LMFDB - Embedded newform 432.3.x.a.125.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(125,432)]

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, 9, 10]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("432.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.x (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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.8
Character	$\chi$	$=$	432.125
Dual form			432.3.x.a.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65125 - 1.12844i) q^{2} +(1.45327 + 3.72666i) q^{4} +(-7.93556 + 2.12633i) q^{5} +(2.99388 - 1.72852i) q^{7} +(1.80558 - 7.79358i) q^{8} +O(q^{10})$	\(q+(-1.65125 - 1.12844i) q^{2} +(1.45327 + 3.72666i) q^{4} +(-7.93556 + 2.12633i) q^{5} +(2.99388 - 1.72852i) q^{7} +(1.80558 - 7.79358i) q^{8} +(15.5030 + 5.44366i) q^{10} +(1.03415 - 3.85948i) q^{11} +(-13.8482 + 3.71061i) q^{13} +(-6.89417 - 0.524181i) q^{14} +(-11.7760 + 10.8317i) q^{16} +30.9102i q^{17} +(-0.373615 - 0.373615i) q^{19} +(-19.4566 - 26.4830i) q^{20} +(-6.06281 + 5.20601i) q^{22} +(14.6209 - 25.3241i) q^{23} +(36.8012 - 21.2472i) q^{25} +(27.0540 + 9.49962i) q^{26} +(10.7925 + 8.64518i) q^{28} +(-5.56448 - 1.49100i) q^{29} +(22.3969 - 38.7926i) q^{31} +(31.6680 - 4.59735i) q^{32} +(34.8802 - 51.0406i) q^{34} +(-20.0827 + 20.0827i) q^{35} +(46.1141 - 46.1141i) q^{37} +(0.195332 + 1.03853i) q^{38} +(2.24337 + 65.6856i) q^{40} +(10.1803 - 17.6328i) q^{41} +(-1.51175 - 0.405073i) q^{43} +(15.8859 - 1.75495i) q^{44} +(-52.7194 + 25.3178i) q^{46} +(39.3321 - 22.7084i) q^{47} +(-18.5245 + 32.0853i) q^{49} +(-84.7440 - 6.44330i) q^{50} +(-33.9533 - 46.2150i) q^{52} +(-24.1685 - 24.1685i) q^{53} +32.8261i q^{55} +(-8.06563 - 26.4540i) q^{56} +(7.50587 + 8.74117i) q^{58} +(28.2635 - 7.57319i) q^{59} +(6.65084 - 24.8213i) q^{61} +(-80.7580 + 38.7829i) q^{62} +(-57.4797 - 28.1439i) q^{64} +(102.003 - 58.8915i) q^{65} +(37.8850 - 10.1512i) q^{67} +(-115.192 + 44.9208i) q^{68} +(55.8237 - 10.4996i) q^{70} +108.615 q^{71} -32.2555i q^{73} +(-128.183 + 24.1092i) q^{74} +(0.849373 - 1.93530i) q^{76} +(-3.57508 - 13.3424i) q^{77} +(2.32341 + 4.02426i) q^{79} +(70.4176 - 110.995i) q^{80} +(-36.7078 + 17.6284i) q^{82} +(-132.223 - 35.4290i) q^{83} +(-65.7252 - 245.290i) q^{85} +(2.03919 + 2.37479i) q^{86} +(-28.2120 - 15.0283i) q^{88} +55.7788 q^{89} +(-35.0459 + 35.0459i) q^{91} +(115.623 + 17.6844i) q^{92} +(-90.5723 - 6.88644i) q^{94} +(3.75927 + 2.17041i) q^{95} +(11.6768 + 20.2248i) q^{97} +(66.7947 - 32.0773i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.65125	−	1.12844i	−0.825626	−	0.564218i
$2$	−1.65125	−	1.12844i	−0.825626	−	0.564218i
$3$		0			0
$3$		0			0
$4$	1.45327	+	3.72666i	0.363317	+	0.931666i
$5$	−7.93556	+	2.12633i	−1.58711	+	0.425265i	−0.941118	−	0.338078i	$-0.890223\pi$
$5$	−7.93556	+	2.12633i	−1.58711	+	0.425265i	−0.645993	+	0.763343i	$0.723557\pi$
$6$		0			0
$7$	2.99388	−	1.72852i	0.427697	−	0.246931i	−0.270668	−	0.962673i	$-0.587245\pi$
$7$	2.99388	−	1.72852i	0.427697	−	0.246931i	0.698365	+	0.715742i	$0.253911\pi$
$8$	1.80558	−	7.79358i	0.225698	−	0.974197i
$9$		0			0
$10$	15.5030	+	5.44366i	1.55030	+	0.544366i
$11$	1.03415	−	3.85948i	0.0940132	−	0.350862i	−0.902855	−	0.429946i	$-0.858533\pi$
$11$	1.03415	−	3.85948i	0.0940132	−	0.350862i	0.996868	+	0.0790835i	$0.0251994\pi$
$12$		0			0
$13$	−13.8482	+	3.71061i	−1.06524	+	0.285431i	−0.748538	−	0.663092i	$-0.769244\pi$
$13$	−13.8482	+	3.71061i	−1.06524	+	0.285431i	−0.316707	+	0.948523i	$0.602577\pi$
$14$	−6.89417	−	0.524181i	−0.492441	−	0.0374415i
$15$		0			0
$16$	−11.7760	+	10.8317i	−0.736002	+	0.676980i
$17$			30.9102i			1.81825i	0.416526	+	0.909124i	$0.363248\pi$
$17$			30.9102i			1.81825i	−0.416526	+	0.909124i	$0.636752\pi$
$18$		0			0
$19$	−0.373615	−	0.373615i	−0.0196639	−	0.0196639i	0.697206	−	0.716870i	$-0.254426\pi$
$19$	−0.373615	−	0.373615i	−0.0196639	−	0.0196639i	−0.716870	+	0.697206i	$0.754426\pi$
$20$	−19.4566	−	26.4830i	−0.972829	−	1.32415i
$21$		0			0
$22$	−6.06281	+	5.20601i	−0.275582	+	0.236637i
$23$	14.6209	−	25.3241i	0.635691	−	1.10105i	−0.350677	−	0.936496i	$-0.614049\pi$
$23$	14.6209	−	25.3241i	0.635691	−	1.10105i	0.986368	−	0.164553i	$-0.0526180\pi$
$24$		0			0
$25$	36.8012	−	21.2472i	1.47205	−	0.849886i
$26$	27.0540	+	9.49962i	1.04054	+	0.365370i
$27$		0			0
$28$	10.7925	+	8.64518i	0.385447	+	0.308757i
$29$	−5.56448	−	1.49100i	−0.191879	−	0.0514137i	0.161600	−	0.986856i	$-0.448335\pi$
$29$	−5.56448	−	1.49100i	−0.191879	−	0.0514137i	−0.353479	+	0.935443i	$0.615001\pi$
$30$		0			0
$31$	22.3969	−	38.7926i	0.722482	−	1.25138i	−0.237520	−	0.971383i	$-0.576335\pi$
$31$	22.3969	−	38.7926i	0.722482	−	1.25138i	0.960002	−	0.279993i	$-0.0903320\pi$
$32$	31.6680	−	4.59735i	0.989626	−	0.143667i
$33$		0			0
$34$	34.8802	−	51.0406i	1.02589	−	1.50119i
$35$	−20.0827	+	20.0827i	−0.573792	+	0.573792i
$36$		0			0
$37$	46.1141	−	46.1141i	1.24633	−	1.24633i	0.288998	−	0.957330i	$-0.406678\pi$
$37$	46.1141	−	46.1141i	1.24633	−	1.24633i	0.957330	−	0.288998i	$-0.0933220\pi$
$38$	0.195332	+	1.03853i	0.00514032	+	0.0273298i
$39$		0			0
$40$	2.24337	+	65.6856i	0.0560842	+	1.64214i
$41$	10.1803	−	17.6328i	0.248301	−	0.430069i	−0.714754	−	0.699376i	$-0.753461\pi$
$41$	10.1803	−	17.6328i	0.248301	−	0.430069i	0.963054	+	0.269307i	$0.0867946\pi$
$42$		0			0
$43$	−1.51175	−	0.405073i	−0.0351571	−	0.00942031i	0.241198	−	0.970476i	$-0.422460\pi$
$43$	−1.51175	−	0.405073i	−0.0351571	−	0.00942031i	−0.276355	+	0.961056i	$0.589126\pi$
$44$	15.8859	−	1.75495i	0.361043	−	0.0398853i
$45$		0			0
$46$	−52.7194	+	25.3178i	−1.14607	+	0.550387i
$47$	39.3321	−	22.7084i	0.836854	−	0.483158i	−0.0193395	−	0.999813i	$-0.506156\pi$
$47$	39.3321	−	22.7084i	0.836854	−	0.483158i	0.856194	+	0.516655i	$0.172823\pi$
$48$		0			0
$49$	−18.5245	+	32.0853i	−0.378050	+	0.654802i
$50$	−84.7440	−	6.44330i	−1.69488	−	0.128866i
$51$		0			0
$52$	−33.9533	−	46.2150i	−0.652948	−	0.888750i
$53$	−24.1685	−	24.1685i	−0.456010	−	0.456010i	0.441333	−	0.897343i	$-0.354506\pi$
$53$	−24.1685	−	24.1685i	−0.456010	−	0.456010i	−0.897343	+	0.441333i	$0.854506\pi$
$54$		0			0
$55$			32.8261i			0.596838i
$56$	−8.06563	−	26.4540i	−0.144029	−	0.472393i
$57$		0			0
$58$	7.50587	+	8.74117i	0.129411	+	0.150710i
$59$	28.2635	−	7.57319i	0.479043	−	0.128359i	−0.0112140	−	0.999937i	$-0.503570\pi$
$59$	28.2635	−	7.57319i	0.479043	−	0.128359i	0.490257	+	0.871578i	$0.336903\pi$
$60$		0			0
$61$	6.65084	−	24.8213i	0.109030	−	0.406906i	−0.889741	−	0.456466i	$-0.849115\pi$
$61$	6.65084	−	24.8213i	0.109030	−	0.406906i	0.998771	+	0.0495597i	$0.0157818\pi$
$62$	−80.7580	+	38.7829i	−1.30255	+	0.625531i
$63$		0			0
$64$	−57.4797	−	28.1439i	−0.898121	−	0.439749i
$65$	102.003	−	58.8915i	1.56928	−	0.906023i
$66$		0			0
$67$	37.8850	−	10.1512i	0.565447	−	0.151511i	0.0352394	−	0.999379i	$-0.488781\pi$
$67$	37.8850	−	10.1512i	0.565447	−	0.151511i	0.530208	+	0.847868i	$0.322114\pi$
$68$	−115.192	+	44.9208i	−1.69400	+	0.660600i
$69$		0			0
$70$	55.8237	−	10.4996i	0.797481	−	0.149994i
$71$	108.615			1.52979			0.764897	−	0.644153i	$-0.222790\pi$
$71$	108.615			1.52979			0.764897	+	0.644153i	$0.222790\pi$
$72$		0			0
$73$		−	32.2555i		−	0.441856i	−0.975290	−	0.220928i	$-0.929091\pi$
$73$		−	32.2555i		−	0.441856i	0.975290	−	0.220928i	$-0.0709086\pi$
$74$	−128.183	+	24.1092i	−1.73220	+	0.325801i
$75$		0			0
$76$	0.849373	−	1.93530i	0.0111760	−	0.0254644i
$77$	−3.57508	−	13.3424i	−0.0464296	−	0.173278i
$78$		0			0
