LMFDB - Embedded newform 288.3.u.a.91.2

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			91.2
Character	$\chi$	$=$	288.91
Dual form			288.3.u.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61758 + 1.17620i) q^{2} +(1.23313 - 3.80518i) q^{4} +(-2.28872 - 0.948019i) q^{5} +(-6.37744 + 6.37744i) q^{7} +(2.48095 + 7.60558i) q^{8} +O(q^{10})$	\(q+(-1.61758 + 1.17620i) q^{2} +(1.23313 - 3.80518i) q^{4} +(-2.28872 - 0.948019i) q^{5} +(-6.37744 + 6.37744i) q^{7} +(2.48095 + 7.60558i) q^{8} +(4.81725 - 1.15849i) q^{10} +(1.79646 + 0.744117i) q^{11} +(16.7036 - 6.91888i) q^{13} +(2.81490 - 17.8171i) q^{14} +(-12.9588 - 9.38456i) q^{16} +6.19811i q^{17} +(-8.50083 - 20.5228i) q^{19} +(-6.42967 + 7.53997i) q^{20} +(-3.78114 + 0.909316i) q^{22} +(-23.6476 - 23.6476i) q^{23} +(-13.3382 - 13.3382i) q^{25} +(-18.8815 + 30.8386i) q^{26} +(16.4031 + 32.1315i) q^{28} +(-14.5725 - 35.1811i) q^{29} -14.1609i q^{31} +(31.9999 - 0.0617869i) q^{32} +(-7.29019 - 10.0259i) q^{34} +(20.6421 - 8.55025i) q^{35} +(-30.0695 - 12.4552i) q^{37} +(37.8896 + 23.1987i) q^{38} +(1.53204 - 19.7590i) q^{40} +(56.9700 - 56.9700i) q^{41} +(54.5034 + 22.5760i) q^{43} +(5.04676 - 5.91825i) q^{44} +(66.0659 + 10.4377i) q^{46} -34.8047 q^{47} -32.3435i q^{49} +(37.2638 + 5.88726i) q^{50} +(-5.72981 - 72.0923i) q^{52} +(-3.92967 + 9.48706i) q^{53} +(-3.40615 - 3.40615i) q^{55} +(-64.3263 - 32.6821i) q^{56} +(64.9521 + 39.7682i) q^{58} +(-9.41777 + 22.7365i) q^{59} +(3.00467 + 7.25391i) q^{61} +(16.6560 + 22.9064i) q^{62} +(-51.6898 + 37.7381i) q^{64} -44.7892 q^{65} +(-55.9040 + 23.1562i) q^{67} +(23.5849 + 7.64307i) q^{68} +(-23.3335 + 38.1099i) q^{70} +(-6.27499 + 6.27499i) q^{71} +(66.4597 - 66.4597i) q^{73} +(63.2896 - 15.2203i) q^{74} +(-88.5756 + 7.03989i) q^{76} +(-16.2024 + 6.71124i) q^{77} -75.8508 q^{79} +(20.7623 + 33.7638i) q^{80} +(-25.1457 + 159.161i) q^{82} +(1.23390 + 2.97891i) q^{83} +(5.87593 - 14.1857i) q^{85} +(-114.717 + 27.5881i) q^{86} +(-1.20252 + 15.5092i) q^{88} +(-36.7030 - 36.7030i) q^{89} +(-62.4018 + 150.651i) q^{91} +(-119.144 + 60.8227i) q^{92} +(56.2994 - 40.9371i) q^{94} +55.0300i q^{95} +90.0528 q^{97} +(38.0423 + 52.3182i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.61758	+	1.17620i	−0.808790	+	0.588098i
$2$	−1.61758	+	1.17620i	−0.808790	+	0.588098i
$3$		0			0
$3$		0			0
$4$	1.23313	−	3.80518i	0.308282	−	0.951295i
$5$	−2.28872	−	0.948019i	−0.457744	−	0.189604i	0.141883	−	0.989883i	$-0.454684\pi$
$5$	−2.28872	−	0.948019i	−0.457744	−	0.189604i	−0.599627	+	0.800280i	$0.704684\pi$
$6$		0			0
$7$	−6.37744	+	6.37744i	−0.911063	+	0.911063i	−0.996356	−	0.0852929i	$-0.972817\pi$
$7$	−6.37744	+	6.37744i	−0.911063	+	0.911063i	0.0852929	+	0.996356i	$0.472817\pi$
$8$	2.48095	+	7.60558i	0.310119	+	0.950698i
$9$		0			0
$10$	4.81725	−	1.15849i	0.481725	−	0.115849i
$11$	1.79646	+	0.744117i	0.163314	+	0.0676470i	0.462843	−	0.886440i	$-0.346829\pi$
$11$	1.79646	+	0.744117i	0.163314	+	0.0676470i	−0.299529	+	0.954087i	$0.596829\pi$
$12$		0			0
$13$	16.7036	−	6.91888i	1.28490	−	0.532221i	0.367436	−	0.930049i	$-0.380236\pi$
$13$	16.7036	−	6.91888i	1.28490	−	0.532221i	0.917460	+	0.397827i	$0.130236\pi$
$14$	2.81490	−	17.8171i	0.201065	−	1.27265i
$15$		0			0
$16$	−12.9588	−	9.38456i	−0.809924	−	0.586535i
$17$			6.19811i			0.364595i	0.983243	+	0.182297i	$0.0583533\pi$
$17$			6.19811i			0.364595i	−0.983243	+	0.182297i	$0.941647\pi$
$18$		0			0
$19$	−8.50083	−	20.5228i	−0.447412	−	1.08015i	−0.973288	−	0.229587i	$-0.926262\pi$
$19$	−8.50083	−	20.5228i	−0.447412	−	1.08015i	0.525876	−	0.850561i	$-0.323738\pi$
$20$	−6.42967	+	7.53997i	−0.321484	+	0.376998i
$21$		0			0
$22$	−3.78114	+	0.909316i	−0.171870	+	0.0413325i
$23$	−23.6476	−	23.6476i	−1.02815	−	1.02815i	−0.999592	−	0.0285625i	$-0.990907\pi$
$23$	−23.6476	−	23.6476i	−1.02815	−	1.02815i	−0.0285625	−	0.999592i	$-0.509093\pi$
$24$		0			0
$25$	−13.3382	−	13.3382i	−0.533527	−	0.533527i
$26$	−18.8815	+	30.8386i	−0.726213	+	1.18610i
$27$		0			0
$28$	16.4031	+	32.1315i	0.585825	+	1.14755i
$29$	−14.5725	−	35.1811i	−0.502500	−	1.21314i	−0.948118	−	0.317919i	$-0.897016\pi$
$29$	−14.5725	−	35.1811i	−0.502500	−	1.21314i	0.445618	−	0.895223i	$-0.352984\pi$
$30$		0			0
$31$		−	14.1609i		−	0.456803i	−0.973567	−	0.228401i	$-0.926650\pi$
$31$		−	14.1609i		−	0.456803i	0.973567	−	0.228401i	$-0.0733498\pi$
$32$	31.9999	−	0.0617869i	0.999998	−	0.00193084i
$33$		0			0
$34$	−7.29019	−	10.0259i	−0.214417	−	0.294880i
$35$	20.6421	−	8.55025i	0.589775	−	0.244293i
$36$		0			0
$37$	−30.0695	−	12.4552i	−0.812689	−	0.336627i	−0.0626629	−	0.998035i	$-0.519959\pi$
$37$	−30.0695	−	12.4552i	−0.812689	−	0.336627i	−0.750027	+	0.661408i	$0.769959\pi$
$38$	37.8896	+	23.1987i	0.997095	+	0.610491i
$39$		0			0
$40$	1.53204	−	19.7590i	0.0383010	−	0.493976i
$41$	56.9700	−	56.9700i	1.38951	−	1.38951i	0.563170	−	0.826341i	$-0.309582\pi$
$41$	56.9700	−	56.9700i	1.38951	−	1.38951i	0.826341	−	0.563170i	$-0.190418\pi$
$42$		0			0
$43$	54.5034	+	22.5760i	1.26752	+	0.525024i	0.912209	−	0.409724i	$-0.134375\pi$
$43$	54.5034	+	22.5760i	1.26752	+	0.525024i	0.355310	+	0.934748i	$0.384375\pi$
$44$	5.04676	−	5.91825i	0.114699	−	0.134506i
$45$		0			0
$46$	66.0659	+	10.4377i	1.43622	+	0.226906i
$47$	−34.8047			−0.740525			−0.370263	−	0.928927i	$-0.620732\pi$
$47$	−34.8047			−0.740525			−0.370263	+	0.928927i	$0.620732\pi$
$48$		0			0
$49$		−	32.3435i		−	0.660072i
$50$	37.2638	+	5.88726i	0.745277	+	0.117745i
$51$		0			0
$52$	−5.72981	−	72.0923i	−0.110189	−	1.38639i
$53$	−3.92967	+	9.48706i	−0.0741447	+	0.179001i	−0.956606	−	0.291383i	$-0.905885\pi$
$53$	−3.92967	+	9.48706i	−0.0741447	+	0.179001i	0.882462	+	0.470384i	$0.155885\pi$
$54$		0			0
$55$	−3.40615	−	3.40615i	−0.0619300	−	0.0619300i
$56$	−64.3263	−	32.6821i	−1.14868	−	0.583608i
$57$		0			0
$58$	64.9521	+	39.7682i	1.11986	+	0.685658i
$59$	−9.41777	+	22.7365i	−0.159623	+	0.385365i	−0.983375	−	0.181586i	$-0.941877\pi$
$59$	−9.41777	+	22.7365i	−0.159623	+	0.385365i	0.823752	+	0.566951i	$0.191877\pi$
$60$		0			0
$61$	3.00467	+	7.25391i	0.0492568	+	0.118916i	0.946593	−	0.322432i	$-0.104500\pi$
$61$	3.00467	+	7.25391i	0.0492568	+	0.118916i	−0.897336	+	0.441348i	$0.854500\pi$
$62$	16.6560	+	22.9064i	0.268644	+	0.369457i
$63$		0			0
$64$	−51.6898	+	37.7381i	−0.807653	+	0.589658i
$65$	−44.7892			−0.689065
$66$		0			0
$67$	−55.9040	+	23.1562i	−0.834388	+	0.345615i	−0.758638	−	0.651512i	$-0.774135\pi$
$67$	−55.9040	+	23.1562i	−0.834388	+	0.345615i	−0.0757497	+	0.997127i	$0.524135\pi$
$68$	23.5849	+	7.64307i	0.346837	+	0.112398i
$69$		0			0
$70$	−23.3335	+	38.1099i	−0.333336	+	0.544427i
$71$	−6.27499	+	6.27499i	−0.0883801	+	0.0883801i	−0.749915	−	0.661535i	$-0.769905\pi$
$71$	−6.27499	+	6.27499i	−0.0883801	+	0.0883801i	0.661535	+	0.749915i	$0.269905\pi$
$72$		0			0
$73$	66.4597	−	66.4597i	0.910406	−	0.910406i	−0.0858977	−	0.996304i	$-0.527376\pi$
$73$	66.4597	−	66.4597i	0.910406	−	0.910406i	0.996304	+	0.0858977i	$0.0273758\pi$
$74$	63.2896	−	15.2203i	0.855265	−	0.205680i
$75$		0			0
$76$	−88.5756	+	7.03989i	−1.16547	+	0.0926301i
$77$	−16.2024	+	6.71124i	−0.210420	+	0.0871589i
$78$		0			0
$79$	−75.8508			−0.960136			−0.480068	−	0.877231i	$-0.659388\pi$
$79$	−75.8508			−0.960136			−0.480068	+	0.877231i	$0.659388\pi$
$80$	20.7623	+	33.7638i	0.259529	+	0.422048i
$81$		0			0
$82$	−25.1457	+	159.161i	−0.306654	+	1.94099i
