LMFDB - Embedded newform 4015.2.a.h.1.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.16679 q^{2} -1.55174 q^{3} +2.69497 q^{4} +1.00000 q^{5} -3.36228 q^{6} +1.94995 q^{7} +1.50584 q^{8} -0.592115 q^{9} +O(q^{10})$	\(q+2.16679 q^{2} -1.55174 q^{3} +2.69497 q^{4} +1.00000 q^{5} -3.36228 q^{6} +1.94995 q^{7} +1.50584 q^{8} -0.592115 q^{9} +2.16679 q^{10} +1.00000 q^{11} -4.18188 q^{12} +4.81875 q^{13} +4.22513 q^{14} -1.55174 q^{15} -2.12709 q^{16} +4.21395 q^{17} -1.28299 q^{18} -4.40411 q^{19} +2.69497 q^{20} -3.02581 q^{21} +2.16679 q^{22} -1.88088 q^{23} -2.33667 q^{24} +1.00000 q^{25} +10.4412 q^{26} +5.57401 q^{27} +5.25505 q^{28} +7.25876 q^{29} -3.36228 q^{30} -7.65096 q^{31} -7.62064 q^{32} -1.55174 q^{33} +9.13074 q^{34} +1.94995 q^{35} -1.59573 q^{36} +8.64926 q^{37} -9.54277 q^{38} -7.47743 q^{39} +1.50584 q^{40} -2.23388 q^{41} -6.55629 q^{42} +9.48096 q^{43} +2.69497 q^{44} -0.592115 q^{45} -4.07546 q^{46} +10.0271 q^{47} +3.30068 q^{48} -3.19769 q^{49} +2.16679 q^{50} -6.53894 q^{51} +12.9864 q^{52} +3.93673 q^{53} +12.0777 q^{54} +1.00000 q^{55} +2.93632 q^{56} +6.83402 q^{57} +15.7282 q^{58} +1.70367 q^{59} -4.18188 q^{60} +4.40338 q^{61} -16.5780 q^{62} -1.15460 q^{63} -12.2581 q^{64} +4.81875 q^{65} -3.36228 q^{66} -2.87650 q^{67} +11.3565 q^{68} +2.91863 q^{69} +4.22513 q^{70} -6.41228 q^{71} -0.891632 q^{72} +1.00000 q^{73} +18.7411 q^{74} -1.55174 q^{75} -11.8689 q^{76} +1.94995 q^{77} -16.2020 q^{78} -11.2340 q^{79} -2.12709 q^{80} -6.87305 q^{81} -4.84034 q^{82} -13.2014 q^{83} -8.15445 q^{84} +4.21395 q^{85} +20.5432 q^{86} -11.2637 q^{87} +1.50584 q^{88} +0.759394 q^{89} -1.28299 q^{90} +9.39633 q^{91} -5.06890 q^{92} +11.8723 q^{93} +21.7266 q^{94} -4.40411 q^{95} +11.8252 q^{96} +13.4213 q^{97} -6.92871 q^{98} -0.592115 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	2.16679	1.53215	0.766075	−	0.642751i	$-0.222207\pi$
$2$	2.16679	1.53215	0.766075	+	0.642751i	$0.222207\pi$
$3$	−1.55174	−0.895895	−0.447948	−	0.894060i	$-0.647845\pi$
$3$	−1.55174	−0.895895	−0.447948	+	0.894060i	$0.647845\pi$
$4$	2.69497	1.34748
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.36228	−1.37265
$7$	1.94995	0.737012	0.368506	−	0.929625i	$-0.379869\pi$
$7$	1.94995	0.737012	0.368506	+	0.929625i	$0.379869\pi$
$8$	1.50584	0.532396
$9$	−0.592115	−0.197372
$10$	2.16679	0.685198
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.18188	−1.20720
$13$	4.81875	1.33648	0.668240	−	0.743945i	$-0.267048\pi$
$13$	4.81875	1.33648	0.668240	+	0.743945i	$0.267048\pi$
$14$	4.22513	1.12921
$15$	−1.55174	−0.400657
$16$	−2.12709	−0.531773
$17$	4.21395	1.02203	0.511017	−	0.859571i	$-0.329269\pi$
$17$	4.21395	1.02203	0.511017	+	0.859571i	$0.329269\pi$
$18$	−1.28299	−0.302403
$19$	−4.40411	−1.01037	−0.505186	−	0.863010i	$-0.668576\pi$
$19$	−4.40411	−1.01037	−0.505186	+	0.863010i	$0.668576\pi$
$20$	2.69497	0.602613
$21$	−3.02581	−0.660286
$22$	2.16679	0.461961
$23$	−1.88088	−0.392190	−0.196095	−	0.980585i	$-0.562826\pi$
$23$	−1.88088	−0.392190	−0.196095	+	0.980585i	$0.562826\pi$
$24$	−2.33667	−0.476971
$25$	1.00000	0.200000
$26$	10.4412	2.04769
$27$	5.57401	1.07272
$28$	5.25505	0.993112
$29$	7.25876	1.34792	0.673959	−	0.738769i	$-0.264592\pi$
$29$	7.25876	1.34792	0.673959	+	0.738769i	$0.264592\pi$
$30$	−3.36228	−0.613866
$31$	−7.65096	−1.37415	−0.687076	−	0.726585i	$-0.741106\pi$
$31$	−7.65096	−1.37415	−0.687076	+	0.726585i	$0.741106\pi$
$32$	−7.62064	−1.34715
$33$	−1.55174	−0.270123
$34$	9.13074	1.56591
$35$	1.94995	0.329602
$36$	−1.59573	−0.265955
$37$	8.64926	1.42193	0.710964	−	0.703228i	$-0.248259\pi$
$37$	8.64926	1.42193	0.710964	+	0.703228i	$0.248259\pi$
$38$	−9.54277	−1.54804
$39$	−7.47743	−1.19735
$40$	1.50584	0.238095
$41$	−2.23388	−0.348873	−0.174437	−	0.984668i	$-0.555810\pi$
$41$	−2.23388	−0.348873	−0.174437	+	0.984668i	$0.555810\pi$
$42$	−6.55629	−1.01166
$43$	9.48096	1.44583	0.722917	−	0.690935i	$-0.242801\pi$
$43$	9.48096	1.44583	0.722917	+	0.690935i	$0.242801\pi$
$44$	2.69497	0.406281
$45$	−0.592115	−0.0882673
$46$	−4.07546	−0.600894
$47$	10.0271	1.46260	0.731302	−	0.682054i	$-0.238913\pi$
$47$	10.0271	1.46260	0.731302	+	0.682054i	$0.238913\pi$
$48$	3.30068	0.476413
$49$	−3.19769	−0.456813
$50$	2.16679	0.306430
$51$	−6.53894	−0.915635
$52$	12.9864	1.80089
$53$	3.93673	0.540751	0.270375	−	0.962755i	$-0.412852\pi$
$53$	3.93673	0.540751	0.270375	+	0.962755i	$0.412852\pi$
$54$	12.0777	1.64357
$55$	1.00000	0.134840
$56$	2.93632	0.392382
$57$	6.83402	0.905188
$58$	15.7282	2.06521
$59$	1.70367	0.221799	0.110899	−	0.993832i	$-0.464627\pi$
$59$	1.70367	0.221799	0.110899	+	0.993832i	$0.464627\pi$
$60$	−4.18188	−0.539878
$61$	4.40338	0.563795	0.281897	−	0.959445i	$-0.409036\pi$
$61$	4.40338	0.563795	0.281897	+	0.959445i	$0.409036\pi$
$62$	−16.5780	−2.10541
$63$	−1.15460	−0.145465
$64$	−12.2581	−1.53226
$65$	4.81875	0.597692
$66$	−3.36228	−0.413868
$67$	−2.87650	−0.351420	−0.175710	−	0.984442i	$-0.556222\pi$
$67$	−2.87650	−0.351420	−0.175710	+	0.984442i	$0.556222\pi$
$68$	11.3565	1.37717
$69$	2.91863	0.351361
$70$	4.22513	0.505000
$71$	−6.41228	−0.760998	−0.380499	−	0.924781i	$-0.624248\pi$
$71$	−6.41228	−0.760998	−0.380499	+	0.924781i	$0.624248\pi$
$72$	−0.891632	−0.105080
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	18.7411	2.17861
$75$	−1.55174	−0.179179
$76$	−11.8689	−1.36146
$77$	1.94995	0.222218
$78$	−16.2020	−1.83451
$79$	−11.2340	−1.26392	−0.631960	−	0.775001i	$-0.717749\pi$
$79$	−11.2340	−1.26392	−0.631960	+	0.775001i	$0.717749\pi$
