LMFDB - Embedded newform 315.3.h.d.181.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(181,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("315.181");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.h (of order $2$, degree $1$, 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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.11
Root			$1.86875 + 3.23677i$ of defining polynomial
Character	$\chi$	$=$	315.181
Dual form			315.3.h.d.181.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.80460 q^{2} +10.4750 q^{4} -2.23607i q^{5} +(2.44621 - 6.55866i) q^{7} +24.6348 q^{8} +O(q^{10})$	\(q+3.80460 q^{2} +10.4750 q^{4} -2.23607i q^{5} +(2.44621 - 6.55866i) q^{7} +24.6348 q^{8} -8.50735i q^{10} -14.4489 q^{11} +16.9427i q^{13} +(9.30684 - 24.9531i) q^{14} +51.8255 q^{16} -13.0093i q^{17} +18.6908i q^{19} -23.4228i q^{20} -54.9723 q^{22} -10.3861 q^{23} -5.00000 q^{25} +64.4602i q^{26} +(25.6240 - 68.7020i) q^{28} +13.7269 q^{29} +42.4383i q^{31} +98.6363 q^{32} -49.4951i q^{34} +(-14.6656 - 5.46988i) q^{35} +28.7434 q^{37} +71.1112i q^{38} -55.0850i q^{40} +28.8060i q^{41} -5.84593 q^{43} -151.352 q^{44} -39.5151 q^{46} -10.5013i q^{47} +(-37.0322 - 32.0877i) q^{49} -19.0230 q^{50} +177.475i q^{52} -81.9074 q^{53} +32.3087i q^{55} +(60.2617 - 161.571i) q^{56} +52.2254 q^{58} -35.1680i q^{59} -68.4826i q^{61} +161.461i q^{62} +167.970 q^{64} +37.8850 q^{65} +47.4637 q^{67} -136.272i q^{68} +(-55.7968 - 20.8107i) q^{70} -47.6548 q^{71} -125.967i q^{73} +109.357 q^{74} +195.786i q^{76} +(-35.3450 + 94.7655i) q^{77} -129.527 q^{79} -115.885i q^{80} +109.595i q^{82} +42.6906i q^{83} -29.0896 q^{85} -22.2414 q^{86} -355.945 q^{88} -25.5329i q^{89} +(111.122 + 41.4453i) q^{91} -108.795 q^{92} -39.9533i q^{94} +41.7940 q^{95} +28.7310i q^{97} +(-140.893 - 122.081i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8	$ 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8} + 16 q^{11} + 40 q^{14} + 92 q^{16} - 88 q^{22} + 64 q^{23} - 60 q^{25} + 88 q^{28} - 104 q^{29} + 228 q^{32} - 60 q^{35} + 32 q^{37} + 152 q^{43} - 192 q^{44} + 200 q^{46} + 60 q^{49} - 20 q^{50} - 176 q^{53} + 368 q^{56} - 400 q^{58} - 20 q^{64} + 240 q^{65} + 168 q^{67} - 60 q^{70} - 32 q^{71} - 184 q^{74} - 8 q^{77} + 120 q^{79} + 120 q^{85} - 400 q^{86} - 536 q^{88} + 24 q^{91} - 192 q^{92} - 884 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8 + 16 * q^11 + 40 * q^14 + 92 * q^16 - 88 * q^22 + 64 * q^23 - 60 * q^25 + 88 * q^28 - 104 * q^29 + 228 * q^32 - 60 * q^35 + 32 * q^37 + 152 * q^43 - 192 * q^44 + 200 * q^46 + 60 * q^49 - 20 * q^50 - 176 * q^53 + 368 * q^56 - 400 * q^58 - 20 * q^64 + 240 * q^65 + 168 * q^67 - 60 * q^70 - 32 * q^71 - 184 * q^74 - 8 * q^77 + 120 * q^79 + 120 * q^85 - 400 * q^86 - 536 * q^88 + 24 * q^91 - 192 * q^92 - 884 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	3.80460			1.90230			0.951150	−	0.308728i	$-0.0999033\pi$
$2$	3.80460			1.90230			0.951150	+	0.308728i	$0.0999033\pi$
$3$		0			0
$3$		0			0
$4$	10.4750			2.61875
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		0			0
$7$	2.44621	−	6.55866i	0.349458	−	0.936952i
$7$	2.44621	−	6.55866i	0.349458	−	0.936952i
$8$	24.6348			3.07935
$9$		0			0
$10$		−	8.50735i		−	0.850735i
$11$	−14.4489			−1.31354			−0.656768	−	0.754092i	$-0.728077\pi$
$11$	−14.4489			−1.31354			−0.656768	+	0.754092i	$0.728077\pi$
$12$		0			0
$13$			16.9427i			1.30329i	0.758526	+	0.651643i	$0.225920\pi$
$13$			16.9427i			1.30329i	−0.758526	+	0.651643i	$0.774080\pi$
$14$	9.30684	−	24.9531i	0.664774	−	1.78236i
$15$		0			0
$16$	51.8255			3.23909
$17$		−	13.0093i		−	0.765251i	−0.923904	−	0.382625i	$-0.875020\pi$
$17$		−	13.0093i		−	0.765251i	0.923904	−	0.382625i	$-0.124980\pi$
$18$		0			0
$19$			18.6908i			0.983729i	0.870672	+	0.491864i	$0.163684\pi$
$19$			18.6908i			0.983729i	−0.870672	+	0.491864i	$0.836316\pi$
$20$		−	23.4228i		−	1.17114i
$21$		0			0
$22$	−54.9723			−2.49874
$23$	−10.3861			−0.451570			−0.225785	−	0.974177i	$-0.572495\pi$
$23$	−10.3861			−0.451570			−0.225785	+	0.974177i	$0.572495\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$			64.4602i			2.47924i
$27$		0			0
$28$	25.6240	−	68.7020i	0.915142	−	2.45364i
$29$	13.7269			0.473341			0.236671	−	0.971590i	$-0.423944\pi$
$29$	13.7269			0.473341			0.236671	+	0.971590i	$0.423944\pi$
$30$		0			0
$31$			42.4383i			1.36898i	0.729024	+	0.684488i	$0.239974\pi$
$31$			42.4383i			1.36898i	−0.729024	+	0.684488i	$0.760026\pi$
$32$	98.6363			3.08238
$33$		0			0
$34$		−	49.4951i		−	1.45574i
$35$	−14.6656	−	5.46988i	−0.419018	−	0.156282i
$36$		0			0
$37$	28.7434			0.776850			0.388425	−	0.921480i	$-0.373019\pi$
$37$	28.7434			0.776850			0.388425	+	0.921480i	$0.373019\pi$
$38$			71.1112i			1.87135i
$39$		0			0
$40$		−	55.0850i		−	1.37713i
$41$			28.8060i			0.702585i	0.936266	+	0.351293i	$0.114258\pi$
$41$			28.8060i			0.702585i	−0.936266	+	0.351293i	$0.885742\pi$
$42$		0			0
$43$	−5.84593			−0.135952			−0.0679759	−	0.997687i	$-0.521654\pi$
$43$	−5.84593			−0.135952			−0.0679759	+	0.997687i	$0.521654\pi$
$44$	−151.352			−3.43982
$45$		0			0
$46$	−39.5151			−0.859023
$47$		−	10.5013i		−	0.223432i	−0.993740	−	0.111716i	$-0.964365\pi$
$47$		−	10.5013i		−	0.223432i	0.993740	−	0.111716i	$-0.0356347\pi$
$48$		0			0
$49$	−37.0322	−	32.0877i	−0.755758	−	0.654851i
$50$	−19.0230			−0.380460
$51$		0			0
$52$			177.475i			3.41298i
$53$	−81.9074			−1.54542			−0.772712	−	0.634757i	$-0.781100\pi$
$53$	−81.9074			−1.54542			−0.772712	+	0.634757i	$0.781100\pi$
$54$		0			0
$55$			32.3087i			0.587432i
$56$	60.2617	−	161.571i	1.07610	−	2.88520i
$57$		0			0
$58$	52.2254			0.900438
$59$		−	35.1680i		−	0.596067i	−0.954555	−	0.298033i	$-0.903669\pi$
$59$		−	35.1680i		−	0.596067i	0.954555	−	0.298033i	$-0.0963307\pi$
$60$		0			0
$61$		−	68.4826i		−	1.12267i	−0.827590	−	0.561333i	$-0.810289\pi$
$61$		−	68.4826i		−	1.12267i	0.827590	−	0.561333i	$-0.189711\pi$
$62$			161.461i			2.60421i
$63$		0			0
$64$	167.970			2.62453
$65$	37.8850			0.582847
$66$		0			0