$83$	1.23390	+	2.97891i	0.0148663	+	0.0358905i	0.931138	−	0.364666i	$-0.118817\pi$
$83$	1.23390	+	2.97891i	0.0148663	+	0.0358905i	−0.916272	+	0.400556i	$0.868817\pi$
$84$		0			0
$85$	5.87593	−	14.1857i	0.0691286	−	0.166891i
$86$	−114.717	+	27.5881i	−1.33392	+	0.320791i
$87$		0			0
$88$	−1.20252	+	15.5092i	−0.0136651	+	0.176241i
$89$	−36.7030	−	36.7030i	−0.412393	−	0.412393i	0.470178	−	0.882572i	$-0.344190\pi$
$89$	−36.7030	−	36.7030i	−0.412393	−	0.412393i	−0.882572	+	0.470178i	$0.844190\pi$
$90$		0			0
$91$	−62.4018	+	150.651i	−0.685734	+	1.65551i
$92$	−119.144	+	60.8227i	−1.29504	+	0.661116i
$93$		0			0
$94$	56.2994	−	40.9371i	0.598929	−	0.435501i
$95$			55.0300i			0.579263i
$96$		0			0
$97$	90.0528			0.928379			0.464189	−	0.885736i	$-0.346346\pi$
$97$	90.0528			0.928379			0.464189	+	0.885736i	$0.346346\pi$
$98$	38.0423	+	52.3182i	0.388187	+	0.533859i
$99$		0			0
$100$	−67.2018	+	34.3064i	−0.672018	+	0.343064i
$101$	20.0870	+	8.32031i	0.198881	+	0.0823793i	0.479901	−	0.877323i	$-0.340673\pi$
$101$	20.0870	+	8.32031i	0.198881	+	0.0823793i	−0.281020	+	0.959702i	$0.590673\pi$
$102$		0			0
$103$	4.88882	−	4.88882i	0.0474642	−	0.0474642i	−0.682976	−	0.730441i	$-0.739315\pi$
$103$	4.88882	−	4.88882i	0.0474642	−	0.0474642i	0.730441	+	0.682976i	$0.239315\pi$
$104$	94.0630	+	109.876i	0.904452	+	1.05650i
$105$		0			0
$106$	−4.80208	−	19.9681i	−0.0453027	−	0.188379i
$107$	51.9710	+	21.5271i	0.485710	+	0.201188i	0.612080	−	0.790795i	$-0.290333\pi$
$107$	51.9710	+	21.5271i	0.485710	+	0.201188i	−0.126371	+	0.991983i	$0.540333\pi$
$108$		0			0
$109$	−49.8054	+	20.6301i	−0.456931	+	0.189267i	−0.599263	−	0.800552i	$-0.704540\pi$
$109$	−49.8054	+	20.6301i	−0.456931	+	0.189267i	0.142333	+	0.989819i	$0.454540\pi$
$110$	9.51602	+	1.50342i	0.0865093	+	0.0136675i
$111$		0			0
$112$	142.493	−	22.7944i	1.27226	−	0.203522i
$113$		−	62.0870i		−	0.549442i	−0.961524	−	0.274721i	$-0.911414\pi$
$113$		−	62.0870i		−	0.549442i	0.961524	−	0.274721i	$-0.0885855\pi$
$114$		0			0
$115$	31.7043	+	76.5410i	0.275690	+	0.665574i
$116$	−151.840	+	12.0681i	−1.30897	+	0.104035i
$117$		0			0
$118$	−11.5086	−	47.8553i	−0.0975304	−	0.405553i
$119$	−39.5281	−	39.5281i	−0.332169	−	0.332169i
$120$		0			0
$121$	−82.8864	−	82.8864i	−0.685011	−	0.685011i
$122$	−13.3923	−	8.19970i	−0.109773	−	0.0672106i
$123$		0			0
$124$	−53.8847	−	17.4622i	−0.434554	−	0.140824i
$125$	41.5830	+	100.390i	0.332664	+	0.803122i
$126$		0			0
$127$			177.045i			1.39406i	0.717043	+	0.697029i	$0.245495\pi$
$127$			177.045i			1.39406i	−0.717043	+	0.697029i	$0.754505\pi$
$128$	39.2250	−	121.842i	0.306445	−	0.951888i
$129$		0			0
$130$	72.4502	−	52.6809i	0.557309	−	0.405238i
$131$	−88.7654	+	36.7678i	−0.677598	+	0.280670i	−0.694823	−	0.719181i	$-0.744517\pi$
$131$	−88.7654	+	36.7678i	−0.677598	+	0.280670i	0.0172241	+	0.999852i	$0.494517\pi$
$132$		0			0
$133$	185.097	+	76.6695i	1.39170	+	0.576462i
$134$	63.1930	−	103.211i	0.471589	−	0.770231i
$135$		0			0
$136$	−47.1402	+	15.3772i	−0.346619	+	0.113068i
$137$	58.5583	−	58.5583i	0.427433	−	0.427433i	−0.460320	−	0.887753i	$-0.652265\pi$
$137$	58.5583	−	58.5583i	0.427433	−	0.427433i	0.887753	+	0.460320i	$0.152265\pi$
$138$		0			0
$139$	−166.832	−	69.1039i	−1.20023	−	0.497151i	−0.309155	−	0.951012i	$-0.600046\pi$
$139$	−166.832	−	69.1039i	−1.20023	−	0.497151i	−0.891072	+	0.453861i	$0.850046\pi$
$140$	−7.08082	−	89.0906i	−0.0505773	−	0.636361i
$141$		0			0
$142$	2.76968	−	17.5309i	0.0195048	−	0.123457i
$143$	35.1558			0.245845
$144$		0			0
$145$			94.3348i			0.650585i
$146$	−29.3343	+	185.673i	−0.200920	+	1.27174i
$147$		0			0
$148$	−84.4739	+	99.0610i	−0.570769	+	0.669331i
$149$	−18.0040	+	43.4655i	−0.120832	+	0.291715i	−0.972709	−	0.232027i	$-0.925464\pi$
$149$	−18.0040	+	43.4655i	−0.120832	+	0.291715i	0.851877	+	0.523742i	$0.175464\pi$
$150$		0			0
$151$	−68.3596	−	68.3596i	−0.452713	−	0.452713i	0.443541	−	0.896254i	$-0.353722\pi$
$151$	−68.3596	−	68.3596i	−0.452713	−	0.452713i	−0.896254	+	0.443541i	$0.853722\pi$
$152$	134.998	−	115.570i	0.888144	−	0.760328i
$153$		0			0
$154$	18.3149	−	29.9131i	0.118928	−	0.194241i
$155$	−13.4248	+	32.4103i	−0.0866115	+	0.209099i
$156$		0			0
$157$	−74.5650	−	180.016i	−0.474936	−	1.14660i	−0.961956	−	0.273206i	$-0.911916\pi$
$157$	−74.5650	−	180.016i	−0.474936	−	1.14660i	0.487020	−	0.873391i	$-0.338084\pi$
$158$	122.695	−	89.2153i	0.776549	−	0.564654i
$159$		0			0
$160$	−73.2975	−	30.1952i	−0.458110	−	0.188720i
$161$	301.622			1.87343
$162$		0			0
$163$	267.123	−	110.646i	1.63879	−	0.678811i	0.642619	−	0.766186i	$-0.277848\pi$
$163$	267.123	−	110.646i	1.63879	−	0.678811i	0.996175	+	0.0873756i	$0.0278480\pi$
$164$	−146.530	−	287.032i	−0.893473	−	1.75020i
$165$		0			0
$166$	−5.49972	−	3.36731i	−0.0331308	−	0.0202850i
$167$	−99.3059	+	99.3059i	−0.594646	+	0.594646i	−0.938883	−	0.344237i	$-0.888138\pi$
$167$	−99.3059	+	99.3059i	−0.594646	+	0.594646i	0.344237	+	0.938883i	$0.388138\pi$
$168$		0			0
$169$	111.640	−	111.640i	0.660592	−	0.660592i
$170$	7.18042	+	29.8578i	0.0422378	+	0.175634i
$171$		0			0
$172$	153.116	−	179.556i	0.890207	−	1.04393i
$173$	−187.259	+	77.5652i	−1.08242	+	0.448354i	−0.851358	−	0.524585i	$-0.824220\pi$
$173$	−187.259	+	77.5652i	−1.08242	+	0.448354i	−0.231063	+	0.972939i	$0.574220\pi$
$174$		0			0
$175$	170.127			0.972153
$176$	−16.2967	−	26.5018i	−0.0925948	−	0.150578i
$177$		0			0
$178$	102.540	+	16.2001i	0.576067	+	0.0910121i
$179$	101.230	+	244.390i	0.565528	+	1.36531i	0.905290	+	0.424795i	$0.139654\pi$
$179$	101.230	+	244.390i	0.565528	+	1.36531i	−0.339761	+	0.940512i	$0.610346\pi$
$180$		0			0
$181$	6.07796	−	14.6735i	0.0335799	−	0.0810690i	−0.906200	−	0.422849i	$-0.861030\pi$
$181$	6.07796	−	14.6735i	0.0335799	−	0.0810690i	0.939780	+	0.341780i	$0.111030\pi$
$182$	−76.2554	−	317.087i	−0.418986	−	1.74224i
$183$		0			0
$184$	121.185	−	238.522i	0.658614	−	1.29631i
$185$	57.0130	+	57.0130i	0.308178	+	0.308178i
$186$		0			0
$187$	−4.61212	+	11.1346i	−0.0246637	+	0.0595435i
$188$	−42.9187	+	132.438i	−0.228291	+	0.704458i
$189$		0			0
$190$	−64.7260	−	89.0154i	−0.340663	−	0.468502i
$191$		−	370.577i		−	1.94019i	−0.242716	−	0.970097i	$-0.578038\pi$
$191$		−	370.577i		−	1.94019i	0.242716	−	0.970097i	$-0.421962\pi$
$192$		0			0
$193$	−132.679			−0.687456			−0.343728	−	0.939069i	$-0.611690\pi$
$193$	−132.679			−0.687456			−0.343728	+	0.939069i	$0.611690\pi$
$194$	−145.668	+	105.920i	−0.750864	+	0.545977i
$195$		0			0
$196$	−123.073	−	39.8837i	−0.627923	−	0.203488i
$197$	−116.390	−	48.2104i	−0.590814	−	0.244723i	0.0671870	−	0.997740i	$-0.478598\pi$
$197$	−116.390	−	48.2104i	−0.590814	−	0.244723i	−0.658001	+	0.753017i	$0.728598\pi$
$198$		0			0
$199$	−89.9950	+	89.9950i	−0.452236	+	0.452236i	−0.896096	−	0.443860i	$-0.853609\pi$
$199$	−89.9950	+	89.9950i	−0.452236	+	0.452236i	0.443860	+	0.896096i	$0.353609\pi$
$200$	68.3532	−	134.536i	0.341766	−	0.672679i
$201$		0			0
$202$	−42.2786	+	10.1675i	−0.209300	+	0.0503340i
$203$	317.301	+	131.430i	1.56306	+	0.647440i
$204$		0			0
$205$	−184.397	+	76.3797i	−0.899498	+	0.372584i
$206$	−2.15785	+	13.6582i	−0.0104750	+	0.0663022i
$207$		0			0
$208$	−281.390	−	67.0961i	−1.35283	−	0.322578i
$209$		−	43.1940i		−	0.206670i
$210$		0			0
$211$	20.9287	+	50.5264i	0.0991883	+	0.239462i	0.965683	−	0.259725i	$-0.0836321\pi$
$211$	20.9287	+	50.5264i	0.0991883	+	0.239462i	−0.866494	+	0.499187i	$0.833632\pi$
