LMFDB - Embedded newform 475.3.c.g.151.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(151,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, 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("475.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.c (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:	$12.9428125571$
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} + 30x^{10} + 329x^{8} + 1620x^{6} + 3479x^{4} + 2470x^{2} + 55 $ x^12 + 30x^10 + 329x^8 + 1620x^6 + 3479x^4 + 2470*x^2 + 55
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.12
Root			$3.38208i$ of defining polynomial
Character	$\chi$	$=$	475.151
Dual form			475.3.c.g.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.38208i q^{2} +4.08851i q^{3} -7.43849 q^{4} -13.8277 q^{6} -4.56923 q^{7} -11.6293i q^{8} -7.71590 q^{9} +O(q^{10})$	\(q+3.38208i q^{2} +4.08851i q^{3} -7.43849 q^{4} -13.8277 q^{6} -4.56923 q^{7} -11.6293i q^{8} -7.71590 q^{9} +6.24529 q^{11} -30.4124i q^{12} -14.4666i q^{13} -15.4535i q^{14} +9.57723 q^{16} -26.6967 q^{17} -26.0958i q^{18} +(-18.2451 - 5.30257i) q^{19} -18.6813i q^{21} +21.1221i q^{22} +33.4334 q^{23} +47.5464 q^{24} +48.9271 q^{26} +5.25004i q^{27} +33.9882 q^{28} +10.3640i q^{29} -30.5308i q^{31} -14.1261i q^{32} +25.5339i q^{33} -90.2906i q^{34} +57.3947 q^{36} +18.1542i q^{37} +(17.9338 - 61.7064i) q^{38} +59.1466 q^{39} +65.5629i q^{41} +63.1819 q^{42} -71.3965 q^{43} -46.4556 q^{44} +113.075i q^{46} -53.1345 q^{47} +39.1566i q^{48} -28.1221 q^{49} -109.150i q^{51} +107.609i q^{52} +21.9762i q^{53} -17.7561 q^{54} +53.1369i q^{56} +(21.6796 - 74.5951i) q^{57} -35.0518 q^{58} +92.9158i q^{59} -27.8117 q^{61} +103.258 q^{62} +35.2557 q^{63} +86.0847 q^{64} -86.3579 q^{66} -60.7093i q^{67} +198.583 q^{68} +136.693i q^{69} -103.561i q^{71} +89.7304i q^{72} +11.9203 q^{73} -61.3990 q^{74} +(135.716 + 39.4432i) q^{76} -28.5362 q^{77} +200.039i q^{78} +9.41895i q^{79} -90.9080 q^{81} -221.739 q^{82} +15.2174 q^{83} +138.961i q^{84} -241.469i q^{86} -42.3732 q^{87} -72.6282i q^{88} +11.8378i q^{89} +66.1010i q^{91} -248.694 q^{92} +124.826 q^{93} -179.705i q^{94} +57.7548 q^{96} +62.0200i q^{97} -95.1114i q^{98} -48.1881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9}+O(q^{10}) $ 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9	$ 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9} + 32 q^{11} - 44 q^{16} + 44 q^{17} + 8 q^{19} - 36 q^{23} + 100 q^{24} + 108 q^{26} + 36 q^{28} - 80 q^{36} + 44 q^{38} + 76 q^{39} - 100 q^{42} - 320 q^{43} - 256 q^{44} + 56 q^{47} + 72 q^{49} - 76 q^{54} - 60 q^{57} - 68 q^{58} - 296 q^{61} + 376 q^{62} + 96 q^{63} + 188 q^{64} + 152 q^{66} + 340 q^{68} + 244 q^{73} + 136 q^{74} + 248 q^{76} + 200 q^{77} - 372 q^{81} - 424 q^{82} + 160 q^{83} - 444 q^{87} - 716 q^{92} - 296 q^{93} - 44 q^{96} - 312 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9 + 32 * q^11 - 44 * q^16 + 44 * q^17 + 8 * q^19 - 36 * q^23 + 100 * q^24 + 108 * q^26 + 36 * q^28 - 80 * q^36 + 44 * q^38 + 76 * q^39 - 100 * q^42 - 320 * q^43 - 256 * q^44 + 56 * q^47 + 72 * q^49 - 76 * q^54 - 60 * q^57 - 68 * q^58 - 296 * q^61 + 376 * q^62 + 96 * q^63 + 188 * q^64 + 152 * q^66 + 340 * q^68 + 244 * q^73 + 136 * q^74 + 248 * q^76 + 200 * q^77 - 372 * q^81 - 424 * q^82 + 160 * q^83 - 444 * q^87 - 716 * q^92 - 296 * q^93 - 44 * q^96 - 312 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$-1$

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 $

$2$			3.38208i			1.69104i	0.533942	+	0.845521i	$0.320710\pi$
$2$			3.38208i			1.69104i	−0.533942	+	0.845521i	$0.679290\pi$
$3$			4.08851i			1.36284i	0.731894	+	0.681418i	$0.238636\pi$
$3$			4.08851i			1.36284i	−0.731894	+	0.681418i	$0.761364\pi$
$4$	−7.43849			−1.85962
$5$		0			0
$5$		0			0
$6$	−13.8277			−2.30461
$7$	−4.56923			−0.652747			−0.326374	−	0.945241i	$-0.605827\pi$
$7$	−4.56923			−0.652747			−0.326374	+	0.945241i	$0.605827\pi$
$8$		−	11.6293i		−	1.45366i
$9$	−7.71590			−0.857323
$10$		0			0
$11$	6.24529			0.567754			0.283877	−	0.958861i	$-0.408379\pi$
$11$	6.24529			0.567754			0.283877	+	0.958861i	$0.408379\pi$
$12$		−	30.4124i		−	2.53436i
$13$		−	14.4666i		−	1.11281i	−0.830911	−	0.556406i	$-0.812180\pi$
$13$		−	14.4666i		−	1.11281i	0.830911	−	0.556406i	$-0.187820\pi$
$14$		−	15.4535i		−	1.10382i
$15$		0			0
$16$	9.57723			0.598577
$17$	−26.6967			−1.57040			−0.785198	−	0.619245i	$-0.787439\pi$
$17$	−26.6967			−1.57040			−0.785198	+	0.619245i	$0.787439\pi$
$18$		−	26.0958i		−	1.44977i
$19$	−18.2451	−	5.30257i	−0.960267	−	0.279083i
$19$	−18.2451	−	5.30257i	−0.960267	−	0.279083i
$20$		0			0
$21$		−	18.6813i		−	0.889588i
$22$			21.1221i			0.960095i
$23$	33.4334			1.45363			0.726813	−	0.686836i	$-0.241001\pi$
$23$	33.4334			1.45363			0.726813	+	0.686836i	$0.241001\pi$
$24$	47.5464			1.98110
$25$		0			0
$26$	48.9271			1.88181
$27$			5.25004i			0.194446i
$28$	33.9882			1.21386
$29$			10.3640i			0.357378i	0.983906	+	0.178689i	$0.0571856\pi$
$29$			10.3640i			0.357378i	−0.983906	+	0.178689i	$0.942814\pi$
$30$		0			0
$31$		−	30.5308i		−	0.984865i	−0.870351	−	0.492433i	$-0.836108\pi$
$31$		−	30.5308i		−	0.984865i	0.870351	−	0.492433i	$-0.163892\pi$
$32$		−	14.1261i		−	0.441442i
$33$			25.5339i			0.773755i
$34$		−	90.2906i		−	2.65561i
$35$		0			0
$36$	57.3947			1.59430
$37$			18.1542i			0.490653i	0.969440	+	0.245327i	$0.0788952\pi$
$37$			18.1542i			0.490653i	−0.969440	+	0.245327i	$0.921105\pi$
$38$	17.9338	−	61.7064i	0.471941	−	1.62385i
$39$	59.1466			1.51658
$40$		0			0
$41$			65.5629i			1.59909i	0.600603	+	0.799547i	$0.294927\pi$
$41$			65.5629i			1.59909i	−0.600603	+	0.799547i	$0.705073\pi$
$42$	63.1819			1.50433
$43$	−71.3965			−1.66038			−0.830191	−	0.557479i	$-0.811769\pi$
$43$	−71.3965			−1.66038			−0.830191	+	0.557479i	$0.811769\pi$
$44$	−46.4556			−1.05581
$45$		0			0
$46$			113.075i			2.45814i
$47$	−53.1345			−1.13052			−0.565261	−	0.824912i	$-0.691224\pi$
$47$	−53.1345			−1.13052			−0.565261	+	0.824912i	$0.691224\pi$
$48$			39.1566i			0.815762i
$49$	−28.1221			−0.573921
$50$		0			0
$51$		−	109.150i		−	2.14019i
$52$			107.609i			2.06941i
$53$			21.9762i			0.414646i	0.978273	+	0.207323i	$0.0664750\pi$
$53$			21.9762i			0.414646i	−0.978273	+	0.207323i	$0.933525\pi$
