LMFDB - Embedded newform 1150.3.d.b.551.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(551,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.551");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.d (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:	$31.3352304014$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.4
Root			$2.26343i$ of defining polynomial
Character	$\chi$	$=$	1150.551
Dual form			1150.3.d.b.551.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -1.43837 q^{3} +2.00000 q^{4} +2.03417 q^{6} +10.1866i q^{7} -2.82843 q^{8} -6.93108 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -1.43837 q^{3} +2.00000 q^{4} +2.03417 q^{6} +10.1866i q^{7} -2.82843 q^{8} -6.93108 q^{9} -13.0237i q^{11} -2.87675 q^{12} -23.2154 q^{13} -14.4060i q^{14} +4.00000 q^{16} -28.2228i q^{17} +9.80202 q^{18} +11.6665i q^{19} -14.6521i q^{21} +18.4183i q^{22} +(17.3999 - 15.0414i) q^{23} +4.06834 q^{24} +32.8315 q^{26} +22.9149 q^{27} +20.3731i q^{28} +42.4794 q^{29} +18.7683 q^{31} -5.65685 q^{32} +18.7330i q^{33} +39.9131i q^{34} -13.8622 q^{36} -1.14094i q^{37} -16.4989i q^{38} +33.3924 q^{39} -72.8198 q^{41} +20.7212i q^{42} -4.96573i q^{43} -26.0474i q^{44} +(-24.6071 + 21.2718i) q^{46} +0.813360 q^{47} -5.75350 q^{48} -54.7661 q^{49} +40.5950i q^{51} -46.4308 q^{52} +26.7286i q^{53} -32.4065 q^{54} -28.8120i q^{56} -16.7808i q^{57} -60.0750 q^{58} +94.0845 q^{59} +74.5293i q^{61} -26.5423 q^{62} -70.6039i q^{63} +8.00000 q^{64} -26.4925i q^{66} +80.0906i q^{67} -56.4456i q^{68} +(-25.0275 + 21.6352i) q^{69} -83.5303 q^{71} +19.6040 q^{72} +8.98897 q^{73} +1.61354i q^{74} +23.3330i q^{76} +132.667 q^{77} -47.2241 q^{78} +80.2841i q^{79} +29.4195 q^{81} +102.983 q^{82} -94.6451i q^{83} -29.3042i q^{84} +7.02261i q^{86} -61.1014 q^{87} +36.8367i q^{88} +136.812i q^{89} -236.485i q^{91} +(34.7997 - 30.0829i) q^{92} -26.9958 q^{93} -1.15026 q^{94} +8.13668 q^{96} -2.32666i q^{97} +77.4509 q^{98} +90.2684i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} - 24 q^{13} + 64 q^{16} + 32 q^{18} - 4 q^{23} - 16 q^{24} + 96 q^{26} + 96 q^{27} - 108 q^{29} - 116 q^{31} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} + 128 q^{47} - 28 q^{49} - 48 q^{52} + 224 q^{54} - 160 q^{58} + 204 q^{59} - 64 q^{62} + 128 q^{64} - 268 q^{69} + 236 q^{71} + 64 q^{72} + 112 q^{73} + 936 q^{77} + 432 q^{78} - 136 q^{81} + 64 q^{82} + 152 q^{87} - 8 q^{92} - 856 q^{93} - 216 q^{94} - 32 q^{96} - 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 - 24 * q^13 + 64 * q^16 + 32 * q^18 - 4 * q^23 - 16 * q^24 + 96 * q^26 + 96 * q^27 - 108 * q^29 - 116 * q^31 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 + 128 * q^47 - 28 * q^49 - 48 * q^52 + 224 * q^54 - 160 * q^58 + 204 * q^59 - 64 * q^62 + 128 * q^64 - 268 * q^69 + 236 * q^71 + 64 * q^72 + 112 * q^73 + 936 * q^77 + 432 * q^78 - 136 * q^81 + 64 * q^82 + 152 * q^87 - 8 * q^92 - 856 * q^93 - 216 * q^94 - 32 * q^96 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−1.43837			−0.479458			−0.239729	−	0.970840i	$-0.577059\pi$
$3$	−1.43837			−0.479458			−0.239729	+	0.970840i	$0.577059\pi$
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	2.03417			0.339028
$7$			10.1866i			1.45522i	0.685989	+	0.727612i	$0.259370\pi$
$7$			10.1866i			1.45522i	−0.685989	+	0.727612i	$0.740630\pi$
$8$	−2.82843			−0.353553
$9$	−6.93108			−0.770120
$10$		0			0
$11$		−	13.0237i		−	1.18397i	−0.805947	−	0.591987i	$-0.798343\pi$
$11$		−	13.0237i		−	1.18397i	0.805947	−	0.591987i	$-0.201657\pi$
$12$	−2.87675			−0.239729
$13$	−23.2154			−1.78580			−0.892900	−	0.450255i	$-0.851333\pi$
$13$	−23.2154			−1.78580			−0.892900	+	0.450255i	$0.851333\pi$
$14$		−	14.4060i		−	1.02900i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	28.2228i		−	1.66016i	−0.557641	−	0.830082i	$-0.688293\pi$
$17$		−	28.2228i		−	1.66016i	0.557641	−	0.830082i	$-0.311707\pi$
$18$	9.80202			0.544557
$19$			11.6665i			0.614027i	0.951705	+	0.307013i	$0.0993297\pi$
$19$			11.6665i			0.614027i	−0.951705	+	0.307013i	$0.900670\pi$
$20$		0			0
$21$		−	14.6521i		−	0.697719i
$22$			18.4183i			0.837197i
$23$	17.3999	−	15.0414i	0.756516	−	0.653976i
$23$	17.3999	−	15.0414i	0.756516	−	0.653976i
$24$	4.06834			0.169514
$25$		0			0
$26$	32.8315			1.26275
$27$	22.9149			0.848699
$28$			20.3731i			0.727612i
$29$	42.4794			1.46481			0.732404	−	0.680870i	$-0.238398\pi$
$29$	42.4794			1.46481			0.732404	+	0.680870i	$0.238398\pi$
$30$		0			0
$31$	18.7683			0.605428			0.302714	−	0.953082i	$-0.402107\pi$
$31$	18.7683			0.605428			0.302714	+	0.953082i	$0.402107\pi$
$32$	−5.65685			−0.176777
$33$			18.7330i			0.567667i
$34$			39.9131i			1.17391i
$35$		0			0
$36$	−13.8622			−0.385060
$37$		−	1.14094i		−	0.0308363i	−0.999881	−	0.0154182i	$-0.995092\pi$
$37$		−	1.14094i		−	0.0308363i	0.999881	−	0.0154182i	$-0.00490795\pi$
$38$		−	16.4989i		−	0.434183i
$39$	33.3924			0.856217
$40$		0			0
$41$	−72.8198			−1.77609			−0.888046	−	0.459755i	$-0.847937\pi$
$41$	−72.8198			−1.77609			−0.888046	+	0.459755i	$0.847937\pi$
$42$			20.7212i			0.493362i
$43$		−	4.96573i		−	0.115482i	−0.998332	−	0.0577411i	$-0.981610\pi$
$43$		−	4.96573i		−	0.115482i	0.998332	−	0.0577411i	$-0.0183898\pi$
$44$		−	26.0474i		−	0.591987i
$45$		0			0
$46$	−24.6071	+	21.2718i	−0.534937	+	0.462431i
$47$	0.813360			0.0173055			0.00865277	−	0.999963i	$-0.497246\pi$
$47$	0.813360			0.0173055			0.00865277	+	0.999963i	$0.497246\pi$
$48$	−5.75350			−0.119865
$49$	−54.7661			−1.11768
$50$		0			0
$51$			40.5950i			0.795980i
$52$	−46.4308			−0.892900
$53$			26.7286i			0.504313i	0.967686	+	0.252157i	$0.0811398\pi$
$53$			26.7286i			0.504313i	−0.967686	+	0.252157i	$0.918860\pi$
$54$	−32.4065			−0.600121
$55$		0			0
$56$		−	28.8120i		−	0.514499i
$57$		−	16.7808i		−	0.294400i
$58$	−60.0750			−1.03578
$59$	94.0845			1.59465			0.797326	−	0.603549i	$-0.206247\pi$
$59$	94.0845			1.59465			0.797326	+	0.603549i	$0.206247\pi$
$60$		0			0
$61$			74.5293i			1.22179i	0.791711	+	0.610896i	$0.209191\pi$
$61$			74.5293i			1.22179i	−0.791711	+	0.610896i	$0.790809\pi$
$62$	−26.5423			−0.428102
$63$		−	70.6039i		−	1.12070i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	26.4925i		−	0.401401i
