LMFDB - Embedded newform 1600.2.j.d.1007.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1600,2,Mod(143,1600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1600.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1007.9
Root			$0.235136 + 1.39453i$ of defining polynomial
Character	$\chi$	$=$	1600.1007
Dual form			1600.2.j.d.143.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.96561i q^{3} +(-0.115101 - 0.115101i) q^{7} -5.79486 q^{9} +(-2.95966 - 2.95966i) q^{11} -1.55822 q^{13} +(-0.299668 - 0.299668i) q^{17} +(-2.26261 - 2.26261i) q^{19} +(0.341344 - 0.341344i) q^{21} +(4.14573 - 4.14573i) q^{23} -8.28846i q^{27} +(-0.289656 + 0.289656i) q^{29} -4.18508i q^{31} +(8.77721 - 8.77721i) q^{33} -1.63643 q^{37} -4.62107i q^{39} -7.61648i q^{41} -6.72651 q^{43} +(-4.38366 + 4.38366i) q^{47} -6.97350i q^{49} +(0.888698 - 0.888698i) q^{51} +11.4324i q^{53} +(6.71003 - 6.71003i) q^{57} +(1.63497 - 1.63497i) q^{59} +(-1.23034 - 1.23034i) q^{61} +(0.666993 + 0.666993i) q^{63} +2.49337 q^{67} +(12.2946 + 12.2946i) q^{69} -8.00096 q^{71} +(-1.12102 - 1.12102i) q^{73} +0.681319i q^{77} +3.62218 q^{79} +7.19579 q^{81} -1.62629i q^{83} +(-0.859007 - 0.859007i) q^{87} +15.7149 q^{89} +(0.179352 + 0.179352i) q^{91} +12.4113 q^{93} +(-9.69217 - 9.69217i) q^{97} +(17.1508 + 17.1508i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} - 10 q^{9} + 2 q^{11} + 6 q^{17} - 2 q^{19} - 16 q^{21} - 2 q^{23} - 14 q^{29} + 8 q^{33} - 8 q^{37} - 44 q^{43} - 38 q^{47} - 8 q^{51} - 24 q^{57} + 10 q^{59} + 14 q^{61} + 6 q^{63} + 12 q^{67}+ \cdots + 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 - 10 * q^9 + 2 * q^11 + 6 * q^17 - 2 * q^19 - 16 * q^21 - 2 * q^23 - 14 * q^29 + 8 * q^33 - 8 * q^37 - 44 * q^43 - 38 * q^47 - 8 * q^51 - 24 * q^57 + 10 * q^59 + 14 * q^61 + 6 * q^63 + 12 * q^67 + 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^79 + 2 * q^81 + 24 * q^87 - 12 * q^89 - 16 * q^93 - 18 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$			2.96561i			1.71220i	0.516813	+	0.856099i	$0.327118\pi$
$3$			2.96561i			1.71220i	−0.516813	+	0.856099i	$0.672882\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.115101	−	0.115101i	−0.0435040	−	0.0435040i	0.685020	−	0.728524i	$-0.259793\pi$
$7$	−0.115101	−	0.115101i	−0.0435040	−	0.0435040i	−0.728524	+	0.685020i	$0.759793\pi$
$8$		0			0
$9$	−5.79486			−1.93162
$10$		0			0
$11$	−2.95966	−	2.95966i	−0.892372	−	0.892372i	0.102374	−	0.994746i	$-0.467356\pi$
$11$	−2.95966	−	2.95966i	−0.892372	−	0.892372i	−0.994746	+	0.102374i	$0.967356\pi$
$12$		0			0
$13$	−1.55822			−0.432172			−0.216086	−	0.976374i	$-0.569329\pi$
$13$	−1.55822			−0.432172			−0.216086	+	0.976374i	$0.569329\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.299668	−	0.299668i	−0.0726801	−	0.0726801i	0.669832	−	0.742512i	$-0.266366\pi$
$17$	−0.299668	−	0.299668i	−0.0726801	−	0.0726801i	−0.742512	+	0.669832i	$0.766366\pi$
$18$		0			0
$19$	−2.26261	−	2.26261i	−0.519079	−	0.519079i	0.398214	−	0.917293i	$-0.369630\pi$
$19$	−2.26261	−	2.26261i	−0.519079	−	0.519079i	−0.917293	+	0.398214i	$0.869630\pi$
$20$		0			0
$21$	0.341344	−	0.341344i	0.0744874	−	0.0744874i
$22$		0			0
$23$	4.14573	−	4.14573i	0.864444	−	0.864444i	−0.127406	−	0.991851i	$-0.540665\pi$
$23$	4.14573	−	4.14573i	0.864444	−	0.864444i	0.991851	+	0.127406i	$0.0406652\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	8.28846i		−	1.59511i
$28$		0			0
$29$	−0.289656	+	0.289656i	−0.0537878	+	0.0537878i	−0.733489	−	0.679701i	$-0.762109\pi$
$29$	−0.289656	+	0.289656i	−0.0537878	+	0.0537878i	0.679701	+	0.733489i	$0.262109\pi$
$30$		0			0
$31$		−	4.18508i		−	0.751663i	−0.926688	−	0.375832i	$-0.877357\pi$
$31$		−	4.18508i		−	0.751663i	0.926688	−	0.375832i	$-0.122643\pi$
$32$		0			0
$33$	8.77721	−	8.77721i	1.52792	−	1.52792i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.63643			−0.269027			−0.134514	−	0.990912i	$-0.542947\pi$
$37$	−1.63643			−0.269027			−0.134514	+	0.990912i	$0.542947\pi$
$38$		0			0
$39$		−	4.62107i		−	0.739964i
$40$		0			0
$41$		−	7.61648i		−	1.18949i	−0.803913	−	0.594747i	$-0.797252\pi$
$41$		−	7.61648i		−	1.18949i	0.803913	−	0.594747i	$-0.202748\pi$
$42$		0			0
$43$	−6.72651			−1.02578			−0.512892	−	0.858453i	$-0.671426\pi$
$43$	−6.72651			−1.02578			−0.512892	+	0.858453i	$0.671426\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.38366	+	4.38366i	−0.639423	+	0.639423i	−0.950413	−	0.310990i	$-0.899339\pi$
$47$	−4.38366	+	4.38366i	−0.639423	+	0.639423i	0.310990	+	0.950413i	$0.399339\pi$
$48$		0			0
$49$		−	6.97350i		−	0.996215i
$50$		0			0
$51$	0.888698	−	0.888698i	0.124443	−	0.124443i
$52$		0			0
$53$			11.4324i			1.57036i	0.619265	+	0.785182i	$0.287431\pi$
$53$			11.4324i			1.57036i	−0.619265	+	0.785182i	$0.712569\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	6.71003	−	6.71003i	0.888766	−	0.888766i
$58$		0			0
$59$	1.63497	−	1.63497i	0.212855	−	0.212855i	−0.592624	−	0.805479i	$-0.701908\pi$
$59$	1.63497	−	1.63497i	0.212855	−	0.212855i	0.805479	+	0.592624i	$0.201908\pi$
$60$		0			0
$61$	−1.23034	−	1.23034i	−0.157528	−	0.157528i	0.623942	−	0.781471i	$-0.285530\pi$
$61$	−1.23034	−	1.23034i	−0.157528	−	0.157528i	−0.781471	+	0.623942i	$0.785530\pi$
$62$		0			0
$63$	0.666993	+	0.666993i	0.0840332	+	0.0840332i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.49337			0.304614			0.152307	−	0.988333i	$-0.451330\pi$
$67$	2.49337			0.304614			0.152307	+	0.988333i	$0.451330\pi$
$68$		0			0
$69$	12.2946	+	12.2946i	1.48010	+	1.48010i
$70$		0			0
$71$	−8.00096			−0.949540			−0.474770	−	0.880110i	$-0.657469\pi$
$71$	−8.00096			−0.949540			−0.474770	+	0.880110i	$0.657469\pi$
$72$		0			0
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	0.638454	−	0.769660i	$-0.279574\pi$
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	−0.769660	+	0.638454i	$0.779574\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			0.681319i			0.0776435i
$78$		0			0
$79$	3.62218			0.407527			0.203763	−	0.979020i	$-0.434683\pi$
