LMFDB - Embedded newform 925.2.c.c.776.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(776,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, 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("925.776");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.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:	$7.38616218697$
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} + 21x^{10} + 162x^{8} + 574x^{6} + 985x^{4} + 765x^{2} + 196 $ x^12 + 21x^10 + 162x^8 + 574x^6 + 985x^4 + 765*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			776.10
Root			$1.66705i$ of defining polynomial
Character	$\chi$	$=$	925.776
Dual form			925.2.c.c.776.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.66705i q^{2} -0.792969 q^{3} -0.779058 q^{4} -1.32192i q^{6} +0.457139 q^{7} +2.03537i q^{8} -2.37120 q^{9} +O(q^{10})$	\(q+1.66705i q^{2} -0.792969 q^{3} -0.779058 q^{4} -1.32192i q^{6} +0.457139 q^{7} +2.03537i q^{8} -2.37120 q^{9} +5.26092 q^{11} +0.617769 q^{12} +0.138100i q^{13} +0.762075i q^{14} -4.95118 q^{16} +1.88972i q^{17} -3.95291i q^{18} +5.01391i q^{19} -0.362497 q^{21} +8.77022i q^{22} -3.03998i q^{23} -1.61399i q^{24} -0.230221 q^{26} +4.25919 q^{27} -0.356138 q^{28} +8.32834i q^{29} +1.34974i q^{31} -4.18313i q^{32} -4.17174 q^{33} -3.15026 q^{34} +1.84730 q^{36} +(-5.81731 - 1.77733i) q^{37} -8.35844 q^{38} -0.109509i q^{39} +3.80342 q^{41} -0.604301i q^{42} +8.37408i q^{43} -4.09856 q^{44} +5.06780 q^{46} -5.12534 q^{47} +3.92613 q^{48} -6.79102 q^{49} -1.49849i q^{51} -0.107588i q^{52} -7.28874 q^{53} +7.10029i q^{54} +0.930449i q^{56} -3.97587i q^{57} -13.8838 q^{58} -1.82213i q^{59} +11.0221i q^{61} -2.25008 q^{62} -1.08397 q^{63} -2.92887 q^{64} -6.95451i q^{66} +5.60855 q^{67} -1.47220i q^{68} +2.41061i q^{69} -6.34319 q^{71} -4.82628i q^{72} +16.3710 q^{73} +(2.96290 - 9.69775i) q^{74} -3.90613i q^{76} +2.40497 q^{77} +0.182558 q^{78} -8.78240i q^{79} +3.73620 q^{81} +6.34050i q^{82} +6.13053 q^{83} +0.282406 q^{84} -13.9600 q^{86} -6.60411i q^{87} +10.7079i q^{88} -12.5184i q^{89} +0.0631312i q^{91} +2.36832i q^{92} -1.07030i q^{93} -8.54421i q^{94} +3.31709i q^{96} -9.97862i q^{97} -11.3210i q^{98} -12.4747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 18 q^{4} + 18 q^{7} + 22 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 - 18 * q^4 + 18 * q^7 + 22 * q^9	$ 12 q - 2 q^{3} - 18 q^{4} + 18 q^{7} + 22 q^{9} + 2 q^{11} + 36 q^{12} + 30 q^{16} - 6 q^{21} - 12 q^{26} - 26 q^{27} - 24 q^{28} + 18 q^{33} + 4 q^{34} - 22 q^{36} - 10 q^{37} - 12 q^{38} - 10 q^{41} + 44 q^{44} - 24 q^{46} - 2 q^{47} - 60 q^{48} + 30 q^{49} + 6 q^{53} + 24 q^{58} - 44 q^{62} + 16 q^{63} - 126 q^{64} - 16 q^{67} + 42 q^{71} + 46 q^{73} + 50 q^{74} - 30 q^{77} - 132 q^{78} - 12 q^{81} + 62 q^{83} - 84 q^{84} - 64 q^{86} - 84 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 18 * q^4 + 18 * q^7 + 22 * q^9 + 2 * q^11 + 36 * q^12 + 30 * q^16 - 6 * q^21 - 12 * q^26 - 26 * q^27 - 24 * q^28 + 18 * q^33 + 4 * q^34 - 22 * q^36 - 10 * q^37 - 12 * q^38 - 10 * q^41 + 44 * q^44 - 24 * q^46 - 2 * q^47 - 60 * q^48 + 30 * q^49 + 6 * q^53 + 24 * q^58 - 44 * q^62 + 16 * q^63 - 126 * q^64 - 16 * q^67 + 42 * q^71 + 46 * q^73 + 50 * q^74 - 30 * q^77 - 132 * q^78 - 12 * q^81 + 62 * q^83 - 84 * q^84 - 64 * q^86 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.66705i			1.17878i	0.807848	+	0.589391i	$0.200632\pi$
$2$			1.66705i			1.17878i	−0.807848	+	0.589391i	$0.799368\pi$
$3$	−0.792969			−0.457821			−0.228910	−	0.973448i	$-0.573516\pi$
$3$	−0.792969			−0.457821			−0.228910	+	0.973448i	$0.573516\pi$
$4$	−0.779058			−0.389529
$5$		0			0
$5$		0			0
$6$		−	1.32192i		−	0.539671i
$7$	0.457139			0.172782			0.0863912	−	0.996261i	$-0.472466\pi$
$7$	0.457139			0.172782			0.0863912	+	0.996261i	$0.472466\pi$
$8$			2.03537i			0.719613i
$9$	−2.37120			−0.790400
$10$		0			0
$11$	5.26092			1.58623			0.793114	−	0.609074i	$-0.208459\pi$
$11$	5.26092			1.58623			0.793114	+	0.609074i	$0.208459\pi$
$12$	0.617769			0.178334
$13$			0.138100i			0.0383022i	0.999817	+	0.0191511i	$0.00609635\pi$
$13$			0.138100i			0.0383022i	−0.999817	+	0.0191511i	$0.993904\pi$
$14$			0.762075i			0.203673i
$15$		0			0
$16$	−4.95118			−1.23780
$17$			1.88972i			0.458324i	0.973388	+	0.229162i	$0.0735986\pi$
$17$			1.88972i			0.458324i	−0.973388	+	0.229162i	$0.926401\pi$
$18$		−	3.95291i		−	0.931710i
$19$			5.01391i			1.15027i	0.818059	+	0.575135i	$0.195050\pi$
$19$			5.01391i			1.15027i	−0.818059	+	0.575135i	$0.804950\pi$
$20$		0			0
$21$	−0.362497			−0.0791034
$22$			8.77022i			1.86982i
$23$		−	3.03998i		−	0.633879i	−0.948446	−	0.316940i	$-0.897345\pi$
$23$		−	3.03998i		−	0.633879i	0.948446	−	0.316940i	$-0.102655\pi$
$24$		−	1.61399i		−	0.329453i
$25$		0			0
$26$	−0.230221			−0.0451500
$27$	4.25919			0.819682
$28$	−0.356138			−0.0673038
$29$			8.32834i			1.54653i	0.634081	+	0.773267i	$0.281379\pi$
$29$			8.32834i			1.54653i	−0.634081	+	0.773267i	$0.718621\pi$
$30$		0			0
$31$			1.34974i			0.242420i	0.992627	+	0.121210i	$0.0386775\pi$
$31$			1.34974i			0.242420i	−0.992627	+	0.121210i	$0.961322\pi$
$32$		−	4.18313i		−	0.739480i
$33$	−4.17174			−0.726208
$34$	−3.15026			−0.540265
$35$		0			0
$36$	1.84730			0.307884
$37$	−5.81731	−	1.77733i	−0.956360	−	0.292191i
$37$	−5.81731	−	1.77733i	−0.956360	−	0.292191i
$38$	−8.35844			−1.35592
$39$		−	0.109509i		−	0.0175355i
$40$		0			0
$41$	3.80342			0.593995			0.296997	−	0.954878i	$-0.404015\pi$
$41$	3.80342			0.593995			0.296997	+	0.954878i	$0.404015\pi$
$42$		−	0.604301i		−	0.0932457i
$43$			8.37408i			1.27704i	0.769607	+	0.638518i	$0.220452\pi$
$43$			8.37408i			1.27704i	−0.769607	+	0.638518i	$0.779548\pi$
$44$	−4.09856			−0.617882
$45$		0			0
$46$	5.06780			0.747206
$47$	−5.12534			−0.747608			−0.373804	−	0.927508i	$-0.621947\pi$
$47$	−5.12534			−0.747608			−0.373804	+	0.927508i	$0.621947\pi$
$48$	3.92613			0.566689
$49$	−6.79102			−0.970146
$50$		0			0
$51$		−	1.49849i		−	0.209830i
$52$		−	0.107588i		−	0.0149198i
$53$	−7.28874			−1.00119			−0.500593	−	0.865683i	$-0.666885\pi$
$53$	−7.28874			−1.00119			−0.500593	+	0.865683i	$0.666885\pi$
$54$			7.10029i			0.966227i
$55$		0			0
$56$			0.930449i			0.124336i
$57$		−	3.97587i		−	0.526617i
