LMFDB - Embedded newform 288.3.u.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	288.19
Dual form			288.3.u.a.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.108191 + 1.99707i) q^{2} +(-3.97659 + 0.432130i) q^{4} +(2.81639 - 1.16659i) q^{5} +(-6.23443 - 6.23443i) q^{7} +(-1.29322 - 7.89478i) q^{8} +O(q^{10})$	\(q+(0.108191 + 1.99707i) q^{2} +(-3.97659 + 0.432130i) q^{4} +(2.81639 - 1.16659i) q^{5} +(-6.23443 - 6.23443i) q^{7} +(-1.29322 - 7.89478i) q^{8} +(2.63447 + 5.49832i) q^{10} +(8.06262 - 3.33965i) q^{11} +(13.3208 + 5.51766i) q^{13} +(11.7761 - 13.1251i) q^{14} +(15.6265 - 3.43680i) q^{16} -4.56488i q^{17} +(13.4421 - 32.4522i) q^{19} +(-10.6955 + 5.85609i) q^{20} +(7.54181 + 15.7403i) q^{22} +(6.75277 - 6.75277i) q^{23} +(-11.1065 + 11.1065i) q^{25} +(-9.57798 + 27.1996i) q^{26} +(27.4859 + 22.0977i) q^{28} +(0.266504 - 0.643399i) q^{29} +0.326715i q^{31} +(8.55419 + 30.8355i) q^{32} +(9.11639 - 0.493878i) q^{34} +(-24.8316 - 10.2856i) q^{35} +(31.5133 - 13.0532i) q^{37} +(66.2637 + 23.3339i) q^{38} +(-12.8522 - 20.7261i) q^{40} +(-15.7509 - 15.7509i) q^{41} +(4.83274 - 2.00179i) q^{43} +(-30.6186 + 16.7645i) q^{44} +(14.2164 + 12.7552i) q^{46} +49.7096 q^{47} +28.7362i q^{49} +(-23.3822 - 20.9789i) q^{50} +(-55.3558 - 16.1852i) q^{52} +(-4.45882 - 10.7645i) q^{53} +(18.8115 - 18.8115i) q^{55} +(-41.1569 + 57.2820i) q^{56} +(1.31375 + 0.462619i) q^{58} +(-13.1268 - 31.6909i) q^{59} +(-35.4023 + 85.4687i) q^{61} +(-0.652473 + 0.0353475i) q^{62} +(-60.6551 + 20.4194i) q^{64} +43.9535 q^{65} +(-41.3348 - 17.1214i) q^{67} +(1.97262 + 18.1527i) q^{68} +(17.8545 - 50.7033i) q^{70} +(-37.6381 - 37.6381i) q^{71} +(-52.2302 - 52.2302i) q^{73} +(29.4777 + 61.5220i) q^{74} +(-39.4303 + 134.858i) q^{76} +(-71.0866 - 29.4450i) q^{77} +26.9061 q^{79} +(40.0011 - 27.9091i) q^{80} +(29.7516 - 33.1598i) q^{82} +(-10.6315 + 25.6667i) q^{83} +(-5.32533 - 12.8565i) q^{85} +(4.52057 + 9.43475i) q^{86} +(-36.7926 - 59.3337i) q^{88} +(103.292 - 103.292i) q^{89} +(-48.6482 - 117.447i) q^{91} +(-23.9349 + 29.7711i) q^{92} +(5.37812 + 99.2736i) q^{94} -107.080i q^{95} +77.9778 q^{97} +(-57.3883 + 3.10900i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

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 $

$2$	0.108191	+	1.99707i	0.0540954	+	0.998536i
$2$	0.108191	+	1.99707i	0.0540954	+	0.998536i
$3$		0			0
$3$		0			0
$4$	−3.97659	+	0.432130i	−0.994147	+	0.108032i
$5$	2.81639	−	1.16659i	0.563278	−	0.233318i	−0.0828294	−	0.996564i	$-0.526396\pi$
$5$	2.81639	−	1.16659i	0.563278	−	0.233318i	0.646108	+	0.763246i	$0.276396\pi$
$6$		0			0
$7$	−6.23443	−	6.23443i	−0.890633	−	0.890633i	0.103950	−	0.994583i	$-0.466852\pi$
$7$	−6.23443	−	6.23443i	−0.890633	−	0.890633i	−0.994583	+	0.103950i	$0.966852\pi$
$8$	−1.29322	−	7.89478i	−0.161653	−	0.986848i
$9$		0			0
$10$	2.63447	+	5.49832i	0.263447	+	0.549832i
$11$	8.06262	−	3.33965i	0.732965	−	0.303604i	0.0151955	−	0.999885i	$-0.495163\pi$
$11$	8.06262	−	3.33965i	0.732965	−	0.303604i	0.717770	+	0.696280i	$0.245163\pi$
$12$		0			0
$13$	13.3208	+	5.51766i	1.02468	+	0.424436i	0.830789	−	0.556588i	$-0.187890\pi$
$13$	13.3208	+	5.51766i	1.02468	+	0.424436i	0.193889	+	0.981023i	$0.437890\pi$
$14$	11.7761	−	13.1251i	0.841150	−	0.937508i
$15$		0			0
$16$	15.6265	−	3.43680i	0.976658	−	0.214800i
$17$		−	4.56488i		−	0.268522i	−0.990946	−	0.134261i	$-0.957134\pi$
$17$		−	4.56488i		−	0.268522i	0.990946	−	0.134261i	$-0.0428661\pi$
$18$		0			0
$19$	13.4421	−	32.4522i	0.707481	−	1.70801i	0.00128016	−	0.999999i	$-0.499593\pi$
$19$	13.4421	−	32.4522i	0.707481	−	1.70801i	0.706201	−	0.708011i	$-0.250407\pi$
$20$	−10.6955	+	5.85609i	−0.534776	+	0.292804i
$21$		0			0
$22$	7.54181	+	15.7403i	0.342810	+	0.715469i
$23$	6.75277	−	6.75277i	0.293599	−	0.293599i	−0.544901	−	0.838500i	$-0.683433\pi$
$23$	6.75277	−	6.75277i	0.293599	−	0.293599i	0.838500	+	0.544901i	$0.183433\pi$
$24$		0			0
$25$	−11.1065	+	11.1065i	−0.444261	+	0.444261i
$26$	−9.57798	+	27.1996i	−0.368384	+	1.04614i
$27$		0			0
$28$	27.4859	+	22.0977i	0.981638	+	0.789203i
$29$	0.266504	−	0.643399i	0.00918981	−	0.0221862i	−0.919218	−	0.393749i	$-0.871178\pi$
$29$	0.266504	−	0.643399i	0.00918981	−	0.0221862i	0.928408	+	0.371563i	$0.121178\pi$
$30$		0			0
$31$			0.326715i			0.0105392i	0.999986	+	0.00526959i	$0.00167737\pi$
$31$			0.326715i			0.0105392i	−0.999986	+	0.00526959i	$0.998323\pi$
$32$	8.55419	+	30.8355i	0.267318	+	0.963608i
$33$		0			0
$34$	9.11639	−	0.493878i	0.268129	−	0.0145258i
$35$	−24.8316	−	10.2856i	−0.709475	−	0.293874i
$36$		0			0
$37$	31.5133	−	13.0532i	0.851710	−	0.352790i	0.0862502	−	0.996274i	$-0.472512\pi$
$37$	31.5133	−	13.0532i	0.851710	−	0.352790i	0.765460	+	0.643484i	$0.222512\pi$
$38$	66.2637	+	23.3339i	1.74378	+	0.614050i
$39$		0			0
$40$	−12.8522	−	20.7261i	−0.321305	−	0.518153i
$41$	−15.7509	−	15.7509i	−0.384169	−	0.384169i	0.488433	−	0.872601i	$-0.337569\pi$
$41$	−15.7509	−	15.7509i	−0.384169	−	0.384169i	−0.872601	+	0.488433i	$0.837569\pi$
$42$		0			0
$43$	4.83274	−	2.00179i	0.112389	−	0.0465531i	−0.325780	−	0.945446i	$-0.605627\pi$
$43$	4.83274	−	2.00179i	0.112389	−	0.0465531i	0.438170	+	0.898892i	$0.355627\pi$
$44$	−30.6186	+	16.7645i	−0.695877	+	0.381011i
$45$		0			0
$46$	14.2164	+	12.7552i	0.309051	+	0.277287i
$47$	49.7096			1.05765			0.528825	−	0.848731i	$-0.322633\pi$
$47$	49.7096			1.05765			0.528825	+	0.848731i	$0.322633\pi$
$48$		0			0
$49$			28.7362i			0.586454i
$50$	−23.3822	−	20.9789i	−0.467643	−	0.419578i
$51$		0			0
$52$	−55.3558	−	16.1852i	−1.06453	−	0.311253i
$53$	−4.45882	−	10.7645i	−0.0841286	−	0.203105i	0.876217	−	0.481917i	$-0.160059\pi$
$53$	−4.45882	−	10.7645i	−0.0841286	−	0.203105i	−0.960346	+	0.278812i	$0.910059\pi$
$54$		0			0
$55$	18.8115	−	18.8115i	0.342027	−	0.342027i
$56$	−41.1569	+	57.2820i	−0.734946	+	1.02289i
$57$		0			0
$58$	1.31375	+	0.462619i	0.0226508	+	0.00797618i
$59$	−13.1268	−	31.6909i	−0.222488	−	0.537134i	0.772739	−	0.634724i	$-0.218886\pi$
$59$	−13.1268	−	31.6909i	−0.222488	−	0.537134i	−0.995227	+	0.0975907i	$0.968886\pi$
$60$		0			0
$61$	−35.4023	+	85.4687i	−0.580366	+	1.40113i	0.312116	+	0.950044i	$0.398962\pi$
$61$	−35.4023	+	85.4687i	−0.580366	+	1.40113i	−0.892482	+	0.451083i	$0.851038\pi$
$62$	−0.652473	+	0.0353475i	−0.0105238	+	0.000570122i
$63$		0			0
$64$	−60.6551	+	20.4194i	−0.947737	+	0.319054i
$65$	43.9535			0.676207
$66$		0			0
$67$	−41.3348	−	17.1214i	−0.616938	−	0.255544i	0.0522539	−	0.998634i	$-0.483359\pi$
$67$	−41.3348	−	17.1214i	−0.616938	−	0.255544i	−0.669192	+	0.743090i	$0.733359\pi$
$68$	1.97262	+	18.1527i	0.0290091	+	0.266951i
$69$		0			0
$70$	17.8545	−	50.7033i	0.255064	−	0.724333i
$71$	−37.6381	−	37.6381i	−0.530114	−	0.530114i	0.390492	−	0.920606i	$-0.372305\pi$
$71$	−37.6381	−	37.6381i	−0.530114	−	0.530114i	−0.920606	+	0.390492i	$0.872305\pi$
$72$		0			0
$73$	−52.2302	−	52.2302i	−0.715482	−	0.715482i	0.252195	−	0.967677i	$-0.418848\pi$
$73$	−52.2302	−	52.2302i	−0.715482	−	0.715482i	−0.967677	+	0.252195i	$0.918848\pi$
$74$	29.4777	+	61.5220i	0.398347	+	0.831379i
$75$		0			0
$76$	−39.4303	+	134.858i	−0.518820	+	1.77445i
$77$	−71.0866	−	29.4450i	−0.923203	−	0.382403i
$78$		0			0
$79$	26.9061			0.340583			0.170292	−	0.985394i	$-0.445529\pi$
$79$	26.9061			0.340583			0.170292	+	0.985394i	$0.445529\pi$
$80$	40.0011	−	27.9091i	0.500014	−	0.348864i
$81$		0			0
$82$	29.7516	−	33.1598i	0.362824	−	0.404388i
