LMFDB - Embedded newform 432.3.x.a.341.44

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			341.44
Character	$\chi$	$=$	432.341
Dual form			432.3.x.a.413.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98351 - 0.256277i) q^{2} +(3.86864 - 1.01666i) q^{4} +(-1.00259 - 3.74171i) q^{5} +(4.65369 - 2.68681i) q^{7} +(7.41296 - 3.00800i) q^{8} +O(q^{10})$	\(q+(1.98351 - 0.256277i) q^{2} +(3.86864 - 1.01666i) q^{4} +(-1.00259 - 3.74171i) q^{5} +(4.65369 - 2.68681i) q^{7} +(7.41296 - 3.00800i) q^{8} +(-2.94756 - 7.16478i) q^{10} +(-12.4933 - 3.34758i) q^{11} +(-3.07587 - 11.4793i) q^{13} +(8.54209 - 6.52195i) q^{14} +(13.9328 - 7.86617i) q^{16} +11.8846i q^{17} +(20.1387 - 20.1387i) q^{19} +(-7.68268 - 13.4560i) q^{20} +(-25.6386 - 3.43821i) q^{22} +(-4.74003 + 8.20998i) q^{23} +(8.65545 - 4.99723i) q^{25} +(-9.04291 - 21.9811i) q^{26} +(15.2719 - 15.1255i) q^{28} +(-5.39392 + 20.1304i) q^{29} +(-19.3613 + 33.5347i) q^{31} +(25.6200 - 19.1733i) q^{32} +(3.04574 + 23.5732i) q^{34} +(-14.7190 - 14.7190i) q^{35} +(9.65467 + 9.65467i) q^{37} +(34.7843 - 45.1065i) q^{38} +(-18.6872 - 24.7213i) q^{40} +(11.7420 - 20.3377i) q^{41} +(19.5292 - 72.8841i) q^{43} +(-51.7356 - 0.249158i) q^{44} +(-7.29789 + 17.4994i) q^{46} +(18.4560 - 10.6556i) q^{47} +(-10.0621 + 17.4281i) q^{49} +(15.8875 - 12.1303i) q^{50} +(-23.5700 - 41.2822i) q^{52} +(21.4244 - 21.4244i) q^{53} +50.1026i q^{55} +(26.4157 - 33.9155i) q^{56} +(-5.53996 + 41.3112i) q^{58} +(6.02423 + 22.4827i) q^{59} +(58.9293 + 15.7901i) q^{61} +(-29.8091 + 71.4783i) q^{62} +(45.9039 - 44.5963i) q^{64} +(-39.8684 + 23.0180i) q^{65} +(24.1615 + 90.1720i) q^{67} +(12.0825 + 45.9771i) q^{68} +(-32.9674 - 25.4232i) q^{70} -124.525 q^{71} +86.4217i q^{73} +(21.6244 + 16.6759i) q^{74} +(57.4353 - 98.3836i) q^{76} +(-67.1344 + 17.9886i) q^{77} +(46.4211 + 80.4037i) q^{79} +(-43.4018 - 44.2460i) q^{80} +(18.0783 - 43.3493i) q^{82} +(-20.2421 + 75.5446i) q^{83} +(44.4685 - 11.9153i) q^{85} +(20.0580 - 149.571i) q^{86} +(-102.682 + 12.7644i) q^{88} +164.215 q^{89} +(-45.1569 - 45.1569i) q^{91} +(-9.99077 + 36.5805i) q^{92} +(33.8770 - 25.8654i) q^{94} +(-95.5439 - 55.1623i) q^{95} +(15.8533 + 27.4588i) q^{97} +(-15.4919 + 37.1475i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.98351	−	0.256277i	0.991756	−	0.128138i
$2$	1.98351	−	0.256277i	0.991756	−	0.128138i
$3$		0			0
$3$		0			0
$4$	3.86864	−	1.01666i	0.967161	−	0.254164i
$5$	−1.00259	−	3.74171i	−0.200517	−	0.748341i	−0.990769	−	0.135559i	$-0.956717\pi$
$5$	−1.00259	−	3.74171i	−0.200517	−	0.748341i	0.790252	−	0.612782i	$-0.209950\pi$
$6$		0			0
$7$	4.65369	−	2.68681i	0.664813	−	0.383830i	−0.129295	−	0.991606i	$-0.541272\pi$
$7$	4.65369	−	2.68681i	0.664813	−	0.383830i	0.794108	+	0.607776i	$0.207938\pi$
$8$	7.41296	−	3.00800i	0.926620	−	0.375999i
$9$		0			0
$10$	−2.94756	−	7.16478i	−0.294756	−	0.716478i
$11$	−12.4933	−	3.34758i	−1.13576	−	0.304325i	−0.358513	−	0.933525i	$-0.616716\pi$
$11$	−12.4933	−	3.34758i	−1.13576	−	0.304325i	−0.777244	+	0.629200i	$0.783383\pi$
$12$		0			0
$13$	−3.07587	−	11.4793i	−0.236605	−	0.883024i	−0.977419	−	0.211312i	$-0.932226\pi$
$13$	−3.07587	−	11.4793i	−0.236605	−	0.883024i	0.740813	−	0.671711i	$-0.234440\pi$
$14$	8.54209	−	6.52195i	0.610149	−	0.465854i
$15$		0			0
$16$	13.9328	−	7.86617i	0.870801	−	0.491635i
$17$			11.8846i			0.699092i	0.936919	+	0.349546i	$0.113664\pi$
$17$			11.8846i			0.699092i	−0.936919	+	0.349546i	$0.886336\pi$
$18$		0			0
$19$	20.1387	−	20.1387i	1.05993	−	1.05993i	0.0618460	−	0.998086i	$-0.480301\pi$
$19$	20.1387	−	20.1387i	1.05993	−	1.05993i	0.998086	−	0.0618460i	$-0.0196988\pi$
$20$	−7.68268	−	13.4560i	−0.384134	−	0.672802i
$21$		0			0
$22$	−25.6386	−	3.43821i	−1.16539	−	0.156282i
$23$	−4.74003	+	8.20998i	−0.206088	+	0.356955i	−0.950479	−	0.310789i	$-0.899407\pi$
$23$	−4.74003	+	8.20998i	−0.206088	+	0.356955i	0.744391	+	0.667744i	$0.232740\pi$
$24$		0			0
$25$	8.65545	−	4.99723i	0.346218	−	0.199889i
$26$	−9.04291	−	21.9811i	−0.347804	−	0.845426i
$27$		0			0
$28$	15.2719	−	15.1255i	0.545425	−	0.540197i
$29$	−5.39392	+	20.1304i	−0.185997	+	0.694151i	0.808418	+	0.588609i	$0.200324\pi$
$29$	−5.39392	+	20.1304i	−0.185997	+	0.694151i	−0.994415	+	0.105542i	$0.966342\pi$
$30$		0			0
$31$	−19.3613	+	33.5347i	−0.624557	+	1.08176i	0.364069	+	0.931372i	$0.381387\pi$
$31$	−19.3613	+	33.5347i	−0.624557	+	1.08176i	−0.988626	+	0.150393i	$0.951946\pi$
$32$	25.6200	−	19.1733i	0.800625	−	0.599166i
$33$		0			0
$34$	3.04574	+	23.5732i	0.0895805	+	0.693329i
$35$	−14.7190	−	14.7190i	−0.420542	−	0.420542i
$36$		0			0
$37$	9.65467	+	9.65467i	0.260937	+	0.260937i	0.825435	−	0.564498i	$-0.190930\pi$
$37$	9.65467	+	9.65467i	0.260937	+	0.260937i	−0.564498	+	0.825435i	$0.690930\pi$
$38$	34.7843	−	45.1065i	0.915376	−	1.18701i
$39$		0			0
$40$	−18.6872	−	24.7213i	−0.467179	−	0.618033i
$41$	11.7420	−	20.3377i	0.286390	−	0.496042i	−0.686555	−	0.727077i	$-0.740878\pi$
$41$	11.7420	−	20.3377i	0.286390	−	0.496042i	0.972945	+	0.231036i	$0.0742114\pi$
$42$		0			0
$43$	19.5292	−	72.8841i	0.454168	−	1.69498i	−0.236353	−	0.971667i	$-0.575952\pi$
$43$	19.5292	−	72.8841i	0.454168	−	1.69498i	0.690521	−	0.723312i	$-0.257381\pi$
$44$	−51.7356	−	0.249158i	−1.17581	−	0.00566269i
$45$		0			0
$46$	−7.29789	+	17.4994i	−0.158650	+	0.380421i
$47$	18.4560	−	10.6556i	0.392682	−	0.226715i	−0.290640	−	0.956833i	$-0.593868\pi$
$47$	18.4560	−	10.6556i	0.392682	−	0.226715i	0.683321	+	0.730118i	$0.260535\pi$
$48$		0			0
$49$	−10.0621	+	17.4281i	−0.205349	+	0.355675i
$50$	15.8875	−	12.1303i	0.317750	−	0.242605i
$51$		0			0
$52$	−23.5700	−	41.2822i	−0.453269	−	0.793889i
$53$	21.4244	−	21.4244i	0.404234	−	0.404234i	−0.475488	−	0.879722i	$-0.657729\pi$
$53$	21.4244	−	21.4244i	0.404234	−	0.404234i	0.879722	+	0.475488i	$0.157729\pi$
$54$		0			0
$55$			50.1026i			0.910956i
$56$	26.4157	−	33.9155i	0.471709	−	0.605634i
$57$		0			0
$58$	−5.53996	+	41.3112i	−0.0955165	+	0.712262i
$59$	6.02423	+	22.4827i	0.102106	+	0.381063i	0.998001	−	0.0632023i	$-0.0201313\pi$
$59$	6.02423	+	22.4827i	0.102106	+	0.381063i	−0.895895	+	0.444266i	$0.853465\pi$
$60$		0			0
$61$	58.9293	+	15.7901i	0.966054	+	0.258853i	0.707161	−	0.707053i	$-0.249976\pi$
$61$	58.9293	+	15.7901i	0.966054	+	0.258853i	0.258893	+	0.965906i	$0.416642\pi$
$62$	−29.8091	+	71.4783i	−0.480793	+	1.15288i
$63$		0			0
$64$	45.9039	−	44.5963i	0.717249	−	0.696817i
$65$	−39.8684	+	23.0180i	−0.613359	+	0.354123i
$66$		0			0
$67$	24.1615	+	90.1720i	0.360620	+	1.34585i	0.873263	+	0.487249i	$0.162000\pi$
$67$	24.1615	+	90.1720i	0.360620	+	1.34585i	−0.512643	+	0.858602i	$0.671334\pi$
$68$	12.0825	+	45.9771i	0.177684	+	0.676134i
$69$		0			0
$70$	−32.9674	−	25.4232i	−0.470963	−	0.363188i
$71$	−124.525			−1.75387			−0.876935	−	0.480609i	$-0.840416\pi$
$71$	−124.525			−1.75387			−0.876935	+	0.480609i	$0.840416\pi$
$72$		0			0
$73$			86.4217i			1.18386i	0.805990	+	0.591930i	$0.201634\pi$
$73$			86.4217i			1.18386i	−0.805990	+	0.591930i	$0.798366\pi$
$74$	21.6244	+	16.6759i	0.292222	+	0.225350i
$75$		0			0
$76$	57.4353	−	98.3836i	0.755728	−	1.29452i
$77$	−67.1344	+	17.9886i	−0.871875	+	0.233618i
$78$		0			0
$79$	46.4211	+	80.4037i	0.587609	+	1.01777i	0.994545	+	0.104311i	$0.0332639\pi$
$79$	46.4211	+	80.4037i	0.587609	+	1.01777i	−0.406936	+	0.913457i	$0.633403\pi$
$80$	−43.4018	−	44.2460i	−0.542522	−	0.553075i
$81$		0			0
$82$	18.0783	−	43.3493i	0.220467	−	0.528650i
