LMFDB - Embedded newform 225.2.m.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (of order $10$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.1
Root			$2.53767i$ of defining polynomial
Character	$\chi$	$=$	225.109
Dual form			225.2.m.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49161 + 2.05302i) q^{2} +(-1.37197 - 4.22249i) q^{4} +(-0.227564 - 2.22446i) q^{5} +1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +O(q^{10})$	\(q+(-1.49161 + 2.05302i) q^{2} +(-1.37197 - 4.22249i) q^{4} +(-0.227564 - 2.22446i) q^{5} +1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +(4.90630 + 2.85082i) q^{10} +(2.40360 + 1.74631i) q^{11} +(3.33228 + 4.58650i) q^{13} +(-2.13624 - 1.55207i) q^{14} +(-5.52731 + 4.01583i) q^{16} +(4.83480 + 1.57092i) q^{17} +(1.65990 - 5.10866i) q^{19} +(-9.08054 + 4.01278i) q^{20} +(-7.17044 + 2.32982i) q^{22} +(2.26908 - 3.12312i) q^{23} +(-4.89643 + 1.01241i) q^{25} -14.3866 q^{26} +(4.39365 - 1.42758i) q^{28} +(0.210038 + 0.646430i) q^{29} +(0.262699 - 0.808503i) q^{31} -4.95495i q^{32} +(-10.4368 + 7.58275i) q^{34} +(2.31463 - 0.236789i) q^{35} +(0.950818 + 1.30869i) q^{37} +(8.01226 + 11.0279i) q^{38} +(2.91595 - 13.5338i) q^{40} +(0.942740 - 0.684941i) q^{41} -5.68601i q^{43} +(4.07613 - 12.5450i) q^{44} +(3.02725 + 9.31693i) q^{46} +(3.12556 - 1.01555i) q^{47} +5.91729 q^{49} +(5.22504 - 11.5626i) q^{50} +(14.7946 - 20.3631i) q^{52} +(-12.0652 + 3.92023i) q^{53} +(3.33763 - 5.74410i) q^{55} +(-1.99080 + 6.12704i) q^{56} +(-1.64043 - 0.533007i) q^{58} +(-2.59846 + 1.88789i) q^{59} +(4.38562 + 3.18634i) q^{61} +(1.26803 + 1.74530i) q^{62} +(-0.881995 - 0.640807i) q^{64} +(9.44416 - 8.45625i) q^{65} +(-0.883665 - 0.287120i) q^{67} -22.5702i q^{68} +(-2.96638 + 5.10517i) q^{70} +(0.436821 + 1.34440i) q^{71} +(-6.65571 + 9.16080i) q^{73} -4.10501 q^{74} -23.8486 q^{76} +(-1.81710 + 2.50103i) q^{77} +(0.447171 + 1.37625i) q^{79} +(10.1909 + 11.3814i) q^{80} +2.95713i q^{82} +(-10.9140 - 3.54616i) q^{83} +(2.39422 - 11.1123i) q^{85} +(11.6735 + 8.48129i) q^{86} +(10.8121 + 14.8816i) q^{88} +(-7.33961 - 5.33254i) q^{89} +(-4.77241 + 3.46736i) q^{91} +(-16.3004 - 5.29633i) q^{92} +(-2.57715 + 7.93164i) q^{94} +(-11.7417 - 2.52984i) q^{95} +(5.73419 - 1.86315i) q^{97} +(-8.82627 + 12.1483i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) $ 16 * q + 2 * q^4 + 30 * q^8	$ 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.49161	+	2.05302i	−1.05473	+	1.45171i	−0.170086	+	0.985429i	$0.554405\pi$
$2$	−1.49161	+	2.05302i	−1.05473	+	1.45171i	−0.884639	+	0.466276i	$0.845595\pi$
$3$		0			0
$3$		0			0
$4$	−1.37197	−	4.22249i	−0.685985	−	2.11124i
$5$	−0.227564	−	2.22446i	−0.101770	−	0.994808i
$5$	−0.227564	−	2.22446i	−0.101770	−	0.994808i
$6$		0			0
$7$			1.04054i			0.393285i	0.980475	+	0.196643i	$0.0630039\pi$
$7$			1.04054i			0.393285i	−0.980475	+	0.196643i	$0.936996\pi$
$8$	5.88835	+	1.91324i	2.08185	+	0.676433i
$9$		0			0
$10$	4.90630	+	2.85082i	1.55151	+	0.901510i
$11$	2.40360	+	1.74631i	0.724711	+	0.526533i	0.887886	−	0.460064i	$-0.152173\pi$
$11$	2.40360	+	1.74631i	0.724711	+	0.526533i	−0.163175	+	0.986597i	$0.552173\pi$
$12$		0			0
$13$	3.33228	+	4.58650i	0.924209	+	1.27207i	0.962076	+	0.272782i	$0.0879439\pi$
$13$	3.33228	+	4.58650i	0.924209	+	1.27207i	−0.0378663	+	0.999283i	$0.512056\pi$
$14$	−2.13624	−	1.55207i	−0.570934	−	0.414808i
$15$		0			0
$16$	−5.52731	+	4.01583i	−1.38183	+	1.00396i
$17$	4.83480	+	1.57092i	1.17261	+	0.381005i	0.829617	−	0.558333i	$-0.188559\pi$
$17$	4.83480	+	1.57092i	1.17261	+	0.381005i	0.342995	+	0.939337i	$0.388559\pi$
$18$		0			0
$19$	1.65990	−	5.10866i	0.380808	−	1.17201i	−0.558668	−	0.829391i	$-0.688687\pi$
$19$	1.65990	−	5.10866i	0.380808	−	1.17201i	0.939476	−	0.342615i	$-0.111313\pi$
$20$	−9.08054	+	4.01278i	−2.03047	+	0.897284i
$21$		0			0
$22$	−7.17044	+	2.32982i	−1.52874	+	0.496719i
$23$	2.26908	−	3.12312i	0.473135	−	0.651215i	−0.504032	−	0.863685i	$-0.668151\pi$
$23$	2.26908	−	3.12312i	0.473135	−	0.651215i	0.977168	+	0.212470i	$0.0681507\pi$
$24$		0			0
$25$	−4.89643	+	1.01241i	−0.979286	+	0.202483i
$26$	−14.3866			−2.82145
$27$		0			0
$28$	4.39365	−	1.42758i	0.830322	−	0.269788i
$29$	0.210038	+	0.646430i	0.0390030	+	0.120039i	0.968662	−	0.248382i	$-0.0798987\pi$
$29$	0.210038	+	0.646430i	0.0390030	+	0.120039i	−0.929659	+	0.368421i	$0.879899\pi$
$30$		0			0
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	−0.924690	−	0.380721i	$-0.875676\pi$
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	0.971872	+	0.235509i	$0.0756759\pi$
$32$		−	4.95495i		−	0.875921i
$33$		0			0
$34$	−10.4368	+	7.58275i	−1.78989	+	1.30043i
$35$	2.31463	−	0.236789i	0.391244	−	0.0400246i
$36$		0			0
$37$	0.950818	+	1.30869i	0.156313	+	0.215147i	0.879990	−	0.474992i	$-0.157549\pi$
$37$	0.950818	+	1.30869i	0.156313	+	0.215147i	−0.723676	+	0.690139i	$0.757549\pi$
$38$	8.01226	+	11.0279i	1.29976	+	1.78897i
$39$		0			0
$40$	2.91595	−	13.5338i	0.461052	−	2.13988i
$41$	0.942740	−	0.684941i	0.147231	−	0.106970i	−0.511731	−	0.859146i	$-0.670996\pi$
$41$	0.942740	−	0.684941i	0.147231	−	0.106970i	0.658962	+	0.752176i	$0.270996\pi$
$42$		0			0
$43$		−	5.68601i		−	0.867109i	−0.901127	−	0.433554i	$-0.857259\pi$
$43$		−	5.68601i		−	0.867109i	0.901127	−	0.433554i	$-0.142741\pi$
$44$	4.07613	−	12.5450i	0.614500	−	1.89124i
$45$		0			0
$46$	3.02725	+	9.31693i	0.446344	+	1.37371i
$47$	3.12556	−	1.01555i	0.455909	−	0.148134i	−0.0720547	−	0.997401i	$-0.522956\pi$
$47$	3.12556	−	1.01555i	0.455909	−	0.148134i	0.527964	+	0.849267i	$0.322956\pi$
$48$		0			0
$49$	5.91729			0.845327
$50$	5.22504	−	11.5626i	0.738932	−	1.63520i
$51$		0			0
$52$	14.7946	−	20.3631i	2.05165	−	2.82385i
$53$	−12.0652	+	3.92023i	−1.65729	+	0.538485i	−0.980301	−	0.197511i	$-0.936714\pi$
$53$	−12.0652	+	3.92023i	−1.65729	+	0.538485i	−0.676986	+	0.735996i	$0.736714\pi$
$54$		0			0
$55$	3.33763	−	5.74410i	0.450046	−	0.774534i
$56$	−1.99080	+	6.12704i	−0.266031	+	0.818760i
$57$		0			0
$58$	−1.64043	−	0.533007i	−0.215399	−	0.0699873i
$59$	−2.59846	+	1.88789i	−0.338290	+	0.245782i	−0.743940	−	0.668246i	$-0.767045\pi$
$59$	−2.59846	+	1.88789i	−0.338290	+	0.245782i	0.405650	+	0.914029i	$0.367045\pi$
$60$		0			0
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	0.832015	−	0.554753i	$-0.187187\pi$
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	−0.270494	+	0.962722i	$0.587187\pi$
$62$	1.26803	+	1.74530i	0.161040	+	0.221653i
$63$		0			0
$64$	−0.881995	−	0.640807i	−0.110249	−	0.0801008i
$65$	9.44416	−	8.45625i	1.17140	−	1.04887i
$66$		0			0
$67$	−0.883665	−	0.287120i	−0.107957	−	0.0350773i	0.254540	−	0.967062i	$-0.418076\pi$
$67$	−0.883665	−	0.287120i	−0.107957	−	0.0350773i	−0.362497	+	0.931985i	$0.618076\pi$
$68$		−	22.5702i		−	2.73703i
$69$		0			0
$70$	−2.96638	+	5.10517i	−0.354551	+	0.610185i
$71$	0.436821	+	1.34440i	0.0518412	+	0.159551i	0.973625	−	0.228153i	$-0.0732685\pi$
$71$	0.436821	+	1.34440i	0.0518412	+	0.159551i	−0.921784	+	0.387703i	$0.873269\pi$
$72$		0			0
$73$	−6.65571	+	9.16080i	−0.778992	+	1.07219i	0.216400	+	0.976305i	$0.430568\pi$
$73$	−6.65571	+	9.16080i	−0.778992	+	1.07219i	−0.995392	+	0.0958862i	$0.969432\pi$
$74$	−4.10501			−0.477198
$75$		0			0
$76$	−23.8486			−2.73562
$77$	−1.81710	+	2.50103i	−0.207078	+	0.285018i
$78$		0			0
$79$	0.447171	+	1.37625i	0.0503106	+	0.154840i	0.973055	−	0.230571i	$-0.0740595\pi$
$79$	0.447171	+	1.37625i	0.0503106	+	0.154840i	−0.922745	+	0.385412i	$0.874059\pi$