$79$	2.32341	+	4.02426i	0.0294102	+	0.0509400i	0.880356	−	0.474314i	$-0.157304\pi$
$79$	2.32341	+	4.02426i	0.0294102	+	0.0509400i	−0.850946	+	0.525254i	$0.823970\pi$
$80$	70.4176	−	110.995i	0.880220	−	1.38744i
$81$		0			0
$82$	−36.7078	+	17.6284i	−0.447656	+	0.214981i
$83$	−132.223	−	35.4290i	−1.59305	−	0.426855i	−0.650113	−	0.759838i	$-0.725278\pi$
$83$	−132.223	−	35.4290i	−1.59305	−	0.426855i	−0.942933	+	0.332983i	$0.891945\pi$
$84$		0			0
$85$	−65.7252	−	245.290i	−0.773238	−	2.88576i
$86$	2.03919	+	2.37479i	0.0237115	+	0.0276139i
$87$		0			0
$88$	−28.2120	−	15.0283i	−0.320590	−	0.170776i
$89$	55.7788			0.626728			0.313364	−	0.949633i	$-0.398544\pi$
$89$	55.7788			0.626728			0.313364	+	0.949633i	$0.398544\pi$
$90$		0			0
$91$	−35.0459	+	35.0459i	−0.385120	+	0.385120i
$92$	115.623	+	17.6844i	1.25677	+	0.192222i
$93$		0			0
$94$	−90.5723	−	6.88644i	−0.963535	−	0.0732600i
$95$	3.75927	+	2.17041i	0.0395712	+	0.0228465i
$96$		0			0
$97$	11.6768	+	20.2248i	0.120379	+	0.208503i	0.919917	−	0.392112i	$-0.128256\pi$
$97$	11.6768	+	20.2248i	0.120379	+	0.208503i	−0.799538	+	0.600616i	$0.794922\pi$
$98$	66.7947	−	32.0773i	0.681579	−	0.327319i
$99$		0			0
$100$	132.663	+	106.268i	1.32663	+	1.06268i
$101$	19.3236	−	72.1167i	0.191323	−	0.714027i	−0.801865	−	0.597505i	$-0.796159\pi$
$101$	19.3236	−	72.1167i	0.191323	−	0.714027i	0.993188	−	0.116522i	$-0.0371745\pi$
$102$		0			0
$103$	12.3067	+	7.10526i	0.119482	+	0.0689831i	0.558550	−	0.829471i	$-0.311358\pi$
$103$	12.3067	+	7.10526i	0.119482	+	0.0689831i	−0.439068	+	0.898454i	$0.644691\pi$
$104$	3.91486	+	114.627i	0.0376428	+	1.10218i
$105$		0			0
$106$	12.6357	+	67.1810i	0.119205	+	0.633783i
$107$	85.8249	+	85.8249i	0.802102	+	0.802102i	0.983424	−	0.181322i	$-0.0580375\pi$
$107$	85.8249	+	85.8249i	0.802102	+	0.802102i	−0.181322	+	0.983424i	$0.558038\pi$
$108$		0			0
$109$	22.7807	+	22.7807i	0.208998	+	0.208998i	0.803841	−	0.594844i	$-0.202786\pi$
$109$	22.7807	+	22.7807i	0.208998	+	0.208998i	−0.594844	+	0.803841i	$0.702786\pi$
$110$	37.0421	−	54.2041i	0.336746	−	0.492765i
$111$		0			0
$112$	−16.5333	+	52.7838i	−0.147618	+	0.471284i
$113$	30.3650	+	17.5313i	0.268717	+	0.155144i	0.628304	−	0.777968i	$-0.283749\pi$
$113$	30.3650	+	17.5313i	0.268717	+	0.155144i	−0.359587	+	0.933111i	$0.617083\pi$
$114$		0			0
$115$	−62.1776	+	232.050i	−0.540674	+	2.01782i
$116$	−2.53024	−	22.9038i	−0.0218124	−	0.197446i
$117$		0			0
$118$	−55.2161	−	19.3883i	−0.467933	−	0.164308i
$119$	53.4289	+	92.5415i	0.448982	+	0.777660i
$120$		0			0
$121$	90.9629	+	52.5175i	0.751760	+	0.434029i
$122$	−38.9914	+	33.4811i	−0.319602	+	0.274435i
$123$		0			0
$124$	177.116	+	27.0897i	1.42835	+	0.218466i
$125$	−101.629	+	101.629i	−0.813028	+	0.813028i
$126$		0			0
$127$	−169.389			−1.33377			−0.666887	−	0.745159i	$-0.732374\pi$
$127$	−169.389			−1.33377			−0.666887	+	0.745159i	$0.732374\pi$
$128$	63.1549	+	111.335i	0.493398	+	0.869804i
$129$		0			0
$130$	−234.888	−	17.8591i	−1.80683	−	0.137378i
$131$	22.7820	+	85.0237i	0.173909	+	0.649036i	0.996735	+	0.0807431i	$0.0257293\pi$
$131$	22.7820	+	85.0237i	0.173909	+	0.649036i	−0.822826	+	0.568293i	$0.807604\pi$
$132$		0			0
$133$	−1.76436	−	0.472758i	−0.0132658	−	0.00355457i
$134$	−74.0126	−	25.9885i	−0.552333	−	0.193944i
$135$		0			0
$136$	240.901	+	55.8110i	1.77133	+	0.410375i
$137$	−125.270	−	216.974i	−0.914378	−	1.58375i	−0.807809	−	0.589444i	$-0.799347\pi$
$137$	−125.270	−	216.974i	−0.914378	−	1.58375i	−0.106569	−	0.994305i	$-0.533987\pi$
$138$		0			0
$139$	14.3732	+	53.6416i	0.103404	+	0.385911i	0.998159	−	0.0606470i	$-0.0193164\pi$
$139$	14.3732	+	53.6416i	0.103404	+	0.385911i	−0.894755	+	0.446558i	$0.852650\pi$
$140$	−104.027	−	45.6559i	−0.743051	−	0.326114i
$141$		0			0
$142$	−179.351	−	122.565i	−1.26304	−	0.863136i
$143$			57.2841i			0.400588i
$144$		0			0
$145$	47.3276			0.326397
$146$	−36.3982	+	53.2620i	−0.249303	+	0.364808i
$147$		0			0
$148$	238.868	+	104.836i	1.61397	+	0.708349i
$149$	95.6864	−	25.6391i	0.642190	−	0.172074i	0.0769950	−	0.997031i	$-0.475467\pi$
$149$	95.6864	−	25.6391i	0.642190	−	0.172074i	0.565195	+	0.824957i	$0.308801\pi$
$150$		0			0
$151$	−86.6167	+	50.0082i	−0.573621	+	0.331180i	−0.758594	−	0.651563i	$-0.774113\pi$
$151$	−86.6167	+	50.0082i	−0.573621	+	0.331180i	0.184973	+	0.982744i	$0.440780\pi$
$152$	−3.58639	+	2.23720i	−0.0235947	+	0.0147184i
$153$		0			0
$154$	−9.15265	+	26.0659i	−0.0594328	+	0.169259i
$155$	−95.2464	+	355.464i	−0.614493	+	2.29332i
$156$		0			0
$157$	−138.066	+	36.9948i	−0.879404	+	0.235636i	−0.670150	−	0.742226i	$-0.733770\pi$
$157$	−138.066	+	36.9948i	−0.879404	+	0.235636i	−0.209254	+	0.977861i	$0.567104\pi$
$158$	0.704584	−	9.26688i	0.00445939	−	0.0586511i
$159$		0			0
$160$	−241.528	+	103.819i	−1.50955	+	0.648870i
$161$		−	101.090i		−	0.627887i
$162$		0			0
$163$	−29.7600	−	29.7600i	−0.182577	−	0.182577i	0.609901	−	0.792478i	$-0.291209\pi$
$163$	−29.7600	−	29.7600i	−0.182577	−	0.182577i	−0.792478	+	0.609901i	$0.791209\pi$
$164$	80.5064	+	12.3134i	0.490893	+	0.0750817i
$165$		0			0
$166$	178.354	+	207.707i	1.07442	+	1.25125i
$167$	−120.494	+	208.701i	−0.721518	+	1.24971i	0.238873	+	0.971051i	$0.423222\pi$
$167$	−120.494	+	208.701i	−0.721518	+	1.24971i	−0.960391	+	0.278655i	$0.910111\pi$
$168$		0			0
$169$	31.6452	−	18.2704i	0.187250	−	0.108109i
$170$	−168.265	+	479.202i	−0.989793	+	2.81883i
$171$		0			0
$172$	−0.687412	−	6.22248i	−0.00399658	−	0.0361772i
$173$	−6.87074	−	1.84101i	−0.0397152	−	0.0106417i	0.238907	−	0.971043i	$-0.423211\pi$
$173$	−6.87074	−	1.84101i	−0.0397152	−	0.0106417i	−0.278622	+	0.960401i	$0.589878\pi$
$174$		0			0
$175$	73.4522	−	127.223i	0.419727	−	0.726988i
$176$	29.6266	+	56.6509i	0.168333	+	0.321880i
$177$		0			0
$178$	−92.1049	−	62.9428i	−0.517443	−	0.353611i
$179$	156.510	−	156.510i	0.874357	−	0.874357i	−0.118586	−	0.992944i	$-0.537836\pi$
$179$	156.510	−	156.510i	0.874357	−	0.874357i	0.992944	+	0.118586i	$0.0378362\pi$
$180$		0			0
$181$	77.8756	−	77.8756i	0.430252	−	0.430252i	−0.458462	−	0.888714i	$-0.651599\pi$
$181$	77.8756	−	77.8756i	0.430252	−	0.430252i	0.888714	+	0.458462i	$0.151599\pi$
$182$	97.4168	−	18.3226i	0.535257	−	0.100674i
$183$		0			0
$184$	−170.966	−	159.674i	−0.929165	−	0.867793i
$185$	−267.888	+	463.995i	−1.44804	+	2.50808i
$186$		0			0
$187$	119.297	+	31.9657i	0.637954	+	0.170939i
$188$	141.787	+	113.576i	0.754185	+	0.604129i
$189$		0			0
$190$	−3.75833	−	7.82599i	−0.0197807	−	0.0411894i
$191$	293.984	−	169.732i	1.53919	−	0.888649i	0.540299	−	0.841473i	$-0.318311\pi$
$191$	293.984	−	169.732i	1.53919	−	0.888649i	0.998887	−	0.0471762i	$-0.0150222\pi$
$192$		0			0
$193$	112.869	−	195.495i	0.584813	−	1.01293i	−0.410086	−	0.912047i	$-0.634501\pi$
$193$	112.869	−	195.495i	0.584813	−	1.01293i	0.994899	−	0.100878i	$-0.0321653\pi$
$194$	3.54105	−	46.5728i	0.0182528	−	0.240066i
$195$		0			0
$196$	−146.492	−	22.4058i	−0.747408	−	0.114316i
$197$	−36.1795	−	36.1795i	−0.183652	−	0.183652i	0.609293	−	0.792945i	$-0.291453\pi$
$197$	−36.1795	−	36.1795i	−0.183652	−	0.183652i	−0.792945	+	0.609293i	$0.791453\pi$
$198$		0			0
$199$		−	132.303i		−	0.664837i	−0.943132	−	0.332419i	$-0.892135\pi$
$199$		−	132.303i		−	0.664837i	0.943132	−	0.332419i	$-0.107865\pi$
$200$	−99.1438	−	325.176i	−0.495719	−	1.62588i
$201$		0			0
$202$	−113.287	+	97.2774i	−0.560828	+	0.481571i
$203$	−19.2366	+	5.15443i	−0.0947616	+	0.0253913i
$204$		0			0
$205$	−43.2934	+	161.573i	−0.211187	+	0.788162i
$206$	−12.3036	−	25.6198i	−0.0597262	−	0.124368i
$207$		0			0
$208$	122.884	−	193.695i	0.590790	−	0.931227i
