LMFDB - Embedded newform 950.3.c.b.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,3,Mod(151,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	950.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:	$25.8856251142$
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} + 68x^{10} + 1670x^{8} + 18282x^{6} + 91461x^{4} + 207270x^{2} + 172225 $ x^12 + 68x^10 + 1670x^8 + 18282x^6 + 91461x^4 + 207270*x^2 + 172225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.3
Root			$-1.89288i$ of defining polynomial
Character	$\chi$	$=$	950.151
Dual form			950.3.c.b.151.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -1.89288i q^{3} -2.00000 q^{4} -2.67694 q^{6} +1.68650 q^{7} +2.82843i q^{8} +5.41699 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -1.89288i q^{3} -2.00000 q^{4} -2.67694 q^{6} +1.68650 q^{7} +2.82843i q^{8} +5.41699 q^{9} +1.04411 q^{11} +3.78577i q^{12} +6.02294i q^{13} -2.38506i q^{14} +4.00000 q^{16} -21.6652 q^{17} -7.66078i q^{18} +(-17.3019 + 7.85143i) q^{19} -3.19234i q^{21} -1.47660i q^{22} -39.8186 q^{23} +5.35389 q^{24} +8.51772 q^{26} -27.2897i q^{27} -3.37299 q^{28} +0.278403i q^{29} -19.8410i q^{31} -5.65685i q^{32} -1.97638i q^{33} +30.6392i q^{34} -10.8340 q^{36} -68.3424i q^{37} +(11.1036 + 24.4686i) q^{38} +11.4007 q^{39} -3.84932i q^{41} -4.51465 q^{42} -65.0642 q^{43} -2.08822 q^{44} +56.3120i q^{46} -9.61045 q^{47} -7.57154i q^{48} -46.1557 q^{49} +41.0097i q^{51} -12.0459i q^{52} +62.0602i q^{53} -38.5935 q^{54} +4.77013i q^{56} +(14.8618 + 32.7505i) q^{57} +0.393722 q^{58} +94.0807i q^{59} -19.4070 q^{61} -28.0595 q^{62} +9.13572 q^{63} -8.00000 q^{64} -2.79503 q^{66} -62.2388i q^{67} +43.3304 q^{68} +75.3720i q^{69} +41.4101i q^{71} +15.3216i q^{72} +3.25235 q^{73} -96.6507 q^{74} +(34.6038 - 15.7029i) q^{76} +1.76089 q^{77} -16.1231i q^{78} +84.1379i q^{79} -2.90334 q^{81} -5.44376 q^{82} -5.58177 q^{83} +6.38468i q^{84} +92.0147i q^{86} +0.526985 q^{87} +2.95319i q^{88} -84.3407i q^{89} +10.1577i q^{91} +79.6372 q^{92} -37.5568 q^{93} +13.5912i q^{94} -10.7078 q^{96} +1.89498i q^{97} +65.2741i q^{98} +5.65594 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{4} - 8 q^{6} - 24 q^{7} - 28 q^{9}+O(q^{10}) $ 12 * q - 24 * q^4 - 8 * q^6 - 24 * q^7 - 28 * q^9	$ 12 q - 24 q^{4} - 8 q^{6} - 24 q^{7} - 28 q^{9} + 4 q^{11} + 48 q^{16} - 12 q^{19} + 32 q^{23} + 16 q^{24} - 16 q^{26} + 48 q^{28} + 56 q^{36} - 8 q^{38} + 100 q^{39} + 72 q^{42} + 188 q^{43} - 8 q^{44} + 180 q^{47} - 108 q^{49} + 112 q^{54} - 92 q^{57} - 120 q^{58} - 76 q^{61} + 64 q^{62} + 84 q^{63} - 96 q^{64} + 8 q^{66} + 124 q^{73} + 72 q^{74} + 24 q^{76} - 184 q^{77} - 132 q^{81} - 96 q^{82} - 500 q^{83} - 432 q^{87} - 64 q^{92} - 452 q^{93} - 32 q^{96} + 128 q^{99}+O(q^{100}) $ 12 * q - 24 * q^4 - 8 * q^6 - 24 * q^7 - 28 * q^9 + 4 * q^11 + 48 * q^16 - 12 * q^19 + 32 * q^23 + 16 * q^24 - 16 * q^26 + 48 * q^28 + 56 * q^36 - 8 * q^38 + 100 * q^39 + 72 * q^42 + 188 * q^43 - 8 * q^44 + 180 * q^47 - 108 * q^49 + 112 * q^54 - 92 * q^57 - 120 * q^58 - 76 * q^61 + 64 * q^62 + 84 * q^63 - 96 * q^64 + 8 * q^66 + 124 * q^73 + 72 * q^74 + 24 * q^76 - 184 * q^77 - 132 * q^81 - 96 * q^82 - 500 * q^83 - 432 * q^87 - 64 * q^92 - 452 * q^93 - 32 * q^96 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		−	1.89288i		−	0.630961i	−0.948932	−	0.315481i	$-0.897834\pi$
$3$		−	1.89288i		−	0.630961i	0.948932	−	0.315481i	$-0.102166\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−2.67694			−0.446157
$7$	1.68650			0.240928			0.120464	−	0.992718i	$-0.461562\pi$
$7$	1.68650			0.240928			0.120464	+	0.992718i	$0.461562\pi$
$8$			2.82843i			0.353553i
$9$	5.41699			0.601888
$10$		0			0
$11$	1.04411			0.0949193			0.0474596	−	0.998873i	$-0.484887\pi$
$11$	1.04411			0.0949193			0.0474596	+	0.998873i	$0.484887\pi$
$12$			3.78577i			0.315481i
$13$			6.02294i			0.463303i	0.972799	+	0.231652i	$0.0744129\pi$
$13$			6.02294i			0.463303i	−0.972799	+	0.231652i	$0.925587\pi$
$14$		−	2.38506i		−	0.170362i
$15$		0			0
$16$	4.00000			0.250000
$17$	−21.6652			−1.27442			−0.637212	−	0.770689i	$-0.719912\pi$
$17$	−21.6652			−1.27442			−0.637212	+	0.770689i	$0.719912\pi$
$18$		−	7.66078i		−	0.425599i
$19$	−17.3019	+	7.85143i	−0.910625	+	0.413233i
$19$	−17.3019	+	7.85143i	−0.910625	+	0.413233i
$20$		0			0
$21$		−	3.19234i		−	0.152016i
$22$		−	1.47660i		−	0.0671181i
$23$	−39.8186			−1.73124			−0.865622	−	0.500698i	$-0.833077\pi$
$23$	−39.8186			−1.73124			−0.865622	+	0.500698i	$0.833077\pi$
$24$	5.35389			0.223079
$25$		0			0
$26$	8.51772			0.327605
$27$		−	27.2897i		−	1.01073i
$28$	−3.37299			−0.120464
$29$			0.278403i			0.00960011i	0.999988	+	0.00480006i	$0.00152791\pi$
$29$			0.278403i			0.00960011i	−0.999988	+	0.00480006i	$0.998472\pi$
$30$		0			0
$31$		−	19.8410i		−	0.640034i	−0.947412	−	0.320017i	$-0.896311\pi$
$31$		−	19.8410i		−	0.640034i	0.947412	−	0.320017i	$-0.103689\pi$
$32$		−	5.65685i		−	0.176777i
$33$		−	1.97638i		−	0.0598904i
$34$			30.6392i			0.901154i
$35$		0			0
$36$	−10.8340			−0.300944
$37$		−	68.3424i		−	1.84709i	−0.383488	−	0.923546i	$-0.625277\pi$
$37$		−	68.3424i		−	1.84709i	0.383488	−	0.923546i	$-0.374723\pi$
$38$	11.1036	+	24.4686i	0.292200	+	0.643909i
$39$	11.4007			0.292326
$40$		0			0
$41$		−	3.84932i		−	0.0938858i	−0.998898	−	0.0469429i	$-0.985052\pi$
$41$		−	3.84932i		−	0.0938858i	0.998898	−	0.0469429i	$-0.0149479\pi$
$42$	−4.51465			−0.107492
$43$	−65.0642			−1.51312			−0.756561	−	0.653924i	$-0.773122\pi$
$43$	−65.0642			−1.51312			−0.756561	+	0.653924i	$0.773122\pi$
$44$	−2.08822			−0.0474596
$45$		0			0
$46$			56.3120i			1.22417i
$47$	−9.61045			−0.204478			−0.102239	−	0.994760i	$-0.532601\pi$
$47$	−9.61045			−0.204478			−0.102239	+	0.994760i	$0.532601\pi$
$48$		−	7.57154i		−	0.157740i
$49$	−46.1557			−0.941954
$50$		0			0
$51$			41.0097i			0.804112i
$52$		−	12.0459i		−	0.231652i
$53$			62.0602i			1.17095i	0.810691	+	0.585474i	$0.199091\pi$
$53$			62.0602i			1.17095i	−0.810691	+	0.585474i	$0.800909\pi$
$54$	−38.5935			−0.714694
$55$		0			0
$56$			4.77013i			0.0851809i
$57$	14.8618	+	32.7505i	0.260734	+	0.574569i
$58$	0.393722			0.00678830
$59$			94.0807i			1.59459i	0.603591	+	0.797294i	$0.293736\pi$
$59$			94.0807i			1.59459i	−0.603591	+	0.797294i	$0.706264\pi$
