LMFDB - Embedded newform 725.2.c.e.376.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(376,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("725.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.16516096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 13x^{2} + 1 $ x^6 + 9x^4 + 13x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			376.6
Root			$2.68667i$ of defining polynomial
Character	$\chi$	$=$	725.376
Dual form			725.2.c.e.376.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68667i q^{2} +2.31446i q^{3} -5.21819 q^{4} -6.21819 q^{6} -4.21819 q^{7} -8.64620i q^{8} -2.35673 q^{9} +O(q^{10})$	\(q+2.68667i q^{2} +2.31446i q^{3} -5.21819 q^{4} -6.21819 q^{6} -4.21819 q^{7} -8.64620i q^{8} -2.35673 q^{9} +2.31446i q^{11} -12.0773i q^{12} +0.643274 q^{13} -11.3329i q^{14} +12.7931 q^{16} +0.586195i q^{17} -6.33174i q^{18} +5.95953i q^{19} -9.76282i q^{21} -6.21819 q^{22} +5.57491 q^{23} +20.0113 q^{24} +1.72826i q^{26} +1.48883i q^{27} +22.0113 q^{28} +(-5.21819 - 1.33061i) q^{29} +0.158221i q^{31} +17.0784i q^{32} -5.35673 q^{33} -1.57491 q^{34} +12.2978 q^{36} -4.04272i q^{37} -16.0113 q^{38} +1.48883i q^{39} -9.76282i q^{41} +26.2295 q^{42} -4.97568i q^{43} -12.0773i q^{44} +14.9779i q^{46} -2.31446i q^{47} +29.6091i q^{48} +10.7931 q^{49} -1.35673 q^{51} -3.35673 q^{52} -13.0796 q^{53} -4.00000 q^{54} +36.4713i q^{56} -13.7931 q^{57} +(3.57491 - 14.0195i) q^{58} -2.64327 q^{59} -0.983848i q^{61} -0.425088 q^{62} +9.94111 q^{63} -20.2978 q^{64} -14.3917i q^{66} -1.57491 q^{67} -3.05888i q^{68} +12.9029i q^{69} -9.35673 q^{71} +20.3767i q^{72} +9.17663i q^{73} +10.8615 q^{74} -31.0980i q^{76} -9.76282i q^{77} -4.00000 q^{78} +4.97568i q^{79} -10.5160 q^{81} +26.2295 q^{82} +8.21819 q^{83} +50.9442i q^{84} +13.3680 q^{86} +(3.07965 - 12.0773i) q^{87} +20.0113 q^{88} +7.29014i q^{89} -2.71345 q^{91} -29.0909 q^{92} -0.366196 q^{93} +6.21819 q^{94} -39.5273 q^{96} -3.05888i q^{97} +28.9975i q^{98} -5.45455i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 12 q^{6} - 14 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 12 * q^6 - 14 * q^9	$ 6 q - 6 q^{4} - 12 q^{6} - 14 q^{9} + 4 q^{13} + 26 q^{16} - 12 q^{22} + 8 q^{23} + 44 q^{24} + 56 q^{28} - 6 q^{29} - 32 q^{33} + 16 q^{34} - 2 q^{36} - 20 q^{38} + 56 q^{42} + 14 q^{49} - 8 q^{51} - 20 q^{52} - 28 q^{53} - 24 q^{54} - 32 q^{57} - 4 q^{58} - 16 q^{59} - 28 q^{62} - 16 q^{63} - 46 q^{64} + 16 q^{67} - 56 q^{71} + 40 q^{74} - 24 q^{78} + 38 q^{81} + 56 q^{82} + 24 q^{83} + 4 q^{86} - 32 q^{87} + 44 q^{88} - 16 q^{91} - 48 q^{92} + 48 q^{93} + 12 q^{94} - 60 q^{96}+O(q^{100}) $ 6 * q - 6 * q^4 - 12 * q^6 - 14 * q^9 + 4 * q^13 + 26 * q^16 - 12 * q^22 + 8 * q^23 + 44 * q^24 + 56 * q^28 - 6 * q^29 - 32 * q^33 + 16 * q^34 - 2 * q^36 - 20 * q^38 + 56 * q^42 + 14 * q^49 - 8 * q^51 - 20 * q^52 - 28 * q^53 - 24 * q^54 - 32 * q^57 - 4 * q^58 - 16 * q^59 - 28 * q^62 - 16 * q^63 - 46 * q^64 + 16 * q^67 - 56 * q^71 + 40 * q^74 - 24 * q^78 + 38 * q^81 + 56 * q^82 + 24 * q^83 + 4 * q^86 - 32 * q^87 + 44 * q^88 - 16 * q^91 - 48 * q^92 + 48 * q^93 + 12 * q^94 - 60 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.68667i			1.89976i	0.312613	+	0.949881i	$0.398796\pi$
$2$			2.68667i			1.89976i	−0.312613	+	0.949881i	$0.601204\pi$
$3$			2.31446i			1.33625i	0.744047	+	0.668127i	$0.232904\pi$
$3$			2.31446i			1.33625i	−0.744047	+	0.668127i	$0.767096\pi$
$4$	−5.21819			−2.60909
$5$		0			0
$5$		0			0
$6$	−6.21819			−2.53856
$7$	−4.21819			−1.59432			−0.797162	−	0.603765i	$-0.793667\pi$
$7$	−4.21819			−1.59432			−0.797162	+	0.603765i	$0.793667\pi$
$8$		−	8.64620i		−	3.05689i
$9$	−2.35673			−0.785575
$10$		0			0
$11$			2.31446i			0.697836i	0.937153	+	0.348918i	$0.113451\pi$
$11$			2.31446i			0.697836i	−0.937153	+	0.348918i	$0.886549\pi$
$12$		−	12.0773i		−	3.48641i
$13$	0.643274			0.178412			0.0892061	−	0.996013i	$-0.471567\pi$
$13$	0.643274			0.178412			0.0892061	+	0.996013i	$0.471567\pi$
$14$		−	11.3329i		−	3.02884i
$15$		0			0
$16$	12.7931			3.19827
$17$			0.586195i			0.142173i	0.997470	+	0.0710866i	$0.0226467\pi$
$17$			0.586195i			0.142173i	−0.997470	+	0.0710866i	$0.977353\pi$
$18$		−	6.33174i		−	1.49241i
$19$			5.95953i			1.36721i	0.729852	+	0.683605i	$0.239589\pi$
$19$			5.95953i			1.36721i	−0.729852	+	0.683605i	$0.760411\pi$
$20$		0			0
$21$		−	9.76282i		−	2.13042i
$22$	−6.21819			−1.32572
$23$	5.57491			1.16245			0.581225	−	0.813743i	$-0.302574\pi$
$23$	5.57491			1.16245			0.581225	+	0.813743i	$0.302574\pi$
$24$	20.0113			4.08479
$25$		0			0
$26$			1.72826i			0.338941i
$27$			1.48883i			0.286526i
$28$	22.0113			4.15974
$29$	−5.21819	−	1.33061i	−0.968993	−	0.247088i
$29$	−5.21819	−	1.33061i	−0.968993	−	0.247088i
$30$		0			0
$31$			0.158221i			0.0284174i	0.999899	+	0.0142087i	$0.00452291\pi$
$31$			0.158221i			0.0284174i	−0.999899	+	0.0142087i	$0.995477\pi$
$32$			17.0784i			3.01907i
$33$	−5.35673			−0.932486
$34$	−1.57491			−0.270095
$35$		0			0
$36$	12.2978			2.04964
$37$		−	4.04272i		−	0.664620i	−0.943170	−	0.332310i	$-0.892172\pi$
$37$		−	4.04272i		−	0.664620i	0.943170	−	0.332310i	$-0.107828\pi$
$38$	−16.0113			−2.59737
$39$			1.48883i			0.238404i
$40$		0			0
$41$		−	9.76282i		−	1.52470i	−0.647167	−	0.762349i	$-0.724046\pi$
$41$		−	9.76282i		−	1.52470i	0.647167	−	0.762349i	$-0.275954\pi$
$42$	26.2295			4.04730
$43$		−	4.97568i		−	0.758785i	−0.925236	−	0.379392i	$-0.876133\pi$
$43$		−	4.97568i		−	0.758785i	0.925236	−	0.379392i	$-0.123867\pi$
$44$		−	12.0773i		−	1.82072i
$45$		0			0
$46$			14.9779i			2.20838i
$47$		−	2.31446i		−	0.337599i	−0.985650	−	0.168799i	$-0.946011\pi$
$47$		−	2.31446i		−	0.337599i	0.985650	−	0.168799i	$-0.0539890\pi$
$48$			29.6091i			4.27371i
$49$	10.7931			1.54187
$50$		0			0
$51$	−1.35673			−0.189980
$52$	−3.35673			−0.465494
$53$	−13.0796			−1.79663			−0.898314	−	0.439354i	$-0.855207\pi$
$53$	−13.0796			−1.79663			−0.898314	+	0.439354i	$0.855207\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$			36.4713i			4.87368i
$57$	−13.7931			−1.82694
$58$	3.57491	−	14.0195i	0.469409	−	1.84086i
$59$	−2.64327			−0.344125			−0.172063	−	0.985086i	$-0.555043\pi$
