LMFDB - Embedded newform 2415.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.42978136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 7x - 9 $ x^6 - x^5 - 8x^4 + 6x^3 + 16x^2 - 7x - 9
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			1.2
Root			$-1.27660$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27660 q^{2} -1.00000 q^{3} -0.370286 q^{4} -1.00000 q^{5} +1.27660 q^{6} -1.00000 q^{7} +3.02591 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.27660 q^{2} -1.00000 q^{3} -0.370286 q^{4} -1.00000 q^{5} +1.27660 q^{6} -1.00000 q^{7} +3.02591 q^{8} +1.00000 q^{9} +1.27660 q^{10} +4.90026 q^{11} +0.370286 q^{12} +4.50637 q^{13} +1.27660 q^{14} +1.00000 q^{15} -3.12232 q^{16} +3.98364 q^{17} -1.27660 q^{18} +8.07358 q^{19} +0.370286 q^{20} +1.00000 q^{21} -6.25569 q^{22} +1.00000 q^{23} -3.02591 q^{24} +1.00000 q^{25} -5.75285 q^{26} -1.00000 q^{27} +0.370286 q^{28} -7.63580 q^{29} -1.27660 q^{30} -5.07594 q^{31} -2.06587 q^{32} -4.90026 q^{33} -5.08553 q^{34} +1.00000 q^{35} -0.370286 q^{36} +5.24695 q^{37} -10.3068 q^{38} -4.50637 q^{39} -3.02591 q^{40} -8.82791 q^{41} -1.27660 q^{42} -4.72888 q^{43} -1.81450 q^{44} -1.00000 q^{45} -1.27660 q^{46} +3.44679 q^{47} +3.12232 q^{48} +1.00000 q^{49} -1.27660 q^{50} -3.98364 q^{51} -1.66865 q^{52} +13.8913 q^{53} +1.27660 q^{54} -4.90026 q^{55} -3.02591 q^{56} -8.07358 q^{57} +9.74788 q^{58} +11.5380 q^{59} -0.370286 q^{60} -11.6241 q^{61} +6.47995 q^{62} -1.00000 q^{63} +8.88193 q^{64} -4.50637 q^{65} +6.25569 q^{66} +0.415644 q^{67} -1.47509 q^{68} -1.00000 q^{69} -1.27660 q^{70} -0.0137499 q^{71} +3.02591 q^{72} +5.23692 q^{73} -6.69827 q^{74} -1.00000 q^{75} -2.98953 q^{76} -4.90026 q^{77} +5.75285 q^{78} +2.49002 q^{79} +3.12232 q^{80} +1.00000 q^{81} +11.2697 q^{82} +14.6322 q^{83} -0.370286 q^{84} -3.98364 q^{85} +6.03690 q^{86} +7.63580 q^{87} +14.8278 q^{88} +2.83796 q^{89} +1.27660 q^{90} -4.50637 q^{91} -0.370286 q^{92} +5.07594 q^{93} -4.40019 q^{94} -8.07358 q^{95} +2.06587 q^{96} -16.9015 q^{97} -1.27660 q^{98} +4.90026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9} - q^{10} - 6 q^{11} - 5 q^{12} + 6 q^{13} - q^{14} + 6 q^{15} - 5 q^{16} + 16 q^{17} + q^{18} - 5 q^{20} + 6 q^{21} - 10 q^{22} + 6 q^{23} - 3 q^{24} + 6 q^{25} + 3 q^{26} - 6 q^{27} - 5 q^{28} - 4 q^{29} + q^{30} + 2 q^{32} + 6 q^{33} - 3 q^{34} + 6 q^{35} + 5 q^{36} - 4 q^{37} + 22 q^{38} - 6 q^{39} - 3 q^{40} + 4 q^{41} + q^{42} - 16 q^{43} - 13 q^{44} - 6 q^{45} + q^{46} + 38 q^{47} + 5 q^{48} + 6 q^{49} + q^{50} - 16 q^{51} + 24 q^{52} + 24 q^{53} - q^{54} + 6 q^{55} - 3 q^{56} + 2 q^{58} + 2 q^{59} + 5 q^{60} - 4 q^{61} + 26 q^{62} - 6 q^{63} + 7 q^{64} - 6 q^{65} + 10 q^{66} - 30 q^{67} + 54 q^{68} - 6 q^{69} + q^{70} - 6 q^{71} + 3 q^{72} + 38 q^{73} - 7 q^{74} - 6 q^{75} + 3 q^{76} + 6 q^{77} - 3 q^{78} - 14 q^{79} + 5 q^{80} + 6 q^{81} + 56 q^{82} + 22 q^{83} + 5 q^{84} - 16 q^{85} + 48 q^{86} + 4 q^{87} - 21 q^{88} + 20 q^{89} - q^{90} - 6 q^{91} + 5 q^{92} + 40 q^{94} - 2 q^{96} + 4 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9 - q^10 - 6 * q^11 - 5 * q^12 + 6 * q^13 - q^14 + 6 * q^15 - 5 * q^16 + 16 * q^17 + q^18 - 5 * q^20 + 6 * q^21 - 10 * q^22 + 6 * q^23 - 3 * q^24 + 6 * q^25 + 3 * q^26 - 6 * q^27 - 5 * q^28 - 4 * q^29 + q^30 + 2 * q^32 + 6 * q^33 - 3 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 + 22 * q^38 - 6 * q^39 - 3 * q^40 + 4 * q^41 + q^42 - 16 * q^43 - 13 * q^44 - 6 * q^45 + q^46 + 38 * q^47 + 5 * q^48 + 6 * q^49 + q^50 - 16 * q^51 + 24 * q^52 + 24 * q^53 - q^54 + 6 * q^55 - 3 * q^56 + 2 * q^58 + 2 * q^59 + 5 * q^60 - 4 * q^61 + 26 * q^62 - 6 * q^63 + 7 * q^64 - 6 * q^65 + 10 * q^66 - 30 * q^67 + 54 * q^68 - 6 * q^69 + q^70 - 6 * q^71 + 3 * q^72 + 38 * q^73 - 7 * q^74 - 6 * q^75 + 3 * q^76 + 6 * q^77 - 3 * q^78 - 14 * q^79 + 5 * q^80 + 6 * q^81 + 56 * q^82 + 22 * q^83 + 5 * q^84 - 16 * q^85 + 48 * q^86 + 4 * q^87 - 21 * q^88 + 20 * q^89 - q^90 - 6 * q^91 + 5 * q^92 + 40 * q^94 - 2 * q^96 + 4 * q^97 + q^98 - 6 * 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 $

$2$	−1.27660	−0.902694	−0.451347	−	0.892348i	$-0.649056\pi$
$2$	−1.27660	−0.902694	−0.451347	+	0.892348i	$0.649056\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.370286	−0.185143
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.27660	0.521171
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.02591	1.06982
$9$	1.00000	0.333333
$10$	1.27660	0.403697
$11$	4.90026	1.47748	0.738742	−	0.673988i	$-0.235420\pi$
$11$	4.90026	1.47748	0.738742	+	0.673988i	$0.235420\pi$
$12$	0.370286	0.106892
$13$	4.50637	1.24984	0.624922	−	0.780687i	$-0.285131\pi$
$13$	4.50637	1.24984	0.624922	+	0.780687i	$0.285131\pi$
$14$	1.27660	0.341186
$15$	1.00000	0.258199
$16$	−3.12232	−0.780579
$17$	3.98364	0.966176	0.483088	−	0.875572i	$-0.339515\pi$
$17$	3.98364	0.966176	0.483088	+	0.875572i	$0.339515\pi$
$18$	−1.27660	−0.300898
$19$	8.07358	1.85221	0.926104	−	0.377269i	$-0.123137\pi$
$19$	8.07358	1.85221	0.926104	+	0.377269i	$0.123137\pi$
$20$	0.370286	0.0827984
$21$	1.00000	0.218218
$22$	−6.25569	−1.33372
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.02591	−0.617662
$25$	1.00000	0.200000
$26$	−5.75285	−1.12823
$27$	−1.00000	−0.192450
$28$	0.370286	0.0699775
$29$	−7.63580	−1.41793	−0.708966	−	0.705243i	$-0.750838\pi$
$29$	−7.63580	−1.41793	−0.708966	+	0.705243i	$0.750838\pi$
$30$	−1.27660	−0.233075
$31$	−5.07594	−0.911665	−0.455832	−	0.890066i	$-0.650658\pi$
$31$	−5.07594	−0.911665	−0.455832	+	0.890066i	$0.650658\pi$
$32$	−2.06587	−0.365197
$33$	−4.90026	−0.853026
$34$	−5.08553	−0.872161
$35$	1.00000	0.169031
$36$	−0.370286	−0.0617143
$37$	5.24695	0.862593	0.431296	−	0.902210i	$-0.358056\pi$
$37$	5.24695	0.862593	0.431296	+	0.902210i	$0.358056\pi$
$38$	−10.3068	−1.67198
$39$	−4.50637	−0.721597
$40$	−3.02591	−0.478439
$41$	−8.82791	−1.37869	−0.689344	−	0.724434i	$-0.742101\pi$
$41$	−8.82791	−1.37869	−0.689344	+	0.724434i	$0.742101\pi$
$42$	−1.27660	−0.196984
$43$	−4.72888	−0.721147	−0.360574	−	0.932731i	$-0.617419\pi$