$67$	47.4637			0.708414			0.354207	−	0.935167i	$-0.384751\pi$
$67$	47.4637			0.708414			0.354207	+	0.935167i	$0.384751\pi$
$68$		−	136.272i		−	2.00400i
$69$		0			0
$70$	−55.7968	−	20.8107i	−0.797098	−	0.297296i
$71$	−47.6548			−0.671194			−0.335597	−	0.942006i	$-0.608938\pi$
$71$	−47.6548			−0.671194			−0.335597	+	0.942006i	$0.608938\pi$
$72$		0			0
$73$		−	125.967i		−	1.72557i	−0.505569	−	0.862786i	$-0.668717\pi$
$73$		−	125.967i		−	1.72557i	0.505569	−	0.862786i	$-0.331283\pi$
$74$	109.357			1.47780
$75$		0			0
$76$			195.786i			2.57614i
$77$	−35.3450	+	94.7655i	−0.459026	+	1.23072i
$78$		0			0
$79$	−129.527			−1.63958			−0.819790	−	0.572665i	$-0.805910\pi$
$79$	−129.527			−1.63958			−0.819790	+	0.572665i	$0.805910\pi$
$80$		−	115.885i		−	1.44857i
$81$		0			0
$82$			109.595i			1.33653i
$83$			42.6906i			0.514345i	0.966365	+	0.257173i	$0.0827909\pi$
$83$			42.6906i			0.514345i	−0.966365	+	0.257173i	$0.917209\pi$
$84$		0			0
$85$	−29.0896			−0.342231
$86$	−22.2414			−0.258621
$87$		0			0
$88$	−355.945			−4.04483
$89$		−	25.5329i		−	0.286886i	−0.989659	−	0.143443i	$-0.954183\pi$
$89$		−	25.5329i		−	0.286886i	0.989659	−	0.143443i	$-0.0458174\pi$
$90$		0			0
$91$	111.122	+	41.4453i	1.22112	+	0.455443i
$92$	−108.795			−1.18255
$93$		0			0
$94$		−	39.9533i		−	0.425035i
$95$	41.7940			0.439937
$96$		0			0
$97$			28.7310i			0.296196i	0.988973	+	0.148098i	$0.0473151\pi$
$97$			28.7310i			0.296196i	−0.988973	+	0.148098i	$0.952685\pi$
$98$	−140.893	−	122.081i	−1.43768	−	1.24572i
$99$		0			0
$100$	−52.3750			−0.523750
$101$			12.4609i			0.123375i	0.998096	+	0.0616875i	$0.0196482\pi$
$101$			12.4609i			0.123375i	−0.998096	+	0.0616875i	$0.980352\pi$
$102$		0			0
$103$		−	38.4795i		−	0.373587i	−0.982399	−	0.186794i	$-0.940190\pi$
$103$		−	38.4795i		−	0.373587i	0.982399	−	0.186794i	$-0.0598096\pi$
$104$			417.380i			4.01326i
$105$		0			0
$106$	−311.625			−2.93986
$107$	87.7985			0.820547			0.410273	−	0.911963i	$-0.365433\pi$
$107$	87.7985			0.820547			0.410273	+	0.911963i	$0.365433\pi$
$108$		0			0
$109$	130.012			1.19277			0.596386	−	0.802698i	$-0.296603\pi$
$109$	130.012			1.19277			0.596386	+	0.802698i	$0.296603\pi$
$110$			122.922i			1.11747i
$111$		0			0
$112$	126.776	−	339.906i	1.13193	−	3.03487i
$113$	158.597			1.40351			0.701757	−	0.712417i	$-0.252399\pi$
$113$	158.597			1.40351			0.701757	+	0.712417i	$0.252399\pi$
$114$		0			0
$115$			23.2241i			0.201948i
$116$	143.789			1.23956
$117$		0			0
$118$		−	133.800i		−	1.13390i
$119$	−85.3234	−	31.8233i	−0.717003	−	0.267423i
$120$		0			0
$121$	87.7709			0.725379
$122$		−	260.549i		−	2.13565i
$123$		0			0
$124$			444.541i			3.58501i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	43.0643			0.339089			0.169545	−	0.985523i	$-0.445770\pi$
$127$	43.0643			0.339089			0.169545	+	0.985523i	$0.445770\pi$
$128$	244.513			1.91026
$129$		0			0
$130$	144.137			1.10875
$131$			0.686731i			0.00524222i	0.999997	+	0.00262111i	$0.000834326\pi$
$131$			0.686731i			0.00524222i	−0.999997	+	0.00262111i	$0.999166\pi$
$132$		0			0
$133$	122.587	+	45.7216i	0.921707	+	0.343772i
$134$	180.581			1.34762
$135$		0			0
$136$		−	320.480i		−	2.35647i
$137$	−76.2084			−0.556266			−0.278133	−	0.960543i	$-0.589716\pi$
$137$	−76.2084			−0.556266			−0.278133	+	0.960543i	$0.589716\pi$
$138$		0			0
$139$		−	49.0445i		−	0.352838i	−0.984315	−	0.176419i	$-0.943549\pi$
$139$		−	49.0445i		−	0.352838i	0.984315	−	0.176419i	$-0.0564514\pi$
$140$	−153.622	−	57.2970i	−1.09730	−	0.409264i
$141$		0			0
$142$	−181.307			−1.27681
$143$		−	244.804i		−	1.71191i
$144$		0			0
$145$		−	30.6943i		−	0.211685i
$146$		−	479.253i		−	3.28256i
$147$		0			0
$148$	301.087			2.03437
$149$	242.344			1.62647			0.813236	−	0.581934i	$-0.197704\pi$
$149$	242.344			1.62647			0.813236	+	0.581934i	$0.197704\pi$
$150$		0			0
$151$	107.704			0.713271			0.356636	−	0.934244i	$-0.383924\pi$
$151$	107.704			0.713271			0.356636	+	0.934244i	$0.383924\pi$
$152$			460.445i			3.02924i
$153$		0			0
$154$	−134.474	+	360.545i	−0.873205	+	2.34120i
$155$	94.8949			0.612225
$156$		0			0
$157$			76.1684i			0.485149i	0.970133	+	0.242575i	$0.0779919\pi$
$157$			76.1684i			0.485149i	−0.970133	+	0.242575i	$0.922008\pi$
$158$	−492.798			−3.11897
$159$		0			0
$160$		−	220.557i		−	1.37848i
$161$	−25.4066	+	68.1191i	−0.157805	+	0.423100i
$162$		0			0
$163$	10.4287			0.0639800			0.0319900	−	0.999488i	$-0.489816\pi$
$163$	10.4287			0.0639800			0.0319900	+	0.999488i	$0.489816\pi$
$164$			301.743i			1.83989i
$165$		0			0
$166$			162.421i			0.978439i
$167$		−	75.7598i		−	0.453652i	−0.973935	−	0.226826i	$-0.927165\pi$
$167$		−	75.7598i		−	0.453652i	0.973935	−	0.226826i	$-0.0728348\pi$
$168$		0			0
$169$	−118.055			−0.698552
$170$	−110.674			−0.651025
$171$		0			0
$172$	−61.2361			−0.356024
$173$			325.843i			1.88349i	0.336333	+	0.941743i	$0.390813\pi$
$173$			325.843i			1.88349i	−0.336333	+	0.941743i	$0.609187\pi$
$174$		0			0
$175$	−12.2310	+	32.7933i	−0.0698916	+	0.187390i
$176$	−748.822			−4.25467
$177$		0			0
$178$		−	97.1424i		−	0.545744i
$179$	30.9215			0.172746			0.0863728	−	0.996263i	$-0.472472\pi$
$179$	30.9215			0.172746			0.0863728	+	0.996263i	$0.472472\pi$
$180$		0			0
$181$		−	211.403i		−	1.16797i	−0.811764	−	0.583985i	$-0.801493\pi$
$181$		−	211.403i		−	1.16797i	0.811764	−	0.583985i	$-0.198507\pi$
$182$	422.773	+	157.683i	2.32293	+	0.866390i
$183$		0			0
$184$	−255.860			−1.39054
$185$		−	64.2723i		−	0.347418i
$186$		0			0
$187$			187.970i			1.00519i
$188$		−	110.001i		−	0.585112i
$189$		0			0
$190$	159.010			0.836892
$191$	−112.093			−0.586874			−0.293437	−	0.955978i	$-0.594799\pi$
$191$	−112.093			−0.586874			−0.293437	+	0.955978i	$0.594799\pi$
$192$		0			0
$193$	−293.541			−1.52094			−0.760470	−	0.649373i	$-0.775031\pi$
$193$	−293.541			−1.52094			−0.760470	+	0.649373i	$0.775031\pi$
$194$			109.310i			0.563453i
$195$		0			0
$196$	−387.912	−	336.118i	−1.97914	−	1.71489i
$197$	90.7583			0.460702			0.230351	−	0.973108i	$-0.426013\pi$
