LMFDB - Embedded newform 1335.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1335,2,Mod(1,1335)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1335, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1335.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1335 = 3 \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1335.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$10.6600286698$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 6x^{7} + 31x^{6} + 13x^{5} - 75x^{4} - 17x^{3} + 52x^{2} + 11x - 1 $ x^9 - 4x^8 - 6x^7 + 31x^6 + 13x^5 - 75x^4 - 17x^3 + 52x^2 + 11x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.89144$ of defining polynomial
Character	$\chi$	$=$	1335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.891444 q^{2} -1.00000 q^{3} -1.20533 q^{4} -1.00000 q^{5} +0.891444 q^{6} +3.64096 q^{7} +2.85737 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.891444 q^{2} -1.00000 q^{3} -1.20533 q^{4} -1.00000 q^{5} +0.891444 q^{6} +3.64096 q^{7} +2.85737 q^{8} +1.00000 q^{9} +0.891444 q^{10} +4.33096 q^{11} +1.20533 q^{12} -1.57936 q^{13} -3.24571 q^{14} +1.00000 q^{15} -0.136530 q^{16} -4.04140 q^{17} -0.891444 q^{18} -3.87139 q^{19} +1.20533 q^{20} -3.64096 q^{21} -3.86080 q^{22} +8.46521 q^{23} -2.85737 q^{24} +1.00000 q^{25} +1.40791 q^{26} -1.00000 q^{27} -4.38855 q^{28} -4.60342 q^{29} -0.891444 q^{30} +4.14525 q^{31} -5.59303 q^{32} -4.33096 q^{33} +3.60268 q^{34} -3.64096 q^{35} -1.20533 q^{36} -5.13942 q^{37} +3.45112 q^{38} +1.57936 q^{39} -2.85737 q^{40} +5.53546 q^{41} +3.24571 q^{42} -4.03101 q^{43} -5.22022 q^{44} -1.00000 q^{45} -7.54626 q^{46} +2.01901 q^{47} +0.136530 q^{48} +6.25657 q^{49} -0.891444 q^{50} +4.04140 q^{51} +1.90364 q^{52} +7.34755 q^{53} +0.891444 q^{54} -4.33096 q^{55} +10.4036 q^{56} +3.87139 q^{57} +4.10369 q^{58} +4.74102 q^{59} -1.20533 q^{60} -14.7844 q^{61} -3.69525 q^{62} +3.64096 q^{63} +5.25893 q^{64} +1.57936 q^{65} +3.86080 q^{66} +2.05578 q^{67} +4.87121 q^{68} -8.46521 q^{69} +3.24571 q^{70} +9.08588 q^{71} +2.85737 q^{72} +13.8742 q^{73} +4.58151 q^{74} -1.00000 q^{75} +4.66629 q^{76} +15.7688 q^{77} -1.40791 q^{78} +4.23690 q^{79} +0.136530 q^{80} +1.00000 q^{81} -4.93455 q^{82} +17.2495 q^{83} +4.38855 q^{84} +4.04140 q^{85} +3.59342 q^{86} +4.60342 q^{87} +12.3751 q^{88} +1.00000 q^{89} +0.891444 q^{90} -5.75037 q^{91} -10.2033 q^{92} -4.14525 q^{93} -1.79984 q^{94} +3.87139 q^{95} +5.59303 q^{96} +6.13872 q^{97} -5.57739 q^{98} +4.33096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9	\( 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9} - 5 q^{10} + 4 q^{11} - 11 q^{12} + 5 q^{13} - q^{14} + 9 q^{15} + 15 q^{16} + 21 q^{17} + 5 q^{18} - 18 q^{19} - 11 q^{20} + 3 q^{21} + 6 q^{22} + 16 q^{23} - 18 q^{24} + 9 q^{25} + 8 q^{26} - 9 q^{27} + 6 q^{28} + 3 q^{29} + 5 q^{30} - 6 q^{31} + 46 q^{32} - 4 q^{33} + 12 q^{34} + 3 q^{35} + 11 q^{36} + 11 q^{37} + 20 q^{38} - 5 q^{39} - 18 q^{40} - q^{41} + q^{42} - 3 q^{43} + 38 q^{44} - 9 q^{45} + 16 q^{46} + 27 q^{47} - 15 q^{48} + 24 q^{49} + 5 q^{50} - 21 q^{51} + 17 q^{52} + 43 q^{53} - 5 q^{54} - 4 q^{55} + 5 q^{56} + 18 q^{57} + 34 q^{58} + 3 q^{59} + 11 q^{60} - 30 q^{61} + 36 q^{62} - 3 q^{63} + 50 q^{64} - 5 q^{65} - 6 q^{66} - 12 q^{67} + 64 q^{68} - 16 q^{69} + q^{70} - 4 q^{71} + 18 q^{72} + 26 q^{73} + 2 q^{74} - 9 q^{75} - 12 q^{76} + 34 q^{77} - 8 q^{78} + q^{79} - 15 q^{80} + 9 q^{81} - 51 q^{82} + 24 q^{83} - 6 q^{84} - 21 q^{85} + 18 q^{86} - 3 q^{87} + 64 q^{88} + 9 q^{89} - 5 q^{90} - 50 q^{91} + 10 q^{92} + 6 q^{93} - 11 q^{94} + 18 q^{95} - 46 q^{96} - 4 q^{97} + 75 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9 - 5 * q^10 + 4 * q^11 - 11 * q^12 + 5 * q^13 - q^14 + 9 * q^15 + 15 * q^16 + 21 * q^17 + 5 * q^18 - 18 * q^19 - 11 * q^20 + 3 * q^21 + 6 * q^22 + 16 * q^23 - 18 * q^24 + 9 * q^25 + 8 * q^26 - 9 * q^27 + 6 * q^28 + 3 * q^29 + 5 * q^30 - 6 * q^31 + 46 * q^32 - 4 * q^33 + 12 * q^34 + 3 * q^35 + 11 * q^36 + 11 * q^37 + 20 * q^38 - 5 * q^39 - 18 * q^40 - q^41 + q^42 - 3 * q^43 + 38 * q^44 - 9 * q^45 + 16 * q^46 + 27 * q^47 - 15 * q^48 + 24 * q^49 + 5 * q^50 - 21 * q^51 + 17 * q^52 + 43 * q^53 - 5 * q^54 - 4 * q^55 + 5 * q^56 + 18 * q^57 + 34 * q^58 + 3 * q^59 + 11 * q^60 - 30 * q^61 + 36 * q^62 - 3 * q^63 + 50 * q^64 - 5 * q^65 - 6 * q^66 - 12 * q^67 + 64 * q^68 - 16 * q^69 + q^70 - 4 * q^71 + 18 * q^72 + 26 * q^73 + 2 * q^74 - 9 * q^75 - 12 * q^76 + 34 * q^77 - 8 * q^78 + q^79 - 15 * q^80 + 9 * q^81 - 51 * q^82 + 24 * q^83 - 6 * q^84 - 21 * q^85 + 18 * q^86 - 3 * q^87 + 64 * q^88 + 9 * q^89 - 5 * q^90 - 50 * q^91 + 10 * q^92 + 6 * q^93 - 11 * q^94 + 18 * q^95 - 46 * q^96 - 4 * q^97 + 75 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−0.891444	−0.630346	−0.315173	−	0.949034i	$-0.602063\pi$
$2$	−0.891444	−0.630346	−0.315173	+	0.949034i	$0.602063\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.20533	−0.602664
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.891444	0.363930
$7$	3.64096	1.37615	0.688076	−	0.725638i	$-0.258455\pi$
$7$	3.64096	1.37615	0.688076	+	0.725638i	$0.258455\pi$
$8$	2.85737	1.01023
$9$	1.00000	0.333333
$10$	0.891444	0.281899
$11$	4.33096	1.30583	0.652916	−	0.757430i	$-0.273545\pi$
$11$	4.33096	1.30583	0.652916	+	0.757430i	$0.273545\pi$
$12$	1.20533	0.347948
$13$	−1.57936	−0.438035	−0.219017	−	0.975721i	$-0.570285\pi$
$13$	−1.57936	−0.438035	−0.219017	+	0.975721i	$0.570285\pi$
$14$	−3.24571	−0.867452
$15$	1.00000	0.258199
$16$	−0.136530	−0.0341324
$17$	−4.04140	−0.980183	−0.490092	−	0.871671i	$-0.663037\pi$
$17$	−4.04140	−0.980183	−0.490092	+	0.871671i	$0.663037\pi$
$18$	−0.891444	−0.210115
$19$	−3.87139	−0.888157	−0.444078	−	0.895988i	$-0.646469\pi$
$19$	−3.87139	−0.888157	−0.444078	+	0.895988i	$0.646469\pi$
$20$	1.20533	0.269519
$21$	−3.64096	−0.794522
$22$	−3.86080	−0.823126
$23$	8.46521	1.76512	0.882559	−	0.470202i	$-0.155819\pi$
$23$	8.46521	1.76512	0.882559	+	0.470202i	$0.155819\pi$
$24$	−2.85737	−0.583258
$25$	1.00000	0.200000
$26$	1.40791	0.276113
$27$	−1.00000	−0.192450
$28$	−4.38855	−0.829358
$29$	−4.60342	−0.854833	−0.427416	−	0.904055i	$-0.640576\pi$
