LMFDB - Embedded newform 925.2.d.f.924.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(924,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.924"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,18,0,0,0,6,-22,0,2,0,20,0,0,30,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			924.3
Root			$-1.36551i$ of defining polynomial
Character	$\chi$	$=$	925.924
Dual form			925.2.d.f.924.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.36551 q^{2} -2.79310i q^{3} -0.135372 q^{4} +3.81402i q^{6} -4.67865i q^{7} +2.91588 q^{8} -4.80143 q^{9} -0.186084 q^{11} +0.378109i q^{12} -4.24161 q^{13} +6.38876i q^{14} -3.71093 q^{16} +3.61534 q^{17} +6.55641 q^{18} -7.92848i q^{19} -13.0679 q^{21} +0.254101 q^{22} -3.32146 q^{23} -8.14435i q^{24} +5.79198 q^{26} +5.03157i q^{27} +0.633360i q^{28} +2.01664i q^{29} +2.04293i q^{31} -0.764435 q^{32} +0.519752i q^{33} -4.93680 q^{34} +0.649980 q^{36} +(2.98085 - 5.30231i) q^{37} +10.8264i q^{38} +11.8473i q^{39} +1.03061 q^{41} +17.8445 q^{42} +4.05248 q^{43} +0.0251907 q^{44} +4.53549 q^{46} -2.78341i q^{47} +10.3650i q^{48} -14.8897 q^{49} -10.0980i q^{51} +0.574197 q^{52} -7.67087i q^{53} -6.87067i q^{54} -13.6424i q^{56} -22.1451 q^{57} -2.75376i q^{58} +9.12948i q^{59} +12.5713i q^{61} -2.78965i q^{62} +22.4642i q^{63} +8.46571 q^{64} -0.709729i q^{66} +7.35469i q^{67} -0.489417 q^{68} +9.27717i q^{69} +15.2343 q^{71} -14.0004 q^{72} +0.622606i q^{73} +(-4.07040 + 7.24038i) q^{74} +1.07330i q^{76} +0.870623i q^{77} -16.1776i q^{78} -0.662906i q^{79} -0.350591 q^{81} -1.40732 q^{82} +9.75304i q^{83} +1.76904 q^{84} -5.53372 q^{86} +5.63270 q^{87} -0.542599 q^{88} -6.06313i q^{89} +19.8450i q^{91} +0.449633 q^{92} +5.70612 q^{93} +3.80078i q^{94} +2.13515i q^{96} -10.2018 q^{97} +20.3322 q^{98} +0.893470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 18 q^{4} + 6 q^{8} - 22 q^{9} + 2 q^{11} + 20 q^{13} + 30 q^{16} + 12 q^{17} - 26 q^{18} - 6 q^{21} - 28 q^{22} - 16 q^{23} - 12 q^{26} + 14 q^{32} - 4 q^{34} - 22 q^{36} - 14 q^{37} - 10 q^{41}+ \cdots + 84 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 18 * q^4 + 6 * q^8 - 22 * q^9 + 2 * q^11 + 20 * q^13 + 30 * q^16 + 12 * q^17 - 26 * q^18 - 6 * q^21 - 28 * q^22 - 16 * q^23 - 12 * q^26 + 14 * q^32 - 4 * q^34 - 22 * q^36 - 14 * q^37 - 10 * q^41 + 72 * q^42 - 12 * q^43 - 44 * q^44 - 24 * q^46 - 30 * q^49 + 80 * q^52 - 32 * q^57 + 126 * q^64 - 40 * q^68 + 42 * q^71 - 178 * q^72 - 50 * q^74 - 12 * q^81 + 96 * q^82 + 84 * q^84 - 64 * q^86 - 56 * q^87 - 72 * q^88 + 16 * q^92 + 76 * q^93 - 28 * q^97 + 118 * q^98 + 84 * q^99

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 $

$2$	−1.36551			−0.965564			−0.482782	−	0.875741i	$-0.660374\pi$
$2$	−1.36551			−0.965564			−0.482782	+	0.875741i	$0.660374\pi$
$3$		−	2.79310i		−	1.61260i	−0.591508	−	0.806299i	$-0.701467\pi$
$3$		−	2.79310i		−	1.61260i	0.591508	−	0.806299i	$-0.298533\pi$
$4$	−0.135372			−0.0676862
$5$		0			0
$5$		0			0
$6$			3.81402i			1.55707i
$7$		−	4.67865i		−	1.76836i	−0.467144	−	0.884181i	$-0.654717\pi$
$7$		−	4.67865i		−	1.76836i	0.467144	−	0.884181i	$-0.345283\pi$
$8$	2.91588			1.03092
$9$	−4.80143			−1.60048
$10$		0			0
$11$	−0.186084			−0.0561065			−0.0280533	−	0.999606i	$-0.508931\pi$
$11$	−0.186084			−0.0561065			−0.0280533	+	0.999606i	$0.508931\pi$
$12$			0.378109i			0.109151i
$13$	−4.24161			−1.17641			−0.588205	−	0.808712i	$-0.700165\pi$
$13$	−4.24161			−1.17641			−0.588205	+	0.808712i	$0.700165\pi$
$14$			6.38876i			1.70747i
$15$		0			0
$16$	−3.71093			−0.927732
$17$	3.61534			0.876849			0.438424	−	0.898768i	$-0.355537\pi$
$17$	3.61534			0.876849			0.438424	+	0.898768i	$0.355537\pi$
$18$	6.55641			1.54536
$19$		−	7.92848i		−	1.81892i	−0.415795	−	0.909459i	$-0.636497\pi$
$19$		−	7.92848i		−	1.81892i	0.415795	−	0.909459i	$-0.363503\pi$
$20$		0			0
$21$	−13.0679			−2.85166
$22$	0.254101			0.0541744
$23$	−3.32146			−0.692572			−0.346286	−	0.938129i	$-0.612557\pi$
$23$	−3.32146			−0.692572			−0.346286	+	0.938129i	$0.612557\pi$
$24$		−	8.14435i		−	1.66246i
$25$		0			0
$26$	5.79198			1.13590
$27$			5.03157i			0.968325i
$28$			0.633360i			0.119694i
$29$			2.01664i			0.374481i	0.982314	+	0.187241i	$0.0599544\pi$
$29$			2.01664i			0.374481i	−0.982314	+	0.187241i	$0.940046\pi$
$30$		0			0
$31$			2.04293i			0.366921i	0.983027	+	0.183461i	$0.0587300\pi$
$31$			2.04293i			0.366921i	−0.983027	+	0.183461i	$0.941270\pi$
$32$	−0.764435			−0.135134
$33$			0.519752i			0.0904773i
$34$	−4.93680			−0.846654
$35$		0			0
$36$	0.649980			0.108330
$37$	2.98085	−	5.30231i	0.490049	−	0.871695i
$37$	2.98085	−	5.30231i	0.490049	−	0.871695i
$38$			10.8264i			1.75628i
$39$			11.8473i			1.89708i
$40$		0			0
$41$	1.03061			0.160955			0.0804774	−	0.996756i	$-0.474356\pi$
$41$	1.03061			0.160955			0.0804774	+	0.996756i	$0.474356\pi$
$42$	17.8445			2.75346
$43$	4.05248			0.617998			0.308999	−	0.951062i	$-0.400006\pi$
$43$	4.05248			0.617998			0.308999	+	0.951062i	$0.400006\pi$
$44$	0.0251907			0.00379764
$45$		0			0
$46$	4.53549			0.668722
$47$		−	2.78341i		−	0.406002i	−0.979179	−	0.203001i	$-0.934931\pi$
$47$		−	2.78341i		−	0.406002i	0.979179	−	0.203001i	$-0.0650694\pi$
$48$			10.3650i			1.49606i
$49$	−14.8897			−2.12711
$50$		0			0
$51$		−	10.0980i		−	1.41401i
$52$	0.574197			0.0796268
$53$		−	7.67087i		−	1.05367i	−0.849966	−	0.526837i	$-0.823378\pi$
$53$		−	7.67087i		−	1.05367i	0.849966	−	0.526837i	$-0.176622\pi$
$54$		−	6.87067i		−	0.934980i
$55$		0			0
$56$		−	13.6424i		−	1.82304i
$57$	−22.1451			−2.93318
$58$		−	2.75376i		−	0.361586i
$59$			9.12948i			1.18856i	0.804259	+	0.594279i	$0.202562\pi$
$59$			9.12948i			1.18856i	−0.804259	+	0.594279i	$0.797438\pi$
$60$		0			0
$61$			12.5713i			1.60959i	0.593550	+	0.804797i	$0.297726\pi$
$61$			12.5713i			1.60959i	−0.593550	+	0.804797i	$0.702274\pi$
$62$		−	2.78965i		−	0.354286i
$63$			22.4642i			2.83022i
$64$	8.46571			1.05821
$65$		0			0
$66$		−	0.709729i		−	0.0873616i
$67$			7.35469i			0.898518i	0.893401	+	0.449259i	$0.148312\pi$
$67$			7.35469i			0.898518i	−0.893401	+	0.449259i	$0.851688\pi$
$68$	−0.489417			−0.0593506