$80$	10.1909	+	11.3814i	1.13937	+	1.27248i
$81$		0			0
$82$			2.95713i			0.326560i
$83$	−10.9140	−	3.54616i	−1.19796	−	0.389242i	−0.358952	−	0.933356i	$-0.616866\pi$
$83$	−10.9140	−	3.54616i	−1.19796	−	0.389242i	−0.839011	+	0.544114i	$0.816866\pi$
$84$		0			0
$85$	2.39422	−	11.1123i	0.259690	−	1.20530i
$86$	11.6735	+	8.48129i	1.25879	+	0.914561i
$87$		0			0
$88$	10.8121	+	14.8816i	1.15257	+	1.58638i
$89$	−7.33961	−	5.33254i	−0.777997	−	0.565248i	0.126380	−	0.991982i	$-0.459664\pi$
$89$	−7.33961	−	5.33254i	−0.777997	−	0.565248i	−0.904377	+	0.426734i	$0.859664\pi$
$90$		0			0
$91$	−4.77241	+	3.46736i	−0.500285	+	0.363478i
$92$	−16.3004	−	5.29633i	−1.69944	−	0.552181i
$93$		0			0
$94$	−2.57715	+	7.93164i	−0.265812	+	0.818086i
$95$	−11.7417	−	2.52984i	−1.20468	−	0.259556i
$96$		0			0
$97$	5.73419	−	1.86315i	0.582219	−	0.189174i	−0.00307549	−	0.999995i	$-0.500979\pi$
$97$	5.73419	−	1.86315i	0.582219	−	0.189174i	0.585294	+	0.810821i	$0.300979\pi$
$98$	−8.82627	+	12.1483i	−0.891587	+	1.22716i
$99$		0			0
$100$	10.9927	+	19.2861i	1.09927	+	1.92861i
$101$	15.3408			1.52647			0.763236	−	0.646120i	$-0.223610\pi$
$101$	15.3408			1.52647			0.763236	+	0.646120i	$0.223610\pi$
$102$		0			0
$103$	−11.4688	+	3.72642i	−1.13005	+	0.367175i	−0.813595	−	0.581432i	$-0.802493\pi$
$103$	−11.4688	+	3.72642i	−1.13005	+	0.367175i	−0.316455	+	0.948608i	$0.602493\pi$
$104$	10.8466	+	33.3824i	1.06360	+	3.27341i
$105$		0			0
$106$	9.94827	−	30.6176i	0.966261	−	2.97385i
$107$		−	6.49787i		−	0.628173i	−0.949394	−	0.314086i	$-0.898302\pi$
$107$		−	6.49787i		−	0.628173i	0.949394	−	0.314086i	$-0.101698\pi$
$108$		0			0
$109$	−1.86929	+	1.35812i	−0.179046	+	0.130084i	−0.673698	−	0.739006i	$-0.735295\pi$
$109$	−1.86929	+	1.35812i	−0.179046	+	0.130084i	0.494653	+	0.869091i	$0.335295\pi$
$110$	6.81431	+	15.4202i	0.649719	+	1.47025i
$111$		0			0
$112$	−4.17861	−	5.75136i	−0.394841	−	0.543453i
$113$	2.27638	+	3.13317i	0.214144	+	0.294744i	0.902553	−	0.430579i	$-0.141691\pi$
$113$	2.27638	+	3.13317i	0.214144	+	0.294744i	−0.688409	+	0.725323i	$0.741691\pi$
$114$		0			0
$115$	−7.46361	−	4.33676i	−0.695985	−	0.404405i
$116$	2.44138	−	1.77376i	0.226676	−	0.164690i
$117$		0			0
$118$		−	8.15067i		−	0.750330i
$119$	−1.63460	+	5.03078i	−0.149844	+	0.461171i
$120$		0			0
$121$	−0.671530	−	2.06676i	−0.0610482	−	0.187887i
$122$	−13.0832	+	4.25101i	−1.18450	+	0.384868i
$123$		0			0
$124$	−3.77431			−0.338943
$125$	3.36632	+	10.6615i	0.301093	+	0.953595i
$126$		0			0
$127$	−6.87342	+	9.46046i	−0.609918	+	0.839480i	−0.996571	−	0.0827456i	$-0.973631\pi$
$127$	−6.87342	+	9.46046i	−0.609918	+	0.839480i	0.386653	+	0.922225i	$0.373631\pi$
$128$	12.0561	−	3.91725i	1.06562	−	0.346239i
$129$		0			0
$130$	3.27388	+	32.0025i	0.287138	+	2.80680i
$131$	2.46042	−	7.57241i	0.214968	−	0.661604i	−0.784188	−	0.620524i	$-0.786920\pi$
$131$	2.46042	−	7.57241i	0.214968	−	0.661604i	0.999156	−	0.0410805i	$-0.0130800\pi$
$132$		0			0
$133$	5.31574	+	1.72719i	0.460933	+	0.149766i
$134$	1.90754	−	1.38591i	0.164787	−	0.119725i
$135$		0			0
$136$	25.4635	+	18.5003i	2.18348	+	1.58639i
$137$	6.49579	+	8.94069i	0.554973	+	0.763854i	0.990676	−	0.136236i	$-0.0435004\pi$
$137$	6.49579	+	8.94069i	0.554973	+	0.763854i	−0.435704	+	0.900090i	$0.643500\pi$
$138$		0			0
$139$	−9.92651	−	7.21204i	−0.841956	−	0.611717i	0.0809604	−	0.996717i	$-0.474201\pi$
$139$	−9.92651	−	7.21204i	−0.841956	−	0.611717i	−0.922916	+	0.385000i	$0.874201\pi$
$140$	−4.17544	−	9.44862i	−0.352889	−	0.798554i
$141$		0			0
$142$	−3.41164	−	1.10851i	−0.286299	−	0.0930241i
$143$			16.8433i			1.40851i
$144$		0			0
$145$	1.39016	−	0.614324i	0.115446	−	0.0510169i
$146$	−8.87961	−	27.3286i	−0.734882	−	2.26173i
$147$		0			0
$148$	4.22143	−	5.81030i	0.346999	−	0.477604i
$149$	−4.62832			−0.379167			−0.189584	−	0.981865i	$-0.560714\pi$
$149$	−4.62832			−0.379167			−0.189584	+	0.981865i	$0.560714\pi$
$150$		0			0
$151$	−4.67249			−0.380242			−0.190121	−	0.981761i	$-0.560888\pi$
$151$	−4.67249			−0.380242			−0.190121	+	0.981761i	$0.560888\pi$
$152$	19.5482	−	26.9058i	1.58557	−	2.18235i
$153$		0			0
$154$	−2.42426	−	7.46110i	−0.195352	−	0.601232i
$155$	−1.85826	−	0.400376i	−0.149259	−	0.0321590i
$156$		0			0
$157$		−	14.9726i		−	1.19494i	−0.801890	−	0.597472i	$-0.796172\pi$
$157$		−	14.9726i		−	1.19494i	0.801890	−	0.597472i	$-0.203828\pi$
$158$	−3.49247	−	1.13477i	−0.277846	−	0.0902777i
$159$		0			0
$160$	−11.0221	+	1.12757i	−0.871373	+	0.0891422i
$161$	3.24972	+	2.36106i	0.256113	+	0.186077i
$162$		0			0
$163$	−7.00123	−	9.63637i	−0.548379	−	0.754779i	0.441412	−	0.897304i	$-0.354478\pi$
$163$	−7.00123	−	9.63637i	−0.548379	−	0.754779i	−0.989791	+	0.142526i	$0.954478\pi$
$164$	−4.18557	−	3.04099i	−0.326838	−	0.237462i
$165$		0			0
$166$	23.5597	−	17.1171i	1.82859	−	1.32855i
$167$	−10.0889	−	3.27809i	−0.780704	−	0.253666i	−0.108563	−	0.994090i	$-0.534625\pi$
$167$	−10.0889	−	3.27809i	−0.780704	−	0.253666i	−0.672141	+	0.740424i	$0.734625\pi$
$168$		0			0
$169$	−5.91461	+	18.2033i	−0.454970	+	1.40025i
$170$	19.2426	+	21.4906i	1.47584	+	1.64825i
$171$		0			0
$172$	−24.0091	+	7.80103i	−1.83068	+	0.594823i
$173$	0.736719	−	1.01401i	0.0560117	−	0.0770935i	−0.780092	−	0.625664i	$-0.784828\pi$
$173$	0.736719	−	1.01401i	0.0560117	−	0.0770935i	0.836104	+	0.548571i	$0.184828\pi$
$174$		0			0
$175$	−1.05345	−	5.09491i	−0.0796335	−	0.385139i
$176$	−20.2983			−1.53004
$177$		0			0
$178$	21.8956	−	7.11432i	1.64115	−	0.533241i
$179$	−6.43105	−	19.7927i	−0.480679	−	1.47938i	−0.838143	−	0.545451i	$-0.816358\pi$
$179$	−6.43105	−	19.7927i	−0.480679	−	1.47938i	0.357464	−	0.933927i	$-0.383642\pi$
$180$		0			0
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	−0.998554	−	0.0537591i	$-0.982880\pi$
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	0.839446	+	0.543443i	$0.182880\pi$
$182$		−	14.9698i		−	1.10964i
$183$		0			0
$184$	19.3364	−	14.0487i	1.42550	−	1.03569i
$185$	2.69475	−	2.41287i	0.198122	−	0.177397i
$186$		0			0
$187$	8.87759	+	12.2189i	0.649193	+	0.893538i
$188$	−8.57633	−	11.8043i	−0.625494	−	0.860918i
$189$		0			0
$190$	22.7079	−	20.3325i	1.64740	−	1.47507i
$191$	6.60494	−	4.79877i	0.477916	−	0.347227i	−0.322602	−	0.946535i	$-0.604558\pi$
$191$	6.60494	−	4.79877i	0.477916	−	0.347227i	0.800518	+	0.599308i	$0.204558\pi$
$192$		0			0
$193$		−	13.9629i		−	1.00507i	−0.864556	−	0.502537i	$-0.832400\pi$
$193$		−	13.9629i		−	1.00507i	0.864556	−	0.502537i	$-0.167600\pi$
$194$	−4.72807	+	14.5515i	−0.339456	+	1.04474i
$195$		0			0
$196$	−8.11834	−	24.9857i	−0.579881	−	1.78469i
$197$	−5.48046	+	1.78071i	−0.390467	+	0.126870i	−0.497669	−	0.867367i	$-0.665811\pi$
$197$	−5.48046	+	1.78071i	−0.390467	+	0.126870i	0.107203	+	0.994237i	$0.465811\pi$
$198$		0			0
$199$	26.5748			1.88384			0.941919	−	0.335841i	$-0.109020\pi$
$199$	26.5748			1.88384			0.941919	+	0.335841i	$0.109020\pi$
$200$	−30.7689	−	3.40660i	−2.17569	−	0.240883i
$201$		0			0
$202$	−22.8825	+	31.4951i	−1.61001	+	2.21599i
$203$	−0.672633	+	0.218552i	−0.0472096	+	0.0153393i
$204$		0			0
$205$	−1.73816	−	1.94122i	−0.121398	−	0.135581i
$206$	9.45644	−	29.1039i	0.658862	−	2.02777i
$207$		0			0
$208$	−36.8371	−	11.9691i	−2.55420	−	0.829909i
$209$	12.9111	−	9.38043i	0.893076	−	0.648858i
$210$		0			0
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.979533	+	0.201285i	$0.0645116\pi$
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.494125	+	0.869391i	$0.335488\pi$