$29$	−4.60342	−0.854833	−0.427416	+	0.904055i	$0.640576\pi$
$30$	−0.891444	−0.162755
$31$	4.14525	0.744508	0.372254	−	0.928131i	$-0.378585\pi$
$31$	4.14525	0.744508	0.372254	+	0.928131i	$0.378585\pi$
$32$	−5.59303	−0.988718
$33$	−4.33096	−0.753923
$34$	3.60268	0.617855
$35$	−3.64096	−0.615434
$36$	−1.20533	−0.200888
$37$	−5.13942	−0.844916	−0.422458	−	0.906383i	$-0.638833\pi$
$37$	−5.13942	−0.844916	−0.422458	+	0.906383i	$0.638833\pi$
$38$	3.45112	0.559846
$39$	1.57936	0.252899
$40$	−2.85737	−0.451790
$41$	5.53546	0.864493	0.432247	−	0.901755i	$-0.357721\pi$
$41$	5.53546	0.864493	0.432247	+	0.901755i	$0.357721\pi$
$42$	3.24571	0.500824
$43$	−4.03101	−0.614724	−0.307362	−	0.951593i	$-0.599446\pi$
$43$	−4.03101	−0.614724	−0.307362	+	0.951593i	$0.599446\pi$
$44$	−5.22022	−0.786978
$45$	−1.00000	−0.149071
$46$	−7.54626	−1.11263
$47$	2.01901	0.294503	0.147252	−	0.989099i	$-0.452957\pi$
$47$	2.01901	0.294503	0.147252	+	0.989099i	$0.452957\pi$
$48$	0.136530	0.0197064
$49$	6.25657	0.893796
$50$	−0.891444	−0.126069
$51$	4.04140	0.565909
$52$	1.90364	0.263988
$53$	7.34755	1.00926	0.504632	−	0.863335i	$-0.331628\pi$
$53$	7.34755	1.00926	0.504632	+	0.863335i	$0.331628\pi$
$54$	0.891444	0.121310
$55$	−4.33096	−0.583986
$56$	10.4036	1.39023
$57$	3.87139	0.512778
$58$	4.10369	0.538840
$59$	4.74102	0.617228	0.308614	−	0.951187i	$-0.400135\pi$
$59$	4.74102	0.617228	0.308614	+	0.951187i	$0.400135\pi$
$60$	−1.20533	−0.155607
$61$	−14.7844	−1.89295	−0.946476	−	0.322775i	$-0.895384\pi$
$61$	−14.7844	−1.89295	−0.946476	+	0.322775i	$0.895384\pi$
$62$	−3.69525	−0.469298
$63$	3.64096	0.458718
$64$	5.25893	0.657367
$65$	1.57936	0.195895
$66$	3.86080	0.475232
$67$	2.05578	0.251153	0.125577	−	0.992084i	$-0.459922\pi$
$67$	2.05578	0.251153	0.125577	+	0.992084i	$0.459922\pi$
$68$	4.87121	0.590721
$69$	−8.46521	−1.01909
$70$	3.24571	0.387937
$71$	9.08588	1.07830	0.539148	−	0.842211i	$-0.318746\pi$
$71$	9.08588	1.07830	0.539148	+	0.842211i	$0.318746\pi$
$72$	2.85737	0.336744
$73$	13.8742	1.62385	0.811926	−	0.583760i	$-0.198419\pi$
$73$	13.8742	1.62385	0.811926	+	0.583760i	$0.198419\pi$
$74$	4.58151	0.532589
$75$	−1.00000	−0.115470
$76$	4.66629	0.535260
$77$	15.7688	1.79702
$78$	−1.40791	−0.159414
$79$	4.23690	0.476689	0.238344	−	0.971181i	$-0.423395\pi$
$79$	4.23690	0.476689	0.238344	+	0.971181i	$0.423395\pi$
$80$	0.136530	0.0152645
$81$	1.00000	0.111111
$82$	−4.93455	−0.544930
$83$	17.2495	1.89338	0.946688	−	0.322152i	$-0.104406\pi$
$83$	17.2495	1.89338	0.946688	+	0.322152i	$0.104406\pi$
$84$	4.38855	0.478830
$85$	4.04140	0.438351
$86$	3.59342	0.387489
$87$	4.60342	0.493538
$88$	12.3751	1.31919
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	0.891444	0.0939664
$91$	−5.75037	−0.602803
$92$	−10.2033	−1.06377
$93$	−4.14525	−0.429842
$94$	−1.79984	−0.185639
$95$	3.87139	0.397196
$96$	5.59303	0.570836
$97$	6.13872	0.623292	0.311646	−	0.950198i	$-0.399120\pi$
$97$	6.13872	0.623292	0.311646	+	0.950198i	$0.399120\pi$
$98$	−5.57739	−0.563401
$99$	4.33096	0.435277
$100$	−1.20533	−0.120533
$101$	−10.5014	−1.04493	−0.522464	−	0.852661i	$-0.674987\pi$
$101$	−10.5014	−1.04493	−0.522464	+	0.852661i	$0.674987\pi$
$102$	−3.60268	−0.356718
$103$	13.2616	1.30670	0.653350	−	0.757056i	$-0.273363\pi$
$103$	13.2616	1.30670	0.653350	+	0.757056i	$0.273363\pi$
$104$	−4.51281	−0.442517
$105$	3.64096	0.355321
$106$	−6.54993	−0.636185
$107$	14.6857	1.41972	0.709862	−	0.704341i	$-0.248757\pi$
$107$	14.6857	1.41972	0.709862	+	0.704341i	$0.248757\pi$
$108$	1.20533	0.115983
$109$	−7.63418	−0.731222	−0.365611	−	0.930768i	$-0.619140\pi$
$109$	−7.63418	−0.731222	−0.365611	+	0.930768i	$0.619140\pi$
$110$	3.86080	0.368113
$111$	5.13942	0.487812
$112$	−0.497099	−0.0469714
$113$	−15.0328	−1.41416	−0.707082	−	0.707131i	$-0.749989\pi$
$113$	−15.0328	−1.41416	−0.707082	+	0.707131i	$0.749989\pi$
$114$	−3.45112	−0.323227
$115$	−8.46521	−0.789384
$116$	5.54862	0.515177
$117$	−1.57936	−0.146012
$118$	−4.22635	−0.389067
$119$	−14.7146	−1.34888
$120$	2.85737	0.260841
$121$	7.75718	0.705198
$122$	13.1795	1.19321
$123$	−5.53546	−0.499115
$124$	−4.99638	−0.448688
$125$	−1.00000	−0.0894427
$126$	−3.24571	−0.289151
$127$	10.6036	0.940916	0.470458	−	0.882422i	$-0.344089\pi$
$127$	10.6036	0.940916	0.470458	+	0.882422i	$0.344089\pi$
$128$	6.49802	0.574349
$129$	4.03101	0.354911
$130$	−1.40791	−0.123482
$131$	10.0863	0.881240	0.440620	−	0.897694i	$-0.354759\pi$
$131$	10.0863	0.881240	0.440620	+	0.897694i	$0.354759\pi$
$132$	5.22022	0.454362
$133$	−14.0956	−1.22224
$134$	−1.83261	−0.158313
$135$	1.00000	0.0860663
$136$	−11.5478	−0.990213
$137$	−8.64359	−0.738472	−0.369236	−	0.929336i	$-0.620381\pi$
$137$	−8.64359	−0.738472	−0.369236	+	0.929336i	$0.620381\pi$
$138$	7.54626	0.642380
$139$	−17.6476	−1.49685	−0.748423	−	0.663221i	$-0.769189\pi$
$139$	−17.6476	−1.49685	−0.748423	+	0.663221i	$0.769189\pi$
$140$	4.38855	0.370900
$141$	−2.01901	−0.170032
$142$	−8.09955	−0.679699
$143$	−6.84012	−0.572000
$144$	−0.136530	−0.0113775
$145$	4.60342	0.382293
$146$	−12.3681	−1.02359
$147$	−6.25657	−0.516034
$148$	6.19469	0.509200
$149$	8.05076	0.659544	0.329772	−	0.944061i	$-0.393028\pi$
$149$	8.05076	0.659544	0.329772	+	0.944061i	$0.393028\pi$
$150$	0.891444	0.0727861
$151$	8.17384	0.665178	0.332589	−	0.943072i	$-0.392078\pi$
$151$	8.17384	0.665178	0.332589	+	0.943072i	$0.392078\pi$
$152$	−11.0620	−0.897245
$153$	−4.04140	−0.326728
$154$	−14.0570	−1.13275
$155$	−4.14525	−0.332954
$156$	−1.90364	−0.152413
$157$	19.0147	1.51754	0.758770	−	0.651359i	$-0.225801\pi$
$157$	19.0147	1.51754	0.758770	+	0.651359i	$0.225801\pi$
$158$	−3.77696	−0.300479
$159$	−7.34755	−0.582699
$160$	5.59303	0.442168
$161$	30.8215	2.42907
$162$	−0.891444	−0.0700384
$163$	−7.89684	−0.618529	−0.309264	−	0.950976i	$-0.600083\pi$
$163$	−7.89684	−0.618529	−0.309264	+	0.950976i	$0.600083\pi$
$164$	−6.67204	−0.520999
$165$	4.33096	0.337164
$166$	−15.3769	−1.19348
$167$	−5.95886	−0.461110	−0.230555	−	0.973059i	$-0.574054\pi$
$167$	−5.95886	−0.461110	−0.230555	+	0.973059i	$0.574054\pi$
$168$	−10.4036	−0.802652
$169$	−10.5056	−0.808126
$170$	−3.60268	−0.276313
$171$	−3.87139	−0.296052
$172$	4.85869	0.370472