$212$	31.2542	+	26.6519i	0.147425	+	0.125716i
$213$		0			0
$214$	−109.387	+	26.3062i	−0.511155	+	0.122926i
$215$	−103.340	−	103.340i	−0.480653	−	0.480653i
$216$		0			0
$217$	90.3102	+	90.3102i	0.416176	+	0.416176i
$218$	56.2993	−	91.9518i	0.258254	−	0.421797i
$219$		0			0
$220$	−17.1612	+	8.76079i	−0.0780057	+	0.0398218i
$221$	42.8840	+	103.531i	0.194045	+	0.468466i
$222$		0			0
$223$		−	52.7540i		−	0.236565i	−0.992980	−	0.118283i	$-0.962261\pi$
$223$		−	52.7540i		−	0.236565i	0.992980	−	0.118283i	$-0.0377388\pi$
$224$	−203.684	+	204.472i	−0.909302	+	0.912820i
$225$		0			0
$226$	73.0264	+	100.431i	0.323126	+	0.444383i
$227$	327.101	−	135.490i	1.44097	−	0.596871i	0.480939	−	0.876754i	$-0.340296\pi$
$227$	327.101	−	135.490i	1.44097	−	0.596871i	0.960034	+	0.279883i	$0.0902957\pi$
$228$		0			0
$229$	245.430	+	101.660i	1.07175	+	0.443932i	0.847606	−	0.530625i	$-0.178043\pi$
$229$	245.430	+	101.660i	1.07175	+	0.443932i	0.224139	+	0.974557i	$0.428043\pi$
$230$	−141.311	−	86.5207i	−0.614398	−	0.376177i
$231$		0			0
$232$	231.419	−	198.115i	0.997497	−	0.853944i
$233$	31.8772	−	31.8772i	0.136812	−	0.136812i	−0.635384	−	0.772196i	$-0.719158\pi$
$233$	31.8772	−	31.8772i	0.136812	−	0.136812i	0.772196	+	0.635384i	$0.219158\pi$
$234$		0			0
$235$	79.6582	+	32.9955i	0.338971	+	0.140406i
$236$	74.9032	+	63.8734i	0.317386	+	0.270650i
$237$		0			0
$238$	110.433	+	17.4471i	0.464002	+	0.0733071i
$239$	−90.0511			−0.376783			−0.188391	−	0.982094i	$-0.560327\pi$
$239$	−90.0511			−0.376783			−0.188391	+	0.982094i	$0.560327\pi$
$240$		0			0
$241$		−	20.9972i		−	0.0871252i	−0.999051	−	0.0435626i	$-0.986129\pi$
$241$		−	20.9972i		−	0.0871252i	0.999051	−	0.0435626i	$-0.0138708\pi$
$242$	231.566	+	36.5848i	0.956884	+	0.151177i
$243$		0			0
$244$	31.3076	−	2.48829i	0.128310	−	0.0101979i
$245$	−30.6623	+	74.0253i	−0.125152	+	0.302144i
$246$		0			0
$247$	−283.990	−	283.990i	−1.14976	−	1.14976i
$248$	107.702	−	35.1324i	0.434281	−	0.141663i
$249$		0			0
$250$	−185.342	−	113.479i	−0.741369	−	0.453918i
$251$	−105.207	+	253.991i	−0.419150	+	1.01192i	0.563444	+	0.826154i	$0.309476\pi$
$251$	−105.207	+	253.991i	−0.419150	+	1.01192i	−0.982594	+	0.185764i	$0.940524\pi$
$252$		0			0
$253$	−24.8853	−	60.0783i	−0.0983607	−	0.237464i
$254$	−208.240	−	286.385i	−0.819842	−	1.12750i
$255$		0			0
$256$	79.8601	+	243.225i	0.311954	+	0.950097i
$257$	−236.584			−0.920561			−0.460281	−	0.887773i	$-0.652251\pi$
$257$	−236.584			−0.920561			−0.460281	+	0.887773i	$0.652251\pi$
$258$		0			0
$259$	271.199	−	112.334i	1.04710	−	0.433723i
$260$	−55.2309	+	170.431i	−0.212427	+	0.655504i
$261$		0			0
$262$	100.339	−	163.880i	0.382973	−	0.625498i
$263$	−32.0070	+	32.0070i	−0.121700	+	0.121700i	−0.765334	−	0.643634i	$-0.777426\pi$
$263$	−32.0070	+	32.0070i	−0.121700	+	0.121700i	0.643634	+	0.765334i	$0.277426\pi$
$264$		0			0
$265$	17.9878	−	17.9878i	0.0678786	−	0.0678786i
$266$	−389.587	+	93.6906i	−1.46461	+	0.352220i
$267$		0			0
$268$	19.1766	+	241.279i	0.0715545	+	0.900296i
$269$	−115.344	+	47.7769i	−0.428787	+	0.177609i	−0.586630	−	0.809855i	$-0.699546\pi$
$269$	−115.344	+	47.7769i	−0.428787	+	0.177609i	0.157844	+	0.987464i	$0.449546\pi$
$270$		0			0
$271$	−55.4325			−0.204548			−0.102274	−	0.994756i	$-0.532612\pi$
$271$	−55.4325			−0.204548			−0.102274	+	0.994756i	$0.532612\pi$
$272$	58.1665	−	80.3199i	0.213847	−	0.295294i
$273$		0			0
$274$	−25.8468	+	163.599i	−0.0943312	+	0.597076i
$275$	−14.0363	−	33.8866i	−0.0510410	−	0.123224i
$276$		0			0
$277$	−35.7881	+	86.4001i	−0.129199	+	0.311914i	−0.975221	−	0.221235i	$-0.928991\pi$
$277$	−35.7881	+	86.4001i	−0.129199	+	0.311914i	0.846022	+	0.533148i	$0.178991\pi$
$278$	351.143	−	84.4454i	1.26310	−	0.303761i
$279$		0			0
$280$	116.242	+	135.783i	0.415149	+	0.484938i
$281$	−13.8509	−	13.8509i	−0.0492914	−	0.0492914i	0.682031	−	0.731323i	$-0.261097\pi$
$281$	−13.8509	−	13.8509i	−0.0492914	−	0.0492914i	−0.731323	+	0.682031i	$0.761097\pi$
$282$		0			0
$283$	−135.615	+	327.403i	−0.479205	+	1.15690i	0.480778	+	0.876843i	$0.340354\pi$
$283$	−135.615	+	327.403i	−0.479205	+	1.15690i	−0.959982	+	0.280060i	$0.909646\pi$
$284$	16.1396	+	31.6153i	0.0568295	+	0.111322i
$285$		0			0
$286$	−56.8674	+	41.3501i	−0.198837	+	0.144581i
$287$			726.645i			2.53186i
$288$		0			0
$289$	250.583			0.867071
$290$	−110.956	−	152.594i	−0.382608	−	0.526187i
$291$		0			0
$292$	−170.938	−	334.844i	−0.585403	−	1.14673i
$293$	412.791	+	170.984i	1.40884	+	0.583562i	0.952031	−	0.306002i	$-0.0989914\pi$
$293$	412.791	+	170.984i	1.40884	+	0.583562i	0.456811	+	0.889564i	$0.348991\pi$
$294$		0			0
$295$	43.1093	−	43.1093i	0.146133	−	0.146133i
$296$	20.1281	−	259.597i	0.0680005	−	0.877016i
$297$		0			0
$298$	−22.0010	−	91.4851i	−0.0738289	−	0.306997i
$299$	−558.615	−	231.386i	−1.86828	−	0.773866i
$300$		0			0
$301$	−491.569	+	203.615i	−1.63312	+	0.676461i
$302$	190.981	+	30.1729i	0.632389	+	0.0999102i
$303$		0			0
$304$	−82.4372	+	345.727i	−0.271175	+	1.13726i
$305$		−	19.4507i		−	0.0637726i
$306$		0			0
$307$	−42.3557	−	102.256i	−0.137967	−	0.333081i	0.839762	−	0.542955i	$-0.182695\pi$
$307$	−42.3557	−	102.256i	−0.137967	−	0.333081i	−0.977728	+	0.209874i	$0.932695\pi$
$308$	5.55785	+	69.9287i	0.0180450	+	0.227041i
$309$		0			0
$310$	−16.4052	−	68.2164i	−0.0529199	−	0.220053i
$311$	−337.326	−	337.326i	−1.08465	−	1.08465i	−0.996069	−	0.0885790i	$-0.971767\pi$
$311$	−337.326	−	337.326i	−1.08465	−	1.08465i	−0.0885790	−	0.996069i	$-0.528233\pi$
$312$		0			0
$313$	−70.0735	−	70.0735i	−0.223877	−	0.223877i	0.586252	−	0.810129i	$-0.300603\pi$
$313$	−70.0735	−	70.0735i	−0.223877	−	0.223877i	−0.810129	+	0.586252i	$0.800603\pi$
$314$	332.348	+	203.487i	1.05843	+	0.648047i
$315$		0			0
$316$	−93.5338	+	288.626i	−0.295993	+	0.913373i
$317$	−32.8632	−	79.3388i	−0.103669	−	0.250280i	0.863530	−	0.504297i	$-0.168248\pi$
$317$	−32.8632	−	79.3388i	−0.103669	−	0.250280i	−0.967200	+	0.254017i	$0.918248\pi$
$318$		0			0
$319$		−	74.0450i		−	0.232116i
$320$	154.080	−	37.3691i	0.481500	−	0.116779i
$321$		0			0
$322$	−487.897	+	354.766i	−1.51521	+	1.10176i
$323$	127.203	−	52.6891i	0.393816	−	0.163124i
$324$		0			0
$325$	−315.081	−	130.511i	−0.969480	−	0.401572i
$326$	−301.952	+	493.168i	−0.926233	+	1.51279i
$327$		0			0
$328$	574.629	+	291.950i	1.75192	+	0.890092i
$329$	221.965	−	221.965i	0.674665	−	0.674665i
$330$		0			0
$331$	124.865	+	51.7206i	0.377234	+	0.156256i	0.563240	−	0.826293i	$-0.309554\pi$
$331$	124.865	+	51.7206i	0.377234	+	0.156256i	−0.186006	+	0.982549i	$0.559554\pi$
$332$	12.8568	−	1.02185i	0.0387254	−	0.00307785i
$333$		0			0
$334$	43.8321	−	277.438i	0.131234	−	0.830654i
$335$	149.901			0.447466
$336$		0			0
$337$			323.529i			0.960027i	0.877261	+	0.480014i	$0.159368\pi$
$337$			323.529i			0.960027i	−0.877261	+	0.480014i	$0.840632\pi$
$338$	−49.2762	+	311.897i	−0.145787	+	0.922772i
$339$		0			0
$340$	−46.7335	−	39.8518i	−0.137452	−	0.117211i
$341$	10.5373	−	25.4394i	0.0309013	−	0.0746024i
$342$		0			0
$343$	−106.226	−	106.226i	−0.309696	−	0.309696i
$344$	−36.4838	+	470.540i	−0.106058	+	1.36785i
$345$		0			0
$346$	211.674	−	345.721i	0.611776	−	0.999193i
$347$	135.065	−	326.076i	0.389236	−	0.939700i	−0.600866	−	0.799350i	$-0.705177\pi$
$347$	135.065	−	326.076i	0.389236	−	0.939700i	0.990102	−	0.140350i	$-0.0448226\pi$
$348$		0			0
$349$	187.869	+	453.555i	0.538305	+	1.29958i	0.925905	+	0.377756i	$0.123304\pi$