$67$			80.0906i			1.19538i	0.801727	+	0.597691i	$0.203915\pi$
$67$			80.0906i			1.19538i	−0.801727	+	0.597691i	$0.796085\pi$
$68$		−	56.4456i		−	0.830082i
$69$	−25.0275	+	21.6352i	−0.362718	+	0.313554i
$70$		0			0
$71$	−83.5303			−1.17648			−0.588241	−	0.808686i	$-0.700179\pi$
$71$	−83.5303			−1.17648			−0.588241	+	0.808686i	$0.700179\pi$
$72$	19.6040			0.272278
$73$	8.98897			0.123137			0.0615683	−	0.998103i	$-0.480390\pi$
$73$	8.98897			0.123137			0.0615683	+	0.998103i	$0.480390\pi$
$74$			1.61354i			0.0218046i
$75$		0			0
$76$			23.3330i			0.307013i
$77$	132.667			1.72295
$78$	−47.2241			−0.605437
$79$			80.2841i			1.01626i	0.861282	+	0.508128i	$0.169662\pi$
$79$			80.2841i			1.01626i	−0.861282	+	0.508128i	$0.830338\pi$
$80$		0			0
$81$	29.4195			0.363204
$82$	102.983			1.25589
$83$		−	94.6451i		−	1.14030i	−0.821540	−	0.570151i	$-0.806885\pi$
$83$		−	94.6451i		−	1.14030i	0.821540	−	0.570151i	$-0.193115\pi$
$84$		−	29.3042i		−	0.348859i
$85$		0			0
$86$			7.02261i			0.0816582i
$87$	−61.1014			−0.702315
$88$			36.8367i			0.418598i
$89$			136.812i			1.53722i	0.639720	+	0.768608i	$0.279050\pi$
$89$			136.812i			1.53722i	−0.639720	+	0.768608i	$0.720950\pi$
$90$		0			0
$91$		−	236.485i		−	2.59874i
$92$	34.7997	−	30.0829i	0.378258	−	0.326988i
$93$	−26.9958			−0.290277
$94$	−1.15026			−0.0122369
$95$		0			0
$96$	8.13668			0.0847571
$97$		−	2.32666i		−	0.0239862i	−0.999928	−	0.0119931i	$-0.996182\pi$
$97$		−	2.32666i		−	0.0239862i	0.999928	−	0.0119931i	$-0.00381761\pi$
$98$	77.4509			0.790316
$99$			90.2684i			0.911802i
$100$		0			0
$101$	12.9918			0.128632			0.0643161	−	0.997930i	$-0.479513\pi$
$101$	12.9918			0.128632			0.0643161	+	0.997930i	$0.479513\pi$
$102$		−	57.4100i		−	0.562843i
$103$			90.3165i			0.876859i	0.898766	+	0.438430i	$0.144465\pi$
$103$			90.3165i			0.876859i	−0.898766	+	0.438430i	$0.855535\pi$
$104$	65.6631			0.631376
$105$		0			0
$106$		−	37.7999i		−	0.356603i
$107$			185.173i			1.73059i	0.501264	+	0.865294i	$0.332869\pi$
$107$			185.173i			1.73059i	−0.501264	+	0.865294i	$0.667131\pi$
$108$	45.8297			0.424349
$109$		−	13.8248i		−	0.126833i	−0.997987	−	0.0634167i	$-0.979800\pi$
$109$		−	13.8248i		−	0.126833i	0.997987	−	0.0634167i	$-0.0201997\pi$
$110$		0			0
$111$			1.64110i			0.0147847i
$112$			40.7463i			0.363806i
$113$		−	178.530i		−	1.57991i	−0.613164	−	0.789956i	$-0.710103\pi$
$113$		−	178.530i		−	1.57991i	0.613164	−	0.789956i	$-0.289897\pi$
$114$			23.7317i			0.208172i
$115$		0			0
$116$	84.9589			0.732404
$117$	160.908			1.37528
$118$	−133.056			−1.12759
$119$	287.493			2.41591
$120$		0			0
$121$	−48.6174			−0.401797
$122$		−	105.400i		−	0.863938i
$123$	104.742			0.851562
$124$	37.5365			0.302714
$125$		0			0
$126$			99.8489i			0.792452i
$127$	112.959			0.889442			0.444721	−	0.895669i	$-0.353303\pi$
$127$	112.959			0.889442			0.444721	+	0.895669i	$0.353303\pi$
$128$	−11.3137			−0.0883883
$129$			7.14258i			0.0553689i
$130$		0			0
$131$	−12.1419			−0.0926860			−0.0463430	−	0.998926i	$-0.514757\pi$
$131$	−12.1419			−0.0926860			−0.0463430	+	0.998926i	$0.514757\pi$
$132$			37.4660i			0.283833i
$133$	−118.842			−0.893546
$134$		−	113.265i		−	0.845263i
$135$		0			0
$136$			79.8261i			0.586957i
$137$			170.543i			1.24484i	0.782685	+	0.622418i	$0.213850\pi$
$137$			170.543i			1.24484i	−0.782685	+	0.622418i	$0.786150\pi$
$138$	35.3943	−	30.5968i	0.256480	−	0.221716i
$139$	38.5478			0.277322			0.138661	−	0.990340i	$-0.455720\pi$
$139$	38.5478			0.277322			0.138661	+	0.990340i	$0.455720\pi$
$140$		0			0
$141$	−1.16992			−0.00829728
$142$	118.130			0.831899
$143$			302.351i			2.11434i
$144$	−27.7243			−0.192530
$145$		0			0
$146$	−12.7123			−0.0870707
$147$	78.7742			0.535879
$148$		−	2.28189i		−	0.0154182i
$149$			81.4125i			0.546393i	0.961958	+	0.273196i	$0.0880808\pi$
$149$			81.4125i			0.546393i	−0.961958	+	0.273196i	$0.911919\pi$
$150$		0			0
$151$	159.680			1.05748			0.528742	−	0.848782i	$-0.322664\pi$
$151$	159.680			1.05748			0.528742	+	0.848782i	$0.322664\pi$
$152$		−	32.9979i		−	0.217091i
$153$			195.614i			1.27853i
$154$	−187.619			−1.21831
$155$		0			0
$156$	66.7849			0.428108
$157$			38.5953i			0.245830i	0.992417	+	0.122915i	$0.0392242\pi$
$157$			38.5953i			0.245830i	−0.992417	+	0.122915i	$0.960776\pi$
$158$		−	113.539i		−	0.718601i
$159$		−	38.4457i		−	0.241797i
$160$		0			0
$161$	153.221	+	177.245i	0.951681	+	1.10090i
$162$	−41.6055			−0.256824
$163$	−150.291			−0.922028			−0.461014	−	0.887393i	$-0.652514\pi$
$163$	−150.291			−0.922028			−0.461014	+	0.887393i	$0.652514\pi$
$164$	−145.640			−0.888046
$165$		0			0
$166$			133.848i			0.806316i
$167$	−27.7604			−0.166230			−0.0831149	−	0.996540i	$-0.526487\pi$
$167$	−27.7604			−0.166230			−0.0831149	+	0.996540i	$0.526487\pi$
$168$			41.4424i			0.246681i
$169$	369.955			2.18908
$170$		0			0
$171$		−	80.8615i		−	0.472874i
$172$		−	9.93146i		−	0.0577411i
$173$	24.0064			0.138765			0.0693826	−	0.997590i	$-0.477897\pi$
$173$	24.0064			0.138765			0.0693826	+	0.997590i	$0.477897\pi$
$174$	86.4104			0.496611
$175$		0			0
$176$		−	52.0949i		−	0.295994i
$177$	−135.329			−0.764569
$178$		−	193.482i		−	1.08698i
$179$	−201.178			−1.12390			−0.561949	−	0.827172i	$-0.689948\pi$
$179$	−201.178			−1.12390			−0.561949	+	0.827172i	$0.689948\pi$
$180$		0			0
$181$		−	202.358i		−	1.11800i	−0.829168	−	0.558999i	$-0.811186\pi$
$181$		−	202.358i		−	1.11800i	0.829168	−	0.558999i	$-0.188814\pi$
$182$			334.441i			1.83759i
$183$		−	107.201i		−	0.585798i
$184$	−49.2142	+	42.5436i	−0.267469	+	0.231215i
$185$		0			0
$186$	38.1778			0.205257
$187$	−367.566			−1.96559
$188$	1.62672			0.00865277
$189$			233.424i			1.23505i
$190$		0			0
$191$			111.302i			0.582735i	0.956611	+	0.291368i	$0.0941103\pi$
$191$			111.302i			0.582735i	−0.956611	+	0.291368i	$0.905890\pi$
$192$	−11.5070			−0.0599323
$193$	164.081			0.850163			0.425081	−	0.905155i	$-0.360246\pi$
$193$	164.081			0.850163			0.425081	+	0.905155i	$0.360246\pi$
$194$			3.29040i			0.0169608i
$195$		0			0
$196$	−109.532			−0.558838
$197$	329.562			1.67290			0.836451	−	0.548042i	$-0.184627\pi$
$197$	329.562			1.67290			0.836451	+	0.548042i	$0.184627\pi$
$198$		−	127.659i		−	0.644742i
