LMFDB - Embedded newform 432.2.y.a.37.1

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:	$1$
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			37.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	432.37
Dual form			432.2.y.a.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-0.500000 + 0.133975i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-0.500000 + 0.133975i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.633975 - 0.366025i) q^{10} +(-0.133975 + 0.500000i) q^{11} +(-1.23205 - 4.59808i) q^{13} +(2.46410 - 2.46410i) q^{14} +(2.00000 - 3.46410i) q^{16} -4.00000 q^{17} +(-3.00000 + 3.00000i) q^{19} +(-0.732051 + 0.732051i) q^{20} -0.732051i q^{22} +(-0.401924 - 0.232051i) q^{23} +(-4.09808 + 2.36603i) q^{25} +(3.36603 + 5.83013i) q^{26} +(-2.46410 + 4.26795i) q^{28} +(3.23205 + 0.866025i) q^{29} +(0.598076 - 1.03590i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(5.46410 - 1.46410i) q^{34} +(0.901924 - 0.901924i) q^{35} +(-7.73205 - 7.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(0.732051 - 1.26795i) q^{40} +(-9.69615 - 5.59808i) q^{41} +(-2.33013 + 8.69615i) q^{43} +(0.267949 + 1.00000i) q^{44} +(0.633975 + 0.169873i) q^{46} +(-4.59808 - 7.96410i) q^{47} +(-0.464102 + 0.803848i) q^{49} +(4.73205 - 4.73205i) q^{50} +(-6.73205 - 6.73205i) q^{52} +(-2.26795 - 2.26795i) q^{53} -0.267949i q^{55} +(1.80385 - 6.73205i) q^{56} -4.73205 q^{58} +(-5.59808 + 1.50000i) q^{59} +(14.4282 + 3.86603i) q^{61} +(-0.437822 + 1.63397i) q^{62} -8.00000i q^{64} +(1.23205 + 2.13397i) q^{65} +(-0.330127 - 1.23205i) q^{67} +(-6.92820 + 4.00000i) q^{68} +(-0.901924 + 1.56218i) q^{70} +10.9282i q^{71} -0.535898i q^{73} +(13.3923 + 7.73205i) q^{74} +(-2.19615 + 8.19615i) q^{76} +(-0.330127 - 1.23205i) q^{77} +(0.866025 + 1.50000i) q^{79} +(-0.535898 + 2.00000i) q^{80} +(15.2942 + 4.09808i) q^{82} +(11.7942 + 3.16025i) q^{83} +(2.00000 - 0.535898i) q^{85} -12.7321i q^{86} +(-0.732051 - 1.26795i) q^{88} -11.8564i q^{89} +(8.29423 + 8.29423i) q^{91} -0.928203 q^{92} +(9.19615 + 9.19615i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(0.339746 - 1.26795i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{5} - 12 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^5 - 12 * q^7 - 8 * q^8	$ 4 q - 2 q^{2} - 2 q^{5} - 12 q^{7} - 8 q^{8} + 6 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 8 q^{16} - 16 q^{17} - 12 q^{19} + 4 q^{20} - 12 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{28} + 6 q^{29} - 8 q^{31} + 8 q^{32} + 8 q^{34} + 14 q^{35} - 24 q^{37} + 12 q^{38} - 4 q^{40} - 18 q^{41} + 8 q^{43} + 8 q^{44} + 6 q^{46} - 8 q^{47} + 12 q^{49} + 12 q^{50} - 20 q^{52} - 16 q^{53} + 28 q^{56} - 12 q^{58} - 12 q^{59} + 30 q^{61} - 26 q^{62} - 2 q^{65} + 16 q^{67} - 14 q^{70} + 12 q^{74} + 12 q^{76} + 16 q^{77} - 16 q^{80} + 30 q^{82} + 16 q^{83} + 8 q^{85} + 4 q^{88} + 2 q^{91} + 24 q^{92} + 16 q^{94} - 6 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^5 - 12 * q^7 - 8 * q^8 + 6 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 8 * q^16 - 16 * q^17 - 12 * q^19 + 4 * q^20 - 12 * q^23 - 6 * q^25 + 10 * q^26 + 4 * q^28 + 6 * q^29 - 8 * q^31 + 8 * q^32 + 8 * q^34 + 14 * q^35 - 24 * q^37 + 12 * q^38 - 4 * q^40 - 18 * q^41 + 8 * q^43 + 8 * q^44 + 6 * q^46 - 8 * q^47 + 12 * q^49 + 12 * q^50 - 20 * q^52 - 16 * q^53 + 28 * q^56 - 12 * q^58 - 12 * q^59 + 30 * q^61 - 26 * q^62 - 2 * q^65 + 16 * q^67 - 14 * q^70 + 12 * q^74 + 12 * q^76 + 16 * q^77 - 16 * q^80 + 30 * q^82 + 16 * q^83 + 8 * q^85 + 4 * q^88 + 2 * q^91 + 24 * q^92 + 16 * 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	−0.500000	+	0.133975i	−0.223607	+	0.0599153i	−0.368883	−	0.929476i	$-0.620260\pi$
$5$	−0.500000	+	0.133975i	−0.223607	+	0.0599153i	0.145276	+	0.989391i	$0.453593\pi$
$6$		0			0
$7$	−2.13397	+	1.23205i	−0.806567	+	0.465671i	−0.845762	−	0.533560i	$-0.820854\pi$
$7$	−2.13397	+	1.23205i	−0.806567	+	0.465671i	0.0391956	+	0.999232i	$0.487520\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	0.633975	−	0.366025i	0.200480	−	0.115747i
$11$	−0.133975	+	0.500000i	−0.0403949	+	0.150756i	−0.983178	−	0.182652i	$-0.941532\pi$
$11$	−0.133975	+	0.500000i	−0.0403949	+	0.150756i	0.942783	+	0.333408i	$0.108199\pi$
$12$		0			0
$13$	−1.23205	−	4.59808i	−0.341709	−	1.27528i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−1.23205	−	4.59808i	−0.341709	−	1.27528i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	2.46410	−	2.46410i	0.658559	−	0.658559i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−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	−0.961844	−	0.273597i	$-0.911786\pi$
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	0.273597	+	0.961844i	$0.411786\pi$
$20$	−0.732051	+	0.732051i	−0.163692	+	0.163692i
$21$		0			0
$22$		−	0.732051i		−	0.156074i
$23$	−0.401924	−	0.232051i	−0.0838069	−	0.0483859i	0.457511	−	0.889204i	$-0.348741\pi$
$23$	−0.401924	−	0.232051i	−0.0838069	−	0.0483859i	−0.541318	+	0.840818i	$0.682074\pi$
$24$		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
$29$	3.23205	+	0.866025i	0.600177	+	0.160817i	0.546100	−	0.837720i	$-0.316112\pi$
$29$	3.23205	+	0.866025i	0.600177	+	0.160817i	0.0540766	+	0.998537i	$0.482778\pi$
$30$		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	$0.132408\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$		0			0
$34$	5.46410	−	1.46410i	0.937086	−	0.251091i
$35$	0.901924	−	0.901924i	0.152453	−	0.152453i
$36$		0			0
$37$	−7.73205	−	7.73205i	−1.27114	−	1.27114i	−0.945490	−	0.325651i	$-0.894416\pi$
$37$	−7.73205	−	7.73205i	−1.27114	−	1.27114i	−0.325651	−	0.945490i	$-0.605584\pi$
$38$	3.00000	−	5.19615i	0.486664	−	0.842927i
$39$		0			0
$40$	0.732051	−	1.26795i	0.115747	−	0.200480i
$41$	−9.69615	−	5.59808i	−1.51428	−	0.874273i	−0.999860	−	0.0167371i	$-0.994672\pi$
$41$	−9.69615	−	5.59808i	−1.51428	−	0.874273i	−0.514425	−	0.857536i	$-0.671994\pi$
$42$		0			0
$43$	−2.33013	+	8.69615i	−0.355341	+	1.32615i	0.524714	+	0.851279i	$0.324172\pi$
$43$	−2.33013	+	8.69615i	−0.355341	+	1.32615i	−0.880055	+	0.474872i	$0.842494\pi$
$44$	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
$50$	4.73205	−	4.73205i	0.669213	−	0.669213i
$51$		0			0
$52$	−6.73205	−	6.73205i	−0.933567	−	0.933567i
$53$	−2.26795	−	2.26795i	−0.311527	−	0.311527i	0.533974	−	0.845501i	$-0.320698\pi$
$53$	−2.26795	−	2.26795i	−0.311527	−	0.311527i	−0.845501	+	0.533974i	$0.820698\pi$
$54$		0			0