$58$	−13.8838			−1.82303
$59$		−	1.82213i		−	0.237222i	−0.992941	−	0.118611i	$-0.962156\pi$
$59$		−	1.82213i		−	0.237222i	0.992941	−	0.118611i	$-0.0378441\pi$
$60$		0			0
$61$			11.0221i			1.41123i	0.708595	+	0.705615i	$0.249329\pi$
$61$			11.0221i			1.41123i	−0.708595	+	0.705615i	$0.750671\pi$
$62$	−2.25008			−0.285761
$63$	−1.08397			−0.136567
$64$	−2.92887			−0.366109
$65$		0			0
$66$		−	6.95451i		−	0.856041i
$67$	5.60855			0.685194			0.342597	−	0.939483i	$-0.388694\pi$
$67$	5.60855			0.685194			0.342597	+	0.939483i	$0.388694\pi$
$68$		−	1.47220i		−	0.178531i
$69$			2.41061i			0.290203i
$70$		0			0
$71$	−6.34319			−0.752798			−0.376399	−	0.926458i	$-0.622838\pi$
$71$	−6.34319			−0.752798			−0.376399	+	0.926458i	$0.622838\pi$
$72$		−	4.82628i		−	0.568782i
$73$	16.3710			1.91608			0.958041	−	0.286632i	$-0.0925357\pi$
$73$	16.3710			1.91608			0.958041	+	0.286632i	$0.0925357\pi$
$74$	2.96290	−	9.69775i	0.344430	−	1.12734i
$75$		0			0
$76$		−	3.90613i		−	0.448064i
$77$	2.40497			0.274072
$78$	0.182558			0.0206706
$79$		−	8.78240i		−	0.988098i	−0.869434	−	0.494049i	$-0.835516\pi$
$79$		−	8.78240i		−	0.988098i	0.869434	−	0.494049i	$-0.164484\pi$
$80$		0			0
$81$	3.73620			0.415133
$82$			6.34050i			0.700191i
$83$	6.13053			0.672913			0.336456	−	0.941699i	$-0.390772\pi$
$83$	6.13053			0.672913			0.336456	+	0.941699i	$0.390772\pi$
$84$	0.282406			0.0308131
$85$		0			0
$86$	−13.9600			−1.50535
$87$		−	6.60411i		−	0.708035i
$88$			10.7079i			1.14147i
$89$		−	12.5184i		−	1.32695i	−0.748200	−	0.663473i	$-0.769082\pi$
$89$		−	12.5184i		−	1.32695i	0.748200	−	0.663473i	$-0.230918\pi$
$90$		0			0
$91$			0.0631312i			0.00661795i
$92$			2.36832i			0.246915i
$93$		−	1.07030i		−	0.110985i
$94$		−	8.54421i		−	0.881268i
$95$		0			0
$96$			3.31709i			0.338549i
$97$		−	9.97862i		−	1.01318i	−0.862188	−	0.506588i	$-0.830907\pi$
$97$		−	9.97862i		−	1.01318i	0.862188	−	0.506588i	$-0.169093\pi$
$98$		−	11.3210i		−	1.14359i
$99$	−12.4747			−1.25375
$100$		0			0
$101$	−7.80963			−0.777087			−0.388544	−	0.921430i	$-0.627022\pi$
$101$	−7.80963			−0.777087			−0.388544	+	0.921430i	$0.627022\pi$
$102$	2.49806			0.247344
$103$			15.6498i			1.54203i	0.636820	+	0.771013i	$0.280250\pi$
$103$			15.6498i			1.54203i	−0.636820	+	0.771013i	$0.719750\pi$
$104$	−0.281086			−0.0275627
$105$		0			0
$106$		−	12.1507i		−	1.18018i
$107$	−5.07998			−0.491100			−0.245550	−	0.969384i	$-0.578969\pi$
$107$	−5.07998			−0.491100			−0.245550	+	0.969384i	$0.578969\pi$
$108$	−3.31816			−0.319290
$109$			4.39200i			0.420678i	0.977629	+	0.210339i	$0.0674567\pi$
$109$			4.39200i			0.420678i	−0.977629	+	0.210339i	$0.932543\pi$
$110$		0			0
$111$	4.61294	+	1.40937i	0.437841	+	0.133771i
$112$	−2.26338			−0.213869
$113$			4.80054i			0.451597i	0.974174	+	0.225799i	$0.0724991\pi$
$113$			4.80054i			0.451597i	−0.974174	+	0.225799i	$0.927501\pi$
$114$	6.62798			0.620767
$115$		0			0
$116$		−	6.48826i		−	0.602420i
$117$		−	0.327464i		−	0.0302741i
$118$	3.03759			0.279633
$119$			0.863866i			0.0791904i
$120$		0			0
$121$	16.6773			1.51612
$122$	−18.3743			−1.66353
$123$	−3.01600			−0.271943
$124$		−	1.05153i		−	0.0944298i
$125$		0			0
$126$		−	1.80703i		−	0.160983i
$127$	16.7072			1.48253			0.741264	−	0.671213i	$-0.234227\pi$
$127$	16.7072			1.48253			0.741264	+	0.671213i	$0.234227\pi$
$128$		−	13.2488i		−	1.17104i
$129$		−	6.64038i		−	0.584653i
$130$		0			0
$131$		−	9.87907i		−	0.863138i	−0.902080	−	0.431569i	$-0.857960\pi$
$131$		−	9.87907i		−	0.863138i	0.902080	−	0.431569i	$-0.142040\pi$
$132$	3.25003			0.282879
$133$			2.29206i			0.198746i
$134$			9.34974i			0.807694i
$135$		0			0
$136$	−3.84628			−0.329816
$137$	2.99424			0.255815			0.127907	−	0.991786i	$-0.459174\pi$
$137$	2.99424			0.255815			0.127907	+	0.991786i	$0.459174\pi$
$138$	−4.01861			−0.342086
$139$	−9.65323			−0.818776			−0.409388	−	0.912360i	$-0.634258\pi$
$139$	−9.65323			−0.818776			−0.409388	+	0.912360i	$0.634258\pi$
$140$		0			0
$141$	4.06424			0.342270
$142$		−	10.5744i		−	0.887385i
$143$			0.726536i			0.0607560i
$144$	11.7403			0.978354
$145$		0			0
$146$			27.2913i			2.25864i
$147$	5.38507			0.444153
$148$	4.53202	+	1.38464i	0.372530	+	0.113817i
$149$	15.9259			1.30470			0.652349	−	0.757919i	$-0.273784\pi$
$149$	15.9259			1.30470			0.652349	+	0.757919i	$0.273784\pi$
$150$		0			0
$151$	14.8529			1.20871			0.604357	−	0.796714i	$-0.293430\pi$
$151$	14.8529			1.20871			0.604357	+	0.796714i	$0.293430\pi$
$152$	−10.2052			−0.827749
$153$		−	4.48091i		−	0.362260i
$154$			4.00921i			0.323072i
$155$		0			0
$156$			0.0853142i			0.00683060i
$157$	−2.31306			−0.184602			−0.0923012	−	0.995731i	$-0.529422\pi$
$157$	−2.31306			−0.184602			−0.0923012	+	0.995731i	$0.529422\pi$
$158$	14.6407			1.16475
$159$	5.77974			0.458363
$160$		0			0
$161$		−	1.38969i		−	0.109523i
$162$			6.22843i			0.489352i
$163$			2.26976i			0.177781i	0.996041	+	0.0888905i	$0.0283321\pi$
$163$			2.26976i			0.177781i	−0.996041	+	0.0888905i	$0.971668\pi$
$164$	−2.96309			−0.231378
$165$		0			0
$166$			10.2199i			0.793218i
$167$		−	2.32540i		−	0.179945i	−0.995944	−	0.0899723i	$-0.971322\pi$
$167$		−	2.32540i		−	0.179945i	0.995944	−	0.0899723i	$-0.0286779\pi$
$168$		−	0.737817i		−	0.0569238i
$169$	12.9809			0.998533
$170$		0			0
$171$		−	11.8890i		−	0.909174i
$172$		−	6.52390i		−	0.497442i
$173$	16.3953			1.24651			0.623257	−	0.782017i	$-0.285809\pi$
$173$	16.3953			1.24651			0.623257	+	0.782017i	$0.285809\pi$
$174$	11.0094			0.834620
$175$		0			0
$176$	−26.0478			−1.96343
$177$			1.44490i			0.108605i
$178$	20.8688			1.56418
$179$		−	9.21241i		−	0.688568i	−0.938866	−	0.344284i	$-0.888122\pi$
$179$		−	9.21241i		−	0.688568i	0.938866	−	0.344284i	$-0.111878\pi$
$180$		0			0
$181$	−1.23679			−0.0919302			−0.0459651	−	0.998943i	$-0.514636\pi$
$181$	−1.23679			−0.0919302			−0.0459651	+	0.998943i	$0.514636\pi$
$182$	−0.105243			−0.00780112
$183$		−	8.74015i		−	0.646090i
$184$	6.18749			0.456148
$185$		0			0
$186$	1.78425			0.130827
$187$			9.94167i			0.727007i
$188$	3.99294			0.291215
$189$	1.94705			0.141627
$190$		0			0
$191$			11.2486i			0.813921i	0.913446	+	0.406960i	$0.133411\pi$
$191$			11.2486i			0.813921i	−0.913446	+	0.406960i	$0.866589\pi$
$192$	2.32251			0.167612