$197$	90.7583			0.460702			0.230351	+	0.973108i	$0.426013\pi$
$198$		0			0
$199$		−	389.421i		−	1.95689i	−0.206505	−	0.978445i	$-0.566209\pi$
$199$		−	389.421i		−	1.95689i	0.206505	−	0.978445i	$-0.433791\pi$
$200$	−123.174			−0.615869
$201$		0			0
$202$			47.4086i			0.234696i
$203$	33.5788	−	90.0301i	0.165413	−	0.443498i
$204$		0			0
$205$	64.4122			0.314206
$206$		−	146.399i		−	0.710676i
$207$		0			0
$208$			878.064i			4.22146i
$209$		−	270.062i		−	1.29216i
$210$		0			0
$211$	−21.1049			−0.100023			−0.0500115	−	0.998749i	$-0.515926\pi$
$211$	−21.1049			−0.100023			−0.0500115	+	0.998749i	$0.515926\pi$
$212$	−857.980			−4.04707
$213$		0			0
$214$	334.038			1.56093
$215$			13.0719i			0.0607995i
$216$		0			0
$217$	278.338	+	103.813i	1.28267	+	0.478400i
$218$	494.645			2.26901
$219$		0			0
$220$			338.434i			1.53834i
$221$	220.412			0.997340
$222$		0			0
$223$			293.039i			1.31408i	0.753857	+	0.657039i	$0.228191\pi$
$223$			293.039i			1.31408i	−0.753857	+	0.657039i	$0.771809\pi$
$224$	241.285	−	646.922i	1.07716	−	2.88805i
$225$		0			0
$226$	603.398			2.66990
$227$		−	73.9333i		−	0.325697i	−0.986651	−	0.162849i	$-0.947932\pi$
$227$		−	73.9333i		−	0.325697i	0.986651	−	0.162849i	$-0.0520682\pi$
$228$		0			0
$229$		−	233.516i		−	1.01972i	−0.860257	−	0.509860i	$-0.829697\pi$
$229$		−	233.516i		−	1.01972i	0.860257	−	0.509860i	$-0.170303\pi$
$230$			88.3583i			0.384167i
$231$		0			0
$232$	338.159			1.45758
$233$	385.429			1.65420			0.827101	−	0.562054i	$-0.189989\pi$
$233$	385.429			1.65420			0.827101	+	0.562054i	$0.189989\pi$
$234$		0			0
$235$	−23.4816			−0.0999218
$236$		−	368.384i		−	1.56095i
$237$		0			0
$238$	−324.621	−	121.075i	−1.36396	−	0.508719i
$239$	−407.373			−1.70449			−0.852244	−	0.523144i	$-0.824759\pi$
$239$	−407.373			−1.70449			−0.852244	+	0.523144i	$0.824759\pi$
$240$		0			0
$241$		−	271.816i		−	1.12787i	−0.825820	−	0.563934i	$-0.809287\pi$
$241$		−	271.816i		−	1.12787i	0.825820	−	0.563934i	$-0.190713\pi$
$242$	333.933			1.37989
$243$		0			0
$244$		−	717.355i		−	2.93998i
$245$	−71.7502	+	82.8064i	−0.292858	+	0.337985i
$246$		0			0
$247$	−316.673			−1.28208
$248$			1045.46i			4.21555i
$249$		0			0
$250$			42.5367i			0.170147i
$251$			442.250i			1.76195i	0.473162	+	0.880976i	$0.343113\pi$
$251$			442.250i			1.76195i	−0.473162	+	0.880976i	$0.656887\pi$
$252$		0			0
$253$	150.068			0.593154
$254$	163.843			0.645049
$255$		0			0
$256$	258.395			1.00935
$257$			390.436i			1.51921i	0.650386	+	0.759604i	$0.274607\pi$
$257$			390.436i			1.51921i	−0.650386	+	0.759604i	$0.725393\pi$
$258$		0			0
$259$	70.3124	−	188.519i	0.271476	−	0.727871i
$260$	396.846			1.52633
$261$		0			0
$262$			2.61274i			0.00997228i
$263$	1.63279			0.00620832			0.00310416	−	0.999995i	$-0.499012\pi$
$263$	1.63279			0.00620832			0.00310416	+	0.999995i	$0.499012\pi$
$264$		0			0
$265$			183.151i			0.691134i
$266$	466.395	+	173.953i	1.75336	+	0.653957i
$267$		0			0
$268$	497.182			1.85516
$269$		−	410.340i		−	1.52543i	−0.646737	−	0.762713i	$-0.723867\pi$
$269$		−	410.340i		−	1.52543i	0.646737	−	0.762713i	$-0.276133\pi$
$270$		0			0
$271$			470.030i			1.73443i	0.497937	+	0.867213i	$0.334091\pi$
$271$			470.030i			1.73443i	−0.497937	+	0.867213i	$0.665909\pi$
$272$		−	674.211i		−	2.47872i
$273$		0			0
$274$	−289.943			−1.05818
$275$	72.2445			0.262707
$276$		0			0
$277$	366.582			1.32340			0.661701	−	0.749768i	$-0.269835\pi$
$277$	366.582			1.32340			0.661701	+	0.749768i	$0.269835\pi$
$278$		−	186.595i		−	0.671204i
$279$		0			0
$280$	−361.284	−	134.749i	−1.29030	−	0.481247i
$281$	−10.1164			−0.0360015			−0.0180008	−	0.999838i	$-0.505730\pi$
$281$	−10.1164			−0.0360015			−0.0180008	+	0.999838i	$0.505730\pi$
$282$		0			0
$283$		−	121.896i		−	0.430729i	−0.976534	−	0.215364i	$-0.930906\pi$
$283$		−	121.896i		−	0.430729i	0.976534	−	0.215364i	$-0.0690939\pi$
$284$	−499.183			−1.75769
$285$		0			0
$286$		−	931.380i		−	3.25657i
$287$	188.929	+	70.4654i	0.658289	+	0.245524i
$288$		0			0
$289$	119.759			0.414391
$290$		−	116.780i		−	0.402688i
$291$		0			0
$292$		−	1319.50i		−	4.51884i
$293$		−	292.803i		−	0.999327i	−0.866220	−	0.499663i	$-0.833457\pi$
$293$		−	292.803i		−	0.999327i	0.866220	−	0.499663i	$-0.166543\pi$
$294$		0			0
$295$	−78.6379			−0.266569
$296$	708.088			2.39219
$297$		0			0
$298$	922.023			3.09404
$299$		−	175.969i		−	0.588525i
$300$		0			0
$301$	−14.3003	+	38.3415i	−0.0475095	+	0.127380i
$302$	409.771			1.35686
$303$		0			0
$304$			968.662i			3.18639i
$305$	−153.132			−0.502071
$306$		0			0
$307$			167.855i			0.546758i	0.961906	+	0.273379i	$0.0881412\pi$
$307$			167.855i			0.546758i	−0.961906	+	0.273379i	$0.911859\pi$
$308$	−370.238	+	992.668i	−1.20207	+	3.22295i
$309$		0			0
$310$	361.037			1.16464
$311$		−	303.739i		−	0.976652i	−0.872661	−	0.488326i	$-0.837608\pi$
$311$		−	303.739i		−	0.976652i	0.872661	−	0.488326i	$-0.162392\pi$
$312$		0			0
$313$			17.2151i			0.0550004i	0.999622	+	0.0275002i	$0.00875470\pi$
$313$			17.2151i			0.0550004i	−0.999622	+	0.0275002i	$0.991245\pi$
$314$			289.790i			0.922899i
$315$		0			0
$316$	−1356.79			−4.29364
$317$	−82.8657			−0.261406			−0.130703	−	0.991422i	$-0.541723\pi$
$317$	−82.8657			−0.261406			−0.130703	+	0.991422i	$0.541723\pi$
$318$		0			0
$319$	−198.339			−0.621751
$320$		−	375.592i		−	1.17372i
$321$		0			0
$322$	−96.6619	+	259.166i	−0.300192	+	0.804863i
$323$	243.154			0.752799
$324$		0			0
$325$		−	84.7135i		−	0.260657i
$326$	39.6772			0.121709
$327$		0			0
$328$			709.629i			2.16350i
$329$	−68.8745	−	25.6883i	−0.209345	−	0.0780800i
$330$		0			0
$331$	−451.490			−1.36402			−0.682009	−	0.731343i	$-0.738894\pi$
$331$	−451.490			−1.36402			−0.682009	+	0.731343i	$0.738894\pi$
$332$			447.184i			1.34694i
$333$		0			0
$334$		−	288.236i		−	0.862982i
$335$		−	106.132i		−	0.316812i
$336$		0			0
$337$	204.157			0.605808			0.302904	−	0.953021i	$-0.402044\pi$
$337$	204.157			0.605808			0.302904	+	0.953021i	$0.402044\pi$
$338$	−449.153			−1.32886
$339$		0			0
$340$	−304.713			−0.896215
$341$		−	613.187i		−	1.79820i
$342$		0			0