$80$	−2.12709	−0.237816
$81$	−6.87305	−0.763673
$82$	−4.84034	−0.534526
$83$	−13.2014	−1.44904	−0.724520	−	0.689254i	$-0.757938\pi$
$83$	−13.2014	−1.44904	−0.724520	+	0.689254i	$0.757938\pi$
$84$	−8.15445	−0.889724
$85$	4.21395	0.457067
$86$	20.5432	2.21523
$87$	−11.2637	−1.20759
$88$	1.50584	0.160523
$89$	0.759394	0.0804956	0.0402478	−	0.999190i	$-0.487185\pi$
$89$	0.759394	0.0804956	0.0402478	+	0.999190i	$0.487185\pi$
$90$	−1.28299	−0.135239
$91$	9.39633	0.985003
$92$	−5.06890	−0.528470
$93$	11.8723	1.23110
$94$	21.7266	2.24093
$95$	−4.40411	−0.451852
$96$	11.8252	1.20691
$97$	13.4213	1.36273	0.681363	−	0.731945i	$-0.261387\pi$
$97$	13.4213	1.36273	0.681363	+	0.731945i	$0.261387\pi$
$98$	−6.92871	−0.699905
$99$	−0.592115	−0.0595098
$100$	2.69497	0.269497
$101$	13.5132	1.34462	0.672309	−	0.740271i	$-0.265303\pi$
$101$	13.5132	1.34462	0.672309	+	0.740271i	$0.265303\pi$
$102$	−14.1685	−1.40289
$103$	2.49746	0.246082	0.123041	−	0.992402i	$-0.460735\pi$
$103$	2.49746	0.246082	0.123041	+	0.992402i	$0.460735\pi$
$104$	7.25628	0.711537
$105$	−3.02581	−0.295289
$106$	8.53005	0.828511
$107$	20.4722	1.97912	0.989560	−	0.144121i	$-0.0460354\pi$
$107$	20.4722	1.97912	0.989560	+	0.144121i	$0.0460354\pi$
$108$	15.0218	1.44547
$109$	9.45065	0.905208	0.452604	−	0.891712i	$-0.350495\pi$
$109$	9.45065	0.905208	0.452604	+	0.891712i	$0.350495\pi$
$110$	2.16679	0.206595
$111$	−13.4214	−1.27390
$112$	−4.14773	−0.391923
$113$	−9.91628	−0.932845	−0.466423	−	0.884562i	$-0.654457\pi$
$113$	−9.91628	−0.932845	−0.466423	+	0.884562i	$0.654457\pi$
$114$	14.8079	1.38688
$115$	−1.88088	−0.175393
$116$	19.5621	1.81630
$117$	−2.85326	−0.263784
$118$	3.69149	0.339829
$119$	8.21700	0.753251
$120$	−2.33667	−0.213308
$121$	1.00000	0.0909091
$122$	9.54118	0.863818
$123$	3.46639	0.312554
$124$	−20.6191	−1.85165
$125$	1.00000	0.0894427
$126$	−2.50176	−0.222875
$127$	12.3837	1.09888	0.549439	−	0.835534i	$-0.314841\pi$
$127$	12.3837	1.09888	0.549439	+	0.835534i	$0.314841\pi$
$128$	−11.3195	−1.00051
$129$	−14.7120	−1.29532
$130$	10.4412	0.915754
$131$	−6.77735	−0.592140	−0.296070	−	0.955166i	$-0.595676\pi$
$131$	−6.77735	−0.592140	−0.296070	+	0.955166i	$0.595676\pi$
$132$	−4.18188	−0.363986
$133$	−8.58780	−0.744657
$134$	−6.23276	−0.538429
$135$	5.57401	0.479735
$136$	6.34555	0.544126
$137$	−12.3842	−1.05805	−0.529027	−	0.848605i	$-0.677443\pi$
$137$	−12.3842	−1.05805	−0.529027	+	0.848605i	$0.677443\pi$
$138$	6.32404	0.538338
$139$	0.678872	0.0575812	0.0287906	−	0.999585i	$-0.490834\pi$
$139$	0.678872	0.0575812	0.0287906	+	0.999585i	$0.490834\pi$
$140$	5.25505	0.444133
$141$	−15.5594	−1.31034
$142$	−13.8940	−1.16596
$143$	4.81875	0.402964
$144$	1.25948	0.104957
$145$	7.25876	0.602807
$146$	2.16679	0.179325
$147$	4.96197	0.409256
$148$	23.3094	1.91602
$149$	19.3630	1.58628	0.793138	−	0.609041i	$-0.208446\pi$
$149$	19.3630	1.58628	0.793138	+	0.609041i	$0.208446\pi$
$150$	−3.36228	−0.274529
$151$	−7.19974	−0.585907	−0.292953	−	0.956127i	$-0.594638\pi$
$151$	−7.19974	−0.585907	−0.292953	+	0.956127i	$0.594638\pi$
$152$	−6.63190	−0.537918
$153$	−2.49514	−0.201721
$154$	4.22513	0.340471
$155$	−7.65096	−0.614540
$156$	−20.1514	−1.61340
$157$	17.5412	1.39994	0.699971	−	0.714172i	$-0.253196\pi$
$157$	17.5412	1.39994	0.699971	+	0.714172i	$0.253196\pi$
$158$	−24.3416	−1.93652
$159$	−6.10876	−0.484456
$160$	−7.62064	−0.602464
$161$	−3.66762	−0.289049
$162$	−14.8924	−1.17006
$163$	11.4664	0.898120	0.449060	−	0.893502i	$-0.351759\pi$
$163$	11.4664	0.898120	0.449060	+	0.893502i	$0.351759\pi$
$164$	−6.02022	−0.470100
$165$	−1.55174	−0.120802
$166$	−28.6046	−2.22015
$167$	−8.58379	−0.664234	−0.332117	−	0.943238i	$-0.607763\pi$
$167$	−8.58379	−0.664234	−0.332117	+	0.943238i	$0.607763\pi$
$168$	−4.55639	−0.351533
$169$	10.2204	0.786181
$170$	9.13074	0.700295
$171$	2.60774	0.199419
$172$	25.5509	1.94824
$173$	−7.57078	−0.575596	−0.287798	−	0.957691i	$-0.592923\pi$
$173$	−7.57078	−0.575596	−0.287798	+	0.957691i	$0.592923\pi$
$174$	−24.4060	−1.85021
$175$	1.94995	0.147402
$176$	−2.12709	−0.160336
$177$	−2.64364	−0.198708
$178$	1.64545	0.123331
$179$	19.5349	1.46011	0.730055	−	0.683389i	$-0.239495\pi$
$179$	19.5349	1.46011	0.730055	+	0.683389i	$0.239495\pi$
$180$	−1.59573	−0.118939
$181$	3.55132	0.263968	0.131984	−	0.991252i	$-0.457865\pi$
$181$	3.55132	0.263968	0.131984	+	0.991252i	$0.457865\pi$
$182$	20.3598	1.50917
$183$	−6.83288	−0.505101
$184$	−2.83231	−0.208800
$185$	8.64926	0.635906
$186$	25.7247	1.88622
$187$	4.21395	0.308155
$188$	27.0227	1.97083
$189$	10.8691	0.790608
$190$	−9.54277	−0.692305
$191$	−23.4059	−1.69359	−0.846796	−	0.531917i	$-0.821472\pi$
$191$	−23.4059	−1.69359	−0.846796	+	0.531917i	$0.821472\pi$
$192$	19.0214	1.37275
$193$	6.26351	0.450858	0.225429	−	0.974260i	$-0.427622\pi$
$193$	6.26351	0.450858	0.225429	+	0.974260i	$0.427622\pi$
$194$	29.0811	2.08790
$195$	−7.47743	−0.535470
$196$	−8.61766	−0.615547
$197$	−17.4535	−1.24351	−0.621754	−	0.783213i	$-0.713580\pi$
$197$	−17.4535	−1.24351	−0.621754	+	0.783213i	$0.713580\pi$
$198$	−1.28299	−0.0911780
$199$	5.74997	0.407605	0.203802	−	0.979012i	$-0.434670\pi$
$199$	5.74997	0.407605	0.203802	+	0.979012i	$0.434670\pi$
$200$	1.50584	0.106479
$201$	4.46357	0.314836
$202$	29.2803	2.06016
$203$	14.1542	0.993433
$204$	−17.6222	−1.23380
$205$	−2.23388	−0.156021
$206$	5.41146	0.377034
$207$	1.11370	0.0774073
$208$	−10.2499	−0.710704
$209$	−4.40411	−0.304639
$210$	−6.55629	−0.452427