$83$	−20.2421	+	75.5446i	−0.243881	+	0.910176i	0.730062	+	0.683381i	$0.239491\pi$
$83$	−20.2421	+	75.5446i	−0.243881	+	0.910176i	−0.973943	+	0.226795i	$0.927175\pi$
$84$		0			0
$85$	44.4685	−	11.9153i	0.523159	−	0.140180i
$86$	20.0580	−	149.571i	0.233232	−	1.73920i
$87$		0			0
$88$	−102.682	+	12.7644i	−1.16684	+	0.145050i
$89$	164.215			1.84511			0.922556	−	0.385863i	$-0.126096\pi$
$89$	164.215			1.84511			0.922556	+	0.385863i	$0.126096\pi$
$90$		0			0
$91$	−45.1569	−	45.1569i	−0.496229	−	0.496229i
$92$	−9.99077	+	36.5805i	−0.108595	+	0.397614i
$93$		0			0
$94$	33.8770	−	25.8654i	0.360394	−	0.275164i
$95$	−95.5439	−	55.1623i	−1.00573	−	0.580656i
$96$		0			0
$97$	15.8533	+	27.4588i	0.163437	+	0.283080i	0.936099	−	0.351737i	$-0.114409\pi$
$97$	15.8533	+	27.4588i	0.163437	+	0.283080i	−0.772662	+	0.634817i	$0.781075\pi$
$98$	−15.4919	+	37.1475i	−0.158081	+	0.379056i
$99$		0			0
$100$	28.4044	−	28.1321i	0.284044	−	0.281321i
$101$	120.067	+	32.1718i	1.18878	+	0.318532i	0.798403	−	0.602123i	$-0.205678\pi$
$101$	120.067	+	32.1718i	1.18878	+	0.318532i	0.390376	+	0.920656i	$0.372345\pi$
$102$		0			0
$103$	−163.306	−	94.2846i	−1.58549	−	0.915384i	−0.994037	−	0.109046i	$-0.965220\pi$
$103$	−163.306	−	94.2846i	−1.58549	−	0.915384i	−0.591455	−	0.806338i	$-0.701446\pi$
$104$	−57.3310	−	75.8434i	−0.551260	−	0.729264i
$105$		0			0
$106$	37.0050	−	47.9862i	0.349104	−	0.452700i
$107$	−96.3954	+	96.3954i	−0.900891	+	0.900891i	−0.995513	−	0.0946220i	$-0.969836\pi$
$107$	−96.3954	+	96.3954i	−0.900891	+	0.900891i	0.0946220	+	0.995513i	$0.469836\pi$
$108$		0			0
$109$	−111.267	+	111.267i	−1.02079	+	1.02079i	−0.0210151	+	0.999779i	$0.506690\pi$
$109$	−111.267	+	111.267i	−1.02079	+	1.02079i	−0.999779	+	0.0210151i	$0.993310\pi$
$110$	12.8401	+	99.3791i	0.116729	+	0.903447i
$111$		0			0
$112$	43.7041	−	74.0415i	0.390215	−	0.661085i
$113$	53.6807	+	30.9926i	0.475051	+	0.274271i	0.718352	−	0.695680i	$-0.244897\pi$
$113$	53.6807	+	30.9926i	0.475051	+	0.274271i	−0.243301	+	0.969951i	$0.578230\pi$
$114$		0			0
$115$	35.4716	+	9.50459i	0.308449	+	0.0826486i
$116$	−0.401466	+	83.3611i	−0.00346092	+	0.718630i
$117$		0			0
$118$	17.7109	+	43.0509i	0.150093	+	0.364838i
$119$	31.9316	+	55.3071i	0.268332	+	0.464765i
$120$		0			0
$121$	40.0879	+	23.1447i	0.331305	+	0.191279i
$122$	120.934	+	16.2176i	0.991259	+	0.132931i
$123$		0			0
$124$	−40.8086	+	149.418i	−0.329101	+	1.20498i
$125$	−95.8540	−	95.8540i	−0.766832	−	0.766832i
$126$		0			0
$127$	−56.7743			−0.447041			−0.223521	−	0.974699i	$-0.571755\pi$
$127$	−56.7743			−0.447041			−0.223521	+	0.974699i	$0.571755\pi$
$128$	79.6220	−	100.221i	0.622047	−	0.782980i
$129$		0			0
$130$	−73.1804	+	55.8739i	−0.562926	+	0.429799i
$131$	−53.4982	+	14.3348i	−0.408383	+	0.109426i	−0.457161	−	0.889384i	$-0.651134\pi$
$131$	−53.4982	+	14.3348i	−0.408383	+	0.109426i	0.0487784	+	0.998810i	$0.484467\pi$
$132$		0			0
$133$	39.6104	−	147.828i	0.297823	−	1.11149i
$134$	71.0337	+	172.665i	0.530102	+	1.28855i
$135$		0			0
$136$	35.7487	+	88.0998i	0.262858	+	0.647792i
$137$	52.5810	+	91.0730i	0.383803	+	0.664766i	0.991602	−	0.129324i	$-0.0412809\pi$
$137$	52.5810	+	91.0730i	0.383803	+	0.664766i	−0.607799	+	0.794091i	$0.707948\pi$
$138$		0			0
$139$	−97.9157	+	26.2364i	−0.704429	+	0.188751i	−0.593214	−	0.805045i	$-0.702141\pi$
$139$	−97.9157	+	26.2364i	−0.704429	+	0.188751i	−0.111216	+	0.993796i	$0.535474\pi$
$140$	−71.9067	−	41.9784i	−0.513619	−	0.299845i
$141$		0			0
$142$	−246.996	+	31.9128i	−1.73941	+	0.224738i
$143$			153.711i			1.07491i
$144$		0			0
$145$	80.7299			0.556758
$146$	22.1479	+	171.419i	0.151698	+	1.17410i
$147$		0			0
$148$	47.1660	+	27.5350i	0.318689	+	0.186047i
$149$	−54.4787	−	203.317i	−0.365629	−	1.36454i	−0.866566	−	0.499062i	$-0.833678\pi$
$149$	−54.4787	−	203.317i	−0.365629	−	1.36454i	0.500938	−	0.865483i	$-0.332989\pi$
$150$		0			0
$151$	−126.469	+	73.0167i	−0.837541	+	0.483554i	−0.856428	−	0.516267i	$-0.827321\pi$
$151$	−126.469	+	73.0167i	−0.837541	+	0.483554i	0.0188867	+	0.999822i	$0.493988\pi$
$152$	88.7102	−	209.865i	0.583620	−	1.38069i
$153$		0			0
$154$	−128.552	+	52.8856i	−0.834752	+	0.343413i
$155$	144.888	+	38.8227i	0.934764	+	0.250469i
$156$		0			0
$157$	27.0148	+	100.820i	0.172069	+	0.642168i	0.997032	+	0.0769830i	$0.0245287\pi$
$157$	27.0148	+	100.820i	0.172069	+	0.642168i	−0.824964	+	0.565185i	$0.808805\pi$
$158$	112.682	+	147.585i	0.713180	+	0.934083i
$159$		0			0
$160$	−97.4272	−	76.6396i	−0.608920	−	0.478998i
$161$			50.9423i			0.316412i
$162$		0			0
$163$	33.4075	−	33.4075i	0.204954	−	0.204954i	−0.597165	−	0.802119i	$-0.703706\pi$
$163$	33.4075	−	33.4075i	0.204954	−	0.204954i	0.802119	+	0.597165i	$0.203706\pi$
$164$	24.7491	−	90.6169i	0.150909	−	0.552542i
$165$		0			0
$166$	−20.7902	+	155.031i	−0.125242	+	0.933923i
$167$	83.3490	−	144.365i	0.499096	−	0.864459i	−0.500904	−	0.865503i	$-0.666999\pi$
$167$	83.3490	−	144.365i	0.499096	−	0.864459i	0.999999	+	0.00104367i	$0.000332212\pi$
$168$		0			0
$169$	24.0448	−	13.8823i	0.142277	−	0.0821437i
$170$	85.1503	−	35.0304i	0.500884	−	0.206061i
$171$		0			0
$172$	1.45355	−	301.817i	0.00845087	−	1.75475i
$173$	18.3433	−	68.4582i	0.106031	−	0.395712i	−0.892429	−	0.451187i	$-0.851001\pi$
$173$	18.3433	−	68.4582i	0.106031	−	0.395712i	0.998460	+	0.0554750i	$0.0176673\pi$
$174$		0			0
$175$	26.8532	−	46.5111i	0.153447	−	0.265778i
$176$	−200.400	+	51.6334i	−1.13864	+	0.293372i
$177$		0			0
$178$	325.722	−	42.0845i	1.82990	−	0.236430i
$179$	145.221	+	145.221i	0.811290	+	0.811290i	0.984827	−	0.173538i	$-0.0555198\pi$
$179$	145.221	+	145.221i	0.811290	+	0.811290i	−0.173538	+	0.984827i	$0.555520\pi$
$180$		0			0
$181$	84.5981	+	84.5981i	0.467393	+	0.467393i	0.901069	−	0.433676i	$-0.142784\pi$
$181$	84.5981	+	84.5981i	0.467393	+	0.467393i	−0.433676	+	0.901069i	$0.642784\pi$
$182$	−101.142	−	77.9965i	−0.555725	−	0.428552i
$183$		0			0
$184$	−10.4421	+	75.1182i	−0.0567505	+	0.408251i
$185$	26.4453	−	45.8046i	0.142948	−	0.247592i
$186$		0			0
$187$	39.7845	−	148.478i	0.212751	−	0.793998i
$188$	60.5668	−	59.9862i	0.322164	−	0.319075i
$189$		0			0
$190$	−203.649	−	84.9294i	−1.07184	−	0.446997i
$191$	9.02196	−	5.20883i	0.0472354	−	0.0272714i	−0.476196	−	0.879339i	$-0.657985\pi$
$191$	9.02196	−	5.20883i	0.0472354	−	0.0272714i	0.523432	+	0.852068i	$0.324652\pi$
$192$		0			0
$193$	81.1839	−	140.615i	0.420642	−	0.728573i	−0.575361	−	0.817900i	$-0.695138\pi$
$193$	81.1839	−	140.615i	0.420642	−	0.728573i	0.996002	+	0.0893270i	$0.0284716\pi$
$194$	38.4824	+	50.4020i	0.198363	+	0.259804i
$195$		0			0
$196$	−21.2083	+	77.6528i	−0.108206	+	0.396188i
$197$	158.587	−	158.587i	0.805013	−	0.805013i	−0.178862	−	0.983874i	$-0.557241\pi$
$197$	158.587	−	158.587i	0.805013	−	0.805013i	0.983874	+	0.178862i	$0.0572414\pi$
$198$		0			0
$199$			88.5298i			0.444874i	0.974947	+	0.222437i	$0.0714011\pi$
$199$			88.5298i			0.444874i	−0.974947	+	0.222437i	$0.928599\pi$
$200$	49.1309	−	63.0798i	0.245654	−	0.315399i
$201$		0			0
$202$	246.399	+	33.0428i	1.21980	+	0.163578i
$203$	28.9849	+	108.173i	0.142783	+	0.532872i
$204$		0			0
$205$	−87.8701	−	23.5447i	−0.428635	−	0.114852i
$206$	−348.082	−	145.163i	−1.68972	−	0.704675i
$207$		0			0
$208$	−133.154	−	135.744i	−0.640162	−	0.652614i
$209$	−319.015	+	184.184i	−1.52639	+	0.881261i
$210$		0			0
$211$	−75.6516	−	282.335i	−0.358538	−	1.33808i	−0.875973	−	0.482360i	$-0.839780\pi$
$211$	−75.6516	−	282.335i	−0.358538	−	1.33808i	0.517435	−	0.855723i	$-0.326887\pi$
