LMFDB - Embedded newform 8015.2.a.j.1.35

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			1.35
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)

$f(q)$	$=$	$q+1.49678 q^{2} +3.16909 q^{3} +0.240365 q^{4} -1.00000 q^{5} +4.74344 q^{6} +1.00000 q^{7} -2.63379 q^{8} +7.04311 q^{9} +O(q^{10})$	\(q+1.49678 q^{2} +3.16909 q^{3} +0.240365 q^{4} -1.00000 q^{5} +4.74344 q^{6} +1.00000 q^{7} -2.63379 q^{8} +7.04311 q^{9} -1.49678 q^{10} -1.64388 q^{11} +0.761738 q^{12} -5.51535 q^{13} +1.49678 q^{14} -3.16909 q^{15} -4.42296 q^{16} -4.91895 q^{17} +10.5420 q^{18} -3.24054 q^{19} -0.240365 q^{20} +3.16909 q^{21} -2.46053 q^{22} -5.69376 q^{23} -8.34672 q^{24} +1.00000 q^{25} -8.25530 q^{26} +12.8130 q^{27} +0.240365 q^{28} +6.56392 q^{29} -4.74344 q^{30} -0.264994 q^{31} -1.35262 q^{32} -5.20958 q^{33} -7.36261 q^{34} -1.00000 q^{35} +1.69292 q^{36} -6.73173 q^{37} -4.85040 q^{38} -17.4786 q^{39} +2.63379 q^{40} +3.54871 q^{41} +4.74344 q^{42} +3.22527 q^{43} -0.395130 q^{44} -7.04311 q^{45} -8.52233 q^{46} +0.458259 q^{47} -14.0167 q^{48} +1.00000 q^{49} +1.49678 q^{50} -15.5886 q^{51} -1.32570 q^{52} +3.98602 q^{53} +19.1783 q^{54} +1.64388 q^{55} -2.63379 q^{56} -10.2696 q^{57} +9.82478 q^{58} +4.48362 q^{59} -0.761738 q^{60} -7.74539 q^{61} -0.396638 q^{62} +7.04311 q^{63} +6.82132 q^{64} +5.51535 q^{65} -7.79763 q^{66} -8.59497 q^{67} -1.18234 q^{68} -18.0440 q^{69} -1.49678 q^{70} -11.8022 q^{71} -18.5501 q^{72} -7.94790 q^{73} -10.0760 q^{74} +3.16909 q^{75} -0.778914 q^{76} -1.64388 q^{77} -26.1618 q^{78} -4.57590 q^{79} +4.42296 q^{80} +19.4761 q^{81} +5.31165 q^{82} -11.7945 q^{83} +0.761738 q^{84} +4.91895 q^{85} +4.82753 q^{86} +20.8016 q^{87} +4.32963 q^{88} -6.03301 q^{89} -10.5420 q^{90} -5.51535 q^{91} -1.36858 q^{92} -0.839788 q^{93} +0.685915 q^{94} +3.24054 q^{95} -4.28658 q^{96} -7.99233 q^{97} +1.49678 q^{98} -11.5780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.49678	1.05839	0.529193	−	0.848501i	$-0.322495\pi$
$2$	1.49678	1.05839	0.529193	+	0.848501i	$0.322495\pi$
$3$	3.16909	1.82967	0.914837	−	0.403824i	$-0.132319\pi$
$3$	3.16909	1.82967	0.914837	+	0.403824i	$0.132319\pi$
$4$	0.240365	0.120183
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.74344	1.93650
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.63379	−0.931187
$9$	7.04311	2.34770
$10$	−1.49678	−0.473325
$11$	−1.64388	−0.495647	−0.247824	−	0.968805i	$-0.579715\pi$
$11$	−1.64388	−0.495647	−0.247824	+	0.968805i	$0.579715\pi$
$12$	0.761738	0.219895
$13$	−5.51535	−1.52968	−0.764842	−	0.644218i	$-0.777183\pi$
$13$	−5.51535	−1.52968	−0.764842	+	0.644218i	$0.777183\pi$
$14$	1.49678	0.400033
$15$	−3.16909	−0.818255
$16$	−4.42296	−1.10574
$17$	−4.91895	−1.19302	−0.596510	−	0.802606i	$-0.703446\pi$
$17$	−4.91895	−1.19302	−0.596510	+	0.802606i	$0.703446\pi$
$18$	10.5420	2.48478
$19$	−3.24054	−0.743432	−0.371716	−	0.928347i	$-0.621230\pi$
$19$	−3.24054	−0.743432	−0.371716	+	0.928347i	$0.621230\pi$
$20$	−0.240365	−0.0537473
$21$	3.16909	0.691551
$22$	−2.46053	−0.524586
$23$	−5.69376	−1.18723	−0.593615	−	0.804749i	$-0.702300\pi$
$23$	−5.69376	−1.18723	−0.593615	+	0.804749i	$0.702300\pi$
$24$	−8.34672	−1.70377
$25$	1.00000	0.200000
$26$	−8.25530	−1.61900
$27$	12.8130	2.46586
$28$	0.240365	0.0454248
$29$	6.56392	1.21889	0.609445	−	0.792828i	$-0.291392\pi$
$29$	6.56392	1.21889	0.609445	+	0.792828i	$0.291392\pi$
$30$	−4.74344	−0.866030
$31$	−0.264994	−0.0475943	−0.0237971	−	0.999717i	$-0.507576\pi$
$31$	−0.264994	−0.0475943	−0.0237971	+	0.999717i	$0.507576\pi$
$32$	−1.35262	−0.239112
$33$	−5.20958	−0.906872
$34$	−7.36261	−1.26268
$35$	−1.00000	−0.169031
$36$	1.69292	0.282153
$37$	−6.73173	−1.10669	−0.553345	−	0.832952i	$-0.686649\pi$
$37$	−6.73173	−1.10669	−0.553345	+	0.832952i	$0.686649\pi$
$38$	−4.85040	−0.786838
$39$	−17.4786	−2.79882
$40$	2.63379	0.416440
$41$	3.54871	0.554215	0.277107	−	0.960839i	$-0.410624\pi$
$41$	3.54871	0.554215	0.277107	+	0.960839i	$0.410624\pi$
$42$	4.74344	0.731929
$43$	3.22527	0.491849	0.245924	−	0.969289i	$-0.420909\pi$
$43$	3.22527	0.491849	0.245924	+	0.969289i	$0.420909\pi$
$44$	−0.395130	−0.0595682
$45$	−7.04311	−1.04992
$46$	−8.52233	−1.25655
$47$	0.458259	0.0668439	0.0334220	−	0.999441i	$-0.489359\pi$
$47$	0.458259	0.0668439	0.0334220	+	0.999441i	$0.489359\pi$
$48$	−14.0167	−2.02314
$49$	1.00000	0.142857
$50$	1.49678	0.211677
$51$	−15.5886	−2.18284
$52$	−1.32570	−0.183841
$53$	3.98602	0.547521	0.273761	−	0.961798i	$-0.411732\pi$
$53$	3.98602	0.547521	0.273761	+	0.961798i	$0.411732\pi$
$54$	19.1783	2.60983
$55$	1.64388	0.221660
$56$	−2.63379	−0.351956
$57$	−10.2696	−1.36024
$58$	9.82478	1.29006
$59$	4.48362	0.583718	0.291859	−	0.956461i	$-0.405726\pi$
$59$	4.48362	0.583718	0.291859	+	0.956461i	$0.405726\pi$
$60$	−0.761738	−0.0983400
$61$	−7.74539	−0.991695	−0.495847	−	0.868410i	$-0.665142\pi$
$61$	−7.74539	−0.991695	−0.495847	+	0.868410i	$0.665142\pi$
$62$	−0.396638	−0.0503731
$63$	7.04311	0.887349
$64$	6.82132	0.852666
$65$	5.51535	0.684095
$66$	−7.79763	−0.959821
$67$	−8.59497	−1.05004	−0.525021	−	0.851089i	$-0.675943\pi$
$67$	−8.59497	−1.05004	−0.525021	+	0.851089i	$0.675943\pi$
$68$	−1.18234	−0.143380
$69$	−18.0440	−2.17224
$70$	−1.49678	−0.178900
$71$	−11.8022	−1.40066	−0.700330	−	0.713819i	$-0.746964\pi$
$71$	−11.8022	−1.40066	−0.700330	+	0.713819i	$0.746964\pi$
$72$	−18.5501	−2.18615
$73$	−7.94790	−0.930231	−0.465116	−	0.885250i	$-0.653987\pi$
$73$	−7.94790	−0.930231	−0.465116	+	0.885250i	$0.653987\pi$
$74$	−10.0760	−1.17131