$83$	−10.6315	+	25.6667i	−0.128090	+	0.309237i	−0.974894	−	0.222667i	$-0.928524\pi$
$83$	−10.6315	+	25.6667i	−0.128090	+	0.309237i	0.846804	+	0.531905i	$0.178524\pi$
$84$		0			0
$85$	−5.32533	−	12.8565i	−0.0626510	−	0.151253i
$86$	4.52057	+	9.43475i	0.0525647	+	0.109706i
$87$		0			0
$88$	−36.7926	−	59.3337i	−0.418097	−	0.674247i
$89$	103.292	−	103.292i	1.16058	−	1.16058i	0.176234	−	0.984348i	$-0.443609\pi$
$89$	103.292	−	103.292i	1.16058	−	1.16058i	0.984348	−	0.176234i	$-0.0563914\pi$
$90$		0			0
$91$	−48.6482	−	117.447i	−0.534596	−	1.29063i
$92$	−23.9349	+	29.7711i	−0.260162	+	0.323599i
$93$		0			0
$94$	5.37812	+	99.2736i	0.0572140	+	1.05610i
$95$		−	107.080i		−	1.12715i
$96$		0			0
$97$	77.9778			0.803895			0.401948	−	0.915663i	$-0.368333\pi$
$97$	77.9778			0.803895			0.401948	+	0.915663i	$0.368333\pi$
$98$	−57.3883	+	3.10900i	−0.585595	+	0.0317245i
$99$		0			0
$100$	39.3667	−	48.9656i	0.393667	−	0.489656i
$101$	−104.064	+	43.1046i	−1.03033	+	0.426778i	−0.832833	−	0.553525i	$-0.813282\pi$
$101$	−104.064	+	43.1046i	−1.03033	+	0.426778i	−0.197500	+	0.980303i	$0.563282\pi$
$102$		0			0
$103$	−76.6571	−	76.6571i	−0.744243	−	0.744243i	0.229148	−	0.973392i	$-0.426406\pi$
$103$	−76.6571	−	76.6571i	−0.744243	−	0.744243i	−0.973392	+	0.229148i	$0.926406\pi$
$104$	26.3339	−	112.301i	0.253211	−	1.07981i
$105$		0			0
$106$	21.0152	−	10.0692i	0.198256	−	0.0949925i
$107$	40.9728	−	16.9715i	0.382923	−	0.158612i	−0.182914	−	0.983129i	$-0.558553\pi$
$107$	40.9728	−	16.9715i	0.382923	−	0.158612i	0.565837	+	0.824517i	$0.308553\pi$
$108$		0			0
$109$	102.183	+	42.3255i	0.937456	+	0.388307i	0.798502	−	0.601992i	$-0.205626\pi$
$109$	102.183	+	42.3255i	0.937456	+	0.388307i	0.138954	+	0.990299i	$0.455626\pi$
$110$	39.6032	+	35.5327i	0.360029	+	0.323024i
$111$		0			0
$112$	−118.849	−	75.9960i	−1.06115	−	0.678536i
$113$			123.602i			1.09383i	0.837190	+	0.546913i	$0.184197\pi$
$113$			123.602i			1.09383i	−0.837190	+	0.546913i	$0.815803\pi$
$114$		0			0
$115$	11.1408	−	26.8962i	0.0968761	−	0.233880i
$116$	−0.781747	+	2.67370i	−0.00673920	+	0.0230491i
$117$		0			0
$118$	61.8688	−	29.6438i	0.524312	−	0.251219i
$119$	−28.4594	+	28.4594i	−0.239155	+	0.239155i
$120$		0			0
$121$	−31.7073	+	31.7073i	−0.262044	+	0.262044i
$122$	−174.517	−	61.4540i	−1.43047	−	0.503721i
$123$		0			0
$124$	−0.141183	−	1.29921i	−0.00113857	−	0.0104775i
$125$	−47.4883	+	114.647i	−0.379906	+	0.917175i
$126$		0			0
$127$			133.213i			1.04892i	0.851434	+	0.524462i	$0.175734\pi$
$127$			133.213i			1.04892i	−0.851434	+	0.524462i	$0.824266\pi$
$128$	−47.3414	−	118.923i	−0.369855	−	0.929090i
$129$		0			0
$130$	4.75536	+	87.7782i	0.0365797	+	0.675217i
$131$	−228.056	−	94.4640i	−1.74089	−	0.721100i	−0.998704	−	0.0509041i	$-0.983790\pi$
$131$	−228.056	−	94.4640i	−1.74089	−	0.721100i	−0.742185	−	0.670195i	$-0.766210\pi$
$132$		0			0
$133$	−286.125	+	118.517i	−2.15132	+	0.891104i
$134$	29.7207	−	84.4010i	0.221796	−	0.629858i
$135$		0			0
$136$	−36.0387	+	5.90341i	−0.264991	+	0.0434075i
$137$	111.817	+	111.817i	0.816180	+	0.816180i	0.985552	−	0.169372i	$-0.0541739\pi$
$137$	111.817	+	111.817i	0.816180	+	0.816180i	−0.169372	+	0.985552i	$0.554174\pi$
$138$		0			0
$139$	31.7750	−	13.1616i	0.228597	−	0.0946880i	−0.265445	−	0.964126i	$-0.585519\pi$
$139$	31.7750	−	13.1616i	0.228597	−	0.0946880i	0.494042	+	0.869438i	$0.335519\pi$
$140$	103.190	+	30.1711i	0.737070	+	0.215508i
$141$		0			0
$142$	71.0939	−	79.2381i	0.500661	−	0.558015i
$143$	125.828			0.879914
$144$		0			0
$145$		−	2.12296i		−	0.0146411i
$146$	98.6566	−	109.958i	0.675730	−	0.753138i
$147$		0			0
$148$	−119.675	+	65.5251i	−0.808613	+	0.442737i
$149$	108.344	+	261.565i	0.727140	+	1.75547i	0.651898	+	0.758307i	$0.273973\pi$
$149$	108.344	+	261.565i	0.727140	+	1.75547i	0.0752422	+	0.997165i	$0.476027\pi$
$150$		0			0
$151$	51.5292	−	51.5292i	0.341253	−	0.341253i	−0.515585	−	0.856838i	$-0.672425\pi$
$151$	51.5292	−	51.5292i	0.341253	−	0.341253i	0.856838	+	0.515585i	$0.172425\pi$
$152$	−273.587	−	64.1548i	−1.79991	−	0.422071i
$153$		0			0
$154$	51.1129	−	145.151i	0.331902	−	0.942538i
$155$	0.381142	+	0.920157i	0.00245898	+	0.00593650i
$156$		0			0
$157$	39.3450	−	94.9872i	0.250605	−	0.605014i	−0.747648	−	0.664095i	$-0.768817\pi$
$157$	39.3450	−	94.9872i	0.250605	−	0.605014i	0.998253	+	0.0590811i	$0.0188171\pi$
$158$	2.91099	+	53.7334i	0.0184240	+	0.340085i
$159$		0			0
$160$	60.0642	+	76.8655i	0.375401	+	0.480410i
$161$	−84.1994			−0.522978
$162$		0			0
$163$	−4.97467	−	2.06057i	−0.0305194	−	0.0126416i	0.367372	−	0.930074i	$-0.380258\pi$
$163$	−4.97467	−	2.06057i	−0.0305194	−	0.0126416i	−0.397891	+	0.917433i	$0.630258\pi$
$164$	69.4413	+	55.8285i	0.423423	+	0.340417i
$165$		0			0
$166$	−52.4085	−	18.4550i	−0.315714	−	0.111174i
$167$	165.012	+	165.012i	0.988097	+	0.988097i	0.999930	−	0.0118333i	$-0.00376674\pi$
$167$	165.012	+	165.012i	0.988097	+	0.988097i	−0.0118333	+	0.999930i	$0.503767\pi$
$168$		0			0
$169$	27.4985	+	27.4985i	0.162713	+	0.162713i
$170$	25.0992	−	12.0260i	0.147642	−	0.0707413i
$171$		0			0
$172$	−18.3528	+	10.0486i	−0.106702	+	0.0584224i
$173$	115.760	+	47.9493i	0.669132	+	0.277163i	0.691275	−	0.722591i	$-0.257049\pi$
$173$	115.760	+	47.9493i	0.669132	+	0.277163i	−0.0221438	+	0.999755i	$0.507049\pi$
$174$		0			0
$175$	138.486			0.791348
$176$	114.513	−	79.8967i	0.650642	−	0.453959i
$177$		0			0
$178$	217.456	+	195.106i	1.22166	+	1.09610i
$179$	44.8368	−	108.246i	0.250485	−	0.604724i	−0.747758	−	0.663971i	$-0.768870\pi$
$179$	44.8368	−	108.246i	0.250485	−	0.604724i	0.998243	+	0.0592467i	$0.0188699\pi$
$180$		0			0
$181$	80.3652	+	194.019i	0.444007	+	1.07193i	0.974530	+	0.224256i	$0.0719953\pi$
$181$	80.3652	+	194.019i	0.444007	+	1.07193i	−0.530524	+	0.847670i	$0.678005\pi$
$182$	229.287	−	109.861i	1.25982	−	0.603630i
$183$		0			0
$184$	−62.0445	−	44.5788i	−0.337198	−	0.242276i
$185$	73.5260	−	73.5260i	0.397438	−	0.397438i
$186$		0			0
$187$	−15.2451	−	36.8049i	−0.0815245	−	0.196818i
$188$	−197.675	+	21.4810i	−1.05146	+	0.114261i
$189$		0			0
$190$	213.846	−	11.5850i	1.12550	−	0.0609738i
$191$			338.117i			1.77025i	0.465357	+	0.885123i	$0.345926\pi$
$191$			338.117i			1.77025i	−0.465357	+	0.885123i	$0.654074\pi$
$192$		0			0
$193$	234.508			1.21507			0.607533	−	0.794295i	$-0.292159\pi$
$193$	234.508			1.21507			0.607533	+	0.794295i	$0.292159\pi$
$194$	8.43648	+	155.727i	0.0434870	+	0.802718i
$195$		0			0
$196$	−12.4178	−	114.272i	−0.0633560	−	0.583022i
$197$	−237.007	+	98.1713i	−1.20308	+	0.498332i	−0.891993	−	0.452050i	$-0.850693\pi$
$197$	−237.007	+	98.1713i	−1.20308	+	0.498332i	−0.311086	+	0.950382i	$0.600693\pi$
$198$		0			0
$199$	39.2172	+	39.2172i	0.197071	+	0.197071i	0.798743	−	0.601672i	$-0.205499\pi$
$199$	39.2172	+	39.2172i	0.197071	+	0.197071i	−0.601672	+	0.798743i	$0.705499\pi$
$200$	102.047	+	73.3204i	0.510234	+	0.366602i
$201$		0			0
$202$	−97.3416	−	203.159i	−0.481889	−	1.00574i
$203$	−5.67273	+	2.34972i	−0.0279445	+	0.0115750i
$204$		0			0
$205$	−62.7356	−	25.9859i	−0.306027	−	0.126761i
$206$	144.796	−	161.383i	0.702894	−	0.783414i
$207$		0			0
$208$	227.121	+	40.4409i	1.09193	+	0.194427i
$209$		−	306.542i		−	1.46671i
$210$		0			0
$211$	−79.9026	+	192.902i	−0.378685	+	0.914227i	0.613528	+	0.789673i	$0.289750\pi$
$211$	−79.9026	+	192.902i	−0.378685	+	0.914227i	−0.992213	+	0.124554i	$0.960250\pi$
$212$	22.3826	+	40.8794i	0.105578	+	0.192827i
