LMFDB - Embedded newform 925.2.c.c.776.8

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			776.8
Root			$1.23687i$ of defining polynomial
Character	$\chi$	$=$	925.776
Dual form			925.2.c.c.776.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.23687i q^{2} +2.43200 q^{3} +0.470165 q^{4} +3.00806i q^{6} +3.53789 q^{7} +3.05526i q^{8} +2.91464 q^{9} +O(q^{10})$	\(q+1.23687i q^{2} +2.43200 q^{3} +0.470165 q^{4} +3.00806i q^{6} +3.53789 q^{7} +3.05526i q^{8} +2.91464 q^{9} -4.65123 q^{11} +1.14344 q^{12} +0.812921i q^{13} +4.37590i q^{14} -2.83862 q^{16} -2.73660i q^{17} +3.60501i q^{18} +3.03816i q^{19} +8.60417 q^{21} -5.75295i q^{22} +8.12140i q^{23} +7.43040i q^{24} -1.00547 q^{26} -0.207606 q^{27} +1.66339 q^{28} -8.69328i q^{29} -6.93173i q^{31} +2.59954i q^{32} -11.3118 q^{33} +3.38480 q^{34} +1.37036 q^{36} +(1.14794 - 5.97346i) q^{37} -3.75780 q^{38} +1.97703i q^{39} +9.49341 q^{41} +10.6422i q^{42} -3.64767i q^{43} -2.18685 q^{44} -10.0451 q^{46} -6.48535 q^{47} -6.90352 q^{48} +5.51669 q^{49} -6.65541i q^{51} +0.382207i q^{52} +6.57491 q^{53} -0.256780i q^{54} +10.8092i q^{56} +7.38882i q^{57} +10.7524 q^{58} +2.79628i q^{59} -9.09068i q^{61} +8.57362 q^{62} +10.3117 q^{63} -8.89251 q^{64} -13.9912i q^{66} +0.863688 q^{67} -1.28665i q^{68} +19.7513i q^{69} -1.16023 q^{71} +8.90497i q^{72} +7.23656 q^{73} +(7.38837 + 1.41984i) q^{74} +1.42844i q^{76} -16.4556 q^{77} -2.44532 q^{78} +2.27116i q^{79} -9.24881 q^{81} +11.7421i q^{82} -8.84553 q^{83} +4.04538 q^{84} +4.51167 q^{86} -21.1421i q^{87} -14.2107i q^{88} -3.58479i q^{89} +2.87603i q^{91} +3.81840i q^{92} -16.8580i q^{93} -8.02151i q^{94} +6.32208i q^{96} -11.9180i q^{97} +6.82341i q^{98} -13.5566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.23687i			0.874596i	0.899317	+	0.437298i	$0.144064\pi$
$2$			1.23687i			0.874596i	−0.899317	+	0.437298i	$0.855936\pi$
$3$	2.43200			1.40412			0.702059	−	0.712119i	$-0.252264\pi$
$3$	2.43200			1.40412			0.702059	+	0.712119i	$0.252264\pi$
$4$	0.470165			0.235082
$5$		0			0
$5$		0			0
$6$			3.00806i			1.22803i
$7$	3.53789			1.33720			0.668599	−	0.743623i	$-0.266894\pi$
$7$	3.53789			1.33720			0.668599	+	0.743623i	$0.266894\pi$
$8$			3.05526i			1.08020i
$9$	2.91464			0.971545
$10$		0			0
$11$	−4.65123			−1.40240			−0.701200	−	0.712965i	$-0.747352\pi$
$11$	−4.65123			−1.40240			−0.701200	+	0.712965i	$0.747352\pi$
$12$	1.14344			0.330083
$13$			0.812921i			0.225464i	0.993625	+	0.112732i	$0.0359601\pi$
$13$			0.812921i			0.225464i	−0.993625	+	0.112732i	$0.964040\pi$
$14$			4.37590i			1.16951i
$15$		0			0
$16$	−2.83862			−0.709654
$17$		−	2.73660i		−	0.663722i	−0.943328	−	0.331861i	$-0.892323\pi$
$17$		−	2.73660i		−	0.663722i	0.943328	−	0.331861i	$-0.107677\pi$
$18$			3.60501i			0.849709i
$19$			3.03816i			0.697002i	0.937308	+	0.348501i	$0.113309\pi$
$19$			3.03816i			0.697002i	−0.937308	+	0.348501i	$0.886691\pi$
$20$		0			0
$21$	8.60417			1.87758
$22$		−	5.75295i		−	1.22653i
$23$			8.12140i			1.69343i	0.532048	+	0.846714i	$0.321423\pi$
$23$			8.12140i			1.69343i	−0.532048	+	0.846714i	$0.678577\pi$
$24$			7.43040i			1.51672i
$25$		0			0
$26$	−1.00547			−0.197190
$27$	−0.207606			−0.0399538
$28$	1.66339			0.314352
$29$		−	8.69328i		−	1.61430i	−0.590346	−	0.807150i	$-0.701009\pi$
$29$		−	8.69328i		−	1.61430i	0.590346	−	0.807150i	$-0.298991\pi$
$30$		0			0
$31$		−	6.93173i		−	1.24498i	−0.782629	−	0.622488i	$-0.786122\pi$
$31$		−	6.93173i		−	1.24498i	0.782629	−	0.622488i	$-0.213878\pi$
$32$			2.59954i			0.459538i
$33$	−11.3118			−1.96913
$34$	3.38480			0.580489
$35$		0			0
$36$	1.37036			0.228393
$37$	1.14794	−	5.97346i	0.188719	−	0.982031i
$37$	1.14794	−	5.97346i	0.188719	−	0.982031i
$38$	−3.75780			−0.609595
$39$			1.97703i			0.316578i
$40$		0			0
$41$	9.49341			1.48262			0.741311	−	0.671162i	$-0.234204\pi$
$41$	9.49341			1.48262			0.741311	+	0.671162i	$0.234204\pi$
$42$			10.6422i			1.64213i
$43$		−	3.64767i		−	0.556264i	−0.960543	−	0.278132i	$-0.910285\pi$
$43$		−	3.64767i		−	0.556264i	0.960543	−	0.278132i	$-0.0897153\pi$
$44$	−2.18685			−0.329679
$45$		0			0
$46$	−10.0451			−1.48107
$47$	−6.48535			−0.945986			−0.472993	−	0.881066i	$-0.656826\pi$
$47$	−6.48535			−0.945986			−0.472993	+	0.881066i	$0.656826\pi$
$48$	−6.90352			−0.996437
$49$	5.51669			0.788099
$50$		0			0
$51$		−	6.65541i		−	0.931944i
$52$			0.382207i			0.0530026i
$53$	6.57491			0.903133			0.451567	−	0.892237i	$-0.350865\pi$
$53$	6.57491			0.903133			0.451567	+	0.892237i	$0.350865\pi$
$54$		−	0.256780i		−	0.0349434i
$55$		0			0
$56$			10.8092i			1.44444i
$57$			7.38882i			0.978673i
$58$	10.7524			1.41186
$59$			2.79628i			0.364044i	0.983294	+	0.182022i	$0.0582642\pi$
$59$			2.79628i			0.364044i	−0.983294	+	0.182022i	$0.941736\pi$
$60$		0			0
$61$		−	9.09068i		−	1.16394i	−0.813209	−	0.581971i	$-0.802282\pi$
$61$		−	9.09068i		−	1.16394i	0.813209	−	0.581971i	$-0.197718\pi$
$62$	8.57362			1.08885
$63$	10.3117			1.29915
$64$	−8.89251			−1.11156
$65$		0			0
$66$		−	13.9912i		−	1.72220i
$67$	0.863688			0.105516			0.0527582	−	0.998607i	$-0.483199\pi$
$67$	0.863688			0.105516			0.0527582	+	0.998607i	$0.483199\pi$
$68$		−	1.28665i		−	0.156029i
$69$			19.7513i			2.37777i
$70$		0			0
$71$	−1.16023			−0.137694			−0.0688471	−	0.997627i	$-0.521932\pi$
$71$	−1.16023			−0.137694			−0.0688471	+	0.997627i	$0.521932\pi$
$72$			8.90497i			1.04946i
$73$	7.23656			0.846975			0.423487	−	0.905902i	$-0.360806\pi$
$73$	7.23656			0.846975			0.423487	+	0.905902i	$0.360806\pi$
$74$	7.38837	+	1.41984i	0.858880	+	0.165053i
$75$		0			0
$76$			1.42844i			0.163853i
$77$	−16.4556			−1.87529
$78$	−2.44532			−0.276877
$79$			2.27116i			0.255525i	0.991805	+	0.127763i	$0.0407796\pi$
$79$			2.27116i			0.255525i	−0.991805	+	0.127763i	$0.959220\pi$
$80$		0			0
$81$	−9.24881			−1.02765
$82$			11.7421i			1.29669i
$83$	−8.84553			−0.970923			−0.485461	−	0.874258i	$-0.661348\pi$