$75$	3.16909	0.365935
$76$	−0.778914	−0.0893475
$77$	−1.64388	−0.187337
$78$	−26.1618	−2.96224
$79$	−4.57590	−0.514829	−0.257414	−	0.966301i	$-0.582870\pi$
$79$	−4.57590	−0.514829	−0.257414	+	0.966301i	$0.582870\pi$
$80$	4.42296	0.494501
$81$	19.4761	2.16401
$82$	5.31165	0.586573
$83$	−11.7945	−1.29461	−0.647305	−	0.762231i	$-0.724104\pi$
$83$	−11.7945	−1.29461	−0.647305	+	0.762231i	$0.724104\pi$
$84$	0.761738	0.0831125
$85$	4.91895	0.533535
$86$	4.82753	0.520566
$87$	20.8016	2.23017
$88$	4.32963	0.461540
$89$	−6.03301	−0.639498	−0.319749	−	0.947502i	$-0.603599\pi$
$89$	−6.03301	−0.639498	−0.319749	+	0.947502i	$0.603599\pi$
$90$	−10.5420	−1.11123
$91$	−5.51535	−0.578166
$92$	−1.36858	−0.142684
$93$	−0.839788	−0.0870819
$94$	0.685915	0.0707467
$95$	3.24054	0.332473
$96$	−4.28658	−0.437497
$97$	−7.99233	−0.811499	−0.405749	−	0.913984i	$-0.632989\pi$
$97$	−7.99233	−0.811499	−0.405749	+	0.913984i	$0.632989\pi$
$98$	1.49678	0.151198
$99$	−11.5780	−1.16363
$100$	0.240365	0.0240365
$101$	−1.59326	−0.158536	−0.0792678	−	0.996853i	$-0.525258\pi$
$101$	−1.59326	−0.158536	−0.0792678	+	0.996853i	$0.525258\pi$
$102$	−23.3327	−2.31029
$103$	19.5599	1.92729	0.963646	−	0.267183i	$-0.0860927\pi$
$103$	19.5599	1.92729	0.963646	+	0.267183i	$0.0860927\pi$
$104$	14.5263	1.42442
$105$	−3.16909	−0.309271
$106$	5.96621	0.579489
$107$	−14.3659	−1.38880	−0.694402	−	0.719587i	$-0.744331\pi$
$107$	−14.3659	−1.38880	−0.694402	+	0.719587i	$0.744331\pi$
$108$	3.07979	0.296353
$109$	4.39821	0.421272	0.210636	−	0.977565i	$-0.432447\pi$
$109$	4.39821	0.421272	0.210636	+	0.977565i	$0.432447\pi$
$110$	2.46053	0.234602
$111$	−21.3334	−2.02488
$112$	−4.42296	−0.417930
$113$	12.6660	1.19151	0.595757	−	0.803165i	$-0.296852\pi$
$113$	12.6660	1.19151	0.595757	+	0.803165i	$0.296852\pi$
$114$	−15.3713	−1.43966
$115$	5.69376	0.530945
$116$	1.57774	0.146489
$117$	−38.8452	−3.59124
$118$	6.71102	0.617799
$119$	−4.91895	−0.450919
$120$	8.34672	0.761948
$121$	−8.29767	−0.754334
$122$	−11.5932	−1.04960
$123$	11.2462	1.01403
$124$	−0.0636952	−0.00572000
$125$	−1.00000	−0.0894427
$126$	10.5420	0.939158
$127$	5.09830	0.452401	0.226200	−	0.974081i	$-0.427370\pi$
$127$	5.09830	0.452401	0.226200	+	0.974081i	$0.427370\pi$
$128$	12.9153	1.14156
$129$	10.2211	0.899922
$130$	8.25530	0.724038
$131$	−5.18403	−0.452931	−0.226466	−	0.974019i	$-0.572717\pi$
$131$	−5.18403	−0.452931	−0.226466	+	0.974019i	$0.572717\pi$
$132$	−1.25220	−0.108990
$133$	−3.24054	−0.280991
$134$	−12.8648	−1.11135
$135$	−12.8130	−1.10276
$136$	12.9555	1.11092
$137$	−6.83321	−0.583801	−0.291900	−	0.956449i	$-0.594288\pi$
$137$	−6.83321	−0.583801	−0.291900	+	0.956449i	$0.594288\pi$
$138$	−27.0080	−2.29907
$139$	10.8259	0.918237	0.459118	−	0.888375i	$-0.348165\pi$
$139$	10.8259	0.918237	0.459118	+	0.888375i	$0.348165\pi$
$140$	−0.240365	−0.0203146
$141$	1.45226	0.122303
$142$	−17.6653	−1.48244
$143$	9.06655	0.758183
$144$	−31.1514	−2.59595
$145$	−6.56392	−0.545104
$146$	−11.8963	−0.984544
$147$	3.16909	0.261382
$148$	−1.61807	−0.133005
$149$	−10.2921	−0.843161	−0.421581	−	0.906791i	$-0.638525\pi$
$149$	−10.2921	−0.843161	−0.421581	+	0.906791i	$0.638525\pi$
$150$	4.74344	0.387300
$151$	1.96012	0.159512	0.0797560	−	0.996814i	$-0.474586\pi$
$151$	1.96012	0.159512	0.0797560	+	0.996814i	$0.474586\pi$
$152$	8.53493	0.692274
$153$	−34.6447	−2.80086
$154$	−2.46053	−0.198275
$155$	0.264994	0.0212848
$156$	−4.20126	−0.336370
$157$	23.4757	1.87356	0.936781	−	0.349917i	$-0.113790\pi$
$157$	23.4757	1.87356	0.936781	+	0.349917i	$0.113790\pi$
$158$	−6.84913	−0.544888
$159$	12.6320	1.00179
$160$	1.35262	0.106934
$161$	−5.69376	−0.448731
$162$	29.1515	2.29036
$163$	−17.4491	−1.36672	−0.683359	−	0.730083i	$-0.739481\pi$
$163$	−17.4491	−1.36672	−0.683359	+	0.730083i	$0.739481\pi$
$164$	0.852985	0.0666070
$165$	5.20958	0.405565
$166$	−17.6538	−1.37020
$167$	11.5284	0.892093	0.446046	−	0.895010i	$-0.352832\pi$
$167$	11.5284	0.892093	0.446046	+	0.895010i	$0.352832\pi$
$168$	−8.34672	−0.643964
$169$	17.4191	1.33993
$170$	7.36261	0.564686
$171$	−22.8235	−1.74536
$172$	0.775242	0.0591116
$173$	10.0160	0.761503	0.380752	−	0.924677i	$-0.375665\pi$
$173$	10.0160	0.761503	0.380752	+	0.924677i	$0.375665\pi$
$174$	31.1356	2.36038
$175$	1.00000	0.0755929
$176$	7.27079	0.548056
$177$	14.2090	1.06801
$178$	−9.03012	−0.676836
$179$	−14.7938	−1.10574	−0.552869	−	0.833268i	$-0.686467\pi$
$179$	−14.7938	−1.10574	−0.552869	+	0.833268i	$0.686467\pi$
$180$	−1.69292	−0.126183
$181$	17.0003	1.26362	0.631810	−	0.775123i	$-0.282312\pi$
$181$	17.0003	1.26362	0.631810	+	0.775123i	$0.282312\pi$
$182$	−8.25530	−0.611923
$183$	−24.5458	−1.81448
$184$	14.9962	1.10553
$185$	6.73173	0.494927
$186$	−1.25698	−0.0921664
$187$	8.08614	0.591317
$188$	0.110150	0.00803348
$189$	12.8130	0.932006
$190$	4.85040	0.351885
$191$	4.53984	0.328492	0.164246	−	0.986419i	$-0.447481\pi$
$191$	4.53984	0.328492	0.164246	+	0.986419i	$0.447481\pi$
$192$	21.6174	1.56010
$193$	−19.6366	−1.41347	−0.706735	−	0.707478i	$-0.749833\pi$
$193$	−19.6366	−1.41347	−0.706735	+	0.707478i	$0.749833\pi$
$194$	−11.9628	−0.858879
$195$	17.4786	1.25167
$196$	0.240365	0.0171689
$197$	−12.3780	−0.881896	−0.440948	−	0.897533i	$-0.645358\pi$
$197$	−12.3780	−0.881896	−0.440948	+	0.897533i	$0.645358\pi$
$198$	−17.3298	−1.23157
$199$	0.905926	0.0642194	0.0321097	−	0.999484i	$-0.489777\pi$
$199$	0.905926	0.0642194	0.0321097	+	0.999484i	$0.489777\pi$
$200$	−2.63379	−0.186237
$201$	−27.2382	−1.92124
$202$	−2.38477	−0.167792