$54$	−17.7561			−0.328816
$55$		0			0
$56$			53.1369i			0.948873i
$57$	21.6796	−	74.5951i	0.380344	−	1.30869i
$58$	−35.0518			−0.604341
$59$			92.9158i			1.57484i	0.616414	+	0.787422i	$0.288585\pi$
$59$			92.9158i			1.57484i	−0.616414	+	0.787422i	$0.711415\pi$
$60$		0			0
$61$	−27.8117			−0.455929			−0.227964	−	0.973669i	$-0.573207\pi$
$61$	−27.8117			−0.455929			−0.227964	+	0.973669i	$0.573207\pi$
$62$	103.258			1.66545
$63$	35.2557			0.559615
$64$	86.0847			1.34507
$65$		0			0
$66$	−86.3579			−1.30845
$67$		−	60.7093i		−	0.906109i	−0.891483	−	0.453055i	$-0.850334\pi$
$67$		−	60.7093i		−	0.906109i	0.891483	−	0.453055i	$-0.149666\pi$
$68$	198.583			2.92035
$69$			136.693i			1.98105i
$70$		0			0
$71$		−	103.561i		−	1.45861i	−0.684188	−	0.729306i	$-0.739843\pi$
$71$		−	103.561i		−	1.45861i	0.684188	−	0.729306i	$-0.260157\pi$
$72$			89.7304i			1.24626i
$73$	11.9203			0.163292			0.0816461	−	0.996661i	$-0.473982\pi$
$73$	11.9203			0.163292			0.0816461	+	0.996661i	$0.473982\pi$
$74$	−61.3990			−0.829716
$75$		0			0
$76$	135.716	+	39.4432i	1.78574	+	0.518989i
$77$	−28.5362			−0.370600
$78$			200.039i			2.56460i
$79$			9.41895i			0.119227i	0.998222	+	0.0596136i	$0.0189869\pi$
$79$			9.41895i			0.119227i	−0.998222	+	0.0596136i	$0.981013\pi$
$80$		0			0
$81$	−90.9080			−1.12232
$82$	−221.739			−2.70414
$83$	15.2174			0.183343			0.0916714	−	0.995789i	$-0.470779\pi$
$83$	15.2174			0.183343			0.0916714	+	0.995789i	$0.470779\pi$
$84$			138.961i			1.65430i
$85$		0			0
$86$		−	241.469i		−	2.80778i
$87$	−42.3732			−0.487048
$88$		−	72.6282i		−	0.825321i
$89$			11.8378i			0.133009i	0.997786	+	0.0665047i	$0.0211847\pi$
$89$			11.8378i			0.133009i	−0.997786	+	0.0665047i	$0.978815\pi$
$90$		0			0
$91$			66.1010i			0.726385i
$92$	−248.694			−2.70320
$93$	124.826			1.34221
$94$		−	179.705i		−	1.91176i
$95$		0			0
$96$	57.7548			0.601613
$97$			62.0200i			0.639381i	0.947522	+	0.319691i	$0.103579\pi$
$97$			62.0200i			0.639381i	−0.947522	+	0.319691i	$0.896421\pi$
$98$		−	95.1114i		−	0.970525i
$99$	−48.1881			−0.486748
$100$		0			0
$101$	139.132			1.37755			0.688773	−	0.724977i	$-0.258150\pi$
$101$	139.132			1.37755			0.688773	+	0.724977i	$0.258150\pi$
$102$	369.154			3.61916
$103$			137.668i			1.33658i	0.743900	+	0.668291i	$0.232974\pi$
$103$			137.668i			1.33658i	−0.743900	+	0.668291i	$0.767026\pi$
$104$	−168.236			−1.61765
$105$		0			0
$106$	−74.3254			−0.701183
$107$		−	126.783i		−	1.18488i	−0.805613	−	0.592442i	$-0.798164\pi$
$107$		−	126.783i		−	1.18488i	0.805613	−	0.592442i	$-0.201836\pi$
$108$		−	39.0524i		−	0.361596i
$109$			18.4688i			0.169438i	0.996405	+	0.0847191i	$0.0269993\pi$
$109$			18.4688i			0.169438i	−0.996405	+	0.0847191i	$0.973001\pi$
$110$		0			0
$111$	−74.2235			−0.668680
$112$	−43.7606			−0.390719
$113$		−	134.320i		−	1.18867i	−0.804216	−	0.594337i	$-0.797414\pi$
$113$		−	134.320i		−	1.18867i	0.804216	−	0.594337i	$-0.202586\pi$
$114$	252.287	+	73.3223i	2.21304	+	0.643178i
$115$		0			0
$116$		−	77.0923i		−	0.664589i
$117$			111.623i			0.954039i
$118$	−314.249			−2.66313
$119$	121.984			1.02507
$120$		0			0
$121$	−81.9964			−0.677656
$122$		−	94.0614i		−	0.770995i
$123$	−268.054			−2.17930
$124$			227.103i			1.83148i
$125$		0			0
$126$			119.238i			0.946333i
$127$		−	76.6711i		−	0.603709i	−0.953354	−	0.301855i	$-0.902394\pi$
$127$		−	76.6711i		−	0.603709i	0.953354	−	0.301855i	$-0.0976057\pi$
$128$			234.641i			1.83313i
$129$		−	291.905i		−	2.26283i
$130$		0			0
$131$	−82.1678			−0.627235			−0.313617	−	0.949549i	$-0.601541\pi$
$131$	−82.1678			−0.627235			−0.313617	+	0.949549i	$0.601541\pi$
$132$		−	189.934i		−	1.43889i
$133$	83.3659	+	24.2287i	0.626812	+	0.182171i
$134$	205.324			1.53227
$135$		0			0
$136$			310.464i			2.28282i
$137$	38.0930			0.278051			0.139026	−	0.990289i	$-0.455603\pi$
$137$	38.0930			0.278051			0.139026	+	0.990289i	$0.455603\pi$
$138$	−462.306			−3.35004
$139$	−46.5503			−0.334894			−0.167447	−	0.985881i	$-0.553552\pi$
$139$	−46.5503			−0.334894			−0.167447	+	0.985881i	$0.553552\pi$
$140$		0			0
$141$		−	217.241i		−	1.54072i
$142$	350.253			2.46657
$143$		−	90.3478i		−	0.631803i
$144$	−73.8970			−0.513173
$145$		0			0
$146$			40.3156i			0.276134i
$147$		−	114.978i		−	0.782160i
$148$		−	135.040i		−	0.912431i
$149$	−210.319			−1.41153			−0.705767	−	0.708444i	$-0.749397\pi$
$149$	−210.319			−1.41153			−0.705767	+	0.708444i	$0.749397\pi$
$150$		0			0
$151$		−	120.965i		−	0.801093i	−0.916276	−	0.400546i	$-0.868820\pi$
$151$		−	120.965i		−	0.801093i	0.916276	−	0.400546i	$-0.131180\pi$
$152$	−61.6651	+	212.177i	−0.405692	+	1.39590i
$153$	205.989			1.34634
$154$		−	96.5117i		−	0.626700i
$155$		0			0
$156$	−439.962			−2.82027
$157$	248.160			1.58064			0.790319	−	0.612695i	$-0.209915\pi$
$157$	248.160			1.58064			0.790319	+	0.612695i	$0.209915\pi$
$158$	−31.8557			−0.201618
$159$	−89.8500			−0.565094
$160$		0			0
$161$	−152.765			−0.948850
$162$		−	307.458i		−	1.89789i
$163$	−26.4077			−0.162010			−0.0810051	−	0.996714i	$-0.525813\pi$
$163$	−26.4077			−0.162010			−0.0810051	+	0.996714i	$0.525813\pi$
$164$		−	487.689i		−	2.97371i
$165$		0			0
$166$			51.4667i			0.310040i
$167$			256.876i			1.53818i	0.639141	+	0.769089i	$0.279290\pi$
$167$			256.876i			1.53818i	−0.639141	+	0.769089i	$0.720710\pi$
$168$	−217.251			−1.29316
$169$	−40.2813			−0.238351
$170$		0			0
$171$	140.777	+	40.9142i	0.823259	+	0.239264i
$172$	531.082			3.08769
$173$		−	135.679i		−	0.784271i	−0.919907	−	0.392136i	$-0.871736\pi$
$173$		−	135.679i		−	0.784271i	0.919907	−	0.392136i	$-0.128264\pi$
$174$		−	143.310i		−	0.823618i
$175$		0			0
$176$	59.8126			0.339844
$177$	−379.887			−2.14626
$178$	−40.0366			−0.224925
$179$			43.6655i			0.243941i	0.992534	+	0.121971i	$0.0389214\pi$
$179$			43.6655i			0.243941i	−0.992534	+	0.121971i	$0.961079\pi$
$180$		0			0
$181$			247.032i			1.36482i	0.730970	+	0.682410i	$0.239068\pi$
$181$			247.032i			1.36482i	−0.730970	+	0.682410i	$0.760932\pi$
$182$	−223.559			−1.22835
$183$		−	113.708i		−	0.621356i
$184$		−	388.806i		−	2.11308i
$185$		0			0
$186$			422.170i			2.26973i
$187$	−166.729			−0.891598
$188$	395.241			2.10234
$189$		−	23.9886i		−	0.126924i
$190$		0			0
$191$	134.807			0.705795			0.352897	−	0.935662i	$-0.385197\pi$