$59$	−2.64327			−0.344125			−0.172063	+	0.985086i	$0.555043\pi$
$60$		0			0
$61$		−	0.983848i		−	0.125969i	−0.998015	−	0.0629844i	$-0.979938\pi$
$61$		−	0.983848i		−	0.125969i	0.998015	−	0.0629844i	$-0.0200618\pi$
$62$	−0.425088			−0.0539862
$63$	9.94111			1.25246
$64$	−20.2978			−2.53723
$65$		0			0
$66$		−	14.3917i		−	1.77150i
$67$	−1.57491			−0.192406			−0.0962031	−	0.995362i	$-0.530670\pi$
$67$	−1.57491			−0.192406			−0.0962031	+	0.995362i	$0.530670\pi$
$68$		−	3.05888i		−	0.370943i
$69$			12.9029i			1.55333i
$70$		0			0
$71$	−9.35673			−1.11044			−0.555220	−	0.831704i	$-0.687366\pi$
$71$	−9.35673			−1.11044			−0.555220	+	0.831704i	$0.687366\pi$
$72$			20.3767i			2.40142i
$73$			9.17663i			1.07404i	0.843568	+	0.537022i	$0.180451\pi$
$73$			9.17663i			1.07404i	−0.843568	+	0.537022i	$0.819549\pi$
$74$	10.8615			1.26262
$75$		0			0
$76$		−	31.0980i		−	3.56718i
$77$		−	9.76282i		−	1.11258i
$78$	−4.00000			−0.452911
$79$			4.97568i			0.559808i	0.960028	+	0.279904i	$0.0903027\pi$
$79$			4.97568i			0.559808i	−0.960028	+	0.279904i	$0.909697\pi$
$80$		0			0
$81$	−10.5160			−1.16845
$82$	26.2295			2.89656
$83$	8.21819			0.902063			0.451032	−	0.892508i	$-0.351056\pi$
$83$	8.21819			0.902063			0.451032	+	0.892508i	$0.351056\pi$
$84$			50.9442i			5.55847i
$85$		0			0
$86$	13.3680			1.44151
$87$	3.07965	−	12.0773i	0.330173	−	1.29482i
$88$	20.0113			2.13321
$89$			7.29014i			0.772754i	0.922341	+	0.386377i	$0.126274\pi$
$89$			7.29014i			0.772754i	−0.922341	+	0.386377i	$0.873726\pi$
$90$		0			0
$91$	−2.71345			−0.284447
$92$	−29.0909			−3.03294
$93$	−0.366196			−0.0379728
$94$	6.21819			0.641357
$95$		0			0
$96$	−39.5273			−4.03424
$97$		−	3.05888i		−	0.310582i	−0.987869	−	0.155291i	$-0.950369\pi$
$97$		−	3.05888i		−	0.310582i	0.987869	−	0.155291i	$-0.0496315\pi$
$98$			28.9975i			2.92919i
$99$		−	5.45455i		−	0.548203i
$100$		0			0
$101$			1.48883i			0.148144i	0.997253	+	0.0740722i	$0.0235995\pi$
$101$			1.48883i			0.148144i	−0.997253	+	0.0740722i	$0.976400\pi$
$102$		−	3.64507i		−	0.360916i
$103$	−11.2978			−1.11321			−0.556604	−	0.830778i	$-0.687896\pi$
$103$	−11.2978			−1.11321			−0.556604	+	0.830778i	$0.687896\pi$
$104$		−	5.56188i		−	0.545387i
$105$		0			0
$106$		−	35.1407i		−	3.41316i
$107$	2.93164			0.283412			0.141706	−	0.989909i	$-0.454741\pi$
$107$	2.93164			0.283412			0.141706	+	0.989909i	$0.454741\pi$
$108$		−	7.76901i		−	0.747573i
$109$	−17.0796			−1.63593			−0.817967	−	0.575265i	$-0.804899\pi$
$109$	−17.0796			−1.63593			−0.817967	+	0.575265i	$0.804899\pi$
$110$		0			0
$111$	9.35673			0.888101
$112$	−53.9637			−5.09909
$113$			13.4891i			1.26895i	0.772944	+	0.634474i	$0.218783\pi$
$113$			13.4891i			1.26895i	−0.772944	+	0.634474i	$0.781217\pi$
$114$		−	37.0575i		−	3.47075i
$115$		0			0
$116$	27.2295	+	6.94338i	2.52819	+	0.644677i
$117$	−1.51602			−0.140156
$118$		−	7.10160i		−	0.653755i
$119$		−	2.47268i		−	0.226670i
$120$		0			0
$121$	5.64327			0.513025
$122$	2.64327			0.239311
$123$	22.5957			2.03738
$124$		−	0.825627i		−	0.0741435i
$125$		0			0
$126$			26.7085i			2.37938i
$127$			11.0934i			0.984383i	0.870487	+	0.492192i	$0.163804\pi$
$127$			11.0934i			0.984383i	−0.870487	+	0.492192i	$0.836196\pi$
$128$		−	20.3767i		−	1.80106i
$129$	11.5160			1.01393
$130$		0			0
$131$			7.13192i			0.623119i	0.950227	+	0.311559i	$0.100851\pi$
$131$			7.13192i			0.623119i	−0.950227	+	0.311559i	$0.899149\pi$
$132$	27.9524			2.43294
$133$		−	25.1384i		−	2.17978i
$134$		−	4.23127i		−	0.365526i
$135$		0			0
$136$	5.06836			0.434608
$137$			14.7894i			1.26354i	0.775154	+	0.631772i	$0.217672\pi$
$137$			14.7894i			1.26354i	−0.775154	+	0.631772i	$0.782328\pi$
$138$	−34.6658			−2.95095
$139$	3.56363			0.302263			0.151131	−	0.988514i	$-0.451708\pi$
$139$	3.56363			0.302263			0.151131	+	0.988514i	$0.451708\pi$
$140$		0			0
$141$	5.35673			0.451118
$142$		−	25.1384i		−	2.10957i
$143$			1.48883i			0.124502i
$144$	−30.1498			−2.51249
$145$		0			0
$146$	−24.6546			−2.04043
$147$			24.9802i			2.06033i
$148$			21.0957i			1.73406i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	4.50655			0.366738			0.183369	−	0.983044i	$-0.441300\pi$
$151$	4.50655			0.366738			0.183369	+	0.983044i	$0.441300\pi$
$152$	51.5273			4.17942
$153$		−	1.38150i		−	0.111688i
$154$	26.2295			2.11363
$155$		0			0
$156$		−	7.76901i		−	0.622018i
$157$		−	16.9456i		−	1.35241i	−0.736714	−	0.676205i	$-0.763624\pi$
$157$		−	16.9456i		−	1.35241i	0.736714	−	0.676205i	$-0.236376\pi$
$158$	−13.3680			−1.06350
$159$		−	30.2723i		−	2.40075i
$160$		0			0
$161$	−23.5160			−1.85332
$162$		−	28.2531i		−	2.21977i
$163$		−	11.0934i		−	0.868905i	−0.900695	−	0.434453i	$-0.856942\pi$
$163$		−	11.0934i		−	0.868905i	0.900695	−	0.434453i	$-0.143058\pi$
$164$			50.9442i			3.97808i
$165$		0			0
$166$			22.0795i			1.71370i
$167$	5.57491			0.431400			0.215700	−	0.976460i	$-0.430797\pi$
$167$	5.57491			0.431400			0.215700	+	0.976460i	$0.430797\pi$
$168$	−84.4113			−6.51248
$169$	−12.5862			−0.968169
$170$		0			0
$171$		−	14.0450i		−	1.07405i
$172$			25.9640i			1.97974i
$173$	−7.79310			−0.592498			−0.296249	−	0.955111i	$-0.595736\pi$
$173$	−7.79310			−0.592498			−0.296249	+	0.955111i	$0.595736\pi$
$174$	32.4477	+	8.27399i	2.45985	+	0.627250i
$175$		0			0
$176$			29.6091i			2.23187i
$177$		−	6.11775i		−	0.459838i
$178$	−19.5862			−1.46805
$179$	−4.43637			−0.331590			−0.165795	−	0.986160i	$-0.553019\pi$
$179$	−4.43637			−0.331590			−0.165795	+	0.986160i	$0.553019\pi$
$180$		0			0
$181$	13.5160			1.00464			0.502319	−	0.864682i	$-0.332480\pi$
$181$	13.5160			1.00464			0.502319	+	0.864682i	$0.332480\pi$
$182$		−	7.29014i		−	0.540381i
$183$	2.27708			0.168326
$184$		−	48.2018i		−	3.55348i
$185$		0			0
$186$		−	0.983848i		−	0.0721393i
$187$	−1.35673			−0.0992136
$188$			12.0773i			0.880827i
$189$		−	6.28017i		−	0.456816i
$190$		0			0
$191$		−	11.5723i		−	0.837342i	−0.908138	−	0.418671i	$-0.862496\pi$
$191$		−	11.5723i		−	0.837342i	0.908138	−	0.418671i	$-0.137504\pi$
$192$		−	46.9785i		−	3.39038i
$193$			9.84404i			0.708589i	0.935134	+	0.354295i	$0.115279\pi$
$193$			9.84404i			0.708589i	−0.935134	+	0.354295i	$0.884721\pi$
$194$	8.21819			0.590031
$195$		0			0
$196$	−56.3204			−4.02289