$43$	−4.72888	−0.721147	−0.360574	+	0.932731i	$0.617419\pi$
$44$	−1.81450	−0.273546
$45$	−1.00000	−0.149071
$46$	−1.27660	−0.188225
$47$	3.44679	0.502767	0.251383	−	0.967888i	$-0.419115\pi$
$47$	3.44679	0.502767	0.251383	+	0.967888i	$0.419115\pi$
$48$	3.12232	0.450668
$49$	1.00000	0.142857
$50$	−1.27660	−0.180539
$51$	−3.98364	−0.557822
$52$	−1.66865	−0.231400
$53$	13.8913	1.90811	0.954055	−	0.299631i	$-0.0968637\pi$
$53$	13.8913	1.90811	0.954055	+	0.299631i	$0.0968637\pi$
$54$	1.27660	0.173724
$55$	−4.90026	−0.660751
$56$	−3.02591	−0.404355
$57$	−8.07358	−1.06937
$58$	9.74788	1.27996
$59$	11.5380	1.50212	0.751060	−	0.660234i	$-0.229543\pi$
$59$	11.5380	1.50212	0.751060	+	0.660234i	$0.229543\pi$
$60$	−0.370286	−0.0478037
$61$	−11.6241	−1.48831	−0.744155	−	0.668007i	$-0.767148\pi$
$61$	−11.6241	−1.48831	−0.744155	+	0.668007i	$0.767148\pi$
$62$	6.47995	0.822955
$63$	−1.00000	−0.125988
$64$	8.88193	1.11024
$65$	−4.50637	−0.558947
$66$	6.25569	0.770022
$67$	0.415644	0.0507790	0.0253895	−	0.999678i	$-0.491917\pi$
$67$	0.415644	0.0507790	0.0253895	+	0.999678i	$0.491917\pi$
$68$	−1.47509	−0.178881
$69$	−1.00000	−0.120386
$70$	−1.27660	−0.152583
$71$	−0.0137499	−0.00163181	−0.000815905	−	1.00000i	$-0.500260\pi$
$71$	−0.0137499	−0.00163181	−0.000815905		1.00000i	$0.500260\pi$
$72$	3.02591	0.356607
$73$	5.23692	0.612935	0.306467	−	0.951881i	$-0.400853\pi$
$73$	5.23692	0.612935	0.306467	+	0.951881i	$0.400853\pi$
$74$	−6.69827	−0.778658
$75$	−1.00000	−0.115470
$76$	−2.98953	−0.342923
$77$	−4.90026	−0.558437
$78$	5.75285	0.651382
$79$	2.49002	0.280149	0.140075	−	0.990141i	$-0.455266\pi$
$79$	2.49002	0.280149	0.140075	+	0.990141i	$0.455266\pi$
$80$	3.12232	0.349086
$81$	1.00000	0.111111
$82$	11.2697	1.24453
$83$	14.6322	1.60610	0.803048	−	0.595914i	$-0.203210\pi$
$83$	14.6322	1.60610	0.803048	+	0.595914i	$0.203210\pi$
$84$	−0.370286	−0.0404015
$85$	−3.98364	−0.432087
$86$	6.03690	0.650976
$87$	7.63580	0.818644
$88$	14.8278	1.58064
$89$	2.83796	0.300823	0.150412	−	0.988623i	$-0.451940\pi$
$89$	2.83796	0.300823	0.150412	+	0.988623i	$0.451940\pi$
$90$	1.27660	0.134566
$91$	−4.50637	−0.472396
$92$	−0.370286	−0.0386050
$93$	5.07594	0.526350
$94$	−4.40019	−0.453845
$95$	−8.07358	−0.828332
$96$	2.06587	0.210847
$97$	−16.9015	−1.71609	−0.858043	−	0.513578i	$-0.828320\pi$
$97$	−16.9015	−1.71609	−0.858043	+	0.513578i	$0.828320\pi$
$98$	−1.27660	−0.128956
$99$	4.90026	0.492495
$100$	−0.370286	−0.0370286
$101$	2.93913	0.292454	0.146227	−	0.989251i	$-0.453287\pi$
$101$	2.93913	0.292454	0.146227	+	0.989251i	$0.453287\pi$
$102$	5.08553	0.503543
$103$	−11.1499	−1.09863	−0.549317	−	0.835614i	$-0.685112\pi$
$103$	−11.1499	−1.09863	−0.549317	+	0.835614i	$0.685112\pi$
$104$	13.6359	1.33711
$105$	−1.00000	−0.0975900
$106$	−17.7336	−1.72244
$107$	−0.0747441	−0.00722579	−0.00361289	−	0.999993i	$-0.501150\pi$
$107$	−0.0747441	−0.00722579	−0.00361289	+	0.999993i	$0.501150\pi$
$108$	0.370286	0.0356308
$109$	10.3065	0.987186	0.493593	−	0.869693i	$-0.335683\pi$
$109$	10.3065	0.987186	0.493593	+	0.869693i	$0.335683\pi$
$110$	6.25569	0.596456
$111$	−5.24695	−0.498018
$112$	3.12232	0.295031
$113$	4.86844	0.457984	0.228992	−	0.973428i	$-0.426457\pi$
$113$	4.86844	0.457984	0.228992	+	0.973428i	$0.426457\pi$
$114$	10.3068	0.965316
$115$	−1.00000	−0.0932505
$116$	2.82743	0.262520
$117$	4.50637	0.416614
$118$	−14.7294	−1.35596
$119$	−3.98364	−0.365180
$120$	3.02591	0.276227
$121$	13.0126	1.18296
$122$	14.8393	1.34349
$123$	8.82791	0.795985
$124$	1.87955	0.168788
$125$	−1.00000	−0.0894427
$126$	1.27660	0.113729
$127$	−17.7348	−1.57371	−0.786856	−	0.617137i	$-0.788292\pi$
$127$	−17.7348	−1.57371	−0.786856	+	0.617137i	$0.788292\pi$
$128$	−7.20695	−0.637011
$129$	4.72888	0.416355
$130$	5.75285	0.504558
$131$	7.24695	0.633169	0.316584	−	0.948564i	$-0.397464\pi$
$131$	7.24695	0.633169	0.316584	+	0.948564i	$0.397464\pi$
$132$	1.81450	0.157932
$133$	−8.07358	−0.700069
$134$	−0.530612	−0.0458379
$135$	1.00000	0.0860663
$136$	12.0542	1.03364
$137$	18.7017	1.59779	0.798896	−	0.601470i	$-0.205418\pi$
$137$	18.7017	1.59779	0.798896	+	0.601470i	$0.205418\pi$
$138$	1.27660	0.108672
$139$	−16.2333	−1.37689	−0.688444	−	0.725289i	$-0.741706\pi$
$139$	−16.2333	−1.37689	−0.688444	+	0.725289i	$0.741706\pi$
$140$	−0.370286	−0.0312949
$141$	−3.44679	−0.290272
$142$	0.0175531	0.00147303
$143$	22.0824	1.84662
$144$	−3.12232	−0.260193
$145$	7.63580	0.634119
$146$	−6.68546	−0.553293
$147$	−1.00000	−0.0824786
$148$	−1.94287	−0.159703
$149$	10.1254	0.829509	0.414755	−	0.909933i	$-0.363867\pi$
$149$	10.1254	0.829509	0.414755	+	0.909933i	$0.363867\pi$
$150$	1.27660	0.104234
$151$	−22.3700	−1.82045	−0.910224	−	0.414116i	$-0.864091\pi$
$151$	−22.3700	−1.82045	−0.910224	+	0.414116i	$0.864091\pi$
$152$	24.4300	1.98153
$153$	3.98364	0.322059
$154$	6.25569	0.504097
$155$	5.07594	0.407709
$156$	1.66865	0.133599
$157$	17.8851	1.42738	0.713692	−	0.700460i	$-0.247022\pi$
$157$	17.8851	1.42738	0.713692	+	0.700460i	$0.247022\pi$
$158$	−3.17876	−0.252889
$159$	−13.8913	−1.10165
$160$	2.06587	0.163321
$161$	−1.00000	−0.0788110
$162$	−1.27660	−0.100299
$163$	1.25644	0.0984119	0.0492060	−	0.998789i	$-0.484331\pi$
$163$	1.25644	0.0984119	0.0492060	+	0.998789i	$0.484331\pi$
$164$	3.26885	0.255254
$165$	4.90026	0.381485
$166$	−18.6795	−1.44981
$167$	11.1566	0.863324	0.431662	−	0.902036i	$-0.357927\pi$
$167$	11.1566	0.863324	0.431662	+	0.902036i	$0.357927\pi$
$168$	3.02591	0.233454
$169$	7.30741	0.562109
$170$	5.08553	0.390042
$171$	8.07358	0.617402
$172$	1.75104	0.133515
$173$	−14.5762	−1.10821	−0.554104	−	0.832448i	$-0.686939\pi$
$173$	−14.5762	−1.10821	−0.554104	+	0.832448i	$0.686939\pi$
$174$	−9.74788	−0.738985
$175$	−1.00000	−0.0755929
$176$	−15.3002	−1.15329
$177$	−11.5380	−0.867249
$178$	−3.62295	−0.271551
$179$	−19.3754	−1.44818	−0.724092	−	0.689704i	$-0.757741\pi$
$179$	−19.3754	−1.44818	−0.724092	+	0.689704i	$0.757741\pi$
$180$	0.370286	0.0275995
$181$	4.63964	0.344862	0.172431	−	0.985022i	$-0.444838\pi$
$181$	4.63964	0.344862	0.172431	+	0.985022i	$0.444838\pi$
