LMFDB - Embedded newform 432.2.y.d.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			253.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	432.253
Dual form			432.2.y.d.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(0.133975 + 0.500000i) q^{5} +(2.13397 - 1.23205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(0.133975 + 0.500000i) q^{5} +(2.13397 - 1.23205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.633975 + 0.366025i) q^{10} +(0.500000 + 0.133975i) q^{11} +(4.59808 - 1.23205i) q^{13} +(0.901924 - 3.36603i) q^{14} -4.00000 q^{16} -4.00000 q^{17} +(-3.00000 - 3.00000i) q^{19} +(1.00000 - 0.267949i) q^{20} +(0.633975 - 0.366025i) q^{22} +(0.401924 + 0.232051i) q^{23} +(4.09808 - 2.36603i) q^{25} +(3.36603 - 5.83013i) q^{26} +(-2.46410 - 4.26795i) q^{28} +(-0.866025 + 3.23205i) q^{29} +(0.598076 - 1.03590i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-4.00000 + 4.00000i) q^{34} +(0.901924 + 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} -6.00000 q^{38} +(0.732051 - 1.26795i) q^{40} +(9.69615 + 5.59808i) q^{41} +(8.69615 + 2.33013i) q^{43} +(0.267949 - 1.00000i) q^{44} +(0.633975 - 0.169873i) q^{46} +(-4.59808 - 7.96410i) q^{47} +(-0.464102 + 0.803848i) q^{49} +(1.73205 - 6.46410i) q^{50} +(-2.46410 - 9.19615i) q^{52} +(-2.26795 + 2.26795i) q^{53} +0.267949i q^{55} +(-6.73205 - 1.80385i) q^{56} +(2.36603 + 4.09808i) q^{58} +(1.50000 + 5.59808i) q^{59} +(-3.86603 + 14.4282i) q^{61} +(-0.437822 - 1.63397i) q^{62} +8.00000i q^{64} +(1.23205 + 2.13397i) q^{65} +(1.23205 - 0.330127i) q^{67} +8.00000i q^{68} +1.80385 q^{70} -10.9282i q^{71} +0.535898i q^{73} +15.4641i q^{74} +(-6.00000 + 6.00000i) q^{76} +(1.23205 - 0.330127i) q^{77} +(0.866025 + 1.50000i) q^{79} +(-0.535898 - 2.00000i) q^{80} +(15.2942 - 4.09808i) q^{82} +(-3.16025 + 11.7942i) q^{83} +(-0.535898 - 2.00000i) q^{85} +(11.0263 - 6.36603i) q^{86} +(-0.732051 - 1.26795i) q^{88} +11.8564i q^{89} +(8.29423 - 8.29423i) q^{91} +(0.464102 - 0.803848i) q^{92} +(-12.5622 - 3.36603i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(0.339746 + 1.26795i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{5} + 12 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^5 + 12 * q^7 - 8 * q^8	$ 4 q + 4 q^{2} + 4 q^{5} + 12 q^{7} - 8 q^{8} + 6 q^{10} + 2 q^{11} + 8 q^{13} + 14 q^{14} - 16 q^{16} - 16 q^{17} - 12 q^{19} + 4 q^{20} + 6 q^{22} + 12 q^{23} + 6 q^{25} + 10 q^{26} + 4 q^{28} - 8 q^{31} - 16 q^{32} - 16 q^{34} + 14 q^{35} - 24 q^{37} - 24 q^{38} - 4 q^{40} + 18 q^{41} + 14 q^{43} + 8 q^{44} + 6 q^{46} - 8 q^{47} + 12 q^{49} + 4 q^{52} - 16 q^{53} - 20 q^{56} + 6 q^{58} + 6 q^{59} - 12 q^{61} - 26 q^{62} - 2 q^{65} - 2 q^{67} + 28 q^{70} - 24 q^{76} - 2 q^{77} - 16 q^{80} + 30 q^{82} + 22 q^{83} - 16 q^{85} + 6 q^{86} + 4 q^{88} + 2 q^{91} - 12 q^{92} - 26 q^{94} - 6 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^5 + 12 * q^7 - 8 * q^8 + 6 * q^10 + 2 * q^11 + 8 * q^13 + 14 * q^14 - 16 * q^16 - 16 * q^17 - 12 * q^19 + 4 * q^20 + 6 * q^22 + 12 * q^23 + 6 * q^25 + 10 * q^26 + 4 * q^28 - 8 * q^31 - 16 * q^32 - 16 * q^34 + 14 * q^35 - 24 * q^37 - 24 * q^38 - 4 * q^40 + 18 * q^41 + 14 * q^43 + 8 * q^44 + 6 * q^46 - 8 * q^47 + 12 * q^49 + 4 * q^52 - 16 * q^53 - 20 * q^56 + 6 * q^58 + 6 * q^59 - 12 * q^61 - 26 * q^62 - 2 * q^65 - 2 * q^67 + 28 * q^70 - 24 * q^76 - 2 * q^77 - 16 * q^80 + 30 * q^82 + 22 * q^83 - 16 * q^85 + 6 * q^86 + 4 * q^88 + 2 * q^91 - 12 * q^92 - 26 * q^94 - 6 * q^95 - 2 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	1.00000i
$5$	0.133975	+	0.500000i	0.0599153	+	0.223607i	0.989391	−	0.145276i	$-0.0464070\pi$
$5$	0.133975	+	0.500000i	0.0599153	+	0.223607i	−0.929476	+	0.368883i	$0.879740\pi$
$6$		0			0
$7$	2.13397	−	1.23205i	0.806567	−	0.465671i	−0.0391956	−	0.999232i	$-0.512480\pi$
$7$	2.13397	−	1.23205i	0.806567	−	0.465671i	0.845762	+	0.533560i	$0.179146\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	0.633975	+	0.366025i	0.200480	+	0.115747i
$11$	0.500000	+	0.133975i	0.150756	+	0.0403949i	0.333408	−	0.942783i	$-0.391801\pi$
$11$	0.500000	+	0.133975i	0.150756	+	0.0403949i	−0.182652	+	0.983178i	$0.558468\pi$
$12$		0			0
$13$	4.59808	−	1.23205i	1.27528	−	0.341709i	0.443227	−	0.896410i	$-0.353834\pi$
$13$	4.59808	−	1.23205i	1.27528	−	0.341709i	0.832050	+	0.554700i	$0.187167\pi$
$14$	0.901924	−	3.36603i	0.241049	−	0.899608i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	1.00000	−	0.267949i	0.223607	−	0.0599153i
$21$		0			0
$22$	0.633975	−	0.366025i	0.135164	−	0.0780369i
$23$	0.401924	+	0.232051i	0.0838069	+	0.0483859i	0.541318	−	0.840818i	$-0.317926\pi$
$23$	0.401924	+	0.232051i	0.0838069	+	0.0483859i	−0.457511	+	0.889204i	$0.651259\pi$
$24$		0			0
$25$	4.09808	−	2.36603i	0.819615	−	0.473205i
$26$	3.36603	−	5.83013i	0.660132	−	1.14338i
$27$		0			0
$28$	−2.46410	−	4.26795i	−0.465671	−	0.806567i
$29$	−0.866025	+	3.23205i	−0.160817	+	0.600177i	0.837720	+	0.546100i	$0.183888\pi$
$29$	−0.866025	+	3.23205i	−0.160817	+	0.600177i	−0.998537	+	0.0540766i	$0.982778\pi$
$30$		0			0
$31$	0.598076	−	1.03590i	0.107418	−	0.186053i	−0.807306	−	0.590133i	$-0.799075\pi$
$31$	0.598076	−	1.03590i	0.107418	−	0.186053i	0.914723	+	0.404081i	$0.132408\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$		0			0
$34$	−4.00000	+	4.00000i	−0.685994	+	0.685994i
$35$	0.901924	+	0.901924i	0.152453	+	0.152453i
$36$		0			0
$37$	−7.73205	+	7.73205i	−1.27114	+	1.27114i	−0.325651	+	0.945490i	$0.605584\pi$
$37$	−7.73205	+	7.73205i	−1.27114	+	1.27114i	−0.945490	+	0.325651i	$0.894416\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$	0.732051	−	1.26795i	0.115747	−	0.200480i
$41$	9.69615	+	5.59808i	1.51428	+	0.874273i	0.999860	+	0.0167371i	$0.00532782\pi$
$41$	9.69615	+	5.59808i	1.51428	+	0.874273i	0.514425	+	0.857536i	$0.328006\pi$
$42$		0			0
$43$	8.69615	+	2.33013i	1.32615	+	0.355341i	0.851279	−	0.524714i	$-0.175828\pi$
$43$	8.69615	+	2.33013i	1.32615	+	0.355341i	0.474872	+	0.880055i	$0.342494\pi$
$44$	0.267949	−	1.00000i	0.0403949	−	0.150756i
$45$		0			0
$46$	0.633975	−	0.169873i	0.0934745	−	0.0250464i
$47$	−4.59808	−	7.96410i	−0.670698	−	1.16168i	−0.977706	−	0.209977i	$-0.932661\pi$
$47$	−4.59808	−	7.96410i	−0.670698	−	1.16168i	0.307008	−	0.951707i	$-0.400672\pi$
$48$		0			0
$49$	−0.464102	+	0.803848i	−0.0663002	+	0.114835i
$50$	1.73205	−	6.46410i	0.244949	−	0.914162i
$51$		0			0
$52$	−2.46410	−	9.19615i	−0.341709	−	1.27528i
$53$	−2.26795	+	2.26795i	−0.311527	+	0.311527i	−0.845501	−	0.533974i	$-0.820698\pi$
$53$	−2.26795	+	2.26795i	−0.311527	+	0.311527i	0.533974	+	0.845501i	$0.320698\pi$
$54$		0			0
$55$			0.267949i			0.0361303i
$56$	−6.73205	−	1.80385i	−0.899608	−	0.241049i
$57$		0			0
$58$	2.36603	+	4.09808i	0.310674	+	0.538104i
$59$	1.50000	+	5.59808i	0.195283	+	0.728807i	0.992193	+	0.124709i	$0.0397998\pi$
$59$	1.50000	+	5.59808i	0.195283	+	0.728807i	−0.796910	+	0.604098i	$0.793533\pi$
$60$		0			0
$61$	−3.86603	+	14.4282i	−0.494994	+	1.84734i	0.0350707	+	0.999385i	$0.488834\pi$
$61$	−3.86603	+	14.4282i	−0.494994	+	1.84734i	−0.530065	+	0.847957i	$0.677832\pi$
$62$	−0.437822	−	1.63397i	−0.0556035	−	0.207515i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	1.23205	+	2.13397i	0.152817	+	0.264687i
$66$		0			0
$67$	1.23205	−	0.330127i	0.150519	−	0.0403314i	−0.182773	−	0.983155i	$-0.558507\pi$
$67$	1.23205	−	0.330127i	0.150519	−	0.0403314i	0.333292	+	0.942824i	$0.391841\pi$
$68$			8.00000i			0.970143i
$69$		0			0
$70$	1.80385			0.215601
$71$		−	10.9282i		−	1.29694i	−0.761241	−	0.648470i	$-0.775409\pi$
$71$		−	10.9282i		−	1.29694i	0.761241	−	0.648470i	$-0.224591\pi$
$72$		0			0
$73$			0.535898i			0.0627222i	0.999508	+	0.0313611i	$0.00998418\pi$
