LMFDB - Embedded newform 8015.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26339 q^{2} +2.16114 q^{3} +3.12292 q^{4} -1.00000 q^{5} -4.89149 q^{6} +1.00000 q^{7} -2.54160 q^{8} +1.67051 q^{9} +O(q^{10})$	\(q-2.26339 q^{2} +2.16114 q^{3} +3.12292 q^{4} -1.00000 q^{5} -4.89149 q^{6} +1.00000 q^{7} -2.54160 q^{8} +1.67051 q^{9} +2.26339 q^{10} +3.90332 q^{11} +6.74905 q^{12} -1.97675 q^{13} -2.26339 q^{14} -2.16114 q^{15} -0.493215 q^{16} -4.28978 q^{17} -3.78101 q^{18} +3.00948 q^{19} -3.12292 q^{20} +2.16114 q^{21} -8.83471 q^{22} -6.89424 q^{23} -5.49274 q^{24} +1.00000 q^{25} +4.47416 q^{26} -2.87321 q^{27} +3.12292 q^{28} -0.0129567 q^{29} +4.89149 q^{30} +2.71807 q^{31} +6.19954 q^{32} +8.43560 q^{33} +9.70943 q^{34} -1.00000 q^{35} +5.21687 q^{36} -6.17690 q^{37} -6.81162 q^{38} -4.27204 q^{39} +2.54160 q^{40} -3.02915 q^{41} -4.89149 q^{42} -4.37775 q^{43} +12.1897 q^{44} -1.67051 q^{45} +15.6043 q^{46} +12.7322 q^{47} -1.06591 q^{48} +1.00000 q^{49} -2.26339 q^{50} -9.27080 q^{51} -6.17324 q^{52} +3.81179 q^{53} +6.50318 q^{54} -3.90332 q^{55} -2.54160 q^{56} +6.50390 q^{57} +0.0293260 q^{58} +10.9348 q^{59} -6.74905 q^{60} +0.472150 q^{61} -6.15205 q^{62} +1.67051 q^{63} -13.0455 q^{64} +1.97675 q^{65} -19.0930 q^{66} -12.1947 q^{67} -13.3966 q^{68} -14.8994 q^{69} +2.26339 q^{70} +2.95523 q^{71} -4.24577 q^{72} -1.89272 q^{73} +13.9807 q^{74} +2.16114 q^{75} +9.39836 q^{76} +3.90332 q^{77} +9.66927 q^{78} +4.11222 q^{79} +0.493215 q^{80} -11.2209 q^{81} +6.85613 q^{82} +2.69093 q^{83} +6.74905 q^{84} +4.28978 q^{85} +9.90854 q^{86} -0.0280012 q^{87} -9.92067 q^{88} -1.81741 q^{89} +3.78101 q^{90} -1.97675 q^{91} -21.5301 q^{92} +5.87413 q^{93} -28.8178 q^{94} -3.00948 q^{95} +13.3980 q^{96} -14.1011 q^{97} -2.26339 q^{98} +6.52053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * 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 $

$2$	−2.26339	−1.60046	−0.800228	−	0.599696i	$-0.795288\pi$
$2$	−2.26339	−1.60046	−0.800228	+	0.599696i	$0.795288\pi$
$3$	2.16114	1.24773	0.623866	−	0.781531i	$-0.285561\pi$
$3$	2.16114	1.24773	0.623866	+	0.781531i	$0.285561\pi$
$4$	3.12292	1.56146
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.89149	−1.99694
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.54160	−0.898591
$9$	1.67051	0.556837
$10$	2.26339	0.715746
$11$	3.90332	1.17689	0.588447	−	0.808536i	$-0.299740\pi$
$11$	3.90332	1.17689	0.588447	+	0.808536i	$0.299740\pi$
$12$	6.74905	1.94828
$13$	−1.97675	−0.548253	−0.274126	−	0.961694i	$-0.588389\pi$
$13$	−1.97675	−0.548253	−0.274126	+	0.961694i	$0.588389\pi$
$14$	−2.26339	−0.604916
$15$	−2.16114	−0.558003
$16$	−0.493215	−0.123304
$17$	−4.28978	−1.04042	−0.520212	−	0.854037i	$-0.674147\pi$
$17$	−4.28978	−1.04042	−0.520212	+	0.854037i	$0.674147\pi$
$18$	−3.78101	−0.891193
$19$	3.00948	0.690422	0.345211	−	0.938525i	$-0.387807\pi$
$19$	3.00948	0.690422	0.345211	+	0.938525i	$0.387807\pi$
$20$	−3.12292	−0.698306
$21$	2.16114	0.471599
$22$	−8.83471	−1.88357
$23$	−6.89424	−1.43755	−0.718774	−	0.695244i	$-0.755296\pi$
$23$	−6.89424	−1.43755	−0.718774	+	0.695244i	$0.755296\pi$
$24$	−5.49274	−1.12120
$25$	1.00000	0.200000
$26$	4.47416	0.877455
$27$	−2.87321	−0.552949
$28$	3.12292	0.590176
$29$	−0.0129567	−0.00240600	−0.00120300	−	0.999999i	$-0.500383\pi$
$29$	−0.0129567	−0.00240600	−0.00120300	+	0.999999i	$0.500383\pi$
$30$	4.89149	0.893059
$31$	2.71807	0.488180	0.244090	−	0.969753i	$-0.421511\pi$
$31$	2.71807	0.488180	0.244090	+	0.969753i	$0.421511\pi$
$32$	6.19954	1.09593
$33$	8.43560	1.46845
$34$	9.70943	1.66515
$35$	−1.00000	−0.169031
$36$	5.21687	0.869478
$37$	−6.17690	−1.01548	−0.507738	−	0.861511i	$-0.669518\pi$
$37$	−6.17690	−1.01548	−0.507738	+	0.861511i	$0.669518\pi$
$38$	−6.81162	−1.10499
$39$	−4.27204	−0.684073
$40$	2.54160	0.401862
$41$	−3.02915	−0.473073	−0.236537	−	0.971623i	$-0.576012\pi$
$41$	−3.02915	−0.473073	−0.236537	+	0.971623i	$0.576012\pi$
$42$	−4.89149	−0.754773
$43$	−4.37775	−0.667601	−0.333800	−	0.942644i	$-0.608331\pi$
$43$	−4.37775	−0.667601	−0.333800	+	0.942644i	$0.608331\pi$
$44$	12.1897	1.83767
$45$	−1.67051	−0.249025
$46$	15.6043	2.30073
$47$	12.7322	1.85718	0.928588	−	0.371112i	$-0.121023\pi$
$47$	12.7322	1.85718	0.928588	+	0.371112i	$0.121023\pi$
$48$	−1.06591	−0.153850
$49$	1.00000	0.142857
$50$	−2.26339	−0.320091
$51$	−9.27080	−1.29817
$52$	−6.17324	−0.856075
$53$	3.81179	0.523590	0.261795	−	0.965123i	$-0.415686\pi$
$53$	3.81179	0.523590	0.261795	+	0.965123i	$0.415686\pi$
$54$	6.50318	0.884971
$55$	−3.90332	−0.526323
$56$	−2.54160	−0.339636
$57$	6.50390	0.861462
$58$	0.0293260	0.00385070
$59$	10.9348	1.42359	0.711794	−	0.702388i	$-0.247883\pi$
$59$	10.9348	1.42359	0.711794	+	0.702388i	$0.247883\pi$
$60$	−6.74905	−0.871299
$61$	0.472150	0.0604526	0.0302263	−	0.999543i	$-0.490377\pi$
$61$	0.472150	0.0604526	0.0302263	+	0.999543i	$0.490377\pi$
$62$	−6.15205	−0.781311
$63$	1.67051	0.210465
$64$	−13.0455	−1.63069
$65$	1.97675	0.245186
$66$	−19.0930	−2.35019
$67$	−12.1947	−1.48981	−0.744907	−	0.667168i	$-0.767506\pi$
$67$	−12.1947	−1.48981	−0.744907	+	0.667168i	$0.767506\pi$
$68$	−13.3966	−1.62458
$69$	−14.8994	−1.79368
$70$	2.26339	0.270526
$71$	2.95523	0.350721	0.175361	−	0.984504i	$-0.443891\pi$
$71$	2.95523	0.350721	0.175361	+	0.984504i	$0.443891\pi$
$72$	−4.24577	−0.500369
$73$	−1.89272	−0.221526	−0.110763	−	0.993847i	$-0.535329\pi$
$73$	−1.89272	−0.221526	−0.110763	+	0.993847i	$0.535329\pi$
$74$	13.9807	1.62522
$75$	2.16114	0.249547
$76$	9.39836	1.07807