$69$			9.27717i			1.11684i
$70$		0			0
$71$	15.2343			1.80798			0.903992	−	0.427549i	$-0.140623\pi$
$71$	15.2343			1.80798			0.903992	+	0.427549i	$0.140623\pi$
$72$	−14.0004			−1.64996
$73$			0.622606i			0.0728705i	0.999336	+	0.0364352i	$0.0116003\pi$
$73$			0.622606i			0.0728705i	−0.999336	+	0.0364352i	$0.988400\pi$
$74$	−4.07040	+	7.24038i	−0.473174	+	0.841677i
$75$		0			0
$76$			1.07330i			0.123116i
$77$			0.870623i			0.0992167i
$78$		−	16.1776i		−	1.83175i
$79$		−	0.662906i		−	0.0745828i	−0.999304	−	0.0372914i	$-0.988127\pi$
$79$		−	0.662906i		−	0.0745828i	0.999304	−	0.0372914i	$-0.0118730\pi$
$80$		0			0
$81$	−0.350591			−0.0389546
$82$	−1.40732			−0.155412
$83$			9.75304i			1.07054i	0.844683	+	0.535268i	$0.179789\pi$
$83$			9.75304i			1.07054i	−0.844683	+	0.535268i	$0.820211\pi$
$84$	1.76904			0.193018
$85$		0			0
$86$	−5.53372			−0.596717
$87$	5.63270			0.603888
$88$	−0.542599			−0.0578413
$89$		−	6.06313i		−	0.642691i	−0.946962	−	0.321345i	$-0.895865\pi$
$89$		−	6.06313i		−	0.642691i	0.946962	−	0.321345i	$-0.104135\pi$
$90$		0			0
$91$			19.8450i			2.08032i
$92$	0.449633			0.0468775
$93$	5.70612			0.591697
$94$			3.80078i			0.392020i
$95$		0			0
$96$			2.13515i			0.217917i
$97$	−10.2018			−1.03584			−0.517919	−	0.855430i	$-0.673293\pi$
$97$	−10.2018			−1.03584			−0.517919	+	0.855430i	$0.673293\pi$
$98$	20.3322			2.05386
$99$	0.893470			0.0897971
$100$		0			0
$101$	5.22165			0.519573			0.259787	−	0.965666i	$-0.416348\pi$
$101$	5.22165			0.519573			0.259787	+	0.965666i	$0.416348\pi$
$102$			13.7890i			1.36531i
$103$	13.4563			1.32589			0.662943	−	0.748670i	$-0.269307\pi$
$103$	13.4563			1.32589			0.662943	+	0.748670i	$0.269307\pi$
$104$	−12.3680			−1.21278
$105$		0			0
$106$			10.4747i			1.01739i
$107$			3.61849i			0.349812i	0.984585	+	0.174906i	$0.0559622\pi$
$107$			3.61849i			0.349812i	−0.984585	+	0.174906i	$0.944038\pi$
$108$		−	0.681135i		−	0.0655423i
$109$			15.9453i			1.52728i	0.645642	+	0.763640i	$0.276590\pi$
$109$			15.9453i			1.52728i	−0.645642	+	0.763640i	$0.723410\pi$
$110$		0			0
$111$	−14.8099	−	8.32583i	−1.40569	−	0.790253i
$112$			17.3621i			1.64057i
$113$	−7.28167			−0.685002			−0.342501	−	0.939517i	$-0.611274\pi$
$113$	−7.28167			−0.685002			−0.342501	+	0.939517i	$0.611274\pi$
$114$	30.2394			2.83218
$115$		0			0
$116$		−	0.272998i		−	0.0253472i
$117$	20.3658			1.88282
$118$		−	12.4664i		−	1.14763i
$119$		−	16.9149i		−	1.55059i
$120$		0			0
$121$	−10.9654			−0.996852
$122$		−	17.1663i		−	1.55417i
$123$		−	2.87861i		−	0.259556i
$124$		−	0.276556i		−	0.0248355i
$125$		0			0
$126$		−	30.6751i		−	2.73276i
$127$		−	12.3627i		−	1.09701i	−0.836148	−	0.548505i	$-0.815197\pi$
$127$		−	12.3627i		−	1.09701i	0.836148	−	0.548505i	$-0.184803\pi$
$128$	−10.0312			−0.886638
$129$		−	11.3190i		−	0.996583i
$130$		0			0
$131$		−	7.80186i		−	0.681652i	−0.940126	−	0.340826i	$-0.889293\pi$
$131$		−	7.80186i		−	0.681652i	0.940126	−	0.340826i	$-0.110707\pi$
$132$		−	0.0703601i		−	0.00612406i
$133$	−37.0945			−3.21651
$134$		−	10.0429i		−	0.867577i
$135$		0			0
$136$	10.5419			0.903961
$137$			1.28562i			0.109838i	0.998491	+	0.0549188i	$0.0174900\pi$
$137$			1.28562i			0.109838i	−0.998491	+	0.0549188i	$0.982510\pi$
$138$		−	12.6681i		−	1.07838i
$139$	−3.93652			−0.333891			−0.166946	−	0.985966i	$-0.553390\pi$
$139$	−3.93652			−0.333891			−0.166946	+	0.985966i	$0.553390\pi$
$140$		0			0
$141$	−7.77434			−0.654718
$142$	−20.8027			−1.74572
$143$	0.789297			0.0660043
$144$	17.8178			1.48481
$145$		0			0
$146$		−	0.850177i		−	0.0703611i
$147$			41.5886i			3.43017i
$148$	−0.403525	+	0.717786i	−0.0331696	+	0.0590017i
$149$	15.5509			1.27398			0.636988	−	0.770873i	$-0.280180\pi$
$149$	15.5509			1.27398			0.636988	+	0.770873i	$0.280180\pi$
$150$		0			0
$151$	15.0928			1.22824			0.614119	−	0.789213i	$-0.289511\pi$
$151$	15.0928			1.22824			0.614119	+	0.789213i	$0.289511\pi$
$152$		−	23.1185i		−	1.87516i
$153$	−17.3588			−1.40337
$154$		−	1.18885i		−	0.0958000i
$155$		0			0
$156$		−	1.60379i		−	0.128406i
$157$		−	6.89821i		−	0.550537i	−0.961367	−	0.275269i	$-0.911233\pi$
$157$		−	6.89821i		−	0.550537i	0.961367	−	0.275269i	$-0.0887668\pi$
$158$			0.905208i			0.0720144i
$159$	−21.4255			−1.69915
$160$		0			0
$161$			15.5399i			1.22472i
$162$	0.478737			0.0376131
$163$	−4.42444			−0.346549			−0.173275	−	0.984874i	$-0.555435\pi$
$163$	−4.42444			−0.346549			−0.173275	+	0.984874i	$0.555435\pi$
$164$	−0.139517			−0.0108944
$165$		0			0
$166$		−	13.3179i		−	1.03367i
$167$	−16.1383			−1.24882			−0.624411	−	0.781096i	$-0.714661\pi$
$167$	−16.1383			−1.24882			−0.624411	+	0.781096i	$0.714661\pi$
$168$	−38.1046			−2.93983
$169$	4.99126			0.383943
$170$		0			0
$171$			38.0680i			2.91113i
$172$	−0.548594			−0.0418299
$173$		−	23.7342i		−	1.80448i	−0.431236	−	0.902239i	$-0.641922\pi$
$173$		−	23.7342i		−	1.80448i	0.431236	−	0.902239i	$-0.358078\pi$
$174$	−7.69152			−0.583093
$175$		0			0
$176$	0.690545			0.0520518
$177$	25.4996			1.91667
$178$			8.27929i			0.620559i
$179$		−	7.66128i		−	0.572631i	−0.958135	−	0.286315i	$-0.907570\pi$
$179$		−	7.66128i		−	0.572631i	0.958135	−	0.286315i	$-0.0924305\pi$
$180$		0			0
$181$	−13.9590			−1.03756			−0.518781	−	0.854907i	$-0.673614\pi$
$181$	−13.9590			−1.03756			−0.518781	+	0.854907i	$0.673614\pi$
$182$		−	27.0986i		−	2.00868i
$183$	35.1130			2.59563
$184$	−9.68497			−0.713985
$185$		0			0
$186$	−7.79178			−0.571321
$187$	−0.672758			−0.0491969
$188$			0.376796i			0.0274807i
$189$	23.5409			1.71235
$190$		0			0
$191$		−	20.7490i		−	1.50134i	−0.660675	−	0.750672i	$-0.729730\pi$
$191$		−	20.7490i		−	1.50134i	0.660675	−	0.750672i	$-0.270270\pi$
$192$		−	23.6456i		−	1.70647i
$193$	−9.18440			−0.661108			−0.330554	−	0.943787i	$-0.607236\pi$
$193$	−9.18440			−0.661108			−0.330554	+	0.943787i	$0.607236\pi$
$194$	13.9307			1.00017
$195$		0			0
$196$	2.01566			0.143976
$197$		−	8.62507i		−	0.614511i	−0.951627	−	0.307255i	$-0.900589\pi$
$197$		−	8.62507i		−	0.614511i	0.951627	−	0.307255i	$-0.0994106\pi$
$198$	−1.22004			−0.0867048
$199$			1.09459i			0.0775938i	0.999247	+	0.0387969i	$0.0123525\pi$