$213$		0			0
$214$	38.3261	+	79.9894i	0.179094	+	0.373782i
$215$	11.2756	−	11.2756i	0.0524448	−	0.0524448i
$216$		0			0
$217$	2.03688	−	2.03688i	0.00938655	−	0.00938655i
$218$	−73.4718	+	208.645i	−0.337026	+	0.957089i
$219$		0			0
$220$	−66.6766	+	82.9346i	−0.303076	+	0.376976i
$221$	25.1875	−	60.8079i	0.113970	−	0.275149i
$222$		0			0
$223$			344.421i			1.54449i	0.635326	+	0.772244i	$0.280866\pi$
$223$			344.421i			1.54449i	−0.635326	+	0.772244i	$0.719134\pi$
$224$	138.911	−	245.572i	0.620139	−	1.09630i
$225$		0			0
$226$	−246.843	+	13.3726i	−1.09222	+	0.0591709i
$227$	−68.2639	−	28.2758i	−0.300722	−	0.124563i	0.227220	−	0.973843i	$-0.427036\pi$
$227$	−68.2639	−	28.2758i	−0.300722	−	0.124563i	−0.527942	+	0.849280i	$0.677036\pi$
$228$		0			0
$229$	−41.8202	+	17.3225i	−0.182621	+	0.0756440i	−0.472120	−	0.881534i	$-0.656511\pi$
$229$	−41.8202	+	17.3225i	−0.182621	+	0.0756440i	0.289499	+	0.957178i	$0.406511\pi$
$230$	54.9189	+	19.3390i	0.238778	+	0.0840824i
$231$		0			0
$232$	−5.42414	−	1.27194i	−0.0233799	−	0.00548248i
$233$	−203.044	−	203.044i	−0.871432	−	0.871432i	0.121197	−	0.992629i	$-0.461327\pi$
$233$	−203.044	−	203.044i	−0.871432	−	0.871432i	−0.992629	+	0.121197i	$0.961327\pi$
$234$		0			0
$235$	140.002	−	57.9906i	0.595752	−	0.246768i
$236$	65.8944	+	120.349i	0.279214	+	0.509954i
$237$		0			0
$238$	−59.9146	−	53.7565i	−0.251742	−	0.225868i
$239$	−87.6710			−0.366824			−0.183412	−	0.983036i	$-0.558714\pi$
$239$	−87.6710			−0.366824			−0.183412	+	0.983036i	$0.558714\pi$
$240$		0			0
$241$			15.4754i			0.0642135i	0.999484	+	0.0321067i	$0.0102216\pi$
$241$			15.4754i			0.0642135i	−0.999484	+	0.0321067i	$0.989778\pi$
$242$	−66.7522	−	59.8913i	−0.275836	−	0.247485i
$243$		0			0
$244$	103.847	−	355.172i	0.425602	−	1.45562i
$245$	33.5233	+	80.9325i	0.136830	+	0.330337i
$246$		0			0
$247$	358.121	−	358.121i	1.44988	−	1.44988i
$248$	2.57934	−	0.422516i	0.0104006	−	0.00170369i
$249$		0			0
$250$	−234.096	−	82.4338i	−0.936383	−	0.329735i
$251$	−95.9530	−	231.651i	−0.382283	−	0.922913i	−0.991524	−	0.129927i	$-0.958526\pi$
$251$	−95.9530	−	231.651i	−0.382283	−	0.922913i	0.609241	−	0.792985i	$-0.291474\pi$
$252$		0			0
$253$	31.8932	−	76.9969i	0.126060	−	0.304336i
$254$	−266.037	+	14.4125i	−1.04739	+	0.0567420i
$255$		0			0
$256$	232.377	−	107.411i	0.907722	−	0.419573i
$257$	131.142			0.510282			0.255141	−	0.966904i	$-0.417878\pi$
$257$	131.142			0.510282			0.255141	+	0.966904i	$0.417878\pi$
$258$		0			0
$259$	−277.847	−	115.088i	−1.07277	−	0.444355i
$260$	−174.785	+	18.9936i	−0.672250	+	0.0730523i
$261$		0			0
$262$	163.978	−	465.665i	0.625870	−	1.77735i
$263$	281.350	+	281.350i	1.06977	+	1.06977i	0.997376	+	0.0723955i	$0.0230644\pi$
$263$	281.350	+	281.350i	1.06977	+	1.06977i	0.0723955	+	0.997376i	$0.476936\pi$
$264$		0			0
$265$	−25.1156	−	25.1156i	−0.0947757	−	0.0947757i
$266$	−267.643	−	558.590i	−1.00618	−	2.09996i
$267$		0			0
$268$	171.770	+	50.2230i	0.640934	+	0.187399i
$269$	−133.290	−	55.2107i	−0.495503	−	0.205244i	0.120915	−	0.992663i	$-0.461417\pi$
$269$	−133.290	−	55.2107i	−0.495503	−	0.205244i	−0.616419	+	0.787419i	$0.711417\pi$
$270$		0			0
$271$	−368.673			−1.36042			−0.680208	−	0.733019i	$-0.738111\pi$
$271$	−368.673			−1.36042			−0.680208	+	0.733019i	$0.738111\pi$
$272$	−15.6886	−	71.3332i	−0.0576787	−	0.262255i
$273$		0			0
$274$	−211.208	+	235.404i	−0.770834	+	0.859137i
$275$	−52.4559	+	126.640i	−0.190749	+	0.460508i
$276$		0			0
$277$	21.6001	+	52.1472i	0.0779786	+	0.188257i	0.958061	−	0.286564i	$-0.0925130\pi$
$277$	21.6001	+	52.1472i	0.0779786	+	0.188257i	−0.880083	+	0.474821i	$0.842513\pi$
$278$	29.7225	+	62.0329i	0.106915	+	0.223140i
$279$		0			0
$280$	−49.0896	+	209.342i	−0.175320	+	0.747649i
$281$	−85.0605	+	85.0605i	−0.302706	+	0.302706i	−0.842072	−	0.539365i	$-0.818664\pi$
$281$	−85.0605	+	85.0605i	−0.302706	+	0.302706i	0.539365	+	0.842072i	$0.318664\pi$
$282$		0			0
$283$	27.0948	+	65.4127i	0.0957414	+	0.231140i	0.964493	−	0.264107i	$-0.0850773\pi$
$283$	27.0948	+	65.4127i	0.0957414	+	0.231140i	−0.868752	+	0.495248i	$0.835077\pi$
$284$	165.936	+	133.407i	0.584281	+	0.469742i
$285$		0			0
$286$	13.6134	+	251.287i	0.0475993	+	0.878626i
$287$			196.396i			0.684306i
$288$		0			0
$289$	268.162			0.927896
$290$	4.23971	−	0.229685i	0.0146197	−	0.000792018i
$291$		0			0
$292$	230.268	+	185.128i	0.788590	+	0.633999i
$293$	321.033	−	132.976i	1.09568	−	0.453844i	0.239694	−	0.970849i	$-0.422953\pi$
$293$	321.033	−	132.976i	1.09568	−	0.453844i	0.855983	+	0.517005i	$0.172953\pi$
$294$		0			0
$295$	−73.9404	−	73.9404i	−0.250645	−	0.250645i
$296$	−143.806	−	231.910i	−0.485831	−	0.783479i
$297$		0			0
$298$	−510.643	+	244.669i	−1.71357	+	0.821039i
$299$	127.212	−	52.6929i	0.425458	−	0.176231i
$300$		0			0
$301$	−42.6094	−	17.6494i	−0.141559	−	0.0586358i
$302$	108.483	+	97.3326i	0.359214	+	0.322293i
$303$		0			0
$304$	98.5222	−	553.313i	0.324086	−	1.82011i
$305$			282.013i			0.924634i
$306$		0			0
$307$	−92.6973	+	223.791i	−0.301946	+	0.728961i	0.697972	+	0.716125i	$0.254086\pi$
$307$	−92.6973	+	223.791i	−0.301946	+	0.728961i	−0.999918	+	0.0128360i	$0.995914\pi$
$308$	295.406	+	86.3722i	0.959112	+	0.280429i
$309$		0			0
$310$	−1.79638	+	0.860719i	−0.00579479	+	0.00277651i
$311$	44.5768	−	44.5768i	0.143334	−	0.143334i	−0.631799	−	0.775133i	$-0.717683\pi$
$311$	44.5768	−	44.5768i	0.143334	−	0.143334i	0.775133	+	0.631799i	$0.217683\pi$
$312$		0			0
$313$	−27.9303	+	27.9303i	−0.0892343	+	0.0892343i	−0.750315	−	0.661081i	$-0.770098\pi$
$313$	−27.9303	+	27.9303i	−0.0892343	+	0.0892343i	0.661081	+	0.750315i	$0.270098\pi$
$314$	193.953	+	68.2980i	0.617685	+	0.217510i
$315$		0			0
$316$	−106.994	+	11.6269i	−0.338590	+	0.0367940i
$317$	125.850	−	303.829i	0.397003	−	0.958450i	−0.591370	−	0.806400i	$-0.701413\pi$
$317$	125.850	−	303.829i	0.397003	−	0.958450i	0.988373	−	0.152049i	$-0.0485873\pi$
$318$		0			0
$319$		−	6.07751i		−	0.0190518i
$320$	−147.008	+	128.269i	−0.459399	+	0.400840i
$321$		0			0
$322$	−9.10960	−	168.152i	−0.0282907	−	0.522212i
$323$	−148.140	−	61.3618i	−0.458639	−	0.189975i
$324$		0			0
$325$	−209.230	+	86.6660i	−0.643785	+	0.266665i
$326$	3.57690	−	10.1577i	0.0109721	−	0.0311586i
$327$		0			0
$328$	−103.981	+	144.719i	−0.317014	+	0.441218i
$329$	−309.911	−	309.911i	−0.941978	−	0.941978i
$330$		0			0
$331$	−169.515	+	70.2155i	−0.512131	+	0.212131i	−0.623756	−	0.781619i	$-0.714394\pi$
$331$	−169.515	+	70.2155i	−0.512131	+	0.212131i	0.111626	+	0.993750i	$0.464394\pi$
$332$	31.1858	−	106.660i	0.0939330	−	0.321265i
$333$		0			0
$334$	−311.688	+	347.394i	−0.933198	+	1.04010i
$335$	−136.389			−0.407131
$336$		0			0
$337$		−	67.3116i		−	0.199738i	−0.995001	−	0.0998689i	$-0.968158\pi$
$337$		−	67.3116i		−	0.199738i	0.995001	−	0.0998689i	$-0.0318423\pi$
$338$	−51.9414	+	57.8916i	−0.153673	+	0.171277i
$339$		0			0
$340$	26.7323	+	48.8238i	0.0786245	+	0.143599i
$341$	1.09111	+	2.63418i	0.00319974	+	0.00772486i
$342$		0			0
$343$	−126.333	+	126.333i	−0.368318	+	0.368318i
$344$	−22.0535	−	35.5646i	−0.0641089	−	0.103386i
$345$		0			0
$346$	−83.2340	+	236.368i	−0.240561	+	0.683145i
$347$	107.157	+	258.699i	0.308809	+	0.745530i	0.999744	+	0.0226140i	$0.00719886\pi$
$347$	107.157	+	258.699i	0.308809	+	0.745530i	−0.690935	+	0.722916i	$0.742801\pi$
$348$		0			0
$349$	165.558	−	399.692i	0.474378	−	1.14525i	−0.487831	−	0.872938i	$-0.662212\pi$
