LMFDB - Embedded newform 2415.2.a.o.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:	$1$
Dimension:	$5$
Coefficient field:	5.5.2508628.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} - 2x^{2} + 23x + 8 $ x^5 - 10x^3 - 2x^2 + 23*x + 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.92367$ 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)

$f(q)$	$=$	$q-1.92367 q^{2} -1.00000 q^{3} +1.70052 q^{4} -1.00000 q^{5} +1.92367 q^{6} -1.00000 q^{7} +0.576096 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.92367 q^{2} -1.00000 q^{3} +1.70052 q^{4} -1.00000 q^{5} +1.92367 q^{6} -1.00000 q^{7} +0.576096 q^{8} +1.00000 q^{9} +1.92367 q^{10} -5.42344 q^{11} -1.70052 q^{12} +2.22315 q^{13} +1.92367 q^{14} +1.00000 q^{15} -4.50927 q^{16} -2.00000 q^{17} -1.92367 q^{18} +6.85685 q^{19} -1.70052 q^{20} +1.00000 q^{21} +10.4329 q^{22} -1.00000 q^{23} -0.576096 q^{24} +1.00000 q^{25} -4.27662 q^{26} -1.00000 q^{27} -1.70052 q^{28} +4.49977 q^{29} -1.92367 q^{30} +0.513131 q^{31} +7.52217 q^{32} +5.42344 q^{33} +3.84735 q^{34} +1.00000 q^{35} +1.70052 q^{36} -2.87557 q^{37} -13.1903 q^{38} -2.22315 q^{39} -0.576096 q^{40} -0.509726 q^{41} -1.92367 q^{42} -3.71002 q^{43} -9.22269 q^{44} -1.00000 q^{45} +1.92367 q^{46} +1.20029 q^{47} +4.50927 q^{48} +1.00000 q^{49} -1.92367 q^{50} +2.00000 q^{51} +3.78052 q^{52} -8.82449 q^{53} +1.92367 q^{54} +5.42344 q^{55} -0.576096 q^{56} -6.85685 q^{57} -8.65609 q^{58} +8.21320 q^{59} +1.70052 q^{60} +2.25789 q^{61} -0.987098 q^{62} -1.00000 q^{63} -5.45167 q^{64} -2.22315 q^{65} -10.4329 q^{66} +6.40059 q^{67} -3.40105 q^{68} +1.00000 q^{69} -1.92367 q^{70} +14.3661 q^{71} +0.576096 q^{72} -1.48687 q^{73} +5.53167 q^{74} -1.00000 q^{75} +11.6602 q^{76} +5.42344 q^{77} +4.27662 q^{78} +13.9713 q^{79} +4.50927 q^{80} +1.00000 q^{81} +0.980547 q^{82} -3.80920 q^{83} +1.70052 q^{84} +2.00000 q^{85} +7.13687 q^{86} -4.49977 q^{87} -3.12443 q^{88} -14.2356 q^{89} +1.92367 q^{90} -2.22315 q^{91} -1.70052 q^{92} -0.513131 q^{93} -2.30897 q^{94} -6.85685 q^{95} -7.52217 q^{96} +8.36611 q^{97} -1.92367 q^{98} -5.42344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9	$ 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9} + q^{11} - 10 q^{12} + 5 q^{15} + 8 q^{16} - 10 q^{17} + 3 q^{19} - 10 q^{20} + 5 q^{21} + 12 q^{22} - 5 q^{23} + 6 q^{24} + 5 q^{25} - 14 q^{26} - 5 q^{27} - 10 q^{28} + 4 q^{29} + 2 q^{31} - 12 q^{32} - q^{33} + 5 q^{35} + 10 q^{36} - 4 q^{37} - 24 q^{38} + 6 q^{40} - 9 q^{41} - 8 q^{43} + 2 q^{44} - 5 q^{45} - 11 q^{47} - 8 q^{48} + 5 q^{49} + 10 q^{51} - 22 q^{52} - 19 q^{53} - q^{55} + 6 q^{56} - 3 q^{57} + 8 q^{58} + 5 q^{59} + 10 q^{60} - 17 q^{61} - 24 q^{62} - 5 q^{63} - 8 q^{64} - 12 q^{66} - 2 q^{67} - 20 q^{68} + 5 q^{69} + 10 q^{71} - 6 q^{72} - 8 q^{73} - 34 q^{74} - 5 q^{75} - 8 q^{76} - q^{77} + 14 q^{78} + 24 q^{79} - 8 q^{80} + 5 q^{81} - 8 q^{82} - 24 q^{83} + 10 q^{84} + 10 q^{85} - 10 q^{86} - 4 q^{87} - 26 q^{88} - 4 q^{89} - 10 q^{92} - 2 q^{93} + 2 q^{94} - 3 q^{95} + 12 q^{96} - 20 q^{97} + q^{99}+O(q^{100}) $ 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9 + q^11 - 10 * q^12 + 5 * q^15 + 8 * q^16 - 10 * q^17 + 3 * q^19 - 10 * q^20 + 5 * q^21 + 12 * q^22 - 5 * q^23 + 6 * q^24 + 5 * q^25 - 14 * q^26 - 5 * q^27 - 10 * q^28 + 4 * q^29 + 2 * q^31 - 12 * q^32 - q^33 + 5 * q^35 + 10 * q^36 - 4 * q^37 - 24 * q^38 + 6 * q^40 - 9 * q^41 - 8 * q^43 + 2 * q^44 - 5 * q^45 - 11 * q^47 - 8 * q^48 + 5 * q^49 + 10 * q^51 - 22 * q^52 - 19 * q^53 - q^55 + 6 * q^56 - 3 * q^57 + 8 * q^58 + 5 * q^59 + 10 * q^60 - 17 * q^61 - 24 * q^62 - 5 * q^63 - 8 * q^64 - 12 * q^66 - 2 * q^67 - 20 * q^68 + 5 * q^69 + 10 * q^71 - 6 * q^72 - 8 * q^73 - 34 * q^74 - 5 * q^75 - 8 * q^76 - q^77 + 14 * q^78 + 24 * q^79 - 8 * q^80 + 5 * q^81 - 8 * q^82 - 24 * q^83 + 10 * q^84 + 10 * q^85 - 10 * q^86 - 4 * q^87 - 26 * q^88 - 4 * q^89 - 10 * q^92 - 2 * q^93 + 2 * q^94 - 3 * q^95 + 12 * q^96 - 20 * q^97 + 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 $

$2$	−1.92367	−1.36024	−0.680122	−	0.733099i	$-0.738073\pi$
$2$	−1.92367	−1.36024	−0.680122	+	0.733099i	$0.738073\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.70052	0.850261
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.92367	0.785337
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.576096	0.203681
$9$	1.00000	0.333333
$10$	1.92367	0.608319
$11$	−5.42344	−1.63523	−0.817615	−	0.575765i	$-0.804704\pi$
$11$	−5.42344	−1.63523	−0.817615	+	0.575765i	$0.804704\pi$
$12$	−1.70052	−0.490899
$13$	2.22315	0.616591	0.308296	−	0.951291i	$-0.400241\pi$
$13$	2.22315	0.616591	0.308296	+	0.951291i	$0.400241\pi$
$14$	1.92367	0.514124
$15$	1.00000	0.258199
$16$	−4.50927	−1.12732
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.92367	−0.453414
$19$	6.85685	1.57307	0.786534	−	0.617547i	$-0.211873\pi$
$19$	6.85685	1.57307	0.786534	+	0.617547i	$0.211873\pi$
$20$	−1.70052	−0.380248
$21$	1.00000	0.218218
$22$	10.4329	2.22431
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.576096	−0.117595
$25$	1.00000	0.200000
$26$	−4.27662	−0.838714
$27$	−1.00000	−0.192450
$28$	−1.70052	−0.321369
$29$	4.49977	0.835586	0.417793	−	0.908542i	$-0.362804\pi$
$29$	4.49977	0.835586	0.417793	+	0.908542i	$0.362804\pi$
$30$	−1.92367	−0.351213
$31$	0.513131	0.0921611	0.0460806	−	0.998938i	$-0.485327\pi$
$31$	0.513131	0.0921611	0.0460806	+	0.998938i	$0.485327\pi$
$32$	7.52217	1.32974
$33$	5.42344	0.944101
$34$	3.84735	0.659815
$35$	1.00000	0.169031
$36$	1.70052	0.283420
$37$	−2.87557	−0.472741	−0.236371	−	0.971663i	$-0.575958\pi$
$37$	−2.87557	−0.472741	−0.236371	+	0.971663i	$0.575958\pi$
$38$	−13.1903	−2.13976
$39$	−2.22315	−0.355989
$40$	−0.576096	−0.0910888
$41$	−0.509726	−0.0796059	−0.0398029	−	0.999208i	$-0.512673\pi$
$41$	−0.509726	−0.0796059	−0.0398029	+	0.999208i	$0.512673\pi$
$42$	−1.92367	−0.296829
$43$	−3.71002	−0.565773	−0.282886	−	0.959153i	$-0.591292\pi$
$43$	−3.71002	−0.565773	−0.282886	+	0.959153i	$0.591292\pi$
$44$	−9.22269	−1.39037