$182$	5.75285	0.426430
$183$	11.6241	0.859276
$184$	3.02591	0.223073
$185$	−5.24695	−0.385763
$186$	−6.47995	−0.475133
$187$	19.5209	1.42751
$188$	−1.27630	−0.0930837
$189$	1.00000	0.0727393
$190$	10.3068	0.747731
$191$	−3.84027	−0.277872	−0.138936	−	0.990301i	$-0.544368\pi$
$191$	−3.84027	−0.277872	−0.138936	+	0.990301i	$0.544368\pi$
$192$	−8.88193	−0.640998
$193$	−5.12537	−0.368932	−0.184466	−	0.982839i	$-0.559056\pi$
$193$	−5.12537	−0.368932	−0.184466	+	0.982839i	$0.559056\pi$
$194$	21.5765	1.54910
$195$	4.50637	0.322708
$196$	−0.370286	−0.0264490
$197$	−8.01081	−0.570746	−0.285373	−	0.958416i	$-0.592118\pi$
$197$	−8.01081	−0.570746	−0.285373	+	0.958416i	$0.592118\pi$
$198$	−6.25569	−0.444572
$199$	−8.69874	−0.616637	−0.308319	−	0.951283i	$-0.599766\pi$
$199$	−8.69874	−0.616637	−0.308319	+	0.951283i	$0.599766\pi$
$200$	3.02591	0.213964
$201$	−0.415644	−0.0293173
$202$	−3.75210	−0.263997
$203$	7.63580	0.535928
$204$	1.47509	0.103277
$205$	8.82791	0.616568
$206$	14.2340	0.991732
$207$	1.00000	0.0695048
$208$	−14.0703	−0.975602
$209$	39.5627	2.73661
$210$	1.27660	0.0880939
$211$	0.133840	0.00921393	0.00460696	−	0.999989i	$-0.498534\pi$
$211$	0.133840	0.00921393	0.00460696	+	0.999989i	$0.498534\pi$
$212$	−5.14373	−0.353273
$213$	0.0137499	0.000942126 0
$214$	0.0954186	0.00652268
$215$	4.72888	0.322507
$216$	−3.02591	−0.205887
$217$	5.07594	0.344577
$218$	−13.1573	−0.891127
$219$	−5.23692	−0.353878
$220$	1.81450	0.122333
$221$	17.9518	1.20757
$222$	6.69827	0.449558
$223$	22.5532	1.51027	0.755136	−	0.655568i	$-0.227571\pi$
$223$	22.5532	1.51027	0.755136	+	0.655568i	$0.227571\pi$
$224$	2.06587	0.138032
$225$	1.00000	0.0666667
$226$	−6.21506	−0.413419
$227$	19.3447	1.28395	0.641976	−	0.766725i	$-0.278115\pi$
$227$	19.3447	1.28395	0.641976	+	0.766725i	$0.278115\pi$
$228$	2.98953	0.197987
$229$	7.01364	0.463474	0.231737	−	0.972778i	$-0.425559\pi$
$229$	7.01364	0.463474	0.231737	+	0.972778i	$0.425559\pi$
$230$	1.27660	0.0841767
$231$	4.90026	0.322413
$232$	−23.1053	−1.51693
$233$	−18.5301	−1.21395	−0.606975	−	0.794721i	$-0.707617\pi$
$233$	−18.5301	−1.21395	−0.606975	+	0.794721i	$0.707617\pi$
$234$	−5.75285	−0.376076
$235$	−3.44679	−0.224844
$236$	−4.27236	−0.278107
$237$	−2.49002	−0.161744
$238$	5.08553	0.329646
$239$	−16.8314	−1.08873	−0.544365	−	0.838848i	$-0.683230\pi$
$239$	−16.8314	−1.08873	−0.544365	+	0.838848i	$0.683230\pi$
$240$	−3.12232	−0.201545
$241$	−15.3101	−0.986207	−0.493104	−	0.869971i	$-0.664138\pi$
$241$	−15.3101	−0.986207	−0.493104	+	0.869971i	$0.664138\pi$
$242$	−16.6119	−1.06785
$243$	−1.00000	−0.0641500
$244$	4.30423	0.275550
$245$	−1.00000	−0.0638877
$246$	−11.2697	−0.718532
$247$	36.3826	2.31497
$248$	−15.3593	−0.975319
$249$	−14.6322	−0.927280
$250$	1.27660	0.0807394
$251$	−15.5681	−0.982647	−0.491324	−	0.870977i	$-0.663487\pi$
$251$	−15.5681	−0.982647	−0.491324	+	0.870977i	$0.663487\pi$
$252$	0.370286	0.0233258
$253$	4.90026	0.308077
$254$	22.6403	1.42058
$255$	3.98364	0.249465
$256$	−8.56344	−0.535215
$257$	10.4474	0.651688	0.325844	−	0.945423i	$-0.394351\pi$
$257$	10.4474	0.651688	0.325844	+	0.945423i	$0.394351\pi$
$258$	−6.03690	−0.375841
$259$	−5.24695	−0.326029
$260$	1.66865	0.103485
$261$	−7.63580	−0.472644
$262$	−9.25147	−0.571558
$263$	4.47873	0.276171	0.138085	−	0.990420i	$-0.455905\pi$
$263$	4.47873	0.276171	0.138085	+	0.990420i	$0.455905\pi$
$264$	−14.8278	−0.912586
$265$	−13.8913	−0.853333
$266$	10.3068	0.631948
$267$	−2.83796	−0.173680
$268$	−0.153907	−0.00940138
$269$	21.7194	1.32426	0.662128	−	0.749391i	$-0.269654\pi$
$269$	21.7194	1.32426	0.662128	+	0.749391i	$0.269654\pi$
$270$	−1.27660	−0.0776916
$271$	14.1313	0.858413	0.429206	−	0.903206i	$-0.358793\pi$
$271$	14.1313	0.858413	0.429206	+	0.903206i	$0.358793\pi$
$272$	−12.4382	−0.754177
$273$	4.50637	0.272738
$274$	−23.8746	−1.44232
$275$	4.90026	0.295497
$276$	0.370286	0.0222886
$277$	−19.7094	−1.18422	−0.592111	−	0.805856i	$-0.701705\pi$
$277$	−19.7094	−1.18422	−0.592111	+	0.805856i	$0.701705\pi$
$278$	20.7234	1.24291
$279$	−5.07594	−0.303888
$280$	3.02591	0.180833
$281$	−19.5815	−1.16814	−0.584068	−	0.811705i	$-0.698540\pi$
$281$	−19.5815	−1.16814	−0.584068	+	0.811705i	$0.698540\pi$
$282$	4.40019	0.262027
$283$	14.6687	0.871963	0.435981	−	0.899956i	$-0.356401\pi$
$283$	14.6687	0.871963	0.435981	+	0.899956i	$0.356401\pi$
$284$	0.00509138	0.000302118 0
$285$	8.07358	0.478238
$286$	−28.1905	−1.66694
$287$	8.82791	0.521095
$288$	−2.06587	−0.121732
$289$	−1.13058	−0.0665046
$290$	−9.74788	−0.572415
$291$	16.9015	0.990783
$292$	−1.93916	−0.113481
$293$	28.1979	1.64734	0.823670	−	0.567070i	$-0.191923\pi$
$293$	28.1979	1.64734	0.823670	+	0.567070i	$0.191923\pi$
$294$	1.27660	0.0744530
$295$	−11.5380	−0.671769
$296$	15.8768	0.922820
$297$	−4.90026	−0.284342
$298$	−12.9262	−0.748793
$299$	4.50637	0.260610
$300$	0.370286	0.0213785
$301$	4.72888	0.272568
$302$	28.5577	1.64331
$303$	−2.93913	−0.168848
$304$	−25.2083	−1.44579
$305$	11.6241	0.665592
$306$	−5.08553	−0.290720
$307$	26.6887	1.52320	0.761602	−	0.648045i	$-0.224413\pi$
$307$	26.6887	1.52320	0.761602	+	0.648045i	$0.224413\pi$
$308$	1.81450	0.103391
$309$	11.1499	0.634297
$310$	−6.47995	−0.368037
$311$	−8.65298	−0.490666	−0.245333	−	0.969439i	$-0.578897\pi$
$311$	−8.65298	−0.490666	−0.245333	+	0.969439i	$0.578897\pi$
$312$	−13.6359	−0.771981
$313$	29.7841	1.68350	0.841750	−	0.539868i	$-0.181526\pi$
$313$	29.7841	1.68350	0.841750	+	0.539868i	$0.181526\pi$
$314$	−22.8321	−1.28849
$315$	1.00000	0.0563436
$316$	−0.922019	−0.0518676
$317$	−3.18540	−0.178910	−0.0894549	−	0.995991i	$-0.528512\pi$
$317$	−3.18540	−0.178910	−0.0894549	+	0.995991i	$0.528512\pi$
$318$	17.7336	0.994451
$319$	−37.4174	−2.09497
$320$	−8.88193	−0.496515
$321$	0.0747441	0.00417181
$322$	1.27660	0.0711423
$323$	32.1623	1.78956
$324$	−0.370286	−0.0205714
$325$	4.50637	0.249969
$326$	−1.60397	−0.0888359
$327$	−10.3065	−0.569952
$328$	−26.7125	−1.47495
$329$	−3.44679	−0.190028
$330$	−6.25569	−0.344364
$331$	9.03447	0.496579	0.248290	−	0.968686i	$-0.420132\pi$