$73$			0.535898i			0.0627222i	−0.999508	+	0.0313611i	$0.990016\pi$
$74$			15.4641i			1.79767i
$75$		0			0
$76$	−6.00000	+	6.00000i	−0.688247	+	0.688247i
$77$	1.23205	−	0.330127i	0.140405	−	0.0376215i
$78$		0			0
$79$	0.866025	+	1.50000i	0.0974355	+	0.168763i	0.910622	−	0.413239i	$-0.135603\pi$
$79$	0.866025	+	1.50000i	0.0974355	+	0.168763i	−0.813187	+	0.582003i	$0.802269\pi$
$80$	−0.535898	−	2.00000i	−0.0599153	−	0.223607i
$81$		0			0
$82$	15.2942	−	4.09808i	1.68897	−	0.452557i
$83$	−3.16025	+	11.7942i	−0.346883	+	1.29458i	0.543514	+	0.839400i	$0.317093\pi$
$83$	−3.16025	+	11.7942i	−0.346883	+	1.29458i	−0.890397	+	0.455185i	$0.849573\pi$
$84$		0			0
$85$	−0.535898	−	2.00000i	−0.0581263	−	0.216930i
$86$	11.0263	−	6.36603i	1.18899	−	0.686466i
$87$		0			0
$88$	−0.732051	−	1.26795i	−0.0780369	−	0.135164i
$89$			11.8564i			1.25678i	0.777900	+	0.628388i	$0.216285\pi$
$89$			11.8564i			1.25678i	−0.777900	+	0.628388i	$0.783715\pi$
$90$		0			0
$91$	8.29423	−	8.29423i	0.869471	−	0.869471i
$92$	0.464102	−	0.803848i	0.0483859	−	0.0838069i
$93$		0			0
$94$	−12.5622	−	3.36603i	−1.29569	−	0.347179i
$95$	1.09808	−	1.90192i	0.112660	−	0.195133i
$96$		0			0
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$	0.339746	+	1.26795i	0.0343195	+	0.128082i
$99$		0			0
$100$	−4.73205	−	8.19615i	−0.473205	−	0.819615i
$101$	1.86603	+	0.500000i	0.185676	+	0.0497519i	0.350459	−	0.936578i	$-0.386026\pi$
$101$	1.86603	+	0.500000i	0.185676	+	0.0497519i	−0.164783	+	0.986330i	$0.552692\pi$
$102$		0			0
$103$	−1.79423	−	1.03590i	−0.176791	−	0.102070i	0.408993	−	0.912537i	$-0.365880\pi$
$103$	−1.79423	−	1.03590i	−0.176791	−	0.102070i	−0.585784	+	0.810467i	$0.699213\pi$
$104$	−11.6603	−	6.73205i	−1.14338	−	0.660132i
$105$		0			0
$106$			4.53590i			0.440565i
$107$	11.3923	−	11.3923i	1.10134	−	1.10134i	0.107086	−	0.994250i	$-0.465848\pi$
$107$	11.3923	−	11.3923i	1.10134	−	1.10134i	0.994250	−	0.107086i	$-0.0341520\pi$
$108$		0			0
$109$	1.73205	+	1.73205i	0.165900	+	0.165900i	0.785175	−	0.619274i	$-0.212573\pi$
$109$	1.73205	+	1.73205i	0.165900	+	0.165900i	−0.619274	+	0.785175i	$0.712573\pi$
$110$	0.267949	+	0.267949i	0.0255480	+	0.0255480i
$111$		0			0
$112$	−8.53590	+	4.92820i	−0.806567	+	0.465671i
$113$	2.76795	−	4.79423i	0.260387	−	0.451003i	−0.705958	−	0.708254i	$-0.749483\pi$
$113$	2.76795	−	4.79423i	0.260387	−	0.451003i	0.966345	+	0.257251i	$0.0828166\pi$
$114$		0			0
$115$	−0.0621778	+	0.232051i	−0.00579811	+	0.0216388i
$116$	6.46410	+	1.73205i	0.600177	+	0.160817i
$117$		0			0
$118$	7.09808	+	4.09808i	0.653431	+	0.377258i
$119$	−8.53590	+	4.92820i	−0.782485	+	0.451768i
$120$		0			0
$121$	−9.29423	−	5.36603i	−0.844930	−	0.487820i
$122$	10.5622	+	18.2942i	0.956255	+	1.65628i
$123$		0			0
$124$	−2.07180	−	1.19615i	−0.186053	−	0.107418i
$125$	3.56218	+	3.56218i	0.318611	+	0.318611i
$126$		0			0
$127$	−20.3923			−1.80952			−0.904762	−	0.425917i	$-0.859952\pi$
$127$	−20.3923			−1.80952			−0.904762	+	0.425917i	$0.859952\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$		0			0
$130$	3.36603	+	0.901924i	0.295220	+	0.0791039i
$131$	−11.6962	+	3.13397i	−1.02190	+	0.273817i	−0.730593	−	0.682814i	$-0.760756\pi$
$131$	−11.6962	+	3.13397i	−1.02190	+	0.273817i	−0.291305	+	0.956630i	$0.594089\pi$
$132$		0			0
$133$	−10.0981	−	2.70577i	−0.875614	−	0.234620i
$134$	0.901924	−	1.56218i	0.0779143	−	0.134952i
$135$		0			0
$136$	8.00000	+	8.00000i	0.685994	+	0.685994i
$137$	14.4282	−	8.33013i	1.23268	−	0.711691i	0.265096	−	0.964222i	$-0.414596\pi$
$137$	14.4282	−	8.33013i	1.23268	−	0.711691i	0.967589	+	0.252531i	$0.0812631\pi$
$138$		0			0
$139$	−1.16025	−	4.33013i	−0.0984115	−	0.367277i	0.899103	−	0.437737i	$-0.144220\pi$
$139$	−1.16025	−	4.33013i	−0.0984115	−	0.367277i	−0.997515	+	0.0704603i	$0.977553\pi$
$140$	1.80385	−	1.80385i	0.152453	−	0.152453i
$141$		0			0
$142$	−10.9282	−	10.9282i	−0.917074	−	0.917074i
$143$	2.46410			0.206059
$144$		0			0
$145$	−1.73205			−0.143839
$146$	0.535898	+	0.535898i	0.0443513	+	0.0443513i
$147$		0			0
$148$	15.4641	+	15.4641i	1.27114	+	1.27114i
$149$	−3.93782	−	14.6962i	−0.322599	−	1.20396i	−0.916704	−	0.399568i	$-0.869160\pi$
$149$	−3.93782	−	14.6962i	−0.322599	−	1.20396i	0.594105	−	0.804388i	$-0.297507\pi$
$150$		0			0
$151$	6.06218	−	3.50000i	0.493333	−	0.284826i	−0.232623	−	0.972567i	$-0.574731\pi$
$151$	6.06218	−	3.50000i	0.493333	−	0.284826i	0.725956	+	0.687741i	$0.241398\pi$
$152$			12.0000i			0.973329i
$153$		0			0
$154$	0.901924	−	1.56218i	0.0726791	−	0.125884i
$155$	0.598076	+	0.160254i	0.0480386	+	0.0128719i
$156$		0			0
$157$	0.866025	−	0.232051i	0.0691164	−	0.0185197i	−0.224095	−	0.974567i	$-0.571943\pi$
$157$	0.866025	−	0.232051i	0.0691164	−	0.0185197i	0.293212	+	0.956048i	$0.405276\pi$
$158$	2.36603	+	0.633975i	0.188231	+	0.0504363i
$159$		0			0
$160$	−2.53590	−	1.46410i	−0.200480	−	0.115747i
$161$	1.14359			0.0901278
$162$		0			0
$163$	11.9282	+	11.9282i	0.934289	+	0.934289i	0.997970	−	0.0636813i	$-0.0202841\pi$
$163$	11.9282	+	11.9282i	0.934289	+	0.934289i	−0.0636813	+	0.997970i	$0.520284\pi$
$164$	11.1962	−	19.3923i	0.874273	−	1.51428i
$165$		0			0
$166$	8.63397	+	14.9545i	0.670126	+	1.16069i
$167$	−8.25833	−	4.76795i	−0.639049	−	0.368955i	0.145199	−	0.989402i	$-0.453618\pi$
$167$	−8.25833	−	4.76795i	−0.639049	−	0.368955i	−0.784248	+	0.620447i	$0.786951\pi$
$168$		0			0
$169$	8.36603	−	4.83013i	0.643540	−	0.371548i
$170$	−2.53590	−	1.46410i	−0.194495	−	0.112291i
$171$		0			0
$172$	4.66025	−	17.3923i	0.355341	−	1.32615i
$173$	−2.40192	+	8.96410i	−0.182615	+	0.681528i	0.812514	+	0.582942i	$0.198099\pi$
$173$	−2.40192	+	8.96410i	−0.182615	+	0.681528i	−0.995129	+	0.0985859i	$0.968568\pi$
$174$		0			0
$175$	5.83013	−	10.0981i	0.440716	−	0.763343i
$176$	−2.00000	−	0.535898i	−0.150756	−	0.0403949i
$177$		0			0
$178$	11.8564	+	11.8564i	0.888675	+	0.888675i
$179$	−7.92820	−	7.92820i	−0.592582	−	0.592582i	0.345746	−	0.938328i	$-0.387626\pi$
$179$	−7.92820	−	7.92820i	−0.592582	−	0.592582i	−0.938328	+	0.345746i	$0.887626\pi$
$180$		0			0
$181$	−4.26795	+	4.26795i	−0.317234	+	0.317234i	−0.847704	−	0.530470i	$-0.822016\pi$
$181$	−4.26795	+	4.26795i	−0.317234	+	0.317234i	0.530470	+	0.847704i	$0.322016\pi$
$182$		−	16.5885i		−	1.22962i
$183$		0			0
$184$	−0.339746	−	1.26795i	−0.0250464	−	0.0934745i
$185$	−4.90192	−	2.83013i	−0.360397	−	0.208075i
$186$		0			0
$187$	−2.00000	−	0.535898i	−0.146254	−	0.0391888i
$188$	−15.9282	+	9.19615i	−1.16168	+	0.670698i
$189$		0			0
$190$	−0.803848	−	3.00000i	−0.0583172	−	0.217643i
$191$	−6.59808	−	11.4282i	−0.477420	−	0.826916i	0.522245	−	0.852795i	$-0.325095\pi$
$191$	−6.59808	−	11.4282i	−0.477420	−	0.826916i	−0.999665	+	0.0258797i	$0.991761\pi$
$192$		0			0
$193$	−1.23205	+	2.13397i	−0.0886850	+	0.153607i	−0.906956	−	0.421226i	$-0.861600\pi$
$193$	−1.23205	+	2.13397i	−0.0886850	+	0.153607i	0.818271	+	0.574833i	$0.194933\pi$
$194$	−1.36603	−	0.366025i	−0.0980749	−	0.0262791i
$195$		0			0
$196$	1.60770	+	0.928203i	0.114835	+	0.0663002i
$197$	−10.4641	+	10.4641i	−0.745536	+	0.745536i	−0.973637	−	0.228101i	$-0.926748\pi$
$197$	−10.4641	+	10.4641i	−0.745536	+	0.745536i	0.228101	+	0.973637i	$0.426748\pi$
$198$		0			0
$199$			5.85641i			0.415150i	0.978219	+	0.207575i	$0.0665570\pi$
$199$			5.85641i			0.415150i	−0.978219	+	0.207575i	$0.933443\pi$
$200$	−12.9282	−	3.46410i	−0.914162	−	0.244949i
$201$		0			0
$202$	2.36603	−	1.36603i	0.166473	−	0.0961132i
$203$	2.13397	+	7.96410i	0.149776	+	0.558970i
$204$		0			0
$205$	−1.50000	+	5.59808i	−0.104765	+	0.390987i
$206$	−2.83013	+	0.758330i	−0.197184	+	0.0528354i
$207$		0			0
$208$	−18.3923	+	4.92820i	−1.27528	+	0.341709i