$45$	−1.00000	−0.149071
$46$	1.92367	0.283630
$47$	1.20029	0.175081	0.0875404	−	0.996161i	$-0.472099\pi$
$47$	1.20029	0.175081	0.0875404	+	0.996161i	$0.472099\pi$
$48$	4.50927	0.650857
$49$	1.00000	0.142857
$50$	−1.92367	−0.272049
$51$	2.00000	0.280056
$52$	3.78052	0.524264
$53$	−8.82449	−1.21214	−0.606069	−	0.795412i	$-0.707254\pi$
$53$	−8.82449	−1.21214	−0.606069	+	0.795412i	$0.707254\pi$
$54$	1.92367	0.261779
$55$	5.42344	0.731297
$56$	−0.576096	−0.0769841
$57$	−6.85685	−0.908211
$58$	−8.65609	−1.13660
$59$	8.21320	1.06927	0.534634	−	0.845084i	$-0.320450\pi$
$59$	8.21320	1.06927	0.534634	+	0.845084i	$0.320450\pi$
$60$	1.70052	0.219537
$61$	2.25789	0.289093	0.144547	−	0.989498i	$-0.453828\pi$
$61$	2.25789	0.289093	0.144547	+	0.989498i	$0.453828\pi$
$62$	−0.987098	−0.125362
$63$	−1.00000	−0.125988
$64$	−5.45167	−0.681459
$65$	−2.22315	−0.275748
$66$	−10.4329	−1.28421
$67$	6.40059	0.781956	0.390978	−	0.920400i	$-0.372137\pi$
$67$	6.40059	0.781956	0.390978	+	0.920400i	$0.372137\pi$
$68$	−3.40105	−0.412437
$69$	1.00000	0.120386
$70$	−1.92367	−0.229923
$71$	14.3661	1.70494	0.852472	−	0.522773i	$-0.175102\pi$
$71$	14.3661	1.70494	0.852472	+	0.522773i	$0.175102\pi$
$72$	0.576096	0.0678936
$73$	−1.48687	−0.174025	−0.0870124	−	0.996207i	$-0.527732\pi$
$73$	−1.48687	−0.174025	−0.0870124	+	0.996207i	$0.527732\pi$
$74$	5.53167	0.643043
$75$	−1.00000	−0.115470
$76$	11.6602	1.33752
$77$	5.42344	0.618059
$78$	4.27662	0.484232
$79$	13.9713	1.57190	0.785948	−	0.618293i	$-0.212175\pi$
$79$	13.9713	1.57190	0.785948	+	0.618293i	$0.212175\pi$
$80$	4.50927	0.504151
$81$	1.00000	0.111111
$82$	0.980547	0.108283
$83$	−3.80920	−0.418114	−0.209057	−	0.977903i	$-0.567039\pi$
$83$	−3.80920	−0.418114	−0.209057	+	0.977903i	$0.567039\pi$
$84$	1.70052	0.185542
$85$	2.00000	0.216930
$86$	7.13687	0.769588
$87$	−4.49977	−0.482426
$88$	−3.12443	−0.333065
$89$	−14.2356	−1.50897	−0.754485	−	0.656317i	$-0.772113\pi$
$89$	−14.2356	−1.50897	−0.754485	+	0.656317i	$0.772113\pi$
$90$	1.92367	0.202773
$91$	−2.22315	−0.233050
$92$	−1.70052	−0.177292
$93$	−0.513131	−0.0532093
$94$	−2.30897	−0.238152
$95$	−6.85685	−0.703498
$96$	−7.52217	−0.767728
$97$	8.36611	0.849450	0.424725	−	0.905322i	$-0.360371\pi$
$97$	8.36611	0.849450	0.424725	+	0.905322i	$0.360371\pi$
$98$	−1.92367	−0.194320
$99$	−5.42344	−0.545077
$100$	1.70052	0.170052
$101$	−2.08923	−0.207886	−0.103943	−	0.994583i	$-0.533146\pi$
$101$	−2.08923	−0.207886	−0.103943	+	0.994583i	$0.533146\pi$
$102$	−3.84735	−0.380944
$103$	2.41054	0.237518	0.118759	−	0.992923i	$-0.462108\pi$
$103$	2.41054	0.237518	0.118759	+	0.992923i	$0.462108\pi$
$104$	1.28075	0.125588
$105$	−1.00000	−0.0975900
$106$	16.9754	1.64880
$107$	−11.3085	−1.09324	−0.546618	−	0.837382i	$-0.684085\pi$
$107$	−11.3085	−1.09324	−0.546618	+	0.837382i	$0.684085\pi$
$108$	−1.70052	−0.163633
$109$	−8.00367	−0.766613	−0.383306	−	0.923621i	$-0.625215\pi$
$109$	−8.00367	−0.766613	−0.383306	+	0.923621i	$0.625215\pi$
$110$	−10.4329	−0.994742
$111$	2.87557	0.272937
$112$	4.50927	0.426086
$113$	2.49100	0.234333	0.117167	−	0.993112i	$-0.462619\pi$
$113$	2.49100	0.234333	0.117167	+	0.993112i	$0.462619\pi$
$114$	13.1903	1.23539
$115$	1.00000	0.0932505
$116$	7.65196	0.710467
$117$	2.22315	0.205530
$118$	−15.7995	−1.45446
$119$	2.00000	0.183340
$120$	0.576096	0.0525902
$121$	18.4138	1.67398
$122$	−4.34345	−0.393237
$123$	0.509726	0.0459605
$124$	0.872592	0.0783611
$125$	−1.00000	−0.0894427
$126$	1.92367	0.171375
$127$	−10.5545	−0.936563	−0.468281	−	0.883579i	$-0.655127\pi$
$127$	−10.5545	−0.936563	−0.468281	+	0.883579i	$0.655127\pi$
$128$	−4.55710	−0.402795
$129$	3.71002	0.326649
$130$	4.27662	0.375084
$131$	16.1712	1.41288	0.706440	−	0.707773i	$-0.250300\pi$
$131$	16.1712	1.41288	0.706440	+	0.707773i	$0.250300\pi$
$132$	9.22269	0.802732
$133$	−6.85685	−0.594564
$134$	−12.3126	−1.06365
$135$	1.00000	0.0860663
$136$	−1.15219	−0.0987997
$137$	−20.1330	−1.72008	−0.860039	−	0.510228i	$-0.829561\pi$
$137$	−20.1330	−1.72008	−0.860039	+	0.510228i	$0.829561\pi$
$138$	−1.92367	−0.163754
$139$	8.68478	0.736633	0.368317	−	0.929700i	$-0.379934\pi$
$139$	8.68478	0.736633	0.368317	+	0.929700i	$0.379934\pi$
$140$	1.70052	0.143720
$141$	−1.20029	−0.101083
$142$	−27.6357	−2.31914
$143$	−12.0571	−1.00827
$144$	−4.50927	−0.375772
$145$	−4.49977	−0.373686
$146$	2.86025	0.236716
$147$	−1.00000	−0.0824786
$148$	−4.88998	−0.401954
$149$	−10.4019	−0.852155	−0.426077	−	0.904687i	$-0.640105\pi$
$149$	−10.4019	−0.852155	−0.426077	+	0.904687i	$0.640105\pi$
$150$	1.92367	0.157067
$151$	1.10868	0.0902231	0.0451116	−	0.998982i	$-0.485636\pi$
$151$	1.10868	0.0902231	0.0451116	+	0.998982i	$0.485636\pi$
$152$	3.95020	0.320404
$153$	−2.00000	−0.161690
$154$	−10.4329	−0.840710
$155$	−0.513131	−0.0412157
$156$	−3.78052	−0.302684
$157$	−2.45626	−0.196031	−0.0980154	−	0.995185i	$-0.531249\pi$
$157$	−2.45626	−0.196031	−0.0980154	+	0.995185i	$0.531249\pi$
$158$	−26.8763	−2.13816
$159$	8.82449	0.699828
$160$	−7.52217	−0.594680
$161$	1.00000	0.0788110
$162$	−1.92367	−0.151138
$163$	24.5088	1.91968	0.959839	−	0.280551i	$-0.0905173\pi$
$163$	24.5088	1.91968	0.959839	+	0.280551i	$0.0905173\pi$
$164$	−0.866801	−0.0676858
$165$	−5.42344	−0.422215
$166$	7.32767	0.568737
$167$	−13.6619	−1.05719	−0.528596	−	0.848874i	$-0.677281\pi$
$167$	−13.6619	−1.05719	−0.528596	+	0.848874i	$0.677281\pi$
$168$	0.576096	0.0444468
$169$	−8.05760	−0.619815
$170$	−3.84735	−0.295078
$171$	6.85685	0.524356
$172$	−6.30897	−0.481055
$173$	1.01290	0.0770095	0.0385048	−	0.999258i	$-0.487741\pi$
$173$	1.01290	0.0770095	0.0385048	+	0.999258i	$0.487741\pi$
$174$	8.65609	0.656217
$175$	−1.00000	−0.0755929
$176$	24.4558	1.84342
$177$	−8.21320	−0.617342
$178$	27.3846	2.05257
$179$	−8.99656	−0.672434	−0.336217	−	0.941784i	$-0.609148\pi$
$179$	−8.99656	−0.672434	−0.336217	+	0.941784i	$0.609148\pi$
$180$	−1.70052	−0.126749
$181$	−12.1152	−0.900515	−0.450258	−	0.892899i	$-0.648668\pi$
$181$	−12.1152	−0.900515	−0.450258	+	0.892899i	$0.648668\pi$