$191$	134.807			0.705795			0.352897	+	0.935662i	$0.385197\pi$
$192$			351.958i			1.83311i
$193$			41.0916i			0.212910i	0.994318	+	0.106455i	$0.0339500\pi$
$193$			41.0916i			0.212910i	−0.994318	+	0.106455i	$0.966050\pi$
$194$	−209.757			−1.08122
$195$		0			0
$196$	209.186			1.06728
$197$	−100.288			−0.509076			−0.254538	−	0.967063i	$-0.581923\pi$
$197$	−100.288			−0.509076			−0.254538	+	0.967063i	$0.581923\pi$
$198$		−	162.976i		−	0.823111i
$199$	−229.156			−1.15154			−0.575770	−	0.817612i	$-0.695297\pi$
$199$	−229.156			−1.15154			−0.575770	+	0.817612i	$0.695297\pi$
$200$		0			0
$201$	248.211			1.23488
$202$			470.557i			2.32949i
$203$		−	47.3553i		−	0.233278i
$204$			811.910i			3.97995i
$205$		0			0
$206$	−465.605			−2.26022
$207$	−257.969			−1.24623
$208$		−	138.550i		−	0.666103i
$209$	−113.946	−	33.1161i	−0.545195	−	0.158450i
$210$		0			0
$211$			194.492i			0.921765i	0.887461	+	0.460882i	$0.152467\pi$
$211$			194.492i			0.921765i	−0.887461	+	0.460882i	$0.847533\pi$
$212$		−	163.470i		−	0.771085i
$213$	423.412			1.98785
$214$	428.789			2.00369
$215$		0			0
$216$	61.0542			0.282658
$217$			139.502i			0.642868i
$218$	−62.4629			−0.286527
$219$			48.7364i			0.222541i
$220$		0			0
$221$			386.210i			1.74756i
$222$		−	251.030i		−	1.13077i
$223$			29.2071i			0.130974i	0.997853	+	0.0654868i	$0.0208600\pi$
$223$			29.2071i			0.130974i	−0.997853	+	0.0654868i	$0.979140\pi$
$224$			64.5456i			0.288150i
$225$		0			0
$226$	454.282			2.01010
$227$		−	313.596i		−	1.38148i	−0.723104	−	0.690740i	$-0.757285\pi$
$227$		−	313.596i		−	1.38148i	0.723104	−	0.690740i	$-0.242715\pi$
$228$	−161.264	+	554.876i	−0.707297	+	2.43366i
$229$	37.9407			0.165680			0.0828400	−	0.996563i	$-0.473601\pi$
$229$	37.9407			0.165680			0.0828400	+	0.996563i	$0.473601\pi$
$230$		0			0
$231$		−	116.670i		−	0.505067i
$232$	120.525			0.519506
$233$	−416.600			−1.78798			−0.893990	−	0.448086i	$-0.852106\pi$
$233$	−416.600			−1.78798			−0.893990	+	0.448086i	$0.852106\pi$
$234$	−377.517			−1.61332
$235$		0			0
$236$		−	691.154i		−	2.92862i
$237$	−38.5095			−0.162487
$238$			412.559i			1.73344i
$239$	−98.2483			−0.411081			−0.205540	−	0.978649i	$-0.565895\pi$
$239$	−98.2483			−0.411081			−0.205540	+	0.978649i	$0.565895\pi$
$240$		0			0
$241$			85.1333i			0.353250i	0.984278	+	0.176625i	$0.0565180\pi$
$241$			85.1333i			0.353250i	−0.984278	+	0.176625i	$0.943482\pi$
$242$		−	277.319i		−	1.14594i
$243$		−	324.428i		−	1.33509i
$244$	206.877			0.847856
$245$		0			0
$246$		−	906.582i		−	3.68529i
$247$	−76.7100	+	263.943i	−0.310567	+	1.06860i
$248$	−355.051			−1.43166
$249$			62.2167i			0.249866i
$250$		0			0
$251$	118.230			0.471036			0.235518	−	0.971870i	$-0.424321\pi$
$251$	118.230			0.471036			0.235518	+	0.971870i	$0.424321\pi$
$252$	−262.250			−1.04067
$253$	208.801			0.825301
$254$	259.308			1.02090
$255$		0			0
$256$	−449.237			−1.75483
$257$			290.346i			1.12975i	0.825176	+	0.564875i	$0.191076\pi$
$257$			290.346i			1.12975i	−0.825176	+	0.564875i	$0.808924\pi$
$258$	987.247			3.82654
$259$		−	82.9506i		−	0.320273i
$260$		0			0
$261$		−	79.9674i		−	0.306388i
$262$		−	277.898i		−	1.06068i
$263$	−451.882			−1.71818			−0.859092	−	0.511822i	$-0.828971\pi$
$263$	−451.882			−1.71818			−0.859092	+	0.511822i	$0.828971\pi$
$264$	296.941			1.12478
$265$		0			0
$266$	−81.9435	+	281.951i	−0.308058	+	1.05996i
$267$	−48.3991			−0.181270
$268$			451.586i			1.68502i
$269$		−	110.442i		−	0.410567i	−0.978703	−	0.205283i	$-0.934188\pi$
$269$		−	110.442i		−	0.410567i	0.978703	−	0.205283i	$-0.0658116\pi$
$270$		0			0
$271$	−502.913			−1.85577			−0.927883	−	0.372871i	$-0.878373\pi$
$271$	−502.913			−1.85577			−0.927883	+	0.372871i	$0.878373\pi$
$272$	−255.681			−0.940002
$273$	−270.255			−0.989944
$274$			128.834i			0.470196i
$275$		0			0
$276$		−	1016.79i		−	3.68401i
$277$	180.350			0.651084			0.325542	−	0.945528i	$-0.394453\pi$
$277$	180.350			0.651084			0.325542	+	0.945528i	$0.394453\pi$
$278$		−	157.437i		−	0.566320i
$279$			235.573i			0.844347i
$280$		0			0
$281$			361.878i			1.28782i	0.765100	+	0.643912i	$0.222690\pi$
$281$			361.878i			1.28782i	−0.765100	+	0.643912i	$0.777310\pi$
$282$	734.727			2.60541
$283$	−39.8981			−0.140983			−0.0704914	−	0.997512i	$-0.522457\pi$
$283$	−39.8981			−0.140983			−0.0704914	+	0.997512i	$0.522457\pi$
$284$			770.341i			2.71247i
$285$		0			0
$286$	305.564			1.06841
$287$		−	299.572i		−	1.04380i
$288$			108.996i			0.378458i
$289$	423.715			1.46614
$290$		0			0
$291$	−253.569			−0.871372
$292$	−88.6693			−0.303662
$293$			335.148i			1.14385i	0.820306	+	0.571925i	$0.193803\pi$
$293$			335.148i			1.14385i	−0.820306	+	0.571925i	$0.806197\pi$
$294$	388.864			1.32267
$295$		0			0
$296$	211.120			0.713243
$297$			32.7880i			0.110397i
$298$		−	711.315i		−	2.38696i
$299$		−	483.666i		−	1.61761i
$300$		0			0
$301$	326.227			1.08381
$302$	409.114			1.35468
$303$			568.843i			1.87737i
$304$	−174.737	−	50.7840i	−0.574793	−	0.167053i
$305$		0			0
$306$			696.674i			2.27671i
$307$			531.973i			1.73281i	0.499341	+	0.866406i	$0.333576\pi$
$307$			531.973i			1.73281i	−0.499341	+	0.866406i	$0.666424\pi$
$308$	212.266			0.689176
$309$	−562.857			−1.82154
$310$		0			0
$311$	−144.171			−0.463572			−0.231786	−	0.972767i	$-0.574457\pi$
$311$	−144.171			−0.463572			−0.231786	+	0.972767i	$0.574457\pi$
$312$		−	687.833i		−	2.20459i
$313$	238.517			0.762036			0.381018	−	0.924568i	$-0.375574\pi$
$313$	238.517			0.762036			0.381018	+	0.924568i	$0.375574\pi$
$314$			839.299i			2.67293i
$315$		0			0
$316$		−	70.0628i		−	0.221718i
$317$			9.36886i			0.0295548i	0.999891	+	0.0147774i	$0.00470396\pi$
$317$			9.36886i			0.0295548i	−0.999891	+	0.0147774i	$0.995296\pi$
$318$		−	303.880i		−	0.955598i
$319$			64.7260i			0.202903i
$320$		0			0
$321$	518.352			1.61480
$322$		−	516.664i		−	1.60455i
$323$	487.084	+	141.561i	1.50800	+	0.438271i
$324$	676.218			2.08709
$325$		0			0
$326$		−	89.3130i		−	0.273966i
$327$	−75.5097			−0.230917
$328$	762.449			2.32454
$329$	242.784			0.737945
$330$		0			0
$331$		−	255.663i		−	0.772396i	−0.922416	−	0.386198i	$-0.873788\pi$
$331$		−	255.663i		−	0.772396i	0.922416	−	0.386198i	$-0.126212\pi$
$332$	−113.195			−0.340948
$333$		−	140.076i		−	0.420648i
$334$	−868.776			−2.60113
$335$		0			0
$336$		−	178.915i		−	0.532486i