$79$	3.62218			0.407527			0.203763	+	0.979020i	$0.434683\pi$
$80$		0			0
$81$	7.19579			0.799532
$82$		0			0
$83$		−	1.62629i		−	0.178509i	−0.996009	−	0.0892545i	$-0.971552\pi$
$83$		−	1.62629i		−	0.178509i	0.996009	−	0.0892545i	$-0.0284484\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.859007	−	0.859007i	−0.0920953	−	0.0920953i
$88$		0			0
$89$	15.7149			1.66577			0.832887	−	0.553443i	$-0.186686\pi$
$89$	15.7149			1.66577			0.832887	+	0.553443i	$0.186686\pi$
$90$		0			0
$91$	0.179352	+	0.179352i	0.0188012	+	0.0188012i
$92$		0			0
$93$	12.4113			1.28700
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.69217	−	9.69217i	−0.984091	−	0.984091i	0.0157848	−	0.999875i	$-0.494975\pi$
$97$	−9.69217	−	9.69217i	−0.984091	−	0.984091i	−0.999875	+	0.0157848i	$0.994975\pi$
$98$		0			0
$99$	17.1508	+	17.1508i	1.72372	+	1.72372i
$100$		0			0
$101$	−12.8067	+	12.8067i	−1.27432	+	1.27432i	−0.330516	+	0.943800i	$0.607223\pi$
$101$	−12.8067	+	12.8067i	−1.27432	+	1.27432i	−0.943800	+	0.330516i	$0.892777\pi$
$102$		0			0
$103$	−4.33738	+	4.33738i	−0.427375	+	0.427375i	−0.887733	−	0.460358i	$-0.847721\pi$
$103$	−4.33738	+	4.33738i	−0.427375	+	0.427375i	0.460358	+	0.887733i	$0.347721\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	11.9807i		−	1.15822i	−0.815251	−	0.579108i	$-0.803401\pi$
$107$		−	11.9807i		−	1.15822i	0.815251	−	0.579108i	$-0.196599\pi$
$108$		0			0
$109$	−4.01503	+	4.01503i	−0.384570	+	0.384570i	−0.872746	−	0.488175i	$-0.837663\pi$
$109$	−4.01503	+	4.01503i	−0.384570	+	0.384570i	0.488175	+	0.872746i	$0.337663\pi$
$110$		0			0
$111$		−	4.85301i		−	0.460628i
$112$		0			0
$113$	−6.47754	+	6.47754i	−0.609356	+	0.609356i	−0.942778	−	0.333422i	$-0.891797\pi$
$113$	−6.47754	+	6.47754i	−0.609356	+	0.609356i	0.333422	+	0.942778i	$0.391797\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	9.02966			0.834792
$118$		0			0
$119$			0.0689840i			0.00632375i
$120$		0			0
$121$			6.51921i			0.592655i
$122$		0			0
$123$	22.5875			2.03665
$124$		0			0
$125$		0			0
$126$		0			0
$127$	12.2756	−	12.2756i	1.08928	−	1.08928i	0.0936781	−	0.995603i	$-0.470138\pi$
$127$	12.2756	−	12.2756i	1.08928	−	1.08928i	0.995603	−	0.0936781i	$-0.0298625\pi$
$128$		0			0
$129$		−	19.9482i		−	1.75634i
$130$		0			0
$131$	−7.99562	+	7.99562i	−0.698581	+	0.698581i	−0.964104	−	0.265524i	$-0.914455\pi$
$131$	−7.99562	+	7.99562i	−0.698581	+	0.698581i	0.265524	+	0.964104i	$0.414455\pi$
$132$		0			0
$133$			0.520857i			0.0451641i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.08551	+	3.08551i	−0.263613	+	0.263613i	−0.826520	−	0.562907i	$-0.809683\pi$
$137$	−3.08551	+	3.08551i	−0.263613	+	0.263613i	0.562907	+	0.826520i	$0.309683\pi$
$138$		0			0
$139$	12.2206	−	12.2206i	1.03654	−	1.03654i	0.0372284	−	0.999307i	$-0.488147\pi$
$139$	12.2206	−	12.2206i	1.03654	−	1.03654i	0.999307	−	0.0372284i	$-0.0118529\pi$
$140$		0			0
$141$	−13.0002	−	13.0002i	−1.09482	−	1.09482i
$142$		0			0
$143$	4.61180	+	4.61180i	0.385658	+	0.385658i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	20.6807			1.70572
$148$		0			0
$149$	−2.59172	−	2.59172i	−0.212322	−	0.212322i	0.592931	−	0.805253i	$-0.297971\pi$
$149$	−2.59172	−	2.59172i	−0.212322	−	0.212322i	−0.805253	+	0.592931i	$0.797971\pi$
$150$		0			0
$151$	16.9594			1.38014			0.690068	−	0.723745i	$-0.257581\pi$
$151$	16.9594			1.38014			0.690068	+	0.723745i	$0.257581\pi$
$152$		0			0
$153$	1.73653	+	1.73653i	0.140390	+	0.140390i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	8.55235i		−	0.682552i	−0.939963	−	0.341276i	$-0.889141\pi$
$157$		−	8.55235i		−	0.682552i	0.939963	−	0.341276i	$-0.110859\pi$
$158$		0			0
$159$	−33.9041			−2.68877
$160$		0			0
$161$	−0.954354			−0.0752136
$162$		0			0
$163$			3.57797i			0.280248i	0.990134	+	0.140124i	$0.0447501\pi$
$163$			3.57797i			0.280248i	−0.990134	+	0.140124i	$0.955250\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.482874	+	0.482874i	0.0373659	+	0.0373659i	0.725543	−	0.688177i	$-0.241589\pi$
$167$	0.482874	+	0.482874i	0.0373659	+	0.0373659i	−0.688177	+	0.725543i	$0.741589\pi$
$168$		0			0
$169$	−10.5720			−0.813227
$170$		0			0
$171$	13.1115	+	13.1115i	1.00266	+	1.00266i
$172$		0			0
$173$	−11.8189			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$173$	−11.8189			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.84870	+	4.84870i	0.364451	+	0.364451i
$178$		0			0
$179$	−4.71524	−	4.71524i	−0.352433	−	0.352433i	0.508581	−	0.861014i	$-0.330170\pi$
$179$	−4.71524	−	4.71524i	−0.352433	−	0.352433i	−0.861014	+	0.508581i	$0.830170\pi$
$180$		0			0
$181$	13.1843	−	13.1843i	0.979983	−	0.979983i	−0.0198205	−	0.999804i	$-0.506309\pi$
$181$	13.1843	−	13.1843i	0.979983	−	0.979983i	0.999804	+	0.0198205i	$0.00630948\pi$
$182$		0			0
$183$	3.64870	−	3.64870i	0.269720	−	0.269720i
$184$		0			0
$185$		0			0
$186$		0			0
$187$			1.77383i			0.129715i
$188$		0			0
$189$	−0.954008	+	0.954008i	−0.0693939	+	0.0693939i
$190$		0			0
$191$		−	13.9872i		−	1.01208i	−0.862510	−	0.506040i	$-0.831109\pi$
$191$		−	13.9872i		−	1.01208i	0.862510	−	0.506040i	$-0.168891\pi$
$192$		0			0
$193$	−3.88875	+	3.88875i	−0.279919	+	0.279919i	−0.833076	−	0.553158i	$-0.813423\pi$
$193$	−3.88875	+	3.88875i	−0.279919	+	0.279919i	0.553158	+	0.833076i	$0.313423\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.3277			1.59078			0.795391	−	0.606097i	$-0.207266\pi$
$197$	22.3277			1.59078			0.795391	+	0.606097i	$0.207266\pi$
$198$		0			0
$199$			9.83847i			0.697431i	0.937229	+	0.348715i	$0.113382\pi$
$199$			9.83847i			0.697431i	−0.937229	+	0.348715i	$0.886618\pi$
$200$		0			0
$201$			7.39437i			0.521559i
$202$		0			0
$203$	0.0666793			0.00467997
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−24.0239	+	24.0239i	−1.66978	+	1.66978i
$208$		0			0
$209$			13.3931i			0.926423i
$210$		0			0
$211$	−11.0531	+	11.0531i	−0.760925	+	0.760925i	−0.976490	−	0.215565i	$-0.930841\pi$
$211$	−11.0531	+	11.0531i	−0.760925	+	0.760925i	0.215565	+	0.976490i	$0.430841\pi$
