi$
$462$		0			0
$463$	1.63560	−	6.10415i	0.0760129	−	0.283684i	−0.917448	−	0.397855i	$-0.869755\pi$
$463$	1.63560	−	6.10415i	0.0760129	−	0.283684i	0.993461	+	0.114171i	$0.0364213\pi$
$464$	−1.07027	+	4.97302i	−0.0496862	+	0.230867i
$465$		0			0
$466$	37.2305	+	12.1231i	1.72467	+	0.561592i
$467$	−22.6544	+	22.6544i	−1.04832	+	1.04832i	−0.0495470	+	0.998772i	$0.515778\pi$
$467$	−22.6544	+	22.6544i	−1.04832	+	1.04832i	−0.998772	+	0.0495470i	$0.984222\pi$
$468$		0			0
$469$		−	9.75400i		−	0.450398i
$470$	14.1631	+	5.62425i	0.653295	+	0.259427i
$471$		0			0
$472$	2.59545	+	6.80011i	0.119465	+	0.313001i
$473$	−2.87721	−	0.770947i	−0.132294	−	0.0354482i
$474$		0			0
$475$	−4.20918	+	5.53659i	−0.193130	+	0.254036i
$476$	−10.5228	−	23.7158i	−0.482313	−	1.08701i
$477$		0			0
$478$	6.44036	−	9.90350i	0.294575	−	0.452975i
$479$	−4.39489	+	7.61217i	−0.200808	+	0.347809i	−0.948789	−	0.315911i	$-0.897690\pi$
$479$	−4.39489	+	7.61217i	−0.200808	+	0.347809i	0.747981	+	0.663720i	$0.231023\pi$
$480$		0			0
$481$	18.4609	+	31.9752i	0.841744	+	1.45794i
$482$	−20.4058	−	1.08243i	−0.929461	−	0.0493036i
$483$		0			0
$484$	8.23224	+	0.875828i	0.374193	+	0.0398104i
$485$	−16.0738	−	18.2462i	−0.729872	−	0.828516i
$486$		0			0
$487$	−0.323226	+	0.323226i	−0.0146468	+	0.0146468i	−0.714392	−	0.699745i	$-0.753297\pi$
$487$	−0.323226	+	0.323226i	−0.0146468	+	0.0146468i	0.699745	+	0.714392i	$0.253297\pi$
$488$	−17.8389	+	21.9435i	−0.807529	+	0.993336i
$489$		0			0
$490$	−0.620773	+	5.31776i	−0.0280437	+	0.240232i
$491$	24.7940	−	14.3148i	1.11894	−	0.646018i	0.177807	−	0.984065i	$-0.443100\pi$
$491$	24.7940	−	14.3148i	1.11894	−	0.646018i	0.941129	+	0.338047i	$0.109766\pi$
$492$		0			0
$493$	1.85352	+	6.91742i	0.0834783	+	0.311545i
$494$	1.57029	+	7.41080i	0.0706507	+	0.333427i
$495$		0			0
$496$	18.2237	+	16.4928i	0.818267	+	0.740548i
$497$	−35.7615	+	9.58226i	−1.60412	+	0.429823i
$498$		0			0
$499$	−13.9388	−	24.1427i	−0.623987	−	1.08078i	−0.988736	−	0.149671i	$-0.952178\pi$
$499$	−13.9388	−	24.1427i	−0.623987	−	1.08078i	0.364749	−	0.931106i	$-0.381155\pi$
$500$	−16.3372	+	15.2675i	−0.730622	+	0.682782i
$501$		0			0
$502$	15.4154	−	7.84220i	0.688023	−	0.350014i
$503$	−10.0328	−	10.0328i	−0.447342	−	0.447342i	0.447128	−	0.894470i	$-0.352447\pi$
$503$	−10.0328	−	10.0328i	−0.447342	−	0.447342i	−0.894470	+	0.447128i	$0.852447\pi$
$504$		0			0
$505$	−16.3088	−	1.03232i	−0.725730	−	0.0459377i
$506$	19.3430	+	6.29852i	0.859901	+	0.280003i
$507$		0			0
$508$	0.122881	+	0.782278i	0.00545197	+	0.0347080i
$509$	7.76593	−	4.48366i	0.344219	−	0.198735i	−0.317917	−	0.948118i	$-0.602983\pi$
$509$	7.76593	−	4.48366i	0.344219	−	0.198735i	0.662136	+	0.749384i	$0.269650\pi$
$510$		0			0
$511$	−9.42056	−	5.43896i	−0.416741	−	0.240605i
$512$	20.1021	+	10.3878i	0.888394	+	0.459081i
$513$		0			0
$514$	−36.0484	+	7.63836i	−1.59003	+	0.336914i
$515$	−38.6036	+	7.76849i	−1.70108	+	0.342321i
$516$		0			0
$517$	3.26688	−	12.1922i	0.143677	−	0.536211i
$518$	31.1922	+	1.65460i	1.37051	+	0.0726990i
$519$		0			0
$520$	0.964175	+	24.3362i	0.0422819	+	1.06721i
$521$	−10.8863			−0.476940			−0.238470	−	0.971150i	$-0.576646\pi$
$521$	−10.8863			−0.476940			−0.238470	+	0.971150i	$0.576646\pi$
$522$		0			0
$523$	12.6943	+	12.6943i	0.555084	+	0.555084i	0.927904	−	0.372820i	$-0.121609\pi$
$523$	12.6943	+	12.6943i	0.555084	+	0.555084i	−0.372820	+	0.927904i	$0.621609\pi$
$524$	1.78937	−	16.8190i	0.0781691	−	0.734741i
$525$		0			0
$526$	3.81939	+	4.24729i	0.166533	+	0.185191i
$527$	33.4235	+	8.95580i	1.45595	+	0.390121i
$528$		0			0
$529$	−6.20001	−	3.57958i	−0.269565	−	0.155634i
$530$	−3.33042	−	22.7136i	−0.144664	−	0.986614i
$531$		0			0
$532$	5.98019	+	2.30431i	0.259274	+	0.0999045i
$533$	0.870388	+	3.24833i	0.0377007	+	0.140701i
$534$		0			0
$535$	−19.8629	−	6.69307i	−0.858749	−	0.289366i
$536$	10.9311	+	4.89186i	0.472153	+	0.211296i
$537$		0			0
$538$	−10.1823	+	5.17999i	−0.438991	+	0.223325i
$539$	4.43456			0.191010
$540$		0			0
$541$	4.26001			0.183152			0.0915761	−	0.995798i	$-0.470810\pi$