$209$	−1.09808	−	1.90192i	−0.0759555	−	0.131559i
$210$		0			0
$211$	1.96410	−	0.526279i	0.135214	−	0.0362306i	−0.190577	−	0.981672i	$-0.561036\pi$
$211$	1.96410	−	0.526279i	0.135214	−	0.0362306i	0.325791	+	0.945442i	$0.394369\pi$
$212$	4.53590	+	4.53590i	0.311527	+	0.311527i
$213$		0			0
$214$		−	22.7846i		−	1.55752i
$215$			4.66025i			0.317827i
$216$		0			0
$217$		−	2.94744i		−	0.200085i
$218$	3.46410			0.234619
$219$		0			0
$220$	0.535898			0.0361303
$221$	−18.3923	+	4.92820i	−1.23720	+	0.331507i
$222$		0			0
$223$	−7.79423	−	13.5000i	−0.521940	−	0.904027i	−0.999674	−	0.0255224i	$-0.991875\pi$
$223$	−7.79423	−	13.5000i	−0.521940	−	0.904027i	0.477734	−	0.878504i	$-0.341458\pi$
$224$	−3.60770	+	13.4641i	−0.241049	+	0.899608i
$225$		0			0
$226$	−2.02628	−	7.56218i	−0.134786	−	0.503029i
$227$	4.62436	−	17.2583i	0.306929	−	1.14548i	−0.624343	−	0.781151i	$-0.714633\pi$
$227$	4.62436	−	17.2583i	0.306929	−	1.14548i	0.931272	−	0.364325i	$-0.118700\pi$
$228$		0			0
$229$	−2.52628	−	9.42820i	−0.166941	−	0.623033i	−0.997785	−	0.0665269i	$-0.978808\pi$
$229$	−2.52628	−	9.42820i	−0.166941	−	0.623033i	0.830843	−	0.556506i	$-0.187858\pi$
$230$	0.169873	+	0.294229i	0.0112011	+	0.0194009i
$231$		0			0
$232$	8.19615	−	4.73205i	0.538104	−	0.310674i
$233$		−	22.9282i		−	1.50208i	−0.660259	−	0.751038i	$-0.729553\pi$
$233$		−	22.9282i		−	1.50208i	0.660259	−	0.751038i	$-0.270447\pi$
$234$		0			0
$235$	3.36603	−	3.36603i	0.219575	−	0.219575i
$236$	11.1962	−	3.00000i	0.728807	−	0.195283i
$237$		0			0
$238$	−3.60770	+	13.4641i	−0.233852	+	0.872748i
$239$	5.59808	−	9.69615i	0.362109	−	0.627192i	−0.626198	−	0.779664i	$-0.715390\pi$
$239$	5.59808	−	9.69615i	0.362109	−	0.627192i	0.988308	+	0.152472i	$0.0487233\pi$
$240$		0			0
$241$	−6.23205	−	10.7942i	−0.401442	−	0.695317i	0.592458	−	0.805601i	$-0.298157\pi$
$241$	−6.23205	−	10.7942i	−0.401442	−	0.695317i	−0.993900	+	0.110284i	$0.964824\pi$
$242$	−14.6603	+	3.92820i	−0.942397	+	0.252514i
$243$		0			0
$244$	28.8564	+	7.73205i	1.84734	+	0.494994i
$245$	−0.464102	−	0.124356i	−0.0296504	−	0.00794479i
$246$		0			0
$247$	−17.4904	−	10.0981i	−1.11289	−	0.642525i
$248$	−3.26795	+	0.875644i	−0.207515	+	0.0556035i
$249$		0			0
$250$	7.12436			0.450584
$251$	−7.39230	+	7.39230i	−0.466598	+	0.466598i	−0.900811	−	0.434212i	$-0.857027\pi$
$251$	−7.39230	+	7.39230i	−0.466598	+	0.466598i	0.434212	+	0.900811i	$0.357027\pi$
$252$		0			0
$253$	0.169873	+	0.169873i	0.0106798	+	0.0106798i
$254$	−20.3923	+	20.3923i	−1.27953	+	1.27953i
$255$		0			0
$256$	16.0000			1.00000
$257$	5.16025	−	8.93782i	0.321888	−	0.557526i	−0.658990	−	0.752152i	$-0.729016\pi$
$257$	5.16025	−	8.93782i	0.321888	−	0.557526i	0.980878	+	0.194626i	$0.0623493\pi$
$258$		0			0
$259$	−6.97372	+	26.0263i	−0.433326	+	1.61719i
$260$	4.26795	−	2.46410i	0.264687	−	0.152817i
$261$		0			0
$262$	−8.56218	+	14.8301i	−0.528973	+	0.916208i
$263$	3.40192	−	1.96410i	0.209772	−	0.121112i	−0.391434	−	0.920206i	$-0.628021\pi$
$263$	3.40192	−	1.96410i	0.209772	−	0.121112i	0.601205	+	0.799095i	$0.294687\pi$
$264$		0			0
$265$	−1.43782	−	0.830127i	−0.0883247	−	0.0509943i
$266$	−12.8038	+	7.39230i	−0.785054	+	0.453251i
$267$		0			0
$268$	−0.660254	−	2.46410i	−0.0403314	−	0.150519i
$269$	−7.73205	−	7.73205i	−0.471431	−	0.471431i	0.430946	−	0.902378i	$-0.358180\pi$
$269$	−7.73205	−	7.73205i	−0.471431	−	0.471431i	−0.902378	+	0.430946i	$0.858180\pi$
$270$		0			0
$271$	−14.9282			−0.906824			−0.453412	−	0.891301i	$-0.649793\pi$
$271$	−14.9282			−0.906824			−0.453412	+	0.891301i	$0.649793\pi$
$272$	16.0000			0.970143
$273$		0			0
$274$	6.09808	−	22.7583i	0.368398	−	1.37488i
$275$	2.36603	−	0.633975i	0.142677	−	0.0382301i
$276$		0			0
$277$	13.7942	+	3.69615i	0.828815	+	0.222080i	0.648197	−	0.761473i	$-0.275523\pi$
$277$	13.7942	+	3.69615i	0.828815	+	0.222080i	0.180618	+	0.983553i	$0.442190\pi$
$278$	−5.49038	−	3.16987i	−0.329291	−	0.190116i
$279$		0			0
$280$		−	3.60770i		−	0.215601i
$281$	16.9641	−	9.79423i	1.01199	−	0.584275i	0.100219	−	0.994965i	$-0.468046\pi$
$281$	16.9641	−	9.79423i	1.01199	−	0.584275i	0.911775	+	0.410691i	$0.134712\pi$
$282$		0			0
$283$	4.16025	+	15.5263i	0.247301	+	0.922942i	0.972213	+	0.234099i	$0.0752141\pi$
$283$	4.16025	+	15.5263i	0.247301	+	0.922942i	−0.724911	+	0.688842i	$0.758119\pi$
$284$	−21.8564			−1.29694
$285$		0			0
$286$	2.46410	−	2.46410i	0.145705	−	0.145705i
$287$	27.5885			1.62850
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	−1.73205	+	1.73205i	−0.101710	+	0.101710i
$291$		0			0
$292$	1.07180			0.0627222
$293$	−3.86603	−	14.4282i	−0.225856	−	0.842905i	−0.982060	−	0.188569i	$-0.939615\pi$
$293$	−3.86603	−	14.4282i	−0.225856	−	0.842905i	0.756204	−	0.654336i	$-0.227052\pi$
$294$		0			0
$295$	−2.59808	+	1.50000i	−0.151266	+	0.0873334i
$296$	30.9282			1.79767
$297$		0			0
$298$	−18.6340	−	10.7583i	−1.07944	−	0.623213i
$299$	2.13397	+	0.571797i	0.123411	+	0.0330679i
$300$		0			0
$301$	21.4282	−	5.74167i	1.23510	−	0.330944i
$302$	2.56218	−	9.56218i	0.147437	−	0.550242i
$303$		0			0
$304$	12.0000	+	12.0000i	0.688247	+	0.688247i
$305$	−7.73205			−0.442736
$306$		0			0
$307$	−5.92820	−	5.92820i	−0.338340	−	0.338340i	0.517402	−	0.855742i	$-0.326899\pi$
$307$	−5.92820	−	5.92820i	−0.338340	−	0.338340i	−0.855742	+	0.517402i	$0.826899\pi$
$308$	−0.660254	−	2.46410i	−0.0376215	−	0.140405i
$309$		0			0
$310$	0.758330	−	0.437822i	0.0430703	−	0.0248666i
$311$	27.1865	+	15.6962i	1.54161	+	0.890047i	0.998738	+	0.0502299i	$0.0159954\pi$
$311$	27.1865	+	15.6962i	1.54161	+	0.890047i	0.542869	+	0.839817i	$0.317338\pi$
$312$		0			0
$313$	7.83975	−	4.52628i	0.443129	−	0.255840i	−0.261795	−	0.965123i	$-0.584314\pi$
$313$	7.83975	−	4.52628i	0.443129	−	0.255840i	0.704924	+	0.709283i	$0.250981\pi$
$314$	0.633975	−	1.09808i	0.0357773	−	0.0619680i
$315$		0			0
$316$	3.00000	−	1.73205i	0.168763	−	0.0974355i
$317$	0.545517	−	2.03590i	0.0306393	−	0.114347i	−0.948913	−	0.315539i	$-0.897815\pi$
$317$	0.545517	−	2.03590i	0.0306393	−	0.114347i	0.979552	+	0.201192i	$0.0644814\pi$
$318$		0			0
$319$	−0.866025	+	1.50000i	−0.0484881	+	0.0839839i
$320$	−4.00000	+	1.07180i	−0.223607	+	0.0599153i
$321$		0			0
$322$	1.14359	−	1.14359i	0.0637300	−	0.0637300i
$323$	12.0000	+	12.0000i	0.667698	+	0.667698i
$324$		0			0
$325$	15.9282	−	15.9282i	0.883538	−	0.883538i
$326$	23.8564			1.32128
$327$		0			0
$328$	−8.19615	−	30.5885i	−0.452557	−	1.68897i
$329$	−19.6244	−	11.3301i	−1.08193	−	0.624650i
$330$		0			0
$331$	−26.3564	−	7.06218i	−1.44868	−	0.388172i	−0.553115	−	0.833105i	$-0.686561\pi$
$331$	−26.3564	−	7.06218i	−1.44868	−	0.388172i	−0.895564	+	0.444933i	$0.853228\pi$
$332$	23.5885	+	6.32051i	1.29458	+	0.346883i
$333$		0			0
$334$	−13.0263	+	3.49038i	−0.712766	+	0.190985i
$335$	0.330127	+	0.571797i	0.0180368	+	0.0312406i
$336$		0			0
$337$	0.696152	−	1.20577i	0.0379218	−	0.0656826i	−0.846442	−	0.532482i	$-0.821260\pi$
$337$	0.696152	−	1.20577i	0.0379218	−	0.0656826i	0.884363	+	0.466799i	$0.154593\pi$
$338$	3.53590	−	13.1962i	0.192328	−	0.717776i
$339$		0			0
$340$	−4.00000	+	1.07180i	−0.216930	+	0.0581263i
$341$	0.437822	−	0.437822i	0.0237094	−	0.0237094i
$342$		0			0
$343$			19.5359i			1.05484i
$344$	−12.7321	−	22.0526i	−0.686466	−	1.18899i
$345$		0			0
$346$	6.56218	+	11.3660i	0.352785	+	0.611041i
$347$	5.23205	+	19.5263i	0.280871	+	1.04823i	0.951804	+	0.306707i	$0.0992273\pi$
$347$	5.23205	+	19.5263i	0.280871	+	1.04823i	−0.670933	+	0.741518i	$0.734106\pi$
$348$		0			0
$349$	−2.13397	+	7.96410i	−0.114229	+	0.426309i	−0.999228	−	0.0392843i	$-0.987492\pi$
$349$	−2.13397	+	7.96410i	−0.114229	+	0.426309i	0.884999	+	0.465593i	$0.154159\pi$
$350$	−4.26795	−	15.9282i	−0.228131	−	0.851398i
$351$		0			0