$209$	−1.82833	+	1.05559i	−0.00874800	+	0.00505066i
$210$		0			0
$211$	138.625	−	37.1444i	0.656989	−	0.176040i	0.0851022	−	0.996372i	$-0.472878\pi$
$211$	138.625	−	37.1444i	0.656989	−	0.176040i	0.571887	+	0.820333i	$0.306212\pi$
$212$	54.9446	−	125.191i	0.259173	−	0.590525i
$213$		0			0
$214$	−44.8707	−	238.566i	−0.209676	−	1.11480i
$215$	12.8579			0.0598043
$216$		0			0
$217$		−	154.854i		−	0.713613i
$218$	−11.9102	−	63.3233i	−0.0546337	−	0.290474i
$219$		0			0
$220$	−122.332	+	47.7051i	−0.556053	+	0.216841i
$221$	−114.696	−	428.050i	−0.518985	−	1.93688i
$222$		0			0
$223$	−81.7039	−	141.515i	−0.366385	−	0.634598i	0.622612	−	0.782531i	$-0.286071\pi$
$223$	−81.7039	−	141.515i	−0.366385	−	0.634598i	−0.988997	+	0.147933i	$0.952738\pi$
$224$	86.8637	−	68.5027i	0.387784	−	0.305816i
$225$		0			0
$226$	−30.3574	−	63.2135i	−0.134325	−	0.279706i
$227$	−219.301	−	58.7614i	−0.966082	−	0.258861i	−0.258909	−	0.965902i	$-0.583363\pi$
$227$	−219.301	−	58.7614i	−0.966082	−	0.258861i	−0.707173	+	0.707041i	$0.750030\pi$
$228$		0			0
$229$	84.5858	+	315.678i	0.369370	+	1.37851i	0.861399	+	0.507929i	$0.169589\pi$
$229$	84.5858	+	315.678i	0.369370	+	1.37851i	−0.492029	+	0.870579i	$0.663744\pi$
$230$	364.524	−	313.009i	1.58489	−	1.36091i
$231$		0			0
$232$	−21.6674	+	40.6751i	−0.0933938	+	0.175324i
$233$	200.291			0.859618			0.429809	−	0.902920i	$-0.358581\pi$
$233$	200.291			0.859618			0.429809	+	0.902920i	$0.358581\pi$
$234$		0			0
$235$	−263.837	+	263.837i	−1.12271	+	1.12271i
$236$	69.2972	+	94.3228i	0.293632	+	0.399673i
$237$		0			0
$238$	16.2026	−	213.100i	0.0680780	−	0.895380i
$239$	122.429	+	70.6841i	0.512253	+	0.295750i	0.733759	−	0.679409i	$-0.237764\pi$
$239$	122.429	+	70.6841i	0.512253	+	0.295750i	−0.221506	+	0.975159i	$0.571097\pi$
$240$		0			0
$241$	184.470	+	319.511i	0.765434	+	1.32577i	0.940017	+	0.341128i	$0.110809\pi$
$241$	184.470	+	319.511i	0.765434	+	1.32577i	−0.174583	+	0.984643i	$0.555858\pi$
$242$	−90.9402	−	189.365i	−0.375786	−	0.782501i
$243$		0			0
$244$	102.166	−	11.2865i	0.418713	−	0.0462562i
$245$	78.7781	−	294.004i	0.321543	−	1.20002i
$246$		0			0
$247$	6.56022	+	3.78755i	0.0265596	+	0.0153342i
$248$	−261.894	−	244.596i	−1.05602	−	0.986273i
$249$		0			0
$250$	282.496	−	53.1331i	1.12998	−	0.212533i
$251$	−248.750	−	248.750i	−0.991035	−	0.991035i	0.00892468	−	0.999960i	$-0.497159\pi$
$251$	−248.750	−	248.750i	−0.991035	−	0.991035i	−0.999960	+	0.00892468i	$0.997159\pi$
$252$		0			0
$253$	−82.6179	−	82.6179i	−0.326553	−	0.326553i
$254$	279.705	+	191.145i	1.10120	+	0.752539i
$255$		0			0
$256$	21.3495	−	255.108i	0.0833964	−	0.996516i
$257$	−436.391	−	251.950i	−1.69802	−	0.980352i	−0.947638	−	0.319347i	$-0.896536\pi$
$257$	−436.391	−	251.950i	−1.69802	−	0.980352i	−0.750382	−	0.661005i	$-0.770130\pi$
$258$		0			0
$259$	58.3511	−	217.769i	0.225294	−	0.840808i
$260$	367.707	+	294.546i	1.41426	+	1.13287i
$261$		0			0
$262$	58.3249	−	166.104i	0.222614	−	0.633983i
$263$	66.7613	+	115.634i	0.253845	+	0.439673i	0.964581	−	0.263786i	$-0.0849712\pi$
$263$	66.7613	+	115.634i	0.253845	+	0.439673i	−0.710736	+	0.703459i	$0.751638\pi$
$264$		0			0
$265$	243.181	+	140.401i	0.917664	+	0.529814i
$266$	2.37992	+	2.77161i	0.00894707	+	0.0104196i
$267$		0			0
$268$	92.8873	+	126.432i	0.346594	+	0.471761i
$269$	−184.417	+	184.417i	−0.685567	+	0.685567i	−0.961249	−	0.275682i	$-0.911096\pi$
$269$	−184.417	+	184.417i	−0.685567	+	0.685567i	0.275682	+	0.961249i	$0.411096\pi$
$270$		0			0
$271$	−145.196			−0.535777			−0.267888	−	0.963450i	$-0.586326\pi$
$271$	−145.196			−0.535777			−0.267888	+	0.963450i	$0.586326\pi$
$272$	−334.810	−	363.999i	−1.23092	−	1.33823i
$273$		0			0
$274$	−37.9887	+	499.637i	−0.138645	+	1.82349i
$275$	−43.9453	−	164.006i	−0.159801	−	0.596386i
$276$		0			0
$277$	38.1040	+	10.2099i	0.137560	+	0.0368590i	0.326942	−	0.945044i	$-0.393982\pi$
$277$	38.1040	+	10.2099i	0.137560	+	0.0368590i	−0.189382	+	0.981903i	$0.560649\pi$
$278$	36.7972	−	104.795i	0.132364	−	0.376961i
$279$		0			0
$280$	120.255	+	192.777i	0.429483	+	0.688490i
$281$	116.712	+	202.150i	0.415344	+	0.719397i	0.995464	−	0.0951340i	$-0.0303279\pi$
$281$	116.712	+	202.150i	0.415344	+	0.719397i	−0.580121	+	0.814531i	$0.696995\pi$
$282$		0			0
$283$	23.7359	+	88.5837i	0.0838726	+	0.313017i	0.995098	−	0.0988906i	$-0.0315294\pi$
$283$	23.7359	+	88.5837i	0.0838726	+	0.313017i	−0.911226	+	0.411907i	$0.864863\pi$
$284$	157.847	+	404.773i	0.555800	+	1.42526i
$285$		0			0
$286$	64.6414	−	94.5906i	0.226019	−	0.330736i
$287$		−	70.3875i		−	0.245253i
$288$		0			0
$289$	−666.441			−2.30603
$290$	−78.1498	−	53.4061i	−0.269482	−	0.184159i
$291$		0			0
$292$	120.205	−	46.8759i	0.411662	−	0.160534i
$293$	−16.2772	+	4.36146i	−0.0555535	+	0.0148855i	−0.286489	−	0.958084i	$-0.592488\pi$
$293$	−16.2772	+	4.36146i	−0.0555535	+	0.0148855i	0.230935	+	0.972969i	$0.425821\pi$
$294$		0			0
$295$	−208.184	+	120.195i	−0.705708	+	0.407441i
$296$	−276.131	−	442.657i	−0.932875	−	1.49546i
$297$		0			0
$298$	−186.934	−	65.6393i	−0.627296	−	0.220266i
$299$	−108.505	+	404.945i	−0.362892	+	1.35433i
$300$		0			0
$301$	−5.22619	+	1.40035i	−0.0173627	+	0.00465233i
$302$	199.457	+	15.1652i	0.660454	+	0.0502160i
$303$		0			0
$304$	8.44657	+	0.352821i	0.0277848	+	0.00116060i
$305$			211.112i			0.692172i
$306$		0			0
$307$	11.3806	+	11.3806i	0.0370705	+	0.0370705i	0.725399	−	0.688329i	$-0.241655\pi$
$307$	11.3806	+	11.3806i	0.0370705	+	0.0370705i	−0.688329	+	0.725399i	$0.741655\pi$
$308$	44.5270	−	32.7132i	0.144568	−	0.106212i
$309$		0			0
$310$	558.394	−	479.482i	1.80127	−	1.54672i
$311$	209.169	−	362.292i	0.672570	−	1.16493i	−0.304603	−	0.952479i	$-0.598524\pi$
$311$	209.169	−	362.292i	0.672570	−	1.16493i	0.977173	−	0.212446i	$-0.0681429\pi$
$312$		0			0
$313$	207.461	−	119.778i	0.662814	−	0.382676i	−0.130534	−	0.991444i	$-0.541669\pi$
$313$	207.461	−	119.778i	0.662814	−	0.382676i	0.793348	+	0.608768i	$0.208336\pi$
$314$	269.729	+	94.7113i	0.859009	+	0.301628i
$315$		0			0
$316$	−11.6205	+	14.5069i	−0.0367738	+	0.0459078i
$317$	−228.911	−	61.3365i	−0.722117	−	0.193491i	−0.121001	−	0.992652i	$-0.538610\pi$
$317$	−228.911	−	61.3365i	−0.722117	−	0.193491i	−0.601116	+	0.799162i	$0.705277\pi$
$318$		0			0
$319$	−11.5090	+	19.9341i	−0.0360783	+	0.0624894i
$320$	515.977	+	101.117i	1.61243	+	0.315991i
$321$		0			0
$322$	−114.073	+	166.925i	−0.354265	+	0.518400i
$323$	11.5485	−	11.5485i	0.0357539	−	0.0357539i
$324$		0			0
$325$	−430.789	+	430.789i	−1.32551	+	1.32551i
$326$	15.5590	+	82.7234i	0.0477271	+	0.253753i
$327$		0			0
$328$	−119.042	−	111.179i	−0.362931	−	0.338960i
$329$	78.5038	−	135.973i	0.238613	−	0.413291i
$330$		0			0
$331$	535.549	+	143.500i	1.61797	+	0.433534i	0.950405	−	0.311015i	$-0.100669\pi$
$331$	535.549	+	143.500i	1.61797	+	0.433534i	0.667567	+	0.744550i	$0.267336\pi$
$332$	−60.1233	−	544.237i	−0.181094	−	1.63927i
$333$		0			0
$334$	434.471	−	208.649i	1.30081	−	0.624697i
$335$	−279.053	+	161.112i	−0.832995	+	0.480930i
$336$		0			0
$337$	306.945	−	531.645i	0.910816	−	1.57758i	0.0979027	−	0.995196i	$-0.468787\pi$
$337$	306.945	−	531.645i	0.910816	−	1.57758i	0.812914	−	0.582384i	$-0.197880\pi$
$338$	−72.8712	−	5.54058i	−0.215595	−	0.0163922i
$339$		0			0
$340$	818.596	−	601.407i	2.40763	−	1.76885i
$341$	−126.558	−	126.558i	−0.371137	−	0.371137i
$342$		0			0
$343$			297.474i			0.867272i
$344$	−5.88657	+	11.0506i	−0.0171121	+	0.0321238i
$345$		0			0
$346$	9.26786	+	10.7932i	0.0267857	+	0.0311941i