$212$	61.1021	−	104.665i	0.288218	−	0.493701i
$213$		0			0
$214$	−166.498	+	215.905i	−0.778026	+	1.00890i
$215$	−292.291			−1.35949
$216$		0			0
$217$			208.080i			0.958895i
$218$	−192.184	+	249.214i	−0.881576	+	1.14318i
$219$		0			0
$220$	50.9371	+	193.829i	0.231532	+	0.881042i
$221$	136.427	−	36.5554i	0.617315	−	0.165409i
$222$		0			0
$223$	−39.5000	−	68.4160i	−0.177130	−	0.306798i	0.763766	−	0.645493i	$-0.223348\pi$
$223$	−39.5000	−	68.4160i	−0.177130	−	0.306798i	−0.940896	+	0.338695i	$0.890015\pi$
$224$	67.7126	−	158.063i	0.302288	−	0.705637i
$225$		0			0
$226$	114.419	+	47.7170i	0.506279	+	0.211137i
$227$	39.7756	−	148.445i	0.175223	−	0.653941i	−0.821290	−	0.570510i	$-0.806745\pi$
$227$	39.7756	−	148.445i	0.175223	−	0.653941i	0.996514	−	0.0834312i	$-0.0265879\pi$
$228$		0			0
$229$	142.591	−	38.2072i	0.622669	−	0.166844i	0.0663280	−	0.997798i	$-0.478872\pi$
$229$	142.591	−	38.2072i	0.622669	−	0.166844i	0.556341	+	0.830954i	$0.312205\pi$
$230$	72.7942	+	9.76192i	0.316497	+	0.0424431i
$231$		0			0
$232$	20.5672	+	165.451i	0.0886517	+	0.713149i
$233$	−232.917			−0.999644			−0.499822	−	0.866128i	$-0.666601\pi$
$233$	−232.917			−0.999644			−0.499822	+	0.866128i	$0.666601\pi$
$234$		0			0
$235$	−58.3739	−	58.3739i	−0.248400	−	0.248400i
$236$	46.1628	+	80.8531i	0.195605	+	0.342598i
$237$		0			0
$238$	77.5106	+	101.519i	0.325675	+	0.426550i
$239$	71.3891	+	41.2165i	0.298699	+	0.172454i	0.641858	−	0.766823i	$-0.278164\pi$
$239$	71.3891	+	41.2165i	0.298699	+	0.172454i	−0.343159	+	0.939277i	$0.611497\pi$
$240$		0			0
$241$	177.458	+	307.367i	0.736342	+	1.27538i	0.954132	+	0.299387i	$0.0967820\pi$
$241$	177.458	+	307.367i	0.736342	+	1.27538i	−0.217790	+	0.975996i	$0.569885\pi$
$242$	85.4462	+	35.6343i	0.353084	+	0.147249i
$243$		0			0
$244$	244.030	+	1.17524i	1.00012	+	0.00481658i
$245$	75.2989	+	20.1763i	0.307342	+	0.0823522i
$246$		0			0
$247$	−293.122	−	169.234i	−1.18673	−	0.685159i
$248$	−42.6521	+	306.830i	−0.171984	+	1.23722i
$249$		0			0
$250$	−214.693	−	165.562i	−0.858771	−	0.662250i
$251$	88.3235	−	88.3235i	0.351886	−	0.351886i	−0.508925	−	0.860811i	$-0.669957\pi$
$251$	88.3235	−	88.3235i	0.351886	−	0.351886i	0.860811	+	0.508925i	$0.169957\pi$
$252$		0			0
$253$	86.7023	−	86.7023i	0.342697	−	0.342697i
$254$	−112.612	+	14.5499i	−0.443356	+	0.0572832i
$255$		0			0
$256$	132.247	−	219.196i	0.516589	−	0.856233i
$257$	224.014	+	129.334i	0.871649	+	0.503247i	0.867896	−	0.496746i	$-0.165472\pi$
$257$	224.014	+	129.334i	0.871649	+	0.503247i	0.00375325	+	0.999993i	$0.498805\pi$
$258$		0			0
$259$	70.8701	+	18.9896i	0.273630	+	0.0733189i
$260$	−130.835	+	129.581i	−0.503212	+	0.498388i
$261$		0			0
$262$	−102.441	+	42.1436i	−0.390995	+	0.160853i
$263$	−217.325	−	376.418i	−0.826331	−	1.43125i	−0.900898	−	0.434031i	$-0.857091\pi$
$263$	−217.325	−	376.418i	−0.826331	−	1.43125i	0.0745671	−	0.997216i	$-0.476243\pi$
$264$		0			0
$265$	−101.644	−	58.6840i	−0.383561	−	0.221449i
$266$	40.6829	−	303.370i	0.152943	−	1.14049i
$267$		0			0
$268$	185.146	+	324.279i	0.690844	+	1.21000i
$269$	−6.46656	−	6.46656i	−0.0240393	−	0.0240393i	0.694985	−	0.719024i	$-0.255411\pi$
$269$	−6.46656	−	6.46656i	−0.0240393	−	0.0240393i	−0.719024	+	0.694985i	$0.755411\pi$
$270$		0			0
$271$	−162.021			−0.597863			−0.298932	−	0.954275i	$-0.596630\pi$
$271$	−162.021			−0.597863			−0.298932	+	0.954275i	$0.596630\pi$
$272$	93.4859	+	165.585i	0.343698	+	0.608770i
$273$		0			0
$274$	127.635	+	167.169i	0.465821	+	0.610106i
$275$	−124.864	+	33.4572i	−0.454051	+	0.121663i
$276$		0			0
$277$	67.8658	−	253.279i	0.245003	−	0.914364i	−0.728379	−	0.685175i	$-0.759726\pi$
$277$	67.8658	−	253.279i	0.245003	−	0.914364i	0.973382	−	0.229189i	$-0.0736075\pi$
$278$	−187.493	+	77.1338i	−0.674436	+	0.277460i
$279$		0			0
$280$	−153.386	−	64.8366i	−0.547807	−	0.231559i
$281$	−128.998	−	223.431i	−0.459067	−	0.795127i	0.539845	−	0.841764i	$-0.318483\pi$
$281$	−128.998	−	223.431i	−0.459067	−	0.795127i	−0.998912	+	0.0466376i	$0.985149\pi$
$282$		0			0
$283$	−65.1839	+	17.4660i	−0.230332	+	0.0617172i	−0.372139	−	0.928177i	$-0.621375\pi$
$283$	−65.1839	+	17.4660i	−0.230332	+	0.0617172i	0.141807	+	0.989894i	$0.454709\pi$
$284$	−481.742	+	126.599i	−1.69628	+	0.445771i
$285$		0			0
$286$	39.3927	+	304.889i	0.137737	+	1.06604i
$287$		−	126.194i		−	0.439700i
$288$		0			0
$289$	147.757			0.511271
$290$	160.129	−	20.6892i	0.552168	−	0.0713421i
$291$		0			0
$292$	87.8612	+	334.335i	0.300895	+	1.14498i
$293$	113.090	+	422.058i	0.385973	+	1.44047i	0.836628	+	0.547772i	$0.184524\pi$
$293$	113.090	+	422.058i	0.385973	+	1.44047i	−0.450655	+	0.892698i	$0.648809\pi$
$294$		0			0
$295$	78.0840	−	45.0818i	0.264691	−	0.152820i
$296$	100.611	+	42.5285i	0.339902	+	0.143677i
$297$		0			0
$298$	−160.165	−	389.321i	−0.537465	−	1.30644i
$299$	108.825	+	29.1595i	0.363962	+	0.0975232i
$300$		0			0
$301$	−104.943	−	391.652i	−0.348647	−	1.30117i
$302$	−232.140	+	177.241i	−0.768675	+	0.586889i
$303$		0			0
$304$	122.174	−	439.003i	0.401890	−	1.44409i
$305$		−	236.327i		−	0.774843i
$306$		0			0
$307$	281.005	−	281.005i	0.915324	−	0.915324i	−0.0813605	−	0.996685i	$-0.525927\pi$
$307$	281.005	−	281.005i	0.915324	−	0.915324i	0.996685	+	0.0813605i	$0.0259265\pi$
$308$	−241.431	+	137.844i	−0.783866	+	0.447546i
$309$		0			0
$310$	297.337	+	39.8738i	0.959152	+	0.128625i
$311$	−93.6716	+	162.244i	−0.301195	+	0.521685i	−0.976407	−	0.215939i	$-0.930719\pi$
$311$	−93.6716	+	162.244i	−0.301195	+	0.521685i	0.675212	+	0.737624i	$0.264052\pi$
$312$		0			0
$313$	147.960	−	85.4249i	0.472716	−	0.272923i	−0.244660	−	0.969609i	$-0.578676\pi$
$313$	147.960	−	85.4249i	0.472716	−	0.272923i	0.717376	+	0.696686i	$0.245343\pi$
$314$	79.4221	+	193.055i	0.252937	+	0.614826i
$315$		0			0
$316$	261.330	+	263.859i	0.826992	+	0.834997i
$317$	148.256	−	553.300i	0.467685	−	1.74543i	−0.180144	−	0.983640i	$-0.557656\pi$
$317$	148.256	−	553.300i	0.467685	−	1.74543i	0.647829	−	0.761786i	$-0.275677\pi$
$318$		0			0
$319$	134.776	−	233.439i	0.422495	−	0.731783i
$320$	−212.889	−	127.047i	−0.665278	−	0.397023i
$321$		0			0
$322$	13.0553	+	101.045i	0.0405445	+	0.313803i
$323$	239.340	+	239.340i	0.740990	+	0.740990i
$324$		0			0
$325$	−83.9877	−	83.9877i	−0.258424	−	0.258424i
$326$	57.7027	−	74.8258i	0.177002	−	0.229527i
$327$		0			0
$328$	25.8671	−	186.082i	0.0788631	−	0.567325i
$329$	57.2591	−	99.1757i	0.174040	−	0.301446i
$330$		0			0
$331$	−17.5294	+	65.4206i	−0.0529589	+	0.197645i	−0.987337	−	0.158638i	$-0.949290\pi$
$331$	−17.5294	+	65.4206i	−0.0529589	+	0.197645i	0.934378	+	0.356284i	$0.115956\pi$
$332$	−1.50661	+	312.835i	−0.00453798	+	0.942273i
$333$		0			0
$334$	128.326	−	307.710i	0.384211	−	0.921286i
$335$	313.173	−	180.811i	0.934845	−	0.539733i
$336$		0			0
$337$	−165.268	+	286.252i	−0.490409	+	0.849413i	−0.999939	−	0.0110397i	$-0.996486\pi$
$337$	−165.268	+	286.252i	−0.490409	+	0.849413i	0.509530	+	0.860453i	$0.329819\pi$
$338$	44.1355	−	33.6978i	0.130578	−	0.0996977i
$339$		0			0
$340$	159.919	−	91.3053i	0.470351	−	0.268545i
$341$	354.147	−	354.147i	1.03855	−	1.03855i
$342$		0			0
$343$			371.447i			1.08294i
$344$	−74.4657	−	599.031i	−0.216470	−	1.74137i
$345$		0			0
$346$	18.8400	−	140.489i	0.0544508	−	0.406037i
$347$	−152.939	−	570.776i	−0.440747	−	1.64489i	−0.726928	−	0.686713i	$-0.759053\pi$
$347$	−152.939	−	570.776i	−0.440747	−	1.64489i	0.286182	−	0.958175i	$-0.407614\pi$
$348$		0			0
$349$	−481.904	−	129.126i	−1.38081	−	0.369988i	−0.509396	−	0.860532i	$-0.670131\pi$
