LMFDB - Embedded newform 925.2.c.c.776.11

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			776.11
Root			$2.59891i$ of defining polynomial
Character	$\chi$	$=$	925.776
Dual form			925.2.c.c.776.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.59891i q^{2} +0.695617 q^{3} -4.75431 q^{4} +1.80784i q^{6} +3.94647 q^{7} -7.15821i q^{8} -2.51612 q^{9} +O(q^{10})$	\(q+2.59891i q^{2} +0.695617 q^{3} -4.75431 q^{4} +1.80784i q^{6} +3.94647 q^{7} -7.15821i q^{8} -2.51612 q^{9} +0.718621 q^{11} -3.30718 q^{12} +6.10237i q^{13} +10.2565i q^{14} +9.09488 q^{16} +2.79750i q^{17} -6.53915i q^{18} +0.449931i q^{19} +2.74523 q^{21} +1.86763i q^{22} +2.47294i q^{23} -4.97937i q^{24} -15.8595 q^{26} -3.83710 q^{27} -18.7628 q^{28} -5.64100i q^{29} +9.09202i q^{31} +9.32032i q^{32} +0.499885 q^{33} -7.27043 q^{34} +11.9624 q^{36} +(-5.67153 + 2.19859i) q^{37} -1.16933 q^{38} +4.24491i q^{39} -10.2570 q^{41} +7.13460i q^{42} +0.724878i q^{43} -3.41655 q^{44} -6.42693 q^{46} +8.44915 q^{47} +6.32655 q^{48} +8.57464 q^{49} +1.94599i q^{51} -29.0126i q^{52} +8.18124 q^{53} -9.97227i q^{54} -28.2497i q^{56} +0.312980i q^{57} +14.6604 q^{58} +6.30955i q^{59} -5.93895i q^{61} -23.6293 q^{62} -9.92979 q^{63} -6.03290 q^{64} +1.29915i q^{66} +0.420184 q^{67} -13.3002i q^{68} +1.72022i q^{69} +12.2858 q^{71} +18.0109i q^{72} -13.1856 q^{73} +(-5.71393 - 14.7398i) q^{74} -2.13912i q^{76} +2.83602 q^{77} -11.0321 q^{78} -10.8733i q^{79} +4.87920 q^{81} -26.6570i q^{82} +3.21802 q^{83} -13.0517 q^{84} -1.88389 q^{86} -3.92397i q^{87} -5.14403i q^{88} -3.67421i q^{89} +24.0828i q^{91} -11.7571i q^{92} +6.32456i q^{93} +21.9586i q^{94} +6.48337i q^{96} -1.64543i q^{97} +22.2847i q^{98} -1.80813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.59891i			1.83770i	0.394602	+	0.918852i	$0.370883\pi$
$2$			2.59891i			1.83770i	−0.394602	+	0.918852i	$0.629117\pi$
$3$	0.695617			0.401615			0.200807	−	0.979631i	$-0.435644\pi$
$3$	0.695617			0.401615			0.200807	+	0.979631i	$0.435644\pi$
$4$	−4.75431			−2.37716
$5$		0			0
$5$		0			0
$6$			1.80784i			0.738049i
$7$	3.94647			1.49163			0.745813	−	0.666155i	$-0.232061\pi$
$7$	3.94647			1.49163			0.745813	+	0.666155i	$0.232061\pi$
$8$		−	7.15821i		−	2.53081i
$9$	−2.51612			−0.838706
$10$		0			0
$11$	0.718621			0.216672			0.108336	−	0.994114i	$-0.465448\pi$
$11$	0.718621			0.216672			0.108336	+	0.994114i	$0.465448\pi$
$12$	−3.30718			−0.954701
$13$			6.10237i			1.69249i	0.532793	+	0.846246i	$0.321143\pi$
$13$			6.10237i			1.69249i	−0.532793	+	0.846246i	$0.678857\pi$
$14$			10.2565i			2.74117i
$15$		0			0
$16$	9.09488			2.27372
$17$			2.79750i			0.678493i	0.940698	+	0.339246i	$0.110172\pi$
$17$			2.79750i			0.678493i	−0.940698	+	0.339246i	$0.889828\pi$
$18$		−	6.53915i		−	1.54129i
$19$			0.449931i			0.103221i	0.998667	+	0.0516107i	$0.0164355\pi$
$19$			0.449931i			0.103221i	−0.998667	+	0.0516107i	$0.983565\pi$
$20$		0			0
$21$	2.74523			0.599059
$22$			1.86763i			0.398180i
$23$			2.47294i			0.515643i	0.966193	+	0.257821i	$0.0830046\pi$
$23$			2.47294i			0.515643i	−0.966193	+	0.257821i	$0.916995\pi$
$24$		−	4.97937i		−	1.01641i
$25$		0			0
$26$	−15.8595			−3.11030
$27$	−3.83710			−0.738451
$28$	−18.7628			−3.54583
$29$		−	5.64100i		−	1.04751i	−0.851870	−	0.523754i	$-0.824531\pi$
$29$		−	5.64100i		−	1.04751i	0.851870	−	0.523754i	$-0.175469\pi$
$30$		0			0
$31$			9.09202i			1.63297i	0.577363	+	0.816487i	$0.304082\pi$
$31$			9.09202i			1.63297i	−0.577363	+	0.816487i	$0.695918\pi$
$32$			9.32032i			1.64762i
$33$	0.499885			0.0870187
$34$	−7.27043			−1.24687
$35$		0			0
$36$	11.9624			1.99374
$37$	−5.67153	+	2.19859i	−0.932393	+	0.361446i
$37$	−5.67153	+	2.19859i	−0.932393	+	0.361446i
$38$	−1.16933			−0.189690
$39$			4.24491i			0.679729i
$40$		0			0
$41$	−10.2570			−1.60187			−0.800937	−	0.598749i	$-0.795665\pi$
$41$	−10.2570			−1.60187			−0.800937	+	0.598749i	$0.795665\pi$
$42$			7.13460i			1.10089i
$43$			0.724878i			0.110543i	0.998471	+	0.0552714i	$0.0176024\pi$
$43$			0.724878i			0.110543i	−0.998471	+	0.0552714i	$0.982398\pi$
$44$	−3.41655			−0.515064
$45$		0			0
$46$	−6.42693			−0.947599
$47$	8.44915			1.23244			0.616218	−	0.787576i	$-0.288664\pi$
$47$	8.44915			1.23244			0.616218	+	0.787576i	$0.288664\pi$
$48$	6.32655			0.913159
$49$	8.57464			1.22495
$50$		0			0
$51$			1.94599i			0.272492i
$52$		−	29.0126i		−	4.02332i
$53$	8.18124			1.12378			0.561890	−	0.827212i	$-0.310074\pi$
$53$	8.18124			1.12378			0.561890	+	0.827212i	$0.310074\pi$
$54$		−	9.97227i		−	1.35705i
$55$		0			0
$56$		−	28.2497i		−	3.77502i
$57$			0.312980i			0.0414552i
$58$	14.6604			1.92501
$59$			6.30955i			0.821434i	0.911763	+	0.410717i	$0.134722\pi$
$59$			6.30955i			0.821434i	−0.911763	+	0.410717i	$0.865278\pi$
$60$		0			0
$61$		−	5.93895i		−	0.760405i	−0.924903	−	0.380202i	$-0.875854\pi$
$61$		−	5.93895i		−	0.760405i	0.924903	−	0.380202i	$-0.124146\pi$
$62$	−23.6293			−3.00093
$63$	−9.92979			−1.25104
$64$	−6.03290			−0.754112
$65$		0			0
$66$			1.29915i			0.159915i
$67$	0.420184			0.0513337			0.0256668	−	0.999671i	$-0.491829\pi$
$67$	0.420184			0.0513337			0.0256668	+	0.999671i	$0.491829\pi$
$68$		−	13.3002i		−	1.61288i
$69$			1.72022i			0.207090i
$70$		0			0
$71$	12.2858			1.45805			0.729026	−	0.684486i	$-0.239973\pi$
$71$	12.2858			1.45805			0.729026	+	0.684486i	$0.239973\pi$
$72$			18.0109i			2.12260i
$73$	−13.1856			−1.54326			−0.771631	−	0.636071i	$-0.780559\pi$
$73$	−13.1856			−1.54326			−0.771631	+	0.636071i	$0.780559\pi$
$74$	−5.71393	−	14.7398i	−0.664231	−	1.71346i
$75$		0			0
$76$		−	2.13912i		−	0.245373i
$77$	2.83602			0.323194
$78$	−11.0321			−1.24914
$79$		−	10.8733i		−	1.22334i	−0.791113	−	0.611670i	$-0.790498\pi$
$79$		−	10.8733i		−	1.22334i	0.791113	−	0.611670i	$-0.209502\pi$
$80$		0			0
$81$	4.87920			0.542133
$82$		−	26.6570i		−	2.94377i
$83$	3.21802			0.353223			0.176612	−	0.984281i	$-0.443486\pi$