$182$	4.27662	0.317004
$183$	−2.25789	−0.166908
$184$	−0.576096	−0.0424704
$185$	2.87557	0.211416
$186$	0.987098	0.0723775
$187$	10.8469	0.793203
$188$	2.04113	0.148864
$189$	1.00000	0.0727393
$190$	13.1903	0.956928
$191$	−11.4893	−0.831333	−0.415667	−	0.909517i	$-0.636452\pi$
$191$	−11.4893	−0.831333	−0.415667	+	0.909517i	$0.636452\pi$
$192$	5.45167	0.393440
$193$	−22.0319	−1.58589	−0.792944	−	0.609294i	$-0.791453\pi$
$193$	−22.0319	−1.58589	−0.792944	+	0.609294i	$0.791453\pi$
$194$	−16.0937	−1.15546
$195$	2.22315	0.159203
$196$	1.70052	0.121466
$197$	−14.9004	−1.06161	−0.530803	−	0.847495i	$-0.678110\pi$
$197$	−14.9004	−1.06161	−0.530803	+	0.847495i	$0.678110\pi$
$198$	10.4329	0.741437
$199$	−14.2837	−1.01254	−0.506272	−	0.862374i	$-0.668977\pi$
$199$	−14.2837	−1.01254	−0.506272	+	0.862374i	$0.668977\pi$
$200$	0.576096	0.0407362
$201$	−6.40059	−0.451463
$202$	4.01899	0.282775
$203$	−4.49977	−0.315822
$204$	3.40105	0.238121
$205$	0.509726	0.0356008
$206$	−4.63710	−0.323082
$207$	−1.00000	−0.0695048
$208$	−10.0248	−0.695094
$209$	−37.1877	−2.57233
$210$	1.92367	0.132746
$211$	13.9366	0.959433	0.479717	−	0.877423i	$-0.340739\pi$
$211$	13.9366	0.959433	0.479717	+	0.877423i	$0.340739\pi$
$212$	−15.0062	−1.03063
$213$	−14.3661	−0.984350
$214$	21.7539	1.48707
$215$	3.71002	0.253021
$216$	−0.576096	−0.0391984
$217$	−0.513131	−0.0348336
$218$	15.3965	1.04278
$219$	1.48687	0.100473
$220$	9.22269	0.621794
$221$	−4.44630	−0.299091
$222$	−5.53167	−0.371261
$223$	−14.3853	−0.963309	−0.481654	−	0.876361i	$-0.659964\pi$
$223$	−14.3853	−0.963309	−0.481654	+	0.876361i	$0.659964\pi$
$224$	−7.52217	−0.502596
$225$	1.00000	0.0666667
$226$	−4.79187	−0.318750
$227$	−16.8926	−1.12120	−0.560601	−	0.828086i	$-0.689430\pi$
$227$	−16.8926	−1.12120	−0.560601	+	0.828086i	$0.689430\pi$
$228$	−11.6602	−0.772217
$229$	14.1418	0.934515	0.467258	−	0.884121i	$-0.345242\pi$
$229$	14.1418	0.934515	0.467258	+	0.884121i	$0.345242\pi$
$230$	−1.92367	−0.126843
$231$	−5.42344	−0.356836
$232$	2.59230	0.170193
$233$	−17.3924	−1.13941	−0.569706	−	0.821848i	$-0.692943\pi$
$233$	−17.3924	−1.13941	−0.569706	+	0.821848i	$0.692943\pi$
$234$	−4.27662	−0.279571
$235$	−1.20029	−0.0782985
$236$	13.9667	0.909157
$237$	−13.9713	−0.907535
$238$	−3.84735	−0.249387
$239$	−4.99179	−0.322892	−0.161446	−	0.986882i	$-0.551616\pi$
$239$	−4.99179	−0.322892	−0.161446	+	0.986882i	$0.551616\pi$
$240$	−4.50927	−0.291072
$241$	−16.7577	−1.07946	−0.539728	−	0.841839i	$-0.681473\pi$
$241$	−16.7577	−1.07946	−0.539728	+	0.841839i	$0.681473\pi$
$242$	−35.4221	−2.27702
$243$	−1.00000	−0.0641500
$244$	3.83960	0.245805
$245$	−1.00000	−0.0638877
$246$	−0.980547	−0.0625174
$247$	15.2438	0.969940
$248$	0.295613	0.0187715
$249$	3.80920	0.241398
$250$	1.92367	0.121664
$251$	−8.99954	−0.568046	−0.284023	−	0.958817i	$-0.591669\pi$
$251$	−8.99954	−0.568046	−0.284023	+	0.958817i	$0.591669\pi$
$252$	−1.70052	−0.107123
$253$	5.42344	0.340969
$254$	20.3035	1.27395
$255$	−2.00000	−0.125245
$256$	19.6697	1.22936
$257$	4.90835	0.306175	0.153087	−	0.988213i	$-0.451078\pi$
$257$	4.90835	0.306175	0.153087	+	0.988213i	$0.451078\pi$
$258$	−7.13687	−0.444322
$259$	2.87557	0.178679
$260$	−3.78052	−0.234458
$261$	4.49977	0.278529
$262$	−31.1080	−1.92186
$263$	11.3061	0.697166	0.348583	−	0.937278i	$-0.386663\pi$
$263$	11.3061	0.697166	0.348583	+	0.937278i	$0.386663\pi$
$264$	3.12443	0.192295
$265$	8.82449	0.542084
$266$	13.1903	0.808752
$267$	14.2356	0.871204
$268$	10.8843	0.664867
$269$	−2.72096	−0.165900	−0.0829499	−	0.996554i	$-0.526434\pi$
$269$	−2.72096	−0.165900	−0.0829499	+	0.996554i	$0.526434\pi$
$270$	−1.92367	−0.117071
$271$	−29.5849	−1.79716	−0.898578	−	0.438815i	$-0.855398\pi$
$271$	−29.5849	−1.79716	−0.898578	+	0.438815i	$0.855398\pi$
$272$	9.01854	0.546829
$273$	2.22315	0.134551
$274$	38.7293	2.33973
$275$	−5.42344	−0.327046
$276$	1.70052	0.102359
$277$	7.22243	0.433954	0.216977	−	0.976177i	$-0.430380\pi$
$277$	7.22243	0.433954	0.216977	+	0.976177i	$0.430380\pi$
$278$	−16.7067	−1.00200
$279$	0.513131	0.0307204
$280$	0.576096	0.0344283
$281$	30.2507	1.80460	0.902302	−	0.431104i	$-0.141876\pi$
$281$	30.2507	1.80460	0.902302	+	0.431104i	$0.141876\pi$
$282$	2.30897	0.137497
$283$	−18.0228	−1.07135	−0.535673	−	0.844426i	$-0.679942\pi$
$283$	−18.0228	−1.07135	−0.535673	+	0.844426i	$0.679942\pi$
$284$	24.4299	1.44965
$285$	6.85685	0.406164
$286$	23.1940	1.37149
$287$	0.509726	0.0300882
$288$	7.52217	0.443248
$289$	−13.0000	−0.764706
$290$	8.65609	0.508303
$291$	−8.36611	−0.490430
$292$	−2.52845	−0.147967
$293$	−1.62522	−0.0949462	−0.0474731	−	0.998873i	$-0.515117\pi$
$293$	−1.62522	−0.0949462	−0.0474731	+	0.998873i	$0.515117\pi$
$294$	1.92367	0.112191
$295$	−8.21320	−0.478191
$296$	−1.65661	−0.0962883
$297$	5.42344	0.314700
$298$	20.0098	1.15914
$299$	−2.22315	−0.128568
$300$	−1.70052	−0.0981797
$301$	3.71002	0.213842
$302$	−2.13274	−0.122725
$303$	2.08923	0.120023
$304$	−30.9194	−1.77335
$305$	−2.25789	−0.129286
$306$	3.84735	0.219938
$307$	−30.8048	−1.75813	−0.879063	−	0.476706i	$-0.841831\pi$
$307$	−30.8048	−1.75813	−0.879063	+	0.476706i	$0.841831\pi$
$308$	9.22269	0.525512
$309$	−2.41054	−0.137131
$310$	0.987098	0.0560634
$311$	11.1869	0.634353	0.317176	−	0.948367i	$-0.397265\pi$
$311$	11.1869	0.634353	0.317176	+	0.948367i	$0.397265\pi$
$312$	−1.28075	−0.0725082
$313$	4.18749	0.236691	0.118346	−	0.992972i	$-0.462241\pi$
$313$	4.18749	0.236691	0.118346	+	0.992972i	$0.462241\pi$
$314$	4.72504	0.266650
$315$	1.00000	0.0563436
$316$	23.7585	1.33652
$317$	−6.64169	−0.373034	−0.186517	−	0.982452i	$-0.559720\pi$
$317$	−6.64169	−0.373034	−0.186517	+	0.982452i	$0.559720\pi$
$318$	−16.9754	−0.951936
$319$	−24.4043	−1.36638
$320$	5.45167	0.304758
$321$	11.3085	0.631180
$322$	−1.92367	−0.107202
$323$	−13.7137	−0.763050
$324$	1.70052	0.0944735
$325$	2.22315	0.123318
$326$	−47.1470	−2.61123
$327$	8.00367	0.442604
$328$	−0.293651	−0.0162142
$329$	−1.20029	−0.0661743
$330$	10.4329	0.574315
$331$	−26.4903	−1.45604	−0.728021	−	0.685555i	$-0.759559\pi$