$337$			59.1258i			0.175448i	0.996145	+	0.0877238i	$0.0279593\pi$
$337$			59.1258i			0.175448i	−0.996145	+	0.0877238i	$0.972041\pi$
$338$		−	136.235i		−	0.403061i
$339$	549.169			1.61997
$340$		0			0
$341$		−	190.674i		−	0.559161i
$342$	−138.375	+	476.120i	−0.404606	+	1.39217i
$343$	352.389			1.02737
$344$			830.289i			2.41363i
$345$		0			0
$346$	458.878			1.32624
$347$	152.643			0.439894			0.219947	−	0.975512i	$-0.429411\pi$
$347$	152.643			0.439894			0.219947	+	0.975512i	$0.429411\pi$
$348$	315.193			0.905726
$349$	−136.603			−0.391411			−0.195706	−	0.980663i	$-0.562700\pi$
$349$	−136.603			−0.391411			−0.195706	+	0.980663i	$0.562700\pi$
$350$		0			0
$351$	75.9500			0.216382
$352$		−	88.2218i		−	0.250630i
$353$	−220.194			−0.623780			−0.311890	−	0.950118i	$-0.600962\pi$
$353$	−220.194			−0.623780			−0.311890	+	0.950118i	$0.600962\pi$
$354$		−	1284.81i		−	3.62941i
$355$		0			0
$356$		−	88.0557i		−	0.247348i
$357$			498.731i			1.39700i
$358$	−147.680			−0.412515
$359$	217.423			0.605635			0.302817	−	0.953049i	$-0.402073\pi$
$359$	217.423			0.605635			0.302817	+	0.953049i	$0.402073\pi$
$360$		0			0
$361$	304.765	+	193.492i	0.844225	+	0.535988i
$362$	−835.484			−2.30797
$363$		−	335.243i		−	0.923534i
$364$		−	491.692i		−	1.35080i
$365$		0			0
$366$	384.571			1.05074
$367$	363.227			0.989718			0.494859	−	0.868973i	$-0.335220\pi$
$367$	363.227			0.989718			0.494859	+	0.868973i	$0.335220\pi$
$368$	320.199			0.870106
$369$		−	505.877i		−	1.37094i
$370$		0			0
$371$		−	100.414i		−	0.270659i
$372$	−928.514			−2.49601
$373$			14.8850i			0.0399061i	0.999801	+	0.0199531i	$0.00635168\pi$
$373$			14.8850i			0.0399061i	−0.999801	+	0.0199531i	$0.993648\pi$
$374$		−	563.891i		−	1.50773i
$375$		0			0
$376$			617.916i			1.64339i
$377$	149.931			0.397695
$378$	81.1316			0.214634
$379$			214.679i			0.566436i	0.959056	+	0.283218i	$0.0914020\pi$
$379$			214.679i			0.566436i	−0.959056	+	0.283218i	$0.908598\pi$
$380$		0			0
$381$	313.470			0.822757
$382$			455.928i			1.19353i
$383$			556.024i			1.45176i	0.687822	+	0.725880i	$0.258567\pi$
$383$			556.024i			1.45176i	−0.687822	+	0.725880i	$0.741433\pi$
$384$	−959.332			−2.49826
$385$		0			0
$386$	−138.975			−0.360040
$387$	550.888			1.42348
$388$		−	461.335i		−	1.18901i
$389$	64.2081			0.165059			0.0825296	−	0.996589i	$-0.473700\pi$
$389$	64.2081			0.165059			0.0825296	+	0.996589i	$0.473700\pi$
$390$		0			0
$391$	−892.562			−2.28277
$392$			327.040i			0.834286i
$393$		−	335.944i		−	0.854818i
$394$		−	339.183i		−	0.860870i
$395$		0			0
$396$	358.447			0.905168
$397$	5.41669			0.0136441			0.00682203	−	0.999977i	$-0.497828\pi$
$397$	5.41669			0.0136441			0.00682203	+	0.999977i	$0.497828\pi$
$398$		−	775.026i		−	1.94730i
$399$	−99.0592	+	340.842i	−0.248269	+	0.854242i
$400$		0			0
$401$			130.654i			0.325820i	0.986641	+	0.162910i	$0.0520881\pi$
$401$			130.654i			0.325820i	−0.986641	+	0.162910i	$0.947912\pi$
$402$			839.469i			2.08823i
$403$	−441.676			−1.09597
$404$	−1034.93			−2.56172
$405$		0			0
$406$	160.160			0.394482
$407$			113.378i			0.278570i
$408$	−1269.33			−3.11111
$409$			473.522i			1.15776i	0.815414	+	0.578878i	$0.196509\pi$
$409$			473.522i			1.15776i	−0.815414	+	0.578878i	$0.803491\pi$
$410$		0			0
$411$			155.744i			0.378938i
$412$		−	1024.04i		−	2.48554i
$413$		−	424.554i		−	1.02798i
$414$		−	872.472i		−	2.10742i
$415$		0			0
$416$	−204.356			−0.491242
$417$		−	190.321i		−	0.456406i
$418$	112.001	−	385.374i	0.267946	−	0.921948i
$419$	−414.091			−0.988284			−0.494142	−	0.869381i	$-0.664518\pi$
$419$	−414.091			−0.988284			−0.494142	+	0.869381i	$0.664518\pi$
$420$		0			0
$421$			238.371i			0.566201i	0.959090	+	0.283100i	$0.0913630\pi$
$421$			238.371i			0.566201i	−0.959090	+	0.283100i	$0.908637\pi$
$422$	−657.790			−1.55874
$423$	409.981			0.969221
$424$	255.568			0.602754
$425$		0			0
$426$			1432.01i			3.36154i
$427$	127.078			0.297606
$428$			943.072i			2.20344i
$429$	369.388			0.861044
$430$		0			0
$431$		−	432.728i		−	1.00401i	−0.864865	−	0.502005i	$-0.832596\pi$
$431$		−	432.728i		−	1.00401i	0.864865	−	0.502005i	$-0.167404\pi$
$432$			50.2808i			0.116391i
$433$			711.686i			1.64362i	0.569764	+	0.821808i	$0.307035\pi$
$433$			711.686i			1.64362i	−0.569764	+	0.821808i	$0.692965\pi$
$434$	−471.809			−1.08712
$435$		0			0
$436$		−	137.380i		−	0.315091i
$437$	−609.994	−	177.283i	−1.39587	−	0.405682i
$438$	−164.831			−0.376325
$439$		−	381.873i		−	0.869870i	−0.900462	−	0.434935i	$-0.856771\pi$
$439$		−	381.873i		−	0.869870i	0.900462	−	0.434935i	$-0.143229\pi$
$440$		0			0
$441$	216.988			0.492036
$442$	−1306.19			−2.95519
$443$	−409.840			−0.925147			−0.462573	−	0.886581i	$-0.653074\pi$
$443$	−409.840			−0.925147			−0.462573	+	0.886581i	$0.653074\pi$
$444$	552.111			1.24349
$445$		0			0
$446$	−98.7809			−0.221482
$447$		−	859.889i		−	1.92369i
$448$	−393.341			−0.877993
$449$			234.199i			0.521601i	0.965393	+	0.260800i	$0.0839864\pi$
$449$			234.199i			0.521601i	−0.965393	+	0.260800i	$0.916014\pi$
$450$		0			0
$451$			409.459i			0.907891i
$452$			999.140i			2.21049i
$453$	494.567			1.09176
$454$	1060.61			2.33614
$455$		0			0
$456$	−867.488	−	252.118i	−1.90239	−	0.552891i
$457$	614.393			1.34440			0.672202	−	0.740367i	$-0.265348\pi$
$457$	614.393			1.34440			0.672202	+	0.740367i	$0.265348\pi$
$458$			128.319i			0.280172i
$459$		−	140.159i		−	0.305357i
$460$		0			0
$461$	−51.6808			−0.112106			−0.0560530	−	0.998428i	$-0.517852\pi$
$461$	−51.6808			−0.112106			−0.0560530	+	0.998428i	$0.517852\pi$
$462$	394.589			0.854089
$463$	−364.290			−0.786804			−0.393402	−	0.919367i	$-0.628702\pi$
$463$	−364.290			−0.786804			−0.393402	+	0.919367i	$0.628702\pi$
$464$			99.2580i			0.213918i
$465$		0			0
$466$		−	1408.97i		−	3.02355i
$467$	358.002			0.766599			0.383300	−	0.923624i	$-0.374788\pi$
$467$	358.002			0.766599			0.383300	+	0.923624i	$0.374788\pi$
$468$		−	830.304i		−	1.77415i
$469$			277.395i			0.591460i
$470$		0			0
$471$			1014.61i			2.15415i
$472$	1080.54			2.28929
$473$	−445.892			−0.942688
$474$		−	130.242i		−	0.274773i
$475$		0			0
$476$	−907.374			−1.90625
$477$		−	169.566i		−	0.355485i
$478$		−	332.284i		−	0.695155i
$479$	−246.301			−0.514198			−0.257099	−	0.966385i	$-0.582767\pi$
$479$	−246.301			−0.514198			−0.257099	+	0.966385i	$0.582767\pi$