$211$	4.57138	0.314707	0.157353	−	0.987542i	$-0.449704\pi$
$211$	4.57138	0.314707	0.157353	+	0.987542i	$0.449704\pi$
$212$	10.6093	0.728653
$213$	9.95017	0.681774
$214$	44.3588	3.03231
$215$	9.48096	0.646596
$216$	8.39359	0.571111
$217$	−14.9190	−1.01277
$218$	20.4775	1.38691
$219$	−1.55174	−0.104857
$220$	2.69497	0.181695
$221$	20.3060	1.36593
$222$	−29.0812	−1.95180
$223$	9.16722	0.613882	0.306941	−	0.951728i	$-0.400694\pi$
$223$	9.16722	0.613882	0.306941	+	0.951728i	$0.400694\pi$
$224$	−14.8599	−0.992867
$225$	−0.592115	−0.0394743
$226$	−21.4865	−1.42926
$227$	−1.31260	−0.0871204	−0.0435602	−	0.999051i	$-0.513870\pi$
$227$	−1.31260	−0.0871204	−0.0435602	+	0.999051i	$0.513870\pi$
$228$	18.4174	1.21972
$229$	−11.1590	−0.737404	−0.368702	−	0.929548i	$-0.620198\pi$
$229$	−11.1590	−0.737404	−0.368702	+	0.929548i	$0.620198\pi$
$230$	−4.07546	−0.268728
$231$	−3.02581	−0.199084
$232$	10.9306	0.717626
$233$	4.34899	0.284912	0.142456	−	0.989801i	$-0.454500\pi$
$233$	4.34899	0.284912	0.142456	+	0.989801i	$0.454500\pi$
$234$	−6.18240	−0.404156
$235$	10.0271	0.654096
$236$	4.59133	0.298870
$237$	17.4322	1.13234
$238$	17.8045	1.15409
$239$	−18.7395	−1.21216	−0.606079	−	0.795405i	$-0.707258\pi$
$239$	−18.7395	−1.21216	−0.606079	+	0.795405i	$0.707258\pi$
$240$	3.30068	0.213058
$241$	−25.5824	−1.64791	−0.823954	−	0.566656i	$-0.808237\pi$
$241$	−25.5824	−1.64791	−0.823954	+	0.566656i	$0.808237\pi$
$242$	2.16679	0.139286
$243$	−6.05688	−0.388549
$244$	11.8670	0.759704
$245$	−3.19769	−0.204293
$246$	7.51093	0.478879
$247$	−21.2223	−1.35034
$248$	−11.5211	−0.731593
$249$	20.4851	1.29819
$250$	2.16679	0.137040
$251$	−28.4822	−1.79778	−0.898891	−	0.438172i	$-0.855626\pi$
$251$	−28.4822	−1.79778	−0.898891	+	0.438172i	$0.855626\pi$
$252$	−3.11160	−0.196012
$253$	−1.88088	−0.118250
$254$	26.8329	1.68365
$255$	−6.53894	−0.409484
$256$	−0.0106063	−0.000662897 0
$257$	−9.96006	−0.621291	−0.310646	−	0.950526i	$-0.600545\pi$
$257$	−9.96006	−0.621291	−0.310646	+	0.950526i	$0.600545\pi$
$258$	−31.8777	−1.98462
$259$	16.8656	1.04798
$260$	12.9864	0.805380
$261$	−4.29802	−0.266041
$262$	−14.6851	−0.907247
$263$	5.96789	0.367996	0.183998	−	0.982927i	$-0.441096\pi$
$263$	5.96789	0.367996	0.183998	+	0.982927i	$0.441096\pi$
$264$	−2.33667	−0.143812
$265$	3.93673	0.241831
$266$	−18.6079	−1.14093
$267$	−1.17838	−0.0721157
$268$	−7.75207	−0.473533
$269$	−9.96780	−0.607748	−0.303874	−	0.952712i	$-0.598280\pi$
$269$	−9.96780	−0.607748	−0.303874	+	0.952712i	$0.598280\pi$
$270$	12.0777	0.735026
$271$	21.7054	1.31851	0.659254	−	0.751920i	$-0.270872\pi$
$271$	21.7054	1.31851	0.659254	+	0.751920i	$0.270872\pi$
$272$	−8.96346	−0.543490
$273$	−14.5806	−0.882460
$274$	−26.8339	−1.62110
$275$	1.00000	0.0603023
$276$	7.86560	0.473453
$277$	−13.4164	−0.806111	−0.403056	−	0.915175i	$-0.632052\pi$
$277$	−13.4164	−0.806111	−0.403056	+	0.915175i	$0.632052\pi$
$278$	1.47097	0.0882230
$279$	4.53025	0.271219
$280$	2.93632	0.175479
$281$	−1.69298	−0.100995	−0.0504973	−	0.998724i	$-0.516081\pi$
$281$	−1.69298	−0.100995	−0.0504973	+	0.998724i	$0.516081\pi$
$282$	−33.7140	−2.00764
$283$	29.2432	1.73833	0.869165	−	0.494523i	$-0.164657\pi$
$283$	29.2432	1.73833	0.869165	+	0.494523i	$0.164657\pi$
$284$	−17.2809	−1.02543
$285$	6.83402	0.404812
$286$	10.4412	0.617401
$287$	−4.35595	−0.257124
$288$	4.51230	0.265890
$289$	0.757389	0.0445523
$290$	15.7282	0.923591
$291$	−20.8263	−1.22086
$292$	2.69497	0.157711
$293$	−11.5818	−0.676618	−0.338309	−	0.941035i	$-0.609855\pi$
$293$	−11.5818	−0.676618	−0.338309	+	0.941035i	$0.609855\pi$
$294$	10.7515	0.627042
$295$	1.70367	0.0991914
$296$	13.0244	0.757029
$297$	5.57401	0.323437
$298$	41.9554	2.43041
$299$	−9.06348	−0.524155
$300$	−4.18188	−0.241441
$301$	18.4874	1.06560
$302$	−15.6003	−0.897697
$303$	−20.9690	−1.20464
$304$	9.36794	0.537288
$305$	4.40338	0.252137
$306$	−5.40645	−0.309066
$307$	−34.8816	−1.99080	−0.995398	−	0.0958277i	$-0.969450\pi$
$307$	−34.8816	−1.99080	−0.995398	+	0.0958277i	$0.969450\pi$
$308$	5.25505	0.299434
$309$	−3.87539	−0.220463
$310$	−16.5780	−0.941567
$311$	24.9007	1.41199	0.705995	−	0.708217i	$-0.250500\pi$
$311$	24.9007	1.41199	0.705995	+	0.708217i	$0.250500\pi$
$312$	−11.2598	−0.637462
$313$	2.25025	0.127192	0.0635958	−	0.997976i	$-0.479743\pi$
$313$	2.25025	0.127192	0.0635958	+	0.997976i	$0.479743\pi$
$314$	38.0081	2.14492
$315$	−1.15460	−0.0650541
$316$	−30.2752	−1.70311
$317$	13.5209	0.759409	0.379704	−	0.925108i	$-0.376026\pi$
$317$	13.5209	0.759409	0.379704	+	0.925108i	$0.376026\pi$
$318$	−13.2364	−0.742259
$319$	7.25876	0.406413
$320$	−12.2581	−0.685250
$321$	−31.7674	−1.77308
$322$	−7.94695	−0.442866
$323$	−18.5587	−1.03263
$324$	−18.5226	−1.02904
$325$	4.81875	0.267296
$326$	24.8453	1.37605
$327$	−14.6649	−0.810972
$328$	−3.36387	−0.185739
$329$	19.5524	1.07796
$330$	−3.36228	−0.185088
$331$	−15.4417	−0.848754	−0.424377	−	0.905486i	$-0.639507\pi$
$331$	−15.4417	−0.848754	−0.424377	+	0.905486i	$0.639507\pi$
$332$	−35.5773	−1.95256
$333$	−5.12136	−0.280649
$334$	−18.5992	−1.01771
$335$	−2.87650	−0.157160
$336$	6.43617	0.351122
$337$	−30.6989	−1.67228	−0.836138	−	0.548519i	$-0.815192\pi$
$337$	−30.6989	−1.67228	−0.836138	+	0.548519i	$0.815192\pi$
$338$	22.1453	1.20455
$339$	15.3875	0.835732
$340$	11.3565	0.615890
$341$	−7.65096	−0.414323
$342$	5.65042	0.305540
$343$	−19.8850	−1.07369
$344$	14.2768	0.769755
$345$	2.91863	0.157134
$346$	−16.4043	−0.881899
$347$	−35.8648	−1.92532	−0.962661	−	0.270708i	$-0.912742\pi$