$347$	372.241	−	99.7417i	1.07274	−	0.287440i	0.321122	−	0.947038i	$-0.395940\pi$
$347$	372.241	−	99.7417i	1.07274	−	0.287440i	0.751619	+	0.659598i	$0.229273\pi$
$348$		0			0
$349$	−43.3586	+	161.816i	−0.124237	+	0.463657i	−0.999811	−	0.0194254i	$-0.993816\pi$
$349$	−43.3586	+	161.816i	−0.124237	+	0.463657i	0.875575	+	0.483083i	$0.160483\pi$
$350$	−264.851	+	127.191i	−0.756717	+	0.363403i
$351$		0			0
$352$	15.0059	−	126.977i	0.0426305	−	0.360729i
$353$	−31.0994	+	17.9552i	−0.0881002	+	0.0508647i	−0.543403	−	0.839472i	$-0.682864\pi$
$353$	−31.0994	+	17.9552i	−0.0881002	+	0.0508647i	0.455303	+	0.890337i	$0.349531\pi$
$354$		0			0
$355$	−861.923	+	230.952i	−2.42795	+	0.650568i
$356$	81.0616	+	207.869i	0.227701	+	0.583901i
$357$		0			0
$358$	−435.049	+	81.8261i	−1.21522	+	0.228564i
$359$	−603.384			−1.68073			−0.840367	−	0.542017i	$-0.817661\pi$
$359$	−603.384			−1.68073			−0.840367	+	0.542017i	$0.817661\pi$
$360$		0			0
$361$		−	360.721i		−	0.999227i
$362$	−216.470	+	40.7147i	−0.597983	+	0.112472i
$363$		0			0
$364$	−181.536	−	79.6733i	−0.498724	−	0.218883i
$365$	68.5857	+	255.965i	0.187906	+	0.701275i
$366$		0			0
$367$	−262.962	−	455.464i	−0.716519	−	1.24105i	−0.962371	−	0.271740i	$-0.912401\pi$
$367$	−262.962	−	455.464i	−0.716519	−	1.24105i	0.245852	−	0.969307i	$-0.420932\pi$
$368$	102.127	+	456.586i	0.277519	+	1.24072i
$369$		0			0
$370$	965.938	−	463.879i	2.61064	−	1.25373i
$371$	−114.133	−	30.5820i	−0.307637	−	0.0824312i
$372$		0			0
$373$	−155.886	−	581.775i	−0.417925	−	1.55972i	−0.778903	−	0.627144i	$-0.784224\pi$
$373$	−155.886	−	581.775i	−0.417925	−	1.55972i	0.360978	−	0.932574i	$-0.382443\pi$
$374$	−160.919	−	187.403i	−0.430265	−	0.501077i
$375$		0			0
$376$	−105.962	−	347.540i	−0.281815	−	0.924309i
$377$	82.5904			0.219073
$378$		0			0
$379$	−84.3968	+	84.3968i	−0.222683	+	0.222683i	−0.809627	−	0.586944i	$-0.800331\pi$
$379$	−84.3968	+	84.3968i	−0.222683	+	0.222683i	0.586944	+	0.809627i	$0.300331\pi$
$380$	−2.62518	+	17.1637i	−0.00690836	+	0.0451677i
$381$		0			0
$382$	−676.974	−	51.4721i	−1.77218	−	0.134744i
$383$	−43.3195	−	25.0105i	−0.113106	−	0.0653016i	0.442380	−	0.896828i	$-0.354134\pi$
$383$	−43.3195	−	25.0105i	−0.113106	−	0.0653016i	−0.555486	+	0.831526i	$0.687468\pi$
$384$		0			0
$385$	56.7405	+	98.2774i	0.147378	+	0.255266i
$386$	−406.978	+	195.446i	−1.05435	+	0.506336i
$387$		0			0
$388$	−58.4016	+	72.9076i	−0.150519	+	0.187906i
$389$	114.891	−	428.778i	0.295349	−	1.10226i	−0.645591	−	0.763684i	$-0.723389\pi$
$389$	114.891	−	428.778i	0.295349	−	1.10226i	0.940940	−	0.338574i	$-0.109945\pi$
$390$		0			0
$391$	782.774	+	451.935i	2.00198	+	1.15584i
$392$	216.612	+	202.304i	0.552581	+	0.516083i
$393$		0			0
$394$	18.9153	+	100.568i	0.0480083	+	0.255248i
$395$	−26.9944	−	26.9944i	−0.0683403	−	0.0683403i
$396$		0			0
$397$	13.5678	+	13.5678i	0.0341758	+	0.0341758i	0.723988	−	0.689812i	$-0.242307\pi$
$397$	13.5678	+	13.5678i	0.0341758	+	0.0341758i	−0.689812	+	0.723988i	$0.742307\pi$
$398$	−149.295	+	218.465i	−0.375113	+	0.548907i
$399$		0			0
$400$	−203.229	+	648.825i	−0.508072	+	1.62206i
$401$	231.764	+	133.809i	0.577964	+	0.333688i	0.760324	−	0.649544i	$-0.225040\pi$
$401$	231.764	+	133.809i	0.577964	+	0.333688i	−0.182360	+	0.983232i	$0.558374\pi$
$402$		0			0
$403$	−166.213	+	620.314i	−0.412438	+	1.53924i
$404$	296.837	−	32.7923i	0.734745	−	0.0811691i
$405$		0			0
$406$	37.5809	+	13.1960i	0.0925639	+	0.0325024i
$407$	−130.288	−	225.665i	−0.320118	−	0.554460i
$408$		0			0
$409$	376.353	+	217.287i	0.920178	+	0.531265i	0.883692	−	0.468069i	$-0.155050\pi$
$409$	376.353	+	217.287i	0.920178	+	0.531265i	0.0364863	+	0.999334i	$0.488383\pi$
$410$	253.813	−	217.944i	0.619056	−	0.531571i
$411$		0			0
$412$	−8.59401	+	56.1886i	−0.0208592	+	0.136380i
$413$	71.5272	−	71.5272i	0.173189	−	0.173189i
$414$		0			0
$415$	1124.59			2.70987
$416$	−421.486	+	181.173i	−1.01319	+	0.435511i
$417$		0			0
$418$	4.21020	+	0.320112i	0.0100722	+	0.000765818i
$419$	26.4380	+	98.6680i	0.0630979	+	0.235484i	0.990272	−	0.139147i	$-0.0444360\pi$
$419$	26.4380	+	98.6680i	0.0630979	+	0.235484i	−0.927174	+	0.374631i	$0.877769\pi$
$420$		0			0
$421$	−402.531	−	107.858i	−0.956130	−	0.256194i	−0.253168	−	0.967422i	$-0.581473\pi$
$421$	−402.531	−	107.858i	−0.956130	−	0.256194i	−0.702961	+	0.711228i	$0.748139\pi$
$422$	−270.819	−	95.0942i	−0.641752	−	0.225342i
$423$		0			0
$424$	−231.998	+	144.721i	−0.547165	+	0.341323i
$425$	656.754	+	1137.53i	1.54530	+	2.67655i
$426$		0			0
$427$	−22.9922	−	85.8080i	−0.0538459	−	0.200955i
$428$	−195.114	+	444.567i	−0.455874	+	1.03871i
$429$		0			0
$430$	−21.2317	−	14.5093i	−0.0493760	−	0.0337426i
$431$		−	665.443i		−	1.54395i	−0.635652	−	0.771976i	$-0.719268\pi$
$431$		−	665.443i		−	1.54395i	0.635652	−	0.771976i	$-0.280732\pi$
$432$		0			0
$433$	482.470			1.11425			0.557124	−	0.830429i	$-0.311905\pi$
$433$	482.470			1.11425			0.557124	+	0.830429i	$0.311905\pi$
$434$	−174.743	+	255.703i	−0.402633	+	0.589177i
$435$		0			0
$436$	−51.7896	+	118.003i	−0.118783	+	0.270648i
$437$	−14.9240	+	3.99888i	−0.0341511	+	0.00915077i
$438$		0			0
$439$	422.092	−	243.695i	0.961485	−	0.555114i	0.0648553	−	0.997895i	$-0.479341\pi$
$439$	422.092	−	243.695i	0.961485	−	0.555114i	0.896630	+	0.442781i	$0.146008\pi$
$440$	255.833	+	59.2703i	0.581438	+	0.134705i
$441$		0			0
$442$	−293.635	+	836.246i	−0.664334	+	1.89196i
$443$	−9.08829	+	33.9180i	−0.0205153	+	0.0765642i	−0.975425	−	0.220334i	$-0.929285\pi$
$443$	−9.08829	+	33.9180i	−0.0205153	+	0.0765642i	0.954909	+	0.296898i	$0.0959521\pi$
$444$		0			0
$445$	−442.636	+	118.604i	−0.994687	+	0.266526i
$446$	−24.7771	+	325.875i	−0.0555541	+	0.730662i
$447$		0			0
$448$	−220.735	+	15.0952i	−0.492711	+	0.0336945i
$449$			515.482i			1.14807i	0.818832	+	0.574034i	$0.194622\pi$
$449$			515.482i			1.14807i	−0.818832	+	0.574034i	$0.805378\pi$
$450$		0			0
$451$	−57.5257	−	57.5257i	−0.127552	−	0.127552i
$452$	−21.2046	+	138.638i	−0.0469127	+	0.306721i
$453$		0			0
$454$	295.812	+	344.497i	0.651569	+	0.758803i
$455$	203.590	−	352.628i	0.447451	−	0.775007i
$456$		0			0
$457$	−233.569	+	134.851i	−0.511091	+	0.295079i	−0.733282	−	0.679925i	$-0.762012\pi$
$457$	−233.569	+	134.851i	−0.511091	+	0.295079i	0.222191	+	0.975003i	$0.428679\pi$
$458$	216.550	−	616.714i	0.472817	−	1.34654i
$459$		0			0
$460$	−955.132	+	105.516i	−2.07637	+	0.229382i
$461$	558.526	+	149.657i	1.21155	+	0.324635i	0.807371	−	0.590044i	$-0.200890\pi$
$461$	558.526	+	149.657i	1.21155	+	0.324635i	0.404182	+	0.914679i	$0.367556\pi$
$462$		0			0
$463$	190.028	−	329.138i	0.410427	−	0.710881i	−0.584509	−	0.811387i	$-0.698713\pi$
$463$	190.028	−	329.138i	0.410427	−	0.710881i	0.994936	+	0.100506i	$0.0320463\pi$
$464$	81.6775	−	42.7146i	0.176029	−	0.0920574i
$465$		0			0
$466$	−330.731	−	226.015i	−0.709723	−	0.485011i
$467$	−182.836	+	182.836i	−0.391512	+	0.391512i	−0.875226	−	0.483714i	$-0.839287\pi$
$467$	−182.836	+	182.836i	−0.391512	+	0.391512i	0.483714	+	0.875226i	$0.339287\pi$
$468$		0			0
$469$	95.8764	−	95.8764i	0.204427	−	0.204427i
$470$	733.384	−	137.938i	1.56039	−	0.293486i
$471$		0			0
$472$	−7.99005	−	233.948i	−0.0169281	−	0.495653i
$473$	−3.12675	+	5.41568i	−0.00661046	+	0.0114496i
$474$		0			0
$475$	−21.6877	−	5.81120i	−0.0456583	−	0.0122341i
$476$	−267.224	+	333.599i	−0.561396	+	0.700838i
$477$		0			0
$478$	−122.398	−	254.870i	−0.256063	−	0.533201i
$479$	−161.071	+	92.9946i	−0.336266	+	0.194143i	−0.658620	−	0.752476i	$-0.728859\pi$
$479$	−161.071	+	92.9946i	−0.336266	+	0.194143i	0.322354	+	0.946619i	$0.395526\pi$
