LMFDB - Embedded newform 8015.2.a.j.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.69745 q^{2} +0.851741 q^{3} +0.881321 q^{4} -1.00000 q^{5} -1.44578 q^{6} +1.00000 q^{7} +1.89890 q^{8} -2.27454 q^{9} +O(q^{10})$	\(q-1.69745 q^{2} +0.851741 q^{3} +0.881321 q^{4} -1.00000 q^{5} -1.44578 q^{6} +1.00000 q^{7} +1.89890 q^{8} -2.27454 q^{9} +1.69745 q^{10} +3.48843 q^{11} +0.750658 q^{12} +1.21654 q^{13} -1.69745 q^{14} -0.851741 q^{15} -4.98592 q^{16} +2.17337 q^{17} +3.86090 q^{18} +6.81744 q^{19} -0.881321 q^{20} +0.851741 q^{21} -5.92142 q^{22} -0.247916 q^{23} +1.61737 q^{24} +1.00000 q^{25} -2.06501 q^{26} -4.49254 q^{27} +0.881321 q^{28} +3.26988 q^{29} +1.44578 q^{30} -9.26914 q^{31} +4.66553 q^{32} +2.97124 q^{33} -3.68918 q^{34} -1.00000 q^{35} -2.00460 q^{36} -8.51487 q^{37} -11.5722 q^{38} +1.03618 q^{39} -1.89890 q^{40} -9.48462 q^{41} -1.44578 q^{42} -1.22649 q^{43} +3.07443 q^{44} +2.27454 q^{45} +0.420824 q^{46} +2.37490 q^{47} -4.24671 q^{48} +1.00000 q^{49} -1.69745 q^{50} +1.85115 q^{51} +1.07216 q^{52} -10.4489 q^{53} +7.62584 q^{54} -3.48843 q^{55} +1.89890 q^{56} +5.80669 q^{57} -5.55044 q^{58} -11.7301 q^{59} -0.750658 q^{60} +8.29191 q^{61} +15.7339 q^{62} -2.27454 q^{63} +2.05235 q^{64} -1.21654 q^{65} -5.04352 q^{66} -3.49856 q^{67} +1.91544 q^{68} -0.211160 q^{69} +1.69745 q^{70} -12.3408 q^{71} -4.31911 q^{72} -15.0502 q^{73} +14.4535 q^{74} +0.851741 q^{75} +6.00835 q^{76} +3.48843 q^{77} -1.75885 q^{78} +3.22838 q^{79} +4.98592 q^{80} +2.99713 q^{81} +16.0996 q^{82} +8.97461 q^{83} +0.750658 q^{84} -2.17337 q^{85} +2.08191 q^{86} +2.78509 q^{87} +6.62416 q^{88} -1.91608 q^{89} -3.86090 q^{90} +1.21654 q^{91} -0.218493 q^{92} -7.89491 q^{93} -4.03126 q^{94} -6.81744 q^{95} +3.97382 q^{96} +11.7682 q^{97} -1.69745 q^{98} -7.93456 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.69745	−1.20028	−0.600138	−	0.799897i	$-0.704888\pi$
$2$	−1.69745	−1.20028	−0.600138	+	0.799897i	$0.704888\pi$
$3$	0.851741	0.491753	0.245877	−	0.969301i	$-0.420924\pi$
$3$	0.851741	0.491753	0.245877	+	0.969301i	$0.420924\pi$
$4$	0.881321	0.440661
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.44578	−0.590239
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.89890	0.671361
$9$	−2.27454	−0.758179
$10$	1.69745	0.536779
$11$	3.48843	1.05180	0.525900	−	0.850546i	$-0.323728\pi$
$11$	3.48843	1.05180	0.525900	+	0.850546i	$0.323728\pi$
$12$	0.750658	0.216696
$13$	1.21654	0.337407	0.168704	−	0.985667i	$-0.446042\pi$
$13$	1.21654	0.337407	0.168704	+	0.985667i	$0.446042\pi$
$14$	−1.69745	−0.453661
$15$	−0.851741	−0.219919
$16$	−4.98592	−1.24648
$17$	2.17337	0.527119	0.263560	−	0.964643i	$-0.415103\pi$
$17$	2.17337	0.527119	0.263560	+	0.964643i	$0.415103\pi$
$18$	3.86090	0.910023
$19$	6.81744	1.56403	0.782013	−	0.623262i	$-0.214193\pi$
$19$	6.81744	1.56403	0.782013	+	0.623262i	$0.214193\pi$
$20$	−0.881321	−0.197069
$21$	0.851741	0.185865
$22$	−5.92142	−1.26245