$77$	3.90332	0.444824
$78$	9.66927	1.09483
$79$	4.11222	0.462661	0.231331	−	0.972875i	$-0.425692\pi$
$79$	4.11222	0.462661	0.231331	+	0.972875i	$0.425692\pi$
$80$	0.493215	0.0551431
$81$	−11.2209	−1.24677
$82$	6.85613	0.757133
$83$	2.69093	0.295368	0.147684	−	0.989035i	$-0.452818\pi$
$83$	2.69093	0.295368	0.147684	+	0.989035i	$0.452818\pi$
$84$	6.74905	0.736382
$85$	4.28978	0.465292
$86$	9.90854	1.06847
$87$	−0.0280012	−0.00300204
$88$	−9.92067	−1.05755
$89$	−1.81741	−0.192645	−0.0963224	−	0.995350i	$-0.530708\pi$
$89$	−1.81741	−0.192645	−0.0963224	+	0.995350i	$0.530708\pi$
$90$	3.78101	0.398554
$91$	−1.97675	−0.207220
$92$	−21.5301	−2.24467
$93$	5.87413	0.609119
$94$	−28.8178	−2.97233
$95$	−3.00948	−0.308766
$96$	13.3980	1.36743
$97$	−14.1011	−1.43175	−0.715874	−	0.698230i	$-0.753971\pi$
$97$	−14.1011	−1.43175	−0.715874	+	0.698230i	$0.753971\pi$
$98$	−2.26339	−0.228637
$99$	6.52053	0.655338
$100$	3.12292	0.312292
$101$	−9.08375	−0.903867	−0.451933	−	0.892052i	$-0.649266\pi$
$101$	−9.08375	−0.903867	−0.451933	+	0.892052i	$0.649266\pi$
$102$	20.9834	2.07767
$103$	−10.6126	−1.04569	−0.522845	−	0.852428i	$-0.675129\pi$
$103$	−10.6126	−1.04569	−0.522845	+	0.852428i	$0.675129\pi$
$104$	5.02412	0.492655
$105$	−2.16114	−0.210905
$106$	−8.62756	−0.837983
$107$	−20.4256	−1.97461	−0.987306	−	0.158827i	$-0.949229\pi$
$107$	−20.4256	−1.97461	−0.987306	+	0.158827i	$0.949229\pi$
$108$	−8.97280	−0.863408
$109$	−2.80770	−0.268929	−0.134465	−	0.990918i	$-0.542931\pi$
$109$	−2.80770	−0.268929	−0.134465	+	0.990918i	$0.542931\pi$
$110$	8.83471	0.842357
$111$	−13.3491	−1.26704
$112$	−0.493215	−0.0466045
$113$	−9.71166	−0.913596	−0.456798	−	0.889570i	$-0.651004\pi$
$113$	−9.71166	−0.913596	−0.456798	+	0.889570i	$0.651004\pi$
$114$	−14.7208	−1.37873
$115$	6.89424	0.642891
$116$	−0.0404627	−0.00375687
$117$	−3.30219	−0.305287
$118$	−24.7496	−2.27839
$119$	−4.28978	−0.393243
$120$	5.49274	0.501417
$121$	4.23587	0.385079
$122$	−1.06866	−0.0967517
$123$	−6.54640	−0.590269
$124$	8.48832	0.762274
$125$	−1.00000	−0.0894427
$126$	−3.78101	−0.336839
$127$	−4.47657	−0.397231	−0.198616	−	0.980077i	$-0.563645\pi$
$127$	−4.47657	−0.397231	−0.198616	+	0.980077i	$0.563645\pi$
$128$	17.1280	1.51391
$129$	−9.46091	−0.832987
$130$	−4.47416	−0.392410
$131$	−7.84749	−0.685638	−0.342819	−	0.939401i	$-0.611382\pi$
$131$	−7.84749	−0.685638	−0.342819	+	0.939401i	$0.611382\pi$
$132$	26.3437	2.29292
$133$	3.00948	0.260955
$134$	27.6012	2.38438
$135$	2.87321	0.247286
$136$	10.9029	0.934916
$137$	10.2618	0.876725	0.438362	−	0.898798i	$-0.355559\pi$
$137$	10.2618	0.876725	0.438362	+	0.898798i	$0.355559\pi$
$138$	33.7231	2.87070
$139$	0.297725	0.0252527	0.0126264	−	0.999920i	$-0.495981\pi$
$139$	0.297725	0.0252527	0.0126264	+	0.999920i	$0.495981\pi$
$140$	−3.12292	−0.263935
$141$	27.5159	2.31726
$142$	−6.68883	−0.561314
$143$	−7.71590	−0.645236
$144$	−0.823921	−0.0686601
$145$	0.0129567	0.00107600
$146$	4.28395	0.354542
$147$	2.16114	0.178248
$148$	−19.2900	−1.58562
$149$	2.85795	0.234133	0.117066	−	0.993124i	$-0.462651\pi$
$149$	2.85795	0.234133	0.117066	+	0.993124i	$0.462651\pi$
$150$	−4.89149	−0.399388
$151$	−0.163031	−0.0132673	−0.00663363	−	0.999978i	$-0.502112\pi$
$151$	−0.163031	−0.0132673	−0.00663363	+	0.999978i	$0.502112\pi$
$152$	−7.64889	−0.620407
$153$	−7.16612	−0.579347
$154$	−8.83471	−0.711921
$155$	−2.71807	−0.218321
$156$	−13.3412	−1.06815
$157$	−13.1505	−1.04952	−0.524762	−	0.851249i	$-0.675846\pi$
$157$	−13.1505	−1.04952	−0.524762	+	0.851249i	$0.675846\pi$
$158$	−9.30755	−0.740469
$159$	8.23781	0.653301
$160$	−6.19954	−0.490116
$161$	−6.89424	−0.543342
$162$	25.3973	1.99540
$163$	21.3019	1.66849	0.834247	−	0.551391i	$-0.185903\pi$
$163$	21.3019	1.66849	0.834247	+	0.551391i	$0.185903\pi$
$164$	−9.45978	−0.738685
$165$	−8.43560	−0.656710
$166$	−6.09062	−0.472724
$167$	−3.27317	−0.253285	−0.126643	−	0.991948i	$-0.540420\pi$
$167$	−3.27317	−0.253285	−0.126643	+	0.991948i	$0.540420\pi$
$168$	−5.49274	−0.423774
$169$	−9.09244	−0.699419
$170$	−9.70943	−0.744679
$171$	5.02737	0.384452
$172$	−13.6714	−1.04243
$173$	11.1646	0.848826	0.424413	−	0.905469i	$-0.360481\pi$
$173$	11.1646	0.848826	0.424413	+	0.905469i	$0.360481\pi$
$174$	0.0633776	0.00480464
$175$	1.00000	0.0755929
$176$	−1.92517	−0.145116
$177$	23.6316	1.77626
$178$	4.11350	0.308320
$179$	8.53189	0.637703	0.318852	−	0.947805i	$-0.396703\pi$
$179$	8.53189	0.637703	0.318852	+	0.947805i	$0.396703\pi$
$180$	−5.21687	−0.388842
$181$	−6.64283	−0.493758	−0.246879	−	0.969046i	$-0.579405\pi$
$181$	−6.64283	−0.493758	−0.246879	+	0.969046i	$0.579405\pi$
$182$	4.47416	0.331647
$183$	1.02038	0.0754287
$184$	17.5224	1.29177
$185$	6.17690	0.454135
$186$	−13.2954	−0.974868
$187$	−16.7444	−1.22447
$188$	39.7615	2.89991
$189$	−2.87321	−0.208995
$190$	6.81162	0.494167
$191$	10.7315	0.776501	0.388250	−	0.921554i	$-0.373080\pi$
$191$	10.7315	0.776501	0.388250	+	0.921554i	$0.373080\pi$
$192$	−28.1931	−2.03466
$193$	13.3940	0.964124	0.482062	−	0.876137i	$-0.339888\pi$
$193$	13.3940	0.964124	0.482062	+	0.876137i	$0.339888\pi$
$194$	31.9162	2.29145
$195$	4.27204	0.305927
$196$	3.12292	0.223066
$197$	−7.79058	−0.555056	−0.277528	−	0.960718i	$-0.589515\pi$
$197$	−7.79058	−0.555056	−0.277528	+	0.960718i	$0.589515\pi$
$198$	−14.7585	−1.04884
$199$	−8.14245	−0.577203	−0.288602	−	0.957449i	$-0.593190\pi$
$199$	−8.14245	−0.577203	−0.288602	+	0.957449i	$0.593190\pi$
$200$	−2.54160	−0.179718
$201$	−26.3543	−1.85889
$202$	20.5600	1.44660
$203$	−0.0129567	−0.000909382 0