$173$	17.0408	1.29559	0.647794	−	0.761816i	$-0.275692\pi$
$173$	17.0408	1.29559	0.647794	+	0.761816i	$0.275692\pi$
$174$	−4.10369	−0.311100
$175$	3.64096	0.275231
$176$	−0.591304	−0.0445712
$177$	−4.74102	−0.356357
$178$	−0.891444	−0.0668165
$179$	15.6647	1.17084	0.585419	−	0.810731i	$-0.300930\pi$
$179$	15.6647	1.17084	0.585419	+	0.810731i	$0.300930\pi$
$180$	1.20533	0.0898398
$181$	−10.9347	−0.812771	−0.406385	−	0.913702i	$-0.633211\pi$
$181$	−10.9347	−0.812771	−0.406385	+	0.913702i	$0.633211\pi$
$182$	5.12613	0.379974
$183$	14.7844	1.09290
$184$	24.1882	1.78318
$185$	5.13942	0.377858
$186$	3.69525	0.270949
$187$	−17.5031	−1.27995
$188$	−2.43357	−0.177487
$189$	−3.64096	−0.264841
$190$	−3.45112	−0.250371
$191$	11.6720	0.844556	0.422278	−	0.906466i	$-0.361231\pi$
$191$	11.6720	0.844556	0.422278	+	0.906466i	$0.361231\pi$
$192$	−5.25893	−0.379531
$193$	−4.60334	−0.331356	−0.165678	−	0.986180i	$-0.552981\pi$
$193$	−4.60334	−0.331356	−0.165678	+	0.986180i	$0.552981\pi$
$194$	−5.47232	−0.392890
$195$	−1.57936	−0.113100
$196$	−7.54122	−0.538659
$197$	21.3603	1.52186	0.760929	−	0.648835i	$-0.224743\pi$
$197$	21.3603	1.52186	0.760929	+	0.648835i	$0.224743\pi$
$198$	−3.86080	−0.274375
$199$	−20.2630	−1.43640	−0.718202	−	0.695835i	$-0.755035\pi$
$199$	−20.2630	−1.43640	−0.718202	+	0.695835i	$0.755035\pi$
$200$	2.85737	0.202047
$201$	−2.05578	−0.145003
$202$	9.36141	0.658666
$203$	−16.7608	−1.17638
$204$	−4.87121	−0.341053
$205$	−5.53546	−0.386613
$206$	−11.8219	−0.823674
$207$	8.46521	0.588372
$208$	0.215629	0.0149512
$209$	−16.7668	−1.15978
$210$	−3.24571	−0.223975
$211$	−15.2602	−1.05055	−0.525276	−	0.850932i	$-0.676038\pi$
$211$	−15.2602	−1.05055	−0.525276	+	0.850932i	$0.676038\pi$
$212$	−8.85620	−0.608247
$213$	−9.08588	−0.622554
$214$	−13.0915	−0.894917
$215$	4.03101	0.274913
$216$	−2.85737	−0.194419
$217$	15.0927	1.02456
$218$	6.80545	0.460923
$219$	−13.8742	−0.937532
$220$	5.22022	0.351947
$221$	6.38281	0.429354
$222$	−4.58151	−0.307491
$223$	−8.24096	−0.551856	−0.275928	−	0.961178i	$-0.588985\pi$
$223$	−8.24096	−0.551856	−0.275928	+	0.961178i	$0.588985\pi$
$224$	−20.3640	−1.36063
$225$	1.00000	0.0666667
$226$	13.4009	0.891413
$227$	−6.21752	−0.412672	−0.206336	−	0.978481i	$-0.566154\pi$
$227$	−6.21752	−0.412672	−0.206336	+	0.978481i	$0.566154\pi$
$228$	−4.66629	−0.309033
$229$	12.9557	0.856134	0.428067	−	0.903747i	$-0.359195\pi$
$229$	12.9557	0.856134	0.428067	+	0.903747i	$0.359195\pi$
$230$	7.54626	0.497585
$231$	−15.7688	−1.03751
$232$	−13.1537	−0.863580
$233$	3.25893	0.213500	0.106750	−	0.994286i	$-0.465956\pi$
$233$	3.25893	0.213500	0.106750	+	0.994286i	$0.465956\pi$
$234$	1.40791	0.0920378
$235$	−2.01901	−0.131706
$236$	−5.71448	−0.371981
$237$	−4.23690	−0.275216
$238$	13.1172	0.850262
$239$	15.9708	1.03307	0.516534	−	0.856267i	$-0.327222\pi$
$239$	15.9708	1.03307	0.516534	+	0.856267i	$0.327222\pi$
$240$	−0.136530	−0.00881295
$241$	9.32756	0.600841	0.300421	−	0.953807i	$-0.402873\pi$
$241$	9.32756	0.600841	0.300421	+	0.953807i	$0.402873\pi$
$242$	−6.91509	−0.444519
$243$	−1.00000	−0.0641500
$244$	17.8201	1.14081
$245$	−6.25657	−0.399718
$246$	4.93455	0.314615
$247$	6.11430	0.389044
$248$	11.8445	0.752127
$249$	−17.2495	−1.09314
$250$	0.891444	0.0563799
$251$	−13.7818	−0.869899	−0.434949	−	0.900455i	$-0.643234\pi$
$251$	−13.7818	−0.869899	−0.434949	+	0.900455i	$0.643234\pi$
$252$	−4.38855	−0.276453
$253$	36.6624	2.30495
$254$	−9.45250	−0.593103
$255$	−4.04140	−0.253082
$256$	−16.3105	−1.01941
$257$	22.7831	1.42117	0.710584	−	0.703612i	$-0.248431\pi$
$257$	22.7831	1.42117	0.710584	+	0.703612i	$0.248431\pi$
$258$	−3.59342	−0.223717
$259$	−18.7124	−1.16273
$260$	−1.90364	−0.118059
$261$	−4.60342	−0.284944
$262$	−8.99133	−0.555486
$263$	−0.550629	−0.0339532	−0.0169766	−	0.999856i	$-0.505404\pi$
$263$	−0.550629	−0.0339532	−0.0169766	+	0.999856i	$0.505404\pi$
$264$	−12.3751	−0.761637
$265$	−7.34755	−0.451356
$266$	12.5654	0.770434
$267$	−1.00000	−0.0611990
$268$	−2.47789	−0.151361
$269$	−11.5809	−0.706098	−0.353049	−	0.935605i	$-0.614855\pi$
$269$	−11.5809	−0.706098	−0.353049	+	0.935605i	$0.614855\pi$
$270$	−0.891444	−0.0542515
$271$	21.1026	1.28189	0.640946	−	0.767586i	$-0.278542\pi$
$271$	21.1026	1.28189	0.640946	+	0.767586i	$0.278542\pi$
$272$	0.551771	0.0334560
$273$	5.75037	0.348028
$274$	7.70528	0.465493
$275$	4.33096	0.261166
$276$	10.2033	0.614169
$277$	17.4880	1.05076	0.525378	−	0.850869i	$-0.323924\pi$
$277$	17.4880	1.05076	0.525378	+	0.850869i	$0.323924\pi$
$278$	15.7318	0.943531
$279$	4.14525	0.248169
$280$	−10.4036	−0.621732
$281$	−5.55849	−0.331592	−0.165796	−	0.986160i	$-0.553019\pi$
$281$	−5.55849	−0.331592	−0.165796	+	0.986160i	$0.553019\pi$
$282$	1.79984	0.107179
$283$	12.6228	0.750350	0.375175	−	0.926954i	$-0.377583\pi$
$283$	12.6228	0.750350	0.375175	+	0.926954i	$0.377583\pi$
$284$	−10.9515	−0.649850
$285$	−3.87139	−0.229321
$286$	6.09759	0.360558
$287$	20.1544	1.18967
$288$	−5.59303	−0.329573
$289$	−0.667098	−0.0392411
$290$	−4.10369	−0.240977
$291$	−6.13872	−0.359858
$292$	−16.7230	−0.978637
$293$	2.15302	0.125781	0.0628904	−	0.998020i	$-0.479968\pi$
$293$	2.15302	0.125781	0.0628904	+	0.998020i	$0.479968\pi$
$294$	5.57739	0.325280
$295$	−4.74102	−0.276033
$296$	−14.6852	−0.853562
$297$	−4.33096	−0.251308
$298$	−7.17680	−0.415741
$299$	−13.3696	−0.773183
$300$	1.20533	0.0695896
$301$	−14.6767	−0.845953
$302$	−7.28652	−0.419292
$303$	10.5014	0.603290
$304$	0.528559	0.0303149
$305$	14.7844	0.846554
$306$	3.60268	0.205952
$307$	−19.2711	−1.09986	−0.549931	−	0.835210i	$-0.685346\pi$
$307$	−19.2711	−1.09986	−0.549931	+	0.835210i	$0.685346\pi$
$308$	−19.0066	−1.08300
$309$	−13.2616	−0.754424
$310$	3.69525	0.209876
$311$	−12.8473	−0.728501	−0.364250	−	0.931301i	$-0.618675\pi$
$311$	−12.8473	−0.728501	−0.364250	+	0.931301i	$0.618675\pi$
$312$	4.51281	0.255487
$313$	4.42924	0.250355	0.125178	−	0.992134i	$-0.460050\pi$
$313$	4.42924	0.250355	0.125178	+	0.992134i	$0.460050\pi$
$314$	−16.9506	−0.956575
$315$	−3.64096	−0.205145
$316$	−5.10686	−0.287283
$317$	21.0082	1.17994	0.589970	−	0.807425i	$-0.299140\pi$
$317$	21.0082	1.17994	0.589970	+	0.807425i	$0.299140\pi$
$318$	6.54993	0.367302