$349$	−481.904	−	129.126i	−1.38081	−	0.369988i	−0.871416	+	0.490544i	$0.836798\pi$
$350$	41.3439	−	99.1372i	0.118125	−	0.283249i
$351$		0			0
$352$	−384.263	+	153.773i	−1.09166	+	0.436856i
$353$	−100.398	+	57.9648i	−0.284413	+	0.164206i	−0.635420	−	0.772167i	$-0.719173\pi$
$353$	−100.398	+	57.9648i	−0.284413	+	0.164206i	0.351006	+	0.936373i	$0.385840\pi$
$354$		0			0
$355$	124.847	+	465.935i	0.351682	+	1.31249i
$356$	635.289	−	166.950i	1.78452	−	0.468961i
$357$		0			0
$358$	325.264	+	250.831i	0.908559	+	0.700644i
$359$	−598.738			−1.66780			−0.833898	−	0.551919i	$-0.813896\pi$
$359$	−598.738			−1.66780			−0.833898	+	0.551919i	$0.813896\pi$
$360$		0			0
$361$		−	450.135i		−	1.24691i
$362$	189.482	+	146.121i	0.523431	+	0.403649i
$363$		0			0
$364$	−220.605	−	128.787i	−0.606057	−	0.353810i
$365$	323.365	−	86.6453i	0.885931	−	0.237384i
$366$		0			0
$367$	−30.0248	−	52.0045i	−0.0818115	−	0.141702i	0.822217	−	0.569175i	$-0.192737\pi$
$367$	−30.0248	−	52.0045i	−0.0818115	−	0.141702i	−0.904028	+	0.427473i	$0.859404\pi$
$368$	−1.46096	+	151.674i	−0.00396999	+	0.412158i
$369$		0			0
$370$	40.7159	−	97.6313i	0.110043	−	0.263868i
$371$	42.1393	−	157.266i	0.113583	−	0.423897i
$372$		0			0
$373$	−599.280	+	160.577i	−1.60665	+	0.430500i	−0.947042	−	0.321111i	$-0.895944\pi$
$373$	−599.280	+	160.577i	−1.60665	+	0.430500i	−0.659607	+	0.751611i	$0.729277\pi$
$374$	40.8616	−	304.703i	0.109256	−	0.814715i
$375$		0			0
$376$	104.762	−	134.505i	0.278622	−	0.357727i
$377$	247.674			0.656960
$378$		0			0
$379$	−128.337	−	128.337i	−0.338620	−	0.338620i	0.517228	−	0.855848i	$-0.326964\pi$
$379$	−128.337	−	128.337i	−0.338620	−	0.338620i	−0.855848	+	0.517228i	$0.826964\pi$
$380$	−425.707	−	116.268i	−1.12028	−	0.305968i
$381$		0			0
$382$	16.5603	−	12.6439i	0.0433515	−	0.0330992i
$383$	56.1996	+	32.4468i	0.146735	+	0.0847176i	0.571570	−	0.820553i	$-0.306335\pi$
$383$	56.1996	+	32.4468i	0.146735	+	0.0847176i	−0.424835	+	0.905271i	$0.639668\pi$
$384$		0			0
$385$	134.616	+	233.162i	0.349652	+	0.605616i
$386$	124.993	−	299.716i	0.323816	−	0.776467i
$387$		0			0
$388$	89.2471	+	90.1109i	0.230018	+	0.232245i
$389$	−399.684	−	107.095i	−1.02747	−	0.275309i	−0.294556	−	0.955634i	$-0.595172\pi$
$389$	−399.684	−	107.095i	−1.02747	−	0.275309i	−0.732910	+	0.680326i	$0.761838\pi$
$390$		0			0
$391$	−97.5720	−	56.3332i	−0.249545	−	0.144075i
$392$	−22.1664	+	159.460i	−0.0565469	+	0.406787i
$393$		0			0
$394$	273.918	−	355.203i	0.695223	−	0.901529i
$395$	254.306	−	254.306i	0.643812	−	0.643812i
$396$		0			0
$397$	−396.576	+	396.576i	−0.998931	+	0.998931i	−0.999999	−	0.00106822i	$-0.999660\pi$
$397$	−396.576	+	396.576i	−0.998931	+	0.998931i	0.00106822	+	0.999999i	$0.499660\pi$
$398$	22.6882	+	175.600i	0.0570054	+	0.441206i
$399$		0			0
$400$	81.2858	−	137.711i	0.203214	−	0.344277i
$401$	−75.9357	−	43.8415i	−0.189366	−	0.109330i	0.402320	−	0.915499i	$-0.368204\pi$
$401$	−75.9357	−	43.8415i	−0.189366	−	0.109330i	−0.591686	+	0.806169i	$0.701537\pi$
$402$		0			0
$403$	444.508	+	119.106i	1.10300	+	0.295547i
$404$	497.203	+	2.39453i	1.23070	+	0.00592704i
$405$		0			0
$406$	85.2141	+	207.134i	0.209887	+	0.510183i
$407$	−88.2992	−	152.939i	−0.216951	−	0.375771i
$408$		0			0
$409$	54.0849	+	31.2259i	0.132237	+	0.0763470i	0.564659	−	0.825324i	$-0.309008\pi$
$409$	54.0849	+	31.2259i	0.132237	+	0.0763470i	−0.432422	+	0.901671i	$0.642341\pi$
$410$	−180.325	−	24.1822i	−0.439818	−	0.0589809i
$411$		0			0
$412$	−727.626	−	198.728i	−1.76608	−	0.482349i
$413$	88.4417	+	88.4417i	0.214145	+	0.214145i
$414$		0			0
$415$	302.960			0.730025
$416$	−298.900	−	235.125i	−0.718510	−	0.565205i
$417$		0			0
$418$	−585.569	+	447.087i	−1.40088	+	1.06959i
$419$	267.062	−	71.5590i	0.637379	−	0.170785i	0.0743629	−	0.997231i	$-0.476308\pi$
$419$	267.062	−	71.5590i	0.637379	−	0.170785i	0.563016	+	0.826446i	$0.309641\pi$
$420$		0			0
$421$	158.502	−	591.536i	0.376488	−	1.40507i	−0.474670	−	0.880164i	$-0.657433\pi$
$421$	158.502	−	591.536i	0.376488	−	1.40507i	0.851158	−	0.524909i	$-0.175901\pi$
$422$	−222.412	−	540.628i	−0.527042	−	1.28111i
$423$		0			0
$424$	94.3737	−	223.263i	0.222580	−	0.526563i
$425$	59.3898	+	102.866i	0.139741	+	0.242038i
$426$		0			0
$427$	316.664	−	84.8498i	0.741601	−	0.198711i
$428$	−274.918	+	470.920i	−0.642333	+	1.10028i
$429$		0			0
$430$	−579.762	+	74.9074i	−1.34828	+	0.174203i
$431$			512.341i			1.18873i	0.804196	+	0.594364i	$0.202596\pi$
$431$			512.341i			1.18873i	−0.804196	+	0.594364i	$0.797404\pi$
$432$		0			0
$433$	92.4308			0.213466			0.106733	−	0.994288i	$-0.465961\pi$
$433$	92.4308			0.213466			0.106733	+	0.994288i	$0.465961\pi$
$434$	53.3261	+	412.730i	0.122871	+	0.950990i
$435$		0			0
$436$	−317.331	+	543.571i	−0.727823	+	1.24672i
$437$	69.8802	+	260.796i	0.159909	+	0.596788i
$438$		0			0
$439$	162.735	−	93.9551i	0.370695	−	0.214021i	−0.303067	−	0.952969i	$-0.598011\pi$
$439$	162.735	−	93.9551i	0.370695	−	0.214021i	0.673762	+	0.738949i	$0.264677\pi$
$440$	150.708	+	371.409i	0.342519	+	0.844110i
$441$		0			0
$442$	261.235	−	107.471i	0.591030	−	0.243147i
$443$	617.132	+	165.360i	1.39307	+	0.373273i	0.875853	−	0.482578i	$-0.160300\pi$
$443$	617.132	+	165.360i	1.39307	+	0.373273i	0.517222	+	0.855852i	$0.326966\pi$
$444$		0			0
$445$	−164.640	−	614.444i	−0.369977	−	1.38077i
$446$	−95.8822	−	125.581i	−0.214982	−	0.281572i
$447$		0			0
$448$	93.8009	−	330.872i	0.209377	−	0.738555i
$449$			182.865i			0.407271i	0.979047	+	0.203635i	$0.0652757\pi$
$449$			182.865i			0.407271i	−0.979047	+	0.203635i	$0.934724\pi$
$450$		0			0
$451$	−214.778	+	214.778i	−0.476227	+	0.476227i
$452$	239.180	+	65.3244i	0.529160	+	0.144523i
$453$		0			0
$454$	40.8525	−	304.636i	0.0899836	−	0.671003i
$455$	−123.690	+	214.237i	−0.271846	+	0.470851i
$456$		0			0
$457$	−408.786	+	236.013i	−0.894500	+	0.516440i	−0.875412	−	0.483378i	$-0.839410\pi$
$457$	−408.786	+	236.013i	−0.894500	+	0.516440i	−0.0190880	+	0.999818i	$0.506076\pi$
$458$	273.040	−	112.327i	0.596157	−	0.245256i
$459$		0			0
$460$	146.890	+	0.707421i	0.319326	+	0.00153787i
$461$	−199.024	+	742.769i	−0.431723	+	1.61121i	0.317066	+	0.948403i	$0.397302\pi$
$461$	−199.024	+	742.769i	−0.431723	+	1.61121i	−0.748789	+	0.662808i	$0.769364\pi$
$462$		0			0
$463$	−64.8072	+	112.249i	−0.139972	+	0.242439i	−0.927486	−	0.373858i	$-0.878035\pi$
$463$	−64.8072	+	112.249i	−0.139972	+	0.242439i	0.787514	+	0.616297i	$0.211368\pi$
$464$	83.1965	+	322.902i	0.179303	+	0.695910i
$465$		0			0
$466$	−461.994	+	59.6912i	−0.991403	+	0.128093i
$467$	64.6941	+	64.6941i	0.138531	+	0.138531i	0.772972	−	0.634440i	$-0.218769\pi$
$467$	64.6941	+	64.6941i	0.138531	+	0.138531i	−0.634440	+	0.772972i	$0.718769\pi$
$468$		0			0
$469$	354.715	+	354.715i	0.756323	+	0.756323i
$470$	−130.745	−	100.826i	−0.278181	−	0.214522i
$471$		0			0
$472$	112.285	+	148.543i	0.237893	+	0.314709i
$473$	−487.970	+	845.189i	−1.03165	+	1.78687i
$474$		0			0
$475$	73.6719	−	274.947i	0.155099	−	0.578836i
$476$	179.760	+	181.500i	0.377647	+	0.381302i
$477$		0			0
$478$	152.164	+	63.4581i	0.318335	+	0.132757i
$479$	−355.298	+	205.131i	−0.741750	+	0.428249i	−0.822705	−	0.568468i	$-0.807536\pi$
$479$	−355.298	+	205.131i	−0.741750	+	0.428249i	0.0809554	+	0.996718i	$0.474203\pi$
$480$		0			0
$481$	81.1324	−	140.525i	0.168674	−	0.292153i
$482$	430.762	+	564.188i	0.893698	+	1.17051i
$483$		0			0
$484$	178.616	+	48.7832i	0.369041	+	0.100792i
$485$	86.8484	−	86.8484i	0.179069	−	0.179069i
$486$		0			0