$331$	−26.4903	−1.45604	−0.728021	+	0.685555i	$0.759559\pi$
$332$	−6.47764	−0.355507
$333$	−2.87557	−0.157580
$334$	26.2811	1.43804
$335$	−6.40059	−0.349701
$336$	−4.50927	−0.246001
$337$	17.5934	0.958373	0.479187	−	0.877713i	$-0.340932\pi$
$337$	17.5934	0.958373	0.479187	+	0.877713i	$0.340932\pi$
$338$	15.5002	0.843099
$339$	−2.49100	−0.135292
$340$	3.40105	0.184448
$341$	−2.78294	−0.150705
$342$	−13.1903	−0.713252
$343$	−1.00000	−0.0539949
$344$	−2.13733	−0.115237
$345$	−1.00000	−0.0538382
$346$	−1.94849	−0.104752
$347$	26.4079	1.41765	0.708826	−	0.705383i	$-0.249225\pi$
$347$	26.4079	1.41765	0.708826	+	0.705383i	$0.249225\pi$
$348$	−7.65196	−0.410188
$349$	−33.6259	−1.79995	−0.899977	−	0.435937i	$-0.856417\pi$
$349$	−33.6259	−1.79995	−0.899977	+	0.435937i	$0.856417\pi$
$350$	1.92367	0.102825
$351$	−2.22315	−0.118663
$352$	−40.7961	−2.17444
$353$	−29.9903	−1.59622	−0.798112	−	0.602510i	$-0.794167\pi$
$353$	−29.9903	−1.59622	−0.798112	+	0.602510i	$0.794167\pi$
$354$	15.7995	0.839735
$355$	−14.3661	−0.762474
$356$	−24.2080	−1.28302
$357$	−2.00000	−0.105851
$358$	17.3065	0.914674
$359$	19.0479	1.00531	0.502655	−	0.864487i	$-0.332357\pi$
$359$	19.0479	1.00531	0.502655	+	0.864487i	$0.332357\pi$
$360$	−0.576096	−0.0303629
$361$	28.0163	1.47454
$362$	23.3057	1.22492
$363$	−18.4138	−0.966472
$364$	−3.78052	−0.198153
$365$	1.48687	0.0778263
$366$	4.34345	0.227036
$367$	−2.07023	−0.108065	−0.0540327	−	0.998539i	$-0.517208\pi$
$367$	−2.07023	−0.108065	−0.0540327	+	0.998539i	$0.517208\pi$
$368$	4.50927	0.235062
$369$	−0.509726	−0.0265353
$370$	−5.53167	−0.287578
$371$	8.82449	0.458145
$372$	−0.872592	−0.0452418
$373$	−27.9046	−1.44484	−0.722422	−	0.691452i	$-0.756971\pi$
$373$	−27.9046	−1.44484	−0.722422	+	0.691452i	$0.756971\pi$
$374$	−20.8659	−1.07895
$375$	1.00000	0.0516398
$376$	0.691485	0.0356606
$377$	10.0037	0.515215
$378$	−1.92367	−0.0989431
$379$	6.14296	0.315543	0.157771	−	0.987476i	$-0.449569\pi$
$379$	6.14296	0.315543	0.157771	+	0.987476i	$0.449569\pi$
$380$	−11.6602	−0.598157
$381$	10.5545	0.540725
$382$	22.1016	1.13082
$383$	4.33180	0.221344	0.110672	−	0.993857i	$-0.464700\pi$
$383$	4.33180	0.221344	0.110672	+	0.993857i	$0.464700\pi$
$384$	4.55710	0.232554
$385$	−5.42344	−0.276404
$386$	42.3821	2.15719
$387$	−3.71002	−0.188591
$388$	14.2268	0.722255
$389$	−14.2479	−0.722399	−0.361200	−	0.932489i	$-0.617633\pi$
$389$	−14.2479	−0.722399	−0.361200	+	0.932489i	$0.617633\pi$
$390$	−4.27662	−0.216555
$391$	2.00000	0.101144
$392$	0.576096	0.0290973
$393$	−16.1712	−0.815727
$394$	28.6634	1.44404
$395$	−13.9713	−0.702973
$396$	−9.22269	−0.463458
$397$	25.7353	1.29162	0.645810	−	0.763498i	$-0.276520\pi$
$397$	25.7353	1.29162	0.645810	+	0.763498i	$0.276520\pi$
$398$	27.4772	1.37731
$399$	6.85685	0.343272
$400$	−4.50927	−0.225463
$401$	−15.1736	−0.757732	−0.378866	−	0.925452i	$-0.623686\pi$
$401$	−15.1736	−0.757732	−0.378866	+	0.925452i	$0.623686\pi$
$402$	12.3126	0.614099
$403$	1.14077	0.0568258
$404$	−3.55278	−0.176757
$405$	−1.00000	−0.0496904
$406$	8.65609	0.429595
$407$	15.5955	0.773041
$408$	1.15219	0.0570420
$409$	−27.2589	−1.34786	−0.673932	−	0.738793i	$-0.735396\pi$
$409$	−27.2589	−1.34786	−0.673932	+	0.738793i	$0.735396\pi$
$410$	−0.980547	−0.0484258
$411$	20.1330	0.993088
$412$	4.09918	0.201952
$413$	−8.21320	−0.404145
$414$	1.92367	0.0945434
$415$	3.80920	0.186986
$416$	16.7229	0.819909
$417$	−8.68478	−0.425295
$418$	71.5371	3.49899
$419$	4.69424	0.229329	0.114664	−	0.993404i	$-0.463421\pi$
$419$	4.69424	0.229329	0.114664	+	0.993404i	$0.463421\pi$
$420$	−1.70052	−0.0829770
$421$	−4.94702	−0.241103	−0.120551	−	0.992707i	$-0.538466\pi$
$421$	−4.94702	−0.241103	−0.120551	+	0.992707i	$0.538466\pi$
$422$	−26.8094	−1.30506
$423$	1.20029	0.0583603
$424$	−5.08376	−0.246889
$425$	−2.00000	−0.0970143
$426$	27.6357	1.33896
$427$	−2.25789	−0.109267
$428$	−19.2304	−0.929536
$429$	12.0571	0.582124
$430$	−7.13687	−0.344170
$431$	4.89012	0.235549	0.117774	−	0.993040i	$-0.462424\pi$
$431$	4.89012	0.235549	0.117774	+	0.993040i	$0.462424\pi$
$432$	4.50927	0.216952
$433$	−31.1553	−1.49723	−0.748613	−	0.663007i	$-0.769280\pi$
$433$	−31.1553	−1.49723	−0.748613	+	0.663007i	$0.769280\pi$
$434$	0.987098	0.0473822
$435$	4.49977	0.215747
$436$	−13.6104	−0.651821
$437$	−6.85685	−0.328007
$438$	−2.86025	−0.136668
$439$	−21.3143	−1.01728	−0.508638	−	0.860980i	$-0.669851\pi$
$439$	−21.3143	−1.01728	−0.508638	+	0.860980i	$0.669851\pi$
$440$	3.12443	0.148951
$441$	1.00000	0.0476190
$442$	8.55324	0.406836
$443$	26.1478	1.24232	0.621161	−	0.783683i	$-0.286661\pi$
$443$	26.1478	1.24232	0.621161	+	0.783683i	$0.286661\pi$
$444$	4.88998	0.232068
$445$	14.2356	0.674832
$446$	27.6726	1.31033
$447$	10.4019	0.491992
$448$	5.45167	0.257567
$449$	36.4979	1.72244	0.861222	−	0.508229i	$-0.169700\pi$
$449$	36.4979	1.72244	0.861222	+	0.508229i	$0.169700\pi$
$450$	−1.92367	−0.0906829
$451$	2.76447	0.130174
$452$	4.23600	0.199245
$453$	−1.10868	−0.0520903
$454$	32.4959	1.52511
$455$	2.22315	0.104223
$456$	−3.95020	−0.184985
$457$	17.1386	0.801709	0.400854	−	0.916142i	$-0.368713\pi$
$457$	17.1386	0.801709	0.400854	+	0.916142i	$0.368713\pi$
$458$	−27.2042	−1.27117
$459$	2.00000	0.0933520
$460$	1.70052	0.0792873
$461$	23.9502	1.11547	0.557737	−	0.830018i	$-0.311670\pi$
$461$	23.9502	1.11547	0.557737	+	0.830018i	$0.311670\pi$
$462$	10.4329	0.485384
$463$	11.0399	0.513067	0.256534	−	0.966535i	$-0.417420\pi$
$463$	11.0399	0.513067	0.256534	+	0.966535i	$0.417420\pi$
$464$	−20.2907	−0.941971
$465$	0.513131	0.0237959
$466$	33.4573	1.54988
$467$	−20.3501	−0.941690	−0.470845	−	0.882216i	$-0.656051\pi$
$467$	−20.3501	−0.941690	−0.470845	+	0.882216i	$0.656051\pi$
$468$	3.78052	0.174755
$469$	−6.40059	−0.295552
$470$	2.30897	0.106505
$471$	2.45626	0.113178
$472$	4.73159	0.217789
$473$	20.1211	0.925169
$474$	26.8763	1.23447
$475$	6.85685	0.314614
$476$	3.40105	0.155887
$477$	−8.82449	−0.404046
$478$	9.60258	0.439212
$479$	−4.72096	−0.215706	−0.107853	−	0.994167i	$-0.534398\pi$