$83$	−8.84553			−0.970923			−0.485461	+	0.874258i	$0.661348\pi$
$84$	4.04538			0.441387
$85$		0			0
$86$	4.51167			0.486506
$87$		−	21.1421i		−	2.26667i
$88$		−	14.2107i		−	1.51487i
$89$		−	3.58479i		−	0.379987i	−0.981785	−	0.189993i	$-0.939153\pi$
$89$		−	3.58479i		−	0.379987i	0.981785	−	0.189993i	$-0.0608467\pi$
$90$		0			0
$91$			2.87603i			0.301490i
$92$			3.81840i			0.398095i
$93$		−	16.8580i		−	1.74809i
$94$		−	8.02151i		−	0.827355i
$95$		0			0
$96$			6.32208i			0.645245i
$97$		−	11.9180i		−	1.21009i	−0.796193	−	0.605043i	$-0.793156\pi$
$97$		−	11.9180i		−	1.21009i	0.796193	−	0.605043i	$-0.206844\pi$
$98$			6.82341i			0.689268i
$99$	−13.5566			−1.36249
$100$		0			0
$101$	−15.9129			−1.58340			−0.791699	−	0.610912i	$-0.790803\pi$
$101$	−15.9129			−1.58340			−0.791699	+	0.610912i	$0.790803\pi$
$102$	8.23184			0.815074
$103$			5.55461i			0.547312i	0.961828	+	0.273656i	$0.0882330\pi$
$103$			5.55461i			0.547312i	−0.961828	+	0.273656i	$0.911767\pi$
$104$	−2.48369			−0.243546
$105$		0			0
$106$			8.13227i			0.789876i
$107$	6.56328			0.634497			0.317248	−	0.948343i	$-0.397241\pi$
$107$	6.56328			0.634497			0.317248	+	0.948343i	$0.397241\pi$
$108$	−0.0976090			−0.00939243
$109$			1.32162i			0.126588i	0.997995	+	0.0632940i	$0.0201606\pi$
$109$			1.32162i			0.126588i	−0.997995	+	0.0632940i	$0.979839\pi$
$110$		0			0
$111$	2.79178	−	14.5275i	0.264984	−	1.37889i
$112$	−10.0427			−0.948948
$113$			17.2264i			1.62053i	0.586065	+	0.810264i	$0.300676\pi$
$113$			17.2264i			1.62053i	−0.586065	+	0.810264i	$0.699324\pi$
$114$	−9.13897			−0.855943
$115$		0			0
$116$		−	4.08727i		−	0.379494i
$117$			2.36937i			0.219048i
$118$	−3.45862			−0.318391
$119$		−	9.68179i		−	0.887528i
$120$		0			0
$121$	10.6340			0.966724
$122$	11.2439			1.01798
$123$	23.0880			2.08178
$124$		−	3.25906i		−	0.292672i
$125$		0			0
$126$			12.7541i			1.13623i
$127$	−9.98928			−0.886406			−0.443203	−	0.896421i	$-0.646158\pi$
$127$	−9.98928			−0.886406			−0.443203	+	0.896421i	$0.646158\pi$
$128$		−	5.79976i		−	0.512631i
$129$		−	8.87114i		−	0.781060i
$130$		0			0
$131$			7.51082i			0.656223i	0.944639	+	0.328112i	$0.106412\pi$
$131$			7.51082i			0.656223i	−0.944639	+	0.328112i	$0.893588\pi$
$132$	−5.31841			−0.462909
$133$			10.7487i			0.932030i
$134$			1.06827i			0.0922841i
$135$		0			0
$136$	8.36102			0.716951
$137$	−13.1670			−1.12493			−0.562467	−	0.826820i	$-0.690148\pi$
$137$	−13.1670			−1.12493			−0.562467	+	0.826820i	$0.690148\pi$
$138$	−24.4296			−2.07959
$139$	−16.1338			−1.36845			−0.684224	−	0.729272i	$-0.739859\pi$
$139$	−16.1338			−1.36845			−0.684224	+	0.729272i	$0.739859\pi$
$140$		0			0
$141$	−15.7724			−1.32828
$142$		−	1.43505i		−	0.120427i
$143$		−	3.78109i		−	0.316190i
$144$	−8.27353			−0.689461
$145$		0			0
$146$			8.95065i			0.740761i
$147$	13.4166			1.10658
$148$	0.539719	−	2.80851i	0.0443646	−	0.230858i
$149$	−10.6008			−0.868450			−0.434225	−	0.900804i	$-0.642978\pi$
$149$	−10.6008			−0.868450			−0.434225	+	0.900804i	$0.642978\pi$
$150$		0			0
$151$	4.48208			0.364747			0.182373	−	0.983229i	$-0.441622\pi$
$151$	4.48208			0.364747			0.182373	+	0.983229i	$0.441622\pi$
$152$	−9.28238			−0.752900
$153$		−	7.97618i		−	0.644836i
$154$		−	20.3533i		−	1.64012i
$155$		0			0
$156$			0.929529i			0.0744218i
$157$	−3.66272			−0.292317			−0.146158	−	0.989261i	$-0.546691\pi$
$157$	−3.66272			−0.292317			−0.146158	+	0.989261i	$0.546691\pi$
$158$	−2.80912			−0.223481
$159$	15.9902			1.26810
$160$		0			0
$161$			28.7326i			2.26445i
$162$		−	11.4395i		−	0.898774i
$163$			5.63155i			0.441097i	0.975376	+	0.220549i	$0.0707847\pi$
$163$			5.63155i			0.441097i	−0.975376	+	0.220549i	$0.929215\pi$
$164$	4.46347			0.348538
$165$		0			0
$166$		−	10.9407i		−	0.849165i
$167$			2.21580i			0.171464i	0.996318	+	0.0857319i	$0.0273229\pi$
$167$			2.21580i			0.171464i	−0.996318	+	0.0857319i	$0.972677\pi$
$168$			26.2880i			2.02816i
$169$	12.3392			0.949166
$170$		0			0
$171$			8.85514i			0.677169i
$172$		−	1.71500i		−	0.130768i
$173$	−7.15889			−0.544280			−0.272140	−	0.962258i	$-0.587731\pi$
$173$	−7.15889			−0.544280			−0.272140	+	0.962258i	$0.587731\pi$
$174$	26.1499			1.98242
$175$		0			0
$176$	13.2031			0.995218
$177$			6.80055i			0.511161i
$178$	4.43390			0.332335
$179$		−	6.96897i		−	0.520885i	−0.965489	−	0.260443i	$-0.916132\pi$
$179$		−	6.96897i		−	0.520885i	0.965489	−	0.260443i	$-0.0838685\pi$
$180$		0			0
$181$	20.0401			1.48957			0.744783	−	0.667307i	$-0.232553\pi$
$181$	20.0401			1.48957			0.744783	+	0.667307i	$0.232553\pi$
$182$	−3.55726			−0.263682
$183$		−	22.1086i		−	1.63431i
$184$	−24.8130			−1.82924
$185$		0			0
$186$	20.8511			1.52887
$187$			12.7285i			0.930804i
$188$	−3.04919			−0.222385
$189$	−0.734488			−0.0534261
$190$		0			0
$191$		−	11.7263i		−	0.848483i	−0.905549	−	0.424242i	$-0.860541\pi$
$191$		−	11.7263i		−	0.848483i	0.905549	−	0.424242i	$-0.139459\pi$
$192$	−21.6266			−1.56077
$193$			20.1235i			1.44852i	0.689528	+	0.724259i	$0.257818\pi$
$193$			20.1235i			1.44852i	−0.689528	+	0.724259i	$0.742182\pi$
$194$	14.7409			1.05834
$195$		0			0
$196$	2.59376			0.185268
$197$	25.7021			1.83120			0.915599	−	0.402093i	$-0.131717\pi$
$197$	25.7021			1.83120			0.915599	+	0.402093i	$0.131717\pi$
$198$		−	16.7677i		−	1.19163i
$199$			17.0365i			1.20768i	0.797104	+	0.603842i	$0.206364\pi$
$199$			17.0365i			1.20768i	−0.797104	+	0.603842i	$0.793636\pi$
$200$		0			0
$201$	2.10049			0.148157
$202$		−	19.6822i		−	1.38483i
$203$		−	30.7559i		−	2.15864i
$204$		−	3.12914i		−	0.219084i
$205$		0			0
$206$	−6.87030			−0.478677
$207$			23.6709i			1.64524i
$208$		−	2.30757i		−	0.160001i
$209$		−	14.1312i		−	0.977476i
$210$		0			0
$211$	1.67107			0.115041			0.0575207	−	0.998344i	$-0.481680\pi$
$211$	1.67107			0.115041			0.0575207	+	0.998344i	$0.481680\pi$
$212$	3.09129			0.212311
$213$	−2.82169			−0.193339
$214$			8.11790i			0.554928i
$215$		0			0