$487$			869.101i			1.78460i	0.451442	+	0.892301i	$0.350910\pi$
$487$			869.101i			1.78460i	−0.451442	+	0.892301i	$0.649090\pi$
$488$	484.337	−	60.2080i	0.992494	−	0.123377i
$489$		0			0
$490$	154.527	+	20.7225i	0.315361	+	0.0422909i
$491$	−104.814	−	391.173i	−0.213471	−	0.796686i	−0.986699	−	0.162558i	$-0.948026\pi$
$491$	−104.814	−	391.173i	−0.213471	−	0.796686i	0.773228	−	0.634129i	$-0.218641\pi$
$492$		0			0
$493$	−239.241	−	64.1044i	−0.485275	−	0.130029i
$494$	−624.783	−	260.558i	−1.26474	−	0.527445i
$495$		0			0
$496$	−5.96746	+	619.532i	−0.0120312	+	1.24906i
$497$	−579.500	+	334.574i	−1.16600	+	0.673188i
$498$		0			0
$499$	59.9492	+	223.734i	0.120139	+	0.448364i	0.999620	−	0.0275699i	$-0.00877689\pi$
$499$	59.9492	+	223.734i	0.120139	+	0.448364i	−0.879481	+	0.475934i	$0.842110\pi$
$500$	−468.276	−	273.374i	−0.936551	−	0.546749i
$501$		0			0
$502$	152.556	−	197.826i	0.303895	−	0.394076i
$503$	543.851			1.08121			0.540607	−	0.841275i	$-0.318195\pi$
$503$	543.851			1.08121			0.540607	+	0.841275i	$0.318195\pi$
$504$		0			0
$505$		−	481.509i		−	0.953484i
$506$	149.755	−	194.195i	0.295959	−	0.383784i
$507$		0			0
$508$	−219.639	+	57.7199i	−0.432361	+	0.113622i
$509$	−665.031	+	178.195i	−1.30655	+	0.350088i	−0.843921	−	0.536467i	$-0.819759\pi$
$509$	−665.031	+	178.195i	−1.30655	+	0.350088i	−0.462624	+	0.886555i	$0.653092\pi$
$510$		0			0
$511$	232.199	+	402.180i	0.454401	+	0.787045i
$512$	206.138	−	468.669i	0.402614	−	0.915370i
$513$		0			0
$514$	477.480	+	199.127i	0.928949	+	0.387407i
$515$	−189.057	+	705.570i	−0.367101	+	1.37004i
$516$		0			0
$517$	−266.248	+	71.3409i	−0.514986	+	0.137990i
$518$	145.438	+	19.5037i	0.280769	+	0.0376520i
$519$		0			0
$520$	−226.304	+	290.555i	−0.435201	+	0.558760i
$521$	51.1580			0.0981920			0.0490960	−	0.998794i	$-0.484366\pi$
$521$	51.1580			0.0981920			0.0490960	+	0.998794i	$0.484366\pi$
$522$		0			0
$523$	628.440	+	628.440i	1.20161	+	1.20161i	0.973678	+	0.227929i	$0.0731955\pi$
$523$	628.440	+	628.440i	1.20161	+	1.20161i	0.227929	+	0.973678i	$0.426804\pi$
$524$	−192.392	+	109.846i	−0.367160	+	0.209629i
$525$		0			0
$526$	−527.534	−	690.934i	−1.00292	−	1.31356i
$527$	−398.545	−	230.100i	−0.756253	−	0.436623i
$528$		0			0
$529$	219.564	+	380.296i	0.415055	+	0.718897i
$530$	−216.651	−	90.3515i	−0.408775	−	0.170475i
$531$		0			0
$532$	2.94818	−	612.165i	0.00554170	−	1.15069i
$533$	−269.580	−	72.2336i	−0.505778	−	0.135523i
$534$		0			0
$535$	457.328	+	264.038i	0.854819	+	0.493530i
$536$	450.345	+	595.764i	0.840197	+	1.11150i
$537$		0			0
$538$	−14.4837	−	11.1693i	−0.0269214	−	0.0207607i
$539$	184.051	−	184.051i	0.341468	−	0.341468i
$540$		0			0
$541$	138.038	−	138.038i	0.255154	−	0.255154i	−0.567926	−	0.823080i	$-0.692254\pi$
$541$	138.038	−	138.038i	0.255154	−	0.255154i	0.823080	+	0.567926i	$0.192254\pi$
$542$	−321.371	+	41.5222i	−0.592935	+	0.0766093i
$543$		0			0
$544$	227.866	+	304.482i	0.418872	+	0.559710i
$545$	527.881	+	304.772i	0.968590	+	0.559215i
$546$		0			0
$547$	−655.476	−	175.634i	−1.19831	−	0.321086i	−0.396145	−	0.918188i	$-0.629652\pi$
$547$	−655.476	−	175.634i	−1.19831	−	0.321086i	−0.802165	+	0.597102i	$0.796319\pi$
$548$	296.007	+	298.872i	0.540159	+	0.545387i
$549$		0			0
$550$	−239.095	+	98.3625i	−0.434718	+	0.178841i
$551$	296.773	+	514.026i	0.538608	+	0.932897i
$552$		0			0
$553$	432.059	+	249.449i	0.781300	+	0.451084i
$554$	69.7033	−	519.774i	0.125818	−	0.938220i
$555$		0			0
$556$	−352.128	+	201.046i	−0.633323	+	0.361594i
$557$	−523.493	−	523.493i	−0.939844	−	0.939844i	0.0584463	−	0.998291i	$-0.481385\pi$
$557$	−523.493	−	523.493i	−0.939844	−	0.939844i	−0.998291	+	0.0584463i	$0.981385\pi$
$558$		0			0
$559$	−896.728			−1.60417
$560$	−320.859	−	89.2949i	−0.572962	−	0.159455i
$561$		0			0
$562$	−313.129	−	410.118i	−0.557168	−	0.729748i
$563$	−535.008	+	143.355i	−0.950281	+	0.254627i	−0.700482	−	0.713670i	$-0.747031\pi$
$563$	−535.008	+	143.355i	−0.950281	+	0.254627i	−0.249800	+	0.968298i	$0.580365\pi$
$564$		0			0
$565$	62.1455	−	231.930i	0.109992	−	0.410496i
$566$	−124.817	+	51.3491i	−0.220525	+	0.0907228i
$567$		0			0
$568$	−923.097	+	374.570i	−1.62517	+	0.659454i
$569$	−281.315	−	487.252i	−0.494402	−	0.856330i	0.505577	−	0.862782i	$-0.331280\pi$
$569$	−281.315	−	487.252i	−0.494402	−	0.856330i	−0.999979	+	0.00645162i	$0.997946\pi$
$570$		0			0
$571$	93.7407	−	25.1177i	0.164169	−	0.0439890i	−0.175798	−	0.984426i	$-0.556251\pi$
$571$	93.7407	−	25.1177i	0.164169	−	0.0439890i	0.339967	+	0.940437i	$0.389584\pi$
$572$	156.272	+	594.655i	0.273202	+	1.03961i
$573$		0			0
$574$	−32.3406	−	250.307i	−0.0563425	−	0.436075i
$575$			94.7480i			0.164779i
$576$		0			0
$577$	−606.259			−1.05071			−0.525354	−	0.850884i	$-0.676067\pi$
$577$	−606.259			−1.05071			−0.525354	+	0.850884i	$0.676067\pi$
$578$	293.078	−	37.8668i	0.507056	−	0.0655134i
$579$		0			0
$580$	312.315	−	82.0746i	0.538474	−	0.141508i
$581$	108.773	+	405.948i	0.187218	+	0.698706i
$582$		0			0
$583$	−339.382	+	195.942i	−0.582130	+	0.336093i
$584$	259.956	+	640.641i	0.445130	+	1.09699i
$585$		0			0
$586$	332.479	+	808.175i	0.567371	+	1.37914i
$587$	−237.410	−	63.6138i	−0.404446	−	0.108371i	0.0508604	−	0.998706i	$-0.483804\pi$
$587$	−237.410	−	63.6138i	−0.404446	−	0.108371i	−0.455307	+	0.890335i	$0.650470\pi$
$588$		0			0
$589$	285.435	+	1065.26i	0.484609	+	1.80858i
$590$	143.327	−	109.431i	0.242927	−	0.185477i
$591$		0			0
$592$	210.462	+	58.5715i	0.355510	+	0.0989384i
$593$			849.686i			1.43286i	0.697659	+	0.716430i	$0.254225\pi$
$593$			849.686i			1.43286i	−0.697659	+	0.716430i	$0.745775\pi$
$594$		0			0
$595$	174.929	−	174.929i	0.293998	−	0.293998i
$596$	−417.462	−	731.176i	−0.700440	−	1.22681i
$597$		0			0
$598$	223.328	+	29.9489i	0.373458	+	0.0500818i
$599$	172.533	−	298.836i	0.288035	−	0.498891i	−0.685306	−	0.728256i	$-0.740331\pi$
$599$	172.533	−	298.836i	0.288035	−	0.498891i	0.973341	+	0.229364i	$0.0736647\pi$
$600$		0			0
$601$	−114.395	+	66.0458i	−0.190341	+	0.109893i	−0.592142	−	0.805834i	$-0.701718\pi$
$601$	−114.395	+	66.0458i	−0.190341	+	0.109893i	0.401801	+	0.915727i	$0.368384\pi$
$602$	−308.526	−	749.951i	−0.512502	−	1.24577i
$603$		0			0
$604$	−415.029	+	411.051i	−0.687135	+	0.680548i
$605$	46.4092	−	173.202i	0.0767095	−	0.286284i
$606$		0			0
$607$	399.074	−	691.216i	0.657453	−	1.13874i	−0.323820	−	0.946119i	$-0.604967\pi$
$607$	399.074	−	691.216i	0.657453	−	1.13874i	0.981273	−	0.192623i	$-0.0616993\pi$
$608$	129.828	−	902.079i	0.213533	−	1.48368i
$609$		0			0
$610$	−60.5652	−	468.758i	−0.0992871	−	0.768455i
$611$	−179.087	−	179.087i	−0.293105	−	0.293105i
$612$		0			0
$613$	−92.1791	−	92.1791i	−0.150374	−	0.150374i	0.627911	−	0.778285i	$-0.283910\pi$
$613$	−92.1791	−	92.1791i	−0.150374	−	0.150374i	−0.778285	+	0.627911i	$0.783910\pi$
$614$	485.361	−	629.391i	0.790490	−	1.02507i
$615$		0			0
$616$	−443.555	+	335.289i	−0.720056	+	0.544300i
$617$	−39.3936	+	68.2317i	−0.0638470	+	0.110586i	−0.896182	−	0.443687i	$-0.853670\pi$
$617$	−39.3936	+	68.2317i	−0.0638470	+	0.110586i	0.832335	+	0.554273i	$0.187004\pi$
$618$		0			0
$619$	128.392	−	479.166i	0.207418	−	0.774096i	−0.781280	−	0.624180i	$-0.785433\pi$
$619$	128.392	−	479.166i	0.207418	−	0.774096i	0.988699	−	0.149916i	$-0.0479003\pi$
$620$	599.991	+	2.88955i	0.967727	+	0.00466057i
$621$		0			0
$622$	−144.219	+	345.819i	−0.231864	+	0.555979i
$623$	764.206	−	441.214i	1.22665	−	0.708209i
$624$		0			0
$625$	−137.625	+	238.373i	−0.220200	+	0.381397i