$55$		−	0.267949i		−	0.0361303i
$56$	1.80385	−	6.73205i	0.241049	−	0.899608i
$57$		0			0
$58$	−4.73205			−0.621349
$59$	−5.59808	+	1.50000i	−0.728807	+	0.195283i	−0.604098	−	0.796910i	$-0.706467\pi$
$59$	−5.59808	+	1.50000i	−0.728807	+	0.195283i	−0.124709	+	0.992193i	$0.539800\pi$
$60$		0			0
$61$	14.4282	+	3.86603i	1.84734	+	0.494994i	0.999385	−	0.0350707i	$-0.0111656\pi$
$61$	14.4282	+	3.86603i	1.84734	+	0.494994i	0.847957	+	0.530065i	$0.177832\pi$
$62$	−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
$67$	−0.330127	−	1.23205i	−0.0403314	−	0.150519i	0.942824	−	0.333292i	$-0.108159\pi$
$67$	−0.330127	−	1.23205i	−0.0403314	−	0.150519i	−0.983155	+	0.182773i	$0.941493\pi$
$68$	−6.92820	+	4.00000i	−0.840168	+	0.485071i
$69$		0			0
$70$	−0.901924	+	1.56218i	−0.107801	+	0.186716i
$71$			10.9282i			1.29694i	0.761241	+	0.648470i	$0.224591\pi$
$71$			10.9282i			1.29694i	−0.761241	+	0.648470i	$0.775409\pi$
$72$		0			0
$73$		−	0.535898i		−	0.0627222i	−0.999508	−	0.0313611i	$-0.990016\pi$
$73$		−	0.535898i		−	0.0627222i	0.999508	−	0.0313611i	$-0.00998418\pi$
$74$	13.3923	+	7.73205i	1.55682	+	0.898833i
$75$		0			0
$76$	−2.19615	+	8.19615i	−0.251916	+	0.940163i
$77$	−0.330127	−	1.23205i	−0.0376215	−	0.140405i
$78$		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
$83$	11.7942	+	3.16025i	1.29458	+	0.346883i	0.839400	−	0.543514i	$-0.182907\pi$
$83$	11.7942	+	3.16025i	1.29458	+	0.346883i	0.455185	+	0.890397i	$0.349573\pi$
$84$		0			0
$85$	2.00000	−	0.535898i	0.216930	−	0.0581263i
$86$		−	12.7321i		−	1.37293i
$87$		0			0
$88$	−0.732051	−	1.26795i	−0.0780369	−	0.135164i
$89$		−	11.8564i		−	1.25678i	−0.777900	−	0.628388i	$-0.783715\pi$
$89$		−	11.8564i		−	1.25678i	0.777900	−	0.628388i	$-0.216285\pi$
$90$		0			0
$91$	8.29423	+	8.29423i	0.869471	+	0.869471i
$92$	−0.928203			−0.0967719
$93$		0			0
$94$	9.19615	+	9.19615i	0.948511	+	0.948511i
$95$	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
$101$	−0.500000	+	1.86603i	−0.0497519	+	0.185676i	−0.986330	−	0.164783i	$-0.947308\pi$
$101$	−0.500000	+	1.86603i	−0.0497519	+	0.185676i	0.936578	+	0.350459i	$0.113974\pi$
$102$		0			0
$103$	1.79423	+	1.03590i	0.176791	+	0.102070i	0.585784	−	0.810467i	$-0.300787\pi$
$103$	1.79423	+	1.03590i	0.176791	+	0.102070i	−0.408993	+	0.912537i	$0.634120\pi$
$104$	11.6603	+	6.73205i	1.14338	+	0.660132i
$105$		0			0
$106$	3.92820	+	2.26795i	0.381541	+	0.220283i
$107$	11.3923	+	11.3923i	1.10134	+	1.10134i	0.994250	+	0.107086i	$0.0341520\pi$
$107$	11.3923	+	11.3923i	1.10134	+	1.10134i	0.107086	+	0.994250i	$0.465848\pi$
$108$		0			0
$109$	1.73205	−	1.73205i	0.165900	−	0.165900i	−0.619274	−	0.785175i	$-0.712573\pi$
$109$	1.73205	−	1.73205i	0.165900	−	0.165900i	0.785175	+	0.619274i	$0.212573\pi$
$110$	0.0980762	+	0.366025i	0.00935120	+	0.0348992i
$111$		0			0
$112$			9.85641i			0.931343i
$113$	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
$115$	0.232051	+	0.0621778i	0.0216388	+	0.00579811i
$116$	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
$122$	−21.1244			−1.91251
$123$		0			0
$124$		−	2.39230i		−	0.214835i
$125$	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	$0.859952\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$		0			0
$130$	−2.46410	−	2.46410i	−0.216116	−	0.216116i
$131$	3.13397	+	11.6962i	0.273817	+	1.02190i	0.956630	+	0.291305i	$0.0940894\pi$
$131$	3.13397	+	11.6962i	0.273817	+	1.02190i	−0.682814	+	0.730593i	$0.739244\pi$
$132$		0			0
$133$	2.70577	−	10.0981i	0.234620	−	0.875614i
$134$	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	−0.967589	−	0.252531i	$-0.918737\pi$
$137$	−14.4282	+	8.33013i	−1.23268	+	0.711691i	−0.265096	+	0.964222i	$0.585404\pi$
$138$		0			0
$139$	4.33013	−	1.16025i	0.367277	−	0.0984115i	−0.0704603	−	0.997515i	$-0.522447\pi$
$139$	4.33013	−	1.16025i	0.367277	−	0.0984115i	0.437737	+	0.899103i	$0.355780\pi$
$140$	0.660254	−	2.46410i	0.0558017	−	0.208255i
$141$		0			0
$142$	−4.00000	−	14.9282i	−0.335673	−	1.25275i
$143$	2.46410			0.206059
$144$		0			0
$145$	−1.73205			−0.143839
$146$	0.196152	+	0.732051i	0.0162337	+	0.0605850i
$147$		0			0
$148$	−21.1244	−	5.66025i	−1.73641	−	0.465270i
$149$	14.6962	−	3.93782i	1.20396	−	0.322599i	0.399568	−	0.916704i	$-0.369160\pi$
$149$	14.6962	−	3.93782i	1.20396	−	0.322599i	0.804388	+	0.594105i	$0.202493\pi$
$150$		0			0
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	−0.725956	−	0.687741i	$-0.758602\pi$
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	0.232623	+	0.972567i	$0.425269\pi$
$152$		−	12.0000i		−	0.973329i
$153$		0			0
$154$	0.901924	+	1.56218i	0.0726791	+	0.125884i
$155$	−0.160254	+	0.598076i	−0.0128719	+	0.0480386i
$156$		0			0
$157$	−0.232051	−	0.866025i	−0.0185197	−	0.0691164i	0.956048	−	0.293212i	$-0.0947240\pi$
$157$	−0.232051	−	0.866025i	−0.0185197	−	0.0691164i	−0.974567	+	0.224095i	$0.928057\pi$
$158$	−1.73205	−	1.73205i	−0.137795	−	0.137795i
$159$		0			0
$160$		−	2.92820i		−	0.231495i
$161$	1.14359			0.0901278
$162$		0			0
$163$	11.9282	−	11.9282i	0.934289	−	0.934289i	−0.0636813	−	0.997970i	$-0.520284\pi$
$163$	11.9282	−	11.9282i	0.934289	−	0.934289i	0.997970	+	0.0636813i	$0.0202841\pi$
$164$	−22.3923			−1.74855
$165$		0			0
$166$	−17.2679			−1.34025
$167$	8.25833	+	4.76795i	0.639049	+	0.368955i	0.784248	−	0.620447i	$-0.213049\pi$
$167$	8.25833	+	4.76795i	0.639049	+	0.368955i	−0.145199	+	0.989402i	$0.546382\pi$
$168$		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
$173$	8.96410	+	2.40192i	0.681528	+	0.182615i	0.582942	−	0.812514i	$-0.301901\pi$
$173$	8.96410	+	2.40192i	0.681528	+	0.182615i	0.0985859	+	0.995129i	$0.468568\pi$
$174$		0			0
$175$	5.83013	−	10.0981i	0.440716	−	0.763343i
$176$	1.46410	+	1.46410i	0.110361	+	0.110361i
$177$		0			0
$178$	4.33975	+	16.1962i	0.325278	+	1.21395i
$179$	−7.92820	+	7.92820i	−0.592582	+	0.592582i	−0.938328	−	0.345746i	$-0.887626\pi$
$179$	−7.92820	+	7.92820i	−0.592582	+	0.592582i	0.345746	+	0.938328i	$0.387626\pi$
$180$		0			0
$181$	−4.26795	−	4.26795i	−0.317234	−	0.317234i	0.530470	−	0.847704i	$-0.322016\pi$
$181$	−4.26795	−	4.26795i	−0.317234	−	0.317234i	−0.847704	+	0.530470i	$0.822016\pi$
$182$	−14.3660	−	8.29423i	−1.06488	−	0.614809i
$183$		0			0
$184$	1.26795	−	0.339746i	0.0934745	−	0.0250464i
$185$	4.90192	+	2.83013i	0.360397	+	0.208075i
$186$		0			0
$187$	0.535898	−	2.00000i	0.0391888	−	0.146254i
$188$	−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	$0.194933\pi$
$194$	1.00000	+	1.00000i	0.0717958	+	0.0717958i