$343$	−301.041	+	164.388i	−0.877669	+	0.479267i
$344$	−144.013			−0.418643
$345$		0			0
$346$			1239.70i			3.58296i
$347$	−146.593			−0.422458			−0.211229	−	0.977437i	$-0.567747\pi$
$347$	−146.593			−0.422458			−0.211229	+	0.977437i	$0.567747\pi$
$348$		0			0
$349$		−	11.4454i		−	0.0327947i	−0.999866	−	0.0163974i	$-0.994780\pi$
$349$		−	11.4454i		−	0.0327947i	0.999866	−	0.0163974i	$-0.00521968\pi$
$350$	−46.5342	+	124.766i	−0.132955	+	0.356473i
$351$		0			0
$352$	−1425.19			−4.04882
$353$			177.817i			0.503730i	0.967762	+	0.251865i	$0.0810439\pi$
$353$			177.817i			0.503730i	−0.967762	+	0.251865i	$0.918956\pi$
$354$		0			0
$355$			106.559i			0.300167i
$356$		−	267.457i		−	0.751283i
$357$		0			0
$358$	117.644			0.328614
$359$	−653.079			−1.81916			−0.909581	−	0.415526i	$-0.863598\pi$
$359$	−653.079			−1.81916			−0.909581	+	0.415526i	$0.863598\pi$
$360$		0			0
$361$	11.6523			0.0322780
$362$		−	804.303i		−	2.22183i
$363$		0			0
$364$	1164.00	+	434.140i	3.19779	+	1.19269i
$365$	−281.670			−0.771699
$366$		0			0
$367$			466.632i			1.27148i	0.771905	+	0.635738i	$0.219304\pi$
$367$			466.632i			1.27148i	−0.771905	+	0.635738i	$0.780696\pi$
$368$	−538.266			−1.46268
$369$		0			0
$370$		−	244.530i		−	0.660893i
$371$	−200.362	+	537.203i	−0.540060	+	1.44799i
$372$		0			0
$373$	−452.082			−1.21202			−0.606008	−	0.795459i	$-0.707230\pi$
$373$	−452.082			−1.21202			−0.606008	+	0.795459i	$0.707230\pi$
$374$			715.149i			1.91216i
$375$		0			0
$376$		−	258.697i		−	0.688024i
$377$			232.571i			0.616899i
$378$		0			0
$379$	326.478			0.861420			0.430710	−	0.902490i	$-0.358263\pi$
$379$	326.478			0.861420			0.430710	+	0.902490i	$0.358263\pi$
$380$	437.792			1.15208
$381$		0			0
$382$	−426.469			−1.11641
$383$			381.262i			0.995462i	0.867331	+	0.497731i	$0.165833\pi$
$383$			381.262i			0.995462i	−0.867331	+	0.497731i	$0.834167\pi$
$384$		0			0
$385$	211.902	+	79.0338i	0.550395	+	0.205283i
$386$	−1116.81			−2.89329
$387$		0			0
$388$			300.957i			0.775662i
$389$	68.8443			0.176978			0.0884888	−	0.996077i	$-0.471796\pi$
$389$	68.8443			0.176978			0.0884888	+	0.996077i	$0.471796\pi$
$390$		0			0
$391$			135.116i			0.345565i
$392$	−912.278	−	790.472i	−2.32724	−	2.01651i
$393$		0			0
$394$	345.299			0.876394
$395$			289.631i			0.733242i
$396$		0			0
$397$			370.531i			0.933328i	0.884435	+	0.466664i	$0.154544\pi$
$397$			370.531i			0.933328i	−0.884435	+	0.466664i	$0.845456\pi$
$398$		−	1481.59i		−	3.72259i
$399$		0			0
$400$	−259.127			−0.647819
$401$	−8.95073			−0.0223210			−0.0111605	−	0.999938i	$-0.503553\pi$
$401$	−8.95073			−0.0223210			−0.0111605	+	0.999938i	$0.503553\pi$
$402$		0			0
$403$	−719.019			−1.78417
$404$			130.528i			0.323088i
$405$		0			0
$406$	127.754	−	342.529i	0.314665	−	0.843667i
$407$	−415.311			−1.02042
$408$		0			0
$409$		−	63.1330i		−	0.154359i	−0.997017	−	0.0771797i	$-0.975408\pi$
$409$		−	63.1330i		−	0.154359i	0.997017	−	0.0771797i	$-0.0245915\pi$
$410$	245.063			0.597714
$411$		0			0
$412$		−	403.072i		−	0.978331i
$413$	−230.655	−	86.0280i	−0.558486	−	0.208300i
$414$		0			0
$415$	95.4592			0.230022
$416$			1671.17i			4.01722i
$417$		0			0
$418$		−	1027.48i		−	2.45808i
$419$			3.58774i			0.00856263i	0.999991	+	0.00428131i	$0.00136279\pi$
$419$			3.58774i			0.00856263i	−0.999991	+	0.00428131i	$0.998637\pi$
$420$		0			0
$421$	119.594			0.284071			0.142035	−	0.989862i	$-0.454635\pi$
$421$	119.594			0.284071			0.142035	+	0.989862i	$0.454635\pi$
$422$	−80.2956			−0.190274
$423$		0			0
$424$	−2017.77			−4.75889
$425$			65.0463i			0.153050i
$426$		0			0
$427$	−449.154	−	167.523i	−1.05188	−	0.392324i
$428$	919.689			2.14881
$429$		0			0
$430$			49.7334i			0.115659i
$431$	404.488			0.938488			0.469244	−	0.883069i	$-0.344527\pi$
$431$	404.488			0.938488			0.469244	+	0.883069i	$0.344527\pi$
$432$		0			0
$433$		−	116.085i		−	0.268094i	−0.990975	−	0.134047i	$-0.957203\pi$
$433$		−	116.085i		−	0.268094i	0.990975	−	0.134047i	$-0.0427974\pi$
$434$	1058.97	+	394.966i	2.44002	+	0.910060i
$435$		0			0
$436$	1361.88			3.12357
$437$		−	194.125i		−	0.444223i
$438$		0			0
$439$		−	58.4183i		−	0.133071i	−0.997784	−	0.0665357i	$-0.978805\pi$
$439$		−	58.4183i		−	0.133071i	0.997784	−	0.0665357i	$-0.0211946\pi$
$440$			795.918i			1.80890i
$441$		0			0
$442$	838.580			1.89724
$443$	−267.301			−0.603388			−0.301694	−	0.953405i	$-0.597552\pi$
$443$	−267.301			−0.603388			−0.301694	+	0.953405i	$0.597552\pi$
$444$		0			0
$445$	−57.0932			−0.128299
$446$			1114.90i			2.49977i
$447$		0			0
$448$	410.888	−	1101.66i	0.917162	−	2.45906i
$449$	−296.478			−0.660307			−0.330154	−	0.943927i	$-0.607101\pi$
$449$	−296.478			−0.660307			−0.330154	+	0.943927i	$0.607101\pi$
$450$		0			0
$451$		−	416.215i		−	0.922872i
$452$	1661.30			3.67545
$453$		0			0
$454$		−	281.287i		−	0.619574i
$455$	92.6746	−	248.475i	0.203680	−	0.546100i
$456$		0			0
$457$	12.1251			0.0265320			0.0132660	−	0.999912i	$-0.495777\pi$
$457$	12.1251			0.0265320			0.0132660	+	0.999912i	$0.495777\pi$
$458$		−	888.435i		−	1.93981i
$459$		0			0
$460$			243.272i			0.528852i
$461$		−	103.948i		−	0.225483i	−0.993624	−	0.112741i	$-0.964037\pi$
$461$		−	103.948i		−	0.225483i	0.993624	−	0.112741i	$-0.0359632\pi$
$462$		0			0
$463$	498.831			1.07739			0.538694	−	0.842501i	$-0.318918\pi$
$463$	498.831			1.07739			0.538694	+	0.842501i	$0.318918\pi$
$464$	711.403			1.53320
$465$		0			0
$466$	1466.40			3.14679
$467$			597.683i			1.27983i	0.768444	+	0.639917i	$0.221031\pi$
$467$			597.683i			1.27983i	−0.768444	+	0.639917i	$0.778969\pi$
$468$		0			0
$469$	116.106	−	311.299i	0.247561	−	0.663750i
$470$	−89.3382			−0.190081
$471$		0			0
$472$		−	866.354i		−	1.83550i
$473$	84.4673			0.178578
$474$		0			0
$475$		−	93.4542i		−	0.196746i
$476$	−893.762	−	333.349i	−1.87765	−	0.700313i
$477$		0			0
$478$	−1549.89			−3.24245
$479$		−	276.703i		−	0.577669i	−0.957379	−	0.288834i	$-0.906732\pi$
$479$		−	276.703i		−	0.577669i	0.957379	−	0.288834i	$-0.0932677\pi$
$480$		0			0
$481$			486.992i			1.01246i
$482$		−	1034.15i		−	2.14554i