$212$		0			0
$213$		−	23.7278i		−	1.62580i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.481706	+	0.481706i	−0.0327004	+	0.0327004i
$218$		0			0
$219$	3.32451	−	3.32451i	0.224650	−	0.224650i
$220$		0			0
$221$	0.466948	+	0.466948i	0.0314103	+	0.0314103i
$222$		0			0
$223$	−5.93975	−	5.93975i	−0.397755	−	0.397755i	0.479686	−	0.877440i	$-0.340751\pi$
$223$	−5.93975	−	5.93975i	−0.397755	−	0.397755i	−0.877440	+	0.479686i	$0.840751\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−23.2105			−1.54054			−0.770269	−	0.637720i	$-0.779878\pi$
$227$	−23.2105			−1.54054			−0.770269	+	0.637720i	$0.779878\pi$
$228$		0			0
$229$	−5.59944	−	5.59944i	−0.370021	−	0.370021i	0.497464	−	0.867485i	$-0.334265\pi$
$229$	−5.59944	−	5.59944i	−0.370021	−	0.370021i	−0.867485	+	0.497464i	$0.834265\pi$
$230$		0			0
$231$	−2.02053			−0.132941
$232$		0			0
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	0.799076	−	0.601230i	$-0.205323\pi$
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	−0.601230	+	0.799076i	$0.705323\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			10.7420i			0.697766i
$238$		0			0
$239$	−0.00138865			−8.98241e−5			−4.49120e−5	−	1.00000i	$-0.500014\pi$
$239$	−0.00138865			−8.98241e−5			−4.49120e−5		1.00000i	$0.500014\pi$
$240$		0			0
$241$	−12.8578			−0.828245			−0.414123	−	0.910221i	$-0.635912\pi$
$241$	−12.8578			−0.828245			−0.414123	+	0.910221i	$0.635912\pi$
$242$		0			0
$243$		−	3.52546i		−	0.226158i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.52565	+	3.52565i	0.224332	+	0.224332i
$248$		0			0
$249$	4.82296			0.305643
$250$		0			0
$251$	9.14111	+	9.14111i	0.576982	+	0.576982i	0.934071	−	0.357089i	$-0.116231\pi$
$251$	9.14111	+	9.14111i	0.576982	+	0.576982i	−0.357089	+	0.934071i	$0.616231\pi$
$252$		0			0
$253$	−24.5399			−1.54281
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−21.2733	−	21.2733i	−1.32699	−	1.32699i	−0.907980	−	0.419013i	$-0.862376\pi$
$257$	−21.2733	−	21.2733i	−1.32699	−	1.32699i	−0.419013	−	0.907980i	$-0.637624\pi$
$258$		0			0
$259$	0.188354	+	0.188354i	0.0117038	+	0.0117038i
$260$		0			0
$261$	1.67851	−	1.67851i	0.103897	−	0.103897i
$262$		0			0
$263$	−16.7214	+	16.7214i	−1.03108	+	1.03108i	−0.0315818	+	0.999501i	$0.510054\pi$
$263$	−16.7214	+	16.7214i	−1.03108	+	1.03108i	−0.999501	+	0.0315818i	$0.989946\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			46.6043i			2.85213i
$268$		0			0
$269$	−15.9096	+	15.9096i	−0.970026	+	0.970026i	−0.999564	−	0.0295378i	$-0.990596\pi$
$269$	−15.9096	+	15.9096i	−0.970026	+	0.970026i	0.0295378	+	0.999564i	$0.490596\pi$
$270$		0			0
$271$			12.3601i			0.750824i	0.926858	+	0.375412i	$0.122499\pi$
$271$			12.3601i			0.750824i	−0.926858	+	0.375412i	$0.877501\pi$
$272$		0			0
$273$	−0.531889	+	0.531889i	−0.0321914	+	0.0321914i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−21.0270			−1.26339			−0.631695	−	0.775217i	$-0.717641\pi$
$277$	−21.0270			−1.26339			−0.631695	+	0.775217i	$0.717641\pi$
$278$		0			0
$279$			24.2520i			1.45193i
$280$		0			0
$281$		−	10.6807i		−	0.637158i	−0.947896	−	0.318579i	$-0.896794\pi$
$281$		−	10.6807i		−	0.637158i	0.947896	−	0.318579i	$-0.103206\pi$
$282$		0			0
$283$	12.5946			0.748673			0.374336	−	0.927293i	$-0.377871\pi$
$283$	12.5946			0.748673			0.374336	+	0.927293i	$0.377871\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.876663	+	0.876663i	−0.0517478	+	0.0517478i
$288$		0			0
$289$		−	16.8204i		−	0.989435i
$290$		0			0
$291$	28.7432	−	28.7432i	1.68496	−	1.68496i
$292$		0			0
$293$			3.43132i			0.200460i	0.994964	+	0.100230i	$0.0319579\pi$
$293$			3.43132i			0.200460i	−0.994964	+	0.100230i	$0.968042\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−24.5310	+	24.5310i	−1.42344	+	1.42344i
$298$		0			0
$299$	−6.45996	+	6.45996i	−0.373589	+	0.373589i
$300$		0			0
$301$	0.774227	+	0.774227i	0.0446257	+	0.0446257i
$302$		0			0
$303$	−37.9798	−	37.9798i	−2.18188	−	2.18188i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−11.8104			−0.674053			−0.337027	−	0.941495i	$-0.609421\pi$
$307$	−11.8104			−0.674053			−0.337027	+	0.941495i	$0.609421\pi$
$308$		0			0
$309$	−12.8630	−	12.8630i	−0.731750	−	0.731750i
$310$		0			0
$311$	−22.6262			−1.28301			−0.641506	−	0.767118i	$-0.721690\pi$
$311$	−22.6262			−1.28301			−0.641506	+	0.767118i	$0.721690\pi$
$312$		0			0
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	0.878486	−	0.477767i	$-0.158554\pi$
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	−0.477767	+	0.878486i	$0.658554\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			25.1265i			1.41124i	0.708589	+	0.705621i	$0.249332\pi$
$317$			25.1265i			1.41124i	−0.708589	+	0.705621i	$0.750668\pi$
$318$		0			0
$319$	1.71457			0.0959974
$320$		0			0
$321$	35.5300			1.98309
$322$		0			0
$323$			1.35606i			0.0754535i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.9070	−	11.9070i	−0.658460	−	0.658460i
$328$		0			0
$329$	1.00913			0.0556349
$330$		0			0
$331$	−5.80829	−	5.80829i	−0.319253	−	0.319253i	0.529227	−	0.848480i	$-0.322482\pi$
$331$	−5.80829	−	5.80829i	−0.319253	−	0.319253i	−0.848480	+	0.529227i	$0.822482\pi$
$332$		0			0
$333$	9.48287			0.519658
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.41679	+	7.41679i	0.404019	+	0.404019i	0.879647	−	0.475628i	$-0.157779\pi$
$337$	7.41679	+	7.41679i	0.404019	+	0.404019i	−0.475628	+	0.879647i	$0.657779\pi$
$338$		0			0
$339$	−19.2099	−	19.2099i	−1.04334	−	1.04334i
$340$		0			0
$341$	−12.3864	+	12.3864i	−0.670763	+	0.670763i
$342$		0			0
$343$	−1.60836	+	1.60836i	−0.0868434	+	0.0868434i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	18.2493i		−	0.979673i	−0.871814	−	0.489837i	$-0.837056\pi$
$347$		−	18.2493i		−	0.979673i	0.871814	−	0.489837i	$-0.162944\pi$
$348$		0			0
$349$	19.4413	−	19.4413i	1.04067	−	1.04067i	0.0415330	−	0.999137i	$-0.486776\pi$
$349$	19.4413	−	19.4413i	1.04067	−	1.04067i	0.999137	−	0.0415330i	$-0.0132242\pi$
$350$		0			0
$351$			12.9152i			0.689364i
$352$		0			0