$199$		−	337.886i		−	1.69792i	−0.528455	−	0.848961i	$-0.677229\pi$
$199$		−	337.886i		−	1.69792i	0.528455	−	0.848961i	$-0.322771\pi$
$200$		0			0
$201$		−	115.200i		−	0.573136i
$202$	−18.3732			−0.0909566
$203$			432.720i			2.13162i
$204$			81.1899i			0.397990i
$205$		0			0
$206$		−	127.727i		−	0.620033i
$207$	−120.600	+	104.253i	−0.582608	+	0.503640i
$208$	−92.8616			−0.446450
$209$	151.941			0.726992
$210$		0			0
$211$	111.656			0.529173			0.264587	−	0.964362i	$-0.414765\pi$
$211$	111.656			0.529173			0.264587	+	0.964362i	$0.414765\pi$
$212$			53.4572i			0.252157i
$213$	120.148			0.564074
$214$		−	261.874i		−	1.22371i
$215$		0			0
$216$	−64.8130			−0.300060
$217$			191.184i			0.881032i
$218$			19.5513i			0.0896847i
$219$	−12.9295			−0.0590389
$220$		0			0
$221$			655.204i			2.96472i
$222$		−	2.32087i		−	0.0104544i
$223$	363.545			1.63025			0.815123	−	0.579288i	$-0.196669\pi$
$223$	363.545			1.63025			0.815123	+	0.579288i	$0.196669\pi$
$224$		−	57.6239i		−	0.257250i
$225$		0			0
$226$			252.480i			1.11717i
$227$		−	11.3368i		−	0.0499418i	−0.999688	−	0.0249709i	$-0.992051\pi$
$227$		−	11.3368i		−	0.0499418i	0.999688	−	0.0249709i	$-0.00794931\pi$
$228$		−	33.5616i		−	0.147200i
$229$		−	112.509i		−	0.491306i	−0.969358	−	0.245653i	$-0.920998\pi$
$229$		−	112.509i		−	0.491306i	0.969358	−	0.245653i	$-0.0790024\pi$
$230$		0			0
$231$	−190.825			−0.826082
$232$	−120.150			−0.517888
$233$	381.634			1.63791			0.818957	−	0.573855i	$-0.194553\pi$
$233$	381.634			1.63791			0.818957	+	0.573855i	$0.194553\pi$
$234$	−227.558			−0.972470
$235$		0			0
$236$	188.169			0.797326
$237$		−	115.479i		−	0.487252i
$238$	−406.577			−1.70831
$239$	139.296			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$239$	139.296			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$240$		0			0
$241$		−	82.3347i		−	0.341638i	−0.985302	−	0.170819i	$-0.945359\pi$
$241$		−	82.3347i		−	0.341638i	0.985302	−	0.170819i	$-0.0546413\pi$
$242$	68.7554			0.284113
$243$	−248.550			−1.02284
$244$			149.059i			0.610896i
$245$		0			0
$246$	−148.128			−0.602145
$247$		−	270.843i		−	1.09653i
$248$	−53.0846			−0.214051
$249$			136.135i			0.546728i
$250$		0			0
$251$		−	323.924i		−	1.29054i	−0.763957	−	0.645268i	$-0.776746\pi$
$251$		−	323.924i		−	1.29054i	0.763957	−	0.645268i	$-0.223254\pi$
$252$		−	141.208i		−	0.560348i
$253$	−195.896	−	226.611i	−0.774291	−	0.895695i
$254$	−159.748			−0.628931
$255$		0			0
$256$	16.0000			0.0625000
$257$	250.796			0.975858			0.487929	−	0.872883i	$-0.337752\pi$
$257$	250.796			0.975858			0.487929	+	0.872883i	$0.337752\pi$
$258$		−	10.1011i		−	0.0391517i
$259$	11.6223			0.0448737
$260$		0			0
$261$	−294.428			−1.12808
$262$	17.1712			0.0655389
$263$		−	276.878i		−	1.05277i	−0.850247	−	0.526384i	$-0.823548\pi$
$263$		−	276.878i		−	1.05277i	0.850247	−	0.526384i	$-0.176452\pi$
$264$		−	52.9849i		−	0.200700i
$265$		0			0
$266$	168.067			0.631833
$267$		−	196.787i		−	0.737031i
$268$			160.181i			0.597691i
$269$	−78.1002			−0.290335			−0.145168	−	0.989407i	$-0.546372\pi$
$269$	−78.1002			−0.290335			−0.145168	+	0.989407i	$0.546372\pi$
$270$		0			0
$271$	331.551			1.22343			0.611717	−	0.791076i	$-0.290479\pi$
$271$	331.551			1.22343			0.611717	+	0.791076i	$0.290479\pi$
$272$		−	112.891i		−	0.415041i
$273$			340.154i			1.24599i
$274$		−	241.184i		−	0.880232i
$275$		0			0
$276$	−50.0550	+	43.2705i	−0.181359	+	0.156777i
$277$	355.974			1.28511			0.642553	−	0.766241i	$-0.277875\pi$
$277$	355.974			1.28511			0.642553	+	0.766241i	$0.277875\pi$
$278$	−54.5148			−0.196097
$279$	−130.084			−0.466252
$280$		0			0
$281$			391.437i			1.39301i	0.717550	+	0.696507i	$0.245264\pi$
$281$			391.437i			1.39301i	−0.717550	+	0.696507i	$0.754736\pi$
$282$	1.65451			0.00586706
$283$		−	133.616i		−	0.472143i	−0.971736	−	0.236071i	$-0.924140\pi$
$283$		−	133.616i		−	0.472143i	0.971736	−	0.236071i	$-0.0758599\pi$
$284$	−167.061			−0.588241
$285$		0			0
$286$		−	427.589i		−	1.49507i
$287$		−	741.783i		−	2.58461i
$288$	39.2081			0.136139
$289$	−507.527			−1.75615
$290$		0			0
$291$			3.34661i			0.0115004i
$292$	17.9779			0.0615683
$293$		−	533.454i		−	1.82066i	−0.413880	−	0.910331i	$-0.635827\pi$
$293$		−	533.454i		−	1.82066i	0.413880	−	0.910331i	$-0.364173\pi$
$294$	−111.403			−0.378923
$295$		0			0
$296$			3.22708i			0.0109023i
$297$		−	298.437i		−	1.00484i
$298$		−	115.135i		−	0.386358i
$299$	−403.945	+	349.193i	−1.35099	+	1.16787i
$300$		0			0
$301$	50.5837			0.168052
$302$	−225.822			−0.747755
$303$	−18.6871			−0.0616737
$304$			46.6660i			0.153507i
$305$		0			0
$306$		−	276.641i		−	0.904054i
$307$	−282.656			−0.920705			−0.460352	−	0.887736i	$-0.652277\pi$
$307$	−282.656			−0.920705			−0.460352	+	0.887736i	$0.652277\pi$
$308$	265.334			0.861474
$309$		−	129.909i		−	0.420417i
$310$		0			0
$311$	−193.206			−0.621241			−0.310620	−	0.950534i	$-0.600537\pi$
$311$	−193.206			−0.621241			−0.310620	+	0.950534i	$0.600537\pi$
$312$	−94.4481			−0.302718
$313$			399.279i			1.27565i	0.770181	+	0.637826i	$0.220166\pi$
$313$			399.279i			1.27565i	−0.770181	+	0.637826i	$0.779834\pi$
$314$		−	54.5820i		−	0.173828i
$315$		0			0
$316$			160.568i			0.508128i
$317$	36.5297			0.115236			0.0576178	−	0.998339i	$-0.481650\pi$
$317$	36.5297			0.115236			0.0576178	+	0.998339i	$0.481650\pi$
$318$			54.3705i			0.170976i
$319$		−	553.241i		−	1.73430i
$320$		0			0
$321$		−	266.348i		−	0.829745i
$322$	−216.687	−	250.662i	−0.672940	−	0.778453i
$323$	329.262			1.01939
$324$	58.8391			0.181602
$325$		0			0
$326$	212.543			0.651973
$327$			19.8853i			0.0608113i
$328$	205.965			0.627943
$329$			8.28534i			0.0251834i
$330$		0			0
$331$	85.9406			0.259639			0.129820	−	0.991538i	$-0.458560\pi$
$331$	85.9406			0.259639			0.129820	+	0.991538i	$0.458560\pi$
$332$		−	189.290i		−	0.570151i
$333$			7.90797i			0.0237476i
$334$	39.2591			0.117542
$335$		0			0
$336$		−	58.6084i		−	0.174430i
$337$			548.713i			1.62823i	0.580706	+	0.814114i	$0.302777\pi$
$337$			548.713i			1.62823i	−0.580706	+	0.814114i	$0.697223\pi$
$338$	−523.195			−1.54791
$339$			256.793i			0.757502i
$340$		0			0
$341$		−	244.433i		−	0.716811i
$342$			114.355i			0.334373i
$343$		−	58.7366i		−	0.171244i