$193$		−	7.19619i		−	0.517993i	−0.965878	−	0.258997i	$-0.916608\pi$
$193$		−	7.19619i		−	0.517993i	0.965878	−	0.258997i	$-0.0833918\pi$
$194$	16.6349			1.19431
$195$		0			0
$196$	5.29060			0.377900
$197$	11.2517			0.801651			0.400825	−	0.916154i	$-0.368723\pi$
$197$	11.2517			0.801651			0.400825	+	0.916154i	$0.368723\pi$
$198$		−	20.7960i		−	1.47790i
$199$			16.1947i			1.14801i	0.818850	+	0.574007i	$0.194612\pi$
$199$			16.1947i			1.14801i	−0.818850	+	0.574007i	$0.805388\pi$
$200$		0			0
$201$	−4.44740			−0.313696
$202$		−	13.0190i		−	0.916017i
$203$			3.80721i			0.267214i
$204$			1.16741i			0.0817350i
$205$		0			0
$206$	−26.0891			−1.81771
$207$			7.20840i			0.501019i
$208$		−	0.683761i		−	0.0474103i
$209$			26.3778i			1.82459i
$210$		0			0
$211$	9.83188			0.676855			0.338427	−	0.940993i	$-0.390105\pi$
$211$	9.83188			0.676855			0.338427	+	0.940993i	$0.390105\pi$
$212$	5.67835			0.389991
$213$	5.02995			0.344646
$214$		−	8.46859i		−	0.578901i
$215$		0			0
$216$			8.66904i			0.589854i
$217$			0.617019i			0.0418860i
$218$	−7.32169			−0.495887
$219$	−12.9817			−0.877222
$220$		0			0
$221$	−0.260971			−0.0175548
$222$	−2.34949	+	7.69001i	−0.157687	+	0.516120i
$223$	−2.13053			−0.142671			−0.0713353	−	0.997452i	$-0.522726\pi$
$223$	−2.13053			−0.142671			−0.0713353	+	0.997452i	$0.522726\pi$
$224$		−	1.91228i		−	0.127769i
$225$		0			0
$226$	−8.00275			−0.532335
$227$			17.8160i			1.18249i	0.806493	+	0.591243i	$0.201363\pi$
$227$			17.8160i			1.18249i	−0.806493	+	0.591243i	$0.798637\pi$
$228$			3.09744i			0.205133i
$229$	8.80568			0.581896			0.290948	−	0.956739i	$-0.406029\pi$
$229$	8.80568			0.581896			0.290948	+	0.956739i	$0.406029\pi$
$230$		0			0
$231$	−1.90707			−0.125476
$232$	−16.9513			−1.11291
$233$	6.55466			0.429410			0.214705	−	0.976679i	$-0.431121\pi$
$233$	6.55466			0.429410			0.214705	+	0.976679i	$0.431121\pi$
$234$	0.545899			0.0356865
$235$		0			0
$236$			1.41955i			0.0924048i
$237$			6.96417i			0.452372i
$238$	−1.44011			−0.0933483
$239$		−	26.9707i		−	1.74459i	−0.488979	−	0.872295i	$-0.662631\pi$
$239$		−	26.9707i		−	1.74459i	0.488979	−	0.872295i	$-0.337369\pi$
$240$		0			0
$241$			28.3465i			1.82596i	0.408005	+	0.912980i	$0.366225\pi$
$241$			28.3465i			1.82596i	−0.408005	+	0.912980i	$0.633775\pi$
$242$			27.8019i			1.78717i
$243$	−15.7403			−1.00974
$244$		−	8.58683i		−	0.549715i
$245$		0			0
$246$		−	5.02782i		−	0.320562i
$247$	−0.692423			−0.0440579
$248$	−2.74722			−0.174449
$249$	−4.86131			−0.308073
$250$		0			0
$251$		−	15.5536i		−	0.981734i	−0.871234	−	0.490867i	$-0.836680\pi$
$251$		−	15.5536i		−	0.981734i	0.871234	−	0.490867i	$-0.163320\pi$
$252$	0.844475			0.0531970
$253$		−	15.9931i		−	1.00548i
$254$			27.8518i			1.74758i
$255$		0			0
$256$	16.2288			1.01430
$257$		−	1.18755i		−	0.0740773i	−0.999314	−	0.0370387i	$-0.988208\pi$
$257$		−	1.18755i		−	0.0740773i	0.999314	−	0.0370387i	$-0.0117925\pi$
$258$	11.0699			0.689179
$259$	−2.65932	−	0.812488i	−0.165242	−	0.0504856i
$260$		0			0
$261$		−	19.7482i		−	1.22238i
$262$	16.4689			1.01745
$263$	−23.9483			−1.47671			−0.738357	−	0.674410i	$-0.764398\pi$
$263$	−23.9483			−1.47671			−0.738357	+	0.674410i	$0.764398\pi$
$264$		−	8.49105i		−	0.522588i
$265$		0			0
$266$	−3.82097			−0.234279
$267$			9.92669i			0.607503i
$268$	−4.36939			−0.266903
$269$	17.0554			1.03989			0.519943	−	0.854201i	$-0.325953\pi$
$269$	17.0554			1.03989			0.519943	+	0.854201i	$0.325953\pi$
$270$		0			0
$271$	−14.3073			−0.869109			−0.434555	−	0.900645i	$-0.643094\pi$
$271$	−14.3073			−0.869109			−0.434555	+	0.900645i	$0.643094\pi$
$272$		−	9.35635i		−	0.567312i
$273$		−	0.0500610i		−	0.00302983i
$274$			4.99155i			0.301550i
$275$		0			0
$276$		−	1.87800i		−	0.113043i
$277$		−	14.4359i		−	0.867368i	−0.901065	−	0.433684i	$-0.857213\pi$
$277$		−	14.4359i		−	0.867368i	0.901065	−	0.433684i	$-0.142787\pi$
$278$		−	16.0924i		−	0.965159i
$279$		−	3.20050i		−	0.191609i
$280$		0			0
$281$		−	31.0773i		−	1.85391i	−0.375167	−	0.926957i	$-0.622415\pi$
$281$		−	31.0773i		−	1.85391i	0.375167	−	0.926957i	$-0.377585\pi$
$282$			6.77529i			0.403462i
$283$			21.5252i			1.27954i	0.768566	+	0.639771i	$0.220971\pi$
$283$			21.5252i			1.27954i	−0.768566	+	0.639771i	$0.779029\pi$
$284$	4.94171			0.293237
$285$		0			0
$286$	−1.21117			−0.0716181
$287$	1.73870			0.102632
$288$			9.91905i			0.584486i
$289$	13.4290			0.789939
$290$		0			0
$291$			7.91273i			0.463853i
$292$	−12.7540			−0.746370
$293$	19.6068			1.14544			0.572722	−	0.819750i	$-0.305887\pi$
$293$	19.6068			1.14544			0.572722	+	0.819750i	$0.305887\pi$
$294$			8.97718i			0.523560i
$295$		0			0
$296$	3.61753	−	11.8404i	0.210265	−	0.688209i
$297$	22.4073			1.30020
$298$			26.5492i			1.53795i
$299$	0.419823			0.0242790
$300$		0			0
$301$			3.82812i			0.220649i
$302$			24.7606i			1.42481i
$303$	6.19279			0.355767
$304$		−	24.8248i		−	1.42380i
$305$		0			0
$306$	7.46990			0.427026
$307$	22.7642			1.29922			0.649610	−	0.760267i	$-0.274932\pi$
$307$	22.7642			1.29922			0.649610	+	0.760267i	$0.274932\pi$
$308$	−1.87362			−0.106759
$309$		−	12.4098i		−	0.705971i
$310$		0			0
$311$			13.1946i			0.748197i	0.927389	+	0.374098i	$0.122048\pi$
$311$			13.1946i			0.748197i	−0.927389	+	0.374098i	$0.877952\pi$
$312$	0.222892			0.0126188
$313$		−	31.9168i		−	1.80405i	−0.431688	−	0.902023i	$-0.642082\pi$
$313$		−	31.9168i		−	1.80405i	0.431688	−	0.902023i	$-0.357918\pi$
$314$		−	3.85599i		−	0.217606i
$315$		0			0
$316$			6.84201i			0.384893i
$317$	−23.2404			−1.30531			−0.652654	−	0.757656i	$-0.726345\pi$
$317$	−23.2404			−1.30531			−0.652654	+	0.757656i	$0.726345\pi$
$318$			9.63512i			0.540311i
$319$			43.8147i			2.45315i
$320$		0			0
$321$	4.02827			0.224836
$322$	2.31669			0.129104
$323$	−9.47489			−0.527197
$324$	−2.91071			−0.161706
$325$		0			0
$326$	−3.78380			−0.209565
$327$		−	3.48272i		−	0.192595i
$328$			7.74138i			0.427446i
$329$	−2.34300			−0.129174
$330$		0			0
$331$		−	9.60258i		−	0.527806i	−0.964549	−	0.263903i	$-0.914990\pi$
$331$		−	9.60258i		−	0.527806i	0.964549	−	0.263903i	$-0.0850098\pi$
$332$	−4.77604			−0.262119
$333$	13.7940	+	4.21441i	0.755907	+	0.230948i
$334$	3.87656			0.212116
$335$		0			0
$336$	1.79479			0.0979139
$337$	11.6079			0.632321			0.316160	−	0.948706i	$-0.397606\pi$