$353$	1.13598	−	1.13598i	0.0604622	−	0.0604622i	−0.676229	−	0.736691i	$-0.736387\pi$
$353$	1.13598	−	1.13598i	0.0604622	−	0.0604622i	0.736691	+	0.676229i	$0.236387\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.204580			−0.0108275
$358$		0			0
$359$		−	28.4140i		−	1.49963i	−0.661645	−	0.749817i	$-0.730141\pi$
$359$		−	28.4140i		−	1.49963i	0.661645	−	0.749817i	$-0.269859\pi$
$360$		0			0
$361$		−	8.76116i		−	0.461114i
$362$		0			0
$363$	−19.3334			−1.01474
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.29692	−	2.29692i	0.119898	−	0.119898i	−0.644612	−	0.764510i	$-0.722981\pi$
$367$	2.29692	−	2.29692i	0.119898	−	0.119898i	0.764510	+	0.644612i	$0.222981\pi$
$368$		0			0
$369$			44.1364i			2.29765i
$370$		0			0
$371$	1.31588	−	1.31588i	0.0683172	−	0.0683172i
$372$		0			0
$373$		−	18.0787i		−	0.936081i	−0.883707	−	0.468040i	$-0.844960\pi$
$373$		−	18.0787i		−	0.936081i	0.883707	−	0.468040i	$-0.155040\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.451348	−	0.451348i	0.0232456	−	0.0232456i
$378$		0			0
$379$	−2.79031	+	2.79031i	−0.143328	+	0.143328i	−0.775130	−	0.631802i	$-0.782316\pi$
$379$	−2.79031	+	2.79031i	−0.143328	+	0.143328i	0.631802	+	0.775130i	$0.282316\pi$
$380$		0			0
$381$	36.4046	+	36.4046i	1.86506	+	1.86506i
$382$		0			0
$383$	8.12206	+	8.12206i	0.415018	+	0.415018i	0.883482	−	0.468464i	$-0.155193\pi$
$383$	8.12206	+	8.12206i	0.415018	+	0.415018i	−0.468464	+	0.883482i	$0.655193\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	38.9792			1.98142
$388$		0			0
$389$	14.4341	+	14.4341i	0.731839	+	0.731839i	0.970984	−	0.239145i	$-0.0768670\pi$
$389$	14.4341	+	14.4341i	0.731839	+	0.731839i	−0.239145	+	0.970984i	$0.576867\pi$
$390$		0			0
$391$	−2.48468			−0.125656
$392$		0			0
$393$	−23.7119	−	23.7119i	−1.19611	−	1.19611i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			35.1624i			1.76475i	0.470549	+	0.882374i	$0.344056\pi$
$397$			35.1624i			1.76475i	−0.470549	+	0.882374i	$0.655944\pi$
$398$		0			0
$399$	−1.54466			−0.0773298
$400$		0			0
$401$	−23.5164			−1.17435			−0.587176	−	0.809459i	$-0.699760\pi$
$401$	−23.5164			−1.17435			−0.587176	+	0.809459i	$0.699760\pi$
$402$		0			0
$403$			6.52128i			0.324848i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.84328	+	4.84328i	0.240072	+	0.240072i
$408$		0			0
$409$	−23.2595			−1.15011			−0.575054	−	0.818115i	$-0.695019\pi$
$409$	−23.2595			−1.15011			−0.575054	+	0.818115i	$0.695019\pi$
$410$		0			0
$411$	−9.15043	−	9.15043i	−0.451357	−	0.451357i
$412$		0			0
$413$	−0.376374			−0.0185201
$414$		0			0
$415$		0			0
$416$		0			0
$417$	36.2415	+	36.2415i	1.77475	+	1.77475i
$418$		0			0
$419$	6.63975	+	6.63975i	0.324373	+	0.324373i	0.850442	−	0.526069i	$-0.176335\pi$
$419$	6.63975	+	6.63975i	0.324373	+	0.324373i	−0.526069	+	0.850442i	$0.676335\pi$
$420$		0			0
$421$	7.28216	−	7.28216i	0.354911	−	0.354911i	−0.507022	−	0.861933i	$-0.669254\pi$
$421$	7.28216	−	7.28216i	0.354911	−	0.354911i	0.861933	+	0.507022i	$0.169254\pi$
$422$		0			0
$423$	25.4027	−	25.4027i	1.23512	−	1.23512i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			0.283225i			0.0137062i
$428$		0			0
$429$	−13.6768	+	13.6768i	−0.660323	+	0.660323i
$430$		0			0
$431$		−	11.7250i		−	0.564771i	−0.959301	−	0.282386i	$-0.908874\pi$
$431$		−	11.7250i		−	0.564771i	0.959301	−	0.282386i	$-0.0911258\pi$
$432$		0			0
$433$	20.8827	−	20.8827i	1.00356	−	1.00356i	0.00356603	−	0.999994i	$-0.498865\pi$
$433$	20.8827	−	20.8827i	1.00356	−	1.00356i	0.999994	−	0.00356603i	$-0.00113511\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−18.7604			−0.897430
$438$		0			0
$439$			7.53661i			0.359703i	0.983694	+	0.179851i	$0.0575617\pi$
$439$			7.53661i			0.359703i	−0.983694	+	0.179851i	$0.942438\pi$
$440$		0			0
$441$			40.4105i			1.92431i
$442$		0			0
$443$	−25.7280			−1.22237			−0.611187	−	0.791486i	$-0.709308\pi$
$443$	−25.7280			−1.22237			−0.611187	+	0.791486i	$0.709308\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.68604	−	7.68604i	0.363537	−	0.363537i
$448$		0			0
$449$			2.33824i			0.110348i	0.998477	+	0.0551741i	$0.0175714\pi$
$449$			2.33824i			0.110348i	−0.998477	+	0.0551741i	$0.982429\pi$
$450$		0			0
$451$	−22.5422	+	22.5422i	−1.06147	+	1.06147i
$452$		0			0
$453$			50.2950i			2.36306i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	−0.418912	−	0.908027i	$-0.637588\pi$
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	0.908027	+	0.418912i	$0.137588\pi$
$458$		0			0
$459$	−2.48378	+	2.48378i	−0.115933	+	0.115933i
$460$		0			0
$461$	15.6903	+	15.6903i	0.730769	+	0.730769i	0.970772	−	0.240003i	$-0.0771484\pi$
$461$	15.6903	+	15.6903i	0.730769	+	0.730769i	−0.240003	+	0.970772i	$0.577148\pi$
$462$		0			0
$463$	19.6332	+	19.6332i	0.912434	+	0.912434i	0.996463	−	0.0840297i	$-0.0267791\pi$
$463$	19.6332	+	19.6332i	0.912434	+	0.912434i	−0.0840297	+	0.996463i	$0.526779\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−24.4862			−1.13309			−0.566543	−	0.824032i	$-0.691719\pi$
$467$	−24.4862			−1.13309			−0.566543	+	0.824032i	$0.691719\pi$
$468$		0			0
$469$	−0.286989	−	0.286989i	−0.0132519	−	0.0132519i
$470$		0			0
$471$	25.3630			1.16866
$472$		0			0
$473$	19.9082	+	19.9082i	0.915380	+	0.915380i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	66.2493i		−	3.03335i
$478$		0			0
$479$	37.0609			1.69335			0.846677	−	0.532108i	$-0.178600\pi$
$479$	37.0609			1.69335			0.846677	+	0.532108i	$0.178600\pi$
$480$		0			0
$481$	2.54991			0.116266
$482$		0			0
$483$		−	2.83024i		−	0.128781i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	20.1912	+	20.1912i	0.914950	+	0.914950i	0.996656	−	0.0817061i	$-0.0260369\pi$
$487$	20.1912	+	20.1912i	0.914950	+	0.914950i	−0.0817061	+	0.996656i	$0.526037\pi$
$488$		0			0
$489$	−10.6109			−0.479840
$490$		0			0
$491$	7.45822	+	7.45822i	0.336585	+	0.336585i	0.855080	−	0.518496i	$-0.173508\pi$
$491$	7.45822	+	7.45822i	0.336585	+	0.336585i	−0.518496	+	0.855080i	$0.673508\pi$
$492$		0			0