$199$			1.09459i			0.0775938i	−0.999247	+	0.0387969i	$0.987647\pi$
$200$		0			0
$201$	20.5424			1.44895
$202$	−7.13023			−0.501681
$203$	9.43517			0.662219
$204$			1.36699i			0.0957087i
$205$		0			0
$206$	−18.3747			−1.28023
$207$	15.9477			1.10844
$208$	15.7403			1.09139
$209$			1.47536i			0.102053i
$210$		0			0
$211$	6.92566			0.476782			0.238391	−	0.971169i	$-0.423380\pi$
$211$	6.92566			0.476782			0.238391	+	0.971169i	$0.423380\pi$
$212$			1.03842i			0.0713192i
$213$		−	42.5511i		−	2.91555i
$214$		−	4.94109i		−	0.337766i
$215$		0			0
$216$			14.6714i			0.998265i
$217$	9.55815			0.648850
$218$		−	21.7735i		−	1.47469i
$219$	1.73900			0.117511
$220$		0			0
$221$	−15.3349			−1.03153
$222$	20.2231	+	11.3690i	1.35729	+	0.763040i
$223$		−	5.75304i		−	0.385252i	−0.981272	−	0.192626i	$-0.938300\pi$
$223$		−	5.75304i		−	0.385252i	0.981272	−	0.192626i	$-0.0617004\pi$
$224$			3.57652i			0.238967i
$225$		0			0
$226$	9.94322			0.661413
$227$	−7.56947			−0.502404			−0.251202	−	0.967935i	$-0.580826\pi$
$227$	−7.56947			−0.502404			−0.251202	+	0.967935i	$0.580826\pi$
$228$	2.99783			0.198536
$229$	19.8975			1.31487			0.657433	−	0.753513i	$-0.271642\pi$
$229$	19.8975			1.31487			0.657433	+	0.753513i	$0.271642\pi$
$230$		0			0
$231$	2.43174			0.159997
$232$			5.88029i			0.386060i
$233$		−	17.7494i		−	1.16280i	−0.813616	−	0.581402i	$-0.802504\pi$
$233$		−	17.7494i		−	1.16280i	0.813616	−	0.581402i	$-0.197496\pi$
$234$	−27.8097			−1.81798
$235$		0			0
$236$		−	1.23588i		−	0.0804489i
$237$	−1.85157			−0.120272
$238$			23.0975i			1.49719i
$239$		−	9.34261i		−	0.604323i	−0.953257	−	0.302162i	$-0.902292\pi$
$239$		−	9.34261i		−	0.604323i	0.953257	−	0.302162i	$-0.0977082\pi$
$240$		0			0
$241$		−	13.0233i		−	0.838903i	−0.907778	−	0.419452i	$-0.862222\pi$
$241$		−	13.0233i		−	0.838903i	0.907778	−	0.419452i	$-0.137778\pi$
$242$	14.9734			0.962524
$243$			16.0739i			1.03114i
$244$		−	1.70181i		−	0.108947i
$245$		0			0
$246$			3.93078i			0.250618i
$247$			33.6295i			2.13979i
$248$			5.95694i			0.378266i
$249$	27.2412			1.72634
$250$		0			0
$251$		−	7.49230i		−	0.472910i	−0.971642	−	0.236455i	$-0.924014\pi$
$251$		−	7.49230i		−	0.472910i	0.971642	−	0.236455i	$-0.0759856\pi$
$252$		−	3.04103i		−	0.191567i
$253$	0.618071			0.0388578
$254$			16.8814i			1.05923i
$255$		0			0
$256$	−3.23372			−0.202107
$257$	−2.57062			−0.160351			−0.0801756	−	0.996781i	$-0.525548\pi$
$257$	−2.57062			−0.160351			−0.0801756	+	0.996781i	$0.525548\pi$
$258$			15.4563i			0.962265i
$259$	−24.8076	−	13.9464i	−1.54147	−	0.866585i
$260$		0			0
$261$		−	9.68277i		−	0.599348i
$262$			10.6535i			0.658178i
$263$			18.2800i			1.12719i	0.826050	+	0.563597i	$0.190583\pi$
$263$			18.2800i			1.12719i	−0.826050	+	0.563597i	$0.809417\pi$
$264$			1.51554i			0.0932748i
$265$		0			0
$266$	50.6531			3.10574
$267$	−16.9350			−1.03640
$268$		−	0.995622i		−	0.0608173i
$269$	2.38487			0.145408			0.0727040	−	0.997354i	$-0.476837\pi$
$269$	2.38487			0.145408			0.0727040	+	0.997354i	$0.476837\pi$
$270$		0			0
$271$	−8.55124			−0.519451			−0.259725	−	0.965683i	$-0.583632\pi$
$271$	−8.55124			−0.519451			−0.259725	+	0.965683i	$0.583632\pi$
$272$	−13.4163			−0.813481
$273$	55.4291			3.35472
$274$		−	1.75553i		−	0.106055i
$275$		0			0
$276$		−	1.25587i		−	0.0755947i
$277$	19.1136			1.14843			0.574214	−	0.818705i	$-0.305308\pi$
$277$	19.1136			1.14843			0.574214	+	0.818705i	$0.305308\pi$
$278$	5.37537			0.322393
$279$		−	9.80898i		−	0.587248i
$280$		0			0
$281$		−	4.61050i		−	0.275039i	−0.990499	−	0.137520i	$-0.956087\pi$
$281$		−	4.61050i		−	0.275039i	0.990499	−	0.137520i	$-0.0439130\pi$
$282$	10.6160			0.632172
$283$	−11.3598			−0.675273			−0.337636	−	0.941277i	$-0.609627\pi$
$283$	−11.3598			−0.675273			−0.337636	+	0.941277i	$0.609627\pi$
$284$	−2.06231			−0.122376
$285$		0			0
$286$	−1.07780			−0.0637314
$287$		−	4.82188i		−	0.284627i
$288$	3.67038			0.216279
$289$	−3.92931			−0.231136
$290$		0			0
$291$			28.4948i			1.67039i
$292$		−	0.0842836i		−	0.00493233i
$293$			14.0612i			0.821466i	0.911756	+	0.410733i	$0.134727\pi$
$293$			14.0612i			0.821466i	−0.911756	+	0.410733i	$0.865273\pi$
$294$		−	56.7898i		−	3.31205i
$295$		0			0
$296$	8.69182	−	15.4609i	0.505201	−	0.898647i
$297$		−	0.936295i		−	0.0543294i
$298$	−21.2349			−1.23011
$299$	14.0883			0.814749
$300$		0			0
$301$		−	18.9601i		−	1.09284i
$302$	−20.6095			−1.18594
$303$		−	14.5846i		−	0.837863i
$304$			29.4220i			1.68747i
$305$		0			0
$306$	23.7037			1.35505
$307$		−	9.03504i		−	0.515657i	−0.966191	−	0.257829i	$-0.916993\pi$
$307$		−	9.03504i		−	0.515657i	0.966191	−	0.257829i	$-0.0830070\pi$
$308$		−	0.117858i		−	0.00671560i
$309$		−	37.5847i		−	2.13812i
$310$		0			0
$311$			28.0432i			1.59019i	0.606487	+	0.795093i	$0.292578\pi$
$311$			28.0432i			1.59019i	−0.606487	+	0.795093i	$0.707422\pi$
$312$			34.5452i			1.95574i
$313$	−15.7374			−0.889528			−0.444764	−	0.895648i	$-0.646713\pi$
$313$	−15.7374			−0.889528			−0.444764	+	0.895648i	$0.646713\pi$
$314$			9.41961i			0.531579i
$315$		0			0
$316$			0.0897392i			0.00504822i
$317$			32.4811i			1.82432i	0.409836	+	0.912159i	$0.365586\pi$
$317$			32.4811i			1.82432i	−0.409836	+	0.912159i	$0.634414\pi$
$318$	29.2568			1.64064
$319$		−	0.375266i		−	0.0210108i
$320$		0			0
$321$	10.1068			0.564107
$322$		−	21.2200i		−	1.18254i
$323$		−	28.6641i		−	1.59492i
$324$	0.0474604			0.00263669
$325$		0			0
$326$	6.04164			0.334615
$327$	44.5368			2.46289
$328$	3.00515			0.165931
$329$	−13.0226			−0.717958
$330$		0			0
$331$		−	23.2086i		−	1.27566i	−0.770177	−	0.637830i	$-0.779832\pi$
$331$		−	23.2086i		−	1.27566i	0.770177	−	0.637830i	$-0.220168\pi$
$332$		−	1.32029i		−	0.0724605i
$333$	−14.3124	+	25.4587i	−0.784312	+	1.39513i
$334$	22.0371			1.20582
$335$		0			0
$336$	48.4942			2.64558
$337$		−	4.46538i		−	0.243245i	−0.992576	−	0.121622i	$-0.961190\pi$
$337$		−	4.46538i		−	0.243245i	0.992576	−	0.121622i	$-0.0388096\pi$
$338$	−6.81563			−0.370721
$339$			20.3385i			1.10463i
$340$		0			0
$341$		−	0.380157i		−	0.0205867i
$342$		−	51.9824i		−	2.81088i
$343$			36.9134i			1.99313i