$344$			14.0452i			0.0408291i
$345$		0			0
$346$	−33.9502			−0.0981219
$347$	−62.0036			−0.178685			−0.0893424	−	0.996001i	$-0.528477\pi$
$347$	−62.0036			−0.178685			−0.0893424	+	0.996001i	$0.528477\pi$
$348$	−122.203			−0.351157
$349$	−131.393			−0.376485			−0.188242	−	0.982123i	$-0.560279\pi$
$349$	−131.393			−0.376485			−0.188242	+	0.982123i	$0.560279\pi$
$350$		0			0
$351$	−531.978			−1.51561
$352$			73.6733i			0.209299i
$353$	176.990			0.501389			0.250694	−	0.968066i	$-0.419341\pi$
$353$	176.990			0.501389			0.250694	+	0.968066i	$0.419341\pi$
$354$	191.384			0.540632
$355$		0			0
$356$			273.624i			0.768608i
$357$	−413.523			−1.15833
$358$	284.508			0.794716
$359$			187.851i			0.523260i	0.965168	+	0.261630i	$0.0842601\pi$
$359$			187.851i			0.523260i	−0.965168	+	0.261630i	$0.915740\pi$
$360$		0			0
$361$	224.893			0.622971
$362$			286.177i			0.790544i
$363$	69.9300			0.192645
$364$		−	472.970i		−	1.29937i
$365$		0			0
$366$			151.605i			0.414222i
$367$		−	128.510i		−	0.350162i	−0.984554	−	0.175081i	$-0.943981\pi$
$367$		−	128.510i		−	0.350162i	0.984554	−	0.175081i	$-0.0560188\pi$
$368$	69.5994	−	60.1658i	0.189129	−	0.163494i
$369$	504.719			1.36780
$370$		0			0
$371$	−272.273			−0.733888
$372$	−53.9916			−0.145139
$373$		−	79.2928i		−	0.212581i	−0.994335	−	0.106291i	$-0.966103\pi$
$373$		−	79.2928i		−	0.212581i	0.994335	−	0.106291i	$-0.0338974\pi$
$374$	519.817			1.38988
$375$		0			0
$376$	−2.30053			−0.00611843
$377$	−986.177			−2.61585
$378$		−	330.111i		−	0.873309i
$379$			402.569i			1.06219i	0.847313	+	0.531094i	$0.178219\pi$
$379$			402.569i			1.06219i	−0.847313	+	0.531094i	$0.821781\pi$
$380$		0			0
$381$	−162.478			−0.426450
$382$		−	157.405i		−	0.412056i
$383$			370.198i			0.966575i	0.875462	+	0.483288i	$0.160557\pi$
$383$			370.198i			0.966575i	−0.875462	+	0.483288i	$0.839443\pi$
$384$	16.2734			0.0423785
$385$		0			0
$386$	−232.046			−0.601156
$387$			34.4179i			0.0889351i
$388$		−	4.65332i		−	0.0119931i
$389$			12.0598i			0.0310021i	0.999880	+	0.0155011i	$0.00493434\pi$
$389$			12.0598i			0.0310021i	−0.999880	+	0.0155011i	$0.995066\pi$
$390$		0			0
$391$	−424.512	−	491.073i	−1.08571	−	1.25594i
$392$	154.902			0.395158
$393$	17.4645			0.0444391
$394$	−466.071			−1.18292
$395$		0			0
$396$			180.537i			0.455901i
$397$	−233.543			−0.588270			−0.294135	−	0.955764i	$-0.595032\pi$
$397$	−233.543			−0.588270			−0.294135	+	0.955764i	$0.595032\pi$
$398$			477.844i			1.20061i
$399$	170.939			0.428418
$400$		0			0
$401$			114.072i			0.284469i	0.989833	+	0.142235i	$0.0454287\pi$
$401$			114.072i			0.284469i	−0.989833	+	0.142235i	$0.954571\pi$
$402$			162.918i			0.405268i
$403$	−435.713			−1.08117
$404$	25.9837			0.0643161
$405$		0			0
$406$		−	611.958i		−	1.50729i
$407$	−14.8593			−0.0365094
$408$		−	114.820i		−	0.281421i
$409$	125.952			0.307950			0.153975	−	0.988075i	$-0.450792\pi$
$409$	125.952			0.307950			0.153975	+	0.988075i	$0.450792\pi$
$410$		0			0
$411$		−	245.304i		−	0.596847i
$412$			180.633i			0.438430i
$413$			958.397i			2.32057i
$414$	170.554	−	147.437i	0.411966	−	0.356127i
$415$		0			0
$416$	131.326			0.315688
$417$	−55.4462			−0.132965
$418$	−214.878			−0.514061
$419$		−	135.868i		−	0.324268i	−0.986769	−	0.162134i	$-0.948162\pi$
$419$		−	135.868i		−	0.324268i	0.986769	−	0.162134i	$-0.0518377\pi$
$420$		0			0
$421$		−	194.111i		−	0.461070i	−0.973064	−	0.230535i	$-0.925952\pi$
$421$		−	194.111i		−	0.461070i	0.973064	−	0.230535i	$-0.0740477\pi$
$422$	−157.905			−0.374182
$423$	−5.63746			−0.0133273
$424$		−	75.5999i		−	0.178302i
$425$		0			0
$426$	−169.915			−0.398861
$427$	−759.198			−1.77798
$428$			370.346i			0.865294i
$429$		−	434.894i		−	1.01374i
$430$		0			0
$431$		−	421.699i		−	0.978420i	−0.872166	−	0.489210i	$-0.837285\pi$
$431$		−	421.699i		−	0.978420i	0.872166	−	0.489210i	$-0.162715\pi$
$432$	91.6595			0.212175
$433$			3.78505i			0.00874144i	0.999990	+	0.00437072i	$0.00139125\pi$
$433$			3.78505i			0.00874144i	−0.999990	+	0.00437072i	$0.998609\pi$
$434$		−	270.375i		−	0.622984i
$435$		0			0
$436$		−	27.6497i		−	0.0634167i
$437$	175.481	+	202.996i	0.401559	+	0.464521i
$438$	18.2851			0.0417468
$439$	−6.17744			−0.0140716			−0.00703581	−	0.999975i	$-0.502240\pi$
$439$	−6.17744			−0.0140716			−0.00703581	+	0.999975i	$0.502240\pi$
$440$		0			0
$441$	379.588			0.860744
$442$		−	926.598i		−	2.09638i
$443$	406.821			0.918331			0.459166	−	0.888351i	$-0.348148\pi$
$443$	406.821			0.918331			0.459166	+	0.888351i	$0.348148\pi$
$444$			3.28221i			0.00739236i
$445$		0			0
$446$	−514.130			−1.15276
$447$		−	117.102i		−	0.261972i
$448$			81.4925i			0.181903i
$449$	−289.981			−0.645837			−0.322918	−	0.946427i	$-0.604664\pi$
$449$	−289.981			−0.645837			−0.322918	+	0.946427i	$0.604664\pi$
$450$		0			0
$451$			948.385i			2.10285i
$452$		−	357.060i		−	0.789956i
$453$	−229.680			−0.507020
$454$			16.0326i			0.0353142i
$455$		0			0
$456$			47.4633i			0.104086i
$457$			224.430i			0.491094i	0.969385	+	0.245547i	$0.0789676\pi$
$457$			224.430i			0.491094i	−0.969385	+	0.245547i	$0.921032\pi$
$458$			159.112i			0.347406i
$459$		−	646.722i		−	1.40898i
$460$		0			0
$461$	534.660			1.15978			0.579891	−	0.814694i	$-0.303095\pi$
$461$	534.660			1.15978			0.579891	+	0.814694i	$0.303095\pi$
$462$	269.867			0.584128
$463$	−166.226			−0.359019			−0.179509	−	0.983756i	$-0.557451\pi$
$463$	−166.226			−0.359019			−0.179509	+	0.983756i	$0.557451\pi$
$464$	169.918			0.366202
$465$		0			0
$466$	−539.712			−1.15818
$467$		−	113.755i		−	0.243587i	−0.992555	−	0.121794i	$-0.961135\pi$
$467$		−	113.755i		−	0.243587i	0.992555	−	0.121794i	$-0.0388646\pi$
$468$	321.815			0.687640
$469$	−815.848			−1.73955
$470$		0			0
$471$		−	55.5145i		−	0.117865i
$472$	−266.111			−0.563795
$473$	−64.6723			−0.136728
$474$			163.312i			0.344539i
$475$		0			0
$476$	574.987			1.20796
$477$		−	185.258i		−	0.388382i
$478$	−196.994			−0.412121
$479$		−	156.314i		−	0.326334i	−0.986598	−	0.163167i	$-0.947829\pi$
$479$		−	156.314i		−	0.326334i	0.986598	−	0.163167i	$-0.0521710\pi$
$480$		0			0
$481$			26.4875i			0.0550675i
$482$			116.439i			0.241574i
$483$	−220.389	−	254.944i	−0.456291	−	0.527835i
$484$	−97.2348			−0.200898