$541$	4.26001			0.183152			0.0915761	+	0.995798i	$0.470810\pi$
$542$	−20.4976	+	10.4276i	−0.880447	+	0.447905i
$543$		0			0
$544$	31.8553	+	0.101266i	1.36578	+	0.00434174i
$545$	−2.52236	+	1.25091i	−0.108046	+	0.0535830i
$546$		0			0
$547$	−6.66574	−	24.8769i	−0.285006	−	1.06366i	−0.948835	−	0.315773i	$-0.897736\pi$
$547$	−6.66574	−	24.8769i	−0.285006	−	1.06366i	0.663828	−	0.747885i	$-0.268931\pi$
$548$	7.05361	−	18.3057i	0.301315	−	0.781980i
$549$		0			0
$550$	14.1296	+	11.9744i	0.602489	+	0.510591i
$551$	−1.53195	−	0.884474i	−0.0652634	−	0.0376799i
$552$		0			0
$553$	26.7385	+	7.16457i	1.13704	+	0.304669i
$554$	−18.3101	−	20.3615i	−0.777923	−	0.865076i
$555$		0			0
$556$	5.41467	+	0.576066i	0.229633	+	0.0244307i
$557$	−21.4199	−	21.4199i	−0.907590	−	0.907590i	0.0884870	−	0.996077i	$-0.471797\pi$
$557$	−21.4199	−	21.4199i	−0.907590	−	0.907590i	−0.996077	+	0.0884870i	$0.971797\pi$
$558$		0			0
$559$	4.37935			0.185227
$560$	17.7046	+	10.5405i	0.748157	+	0.445418i
$561$		0			0
$562$	−0.0463757	−	0.00246002i	−0.00195624	−	0.000103770i
$563$	4.95307	−	18.4851i	0.208747	−	0.779054i	−0.779528	−	0.626368i	$-0.784541\pi$
$563$	4.95307	−	18.4851i	0.208747	−	0.779054i	0.988275	−	0.152686i	$-0.0487924\pi$
$564$		0			0
$565$	3.18234	+	15.8138i	0.133882	+	0.665293i
$566$	43.3225	−	9.17970i	1.82098	−	0.385852i
$567$		0			0
$568$	7.19655	−	44.8830i	0.301960	−	1.88325i
$569$	20.9519	+	12.0966i	0.878351	+	0.507116i	0.870114	−	0.492850i	$-0.164045\pi$
$569$	20.9519	+	12.0966i	0.878351	+	0.507116i	0.00823692	+	0.999966i	$0.497378\pi$
$570$		0			0
$571$	16.2507	−	9.38236i	0.680071	−	0.392639i	−0.119811	−	0.992797i	$-0.538229\pi$
$571$	16.2507	−	9.38236i	0.680071	−	0.392639i	0.799882	+	0.600157i	$0.204895\pi$
$572$	19.9289	−	3.13046i	0.833270	−	0.130891i
$573$		0			0
$574$	2.70525	+	0.880891i	0.112915	+	0.0367677i
$575$	−16.8130	−	21.7095i	−0.701151	−	0.905348i
$576$		0			0
$577$	−11.3343	−	11.3343i	−0.471855	−	0.471855i	0.430660	−	0.902514i	$-0.358281\pi$
$577$	−11.3343	−	11.3343i	−0.471855	−	0.471855i	−0.902514	+	0.430660i	$0.858281\pi$
$578$	18.5436	−	9.43358i	0.771312	−	0.392385i
$579$		0			0
$580$	−4.37615	−	3.63247i	−0.181710	−	0.150830i
$581$	−17.4203	−	30.1728i	−0.722714	−	1.25178i
$582$		0			0
$583$	−18.3667	+	4.92134i	−0.760670	+	0.203821i
$584$	10.8200	−	7.82969i	0.447734	−	0.323995i
$585$		0			0
$586$	0.647267	+	3.05470i	0.0267384	+	0.126189i
$587$	0.771445	+	2.87907i	0.0318409	+	0.118832i	0.980017	−	0.198913i	$-0.0637411\pi$
$587$	0.771445	+	2.87907i	0.0318409	+	0.118832i	−0.948176	+	0.317745i	$0.897074\pi$
$588$		0			0
$589$	−7.40207	+	4.27359i	−0.304997	+	0.176090i
$590$	−8.08283	−	0.943555i	−0.332765	−	0.0388456i
$591$		0			0
$592$	−17.4979	+	34.1268i	−0.719160	+	1.40260i
$593$	−4.55102	+	4.55102i	−0.186888	+	0.186888i	−0.794349	−	0.607461i	$-0.792188\pi$
$593$	−4.55102	+	4.55102i	−0.186888	+	0.186888i	0.607461	+	0.794349i	$0.292188\pi$
$594$		0			0
$595$	28.9500	+	1.83249i	1.18683	+	0.0751248i
$596$	−1.35245	+	12.7121i	−0.0553983	+	0.520710i
$597$		0			0
$598$	−29.8661	−	1.58426i	−1.22132	−	0.0647851i
$599$	0.248880	+	0.431072i	0.0101689	+	0.0176131i	0.871065	−	0.491168i	$-0.163430\pi$
$599$	0.248880	+	0.431072i	0.0101689	+	0.0176131i	−0.860896	+	0.508781i	$0.830096\pi$
$600$		0			0
$601$	−2.70011	+	4.67672i	−0.110140	+	0.190767i	−0.915826	−	0.401574i	$-0.868463\pi$
$601$	−2.70011	+	4.67672i	−0.110140	+	0.190767i	0.805687	+	0.592342i	$0.201796\pi$
$602$	2.01984	−	3.10596i	0.0823226	−	0.126589i
$603$		0			0
$604$	11.2567	−	4.99465i	0.458028	−	0.203230i
$605$	−5.12507	+	7.70745i	−0.208364	+	0.313352i
$606$		0			0
$607$	43.5030	+	11.6566i	1.76573	+	0.473126i	0.987867	−	0.155305i	$-0.0496360\pi$
$607$	43.5030	+	11.6566i	1.76573	+	0.473126i	0.777865	+	0.628431i	$0.216303\pi$
$608$	−5.58161	+	5.54623i	−0.226364	+	0.224929i
$609$		0			0
$610$	−12.5274	−	29.0301i	−0.507218	−	1.17539i
$611$			18.5575i			0.750755i
$612$		0			0
$613$	17.4214	−	17.4214i	0.703643	−	0.703643i	−0.261548	−	0.965191i	$-0.584233\pi$
$613$	17.4214	−	17.4214i	0.703643	−	0.703643i	0.965191	+	0.261548i	$0.0842328\pi$