$344$	11.8166			0.637106
$345$		0			0
$346$			32.4094i			1.74234i
$347$	9.36350			0.502659			0.251330	−	0.967902i	$-0.419132\pi$
$347$	9.36350			0.502659			0.251330	+	0.967902i	$0.419132\pi$
$348$	−0.762511			−0.0408749
$349$	−15.2015			−0.813720			−0.406860	−	0.913490i	$-0.633376\pi$
$349$	−15.2015			−0.813720			−0.406860	+	0.913490i	$0.633376\pi$
$350$		0			0
$351$		−	21.3419i		−	1.13915i
$352$	0.142249			0.00758192
$353$	4.76686			0.253714			0.126857	−	0.991921i	$-0.459511\pi$
$353$	4.76686			0.253714			0.126857	+	0.991921i	$0.459511\pi$
$354$	−34.8200			−1.85066
$355$		0			0
$356$			0.820781i			0.0435013i
$357$	−47.2451			−2.50048
$358$			10.4616i			0.552911i
$359$	−4.76777			−0.251633			−0.125817	−	0.992054i	$-0.540155\pi$
$359$	−4.76777			−0.251633			−0.125817	+	0.992054i	$0.540155\pi$
$360$		0			0
$361$	−43.8607			−2.30846
$362$	19.0612			1.00183
$363$			30.6274i			1.60752i
$364$		−	2.68647i		−	0.140809i
$365$		0			0
$366$	−47.9473			−2.50625
$367$		−	13.5255i		−	0.706027i	−0.935618	−	0.353014i	$-0.885157\pi$
$367$		−	13.5255i		−	0.706027i	0.935618	−	0.353014i	$-0.114843\pi$
$368$	12.3257			0.642521
$369$	−4.94842			−0.257604
$370$		0			0
$371$	−35.8893			−1.86328
$372$	−0.772450			−0.0400497
$373$			17.6980i			0.916366i	0.888858	+	0.458183i	$0.151500\pi$
$373$			17.6980i			0.916366i	−0.888858	+	0.458183i	$0.848500\pi$
$374$	0.918660			0.0475028
$375$		0			0
$376$		−	8.11608i		−	0.418555i
$377$		−	8.55382i		−	0.440544i
$378$	−32.1455			−1.65338
$379$	−10.1646			−0.522123			−0.261061	−	0.965322i	$-0.584073\pi$
$379$	−10.1646			−0.522123			−0.261061	+	0.965322i	$0.584073\pi$
$380$		0			0
$381$	−34.5302			−1.76904
$382$			28.3330i			1.44964i
$383$	−36.9494			−1.88802			−0.944012	−	0.329911i	$-0.892981\pi$
$383$	−36.9494			−1.88802			−0.944012	+	0.329911i	$0.892981\pi$
$384$			28.0181i			1.42979i
$385$		0			0
$386$	12.5414			0.638342
$387$	−19.4577			−0.989090
$388$	1.38105			0.0701120
$389$		−	24.8802i		−	1.26148i	−0.775995	−	0.630739i	$-0.782752\pi$
$389$		−	24.8802i		−	1.26148i	0.775995	−	0.630739i	$-0.217248\pi$
$390$		0			0
$391$	−12.0082			−0.607281
$392$	−43.4167			−2.19288
$393$	−21.7914			−1.09923
$394$			11.7776i			0.593349i
$395$		0			0
$396$	−0.120951			−0.00607802
$397$		−	3.14936i		−	0.158062i	−0.996872	−	0.0790308i	$-0.974817\pi$
$397$		−	3.14936i		−	0.158062i	0.996872	−	0.0790308i	$-0.0251826\pi$
$398$		−	1.49468i		−	0.0749218i
$399$			103.609i			5.18693i
$400$		0			0
$401$		−	37.0988i		−	1.85263i	−0.376756	−	0.926313i	$-0.622960\pi$
$401$		−	37.0988i		−	1.85263i	0.376756	−	0.926313i	$-0.377040\pi$
$402$	−28.0509			−1.39905
$403$		−	8.66531i		−	0.431650i
$404$	−0.706867			−0.0351679
$405$		0			0
$406$	−12.8839			−0.639415
$407$	−0.554690	+	0.986677i	−0.0274950	+	0.0489077i
$408$		−	29.4446i		−	1.45773i
$409$			16.6487i			0.823226i	0.911359	+	0.411613i	$0.135034\pi$
$409$			16.6487i			0.823226i	−0.911359	+	0.411613i	$0.864966\pi$
$410$		0			0
$411$	3.59086			0.177124
$412$	−1.82161			−0.0897441
$413$	42.7136			2.10180
$414$	−21.7768			−1.07027
$415$		0			0
$416$	3.24244			0.158974
$417$			10.9951i			0.538433i
$418$		−	2.01463i		−	0.0985388i
$419$	8.08323			0.394892			0.197446	−	0.980314i	$-0.436735\pi$
$419$	8.08323			0.394892			0.197446	+	0.980314i	$0.436735\pi$
$420$		0			0
$421$			14.4462i			0.704067i	0.935987	+	0.352034i	$0.114510\pi$
$421$			14.4462i			0.704067i	−0.935987	+	0.352034i	$0.885490\pi$
$422$	−9.45708			−0.460363
$423$			13.3643i			0.649795i
$424$		−	22.3673i		−	1.08625i
$425$		0			0
$426$			58.1041i			2.81515i
$427$	58.8169			2.84635
$428$		−	0.489843i		−	0.0236775i
$429$		−	2.20459i		−	0.106438i
$430$		0			0
$431$		−	13.8283i		−	0.666086i	−0.942912	−	0.333043i	$-0.891925\pi$
$431$		−	13.8283i		−	0.666086i	0.942912	−	0.333043i	$-0.108075\pi$
$432$		−	18.6718i		−	0.898347i
$433$		−	18.0931i		−	0.869497i	−0.900552	−	0.434749i	$-0.856837\pi$
$433$		−	18.0931i		−	0.869497i	0.900552	−	0.434749i	$-0.143163\pi$
$434$	−13.0518			−0.626506
$435$		0			0
$436$		−	2.15855i		−	0.103376i
$437$			26.3341i			1.25973i
$438$	−2.37463			−0.113464
$439$		−	0.179590i		−	0.00857135i	−0.999991	−	0.00428567i	$-0.998636\pi$
$439$		−	0.179590i		−	0.00857135i	0.999991	−	0.00428567i	$-0.00136418\pi$
$440$		0			0
$441$	71.4920			3.40438
$442$	20.9400			0.996013
$443$		−	3.43515i		−	0.163209i	−0.996665	−	0.0816045i	$-0.973996\pi$
$443$		−	3.43515i		−	0.163209i	0.996665	−	0.0816045i	$-0.0260044\pi$
$444$	2.00485	+	1.12709i	0.0951461	+	0.0534892i
$445$		0			0
$446$			7.85586i			0.371986i
$447$		−	43.4352i		−	2.05441i
$448$		−	39.6081i		−	1.87130i
$449$			26.3383i			1.24298i	0.783422	+	0.621490i	$0.213472\pi$
$449$			26.3383i			1.24298i	−0.783422	+	0.621490i	$0.786528\pi$
$450$		0			0
$451$	−0.191781			−0.00903062
$452$	0.985737			0.0463652
$453$		−	42.1559i		−	1.98066i
$454$	10.3362			0.485103
$455$		0			0
$456$	−64.5723			−3.02388
$457$	−9.74641			−0.455918			−0.227959	−	0.973671i	$-0.573205\pi$
$457$	−9.74641			−0.455918			−0.227959	+	0.973671i	$0.573205\pi$
$458$	−27.1704			−1.26959
$459$			18.1908i			0.849075i
$460$		0			0
$461$		−	17.7513i		−	0.826763i	−0.910558	−	0.413381i	$-0.864348\pi$
$461$		−	17.7513i		−	0.826763i	0.910558	−	0.413381i	$-0.135652\pi$
$462$	−3.32057			−0.154487
$463$	32.0881			1.49126			0.745629	−	0.666361i	$-0.232149\pi$
$463$	32.0881			1.49126			0.745629	+	0.666361i	$0.232149\pi$
$464$		−	7.48362i		−	0.347419i
$465$		0			0
$466$			24.2371i			1.12276i
$467$	−28.3944			−1.31393			−0.656967	−	0.753919i	$-0.728161\pi$
$467$	−28.3944			−1.31393			−0.656967	+	0.753919i	$0.728161\pi$
$468$	−2.75696			−0.127441
$469$	34.4100			1.58891
$470$		0			0
$471$	−19.2674			−0.887796
$472$			26.6205i			1.22531i
$473$	−0.754103			−0.0346737
$474$	2.52834			0.116130
$475$		0			0
$476$			2.28981i			0.104953i
$477$			36.8311i			1.68638i
$478$			12.7575i			0.583513i
$479$			1.49825i			0.0684567i	0.999414	+	0.0342283i	$0.0108973\pi$
$479$			1.49825i			0.0684567i	−0.999414	+	0.0342283i	$0.989103\pi$
$480$		0			0
$481$	−12.6436	+	22.4903i	−0.576500	+	1.02547i
$482$			17.7835i			0.810015i
$483$	43.4046			1.97498