$483$		0			0
$484$	919.399			1.89958
$485$	64.2444			0.132463
$486$		0			0
$487$	−542.653			−1.11428			−0.557138	−	0.830420i	$-0.688101\pi$
$487$	−542.653			−1.11428			−0.557138	+	0.830420i	$0.688101\pi$
$488$		−	1687.05i		−	3.45708i
$489$		0			0
$490$	−272.981	+	315.045i	−0.557104	+	0.642950i
$491$	−574.817			−1.17071			−0.585353	−	0.810778i	$-0.699044\pi$
$491$	−574.817			−1.17071			−0.585353	+	0.810778i	$0.699044\pi$
$492$		0			0
$493$		−	178.577i		−	0.362225i
$494$	−1204.82			−2.43890
$495$		0			0
$496$			2199.38i			4.43424i
$497$	−116.573	+	312.552i	−0.234554	+	0.628877i
$498$		0			0
$499$	−549.967			−1.10214			−0.551070	−	0.834459i	$-0.685780\pi$
$499$	−549.967			−1.10214			−0.551070	+	0.834459i	$0.685780\pi$
$500$			117.114i			0.234228i
$501$		0			0
$502$			1682.58i			3.35176i
$503$			397.053i			0.789369i	0.918817	+	0.394685i	$0.129146\pi$
$503$			397.053i			0.789369i	−0.918817	+	0.394685i	$0.870854\pi$
$504$		0			0
$505$	27.8634			0.0551750
$506$	570.949			1.12836
$507$		0			0
$508$	451.098			0.887989
$509$			557.813i			1.09590i	0.836511	+	0.547950i	$0.184592\pi$
$509$			557.813i			1.09590i	−0.836511	+	0.547950i	$0.815408\pi$
$510$		0			0
$511$	−826.174	−	308.141i	−1.61678	−	0.603015i
$512$	5.03806			0.00983995
$513$		0			0
$514$			1485.45i			2.88999i
$515$	−86.0428			−0.167073
$516$		0			0
$517$			151.732i			0.293486i
$518$	267.511	−	717.238i	0.516430	−	1.38463i
$519$		0			0
$520$	933.289			1.79479
$521$		−	287.300i		−	0.551439i	−0.961238	−	0.275719i	$-0.911084\pi$
$521$		−	287.300i		−	0.551439i	0.961238	−	0.275719i	$-0.0889161\pi$
$522$		0			0
$523$		−	1012.28i		−	1.93553i	−0.251853	−	0.967766i	$-0.581040\pi$
$523$		−	1012.28i		−	1.93553i	0.251853	−	0.967766i	$-0.418960\pi$
$524$			7.19350i			0.0137281i
$525$		0			0
$526$	6.21211			0.0118101
$527$	552.091			1.04761
$528$		0			0
$529$	−421.128			−0.796084
$530$			696.815i			1.31475i
$531$		0			0
$532$	1284.10	+	478.934i	2.41372	+	0.900252i
$533$	−488.051			−0.915669
$534$		0			0
$535$		−	196.323i		−	0.366960i
$536$	1169.26			2.18145
$537$		0			0
$538$		−	1561.18i		−	2.90182i
$539$	535.074	+	463.632i	0.992716	+	0.860170i
$540$		0			0
$541$	526.853			0.973851			0.486925	−	0.873444i	$-0.338118\pi$
$541$	526.853			0.973851			0.486925	+	0.873444i	$0.338118\pi$
$542$			1788.28i			3.29940i
$543$		0			0
$544$		−	1283.19i		−	2.35880i
$545$		−	290.716i		−	0.533424i
$546$		0			0
$547$	−250.549			−0.458042			−0.229021	−	0.973421i	$-0.573553\pi$
$547$	−250.549			−0.458042			−0.229021	+	0.973421i	$0.573553\pi$
$548$	−798.282			−1.45672
$549$		0			0
$550$	274.862			0.499748
$551$			256.567i			0.465640i
$552$		0			0
$553$	−316.849	+	849.522i	−0.572964	+	1.53621i
$554$	1394.70			2.51751
$555$		0			0
$556$		−	513.741i		−	0.923994i
$557$	64.1496			0.115170			0.0575849	−	0.998341i	$-0.481660\pi$
$557$	64.1496			0.115170			0.0575849	+	0.998341i	$0.481660\pi$
$558$		0			0
$559$		−	99.0459i		−	0.177184i
$560$	−760.053	−	283.479i	−1.35724	−	0.506213i
$561$		0			0
$562$	−38.4890			−0.0684857
$563$		−	17.3869i		−	0.0308826i	−0.999881	−	0.0154413i	$-0.995085\pi$
$563$		−	17.3869i		−	0.0308826i	0.999881	−	0.0154413i	$-0.00491531\pi$
$564$		0			0
$565$		−	354.634i		−	0.627670i
$566$		−	463.767i		−	0.819376i
$567$		0			0
$568$	−1173.96			−2.06684
$569$	−174.914			−0.307405			−0.153703	−	0.988117i	$-0.549120\pi$
$569$	−174.914			−0.307405			−0.153703	+	0.988117i	$0.549120\pi$
$570$		0			0
$571$	−376.637			−0.659609			−0.329805	−	0.944049i	$-0.606983\pi$
$571$	−376.637			−0.659609			−0.329805	+	0.944049i	$0.606983\pi$
$572$		−	2564.32i		−	4.48307i
$573$		0			0
$574$	718.799	+	268.093i	1.25226	+	0.467060i
$575$	51.9306			0.0903141
$576$		0			0
$577$		−	448.775i		−	0.777773i	−0.921286	−	0.388886i	$-0.872860\pi$
$577$		−	448.775i		−	0.777773i	0.921286	−	0.388886i	$-0.127140\pi$
$578$	455.636			0.788297
$579$		0			0
$580$		−	321.522i		−	0.554349i
$581$	279.994	+	104.430i	0.481917	+	0.179742i
$582$		0			0
$583$	1183.47			2.02997
$584$		−	3103.16i		−	5.31363i
$585$		0			0
$586$		−	1114.00i		−	1.90102i
$587$			275.916i			0.470044i	0.971990	+	0.235022i	$0.0755162\pi$
$587$			275.916i			0.470044i	−0.971990	+	0.235022i	$0.924484\pi$
$588$		0			0
$589$	−793.207			−1.34670
$590$	−299.186			−0.507095
$591$		0			0
$592$	1489.64			2.51629
$593$			893.938i			1.50748i	0.657171	+	0.753742i	$0.271753\pi$
$593$			893.938i			1.50748i	−0.657171	+	0.753742i	$0.728247\pi$
$594$		0			0
$595$	−71.1591	+	190.789i	−0.119595	+	0.320654i
$596$	2538.55			4.25932
$597$		0			0
$598$		−	669.492i		−	1.11955i
$599$	122.407			0.204352			0.102176	−	0.994766i	$-0.467419\pi$
$599$	122.407			0.204352			0.102176	+	0.994766i	$0.467419\pi$
$600$		0			0
$601$			594.921i			0.989885i	0.868926	+	0.494943i	$0.164811\pi$
$601$			594.921i			0.989885i	−0.868926	+	0.494943i	$0.835189\pi$
$602$	−54.4071	+	145.874i	−0.0903773	+	0.242316i
$603$		0			0
$604$	1128.20			1.86788
$605$		−	196.262i		−	0.324399i
$606$		0			0
$607$			539.772i			0.889246i	0.895718	+	0.444623i	$0.146662\pi$
$607$			539.772i			0.889246i	−0.895718	+	0.444623i	$0.853338\pi$
$608$			1843.60i			3.03223i
$609$		0			0
$610$	−582.605			−0.955091
$611$	177.920			0.291195
$612$		0			0
$613$	1180.07			1.92508			0.962540	−	0.271140i	$-0.0874006\pi$
$613$	1180.07			1.92508			0.962540	+	0.271140i	$0.0874006\pi$
$614$			638.620i			1.04010i
$615$		0			0
$616$	−870.715	+	2334.53i	−1.41350	+	3.78982i
$617$	777.688			1.26043			0.630217	−	0.776419i	$-0.282966\pi$
$617$	777.688			1.26043			0.630217	+	0.776419i	$0.282966\pi$
$618$		0			0
$619$		−	285.107i		−	0.460592i	−0.973121	−	0.230296i	$-0.926030\pi$
$619$		−	285.107i		−	0.460592i	0.973121	−	0.230296i	$-0.0739695\pi$
$620$	994.023			1.60326
$621$		0			0
$622$		−	1155.60i		−	1.85789i
$623$	−167.462	−	62.4586i	−0.268799	−	0.100255i
$624$		0			0
$625$	25.0000			0.0400000
$626$			65.4967i			0.104627i
$627$		0			0
$628$			797.863i			1.27048i
$629$		−	373.931i		−	0.594485i
$630$		0			0
$631$	506.946			0.803401			0.401700	−	0.915771i	$-0.368419\pi$