$83$	3.21802			0.353223			0.176612	+	0.984281i	$0.443486\pi$
$84$	−13.0517			−1.42406
$85$		0			0
$86$	−1.88389			−0.203145
$87$		−	3.92397i		−	0.420694i
$88$		−	5.14403i		−	0.548356i
$89$		−	3.67421i		−	0.389465i	−0.980856	−	0.194733i	$-0.937616\pi$
$89$		−	3.67421i		−	0.389465i	0.980856	−	0.194733i	$-0.0623839\pi$
$90$		0			0
$91$			24.0828i			2.52456i
$92$		−	11.7571i		−	1.22576i
$93$			6.32456i			0.655826i
$94$			21.9586i			2.26485i
$95$		0			0
$96$			6.48337i			0.661707i
$97$		−	1.64543i		−	0.167068i	−0.996505	−	0.0835342i	$-0.973379\pi$
$97$		−	1.64543i		−	0.167068i	0.996505	−	0.0835342i	$-0.0266208\pi$
$98$			22.2847i			2.25109i
$99$	−1.80813			−0.181724
$100$		0			0
$101$	7.10396			0.706870			0.353435	−	0.935459i	$-0.385013\pi$
$101$	7.10396			0.706870			0.353435	+	0.935459i	$0.385013\pi$
$102$	−5.05743			−0.500761
$103$			13.9330i			1.37286i	0.727195	+	0.686431i	$0.240824\pi$
$103$			13.9330i			1.37286i	−0.727195	+	0.686431i	$0.759176\pi$
$104$	43.6820			4.28337
$105$		0			0
$106$			21.2623i			2.06518i
$107$	15.4326			1.49192			0.745962	−	0.665988i	$-0.231990\pi$
$107$	15.4326			1.49192			0.745962	+	0.665988i	$0.231990\pi$
$108$	18.2428			1.75541
$109$			0.190894i			0.0182843i	0.999958	+	0.00914215i	$0.00291008\pi$
$109$			0.190894i			0.0182843i	−0.999958	+	0.00914215i	$0.997090\pi$
$110$		0			0
$111$	−3.94521	+	1.52938i	−0.374463	+	0.145162i
$112$	35.8927			3.39154
$113$			0.0160019i			0.00150534i	1.00000		0.000752668i	$0.000239582\pi$
$113$			0.0160019i			0.00150534i	−1.00000		0.000752668i	$0.999760\pi$
$114$	−0.813405			−0.0761824
$115$		0			0
$116$			26.8191i			2.49009i
$117$		−	15.3543i		−	1.41950i
$118$	−16.3979			−1.50955
$119$			11.0402i			1.01206i
$120$		0			0
$121$	−10.4836			−0.953053
$122$	15.4348			1.39740
$123$	−7.13494			−0.643336
$124$		−	43.2263i		−	3.88184i
$125$		0			0
$126$		−	25.8066i		−	2.29903i
$127$	9.55415			0.847794			0.423897	−	0.905710i	$-0.360662\pi$
$127$	9.55415			0.847794			0.423897	+	0.905710i	$0.360662\pi$
$128$			2.96172i			0.261781i
$129$			0.504237i			0.0443956i
$130$		0			0
$131$		−	11.9379i		−	1.04302i	−0.853246	−	0.521508i	$-0.825370\pi$
$131$		−	11.9379i		−	1.04302i	0.853246	−	0.521508i	$-0.174630\pi$
$132$	−2.37661			−0.206857
$133$			1.77564i			0.153968i
$134$			1.09202i			0.0943361i
$135$		0			0
$136$	20.0251			1.71713
$137$	8.83881			0.755151			0.377575	−	0.925979i	$-0.376758\pi$
$137$	8.83881			0.755151			0.377575	+	0.925979i	$0.376758\pi$
$138$	−4.47068			−0.380569
$139$	−9.81373			−0.832390			−0.416195	−	0.909275i	$-0.636637\pi$
$139$	−9.81373			−0.832390			−0.416195	+	0.909275i	$0.636637\pi$
$140$		0			0
$141$	5.87737			0.494964
$142$			31.9296i			2.67947i
$143$			4.38529i			0.366716i
$144$	−22.8838			−1.90698
$145$		0			0
$146$		−	34.2682i		−	2.83606i
$147$	5.96466			0.491957
$148$	26.9642	−	10.4528i	2.21644	−	0.859214i
$149$	4.27012			0.349822			0.174911	−	0.984584i	$-0.444036\pi$
$149$	4.27012			0.349822			0.174911	+	0.984584i	$0.444036\pi$
$150$		0			0
$151$	−1.86860			−0.152065			−0.0760323	−	0.997105i	$-0.524225\pi$
$151$	−1.86860			−0.152065			−0.0760323	+	0.997105i	$0.524225\pi$
$152$	3.22070			0.261233
$153$		−	7.03883i		−	0.569056i
$154$			7.37054i			0.593935i
$155$		0			0
$156$		−	20.1816i		−	1.61582i
$157$	−20.2075			−1.61274			−0.806368	−	0.591414i	$-0.798570\pi$
$157$	−20.2075			−1.61274			−0.806368	+	0.591414i	$0.798570\pi$
$158$	28.2586			2.24814
$159$	5.69101			0.451326
$160$		0			0
$161$			9.75937i			0.769146i
$162$			12.6806i			0.996280i
$163$		−	12.3406i		−	0.966588i	−0.875458	−	0.483294i	$-0.839440\pi$
$163$		−	12.3406i		−	0.966588i	0.875458	−	0.483294i	$-0.160560\pi$
$164$	48.7650			3.80791
$165$		0			0
$166$			8.36333i			0.649120i
$167$		−	9.45916i		−	0.731972i	−0.930620	−	0.365986i	$-0.880732\pi$
$167$		−	9.45916i		−	0.731972i	0.930620	−	0.365986i	$-0.119268\pi$
$168$		−	19.6509i		−	1.51610i
$169$	−24.2389			−1.86453
$170$		0			0
$171$		−	1.13208i		−	0.0865723i
$172$		−	3.44630i		−	0.262778i
$173$	7.55996			0.574773			0.287387	−	0.957815i	$-0.407214\pi$
$173$	7.55996			0.574773			0.287387	+	0.957815i	$0.407214\pi$
$174$	10.1980			0.773112
$175$		0			0
$176$	6.53577			0.492652
$177$			4.38903i			0.329900i
$178$	9.54892			0.715722
$179$			5.56293i			0.415793i	0.978151	+	0.207897i	$0.0666618\pi$
$179$			5.56293i			0.415793i	−0.978151	+	0.207897i	$0.933338\pi$
$180$		0			0
$181$	6.96840			0.517957			0.258979	−	0.965883i	$-0.416614\pi$
$181$	6.96840			0.517957			0.258979	+	0.965883i	$0.416614\pi$
$182$	−62.5890			−4.63940
$183$		−	4.13123i		−	0.305390i
$184$	17.7018			1.30499
$185$		0			0
$186$	−16.4369			−1.20522
$187$			2.01034i			0.147011i
$188$	−40.1699			−2.92969
$189$	−15.1430			−1.10149
$190$		0			0
$191$		−	4.36368i		−	0.315745i	−0.987460	−	0.157873i	$-0.949536\pi$
$191$		−	4.36368i		−	0.315745i	0.987460	−	0.157873i	$-0.0504635\pi$
$192$	−4.19658			−0.302862
$193$			21.9631i			1.58094i	0.612500	+	0.790470i	$0.290164\pi$
$193$			21.9631i			1.58094i	−0.612500	+	0.790470i	$0.709836\pi$
$194$	4.27633			0.307022
$195$		0			0
$196$	−40.7665			−2.91190
$197$	18.0892			1.28880			0.644400	−	0.764689i	$-0.277107\pi$
$197$	18.0892			1.28880			0.644400	+	0.764689i	$0.277107\pi$
$198$		−	4.69917i		−	0.333956i
$199$			4.03777i			0.286230i	0.989706	+	0.143115i	$0.0457119\pi$
$199$			4.03777i			0.286230i	−0.989706	+	0.143115i	$0.954288\pi$
$200$		0			0
$201$	0.292287			0.0206164
$202$			18.4625i			1.29902i
$203$		−	22.2621i		−	1.56249i
$204$		−	9.25183i		−	0.647757i
$205$		0			0
$206$	−36.2106			−2.52291
$207$		−	6.22220i		−	0.432472i
$208$			55.5003i			3.84825i
$209$			0.323330i			0.0223652i
$210$		0			0
$211$	19.5367			1.34496			0.672482	−	0.740113i	$-0.265228\pi$
$211$	19.5367			1.34496			0.672482	+	0.740113i	$0.265228\pi$
$212$	−38.8962			−2.67140
$213$	8.54619			0.585575
$214$			40.1078i			2.74172i
$215$		0			0
$216$			27.4668i			1.86888i