$216$		−	0.634290i		−	0.0431580i
$217$		−	24.5237i		−	1.66478i
$218$	−1.63466			−0.110713
$219$	17.5993			1.18925
$220$		0			0
$221$	2.22464			0.149645
$222$	17.9685	+	3.45306i	1.20597	+	0.231754i
$223$	12.8455			0.860200			0.430100	−	0.902781i	$-0.358478\pi$
$223$	12.8455			0.860200			0.430100	+	0.902781i	$0.358478\pi$
$224$			9.19689i			0.614493i
$225$		0			0
$226$	−21.3068			−1.41731
$227$		−	21.3404i		−	1.41641i	−0.706006	−	0.708206i	$-0.749505\pi$
$227$		−	21.3404i		−	1.41641i	0.706006	−	0.708206i	$-0.250495\pi$
$228$			3.47396i			0.230069i
$229$	20.1887			1.33410			0.667052	−	0.745011i	$-0.267556\pi$
$229$	20.1887			1.33410			0.667052	+	0.745011i	$0.267556\pi$
$230$		0			0
$231$	−40.0200			−2.63312
$232$	26.5602			1.74376
$233$	−14.6861			−0.962121			−0.481061	−	0.876687i	$-0.659748\pi$
$233$	−14.6861			−0.962121			−0.481061	+	0.876687i	$0.659748\pi$
$234$	−2.93059			−0.191579
$235$		0			0
$236$			1.31471i			0.0855804i
$237$			5.52346i			0.358787i
$238$	11.9751			0.776228
$239$			0.182536i			0.0118073i	0.999983	+	0.00590364i	$0.00187920\pi$
$239$			0.182536i			0.0118073i	−0.999983	+	0.00590364i	$0.998121\pi$
$240$		0			0
$241$			2.67973i			0.172616i	0.996268	+	0.0863082i	$0.0275070\pi$
$241$			2.67973i			0.172616i	−0.996268	+	0.0863082i	$0.972493\pi$
$242$			13.1528i			0.845493i
$243$	−21.8703			−1.40298
$244$		−	4.27412i		−	0.273622i
$245$		0			0
$246$			28.5567i			1.82071i
$247$	−2.46979			−0.157149
$248$	21.1783			1.34482
$249$	−21.5123			−1.36329
$250$		0			0
$251$		−	30.1714i		−	1.90440i	−0.305473	−	0.952201i	$-0.598815\pi$
$251$		−	30.1714i		−	1.90440i	0.305473	−	0.952201i	$-0.401185\pi$
$252$	4.84819			0.305407
$253$		−	37.7745i		−	2.37486i
$254$		−	12.3554i		−	0.775246i
$255$		0			0
$256$	−10.6115			−0.663219
$257$		−	8.00807i		−	0.499530i	−0.968307	−	0.249765i	$-0.919647\pi$
$257$		−	8.00807i		−	0.499530i	0.968307	−	0.249765i	$-0.0803533\pi$
$258$	10.9724			0.683112
$259$	4.06127	−	21.1335i	0.252355	−	1.31317i
$260$		0			0
$261$		−	25.3377i		−	1.56837i
$262$	−9.28987			−0.573930
$263$	−24.9112			−1.53609			−0.768044	−	0.640397i	$-0.778770\pi$
$263$	−24.9112			−1.53609			−0.768044	+	0.640397i	$0.778770\pi$
$264$		−	34.5605i		−	2.12705i
$265$		0			0
$266$	−13.2947			−0.815150
$267$		−	8.71821i		−	0.533546i
$268$	0.406076			0.0248050
$269$	−16.0552			−0.978902			−0.489451	−	0.872031i	$-0.662803\pi$
$269$	−16.0552			−0.978902			−0.489451	+	0.872031i	$0.662803\pi$
$270$		0			0
$271$	8.77834			0.533246			0.266623	−	0.963801i	$-0.414092\pi$
$271$	8.77834			0.533246			0.266623	+	0.963801i	$0.414092\pi$
$272$			7.76814i			0.471013i
$273$			6.99451i			0.423327i
$274$		−	16.2858i		−	0.983862i
$275$		0			0
$276$			9.28635i			0.558972i
$277$			24.4345i			1.46813i	0.679081	+	0.734064i	$0.262379\pi$
$277$			24.4345i			1.46813i	−0.679081	+	0.734064i	$0.737621\pi$
$278$		−	19.9553i		−	1.19684i
$279$		−	20.2035i		−	1.20955i
$280$		0			0
$281$			25.9947i			1.55071i	0.631524	+	0.775356i	$0.282430\pi$
$281$			25.9947i			1.55071i	−0.631524	+	0.775356i	$0.717570\pi$
$282$		−	19.5083i		−	1.16170i
$283$		−	11.3564i		−	0.675066i	−0.941314	−	0.337533i	$-0.890407\pi$
$283$		−	11.3564i		−	0.675066i	0.941314	−	0.337533i	$-0.109593\pi$
$284$	−0.545501			−0.0323695
$285$		0			0
$286$	4.67669			0.276539
$287$	33.5867			1.98256
$288$			7.57670i			0.446462i
$289$	9.51104			0.559473
$290$		0			0
$291$		−	28.9845i		−	1.69910i
$292$	3.40237			0.199109
$293$	30.9868			1.81027			0.905135	−	0.425125i	$-0.139770\pi$
$293$	30.9868			1.81027			0.905135	+	0.425125i	$0.139770\pi$
$294$			16.5945i			0.967813i
$295$		0			0
$296$	18.2505	+	3.50724i	1.06079	+	0.203854i
$297$	0.965623			0.0560311
$298$		−	13.1117i		−	0.759543i
$299$	−6.60206			−0.381807
$300$		0			0
$301$		−	12.9051i		−	0.743835i
$302$			5.54373i			0.319006i
$303$	−38.7003			−2.22328
$304$		−	8.62417i		−	0.494630i
$305$		0			0
$306$	9.86546			0.563971
$307$	−16.7038			−0.953338			−0.476669	−	0.879083i	$-0.658156\pi$
$307$	−16.7038			−0.953338			−0.476669	+	0.879083i	$0.658156\pi$
$308$	−7.73683			−0.440847
$309$			13.5088i			0.768490i
$310$		0			0
$311$		−	19.0378i		−	1.07954i	−0.841813	−	0.539769i	$-0.818512\pi$
$311$		−	19.0378i		−	1.07954i	0.841813	−	0.539769i	$-0.181488\pi$
$312$	−6.04033			−0.341966
$313$			11.7324i			0.663153i	0.943428	+	0.331576i	$0.107580\pi$
$313$			11.7324i			0.663153i	−0.943428	+	0.331576i	$0.892420\pi$
$314$		−	4.53029i		−	0.255659i
$315$		0			0
$316$			1.06782i			0.0600695i
$317$	22.9458			1.28876			0.644382	−	0.764704i	$-0.277115\pi$
$317$	22.9458			1.28876			0.644382	+	0.764704i	$0.277115\pi$
$318$			19.7777i			1.10908i
$319$			40.4344i			2.26389i
$320$		0			0
$321$	15.9619			0.890908
$322$	−35.5384			−1.98048
$323$	8.31422			0.462616
$324$	−4.34846			−0.241581
$325$		0			0
$326$	−6.96547			−0.385782
$327$			3.21418i			0.177744i
$328$			29.0049i			1.60152i
$329$	−22.9445			−1.26497
$330$		0			0
$331$			1.98109i			0.108890i	0.998517	+	0.0544452i	$0.0173390\pi$
$331$			1.98109i			0.108890i	−0.998517	+	0.0544452i	$0.982661\pi$
$332$	−4.15886			−0.228247
$333$	3.34581	−	17.4105i	0.183349	−	0.954088i
$334$	−2.74065			−0.149962
$335$		0			0
$336$	−24.4239			−1.33243
$337$	5.08513			0.277005			0.138502	−	0.990362i	$-0.455771\pi$
$337$	5.08513			0.277005			0.138502	+	0.990362i	$0.455771\pi$
$338$			15.2619i			0.830137i
$339$			41.8948i			2.27541i
$340$		0			0
$341$			32.2411i			1.74595i
$342$	−10.9526			−0.592249
$343$	−5.24778			−0.283354
$344$	11.1446			0.600875
$345$		0			0
$346$		−	8.85458i		−	0.476025i
$347$			30.3201i			1.62767i	0.581097	+	0.813834i	$0.302624\pi$
$347$			30.3201i			1.62767i	−0.581097	+	0.813834i	$0.697376\pi$
$348$		−	9.94026i		−	0.532854i
$349$	−1.60060			−0.0856782			−0.0428391	−	0.999082i	$-0.513640\pi$
$349$	−1.60060			−0.0856782			−0.0428391	+	0.999082i	$0.513640\pi$
$350$		0			0
$351$		−	0.168767i		−	0.00900813i
$352$		−	12.0911i		−	0.644455i