$349$	187.869	+	453.555i	0.538305	+	1.29958i	−0.387600	+	0.921828i	$0.626696\pi$
$350$	−275.194	+	200.102i	−0.786267	+	0.571721i
$351$		0			0
$352$	57.5325	+	23.7007i	0.163445	+	0.0673315i
$353$	70.5556			0.199874			0.0999372	−	0.994994i	$-0.468136\pi$
$353$	70.5556			0.199874			0.0999372	+	0.994994i	$0.468136\pi$
$354$		0			0
$355$	20.3105	−	8.41289i	0.0572127	−	0.0236983i
$356$	−184.921	+	94.4020i	−0.519441	+	0.265174i
$357$		0			0
$358$	−451.197	−	276.254i	−1.26033	−	0.771660i
$359$	409.567	−	409.567i	1.14086	−	1.14086i	0.152561	−	0.988294i	$-0.451248\pi$
$359$	409.567	−	409.567i	1.14086	−	1.14086i	0.988294	−	0.152561i	$-0.0487522\pi$
$360$		0			0
$361$	−93.6563	+	93.6563i	−0.259436	+	0.259436i
$362$	7.42731	+	30.8844i	0.0205174	+	0.0853161i
$363$		0			0
$364$	496.306	+	423.223i	1.36348	+	1.16270i
$365$	−215.113	+	89.1026i	−0.589350	+	0.244117i
$366$		0			0
$367$	513.680			1.39967			0.699837	−	0.714303i	$-0.253256\pi$
$367$	513.680			1.39967			0.699837	+	0.714303i	$0.253256\pi$
$368$	84.5217	+	528.365i	0.229678	+	1.43578i
$369$		0			0
$370$	−159.281	−	25.1646i	−0.430490	−	0.0680126i
$371$	−35.4419	−	85.5644i	−0.0955308	−	0.230632i
$372$		0			0
$373$	−46.5164	+	112.301i	−0.124709	+	0.301074i	−0.973887	−	0.227032i	$-0.927098\pi$
$373$	−46.5164	+	112.301i	−0.124709	+	0.301074i	0.849178	+	0.528106i	$0.177098\pi$
$374$	−5.63604	−	23.4359i	−0.0150696	−	0.0626629i
$375$		0			0
$376$	−86.3486	−	264.710i	−0.229651	−	0.704016i
$377$	−486.828	−	486.828i	−1.29132	−	1.29132i
$378$		0			0
$379$	172.090	−	415.462i	0.454064	−	1.09621i	−0.516699	−	0.856167i	$-0.672840\pi$
$379$	172.090	−	415.462i	0.454064	−	1.09621i	0.970763	−	0.240040i	$-0.0771604\pi$
$380$	209.399	+	67.8591i	0.551050	+	0.178576i
$381$		0			0
$382$	435.871	+	599.438i	1.14102	+	1.56921i
$383$		−	430.627i		−	1.12435i	−0.827017	−	0.562177i	$-0.809964\pi$
$383$		−	430.627i		−	1.12435i	0.827017	−	0.562177i	$-0.190036\pi$
$384$		0			0
$385$	43.4451			0.112844
$386$	214.619	−	156.056i	0.556008	−	0.404291i
$387$		0			0
$388$	111.047	−	342.667i	0.286203	−	0.883162i
$389$	−55.8615	−	23.1386i	−0.143603	−	0.0594823i	0.309725	−	0.950826i	$-0.399763\pi$
$389$	−55.8615	−	23.1386i	−0.143603	−	0.0594823i	−0.453327	+	0.891344i	$0.649763\pi$
$390$		0			0
$391$	146.570	−	146.570i	0.374860	−	0.374860i
$392$	245.991	−	80.2426i	0.627529	−	0.204701i
$393$		0			0
$394$	244.975	−	58.9135i	0.621765	−	0.149527i
$395$	173.601	+	71.9080i	0.439497	+	0.182046i
$396$		0			0
$397$	−67.6641	+	28.0274i	−0.170439	+	0.0705979i	−0.466271	−	0.884642i	$-0.654403\pi$
$397$	−67.6641	+	28.0274i	−0.170439	+	0.0705979i	0.295833	+	0.955240i	$0.404403\pi$
$398$	39.7224	−	251.426i	0.0998051	−	0.631723i
$399$		0			0
$400$	47.6736	+	298.019i	0.119184	+	0.745048i
$401$			536.024i			1.33672i	0.743839	+	0.668359i	$0.233003\pi$
$401$			536.024i			1.33672i	−0.743839	+	0.668359i	$0.766997\pi$
$402$		0			0
$403$	−97.9774	−	236.538i	−0.243120	−	0.586944i
$404$	56.4301	−	66.1746i	0.139679	−	0.163799i
$405$		0			0
$406$	−667.847	+	160.609i	−1.64494	+	0.395588i
$407$	−44.7505	−	44.7505i	−0.109952	−	0.109952i
$408$		0			0
$409$	−540.379	−	540.379i	−1.32122	−	1.32122i	−0.912790	−	0.408430i	$-0.866077\pi$
$409$	−540.379	−	540.379i	−1.32122	−	1.32122i	−0.408430	−	0.912790i	$-0.633923\pi$
$410$	208.439	−	340.437i	0.508389	−	0.830335i
$411$		0			0
$412$	−12.5743	−	24.6314i	−0.0305201	−	0.0597849i
$413$	−84.9395	−	205.062i	−0.205665	−	0.496518i
$414$		0			0
$415$		−	7.98765i		−	0.0192474i
$416$	534.088	−	222.436i	1.28387	−	0.534701i
$417$		0			0
$418$	50.8045	+	69.8697i	0.121542	+	0.167152i
$419$	341.184	−	141.323i	0.814281	−	0.337286i	0.0636205	−	0.997974i	$-0.479735\pi$
$419$	341.184	−	141.323i	0.814281	−	0.337286i	0.750661	+	0.660688i	$0.229735\pi$
$420$		0			0
$421$	339.196	+	140.500i	0.805692	+	0.333728i	0.747234	−	0.664561i	$-0.231382\pi$
$421$	339.196	+	140.500i	0.805692	+	0.333728i	0.0584581	+	0.998290i	$0.481382\pi$
$422$	−93.2828	−	57.1142i	−0.221049	−	0.135342i
$423$		0			0
$424$	−81.9039	−	6.35051i	−0.193170	−	0.0149776i
$425$	82.6714	−	82.6714i	0.194521	−	0.194521i
$426$		0			0
$427$	−65.4234	−	27.0993i	−0.153216	−	0.0634643i
$428$	146.001	−	171.213i	0.341125	−	0.400031i
$429$		0			0
$430$	288.710	+	45.6129i	0.671419	+	0.106077i
$431$	−154.504			−0.358478			−0.179239	−	0.983806i	$-0.557363\pi$
$431$	−154.504			−0.358478			−0.179239	+	0.983806i	$0.557363\pi$
$432$		0			0
$433$			506.808i			1.17046i	0.810868	+	0.585228i	$0.198995\pi$
$433$			506.808i			1.17046i	−0.810868	+	0.585228i	$0.801005\pi$
$434$	−252.306	−	39.8615i	−0.581351	−	0.0918468i
$435$		0			0
$436$	17.0846	+	214.958i	0.0391850	+	0.493023i
$437$	−284.291	+	686.338i	−0.650550	+	1.57057i
$438$		0			0
$439$	−144.746	−	144.746i	−0.329718	−	0.329718i	0.522761	−	0.852479i	$-0.324902\pi$
$439$	−144.746	−	144.746i	−0.329718	−	0.329718i	−0.852479	+	0.522761i	$0.824902\pi$
$440$	17.4553	−	34.3563i	0.0396711	−	0.0780824i
$441$		0			0
$442$	−191.141	−	117.030i	−0.432446	−	0.264773i
$443$	−230.959	+	557.584i	−0.521351	+	1.25865i	0.415713	+	0.909496i	$0.363532\pi$
$443$	−230.959	+	557.584i	−0.521351	+	1.25865i	−0.937064	+	0.349158i	$0.886468\pi$
$444$		0			0
$445$	49.2078	+	118.798i	0.110579	+	0.266962i
$446$	62.0490	+	85.3338i	0.139123	+	0.191331i
$447$		0			0
$448$	88.9759	−	570.321i	0.198607	−	1.27304i
$449$	0.201052			0.000447778			0.000223889	−	1.00000i	$-0.499929\pi$
$449$	0.201052			0.000447778			0.000223889		1.00000i	$0.499929\pi$
$450$		0			0
$451$	144.736	−	59.9518i	0.320923	−	0.132931i
$452$	−236.252	−	76.5613i	−0.522681	−	0.169383i
$453$		0			0
$454$	−369.750	+	603.900i	−0.814427	+	1.33018i
$455$	285.641	−	285.641i	0.627782	−	0.627782i
$456$		0			0
$457$	226.835	−	226.835i	0.496358	−	0.496358i	−0.413944	−	0.910302i	$-0.635849\pi$
$457$	226.835	−	226.835i	0.496358	−	0.496358i	0.910302	+	0.413944i	$0.135849\pi$
$458$	−516.575	+	124.230i	−1.12789	+	0.271244i
$459$		0			0
$460$	330.348	−	26.2557i	0.718147	−	0.0570775i
$461$	−496.600	+	205.699i	−1.07722	+	0.446201i	−0.849535	−	0.527533i	$-0.823117\pi$
$461$	−496.600	+	205.699i	−1.07722	+	0.446201i	−0.227690	+	0.973734i	$0.573117\pi$
$462$		0			0
$463$	−520.019			−1.12315			−0.561576	−	0.827425i	$-0.689805\pi$
$463$	−520.019			−1.12315			−0.561576	+	0.827425i	$0.689805\pi$
$464$	−141.317	+	592.661i	−0.304564	+	1.27729i
$465$		0			0
$466$	−14.0701	+	89.0576i	−0.0301933	+	0.191111i
$467$	−35.4966	−	85.6964i	−0.0760099	−	0.183504i	0.881307	−	0.472544i	$-0.156664\pi$
$467$	−35.4966	−	85.6964i	−0.0760099	−	0.183504i	−0.957317	+	0.289040i	$0.906664\pi$
$468$		0			0
$469$	208.847	−	504.202i	0.445303	−	1.07506i
$470$	−167.663	+	40.3207i	−0.356729	+	0.0857888i
$471$		0			0
$472$	−196.289	−	15.2195i	−0.415868	−	0.0322448i
$473$	81.1137	+	81.1137i	0.171488	+	0.171488i
$474$		0			0
$475$	−160.351	+	387.122i	−0.337582	+	0.814994i
$476$	−199.155	+	101.668i	−0.418392	+	0.213589i
$477$		0			0
$478$	145.665	−	105.918i	0.304738	−	0.221585i
$479$		−	163.116i		−	0.340535i	−0.985398	−	0.170268i	$-0.945537\pi$
$479$		−	163.116i		−	0.340535i	0.985398	−	0.170268i	$-0.0544632\pi$
$480$		0			0
$481$	−588.447			−1.22338
$482$	24.6968	+	33.9646i	0.0512381	+	0.0704660i
$483$		0			0
$484$	−417.607	+	213.188i	−0.862825	+	0.440471i
$485$	−206.106	−	85.3718i	−0.424960	−	0.176024i
$486$		0			0
$487$	371.724	−	371.724i	0.763294	−	0.763294i	−0.213622	−	0.976916i	$-0.568526\pi$