$60$		0			0
$61$	−19.4070			−0.318148			−0.159074	−	0.987267i	$-0.550851\pi$
$61$	−19.4070			−0.318148			−0.159074	+	0.987267i	$0.550851\pi$
$62$	−28.0595			−0.452572
$63$	9.13572			0.145012
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−2.79503			−0.0423489
$67$		−	62.2388i		−	0.928937i	−0.885590	−	0.464469i	$-0.846245\pi$
$67$		−	62.2388i		−	0.928937i	0.885590	−	0.464469i	$-0.153755\pi$
$68$	43.3304			0.637212
$69$			75.3720i			1.09235i
$70$		0			0
$71$			41.4101i			0.583241i	0.956534	+	0.291621i	$0.0941945\pi$
$71$			41.4101i			0.583241i	−0.956534	+	0.291621i	$0.905805\pi$
$72$			15.3216i			0.212799i
$73$	3.25235			0.0445527			0.0222763	−	0.999752i	$-0.492909\pi$
$73$	3.25235			0.0445527			0.0222763	+	0.999752i	$0.492909\pi$
$74$	−96.6507			−1.30609
$75$		0			0
$76$	34.6038	−	15.7029i	0.455313	−	0.206617i
$77$	1.76089			0.0228687
$78$		−	16.1231i		−	0.206706i
$79$			84.1379i			1.06504i	0.846418	+	0.532519i	$0.178754\pi$
$79$			84.1379i			1.06504i	−0.846418	+	0.532519i	$0.821246\pi$
$80$		0			0
$81$	−2.90334			−0.0358437
$82$	−5.44376			−0.0663873
$83$	−5.58177			−0.0672503			−0.0336251	−	0.999435i	$-0.510705\pi$
$83$	−5.58177			−0.0672503			−0.0336251	+	0.999435i	$0.510705\pi$
$84$			6.38468i			0.0760081i
$85$		0			0
$86$			92.0147i			1.06994i
$87$	0.526985			0.00605730
$88$			2.95319i			0.0335590i
$89$		−	84.3407i		−	0.947648i	−0.880619	−	0.473824i	$-0.842873\pi$
$89$		−	84.3407i		−	0.947648i	0.880619	−	0.473824i	$-0.157127\pi$
$90$		0			0
$91$			10.1577i			0.111623i
$92$	79.6372			0.865622
$93$	−37.5568			−0.403837
$94$			13.5912i			0.144588i
$95$		0			0
$96$	−10.7078			−0.111539
$97$			1.89498i			0.0195359i	0.999952	+	0.00976795i	$0.00310928\pi$
$97$			1.89498i			0.0195359i	−0.999952	+	0.00976795i	$0.996891\pi$
$98$			65.2741i			0.666062i
$99$	5.65594			0.0571307
$100$		0			0
$101$	15.0979			0.149484			0.0747418	−	0.997203i	$-0.476187\pi$
$101$	15.0979			0.149484			0.0747418	+	0.997203i	$0.476187\pi$
$102$	57.9965			0.568593
$103$			143.352i			1.39177i	0.718155	+	0.695883i	$0.244987\pi$
$103$			143.352i			1.39177i	−0.718155	+	0.695883i	$0.755013\pi$
$104$	−17.0354			−0.163802
$105$		0			0
$106$	87.7664			0.827985
$107$		−	118.658i		−	1.10895i	−0.832200	−	0.554475i	$-0.812919\pi$
$107$		−	118.658i		−	1.10895i	0.832200	−	0.554475i	$-0.187081\pi$
$108$			54.5794i			0.505365i
$109$			62.2344i			0.570957i	0.958385	+	0.285479i	$0.0921526\pi$
$109$			62.2344i			0.570957i	−0.958385	+	0.285479i	$0.907847\pi$
$110$		0			0
$111$	−129.364			−1.16544
$112$	6.74598			0.0602320
$113$		−	88.8122i		−	0.785949i	−0.919549	−	0.392974i	$-0.871446\pi$
$113$		−	88.8122i		−	0.785949i	0.919549	−	0.392974i	$-0.128554\pi$
$114$	46.3161	−	21.0178i	0.406282	−	0.184367i
$115$		0			0
$116$		−	0.556806i		−	0.00480006i
$117$			32.6262i			0.278856i
$118$	133.050			1.12754
$119$	−36.5383			−0.307044
$120$		0			0
$121$	−119.910			−0.990990
$122$			27.4456i			0.224964i
$123$	−7.28632			−0.0592383
$124$			39.6821i			0.320017i
$125$		0			0
$126$		−	12.9199i		−	0.102539i
$127$		−	9.31099i		−	0.0733149i	−0.999328	−	0.0366574i	$-0.988329\pi$
$127$		−	9.31099i		−	0.0733149i	0.999328	−	0.0366574i	$-0.0116710\pi$
$128$			11.3137i			0.0883883i
$129$			123.159i			0.954721i
$130$		0			0
$131$	147.708			1.12754			0.563769	−	0.825932i	$-0.309351\pi$
$131$	147.708			1.12754			0.563769	+	0.825932i	$0.309351\pi$
$132$			3.95277i			0.0299452i
$133$	−29.1795	+	13.2414i	−0.219395	+	0.0995594i
$134$	−88.0189			−0.656858
$135$		0			0
$136$		−	61.2785i		−	0.450577i
$137$	147.080			1.07358			0.536789	−	0.843716i	$-0.319637\pi$
$137$	147.080			1.07358			0.536789	+	0.843716i	$0.319637\pi$
$138$	106.592			0.772407
$139$	−78.4626			−0.564479			−0.282240	−	0.959344i	$-0.591077\pi$
$139$	−78.4626			−0.564479			−0.282240	+	0.959344i	$0.591077\pi$
$140$		0			0
$141$			18.1915i			0.129018i
$142$	58.5628			0.412414
$143$			6.28862i			0.0439764i
$144$	21.6680			0.150472
$145$		0			0
$146$		−	4.59951i		−	0.0315035i
$147$			87.3675i			0.594337i
$148$			136.685i			0.923546i
$149$	135.184			0.907273			0.453637	−	0.891187i	$-0.350126\pi$
$149$	135.184			0.907273			0.453637	+	0.891187i	$0.350126\pi$
$150$		0			0
$151$		−	168.771i		−	1.11769i	−0.829272	−	0.558846i	$-0.811244\pi$
$151$		−	168.771i		−	1.11769i	0.829272	−	0.558846i	$-0.188756\pi$
$152$	−22.2072	−	48.9371i	−0.146100	−	0.321955i
$153$	−117.360			−0.767060
$154$		−	2.49027i		−	0.0161706i
$155$		0			0
$156$	−22.8015			−0.146163
$157$	4.58432			0.0291995			0.0145998	−	0.999893i	$-0.495353\pi$
$157$	4.58432			0.0291995			0.0145998	+	0.999893i	$0.495353\pi$
$158$	118.989			0.753095
$159$	117.473			0.738823
$160$		0			0
$161$	−67.1539			−0.417105
$162$			4.10594i			0.0253453i
$163$	−187.644			−1.15119			−0.575596	−	0.817734i	$-0.695230\pi$
$163$	−187.644			−1.15119			−0.575596	+	0.817734i	$0.695230\pi$
$164$			7.69864i			0.0469429i
$165$		0			0
$166$			7.89382i			0.0475531i
$167$		−	108.235i		−	0.648112i	−0.946038	−	0.324056i	$-0.894953\pi$
$167$		−	108.235i		−	0.648112i	0.946038	−	0.324056i	$-0.105047\pi$
$168$	9.02930			0.0537458
$169$	132.724			0.785350
$170$		0			0
$171$	−93.7241	+	42.5311i	−0.548094	+	0.248720i
$172$	130.128			0.756561
$173$		−	102.097i		−	0.590155i	−0.955473	−	0.295078i	$-0.904655\pi$
$173$		−	102.097i		−	0.590155i	0.955473	−	0.295078i	$-0.0953455\pi$
$174$		−	0.745270i		−	0.00428316i
$175$		0			0
$176$	4.17645			0.0237298
$177$	178.084			1.00612
$178$	−119.276			−0.670089
$179$			121.752i			0.680181i	0.940393	+	0.340090i	$0.110458\pi$
$179$			121.752i			0.680181i	−0.940393	+	0.340090i	$0.889542\pi$
$180$		0			0
$181$		−	40.3187i		−	0.222755i	−0.993778	−	0.111378i	$-0.964474\pi$
$181$		−	40.3187i		−	0.222755i	0.993778	−	0.111378i	$-0.0355263\pi$
$182$	14.3651			0.0789291
$183$			36.7352i			0.200739i
$184$		−	112.624i		−	0.612087i
$185$		0			0
$186$			53.1133i			0.285556i
$187$	−22.6209			−0.120967
$188$	19.2209			0.102239
$189$		−	46.0239i		−	0.243513i
$190$		0			0
$191$	−226.244			−1.18452			−0.592261	−	0.805746i	$-0.701765\pi$
$191$	−226.244			−1.18452			−0.592261	+	0.805746i	$0.701765\pi$
$192$			15.1431i			0.0788702i
$193$		−	6.91887i		−	0.0358491i	−0.999839	−	0.0179245i	$-0.994294\pi$
$193$		−	6.91887i		−	0.0358491i	0.999839	−	0.0179245i	$-0.00570587\pi$