$352$	−2.53590	+	1.46410i	−0.135164	+	0.0780369i
$353$	15.2321	+	26.3827i	0.810720	+	1.40421i	0.912361	+	0.409387i	$0.134258\pi$
$353$	15.2321	+	26.3827i	0.810720	+	1.40421i	−0.101640	+	0.994821i	$0.532409\pi$
$354$		0			0
$355$	5.46410	−	1.46410i	0.290004	−	0.0777064i
$356$	23.7128			1.25678
$357$		0			0
$358$	−15.8564			−0.838037
$359$			15.0718i			0.795459i	0.917503	+	0.397730i	$0.130202\pi$
$359$			15.0718i			0.795459i	−0.917503	+	0.397730i	$0.869798\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$			8.53590i			0.448637i
$363$		0			0
$364$	−16.5885	−	16.5885i	−0.869471	−	0.869471i
$365$	−0.267949	+	0.0717968i	−0.0140251	+	0.00375801i
$366$		0			0
$367$	15.4545	+	26.7679i	0.806717	+	1.39728i	0.915125	+	0.403169i	$0.132091\pi$
$367$	15.4545	+	26.7679i	0.806717	+	1.39728i	−0.108408	+	0.994106i	$0.534575\pi$
$368$	−1.60770	−	0.928203i	−0.0838069	−	0.0483859i
$369$		0			0
$370$	−7.73205	+	2.07180i	−0.401970	+	0.107708i
$371$	−2.04552	+	7.63397i	−0.106198	+	0.396336i
$372$		0			0
$373$	3.59808	+	13.4282i	0.186301	+	0.695286i	0.994348	+	0.106168i	$0.0338581\pi$
$373$	3.59808	+	13.4282i	0.186301	+	0.695286i	−0.808047	+	0.589118i	$0.799475\pi$
$374$	−2.53590	+	1.46410i	−0.131128	+	0.0757069i
$375$		0			0
$376$	−6.73205	+	25.1244i	−0.347179	+	1.29569i
$377$			15.9282i			0.820344i
$378$		0			0
$379$	15.5885	−	15.5885i	0.800725	−	0.800725i	−0.182484	−	0.983209i	$-0.558414\pi$
$379$	15.5885	−	15.5885i	0.800725	−	0.800725i	0.983209	+	0.182484i	$0.0584137\pi$
$380$	−3.80385	−	2.19615i	−0.195133	−	0.112660i
$381$		0			0
$382$	−18.0263	−	4.83013i	−0.922305	−	0.247131i
$383$	−12.3301	+	21.3564i	−0.630040	+	1.09126i	0.357503	+	0.933912i	$0.383628\pi$
$383$	−12.3301	+	21.3564i	−0.630040	+	1.09126i	−0.987543	+	0.157349i	$0.949705\pi$
$384$		0			0
$385$	0.330127	+	0.571797i	0.0168248	+	0.0291415i
$386$	0.901924	+	3.36603i	0.0459067	+	0.171326i
$387$		0			0
$388$	−1.73205	+	1.00000i	−0.0879316	+	0.0507673i
$389$	−7.59808	−	2.03590i	−0.385238	−	0.103224i	0.0610019	−	0.998138i	$-0.480570\pi$
$389$	−7.59808	−	2.03590i	−0.385238	−	0.103224i	−0.446240	+	0.894914i	$0.647237\pi$
$390$		0			0
$391$	−1.60770	−	0.928203i	−0.0813046	−	0.0469413i
$392$	2.53590	−	0.679492i	0.128082	−	0.0343195i
$393$		0			0
$394$			20.9282i			1.05435i
$395$	−0.633975	+	0.633975i	−0.0318987	+	0.0318987i
$396$		0			0
$397$	−21.0526	−	21.0526i	−1.05660	−	1.05660i	−0.998299	−	0.0582984i	$-0.981433\pi$
$397$	−21.0526	−	21.0526i	−1.05660	−	1.05660i	−0.0582984	−	0.998299i	$-0.518567\pi$
$398$	5.85641	+	5.85641i	0.293555	+	0.293555i
$399$		0			0
$400$	−16.3923	+	9.46410i	−0.819615	+	0.473205i
$401$	−1.16025	+	2.00962i	−0.0579403	+	0.100356i	−0.893541	−	0.448982i	$-0.851787\pi$
$401$	−1.16025	+	2.00962i	−0.0579403	+	0.100356i	0.835600	+	0.549338i	$0.185120\pi$
$402$		0			0
$403$	1.47372	−	5.50000i	0.0734112	−	0.273975i
$404$	1.00000	−	3.73205i	0.0497519	−	0.185676i
$405$		0			0
$406$	10.0981	+	5.83013i	0.501159	+	0.289344i
$407$	−4.90192	+	2.83013i	−0.242979	+	0.140284i
$408$		0			0
$409$	4.62436	+	2.66987i	0.228660	+	0.132017i	0.609954	−	0.792437i	$-0.291188\pi$
$409$	4.62436	+	2.66987i	0.228660	+	0.132017i	−0.381294	+	0.924454i	$0.624521\pi$
$410$	4.09808	+	7.09808i	0.202390	+	0.350549i
$411$		0			0
$412$	−2.07180	+	3.58846i	−0.102070	+	0.176791i
$413$	10.0981	+	10.0981i	0.496894	+	0.496894i
$414$		0			0
$415$	−6.32051			−0.310262
$416$	−13.4641	+	23.3205i	−0.660132	+	1.14338i
$417$		0			0
$418$	−3.00000	−	0.803848i	−0.146735	−	0.0393175i
$419$	−1.96410	+	0.526279i	−0.0959526	+	0.0257104i	−0.306476	−	0.951878i	$-0.599150\pi$
$419$	−1.96410	+	0.526279i	−0.0959526	+	0.0257104i	0.210523	+	0.977589i	$0.432483\pi$
$420$		0			0
$421$	10.7942	+	2.89230i	0.526079	+	0.140962i	0.512077	−	0.858940i	$-0.328876\pi$
$421$	10.7942	+	2.89230i	0.526079	+	0.140962i	0.0140017	+	0.999902i	$0.495543\pi$
$422$	1.43782	−	2.49038i	0.0699921	−	0.121230i
$423$		0			0
$424$	9.07180			0.440565
$425$	−16.3923	+	9.46410i	−0.795144	+	0.459076i
$426$		0			0
$427$	9.52628	+	35.5526i	0.461009	+	1.72051i
$428$	−22.7846	−	22.7846i	−1.10134	−	1.10134i
$429$		0			0
$430$	4.66025	+	4.66025i	0.224737	+	0.224737i
$431$	−31.3205			−1.50866			−0.754328	−	0.656498i	$-0.772037\pi$
$431$	−31.3205			−1.50866			−0.754328	+	0.656498i	$0.772037\pi$
$432$		0			0
$433$	24.3923			1.17222			0.586110	−	0.810232i	$-0.300659\pi$
$433$	24.3923			1.17222			0.586110	+	0.810232i	$0.300659\pi$
$434$	−2.94744	−	2.94744i	−0.141482	−	0.141482i
$435$		0			0
$436$	3.46410	−	3.46410i	0.165900	−	0.165900i
$437$	−0.509619	−	1.90192i	−0.0243784	−	0.0909814i
$438$		0			0
$439$	18.0622	−	10.4282i	0.862061	−	0.497711i	−0.00264111	−	0.999997i	$-0.500841\pi$
$439$	18.0622	−	10.4282i	0.862061	−	0.497711i	0.864702	+	0.502286i	$0.167507\pi$
$440$	0.535898	−	0.535898i	0.0255480	−	0.0255480i
$441$		0			0
$442$	−13.4641	+	23.3205i	−0.640422	+	1.10924i
$443$	−16.1603	−	4.33013i	−0.767797	−	0.205731i	−0.146399	−	0.989226i	$-0.546768\pi$
$443$	−16.1603	−	4.33013i	−0.767797	−	0.205731i	−0.621398	+	0.783495i	$0.713435\pi$
$444$		0			0
$445$	−5.92820	+	1.58846i	−0.281024	+	0.0753001i
$446$	−21.2942	−	5.70577i	−1.00831	−	0.270176i
$447$		0			0
$448$	9.85641	+	17.0718i	0.465671	+	0.806567i
$449$	−0.679492			−0.0320672			−0.0160336	−	0.999871i	$-0.505104\pi$
$449$	−0.679492			−0.0320672			−0.0160336	+	0.999871i	$0.505104\pi$
$450$		0			0
$451$	4.09808	+	4.09808i	0.192971	+	0.192971i
$452$	−9.58846	−	5.53590i	−0.451003	−	0.260387i
$453$		0			0
$454$	−12.6340	−	21.8827i	−0.592942	−	1.02701i
$455$	5.25833	+	3.03590i	0.246514	+	0.142325i
$456$		0			0
$457$	19.0359	−	10.9904i	0.890462	−	0.514108i	0.0163683	−	0.999866i	$-0.494790\pi$
$457$	19.0359	−	10.9904i	0.890462	−	0.514108i	0.874094	+	0.485758i	$0.161456\pi$
$458$	−11.9545	−	6.90192i	−0.558596	−	0.322506i
$459$		0			0
$460$	0.464102	+	0.124356i	0.0216388	+	0.00579811i
$461$	0.598076	−	2.23205i	0.0278552	−	0.103957i	−0.950599	−	0.310423i	$-0.899529\pi$
$461$	0.598076	−	2.23205i	0.0278552	−	0.103957i	0.978454	+	0.206466i	$0.0661961\pi$
$462$		0			0
$463$	3.33013	−	5.76795i	0.154764	−	0.268059i	−0.778209	−	0.628005i	$-0.783872\pi$
$463$	3.33013	−	5.76795i	0.154764	−	0.268059i	0.932973	+	0.359946i	$0.117205\pi$
$464$	3.46410	−	12.9282i	0.160817	−	0.600177i
$465$		0			0
$466$	−22.9282	−	22.9282i	−1.06213	−	1.06213i
$467$	19.7846	+	19.7846i	0.915523	+	0.915523i	0.996700	−	0.0811771i	$-0.0258679\pi$
$467$	19.7846	+	19.7846i	0.915523	+	0.915523i	−0.0811771	+	0.996700i	$0.525868\pi$
$468$		0			0
$469$	2.22243	−	2.22243i	0.102622	−	0.102622i
$470$		−	6.73205i		−	0.310526i
$471$		0			0
$472$	8.19615	−	14.1962i	0.377258	−	0.653431i
$473$	4.03590	+	2.33013i	0.185571	+	0.107139i
$474$		0			0
$475$	−19.3923	−	5.19615i	−0.889780	−	0.238416i
$476$	9.85641	+	17.0718i	0.451768	+	0.782485i
$477$		0			0
$478$	−4.09808	−	15.2942i	−0.187442	−	0.699542i
$479$	−0.669873	−	1.16025i	−0.0306073	−	0.0530134i	0.850316	−	0.526272i	$-0.176411\pi$
$479$	−0.669873	−	1.16025i	−0.0306073	−	0.0530134i	−0.880923	+	0.473259i	$0.843077\pi$
$480$		0			0
$481$	−26.0263	+	45.0788i	−1.18670	+	2.05542i
$482$	−17.0263	−	4.56218i	−0.775526	−	0.207802i
$483$		0			0
$484$	−10.7321	+	18.5885i	−0.487820	+	0.844930i
$485$	0.366025	−	0.366025i	0.0166204	−	0.0166204i
$486$		0			0
$487$			34.7846i			1.57624i	0.615521	+	0.788121i	$0.288946\pi$
$487$			34.7846i			1.57624i	−0.615521	+	0.788121i	$0.711054\pi$
$488$	36.5885	−	21.1244i	1.65628	−	0.956255i
$489$		0			0
$490$	−0.588457	+	0.339746i	−0.0265838	+	0.0153482i
$491$	−0.500000	−	1.86603i	−0.0225647	−	0.0842125i	0.953725	−	0.300679i	$-0.0972134\pi$
$491$	−0.500000	−	1.86603i	−0.0225647	−	0.0842125i	−0.976290	+	0.216467i	$0.930547\pi$