$487$	371.724	−	371.724i	0.763294	−	0.763294i	0.976916	+	0.213622i	$0.0685262\pi$
$488$	−47.7158	+	40.8488i	−0.0977782	+	0.0837066i
$489$		0			0
$490$	−37.4695	−	155.807i	−0.0764684	−	0.317973i
$491$	−281.201	−	116.477i	−0.572710	−	0.237224i	0.0774824	−	0.996994i	$-0.475312\pi$
$491$	−281.201	−	116.477i	−0.572710	−	0.237224i	−0.650193	+	0.759769i	$0.725312\pi$
$492$		0			0
$493$	218.056	−	90.3220i	0.442305	−	0.183209i
$494$	793.403	+	125.349i	1.60608	+	0.253742i
$495$		0			0
$496$	−132.894	+	183.508i	−0.267931	+	0.369975i
$497$		−	80.0367i		−	0.161040i
$498$		0			0
$499$	−236.126	−	570.059i	−0.473199	−	1.14240i	−0.962741	−	0.270424i	$-0.912836\pi$
$499$	−236.126	−	570.059i	−0.473199	−	1.14240i	0.489542	−	0.871980i	$-0.337164\pi$
$500$	433.280	−	34.4366i	0.866560	−	0.0688732i
$501$		0			0
$502$	−128.563	−	534.595i	−0.256102	−	1.06493i
$503$	−12.8902	−	12.8902i	−0.0256266	−	0.0256266i	0.694177	−	0.719804i	$-0.255768\pi$
$503$	−12.8902	−	12.8902i	−0.0256266	−	0.0256266i	−0.719804	+	0.694177i	$0.755768\pi$
$504$		0			0
$505$	−38.0857	−	38.0857i	−0.0754173	−	0.0754173i
$506$	110.918	+	67.9116i	0.219205	+	0.134213i
$507$		0			0
$508$	673.690	+	218.320i	1.32616	+	0.429764i
$509$	−59.1272	−	142.746i	−0.116163	−	0.280443i	0.855095	−	0.518472i	$-0.173499\pi$
$509$	−59.1272	−	142.746i	−0.116163	−	0.280443i	−0.971258	+	0.238028i	$0.923499\pi$
$510$		0			0
$511$			847.685i			1.65888i
$512$	−415.260	−	299.505i	−0.811055	−	0.584970i
$513$		0			0
$514$	382.694	−	278.269i	0.744541	−	0.541380i
$515$	−15.8238	+	6.55444i	−0.0307259	+	0.0127271i
$516$		0			0
$517$	−62.5251	−	25.8988i	−0.120938	−	0.0500943i
$518$	−306.559	+	500.692i	−0.591812	+	0.966588i
$519$		0			0
$520$	−111.120	−	340.648i	−0.213692	−	0.655093i
$521$	−119.838	+	119.838i	−0.230015	+	0.230015i	−0.812699	−	0.582684i	$-0.802003\pi$
$521$	−119.838	+	119.838i	−0.230015	+	0.230015i	0.582684	+	0.812699i	$0.302003\pi$
$522$		0			0
$523$	−689.004	−	285.395i	−1.31741	−	0.545688i	−0.390370	−	0.920658i	$-0.627653\pi$
$523$	−689.004	−	285.395i	−1.31741	−	0.545688i	−0.927037	+	0.374970i	$0.877653\pi$
$524$	30.4490	+	383.108i	0.0581087	+	0.731122i
$525$		0			0
$526$	14.1274	−	89.4203i	0.0268582	−	0.170001i
$527$	87.7707			0.166548
$528$		0			0
$529$			589.413i			1.11420i
$530$	−7.93955	+	50.2540i	−0.0149803	+	0.0948188i
$531$		0			0
$532$	519.989	−	609.782i	0.977423	−	1.14621i
$533$	557.438	−	1345.77i	1.04585	−	2.52490i
$534$		0			0
$535$	−98.5390	−	98.5390i	−0.184185	−	0.184185i
$536$	−314.811	−	367.733i	−0.587334	−	0.686069i
$537$		0			0
$538$	130.383	−	212.950i	0.242347	−	0.395817i
$539$	24.0673	−	58.1037i	0.0446519	−	0.107799i
$540$		0			0
$541$	−294.810	−	711.735i	−0.544936	−	1.31559i	−0.921204	−	0.389081i	$-0.872793\pi$
$541$	−294.810	−	711.735i	−0.544936	−	1.31559i	0.376267	−	0.926511i	$-0.377207\pi$
$542$	89.6665	−	65.1995i	0.165436	−	0.120294i
$543$		0			0
$544$	0.382962	+	198.339i	0.000703974	+	0.364594i
$545$	133.549			0.245043
$546$		0			0
$547$	518.930	−	214.948i	0.948683	−	0.392957i	0.145948	−	0.989292i	$-0.453377\pi$
$547$	518.930	−	214.948i	0.948683	−	0.392957i	0.802736	+	0.596335i	$0.203377\pi$
$548$	−150.615	−	295.035i	−0.274845	−	0.538385i
$549$		0			0
$550$	62.5621	+	38.3049i	0.113749	+	0.0696452i
$551$	−598.138	+	598.138i	−1.08555	+	1.08555i
$552$		0			0
$553$	483.734	−	483.734i	0.874745	−	0.874745i
$554$	−43.7333	−	181.853i	−0.0789410	−	0.328254i
$555$		0			0
$556$	−468.678	+	549.610i	−0.842946	+	0.988508i
$557$	883.511	−	365.962i	1.58620	−	0.657024i	0.596816	−	0.802378i	$-0.296432\pi$
$557$	883.511	−	365.962i	1.58620	−	0.657024i	0.989380	+	0.145355i	$0.0464323\pi$
$558$		0			0
$559$	1066.61			1.90806
$560$	−347.737	−	82.9164i	−0.620959	−	0.148065i
$561$		0			0
$562$	38.6963	+	6.11357i	0.0688546	+	0.0108782i
$563$	−385.055	−	929.606i	−0.683935	−	1.65117i	−0.756656	−	0.653813i	$-0.773168\pi$
$563$	−385.055	−	929.606i	−0.683935	−	1.65117i	0.0727214	−	0.997352i	$-0.476832\pi$
$564$		0			0
$565$	−58.8596	+	142.100i	−0.104176	+	0.251504i
$566$	−165.722	−	689.111i	−0.292796	−	1.21751i
$567$		0			0
$568$	−63.2928	−	32.1570i	−0.111431	−	0.0566145i
$569$	503.029	+	503.029i	0.884058	+	0.884058i	0.993944	−	0.109886i	$-0.0350485\pi$
$569$	503.029	+	503.029i	0.884058	+	0.884058i	−0.109886	+	0.993944i	$0.535049\pi$
$570$		0			0
$571$	−48.1525	+	116.250i	−0.0843301	+	0.203591i	−0.960419	−	0.278558i	$-0.910144\pi$
$571$	−48.1525	+	116.250i	−0.0843301	+	0.203591i	0.876089	+	0.482149i	$0.160144\pi$
$572$	43.3517	−	133.774i	0.0757897	−	0.233871i
$573$		0			0
$574$	−854.677	−	1175.41i	−1.48898	−	2.04775i
$575$			630.830i			1.09710i
$576$		0			0
$577$	−11.8629			−0.0205595			−0.0102798	−	0.999947i	$-0.503272\pi$
$577$	−11.8629			−0.0205595			−0.0102798	+	0.999947i	$0.503272\pi$
$578$	−405.339	+	294.735i	−0.701278	+	0.509922i
$579$		0			0
$580$	358.961	+	116.327i	0.618898	+	0.200564i
$581$	−26.8670	−	11.1287i	−0.0462426	−	0.0191543i
$582$		0			0
$583$	−14.1190	+	14.1190i	−0.0242178	+	0.0242178i
$584$	670.347	+	340.581i	1.14786	+	0.583187i
$585$		0			0
$586$	−868.832	+	208.943i	−1.48265	+	0.356558i
$587$	496.631	+	205.711i	0.846049	+	0.350445i	0.763236	−	0.646120i	$-0.223610\pi$
$587$	496.631	+	205.711i	0.846049	+	0.350445i	0.0828132	+	0.996565i	$0.473610\pi$
$588$		0			0
$589$	−290.621	+	120.379i	−0.493414	+	0.204379i
$590$	−19.0278	+	120.438i	−0.0322505	+	0.204132i
$591$		0			0
$592$	272.778	+	443.593i	0.460773	+	0.749313i
$593$			410.471i			0.692193i	0.938199	+	0.346097i	$0.112493\pi$
$593$			410.471i			0.692193i	−0.938199	+	0.346097i	$0.887507\pi$
$594$		0			0
$595$	52.9954	+	127.942i	0.0890678	+	0.215029i
$596$	143.193	+	122.107i	0.240256	+	0.204878i
$597$		0			0
$598$	1175.76	−	282.755i	1.96615	−	0.472835i
$599$	565.778	+	565.778i	0.944537	+	0.944537i	0.998541	−	0.0540033i	$-0.0171982\pi$
$599$	565.778	+	565.778i	0.944537	+	0.944537i	−0.0540033	+	0.998541i	$0.517198\pi$
$600$		0			0
$601$	224.391	+	224.391i	0.373362	+	0.373362i	0.868700	−	0.495338i	$-0.164956\pi$
$601$	224.391	+	224.391i	0.373362	+	0.373362i	−0.495338	+	0.868700i	$0.664956\pi$
$602$	555.662	−	907.544i	0.923026	−	1.50755i
$603$		0			0
$604$	−344.417	+	175.824i	−0.570226	+	0.291100i
$605$	111.126	+	268.282i	0.183679	+	0.443441i
$606$		0			0
$607$			19.8654i			0.0327271i	0.999866	+	0.0163636i	$0.00520892\pi$
$607$			19.8654i			0.0327271i	−0.999866	+	0.0163636i	$0.994791\pi$
$608$	−273.294	−	656.204i	−0.449497	−	1.07928i
$609$		0			0
$610$	22.8778	+	31.4630i	0.0375045	+	0.0515787i
$611$	−581.365	+	240.809i	−0.951498	+	0.394123i
$612$		0			0
$613$	905.460	+	375.054i	1.47710	+	0.611833i	0.968464	−	0.249152i	$-0.0801518\pi$
$613$	905.460	+	375.054i	1.47710	+	0.611833i	0.508631	+	0.860985i	$0.330152\pi$
$614$	188.787	+	115.588i	0.307470	+	0.188255i
$615$		0			0
$616$	−91.2401	−	106.578i	−0.148117	−	0.173016i
$617$	−673.907	+	673.907i	−1.09223	+	1.09223i	−0.0969409	+	0.995290i	$0.530906\pi$
$617$	−673.907	+	673.907i	−1.09223	+	1.09223i	−0.995290	+	0.0969409i	$0.969094\pi$
$618$		0			0
$619$	354.963	+	147.030i	0.573446	+	0.237529i	0.650511	−	0.759497i	$-0.274555\pi$
$619$	354.963	+	147.030i	0.573446	+	0.237529i	−0.0770649	+	0.997026i	$0.524555\pi$
$620$	106.773	+	91.0498i	0.172214	+	0.146855i
$621$		0			0
$622$	942.412	+	148.890i	1.51513	+	0.239374i
$623$	468.143			0.751433
$624$		0			0
$625$			202.389i			0.323822i
$626$	195.770	+	30.9294i	0.312731	+	0.0494080i
$627$		0			0