$194$	2.67991			0.0138140
$195$		0			0
$196$	92.3115			0.470977
$197$	−235.124			−1.19352			−0.596762	−	0.802419i	$-0.703546\pi$
$197$	−235.124			−1.19352			−0.596762	+	0.802419i	$0.703546\pi$
$198$		−	7.99871i		−	0.0403975i
$199$	39.9542			0.200775			0.100388	−	0.994948i	$-0.467992\pi$
$199$	39.9542			0.200775			0.100388	+	0.994948i	$0.467992\pi$
$200$		0			0
$201$	−117.811			−0.586124
$202$		−	21.3516i		−	0.105701i
$203$			0.469526i			0.00231293i
$204$		−	82.0195i		−	0.402056i
$205$		0			0
$206$	202.730			0.984128
$207$	−215.697			−1.04201
$208$			24.0918i			0.115826i
$209$	−18.0651	+	8.19777i	−0.0864359	+	0.0392238i
$210$		0			0
$211$			244.243i			1.15755i	0.815487	+	0.578776i	$0.196469\pi$
$211$			244.243i			1.15755i	−0.815487	+	0.578776i	$0.803531\pi$
$212$		−	124.120i		−	0.585474i
$213$	78.3846			0.368003
$214$	−167.807			−0.784146
$215$		0			0
$216$	77.1869			0.357347
$217$		−	33.4618i		−	0.154202i
$218$	88.0127			0.403728
$219$		−	6.15632i		−	0.0281110i
$220$		0			0
$221$		−	130.488i		−	0.590444i
$222$			182.949i			0.824093i
$223$		−	336.370i		−	1.50839i	−0.656653	−	0.754193i	$-0.728028\pi$
$223$		−	336.370i		−	1.50839i	0.656653	−	0.754193i	$-0.271972\pi$
$224$		−	9.54026i		−	0.0425904i
$225$		0			0
$226$	−125.599			−0.555750
$227$			288.533i			1.27107i	0.772071	+	0.635536i	$0.219221\pi$
$227$			288.533i			1.27107i	−0.772071	+	0.635536i	$0.780779\pi$
$228$	−29.7237	−	65.5009i	−0.130367	−	0.287285i
$229$	412.489			1.80126			0.900632	−	0.434583i	$-0.143104\pi$
$229$	412.489			1.80126			0.900632	+	0.434583i	$0.143104\pi$
$230$		0			0
$231$		−	3.33316i		−	0.0144293i
$232$	−0.787443			−0.00339415
$233$	−33.7493			−0.144847			−0.0724234	−	0.997374i	$-0.523073\pi$
$233$	−33.7493			−0.144847			−0.0724234	+	0.997374i	$0.523073\pi$
$234$	46.1404			0.197181
$235$		0			0
$236$		−	188.161i		−	0.797294i
$237$	159.263			0.671998
$238$			51.6729i			0.217113i
$239$	−197.741			−0.827368			−0.413684	−	0.910421i	$-0.635758\pi$
$239$	−197.741			−0.827368			−0.413684	+	0.910421i	$0.635758\pi$
$240$		0			0
$241$		−	348.779i		−	1.44722i	−0.690211	−	0.723608i	$-0.742482\pi$
$241$		−	348.779i		−	1.44722i	0.690211	−	0.723608i	$-0.257518\pi$
$242$			169.578i			0.700736i
$243$		−	240.112i		−	0.988113i
$244$	38.8140			0.159074
$245$		0			0
$246$			10.3044i			0.0418878i
$247$	−47.2887	−	104.208i	−0.191452	−	0.421895i
$248$	56.1189			0.226286
$249$			10.5657i			0.0424323i
$250$		0			0
$251$	70.8555			0.282293			0.141146	−	0.989989i	$-0.454921\pi$
$251$	70.8555			0.282293			0.141146	+	0.989989i	$0.454921\pi$
$252$	−18.2714			−0.0725058
$253$	−41.5751			−0.164328
$254$	−13.1677			−0.0518414
$255$		0			0
$256$	16.0000			0.0625000
$257$			513.143i			1.99667i	0.0577124	+	0.998333i	$0.481619\pi$
$257$			513.143i			1.99667i	−0.0577124	+	0.998333i	$0.518381\pi$
$258$	174.173			0.675090
$259$		−	115.259i		−	0.445016i
$260$		0			0
$261$			1.50811i			0.00577819i
$262$		−	208.890i		−	0.797290i
$263$	−39.7483			−0.151134			−0.0755670	−	0.997141i	$-0.524077\pi$
$263$	−39.7483			−0.151134			−0.0755670	+	0.997141i	$0.524077\pi$
$264$	5.59006			0.0211745
$265$		0			0
$266$	18.7262	+	41.2661i	0.0703991	+	0.155136i
$267$	−159.647			−0.597930
$268$			124.478i			0.464469i
$269$		−	516.941i		−	1.92172i	−0.277043	−	0.960858i	$-0.589354\pi$
$269$		−	516.941i		−	1.92172i	0.277043	−	0.960858i	$-0.410646\pi$
$270$		0			0
$271$	147.956			0.545963			0.272982	−	0.962019i	$-0.411990\pi$
$271$	147.956			0.545963			0.272982	+	0.962019i	$0.411990\pi$
$272$	−86.6608			−0.318606
$273$	19.2273			0.0704296
$274$		−	208.003i		−	0.759135i
$275$		0			0
$276$		−	150.744i		−	0.546174i
$277$	−400.546			−1.44601			−0.723007	−	0.690840i	$-0.757241\pi$
$277$	−400.546			−1.44601			−0.723007	+	0.690840i	$0.757241\pi$
$278$			110.963i			0.399147i
$279$		−	107.479i		−	0.385228i
$280$		0			0
$281$			251.143i			0.893748i	0.894597	+	0.446874i	$0.147463\pi$
$281$			251.143i			0.893748i	−0.894597	+	0.446874i	$0.852537\pi$
$282$	25.7266			0.0912292
$283$	−420.587			−1.48617			−0.743087	−	0.669195i	$-0.766639\pi$
$283$	−420.587			−1.48617			−0.743087	+	0.669195i	$0.766639\pi$
$284$		−	82.8203i		−	0.291621i
$285$		0			0
$286$	8.89346			0.0310960
$287$		−	6.49186i		−	0.0226197i
$288$		−	30.6431i		−	0.106400i
$289$	180.381			0.624156
$290$		0			0
$291$	3.58698			0.0123264
$292$	−6.50469			−0.0222763
$293$		−	335.367i		−	1.14460i	−0.820045	−	0.572299i	$-0.806052\pi$
$293$		−	335.367i		−	1.14460i	0.820045	−	0.572299i	$-0.193948\pi$
$294$	123.556			0.420259
$295$		0			0
$296$	193.301			0.653046
$297$		−	28.4935i		−	0.0959377i
$298$		−	191.179i		−	0.641539i
$299$		−	239.825i		−	0.802091i
$300$		0			0
$301$	−109.730			−0.364553
$302$	−238.679			−0.790327
$303$		−	28.5785i		−	0.0943185i
$304$	−69.2075	+	31.4057i	−0.227656	+	0.103308i
$305$		0			0
$306$			165.972i			0.542393i
$307$		−	311.594i		−	1.01497i	−0.861662	−	0.507483i	$-0.830576\pi$
$307$		−	311.594i		−	1.01497i	0.861662	−	0.507483i	$-0.169424\pi$
$308$	−3.52178			−0.0114343
$309$	271.349			0.878151
$310$		0			0
$311$	288.128			0.926457			0.463228	−	0.886239i	$-0.346691\pi$
$311$	288.128			0.926457			0.463228	+	0.886239i	$0.346691\pi$
$312$			32.2461i			0.103353i
$313$	137.897			0.440567			0.220284	−	0.975436i	$-0.429302\pi$
$313$	137.897			0.440567			0.220284	+	0.975436i	$0.429302\pi$
$314$		−	6.48321i		−	0.0206472i
$315$		0			0
$316$		−	168.276i		−	0.532519i
$317$			288.819i			0.911101i	0.890210	+	0.455551i	$0.150558\pi$
$317$			288.819i			0.911101i	−0.890210	+	0.455551i	$0.849442\pi$
$318$		−	166.132i		−	0.522426i
$319$			0.290684i			0.000911236i
$320$		0			0
$321$	−224.605			−0.699705
$322$			94.9700i			0.294938i
$323$	374.849	−	170.103i	1.16052	−	0.526634i
$324$	5.80668			0.0179218
$325$		0			0
$326$			265.369i			0.814016i
$327$	117.802			0.360252
$328$	10.8875			0.0331937
$329$	−16.2080			−0.0492644
$330$		0			0
$331$		−	114.877i		−	0.347060i	−0.984829	−	0.173530i	$-0.944483\pi$
$331$		−	114.877i		−	0.347060i	0.984829	−	0.173530i	$-0.0555173\pi$
$332$	11.1635			0.0336251
$333$		−	370.210i		−	1.11174i
$334$	−153.067			−0.458284
$335$		0			0
$336$		−	12.7694i		−	0.0380041i
$337$		−	11.1235i		−	0.0330075i	−0.999864	−	0.0165038i	$-0.994746\pi$