$492$		0			0
$493$	3.46410	−	12.9282i	0.156015	−	0.582257i
$494$	−27.5885	+	7.39230i	−1.24126	+	0.332596i
$495$		0			0
$496$	−2.39230	+	4.14359i	−0.107418	+	0.186053i
$497$	−13.4641	−	23.3205i	−0.603947	−	1.04607i
$498$		0			0
$499$	−2.50000	+	0.669873i	−0.111915	+	0.0299876i	−0.314342	−	0.949310i	$-0.601784\pi$
$499$	−2.50000	+	0.669873i	−0.111915	+	0.0299876i	0.202427	+	0.979297i	$0.435117\pi$
$500$	7.12436	−	7.12436i	0.318611	−	0.318611i
$501$		0			0
$502$			14.7846i			0.659869i
$503$			13.8564i			0.617827i	0.951090	+	0.308913i	$0.0999653\pi$
$503$			13.8564i			0.617827i	−0.951090	+	0.308913i	$0.900035\pi$
$504$		0			0
$505$			1.00000i			0.0444994i
$506$	0.339746			0.0151036
$507$		0			0
$508$			40.7846i			1.80952i
$509$	21.2583	−	5.69615i	0.942259	−	0.252478i	0.245185	−	0.969476i	$-0.421151\pi$
$509$	21.2583	−	5.69615i	0.942259	−	0.252478i	0.697074	+	0.716999i	$0.254485\pi$
$510$		0			0
$511$	0.660254	+	1.14359i	0.0292079	+	0.0505896i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	−3.77757	−	14.0981i	−0.166621	−	0.621839i
$515$	0.277568	−	1.03590i	0.0122311	−	0.0456471i
$516$		0			0
$517$	−1.23205	−	4.59808i	−0.0541855	−	0.202223i
$518$	19.0526	+	33.0000i	0.837121	+	1.44994i
$519$		0			0
$520$	1.80385	−	6.73205i	0.0791039	−	0.295220i
$521$			14.1436i			0.619642i	0.950795	+	0.309821i	$0.100269\pi$
$521$			14.1436i			0.619642i	−0.950795	+	0.309821i	$0.899731\pi$
$522$		0			0
$523$	−2.12436	+	2.12436i	−0.0928916	+	0.0928916i	−0.752026	−	0.659134i	$-0.770923\pi$
$523$	−2.12436	+	2.12436i	−0.0928916	+	0.0928916i	0.659134	+	0.752026i	$0.270923\pi$
$524$	6.26795	+	23.3923i	0.273817	+	1.02190i
$525$		0			0
$526$	1.43782	−	5.36603i	0.0626920	−	0.233970i
$527$	−2.39230	+	4.14359i	−0.104210	+	0.180498i
$528$		0			0
$529$	−11.3923	−	19.7321i	−0.495318	−	0.857915i
$530$	−2.26795	+	0.607695i	−0.0985134	+	0.0263966i
$531$		0			0
$532$	−5.41154	+	20.1962i	−0.234620	+	0.875614i
$533$	51.4808	+	13.7942i	2.22988	+	0.597494i
$534$		0			0
$535$	7.22243	+	4.16987i	0.312253	+	0.180279i
$536$	−3.12436	−	1.80385i	−0.134952	−	0.0779143i
$537$		0			0
$538$	−15.4641			−0.666705
$539$	−0.339746	+	0.339746i	−0.0146339	+	0.0146339i
$540$		0			0
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	0.306856	−	0.951756i	$-0.400723\pi$
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	−0.951756	+	0.306856i	$0.900723\pi$
$542$	−14.9282	+	14.9282i	−0.641221	+	0.641221i
$543$		0			0
$544$	16.0000	−	16.0000i	0.685994	−	0.685994i
$545$	−0.633975	+	1.09808i	−0.0271565	+	0.0470364i
$546$		0			0
$547$	7.57180	−	28.2583i	0.323747	−	1.20824i	−0.591819	−	0.806071i	$-0.701590\pi$
$547$	7.57180	−	28.2583i	0.323747	−	1.20824i	0.915566	−	0.402168i	$-0.131743\pi$
$548$	−16.6603	−	28.8564i	−0.711691	−	1.23268i
$549$		0			0
$550$	1.73205	−	3.00000i	0.0738549	−	0.127920i
$551$	12.2942	−	7.09808i	0.523752	−	0.302388i
$552$		0			0
$553$	3.69615	+	2.13397i	0.157176	+	0.0907458i
$554$	17.4904	−	10.0981i	0.743095	−	0.429026i
$555$		0			0
$556$	−8.66025	+	2.32051i	−0.367277	+	0.0984115i
$557$	−27.9808	−	27.9808i	−1.18558	−	1.18558i	−0.978276	−	0.207307i	$-0.933530\pi$
$557$	−27.9808	−	27.9808i	−1.18558	−	1.18558i	−0.207307	−	0.978276i	$-0.566470\pi$
$558$		0			0
$559$	42.8564			1.81263
$560$	−3.60770	−	3.60770i	−0.152453	−	0.152453i
$561$		0			0
$562$	7.16987	−	26.7583i	0.302443	−	1.12873i
$563$	29.3564	−	7.86603i	1.23723	−	0.331513i	0.419836	−	0.907600i	$-0.362088\pi$
$563$	29.3564	−	7.86603i	1.23723	−	0.331513i	0.817389	+	0.576086i	$0.195421\pi$
$564$		0			0
$565$	2.76795	+	0.741670i	0.116448	+	0.0312023i
$566$	19.6865	+	11.3660i	0.827487	+	0.477750i
$567$		0			0
$568$	−21.8564	+	21.8564i	−0.917074	+	0.917074i
$569$	−24.4808	+	14.1340i	−1.02629	+	0.592527i	−0.915919	−	0.401364i	$-0.868536\pi$
$569$	−24.4808	+	14.1340i	−1.02629	+	0.592527i	−0.110368	+	0.993891i	$0.535203\pi$
$570$		0			0
$571$	1.44744	+	5.40192i	0.0605735	+	0.226063i	0.989576	−	0.144009i	$-0.0459995\pi$
$571$	1.44744	+	5.40192i	0.0605735	+	0.226063i	−0.929003	+	0.370073i	$0.879333\pi$
$572$		−	4.92820i		−	0.206059i
$573$		0			0
$574$	27.5885	−	27.5885i	1.15152	−	1.15152i
$575$	2.19615			0.0915859
$576$		0			0
$577$	37.1769			1.54770			0.773848	−	0.633372i	$-0.218330\pi$
$577$	37.1769			1.54770			0.773848	+	0.633372i	$0.218330\pi$
$578$	−1.00000	+	1.00000i	−0.0415945	+	0.0415945i
$579$		0			0
$580$			3.46410i			0.143839i
$581$	7.78719	+	29.0622i	0.323067	+	1.20570i
$582$		0			0
$583$	−1.43782	+	0.830127i	−0.0595485	+	0.0343803i
$584$	1.07180	−	1.07180i	0.0443513	−	0.0443513i
$585$		0			0
$586$	−18.2942	−	10.5622i	−0.755728	−	0.436320i
$587$	2.96410	+	0.794229i	0.122342	+	0.0327813i	0.319470	−	0.947596i	$-0.396495\pi$
$587$	2.96410	+	0.794229i	0.122342	+	0.0327813i	−0.197129	+	0.980378i	$0.563162\pi$
$588$		0			0
$589$	−4.90192	+	1.31347i	−0.201980	+	0.0541204i
$590$	−1.09808	+	4.09808i	−0.0452071	+	0.168715i
$591$		0			0
$592$	30.9282	−	30.9282i	1.27114	−	1.27114i
$593$	−1.46410			−0.0601234			−0.0300617	−	0.999548i	$-0.509570\pi$
$593$	−1.46410			−0.0601234			−0.0300617	+	0.999548i	$0.509570\pi$
$594$		0			0
$595$	−3.60770	−	3.60770i	−0.147901	−	0.147901i
$596$	−29.3923	+	7.87564i	−1.20396	+	0.322599i
$597$		0			0
$598$	2.70577	−	1.56218i	0.110647	−	0.0638822i
$599$	−30.3109	−	17.5000i	−1.23847	−	0.715031i	−0.269688	−	0.962948i	$-0.586921\pi$
$599$	−30.3109	−	17.5000i	−1.23847	−	0.715031i	−0.968781	+	0.247917i	$0.920254\pi$
$600$		0			0
$601$	−30.2321	+	17.4545i	−1.23319	+	0.711983i	−0.967694	−	0.252128i	$-0.918869\pi$
$601$	−30.2321	+	17.4545i	−1.23319	+	0.711983i	−0.265497	+	0.964112i	$0.585536\pi$
$602$	15.6865	−	27.1699i	0.639335	−	1.10736i
$603$		0			0
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	1.43782	−	5.36603i	0.0584558	−	0.218160i
$606$		0			0
$607$	−4.59808	+	7.96410i	−0.186630	+	0.323253i	−0.944125	−	0.329589i	$-0.893090\pi$
$607$	−4.59808	+	7.96410i	−0.186630	+	0.323253i	0.757494	+	0.652842i	$0.226423\pi$
$608$	24.0000			0.973329
$609$		0			0
$610$	−7.73205	+	7.73205i	−0.313062	+	0.313062i
$611$	−30.9545	−	30.9545i	−1.25228	−	1.25228i
$612$		0			0
$613$	−7.58846	+	7.58846i	−0.306495	+	0.306495i	−0.843548	−	0.537053i	$-0.819537\pi$
$613$	−7.58846	+	7.58846i	−0.306495	+	0.306495i	0.537053	+	0.843548i	$0.319537\pi$
$614$	−11.8564			−0.478486
$615$		0			0
$616$	−3.12436	−	1.80385i	−0.125884	−	0.0726791i
$617$	8.08846	+	4.66987i	0.325629	+	0.188002i	0.653899	−	0.756582i	$-0.273132\pi$
$617$	8.08846	+	4.66987i	0.325629	+	0.188002i	−0.328270	+	0.944584i	$0.606466\pi$
$618$		0			0
$619$	−33.0885	−	8.86603i	−1.32994	−	0.356356i	−0.477246	−	0.878770i	$-0.658365\pi$
$619$	−33.0885	−	8.86603i	−1.32994	−	0.356356i	−0.852692	+	0.522414i	$0.825031\pi$
$620$	0.320508	−	1.19615i	0.0128719	−	0.0480386i
$621$		0			0
$622$	42.8827	−	11.4904i	1.71944	−	0.460722i
$623$	14.6077	+	25.3013i	0.585245	+	1.01367i
$624$		0			0
$625$	10.5263	−	18.2321i	0.421051	−	0.729282i
$626$	3.31347	−	12.3660i	0.132433	−	0.494246i
$627$		0			0
$628$	−0.464102	−	1.73205i	−0.0185197	−	0.0691164i
$629$	30.9282	−	30.9282i	1.23319	−	1.23319i
$630$		0			0
$631$		−	32.2487i		−	1.28380i	−0.766788	−	0.641900i	$-0.778146\pi$
$631$		−	32.2487i		−	1.28380i	0.766788	−	0.641900i	$-0.221854\pi$
$632$	1.26795	−	4.73205i	0.0504363	−	0.188231i
$633$		0			0
$634$	−1.49038	−	2.58142i	−0.0591906	−	0.102521i
$635$	−2.73205	−	10.1962i	−0.108418	−	0.404622i
$636$		0			0
$637$	−1.14359	+	4.26795i	−0.0453108	+	0.169102i
$638$	0.633975	+	2.36603i	0.0250993	+	0.0936718i
$639$		0			0
$640$	−2.92820	+	5.07180i	−0.115747	+	0.200480i
$641$	−5.76795	−	9.99038i	−0.227820	−	0.394596i	0.729342	−	0.684150i	$-0.239827\pi$