$480$		0			0
$481$	−467.485	+	809.708i	−0.971903	+	1.68338i
$482$	55.9413	−	735.755i	0.116061	−	1.52646i
$483$		0			0
$484$	−63.5214	+	415.310i	−0.131242	+	0.858079i
$485$	−135.667	−	135.667i	−0.279725	−	0.279725i
$486$		0			0
$487$		−	359.645i		−	0.738490i	−0.929332	−	0.369245i	$-0.879616\pi$
$487$		−	359.645i		−	0.738490i	0.929332	−	0.369245i	$-0.120384\pi$
$488$	−181.438	−	96.6507i	−0.371799	−	0.198055i
$489$		0			0
$490$	−461.847	+	396.578i	−0.942544	+	0.809344i
$491$	−763.337	+	204.536i	−1.55466	+	0.416569i	−0.930968	−	0.365102i	$-0.881034\pi$
$491$	−763.337	+	204.536i	−1.55466	+	0.416569i	−0.623691	+	0.781671i	$0.714368\pi$
$492$		0			0
$493$	46.0871	−	171.999i	0.0934829	−	0.348883i
$494$	−6.55858	−	13.6570i	−0.0132765	−	0.0276457i
$495$		0			0
$496$	156.442	+	699.419i	0.315408	+	1.41012i
$497$	325.181	−	187.744i	0.654288	−	0.377754i
$498$		0			0
$499$	−195.524	+	52.3905i	−0.391832	+	0.104991i	−0.449355	−	0.893353i	$-0.648346\pi$
$499$	−195.524	+	52.3905i	−0.391832	+	0.104991i	0.0575236	+	0.998344i	$0.481680\pi$
$500$	−526.429	−	231.042i	−1.05286	−	0.462084i
$501$		0			0
$502$	130.051	+	691.447i	0.259065	+	1.37738i
$503$	146.874			0.291995			0.145998	−	0.989285i	$-0.453361\pi$
$503$	146.874			0.291995			0.145998	+	0.989285i	$0.453361\pi$
$504$		0			0
$505$			613.375i			1.21460i
$506$	43.1941	+	229.652i	0.0853637	+	0.453858i
$507$		0			0
$508$	−246.168	−	631.257i	−0.484583	−	1.24263i
$509$	−95.2179	−	355.358i	−0.187069	−	0.698150i	−0.994178	−	0.107748i	$-0.965636\pi$
$509$	−95.2179	−	355.358i	−0.187069	−	0.698150i	0.807110	−	0.590402i	$-0.201031\pi$
$510$		0			0
$511$	−55.7542	−	96.5691i	−0.109108	−	0.188981i
$512$	−323.126	+	397.156i	−0.631106	+	0.775696i
$513$		0			0
$514$	436.282	+	908.473i	0.848797	+	1.76746i
$515$	−112.768	−	30.2162i	−0.218968	−	0.0586722i
$516$		0			0
$517$	−46.9676	−	175.286i	−0.0908465	−	0.339044i
$518$	−342.091	+	293.747i	−0.660407	+	0.567078i
$519$		0			0
$520$	−274.800	−	901.302i	−0.528462	−	1.73327i
$521$	317.610			0.609616			0.304808	−	0.952414i	$-0.401408\pi$
$521$	317.610			0.609616			0.304808	+	0.952414i	$0.401408\pi$
$522$		0			0
$523$	307.029	−	307.029i	0.587053	−	0.587053i	−0.349779	−	0.936832i	$-0.613743\pi$
$523$	307.029	−	307.029i	0.587053	−	0.587053i	0.936832	+	0.349779i	$0.113743\pi$
$524$	−283.746	+	208.463i	−0.541501	+	0.397831i
$525$		0			0
$526$	20.2457	−	266.277i	0.0384899	−	0.506230i
$527$	1199.09	+	692.294i	2.27531	+	1.31365i
$528$		0			0
$529$	−163.041	−	282.395i	−0.308206	−	0.533828i
$530$	−243.120	−	506.251i	−0.458717	−	0.955190i
$531$		0			0
$532$	−0.802274	−	7.26221i	−0.00150803	−	0.0136508i
$533$	−75.5504	+	281.958i	−0.141746	+	0.529002i
$534$		0			0
$535$	−863.560	−	498.577i	−1.61413	−	0.931919i
$536$	−10.7100	−	313.588i	−0.0199814	−	0.585053i
$537$		0			0
$538$	512.623	−	96.4166i	0.952831	−	0.179213i
$539$	104.676	+	104.676i	0.194203	+	0.194203i
$540$		0			0
$541$	122.834	+	122.834i	0.227049	+	0.227049i	0.811459	−	0.584409i	$-0.198674\pi$
$541$	122.834	+	122.834i	0.227049	+	0.227049i	−0.584409	+	0.811459i	$0.698674\pi$
$542$	239.754	+	163.844i	0.442351	+	0.302295i
$543$		0			0
$544$	142.105	+	978.866i	0.261223	+	1.79939i
$545$	−229.217	−	132.339i	−0.420582	−	0.242823i
$546$		0			0
$547$	34.4641	−	128.622i	0.0630056	−	0.235140i	−0.927241	−	0.374465i	$-0.877826\pi$
$547$	34.4641	−	128.622i	0.0630056	−	0.235140i	0.990247	+	0.139325i	$0.0444931\pi$
$548$	626.537	−	782.159i	1.14332	−	1.42730i
$549$		0			0
$550$	−112.506	+	320.405i	−0.204555	+	0.582554i
$551$	1.52191	+	2.63603i	0.00276209	+	0.00478408i
$552$		0			0
$553$	13.9120	+	8.03210i	0.0251573	+	0.0145246i
$554$	−51.3981	−	59.8571i	−0.0927764	−	0.108045i
$555$		0			0
$556$	−179.016	+	131.520i	−0.321971	+	0.236546i
$557$	−144.109	+	144.109i	−0.258723	+	0.258723i	−0.824535	−	0.565811i	$-0.808563\pi$
$557$	−144.109	+	144.109i	−0.258723	+	0.258723i	0.565811	+	0.824535i	$0.308563\pi$
$558$		0			0
$559$	22.4381			0.0401397
$560$	18.9650	−	454.024i	0.0338661	−	0.810757i
$561$		0			0
$562$	35.3934	−	465.503i	0.0629775	−	0.828297i
$563$	117.955	+	440.213i	0.209511	+	0.781906i	0.988027	+	0.154281i	$0.0493061\pi$
$563$	117.955	+	440.213i	0.209511	+	0.781906i	−0.778516	+	0.627625i	$0.784027\pi$
$564$		0			0
$565$	−278.241	−	74.5543i	−0.492461	−	0.131955i
$566$	60.7670	−	173.059i	0.107362	−	0.305757i
$567$		0			0
$568$	196.114	−	846.502i	0.345271	−	1.49032i
$569$	−36.6164	−	63.4215i	−0.0643522	−	0.111461i	0.832054	−	0.554694i	$-0.187165\pi$
$569$	−36.6164	−	63.4215i	−0.0643522	−	0.111461i	−0.896406	+	0.443233i	$0.853831\pi$
$570$		0			0
$571$	−259.035	−	966.734i	−0.453652	−	1.69305i	−0.692020	−	0.721879i	$-0.743279\pi$
$571$	−259.035	−	966.734i	−0.453652	−	1.69305i	0.238367	−	0.971175i	$-0.423388\pi$
$572$	−213.479	+	83.2492i	−0.373214	+	0.145541i
$573$		0			0
$574$	−79.4278	+	116.228i	−0.138376	+	0.202487i
$575$		−	1242.61i		−	2.16106i
$576$		0			0
$577$	−314.306			−0.544725			−0.272362	−	0.962195i	$-0.587805\pi$
$577$	−314.306			−0.544725			−0.272362	+	0.962195i	$0.587805\pi$
$578$	1100.46	+	752.036i	1.90392	+	1.30110i
$579$		0			0
$580$	68.7797	+	176.374i	0.118586	+	0.304093i
$581$	−457.099	+	122.479i	−0.786745	+	0.210808i
$582$		0			0
$583$	−118.272	+	68.2843i	−0.202868	+	0.117126i
$584$	−251.386	−	58.2400i	−0.430455	−	0.0997261i
$585$		0			0
$586$	31.7994	+	11.1659i	0.0542651	+	0.0190544i
$587$	190.651	−	711.520i	0.324789	−	1.21213i	−0.589734	−	0.807597i	$-0.700768\pi$
$587$	190.651	−	711.520i	0.324789	−	1.21213i	0.914524	−	0.404533i	$-0.132566\pi$
$588$		0			0
$589$	−22.8613	+	6.12567i	−0.0388138	+	0.0104001i
$590$	479.396	+	36.4497i	0.812536	+	0.0617792i
$591$		0			0
$592$	−43.5477	+	1042.53i	−0.0735603	+	1.76104i
$593$			360.066i			0.607194i	0.952801	+	0.303597i	$0.0981876\pi$
$593$			360.066i			0.607194i	−0.952801	+	0.303597i	$0.901812\pi$
$594$		0			0
$595$	−620.761	−	620.761i	−1.04330	−	1.04330i
$596$	234.606	+	319.330i	0.393634	+	0.535789i
$597$		0			0
$598$	636.124	−	546.226i	1.06375	−	0.913422i
$599$	−274.206	+	474.939i	−0.457773	+	0.792887i	−0.998843	−	0.0480912i	$-0.984686\pi$
$599$	−274.206	+	474.939i	−0.457773	+	0.792887i	0.541070	+	0.840978i	$0.318020\pi$
$600$		0			0
$601$	−5.92579	+	3.42126i	−0.00985989	+	0.00569261i	−0.504922	−	0.863165i	$-0.668479\pi$
$601$	−5.92579	+	3.42126i	−0.00985989	+	0.00569261i	0.495062	+	0.868858i	$0.335145\pi$
$602$	10.2100	+	3.58508i	0.0169601	+	0.00595528i
$603$		0			0
$604$	−312.241	−	250.116i	−0.516955	−	0.414099i
$605$	−833.511	−	223.339i	−1.37770	−	0.369155i
$606$		0			0
$607$	75.2267	−	130.296i	0.123932	−	0.214656i	−0.797383	−	0.603474i	$-0.793783\pi$
$607$	75.2267	−	130.296i	0.123932	−	0.214656i	0.921315	+	0.388817i	$0.127116\pi$
$608$	−13.5493	−	10.1140i	−0.0222850	−	0.0166349i
$609$		0			0
$610$	238.227	−	348.600i	0.390535	−	0.571475i
$611$	−460.417	+	460.417i	−0.753546	+	0.753546i
$612$		0			0
$613$	150.641	−	150.641i	0.245744	−	0.245744i	−0.573477	−	0.819221i	$-0.694406\pi$
$613$	150.641	−	150.641i	0.245744	−	0.245744i	0.819221	+	0.573477i	$0.194406\pi$
$614$	−5.95000	−	31.6346i	−0.00969055	−	0.0515222i
$615$		0			0
$616$	−110.440	+	3.77186i	−0.179286	+	0.00612316i
$617$	149.034	−	258.134i	0.241545	−	0.418369i	−0.719609	−	0.694379i	$-0.755679\pi$
$617$	149.034	−	258.134i	0.241545	−	0.418369i	0.961155	+	0.276010i	$0.0890124\pi$
$618$		0			0
$619$	942.062	+	252.425i	1.52191	+	0.407794i	0.920370	−	0.391049i	$-0.127888\pi$
$619$	942.062	+	252.425i	1.52191	+	0.407794i	0.601540	+	0.798843i	$0.294554\pi$