$195$		0			0
$196$			1.85641i			0.132600i
$197$	−10.4641	−	10.4641i	−0.745536	−	0.745536i	0.228101	−	0.973637i	$-0.426748\pi$
$197$	−10.4641	−	10.4641i	−0.745536	−	0.745536i	−0.973637	+	0.228101i	$0.926748\pi$
$198$		0			0
$199$		−	5.85641i		−	0.415150i	−0.978219	−	0.207575i	$-0.933443\pi$
$199$		−	5.85641i		−	0.415150i	0.978219	−	0.207575i	$-0.0665570\pi$
$200$	3.46410	−	12.9282i	0.244949	−	0.914162i
$201$		0			0
$202$		−	2.73205i		−	0.192226i
$203$	−7.96410	+	2.13397i	−0.558970	+	0.149776i
$204$		0			0
$205$	5.59808	+	1.50000i	0.390987	+	0.104765i
$206$	−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
$211$	−0.526279	−	1.96410i	−0.0362306	−	0.135214i	0.945442	−	0.325791i	$-0.105631\pi$
$211$	−0.526279	−	1.96410i	−0.0362306	−	0.135214i	−0.981672	+	0.190577i	$0.938964\pi$
$212$	−6.19615	−	1.66025i	−0.425553	−	0.114027i
$213$		0			0
$214$	−19.7321	−	11.3923i	−1.34886	−	0.778762i
$215$		−	4.66025i		−	0.317827i
$216$		0			0
$217$			2.94744i			0.200085i
$218$	−1.73205	+	3.00000i	−0.117309	+	0.203186i
$219$		0			0
$220$	−0.267949	−	0.464102i	−0.0180651	−	0.0312897i
$221$	4.92820	+	18.3923i	0.331507	+	1.23720i
$222$		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
$227$	−17.2583	−	4.62436i	−1.14548	−	0.306929i	−0.364325	−	0.931272i	$-0.618700\pi$
$227$	−17.2583	−	4.62436i	−1.14548	−	0.306929i	−0.781151	+	0.624343i	$0.785367\pi$
$228$		0			0
$229$	9.42820	−	2.52628i	0.623033	−	0.166941i	0.0665269	−	0.997785i	$-0.478808\pi$
$229$	9.42820	−	2.52628i	0.623033	−	0.166941i	0.556506	+	0.830843i	$0.312142\pi$
$230$	−0.339746			−0.0224022
$231$		0			0
$232$	−8.19615	+	4.73205i	−0.538104	+	0.310674i
$233$			22.9282i			1.50208i	0.660259	+	0.751038i	$0.270447\pi$
$233$			22.9282i			1.50208i	−0.660259	+	0.751038i	$0.729553\pi$
$234$		0			0
$235$	3.36603	+	3.36603i	0.219575	+	0.219575i
$236$	−8.19615	+	8.19615i	−0.533524	+	0.533524i
$237$		0			0
$238$	−9.85641	+	9.85641i	−0.638896	+	0.638896i
$239$	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
$245$	0.124356	−	0.464102i	0.00794479	−	0.0296504i
$246$		0			0
$247$	17.4904	+	10.0981i	1.11289	+	0.642525i
$248$	0.875644	+	3.26795i	0.0556035	+	0.207515i
$249$		0			0
$250$	−3.56218	+	6.16987i	−0.225292	+	0.390217i
$251$	−7.39230	−	7.39230i	−0.466598	−	0.466598i	0.434212	−	0.900811i	$-0.357027\pi$
$251$	−7.39230	−	7.39230i	−0.466598	−	0.466598i	−0.900811	+	0.434212i	$0.857027\pi$
$252$		0			0
$253$	0.169873	−	0.169873i	0.0106798	−	0.0106798i
$254$	27.8564	−	7.46410i	1.74787	−	0.468339i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	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
$259$	26.0263	+	6.97372i	1.61719	+	0.433326i
$260$	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	−0.601205	−	0.799095i	$-0.705313\pi$
$263$	−3.40192	+	1.96410i	−0.209772	+	0.121112i	0.391434	+	0.920206i	$0.371979\pi$
$264$		0			0
$265$	1.43782	+	0.830127i	0.0883247	+	0.0509943i
$266$			14.7846i			0.906503i
$267$		0			0
$268$	−1.80385	−	1.80385i	−0.110188	−	0.110188i
$269$	−7.73205	+	7.73205i	−0.471431	+	0.471431i	−0.902378	−	0.430946i	$-0.858180\pi$
$269$	−7.73205	+	7.73205i	−0.471431	+	0.471431i	0.430946	+	0.902378i	$0.358180\pi$
$270$		0			0
$271$	−14.9282			−0.906824			−0.453412	−	0.891301i	$-0.649793\pi$
$271$	−14.9282			−0.906824			−0.453412	+	0.891301i	$0.649793\pi$
$272$	−8.00000	+	13.8564i	−0.485071	+	0.840168i
$273$		0			0
$274$	16.6603	−	16.6603i	1.00648	−	1.00648i
$275$	−0.633975	−	2.36603i	−0.0382301	−	0.142677i
$276$		0			0
$277$	−3.69615	+	13.7942i	−0.222080	+	0.828815i	0.761473	+	0.648197i	$0.224477\pi$
$277$	−3.69615	+	13.7942i	−0.222080	+	0.828815i	−0.983553	+	0.180618i	$0.942190\pi$
$278$	−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	−0.911775	−	0.410691i	$-0.865288\pi$
$281$	−16.9641	+	9.79423i	−1.01199	+	0.584275i	−0.100219	+	0.994965i	$0.531954\pi$
$282$		0			0
$283$	−15.5263	+	4.16025i	−0.922942	+	0.247301i	−0.688842	−	0.724911i	$-0.741881\pi$
$283$	−15.5263	+	4.16025i	−0.922942	+	0.247301i	−0.234099	+	0.972213i	$0.575214\pi$
$284$	10.9282	+	18.9282i	0.648470	+	1.12318i
$285$		0			0
$286$	−3.36603	+	0.901924i	−0.199037	+	0.0533319i
$287$	27.5885			1.62850
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	2.36603	−	0.633975i	0.138938	−	0.0372283i
$291$		0			0
$292$	−0.535898	−	0.928203i	−0.0313611	−	0.0543190i
$293$	14.4282	−	3.86603i	0.842905	−	0.225856i	0.188569	−	0.982060i	$-0.439615\pi$
$293$	14.4282	−	3.86603i	0.842905	−	0.225856i	0.654336	+	0.756204i	$0.272948\pi$
$294$		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
$299$	−0.571797	+	2.13397i	−0.0330679	+	0.123411i
$300$		0			0
$301$	−5.74167	−	21.4282i	−0.330944	−	1.23510i
$302$	7.00000	−	7.00000i	0.402805	−	0.402805i
$303$		0			0
$304$	4.39230	+	16.3923i	0.251916	+	0.940163i
$305$	−7.73205			−0.442736
$306$		0			0
$307$	−5.92820	+	5.92820i	−0.338340	+	0.338340i	−0.855742	−	0.517402i	$-0.826899\pi$
$307$	−5.92820	+	5.92820i	−0.338340	+	0.338340i	0.517402	+	0.855742i	$0.326899\pi$
$308$	−1.80385	−	1.80385i	−0.102784	−	0.102784i
$309$		0			0
$310$		−	0.875644i		−	0.0497333i
$311$	−27.1865	−	15.6962i	−1.54161	−	0.890047i	−0.998738	−	0.0502299i	$-0.984005\pi$
$311$	−27.1865	−	15.6962i	−1.54161	−	0.890047i	−0.542869	−	0.839817i	$-0.682662\pi$
$312$		0			0
$313$	−7.83975	+	4.52628i	−0.443129	+	0.255840i	−0.704924	−	0.709283i	$-0.749019\pi$
$313$	−7.83975	+	4.52628i	−0.443129	+	0.255840i	0.261795	+	0.965123i	$0.415686\pi$
$314$	0.633975	+	1.09808i	0.0357773	+	0.0619680i
$315$		0			0
$316$	3.00000	+	1.73205i	0.168763	+	0.0974355i
$317$	−2.03590	−	0.545517i	−0.114347	−	0.0306393i	0.201192	−	0.979552i	$-0.435519\pi$
$317$	−2.03590	−	0.545517i	−0.114347	−	0.0306393i	−0.315539	+	0.948913i	$0.602185\pi$
$318$		0			0
$319$	−0.866025	+	1.50000i	−0.0484881	+	0.0839839i
$320$	1.07180	+	4.00000i	0.0599153	+	0.223607i
$321$		0			0
$322$	−1.56218	+	0.418584i	−0.0870568	+	0.0233268i
$323$	12.0000	−	12.0000i	0.667698	−	0.667698i
$324$		0			0
$325$	15.9282	+	15.9282i	0.883538	+	0.883538i
$326$	−11.9282	+	20.6603i	−0.660642	+	1.14427i
$327$		0			0
$328$	30.5885	−	8.19615i	1.68897	−	0.452557i
$329$	19.6244	+	11.3301i	1.08193	+	0.624650i
$330$		0			0
$331$	7.06218	−	26.3564i	0.388172	−	1.44868i	−0.444933	−	0.895564i	$-0.646772\pi$
$331$	7.06218	−	26.3564i	0.388172	−	1.44868i	0.833105	−	0.553115i	$-0.186561\pi$
$332$	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	$0.154593\pi$