$349$	165.558	−	399.692i	0.474378	−	1.14525i	0.962209	−	0.272311i	$-0.0877881\pi$
$350$	14.9829	+	276.566i	0.0428083	+	0.790189i
$351$		0			0
$352$	171.949	+	220.047i	0.488491	+	0.625133i
$353$	574.524			1.62755			0.813773	−	0.581183i	$-0.197410\pi$
$353$	574.524			1.62755			0.813773	+	0.581183i	$0.197410\pi$
$354$		0			0
$355$	−149.912	−	62.0955i	−0.422287	−	0.174917i
$356$	−366.114	+	455.385i	−1.02841	+	1.27917i
$357$		0			0
$358$	221.025	+	77.8311i	0.617389	+	0.217405i
$359$	−499.243	−	499.243i	−1.39065	−	1.39065i	−0.823868	−	0.566782i	$-0.808188\pi$
$359$	−499.243	−	499.243i	−1.39065	−	1.39065i	−0.566782	−	0.823868i	$-0.691812\pi$
$360$		0			0
$361$	−617.189	−	617.189i	−1.70966	−	1.70966i
$362$	−378.774	+	181.486i	−1.04634	+	0.501343i
$363$		0			0
$364$	244.206	+	446.017i	0.670897	+	1.22532i
$365$	−208.032	−	86.1696i	−0.569950	−	0.236081i
$366$		0			0
$367$	295.566			0.805357			0.402679	−	0.915341i	$-0.368079\pi$
$367$	295.566			0.805357			0.402679	+	0.915341i	$0.368079\pi$
$368$	82.3144	−	128.730i	0.223681	−	0.349811i
$369$		0			0
$370$	154.792	+	138.882i	0.418355	+	0.375356i
$371$	−39.3126	+	94.9090i	−0.105964	+	0.255819i
$372$		0			0
$373$	−133.878	−	323.209i	−0.358921	−	0.866512i	−0.995452	−	0.0952612i	$-0.969631\pi$
$373$	−133.878	−	323.209i	−0.358921	−	0.866512i	0.636531	−	0.771251i	$-0.280369\pi$
$374$	71.8526	−	34.4275i	0.192119	−	0.0920521i
$375$		0			0
$376$	−64.2856	−	392.446i	−0.170972	−	1.04374i
$377$	7.10011	−	7.10011i	0.0188332	−	0.0188332i
$378$		0			0
$379$	170.642	+	411.967i	0.450244	+	1.08698i	0.972229	+	0.234030i	$0.0751915\pi$
$379$	170.642	+	411.967i	0.450244	+	1.08698i	−0.521986	+	0.852954i	$0.674809\pi$
$380$	46.2722	+	425.811i	0.121769	+	1.12056i
$381$		0			0
$382$	−675.244	+	36.5812i	−1.76765	+	0.0957622i
$383$			254.902i			0.665540i	0.943008	+	0.332770i	$0.107983\pi$
$383$			254.902i			0.665540i	−0.943008	+	0.332770i	$0.892017\pi$
$384$		0			0
$385$	−234.558			−0.609242
$386$	25.3716	+	468.328i	0.0657294	+	1.21329i
$387$		0			0
$388$	−310.086	+	33.6965i	−0.799190	+	0.0868467i
$389$	−687.246	+	284.667i	−1.76670	+	0.731791i	−0.771247	+	0.636536i	$0.780367\pi$
$389$	−687.246	+	284.667i	−1.76670	+	0.731791i	−0.995453	+	0.0952550i	$0.969633\pi$
$390$		0			0
$391$	−30.8256	−	30.8256i	−0.0788379	−	0.0788379i
$392$	226.866	−	37.1624i	0.578741	−	0.0948020i
$393$		0			0
$394$	−221.697	−	462.698i	−0.562683	−	1.17436i
$395$	75.7781	−	31.3883i	0.191843	−	0.0794640i
$396$		0			0
$397$	−56.8981	−	23.5679i	−0.143320	−	0.0593651i	0.309871	−	0.950779i	$-0.399714\pi$
$397$	−56.8981	−	23.5679i	−0.143320	−	0.0593651i	−0.453191	+	0.891414i	$0.649714\pi$
$398$	−74.0766	+	82.5625i	−0.186122	+	0.207443i
$399$		0			0
$400$	−135.386	+	211.728i	−0.338464	+	0.529319i
$401$		−	704.010i		−	1.75564i	−0.478994	−	0.877818i	$-0.658999\pi$
$401$		−	704.010i		−	1.75564i	0.478994	−	0.877818i	$-0.341001\pi$
$402$		0			0
$403$	−1.80270	+	4.35211i	−0.00447321	+	0.0107993i
$404$	395.192	−	216.378i	0.978197	−	0.535589i
$405$		0			0
$406$	−5.30630	−	11.0746i	−0.0130697	−	0.0272774i
$407$	210.486	−	210.486i	0.517166	−	0.517166i
$408$		0			0
$409$	528.488	−	528.488i	1.29215	−	1.29215i	0.358690	−	0.933457i	$-0.383224\pi$
$409$	528.488	−	528.488i	1.29215	−	1.29215i	0.933457	−	0.358690i	$-0.116776\pi$
$410$	45.1083	−	128.099i	0.110020	−	0.312436i
$411$		0			0
$412$	337.959	+	271.708i	0.820290	+	0.659485i
$413$	−115.737	+	279.413i	−0.280234	+	0.676544i
$414$		0			0
$415$			84.6901i			0.204072i
$416$	−56.1909	+	457.953i	−0.135074	+	1.10085i
$417$		0			0
$418$	612.186	−	33.1650i	1.46456	−	0.0793421i
$419$	153.485	+	63.5754i	0.366312	+	0.151731i	0.558244	−	0.829677i	$-0.311475\pi$
$419$	153.485	+	63.5754i	0.366312	+	0.151731i	−0.191932	+	0.981408i	$0.561475\pi$
$420$		0			0
$421$	−240.175	+	99.4838i	−0.570487	+	0.236304i	−0.649231	−	0.760591i	$-0.724909\pi$
$421$	−240.175	+	99.4838i	−0.570487	+	0.236304i	0.0787437	+	0.996895i	$0.474909\pi$
$422$	−393.884	−	138.701i	−0.933373	−	0.328675i
$423$		0			0
$424$	−79.2174	+	49.1224i	−0.186834	+	0.115855i
$425$	50.7000	+	50.7000i	0.119294	+	0.119294i
$426$		0			0
$427$	753.562	−	312.136i	1.76478	−	0.730997i
$428$	−155.598	+	85.1941i	−0.363547	+	0.199052i
$429$		0			0
$430$	23.7381	+	21.2983i	0.0552050	+	0.0495310i
$431$	607.318			1.40909			0.704546	−	0.709659i	$-0.251151\pi$
$431$	607.318			1.40909			0.704546	+	0.709659i	$0.251151\pi$
$432$		0			0
$433$			233.380i			0.538984i	0.963003	+	0.269492i	$0.0868557\pi$
$433$			233.380i			0.538984i	−0.963003	+	0.269492i	$0.913144\pi$
$434$	4.28817	+	3.84743i	0.00988057	+	0.00886504i
$435$		0			0
$436$	−424.629	−	124.155i	−0.973919	−	0.284759i
$437$	−128.371	−	309.914i	−0.293754	−	0.709185i
$438$		0			0
$439$	−496.850	+	496.850i	−1.13178	+	1.13178i	−0.141896	+	0.989882i	$0.545320\pi$
$439$	−496.850	+	496.850i	−1.13178	+	1.13178i	−0.989882	+	0.141896i	$0.954680\pi$
$440$	−172.840	−	124.185i	−0.392819	−	0.282239i
$441$		0			0
$442$	124.163	+	43.7223i	0.280911	+	0.0989193i
$443$	−59.8483	−	144.487i	−0.135098	−	0.326155i	0.841824	−	0.539752i	$-0.181482\pi$
$443$	−59.8483	−	144.487i	−0.135098	−	0.326155i	−0.976922	+	0.213597i	$0.931482\pi$
$444$		0			0
$445$	170.411	−	411.409i	0.382947	−	0.924515i
$446$	−687.833	+	37.2632i	−1.54223	+	0.0835497i
$447$		0			0
$448$	505.454	+	250.847i	1.12825	+	0.559926i
$449$	15.4530			0.0344165			0.0172082	−	0.999852i	$-0.494522\pi$
$449$	15.4530			0.0344165			0.0172082	+	0.999852i	$0.494522\pi$
$450$		0			0
$451$	−179.596	−	74.3911i	−0.398217	−	0.164947i
$452$	−53.4122	−	491.516i	−0.118169	−	1.08742i
$453$		0			0
$454$	49.0833	−	139.387i	0.108113	−	0.307020i
$455$	−274.025	−	274.025i	−0.602253	−	0.602253i
$456$		0			0
$457$	−93.8365	−	93.8365i	−0.205332	−	0.205332i	0.596948	−	0.802280i	$-0.296380\pi$
$457$	−93.8365	−	93.8365i	−0.205332	−	0.205332i	−0.802280	+	0.596948i	$0.796380\pi$
$458$	−39.1188	−	81.6438i	−0.0854122	−	0.178261i
$459$		0			0
$460$	−32.6796	+	111.769i	−0.0710426	+	0.242977i
$461$	574.348	+	237.903i	1.24588	+	0.516058i	0.905546	−	0.424248i	$-0.139462\pi$
$461$	574.348	+	237.903i	1.24588	+	0.516058i	0.340329	+	0.940306i	$0.389462\pi$
$462$		0			0
$463$	568.089			1.22697			0.613487	−	0.789705i	$-0.289766\pi$
$463$	568.089			1.22697			0.613487	+	0.789705i	$0.289766\pi$
$464$	1.95330	−	10.9700i	0.00420971	−	0.0236423i
$465$		0			0
$466$	383.525	−	427.460i	0.823016	−	0.917296i
$467$	156.459	−	377.726i	0.335030	−	0.808835i	−0.663147	−	0.748489i	$-0.730780\pi$
$467$	156.459	−	377.726i	0.335030	−	0.808835i	0.998178	−	0.0603459i	$-0.0192204\pi$
$468$		0			0
$469$	150.957	+	364.442i	0.321869	+	0.777061i
$470$	130.958	+	273.319i	0.278635	+	0.581530i
$471$		0			0
$472$	−233.217	+	144.617i	−0.494103	+	0.306391i
$473$	32.2793	−	32.2793i	0.0682437	−	0.0682437i
$474$		0			0
$475$	211.136	+	509.727i	0.444497	+	1.07311i
$476$	100.873	−	125.470i	0.211919	−	0.263592i
$477$		0			0
$478$	−9.48520	−	175.085i	−0.0198435	−	0.366287i
$479$		−	327.880i		−	0.684509i	−0.939607	−	0.342254i	$-0.888810\pi$
$479$		−	327.880i		−	0.684509i	0.939607	−	0.342254i	$-0.111190\pi$
$480$		0			0
$481$	491.806			1.02247
$482$	−30.9056	+	1.67430i	−0.0641194	+	0.00347365i
$483$		0			0
$484$	112.385	−	139.789i	0.232201	−	0.288820i
$485$	219.616	−	90.9680i	0.452817	−	0.187563i
$486$		0			0
$487$	−147.493	−	147.493i	−0.302861	−	0.302861i	0.539271	−	0.842132i	$-0.318700\pi$