$631$	506.946			0.803401			0.401700	+	0.915771i	$0.368419\pi$
$632$	−3190.86			−5.04883
$633$		0			0
$634$	−315.271			−0.497273
$635$		−	96.2947i		−	0.151645i
$636$		0			0
$637$	543.652	−	627.425i	0.853457	−	0.984969i
$638$	−754.600			−1.18276
$639$		0			0
$640$		−	546.747i		−	0.854293i
$641$	−537.896			−0.839152			−0.419576	−	0.907720i	$-0.637821\pi$
$641$	−537.896			−0.839152			−0.419576	+	0.907720i	$0.637821\pi$
$642$		0			0
$643$			673.330i			1.04717i	0.851973	+	0.523585i	$0.175406\pi$
$643$			673.330i			1.04717i	−0.851973	+	0.523585i	$0.824594\pi$
$644$	−266.134	+	713.547i	−0.413251	+	1.10799i
$645$		0			0
$646$	925.104			1.43205
$647$		−	1082.21i		−	1.67266i	−0.548224	−	0.836332i	$-0.684696\pi$
$647$		−	1082.21i		−	1.67266i	0.548224	−	0.836332i	$-0.315304\pi$
$648$		0			0
$649$			508.138i			0.782956i
$650$		−	322.301i		−	0.495848i
$651$		0			0
$652$	109.241			0.167547
$653$	491.429			0.752571			0.376285	−	0.926504i	$-0.377201\pi$
$653$	491.429			0.752571			0.376285	+	0.926504i	$0.377201\pi$
$654$		0			0
$655$	1.53558			0.00234439
$656$			1492.88i			2.27574i
$657$		0			0
$658$	−262.040	−	97.7339i	−0.398237	−	0.148532i
$659$	−248.373			−0.376893			−0.188447	−	0.982083i	$-0.560345\pi$
$659$	−248.373			−0.376893			−0.188447	+	0.982083i	$0.560345\pi$
$660$		0			0
$661$		−	681.545i		−	1.03108i	−0.856865	−	0.515541i	$-0.827591\pi$
$661$		−	681.545i		−	1.03108i	0.856865	−	0.515541i	$-0.172409\pi$
$662$	−1717.74			−2.59477
$663$		0			0
$664$			1051.67i			1.58385i
$665$	102.237	−	274.113i	0.153739	−	0.412200i
$666$		0			0
$667$	−142.569			−0.213747
$668$		−	793.584i		−	1.18800i
$669$		0			0
$670$		−	403.791i		−	0.602672i
$671$			989.499i			1.47466i
$672$		0			0
$673$	86.1498			0.128009			0.0640043	−	0.997950i	$-0.479613\pi$
$673$	86.1498			0.128009			0.0640043	+	0.997950i	$0.479613\pi$
$674$	776.737			1.15243
$675$		0			0
$676$	−1236.63			−1.82933
$677$		−	793.846i		−	1.17259i	−0.810096	−	0.586297i	$-0.800585\pi$
$677$		−	793.846i		−	1.17259i	0.810096	−	0.586297i	$-0.199415\pi$
$678$		0			0
$679$	188.437	+	70.2819i	0.277521	+	0.103508i
$680$	−716.615			−1.05385
$681$		0			0
$682$		−	2332.93i		−	3.42072i
$683$	186.736			0.273406			0.136703	−	0.990612i	$-0.456349\pi$
$683$	186.736			0.273406			0.136703	+	0.990612i	$0.456349\pi$
$684$		0			0
$685$			170.407i			0.248770i
$686$	−1145.34	+	625.433i	−1.66959	+	0.911709i
$687$		0			0
$688$	−302.968			−0.440361
$689$		−	1387.73i		−	2.01413i
$690$		0			0
$691$			1030.46i			1.49126i	0.666361	+	0.745630i	$0.267851\pi$
$691$			1030.46i			1.49126i	−0.666361	+	0.745630i	$0.732149\pi$
$692$			3413.20i			4.93238i
$693$		0			0
$694$	−557.727			−0.803642
$695$	−109.667			−0.157794
$696$		0			0
$697$	374.745			0.537654
$698$		−	43.5450i		−	0.0623854i
$699$		0			0
$700$	−128.120	+	343.510i	−0.183028	+	0.490728i
$701$	1143.88			1.63179			0.815893	−	0.578203i	$-0.196246\pi$
$701$	1143.88			1.63179			0.815893	+	0.578203i	$0.196246\pi$
$702$		0			0
$703$			537.239i			0.764210i
$704$	−2426.98			−3.44741
$705$		0			0
$706$			676.521i			0.958246i
$707$	81.7267	+	30.4818i	0.115596	+	0.0431143i
$708$		0			0
$709$	−316.757			−0.446766			−0.223383	−	0.974731i	$-0.571710\pi$
$709$	−316.757			−0.446766			−0.223383	+	0.974731i	$0.571710\pi$
$710$			405.416i			0.571008i
$711$		0			0
$712$		−	628.996i		−	0.883422i
$713$		−	440.769i		−	0.618190i
$714$		0			0
$715$	−547.397			−0.765591
$716$	323.902			0.452377
$717$		0			0
$718$	−2484.71			−3.46059
$719$		−	1145.95i		−	1.59381i	−0.604104	−	0.796906i	$-0.706469\pi$
$719$		−	1145.95i		−	1.59381i	0.604104	−	0.796906i	$-0.293531\pi$
$720$		0			0
$721$	−252.374	−	94.1288i	−0.350034	−	0.130553i
$722$	44.3325			0.0614024
$723$		0			0
$724$		−	2214.44i		−	3.05862i
$725$	−68.6345			−0.0946683
$726$		0			0
$727$			149.829i			0.206093i	0.994677	+	0.103046i	$0.0328590\pi$
$727$			149.829i			0.206093i	−0.994677	+	0.103046i	$0.967141\pi$
$728$	2737.45	+	1021.00i	3.76024	+	1.40247i
$729$		0			0
$730$	−1071.64			−1.46800
$731$			76.0512i			0.104037i
$732$		0			0
$733$			70.3231i			0.0959388i	0.998849	+	0.0479694i	$0.0152750\pi$
$733$			70.3231i			0.0959388i	−0.998849	+	0.0479694i	$0.984725\pi$
$734$			1775.35i			2.41873i
$735$		0			0
$736$	−1024.45			−1.39191
$737$	−685.799			−0.930528
$738$		0			0
$739$	774.145			1.04756			0.523779	−	0.851854i	$-0.324522\pi$
$739$	774.145			1.04756			0.523779	+	0.851854i	$0.324522\pi$
$740$		−	673.252i		−	0.909800i
$741$		0			0
$742$	−762.299	+	2043.84i	−1.02736	+	2.75451i
$743$	−1071.79			−1.44252			−0.721260	−	0.692665i	$-0.756437\pi$
$743$	−1071.79			−1.44252			−0.721260	+	0.692665i	$0.756437\pi$
$744$		0			0
$745$		−	541.898i		−	0.727380i
$746$	−1719.99			−2.30562
$747$		0			0
$748$			1968.98i			2.63233i
$749$	214.773	−	575.841i	0.286747	−	0.768813i
$750$		0			0
$751$	361.789			0.481742			0.240871	−	0.970557i	$-0.422567\pi$
$751$	361.789			0.481742			0.240871	+	0.970557i	$0.422567\pi$
$752$		−	544.235i		−	0.723717i
$753$		0			0
$754$			884.839i			1.17353i
$755$		−	240.833i		−	0.318985i
$756$		0			0
$757$	812.552			1.07338			0.536692	−	0.843778i	$-0.319674\pi$
$757$	812.552			1.07338			0.536692	+	0.843778i	$0.319674\pi$
$758$	1242.12			1.63868
$759$		0			0
$760$	1029.59			1.35472
$761$		−	728.812i		−	0.957703i	−0.877896	−	0.478851i	$-0.841053\pi$
$761$		−	728.812i		−	0.957703i	0.877896	−	0.478851i	$-0.158947\pi$
$762$		0			0
$763$	318.036	−	852.706i	0.416824	−	1.11757i
$764$	−1174.17			−1.53688
$765$		0			0
$766$			1450.55i			1.89367i
$767$	595.840			0.776845
$768$		0			0
$769$			624.378i			0.811935i	0.913888	+	0.405967i	$0.133065\pi$
$769$			624.378i			0.811935i	−0.913888	+	0.405967i	$0.866935\pi$
$770$	806.203	+	300.692i	1.04702	+	0.390509i
$771$		0			0
$772$	−3074.84			−3.98296
$773$			34.6106i			0.0447744i	0.999749	+	0.0223872i	$0.00712666\pi$
$773$			34.6106i			0.0447744i	−0.999749	+	0.0223872i	$0.992873\pi$
$774$		0			0
$775$		−	212.191i		−	0.273795i
$776$			707.781i			0.912089i
$777$		0			0
$778$	261.925			0.336665