$614$	39.2185	+	12.7704i	1.58273	+	0.515372i
$615$		0			0
$616$	6.97139	−	15.5780i	0.280885	−	0.627654i
$617$	5.98685	−	22.3432i	0.241021	−	0.899504i	−0.734320	−	0.678803i	$-0.762499\pi$
$617$	5.98685	−	22.3432i	0.241021	−	0.899504i	0.975342	−	0.220701i	$-0.0708345\pi$
$618$		0			0
$619$	−9.49187	+	16.4404i	−0.381510	+	0.660795i	−0.991278	−	0.131785i	$-0.957929\pi$
$619$	−9.49187	+	16.4404i	−0.381510	+	0.660795i	0.609768	+	0.792580i	$0.291263\pi$
$620$	−25.7722	+	9.53610i	−1.03504	+	0.382979i
$621$		0			0
$622$	21.4359	+	13.9400i	0.859501	+	0.558944i
$623$	−25.9626	+	6.95665i	−1.04017	+	0.278712i
$624$		0			0
$625$	−6.68616	−	24.0893i	−0.267446	−	0.963573i
$626$	−35.2248	+	31.6761i	−1.40787	+	1.26603i
$627$		0			0
$628$	9.18877	+	11.3767i	0.366672	+	0.453981i
$629$			53.9917i			2.15279i
$630$		0			0
$631$			40.9537i			1.63034i	0.579221	+	0.815171i	$0.303357\pi$
$631$			40.9537i			1.63034i	−0.579221	+	0.815171i	$0.696643\pi$
$632$	−21.4392	+	26.3722i	−0.852806	+	1.04903i
$633$		0			0
$634$	−6.64716	−	7.39186i	−0.263992	−	0.293568i
$635$	−0.838987	−	0.282707i	−0.0332942	−	0.0112189i
$636$		0			0
$637$	−6.29761	+	1.68744i	−0.249520	+	0.0668588i
$638$	−2.56817	+	3.94913i	−0.101675	+	0.156348i
$639$		0			0
$640$	−20.6919	+	14.5550i	−0.817918	+	0.575335i
$641$	20.4757	−	35.4650i	0.808743	−	1.40078i	−0.104992	−	0.994473i	$-0.533482\pi$
$641$	20.4757	−	35.4650i	0.808743	−	1.40078i	0.913735	−	0.406311i	$-0.133185\pi$
$642$		0			0
$643$	−1.67519	+	6.25190i	−0.0660631	+	0.246551i	−0.991059	−	0.133427i	$-0.957402\pi$
$643$	−1.67519	+	6.25190i	−0.0660631	+	0.246551i	0.924995	+	0.379978i	$0.124068\pi$
$644$	−14.8984	+	20.4512i	−0.587080	+	0.805889i
$645$		0			0
$646$	−3.42987	+	10.5333i	−0.134946	+	0.414426i
$647$	0.935732	−	0.935732i	0.0367874	−	0.0367874i	−0.688474	−	0.725261i	$-0.741719\pi$
$647$	0.935732	−	0.935732i	0.0367874	−	0.0367874i	0.725261	+	0.688474i	$0.241719\pi$
$648$		0			0
$649$			6.74039i			0.264583i
$650$	−24.6223	−	11.6285i	−0.965764	−	0.456107i
$651$		0			0
$652$	−4.13445	+	0.649444i	−0.161918	+	0.0254342i
$653$	21.6131	+	5.79120i	0.845784	+	0.226627i	0.655588	−	0.755119i	$-0.272421\pi$
$653$	21.6131	+	5.79120i	0.845784	+	0.226627i	0.190196	+	0.981746i	$0.439088\pi$
$654$		0			0
$655$	15.7468	+	10.4708i	0.615279	+	0.409130i
$656$	−2.34394	+	2.58994i	−0.0915157	+	0.101120i
$657$		0			0
$658$	13.1615	+	8.55906i	0.513088	+	0.333667i
$659$	9.62899	−	16.6779i	0.375092	−	0.649679i	−0.615249	−	0.788333i	$-0.710944\pi$
$659$	9.62899	−	16.6779i	0.375092	−	0.649679i	0.990341	+	0.138654i	$0.0442777\pi$
$660$		0			0
$661$	3.27298	+	5.66897i	0.127304	+	0.220497i	0.922631	−	0.385683i	$-0.126034\pi$
$661$	3.27298	+	5.66897i	0.127304	+	0.220497i	−0.795327	+	0.606180i	$0.792701\pi$
$662$	0.241274	−	4.54846i	0.00937740	−	0.176781i
$663$		0			0
$664$	42.5508	−	4.39023i	1.65129	−	0.170374i
$665$	−5.37654	+	4.73640i	−0.208493	+	0.183670i
$666$		0			0
$667$	4.93841	−	4.93841i	0.191216	−	0.191216i
$668$	17.0885	−	13.8021i	0.661174	−	0.534018i
$669$		0			0
$670$	−10.5016	+	8.30609i	−0.405713	+	0.320892i
$671$	−22.6800	+	13.0943i	−0.875553	+	0.505501i
$672$		0			0
$673$	5.08274	+	18.9690i	0.195925	+	0.731203i	0.992025	+	0.126038i	$0.0402261\pi$
$673$	5.08274	+	18.9690i	0.195925	+	0.731203i	−0.796100	+	0.605165i	$0.793107\pi$
$674$	0.111972	−	0.0237260i	0.00431301	−	0.000913892i
$675$		0			0
$676$	−3.34464	+	1.48403i	−0.128640	+	0.0570783i
$677$	−18.9141	+	5.06802i	−0.726928	+	0.194780i	−0.603261	−	0.797544i	$-0.706132\pi$
$677$	−18.9141	+	5.06802i	−0.726928	+	0.194780i	−0.123667	+	0.992324i	$0.539466\pi$
$678$		0			0
$679$	−12.5259	−	21.6954i	−0.480699	−	0.832594i
$680$	−16.5727	+	31.5247i	−0.635535	+	1.20892i
$681$		0			0
$682$	10.3205	+	20.2870i	0.395193	+	0.776831i
$683$	30.2810	+	30.2810i	1.15867	+	1.15867i	0.984762	+	0.173909i	$0.0556399\pi$
$683$	30.2810	+	30.2810i	1.15867	+	1.15867i	0.173909	+	0.984762i	$0.444360\pi$
$684$		0			0
$685$	14.4984	+	16.4579i	0.553955	+	0.628823i
$686$	−8.76881	+	26.9294i	−0.334795	+	1.02817i