$212$	33.1063	+	45.5669i	2.27375	+	3.12954i
$213$		0			0
$214$	13.3403	+	9.69227i	0.911922	+	0.662550i
$215$	−12.6483	+	1.29393i	−0.862607	+	0.0882454i
$216$		0			0
$217$	0.841277	+	0.273347i	0.0571096	+	0.0185560i
$218$		−	5.86348i		−	0.397125i
$219$		0			0
$220$	−28.8335	−	6.21238i	−1.94395	−	0.418839i
$221$	8.90591	+	27.4096i	0.599076	+	1.84377i
$222$		0			0
$223$	−16.1321	+	22.2039i	−1.08029	+	1.48689i	−0.221081	+	0.975255i	$0.570958\pi$
$223$	−16.1321	+	22.2039i	−1.08029	+	1.48689i	−0.859205	+	0.511631i	$0.829042\pi$
$224$	5.15581			0.344487
$225$		0			0
$226$	−9.82792			−0.653744
$227$	0.0765066	−	0.105302i	0.00507792	−	0.00698916i	−0.806470	−	0.591274i	$-0.798625\pi$
$227$	0.0765066	−	0.105302i	0.00507792	−	0.00698916i	0.811548	+	0.584285i	$0.198625\pi$
$228$		0			0
$229$	−0.873064	−	2.68702i	−0.0576937	−	0.177563i	0.918057	−	0.396449i	$-0.129758\pi$
$229$	−0.873064	−	2.68702i	−0.0576937	−	0.177563i	−0.975750	+	0.218886i	$0.929758\pi$
$230$	20.0362	−	8.85420i	1.32115	−	0.583829i
$231$		0			0
$232$			4.20826i			0.276286i
$233$	−7.59617	−	2.46815i	−0.497642	−	0.161694i	0.0494328	−	0.998777i	$-0.484259\pi$
$233$	−7.59617	−	2.46815i	−0.497642	−	0.161694i	−0.547075	+	0.837084i	$0.684259\pi$
$234$		0			0
$235$	−2.97032	−	6.72157i	−0.193763	−	0.438467i
$236$	11.5366	+	8.38182i	0.750968	+	0.545610i
$237$		0			0
$238$	−7.89012	−	10.8598i	−0.511441	−	0.703938i
$239$	15.4214	+	11.2043i	0.997528	+	0.724747i	0.961557	−	0.274606i	$-0.0885475\pi$
$239$	15.4214	+	11.2043i	0.997528	+	0.724747i	0.0359713	+	0.999353i	$0.488548\pi$
$240$		0			0
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.981162	−	0.193184i	$-0.938118\pi$
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.119467	+	0.992838i	$0.538118\pi$
$242$	5.24476	+	1.70413i	0.337146	+	0.109545i
$243$		0			0
$244$	7.43735	−	22.8898i	0.476127	−	1.46537i
$245$	−1.34656	−	13.1628i	−0.0860287	−	0.840938i
$246$		0			0
$247$	28.9621	−	9.41036i	1.84281	−	0.598767i
$248$	3.09373	−	4.25815i	0.196452	−	0.270393i
$249$		0			0
$250$	−26.9095	−	8.99165i	−1.70191	−	0.568682i
$251$	−30.2224			−1.90762			−0.953811	−	0.300408i	$-0.902877\pi$
$251$	−30.2224			−1.90762			−0.953811	+	0.300408i	$0.902877\pi$
$252$		0			0
$253$	10.9079	−	3.54419i	0.685773	−	0.222821i
$254$	−9.17007	−	28.2226i	−0.575381	−	1.77084i
$255$		0			0
$256$	−9.26692	+	28.5207i	−0.579183	+	1.78254i
$257$			5.10215i			0.318263i	0.987257	+	0.159132i	$0.0508695\pi$
$257$			5.10215i			0.318263i	−0.987257	+	0.159132i	$0.949131\pi$
$258$		0			0
$259$	−1.36174	+	0.989360i	−0.0846142	+	0.0614758i
$260$	−48.6635	−	28.2761i	−3.01798	−	1.75361i
$261$		0			0
$262$	11.8763	+	16.3464i	0.733722	+	1.00988i
$263$	3.77088	+	5.19017i	0.232522	+	0.320040i	0.909295	−	0.416153i	$-0.136622\pi$
$263$	3.77088	+	5.19017i	0.232522	+	0.320040i	−0.676772	+	0.736192i	$0.736622\pi$
$264$		0			0
$265$	11.4660	+	25.9465i	0.704351	+	1.59388i
$266$	−11.4749	+	8.33704i	−0.703574	+	0.511177i
$267$		0			0
$268$			4.12518i			0.251986i
$269$	−5.39518	+	16.6047i	−0.328950	+	1.01240i	0.640676	+	0.767811i	$0.278654\pi$
$269$	−5.39518	+	16.6047i	−0.328950	+	1.01240i	−0.969626	+	0.244592i	$0.921346\pi$
$270$		0			0
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	0.950159	−	0.311765i	$-0.100920\pi$
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	−0.951946	+	0.306266i	$0.900920\pi$
$272$	−33.0320	+	10.7328i	−2.00286	+	0.650769i
$273$		0			0
$274$	−28.0446			−1.69424
$275$	−13.5370	−	6.11727i	−0.816313	−	0.368885i
$276$		0			0
$277$	10.8157	−	14.8865i	0.649851	−	0.894443i	−0.349242	−	0.937033i	$-0.613561\pi$
$277$	10.8157	−	14.8865i	0.649851	−	0.894443i	0.999093	+	0.0425895i	$0.0135608\pi$
$278$	29.6129	−	9.62182i	1.77606	−	0.577078i
$279$		0			0
$280$	14.0824	+	3.03415i	0.841583	+	0.181325i
$281$	−5.54254	+	17.0582i	−0.330640	+	1.01761i	0.638189	+	0.769879i	$0.279684\pi$
$281$	−5.54254	+	17.0582i	−0.330640	+	1.01761i	−0.968830	+	0.247727i	$0.920316\pi$
$282$		0			0
$283$	−21.1514	−	6.87252i	−1.25732	−	0.408529i	−0.396783	−	0.917912i	$-0.629874\pi$
$283$	−21.1514	−	6.87252i	−1.25732	−	0.408529i	−0.860540	+	0.509383i	$0.829874\pi$
$284$	5.07740	−	3.68895i	0.301288	−	0.218899i
$285$		0			0
$286$	−34.5796	−	25.1236i	−2.04474	−	1.48559i
$287$	0.712705	+	0.980955i	0.0420697	+	0.0579039i
$288$		0			0
$289$	7.15424	+	5.19786i	0.420837	+	0.305756i
$290$	−0.812350	+	3.77036i	−0.0477028	+	0.221403i
$291$		0			0
$292$	47.8128	+	15.5353i	2.79803	+	0.909136i
$293$			18.7316i			1.09431i	0.837031	+	0.547155i	$0.184289\pi$
$293$			18.7316i			1.09431i	−0.837031	+	0.547155i	$0.815711\pi$
$294$		0			0
$295$	4.79084	+	5.35054i	0.278934	+	0.311520i
$296$	3.09491	+	9.52517i	0.179888	+	0.553639i
$297$		0			0
$298$	6.90364	−	9.50204i	0.399917	−	0.550439i
$299$	21.8854			1.26566
$300$		0			0
$301$	5.91650			0.341021
$302$	6.96952	−	9.59272i	0.401051	−	0.551999i
$303$		0			0
$304$	11.3407	+	34.9030i	0.650433	+	2.00183i
$305$	6.08987	−	10.4807i	0.348705	−	0.600125i
$306$		0			0
$307$			7.03850i			0.401708i	0.979621	+	0.200854i	$0.0643717\pi$
$307$			7.03850i			0.401708i	−0.979621	+	0.200854i	$0.935628\pi$
$308$	13.0536	+	4.24136i	0.743796	+	0.241674i
$309$		0			0
$310$	3.59378	−	3.21785i	0.204113	−	0.182762i
$311$	−23.6872	−	17.2098i	−1.34318	−	0.975876i	−0.999321	−	0.0368546i	$-0.988266\pi$
$311$	−23.6872	−	17.2098i	−1.34318	−	0.975876i	−0.343858	−	0.939022i	$-0.611734\pi$
$312$		0			0
$313$	9.19024	+	12.6493i	0.519463	+	0.714980i	0.985479	−	0.169796i	$-0.0543110\pi$
$313$	9.19024	+	12.6493i	0.519463	+	0.714980i	−0.466016	+	0.884776i	$0.654311\pi$
$314$	30.7391	+	22.3333i	1.73471	+	1.26034i
$315$		0			0
$316$	5.19769	−	3.77635i	0.292393	−	0.212436i
$317$	−5.93596	−	1.92871i	−0.333397	−	0.108327i	0.137535	−	0.990497i	$-0.456082\pi$
$317$	−5.93596	−	1.92871i	−0.333397	−	0.108327i	−0.470932	+	0.882170i	$0.656082\pi$
$318$		0			0
$319$	−0.624024	+	1.92055i	−0.0349386	+	0.107530i
$320$	−1.22474	+	2.10778i	−0.0684649	+	0.117829i
$321$		0			0
$322$	−9.69460	+	3.14997i	−0.540259	+	0.175541i
$323$	16.0506	−	22.0918i	0.893080	−	1.22922i
$324$		0			0
$325$	−20.9597	−	19.0838i	−1.16264	−	1.05858i
$326$	30.2268			1.67411
$327$		0			0
$328$	6.86164	−	2.22948i	0.378871	−	0.123103i
$329$	1.05672	+	3.25225i	0.0582589	+	0.179302i
$330$		0			0
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	−0.585862	−	0.810411i	$-0.699244\pi$
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	0.950320	−	0.311275i	$-0.100756\pi$
$332$			50.9493i			2.79621i
$333$		0			0
$334$	21.7787	−	15.8231i	1.19168	−	0.865804i
$335$	−0.437596	+	2.03101i	−0.0239084	+	0.110966i
$336$		0			0
$337$	−20.4262	−	28.1142i	−1.11269	−	1.53148i	−0.817399	−	0.576072i	$-0.804585\pi$
$337$	−20.4262	−	28.1142i	−1.11269	−	1.53148i	−0.295287	−	0.955409i	$-0.595415\pi$
$338$	−28.5495	−	39.2950i	−1.55289	−	2.13736i
$339$		0			0
$340$	−50.2064	+	5.13616i	−2.72282	+	0.278547i
$341$	2.04332	−	1.48456i	0.110652	−	0.0803935i
$342$		0			0
$343$			13.4409i			0.725740i
$344$	10.8787	−	33.4812i	0.586541	−	1.80519i
$345$		0			0
$346$	0.982882	+	3.02500i	0.0528401	+	0.162625i
$347$	27.3182	−	8.87623i	1.46652	−	0.476501i	0.536465	−	0.843922i	$-0.319759\pi$
$347$	27.3182	−	8.87623i	1.46652	−	0.476501i	0.930055	+	0.367421i	$0.119759\pi$
$348$		0			0
$349$	12.2834			0.657515			0.328758	−	0.944414i	$-0.393370\pi$
$349$	12.2834			0.657515			0.328758	+	0.944414i	$0.393370\pi$
$350$	12.0313	+	5.43684i	0.643100	+	0.290611i