$217$			35.8814i			2.43579i
$218$	−0.496115			−0.0336011
$219$	−9.17215			−0.619796
$220$		0			0
$221$	−17.0713			−1.14834
$222$	−3.97471	−	10.2532i	−0.266765	−	0.688152i
$223$	0.781981			0.0523653			0.0261827	−	0.999657i	$-0.491665\pi$
$223$	0.781981			0.0523653			0.0261827	+	0.999657i	$0.491665\pi$
$224$			36.7824i			2.45763i
$225$		0			0
$226$	−0.0415875			−0.00276636
$227$			11.8767i			0.788283i	0.919050	+	0.394142i	$0.128958\pi$
$227$			11.8767i			0.788283i	−0.919050	+	0.394142i	$0.871042\pi$
$228$		−	1.48800i		−	0.0985455i
$229$	20.5496			1.35796			0.678979	−	0.734157i	$-0.262423\pi$
$229$	20.5496			1.35796			0.678979	+	0.734157i	$0.262423\pi$
$230$		0			0
$231$	1.97278			0.129799
$232$	−40.3794			−2.65104
$233$	−5.24600			−0.343677			−0.171838	−	0.985125i	$-0.554971\pi$
$233$	−5.24600			−0.343677			−0.171838	+	0.985125i	$0.554971\pi$
$234$	39.9043			2.60863
$235$		0			0
$236$		−	29.9976i		−	1.95268i
$237$		−	7.56364i		−	0.491311i
$238$	−28.6926			−1.85986
$239$		−	22.3874i		−	1.44812i	−0.689737	−	0.724060i	$-0.742274\pi$
$239$		−	22.3874i		−	1.44812i	0.689737	−	0.724060i	$-0.257726\pi$
$240$		0			0
$241$		−	5.46508i		−	0.352037i	−0.984387	−	0.176019i	$-0.943678\pi$
$241$		−	5.46508i		−	0.352037i	0.984387	−	0.176019i	$-0.0563219\pi$
$242$		−	27.2459i		−	1.75143i
$243$	14.9054			0.956179
$244$			28.2356i			1.80760i
$245$		0			0
$246$		−	18.5430i		−	1.18226i
$247$	−2.74565			−0.174701
$248$	65.0825			4.13275
$249$	2.23851			0.141860
$250$		0			0
$251$			28.1566i			1.77723i	0.458655	+	0.888615i	$0.348331\pi$
$251$			28.1566i			1.77723i	−0.458655	+	0.888615i	$0.651669\pi$
$252$	47.2093			2.97391
$253$			1.77710i			0.111725i
$254$			24.8303i			1.55799i
$255$		0			0
$256$	−19.7630			−1.23519
$257$		−	16.4235i		−	1.02447i	−0.858845	−	0.512236i	$-0.828817\pi$
$257$		−	16.4235i		−	1.02447i	0.858845	−	0.512236i	$-0.171183\pi$
$258$	−1.31046			−0.0815860
$259$	−22.3825	+	8.67667i	−1.39078	+	0.539142i
$260$		0			0
$261$			14.1934i			0.878551i
$262$	31.0254			1.91676
$263$	6.97704			0.430222			0.215111	−	0.976590i	$-0.430989\pi$
$263$	6.97704			0.430222			0.215111	+	0.976590i	$0.430989\pi$
$264$		−	3.57828i		−	0.220228i
$265$		0			0
$266$	−4.61473			−0.282947
$267$		−	2.55584i		−	0.156415i
$268$	−1.99769			−0.122028
$269$	4.25543			0.259458			0.129729	−	0.991549i	$-0.458589\pi$
$269$	4.25543			0.259458			0.129729	+	0.991549i	$0.458589\pi$
$270$		0			0
$271$	13.3537			0.811182			0.405591	−	0.914055i	$-0.367066\pi$
$271$	13.3537			0.811182			0.405591	+	0.914055i	$0.367066\pi$
$272$			25.4429i			1.54270i
$273$			16.7524i			1.01390i
$274$			22.9713i			1.38774i
$275$		0			0
$276$		−	8.17844i		−	0.492284i
$277$			21.3853i			1.28492i	0.766319	+	0.642460i	$0.222086\pi$
$277$			21.3853i			1.28492i	−0.766319	+	0.642460i	$0.777914\pi$
$278$		−	25.5050i		−	1.52969i
$279$		−	22.8766i		−	1.36959i
$280$		0			0
$281$		−	16.5074i		−	0.984747i	−0.870384	−	0.492374i	$-0.836129\pi$
$281$		−	16.5074i		−	0.984747i	0.870384	−	0.492374i	$-0.163871\pi$
$282$			15.2747i			0.909598i
$283$		−	29.5408i		−	1.75602i	−0.478643	−	0.878010i	$-0.658871\pi$
$283$		−	29.5408i		−	1.75602i	0.478643	−	0.878010i	$-0.341129\pi$
$284$	−58.4104			−3.46602
$285$		0			0
$286$	−11.3969			−0.673916
$287$	−40.4789			−2.38940
$288$		−	23.4510i		−	1.38187i
$289$	9.17401			0.539648
$290$		0			0
$291$		−	1.14459i		−	0.0670971i
$292$	62.6887			3.66858
$293$	−8.51399			−0.497393			−0.248696	−	0.968581i	$-0.580002\pi$
$293$	−8.51399			−0.497393			−0.248696	+	0.968581i	$0.580002\pi$
$294$			15.5016i			0.904072i
$295$		0			0
$296$	15.7380	+	40.5979i	0.914750	+	2.35971i
$297$	−2.75742			−0.160002
$298$			11.0976i			0.642869i
$299$	−15.0908			−0.872721
$300$		0			0
$301$			2.86071i			0.164889i
$302$		−	4.85632i		−	0.279450i
$303$	4.94163			0.283889
$304$			4.09207i			0.234696i
$305$		0			0
$306$	18.2933			1.04576
$307$	−10.6933			−0.610297			−0.305149	−	0.952305i	$-0.598706\pi$
$307$	−10.6933			−0.610297			−0.305149	+	0.952305i	$0.598706\pi$
$308$	−13.4833			−0.768283
$309$			9.69205i			0.551361i
$310$		0			0
$311$		−	17.4716i		−	0.990725i	−0.868686	−	0.495363i	$-0.835035\pi$
$311$		−	17.4716i		−	0.990725i	0.868686	−	0.495363i	$-0.164965\pi$
$312$	30.3859			1.72026
$313$		−	24.0536i		−	1.35959i	−0.733403	−	0.679794i	$-0.762069\pi$
$313$		−	24.0536i		−	1.35959i	0.733403	−	0.679794i	$-0.237931\pi$
$314$		−	52.5175i		−	2.96373i
$315$		0			0
$316$			51.6950i			2.90807i
$317$	10.9159			0.613097			0.306548	−	0.951855i	$-0.400826\pi$
$317$	10.9159			0.613097			0.306548	+	0.951855i	$0.400826\pi$
$318$			14.7904i			0.829404i
$319$		−	4.05374i		−	0.226966i
$320$		0			0
$321$	10.7352			0.599178
$322$	−25.3637			−1.41346
$323$	−1.25868			−0.0700349
$324$	−23.1972			−1.28874
$325$		0			0
$326$	32.0720			1.77630
$327$			0.132789i			0.00734324i
$328$			73.4217i			4.05403i
$329$	33.3443			1.83833
$330$		0			0
$331$		−	16.4312i		−	0.903140i	−0.892236	−	0.451570i	$-0.850864\pi$
$331$		−	16.4312i		−	0.903140i	0.892236	−	0.451570i	$-0.149136\pi$
$332$	−15.2995			−0.839668
$333$	14.2702	−	5.53191i	0.782003	−	0.303147i
$334$	24.5835			1.34515
$335$		0			0
$336$	24.9675			1.36209
$337$	4.83030			0.263123			0.131562	−	0.991308i	$-0.458001\pi$
$337$	4.83030			0.263123			0.131562	+	0.991308i	$0.458001\pi$
$338$		−	62.9946i		−	3.42645i
$339$			0.0111312i			0.000604565i
$340$		0			0
$341$			6.53371i			0.353820i
$342$	2.94217			0.159094
$343$	6.21427			0.335539
$344$	5.18882			0.279763
$345$		0			0
$346$			19.6476i			1.05626i
$347$			13.7503i			0.738156i	0.929399	+	0.369078i	$0.120326\pi$
$347$			13.7503i			0.738156i	−0.929399	+	0.369078i	$0.879674\pi$
$348$			18.6558i			1.00006i
$349$	1.81127			0.0969551			0.0484775	−	0.998824i	$-0.484563\pi$
$349$	1.81127			0.0969551			0.0484775	+	0.998824i	$0.484563\pi$
$350$		0			0
$351$		−	23.4154i		−	1.24982i
$352$			6.69778i			0.356993i