$628$	−776.940	+	61.7503i	−1.23717	+	0.0983286i
$629$	77.1987	−	186.374i	0.122732	−	0.296302i
$630$		0			0
$631$	−494.698	−	494.698i	−0.783991	−	0.783991i	0.196511	−	0.980502i	$-0.437039\pi$
$631$	−494.698	−	494.698i	−0.783991	−	0.783991i	−0.980502	+	0.196511i	$0.937039\pi$
$632$	−188.182	−	576.889i	−0.297756	−	0.912800i
$633$		0			0
$634$	146.477	+	89.6833i	0.231036	+	0.141456i
$635$	167.843	−	405.208i	0.264319	−	0.638122i
$636$		0			0
$637$	−223.781	−	540.255i	−0.351304	−	0.848124i
$638$	87.0914	+	119.774i	0.136507	+	0.187733i
$639$		0			0
$640$	−205.283	+	241.676i	−0.320755	+	0.377618i
$641$	−440.457			−0.687141			−0.343571	−	0.939127i	$-0.611636\pi$
$641$	−440.457			−0.687141			−0.343571	+	0.939127i	$0.611636\pi$
$642$		0			0
$643$	−211.055	+	87.4220i	−0.328235	+	0.135960i	−0.540715	−	0.841206i	$-0.681846\pi$
$643$	−211.055	+	87.4220i	−0.328235	+	0.135960i	0.212479	+	0.977166i	$0.431846\pi$
$644$	371.939	−	1147.72i	0.577545	−	1.78218i
$645$		0			0
$646$	−143.788	+	234.844i	−0.222582	+	0.363535i
$647$	−515.935	+	515.935i	−0.797426	+	0.797426i	−0.982689	−	0.185263i	$-0.940686\pi$
$647$	−515.935	+	515.935i	−0.797426	+	0.797426i	0.185263	+	0.982689i	$0.440686\pi$
$648$		0			0
$649$	−33.8372	+	33.8372i	−0.0521375	+	0.0521375i
$650$	663.175	−	159.485i	1.02027	−	0.245362i
$651$		0			0
$652$	−91.6307	−	1152.89i	−0.140538	−	1.76824i
$653$	613.161	−	253.980i	0.938991	−	0.388943i	0.139909	−	0.990164i	$-0.455319\pi$
$653$	613.161	−	253.980i	0.938991	−	0.388943i	0.799082	+	0.601222i	$0.205319\pi$
$654$		0			0
$655$	238.016			0.363383
$656$	−1272.90	+	203.623i	−1.94040	+	0.310402i
$657$		0			0
$658$	−97.9719	+	620.120i	−0.148893	+	0.942431i
$659$	19.4679	+	46.9996i	0.0295416	+	0.0713196i	0.937962	−	0.346738i	$-0.112711\pi$
$659$	19.4679	+	46.9996i	0.0295416	+	0.0713196i	−0.908420	+	0.418058i	$0.862711\pi$
$660$		0			0
$661$	46.1458	−	111.406i	0.0698122	−	0.168541i	−0.885122	−	0.465359i	$-0.845925\pi$
$661$	46.1458	−	111.406i	0.0698122	−	0.168541i	0.954934	+	0.296817i	$0.0959253\pi$
$662$	−262.812	+	63.2029i	−0.396997	+	0.0954726i
$663$		0			0
$664$	−19.5951	+	16.7751i	−0.0295107	+	0.0252637i
$665$	−350.950	−	350.950i	−0.527745	−	0.527745i
$666$		0			0
$667$	−487.344	+	1176.55i	−0.730650	+	1.76395i
$668$	255.420	+	500.334i	0.382365	+	0.749003i
$669$		0			0
$670$	−242.477	+	176.313i	−0.361906	+	0.263154i
$671$			15.2672i			0.0227528i
$672$		0			0
$673$	−352.344			−0.523542			−0.261771	−	0.965130i	$-0.584306\pi$
$673$	−352.344			−0.523542			−0.261771	+	0.965130i	$0.584306\pi$
$674$	−380.533	−	523.334i	−0.564590	−	0.776460i
$675$		0			0
$676$	−287.144	−	562.477i	−0.424769	−	0.832066i
$677$	1178.26	+	488.051i	1.74041	+	0.720902i	0.998742	+	0.0501357i	$0.0159654\pi$
$677$	1178.26	+	488.051i	1.74041	+	0.720902i	0.741669	+	0.670766i	$0.234035\pi$
$678$		0			0
$679$	−574.306	+	574.306i	−0.845812	+	0.845812i
$680$	122.469	+	9.49575i	0.180101	+	0.0139643i
$681$		0			0
$682$	12.8767	+	53.5443i	0.0188808	+	0.0785106i
$683$	414.446	+	171.669i	0.606802	+	0.251346i	0.664861	−	0.746967i	$-0.268491\pi$
$683$	414.446	+	171.669i	0.606802	+	0.251346i	−0.0580582	+	0.998313i	$0.518491\pi$
$684$		0			0
$685$	−189.538	+	78.5093i	−0.276698	+	0.114612i
$686$	296.771	+	46.8864i	0.432611	+	0.0683476i
$687$		0			0
$688$	−494.431	−	804.048i	−0.718650	−	1.16867i
$689$			185.657i			0.269459i
$690$		0			0
$691$	268.707	+	648.715i	0.388866	+	0.938806i	0.990181	+	0.139794i	$0.0446439\pi$
$691$	268.707	+	648.715i	0.388866	+	0.938806i	−0.601314	+	0.799012i	$0.705356\pi$
$692$	64.2350	+	808.202i	0.0928251	+	1.16792i
$693$		0			0
$694$	165.050	+	686.316i	0.237825	+	0.988928i
$695$	316.319	+	316.319i	0.455136	+	0.455136i
$696$		0			0
$697$	353.106	+	353.106i	0.506608	+	0.506608i
$698$	−837.361	−	512.691i	−1.19966	−	0.734514i
$699$		0			0
$700$	209.788	−	647.363i	0.299698	−	0.924804i
$701$	−464.382	−	1121.12i	−0.662457	−	1.59931i	−0.793941	−	0.607995i	$-0.791974\pi$
$701$	−464.382	−	1121.12i	−0.662457	−	1.59931i	0.131484	−	0.991318i	$-0.458026\pi$
$702$		0			0
$703$			722.990i			1.02844i
$704$	−120.940	+	29.3317i	−0.171790	+	0.0416643i
$705$		0			0
$706$	−114.129	+	82.9872i	−0.161656	+	0.117546i
$707$	−181.166	+	75.0414i	−0.256246	+	0.106141i
$708$		0			0
$709$	591.984	+	245.208i	0.834957	+	0.345850i	0.758863	−	0.651250i	$-0.225755\pi$
$709$	591.984	+	245.208i	0.834957	+	0.345850i	0.0760937	+	0.997101i	$0.475755\pi$
$710$	−22.9587	+	37.4976i	−0.0323362	+	0.0528136i
$711$		0			0
$712$	188.090	−	370.206i	0.264171	−	0.519952i
$713$	−334.870	+	334.870i	−0.469664	+	0.469664i
$714$		0			0
$715$	−80.4619	−	33.3284i	−0.112534	−	0.0466132i
$716$	1054.78	−	83.8325i	1.47315	−	0.117084i
$717$		0			0
$718$	−180.777	+	1144.24i	−0.251778	+	1.59365i
$719$	906.230			1.26040			0.630202	−	0.776432i	$-0.282972\pi$
$719$	906.230			1.26040			0.630202	+	0.776432i	$0.282972\pi$
$720$		0			0
$721$			62.3563i			0.0864858i
$722$	41.3384	−	261.655i	0.0572555	−	0.362402i
$723$		0			0
$724$	−48.3404	−	41.2220i	−0.0667685	−	0.0569365i
$725$	−274.881	+	663.622i	−0.379147	+	0.915341i
$726$		0			0
$727$	317.957	+	317.957i	0.437355	+	0.437355i	0.891121	−	0.453766i	$-0.149920\pi$
$727$	317.957	+	317.957i	0.437355	+	0.437355i	−0.453766	+	0.891121i	$0.649920\pi$
$728$	−1300.61	−	100.844i	−1.78655	−	0.138522i
$729$		0			0
$730$	243.160	−	397.145i	0.333096	−	0.544034i
$731$	−139.929	+	337.818i	−0.191421	+	0.462131i
$732$		0			0
$733$	−159.623	−	385.363i	−0.217766	−	0.525734i	0.776811	−	0.629734i	$-0.216836\pi$
$733$	−159.623	−	385.363i	−0.217766	−	0.525734i	−0.994577	+	0.103999i	$0.966836\pi$
$734$	−830.919	+	604.188i	−1.13204	+	0.823145i
$735$		0			0
$736$	−758.181	−	755.259i	−1.03014	−	1.02617i
$737$	−117.660			−0.159647
$738$		0			0
$739$	−380.514	+	157.614i	−0.514904	+	0.213280i	−0.624977	−	0.780643i	$-0.714892\pi$
$739$	−380.514	+	157.614i	−0.514904	+	0.213280i	0.110073	+	0.993924i	$0.464892\pi$
$740$	287.249	−	146.640i	0.388174	−	0.198162i
$741$		0			0
$742$	157.971	+	96.7206i	0.212898	+	0.130351i
$743$	−5.76228	+	5.76228i	−0.00775542	+	0.00775542i	−0.710974	−	0.703218i	$-0.751746\pi$
$743$	−5.76228	+	5.76228i	−0.00775542	+	0.00775542i	0.703218	+	0.710974i	$0.251746\pi$
$744$		0			0
$745$	82.4123	−	82.4123i	0.110620	−	0.110620i
$746$	−56.8434	−	236.367i	−0.0761975	−	0.316847i
$747$		0			0
$748$	36.6819	+	31.2804i	0.0490400	+	0.0418187i
$749$	−468.729	+	194.154i	−0.625807	+	0.259218i
$750$		0			0
$751$	−302.377			−0.402632			−0.201316	−	0.979526i	$-0.564522\pi$
$751$	−302.377			−0.402632			−0.201316	+	0.979526i	$0.564522\pi$
$752$	451.026	+	326.627i	0.599769	+	0.434344i
$753$		0			0
$754$	1360.09	+	214.878i	1.80383	+	0.284985i
$755$	91.6499	+	221.262i	0.121391	+	0.293063i
$756$		0			0
$757$	−9.31627	+	22.4915i	−0.0123068	+	0.0297113i	−0.929914	−	0.367778i	$-0.880119\pi$
$757$	−9.31627	+	22.4915i	−0.0123068	+	0.0297113i	0.917607	+	0.397490i	$0.130119\pi$
$758$	210.295	+	874.455i	0.277434	+	1.15363i
$759$		0			0
$760$	−418.535	+	136.526i	−0.550704	+	0.179640i
$761$	163.034	+	163.034i	0.214236	+	0.214236i	0.806064	−	0.591828i	$-0.201594\pi$
$761$	163.034	+	163.034i	0.214236	+	0.214236i	−0.591828	+	0.806064i	$0.701594\pi$
$762$		0			0
$763$	186.064	−	449.198i	0.243859	−	0.588727i
$764$	−1410.11	−	456.970i	−1.84570	−	0.598128i
$765$		0			0
$766$	506.502	+	696.574i	0.661229	+	0.909365i
$767$			444.943i			0.580109i
$768$		0			0