$641$	−5.76795	−	9.99038i	−0.227820	−	0.394596i	−0.957162	+	0.289553i	$0.906493\pi$
$642$		0			0
$643$	1.03590	−	0.277568i	0.0408518	−	0.0109462i	−0.238335	−	0.971183i	$-0.576602\pi$
$643$	1.03590	−	0.277568i	0.0408518	−	0.0109462i	0.279187	+	0.960237i	$0.409935\pi$
$644$		−	2.28719i		−	0.0901278i
$645$		0			0
$646$	24.0000			0.944267
$647$		−	46.3923i		−	1.82387i	−0.410335	−	0.911935i	$-0.634588\pi$
$647$		−	46.3923i		−	1.82387i	0.410335	−	0.911935i	$-0.365412\pi$
$648$		0			0
$649$			3.00000i			0.117760i
$650$		−	31.8564i		−	1.24951i
$651$		0			0
$652$	23.8564	−	23.8564i	0.934289	−	0.934289i
$653$	21.3301	−	5.71539i	0.834712	−	0.223661i	0.183944	−	0.982937i	$-0.441114\pi$
$653$	21.3301	−	5.71539i	0.834712	−	0.223661i	0.650768	+	0.759276i	$0.274447\pi$
$654$		0			0
$655$	−3.13397	−	5.42820i	−0.122455	−	0.212097i
$656$	−38.7846	−	22.3923i	−1.51428	−	0.874273i
$657$		0			0
$658$	−30.9545	+	8.29423i	−1.20673	+	0.323343i
$659$	2.23205	−	8.33013i	0.0869484	−	0.324496i	−0.908728	−	0.417390i	$-0.862945\pi$
$659$	2.23205	−	8.33013i	0.0869484	−	0.324496i	0.995676	+	0.0928939i	$0.0296117\pi$
$660$		0			0
$661$	4.20577	+	15.6962i	0.163586	+	0.610510i	0.998216	+	0.0596998i	$0.0190143\pi$
$661$	4.20577	+	15.6962i	0.163586	+	0.610510i	−0.834631	+	0.550810i	$0.814319\pi$
$662$	−33.4186	+	19.2942i	−1.29885	+	0.749891i
$663$		0			0
$664$	29.9090	−	17.2679i	1.16069	−	0.670126i
$665$		−	5.41154i		−	0.209851i
$666$		0			0
$667$	−1.09808	+	1.09808i	−0.0425177	+	0.0425177i
$668$	−9.53590	+	16.5167i	−0.368955	+	0.639049i
$669$		0			0
$670$	0.901924	+	0.241670i	0.0348444	+	0.00933652i
$671$	−3.86603	+	6.69615i	−0.149246	+	0.258502i
$672$		0			0
$673$	3.83975	+	6.65064i	0.148011	+	0.256363i	0.930492	−	0.366311i	$-0.119379\pi$
$673$	3.83975	+	6.65064i	0.148011	+	0.256363i	−0.782481	+	0.622674i	$0.786046\pi$
$674$	−0.509619	−	1.90192i	−0.0196298	−	0.0732594i
$675$		0			0
$676$	−9.66025	−	16.7321i	−0.371548	−	0.643540i
$677$	−45.6506	−	12.2321i	−1.75450	−	0.470116i	−0.768920	−	0.639345i	$-0.779205\pi$
$677$	−45.6506	−	12.2321i	−1.75450	−	0.470116i	−0.985577	+	0.169229i	$0.945872\pi$
$678$		0			0
$679$	−2.13397	−	1.23205i	−0.0818944	−	0.0472818i
$680$	−2.92820	+	5.07180i	−0.112291	+	0.194495i
$681$		0			0
$682$		−	0.875644i		−	0.0335302i
$683$	5.39230	−	5.39230i	0.206331	−	0.206331i	−0.596375	−	0.802706i	$-0.703393\pi$
$683$	5.39230	−	5.39230i	0.206331	−	0.206331i	0.802706	+	0.596375i	$0.203393\pi$
$684$		0			0
$685$	6.09808	+	6.09808i	0.232996	+	0.232996i
$686$	19.5359	+	19.5359i	0.745884	+	0.745884i
$687$		0			0
$688$	−34.7846	−	9.32051i	−1.32615	−	0.355341i
$689$	−7.63397	+	13.2224i	−0.290831	+	0.503735i
$690$		0			0
$691$	4.96410	−	18.5263i	0.188843	−	0.704773i	−0.804932	−	0.593367i	$-0.797798\pi$
$691$	4.96410	−	18.5263i	0.188843	−	0.704773i	0.993775	−	0.111405i	$-0.0355352\pi$
$692$	17.9282	+	4.80385i	0.681528	+	0.182615i
$693$		0			0
$694$	24.7583	+	14.2942i	0.939813	+	0.542601i
$695$	2.00962	−	1.16025i	0.0762292	−	0.0440109i
$696$		0			0
$697$	−38.7846	−	22.3923i	−1.46907	−	0.848169i
$698$	5.83013	+	10.0981i	0.220674	+	0.382218i
$699$		0			0
$700$	−20.1962	−	11.6603i	−0.763343	−	0.440716i
$701$	21.0526	+	21.0526i	0.795144	+	0.795144i	0.982325	−	0.187181i	$-0.0599352\pi$
$701$	21.0526	+	21.0526i	0.795144	+	0.795144i	−0.187181	+	0.982325i	$0.559935\pi$
$702$		0			0
$703$	46.3923			1.74972
$704$	−1.07180	+	4.00000i	−0.0403949	+	0.150756i
$705$		0			0
$706$	41.6147	+	11.1506i	1.56619	+	0.419660i
$707$	4.59808	−	1.23205i	0.172928	−	0.0463360i
$708$		0			0
$709$	−40.1147	−	10.7487i	−1.50654	−	0.403676i	−0.591256	−	0.806484i	$-0.701368\pi$
$709$	−40.1147	−	10.7487i	−1.50654	−	0.403676i	−0.915285	+	0.402808i	$0.868034\pi$
$710$	4.00000	−	6.92820i	0.150117	−	0.260011i
$711$		0			0
$712$	23.7128	−	23.7128i	0.888675	−	0.888675i
$713$	0.480762	−	0.277568i	0.0180047	−	0.0103950i
$714$		0			0
$715$	0.330127	+	1.23205i	0.0123461	+	0.0460761i
$716$	−15.8564	+	15.8564i	−0.592582	+	0.592582i
$717$		0			0
$718$	15.0718	+	15.0718i	0.562474	+	0.562474i
$719$	−23.3205			−0.869708			−0.434854	−	0.900501i	$-0.643200\pi$
$719$	−23.3205			−0.869708			−0.434854	+	0.900501i	$0.643200\pi$
$720$		0			0
$721$	−5.10512			−0.190125
$722$	−1.00000	−	1.00000i	−0.0372161	−	0.0372161i
$723$		0			0
$724$	8.53590	+	8.53590i	0.317234	+	0.317234i
$725$	4.09808	+	15.2942i	0.152199	+	0.568013i
$726$		0			0
$727$	−9.06218	+	5.23205i	−0.336098	+	0.194046i	−0.658545	−	0.752541i	$-0.728828\pi$
$727$	−9.06218	+	5.23205i	−0.336098	+	0.194046i	0.322447	+	0.946587i	$0.395494\pi$
$728$	−33.1769			−1.22962
$729$		0			0
$730$	−0.196152	+	0.339746i	−0.00725993	+	0.0125746i
$731$	−34.7846	−	9.32051i	−1.28656	−	0.344731i
$732$		0			0
$733$	27.5263	−	7.37564i	1.01671	−	0.272426i	0.288277	−	0.957547i	$-0.406917\pi$
$733$	27.5263	−	7.37564i	1.01671	−	0.272426i	0.728429	+	0.685121i	$0.240251\pi$
$734$	42.2224	+	11.3135i	1.55846	+	0.417588i
$735$		0			0
$736$	−2.53590	+	0.679492i	−0.0934745	+	0.0250464i
$737$	0.660254			0.0243208
$738$		0			0
$739$	−29.7321	−	29.7321i	−1.09371	−	1.09371i	−0.995129	−	0.0985823i	$-0.968569\pi$
$739$	−29.7321	−	29.7321i	−1.09371	−	1.09371i	−0.0985823	−	0.995129i	$-0.531431\pi$
$740$	−5.66025	+	9.80385i	−0.208075	+	0.360397i
$741$		0			0
$742$	5.58846	+	9.67949i	0.205159	+	0.355345i
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.884072	−	0.467351i	$-0.154791\pi$
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.0372984	+	0.999304i	$0.488125\pi$
$744$		0			0
$745$	6.82051	−	3.93782i	0.249884	−	0.144271i
$746$	17.0263	+	9.83013i	0.623376	+	0.359907i
$747$		0			0
$748$	−1.07180	+	4.00000i	−0.0391888	+	0.146254i
$749$	10.2750	−	38.3468i	0.375440	−	1.40116i
$750$		0			0
$751$	4.72243	−	8.17949i	0.172324	−	0.298474i	−0.766908	−	0.641757i	$-0.778206\pi$
$751$	4.72243	−	8.17949i	0.172324	−	0.298474i	0.939232	+	0.343283i	$0.111539\pi$
$752$	18.3923	+	31.8564i	0.670698	+	1.16168i
$753$		0			0
$754$	15.9282	+	15.9282i	0.580071	+	0.580071i
$755$	2.56218	+	2.56218i	0.0932472	+	0.0932472i
$756$		0			0
$757$	8.46410	−	8.46410i	0.307633	−	0.307633i	−0.536358	−	0.843991i	$-0.680200\pi$
$757$	8.46410	−	8.46410i	0.307633	−	0.307633i	0.843991	+	0.536358i	$0.180200\pi$
$758$		−	31.1769i		−	1.13240i
$759$		0			0
$760$	−6.00000	+	1.60770i	−0.217643	+	0.0583172i
$761$	−25.2846	−	14.5981i	−0.916566	−	0.529180i	−0.0340283	−	0.999421i	$-0.510834\pi$
$761$	−25.2846	−	14.5981i	−0.916566	−	0.529180i	−0.882538	+	0.470241i	$0.844167\pi$
$762$		0			0
$763$	5.83013	+	1.56218i	0.211065	+	0.0565546i
$764$	−22.8564	+	13.1962i	−0.826916	+	0.477420i
$765$		0			0
$766$	9.02628	+	33.6865i	0.326133	+	1.21714i
$767$	13.7942	+	23.8923i	0.498081	+	0.862701i
$768$		0			0
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	−0.922207	−	0.386698i	$-0.873616\pi$
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	0.795993	+	0.605305i	$0.206949\pi$
$770$	0.901924	+	0.241670i	0.0325031	+	0.00870917i
$771$		0			0
$772$	4.26795	+	2.46410i	0.153607	+	0.0886850i
$773$	−7.58846	+	7.58846i	−0.272938	+	0.272938i	−0.830282	−	0.557344i	$-0.811821\pi$
$773$	−7.58846	+	7.58846i	−0.272938	+	0.272938i	0.557344	+	0.830282i	$0.311821\pi$
$774$		0			0
$775$		−	5.66025i		−	0.203322i
$776$	−0.732051	+	2.73205i	−0.0262791	+	0.0980749i
$777$		0			0
$778$	−9.63397	+	5.56218i	−0.345395	+	0.199414i
$779$	−12.2942	−	45.8827i	−0.440486	−	1.64392i
$780$		0			0
$781$	1.46410	−	5.46410i	0.0523897	−	0.195521i
$782$	−2.53590	+	0.679492i	−0.0906835	+	0.0242986i
$783$		0			0
$784$	1.85641	−	3.21539i	0.0663002	−	0.114835i
$785$	0.232051	+	0.401924i	0.00828225	+	0.0143453i
$786$		0			0
$787$	−33.8205	+	9.06218i	−1.20557	+	0.323032i	−0.805023	−	0.593244i	$-0.797847\pi$