$353$		−	7.00767i		−	0.372981i	−0.982457	−	0.186490i	$-0.940289\pi$
$353$		−	7.00767i		−	0.372981i	0.982457	−	0.186490i	$-0.0597113\pi$
$354$	−8.41136			−0.447059
$355$		0			0
$356$		−	1.68544i		−	0.0893282i
$357$		−	23.5461i		−	1.24619i
$358$	8.61967			0.455564
$359$	1.90720			0.100658			0.0503291	−	0.998733i	$-0.483973\pi$
$359$	1.90720			0.100658			0.0503291	+	0.998733i	$0.483973\pi$
$360$		0			0
$361$	9.76957			0.514188
$362$			24.7868i			1.30277i
$363$	25.8618			1.35739
$364$			1.35221i			0.0708750i
$365$		0			0
$366$	27.3453			1.42936
$367$	−3.73972			−0.195212			−0.0976058	−	0.995225i	$-0.531118\pi$
$367$	−3.73972			−0.195212			−0.0976058	+	0.995225i	$0.531118\pi$
$368$		−	23.0535i		−	1.20175i
$369$	27.6698			1.44043
$370$		0			0
$371$	23.2613			1.20767
$372$		−	7.92604i		−	0.410946i
$373$	−20.9597			−1.08525			−0.542625	−	0.839975i	$-0.682570\pi$
$373$	−20.9597			−1.08525			−0.542625	+	0.839975i	$0.682570\pi$
$374$	−15.7435			−0.814077
$375$		0			0
$376$		−	19.8144i		−	1.02185i
$377$	7.06695			0.363966
$378$		−	0.908462i		−	0.0467263i
$379$	10.7162			0.550453			0.275226	−	0.961379i	$-0.411247\pi$
$379$	10.7162			0.550453			0.275226	+	0.961379i	$0.411247\pi$
$380$		0			0
$381$	−24.2940			−1.24462
$382$	14.5038			0.742080
$383$			17.7375i			0.906346i	0.891423	+	0.453173i	$0.149708\pi$
$383$			17.7375i			0.906346i	−0.891423	+	0.453173i	$0.850292\pi$
$384$		−	14.1050i		−	0.719794i
$385$		0			0
$386$	−24.8900			−1.26687
$387$		−	10.6316i		−	0.540436i
$388$		−	5.60341i		−	0.284470i
$389$		−	0.603404i		−	0.0305938i	−0.999883	−	0.0152969i	$-0.995131\pi$
$389$		−	0.603404i		−	0.0305938i	0.999883	−	0.0152969i	$-0.00486934\pi$
$390$		0			0
$391$	22.2250			1.12397
$392$			16.8549i			0.851303i
$393$			18.2663i			0.921414i
$394$			31.7900i			1.60156i
$395$		0			0
$396$	−6.37386			−0.320298
$397$	−22.1477			−1.11156			−0.555780	−	0.831329i	$-0.687580\pi$
$397$	−22.1477			−1.11156			−0.555780	+	0.831329i	$0.687580\pi$
$398$	−21.0718			−1.05623
$399$			26.1409i			1.30868i
$400$		0			0
$401$			10.8898i			0.543813i	0.962324	+	0.271907i	$0.0876541\pi$
$401$			10.8898i			0.543813i	−0.962324	+	0.271907i	$0.912346\pi$
$402$			2.59803i			0.129578i
$403$	5.63496			0.280697
$404$	−7.48171			−0.372229
$405$		0			0
$406$	38.0409			1.88794
$407$	−5.33932	+	27.7840i	−0.264660	+	1.37720i
$408$	20.3340			1.00668
$409$		−	20.3229i		−	1.00490i	−0.864605	−	0.502452i	$-0.832431\pi$
$409$		−	20.3229i		−	1.00490i	0.864605	−	0.502452i	$-0.167569\pi$
$410$		0			0
$411$	−32.0222			−1.57954
$412$			2.61158i			0.128663i
$413$			9.89293i			0.486799i
$414$	−29.2777			−1.43892
$415$		0			0
$416$	−2.11322			−0.103609
$417$	−39.2374			−1.92146
$418$	17.4784			0.854896
$419$	5.89713			0.288094			0.144047	−	0.989571i	$-0.453988\pi$
$419$	5.89713			0.288094			0.144047	+	0.989571i	$0.453988\pi$
$420$		0			0
$421$		−	19.0939i		−	0.930579i	−0.885159	−	0.465289i	$-0.845950\pi$
$421$		−	19.0939i		−	0.930579i	0.885159	−	0.465289i	$-0.154050\pi$
$422$			2.06689i			0.100615i
$423$	−18.9024			−0.919068
$424$			20.0881i			0.975562i
$425$		0			0
$426$		−	3.49005i		−	0.169093i
$427$		−	32.1619i		−	1.55642i
$428$	3.08583			0.149159
$429$		−	9.19561i		−	0.443968i
$430$		0			0
$431$			36.1889i			1.74316i	0.490256	+	0.871579i	$0.336903\pi$
$431$			36.1889i			1.74316i	−0.490256	+	0.871579i	$0.663097\pi$
$432$	0.589313			0.0283534
$433$	12.6173			0.606349			0.303175	−	0.952935i	$-0.401953\pi$
$433$	12.6173			0.606349			0.303175	+	0.952935i	$0.401953\pi$
$434$	30.3326			1.45601
$435$		0			0
$436$			0.621378i			0.0297586i
$437$	−24.6741			−1.18032
$438$			21.7680i			1.04011i
$439$			35.3892i			1.68903i	0.535530	+	0.844516i	$0.320112\pi$
$439$			35.3892i			1.68903i	−0.535530	+	0.844516i	$0.679888\pi$
$440$		0			0
$441$	16.0792			0.765674
$442$			2.75158i			0.130879i
$443$	9.80109			0.465664			0.232832	−	0.972517i	$-0.425201\pi$
$443$	9.80109			0.465664			0.232832	+	0.972517i	$0.425201\pi$
$444$	1.31260	−	6.83031i	0.0622931	−	0.324152i
$445$		0			0
$446$			15.8882i			0.752327i
$447$	−25.7811			−1.21941
$448$	−31.4607			−1.48638
$449$		−	36.2738i		−	1.71187i	−0.517087	−	0.855933i	$-0.672984\pi$
$449$		−	36.2738i		−	1.71187i	0.517087	−	0.855933i	$-0.327016\pi$
$450$		0			0
$451$	−44.1561			−2.07923
$452$			8.09927i			0.380958i
$453$	10.9004			0.512147
$454$	26.3952			1.23879
$455$		0			0
$456$	−22.5748			−1.05716
$457$			0.507576i			0.0237434i	0.999930	+	0.0118717i	$0.00377897\pi$
$457$			0.507576i			0.0237434i	−0.999930	+	0.0118717i	$0.996221\pi$
$458$			24.9706i			1.16680i
$459$			0.568134i			0.0265182i
$460$		0			0
$461$			11.8855i			0.553561i	0.960933	+	0.276781i	$0.0892676\pi$
$461$			11.8855i			0.553561i	−0.960933	+	0.276781i	$0.910732\pi$
$462$		−	49.4993i		−	2.30292i
$463$			36.0142i			1.67372i	0.547416	+	0.836861i	$0.315612\pi$
$463$			36.0142i			1.67372i	−0.547416	+	0.836861i	$0.684388\pi$
$464$			24.6769i			1.14559i
$465$		0			0
$466$		−	18.1648i		−	0.841467i
$467$			22.5404i			1.04304i	0.853238	+	0.521522i	$0.174635\pi$
$467$			22.5404i			1.04304i	−0.853238	+	0.521522i	$0.825365\pi$
$468$			1.11399i			0.0514944i
$469$	3.05564			0.141096
$470$		0			0
$471$	−8.90774			−0.410447
$472$	−8.54335			−0.393240
$473$			16.9661i			0.780104i
$474$	−6.83178			−0.313794
$475$		0			0
$476$		−	4.55204i		−	0.208642i
$477$	19.1635			0.877435
$478$	−0.225772			−0.0103266
$479$			13.2005i			0.603148i	0.953443	+	0.301574i	$0.0975120\pi$
$479$			13.2005i			0.603148i	−0.953443	+	0.301574i	$0.902488\pi$
$480$		0			0
$481$	4.85595	+	0.933181i	0.221412	+	0.0425494i
$482$	−3.31446			−0.150970
$483$			69.8779i			3.17955i
$484$	4.99972			0.227260
$485$		0			0
$486$		−	27.0506i		−	1.22704i
$487$			17.2431i			0.781359i	0.920527	+	0.390680i	$0.127760\pi$
$487$			17.2431i			0.781359i	−0.920527	+	0.390680i	$0.872240\pi$
$488$	27.7744			1.25729
$489$			13.6959i			0.619352i
$490$		0			0