$331$	9.03447	0.496579	0.248290	+	0.968686i	$0.420132\pi$
$332$	−5.41811	−0.297357
$333$	5.24695	0.287531
$334$	−14.2425	−0.779317
$335$	−0.415644	−0.0227091
$336$	−3.12232	−0.170336
$337$	15.3133	0.834166	0.417083	−	0.908868i	$-0.363052\pi$
$337$	15.3133	0.834166	0.417083	+	0.908868i	$0.363052\pi$
$338$	−9.32866	−0.507412
$339$	−4.86844	−0.264417
$340$	1.47509	0.0799978
$341$	−24.8734	−1.34697
$342$	−10.3068	−0.557326
$343$	−1.00000	−0.0539949
$344$	−14.3092	−0.771499
$345$	1.00000	0.0538382
$346$	18.6080	1.00037
$347$	−0.274739	−0.0147488	−0.00737438	−	0.999973i	$-0.502347\pi$
$347$	−0.274739	−0.0147488	−0.00737438	+	0.999973i	$0.502347\pi$
$348$	−2.82743	−0.151566
$349$	11.9953	0.642094	0.321047	−	0.947063i	$-0.395965\pi$
$349$	11.9953	0.642094	0.321047	+	0.947063i	$0.395965\pi$
$350$	1.27660	0.0682373
$351$	−4.50637	−0.240532
$352$	−10.1233	−0.539573
$353$	20.2066	1.07549	0.537745	−	0.843107i	$-0.319276\pi$
$353$	20.2066	1.07549	0.537745	+	0.843107i	$0.319276\pi$
$354$	14.7294	0.782861
$355$	0.0137499	0.000729767 0
$356$	−1.05086	−0.0556953
$357$	3.98364	0.210837
$358$	24.7346	1.30727
$359$	32.6414	1.72275	0.861373	−	0.507973i	$-0.169605\pi$
$359$	32.6414	1.72275	0.861373	+	0.507973i	$0.169605\pi$
$360$	−3.02591	−0.159480
$361$	46.1828	2.43067
$362$	−5.92298	−0.311305
$363$	−13.0126	−0.682982
$364$	1.66865	0.0874609
$365$	−5.23692	−0.274113
$366$	−14.8393	−0.775664
$367$	3.25575	0.169949	0.0849743	−	0.996383i	$-0.472919\pi$
$367$	3.25575	0.169949	0.0849743	+	0.996383i	$0.472919\pi$
$368$	−3.12232	−0.162762
$369$	−8.82791	−0.459562
$370$	6.69827	0.348226
$371$	−13.8913	−0.721198
$372$	−1.87955	−0.0974500
$373$	7.53712	0.390257	0.195129	−	0.980778i	$-0.437488\pi$
$373$	7.53712	0.390257	0.195129	+	0.980778i	$0.437488\pi$
$374$	−24.9204	−1.28860
$375$	1.00000	0.0516398
$376$	10.4297	0.537871
$377$	−34.4098	−1.77219
$378$	−1.27660	−0.0656614
$379$	−18.3325	−0.941675	−0.470838	−	0.882220i	$-0.656048\pi$
$379$	−18.3325	−0.941675	−0.470838	+	0.882220i	$0.656048\pi$
$380$	2.98953	0.153360
$381$	17.7348	0.908583
$382$	4.90250	0.250834
$383$	−4.54692	−0.232337	−0.116168	−	0.993230i	$-0.537061\pi$
$383$	−4.54692	−0.232337	−0.116168	+	0.993230i	$0.537061\pi$
$384$	7.20695	0.367778
$385$	4.90026	0.249740
$386$	6.54306	0.333033
$387$	−4.72888	−0.240382
$388$	6.25838	0.317721
$389$	0.0546609	0.00277142	0.00138571	−	0.999999i	$-0.499559\pi$
$389$	0.0546609	0.00277142	0.00138571	+	0.999999i	$0.499559\pi$
$390$	−5.75285	−0.291307
$391$	3.98364	0.201462
$392$	3.02591	0.152832
$393$	−7.24695	−0.365560
$394$	10.2266	0.515209
$395$	−2.49002	−0.125286
$396$	−1.81450	−0.0911819
$397$	4.38391	0.220022	0.110011	−	0.993930i	$-0.464911\pi$
$397$	4.38391	0.220022	0.110011	+	0.993930i	$0.464911\pi$
$398$	11.1048	0.556635
$399$	8.07358	0.404185
$400$	−3.12232	−0.156116
$401$	28.4337	1.41991	0.709955	−	0.704247i	$-0.248715\pi$
$401$	28.4337	1.41991	0.709955	+	0.704247i	$0.248715\pi$
$402$	0.530612	0.0264645
$403$	−22.8741	−1.13944
$404$	−1.08832	−0.0541458
$405$	−1.00000	−0.0496904
$406$	−9.74788	−0.483779
$407$	25.7114	1.27447
$408$	−12.0542	−0.596770
$409$	−6.09312	−0.301285	−0.150643	−	0.988588i	$-0.548134\pi$
$409$	−6.09312	−0.301285	−0.150643	+	0.988588i	$0.548134\pi$
$410$	−11.2697	−0.556572
$411$	−18.7017	−0.922485
$412$	4.12866	0.203405
$413$	−11.5380	−0.567748
$414$	−1.27660	−0.0627416
$415$	−14.6322	−0.718268
$416$	−9.30958	−0.456440
$417$	16.2333	0.794947
$418$	−50.5058	−2.47032
$419$	28.3838	1.38664	0.693320	−	0.720630i	$-0.256147\pi$
$419$	28.3838	1.38664	0.693320	+	0.720630i	$0.256147\pi$
$420$	0.370286	0.0180681
$421$	−10.2520	−0.499652	−0.249826	−	0.968291i	$-0.580373\pi$
$421$	−10.2520	−0.499652	−0.249826	+	0.968291i	$0.580373\pi$
$422$	−0.170860	−0.00831736
$423$	3.44679	0.167589
$424$	42.0337	2.04134
$425$	3.98364	0.193235
$426$	−0.0175531	−0.000850451 0
$427$	11.6241	0.562528
$428$	0.0276767	0.00133780
$429$	−22.0824	−1.06615
$430$	−6.03690	−0.291125
$431$	−36.1581	−1.74167	−0.870836	−	0.491573i	$-0.836422\pi$
$431$	−36.1581	−1.74167	−0.870836	+	0.491573i	$0.836422\pi$
$432$	3.12232	0.150223
$433$	−1.73863	−0.0835531	−0.0417766	−	0.999127i	$-0.513302\pi$
$433$	−1.73863	−0.0835531	−0.0417766	+	0.999127i	$0.513302\pi$
$434$	−6.47995	−0.311048
$435$	−7.63580	−0.366109
$436$	−3.81636	−0.182771
$437$	8.07358	0.386212
$438$	6.68546	0.319444
$439$	−18.7589	−0.895311	−0.447656	−	0.894206i	$-0.647741\pi$
$439$	−18.7589	−0.895311	−0.447656	+	0.894206i	$0.647741\pi$
$440$	−14.8278	−0.706886
$441$	1.00000	0.0476190
$442$	−22.9173	−1.09007
$443$	12.5021	0.593991	0.296996	−	0.954879i	$-0.404015\pi$
$443$	12.5021	0.593991	0.296996	+	0.954879i	$0.404015\pi$
$444$	1.94287	0.0922045
$445$	−2.83796	−0.134532
$446$	−28.7914	−1.36331
$447$	−10.1254	−0.478917
$448$	−8.88193	−0.419632
$449$	3.09266	0.145952	0.0729758	−	0.997334i	$-0.476750\pi$
$449$	3.09266	0.145952	0.0729758	+	0.997334i	$0.476750\pi$
$450$	−1.27660	−0.0601796
$451$	−43.2590	−2.03699
$452$	−1.80271	−0.0847925
$453$	22.3700	1.05104
$454$	−24.6955	−1.15902
$455$	4.50637	0.211262
$456$	−24.4300	−1.14404
$457$	9.70083	0.453786	0.226893	−	0.973920i	$-0.427143\pi$
$457$	9.70083	0.453786	0.226893	+	0.973920i	$0.427143\pi$
$458$	−8.95362	−0.418375
$459$	−3.98364	−0.185941
$460$	0.370286	0.0172647
$461$	−30.4866	−1.41990	−0.709951	−	0.704251i	$-0.751283\pi$
$461$	−30.4866	−1.41990	−0.709951	+	0.704251i	$0.751283\pi$
$462$	−6.25569	−0.291041
$463$	−33.0357	−1.53530	−0.767650	−	0.640869i	$-0.778574\pi$
$463$	−33.0357	−1.53530	−0.767650	+	0.640869i	$0.778574\pi$
$464$	23.8414	1.10681
$465$	−5.07594	−0.235391
$466$	23.6556	1.09583
$467$	−37.8632	−1.75210	−0.876049	−	0.482222i	$-0.839830\pi$
$467$	−37.8632	−1.75210	−0.876049	+	0.482222i	$0.839830\pi$
$468$	−1.66865	−0.0771332
$469$	−0.415644	−0.0191927
$470$	4.40019	0.202965
$471$	−17.8851	−0.824100
$472$	34.9130	1.60700
$473$	−23.1727	−1.06548
$474$	3.17876	0.146005
$475$	8.07358	0.370441
$476$	1.47509	0.0676105
$477$	13.8913	0.636037
$478$	21.4870	0.982791
$479$	23.2812	1.06375	0.531873	−	0.846824i	$-0.321489\pi$