$338$	9.66025	−	9.66025i	0.525449	−	0.525449i
$339$		0			0
$340$	2.92820	−	2.92820i	0.158804	−	0.158804i
$341$	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
$346$	−13.1244			−0.705570
$347$	−19.5263	+	5.23205i	−1.04823	+	0.280871i	−0.741518	−	0.670933i	$-0.765894\pi$
$347$	−19.5263	+	5.23205i	−1.04823	+	0.280871i	−0.306707	+	0.951804i	$0.599227\pi$
$348$		0			0
$349$	7.96410	+	2.13397i	0.426309	+	0.114229i	0.465593	−	0.884999i	$-0.345841\pi$
$349$	7.96410	+	2.13397i	0.426309	+	0.114229i	−0.0392843	+	0.999228i	$0.512508\pi$
$350$	−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
$355$	−1.46410	−	5.46410i	−0.0777064	−	0.290004i
$356$	−11.8564	−	20.5359i	−0.628388	−	1.08840i
$357$		0			0
$358$	7.92820	−	13.7321i	0.419019	−	0.725761i
$359$		−	15.0718i		−	0.795459i	−0.917503	−	0.397730i	$-0.869798\pi$
$359$		−	15.0718i		−	0.795459i	0.917503	−	0.397730i	$-0.130202\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$	7.39230	+	4.26795i	0.388531	+	0.224318i
$363$		0			0
$364$	22.6603	+	6.07180i	1.18772	+	0.318249i
$365$	0.0717968	+	0.267949i	0.00375801	+	0.0140251i
$366$		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
$371$	7.63397	+	2.04552i	0.396336	+	0.106198i
$372$		0			0
$373$	−13.4282	+	3.59808i	−0.695286	+	0.186301i	−0.589118	−	0.808047i	$-0.700525\pi$
$373$	−13.4282	+	3.59808i	−0.695286	+	0.186301i	−0.106168	+	0.994348i	$0.533858\pi$
$374$			2.92820i			0.151414i
$375$		0			0
$376$	25.1244	+	6.73205i	1.29569	+	0.347179i
$377$		−	15.9282i		−	0.820344i
$378$		0			0
$379$	15.5885	+	15.5885i	0.800725	+	0.800725i	0.983209	−	0.182484i	$-0.0584137\pi$
$379$	15.5885	+	15.5885i	0.800725	+	0.800725i	−0.182484	+	0.983209i	$0.558414\pi$
$380$		−	4.39230i		−	0.225320i
$381$		0			0
$382$	13.1962	+	13.1962i	0.675174	+	0.675174i
$383$	−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
$389$	2.03590	−	7.59808i	0.103224	−	0.385238i	−0.894914	−	0.446240i	$-0.852763\pi$
$389$	2.03590	−	7.59808i	0.103224	−	0.385238i	0.998138	+	0.0610019i	$0.0194296\pi$
$390$		0			0
$391$	1.60770	+	0.928203i	0.0813046	+	0.0469413i
$392$	−0.679492	−	2.53590i	−0.0343195	−	0.128082i
$393$		0			0
$394$	18.1244	+	10.4641i	0.913092	+	0.527174i
$395$	−0.633975	−	0.633975i	−0.0318987	−	0.0318987i
$396$		0			0
$397$	−21.0526	+	21.0526i	−1.05660	+	1.05660i	−0.0582984	+	0.998299i	$0.518567\pi$
$397$	−21.0526	+	21.0526i	−1.05660	+	1.05660i	−0.998299	+	0.0582984i	$0.981433\pi$
$398$	2.14359	+	8.00000i	0.107449	+	0.401004i
$399$		0			0
$400$			18.9282i			0.946410i
$401$	−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
$403$	−5.50000	−	1.47372i	−0.273975	−	0.0734112i
$404$	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	0.381294	−	0.924454i	$-0.375479\pi$
$409$	−4.62436	−	2.66987i	−0.228660	−	0.132017i	−0.609954	+	0.792437i	$0.708812\pi$
$410$	−8.19615			−0.404779
$411$		0			0
$412$	4.14359			0.204140
$413$	10.0981	−	10.0981i	0.496894	−	0.496894i
$414$		0			0
$415$	−6.32051			−0.310262
$416$	26.9282			1.32026
$417$		0			0
$418$	2.19615	+	2.19615i	0.107417	+	0.107417i
$419$	0.526279	+	1.96410i	0.0257104	+	0.0959526i	0.977589	−	0.210523i	$-0.0675168\pi$
$419$	0.526279	+	1.96410i	0.0257104	+	0.0959526i	−0.951878	+	0.306476i	$0.900850\pi$
$420$		0			0
$421$	−2.89230	+	10.7942i	−0.140962	+	0.526079i	0.858940	+	0.512077i	$0.171124\pi$
$421$	−2.89230	+	10.7942i	−0.140962	+	0.526079i	−0.999902	+	0.0140017i	$0.995543\pi$
$422$	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
$427$	−35.5526	+	9.52628i	−1.72051	+	0.461009i
$428$	31.1244	+	8.33975i	1.50445	+	0.403117i
$429$		0			0
$430$	1.70577	+	6.36603i	0.0822596	+	0.306997i
$431$	−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	$0.300659\pi$
$434$	−1.07884	−	4.02628i	−0.0517859	−	0.193268i
$435$		0			0
$436$	1.26795	−	4.73205i	0.0607238	−	0.226624i
$437$	1.90192	−	0.509619i	0.0909814	−	0.0243784i
$438$		0			0
$439$	−18.0622	+	10.4282i	−0.862061	+	0.497711i	−0.864702	−	0.502286i	$-0.832493\pi$
$439$	−18.0622	+	10.4282i	−0.862061	+	0.497711i	0.00264111	+	0.999997i	$0.499159\pi$
$440$	0.535898	+	0.535898i	0.0255480	+	0.0255480i
$441$		0			0
$442$	−13.4641	−	23.3205i	−0.640422	−	1.10924i
$443$	4.33013	−	16.1603i	0.205731	−	0.767797i	−0.783495	−	0.621398i	$-0.786565\pi$
$443$	4.33013	−	16.1603i	0.205731	−	0.767797i	0.989226	−	0.146399i	$-0.0467683\pi$
$444$		0			0
$445$	1.58846	+	5.92820i	0.0753001	+	0.281024i
$446$	15.5885	+	15.5885i	0.738135	+	0.738135i
$447$		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
$452$		−	11.0718i		−	0.520774i
$453$		0			0
$454$	25.2679			1.18588
$455$	−5.25833	−	3.03590i	−0.246514	−	0.142325i
$456$		0			0
$457$	−19.0359	+	10.9904i	−0.890462	+	0.514108i	−0.874094	−	0.485758i	$-0.838544\pi$
$457$	−19.0359	+	10.9904i	−0.890462	+	0.514108i	−0.0163683	+	0.999866i	$0.505210\pi$
$458$	−11.9545	+	6.90192i	−0.558596	+	0.322506i
$459$		0			0
$460$	0.464102	−	0.124356i	0.0216388	−	0.00579811i
$461$	−2.23205	−	0.598076i	−0.103957	−	0.0278552i	0.206466	−	0.978454i	$-0.433804\pi$
$461$	−2.23205	−	0.598076i	−0.103957	−	0.0278552i	−0.310423	+	0.950599i	$0.600471\pi$
$462$		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	$0.117205\pi$
$464$	9.46410	−	9.46410i	0.439360	−	0.439360i
$465$		0			0
$466$	−8.39230	−	31.3205i	−0.388766	−	1.45089i
$467$	19.7846	−	19.7846i	0.915523	−	0.915523i	−0.0811771	−	0.996700i	$-0.525868\pi$
$467$	19.7846	−	19.7846i	0.915523	−	0.915523i	0.996700	+	0.0811771i	$0.0258679\pi$
$468$		0			0
$469$	2.22243	+	2.22243i	0.102622	+	0.102622i
$470$	−5.83013	−	3.36603i	−0.268924	−	0.155263i
$471$		0			0
$472$	8.19615	−	14.1962i	0.377258	−	0.653431i
$473$	−4.03590	−	2.33013i	−0.185571	−	0.107139i
$474$		0			0
$475$	5.19615	−	19.3923i	0.238416	−	0.889780i
$476$	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
$482$	12.4641	+	12.4641i	0.567724	+	0.567724i
$483$		0			0
$484$	21.4641			0.975641
$485$	0.366025	+	0.366025i	0.0166204	+	0.0166204i
$486$		0			0
$487$		−	34.7846i		−	1.57624i	−0.615521	−	0.788121i	$-0.711054\pi$
$487$		−	34.7846i		−	1.57624i	0.615521	−	0.788121i	$-0.288946\pi$
$488$	−36.5885	+	21.1244i	−1.65628	+	0.956255i
$489$		0			0
$490$			0.679492i			0.0306963i
$491$	1.86603	−	0.500000i	0.0842125	−	0.0225647i	−0.216467	−	0.976290i	$-0.569453\pi$
$491$	1.86603	−	0.500000i	0.0842125	−	0.0225647i	0.300679	+	0.953725i	$0.402787\pi$
$492$		0			0
$493$	−12.9282	−	3.46410i	−0.582257	−	0.156015i
$494$	−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