$197$	5.14982			0.366910			0.183455	−	0.983028i	$-0.441272\pi$
$197$	5.14982			0.366910			0.183455	+	0.983028i	$0.441272\pi$
$198$	14.6546			1.04145
$199$	−17.7931			−1.26132			−0.630660	−	0.776060i	$-0.717216\pi$
$199$	−17.7931			−1.26132			−0.630660	+	0.776060i	$0.717216\pi$
$200$		0			0
$201$		−	3.64507i		−	0.257104i
$202$	−4.00000			−0.281439
$203$	22.0113	+	5.61277i	1.54489	+	0.393939i
$204$	7.07965			0.495674
$205$		0			0
$206$		−	30.3535i		−	2.11483i
$207$	−13.1385			−0.913192
$208$	8.22947			0.570611
$209$	−13.7931			−0.954089
$210$		0			0
$211$			18.8624i			1.29854i	0.760556	+	0.649272i	$0.224926\pi$
$211$			18.8624i			1.29854i	−0.760556	+	0.649272i	$0.775074\pi$
$212$	68.2520			4.68757
$213$		−	21.6558i		−	1.48383i
$214$			7.87634i			0.538415i
$215$		0			0
$216$	12.8727			0.875879
$217$		−	0.667406i		−	0.0453065i
$218$		−	45.8873i		−	3.10788i
$219$	−21.2389			−1.43519
$220$		0			0
$221$			0.377084i			0.0253654i
$222$			25.1384i			1.68718i
$223$	−13.5749			−0.909043			−0.454522	−	0.890736i	$-0.650190\pi$
$223$	−13.5749			−0.909043			−0.454522	+	0.890736i	$0.650190\pi$
$224$		−	72.0399i		−	4.81337i
$225$		0			0
$226$	−36.2408			−2.41070
$227$	−7.00181			−0.464727			−0.232363	−	0.972629i	$-0.574646\pi$
$227$	−7.00181			−0.464727			−0.232363	+	0.972629i	$0.574646\pi$
$228$	71.9750			4.76666
$229$		−	24.1546i		−	1.59618i	−0.602539	−	0.798089i	$-0.705844\pi$
$229$		−	24.1546i		−	1.59618i	0.602539	−	0.798089i	$-0.294156\pi$
$230$		0			0
$231$	22.5957			1.48669
$232$	−11.5047	+	45.1175i	−0.755323	+	2.96211i
$233$	−5.14982			−0.337376			−0.168688	−	0.985669i	$-0.553953\pi$
$233$	−5.14982			−0.337376			−0.168688	+	0.985669i	$0.553953\pi$
$234$		−	4.07305i		−	0.266263i
$235$		0			0
$236$	13.7931			0.897854
$237$	−11.5160			−0.748046
$238$	6.64327			0.430620
$239$	14.6433			0.947195			0.473597	−	0.880741i	$-0.342955\pi$
$239$	14.6433			0.947195			0.473597	+	0.880741i	$0.342955\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$			15.1616i			0.974625i
$243$		−	19.8724i		−	1.27482i
$244$			5.13390i			0.328665i
$245$		0			0
$246$			60.7071i			3.87054i
$247$			3.83361i			0.243927i
$248$	1.36801			0.0868688
$249$			19.0207i			1.20539i
$250$		0			0
$251$			22.6354i			1.42873i	0.699771	+	0.714367i	$0.253285\pi$
$251$			22.6354i			1.42873i	−0.699771	+	0.714367i	$0.746715\pi$
$252$	−51.8746			−3.26779
$253$			12.9029i			0.811199i
$254$	−29.8044			−1.87009
$255$		0			0
$256$	14.1498			0.884364
$257$	−10.9204			−0.681193			−0.340596	−	0.940210i	$-0.610629\pi$
$257$	−10.9204			−0.681193			−0.340596	+	0.940210i	$0.610629\pi$
$258$			30.9397i			1.92622i
$259$			17.0530i			1.05962i
$260$		0			0
$261$	12.2978	+	3.13589i	0.761217	+	0.194107i
$262$	−19.1611			−1.18378
$263$			9.92105i			0.611758i	0.952070	+	0.305879i	$0.0989503\pi$
$263$			9.92105i			0.611758i	−0.952070	+	0.305879i	$0.901050\pi$
$264$			46.3153i			2.85051i
$265$		0			0
$266$	67.5386			4.14106
$267$	−16.8727			−1.03260
$268$	8.21819			0.502006
$269$			12.4240i			0.757508i	0.925497	+	0.378754i	$0.123647\pi$
$269$			12.4240i			0.757508i	−0.925497	+	0.378754i	$0.876353\pi$
$270$		0			0
$271$			27.2643i			1.65619i	0.560587	+	0.828095i	$0.310575\pi$
$271$			27.2643i			1.65619i	−0.560587	+	0.828095i	$0.689425\pi$
$272$			7.49925i			0.454709i
$273$		−	6.28017i		−	0.380093i
$274$	−39.7342			−2.40043
$275$		0			0
$276$		−	67.3298i		−	4.05278i
$277$	2.92035			0.175467			0.0877335	−	0.996144i	$-0.472038\pi$
$277$	2.92035			0.175467			0.0877335	+	0.996144i	$0.472038\pi$
$278$			9.57428i			0.574227i
$279$		−	0.372884i		−	0.0223240i
$280$		0			0
$281$	−18.3662			−1.09564			−0.547818	−	0.836598i	$-0.684541\pi$
$281$	−18.3662			−1.09564			−0.547818	+	0.836598i	$0.684541\pi$
$282$			14.3917i			0.857016i
$283$	14.8615			0.883422			0.441711	−	0.897157i	$-0.354372\pi$
$283$	14.8615			0.883422			0.441711	+	0.897157i	$0.354372\pi$
$284$	48.8251			2.89724
$285$		0			0
$286$	−4.00000			−0.236525
$287$			41.1814i			2.43086i
$288$		−	40.2491i		−	2.37170i
$289$	16.6564			0.979787
$290$		0			0
$291$	7.07965			0.415016
$292$		−	47.8854i		−	2.80228i
$293$			1.57004i			0.0917229i	0.998948	+	0.0458615i	$0.0146033\pi$
$293$			1.57004i			0.0917229i	−0.998948	+	0.0458615i	$0.985397\pi$
$294$	−67.1135			−3.91414
$295$		0			0
$296$	−34.9542			−2.03167
$297$	−3.44584			−0.199948
$298$			16.1200i			0.933807i
$299$	3.58620			0.207395
$300$		0			0
$301$			20.9884i			1.20975i
$302$			12.1076i			0.696714i
$303$	−3.44584			−0.197959
$304$			76.2409i			4.37271i
$305$		0			0
$306$	3.71164			0.212180
$307$			4.65924i			0.265917i	0.991122	+	0.132958i	$0.0424477\pi$
$307$			4.65924i			0.265917i	−0.991122	+	0.132958i	$0.957552\pi$
$308$			50.9442i			2.90282i
$309$		−	26.1484i		−	1.48753i
$310$		0			0
$311$			21.6516i			1.22775i	0.789404	+	0.613874i	$0.210390\pi$
$311$			21.6516i			1.22775i	−0.789404	+	0.613874i	$0.789610\pi$
$312$	12.8727			0.728776
$313$	−11.3567			−0.641920			−0.320960	−	0.947093i	$-0.604006\pi$
$313$	−11.3567			−0.641920			−0.320960	+	0.947093i	$0.604006\pi$
$314$	45.5273			2.56925
$315$		0			0
$316$		−	25.9640i		−	1.46059i
$317$		−	9.36517i		−	0.526000i	−0.964796	−	0.263000i	$-0.915288\pi$
$317$		−	9.36517i		−	0.526000i	0.964796	−	0.263000i	$-0.0847120\pi$
$318$	81.3317			4.56085
$319$	3.07965	−	12.0773i	0.172427	−	0.676198i
$320$		0			0
$321$			6.78516i			0.378711i
$322$		−	63.1797i		−	3.52087i
$323$	−3.49345			−0.194381
$324$	54.8746			3.04859
$325$		0			0
$326$	29.8044			1.65071
$327$		−	39.5302i		−	2.18602i
$328$	−84.4113			−4.66084
$329$			9.76282i			0.538242i
$330$		0			0
$331$		−	18.5115i		−	1.01748i	−0.860919	−	0.508741i	$-0.830111\pi$
$331$		−	18.5115i		−	1.01748i	0.860919	−	0.508741i	$-0.169889\pi$
$332$	−42.8840			−2.35357
$333$			9.52759i			0.522109i
$334$			14.9779i			0.819556i
$335$		0			0
$336$		−	124.897i		−	6.81368i
$337$			18.8116i			1.02473i	0.858768	+	0.512365i	$0.171231\pi$
$337$			18.8116i			1.02473i	−0.858768	+	0.512365i	$0.828769\pi$
$338$		−	33.8149i		−	1.83929i
$339$	−31.2200			−1.69564
$340$		0			0
$341$	−0.366196			−0.0198306
$342$	37.7342			2.04043
$343$	−16.0000			−0.863919
$344$	−43.0208			−2.31952
$345$		0			0