$493$	0.173601			0.00781860
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.920917	+	0.920917i	0.0413088	+	0.0413088i
$498$		0			0
$499$	8.17420	+	8.17420i	0.365927	+	0.365927i	0.865990	−	0.500062i	$-0.166689\pi$
$499$	8.17420	+	8.17420i	0.365927	+	0.365927i	−0.500062	+	0.865990i	$0.666689\pi$
$500$		0			0
$501$	−1.43202	+	1.43202i	−0.0639778	+	0.0639778i
$502$		0			0
$503$	−29.2327	+	29.2327i	−1.30342	+	1.30342i	−0.377348	+	0.926072i	$0.623164\pi$
$503$	−29.2327	+	29.2327i	−1.30342	+	1.30342i	−0.926072	+	0.377348i	$0.876836\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	31.3523i		−	1.39241i
$508$		0			0
$509$	20.0340	−	20.0340i	0.887992	−	0.887992i	−0.106338	−	0.994330i	$-0.533912\pi$
$509$	20.0340	−	20.0340i	0.887992	−	0.887992i	0.994330	+	0.106338i	$0.0339125\pi$
$510$		0			0
$511$			0.258061i			0.0114159i
$512$		0			0
$513$	−18.7536	+	18.7536i	−0.827991	+	0.827991i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	25.9483			1.14121
$518$		0			0
$519$		−	35.0504i		−	1.53854i
$520$		0			0
$521$			5.89264i			0.258161i	0.991634	+	0.129081i	$0.0412026\pi$
$521$			5.89264i			0.258161i	−0.991634	+	0.129081i	$0.958797\pi$
$522$		0			0
$523$	−24.6537			−1.07803			−0.539015	−	0.842296i	$-0.681203\pi$
$523$	−24.6537			−1.07803			−0.539015	+	0.842296i	$0.681203\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.25413	+	1.25413i	−0.0546309	+	0.0546309i
$528$		0			0
$529$		−	11.3742i		−	0.494528i
$530$		0			0
$531$	−9.47444	+	9.47444i	−0.411156	+	0.411156i
$532$		0			0
$533$			11.8681i			0.514066i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	13.9836	−	13.9836i	0.603435	−	0.603435i
$538$		0			0
$539$	−20.6392	+	20.6392i	−0.888994	+	0.888994i
$540$		0			0
$541$	−27.1762	−	27.1762i	−1.16840	−	1.16840i	−0.982585	−	0.185812i	$-0.940508\pi$
$541$	−27.1762	−	27.1762i	−1.16840	−	1.16840i	−0.185812	−	0.982585i	$-0.559492\pi$
$542$		0			0
$543$	39.0996	+	39.0996i	1.67792	+	1.67792i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.69225			0.157869			0.0789347	−	0.996880i	$-0.474848\pi$
$547$	3.69225			0.157869			0.0789347	+	0.996880i	$0.474848\pi$
$548$		0			0
$549$	7.12962	+	7.12962i	0.304285	+	0.304285i
$550$		0			0
$551$	1.31076			0.0558402
$552$		0			0
$553$	−0.416915	−	0.416915i	−0.0177290	−	0.0177290i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	12.2117i		−	0.517426i	−0.965954	−	0.258713i	$-0.916702\pi$
$557$		−	12.2117i		−	0.517426i	0.965954	−	0.258713i	$-0.0832984\pi$
$558$		0			0
$559$	10.4814			0.443315
$560$		0			0
$561$	−5.26049			−0.222098
$562$		0			0
$563$			12.2211i			0.515057i	0.966271	+	0.257528i	$0.0829081\pi$
$563$			12.2211i			0.515057i	−0.966271	+	0.257528i	$0.917092\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.828241	−	0.828241i	−0.0347829	−	0.0347829i
$568$		0			0
$569$	30.9592			1.29788			0.648938	−	0.760841i	$-0.275213\pi$
$569$	30.9592			1.29788			0.648938	+	0.760841i	$0.275213\pi$
$570$		0			0
$571$	−30.1508	−	30.1508i	−1.26177	−	1.26177i	−0.950233	−	0.311539i	$-0.899156\pi$
$571$	−30.1508	−	30.1508i	−1.26177	−	1.26177i	−0.311539	−	0.950233i	$-0.600844\pi$
$572$		0			0
$573$	41.4806			1.73288
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.98215	−	1.98215i	−0.0825181	−	0.0825181i	0.664643	−	0.747161i	$-0.268584\pi$
$577$	−1.98215	−	1.98215i	−0.0825181	−	0.0825181i	−0.747161	+	0.664643i	$0.768584\pi$
$578$		0			0
$579$	−11.5325	−	11.5325i	−0.479276	−	0.479276i
$580$		0			0
$581$	−0.187188	+	0.187188i	−0.00776586	+	0.00776586i
$582$		0			0
$583$	33.8361	−	33.8361i	1.40135	−	1.40135i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			26.9680i			1.11309i	0.830818	+	0.556544i	$0.187873\pi$
$587$			26.9680i			1.11309i	−0.830818	+	0.556544i	$0.812127\pi$
$588$		0			0
$589$	−9.46923	+	9.46923i	−0.390173	+	0.390173i
$590$		0			0
$591$			66.2153i			2.72373i
$592$		0			0
$593$	−16.6701	+	16.6701i	−0.684560	+	0.684560i	−0.961024	−	0.276464i	$-0.910837\pi$
$593$	−16.6701	+	16.6701i	−0.684560	+	0.684560i	0.276464	+	0.961024i	$0.410837\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−29.1771			−1.19414
$598$		0			0
$599$			28.8376i			1.17827i	0.808033	+	0.589137i	$0.200532\pi$
$599$			28.8376i			1.17827i	−0.808033	+	0.589137i	$0.799468\pi$
$600$		0			0
$601$			1.91377i			0.0780642i	0.999238	+	0.0390321i	$0.0124275\pi$
$601$			1.91377i			0.0780642i	−0.999238	+	0.0390321i	$0.987573\pi$
$602$		0			0
$603$	−14.4487			−0.588397
$604$		0			0
$605$		0			0
$606$		0			0
$607$	7.89049	−	7.89049i	0.320265	−	0.320265i	−0.528604	−	0.848869i	$-0.677284\pi$
$607$	7.89049	−	7.89049i	0.320265	−	0.320265i	0.848869	+	0.528604i	$0.177284\pi$
$608$		0			0
$609$			0.197745i			0.00801303i
$610$		0			0
$611$	6.83071	−	6.83071i	0.276341	−	0.276341i
$612$		0			0
$613$		−	40.1035i		−	1.61976i	−0.586592	−	0.809882i	$-0.699531\pi$
$613$		−	40.1035i		−	1.61976i	0.586592	−	0.809882i	$-0.300469\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.5821	−	14.5821i	0.587052	−	0.587052i	−0.349780	−	0.936832i	$-0.613744\pi$
$617$	14.5821	−	14.5821i	0.587052	−	0.587052i	0.936832	+	0.349780i	$0.113744\pi$
$618$		0			0
$619$	−4.01752	+	4.01752i	−0.161478	+	0.161478i	−0.783221	−	0.621743i	$-0.786425\pi$
$619$	−4.01752	+	4.01752i	−0.161478	+	0.161478i	0.621743	+	0.783221i	$0.286425\pi$
$620$		0			0
$621$	−34.3617	−	34.3617i	−1.37889	−	1.37889i
$622$		0			0
$623$	−1.80880	−	1.80880i	−0.0724679	−	0.0724679i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−39.7189			−1.58622
$628$		0			0
$629$	0.490385	+	0.490385i	0.0195529	+	0.0195529i
$630$		0			0
$631$	26.9309			1.07210			0.536052	−	0.844185i	$-0.319915\pi$
$631$	26.9309			1.07210			0.536052	+	0.844185i	$0.319915\pi$
$632$		0			0
$633$	−32.7791	−	32.7791i	−1.30285	−	1.30285i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			10.8662i			0.430536i
$638$		0			0
$639$	46.3644			1.83415
$640$		0			0
$641$	18.6880			0.738131			0.369065	−	0.929403i	$-0.379678\pi$
$641$	18.6880			0.738131			0.369065	+	0.929403i	$0.379678\pi$