$487$	−147.493	−	147.493i	−0.302861	−	0.302861i	−0.842132	+	0.539271i	$0.818700\pi$
$488$	720.540	+	168.963i	1.47652	+	0.346236i
$489$		0			0
$490$	−158.001	+	75.7047i	−0.322451	+	0.154499i
$491$	−598.802	+	248.032i	−1.21956	+	0.505157i	−0.897269	−	0.441485i	$-0.854452\pi$
$491$	−598.802	+	248.032i	−1.21956	+	0.505157i	−0.322288	+	0.946642i	$0.604452\pi$
$492$		0			0
$493$	−2.93704	−	1.21656i	−0.00595748	−	0.00246767i
$494$	753.938	+	676.447i	1.52619	+	1.36933i
$495$		0			0
$496$	1.12285	+	5.10542i	0.00226382	+	0.0102932i
$497$			469.304i			0.944274i
$498$		0			0
$499$	58.1446	−	140.373i	0.116522	−	0.281309i	−0.854849	−	0.518877i	$-0.826350\pi$
$499$	58.1446	−	140.373i	0.116522	−	0.281309i	0.971371	+	0.237568i	$0.0763502\pi$
$500$	139.299	−	476.425i	0.278598	−	0.952849i
$501$		0			0
$502$	452.242	−	216.688i	0.900881	−	0.431648i
$503$	256.204	−	256.204i	0.509351	−	0.509351i	−0.404976	−	0.914327i	$-0.632720\pi$
$503$	256.204	−	256.204i	0.509351	−	0.509351i	0.914327	+	0.404976i	$0.132720\pi$
$504$		0			0
$505$	−242.799	+	242.799i	−0.480789	+	0.480789i
$506$	157.219	+	55.3626i	0.310709	+	0.109412i
$507$		0			0
$508$	−57.5655	−	529.735i	−0.113318	−	1.04279i
$509$	229.271	−	553.510i	0.450435	−	1.08745i	−0.521722	−	0.853115i	$-0.674710\pi$
$509$	229.271	−	553.510i	0.450435	−	1.08745i	0.972157	−	0.234331i	$-0.0752898\pi$
$510$		0			0
$511$			651.251i			1.27446i
$512$	239.648	+	452.452i	0.468062	+	0.883696i
$513$		0			0
$514$	14.1884	+	261.901i	0.0276039	+	0.509534i
$515$	−305.324	−	126.469i	−0.592861	−	0.245571i
$516$		0			0
$517$	400.789	−	166.012i	0.775221	−	0.321107i
$518$	199.778	−	567.331i	0.385672	−	1.09523i
$519$		0			0
$520$	−56.8417	−	347.003i	−0.109311	−	0.667314i
$521$	−80.7376	−	80.7376i	−0.154967	−	0.154967i	0.625365	−	0.780332i	$-0.284950\pi$
$521$	−80.7376	−	80.7376i	−0.154967	−	0.154967i	−0.780332	+	0.625365i	$0.784950\pi$
$522$		0			0
$523$	123.197	−	51.0300i	0.235559	−	0.0975717i	−0.261781	−	0.965127i	$-0.584310\pi$
$523$	123.197	−	51.0300i	0.235559	−	0.0975717i	0.497341	+	0.867555i	$0.334310\pi$
$524$	947.707	+	277.095i	1.80860	+	0.528807i
$525$		0			0
$526$	−531.436	+	592.315i	−1.01034	+	1.12607i
$527$	1.49141			0.00283001
$528$		0			0
$529$			437.800i			0.827599i
$530$	47.4403	−	52.8748i	0.0895100	−	0.0997639i
$531$		0			0
$532$	1086.59	−	594.936i	2.04246	−	1.11830i
$533$	−122.907	−	296.723i	−0.230594	−	0.556704i
$534$		0			0
$535$	95.5966	−	95.5966i	0.178685	−	0.178685i
$536$	−81.7149	+	348.471i	−0.152453	+	0.650133i
$537$		0			0
$538$	95.8389	−	272.164i	0.178139	−	0.505881i
$539$	95.9689	+	231.689i	0.178050	+	0.429850i
$540$		0			0
$541$	184.993	−	446.613i	0.341947	−	0.825532i	−0.655572	−	0.755132i	$-0.727573\pi$
$541$	184.993	−	446.613i	0.341947	−	0.825532i	0.997519	−	0.0703996i	$-0.0224275\pi$
$542$	−39.8870	−	736.266i	−0.0735923	−	1.35842i
$543$		0			0
$544$	140.760	−	39.0489i	0.258750	−	0.0717810i
$545$	337.163			0.618648
$546$		0			0
$547$	−570.529	−	236.321i	−1.04302	−	0.432031i	−0.205622	−	0.978632i	$-0.565922\pi$
$547$	−570.529	−	236.321i	−1.04302	−	0.432031i	−0.837394	+	0.546600i	$0.815922\pi$
$548$	−492.968	−	396.330i	−0.899577	−	0.723230i
$549$		0			0
$550$	−258.584	−	91.0569i	−0.470152	−	0.165558i
$551$	−17.2973	−	17.2973i	−0.0313926	−	0.0313926i
$552$		0			0
$553$	−167.744	−	167.744i	−0.303335	−	0.303335i
$554$	−101.805	+	48.7787i	−0.183763	+	0.0880482i
$555$		0			0
$556$	−120.669	+	66.0693i	−0.217030	+	0.118830i
$557$	−340.362	−	140.983i	−0.611063	−	0.253111i	0.0556199	−	0.998452i	$-0.482286\pi$
$557$	−340.362	−	140.983i	−0.611063	−	0.253111i	−0.666683	+	0.745341i	$0.732286\pi$
$558$		0			0
$559$	75.4212			0.134922
$560$	−423.381	−	75.3867i	−0.756038	−	0.134619i
$561$		0			0
$562$	−179.075	−	160.669i	−0.318638	−	0.285888i
$563$	−241.885	+	583.963i	−0.429637	+	1.03723i	0.549766	+	0.835319i	$0.314717\pi$
$563$	−241.885	+	583.963i	−0.429637	+	1.03723i	−0.979403	+	0.201916i	$0.935283\pi$
$564$		0			0
$565$	144.193	+	348.113i	0.255209	+	0.616128i
$566$	−127.702	+	61.1873i	−0.225623	+	0.108105i
$567$		0			0
$568$	−248.470	+	345.819i	−0.437447	+	0.608836i
$569$	−88.6373	+	88.6373i	−0.155777	+	0.155777i	−0.780693	−	0.624915i	$-0.785134\pi$
$569$	−88.6373	+	88.6373i	−0.155777	+	0.155777i	0.624915	+	0.780693i	$0.285134\pi$
$570$		0			0
$571$	−160.453	−	387.367i	−0.281003	−	0.678401i	0.718857	−	0.695158i	$-0.244666\pi$
$571$	−160.453	−	387.367i	−0.281003	−	0.678401i	−0.999860	+	0.0167573i	$0.994666\pi$
$572$	−500.365	+	54.3739i	−0.874764	+	0.0950592i
$573$		0			0
$574$	−392.217	+	21.2482i	−0.683304	+	0.0370178i
$575$			150.000i			0.260869i
$576$		0			0
$577$	−501.285			−0.868778			−0.434389	−	0.900725i	$-0.643036\pi$
$577$	−501.285			−0.868778			−0.434389	+	0.900725i	$0.643036\pi$
$578$	29.0126	+	535.538i	0.0501949	+	0.926537i
$579$		0			0
$580$	0.917395	+	8.44215i	0.00158172	+	0.0145554i
$581$	226.299	−	93.7360i	0.389498	−	0.161336i
$582$		0			0
$583$	−71.8995	−	71.8995i	−0.123327	−	0.123327i
$584$	−344.800	+	479.891i	−0.590412	+	0.821731i
$585$		0			0
$586$	300.296	+	626.739i	0.512451	+	1.06952i
$587$	805.600	−	333.691i	1.37240	−	0.568468i	0.429964	−	0.902846i	$-0.358526\pi$
$587$	805.600	−	333.691i	1.37240	−	0.568468i	0.942439	+	0.334378i	$0.108526\pi$
$588$		0			0
$589$	10.6026	+	4.39175i	0.0180010	+	0.00745628i
$590$	139.665	−	155.664i	0.236720	−	0.263837i
$591$		0			0
$592$	447.582	−	312.282i	0.756050	−	0.527503i
$593$			1035.33i			1.74591i	0.487798	+	0.872957i	$0.337800\pi$
$593$			1035.33i			1.74591i	−0.487798	+	0.872957i	$0.662200\pi$
$594$		0			0
$595$	−46.9525	+	113.353i	−0.0789117	+	0.190510i
$596$	−543.869	−	993.319i	−0.912532	−	1.66664i
$597$		0			0
$598$	118.995	+	248.351i	0.198988	+	0.415302i
$599$	−361.938	+	361.938i	−0.604237	+	0.604237i	−0.941434	−	0.337197i	$-0.890521\pi$
$599$	−361.938	+	361.938i	−0.604237	+	0.604237i	0.337197	+	0.941434i	$0.390521\pi$
$600$		0			0
$601$	−221.839	+	221.839i	−0.369116	+	0.369116i	−0.867155	−	0.498039i	$-0.834054\pi$
$601$	−221.839	+	221.839i	−0.369116	+	0.369116i	0.498039	+	0.867155i	$0.334054\pi$
$602$	30.6371	−	87.0034i	0.0508922	−	0.144524i
$603$		0			0
$604$	−182.643	+	227.178i	−0.302390	+	0.376122i
$605$	−52.3109	+	126.290i	−0.0864642	+	0.208743i
$606$		0			0
$607$			465.834i			0.767437i	0.923450	+	0.383719i	$0.125357\pi$
$607$			465.834i			0.767437i	−0.923450	+	0.383719i	$0.874643\pi$
$608$	1115.67	+	136.892i	1.83498	+	0.225152i
$609$		0			0
$610$	−563.201	+	30.5113i	−0.923280	+	0.0500185i
$611$	662.172	+	274.281i	1.08375	+	0.448905i
$612$		0			0
$613$	292.579	−	121.190i	0.477290	−	0.197700i	−0.131051	−	0.991376i	$-0.541835\pi$
$613$	292.579	−	121.190i	0.477290	−	0.197700i	0.608341	+	0.793676i	$0.291835\pi$
$614$	−456.956	−	160.911i	−0.744227	−	0.262070i
$615$		0			0
$616$	−140.531	+	599.292i	−0.228135	+	0.972877i
$617$	226.657	+	226.657i	0.367354	+	0.367354i	0.866511	−	0.499158i	$-0.166357\pi$
$617$	226.657	+	226.657i	0.367354	+	0.367354i	−0.499158	+	0.866511i	$0.666357\pi$
$618$		0			0
$619$	756.530	−	313.365i	1.22218	−	0.506244i	0.324078	−	0.946030i	$-0.394946\pi$
$619$	756.530	−	313.365i	1.22218	−	0.506244i	0.898102	+	0.439787i	$0.144946\pi$
$620$	−1.91327	−	3.49438i	−0.00308592	−	0.00563610i
$621$		0			0
$622$	93.8459	+	84.2003i	0.150878	+	0.135370i
$623$	−1287.93			−2.06730
$624$		0			0
$625$		−	14.3854i		−	0.0230167i
$626$	−58.8007	−	52.7570i	−0.0939308	−	0.0842764i
$627$		0			0