$23$	−0.247916	−0.0516940	−0.0258470	−	0.999666i	$-0.508228\pi$
$23$	−0.247916	−0.0516940	−0.0258470	+	0.999666i	$0.508228\pi$
$24$	1.61737	0.330144
$25$	1.00000	0.200000
$26$	−2.06501	−0.404982
$27$	−4.49254	−0.864590
$28$	0.881321	0.166554
$29$	3.26988	0.607201	0.303601	−	0.952799i	$-0.401811\pi$
$29$	3.26988	0.607201	0.303601	+	0.952799i	$0.401811\pi$
$30$	1.44578	0.263963
$31$	−9.26914	−1.66479	−0.832393	−	0.554185i	$-0.813030\pi$
$31$	−9.26914	−1.66479	−0.832393	+	0.554185i	$0.813030\pi$
$32$	4.66553	0.824757
$33$	2.97124	0.517226
$34$	−3.68918	−0.632688
$35$	−1.00000	−0.169031
$36$	−2.00460	−0.334100
$37$	−8.51487	−1.39984	−0.699918	−	0.714223i	$-0.746780\pi$
$37$	−8.51487	−1.39984	−0.699918	+	0.714223i	$0.746780\pi$
$38$	−11.5722	−1.87726
$39$	1.03618	0.165921
$40$	−1.89890	−0.300242
$41$	−9.48462	−1.48125	−0.740624	−	0.671919i	$-0.765470\pi$
$41$	−9.48462	−1.48125	−0.740624	+	0.671919i	$0.765470\pi$
$42$	−1.44578	−0.223089
$43$	−1.22649	−0.187039	−0.0935193	−	0.995617i	$-0.529812\pi$
$43$	−1.22649	−0.187039	−0.0935193	+	0.995617i	$0.529812\pi$
$44$	3.07443	0.463487
$45$	2.27454	0.339068
$46$	0.420824	0.0620470
$47$	2.37490	0.346415	0.173207	−	0.984885i	$-0.444587\pi$
$47$	2.37490	0.346415	0.173207	+	0.984885i	$0.444587\pi$
$48$	−4.24671	−0.612960
$49$	1.00000	0.142857
$50$	−1.69745	−0.240055
$51$	1.85115	0.259213
$52$	1.07216	0.148682
$53$	−10.4489	−1.43527	−0.717633	−	0.696421i	$-0.754775\pi$
$53$	−10.4489	−1.43527	−0.717633	+	0.696421i	$0.754775\pi$
$54$	7.62584	1.03775
$55$	−3.48843	−0.470380
$56$	1.89890	0.253751
$57$	5.80669	0.769115
$58$	−5.55044	−0.728808
$59$	−11.7301	−1.52713	−0.763563	−	0.645733i	$-0.776552\pi$
$59$	−11.7301	−1.52713	−0.763563	+	0.645733i	$0.776552\pi$
$60$	−0.750658	−0.0969095
$61$	8.29191	1.06167	0.530835	−	0.847475i	$-0.321878\pi$
$61$	8.29191	1.06167	0.530835	+	0.847475i	$0.321878\pi$
$62$	15.7339	1.99820
$63$	−2.27454	−0.286565
$64$	2.05235	0.256544
$65$	−1.21654	−0.150893
$66$	−5.04352	−0.620814
$67$	−3.49856	−0.427418	−0.213709	−	0.976897i	$-0.568554\pi$
$67$	−3.49856	−0.427418	−0.213709	+	0.976897i	$0.568554\pi$
$68$	1.91544	0.232281
$69$	−0.211160	−0.0254207
$70$	1.69745	0.202884
$71$	−12.3408	−1.46458	−0.732291	−	0.680991i	$-0.761549\pi$
$71$	−12.3408	−1.46458	−0.732291	+	0.680991i	$0.761549\pi$
$72$	−4.31911	−0.509012
$73$	−15.0502	−1.76149	−0.880747	−	0.473586i	$-0.842959\pi$
$73$	−15.0502	−1.76149	−0.880747	+	0.473586i	$0.842959\pi$
$74$	14.4535	1.68019
$75$	0.851741	0.0983506
$76$	6.00835	0.689205
$77$	3.48843	0.397543
$78$	−1.75885	−0.199151
$79$	3.22838	0.363221	0.181610	−	0.983371i	$-0.441869\pi$
$79$	3.22838	0.363221	0.181610	+	0.983371i	$0.441869\pi$
$80$	4.98592	0.557442
$81$	2.99713	0.333014
$82$	16.0996	1.77791
$83$	8.97461	0.985091	0.492546	−	0.870287i	$-0.336066\pi$
$83$	8.97461	0.985091	0.492546	+	0.870287i	$0.336066\pi$
$84$	0.750658	0.0819035
$85$	−2.17337	−0.235735
$86$	2.08191	0.224498