$347$	−35.8648	−1.92532	−0.962661	+	0.270708i	$0.912742\pi$
$348$	−30.3552	−1.62721
$349$	−7.53209	−0.403184	−0.201592	−	0.979470i	$-0.564611\pi$
$349$	−7.53209	−0.403184	−0.201592	+	0.979470i	$0.564611\pi$
$350$	4.22513	0.225843
$351$	26.8598	1.43367
$352$	−7.62064	−0.406181
$353$	−9.17969	−0.488585	−0.244293	−	0.969702i	$-0.578556\pi$
$353$	−9.17969	−0.488585	−0.244293	+	0.969702i	$0.578556\pi$
$354$	−5.72821	−0.304451
$355$	−6.41228	−0.340328
$356$	2.04654	0.108466
$357$	−12.7506	−0.674834
$358$	42.3280	2.23711
$359$	1.64909	0.0870356	0.0435178	−	0.999053i	$-0.486143\pi$
$359$	1.64909	0.0870356	0.0435178	+	0.999053i	$0.486143\pi$
$360$	−0.891632	−0.0469931
$361$	0.396185	0.0208518
$362$	7.69496	0.404438
$363$	−1.55174	−0.0814450
$364$	25.3228	1.32727
$365$	1.00000	0.0523424
$366$	−14.8054	−0.773890
$367$	−14.7948	−0.772281	−0.386140	−	0.922440i	$-0.626192\pi$
$367$	−14.7948	−0.772281	−0.386140	+	0.922440i	$0.626192\pi$
$368$	4.00080	0.208556
$369$	1.32271	0.0688577
$370$	18.7411	0.974303
$371$	7.67643	0.398540
$372$	31.9954	1.65888
$373$	−9.19415	−0.476055	−0.238028	−	0.971258i	$-0.576501\pi$
$373$	−9.19415	−0.476055	−0.238028	+	0.971258i	$0.576501\pi$
$374$	9.13074	0.472139
$375$	−1.55174	−0.0801313
$376$	15.0992	0.778684
$377$	34.9782	1.80147
$378$	23.5509	1.21133
$379$	−33.6000	−1.72592	−0.862958	−	0.505276i	$-0.831391\pi$
$379$	−33.6000	−1.72592	−0.862958	+	0.505276i	$0.831391\pi$
$380$	−11.8689	−0.608863
$381$	−19.2163	−0.984480
$382$	−50.7156	−2.59484
$383$	13.4040	0.684913	0.342456	−	0.939534i	$-0.388741\pi$
$383$	13.4040	0.684913	0.342456	+	0.939534i	$0.388741\pi$
$384$	17.5648	0.896350
$385$	1.94995	0.0993787
$386$	13.5717	0.690781
$387$	−5.61382	−0.285367
$388$	36.1699	1.83625
$389$	19.8956	1.00875	0.504373	−	0.863486i	$-0.331724\pi$
$389$	19.8956	1.00875	0.504373	+	0.863486i	$0.331724\pi$
$390$	−16.2020	−0.820420
$391$	−7.92593	−0.400832
$392$	−4.81522	−0.243205
$393$	10.5167	0.530495
$394$	−37.8179	−1.90524
$395$	−11.2340	−0.565242
$396$	−1.59573	−0.0801885
$397$	1.34682	0.0675951	0.0337976	−	0.999429i	$-0.489240\pi$
$397$	1.34682	0.0675951	0.0337976	+	0.999429i	$0.489240\pi$
$398$	12.4590	0.624511
$399$	13.3260	0.667134
$400$	−2.12709	−0.106355
$401$	10.8908	0.543863	0.271931	−	0.962317i	$-0.412338\pi$
$401$	10.8908	0.543863	0.271931	+	0.962317i	$0.412338\pi$
$402$	9.67160	0.482376
$403$	−36.8681	−1.83653
$404$	36.4177	1.81185
$405$	−6.87305	−0.341525
$406$	30.6692	1.52209
$407$	8.64926	0.428728
$408$	−9.84662	−0.487480
$409$	12.9572	0.640694	0.320347	−	0.947300i	$-0.396200\pi$
$409$	12.9572	0.640694	0.320347	+	0.947300i	$0.396200\pi$
$410$	−4.84034	−0.239047
$411$	19.2170	0.947905
$412$	6.73056	0.331591
$413$	3.32207	0.163468
$414$	2.41314	0.118600
$415$	−13.2014	−0.648030
$416$	−36.7220	−1.80044
$417$	−1.05343	−0.0515867
$418$	−9.54277	−0.466752
$419$	8.26835	0.403935	0.201968	−	0.979392i	$-0.435266\pi$
$419$	8.26835	0.403935	0.201968	+	0.979392i	$0.435266\pi$
$420$	−8.15445	−0.397897
$421$	−30.1123	−1.46759	−0.733793	−	0.679373i	$-0.762252\pi$
$421$	−30.1123	−1.46759	−0.733793	+	0.679373i	$0.762252\pi$
$422$	9.90520	0.482178
$423$	−5.93720	−0.288677
$424$	5.92809	0.287893
$425$	4.21395	0.204407
$426$	21.5599	1.04458
$427$	8.58637	0.415524
$428$	55.1718	2.66683
$429$	−7.47743	−0.361014
$430$	20.5432	0.990682
$431$	−7.15441	−0.344616	−0.172308	−	0.985043i	$-0.555122\pi$
$431$	−7.15441	−0.344616	−0.172308	+	0.985043i	$0.555122\pi$
$432$	−11.8564	−0.570443
$433$	−0.899348	−0.0432199	−0.0216100	−	0.999766i	$-0.506879\pi$
$433$	−0.899348	−0.0432199	−0.0216100	+	0.999766i	$0.506879\pi$
$434$	−32.3263	−1.55171
$435$	−11.2637	−0.540052
$436$	25.4692	1.21975
$437$	8.28359	0.396258
$438$	−3.36228	−0.160656
$439$	−37.4454	−1.78717	−0.893586	−	0.448892i	$-0.851819\pi$
$439$	−37.4454	−1.78717	−0.893586	+	0.448892i	$0.851819\pi$
$440$	1.50584	0.0717882
$441$	1.89340	0.0901619
$442$	43.9987	2.09281
$443$	9.78194	0.464754	0.232377	−	0.972626i	$-0.425350\pi$
$443$	9.78194	0.464754	0.232377	+	0.972626i	$0.425350\pi$
$444$	−36.1701	−1.71656
$445$	0.759394	0.0359987
$446$	19.8634	0.940560
$447$	−30.0462	−1.42114
$448$	−23.9027	−1.12930
$449$	36.4694	1.72110	0.860550	−	0.509366i	$-0.170120\pi$
$449$	36.4694	1.72110	0.860550	+	0.509366i	$0.170120\pi$
$450$	−1.28299	−0.0604806
$451$	−2.23388	−0.105189
$452$	−26.7240	−1.25699
$453$	11.1721	0.524911
$454$	−2.84413	−0.133481
$455$	9.39633	0.440507
$456$	10.2910	0.481918
$457$	−31.4810	−1.47262	−0.736309	−	0.676646i	$-0.763433\pi$
$457$	−31.4810	−1.47262	−0.736309	+	0.676646i	$0.763433\pi$
$458$	−24.1791	−1.12981
$459$	23.4886	1.09636
$460$	−5.06890	−0.236339
$461$	−27.4084	−1.27654	−0.638268	−	0.769814i	$-0.720349\pi$
$461$	−27.4084	−1.27654	−0.638268	+	0.769814i	$0.720349\pi$
$462$	−6.55629	−0.305026
$463$	7.66368	0.356161	0.178081	−	0.984016i	$-0.443011\pi$
$463$	7.66368	0.356161	0.178081	+	0.984016i	$0.443011\pi$
$464$	−15.4401	−0.716786
$465$	11.8723	0.550563
$466$	9.42333	0.436527
$467$	39.5011	1.82789	0.913947	−	0.405833i	$-0.133019\pi$
$467$	39.5011	1.82789	0.913947	+	0.405833i	$0.133019\pi$
$468$	−7.68943	−0.355444
$469$	−5.60904	−0.259001
$470$	21.7266	1.00217
$471$	−27.2193	−1.25420
$472$	2.56546	0.118085
$473$	9.48096	0.435935
$474$	37.7718	1.73491
$475$	−4.40411	−0.202074
$476$	22.1445	1.01499
$477$	−2.33100	−0.106729
$478$	−40.6045	−1.85721
$479$	−13.3454	−0.609765	−0.304882	−	0.952390i	$-0.598617\pi$
$479$	−13.3454	−0.609765	−0.304882	+	0.952390i	$0.598617\pi$
$480$	11.8252	0.539745