$351$		0			0
$352$	8.65291	−	11.9097i	0.461201	−	0.634789i
$353$	25.6575	−	8.33663i	1.36561	−	0.443714i	0.467699	−	0.883888i	$-0.345083\pi$
$353$	25.6575	−	8.33663i	1.36561	−	0.443714i	0.897913	+	0.440174i	$0.145083\pi$
$354$		0			0
$355$	2.89115	−	1.27763i	0.153446	−	0.0678094i
$356$	−12.4469	+	38.3075i	−0.659682	+	2.03029i
$357$		0			0
$358$	50.2275	+	16.3199i	2.65461	+	0.862533i
$359$	−13.2875	+	9.65393i	−0.701287	+	0.509515i	−0.880351	−	0.474322i	$-0.842693\pi$
$359$	−13.2875	+	9.65393i	−0.701287	+	0.509515i	0.179064	+	0.983837i	$0.442693\pi$
$360$		0			0
$361$	−7.97178	−	5.79184i	−0.419567	−	0.304834i
$362$	−10.3325	−	14.2214i	−0.543062	−	0.747460i
$363$		0			0
$364$	21.1885	+	15.3943i	1.11058	+	0.806883i
$365$	21.8924	+	12.7207i	1.14590	+	0.665831i
$366$		0			0
$367$	−28.4321	−	9.23816i	−1.48415	−	0.482228i	−0.548797	−	0.835956i	$-0.684914\pi$
$367$	−28.4321	−	9.23816i	−1.48415	−	0.482228i	−0.935349	+	0.353727i	$0.884914\pi$
$368$			26.3747i			1.37487i
$369$		0			0
$370$	0.934153	+	9.13143i	0.0485643	+	0.474720i
$371$	−4.07914	−	12.5543i	−0.211778	−	0.651787i
$372$		0			0
$373$	14.5951	−	20.0885i	0.755706	−	1.04014i	−0.241853	−	0.970313i	$-0.577755\pi$
$373$	14.5951	−	20.0885i	0.755706	−	1.04014i	0.997559	−	0.0698276i	$-0.0222449\pi$
$374$	−38.3276			−1.98187
$375$		0			0
$376$	20.3474			1.04934
$377$	−2.26494	+	3.11742i	−0.116650	+	0.160556i
$378$		0			0
$379$	−5.99389	−	18.4473i	−0.307885	−	0.947574i	−0.978585	−	0.205845i	$-0.934006\pi$
$379$	−5.99389	−	18.4473i	−0.307885	−	0.947574i	0.670699	−	0.741729i	$-0.265994\pi$
$380$	5.42708	+	53.0502i	0.278403	+	2.72142i
$381$		0			0
$382$			20.7179i			1.06002i
$383$	−10.7002	−	3.47670i	−0.546754	−	0.177651i	0.0225986	−	0.999745i	$-0.492806\pi$
$383$	−10.7002	−	3.47670i	−0.546754	−	0.177651i	−0.569353	+	0.822094i	$0.692806\pi$
$384$		0			0
$385$	5.97694	+	3.47292i	0.304613	+	0.176997i
$386$	28.6662	+	20.8272i	1.45907	+	1.06008i
$387$		0			0
$388$	−15.7343	−	21.6564i	−0.798786	−	1.09944i
$389$	−12.0558	−	8.75903i	−0.611252	−	0.444100i	0.238603	−	0.971117i	$-0.423310\pi$
$389$	−12.0558	−	8.75903i	−0.611252	−	0.444100i	−0.849855	+	0.527017i	$0.823310\pi$
$390$		0			0
$391$	15.8767	−	11.5351i	0.802920	−	0.583356i
$392$	34.8431	+	11.3212i	1.75984	+	0.571807i
$393$		0			0
$394$	4.51886	−	13.9076i	0.227657	−	0.700656i
$395$	2.95965	−	1.30790i	0.148916	−	0.0658075i
$396$		0			0
$397$	−22.9172	+	7.44626i	−1.15018	+	0.373717i	−0.821212	−	0.570623i	$-0.806702\pi$
$397$	−22.9172	+	7.44626i	−1.15018	+	0.373717i	−0.328971	+	0.944340i	$0.606702\pi$
$398$	−39.6392	+	54.5586i	−1.98693	+	2.73478i
$399$		0			0
$400$	22.9984	−	25.2591i	1.14992	−	1.26296i
$401$	−13.4580			−0.672059			−0.336030	−	0.941851i	$-0.609084\pi$
$401$	−13.4580			−0.672059			−0.336030	+	0.941851i	$0.609084\pi$
$402$		0			0
$403$	4.58358	−	1.48930i	0.228325	−	0.0741872i
$404$	−21.0472	−	64.7765i	−1.04714	−	3.22275i
$405$		0			0
$406$	0.554613	−	1.70692i	0.0275250	−	0.0847132i
$407$			4.80598i			0.238224i
$408$		0			0
$409$	−28.6988	+	20.8509i	−1.41906	+	1.03101i	−0.427140	+	0.904186i	$0.640479\pi$
$409$	−28.6988	+	20.8509i	−1.41906	+	1.03101i	−0.991925	+	0.126825i	$0.959521\pi$
$410$	6.57801	−	0.672936i	0.324865	−	0.0332340i
$411$		0			0
$412$	31.4696	+	43.3141i	1.55039	+	2.13393i
$413$	−1.96441	−	2.70379i	−0.0966625	−	0.133045i
$414$		0			0
$415$	−5.40466	+	25.0846i	−0.265304	+	1.23136i
$416$	22.7259	−	16.5113i	1.11423	−	0.809534i
$417$		0			0
$418$			40.4986i			1.98085i
$419$	4.88617	−	15.0381i	0.238705	−	0.734659i	−0.757903	−	0.652367i	$-0.773776\pi$
$419$	4.88617	−	15.0381i	0.238705	−	0.734659i	0.996608	−	0.0822916i	$-0.0262239\pi$
$420$		0			0
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	0.999840	−	0.0178752i	$-0.00569015\pi$
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	−0.819394	+	0.573230i	$0.805690\pi$
$422$	−63.8590	+	20.7491i	−3.10861	+	1.01005i
$423$		0			0
$424$	−78.5447			−3.81447
$425$	−25.2637	−	2.79709i	−1.22547	−	0.135679i
$426$		0			0
$427$	−3.31550	+	4.56340i	−0.160448	+	0.220838i
$428$	−27.4372	+	8.91488i	−1.32623	+	0.430917i
$429$		0			0
$430$	16.2098	−	27.8973i	0.781707	−	1.34532i
$431$	−4.52486	+	13.9261i	−0.217955	+	0.670797i	0.780976	+	0.624562i	$0.214722\pi$
$431$	−4.52486	+	13.9261i	−0.217955	+	0.670797i	−0.998931	+	0.0462350i	$0.985278\pi$
$432$		0			0
$433$	4.06380	+	1.32041i	0.195294	+	0.0634547i	0.405031	−	0.914303i	$-0.367261\pi$
$433$	4.06380	+	1.32041i	0.195294	+	0.0634547i	−0.209737	+	0.977758i	$0.567261\pi$
$434$	−1.81604	+	1.31943i	−0.0871728	+	0.0633347i
$435$		0			0
$436$	8.29926	+	6.02976i	0.397462	+	0.288773i
$437$	−12.1885	−	16.7760i	−0.583055	−	0.802506i
$438$		0			0
$439$	−16.4289	−	11.9363i	−0.784111	−	0.569690i	0.122099	−	0.992518i	$-0.461037\pi$
$439$	−16.4289	−	11.9363i	−0.784111	−	0.569690i	−0.906210	+	0.422828i	$0.861037\pi$
$440$	30.6430	−	27.4376i	1.46085	−	1.30803i
$441$		0			0
$442$	−69.5565	−	22.6003i	−3.30847	−	1.07499i
$443$		−	19.0543i		−	0.905299i	−0.891689	−	0.452649i	$-0.850479\pi$
$443$		−	19.0543i		−	0.905299i	0.891689	−	0.452649i	$-0.149521\pi$
$444$		0			0
$445$	−10.1918	+	17.5401i	−0.483136	+	0.831483i
$446$	−21.5224	−	66.2391i	−1.01912	−	3.13651i
$447$		0			0
$448$	0.666782	−	0.917747i	0.0315025	−	0.0433595i
$449$	29.4793			1.39122			0.695608	−	0.718421i	$-0.255135\pi$
$449$	29.4793			1.39122			0.695608	+	0.718421i	$0.255135\pi$
$450$		0			0
$451$	3.46209			0.163023
$452$	10.1066	−	13.9106i	0.475376	−	0.654299i
$453$		0			0
$454$	0.102070	+	0.314139i	0.00479038	+	0.0147433i
$455$	8.79903	+	9.82698i	0.412505	+	0.460696i
$456$		0			0
$457$		−	28.3015i		−	1.32389i	−0.749553	−	0.661945i	$-0.769731\pi$
$457$		−	28.3015i		−	1.32389i	0.749553	−	0.661945i	$-0.230269\pi$
$458$	6.81877	+	2.21555i	0.318620	+	0.103526i
$459$		0			0
$460$	−8.07208	+	37.4649i	−0.376362	+	1.74681i
$461$	−13.3953	−	9.73223i	−0.623879	−	0.453275i	0.230395	−	0.973097i	$-0.425998\pi$
$461$	−13.3953	−	9.73223i	−0.623879	−	0.453275i	−0.854274	+	0.519822i	$0.825998\pi$
$462$		0			0
$463$	−5.41311	−	7.45051i	−0.251569	−	0.346254i	0.664491	−	0.747296i	$-0.268648\pi$
$463$	−5.41311	−	7.45051i	−0.251569	−	0.346254i	−0.916060	+	0.401042i	$0.868648\pi$
$464$	−3.75689	−	2.72954i	−0.174409	−	0.126716i
$465$		0			0
$466$	16.3977	−	11.9136i	0.759607	−	0.551887i
$467$	10.0929	+	3.27938i	0.467043	+	0.151752i	0.533079	−	0.846066i	$-0.321035\pi$
$467$	10.0929	+	3.27938i	0.467043	+	0.151752i	−0.0660353	+	0.997817i	$0.521035\pi$
$468$		0			0
$469$	0.298759	−	0.919485i	0.0137954	−	0.0424579i
$470$	18.2301	+	3.92780i	0.840890	+	0.181176i
$471$		0			0
$472$	−18.9126	+	6.14508i	−0.870524	+	0.282850i
$473$	9.92956	−	13.6669i	0.456562	−	0.628403i
$474$		0			0
$475$	−2.95552	+	26.6947i	−0.135609	+	1.22484i
$476$	23.4850			1.07644
$477$		0			0
$478$	−46.0054	+	14.9480i	−2.10424	+	0.683708i
$479$	10.3849	+	31.9613i	0.474496	+	1.46035i	0.846636	+	0.532172i	$0.178624\pi$
$479$	10.3849	+	31.9613i	0.474496	+	1.46035i	−0.372140	+	0.928177i	$0.621376\pi$
$480$		0			0
$481$	−2.83390	+	8.72184i	−0.129215	+	0.397682i
$482$		−	53.5954i		−	2.44120i
$483$		0			0
$484$	−7.80554	+	5.67106i	−0.354797	+	0.257775i
$485$	−5.44940	−	12.3315i	−0.247444	−	0.559944i
$486$		0			0
$487$	17.1919	+	23.6626i	0.779039	+	1.07226i	0.995387	+	0.0959389i	$0.0305853\pi$
$487$	17.1919	+	23.6626i	0.779039	+	1.07226i	−0.216348	+	0.976316i	$0.569415\pi$
$488$	19.7279	+	27.1531i	0.893038	+	1.22916i