$204$	−28.9520	−2.02704
$205$	3.02915	0.211565
$206$	24.0204	1.67358
$207$	−11.5169	−0.800480
$208$	0.974965	0.0676017
$209$	11.7469	0.812553
$210$	4.89149	0.337545
$211$	−3.39401	−0.233653	−0.116827	−	0.993152i	$-0.537272\pi$
$211$	−3.39401	−0.233653	−0.116827	+	0.993152i	$0.537272\pi$
$212$	11.9039	0.817565
$213$	6.38666	0.437606
$214$	46.2309	3.16028
$215$	4.37775	0.298560
$216$	7.30255	0.496875
$217$	2.71807	0.184515
$218$	6.35492	0.430410
$219$	−4.09042	−0.276405
$220$	−12.1897	−0.821832
$221$	8.47984	0.570416
$222$	30.2142	2.02785
$223$	−5.08760	−0.340691	−0.170345	−	0.985384i	$-0.554488\pi$
$223$	−5.08760	−0.340691	−0.170345	+	0.985384i	$0.554488\pi$
$224$	6.19954	0.414224
$225$	1.67051	0.111367
$226$	21.9812	1.46217
$227$	21.1394	1.40307	0.701535	−	0.712635i	$-0.252499\pi$
$227$	21.1394	1.40307	0.701535	+	0.712635i	$0.252499\pi$
$228$	20.3111	1.34514
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−15.6043	−1.02892
$231$	8.43560	0.555022
$232$	0.0329308	0.00216201
$233$	10.7233	0.702508	0.351254	−	0.936280i	$-0.385755\pi$
$233$	10.7233	0.702508	0.351254	+	0.936280i	$0.385755\pi$
$234$	7.47413	0.488599
$235$	−12.7322	−0.830555
$236$	34.1485	2.22287
$237$	8.88708	0.577278
$238$	9.70943	0.629369
$239$	−0.963981	−0.0623547	−0.0311774	−	0.999514i	$-0.509926\pi$
$239$	−0.963981	−0.0623547	−0.0311774	+	0.999514i	$0.509926\pi$
$240$	1.06591	0.0688039
$241$	−21.5751	−1.38978	−0.694888	−	0.719118i	$-0.744546\pi$
$241$	−21.5751	−1.38978	−0.694888	+	0.719118i	$0.744546\pi$
$242$	−9.58742	−0.616303
$243$	−15.6303	−1.00269
$244$	1.47449	0.0943943
$245$	−1.00000	−0.0638877
$246$	14.8170	0.944699
$247$	−5.94900	−0.378526
$248$	−6.90826	−0.438675
$249$	5.81547	0.368540
$250$	2.26339	0.143149
$251$	−28.8833	−1.82310	−0.911549	−	0.411191i	$-0.865113\pi$
$251$	−28.8833	−1.82310	−0.911549	+	0.411191i	$0.865113\pi$
$252$	5.21687	0.328632
$253$	−26.9104	−1.69184
$254$	10.1322	0.635751
$255$	9.27080	0.580560
$256$	−12.6762	−0.792262
$257$	−0.275540	−0.0171877	−0.00859385	−	0.999963i	$-0.502736\pi$
$257$	−0.275540	−0.0171877	−0.00859385	+	0.999963i	$0.502736\pi$
$258$	21.4137	1.33316
$259$	−6.17690	−0.383814
$260$	6.17324	0.382848
$261$	−0.0216443	−0.00133975
$262$	17.7619	1.09733
$263$	−21.9605	−1.35415	−0.677073	−	0.735916i	$-0.736752\pi$
$263$	−21.9605	−1.35415	−0.677073	+	0.735916i	$0.736752\pi$
$264$	−21.4399	−1.31954
$265$	−3.81179	−0.234157
$266$	−6.81162	−0.417647
$267$	−3.92767	−0.240369
$268$	−38.0829	−2.32629
$269$	−23.6050	−1.43922	−0.719611	−	0.694377i	$-0.755680\pi$
$269$	−23.6050	−1.43922	−0.719611	+	0.694377i	$0.755680\pi$
$270$	−6.50318	−0.395771
$271$	−17.9142	−1.08821	−0.544104	−	0.839018i	$-0.683130\pi$
$271$	−17.9142	−1.08821	−0.544104	+	0.839018i	$0.683130\pi$
$272$	2.11578	0.128288
$273$	−4.27204	−0.258555
$274$	−23.2264	−1.40316
$275$	3.90332	0.235379
$276$	−46.5296	−2.80075
$277$	10.6535	0.640105	0.320053	−	0.947400i	$-0.396299\pi$
$277$	10.6535	0.640105	0.320053	+	0.947400i	$0.396299\pi$
$278$	−0.673867	−0.0404158
$279$	4.54057	0.271837
$280$	2.54160	0.151890
$281$	8.29851	0.495048	0.247524	−	0.968882i	$-0.420383\pi$
$281$	8.29851	0.495048	0.247524	+	0.968882i	$0.420383\pi$
$282$	−62.2792	−3.70867
$283$	−19.6601	−1.16867	−0.584336	−	0.811512i	$-0.698645\pi$
$283$	−19.6601	−1.16867	−0.584336	+	0.811512i	$0.698645\pi$
$284$	9.22894	0.547637
$285$	−6.50390	−0.385258
$286$	17.4641	1.03267
$287$	−3.02915	−0.178805
$288$	10.3564	0.610256
$289$	1.40221	0.0824828
$290$	−0.0293260	−0.00172208
$291$	−30.4744	−1.78644
$292$	−5.91080	−0.345904
$293$	−22.4692	−1.31266	−0.656332	−	0.754472i	$-0.727893\pi$
$293$	−22.4692	−1.31266	−0.656332	+	0.754472i	$0.727893\pi$
$294$	−4.89149	−0.285277
$295$	−10.9348	−0.636648
$296$	15.6992	0.912498
$297$	−11.2150	−0.650763
$298$	−6.46866	−0.374719
$299$	13.6282	0.788140
$300$	6.74905	0.389657
$301$	−4.37775	−0.252329
$302$	0.369002	0.0212337
$303$	−19.6312	−1.12778
$304$	−1.48432	−0.0851317
$305$	−0.472150	−0.0270352
$306$	16.2197	0.927219
$307$	31.1212	1.77618	0.888090	−	0.459670i	$-0.152032\pi$
$307$	31.1212	1.77618	0.888090	+	0.459670i	$0.152032\pi$
$308$	12.1897	0.694575
$309$	−22.9353	−1.30474
$310$	6.15205	0.349413
$311$	−4.66892	−0.264750	−0.132375	−	0.991200i	$-0.542260\pi$
$311$	−4.66892	−0.264750	−0.132375	+	0.991200i	$0.542260\pi$
$312$	10.8578	0.614702
$313$	−12.9832	−0.733855	−0.366927	−	0.930250i	$-0.619590\pi$
$313$	−12.9832	−0.733855	−0.366927	+	0.930250i	$0.619590\pi$
$314$	29.7647	1.67972
$315$	−1.67051	−0.0941226
$316$	12.8421	0.722427
$317$	22.2549	1.24996	0.624980	−	0.780640i	$-0.285107\pi$
$317$	22.2549	1.24996	0.624980	+	0.780640i	$0.285107\pi$
$318$	−18.6453	−1.04558
$319$	−0.0505741	−0.00283161
$320$	13.0455	0.729267
$321$	−44.1424	−2.46379
$322$	15.6043	0.869595
$323$	−12.9100	−0.718332
$324$	−35.0420	−1.94678
$325$	−1.97675	−0.109651
$326$	−48.2144	−2.67035
$327$	−6.06783	−0.335552
$328$	7.69888	0.425099
$329$	12.7322	0.701947
$330$	19.0930	1.05104
$331$	−16.0368	−0.881460	−0.440730	−	0.897640i	$-0.645280\pi$
$331$	−16.0368	−0.881460	−0.440730	+	0.897640i	$0.645280\pi$
$332$	8.40356	0.461205
$333$	−10.3186	−0.565455
$334$	7.40845	0.405372
$335$	12.1947	0.666265
$336$	−1.06591	−0.0581499
$337$	9.50296	0.517659	0.258830	−	0.965923i	$-0.416663\pi$
$337$	9.50296	0.517659	0.258830	+	0.965923i	$0.416663\pi$
$338$	20.5797	1.11939
$339$	−20.9882	−1.13992
$340$	13.3966	0.726534
$341$	10.6095	0.574537
$342$	−11.3789	−0.615299
$343$	1.00000	0.0539949
$344$	11.1265	0.599900
$345$	14.8994	0.802156