$337$		−	11.1235i		−	0.0330075i	0.999864	−	0.0165038i	$-0.00525355\pi$
$338$		−	187.700i		−	0.555327i
$339$	−168.111			−0.495903
$340$		0			0
$341$		−	20.7163i		−	0.0607515i
$342$	60.1481	+	132.546i	0.175872	+	0.387561i
$343$	−160.480			−0.467871
$344$		−	184.029i		−	0.534969i
$345$		0			0
$346$	−144.387			−0.417303
$347$	−258.149			−0.743944			−0.371972	−	0.928244i	$-0.621318\pi$
$347$	−258.149			−0.743944			−0.371972	+	0.928244i	$0.621318\pi$
$348$	−1.05397			−0.00302865
$349$	−465.062			−1.33256			−0.666278	−	0.745703i	$-0.732114\pi$
$349$	−465.062			−1.33256			−0.666278	+	0.745703i	$0.732114\pi$
$350$		0			0
$351$	164.364			0.468274
$352$		−	5.90639i		−	0.0167795i
$353$	506.379			1.43450			0.717251	−	0.696815i	$-0.245400\pi$
$353$	506.379			1.43450			0.717251	+	0.696815i	$0.245400\pi$
$354$		−	251.849i		−	0.711437i
$355$		0			0
$356$			168.681i			0.473824i
$357$			69.1627i			0.193733i
$358$	172.184			0.480960
$359$	−2.91049			−0.00810722			−0.00405361	−	0.999992i	$-0.501290\pi$
$359$	−2.91049			−0.00810722			−0.00405361	+	0.999992i	$0.501290\pi$
$360$		0			0
$361$	237.710	−	271.689i	0.658477	−	0.752601i
$362$	−57.0192			−0.157512
$363$			226.975i			0.625277i
$364$		−	20.3153i		−	0.0558113i
$365$		0			0
$366$	51.9514			0.141944
$367$	−382.586			−1.04247			−0.521234	−	0.853414i	$-0.674528\pi$
$367$	−382.586			−1.04247			−0.521234	+	0.853414i	$0.674528\pi$
$368$	−159.274			−0.432811
$369$		−	20.8517i		−	0.0565087i
$370$		0			0
$371$			104.664i			0.282114i
$372$	75.1136			0.201918
$373$			394.786i			1.05841i	0.848495	+	0.529204i	$0.177509\pi$
$373$			394.786i			1.05841i	−0.848495	+	0.529204i	$0.822491\pi$
$374$			31.9908i			0.0855368i
$375$		0			0
$376$		−	27.1825i		−	0.0722938i
$377$	−1.67681			−0.00444776
$378$	−65.0877			−0.172190
$379$		−	614.957i		−	1.62258i	−0.584645	−	0.811289i	$-0.698766\pi$
$379$		−	614.957i		−	1.62258i	0.584645	−	0.811289i	$-0.301234\pi$
$380$		0			0
$381$	−17.6246			−0.0462589
$382$			319.957i			0.837584i
$383$			445.383i			1.16288i	0.813589	+	0.581440i	$0.197511\pi$
$383$			445.383i			1.16288i	−0.813589	+	0.581440i	$0.802489\pi$
$384$	21.4155			0.0557696
$385$		0			0
$386$	−9.78477			−0.0253491
$387$	−352.452			−0.910729
$388$		−	3.78996i		−	0.00976795i
$389$	116.462			0.299387			0.149694	−	0.988732i	$-0.452171\pi$
$389$	116.462			0.299387			0.149694	+	0.988732i	$0.452171\pi$
$390$		0			0
$391$	862.679			2.20634
$392$		−	130.548i		−	0.333031i
$393$		−	279.593i		−	0.711433i
$394$			332.516i			0.843948i
$395$		0			0
$396$	−11.3119			−0.0285654
$397$	310.718			0.782665			0.391332	−	0.920249i	$-0.372014\pi$
$397$	310.718			0.782665			0.391332	+	0.920249i	$0.372014\pi$
$398$		−	56.5038i		−	0.141969i
$399$	25.0644	+	55.2335i	0.0628181	+	0.138430i
$400$		0			0
$401$			462.347i			1.15299i	0.817102	+	0.576493i	$0.195579\pi$
$401$			462.347i			1.15299i	−0.817102	+	0.576493i	$0.804421\pi$
$402$			166.610i			0.414452i
$403$	119.501			0.296530
$404$	−30.1957			−0.0747418
$405$		0			0
$406$	0.664010			0.00163549
$407$		−	71.3571i		−	0.175325i
$408$	−115.993			−0.284297
$409$		−	552.392i		−	1.35059i	−0.737547	−	0.675296i	$-0.764016\pi$
$409$		−	552.392i		−	1.35059i	0.737547	−	0.675296i	$-0.235984\pi$
$410$		0			0
$411$		−	278.406i		−	0.677387i
$412$		−	286.704i		−	0.695883i
$413$			158.667i			0.384181i
$414$			305.042i			0.736816i
$415$		0			0
$416$	34.0709			0.0819012
$417$			148.521i			0.356165i
$418$	11.5934	+	25.5479i	0.0277354	+	0.0611194i
$419$	−35.7864			−0.0854090			−0.0427045	−	0.999088i	$-0.513597\pi$
$419$	−35.7864			−0.0854090			−0.0427045	+	0.999088i	$0.513597\pi$
$420$		0			0
$421$		−	669.640i		−	1.59059i	−0.606221	−	0.795297i	$-0.707315\pi$
$421$		−	669.640i		−	1.59059i	0.606221	−	0.795297i	$-0.292685\pi$
$422$	345.412			0.818513
$423$	−52.0597			−0.123073
$424$	−175.533			−0.413992
$425$		0			0
$426$		−	110.853i		−	0.260217i
$427$	−32.7298			−0.0766506
$428$			237.315i			0.554475i
$429$	11.9036			0.0277474
$430$		0			0
$431$			174.646i			0.405212i	0.979260	+	0.202606i	$0.0649411\pi$
$431$			174.646i			0.405212i	−0.979260	+	0.202606i	$0.935059\pi$
$432$		−	109.159i		−	0.252682i
$433$			111.608i			0.257755i	0.991661	+	0.128877i	$0.0411374\pi$
$433$			111.608i			0.257755i	−0.991661	+	0.128877i	$0.958863\pi$
$434$	−47.3222			−0.109037
$435$		0			0
$436$		−	124.469i		−	0.285479i
$437$	688.937	−	312.633i	1.57651	−	0.715408i
$438$	−8.70634			−0.0198775
$439$			93.1300i			0.212141i	0.994359	+	0.106071i	$0.0338270\pi$
$439$			93.1300i			0.212141i	−0.994359	+	0.106071i	$0.966173\pi$
$440$		0			0
$441$	−250.025			−0.566950
$442$	−184.538			−0.417507
$443$	796.123			1.79712			0.898558	−	0.438854i	$-0.144616\pi$
$443$	796.123			1.79712			0.898558	+	0.438854i	$0.144616\pi$
$444$	258.729			0.582722
$445$		0			0
$446$	−475.699			−1.06659
$447$		−	255.887i		−	0.572454i
$448$	−13.4920			−0.0301160
$449$		−	186.109i		−	0.414496i	−0.978288	−	0.207248i	$-0.933549\pi$
$449$		−	186.109i		−	0.414496i	0.978288	−	0.207248i	$-0.0664508\pi$
$450$		0			0
$451$		−	4.01912i		−	0.00891157i
$452$			177.624i			0.392974i
$453$	−319.465			−0.705220
$454$	408.048			0.898784
$455$		0			0
$456$	−92.6323	+	42.0357i	−0.203141	+	0.0921834i
$457$	576.986			1.26255			0.631276	−	0.775558i	$-0.282532\pi$
$457$	576.986			1.26255			0.631276	+	0.775558i	$0.282532\pi$
$458$		−	583.348i		−	1.27369i
$459$			591.237i			1.28810i
$460$		0			0
$461$	223.865			0.485608			0.242804	−	0.970075i	$-0.421933\pi$
$461$	223.865			0.485608			0.242804	+	0.970075i	$0.421933\pi$
$462$	−4.71380			−0.0102030
$463$	−452.579			−0.977492			−0.488746	−	0.872426i	$-0.662545\pi$
$463$	−452.579			−0.977492			−0.488746	+	0.872426i	$0.662545\pi$
$464$			1.11361i			0.00240003i
$465$		0			0
$466$			47.7287i			0.102422i
$467$	69.9506			0.149787			0.0748936	−	0.997192i	$-0.476138\pi$
$467$	69.9506			0.149787			0.0748936	+	0.997192i	$0.476138\pi$
$468$		−	65.2524i		−	0.139428i
$469$		−	104.965i		−	0.223807i
$470$		0			0
$471$		−	8.67760i		−	0.0184238i
$472$	−266.100			−0.563772
$473$	−67.9343			−0.143624
$474$		−	225.232i		−	0.475174i
$475$		0			0
$476$	73.0765			0.153522
$477$			336.179i			0.704779i
$478$			279.648i			0.585037i
$479$	−137.500			−0.287055			−0.143528	−	0.989646i	$-0.545845\pi$
$479$	−137.500			−0.287055			−0.143528	+	0.989646i	$0.545845\pi$