$489$		0			0
$490$	29.0320	+	16.8691i	1.31153	+	0.762070i
$491$	11.2898	−	8.20251i	0.509501	−	0.370174i	−0.303133	−	0.952948i	$-0.598033\pi$
$491$	11.2898	−	8.20251i	0.509501	−	0.370174i	0.812634	+	0.582774i	$0.198033\pi$
$492$		0			0
$493$			3.45531i			0.155619i
$494$	−23.8804	+	73.4964i	−1.07443	+	3.30676i
$495$		0			0
$496$	1.79479	+	5.52380i	0.0805885	+	0.248026i
$497$	−1.39889	+	0.454528i	−0.0627490	+	0.0203884i
$498$		0			0
$499$	35.7533			1.60054			0.800268	−	0.599642i	$-0.204690\pi$
$499$	35.7533			1.60054			0.800268	+	0.599642i	$0.204690\pi$
$500$	40.3996	−	28.8415i	1.80673	−	1.28983i
$501$		0			0
$502$	45.0800	−	62.0472i	2.01202	−	2.76930i
$503$	−11.0744	+	3.59828i	−0.493782	+	0.160439i	−0.545314	−	0.838232i	$-0.683590\pi$
$503$	−11.0744	+	3.59828i	−0.493782	+	0.160439i	0.0515323	+	0.998671i	$0.483590\pi$
$504$		0			0
$505$	−3.49103	−	34.1251i	−0.155349	−	1.51855i
$506$	−8.99399	+	27.6807i	−0.399832	+	1.23056i
$507$		0			0
$508$	49.3768	+	16.0435i	2.19074	+	0.711815i
$509$	6.90384	−	5.01594i	0.306007	−	0.222327i	−0.424174	−	0.905581i	$-0.639436\pi$
$509$	6.90384	−	5.01594i	0.306007	−	0.222327i	0.730181	+	0.683253i	$0.239436\pi$
$510$		0			0
$511$	−9.53214	−	6.92551i	−0.421677	−	0.306366i
$512$	−29.8288	−	41.0558i	−1.31826	−	1.81443i
$513$		0			0
$514$	−10.4748	−	7.61040i	−0.462025	−	0.335681i
$515$	10.8991	+	24.6638i	0.480274	+	1.08682i
$516$		0			0
$517$	9.28605	+	3.01722i	0.408400	+	0.132697i
$518$		−	4.27141i		−	0.187675i
$519$		0			0
$520$	71.7894	−	31.7244i	3.14817	−	1.39121i
$521$	−0.390998	−	1.20337i	−0.0171299	−	0.0527205i	0.942126	−	0.335259i	$-0.108824\pi$
$521$	−0.390998	−	1.20337i	−0.0171299	−	0.0527205i	−0.959256	+	0.282538i	$0.908824\pi$
$522$		0			0
$523$	15.9998	−	22.0218i	0.699621	−	0.962946i	−0.300337	−	0.953833i	$-0.597099\pi$
$523$	15.9998	−	22.0218i	0.699621	−	0.962946i	0.999958	−	0.00911285i	$-0.00290075\pi$
$524$	−35.3500			−1.54427
$525$		0			0
$526$	−16.2802			−0.709850
$527$	2.54019	−	3.49628i	0.110653	−	0.152300i
$528$		0			0
$529$	2.50224	+	7.70110i	0.108793	+	0.334831i
$530$	−70.3715	−	15.1620i	−3.05674	−	0.658597i
$531$		0			0
$532$		−	24.8153i		−	1.07588i
$533$	6.28296	+	2.04146i	0.272145	+	0.0884253i
$534$		0			0
$535$	−14.4542	+	1.47868i	−0.624911	+	0.0639290i
$536$	−4.65400	−	3.38133i	−0.201022	−	0.146051i
$537$		0			0
$538$	−26.0422	−	35.8440i	−1.12276	−	1.54535i
$539$	14.2228	+	10.3334i	0.612618	+	0.445093i
$540$		0			0
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.973492	−	0.228719i	$-0.926546\pi$
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.0833007	+	0.996524i	$0.526546\pi$
$542$	0.229728	+	0.0746431i	0.00986766	+	0.00320620i
$543$		0			0
$544$	7.78385	−	23.9562i	0.333730	−	1.02711i
$545$	3.44647	+	3.84910i	0.147630	+	0.164877i
$546$		0			0
$547$	10.8200	−	3.51564i	0.462631	−	0.150318i	−0.0684223	−	0.997656i	$-0.521797\pi$
$547$	10.8200	−	3.51564i	0.462631	−	0.150318i	0.531053	+	0.847339i	$0.321797\pi$
$548$	28.8399	−	39.6947i	1.23198	−	1.69568i
$549$		0			0
$550$	32.7508	−	18.6672i	1.39650	−	0.795974i
$551$	3.65103			0.155539
$552$		0			0
$553$	−1.43204	+	0.465297i	−0.0608964	+	0.0197864i
$554$	14.4296	+	44.4096i	0.613053	+	1.88678i
$555$		0			0
$556$	−16.8339	+	51.8093i	−0.713914	+	2.19720i
$557$		−	45.7532i		−	1.93862i	−0.245833	−	0.969312i	$-0.579062\pi$
$557$		−	45.7532i		−	1.93862i	0.245833	−	0.969312i	$-0.420938\pi$
$558$		0			0
$559$	26.0789	−	18.9474i	1.10302	−	0.801390i
$560$	−11.8428	+	10.6039i	−0.500448	+	0.448098i
$561$		0			0
$562$	−26.7535	−	36.8231i	−1.12853	−	1.55329i
$563$	5.25650	+	7.23495i	0.221535	+	0.304917i	0.905289	−	0.424796i	$-0.139654\pi$
$563$	5.25650	+	7.23495i	0.221535	+	0.304917i	−0.683754	+	0.729712i	$0.739654\pi$
$564$		0			0
$565$	6.45158	−	5.77671i	0.271420	−	0.243028i
$566$	45.6591	−	33.1733i	1.91919	−	1.39438i
$567$		0			0
$568$			8.75203i			0.367227i
$569$	−0.707365	+	2.17704i	−0.0296543	+	0.0912665i	−0.964788	−	0.263028i	$-0.915279\pi$
$569$	−0.707365	+	2.17704i	−0.0296543	+	0.0912665i	0.935134	+	0.354294i	$0.115279\pi$
$570$		0			0
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	−0.926774	−	0.375618i	$-0.877430\pi$
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	0.528993	−	0.848626i	$-0.322570\pi$
$572$	71.1206	−	23.1085i	2.97370	−	0.966214i
$573$		0			0
$574$	−3.07700			−0.128431
$575$	−7.94849	+	17.5894i	−0.331475	+	0.733528i
$576$		0			0
$577$	−3.87484	+	5.33326i	−0.161312	+	0.222027i	−0.882020	−	0.471212i	$-0.843817\pi$
$577$	−3.87484	+	5.33326i	−0.161312	+	0.222027i	0.720708	+	0.693238i	$0.243817\pi$
$578$	−21.3426	+	6.93464i	−0.887736	+	0.288443i
$579$		0			0
$580$	−4.50123	−	5.02709i	−0.186904	−	0.208739i
$581$	3.68991	−	11.3564i	0.153083	−	0.471141i
$582$		0			0
$583$	−35.8459	−	11.6470i	−1.48458	−	0.482371i
$584$	−56.7180	+	41.2081i	−2.34701	+	1.70520i
$585$		0			0
$586$	−38.4563	−	27.9401i	−1.58861	−	1.15420i
$587$	−3.25499	−	4.48010i	−0.134348	−	0.184914i	0.736543	−	0.676391i	$-0.236457\pi$
$587$	−3.25499	−	4.48010i	−0.134348	−	0.184914i	−0.870890	+	0.491477i	$0.836457\pi$
$588$		0			0
$589$	−3.69431	−	2.68408i	−0.152222	−	0.110595i
$590$	−18.1308	+	1.85480i	−0.746434	+	0.0763609i
$591$		0			0
$592$	−10.5109	−	3.41521i	−0.431997	−	0.140364i
$593$		−	1.88122i		−	0.0772524i	−0.999254	−	0.0386262i	$-0.987702\pi$
$593$		−	1.88122i		−	0.0772524i	0.999254	−	0.0386262i	$-0.0122982\pi$
$594$		0			0
$595$	11.5627	+	2.49128i	0.474026	+	0.102132i
$596$	6.34992	+	19.5430i	0.260103	+	0.800514i
$597$		0			0
$598$	−32.6444	+	44.9311i	−1.33493	+	1.83737i
$599$	17.8272			0.728400			0.364200	−	0.931321i	$-0.381342\pi$
$599$	17.8272			0.728400			0.364200	+	0.931321i	$0.381342\pi$
$600$		0			0
$601$	33.0994			1.35015			0.675077	−	0.737747i	$-0.264110\pi$
$601$	33.0994			1.35015			0.675077	+	0.737747i	$0.264110\pi$
$602$	−8.82509	+	12.1467i	−0.359684	+	0.495062i
$603$		0			0
$604$	6.41052	+	19.7295i	0.260840	+	0.802784i
$605$	−4.44460	+	1.96411i	−0.180699	+	0.0798525i
$606$		0			0
$607$		−	23.4603i		−	0.952226i	−0.879384	−	0.476113i	$-0.842045\pi$
$607$		−	23.4603i		−	0.952226i	0.879384	−	0.476113i	$-0.157955\pi$
$608$	−25.3132	−	8.22475i	−1.02658	−	0.333558i
$609$		0			0
$610$	12.4335	+	28.1358i	0.503416	+	1.13918i
$611$	15.0731	+	10.9512i	0.609792	+	0.443039i
$612$		0			0
$613$	27.7600	+	38.2083i	1.12121	+	1.54322i	0.803769	+	0.594942i	$0.202825\pi$
$613$	27.7600	+	38.2083i	1.12121	+	1.54322i	0.317445	+	0.948277i	$0.397175\pi$
$614$	−14.4502	−	10.4987i	−0.583162	−	0.423692i
$615$		0			0
$616$	−15.4848	+	11.2504i	−0.623901	+	0.453290i
$617$	−15.4735	−	5.02765i	−0.622941	−	0.202406i	−0.0194952	−	0.999810i	$-0.506206\pi$
$617$	−15.4735	−	5.02765i	−0.622941	−	0.202406i	−0.603446	+	0.797404i	$0.706206\pi$
$618$		0			0
$619$	−10.9577	+	33.7244i	−0.440428	+	1.35550i	0.446993	+	0.894537i	$0.352495\pi$
$619$	−10.9577	+	33.7244i	−0.440428	+	1.35550i	−0.887421	+	0.460960i	$0.847505\pi$
$620$	0.858898	+	8.39580i	0.0344942	+	0.337183i
$621$		0			0
$622$	70.6640	−	22.9601i	2.83337	−	0.920617i
$623$	5.54869	−	7.63712i	0.222304	−	0.305975i
$624$		0			0
$625$	22.9500	−	9.91443i	0.918001	−	0.396577i
$626$	−39.6775			−1.58583
$627$		0			0
$628$	−63.2217	+	20.5420i	−2.52282	+	0.819714i
$629$	2.54117	+	7.82091i	0.101323	+	0.311840i
$630$		0			0
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	0.593599	+	0.804761i	$0.297706\pi$
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	−0.953258	+	0.302156i	$0.902294\pi$