$346$	−25.2697	−1.35851
$347$	−1.15561	−0.0620363	−0.0310182	−	0.999519i	$-0.509875\pi$
$347$	−1.15561	−0.0620363	−0.0310182	+	0.999519i	$0.509875\pi$
$348$	−0.0874455	−0.00468757
$349$	−10.1713	−0.544455	−0.272227	−	0.962233i	$-0.587760\pi$
$349$	−10.1713	−0.544455	−0.272227	+	0.962233i	$0.587760\pi$
$350$	−2.26339	−0.120983
$351$	5.67963	0.303156
$352$	24.1987	1.28980
$353$	−26.4025	−1.40526	−0.702631	−	0.711554i	$-0.747992\pi$
$353$	−26.4025	−1.40526	−0.702631	+	0.711554i	$0.747992\pi$
$354$	−53.4874	−2.84282
$355$	−2.95523	−0.156847
$356$	−5.67562	−0.300807
$357$	−9.27080	−0.490663
$358$	−19.3110	−1.02062
$359$	32.9215	1.73753	0.868764	−	0.495226i	$-0.164915\pi$
$359$	32.9215	1.73753	0.868764	+	0.495226i	$0.164915\pi$
$360$	4.24577	0.223772
$361$	−9.94303	−0.523318
$362$	15.0353	0.790237
$363$	9.15430	0.480476
$364$	−6.17324	−0.323566
$365$	1.89272	0.0990694
$366$	−2.30951	−0.120720
$367$	18.8537	0.984154	0.492077	−	0.870552i	$-0.336238\pi$
$367$	18.8537	0.984154	0.492077	+	0.870552i	$0.336238\pi$
$368$	3.40034	0.177255
$369$	−5.06022	−0.263425
$370$	−13.9807	−0.726823
$371$	3.81179	0.197898
$372$	18.3444	0.951114
$373$	7.11896	0.368606	0.184303	−	0.982869i	$-0.440997\pi$
$373$	7.11896	0.368606	0.184303	+	0.982869i	$0.440997\pi$
$374$	37.8990	1.95971
$375$	−2.16114	−0.111601
$376$	−32.3601	−1.66884
$377$	0.0256122	0.00131910
$378$	6.50318	0.334488
$379$	1.29138	0.0663335	0.0331668	−	0.999450i	$-0.489441\pi$
$379$	1.29138	0.0663335	0.0331668	+	0.999450i	$0.489441\pi$
$380$	−9.39836	−0.482126
$381$	−9.67448	−0.495639
$382$	−24.2894	−1.24276
$383$	23.3878	1.19506	0.597530	−	0.801847i	$-0.296149\pi$
$383$	23.3878	1.19506	0.597530	+	0.801847i	$0.296149\pi$
$384$	37.0159	1.88896
$385$	−3.90332	−0.198931
$386$	−30.3159	−1.54304
$387$	−7.31308	−0.371745
$388$	−44.0365	−2.23562
$389$	6.99677	0.354750	0.177375	−	0.984143i	$-0.443239\pi$
$389$	6.99677	0.354750	0.177375	+	0.984143i	$0.443239\pi$
$390$	−9.66927	−0.489622
$391$	29.5748	1.49566
$392$	−2.54160	−0.128370
$393$	−16.9595	−0.855493
$394$	17.6331	0.888342
$395$	−4.11222	−0.206908
$396$	20.3631	1.02328
$397$	1.41754	0.0711444	0.0355722	−	0.999367i	$-0.488675\pi$
$397$	1.41754	0.0711444	0.0355722	+	0.999367i	$0.488675\pi$
$398$	18.4295	0.923788
$399$	6.50390	0.325602
$400$	−0.493215	−0.0246608
$401$	−6.32584	−0.315898	−0.157949	−	0.987447i	$-0.550488\pi$
$401$	−6.32584	−0.315898	−0.157949	+	0.987447i	$0.550488\pi$
$402$	59.6500	2.97507
$403$	−5.37296	−0.267646
$404$	−28.3678	−1.41135
$405$	11.2209	0.557572
$406$	0.0293260	0.00145543
$407$	−24.1104	−1.19511
$408$	23.5627	1.16653
$409$	9.00934	0.445483	0.222742	−	0.974878i	$-0.428499\pi$
$409$	9.00934	0.445483	0.222742	+	0.974878i	$0.428499\pi$
$410$	−6.85613	−0.338600
$411$	22.1771	1.09392
$412$	−33.1423	−1.63280
$413$	10.9348	0.538066
$414$	26.0672	1.28113
$415$	−2.69093	−0.132093
$416$	−12.2550	−0.600849
$417$	0.643424	0.0315086
$418$	−26.5879	−1.30046
$419$	11.3606	0.555004	0.277502	−	0.960725i	$-0.410493\pi$
$419$	11.3606	0.555004	0.277502	+	0.960725i	$0.410493\pi$
$420$	−6.74905	−0.329320
$421$	40.1402	1.95631	0.978156	−	0.207873i	$-0.0666541\pi$
$421$	40.1402	1.95631	0.978156	+	0.207873i	$0.0666541\pi$
$422$	7.68196	0.373952
$423$	21.2692	1.03414
$424$	−9.68805	−0.470493
$425$	−4.28978	−0.208085
$426$	−14.4555	−0.700370
$427$	0.472150	0.0228489
$428$	−63.7873	−3.08328
$429$	−16.6751	−0.805082
$430$	−9.90854	−0.477832
$431$	−37.8272	−1.82207	−0.911037	−	0.412325i	$-0.864717\pi$
$431$	−37.8272	−1.82207	−0.911037	+	0.412325i	$0.864717\pi$
$432$	1.41711	0.0681807
$433$	−3.97938	−0.191237	−0.0956183	−	0.995418i	$-0.530483\pi$
$433$	−3.97938	−0.191237	−0.0956183	+	0.995418i	$0.530483\pi$
$434$	−6.15205	−0.295308
$435$	0.0280012	0.00134256
$436$	−8.76823	−0.419922
$437$	−20.7481	−0.992515
$438$	9.25820	0.442374
$439$	−19.4430	−0.927966	−0.463983	−	0.885844i	$-0.653580\pi$
$439$	−19.4430	−0.927966	−0.463983	+	0.885844i	$0.653580\pi$
$440$	9.92067	0.472949
$441$	1.67051	0.0795481
$442$	−19.1932	−0.912925
$443$	−11.4804	−0.545451	−0.272726	−	0.962092i	$-0.587925\pi$
$443$	−11.4804	−0.545451	−0.272726	+	0.962092i	$0.587925\pi$
$444$	−41.6882	−1.97844
$445$	1.81741	0.0861534
$446$	11.5152	0.545261
$447$	6.17643	0.292135
$448$	−13.0455	−0.616343
$449$	17.1075	0.807354	0.403677	−	0.914902i	$-0.367732\pi$
$449$	17.1075	0.807354	0.403677	+	0.914902i	$0.367732\pi$
$450$	−3.78101	−0.178239
$451$	−11.8237	−0.556757
$452$	−30.3287	−1.42654
$453$	−0.352332	−0.0165540
$454$	−47.8466	−2.24555
$455$	1.97675	0.0926717
$456$	−16.5303	−0.774102
$457$	−1.98759	−0.0929753	−0.0464877	−	0.998919i	$-0.514803\pi$
$457$	−1.98759	−0.0929753	−0.0464877	+	0.998919i	$0.514803\pi$
$458$	−2.26339	−0.105761
$459$	12.3254	0.575302
$460$	21.5301	1.00385
$461$	0.0998380	0.00464992	0.00232496	−	0.999997i	$-0.499260\pi$
$461$	0.0998380	0.00464992	0.00232496	+	0.999997i	$0.499260\pi$
$462$	−19.0930	−0.888288
$463$	−9.43220	−0.438351	−0.219176	−	0.975685i	$-0.570337\pi$
$463$	−9.43220	−0.438351	−0.219176	+	0.975685i	$0.570337\pi$
$464$	0.00639044	0.000296669 0
$465$	−5.87413	−0.272406
$466$	−24.2710	−1.12433
$467$	−17.7045	−0.819265	−0.409633	−	0.912251i	$-0.634343\pi$
$467$	−17.7045	−0.819265	−0.409633	+	0.912251i	$0.634343\pi$
$468$	−10.3125	−0.476694
$469$	−12.1947	−0.563097
$470$	28.8178	1.32927
$471$	−28.4200	−1.30953
$472$	−27.7918	−1.27922
$473$	−17.0877	−0.785695
$474$	−20.1149	−0.923907
$475$	3.00948	0.138084
$476$	−13.3966	−0.614034
$477$	6.36764	0.291554
$478$	2.18186	0.0997960