$346$		−	20.9375i		−	1.12561i
$347$	25.2313			1.35449			0.677243	−	0.735759i	$-0.263174\pi$
$347$	25.2313			1.35449			0.677243	+	0.735759i	$0.263174\pi$
$348$	−16.0702	+	63.0215i	−0.861452	+	3.37831i
$349$	2.85018			0.152566			0.0762832	−	0.997086i	$-0.475695\pi$
$349$	2.85018			0.152566			0.0762832	+	0.997086i	$0.475695\pi$
$350$		0			0
$351$			0.957728i			0.0511197i
$352$	−39.5273			−2.10681
$353$	30.0927			1.60168			0.800838	−	0.598881i	$-0.204388\pi$
$353$	30.0927			1.60168			0.800838	+	0.598881i	$0.204388\pi$
$354$	16.4364			0.873583
$355$		0			0
$356$		−	38.0413i		−	2.01619i
$357$	5.72292			0.302889
$358$		−	11.9191i		−	0.629942i
$359$			23.6193i			1.24658i	0.781992	+	0.623289i	$0.214204\pi$
$359$			23.6193i			1.24658i	−0.781992	+	0.623289i	$0.785796\pi$
$360$		0			0
$361$	−16.5160			−0.869264
$362$			36.3131i			1.90857i
$363$			13.0611i			0.685532i
$364$	14.1593			0.742149
$365$		0			0
$366$			6.11775i			0.319780i
$367$			17.2112i			0.898417i	0.893427	+	0.449208i	$0.148294\pi$
$367$			17.2112i			0.898417i	−0.893427	+	0.449208i	$0.851706\pi$
$368$	71.3204			3.71783
$369$			23.0083i			1.19776i
$370$		0			0
$371$	55.1724			2.86441
$372$	1.91088			0.0990746
$373$	−22.8727			−1.18431			−0.592153	−	0.805826i	$-0.701722\pi$
$373$	−22.8727			−1.18431			−0.592153	+	0.805826i	$0.701722\pi$
$374$		−	3.64507i		−	0.188482i
$375$		0			0
$376$	−20.0113			−1.03200
$377$	−3.35673	−	0.855948i	−0.172880	−	0.0440836i
$378$	16.8727			0.867840
$379$		−	27.2643i		−	1.40047i	−0.713910	−	0.700237i	$-0.753077\pi$
$379$		−	27.2643i		−	1.40047i	0.713910	−	0.700237i	$-0.246923\pi$
$380$		0			0
$381$	−25.6753			−1.31539
$382$	31.0909			1.59075
$383$	−37.2313			−1.90243			−0.951215	−	0.308529i	$-0.900163\pi$
$383$	−37.2313			−1.90243			−0.951215	+	0.308529i	$0.900163\pi$
$384$	47.1611			2.40668
$385$		0			0
$386$	−26.4477			−1.34615
$387$			11.7263i			0.596082i
$388$			15.9618i			0.810337i
$389$		−	23.6496i		−	1.19908i	−0.800344	−	0.599541i	$-0.795350\pi$
$389$		−	23.6496i		−	1.19908i	0.800344	−	0.599541i	$-0.204650\pi$
$390$		0			0
$391$			3.26799i			0.165269i
$392$		−	93.3193i		−	4.71334i
$393$	−16.5066			−0.832645
$394$			13.8359i			0.697041i
$395$		0			0
$396$			28.4628i			1.43031i
$397$	30.0226			1.50679			0.753395	−	0.657568i	$-0.228415\pi$
$397$	30.0226			1.50679			0.753395	+	0.657568i	$0.228415\pi$
$398$		−	47.8042i		−	2.39621i
$399$	58.1819			2.91274
$400$		0			0
$401$	−32.3698			−1.61647			−0.808236	−	0.588859i	$-0.799577\pi$
$401$	−32.3698			−1.61647			−0.808236	+	0.588859i	$0.799577\pi$
$402$	9.79310			0.488435
$403$			0.101780i			0.00507000i
$404$		−	7.76901i		−	0.386523i
$405$		0			0
$406$	−15.0796	+	59.1370i	−0.748390	+	2.93492i
$407$	9.35673			0.463796
$408$			11.7305i			0.580747i
$409$		−	24.5055i		−	1.21172i	−0.795571	−	0.605860i	$-0.792829\pi$
$409$		−	24.5055i		−	1.21172i	0.795571	−	0.605860i	$-0.207171\pi$
$410$		0			0
$411$	−34.2295			−1.68842
$412$	58.9542			2.90447
$413$	11.1498			0.548647
$414$		−	35.2989i		−	1.73485i
$415$		0			0
$416$			10.9861i			0.538638i
$417$			8.24787i			0.403900i
$418$		−	37.0575i		−	1.81254i
$419$	6.22947			0.304330			0.152165	−	0.988355i	$-0.451376\pi$
$419$	6.22947			0.304330			0.152165	+	0.988355i	$0.451376\pi$
$420$		0			0
$421$		−	32.9074i		−	1.60381i	−0.597452	−	0.801905i	$-0.703820\pi$
$421$		−	32.9074i		−	1.60381i	0.597452	−	0.801905i	$-0.296180\pi$
$422$	−50.6771			−2.46692
$423$			5.45455i			0.265209i
$424$			113.089i			5.49210i
$425$		0			0
$426$	58.1819			2.81892
$427$			4.15006i			0.200835i
$428$	−15.2978			−0.739449
$429$	−3.44584			−0.166367
$430$		0			0
$431$	3.00947			0.144961			0.0724806	−	0.997370i	$-0.476908\pi$
$431$	3.00947			0.144961			0.0724806	+	0.997370i	$0.476908\pi$
$432$			19.0468i			0.916389i
$433$			34.3150i			1.64908i	0.565807	+	0.824538i	$0.308565\pi$
$433$			34.3150i			1.64908i	−0.565807	+	0.824538i	$0.691435\pi$
$434$	1.79310			0.0860715
$435$		0			0
$436$	89.1248			4.26830
$437$			33.2239i			1.58931i
$438$		−	57.0620i		−	2.72653i
$439$	29.8157			1.42302			0.711512	−	0.702674i	$-0.248011\pi$
$439$	29.8157			1.42302			0.711512	+	0.702674i	$0.248011\pi$
$440$		0			0
$441$	−25.4364			−1.21126
$442$	−1.01310			−0.0481883
$443$			27.9579i			1.32832i	0.747591	+	0.664159i	$0.231210\pi$
$443$			27.9579i			1.32832i	−0.747591	+	0.664159i	$0.768790\pi$
$444$	−48.8251			−2.31714
$445$		0			0
$446$		−	36.4713i		−	1.72697i
$447$			13.8868i			0.656821i
$448$	85.6201			4.04517
$449$		−	4.27796i		−	0.201889i	−0.994892	−	0.100945i	$-0.967814\pi$
$449$		−	4.27796i		−	0.201889i	0.994892	−	0.100945i	$-0.0321865\pi$
$450$		0			0
$451$	22.5957			1.06399
$452$		−	70.3887i		−	3.31081i
$453$			10.4302i			0.490055i
$454$		−	18.8116i		−	0.882870i
$455$		0			0
$456$			119.258i			5.58476i
$457$	10.3662			0.484910			0.242455	−	0.970163i	$-0.422047\pi$
$457$	10.3662			0.484910			0.242455	+	0.970163i	$0.422047\pi$
$458$	64.8953			3.03236
$459$	−0.872747			−0.0407363
$460$		0			0
$461$			13.0915i			0.609730i	0.952396	+	0.304865i	$0.0986113\pi$
$461$			13.0915i			0.609730i	−0.952396	+	0.304865i	$0.901389\pi$
$462$			60.7071i			2.82435i
$463$	33.4571			1.55488			0.777442	−	0.628954i	$-0.216517\pi$
$463$	33.4571			1.55488			0.777442	+	0.628954i	$0.216517\pi$
$464$	−66.7568	−	17.0226i	−3.09911	−	0.790257i
$465$		0			0
$466$		−	13.8359i		−	0.640934i
$467$		−	32.5868i		−	1.50794i	−0.656911	−	0.753968i	$-0.728137\pi$
$467$		−	32.5868i		−	1.50794i	0.656911	−	0.753968i	$-0.271863\pi$
$468$	7.91088			0.365681
$469$	6.64327			0.306758
$470$		0			0
$471$	39.2200			1.80716
$472$			22.8543i			1.05195i
$473$	11.5160			0.529507
$474$		−	30.9397i		−	1.42111i
$475$		0			0
$476$			12.9029i			0.591404i
$477$	30.8251			1.41139
$478$			39.3416i			1.79944i
$479$			36.5222i			1.66874i	0.551204	+	0.834370i	$0.314169\pi$
$479$			36.5222i			1.66874i	−0.551204	+	0.834370i	$0.685831\pi$
$480$		0			0
$481$		−	2.60058i		−	0.118576i
$482$			5.37334i			0.244749i
$483$		−	54.4269i		−	2.47651i
$484$	−29.4477			−1.33853
$485$		0			0
$486$	53.3906			2.42185
$487$	−25.9411			−1.17550			−0.587752	−	0.809041i	$-0.699987\pi$
$487$	−25.9411			−1.17550			−0.587752	+	0.809041i	$0.699987\pi$