$779$	−538.408			−0.691153
$780$		0			0
$781$	688.559			0.881638
$782$			514.062i			0.657368i
$783$		0			0
$784$	−1919.21	−	1662.96i	−2.44797	−	2.12112i
$785$	170.318			0.216965
$786$		0			0
$787$		−	563.953i		−	0.716586i	−0.933609	−	0.358293i	$-0.883359\pi$
$787$		−	563.953i		−	0.716586i	0.933609	−	0.358293i	$-0.116641\pi$
$788$	950.692			1.20646
$789$		0			0
$790$			1101.93i			1.39485i
$791$	387.961	−	1040.18i	0.490469	−	1.31502i
$792$		0			0
$793$	1160.28			1.46315
$794$			1409.72i			1.77547i
$795$		0			0
$796$		−	4079.18i		−	5.12460i
$797$			887.777i			1.11390i	0.830546	+	0.556949i	$0.188028\pi$
$797$			887.777i			1.11390i	−0.830546	+	0.556949i	$0.811972\pi$
$798$		0			0
$799$	−136.614			−0.170981
$800$	−493.181			−0.616477
$801$		0			0
$802$	−34.0540			−0.0424613
$803$			1820.08i			2.26660i
$804$		0			0
$805$	152.319	+	56.8108i	0.189216	+	0.0705725i
$806$	−2735.58			−3.39402
$807$		0			0
$808$			306.971i			0.379914i
$809$	1338.15			1.65408			0.827041	−	0.562142i	$-0.190023\pi$
$809$	1338.15			1.65408			0.827041	+	0.562142i	$0.190023\pi$
$810$		0			0
$811$		−	1002.03i		−	1.23555i	−0.786353	−	0.617777i	$-0.788033\pi$
$811$		−	1002.03i		−	1.23555i	0.786353	−	0.617777i	$-0.211967\pi$
$812$	351.738	−	943.065i	0.433175	−	1.16141i
$813$		0			0
$814$	−1580.09			−1.94115
$815$		−	23.3194i		−	0.0286127i
$816$		0			0
$817$		−	109.265i		−	0.133740i
$818$		−	240.196i		−	0.293638i
$819$		0			0
$820$	674.717			0.822825
$821$	519.980			0.633349			0.316675	−	0.948534i	$-0.397434\pi$
$821$	519.980			0.633349			0.316675	+	0.948534i	$0.397434\pi$
$822$		0			0
$823$	−35.2676			−0.0428524			−0.0214262	−	0.999770i	$-0.506821\pi$
$823$	−35.2676			−0.0428524			−0.0214262	+	0.999770i	$0.506821\pi$
$824$		−	947.933i		−	1.15040i
$825$		0			0
$826$	−877.550	−	327.302i	−1.06241	−	0.396250i
$827$	1047.83			1.26703			0.633514	−	0.773731i	$-0.281612\pi$
$827$	1047.83			1.26703			0.633514	+	0.773731i	$0.281612\pi$
$828$		0			0
$829$			125.947i			0.151926i	0.997111	+	0.0759632i	$0.0242031\pi$
$829$			125.947i			0.151926i	−0.997111	+	0.0759632i	$0.975797\pi$
$830$	363.184			0.437571
$831$		0			0
$832$			2845.86i			3.42051i
$833$	−417.437	+	481.761i	−0.501125	+	0.578345i
$834$		0			0
$835$	−169.404			−0.202879
$836$		−	2828.90i		−	3.38385i
$837$		0			0
$838$			13.6499i			0.0162887i
$839$		−	456.709i		−	0.544349i	−0.962248	−	0.272174i	$-0.912257\pi$
$839$		−	456.709i		−	0.544349i	0.962248	−	0.272174i	$-0.0877427\pi$
$840$		0			0
$841$	−652.572			−0.775948
$842$	455.007			0.540388
$843$		0			0
$844$	−221.073			−0.261935
$845$			263.980i			0.312402i
$846$		0			0
$847$	214.706	−	575.660i	0.253489	−	0.679645i
$848$	−4244.89			−5.00577
$849$		0			0
$850$			247.475i			0.291147i
$851$	−298.533			−0.350802
$852$		0			0
$853$			815.418i			0.955941i	0.878376	+	0.477971i	$0.158627\pi$
$853$			815.418i			0.955941i	−0.878376	+	0.477971i	$0.841373\pi$
$854$	−1708.85	−	637.356i	−2.00100	−	0.746319i
$855$		0			0
$856$	2162.90			2.52675
$857$		−	609.807i		−	0.711560i	−0.934570	−	0.355780i	$-0.884215\pi$
$857$		−	609.807i		−	0.711560i	0.934570	−	0.355780i	$-0.115785\pi$
$858$		0			0
$859$		−	136.971i		−	0.159454i	−0.996817	−	0.0797272i	$-0.974595\pi$
$859$		−	136.971i		−	0.159454i	0.996817	−	0.0797272i	$-0.0254049\pi$
$860$			136.928i			0.159219i
$861$		0			0
$862$	1538.92			1.78529
$863$	−305.240			−0.353696			−0.176848	−	0.984238i	$-0.556590\pi$
$863$	−305.240			−0.353696			−0.176848	+	0.984238i	$0.556590\pi$
$864$		0			0
$865$	728.607			0.842321
$866$		−	441.657i		−	0.509996i
$867$		0			0
$868$	2915.59	+	1087.44i	3.35898	+	1.25281i
$869$	1871.52			2.15365
$870$		0			0
$871$			804.164i			0.923266i
$872$	3202.82			3.67296
$873$		0			0
$874$		−	738.570i		−	0.845045i
$875$	73.3281	+	27.3494i	0.0838035	+	0.0312565i
$876$		0			0
$877$	621.320			0.708461			0.354231	−	0.935158i	$-0.384743\pi$
$877$	621.320			0.708461			0.354231	+	0.935158i	$0.384743\pi$
$878$		−	222.258i		−	0.253142i
$879$		0			0
$880$			1674.42i			1.90275i
$881$			739.549i			0.839443i	0.907653	+	0.419721i	$0.137872\pi$
$881$			739.549i			0.839443i	−0.907653	+	0.419721i	$0.862128\pi$
$882$		0			0
$883$	643.821			0.729129			0.364564	−	0.931178i	$-0.381218\pi$
$883$	643.821			0.729129			0.364564	+	0.931178i	$0.381218\pi$
$884$	2308.82			2.61178
$885$		0			0
$886$	−1016.97			−1.14782
$887$		−	926.753i		−	1.04482i	−0.852695	−	0.522409i	$-0.825034\pi$
$887$		−	926.753i		−	1.04482i	0.852695	−	0.522409i	$-0.174966\pi$
$888$		0			0
$889$	105.344	−	282.444i	0.118497	−	0.317710i
$890$	−217.217			−0.244064
$891$		0			0
$892$			3069.58i			3.44124i
$893$	196.278			0.219796
$894$		0			0
$895$		−	69.1425i		−	0.0772542i
$896$	598.128	−	1603.68i	0.667554	−	1.78982i
$897$		0			0
$898$	−1127.98			−1.25610
$899$			582.546i			0.647994i
$900$		0			0
$901$			1065.56i			1.18264i
$902$		−	1583.53i		−	1.75558i
$903$		0			0
$904$	3907.00			4.32190
$905$	−472.711			−0.522332
$906$		0			0
$907$	−1540.97			−1.69898			−0.849489	−	0.527607i	$-0.823090\pi$
$907$	−1540.97			−1.69898			−0.849489	+	0.527607i	$0.823090\pi$
$908$		−	774.450i		−	0.852919i
$909$		0			0
$910$	352.590	−	945.349i	0.387461	−	1.03885i
$911$	1187.49			1.30350			0.651748	−	0.758435i	$-0.274036\pi$
$911$	1187.49			1.30350			0.651748	+	0.758435i	$0.274036\pi$
$912$		0			0
$913$		−	616.833i		−	0.675611i
$914$	46.1312			0.0504718
$915$		0			0
$916$		−	2446.08i		−	2.67039i
$917$	4.50404	+	1.67988i	0.00491171	+	0.00183194i
$918$		0			0
$919$	223.009			0.242665			0.121333	−	0.992612i	$-0.461283\pi$
$919$	223.009			0.242665			0.121333	+	0.992612i	$0.461283\pi$
$920$			572.120i			0.621869i
$921$		0			0
$922$		−	395.479i		−	0.428936i
$923$		−	807.401i		−	0.874757i
$924$		0			0
$925$	−143.717			−0.155370
$926$	1897.85			2.04952
$927$		0			0
$928$	1353.97			1.45902
$929$			1482.17i			1.59545i	0.603024	+	0.797723i	$0.293962\pi$
$929$			1482.17i			1.59545i	−0.603024	+	0.797723i	$0.706038\pi$
$930$		0			0
$931$	599.746	−	692.162i	0.644195	−	0.743461i
$932$	4037.36			4.33194
$933$		0			0