$484$	1.48441			0.0674731
$485$		0			0
$486$		−	21.9492i		−	0.995635i
$487$	−31.5505			−1.42969			−0.714844	−	0.699284i	$-0.753502\pi$
$487$	−31.5505			−1.42969			−0.714844	+	0.699284i	$0.753502\pi$
$488$			36.6565i			1.65936i
$489$			12.3579i			0.558845i
$490$		0			0
$491$	16.9549			0.765166			0.382583	−	0.923921i	$-0.375035\pi$
$491$	16.9549			0.765166			0.382583	+	0.923921i	$0.375035\pi$
$492$			0.389684i			0.0175683i
$493$			7.29086i			0.328364i
$494$		−	45.9215i		−	2.06611i
$495$		0			0
$496$		−	7.58117i		−	0.340405i
$497$		−	71.2761i		−	3.19717i
$498$	−37.1983			−1.66690
$499$		−	15.1962i		−	0.680274i	−0.940376	−	0.340137i	$-0.889527\pi$
$499$		−	15.1962i		−	0.680274i	0.940376	−	0.340137i	$-0.110473\pi$
$500$		0			0
$501$			45.0761i			2.01385i
$502$			10.2308i			0.456625i
$503$	−2.02764			−0.0904081			−0.0452040	−	0.998978i	$-0.514394\pi$
$503$	−2.02764			−0.0904081			−0.0452040	+	0.998978i	$0.514394\pi$
$504$			65.5029i			2.91773i
$505$		0			0
$506$	−0.843984			−0.0375197
$507$		−	13.9411i		−	0.619146i
$508$			1.67356i			0.0742524i
$509$	4.66055			0.206575			0.103288	−	0.994652i	$-0.467064\pi$
$509$	4.66055			0.206575			0.103288	+	0.994652i	$0.467064\pi$
$510$		0			0
$511$	2.91295			0.128861
$512$	24.4780			1.08179
$513$	39.8927			1.76130
$514$	3.51022			0.154829
$515$		0			0
$516$			1.53228i			0.0674549i
$517$			0.517948i			0.0227793i
$518$	33.8752	+	19.0440i	1.48839	+	0.836744i
$519$	−66.2921			−2.90990
$520$		0			0
$521$	23.5400			1.03130			0.515652	−	0.856798i	$-0.327550\pi$
$521$	23.5400			1.03130			0.515652	+	0.856798i	$0.327550\pi$
$522$			13.2219i			0.578709i
$523$	−11.4942			−0.502607			−0.251303	−	0.967908i	$-0.580859\pi$
$523$	−11.4942			−0.502607			−0.251303	+	0.967908i	$0.580859\pi$
$524$			1.05616i			0.0461384i
$525$		0			0
$526$		−	24.9616i		−	1.08838i
$527$			7.38589i			0.321734i
$528$		−	1.92876i		−	0.0839387i
$529$	−11.9679			−0.520345
$530$		0			0
$531$		−	43.8345i		−	1.90226i
$532$	5.02158			0.217713
$533$	−4.37146			−0.189349
$534$	23.1249			1.00071
$535$		0			0
$536$			21.4454i			0.926300i
$537$	−21.3987			−0.923423
$538$	−3.25657			−0.140401
$539$	2.77075			0.119345
$540$		0			0
$541$			27.6299i			1.18790i	0.804500	+	0.593952i	$0.202433\pi$
$541$			27.6299i			1.18790i	−0.804500	+	0.593952i	$0.797567\pi$
$542$	11.6768			0.501563
$543$			38.9888i			1.67317i
$544$	−2.76369			−0.118492
$545$		0			0
$546$	−75.6892			−3.23920
$547$	−32.6357			−1.39540			−0.697700	−	0.716390i	$-0.745793\pi$
$547$	−32.6357			−1.39540			−0.697700	+	0.716390i	$0.745793\pi$
$548$		−	0.174037i		−	0.00743449i
$549$		−	60.3603i		−	2.57612i
$550$		0			0
$551$	15.9889			0.681151
$552$			27.0511i			1.15137i
$553$	−3.10150			−0.131889
$554$	−26.0999			−1.10888
$555$		0			0
$556$	0.532896			0.0225998
$557$	23.9676			1.01554			0.507771	−	0.861492i	$-0.330470\pi$
$557$	23.9676			1.01554			0.507771	+	0.861492i	$0.330470\pi$
$558$			13.3943i			0.567026i
$559$	−17.1891			−0.727020
$560$		0			0
$561$			1.87908i			0.0793349i
$562$			6.29570i			0.265568i
$563$	−15.7977			−0.665792			−0.332896	−	0.942964i	$-0.608026\pi$
$563$	−15.7977			−0.665792			−0.332896	+	0.942964i	$0.608026\pi$
$564$	1.05243			0.0443153
$565$		0			0
$566$	15.5120			0.652019
$567$			1.64029i			0.0688858i
$568$	44.4215			1.86389
$569$		−	24.2188i		−	1.01530i	−0.861562	−	0.507652i	$-0.830514\pi$
$569$		−	24.2188i		−	1.01530i	0.861562	−	0.507652i	$-0.169486\pi$
$570$		0			0
$571$	24.0429			1.00617			0.503083	−	0.864238i	$-0.332199\pi$
$571$	24.0429			1.00617			0.503083	+	0.864238i	$0.332199\pi$
$572$	−0.106849			−0.00446758
$573$	−57.9540			−2.42106
$574$			6.58434i			0.274825i
$575$		0			0
$576$	−40.6475			−1.69364
$577$	−23.8305			−0.992076			−0.496038	−	0.868301i	$-0.665212\pi$
$577$	−23.8305			−0.992076			−0.496038	+	0.868301i	$0.665212\pi$
$578$	5.36553			0.223176
$579$			25.6530i			1.06610i
$580$		0			0
$581$	45.6310			1.89309
$582$		−	38.9100i		−	1.61287i
$583$			1.42743i			0.0591180i
$584$			1.81544i			0.0751236i
$585$		0			0
$586$		−	19.2008i		−	0.793178i
$587$	7.16402			0.295691			0.147845	−	0.989010i	$-0.452766\pi$
$587$	7.16402			0.295691			0.147845	+	0.989010i	$0.452766\pi$
$588$		−	5.62995i		−	0.232175i
$589$	16.1973			0.667399
$590$		0			0
$591$	−24.0907			−0.990959
$592$	−11.0617	+	19.6765i	−0.454635	+	0.808699i
$593$			33.0533i			1.35734i	0.734445	+	0.678668i	$0.237442\pi$
$593$			33.0533i			1.35734i	−0.734445	+	0.678668i	$0.762558\pi$
$594$			1.27852i			0.0524585i
$595$		0			0
$596$	−2.10516			−0.0862306
$597$	3.05732			0.125128
$598$	−19.2378			−0.786692
$599$	40.2670			1.64527			0.822633	−	0.568572i	$-0.192504\pi$
$599$	40.2670			1.64527			0.822633	+	0.568572i	$0.192504\pi$
$600$		0			0
$601$	6.28442			0.256347			0.128173	−	0.991752i	$-0.459089\pi$
$601$	6.28442			0.256347			0.128173	+	0.991752i	$0.459089\pi$
$602$			25.8903i			1.05521i
$603$		−	35.3130i		−	1.43806i
$604$	−2.04315			−0.0831348
$605$		0			0
$606$			19.9155i			0.809010i
$607$	26.3428			1.06922			0.534611	−	0.845098i	$-0.320458\pi$
$607$	26.3428			1.06922			0.534611	+	0.845098i	$0.320458\pi$
$608$			6.06081i			0.245798i
$609$		−	26.3534i		−	1.06789i
$610$		0			0
$611$			11.8061i			0.477625i
$612$	2.34990			0.0949891
$613$		−	29.2189i		−	1.18014i	−0.807352	−	0.590070i	$-0.799100\pi$
$613$		−	29.2189i		−	1.18014i	0.807352	−	0.590070i	$-0.200900\pi$
$614$			12.3375i			0.497900i
$615$		0			0
$616$			2.53863i			0.102284i
$617$		−	6.55954i		−	0.264077i	−0.991245	−	0.132039i	$-0.957848\pi$
$617$		−	6.55954i		−	0.264077i	0.991245	−	0.132039i	$-0.0421523\pi$
$618$			51.3225i			2.06449i
$619$	−11.6979			−0.470177			−0.235088	−	0.971974i	$-0.575538\pi$
$619$	−11.6979			−0.470177			−0.235088	+	0.971974i	$0.575538\pi$
$620$		0			0
$621$		−	16.7121i		−	0.670635i
$622$		−	38.2934i		−	1.53543i
$623$	−28.3673			−1.13651
$624$		−	43.9643i		−	1.75998i
$625$		0			0
$626$	21.4896			0.858897
$627$	4.12084			0.164571
$628$			0.933828i			0.0372638i
$629$	10.7768	−	19.1697i	0.429699	−	0.764345i
$630$		0			0
$631$			7.02214i			0.279547i	0.990183	+	0.139774i	$0.0446375\pi$