$480$		0			0
$481$	411.622			0.855763
$482$	−493.248			−1.02334
$483$			127.115i			0.263177i
$484$	239.820			0.495495
$485$		0			0
$486$	−339.569			−0.698702
$487$		−	329.190i		−	0.675954i	−0.941154	−	0.337977i	$-0.890257\pi$
$487$		−	329.190i		−	0.675954i	0.941154	−	0.337977i	$-0.109743\pi$
$488$		−	54.8913i		−	0.112482i
$489$			355.189i			0.726358i
$490$		0			0
$491$	−438.255			−0.892576			−0.446288	−	0.894889i	$-0.647254\pi$
$491$	−438.255			−0.892576			−0.446288	+	0.894889i	$0.647254\pi$
$492$	14.5726			0.0296192
$493$		−	6.03166i		−	0.0122346i
$494$	−147.373	+	66.8763i	−0.298325	+	0.135377i
$495$		0			0
$496$		−	79.3642i		−	0.160008i
$497$			69.8380i			0.140519i
$498$	14.9421			0.0300042
$499$	−695.692			−1.39417			−0.697086	−	0.716988i	$-0.745520\pi$
$499$	−695.692			−1.39417			−0.697086	+	0.716988i	$0.745520\pi$
$500$		0			0
$501$	−204.876			−0.408934
$502$		−	100.205i		−	0.199611i
$503$	−34.2415			−0.0680746			−0.0340373	−	0.999421i	$-0.510837\pi$
$503$	−34.2415			−0.0680746			−0.0340373	+	0.999421i	$0.510837\pi$
$504$			25.8397i			0.0512693i
$505$		0			0
$506$			58.7961i			0.116198i
$507$		−	251.232i		−	0.495526i
$508$			18.6220i			0.0366574i
$509$			391.055i			0.768281i	0.923275	+	0.384140i	$0.125502\pi$
$509$			391.055i			0.768281i	−0.923275	+	0.384140i	$0.874498\pi$
$510$		0			0
$511$	5.48507			0.0107340
$512$		−	22.6274i		−	0.0441942i
$513$	214.263	+	472.163i	0.417667	+	0.920396i
$514$	725.694			1.41186
$515$		0			0
$516$		−	246.318i		−	0.477361i
$517$	−10.0344			−0.0194089
$518$	−163.001			−0.314674
$519$	−193.258			−0.372365
$520$		0			0
$521$		−	423.418i		−	0.812702i	−0.913717	−	0.406351i	$-0.866801\pi$
$521$		−	423.418i		−	0.812702i	0.913717	−	0.406351i	$-0.133199\pi$
$522$	2.13279			0.00408580
$523$		−	277.177i		−	0.529976i	−0.964252	−	0.264988i	$-0.914632\pi$
$523$		−	277.177i		−	0.529976i	0.964252	−	0.264988i	$-0.0853680\pi$
$524$	−295.415			−0.563769
$525$		0			0
$526$			56.2125i			0.106868i
$527$			429.860i			0.815674i
$528$		−	7.90553i		−	0.0149726i
$529$	1056.52			1.99721
$530$		0			0
$531$			509.634i			0.959762i
$532$	58.3591	−	26.4828i	0.109698	−	0.0497797i
$533$	23.1842			0.0434976
$534$			225.775i			0.422800i
$535$		0			0
$536$	176.038			0.328429
$537$	230.463			0.429168
$538$	−731.066			−1.35886
$539$	−48.1918			−0.0894096
$540$		0			0
$541$	−562.342			−1.03945			−0.519725	−	0.854334i	$-0.673965\pi$
$541$	−562.342			−1.03945			−0.519725	+	0.854334i	$0.673965\pi$
$542$		−	209.241i		−	0.386054i
$543$	−76.3186			−0.140550
$544$			122.557i			0.225288i
$545$		0			0
$546$		−	27.1915i		−	0.0498012i
$547$			727.214i			1.32946i	0.747084	+	0.664729i	$0.231453\pi$
$547$			727.214i			1.32946i	−0.747084	+	0.664729i	$0.768547\pi$
$548$	−294.161			−0.536789
$549$	−105.128			−0.191489
$550$		0			0
$551$	−2.18586	−	4.81690i	−0.00396708	−	0.00874210i
$552$	−213.184			−0.386204
$553$			141.898i			0.256597i
$554$			566.458i			1.02249i
$555$		0			0
$556$	156.925			0.282240
$557$	692.987			1.24414			0.622071	−	0.782961i	$-0.286291\pi$
$557$	692.987			1.24414			0.622071	+	0.782961i	$0.286291\pi$
$558$	−151.998			−0.272398
$559$		−	391.878i		−	0.701034i
$560$		0			0
$561$			42.8187i			0.0763257i
$562$	355.170			0.631975
$563$			285.285i			0.506723i	0.967372	+	0.253362i	$0.0815363\pi$
$563$			285.285i			0.506723i	−0.967372	+	0.253362i	$0.918464\pi$
$564$		−	36.3829i		−	0.0645088i
$565$		0			0
$566$			594.800i			1.05088i
$567$	−4.89647			−0.00863574
$568$	−117.126			−0.206207
$569$			843.131i			1.48178i	0.671628	+	0.740888i	$0.265595\pi$
$569$			843.131i			1.48178i	−0.671628	+	0.740888i	$0.734405\pi$
$570$		0			0
$571$	−798.131			−1.39778			−0.698889	−	0.715230i	$-0.746322\pi$
$571$	−798.131			−1.39778			−0.698889	+	0.715230i	$0.746322\pi$
$572$		−	12.5772i		−	0.0219882i
$573$			428.253i			0.747388i
$574$	−9.18087			−0.0159946
$575$		0			0
$576$	−43.3359			−0.0752360
$577$	28.4942			0.0493834			0.0246917	−	0.999695i	$-0.492140\pi$
$577$	28.4942			0.0493834			0.0246917	+	0.999695i	$0.492140\pi$
$578$		−	255.097i		−	0.441345i
$579$	−13.0966			−0.0226194
$580$		0			0
$581$	−9.41364			−0.0162025
$582$		−	5.07276i		−	0.00871608i
$583$			64.7978i			0.111145i
$584$			9.19902i			0.0157518i
$585$		0			0
$586$	−474.281			−0.809352
$587$	−546.088			−0.930303			−0.465151	−	0.885231i	$-0.654000\pi$
$587$	−546.088			−0.930303			−0.465151	+	0.885231i	$0.654000\pi$
$588$		−	174.735i		−	0.297168i
$589$	155.781	+	343.287i	0.264483	+	0.582831i
$590$		0			0
$591$			445.063i			0.753067i
$592$		−	273.370i		−	0.461773i
$593$	1058.29			1.78464			0.892318	−	0.451407i	$-0.149078\pi$
$593$	1058.29			1.78464			0.892318	+	0.451407i	$0.149078\pi$
$594$	−40.2959			−0.0678382
$595$		0			0
$596$	−270.367			−0.453637
$597$		−	75.6288i		−	0.126681i
$598$	−339.164			−0.567164
$599$		−	554.840i		−	0.926278i	−0.886286	−	0.463139i	$-0.846723\pi$
$599$		−	554.840i		−	0.926278i	0.886286	−	0.463139i	$-0.153277\pi$
$600$		0			0
$601$		−	662.009i		−	1.10151i	−0.834666	−	0.550756i	$-0.814339\pi$
$601$		−	662.009i		−	1.10151i	0.834666	−	0.550756i	$-0.185661\pi$
$602$			155.182i			0.257778i
$603$		−	337.147i		−	0.559116i
$604$			337.543i			0.558846i
$605$		0			0
$606$	−40.4161			−0.0666932
$607$		−	895.503i		−	1.47529i	−0.675187	−	0.737646i	$-0.735937\pi$
$607$		−	895.503i		−	1.47529i	0.675187	−	0.737646i	$-0.264063\pi$
$608$	44.4144	+	97.8742i	0.0730500	+	0.160977i
$609$	0.888758			0.00145937
$610$		0			0
$611$		−	57.8832i		−	0.0947351i
$612$	234.720			0.383530
$613$	548.725			0.895146			0.447573	−	0.894247i	$-0.352288\pi$
$613$	548.725			0.895146			0.447573	+	0.894247i	$0.352288\pi$
$614$	−440.661			−0.717689
$615$		0			0
$616$			4.98055i			0.00808531i
$617$	763.924			1.23813			0.619063	−	0.785341i	$-0.287513\pi$
$617$	763.924			1.23813			0.619063	+	0.785341i	$0.287513\pi$
$618$		−	383.745i		−	0.620947i
$619$	−508.039			−0.820741			−0.410370	−	0.911919i	$-0.634601\pi$
$619$	−508.039			−0.820741			−0.410370	+	0.911919i	$0.634601\pi$
$620$		0			0
$621$			1086.64i			1.74982i
$622$		−	407.475i		−	0.655104i
$623$		−	142.240i		−	0.228315i
$624$	45.6029			0.0730816
$625$		0			0
$626$		−	195.016i		−	0.311528i
$627$	15.5174	+	34.1951i	0.0247487	+	0.0545377i
$628$	−9.16865			−0.0145998