$499$	0.669873	+	2.50000i	0.0299876	+	0.111915i	0.979297	−	0.202427i	$-0.0648828\pi$
$499$	0.669873	+	2.50000i	0.0299876	+	0.111915i	−0.949310	+	0.314342i	$0.898216\pi$
$500$	2.60770	−	9.73205i	0.116620	−	0.435231i
$501$		0			0
$502$	12.8038	+	7.39230i	0.571464	+	0.329935i
$503$		−	13.8564i		−	0.617827i	−0.951090	−	0.308913i	$-0.900035\pi$
$503$		−	13.8564i		−	0.617827i	0.951090	−	0.308913i	$-0.0999653\pi$
$504$		0			0
$505$		−	1.00000i		−	0.0444994i
$506$	−0.169873	+	0.294229i	−0.00755178	+	0.0130801i
$507$		0			0
$508$	−35.3205	+	20.3923i	−1.56709	+	0.904762i
$509$	−5.69615	−	21.2583i	−0.252478	−	0.942259i	−0.969476	−	0.245185i	$-0.921151\pi$
$509$	−5.69615	−	21.2583i	−0.252478	−	0.942259i	0.716999	−	0.697074i	$-0.245515\pi$
$510$		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
$515$	−1.03590	−	0.277568i	−0.0456471	−	0.0122311i
$516$		0			0
$517$	4.59808	−	1.23205i	0.202223	−	0.0541855i
$518$	−38.1051			−1.67424
$519$		0			0
$520$	−6.73205	−	1.80385i	−0.295220	−	0.0791039i
$521$		−	14.1436i		−	0.619642i	−0.950795	−	0.309821i	$-0.899731\pi$
$521$		−	14.1436i		−	0.619642i	0.950795	−	0.309821i	$-0.100269\pi$
$522$		0			0
$523$	−2.12436	−	2.12436i	−0.0928916	−	0.0928916i	0.659134	−	0.752026i	$-0.270923\pi$
$523$	−2.12436	−	2.12436i	−0.0928916	−	0.0928916i	−0.752026	+	0.659134i	$0.770923\pi$
$524$	17.1244	+	17.1244i	0.748081	+	0.748081i
$525$		0			0
$526$	3.92820	−	3.92820i	0.171278	−	0.171278i
$527$	−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
$533$	−13.7942	+	51.4808i	−0.597494	+	2.22988i
$534$		0			0
$535$	−7.22243	−	4.16987i	−0.312253	−	0.180279i
$536$	3.12436	+	1.80385i	0.134952	+	0.0779143i
$537$		0			0
$538$	7.73205	−	13.3923i	0.333352	−	0.577383i
$539$	−0.339746	−	0.339746i	−0.0146339	−	0.0146339i
$540$		0			0
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	−0.951756	−	0.306856i	$-0.900723\pi$
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	0.306856	+	0.951756i	$0.400723\pi$
$542$	20.3923	−	5.46410i	0.875924	−	0.234703i
$543$		0			0
$544$	5.85641	−	21.8564i	0.251091	−	0.937086i
$545$	−0.633975	+	1.09808i	−0.0271565	+	0.0470364i
$546$		0			0
$547$	−28.2583	−	7.57180i	−1.20824	−	0.323747i	−0.402168	−	0.915566i	$-0.631743\pi$
$547$	−28.2583	−	7.57180i	−1.20824	−	0.323747i	−0.806071	+	0.591819i	$0.798410\pi$
$548$	−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
$554$		−	20.1962i		−	0.858052i
$555$		0			0
$556$	6.33975	−	6.33975i	0.268865	−	0.268865i
$557$	−27.9808	+	27.9808i	−1.18558	+	1.18558i	−0.207307	+	0.978276i	$0.566470\pi$
$557$	−27.9808	+	27.9808i	−1.18558	+	1.18558i	−0.978276	+	0.207307i	$0.933530\pi$
$558$		0			0
$559$	42.8564			1.81263
$560$	−1.32051	−	4.92820i	−0.0558017	−	0.208255i
$561$		0			0
$562$	19.5885	−	19.5885i	0.826289	−	0.826289i
$563$	−7.86603	−	29.3564i	−0.331513	−	1.23723i	−0.907600	−	0.419836i	$-0.862088\pi$
$563$	−7.86603	−	29.3564i	−0.331513	−	1.23723i	0.576086	−	0.817389i	$-0.304579\pi$
$564$		0			0
$565$	−0.741670	+	2.76795i	−0.0312023	+	0.116448i
$566$	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	0.110368	−	0.993891i	$-0.464797\pi$
$569$	24.4808	−	14.1340i	1.02629	−	0.592527i	0.915919	+	0.401364i	$0.131464\pi$
$570$		0			0
$571$	−5.40192	+	1.44744i	−0.226063	+	0.0605735i	−0.370073	−	0.929003i	$-0.620667\pi$
$571$	−5.40192	+	1.44744i	−0.226063	+	0.0605735i	0.144009	+	0.989576i	$0.454001\pi$
$572$	4.26795	−	2.46410i	0.178452	−	0.103029i
$573$		0			0
$574$	−37.6865	+	10.0981i	−1.57301	+	0.421486i
$575$	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	$0.218330\pi$
$578$	1.36603	−	0.366025i	0.0568192	−	0.0152246i
$579$		0			0
$580$	−3.00000	+	1.73205i	−0.124568	+	0.0719195i
$581$	−29.0622	+	7.78719i	−1.20570	+	0.323067i
$582$		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
$587$	−0.794229	+	2.96410i	−0.0327813	+	0.122342i	−0.980378	−	0.197129i	$-0.936838\pi$
$587$	−0.794229	+	2.96410i	−0.0327813	+	0.122342i	0.947596	+	0.319470i	$0.103505\pi$
$588$		0			0
$589$	1.31347	+	4.90192i	0.0541204	+	0.201980i
$590$	−3.00000	+	3.00000i	−0.123508	+	0.123508i
$591$		0			0
$592$	−42.2487	+	11.3205i	−1.73641	+	0.465270i
$593$	−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
$596$	21.5167	−	21.5167i	0.881357	−	0.881357i
$597$		0			0
$598$		−	3.12436i		−	0.127764i
$599$	30.3109	+	17.5000i	1.23847	+	0.715031i	0.968781	−	0.247917i	$-0.0797461\pi$
$599$	30.3109	+	17.5000i	1.23847	+	0.715031i	0.269688	+	0.962948i	$0.413079\pi$
$600$		0			0
$601$	30.2321	−	17.4545i	1.23319	−	0.711983i	0.265497	−	0.964112i	$-0.414464\pi$
$601$	30.2321	−	17.4545i	1.23319	−	0.711983i	0.967694	+	0.252128i	$0.0811305\pi$
$602$	15.6865	+	27.1699i	0.639335	+	1.10736i
$603$		0			0
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$	−5.36603	−	1.43782i	−0.218160	−	0.0584558i
$606$		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	$0.226423\pi$
$608$	−12.0000	−	20.7846i	−0.486664	−	0.842927i
$609$		0			0
$610$	10.5622	−	2.83013i	0.427650	−	0.114588i
$611$	−30.9545	+	30.9545i	−1.25228	+	1.25228i
$612$		0			0
$613$	−7.58846	−	7.58846i	−0.306495	−	0.306495i	0.537053	−	0.843548i	$-0.319537\pi$
$613$	−7.58846	−	7.58846i	−0.306495	−	0.306495i	−0.843548	+	0.537053i	$0.819537\pi$
$614$	5.92820	−	10.2679i	0.239243	−	0.414381i
$615$		0			0
$616$	3.12436	+	1.80385i	0.125884	+	0.0726791i
$617$	−8.08846	−	4.66987i	−0.325629	−	0.188002i	0.328270	−	0.944584i	$-0.393534\pi$
$617$	−8.08846	−	4.66987i	−0.325629	−	0.188002i	−0.653899	+	0.756582i	$0.726868\pi$
$618$		0			0
$619$	8.86603	−	33.0885i	0.356356	−	1.32994i	−0.522414	−	0.852692i	$-0.674969\pi$
$619$	8.86603	−	33.0885i	0.356356	−	1.32994i	0.878770	−	0.477246i	$-0.158365\pi$
$620$	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
$626$	9.05256	−	9.05256i	0.361813	−	0.361813i
$627$		0			0
$628$	−1.26795	−	1.26795i	−0.0505967	−	0.0505967i
$629$	30.9282	+	30.9282i	1.23319	+	1.23319i
$630$		0			0
$631$			32.2487i			1.28380i	0.766788	+	0.641900i	$0.221854\pi$
$631$			32.2487i			1.28380i	−0.766788	+	0.641900i	$0.778146\pi$
$632$	−4.73205	−	1.26795i	−0.188231	−	0.0504363i
$633$		0			0
$634$	2.98076			0.118381
$635$	10.1962	−	2.73205i	0.404622	−	0.108418i
$636$		0			0
$637$	4.26795	+	1.14359i	0.169102	+	0.0453108i
$638$	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
$643$	−0.277568	−	1.03590i	−0.0109462	−	0.0408518i	0.960237	−	0.279187i	$-0.0900650\pi$
$643$	−0.277568	−	1.03590i	−0.0109462	−	0.0408518i	−0.971183	+	0.238335i	$0.923398\pi$