$479$	17.2654	0.788875	0.394437	−	0.918923i	$-0.370940\pi$
$479$	17.2654	0.788875	0.394437	+	0.918923i	$0.370940\pi$
$480$	−13.3980	−0.611534
$481$	12.2102	0.556738
$482$	48.8329	2.22428
$483$	−14.8994	−0.677946
$484$	13.2283	0.601286
$485$	14.1011	0.640297
$486$	35.3775	1.60475
$487$	−29.2829	−1.32694	−0.663468	−	0.748205i	$-0.730916\pi$
$487$	−29.2829	−1.32694	−0.663468	+	0.748205i	$0.730916\pi$
$488$	−1.20002	−0.0543222
$489$	46.0363	2.08183
$490$	2.26339	0.102249
$491$	−17.0833	−0.770960	−0.385480	−	0.922716i	$-0.625964\pi$
$491$	−17.0833	−0.770960	−0.385480	+	0.922716i	$0.625964\pi$
$492$	−20.4439	−0.921681
$493$	0.0555814	0.00250326
$494$	13.4649	0.605814
$495$	−6.52053	−0.293076
$496$	−1.34060	−0.0601945
$497$	2.95523	0.132560
$498$	−13.1627	−0.589833
$499$	6.34905	0.284222	0.142111	−	0.989851i	$-0.454611\pi$
$499$	6.34905	0.284222	0.142111	+	0.989851i	$0.454611\pi$
$500$	−3.12292	−0.139661
$501$	−7.07376	−0.316032
$502$	65.3741	2.91779
$503$	8.46227	0.377314	0.188657	−	0.982043i	$-0.439587\pi$
$503$	8.46227	0.377314	0.188657	+	0.982043i	$0.439587\pi$
$504$	−4.24577	−0.189122
$505$	9.08375	0.404222
$506$	60.9086	2.70772
$507$	−19.6500	−0.872688
$508$	−13.9800	−0.620261
$509$	0.335274	0.0148608	0.00743039	−	0.999972i	$-0.497635\pi$
$509$	0.335274	0.0148608	0.00743039	+	0.999972i	$0.497635\pi$
$510$	−20.9834	−0.929161
$511$	−1.89272	−0.0837289
$512$	−5.56482	−0.245932
$513$	−8.64686	−0.381768
$514$	0.623653	0.0275081
$515$	10.6126	0.467647
$516$	−29.5457	−1.30068
$517$	49.6976	2.18570
$518$	13.9807	0.614277
$519$	24.1281	1.05911
$520$	−5.02412	−0.220322
$521$	26.2025	1.14795	0.573976	−	0.818872i	$-0.305400\pi$
$521$	26.2025	1.14795	0.573976	+	0.818872i	$0.305400\pi$
$522$	0.0489894	0.00214421
$523$	−23.8471	−1.04276	−0.521380	−	0.853325i	$-0.674582\pi$
$523$	−23.8471	−1.04276	−0.521380	+	0.853325i	$0.674582\pi$
$524$	−24.5071	−1.07060
$525$	2.16114	0.0943197
$526$	49.7052	2.16725
$527$	−11.6599	−0.507915
$528$	−4.16056	−0.181065
$529$	24.5305	1.06654
$530$	8.62756	0.374757
$531$	18.2667	0.792706
$532$	9.39836	0.407471
$533$	5.98788	0.259364
$534$	8.88983	0.384700
$535$	20.4256	0.883074
$536$	30.9939	1.33873
$537$	18.4386	0.795683
$538$	53.4272	2.30341
$539$	3.90332	0.168128
$540$	8.97280	0.386128
$541$	−13.4751	−0.579339	−0.289670	−	0.957127i	$-0.593545\pi$
$541$	−13.4751	−0.579339	−0.289670	+	0.957127i	$0.593545\pi$
$542$	40.5466	1.74163
$543$	−14.3561	−0.616077
$544$	−26.5946	−1.14024
$545$	2.80770	0.120269
$546$	9.66927	0.413806
$547$	−4.11322	−0.175869	−0.0879344	−	0.996126i	$-0.528027\pi$
$547$	−4.11322	−0.175869	−0.0879344	+	0.996126i	$0.528027\pi$
$548$	32.0468	1.36897
$549$	0.788731	0.0336622
$550$	−8.83471	−0.376713
$551$	−0.0389929	−0.00166116
$552$	37.8683	1.61178
$553$	4.11222	0.174870
$554$	−24.1129	−1.02446
$555$	13.3491	0.566639
$556$	0.929771	0.0394311
$557$	14.0165	0.593898	0.296949	−	0.954893i	$-0.404031\pi$
$557$	14.0165	0.593898	0.296949	+	0.954893i	$0.404031\pi$
$558$	−10.2771	−0.435063
$559$	8.65373	0.366014
$560$	0.493215	0.0208421
$561$	−36.1869	−1.52781
$562$	−18.7827	−0.792302
$563$	−41.4274	−1.74596	−0.872979	−	0.487757i	$-0.837815\pi$
$563$	−41.4274	−1.74596	−0.872979	+	0.487757i	$0.837815\pi$
$564$	85.9300	3.61831
$565$	9.71166	0.408573
$566$	44.4984	1.87041
$567$	−11.2209	−0.471235
$568$	−7.51101	−0.315155
$569$	−9.01439	−0.377903	−0.188952	−	0.981986i	$-0.560509\pi$
$569$	−9.01439	−0.377903	−0.188952	+	0.981986i	$0.560509\pi$
$570$	14.7208	0.616588
$571$	18.4896	0.773767	0.386883	−	0.922129i	$-0.373552\pi$
$571$	18.4896	0.773767	0.386883	+	0.922129i	$0.373552\pi$
$572$	−24.0961	−1.00751
$573$	23.1921	0.968865
$574$	6.85613	0.286169
$575$	−6.89424	−0.287510
$576$	−21.7927	−0.908028
$577$	13.5574	0.564402	0.282201	−	0.959355i	$-0.408935\pi$
$577$	13.5574	0.564402	0.282201	+	0.959355i	$0.408935\pi$
$578$	−3.17374	−0.132010
$579$	28.9463	1.20297
$580$	0.0404627	0.00168012
$581$	2.69093	0.111639
$582$	68.9753	2.85912
$583$	14.8786	0.616210
$584$	4.81053	0.199061
$585$	3.30219	0.136529
$586$	50.8565	2.10086
$587$	32.4260	1.33837	0.669183	−	0.743098i	$-0.266644\pi$
$587$	32.4260	1.33837	0.669183	+	0.743098i	$0.266644\pi$
$588$	6.74905	0.278326
$589$	8.17999	0.337051
$590$	24.7496	1.01893
$591$	−16.8365	−0.692561
$592$	3.04654	0.125212
$593$	3.67080	0.150742	0.0753708	−	0.997156i	$-0.475986\pi$
$593$	3.67080	0.150742	0.0753708	+	0.997156i	$0.475986\pi$
$594$	25.3840	1.04152
$595$	4.28978	0.175864
$596$	8.92516	0.365589
$597$	−17.5969	−0.720195
$598$	−30.8459	−1.26138
$599$	26.4338	1.08006	0.540028	−	0.841647i	$-0.318413\pi$
$599$	26.4338	1.08006	0.540028	+	0.841647i	$0.318413\pi$
$600$	−5.49274	−0.224240
$601$	−28.6981	−1.17062	−0.585311	−	0.810809i	$-0.699027\pi$
$601$	−28.6981	−1.17062	−0.585311	+	0.810809i	$0.699027\pi$
$602$	9.90854	0.403842
$603$	−20.3713	−0.829584
$604$	−0.509132	−0.0207163
$605$	−4.23587	−0.172213
$606$	44.4330	1.80497
$607$	−22.7000	−0.921367	−0.460683	−	0.887565i	$-0.652396\pi$
$607$	−22.7000	−0.921367	−0.460683	+	0.887565i	$0.652396\pi$
$608$	18.6574	0.756657
$609$	−0.0280012	−0.00113467
$610$	1.06866	0.0432687
$611$	−25.1684	−1.01820
$612$	−22.3792	−0.904626
$613$	−16.6516	−0.672553	−0.336276	−	0.941763i	$-0.609168\pi$
$613$	−16.6516	−0.672553	−0.336276	+	0.941763i	$0.609168\pi$
$614$	−70.4393	−2.84270
$615$	6.54640	0.263976
$616$	−9.92067	−0.399715
$617$	−32.3622	−1.30285	−0.651427	−	0.758711i	$-0.725829\pi$
$617$	−32.3622	−1.30285	−0.651427	+	0.758711i	$0.725829\pi$
$618$	51.9114	2.08818