$485$		0			0
$486$	351.503			0.723257
$487$	207.919			0.426938			0.213469	−	0.976950i	$-0.431524\pi$
$487$	207.919			0.426938			0.213469	+	0.976950i	$0.431524\pi$
$488$		−	210.801i		−	0.431969i
$489$	216.174			0.442074
$490$		0			0
$491$	−463.345			−0.943676			−0.471838	−	0.881685i	$-0.656409\pi$
$491$	−463.345			−0.943676			−0.471838	+	0.881685i	$0.656409\pi$
$492$	209.484			0.425781
$493$		−	1198.89i		−	2.43182i
$494$			383.029i			0.775363i
$495$		0			0
$496$	75.0730			0.151357
$497$		−	850.886i		−	1.71204i
$498$		−	192.524i		−	0.386595i
$499$	−50.7777			−0.101759			−0.0508794	−	0.998705i	$-0.516202\pi$
$499$	−50.7777			−0.101759			−0.0508794	+	0.998705i	$0.516202\pi$
$500$		0			0
$501$	39.9298			0.0797003
$502$			458.098i			0.912546i
$503$			91.1857i			0.181284i	0.995884	+	0.0906419i	$0.0288919\pi$
$503$			91.1857i			0.181284i	−0.995884	+	0.0906419i	$0.971108\pi$
$504$			199.698i			0.396226i
$505$		0			0
$506$	277.038	+	320.476i	0.547506	+	0.633352i
$507$	−532.134			−1.04957
$508$	225.918			0.444721
$509$	317.681			0.624128			0.312064	−	0.950061i	$-0.398980\pi$
$509$	317.681			0.624128			0.312064	+	0.950061i	$0.398980\pi$
$510$		0			0
$511$			91.5667i			0.179191i
$512$	−22.6274			−0.0441942
$513$			267.337i			0.521124i
$514$	−354.678			−0.690036
$515$		0			0
$516$			14.2852i			0.0276844i
$517$		−	10.5930i		−	0.0204893i
$518$	−16.4364			−0.0317305
$519$	−34.5302			−0.0665322
$520$		0			0
$521$		−	522.346i		−	1.00258i	−0.865279	−	0.501291i	$-0.832858\pi$
$521$		−	522.346i		−	1.00258i	0.865279	−	0.501291i	$-0.167142\pi$
$522$	416.385			0.797671
$523$		−	245.926i		−	0.470221i	−0.971969	−	0.235111i	$-0.924455\pi$
$523$		−	245.926i		−	0.470221i	0.971969	−	0.235111i	$-0.0755452\pi$
$524$	−24.2837			−0.0463430
$525$		0			0
$526$			391.564i			0.744419i
$527$		−	529.693i		−	1.00511i
$528$			74.9320i			0.141917i
$529$	76.5101	−	523.438i	0.144632	−	0.989486i
$530$		0			0
$531$	−652.107			−1.22807
$532$	−237.683			−0.446773
$533$	1690.54			3.17174
$534$			278.299i			0.521160i
$535$		0			0
$536$		−	226.530i		−	0.422631i
$537$	289.369			0.538862
$538$	110.450			0.205298
$539$			713.258i			1.32330i
$540$		0			0
$541$	−307.138			−0.567723			−0.283861	−	0.958865i	$-0.591616\pi$
$541$	−307.138			−0.567723			−0.283861	+	0.958865i	$0.591616\pi$
$542$	−468.884			−0.865099
$543$			291.066i			0.536033i
$544$			159.652i			0.293478i
$545$		0			0
$546$		−	481.051i		−	0.881046i
$547$	712.547			1.30265			0.651323	−	0.758801i	$-0.274214\pi$
$547$	712.547			1.30265			0.651323	+	0.758801i	$0.274214\pi$
$548$			341.085i			0.622418i
$549$		−	516.569i		−	0.940926i
$550$		0			0
$551$			495.587i			0.899432i
$552$	70.7885	−	61.1937i	0.128240	−	0.110858i
$553$	−817.820			−1.47888
$554$	−503.424			−0.908707
$555$		0			0
$556$	77.0956			0.138661
$557$			1.17109i			0.00210250i	0.999999	+	0.00105125i	$0.000334623\pi$
$557$			1.17109i			0.00210250i	−0.999999	+	0.00105125i	$0.999665\pi$
$558$	183.967			0.329690
$559$			115.281i			0.206228i
$560$		0			0
$561$	528.698			0.942420
$562$		−	553.575i		−	0.985010i
$563$			900.058i			1.59868i	0.600878	+	0.799341i	$0.294818\pi$
$563$			900.058i			1.59868i	−0.600878	+	0.799341i	$0.705182\pi$
$564$	−2.33983			−0.00414864
$565$		0			0
$566$			188.962i			0.333855i
$567$			299.684i			0.528543i
$568$	236.259			0.415949
$569$			589.836i			1.03662i	0.855193	+	0.518309i	$0.173438\pi$
$569$			589.836i			1.03662i	−0.855193	+	0.518309i	$0.826562\pi$
$570$		0			0
$571$		−	117.755i		−	0.206225i	−0.994670	−	0.103113i	$-0.967120\pi$
$571$		−	117.755i		−	0.206225i	0.994670	−	0.103113i	$-0.0328802\pi$
$572$			604.702i			1.05717i
$573$		−	160.095i		−	0.279397i
$574$			1049.04i			1.82760i
$575$		0			0
$576$	−55.4486			−0.0962650
$577$	403.533			0.699365			0.349682	−	0.936868i	$-0.386290\pi$
$577$	403.533			0.699365			0.349682	+	0.936868i	$0.386290\pi$
$578$	717.751			1.24178
$579$	−236.011			−0.407618
$580$		0			0
$581$	964.109			1.65940
$582$		−	4.73282i		−	0.00813200i
$583$	348.106			0.597094
$584$	−25.4246			−0.0435354
$585$		0			0
$586$			754.418i			1.28740i
$587$	−607.731			−1.03532			−0.517659	−	0.855587i	$-0.673196\pi$
$587$	−607.731			−1.03532			−0.517659	+	0.855587i	$0.673196\pi$
$588$	157.548			0.267939
$589$			218.960i			0.371749i
$590$		0			0
$591$	−474.033			−0.802087
$592$		−	4.56377i		−	0.00770908i
$593$	−428.555			−0.722690			−0.361345	−	0.932432i	$-0.617682\pi$
$593$	−428.555			−0.722690			−0.361345	+	0.932432i	$0.617682\pi$
$594$			422.053i			0.710528i
$595$		0			0
$596$			162.825i			0.273196i
$597$			486.007i			0.814083i
$598$	571.264	−	493.834i	0.955291	−	0.825809i
$599$	−162.171			−0.270736			−0.135368	−	0.990795i	$-0.543222\pi$
$599$	−162.171			−0.270736			−0.135368	+	0.990795i	$0.543222\pi$
$600$		0			0
$601$	957.407			1.59302			0.796512	−	0.604623i	$-0.206676\pi$
$601$	957.407			1.59302			0.796512	+	0.604623i	$0.206676\pi$
$602$	−71.5362			−0.118831
$603$		−	555.114i		−	0.920587i
$604$	319.360			0.528742
$605$		0			0
$606$	26.4276			0.0436099
$607$	989.893			1.63080			0.815398	−	0.578901i	$-0.196518\pi$
$607$	989.893			1.63080			0.815398	+	0.578901i	$0.196518\pi$
$608$		−	65.9958i		−	0.108546i
$609$		−	622.413i		−	1.02202i
$610$		0			0
$611$	−18.8825			−0.0309042
$612$			391.229i			0.639263i
$613$		−	134.181i		−	0.218892i	−0.993993	−	0.109446i	$-0.965092\pi$
$613$		−	134.181i		−	0.218892i	0.993993	−	0.109446i	$-0.0349076\pi$
$614$	399.736			0.651037
$615$		0			0
$616$	−375.239			−0.609154
$617$			151.269i			0.245168i	0.992458	+	0.122584i	$0.0391181\pi$
$617$			151.269i			0.245168i	−0.992458	+	0.122584i	$0.960882\pi$
$618$			183.719i			0.297280i
$619$			115.852i			0.187159i	0.995612	+	0.0935797i	$0.0298310\pi$
$619$			115.852i			0.187159i	−0.995612	+	0.0935797i	$0.970169\pi$
$620$		0			0
$621$	398.715	−	344.673i	0.642054	−	0.555028i
$622$	273.234			0.439284
$623$	−1393.65			−2.23699
$624$	133.570			0.214054
$625$		0			0
$626$		−	564.665i		−	0.902022i
$627$	−218.549			−0.348563
$628$			77.1906i			0.122915i
$629$	−32.2006			−0.0511934
$630$		0			0
$631$			730.187i			1.15719i	0.815615	+	0.578595i	$0.196399\pi$
$631$			730.187i			1.15719i	−0.815615	+	0.578595i	$0.803601\pi$