$491$	−0.973893			−0.0439512			−0.0219756	−	0.999759i	$-0.506996\pi$
$491$	−0.973893			−0.0439512			−0.0219756	+	0.999759i	$0.506996\pi$
$492$	10.8552			0.489389
$493$	−23.7900			−1.07145
$494$		−	3.05479i		−	0.137442i
$495$		0			0
$496$			19.6765i			0.883502i
$497$	−4.10478			−0.184125
$498$		−	26.6079i		−	1.19233i
$499$		−	15.4479i		−	0.691541i	−0.938319	−	0.345771i	$-0.887618\pi$
$499$		−	15.4479i		−	0.691541i	0.938319	−	0.345771i	$-0.112382\pi$
$500$		0			0
$501$			5.38883i			0.240755i
$502$	37.3179			1.66558
$503$			29.1794i			1.30104i	0.759487	+	0.650522i	$0.225450\pi$
$503$			29.1794i			1.30104i	−0.759487	+	0.650522i	$0.774550\pi$
$504$			31.5048i			1.40334i
$505$		0			0
$506$	46.7220			2.07704
$507$	30.0089			1.33274
$508$	−4.69661			−0.208378
$509$	0.535077			0.0237169			0.0118584	−	0.999930i	$-0.496225\pi$
$509$	0.535077			0.0237169			0.0118584	+	0.999930i	$0.496225\pi$
$510$		0			0
$511$	25.6022			1.13257
$512$		−	24.7245i		−	1.09268i
$513$		−	0.630740i		−	0.0278479i
$514$	9.90490			0.436886
$515$		0			0
$516$		−	4.17090i		−	0.183613i
$517$	30.1649			1.32665
$518$	26.1393	+	5.02325i	1.14849	+	0.220709i
$519$	−17.4104			−0.764233
$520$		0			0
$521$	−32.7830			−1.43625			−0.718125	−	0.695914i	$-0.754999\pi$
$521$	−32.7830			−1.43625			−0.718125	+	0.695914i	$0.754999\pi$
$522$	31.3394			1.37169
$523$		−	19.3262i		−	0.845078i	−0.906345	−	0.422539i	$-0.861139\pi$
$523$		−	19.3262i		−	0.845078i	0.906345	−	0.422539i	$-0.138861\pi$
$524$			3.53132i			0.154267i
$525$		0			0
$526$		−	30.8118i		−	1.34346i
$527$	−18.9694			−0.826318
$528$	32.1099			1.39740
$529$	−42.9571			−1.86770
$530$		0			0
$531$			8.15013i			0.353685i
$532$			5.05366i			0.219104i
$533$			7.71740i			0.334278i
$534$	10.7833			0.466637
$535$		0			0
$536$			2.63879i			0.113979i
$537$		−	16.9485i		−	0.731384i
$538$		−	19.8581i		−	0.856143i
$539$	−25.6594			−1.10523
$540$		0			0
$541$		−	0.555496i		−	0.0238827i	−0.999929	−	0.0119413i	$-0.996199\pi$
$541$		−	0.555496i		−	0.0238827i	0.999929	−	0.0119413i	$-0.00380113\pi$
$542$			10.8576i			0.466375i
$543$	48.7375			2.09152
$544$	7.11388			0.305005
$545$		0			0
$546$	−8.65127			−0.370240
$547$		−	20.0085i		−	0.855501i	−0.903897	−	0.427750i	$-0.859306\pi$
$547$		−	20.0085i		−	0.855501i	0.903897	−	0.427750i	$-0.140694\pi$
$548$	−6.19066			−0.264452
$549$		−	26.4960i		−	1.13082i
$550$		0			0
$551$	26.4116			1.12517
$552$	−60.3452			−2.56846
$553$			8.03512i			0.341688i
$554$	−30.2222			−1.28402
$555$		0			0
$556$	−7.58553			−0.321698
$557$		−	9.16672i		−	0.388406i	−0.980961	−	0.194203i	$-0.937788\pi$
$557$		−	9.16672i		−	0.388406i	0.980961	−	0.194203i	$-0.0622121\pi$
$558$	24.9890			1.05787
$559$	2.96527			0.125417
$560$		0			0
$561$			30.9559i			1.30696i
$562$	−32.1519			−1.35625
$563$		−	16.9848i		−	0.715824i	−0.933755	−	0.357912i	$-0.883489\pi$
$563$		−	16.9848i		−	0.715824i	0.933755	−	0.357912i	$-0.116511\pi$
$564$	−7.41563			−0.312254
$565$		0			0
$566$	14.0463			0.590410
$567$	−32.7213			−1.37417
$568$		−	3.54481i		−	0.148737i
$569$			9.03214i			0.378647i	0.981915	+	0.189323i	$0.0606295\pi$
$569$			9.03214i			0.378647i	−0.981915	+	0.189323i	$0.939371\pi$
$570$		0			0
$571$	−34.0157			−1.42351			−0.711757	−	0.702426i	$-0.752100\pi$
$571$	−34.0157			−1.42351			−0.711757	+	0.702426i	$0.752100\pi$
$572$		−	1.77773i		−	0.0743308i
$573$		−	28.5183i		−	1.19137i
$574$			41.5422i			1.73394i
$575$		0			0
$576$	−25.9184			−1.07993
$577$		−	27.7330i		−	1.15454i	−0.816553	−	0.577270i	$-0.804118\pi$
$577$		−	27.7330i		−	1.15454i	0.816553	−	0.577270i	$-0.195882\pi$
$578$			11.7639i			0.489313i
$579$			48.9403i			2.03389i
$580$		0			0
$581$	−31.2945			−1.29832
$582$	35.8499			1.48603
$583$	−30.5814			−1.26655
$584$			22.1096i			0.914900i
$585$		0			0
$586$			38.3265i			1.58325i
$587$		−	1.34861i		−	0.0556631i	−0.999613	−	0.0278316i	$-0.991140\pi$
$587$		−	1.34861i		−	0.0556631i	0.999613	−	0.0278316i	$-0.00886021\pi$
$588$	6.30802			0.260138
$589$	21.0597			0.867751
$590$		0			0
$591$	62.5075			2.57122
$592$	−3.25855	+	16.9564i	−0.133925	+	0.696902i
$593$	−20.0829			−0.824707			−0.412354	−	0.911024i	$-0.635293\pi$
$593$	−20.0829			−0.824707			−0.412354	+	0.911024i	$0.635293\pi$
$594$			1.19435i			0.0490046i
$595$		0			0
$596$	−4.98411			−0.204157
$597$			41.4327i			1.69573i
$598$		−	8.16585i		−	0.333927i
$599$	23.1973			0.947816			0.473908	−	0.880574i	$-0.342843\pi$
$599$	23.1973			0.947816			0.473908	+	0.880574i	$0.342843\pi$
$600$		0			0
$601$	−26.7983			−1.09313			−0.546563	−	0.837418i	$-0.684064\pi$
$601$	−26.7983			−1.09313			−0.546563	+	0.837418i	$0.684064\pi$
$602$	15.9618			0.650555
$603$	2.51734			0.102514
$604$	2.10732			0.0857456
$605$		0			0
$606$		−	47.8671i		−	1.94447i
$607$			42.0133i			1.70527i	0.522510	+	0.852633i	$0.324996\pi$
$607$			42.0133i			1.70527i	−0.522510	+	0.852633i	$0.675004\pi$
$608$	−7.89782			−0.320299
$609$		−	74.7984i		−	3.03098i
$610$		0			0
$611$		−	5.27208i		−	0.213286i
$612$		−	3.75012i		−	0.151590i
$613$	−39.3574			−1.58963			−0.794816	−	0.606850i	$-0.792433\pi$
$613$	−39.3574			−1.58963			−0.794816	+	0.606850i	$0.792433\pi$
$614$		−	20.6604i		−	0.833785i
$615$		0			0
$616$		−	50.2760i		−	2.02568i
$617$	7.73995			0.311599			0.155799	−	0.987789i	$-0.450205\pi$
$617$	7.73995			0.311599			0.155799	+	0.987789i	$0.450205\pi$
$618$	−16.7086			−0.672118
$619$	18.4650			0.742172			0.371086	−	0.928599i	$-0.378986\pi$
$619$	18.4650			0.742172			0.371086	+	0.928599i	$0.378986\pi$
$620$		0			0
$621$		−	1.68605i		−	0.0676589i
$622$	23.5472			0.944159
$623$		−	12.6826i		−	0.508118i
$624$		−	5.61202i		−	0.224661i
$625$		0			0
$626$	−14.5114			−0.579991
$627$		−	34.3671i		−	1.37249i
$628$	−1.72208			−0.0687185
$629$	−16.3470	−	3.14144i	−0.651796	−	0.125257i
$630$		0			0
$631$		−	15.5190i		−	0.617803i	−0.951094	−	0.308902i	$-0.900039\pi$
$631$		−	15.5190i		−	0.617803i	0.951094	−	0.308902i	$-0.0999614\pi$