$687$		0			0
$688$	2.46780	+	3.82131i	0.0940838	+	0.145686i
$689$	24.2102	−	13.9778i	0.922336	−	0.532511i
$690$		0			0
$691$	−13.6413	−	7.87579i	−0.518938	−	0.299609i	0.217562	−	0.976046i	$-0.430190\pi$
$691$	−13.6413	−	7.87579i	−0.518938	−	0.299609i	−0.736500	+	0.676437i	$0.763523\pi$
$692$	2.83906	+	1.09396i	0.107925	+	0.0415860i
$693$		0			0
$694$	−6.75162	−	31.8635i	−0.256288	−	1.20952i
$695$	−3.37096	+	5.06949i	−0.127868	+	0.192297i
$696$		0			0
$697$	−1.27279	+	4.75013i	−0.0482105	+	0.179924i
$698$	0.399511	−	7.53151i	0.0151217	−	0.285072i
$699$		0			0
$700$	−19.6035	+	12.0995i	−0.740943	+	0.457318i
$701$	−22.6447			−0.855279			−0.427640	−	0.903949i	$-0.640655\pi$
$701$	−22.6447			−0.855279			−0.427640	+	0.903949i	$0.640655\pi$
$702$		0			0
$703$	−9.43032	−	9.43032i	−0.355671	−	0.355671i
$704$	13.9616	+	15.6254i	0.526199	+	0.588906i
$705$		0			0
$706$	1.52389	−	1.37036i	0.0573522	−	0.0515742i
$707$	−16.2619	−	4.35736i	−0.611591	−	0.163875i
$708$		0			0
$709$	4.34364	+	2.50780i	0.163129	+	0.0941824i	0.579342	−	0.815085i	$-0.303310\pi$
$709$	4.34364	+	2.50780i	0.163129	+	0.0941824i	−0.416213	+	0.909267i	$0.636643\pi$
$710$	40.7696	+	30.3427i	1.53006	+	1.13874i
$711$		0			0
$712$	5.22465	−	32.5847i	0.195802	−	1.22117i
$713$	−8.73384	−	32.5952i	−0.327085	−	1.22070i
$714$		0			0
$715$	−7.20211	+	21.3736i	−0.269344	+	0.799328i
$716$	3.62784	−	4.97997i	0.135579	−	0.186110i
$717$		0			0
$718$	−0.0724382	−	0.142392i	−0.00270337	−	0.00531401i
$719$	42.5143			1.58552			0.792758	−	0.609537i	$-0.208645\pi$
$719$	42.5143			1.58552			0.792758	+	0.609537i	$0.208645\pi$
$720$		0			0
$721$	−40.5682			−1.51084
$722$	10.9428	+	21.5103i	0.407250	+	0.800531i
$723$		0			0
$724$	−13.5317	+	18.5751i	−0.502903	+	0.690338i
$725$	5.86365	−	2.45958i	0.217771	−	0.0913464i
$726$		0			0
$727$	−7.69210	−	28.7073i	−0.285284	−	1.06469i	−0.948631	−	0.316383i	$-0.897531\pi$
$727$	−7.69210	−	28.7073i	−0.285284	−	1.06469i	0.663347	−	0.748312i	$-0.269135\pi$
$728$	−3.97248	+	24.7753i	−0.147230	+	0.918235i
$729$		0			0
$730$	2.16630	+	14.7742i	0.0801782	+	0.546818i
$731$	5.54607	+	3.20202i	0.205129	+	0.118431i
$732$		0			0
$733$	−26.4513	−	7.08762i	−0.977003	−	0.261787i	−0.265221	−	0.964188i	$-0.585445\pi$
$733$	−26.4513	−	7.08762i	−0.977003	−	0.261787i	−0.711782	+	0.702401i	$0.752112\pi$
$734$	19.9829	−	17.9697i	0.737584	−	0.663275i
$735$		0			0
$736$	−15.4474	−	26.9531i	−0.569398	−	0.993506i
$737$	7.84202	+	7.84202i	0.288864	+	0.288864i
$738$		0			0
$739$	−44.5392			−1.63840			−0.819201	−	0.573506i	$-0.805583\pi$
$739$	−44.5392			−1.63840			−0.819201	+	0.573506i	$0.805583\pi$
$740$	−24.7805	−	34.9920i	−0.910950	−	1.28633i
$741$		0			0
$742$	1.25279	−	23.6174i	0.0459914	−	0.867021i
$743$	8.69212	−	32.4394i	0.318883	−	1.19009i	−0.601437	−	0.798921i	$-0.705405\pi$
$743$	8.69212	−	32.4394i	0.318883	−	1.19009i	0.920320	−	0.391167i	$-0.127929\pi$
$744$		0			0
$745$	−11.9018	−	7.91408i	−0.436047	−	0.289949i
$746$	5.85155	+	27.6157i	0.214240	+	1.01108i
$747$		0			0
$748$	27.5271	+	10.6068i	1.00649	+	0.387825i
$749$	−18.7010	−	10.7970i	−0.683320	−	0.394515i
$750$		0			0
$751$	−0.355525	+	0.205263i	−0.0129733	+	0.00749014i	−0.506473	−	0.862256i	$-0.669051\pi$
$751$	−0.355525	+	0.205263i	−0.0129733	+	0.00749014i	0.493499	+	0.869746i	$0.335718\pi$
$752$	−16.1928	+	10.4573i	−0.590490	+	0.381337i
$753$		0			0
$754$	2.14438	−	6.58548i	0.0780938	−	0.239829i
$755$	−0.869791	+	13.7411i	−0.0316549	+	0.500089i
$756$		0			0
$757$	−8.14993	−	8.14993i	−0.296214	−	0.296214i	0.543315	−	0.839529i	$-0.317169\pi$
$757$	−8.14993	−	8.14993i	−0.296214	−	0.296214i	−0.839529	+	0.543315i	$0.817169\pi$
$758$	−20.6325	−	40.5572i	−0.749405	−	1.47310i
$759$		0			0
$760$	−2.61154	−	8.40081i	−0.0947307	−	0.304729i
$761$	15.1889	+	26.3080i	0.550598	+	0.953664i	0.998231	+	0.0594465i	$0.0189336\pi$
$761$	15.1889	+	26.3080i	0.550598	+	0.953664i	−0.447634	+	0.894217i	$0.647733\pi$
$762$		0			0
$763$	−2.80180	+	0.750741i	−0.101432	+	0.0271786i
$764$	3.71329	−	1.64761i	0.134342	−	0.0596084i