$644$	1.98076	−	1.14359i	0.0780530	−	0.0450639i
$645$		0			0
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$			46.3923i			1.82387i	0.410335	+	0.911935i	$0.365412\pi$
$647$			46.3923i			1.82387i	−0.410335	+	0.911935i	$0.634588\pi$
$648$		0			0
$649$		−	3.00000i		−	0.117760i
$650$	−27.5885	−	15.9282i	−1.08211	−	0.624756i
$651$		0			0
$652$	8.73205	−	32.5885i	0.341974	−	1.27626i
$653$	−5.71539	−	21.3301i	−0.223661	−	0.834712i	−0.982937	−	0.183944i	$-0.941114\pi$
$653$	−5.71539	−	21.3301i	−0.223661	−	0.834712i	0.759276	−	0.650768i	$-0.225553\pi$
$654$		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
$659$	−8.33013	−	2.23205i	−0.324496	−	0.0869484i	0.0928939	−	0.995676i	$-0.470388\pi$
$659$	−8.33013	−	2.23205i	−0.324496	−	0.0869484i	−0.417390	+	0.908728i	$0.637055\pi$
$660$		0			0
$661$	−15.6962	+	4.20577i	−0.610510	+	0.163586i	−0.550810	−	0.834631i	$-0.685681\pi$
$661$	−15.6962	+	4.20577i	−0.610510	+	0.163586i	−0.0596998	+	0.998216i	$0.519014\pi$
$662$			38.5885i			1.49978i
$663$		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
$668$	19.0718			0.737910
$669$		0			0
$670$	−0.660254	−	0.660254i	−0.0255078	−	0.0255078i
$671$	−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
$677$	12.2321	−	45.6506i	0.470116	−	1.75450i	−0.169229	−	0.985577i	$-0.554128\pi$
$677$	12.2321	−	45.6506i	0.470116	−	1.75450i	0.639345	−	0.768920i	$-0.279205\pi$
$678$		0			0
$679$	2.13397	+	1.23205i	0.0818944	+	0.0472818i
$680$	−2.92820	+	5.07180i	−0.112291	+	0.194495i
$681$		0			0
$682$	−0.758330	−	0.437822i	−0.0290380	−	0.0167651i
$683$	5.39230	+	5.39230i	0.206331	+	0.206331i	0.802706	−	0.596375i	$-0.203393\pi$
$683$	5.39230	+	5.39230i	0.206331	+	0.206331i	−0.596375	+	0.802706i	$0.703393\pi$
$684$		0			0
$685$	6.09808	−	6.09808i	0.232996	−	0.232996i
$686$	7.15064	+	26.6865i	0.273013	+	1.01890i
$687$		0			0
$688$	25.4641	+	25.4641i	0.970810	+	0.970810i
$689$	−7.63397	+	13.2224i	−0.290831	+	0.503735i
$690$		0			0
$691$	−18.5263	−	4.96410i	−0.704773	−	0.188843i	−0.111405	−	0.993775i	$-0.535535\pi$
$691$	−18.5263	−	4.96410i	−0.704773	−	0.188843i	−0.593367	+	0.804932i	$0.702202\pi$
$692$	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
$698$	−11.6603			−0.441347
$699$		0			0
$700$		−	23.3205i		−	0.881432i
$701$	21.0526	−	21.0526i	0.795144	−	0.795144i	−0.187181	−	0.982325i	$-0.559935\pi$
$701$	21.0526	−	21.0526i	0.795144	−	0.795144i	0.982325	+	0.187181i	$0.0599352\pi$
$702$		0			0
$703$	46.3923			1.74972
$704$	4.00000	+	1.07180i	0.150756	+	0.0403949i
$705$		0			0
$706$	−30.4641	−	30.4641i	−1.14653	−	1.14653i
$707$	−1.23205	−	4.59808i	−0.0463360	−	0.172928i
$708$		0			0
$709$	10.7487	−	40.1147i	0.403676	−	1.50654i	−0.402808	−	0.915285i	$-0.631966\pi$
$709$	10.7487	−	40.1147i	0.403676	−	1.50654i	0.806484	−	0.591256i	$-0.201368\pi$
$710$	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
$715$	−1.23205	+	0.330127i	−0.0460761	+	0.0123461i
$716$	−5.80385	+	21.6603i	−0.216900	+	0.809482i
$717$		0			0
$718$	5.51666	+	20.5885i	0.205880	+	0.768354i
$719$	−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
$722$	−0.366025	−	1.36603i	−0.0136221	−	0.0508382i
$723$		0			0
$724$	−11.6603	−	3.12436i	−0.433350	−	0.116116i
$725$	−15.2942	+	4.09808i	−0.568013	+	0.152199i
$726$		0			0
$727$	9.06218	−	5.23205i	0.336098	−	0.194046i	−0.322447	−	0.946587i	$-0.604506\pi$
$727$	9.06218	−	5.23205i	0.336098	−	0.194046i	0.658545	+	0.752541i	$0.271172\pi$
$728$	−33.1769			−1.22962
$729$		0			0
$730$	−0.196152	−	0.339746i	−0.00725993	−	0.0125746i
$731$	9.32051	−	34.7846i	0.344731	−	1.28656i
$732$		0			0
$733$	−7.37564	−	27.5263i	−0.272426	−	1.01671i	−0.957547	−	0.288277i	$-0.906917\pi$
$733$	−7.37564	−	27.5263i	−0.272426	−	1.01671i	0.685121	−	0.728429i	$-0.259749\pi$
$734$	−30.9090	−	30.9090i	−1.14087	−	1.14087i
$735$		0			0
$736$	1.85641	−	1.85641i	0.0684280	−	0.0684280i
$737$	0.660254			0.0243208
$738$		0			0
$739$	−29.7321	+	29.7321i	−1.09371	+	1.09371i	−0.0985823	+	0.995129i	$0.531431\pi$
$739$	−29.7321	+	29.7321i	−1.09371	+	1.09371i	−0.995129	+	0.0985823i	$0.968569\pi$
$740$	11.3205			0.416150
$741$		0			0
$742$	−11.1769			−0.410317
$743$	−25.1147	−	14.5000i	−0.921370	−	0.531953i	−0.0372984	−	0.999304i	$-0.511875\pi$
$743$	−25.1147	−	14.5000i	−0.921370	−	0.531953i	−0.884072	+	0.467351i	$0.845209\pi$
$744$		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
$749$	−38.3468	−	10.2750i	−1.40116	−	0.375440i
$750$		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	$0.111539\pi$
$752$	−36.7846			−1.34140
$753$		0			0
$754$	5.83013	+	21.7583i	0.212321	+	0.792392i
$755$	2.56218	−	2.56218i	0.0932472	−	0.0932472i
$756$		0			0
$757$	8.46410	+	8.46410i	0.307633	+	0.307633i	0.843991	−	0.536358i	$-0.180200\pi$
$757$	8.46410	+	8.46410i	0.307633	+	0.307633i	−0.536358	+	0.843991i	$0.680200\pi$
$758$	−27.0000	−	15.5885i	−0.980684	−	0.566198i
$759$		0			0
$760$	1.60770	+	6.00000i	0.0583172	+	0.217643i
$761$	25.2846	+	14.5981i	0.916566	+	0.529180i	0.882538	−	0.470241i	$-0.155833\pi$
$761$	25.2846	+	14.5981i	0.916566	+	0.529180i	0.0340283	+	0.999421i	$0.489166\pi$
$762$		0			0
$763$	−1.56218	+	5.83013i	−0.0565546	+	0.211065i
$764$	−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	$0.206949\pi$
$770$	−0.660254	−	0.660254i	−0.0237939	−	0.0237939i
$771$		0			0
$772$			4.92820i			0.177370i
$773$	−7.58846	−	7.58846i	−0.272938	−	0.272938i	0.557344	−	0.830282i	$-0.311821\pi$
$773$	−7.58846	−	7.58846i	−0.272938	−	0.272938i	−0.830282	+	0.557344i	$0.811821\pi$
$774$		0			0
$775$			5.66025i			0.203322i
$776$	2.73205	+	0.732051i	0.0980749	+	0.0262791i
$777$		0			0
$778$			11.1244i			0.398827i
$779$	45.8827	−	12.2942i	1.64392	−	0.440486i
$780$		0			0
$781$	−5.46410	−	1.46410i	−0.195521	−	0.0523897i
$782$	−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
$787$	9.06218	+	33.8205i	0.323032	+	1.20557i	0.916276	+	0.400548i	$0.131180\pi$
$787$	9.06218	+	33.8205i	0.323032	+	1.20557i	−0.593244	+	0.805023i	$0.702153\pi$
$788$	−28.5885	−	7.66025i	−1.01842	−	0.272885i
$789$		0			0
$790$	1.09808	+	0.633975i	0.0390678	+	0.0225558i
$791$			13.6410i			0.485019i
$792$		0			0
$793$		−	71.1051i		−	2.52502i
$794$	21.0526	−	36.4641i	0.747127	−	1.29406i
$795$		0			0
$796$	−5.85641	−	10.1436i	−0.207575	−	0.359530i
$797$	−0.284610	−	1.06218i	−0.0100814	−	0.0376243i	0.960702	−	0.277582i	$-0.0895331\pi$
$797$	−0.284610	−	1.06218i	−0.0100814	−	0.0376243i	−0.970783	+	0.239958i	$0.922866\pi$