$479$	−4.72096	−0.215706	−0.107853	+	0.994167i	$0.534398\pi$
$480$	7.52217	0.343339
$481$	−6.39283	−0.291488
$482$	32.2363	1.46832
$483$	−1.00000	−0.0455016
$484$	31.3130	1.42332
$485$	−8.36611	−0.379886
$486$	1.92367	0.0872596
$487$	35.3055	1.59985	0.799923	−	0.600102i	$-0.204873\pi$
$487$	35.3055	1.59985	0.799923	+	0.600102i	$0.204873\pi$
$488$	1.30076	0.0588828
$489$	−24.5088	−1.10833
$490$	1.92367	0.0869027
$491$	−16.6058	−0.749409	−0.374704	−	0.927144i	$-0.622256\pi$
$491$	−16.6058	−0.749409	−0.374704	+	0.927144i	$0.622256\pi$
$492$	0.866801	0.0390784
$493$	−8.99954	−0.405319
$494$	−29.3241	−1.31935
$495$	5.42344	0.243766
$496$	−2.31385	−0.103895
$497$	−14.3661	−0.644408
$498$	−7.32767	−0.328361
$499$	−2.30439	−0.103158	−0.0515792	−	0.998669i	$-0.516425\pi$
$499$	−2.30439	−0.103158	−0.0515792	+	0.998669i	$0.516425\pi$
$500$	−1.70052	−0.0760497
$501$	13.6619	0.610370
$502$	17.3122	0.772681
$503$	0.449466	0.0200407	0.0100204	−	0.999950i	$-0.496810\pi$
$503$	0.449466	0.0200407	0.0100204	+	0.999950i	$0.496810\pi$
$504$	−0.576096	−0.0256614
$505$	2.08923	0.0929694
$506$	−10.4329	−0.463801
$507$	8.05760	0.357850
$508$	−17.9482	−0.796323
$509$	16.3255	0.723616	0.361808	−	0.932253i	$-0.382160\pi$
$509$	16.3255	0.723616	0.361808	+	0.932253i	$0.382160\pi$
$510$	3.84735	0.170363
$511$	1.48687	0.0657752
$512$	−28.7239	−1.26943
$513$	−6.85685	−0.302737
$514$	−9.44207	−0.416472
$515$	−2.41054	−0.106221
$516$	6.30897	0.277737
$517$	−6.50973	−0.286297
$518$	−5.53167	−0.243047
$519$	−1.01290	−0.0444615
$520$	−1.28075	−0.0561646
$521$	24.8660	1.08940	0.544701	−	0.838631i	$-0.316643\pi$
$521$	24.8660	1.08940	0.544701	+	0.838631i	$0.316643\pi$
$522$	−8.65609	−0.378867
$523$	2.78831	0.121924	0.0609621	−	0.998140i	$-0.480583\pi$
$523$	2.78831	0.121924	0.0609621	+	0.998140i	$0.480583\pi$
$524$	27.4994	1.20132
$525$	1.00000	0.0436436
$526$	−21.7493	−0.948315
$527$	−1.02626	−0.0447047
$528$	−24.4558	−1.06430
$529$	1.00000	0.0434783
$530$	−16.9754	−0.737366
$531$	8.21320	0.356422
$532$	−11.6602	−0.505535
$533$	−1.13320	−0.0490843
$534$	−27.3846	−1.18505
$535$	11.3085	0.488910
$536$	3.68735	0.159269
$537$	8.99656	0.388230
$538$	5.23424	0.225664
$539$	−5.42344	−0.233604
$540$	1.70052	0.0731789
$541$	−39.6952	−1.70663	−0.853315	−	0.521395i	$-0.825412\pi$
$541$	−39.6952	−1.70663	−0.853315	+	0.521395i	$0.825412\pi$
$542$	56.9117	2.44457
$543$	12.1152	0.519913
$544$	−15.0443	−0.645021
$545$	8.00367	0.342840
$546$	−4.27662	−0.183022
$547$	35.8341	1.53216	0.766078	−	0.642748i	$-0.222206\pi$
$547$	35.8341	1.53216	0.766078	+	0.642748i	$0.222206\pi$
$548$	−34.2366	−1.46252
$549$	2.25789	0.0963645
$550$	10.4329	0.444862
$551$	30.8542	1.31443
$552$	0.576096	0.0245203
$553$	−13.9713	−0.594121
$554$	−13.8936	−0.590282
$555$	−2.87557	−0.122061
$556$	14.7687	0.626331
$557$	−10.2118	−0.432686	−0.216343	−	0.976317i	$-0.569413\pi$
$557$	−10.2118	−0.432686	−0.216343	+	0.976317i	$0.569413\pi$
$558$	−0.987098	−0.0417872
$559$	−8.24794	−0.348851
$560$	−4.50927	−0.190551
$561$	−10.8469	−0.457956
$562$	−58.1925	−2.45470
$563$	−22.7507	−0.958827	−0.479414	−	0.877589i	$-0.659151\pi$
$563$	−22.7507	−0.958827	−0.479414	+	0.877589i	$0.659151\pi$
$564$	−2.04113	−0.0859469
$565$	−2.49100	−0.104797
$566$	34.6700	1.45729
$567$	−1.00000	−0.0419961
$568$	8.27626	0.347264
$569$	−20.4830	−0.858692	−0.429346	−	0.903140i	$-0.641256\pi$
$569$	−20.4830	−0.858692	−0.429346	+	0.903140i	$0.641256\pi$
$570$	−13.1903	−0.552482
$571$	−22.1571	−0.927246	−0.463623	−	0.886032i	$-0.653451\pi$
$571$	−22.1571	−0.927246	−0.463623	+	0.886032i	$0.653451\pi$
$572$	−20.5034	−0.857292
$573$	11.4893	0.479970
$574$	−0.980547	−0.0409273
$575$	−1.00000	−0.0417029
$576$	−5.45167	−0.227153
$577$	12.6331	0.525923	0.262961	−	0.964806i	$-0.415301\pi$
$577$	12.6331	0.525923	0.262961	+	0.964806i	$0.415301\pi$
$578$	25.0078	1.04019
$579$	22.0319	0.915613
$580$	−7.65196	−0.317730
$581$	3.80920	0.158032
$582$	16.0937	0.667104
$583$	47.8591	1.98212
$584$	−0.856579	−0.0354455
$585$	−2.22315	−0.0919160
$586$	3.12639	0.129150
$587$	24.6745	1.01843	0.509213	−	0.860641i	$-0.329937\pi$
$587$	24.6745	1.01843	0.509213	+	0.860641i	$0.329937\pi$
$588$	−1.70052	−0.0701284
$589$	3.51846	0.144976
$590$	15.7995	0.650456
$591$	14.9004	0.612919
$592$	12.9667	0.532929
$593$	−9.95232	−0.408693	−0.204346	−	0.978899i	$-0.565507\pi$
$593$	−9.95232	−0.408693	−0.204346	+	0.978899i	$0.565507\pi$
$594$	−10.4329	−0.428069
$595$	−2.00000	−0.0819920
$596$	−17.6886	−0.724554
$597$	14.2837	0.584593
$598$	4.27662	0.174884
$599$	−14.4691	−0.591192	−0.295596	−	0.955313i	$-0.595518\pi$
$599$	−14.4691	−0.591192	−0.295596	+	0.955313i	$0.595518\pi$
$600$	−0.576096	−0.0235190
$601$	−10.4417	−0.425926	−0.212963	−	0.977060i	$-0.568311\pi$
$601$	−10.4417	−0.425926	−0.212963	+	0.977060i	$0.568311\pi$
$602$	−7.13687	−0.290877
$603$	6.40059	0.260652
$604$	1.88534	0.0767133
$605$	−18.4138	−0.748626
$606$	−4.01899	−0.163260
$607$	−4.86111	−0.197306	−0.0986532	−	0.995122i	$-0.531453\pi$
$607$	−4.86111	−0.197306	−0.0986532	+	0.995122i	$0.531453\pi$
$608$	51.5784	2.09178
$609$	4.49977	0.182340
$610$	4.34345	0.175861
$611$	2.66843	0.107953
$612$	−3.40105	−0.137479
$613$	−12.4866	−0.504328	−0.252164	−	0.967685i	$-0.581142\pi$
$613$	−12.4866	−0.504328	−0.252164	+	0.967685i	$0.581142\pi$
$614$	59.2585	2.39148
$615$	−0.509726	−0.0205541
$616$	3.12443	0.125887
$617$	32.2716	1.29921	0.649603	−	0.760273i	$-0.274935\pi$
$617$	32.2716	1.29921	0.649603	+	0.760273i	$0.274935\pi$
$618$	4.63710	0.186531
$619$	22.1051	0.888478	0.444239	−	0.895908i	$-0.353474\pi$
$619$	22.1051	0.888478	0.444239	+	0.895908i	$0.353474\pi$
$620$	−0.872592	−0.0350441
$621$	1.00000	0.0401286
$622$	−21.5200	−0.862874
$623$	14.2356	0.570337
$624$	10.0248	0.401313
$625$	1.00000	0.0400000
$626$	−8.05537	−0.321958
$627$	37.1877	1.48513
$628$	−4.17692	−0.166677
$629$	5.75115	0.229313
$630$	−1.92367	−0.0766410
$631$	32.4394	1.29139	0.645695	−	0.763595i	$-0.276568\pi$