$769$	180.205			0.234337			0.117168	−	0.993112i	$-0.462618\pi$
$769$	180.205			0.234337			0.117168	+	0.993112i	$0.462618\pi$
$770$	−70.2759	+	51.0999i	−0.0912674	+	0.0663635i
$771$		0			0
$772$	−163.610	+	504.868i	−0.211931	+	0.653974i
$773$	−196.725	−	81.4860i	−0.254495	−	0.105415i	0.251789	−	0.967782i	$-0.418981\pi$
$773$	−196.725	−	81.4860i	−0.254495	−	0.105415i	−0.506284	+	0.862367i	$0.668981\pi$
$774$		0			0
$775$	−188.880	+	188.880i	−0.243716	+	0.243716i
$776$	223.416	+	684.904i	0.287908	+	0.882608i
$777$		0			0
$778$	117.576	−	28.2755i	0.151126	−	0.0363439i
$779$	−1653.48	−	684.892i	−2.12256	−	0.879194i
$780$		0			0
$781$	−15.9421	+	6.60342i	−0.0204124	+	0.00845508i
$782$	−64.6938	+	409.484i	−0.0827286	+	0.523637i
$783$		0			0
$784$	−303.530	+	419.133i	−0.387155	+	0.534608i
$785$			482.695i			0.614898i
$786$		0			0
$787$	80.6847	+	194.790i	0.102522	+	0.247510i	0.966814	−	0.255480i	$-0.0822334\pi$
$787$	80.6847	+	194.790i	0.102522	+	0.247510i	−0.864293	+	0.502990i	$0.832233\pi$
$788$	−326.974	+	383.436i	−0.414941	+	0.486594i
$789$		0			0
$790$	−365.392	+	87.8721i	−0.462521	+	0.111230i
$791$	395.956	+	395.956i	0.500576	+	0.500576i
$792$		0			0
$793$	100.378	+	100.378i	0.126580	+	0.126580i
$794$	76.4864	−	124.923i	0.0963305	−	0.157333i
$795$		0			0
$796$	231.472	+	453.423i	0.290794	+	0.569627i
$797$	256.509	+	619.268i	0.321843	+	0.776999i	0.999147	+	0.0412950i	$0.0131483\pi$
$797$	256.509	+	619.268i	0.321843	+	0.776999i	−0.677304	+	0.735704i	$0.736852\pi$
$798$		0			0
$799$		−	215.723i		−	0.269992i
$800$	−427.645	−	425.996i	−0.534556	−	0.532495i
$801$		0			0
$802$	−630.469	−	867.061i	−0.786120	−	1.08112i
$803$	168.846	−	69.9382i	0.210269	−	0.0870961i
$804$		0			0
$805$	−690.328	−	285.943i	−0.857551	−	0.355209i
$806$	436.702	+	267.379i	0.541813	+	0.331736i
$807$		0			0
$808$	−13.4460	+	173.416i	−0.0166411	+	0.214623i
$809$	1008.10	−	1008.10i	1.24611	−	1.24611i	0.288683	−	0.957425i	$-0.406783\pi$
$809$	1008.10	−	1008.10i	1.24611	−	1.24611i	0.957425	−	0.288683i	$-0.0932175\pi$
$810$		0			0
$811$	−1271.85	−	526.816i	−1.56825	−	0.649588i	−0.581748	−	0.813369i	$-0.697631\pi$
$811$	−1271.85	−	526.816i	−1.56825	−	0.649588i	−0.986497	+	0.163780i	$0.947631\pi$
$812$	891.389	−	1045.32i	1.09777	−	1.28734i
$813$		0			0
$814$	125.023	+	19.7522i	0.153591	+	0.0242656i
$815$	−716.266			−0.878854
$816$		0			0
$817$		−	1310.48i		−	1.60401i
$818$	1509.70	+	238.515i	1.84560	+	0.291583i
$819$		0			0
$820$	63.2532	+	795.850i	0.0771381	+	0.970548i
$821$	119.922	−	289.516i	0.146068	−	0.352639i	−0.833865	−	0.551969i	$-0.813877\pi$
$821$	119.922	−	289.516i	0.146068	−	0.352639i	0.979932	+	0.199330i	$0.0638767\pi$
$822$		0			0
$823$	607.735	+	607.735i	0.738439	+	0.738439i	0.972276	−	0.233837i	$-0.0751282\pi$
$823$	607.735	+	607.735i	0.738439	+	0.738439i	−0.233837	+	0.972276i	$0.575128\pi$
$824$	49.3112	+	25.0534i	0.0598437	+	0.0304046i
$825$		0			0
$826$	378.590	+	231.799i	0.458341	+	0.280628i
$827$	−246.520	+	595.152i	−0.298090	+	0.719652i	0.701883	+	0.712292i	$0.252343\pi$
$827$	−246.520	+	595.152i	−0.298090	+	0.719652i	−0.999973	+	0.00736012i	$0.997657\pi$
$828$		0			0
$829$	393.211	+	949.295i	0.474319	+	1.14511i	0.962236	+	0.272218i	$0.0877571\pi$
$829$	393.211	+	949.295i	0.474319	+	1.14511i	−0.487916	+	0.872890i	$0.662243\pi$
$830$	9.39504	+	12.9207i	0.0113193	+	0.0155671i
$831$		0			0
$832$	−602.303	+	988.000i	−0.723921	+	1.18750i
$833$	200.469			0.240659
$834$		0			0
$835$	321.428	−	133.140i	0.384943	−	0.159449i
$836$	−164.361	−	53.2637i	−0.196604	−	0.0637126i
$837$		0			0
$838$	−385.669	+	629.900i	−0.460225	+	0.751671i
$839$	575.067	−	575.067i	0.685420	−	0.685420i	−0.275796	−	0.961216i	$-0.588941\pi$
$839$	575.067	−	575.067i	0.685420	−	0.685420i	0.961216	+	0.275796i	$0.0889415\pi$
$840$		0			0
$841$	−430.678	+	430.678i	−0.512102	+	0.512102i
$842$	−713.932	+	171.692i	−0.847900	+	0.203909i
$843$		0			0
$844$	218.070	−	17.3319i	0.258377	−	0.0205355i
$845$	−361.350	+	149.676i	−0.427633	+	0.177131i
$846$		0			0
$847$	1057.21			1.24818
$848$	139.956	−	86.0626i	0.165042	−	0.101489i
$849$		0			0
$850$	−36.4899	+	230.965i	−0.0429293	+	0.271724i
$851$	416.535	+	1005.61i	0.489466	+	1.18167i
$852$		0			0
$853$	304.017	−	733.961i	0.356409	−	0.860447i	−0.639390	−	0.768882i	$-0.720813\pi$
$853$	304.017	−	733.961i	0.356409	−	0.860447i	0.995799	−	0.0915645i	$-0.0291868\pi$
$854$	137.702	−	33.1155i	0.161243	−	0.0387769i
$855$		0			0
$856$	−34.7887	+	448.677i	−0.0406410	+	0.524155i
$857$	241.394	+	241.394i	0.281673	+	0.281673i	0.833776	−	0.552103i	$-0.186174\pi$
$857$	241.394	+	241.394i	0.281673	+	0.281673i	−0.552103	+	0.833776i	$0.686174\pi$
$858$		0			0
$859$	443.212	−	1070.01i	0.515963	−	1.24564i	−0.424401	−	0.905474i	$-0.639515\pi$
$859$	443.212	−	1070.01i	0.515963	−	1.24564i	0.940364	−	0.340170i	$-0.110485\pi$
$860$	−520.661	+	265.797i	−0.605420	+	0.309066i
$861$		0			0
$862$	249.922	−	181.727i	0.289933	−	0.210820i
$863$		−	167.859i		−	0.194507i	−0.995260	−	0.0972533i	$-0.968994\pi$
$863$		−	167.859i		−	0.194507i	0.995260	−	0.0972533i	$-0.0310057\pi$
$864$		0			0
$865$	502.117			0.580482
$866$	−596.105	−	819.802i	−0.688343	−	0.946654i
$867$		0			0
$868$	455.011	−	232.282i	0.524206	−	0.267606i
$869$	−136.263	−	56.4418i	−0.156804	−	0.0649503i
$870$		0			0
$871$	−773.586	+	773.586i	−0.888158	+	0.888158i
$872$	−280.469	−	327.617i	−0.321638	−	0.375708i
$873$		0			0
$874$	−347.405	−	1444.59i	−0.397488	−	1.65285i
$875$	−905.426	−	375.040i	−1.03477	−	0.428617i
$876$		0			0
$877$	659.079	−	272.999i	0.751515	−	0.311288i	0.0261554	−	0.999658i	$-0.491674\pi$
$877$	659.079	−	272.999i	0.751515	−	0.311288i	0.725360	+	0.688370i	$0.241674\pi$
$878$	404.388	+	63.8887i	0.460579	+	0.0727662i
$879$		0			0
$880$	12.1744	+	76.1048i	0.0138345	+	0.0864827i
$881$		−	806.984i		−	0.915987i	−0.888956	−	0.457993i	$-0.848568\pi$
$881$		−	806.984i		−	0.915987i	0.888956	−	0.457993i	$-0.151432\pi$
$882$		0			0
$883$	−118.704	−	286.577i	−0.134433	−	0.324549i	0.842300	−	0.539009i	$-0.181201\pi$
$883$	−118.704	−	286.577i	−0.134433	−	0.324549i	−0.976733	+	0.214459i	$0.931201\pi$
$884$	446.836	−	35.5140i	0.505470	−	0.0401742i
$885$		0			0
$886$	−282.233	−	1173.59i	−0.318547	−	1.32459i
$887$	−727.865	−	727.865i	−0.820592	−	0.820592i	0.165601	−	0.986193i	$-0.447044\pi$
$887$	−727.865	−	727.865i	−0.820592	−	0.820592i	−0.986193	+	0.165601i	$0.947044\pi$
$888$		0			0
$889$	−1129.10	−	1129.10i	−1.27008	−	1.27008i
$890$	−219.327	−	134.288i	−0.246435	−	0.150885i
$891$		0			0
$892$	−200.738	−	65.0525i	−0.225043	−	0.0729288i
$893$	295.869	+	714.290i	0.331320	+	0.799877i
$894$		0			0
$895$		−	655.308i		−	0.732188i
$896$	526.883	+	1027.19i	0.588040	+	1.14642i
$897$		0			0
$898$	−0.325218	+	0.236477i	−0.000362158	+	0.000263337i
$899$	−498.196	+	206.359i	−0.554167	+	0.229543i
$900$		0			0
$901$	−58.8018	−	24.3565i	−0.0652628	−	0.0270328i
$902$	−163.608	+	267.215i	−0.181383	+	0.296247i
$903$		0			0
$904$	472.208	−	154.035i	0.522353	−	0.170392i
$905$	−27.8215	+	27.8215i	−0.0307420	+	0.0307420i
$906$		0			0
$907$	711.116	+	294.554i	0.784031	+	0.324756i	0.738541	−	0.674209i	$-0.235515\pi$
$907$	711.116	+	294.554i	0.784031	+	0.324756i	0.0454897	+	0.998965i	$0.485515\pi$
$908$	−112.205	−	1411.75i	−0.123573	−	1.55480i
$909$		0			0
$910$	−126.077	+	798.016i	−0.138547	+	0.876941i
$911$	758.696			0.832817			0.416409	−	0.909178i	$-0.363289\pi$