$488$	−8.50655			−0.385073
$489$	25.6753			1.16108
$490$		0			0
$491$		−	26.3411i		−	1.18876i	−0.804185	−	0.594379i	$-0.797398\pi$
$491$		−	26.3411i		−	1.18876i	0.804185	−	0.594379i	$-0.202602\pi$
$492$	−117.908			−5.31572
$493$	0.779998	−	3.05888i	0.0351294	−	0.137765i
$494$	−10.2996			−0.463403
$495$		0			0
$496$			2.02414i			0.0908865i
$497$	39.4684			1.77040
$498$	−51.1022			−2.28995
$499$	−21.0131			−0.940676			−0.470338	−	0.882486i	$-0.655868\pi$
$499$	−21.0131			−0.940676			−0.470338	+	0.882486i	$0.655868\pi$
$500$		0			0
$501$			12.9029i			0.576460i
$502$	−60.8139			−2.71426
$503$		−	14.5500i		−	0.648751i	−0.945928	−	0.324375i	$-0.894846\pi$
$503$		−	14.5500i		−	0.648751i	0.945928	−	0.324375i	$-0.105154\pi$
$504$		−	85.9528i		−	3.82864i
$505$		0			0
$506$	−34.6658			−1.54108
$507$		−	29.1303i		−	1.29372i
$508$		−	57.8876i		−	2.56835i
$509$	−12.2295			−0.542062			−0.271031	−	0.962571i	$-0.587365\pi$
$509$	−12.2295			−0.542062			−0.271031	+	0.962571i	$0.587365\pi$
$510$		0			0
$511$		−	38.7087i		−	1.71237i
$512$		−	2.73756i		−	0.120984i
$513$	−8.87275			−0.391741
$514$		−	29.3394i		−	1.29410i
$515$		0			0
$516$	−60.0927			−2.64544
$517$	5.35673			0.235589
$518$	−45.8157			−2.01302
$519$		−	18.0368i		−	0.791728i
$520$		0			0
$521$	17.5160			0.767391			0.383695	−	0.923460i	$-0.374651\pi$
$521$	17.5160			0.767391			0.383695	+	0.923460i	$0.374651\pi$
$522$	−8.42509	+	33.0402i	−0.368756	+	1.44613i
$523$	10.8840			0.475926			0.237963	−	0.971274i	$-0.423520\pi$
$523$	10.8840			0.475926			0.237963	+	0.971274i	$0.423520\pi$
$524$		−	37.2157i		−	1.62578i
$525$		0			0
$526$	−26.6546			−1.16219
$527$	−0.0927485			−0.00404019
$528$	−68.5291			−2.98235
$529$	8.07965			0.351289
$530$		0			0
$531$	6.22947			0.270336
$532$			131.177i			5.68724i
$533$		−	6.28017i		−	0.272025i
$534$		−	45.3315i		−	1.96168i
$535$		0			0
$536$			13.6170i			0.588165i
$537$		−	10.2678i		−	0.443089i
$538$	−33.3793			−1.43908
$539$			24.9802i			1.07597i
$540$		0			0
$541$			35.7572i			1.53732i	0.639657	+	0.768661i	$0.279077\pi$
$541$			35.7572i			1.53732i	−0.639657	+	0.768661i	$0.720923\pi$
$542$	−73.2502			−3.14637
$543$			31.2823i			1.34245i
$544$	−10.0113			−0.429230
$545$		0			0
$546$	16.8727			0.722087
$547$	−12.6320			−0.540105			−0.270052	−	0.962846i	$-0.587041\pi$
$547$	−12.6320			−0.540105			−0.270052	+	0.962846i	$0.587041\pi$
$548$		−	77.1738i		−	3.29670i
$549$			2.31866i			0.0989580i
$550$		0			0
$551$	7.92982	−	31.0980i	0.337822	−	1.32482i
$552$	111.561			4.74836
$553$		−	20.9884i		−	0.892516i
$554$			7.84602i			0.333345i
$555$		0			0
$556$	−18.5957			−0.788632
$557$	21.0095			0.890200			0.445100	−	0.895481i	$-0.353168\pi$
$557$	21.0095			0.890200			0.445100	+	0.895481i	$0.353168\pi$
$558$	1.00181			0.0424102
$559$		−	3.20073i		−	0.135376i
$560$		0			0
$561$		−	3.14009i		−	0.132575i
$562$		−	49.3439i		−	2.08145i
$563$			45.6782i			1.92511i	0.271090	+	0.962554i	$0.412616\pi$
$563$			45.6782i			1.92511i	−0.271090	+	0.962554i	$0.587384\pi$
$564$	−27.9524			−1.17701
$565$		0			0
$566$			39.9278i			1.67829i
$567$	44.3585			1.86288
$568$			80.9001i			3.39449i
$569$			38.5463i			1.61595i	0.589220	+	0.807973i	$0.299435\pi$
$569$			38.5463i			1.61595i	−0.589220	+	0.807973i	$0.700565\pi$
$570$		0			0
$571$	−25.7229			−1.07647			−0.538235	−	0.842795i	$-0.680909\pi$
$571$	−25.7229			−1.07647			−0.538235	+	0.842795i	$0.680909\pi$
$572$		−	7.76901i		−	0.324839i
$573$	26.7836			1.11890
$574$	−110.641			−4.61806
$575$		0			0
$576$	47.8364			1.99318
$577$		−	31.7145i		−	1.32029i	−0.751138	−	0.660145i	$-0.770495\pi$
$577$		−	31.7145i		−	1.32029i	0.751138	−	0.660145i	$-0.229505\pi$
$578$			44.7502i			1.86136i
$579$	−22.7836			−0.946855
$580$		0			0
$581$	−34.6658			−1.43818
$582$			19.0207i			0.788432i
$583$		−	30.2723i		−	1.25375i
$584$	79.3430			3.28324
$585$		0			0
$586$	−4.21819			−0.174252
$587$	−37.5975			−1.55181			−0.775907	−	0.630847i	$-0.782707\pi$
$587$	−37.5975			−1.55181			−0.775907	+	0.630847i	$0.782707\pi$
$588$		−	130.351i		−	5.37560i
$589$	−0.942924			−0.0388525
$590$		0			0
$591$			11.9191i			0.490285i
$592$		−	51.7190i		−	2.12564i
$593$	−36.2295			−1.48777			−0.743883	−	0.668310i	$-0.767018\pi$
$593$	−36.2295			−1.48777			−0.743883	+	0.668310i	$0.767018\pi$
$594$		−	9.25784i		−	0.379854i
$595$		0			0
$596$	−31.3091			−1.28247
$597$		−	41.1814i		−	1.68544i
$598$			9.63492i			0.394001i
$599$		−	3.48685i		−	0.142469i	−0.997460	−	0.0712344i	$-0.977306\pi$
$599$		−	3.48685i		−	0.142469i	0.997460	−	0.0712344i	$-0.0226938\pi$
$600$		0			0
$601$		−	4.81746i		−	0.196508i	−0.995161	−	0.0982542i	$-0.968674\pi$
$601$		−	4.81746i		−	0.196508i	0.995161	−	0.0982542i	$-0.0313258\pi$
$602$	−56.3888			−2.29823
$603$	3.71164			0.151150
$604$	−23.5160			−0.956853
$605$		0			0
$606$		−	9.25784i		−	0.376074i
$607$			7.57626i			0.307511i	0.988109	+	0.153756i	$0.0491368\pi$
$607$			7.57626i			0.307511i	−0.988109	+	0.153756i	$0.950863\pi$
$608$	−101.779			−4.12770
$609$	−12.9905	+	50.9442i	−0.526403	+	2.06436i
$610$		0			0
$611$		−	1.48883i		−	0.0602317i
$612$			7.20893i			0.291404i
$613$	−4.15930			−0.167992			−0.0839962	−	0.996466i	$-0.526768\pi$
$613$	−4.15930			−0.167992			−0.0839962	+	0.996466i	$0.526768\pi$
$614$	−12.5178			−0.505179
$615$		0			0
$616$	−84.4113			−3.40103
$617$			25.7246i			1.03563i	0.855491	+	0.517817i	$0.173255\pi$
$617$			25.7246i			1.03563i	−0.855491	+	0.517817i	$0.826745\pi$
$618$	70.2520			2.82595
$619$		−	31.1997i		−	1.25402i	−0.779010	−	0.627012i	$-0.784278\pi$
$619$		−	31.1997i		−	1.25402i	0.779010	−	0.627012i	$-0.215722\pi$
$620$		0			0
$621$			8.30011i			0.333072i
$622$	−58.1706			−2.33243
$623$		−	30.7512i		−	1.23202i
$624$			19.0468i			0.762482i
$625$		0			0
$626$		−	30.5118i		−	1.21949i
$627$		−	31.9236i		−	1.27490i
$628$			88.4255i			3.52856i
$629$	2.36983			0.0944912
$630$		0			0
$631$	22.1593			0.882148			0.441074	−	0.897471i	$-0.354598\pi$
$631$	22.1593			0.882148			0.441074	+	0.897471i	$0.354598\pi$
$632$	43.0208			1.71127
$633$	−43.6564			−1.73519
$634$	25.1611			0.999275
$635$		0			0
$636$			157.967i			6.26378i
$637$	6.94292			0.275089
$638$	32.4477	+	8.27399i	1.28462	+	0.327570i