$631$	32.4394	1.29139	0.645695	+	0.763595i	$0.276568\pi$
$632$	8.04882	0.320165
$633$	−13.9366	−0.553929
$634$	12.7764	0.507417
$635$	10.5545	0.418844
$636$	15.0062	0.595036
$637$	2.22315	0.0880845
$638$	46.9458	1.85860
$639$	14.3661	0.568315
$640$	4.55710	0.180135
$641$	−28.5418	−1.12733	−0.563666	−	0.826003i	$-0.690609\pi$
$641$	−28.5418	−1.12733	−0.563666	+	0.826003i	$0.690609\pi$
$642$	−21.7539	−0.858558
$643$	−29.5127	−1.16387	−0.581934	−	0.813236i	$-0.697704\pi$
$643$	−29.5127	−1.16387	−0.581934	+	0.813236i	$0.697704\pi$
$644$	1.70052	0.0670100
$645$	−3.71002	−0.146082
$646$	26.3807	1.03793
$647$	47.3915	1.86315	0.931576	−	0.363547i	$-0.118434\pi$
$647$	47.3915	1.86315	0.931576	+	0.363547i	$0.118434\pi$
$648$	0.576096	0.0226312
$649$	−44.5438	−1.74850
$650$	−4.27662	−0.167743
$651$	0.513131	0.0201112
$652$	41.6778	1.63223
$653$	41.8241	1.63670	0.818351	−	0.574718i	$-0.194888\pi$
$653$	41.8241	1.63670	0.818351	+	0.574718i	$0.194888\pi$
$654$	−15.3965	−0.602049
$655$	−16.1712	−0.631859
$656$	2.29849	0.0897410
$657$	−1.48687	−0.0580083
$658$	2.30897	0.0900132
$659$	24.3749	0.949511	0.474755	−	0.880118i	$-0.342537\pi$
$659$	24.3749	0.949511	0.474755	+	0.880118i	$0.342537\pi$
$660$	−9.22269	−0.358993
$661$	28.0708	1.09183	0.545913	−	0.837842i	$-0.316183\pi$
$661$	28.0708	1.09183	0.545913	+	0.837842i	$0.316183\pi$
$662$	50.9588	1.98057
$663$	4.44630	0.172680
$664$	−2.19447	−0.0851619
$665$	6.85685	0.265897
$666$	5.53167	0.214348
$667$	−4.49977	−0.174232
$668$	−23.2324	−0.898889
$669$	14.3853	0.556166
$670$	12.3126	0.475679
$671$	−12.2456	−0.472734
$672$	7.52217	0.290174
$673$	−1.26133	−0.0486208	−0.0243104	−	0.999704i	$-0.507739\pi$
$673$	−1.26133	−0.0486208	−0.0243104	+	0.999704i	$0.507739\pi$
$674$	−33.8440	−1.30362
$675$	−1.00000	−0.0384900
$676$	−13.7021	−0.527005
$677$	5.15954	0.198297	0.0991485	−	0.995073i	$-0.468388\pi$
$677$	5.15954	0.198297	0.0991485	+	0.995073i	$0.468388\pi$
$678$	4.79187	0.184031
$679$	−8.36611	−0.321062
$680$	1.15219	0.0441846
$681$	16.8926	0.647326
$682$	5.35347	0.204995
$683$	32.6616	1.24976	0.624880	−	0.780721i	$-0.285148\pi$
$683$	32.6616	1.24976	0.624880	+	0.780721i	$0.285148\pi$
$684$	11.6602	0.445840
$685$	20.1330	0.769243
$686$	1.92367	0.0734462
$687$	−14.1418	−0.539542
$688$	16.7295	0.637805
$689$	−19.6182	−0.747393
$690$	1.92367	0.0732330
$691$	−39.2873	−1.49456	−0.747280	−	0.664509i	$-0.768641\pi$
$691$	−39.2873	−1.49456	−0.747280	+	0.664509i	$0.768641\pi$
$692$	1.72246	0.0654782
$693$	5.42344	0.206020
$694$	−50.8003	−1.92835
$695$	−8.68478	−0.329432
$696$	−2.59230	−0.0982609
$697$	1.01945	0.0386145
$698$	64.6853	2.44838
$699$	17.3924	0.657840
$700$	−1.70052	−0.0642737
$701$	18.7412	0.707847	0.353923	−	0.935274i	$-0.384847\pi$
$701$	18.7412	0.707847	0.353923	+	0.935274i	$0.384847\pi$
$702$	4.27662	0.161411
$703$	−19.7174	−0.743654
$704$	29.5668	1.11434
$705$	1.20029	0.0452057
$706$	57.6916	2.17125
$707$	2.08923	0.0785735
$708$	−13.9667	−0.524902
$709$	−14.9354	−0.560909	−0.280455	−	0.959867i	$-0.590485\pi$
$709$	−14.9354	−0.560909	−0.280455	+	0.959867i	$0.590485\pi$
$710$	27.6357	1.03715
$711$	13.9713	0.523965
$712$	−8.20107	−0.307348
$713$	−0.513131	−0.0192169
$714$	3.84735	0.143983
$715$	12.0571	0.450911
$716$	−15.2989	−0.571745
$717$	4.99179	0.186422
$718$	−36.6420	−1.36747
$719$	−38.9021	−1.45080	−0.725402	−	0.688326i	$-0.758346\pi$
$719$	−38.9021	−1.45080	−0.725402	+	0.688326i	$0.758346\pi$
$720$	4.50927	0.168050
$721$	−2.41054	−0.0897733
$722$	−53.8943	−2.00574
$723$	16.7577	0.623224
$724$	−20.6022	−0.765674
$725$	4.49977	0.167117
$726$	35.4221	1.31464
$727$	−33.9249	−1.25821	−0.629103	−	0.777322i	$-0.716578\pi$
$727$	−33.9249	−1.25821	−0.629103	+	0.777322i	$0.716578\pi$
$728$	−1.28075	−0.0474677
$729$	1.00000	0.0370370
$730$	−2.86025	−0.105863
$731$	7.42004	0.274440
$732$	−3.83960	−0.141916
$733$	−17.6062	−0.650302	−0.325151	−	0.945662i	$-0.605415\pi$
$733$	−17.6062	−0.650302	−0.325151	+	0.945662i	$0.605415\pi$
$734$	3.98246	0.146995
$735$	1.00000	0.0368856
$736$	−7.52217	−0.277271
$737$	−34.7132	−1.27868
$738$	0.980547	0.0360944
$739$	44.4269	1.63427	0.817135	−	0.576446i	$-0.195561\pi$
$739$	44.4269	1.63427	0.817135	+	0.576446i	$0.195561\pi$
$740$	4.88998	0.179759
$741$	−15.2438	−0.559995
$742$	−16.9754	−0.623188
$743$	−37.8431	−1.38833	−0.694165	−	0.719816i	$-0.744226\pi$
$743$	−37.8431	−1.38833	−0.694165	+	0.719816i	$0.744226\pi$
$744$	−0.295613	−0.0108377
$745$	10.4019	0.381095
$746$	53.6793	1.96534
$747$	−3.80920	−0.139371
$748$	18.4454	0.674430
$749$	11.3085	0.413204
$750$	−1.92367	−0.0702427
$751$	−32.7961	−1.19675	−0.598373	−	0.801218i	$-0.704186\pi$
$751$	−32.7961	−1.19675	−0.598373	+	0.801218i	$0.704186\pi$
$752$	−5.41245	−0.197372
$753$	8.99954	0.327962
$754$	−19.2438	−0.700818
$755$	−1.10868	−0.0403490
$756$	1.70052	0.0618474
$757$	14.8114	0.538329	0.269165	−	0.963094i	$-0.413252\pi$
$757$	14.8114	0.538329	0.269165	+	0.963094i	$0.413252\pi$
$758$	−11.8171	−0.429215
$759$	−5.42344	−0.196859
$760$	−3.95020	−0.143289
$761$	47.5719	1.72448	0.862240	−	0.506500i	$-0.169061\pi$
$761$	47.5719	1.72448	0.862240	+	0.506500i	$0.169061\pi$
$762$	−20.3035	−0.735517
$763$	8.00367	0.289752
$764$	−19.5377	−0.706851
$765$	2.00000	0.0723102
$766$	−8.33297	−0.301082
$767$	18.2592	0.659301
$768$	−19.6697	−0.709770
$769$	23.1177	0.833647	0.416824	−	0.908987i	$-0.363143\pi$
$769$	23.1177	0.833647	0.416824	+	0.908987i	$0.363143\pi$
$770$	10.4329	0.375977
$771$	−4.90835	−0.176770
$772$	−37.4657	−1.34842
$773$	28.3812	1.02080	0.510401	−	0.859937i	$-0.329497\pi$
$773$	28.3812	1.02080	0.510401	+	0.859937i	$0.329497\pi$
$774$	7.13687	0.256529
$775$	0.513131	0.0184322
$776$	4.81969	0.173017
$777$	−2.87557	−0.103161
$778$	27.4084	0.982638
$779$	−3.49511	−0.125225
$780$	3.78052	0.135364
$781$	−77.9138	−2.78798
$782$	−3.84735	−0.137581
$783$	−4.49977	−0.160809
$784$	−4.50927	−0.161045
$785$	2.45626	0.0876676
$786$	31.1080	1.10959
$787$	12.5947	0.448952	0.224476	−	0.974480i	$-0.427933\pi$