$765$		0			0
$766$	−2.97740	+	0.630887i	−0.107578	+	0.0227949i
$767$	−2.56485	−	9.57216i	−0.0926115	−	0.345631i
$768$		0			0
$769$	−36.2266	+	20.9154i	−1.30636	+	0.754229i	−0.981487	−	0.191527i	$-0.938656\pi$
$769$	−36.2266	+	20.9154i	−1.30636	+	0.754229i	−0.324876	+	0.945756i	$0.605323\pi$
$770$	11.8370	+	14.9659i	0.426576	+	0.539332i
$771$		0			0
$772$	14.1464	−	11.4258i	0.509140	−	0.411223i
$773$	15.5606	−	15.5606i	0.559675	−	0.559675i	−0.369540	−	0.929215i	$-0.620485\pi$
$773$	15.5606	−	15.5606i	0.559675	−	0.559675i	0.929215	+	0.369540i	$0.120485\pi$
$774$		0			0
$775$	3.87397	−	30.4782i	0.139157	−	1.09481i
$776$	30.5957	−	3.15675i	1.09832	−	0.113321i
$777$		0			0
$778$	−0.329164	+	6.20534i	−0.0118011	+	0.222472i
$779$	−0.607360	−	1.05198i	−0.0217609	−	0.0376910i
$780$		0			0
$781$	21.0475	−	36.4554i	0.753140	−	1.30448i
$782$	−36.6644	−	23.8433i	−1.31112	−	0.852635i
$783$		0			0
$784$	−5.02116	−	4.54425i	−0.179327	−	0.162295i
$785$	−16.0289	+	3.22561i	−0.572095	+	0.115127i
$786$		0			0
$787$	−7.73707	−	2.07314i	−0.275797	−	0.0738995i	0.118270	−	0.992982i	$-0.462265\pi$
$787$	−7.73707	−	2.07314i	−0.275797	−	0.0738995i	−0.394066	+	0.919082i	$0.628932\pi$
$788$	−34.0595	+	5.35011i	−1.21332	+	0.190590i
$789$		0			0
$790$	−15.0557	−	34.8890i	−0.535657	−	1.24130i
$791$			16.6186i			0.590891i
$792$		0			0
$793$	27.2257	−	27.2257i	0.966814	−	0.966814i
$794$	−2.00262	+	6.15013i	−0.0710704	+	0.218260i
$795$		0			0
$796$	−11.7320	+	16.1046i	−0.415829	+	0.570812i
$797$	−4.37720	+	16.3359i	−0.155048	+	0.578649i	0.844053	+	0.536260i	$0.180163\pi$
$797$	−4.37720	+	16.3359i	−0.155048	+	0.578649i	−0.999101	+	0.0423885i	$0.986503\pi$
$798$		0			0
$799$	−13.5685	+	23.5014i	−0.480021	+	0.831420i
$800$	−3.72808	−	28.0375i	−0.131807	−	0.991275i
$801$		0			0
$802$	6.77129	−	10.4124i	0.239103	−	0.367674i
$803$	11.9467	−	3.20112i	0.421591	−	0.112965i
$804$		0			0
$805$	−12.5686	−	25.3436i	−0.442985	−	0.893244i
$806$	−22.3760	−	24.8829i	−0.788161	−	0.876462i
$807$		0			0
$808$	13.0389	−	16.0391i	0.458708	−	0.564253i
$809$			16.2278i			0.570538i	0.958447	+	0.285269i	$0.0920829\pi$
$809$			16.2278i			0.570538i	−0.958447	+	0.285269i	$0.907917\pi$
$810$		0			0
$811$			12.9382i			0.454320i	0.973857	+	0.227160i	$0.0729441\pi$
$811$			12.9382i			0.454320i	−0.973857	+	0.227160i	$0.927056\pi$
$812$	−3.68158	−	4.55821i	−0.129198	−	0.159962i
$813$		0			0
$814$	−26.4082	+	23.7476i	−0.925606	+	0.832354i
$815$	1.49415	−	4.43417i	0.0523378	−	0.155322i
$816$		0			0
$817$	−1.52796	+	0.409416i	−0.0534566	+	0.0143237i
$818$	−33.5391	−	21.8109i	−1.17267	−	0.762599i
$819$		0			0
$820$	−1.35526	−	3.66273i	−0.0473279	−	0.127908i
$821$	−12.9039	+	22.3502i	−0.450350	+	0.780029i	−0.998408	−	0.0564117i	$-0.982034\pi$
$821$	−12.9039	+	22.3502i	−0.450350	+	0.780029i	0.548058	+	0.836440i	$0.315367\pi$
$822$		0			0
$823$	−10.1300	+	37.8058i	−0.353111	+	1.31783i	0.529734	+	0.848164i	$0.322292\pi$
$823$	−10.1300	+	37.8058i	−0.353111	+	1.31783i	−0.882845	+	0.469665i	$0.844375\pi$
$824$	20.3459	−	45.4641i	0.708783	−	1.58382i
$825$		0			0
$826$	−7.97181	−	2.59580i	−0.277375	−	0.0903195i
$827$	3.53251	−	3.53251i	0.122837	−	0.122837i	−0.643016	−	0.765853i	$-0.722317\pi$
$827$	3.53251	−	3.53251i	0.122837	−	0.122837i	0.765853	+	0.643016i	$0.222317\pi$
$828$		0			0
$829$		−	37.8119i		−	1.31326i	−0.754213	−	0.656630i	$-0.771981\pi$
$829$		−	37.8119i		−	1.31326i	0.754213	−	0.656630i	$-0.228019\pi$
$830$	−17.6511	+	44.4493i	−0.612679	+	1.54286i
$831$		0			0
$832$	−25.7730	−	16.8773i	−0.893518	−	0.585115i
$833$	−9.20916	−	2.46759i	−0.319079	−	0.0854968i
$834$		0			0
$835$	4.84505	+	24.0763i	0.167670	+	0.833194i
$836$	−6.66057	+	2.95533i	−0.230361	+	0.102212i
$837$		0			0
$838$	−17.9439	+	27.5927i	−0.619861	+	0.953174i
$839$	−9.58136	+	16.5954i	−0.330785	+	0.572937i	−0.982666	−	0.185385i	$-0.940647\pi$
$839$	−9.58136	+	16.5954i	−0.330785	+	0.572937i	0.651881	+	0.758321i	$0.273980\pi$
$840$		0			0
$841$	−13.6914	−	23.7141i	−0.472116	−	0.817729i
$842$	26.1525	+	1.38727i	0.901276	+	0.0478085i
$843$		0			0