$629$			1480.65i			2.35398i
$630$		0			0
$631$	673.489			1.06734			0.533668	−	0.845694i	$-0.320813\pi$
$631$	673.489			1.06734			0.533668	+	0.845694i	$0.320813\pi$
$632$	−237.978			−0.376548
$633$	462.325			0.730371
$634$	408.452			0.644246
$635$		0			0
$636$	−234.946			−0.369411
$637$		−	277.993i		−	0.436410i
$638$	0.411089			0.000644341
$639$			224.318i			0.351046i
$640$		0			0
$641$			1084.01i			1.69112i	0.533878	+	0.845562i	$0.320734\pi$
$641$			1084.01i			1.69112i	−0.533878	+	0.845562i	$0.679266\pi$
$642$			317.640i			0.494766i
$643$	−579.940			−0.901929			−0.450964	−	0.892542i	$-0.648920\pi$
$643$	−579.940			−0.901929			−0.450964	+	0.892542i	$0.648920\pi$
$644$	134.308			0.208553
$645$		0			0
$646$	−240.562	−	530.116i	−0.372387	−	0.820613i
$647$	585.847			0.905482			0.452741	−	0.891642i	$-0.350446\pi$
$647$	585.847			0.905482			0.452741	+	0.891642i	$0.350446\pi$
$648$		−	8.21188i		−	0.0126727i
$649$			98.2307i			0.151357i
$650$		0			0
$651$	−63.3394			−0.0972955
$652$	375.289			0.575596
$653$	−715.361			−1.09550			−0.547749	−	0.836642i	$-0.684515\pi$
$653$	−715.361			−1.09550			−0.547749	+	0.836642i	$0.684515\pi$
$654$		−	166.598i		−	0.254737i
$655$		0			0
$656$		−	15.3973i		−	0.0234715i
$657$	17.6179			0.0268157
$658$			22.9215i			0.0348352i
$659$			669.081i			1.01530i	0.861564	+	0.507649i	$0.169485\pi$
$659$			669.081i			1.01530i	−0.861564	+	0.507649i	$0.830515\pi$
$660$		0			0
$661$			291.273i			0.440655i	0.975426	+	0.220327i	$0.0707126\pi$
$661$			291.273i			0.440655i	−0.975426	+	0.220327i	$0.929287\pi$
$662$	−162.460			−0.245408
$663$	−246.999			−0.372548
$664$		−	15.7876i		−	0.0237766i
$665$		0			0
$666$	−523.556			−0.786120
$667$		−	11.0856i		−	0.0166201i
$668$			216.469i			0.324056i
$669$	−636.710			−0.951734
$670$		0			0
$671$	−20.2631			−0.0301983
$672$	−18.0586			−0.0268729
$673$			1212.39i			1.80147i	0.434372	+	0.900734i	$0.356970\pi$
$673$			1212.39i			1.80147i	−0.434372	+	0.900734i	$0.643030\pi$
$674$	−15.7311			−0.0233398
$675$		0			0
$676$	−265.448			−0.392675
$677$		−	158.703i		−	0.234421i	−0.993107	−	0.117211i	$-0.962605\pi$
$677$		−	158.703i		−	0.234421i	0.993107	−	0.117211i	$-0.0373953\pi$
$678$			237.745i			0.350657i
$679$			3.19588i			0.00470674i
$680$		0			0
$681$	546.160			0.801998
$682$	−29.2972			−0.0429578
$683$		−	109.346i		−	0.160097i	−0.996791	−	0.0800483i	$-0.974493\pi$
$683$		−	109.346i		−	0.160097i	0.996791	−	0.0800483i	$-0.0255075\pi$
$684$	187.448	−	85.0622i	0.274047	−	0.124360i
$685$		0			0
$686$			226.953i			0.330835i
$687$		−	780.795i		−	1.13653i
$688$	−260.257			−0.378280
$689$	−373.785			−0.542503
$690$		0			0
$691$	487.341			0.705269			0.352634	−	0.935761i	$-0.385286\pi$
$691$	487.341			0.705269			0.352634	+	0.935761i	$0.385286\pi$
$692$			204.194i			0.295078i
$693$	9.53872			0.0137644
$694$			365.077i			0.526048i
$695$		0			0
$696$			1.49054i			0.00214158i
$697$			83.3963i			0.119650i
$698$			657.697i			0.942259i
$699$			63.8835i			0.0913927i
$700$		0			0
$701$	−925.556			−1.32034			−0.660168	−	0.751118i	$-0.729515\pi$
$701$	−925.556			−1.32034			−0.660168	+	0.751118i	$0.729515\pi$
$702$		−	232.446i		−	0.331120i
$703$	536.585	+	1182.45i	0.763279	+	1.68201i
$704$	−8.35290			−0.0118649
$705$		0			0
$706$		−	716.128i		−	1.01435i
$707$	25.4625			0.0360148
$708$	−356.168			−0.503062
$709$	−181.394			−0.255845			−0.127923	−	0.991784i	$-0.540831\pi$
$709$	−181.394			−0.255845			−0.127923	+	0.991784i	$0.540831\pi$
$710$		0			0
$711$			455.774i			0.641033i
$712$	238.552			0.335044
$713$			790.043i			1.10805i
$714$	97.8108			0.136990
$715$		0			0
$716$		−	243.505i		−	0.340090i
$717$			374.301i			0.522037i
$718$			4.11606i			0.00573267i
$719$	−783.075			−1.08912			−0.544559	−	0.838723i	$-0.683303\pi$
$719$	−783.075			−1.08912			−0.544559	+	0.838723i	$0.683303\pi$
$720$		0			0
$721$			241.762i			0.335315i
$722$	−384.226	−	336.173i	−0.532169	−	0.465613i
$723$	−660.199			−0.913138
$724$			80.6374i			0.111378i
$725$		0			0
$726$	320.992			0.442137
$727$	−790.679			−1.08759			−0.543796	−	0.839217i	$-0.683013\pi$
$727$	−790.679			−1.08759			−0.543796	+	0.839217i	$0.683013\pi$
$728$	−28.7302			−0.0394646
$729$	−480.633			−0.659305
$730$		0			0
$731$	1409.63			1.92836
$732$		−	73.4704i		−	0.100369i
$733$	820.219			1.11899			0.559494	−	0.828834i	$-0.310995\pi$
$733$	820.219			1.11899			0.559494	+	0.828834i	$0.310995\pi$
$734$			541.058i			0.737136i
$735$		0			0
$736$			225.248i			0.306044i
$737$		−	64.9843i		−	0.0881740i
$738$	−29.4888			−0.0399577
$739$	19.5055			0.0263944			0.0131972	−	0.999913i	$-0.495799\pi$
$739$	19.5055			0.0263944			0.0131972	+	0.999913i	$0.495799\pi$
$740$		0			0
$741$	−197.254	+	89.5120i	−0.266200	+	0.120799i
$742$	148.018			0.199485
$743$		−	1204.63i		−	1.62131i	−0.585527	−	0.810653i	$-0.699113\pi$
$743$		−	1204.63i		−	1.62131i	0.585527	−	0.810653i	$-0.300887\pi$
$744$		−	106.227i		−	0.142778i
$745$		0			0
$746$	558.312			0.748407
$747$	−30.2364			−0.0404771
$748$	45.2418			0.0604837
$749$		−	200.116i		−	0.267177i
$750$		0			0
$751$		−	1442.98i		−	1.92141i	−0.277575	−	0.960704i	$-0.589531\pi$
$751$		−	1442.98i		−	1.92141i	0.277575	−	0.960704i	$-0.410469\pi$
$752$	−38.4418			−0.0511194
$753$		−	134.121i		−	0.178116i
$754$			2.37136i			0.00314504i
$755$		0			0
$756$			92.0479i			0.121756i
$757$	947.346			1.25145			0.625724	−	0.780044i	$-0.284804\pi$
$757$	947.346			1.25145			0.625724	+	0.780044i	$0.284804\pi$
$758$	−869.681			−1.14734
$759$			78.6969i			0.103685i
$760$		0			0
$761$	−892.677			−1.17303			−0.586516	−	0.809938i	$-0.699501\pi$
$761$	−892.677			−1.17303			−0.586516	+	0.809938i	$0.699501\pi$
$762$			24.9250i			0.0327099i
$763$			104.958i			0.137560i
$764$	452.487			0.592261
$765$		0			0
$766$	629.867			0.822281
$767$	−566.642			−0.738777
$768$		−	30.2862i		−	0.0394351i
$769$	−629.290			−0.818322			−0.409161	−	0.912462i	$-0.634179\pi$
$769$	−629.290			−0.818322			−0.409161	+	0.912462i	$0.634179\pi$
$770$		0			0
$771$	971.321			1.25982
$772$			13.8377i			0.0179245i
$773$			291.337i			0.376892i	0.982084	+	0.188446i	$0.0603450\pi$
$773$			291.337i			0.376892i	−0.982084	+	0.188446i	$0.939655\pi$
$774$			498.442i			0.643983i
$775$		0			0
$776$	−5.35982			−0.00690698
$777$	−218.172			−0.280788