$639$	22.0512			0.872333
$640$		0			0
$641$			22.3754i			0.883776i	0.897070	+	0.441888i	$0.145691\pi$
$641$			22.3754i			0.883776i	−0.897070	+	0.441888i	$0.854309\pi$
$642$	−18.2295			−0.719460
$643$	20.1480			0.794560			0.397280	−	0.917697i	$-0.369954\pi$
$643$	20.1480			0.794560			0.397280	+	0.917697i	$0.369954\pi$
$644$	122.711			4.83549
$645$		0			0
$646$		−	9.38574i		−	0.369277i
$647$	−34.9542			−1.37419			−0.687096	−	0.726567i	$-0.741115\pi$
$647$	−34.9542			−1.37419			−0.687096	+	0.726567i	$0.741115\pi$
$648$			90.9236i			3.57182i
$649$		−	6.11775i		−	0.240143i
$650$		0			0
$651$	1.54468			0.0605410
$652$			57.8876i			2.26705i
$653$			17.3227i			0.677890i	0.940806	+	0.338945i	$0.110070\pi$
$653$			17.3227i			0.677890i	−0.940806	+	0.338945i	$0.889930\pi$
$654$	106.204			4.15292
$655$		0			0
$656$		−	124.897i		−	4.87640i
$657$		−	21.6268i		−	0.843742i
$658$	−26.2295			−1.02253
$659$			17.1851i			0.669435i	0.942318	+	0.334718i	$0.108641\pi$
$659$			17.1851i			0.669435i	−0.942318	+	0.334718i	$0.891359\pi$
$660$		0			0
$661$	24.0891			0.936958			0.468479	−	0.883475i	$-0.344802\pi$
$661$	24.0891			0.936958			0.468479	+	0.883475i	$0.344802\pi$
$662$	49.7342			1.93297
$663$	−0.872747			−0.0338947
$664$		−	71.0561i		−	2.75751i
$665$		0			0
$666$	−25.5975			−0.991882
$667$	−29.0909	−	7.41804i	−1.12641	−	0.287228i
$668$	−29.0909			−1.12556
$669$		−	31.4186i		−	1.21471i
$670$		0			0
$671$	2.27708			0.0879056
$672$	166.734			6.43189
$673$	31.4495			1.21229			0.606144	−	0.795355i	$-0.292715\pi$
$673$	31.4495			1.21229			0.606144	+	0.795355i	$0.292715\pi$
$674$	−50.5404			−1.94674
$675$		0			0
$676$	65.6771			2.52604
$677$		−	29.0187i		−	1.11528i	−0.830083	−	0.557640i	$-0.811707\pi$
$677$		−	29.0187i		−	1.11528i	0.830083	−	0.557640i	$-0.188293\pi$
$678$		−	83.8778i		−	3.22131i
$679$			12.9029i			0.495168i
$680$		0			0
$681$		−	16.2054i		−	0.620993i
$682$		−	0.983848i		−	0.0376735i
$683$	−12.2884			−0.470201			−0.235101	−	0.971971i	$-0.575542\pi$
$683$	−12.2884			−0.470201			−0.235101	+	0.971971i	$0.575542\pi$
$684$			73.2893i			2.80229i
$685$		0			0
$686$		−	42.9867i		−	1.64124i
$687$	55.9048			2.13290
$688$		−	63.6544i		−	2.42680i
$689$	−8.41380			−0.320540
$690$		0			0
$691$	−41.6753			−1.58540			−0.792702	−	0.609609i	$-0.791326\pi$
$691$	−41.6753			−1.58540			−0.792702	+	0.609609i	$0.791326\pi$
$692$	40.6658			1.54588
$693$			23.0083i			0.874013i
$694$			67.7881i			2.57320i
$695$		0			0
$696$	−104.423	−	26.6273i	−3.95813	−	1.00930i
$697$	5.72292			0.216771
$698$			7.65748i			0.289840i
$699$		−	11.9191i		−	0.450820i
$700$		0			0
$701$	27.8157			1.05058			0.525292	−	0.850922i	$-0.323956\pi$
$701$	27.8157			1.05058			0.525292	+	0.850922i	$0.323956\pi$
$702$	−2.57310			−0.0971153
$703$	24.0927			0.908675
$704$		−	46.9785i		−	1.77057i
$705$		0			0
$706$			80.8492i			3.04280i
$707$		−	6.28017i		−	0.236190i
$708$			31.9236i			1.19976i
$709$	−0.643274			−0.0241587			−0.0120793	−	0.999927i	$-0.503845\pi$
$709$	−0.643274			−0.0241587			−0.0120793	+	0.999927i	$0.503845\pi$
$710$		0			0
$711$		−	11.7263i		−	0.439771i
$712$	63.0320			2.36223
$713$			0.882069i			0.0330337i
$714$			15.3756i			0.575417i
$715$		0			0
$716$	23.1498			0.865150
$717$			33.8913i			1.26569i
$718$	−63.4571			−2.36820
$719$	21.2389			0.792079			0.396039	−	0.918233i	$-0.370384\pi$
$719$	21.2389			0.792079			0.396039	+	0.918233i	$0.370384\pi$
$720$		0			0
$721$	47.6564			1.77482
$722$		−	44.3731i		−	1.65139i
$723$			4.62892i			0.172151i
$724$	−70.5291			−2.62119
$725$		0			0
$726$	−35.0909			−1.30235
$727$		−	19.0771i		−	0.707531i	−0.935334	−	0.353765i	$-0.884901\pi$
$727$		−	19.0771i		−	0.707531i	0.935334	−	0.353765i	$-0.115099\pi$
$728$			23.4610i			0.869524i
$729$	14.4458			0.535031
$730$		0			0
$731$	2.91672			0.107879
$732$	−11.8822			−0.439179
$733$		−	39.4835i		−	1.45836i	−0.684324	−	0.729178i	$-0.739903\pi$
$733$		−	39.4835i		−	1.45836i	0.684324	−	0.729178i	$-0.260097\pi$
$734$	−46.2408			−1.70678
$735$		0			0
$736$			95.2107i			3.50951i
$737$		−	3.64507i		−	0.134268i
$738$	−61.8157			−2.27547
$739$			5.95953i			0.219225i	0.993974	+	0.109612i	$0.0349610\pi$
$739$			5.95953i			0.219225i	−0.993974	+	0.109612i	$0.965039\pi$
$740$		0			0
$741$	−8.87275			−0.325948
$742$			148.230i			5.44169i
$743$			18.0065i			0.660594i	0.943877	+	0.330297i	$0.107149\pi$
$743$			18.0065i			0.660594i	−0.943877	+	0.330297i	$0.892851\pi$
$744$			3.16621i			0.116079i
$745$		0			0
$746$		−	61.4515i		−	2.24990i
$747$	−19.3680			−0.708638
$748$	7.07965			0.258858
$749$	−12.3662			−0.451851
$750$		0			0
$751$		−	25.8623i		−	0.943727i	−0.881671	−	0.471864i	$-0.843581\pi$
$751$		−	25.8623i		−	0.943727i	0.881671	−	0.471864i	$-0.156419\pi$
$752$		−	29.6091i		−	1.07973i
$753$	−52.3888			−1.90915
$754$	2.29965	−	9.01841i	0.0837483	−	0.328431i
$755$		0			0
$756$			32.7711i			1.19187i
$757$			53.0193i			1.92702i	0.267676	+	0.963509i	$0.413744\pi$
$757$			53.0193i			1.92702i	−0.267676	+	0.963509i	$0.586256\pi$
$758$	73.2502			2.66057
$759$	−29.8633			−1.08397
$760$		0			0
$761$	−34.8953			−1.26495			−0.632477	−	0.774579i	$-0.717962\pi$
$761$	−34.8953			−1.26495			−0.632477	+	0.774579i	$0.717962\pi$
$762$		−	68.9811i		−	2.49892i
$763$	72.0451			2.60821
$764$			60.3864i			2.18470i
$765$		0			0
$766$		−	100.028i		−	3.61416i
$767$	−1.70035			−0.0613961
$768$			32.7492i			1.18174i
$769$		−	30.5888i		−	1.10306i	−0.834155	−	0.551530i	$-0.814044\pi$
$769$		−	30.5888i		−	1.10306i	0.834155	−	0.551530i	$-0.185956\pi$
$770$		0			0
$771$		−	25.2747i		−	0.910247i
$772$		−	51.3680i		−	1.84878i
$773$		−	11.9658i		−	0.430378i	−0.976572	−	0.215189i	$-0.930963\pi$
$773$		−	11.9658i		−	0.430378i	0.976572	−	0.215189i	$-0.0690368\pi$
$774$	−31.5047			−1.13241
$775$		0			0
$776$	−26.4477			−0.949416
$777$	−39.4684			−1.41592
$778$	63.5386			2.27797
$779$	58.1819			2.08458
$780$		0			0
$781$		−	21.6558i		−	0.774904i
$782$	−8.78000			−0.313972
$783$	1.98106	−	7.76901i	0.0707973	−	0.277642i
$784$	138.077			4.93133
$785$		0			0
$786$		−	44.3476i		−	1.58183i
$787$	21.2087			0.756009			0.378005	−	0.925804i	$-0.376610\pi$
$787$	21.2087			0.756009			0.378005	+	0.925804i	$0.376610\pi$