$203$	6.56392	0.460697
$204$	−3.74695	−0.262339
$205$	−3.54871	−0.247852
$206$	29.2769	2.03982
$207$	−40.1017	−2.78726
$208$	24.3942	1.69143
$209$	5.32705	0.368480
$210$	−4.74344	−0.327329
$211$	13.6349	0.938662	0.469331	−	0.883022i	$-0.344495\pi$
$211$	13.6349	0.938662	0.469331	+	0.883022i	$0.344495\pi$
$212$	0.958100	0.0658026
$213$	−37.4021	−2.56275
$214$	−21.5027	−1.46989
$215$	−3.22527	−0.219961
$216$	−33.7467	−2.29617
$217$	−0.264994	−0.0179889
$218$	6.58317	0.445869
$219$	−25.1876	−1.70202
$220$	0.395130	0.0266397
$221$	27.1297	1.82494
$222$	−31.9316	−2.14311
$223$	−18.4378	−1.23469	−0.617344	−	0.786693i	$-0.711791\pi$
$223$	−18.4378	−1.23469	−0.617344	+	0.786693i	$0.711791\pi$
$224$	−1.35262	−0.0903759
$225$	7.04311	0.469541
$226$	18.9582	1.26108
$227$	11.2102	0.744046	0.372023	−	0.928224i	$-0.378664\pi$
$227$	11.2102	0.744046	0.372023	+	0.928224i	$0.378664\pi$
$228$	−2.46845	−0.163477
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	8.52233	0.561946
$231$	−5.20958	−0.342765
$232$	−17.2880	−1.13501
$233$	−12.3246	−0.807410	−0.403705	−	0.914889i	$-0.632278\pi$
$233$	−12.3246	−0.807410	−0.403705	+	0.914889i	$0.632278\pi$
$234$	−58.1430	−3.80093
$235$	−0.458259	−0.0298935
$236$	1.07771	0.0701528
$237$	−14.5014	−0.941968
$238$	−7.36261	−0.477247
$239$	14.7798	0.956027	0.478014	−	0.878352i	$-0.341357\pi$
$239$	14.7798	0.956027	0.478014	+	0.878352i	$0.341357\pi$
$240$	14.0167	0.904776
$241$	18.1426	1.16867	0.584335	−	0.811513i	$-0.301355\pi$
$241$	18.1426	1.16867	0.584335	+	0.811513i	$0.301355\pi$
$242$	−12.4198	−0.798377
$243$	23.2825	1.49357
$244$	−1.86172	−0.119184
$245$	−1.00000	−0.0638877
$246$	16.8331	1.07324
$247$	17.8727	1.13722
$248$	0.697939	0.0443192
$249$	−37.3777	−2.36871
$250$	−1.49678	−0.0946650
$251$	15.0922	0.952610	0.476305	−	0.879280i	$-0.341976\pi$
$251$	15.0922	0.952610	0.476305	+	0.879280i	$0.341976\pi$
$252$	1.69292	0.106644
$253$	9.35982	0.588447
$254$	7.63106	0.478815
$255$	15.5886	0.976194
$256$	5.68878	0.355549
$257$	1.92525	0.120094	0.0600469	−	0.998196i	$-0.480875\pi$
$257$	1.92525	0.120094	0.0600469	+	0.998196i	$0.480875\pi$
$258$	15.2989	0.952466
$259$	−6.73173	−0.418289
$260$	1.32570	0.0822164
$261$	46.2304	2.86159
$262$	−7.75938	−0.479376
$263$	7.51940	0.463666	0.231833	−	0.972756i	$-0.425528\pi$
$263$	7.51940	0.463666	0.231833	+	0.972756i	$0.425528\pi$
$264$	13.7210	0.844468
$265$	−3.98602	−0.244859
$266$	−4.85040	−0.297397
$267$	−19.1191	−1.17007
$268$	−2.06593	−0.126197
$269$	−3.95622	−0.241215	−0.120607	−	0.992700i	$-0.538484\pi$
$269$	−3.95622	−0.241215	−0.120607	+	0.992700i	$0.538484\pi$
$270$	−19.1783	−1.16715
$271$	22.4220	1.36204	0.681021	−	0.732264i	$-0.261536\pi$
$271$	22.4220	1.36204	0.681021	+	0.732264i	$0.261536\pi$
$272$	21.7563	1.31917
$273$	−17.4786	−1.05785
$274$	−10.2278	−0.617887
$275$	−1.64388	−0.0991294
$276$	−4.33715	−0.261066
$277$	22.6517	1.36101	0.680505	−	0.732744i	$-0.261761\pi$
$277$	22.6517	1.36101	0.680505	+	0.732744i	$0.261761\pi$
$278$	16.2040	0.971850
$279$	−1.86638	−0.111737
$280$	2.63379	0.157399
$281$	11.8918	0.709405	0.354703	−	0.934979i	$-0.384582\pi$
$281$	11.8918	0.709405	0.354703	+	0.934979i	$0.384582\pi$
$282$	2.17372	0.129443
$283$	13.9270	0.827875	0.413938	−	0.910305i	$-0.364153\pi$
$283$	13.9270	0.827875	0.413938	+	0.910305i	$0.364153\pi$
$284$	−2.83683	−0.168335
$285$	10.2696	0.608316
$286$	13.5707	0.802451
$287$	3.54871	0.209473
$288$	−9.52667	−0.561365
$289$	7.19605	0.423297
$290$	−9.82478	−0.576931
$291$	−25.3284	−1.48478
$292$	−1.91040	−0.111798
$293$	−6.35429	−0.371222	−0.185611	−	0.982623i	$-0.559426\pi$
$293$	−6.35429	−0.371222	−0.185611	+	0.982623i	$0.559426\pi$
$294$	4.74344	0.276643
$295$	−4.48362	−0.261047
$296$	17.7300	1.03054
$297$	−21.0629	−1.22219
$298$	−15.4051	−0.892391
$299$	31.4031	1.81609
$300$	0.761738	0.0439790
$301$	3.22527	0.185901
$302$	2.93387	0.168825
$303$	−5.04919	−0.290068
$304$	14.3328	0.822041
$305$	7.74539	0.443499
$306$	−51.8557	−2.96439
$307$	−14.6029	−0.833432	−0.416716	−	0.909037i	$-0.636819\pi$
$307$	−14.6029	−0.833432	−0.416716	+	0.909037i	$0.636819\pi$
$308$	−0.395130	−0.0225146
$309$	61.9869	3.52631
$310$	0.396638	0.0225275
$311$	13.4629	0.763410	0.381705	−	0.924284i	$-0.375337\pi$
$311$	13.4629	0.763410	0.381705	+	0.924284i	$0.375337\pi$
$312$	46.0351	2.60623
$313$	18.8589	1.06597	0.532983	−	0.846126i	$-0.321071\pi$
$313$	18.8589	1.06597	0.532983	+	0.846126i	$0.321071\pi$
$314$	35.1380	1.98295
$315$	−7.04311	−0.396834
$316$	−1.09989	−0.0618734
$317$	−20.9004	−1.17388	−0.586942	−	0.809629i	$-0.699668\pi$
$317$	−20.9004	−1.17388	−0.586942	+	0.809629i	$0.699668\pi$
$318$	18.9074	1.06028
$319$	−10.7903	−0.604139
$320$	−6.82132	−0.381324
$321$	−45.5268	−2.54106
$322$	−8.52233	−0.474931
$323$	15.9401	0.886929
$324$	4.68137	0.260076
$325$	−5.51535	−0.305937
$326$	−26.1175	−1.44652
$327$	13.9383	0.770790
$328$	−9.34656	−0.516078
$329$	0.458259	0.0252646
$330$	7.79763	0.429245
$331$	12.2297	0.672204	0.336102	−	0.941826i	$-0.390891\pi$
$331$	12.2297	0.672204	0.336102	+	0.941826i	$0.390891\pi$
$332$	−2.83498	−0.155590
$333$	−47.4123	−2.59818
$334$	17.2555	0.944179
$335$	8.59497	0.469593
$336$	−14.0167	−0.764675
$337$	3.09249	0.168459	0.0842293	−	0.996446i	$-0.473157\pi$
$337$	3.09249	0.168459	0.0842293	+	0.996446i	$0.473157\pi$
$338$	26.0727	1.41817
$339$	40.1395	2.18008
$340$	1.18234	0.0641216
$341$	0.435616	0.0235900
$342$	−34.1619	−1.84726
$343$	1.00000	0.0539949
$344$	−8.49469	−0.458003
$345$	18.0440	0.971457
$346$	14.9918	0.805965