$337$	11.6079			0.632321			0.316160	+	0.948706i	$0.397606\pi$
$338$			21.6399i			1.17705i
$339$		−	3.80668i		−	0.206750i
$340$		0			0
$341$			7.10087i			0.384534i
$342$	19.8195			1.07172
$343$	−6.30442			−0.340407
$344$	−17.0444			−0.918971
$345$		0			0
$346$			27.3318i			1.46937i
$347$		−	24.4354i		−	1.31176i	−0.754864	−	0.655881i	$-0.772297\pi$
$347$		−	24.4354i		−	1.31176i	0.754864	−	0.655881i	$-0.227703\pi$
$348$			5.14499i			0.275800i
$349$	9.47566			0.507220			0.253610	−	0.967307i	$-0.418382\pi$
$349$	9.47566			0.507220			0.253610	+	0.967307i	$0.418382\pi$
$350$		0			0
$351$			0.588197i			0.0313956i
$352$		−	22.0071i		−	1.17298i
$353$		−	21.3399i		−	1.13581i	−0.823095	−	0.567903i	$-0.807755\pi$
$353$		−	21.3399i		−	1.13581i	0.823095	−	0.567903i	$-0.192245\pi$
$354$	−2.40871			−0.128022
$355$		0			0
$356$			9.75255i			0.516884i
$357$		−	0.685018i		−	0.0362550i
$358$	15.3576			0.811672
$359$	−18.9477			−1.00002			−0.500011	−	0.866019i	$-0.666671\pi$
$359$	−18.9477			−1.00002			−0.500011	+	0.866019i	$0.666671\pi$
$360$		0			0
$361$	−6.13930			−0.323121
$362$		−	2.06180i		−	0.108366i
$363$	−13.2246			−0.694110
$364$		−	0.0491829i		−	0.00257788i
$365$		0			0
$366$	14.5703			0.761600
$367$	−20.7101			−1.08106			−0.540530	−	0.841325i	$-0.681776\pi$
$367$	−20.7101			−1.08106			−0.540530	+	0.841325i	$0.681776\pi$
$368$			15.0515i			0.784614i
$369$	−9.01868			−0.469494
$370$		0			0
$371$	−3.33197			−0.172987
$372$			0.833827i			0.0432319i
$373$	−2.73793			−0.141765			−0.0708823	−	0.997485i	$-0.522581\pi$
$373$	−2.73793			−0.141765			−0.0708823	+	0.997485i	$0.522581\pi$
$374$	−16.5733			−0.856983
$375$		0			0
$376$		−	10.4320i		−	0.537988i
$377$	−1.15015			−0.0592356
$378$			3.24582i			0.166947i
$379$	−36.3096			−1.86510			−0.932549	−	0.361042i	$-0.882421\pi$
$379$	−36.3096			−1.86510			−0.932549	+	0.361042i	$0.882421\pi$
$380$		0			0
$381$	−13.2483			−0.678732
$382$	−18.7520			−0.959436
$383$		−	33.0211i		−	1.68730i	−0.536894	−	0.843650i	$-0.680402\pi$
$383$		−	33.0211i		−	1.68730i	0.536894	−	0.843650i	$-0.319598\pi$
$384$			10.5059i			0.536128i
$385$		0			0
$386$	11.9964			0.610602
$387$		−	19.8566i		−	1.00937i
$388$			7.77393i			0.394661i
$389$		−	22.3187i		−	1.13160i	−0.824542	−	0.565801i	$-0.808567\pi$
$389$		−	22.3187i		−	1.13160i	0.824542	−	0.565801i	$-0.191433\pi$
$390$		0			0
$391$	5.74471			0.290522
$392$		−	13.8223i		−	0.698129i
$393$			7.83379i			0.395163i
$394$			18.7572i			0.944972i
$395$		0			0
$396$	9.71852			0.488374
$397$	1.45788			0.0731688			0.0365844	−	0.999331i	$-0.488352\pi$
$397$	1.45788			0.0731688			0.0365844	+	0.999331i	$0.488352\pi$
$398$	−26.9975			−1.35326
$399$		−	1.81753i		−	0.0909902i
$400$		0			0
$401$		−	11.0618i		−	0.552402i	−0.961100	−	0.276201i	$-0.910925\pi$
$401$		−	11.0618i		−	0.552402i	0.961100	−	0.276201i	$-0.0890755\pi$
$402$		−	7.41405i		−	0.369779i
$403$	−0.186400			−0.00928523
$404$	6.08416			0.302698
$405$		0			0
$406$	−6.34682			−0.314987
$407$	−30.6044	−	9.35040i	−1.51700	−	0.463482i
$408$	3.04998			0.150997
$409$			3.81802i			0.188789i	0.995535	+	0.0943944i	$0.0300915\pi$
$409$			3.81802i			0.188789i	−0.995535	+	0.0943944i	$0.969909\pi$
$410$		0			0
$411$	−2.37434			−0.117117
$412$		−	12.1921i		−	0.600664i
$413$		−	0.832970i		−	0.0409878i
$414$	−12.0168			−0.590592
$415$		0			0
$416$	0.577693			0.0283237
$417$	7.65470			0.374852
$418$	−43.9731			−2.15079
$419$	17.8037			0.869766			0.434883	−	0.900487i	$-0.356790\pi$
$419$	17.8037			0.869766			0.434883	+	0.900487i	$0.356790\pi$
$420$		0			0
$421$		−	10.6200i		−	0.517586i	−0.965933	−	0.258793i	$-0.916675\pi$
$421$		−	10.6200i		−	0.517586i	0.965933	−	0.258793i	$-0.0833248\pi$
$422$			16.3902i			0.797865i
$423$	12.1532			0.590910
$424$		−	14.8353i		−	0.720466i
$425$		0			0
$426$			8.38518i			0.406263i
$427$			5.03862i			0.243836i
$428$	3.95760			0.191298
$429$		−	0.576120i		−	0.0278153i
$430$		0			0
$431$		−	18.4796i		−	0.890130i	−0.895498	−	0.445065i	$-0.853181\pi$
$431$		−	18.4796i		−	0.890130i	0.895498	−	0.445065i	$-0.146819\pi$
$432$	−21.0881			−1.01460
$433$	17.2076			0.826944			0.413472	−	0.910517i	$-0.364316\pi$
$433$	17.2076			0.826944			0.413472	+	0.910517i	$0.364316\pi$
$434$	−1.02860			−0.0493745
$435$		0			0
$436$		−	3.42163i		−	0.163866i
$437$	15.2422			0.729132
$438$		−	21.6411i		−	1.03405i
$439$			32.5745i			1.55470i	0.629071	+	0.777348i	$0.283436\pi$
$439$			32.5745i			1.55470i	−0.629071	+	0.777348i	$0.716564\pi$
$440$		0			0
$441$	16.1029			0.766804
$442$		−	0.435052i		−	0.0206933i
$443$	−32.5059			−1.54440			−0.772200	−	0.635379i	$-0.780844\pi$
$443$	−32.5059			−1.54440			−0.772200	+	0.635379i	$0.780844\pi$
$444$	−3.59375	−	1.09798i	−0.170552	−	0.0521078i
$445$		0			0
$446$		−	3.55169i		−	0.168178i
$447$	−12.6287			−0.597317
$448$	−1.33890			−0.0632573
$449$		−	36.4293i		−	1.71920i	−0.510965	−	0.859601i	$-0.670712\pi$
$449$		−	36.4293i		−	1.71920i	0.510965	−	0.859601i	$-0.329288\pi$
$450$		0			0
$451$	20.0095			0.942211
$452$		−	3.73990i		−	0.175910i
$453$	−11.7779			−0.553374
$454$	−29.7001			−1.39390
$455$		0			0
$456$	8.09238			0.378960
$457$			9.37134i			0.438373i	0.975683	+	0.219186i	$0.0703403\pi$
$457$			9.37134i			0.438373i	−0.975683	+	0.219186i	$0.929660\pi$
$458$			14.6795i			0.685929i
$459$			8.04868i			0.375680i
$460$		0			0
$461$			30.6799i			1.42891i	0.699684	+	0.714453i	$0.253324\pi$
$461$			30.6799i			1.42891i	−0.699684	+	0.714453i	$0.746676\pi$
$462$		−	3.17918i		−	0.147909i
$463$		−	17.1388i		−	0.796508i	−0.917275	−	0.398254i	$-0.869616\pi$
$463$		−	17.1388i		−	0.796508i	0.917275	−	0.398254i	$-0.130384\pi$
$464$		−	41.2351i		−	1.91429i
$465$		0			0
$466$			10.9269i			0.506181i
$467$			1.02961i			0.0476449i	0.999716	+	0.0238224i	$0.00758363\pi$
$467$			1.02961i			0.0476449i	−0.999716	+	0.0238224i	$0.992416\pi$
$468$			0.255114i			0.0117926i
$469$	2.56389			0.118389
$470$		0			0
$471$	1.83419			0.0845148
$472$	3.70872			0.170708
$473$			44.0554i			2.02567i
$474$	−11.6096			−0.533248
$475$		0			0
$476$		−	0.673002i		−	0.0308470i
$477$	17.2831			0.791337
$478$	44.9616			2.05649
$479$			16.2375i			0.741910i	0.928651	+	0.370955i	$0.120970\pi$
$479$			16.2375i			0.741910i	−0.928651	+	0.370955i	$0.879030\pi$
$480$		0			0