$628$	−115.412	+	394.727i	−0.183777	+	0.628546i
$629$	−59.5864	−	143.854i	−0.0947320	−	0.228703i
$630$		0			0
$631$	338.810	−	338.810i	0.536941	−	0.536941i	−0.385688	−	0.922629i	$-0.626036\pi$
$631$	338.810	−	338.810i	0.536941	−	0.536941i	0.922629	+	0.385688i	$0.126036\pi$
$632$	−34.7956	−	212.418i	−0.0550563	−	0.336104i
$633$		0			0
$634$	620.383	+	218.460i	0.978522	+	0.344574i
$635$	155.405	+	375.181i	0.244733	+	0.590837i
$636$		0			0
$637$	−158.557	+	382.790i	−0.248912	+	0.600927i
$638$	12.1372	−	0.657531i	0.0190239	−	0.00103061i
$639$		0			0
$640$	−272.067	−	279.707i	−0.425104	−	0.437042i
$641$	−729.839			−1.13859			−0.569297	−	0.822132i	$-0.692785\pi$
$641$	−729.839			−1.13859			−0.569297	+	0.822132i	$0.692785\pi$
$642$		0			0
$643$	−370.578	−	153.498i	−0.576327	−	0.238722i	0.0754293	−	0.997151i	$-0.475967\pi$
$643$	−370.578	−	153.498i	−0.576327	−	0.238722i	−0.651756	+	0.758429i	$0.725967\pi$
$644$	334.826	−	36.3850i	0.519917	−	0.0564985i
$645$		0			0
$646$	106.516	−	302.486i	0.164886	−	0.468244i
$647$	179.567	+	179.567i	0.277538	+	0.277538i	0.832126	−	0.554587i	$-0.187124\pi$
$647$	179.567	+	179.567i	0.277538	+	0.277538i	−0.554587	+	0.832126i	$0.687124\pi$
$648$		0			0
$649$	−211.673	−	211.673i	−0.326152	−	0.326152i
$650$	−195.715	−	408.471i	−0.301100	−	0.628417i
$651$		0			0
$652$	20.6726	+	6.04436i	0.0317065	+	0.00927049i
$653$	964.894	+	399.672i	1.47763	+	0.612056i	0.968585	−	0.248683i	$-0.0799976\pi$
$653$	964.894	+	399.672i	1.47763	+	0.612056i	0.509048	+	0.860738i	$0.329998\pi$
$654$		0			0
$655$	−752.497			−1.14885
$656$	−300.265	−	191.999i	−0.457721	−	0.292682i
$657$		0			0
$658$	585.385	−	652.444i	0.889642	−	0.991556i
$659$	−233.939	+	564.778i	−0.354990	+	0.857023i	0.640998	+	0.767542i	$0.278521\pi$
$659$	−233.939	+	564.778i	−0.354990	+	0.857023i	−0.995989	+	0.0894804i	$0.971479\pi$
$660$		0			0
$661$	281.181	+	678.831i	0.425387	+	1.02698i	0.980732	+	0.195356i	$0.0625862\pi$
$661$	281.181	+	678.831i	0.425387	+	1.02698i	−0.555345	+	0.831620i	$0.687414\pi$
$662$	−158.565	−	330.937i	−0.239525	−	0.499905i
$663$		0			0
$664$	216.382	+	50.7405i	0.325876	+	0.0764165i
$665$	−667.580	+	667.580i	−1.00388	+	1.00388i
$666$		0			0
$667$	−2.54508	−	6.14437i	−0.00381571	−	0.00921195i
$668$	−727.492	−	584.879i	−1.08906	−	0.875567i
$669$		0			0
$670$	−14.7560	−	272.378i	−0.0220239	−	0.406534i
$671$			807.333i			1.20318i
$672$		0			0
$673$	705.345			1.04806			0.524031	−	0.851699i	$-0.324428\pi$
$673$	705.345			1.04806			0.524031	+	0.851699i	$0.324428\pi$
$674$	134.426	−	7.28250i	0.199445	−	0.0108049i
$675$		0			0
$676$	−121.233	−	97.4673i	−0.179339	−	0.144182i
$677$	10.4550	−	4.33061i	0.0154432	−	0.00639676i	−0.374948	−	0.927046i	$-0.622340\pi$
$677$	10.4550	−	4.33061i	0.0154432	−	0.00639676i	0.390392	+	0.920649i	$0.372340\pi$
$678$		0			0
$679$	−486.147	−	486.147i	−0.715976	−	0.715976i
$680$	−94.6123	+	58.6687i	−0.139136	+	0.0862775i
$681$		0			0
$682$	−5.14259	+	2.46402i	−0.00754046	+	0.00361294i
$683$	307.101	−	127.205i	0.449635	−	0.186245i	−0.146363	−	0.989231i	$-0.546757\pi$
$683$	307.101	−	127.205i	0.449635	−	0.186245i	0.595998	+	0.802986i	$0.296757\pi$
$684$		0			0
$685$	445.364	+	184.476i	0.650166	+	0.269308i
$686$	−265.964	−	238.628i	−0.387703	−	0.347854i
$687$		0			0
$688$	68.6392	−	47.8901i	0.0997662	−	0.0696077i
$689$		−	167.995i		−	0.243824i
$690$		0			0
$691$	−243.176	+	587.078i	−0.351919	+	0.849607i	0.644465	+	0.764634i	$0.277080\pi$
$691$	−243.176	+	587.078i	−0.351919	+	0.849607i	−0.996383	+	0.0849727i	$0.972920\pi$
$692$	−481.049	−	140.651i	−0.695158	−	0.203253i
$693$		0			0
$694$	−505.047	+	241.988i	−0.727734	+	0.348686i
$695$	74.1366	−	74.1366i	0.106671	−	0.106671i
$696$		0			0
$697$	−71.9010	+	71.9010i	−0.103158	+	0.103158i
$698$	816.125	+	287.388i	1.16923	+	0.411730i
$699$		0			0
$700$	−550.701	+	59.8438i	−0.786716	+	0.0854912i
$701$	−65.7383	+	158.706i	−0.0937779	+	0.226400i	−0.963807	−	0.266600i	$-0.914100\pi$
$701$	−65.7383	+	158.706i	−0.0937779	+	0.226400i	0.870029	+	0.493000i	$0.164100\pi$
$702$		0			0
$703$		−	1198.14i		−	1.70432i
$704$	−420.846	+	367.201i	−0.597792	+	0.521592i
$705$		0			0
$706$	62.1582	+	1147.37i	0.0880428	+	1.62516i
$707$	917.510	+	380.045i	1.29775	+	0.537546i
$708$		0			0
$709$	−1029.00	+	426.228i	−1.45135	+	0.601167i	−0.962519	−	0.271214i	$-0.912575\pi$
$709$	−1029.00	+	426.228i	−1.45135	+	0.601167i	−0.488827	+	0.872381i	$0.662575\pi$
$710$	107.790	−	306.103i	0.151817	−	0.431131i
$711$		0			0
$712$	−949.046	−	681.887i	−1.33293	−	0.957706i
$713$	2.20623	+	2.20623i	0.00309429	+	0.00309429i
$714$		0			0
$715$	354.380	−	146.789i	0.495637	−	0.205299i
$716$	−131.521	+	449.824i	−0.183689	+	0.628245i
$717$		0			0
$718$	943.011	−	1051.04i	1.31339	−	1.46384i
$719$	439.735			0.611592			0.305796	−	0.952097i	$-0.401077\pi$
$719$	439.735			0.611592			0.305796	+	0.952097i	$0.401077\pi$
$720$		0			0
$721$			955.826i			1.32570i
$722$	1165.80	−	1299.34i	1.61468	−	1.79965i
$723$		0			0
$724$	−403.421	−	736.805i	−0.557211	−	1.01769i
$725$	4.18599	+	10.1059i	0.00577378	+	0.0139391i
$726$		0			0
$727$	137.308	−	137.308i	0.188869	−	0.188869i	−0.606338	−	0.795207i	$-0.707362\pi$
$727$	137.308	−	137.308i	0.188869	−	0.188869i	0.795207	+	0.606338i	$0.207362\pi$
$728$	−864.307	+	535.953i	−1.18723	+	0.736199i
$729$		0			0
$730$	149.580	−	424.777i	0.204904	−	0.581886i
$731$	−9.13791	−	22.0609i	−0.0125006	−	0.0301790i
$732$		0			0
$733$	57.7693	−	139.467i	0.0788121	−	0.190269i	−0.879562	−	0.475784i	$-0.842164\pi$
$733$	57.7693	−	139.467i	0.0788121	−	0.190269i	0.958374	+	0.285514i	$0.0921645\pi$
$734$	31.9775	+	590.267i	0.0435661	+	0.804178i
$735$		0			0
$736$	265.989	+	150.460i	0.361399	+	0.204430i
$737$	−390.447			−0.529778
$738$		0			0
$739$	536.590	+	222.263i	0.726103	+	0.300762i	0.714950	−	0.699176i	$-0.246450\pi$
$739$	536.590	+	222.263i	0.726103	+	0.300762i	0.0111538	+	0.999938i	$0.496450\pi$
$740$	−260.610	+	324.155i	−0.352176	+	0.438048i
$741$		0			0
$742$	−193.793	−	68.2418i	−0.261177	−	0.0919700i
$743$	−907.324	−	907.324i	−1.22116	−	1.22116i	−0.967219	−	0.253944i	$-0.918272\pi$
$743$	−907.324	−	907.324i	−1.22116	−	1.22116i	−0.253944	−	0.967219i	$-0.581728\pi$
$744$		0			0
$745$	610.278	+	610.278i	0.819165	+	0.819165i
$746$	630.987	−	302.331i	0.845827	−	0.405270i
$747$		0			0
$748$	76.5279	+	139.770i	0.102310	+	0.186858i
$749$	−361.249	−	149.634i	−0.482309	−	0.199779i
$750$		0			0
$751$	−662.862			−0.882639			−0.441320	−	0.897350i	$-0.645489\pi$
$751$	−662.862			−0.882639			−0.441320	+	0.897350i	$0.645489\pi$
$752$	776.788	−	170.842i	1.03296	−	0.227184i
$753$		0			0
$754$	14.9476	+	13.4113i	0.0198244	+	0.0177868i
$755$	85.0132	−	205.240i	0.112600	−	0.271841i
$756$		0			0
$757$	76.1190	+	183.767i	0.100553	+	0.242757i	0.966148	−	0.257988i	$-0.0830594\pi$
$757$	76.1190	+	183.767i	0.100553	+	0.242757i	−0.865595	+	0.500745i	$0.833059\pi$
$758$	−804.266	+	385.356i	−1.06104	+	0.508385i
$759$		0			0
$760$	−845.370	+	138.478i	−1.11233	+	0.182208i
$761$	−435.811	+	435.811i	−0.572683	+	0.572683i	−0.932877	−	0.360195i	$-0.882710\pi$
$761$	−435.811	+	435.811i	−0.572683	+	0.572683i	0.360195	+	0.932877i	$0.382710\pi$
$762$		0			0
$763$	−373.176	−	900.926i	−0.489090	−	1.18077i
$764$	−146.110	−	1344.55i	−0.191244	−	1.75989i
$765$		0			0
$766$	−509.057	+	27.5780i	−0.664565	+	0.0360026i
$767$		−	494.578i		−	0.644821i
$768$		0			0