$347$	6.21305	0.333534	0.166767	−	0.985996i	$-0.446667\pi$
$347$	6.21305	0.333534	0.166767	+	0.985996i	$0.446667\pi$
$348$	4.99999	0.268028
$349$	−6.85518	−0.366950	−0.183475	−	0.983024i	$-0.558735\pi$
$349$	−6.85518	−0.366950	−0.183475	+	0.983024i	$0.558735\pi$
$350$	1.49678	0.0800065
$351$	−70.6680	−3.77198
$352$	2.22354	0.118515
$353$	−17.3249	−0.922114	−0.461057	−	0.887371i	$-0.652530\pi$
$353$	−17.3249	−0.922114	−0.461057	+	0.887371i	$0.652530\pi$
$354$	21.2678	1.13037
$355$	11.8022	0.626394
$356$	−1.45013	−0.0768566
$357$	−15.5886	−0.825035
$358$	−22.1431	−1.17030
$359$	28.7450	1.51710	0.758551	−	0.651614i	$-0.225908\pi$
$359$	28.7450	1.51710	0.758551	+	0.651614i	$0.225908\pi$
$360$	18.5501	0.977677
$361$	−8.49888	−0.447310
$362$	25.4458	1.33740
$363$	−26.2960	−1.38018
$364$	−1.32570	−0.0694855
$365$	7.94790	0.416012
$366$	−36.7398	−1.92042
$367$	−18.3798	−0.959417	−0.479709	−	0.877428i	$-0.659258\pi$
$367$	−18.3798	−0.959417	−0.479709	+	0.877428i	$0.659258\pi$
$368$	25.1832	1.31277
$369$	24.9939	1.30113
$370$	10.0760	0.523824
$371$	3.98602	0.206944
$372$	−0.201856	−0.0104657
$373$	18.5440	0.960171	0.480086	−	0.877222i	$-0.340606\pi$
$373$	18.5440	0.960171	0.480086	+	0.877222i	$0.340606\pi$
$374$	12.1032	0.625842
$375$	−3.16909	−0.163651
$376$	−1.20696	−0.0622442
$377$	−36.2024	−1.86452
$378$	19.1783	0.986423
$379$	7.24871	0.372341	0.186171	−	0.982517i	$-0.440392\pi$
$379$	7.24871	0.372341	0.186171	+	0.982517i	$0.440392\pi$
$380$	0.778914	0.0399574
$381$	16.1570	0.827746
$382$	6.79517	0.347671
$383$	−4.35119	−0.222335	−0.111168	−	0.993802i	$-0.535459\pi$
$383$	−4.35119	−0.222335	−0.111168	+	0.993802i	$0.535459\pi$
$384$	40.9297	2.08869
$385$	1.64388	0.0837796
$386$	−29.3917	−1.49600
$387$	22.7159	1.15471
$388$	−1.92108	−0.0975280
$389$	−25.6070	−1.29833	−0.649163	−	0.760649i	$-0.724881\pi$
$389$	−25.6070	−1.29833	−0.649163	+	0.760649i	$0.724881\pi$
$390$	26.1618	1.32475
$391$	28.0073	1.41639
$392$	−2.63379	−0.133027
$393$	−16.4287	−0.828716
$394$	−18.5272	−0.933388
$395$	4.57590	0.230238
$396$	−2.78295	−0.139848
$397$	−25.0723	−1.25834	−0.629172	−	0.777266i	$-0.716606\pi$
$397$	−25.0723	−1.25834	−0.629172	+	0.777266i	$0.716606\pi$
$398$	1.35598	0.0679689
$399$	−10.2696	−0.514121
$400$	−4.42296	−0.221148
$401$	22.2812	1.11267	0.556336	−	0.830957i	$-0.312207\pi$
$401$	22.2812	1.11267	0.556336	+	0.830957i	$0.312207\pi$
$402$	−40.7697	−2.03341
$403$	1.46153	0.0728042
$404$	−0.382965	−0.0190532
$405$	−19.4761	−0.967774
$406$	9.82478	0.487596
$407$	11.0661	0.548527
$408$	41.0571	2.03263
$409$	−7.97535	−0.394356	−0.197178	−	0.980368i	$-0.563178\pi$
$409$	−7.97535	−0.394356	−0.197178	+	0.980368i	$0.563178\pi$
$410$	−5.31165	−0.262324
$411$	−21.6550	−1.06816
$412$	4.70151	0.231627
$413$	4.48362	0.220625
$414$	−60.0237	−2.95000
$415$	11.7945	0.578967
$416$	7.46019	0.365766
$417$	34.3081	1.68007
$418$	7.97345	0.389994
$419$	−12.8154	−0.626075	−0.313038	−	0.949741i	$-0.601347\pi$
$419$	−12.8154	−0.626075	−0.313038	+	0.949741i	$0.601347\pi$
$420$	−0.761738	−0.0371690
$421$	39.3652	1.91854	0.959272	−	0.282484i	$-0.0911584\pi$
$421$	39.3652	1.91854	0.959272	+	0.282484i	$0.0911584\pi$
$422$	20.4084	0.993467
$423$	3.22757	0.156930
$424$	−10.4983	−0.509845
$425$	−4.91895	−0.238604
$426$	−55.9829	−2.71238
$427$	−7.74539	−0.374825
$428$	−3.45306	−0.166910
$429$	28.7327	1.38723
$430$	−4.82753	−0.232804
$431$	−24.1320	−1.16240	−0.581200	−	0.813761i	$-0.697417\pi$
$431$	−24.1320	−1.16240	−0.581200	+	0.813761i	$0.697417\pi$
$432$	−56.6712	−2.72659
$433$	−34.3647	−1.65146	−0.825732	−	0.564062i	$-0.809238\pi$
$433$	−34.3647	−1.65146	−0.825732	+	0.564062i	$0.809238\pi$
$434$	−0.396638	−0.0190393
$435$	−20.8016	−0.997363
$436$	1.05718	0.0506296
$437$	18.4509	0.882624
$438$	−37.7004	−1.80139
$439$	−38.3381	−1.82978	−0.914889	−	0.403706i	$-0.867722\pi$
$439$	−38.3381	−1.82978	−0.914889	+	0.403706i	$0.867722\pi$
$440$	−4.32963	−0.206407
$441$	7.04311	0.335386
$442$	40.6074	1.93150
$443$	18.8680	0.896445	0.448223	−	0.893922i	$-0.352057\pi$
$443$	18.8680	0.896445	0.448223	+	0.893922i	$0.352057\pi$
$444$	−5.12782	−0.243355
$445$	6.03301	0.285992
$446$	−27.5975	−1.30678
$447$	−32.6165	−1.54271
$448$	6.82132	0.322277
$449$	−28.6429	−1.35174	−0.675871	−	0.737020i	$-0.736232\pi$
$449$	−28.6429	−1.35174	−0.675871	+	0.737020i	$0.736232\pi$
$450$	10.5420	0.496956
$451$	−5.83363	−0.274695
$452$	3.04446	0.143199
$453$	6.21178	0.291855
$454$	16.7792	0.787488
$455$	5.51535	0.258564
$456$	27.0479	1.26663
$457$	−20.9061	−0.977948	−0.488974	−	0.872298i	$-0.662629\pi$
$457$	−20.9061	−0.977948	−0.488974	+	0.872298i	$0.662629\pi$
$458$	1.49678	0.0699402
$459$	−63.0263	−2.94182
$460$	1.36858	0.0638104
$461$	−18.6596	−0.869067	−0.434533	−	0.900656i	$-0.643087\pi$
$461$	−18.6596	−0.869067	−0.434533	+	0.900656i	$0.643087\pi$
$462$	−7.79763	−0.362778
$463$	−37.2830	−1.73269	−0.866344	−	0.499447i	$-0.833536\pi$
$463$	−37.2830	−1.73269	−0.866344	+	0.499447i	$0.833536\pi$
$464$	−29.0319	−1.34777
$465$	0.839788	0.0389442
$466$	−18.4473	−0.854552
$467$	−23.5339	−1.08902	−0.544510	−	0.838754i	$-0.683284\pi$
$467$	−23.5339	−1.08902	−0.544510	+	0.838754i	$0.683284\pi$
$468$	−9.33705	−0.431605
$469$	−8.59497	−0.396879
$470$	−0.685915	−0.0316389
$471$	74.3964	3.42801
$472$	−11.8089	−0.543551
$473$	−5.30194	−0.243783
$474$	−21.7055	−0.996966
$475$	−3.24054	−0.148686
$476$	−1.18234	−0.0541926
$477$	28.0740	1.28542
$478$	22.1222	1.01185
$479$	−32.7965	−1.49851	−0.749254	−	0.662282i	$-0.769588\pi$