$353$		−	5.67980i		−	0.302305i	−0.988510	−	0.151153i	$-0.951701\pi$
$353$		−	5.67980i		−	0.302305i	0.988510	−	0.151153i	$-0.0482985\pi$
$354$	−11.4067			−0.606258
$355$		0			0
$356$			17.4683i			0.925820i
$357$			7.67978i			0.406457i
$358$	−14.4575			−0.764105
$359$	14.8495			0.783727			0.391863	−	0.920023i	$-0.371831\pi$
$359$	14.8495			0.783727			0.391863	+	0.920023i	$0.371831\pi$
$360$		0			0
$361$	18.7976			0.989345
$362$			18.1102i			0.951852i
$363$	−7.29256			−0.382760
$364$		−	114.497i		−	6.00129i
$365$		0			0
$366$	10.7367			0.561216
$367$	−13.9448			−0.727911			−0.363955	−	0.931416i	$-0.618574\pi$
$367$	−13.9448			−0.727911			−0.363955	+	0.931416i	$0.618574\pi$
$368$			22.4910i			1.17243i
$369$	25.8078			1.34350
$370$		0			0
$371$	32.2870			1.67626
$372$		−	30.0690i		−	1.55900i
$373$	25.4235			1.31638			0.658190	−	0.752852i	$-0.271322\pi$
$373$	25.4235			1.31638			0.658190	+	0.752852i	$0.271322\pi$
$374$	−5.22468			−0.270162
$375$		0			0
$376$		−	60.4808i		−	3.11906i
$377$	34.4235			1.77290
$378$		−	39.3553i		−	2.02422i
$379$	−21.8097			−1.12029			−0.560145	−	0.828394i	$-0.689255\pi$
$379$	−21.8097			−1.12029			−0.560145	+	0.828394i	$0.689255\pi$
$380$		0			0
$381$	6.64603			0.340486
$382$	11.3408			0.580246
$383$			9.28107i			0.474241i	0.971480	+	0.237120i	$0.0762035\pi$
$383$			9.28107i			0.474241i	−0.971480	+	0.237120i	$0.923796\pi$
$384$			2.06022i			0.105135i
$385$		0			0
$386$	−57.0801			−2.90530
$387$		−	1.82388i		−	0.0927129i
$388$			7.82290i			0.397148i
$389$			10.3649i			0.525524i	0.964861	+	0.262762i	$0.0846333\pi$
$389$			10.3649i			0.525524i	−0.964861	+	0.262762i	$0.915367\pi$
$390$		0			0
$391$	−6.91803			−0.349860
$392$		−	61.3790i		−	3.10011i
$393$		−	8.30418i		−	0.418891i
$394$			47.0120i			2.36843i
$395$		0			0
$396$	8.59644			0.431987
$397$	−2.37369			−0.119132			−0.0595660	−	0.998224i	$-0.518972\pi$
$397$	−2.37369			−0.119132			−0.0595660	+	0.998224i	$0.518972\pi$
$398$	−10.4938			−0.526007
$399$			1.23517i			0.0618356i
$400$		0			0
$401$		−	21.2783i		−	1.06259i	−0.847188	−	0.531294i	$-0.821706\pi$
$401$		−	21.2783i		−	1.06259i	0.847188	−	0.531294i	$-0.178294\pi$
$402$			0.759627i			0.0378868i
$403$	−55.4828			−2.76380
$404$	−33.7745			−1.68034
$405$		0			0
$406$	57.8570			2.87139
$407$	−4.07568	+	1.57995i	−0.202024	+	0.0783153i
$408$	13.9298			0.689626
$409$			26.7602i			1.32321i	0.749854	+	0.661604i	$0.230124\pi$
$409$			26.7602i			1.32321i	−0.749854	+	0.661604i	$0.769876\pi$
$410$		0			0
$411$	6.14843			0.303280
$412$		−	66.2420i		−	3.26351i
$413$			24.9005i			1.22527i
$414$	16.1709			0.794757
$415$		0			0
$416$	−56.8760			−2.78858
$417$	−6.82659			−0.334300
$418$	−0.840304			−0.0411006
$419$	−20.9669			−1.02430			−0.512150	−	0.858896i	$-0.671151\pi$
$419$	−20.9669			−1.02430			−0.512150	+	0.858896i	$0.671151\pi$
$420$		0			0
$421$			5.49355i			0.267739i	0.990999	+	0.133870i	$0.0427403\pi$
$421$			5.49355i			0.267739i	−0.990999	+	0.133870i	$0.957260\pi$
$422$			50.7742i			2.47165i
$423$	−21.2591			−1.03365
$424$		−	58.5630i		−	2.84407i
$425$		0			0
$426$			22.2107i			1.07611i
$427$		−	23.4379i		−	1.13424i
$428$	−73.3714			−3.54654
$429$			3.05048i			0.147279i
$430$		0			0
$431$		−	9.10706i		−	0.438672i	−0.975649	−	0.219336i	$-0.929611\pi$
$431$		−	9.10706i		−	0.438672i	0.975649	−	0.219336i	$-0.0703890\pi$
$432$	−34.8980			−1.67903
$433$	8.92491			0.428904			0.214452	−	0.976735i	$-0.431203\pi$
$433$	8.92491			0.428904			0.214452	+	0.976735i	$0.431203\pi$
$434$	−93.2524			−4.47626
$435$		0			0
$436$		−	0.907568i		−	0.0434646i
$437$	−1.11265			−0.0532253
$438$		−	23.8376i		−	1.13900i
$439$		−	7.39067i		−	0.352737i	−0.984324	−	0.176369i	$-0.943565\pi$
$439$		−	7.39067i		−	0.352737i	0.984324	−	0.176369i	$-0.0564351\pi$
$440$		0			0
$441$	−21.5748			−1.02737
$442$		−	44.3668i		−	2.11032i
$443$	25.3625			1.20501			0.602504	−	0.798116i	$-0.294170\pi$
$443$	25.3625			1.20501			0.602504	+	0.798116i	$0.294170\pi$
$444$	18.7568	−	7.27114i	0.890156	−	0.345073i
$445$		0			0
$446$			2.03230i			0.0962320i
$447$	2.97037			0.140494
$448$	−23.8087			−1.12485
$449$		−	31.2928i		−	1.47680i	−0.674364	−	0.738399i	$-0.735582\pi$
$449$		−	31.2928i		−	1.47680i	0.674364	−	0.738399i	$-0.264418\pi$
$450$		0			0
$451$	−7.37089			−0.347082
$452$		−	0.0760782i		−	0.00357842i
$453$	−1.29983			−0.0610713
$454$	−30.8664			−1.44863
$455$		0			0
$456$	2.24037			0.104915
$457$		−	17.8651i		−	0.835696i	−0.908517	−	0.417848i	$-0.862784\pi$
$457$		−	17.8651i		−	0.835696i	0.908517	−	0.417848i	$-0.137216\pi$
$458$			53.4066i			2.49553i
$459$		−	10.7343i		−	0.501033i
$460$		0			0
$461$			25.4342i			1.18459i	0.805722	+	0.592294i	$0.201778\pi$
$461$			25.4342i			1.18459i	−0.805722	+	0.592294i	$0.798222\pi$
$462$			5.12707i			0.238533i
$463$			13.3243i			0.619234i	0.950861	+	0.309617i	$0.100201\pi$
$463$			13.3243i			0.619234i	−0.950861	+	0.309617i	$0.899799\pi$
$464$		−	51.3042i		−	2.38174i
$465$		0			0
$466$		−	13.6339i		−	0.631576i
$467$			20.8614i			0.965351i	0.875799	+	0.482675i	$0.160335\pi$
$467$			20.8614i			0.965351i	−0.875799	+	0.482675i	$0.839665\pi$
$468$			72.9990i			3.37438i
$469$	1.65825			0.0765707
$470$		0			0
$471$	−14.0567			−0.647698
$472$	45.1651			2.07889
$473$			0.520912i			0.0239516i
$474$	19.6572			0.902885
$475$		0			0
$476$		−	52.4888i		−	2.40582i
$477$	−20.5850			−0.942521
$478$	58.1827			2.66122
$479$		−	19.2531i		−	0.879696i	−0.898072	−	0.439848i	$-0.855032\pi$
$479$		−	19.2531i		−	0.879696i	0.898072	−	0.439848i	$-0.144968\pi$
$480$		0			0
$481$	−13.4166	−	34.6097i	−0.611744	−	1.57807i
$482$	14.2032			0.646940
$483$			6.78878i			0.308900i
$484$	49.8423			2.26556
$485$		0			0
$486$			38.7376i			1.75718i
$487$			33.8595i			1.53432i	0.641456	+	0.767159i	$0.278331\pi$
$487$			33.8595i			1.53432i	−0.641456	+	0.767159i	$0.721669\pi$
$488$	−42.5122			−1.92444
$489$		−	8.58430i		−	0.388196i
$490$		0			0