$481$	0.245450	−	0.803373i	0.0111916	−	0.0366307i
$482$	−47.2551			−2.15241
$483$			1.10198i			0.0501420i
$484$	−12.9926			−0.590572
$485$		0			0
$486$		−	26.2398i		−	1.19026i
$487$		−	36.6422i		−	1.66042i	−0.557453	−	0.830209i	$-0.688221\pi$
$487$		−	36.6422i		−	1.66042i	0.557453	−	0.830209i	$-0.311779\pi$
$488$	−22.4340			−1.01554
$489$		−	1.79985i		−	0.0813918i
$490$		0			0
$491$	−14.8738			−0.671244			−0.335622	−	0.941997i	$-0.608947\pi$
$491$	−14.8738			−0.671244			−0.335622	+	0.941997i	$0.608947\pi$
$492$	2.34964			0.105930
$493$	−15.7382			−0.708814
$494$		−	1.15431i		−	0.0519346i
$495$		0			0
$496$		−	6.68281i		−	0.300067i
$497$	−2.89972			−0.130070
$498$		−	8.10406i		−	0.363151i
$499$		−	26.4807i		−	1.18544i	−0.805409	−	0.592719i	$-0.798054\pi$
$499$		−	26.4807i		−	1.18544i	0.805409	−	0.592719i	$-0.201946\pi$
$500$		0			0
$501$			1.84397i			0.0823824i
$502$	25.9286			1.15725
$503$			17.6990i			0.789158i	0.918862	+	0.394579i	$0.129110\pi$
$503$			17.6990i			0.789158i	−0.918862	+	0.394579i	$0.870890\pi$
$504$		−	2.20628i		−	0.0982756i
$505$		0			0
$506$	26.6613			1.18524
$507$	−10.2935			−0.457149
$508$	−13.0159			−0.577488
$509$	2.24594			0.0995497			0.0497748	−	0.998760i	$-0.484150\pi$
$509$	2.24594			0.0995497			0.0497748	+	0.998760i	$0.484150\pi$
$510$		0			0
$511$	7.48383			0.331065
$512$			0.556460i			0.0245923i
$513$			21.3552i			0.942856i
$514$	1.97971			0.0873211
$515$		0			0
$516$			5.17325i			0.227739i
$517$	−26.9640			−1.18588
$518$	1.35446	−	4.43322i	0.0595115	−	0.194785i
$519$	−13.0010			−0.570680
$520$		0			0
$521$	−2.22293			−0.0973883			−0.0486941	−	0.998814i	$-0.515506\pi$
$521$	−2.22293			−0.0973883			−0.0486941	+	0.998814i	$0.515506\pi$
$522$	32.9212			1.44092
$523$		−	40.2668i		−	1.76074i	−0.474284	−	0.880372i	$-0.657293\pi$
$523$		−	40.2668i		−	1.76074i	0.474284	−	0.880372i	$-0.342707\pi$
$524$			7.69637i			0.336218i
$525$		0			0
$526$		−	39.9230i		−	1.74073i
$527$	−2.55063			−0.111107
$528$	20.6551			0.898897
$529$	13.7585			0.598197
$530$		0			0
$531$			4.32065i			0.187500i
$532$		−	1.78565i		−	0.0774175i
$533$			0.525255i			0.0227513i
$534$	−16.5483			−0.716115
$535$		0			0
$536$			11.4155i			0.493074i
$537$			7.30515i			0.315241i
$538$			28.4322i			1.22580i
$539$	−35.7270			−1.53887
$540$		0			0
$541$		−	6.76907i		−	0.291025i	−0.989356	−	0.145513i	$-0.953517\pi$
$541$		−	6.76907i		−	0.291025i	0.989356	−	0.145513i	$-0.0464831\pi$
$542$		−	23.8511i		−	1.02449i
$543$	0.980739			0.0420875
$544$	7.90495			0.338922
$545$		0			0
$546$	0.0834543			0.00357151
$547$			43.0574i			1.84100i	0.390742	+	0.920500i	$0.372219\pi$
$547$			43.0574i			1.84100i	−0.390742	+	0.920500i	$0.627781\pi$
$548$	−2.33269			−0.0996474
$549$		−	26.1355i		−	1.11544i
$550$		0			0
$551$	−41.7575			−1.77893
$552$	−4.90648			−0.208834
$553$		−	4.01478i		−	0.170726i
$554$	24.0653			1.02244
$555$		0			0
$556$	7.52043			0.318937
$557$			23.3255i			0.988333i	0.869367	+	0.494167i	$0.164527\pi$
$557$			23.3255i			0.988333i	−0.869367	+	0.494167i	$0.835473\pi$
$558$	5.33540			0.225866
$559$	−1.15646			−0.0489132
$560$		0			0
$561$		−	7.88343i		−	0.332839i
$562$	51.8074			2.18536
$563$			23.3263i			0.983088i	0.870853	+	0.491544i	$0.163567\pi$
$563$			23.3263i			0.983088i	−0.870853	+	0.491544i	$0.836433\pi$
$564$	−3.16628			−0.133324
$565$		0			0
$566$	−35.8836			−1.50830
$567$	1.70796			0.0717277
$568$		−	12.9107i		−	0.541723i
$569$			24.2148i			1.01514i	0.861611	+	0.507570i	$0.169456\pi$
$569$			24.2148i			1.01514i	−0.861611	+	0.507570i	$0.830544\pi$
$570$		0			0
$571$	40.9431			1.71342			0.856708	−	0.515802i	$-0.172506\pi$
$571$	40.9431			1.71342			0.856708	+	0.515802i	$0.172506\pi$
$572$		−	0.566014i		−	0.0236662i
$573$		−	8.91979i		−	0.372630i
$574$			2.89849i			0.120981i
$575$		0			0
$576$	6.94495			0.289373
$577$			18.5609i			0.772702i	0.922352	+	0.386351i	$0.126265\pi$
$577$			18.5609i			0.772702i	−0.922352	+	0.386351i	$0.873735\pi$
$578$			22.3868i			0.931166i
$579$			5.70635i			0.237148i
$580$		0			0
$581$	2.80251			0.116267
$582$	−13.1909			−0.546782
$583$	−38.3455			−1.58811
$584$			33.3211i			1.37884i
$585$		0			0
$586$			32.6856i			1.35023i
$587$			13.3626i			0.551532i	0.961225	+	0.275766i	$0.0889315\pi$
$587$			13.3626i			0.551532i	−0.961225	+	0.275766i	$0.911069\pi$
$588$	−4.19528			−0.173011
$589$	−6.76747			−0.278849
$590$		0			0
$591$	−8.92225			−0.367012
$592$	28.8026	+	8.79989i	1.18378	+	0.361673i
$593$	31.4142			1.29003			0.645014	−	0.764171i	$-0.276852\pi$
$593$	31.4142			1.29003			0.645014	+	0.764171i	$0.276852\pi$
$594$			37.3541i			1.53266i
$595$		0			0
$596$	−12.4072			−0.508218
$597$		−	12.8419i		−	0.525585i
$598$			0.699866i			0.0286196i
$599$	−10.2378			−0.418303			−0.209152	−	0.977883i	$-0.567070\pi$
$599$	−10.2378			−0.418303			−0.209152	+	0.977883i	$0.567070\pi$
$600$		0			0
$601$	−43.6048			−1.77868			−0.889339	−	0.457249i	$-0.848835\pi$
$601$	−43.6048			−1.77868			−0.889339	+	0.457249i	$0.848835\pi$
$602$	−6.38168			−0.260098
$603$	−13.2990			−0.541577
$604$	−11.5713			−0.470829
$605$		0			0
$606$			10.3237i			0.419371i
$607$			2.73875i			0.111162i	0.998454	+	0.0555811i	$0.0177011\pi$
$607$			2.73875i			0.111162i	−0.998454	+	0.0555811i	$0.982299\pi$
$608$	20.9739			0.850602
$609$		−	3.01900i		−	0.122336i
$610$		0			0
$611$		−	0.707812i		−	0.0286350i
$612$			3.49089i			0.141111i
$613$	12.8562			0.519257			0.259628	−	0.965709i	$-0.416400\pi$
$613$	12.8562			0.519257			0.259628	+	0.965709i	$0.416400\pi$
$614$			37.9490i			1.53150i
$615$		0			0
$616$			4.89502i			0.197226i
$617$	−33.6136			−1.35323			−0.676616	−	0.736336i	$-0.736554\pi$
$617$	−33.6136			−1.35323			−0.676616	+	0.736336i	$0.736554\pi$
$618$	20.6878			0.832187
$619$	−15.7485			−0.632984			−0.316492	−	0.948595i	$-0.602505\pi$
$619$	−15.7485			−0.632984			−0.316492	+	0.948595i	$0.602505\pi$
$620$		0			0
$621$		−	12.9479i		−	0.519580i
$622$	−21.9961			−0.881961
$623$		−	5.72265i		−	0.229273i
$624$			0.542201i			0.0217054i
$625$		0			0
$626$	53.2070			2.12658
$627$		−	20.9168i		−	0.835335i
$628$	1.80201			0.0719080
$629$	3.35866	−	10.9931i	0.133918	−	0.438323i
$630$		0			0
$631$		−	17.5933i		−	0.700377i	−0.936679	−	0.350188i	$-0.886118\pi$
$631$		−	17.5933i		−	0.700377i	0.936679	−	0.350188i	$-0.113882\pi$