$319$	−19.9372	−1.11627
$320$	−5.25893	−0.293983
$321$	−14.6857	−0.819678
$322$	−27.4756	−1.53116
$323$	15.6458	0.870556
$324$	−1.20533	−0.0669627
$325$	−1.57936	−0.0876069
$326$	7.03959	0.389887
$327$	7.63418	0.422171
$328$	15.8168	0.873339
$329$	7.35114	0.405282
$330$	−3.86080	−0.212530
$331$	20.8474	1.14587	0.572937	−	0.819599i	$-0.305804\pi$
$331$	20.8474	1.14587	0.572937	+	0.819599i	$0.305804\pi$
$332$	−20.7913	−1.14107
$333$	−5.13942	−0.281639
$334$	5.31199	0.290659
$335$	−2.05578	−0.112319
$336$	0.497099	0.0271190
$337$	21.9591	1.19619	0.598094	−	0.801426i	$-0.295925\pi$
$337$	21.9591	1.19619	0.598094	+	0.801426i	$0.295925\pi$
$338$	9.36518	0.509399
$339$	15.0328	0.816468
$340$	−4.87121	−0.264178
$341$	17.9529	0.972203
$342$	3.45112	0.186615
$343$	−2.70678	−0.146152
$344$	−11.5181	−0.621014
$345$	8.46521	0.455751
$346$	−15.1909	−0.816669
$347$	34.5428	1.85435	0.927176	−	0.374626i	$-0.122229\pi$
$347$	34.5428	1.85435	0.927176	+	0.374626i	$0.122229\pi$
$348$	−5.54862	−0.297437
$349$	−7.28304	−0.389852	−0.194926	−	0.980818i	$-0.562447\pi$
$349$	−7.28304	−0.389852	−0.194926	+	0.980818i	$0.562447\pi$
$350$	−3.24571	−0.173490
$351$	1.57936	0.0842998
$352$	−24.2232	−1.29110
$353$	−13.1365	−0.699184	−0.349592	−	0.936902i	$-0.613680\pi$
$353$	−13.1365	−0.699184	−0.349592	+	0.936902i	$0.613680\pi$
$354$	4.22635	0.224628
$355$	−9.08588	−0.482228
$356$	−1.20533	−0.0638822
$357$	14.7146	0.778777
$358$	−13.9642	−0.738033
$359$	−5.40281	−0.285149	−0.142575	−	0.989784i	$-0.545538\pi$
$359$	−5.40281	−0.285149	−0.142575	+	0.989784i	$0.545538\pi$
$360$	−2.85737	−0.150597
$361$	−4.01237	−0.211177
$362$	9.74768	0.512327
$363$	−7.75718	−0.407146
$364$	6.93108	0.363287
$365$	−13.8742	−0.726209
$366$	−13.1795	−0.688903
$367$	−18.3751	−0.959175	−0.479587	−	0.877494i	$-0.659214\pi$
$367$	−18.3751	−0.959175	−0.479587	+	0.877494i	$0.659214\pi$
$368$	−1.15575	−0.0602477
$369$	5.53546	0.288164
$370$	−4.58151	−0.238181
$371$	26.7521	1.38890
$372$	4.99638	0.259050
$373$	7.80100	0.403921	0.201960	−	0.979394i	$-0.435269\pi$
$373$	7.80100	0.403921	0.201960	+	0.979394i	$0.435269\pi$
$374$	15.6030	0.806814
$375$	1.00000	0.0516398
$376$	5.76907	0.297517
$377$	7.27043	0.374446
$378$	3.24571	0.166941
$379$	2.27380	0.116797	0.0583986	−	0.998293i	$-0.481401\pi$
$379$	2.27380	0.116797	0.0583986	+	0.998293i	$0.481401\pi$
$380$	−4.66629	−0.239376
$381$	−10.6036	−0.543238
$382$	−10.4049	−0.532362
$383$	−37.6645	−1.92457	−0.962284	−	0.272047i	$-0.912299\pi$
$383$	−37.6645	−1.92457	−0.962284	+	0.272047i	$0.912299\pi$
$384$	−6.49802	−0.331601
$385$	−15.7688	−0.803654
$386$	4.10362	0.208869
$387$	−4.03101	−0.204908
$388$	−7.39916	−0.375636
$389$	−17.0462	−0.864276	−0.432138	−	0.901807i	$-0.642241\pi$
$389$	−17.0462	−0.864276	−0.432138	+	0.901807i	$0.642241\pi$
$390$	1.40791	0.0712922
$391$	−34.2113	−1.73014
$392$	17.8773	0.902942
$393$	−10.0863	−0.508784
$394$	−19.0415	−0.959298
$395$	−4.23690	−0.213182
$396$	−5.22022	−0.262326
$397$	14.9629	0.750968	0.375484	−	0.926829i	$-0.377476\pi$
$397$	14.9629	0.750968	0.375484	+	0.926829i	$0.377476\pi$
$398$	18.0633	0.905431
$399$	14.0956	0.705660
$400$	−0.136530	−0.00682648
$401$	4.52568	0.226002	0.113001	−	0.993595i	$-0.463954\pi$
$401$	4.52568	0.226002	0.113001	+	0.993595i	$0.463954\pi$
$402$	1.83261	0.0914023
$403$	−6.54682	−0.326120
$404$	12.6576	0.629740
$405$	−1.00000	−0.0496904
$406$	14.9414	0.741527
$407$	−22.2586	−1.10332
$408$	11.5478	0.571700
$409$	15.5609	0.769435	0.384718	−	0.923034i	$-0.374299\pi$
$409$	15.5609	0.769435	0.384718	+	0.923034i	$0.374299\pi$
$410$	4.93455	0.243700
$411$	8.64359	0.426357
$412$	−15.9845	−0.787501
$413$	17.2618	0.849400
$414$	−7.54626	−0.370878
$415$	−17.2495	−0.846743
$416$	8.83339	0.433093
$417$	17.6476	0.864205
$418$	14.9467	0.731065
$419$	−23.2741	−1.13701	−0.568507	−	0.822678i	$-0.692479\pi$
$419$	−23.2741	−1.13701	−0.568507	+	0.822678i	$0.692479\pi$
$420$	−4.38855	−0.214139
$421$	1.37894	0.0672053	0.0336026	−	0.999435i	$-0.489302\pi$
$421$	1.37894	0.0672053	0.0336026	+	0.999435i	$0.489302\pi$
$422$	13.6036	0.662211
$423$	2.01901	0.0981678
$424$	20.9947	1.01959
$425$	−4.04140	−0.196037
$426$	8.09955	0.392424
$427$	−53.8295	−2.60499
$428$	−17.7011	−0.855616
$429$	6.84012	0.330244
$430$	−3.59342	−0.173290
$431$	33.3212	1.60503	0.802513	−	0.596635i	$-0.203496\pi$
$431$	33.3212	1.60503	0.802513	+	0.596635i	$0.203496\pi$
$432$	0.136530	0.00656878
$433$	−4.59832	−0.220981	−0.110491	−	0.993877i	$-0.535242\pi$
$433$	−4.59832	−0.220981	−0.110491	+	0.993877i	$0.535242\pi$
$434$	−13.4543	−0.645825
$435$	−4.60342	−0.220717
$436$	9.20169	0.440681
$437$	−32.7721	−1.56770
$438$	12.3681	0.590969
$439$	4.93623	0.235593	0.117797	−	0.993038i	$-0.462417\pi$
$439$	4.93623	0.235593	0.117797	+	0.993038i	$0.462417\pi$
$440$	−12.3751	−0.589962
$441$	6.25657	0.297932
$442$	−5.68992	−0.270642
$443$	−7.06699	−0.335763	−0.167881	−	0.985807i	$-0.553693\pi$
$443$	−7.06699	−0.335763	−0.167881	+	0.985807i	$0.553693\pi$
$444$	−6.19469	−0.293987
$445$	−1.00000	−0.0474045
$446$	7.34636	0.347860
$447$	−8.05076	−0.380788
$448$	19.1476	0.904637
$449$	17.4236	0.822270	0.411135	−	0.911574i	$-0.365132\pi$
$449$	17.4236	0.822270	0.411135	+	0.911574i	$0.365132\pi$
$450$	−0.891444	−0.0420231
$451$	23.9738	1.12888
$452$	18.1194	0.852266
$453$	−8.17384	−0.384040
$454$	5.54257	0.260126
$455$	5.75037	0.269582
$456$	11.0620	0.518025
$457$	−32.3360	−1.51262	−0.756308	−	0.654216i	$-0.772999\pi$
$457$	−32.3360	−1.51262	−0.756308	+	0.654216i	$0.772999\pi$
$458$	−11.5492	−0.539661
$459$	4.04140	0.188636
$460$	10.2033	0.475733
$461$	−18.8138	−0.876247	−0.438124	−	0.898915i	$-0.644357\pi$
$461$	−18.8138	−0.876247	−0.438124	+	0.898915i	$0.644357\pi$
$462$	14.0570	0.653992
$463$	−2.66483	−0.123845	−0.0619225	−	0.998081i	$-0.519723\pi$
$463$	−2.66483	−0.123845	−0.0619225	+	0.998081i	$0.519723\pi$
$464$	0.628503	0.0291775
$465$	4.14525	0.192231
$466$	−2.90515	−0.134579
$467$	−36.0626	−1.66878	−0.834388	−	0.551177i	$-0.814179\pi$
$467$	−36.0626	−1.66878	−0.834388	+	0.551177i	$0.814179\pi$
$468$	1.90364	0.0879959
$469$	7.48500	0.345625
$470$	1.79984	0.0830203
$471$	−19.0147	−0.876152
$472$	13.5468	0.623544