$632$			8.95939i			0.356385i
$633$		0			0
$634$	12.8138	−	9.30978i	0.508901	−	0.369738i
$635$	22.6085	+	13.1368i	0.897192	+	0.521317i
$636$		0			0
$637$	19.7181	+	27.1396i	0.781259	+	1.07531i
$638$	−3.01213	−	4.14583i	−0.119251	−	0.164135i
$639$		0			0
$640$	−11.4573	−	25.9268i	−0.452889	−	1.02485i
$641$	−12.7145	+	9.23764i	−0.502194	+	0.364865i	−0.809854	−	0.586631i	$-0.800454\pi$
$641$	−12.7145	+	9.23764i	−0.502194	+	0.364865i	0.307661	+	0.951496i	$0.400454\pi$
$642$		0			0
$643$		−	8.08055i		−	0.318666i	−0.987225	−	0.159333i	$-0.949066\pi$
$643$		−	8.08055i		−	0.318666i	0.987225	−	0.159333i	$-0.0509343\pi$
$644$	5.51102	−	16.9612i	0.217165	−	0.668364i
$645$		0			0
$646$	21.4137	+	65.9045i	0.842510	+	2.59298i
$647$	−10.4800	+	3.40516i	−0.412011	+	0.133870i	−0.507686	−	0.861542i	$-0.669499\pi$
$647$	−10.4800	+	3.40516i	−0.412011	+	0.133870i	0.0956751	+	0.995413i	$0.469499\pi$
$648$		0			0
$649$	−9.54248			−0.374575
$650$	70.4431	−	14.5652i	2.76301	−	0.571295i
$651$		0			0
$652$	−31.0840	+	42.7834i	−1.21734	+	1.67553i
$653$	−29.5646	+	9.60613i	−1.15695	+	0.375917i	−0.823758	−	0.566941i	$-0.808127\pi$
$653$	−29.5646	+	9.60613i	−1.15695	+	0.375917i	−0.333195	+	0.942858i	$0.608127\pi$
$654$		0			0
$655$	−17.4044	−	3.74990i	−0.680047	−	0.146521i
$656$	−2.46021	+	7.57176i	−0.0960552	+	0.295628i
$657$		0			0
$658$	−8.25315	−	2.68161i	−0.321741	−	0.104540i
$659$	−26.2325	+	19.0590i	−1.02187	+	0.742435i	−0.966666	−	0.256040i	$-0.917582\pi$
$659$	−26.2325	+	19.0590i	−1.02187	+	0.742435i	−0.0552080	+	0.998475i	$0.517582\pi$
$660$		0			0
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	0.314490	−	0.949261i	$-0.398166\pi$
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	−0.805618	+	0.592436i	$0.798166\pi$
$662$	32.0061	+	44.0527i	1.24395	+	1.71216i
$663$		0			0
$664$	−57.4806	−	41.7621i	−2.23068	−	1.62068i
$665$	2.63239	−	12.2177i	0.102080	−	0.473782i
$666$		0			0
$667$	2.49547	+	0.810827i	0.0966249	+	0.0313953i
$668$			47.0978i			1.82227i
$669$		0			0
$670$	−3.51699	−	3.92787i	−0.135873	−	0.151747i
$671$	4.97691	+	15.3173i	0.192131	+	0.591320i
$672$		0			0
$673$	18.2373	−	25.1014i	0.702995	−	0.967589i	−0.296925	−	0.954901i	$-0.595961\pi$
$673$	18.2373	−	25.1014i	0.702995	−	0.967589i	0.999919	−	0.0126883i	$-0.00403893\pi$
$674$	88.1870			3.39684
$675$		0			0
$676$	84.9778			3.26838
$677$	−13.5716	+	18.6796i	−0.521597	+	0.717917i	−0.985821	−	0.167801i	$-0.946333\pi$
$677$	−13.5716	+	18.6796i	−0.521597	+	0.717917i	0.464224	+	0.885718i	$0.346333\pi$
$678$		0			0
$679$	1.93868	+	5.96663i	0.0743995	+	0.228978i
$680$	35.3586	−	60.8524i	1.35594	−	2.33358i
$681$		0			0
$682$			6.40936i			0.245427i
$683$	39.3301	+	12.7791i	1.50492	+	0.488979i	0.941449	−	0.337154i	$-0.109464\pi$
$683$	39.3301	+	12.7791i	1.50492	+	0.488979i	0.563474	+	0.826134i	$0.309464\pi$
$684$		0			0
$685$	18.4100	−	16.4842i	0.703409	−	0.629829i
$686$	−27.5944	−	20.0485i	−1.05356	−	0.765457i
$687$		0			0
$688$	22.8340	+	31.4283i	0.870539	+	1.19819i
$689$	−58.1849	−	42.2738i	−2.21667	−	1.61050i
$690$		0			0
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	−0.654429	−	0.756123i	$-0.727091\pi$
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	0.516886	+	0.856054i	$0.327091\pi$
$692$	−5.29239	−	1.71960i	−0.201186	−	0.0653694i
$693$		0			0
$694$	−22.5250	+	69.3248i	−0.855037	+	2.63153i
$695$	−13.7840	+	23.7223i	−0.522855	+	0.899839i
$696$		0			0
$697$	5.63395	−	1.83058i	0.213401	−	0.0693382i
$698$	−18.3220	+	25.2181i	−0.693498	+	0.954518i
$699$		0			0
$700$	−20.0679	+	11.4382i	−0.758495	+	0.432325i
$701$	25.2265			0.952791			0.476396	−	0.879231i	$-0.341943\pi$
$701$	25.2265			0.952791			0.476396	+	0.879231i	$0.341943\pi$
$702$		0			0
$703$	8.26391	−	2.68511i	0.311679	−	0.101271i
$704$	−1.00091	−	3.08048i	−0.0377231	−	0.116100i
$705$		0			0
$706$	−21.1556	+	65.1104i	−0.796203	+	2.45046i
$707$			15.9627i			0.600339i
$708$		0			0
$709$	1.26199	−	0.916889i	0.0473950	−	0.0344345i	−0.563836	−	0.825887i	$-0.690675\pi$
$709$	1.26199	−	0.916889i	0.0473950	−	0.0344345i	0.611231	+	0.791453i	$0.290675\pi$
$710$	−1.68947	+	7.84131i	−0.0634045	+	0.294279i
$711$		0			0
$712$	−33.0158	−	45.4423i	−1.23732	−	1.70302i
$713$	−1.92897	−	2.65500i	−0.0722404	−	0.0994304i
$714$		0			0
$715$	37.4672	−	3.83293i	1.40119	−	0.143343i
$716$	−74.7514	+	54.3100i	−2.79359	+	2.02966i
$717$		0			0
$718$		−	41.6794i		−	1.55546i
$719$	8.94304	−	27.5238i	0.333519	−	1.02647i	−0.633928	−	0.773392i	$-0.718558\pi$
$719$	8.94304	−	27.5238i	0.333519	−	1.02647i	0.967447	−	0.253074i	$-0.0814416\pi$
$720$		0			0
$721$	−3.87748	−	11.9336i	−0.144405	−	0.444432i
$722$	23.7815	−	7.72709i	0.885057	−	0.287572i
$723$		0			0
$724$	30.7547			1.14299
$725$	−1.68289	−	2.95255i	−0.0625009	−	0.109655i
$726$		0			0
$727$	−21.7242	+	29.9008i	−0.805707	+	1.10896i	0.186265	+	0.982500i	$0.440362\pi$
$727$	−21.7242	+	29.9008i	−0.805707	+	1.10896i	−0.991972	+	0.126461i	$0.959638\pi$
$728$	−34.7355	+	11.2863i	−1.28739	+	0.418297i
$729$		0			0
$730$	−58.7707	+	25.9713i	−2.17520	+	0.961243i
$731$	8.93229	−	27.4907i	0.330372	−	1.01678i
$732$		0			0
$733$	3.95793	+	1.28601i	0.146189	+	0.0474998i	0.381198	−	0.924494i	$-0.375512\pi$
$733$	3.95793	+	1.28601i	0.146189	+	0.0474998i	−0.235008	+	0.971993i	$0.575512\pi$
$734$	61.3757	−	44.5921i	2.26542	−	1.64592i
$735$		0			0
$736$	−15.4749	−	11.2432i	−0.570413	−	0.414429i
$737$	−1.62257	−	2.23328i	−0.0597682	−	0.0822638i
$738$		0			0
$739$	15.3371	+	11.1431i	0.564184	+	0.409904i	0.832988	−	0.553291i	$-0.186628\pi$
$739$	15.3371	+	11.1431i	0.564184	+	0.409904i	−0.268804	+	0.963195i	$0.586628\pi$
$740$	−13.8854	−	8.06818i	−0.510438	−	0.296592i
$741$		0			0
$742$	31.8587	+	10.3515i	1.16957	+	0.380016i
$743$		−	11.7060i		−	0.429452i	−0.976674	−	0.214726i	$-0.931114\pi$
$743$		−	11.7060i		−	0.429452i	0.976674	−	0.214726i	$-0.0688859\pi$
$744$		0			0
$745$	1.05324	+	10.2955i	0.0385877	+	0.377198i
$746$	19.4718	+	59.9281i	0.712915	+	2.19413i
$747$		0			0
$748$	39.4146	−	54.2495i	1.44114	−	1.98356i
$749$	6.76126			0.247051
$750$		0			0
$751$	−4.95672			−0.180873			−0.0904367	−	0.995902i	$-0.528826\pi$
$751$	−4.95672			−0.180873			−0.0904367	+	0.995902i	$0.528826\pi$
$752$	−13.1976	+	18.1650i	−0.481268	+	0.662408i
$753$		0			0
$754$	−3.02174	−	9.29995i	−0.110045	−	0.338684i
$755$	1.06329	+	10.3938i	0.0386971	+	0.378268i
$756$		0			0
$757$			18.6020i			0.676101i	0.941128	+	0.338051i	$0.109768\pi$
$757$			18.6020i			0.676101i	−0.941128	+	0.338051i	$0.890232\pi$
$758$	46.8132	+	15.2105i	1.70033	+	0.552472i
$759$		0			0
$760$	−64.2993	−	37.3614i	−2.33238	−	1.35524i
$761$	−9.18925	−	6.67638i	−0.333110	−	0.242019i	0.408639	−	0.912696i	$-0.366003\pi$
$761$	−9.18925	−	6.67638i	−0.333110	−	0.242019i	−0.741749	+	0.670677i	$0.766003\pi$
$762$		0			0
$763$	−1.41317	−	1.94507i	−0.0511603	−	0.0704161i
$764$	−29.3245	−	21.3055i	−1.06092	−	0.770806i
$765$		0			0
$766$	23.0982	−	16.7818i	0.834572	−	0.606352i
$767$	−17.3176	−	5.62682i	−0.625302	−	0.203173i
$768$		0			0
$769$	−2.24803	+	6.91872i	−0.0810660	+	0.249495i	−0.983373	−	0.181599i	$-0.941873\pi$
$769$	−2.24803	+	6.91872i	−0.0810660	+	0.249495i	0.902307	+	0.431095i	$0.141873\pi$
$770$	−16.0452	+	7.09054i	−0.578230	+	0.255525i
$771$		0			0
$772$	−58.9584	+	19.1567i	−2.12196	+	0.689466i
$773$	5.47985	−	7.54237i	0.197097	−	0.271280i	−0.699017	−	0.715105i	$-0.746379\pi$