$787$	−33.8205	+	9.06218i	−1.20557	+	0.323032i	−0.400548	+	0.916276i	$0.631180\pi$
$788$	20.9282	+	20.9282i	0.745536	+	0.745536i
$789$		0			0
$790$			1.26795i			0.0451116i
$791$		−	13.6410i		−	0.485019i
$792$		0			0
$793$			71.1051i			2.52502i
$794$	−42.1051			−1.49425
$795$		0			0
$796$	11.7128			0.415150
$797$	1.06218	−	0.284610i	0.0376243	−	0.0100814i	−0.239958	−	0.970783i	$-0.577134\pi$
$797$	1.06218	−	0.284610i	0.0376243	−	0.0100814i	0.277582	+	0.960702i	$0.410467\pi$
$798$		0			0
$799$	18.3923	+	31.8564i	0.650673	+	1.12700i
$800$	−6.92820	+	25.8564i	−0.244949	+	0.914162i
$801$		0			0
$802$	0.849365	+	3.16987i	0.0299921	+	0.111932i
$803$	−0.0717968	+	0.267949i	−0.00253365	+	0.00945572i
$804$		0			0
$805$	0.153212	+	0.571797i	0.00540003	+	0.0201532i
$806$	−4.02628	−	6.97372i	−0.141820	−	0.245639i
$807$		0			0
$808$	−2.73205	−	4.73205i	−0.0961132	−	0.166473i
$809$		−	32.6410i		−	1.14760i	−0.818997	−	0.573799i	$-0.805469\pi$
$809$		−	32.6410i		−	1.14760i	0.818997	−	0.573799i	$-0.194531\pi$
$810$		0			0
$811$	−11.5359	+	11.5359i	−0.405080	+	0.405080i	−0.880019	−	0.474939i	$-0.842470\pi$
$811$	−11.5359	+	11.5359i	−0.405080	+	0.405080i	0.474939	+	0.880019i	$0.342470\pi$
$812$	15.9282	−	4.26795i	0.558970	−	0.149776i
$813$		0			0
$814$	−2.07180	+	7.73205i	−0.0726164	+	0.271008i
$815$	−4.36603	+	7.56218i	−0.152935	+	0.264892i
$816$		0			0
$817$	−19.0981	−	33.0788i	−0.668157	−	1.15728i
$818$	7.29423	−	1.95448i	0.255037	−	0.0683369i
$819$		0			0
$820$	11.1962	+	3.00000i	0.390987	+	0.104765i
$821$	18.7224	+	5.01666i	0.653417	+	0.175083i	0.570273	−	0.821455i	$-0.306837\pi$
$821$	18.7224	+	5.01666i	0.653417	+	0.175083i	0.0831439	+	0.996538i	$0.473504\pi$
$822$		0			0
$823$	−6.65064	−	3.83975i	−0.231827	−	0.133845i	0.379588	−	0.925156i	$-0.376066\pi$
$823$	−6.65064	−	3.83975i	−0.231827	−	0.133845i	−0.611414	+	0.791311i	$0.709399\pi$
$824$	1.51666	+	5.66025i	0.0528354	+	0.197184i
$825$		0			0
$826$	20.1962			0.702714
$827$	10.6077	−	10.6077i	0.368866	−	0.368866i	−0.498198	−	0.867063i	$-0.666005\pi$
$827$	10.6077	−	10.6077i	0.368866	−	0.368866i	0.867063	+	0.498198i	$0.166005\pi$
$828$		0			0
$829$	−17.7321	−	17.7321i	−0.615860	−	0.615860i	0.328607	−	0.944467i	$-0.393421\pi$
$829$	−17.7321	−	17.7321i	−0.615860	−	0.615860i	−0.944467	+	0.328607i	$0.893421\pi$
$830$	−6.32051	+	6.32051i	−0.219388	+	0.219388i
$831$		0			0
$832$	9.85641	+	36.7846i	0.341709	+	1.27528i
$833$	1.85641	−	3.21539i	0.0643207	−	0.111407i
$834$		0			0
$835$	1.27757	−	4.76795i	0.0442121	−	0.165002i
$836$	−3.80385	+	2.19615i	−0.131559	+	0.0759555i
$837$		0			0
$838$	−1.43782	+	2.49038i	−0.0496687	+	0.0860288i
$839$	−29.2583	+	16.8923i	−1.01011	+	0.583187i	−0.911224	−	0.411912i	$-0.864861\pi$
$839$	−29.2583	+	16.8923i	−1.01011	+	0.583187i	−0.0988859	+	0.995099i	$0.531528\pi$
$840$		0			0
$841$	15.4186	+	8.90192i	0.531675	+	0.306963i
$842$	13.6865	−	7.90192i	0.471669	−	0.272318i
$843$		0			0
$844$	−1.05256	−	3.92820i	−0.0362306	−	0.135214i
$845$	3.53590	+	3.53590i	0.121639	+	0.121639i
$846$		0			0
$847$	−26.4449			−0.908656
$848$	9.07180	−	9.07180i	0.311527	−	0.311527i
$849$		0			0
$850$	−6.92820	+	25.8564i	−0.237635	+	0.886867i
$851$	−4.90192	+	1.31347i	−0.168036	+	0.0450251i
$852$		0			0
$853$	10.0622	+	2.69615i	0.344522	+	0.0923145i	0.426931	−	0.904284i	$-0.359595\pi$
$853$	10.0622	+	2.69615i	0.344522	+	0.0923145i	−0.0824088	+	0.996599i	$0.526261\pi$
$854$	45.0788	+	26.0263i	1.54257	+	0.890601i
$855$		0			0
$856$	−45.5692			−1.55752
$857$	−42.3564	+	24.4545i	−1.44687	+	0.835349i	−0.998293	−	0.0583966i	$-0.981401\pi$
$857$	−42.3564	+	24.4545i	−1.44687	+	0.835349i	−0.448574	+	0.893746i	$0.648068\pi$
$858$		0			0
$859$	−4.50000	−	16.7942i	−0.153538	−	0.573012i	−0.999226	−	0.0393342i	$-0.987476\pi$
$859$	−4.50000	−	16.7942i	−0.153538	−	0.573012i	0.845688	−	0.533677i	$-0.179190\pi$
$860$	9.32051			0.317827
$861$		0			0
$862$	−31.3205	+	31.3205i	−1.06678	+	1.06678i
$863$	33.4641			1.13913			0.569566	−	0.821946i	$-0.307111\pi$
$863$	33.4641			1.13913			0.569566	+	0.821946i	$0.307111\pi$
$864$		0			0
$865$	−4.80385			−0.163336
$866$	24.3923	−	24.3923i	0.828884	−	0.828884i
$867$		0			0
$868$	−5.89488			−0.200085
$869$	0.232051	+	0.866025i	0.00787178	+	0.0293779i
$870$		0			0
$871$	5.25833	−	3.03590i	0.178172	−	0.102867i
$872$		−	6.92820i		−	0.234619i
$873$		0			0
$874$	−2.41154	−	1.39230i	−0.0815716	−	0.0470954i
$875$	11.9904	+	3.21281i	0.405349	+	0.108613i
$876$		0			0
$877$	33.3827	−	8.94486i	1.12725	−	0.302047i	0.353438	−	0.935458i	$-0.385013\pi$
$877$	33.3827	−	8.94486i	1.12725	−	0.302047i	0.773815	+	0.633411i	$0.218346\pi$
$878$	7.63397	−	28.4904i	0.257634	−	0.961504i
$879$		0			0
$880$		−	1.07180i		−	0.0361303i
$881$	3.32051			0.111871			0.0559354	−	0.998434i	$-0.482186\pi$
$881$	3.32051			0.111871			0.0559354	+	0.998434i	$0.482186\pi$
$882$		0			0
$883$	−3.00000	−	3.00000i	−0.100958	−	0.100958i	0.654824	−	0.755782i	$-0.272743\pi$
$883$	−3.00000	−	3.00000i	−0.100958	−	0.100958i	−0.755782	+	0.654824i	$0.772743\pi$
$884$	9.85641	+	36.7846i	0.331507	+	1.23720i
$885$		0			0
$886$	−20.4904	+	11.8301i	−0.688388	+	0.397441i
$887$	−21.0622	−	12.1603i	−0.707199	−	0.408301i	0.102824	−	0.994700i	$-0.467212\pi$
$887$	−21.0622	−	12.1603i	−0.707199	−	0.408301i	−0.810023	+	0.586398i	$0.800545\pi$
$888$		0			0
$889$	−43.5167	+	25.1244i	−1.45950	+	0.842644i
$890$	−4.33975	+	7.51666i	−0.145469	+	0.251959i
$891$		0			0
$892$	−27.0000	+	15.5885i	−0.904027	+	0.521940i
$893$	−10.0981	+	37.6865i	−0.337919	+	1.26113i
$894$		0			0
$895$	2.90192	−	5.02628i	0.0970006	−	0.168010i
$896$	26.9282	+	7.21539i	0.899608	+	0.241049i
$897$		0			0
$898$	−0.679492	+	0.679492i	−0.0226749	+	0.0226749i
$899$	2.83013	+	2.83013i	0.0943900	+	0.0943900i
$900$		0			0
$901$	9.07180	−	9.07180i	0.302225	−	0.302225i
$902$	8.19615			0.272902
$903$		0			0
$904$	−15.1244	+	4.05256i	−0.503029	+	0.134786i
$905$	−2.70577	−	1.56218i	−0.0899429	−	0.0519285i
$906$		0			0
$907$	11.4282	+	3.06218i	0.379467	+	0.101678i	0.443510	−	0.896269i	$-0.353733\pi$
$907$	11.4282	+	3.06218i	0.379467	+	0.101678i	−0.0640432	+	0.997947i	$0.520400\pi$
$908$	−34.5167	−	9.24871i	−1.14548	−	0.306929i
$909$		0			0
$910$	8.29423	−	2.22243i	0.274951	−	0.0736729i
$911$	5.86603	+	10.1603i	0.194350	+	0.336624i	0.946687	−	0.322154i	$-0.104407\pi$
$911$	5.86603	+	10.1603i	0.194350	+	0.336624i	−0.752337	+	0.658778i	$0.771074\pi$
$912$		0			0
$913$	−3.16025	+	5.47372i	−0.104589	+	0.181154i
$914$	8.04552	−	30.0263i	0.266122	−	0.993181i
$915$		0			0
$916$	−18.8564	+	5.05256i	−0.623033	+	0.166941i
$917$	−21.0981	+	21.0981i	−0.696720	+	0.696720i
$918$		0			0
$919$		−	43.4641i		−	1.43375i	−0.697203	−	0.716874i	$-0.745572\pi$
$919$		−	43.4641i		−	1.43375i	0.697203	−	0.716874i	$-0.254428\pi$
$920$	0.588457	−	0.339746i	0.0194009	−	0.0112011i
$921$		0			0
$922$	−1.63397	−	2.83013i	−0.0538121	−	0.0932053i
$923$	−13.4641	−	50.2487i	−0.443176	−	1.65396i
$924$		0			0
$925$	−13.3923	+	49.9808i	−0.440336	+	1.64336i
$926$	−2.43782	−	9.09808i	−0.0801118	−	0.298981i
$927$		0			0
$928$	−9.46410	−	16.3923i	−0.310674	−	0.538104i
$929$	18.3564	+	31.7942i	0.602254	+	1.04313i	0.992479	+	0.122415i	$0.0390640\pi$
$929$	18.3564	+	31.7942i	0.602254	+	1.04313i	−0.390225	+	0.920720i	$0.627603\pi$
$930$		0			0
$931$	3.80385	−	1.01924i	0.124666	−	0.0334042i
$932$	−45.8564			−1.50208
$933$		0			0
$934$	39.5692			1.29474
$935$		−	1.07180i		−	0.0350515i
$936$		0			0
$937$			32.9282i			1.07572i	0.843035	+	0.537859i	$0.180767\pi$
$937$			32.9282i			1.07572i	−0.843035	+	0.537859i	$0.819233\pi$
$938$		−	4.44486i		−	0.145130i
$939$		0			0
$940$	−6.73205	−	6.73205i	−0.219575	−	0.219575i