$631$			7.02214i			0.279547i	−0.990183	+	0.139774i	$0.955363\pi$
$632$		−	1.93296i		−	0.0768888i
$633$		−	19.3441i		−	0.768858i
$634$		−	44.3533i		−	1.76150i
$635$		0			0
$636$	2.90042			0.115009
$637$	63.1565			2.50235
$638$			0.512430i			0.0202873i
$639$	−73.1466			−2.89363
$640$		0			0
$641$	36.0787			1.42502			0.712511	−	0.701661i	$-0.247558\pi$
$641$	36.0787			1.42502			0.712511	+	0.701661i	$0.247558\pi$
$642$	−13.8010			−0.544681
$643$	46.9144			1.85012			0.925062	−	0.379817i	$-0.124013\pi$
$643$	46.9144			1.85012			0.925062	+	0.379817i	$0.124013\pi$
$644$		−	2.10368i		−	0.0828965i
$645$		0			0
$646$			39.1413i			1.53999i
$647$	−6.09043			−0.239439			−0.119720	−	0.992808i	$-0.538200\pi$
$647$	−6.09043			−0.239439			−0.119720	+	0.992808i	$0.538200\pi$
$648$	−1.02228			−0.0401590
$649$		−	1.69885i		−	0.0666858i
$650$		0			0
$651$		−	26.6969i		−	1.04633i
$652$	0.598947			0.0234566
$653$	37.3874			1.46308			0.731540	−	0.681798i	$-0.238802\pi$
$653$	37.3874			1.46308			0.731540	+	0.681798i	$0.238802\pi$
$654$	−60.8156			−2.37808
$655$		0			0
$656$	−3.82454			−0.149323
$657$		−	2.98940i		−	0.116627i
$658$	17.7825			0.693234
$659$	−6.06336			−0.236195			−0.118098	−	0.993002i	$-0.537680\pi$
$659$	−6.06336			−0.236195			−0.118098	+	0.993002i	$0.537680\pi$
$660$		0			0
$661$			1.09225i			0.0424835i	0.999774	+	0.0212418i	$0.00676197\pi$
$661$			1.09225i			0.0424835i	−0.999774	+	0.0212418i	$0.993238\pi$
$662$			31.6917i			1.23173i
$663$			42.8319i			1.66345i
$664$			28.4387i			1.10364i
$665$		0			0
$666$	19.5437	−	34.7641i	0.757303	−	1.34708i
$667$		−	6.69820i		−	0.259355i
$668$	2.18469			0.0845280
$669$	−16.0688			−0.621257
$670$		0			0
$671$		−	2.33933i		−	0.0903087i
$672$	9.98960			0.385357
$673$			10.6301i			0.409762i	0.978787	+	0.204881i	$0.0656807\pi$
$673$			10.6301i			0.409762i	−0.978787	+	0.204881i	$0.934319\pi$
$674$			6.09753i			0.234868i
$675$		0			0
$676$	−0.675678			−0.0259876
$677$			15.3033i			0.588153i	0.955782	+	0.294076i	$0.0950120\pi$
$677$			15.3033i			0.588153i	−0.955782	+	0.294076i	$0.904988\pi$
$678$		−	27.7724i		−	1.06659i
$679$			47.7308i			1.83174i
$680$		0			0
$681$			21.1423i			0.810175i
$682$			0.519110i			0.0198777i
$683$	23.6010			0.903066			0.451533	−	0.892255i	$-0.350877\pi$
$683$	23.6010			0.903066			0.451533	+	0.892255i	$0.350877\pi$
$684$		−	5.15335i		−	0.197043i
$685$		0			0
$686$		−	50.4057i		−	1.92450i
$687$		−	55.5759i		−	2.12035i
$688$	−15.0385			−0.573337
$689$			32.5368i			1.23955i
$690$		0			0
$691$	−32.4523			−1.23454			−0.617271	−	0.786751i	$-0.711762\pi$
$691$	−32.4523			−1.23454			−0.617271	+	0.786751i	$0.711762\pi$
$692$			3.21296i			0.122138i
$693$		−	4.18023i		−	0.158794i
$694$	−12.7860			−0.485350
$695$		0			0
$696$	16.4243			0.622560
$697$	3.72602			0.141133
$698$	20.7579			0.785699
$699$	−49.5760			−1.87514
$700$		0			0
$701$			29.6756i			1.12083i	0.828211	+	0.560416i	$0.189359\pi$
$701$			29.6756i			1.12083i	−0.828211	+	0.560416i	$0.810641\pi$
$702$			29.1427i			1.09992i
$703$	−42.0392	−	23.6336i	−1.58554	−	0.891359i
$704$	−1.57533			−0.0593727
$705$		0			0
$706$	−6.50921			−0.244977
$707$		−	24.4302i		−	0.918794i
$708$	−3.45194			−0.129732
$709$			2.33245i			0.0875969i	0.999040	+	0.0437985i	$0.0139459\pi$
$709$			2.33245i			0.0875969i	−0.999040	+	0.0437985i	$0.986054\pi$
$710$		0			0
$711$			3.18289i			0.119368i
$712$		−	17.6794i		−	0.662562i
$713$		−	6.78550i		−	0.254119i
$714$	64.5138			2.41437
$715$		0			0
$716$			1.03713i			0.0387592i
$717$	−26.0949			−0.974531
$718$	6.51045			0.242968
$719$	38.0117			1.41760			0.708799	−	0.705410i	$-0.249237\pi$
$719$	38.0117			1.41760			0.708799	+	0.705410i	$0.249237\pi$
$720$		0			0
$721$		−	62.9572i		−	2.34465i
$722$	59.8924			2.22897
$723$	−36.3754			−1.35281
$724$	1.88966			0.0702286
$725$		0			0
$726$		−	41.8222i		−	1.55217i
$727$	11.8176			0.438289			0.219145	−	0.975692i	$-0.429673\pi$
$727$	11.8176			0.438289			0.219145	+	0.975692i	$0.429673\pi$
$728$			57.8656i			2.14464i
$729$	43.8444			1.62387
$730$		0			0
$731$	14.6511			0.541891
$732$	−4.75333			−0.175688
$733$		−	26.8937i		−	0.993340i	−0.867939	−	0.496670i	$-0.834556\pi$
$733$		−	26.8937i		−	0.993340i	0.867939	−	0.496670i	$-0.165444\pi$
$734$			18.4693i			0.681715i
$735$		0			0
$736$	2.53904			0.0935902
$737$		−	1.36859i		−	0.0504127i
$738$	6.75713			0.248733
$739$	19.0328			0.700134			0.350067	−	0.936725i	$-0.386159\pi$
$739$	19.0328			0.700134			0.350067	+	0.936725i	$0.386159\pi$
$740$		0			0
$741$	93.9307			3.45063
$742$	49.0073			1.79912
$743$		−	22.1010i		−	0.810806i	−0.914138	−	0.405403i	$-0.867131\pi$
$743$		−	22.1010i		−	0.810806i	0.914138	−	0.405403i	$-0.132869\pi$
$744$	16.6383			0.609991
$745$		0			0
$746$		−	24.1668i		−	0.884810i
$747$		−	46.8285i		−	1.71337i
$748$	0.0910728			0.00332995
$749$	16.9296			0.618595
$750$		0			0
$751$	−35.7157			−1.30328			−0.651641	−	0.758527i	$-0.725919\pi$
$751$	−35.7157			−1.30328			−0.651641	+	0.758527i	$0.725919\pi$
$752$			10.3290i			0.376661i
$753$	−20.9268			−0.762614
$754$			11.6804i			0.425373i
$755$		0			0
$756$	−3.18679			−0.115902
$757$	9.16811			0.333221			0.166610	−	0.986023i	$-0.446718\pi$
$757$	9.16811			0.333221			0.166610	+	0.986023i	$0.446718\pi$
$758$	13.8800			0.504143
$759$		−	1.72634i		−	0.0626620i
$760$		0			0
$761$	−33.4346			−1.21200			−0.606001	−	0.795464i	$-0.707227\pi$
$761$	−33.4346			−1.21200			−0.606001	+	0.795464i	$0.707227\pi$
$762$	47.1515			1.70812
$763$	74.6023			2.70079
$764$			2.80884i			0.101620i
$765$		0			0
$766$	50.4549			1.82301
$767$		−	38.7237i		−	1.39823i
$768$			9.03210i			0.325918i
$769$		−	33.3999i		−	1.20443i	−0.798333	−	0.602216i	$-0.794284\pi$
$769$		−	33.3999i		−	1.20443i	0.798333	−	0.602216i	$-0.205716\pi$
$770$		0			0
$771$			7.18002i			0.258582i
$772$	1.24331			0.0447479
$773$			33.6561i			1.21053i	0.796026	+	0.605263i	$0.206932\pi$
$773$			33.6561i			1.21053i	−0.796026	+	0.605263i	$0.793068\pi$
$774$	26.5698			0.955030
$775$		0			0
$776$	−29.7473			−1.06787
$777$	−38.9537	+	69.2903i	−1.39745	+	2.48578i
$778$			33.9743i			1.21804i
$779$		−	8.17120i		−	0.292764i
$780$		0			0