$619$	−34.5232	−1.38760	−0.693802	−	0.720166i	$-0.744066\pi$
$619$	−34.5232	−1.38760	−0.693802	+	0.720166i	$0.744066\pi$
$620$	−8.48832	−0.340899
$621$	19.8086	0.794891
$622$	10.5676	0.423721
$623$	−1.81741	−0.0728129
$624$	2.10703	0.0843488
$625$	1.00000	0.0400000
$626$	29.3860	1.17450
$627$	25.3868	1.01385
$628$	−41.0680	−1.63879
$629$	26.4975	1.05653
$630$	3.78101	0.150639
$631$	5.65995	0.225319	0.112659	−	0.993634i	$-0.464063\pi$
$631$	5.65995	0.225319	0.112659	+	0.993634i	$0.464063\pi$
$632$	−10.4516	−0.415743
$633$	−7.33493	−0.291537
$634$	−50.3715	−2.00051
$635$	4.47657	0.177647
$636$	25.7260	1.02010
$637$	−1.97675	−0.0783219
$638$	0.114469	0.00453186
$639$	4.93674	0.195295
$640$	−17.1280	−0.677043
$641$	28.4813	1.12495	0.562473	−	0.826816i	$-0.309850\pi$
$641$	28.4813	1.12495	0.562473	+	0.826816i	$0.309850\pi$
$642$	99.9113	3.94319
$643$	−16.8517	−0.664566	−0.332283	−	0.943180i	$-0.607819\pi$
$643$	−16.8517	−0.664566	−0.332283	+	0.943180i	$0.607819\pi$
$644$	−21.5301	−0.848407
$645$	9.46091	0.372523
$646$	29.2203	1.14966
$647$	−38.3599	−1.50808	−0.754042	−	0.656827i	$-0.771898\pi$
$647$	−38.3599	−1.50808	−0.754042	+	0.656827i	$0.771898\pi$
$648$	28.5191	1.12034
$649$	42.6819	1.67541
$650$	4.47416	0.175491
$651$	5.87413	0.230225
$652$	66.5241	2.60528
$653$	−43.9415	−1.71956	−0.859782	−	0.510661i	$-0.829401\pi$
$653$	−43.9415	−1.71956	−0.859782	+	0.510661i	$0.829401\pi$
$654$	13.7339	0.537036
$655$	7.84749	0.306627
$656$	1.49402	0.0583317
$657$	−3.16180	−0.123354
$658$	−28.8178	−1.12343
$659$	8.79340	0.342542	0.171271	−	0.985224i	$-0.445213\pi$
$659$	8.79340	0.342542	0.171271	+	0.985224i	$0.445213\pi$
$660$	−26.3437	−1.02543
$661$	1.29233	0.0502658	0.0251329	−	0.999684i	$-0.491999\pi$
$661$	1.29233	0.0502658	0.0251329	+	0.999684i	$0.491999\pi$
$662$	36.2974	1.41074
$663$	18.3261	0.711726
$664$	−6.83927	−0.265415
$665$	−3.00948	−0.116703
$666$	23.3549	0.904985
$667$	0.0893266	0.00345874
$668$	−10.2218	−0.395495
$669$	−10.9950	−0.425091
$670$	−27.6012	−1.06633
$671$	1.84295	0.0711463
$672$	13.3980	0.516841
$673$	−48.2612	−1.86033	−0.930167	−	0.367137i	$-0.880338\pi$
$673$	−48.2612	−1.86033	−0.930167	+	0.367137i	$0.880338\pi$
$674$	−21.5089	−0.828491
$675$	−2.87321	−0.110590
$676$	−28.3950	−1.09211
$677$	39.0178	1.49957	0.749787	−	0.661679i	$-0.230156\pi$
$677$	39.0178	1.49957	0.749787	+	0.661679i	$0.230156\pi$
$678$	47.5045	1.82440
$679$	−14.1011	−0.541150
$680$	−10.9029	−0.418107
$681$	45.6851	1.75066
$682$	−24.0134	−0.919521
$683$	−32.9746	−1.26174	−0.630869	−	0.775889i	$-0.717302\pi$
$683$	−32.9746	−1.26174	−0.630869	+	0.775889i	$0.717302\pi$
$684$	15.7001	0.600307
$685$	−10.2618	−0.392083
$686$	−2.26339	−0.0864165
$687$	2.16114	0.0824525
$688$	2.15917	0.0823177
$689$	−7.53498	−0.287060
$690$	−33.7231	−1.28382
$691$	40.0805	1.52473	0.762367	−	0.647145i	$-0.224037\pi$
$691$	40.0805	1.52473	0.762367	+	0.647145i	$0.224037\pi$
$692$	34.8660	1.32541
$693$	6.52053	0.247694
$694$	2.61559	0.0992864
$695$	−0.297725	−0.0112934
$696$	0.0711679	0.00269761
$697$	12.9944	0.492197
$698$	23.0215	0.871376
$699$	23.1745	0.876542
$700$	3.12292	0.118035
$701$	49.2280	1.85932	0.929658	−	0.368422i	$-0.120102\pi$
$701$	49.2280	1.85932	0.929658	+	0.368422i	$0.120102\pi$
$702$	−12.8552	−0.485188
$703$	−18.5893	−0.701107
$704$	−50.9208	−1.91915
$705$	−27.5159	−1.03631
$706$	59.7590	2.24906
$707$	−9.08375	−0.341630
$708$	73.7995	2.77355
$709$	34.7389	1.30465	0.652324	−	0.757940i	$-0.273794\pi$
$709$	34.7389	1.30465	0.652324	+	0.757940i	$0.273794\pi$
$710$	6.68883	0.251027
$711$	6.86951	0.257627
$712$	4.61912	0.173109
$713$	−18.7390	−0.701783
$714$	20.9834	0.785284
$715$	7.71590	0.288558
$716$	26.6444	0.995747
$717$	−2.08329	−0.0778020
$718$	−74.5140	−2.78084
$719$	6.27008	0.233835	0.116917	−	0.993142i	$-0.462699\pi$
$719$	6.27008	0.233835	0.116917	+	0.993142i	$0.462699\pi$
$720$	0.823921	0.0307057
$721$	−10.6126	−0.395234
$722$	22.5049	0.837547
$723$	−46.6268	−1.73407
$724$	−20.7450	−0.770982
$725$	−0.0129567	−0.000481200 0
$726$	−20.7197	−0.768981
$727$	26.8585	0.996128	0.498064	−	0.867140i	$-0.334044\pi$
$727$	26.8585	0.996128	0.498064	+	0.867140i	$0.334044\pi$
$728$	5.02412	0.186206
$729$	−0.116489	−0.00431442
$730$	−4.28395	−0.158556
$731$	18.7796	0.694588
$732$	3.18656	0.117779
$733$	−9.09623	−0.335977	−0.167988	−	0.985789i	$-0.553727\pi$
$733$	−9.09623	−0.335977	−0.167988	+	0.985789i	$0.553727\pi$
$734$	−42.6732	−1.57510
$735$	−2.16114	−0.0797147
$736$	−42.7411	−1.57546
$737$	−47.5996	−1.75335
$738$	11.4532	0.421599
$739$	43.4774	1.59934	0.799670	−	0.600440i	$-0.205008\pi$
$739$	43.4774	1.59934	0.799670	+	0.600440i	$0.205008\pi$
$740$	19.2900	0.709113
$741$	−12.8566	−0.472299
$742$	−8.62756	−0.316728
$743$	−9.40210	−0.344929	−0.172465	−	0.985016i	$-0.555173\pi$
$743$	−9.40210	−0.344929	−0.172465	+	0.985016i	$0.555173\pi$
$744$	−14.9297	−0.547349
$745$	−2.85795	−0.104707
$746$	−16.1130	−0.589937
$747$	4.49523	0.164472
$748$	−52.2913	−1.91196
$749$	−20.4256	−0.746333
$750$	4.89149	0.178612
$751$	−31.6734	−1.15578	−0.577889	−	0.816115i	$-0.696123\pi$
$751$	−31.6734	−1.15578	−0.577889	+	0.816115i	$0.696123\pi$
$752$	−6.27970	−0.228997
$753$	−62.4208	−2.27474
$754$	−0.0579704	−0.00211116
$755$	0.163031	0.00593330
$756$	−8.97280	−0.326337
$757$	−40.2704	−1.46365	−0.731827	−	0.681491i	$-0.761332\pi$
$757$	−40.2704	−1.46365	−0.731827	+	0.681491i	$0.761332\pi$
$758$	−2.92288	−0.106164
$759$	−58.1570	−2.11097
$760$	7.64889	0.277454
$761$	38.9769	1.41291	0.706455	−	0.707758i	$-0.250293\pi$