$473$	−17.4581	−0.802726
$474$	3.77696	0.173482
$475$	−3.87139	−0.177631
$476$	17.7359	0.812922
$477$	7.34755	0.336421
$478$	−14.2371	−0.651190
$479$	13.3114	0.608214	0.304107	−	0.952638i	$-0.401642\pi$
$479$	13.3114	0.608214	0.304107	+	0.952638i	$0.401642\pi$
$480$	−5.59303	−0.255286
$481$	8.11698	0.370103
$482$	−8.31500	−0.378738
$483$	−30.8215	−1.40242
$484$	−9.34994	−0.424997
$485$	−6.13872	−0.278745
$486$	0.891444	0.0404367
$487$	36.8868	1.67150	0.835750	−	0.549111i	$-0.185033\pi$
$487$	36.8868	1.67150	0.835750	+	0.549111i	$0.185033\pi$
$488$	−42.2446	−1.91232
$489$	7.89684	0.357108
$490$	5.57739	0.251961
$491$	−36.6260	−1.65291	−0.826454	−	0.563004i	$-0.809646\pi$
$491$	−36.6260	−1.65291	−0.826454	+	0.563004i	$0.809646\pi$
$492$	6.67204	0.300799
$493$	18.6042	0.837893
$494$	−5.45055	−0.245232
$495$	−4.33096	−0.194662
$496$	−0.565949	−0.0254119
$497$	33.0813	1.48390
$498$	15.3769	0.689057
$499$	43.5384	1.94905	0.974523	−	0.224288i	$-0.0720057\pi$
$499$	43.5384	1.94905	0.974523	+	0.224288i	$0.0720057\pi$
$500$	1.20533	0.0539039
$501$	5.95886	0.266222
$502$	12.2857	0.548337
$503$	−33.6446	−1.50014	−0.750070	−	0.661358i	$-0.769980\pi$
$503$	−33.6446	−1.50014	−0.750070	+	0.661358i	$0.769980\pi$
$504$	10.4036	0.463412
$505$	10.5014	0.467306
$506$	−32.6825	−1.45291
$507$	10.5056	0.466572
$508$	−12.7808	−0.567056
$509$	−25.4064	−1.12612	−0.563058	−	0.826417i	$-0.690375\pi$
$509$	−25.4064	−1.12612	−0.563058	+	0.826417i	$0.690375\pi$
$510$	3.60268	0.159529
$511$	50.5154	2.23467
$512$	1.54385	0.0682290
$513$	3.87139	0.170926
$514$	−20.3098	−0.895828
$515$	−13.2616	−0.584374
$516$	−4.85869	−0.213892
$517$	8.74426	0.384572
$518$	16.6811	0.732924
$519$	−17.0408	−0.748008
$520$	4.51281	0.197900
$521$	−39.1230	−1.71401	−0.857006	−	0.515307i	$-0.827678\pi$
$521$	−39.1230	−1.71401	−0.857006	+	0.515307i	$0.827678\pi$
$522$	4.10369	0.179613
$523$	−10.5640	−0.461929	−0.230965	−	0.972962i	$-0.574188\pi$
$523$	−10.5640	−0.461929	−0.230965	+	0.972962i	$0.574188\pi$
$524$	−12.1572	−0.531092
$525$	−3.64096	−0.158904
$526$	0.490855	0.0214023
$527$	−16.7526	−0.729754
$528$	0.591304	0.0257332
$529$	48.6597	2.11564
$530$	6.54993	0.284511
$531$	4.74102	0.205743
$532$	16.9898	0.736600
$533$	−8.74246	−0.378678
$534$	0.891444	0.0385766
$535$	−14.6857	−0.634920
$536$	5.87412	0.253723
$537$	−15.6647	−0.675983
$538$	10.3237	0.445086
$539$	27.0969	1.16715
$540$	−1.20533	−0.0518690
$541$	−12.3516	−0.531037	−0.265519	−	0.964106i	$-0.585543\pi$
$541$	−12.3516	−0.531037	−0.265519	+	0.964106i	$0.585543\pi$
$542$	−18.8118	−0.808036
$543$	10.9347	0.469253
$544$	22.6037	0.969124
$545$	7.63418	0.327013
$546$	−5.12613	−0.219378
$547$	26.7753	1.14483	0.572414	−	0.819965i	$-0.306007\pi$
$547$	26.7753	1.14483	0.572414	+	0.819965i	$0.306007\pi$
$548$	10.4184	0.445050
$549$	−14.7844	−0.630984
$550$	−3.86080	−0.164625
$551$	17.8216	0.759226
$552$	−24.1882	−1.02952
$553$	15.4264	0.655997
$554$	−15.5896	−0.662339
$555$	−5.13942	−0.218156
$556$	21.2711	0.902095
$557$	28.8270	1.22144	0.610719	−	0.791847i	$-0.290881\pi$
$557$	28.8270	1.22144	0.610719	+	0.791847i	$0.290881\pi$
$558$	−3.69525	−0.156433
$559$	6.36640	0.269270
$560$	0.497099	0.0210062
$561$	17.5031	0.738982
$562$	4.95508	0.209018
$563$	4.36594	0.184002	0.0920012	−	0.995759i	$-0.470674\pi$
$563$	4.36594	0.184002	0.0920012	+	0.995759i	$0.470674\pi$
$564$	2.43357	0.102472
$565$	15.0328	0.632433
$566$	−11.2526	−0.472980
$567$	3.64096	0.152906
$568$	25.9617	1.08933
$569$	6.39205	0.267969	0.133984	−	0.990983i	$-0.457223\pi$
$569$	6.39205	0.267969	0.133984	+	0.990983i	$0.457223\pi$
$570$	3.45112	0.144552
$571$	36.7859	1.53944	0.769722	−	0.638380i	$-0.220395\pi$
$571$	36.7859	1.53944	0.769722	+	0.638380i	$0.220395\pi$
$572$	8.24459	0.344724
$573$	−11.6720	−0.487605
$574$	−17.9665	−0.749907
$575$	8.46521	0.353023
$576$	5.25893	0.219122
$577$	−20.3844	−0.848612	−0.424306	−	0.905519i	$-0.639482\pi$
$577$	−20.3844	−0.848612	−0.424306	+	0.905519i	$0.639482\pi$
$578$	0.594681	0.0247355
$579$	4.60334	0.191308
$580$	−5.54862	−0.230394
$581$	62.8046	2.60557
$582$	5.47232	0.226835
$583$	31.8219	1.31793
$584$	39.6437	1.64047
$585$	1.57936	0.0652984
$586$	−1.91930	−0.0792854
$587$	−32.3272	−1.33429	−0.667143	−	0.744930i	$-0.732483\pi$
$587$	−32.3272	−1.33429	−0.667143	+	0.744930i	$0.732483\pi$
$588$	7.54122	0.310995
$589$	−16.0478	−0.661240
$590$	4.22635	0.173996
$591$	−21.3603	−0.878646
$592$	0.701683	0.0288390
$593$	−0.138120	−0.00567190	−0.00283595	−	0.999996i	$-0.500903\pi$
$593$	−0.138120	−0.00567190	−0.00283595	+	0.999996i	$0.500903\pi$
$594$	3.86080	0.158411
$595$	14.7146	0.603238
$596$	−9.70380	−0.397483
$597$	20.2630	0.829308
$598$	11.9182	0.487373
$599$	1.46178	0.0597269	0.0298634	−	0.999554i	$-0.490493\pi$
$599$	1.46178	0.0597269	0.0298634	+	0.999554i	$0.490493\pi$
$600$	−2.85737	−0.116652
$601$	−26.7601	−1.09157	−0.545784	−	0.837926i	$-0.683768\pi$
$601$	−26.7601	−1.09157	−0.545784	+	0.837926i	$0.683768\pi$
$602$	13.0835	0.533243
$603$	2.05578	0.0837178
$604$	−9.85216	−0.400879
$605$	−7.75718	−0.315374
$606$	−9.36141	−0.380281
$607$	−5.30554	−0.215345	−0.107673	−	0.994186i	$-0.534340\pi$
$607$	−5.30554	−0.215345	−0.107673	+	0.994186i	$0.534340\pi$
$608$	21.6528	0.878136
$609$	16.7608	0.679184
$610$	−13.1795	−0.533622
$611$	−3.18874	−0.129003
$612$	4.87121	0.196907
$613$	30.0385	1.21324	0.606621	−	0.794991i	$-0.292525\pi$
$613$	30.0385	1.21324	0.606621	+	0.794991i	$0.292525\pi$
$614$	17.1791	0.693294
$615$	5.53546	0.223211
$616$	45.0574	1.81541
$617$	3.19073	0.128454	0.0642269	−	0.997935i	$-0.479542\pi$
$617$	3.19073	0.128454	0.0642269	+	0.997935i	$0.479542\pi$
$618$	11.8219	0.475548
$619$	−0.490182	−0.0197021	−0.00985105	−	0.999951i	$-0.503136\pi$
$619$	−0.490182	−0.0197021	−0.00985105	+	0.999951i	$0.503136\pi$
$620$	4.99638	0.200659
$621$	−8.46521	−0.339697
$622$	11.4526	0.459208
$623$	3.64096	0.145872
$624$	−0.215629	−0.00863207
$625$	1.00000	0.0400000
$626$	−3.94842	−0.157810
$627$	16.7668	0.669602
$628$	−22.9190	−0.914566
$629$	20.7705	0.828172
$630$	3.24571	0.129312
$631$	−38.7287	−1.54176	−0.770882	−	0.636977i	$-0.780184\pi$
$631$	−38.7287	−1.54176	−0.770882	+	0.636977i	$0.780184\pi$