$480$		0			0
$481$	262.628			0.546005
$482$	−287.928			−0.597361
$483$		−	624.580i		−	1.29313i
$484$	609.930			1.26018
$485$		0			0
$486$	1097.24			2.25770
$487$		−	732.073i		−	1.50323i	−0.659603	−	0.751614i	$-0.729275\pi$
$487$		−	732.073i		−	1.50323i	0.659603	−	0.751614i	$-0.270725\pi$
$488$			323.430i			0.662766i
$489$		−	107.968i		−	0.220793i
$490$		0			0
$491$	284.304			0.579030			0.289515	−	0.957173i	$-0.406506\pi$
$491$	284.304			0.579030			0.289515	+	0.957173i	$0.406506\pi$
$492$	1993.92			4.05268
$493$		−	276.684i		−	0.561225i
$494$	−892.679	−	259.440i	−1.80704	−	0.525182i
$495$		0			0
$496$		−	292.401i		−	0.589517i
$497$			473.196i			0.952105i
$498$	−210.422			−0.422534
$499$	−161.653			−0.323955			−0.161977	−	0.986794i	$-0.551787\pi$
$499$	−161.653			−0.323955			−0.161977	+	0.986794i	$0.551787\pi$
$500$		0			0
$501$	−1050.24			−2.09629
$502$			399.864i			0.796542i
$503$	232.214			0.461658			0.230829	−	0.972994i	$-0.425856\pi$
$503$	232.214			0.461658			0.230829	+	0.972994i	$0.425856\pi$
$504$		−	409.999i		−	0.813490i
$505$		0			0
$506$			706.183i			1.39562i
$507$		−	164.690i		−	0.324833i
$508$			570.317i			1.12267i
$509$		−	164.016i		−	0.322232i	−0.986935	−	0.161116i	$-0.948491\pi$
$509$		−	164.016i		−	0.322232i	0.986935	−	0.161116i	$-0.0515094\pi$
$510$		0			0
$511$	−54.4667			−0.106589
$512$		−	580.794i		−	1.13436i
$513$	27.8387	−	95.7873i	0.0542665	−	0.186720i
$514$	−981.974			−1.91046
$515$		0			0
$516$			2171.33i			4.20801i
$517$	−331.840			−0.641857
$518$	280.546			0.541595
$519$	554.725			1.06883
$520$		0			0
$521$		−	917.279i		−	1.76061i	−0.474407	−	0.880306i	$-0.657337\pi$
$521$		−	917.279i		−	1.76061i	0.474407	−	0.880306i	$-0.342663\pi$
$522$	270.456			0.518116
$523$			552.428i			1.05627i	0.849161	+	0.528134i	$0.177108\pi$
$523$			552.428i			1.05627i	−0.849161	+	0.528134i	$0.822892\pi$
$524$	611.204			1.16642
$525$		0			0
$526$		−	1528.30i		−	2.90552i
$527$			815.073i			1.54663i
$528$			244.544i			0.463152i
$529$	588.791			1.11303
$530$		0			0
$531$		−	716.930i		−	1.35015i
$532$	−620.117	−	180.225i	−1.16563	−	0.338769i
$533$	948.469			1.77949
$534$		−	163.690i		−	0.306535i
$535$		0			0
$536$	−706.006			−1.31717
$537$	−178.527			−0.332452
$538$	373.526			0.694286
$539$	−175.631			−0.325846
$540$		0			0
$541$	629.744			1.16404			0.582018	−	0.813176i	$-0.302263\pi$
$541$	629.744			1.16404			0.582018	+	0.813176i	$0.302263\pi$
$542$		−	1700.89i		−	3.13818i
$543$	−1009.99			−1.86003
$544$			377.122i			0.693238i
$545$		0			0
$546$		−	914.024i		−	1.67404i
$547$		−	290.138i		−	0.530416i	−0.964191	−	0.265208i	$-0.914559\pi$
$547$		−	290.138i		−	0.530416i	0.964191	−	0.265208i	$-0.0854407\pi$
$548$	−283.354			−0.517070
$549$	214.592			0.390878
$550$		0			0
$551$	54.9557	−	189.091i	0.0997381	−	0.343178i
$552$	1589.64			2.87978
$553$		−	43.0374i		−	0.0778253i
$554$			609.960i			1.10101i
$555$		0			0
$556$	346.264			0.622777
$557$	−2.72609			−0.00489423			−0.00244712	−	0.999997i	$-0.500779\pi$
$557$	−2.72609			−0.00489423			−0.00244712	+	0.999997i	$0.500779\pi$
$558$	−796.727			−1.42783
$559$			1032.86i			1.84769i
$560$		0			0
$561$		−	681.672i		−	1.21510i
$562$	−1223.90			−2.17776
$563$		−	92.3767i		−	0.164079i	−0.996629	−	0.0820397i	$-0.973857\pi$
$563$		−	92.3767i		−	0.164079i	0.996629	−	0.0820397i	$-0.0261434\pi$
$564$			1615.94i			2.86515i
$565$		0			0
$566$		−	134.939i		−	0.238408i
$567$	415.379			0.732592
$568$	−1204.34			−2.12033
$569$		−	675.420i		−	1.18703i	−0.804823	−	0.593515i	$-0.797740\pi$
$569$		−	675.420i		−	1.18703i	0.804823	−	0.593515i	$-0.202260\pi$
$570$		0			0
$571$	−673.447			−1.17942			−0.589708	−	0.807616i	$-0.700757\pi$
$571$	−673.447			−1.17942			−0.589708	+	0.807616i	$0.700757\pi$
$572$			672.052i			1.17492i
$573$			551.159i			0.961882i
$574$	1013.18			1.76512
$575$		0			0
$576$	−664.221			−1.15316
$577$	−380.054			−0.658672			−0.329336	−	0.944213i	$-0.606825\pi$
$577$	−380.054			−0.658672			−0.329336	+	0.944213i	$0.606825\pi$
$578$			1433.04i			2.47931i
$579$	−168.003			−0.290161
$580$		0			0
$581$	−69.5320			−0.119676
$582$		−	857.593i		−	1.47353i
$583$			137.248i			0.235417i
$584$		−	138.625i		−	0.237371i
$585$		0			0
$586$	−1133.50			−1.93430
$587$	934.331			1.59171			0.795853	−	0.605490i	$-0.207023\pi$
$587$	934.331			1.59171			0.795853	+	0.605490i	$0.207023\pi$
$588$			855.260i			1.45452i
$589$	−161.892	+	557.037i	−0.274859	+	0.945734i
$590$		0			0
$591$		−	410.029i		−	0.693788i
$592$			173.867i			0.293694i
$593$	1086.40			1.83204			0.916020	−	0.401133i	$-0.131384\pi$
$593$	1086.40			1.83204			0.916020	+	0.401133i	$0.131384\pi$
$594$	−110.892			−0.186687
$595$		0			0
$596$	1564.45			2.62492
$597$		−	936.907i		−	1.56936i
$598$	1635.80			2.73545
$599$			639.332i			1.06733i	0.845695	+	0.533666i	$0.179186\pi$
$599$			639.332i			1.06733i	−0.845695	+	0.533666i	$0.820814\pi$
$600$		0			0
$601$		−	1185.57i		−	1.97265i	−0.164800	−	0.986327i	$-0.552698\pi$
$601$		−	1185.57i		−	1.97265i	0.164800	−	0.986327i	$-0.447302\pi$
$602$			1103.33i			1.83277i
$603$			468.427i			0.776828i
$604$			899.798i			1.48973i
$605$		0			0
$606$	−1923.88			−3.17471
$607$			468.485i			0.771804i	0.922540	+	0.385902i	$0.126110\pi$
$607$			468.485i			0.771804i	−0.922540	+	0.385902i	$0.873890\pi$
$608$	−74.9049	+	257.732i	−0.123199	+	0.423902i
$609$	193.613			0.317919
$610$		0			0
$611$			768.673i			1.25806i
$612$	−1532.25			−2.50368
$613$	−489.776			−0.798982			−0.399491	−	0.916737i	$-0.630813\pi$
$613$	−489.776			−0.798982			−0.399491	+	0.916737i	$0.630813\pi$
$614$	−1799.18			−2.93026
$615$		0			0
$616$			331.855i			0.538726i
$617$	−916.972			−1.48618			−0.743089	−	0.669193i	$-0.766640\pi$
$617$	−916.972			−1.48618			−0.743089	+	0.669193i	$0.766640\pi$
$618$		−	1903.63i		−	3.08031i
$619$	−248.052			−0.400730			−0.200365	−	0.979721i	$-0.564213\pi$
$619$	−248.052			−0.400730			−0.200365	+	0.979721i	$0.564213\pi$
$620$		0			0
$621$			175.527i			0.282651i
$622$		−	487.598i		−	0.783919i
$623$		−	54.0898i		−	0.0868216i
$624$	566.461			0.907790
$625$		0			0
$626$			806.686i			1.28864i
$627$	135.396	−	465.868i	0.215942	−	0.743012i
$628$	−1845.94			−2.93939
$629$		−	484.657i		−	0.770520i
$630$		0			0