$798$		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
$803$	0.267949	+	0.0717968i	0.00945572	+	0.00253365i
$804$		0			0
$805$	−0.571797	+	0.153212i	−0.0201532	+	0.00540003i
$806$	8.05256			0.283639
$807$		0			0
$808$	−2.73205	−	4.73205i	−0.0961132	−	0.166473i
$809$			32.6410i			1.14760i	0.818997	+	0.573799i	$0.194531\pi$
$809$			32.6410i			1.14760i	−0.818997	+	0.573799i	$0.805469\pi$
$810$		0			0
$811$	−11.5359	−	11.5359i	−0.405080	−	0.405080i	0.474939	−	0.880019i	$-0.342470\pi$
$811$	−11.5359	−	11.5359i	−0.405080	−	0.405080i	−0.880019	+	0.474939i	$0.842470\pi$
$812$	−11.6603	+	11.6603i	−0.409195	+	0.409195i
$813$		0			0
$814$	−5.66025	+	5.66025i	−0.198392	+	0.198392i
$815$	−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
$821$	−5.01666	+	18.7224i	−0.175083	+	0.653417i	0.821455	+	0.570273i	$0.193163\pi$
$821$	−5.01666	+	18.7224i	−0.175083	+	0.653417i	−0.996538	+	0.0831439i	$0.973504\pi$
$822$		0			0
$823$	6.65064	+	3.83975i	0.231827	+	0.133845i	0.611414	−	0.791311i	$-0.290601\pi$
$823$	6.65064	+	3.83975i	0.231827	+	0.133845i	−0.379588	+	0.925156i	$0.623934\pi$
$824$	−5.66025	+	1.51666i	−0.197184	+	0.0528354i
$825$		0			0
$826$	−10.0981	+	17.4904i	−0.351357	+	0.608568i
$827$	10.6077	+	10.6077i	0.368866	+	0.368866i	0.867063	−	0.498198i	$-0.166005\pi$
$827$	10.6077	+	10.6077i	0.368866	+	0.368866i	−0.498198	+	0.867063i	$0.666005\pi$
$828$		0			0
$829$	−17.7321	+	17.7321i	−0.615860	+	0.615860i	−0.944467	−	0.328607i	$-0.893421\pi$
$829$	−17.7321	+	17.7321i	−0.615860	+	0.615860i	0.328607	+	0.944467i	$0.393421\pi$
$830$	8.63397	−	2.31347i	0.299690	−	0.0803016i
$831$		0			0
$832$	−36.7846	+	9.85641i	−1.27528	+	0.341709i
$833$	1.85641	−	3.21539i	0.0643207	−	0.111407i
$834$		0			0
$835$	−4.76795	−	1.27757i	−0.165002	−	0.0442121i
$836$	−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	0.0988859	−	0.995099i	$-0.468472\pi$
$839$	29.2583	−	16.8923i	1.01011	−	0.583187i	0.911224	+	0.411912i	$0.135139\pi$
$840$		0			0
$841$	−15.4186	−	8.90192i	−0.531675	−	0.306963i
$842$		−	15.8038i		−	0.544637i
$843$		0			0
$844$	−2.87564	−	2.87564i	−0.0989838	−	0.0989838i
$845$	3.53590	−	3.53590i	0.121639	−	0.121639i
$846$		0			0
$847$	−26.4449			−0.908656
$848$	−12.3923	+	3.32051i	−0.425553	+	0.114027i
$849$		0			0
$850$	−18.9282	+	18.9282i	−0.649232	+	0.649232i
$851$	1.31347	+	4.90192i	0.0450251	+	0.168036i
$852$		0			0
$853$	−2.69615	+	10.0622i	−0.0923145	+	0.344522i	−0.996599	−	0.0824088i	$-0.973739\pi$
$853$	−2.69615	+	10.0622i	−0.0923145	+	0.344522i	0.904284	+	0.426931i	$0.140405\pi$
$854$	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	0.448574	−	0.893746i	$-0.351932\pi$
$857$	42.3564	−	24.4545i	1.44687	−	0.835349i	0.998293	+	0.0583966i	$0.0185988\pi$
$858$		0			0
$859$	16.7942	−	4.50000i	0.573012	−	0.153538i	0.0393342	−	0.999226i	$-0.487476\pi$
$859$	16.7942	−	4.50000i	0.573012	−	0.153538i	0.533677	+	0.845688i	$0.320810\pi$
$860$	−4.66025	−	8.07180i	−0.158913	−	0.275246i
$861$		0			0
$862$	42.7846	−	11.4641i	1.45725	−	0.390469i
$863$	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
$866$	−33.3205	+	8.92820i	−1.13228	+	0.303393i
$867$		0			0
$868$	2.94744	+	5.10512i	0.100043	+	0.173279i
$869$	−0.866025	+	0.232051i	−0.0293779	+	0.00787178i
$870$		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
$875$	−3.21281	+	11.9904i	−0.108613	+	0.405349i
$876$		0			0
$877$	−8.94486	−	33.3827i	−0.302047	−	1.12725i	−0.935458	−	0.353438i	$-0.885013\pi$
$877$	−8.94486	−	33.3827i	−0.302047	−	1.12725i	0.633411	−	0.773815i	$-0.281654\pi$
$878$	20.8564	−	20.8564i	0.703870	−	0.703870i
$879$		0			0
$880$	−0.928203	−	0.535898i	−0.0312897	−	0.0180651i
$881$	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	−0.755782	−	0.654824i	$-0.772743\pi$
$883$	−3.00000	+	3.00000i	−0.100958	+	0.100958i	0.654824	+	0.755782i	$0.272743\pi$
$884$	26.9282	+	26.9282i	0.905693	+	0.905693i
$885$		0			0
$886$			23.6603i			0.794882i
$887$	21.0622	+	12.1603i	0.707199	+	0.408301i	0.810023	−	0.586398i	$-0.199455\pi$
$887$	21.0622	+	12.1603i	0.707199	+	0.408301i	−0.102824	+	0.994700i	$0.532788\pi$
$888$		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
$893$	37.6865	+	10.0981i	1.26113	+	0.337919i
$894$		0			0
$895$	2.90192	−	5.02628i	0.0970006	−	0.168010i
$896$	−19.7128	−	19.7128i	−0.658559	−	0.658559i
$897$		0			0
$898$	0.928203	−	0.248711i	0.0309745	−	0.00829960i
$899$	2.83013	−	2.83013i	0.0943900	−	0.0943900i
$900$		0			0
$901$	9.07180	+	9.07180i	0.302225	+	0.302225i
$902$	−4.09808	+	7.09808i	−0.136451	+	0.236340i
$903$		0			0
$904$	4.05256	+	15.1244i	0.134786	+	0.503029i
$905$	2.70577	+	1.56218i	0.0899429	+	0.0519285i
$906$		0			0
$907$	−3.06218	+	11.4282i	−0.101678	+	0.379467i	−0.997947	−	0.0640432i	$-0.979600\pi$
$907$	−3.06218	+	11.4282i	−0.101678	+	0.379467i	0.896269	+	0.443510i	$0.146267\pi$
$908$	−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
$914$	21.9808	−	21.9808i	0.727059	−	0.727059i
$915$		0			0
$916$	13.8038	−	13.8038i	0.456092	−	0.456092i
$917$	−21.0981	−	21.0981i	−0.696720	−	0.696720i
$918$		0			0
$919$			43.4641i			1.43375i	0.697203	+	0.716874i	$0.254428\pi$
$919$			43.4641i			1.43375i	−0.697203	+	0.716874i	$0.745572\pi$
$920$	−0.588457	+	0.339746i	−0.0194009	+	0.0112011i
$921$		0			0
$922$	3.26795			0.107624
$923$	50.2487	−	13.4641i	1.65396	−	0.443176i
$924$		0			0
$925$	49.9808	+	13.3923i	1.64336	+	0.440336i
$926$	−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
$931$	−1.01924	−	3.80385i	−0.0334042	−	0.124666i
$932$	22.9282	+	39.7128i	0.751038	+	1.30084i
$933$		0			0
$934$	−19.7846	+	34.2679i	−0.647372	+	1.12128i
$935$			1.07180i			0.0350515i
$936$		0			0
$937$		−	32.9282i		−	1.07572i	−0.843035	−	0.537859i	$-0.819233\pi$
$937$		−	32.9282i		−	1.07572i	0.843035	−	0.537859i	$-0.180767\pi$
$938$	−3.84936	−	2.22243i	−0.125686	−	0.0725650i
$939$		0			0
$940$	9.19615	+	2.46410i	0.299945	+	0.0803701i
$941$	2.91154	+	10.8660i	0.0949136	+	0.354222i	0.997006	−	0.0773199i	$-0.0246363\pi$
$941$	2.91154	+	10.8660i	0.0949136	+	0.354222i	−0.902093	+	0.431542i	$0.857970\pi$
$942$		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
$947$	14.9904	+	4.01666i	0.487122	+	0.130524i	0.494017	−	0.869452i	$-0.335528\pi$
$947$	14.9904	+	4.01666i	0.487122	+	0.130524i	−0.00689497	+	0.999976i	$0.502195\pi$
$948$		0			0
$949$	−2.46410	+	0.660254i	−0.0799881	+	0.0214328i
$950$			28.3923i			0.921168i
$951$		0			0
$952$	−7.21539	+	26.9282i	−0.233852	+	0.872748i