$778$		−	164.702i		−	0.211699i
$779$	30.2227	+	66.6005i	0.0387967	+	0.0854948i
$780$		0			0
$781$			43.2368i			0.0553609i
$782$		−	1220.01i		−	1.56012i
$783$	7.59754			0.00970311
$784$	−184.623			−0.235488
$785$		0			0
$786$	−395.405			−0.503059
$787$		−	889.115i		−	1.12975i	−0.825176	−	0.564876i	$-0.808924\pi$
$787$		−	889.115i		−	1.12975i	0.825176	−	0.564876i	$-0.191076\pi$
$788$	470.248			0.596762
$789$			75.2388i			0.0953598i
$790$		0			0
$791$		−	149.781i		−	0.189357i
$792$			15.9974i			0.0201988i
$793$		−	116.887i		−	0.147399i
$794$		−	439.421i		−	0.553427i
$795$		0			0
$796$	−79.9085			−0.100388
$797$			800.716i			1.00466i	0.864675	+	0.502331i	$0.167524\pi$
$797$			800.716i			1.00466i	−0.864675	+	0.502331i	$0.832476\pi$
$798$	78.1120	−	35.4465i	0.0978847	−	0.0444191i
$799$	208.212			0.260591
$800$		0			0
$801$		−	456.873i		−	0.570378i
$802$	653.858			0.815284
$803$	3.39581			0.00422891
$804$	235.622			0.293062
$805$		0			0
$806$		−	169.000i		−	0.209678i
$807$	−978.510			−1.21253
$808$			42.7032i			0.0528505i
$809$	−327.560			−0.404894			−0.202447	−	0.979293i	$-0.564889\pi$
$809$	−327.560			−0.404894			−0.202447	+	0.979293i	$0.564889\pi$
$810$		0			0
$811$			414.555i			0.511166i	0.966787	+	0.255583i	$0.0822673\pi$
$811$			414.555i			0.511166i	−0.966787	+	0.255583i	$0.917733\pi$
$812$		−	0.939051i		−	0.00115647i
$813$		−	280.064i		−	0.344482i
$814$	−100.914			−0.123973
$815$		0			0
$816$			164.039i			0.201028i
$817$	1125.73	−	510.847i	1.37789	−	0.625272i
$818$	−781.201			−0.955013
$819$			55.0239i			0.0671843i
$820$		0			0
$821$	−594.805			−0.724489			−0.362244	−	0.932083i	$-0.617989\pi$
$821$	−594.805			−0.724489			−0.362244	+	0.932083i	$0.617989\pi$
$822$	−393.726			−0.478985
$823$	704.177			0.855622			0.427811	−	0.903868i	$-0.359285\pi$
$823$	704.177			0.855622			0.427811	+	0.903868i	$0.359285\pi$
$824$	−405.461			−0.492064
$825$		0			0
$826$	224.388			0.271657
$827$			829.642i			1.00319i	0.865101	+	0.501597i	$0.167254\pi$
$827$			829.642i			1.00319i	−0.865101	+	0.501597i	$0.832746\pi$
$828$	431.394			0.521007
$829$		−	693.036i		−	0.835990i	−0.908449	−	0.417995i	$-0.862733\pi$
$829$		−	693.036i		−	0.835990i	0.908449	−	0.417995i	$-0.137267\pi$
$830$		0			0
$831$			758.188i			0.912380i
$832$		−	48.1835i		−	0.0579129i
$833$	999.973			1.20045
$834$	210.040			0.251846
$835$		0			0
$836$	36.1302	−	16.3955i	0.0432179	−	0.0196119i
$837$	−541.456			−0.646901
$838$			50.6096i			0.0603933i
$839$		−	1482.55i		−	1.76704i	−0.468391	−	0.883521i	$-0.655166\pi$
$839$		−	1482.55i		−	1.76704i	0.468391	−	0.883521i	$-0.344834\pi$
$840$		0			0
$841$	840.922			0.999908
$842$	−947.014			−1.12472
$843$	475.385			0.563921
$844$		−	488.487i		−	0.578776i
$845$		0			0
$846$			73.6235i			0.0870254i
$847$	−202.227			−0.238757
$848$			248.241i			0.292737i
$849$			796.123i			0.937718i
$850$		0			0
$851$			2721.30i			3.19777i
$852$	−156.769			−0.184001
$853$	−1327.68			−1.55648			−0.778240	−	0.627966i	$-0.783888\pi$
$853$	−1327.68			−1.55648			−0.778240	+	0.627966i	$0.783888\pi$
$854$			46.2870i			0.0542002i
$855$		0			0
$856$	335.615			0.392073
$857$		−	274.944i		−	0.320822i	−0.987050	−	0.160411i	$-0.948718\pi$
$857$		−	274.944i		−	0.320822i	0.987050	−	0.160411i	$-0.0512819\pi$
$858$		−	16.8343i		−	0.0196204i
$859$	−182.211			−0.212120			−0.106060	−	0.994360i	$-0.533824\pi$
$859$	−182.211			−0.212120			−0.106060	+	0.994360i	$0.533824\pi$
$860$		0			0
$861$	−12.2883			−0.0142722
$862$	246.987			0.286528
$863$			173.434i			0.200966i	0.994939	+	0.100483i	$0.0320389\pi$
$863$			173.434i			0.200966i	−0.994939	+	0.100483i	$0.967961\pi$
$864$	−154.374			−0.178673
$865$		0			0
$866$	157.837			0.182260
$867$		−	341.441i		−	0.393818i
$868$			66.9236i			0.0771010i
$869$			87.8494i			0.101093i
$870$		0			0
$871$	374.860			0.430379
$872$	−176.025			−0.201864
$873$			10.2651i			0.0117584i
$874$	−442.130	−	974.304i	−0.505869	−	1.11476i
$875$		0			0
$876$			12.3126i			0.0140555i
$877$		−	708.930i		−	0.808358i	−0.914680	−	0.404179i	$-0.867557\pi$
$877$		−	708.930i		−	0.808358i	0.914680	−	0.404179i	$-0.132443\pi$
$878$	131.706			0.150006
$879$	−634.811			−0.722197
$880$		0			0
$881$	−188.482			−0.213941			−0.106970	−	0.994262i	$-0.534115\pi$
$881$	−188.482			−0.213941			−0.106970	+	0.994262i	$0.534115\pi$
$882$			353.589i			0.400894i
$883$	−227.812			−0.257998			−0.128999	−	0.991645i	$-0.541176\pi$
$883$	−227.812			−0.257998			−0.128999	+	0.991645i	$0.541176\pi$
$884$			260.976i			0.295222i
$885$		0			0
$886$		−	1125.89i		−	1.27075i
$887$			799.124i			0.900928i	0.892794	+	0.450464i	$0.148742\pi$
$887$			799.124i			0.900928i	−0.892794	+	0.450464i	$0.851258\pi$
$888$		−	365.897i		−	0.412047i
$889$		−	15.7029i		−	0.0176636i
$890$		0			0
$891$	−3.03141			−0.00340226
$892$			672.740i			0.754193i
$893$	166.279	−	75.4558i	0.186203	−	0.0844969i
$894$	−361.879			−0.404786
$895$		0			0
$896$			19.0805i			0.0212952i
$897$	−453.961			−0.506088
$898$	−263.198			−0.293093
$899$	5.52381			0.00614439
$900$		0			0
$901$		−	1344.55i		−	1.49228i
$902$	−5.68389			−0.00630143
$903$			207.707i			0.230019i
$904$	251.199			0.277875
$905$		0			0
$906$			451.791i			0.498666i
$907$			182.629i			0.201355i	0.994919	+	0.100677i	$0.0321010\pi$
$907$			182.629i			0.201355i	−0.994919	+	0.100677i	$0.967899\pi$
$908$		−	577.067i		−	0.635536i
$909$	81.7849			0.0899724
$910$		0			0
$911$		−	1124.39i		−	1.23423i	−0.786872	−	0.617116i	$-0.788301\pi$
$911$		−	1124.39i		−	1.23423i	0.786872	−	0.617116i	$-0.211699\pi$
$912$	59.4474	+	131.002i	0.0651835	+	0.143642i
$913$	−5.82800			−0.00638335
$914$		−	815.982i		−	0.892759i
$915$		0			0
$916$	−824.979			−0.900632
$917$	249.108			0.271656
$918$	836.135			0.910823
$919$	985.231			1.07207			0.536034	−	0.844196i	$-0.319922\pi$
$919$	985.231			1.07207			0.536034	+	0.844196i	$0.319922\pi$
$920$		0			0
$921$	−589.812			−0.640404
$922$		−	316.593i		−	0.343377i
$923$	−249.411			−0.270218
$924$			6.66632i			0.00721463i
$925$		0			0
$926$			640.043i			0.691191i
$927$			776.536i			0.837687i
$928$	1.57489			0.00169708
$929$	842.513			0.906903			0.453452	−	0.891281i	$-0.350193\pi$
$929$	842.513			0.906903			0.453452	+	0.891281i	$0.350193\pi$
$930$		0			0
$931$	798.581	−	362.388i	0.857767	−	0.389246i
$932$	67.4986			0.0724234