$631$	198.320			0.314295			0.157148	−	0.987575i	$-0.449770\pi$
$631$	198.320			0.314295			0.157148	+	0.987575i	$0.449770\pi$
$632$	109.536			0.173316
$633$	−795.184			−1.25621
$634$	−31.6863			−0.0499784
$635$		0			0
$636$	668.348			1.05086
$637$			406.830i			0.638666i
$638$	−218.909			−0.343117
$639$			799.070i			1.25050i
$640$		0			0
$641$			669.775i			1.04489i	0.852673	+	0.522445i	$0.174980\pi$
$641$			669.775i			1.04489i	−0.852673	+	0.522445i	$0.825020\pi$
$642$			1753.11i			2.73070i
$643$	104.564			0.162619			0.0813096	−	0.996689i	$-0.474090\pi$
$643$	104.564			0.162619			0.0813096	+	0.996689i	$0.474090\pi$
$644$	1136.34			1.76450
$645$		0			0
$646$	−478.773	+	1647.36i	−0.741134	+	2.55009i
$647$	−504.773			−0.780175			−0.390087	−	0.920778i	$-0.627555\pi$
$647$	−504.773			−0.780175			−0.390087	+	0.920778i	$0.627555\pi$
$648$			1057.19i			1.63147i
$649$			580.286i			0.894124i
$650$		0			0
$651$	−570.357			−0.876124
$652$	196.433			0.301278
$653$	799.353			1.22412			0.612062	−	0.790810i	$-0.290340\pi$
$653$	799.353			1.22412			0.612062	+	0.790810i	$0.290340\pi$
$654$		−	255.380i		−	0.390490i
$655$		0			0
$656$			627.910i			0.957180i
$657$	−91.9761			−0.139994
$658$			821.115i			1.24790i
$659$		−	1147.64i		−	1.74149i	−0.491732	−	0.870747i	$-0.663636\pi$
$659$		−	1147.64i		−	1.74149i	0.491732	−	0.870747i	$-0.336364\pi$
$660$		0			0
$661$		−	989.094i		−	1.49636i	−0.663496	−	0.748180i	$-0.730928\pi$
$661$		−	989.094i		−	1.49636i	0.663496	−	0.748180i	$-0.269072\pi$
$662$	864.675			1.30616
$663$	−1579.02			−2.38163
$664$		−	176.968i		−	0.266518i
$665$		0			0
$666$	473.748			0.711334
$667$			346.502i			0.519494i
$668$		−	1910.77i		−	2.86043i
$669$	−119.414			−0.178496
$670$		0			0
$671$	−173.692			−0.258855
$672$	−263.895			−0.392701
$673$			502.564i			0.746752i	0.927680	+	0.373376i	$0.121800\pi$
$673$			502.564i			0.746752i	−0.927680	+	0.373376i	$0.878200\pi$
$674$	−199.969			−0.296689
$675$		0			0
$676$	299.632			0.443243
$677$			825.425i			1.21924i	0.792694	+	0.609620i	$0.208678\pi$
$677$			825.425i			1.21924i	−0.792694	+	0.609620i	$0.791322\pi$
$678$			1857.34i			2.73944i
$679$		−	283.384i		−	0.417354i
$680$		0			0
$681$	1282.14			1.88273
$682$	644.875			0.945564
$683$		−	627.488i		−	0.918723i	−0.888249	−	0.459362i	$-0.848078\pi$
$683$		−	627.488i		−	0.918723i	0.888249	−	0.459362i	$-0.151922\pi$
$684$	−1047.17	−	304.340i	−1.53095	−	0.444941i
$685$		0			0
$686$			1191.81i			1.73733i
$687$			155.121i			0.225795i
$688$	−683.780			−0.993866
$689$	317.920			0.461423
$690$		0			0
$691$	−545.404			−0.789297			−0.394649	−	0.918832i	$-0.629134\pi$
$691$	−545.404			−0.789297			−0.394649	+	0.918832i	$0.629134\pi$
$692$			1009.25i			1.45845i
$693$	220.182			0.317723
$694$			516.253i			0.743880i
$695$		0			0
$696$			492.769i			0.708002i
$697$		−	1750.31i		−	2.51121i
$698$		−	462.001i		−	0.661893i
$699$		−	1703.27i		−	2.43673i
$700$		0			0
$701$	−544.518			−0.776774			−0.388387	−	0.921496i	$-0.626968\pi$
$701$	−544.518			−0.776774			−0.388387	+	0.921496i	$0.626968\pi$
$702$			256.869i			0.365911i
$703$	96.2639	−	331.224i	0.136933	−	0.471158i
$704$	537.624			0.763670
$705$		0			0
$706$		−	744.716i		−	1.05484i
$707$	−635.727			−0.899190
$708$	2825.79			3.99123
$709$	−191.235			−0.269725			−0.134863	−	0.990864i	$-0.543059\pi$
$709$	−191.235			−0.269725			−0.134863	+	0.990864i	$0.543059\pi$
$710$		0			0
$711$		−	72.6757i		−	0.102216i
$712$	137.666			0.193351
$713$		−	1020.75i		−	1.43162i
$714$	−1686.75			−2.36239
$715$		0			0
$716$		−	324.805i		−	0.453639i
$717$		−	401.689i		−	0.560236i
$718$			735.343i			1.02415i
$719$	996.287			1.38566			0.692828	−	0.721102i	$-0.256364\pi$
$719$	996.287			1.38566			0.692828	+	0.721102i	$0.256364\pi$
$720$		0			0
$721$		−	629.037i		−	0.872450i
$722$	−654.405	+	1030.74i	−0.906379	+	1.42762i
$723$	−348.068			−0.481422
$724$		−	1837.55i		−	2.53805i
$725$		0			0
$726$	1133.82			1.56173
$727$	623.938			0.858237			0.429119	−	0.903248i	$-0.358824\pi$
$727$	623.938			0.858237			0.429119	+	0.903248i	$0.358824\pi$
$728$	768.707			1.05592
$729$	508.254			0.697193
$730$		0			0
$731$	1906.05			2.60746
$732$			845.818i			1.15549i
$733$	−331.044			−0.451629			−0.225814	−	0.974170i	$-0.572504\pi$
$733$	−331.044			−0.451629			−0.225814	+	0.974170i	$0.572504\pi$
$734$			1228.46i			1.67366i
$735$		0			0
$736$		−	472.284i		−	0.641691i
$737$		−	379.147i		−	0.514447i
$738$	1710.92			2.31832
$739$	−835.615			−1.13074			−0.565368	−	0.824838i	$-0.691266\pi$
$739$	−835.615			−1.13074			−0.565368	+	0.824838i	$0.691266\pi$
$740$		0			0
$741$	−1079.13	−	313.630i	−1.45632	−	0.423252i
$742$	339.610			0.457695
$743$			209.741i			0.282290i	0.989989	+	0.141145i	$0.0450783\pi$
$743$			209.741i			0.282290i	−0.989989	+	0.141145i	$0.954922\pi$
$744$		−	1451.63i		−	1.95112i
$745$		0			0
$746$	−50.3423			−0.0674829
$747$	−117.416			−0.157184
$748$	1240.21			1.65804
$749$			579.299i			0.773430i
$750$		0			0
$751$			1097.59i			1.46150i	0.682643	+	0.730752i	$0.260831\pi$
$751$			1097.59i			1.46150i	−0.682643	+	0.730752i	$0.739169\pi$
$752$	−508.881			−0.676704
$753$			483.385i			0.641945i
$754$			507.079i			0.672519i
$755$		0			0
$756$			178.439i			0.236031i
$757$	−551.713			−0.728816			−0.364408	−	0.931239i	$-0.618729\pi$
$757$	−551.713			−0.728816			−0.364408	+	0.931239i	$0.618729\pi$
$758$	−726.063			−0.957867
$759$			853.685i			1.12475i
$760$		0			0
$761$	1115.81			1.46624			0.733119	−	0.680101i	$-0.238064\pi$
$761$	1115.81			1.46624			0.733119	+	0.680101i	$0.238064\pi$
$762$			1060.18i			1.39132i
$763$		−	84.3880i		−	0.110600i
$764$	−1002.76			−1.31251
$765$		0			0
$766$	−1880.52			−2.45499
$767$	1344.17			1.75251
$768$		−	1836.71i		−	2.39155i
$769$	1432.18			1.86239			0.931195	−	0.364522i	$-0.118768\pi$
$769$	1432.18			1.86239			0.931195	+	0.364522i	$0.118768\pi$
$770$		0			0
$771$	−1187.08			−1.53967
$772$		−	305.660i		−	0.395932i
$773$		−	753.633i		−	0.974946i	−0.873138	−	0.487473i	$-0.837919\pi$
$773$		−	753.633i		−	0.974946i	0.873138	−	0.487473i	$-0.162081\pi$
$774$			1863.15i			2.40717i
$775$		0			0
$776$	721.248			0.929443
$777$	339.144			0.436479
$778$			217.157i			0.279122i
$779$	347.652	−	1196.20i	0.446280	−	1.53556i
$780$		0			0
$781$		−	646.771i		−	0.828132i
$782$		−	3018.72i		−	3.86026i