$788$	−26.8727			−0.957302
$789$	−22.9619			−0.817464
$790$		0			0
$791$		−	56.8996i		−	2.02312i
$792$	−47.1611			−1.67580
$793$		−	0.632884i		−	0.0224744i
$794$			80.6607i			2.86254i
$795$		0			0
$796$	92.8477			3.29090
$797$			8.32068i			0.294734i	0.989082	+	0.147367i	$0.0470798\pi$
$797$			8.32068i			0.294734i	−0.989082	+	0.147367i	$0.952920\pi$
$798$			156.315i			5.53350i
$799$	1.35673			0.0479975
$800$		0			0
$801$		−	17.1809i		−	0.607056i
$802$		−	86.9670i		−	3.07091i
$803$	−21.2389			−0.749506
$804$			19.0207i			0.670807i
$805$		0			0
$806$	−0.273448			−0.00963179
$807$	−28.7550			−1.01222
$808$	12.8727			0.452862
$809$			23.4610i			0.824846i	0.910992	+	0.412423i	$0.135317\pi$
$809$			23.4610i			0.824846i	−0.910992	+	0.412423i	$0.864683\pi$
$810$		0			0
$811$	−7.00947			−0.246136			−0.123068	−	0.992398i	$-0.539273\pi$
$811$	−7.00947			−0.246136			−0.123068	+	0.992398i	$0.539273\pi$
$812$	−114.859	−	29.2885i	−4.03076	−	1.02782i
$813$	−63.1022			−2.21309
$814$			25.1384i			0.881101i
$815$		0			0
$816$	−17.3567			−0.607607
$817$	29.6527			1.03742
$818$	65.8382			2.30198
$819$	6.39486			0.223455
$820$		0			0
$821$	1.44584			0.0504603			0.0252302	−	0.999682i	$-0.491968\pi$
$821$	1.44584			0.0504603			0.0252302	+	0.999682i	$0.491968\pi$
$822$		−	91.9632i		−	3.20759i
$823$			47.1671i			1.64414i	0.569386	+	0.822070i	$0.307181\pi$
$823$			47.1671i			1.64414i	−0.569386	+	0.822070i	$0.692819\pi$
$824$			97.6833i			3.40296i
$825$		0			0
$826$			29.9559i			1.04230i
$827$		−	20.1366i		−	0.700219i	−0.936709	−	0.350109i	$-0.886144\pi$
$827$		−	20.1366i		−	0.700219i	0.936709	−	0.350109i	$-0.113856\pi$
$828$	68.5593			2.38260
$829$		−	12.8011i		−	0.444602i	−0.974978	−	0.222301i	$-0.928643\pi$
$829$		−	12.8011i		−	0.444602i	0.974978	−	0.222301i	$-0.0713567\pi$
$830$		0			0
$831$			6.75904i			0.234468i
$832$	−13.0571			−0.452673
$833$			6.32686i			0.219213i
$834$	−22.1593			−0.767314
$835$		0			0
$836$	71.9750			2.48931
$837$	−0.235565			−0.00814231
$838$			16.7365i			0.578154i
$839$			16.8341i			0.581178i	0.956848	+	0.290589i	$0.0938512\pi$
$839$			16.8341i			0.581178i	−0.956848	+	0.290589i	$0.906149\pi$
$840$		0			0
$841$	25.4589	+	13.8868i	0.877895	+	0.478854i
$842$	88.4113			3.04686
$843$		−	42.5078i		−	1.46405i
$844$		−	98.4278i		−	3.38802i
$845$		0			0
$846$	−14.6546			−0.503834
$847$	−23.8044			−0.817928
$848$	−167.329			−5.74611
$849$			34.3963i			1.18048i
$850$		0			0
$851$		−	22.5378i		−	0.772587i
$852$			113.004i			3.87145i
$853$		−	40.1164i		−	1.37356i	−0.726866	−	0.686779i	$-0.759024\pi$
$853$		−	40.1164i		−	1.37356i	0.726866	−	0.686779i	$-0.240976\pi$
$854$	−11.1498			−0.381539
$855$		0			0
$856$		−	25.3475i		−	0.866361i
$857$	−15.2389			−0.520552			−0.260276	−	0.965534i	$-0.583814\pi$
$857$	−15.2389			−0.520552			−0.260276	+	0.965534i	$0.583814\pi$
$858$		−	9.25784i		−	0.316057i
$859$			10.7770i			0.367706i	0.982954	+	0.183853i	$0.0588571\pi$
$859$			10.7770i			0.367706i	−0.982954	+	0.183853i	$0.941143\pi$
$860$		0			0
$861$	−95.3128			−3.24825
$862$			8.08545i			0.275392i
$863$	32.1004			1.09271			0.546355	−	0.837554i	$-0.316015\pi$
$863$	32.1004			1.09271			0.546355	+	0.837554i	$0.316015\pi$
$864$	−25.4269			−0.865041
$865$		0			0
$866$	−92.1932			−3.13285
$867$			38.5505i			1.30924i
$868$			3.48265i			0.118209i
$869$	−11.5160			−0.390654
$870$		0			0
$871$	−1.01310			−0.0343276
$872$			147.674i			5.00087i
$873$			7.20893i			0.243985i
$874$	−89.2615			−3.01932
$875$		0			0
$876$	110.829			3.74456
$877$	−28.2520			−0.954004			−0.477002	−	0.878902i	$-0.658277\pi$
$877$	−28.2520			−0.954004			−0.477002	+	0.878902i	$0.658277\pi$
$878$			80.1048i			2.70341i
$879$	−3.63380			−0.122565
$880$		0			0
$881$			8.59043i			0.289419i	0.989474	+	0.144710i	$0.0462248\pi$
$881$			8.59043i			0.289419i	−0.989474	+	0.144710i	$0.953775\pi$
$882$		−	68.3391i		−	2.30110i
$883$	34.7913			1.17082			0.585410	−	0.810737i	$-0.300934\pi$
$883$	34.7913			1.17082			0.585410	+	0.810737i	$0.300934\pi$
$884$		−	1.96770i		−	0.0661808i
$885$		0			0
$886$	−75.1135			−2.52349
$887$		−	40.3558i		−	1.35501i	−0.735516	−	0.677507i	$-0.763060\pi$
$887$		−	40.3558i		−	1.35501i	0.735516	−	0.677507i	$-0.236940\pi$
$888$		−	80.9001i		−	2.71483i
$889$		−	46.7942i		−	1.56943i
$890$		0			0
$891$		−	24.3389i		−	0.815384i
$892$	70.8364			2.37178
$893$	13.7931			0.461568
$894$	−37.3091			−1.24780
$895$		0			0
$896$			85.9528i			2.87148i
$897$			8.30011i			0.277133i
$898$	11.4934			0.383541
$899$	0.210531	−	0.825627i	0.00702160	−	0.0275362i
$900$		0			0
$901$		−	7.66723i		−	0.255432i
$902$			60.7071i			2.02132i
$903$	−48.5767			−1.61653
$904$	116.630			3.87904
$905$		0			0
$906$	−28.0226			−0.930988
$907$			8.59463i			0.285380i	0.989767	+	0.142690i	$0.0455752\pi$
$907$			8.59463i			0.285380i	−0.989767	+	0.142690i	$0.954425\pi$
$908$	36.5368			1.21252
$909$		−	3.50877i		−	0.116379i
$910$		0			0
$911$			12.9332i			0.428497i	0.976779	+	0.214249i	$0.0687303\pi$
$911$			12.9332i			0.428497i	−0.976779	+	0.214249i	$0.931270\pi$
$912$	−176.456			−5.84306
$913$			19.0207i			0.629492i
$914$			27.8505i			0.921214i
$915$		0			0
$916$			126.043i			4.16458i
$917$		−	30.0838i		−	0.993454i
$918$		−	2.34478i		−	0.0773893i
$919$	52.1153			1.71913			0.859563	−	0.511030i	$-0.170736\pi$
$919$	52.1153			1.71913			0.859563	+	0.511030i	$0.170736\pi$
$920$		0			0
$921$	−10.7836			−0.355333
$922$	−35.1724			−1.15834
$923$	−6.01894			−0.198116
$924$	−117.908			−3.87890
$925$		0			0
$926$			89.8882i			2.95391i
$927$	26.6259			0.874509
$928$	22.7247	−	89.1184i	0.745976	−	2.92545i
$929$	−26.5993			−0.872695			−0.436347	−	0.899778i	$-0.643728\pi$
$929$	−26.5993			−0.872695			−0.436347	+	0.899778i	$0.643728\pi$
$930$		0			0
$931$			64.3218i			2.10806i
$932$	26.8727			0.880246
$933$	−50.1117			−1.64058
$934$	87.5499			2.86472
$935$		0			0
$936$			13.1078i			0.428443i
$937$	14.5291			0.474646			0.237323	−	0.971431i	$-0.423730\pi$
$937$	14.5291			0.474646			0.237323	+	0.971431i	$0.423730\pi$
$938$			17.8483i			0.582767i
$939$		−	26.2847i		−	0.857768i
$940$		0			0
$941$	3.14619			0.102563			0.0512815	−	0.998684i	$-0.483669\pi$
$941$	3.14619			0.102563			0.0512815	+	0.998684i	$0.483669\pi$