$773$	5.47985	−	7.54237i	0.197097	−	0.271280i	0.896114	+	0.443825i	$0.146379\pi$
$774$		0			0
$775$	−0.467745	+	4.22474i	−0.0168019	+	0.151757i
$776$	37.3296			1.34005
$777$		0			0
$778$	35.9649	−	11.6857i	1.28941	−	0.418953i
$779$	−1.93427	−	5.95307i	−0.0693024	−	0.213291i
$780$		0			0
$781$	−1.29780	+	3.99421i	−0.0464389	+	0.142924i
$782$			49.8011i			1.78088i
$783$		0			0
$784$	−32.7067	+	23.7628i	−1.16810	+	0.848671i
$785$	−33.3060	+	3.40723i	−1.18874	+	0.121609i
$786$		0			0
$787$	8.73787	+	12.0266i	0.311471	+	0.428704i	0.935839	−	0.352427i	$-0.114643\pi$
$787$	8.73787	+	12.0266i	0.311471	+	0.428704i	−0.624368	+	0.781130i	$0.714643\pi$
$788$	15.0381	+	20.6981i	0.535708	+	0.737339i
$789$		0			0
$790$	−1.72949	+	8.02709i	−0.0615326	+	0.285591i
$791$	−3.26017	+	2.36865i	−0.115918	+	0.0842196i
$792$		0			0
$793$			30.7324i			1.09134i
$794$	18.8962	−	58.1565i	0.670600	−	2.06390i
$795$		0			0
$796$	−36.4598	−	112.212i	−1.29228	−	3.97724i
$797$	9.10680	−	2.95898i	0.322580	−	0.104812i	−0.143251	−	0.989686i	$-0.545756\pi$
$797$	9.10680	−	2.95898i	0.322580	−	0.104812i	0.465831	+	0.884874i	$0.345756\pi$
$798$		0			0
$799$	16.7068			0.591044
$800$	5.01646	+	24.2616i	0.177359	+	0.857777i
$801$		0			0
$802$	20.0740	−	27.6295i	0.708838	−	0.975632i
$803$	−31.9953	+	10.3959i	−1.12909	+	0.366863i
$804$		0			0
$805$	4.51255	−	7.76615i	0.159047	−	0.273721i
$806$	−3.77935	+	11.6316i	−0.133122	+	0.409707i
$807$		0			0
$808$	90.3323	+	29.3508i	3.17788	+	1.03256i
$809$	−33.2859	+	24.1836i	−1.17027	+	0.850250i	−0.991041	−	0.133557i	$-0.957360\pi$
$809$	−33.2859	+	24.1836i	−1.17027	+	0.850250i	−0.179228	+	0.983808i	$0.557360\pi$
$810$		0			0
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.236868	−	0.971542i	$-0.576121\pi$
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.997187	+	0.0749479i	$0.976121\pi$
$812$	1.84566	+	2.54034i	0.0647701	+	0.0891484i
$813$		0			0
$814$	−9.86679	−	7.16864i	−0.345831	−	0.251261i
$815$	−19.8425	+	17.7668i	−0.695052	+	0.622345i
$816$		0			0
$817$	−29.0479	−	9.43823i	−1.01626	−	0.330202i
$818$		−	90.0206i		−	3.14750i
$819$		0			0
$820$	−5.81207	+	10.0026i	−0.202966	+	0.349307i
$821$	−5.39595	−	16.6070i	−0.188320	−	0.579589i	0.811670	−	0.584116i	$-0.198559\pi$
$821$	−5.39595	−	16.6070i	−0.188320	−	0.579589i	−0.999990	+	0.00452746i	$0.998559\pi$
$822$		0			0
$823$	−1.30756	+	1.79970i	−0.0455787	+	0.0627337i	−0.831198	−	0.555976i	$-0.812344\pi$
$823$	−1.30756	+	1.79970i	−0.0455787	+	0.0627337i	0.785619	+	0.618710i	$0.212344\pi$
$824$	−74.6616			−2.60096
$825$		0			0
$826$	8.48106			0.295094
$827$	18.4888	−	25.4476i	0.642918	−	0.884900i	−0.355849	−	0.934543i	$-0.615808\pi$
$827$	18.4888	−	25.4476i	0.642918	−	0.884900i	0.998767	+	0.0496432i	$0.0158084\pi$
$828$		0			0
$829$	−16.4690	−	50.6862i	−0.571990	−	1.76041i	−0.646206	−	0.763163i	$-0.723645\pi$
$829$	−16.4690	−	50.6862i	−0.571990	−	1.76041i	0.0742155	−	0.997242i	$-0.476355\pi$
$830$	−43.4376	−	48.5123i	−1.50774	−	1.68389i
$831$		0			0
$832$		−	6.18061i		−	0.214274i
$833$	28.6089	+	9.29560i	0.991240	+	0.322073i
$834$		0			0
$835$	−4.99609	+	23.1883i	−0.172897	+	0.802466i
$836$	−57.3223	−	41.6471i	−1.98253	−	1.44040i
$837$		0			0
$838$	23.5853	+	32.4623i	0.814739	+	1.12139i
$839$	6.77415	+	4.92171i	0.233870	+	0.169916i	0.698548	−	0.715563i	$-0.253830\pi$
$839$	6.77415	+	4.92171i	0.233870	+	0.169916i	−0.464678	+	0.885480i	$0.653830\pi$
$840$		0			0
$841$	23.0877	−	16.7742i	0.796129	−	0.578421i
$842$	−28.9166	−	9.39558i	−0.996532	−	0.323793i
$843$		0			0
$844$	36.3015	−	111.725i	1.24955	−	3.84572i
$845$	41.8384	+	9.01438i	1.43928	+	0.310104i
$846$		0			0
$847$	2.15054	−	0.698751i	0.0738933	−	0.0240094i
$848$	50.9453	−	70.1202i	1.74947	−	2.40794i
$849$		0			0
$850$	43.4260	−	47.6947i	1.48950	−	1.63592i
$851$	6.24467			0.214064
$852$		0			0
$853$	1.16381	−	0.378146i	0.0398482	−	0.0129475i	−0.289025	−	0.957322i	$-0.593331\pi$
$853$	1.16381	−	0.378146i	0.0398482	−	0.0129475i	0.328873	+	0.944374i	$0.393331\pi$
$854$	−4.42332	−	13.6136i	−0.151363	−	0.465847i
$855$		0			0
$856$	12.4320	−	38.2618i	0.424917	−	1.30776i
$857$		−	14.3684i		−	0.490816i	−0.969420	−	0.245408i	$-0.921078\pi$
$857$		−	14.3684i		−	0.490816i	0.969420	−	0.245408i	$-0.0789219\pi$
$858$		0			0
$859$	−8.34015	+	6.05947i	−0.284562	+	0.206747i	−0.720905	−	0.693034i	$-0.756274\pi$
$859$	−8.34015	+	6.05947i	−0.284562	+	0.206747i	0.436343	+	0.899781i	$0.356274\pi$
$860$	22.8167	+	51.6320i	0.778043	+	1.76064i
$861$		0			0
$862$	−21.8413	−	30.0619i	−0.743916	−	1.02391i
$863$	17.7937	+	24.4909i	0.605703	+	0.833679i	0.996215	−	0.0869190i	$-0.0277021\pi$
$863$	17.7937	+	24.4909i	0.605703	+	0.833679i	−0.390512	+	0.920598i	$0.627702\pi$
$864$		0			0
$865$	−2.42327	−	1.40805i	−0.0823935	−	0.0478751i
$866$	−8.77241	+	6.37353i	−0.298099	+	0.216581i
$867$		0			0
$868$		−	3.92730i		−	0.133301i
$869$	−1.32855	+	4.08885i	−0.0450679	+	0.138705i
$870$		0			0
$871$	−1.62775	−	5.00969i	−0.0551541	−	0.169747i
$872$	−13.6055	+	4.42068i	−0.460739	+	0.149703i
$873$		0			0
$874$	52.6220			1.77996
$875$	−11.0937	+	3.50278i	−0.375035	+	0.118416i
$876$		0			0
$877$	−18.0065	+	24.7839i	−0.608037	+	0.836892i	−0.996414	−	0.0846091i	$-0.973036\pi$
$877$	−18.0065	+	24.7839i	−0.608037	+	0.836892i	0.388377	+	0.921501i	$0.373036\pi$
$878$	49.0111	−	15.9247i	1.65404	−	0.537431i
$879$		0			0
$880$	4.61917	+	45.1527i	0.155712	+	1.52210i
$881$	−4.70359	+	14.4762i	−0.158468	+	0.487714i	−0.998496	−	0.0548293i	$-0.982539\pi$
$881$	−4.70359	+	14.4762i	−0.158468	+	0.487714i	0.840028	+	0.542543i	$0.182539\pi$
$882$		0			0
$883$	38.2310	+	12.4220i	1.28658	+	0.418034i	0.870892	−	0.491475i	$-0.163542\pi$
$883$	38.2310	+	12.4220i	1.28658	+	0.418034i	0.415684	+	0.909509i	$0.363542\pi$
$884$	103.518	−	75.2102i	3.48169	−	2.52959i
$885$		0			0
$886$	39.1189	+	28.4216i	1.31423	+	0.954842i
$887$	18.7169	+	25.7617i	0.628453	+	0.864992i	0.997934	−	0.0642465i	$-0.0204644\pi$
$887$	18.7169	+	25.7617i	0.628453	+	0.864992i	−0.369481	+	0.929238i	$0.620464\pi$
$888$		0			0
$889$	−9.84394	−	7.15204i	−0.330155	−	0.239872i
$890$	−20.8082	−	47.0869i	−0.697491	−	1.57836i
$891$		0			0
$892$	115.889	+	37.6545i	3.88024	+	1.26077i
$893$		−	17.6531i		−	0.590739i
$894$		0			0
$895$	−42.5646	+	18.8097i	−1.42278	+	0.628739i
$896$	4.07604	+	12.5448i	0.136171	+	0.419091i
$897$		0			0
$898$	−43.9716	+	60.5217i	−1.46735	+	2.01964i
$899$	0.577817			0.0192713
$900$		0			0
$901$	−64.4914			−2.14852
$902$	−5.16407	+	7.10774i	−0.171945	+	0.236662i
$903$		0			0
$904$	7.40962	+	22.8045i	0.246440	+	0.758465i
$905$	15.1419	+	3.26243i	0.503334	+	0.108447i
$906$		0			0
$907$			28.8507i			0.957970i	0.877823	+	0.478985i	$0.158995\pi$
$907$			28.8507i			0.957970i	−0.877823	+	0.478985i	$0.841005\pi$
$908$	−0.549602	−	0.178577i	−0.0182392	−	0.00592627i
$909$		0			0
$910$	−33.2997	+	3.40659i	−1.10387	+	0.112927i
$911$	39.1370	+	28.4347i	1.29667	+	0.942084i	0.999917	−	0.0128711i	$-0.00409711\pi$
$911$	39.1370	+	28.4347i	1.29667	+	0.942084i	0.296750	+	0.954955i	$0.404097\pi$
$912$		0			0
$913$	−20.0400	−	27.5827i	−0.663228	−	0.912855i
$914$	58.1036	+	42.2148i	1.92190	+	1.39634i
$915$		0			0
$916$	−10.1481	+	7.37301i	−0.335302	+	0.243611i
$917$	7.87936	+	2.56016i	0.260199	+	0.0845439i
$918$		0			0
$919$	2.58963	−	7.97006i	0.0854240	−	0.262908i	−0.899216	−	0.437505i	$-0.855862\pi$
$919$	2.58963	−	7.97006i	0.0854240	−	0.262908i	0.984640	+	0.174597i	$0.0558622\pi$