$479$	−32.7965	−1.49851	−0.749254	+	0.662282i	$0.769588\pi$
$480$	4.28658	0.195655
$481$	37.1279	1.69289
$482$	27.1556	1.23690
$483$	−18.0440	−0.821031
$484$	−1.99447	−0.0906578
$485$	7.99233	0.362913
$486$	34.8488	1.58078
$487$	−4.59290	−0.208124	−0.104062	−	0.994571i	$-0.533184\pi$
$487$	−4.59290	−0.208124	−0.104062	+	0.994571i	$0.533184\pi$
$488$	20.3998	0.923454
$489$	−55.2976	−2.50065
$490$	−1.49678	−0.0676179
$491$	7.58989	0.342527	0.171263	−	0.985225i	$-0.445215\pi$
$491$	7.58989	0.342527	0.171263	+	0.985225i	$0.445215\pi$
$492$	2.70318	0.121869
$493$	−32.2876	−1.45416
$494$	26.7516	1.20361
$495$	11.5780	0.520392
$496$	1.17205	0.0526268
$497$	−11.8022	−0.529400
$498$	−55.9463	−2.50701
$499$	−36.9388	−1.65361	−0.826803	−	0.562491i	$-0.809843\pi$
$499$	−36.9388	−1.65361	−0.826803	+	0.562491i	$0.809843\pi$
$500$	−0.240365	−0.0107495
$501$	36.5344	1.63224
$502$	22.5897	1.00823
$503$	43.5198	1.94045	0.970227	−	0.242198i	$-0.0778684\pi$
$503$	43.5198	1.94045	0.970227	+	0.242198i	$0.0778684\pi$
$504$	−18.5501	−0.826287
$505$	1.59326	0.0708993
$506$	14.0096	0.622805
$507$	55.2027	2.45164
$508$	1.22545	0.0543707
$509$	21.5065	0.953258	0.476629	−	0.879105i	$-0.341859\pi$
$509$	21.5065	0.953258	0.476629	+	0.879105i	$0.341859\pi$
$510$	23.3327	1.03319
$511$	−7.94790	−0.351594
$512$	−17.3157	−0.765254
$513$	−41.5210	−1.83320
$514$	2.88168	0.127106
$515$	−19.5599	−0.861911
$516$	2.45681	0.108155
$517$	−0.753321	−0.0331310
$518$	−10.0760	−0.442712
$519$	31.7416	1.39330
$520$	−14.5263	−0.637021
$521$	−13.7144	−0.600840	−0.300420	−	0.953807i	$-0.597127\pi$
$521$	−13.7144	−0.600840	−0.300420	+	0.953807i	$0.597127\pi$
$522$	69.1970	3.02867
$523$	29.0750	1.27136	0.635680	−	0.771953i	$-0.280720\pi$
$523$	29.0750	1.27136	0.635680	+	0.771953i	$0.280720\pi$
$524$	−1.24606	−0.0544344
$525$	3.16909	0.138310
$526$	11.2549	0.490738
$527$	1.30349	0.0567809
$528$	23.0418	1.00276
$529$	9.41885	0.409515
$530$	−5.96621	−0.259156
$531$	31.5787	1.37040
$532$	−0.778914	−0.0337702
$533$	−19.5724	−0.847773
$534$	−28.6172	−1.23839
$535$	14.3659	0.621092
$536$	22.6374	0.977786
$537$	−46.8827	−2.02314
$538$	−5.92161	−0.255299
$539$	−1.64388	−0.0708067
$540$	−3.07979	−0.132533
$541$	36.0452	1.54971	0.774853	−	0.632142i	$-0.217824\pi$
$541$	36.0452	1.54971	0.774853	+	0.632142i	$0.217824\pi$
$542$	33.5610	1.44157
$543$	53.8753	2.31201
$544$	6.65348	0.285266
$545$	−4.39821	−0.188399
$546$	−26.1618	−1.11962
$547$	−26.2986	−1.12445	−0.562224	−	0.826985i	$-0.690054\pi$
$547$	−26.2986	−1.12445	−0.562224	+	0.826985i	$0.690054\pi$
$548$	−1.64247	−0.0701627
$549$	−54.5516	−2.32821
$550$	−2.46053	−0.104917
$551$	−21.2707	−0.906161
$552$	47.5242	2.02276
$553$	−4.57590	−0.194587
$554$	33.9047	1.44047
$555$	21.3334	0.905554
$556$	2.60216	0.110356
$557$	−15.1803	−0.643208	−0.321604	−	0.946874i	$-0.604222\pi$
$557$	−15.1803	−0.643208	−0.321604	+	0.946874i	$0.604222\pi$
$558$	−2.79357	−0.118261
$559$	−17.7885	−0.752373
$560$	4.42296	0.186904
$561$	25.6257	1.08192
$562$	17.7995	0.750825
$563$	−15.7027	−0.661790	−0.330895	−	0.943668i	$-0.607351\pi$
$563$	−15.7027	−0.661790	−0.330895	+	0.943668i	$0.607351\pi$
$564$	0.349073	0.0146986
$565$	−12.6660	−0.532861
$566$	20.8457	0.876212
$567$	19.4761	0.817918
$568$	31.0845	1.30428
$569$	43.0053	1.80288	0.901439	−	0.432907i	$-0.142512\pi$
$569$	43.0053	1.80288	0.901439	+	0.432907i	$0.142512\pi$
$570$	15.3713	0.643834
$571$	−12.4355	−0.520410	−0.260205	−	0.965553i	$-0.583790\pi$
$571$	−12.4355	−0.520410	−0.260205	+	0.965553i	$0.583790\pi$
$572$	2.17928	0.0911204
$573$	14.3872	0.601032
$574$	5.31165	0.221704
$575$	−5.69376	−0.237446
$576$	48.0433	2.00181
$577$	−28.6368	−1.19216	−0.596082	−	0.802923i	$-0.703277\pi$
$577$	−28.6368	−1.19216	−0.596082	+	0.802923i	$0.703277\pi$
$578$	10.7709	0.448012
$579$	−62.2299	−2.58619
$580$	−1.57774	−0.0655121
$581$	−11.7945	−0.489316
$582$	−37.9112	−1.57147
$583$	−6.55251	−0.271377
$584$	20.9331	0.866219
$585$	38.8452	1.60605
$586$	−9.51101	−0.392896
$587$	11.4882	0.474169	0.237084	−	0.971489i	$-0.423808\pi$
$587$	11.4882	0.474169	0.237084	+	0.971489i	$0.423808\pi$
$588$	0.761738	0.0314136
$589$	0.858723	0.0353831
$590$	−6.71102	−0.276288
$591$	−39.2270	−1.61358
$592$	29.7741	1.22371
$593$	−7.15138	−0.293672	−0.146836	−	0.989161i	$-0.546909\pi$
$593$	−7.15138	−0.293672	−0.146836	+	0.989161i	$0.546909\pi$
$594$	−31.5267	−1.29355
$595$	4.91895	0.201657
$596$	−2.47386	−0.101333
$597$	2.87096	0.117500
$598$	47.0036	1.92212
$599$	11.8157	0.482775	0.241387	−	0.970429i	$-0.422398\pi$
$599$	11.8157	0.482775	0.241387	+	0.970429i	$0.422398\pi$
$600$	−8.34672	−0.340754
$601$	18.1856	0.741806	0.370903	−	0.928672i	$-0.379048\pi$
$601$	18.1856	0.741806	0.370903	+	0.928672i	$0.379048\pi$
$602$	4.82753	0.196755
$603$	−60.5353	−2.46519
$604$	0.471144	0.0191706
$605$	8.29767	0.337348
$606$	−7.55755	−0.307004
$607$	−19.7084	−0.799938	−0.399969	−	0.916529i	$-0.630979\pi$
$607$	−19.7084	−0.799938	−0.399969	+	0.916529i	$0.630979\pi$
$608$	4.38323	0.177764
$609$	20.8016	0.842925
$610$	11.5932	0.469394
$611$	−2.52746	−0.102250
$612$	−8.32738	−0.336614
$613$	2.97669	0.120227	0.0601137	−	0.998192i	$-0.480854\pi$
$613$	2.97669	0.120227	0.0601137	+	0.998192i	$0.480854\pi$
$614$	−21.8574	−0.882094
$615$	−11.2462	−0.453489
$616$	4.32963	0.174446
$617$	−28.1435	−1.13301	−0.566507	−	0.824057i	$-0.691706\pi$
$617$	−28.1435	−1.13301	−0.566507	+	0.824057i	$0.691706\pi$
$618$	92.7811	3.73220
$619$	15.3202	0.615770	0.307885	−	0.951424i	$-0.400379\pi$