$481$	41.6786	1.90038
$482$	−55.4317	−2.52484
$483$	5.69118	0.258958
$484$	2.69497	0.122498
$485$	13.4213	0.609430
$486$	−13.1240	−0.595315
$487$	33.7228	1.52813	0.764064	−	0.645140i	$-0.223201\pi$
$487$	33.7228	1.52813	0.764064	+	0.645140i	$0.223201\pi$
$488$	6.63079	0.300162
$489$	−17.7929	−0.804622
$490$	−6.92871	−0.313007
$491$	−30.0614	−1.35665	−0.678327	−	0.734760i	$-0.737295\pi$
$491$	−30.0614	−1.35665	−0.678327	+	0.734760i	$0.737295\pi$
$492$	9.34180	0.421161
$493$	30.5881	1.37762
$494$	−45.9842	−2.06893
$495$	−0.592115	−0.0266136
$496$	16.2743	0.730737
$497$	−12.5036	−0.560865
$498$	44.3868	1.98902
$499$	−18.3728	−0.822479	−0.411239	−	0.911527i	$-0.634904\pi$
$499$	−18.3728	−0.822479	−0.411239	+	0.911527i	$0.634904\pi$
$500$	2.69497	0.120523
$501$	13.3198	0.595084
$502$	−61.7149	−2.75447
$503$	10.7773	0.480536	0.240268	−	0.970707i	$-0.422765\pi$
$503$	10.7773	0.480536	0.240268	+	0.970707i	$0.422765\pi$
$504$	−1.73864	−0.0774452
$505$	13.5132	0.601331
$506$	−4.07546	−0.181176
$507$	−15.8593	−0.704336
$508$	33.3737	1.48072
$509$	−1.28153	−0.0568029	−0.0284015	−	0.999597i	$-0.509042\pi$
$509$	−1.28153	−0.0568029	−0.0284015	+	0.999597i	$0.509042\pi$
$510$	−14.1685	−0.627391
$511$	1.94995	0.0862608
$512$	22.6159	0.999492
$513$	−24.5486	−1.08385
$514$	−21.5813	−0.951911
$515$	2.49746	0.110051
$516$	−39.6482	−1.74541
$517$	10.0271	0.440992
$518$	36.5442	1.60566
$519$	11.7479	0.515673
$520$	7.25628	0.318209
$521$	−6.86809	−0.300897	−0.150448	−	0.988618i	$-0.548072\pi$
$521$	−6.86809	−0.300897	−0.150448	+	0.988618i	$0.548072\pi$
$522$	−9.31290	−0.407615
$523$	29.4123	1.28611	0.643055	−	0.765820i	$-0.277667\pi$
$523$	29.4123	1.28611	0.643055	+	0.765820i	$0.277667\pi$
$524$	−18.2647	−0.797898
$525$	−3.02581	−0.132057
$526$	12.9311	0.563824
$527$	−32.2408	−1.40443
$528$	3.30068	0.143644
$529$	−19.4623	−0.846187
$530$	8.53005	0.370522
$531$	−1.00877	−0.0437768
$532$	−23.1438	−1.00341
$533$	−10.7645	−0.466262
$534$	−2.55330	−0.110492
$535$	20.4722	0.885089
$536$	−4.33156	−0.187095
$537$	−30.3131	−1.30810
$538$	−21.5981	−0.931160
$539$	−3.19769	−0.137734
$540$	15.0218	0.646434
$541$	3.98769	0.171444	0.0857221	−	0.996319i	$-0.472680\pi$
$541$	3.98769	0.171444	0.0857221	+	0.996319i	$0.472680\pi$
$542$	47.0310	2.02015
$543$	−5.51072	−0.236488
$544$	−32.1130	−1.37683
$545$	9.45065	0.404821
$546$	−31.5931	−1.35206
$547$	−37.5589	−1.60590	−0.802952	−	0.596044i	$-0.796738\pi$
$547$	−37.5589	−1.60590	−0.802952	+	0.596044i	$0.796738\pi$
$548$	−33.3750	−1.42571
$549$	−2.60731	−0.111277
$550$	2.16679	0.0923921
$551$	−31.9684	−1.36190
$552$	4.39499	0.187063
$553$	−21.9057	−0.931525
$554$	−29.0704	−1.23508
$555$	−13.4214	−0.569705
$556$	1.82954	0.0775896
$557$	32.4083	1.37319	0.686593	−	0.727042i	$-0.259106\pi$
$557$	32.4083	1.37319	0.686593	+	0.727042i	$0.259106\pi$
$558$	9.81608	0.415548
$559$	45.6864	1.93233
$560$	−4.14773	−0.175273
$561$	−6.53894	−0.276074
$562$	−3.66832	−0.154739
$563$	−14.1610	−0.596816	−0.298408	−	0.954438i	$-0.596456\pi$
$563$	−14.1610	−0.596816	−0.298408	+	0.954438i	$0.596456\pi$
$564$	−41.9321	−1.76566
$565$	−9.91628	−0.417181
$566$	63.3638	2.66338
$567$	−13.4021	−0.562836
$568$	−9.65588	−0.405152
$569$	36.3825	1.52523	0.762617	−	0.646851i	$-0.223914\pi$
$569$	36.3825	1.52523	0.762617	+	0.646851i	$0.223914\pi$
$570$	14.8079	0.620233
$571$	−29.5479	−1.23654	−0.618271	−	0.785965i	$-0.712167\pi$
$571$	−29.5479	−1.23654	−0.618271	+	0.785965i	$0.712167\pi$
$572$	12.9864	0.542987
$573$	36.3198	1.51728
$574$	−9.43842	−0.393952
$575$	−1.88088	−0.0784380
$576$	7.25822	0.302426
$577$	25.0442	1.04260	0.521301	−	0.853373i	$-0.325447\pi$
$577$	25.0442	1.04260	0.521301	+	0.853373i	$0.325447\pi$
$578$	1.64110	0.0682607
$579$	−9.71932	−0.403921
$580$	19.5621	0.812273
$581$	−25.7421	−1.06796
$582$	−45.1262	−1.87054
$583$	3.93673	0.163043
$584$	1.50584	0.0623122
$585$	−2.85326	−0.117968
$586$	−25.0954	−1.03668
$587$	−10.4384	−0.430838	−0.215419	−	0.976522i	$-0.569112\pi$
$587$	−10.4384	−0.430838	−0.215419	+	0.976522i	$0.569112\pi$
$588$	13.3723	0.551466
$589$	33.6957	1.38841
$590$	3.69149	0.151976
$591$	27.0832	1.11405
$592$	−18.3978	−0.756143
$593$	7.20045	0.295687	0.147844	−	0.989011i	$-0.452767\pi$
$593$	7.20045	0.295687	0.147844	+	0.989011i	$0.452767\pi$
$594$	12.0777	0.495554
$595$	8.21700	0.336864
$596$	52.1826	2.13748
$597$	−8.92244	−0.365171
$598$	−19.6386	−0.803084
$599$	22.3071	0.911442	0.455721	−	0.890123i	$-0.349381\pi$
$599$	22.3071	0.911442	0.455721	+	0.890123i	$0.349381\pi$
$600$	−2.33667	−0.0953942
$601$	12.8397	0.523743	0.261871	−	0.965103i	$-0.415660\pi$
$601$	12.8397	0.523743	0.261871	+	0.965103i	$0.415660\pi$
$602$	40.0583	1.63265
$603$	1.70322	0.0693604
$604$	−19.4031	−0.789499
$605$	1.00000	0.0406558
$606$	−45.4353	−1.84568
$607$	−20.5528	−0.834212	−0.417106	−	0.908858i	$-0.636956\pi$
$607$	−20.5528	−0.834212	−0.417106	+	0.908858i	$0.636956\pi$
$608$	33.5621	1.36112
$609$	−21.9636	−0.890012
$610$	9.54118	0.386311
$611$	48.3181	1.95474
$612$	−6.72433	−0.271815
$613$	−21.7850	−0.879888	−0.439944	−	0.898025i	$-0.645002\pi$
$613$	−21.7850	−0.879888	−0.439944	+	0.898025i	$0.645002\pi$
$614$	−75.5809	−3.05020
$615$	3.46639	0.139778
$616$	2.93632	0.118308
$617$	−43.1861	−1.73861	−0.869304	−	0.494277i	$-0.835433\pi$
$617$	−43.1861	−1.73861	−0.869304	+	0.494277i	$0.835433\pi$
$618$	−8.39715	−0.337783
$619$	25.0202	1.00565	0.502823	−	0.864390i	$-0.332295\pi$
$619$	25.0202	1.00565	0.502823	+	0.864390i	$0.332295\pi$