$479$	23.2812	1.06375	0.531873	+	0.846824i	$0.321489\pi$
$480$	−2.06587	−0.0942936
$481$	23.6447	1.07811
$482$	19.5449	0.890244
$483$	1.00000	0.0455016
$484$	−4.81836	−0.219017
$485$	16.9015	0.767457
$486$	1.27660	0.0579079
$487$	0.794155	0.0359866	0.0179933	−	0.999838i	$-0.494272\pi$
$487$	0.794155	0.0359866	0.0179933	+	0.999838i	$0.494272\pi$
$488$	−35.1734	−1.59223
$489$	−1.25644	−0.0568182
$490$	1.27660	0.0576710
$491$	2.99262	0.135055	0.0675274	−	0.997717i	$-0.478489\pi$
$491$	2.99262	0.135055	0.0675274	+	0.997717i	$0.478489\pi$
$492$	−3.26885	−0.147371
$493$	−30.4183	−1.36997
$494$	−46.4461	−2.08971
$495$	−4.90026	−0.220250
$496$	15.8487	0.711627
$497$	0.0137499	0.000616766 0
$498$	18.6795	0.837050
$499$	−2.36763	−0.105990	−0.0529948	−	0.998595i	$-0.516877\pi$
$499$	−2.36763	−0.105990	−0.0529948	+	0.998595i	$0.516877\pi$
$500$	0.370286	0.0165597
$501$	−11.1566	−0.498440
$502$	19.8742	0.887030
$503$	9.62369	0.429099	0.214549	−	0.976713i	$-0.431172\pi$
$503$	9.62369	0.429099	0.214549	+	0.976713i	$0.431172\pi$
$504$	−3.02591	−0.134785
$505$	−2.93913	−0.130789
$506$	−6.25569	−0.278099
$507$	−7.30741	−0.324534
$508$	6.56696	0.291362
$509$	9.45127	0.418920	0.209460	−	0.977817i	$-0.432829\pi$
$509$	9.45127	0.418920	0.209460	+	0.977817i	$0.432829\pi$
$510$	−5.08553	−0.225191
$511$	−5.23692	−0.231668
$512$	25.3460	1.12015
$513$	−8.07358	−0.356457
$514$	−13.3371	−0.588275
$515$	11.1499	0.491324
$516$	−1.75104	−0.0770851
$517$	16.8902	0.742830
$518$	6.69827	0.294305
$519$	14.5762	0.639824
$520$	−13.6359	−0.597974
$521$	26.6167	1.16610	0.583049	−	0.812437i	$-0.301860\pi$
$521$	26.6167	1.16610	0.583049	+	0.812437i	$0.301860\pi$
$522$	9.74788	0.426653
$523$	−37.0328	−1.61933	−0.809666	−	0.586891i	$-0.800352\pi$
$523$	−37.0328	−1.61933	−0.809666	+	0.586891i	$0.800352\pi$
$524$	−2.68344	−0.117227
$525$	1.00000	0.0436436
$526$	−5.71756	−0.249298
$527$	−20.2207	−0.880828
$528$	15.3002	0.665854
$529$	1.00000	0.0434783
$530$	17.7336	0.770299
$531$	11.5380	0.500707
$532$	2.98953	0.129613
$533$	−39.7819	−1.72314
$534$	3.62295	0.156780
$535$	0.0747441	0.00323147
$536$	1.25770	0.0543245
$537$	19.3754	0.836109
$538$	−27.7270	−1.19540
$539$	4.90026	0.211069
$540$	−0.370286	−0.0159346
$541$	1.13558	0.0488224	0.0244112	−	0.999702i	$-0.492229\pi$
$541$	1.13558	0.0488224	0.0244112	+	0.999702i	$0.492229\pi$
$542$	−18.0400	−0.774884
$543$	−4.63964	−0.199106
$544$	−8.22969	−0.352845
$545$	−10.3065	−0.441483
$546$	−5.75285	−0.246199
$547$	−21.0464	−0.899877	−0.449939	−	0.893059i	$-0.648554\pi$
$547$	−21.0464	−0.899877	−0.449939	+	0.893059i	$0.648554\pi$
$548$	−6.92496	−0.295820
$549$	−11.6241	−0.496103
$550$	−6.25569	−0.266743
$551$	−61.6483	−2.62630
$552$	−3.02591	−0.128791
$553$	−2.49002	−0.105886
$554$	25.1611	1.06899
$555$	5.24695	0.222720
$556$	6.01095	0.254921
$557$	25.0999	1.06351	0.531757	−	0.846897i	$-0.321532\pi$
$557$	25.0999	1.06351	0.531757	+	0.846897i	$0.321532\pi$
$558$	6.47995	0.274318
$559$	−21.3101	−0.901321
$560$	−3.12232	−0.131942
$561$	−19.5209	−0.824173
$562$	24.9978	1.05447
$563$	15.6922	0.661346	0.330673	−	0.943745i	$-0.392724\pi$
$563$	15.6922	0.661346	0.330673	+	0.943745i	$0.392724\pi$
$564$	1.27630	0.0537419
$565$	−4.86844	−0.204817
$566$	−18.7261	−0.787116
$567$	−1.00000	−0.0419961
$568$	−0.0416059	−0.00174575
$569$	37.1169	1.55602	0.778011	−	0.628250i	$-0.216229\pi$
$569$	37.1169	1.55602	0.778011	+	0.628250i	$0.216229\pi$
$570$	−10.3068	−0.431703
$571$	20.0947	0.840936	0.420468	−	0.907307i	$-0.361866\pi$
$571$	20.0947	0.840936	0.420468	+	0.907307i	$0.361866\pi$
$572$	−8.17680	−0.341889
$573$	3.84027	0.160430
$574$	−11.2697	−0.470389
$575$	1.00000	0.0417029
$576$	8.88193	0.370080
$577$	−9.32873	−0.388360	−0.194180	−	0.980966i	$-0.562205\pi$
$577$	−9.32873	−0.388360	−0.194180	+	0.980966i	$0.562205\pi$
$578$	1.44330	0.0600333
$579$	5.12537	0.213003
$580$	−2.82743	−0.117403
$581$	−14.6322	−0.607047
$582$	−21.5765	−0.894374
$583$	68.0707	2.81920
$584$	15.8465	0.655731
$585$	−4.50637	−0.186316
$586$	−35.9975	−1.48704
$587$	−40.7683	−1.68269	−0.841343	−	0.540502i	$-0.818235\pi$
$587$	−40.7683	−1.68269	−0.841343	+	0.540502i	$0.818235\pi$
$588$	0.370286	0.0152703
$589$	−40.9810	−1.68859
$590$	14.7294	0.606402
$591$	8.01081	0.329521
$592$	−16.3826	−0.673322
$593$	21.5790	0.886143	0.443072	−	0.896486i	$-0.353889\pi$
$593$	21.5790	0.886143	0.443072	+	0.896486i	$0.353889\pi$
$594$	6.25569	0.256674
$595$	3.98364	0.163313
$596$	−3.74931	−0.153578
$597$	8.69874	0.356016
$598$	−5.75285	−0.235252
$599$	−30.2136	−1.23450	−0.617248	−	0.786769i	$-0.711752\pi$
$599$	−30.2136	−1.23450	−0.617248	+	0.786769i	$0.711752\pi$
$600$	−3.02591	−0.123532
$601$	47.4917	1.93723	0.968613	−	0.248572i	$-0.0799614\pi$
$601$	47.4917	1.93723	0.968613	+	0.248572i	$0.0799614\pi$
$602$	−6.03690	−0.246046
$603$	0.415644	0.0169263
$604$	8.28331	0.337043
$605$	−13.0126	−0.529035
$606$	3.75210	0.152419
$607$	−35.9283	−1.45828	−0.729142	−	0.684363i	$-0.760081\pi$
$607$	−35.9283	−1.45828	−0.729142	+	0.684363i	$0.760081\pi$
$608$	−16.6790	−0.676421
$609$	−7.63580	−0.309418
$610$	−14.8393	−0.600826
$611$	15.5325	0.628380
$612$	−1.47509	−0.0596269
$613$	23.8546	0.963480	0.481740	−	0.876314i	$-0.340005\pi$
$613$	23.8546	0.963480	0.481740	+	0.876314i	$0.340005\pi$
$614$	−34.0708	−1.37499
$615$	−8.82791	−0.355976
$616$	−14.8278	−0.597428
$617$	−12.3866	−0.498667	−0.249333	−	0.968418i	$-0.580212\pi$
$617$	−12.3866	−0.498667	−0.249333	+	0.968418i	$0.580212\pi$
$618$	−14.2340	−0.572576
$619$	24.8467	0.998671	0.499336	−	0.866409i	$-0.333577\pi$
$619$	24.8467	0.998671	0.499336	+	0.866409i	$0.333577\pi$
$620$	−1.87955	−0.0754844
$621$	−1.00000	−0.0401286
$622$	11.0464	0.442921
$623$	−2.83796	−0.113700
$624$	14.0703	0.563264
$625$	1.00000	0.0400000
$626$	−38.0225	−1.51969
$627$	−39.5627	−1.57998
$628$	−6.62258	−0.264270
$629$	20.9020	0.833416
$630$	−1.27660	−0.0508611
$631$	26.7079	1.06323	0.531613	−	0.846987i	$-0.321586\pi$
$631$	26.7079	1.06323	0.531613	+	0.846987i	$0.321586\pi$
$632$	7.53458	0.299710
$633$	−0.133840	−0.00531966
$634$	4.06649	0.161501