$619$	15.3202	0.615770	0.307885	+	0.951424i	$0.400379\pi$
$620$	0.0636952	0.00255806
$621$	−72.9539	−2.92754
$622$	20.1511	0.807984
$623$	−6.03301	−0.241708
$624$	77.3072	3.09476
$625$	1.00000	0.0400000
$626$	28.2276	1.12820
$627$	16.8819	0.674197
$628$	5.64273	0.225170
$629$	33.1130	1.32030
$630$	−10.5420	−0.420004
$631$	−14.7317	−0.586458	−0.293229	−	0.956042i	$-0.594730\pi$
$631$	−14.7317	−0.586458	−0.293229	+	0.956042i	$0.594730\pi$
$632$	12.0520	0.479402
$633$	43.2100	1.71744
$634$	−31.2834	−1.24242
$635$	−5.09830	−0.202320
$636$	3.03630	0.120397
$637$	−5.51535	−0.218526
$638$	−16.1507	−0.639413
$639$	−83.1240	−3.28833
$640$	−12.9153	−0.510522
$641$	−11.5205	−0.455034	−0.227517	−	0.973774i	$-0.573061\pi$
$641$	−11.5205	−0.455034	−0.227517	+	0.973774i	$0.573061\pi$
$642$	−68.1438	−2.68942
$643$	−8.38515	−0.330678	−0.165339	−	0.986237i	$-0.552872\pi$
$643$	−8.38515	−0.330678	−0.165339	+	0.986237i	$0.552872\pi$
$644$	−1.36858	−0.0539296
$645$	−10.2211	−0.402457
$646$	23.8588	0.938714
$647$	−39.0492	−1.53518	−0.767591	−	0.640940i	$-0.778545\pi$
$647$	−39.0492	−1.53518	−0.767591	+	0.640940i	$0.778545\pi$
$648$	−51.2960	−2.01510
$649$	−7.37052	−0.289318
$650$	−8.25530	−0.323799
$651$	−0.839788	−0.0329139
$652$	−4.19415	−0.164256
$653$	−22.6305	−0.885599	−0.442799	−	0.896621i	$-0.646015\pi$
$653$	−22.6305	−0.885599	−0.442799	+	0.896621i	$0.646015\pi$
$654$	20.8626	0.815794
$655$	5.18403	0.202557
$656$	−15.6958	−0.612817
$657$	−55.9779	−2.18391
$658$	0.685915	0.0267398
$659$	3.44052	0.134024	0.0670118	−	0.997752i	$-0.478653\pi$
$659$	3.44052	0.134024	0.0670118	+	0.997752i	$0.478653\pi$
$660$	1.25220	0.0487419
$661$	45.4146	1.76642	0.883211	−	0.468976i	$-0.155377\pi$
$661$	45.4146	1.76642	0.883211	+	0.468976i	$0.155377\pi$
$662$	18.3052	0.711452
$663$	85.9765	3.33905
$664$	31.0642	1.20552
$665$	3.24054	0.125663
$666$	−70.9661	−2.74988
$667$	−37.3734	−1.44710
$668$	2.77102	0.107214
$669$	−58.4311	−2.25908
$670$	12.8648	0.497012
$671$	12.7324	0.491531
$672$	−4.28658	−0.165358
$673$	−21.3123	−0.821528	−0.410764	−	0.911742i	$-0.634738\pi$
$673$	−21.3123	−0.821528	−0.410764	+	0.911742i	$0.634738\pi$
$674$	4.62879	0.178294
$675$	12.8130	0.493171
$676$	4.18695	0.161037
$677$	27.1070	1.04181	0.520903	−	0.853616i	$-0.325595\pi$
$677$	27.1070	1.04181	0.520903	+	0.853616i	$0.325595\pi$
$678$	60.0803	2.30737
$679$	−7.99233	−0.306718
$680$	−12.9555	−0.496821
$681$	35.5260	1.36136
$682$	0.652024	0.0249673
$683$	14.7166	0.563115	0.281558	−	0.959544i	$-0.409149\pi$
$683$	14.7166	0.563115	0.281558	+	0.959544i	$0.409149\pi$
$684$	−5.48598	−0.209762
$685$	6.83321	0.261084
$686$	1.49678	0.0571475
$687$	3.16909	0.120908
$688$	−14.2652	−0.543856
$689$	−21.9843	−0.837535
$690$	27.0080	1.02818
$691$	−35.5409	−1.35204	−0.676020	−	0.736884i	$-0.736297\pi$
$691$	−35.5409	−1.35204	−0.676020	+	0.736884i	$0.736297\pi$
$692$	2.40750	0.0915194
$693$	−11.5780	−0.439812
$694$	9.29960	0.353008
$695$	−10.8259	−0.410648
$696$	−54.7873	−2.07671
$697$	−17.4559	−0.661189
$698$	−10.2607	−0.388375
$699$	−39.0577	−1.47730
$700$	0.240365	0.00908495
$701$	9.80265	0.370241	0.185121	−	0.982716i	$-0.440732\pi$
$701$	9.80265	0.370241	0.185121	+	0.982716i	$0.440732\pi$
$702$	−105.775	−3.99221
$703$	21.8145	0.822748
$704$	−11.2134	−0.422621
$705$	−1.45226	−0.0546954
$706$	−25.9317	−0.975953
$707$	−1.59326	−0.0599208
$708$	3.41535	0.128357
$709$	−28.8134	−1.08211	−0.541055	−	0.840987i	$-0.681975\pi$
$709$	−28.8134	−1.08211	−0.541055	+	0.840987i	$0.681975\pi$
$710$	17.6653	0.662967
$711$	−32.2285	−1.20866
$712$	15.8897	0.595492
$713$	1.50881	0.0565053
$714$	−23.3327	−0.873206
$715$	−9.06655	−0.339070
$716$	−3.55590	−0.132890
$717$	46.8385	1.74922
$718$	43.0251	1.60568
$719$	−4.81253	−0.179477	−0.0897386	−	0.995965i	$-0.528603\pi$
$719$	−4.81253	−0.179477	−0.0897386	+	0.995965i	$0.528603\pi$
$720$	31.1514	1.16094
$721$	19.5599	0.728448
$722$	−12.7210	−0.473427
$723$	57.4956	2.13828
$724$	4.08627	0.151865
$725$	6.56392	0.243778
$726$	−39.3595	−1.46077
$727$	−29.7155	−1.10209	−0.551043	−	0.834477i	$-0.685770\pi$
$727$	−29.7155	−1.10209	−0.551043	+	0.834477i	$0.685770\pi$
$728$	14.5263	0.538381
$729$	15.3559	0.568738
$730$	11.8963	0.440302
$731$	−15.8649	−0.586785
$732$	−5.89996	−0.218069
$733$	−20.7358	−0.765894	−0.382947	−	0.923770i	$-0.625091\pi$
$733$	−20.7358	−0.765894	−0.382947	+	0.923770i	$0.625091\pi$
$734$	−27.5106	−1.01543
$735$	−3.16909	−0.116894
$736$	7.70150	0.283881
$737$	14.1291	0.520451
$738$	37.4105	1.37710
$739$	−36.9328	−1.35859	−0.679297	−	0.733863i	$-0.737715\pi$
$739$	−36.9328	−1.35859	−0.679297	+	0.733863i	$0.737715\pi$
$740$	1.61807	0.0594816
$741$	56.6403	2.08073
$742$	5.96621	0.219026
$743$	36.7215	1.34718	0.673590	−	0.739105i	$-0.264751\pi$
$743$	36.7215	1.34718	0.673590	+	0.739105i	$0.264751\pi$
$744$	2.21183	0.0810896
$745$	10.2921	0.377073
$746$	27.7564	1.01623
$747$	−83.0697	−3.03936
$748$	1.94363	0.0710660
$749$	−14.3659	−0.524919
$750$	−4.74344	−0.173206
$751$	22.0355	0.804087	0.402044	−	0.915620i	$-0.368300\pi$
$751$	22.0355	0.804087	0.402044	+	0.915620i	$0.368300\pi$
$752$	−2.02686	−0.0739119
$753$	47.8284	1.74296
$754$	−54.1872	−1.97338
$755$	−1.96012	−0.0713359
$756$	3.07979	0.112011
$757$	38.8723	1.41284	0.706418	−	0.707795i	$-0.250310\pi$
$757$	38.8723	1.41284	0.706418	+	0.707795i	$0.250310\pi$
$758$	10.8498	0.394081
$759$	29.6621	1.07667
$760$	−8.53493	−0.309594
$761$	26.5062	0.960850	0.480425	−	0.877036i	$-0.340482\pi$
$761$	26.5062	0.960850	0.480425	+	0.877036i	$0.340482\pi$