$942$			105.371i			3.43318i
$943$		−	54.4269i		−	1.77238i
$944$	−33.8157			−1.10061
$945$		0			0
$946$			30.9397i			1.00594i
$947$			51.7960i			1.68314i	0.540145	+	0.841572i	$0.318369\pi$
$947$			51.7960i			1.68314i	−0.540145	+	0.841572i	$0.681631\pi$
$948$	60.0927			1.95172
$949$			5.90309i			0.191622i
$950$		0			0
$951$	21.6753			0.702870
$952$	−21.3793			−0.692907
$953$	10.5542			0.341883			0.170941	−	0.985281i	$-0.445319\pi$
$953$	10.5542			0.341883			0.170941	+	0.985281i	$0.445319\pi$
$954$			82.8169i			2.68130i
$955$		0			0
$956$	−76.4113			−2.47132
$957$	27.9524	+	7.12772i	0.903573	+	0.230407i
$958$	−98.1230			−3.17021
$959$		−	62.3844i		−	2.01450i
$960$		0			0
$961$	30.9750			0.999192
$962$	6.98690			0.225267
$963$	−6.90907			−0.222642
$964$	−10.4364			−0.336133
$965$		0			0
$966$	146.227			4.70478
$967$		−	21.0448i		−	0.676755i	−0.941010	−	0.338378i	$-0.890122\pi$
$967$		−	21.0448i		−	0.676755i	0.941010	−	0.338378i	$-0.109878\pi$
$968$		−	48.7929i		−	1.56826i
$969$		−	8.08545i		−	0.259742i
$970$		0			0
$971$			1.01417i			0.0325462i	0.999868	+	0.0162731i	$0.00518012\pi$
$971$			1.01417i			0.0325462i	−0.999868	+	0.0162731i	$0.994820\pi$
$972$			103.698i			3.32611i
$973$	−15.0320			−0.481905
$974$		−	69.6952i		−	2.23318i
$975$		0			0
$976$		−	12.5865i		−	0.402883i
$977$	−9.95239			−0.318405			−0.159203	−	0.987246i	$-0.550892\pi$
$977$	−9.95239			−0.318405			−0.159203	+	0.987246i	$0.550892\pi$
$978$			68.9811i			2.20577i
$979$	−16.8727			−0.539255
$980$		0			0
$981$	40.2520			1.28515
$982$	70.7699			2.25836
$983$			15.4059i			0.491372i	0.969349	+	0.245686i	$0.0790133\pi$
$983$			15.4059i			0.491372i	−0.969349	+	0.245686i	$0.920987\pi$
$984$		−	195.367i		−	6.22806i
$985$		0			0
$986$	8.21819	+	2.09560i	0.261720	+	0.0667374i
$987$	−22.5957			−0.719228
$988$		−	20.0045i		−	0.636428i
$989$		−	27.7390i		−	0.882049i
$990$		0			0
$991$	−8.92035			−0.283364			−0.141682	−	0.989912i	$-0.545251\pi$
$991$	−8.92035			−0.283364			−0.141682	+	0.989912i	$0.545251\pi$
$992$	−2.70217			−0.0857938
$993$	42.8441			1.35962
$994$			106.039i			3.36334i
$995$		0			0
$996$		−	99.2534i		−	3.14496i
$997$			1.19296i			0.0377814i	0.999822	+	0.0188907i	$0.00601345\pi$
$997$			1.19296i			0.0377814i	−0.999822	+	0.0188907i	$0.993987\pi$
$998$		−	56.4552i		−	1.78706i
$999$	6.01894			0.190431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.c.e.376.6		6
5.2	odd	4		725.2.d.c.724.1		12
5.3	odd	4		725.2.d.c.724.12		12
5.4	even	2		145.2.c.b.86.1	✓	6
15.14	odd	2		1305.2.d.b.811.6		6
20.19	odd	2		2320.2.g.i.1681.5		6
29.28	even	2	inner	725.2.c.e.376.1		6
145.28	odd	4		725.2.d.c.724.2		12
145.57	odd	4		725.2.d.c.724.11		12
145.99	odd	4		4205.2.a.m.1.6		6
145.104	odd	4		4205.2.a.m.1.1		6
145.144	even	2		145.2.c.b.86.6	yes	6
435.434	odd	2		1305.2.d.b.811.1		6
580.579	odd	2		2320.2.g.i.1681.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.c.b.86.1	✓	6	5.4	even	2
145.2.c.b.86.6	yes	6	145.144	even	2
725.2.c.e.376.1		6	29.28	even	2	inner
725.2.c.e.376.6		6	1.1	even	1	trivial
725.2.d.c.724.1		12	5.2	odd	4
725.2.d.c.724.2		12	145.28	odd	4
725.2.d.c.724.11		12	145.57	odd	4
725.2.d.c.724.12		12	5.3	odd	4
1305.2.d.b.811.1		6	435.434	odd	2
1305.2.d.b.811.6		6	15.14	odd	2
2320.2.g.i.1681.2		6	580.579	odd	2
2320.2.g.i.1681.5		6	20.19	odd	2
4205.2.a.m.1.1		6	145.104	odd	4
4205.2.a.m.1.6		6	145.99	odd	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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.68667i q^{2} +2.31446i q^{3} -5.21819 q^{4} -6.21819 q^{6} -4.21819 q^{7} -8.64620i q^{8} -2.35673 q^{9} +O(q^{10})\)	\(q+2.68667i q^{2} +2.31446i q^{3} -5.21819 q^{4} -6.21819 q^{6} -4.21819 q^{7} -8.64620i q^{8} -2.35673 q^{9} +2.31446i q^{11} -12.0773i q^{12} +0.643274 q^{13} -11.3329i q^{14} +12.7931 q^{16} +0.586195i q^{17} -6.33174i q^{18} +5.95953i q^{19} -9.76282i q^{21} -6.21819 q^{22} +5.57491 q^{23} +20.0113 q^{24} +1.72826i q^{26} +1.48883i q^{27} +22.0113 q^{28} +(-5.21819 - 1.33061i) q^{29} +0.158221i q^{31} +17.0784i q^{32} -5.35673 q^{33} -1.57491 q^{34} +12.2978 q^{36} -4.04272i q^{37} -16.0113 q^{38} +1.48883i q^{39} -9.76282i q^{41} +26.2295 q^{42} -4.97568i q^{43} -12.0773i q^{44} +14.9779i q^{46} -2.31446i q^{47} +29.6091i q^{48} +10.7931 q^{49} -1.35673 q^{51} -3.35673 q^{52} -13.0796 q^{53} -4.00000 q^{54} +36.4713i q^{56} -13.7931 q^{57} +(3.57491 - 14.0195i) q^{58} -2.64327 q^{59} -0.983848i q^{61} -0.425088 q^{62} +9.94111 q^{63} -20.2978 q^{64} -14.3917i q^{66} -1.57491 q^{67} -3.05888i q^{68} +12.9029i q^{69} -9.35673 q^{71} +20.3767i q^{72} +9.17663i q^{73} +10.8615 q^{74} -31.0980i q^{76} -9.76282i q^{77} -4.00000 q^{78} +4.97568i q^{79} -10.5160 q^{81} +26.2295 q^{82} +8.21819 q^{83} +50.9442i q^{84} +13.3680 q^{86} +(3.07965 - 12.0773i) q^{87} +20.0113 q^{88} +7.29014i q^{89} -2.71345 q^{91} -29.0909 q^{92} -0.366196 q^{93} +6.21819 q^{94} -39.5273 q^{96} -3.05888i q^{97} +28.9975i q^{98} -5.45455i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 12 q^{6} - 14 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 12 * q^6 - 14 * q^9	\( 6 q - 6 q^{4} - 12 q^{6} - 14 q^{9} + 4 q^{13} + 26 q^{16} - 12 q^{22} + 8 q^{23} + 44 q^{24} + 56 q^{28} - 6 q^{29} - 32 q^{33} + 16 q^{34} - 2 q^{36} - 20 q^{38} + 56 q^{42} + 14 q^{49} - 8 q^{51} - 20 q^{52} - 28 q^{53} - 24 q^{54} - 32 q^{57} - 4 q^{58} - 16 q^{59} - 28 q^{62} - 16 q^{63} - 46 q^{64} + 16 q^{67} - 56 q^{71} + 40 q^{74} - 24 q^{78} + 38 q^{81} + 56 q^{82} + 24 q^{83} + 4 q^{86} - 32 q^{87} + 44 q^{88} - 16 q^{91} - 48 q^{92} + 48 q^{93} + 12 q^{94} - 60 q^{96}+O(q^{100}) \) 6 * q - 6 * q^4 - 12 * q^6 - 14 * q^9 + 4 * q^13 + 26 * q^16 - 12 * q^22 + 8 * q^23 + 44 * q^24 + 56 * q^28 - 6 * q^29 - 32 * q^33 + 16 * q^34 - 2 * q^36 - 20 * q^38 + 56 * q^42 + 14 * q^49 - 8 * q^51 - 20 * q^52 - 28 * q^53 - 24 * q^54 - 32 * q^57 - 4 * q^58 - 16 * q^59 - 28 * q^62 - 16 * q^63 - 46 * q^64 + 16 * q^67 - 56 * q^71 + 40 * q^74 - 24 * q^78 + 38 * q^81 + 56 * q^82 + 24 * q^83 + 4 * q^86 - 32 * q^87 + 44 * q^88 - 16 * q^91 - 48 * q^92 + 48 * q^93 + 12 * q^94 - 60 * q^96

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