$632$	12.1064	0.481567
$633$	15.2602	0.606537
$634$	−18.7277	−0.743770
$635$	−10.6036	−0.420790
$636$	8.85620	0.351171
$637$	−9.88136	−0.391514
$638$	17.7729	0.703635
$639$	9.08588	0.359432
$640$	−6.49802	−0.256857
$641$	48.2249	1.90477	0.952385	−	0.304897i	$-0.0986221\pi$
$641$	48.2249	1.90477	0.952385	+	0.304897i	$0.0986221\pi$
$642$	13.0915	0.516681
$643$	29.9571	1.18139	0.590696	−	0.806894i	$-0.298853\pi$
$643$	29.9571	1.18139	0.590696	+	0.806894i	$0.298853\pi$
$644$	−37.1500	−1.46391
$645$	−4.03101	−0.158721
$646$	−13.9474	−0.548752
$647$	−21.9578	−0.863250	−0.431625	−	0.902053i	$-0.642060\pi$
$647$	−21.9578	−0.863250	−0.431625	+	0.902053i	$0.642060\pi$
$648$	2.85737	0.112248
$649$	20.5331	0.805996
$650$	1.40791	0.0552227
$651$	−15.0927	−0.591528
$652$	9.51828	0.372765
$653$	−45.7267	−1.78943	−0.894713	−	0.446642i	$-0.852620\pi$
$653$	−45.7267	−1.78943	−0.894713	+	0.446642i	$0.852620\pi$
$654$	−6.80545	−0.266114
$655$	−10.0863	−0.394103
$656$	−0.755754	−0.0295072
$657$	13.8742	0.541284
$658$	−6.55313	−0.255468
$659$	−48.1741	−1.87660	−0.938298	−	0.345828i	$-0.887598\pi$
$659$	−48.1741	−1.87660	−0.938298	+	0.345828i	$0.887598\pi$
$660$	−5.22022	−0.203197
$661$	7.24751	0.281895	0.140948	−	0.990017i	$-0.454985\pi$
$661$	7.24751	0.281895	0.140948	+	0.990017i	$0.454985\pi$
$662$	−18.5842	−0.722297
$663$	−6.38281	−0.247888
$664$	49.2881	1.91275
$665$	14.0956	0.546602
$666$	4.58151	0.177530
$667$	−38.9689	−1.50888
$668$	7.18237	0.277894
$669$	8.24096	0.318614
$670$	1.83261	0.0707999
$671$	−64.0307	−2.47188
$672$	20.3640	0.785558
$673$	−17.9965	−0.693715	−0.346858	−	0.937918i	$-0.612751\pi$
$673$	−17.9965	−0.693715	−0.346858	+	0.937918i	$0.612751\pi$
$674$	−19.5753	−0.754013
$675$	−1.00000	−0.0384900
$676$	12.6627	0.487028
$677$	−9.42242	−0.362133	−0.181067	−	0.983471i	$-0.557955\pi$
$677$	−9.42242	−0.362133	−0.181067	+	0.983471i	$0.557955\pi$
$678$	−13.4009	−0.514657
$679$	22.3508	0.857745
$680$	11.5478	0.442837
$681$	6.21752	0.238256
$682$	−16.0040	−0.612824
$683$	34.3152	1.31304	0.656518	−	0.754310i	$-0.272029\pi$
$683$	34.3152	1.31304	0.656518	+	0.754310i	$0.272029\pi$
$684$	4.66629	0.178420
$685$	8.64359	0.330255
$686$	2.41294	0.0921266
$687$	−12.9557	−0.494289
$688$	0.550352	0.0209820
$689$	−11.6044	−0.442092
$690$	−7.54626	−0.287281
$691$	18.6125	0.708051	0.354026	−	0.935236i	$-0.384813\pi$
$691$	18.6125	0.708051	0.354026	+	0.935236i	$0.384813\pi$
$692$	−20.5397	−0.780804
$693$	15.7688	0.599008
$694$	−30.7929	−1.16888
$695$	17.6476	0.669410
$696$	13.1537	0.498588
$697$	−22.3710	−0.847362
$698$	6.49242	0.245742
$699$	−3.25893	−0.123264
$700$	−4.38855	−0.165872
$701$	18.4560	0.697073	0.348537	−	0.937295i	$-0.386679\pi$
$701$	18.4560	0.697073	0.348537	+	0.937295i	$0.386679\pi$
$702$	−1.40791	−0.0531381
$703$	19.8967	0.750418
$704$	22.7762	0.858411
$705$	2.01901	0.0760404
$706$	11.7104	0.440728
$707$	−38.2351	−1.43798
$708$	5.71448	0.214763
$709$	−8.29517	−0.311532	−0.155766	−	0.987794i	$-0.549785\pi$
$709$	−8.29517	−0.311532	−0.155766	+	0.987794i	$0.549785\pi$
$710$	8.09955	0.303971
$711$	4.23690	0.158896
$712$	2.85737	0.107084
$713$	35.0904	1.31414
$714$	−13.1172	−0.490899
$715$	6.84012	0.255806
$716$	−18.8811	−0.705621
$717$	−15.9708	−0.596442
$718$	4.81630	0.179743
$719$	6.54967	0.244261	0.122131	−	0.992514i	$-0.461027\pi$
$719$	6.54967	0.244261	0.122131	+	0.992514i	$0.461027\pi$
$720$	0.136530	0.00508816
$721$	48.2848	1.79822
$722$	3.57680	0.133115
$723$	−9.32756	−0.346896
$724$	13.1799	0.489828
$725$	−4.60342	−0.170967
$726$	6.91509	0.256643
$727$	−43.9969	−1.63176	−0.815878	−	0.578224i	$-0.803746\pi$
$727$	−43.9969	−1.63176	−0.815878	+	0.578224i	$0.803746\pi$
$728$	−16.4309	−0.608971
$729$	1.00000	0.0370370
$730$	12.3681	0.457763
$731$	16.2909	0.602542
$732$	−17.8201	−0.658649
$733$	16.3217	0.602857	0.301429	−	0.953489i	$-0.402536\pi$
$733$	16.3217	0.602857	0.301429	+	0.953489i	$0.402536\pi$
$734$	16.3804	0.604612
$735$	6.25657	0.230777
$736$	−47.3462	−1.74520
$737$	8.90348	0.327964
$738$	−4.93455	−0.181643
$739$	7.56278	0.278201	0.139101	−	0.990278i	$-0.455579\pi$
$739$	7.56278	0.278201	0.139101	+	0.990278i	$0.455579\pi$
$740$	−6.19469	−0.227721
$741$	−6.11430	−0.224614
$742$	−23.8480	−0.875488
$743$	−22.5633	−0.827767	−0.413883	−	0.910330i	$-0.635828\pi$
$743$	−22.5633	−0.827767	−0.413883	+	0.910330i	$0.635828\pi$
$744$	−11.8445	−0.434240
$745$	−8.05076	−0.294957
$746$	−6.95416	−0.254610
$747$	17.2495	0.631125
$748$	21.0970	0.771383
$749$	53.4702	1.95376
$750$	−0.891444	−0.0325509
$751$	−39.6351	−1.44631	−0.723153	−	0.690688i	$-0.757308\pi$
$751$	−39.6351	−1.44631	−0.723153	+	0.690688i	$0.757308\pi$
$752$	−0.275655	−0.0100521
$753$	13.7818	0.502236
$754$	−6.48119	−0.236031
$755$	−8.17384	−0.297476
$756$	4.38855	0.159610
$757$	−16.1353	−0.586449	−0.293224	−	0.956044i	$-0.594728\pi$
$757$	−16.1353	−0.586449	−0.293224	+	0.956044i	$0.594728\pi$
$758$	−2.02696	−0.0736226
$759$	−36.6624	−1.33076
$760$	11.0620	0.401260
$761$	−11.4845	−0.416314	−0.208157	−	0.978095i	$-0.566747\pi$
$761$	−11.4845	−0.416314	−0.208157	+	0.978095i	$0.566747\pi$
$762$	9.45250	0.342428
$763$	−27.7957	−1.00627
$764$	−14.0686	−0.508983
$765$	4.04140	0.146117
$766$	33.5758	1.21314
$767$	−7.48776	−0.270367
$768$	16.3105	0.588554
$769$	4.05249	0.146136	0.0730682	−	0.997327i	$-0.476721\pi$
$769$	4.05249	0.146136	0.0730682	+	0.997327i	$0.476721\pi$
$770$	14.0570	0.506580
$771$	−22.7831	−0.820512
$772$	5.54854	0.199696
$773$	34.6875	1.24762	0.623812	−	0.781575i	$-0.285583\pi$
$773$	34.6875	1.24762	0.623812	+	0.781575i	$0.285583\pi$
$774$	3.59342	0.129163
$775$	4.14525	0.148902
$776$	17.5406	0.629670
$777$	18.7124	0.671304
$778$	15.1957	0.544793
$779$	−21.4299	−0.767805
$780$	1.90364	0.0681613
$781$	39.3505	1.40807
$782$	30.4974	1.09059
$783$	4.60342	0.164513
$784$	−0.854208	−0.0305074
$785$	−19.0147	−0.678664
$786$	8.99133	0.320710
$787$	−3.48999	−0.124405	−0.0622023	−	0.998064i	$-0.519812\pi$
$787$	−3.48999	−0.124405	−0.0622023	+	0.998064i	$0.519812\pi$
$788$	−25.7462	−0.917169
$789$	0.550629	0.0196029
$790$	3.77696	0.134378
$791$	−54.7337	−1.94611
$792$	12.3751	0.439732
$793$	23.3499	0.829179