$787$	12.5947	0.448952	0.224476	+	0.974480i	$0.427933\pi$
$788$	−25.3384	−0.902643
$789$	−11.3061	−0.402509
$790$	26.8763	0.956215
$791$	−2.49100	−0.0885697
$792$	−3.12443	−0.111022
$793$	5.01963	0.178252
$794$	−49.5064	−1.75692
$795$	−8.82449	−0.312972
$796$	−24.2898	−0.860927
$797$	−23.3496	−0.827087	−0.413543	−	0.910484i	$-0.635709\pi$
$797$	−23.3496	−0.827087	−0.413543	+	0.910484i	$0.635709\pi$
$798$	−13.1903	−0.466933
$799$	−2.40059	−0.0849267
$800$	7.52217	0.265949
$801$	−14.2356	−0.502990
$802$	29.1890	1.03070
$803$	8.06395	0.284571
$804$	−10.8843	−0.383861
$805$	−1.00000	−0.0352454
$806$	−2.19447	−0.0772968
$807$	2.72096	0.0957823
$808$	−1.20360	−0.0423424
$809$	−31.1453	−1.09501	−0.547505	−	0.836802i	$-0.684422\pi$
$809$	−31.1453	−1.09501	−0.547505	+	0.836802i	$0.684422\pi$
$810$	1.92367	0.0675910
$811$	−13.2746	−0.466135	−0.233068	−	0.972461i	$-0.574876\pi$
$811$	−13.2746	−0.466135	−0.233068	+	0.972461i	$0.574876\pi$
$812$	−7.65196	−0.268531
$813$	29.5849	1.03759
$814$	−30.0007	−1.05152
$815$	−24.5088	−0.858506
$816$	−9.01854	−0.315712
$817$	−25.4390	−0.889999
$818$	52.4372	1.83342
$819$	−2.22315	−0.0776832
$820$	0.866801	0.0302700
$821$	37.2251	1.29916	0.649582	−	0.760291i	$-0.274944\pi$
$821$	37.2251	1.29916	0.649582	+	0.760291i	$0.274944\pi$
$822$	−38.7293	−1.35084
$823$	−36.7717	−1.28178	−0.640890	−	0.767633i	$-0.721434\pi$
$823$	−36.7717	−1.28178	−0.640890	+	0.767633i	$0.721434\pi$
$824$	1.38870	0.0483778
$825$	5.42344	0.188820
$826$	15.7995	0.549735
$827$	−14.7778	−0.513873	−0.256936	−	0.966428i	$-0.582713\pi$
$827$	−14.7778	−0.513873	−0.256936	+	0.966428i	$0.582713\pi$
$828$	−1.70052	−0.0590973
$829$	−18.1364	−0.629904	−0.314952	−	0.949108i	$-0.601988\pi$
$829$	−18.1364	−0.629904	−0.314952	+	0.949108i	$0.601988\pi$
$830$	−7.32767	−0.254347
$831$	−7.22243	−0.250543
$832$	−12.1199	−0.420181
$833$	−2.00000	−0.0692959
$834$	16.7067	0.578505
$835$	13.6619	0.472790
$836$	−63.2386	−2.18715
$837$	−0.513131	−0.0177364
$838$	−9.03019	−0.311943
$839$	−51.1737	−1.76671	−0.883356	−	0.468703i	$-0.844722\pi$
$839$	−51.1737	−1.76671	−0.883356	+	0.468703i	$0.844722\pi$
$840$	−0.576096	−0.0198772
$841$	−8.75206	−0.301795
$842$	9.51645	0.327958
$843$	−30.2507	−1.04189
$844$	23.6995	0.815769
$845$	8.05760	0.277190
$846$	−2.30897	−0.0793842
$847$	−18.4138	−0.632704
$848$	39.7920	1.36646
$849$	18.0228	0.618542
$850$	3.84735	0.131963
$851$	2.87557	0.0985734
$852$	−24.4299	−0.836955
$853$	54.9377	1.88103	0.940515	−	0.339751i	$-0.110343\pi$
$853$	54.9377	1.88103	0.940515	+	0.339751i	$0.110343\pi$
$854$	4.34345	0.148630
$855$	−6.85685	−0.234499
$856$	−6.51479	−0.222671
$857$	−36.3465	−1.24157	−0.620786	−	0.783980i	$-0.713186\pi$
$857$	−36.3465	−1.24157	−0.620786	+	0.783980i	$0.713186\pi$
$858$	−23.1940	−0.791830
$859$	−4.25059	−0.145028	−0.0725141	−	0.997367i	$-0.523102\pi$
$859$	−4.25059	−0.145028	−0.0725141	+	0.997367i	$0.523102\pi$
$860$	6.30897	0.215134
$861$	−0.509726	−0.0173714
$862$	−9.40699	−0.320403
$863$	−15.8723	−0.540300	−0.270150	−	0.962818i	$-0.587073\pi$
$863$	−15.8723	−0.540300	−0.270150	+	0.962818i	$0.587073\pi$
$864$	−7.52217	−0.255909
$865$	−1.01290	−0.0344397
$866$	59.9326	2.03659
$867$	13.0000	0.441503
$868$	−0.872592	−0.0296177
$869$	−75.7727	−2.57041
$870$	−8.65609	−0.293469
$871$	14.2295	0.482147
$872$	−4.61089	−0.156144
$873$	8.36611	0.283150
$874$	13.1903	0.446170
$875$	1.00000	0.0338062
$876$	2.52845	0.0854285
$877$	5.33762	0.180239	0.0901194	−	0.995931i	$-0.471275\pi$
$877$	5.33762	0.180239	0.0901194	+	0.995931i	$0.471275\pi$
$878$	41.0018	1.38374
$879$	1.62522	0.0548172
$880$	−24.4558	−0.824404
$881$	18.1211	0.610515	0.305257	−	0.952270i	$-0.401257\pi$
$881$	18.1211	0.610515	0.305257	+	0.952270i	$0.401257\pi$
$882$	−1.92367	−0.0647735
$883$	−3.10921	−0.104633	−0.0523166	−	0.998631i	$-0.516660\pi$
$883$	−3.10921	−0.104633	−0.0523166	+	0.998631i	$0.516660\pi$
$884$	−7.56104	−0.254305
$885$	8.21320	0.276084
$886$	−50.2999	−1.68986
$887$	−4.21846	−0.141642	−0.0708210	−	0.997489i	$-0.522562\pi$
$887$	−4.21846	−0.141642	−0.0708210	+	0.997489i	$0.522562\pi$
$888$	1.65661	0.0555921
$889$	10.5545	0.353987
$890$	−27.3846	−0.917935
$891$	−5.42344	−0.181692
$892$	−24.4625	−0.819064
$893$	8.23023	0.275414
$894$	−20.0098	−0.669228
$895$	8.99656	0.300722
$896$	4.55710	0.152242
$897$	2.22315	0.0742289
$898$	−70.2101	−2.34294
$899$	2.30897	0.0770086
$900$	1.70052	0.0566841
$901$	17.6490	0.587973
$902$	−5.31794	−0.177068
$903$	−3.71002	−0.123462
$904$	1.43506	0.0477292
$905$	12.1152	0.402723
$906$	2.13274	0.0708555
$907$	4.97282	0.165120	0.0825599	−	0.996586i	$-0.473690\pi$
$907$	4.97282	0.165120	0.0825599	+	0.996586i	$0.473690\pi$
$908$	−28.7263	−0.953315
$909$	−2.08923	−0.0692953
$910$	−4.27662	−0.141769
$911$	−44.0386	−1.45906	−0.729532	−	0.683946i	$-0.760262\pi$
$911$	−44.0386	−1.45906	−0.729532	+	0.683946i	$0.760262\pi$
$912$	30.9194	1.02384
$913$	20.6590	0.683713
$914$	−32.9690	−1.09052
$915$	2.25789	0.0746436
$916$	24.0484	0.794582
$917$	−16.1712	−0.534018
$918$	−3.84735	−0.126981
$919$	43.3596	1.43030	0.715151	−	0.698970i	$-0.246358\pi$
$919$	43.3596	1.43030	0.715151	+	0.698970i	$0.246358\pi$
$920$	0.576096	0.0189933
$921$	30.8048	1.01505
$922$	−46.0724	−1.51731
$923$	31.9380	1.05125
$924$	−9.22269	−0.303404
$925$	−2.87557	−0.0945483
$926$	−21.2372	−0.697896
$927$	2.41054	0.0791726
$928$	33.8480	1.11112
$929$	−35.5707	−1.16704	−0.583518	−	0.812100i	$-0.698324\pi$
$929$	−35.5707	−1.16704	−0.583518	+	0.812100i	$0.698324\pi$
$930$	−0.987098	−0.0323682
$931$	6.85685	0.224724
$932$	−29.5761	−0.968799
$933$	−11.1869	−0.366244
$934$	39.1470	1.28093
$935$	−10.8469	−0.354731
$936$	1.28075	0.0418626
$937$	31.7839	1.03834	0.519168	−	0.854672i	$-0.326242\pi$
$937$	31.7839	1.03834	0.519168	+	0.854672i	$0.326242\pi$
$938$	12.3126	0.402022
$939$	−4.18749	−0.136654
$940$	−2.04113	−0.0665742
$941$	52.0775	1.69768	0.848839	−	0.528651i	$-0.177302\pi$
$941$	52.0775	1.69768	0.848839	+	0.528651i	$0.177302\pi$
$942$	−4.72504	−0.153950
$943$	0.509726	0.0165990