$762$	24.1835	0.876075
$763$	4.39821	0.159226
$764$	1.09122	0.0394790
$765$	34.6447	1.25258
$766$	−6.51280	−0.235317
$767$	−24.7288	−0.892904
$768$	18.0282	0.650538
$769$	37.5353	1.35356	0.676779	−	0.736187i	$-0.263375\pi$
$769$	37.5353	1.35356	0.676779	+	0.736187i	$0.263375\pi$
$770$	2.46053	0.0886713
$771$	6.10128	0.219732
$772$	−4.71994	−0.169875
$773$	16.7910	0.603932	0.301966	−	0.953319i	$-0.402357\pi$
$773$	16.7910	0.603932	0.301966	+	0.953319i	$0.402357\pi$
$774$	34.0008	1.22213
$775$	−0.264994	−0.00951885
$776$	21.0502	0.755657
$777$	−21.3334	−0.765333
$778$	−38.3282	−1.37413
$779$	−11.4997	−0.412021
$780$	4.20126	0.150429
$781$	19.4013	0.694233
$782$	41.9209	1.49909
$783$	84.1034	3.00561
$784$	−4.42296	−0.157963
$785$	−23.4757	−0.837882
$786$	−24.5902	−0.877102
$787$	31.3332	1.11691	0.558454	−	0.829535i	$-0.311395\pi$
$787$	31.3332	1.11691	0.558454	+	0.829535i	$0.311395\pi$
$788$	−2.97524	−0.105989
$789$	23.8296	0.848357
$790$	6.84913	0.243681
$791$	12.6660	0.450350
$792$	30.4941	1.08356
$793$	42.7185	1.51698
$794$	−37.5279	−1.33181
$795$	−12.6320	−0.448012
$796$	0.217753	0.00771805
$797$	−2.60473	−0.0922643	−0.0461322	−	0.998935i	$-0.514690\pi$
$797$	−2.60473	−0.0922643	−0.0461322	+	0.998935i	$0.514690\pi$
$798$	−15.3713	−0.544139
$799$	−2.25415	−0.0797462
$800$	−1.35262	−0.0478224
$801$	−42.4912	−1.50135
$802$	33.3502	1.17764
$803$	13.0654	0.461066
$804$	−6.54712	−0.230899
$805$	5.69376	0.200679
$806$	2.18760	0.0770550
$807$	−12.5376	−0.441344
$808$	4.19633	0.147626
$809$	−43.2111	−1.51922	−0.759611	−	0.650378i	$-0.774610\pi$
$809$	−43.2111	−1.51922	−0.759611	+	0.650378i	$0.774610\pi$
$810$	−29.1515	−1.02428
$811$	−2.32993	−0.0818149	−0.0409075	−	0.999163i	$-0.513025\pi$
$811$	−2.32993	−0.0818149	−0.0409075	+	0.999163i	$0.513025\pi$
$812$	1.57774	0.0553678
$813$	71.0574	2.49209
$814$	16.5636	0.580554
$815$	17.4491	0.611215
$816$	68.9476	2.41365
$817$	−10.4516	−0.365656
$818$	−11.9374	−0.417381
$819$	−38.8452	−1.35736
$820$	−0.852985	−0.0297875
$821$	−8.11301	−0.283146	−0.141573	−	0.989928i	$-0.545216\pi$
$821$	−8.11301	−0.283146	−0.141573	+	0.989928i	$0.545216\pi$
$822$	−32.4129	−1.13053
$823$	6.61681	0.230648	0.115324	−	0.993328i	$-0.463209\pi$
$823$	6.61681	0.230648	0.115324	+	0.993328i	$0.463209\pi$
$824$	−51.5167	−1.79467
$825$	−5.20958	−0.181374
$826$	6.71102	0.233506
$827$	40.1246	1.39527	0.697634	−	0.716454i	$-0.254236\pi$
$827$	40.1246	1.39527	0.697634	+	0.716454i	$0.254236\pi$
$828$	−9.63907	−0.334981
$829$	−43.1622	−1.49909	−0.749543	−	0.661955i	$-0.769727\pi$
$829$	−43.1622	−1.49909	−0.749543	+	0.661955i	$0.769727\pi$
$830$	17.6538	0.612771
$831$	71.7852	2.49020
$832$	−37.6220	−1.30431
$833$	−4.91895	−0.170431
$834$	51.3518	1.77817
$835$	−11.5284	−0.398956
$836$	1.28044	0.0442848
$837$	−3.39535	−0.117361
$838$	−19.1820	−0.662630
$839$	35.2634	1.21743	0.608714	−	0.793390i	$-0.291686\pi$
$839$	35.2634	1.21743	0.608714	+	0.793390i	$0.291686\pi$
$840$	8.34672	0.287989
$841$	14.0851	0.485693
$842$	58.9213	2.03056
$843$	37.6861	1.29798
$844$	3.27734	0.112811
$845$	−17.4191	−0.599236
$846$	4.83098	0.166092
$847$	−8.29767	−0.285111
$848$	−17.6300	−0.605416
$849$	44.1359	1.51474
$850$	−7.36261	−0.252535
$851$	38.3288	1.31390
$852$	−8.99017	−0.307998
$853$	−16.7582	−0.573789	−0.286894	−	0.957962i	$-0.592623\pi$
$853$	−16.7582	−0.573789	−0.286894	+	0.957962i	$0.592623\pi$
$854$	−11.5932	−0.396710
$855$	22.8235	0.780547
$856$	37.8368	1.29324
$857$	−29.1560	−0.995949	−0.497975	−	0.867192i	$-0.665923\pi$
$857$	−29.1560	−0.995949	−0.497975	+	0.867192i	$0.665923\pi$
$858$	43.0067	1.46822
$859$	−22.9652	−0.783563	−0.391782	−	0.920058i	$-0.628141\pi$
$859$	−22.9652	−0.783563	−0.391782	+	0.920058i	$0.628141\pi$
$860$	−0.775242	−0.0264355
$861$	11.2462	0.383268
$862$	−36.1205	−1.23027
$863$	50.0883	1.70503	0.852514	−	0.522705i	$-0.175077\pi$
$863$	50.0883	1.70503	0.852514	+	0.522705i	$0.175077\pi$
$864$	−17.3311	−0.589616
$865$	−10.0160	−0.340555
$866$	−51.4366	−1.74789
$867$	22.8049	0.774495
$868$	−0.0636952	−0.00216196
$869$	7.52220	0.255173
$870$	−31.1356	−1.05560
$871$	47.4043	1.60623
$872$	−11.5840	−0.392283
$873$	−56.2909	−1.90516
$874$	27.6170	0.934158
$875$	−1.00000	−0.0338062
$876$	−6.05422	−0.204553
$877$	−39.9641	−1.34949	−0.674746	−	0.738050i	$-0.735747\pi$
$877$	−39.9641	−1.34949	−0.674746	+	0.738050i	$0.735747\pi$
$878$	−57.3839	−1.93661
$879$	−20.1373	−0.679215
$880$	−7.27079	−0.245098
$881$	21.1223	0.711630	0.355815	−	0.934556i	$-0.384203\pi$
$881$	21.1223	0.711630	0.355815	+	0.934556i	$0.384203\pi$
$882$	10.5420	0.354968
$883$	−52.3055	−1.76022	−0.880110	−	0.474769i	$-0.842532\pi$
$883$	−52.3055	−1.76022	−0.880110	+	0.474769i	$0.842532\pi$
$884$	6.52104	0.219326
$885$	−14.2090	−0.477630
$886$	28.2413	0.948786
$887$	57.4026	1.92739	0.963695	−	0.267005i	$-0.0860341\pi$
$887$	57.4026	1.92739	0.963695	+	0.267005i	$0.0860341\pi$
$888$	56.1879	1.88554
$889$	5.09830	0.170991
$890$	9.03012	0.302690
$891$	−32.0162	−1.07258
$892$	−4.43181	−0.148388
$893$	−1.48501	−0.0496939
$894$	−48.8200	−1.63278
$895$	14.7938	0.494501
$896$	12.9153	0.431470
$897$	99.5191	3.32284
$898$	−42.8723	−1.43067
$899$	−1.73940	−0.0580122
$900$	1.69292	0.0564306
$901$	−19.6070	−0.653204
$902$	−8.73169	−0.290733
$903$	10.2211	0.340139
$904$	−33.3596	−1.10952
$905$	−17.0003	−0.565108
$906$	9.29769	0.308895
$907$	15.8866	0.527507	0.263754	−	0.964590i	$-0.415039\pi$
$907$	15.8866	0.527507	0.263754	+	0.964590i	$0.415039\pi$
$908$	2.69454	0.0894214
$909$	−11.2215	−0.372195