$642$		0			0
$643$		−	29.6249i		−	1.16829i	−0.811648	−	0.584146i	$-0.801429\pi$
$643$		−	29.6249i		−	1.16829i	0.811648	−	0.584146i	$-0.198571\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.04426	−	5.04426i	−0.198310	−	0.198310i	0.600965	−	0.799275i	$-0.294783\pi$
$647$	−5.04426	−	5.04426i	−0.198310	−	0.198310i	−0.799275	+	0.600965i	$0.794783\pi$
$648$		0			0
$649$	−9.67794			−0.379893
$650$		0			0
$651$	−1.42855	−	1.42855i	−0.0559895	−	0.0559895i
$652$		0			0
$653$	−3.04934			−0.119330			−0.0596649	−	0.998218i	$-0.519003\pi$
$653$	−3.04934			−0.119330			−0.0596649	+	0.998218i	$0.519003\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.49615	+	6.49615i	0.253439	+	0.253439i
$658$		0			0
$659$	22.0441	+	22.0441i	0.858718	+	0.858718i	0.991187	−	0.132469i	$-0.0422906\pi$
$659$	22.0441	+	22.0441i	0.858718	+	0.858718i	−0.132469	+	0.991187i	$0.542291\pi$
$660$		0			0
$661$	8.09788	−	8.09788i	0.314971	−	0.314971i	−0.531861	−	0.846832i	$-0.678507\pi$
$661$	8.09788	−	8.09788i	0.314971	−	0.314971i	0.846832	+	0.531861i	$0.178507\pi$
$662$		0			0
$663$	−1.38479	+	1.38479i	−0.0537807	+	0.0537807i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			2.40167i			0.0929931i
$668$		0			0
$669$	17.6150	−	17.6150i	0.681035	−	0.681035i
$670$		0			0
$671$			7.28276i			0.281148i
$672$		0			0
$673$	27.1768	−	27.1768i	1.04759	−	1.04759i	0.0487786	−	0.998810i	$-0.484467\pi$
$673$	27.1768	−	27.1768i	1.04759	−	1.04759i	0.998810	−	0.0487786i	$-0.0155329\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.6501			−1.10111			−0.550557	−	0.834798i	$-0.685585\pi$
$677$	−28.6501			−1.10111			−0.550557	+	0.834798i	$0.685585\pi$
$678$		0			0
$679$			2.23115i			0.0856238i
$680$		0			0
$681$		−	68.8334i		−	2.63770i
$682$		0			0
$683$	30.8472			1.18034			0.590168	−	0.807281i	$-0.299062\pi$
$683$	30.8472			1.18034			0.590168	+	0.807281i	$0.299062\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	16.6058	−	16.6058i	0.633549	−	0.633549i
$688$		0			0
$689$		−	17.8142i		−	0.678668i
$690$		0			0
$691$	−0.253186	+	0.253186i	−0.00963164	+	0.00963164i	−0.711906	−	0.702275i	$-0.752168\pi$
$691$	−0.253186	+	0.253186i	−0.00963164	+	0.00963164i	0.702275	+	0.711906i	$0.252168\pi$
$692$		0			0
$693$		−	3.94815i		−	0.149978i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.28241	+	2.28241i	−0.0864525	+	0.0864525i
$698$		0			0
$699$	−8.95608	+	8.95608i	−0.338750	+	0.338750i
$700$		0			0
$701$	10.5238	+	10.5238i	0.397479	+	0.397479i	0.877343	−	0.479864i	$-0.159314\pi$
$701$	10.5238	+	10.5238i	0.397479	+	0.397479i	−0.479864	+	0.877343i	$0.659314\pi$
$702$		0			0
$703$	3.70261	+	3.70261i	0.139646	+	0.139646i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.94813			0.110876
$708$		0			0
$709$	−1.58968	−	1.58968i	−0.0597015	−	0.0597015i	0.676626	−	0.736327i	$-0.263442\pi$
$709$	−1.58968	−	1.58968i	−0.0597015	−	0.0597015i	−0.736327	+	0.676626i	$0.763442\pi$
$710$		0			0
$711$	−20.9900			−0.787186
$712$		0			0
$713$	−17.3502	−	17.3502i	−0.649771	−	0.649771i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	0.00411819i		−	0.000153797i
$718$		0			0
$719$	−22.8919			−0.853722			−0.426861	−	0.904317i	$-0.640381\pi$
$719$	−22.8919			−0.853722			−0.426861	+	0.904317i	$0.640381\pi$
$720$		0			0
$721$	0.998472			0.0371850
$722$		0			0
$723$		−	38.1313i		−	1.41812i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	20.1893	+	20.1893i	0.748780	+	0.748780i	0.974250	−	0.225470i	$-0.0723919\pi$
$727$	20.1893	+	20.1893i	0.748780	+	0.748780i	−0.225470	+	0.974250i	$0.572392\pi$
$728$		0			0
$729$	32.0425			1.18676
$730$		0			0
$731$	2.01572	+	2.01572i	0.0745540	+	0.0745540i
$732$		0			0
$733$	14.3253			0.529118			0.264559	−	0.964370i	$-0.414774\pi$
$733$	14.3253			0.529118			0.264559	+	0.964370i	$0.414774\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.37954	−	7.37954i	−0.271829	−	0.271829i
$738$		0			0
$739$	−32.3401	−	32.3401i	−1.18965	−	1.18965i	−0.977164	−	0.212487i	$-0.931844\pi$
$739$	−32.3401	−	32.3401i	−1.18965	−	1.18965i	−0.212487	−	0.977164i	$-0.568156\pi$
$740$		0			0
$741$	−10.4557	+	10.4557i	−0.384100	+	0.384100i
$742$		0			0
$743$	−6.06842	+	6.06842i	−0.222629	+	0.222629i	−0.809605	−	0.586976i	$-0.800318\pi$
$743$	−6.06842	+	6.06842i	−0.222629	+	0.222629i	0.586976	+	0.809605i	$0.300318\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			9.42414i			0.344811i
$748$		0			0
$749$	−1.37898	+	1.37898i	−0.0503870	+	0.0503870i
$750$		0			0
$751$		−	49.6431i		−	1.81150i	−0.423810	−	0.905751i	$-0.639308\pi$
$751$		−	49.6431i		−	1.81150i	0.423810	−	0.905751i	$-0.360692\pi$
$752$		0			0
$753$	−27.1090	+	27.1090i	−0.987907	+	0.987907i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	9.18443			0.333814			0.166907	−	0.985973i	$-0.446622\pi$
$757$	9.18443			0.333814			0.166907	+	0.985973i	$0.446622\pi$
$758$		0			0
$759$		−	72.7759i		−	2.64160i
$760$		0			0
$761$		−	4.75310i		−	0.172300i	−0.996282	−	0.0861499i	$-0.972544\pi$
$761$		−	4.75310i		−	0.172300i	0.996282	−	0.0861499i	$-0.0274564\pi$
$762$		0			0
$763$	0.924267			0.0334607
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.54765	+	2.54765i	−0.0919902	+	0.0919902i
$768$		0			0
$769$			19.4153i			0.700135i	0.936724	+	0.350067i	$0.113841\pi$
$769$			19.4153i			0.700135i	−0.936724	+	0.350067i	$0.886159\pi$
$770$		0			0
$771$	63.0884	−	63.0884i	2.27207	−	2.27207i
$772$		0			0
$773$			26.0890i			0.938356i	0.883104	+	0.469178i	$0.155450\pi$
$773$			26.0890i			0.938356i	−0.883104	+	0.469178i	$0.844550\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.558586	+	0.558586i	−0.0200392	+	0.0200392i
$778$		0			0
$779$	−17.2331	+	17.2331i	−0.617442	+	0.617442i
$780$		0			0
$781$	23.6802	+	23.6802i	0.847343	+	0.847343i
$782$		0			0
$783$	2.40080	+	2.40080i	0.0857977	+	0.0857977i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−14.2339			−0.507384			−0.253692	−	0.967285i	$-0.581645\pi$
$787$	−14.2339			−0.507384			−0.253692	+	0.967285i	$0.581645\pi$
$788$		0			0