$626$	271.588	−	207.360i	0.433847	−	0.331246i
$627$		0			0
$628$	207.010	+	362.574i	0.329634	+	0.577347i
$629$	−114.742	+	114.742i	−0.182419	+	0.182419i
$630$		0			0
$631$		−	806.396i		−	1.27797i	−0.769221	−	0.638983i	$-0.779355\pi$
$631$		−	806.396i		−	1.27797i	0.769221	−	0.638983i	$-0.220645\pi$
$632$	585.972	+	456.395i	0.927170	+	0.722144i
$633$		0			0
$634$	152.270	−	1135.47i	0.240174	−	1.79097i
$635$	56.9212	+	212.433i	0.0896396	+	0.334540i
$636$		0			0
$637$	231.012	+	61.8995i	0.362656	+	0.0971734i
$638$	207.505	−	497.569i	0.325243	−	0.779889i
$639$		0			0
$640$	−454.827	−	197.441i	−0.710667	−	0.308502i
$641$	103.969	−	60.0266i	0.162198	−	0.0936453i	−0.416704	−	0.909042i	$-0.636815\pi$
$641$	103.969	−	60.0266i	0.162198	−	0.0936453i	0.578902	+	0.815397i	$0.303481\pi$
$642$		0			0
$643$	210.532	+	785.714i	0.327421	+	1.22195i	0.911856	+	0.410511i	$0.134649\pi$
$643$	210.532	+	785.714i	0.327421	+	1.22195i	−0.584435	+	0.811440i	$0.698684\pi$
$644$	51.7908	+	197.077i	0.0804205	+	0.306021i
$645$		0			0
$646$	536.070	+	413.396i	0.829830	+	0.639932i
$647$	825.493			1.27588			0.637939	−	0.770087i	$-0.279787\pi$
$647$	825.493			1.27588			0.637939	+	0.770087i	$0.279787\pi$
$648$		0			0
$649$		−	301.051i		−	0.463869i
$650$	−188.115	−	145.067i	−0.289407	−	0.223179i
$651$		0			0
$652$	95.2778	−	163.206i	0.146132	−	0.250316i
$653$	45.5134	−	12.1953i	0.0696989	−	0.0186758i	−0.223801	−	0.974635i	$-0.571847\pi$
$653$	45.5134	−	12.1953i	0.0696989	−	0.0186758i	0.293500	+	0.955959i	$0.405180\pi$
$654$		0			0
$655$	107.273	+	185.803i	0.163776	+	0.283668i
$656$	3.61907	−	375.726i	0.00551688	−	0.572753i
$657$		0			0
$658$	88.1578	−	211.391i	0.133978	−	0.321262i
$659$	−144.063	+	537.650i	−0.218608	+	0.815857i	0.766257	+	0.642534i	$0.222117\pi$
$659$	−144.063	+	537.650i	−0.218608	+	0.815857i	−0.984865	+	0.173323i	$0.944550\pi$
$660$		0			0
$661$	−908.098	+	243.324i	−1.37382	+	0.368115i	−0.868874	−	0.495033i	$-0.835156\pi$
$661$	−908.098	+	243.324i	−1.37382	+	0.368115i	−0.504950	+	0.863148i	$0.668489\pi$
$662$	−18.0040	+	134.255i	−0.0271964	+	0.202802i
$663$		0			0
$664$	77.1839	+	620.897i	0.116241	+	0.935086i
$665$	−592.842			−0.891492
$666$		0			0
$667$	−139.703	−	139.703i	−0.209449	−	0.209449i
$668$	175.678	−	643.233i	0.262991	−	0.962924i
$669$		0			0
$670$	574.845	−	438.899i	0.857978	−	0.655073i
$671$	−683.365	−	394.541i	−1.01843	−	0.587989i
$672$		0			0
$673$	642.305	+	1112.50i	0.954390	+	1.65305i	0.735757	+	0.677246i	$0.236827\pi$
$673$	642.305	+	1112.50i	0.954390	+	1.65305i	0.218633	+	0.975807i	$0.429840\pi$
$674$	−254.451	+	610.139i	−0.377524	+	0.905251i
$675$		0			0
$676$	78.9073	−	78.1509i	0.116727	−	0.115608i
$677$	−81.0177	−	21.7086i	−0.119672	−	0.0320659i	0.198486	−	0.980104i	$-0.436398\pi$
$677$	−81.0177	−	21.7086i	−0.119672	−	0.0320659i	−0.318158	+	0.948038i	$0.603064\pi$
$678$		0			0
$679$	147.553	+	85.1898i	0.217309	+	0.125464i
$680$	293.802	−	222.089i	0.432062	−	0.326601i
$681$		0			0
$682$	611.695	−	793.214i	0.896913	−	1.16307i
$683$	−422.773	+	422.773i	−0.618994	+	0.618994i	−0.945273	−	0.326280i	$-0.894205\pi$
$683$	−422.773	+	422.773i	−0.618994	+	0.618994i	0.326280	+	0.945273i	$0.394205\pi$
$684$		0			0
$685$	288.051	−	288.051i	0.420513	−	0.420513i
$686$	95.1933	+	736.770i	0.138766	+	1.07401i
$687$		0			0
$688$	−301.221	−	1169.10i	−0.437822	−	1.69928i
$689$	−311.836	−	180.039i	−0.452592	−	0.261304i
$690$		0			0
$691$	−504.924	−	135.294i	−0.730715	−	0.195795i	−0.125768	−	0.992060i	$-0.540139\pi$
$691$	−504.924	−	135.294i	−0.730715	−	0.195795i	−0.604948	+	0.796265i	$0.706806\pi$
$692$	1.36528	−	283.489i	0.00197295	−	0.409667i
$693$		0			0
$694$	−449.633	−	1092.95i	−0.647887	−	1.57485i
$695$	196.338	+	340.067i	0.282501	+	0.489306i
$696$		0			0
$697$	241.705	+	139.548i	0.346779	+	0.200213i
$698$	−988.954	−	132.622i	−1.41684	−	0.190002i
$699$		0			0
$700$	56.5996	−	207.235i	0.0808566	−	0.296050i
$701$	−387.399	−	387.399i	−0.552638	−	0.552638i	0.374563	−	0.927201i	$-0.377793\pi$
$701$	−387.399	−	387.399i	−0.552638	−	0.552638i	−0.927201	+	0.374563i	$0.877793\pi$
$702$		0			0
$703$	388.865			0.553151
$704$	−722.782	+	403.489i	−1.02668	+	0.573138i
$705$		0			0
$706$	−184.286	+	140.704i	−0.261028	+	0.199297i
$707$	645.192	−	172.879i	0.912578	−	0.244524i
$708$		0			0
$709$	42.2947	−	157.846i	0.0596540	−	0.222632i	−0.929663	−	0.368410i	$-0.879902\pi$
$709$	42.2947	−	157.846i	0.0596540	−	0.222632i	0.989317	+	0.145779i	$0.0465688\pi$
$710$	367.044	+	892.193i	0.516963	+	1.25661i
$711$		0			0
$712$	1217.32	−	493.958i	1.70972	−	0.693761i
$713$	−183.546	−	317.911i	−0.257428	−	0.445878i
$714$		0			0
$715$	575.143	−	154.109i	0.804396	−	0.215537i
$716$	709.448	+	414.168i	0.990849	+	0.578447i
$717$		0			0
$718$	−1187.61	+	153.443i	−1.65405	+	0.213709i
$719$		−	480.946i		−	0.668909i	−0.942412	−	0.334455i	$-0.891448\pi$
$719$		−	480.946i		−	0.668909i	0.942412	−	0.334455i	$-0.108552\pi$
$720$		0			0
$721$	−1013.30			−1.40541
$722$	−115.359	−	892.848i	−0.159777	−	1.23663i
$723$		0			0
$724$	413.287	+	241.273i	0.570838	+	0.333249i
$725$	53.9093	+	201.192i	0.0743576	+	0.277506i
$726$		0			0
$727$	−45.9366	+	26.5215i	−0.0631865	+	0.0364807i	−0.531260	−	0.847209i	$-0.678281\pi$
$727$	−45.9366	+	26.5215i	−0.0631865	+	0.0364807i	0.468074	+	0.883689i	$0.344948\pi$
$728$	−470.578	−	198.914i	−0.646398	−	0.273234i
$729$		0			0
$730$	619.193	−	254.733i	0.848209	−	0.348949i
$731$	866.196	+	232.096i	1.18495	+	0.317505i
$732$		0			0
$733$	165.745	+	618.567i	0.226118	+	0.843884i	0.981953	+	0.189123i	$0.0605644\pi$
$733$	165.745	+	618.567i	0.226118	+	0.843884i	−0.755835	+	0.654762i	$0.772769\pi$
$734$	−72.8822	−	95.4570i	−0.0992945	−	0.130050i
$735$		0			0
$736$	35.9727	+	301.222i	0.0488760	+	0.409269i
$737$		−	1207.43i		−	1.63831i
$738$		0			0
$739$	726.916	−	726.916i	0.983648	−	0.983648i	−0.0162206	−	0.999868i	$-0.505163\pi$
$739$	726.916	−	726.916i	0.983648	−	0.983648i	0.999868	+	0.0162206i	$0.00516340\pi$
$740$	55.7399	−	204.087i	0.0753242	−	0.275794i
$741$		0			0
$742$	43.2801	−	322.738i	0.0583290	−	0.434957i
$743$	440.165	−	762.388i	0.592415	−	1.02609i	−0.401491	−	0.915863i	$-0.631508\pi$
$743$	440.165	−	762.388i	0.592415	−	1.02609i	0.993906	−	0.110230i	$-0.0351589\pi$
$744$		0			0
$745$	−706.134	+	407.686i	−0.947830	+	0.547230i
$746$	−1147.53	+	472.087i	−1.53824	+	0.632825i
$747$		0			0
$748$	2.96114	−	614.855i	0.00395874	−	0.821998i
$749$	−189.598	+	707.590i	−0.253135	+	0.944713i
$750$		0			0
$751$	−428.427	+	742.057i	−0.570475	+	0.988092i	0.426042	+	0.904703i	$0.359908\pi$
$751$	−428.427	+	742.057i	−0.570475	+	0.988092i	−0.996517	+	0.0833883i	$0.973426\pi$
$752$	173.326	−	293.641i	0.230487	−	0.390480i
$753$		0			0
$754$	491.264	−	63.4731i	0.651544	−	0.0841818i
$755$	400.003	+	400.003i	0.529805	+	0.529805i
$756$		0			0
$757$	−119.448	−	119.448i	−0.157791	−	0.157791i	0.623796	−	0.781587i	$-0.285590\pi$
$757$	−119.448	−	119.448i	−0.157791	−	0.157791i	−0.781587	+	0.623796i	$0.785590\pi$
$758$	−287.448	−	221.668i	−0.379219	−	0.292439i
$759$		0			0
$760$	−874.191	−	121.520i	−1.15025	−	0.159895i
$761$	132.802	−	230.020i	0.174510	−	0.302260i	−0.765482	−	0.643458i	$-0.777499\pi$
$761$	132.802	−	230.020i	0.174510	−	0.302260i	0.939992	+	0.341198i	$0.110833\pi$
$762$		0			0
$763$	−218.848	+	816.752i	−0.286826	+	1.07045i
$764$	29.6072	−	29.3233i	0.0387528	−	0.0383813i
$765$		0			0
$766$	119.788	+	49.9561i	0.156381	+	0.0652168i
$767$	239.556	−	138.308i	0.312329	−	0.180323i