$620$	−1463.11	+	161.634i	−2.35986	+	0.260700i
$621$		0			0
$622$	−754.214	+	362.201i	−1.21256	+	0.582317i
$623$	166.995	−	96.4147i	0.268050	−	0.154759i
$624$		0			0
$625$	59.2047	−	102.546i	0.0947276	−	0.164073i
$626$	−477.731	−	36.3231i	−0.763149	−	0.0580241i
$627$		0			0
$628$	−338.515	−	460.764i	−0.539036	−	0.733700i
$629$	1425.40	+	1425.40i	2.26613	+	2.26613i
$630$		0			0
$631$		−	678.160i		−	1.07474i	−0.843347	−	0.537369i	$-0.819418\pi$
$631$		−	678.160i		−	1.07474i	0.843347	−	0.537369i	$-0.180582\pi$
$632$	35.5585	−	10.8415i	0.0562634	−	0.0171543i
$633$		0			0
$634$	308.776	+	359.593i	0.487028	+	0.567182i
$635$	1344.20	−	360.177i	2.11685	−	0.567208i
$636$		0			0
$637$	137.474	−	513.060i	0.215815	−	0.805432i
$638$	41.4986	−	19.9291i	0.0650448	−	0.0312369i
$639$		0			0
$640$	−737.904	−	749.216i	−1.15297	−	1.17065i
$641$	−612.449	+	353.597i	−0.955458	+	0.551634i	−0.894772	−	0.446523i	$-0.852662\pi$
$641$	−612.449	+	353.597i	−0.955458	+	0.551634i	−0.0606860	+	0.998157i	$0.519329\pi$
$642$		0			0
$643$	854.507	−	228.964i	1.32894	−	0.356088i	0.476619	−	0.879110i	$-0.341862\pi$
$643$	854.507	−	228.964i	1.32894	−	0.356088i	0.852319	+	0.523022i	$0.175196\pi$
$644$	376.728	−	146.911i	0.584981	−	0.228122i
$645$		0			0
$646$	−32.1012	+	6.03776i	−0.0496923	+	0.00934637i
$647$	199.887			0.308944			0.154472	−	0.987997i	$-0.450632\pi$
$647$	199.887			0.308944			0.154472	+	0.987997i	$0.450632\pi$
$648$		0			0
$649$		−	116.914i		−	0.180145i
$650$	1197.46	−	225.224i	1.84225	−	0.346498i
$651$		0			0
$652$	67.6562	−	154.155i	0.103767	−	0.236433i
$653$	138.705	+	517.655i	0.212413	+	0.792734i	0.987061	+	0.160343i	$0.0512599\pi$
$653$	138.705	+	517.655i	0.212413	+	0.792734i	−0.774649	+	0.632392i	$0.782073\pi$
$654$		0			0
$655$	−361.576	−	626.269i	−0.552025	−	0.956135i
$656$	71.1095	+	317.915i	0.108399	+	0.484626i
$657$		0			0
$658$	−283.066	+	135.939i	−0.430191	+	0.206594i
$659$	229.743	+	61.5594i	0.348624	+	0.0934134i	0.428882	−	0.903361i	$-0.358908\pi$
$659$	229.743	+	61.5594i	0.348624	+	0.0934134i	−0.0802580	+	0.996774i	$0.525574\pi$
$660$		0			0
$661$	110.816	+	413.571i	0.167649	+	0.625675i	0.997687	+	0.0679689i	$0.0216519\pi$
$661$	110.816	+	413.571i	0.167649	+	0.625675i	−0.830038	+	0.557707i	$0.811681\pi$
$662$	−722.396	−	841.286i	−1.09123	−	1.27083i
$663$		0			0
$664$	−514.858	+	966.519i	−0.775389	+	1.45560i
$665$	15.0064			0.0225660
$666$		0			0
$667$	−119.116	+	119.116i	−0.178585	+	0.178585i
$668$	−952.867	−	145.740i	−1.42645	−	0.218174i
$669$		0			0
$670$	642.591	+	48.8579i	0.959092	+	0.0729222i
$671$	−88.9193	−	51.3376i	−0.132518	−	0.0765091i
$672$		0			0
$673$	36.9545	+	64.0071i	0.0549102	+	0.0951072i	0.892174	−	0.451692i	$-0.149179\pi$
$673$	36.9545	+	64.0071i	0.0549102	+	0.0951072i	−0.837264	+	0.546799i	$0.815846\pi$
$674$	−1106.77	+	531.512i	−1.64209	+	0.788593i
$675$		0			0
$676$	114.077	+	91.3793i	0.168752	+	0.135176i
$677$	33.8203	−	126.219i	0.0499562	−	0.186439i	−0.936439	−	0.350830i	$-0.885899\pi$
$677$	33.8203	−	126.219i	0.0499562	−	0.186439i	0.986395	+	0.164391i	$0.0525660\pi$
$678$		0			0
$679$	69.9179	+	40.3671i	0.102972	+	0.0594509i
$680$	−2030.36	+	69.3430i	−2.98582	+	0.101975i
$681$		0			0
$682$	66.1666	+	351.791i	0.0970185	+	0.515823i
$683$	−619.224	−	619.224i	−0.906624	−	0.906624i	0.0893737	−	0.995998i	$-0.471513\pi$
$683$	−619.224	−	619.224i	−0.906624	−	0.906624i	−0.995998	+	0.0893737i	$0.971513\pi$
$684$		0			0
$685$	1455.44	+	1455.44i	2.12473	+	2.12473i
$686$	335.680	−	491.205i	0.489330	−	0.716042i
$687$		0			0
$688$	22.1901	−	11.6047i	0.0322530	−	0.0168673i
$689$	424.370	+	245.010i	0.615922	+	0.355603i
$690$		0			0
$691$	−80.0807	+	298.865i	−0.115891	+	0.432511i	−0.999352	−	0.0359935i	$-0.988540\pi$
$691$	−80.0807	+	298.865i	−0.115891	+	0.432511i	0.883461	+	0.468505i	$0.155207\pi$
$692$	−3.12421	−	28.2804i	−0.00451475	−	0.0408676i
$693$		0			0
$694$	−727.216	−	255.351i	−1.04786	−	0.367941i
$695$	−228.119	−	395.114i	−0.328229	−	0.568509i
$696$		0			0
$697$	545.035	+	314.676i	0.781973	+	0.451472i
$698$	254.195	−	218.272i	0.364177	−	0.312711i
$699$		0			0
$700$	580.863	+	88.8425i	0.829804	+	0.126918i
$701$	627.258	−	627.258i	0.894805	−	0.894805i	−0.100166	−	0.994971i	$-0.531937\pi$
$701$	627.258	−	627.258i	0.894805	−	0.894805i	0.994971	+	0.100166i	$0.0319372\pi$
$702$		0			0
$703$	−34.4578			−0.0490154
$704$	−168.063	+	192.737i	−0.238726	+	0.273774i
$705$		0			0
$706$	71.6142	+	5.44501i	0.101437	+	0.00771248i
$707$	−66.8024	−	249.310i	−0.0944872	−	0.352631i
$708$		0			0
$709$	435.452	+	116.679i	0.614178	+	0.164569i	0.552480	−	0.833526i	$-0.313682\pi$
$709$	435.452	+	116.679i	0.614178	+	0.164569i	0.0616984	+	0.998095i	$0.480348\pi$
$710$	1683.87	+	591.265i	2.37164	+	0.832768i
$711$		0			0
$712$	100.713	−	434.717i	0.141451	−	0.610557i
$713$	−654.926	−	1134.37i	−0.918550	−	1.59098i
$714$		0			0
$715$	−121.805	−	454.582i	−0.170356	−	0.635778i
$716$	810.711	+	355.809i	1.13228	+	0.496940i
$717$		0			0
$718$	996.339	+	680.879i	1.38766	+	0.948300i
$719$			608.687i			0.846574i	0.905996	+	0.423287i	$0.139124\pi$
$719$			608.687i			0.846574i	−0.905996	+	0.423287i	$0.860876\pi$
$720$		0			0
$721$	49.1263			0.0681363
$722$	−407.050	+	595.641i	−0.563781	+	0.824988i
$723$		0			0
$724$	403.390	+	177.042i	0.557169	+	0.244533i
$725$	−236.459	+	63.3590i	−0.326150	+	0.0873917i
$726$		0			0
$727$	−712.721	+	411.490i	−0.980359	+	0.566011i	−0.902379	−	0.430944i	$-0.858181\pi$
$727$	−712.721	+	411.490i	−0.980359	+	0.566011i	−0.0779806	+	0.996955i	$0.524847\pi$
$728$	209.855	+	336.412i	0.288262	+	0.462104i
$729$		0			0
$730$	175.588	−	500.058i	0.240531	−	0.685011i
$731$	12.5209	−	46.7286i	0.0171285	−	0.0639243i
$732$		0			0
$733$	−694.142	+	185.995i	−0.946988	+	0.253745i	−0.699084	−	0.715040i	$-0.746408\pi$
$733$	−694.142	+	185.995i	−0.946988	+	0.253745i	−0.247904	+	0.968785i	$0.579742\pi$
$734$	−79.7446	+	1048.82i	−0.108644	+	1.42891i
$735$		0			0
$736$	346.591	−	869.183i	0.470912	−	1.18095i
$737$		−	156.714i		−	0.212638i
$738$		0			0
$739$	772.871	+	772.871i	1.04583	+	1.04583i	0.998898	+	0.0469350i	$0.0149454\pi$
$739$	772.871	+	772.871i	1.04583	+	1.04583i	0.0469350	+	0.998898i	$0.485055\pi$
$740$	−2118.46	−	324.018i	−2.86279	−	0.437862i
$741$		0			0
$742$	153.953	+	179.291i	0.207484	+	0.241632i
$743$	39.7288	−	68.8122i	0.0534707	−	0.0926140i	−0.838051	−	0.545592i	$-0.816305\pi$
$743$	39.7288	−	68.8122i	0.0534707	−	0.0926140i	0.891522	+	0.452978i	$0.149638\pi$
$744$		0			0
$745$	−704.807	+	406.921i	−0.946050	+	0.546202i
$746$	−399.088	+	1136.56i	−0.534971	+	1.52355i
$747$		0			0
$748$	54.2460	+	491.036i	0.0725214	+	0.656465i
$749$	405.300	+	108.600i	0.541121	+	0.144993i
$750$		0			0
$751$	−708.730	+	1227.56i	−0.943715	+	1.63456i	−0.185410	+	0.982661i	$0.559361\pi$
$751$	−708.730	+	1227.56i	−0.943715	+	1.63456i	−0.758305	+	0.651900i	$0.773972\pi$
$752$	−217.206	+	693.448i	−0.288838	+	0.922138i
$753$		0			0
$754$	−136.378	−	93.1980i	−0.180872	−	0.123605i
$755$	581.018	−	581.018i	0.769561	−	0.769561i
$756$		0			0
$757$	−279.258	+	279.258i	−0.368901	+	0.368901i	−0.867076	−	0.498175i	$-0.834004\pi$
$757$	−279.258	+	279.258i	−0.368901	+	0.368901i	0.498175	+	0.867076i	$0.334004\pi$
$758$	234.597	−	44.1241i	0.309495	−	0.0582112i
$759$		0			0
$760$	23.7030	−	25.3793i	0.0311881	−	0.0333938i
$761$	462.701	−	801.421i	0.608017	−	1.05312i	−0.383550	−	0.923520i	$-0.625299\pi$
$761$	462.701	−	801.421i	0.608017	−	1.05312i	0.991567	−	0.129596i	$-0.0413679\pi$
$762$		0			0
$763$	107.580	+	28.8259i	0.140996	+	0.0377797i