$620$	−20.6191	−0.828082
$621$	−10.4840	−0.420710
$622$	53.9546	2.16338
$623$	1.48078	0.0593263
$624$	15.9052	0.636717
$625$	1.00000	0.0400000
$626$	4.87581	0.194877
$627$	6.83402	0.272924
$628$	47.2730	1.88640
$629$	36.4475	1.45326
$630$	−2.50176	−0.0996726
$631$	13.0581	0.519835	0.259917	−	0.965631i	$-0.416305\pi$
$631$	13.0581	0.519835	0.259917	+	0.965631i	$0.416305\pi$
$632$	−16.9166	−0.672906
$633$	−7.09357	−0.281944
$634$	29.2969	1.16353
$635$	12.3837	0.491433
$636$	−16.4629	−0.652796
$637$	−15.4089	−0.610521
$638$	15.7282	0.622685
$639$	3.79681	0.150199
$640$	−11.3195	−0.447441
$641$	−33.7241	−1.33202	−0.666011	−	0.745942i	$-0.731999\pi$
$641$	−33.7241	−1.33202	−0.666011	+	0.745942i	$0.731999\pi$
$642$	−68.8332	−2.71663
$643$	−8.37513	−0.330283	−0.165141	−	0.986270i	$-0.552808\pi$
$643$	−8.37513	−0.330283	−0.165141	+	0.986270i	$0.552808\pi$
$644$	−9.88411	−0.389489
$645$	−14.7120	−0.579282
$646$	−40.2128	−1.58215
$647$	−41.5679	−1.63420	−0.817101	−	0.576495i	$-0.804420\pi$
$647$	−41.5679	−1.63420	−0.817101	+	0.576495i	$0.804420\pi$
$648$	−10.3497	−0.406576
$649$	1.70367	0.0668749
$650$	10.4412	0.409538
$651$	23.1503	0.907334
$652$	30.9016	1.21020
$653$	−29.0280	−1.13595	−0.567977	−	0.823044i	$-0.692274\pi$
$653$	−29.0280	−1.13595	−0.567977	+	0.823044i	$0.692274\pi$
$654$	−31.7757	−1.24253
$655$	−6.77735	−0.264813
$656$	4.75166	0.185521
$657$	−0.592115	−0.0231006
$658$	42.3658	1.65159
$659$	−9.58468	−0.373366	−0.186683	−	0.982420i	$-0.559774\pi$
$659$	−9.58468	−0.373366	−0.186683	+	0.982420i	$0.559774\pi$
$660$	−4.18188	−0.162779
$661$	−11.2956	−0.439347	−0.219673	−	0.975573i	$-0.570499\pi$
$661$	−11.2956	−0.439347	−0.219673	+	0.975573i	$0.570499\pi$
$662$	−33.4589	−1.30042
$663$	−31.5095	−1.22373
$664$	−19.8792	−0.771463
$665$	−8.58780	−0.333021
$666$	−11.0969	−0.429996
$667$	−13.6528	−0.528640
$668$	−23.1330	−0.895043
$669$	−14.2251	−0.549974
$670$	−6.23276	−0.240793
$671$	4.40338	0.169990
$672$	23.0586	0.889505
$673$	−44.4062	−1.71173	−0.855866	−	0.517198i	$-0.826975\pi$
$673$	−44.4062	−1.71173	−0.855866	+	0.517198i	$0.826975\pi$
$674$	−66.5180	−2.56218
$675$	5.57401	0.214544
$676$	27.5435	1.05937
$677$	24.8891	0.956564	0.478282	−	0.878206i	$-0.341260\pi$
$677$	24.8891	0.956564	0.478282	+	0.878206i	$0.341260\pi$
$678$	33.3413	1.28047
$679$	26.1709	1.00435
$680$	6.34555	0.243341
$681$	2.03681	0.0780508
$682$	−16.5780	−0.634804
$683$	2.76730	0.105888	0.0529440	−	0.998597i	$-0.483140\pi$
$683$	2.76730	0.105888	0.0529440	+	0.998597i	$0.483140\pi$
$684$	7.02777	0.268714
$685$	−12.3842	−0.473176
$686$	−43.0866	−1.64505
$687$	17.3158	0.660637
$688$	−20.1669	−0.768855
$689$	18.9701	0.722703
$690$	6.32404	0.240752
$691$	18.7364	0.712766	0.356383	−	0.934340i	$-0.384010\pi$
$691$	18.7364	0.712766	0.356383	+	0.934340i	$0.384010\pi$
$692$	−20.4030	−0.775605
$693$	−1.15460	−0.0438595
$694$	−77.7114	−2.94988
$695$	0.678872	0.0257511
$696$	−16.9613	−0.642918
$697$	−9.41345	−0.356560
$698$	−16.3204	−0.617738
$699$	−6.74848	−0.255251
$700$	5.25505	0.198622
$701$	23.0464	0.870449	0.435224	−	0.900322i	$-0.356669\pi$
$701$	23.0464	0.870449	0.435224	+	0.900322i	$0.356669\pi$
$702$	58.1994	2.19660
$703$	−38.0923	−1.43668
$704$	−12.2581	−0.461995
$705$	−15.5594	−0.586002
$706$	−19.8904	−0.748586
$707$	26.3502	0.991000
$708$	−7.12453	−0.267756
$709$	−24.9522	−0.937098	−0.468549	−	0.883437i	$-0.655223\pi$
$709$	−24.9522	−0.937098	−0.468549	+	0.883437i	$0.655223\pi$
$710$	−13.8940	−0.521434
$711$	6.65180	0.249462
$712$	1.14353	0.0428555
$713$	14.3905	0.538929
$714$	−27.6279	−1.03395
$715$	4.81875	0.180211
$716$	52.6460	1.96747
$717$	29.0788	1.08597
$718$	3.57322	0.133352
$719$	13.7898	0.514272	0.257136	−	0.966375i	$-0.417221\pi$
$719$	13.7898	0.514272	0.257136	+	0.966375i	$0.417221\pi$
$720$	1.25948	0.0469382
$721$	4.86992	0.181365
$722$	0.858447	0.0319481
$723$	39.6972	1.47635
$724$	9.57070	0.355692
$725$	7.25876	0.269584
$726$	−3.36228	−0.124786
$727$	−2.42606	−0.0899776	−0.0449888	−	0.998987i	$-0.514325\pi$
$727$	−2.42606	−0.0899776	−0.0449888	+	0.998987i	$0.514325\pi$
$728$	14.1494	0.524411
$729$	30.0178	1.11177
$730$	2.16679	0.0801964
$731$	39.9523	1.47769
$732$	−18.4144	−0.680615
$733$	0.227881	0.00841697	0.00420849	−	0.999991i	$-0.498660\pi$
$733$	0.227881	0.00841697	0.00420849	+	0.999991i	$0.498660\pi$
$734$	−32.0571	−1.18325
$735$	4.96197	0.183025
$736$	14.3335	0.528340
$737$	−2.87650	−0.105957
$738$	2.86604	0.105500
$739$	26.7447	0.983818	0.491909	−	0.870647i	$-0.336299\pi$
$739$	26.7447	0.983818	0.491909	+	0.870647i	$0.336299\pi$
$740$	23.3094	0.856872
$741$	32.9314	1.20977
$742$	16.6332	0.610623
$743$	1.62313	0.0595468	0.0297734	−	0.999557i	$-0.490521\pi$
$743$	1.62313	0.0595468	0.0297734	+	0.999557i	$0.490521\pi$
$744$	17.8778	0.655431
$745$	19.3630	0.709405
$746$	−19.9218	−0.729388
$747$	7.81674	0.286000
$748$	11.3565	0.415233
$749$	39.9198	1.45864
$750$	−3.36228	−0.122773
$751$	19.2812	0.703580	0.351790	−	0.936079i	$-0.385573\pi$
$751$	19.2812	0.703580	0.351790	+	0.936079i	$0.385573\pi$
$752$	−21.3286	−0.777773
$753$	44.1969	1.61062
$754$	75.7902	2.76012
$755$	−7.19974	−0.262026
$756$	29.2917	1.06533
$757$	−37.4189	−1.36001	−0.680006	−	0.733207i	$-0.738023\pi$
$757$	−37.4189	−1.36001	−0.680006	+	0.733207i	$0.738023\pi$
$758$	−72.8040	−2.64436
$759$	2.91863	0.105939
$760$	−6.63190	−0.240564
$761$	22.8810	0.829436	0.414718	−	0.909950i	$-0.363880\pi$
$761$	22.8810	0.829436	0.414718	+	0.909950i	$0.363880\pi$