$632$		−	227.078i		−	0.359300i
$633$	−160.602			−0.253716
$634$	−51.6608			−0.0814839
$635$		0			0
$636$		−	76.8915i		−	0.120899i
$637$	1271.42			1.99594
$638$			782.400i			1.22633i
$639$	578.955			0.906032
$640$		0			0
$641$		−	725.551i		−	1.13190i	−0.824438	−	0.565952i	$-0.808509\pi$
$641$		−	725.551i		−	1.13190i	0.824438	−	0.565952i	$-0.191491\pi$
$642$			376.673i			0.586718i
$643$		−	505.908i		−	0.786792i	−0.919369	−	0.393396i	$-0.871300\pi$
$643$		−	505.908i		−	0.786792i	0.919369	−	0.393396i	$-0.128700\pi$
$644$	306.441	+	354.490i	0.475840	+	0.550450i
$645$		0			0
$646$	−465.646			−0.720815
$647$	324.943			0.502230			0.251115	−	0.967957i	$-0.419203\pi$
$647$	324.943			0.502230			0.251115	+	0.967957i	$0.419203\pi$
$648$	−83.2110			−0.128412
$649$		−	1225.33i		−	1.88803i
$650$		0			0
$651$		−	274.994i		−	0.422418i
$652$	−300.581			−0.461014
$653$	146.801			0.224810			0.112405	−	0.993662i	$-0.464145\pi$
$653$	146.801			0.224810			0.112405	+	0.993662i	$0.464145\pi$
$654$		−	28.1220i		−	0.0430001i
$655$		0			0
$656$	−291.279			−0.444023
$657$	−62.3033			−0.0948299
$658$		−	11.7172i		−	0.0178074i
$659$			366.667i			0.556399i	0.960523	+	0.278200i	$0.0897377\pi$
$659$			366.667i			0.556399i	−0.960523	+	0.278200i	$0.910262\pi$
$660$		0			0
$661$			1241.87i			1.87878i	0.342852	+	0.939389i	$0.388607\pi$
$661$			1241.87i			1.87878i	−0.342852	+	0.939389i	$0.611393\pi$
$662$	−121.538			−0.183593
$663$		−	942.428i		−	1.42146i
$664$			267.697i			0.403158i
$665$		0			0
$666$		−	11.1836i		−	0.0167921i
$667$	739.136	−	638.952i	1.10815	−	0.957949i
$668$	−55.5208			−0.0831149
$669$	−522.914			−0.781635
$670$		0			0
$671$	970.649			1.44657
$672$			82.8848i			0.123340i
$673$	−812.966			−1.20797			−0.603987	−	0.796994i	$-0.706422\pi$
$673$	−812.966			−1.20797			−0.603987	+	0.796994i	$0.706422\pi$
$674$		−	775.997i		−	1.15133i
$675$		0			0
$676$	739.910			1.09454
$677$			1053.03i			1.55544i	0.628610	+	0.777721i	$0.283624\pi$
$677$			1053.03i			1.55544i	−0.628610	+	0.777721i	$0.716376\pi$
$678$		−	363.160i		−	0.535635i
$679$	23.7007			0.0349053
$680$		0			0
$681$			16.3066i			0.0239450i
$682$			345.680i			0.506862i
$683$	−947.718			−1.38758			−0.693791	−	0.720177i	$-0.744061\pi$
$683$	−947.718			−1.38758			−0.693791	+	0.720177i	$0.744061\pi$
$684$		−	161.723i		−	0.236437i
$685$		0			0
$686$			83.0661i			0.121088i
$687$			161.830i			0.235561i
$688$		−	19.8629i		−	0.0288705i
$689$		−	620.515i		−	0.900602i
$690$		0			0
$691$	−600.541			−0.869090			−0.434545	−	0.900650i	$-0.643091\pi$
$691$	−600.541			−0.869090			−0.434545	+	0.900650i	$0.643091\pi$
$692$	48.0128			0.0693826
$693$	−919.525			−1.32688
$694$	87.6863			0.126349
$695$		0			0
$696$	172.821			0.248306
$697$			2055.18i			2.94861i
$698$	185.818			0.266215
$699$	−548.932			−0.785311
$700$		0			0
$701$			907.376i			1.29440i	0.762319	+	0.647201i	$0.224061\pi$
$701$			907.376i			1.29440i	−0.762319	+	0.647201i	$0.775939\pi$
$702$	752.330			1.07170
$703$	13.3108			0.0189343
$704$		−	104.190i		−	0.147997i
$705$		0			0
$706$	−250.302			−0.354536
$707$			132.342i			0.187188i
$708$	−270.657			−0.382285
$709$			657.300i			0.927081i	0.886076	+	0.463540i	$0.153421\pi$
$709$			657.300i			0.927081i	−0.886076	+	0.463540i	$0.846579\pi$
$710$		0			0
$711$		−	556.456i		−	0.782638i
$712$		−	386.963i		−	0.543488i
$713$	326.565	−	282.302i	0.458015	−	0.395935i
$714$	584.810			0.819062
$715$		0			0
$716$	−402.356			−0.561949
$717$	−200.360			−0.279442
$718$		−	265.661i		−	0.370001i
$719$	1095.72			1.52395			0.761975	−	0.647606i	$-0.224230\pi$
$719$	1095.72			1.52395			0.761975	+	0.647606i	$0.224230\pi$
$720$		0			0
$721$	−920.015			−1.27603
$722$	−318.046			−0.440507
$723$			118.428i			0.163801i
$724$		−	404.715i		−	0.558999i
$725$		0			0
$726$	−98.8960			−0.136220
$727$		−	814.942i		−	1.12097i	−0.828166	−	0.560483i	$-0.810616\pi$
$727$		−	814.942i		−	1.12097i	0.828166	−	0.560483i	$-0.189384\pi$
$728$			668.881i			0.918793i
$729$	92.7324			0.127205
$730$		0			0
$731$	−140.147			−0.191719
$732$		−	214.402i		−	0.292899i
$733$			742.293i			1.01268i	0.862335	+	0.506339i	$0.169001\pi$
$733$			742.293i			1.01268i	−0.862335	+	0.506339i	$0.830999\pi$
$734$			181.740i			0.247602i
$735$		0			0
$736$	−98.4285	+	85.0872i	−0.133734	+	0.115608i
$737$	1043.08			1.41530
$738$	−713.781			−0.967183
$739$	−288.013			−0.389733			−0.194866	−	0.980830i	$-0.562427\pi$
$739$	−288.013			−0.389733			−0.194866	+	0.980830i	$0.562427\pi$
$740$		0			0
$741$			389.573i			0.525740i
$742$	385.052			0.518937
$743$		−	199.651i		−	0.268709i	−0.990933	−	0.134354i	$-0.957104\pi$
$743$		−	199.651i		−	0.268709i	0.990933	−	0.134354i	$-0.0428961\pi$
$744$	76.3556			0.102629
$745$		0			0
$746$			112.137i			0.150318i
$747$			655.993i			0.878170i
$748$	−735.132			−0.982797
$749$	−1886.28			−2.51839
$750$		0			0
$751$			610.667i			0.813138i	0.913620	+	0.406569i	$0.133275\pi$
$751$			610.667i			0.813138i	−0.913620	+	0.406569i	$0.866725\pi$
$752$	3.25344			0.00432638
$753$			465.925i			0.618758i
$754$	1394.67			1.84969
$755$		0			0
$756$			466.847i			0.617523i
$757$		−	241.235i		−	0.318672i	−0.987224	−	0.159336i	$-0.949065\pi$
$757$		−	241.235i		−	0.318672i	0.987224	−	0.159336i	$-0.0509354\pi$
$758$		−	569.319i		−	0.751080i
$759$	281.771	+	325.952i	0.371240	+	0.429449i
$760$		0			0
$761$	568.126			0.746552			0.373276	−	0.927720i	$-0.378235\pi$
$761$	568.126			0.746552			0.373276	+	0.927720i	$0.378235\pi$
$762$	229.778			0.301546
$763$	140.828			0.184571
$764$			222.605i			0.291368i
$765$		0			0
$766$		−	523.539i		−	0.683472i
$767$	−2184.21			−2.84773
$768$	−23.0140			−0.0299661
$769$		−	425.966i		−	0.553922i	−0.960881	−	0.276961i	$-0.910673\pi$
$769$		−	425.966i		−	0.553922i	0.960881	−	0.276961i	$-0.0893273\pi$
$770$		0			0
$771$	−360.738			−0.467883
$772$	328.163			0.425081
$773$		−	849.417i		−	1.09886i	−0.835540	−	0.549429i	$-0.814845\pi$
$773$		−	849.417i		−	1.09886i	0.835540	−	0.549429i	$-0.185155\pi$
$774$		−	48.6742i		−	0.0628866i
$775$		0			0
$776$			6.58079i			0.00848040i
$777$	−16.7172			−0.0215151
$778$		−	17.0552i		−	0.0219218i
$779$		−	849.553i		−	1.09057i
$780$		0			0
$781$			1087.87i			1.39293i