$761$	38.9769	1.41291	0.706455	+	0.707758i	$0.250293\pi$
$762$	21.8971	0.793248
$763$	−2.80770	−0.101646
$764$	33.5135	1.21247
$765$	7.16612	0.259092
$766$	−52.9356	−1.91264
$767$	−21.6154	−0.780486
$768$	−27.3950	−0.988532
$769$	2.52568	0.0910783	0.0455392	−	0.998963i	$-0.485499\pi$
$769$	2.52568	0.0910783	0.0455392	+	0.998963i	$0.485499\pi$
$770$	8.83471	0.318381
$771$	−0.595479	−0.0214456
$772$	41.8285	1.50544
$773$	25.2693	0.908874	0.454437	−	0.890779i	$-0.349840\pi$
$773$	25.2693	0.908874	0.454437	+	0.890779i	$0.349840\pi$
$774$	16.5523	0.594961
$775$	2.71807	0.0976361
$776$	35.8393	1.28656
$777$	−13.3491	−0.478897
$778$	−15.8364	−0.567763
$779$	−9.11615	−0.326620
$780$	13.3412	0.477692
$781$	11.5352	0.412762
$782$	−66.9391	−2.39374
$783$	0.0372273	0.00133040
$784$	−0.493215	−0.0176148
$785$	13.1505	0.469362
$786$	38.3859	1.36918
$787$	−14.1724	−0.505191	−0.252596	−	0.967572i	$-0.581284\pi$
$787$	−14.1724	−0.505191	−0.252596	+	0.967572i	$0.581284\pi$
$788$	−24.3293	−0.866697
$789$	−47.4597	−1.68961
$790$	9.30755	0.331148
$791$	−9.71166	−0.345307
$792$	−16.5726	−0.588881
$793$	−0.933324	−0.0331433
$794$	−3.20845	−0.113863
$795$	−8.23781	−0.292165
$796$	−25.4282	−0.901279
$797$	22.3237	0.790746	0.395373	−	0.918521i	$-0.370615\pi$
$797$	22.3237	0.790746	0.395373	+	0.918521i	$0.370615\pi$
$798$	−14.7208	−0.521112
$799$	−54.6182	−1.93225
$800$	6.19954	0.219187
$801$	−3.03600	−0.107272
$802$	14.3178	0.505580
$803$	−7.38787	−0.260712
$804$	−82.3024	−2.90258
$805$	6.89424	0.242990
$806$	12.1611	0.428356
$807$	−51.0136	−1.79576
$808$	23.0873	0.812207
$809$	−28.5386	−1.00336	−0.501681	−	0.865052i	$-0.667285\pi$
$809$	−28.5386	−1.00336	−0.501681	+	0.865052i	$0.667285\pi$
$810$	−25.3973	−0.892370
$811$	−49.4079	−1.73495	−0.867473	−	0.497483i	$-0.834258\pi$
$811$	−49.4079	−1.73495	−0.867473	+	0.497483i	$0.834258\pi$
$812$	−0.0404627	−0.00141996
$813$	−38.7149	−1.35779
$814$	54.5711	1.91272
$815$	−21.3019	−0.746173
$816$	4.57250	0.160069
$817$	−13.1747	−0.460926
$818$	−20.3916	−0.712976
$819$	−3.30219	−0.115388
$820$	9.45978	0.330350
$821$	10.5692	0.368868	0.184434	−	0.982845i	$-0.440955\pi$
$821$	10.5692	0.368868	0.184434	+	0.982845i	$0.440955\pi$
$822$	−50.1955	−1.75077
$823$	26.8982	0.937613	0.468806	−	0.883301i	$-0.344684\pi$
$823$	26.8982	0.937613	0.468806	+	0.883301i	$0.344684\pi$
$824$	26.9730	0.939647
$825$	8.43560	0.293690
$826$	−24.7496	−0.861150
$827$	53.1853	1.84943	0.924717	−	0.380656i	$-0.124302\pi$
$827$	53.1853	1.84943	0.924717	+	0.380656i	$0.124302\pi$
$828$	−35.9663	−1.24992
$829$	−21.0463	−0.730969	−0.365485	−	0.930817i	$-0.619097\pi$
$829$	−21.0463	−0.730969	−0.365485	+	0.930817i	$0.619097\pi$
$830$	6.09062	0.211408
$831$	23.0236	0.798680
$832$	25.7878	0.894030
$833$	−4.28978	−0.148632
$834$	−1.45632	−0.0504282
$835$	3.27317	0.113273
$836$	36.6848	1.26877
$837$	−7.80959	−0.269939
$838$	−25.7135	−0.888260
$839$	−21.6081	−0.745995	−0.372998	−	0.927832i	$-0.621670\pi$
$839$	−21.6081	−0.745995	−0.372998	+	0.927832i	$0.621670\pi$
$840$	5.49274	0.189518
$841$	−28.9998	−0.999994
$842$	−90.8527	−3.13099
$843$	17.9342	0.617687
$844$	−10.5992	−0.364840
$845$	9.09244	0.312790
$846$	−48.1404	−1.65510
$847$	4.23587	0.145546
$848$	−1.88003	−0.0645607
$849$	−42.4881	−1.45819
$850$	9.70943	0.333031
$851$	42.5850	1.45980
$852$	19.9450	0.683305
$853$	−11.0517	−0.378404	−0.189202	−	0.981938i	$-0.560590\pi$
$853$	−11.0517	−0.378404	−0.189202	+	0.981938i	$0.560590\pi$
$854$	−1.06866	−0.0365687
$855$	−5.02737	−0.171932
$856$	51.9136	1.77437
$857$	9.21768	0.314870	0.157435	−	0.987529i	$-0.449678\pi$
$857$	9.21768	0.314870	0.157435	+	0.987529i	$0.449678\pi$
$858$	37.7422	1.28850
$859$	−23.8202	−0.812735	−0.406367	−	0.913710i	$-0.633205\pi$
$859$	−23.8202	−0.812735	−0.406367	+	0.913710i	$0.633205\pi$
$860$	13.6714	0.466189
$861$	−6.54640	−0.223101
$862$	85.6177	2.91615
$863$	−42.8269	−1.45785	−0.728923	−	0.684596i	$-0.759979\pi$
$863$	−42.8269	−1.45785	−0.728923	+	0.684596i	$0.759979\pi$
$864$	−17.8126	−0.605996
$865$	−11.1646	−0.379606
$866$	9.00687	0.306066
$867$	3.03036	0.102916
$868$	8.48832	0.288113
$869$	16.0513	0.544503
$870$	−0.0633776	−0.00214870
$871$	24.1058	0.816795
$872$	7.13606	0.241658
$873$	−23.5560	−0.797250
$874$	46.9609	1.58848
$875$	−1.00000	−0.0338062
$876$	−12.7741	−0.431595
$877$	−3.59095	−0.121258	−0.0606289	−	0.998160i	$-0.519311\pi$
$877$	−3.59095	−0.121258	−0.0606289	+	0.998160i	$0.519311\pi$
$878$	44.0071	1.48517
$879$	−48.5590	−1.63785
$880$	1.92517	0.0648976
$881$	12.8070	0.431478	0.215739	−	0.976451i	$-0.430784\pi$
$881$	12.8070	0.431478	0.215739	+	0.976451i	$0.430784\pi$
$882$	−3.78101	−0.127313
$883$	−37.1391	−1.24983	−0.624916	−	0.780692i	$-0.714867\pi$
$883$	−37.1391	−1.24983	−0.624916	+	0.780692i	$0.714867\pi$
$884$	26.4819	0.890681
$885$	−23.6316	−0.794366
$886$	25.9846	0.872971
$887$	10.5169	0.353122	0.176561	−	0.984290i	$-0.443503\pi$
$887$	10.5169	0.353122	0.176561	+	0.984290i	$0.443503\pi$
$888$	33.9281	1.13855
$889$	−4.47657	−0.150139
$890$	−4.11350	−0.137885
$891$	−43.7988	−1.46732
$892$	−15.8882	−0.531975
$893$	38.3172	1.28224
$894$	−13.9796	−0.467549
$895$	−8.53189	−0.285189
$896$	17.1280	0.572205
$897$	29.4524	0.983388
$898$	−38.7209	−1.29213
$899$	−0.0352173	−0.00117456
$900$	5.21687	0.173896
$901$	−16.3518	−0.544756
$902$	26.7616	0.891065
$903$	−9.46091	−0.314839
$904$	24.6832	0.820950
$905$	6.64283	0.220815
$906$	0.797463	0.0264939
$907$	−41.7177	−1.38521	−0.692606	−	0.721316i	$-0.743538\pi$
$907$	−41.7177	−1.38521	−0.692606	+	0.721316i	$0.743538\pi$