$632$	−6.93898			−0.276018
$633$	4.06405			0.161532
$634$			28.3809i			1.12715i
$635$		0			0
$636$	7.51803			0.298109
$637$			4.48464i			0.177688i
$638$	−50.0120			−1.97999
$639$	−3.38166			−0.133776
$640$		0			0
$641$	34.5202			1.36346			0.681732	−	0.731602i	$-0.261227\pi$
$641$	34.5202			1.36346			0.681732	+	0.731602i	$0.261227\pi$
$642$			19.7427i			0.779184i
$643$			6.59477i			0.260072i	0.991509	+	0.130036i	$0.0415093\pi$
$643$			6.59477i			0.260072i	−0.991509	+	0.130036i	$0.958491\pi$
$644$			13.5091i			0.532332i
$645$		0			0
$646$			10.2836i			0.404602i
$647$			6.12397i			0.240758i	0.992728	+	0.120379i	$0.0384110\pi$
$647$			6.12397i			0.240758i	−0.992728	+	0.120379i	$0.961589\pi$
$648$		−	28.2575i		−	1.11006i
$649$		−	13.0061i		−	0.510535i
$650$		0			0
$651$		−	59.6418i		−	2.33755i
$652$			2.64776i			0.103694i
$653$		−	19.4230i		−	0.760082i	−0.924970	−	0.380041i	$-0.875910\pi$
$653$		−	19.4230i		−	0.760082i	0.924970	−	0.380041i	$-0.124090\pi$
$654$	−3.97550			−0.155454
$655$		0			0
$656$	−26.9481			−1.05215
$657$	21.0919			0.822875
$658$		−	28.3792i		−	1.10634i
$659$	20.7540			0.808461			0.404231	−	0.914657i	$-0.367539\pi$
$659$	20.7540			0.808461			0.404231	+	0.914657i	$0.367539\pi$
$660$		0			0
$661$			37.6403i			1.46404i	0.681284	+	0.732019i	$0.261422\pi$
$661$			37.6403i			1.46404i	−0.681284	+	0.732019i	$0.738578\pi$
$662$	−2.45034			−0.0952350
$663$	5.41032			0.210120
$664$		−	27.0254i		−	1.04879i
$665$		0			0
$666$	21.5344	+	4.13832i	0.834441	+	0.160357i
$667$	70.6016			2.73370
$668$			1.04179i			0.0403081i
$669$	31.2403			1.20782
$670$		0			0
$671$			42.2829i			1.63231i
$672$			22.3669i			0.862820i
$673$	17.1811			0.662281			0.331141	−	0.943581i	$-0.392567\pi$
$673$	17.1811			0.662281			0.331141	+	0.943581i	$0.392567\pi$
$674$			6.28962i			0.242267i
$675$		0			0
$676$	5.80144			0.223132
$677$	16.6649			0.640483			0.320242	−	0.947336i	$-0.396236\pi$
$677$	16.6649			0.640483			0.320242	+	0.947336i	$0.396236\pi$
$678$	−51.8182			−1.99006
$679$		−	42.1645i		−	1.61813i
$680$		0			0
$681$		−	51.8999i		−	1.98881i
$682$	−39.8779			−1.52700
$683$		−	31.8739i		−	1.21962i	−0.792548	−	0.609810i	$-0.791246\pi$
$683$		−	31.8739i		−	1.21962i	0.792548	−	0.609810i	$-0.208754\pi$
$684$			4.16337i			0.159191i
$685$		0			0
$686$		−	6.49080i		−	0.247820i
$687$	49.0988			1.87324
$688$			10.3543i			0.394755i
$689$			5.34488i			0.203624i
$690$		0			0
$691$	−0.304841			−0.0115967			−0.00579834	−	0.999983i	$-0.501846\pi$
$691$	−0.304841			−0.0115967			−0.00579834	+	0.999983i	$0.501846\pi$
$692$	−3.36586			−0.127951
$693$	−47.9620			−1.82193
$694$	−37.5019			−1.42355
$695$		0			0
$696$	64.5945			2.44845
$697$		−	25.9796i		−	0.984049i
$698$		−	1.97973i		−	0.0749338i
$699$	−35.7167			−1.35093
$700$		0			0
$701$		−	7.79427i		−	0.294386i	−0.989108	−	0.147193i	$-0.952976\pi$
$701$		−	7.79427i		−	0.294386i	0.989108	−	0.147193i	$-0.0470238\pi$
$702$	0.208742			0.00787847
$703$	18.1483	+	3.48761i	0.684478	+	0.131538i
$704$	41.3611			1.55886
$705$		0			0
$706$	8.66754			0.326207
$707$	−56.2983			−2.11732
$708$			3.19738i			0.120165i
$709$			16.8307i			0.632090i	0.948744	+	0.316045i	$0.102355\pi$
$709$			16.8307i			0.632090i	−0.948744	+	0.316045i	$0.897645\pi$
$710$		0			0
$711$			6.61960i			0.248254i
$712$	10.9525			0.410461
$713$	56.2954			2.10828
$714$	29.1234			1.08992
$715$		0			0
$716$		−	3.27656i		−	0.122451i
$717$			0.443928i			0.0165788i
$718$			2.35895i			0.0880352i
$719$	22.3120			0.832097			0.416049	−	0.909342i	$-0.363415\pi$
$719$	22.3120			0.832097			0.416049	+	0.909342i	$0.363415\pi$
$720$		0			0
$721$			19.6516i			0.731865i
$722$			12.0836i			0.449706i
$723$			6.51711i			0.242374i
$724$	9.42213			0.350171
$725$		0			0
$726$			31.9876i			1.18717i
$727$			18.1887i			0.674583i	0.941400	+	0.337291i	$0.109511\pi$
$727$			18.1887i			0.674583i	−0.941400	+	0.337291i	$0.890489\pi$
$728$	−8.78702			−0.325669
$729$	−25.4422			−0.942304
$730$		0			0
$731$	−9.98219			−0.369205
$732$		−	10.3947i		−	0.384198i
$733$	3.92923			0.145129			0.0725646	−	0.997364i	$-0.476882\pi$
$733$	3.92923			0.145129			0.0725646	+	0.997364i	$0.476882\pi$
$734$		−	4.62552i		−	0.170731i
$735$		0			0
$736$	−21.1119			−0.778194
$737$	−4.01722			−0.147976
$738$			34.2239i			1.25980i
$739$	22.6573			0.833463			0.416731	−	0.909030i	$-0.363176\pi$
$739$	22.6573			0.833463			0.416731	+	0.909030i	$0.363176\pi$
$740$		0			0
$741$	−6.00653			−0.220655
$742$			28.7711i			1.05622i
$743$	17.5427			0.643580			0.321790	−	0.946811i	$-0.395715\pi$
$743$	17.5427			0.643580			0.321790	+	0.946811i	$0.395715\pi$
$744$	51.5056			1.88829
$745$		0			0
$746$		−	25.9243i		−	0.949156i
$747$	−25.7815			−0.943295
$748$			5.98452i			0.218816i
$749$	23.2202			0.848448
$750$		0			0
$751$	−39.0372			−1.42449			−0.712244	−	0.701932i	$-0.752321\pi$
$751$	−39.0372			−1.42449			−0.712244	+	0.701932i	$0.752321\pi$
$752$	18.4094			0.671323
$753$		−	73.3769i		−	2.67400i
$754$			8.74086i			0.318324i
$755$		0			0
$756$	−0.345330			−0.0125595
$757$			43.1487i			1.56827i	0.620592	+	0.784134i	$0.286892\pi$
$757$			43.1487i			1.56827i	−0.620592	+	0.784134i	$0.713108\pi$
$758$			13.2545i			0.481423i
$759$		−	91.8677i		−	3.33459i
$760$		0			0
$761$	−21.7502			−0.788446			−0.394223	−	0.919015i	$-0.628986\pi$
$761$	−21.7502			−0.788446			−0.394223	+	0.919015i	$0.628986\pi$
$762$		−	30.0484i		−	1.08854i
$763$			4.67574i			0.169273i
$764$		−	5.51328i		−	0.199464i
$765$		0			0
$766$	−21.9389			−0.792686
$767$	−2.27315			−0.0820788
$768$	−25.8072			−0.931237
$769$		−	25.6657i		−	0.925527i	−0.886482	−	0.462764i	$-0.846858\pi$
$769$		−	25.6657i		−	0.925527i	0.886482	−	0.462764i	$-0.153142\pi$
$770$		0			0
$771$		−	19.4756i		−	0.701398i
$772$			9.46134i			0.340521i
$773$	40.9962			1.47453			0.737265	−	0.675604i	$-0.236117\pi$
$773$	40.9962			1.47453			0.737265	+	0.675604i	$0.236117\pi$
$774$	13.1499			0.472663