$941$	−10.8660	+	2.91154i	−0.354222	+	0.0949136i	−0.431542	−	0.902093i	$-0.642030\pi$
$941$	−10.8660	+	2.91154i	−0.354222	+	0.0949136i	0.0773199	+	0.997006i	$0.475364\pi$
$942$		0			0
$943$	2.59808	+	4.50000i	0.0846050	+	0.146540i
$944$	−6.00000	−	22.3923i	−0.195283	−	0.728807i
$945$		0			0
$946$	6.36603	−	1.70577i	0.206977	−	0.0554594i
$947$	−4.01666	+	14.9904i	−0.130524	+	0.487122i	−0.999976	−	0.00689497i	$-0.997805\pi$
$947$	−4.01666	+	14.9904i	−0.130524	+	0.487122i	0.869452	+	0.494017i	$0.164472\pi$
$948$		0			0
$949$	0.660254	+	2.46410i	0.0214328	+	0.0799881i
$950$	−24.5885	+	14.1962i	−0.797755	+	0.460584i
$951$		0			0
$952$	26.9282	+	7.21539i	0.872748	+	0.233852i
$953$			39.4641i			1.27837i	0.769054	+	0.639184i	$0.220728\pi$
$953$			39.4641i			1.27837i	−0.769054	+	0.639184i	$0.779272\pi$
$954$		0			0
$955$	4.83013	−	4.83013i	0.156299	−	0.156299i
$956$	−19.3923	−	11.1962i	−0.627192	−	0.362109i
$957$		0			0
$958$	−1.83013	−	0.490381i	−0.0591287	−	0.0158435i
$959$	20.5263	−	35.5526i	0.662828	−	1.14805i
$960$		0			0
$961$	14.7846	+	25.6077i	0.476923	+	0.826055i
$962$	19.0526	+	71.1051i	0.614279	+	2.29252i
$963$		0			0
$964$	−21.5885	+	12.4641i	−0.695317	+	0.401442i
$965$	−1.23205	−	0.330127i	−0.0396611	−	0.0106272i
$966$		0			0
$967$	−14.9378	−	8.62436i	−0.480368	−	0.277341i	0.240202	−	0.970723i	$-0.422786\pi$
$967$	−14.9378	−	8.62436i	−0.480368	−	0.277341i	−0.720570	+	0.693382i	$0.756120\pi$
$968$	7.85641	+	29.3205i	0.252514	+	0.942397i
$969$		0			0
$970$		−	0.732051i		−	0.0235047i
$971$	−27.9808	+	27.9808i	−0.897945	+	0.897945i	−0.995254	−	0.0973088i	$-0.968977\pi$
$971$	−27.9808	+	27.9808i	−0.897945	+	0.897945i	0.0973088	+	0.995254i	$0.468977\pi$
$972$		0			0
$973$	−7.81089	−	7.81089i	−0.250406	−	0.250406i
$974$	34.7846	+	34.7846i	1.11457	+	1.11457i
$975$		0			0
$976$	15.4641	−	57.7128i	0.494994	−	1.84734i
$977$	−17.2846	+	29.9378i	−0.552984	+	0.957796i	0.445074	+	0.895494i	$0.353177\pi$
$977$	−17.2846	+	29.9378i	−0.552984	+	0.957796i	−0.998057	+	0.0623018i	$0.980156\pi$
$978$		0			0
$979$	−1.58846	+	5.92820i	−0.0507673	+	0.189466i
$980$	−0.248711	+	0.928203i	−0.00794479	+	0.0296504i
$981$		0			0
$982$	−2.36603	−	1.36603i	−0.0755029	−	0.0435916i
$983$	40.9186	−	23.6244i	1.30510	−	0.753500i	0.323826	−	0.946117i	$-0.395031\pi$
$983$	40.9186	−	23.6244i	1.30510	−	0.753500i	0.981274	+	0.192617i	$0.0616974\pi$
$984$		0			0
$985$	−6.63397	−	3.83013i	−0.211376	−	0.122038i
$986$	−9.46410	−	16.3923i	−0.301398	−	0.522037i
$987$		0			0
$988$	−20.1962	+	34.9808i	−0.642525	+	1.11289i
$989$	2.95448	+	2.95448i	0.0939471	+	0.0939471i
$990$		0			0
$991$	−23.6077			−0.749923			−0.374962	−	0.927040i	$-0.622344\pi$
$991$	−23.6077			−0.749923			−0.374962	+	0.927040i	$0.622344\pi$
$992$	1.75129	+	6.53590i	0.0556035	+	0.207515i
$993$		0			0
$994$	−36.7846	−	9.85641i	−1.16674	−	0.312626i
$995$	−2.92820	+	0.784610i	−0.0928303	+	0.0248738i
$996$		0			0
$997$	11.0622	+	2.96410i	0.350343	+	0.0938740i	0.429699	−	0.902972i	$-0.358620\pi$
$997$	11.0622	+	2.96410i	0.350343	+	0.0938740i	−0.0793561	+	0.996846i	$0.525286\pi$
$998$	−1.83013	+	3.16987i	−0.0579317	+	0.100341i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.d.253.1		4
3.2	odd	2		144.2.x.a.13.1	✓	4
4.3	odd	2		1728.2.bc.c.145.1		4
9.2	odd	6		144.2.x.d.61.1	yes	4
9.7	even	3		432.2.y.a.397.1		4
12.11	even	2		576.2.bb.a.337.1		4
16.5	even	4		432.2.y.a.37.1		4
16.11	odd	4		1728.2.bc.b.1009.1		4
36.7	odd	6		1728.2.bc.b.721.1		4
36.11	even	6		576.2.bb.b.529.1		4
48.5	odd	4		144.2.x.d.85.1	yes	4
48.11	even	4		576.2.bb.b.49.1		4
144.11	even	12		576.2.bb.a.241.1		4
144.43	odd	12		1728.2.bc.c.1585.1		4
144.101	odd	12		144.2.x.a.133.1	yes	4
144.133	even	12	inner	432.2.y.d.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.13.1	✓	4	3.2	odd	2
144.2.x.a.133.1	yes	4	144.101	odd	12
144.2.x.d.61.1	yes	4	9.2	odd	6
144.2.x.d.85.1	yes	4	48.5	odd	4
432.2.y.a.37.1		4	16.5	even	4
432.2.y.a.397.1		4	9.7	even	3
432.2.y.d.181.1		4	144.133	even	12	inner
432.2.y.d.253.1		4	1.1	even	1	trivial
576.2.bb.a.241.1		4	144.11	even	12
576.2.bb.a.337.1		4	12.11	even	2
576.2.bb.b.49.1		4	48.11	even	4
576.2.bb.b.529.1		4	36.11	even	6
1728.2.bc.b.721.1		4	36.7	odd	6
1728.2.bc.b.1009.1		4	16.11	odd	4
1728.2.bc.c.145.1		4	4.3	odd	2
1728.2.bc.c.1585.1		4	144.43	odd	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(0.133975 + 0.500000i) q^{5} +(2.13397 - 1.23205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(0.133975 + 0.500000i) q^{5} +(2.13397 - 1.23205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.633975 + 0.366025i) q^{10} +(0.500000 + 0.133975i) q^{11} +(4.59808 - 1.23205i) q^{13} +(0.901924 - 3.36603i) q^{14} -4.00000 q^{16} -4.00000 q^{17} +(-3.00000 - 3.00000i) q^{19} +(1.00000 - 0.267949i) q^{20} +(0.633975 - 0.366025i) q^{22} +(0.401924 + 0.232051i) q^{23} +(4.09808 - 2.36603i) q^{25} +(3.36603 - 5.83013i) q^{26} +(-2.46410 - 4.26795i) q^{28} +(-0.866025 + 3.23205i) q^{29} +(0.598076 - 1.03590i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-4.00000 + 4.00000i) q^{34} +(0.901924 + 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} -6.00000 q^{38} +(0.732051 - 1.26795i) q^{40} +(9.69615 + 5.59808i) q^{41} +(8.69615 + 2.33013i) q^{43} +(0.267949 - 1.00000i) q^{44} +(0.633975 - 0.169873i) q^{46} +(-4.59808 - 7.96410i) q^{47} +(-0.464102 + 0.803848i) q^{49} +(1.73205 - 6.46410i) q^{50} +(-2.46410 - 9.19615i) q^{52} +(-2.26795 + 2.26795i) q^{53} +0.267949i q^{55} +(-6.73205 - 1.80385i) q^{56} +(2.36603 + 4.09808i) q^{58} +(1.50000 + 5.59808i) q^{59} +(-3.86603 + 14.4282i) q^{61} +(-0.437822 - 1.63397i) q^{62} +8.00000i q^{64} +(1.23205 + 2.13397i) q^{65} +(1.23205 - 0.330127i) q^{67} +8.00000i q^{68} +1.80385 q^{70} -10.9282i q^{71} +0.535898i q^{73} +15.4641i q^{74} +(-6.00000 + 6.00000i) q^{76} +(1.23205 - 0.330127i) q^{77} +(0.866025 + 1.50000i) q^{79} +(-0.535898 - 2.00000i) q^{80} +(15.2942 - 4.09808i) q^{82} +(-3.16025 + 11.7942i) q^{83} +(-0.535898 - 2.00000i) q^{85} +(11.0263 - 6.36603i) q^{86} +(-0.732051 - 1.26795i) q^{88} +11.8564i q^{89} +(8.29423 - 8.29423i) q^{91} +(0.464102 - 0.803848i) q^{92} +(-12.5622 - 3.36603i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(0.339746 + 1.26795i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{5} + 12 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^5 + 12 * q^7 - 8 * q^8	\( 4 q + 4 q^{2} + 4 q^{5} + 12 q^{7} - 8 q^{8} + 6 q^{10} + 2 q^{11} + 8 q^{13} + 14 q^{14} - 16 q^{16} - 16 q^{17} - 12 q^{19} + 4 q^{20} + 6 q^{22} + 12 q^{23} + 6 q^{25} + 10 q^{26} + 4 q^{28} - 8 q^{31} - 16 q^{32} - 16 q^{34} + 14 q^{35} - 24 q^{37} - 24 q^{38} - 4 q^{40} + 18 q^{41} + 14 q^{43} + 8 q^{44} + 6 q^{46} - 8 q^{47} + 12 q^{49} + 4 q^{52} - 16 q^{53} - 20 q^{56} + 6 q^{58} + 6 q^{59} - 12 q^{61} - 26 q^{62} - 2 q^{65} - 2 q^{67} + 28 q^{70} - 24 q^{76} - 2 q^{77} - 16 q^{80} + 30 q^{82} + 22 q^{83} - 16 q^{85} + 6 q^{86} + 4 q^{88} + 2 q^{91} - 12 q^{92} - 26 q^{94} - 6 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^5 + 12 * q^7 - 8 * q^8 + 6 * q^10 + 2 * q^11 + 8 * q^13 + 14 * q^14 - 16 * q^16 - 16 * q^17 - 12 * q^19 + 4 * q^20 + 6 * q^22 + 12 * q^23 + 6 * q^25 + 10 * q^26 + 4 * q^28 - 8 * q^31 - 16 * q^32 - 16 * q^34 + 14 * q^35 - 24 * q^37 - 24 * q^38 - 4 * q^40 + 18 * q^41 + 14 * q^43 + 8 * q^44 + 6 * q^46 - 8 * q^47 + 12 * q^49 + 4 * q^52 - 16 * q^53 - 20 * q^56 + 6 * q^58 + 6 * q^59 - 12 * q^61 - 26 * q^62 - 2 * q^65 - 2 * q^67 + 28 * q^70 - 24 * q^76 - 2 * q^77 - 16 * q^80 + 30 * q^82 + 22 * q^83 - 16 * q^85 + 6 * q^86 + 4 * q^88 + 2 * q^91 - 12 * q^92 - 26 * q^94 - 6 * q^95 - 2 * q^97 + 36 * q^98

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