$944$	−37.0355	−1.20540
$945$	−1.00000	−0.0325300
$946$	−38.7064	−1.25845
$947$	−10.4151	−0.338447	−0.169223	−	0.985578i	$-0.554126\pi$
$947$	−10.4151	−0.338447	−0.169223	+	0.985578i	$0.554126\pi$
$948$	−23.7585	−0.771642
$949$	−3.30553	−0.107302
$950$	−13.1903	−0.427951
$951$	6.64169	0.215371
$952$	1.15219	0.0373428
$953$	−50.0252	−1.62047	−0.810237	−	0.586103i	$-0.800662\pi$
$953$	−50.0252	−1.62047	−0.810237	+	0.586103i	$0.800662\pi$
$954$	16.9754	0.549600
$955$	11.4893	0.371784
$956$	−8.48865	−0.274543
$957$	24.4043	0.788878
$958$	9.08159	0.293413
$959$	20.1330	0.650129
$960$	−5.45167	−0.175952
$961$	−30.7367	−0.991506
$962$	12.2977	0.396495
$963$	−11.3085	−0.364412
$964$	−28.4968	−0.917820
$965$	22.0319	0.709231
$966$	1.92367	0.0618932
$967$	−26.5464	−0.853673	−0.426837	−	0.904329i	$-0.640372\pi$
$967$	−26.5464	−0.853673	−0.426837	+	0.904329i	$0.640372\pi$
$968$	10.6081	0.340957
$969$	13.7137	0.440547
$970$	16.0937	0.516737
$971$	−42.2203	−1.35491	−0.677457	−	0.735562i	$-0.736918\pi$
$971$	−42.2203	−1.35491	−0.677457	+	0.735562i	$0.736918\pi$
$972$	−1.70052	−0.0545443
$973$	−8.68478	−0.278421
$974$	−67.9163	−2.17618
$975$	−2.22315	−0.0711978
$976$	−10.1814	−0.325900
$977$	−12.2333	−0.391377	−0.195688	−	0.980666i	$-0.562694\pi$
$977$	−12.2333	−0.391377	−0.195688	+	0.980666i	$0.562694\pi$
$978$	47.1470	1.50759
$979$	77.2060	2.46751
$980$	−1.70052	−0.0543212
$981$	−8.00367	−0.255538
$982$	31.9441	1.01938
$983$	−48.8515	−1.55812	−0.779060	−	0.626949i	$-0.784304\pi$
$983$	−48.8515	−1.55812	−0.779060	+	0.626949i	$0.784304\pi$
$984$	0.293651	0.00936127
$985$	14.9004	0.474765
$986$	17.3122	0.551332
$987$	1.20029	0.0382058
$988$	25.9224	0.824703
$989$	3.71002	0.117972
$990$	−10.4329	−0.331581
$991$	55.8555	1.77431	0.887154	−	0.461473i	$-0.152679\pi$
$991$	55.8555	1.77431	0.887154	+	0.461473i	$0.152679\pi$
$992$	3.85986	0.122551
$993$	26.4903	0.840646
$994$	27.6357	0.876552
$995$	14.2837	0.452824
$996$	6.47764	0.205252
$997$	−53.1825	−1.68431	−0.842153	−	0.539238i	$-0.818712\pi$
$997$	−53.1825	−1.68431	−0.842153	+	0.539238i	$0.818712\pi$
$998$	4.43289	0.140321
$999$	2.87557	0.0909791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.o.1.2	✓	5
3.2	odd	2		7245.2.a.bg.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.o.1.2	✓	5	1.1	even	1	trivial
7245.2.a.bg.1.4		5	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)

\(f(q)\)	\(=\)	\(q-1.92367 q^{2} -1.00000 q^{3} +1.70052 q^{4} -1.00000 q^{5} +1.92367 q^{6} -1.00000 q^{7} +0.576096 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.92367 q^{2} -1.00000 q^{3} +1.70052 q^{4} -1.00000 q^{5} +1.92367 q^{6} -1.00000 q^{7} +0.576096 q^{8} +1.00000 q^{9} +1.92367 q^{10} -5.42344 q^{11} -1.70052 q^{12} +2.22315 q^{13} +1.92367 q^{14} +1.00000 q^{15} -4.50927 q^{16} -2.00000 q^{17} -1.92367 q^{18} +6.85685 q^{19} -1.70052 q^{20} +1.00000 q^{21} +10.4329 q^{22} -1.00000 q^{23} -0.576096 q^{24} +1.00000 q^{25} -4.27662 q^{26} -1.00000 q^{27} -1.70052 q^{28} +4.49977 q^{29} -1.92367 q^{30} +0.513131 q^{31} +7.52217 q^{32} +5.42344 q^{33} +3.84735 q^{34} +1.00000 q^{35} +1.70052 q^{36} -2.87557 q^{37} -13.1903 q^{38} -2.22315 q^{39} -0.576096 q^{40} -0.509726 q^{41} -1.92367 q^{42} -3.71002 q^{43} -9.22269 q^{44} -1.00000 q^{45} +1.92367 q^{46} +1.20029 q^{47} +4.50927 q^{48} +1.00000 q^{49} -1.92367 q^{50} +2.00000 q^{51} +3.78052 q^{52} -8.82449 q^{53} +1.92367 q^{54} +5.42344 q^{55} -0.576096 q^{56} -6.85685 q^{57} -8.65609 q^{58} +8.21320 q^{59} +1.70052 q^{60} +2.25789 q^{61} -0.987098 q^{62} -1.00000 q^{63} -5.45167 q^{64} -2.22315 q^{65} -10.4329 q^{66} +6.40059 q^{67} -3.40105 q^{68} +1.00000 q^{69} -1.92367 q^{70} +14.3661 q^{71} +0.576096 q^{72} -1.48687 q^{73} +5.53167 q^{74} -1.00000 q^{75} +11.6602 q^{76} +5.42344 q^{77} +4.27662 q^{78} +13.9713 q^{79} +4.50927 q^{80} +1.00000 q^{81} +0.980547 q^{82} -3.80920 q^{83} +1.70052 q^{84} +2.00000 q^{85} +7.13687 q^{86} -4.49977 q^{87} -3.12443 q^{88} -14.2356 q^{89} +1.92367 q^{90} -2.22315 q^{91} -1.70052 q^{92} -0.513131 q^{93} -2.30897 q^{94} -6.85685 q^{95} -7.52217 q^{96} +8.36611 q^{97} -1.92367 q^{98} -5.42344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9} + q^{11} - 10 q^{12} + 5 q^{15} + 8 q^{16} - 10 q^{17} + 3 q^{19} - 10 q^{20} + 5 q^{21} + 12 q^{22} - 5 q^{23} + 6 q^{24} + 5 q^{25} - 14 q^{26} - 5 q^{27} - 10 q^{28} + 4 q^{29} + 2 q^{31} - 12 q^{32} - q^{33} + 5 q^{35} + 10 q^{36} - 4 q^{37} - 24 q^{38} + 6 q^{40} - 9 q^{41} - 8 q^{43} + 2 q^{44} - 5 q^{45} - 11 q^{47} - 8 q^{48} + 5 q^{49} + 10 q^{51} - 22 q^{52} - 19 q^{53} - q^{55} + 6 q^{56} - 3 q^{57} + 8 q^{58} + 5 q^{59} + 10 q^{60} - 17 q^{61} - 24 q^{62} - 5 q^{63} - 8 q^{64} - 12 q^{66} - 2 q^{67} - 20 q^{68} + 5 q^{69} + 10 q^{71} - 6 q^{72} - 8 q^{73} - 34 q^{74} - 5 q^{75} - 8 q^{76} - q^{77} + 14 q^{78} + 24 q^{79} - 8 q^{80} + 5 q^{81} - 8 q^{82} - 24 q^{83} + 10 q^{84} + 10 q^{85} - 10 q^{86} - 4 q^{87} - 26 q^{88} - 4 q^{89} - 10 q^{92} - 2 q^{93} + 2 q^{94} - 3 q^{95} + 12 q^{96} - 20 q^{97} + q^{99}+O(q^{100}) \) 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9 + q^11 - 10 * q^12 + 5 * q^15 + 8 * q^16 - 10 * q^17 + 3 * q^19 - 10 * q^20 + 5 * q^21 + 12 * q^22 - 5 * q^23 + 6 * q^24 + 5 * q^25 - 14 * q^26 - 5 * q^27 - 10 * q^28 + 4 * q^29 + 2 * q^31 - 12 * q^32 - q^33 + 5 * q^35 + 10 * q^36 - 4 * q^37 - 24 * q^38 + 6 * q^40 - 9 * q^41 - 8 * q^43 + 2 * q^44 - 5 * q^45 - 11 * q^47 - 8 * q^48 + 5 * q^49 + 10 * q^51 - 22 * q^52 - 19 * q^53 - q^55 + 6 * q^56 - 3 * q^57 + 8 * q^58 + 5 * q^59 + 10 * q^60 - 17 * q^61 - 24 * q^62 - 5 * q^63 - 8 * q^64 - 12 * q^66 - 2 * q^67 - 20 * q^68 + 5 * q^69 + 10 * q^71 - 6 * q^72 - 8 * q^73 - 34 * q^74 - 5 * q^75 - 8 * q^76 - q^77 + 14 * q^78 + 24 * q^79 - 8 * q^80 + 5 * q^81 - 8 * q^82 - 24 * q^83 + 10 * q^84 + 10 * q^85 - 10 * q^86 - 4 * q^87 - 26 * q^88 - 4 * q^89 - 10 * q^92 - 2 * q^93 + 2 * q^94 - 3 * q^95 + 12 * q^96 - 20 * q^97 + q^99

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