$769$	−1422.48			−1.84978			−0.924889	−	0.380237i	$-0.875843\pi$
$769$	−1422.48			−1.84978			−0.924889	+	0.380237i	$0.875843\pi$
$770$	−25.3770	−	468.429i	−0.0329572	−	0.608350i
$771$		0			0
$772$	−932.540	+	101.338i	−1.20795	+	0.131266i
$773$	0.439715	−	0.182136i	0.000568842	−	0.000235622i	−0.382399	−	0.923997i	$-0.624902\pi$
$773$	0.439715	−	0.182136i	0.000568842	−	0.000235622i	0.382968	+	0.923762i	$0.374902\pi$
$774$		0			0
$775$	−3.62867	−	3.62867i	−0.00468215	−	0.00468215i
$776$	−100.843	−	615.618i	−0.129952	−	0.793322i
$777$		0			0
$778$	−642.854	−	1341.68i	−0.826290	−	1.72453i
$779$	−722.878	+	299.426i	−0.927956	+	0.384372i
$780$		0			0
$781$	−429.160	−	177.764i	−0.549500	−	0.227610i
$782$	58.2259	−	64.8960i	0.0744576	−	0.0829872i
$783$		0			0
$784$	98.7608	+	449.048i	0.125970	+	0.572765i
$785$		−	313.420i		−	0.399262i
$786$		0			0
$787$	23.0303	−	55.6002i	0.0292635	−	0.0706482i	−0.908572	−	0.417728i	$-0.862827\pi$
$787$	23.0303	−	55.6002i	0.0292635	−	0.0706482i	0.937836	+	0.347079i	$0.112827\pi$
$788$	900.055	−	492.805i	1.14220	−	0.625386i
$789$		0			0
$790$	70.8832	+	147.938i	0.0897255	+	0.187264i
$791$	770.590	−	770.590i	0.974197	−	0.974197i
$792$		0			0
$793$	−943.175	+	943.175i	−1.18938	+	1.18938i
$794$	40.9110	−	116.179i	0.0515252	−	0.146322i
$795$		0			0
$796$	−172.898	−	139.004i	−0.217208	−	0.174628i
$797$	−49.3444	+	119.128i	−0.0619127	+	0.149470i	−0.951808	−	0.306694i	$-0.900777\pi$
$797$	−49.3444	+	119.128i	−0.0619127	+	0.149470i	0.889895	+	0.456165i	$0.150777\pi$
$798$		0			0
$799$		−	226.918i		−	0.284003i
$800$	−437.482	−	247.468i	−0.546853	−	0.309335i
$801$		0			0
$802$	1405.96	−	76.1674i	1.75307	−	0.0949718i
$803$	−595.542	−	246.682i	−0.741647	−	0.307200i
$804$		0			0
$805$	−237.138	+	98.2260i	−0.294582	+	0.122020i
$806$	−8.88651	−	3.12927i	−0.0110254	−	0.00388247i
$807$		0			0
$808$	474.879	+	765.816i	0.587721	+	0.947792i
$809$	−29.6470	−	29.6470i	−0.0366465	−	0.0366465i	0.688546	−	0.725193i	$-0.258249\pi$
$809$	−29.6470	−	29.6470i	−0.0366465	−	0.0366465i	−0.725193	+	0.688546i	$0.758249\pi$
$810$		0			0
$811$	−755.209	+	312.818i	−0.931207	+	0.385719i	−0.796136	−	0.605117i	$-0.793126\pi$
$811$	−755.209	+	312.818i	−0.931207	+	0.385719i	−0.135071	+	0.990836i	$0.543126\pi$
$812$	21.5427	−	11.7952i	0.0265304	−	0.0145261i
$813$		0			0
$814$	443.129	+	397.584i	0.544385	+	0.488432i
$815$	−16.4144			−0.0201404
$816$		0			0
$817$		−	183.741i		−	0.224897i
$818$	1112.61	+	998.251i	1.36015	+	1.22036i
$819$		0			0
$820$	260.703	+	76.2254i	0.317930	+	0.0929578i
$821$	−120.712	−	291.425i	−0.147031	−	0.354964i	0.833156	−	0.553038i	$-0.186531\pi$
$821$	−120.712	−	291.425i	−0.147031	−	0.354964i	−0.980187	+	0.198074i	$0.936531\pi$
$822$		0			0
$823$	173.105	−	173.105i	0.210334	−	0.210334i	−0.594076	−	0.804409i	$-0.702482\pi$
$823$	173.105	−	173.105i	0.210334	−	0.210334i	0.804409	+	0.594076i	$0.202482\pi$
$824$	−506.056	+	704.326i	−0.614146	+	0.854764i
$825$		0			0
$826$	−570.529	−	200.904i	−0.690713	−	0.243225i
$827$	59.9551	+	144.744i	0.0724971	+	0.175023i	0.955974	−	0.293451i	$-0.0948038\pi$
$827$	59.9551	+	144.744i	0.0724971	+	0.175023i	−0.883477	+	0.468475i	$0.844804\pi$
$828$		0			0
$829$	259.829	−	627.283i	0.313425	−	0.756674i	−0.686149	−	0.727461i	$-0.740700\pi$
$829$	259.829	−	627.283i	0.313425	−	0.756674i	0.999573	−	0.0292124i	$-0.00929993\pi$
$830$	−169.132	+	9.16269i	−0.203774	+	0.0110394i
$831$		0			0
$832$	−920.644	−	62.6710i	−1.10654	−	0.0753257i
$833$	131.178			0.157476
$834$		0			0
$835$	657.240	+	272.238i	0.787114	+	0.326033i
$836$	132.466	+	1218.99i	0.158452	+	1.45812i
$837$		0			0
$838$	−110.359	+	313.398i	−0.131693	+	0.373983i
$839$	−182.343	−	182.343i	−0.217333	−	0.217333i	0.590040	−	0.807374i	$-0.299112\pi$
$839$	−182.343	−	182.343i	−0.217333	−	0.217333i	−0.807374	+	0.590040i	$0.799112\pi$
$840$		0			0
$841$	594.334	+	594.334i	0.706699	+	0.706699i
$842$	−224.661	−	468.884i	−0.266818	−	0.556869i
$843$		0			0
$844$	234.381	−	801.620i	0.277703	−	0.949787i
$845$	109.526	+	45.3671i	0.129617	+	0.0536889i
$846$		0			0
$847$	395.354			0.466770
$848$	−106.671	−	152.888i	−0.125792	−	0.180293i
$849$		0			0
$850$	−95.7663	+	106.737i	−0.112666	+	0.125573i
$851$	124.657	−	300.947i	0.146482	−	0.353640i
$852$		0			0
$853$	−300.757	−	726.092i	−0.352588	−	0.851222i	−0.996299	−	0.0859535i	$-0.972606\pi$
$853$	−300.757	−	726.092i	−0.352588	−	0.851222i	0.643712	−	0.765268i	$-0.277394\pi$
$854$	704.886	+	1471.15i	0.825393	+	1.72266i
$855$		0			0
$856$	−186.973	−	301.523i	−0.218426	−	0.352247i
$857$	545.430	−	545.430i	0.636441	−	0.636441i	−0.313235	−	0.949676i	$-0.601413\pi$
$857$	545.430	−	545.430i	0.636441	−	0.636441i	0.949676	+	0.313235i	$0.101413\pi$
$858$		0			0
$859$	230.652	+	556.843i	0.268512	+	0.648246i	0.999414	−	0.0342370i	$-0.0109001\pi$
$859$	230.652	+	556.843i	0.268512	+	0.648246i	−0.730901	+	0.682483i	$0.760900\pi$
$860$	−39.9660	+	49.7111i	−0.0464721	+	0.0578036i
$861$		0			0
$862$	65.7063	+	1212.86i	0.0762254	+	1.40703i
$863$		−	980.846i		−	1.13655i	−0.822837	−	0.568277i	$-0.807610\pi$
$863$		−	980.846i		−	1.13655i	0.822837	−	0.568277i	$-0.192390\pi$
$864$		0			0
$865$	381.962			0.441574
$866$	−466.076	+	25.2496i	−0.538195	+	0.0291565i
$867$		0			0
$868$	−7.21964	+	8.98004i	−0.00831756	+	0.0103457i
$869$	216.933	−	89.8568i	0.249636	−	0.103403i
$870$		0			0
$871$	−456.143	−	456.143i	−0.523701	−	0.523701i
$872$	202.005	−	861.446i	0.231657	−	0.987897i
$873$		0			0
$874$	605.032	−	289.895i	0.692256	−	0.331688i
$875$	1010.82	−	418.696i	1.15522	−	0.478509i
$876$		0			0
$877$	1395.56	+	578.059i	1.59129	+	0.659132i	0.990150	−	0.140014i	$-0.0447146\pi$
$877$	1395.56	+	578.059i	1.59129	+	0.659132i	0.601137	+	0.799146i	$0.294715\pi$
$878$	−1046.00	−	938.491i	−1.19134	−	1.06890i
$879$		0			0
$880$	229.307	−	358.610i	0.260576	−	0.407511i
$881$			1513.62i			1.71807i	0.511914	+	0.859037i	$0.328937\pi$
$881$			1513.62i			1.71807i	−0.511914	+	0.859037i	$0.671063\pi$
$882$		0			0
$883$	−91.3318	+	220.494i	−0.103434	+	0.249711i	−0.967121	−	0.254317i	$-0.918149\pi$
$883$	−91.3318	+	220.494i	−0.103434	+	0.249711i	0.863687	+	0.504028i	$0.168149\pi$
$884$	−73.8833	+	252.692i	−0.0835784	+	0.285851i
$885$		0			0
$886$	282.075	−	135.153i	0.318369	−	0.152543i
$887$	−892.828	+	892.828i	−1.00657	+	1.00657i	−0.00659168	+	0.999978i	$0.502098\pi$
$887$	−892.828	+	892.828i	−1.00657	+	1.00657i	−0.999978	+	0.00659168i	$0.997902\pi$
$888$		0			0
$889$	830.510	−	830.510i	0.934207	−	0.934207i
$890$	840.050	+	295.813i	0.943877	+	0.332374i
$891$		0			0
$892$	−148.834	−	1369.62i	−0.166855	−	1.53545i
$893$	668.203	−	1613.19i	0.748268	−	1.80648i
$894$		0			0
$895$		−	357.168i		−	0.399071i
$896$	−446.273	+	1036.57i	−0.498073	+	1.15688i
$897$		0			0
$898$	1.67187	+	30.8608i	0.00186177	+	0.0343661i
$899$	0.210208	+	0.0870710i	0.000233824	+	9.68531e-5i
$900$		0			0
$901$	−49.1388	+	20.3540i	−0.0545381	+	0.0225904i
$902$	129.134	−	366.715i	0.143164	−	0.406557i
$903$		0			0
$904$	975.813	−	159.845i	1.07944	−	0.176820i
$905$	452.680	+	452.680i	0.500199	+	0.500199i
$906$		0			0
$907$	−469.078	+	194.298i	−0.517175	+	0.214221i	−0.625976	−	0.779843i	$-0.715299\pi$
$907$	−469.078	+	194.298i	−0.517175	+	0.214221i	0.108800	+	0.994064i	$0.465299\pi$
$908$	283.676	+	82.9425i	0.312419	+	0.0913464i
$909$		0			0
$910$	517.600	−	576.894i	0.568792	−	0.633950i
$911$	−469.566			−0.515441			−0.257720	−	0.966220i	$-0.582971\pi$