$934$			2273.95i			2.43463i
$935$	420.313			0.449532
$936$		0			0
$937$		−	836.508i		−	0.892751i	−0.894846	−	0.446376i	$-0.852715\pi$
$937$		−	836.508i		−	0.892751i	0.894846	−	0.446376i	$-0.147285\pi$
$938$	441.737	−	1184.37i	0.470935	−	1.26265i
$939$		0			0
$940$	−245.970			−0.261670
$941$			1637.85i			1.74055i	0.492569	+	0.870273i	$0.336058\pi$
$941$			1637.85i			1.74055i	−0.492569	+	0.870273i	$0.663942\pi$
$942$		0			0
$943$		−	299.183i		−	0.317267i
$944$		−	1822.60i		−	1.93072i
$945$		0			0
$946$	321.364			0.339709
$947$	−748.381			−0.790265			−0.395133	−	0.918624i	$-0.629301\pi$
$947$	−748.381			−0.790265			−0.395133	+	0.918624i	$0.629301\pi$
$948$		0			0
$949$	2134.22			2.24891
$950$		−	355.556i		−	0.374270i
$951$		0			0
$952$	−2101.92	−	783.960i	−2.20790	−	0.823487i
$953$	942.124			0.988588			0.494294	−	0.869295i	$-0.335427\pi$
$953$	942.124			0.988588			0.494294	+	0.869295i	$0.335427\pi$
$954$		0			0
$955$			250.648i			0.262458i
$956$	−4267.23			−4.46362
$957$		0			0
$958$		−	1052.75i		−	1.09890i
$959$	−186.421	+	499.825i	−0.194391	+	0.521194i
$960$		0			0
$961$	−840.008			−0.874098
$962$			1852.81i			1.92600i
$963$		0			0
$964$		−	2847.27i		−	2.95360i
$965$			656.379i			0.680185i
$966$		0			0
$967$	−1654.90			−1.71138			−0.855690	−	0.517489i	$-0.826867\pi$
$967$	−1654.90			−1.71138			−0.855690	+	0.517489i	$0.826867\pi$
$968$	2162.21			2.23369
$969$		0			0
$970$	244.424			0.251984
$971$		−	354.436i		−	0.365022i	−0.983204	−	0.182511i	$-0.941578\pi$
$971$		−	354.436i		−	0.365022i	0.983204	−	0.182511i	$-0.0584224\pi$
$972$		0			0
$973$	−321.666	−	119.973i	−0.330592	−	0.123302i
$974$	−2064.58			−2.11969
$975$		0			0
$976$		−	3549.14i		−	3.63642i
$977$	−1726.63			−1.76727			−0.883637	−	0.468173i	$-0.844912\pi$
$977$	−1726.63			−1.76727			−0.883637	+	0.468173i	$0.844912\pi$
$978$		0			0
$979$			368.922i			0.376836i
$980$	−751.583	+	867.397i	−0.766922	+	0.885099i
$981$		0			0
$982$	−2186.95			−2.22704
$983$			1635.34i			1.66362i	0.555062	+	0.831809i	$0.312694\pi$
$983$			1635.34i			1.66362i	−0.555062	+	0.831809i	$0.687306\pi$
$984$		0			0
$985$		−	202.942i		−	0.206032i
$986$		−	679.414i		−	0.689061i
$987$		0			0
$988$	−3317.15			−3.35744
$989$	60.7165			0.0613919
$990$		0			0
$991$	−313.579			−0.316427			−0.158213	−	0.987405i	$-0.550573\pi$
$991$	−313.579			−0.316427			−0.158213	+	0.987405i	$0.550573\pi$
$992$			4185.95i			4.21971i
$993$		0			0
$994$	−443.515	+	1189.13i	−0.446192	+	1.19631i
$995$	−870.772			−0.875148
$996$		0			0
$997$		−	17.3708i		−	0.0174231i	−0.999962	−	0.00871155i	$-0.997227\pi$
$997$		−	17.3708i		−	0.0174231i	0.999962	−	0.00871155i	$-0.00277301\pi$
$998$	−2092.41			−2.09660
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.h.d.181.11		12
3.2	odd	2		105.3.h.a.76.2	yes	12
7.6	odd	2	inner	315.3.h.d.181.12		12
12.11	even	2		1680.3.s.c.1441.5		12
15.2	even	4		525.3.e.c.349.3		24
15.8	even	4		525.3.e.c.349.12		24
15.14	odd	2		525.3.h.d.76.11		12
21.20	even	2		105.3.h.a.76.1	✓	12
84.83	odd	2		1680.3.s.c.1441.8		12
105.62	odd	4		525.3.e.c.349.11		24
105.83	odd	4		525.3.e.c.349.4		24
105.104	even	2		525.3.h.d.76.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.1	✓	12	21.20	even	2
105.3.h.a.76.2	yes	12	3.2	odd	2
315.3.h.d.181.11		12	1.1	even	1	trivial
315.3.h.d.181.12		12	7.6	odd	2	inner
525.3.e.c.349.3		24	15.2	even	4
525.3.e.c.349.4		24	105.83	odd	4
525.3.e.c.349.11		24	105.62	odd	4
525.3.e.c.349.12		24	15.8	even	4
525.3.h.d.76.11		12	15.14	odd	2
525.3.h.d.76.12		12	105.104	even	2
1680.3.s.c.1441.5		12	12.11	even	2
1680.3.s.c.1441.8		12	84.83	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.80460 q^{2} +10.4750 q^{4} -2.23607i q^{5} +(2.44621 - 6.55866i) q^{7} +24.6348 q^{8} +O(q^{10})\)	\(q+3.80460 q^{2} +10.4750 q^{4} -2.23607i q^{5} +(2.44621 - 6.55866i) q^{7} +24.6348 q^{8} -8.50735i q^{10} -14.4489 q^{11} +16.9427i q^{13} +(9.30684 - 24.9531i) q^{14} +51.8255 q^{16} -13.0093i q^{17} +18.6908i q^{19} -23.4228i q^{20} -54.9723 q^{22} -10.3861 q^{23} -5.00000 q^{25} +64.4602i q^{26} +(25.6240 - 68.7020i) q^{28} +13.7269 q^{29} +42.4383i q^{31} +98.6363 q^{32} -49.4951i q^{34} +(-14.6656 - 5.46988i) q^{35} +28.7434 q^{37} +71.1112i q^{38} -55.0850i q^{40} +28.8060i q^{41} -5.84593 q^{43} -151.352 q^{44} -39.5151 q^{46} -10.5013i q^{47} +(-37.0322 - 32.0877i) q^{49} -19.0230 q^{50} +177.475i q^{52} -81.9074 q^{53} +32.3087i q^{55} +(60.2617 - 161.571i) q^{56} +52.2254 q^{58} -35.1680i q^{59} -68.4826i q^{61} +161.461i q^{62} +167.970 q^{64} +37.8850 q^{65} +47.4637 q^{67} -136.272i q^{68} +(-55.7968 - 20.8107i) q^{70} -47.6548 q^{71} -125.967i q^{73} +109.357 q^{74} +195.786i q^{76} +(-35.3450 + 94.7655i) q^{77} -129.527 q^{79} -115.885i q^{80} +109.595i q^{82} +42.6906i q^{83} -29.0896 q^{85} -22.2414 q^{86} -355.945 q^{88} -25.5329i q^{89} +(111.122 + 41.4453i) q^{91} -108.795 q^{92} -39.9533i q^{94} +41.7940 q^{95} +28.7310i q^{97} +(-140.893 - 122.081i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8	\( 12 q + 4 q^{2} + 44 q^{4} - 8 q^{7} - 4 q^{8} + 16 q^{11} + 40 q^{14} + 92 q^{16} - 88 q^{22} + 64 q^{23} - 60 q^{25} + 88 q^{28} - 104 q^{29} + 228 q^{32} - 60 q^{35} + 32 q^{37} + 152 q^{43} - 192 q^{44} + 200 q^{46} + 60 q^{49} - 20 q^{50} - 176 q^{53} + 368 q^{56} - 400 q^{58} - 20 q^{64} + 240 q^{65} + 168 q^{67} - 60 q^{70} - 32 q^{71} - 184 q^{74} - 8 q^{77} + 120 q^{79} + 120 q^{85} - 400 q^{86} - 536 q^{88} + 24 q^{91} - 192 q^{92} - 884 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 44 * q^4 - 8 * q^7 - 4 * q^8 + 16 * q^11 + 40 * q^14 + 92 * q^16 - 88 * q^22 + 64 * q^23 - 60 * q^25 + 88 * q^28 - 104 * q^29 + 228 * q^32 - 60 * q^35 + 32 * q^37 + 152 * q^43 - 192 * q^44 + 200 * q^46 + 60 * q^49 - 20 * q^50 - 176 * q^53 + 368 * q^56 - 400 * q^58 - 20 * q^64 + 240 * q^65 + 168 * q^67 - 60 * q^70 - 32 * q^71 - 184 * q^74 - 8 * q^77 + 120 * q^79 + 120 * q^85 - 400 * q^86 - 536 * q^88 + 24 * q^91 - 192 * q^92 - 884 * q^98

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