$762$	−41.6376	−1.50837
$763$	18.4283	0.667150
$764$	−63.0781	−2.28209
$765$	−2.49514	−0.0902122
$766$	29.0436	1.04939
$767$	8.20956	0.296430
$768$	0.0164582	0.000593886 0
$769$	−22.0616	−0.795562	−0.397781	−	0.917480i	$-0.630220\pi$
$769$	−22.0616	−0.795562	−0.397781	+	0.917480i	$0.630220\pi$
$770$	4.22513	0.152263
$771$	15.4554	0.556612
$772$	16.8800	0.607523
$773$	−3.32179	−0.119477	−0.0597383	−	0.998214i	$-0.519027\pi$
$773$	−3.32179	−0.119477	−0.0597383	+	0.998214i	$0.519027\pi$
$774$	−12.1640	−0.437224
$775$	−7.65096	−0.274831
$776$	20.2104	0.725510
$777$	−26.1710	−0.938880
$778$	43.1095	1.54555
$779$	9.83824	0.352492
$780$	−20.1514	−0.721536
$781$	−6.41228	−0.229449
$782$	−17.1738	−0.614134
$783$	40.4605	1.44594
$784$	6.80178	0.242921
$785$	17.5412	0.626073
$786$	22.7874	0.812798
$787$	9.25098	0.329762	0.164881	−	0.986313i	$-0.447276\pi$
$787$	9.25098	0.329762	0.164881	+	0.986313i	$0.447276\pi$
$788$	−47.0365	−1.67561
$789$	−9.26058	−0.329685
$790$	−24.3416	−0.866036
$791$	−19.3363	−0.687519
$792$	−0.891632	−0.0316828
$793$	21.2188	0.753501
$794$	2.91828	0.103566
$795$	−6.10876	−0.216655
$796$	15.4960	0.549240
$797$	21.8175	0.772817	0.386408	−	0.922328i	$-0.373716\pi$
$797$	21.8175	0.772817	0.386408	+	0.922328i	$0.373716\pi$
$798$	28.8746	1.02215
$799$	42.2537	1.49483
$800$	−7.62064	−0.269430
$801$	−0.449649	−0.0158876
$802$	23.5981	0.833279
$803$	1.00000	0.0352892
$804$	12.0292	0.424236
$805$	−3.66762	−0.129267
$806$	−79.8852	−2.81384
$807$	15.4674	0.544478
$808$	20.3488	0.715869
$809$	28.7077	1.00931	0.504654	−	0.863322i	$-0.331620\pi$
$809$	28.7077	1.00931	0.504654	+	0.863322i	$0.331620\pi$
$810$	−14.8924	−0.523267
$811$	−37.1137	−1.30324	−0.651619	−	0.758547i	$-0.725910\pi$
$811$	−37.1137	−1.30324	−0.651619	+	0.758547i	$0.725910\pi$
$812$	38.1452	1.33863
$813$	−33.6810	−1.18125
$814$	18.7411	0.656875
$815$	11.4664	0.401652
$816$	13.9089	0.486910
$817$	−41.7552	−1.46083
$818$	28.0756	0.981640
$819$	−5.56371	−0.194412
$820$	−6.02022	−0.210235
$821$	−40.9076	−1.42768	−0.713842	−	0.700306i	$-0.753047\pi$
$821$	−40.9076	−1.42768	−0.713842	+	0.700306i	$0.753047\pi$
$822$	41.6392	1.45233
$823$	−5.94004	−0.207057	−0.103528	−	0.994626i	$-0.533013\pi$
$823$	−5.94004	−0.207057	−0.103528	+	0.994626i	$0.533013\pi$
$824$	3.76078	0.131013
$825$	−1.55174	−0.0540245
$826$	7.19822	0.250458
$827$	16.1004	0.559865	0.279932	−	0.960020i	$-0.409688\pi$
$827$	16.1004	0.559865	0.279932	+	0.960020i	$0.409688\pi$
$828$	3.00137	0.104305
$829$	0.496916	0.0172586	0.00862930	−	0.999963i	$-0.497253\pi$
$829$	0.496916	0.0172586	0.00862930	+	0.999963i	$0.497253\pi$
$830$	−28.6046	−0.992880
$831$	20.8187	0.722191
$832$	−59.0688	−2.04784
$833$	−13.4749	−0.466878
$834$	−2.28256	−0.0790385
$835$	−8.58379	−0.297054
$836$	−11.8689	−0.410495
$837$	−42.6465	−1.47408
$838$	17.9158	0.618890
$839$	14.5469	0.502216	0.251108	−	0.967959i	$-0.419205\pi$
$839$	14.5469	0.502216	0.251108	+	0.967959i	$0.419205\pi$
$840$	−4.55639	−0.157211
$841$	23.6896	0.816884
$842$	−65.2470	−2.24856
$843$	2.62705	0.0904805
$844$	12.3197	0.424062
$845$	10.2204	0.351591
$846$	−12.8647	−0.442296
$847$	1.94995	0.0670011
$848$	−8.37378	−0.287557
$849$	−45.3778	−1.55736
$850$	9.13074	0.313182
$851$	−16.2682	−0.557667
$852$	26.8154	0.918679
$853$	−21.5553	−0.738041	−0.369020	−	0.929421i	$-0.620307\pi$
$853$	−21.5553	−0.738041	−0.369020	+	0.929421i	$0.620307\pi$
$854$	18.6048	0.636645
$855$	2.60774	0.0891828
$856$	30.8279	1.05368
$857$	−2.55162	−0.0871617	−0.0435808	−	0.999050i	$-0.513877\pi$
$857$	−2.55162	−0.0871617	−0.0435808	+	0.999050i	$0.513877\pi$
$858$	−16.2020	−0.553127
$859$	−28.7103	−0.979582	−0.489791	−	0.871840i	$-0.662927\pi$
$859$	−28.7103	−0.979582	−0.489791	+	0.871840i	$0.662927\pi$
$860$	25.5509	0.871277
$861$	6.75929	0.230356
$862$	−15.5021	−0.528003
$863$	−46.3886	−1.57909	−0.789544	−	0.613694i	$-0.789683\pi$
$863$	−46.3886	−1.57909	−0.789544	+	0.613694i	$0.789683\pi$
$864$	−42.4776	−1.44512
$865$	−7.57078	−0.257414
$866$	−1.94870	−0.0662194
$867$	−1.17527	−0.0399142
$868$	−40.2062	−1.36469
$869$	−11.2340	−0.381086
$870$	−24.4060	−0.827441
$871$	−13.8611	−0.469667
$872$	14.2312	0.481929
$873$	−7.94696	−0.268964
$874$	17.9488	0.607127
$875$	1.94995	0.0659204
$876$	−4.18188	−0.141292
$877$	58.7918	1.98526	0.992630	−	0.121187i	$-0.0386699\pi$
$877$	58.7918	1.98526	0.992630	+	0.121187i	$0.0386699\pi$
$878$	−81.1363	−2.73822
$879$	17.9720	0.606179
$880$	−2.12709	−0.0717042
$881$	−1.48250	−0.0499468	−0.0249734	−	0.999688i	$-0.507950\pi$
$881$	−1.48250	−0.0499468	−0.0249734	+	0.999688i	$0.507950\pi$
$882$	4.10259	0.138142
$883$	−15.5334	−0.522741	−0.261370	−	0.965239i	$-0.584174\pi$
$883$	−15.5334	−0.522741	−0.261370	+	0.965239i	$0.584174\pi$
$884$	54.7239	1.84056
$885$	−2.64364	−0.0888651
$886$	21.1954	0.712072
$887$	−3.25122	−0.109165	−0.0545827	−	0.998509i	$-0.517383\pi$
$887$	−3.25122	−0.109165	−0.0545827	+	0.998509i	$0.517383\pi$
$888$	−20.2105	−0.678219
$889$	24.1477	0.809887
$890$	1.64545	0.0551555
$891$	−6.87305	−0.230256
$892$	24.7053	0.827196
$893$	−44.1605	−1.47777
$894$	−65.1038	−2.17740
$895$	19.5349	0.652981
$896$	−22.0724	−0.737387
$897$	14.0641	0.469588
$898$	79.0215	2.63698
$899$	−55.5365	−1.85225
$900$	−1.59573	−0.0531910
$901$	16.5892	0.552666
$902$	−4.84034	−0.161166
$903$	−28.6876	−0.954663
$904$	−14.9324	−0.496643
$905$	3.55132	0.118050
$906$	24.2076	0.804242
$907$	−32.1843	−1.06866	−0.534331	−	0.845275i	$-0.679437\pi$
$907$	−32.1843	−1.06866	−0.534331	+	0.845275i	$0.679437\pi$