$491$	−11.7655			−0.530972			−0.265486	−	0.964115i	$-0.585532\pi$
$491$	−11.7655			−0.530972			−0.265486	+	0.964115i	$0.585532\pi$
$492$	33.9217			1.52931
$493$	15.7807			0.710726
$494$		−	7.13568i		−	0.321049i
$495$		0			0
$496$			82.6908i			3.71293i
$497$	48.4854			2.17487
$498$			5.81767i			0.260696i
$499$			4.63787i			0.207620i	0.994597	+	0.103810i	$0.0331033\pi$
$499$			4.63787i			0.207620i	−0.994597	+	0.103810i	$0.966897\pi$
$500$		0			0
$501$		−	6.57995i		−	0.293971i
$502$	−73.1764			−3.26602
$503$		−	11.4479i		−	0.510434i	−0.966884	−	0.255217i	$-0.917853\pi$
$503$		−	11.4479i		−	0.510434i	0.966884	−	0.255217i	$-0.0821470\pi$
$504$			71.0795i			3.16613i
$505$		0			0
$506$	−4.61852			−0.205318
$507$	−16.8610			−0.748822
$508$	−45.4234			−2.01534
$509$	14.9280			0.661671			0.330835	−	0.943688i	$-0.392669\pi$
$509$	14.9280			0.661671			0.330835	+	0.943688i	$0.392669\pi$
$510$		0			0
$511$	−52.0367			−2.30197
$512$		−	45.4388i		−	2.00813i
$513$		−	1.72643i		−	0.0762239i
$514$	42.6832			1.88268
$515$		0			0
$516$		−	2.39730i		−	0.105535i
$517$	6.07174			0.267035
$518$	−22.5499	−	58.1701i	−0.990784	−	2.55585i
$519$	5.25884			0.230837
$520$		0			0
$521$	−16.9859			−0.744165			−0.372083	−	0.928200i	$-0.621356\pi$
$521$	−16.9859			−0.744165			−0.372083	+	0.928200i	$0.621356\pi$
$522$	−36.8874			−1.61452
$523$		−	6.19069i		−	0.270700i	−0.990798	−	0.135350i	$-0.956784\pi$
$523$		−	6.19069i		−	0.270700i	0.990798	−	0.135350i	$-0.0432159\pi$
$524$			56.7564i			2.47941i
$525$		0			0
$526$			18.1327i			0.790622i
$527$	−25.4349			−1.10796
$528$	4.54639			0.197856
$529$	16.8846			0.734113
$530$		0			0
$531$		−	15.8756i		−	0.688941i
$532$		−	8.44196i		−	0.366005i
$533$		−	62.5919i		−	2.71116i
$534$	6.64239			0.287444
$535$		0			0
$536$		−	3.00777i		−	0.129916i
$537$			3.86967i			0.166989i
$538$			11.0595i			0.476807i
$539$	6.16191			0.265412
$540$		0			0
$541$		−	36.5725i		−	1.57238i	−0.617988	−	0.786188i	$-0.712052\pi$
$541$		−	36.5725i		−	1.57238i	0.617988	−	0.786188i	$-0.287948\pi$
$542$			34.7051i			1.49071i
$543$	4.84734			0.208019
$544$	−26.0736			−1.11790
$545$		0			0
$546$	−43.5379			−1.86325
$547$		−	23.7093i		−	1.01374i	−0.862024	−	0.506868i	$-0.830803\pi$
$547$		−	23.7093i		−	1.01374i	0.862024	−	0.506868i	$-0.169197\pi$
$548$	−42.0225			−1.79511
$549$			14.9431i			0.637756i
$550$		0			0
$551$	2.53806			0.108125
$552$	12.3137			0.524104
$553$		−	42.9111i		−	1.82477i
$554$	−55.5785			−2.36130
$555$		0			0
$556$	46.6576			1.97872
$557$		−	38.5915i		−	1.63518i	−0.575803	−	0.817588i	$-0.695311\pi$
$557$		−	38.5915i		−	1.63518i	0.575803	−	0.817588i	$-0.304689\pi$
$558$	59.4541			2.51689
$559$	−4.42347			−0.187093
$560$		0			0
$561$			1.39843i			0.0590416i
$562$	42.9011			1.80967
$563$			29.8755i			1.25910i	0.776958	+	0.629552i	$0.216762\pi$
$563$			29.8755i			1.25910i	−0.776958	+	0.629552i	$0.783238\pi$
$564$	−27.9429			−1.17661
$565$		0			0
$566$	76.7738			3.22705
$567$	19.2556			0.808660
$568$		−	87.9441i		−	3.69005i
$569$			11.9663i			0.501652i	0.968032	+	0.250826i	$0.0807023\pi$
$569$			11.9663i			0.501652i	−0.968032	+	0.250826i	$0.919298\pi$
$570$		0			0
$571$	33.0510			1.38314			0.691571	−	0.722308i	$-0.256919\pi$
$571$	33.0510			1.38314			0.691571	+	0.722308i	$0.256919\pi$
$572$		−	20.8490i		−	0.871742i
$573$		−	3.03545i		−	0.126808i
$574$		−	105.201i		−	4.39100i
$575$		0			0
$576$	15.1795			0.632478
$577$			16.7283i			0.696407i	0.937419	+	0.348203i	$0.113208\pi$
$577$			16.7283i			0.696407i	−0.937419	+	0.348203i	$0.886792\pi$
$578$			23.8424i			0.991713i
$579$			15.2779i			0.634929i
$580$		0			0
$581$	12.6998			0.526877
$582$	2.97468			0.123305
$583$	5.87921			0.243492
$584$			94.3855i			3.90570i
$585$		0			0
$586$		−	22.1271i		−	0.914061i
$587$		−	28.5959i		−	1.18028i	−0.807301	−	0.590140i	$-0.799072\pi$
$587$		−	28.5959i		−	1.18028i	0.807301	−	0.590140i	$-0.200928\pi$
$588$	−28.3579			−1.16946
$589$	−4.09078			−0.168558
$590$		0			0
$591$	12.5831			0.517601
$592$	−51.5818	+	19.9959i	−2.12000	+	0.821827i
$593$	−30.9346			−1.27033			−0.635166	−	0.772376i	$-0.719068\pi$
$593$	−30.9346			−1.27033			−0.635166	+	0.772376i	$0.719068\pi$
$594$		−	7.16628i		−	0.294036i
$595$		0			0
$596$	−20.3015			−0.831582
$597$			2.80874i			0.114954i
$598$		−	39.2195i		−	1.60380i
$599$	−5.03474			−0.205714			−0.102857	−	0.994696i	$-0.532798\pi$
$599$	−5.03474			−0.205714			−0.102857	+	0.994696i	$0.532798\pi$
$600$		0			0
$601$	−13.3580			−0.544883			−0.272442	−	0.962172i	$-0.587831\pi$
$601$	−13.3580			−0.544883			−0.272442	+	0.962172i	$0.587831\pi$
$602$	−7.43471			−0.303016
$603$	−1.05723			−0.0430539
$604$	8.88391			0.361481
$605$		0			0
$606$			12.8428i			0.521705i
$607$			18.1262i			0.735721i	0.929881	+	0.367860i	$0.119910\pi$
$607$			18.1262i			0.735721i	−0.929881	+	0.367860i	$0.880090\pi$
$608$	−4.19351			−0.170069
$609$		−	15.4859i		−	0.627519i
$610$		0			0
$611$			51.5598i			2.08589i
$612$			33.4648i			1.35273i
$613$	30.6392			1.23750			0.618752	−	0.785586i	$-0.287639\pi$
$613$	30.6392			1.23750			0.618752	+	0.785586i	$0.287639\pi$
$614$		−	27.7908i		−	1.12155i
$615$		0			0
$616$		−	20.3008i		−	0.817942i
$617$	−47.1052			−1.89638			−0.948192	−	0.317697i	$-0.897091\pi$
$617$	−47.1052			−1.89638			−0.948192	+	0.317697i	$0.897091\pi$
$618$	−25.1887			−1.01324
$619$	5.80693			0.233400			0.116700	−	0.993167i	$-0.462768\pi$
$619$	5.80693			0.233400			0.116700	+	0.993167i	$0.462768\pi$
$620$		0			0
$621$		−	9.48891i		−	0.380777i
$622$	45.4071			1.82066
$623$		−	14.5002i		−	0.580936i
$624$			38.6069i			1.54551i
$625$		0			0
$626$	62.5130			2.49852
$627$			0.224914i			0.00898219i
$628$	96.0730			3.83373
$629$	−6.15055	−	15.8661i	−0.245238	−	0.632622i
$630$		0			0
$631$		−	39.7661i		−	1.58306i	−0.611128	−	0.791532i	$-0.709284\pi$
$631$		−	39.7661i		−	1.58306i	0.611128	−	0.791532i	$-0.290716\pi$
$632$	−77.8332			−3.09604
$633$	13.5901			0.540157