$911$	−469.566			−0.515441			−0.257720	+	0.966220i	$0.582971\pi$
$912$		0			0
$913$			242.446i			0.265549i
$914$	177.246	−	197.550i	0.193923	−	0.216138i
$915$		0			0
$916$	158.816	−	86.9562i	0.173380	−	0.0949303i
$917$	832.872	+	2010.73i	0.908257	+	2.19273i
$918$		0			0
$919$	737.868	−	737.868i	0.802903	−	0.802903i	−0.180645	−	0.983548i	$-0.557819\pi$
$919$	737.868	−	737.868i	0.802903	−	0.802903i	0.983548	+	0.180645i	$0.0578186\pi$
$920$	−226.747	−	53.1710i	−0.246464	−	0.0577946i
$921$		0			0
$922$	−412.970	+	1172.75i	−0.447907	+	1.27197i
$923$	−293.696	−	709.045i	−0.318197	−	0.768196i
$924$		0			0
$925$	−205.027	+	494.979i	−0.221651	+	0.535113i
$926$	61.4620	+	1134.51i	0.0663736	+	1.22518i
$927$		0			0
$928$	22.1192	+	2.71403i	0.0238354	+	0.00292461i
$929$	−796.539			−0.857416			−0.428708	−	0.903443i	$-0.641031\pi$
$929$	−796.539			−0.857416			−0.428708	+	0.903443i	$0.641031\pi$
$930$		0			0
$931$	932.554	+	386.277i	1.00167	+	0.414905i
$932$	895.162	+	719.680i	0.960475	+	0.772189i
$933$		0			0
$934$	771.273	+	271.594i	0.825774	+	0.290786i
$935$	−85.8723	−	85.8723i	−0.0918420	−	0.0918420i
$936$		0			0
$937$	764.262	+	764.262i	0.815648	+	0.815648i	0.985474	−	0.169826i	$-0.0543206\pi$
$937$	764.262	+	764.262i	0.815648	+	0.815648i	−0.169826	+	0.985474i	$0.554321\pi$
$938$	−711.484	+	340.900i	−0.758511	+	0.363433i
$939$		0			0
$940$	−531.670	+	291.104i	−0.565606	+	0.309685i
$941$	−113.549	−	47.0336i	−0.120669	−	0.0499826i	0.321532	−	0.946899i	$-0.395802\pi$
$941$	−113.549	−	47.0336i	−0.120669	−	0.0499826i	−0.442201	+	0.896916i	$0.645802\pi$
$942$		0			0
$943$	−212.725			−0.225583
$944$	−314.042	−	450.104i	−0.332671	−	0.476805i
$945$		0			0
$946$	67.9563	+	60.9717i	0.0718354	+	0.0644521i
$947$	−396.726	+	957.782i	−0.418930	+	1.01139i	0.563729	+	0.825960i	$0.309366\pi$
$947$	−396.726	+	957.782i	−0.418930	+	1.01139i	−0.982658	+	0.185425i	$0.940634\pi$
$948$		0			0
$949$	−407.560	−	983.937i	−0.429463	−	1.03681i
$950$	−995.118	+	476.801i	−1.04749	+	0.501896i
$951$		0			0
$952$	261.485	+	187.877i	0.274670	+	0.197349i
$953$	−391.136	+	391.136i	−0.410426	+	0.410426i	−0.881887	−	0.471461i	$-0.843727\pi$
$953$	−391.136	+	391.136i	−0.410426	+	0.410426i	0.471461	+	0.881887i	$0.343727\pi$
$954$		0			0
$955$	394.443	+	952.270i	0.413030	+	0.997142i
$956$	348.632	−	37.8852i	0.364677	−	0.0396289i
$957$		0			0
$958$	654.799	−	35.4736i	0.683506	−	0.0370288i
$959$		−	1394.23i		−	1.45383i
$960$		0			0
$961$	960.893			0.999889
$962$	53.2089	+	982.171i	0.0553107	+	1.02097i
$963$		0			0
$964$	−6.68740	−	61.5395i	−0.00693713	−	0.0638377i
$965$	660.465	−	273.574i	0.684420	−	0.283496i
$966$		0			0
$967$	−22.8939	−	22.8939i	−0.0236752	−	0.0236752i	0.695170	−	0.718845i	$-0.255329\pi$
$967$	−22.8939	−	22.8939i	−0.0236752	−	0.0236752i	−0.718845	+	0.695170i	$0.755329\pi$
$968$	291.327	+	209.318i	0.300958	+	0.216237i
$969$		0			0
$970$	205.430	+	428.747i	0.211784	+	0.442007i
$971$	619.006	−	256.401i	0.637493	−	0.264058i	−0.0404399	−	0.999182i	$-0.512876\pi$
$971$	619.006	−	256.401i	0.637493	−	0.264058i	0.677933	+	0.735124i	$0.262876\pi$
$972$		0			0
$973$	−280.154	−	116.044i	−0.287928	−	0.119264i
$974$	278.597	−	310.512i	0.286034	−	0.318801i
$975$		0			0
$976$	−259.476	+	1457.25i	−0.265856	+	1.49308i
$977$		−	430.856i		−	0.440999i	−0.975387	−	0.220500i	$-0.929231\pi$
$977$		−	430.856i		−	0.440999i	0.975387	−	0.220500i	$-0.0707688\pi$
$978$		0			0
$979$	487.844	−	1177.76i	0.498309	−	1.20302i
$980$	−168.282	−	307.349i	−0.171716	−	0.313621i
$981$		0			0
$982$	−560.123	−	1169.02i	−0.570390	−	1.19044i
$983$	−154.209	+	154.209i	−0.156876	+	0.156876i	−0.781181	−	0.624305i	$-0.785382\pi$
$983$	−154.209	+	154.209i	−0.156876	+	0.156876i	0.624305	+	0.781181i	$0.285382\pi$
$984$		0			0
$985$	−552.978	+	552.978i	−0.561399	+	0.561399i
$986$	2.11180	−	5.99710i	0.00214178	−	0.00608225i
$987$		0			0
$988$	−1269.34	+	1578.85i	−1.28476	+	1.59803i
$989$	19.1168	−	46.1520i	0.0193294	−	0.0466653i
$990$		0			0
$991$		−	966.543i		−	0.975320i	−0.873033	−	0.487660i	$-0.837850\pi$
$991$		−	966.543i		−	0.975320i	0.873033	−	0.487660i	$-0.162150\pi$
$992$	−10.0744	+	2.79478i	−0.0101556	+	0.00281732i
$993$		0			0
$994$	−937.234	+	50.7744i	−0.942891	+	0.0510809i
$995$	156.201	+	64.7007i	0.156986	+	0.0650258i
$996$		0			0
$997$	732.694	−	303.492i	0.734899	−	0.304405i	0.0163357	−	0.999867i	$-0.494800\pi$
$997$	732.694	−	303.492i	0.734899	−	0.304405i	0.718564	+	0.695461i	$0.244800\pi$
$998$	286.626	+	100.932i	0.287201	+	0.101134i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.19.4		28
3.2	odd	2		32.3.h.a.19.4	✓	28
12.11	even	2		128.3.h.a.111.1		28
24.5	odd	2		256.3.h.b.223.1		28
24.11	even	2		256.3.h.a.223.7		28
32.27	odd	8	inner	288.3.u.a.91.4		28
96.5	odd	8		128.3.h.a.15.1		28
96.11	even	8		256.3.h.b.31.1		28
96.53	odd	8		256.3.h.a.31.7		28
96.59	even	8		32.3.h.a.27.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.4	✓	28	3.2	odd	2
32.3.h.a.27.4	yes	28	96.59	even	8
128.3.h.a.15.1		28	96.5	odd	8
128.3.h.a.111.1		28	12.11	even	2
256.3.h.a.31.7		28	96.53	odd	8
256.3.h.a.223.7		28	24.11	even	2
256.3.h.b.31.1		28	96.11	even	8
256.3.h.b.223.1		28	24.5	odd	2
288.3.u.a.19.4		28	1.1	even	1	trivial
288.3.u.a.91.4		28	32.27	odd	8	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.108191 + 1.99707i) q^{2} +(-3.97659 + 0.432130i) q^{4} +(2.81639 - 1.16659i) q^{5} +(-6.23443 - 6.23443i) q^{7} +(-1.29322 - 7.89478i) q^{8} +O(q^{10})\)	\(q+(0.108191 + 1.99707i) q^{2} +(-3.97659 + 0.432130i) q^{4} +(2.81639 - 1.16659i) q^{5} +(-6.23443 - 6.23443i) q^{7} +(-1.29322 - 7.89478i) q^{8} +(2.63447 + 5.49832i) q^{10} +(8.06262 - 3.33965i) q^{11} +(13.3208 + 5.51766i) q^{13} +(11.7761 - 13.1251i) q^{14} +(15.6265 - 3.43680i) q^{16} -4.56488i q^{17} +(13.4421 - 32.4522i) q^{19} +(-10.6955 + 5.85609i) q^{20} +(7.54181 + 15.7403i) q^{22} +(6.75277 - 6.75277i) q^{23} +(-11.1065 + 11.1065i) q^{25} +(-9.57798 + 27.1996i) q^{26} +(27.4859 + 22.0977i) q^{28} +(0.266504 - 0.643399i) q^{29} +0.326715i q^{31} +(8.55419 + 30.8355i) q^{32} +(9.11639 - 0.493878i) q^{34} +(-24.8316 - 10.2856i) q^{35} +(31.5133 - 13.0532i) q^{37} +(66.2637 + 23.3339i) q^{38} +(-12.8522 - 20.7261i) q^{40} +(-15.7509 - 15.7509i) q^{41} +(4.83274 - 2.00179i) q^{43} +(-30.6186 + 16.7645i) q^{44} +(14.2164 + 12.7552i) q^{46} +49.7096 q^{47} +28.7362i q^{49} +(-23.3822 - 20.9789i) q^{50} +(-55.3558 - 16.1852i) q^{52} +(-4.45882 - 10.7645i) q^{53} +(18.8115 - 18.8115i) q^{55} +(-41.1569 + 57.2820i) q^{56} +(1.31375 + 0.462619i) q^{58} +(-13.1268 - 31.6909i) q^{59} +(-35.4023 + 85.4687i) q^{61} +(-0.652473 + 0.0353475i) q^{62} +(-60.6551 + 20.4194i) q^{64} +43.9535 q^{65} +(-41.3348 - 17.1214i) q^{67} +(1.97262 + 18.1527i) q^{68} +(17.8545 - 50.7033i) q^{70} +(-37.6381 - 37.6381i) q^{71} +(-52.2302 - 52.2302i) q^{73} +(29.4777 + 61.5220i) q^{74} +(-39.4303 + 134.858i) q^{76} +(-71.0866 - 29.4450i) q^{77} +26.9061 q^{79} +(40.0011 - 27.9091i) q^{80} +(29.7516 - 33.1598i) q^{82} +(-10.6315 + 25.6667i) q^{83} +(-5.32533 - 12.8565i) q^{85} +(4.52057 + 9.43475i) q^{86} +(-36.7926 - 59.3337i) q^{88} +(103.292 - 103.292i) q^{89} +(-48.6482 - 117.447i) q^{91} +(-23.9349 + 29.7711i) q^{92} +(5.37812 + 99.2736i) q^{94} -107.080i q^{95} +77.9778 q^{97} +(-57.3883 + 3.10900i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

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