$908$	66.0165	2.19084
$909$	−15.1745	−0.503306
$910$	−4.47416	−0.148317
$911$	22.8665	0.757602	0.378801	−	0.925478i	$-0.376336\pi$
$911$	22.8665	0.757602	0.378801	+	0.925478i	$0.376336\pi$
$912$	−3.20782	−0.106222
$913$	10.5036	0.347617
$914$	4.49867	0.148803
$915$	−1.02038	−0.0337327
$916$	3.12292	0.103184
$917$	−7.84749	−0.259147
$918$	−27.8972	−0.920745
$919$	43.3379	1.42959	0.714793	−	0.699336i	$-0.246521\pi$
$919$	43.3379	1.42959	0.714793	+	0.699336i	$0.246521\pi$
$920$	−17.5224	−0.577696
$921$	67.2571	2.21620
$922$	−0.225972	−0.00744199
$923$	−5.84176	−0.192284
$924$	26.3437	0.866644
$925$	−6.17690	−0.203095
$926$	21.3487	0.701562
$927$	−17.7284	−0.582278
$928$	−0.0803256	−0.00263682
$929$	44.7000	1.46656	0.733279	−	0.679928i	$-0.237989\pi$
$929$	44.7000	1.46656	0.733279	+	0.679928i	$0.237989\pi$
$930$	13.2954	0.435974
$931$	3.00948	0.0986317
$932$	33.4880	1.09694
$933$	−10.0902	−0.330337
$934$	40.0721	1.31120
$935$	16.7444	0.547599
$936$	8.39284	0.274329
$937$	49.0503	1.60240	0.801201	−	0.598395i	$-0.204195\pi$
$937$	49.0503	1.60240	0.801201	+	0.598395i	$0.204195\pi$
$938$	27.6012	0.901212
$939$	−28.0585	−0.915654
$940$	−39.7615	−1.29688
$941$	18.7777	0.612137	0.306068	−	0.952010i	$-0.400986\pi$
$941$	18.7777	0.612137	0.306068	+	0.952010i	$0.400986\pi$
$942$	64.3255	2.09584
$943$	20.8837	0.680065
$944$	−5.39320	−0.175534
$945$	2.87321	0.0934655
$946$	38.6762	1.25747
$947$	−34.0029	−1.10495	−0.552473	−	0.833531i	$-0.686316\pi$
$947$	−34.0029	−1.10495	−0.552473	+	0.833531i	$0.686316\pi$
$948$	27.7536	0.901396
$949$	3.74144	0.121452
$950$	−6.81162	−0.220998
$951$	48.0959	1.55962
$952$	10.9029	0.353365
$953$	−0.882107	−0.0285743	−0.0142871	−	0.999898i	$-0.504548\pi$
$953$	−0.882107	−0.0285743	−0.0142871	+	0.999898i	$0.504548\pi$
$954$	−14.4124	−0.466620
$955$	−10.7315	−0.347262
$956$	−3.01043	−0.0973644
$957$	−0.109298	−0.00353309
$958$	−39.0782	−1.26256
$959$	10.2618	0.331371
$960$	28.1931	0.909930
$961$	−23.6121	−0.761680
$962$	−27.6364	−0.891034
$963$	−34.1211	−1.09954
$964$	−67.3774	−2.17008
$965$	−13.3940	−0.431169
$966$	33.7231	1.08502
$967$	−22.7401	−0.731271	−0.365636	−	0.930758i	$-0.619148\pi$
$967$	−22.7401	−0.731271	−0.365636	+	0.930758i	$0.619148\pi$
$968$	−10.7659	−0.346029
$969$	−27.9003	−0.896286
$970$	−31.9162	−1.02477
$971$	−45.1914	−1.45026	−0.725130	−	0.688611i	$-0.758221\pi$
$971$	−45.1914	−1.45026	−0.725130	+	0.688611i	$0.758221\pi$
$972$	−48.8122	−1.56565
$973$	0.297725	0.00954463
$974$	66.2786	2.12370
$975$	−4.27204	−0.136815
$976$	−0.232871	−0.00745403
$977$	−5.04678	−0.161461	−0.0807304	−	0.996736i	$-0.525725\pi$
$977$	−5.04678	−0.161461	−0.0807304	+	0.996736i	$0.525725\pi$
$978$	−104.198	−3.33188
$979$	−7.09392	−0.226723
$980$	−3.12292	−0.0997580
$981$	−4.69030	−0.149750
$982$	38.6662	1.23389
$983$	10.7958	0.344334	0.172167	−	0.985068i	$-0.444923\pi$
$983$	10.7958	0.344334	0.172167	+	0.985068i	$0.444923\pi$
$984$	16.6383	0.530410
$985$	7.79058	0.248228
$986$	−0.125802	−0.00400636
$987$	27.5159	0.875842
$988$	−18.5782	−0.591053
$989$	30.1812	0.959708
$990$	14.7585	0.469055
$991$	−57.8595	−1.83797	−0.918984	−	0.394296i	$-0.870989\pi$
$991$	−57.8595	−1.83797	−0.918984	+	0.394296i	$0.870989\pi$
$992$	16.8508	0.535013
$993$	−34.6576	−1.09983
$994$	−6.68883	−0.212157
$995$	8.14245	0.258133
$996$	18.1612	0.575461
$997$	41.2547	1.30655	0.653274	−	0.757121i	$-0.273395\pi$
$997$	41.2547	1.30655	0.653274	+	0.757121i	$0.273395\pi$
$998$	−14.3704	−0.454886
$999$	17.7475	0.561507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.6	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.6	✓	45	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26339 q^{2} +2.16114 q^{3} +3.12292 q^{4} -1.00000 q^{5} -4.89149 q^{6} +1.00000 q^{7} -2.54160 q^{8} +1.67051 q^{9} +O(q^{10})\)	\(q-2.26339 q^{2} +2.16114 q^{3} +3.12292 q^{4} -1.00000 q^{5} -4.89149 q^{6} +1.00000 q^{7} -2.54160 q^{8} +1.67051 q^{9} +2.26339 q^{10} +3.90332 q^{11} +6.74905 q^{12} -1.97675 q^{13} -2.26339 q^{14} -2.16114 q^{15} -0.493215 q^{16} -4.28978 q^{17} -3.78101 q^{18} +3.00948 q^{19} -3.12292 q^{20} +2.16114 q^{21} -8.83471 q^{22} -6.89424 q^{23} -5.49274 q^{24} +1.00000 q^{25} +4.47416 q^{26} -2.87321 q^{27} +3.12292 q^{28} -0.0129567 q^{29} +4.89149 q^{30} +2.71807 q^{31} +6.19954 q^{32} +8.43560 q^{33} +9.70943 q^{34} -1.00000 q^{35} +5.21687 q^{36} -6.17690 q^{37} -6.81162 q^{38} -4.27204 q^{39} +2.54160 q^{40} -3.02915 q^{41} -4.89149 q^{42} -4.37775 q^{43} +12.1897 q^{44} -1.67051 q^{45} +15.6043 q^{46} +12.7322 q^{47} -1.06591 q^{48} +1.00000 q^{49} -2.26339 q^{50} -9.27080 q^{51} -6.17324 q^{52} +3.81179 q^{53} +6.50318 q^{54} -3.90332 q^{55} -2.54160 q^{56} +6.50390 q^{57} +0.0293260 q^{58} +10.9348 q^{59} -6.74905 q^{60} +0.472150 q^{61} -6.15205 q^{62} +1.67051 q^{63} -13.0455 q^{64} +1.97675 q^{65} -19.0930 q^{66} -12.1947 q^{67} -13.3966 q^{68} -14.8994 q^{69} +2.26339 q^{70} +2.95523 q^{71} -4.24577 q^{72} -1.89272 q^{73} +13.9807 q^{74} +2.16114 q^{75} +9.39836 q^{76} +3.90332 q^{77} +9.66927 q^{78} +4.11222 q^{79} +0.493215 q^{80} -11.2209 q^{81} +6.85613 q^{82} +2.69093 q^{83} +6.74905 q^{84} +4.28978 q^{85} +9.90854 q^{86} -0.0280012 q^{87} -9.92067 q^{88} -1.81741 q^{89} +3.78101 q^{90} -1.97675 q^{91} -21.5301 q^{92} +5.87413 q^{93} -28.8178 q^{94} -3.00948 q^{95} +13.3980 q^{96} -14.1011 q^{97} -2.26339 q^{98} +6.52053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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