$632$	17.8755			0.711048
$633$	−7.79637			−0.309878
$634$		−	38.7429i		−	1.53868i
$635$		0			0
$636$	−4.50276			−0.178546
$637$		−	0.937844i		−	0.0371587i
$638$	−73.0414			−2.89174
$639$	15.0410			0.595012
$640$		0			0
$641$	12.2855			0.485249			0.242625	−	0.970120i	$-0.421992\pi$
$641$	12.2855			0.485249			0.242625	+	0.970120i	$0.421992\pi$
$642$			6.71532i			0.265033i
$643$			27.1945i			1.07245i	0.844076	+	0.536224i	$0.180150\pi$
$643$			27.1945i			1.07245i	−0.844076	+	0.536224i	$0.819850\pi$
$644$			1.08265i			0.0426625i
$645$		0			0
$646$		−	15.7951i		−	0.621451i
$647$			28.9910i			1.13976i	0.821730	+	0.569878i	$0.193009\pi$
$647$			28.9910i			1.13976i	−0.821730	+	0.569878i	$0.806991\pi$
$648$			7.60455i			0.298735i
$649$		−	9.58611i		−	0.376288i
$650$		0			0
$651$		−	0.489277i		−	0.0191763i
$652$		−	1.76827i		−	0.0692509i
$653$		−	9.88689i		−	0.386904i	−0.981110	−	0.193452i	$-0.938032\pi$
$653$		−	9.88689i		−	0.386904i	0.981110	−	0.193452i	$-0.0619684\pi$
$654$	5.80587			0.227027
$655$		0			0
$656$	−18.8315			−0.735245
$657$	−38.8189			−1.51447
$658$		−	3.90589i		−	0.152268i
$659$	21.9914			0.856664			0.428332	−	0.903621i	$-0.359101\pi$
$659$	21.9914			0.856664			0.428332	+	0.903621i	$0.359101\pi$
$660$		0			0
$661$		−	20.2762i		−	0.788653i	−0.918970	−	0.394326i	$-0.870978\pi$
$661$		−	20.2762i		−	0.788653i	0.918970	−	0.394326i	$-0.129022\pi$
$662$	16.0080			0.622168
$663$	0.206942			0.00803696
$664$			12.4779i			0.484236i
$665$		0			0
$666$	−7.02563	+	22.9953i	−0.272238	+	0.891050i
$667$	25.3180			0.980316
$668$			1.81162i			0.0700937i
$669$	1.68944			0.0653175
$670$		0			0
$671$			57.9862i			2.23853i
$672$			1.51637i			0.0584954i
$673$	−31.0399			−1.19650			−0.598251	−	0.801309i	$-0.704137\pi$
$673$	−31.0399			−1.19650			−0.598251	+	0.801309i	$0.704137\pi$
$674$			19.3509i			0.745369i
$675$		0			0
$676$	−10.1129			−0.388958
$677$	32.5996			1.25291			0.626453	−	0.779459i	$-0.284506\pi$
$677$	32.5996			1.25291			0.626453	+	0.779459i	$0.284506\pi$
$678$	6.34593			0.243714
$679$		−	4.56162i		−	0.175059i
$680$		0			0
$681$		−	14.1275i		−	0.541367i
$682$	−11.8375			−0.453282
$683$		−	8.66313i		−	0.331485i	−0.986169	−	0.165743i	$-0.946998\pi$
$683$		−	8.66313i		−	0.331485i	0.986169	−	0.165743i	$-0.0530021\pi$
$684$			9.26222i			0.354150i
$685$		0			0
$686$		−	10.5098i		−	0.401266i
$687$	−6.98263			−0.266404
$688$		−	41.4616i		−	1.58071i
$689$		−	1.00658i		−	0.0383476i
$690$		0			0
$691$	21.5237			0.818801			0.409400	−	0.912355i	$-0.365738\pi$
$691$	21.5237			0.818801			0.409400	+	0.912355i	$0.365738\pi$
$692$	−12.7729			−0.485553
$693$	−5.70268			−0.216627
$694$	40.7351			1.54628
$695$		0			0
$696$	13.4418			0.509511
$697$			7.18741i			0.272242i
$698$			15.7964i			0.597903i
$699$	−5.19764			−0.196593
$700$		0			0
$701$			8.50098i			0.321078i	0.987030	+	0.160539i	$0.0513232\pi$
$701$			8.50098i			0.321078i	−0.987030	+	0.160539i	$0.948677\pi$
$702$	−0.980554			−0.0370086
$703$	8.91138	−	29.1675i	0.336099	−	1.10007i
$704$	−15.4086			−0.580733
$705$		0			0
$706$	35.5746			1.33887
$707$	−3.57009			−0.134267
$708$		−	1.12566i		−	0.0423048i
$709$			47.5830i			1.78702i	0.449047	+	0.893508i	$0.351764\pi$
$709$			47.5830i			1.78702i	−0.449047	+	0.893508i	$0.648236\pi$
$710$		0			0
$711$			20.8248i			0.780993i
$712$	25.4796			0.954887
$713$	4.10318			0.153665
$714$	1.14196			0.0427368
$715$		0			0
$716$			7.17700i			0.268217i
$717$			21.3869i			0.798710i
$718$		−	31.5868i		−	1.17881i
$719$	51.2046			1.90961			0.954805	−	0.297232i	$-0.0960636\pi$
$719$	51.2046			1.90961			0.954805	+	0.297232i	$0.0960636\pi$
$720$		0			0
$721$			7.15416i			0.266435i
$722$		−	10.2345i		−	0.380889i
$723$		−	22.4779i		−	0.835962i
$724$	0.963535			0.0358095
$725$		0			0
$726$		−	22.0460i		−	0.818205i
$727$			23.8580i			0.884844i	0.896807	+	0.442422i	$0.145881\pi$
$727$			23.8580i			0.884844i	−0.896807	+	0.442422i	$0.854119\pi$
$728$	−0.128495			−0.00476236
$729$	1.27295			0.0471462
$730$		0			0
$731$	−15.8247			−0.585296
$732$			6.80908i			0.251671i
$733$	−26.6577			−0.984626			−0.492313	−	0.870418i	$-0.663848\pi$
$733$	−26.6577			−0.984626			−0.492313	+	0.870418i	$0.663848\pi$
$734$		−	34.5249i		−	1.27434i
$735$		0			0
$736$	−12.7166			−0.468741
$737$	29.5061			1.08687
$738$		−	15.0346i		−	0.553431i
$739$	−8.24275			−0.303214			−0.151607	−	0.988441i	$-0.548445\pi$
$739$	−8.24275			−0.303214			−0.151607	+	0.988441i	$0.548445\pi$
$740$		0			0
$741$	0.549070			0.0201706
$742$		−	5.55457i		−	0.203915i
$743$	33.2722			1.22064			0.610319	−	0.792155i	$-0.291041\pi$
$743$	33.2722			1.22064			0.610319	+	0.792155i	$0.291041\pi$
$744$	2.17846			0.0798662
$745$		0			0
$746$		−	4.56427i		−	0.167110i
$747$	−14.5367			−0.531870
$748$		−	7.74514i		−	0.283190i
$749$	−2.32226			−0.0848536
$750$		0			0
$751$	−30.0582			−1.09684			−0.548421	−	0.836203i	$-0.684771\pi$
$751$	−30.0582			−1.09684			−0.548421	+	0.836203i	$0.684771\pi$
$752$	25.3765			0.925386
$753$			12.3335i			0.449458i
$754$		−	1.91735i		−	0.0698259i
$755$		0			0
$756$	−1.51686			−0.0551677
$757$			35.3038i			1.28314i	0.767066	+	0.641568i	$0.221716\pi$
$757$			35.3038i			1.28314i	−0.767066	+	0.641568i	$0.778284\pi$
$758$		−	60.5299i		−	2.19855i
$759$			12.6820i			0.460328i
$760$		0			0
$761$	−46.3252			−1.67929			−0.839644	−	0.543137i	$-0.817236\pi$
$761$	−46.3252			−1.67929			−0.839644	+	0.543137i	$0.817236\pi$
$762$		−	22.0856i		−	0.800078i
$763$			2.00776i			0.0726857i
$764$		−	8.76332i		−	0.317046i
$765$		0			0
$766$	55.0479			1.98896
$767$	0.251638			0.00908611
$768$	−12.8689			−0.464366
$769$			40.2977i			1.45317i	0.687075	+	0.726586i	$0.258894\pi$
$769$			40.2977i			1.45317i	−0.687075	+	0.726586i	$0.741106\pi$
$770$		0			0
$771$			0.941690i			0.0339141i
$772$			5.60625i			0.201773i
$773$	47.2815			1.70060			0.850299	−	0.526301i	$-0.176421\pi$
$773$	47.2815			1.70060			0.850299	+	0.526301i	$0.176421\pi$
$774$	33.1020			1.18983
$775$		0			0
$776$	20.3102			0.729094
$777$	2.10876	+	0.644277i	0.0756513	+	0.0231133i
$778$	37.2064			1.33391
$779$			19.0700i			0.683255i
$780$		0			0
$781$	−33.3710			−1.19411
$782$			9.57672i			0.342463i
$783$			35.4720i			1.26767i
$784$	33.6236			1.20084
$785$		0			0