$794$	−13.3386	−0.473370
$795$	7.34755	0.260591
$796$	24.4235	0.865669
$797$	−39.0614	−1.38363	−0.691813	−	0.722076i	$-0.743188\pi$
$797$	−39.0614	−1.38363	−0.691813	+	0.722076i	$0.743188\pi$
$798$	−12.5654	−0.444810
$799$	−8.15964	−0.288667
$800$	−5.59303	−0.197744
$801$	1.00000	0.0353333
$802$	−4.03439	−0.142459
$803$	60.0886	2.12048
$804$	2.47789	0.0873883
$805$	−30.8215	−1.08631
$806$	5.83612	0.205569
$807$	11.5809	0.407666
$808$	−30.0064	−1.05562
$809$	−48.9260	−1.72015	−0.860073	−	0.510171i	$-0.829582\pi$
$809$	−48.9260	−1.72015	−0.860073	+	0.510171i	$0.829582\pi$
$810$	0.891444	0.0313221
$811$	44.2201	1.55278	0.776389	−	0.630254i	$-0.217049\pi$
$811$	44.2201	1.55278	0.776389	+	0.630254i	$0.217049\pi$
$812$	20.2023	0.708962
$813$	−21.1026	−0.740101
$814$	19.8423	0.695472
$815$	7.89684	0.276614
$816$	−0.551771	−0.0193158
$817$	15.6056	0.545971
$818$	−13.8716	−0.485011
$819$	−5.75037	−0.200934
$820$	6.67204	0.232998
$821$	−13.2757	−0.463326	−0.231663	−	0.972796i	$-0.574417\pi$
$821$	−13.2757	−0.463326	−0.231663	+	0.972796i	$0.574417\pi$
$822$	−7.70528	−0.268752
$823$	−52.8359	−1.84175	−0.920873	−	0.389864i	$-0.872522\pi$
$823$	−52.8359	−1.84175	−0.920873	+	0.389864i	$0.872522\pi$
$824$	37.8932	1.32007
$825$	−4.33096	−0.150785
$826$	−15.3880	−0.535416
$827$	42.8247	1.48916	0.744581	−	0.667532i	$-0.232649\pi$
$827$	42.8247	1.48916	0.744581	+	0.667532i	$0.232649\pi$
$828$	−10.2033	−0.354591
$829$	−5.81578	−0.201990	−0.100995	−	0.994887i	$-0.532203\pi$
$829$	−5.81578	−0.201990	−0.100995	+	0.994887i	$0.532203\pi$
$830$	15.3769	0.533741
$831$	−17.4880	−0.606654
$832$	−8.30573	−0.287949
$833$	−25.2853	−0.876084
$834$	−15.7318	−0.544748
$835$	5.95886	0.206215
$836$	20.2095	0.698960
$837$	−4.14525	−0.143281
$838$	20.7476	0.716712
$839$	27.5758	0.952023	0.476011	−	0.879439i	$-0.342082\pi$
$839$	27.5758	0.952023	0.476011	+	0.879439i	$0.342082\pi$
$840$	10.4036	0.358957
$841$	−7.80857	−0.269261
$842$	−1.22924	−0.0423626
$843$	5.55849	0.191445
$844$	18.3935	0.633130
$845$	10.5056	0.361405
$846$	−1.79984	−0.0618797
$847$	28.2436	0.970460
$848$	−1.00316	−0.0344486
$849$	−12.6228	−0.433215
$850$	3.60268	0.123571
$851$	−43.5063	−1.49138
$852$	10.9515	0.375191
$853$	−57.6857	−1.97512	−0.987560	−	0.157240i	$-0.949740\pi$
$853$	−57.6857	−1.97512	−0.987560	+	0.157240i	$0.949740\pi$
$854$	47.9860	1.64205
$855$	3.87139	0.132399
$856$	41.9626	1.43425
$857$	−38.6275	−1.31949	−0.659746	−	0.751489i	$-0.729336\pi$
$857$	−38.6275	−1.31949	−0.659746	+	0.751489i	$0.729336\pi$
$858$	−6.09759	−0.208168
$859$	−21.7778	−0.743050	−0.371525	−	0.928423i	$-0.621165\pi$
$859$	−21.7778	−0.743050	−0.371525	+	0.928423i	$0.621165\pi$
$860$	−4.85869	−0.165680
$861$	−20.1544	−0.686859
$862$	−29.7040	−1.01172
$863$	18.4365	0.627586	0.313793	−	0.949491i	$-0.398400\pi$
$863$	18.4365	0.627586	0.313793	+	0.949491i	$0.398400\pi$
$864$	5.59303	0.190279
$865$	−17.0408	−0.579405
$866$	4.09914	0.139295
$867$	0.667098	0.0226558
$868$	−18.1916	−0.617463
$869$	18.3498	0.622476
$870$	4.10369	0.139128
$871$	−3.24681	−0.110014
$872$	−21.8137	−0.738705
$873$	6.13872	0.207764
$874$	29.2145	0.988194
$875$	−3.64096	−0.123087
$876$	16.7230	0.565017
$877$	4.62129	0.156050	0.0780249	−	0.996951i	$-0.475139\pi$
$877$	4.62129	0.156050	0.0780249	+	0.996951i	$0.475139\pi$
$878$	−4.40037	−0.148505
$879$	−2.15302	−0.0726196
$880$	0.591304	0.0199328
$881$	36.2322	1.22069	0.610347	−	0.792134i	$-0.291030\pi$
$881$	36.2322	1.22069	0.610347	+	0.792134i	$0.291030\pi$
$882$	−5.57739	−0.187800
$883$	−19.2717	−0.648545	−0.324273	−	0.945964i	$-0.605120\pi$
$883$	−19.2717	−0.648545	−0.324273	+	0.945964i	$0.605120\pi$
$884$	−7.69338	−0.258756
$885$	4.74102	0.159368
$886$	6.29982	0.211647
$887$	48.4068	1.62534	0.812671	−	0.582722i	$-0.198012\pi$
$887$	48.4068	1.62534	0.812671	+	0.582722i	$0.198012\pi$
$888$	14.6852	0.492804
$889$	38.6072	1.29484
$890$	0.891444	0.0298813
$891$	4.33096	0.145092
$892$	9.93306	0.332583
$893$	−7.81638	−0.261565
$894$	7.17680	0.240028
$895$	−15.6647	−0.523614
$896$	23.6590	0.790392
$897$	13.3696	0.446397
$898$	−15.5322	−0.518315
$899$	−19.0823	−0.636430
$900$	−1.20533	−0.0401776
$901$	−29.6944	−0.989263
$902$	−21.3713	−0.711587
$903$	14.6767	0.488411
$904$	−42.9542	−1.42864
$905$	10.9347	0.363482
$906$	7.28652	0.242078
$907$	−32.5739	−1.08160	−0.540800	−	0.841151i	$-0.681878\pi$
$907$	−32.5739	−1.08160	−0.540800	+	0.841151i	$0.681878\pi$
$908$	7.49415	0.248702
$909$	−10.5014	−0.348309
$910$	−5.12613	−0.169930
$911$	7.76551	0.257283	0.128641	−	0.991691i	$-0.458938\pi$
$911$	7.76551	0.257283	0.128641	+	0.991691i	$0.458938\pi$
$912$	−0.528559	−0.0175023
$913$	74.7067	2.47243
$914$	28.8258	0.953471
$915$	−14.7844	−0.488758
$916$	−15.6158	−0.515961
$917$	36.7236	1.21272
$918$	−3.60268	−0.118906
$919$	15.1765	0.500627	0.250314	−	0.968165i	$-0.419466\pi$
$919$	15.1765	0.500627	0.250314	+	0.968165i	$0.419466\pi$
$920$	−24.1882	−0.797462
$921$	19.2711	0.635006
$922$	16.7715	0.552339
$923$	−14.3498	−0.472331
$924$	19.0066	0.625271
$925$	−5.13942	−0.168983
$926$	2.37554	0.0780652
$927$	13.2616	0.435567
$928$	25.7470	0.845188
$929$	6.13515	0.201288	0.100644	−	0.994923i	$-0.467910\pi$
$929$	6.13515	0.201288	0.100644	+	0.994923i	$0.467910\pi$
$930$	−3.69525	−0.121172
$931$	−24.2216	−0.793831
$932$	−3.92808	−0.128668
$933$	12.8473	0.420600
$934$	32.1478	1.05191
$935$	17.5031	0.572413
$936$	−4.51281	−0.147506
$937$	48.9924	1.60051	0.800257	−	0.599658i	$-0.204697\pi$
$937$	48.9924	1.60051	0.800257	+	0.599658i	$0.204697\pi$
$938$	−6.67246	−0.217864
$939$	−4.42924	−0.144543
$940$	2.43357	0.0793744
$941$	17.2926	0.563724	0.281862	−	0.959455i	$-0.409048\pi$
$941$	17.2926	0.563724	0.281862	+	0.959455i	$0.409048\pi$
$942$	16.9506	0.552279
$943$	46.8588	1.52593
$944$	−0.647289	−0.0210675
$945$	3.64096	0.118440
$946$	15.5629	0.505995
$947$	−31.6953	−1.02996	−0.514980	−	0.857202i	$-0.672201\pi$
$947$	−31.6953	−1.02996	−0.514980	+	0.857202i	$0.672201\pi$
$948$	5.10686	0.165863
$949$	−21.9123	−0.711304
$950$	3.45112	0.111969
$951$	−21.0082	−0.681238
$952$	−42.0449	−1.36268
$953$	−31.8797	−1.03268	−0.516342	−	0.856382i	$-0.672707\pi$