$634$			28.3693i			1.12669i
$635$		0			0
$636$	−27.0568			−1.07287
$637$			52.3256i			2.07322i
$638$	10.5353			0.417096
$639$	−30.9124			−1.22288
$640$		0			0
$641$	−19.3478			−0.764194			−0.382097	−	0.924122i	$-0.624798\pi$
$641$	−19.3478			−0.764194			−0.382097	+	0.924122i	$0.624798\pi$
$642$			27.8997i			1.10111i
$643$		−	11.2470i		−	0.443537i	−0.975099	−	0.221768i	$-0.928817\pi$
$643$		−	11.2470i		−	0.443537i	0.975099	−	0.221768i	$-0.0711829\pi$
$644$		−	46.3991i		−	1.82838i
$645$		0			0
$646$		−	3.27120i		−	0.128703i
$647$		−	3.01746i		−	0.118629i	−0.998239	−	0.0593144i	$-0.981109\pi$
$647$		−	3.01746i		−	0.118629i	0.998239	−	0.0593144i	$-0.0188914\pi$
$648$		−	34.9263i		−	1.37203i
$649$			4.53418i			0.177982i
$650$		0			0
$651$			24.9597i			0.978248i
$652$			58.6709i			2.29773i
$653$			35.7962i			1.40081i	0.713743	+	0.700407i	$0.246998\pi$
$653$			35.7962i			1.40081i	−0.713743	+	0.700407i	$0.753002\pi$
$654$	−0.345106			−0.0134947
$655$		0			0
$656$	−93.2861			−3.64221
$657$	33.1766			1.29434
$658$			86.6588i			3.37831i
$659$	−4.68867			−0.182645			−0.0913223	−	0.995821i	$-0.529109\pi$
$659$	−4.68867			−0.182645			−0.0913223	+	0.995821i	$0.529109\pi$
$660$		0			0
$661$		−	17.4911i		−	0.680324i	−0.940367	−	0.340162i	$-0.889518\pi$
$661$		−	17.4911i		−	0.680324i	0.940367	−	0.340162i	$-0.110482\pi$
$662$	42.7031			1.65970
$663$	−11.8751			−0.461191
$664$		−	23.0352i		−	0.893941i
$665$		0			0
$666$	14.3769	+	37.0870i	0.557094	+	1.43709i
$667$	13.9498			0.540140
$668$			44.9718i			1.74001i
$669$	0.543959			0.0210307
$670$		0			0
$671$		−	4.26785i		−	0.164759i
$672$			25.5865i			0.987019i
$673$	3.52297			0.135800			0.0679002	−	0.997692i	$-0.478370\pi$
$673$	3.52297			0.135800			0.0679002	+	0.997692i	$0.478370\pi$
$674$			12.5535i			0.483543i
$675$		0			0
$676$	115.239			4.43228
$677$	−31.6661			−1.21703			−0.608513	−	0.793544i	$-0.708234\pi$
$677$	−31.6661			−1.21703			−0.608513	+	0.793544i	$0.708234\pi$
$678$	−0.0289290			−0.00111101
$679$		−	6.49365i		−	0.249204i
$680$		0			0
$681$			8.26162i			0.316586i
$682$	−16.9805			−0.650217
$683$			6.02306i			0.230466i	0.993338	+	0.115233i	$0.0367615\pi$
$683$			6.02306i			0.230466i	−0.993338	+	0.115233i	$0.963239\pi$
$684$			5.38226i			0.205796i
$685$		0			0
$686$			16.1503i			0.616621i
$687$	14.2947			0.545376
$688$			6.59267i			0.251343i
$689$			49.9249i			1.90199i
$690$		0			0
$691$	−21.1596			−0.804950			−0.402475	−	0.915431i	$-0.631850\pi$
$691$	−21.1596			−0.804950			−0.402475	+	0.915431i	$0.631850\pi$
$692$	−35.9424			−1.36633
$693$	−7.13575			−0.271065
$694$	−35.7358			−1.35651
$695$		0			0
$696$	−28.0886			−1.06470
$697$		−	28.6939i		−	1.08686i
$698$			4.70732i			0.178175i
$699$	−3.64920			−0.138026
$700$		0			0
$701$			14.1969i			0.536210i	0.963390	+	0.268105i	$0.0863974\pi$
$701$			14.1969i			0.536210i	−0.963390	+	0.268105i	$0.913603\pi$
$702$	60.8545			2.29680
$703$	−0.989215	−	2.55180i	−0.0373089	−	0.0962428i
$704$	−4.33536			−0.163395
$705$		0			0
$706$	14.7613			0.555548
$707$	28.0356			1.05439
$708$		−	20.8668i		−	0.784224i
$709$			11.9225i			0.447758i	0.974617	+	0.223879i	$0.0718721\pi$
$709$			11.9225i			0.447758i	−0.974617	+	0.223879i	$0.928128\pi$
$710$		0			0
$711$			27.3585i			1.02602i
$712$	−26.3007			−0.985662
$713$	−22.4840			−0.842032
$714$	−19.9590			−0.746948
$715$		0			0
$716$		−	26.4479i		−	0.988406i
$717$		−	15.5730i		−	0.581586i
$718$			38.5925i			1.44026i
$719$	−13.6063			−0.507431			−0.253715	−	0.967279i	$-0.581653\pi$
$719$	−13.6063			−0.507431			−0.253715	+	0.967279i	$0.581653\pi$
$720$		0			0
$721$			54.9863i			2.04780i
$722$			48.8531i			1.81812i
$723$		−	3.80160i		−	0.141383i
$724$	−33.1300			−1.23127
$725$		0			0
$726$		−	18.9527i		−	0.703400i
$727$		−	5.35589i		−	0.198639i	−0.995056	−	0.0993195i	$-0.968333\pi$
$727$		−	5.35589i		−	0.198639i	0.995056	−	0.0993195i	$-0.0316666\pi$
$728$	172.390			6.38919
$729$	−4.26917			−0.158118
$730$		0			0
$731$	−2.02784			−0.0750025
$732$			19.6412i			0.725959i
$733$	−3.86939			−0.142919			−0.0714596	−	0.997443i	$-0.522766\pi$
$733$	−3.86939			−0.142919			−0.0714596	+	0.997443i	$0.522766\pi$
$734$		−	36.2411i		−	1.33768i
$735$		0			0
$736$	−23.0486			−0.849581
$737$	0.301953			0.0111226
$738$			67.0721i			2.46896i
$739$	−11.2514			−0.413888			−0.206944	−	0.978353i	$-0.566352\pi$
$739$	−11.2514			−0.413888			−0.206944	+	0.978353i	$0.566352\pi$
$740$		0			0
$741$	−1.90992			−0.0701626
$742$			83.9110i			3.08047i
$743$	−37.7018			−1.38315			−0.691573	−	0.722307i	$-0.743082\pi$
$743$	−37.7018			−1.38315			−0.691573	+	0.722307i	$0.743082\pi$
$744$	45.2725			1.65977
$745$		0			0
$746$			66.0733i			2.41912i
$747$	−8.09691			−0.296251
$748$		−	9.55778i		−	0.349467i
$749$	60.9043			2.22539
$750$		0			0
$751$	8.10716			0.295835			0.147917	−	0.989000i	$-0.452743\pi$
$751$	8.10716			0.295835			0.147917	+	0.989000i	$0.452743\pi$
$752$	76.8440			2.80221
$753$			19.5862i			0.713761i
$754$			89.4633i			3.25806i
$755$		0			0
$756$	71.9947			2.61842
$757$		−	1.81739i		−	0.0660543i	−0.999454	−	0.0330272i	$-0.989485\pi$
$757$		−	1.81739i		−	0.0660543i	0.999454	−	0.0330272i	$-0.0105148\pi$
$758$		−	56.6814i		−	2.05876i
$759$			1.23618i			0.0448706i
$760$		0			0
$761$	18.2277			0.660754			0.330377	−	0.943849i	$-0.392824\pi$
$761$	18.2277			0.660754			0.330377	+	0.943849i	$0.392824\pi$
$762$			17.2724i			0.625713i
$763$			0.753356i			0.0272733i
$764$			20.7463i			0.750576i
$765$		0			0
$766$	−24.1206			−0.871514
$767$	−38.5032			−1.39027
$768$	−13.7475			−0.496070
$769$			47.2379i			1.70344i	0.523996	+	0.851721i	$0.324441\pi$
$769$			47.2379i			1.70344i	−0.523996	+	0.851721i	$0.675559\pi$
$770$		0			0
$771$		−	11.4245i		−	0.411442i
$772$		−	104.420i		−	3.75814i
$773$	39.6547			1.42628			0.713141	−	0.701021i	$-0.247272\pi$
$773$	39.6547			1.42628			0.713141	+	0.701021i	$0.247272\pi$
$774$	4.74009			0.170379