$768$		0			0
$769$	750.091	−	1299.20i	0.975411	−	1.68946i	0.296838	−	0.954928i	$-0.404068\pi$
$769$	750.091	−	1299.20i	0.975411	−	1.68946i	0.678573	−	0.734533i	$-0.262599\pi$
$770$	326.767	+	427.981i	0.424373	+	0.555819i
$771$		0			0
$772$	171.115	−	626.524i	0.221651	−	0.811559i
$773$	−572.185	+	572.185i	−0.740213	+	0.740213i	−0.972619	−	0.232406i	$-0.925340\pi$
$773$	−572.185	+	572.185i	−0.740213	+	0.740213i	0.232406	+	0.972619i	$0.425340\pi$
$774$		0			0
$775$			387.010i			0.499368i
$776$	200.116	+	155.864i	0.257882	+	0.200856i
$777$		0			0
$778$	−820.225	−	109.995i	−1.05427	−	0.141381i
$779$	−173.107	−	646.043i	−0.222217	−	0.829324i
$780$		0			0
$781$	1555.73	+	416.856i	1.99197	+	0.533747i
$782$	−207.972	−	86.7322i	−0.265949	−	0.110911i
$783$		0			0
$784$	−3.10131	+	321.973i	−0.00395575	+	0.410679i
$785$	350.156	−	202.163i	0.446058	−	0.257532i
$786$		0			0
$787$	98.7267	+	368.453i	0.125447	+	0.468174i	0.999855	−	0.0170167i	$-0.00541686\pi$
$787$	98.7267	+	368.453i	0.125447	+	0.468174i	−0.874408	+	0.485191i	$0.838750\pi$
$788$	452.290	−	774.748i	0.573971	−	0.983182i
$789$		0			0
$790$	439.246	−	569.591i	0.556008	−	0.721002i
$791$	333.085			0.421093
$792$		0			0
$793$		−	725.036i		−	0.914295i
$794$	−684.980	+	888.246i	−0.862695	+	1.11870i
$795$		0			0
$796$	90.0045	+	342.490i	0.113071	+	0.430264i
$797$	796.594	−	213.447i	0.999491	−	0.267813i	0.278259	−	0.960506i	$-0.410243\pi$
$797$	796.594	−	213.447i	0.999491	−	0.267813i	0.721232	+	0.692693i	$0.243576\pi$
$798$		0			0
$799$	126.637	+	219.342i	0.158495	+	0.274521i
$800$	125.939	−	293.982i	0.157424	−	0.367478i
$801$		0			0
$802$	−161.855	−	67.4996i	−0.201814	−	0.0841641i
$803$	289.303	−	1079.69i	0.360278	−	1.34458i
$804$		0			0
$805$	190.611	−	51.0741i	0.236784	−	0.0634460i
$806$	912.211	+	122.330i	1.13178	+	0.151774i
$807$		0			0
$808$	986.822	−	122.672i	1.22131	−	0.151822i
$809$	371.253			0.458904			0.229452	−	0.973320i	$-0.426307\pi$
$809$	371.253			0.458904			0.229452	+	0.973320i	$0.426307\pi$
$810$		0			0
$811$	−682.431	−	682.431i	−0.841468	−	0.841468i	0.147582	−	0.989050i	$-0.452851\pi$
$811$	−682.431	−	682.431i	−0.841468	−	0.841468i	−0.989050	+	0.147582i	$0.952851\pi$
$812$	222.107	+	389.015i	0.273531	+	0.479083i
$813$		0			0
$814$	−214.337	−	280.727i	−0.263314	−	0.344873i
$815$	−158.495	−	91.5072i	−0.194473	−	0.112279i
$816$		0			0
$817$	−1074.50	−	1861.09i	−1.31518	−	2.27795i
$818$	115.281	+	48.0763i	0.140930	+	0.0587730i
$819$		0			0
$820$	−363.875	−	1.75242i	−0.443750	−	0.00213710i
$821$	124.780	+	33.4347i	0.151986	+	0.0407244i	0.334010	−	0.942570i	$-0.391598\pi$
$821$	124.780	+	33.4347i	0.151986	+	0.0407244i	−0.182024	+	0.983294i	$0.558265\pi$
$822$		0			0
$823$	−364.270	−	210.311i	−0.442613	−	0.255543i	0.262093	−	0.965043i	$-0.415587\pi$
$823$	−364.270	−	210.311i	−0.442613	−	0.255543i	−0.704705	+	0.709500i	$0.748921\pi$
$824$	−1494.19	−	207.705i	−1.81333	−	0.252069i
$825$		0			0
$826$	198.091	+	152.760i	0.239819	+	0.184939i
$827$	−646.935	+	646.935i	−0.782268	+	0.782268i	−0.980213	−	0.197945i	$-0.936573\pi$
$827$	−646.935	+	646.935i	−0.782268	+	0.782268i	0.197945	+	0.980213i	$0.436573\pi$
$828$		0			0
$829$	626.764	−	626.764i	0.756048	−	0.756048i	−0.219553	−	0.975601i	$-0.570460\pi$
$829$	626.764	−	626.764i	0.756048	−	0.756048i	0.975601	+	0.219553i	$0.0704598\pi$
$830$	600.926	−	77.6417i	0.724007	−	0.0935442i
$831$		0			0
$832$	−653.129	−	389.773i	−0.785011	−	0.468477i
$833$	−207.125	−	119.584i	−0.248650	−	0.143558i
$834$		0			0
$835$	−623.735	−	167.129i	−0.746988	−	0.200155i
$836$	−1046.91	+	1036.87i	−1.25228	+	1.24027i
$837$		0			0
$838$	511.381	−	210.380i	0.610240	−	0.251050i
$839$	−441.149	−	764.093i	−0.525804	−	0.910719i	−0.999548	−	0.0300564i	$-0.990431\pi$
$839$	−441.149	−	764.093i	−0.525804	−	0.910719i	0.473744	−	0.880662i	$-0.342902\pi$
$840$		0			0
$841$	352.189	+	203.337i	0.418775	+	0.241780i
$842$	162.793	−	1213.94i	0.193341	−	1.44173i
$843$		0			0
$844$	−579.707	−	1015.34i	−0.686857	−	1.20301i
$845$	−76.0504	−	76.0504i	−0.0900005	−	0.0900005i
$846$		0			0
$847$	248.742			0.293674
$848$	129.974	−	467.030i	0.153272	−	0.550743i
$849$		0			0
$850$	144.163	+	188.816i	0.169603	+	0.222137i
$851$	−125.028	+	33.5012i	−0.146919	+	0.0393668i
$852$		0			0
$853$	−191.702	+	715.440i	−0.224738	+	0.838734i	0.757771	+	0.652520i	$0.226288\pi$
$853$	−191.702	+	715.440i	−0.224738	+	0.838734i	−0.982509	+	0.186214i	$0.940378\pi$
$854$	606.361	−	249.454i	0.710025	−	0.292101i
$855$		0			0
$856$	−424.618	+	1004.53i	−0.496049	+	1.17352i
$857$	454.964	+	788.022i	0.530880	+	0.919512i	0.999351	+	0.0360325i	$0.0114720\pi$
$857$	454.964	+	788.022i	0.530880	+	0.919512i	−0.468470	+	0.883479i	$0.655195\pi$
$858$		0			0
$859$	−133.228	+	35.6983i	−0.155097	+	0.0415580i	−0.335532	−	0.942029i	$-0.608916\pi$
$859$	−133.228	+	35.6983i	−0.155097	+	0.0415580i	0.180435	+	0.983587i	$0.442249\pi$
$860$	−1130.77	+	297.159i	−1.31485	+	0.345534i
$861$		0			0
$862$	131.301	+	1016.24i	0.152322	+	1.17893i
$863$			512.214i			0.593527i	0.954951	+	0.296764i	$0.0959073\pi$
$863$			512.214i			0.593527i	−0.954951	+	0.296764i	$0.904093\pi$
$864$		0			0
$865$	−274.541			−0.317389
$866$	183.338	−	23.6879i	0.211706	−	0.0273532i
$867$		0			0
$868$	211.546	+	804.988i	0.243717	+	0.927406i
$869$	−310.796	−	1159.91i	−0.357648	−	1.33476i
$870$		0			0
$871$	960.794	−	554.715i	1.10309	−	0.636871i
$872$	−490.125	+	1159.50i	−0.562070	+	1.32971i
$873$		0			0
$874$	205.444	+	499.384i	0.235062	+	0.571378i
$875$	−703.616	−	188.533i	−0.804133	−	0.215467i
$876$		0			0
$877$	−259.253	−	967.546i	−0.295614	−	1.10325i	−0.940729	−	0.339160i	$-0.889857\pi$
$877$	−259.253	−	967.546i	−0.295614	−	1.10325i	0.645115	−	0.764085i	$-0.276809\pi$
$878$	298.708	−	228.066i	0.340215	−	0.259757i
$879$		0			0
$880$	394.115	+	698.070i	0.447858	+	0.793262i
$881$			18.4946i			0.0209928i	0.999945	+	0.0104964i	$0.00334117\pi$
$881$			18.4946i			0.0209928i	−0.999945	+	0.0104964i	$0.996659\pi$
$882$		0			0
$883$	162.276	−	162.276i	0.183778	−	0.183778i	−0.609222	−	0.793000i	$-0.708518\pi$
$883$	162.276	−	162.276i	0.183778	−	0.183778i	0.793000	+	0.609222i	$0.208518\pi$
$884$	490.621	−	280.119i	0.555002	−	0.316876i
$885$		0			0
$886$	1266.47	+	169.837i	1.42942	+	0.191690i
$887$	−252.776	+	437.820i	−0.284978	+	0.493596i	−0.972604	−	0.232469i	$-0.925320\pi$
$887$	−252.776	+	437.820i	−0.284978	+	0.493596i	0.687626	+	0.726065i	$0.258653\pi$
$888$		0			0
$889$	−264.210	+	152.542i	−0.297199	+	0.171588i
$890$	−484.033	−	1176.56i	−0.543857	−	1.32198i
$891$		0			0
$892$	−222.367	−	224.519i	−0.249290	−	0.251703i
$893$	157.091	−	586.271i	0.175913	−	0.656518i
$894$		0			0
$895$	397.777	−	688.970i	0.444444	−	0.769799i
$896$	101.260	−	680.329i	0.113014	−	0.759295i
$897$		0			0
$898$	46.8640	+	362.714i	0.0521871	+	0.403913i
$899$	−570.633	−	570.633i	−0.634742	−	0.634742i
$900$		0			0
$901$	254.620	+	254.620i	0.282597	+	0.282597i
$902$	−370.973	+	481.059i	−0.411278	+	0.533324i
$903$		0			0
$904$	491.159	+	68.2753i	0.543317	+	0.0755258i
$905$	231.724	−	401.358i	0.256049	−	0.443490i
$906$		0			0
$907$	−258.798	+	965.847i	−0.285334	+	1.06488i	0.663261	+	0.748388i	$0.269172\pi$
$907$	−258.798	+	965.847i	−0.285334	+	1.06488i	−0.948595	+	0.316493i	$0.897495\pi$
$908$	2.96048	−	614.718i	0.00326044	−	0.677002i
$909$		0			0
$910$	−190.437	+	456.641i	−0.209271	+	0.501804i
$911$	−452.086	+	261.012i	−0.496252	+	0.286512i	−0.727165	−	0.686463i	$-0.759162\pi$