$786$	−13.0593			−0.465811
$787$	8.68346			0.309532			0.154766	−	0.987951i	$-0.450538\pi$
$787$	8.68346			0.309532			0.154766	+	0.987951i	$0.450538\pi$
$788$	−8.76574			−0.312266
$789$	18.9902			0.676070
$790$		0			0
$791$			2.19452i			0.0780281i
$792$		−	25.3907i		−	0.902218i
$793$	−1.52215			−0.0540532
$794$			2.43036i			0.0862502i
$795$		0			0
$796$		−	12.6166i		−	0.447185i
$797$		−	52.3316i		−	1.85368i	−0.375456	−	0.926840i	$-0.622514\pi$
$797$		−	52.3316i		−	1.85368i	0.375456	−	0.926840i	$-0.377486\pi$
$798$	3.02991			0.107258
$799$		−	9.68546i		−	0.342647i
$800$		0			0
$801$			29.6836i			1.04882i
$802$	18.4406			0.651162
$803$	86.1266			3.03934
$804$	3.46479			0.122194
$805$		0			0
$806$		−	0.310738i		−	0.0109453i
$807$	−13.5244			−0.476081
$808$		−	15.8955i		−	0.559202i
$809$			9.14324i			0.321459i	0.986998	+	0.160730i	$0.0513847\pi$
$809$			9.14324i			0.321459i	−0.986998	+	0.160730i	$0.948615\pi$
$810$		0			0
$811$	33.5344			1.17755			0.588776	−	0.808296i	$-0.299610\pi$
$811$	33.5344			1.17755			0.588776	+	0.808296i	$0.299610\pi$
$812$		−	2.96604i		−	0.104088i
$813$	11.3453			0.397896
$814$	15.5876	−	51.0191i	0.546345	−	1.78822i
$815$		0			0
$816$			7.41929i			0.259727i
$817$	−41.9869			−1.46894
$818$	−6.36483			−0.222541
$819$		−	0.149697i		−	0.00523083i
$820$		0			0
$821$	−16.2272			−0.566332			−0.283166	−	0.959071i	$-0.591385\pi$
$821$	−16.2272			−0.566332			−0.283166	+	0.959071i	$0.591385\pi$
$822$		−	3.95814i		−	0.138056i
$823$	−9.20787			−0.320966			−0.160483	−	0.987039i	$-0.551305\pi$
$823$	−9.20787			−0.320966			−0.160483	+	0.987039i	$0.551305\pi$
$824$	−31.8533			−1.10966
$825$		0			0
$826$	1.38860			0.0483157
$827$		−	36.0594i		−	1.25391i	−0.779056	−	0.626954i	$-0.784301\pi$
$827$		−	36.0594i		−	1.25391i	0.779056	−	0.626954i	$-0.215699\pi$
$828$		−	5.61576i		−	0.195161i
$829$		−	44.6192i		−	1.54969i	−0.632152	−	0.774845i	$-0.717828\pi$
$829$		−	44.6192i		−	1.54969i	0.632152	−	0.774845i	$-0.282172\pi$
$830$		0			0
$831$			11.4472i			0.397099i
$832$		−	0.404479i		−	0.0140228i
$833$		−	12.8331i		−	0.444642i
$834$			12.7608i			0.441870i
$835$		0			0
$836$		−	20.5498i		−	0.710731i
$837$			5.74880i			0.198708i
$838$			29.6796i			1.02527i
$839$	19.9712			0.689482			0.344741	−	0.938698i	$-0.387967\pi$
$839$	19.9712			0.689482			0.344741	+	0.938698i	$0.387967\pi$
$840$		0			0
$841$	−40.3612			−1.39177
$842$	17.7040			0.610122
$843$			24.6433i			0.848760i
$844$	−7.65961			−0.263655
$845$		0			0
$846$			20.2600i			0.696554i
$847$	7.62385			0.261958
$848$	36.0879			1.23926
$849$		−	17.0688i		−	0.585800i
$850$		0			0
$851$	−5.40305	+	17.6845i	−0.185214	+	0.606217i
$852$	−3.91862			−0.134250
$853$			43.5931i			1.49260i	0.665609	+	0.746300i	$0.268172\pi$
$853$			43.5931i			1.49260i	−0.665609	+	0.746300i	$0.731828\pi$
$854$	−8.39963			−0.287429
$855$		0			0
$856$		−	10.3397i		−	0.353402i
$857$			24.4715i			0.835932i	0.908463	+	0.417966i	$0.137257\pi$
$857$			24.4715i			0.835932i	−0.908463	+	0.417966i	$0.862743\pi$
$858$	0.960421			0.0327882
$859$			10.0825i			0.344009i	0.985096	+	0.172005i	$0.0550244\pi$
$859$			10.0825i			0.344009i	−0.985096	+	0.172005i	$0.944976\pi$
$860$		0			0
$861$	−1.37873			−0.0469870
$862$	30.8064			1.04927
$863$	−39.8556			−1.35670			−0.678349	−	0.734739i	$-0.737304\pi$
$863$	−39.8556			−1.35670			−0.678349	+	0.734739i	$0.737304\pi$
$864$		−	17.8168i		−	0.606139i
$865$		0			0
$866$			28.6859i			0.974787i
$867$	−10.6487			−0.361650
$868$		−	0.480694i		−	0.0163158i
$869$		−	46.2035i		−	1.56735i
$870$		0			0
$871$			0.774544i			0.0262444i
$872$	−8.93936			−0.302725
$873$			23.6613i			0.800814i
$874$			25.4095i			0.859489i
$875$		0			0
$876$	10.1135			0.341703
$877$	13.9320			0.470450			0.235225	−	0.971941i	$-0.424417\pi$
$877$	13.9320			0.470450			0.235225	+	0.971941i	$0.424417\pi$
$878$	−54.3033			−1.83265
$879$	−15.5476			−0.524408
$880$		0			0
$881$	−27.1930			−0.916155			−0.458077	−	0.888912i	$-0.651462\pi$
$881$	−27.1930			−0.916155			−0.458077	+	0.888912i	$0.651462\pi$
$882$			26.8443i			0.903895i
$883$			26.8384i			0.903185i	0.892224	+	0.451592i	$0.149144\pi$
$883$			26.8384i			0.903185i	−0.892224	+	0.451592i	$0.850856\pi$
$884$	0.203312			0.00683812
$885$		0			0
$886$		−	54.1889i		−	1.82051i
$887$	−24.3451			−0.817430			−0.408715	−	0.912662i	$-0.634023\pi$
$887$	−24.3451			−0.817430			−0.408715	+	0.912662i	$0.634023\pi$
$888$	−2.86859	+	9.38906i	−0.0962635	+	0.315076i
$889$	7.63754			0.256155
$890$		0			0
$891$	19.6558			0.658495
$892$	1.65980			0.0555743
$893$		−	25.6980i		−	0.859951i
$894$		−	21.0527i		−	0.704107i
$895$		0			0
$896$		−	6.05657i		−	0.202336i
$897$	−0.332906			−0.0111154
$898$	60.7294			2.02657
$899$	−11.2411			−0.374911
$900$		0			0
$901$		−	13.7737i		−	0.458868i
$902$			33.3569i			1.11066i
$903$		−	3.03558i		−	0.101018i
$904$	−9.77089			−0.324975
$905$		0			0
$906$		−	19.6344i		−	0.652308i
$907$			9.65604i			0.320624i	0.987066	+	0.160312i	$0.0512500\pi$
$907$			9.65604i			0.320624i	−0.987066	+	0.160312i	$0.948750\pi$
$908$		−	13.8797i		−	0.460613i
$909$	18.5182			0.614210
$910$		0			0
$911$			21.9698i			0.727892i	0.931420	+	0.363946i	$0.118571\pi$
$911$			21.9698i			0.727892i	−0.931420	+	0.363946i	$0.881429\pi$
$912$			19.6853i			0.651845i
$913$	32.2522			1.06739
$914$	−15.6225			−0.516747
$915$		0			0
$916$	−6.86014			−0.226665
$917$		−	4.51611i		−	0.149135i
$918$	−13.4176			−0.442846
$919$		−	37.3495i		−	1.23205i	−0.787728	−	0.616023i	$-0.788743\pi$
$919$		−	37.3495i		−	1.23205i	0.787728	−	0.616023i	$-0.211257\pi$
$920$		0			0
$921$	−18.0513			−0.594810
$922$	−51.1449			−1.68437
$923$		−	0.875997i		−	0.0288338i
$924$	1.48572			0.0488765
$925$		0			0
$926$	28.5713			0.938910
$927$		−	37.1089i		−	1.21882i
$928$	34.8385			1.14363
$929$	45.8488			1.50425			0.752125	−	0.659021i	$-0.229029\pi$
$929$	45.8488			1.50425			0.752125	+	0.659021i	$0.229029\pi$
$930$		0			0
$931$		−	34.0496i		−	1.11593i
$932$	−5.10646			−0.167268
$933$		−	10.4629i		−	0.342540i
$934$	−1.71642			−0.0561629
$935$		0			0
$936$	0.666511			0.0217856
$937$	−38.6792			−1.26359			−0.631797	−	0.775134i	$-0.717682\pi$
$937$	−38.6792			−1.26359			−0.631797	+	0.775134i	$0.717682\pi$
$938$			4.27413i			0.139555i
$939$			25.3090i			0.825929i