$781$	−2.83487			−0.101440
$782$	16.3974			0.586368
$783$	−10.1469			−0.362620
$784$	55.2548			1.97339
$785$		0			0
$786$	29.7565			1.06138
$787$			1.05415i			0.0375764i	0.999823	+	0.0187882i	$0.00598083\pi$
$787$			1.05415i			0.0375764i	−0.999823	+	0.0187882i	$0.994019\pi$
$788$			1.16760i			0.0415939i
$789$	51.0579			1.81771
$790$		0			0
$791$			34.0684i			1.21133i
$792$	2.60525			0.0925735
$793$		−	53.3227i		−	1.89354i
$794$			4.30049i			0.152619i
$795$		0			0
$796$		−	0.148178i		−	0.00525203i
$797$	−26.3106			−0.931970			−0.465985	−	0.884793i	$-0.654300\pi$
$797$	−26.3106			−0.931970			−0.465985	+	0.884793i	$0.654300\pi$
$798$		−	141.479i		−	5.00832i
$799$		−	10.0630i		−	0.356002i
$800$		0			0
$801$			29.1117i			1.02861i
$802$			50.6589i			1.78883i
$803$		−	0.115857i		−	0.00408851i
$804$	−2.78087			−0.0980739
$805$		0			0
$806$			11.8326i			0.416786i
$807$		−	6.66118i		−	0.234485i
$808$	15.2257			0.535638
$809$			15.9357i			0.560271i	0.959960	+	0.280136i	$0.0903794\pi$
$809$			15.9357i			0.560271i	−0.959960	+	0.280136i	$0.909621\pi$
$810$		0			0
$811$	14.8155			0.520242			0.260121	−	0.965576i	$-0.416238\pi$
$811$	14.8155			0.520242			0.260121	+	0.965576i	$0.416238\pi$
$812$	−1.27726			−0.0448231
$813$			23.8845i			0.837665i
$814$	0.757437	−	1.34732i	0.0265481	−	0.0472236i
$815$		0			0
$816$			37.4730i			1.31182i
$817$		−	32.1300i		−	1.12409i
$818$		−	22.7340i		−	0.794877i
$819$		−	95.2843i		−	3.32950i
$820$		0			0
$821$	−15.9564			−0.556882			−0.278441	−	0.960453i	$-0.589818\pi$
$821$	−15.9564			−0.556882			−0.278441	+	0.960453i	$0.589818\pi$
$822$	−4.90337			−0.171025
$823$			10.3719i			0.361542i	0.983525	+	0.180771i	$0.0578592\pi$
$823$			10.3719i			0.361542i	−0.983525	+	0.180771i	$0.942141\pi$
$824$	39.2369			1.36688
$825$		0			0
$826$	−58.3261			−2.02942
$827$	−54.8138			−1.90606			−0.953032	−	0.302871i	$-0.902055\pi$
$827$	−54.8138			−1.90606			−0.953032	+	0.302871i	$0.902055\pi$
$828$	−2.15888			−0.0750263
$829$		−	18.7538i		−	0.651347i	−0.945482	−	0.325674i	$-0.894409\pi$
$829$		−	18.7538i		−	0.651347i	0.945482	−	0.325674i	$-0.105591\pi$
$830$		0			0
$831$		−	53.3864i		−	1.85195i
$832$	−35.9082			−1.24489
$833$	−53.8315			−1.86515
$834$		−	15.0140i		−	0.519891i
$835$		0			0
$836$		−	0.199724i		−	0.00690758i
$837$	−10.2791			−0.355299
$838$	−11.0378			−0.381293
$839$	27.0261			0.933043			0.466522	−	0.884510i	$-0.345507\pi$
$839$	27.0261			0.933043			0.466522	+	0.884510i	$0.345507\pi$
$840$		0			0
$841$	24.9331			0.859764
$842$		−	19.7266i		−	0.679822i
$843$	−12.8776			−0.443528
$844$	−0.937543			−0.0322716
$845$		0			0
$846$		−	18.2492i		−	0.627419i
$847$			51.3031i			1.76280i
$848$			28.4660i			0.977528i
$849$			31.7292i			1.08894i
$850$		0			0
$851$	−9.90078	+	17.6114i	−0.339394	+	0.603711i
$852$			5.76024i			0.197343i
$853$	−32.8016			−1.12311			−0.561553	−	0.827441i	$-0.689796\pi$
$853$	−32.8016			−1.12311			−0.561553	+	0.827441i	$0.689796\pi$
$854$	−80.3152			−2.74833
$855$		0			0
$856$			10.5511i			0.360628i
$857$	44.9972			1.53707			0.768537	−	0.639805i	$-0.220985\pi$
$857$	44.9972			1.53707			0.768537	+	0.639805i	$0.220985\pi$
$858$			3.01039i			0.102773i
$859$		−	38.4263i		−	1.31109i	−0.755157	−	0.655543i	$-0.772440\pi$
$859$		−	38.4263i		−	1.31109i	0.755157	−	0.655543i	$-0.227560\pi$
$860$		0			0
$861$	−13.4680			−0.458989
$862$			18.8827i			0.643149i
$863$		−	11.3362i		−	0.385890i	−0.981210	−	0.192945i	$-0.938196\pi$
$863$		−	11.3362i		−	0.385890i	0.981210	−	0.192945i	$-0.0618039\pi$
$864$		−	3.84631i		−	0.130854i
$865$		0			0
$866$			24.7063i			0.839555i
$867$			10.9750i			0.372729i
$868$	−1.29391			−0.0439182
$869$			0.123356i			0.00418458i
$870$		0			0
$871$		−	31.1957i		−	1.05703i
$872$			46.4945i			1.57450i
$873$	48.9833			1.65783
$874$		−	35.9596i		−	1.21635i
$875$		0			0
$876$	−0.235413			−0.00795386
$877$		−	15.7379i		−	0.531433i	−0.964051	−	0.265716i	$-0.914392\pi$
$877$		−	15.7379i		−	0.531433i	0.964051	−	0.265716i	$-0.0856085\pi$
$878$			0.245232i			0.00827618i
$879$	39.2745			1.32469
$880$		0			0
$881$	−19.4357			−0.654804			−0.327402	−	0.944885i	$-0.606173\pi$
$881$	−19.4357			−0.654804			−0.327402	+	0.944885i	$0.606173\pi$
$882$	−97.6233			−3.28715
$883$	20.2319			0.680858			0.340429	−	0.940270i	$-0.389428\pi$
$883$	20.2319			0.680858			0.340429	+	0.940270i	$0.389428\pi$
$884$	2.07592			0.0698207
$885$		0			0
$886$			4.69075i			0.157589i
$887$		−	10.5339i		−	0.353695i	−0.984238	−	0.176847i	$-0.943410\pi$
$887$		−	10.5339i		−	0.353695i	0.984238	−	0.176847i	$-0.0565899\pi$
$888$	−43.1839	−	24.2771i	−1.44916	−	0.814687i
$889$	−57.8406			−1.93991
$890$		0			0
$891$	0.0652395			0.00218561
$892$			0.778803i			0.0260762i
$893$	−22.0682			−0.738483
$894$			59.3113i			1.98367i
$895$		0			0
$896$			46.9323i			1.56790i
$897$		−	39.3501i		−	1.31386i
$898$		−	35.9653i		−	1.20018i
$899$	−4.11986			−0.137405
$900$		0			0
$901$		−	27.7328i		−	0.923914i
$902$	0.261880			0.00871964
$903$	−52.9576			−1.76232
$904$	−21.2325			−0.706182
$905$		0			0
$906$			57.5644i			1.91245i
$907$	9.71635			0.322626			0.161313	−	0.986903i	$-0.448427\pi$
$907$	9.71635			0.322626			0.161313	+	0.986903i	$0.448427\pi$
$908$	1.02470			0.0340058
$909$	−25.0713			−0.831564
$910$		0			0
$911$			9.06312i			0.300274i	0.988665	+	0.150137i	$0.0479715\pi$
$911$			9.06312i			0.300274i	−0.988665	+	0.150137i	$0.952028\pi$
$912$	82.1787			2.72121
$913$		−	1.81489i		−	0.0600640i
$914$	13.3089			0.440218
$915$		0			0
$916$	−2.69358			−0.0889983
$917$	−36.5022			−1.20541
$918$		−	24.8398i		−	0.819836i
$919$		−	16.9169i		−	0.558036i	−0.960286	−	0.279018i	$-0.909991\pi$
$919$		−	16.9169i		−	0.558036i	0.960286	−	0.279018i	$-0.0900089\pi$
$920$		0			0
$921$	−25.2358			−0.831548
$922$			24.2397i			0.798292i
$923$	−64.6182			−2.12693
$924$	−0.329190			−0.0108296
$925$		0			0
$926$	−43.8167			−1.43991
$927$	−64.6093			−2.12205
$928$		−	1.54159i		−	0.0506053i
$929$	22.5222			0.738930			0.369465	−	0.929245i	$-0.379541\pi$
$929$	22.5222			0.738930			0.369465	+	0.929245i	$0.379541\pi$
$930$		0			0
$931$			118.053i			3.86903i