$635$	17.7348	0.703785
$636$	5.14373	0.203962
$637$	4.50637	0.178549
$638$	47.7672	1.89112
$639$	−0.0137499	−0.000543936 0
$640$	7.20695	0.284880
$641$	−16.7496	−0.661569	−0.330784	−	0.943706i	$-0.607313\pi$
$641$	−16.7496	−0.661569	−0.330784	+	0.943706i	$0.607313\pi$
$642$	−0.0954186	−0.00376587
$643$	37.2806	1.47021	0.735103	−	0.677956i	$-0.237134\pi$
$643$	37.2806	1.47021	0.735103	+	0.677956i	$0.237134\pi$
$644$	0.370286	0.0145913
$645$	−4.72888	−0.186199
$646$	−41.0585	−1.61542
$647$	29.4555	1.15802	0.579008	−	0.815322i	$-0.303440\pi$
$647$	29.4555	1.15802	0.579008	+	0.815322i	$0.303440\pi$
$648$	3.02591	0.118869
$649$	56.5392	2.21936
$650$	−5.75285	−0.225645
$651$	−5.07594	−0.198942
$652$	−0.465242	−0.0182203
$653$	14.2991	0.559567	0.279784	−	0.960063i	$-0.409737\pi$
$653$	14.2991	0.559567	0.279784	+	0.960063i	$0.409737\pi$
$654$	13.1573	0.514493
$655$	−7.24695	−0.283162
$656$	27.5635	1.07617
$657$	5.23692	0.204312
$658$	4.40019	0.171537
$659$	37.4967	1.46066	0.730332	−	0.683092i	$-0.239365\pi$
$659$	37.4967	1.46066	0.730332	+	0.683092i	$0.239365\pi$
$660$	−1.81450	−0.0706292
$661$	−38.5966	−1.50123	−0.750616	−	0.660738i	$-0.770243\pi$
$661$	−38.5966	−1.50123	−0.750616	+	0.660738i	$0.770243\pi$
$662$	−11.5334	−0.448259
$663$	−17.9518	−0.697190
$664$	44.2759	1.71824
$665$	8.07358	0.313080
$666$	−6.69827	−0.259553
$667$	−7.63580	−0.295659
$668$	−4.13113	−0.159838
$669$	−22.5532	−0.871956
$670$	0.530612	0.0204993
$671$	−56.9610	−2.19895
$672$	−2.06587	−0.0796926
$673$	−37.2134	−1.43447	−0.717235	−	0.696831i	$-0.754593\pi$
$673$	−37.2134	−1.43447	−0.717235	+	0.696831i	$0.754593\pi$
$674$	−19.5489	−0.752997
$675$	−1.00000	−0.0384900
$676$	−2.70583	−0.104070
$677$	−39.7033	−1.52592	−0.762960	−	0.646446i	$-0.776255\pi$
$677$	−39.7033	−1.52592	−0.762960	+	0.646446i	$0.776255\pi$
$678$	6.21506	0.238688
$679$	16.9015	0.648620
$680$	−12.0542	−0.462256
$681$	−19.3447	−0.741290
$682$	31.7535	1.21590
$683$	−0.378741	−0.0144921	−0.00724605	−	0.999974i	$-0.502307\pi$
$683$	−0.378741	−0.0144921	−0.00724605	+	0.999974i	$0.502307\pi$
$684$	−2.98953	−0.114308
$685$	−18.7017	−0.714554
$686$	1.27660	0.0487409
$687$	−7.01364	−0.267587
$688$	14.7651	0.562913
$689$	62.5992	2.38484
$690$	−1.27660	−0.0485994
$691$	29.4083	1.11874	0.559372	−	0.828917i	$-0.311042\pi$
$691$	29.4083	1.11874	0.559372	+	0.828917i	$0.311042\pi$
$692$	5.39736	0.205177
$693$	−4.90026	−0.186146
$694$	0.350732	0.0133136
$695$	16.2333	0.615763
$696$	23.1053	0.875803
$697$	−35.1672	−1.33205
$698$	−15.3132	−0.579614
$699$	18.5301	0.700874
$700$	0.370286	0.0139955
$701$	−16.8501	−0.636419	−0.318210	−	0.948020i	$-0.603082\pi$
$701$	−16.8501	−0.636419	−0.318210	+	0.948020i	$0.603082\pi$
$702$	5.75285	0.217127
$703$	42.3617	1.59770
$704$	43.5238	1.64036
$705$	3.44679	0.129814
$706$	−25.7958	−0.970839
$707$	−2.93913	−0.110537
$708$	4.27236	0.160565
$709$	−12.9703	−0.487111	−0.243555	−	0.969887i	$-0.578314\pi$
$709$	−12.9703	−0.487111	−0.243555	+	0.969887i	$0.578314\pi$
$710$	−0.0175531	−0.000658757 0
$711$	2.49002	0.0933830
$712$	8.58742	0.321827
$713$	−5.07594	−0.190095
$714$	−5.08553	−0.190321
$715$	−22.0824	−0.825835
$716$	7.17443	0.268121
$717$	16.8314	0.628579
$718$	−41.6701	−1.55511
$719$	−28.5189	−1.06357	−0.531787	−	0.846878i	$-0.678479\pi$
$719$	−28.5189	−1.06357	−0.531787	+	0.846878i	$0.678479\pi$
$720$	3.12232	0.116362
$721$	11.1499	0.415245
$722$	−58.9570	−2.19415
$723$	15.3101	0.569387
$724$	−1.71799	−0.0638487
$725$	−7.63580	−0.283586
$726$	16.6119	0.616524
$727$	−47.5256	−1.76263	−0.881313	−	0.472532i	$-0.843340\pi$
$727$	−47.5256	−1.76263	−0.881313	+	0.472532i	$0.843340\pi$
$728$	−13.6359	−0.505380
$729$	1.00000	0.0370370
$730$	6.68546	0.247440
$731$	−18.8382	−0.696755
$732$	−4.30423	−0.159089
$733$	20.6587	0.763046	0.381523	−	0.924359i	$-0.375400\pi$
$733$	20.6587	0.763046	0.381523	+	0.924359i	$0.375400\pi$
$734$	−4.15629	−0.153412
$735$	1.00000	0.0368856
$736$	−2.06587	−0.0761489
$737$	2.03676	0.0750252
$738$	11.2697	0.414844
$739$	19.6839	0.724084	0.362042	−	0.932162i	$-0.382080\pi$
$739$	19.6839	0.724084	0.362042	+	0.932162i	$0.382080\pi$
$740$	1.94287	0.0714213
$741$	−36.3826	−1.33655
$742$	17.7336	0.651021
$743$	−23.9674	−0.879280	−0.439640	−	0.898174i	$-0.644894\pi$
$743$	−23.9674	−0.879280	−0.439640	+	0.898174i	$0.644894\pi$
$744$	15.3593	0.563101
$745$	−10.1254	−0.370968
$746$	−9.62190	−0.352283
$747$	14.6322	0.535365
$748$	−7.22831	−0.264293
$749$	0.0747441	0.00273109
$750$	−1.27660	−0.0466149
$751$	−49.9941	−1.82431	−0.912156	−	0.409843i	$-0.865583\pi$
$751$	−49.9941	−1.82431	−0.912156	+	0.409843i	$0.865583\pi$
$752$	−10.7620	−0.392449
$753$	15.5681	0.567332
$754$	43.9276	1.59975
$755$	22.3700	0.814129
$756$	−0.370286	−0.0134672
$757$	3.78026	0.137396	0.0686979	−	0.997638i	$-0.478116\pi$
$757$	3.78026	0.137396	0.0686979	+	0.997638i	$0.478116\pi$
$758$	23.4033	0.850045
$759$	−4.90026	−0.177868
$760$	−24.4300	−0.886168
$761$	37.9329	1.37507	0.687534	−	0.726153i	$-0.258693\pi$
$761$	37.9329	1.37507	0.687534	+	0.726153i	$0.258693\pi$
$762$	−22.6403	−0.820172
$763$	−10.3065	−0.373121
$764$	1.42200	0.0514461
$765$	−3.98364	−0.144029
$766$	5.80461	0.209729
$767$	51.9946	1.87741
$768$	8.56344	0.309006
$769$	−17.0955	−0.616481	−0.308240	−	0.951308i	$-0.599740\pi$
$769$	−17.0955	−0.616481	−0.308240	+	0.951308i	$0.599740\pi$
$770$	−6.25569	−0.225439
$771$	−10.4474	−0.376253
$772$	1.89785	0.0683052
$773$	20.8751	0.750827	0.375413	−	0.926857i	$-0.377501\pi$
$773$	20.8751	0.750827	0.375413	+	0.926857i	$0.377501\pi$
$774$	6.03690	0.216992
$775$	−5.07594	−0.182333
$776$	−51.1424	−1.83591
$777$	5.24695	0.188233
$778$	−0.0697803	−0.00250174
$779$	−71.2728	−2.55361
$780$	−1.66865	−0.0597471
$781$	−0.0673779	−0.00241097
$782$	−5.08553	−0.181858
$783$	7.63580	0.272881
$784$	−3.12232	−0.111511
$785$	−17.8851	−0.638345
$786$	9.25147	0.329989
$787$	29.7743	1.06134	0.530670	−	0.847579i	$-0.321940\pi$
$787$	29.7743	1.06134	0.530670	+	0.847579i	$0.321940\pi$
$788$	2.96629	0.105670
$789$	−4.47873	−0.159447
$790$	3.17876	0.113095