$933$		−	545.393i		−	0.584559i
$934$		−	98.9251i		−	0.105916i
$935$		0			0
$936$	−92.2808			−0.0985906
$937$	612.166			0.653326			0.326663	−	0.945141i	$-0.394076\pi$
$937$	612.166			0.653326			0.326663	+	0.945141i	$0.394076\pi$
$938$	−148.444			−0.158255
$939$		−	261.024i		−	0.277981i
$940$		0			0
$941$		−	760.768i		−	0.808467i	−0.914656	−	0.404234i	$-0.867538\pi$
$941$		−	760.768i		−	0.808467i	0.914656	−	0.404234i	$-0.132462\pi$
$942$	−12.2720			−0.0130276
$943$			153.275i			0.162539i
$944$			376.323i			0.398647i
$945$		0			0
$946$			96.0736i			0.101558i
$947$	−23.9008			−0.0252384			−0.0126192	−	0.999920i	$-0.504017\pi$
$947$	−23.9008			−0.0252384			−0.0126192	+	0.999920i	$0.504017\pi$
$948$	−318.527			−0.335999
$949$			19.5887i			0.0206414i
$950$		0			0
$951$	546.701			0.574870
$952$		−	103.346i		−	0.108557i
$953$		−	52.0625i		−	0.0546301i	−0.999627	−	0.0273150i	$-0.991304\pi$
$953$		−	52.0625i		−	0.0546301i	0.999627	−	0.0273150i	$-0.00869573\pi$
$954$	475.429			0.498354
$955$		0			0
$956$	395.482			0.413684
$957$	0.550231			0.000574955
$958$			194.454i			0.202979i
$959$	248.050			0.258655
$960$		0			0
$961$	567.333			0.590357
$962$		−	582.122i		−	0.605116i
$963$		−	642.767i		−	0.667463i
$964$			697.558i			0.723608i
$965$		0			0
$966$	179.767			0.186094
$967$	−987.119			−1.02081			−0.510403	−	0.859935i	$-0.670504\pi$
$967$	−987.119			−1.02081			−0.510403	+	0.859935i	$0.670504\pi$
$968$		−	339.156i		−	0.350368i
$969$	−321.985	−	709.545i	−0.332286	−	0.732245i
$970$		0			0
$971$			1204.48i			1.24045i	0.784422	+	0.620227i	$0.212960\pi$
$971$			1204.48i			1.24045i	−0.784422	+	0.620227i	$0.787040\pi$
$972$			480.223i			0.494057i
$973$	−132.327			−0.135999
$974$	−465.544			−0.477972
$975$		0			0
$976$	−77.6280			−0.0795369
$977$			556.615i			0.569719i	0.958569	+	0.284859i	$0.0919469\pi$
$977$			556.615i			0.569719i	−0.958569	+	0.284859i	$0.908053\pi$
$978$	502.313			0.513613
$979$		−	88.0611i		−	0.0899501i
$980$		0			0
$981$			337.123i			0.343652i
$982$			619.786i			0.631146i
$983$		−	462.624i		−	0.470625i	−0.971920	−	0.235312i	$-0.924389\pi$
$983$		−	462.624i		−	0.470625i	0.971920	−	0.235312i	$-0.0756113\pi$
$984$		−	20.6088i		−	0.0209439i
$985$		0			0
$986$	−8.53006			−0.00865118
$987$			30.6798i			0.0310839i
$988$	94.5774	+	208.416i	0.0957261	+	0.210948i
$989$	2590.77			2.61958
$990$		0			0
$991$		−	1691.69i		−	1.70706i	−0.521046	−	0.853528i	$-0.674458\pi$
$991$		−	1691.69i		−	1.70706i	0.521046	−	0.853528i	$-0.325542\pi$
$992$	−112.238			−0.113143
$993$	−217.448			−0.218981
$994$	98.7659			0.0993620
$995$		0			0
$996$		−	21.1313i		−	0.0212162i
$997$	−742.809			−0.745044			−0.372522	−	0.928023i	$-0.621507\pi$
$997$	−742.809			−0.745044			−0.372522	+	0.928023i	$0.621507\pi$
$998$			983.857i			0.985828i
$999$	−1865.04			−1.86691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.3.c.b.151.3	✓	12
5.2	odd	4		950.3.d.b.949.18		24
5.3	odd	4		950.3.d.b.949.7		24
5.4	even	2		950.3.c.c.151.10	yes	12
19.18	odd	2	inner	950.3.c.b.151.10	yes	12
95.18	even	4		950.3.d.b.949.19		24
95.37	even	4		950.3.d.b.949.6		24
95.94	odd	2		950.3.c.c.151.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.3.c.b.151.3	✓	12	1.1	even	1	trivial
950.3.c.b.151.10	yes	12	19.18	odd	2	inner
950.3.c.c.151.3	yes	12	95.94	odd	2
950.3.c.c.151.10	yes	12	5.4	even	2
950.3.d.b.949.6		24	95.37	even	4
950.3.d.b.949.7		24	5.3	odd	4
950.3.d.b.949.18		24	5.2	odd	4
950.3.d.b.949.19		24	95.18	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	950.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -1.89288i q^{3} -2.00000 q^{4} -2.67694 q^{6} +1.68650 q^{7} +2.82843i q^{8} +5.41699 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -1.89288i q^{3} -2.00000 q^{4} -2.67694 q^{6} +1.68650 q^{7} +2.82843i q^{8} +5.41699 q^{9} +1.04411 q^{11} +3.78577i q^{12} +6.02294i q^{13} -2.38506i q^{14} +4.00000 q^{16} -21.6652 q^{17} -7.66078i q^{18} +(-17.3019 + 7.85143i) q^{19} -3.19234i q^{21} -1.47660i q^{22} -39.8186 q^{23} +5.35389 q^{24} +8.51772 q^{26} -27.2897i q^{27} -3.37299 q^{28} +0.278403i q^{29} -19.8410i q^{31} -5.65685i q^{32} -1.97638i q^{33} +30.6392i q^{34} -10.8340 q^{36} -68.3424i q^{37} +(11.1036 + 24.4686i) q^{38} +11.4007 q^{39} -3.84932i q^{41} -4.51465 q^{42} -65.0642 q^{43} -2.08822 q^{44} +56.3120i q^{46} -9.61045 q^{47} -7.57154i q^{48} -46.1557 q^{49} +41.0097i q^{51} -12.0459i q^{52} +62.0602i q^{53} -38.5935 q^{54} +4.77013i q^{56} +(14.8618 + 32.7505i) q^{57} +0.393722 q^{58} +94.0807i q^{59} -19.4070 q^{61} -28.0595 q^{62} +9.13572 q^{63} -8.00000 q^{64} -2.79503 q^{66} -62.2388i q^{67} +43.3304 q^{68} +75.3720i q^{69} +41.4101i q^{71} +15.3216i q^{72} +3.25235 q^{73} -96.6507 q^{74} +(34.6038 - 15.7029i) q^{76} +1.76089 q^{77} -16.1231i q^{78} +84.1379i q^{79} -2.90334 q^{81} -5.44376 q^{82} -5.58177 q^{83} +6.38468i q^{84} +92.0147i q^{86} +0.526985 q^{87} +2.95319i q^{88} -84.3407i q^{89} +10.1577i q^{91} +79.6372 q^{92} -37.5568 q^{93} +13.5912i q^{94} -10.7078 q^{96} +1.89498i q^{97} +65.2741i q^{98} +5.65594 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{4} - 8 q^{6} - 24 q^{7} - 28 q^{9}+O(q^{10}) \) 12 * q - 24 * q^4 - 8 * q^6 - 24 * q^7 - 28 * q^9	\( 12 q - 24 q^{4} - 8 q^{6} - 24 q^{7} - 28 q^{9} + 4 q^{11} + 48 q^{16} - 12 q^{19} + 32 q^{23} + 16 q^{24} - 16 q^{26} + 48 q^{28} + 56 q^{36} - 8 q^{38} + 100 q^{39} + 72 q^{42} + 188 q^{43} - 8 q^{44} + 180 q^{47} - 108 q^{49} + 112 q^{54} - 92 q^{57} - 120 q^{58} - 76 q^{61} + 64 q^{62} + 84 q^{63} - 96 q^{64} + 8 q^{66} + 124 q^{73} + 72 q^{74} + 24 q^{76} - 184 q^{77} - 132 q^{81} - 96 q^{82} - 500 q^{83} - 432 q^{87} - 64 q^{92} - 452 q^{93} - 32 q^{96} + 128 q^{99}+O(q^{100}) \) 12 * q - 24 * q^4 - 8 * q^6 - 24 * q^7 - 28 * q^9 + 4 * q^11 + 48 * q^16 - 12 * q^19 + 32 * q^23 + 16 * q^24 - 16 * q^26 + 48 * q^28 + 56 * q^36 - 8 * q^38 + 100 * q^39 + 72 * q^42 + 188 * q^43 - 8 * q^44 + 180 * q^47 - 108 * q^49 + 112 * q^54 - 92 * q^57 - 120 * q^58 - 76 * q^61 + 64 * q^62 + 84 * q^63 - 96 * q^64 + 8 * q^66 + 124 * q^73 + 72 * q^74 + 24 * q^76 - 184 * q^77 - 132 * q^81 - 96 * q^82 - 500 * q^83 - 432 * q^87 - 64 * q^92 - 452 * q^93 - 32 * q^96 + 128 * q^99

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