$775$		0			0
$776$	−11.7783			−0.422818
$777$	−15.5697	+	6.03564i	−0.558558	+	0.216527i
$778$	−26.9375			−0.965757
$779$		−	4.61494i		−	0.165348i
$780$		0			0
$781$	8.82881			0.315920
$782$		−	17.9793i		−	0.642939i
$783$			21.6451i			0.773533i
$784$	77.9853			2.78519
$785$		0			0
$786$	21.5818			0.769797
$787$	3.05948			0.109059			0.0545293	−	0.998512i	$-0.482634\pi$
$787$	3.05948			0.109059			0.0545293	+	0.998512i	$0.482634\pi$
$788$	−86.0016			−3.06368
$789$	4.85334			0.172784
$790$		0			0
$791$			0.0631512i			0.00224540i
$792$			12.9430i			0.459909i
$793$	36.2417			1.28698
$794$		−	6.16900i		−	0.218930i
$795$		0			0
$796$		−	19.1969i		−	0.680414i
$797$			14.4075i			0.510341i	0.966896	+	0.255170i	$0.0821315\pi$
$797$			14.4075i			0.510341i	−0.966896	+	0.255170i	$0.917868\pi$
$798$	−3.21008			−0.113636
$799$			23.6365i			0.836199i
$800$		0			0
$801$			9.24474i			0.326647i
$802$	55.3003			1.95272
$803$	−9.47547			−0.334382
$804$	−1.38963			−0.0490083
$805$		0			0
$806$		−	144.195i		−	5.07904i
$807$	2.96015			0.104202
$808$		−	50.8516i		−	1.78895i
$809$			40.6464i			1.42905i	0.699610	+	0.714525i	$0.253357\pi$
$809$			40.6464i			1.42905i	−0.699610	+	0.714525i	$0.746643\pi$
$810$		0			0
$811$	21.4607			0.753588			0.376794	−	0.926297i	$-0.377026\pi$
$811$	21.4607			0.753588			0.376794	+	0.926297i	$0.377026\pi$
$812$			105.841i			3.71428i
$813$	9.28908			0.325782
$814$	−4.10615	−	10.5923i	−0.143920	−	0.371260i
$815$		0			0
$816$			17.6985i			0.619571i
$817$	−0.326145			−0.0114104
$818$	−69.5473			−2.43166
$819$		−	60.5952i		−	2.11737i
$820$		0			0
$821$	−30.5319			−1.06557			−0.532785	−	0.846251i	$-0.678855\pi$
$821$	−30.5319			−1.06557			−0.532785	+	0.846251i	$0.678855\pi$
$822$			15.9792i			0.557338i
$823$	−42.2325			−1.47213			−0.736067	−	0.676909i	$-0.763319\pi$
$823$	−42.2325			−1.47213			−0.736067	+	0.676909i	$0.763319\pi$
$824$	99.7355			3.47445
$825$		0			0
$826$	−64.7140			−2.25169
$827$		−	42.1551i		−	1.46588i	−0.680295	−	0.732938i	$-0.738149\pi$
$827$		−	42.1551i		−	1.46588i	0.680295	−	0.732938i	$-0.261851\pi$
$828$			29.5823i			1.02806i
$829$			40.9058i			1.42072i	0.703840	+	0.710359i	$0.251467\pi$
$829$			40.9058i			1.42072i	−0.703840	+	0.710359i	$0.748533\pi$
$830$		0			0
$831$			14.8760i			0.516043i
$832$		−	36.8149i		−	1.27633i
$833$			23.9875i			0.831118i
$834$		−	17.7417i		−	0.614344i
$835$		0			0
$836$		−	1.53721i		−	0.0531656i
$837$		−	34.8870i		−	1.20587i
$838$		−	54.4910i		−	1.88236i
$839$	−3.87962			−0.133939			−0.0669696	−	0.997755i	$-0.521333\pi$
$839$	−3.87962			−0.133939			−0.0669696	+	0.997755i	$0.521333\pi$
$840$		0			0
$841$	−2.82089			−0.0972722
$842$	−14.2772			−0.492025
$843$		−	11.4828i		−	0.395489i
$844$	−92.8838			−3.19719
$845$		0			0
$846$		−	55.2503i		−	1.89954i
$847$	−41.3732			−1.42160
$848$	74.4074			2.55516
$849$		−	20.5491i		−	0.705243i
$850$		0			0
$851$	−5.43697	−	14.0253i	−0.186377	−	0.480782i
$852$	−40.6313			−1.39200
$853$			33.9215i			1.16145i	0.814100	+	0.580725i	$0.197231\pi$
$853$			33.9215i			1.16145i	−0.814100	+	0.580725i	$0.802769\pi$
$854$	60.9129			2.08440
$855$		0			0
$856$		−	110.470i		−	3.77577i
$857$		−	8.94674i		−	0.305615i	−0.988256	−	0.152807i	$-0.951169\pi$
$857$		−	8.94674i		−	0.305615i	0.988256	−	0.152807i	$-0.0488314\pi$
$858$	−7.92791			−0.270654
$859$			3.31270i			0.113028i	0.998402	+	0.0565139i	$0.0179985\pi$
$859$			3.31270i			0.113028i	−0.998402	+	0.0565139i	$0.982001\pi$
$860$		0			0
$861$	−28.1578			−0.959616
$862$	23.6684			0.806149
$863$	−4.64920			−0.158260			−0.0791302	−	0.996864i	$-0.525214\pi$
$863$	−4.64920			−0.158260			−0.0791302	+	0.996864i	$0.525214\pi$
$864$		−	35.7631i		−	1.21668i
$865$		0			0
$866$			23.1950i			0.788198i
$867$	6.38160			0.216730
$868$		−	170.591i		−	5.79025i
$869$		−	7.81377i		−	0.265064i
$870$		0			0
$871$			2.56412i			0.0868818i
$872$	1.36646			0.0462740
$873$			4.14010i			0.140121i
$874$		−	2.89168i		−	0.0978124i
$875$		0			0
$876$	43.6073			1.47335
$877$	−26.5496			−0.896516			−0.448258	−	0.893904i	$-0.647955\pi$
$877$	−26.5496			−0.896516			−0.448258	+	0.893904i	$0.647955\pi$
$878$	19.2077			0.648227
$879$	−5.92248			−0.199760
$880$		0			0
$881$	−13.1533			−0.443148			−0.221574	−	0.975144i	$-0.571119\pi$
$881$	−13.1533			−0.443148			−0.221574	+	0.975144i	$0.571119\pi$
$882$		−	56.0709i		−	1.88800i
$883$			14.2511i			0.479587i	0.970824	+	0.239794i	$0.0770798\pi$
$883$			14.2511i			0.479587i	−0.970824	+	0.239794i	$0.922920\pi$
$884$	81.1626			2.72979
$885$		0			0
$886$			65.9148i			2.21445i
$887$	−34.2013			−1.14837			−0.574183	−	0.818727i	$-0.694680\pi$
$887$	−34.2013			−1.14837			−0.574183	+	0.818727i	$0.694680\pi$
$888$	10.9476	+	28.2406i	0.367377	+	0.947693i
$889$	37.7052			1.26459
$890$		0			0
$891$	3.50629			0.117465
$892$	−3.71778			−0.124481
$893$			3.80154i			0.127214i
$894$			7.71971i			0.258186i
$895$		0			0
$896$			11.6883i			0.390480i
$897$	−10.4974			−0.350497
$898$	81.3270			2.71392
$899$	51.2881			1.71055
$900$		0			0
$901$			22.8870i			0.762476i
$902$		−	19.1563i		−	0.637834i
$903$			1.98996i			0.0662216i
$904$	0.114545			0.00380972
$905$		0			0
$906$		−	3.37814i		−	0.112231i
$907$			17.7684i			0.589991i	0.955499	+	0.294995i	$0.0953181\pi$
$907$			17.7684i			0.589991i	−0.955499	+	0.294995i	$0.904682\pi$
$908$		−	56.4655i		−	1.87387i
$909$	−17.8744			−0.592856
$910$		0			0
$911$		−	23.8206i		−	0.789213i	−0.918850	−	0.394606i	$-0.870881\pi$
$911$		−	23.8206i		−	0.789213i	0.918850	−	0.394606i	$-0.129119\pi$
$912$			2.84651i			0.0942575i
$913$	2.31254			0.0765337
$914$	46.4298			1.53576
$915$		0			0
$916$	−97.6995			−3.22808
$917$		−	47.1125i		−	1.55579i
$918$	27.8974			0.920751
$919$			4.18679i			0.138110i	0.997613	+	0.0690548i	$0.0219983\pi$
$919$			4.18679i			0.138110i	−0.997613	+	0.0690548i	$0.978002\pi$
$920$		0			0
$921$	−7.43842			−0.245104
$922$	−66.1011			−2.17692