$910$	8.25530	0.273660
$911$	8.65365	0.286708	0.143354	−	0.989671i	$-0.454211\pi$
$911$	8.65365	0.286708	0.143354	+	0.989671i	$0.454211\pi$
$912$	45.4218	1.50407
$913$	19.3886	0.641669
$914$	−31.2920	−1.03505
$915$	24.5458	0.811459
$916$	0.240365	0.00794189
$917$	−5.18403	−0.171192
$918$	−94.3368	−3.11358
$919$	−9.44789	−0.311657	−0.155828	−	0.987784i	$-0.549805\pi$
$919$	−9.44789	−0.311657	−0.155828	+	0.987784i	$0.549805\pi$
$920$	−14.9962	−0.494410
$921$	−46.2779	−1.52491
$922$	−27.9295	−0.919809
$923$	65.0932	2.14257
$924$	−1.25220	−0.0411944
$925$	−6.73173	−0.221338
$926$	−55.8047	−1.83385
$927$	137.762	4.52471
$928$	−8.87851	−0.291452
$929$	−16.4792	−0.540664	−0.270332	−	0.962767i	$-0.587134\pi$
$929$	−16.4792	−0.540664	−0.270332	+	0.962767i	$0.587134\pi$
$930$	1.25698	0.0412180
$931$	−3.24054	−0.106205
$932$	−2.96240	−0.0970367
$933$	42.6651	1.39679
$934$	−35.2252	−1.15260
$935$	−8.08614	−0.264445
$936$	102.310	3.34412
$937$	56.5463	1.84729	0.923644	−	0.383251i	$-0.125196\pi$
$937$	56.5463	1.84729	0.923644	+	0.383251i	$0.125196\pi$
$938$	−12.8648	−0.420051
$939$	59.7653	1.95037
$940$	−0.110150	−0.00359268
$941$	22.5946	0.736564	0.368282	−	0.929714i	$-0.379946\pi$
$941$	22.5946	0.736564	0.368282	+	0.929714i	$0.379946\pi$
$942$	111.355	3.62816
$943$	−20.2055	−0.657980
$944$	−19.8309	−0.645440
$945$	−12.8130	−0.416806
$946$	−7.93586	−0.258017
$947$	−13.4723	−0.437792	−0.218896	−	0.975748i	$-0.570246\pi$
$947$	−13.4723	−0.437792	−0.218896	+	0.975748i	$0.570246\pi$
$948$	−3.48563	−0.113208
$949$	43.8355	1.42296
$950$	−4.85040	−0.157368
$951$	−66.2352	−2.14782
$952$	12.9555	0.419890
$953$	−22.3552	−0.724156	−0.362078	−	0.932148i	$-0.617933\pi$
$953$	−22.3552	−0.724156	−0.362078	+	0.932148i	$0.617933\pi$
$954$	42.0207	1.36047
$955$	−4.53984	−0.146906
$956$	3.55256	0.114898
$957$	−34.1953	−1.10538
$958$	−49.0893	−1.58600
$959$	−6.83321	−0.220656
$960$	−21.6174	−0.697698
$961$	−30.9298	−0.997735
$962$	55.5724	1.79173
$963$	−101.181	−3.26050
$964$	4.36086	0.140454
$965$	19.6366	0.632123
$966$	−27.0080	−0.868968
$967$	50.3440	1.61895	0.809477	−	0.587151i	$-0.199751\pi$
$967$	50.3440	1.61895	0.809477	+	0.587151i	$0.199751\pi$
$968$	21.8544	0.702426
$969$	50.5154	1.62279
$970$	11.9628	0.384103
$971$	−26.9334	−0.864335	−0.432168	−	0.901793i	$-0.642251\pi$
$971$	−26.9334	−0.864335	−0.432168	+	0.901793i	$0.642251\pi$
$972$	5.59629	0.179501
$973$	10.8259	0.347061
$974$	−6.87458	−0.220276
$975$	−17.4786	−0.559764
$976$	34.2575	1.09656
$977$	−52.9277	−1.69331	−0.846654	−	0.532144i	$-0.821386\pi$
$977$	−52.9277	−1.69331	−0.846654	+	0.532144i	$0.821386\pi$
$978$	−82.7687	−2.64665
$979$	9.91752	0.316965
$980$	−0.240365	−0.00767819
$981$	30.9771	0.989022
$982$	11.3604	0.362526
$983$	38.5633	1.22998	0.614989	−	0.788536i	$-0.289161\pi$
$983$	38.5633	1.22998	0.614989	+	0.788536i	$0.289161\pi$
$984$	−29.6201	−0.944253
$985$	12.3780	0.394396
$986$	−48.3276	−1.53906
$987$	1.45226	0.0462260
$988$	4.29598	0.136673
$989$	−18.3639	−0.583937
$990$	17.3298	0.550776
$991$	10.6067	0.336932	0.168466	−	0.985707i	$-0.446119\pi$
$991$	10.6067	0.336932	0.168466	+	0.985707i	$0.446119\pi$
$992$	0.358436	0.0113804
$993$	38.7569	1.22991
$994$	−17.6653	−0.560310
$995$	−0.905926	−0.0287198
$996$	−8.98429	−0.284678
$997$	−19.1681	−0.607059	−0.303529	−	0.952822i	$-0.598165\pi$
$997$	−19.1681	−0.607059	−0.303529	+	0.952822i	$0.598165\pi$
$998$	−55.2894	−1.75016
$999$	−86.2534	−2.72894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.35	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.35	✓	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)

\(f(q)\)	\(=\)	\(q+1.49678 q^{2} +3.16909 q^{3} +0.240365 q^{4} -1.00000 q^{5} +4.74344 q^{6} +1.00000 q^{7} -2.63379 q^{8} +7.04311 q^{9} +O(q^{10})\)	\(q+1.49678 q^{2} +3.16909 q^{3} +0.240365 q^{4} -1.00000 q^{5} +4.74344 q^{6} +1.00000 q^{7} -2.63379 q^{8} +7.04311 q^{9} -1.49678 q^{10} -1.64388 q^{11} +0.761738 q^{12} -5.51535 q^{13} +1.49678 q^{14} -3.16909 q^{15} -4.42296 q^{16} -4.91895 q^{17} +10.5420 q^{18} -3.24054 q^{19} -0.240365 q^{20} +3.16909 q^{21} -2.46053 q^{22} -5.69376 q^{23} -8.34672 q^{24} +1.00000 q^{25} -8.25530 q^{26} +12.8130 q^{27} +0.240365 q^{28} +6.56392 q^{29} -4.74344 q^{30} -0.264994 q^{31} -1.35262 q^{32} -5.20958 q^{33} -7.36261 q^{34} -1.00000 q^{35} +1.69292 q^{36} -6.73173 q^{37} -4.85040 q^{38} -17.4786 q^{39} +2.63379 q^{40} +3.54871 q^{41} +4.74344 q^{42} +3.22527 q^{43} -0.395130 q^{44} -7.04311 q^{45} -8.52233 q^{46} +0.458259 q^{47} -14.0167 q^{48} +1.00000 q^{49} +1.49678 q^{50} -15.5886 q^{51} -1.32570 q^{52} +3.98602 q^{53} +19.1783 q^{54} +1.64388 q^{55} -2.63379 q^{56} -10.2696 q^{57} +9.82478 q^{58} +4.48362 q^{59} -0.761738 q^{60} -7.74539 q^{61} -0.396638 q^{62} +7.04311 q^{63} +6.82132 q^{64} +5.51535 q^{65} -7.79763 q^{66} -8.59497 q^{67} -1.18234 q^{68} -18.0440 q^{69} -1.49678 q^{70} -11.8022 q^{71} -18.5501 q^{72} -7.94790 q^{73} -10.0760 q^{74} +3.16909 q^{75} -0.778914 q^{76} -1.64388 q^{77} -26.1618 q^{78} -4.57590 q^{79} +4.42296 q^{80} +19.4761 q^{81} +5.31165 q^{82} -11.7945 q^{83} +0.761738 q^{84} +4.91895 q^{85} +4.82753 q^{86} +20.8016 q^{87} +4.32963 q^{88} -6.03301 q^{89} -10.5420 q^{90} -5.51535 q^{91} -1.36858 q^{92} -0.839788 q^{93} +0.685915 q^{94} +3.24054 q^{95} -4.28658 q^{96} -7.99233 q^{97} +1.49678 q^{98} -11.5780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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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