$791$	−4.86844	−0.173102
$792$	14.8278	0.526882
$793$	−52.3824	−1.86015
$794$	−5.59652	−0.198613
$795$	13.8913	0.492672
$796$	3.22102	0.114166
$797$	23.3339	0.826530	0.413265	−	0.910611i	$-0.364388\pi$
$797$	23.3339	0.826530	0.413265	+	0.910611i	$0.364388\pi$
$798$	−10.3068	−0.364855
$799$	13.7308	0.485761
$800$	−2.06587	−0.0730395
$801$	2.83796	0.100274
$802$	−36.2985	−1.28174
$803$	25.6623	0.905601
$804$	0.153907	0.00542789
$805$	1.00000	0.0352454
$806$	29.2011	1.02856
$807$	−21.7194	−0.764559
$808$	8.89354	0.312874
$809$	−4.03632	−0.141909	−0.0709547	−	0.997480i	$-0.522605\pi$
$809$	−4.03632	−0.141909	−0.0709547	+	0.997480i	$0.522605\pi$
$810$	1.27660	0.0448552
$811$	1.22018	0.0428463	0.0214231	−	0.999770i	$-0.493180\pi$
$811$	1.22018	0.0428463	0.0214231	+	0.999770i	$0.493180\pi$
$812$	−2.82743	−0.0992233
$813$	−14.1313	−0.495605
$814$	−32.8232	−1.15045
$815$	−1.25644	−0.0440112
$816$	12.4382	0.435424
$817$	−38.1790	−1.33571
$818$	7.77849	0.271969
$819$	−4.50637	−0.157465
$820$	−3.26885	−0.114153
$821$	−15.7740	−0.550515	−0.275258	−	0.961371i	$-0.588763\pi$
$821$	−15.7740	−0.550515	−0.275258	+	0.961371i	$0.588763\pi$
$822$	23.8746	0.832722
$823$	−27.2866	−0.951152	−0.475576	−	0.879675i	$-0.657760\pi$
$823$	−27.2866	−0.951152	−0.475576	+	0.879675i	$0.657760\pi$
$824$	−33.7387	−1.17534
$825$	−4.90026	−0.170605
$826$	14.7294	0.512503
$827$	−22.1178	−0.769111	−0.384555	−	0.923102i	$-0.625645\pi$
$827$	−22.1178	−0.769111	−0.384555	+	0.923102i	$0.625645\pi$
$828$	−0.370286	−0.0128683
$829$	−9.81595	−0.340922	−0.170461	−	0.985364i	$-0.554526\pi$
$829$	−9.81595	−0.340922	−0.170461	+	0.985364i	$0.554526\pi$
$830$	18.6795	0.648376
$831$	19.7094	0.683711
$832$	40.0253	1.38763
$833$	3.98364	0.138025
$834$	−20.7234	−0.717594
$835$	−11.1566	−0.386090
$836$	−14.6495	−0.506663
$837$	5.07594	0.175450
$838$	−36.2348	−1.25171
$839$	10.5603	0.364583	0.182291	−	0.983245i	$-0.441649\pi$
$839$	10.5603	0.364583	0.182291	+	0.983245i	$0.441649\pi$
$840$	−3.02591	−0.104404
$841$	29.3054	1.01053
$842$	13.0877	0.451033
$843$	19.5815	0.674424
$844$	−0.0495591	−0.00170589
$845$	−7.30741	−0.251383
$846$	−4.40019	−0.151282
$847$	−13.0126	−0.447117
$848$	−43.3729	−1.48943
$849$	−14.6687	−0.503428
$850$	−5.08553	−0.174432
$851$	5.24695	0.179863
$852$	−0.00509138	−0.000174428 0
$853$	24.5300	0.839890	0.419945	−	0.907550i	$-0.362049\pi$
$853$	24.5300	0.839890	0.419945	+	0.907550i	$0.362049\pi$
$854$	−14.8393	−0.507791
$855$	−8.07358	−0.276111
$856$	−0.226169	−0.00773031
$857$	10.6203	0.362781	0.181391	−	0.983411i	$-0.441940\pi$
$857$	10.6203	0.362781	0.181391	+	0.983411i	$0.441940\pi$
$858$	28.1905	0.962406
$859$	−13.7045	−0.467593	−0.233797	−	0.972286i	$-0.575115\pi$
$859$	−13.7045	−0.467593	−0.233797	+	0.972286i	$0.575115\pi$
$860$	−1.75104	−0.0597099
$861$	−8.82791	−0.300854
$862$	46.1595	1.57220
$863$	35.3808	1.20438	0.602189	−	0.798354i	$-0.294295\pi$
$863$	35.3808	1.20438	0.602189	+	0.798354i	$0.294295\pi$
$864$	2.06587	0.0702823
$865$	14.5762	0.495605
$866$	2.21954	0.0754229
$867$	1.13058	0.0383964
$868$	−1.87955	−0.0637960
$869$	12.2017	0.413916
$870$	9.74788	0.330484
$871$	1.87305	0.0634658
$872$	31.1867	1.05611
$873$	−16.9015	−0.572029
$874$	−10.3068	−0.348631
$875$	1.00000	0.0338062
$876$	1.93916	0.0655180
$877$	−33.2454	−1.12262	−0.561308	−	0.827607i	$-0.689702\pi$
$877$	−33.2454	−1.12262	−0.561308	+	0.827607i	$0.689702\pi$
$878$	23.9476	0.808193
$879$	−28.1979	−0.951092
$880$	15.3002	0.515768
$881$	−3.78991	−0.127685	−0.0638427	−	0.997960i	$-0.520336\pi$
$881$	−3.78991	−0.127685	−0.0638427	+	0.997960i	$0.520336\pi$
$882$	−1.27660	−0.0429854
$883$	−46.0928	−1.55115	−0.775573	−	0.631258i	$-0.782539\pi$
$883$	−46.0928	−1.55115	−0.775573	+	0.631258i	$0.782539\pi$
$884$	−6.64730	−0.223573
$885$	11.5380	0.387846
$886$	−15.9602	−0.536193
$887$	−7.77075	−0.260916	−0.130458	−	0.991454i	$-0.541645\pi$
$887$	−7.77075	−0.260916	−0.130458	+	0.991454i	$0.541645\pi$
$888$	−15.8768	−0.532791
$889$	17.7348	0.594807
$890$	3.62295	0.121441
$891$	4.90026	0.164165
$892$	−8.35112	−0.279616
$893$	27.8280	0.931228
$894$	12.9262	0.432316
$895$	19.3754	0.647647
$896$	7.20695	0.240767
$897$	−4.50637	−0.150463
$898$	−3.94810	−0.131750
$899$	38.7588	1.29268
$900$	−0.370286	−0.0123429
$901$	55.3378	1.84357
$902$	55.2246	1.83878
$903$	−4.72888	−0.157367
$904$	14.7315	0.489961
$905$	−4.63964	−0.154227
$906$	−28.5577	−0.948765
$907$	3.00779	0.0998719	0.0499360	−	0.998752i	$-0.484098\pi$
$907$	3.00779	0.0998719	0.0499360	+	0.998752i	$0.484098\pi$
$908$	−7.16306	−0.237715
$909$	2.93913	0.0974847
$910$	−5.75285	−0.190705
$911$	10.8287	0.358769	0.179385	−	0.983779i	$-0.442589\pi$
$911$	10.8287	0.358769	0.179385	+	0.983779i	$0.442589\pi$
$912$	25.2083	0.834730
$913$	71.7017	2.37298
$914$	−12.3841	−0.409630
$915$	−11.6241	−0.384280
$916$	−2.59705	−0.0858089
$917$	−7.24695	−0.239315
$918$	5.08553	0.167848
$919$	−18.7216	−0.617568	−0.308784	−	0.951132i	$-0.599922\pi$
$919$	−18.7216	−0.617568	−0.308784	+	0.951132i	$0.599922\pi$
$920$	−3.02591	−0.0997614
$921$	−26.6887	−0.879422
$922$	38.9193	1.28174
$923$	−0.0619621	−0.00203951
$924$	−1.81450	−0.0596926
$925$	5.24695	0.172519
$926$	42.1735	1.38591
$927$	−11.1499	−0.366212
$928$	15.7746	0.517825
$929$	37.1627	1.21927	0.609634	−	0.792683i	$-0.291316\pi$
$929$	37.1627	1.21927	0.609634	+	0.792683i	$0.291316\pi$
$930$	6.47995	0.212486
$931$	8.07358	0.264601
$932$	6.86145	0.224754
$933$	8.65298	0.283286
$934$	48.3362	1.58161
$935$	−19.5209	−0.638402
$936$	13.6359	0.445703
$937$	55.6539	1.81813	0.909067	−	0.416650i	$-0.136796\pi$
$937$	55.6539	1.81813	0.909067	+	0.416650i	$0.136796\pi$
$938$	0.530612	0.0173251
$939$	−29.7841	−0.971969
$940$	1.27630	0.0416283
$941$	−17.4038	−0.567348	−0.283674	−	0.958921i	$-0.591553\pi$
$941$	−17.4038	−0.567348	−0.283674	+	0.958921i	$0.591553\pi$
$942$	22.8321	0.743910
$943$	−8.82791	−0.287476
$944$	−36.0253	−1.17252
$945$	−1.00000	−0.0325300
$946$	29.5824	0.961806
$947$	1.49523	0.0485884	0.0242942	−	0.999705i	$-0.492266\pi$
$947$	1.49523	0.0485884	0.0242942	+	0.999705i	$0.492266\pi$