$923$			74.9723i			2.46774i
$924$	−9.37922			−0.308554
$925$		0			0
$926$	−34.6287			−1.13797
$927$		−	35.0571i		−	1.15143i
$928$	52.5760			1.72589
$929$	−11.8463			−0.388664			−0.194332	−	0.980936i	$-0.562254\pi$
$929$	−11.8463			−0.388664			−0.194332	+	0.980936i	$0.562254\pi$
$930$		0			0
$931$			3.85800i			0.126441i
$932$	24.9411			0.816973
$933$		−	12.1536i		−	0.397890i
$934$	−54.2169			−1.77403
$935$		0			0
$936$	−109.909			−3.59249
$937$	−4.87951			−0.159407			−0.0797033	−	0.996819i	$-0.525397\pi$
$937$	−4.87951			−0.159407			−0.0797033	+	0.996819i	$0.525397\pi$
$938$			4.30963i			0.140714i
$939$		−	16.7321i		−	0.546030i
$940$		0			0
$941$	−24.7262			−0.806051			−0.403025	−	0.915189i	$-0.632041\pi$
$941$	−24.7262			−0.806051			−0.403025	+	0.915189i	$0.632041\pi$
$942$		−	36.5320i		−	1.19028i
$943$		−	25.3649i		−	0.825994i
$944$			57.3846i			1.86771i
$945$		0			0
$946$	−1.35380			−0.0440159
$947$			31.4176i			1.02094i	0.859897	+	0.510468i	$0.170528\pi$
$947$			31.4176i			1.02094i	−0.859897	+	0.510468i	$0.829472\pi$
$948$			35.9599i			1.16792i
$949$		−	80.4636i		−	2.61196i
$950$		0			0
$951$	7.59327			0.246229
$952$	79.0283			2.56132
$953$	32.3909			1.04925			0.524623	−	0.851335i	$-0.324206\pi$
$953$	32.3909			1.04925			0.524623	+	0.851335i	$0.324206\pi$
$954$		−	53.4984i		−	1.73207i
$955$		0			0
$956$			106.437i			3.44241i
$957$		−	2.81985i		−	0.0911528i
$958$	50.0370			1.61662
$959$	34.8821			1.12640
$960$		0			0
$961$	−51.6648			−1.66661
$962$	89.9474	−	34.8685i	2.90002	−	1.12421i
$963$	−38.8302			−1.25129
$964$			25.9827i			0.836847i
$965$		0			0
$966$	−17.6434			−0.567667
$967$			55.8879i			1.79723i	0.438735	+	0.898616i	$0.355427\pi$
$967$			55.8879i			1.79723i	−0.438735	+	0.898616i	$0.644573\pi$
$968$			75.0437i			2.41199i
$969$	−0.875560			−0.0281270
$970$		0			0
$971$	−17.8598			−0.573148			−0.286574	−	0.958058i	$-0.592516\pi$
$971$	−17.8598			−0.573148			−0.286574	+	0.958058i	$0.592516\pi$
$972$	−70.8648			−2.27299
$973$	−38.7296			−1.24161
$974$	−87.9976			−2.81962
$975$		0			0
$976$		−	54.0140i		−	1.72895i
$977$		−	47.1359i		−	1.50801i	−0.656868	−	0.754006i	$-0.728119\pi$
$977$		−	47.1359i		−	1.50801i	0.656868	−	0.754006i	$-0.271881\pi$
$978$	22.3098			0.713389
$979$		−	2.64036i		−	0.0843863i
$980$		0			0
$981$		−	0.480311i		−	0.0153351i
$982$		−	30.5776i		−	0.975769i
$983$	−30.2430			−0.964601			−0.482301	−	0.876006i	$-0.660199\pi$
$983$	−30.2430			−0.964601			−0.482301	+	0.876006i	$0.660199\pi$
$984$			51.0734i			1.62816i
$985$		0			0
$986$			41.0125i			1.30610i
$987$	23.1949			0.738301
$988$	13.0537			0.415292
$989$	−1.79258			−0.0570006
$990$		0			0
$991$			3.34332i			0.106204i	0.998589	+	0.0531020i	$0.0169109\pi$
$991$			3.34332i			0.106204i	−0.998589	+	0.0531020i	$0.983089\pi$
$992$	−84.7406			−2.69052
$993$		−	11.4298i		−	0.362714i
$994$			126.009i			3.99677i
$995$		0			0
$996$	−10.6426			−0.337223
$997$			15.3402i			0.485828i	0.970048	+	0.242914i	$0.0781033\pi$
$997$			15.3402i			0.485828i	−0.970048	+	0.242914i	$0.921897\pi$
$998$	−12.0534			−0.381544
$999$	21.7622	−	8.43622i	0.688527	−	0.266910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.c.c.776.11		12
5.2	odd	4		925.2.d.f.924.1		12
5.3	odd	4		925.2.d.e.924.12		12
5.4	even	2		185.2.c.b.36.2	✓	12
15.14	odd	2		1665.2.e.e.406.11		12
20.19	odd	2		2960.2.p.h.961.8		12
37.36	even	2	inner	925.2.c.c.776.2		12
185.73	odd	4		925.2.d.f.924.2		12
185.147	odd	4		925.2.d.e.924.11		12
185.154	odd	4		6845.2.a.i.1.1		6
185.179	odd	4		6845.2.a.h.1.6		6
185.184	even	2		185.2.c.b.36.11	yes	12
555.554	odd	2		1665.2.e.e.406.2		12
740.739	odd	2		2960.2.p.h.961.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.2	✓	12	5.4	even	2
185.2.c.b.36.11	yes	12	185.184	even	2
925.2.c.c.776.2		12	37.36	even	2	inner
925.2.c.c.776.11		12	1.1	even	1	trivial
925.2.d.e.924.11		12	185.147	odd	4
925.2.d.e.924.12		12	5.3	odd	4
925.2.d.f.924.1		12	5.2	odd	4
925.2.d.f.924.2		12	185.73	odd	4
1665.2.e.e.406.2		12	555.554	odd	2
1665.2.e.e.406.11		12	15.14	odd	2
2960.2.p.h.961.7		12	740.739	odd	2
2960.2.p.h.961.8		12	20.19	odd	2
6845.2.a.h.1.6		6	185.179	odd	4
6845.2.a.i.1.1		6	185.154	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)

\(f(q)\)	\(=\)	\(q+2.59891i q^{2} +0.695617 q^{3} -4.75431 q^{4} +1.80784i q^{6} +3.94647 q^{7} -7.15821i q^{8} -2.51612 q^{9} +O(q^{10})\)	\(q+2.59891i q^{2} +0.695617 q^{3} -4.75431 q^{4} +1.80784i q^{6} +3.94647 q^{7} -7.15821i q^{8} -2.51612 q^{9} +0.718621 q^{11} -3.30718 q^{12} +6.10237i q^{13} +10.2565i q^{14} +9.09488 q^{16} +2.79750i q^{17} -6.53915i q^{18} +0.449931i q^{19} +2.74523 q^{21} +1.86763i q^{22} +2.47294i q^{23} -4.97937i q^{24} -15.8595 q^{26} -3.83710 q^{27} -18.7628 q^{28} -5.64100i q^{29} +9.09202i q^{31} +9.32032i q^{32} +0.499885 q^{33} -7.27043 q^{34} +11.9624 q^{36} +(-5.67153 + 2.19859i) q^{37} -1.16933 q^{38} +4.24491i q^{39} -10.2570 q^{41} +7.13460i q^{42} +0.724878i q^{43} -3.41655 q^{44} -6.42693 q^{46} +8.44915 q^{47} +6.32655 q^{48} +8.57464 q^{49} +1.94599i q^{51} -29.0126i q^{52} +8.18124 q^{53} -9.97227i q^{54} -28.2497i q^{56} +0.312980i q^{57} +14.6604 q^{58} +6.30955i q^{59} -5.93895i q^{61} -23.6293 q^{62} -9.92979 q^{63} -6.03290 q^{64} +1.29915i q^{66} +0.420184 q^{67} -13.3002i q^{68} +1.72022i q^{69} +12.2858 q^{71} +18.0109i q^{72} -13.1856 q^{73} +(-5.71393 - 14.7398i) q^{74} -2.13912i q^{76} +2.83602 q^{77} -11.0321 q^{78} -10.8733i q^{79} +4.87920 q^{81} -26.6570i q^{82} +3.21802 q^{83} -13.0517 q^{84} -1.88389 q^{86} -3.92397i q^{87} -5.14403i q^{88} -3.67421i q^{89} +24.0828i q^{91} -11.7571i q^{92} +6.32456i q^{93} +21.9586i q^{94} +6.48337i q^{96} -1.64543i q^{97} +22.2847i q^{98} -1.80813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 18 q^{4} + 18 q^{7} + 22 q^{9}+O(q^{10}) \) 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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