$844$	1.02606	−	9.64431i	0.0353184	−	0.331971i
$845$	0.258436	−	4.08282i	0.00889048	−	0.140453i
$846$		0			0
$847$	−6.74279	+	6.74279i	−0.231685	+	0.231685i
$848$	25.8393	+	13.2487i	0.887325	+	0.454961i
$849$		0			0
$850$	−22.6796	−	32.7294i	−0.777904	−	1.12261i
$851$	45.5994	−	26.3268i	1.56313	−	0.902471i
$852$		0			0
$853$	9.70091	+	36.2043i	0.332153	+	1.23961i	0.906923	+	0.421296i	$0.138425\pi$
$853$	9.70091	+	36.2043i	0.332153	+	1.23961i	−0.574770	+	0.818315i	$0.694909\pi$
$854$	−6.75221	−	31.8663i	−0.231056	−	1.09044i
$855$		0			0
$856$	21.4790	−	15.5429i	0.734139	−	0.531247i
$857$	32.3452	−	8.66686i	1.10489	−	0.296054i	0.340135	−	0.940377i	$-0.389527\pi$
$857$	32.3452	−	8.66686i	1.10489	−	0.296054i	0.764754	+	0.644322i	$0.222860\pi$
$858$		0			0
$859$	−21.5581	−	37.3397i	−0.735551	−	1.27401i	−0.954481	−	0.298272i	$-0.903590\pi$
$859$	−21.5581	−	37.3397i	−0.735551	−	1.27401i	0.218930	−	0.975741i	$-0.429744\pi$
$860$	−5.06403	+	0.470243i	−0.172682	+	0.0160352i
$861$		0			0
$862$	−0.806366	+	0.410218i	−0.0274649	+	0.0139721i
$863$	24.3583	+	24.3583i	0.829165	+	0.829165i	0.987401	−	0.158236i	$-0.0505807\pi$
$863$	24.3583	+	24.3583i	0.829165	+	0.829165i	−0.158236	+	0.987401i	$0.550581\pi$
$864$		0			0
$865$	−2.55248	+	2.24858i	−0.0867868	+	0.0764539i
$866$	27.9241	+	9.09271i	0.948898	+	0.308983i
$867$		0			0
$868$	−27.9679	+	4.39323i	−0.949292	+	0.149116i
$869$	−27.2574	+	15.7371i	−0.924644	+	0.533844i
$870$		0			0
$871$	−14.1206	−	8.15256i	−0.478460	−	0.276239i
$872$	0.563828	−	3.51645i	0.0190936	−	0.119082i
$873$		0			0
$874$	10.5684	−	2.23937i	0.357482	−	0.0757477i
$875$	−1.85686	−	25.6889i	−0.0627732	−	0.868445i
$876$		0			0
$877$	−10.6529	+	39.7573i	−0.359724	+	1.34251i	0.514709	+	0.857365i	$0.327900\pi$
$877$	−10.6529	+	39.7573i	−0.359724	+	1.34251i	−0.874434	+	0.485145i	$0.838767\pi$
$878$	−34.2253	−	1.81549i	−1.15505	−	0.0612698i
$879$		0			0
$880$	−22.7085	+	5.75980i	−0.765504	+	0.194163i
$881$	3.73398			0.125801			0.0629004	−	0.998020i	$-0.479965\pi$
$881$	3.73398			0.125801			0.0629004	+	0.998020i	$0.479965\pi$
$882$		0			0
$883$	1.79967	+	1.79967i	0.0605638	+	0.0605638i	0.736740	−	0.676176i	$-0.236364\pi$
$883$	1.79967	+	1.79967i	0.0605638	+	0.0605638i	−0.676176	+	0.736740i	$0.736364\pi$
$884$	−43.1279	−	4.58838i	−1.45055	−	0.154324i
$885$		0			0
$886$	11.4944	+	12.7821i	0.386161	+	0.429424i
$887$	−52.3674	−	14.0318i	−1.75832	−	0.471142i	−0.771954	−	0.635679i	$-0.780720\pi$
$887$	−52.3674	−	14.0318i	−1.75832	−	0.471142i	−0.986371	+	0.164537i	$0.947387\pi$
$888$		0			0
$889$	−0.789909	−	0.456054i	−0.0264927	−	0.0152956i
$890$	29.5985	+	22.0286i	0.992144	+	0.738399i
$891$		0			0
$892$	−4.23253	+	10.9844i	−0.141716	+	0.367783i
$893$	−1.73490	−	6.47473i	−0.0580561	−	0.216668i
$894$		0			0
$895$	3.06052	+	6.17130i	0.102302	+	0.206284i
$896$	−23.8569	+	10.4948i	−0.797002	+	0.350606i
$897$		0			0
$898$	−40.9210	+	20.8175i	−1.36555	+	0.694689i
$899$	7.81433			0.260623
$900$		0			0
$901$	40.8802			1.36192
$902$	−2.88318	+	1.46675i	−0.0959995	+	0.0488373i
$903$		0			0
$904$	−18.6242	−	8.33464i	−0.619432	−	0.277206i
$905$	−11.4156	−	23.0187i	−0.379468	−	0.765168i
$906$		0			0
$907$	13.7004	+	51.1304i	0.454913	+	1.69776i	0.688344	+	0.725384i	$0.258338\pi$
$907$	13.7004	+	51.1304i	0.454913	+	1.69776i	−0.233431	+	0.972373i	$0.574995\pi$
$908$	−23.4386	−	9.03145i	−0.777837	−	0.299719i
$909$		0			0
$910$	−22.5048	−	16.7491i	−0.746026	−	0.555227i
$911$	−43.9674	−	25.3846i	−1.45670	−	0.841028i	−0.457856	−	0.889026i	$-0.651383\pi$
$911$	−43.9674	−	25.3846i	−1.45670	−	0.841028i	−0.998847	+	0.0479979i	$0.984716\pi$
$912$		0			0
$913$	38.2638	+	10.2528i	1.26635	+	0.339317i
$914$	28.8501	+	32.0823i	0.954277	+	1.06119i
$915$		0			0
$916$	−3.07877	+	28.9385i	−0.101725	+	0.956154i
$917$	13.7760	+	13.7760i	0.454922	+	0.454922i
$918$		0			0
$919$	56.4654			1.86262			0.931311	−	0.364225i	$-0.118666\pi$
$919$	56.4654			1.86262			0.931311	+	0.364225i	$0.118666\pi$
$920$	34.7056	−	1.37500i	1.14421	−	0.0453323i
$921$		0			0
$922$	6.47151	+	0.343284i	0.213128	+	0.0113054i