$782$	600.350	+	694.482i	0.767711	+	0.888084i
$783$	973.411			1.24318
$784$	−219.064			−0.279419
$785$		0			0
$786$	−24.6986			−0.0314232
$787$			1448.81i			1.84093i	0.390828	+	0.920464i	$0.372189\pi$
$787$			1448.81i			1.84093i	−0.390828	+	0.920464i	$0.627811\pi$
$788$	659.123			0.836451
$789$			398.254i			0.504758i
$790$		0			0
$791$	1818.61			2.29912
$792$		−	255.318i		−	0.322371i
$793$		−	1730.23i		−	2.18188i
$794$	330.280			0.415970
$795$		0			0
$796$		−	675.773i		−	0.848961i
$797$		−	405.786i		−	0.509141i	−0.967054	−	0.254571i	$-0.918066\pi$
$797$		−	405.786i		−	0.509141i	0.967054	−	0.254571i	$-0.0819342\pi$
$798$	−241.744			−0.302937
$799$		−	22.9553i		−	0.0287300i
$800$		0			0
$801$		−	948.256i		−	1.18384i
$802$		−	161.322i		−	0.201150i
$803$		−	117.070i		−	0.145791i
$804$		−	230.401i		−	0.286568i
$805$		0			0
$806$	616.191			0.764504
$807$	112.337			0.139204
$808$	−36.7465			−0.0454783
$809$	755.183			0.933477			0.466739	−	0.884395i	$-0.345429\pi$
$809$	755.183			0.933477			0.466739	+	0.884395i	$0.345429\pi$
$810$		0			0
$811$	−1132.66			−1.39662			−0.698311	−	0.715795i	$-0.746065\pi$
$811$	−1132.66			−1.39662			−0.698311	+	0.715795i	$0.746065\pi$
$812$			865.439i			1.06581i
$813$	−476.894			−0.586586
$814$	21.0143			0.0258161
$815$		0			0
$816$			162.380i			0.198995i
$817$	57.9328			0.0709091
$818$	−178.122			−0.217754
$819$			1639.10i			2.00134i
$820$		0			0
$821$	167.684			0.204244			0.102122	−	0.994772i	$-0.467437\pi$
$821$	167.684			0.204244			0.102122	+	0.994772i	$0.467437\pi$
$822$			346.913i			0.422035i
$823$	403.176			0.489886			0.244943	−	0.969538i	$-0.421231\pi$
$823$	403.176			0.489886			0.244943	+	0.969538i	$0.421231\pi$
$824$		−	255.454i		−	0.310016i
$825$		0			0
$826$		−	1355.38i		−	1.64089i
$827$			901.234i			1.08976i	0.838513	+	0.544881i	$0.183425\pi$
$827$			901.234i			1.08976i	−0.838513	+	0.544881i	$0.816575\pi$
$828$	−241.200	+	208.507i	−0.291304	+	0.251820i
$829$	−455.150			−0.549034			−0.274517	−	0.961582i	$-0.588518\pi$
$829$	−455.150			−0.549034			−0.274517	+	0.961582i	$0.588518\pi$
$830$		0			0
$831$	−512.024			−0.616155
$832$	−185.723			−0.223225
$833$			1545.65i			1.85553i
$834$	78.4128			0.0940201
$835$		0			0
$836$	303.883			0.363496
$837$	430.072			0.513826
$838$			192.147i			0.229292i
$839$			150.136i			0.178946i	0.995989	+	0.0894730i	$0.0285183\pi$
$839$			150.136i			0.178946i	−0.995989	+	0.0894730i	$0.971482\pi$
$840$		0			0
$841$	963.503			1.14566
$842$			274.514i			0.326026i
$843$		−	563.033i		−	0.667892i
$844$	223.311			0.264587
$845$		0			0
$846$	7.97257			0.00942385
$847$		−	495.244i		−	0.584704i
$848$			106.914i			0.126078i
$849$			192.190i			0.226373i
$850$		0			0
$851$	−17.1614	−	19.8523i	−0.0201662	−	0.0233281i
$852$	240.296			0.282037
$853$	−582.826			−0.683266			−0.341633	−	0.939833i	$-0.610980\pi$
$853$	−582.826			−0.683266			−0.341633	+	0.939833i	$0.610980\pi$
$854$	1073.67			1.25722
$855$		0			0
$856$		−	523.748i		−	0.611856i
$857$	435.647			0.508339			0.254170	−	0.967160i	$-0.418198\pi$
$857$	435.647			0.508339			0.254170	+	0.967160i	$0.418198\pi$
$858$			615.033i			0.716822i
$859$	−427.848			−0.498076			−0.249038	−	0.968494i	$-0.580114\pi$
$859$	−427.848			−0.498076			−0.249038	+	0.968494i	$0.580114\pi$
$860$		0			0
$861$			1066.96i			1.23921i
$862$			596.373i			0.691848i
$863$	698.719			0.809640			0.404820	−	0.914396i	$-0.367334\pi$
$863$	698.719			0.809640			0.404820	+	0.914396i	$0.367334\pi$
$864$	−129.626			−0.150030
$865$		0			0
$866$		−	5.35286i		−	0.00618113i
$867$	730.013			0.841999
$868$			382.368i			0.440516i
$869$	1045.60			1.20322
$870$		0			0
$871$		−	1859.34i		−	2.13471i
$872$			39.1025i			0.0448424i
$873$			16.1263i			0.0184722i
$874$	−248.168	−	287.079i	−0.283945	−	0.328466i
$875$		0			0
$876$	−25.8590			−0.0295194
$877$	−779.272			−0.888566			−0.444283	−	0.895887i	$-0.646541\pi$
$877$	−779.272			−0.888566			−0.444283	+	0.895887i	$0.646541\pi$
$878$	8.73622			0.00995014
$879$			767.307i			0.872932i
$880$		0			0
$881$			1612.85i			1.83070i	0.402659	+	0.915350i	$0.368086\pi$
$881$			1612.85i			1.83070i	−0.402659	+	0.915350i	$0.631914\pi$
$882$	−536.818			−0.608638
$883$	336.489			0.381075			0.190537	−	0.981680i	$-0.438977\pi$
$883$	336.489			0.381075			0.190537	+	0.981680i	$0.438977\pi$
$884$			1310.41i			1.48236i
$885$		0			0
$886$	−575.331			−0.649358
$887$	12.5177			0.0141124			0.00705619	−	0.999975i	$-0.497754\pi$
$887$	12.5177			0.0141124			0.00705619	+	0.999975i	$0.497754\pi$
$888$		−	4.64174i		−	0.00522719i
$889$			1150.67i			1.29434i
$890$		0			0
$891$		−	383.152i		−	0.430025i
$892$	727.090			0.815123
$893$			9.48907i			0.0106261i
$894$			165.607i			0.185242i
$895$		0			0
$896$		−	115.248i		−	0.128625i
$897$	581.024	−	502.271i	0.647741	−	0.559945i
$898$	410.095			0.456676
$899$	797.265			0.886835
$900$		0			0
$901$	754.356			0.837243
$902$		−	1341.22i		−	1.48694i
$903$	−72.7584			−0.0805741
$904$			504.959i			0.558583i
$905$		0			0
$906$	324.817			0.358517
$907$		−	1320.74i		−	1.45616i	−0.685492	−	0.728080i	$-0.740413\pi$
$907$		−	1320.74i		−	1.45616i	0.685492	−	0.728080i	$-0.259587\pi$
$908$		−	22.6736i		−	0.0249709i
$909$	−90.0475			−0.0990621
$910$		0			0
$911$		−	1388.64i		−	1.52430i	−0.647398	−	0.762152i	$-0.724143\pi$
$911$		−	1388.64i		−	1.52430i	0.647398	−	0.762152i	$-0.275857\pi$
$912$		−	67.1233i		−	0.0736001i
$913$	−1232.63			−1.35009
$914$		−	317.392i		−	0.347256i
$915$		0			0
$916$		−	225.018i		−	0.245653i
$917$		−	123.684i		−	0.134879i
$918$			914.602i			0.996299i
$919$		−	814.108i		−	0.885863i	−0.896555	−	0.442932i	$-0.853938\pi$
$919$		−	814.108i		−	0.885863i	0.896555	−	0.442932i	$-0.146062\pi$
$920$		0			0
$921$	406.566			0.441440
$922$	−756.123			−0.820090
$923$	1939.19			2.10096
$924$	−381.650			−0.413041
$925$		0			0
$926$	235.078			0.253864
$927$		−	625.991i		−	0.675286i
$928$	−240.300			−0.258944
$929$	951.041			1.02373			0.511863	−	0.859067i	$-0.328956\pi$
$929$	951.041			1.02373			0.511863	+	0.859067i	$0.328956\pi$
$930$		0			0
$931$		−	638.929i		−	0.686283i
$932$	763.268			0.818957
$933$	277.903			0.297859
$934$			160.874i			0.172242i
$935$		0			0
$936$	−455.116			−0.486235