$764$	1059.77	+	848.915i	1.38714	+	1.11114i
$765$		0			0
$766$	43.3086	+	90.1819i	0.0565387	+	0.117731i
$767$	−363.297	+	209.750i	−0.473660	+	0.273468i
$768$		0			0
$769$	462.791	−	801.578i	0.601809	−	1.04236i	−0.390738	−	0.920502i	$-0.627780\pi$
$769$	462.791	−	801.578i	0.601809	−	1.04236i	0.992547	−	0.121862i	$-0.0388865\pi$
$770$	17.2068	−	226.309i	0.0223465	−	0.293907i
$771$		0			0
$772$	892.571	+	136.518i	1.15618	+	0.176837i
$773$	216.688	+	216.688i	0.280321	+	0.280321i	0.833237	−	0.552916i	$-0.186485\pi$
$773$	216.688	+	216.688i	0.280321	+	0.280321i	−0.552916	+	0.833237i	$0.686485\pi$
$774$		0			0
$775$		−	1903.49i		−	2.45611i
$776$	178.707	−	54.4865i	0.230293	−	0.0702145i
$777$		0			0
$778$	−673.562	+	578.374i	−0.865761	+	0.743412i
$779$	−10.3914	+	2.78437i	−0.0133394	+	0.00357429i
$780$		0			0
$781$	112.324	−	419.199i	0.143821	−	0.536747i
$782$	−782.578	−	1629.57i	−1.00074	−	2.08385i
$783$		0			0
$784$	−129.393	−	578.488i	−0.165042	−	0.737867i
$785$	1016.97	−	587.148i	1.29550	−	0.747960i
$786$		0			0
$787$	811.343	−	217.399i	1.03093	−	0.276237i	0.296581	−	0.955008i	$-0.404154\pi$
$787$	811.343	−	217.399i	1.03093	−	0.276237i	0.734350	+	0.678771i	$0.237487\pi$
$788$	82.2504	−	187.408i	0.104379	−	0.237827i
$789$		0			0
$790$	14.1131	+	75.0360i	0.0178647	+	0.0949823i
$791$	121.212			0.153239
$792$		0			0
$793$			368.408i			0.464575i
$794$	−7.09346	−	37.7142i	−0.00893383	−	0.0474990i
$795$		0			0
$796$	493.047	−	192.271i	0.619406	−	0.241547i
$797$	−116.745	−	435.698i	−0.146481	−	0.546673i	−0.999685	−	0.0250964i	$-0.992011\pi$
$797$	−116.745	−	435.698i	−0.146481	−	0.546673i	0.853204	−	0.521577i	$-0.174656\pi$
$798$		0			0
$799$	701.922	+	1215.77i	0.878501	+	1.52161i
$800$	1067.74	−	842.044i	1.33467	−	1.05255i
$801$		0			0
$802$	−231.706	−	482.482i	−0.288910	−	0.601599i
$803$	−124.490	−	33.3569i	−0.155031	−	0.0415403i
$804$		0			0
$805$	214.950	+	802.204i	0.267019	+	0.996527i
$806$	974.442	−	836.734i	1.20899	−	1.03813i
$807$		0			0
$808$	−527.157	−	280.813i	−0.652422	−	0.347541i
$809$	−814.365			−1.00663			−0.503316	−	0.864102i	$-0.667887\pi$
$809$	−814.365			−1.00663			−0.503316	+	0.864102i	$0.667887\pi$
$810$		0			0
$811$	417.721	−	417.721i	0.515069	−	0.515069i	−0.401006	−	0.916075i	$-0.631339\pi$
$811$	417.721	−	417.721i	0.515069	−	0.515069i	0.916075	+	0.401006i	$0.131339\pi$
$812$	−47.1648	−	64.1976i	−0.0580847	−	0.0790610i
$813$		0			0
$814$	−39.5105	+	519.652i	−0.0485386	+	0.638393i
$815$	299.441	+	172.883i	0.367413	+	0.212126i
$816$		0			0
$817$	0.413472	+	0.716155i	0.000506086	+	0.000876566i
$818$	−376.259	−	783.486i	−0.459974	−	0.957807i
$819$		0			0
$820$	−665.046	+	73.4692i	−0.811031	+	0.0895966i
$821$	200.307	−	747.558i	0.243980	−	0.910545i	−0.729914	−	0.683539i	$-0.760440\pi$
$821$	200.307	−	747.558i	0.243980	−	0.910545i	0.973893	−	0.227006i	$-0.0728936\pi$
$822$		0			0
$823$	708.953	+	409.314i	0.861426	+	0.497344i	0.864489	−	0.502651i	$-0.167642\pi$
$823$	708.953	+	409.314i	0.861426	+	0.497344i	−0.00306374	+	0.999995i	$0.500975\pi$
$824$	77.5961	−	83.0838i	0.0941700	−	0.100830i
$825$		0			0
$826$	−198.823	+	37.3957i	−0.240706	+	0.0452732i
$827$	193.297	+	193.297i	0.233733	+	0.233733i	0.814249	−	0.580516i	$-0.197149\pi$
$827$	193.297	+	193.297i	0.233733	+	0.233733i	−0.580516	+	0.814249i	$0.697149\pi$
$828$		0			0
$829$	−373.959	−	373.959i	−0.451096	−	0.451096i	0.444622	−	0.895718i	$-0.353338\pi$
$829$	−373.959	−	373.959i	−0.451096	−	0.451096i	−0.895718	+	0.444622i	$0.853338\pi$
$830$	−1856.99	−	1269.03i	−2.23734	−	1.52895i
$831$		0			0
$832$	900.421	+	176.458i	1.08224	+	0.212088i
$833$	−991.763	−	572.595i	−1.19059	−	0.687389i
$834$		0			0
$835$	512.417	−	1912.37i	0.613673	−	2.29026i
$836$	−6.59087	−	5.27952i	−0.00788382	−	0.00631522i
$837$		0			0
$838$	67.6846	−	192.759i	0.0807692	−	0.230023i
$839$	240.931	+	417.305i	0.287164	+	0.497383i	0.973132	−	0.230249i	$-0.0739541\pi$
$839$	240.931	+	417.305i	0.287164	+	0.497383i	−0.685967	+	0.727632i	$0.740621\pi$
$840$		0			0
$841$	−699.587	−	403.907i	−0.831851	−	0.480270i
$842$	542.969	+	632.330i	0.644856	+	0.750986i
$843$		0			0
$844$	339.883	+	462.627i	0.402705	+	0.548136i
$845$	−212.274	+	212.274i	−0.251211	+	0.251211i
$846$		0			0
$847$	363.109			0.428701
$848$	546.395	+	22.8235i	0.644334	+	0.0269145i
$849$		0			0
$850$	199.164	−	2619.46i	0.234311	−	3.08171i
$851$	−493.570	−	1842.03i	−0.579989	−	2.16455i
$852$		0			0
$853$	−258.984	−	69.3945i	−0.303615	−	0.0813535i	0.103795	−	0.994599i	$-0.466901\pi$
$853$	−258.984	−	69.3945i	−0.303615	−	0.0813535i	−0.407410	+	0.913245i	$0.633568\pi$
$854$	−58.8629	+	167.636i	−0.0689261	+	0.196295i
$855$		0			0
$856$	823.848	−	513.919i	0.962439	−	0.600373i
$857$	56.9837	+	98.6987i	0.0664921	+	0.115168i	0.897355	−	0.441310i	$-0.145486\pi$
$857$	56.9837	+	98.6987i	0.0664921	+	0.115168i	−0.830863	+	0.556477i	$0.812153\pi$
$858$		0			0
$859$	29.2485	+	109.157i	0.0340494	+	0.127074i	0.980859	−	0.194721i	$-0.0623803\pi$
$859$	29.2485	+	109.157i	0.0340494	+	0.127074i	−0.946809	+	0.321796i	$0.895714\pi$
$860$	18.6860	+	47.9171i	0.0217279	+	0.0557176i
$861$		0			0
$862$	−750.910	+	1098.81i	−0.871125	+	1.27473i
$863$			856.201i			0.992121i	0.868288	+	0.496061i	$0.165221\pi$
$863$			856.201i			0.992121i	−0.868288	+	0.496061i	$0.834779\pi$
$864$		0			0
$865$	58.4377			0.0675580
$866$	−796.679	−	544.436i	−0.919953	−	0.628679i
$867$		0			0
$868$	577.089	−	225.044i	0.664849	−	0.259268i
$869$	17.9343	−	4.80548i	0.0206379	−	0.00552990i
$870$		0			0
$871$	−486.970	+	281.153i	−0.559094	+	0.322793i
$872$	218.676	−	136.411i	0.250775	−	0.156435i
$873$		0			0
$874$	29.1558	+	10.2376i	0.0333591	+	0.0117136i
$875$	−128.597	+	479.931i	−0.146968	+	0.548492i
$876$		0			0
$877$	−836.328	+	224.093i	−0.953623	+	0.255523i	−0.701899	−	0.712276i	$-0.747664\pi$
$877$	−836.328	+	224.093i	−0.953623	+	0.255523i	−0.251724	+	0.967799i	$0.580998\pi$
$878$	−971.974	−	73.9017i	−1.10703	−	0.0841704i
$879$		0			0
$880$	−355.562	−	386.561i	−0.404047	−	0.439274i
$881$		−	574.718i		−	0.652347i	−0.945310	−	0.326174i	$-0.894241\pi$
$881$		−	574.718i		−	0.652347i	0.945310	−	0.326174i	$-0.105759\pi$
$882$		0			0
$883$	488.857	+	488.857i	0.553632	+	0.553632i	0.927487	−	0.373855i	$-0.121964\pi$
$883$	488.857	+	488.857i	0.553632	+	0.553632i	−0.373855	+	0.927487i	$0.621964\pi$
$884$	1428.52	−	1049.50i	1.61597	−	1.18722i
$885$		0			0
$886$	53.2813	−	45.7516i	0.0601369	−	0.0516383i
$887$	−366.906	+	635.500i	−0.413648	+	0.716460i	−0.995286	−	0.0969885i	$-0.969079\pi$
$887$	−366.906	+	635.500i	−0.413648	+	0.716460i	0.581637	+	0.813448i	$0.302412\pi$
$888$		0			0
$889$	−507.131	+	292.792i	−0.570452	+	0.329350i
$890$	864.740	+	303.641i	0.971618	+	0.341170i
$891$		0			0
$892$	408.642	−	510.143i	0.458119	−	0.571909i
$893$	−23.1793	−	6.21087i	−0.0259566	−	0.00695506i
$894$		0			0
$895$	−909.203	+	1574.79i	−1.01587	+	1.75954i
$896$	381.523	+	224.159i	0.425807	+	0.250177i
$897$		0			0
$898$	581.688	−	851.191i	0.647760	−	0.947875i
$899$	−182.467	+	182.467i	−0.202967	+	0.202967i
$900$		0			0
$901$	747.055	−	747.055i	0.829140	−	0.829140i
$902$	30.0754	+	159.904i	0.0333431	+	0.177277i
$903$		0			0
$904$	191.458	−	204.998i	0.211790	−	0.226768i
$905$	−452.397	+	783.575i	−0.499887	+	0.865829i
$906$		0			0
$907$	−992.430	−	265.921i	−1.09419	−	0.293187i	−0.333793	−	0.942646i	$-0.608329\pi$
$907$	−992.430	−	265.921i	−1.09419	−	0.293187i	−0.760396	+	0.649459i	$0.774995\pi$
$908$	−99.7186	−	902.656i	−0.109822	−	0.994114i
$909$		0			0