$923$	−16.0180	+	59.7801i	−0.527240	+	1.96769i
$924$		0			0
$925$	47.5004	−	6.46974i	1.56180	−	0.212724i
$926$	−8.74298	+	1.85257i	−0.287312	+	0.0608792i
$927$		0			0
$928$	6.95470	−	1.83983i	0.228299	−	0.0603954i
$929$	10.4238	+	6.01820i	0.341994	+	0.197451i	0.661154	−	0.750251i	$-0.270067\pi$
$929$	10.4238	+	6.01820i	0.341994	+	0.197451i	−0.319159	+	0.947701i	$0.603400\pi$
$930$		0			0
$931$	2.03949	−	1.17750i	0.0668416	−	0.0385910i
$932$	−8.59269	−	54.7022i	−0.281463	−	1.79183i
$933$		0			0
$934$	43.0822	+	14.0286i	1.40969	+	0.459028i
$935$	−24.7485	+	21.8019i	−0.809361	+	0.712998i
$936$		0			0
$937$	32.1820	+	32.1820i	1.05134	+	1.05134i	0.998609	+	0.0527320i	$0.0167929\pi$
$937$	32.1820	+	32.1820i	1.05134	+	1.05134i	0.0527320	+	0.998609i	$0.483207\pi$
$938$	−12.2947	+	6.25464i	−0.401438	+	0.204221i
$939$		0			0
$940$	−1.99265	−	21.4588i	−0.0649931	−	0.699909i
$941$	6.28114	+	10.8792i	0.204759	+	0.354653i	0.950056	−	0.312080i	$-0.101026\pi$
$941$	6.28114	+	10.8792i	0.204759	+	0.354653i	−0.745297	+	0.666733i	$0.767692\pi$
$942$		0			0
$943$	4.63240	−	1.24125i	0.150852	−	0.0404206i
$944$	6.90712	−	7.63201i	0.224808	−	0.248401i
$945$		0			0
$946$	0.873215	+	4.12104i	0.0283907	+	0.133986i
$947$	9.68517	+	36.1455i	0.314726	+	1.17457i	0.924245	+	0.381801i	$0.124696\pi$
$947$	9.68517	+	36.1455i	0.314726	+	1.17457i	−0.609519	+	0.792771i	$0.708637\pi$
$948$		0			0
$949$	−15.7477	+	9.09195i	−0.511193	+	0.295137i
$950$	9.67786	+	1.75532i	0.313991	+	0.0569500i
$951$		0			0
$952$	−23.1456	+	28.4713i	−0.750154	+	0.922759i
$953$	6.99153	−	6.99153i	0.226478	−	0.226478i	−0.584742	−	0.811220i	$-0.698804\pi$
$953$	6.99153	−	6.99153i	0.226478	−	0.226478i	0.811220	+	0.584742i	$0.198804\pi$
$954$		0			0
$955$	−0.286922	+	4.53284i	−0.00928457	+	0.146679i
$956$	−16.6130	−	1.76746i	−0.537302	−	0.0571636i
$957$		0			0
$958$	12.4132	+	0.658461i	0.401051	+	0.0212739i
$959$	11.2982	+	19.5691i	0.364838	+	0.631918i
$960$		0			0
$961$	3.37858	−	5.85187i	0.108986	−	0.188770i
$962$	28.4663	−	43.7733i	0.917791	−	1.41131i
$963$		0			0
$964$	11.7206	+	26.4153i	0.377496	+	0.850779i
$965$	4.01089	+	19.9311i	0.129115	+	0.641605i
$966$		0			0
$967$	−49.5314	−	13.2719i	−1.59282	−	0.426796i	−0.649958	−	0.759970i	$-0.725214\pi$
$967$	−49.5314	−	13.2719i	−1.59282	−	0.426796i	−0.942865	+	0.333174i	$0.891880\pi$
$968$	−4.17486	−	10.9382i	−0.134185	−	0.351567i
$969$		0			0
$970$	−12.6918	+	31.9608i	−0.407511	+	1.02620i
$971$		−	3.58160i		−	0.114939i	−0.998347	−	0.0574694i	$-0.981697\pi$
$971$		−	3.58160i		−	0.114939i	0.998347	−	0.0574694i	$-0.0183032\pi$
$972$		0			0
$973$	−4.43500	+	4.43500i	−0.142180	+	0.142180i
$974$	0.614685	+	0.200155i	0.0196958	+	0.00641339i
$975$		0			0
$976$	39.0984	+	8.41460i	1.25151	+	0.269345i
$977$	−8.71028	+	32.5072i	−0.278666	+	1.04000i	0.674678	+	0.738112i	$0.264283\pi$
$977$	−8.71028	+	32.5072i	−0.278666	+	1.04000i	−0.953344	+	0.301885i	$0.902384\pi$
$978$		0			0
$979$	15.2804	−	26.4664i	0.488363	−	0.845869i
$980$	7.10100	−	2.62748i	0.226833	−	0.0839317i
$981$		0			0
$982$	−33.9424	−	22.0731i	−1.08315	−	0.704382i
$983$	−3.85218	+	1.03219i	−0.122866	+	0.0329217i	−0.319728	−	0.947509i	$-0.603591\pi$
$983$	−3.85218	+	1.03219i	−0.122866	+	0.0329217i	0.196862	+	0.980431i	$0.436925\pi$
$984$		0			0
$985$	12.3088	−	36.5286i	0.392190	−	1.16390i
$986$	7.53074	−	6.77204i	0.239828	−	0.215666i
$987$		0			0
$988$	8.33424	−	6.73141i	0.265148	−	0.214155i
$989$		−	6.24533i		−	0.198590i
$990$		0			0
$991$			37.3787i			1.18737i	0.804696	+	0.593687i	$0.202328\pi$
$991$			37.3787i			1.18737i	−0.804696	+	0.593687i	$0.797672\pi$
$992$	9.10313	−	33.5464i	0.289025	−	1.06510i
$993$		0			0
$994$	35.0099	+	38.9322i	1.11045	+	1.23485i
$995$	−9.89733	−	19.9572i	−0.313766	−	0.632686i
$996$		0			0
$997$	3.84805	−	1.03108i	0.121869	−	0.0326547i	−0.197369	−	0.980329i	$-0.563240\pi$
$997$	3.84805	−	1.03108i	0.121869	−	0.0326547i	0.319238	+	0.947675i	$0.396573\pi$
$998$	−21.4934	+	33.0509i	−0.680361	+	1.04621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.y.a.127.11		128