$911$	758.696			0.832817			0.416409	+	0.909178i	$0.363289\pi$
$912$		0			0
$913$			6.26965i			0.00686708i
$914$	−100.122	+	633.727i	−0.109542	+	0.693356i
$915$		0			0
$916$	689.483	−	808.544i	0.752710	−	0.882690i
$917$	331.611	−	800.581i	0.361626	−	0.873043i
$918$		0			0
$919$	949.647	+	949.647i	1.03335	+	1.03335i	0.999424	+	0.0339243i	$0.0108005\pi$
$919$	949.647	+	949.647i	1.03335	+	1.03335i	0.0339243	+	0.999424i	$0.489199\pi$
$920$	−503.482	+	431.024i	−0.547263	+	0.468505i
$921$		0			0
$922$	561.349	−	916.833i	0.608838	−	0.994396i
$923$	−61.3993	+	148.231i	−0.0665215	+	0.160597i
$924$		0			0
$925$	234.943	+	567.202i	0.253992	+	0.613191i
$926$	841.172	−	611.644i	0.908393	−	0.660523i
$927$		0			0
$928$	−468.493	−	1124.89i	−0.504842	−	1.21217i
$929$	−222.645			−0.239661			−0.119830	−	0.992794i	$-0.538235\pi$
$929$	−222.645			−0.239661			−0.119830	+	0.992794i	$0.538235\pi$
$930$		0			0
$931$	−663.780	+	274.947i	−0.712975	+	0.295324i
$932$	−81.9896	−	160.607i	−0.0879717	−	0.172325i
$933$		0			0
$934$	158.214	+	96.8699i	0.169394	+	0.103715i
$935$	21.1117	−	21.1117i	0.0225794	−	0.0225794i
$936$		0			0
$937$	−1027.40	+	1027.40i	−1.09648	+	1.09648i	−0.101659	+	0.994819i	$0.532415\pi$
$937$	−1027.40	+	1027.40i	−1.09648	+	1.09648i	−0.994819	+	0.101659i	$0.967585\pi$
$938$	255.213	+	1061.23i	0.272082	+	1.13138i
$939$		0			0
$940$	223.783	−	262.426i	0.238067	−	0.279177i
$941$	892.441	−	369.661i	0.948397	−	0.392839i	0.145769	−	0.989319i	$-0.453434\pi$
$941$	892.441	−	369.661i	0.948397	−	0.392839i	0.802628	+	0.596480i	$0.203434\pi$
$942$		0			0
$943$	−2694.40			−2.85726
$944$	335.415	−	206.256i	0.355313	−	0.218491i
$945$		0			0
$946$	−226.613	−	35.8023i	−0.239549	−	0.0378460i
$947$	−385.441	−	930.536i	−0.407012	−	0.982615i	−0.985919	−	0.167221i	$-0.946521\pi$
$947$	−385.441	−	930.536i	−0.407012	−	0.982615i	0.578907	−	0.815394i	$-0.303479\pi$
$948$		0			0
$949$	650.293	−	1569.95i	0.685240	−	1.65432i
$950$	−195.950	−	814.805i	−0.206263	−	0.857690i
$951$		0			0
$952$	202.567	−	398.701i	0.212780	−	0.418804i
$953$	−648.910	−	648.910i	−0.680913	−	0.680913i	0.279293	−	0.960206i	$-0.409900\pi$
$953$	−648.910	−	648.910i	−0.680913	−	0.680913i	−0.960206	+	0.279293i	$0.909900\pi$
$954$		0			0
$955$	−351.314	+	848.148i	−0.367868	+	0.888113i
$956$	−111.045	+	342.661i	−0.116156	+	0.358432i
$957$		0			0
$958$	191.857	+	263.854i	0.200268	+	0.275422i
$959$			746.905i			0.778837i
$960$		0			0
$961$	760.470			0.791331
$962$	951.859	−	692.128i	0.989459	−	0.719468i
$963$		0			0
$964$	−79.8980	−	25.8922i	−0.0828818	−	0.0268592i
$965$	303.665	+	125.782i	0.314679	+	0.130344i
$966$		0			0
$967$	−41.2757	+	41.2757i	−0.0426842	+	0.0426842i	−0.728127	−	0.685443i	$-0.759609\pi$
$967$	−41.2757	+	41.2757i	−0.0426842	+	0.0426842i	0.685443	+	0.728127i	$0.259609\pi$
$968$	424.762	−	836.036i	0.438804	−	0.863674i
$969$		0			0
$970$	433.806	−	104.325i	0.447223	−	0.107551i
$971$	213.816	+	88.5653i	0.220201	+	0.0912104i	0.490057	−	0.871690i	$-0.336976\pi$
$971$	213.816	+	88.5653i	0.220201	+	0.0912104i	−0.269856	+	0.962901i	$0.586976\pi$
$972$		0			0
$973$	1504.67	−	623.253i	1.54642	−	0.640547i
$974$	−164.073	+	1038.51i	−0.168453	+	1.06624i
$975$		0			0
$976$	29.1379	−	122.199i	0.0298544	−	0.125204i
$977$		−	314.091i		−	0.321485i	−0.986996	−	0.160742i	$-0.948611\pi$
$977$		−	314.091i		−	0.321485i	0.986996	−	0.160742i	$-0.0513888\pi$
$978$		0			0
$979$	−38.6240	−	93.2467i	−0.0394526	−	0.0952469i
$980$	243.869	+	207.958i	0.248846	+	0.212202i
$981$		0			0
$982$	591.865	−	142.336i	0.602713	−	0.144945i
$983$	8.50847	+	8.50847i	0.00865562	+	0.00865562i	0.711421	−	0.702766i	$-0.248052\pi$
$983$	8.50847	+	8.50847i	0.00865562	+	0.00865562i	−0.702766	+	0.711421i	$0.748052\pi$
$984$		0			0
$985$	220.680	+	220.680i	0.224041	+	0.224041i
$986$	−246.488	+	402.580i	−0.249987	+	0.408296i
$987$		0			0
$988$	−1430.83	+	730.436i	−1.44821	+	0.739307i
$989$	−755.003	−	1822.74i	−0.763400	−	1.84301i
$990$		0			0
$991$		−	93.7233i		−	0.0945745i	−0.998881	−	0.0472872i	$-0.984942\pi$
$991$		−	93.7233i		−	0.0945745i	0.998881	−	0.0472872i	$-0.0150576\pi$
$992$	−0.874957	−	453.147i	−0.000882013	−	0.456802i
$993$		0			0
$994$	94.1388	+	129.466i	0.0947070	+	0.130247i
$995$	291.291	−	120.657i	0.292754	−	0.121263i
$996$		0			0
$997$	−287.749	−	119.189i	−0.288614	−	0.119548i	0.233679	−	0.972314i	$-0.424923\pi$
$997$	−287.749	−	119.189i	−0.288614	−	0.119548i	−0.522294	+	0.852766i	$0.674923\pi$
$998$	1052.45	+	644.386i	1.05456	+	0.645677i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.91.2		28
3.2	odd	2		32.3.h.a.27.6	yes	28
12.11	even	2		128.3.h.a.15.5		28
24.5	odd	2		256.3.h.b.31.5		28
24.11	even	2		256.3.h.a.31.3		28
32.19	odd	8	inner	288.3.u.a.19.2		28
96.29	odd	8		256.3.h.a.223.3		28
96.35	even	8		256.3.h.b.223.5		28
96.77	odd	8		128.3.h.a.111.5		28
96.83	even	8		32.3.h.a.19.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.6	✓	28	96.83	even	8
32.3.h.a.27.6	yes	28	3.2	odd	2
128.3.h.a.15.5		28	12.11	even	2
128.3.h.a.111.5		28	96.77	odd	8
256.3.h.a.31.3		28	24.11	even	2
256.3.h.a.223.3		28	96.29	odd	8
256.3.h.b.31.5		28	24.5	odd	2
256.3.h.b.223.5		28	96.35	even	8
288.3.u.a.19.2		28	32.19	odd	8	inner
288.3.u.a.91.2		28	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.61758 + 1.17620i) q^{2} +(1.23313 - 3.80518i) q^{4} +(-2.28872 - 0.948019i) q^{5} +(-6.37744 + 6.37744i) q^{7} +(2.48095 + 7.60558i) q^{8} +O(q^{10})\)	\(q+(-1.61758 + 1.17620i) q^{2} +(1.23313 - 3.80518i) q^{4} +(-2.28872 - 0.948019i) q^{5} +(-6.37744 + 6.37744i) q^{7} +(2.48095 + 7.60558i) q^{8} +(4.81725 - 1.15849i) q^{10} +(1.79646 + 0.744117i) q^{11} +(16.7036 - 6.91888i) q^{13} +(2.81490 - 17.8171i) q^{14} +(-12.9588 - 9.38456i) q^{16} +6.19811i q^{17} +(-8.50083 - 20.5228i) q^{19} +(-6.42967 + 7.53997i) q^{20} +(-3.78114 + 0.909316i) q^{22} +(-23.6476 - 23.6476i) q^{23} +(-13.3382 - 13.3382i) q^{25} +(-18.8815 + 30.8386i) q^{26} +(16.4031 + 32.1315i) q^{28} +(-14.5725 - 35.1811i) q^{29} -14.1609i q^{31} +(31.9999 - 0.0617869i) q^{32} +(-7.29019 - 10.0259i) q^{34} +(20.6421 - 8.55025i) q^{35} +(-30.0695 - 12.4552i) q^{37} +(37.8896 + 23.1987i) q^{38} +(1.53204 - 19.7590i) q^{40} +(56.9700 - 56.9700i) q^{41} +(54.5034 + 22.5760i) q^{43} +(5.04676 - 5.91825i) q^{44} +(66.0659 + 10.4377i) q^{46} -34.8047 q^{47} -32.3435i q^{49} +(37.2638 + 5.88726i) q^{50} +(-5.72981 - 72.0923i) q^{52} +(-3.92967 + 9.48706i) q^{53} +(-3.40615 - 3.40615i) q^{55} +(-64.3263 - 32.6821i) q^{56} +(64.9521 + 39.7682i) q^{58} +(-9.41777 + 22.7365i) q^{59} +(3.00467 + 7.25391i) q^{61} +(16.6560 + 22.9064i) q^{62} +(-51.6898 + 37.7381i) q^{64} -44.7892 q^{65} +(-55.9040 + 23.1562i) q^{67} +(23.5849 + 7.64307i) q^{68} +(-23.3335 + 38.1099i) q^{70} +(-6.27499 + 6.27499i) q^{71} +(66.4597 - 66.4597i) q^{73} +(63.2896 - 15.2203i) q^{74} +(-88.5756 + 7.03989i) q^{76} +(-16.2024 + 6.71124i) q^{77} -75.8508 q^{79} +(20.7623 + 33.7638i) q^{80} +(-25.1457 + 159.161i) q^{82} +(1.23390 + 2.97891i) q^{83} +(5.87593 - 14.1857i) q^{85} +(-114.717 + 27.5881i) q^{86} +(-1.20252 + 15.5092i) q^{88} +(-36.7030 - 36.7030i) q^{89} +(-62.4018 + 150.651i) q^{91} +(-119.144 + 60.8227i) q^{92} +(56.2994 - 40.9371i) q^{94} +55.0300i q^{95} +90.0528 q^{97} +(38.0423 + 52.3182i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 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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