$937$			25.4596i			0.0271713i	0.999908	+	0.0135857i	$0.00432459\pi$
$937$			25.4596i			0.0271713i	−0.999908	+	0.0135857i	$0.995675\pi$
$938$	1153.78			1.23005
$939$		−	574.313i		−	0.611622i
$940$		0			0
$941$			1304.69i			1.38650i	0.720698	+	0.693249i	$0.243821\pi$
$941$			1304.69i			1.38650i	−0.720698	+	0.693249i	$0.756179\pi$
$942$			78.5093i			0.0833432i
$943$	−1267.05	+	1095.31i	−1.34364	+	1.16152i
$944$	376.338			0.398663
$945$		0			0
$946$	91.4605			0.0966813
$947$	25.1178			0.0265236			0.0132618	−	0.999912i	$-0.495779\pi$
$947$	25.1178			0.0265236			0.0132618	+	0.999912i	$0.495779\pi$
$948$		−	230.957i		−	0.243626i
$949$	−208.683			−0.219897
$950$		0			0
$951$	−52.5434			−0.0552507
$952$	−813.154			−0.854153
$953$			663.560i			0.696286i	0.937442	+	0.348143i	$0.113188\pi$
$953$			663.560i			0.696286i	−0.937442	+	0.348143i	$0.886812\pi$
$954$			261.994i			0.274627i
$955$		0			0
$956$	278.592			0.291414
$957$			795.767i			0.831523i
$958$			221.061i			0.230753i
$959$	−1737.24			−1.81152
$960$		0			0
$961$	−608.753			−0.633457
$962$		−	37.4589i		−	0.0389386i
$963$		−	1283.45i		−	1.33276i
$964$		−	164.669i		−	0.170819i
$965$		0			0
$966$	311.677	+	360.546i	0.322647	+	0.373236i
$967$	661.312			0.683880			0.341940	−	0.939722i	$-0.388916\pi$
$967$	661.312			0.683880			0.341940	+	0.939722i	$0.388916\pi$
$968$	137.511			0.142057
$969$	−473.602			−0.488753
$970$		0			0
$971$		−	1198.53i		−	1.23433i	−0.786834	−	0.617165i	$-0.788281\pi$
$971$		−	1198.53i		−	1.23433i	0.786834	−	0.617165i	$-0.211719\pi$
$972$	−497.100			−0.511420
$973$			392.670i			0.403566i
$974$	−294.042			−0.301891
$975$		0			0
$976$			298.117i			0.305448i
$977$		−	1156.31i		−	1.18353i	−0.806110	−	0.591765i	$-0.798431\pi$
$977$		−	1156.31i		−	1.18353i	0.806110	−	0.591765i	$-0.201569\pi$
$978$	−305.717			−0.312594
$979$	1781.80			1.82002
$980$		0			0
$981$			95.8210i			0.0976768i
$982$	655.268			0.667279
$983$		−	534.831i		−	0.544080i	−0.962286	−	0.272040i	$-0.912302\pi$
$983$		−	534.831i		−	0.544080i	0.962286	−	0.272040i	$-0.0876983\pi$
$984$	−296.255			−0.301073
$985$		0			0
$986$			1695.48i			1.71956i
$987$		−	11.9174i		−	0.0120744i
$988$		−	541.685i		−	0.548265i
$989$	−74.6918	−	86.4030i	−0.0755225	−	0.0873640i
$990$		0			0
$991$	−217.485			−0.219461			−0.109730	−	0.993961i	$-0.534999\pi$
$991$	−217.485			−0.219461			−0.109730	+	0.993961i	$0.534999\pi$
$992$	−106.169			−0.107025
$993$	−123.615			−0.124486
$994$			1203.33i			1.21060i
$995$		0			0
$996$			272.270i			0.273364i
$997$	248.055			0.248801			0.124400	−	0.992232i	$-0.460299\pi$
$997$	248.055			0.248801			0.124400	+	0.992232i	$0.460299\pi$
$998$	71.8105			0.0719544
$999$		−	26.1446i		−	0.0261707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.3.d.b.551.4		16
5.2	odd	4		1150.3.c.c.1149.1		32
5.3	odd	4		1150.3.c.c.1149.32		32
5.4	even	2		230.3.d.a.91.13	✓	16
15.14	odd	2		2070.3.c.a.91.5		16
20.19	odd	2		1840.3.k.d.321.7		16
23.22	odd	2	inner	1150.3.d.b.551.3		16
115.22	even	4		1150.3.c.c.1149.31		32
115.68	even	4		1150.3.c.c.1149.2		32
115.114	odd	2		230.3.d.a.91.14	yes	16
345.344	even	2		2070.3.c.a.91.4		16
460.459	even	2		1840.3.k.d.321.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.13	✓	16	5.4	even	2
230.3.d.a.91.14	yes	16	115.114	odd	2
1150.3.c.c.1149.1		32	5.2	odd	4
1150.3.c.c.1149.2		32	115.68	even	4
1150.3.c.c.1149.31		32	115.22	even	4
1150.3.c.c.1149.32		32	5.3	odd	4
1150.3.d.b.551.3		16	23.22	odd	2	inner
1150.3.d.b.551.4		16	1.1	even	1	trivial
1840.3.k.d.321.7		16	20.19	odd	2
1840.3.k.d.321.8		16	460.459	even	2
2070.3.c.a.91.4		16	345.344	even	2
2070.3.c.a.91.5		16	15.14	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -1.43837 q^{3} +2.00000 q^{4} +2.03417 q^{6} +10.1866i q^{7} -2.82843 q^{8} -6.93108 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -1.43837 q^{3} +2.00000 q^{4} +2.03417 q^{6} +10.1866i q^{7} -2.82843 q^{8} -6.93108 q^{9} -13.0237i q^{11} -2.87675 q^{12} -23.2154 q^{13} -14.4060i q^{14} +4.00000 q^{16} -28.2228i q^{17} +9.80202 q^{18} +11.6665i q^{19} -14.6521i q^{21} +18.4183i q^{22} +(17.3999 - 15.0414i) q^{23} +4.06834 q^{24} +32.8315 q^{26} +22.9149 q^{27} +20.3731i q^{28} +42.4794 q^{29} +18.7683 q^{31} -5.65685 q^{32} +18.7330i q^{33} +39.9131i q^{34} -13.8622 q^{36} -1.14094i q^{37} -16.4989i q^{38} +33.3924 q^{39} -72.8198 q^{41} +20.7212i q^{42} -4.96573i q^{43} -26.0474i q^{44} +(-24.6071 + 21.2718i) q^{46} +0.813360 q^{47} -5.75350 q^{48} -54.7661 q^{49} +40.5950i q^{51} -46.4308 q^{52} +26.7286i q^{53} -32.4065 q^{54} -28.8120i q^{56} -16.7808i q^{57} -60.0750 q^{58} +94.0845 q^{59} +74.5293i q^{61} -26.5423 q^{62} -70.6039i q^{63} +8.00000 q^{64} -26.4925i q^{66} +80.0906i q^{67} -56.4456i q^{68} +(-25.0275 + 21.6352i) q^{69} -83.5303 q^{71} +19.6040 q^{72} +8.98897 q^{73} +1.61354i q^{74} +23.3330i q^{76} +132.667 q^{77} -47.2241 q^{78} +80.2841i q^{79} +29.4195 q^{81} +102.983 q^{82} -94.6451i q^{83} -29.3042i q^{84} +7.02261i q^{86} -61.1014 q^{87} +36.8367i q^{88} +136.812i q^{89} -236.485i q^{91} +(34.7997 - 30.0829i) q^{92} -26.9958 q^{93} -1.15026 q^{94} +8.13668 q^{96} -2.32666i q^{97} +77.4509 q^{98} +90.2684i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} - 24 q^{13} + 64 q^{16} + 32 q^{18} - 4 q^{23} - 16 q^{24} + 96 q^{26} + 96 q^{27} - 108 q^{29} - 116 q^{31} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} + 128 q^{47} - 28 q^{49} - 48 q^{52} + 224 q^{54} - 160 q^{58} + 204 q^{59} - 64 q^{62} + 128 q^{64} - 268 q^{69} + 236 q^{71} + 64 q^{72} + 112 q^{73} + 936 q^{77} + 432 q^{78} - 136 q^{81} + 64 q^{82} + 152 q^{87} - 8 q^{92} - 856 q^{93} - 216 q^{94} - 32 q^{96} - 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 - 24 * q^13 + 64 * q^16 + 32 * q^18 - 4 * q^23 - 16 * q^24 + 96 * q^26 + 96 * q^27 - 108 * q^29 - 116 * q^31 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 + 128 * q^47 - 28 * q^49 - 48 * q^52 + 224 * q^54 - 160 * q^58 + 204 * q^59 - 64 * q^62 + 128 * q^64 - 268 * q^69 + 236 * q^71 + 64 * q^72 + 112 * q^73 + 936 * q^77 + 432 * q^78 - 136 * q^81 + 64 * q^82 + 152 * q^87 - 8 * q^92 - 856 * q^93 - 216 * q^94 - 32 * q^96 - 256 * q^98

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