3.2	odd	2		180.2.x.a.7.22	yes	128
4.3	odd	2	inner	540.2.y.a.127.16		128
5.3	odd	4	inner	540.2.y.a.343.6		128
9.4	even	3	inner	540.2.y.a.307.32		128
9.5	odd	6		180.2.x.a.67.1	yes	128
12.11	even	2		180.2.x.a.7.17	✓	128
15.2	even	4		900.2.bf.e.43.6		128
15.8	even	4		180.2.x.a.43.27	yes	128
15.14	odd	2		900.2.bf.e.7.11		128
20.3	even	4	inner	540.2.y.a.343.32		128
36.23	even	6		180.2.x.a.67.27	yes	128
36.31	odd	6	inner	540.2.y.a.307.6		128
45.13	odd	12	inner	540.2.y.a.523.16		128
45.14	odd	6		900.2.bf.e.607.32		128
45.23	even	12		180.2.x.a.103.17	yes	128
45.32	even	12		900.2.bf.e.643.16		128
60.23	odd	4		180.2.x.a.43.1	yes	128
60.47	odd	4		900.2.bf.e.43.32		128
60.59	even	2		900.2.bf.e.7.16		128
180.23	odd	12		180.2.x.a.103.22	yes	128
180.59	even	6		900.2.bf.e.607.6		128
180.103	even	12	inner	540.2.y.a.523.11		128
180.167	odd	12		900.2.bf.e.643.11		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.17	✓	128	12.11	even	2
180.2.x.a.7.22	yes	128	3.2	odd	2
180.2.x.a.43.1	yes	128	60.23	odd	4
180.2.x.a.43.27	yes	128	15.8	even	4
180.2.x.a.67.1	yes	128	9.5	odd	6
180.2.x.a.67.27	yes	128	36.23	even	6
180.2.x.a.103.17	yes	128	45.23	even	12
180.2.x.a.103.22	yes	128	180.23	odd	12
540.2.y.a.127.11		128	1.1	even	1	trivial
540.2.y.a.127.16		128	4.3	odd	2	inner
540.2.y.a.307.6		128	36.31	odd	6	inner
540.2.y.a.307.32		128	9.4	even	3	inner
540.2.y.a.343.6		128	5.3	odd	4	inner
540.2.y.a.343.32		128	20.3	even	4	inner
540.2.y.a.523.11		128	180.103	even	12	inner
540.2.y.a.523.16		128	45.13	odd	12	inner
900.2.bf.e.7.11		128	15.14	odd	2
900.2.bf.e.7.16		128	60.59	even	2
900.2.bf.e.43.6		128	15.2	even	4
900.2.bf.e.43.32		128	60.47	odd	4
900.2.bf.e.607.6		128	180.59	even	6
900.2.bf.e.607.32		128	45.14	odd	6
900.2.bf.e.643.11		128	180.167	odd	12
900.2.bf.e.643.16		128	45.32	even	12

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.641238 - 1.26048i) q^{2} +(-1.17763 + 1.61654i) q^{4} +(-0.993469 - 2.00325i) q^{5} +(-0.596237 - 2.22519i) q^{7} +(2.79276 + 0.447791i) q^{8} +O(q^{10})\)	\(q+(-0.641238 - 1.26048i) q^{2} +(-1.17763 + 1.61654i) q^{4} +(-0.993469 - 2.00325i) q^{5} +(-0.596237 - 2.22519i) q^{7} +(2.79276 + 0.447791i) q^{8} +(-1.88801 + 2.53681i) q^{10} +(2.26837 + 1.30964i) q^{11} +(-3.71970 - 0.996690i) q^{13} +(-2.42248 + 2.17842i) q^{14} +(-1.22639 - 3.80736i) q^{16} +(-3.98193 - 3.98193i) q^{17} +1.39099 q^{19} +(4.40827 + 0.753104i) q^{20} +(0.196216 - 3.69903i) q^{22} +(-1.42137 + 5.30461i) q^{23} +(-3.02604 + 3.98034i) q^{25} +(1.12890 + 5.32773i) q^{26} +(4.29924 + 1.65660i) q^{28} +(-1.10134 - 0.635861i) q^{29} +(-5.32145 + 3.07234i) q^{31} +(-4.01270 + 3.98726i) q^{32} +(-2.46578 + 7.57251i) q^{34} +(-3.86527 + 3.40507i) q^{35} +(-6.77959 - 6.77959i) q^{37} +(-0.891954 - 1.75331i) q^{38} +(-1.87748 - 6.03946i) q^{40} +(-0.436639 - 0.756282i) q^{41} +(-1.09847 + 0.294335i) q^{43} +(-4.78838 + 2.12463i) q^{44} +(7.59779 - 1.60991i) q^{46} +(-1.24724 - 4.65477i) q^{47} +(1.46622 - 0.846521i) q^{49} +(6.95755 + 1.26192i) q^{50} +(5.99160 - 4.83930i) q^{52} +(-5.13321 + 5.13321i) q^{53} +(0.369993 - 5.84520i) q^{55} +(-0.668726 - 6.48139i) q^{56} +(-0.0952674 + 1.79596i) q^{58} +(1.28669 + 2.22860i) q^{59} +(-4.99920 + 8.65887i) q^{61} +(7.28495 + 4.73749i) q^{62} +(7.59897 + 2.50114i) q^{64} +(1.69878 + 8.44167i) q^{65} +(4.08982 + 1.09586i) q^{67} +(11.1262 - 1.74771i) q^{68} +(6.77058 + 2.68864i) q^{70} -16.0712i q^{71} +(3.33894 - 3.33894i) q^{73} +(-4.19822 + 12.8929i) q^{74} +(-1.63806 + 2.24858i) q^{76} +(1.56171 - 5.82840i) q^{77} +(-6.00816 + 10.4064i) q^{79} +(-6.40872 + 6.23926i) q^{80} +(-0.673289 + 1.03533i) q^{82} +(14.6085 - 3.91434i) q^{83} +(-4.02089 + 11.9327i) q^{85} +(1.07539 + 1.19587i) q^{86} +(5.74855 + 4.67326i) q^{88} -11.6676i q^{89} +8.87129i q^{91} +(-6.90126 - 8.54454i) q^{92} +(-5.06748 + 4.55695i) q^{94} +(-1.38190 - 2.78650i) q^{95} +(10.5041 - 2.81456i) q^{97} +(-2.00722 - 1.30532i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

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