$775$		0			0
$776$	36.4125			1.30713
$777$	9.87703	−	51.3967i	0.354336	−	1.84384i
$778$	0.746329			0.0267572
$779$			28.8425i			1.03339i
$780$		0			0
$781$	5.39651			0.193102
$782$			27.4893i			0.983016i
$783$			1.80478i			0.0644974i
$784$	−15.6598			−0.559278
$785$		0			0
$786$	−22.5930			−0.805865
$787$	7.54502			0.268951			0.134476	−	0.990917i	$-0.457065\pi$
$787$	7.54502			0.268951			0.134476	+	0.990917i	$0.457065\pi$
$788$	12.0842			0.430482
$789$	−60.5840			−2.15685
$790$		0			0
$791$			60.9453i			2.16697i
$792$		−	41.4191i		−	1.47176i
$793$	7.39001			0.262427
$794$		−	27.3937i		−	0.972165i
$795$		0			0
$796$			8.00995i			0.283905i
$797$			9.06241i			0.321007i	0.987035	+	0.160503i	$0.0513118\pi$
$797$			9.06241i			0.321007i	−0.987035	+	0.160503i	$0.948688\pi$
$798$	−32.3327			−1.14457
$799$			17.7478i			0.627872i
$800$		0			0
$801$		−	10.4484i		−	0.369174i
$802$	−13.4693			−0.475616
$803$	−33.6589			−1.18780
$804$	0.987578			0.0348292
$805$		0			0
$806$			6.96968i			0.245496i
$807$	−39.0462			−1.37449
$808$		−	48.6182i		−	1.71038i
$809$			22.7076i			0.798355i	0.916874	+	0.399178i	$0.130704\pi$
$809$			22.7076i			0.798355i	−0.916874	+	0.399178i	$0.869296\pi$
$810$		0			0
$811$	−1.50322			−0.0527850			−0.0263925	−	0.999652i	$-0.508402\pi$
$811$	−1.50322			−0.0527850			−0.0263925	+	0.999652i	$0.508402\pi$
$812$		−	14.4603i		−	0.507458i
$813$	21.3489			0.748740
$814$	−34.3650	−	6.60401i	−1.20449	−	0.231471i
$815$		0			0
$816$			18.8921i			0.661357i
$817$	11.0822			0.387717
$818$	25.1367			0.878885
$819$			8.38258i			0.292911i
$820$		0			0
$821$	15.7647			0.550192			0.275096	−	0.961417i	$-0.411290\pi$
$821$	15.7647			0.550192			0.275096	+	0.961417i	$0.411290\pi$
$822$		−	39.6071i		−	1.38146i
$823$	−43.0343			−1.50008			−0.750040	−	0.661393i	$-0.769966\pi$
$823$	−43.0343			−1.50008			−0.750040	+	0.661393i	$0.769966\pi$
$824$	−16.9708			−0.591205
$825$		0			0
$826$	−12.2362			−0.425752
$827$		−	21.0281i		−	0.731220i	−0.930768	−	0.365610i	$-0.880860\pi$
$827$		−	21.0281i		−	0.731220i	0.930768	−	0.365610i	$-0.119140\pi$
$828$			11.1292i			0.386768i
$829$		−	9.83380i		−	0.341542i	−0.985311	−	0.170771i	$-0.945374\pi$
$829$		−	9.83380i		−	0.341542i	0.985311	−	0.170771i	$-0.0546258\pi$
$830$		0			0
$831$			59.4248i			2.06142i
$832$		−	7.22891i		−	0.250617i
$833$		−	15.0970i		−	0.523079i
$834$		−	48.5313i		−	1.68050i
$835$		0			0
$836$		−	6.64399i		−	0.229787i
$837$			1.43907i			0.0497415i
$838$			7.29396i			0.251966i
$839$	42.1023			1.45353			0.726766	−	0.686886i	$-0.241023\pi$
$839$	42.1023			1.45353			0.726766	+	0.686886i	$0.241023\pi$
$840$		0			0
$841$	−46.5731			−1.60597
$842$	23.6166			0.813880
$843$			63.2191i			2.17738i
$844$	0.785679			0.0270442
$845$		0			0
$846$		−	23.3798i		−	0.803813i
$847$	37.6218			1.29270
$848$	−18.6636			−0.640912
$849$		−	27.6187i		−	0.947872i
$850$		0			0
$851$	48.5129	+	9.32284i	1.66300	+	0.319583i
$852$	−1.32666			−0.0454506
$853$		−	40.1419i		−	1.37443i	−0.726453	−	0.687216i	$-0.758832\pi$
$853$		−	40.1419i		−	1.37443i	0.726453	−	0.687216i	$-0.241168\pi$
$854$	39.7799			1.36124
$855$		0			0
$856$			20.0525i			0.685382i
$857$		−	33.0976i		−	1.13059i	−0.824888	−	0.565296i	$-0.808762\pi$
$857$		−	33.0976i		−	1.13059i	0.824888	−	0.565296i	$-0.191238\pi$
$858$	11.3737			0.388293
$859$			12.8778i			0.439383i	0.975569	+	0.219692i	$0.0705051\pi$
$859$			12.8778i			0.439383i	−0.975569	+	0.219692i	$0.929495\pi$
$860$		0			0
$861$	81.6829			2.78375
$862$	−44.7608			−1.52456
$863$	22.4100			0.762847			0.381423	−	0.924400i	$-0.375434\pi$
$863$	22.4100			0.762847			0.381423	+	0.924400i	$0.375434\pi$
$864$		−	0.539679i		−	0.0183603i
$865$		0			0
$866$			15.6059i			0.530310i
$867$	23.1309			0.785566
$868$		−	11.5302i		−	0.391361i
$869$		−	10.5637i		−	0.358348i
$870$		0			0
$871$			0.702111i			0.0237901i
$872$	−4.03789			−0.136740
$873$		−	34.7365i		−	1.17565i
$874$		−	30.5186i		−	1.03231i
$875$		0			0
$876$	8.27458			0.279572
$877$	−20.8988			−0.705703			−0.352852	−	0.935679i	$-0.614788\pi$
$877$	−20.8988			−0.705703			−0.352852	+	0.935679i	$0.614788\pi$
$878$	−43.7716			−1.47722
$879$	75.3600			2.54183
$880$		0			0
$881$	−6.33856			−0.213551			−0.106776	−	0.994283i	$-0.534053\pi$
$881$	−6.33856			−0.213551			−0.106776	+	0.994283i	$0.534053\pi$
$882$			19.8877i			0.669655i
$883$			48.5707i			1.63454i	0.576258	+	0.817268i	$0.304512\pi$
$883$			48.5707i			1.63454i	−0.576258	+	0.817268i	$0.695488\pi$
$884$	1.04595			0.0351790
$885$		0			0
$886$			12.1226i			0.407268i
$887$	−21.3315			−0.716243			−0.358121	−	0.933675i	$-0.616583\pi$
$887$	−21.3315			−0.716243			−0.358121	+	0.933675i	$0.616583\pi$
$888$	44.3852	+	8.52962i	1.48947	+	0.286235i
$889$	−35.3410			−1.18530
$890$		0			0
$891$	43.0183			1.44117
$892$	6.03951			0.202218
$893$		−	19.7036i		−	0.659354i
$894$		−	31.8878i		−	1.06649i
$895$		0			0
$896$		−	20.5189i		−	0.685489i
$897$	−16.0562			−0.536102
$898$	44.8658			1.49719
$899$	−60.2595			−2.00977
$900$		0			0
$901$		−	17.9929i		−	0.599429i
$902$		−	54.6151i		−	1.81848i
$903$		−	31.3851i		−	1.04443i
$904$	−52.6313			−1.75049
$905$		0			0
$906$			13.4824i			0.447922i
$907$			15.1452i			0.502888i	0.967872	+	0.251444i	$0.0809054\pi$
$907$			15.1452i			0.502888i	−0.967872	+	0.251444i	$0.919095\pi$
$908$		−	10.0335i		−	0.332974i
$909$	−46.3804			−1.53834
$910$		0			0
$911$		−	22.2508i		−	0.737202i	−0.929588	−	0.368601i	$-0.879837\pi$
$911$		−	22.2508i		−	0.737202i	0.929588	−	0.368601i	$-0.120163\pi$
$912$		−	20.9740i		−	0.694519i
$913$	41.1426			1.36162
$914$	−0.627804			−0.0207659
$915$		0			0
$916$	9.49199			0.313624
$917$			26.5725i			0.877501i
$918$	−0.702705			−0.0231927
$919$		−	9.88176i		−	0.325969i	−0.986629	−	0.162985i	$-0.947888\pi$
$919$		−	9.88176i		−	0.325969i	0.986629	−	0.162985i	$-0.0521121\pi$
$920$		0			0
$921$	−40.6237			−1.33860
$922$	−14.7007			−0.484142