$953$		−	39.4641i		−	1.27837i	−0.769054	−	0.639184i	$-0.779272\pi$
$953$		−	39.4641i		−	1.27837i	0.769054	−	0.639184i	$-0.220728\pi$
$954$		0			0
$955$	4.83013	+	4.83013i	0.156299	+	0.156299i
$956$		−	22.3923i		−	0.724219i
$957$		0			0
$958$	1.33975	+	1.33975i	0.0432852	+	0.0432852i
$959$	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
$965$	0.330127	−	1.23205i	0.0106272	−	0.0396611i
$966$		0			0
$967$	14.9378	+	8.62436i	0.480368	+	0.277341i	0.720570	−	0.693382i	$-0.243880\pi$
$967$	14.9378	+	8.62436i	0.480368	+	0.277341i	−0.240202	+	0.970723i	$0.577214\pi$
$968$	−29.3205	+	7.85641i	−0.942397	+	0.252514i
$969$		0			0
$970$	−0.633975	−	0.366025i	−0.0203557	−	0.0117524i
$971$	−27.9808	−	27.9808i	−0.897945	−	0.897945i	0.0973088	−	0.995254i	$-0.468977\pi$
$971$	−27.9808	−	27.9808i	−0.897945	−	0.897945i	−0.995254	+	0.0973088i	$0.968977\pi$
$972$		0			0
$973$	−7.81089	+	7.81089i	−0.250406	+	0.250406i
$974$	12.7321	+	47.5167i	0.407961	+	1.52253i
$975$		0			0
$976$	42.2487	−	42.2487i	1.35235	−	1.35235i
$977$	−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
$979$	5.92820	+	1.58846i	0.189466	+	0.0507673i
$980$	−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	−0.981274	−	0.192617i	$-0.938303\pi$
$983$	−40.9186	+	23.6244i	−1.30510	+	0.753500i	−0.323826	+	0.946117i	$0.604969\pi$
$984$		0			0
$985$	6.63397	+	3.83013i	0.211376	+	0.122038i
$986$	18.9282			0.602797
$987$		0			0
$988$	40.3923			1.28505
$989$	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	$0.622344\pi$
$992$	4.78461	+	4.78461i	0.151912	+	0.151912i
$993$		0			0
$994$	26.9282	+	26.9282i	0.854111	+	0.854111i
$995$	0.784610	+	2.92820i	0.0248738	+	0.0928303i
$996$		0			0
$997$	−2.96410	+	11.0622i	−0.0938740	+	0.350343i	−0.996846	−	0.0793561i	$-0.974714\pi$
$997$	−2.96410	+	11.0622i	−0.0938740	+	0.350343i	0.902972	+	0.429699i	$0.141380\pi$
$998$	−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.a.37.1		4
3.2	odd	2		144.2.x.d.85.1	yes	4
4.3	odd	2		1728.2.bc.b.1009.1		4
9.2	odd	6		144.2.x.a.133.1	yes	4
9.7	even	3		432.2.y.d.181.1		4
12.11	even	2		576.2.bb.b.49.1		4
16.3	odd	4		1728.2.bc.c.145.1		4
16.13	even	4		432.2.y.d.253.1		4
36.7	odd	6		1728.2.bc.c.1585.1		4
36.11	even	6		576.2.bb.a.241.1		4
48.29	odd	4		144.2.x.a.13.1	✓	4
48.35	even	4		576.2.bb.a.337.1		4
144.29	odd	12		144.2.x.d.61.1	yes	4
144.61	even	12	inner	432.2.y.a.397.1		4
144.83	even	12		576.2.bb.b.529.1		4
144.115	odd	12		1728.2.bc.b.721.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.13.1	✓	4	48.29	odd	4
144.2.x.a.133.1	yes	4	9.2	odd	6
144.2.x.d.61.1	yes	4	144.29	odd	12
144.2.x.d.85.1	yes	4	3.2	odd	2
432.2.y.a.37.1		4	1.1	even	1	trivial
432.2.y.a.397.1		4	144.61	even	12	inner
432.2.y.d.181.1		4	9.7	even	3
432.2.y.d.253.1		4	16.13	even	4
576.2.bb.a.241.1		4	36.11	even	6
576.2.bb.a.337.1		4	48.35	even	4
576.2.bb.b.49.1		4	12.11	even	2
576.2.bb.b.529.1		4	144.83	even	12
1728.2.bc.b.721.1		4	144.115	odd	12
1728.2.bc.b.1009.1		4	4.3	odd	2
1728.2.bc.c.145.1		4	16.3	odd	4
1728.2.bc.c.1585.1		4	36.7	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-0.500000 + 0.133975i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-0.500000 + 0.133975i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.633975 - 0.366025i) q^{10} +(-0.133975 + 0.500000i) q^{11} +(-1.23205 - 4.59808i) q^{13} +(2.46410 - 2.46410i) q^{14} +(2.00000 - 3.46410i) q^{16} -4.00000 q^{17} +(-3.00000 + 3.00000i) q^{19} +(-0.732051 + 0.732051i) q^{20} -0.732051i q^{22} +(-0.401924 - 0.232051i) q^{23} +(-4.09808 + 2.36603i) q^{25} +(3.36603 + 5.83013i) q^{26} +(-2.46410 + 4.26795i) q^{28} +(3.23205 + 0.866025i) q^{29} +(0.598076 - 1.03590i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(5.46410 - 1.46410i) q^{34} +(0.901924 - 0.901924i) q^{35} +(-7.73205 - 7.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(0.732051 - 1.26795i) q^{40} +(-9.69615 - 5.59808i) q^{41} +(-2.33013 + 8.69615i) q^{43} +(0.267949 + 1.00000i) q^{44} +(0.633975 + 0.169873i) q^{46} +(-4.59808 - 7.96410i) q^{47} +(-0.464102 + 0.803848i) q^{49} +(4.73205 - 4.73205i) q^{50} +(-6.73205 - 6.73205i) q^{52} +(-2.26795 - 2.26795i) q^{53} -0.267949i q^{55} +(1.80385 - 6.73205i) q^{56} -4.73205 q^{58} +(-5.59808 + 1.50000i) q^{59} +(14.4282 + 3.86603i) q^{61} +(-0.437822 + 1.63397i) q^{62} -8.00000i q^{64} +(1.23205 + 2.13397i) q^{65} +(-0.330127 - 1.23205i) q^{67} +(-6.92820 + 4.00000i) q^{68} +(-0.901924 + 1.56218i) q^{70} +10.9282i q^{71} -0.535898i q^{73} +(13.3923 + 7.73205i) q^{74} +(-2.19615 + 8.19615i) q^{76} +(-0.330127 - 1.23205i) q^{77} +(0.866025 + 1.50000i) q^{79} +(-0.535898 + 2.00000i) q^{80} +(15.2942 + 4.09808i) q^{82} +(11.7942 + 3.16025i) q^{83} +(2.00000 - 0.535898i) q^{85} -12.7321i q^{86} +(-0.732051 - 1.26795i) q^{88} -11.8564i q^{89} +(8.29423 + 8.29423i) q^{91} -0.928203 q^{92} +(9.19615 + 9.19615i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(0.339746 - 1.26795i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{5} - 12 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^5 - 12 * q^7 - 8 * q^8	\( 4 q - 2 q^{2} - 2 q^{5} - 12 q^{7} - 8 q^{8} + 6 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 8 q^{16} - 16 q^{17} - 12 q^{19} + 4 q^{20} - 12 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{28} + 6 q^{29} - 8 q^{31} + 8 q^{32} + 8 q^{34} + 14 q^{35} - 24 q^{37} + 12 q^{38} - 4 q^{40} - 18 q^{41} + 8 q^{43} + 8 q^{44} + 6 q^{46} - 8 q^{47} + 12 q^{49} + 12 q^{50} - 20 q^{52} - 16 q^{53} + 28 q^{56} - 12 q^{58} - 12 q^{59} + 30 q^{61} - 26 q^{62} - 2 q^{65} + 16 q^{67} - 14 q^{70} + 12 q^{74} + 12 q^{76} + 16 q^{77} - 16 q^{80} + 30 q^{82} + 16 q^{83} + 8 q^{85} + 4 q^{88} + 2 q^{91} + 24 q^{92} + 16 q^{94} - 6 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^5 - 12 * q^7 - 8 * q^8 + 6 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 8 * q^16 - 16 * q^17 - 12 * q^19 + 4 * q^20 - 12 * q^23 - 6 * q^25 + 10 * q^26 + 4 * q^28 + 6 * q^29 - 8 * q^31 + 8 * q^32 + 8 * q^34 + 14 * q^35 - 24 * q^37 + 12 * q^38 - 4 * q^40 - 18 * q^41 + 8 * q^43 + 8 * q^44 + 6 * q^46 - 8 * q^47 + 12 * q^49 + 12 * q^50 - 20 * q^52 - 16 * q^53 + 28 * q^56 - 12 * q^58 - 12 * q^59 + 30 * q^61 - 26 * q^62 - 2 * q^65 + 16 * q^67 - 14 * q^70 + 12 * q^74 + 12 * q^76 + 16 * q^77 - 16 * q^80 + 30 * q^82 + 16 * q^83 + 8 * q^85 + 4 * q^88 + 2 * q^91 + 24 * q^92 + 16 * q^94 - 6 * q^95 - 2 * q^97 + 36 * q^98

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