$789$	−49.5891	−	49.5891i	−1.76542	−	1.76542i
$790$		0			0
$791$	1.49114			0.0530189
$792$		0			0
$793$	1.91713	+	1.91713i	0.0680794	+	0.0680794i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	19.8283i		−	0.702353i	−0.936309	−	0.351176i	$-0.885782\pi$
$797$		−	19.8283i		−	0.702353i	0.936309	−	0.351176i	$-0.114218\pi$
$798$		0			0
$799$	2.62729			0.0929467
$800$		0			0
$801$	−91.0655			−3.21764
$802$		0			0
$803$			6.63568i			0.234168i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−47.1817	−	47.1817i	−1.66088	−	1.66088i
$808$		0			0
$809$	−21.3864			−0.751907			−0.375954	−	0.926639i	$-0.622685\pi$
$809$	−21.3864			−0.751907			−0.375954	+	0.926639i	$0.622685\pi$
$810$		0			0
$811$	9.90624	+	9.90624i	0.347855	+	0.347855i	0.859310	−	0.511455i	$-0.170893\pi$
$811$	9.90624	+	9.90624i	0.347855	+	0.347855i	−0.511455	+	0.859310i	$0.670893\pi$
$812$		0			0
$813$	−36.6553			−1.28556
$814$		0			0
$815$		0			0
$816$		0			0
$817$	15.2195	+	15.2195i	0.532463	+	0.532463i
$818$		0			0
$819$	−1.03932	−	1.03932i	−0.0363168	−	0.0363168i
$820$		0			0
$821$	22.6209	−	22.6209i	0.789474	−	0.789474i	−0.191934	−	0.981408i	$-0.561476\pi$
$821$	22.6209	−	22.6209i	0.789474	−	0.789474i	0.981408	+	0.191934i	$0.0614759\pi$
$822$		0			0
$823$	4.89892	−	4.89892i	0.170766	−	0.170766i	−0.616550	−	0.787316i	$-0.711470\pi$
$823$	4.89892	−	4.89892i	0.170766	−	0.170766i	0.787316	+	0.616550i	$0.211470\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1.05434i			0.0366630i	0.999832	+	0.0183315i	$0.00583542\pi$
$827$			1.05434i			0.0366630i	−0.999832	+	0.0183315i	$0.994165\pi$
$828$		0			0
$829$	−11.7754	+	11.7754i	−0.408978	+	0.408978i	−0.881382	−	0.472404i	$-0.843386\pi$
$829$	−11.7754	+	11.7754i	−0.408978	+	0.408978i	0.472404	+	0.881382i	$0.343386\pi$
$830$		0			0
$831$		−	62.3580i		−	2.16317i
$832$		0			0
$833$	−2.08973	+	2.08973i	−0.0724050	+	0.0724050i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−34.6879			−1.19899
$838$		0			0
$839$			41.1678i			1.42127i	0.703560	+	0.710636i	$0.251593\pi$
$839$			41.1678i			1.42127i	−0.703560	+	0.710636i	$0.748407\pi$
$840$		0			0
$841$			28.8322i			0.994214i
$842$		0			0
$843$	31.6749			1.09094
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.750366	−	0.750366i	0.0257829	−	0.0257829i
$848$		0			0
$849$			37.3508i			1.28188i
$850$		0			0
$851$	−6.78419	+	6.78419i	−0.232559	+	0.232559i
$852$		0			0
$853$			11.7179i			0.401212i	0.979672	+	0.200606i	$0.0642911\pi$
$853$			11.7179i			0.401212i	−0.979672	+	0.200606i	$0.935709\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.2154	+	12.2154i	−0.417270	+	0.417270i	−0.884262	−	0.466992i	$-0.845338\pi$
$857$	−12.2154	+	12.2154i	−0.417270	+	0.417270i	0.466992	+	0.884262i	$0.345338\pi$
$858$		0			0
$859$	17.2170	−	17.2170i	0.587436	−	0.587436i	−0.349500	−	0.936936i	$-0.613649\pi$
$859$	17.2170	−	17.2170i	0.587436	−	0.587436i	0.936936	+	0.349500i	$0.113649\pi$
$860$		0			0
$861$	−2.59984	−	2.59984i	−0.0886024	−	0.0886024i
$862$		0			0
$863$	11.1929	+	11.1929i	0.381011	+	0.381011i	0.871466	−	0.490455i	$-0.163169\pi$
$863$	11.1929	+	11.1929i	0.381011	+	0.381011i	−0.490455	+	0.871466i	$0.663169\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	49.8828			1.69411
$868$		0			0
$869$	−10.7204	−	10.7204i	−0.363665	−	0.363665i
$870$		0			0
$871$	−3.88522			−0.131646
$872$		0			0
$873$	56.1647	+	56.1647i	1.90089	+	1.90089i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	43.1739i		−	1.45788i	−0.684578	−	0.728940i	$-0.740013\pi$
$877$		−	43.1739i		−	1.45788i	0.684578	−	0.728940i	$-0.259987\pi$
$878$		0			0
$879$	−10.1760			−0.343227
$880$		0			0
$881$	−33.4204			−1.12596			−0.562981	−	0.826470i	$-0.690346\pi$
$881$	−33.4204			−1.12596			−0.562981	+	0.826470i	$0.690346\pi$
$882$		0			0
$883$		−	2.00362i		−	0.0674270i	−0.999432	−	0.0337135i	$-0.989267\pi$
$883$		−	2.00362i		−	0.0674270i	0.999432	−	0.0337135i	$-0.0107334\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.1765	−	16.1765i	−0.543154	−	0.543154i	0.381298	−	0.924452i	$-0.375477\pi$
$887$	−16.1765	−	16.1765i	−0.543154	−	0.543154i	−0.924452	+	0.381298i	$0.875477\pi$
$888$		0			0
$889$	−2.82586			−0.0947762
$890$		0			0
$891$	−21.2971	−	21.2971i	−0.713480	−	0.713480i
$892$		0			0
$893$	19.8371			0.663822
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−19.1577	−	19.1577i	−0.639658	−	0.639658i
$898$		0			0
$899$	1.21223	+	1.21223i	0.0404303	+	0.0404303i
$900$		0			0
$901$	3.42593	−	3.42593i	0.114134	−	0.114134i
$902$		0			0
$903$	−2.29606	+	2.29606i	−0.0764080	+	0.0764080i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	29.7116i		−	0.986559i	−0.869871	−	0.493279i	$-0.835798\pi$
$907$		−	29.7116i		−	0.986559i	0.869871	−	0.493279i	$-0.164202\pi$
$908$		0			0
$909$	74.2131	−	74.2131i	2.46149	−	2.46149i
$910$		0			0
$911$			44.6931i			1.48075i	0.672195	+	0.740374i	$0.265352\pi$
$911$			44.6931i			1.48075i	−0.672195	+	0.740374i	$0.734648\pi$
$912$		0			0
$913$	−4.81328	+	4.81328i	−0.159296	+	0.159296i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.84061			0.0607821
$918$		0			0
$919$			40.1278i			1.32369i	0.749639	+	0.661847i	$0.230227\pi$
$919$			40.1278i			1.32369i	−0.749639	+	0.661847i	$0.769773\pi$
$920$		0			0
$921$		−	35.0250i		−	1.15411i
$922$		0			0
$923$	12.4673			0.410365
$924$		0			0
$925$		0			0
$926$		0			0
$927$	25.1345	−	25.1345i	0.825525	−	0.825525i
$928$		0			0
$929$			27.7519i			0.910512i	0.890361	+	0.455256i	$0.150452\pi$
$929$			27.7519i			0.910512i	−0.890361	+	0.455256i	$0.849548\pi$
$930$		0			0
$931$	−15.7783	+	15.7783i	−0.517114	+	0.517114i
$932$		0			0
$933$		−	67.1004i		−	2.19677i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	−0.930591	−	0.366060i	$-0.880706\pi$
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	0.366060	+	0.930591i	$0.380706\pi$
$938$		0			0
$939$	−21.0245	+	21.0245i	−0.686110	+	0.686110i
$940$		0			0
$941$	−4.81532	−	4.81532i	−0.156975	−	0.156975i	0.624250	−	0.781225i	$-0.285405\pi$