$911$	−452.086	+	261.012i	−0.496252	+	0.286512i	0.230912	+	0.972975i	$0.425829\pi$
$912$		0			0
$913$	505.783	−	876.042i	0.553979	−	0.959520i
$914$	−750.348	+	572.897i	−0.820950	+	0.626802i
$915$		0			0
$916$	512.791	−	292.776i	0.559815	−	0.319625i
$917$	−210.449	+	210.449i	−0.229497	+	0.229497i
$918$		0			0
$919$		−	495.997i		−	0.539713i	−0.962901	−	0.269857i	$-0.913024\pi$
$919$		−	495.997i		−	0.539713i	0.962901	−	0.269857i	$-0.0869763\pi$
$920$	291.539	−	36.2413i	0.316891	−	0.0393927i
$921$		0			0
$922$	−204.413	+	1524.30i	−0.221706	+	1.65325i
$923$	383.022	+	1429.46i	0.414975	+	1.54871i
$924$		0			0
$925$	131.812	+	35.3189i	0.142500	+	0.0381826i
$926$	−99.7789	+	239.257i	−0.107753	+	0.258376i
$927$		0			0
$928$	247.774	+	619.160i	0.266997	+	0.667198i
$929$	1037.03	−	598.731i	1.11629	−	0.644490i	0.175838	−	0.984419i	$-0.443736\pi$
$929$	1037.03	−	598.731i	1.11629	−	0.644490i	0.940451	+	0.339929i	$0.110403\pi$
$930$		0			0
$931$	148.341	+	553.617i	0.159335	+	0.594647i
$932$	−901.073	+	236.797i	−0.966816	+	0.254074i
$933$		0			0
$934$	144.901	+	111.742i	0.155140	+	0.119638i
$935$	−595.447			−0.636842
$936$		0			0
$937$			219.908i			0.234694i	0.993091	+	0.117347i	$0.0374390\pi$
$937$			219.908i			0.234694i	−0.993091	+	0.117347i	$0.962561\pi$
$938$	794.488	+	612.677i	0.847002	+	0.653174i
$939$		0			0
$940$	−285.174	−	166.482i	−0.303377	−	0.177108i
$941$	−7.40638	+	1.98453i	−0.00787075	+	0.00210896i	−0.262752	−	0.964863i	$-0.584630\pi$
$941$	−7.40638	+	1.98453i	−0.00787075	+	0.00210896i	0.254882	+	0.966972i	$0.417964\pi$
$942$		0			0
$943$	111.315	+	192.803i	0.118043	+	0.204457i
$944$	260.787	+	265.860i	0.276258	+	0.281632i
$945$		0			0
$946$	−751.293	+	1801.50i	−0.794178	+	1.90433i
$947$	206.974	−	772.438i	0.218558	−	0.815668i	−0.766326	−	0.642452i	$-0.777917\pi$
$947$	206.974	−	772.438i	0.218558	−	0.815668i	0.984884	−	0.173217i	$-0.0554160\pi$
$948$		0			0
$949$	992.062	−	265.822i	1.04538	−	0.280108i
$950$	75.6665	−	564.242i	0.0796489	−	0.593938i
$951$		0			0
$952$	403.071	+	313.939i	0.423394	+	0.329768i
$953$	−11.2506			−0.0118054			−0.00590272	−	0.999983i	$-0.501879\pi$
$953$	−11.2506			−0.0118054			−0.00590272	+	0.999983i	$0.501879\pi$
$954$		0			0
$955$	−28.5352	−	28.5352i	−0.0298798	−	0.0298798i
$956$	318.082	+	86.8738i	0.332722	+	0.0908722i
$957$		0			0
$958$	−652.168	+	497.936i	−0.680760	+	0.519766i
$959$	489.391	+	282.550i	0.510314	+	0.294630i
$960$		0			0
$961$	−269.217	−	466.298i	−0.280143	−	0.485222i
$962$	124.914	−	299.526i	0.129848	−	0.311358i
$963$		0			0
$964$	999.011	+	1008.68i	1.03632	+	1.04635i
$965$	−607.532	−	162.788i	−0.629567	−	0.168692i
$966$		0			0
$967$	206.224	+	119.064i	0.213262	+	0.123127i	0.602826	−	0.797872i	$-0.294041\pi$
$967$	206.224	+	119.064i	0.213262	+	0.123127i	−0.389564	+	0.920999i	$0.627374\pi$
$968$	366.789	+	50.9869i	0.378914	+	0.0526724i
$969$		0			0
$970$	150.008	−	194.522i	0.154647	−	0.200538i
$971$	−956.820	+	956.820i	−0.985396	+	0.985396i	−0.999895	−	0.0144987i	$-0.995385\pi$
$971$	−956.820	+	956.820i	−0.985396	+	0.985396i	0.0144987	+	0.999895i	$0.495385\pi$
$972$		0			0
$973$	−385.177	+	385.177i	−0.395865	+	0.395865i
$974$	222.730	+	1723.87i	0.228676	+	1.76989i
$975$		0			0
$976$	945.258	−	243.548i	0.968502	−	0.249537i
$977$	−25.8436	−	14.9208i	−0.0264520	−	0.0152720i	0.486716	−	0.873560i	$-0.338195\pi$
$977$	−25.8436	−	14.9208i	−0.0264520	−	0.0152720i	−0.513168	+	0.858288i	$0.671528\pi$
$978$		0			0
$979$	−2051.59	−	549.722i	−2.09560	−	0.561514i
$980$	311.817	+	1.50171i	0.318181	+	0.00153236i
$981$		0			0
$982$	−308.149	−	749.035i	−0.313798	−	0.762765i
$983$	626.105	+	1084.45i	0.636933	+	1.10320i	0.986102	+	0.166141i	$0.0531306\pi$
$983$	626.105	+	1084.45i	0.636933	+	1.10320i	−0.349169	+	0.937060i	$0.613536\pi$
$984$		0			0
$985$	−752.386	−	434.390i	−0.763843	−	0.441005i
$986$	−490.966	−	65.8400i	−0.497937	−	0.0667748i
$987$		0			0
$988$	−1306.04	−	356.702i	−1.32190	−	0.361035i
$989$	505.808	+	505.808i	0.511433	+	0.511433i
$990$		0			0
$991$	−702.277			−0.708655			−0.354328	−	0.935121i	$-0.615290\pi$
$991$	−702.277			−0.708655			−0.354328	+	0.935121i	$0.615290\pi$
$992$	146.935	+	1230.38i	0.148120	+	1.24030i
$993$		0			0
$994$	−1063.70	+	812.145i	−1.07012	+	0.817047i
$995$	331.253	−	88.7589i	0.332917	−	0.0892049i
$996$		0			0
$997$	−210.524	+	785.686i	−0.211157	+	0.788050i	0.776327	+	0.630331i	$0.217081\pi$
$997$	−210.524	+	785.686i	−0.211157	+	0.788050i	−0.987484	+	0.157719i	$0.949586\pi$
$998$	176.248	+	428.415i	0.176601	+	0.429273i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.x.a.341.44		184
3.2	odd	2		144.3.w.a.5.3	✓	184
9.2	odd	6	inner	432.3.x.a.197.33		184
9.7	even	3		144.3.w.a.101.14	yes	184
16.13	even	4	inner	432.3.x.a.125.33		184
48.29	odd	4		144.3.w.a.77.14	yes	184
144.29	odd	12	inner	432.3.x.a.413.44		184
144.61	even	12		144.3.w.a.29.3	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.3	✓	184	3.2	odd	2
144.3.w.a.29.3	yes	184	144.61	even	12
144.3.w.a.77.14	yes	184	48.29	odd	4
144.3.w.a.101.14	yes	184	9.7	even	3
432.3.x.a.125.33		184	16.13	even	4	inner
432.3.x.a.197.33		184	9.2	odd	6	inner
432.3.x.a.341.44		184	1.1	even	1	trivial
432.3.x.a.413.44		184	144.29	odd	12	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)

\(f(q)\)	\(=\)	\(q+(1.98351 - 0.256277i) q^{2} +(3.86864 - 1.01666i) q^{4} +(-1.00259 - 3.74171i) q^{5} +(4.65369 - 2.68681i) q^{7} +(7.41296 - 3.00800i) q^{8} +O(q^{10})\)	\(q+(1.98351 - 0.256277i) q^{2} +(3.86864 - 1.01666i) q^{4} +(-1.00259 - 3.74171i) q^{5} +(4.65369 - 2.68681i) q^{7} +(7.41296 - 3.00800i) q^{8} +(-2.94756 - 7.16478i) q^{10} +(-12.4933 - 3.34758i) q^{11} +(-3.07587 - 11.4793i) q^{13} +(8.54209 - 6.52195i) q^{14} +(13.9328 - 7.86617i) q^{16} +11.8846i q^{17} +(20.1387 - 20.1387i) q^{19} +(-7.68268 - 13.4560i) q^{20} +(-25.6386 - 3.43821i) q^{22} +(-4.74003 + 8.20998i) q^{23} +(8.65545 - 4.99723i) q^{25} +(-9.04291 - 21.9811i) q^{26} +(15.2719 - 15.1255i) q^{28} +(-5.39392 + 20.1304i) q^{29} +(-19.3613 + 33.5347i) q^{31} +(25.6200 - 19.1733i) q^{32} +(3.04574 + 23.5732i) q^{34} +(-14.7190 - 14.7190i) q^{35} +(9.65467 + 9.65467i) q^{37} +(34.7843 - 45.1065i) q^{38} +(-18.6872 - 24.7213i) q^{40} +(11.7420 - 20.3377i) q^{41} +(19.5292 - 72.8841i) q^{43} +(-51.7356 - 0.249158i) q^{44} +(-7.29789 + 17.4994i) q^{46} +(18.4560 - 10.6556i) q^{47} +(-10.0621 + 17.4281i) q^{49} +(15.8875 - 12.1303i) q^{50} +(-23.5700 - 41.2822i) q^{52} +(21.4244 - 21.4244i) q^{53} +50.1026i q^{55} +(26.4157 - 33.9155i) q^{56} +(-5.53996 + 41.3112i) q^{58} +(6.02423 + 22.4827i) q^{59} +(58.9293 + 15.7901i) q^{61} +(-29.8091 + 71.4783i) q^{62} +(45.9039 - 44.5963i) q^{64} +(-39.8684 + 23.0180i) q^{65} +(24.1615 + 90.1720i) q^{67} +(12.0825 + 45.9771i) q^{68} +(-32.9674 - 25.4232i) q^{70} -124.525 q^{71} +86.4217i q^{73} +(21.6244 + 16.6759i) q^{74} +(57.4353 - 98.3836i) q^{76} +(-67.1344 + 17.9886i) q^{77} +(46.4211 + 80.4037i) q^{79} +(-43.4018 - 44.2460i) q^{80} +(18.0783 - 43.3493i) q^{82} +(-20.2421 + 75.5446i) q^{83} +(44.4685 - 11.9153i) q^{85} +(20.0580 - 149.571i) q^{86} +(-102.682 + 12.7644i) q^{88} +164.215 q^{89} +(-45.1569 - 45.1569i) q^{91} +(-9.99077 + 36.5805i) q^{92} +(33.8770 - 25.8654i) q^{94} +(-95.5439 - 55.1623i) q^{95} +(15.8533 + 27.4588i) q^{97} +(-15.4919 + 37.1475i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 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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