$953$	−31.8797	−1.03268	−0.516342	+	0.856382i	$0.672707\pi$
$954$	−6.54993	−0.212062
$955$	−11.6720	−0.377697
$956$	−19.2501	−0.622593
$957$	19.9372	0.644478
$958$	−11.8664	−0.383386
$959$	−31.4710	−1.01625
$960$	5.25893	0.169731
$961$	−13.8169	−0.445708
$962$	−7.23583	−0.233293
$963$	14.6857	0.473241
$964$	−11.2428	−0.362105
$965$	4.60334	0.148187
$966$	27.4756	0.884013
$967$	34.1950	1.09964	0.549818	−	0.835284i	$-0.314697\pi$
$967$	34.1950	1.09964	0.549818	+	0.835284i	$0.314697\pi$
$968$	22.1651	0.712414
$969$	−15.6458	−0.502616
$970$	5.47232	0.175706
$971$	−26.2314	−0.841807	−0.420903	−	0.907105i	$-0.638287\pi$
$971$	−26.2314	−0.841807	−0.420903	+	0.907105i	$0.638287\pi$
$972$	1.20533	0.0386609
$973$	−64.2540	−2.05989
$974$	−32.8825	−1.05362
$975$	1.57936	0.0505799
$976$	2.01851	0.0646110
$977$	11.3282	0.362423	0.181211	−	0.983444i	$-0.441998\pi$
$977$	11.3282	0.362423	0.181211	+	0.983444i	$0.441998\pi$
$978$	−7.03959	−0.225101
$979$	4.33096	0.138418
$980$	7.54122	0.240896
$981$	−7.63418	−0.243741
$982$	32.6500	1.04190
$983$	53.1093	1.69392	0.846962	−	0.531653i	$-0.178429\pi$
$983$	53.1093	1.69392	0.846962	+	0.531653i	$0.178429\pi$
$984$	−15.8168	−0.504223
$985$	−21.3603	−0.680596
$986$	−16.5846	−0.528162
$987$	−7.35114	−0.233989
$988$	−7.36973	−0.234462
$989$	−34.1233	−1.08506
$990$	3.86080	0.122704
$991$	−32.5725	−1.03470	−0.517350	−	0.855774i	$-0.673081\pi$
$991$	−32.5725	−1.03470	−0.517350	+	0.855774i	$0.673081\pi$
$992$	−23.1845	−0.736108
$993$	−20.8474	−0.661571
$994$	−29.4901	−0.935370
$995$	20.2630	0.642379
$996$	20.7913	0.658797
$997$	−4.20259	−0.133098	−0.0665488	−	0.997783i	$-0.521199\pi$
$997$	−4.20259	−0.133098	−0.0665488	+	0.997783i	$0.521199\pi$
$998$	−38.8120	−1.22857
$999$	5.13942	0.162604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1335.2.a.h.1.3	✓	9
3.2	odd	2		4005.2.a.q.1.7		9
5.4	even	2		6675.2.a.x.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1335.2.a.h.1.3	✓	9	1.1	even	1	trivial
4005.2.a.q.1.7		9	3.2	odd	2
6675.2.a.x.1.7		9	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1335 = 3 \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1335.a (trivial)

\(f(q)\)	\(=\)	\(q-0.891444 q^{2} -1.00000 q^{3} -1.20533 q^{4} -1.00000 q^{5} +0.891444 q^{6} +3.64096 q^{7} +2.85737 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.891444 q^{2} -1.00000 q^{3} -1.20533 q^{4} -1.00000 q^{5} +0.891444 q^{6} +3.64096 q^{7} +2.85737 q^{8} +1.00000 q^{9} +0.891444 q^{10} +4.33096 q^{11} +1.20533 q^{12} -1.57936 q^{13} -3.24571 q^{14} +1.00000 q^{15} -0.136530 q^{16} -4.04140 q^{17} -0.891444 q^{18} -3.87139 q^{19} +1.20533 q^{20} -3.64096 q^{21} -3.86080 q^{22} +8.46521 q^{23} -2.85737 q^{24} +1.00000 q^{25} +1.40791 q^{26} -1.00000 q^{27} -4.38855 q^{28} -4.60342 q^{29} -0.891444 q^{30} +4.14525 q^{31} -5.59303 q^{32} -4.33096 q^{33} +3.60268 q^{34} -3.64096 q^{35} -1.20533 q^{36} -5.13942 q^{37} +3.45112 q^{38} +1.57936 q^{39} -2.85737 q^{40} +5.53546 q^{41} +3.24571 q^{42} -4.03101 q^{43} -5.22022 q^{44} -1.00000 q^{45} -7.54626 q^{46} +2.01901 q^{47} +0.136530 q^{48} +6.25657 q^{49} -0.891444 q^{50} +4.04140 q^{51} +1.90364 q^{52} +7.34755 q^{53} +0.891444 q^{54} -4.33096 q^{55} +10.4036 q^{56} +3.87139 q^{57} +4.10369 q^{58} +4.74102 q^{59} -1.20533 q^{60} -14.7844 q^{61} -3.69525 q^{62} +3.64096 q^{63} +5.25893 q^{64} +1.57936 q^{65} +3.86080 q^{66} +2.05578 q^{67} +4.87121 q^{68} -8.46521 q^{69} +3.24571 q^{70} +9.08588 q^{71} +2.85737 q^{72} +13.8742 q^{73} +4.58151 q^{74} -1.00000 q^{75} +4.66629 q^{76} +15.7688 q^{77} -1.40791 q^{78} +4.23690 q^{79} +0.136530 q^{80} +1.00000 q^{81} -4.93455 q^{82} +17.2495 q^{83} +4.38855 q^{84} +4.04140 q^{85} +3.59342 q^{86} +4.60342 q^{87} +12.3751 q^{88} +1.00000 q^{89} +0.891444 q^{90} -5.75037 q^{91} -10.2033 q^{92} -4.14525 q^{93} -1.79984 q^{94} +3.87139 q^{95} +5.59303 q^{96} +6.13872 q^{97} -5.57739 q^{98} +4.33096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9	\( 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9} - 5 q^{10} + 4 q^{11} - 11 q^{12} + 5 q^{13} - q^{14} + 9 q^{15} + 15 q^{16} + 21 q^{17} + 5 q^{18} - 18 q^{19} - 11 q^{20} + 3 q^{21} + 6 q^{22} + 16 q^{23} - 18 q^{24} + 9 q^{25} + 8 q^{26} - 9 q^{27} + 6 q^{28} + 3 q^{29} + 5 q^{30} - 6 q^{31} + 46 q^{32} - 4 q^{33} + 12 q^{34} + 3 q^{35} + 11 q^{36} + 11 q^{37} + 20 q^{38} - 5 q^{39} - 18 q^{40} - q^{41} + q^{42} - 3 q^{43} + 38 q^{44} - 9 q^{45} + 16 q^{46} + 27 q^{47} - 15 q^{48} + 24 q^{49} + 5 q^{50} - 21 q^{51} + 17 q^{52} + 43 q^{53} - 5 q^{54} - 4 q^{55} + 5 q^{56} + 18 q^{57} + 34 q^{58} + 3 q^{59} + 11 q^{60} - 30 q^{61} + 36 q^{62} - 3 q^{63} + 50 q^{64} - 5 q^{65} - 6 q^{66} - 12 q^{67} + 64 q^{68} - 16 q^{69} + q^{70} - 4 q^{71} + 18 q^{72} + 26 q^{73} + 2 q^{74} - 9 q^{75} - 12 q^{76} + 34 q^{77} - 8 q^{78} + q^{79} - 15 q^{80} + 9 q^{81} - 51 q^{82} + 24 q^{83} - 6 q^{84} - 21 q^{85} + 18 q^{86} - 3 q^{87} + 64 q^{88} + 9 q^{89} - 5 q^{90} - 50 q^{91} + 10 q^{92} + 6 q^{93} - 11 q^{94} + 18 q^{95} - 46 q^{96} - 4 q^{97} + 75 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9 - 5 * q^10 + 4 * q^11 - 11 * q^12 + 5 * q^13 - q^14 + 9 * q^15 + 15 * q^16 + 21 * q^17 + 5 * q^18 - 18 * q^19 - 11 * q^20 + 3 * q^21 + 6 * q^22 + 16 * q^23 - 18 * q^24 + 9 * q^25 + 8 * q^26 - 9 * q^27 + 6 * q^28 + 3 * q^29 + 5 * q^30 - 6 * q^31 + 46 * q^32 - 4 * q^33 + 12 * q^34 + 3 * q^35 + 11 * q^36 + 11 * q^37 + 20 * q^38 - 5 * q^39 - 18 * q^40 - q^41 + q^42 - 3 * q^43 + 38 * q^44 - 9 * q^45 + 16 * q^46 + 27 * q^47 - 15 * q^48 + 24 * q^49 + 5 * q^50 - 21 * q^51 + 17 * q^52 + 43 * q^53 - 5 * q^54 - 4 * q^55 + 5 * q^56 + 18 * q^57 + 34 * q^58 + 3 * q^59 + 11 * q^60 - 30 * q^61 + 36 * q^62 - 3 * q^63 + 50 * q^64 - 5 * q^65 - 6 * q^66 - 12 * q^67 + 64 * q^68 - 16 * q^69 + q^70 - 4 * q^71 + 18 * q^72 + 26 * q^73 + 2 * q^74 - 9 * q^75 - 12 * q^76 + 34 * q^77 - 8 * q^78 + q^79 - 15 * q^80 + 9 * q^81 - 51 * q^82 + 24 * q^83 - 6 * q^84 - 21 * q^85 + 18 * q^86 - 3 * q^87 + 64 * q^88 + 9 * q^89 - 5 * q^90 - 50 * q^91 + 10 * q^92 + 6 * q^93 - 11 * q^94 + 18 * q^95 - 46 * q^96 - 4 * q^97 + 75 * q^98 + 4 * q^99

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