$783$	−54.4112			−0.0694907
$784$	−269.332			−0.343536
$785$		0			0
$786$	1136.19			1.44553
$787$		−	1196.41i		−	1.52022i	−0.649795	−	0.760110i	$-0.725145\pi$
$787$		−	1196.41i		−	1.52022i	0.649795	−	0.760110i	$-0.274855\pi$
$788$	745.992			0.946691
$789$		−	1847.52i		−	2.34160i
$790$		0			0
$791$			613.740i			0.775904i
$792$			560.392i			0.707566i
$793$			402.339i			0.507363i
$794$			18.3197i			0.0230727i
$795$		0			0
$796$	1704.58			2.14143
$797$		−	1345.94i		−	1.68876i	−0.535747	−	0.844379i	$-0.679970\pi$
$797$		−	1345.94i		−	1.68876i	0.535747	−	0.844379i	$-0.320030\pi$
$798$	−1152.76	−	335.027i	−1.44456	−	0.419833i
$799$	1418.52			1.77537
$800$		0			0
$801$		−	91.3397i		−	0.114032i
$802$	−441.883			−0.550976
$803$	74.4459			0.0927097
$804$	−1846.31			−2.29641
$805$		0			0
$806$		−	1493.79i		−	1.85333i
$807$	451.545			0.559535
$808$		−	1618.01i		−	2.00248i
$809$	73.4294			0.0907657			0.0453828	−	0.998970i	$-0.485549\pi$
$809$	73.4294			0.0907657			0.0453828	+	0.998970i	$0.485549\pi$
$810$		0			0
$811$			420.830i			0.518903i	0.965756	+	0.259451i	$0.0835418\pi$
$811$			420.830i			0.518903i	−0.965756	+	0.259451i	$0.916458\pi$
$812$			352.253i			0.433809i
$813$		−	2056.16i		−	2.52911i
$814$	−383.454			−0.471074
$815$		0			0
$816$		−	1045.35i		−	1.28107i
$817$	1302.63	+	378.585i	1.59441	+	0.463384i
$818$	−1601.49			−1.95781
$819$		−	510.029i		−	0.622746i
$820$		0			0
$821$	−80.2743			−0.0977762			−0.0488881	−	0.998804i	$-0.515568\pi$
$821$	−80.2743			−0.0977762			−0.0488881	+	0.998804i	$0.515568\pi$
$822$	−526.738			−0.640800
$823$	444.054			0.539555			0.269778	−	0.962923i	$-0.413050\pi$
$823$	444.054			0.539555			0.269778	+	0.962923i	$0.413050\pi$
$824$	1600.98			1.94294
$825$		0			0
$826$	1435.88			1.73835
$827$			257.906i			0.311857i	0.987768	+	0.155929i	$0.0498370\pi$
$827$			257.906i			0.311857i	−0.987768	+	0.155929i	$0.950163\pi$
$828$	1918.90			2.31751
$829$			610.791i			0.736781i	0.929671	+	0.368391i	$0.120091\pi$
$829$			610.791i			0.736781i	−0.929671	+	0.368391i	$0.879909\pi$
$830$		0			0
$831$			737.364i			0.887321i
$832$		−	1245.35i		−	1.49681i
$833$	750.769			0.901283
$834$	643.683			0.771802
$835$		0			0
$836$	847.585	+	246.334i	1.01386	+	0.294658i
$837$	160.288			0.191503
$838$		−	1400.49i		−	1.67123i
$839$		−	168.780i		−	0.201168i	−0.994929	−	0.100584i	$-0.967929\pi$
$839$		−	168.780i		−	0.201168i	0.994929	−	0.100584i	$-0.0320711\pi$
$840$		0			0
$841$	733.588			0.872281
$842$	−806.189			−0.957470
$843$	−1479.54			−1.75509
$844$		−	1446.73i		−	1.71414i
$845$		0			0
$846$			1386.59i			1.63899i
$847$	374.660			0.442338
$848$			210.471i			0.248197i
$849$		−	163.124i		−	0.192136i
$850$		0			0
$851$			606.955i			0.713226i
$852$	−3149.55			−3.69665
$853$	−932.527			−1.09323			−0.546616	−	0.837383i	$-0.684084\pi$
$853$	−932.527			−1.09323			−0.546616	+	0.837383i	$0.684084\pi$
$854$			429.788i			0.503265i
$855$		0			0
$856$	−1474.39			−1.72242
$857$		−	658.085i		−	0.767893i	−0.923355	−	0.383947i	$-0.874565\pi$
$857$		−	658.085i		−	0.767893i	0.923355	−	0.383947i	$-0.125435\pi$
$858$			1249.30i			1.45606i
$859$	−634.851			−0.739058			−0.369529	−	0.929219i	$-0.620481\pi$
$859$	−634.851			−0.739058			−0.369529	+	0.929219i	$0.620481\pi$
$860$		0			0
$861$	1224.80			1.42253
$862$	1463.52			1.69782
$863$		−	168.480i		−	0.195226i	−0.995224	−	0.0976130i	$-0.968879\pi$
$863$		−	168.480i		−	0.195226i	0.995224	−	0.0976130i	$-0.0311207\pi$
$864$	74.1627			0.0858365
$865$		0			0
$866$	−2406.98			−2.77943
$867$			1732.36i			1.99811i
$868$		−	1037.69i		−	1.19549i
$869$			58.8241i			0.0676917i
$870$		0			0
$871$	−878.255			−1.00833
$872$	214.778			0.246306
$873$		−	478.540i		−	0.548156i
$874$	599.586	−	2063.05i	0.686025	−	2.36047i
$875$		0			0
$876$		−	362.525i		−	0.413842i
$877$		−	352.865i		−	0.402355i	−0.979555	−	0.201177i	$-0.935523\pi$
$877$		−	352.865i		−	0.402355i	0.979555	−	0.201177i	$-0.0644768\pi$
$878$	1291.53			1.47099
$879$	−1370.26			−1.55888
$880$		0			0
$881$	868.676			0.986011			0.493006	−	0.870026i	$-0.335898\pi$
$881$	868.676			0.986011			0.493006	+	0.870026i	$0.335898\pi$
$882$			733.871i			0.832053i
$883$	220.851			0.250114			0.125057	−	0.992150i	$-0.460089\pi$
$883$	220.851			0.250114			0.125057	+	0.992150i	$0.460089\pi$
$884$		−	2872.82i		−	3.24980i
$885$		0			0
$886$		−	1386.11i		−	1.56446i
$887$			1308.29i			1.47496i	0.675367	+	0.737482i	$0.263985\pi$
$887$			1308.29i			1.47496i	−0.675367	+	0.737482i	$0.736015\pi$
$888$			863.166i			0.972034i
$889$			350.328i			0.394070i
$890$		0			0
$891$	−567.747			−0.637202
$892$		−	217.257i		−	0.243562i
$893$	969.443	+	281.750i	1.08560	+	0.315509i
$894$	2908.22			3.25304
$895$		0			0
$896$		−	1072.13i		−	1.19657i
$897$	1977.47			2.20454
$898$	−792.080			−0.882049
$899$	316.420			0.351969
$900$		0			0
$901$		−	586.693i		−	0.651158i
$902$	−1384.82			−1.53528
$903$			1333.78i			1.47706i
$904$	−1562.05			−1.72793
$905$		0			0
$906$			1672.67i			1.84621i
$907$			723.418i			0.797594i	0.917039	+	0.398797i	$0.130572\pi$
$907$			723.418i			0.797594i	−0.917039	+	0.398797i	$0.869428\pi$
$908$			2332.68i			2.56903i
$909$	−1073.53			−1.18100
$910$		0			0
$911$		−	572.989i		−	0.628967i	−0.949263	−	0.314483i	$-0.898169\pi$
$911$		−	572.989i		−	0.628967i	0.949263	−	0.314483i	$-0.101831\pi$
$912$	207.631	−	714.415i	0.227665	−	0.783349i
$913$	95.0373			0.104093
$914$			2077.93i			2.27345i
$915$		0			0
$916$	−282.222			−0.308102
$917$	375.443			0.409426
$918$	474.029			0.516372
$919$	11.3971			0.0124016			0.00620079	−	0.999981i	$-0.498026\pi$
$919$	11.3971			0.0124016			0.00620079	+	0.999981i	$0.498026\pi$
$920$		0			0
$921$	−2174.98			−2.36154
$922$		−	174.789i		−	0.189576i
$923$	−1498.18			−1.62316
$924$			867.852i			0.939234i
$925$		0			0
$926$		−	1232.06i		−	1.33052i
$927$		−	1062.23i		−	1.14588i
$928$	146.403			0.157762
$929$	81.6994			0.0879434			0.0439717	−	0.999033i	$-0.485999\pi$
$929$	81.6994			0.0879434			0.0439717	+	0.999033i	$0.485999\pi$
$930$		0			0
$931$	513.090	+	149.120i	0.551117	+	0.160172i
$932$	3098.87			3.32497
$933$		−	589.443i		−	0.631772i
$934$			1210.79i			1.29635i
$935$		0			0
$936$	1298.09			1.38685
$937$	−1797.25			−1.91809			−0.959044	−	0.283257i	$-0.908585\pi$
$937$	−1797.25			−1.91809			−0.959044	+	0.283257i	$0.908585\pi$