$920$	−35.6511	−	39.8161i	−1.17538	−	1.31270i
$921$		0			0
$922$	39.9609	−	12.9841i	1.31604	−	0.427608i
$923$	−4.71046	+	6.48340i	−0.155047	+	0.213404i
$924$		0			0
$925$	−5.98055	−	5.44528i	−0.196639	−	0.179040i
$926$	23.3703			0.767995
$927$		0			0
$928$	3.20303	−	1.04073i	0.105145	−	0.0341636i
$929$	4.42283	+	13.6121i	0.145108	+	0.446597i	0.997025	−	0.0770801i	$-0.0245597\pi$
$929$	4.42283	+	13.6121i	0.145108	+	0.446597i	−0.851917	+	0.523677i	$0.824560\pi$
$930$		0			0
$931$	9.82212	−	30.2294i	0.321907	−	0.990728i
$932$			35.4610i			1.16156i
$933$		0			0
$934$	−21.7873	+	15.8294i	−0.712901	+	0.517953i
$935$	25.1603	−	22.5284i	0.822830	−	0.736758i
$936$		0			0
$937$	−12.8869	−	17.7372i	−0.420996	−	0.579451i	0.544862	−	0.838526i	$-0.316582\pi$
$937$	−12.8869	−	17.7372i	−0.420996	−	0.579451i	−0.965857	+	0.259075i	$0.916582\pi$
$938$	1.44209	+	1.98487i	0.0470859	+	0.0648082i
$939$		0			0
$940$	−24.3065	+	21.7639i	−0.792792	+	0.709861i
$941$	18.1167	−	13.1625i	0.590586	−	0.429086i	−0.251939	−	0.967743i	$-0.581068\pi$
$941$	18.1167	−	13.1625i	0.590586	−	0.429086i	0.842525	+	0.538657i	$0.181068\pi$
$942$		0			0
$943$		−	4.49847i		−	0.146490i
$944$	6.78104	−	20.8699i	0.220704	−	0.679257i
$945$		0			0
$946$	13.2474	+	40.7712i	0.430709	+	1.32559i
$947$	−41.4316	+	13.4619i	−1.34635	+	0.437454i	−0.891462	−	0.453096i	$-0.850319\pi$
$947$	−41.4316	+	13.4619i	−1.34635	+	0.437454i	−0.454884	+	0.890550i	$0.650319\pi$
$948$		0			0
$949$	−64.1947			−2.08385
$950$	−50.3963	−	45.8857i	−1.63507	−	1.48873i
$951$		0			0
$952$	−19.2502	+	26.4957i	−0.623903	+	0.858729i
$953$	2.25561	−	0.732893i	0.0730664	−	0.0237407i	−0.272256	−	0.962225i	$-0.587770\pi$
$953$	2.25561	−	0.732893i	0.0730664	−	0.0237407i	0.345322	+	0.938484i	$0.387770\pi$
$954$		0			0
$955$	−12.1777	−	13.6004i	−0.394061	−	0.440098i
$956$	26.1524	−	80.4887i	0.845828	−	2.60319i
$957$		0			0
$958$	−81.1073	−	26.3534i	−2.62046	−	0.851439i
$959$	−9.30310	+	6.75910i	−0.300413	+	0.218263i
$960$		0			0
$961$	24.4949	+	17.7966i	0.790157	+	0.574082i
$962$	−13.6791	−	18.8276i	−0.441031	−	0.607027i
$963$		0			0
$964$	75.8598	+	55.1154i	2.44328	+	1.77515i
$965$	−31.0600	+	3.17746i	−0.999856	+	0.102286i
$966$		0			0
$967$	18.8174	+	6.11413i	0.605125	+	0.196617i	0.595525	−	0.803337i	$-0.296944\pi$
$967$	18.8174	+	6.11413i	0.605125	+	0.196617i	0.00960036	+	0.999954i	$0.496944\pi$
$968$		−	13.4546i		−	0.432447i
$969$		0			0
$970$	33.4452	+	7.20599i	1.07386	+	0.231371i
$971$	−15.2604	−	46.9668i	−0.489731	−	1.50724i	−0.825010	−	0.565118i	$-0.808831\pi$
$971$	−15.2604	−	46.9668i	−0.489731	−	1.50724i	0.335279	−	0.942119i	$-0.391169\pi$
$972$		0			0
$973$	7.50438	−	10.3289i	0.240579	−	0.331129i
$974$	−74.2234			−2.37827
$975$		0			0
$976$	−37.0365			−1.18551
$977$	−28.0757	+	38.6429i	−0.898221	+	1.23630i	0.0728110	+	0.997346i	$0.476803\pi$
$977$	−28.0757	+	38.6429i	−0.898221	+	1.23630i	−0.971032	+	0.238949i	$0.923197\pi$
$978$		0			0
$979$	−8.32916	−	25.6345i	−0.266201	−	0.819283i
$980$	−53.7321	+	23.7447i	−1.71641	+	0.758498i
$981$		0			0
$982$			35.4131i			1.13008i
$983$	−49.3867	−	16.0467i	−1.57519	−	0.511810i	−0.614379	−	0.789011i	$-0.710593\pi$
$983$	−49.3867	−	16.0467i	−1.57519	−	0.511810i	−0.960812	+	0.277201i	$0.910593\pi$
$984$		0			0
$985$	5.20827	+	11.7858i	0.165949	+	0.375528i
$986$	−7.09383	−	5.15397i	−0.225914	−	0.164136i
$987$		0			0
$988$	−79.4703	−	109.381i	−2.52829	−	3.47989i
$989$	−17.7581	−	12.9020i	−0.564674	−	0.410260i
$990$		0			0
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	−0.357083	−	0.934073i	$-0.616229\pi$
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	0.778011	+	0.628250i	$0.216229\pi$
$992$	−4.00610	−	1.30166i	−0.127194	−	0.0413277i
$993$		0			0
$994$	1.15344	−	3.54994i	0.0365850	−	0.112597i
$995$	−6.04747	−	59.1145i	−0.191718	−	1.87406i
$996$		0			0
$997$	−21.1625	+	6.87610i	−0.670222	+	0.217768i	−0.624309	−	0.781177i	$-0.714620\pi$
$997$	−21.1625	+	6.87610i	−0.670222	+	0.217768i	−0.0459126	+	0.998945i	$0.514620\pi$
$998$	−53.3299	+	73.4022i	−1.68813	+	2.32351i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.b.109.1		16
3.2	odd	2		75.2.i.a.34.4	✓	16
15.2	even	4		375.2.g.e.76.4		16
15.8	even	4		375.2.g.d.76.1		16
15.14	odd	2		375.2.i.c.49.1		16
25.8	odd	20		5625.2.a.t.1.1		8
25.14	even	10	inner	225.2.m.b.64.1		16
25.17	odd	20		5625.2.a.bd.1.8		8
75.2	even	20		375.2.g.e.301.4		16
75.8	even	20		1875.2.a.p.1.8		8
75.11	odd	10		375.2.i.c.199.1		16
75.14	odd	10		75.2.i.a.64.4	yes	16
75.17	even	20		1875.2.a.m.1.1		8
75.23	even	20		375.2.g.d.301.1		16
75.44	odd	10		1875.2.b.h.1249.1		16
75.56	odd	10		1875.2.b.h.1249.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.4	✓	16	3.2	odd	2
75.2.i.a.64.4	yes	16	75.14	odd	10
225.2.m.b.64.1		16	25.14	even	10	inner
225.2.m.b.109.1		16	1.1	even	1	trivial
375.2.g.d.76.1		16	15.8	even	4
375.2.g.d.301.1		16	75.23	even	20
375.2.g.e.76.4		16	15.2	even	4
375.2.g.e.301.4		16	75.2	even	20
375.2.i.c.49.1		16	15.14	odd	2
375.2.i.c.199.1		16	75.11	odd	10
1875.2.a.m.1.1		8	75.17	even	20
1875.2.a.p.1.8		8	75.8	even	20
1875.2.b.h.1249.1		16	75.44	odd	10
1875.2.b.h.1249.16		16	75.56	odd	10
5625.2.a.t.1.1		8	25.8	odd	20
5625.2.a.bd.1.8		8	25.17	odd	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49161 + 2.05302i) q^{2} +(-1.37197 - 4.22249i) q^{4} +(-0.227564 - 2.22446i) q^{5} +1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +O(q^{10})\)	\(q+(-1.49161 + 2.05302i) q^{2} +(-1.37197 - 4.22249i) q^{4} +(-0.227564 - 2.22446i) q^{5} +1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +(4.90630 + 2.85082i) q^{10} +(2.40360 + 1.74631i) q^{11} +(3.33228 + 4.58650i) q^{13} +(-2.13624 - 1.55207i) q^{14} +(-5.52731 + 4.01583i) q^{16} +(4.83480 + 1.57092i) q^{17} +(1.65990 - 5.10866i) q^{19} +(-9.08054 + 4.01278i) q^{20} +(-7.17044 + 2.32982i) q^{22} +(2.26908 - 3.12312i) q^{23} +(-4.89643 + 1.01241i) q^{25} -14.3866 q^{26} +(4.39365 - 1.42758i) q^{28} +(0.210038 + 0.646430i) q^{29} +(0.262699 - 0.808503i) q^{31} -4.95495i q^{32} +(-10.4368 + 7.58275i) q^{34} +(2.31463 - 0.236789i) q^{35} +(0.950818 + 1.30869i) q^{37} +(8.01226 + 11.0279i) q^{38} +(2.91595 - 13.5338i) q^{40} +(0.942740 - 0.684941i) q^{41} -5.68601i q^{43} +(4.07613 - 12.5450i) q^{44} +(3.02725 + 9.31693i) q^{46} +(3.12556 - 1.01555i) q^{47} +5.91729 q^{49} +(5.22504 - 11.5626i) q^{50} +(14.7946 - 20.3631i) q^{52} +(-12.0652 + 3.92023i) q^{53} +(3.33763 - 5.74410i) q^{55} +(-1.99080 + 6.12704i) q^{56} +(-1.64043 - 0.533007i) q^{58} +(-2.59846 + 1.88789i) q^{59} +(4.38562 + 3.18634i) q^{61} +(1.26803 + 1.74530i) q^{62} +(-0.881995 - 0.640807i) q^{64} +(9.44416 - 8.45625i) q^{65} +(-0.883665 - 0.287120i) q^{67} -22.5702i q^{68} +(-2.96638 + 5.10517i) q^{70} +(0.436821 + 1.34440i) q^{71} +(-6.65571 + 9.16080i) q^{73} -4.10501 q^{74} -23.8486 q^{76} +(-1.81710 + 2.50103i) q^{77} +(0.447171 + 1.37625i) q^{79} +(10.1909 + 11.3814i) q^{80} +2.95713i q^{82} +(-10.9140 - 3.54616i) q^{83} +(2.39422 - 11.1123i) q^{85} +(11.6735 + 8.48129i) q^{86} +(10.8121 + 14.8816i) q^{88} +(-7.33961 - 5.33254i) q^{89} +(-4.77241 + 3.46736i) q^{91} +(-16.3004 - 5.29633i) q^{92} +(-2.57715 + 7.93164i) q^{94} +(-11.7417 - 2.52984i) q^{95} +(5.73419 - 1.86315i) q^{97} +(-8.82627 + 12.1483i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) \) 16 * q + 2 * q^4 + 30 * q^8	\( 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

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