$948$	0.922019	0.0299458
$949$	23.5995	0.766073
$950$	−10.3068	−0.334395
$951$	3.18540	0.103294
$952$	−12.0542	−0.390678
$953$	0.362277	0.0117353	0.00586765	−	0.999983i	$-0.498132\pi$
$953$	0.362277	0.0117353	0.00586765	+	0.999983i	$0.498132\pi$
$954$	−17.7336	−0.574147
$955$	3.84027	0.124268
$956$	6.23242	0.201571
$957$	37.4174	1.20953
$958$	−29.7208	−0.960237
$959$	−18.7017	−0.603908
$960$	8.88193	0.286663
$961$	−5.23488	−0.168867
$962$	−30.1849	−0.973200
$963$	−0.0747441	−0.00240860
$964$	5.66910	0.182589
$965$	5.12537	0.164992
$966$	−1.27660	−0.0410740
$967$	29.3252	0.943036	0.471518	−	0.881857i	$-0.343706\pi$
$967$	29.3252	0.943036	0.471518	+	0.881857i	$0.343706\pi$
$968$	39.3749	1.26556
$969$	−32.1623	−1.03320
$970$	−21.5765	−0.692779
$971$	−32.0712	−1.02921	−0.514607	−	0.857426i	$-0.672062\pi$
$971$	−32.0712	−1.02921	−0.514607	+	0.857426i	$0.672062\pi$
$972$	0.370286	0.0118769
$973$	16.2333	0.520415
$974$	−1.01382	−0.0324849
$975$	−4.50637	−0.144319
$976$	36.2940	1.16174
$977$	−15.0727	−0.482218	−0.241109	−	0.970498i	$-0.577511\pi$
$977$	−15.0727	−0.482218	−0.241109	+	0.970498i	$0.577511\pi$
$978$	1.60397	0.0512894
$979$	13.9067	0.444461
$980$	0.370286	0.0118283
$981$	10.3065	0.329062
$982$	−3.82038	−0.121913
$983$	9.08586	0.289794	0.144897	−	0.989447i	$-0.453715\pi$
$983$	9.08586	0.289794	0.144897	+	0.989447i	$0.453715\pi$
$984$	26.7125	0.851563
$985$	8.01081	0.255245
$986$	38.8321	1.23667
$987$	3.44679	0.109713
$988$	−13.4720	−0.428600
$989$	−4.72888	−0.150370
$990$	6.25569	0.198819
$991$	−5.52857	−0.175621	−0.0878104	−	0.996137i	$-0.527987\pi$
$991$	−5.52857	−0.175621	−0.0878104	+	0.996137i	$0.527987\pi$
$992$	10.4862	0.332938
$993$	−9.03447	−0.286700
$994$	−0.0175531	−0.000556751 0
$995$	8.69874	0.275768
$996$	5.41811	0.171679
$997$	−44.5505	−1.41093	−0.705464	−	0.708746i	$-0.749261\pi$
$997$	−44.5505	−1.41093	−0.705464	+	0.708746i	$0.749261\pi$
$998$	3.02252	0.0956763
$999$	−5.24695	−0.166006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.p.1.2	✓	6
3.2	odd	2		7245.2.a.bk.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.p.1.2	✓	6	1.1	even	1	trivial
7245.2.a.bk.1.5		6	3.2	odd	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:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q-1.27660 q^{2} -1.00000 q^{3} -0.370286 q^{4} -1.00000 q^{5} +1.27660 q^{6} -1.00000 q^{7} +3.02591 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.27660 q^{2} -1.00000 q^{3} -0.370286 q^{4} -1.00000 q^{5} +1.27660 q^{6} -1.00000 q^{7} +3.02591 q^{8} +1.00000 q^{9} +1.27660 q^{10} +4.90026 q^{11} +0.370286 q^{12} +4.50637 q^{13} +1.27660 q^{14} +1.00000 q^{15} -3.12232 q^{16} +3.98364 q^{17} -1.27660 q^{18} +8.07358 q^{19} +0.370286 q^{20} +1.00000 q^{21} -6.25569 q^{22} +1.00000 q^{23} -3.02591 q^{24} +1.00000 q^{25} -5.75285 q^{26} -1.00000 q^{27} +0.370286 q^{28} -7.63580 q^{29} -1.27660 q^{30} -5.07594 q^{31} -2.06587 q^{32} -4.90026 q^{33} -5.08553 q^{34} +1.00000 q^{35} -0.370286 q^{36} +5.24695 q^{37} -10.3068 q^{38} -4.50637 q^{39} -3.02591 q^{40} -8.82791 q^{41} -1.27660 q^{42} -4.72888 q^{43} -1.81450 q^{44} -1.00000 q^{45} -1.27660 q^{46} +3.44679 q^{47} +3.12232 q^{48} +1.00000 q^{49} -1.27660 q^{50} -3.98364 q^{51} -1.66865 q^{52} +13.8913 q^{53} +1.27660 q^{54} -4.90026 q^{55} -3.02591 q^{56} -8.07358 q^{57} +9.74788 q^{58} +11.5380 q^{59} -0.370286 q^{60} -11.6241 q^{61} +6.47995 q^{62} -1.00000 q^{63} +8.88193 q^{64} -4.50637 q^{65} +6.25569 q^{66} +0.415644 q^{67} -1.47509 q^{68} -1.00000 q^{69} -1.27660 q^{70} -0.0137499 q^{71} +3.02591 q^{72} +5.23692 q^{73} -6.69827 q^{74} -1.00000 q^{75} -2.98953 q^{76} -4.90026 q^{77} +5.75285 q^{78} +2.49002 q^{79} +3.12232 q^{80} +1.00000 q^{81} +11.2697 q^{82} +14.6322 q^{83} -0.370286 q^{84} -3.98364 q^{85} +6.03690 q^{86} +7.63580 q^{87} +14.8278 q^{88} +2.83796 q^{89} +1.27660 q^{90} -4.50637 q^{91} -0.370286 q^{92} +5.07594 q^{93} -4.40019 q^{94} -8.07358 q^{95} +2.06587 q^{96} -16.9015 q^{97} -1.27660 q^{98} +4.90026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9} - q^{10} - 6 q^{11} - 5 q^{12} + 6 q^{13} - q^{14} + 6 q^{15} - 5 q^{16} + 16 q^{17} + q^{18} - 5 q^{20} + 6 q^{21} - 10 q^{22} + 6 q^{23} - 3 q^{24} + 6 q^{25} + 3 q^{26} - 6 q^{27} - 5 q^{28} - 4 q^{29} + q^{30} + 2 q^{32} + 6 q^{33} - 3 q^{34} + 6 q^{35} + 5 q^{36} - 4 q^{37} + 22 q^{38} - 6 q^{39} - 3 q^{40} + 4 q^{41} + q^{42} - 16 q^{43} - 13 q^{44} - 6 q^{45} + q^{46} + 38 q^{47} + 5 q^{48} + 6 q^{49} + q^{50} - 16 q^{51} + 24 q^{52} + 24 q^{53} - q^{54} + 6 q^{55} - 3 q^{56} + 2 q^{58} + 2 q^{59} + 5 q^{60} - 4 q^{61} + 26 q^{62} - 6 q^{63} + 7 q^{64} - 6 q^{65} + 10 q^{66} - 30 q^{67} + 54 q^{68} - 6 q^{69} + q^{70} - 6 q^{71} + 3 q^{72} + 38 q^{73} - 7 q^{74} - 6 q^{75} + 3 q^{76} + 6 q^{77} - 3 q^{78} - 14 q^{79} + 5 q^{80} + 6 q^{81} + 56 q^{82} + 22 q^{83} + 5 q^{84} - 16 q^{85} + 48 q^{86} + 4 q^{87} - 21 q^{88} + 20 q^{89} - q^{90} - 6 q^{91} + 5 q^{92} + 40 q^{94} - 2 q^{96} + 4 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9 - q^10 - 6 * q^11 - 5 * q^12 + 6 * q^13 - q^14 + 6 * q^15 - 5 * q^16 + 16 * q^17 + q^18 - 5 * q^20 + 6 * q^21 - 10 * q^22 + 6 * q^23 - 3 * q^24 + 6 * q^25 + 3 * q^26 - 6 * q^27 - 5 * q^28 - 4 * q^29 + q^30 + 2 * q^32 + 6 * q^33 - 3 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 + 22 * q^38 - 6 * q^39 - 3 * q^40 + 4 * q^41 + q^42 - 16 * q^43 - 13 * q^44 - 6 * q^45 + q^46 + 38 * q^47 + 5 * q^48 + 6 * q^49 + q^50 - 16 * q^51 + 24 * q^52 + 24 * q^53 - q^54 + 6 * q^55 - 3 * q^56 + 2 * q^58 + 2 * q^59 + 5 * q^60 - 4 * q^61 + 26 * q^62 - 6 * q^63 + 7 * q^64 - 6 * q^65 + 10 * q^66 - 30 * q^67 + 54 * q^68 - 6 * q^69 + q^70 - 6 * q^71 + 3 * q^72 + 38 * q^73 - 7 * q^74 - 6 * q^75 + 3 * q^76 + 6 * q^77 - 3 * q^78 - 14 * q^79 + 5 * q^80 + 6 * q^81 + 56 * q^82 + 22 * q^83 + 5 * q^84 - 16 * q^85 + 48 * q^86 + 4 * q^87 - 21 * q^88 + 20 * q^89 - q^90 - 6 * q^91 + 5 * q^92 + 40 * q^94 - 2 * q^96 + 4 * q^97 + q^98 - 6 * q^99

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