$910$	−734.097	+	352.540i	−0.806700	+	0.387407i
$911$	−636.932	+	367.733i	−0.699157	+	0.403659i	−0.807033	−	0.590506i	$-0.798928\pi$
$911$	−636.932	+	367.733i	−0.699157	+	0.403659i	0.107876	+	0.994164i	$0.465595\pi$
$912$		0			0
$913$	−273.475	+	473.673i	−0.299535	+	0.518809i
$914$	537.851	+	40.8942i	0.588459	+	0.0447420i
$915$		0			0
$916$	−1053.50	+	773.988i	−1.15011	+	0.844965i
$917$	215.172	+	215.172i	0.234647	+	0.234647i
$918$		0			0
$919$			994.090i			1.08171i	0.841116	+	0.540854i	$0.181899\pi$
$919$			994.090i			1.08171i	−0.841116	+	0.540854i	$0.818101\pi$
$920$	1696.23	+	903.571i	1.84373	+	0.982143i
$921$		0			0
$922$	−753.390	−	877.381i	−0.817126	−	0.951607i
$923$	−1504.12	+	403.029i	−1.62960	+	0.436651i
$924$		0			0
$925$	717.259	−	2676.85i	0.775415	−	2.89389i
$926$	−685.195	+	329.055i	−0.739951	+	0.355351i
$927$		0			0
$928$	−183.071	−	21.6351i	−0.197275	−	0.0233137i
$929$	670.208	−	386.945i	0.721430	−	0.416518i	−0.0938490	−	0.995586i	$-0.529917\pi$
$929$	670.208	−	386.945i	0.721430	−	0.416518i	0.815279	+	0.579069i	$0.196584\pi$
$930$		0			0
$931$	18.9085	−	5.06653i	0.0203099	−	0.00544203i
$932$	291.076	+	746.417i	0.312314	+	0.800876i
$933$		0			0
$934$	508.227	−	95.5898i	0.544140	−	0.102345i
$935$	−1014.66			−1.08520
$936$		0			0
$937$		−	1692.63i		−	1.80644i	−0.429180	−	0.903219i	$-0.641197\pi$
$937$		−	1692.63i		−	1.80644i	0.429180	−	0.903219i	$-0.358803\pi$
$938$	−266.507	+	50.1258i	−0.284122	+	0.0534391i
$939$		0			0
$940$	−1366.66	−	599.805i	−1.45389	−	0.638091i
$941$	192.505	+	718.438i	0.204575	+	0.763483i	0.989579	+	0.143993i	$0.0459941\pi$
$941$	192.505	+	718.438i	0.204575	+	0.763483i	−0.785004	+	0.619491i	$0.787339\pi$
$942$		0			0
$943$	−297.691	−	515.616i	−0.315685	−	0.546782i
$944$	−250.802	+	395.324i	−0.265680	+	0.418775i
$945$		0			0
$946$	11.2743	−	5.41433i	0.0119179	−	0.00572339i
$947$	69.1063	+	18.5170i	0.0729740	+	0.0195533i	0.295121	−	0.955460i	$-0.404640\pi$
$947$	69.1063	+	18.5170i	0.0729740	+	0.0195533i	−0.222147	+	0.975013i	$0.571307\pi$
$948$		0			0
$949$	119.688	+	446.680i	0.126120	+	0.470685i
$950$	29.2543	+	34.0689i	0.0307940	+	0.0358620i
$951$		0			0
$952$	817.700	−	249.310i	0.858928	−	0.261881i
$953$	−1187.41			−1.24597			−0.622985	−	0.782234i	$-0.714080\pi$
$953$	−1187.41			−1.24597			−0.622985	+	0.782234i	$0.714080\pi$
$954$		0			0
$955$	−1972.02	+	1972.02i	−2.06495	+	2.06495i
$956$	−85.4945	+	558.973i	−0.0894294	+	0.584700i
$957$		0			0
$958$	370.908	+	28.2011i	0.387169	+	0.0294374i
$959$	−750.086	−	433.062i	−0.782154	−	0.451577i
$960$		0			0
$961$	−522.745	−	905.421i	−0.543960	−	0.942166i
$962$	1685.64	−	809.506i	1.75222	−	0.841482i
$963$		0			0
$964$	−922.625	+	1151.79i	−0.957080	+	1.19480i
$965$	−479.992	+	1791.35i	−0.497401	+	1.85633i
$966$		0			0
$967$	−6.67685	−	3.85488i	−0.00690470	−	0.00398643i	0.496544	−	0.868012i	$-0.334602\pi$
$967$	−6.67685	−	3.85488i	−0.00690470	−	0.00398643i	−0.503448	+	0.864025i	$0.667936\pi$
$968$	573.540	−	614.102i	0.592500	−	0.634403i
$969$		0			0
$970$	70.9288	+	377.111i	0.0731224	+	0.388774i
$971$	217.341	+	217.341i	0.223832	+	0.223832i	0.810110	−	0.586278i	$-0.199407\pi$
$971$	217.341	+	217.341i	0.223832	+	0.223832i	−0.586278	+	0.810110i	$0.699407\pi$
$972$		0			0
$973$	135.752	+	135.752i	0.139519	+	0.139519i
$974$	−405.836	+	593.864i	−0.416669	+	0.609717i
$975$		0			0
$976$	190.535	+	364.335i	0.195221	+	0.373295i
$977$	51.1038	+	29.5048i	0.0523069	+	0.0301994i	0.525925	−	0.850531i	$-0.323719\pi$
$977$	51.1038	+	29.5048i	0.0523069	+	0.0301994i	−0.473619	+	0.880730i	$0.657052\pi$
$978$		0			0
$979$	57.6834	−	215.277i	0.0589207	−	0.219895i
$980$	1210.14	−	133.687i	1.23483	−	0.136415i
$981$		0			0
$982$	1491.27	+	523.637i	1.51860	+	0.533235i
$983$	111.503	+	193.129i	0.113432	+	0.196469i	0.917152	−	0.398538i	$-0.130482\pi$
$983$	111.503	+	193.129i	0.113432	+	0.196469i	−0.803720	+	0.595008i	$0.797149\pi$
$984$		0			0
$985$	364.034	+	210.175i	0.369578	+	0.213376i
$986$	−270.191	+	232.008i	−0.274028	+	0.235302i
$987$		0			0
$988$	−4.58114	+	29.9520i	−0.00463678	+	0.0303158i
$989$	−32.3613	+	32.3613i	−0.0327212	+	0.0327212i
$990$		0			0
$991$	−718.786			−0.725314			−0.362657	−	0.931923i	$-0.618130\pi$
$991$	−718.786			−0.725314			−0.362657	+	0.931923i	$0.618130\pi$
$992$	530.923	−	1331.45i	0.535205	−	1.34219i
$993$		0			0
$994$	−748.813	−	56.9341i	−0.753333	−	0.0572778i
$995$	281.319	+	1049.89i	0.282732	+	1.05517i
$996$		0			0
$997$	500.410	+	134.084i	0.501916	+	0.134488i	0.500889	−	0.865512i	$-0.333007\pi$
$997$	500.410	+	134.084i	0.501916	+	0.134488i	0.00102666	+	0.999999i	$0.499673\pi$
$998$	381.979	+	134.126i	0.382744	+	0.134395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.x.a.125.8		184
3.2	odd	2		144.3.w.a.77.39	yes	184
9.2	odd	6	inner	432.3.x.a.413.24		184
9.7	even	3		144.3.w.a.29.23	yes	184
16.5	even	4	inner	432.3.x.a.341.24		184
48.5	odd	4		144.3.w.a.5.23	✓	184
144.101	odd	12	inner	432.3.x.a.197.8		184
144.133	even	12		144.3.w.a.101.39	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.23	✓	184	48.5	odd	4
144.3.w.a.29.23	yes	184	9.7	even	3
144.3.w.a.77.39	yes	184	3.2	odd	2
144.3.w.a.101.39	yes	184	144.133	even	12
432.3.x.a.125.8		184	1.1	even	1	trivial
432.3.x.a.197.8		184	144.101	odd	12	inner
432.3.x.a.341.24		184	16.5	even	4	inner
432.3.x.a.413.24		184	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.65125 - 1.12844i) q^{2} +(1.45327 + 3.72666i) q^{4} +(-7.93556 + 2.12633i) q^{5} +(2.99388 - 1.72852i) q^{7} +(1.80558 - 7.79358i) q^{8} +O(q^{10})\)	\(q+(-1.65125 - 1.12844i) q^{2} +(1.45327 + 3.72666i) q^{4} +(-7.93556 + 2.12633i) q^{5} +(2.99388 - 1.72852i) q^{7} +(1.80558 - 7.79358i) q^{8} +(15.5030 + 5.44366i) q^{10} +(1.03415 - 3.85948i) q^{11} +(-13.8482 + 3.71061i) q^{13} +(-6.89417 - 0.524181i) q^{14} +(-11.7760 + 10.8317i) q^{16} +30.9102i q^{17} +(-0.373615 - 0.373615i) q^{19} +(-19.4566 - 26.4830i) q^{20} +(-6.06281 + 5.20601i) q^{22} +(14.6209 - 25.3241i) q^{23} +(36.8012 - 21.2472i) q^{25} +(27.0540 + 9.49962i) q^{26} +(10.7925 + 8.64518i) q^{28} +(-5.56448 - 1.49100i) q^{29} +(22.3969 - 38.7926i) q^{31} +(31.6680 - 4.59735i) q^{32} +(34.8802 - 51.0406i) q^{34} +(-20.0827 + 20.0827i) q^{35} +(46.1141 - 46.1141i) q^{37} +(0.195332 + 1.03853i) q^{38} +(2.24337 + 65.6856i) q^{40} +(10.1803 - 17.6328i) q^{41} +(-1.51175 - 0.405073i) q^{43} +(15.8859 - 1.75495i) q^{44} +(-52.7194 + 25.3178i) q^{46} +(39.3321 - 22.7084i) q^{47} +(-18.5245 + 32.0853i) q^{49} +(-84.7440 - 6.44330i) q^{50} +(-33.9533 - 46.2150i) q^{52} +(-24.1685 - 24.1685i) q^{53} +32.8261i q^{55} +(-8.06563 - 26.4540i) q^{56} +(7.50587 + 8.74117i) q^{58} +(28.2635 - 7.57319i) q^{59} +(6.65084 - 24.8213i) q^{61} +(-80.7580 + 38.7829i) q^{62} +(-57.4797 - 28.1439i) q^{64} +(102.003 - 58.8915i) q^{65} +(37.8850 - 10.1512i) q^{67} +(-115.192 + 44.9208i) q^{68} +(55.8237 - 10.4996i) q^{70} +108.615 q^{71} -32.2555i q^{73} +(-128.183 + 24.1092i) q^{74} +(0.849373 - 1.93530i) q^{76} +(-3.57508 - 13.3424i) q^{77} +(2.32341 + 4.02426i) q^{79} +(70.4176 - 110.995i) q^{80} +(-36.7078 + 17.6284i) q^{82} +(-132.223 - 35.4290i) q^{83} +(-65.7252 - 245.290i) q^{85} +(2.03919 + 2.37479i) q^{86} +(-28.2120 - 15.0283i) q^{88} +55.7788 q^{89} +(-35.0459 + 35.0459i) q^{91} +(115.623 + 17.6844i) q^{92} +(-90.5723 - 6.88644i) q^{94} +(3.75927 + 2.17041i) q^{95} +(11.6768 + 20.2248i) q^{97} +(66.7947 - 32.0773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

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