$923$		−	0.943178i		−	0.0310451i
$924$	−18.8160			−0.619001
$925$		0			0
$926$	−44.5447			−1.46383
$927$			16.1897i			0.531738i
$928$	22.5985			0.741832
$929$	−53.9902			−1.77136			−0.885681	−	0.464294i	$-0.846308\pi$
$929$	−53.9902			−1.77136			−0.885681	+	0.464294i	$0.846308\pi$
$930$		0			0
$931$			16.7606i			0.549307i
$932$	−6.90491			−0.226178
$933$		−	46.3001i		−	1.51580i
$934$	−27.8794			−0.912241
$935$		0			0
$936$	−7.23904			−0.236616
$937$	21.3136			0.696285			0.348143	−	0.937442i	$-0.386813\pi$
$937$	21.3136			0.696285			0.348143	+	0.937442i	$0.386813\pi$
$938$			3.77941i			0.123402i
$939$			28.5332i			0.931144i
$940$		0			0
$941$	53.6144			1.74778			0.873889	−	0.486125i	$-0.161590\pi$
$941$	53.6144			1.74778			0.873889	+	0.486125i	$0.161590\pi$
$942$		−	11.0177i		−	0.358975i
$943$			77.0998i			2.51071i
$944$		−	7.93755i		−	0.258345i
$945$		0			0
$946$	−20.9848			−0.682276
$947$		−	10.6038i		−	0.344576i	−0.985047	−	0.172288i	$-0.944884\pi$
$947$		−	10.6038i		−	0.344576i	0.985047	−	0.172288i	$-0.0551160\pi$
$948$			2.59694i			0.0843446i
$949$			5.88275i			0.190962i
$950$		0			0
$951$	55.8042			1.80958
$952$	29.5804			0.958706
$953$	3.09422			0.100232			0.0501159	−	0.998743i	$-0.484041\pi$
$953$	3.09422			0.100232			0.0501159	+	0.998743i	$0.484041\pi$
$954$			23.7026i			0.767400i
$955$		0			0
$956$			0.0858220i			0.00277568i
$957$			98.3367i			3.17877i
$958$	−16.3273			−0.527511
$959$	−46.5835			−1.50426
$960$		0			0
$961$	−17.0489			−0.549966
$962$	−1.15422	+	6.00616i	−0.0372135	+	0.193646i
$963$	19.1296			0.616442
$964$			1.25991i			0.0405791i
$965$		0			0
$966$	−86.4295			−2.78082
$967$		−	54.4946i		−	1.75243i	−0.481921	−	0.876215i	$-0.660061\pi$
$967$		−	54.4946i		−	1.75243i	0.481921	−	0.876215i	$-0.339939\pi$
$968$			32.4895i			1.04425i
$969$	20.2202			0.649567
$970$		0			0
$971$	−29.1731			−0.936208			−0.468104	−	0.883673i	$-0.655063\pi$
$971$	−29.1731			−0.936208			−0.468104	+	0.883673i	$0.655063\pi$
$972$	−10.2826			−0.329816
$973$	−57.0796			−1.82989
$974$	−21.3274			−0.683373
$975$		0			0
$976$			25.8049i			0.825996i
$977$			0.625130i			0.0199997i	0.999950	+	0.00999984i	$0.00318310\pi$
$977$			0.625130i			0.0199997i	−0.999950	+	0.00999984i	$0.996817\pi$
$978$	−16.9400			−0.541682
$979$			16.6737i			0.532893i
$980$		0			0
$981$			3.85203i			0.122986i
$982$		−	1.20457i		−	0.0384395i
$983$	−3.97152			−0.126672			−0.0633359	−	0.997992i	$-0.520174\pi$
$983$	−3.97152			−0.126672			−0.0633359	+	0.997992i	$0.520174\pi$
$984$			70.5399i			2.24873i
$985$		0			0
$986$		−	29.4250i		−	0.937083i
$987$	−55.8011			−1.77617
$988$	−1.16121			−0.0369429
$989$	29.6242			0.941993
$990$		0			0
$991$			49.4776i			1.57171i	0.618412	+	0.785854i	$0.287776\pi$
$991$			49.4776i			1.57171i	−0.618412	+	0.785854i	$0.712224\pi$
$992$	18.0193			0.572113
$993$			4.81801i			0.152895i
$994$		−	5.07706i		−	0.161035i
$995$		0			0
$996$	−10.1143			−0.320485
$997$		−	7.71177i		−	0.244234i	−0.992516	−	0.122117i	$-0.961032\pi$
$997$		−	7.71177i		−	0.244234i	0.992516	−	0.122117i	$-0.0389683\pi$
$998$	19.1069			0.604819
$999$	−0.238318	+	1.24013i	−0.00754005	+	0.0392358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.c.c.776.8		12
5.2	odd	4		925.2.d.e.924.5		12
5.3	odd	4		925.2.d.f.924.8		12
5.4	even	2		185.2.c.b.36.5	✓	12
15.14	odd	2		1665.2.e.e.406.8		12
20.19	odd	2		2960.2.p.h.961.11		12
37.36	even	2	inner	925.2.c.c.776.5		12
185.73	odd	4		925.2.d.e.924.6		12
185.147	odd	4		925.2.d.f.924.7		12
185.154	odd	4		6845.2.a.h.1.3		6
185.179	odd	4		6845.2.a.i.1.4		6
185.184	even	2		185.2.c.b.36.8	yes	12
555.554	odd	2		1665.2.e.e.406.5		12
740.739	odd	2		2960.2.p.h.961.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.5	✓	12	5.4	even	2
185.2.c.b.36.8	yes	12	185.184	even	2
925.2.c.c.776.5		12	37.36	even	2	inner
925.2.c.c.776.8		12	1.1	even	1	trivial
925.2.d.e.924.5		12	5.2	odd	4
925.2.d.e.924.6		12	185.73	odd	4
925.2.d.f.924.7		12	185.147	odd	4
925.2.d.f.924.8		12	5.3	odd	4
1665.2.e.e.406.5		12	555.554	odd	2
1665.2.e.e.406.8		12	15.14	odd	2
2960.2.p.h.961.11		12	20.19	odd	2
2960.2.p.h.961.12		12	740.739	odd	2
6845.2.a.h.1.3		6	185.154	odd	4
6845.2.a.i.1.4		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)

\(f(q)\)	\(=\)	\(q+1.23687i q^{2} +2.43200 q^{3} +0.470165 q^{4} +3.00806i q^{6} +3.53789 q^{7} +3.05526i q^{8} +2.91464 q^{9} +O(q^{10})\)	\(q+1.23687i q^{2} +2.43200 q^{3} +0.470165 q^{4} +3.00806i q^{6} +3.53789 q^{7} +3.05526i q^{8} +2.91464 q^{9} -4.65123 q^{11} +1.14344 q^{12} +0.812921i q^{13} +4.37590i q^{14} -2.83862 q^{16} -2.73660i q^{17} +3.60501i q^{18} +3.03816i q^{19} +8.60417 q^{21} -5.75295i q^{22} +8.12140i q^{23} +7.43040i q^{24} -1.00547 q^{26} -0.207606 q^{27} +1.66339 q^{28} -8.69328i q^{29} -6.93173i q^{31} +2.59954i q^{32} -11.3118 q^{33} +3.38480 q^{34} +1.37036 q^{36} +(1.14794 - 5.97346i) q^{37} -3.75780 q^{38} +1.97703i q^{39} +9.49341 q^{41} +10.6422i q^{42} -3.64767i q^{43} -2.18685 q^{44} -10.0451 q^{46} -6.48535 q^{47} -6.90352 q^{48} +5.51669 q^{49} -6.65541i q^{51} +0.382207i q^{52} +6.57491 q^{53} -0.256780i q^{54} +10.8092i q^{56} +7.38882i q^{57} +10.7524 q^{58} +2.79628i q^{59} -9.09068i q^{61} +8.57362 q^{62} +10.3117 q^{63} -8.89251 q^{64} -13.9912i q^{66} +0.863688 q^{67} -1.28665i q^{68} +19.7513i q^{69} -1.16023 q^{71} +8.90497i q^{72} +7.23656 q^{73} +(7.38837 + 1.41984i) q^{74} +1.42844i q^{76} -16.4556 q^{77} -2.44532 q^{78} +2.27116i q^{79} -9.24881 q^{81} +11.7421i q^{82} -8.84553 q^{83} +4.04538 q^{84} +4.51167 q^{86} -21.1421i q^{87} -14.2107i q^{88} -3.58479i q^{89} +2.87603i q^{91} +3.81840i q^{92} -16.8580i q^{93} -8.02151i q^{94} +6.32208i q^{96} -11.9180i q^{97} +6.82341i q^{98} -13.5566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 18 q^{4} + 18 q^{7} + 22 q^{9}+O(q^{10}) \) 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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