$940$		0			0
$941$	12.7148			0.414490			0.207245	−	0.978289i	$-0.433550\pi$
$941$	12.7148			0.414490			0.207245	+	0.978289i	$0.433550\pi$
$942$			3.05768i			0.0996246i
$943$		−	11.5623i		−	0.376521i
$944$			9.02173i			0.293632i
$945$		0			0
$946$	−73.4425			−2.38782
$947$			26.7650i			0.869746i	0.900492	+	0.434873i	$0.143207\pi$
$947$			26.7650i			0.869746i	−0.900492	+	0.434873i	$0.856793\pi$
$948$		−	5.42550i		−	0.176212i
$949$			2.26084i			0.0733901i
$950$		0			0
$951$	18.4289			0.597597
$952$	−1.75829			−0.0569864
$953$	25.1648			0.815167			0.407584	−	0.913168i	$-0.366371\pi$
$953$	25.1648			0.815167			0.407584	+	0.913168i	$0.366371\pi$
$954$			28.8118i			0.932815i
$955$		0			0
$956$			21.0118i			0.679569i
$957$		−	34.7437i		−	1.12310i
$958$	−27.0687			−0.874551
$959$	1.36878			0.0442003
$960$		0			0
$961$	29.1782			0.941232
$962$	1.33926	+	0.409178i	0.0431796	+	0.0131924i
$963$	12.0457			0.388166
$964$		−	22.0836i		−	0.711264i
$965$		0			0
$966$	−1.83706			−0.0591065
$967$		−	4.54109i		−	0.146032i	−0.997331	−	0.0730158i	$-0.976738\pi$
$967$		−	4.54109i		−	0.146032i	0.997331	−	0.0730158i	$-0.0232624\pi$
$968$			33.9445i			1.09102i
$969$	7.51329			0.241362
$970$		0			0
$971$	2.99500			0.0961141			0.0480571	−	0.998845i	$-0.484697\pi$
$971$	2.99500			0.0961141			0.0480571	+	0.998845i	$0.484697\pi$
$972$	12.2626			0.393323
$973$	−4.41287			−0.141470
$974$	61.0844			1.95727
$975$		0			0
$976$		−	54.5722i		−	1.74681i
$977$		−	56.8670i		−	1.81934i	−0.415336	−	0.909668i	$-0.636336\pi$
$977$		−	56.8670i		−	1.81934i	0.415336	−	0.909668i	$-0.363664\pi$
$978$	3.00043			0.0959433
$979$		−	65.8582i		−	2.10484i
$980$		0			0
$981$		−	10.4143i		−	0.332504i
$982$		−	24.7954i		−	0.791251i
$983$	−23.8530			−0.760791			−0.380396	−	0.924824i	$-0.624212\pi$
$983$	−23.8530			−0.760791			−0.380396	+	0.924824i	$0.624212\pi$
$984$		−	6.13867i		−	0.195694i
$985$		0			0
$986$		−	26.2364i		−	0.835538i
$987$	1.85792			0.0591383
$988$	0.539438			0.0171618
$989$	25.4570			0.809486
$990$		0			0
$991$			13.6197i			0.432645i	0.976322	+	0.216323i	$0.0694063\pi$
$991$			13.6197i			0.432645i	−0.976322	+	0.216323i	$0.930594\pi$
$992$	5.64614			0.179265
$993$			7.61455i			0.241640i
$994$		−	4.83398i		−	0.153325i
$995$		0			0
$996$	3.78725			0.120004
$997$			19.9740i			0.632584i	0.948662	+	0.316292i	$0.102438\pi$
$997$			19.9740i			0.632584i	−0.948662	+	0.316292i	$0.897562\pi$
$998$	44.1447			1.39737
$999$	−24.7770	−	7.57000i	−0.783911	−	0.239504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.c.c.776.10		12
5.2	odd	4		925.2.d.e.924.4		12
5.3	odd	4		925.2.d.f.924.9		12
5.4	even	2		185.2.c.b.36.3	✓	12
15.14	odd	2		1665.2.e.e.406.10		12
20.19	odd	2		2960.2.p.h.961.5		12
37.36	even	2	inner	925.2.c.c.776.3		12
185.73	odd	4		925.2.d.e.924.3		12
185.147	odd	4		925.2.d.f.924.10		12
185.154	odd	4		6845.2.a.h.1.2		6
185.179	odd	4		6845.2.a.i.1.5		6
185.184	even	2		185.2.c.b.36.10	yes	12
555.554	odd	2		1665.2.e.e.406.3		12
740.739	odd	2		2960.2.p.h.961.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.3	✓	12	5.4	even	2
185.2.c.b.36.10	yes	12	185.184	even	2
925.2.c.c.776.3		12	37.36	even	2	inner
925.2.c.c.776.10		12	1.1	even	1	trivial
925.2.d.e.924.3		12	185.73	odd	4
925.2.d.e.924.4		12	5.2	odd	4
925.2.d.f.924.9		12	5.3	odd	4
925.2.d.f.924.10		12	185.147	odd	4
1665.2.e.e.406.3		12	555.554	odd	2
1665.2.e.e.406.10		12	15.14	odd	2
2960.2.p.h.961.5		12	20.19	odd	2
2960.2.p.h.961.6		12	740.739	odd	2
6845.2.a.h.1.2		6	185.154	odd	4
6845.2.a.i.1.5		6	185.179	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.66705i q^{2} -0.792969 q^{3} -0.779058 q^{4} -1.32192i q^{6} +0.457139 q^{7} +2.03537i q^{8} -2.37120 q^{9} +O(q^{10})\)	\(q+1.66705i q^{2} -0.792969 q^{3} -0.779058 q^{4} -1.32192i q^{6} +0.457139 q^{7} +2.03537i q^{8} -2.37120 q^{9} +5.26092 q^{11} +0.617769 q^{12} +0.138100i q^{13} +0.762075i q^{14} -4.95118 q^{16} +1.88972i q^{17} -3.95291i q^{18} +5.01391i q^{19} -0.362497 q^{21} +8.77022i q^{22} -3.03998i q^{23} -1.61399i q^{24} -0.230221 q^{26} +4.25919 q^{27} -0.356138 q^{28} +8.32834i q^{29} +1.34974i q^{31} -4.18313i q^{32} -4.17174 q^{33} -3.15026 q^{34} +1.84730 q^{36} +(-5.81731 - 1.77733i) q^{37} -8.35844 q^{38} -0.109509i q^{39} +3.80342 q^{41} -0.604301i q^{42} +8.37408i q^{43} -4.09856 q^{44} +5.06780 q^{46} -5.12534 q^{47} +3.92613 q^{48} -6.79102 q^{49} -1.49849i q^{51} -0.107588i q^{52} -7.28874 q^{53} +7.10029i q^{54} +0.930449i q^{56} -3.97587i q^{57} -13.8838 q^{58} -1.82213i q^{59} +11.0221i q^{61} -2.25008 q^{62} -1.08397 q^{63} -2.92887 q^{64} -6.95451i q^{66} +5.60855 q^{67} -1.47220i q^{68} +2.41061i q^{69} -6.34319 q^{71} -4.82628i q^{72} +16.3710 q^{73} +(2.96290 - 9.69775i) q^{74} -3.90613i q^{76} +2.40497 q^{77} +0.182558 q^{78} -8.78240i q^{79} +3.73620 q^{81} +6.34050i q^{82} +6.13053 q^{83} +0.282406 q^{84} -13.9600 q^{86} -6.60411i q^{87} +10.7079i q^{88} -12.5184i q^{89} +0.0631312i q^{91} +2.36832i q^{92} -1.07030i q^{93} -8.54421i q^{94} +3.31709i q^{96} -9.97862i q^{97} -11.3210i q^{98} -12.4747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 18 q^{4} + 18 q^{7} + 22 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 - 18 * q^4 + 18 * q^7 + 22 * q^9	\( 12 q - 2 q^{3} - 18 q^{4} + 18 q^{7} + 22 q^{9} + 2 q^{11} + 36 q^{12} + 30 q^{16} - 6 q^{21} - 12 q^{26} - 26 q^{27} - 24 q^{28} + 18 q^{33} + 4 q^{34} - 22 q^{36} - 10 q^{37} - 12 q^{38} - 10 q^{41} + 44 q^{44} - 24 q^{46} - 2 q^{47} - 60 q^{48} + 30 q^{49} + 6 q^{53} + 24 q^{58} - 44 q^{62} + 16 q^{63} - 126 q^{64} - 16 q^{67} + 42 q^{71} + 46 q^{73} + 50 q^{74} - 30 q^{77} - 132 q^{78} - 12 q^{81} + 62 q^{83} - 84 q^{84} - 64 q^{86} - 84 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 18 * q^4 + 18 * q^7 + 22 * q^9 + 2 * q^11 + 36 * q^12 + 30 * q^16 - 6 * q^21 - 12 * q^26 - 26 * q^27 - 24 * q^28 + 18 * q^33 + 4 * q^34 - 22 * q^36 - 10 * q^37 - 12 * q^38 - 10 * q^41 + 44 * q^44 - 24 * q^46 - 2 * q^47 - 60 * q^48 + 30 * q^49 + 6 * q^53 + 24 * q^58 - 44 * q^62 + 16 * q^63 - 126 * q^64 - 16 * q^67 + 42 * q^71 + 46 * q^73 + 50 * q^74 - 30 * q^77 - 132 * q^78 - 12 * q^81 + 62 * q^83 - 84 * q^84 - 64 * q^86 - 84 * q^99

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