$941$	−4.81532	−	4.81532i	−0.156975	−	0.156975i	−0.781225	+	0.624250i	$0.785405\pi$
$942$		0			0
$943$	−31.5759	−	31.5759i	−1.02825	−	1.02825i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.37347			0.109623			0.0548115	−	0.998497i	$-0.482544\pi$
$947$	3.37347			0.109623			0.0548115	+	0.998497i	$0.482544\pi$
$948$		0			0
$949$	1.74680	+	1.74680i	0.0567034	+	0.0567034i
$950$		0			0
$951$	−74.5153			−2.41632
$952$		0			0
$953$	14.3663	+	14.3663i	0.465369	+	0.465369i	0.900410	−	0.435041i	$-0.143266\pi$
$953$	14.3663	+	14.3663i	0.465369	+	0.465369i	−0.435041	+	0.900410i	$0.643266\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			5.08475i			0.164366i
$958$		0			0
$959$	0.710289			0.0229364
$960$		0			0
$961$	13.4851			0.435003
$962$		0			0
$963$			69.4263i			2.23723i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.8576	−	11.8576i	−0.381315	−	0.381315i	0.490260	−	0.871576i	$-0.336902\pi$
$967$	−11.8576	−	11.8576i	−0.381315	−	0.381315i	−0.871576	+	0.490260i	$0.836902\pi$
$968$		0			0
$969$	−4.02156			−0.129191
$970$		0			0
$971$	14.6082	+	14.6082i	0.468799	+	0.468799i	0.901525	−	0.432726i	$-0.142448\pi$
$971$	14.6082	+	14.6082i	0.468799	+	0.468799i	−0.432726	+	0.901525i	$0.642448\pi$
$972$		0			0
$973$	−2.81319			−0.0901869
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.9249	−	12.9249i	−0.413504	−	0.413504i	0.469454	−	0.882957i	$-0.344451\pi$
$977$	−12.9249	−	12.9249i	−0.413504	−	0.413504i	−0.882957	+	0.469454i	$0.844451\pi$
$978$		0			0
$979$	−46.5108	−	46.5108i	−1.48649	−	1.48649i
$980$		0			0
$981$	23.2665	−	23.2665i	0.742843	−	0.742843i
$982$		0			0
$983$	−0.133323	+	0.133323i	−0.00425235	+	0.00425235i	−0.709230	−	0.704977i	$-0.750957\pi$
$983$	−0.133323	+	0.133323i	−0.00425235	+	0.00425235i	0.704977	+	0.709230i	$0.250957\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			2.99268i			0.0952580i
$988$		0			0
$989$	−27.8863	+	27.8863i	−0.886733	+	0.886733i
$990$		0			0
$991$			47.9032i			1.52170i	0.648930	+	0.760848i	$0.275217\pi$
$991$			47.9032i			1.52170i	−0.648930	+	0.760848i	$0.724783\pi$
$992$		0			0
$993$	17.2251	−	17.2251i	0.546624	−	0.546624i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	54.9379			1.73990			0.869951	−	0.493138i	$-0.164150\pi$
$997$	54.9379			1.73990			0.869951	+	0.493138i	$0.164150\pi$
$998$		0			0
$999$			13.5635i			0.429129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.d.1007.9		18
4.3	odd	2		400.2.j.d.307.9		18
5.2	odd	4		320.2.s.b.303.9		18
5.3	odd	4		1600.2.s.d.943.1		18
5.4	even	2		320.2.j.b.47.1		18
16.5	even	4		400.2.s.d.107.5		18
16.11	odd	4		1600.2.s.d.207.1		18
20.3	even	4		400.2.s.d.243.5		18
20.7	even	4		80.2.s.b.3.5	yes	18
20.19	odd	2		80.2.j.b.67.1	yes	18
40.19	odd	2		640.2.j.d.607.1		18
40.27	even	4		640.2.s.d.223.9		18
40.29	even	2		640.2.j.c.607.9		18
40.37	odd	4		640.2.s.c.223.1		18
60.47	odd	4		720.2.z.g.163.5		18
60.59	even	2		720.2.bd.g.307.9		18
80.19	odd	4		640.2.s.c.287.1		18
80.27	even	4		320.2.j.b.143.9		18
80.29	even	4		640.2.s.d.287.9		18
80.37	odd	4		80.2.j.b.43.1	✓	18
80.43	even	4	inner	1600.2.j.d.143.1		18
80.53	odd	4		400.2.j.d.43.9		18
80.59	odd	4		320.2.s.b.207.9		18
80.67	even	4		640.2.j.c.543.1		18
80.69	even	4		80.2.s.b.27.5	yes	18
80.77	odd	4		640.2.j.d.543.9		18
240.149	odd	4		720.2.z.g.667.5		18
240.197	even	4		720.2.bd.g.523.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.1	✓	18	80.37	odd	4
80.2.j.b.67.1	yes	18	20.19	odd	2
80.2.s.b.3.5	yes	18	20.7	even	4
80.2.s.b.27.5	yes	18	80.69	even	4
320.2.j.b.47.1		18	5.4	even	2
320.2.j.b.143.9		18	80.27	even	4
320.2.s.b.207.9		18	80.59	odd	4
320.2.s.b.303.9		18	5.2	odd	4
400.2.j.d.43.9		18	80.53	odd	4
400.2.j.d.307.9		18	4.3	odd	2
400.2.s.d.107.5		18	16.5	even	4
400.2.s.d.243.5		18	20.3	even	4
640.2.j.c.543.1		18	80.67	even	4
640.2.j.c.607.9		18	40.29	even	2
640.2.j.d.543.9		18	80.77	odd	4
640.2.j.d.607.1		18	40.19	odd	2
640.2.s.c.223.1		18	40.37	odd	4
640.2.s.c.287.1		18	80.19	odd	4
640.2.s.d.223.9		18	40.27	even	4
640.2.s.d.287.9		18	80.29	even	4
720.2.z.g.163.5		18	60.47	odd	4
720.2.z.g.667.5		18	240.149	odd	4
720.2.bd.g.307.9		18	60.59	even	2
720.2.bd.g.523.9		18	240.197	even	4
1600.2.j.d.143.1		18	80.43	even	4	inner
1600.2.j.d.1007.9		18	1.1	even	1	trivial
1600.2.s.d.207.1		18	16.11	odd	4
1600.2.s.d.943.1		18	5.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.96561i q^{3} +(-0.115101 - 0.115101i) q^{7} -5.79486 q^{9} +(-2.95966 - 2.95966i) q^{11} -1.55822 q^{13} +(-0.299668 - 0.299668i) q^{17} +(-2.26261 - 2.26261i) q^{19} +(0.341344 - 0.341344i) q^{21} +(4.14573 - 4.14573i) q^{23} -8.28846i q^{27} +(-0.289656 + 0.289656i) q^{29} -4.18508i q^{31} +(8.77721 - 8.77721i) q^{33} -1.63643 q^{37} -4.62107i q^{39} -7.61648i q^{41} -6.72651 q^{43} +(-4.38366 + 4.38366i) q^{47} -6.97350i q^{49} +(0.888698 - 0.888698i) q^{51} +11.4324i q^{53} +(6.71003 - 6.71003i) q^{57} +(1.63497 - 1.63497i) q^{59} +(-1.23034 - 1.23034i) q^{61} +(0.666993 + 0.666993i) q^{63} +2.49337 q^{67} +(12.2946 + 12.2946i) q^{69} -8.00096 q^{71} +(-1.12102 - 1.12102i) q^{73} +0.681319i q^{77} +3.62218 q^{79} +7.19579 q^{81} -1.62629i q^{83} +(-0.859007 - 0.859007i) q^{87} +15.7149 q^{89} +(0.179352 + 0.179352i) q^{91} +12.4113 q^{93} +(-9.69217 - 9.69217i) q^{97} +(17.1508 + 17.1508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} - 10 q^{9} + 2 q^{11} + 6 q^{17} - 2 q^{19} - 16 q^{21} - 2 q^{23} - 14 q^{29} + 8 q^{33} - 8 q^{37} - 44 q^{43} - 38 q^{47} - 8 q^{51} - 24 q^{57} + 10 q^{59} + 14 q^{61} + 6 q^{63} + 12 q^{67}+ \cdots + 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 - 10 * q^9 + 2 * q^11 + 6 * q^17 - 2 * q^19 - 16 * q^21 - 2 * q^23 - 14 * q^29 + 8 * q^33 - 8 * q^37 - 44 * q^43 - 38 * q^47 - 8 * q^51 - 24 * q^57 + 10 * q^59 + 14 * q^61 + 6 * q^63 + 12 * q^67 + 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^79 + 2 * q^81 + 24 * q^87 - 12 * q^89 - 16 * q^93 - 18 * q^97 + 22 * q^99

Introduction

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