$938$	−938.173			−1.00018
$939$			975.180i			1.03853i
$940$		0			0
$941$			265.809i			0.282475i	0.989976	+	0.141237i	$0.0451081\pi$
$941$			265.809i			0.282475i	−0.989976	+	0.141237i	$0.954892\pi$
$942$	−3431.48			−3.64276
$943$			2191.99i			2.32448i
$944$			889.876i			0.942665i
$945$		0			0
$946$		−	1508.04i		−	1.59413i
$947$	−1177.82			−1.24373			−0.621867	−	0.783123i	$-0.713626\pi$
$947$	−1177.82			−1.24373			−0.621867	+	0.783123i	$0.713626\pi$
$948$	286.453			0.302165
$949$		−	172.446i		−	0.181714i
$950$		0			0
$951$	−38.3047			−0.0402783
$952$		−	1418.58i		−	1.49011i
$953$		−	181.390i		−	0.190336i	−0.995461	−	0.0951681i	$-0.969661\pi$
$953$		−	181.390i		−	0.190336i	0.995461	−	0.0951681i	$-0.0303388\pi$
$954$	573.488			0.601140
$955$		0			0
$956$	730.820			0.764456
$957$	−264.633			−0.276523
$958$		−	833.009i		−	0.869530i
$959$	−174.056			−0.181497
$960$		0			0
$961$	28.8690			0.0300405
$962$			888.231i			0.923318i
$963$			978.242i			1.01583i
$964$		−	633.264i		−	0.656912i
$965$		0			0
$966$	2112.38			2.18673
$967$	−1536.16			−1.58859			−0.794293	−	0.607535i	$-0.792159\pi$
$967$	−1536.16			−1.58859			−0.794293	+	0.607535i	$0.792159\pi$
$968$			953.559i			0.985081i
$969$	−578.775	+	1991.45i	−0.597291	+	2.05516i
$970$		0			0
$971$		−	54.9334i		−	0.0565741i	−0.999600	−	0.0282870i	$-0.990995\pi$
$971$		−	54.9334i		−	0.0565741i	0.999600	−	0.0282870i	$-0.00900524\pi$
$972$			2413.25i			2.48277i
$973$	212.699			0.218601
$974$	2475.93			2.54202
$975$		0			0
$976$	−266.359			−0.272908
$977$		−	259.857i		−	0.265975i	−0.991118	−	0.132987i	$-0.957543\pi$
$977$		−	259.857i		−	0.265975i	0.991118	−	0.132987i	$-0.0424570\pi$
$978$	365.157			0.373371
$979$			73.9308i			0.0755166i
$980$		0			0
$981$		−	142.503i		−	0.145263i
$982$			961.540i			0.979165i
$983$		−	895.533i		−	0.911020i	−0.890231	−	0.455510i	$-0.849457\pi$
$983$		−	895.533i		−	0.911020i	0.890231	−	0.455510i	$-0.150543\pi$
$984$			3117.28i			3.16797i
$985$		0			0
$986$	935.769			0.949055
$987$			992.624i			1.00570i
$988$	570.607	−	1963.34i	0.577537	−	1.98719i
$989$	−2387.02			−2.41357
$990$		0			0
$991$		−	1321.52i		−	1.33352i	−0.745272	−	0.666761i	$-0.767680\pi$
$991$		−	1321.52i		−	1.33352i	0.745272	−	0.666761i	$-0.232320\pi$
$992$	−431.282			−0.434760
$993$	1045.28			1.05265
$994$	−1600.39			−1.61005
$995$		0			0
$996$		−	462.798i		−	0.464657i
$997$	−1012.20			−1.01525			−0.507624	−	0.861579i	$-0.669476\pi$
$997$	−1012.20			−1.01525			−0.507624	+	0.861579i	$0.669476\pi$
$998$		−	546.726i		−	0.547821i
$999$	−95.3101			−0.0954055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.3.c.g.151.12		12
5.2	odd	4		475.3.d.c.474.2		24
5.3	odd	4		475.3.d.c.474.23		24
5.4	even	2		95.3.c.a.56.1	✓	12
15.14	odd	2		855.3.e.a.721.12		12
19.18	odd	2	inner	475.3.c.g.151.1		12
20.19	odd	2		1520.3.h.a.721.10		12
95.18	even	4		475.3.d.c.474.1		24
95.37	even	4		475.3.d.c.474.24		24
95.94	odd	2		95.3.c.a.56.12	yes	12
285.284	even	2		855.3.e.a.721.1		12
380.379	even	2		1520.3.h.a.721.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.3.c.a.56.1	✓	12	5.4	even	2
95.3.c.a.56.12	yes	12	95.94	odd	2
475.3.c.g.151.1		12	19.18	odd	2	inner
475.3.c.g.151.12		12	1.1	even	1	trivial
475.3.d.c.474.1		24	95.18	even	4
475.3.d.c.474.2		24	5.2	odd	4
475.3.d.c.474.23		24	5.3	odd	4
475.3.d.c.474.24		24	95.37	even	4
855.3.e.a.721.1		12	285.284	even	2
855.3.e.a.721.12		12	15.14	odd	2
1520.3.h.a.721.3		12	380.379	even	2
1520.3.h.a.721.10		12	20.19	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.38208i q^{2} +4.08851i q^{3} -7.43849 q^{4} -13.8277 q^{6} -4.56923 q^{7} -11.6293i q^{8} -7.71590 q^{9} +O(q^{10})\)	\(q+3.38208i q^{2} +4.08851i q^{3} -7.43849 q^{4} -13.8277 q^{6} -4.56923 q^{7} -11.6293i q^{8} -7.71590 q^{9} +6.24529 q^{11} -30.4124i q^{12} -14.4666i q^{13} -15.4535i q^{14} +9.57723 q^{16} -26.6967 q^{17} -26.0958i q^{18} +(-18.2451 - 5.30257i) q^{19} -18.6813i q^{21} +21.1221i q^{22} +33.4334 q^{23} +47.5464 q^{24} +48.9271 q^{26} +5.25004i q^{27} +33.9882 q^{28} +10.3640i q^{29} -30.5308i q^{31} -14.1261i q^{32} +25.5339i q^{33} -90.2906i q^{34} +57.3947 q^{36} +18.1542i q^{37} +(17.9338 - 61.7064i) q^{38} +59.1466 q^{39} +65.5629i q^{41} +63.1819 q^{42} -71.3965 q^{43} -46.4556 q^{44} +113.075i q^{46} -53.1345 q^{47} +39.1566i q^{48} -28.1221 q^{49} -109.150i q^{51} +107.609i q^{52} +21.9762i q^{53} -17.7561 q^{54} +53.1369i q^{56} +(21.6796 - 74.5951i) q^{57} -35.0518 q^{58} +92.9158i q^{59} -27.8117 q^{61} +103.258 q^{62} +35.2557 q^{63} +86.0847 q^{64} -86.3579 q^{66} -60.7093i q^{67} +198.583 q^{68} +136.693i q^{69} -103.561i q^{71} +89.7304i q^{72} +11.9203 q^{73} -61.3990 q^{74} +(135.716 + 39.4432i) q^{76} -28.5362 q^{77} +200.039i q^{78} +9.41895i q^{79} -90.9080 q^{81} -221.739 q^{82} +15.2174 q^{83} +138.961i q^{84} -241.469i q^{86} -42.3732 q^{87} -72.6282i q^{88} +11.8378i q^{89} +66.1010i q^{91} -248.694 q^{92} +124.826 q^{93} -179.705i q^{94} +57.7548 q^{96} +62.0200i q^{97} -95.1114i q^{98} -48.1881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9}+O(q^{10}) \) 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9	\( 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9} + 32 q^{11} - 44 q^{16} + 44 q^{17} + 8 q^{19} - 36 q^{23} + 100 q^{24} + 108 q^{26} + 36 q^{28} - 80 q^{36} + 44 q^{38} + 76 q^{39} - 100 q^{42} - 320 q^{43} - 256 q^{44} + 56 q^{47} + 72 q^{49} - 76 q^{54} - 60 q^{57} - 68 q^{58} - 296 q^{61} + 376 q^{62} + 96 q^{63} + 188 q^{64} + 152 q^{66} + 340 q^{68} + 244 q^{73} + 136 q^{74} + 248 q^{76} + 200 q^{77} - 372 q^{81} - 424 q^{82} + 160 q^{83} - 444 q^{87} - 716 q^{92} - 296 q^{93} - 44 q^{96} - 312 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9 + 32 * q^11 - 44 * q^16 + 44 * q^17 + 8 * q^19 - 36 * q^23 + 100 * q^24 + 108 * q^26 + 36 * q^28 - 80 * q^36 + 44 * q^38 + 76 * q^39 - 100 * q^42 - 320 * q^43 - 256 * q^44 + 56 * q^47 + 72 * q^49 - 76 * q^54 - 60 * q^57 - 68 * q^58 - 296 * q^61 + 376 * q^62 + 96 * q^63 + 188 * q^64 + 152 * q^66 + 340 * q^68 + 244 * q^73 + 136 * q^74 + 248 * q^76 + 200 * q^77 - 372 * q^81 - 424 * q^82 + 160 * q^83 - 444 * q^87 - 716 * q^92 - 296 * q^93 - 44 * q^96 - 312 * q^99

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