$932$			2.40278i			0.0787058i
$933$	78.3277			2.56433
$934$	38.7729			1.26869
$935$		0			0
$936$	59.3842			1.94103
$937$			30.8630i			1.00825i	0.863630	+	0.504126i	$0.168185\pi$
$937$			30.8630i			1.00825i	−0.863630	+	0.504126i	$0.831815\pi$
$938$	−46.9873			−1.53419
$939$			43.9561i			1.43445i
$940$		0			0
$941$	−54.0573			−1.76222			−0.881108	−	0.472914i	$-0.843202\pi$
$941$	−54.0573			−1.76222			−0.881108	+	0.472914i	$0.843202\pi$
$942$	26.3099			0.857224
$943$	−3.42314			−0.111473
$944$		−	33.8789i		−	1.10266i
$945$		0			0
$946$	1.02974			0.0334797
$947$	53.5495			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$947$	53.5495			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$948$	0.250651			0.00814076
$949$		−	2.64085i		−	0.0857256i
$950$		0			0
$951$	90.7230			2.94189
$952$		−	49.3218i		−	1.59853i
$953$		−	32.2122i		−	1.04346i	−0.853112	−	0.521728i	$-0.825288\pi$
$953$		−	32.2122i		−	1.04346i	0.853112	−	0.521728i	$-0.174712\pi$
$954$		−	50.2934i		−	1.62831i
$955$		0			0
$956$			1.26473i			0.0409043i
$957$	−1.04816			−0.0338821
$958$		−	2.04588i		−	0.0660993i
$959$	6.01495			0.194233
$960$		0			0
$961$	26.8264			0.865369
$962$	17.2650	−	30.7109i	0.556647	−	0.990158i
$963$		−	17.3739i		−	0.559866i
$964$			1.76299i			0.0567822i
$965$		0			0
$966$	−59.2696			−1.90697
$967$	−25.9095			−0.833193			−0.416597	−	0.909091i	$-0.636777\pi$
$967$	−25.9095			−0.833193			−0.416597	+	0.909091i	$0.636777\pi$
$968$	−31.9737			−1.02767
$969$	−80.0619			−2.57196
$970$		0			0
$971$	7.44649			0.238969			0.119485	−	0.992836i	$-0.461876\pi$
$971$	7.44649			0.238969			0.119485	+	0.992836i	$0.461876\pi$
$972$		−	2.17597i		−	0.0697942i
$973$			18.4176i			0.590441i
$974$	43.0826			1.38046
$975$		0			0
$976$		−	46.6513i		−	1.49327i
$977$	5.21832			0.166949			0.0834744	−	0.996510i	$-0.473398\pi$
$977$	5.21832			0.166949			0.0834744	+	0.996510i	$0.473398\pi$
$978$		−	16.8749i		−	0.539600i
$979$			1.12825i			0.0360591i
$980$		0			0
$981$		−	76.5600i		−	2.44437i
$982$	−23.1522			−0.738816
$983$		−	30.9100i		−	0.985874i	−0.870065	−	0.492937i	$-0.835923\pi$
$983$		−	30.9100i		−	0.985874i	0.870065	−	0.492937i	$-0.164077\pi$
$984$		−	8.39369i		−	0.267581i
$985$		0			0
$986$		−	9.95576i		−	0.317056i
$987$			36.3734i			1.15778i
$988$		−	4.55251i		−	0.144834i
$989$	−13.4601			−0.428008
$990$		0			0
$991$		−	37.9145i		−	1.20439i	−0.798348	−	0.602196i	$-0.794292\pi$
$991$		−	37.9145i		−	1.20439i	0.798348	−	0.602196i	$-0.205708\pi$
$992$		−	1.56169i		−	0.0495836i
$993$	−64.8240			−2.05713
$994$			97.3285i			3.08707i
$995$		0			0
$996$	−3.68771			−0.116850
$997$	−43.7248			−1.38478			−0.692389	−	0.721525i	$-0.743442\pi$
$997$	−43.7248			−1.38478			−0.692389	+	0.721525i	$0.743442\pi$
$998$			20.7506i			0.656848i
$999$	26.6789	+	14.9984i	0.844084	+	0.474527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.d.f.924.3		12
5.2	odd	4		925.2.c.c.776.4		12
5.3	odd	4		185.2.c.b.36.9	yes	12
5.4	even	2		925.2.d.e.924.10		12
15.8	even	4		1665.2.e.e.406.4		12
20.3	even	4		2960.2.p.h.961.3		12
37.36	even	2		925.2.d.e.924.9		12
185.43	even	4		6845.2.a.h.1.5		6
185.68	even	4		6845.2.a.i.1.2		6
185.73	odd	4		185.2.c.b.36.4	✓	12
185.147	odd	4		925.2.c.c.776.9		12
185.184	even	2	inner	925.2.d.f.924.4		12
555.443	even	4		1665.2.e.e.406.9		12
740.443	even	4		2960.2.p.h.961.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.4	✓	12	185.73	odd	4
185.2.c.b.36.9	yes	12	5.3	odd	4
925.2.c.c.776.4		12	5.2	odd	4
925.2.c.c.776.9		12	185.147	odd	4
925.2.d.e.924.9		12	37.36	even	2
925.2.d.e.924.10		12	5.4	even	2
925.2.d.f.924.3		12	1.1	even	1	trivial
925.2.d.f.924.4		12	185.184	even	2	inner
1665.2.e.e.406.4		12	15.8	even	4
1665.2.e.e.406.9		12	555.443	even	4
2960.2.p.h.961.3		12	20.3	even	4
2960.2.p.h.961.4		12	740.443	even	4
6845.2.a.h.1.5		6	185.43	even	4
6845.2.a.i.1.2		6	185.68	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.36551 q^{2} -2.79310i q^{3} -0.135372 q^{4} +3.81402i q^{6} -4.67865i q^{7} +2.91588 q^{8} -4.80143 q^{9} -0.186084 q^{11} +0.378109i q^{12} -4.24161 q^{13} +6.38876i q^{14} -3.71093 q^{16} +3.61534 q^{17} +6.55641 q^{18} -7.92848i q^{19} -13.0679 q^{21} +0.254101 q^{22} -3.32146 q^{23} -8.14435i q^{24} +5.79198 q^{26} +5.03157i q^{27} +0.633360i q^{28} +2.01664i q^{29} +2.04293i q^{31} -0.764435 q^{32} +0.519752i q^{33} -4.93680 q^{34} +0.649980 q^{36} +(2.98085 - 5.30231i) q^{37} +10.8264i q^{38} +11.8473i q^{39} +1.03061 q^{41} +17.8445 q^{42} +4.05248 q^{43} +0.0251907 q^{44} +4.53549 q^{46} -2.78341i q^{47} +10.3650i q^{48} -14.8897 q^{49} -10.0980i q^{51} +0.574197 q^{52} -7.67087i q^{53} -6.87067i q^{54} -13.6424i q^{56} -22.1451 q^{57} -2.75376i q^{58} +9.12948i q^{59} +12.5713i q^{61} -2.78965i q^{62} +22.4642i q^{63} +8.46571 q^{64} -0.709729i q^{66} +7.35469i q^{67} -0.489417 q^{68} +9.27717i q^{69} +15.2343 q^{71} -14.0004 q^{72} +0.622606i q^{73} +(-4.07040 + 7.24038i) q^{74} +1.07330i q^{76} +0.870623i q^{77} -16.1776i q^{78} -0.662906i q^{79} -0.350591 q^{81} -1.40732 q^{82} +9.75304i q^{83} +1.76904 q^{84} -5.53372 q^{86} +5.63270 q^{87} -0.542599 q^{88} -6.06313i q^{89} +19.8450i q^{91} +0.449633 q^{92} +5.70612 q^{93} +3.80078i q^{94} +2.13515i q^{96} -10.2018 q^{97} +20.3322 q^{98} +0.893470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 18 q^{4} + 6 q^{8} - 22 q^{9} + 2 q^{11} + 20 q^{13} + 30 q^{16} + 12 q^{17} - 26 q^{18} - 6 q^{21} - 28 q^{22} - 16 q^{23} - 12 q^{26} + 14 q^{32} - 4 q^{34} - 22 q^{36} - 14 q^{37} - 10 q^{41}+ \cdots + 84 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 18 * q^4 + 6 * q^8 - 22 * q^9 + 2 * q^11 + 20 * q^13 + 30 * q^16 + 12 * q^17 - 26 * q^18 - 6 * q^21 - 28 * q^22 - 16 * q^23 - 12 * q^26 + 14 * q^32 - 4 * q^34 - 22 * q^36 - 14 * q^37 - 10 * q^41 + 72 * q^42 - 12 * q^43 - 44 * q^44 - 24 * q^46 - 30 * q^49 + 80 * q^52 - 32 * q^57 + 126 * q^64 - 40 * q^68 + 42 * q^71 - 178 * q^72 - 50 * q^74 - 12 * q^81 + 96 * q^82 + 84 * q^84 - 64 * q^86 - 56 * q^87 - 72 * q^88 + 16 * q^92 + 76 * q^93 - 28 * q^97 + 118 * q^98 + 84 * q^99

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