$908$	−3.53742	−0.117393
$909$	−8.00139	−0.265389
$910$	20.3598	0.674922
$911$	−40.5657	−1.34400	−0.672001	−	0.740550i	$-0.734565\pi$
$911$	−40.5657	−1.34400	−0.672001	+	0.740550i	$0.734565\pi$
$912$	−14.5366	−0.481354
$913$	−13.2014	−0.436902
$914$	−68.2126	−2.25627
$915$	−6.83288	−0.225888
$916$	−30.0730	−0.993640
$917$	−13.2155	−0.436414
$918$	50.8949	1.67978
$919$	−41.2378	−1.36031	−0.680154	−	0.733069i	$-0.738087\pi$
$919$	−41.2378	−1.36031	−0.680154	+	0.733069i	$0.738087\pi$
$920$	−2.83231	−0.0933784
$921$	54.1270	1.78354
$922$	−59.3881	−1.95584
$923$	−30.8992	−1.01706
$924$	−8.15445	−0.268262
$925$	8.64926	0.284386
$926$	16.6056	0.545692
$927$	−1.47878	−0.0485696
$928$	−55.3164	−1.81585
$929$	−57.4522	−1.88495	−0.942473	−	0.334282i	$-0.891506\pi$
$929$	−57.4522	−1.88495	−0.942473	+	0.334282i	$0.891506\pi$
$930$	25.7247	0.843545
$931$	14.0830	0.461551
$932$	11.7204	0.383914
$933$	−38.6393	−1.26500
$934$	85.5905	2.80061
$935$	4.21395	0.137811
$936$	−4.29655	−0.140437
$937$	45.6087	1.48997	0.744986	−	0.667080i	$-0.232456\pi$
$937$	45.6087	1.48997	0.744986	+	0.667080i	$0.232456\pi$
$938$	−12.1536	−0.396829
$939$	−3.49179	−0.113950
$940$	27.0227	0.881383
$941$	−8.47612	−0.276314	−0.138157	−	0.990410i	$-0.544118\pi$
$941$	−8.47612	−0.276314	−0.138157	+	0.990410i	$0.544118\pi$
$942$	−58.9785	−1.92162
$943$	4.20165	0.136825
$944$	−3.62386	−0.117947
$945$	10.8691	0.353571
$946$	20.5432	0.667918
$947$	41.6946	1.35489	0.677447	−	0.735572i	$-0.263087\pi$
$947$	41.6946	1.35489	0.677447	+	0.735572i	$0.263087\pi$
$948$	46.9791	1.52581
$949$	4.81875	0.156423
$950$	−9.54277	−0.309608
$951$	−20.9809	−0.680351
$952$	12.3735	0.401028
$953$	−32.8866	−1.06530	−0.532651	−	0.846335i	$-0.678804\pi$
$953$	−32.8866	−1.06530	−0.532651	+	0.846335i	$0.678804\pi$
$954$	−5.05077	−0.163525
$955$	−23.4059	−0.757398
$956$	−50.5023	−1.63336
$957$	−11.2637	−0.364103
$958$	−28.9165	−0.934251
$959$	−24.1486	−0.779798
$960$	19.0214	0.613912
$961$	27.5372	0.888295
$962$	90.3087	2.91167
$963$	−12.1219	−0.390622
$964$	−68.9438	−2.22053
$965$	6.26351	0.201630
$966$	12.3316	0.396762
$967$	52.5000	1.68829	0.844143	−	0.536118i	$-0.180110\pi$
$967$	52.5000	1.68829	0.844143	+	0.536118i	$0.180110\pi$
$968$	1.50584	0.0483996
$969$	28.7982	0.925132
$970$	29.0811	0.933738
$971$	6.22032	0.199619	0.0998097	−	0.995007i	$-0.468177\pi$
$971$	6.22032	0.199619	0.0998097	+	0.995007i	$0.468177\pi$
$972$	−16.3231	−0.523563
$973$	1.32377	0.0424380
$974$	73.0702	2.34132
$975$	−7.47743	−0.239469
$976$	−9.36639	−0.299811
$977$	−18.3479	−0.587002	−0.293501	−	0.955959i	$-0.594820\pi$
$977$	−18.3479	−0.587002	−0.293501	+	0.955959i	$0.594820\pi$
$978$	−38.5534	−1.23280
$979$	0.759394	0.0242703
$980$	−8.61766	−0.275281
$981$	−5.59587	−0.178662
$982$	−65.1367	−2.07860
$983$	17.0464	0.543696	0.271848	−	0.962340i	$-0.412365\pi$
$983$	17.0464	0.543696	0.271848	+	0.962340i	$0.412365\pi$
$984$	5.21984	0.166402
$985$	−17.4535	−0.556114
$986$	66.2778	2.11072
$987$	−30.3401	−0.965737
$988$	−57.1934	−1.81956
$989$	−17.8325	−0.567042
$990$	−1.28299	−0.0407760
$991$	−34.6261	−1.09994	−0.549968	−	0.835186i	$-0.685360\pi$
$991$	−34.6261	−1.09994	−0.549968	+	0.835186i	$0.685360\pi$
$992$	58.3052	1.85119
$993$	23.9615	0.760395
$994$	−27.0927	−0.859329
$995$	5.74997	0.182286
$996$	55.2065	1.74929
$997$	28.3564	0.898055	0.449028	−	0.893518i	$-0.351770\pi$
$997$	28.3564	0.898055	0.449028	+	0.893518i	$0.351770\pi$
$998$	−39.8099	−1.26016
$999$	48.2111	1.52533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.31	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.31	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.16679 q^{2} -1.55174 q^{3} +2.69497 q^{4} +1.00000 q^{5} -3.36228 q^{6} +1.94995 q^{7} +1.50584 q^{8} -0.592115 q^{9} +O(q^{10})\)	\(q+2.16679 q^{2} -1.55174 q^{3} +2.69497 q^{4} +1.00000 q^{5} -3.36228 q^{6} +1.94995 q^{7} +1.50584 q^{8} -0.592115 q^{9} +2.16679 q^{10} +1.00000 q^{11} -4.18188 q^{12} +4.81875 q^{13} +4.22513 q^{14} -1.55174 q^{15} -2.12709 q^{16} +4.21395 q^{17} -1.28299 q^{18} -4.40411 q^{19} +2.69497 q^{20} -3.02581 q^{21} +2.16679 q^{22} -1.88088 q^{23} -2.33667 q^{24} +1.00000 q^{25} +10.4412 q^{26} +5.57401 q^{27} +5.25505 q^{28} +7.25876 q^{29} -3.36228 q^{30} -7.65096 q^{31} -7.62064 q^{32} -1.55174 q^{33} +9.13074 q^{34} +1.94995 q^{35} -1.59573 q^{36} +8.64926 q^{37} -9.54277 q^{38} -7.47743 q^{39} +1.50584 q^{40} -2.23388 q^{41} -6.55629 q^{42} +9.48096 q^{43} +2.69497 q^{44} -0.592115 q^{45} -4.07546 q^{46} +10.0271 q^{47} +3.30068 q^{48} -3.19769 q^{49} +2.16679 q^{50} -6.53894 q^{51} +12.9864 q^{52} +3.93673 q^{53} +12.0777 q^{54} +1.00000 q^{55} +2.93632 q^{56} +6.83402 q^{57} +15.7282 q^{58} +1.70367 q^{59} -4.18188 q^{60} +4.40338 q^{61} -16.5780 q^{62} -1.15460 q^{63} -12.2581 q^{64} +4.81875 q^{65} -3.36228 q^{66} -2.87650 q^{67} +11.3565 q^{68} +2.91863 q^{69} +4.22513 q^{70} -6.41228 q^{71} -0.891632 q^{72} +1.00000 q^{73} +18.7411 q^{74} -1.55174 q^{75} -11.8689 q^{76} +1.94995 q^{77} -16.2020 q^{78} -11.2340 q^{79} -2.12709 q^{80} -6.87305 q^{81} -4.84034 q^{82} -13.2014 q^{83} -8.15445 q^{84} +4.21395 q^{85} +20.5432 q^{86} -11.2637 q^{87} +1.50584 q^{88} +0.759394 q^{89} -1.28299 q^{90} +9.39633 q^{91} -5.06890 q^{92} +11.8723 q^{93} +21.7266 q^{94} -4.40411 q^{95} +11.8252 q^{96} +13.4213 q^{97} -6.92871 q^{98} -0.592115 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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