$87$	2.78509	0.298593
$88$	6.62416	0.706138
$89$	−1.91608	−0.203104	−0.101552	−	0.994830i	$-0.532381\pi$
$89$	−1.91608	−0.203104	−0.101552	+	0.994830i	$0.532381\pi$
$90$	−3.86090	−0.406975
$91$	1.21654	0.127528
$92$	−0.218493	−0.0227795
$93$	−7.89491	−0.818664
$94$	−4.03126	−0.415793
$95$	−6.81744	−0.699454
$96$	3.97382	0.405577
$97$	11.7682	1.19488	0.597440	−	0.801914i	$-0.296185\pi$
$97$	11.7682	1.19488	0.597440	+	0.801914i	$0.296185\pi$
$98$	−1.69745	−0.171468
$99$	−7.93456	−0.797453
$100$	0.881321	0.0881321
$101$	−8.11852	−0.807823	−0.403911	−	0.914798i	$-0.632350\pi$
$101$	−8.11852	−0.807823	−0.403911	+	0.914798i	$0.632350\pi$
$102$	−3.14222	−0.311126
$103$	5.70371	0.562003	0.281001	−	0.959707i	$-0.409333\pi$
$103$	5.70371	0.562003	0.281001	+	0.959707i	$0.409333\pi$
$104$	2.31008	0.226522
$105$	−0.851741	−0.0831214
$106$	17.7364	1.72271
$107$	12.0745	1.16729	0.583643	−	0.812010i	$-0.301627\pi$
$107$	12.0745	1.16729	0.583643	+	0.812010i	$0.301627\pi$
$108$	−3.95937	−0.380991
$109$	1.87641	0.179728	0.0898638	−	0.995954i	$-0.471357\pi$
$109$	1.87641	0.179728	0.0898638	+	0.995954i	$0.471357\pi$
$110$	5.92142	0.564585
$111$	−7.25247	−0.688374
$112$	−4.98592	−0.471125
$113$	7.67031	0.721562	0.360781	−	0.932651i	$-0.382510\pi$
$113$	7.67031	0.721562	0.360781	+	0.932651i	$0.382510\pi$
$114$	−9.85654	−0.923150
$115$	0.247916	0.0231183
$116$	2.88181	0.267570
$117$	−2.76706	−0.255815
$118$	19.9112	1.83297
$119$	2.17337	0.199232
$120$	−1.61737	−0.147645
$121$	1.16913	0.106285
$122$	−14.0751	−1.27430
$123$	−8.07844	−0.728409
$124$	−8.16909	−0.733606
$125$	−1.00000	−0.0894427
$126$	3.86090	0.343957
$127$	15.6329	1.38720	0.693598	−	0.720362i	$-0.256024\pi$
$127$	15.6329	1.38720	0.693598	+	0.720362i	$0.256024\pi$
$128$	−12.8148	−1.13268
$129$	−1.04466	−0.0919768
$130$	2.06501	0.181113
$131$	5.79730	0.506512	0.253256	−	0.967399i	$-0.418498\pi$
$131$	5.79730	0.506512	0.253256	+	0.967399i	$0.418498\pi$
$132$	2.61862	0.227921
$133$	6.81744	0.591147
$134$	5.93862	0.513019
$135$	4.49254	0.386656
$136$	4.12700	0.353887
$137$	−5.39105	−0.460588	−0.230294	−	0.973121i	$-0.573969\pi$
$137$	−5.39105	−0.460588	−0.230294	+	0.973121i	$0.573969\pi$
$138$	0.358433	0.0305118
$139$	−14.9369	−1.26694	−0.633468	−	0.773769i	$-0.718369\pi$
$139$	−14.9369	−1.26694	−0.633468	+	0.773769i	$0.718369\pi$
$140$	−0.881321	−0.0744853
$141$	2.02280	0.170351
$142$	20.9478	1.75790
$143$	4.24381	0.354885
$144$	11.3406	0.945054
$145$	−3.26988	−0.271549
$146$	25.5469	2.11428
$147$	0.851741	0.0702504
$148$	−7.50434	−0.616853
$149$	6.79656	0.556796	0.278398	−	0.960466i	$-0.410197\pi$
$149$	6.79656	0.556796	0.278398	+	0.960466i	$0.410197\pi$
$150$	−1.44578	−0.118048
$151$	−8.98439	−0.731139	−0.365570	−	0.930784i	$-0.619126\pi$
$151$	−8.98439	−0.731139	−0.365570	+	0.930784i	$0.619126\pi$
$152$	12.9456	1.05003
$153$	−4.94341	−0.399651
$154$	−5.92142	−0.477161
$155$	9.26914	0.744515
$156$	0.913205	0.0731149
$157$	0.512503	0.0409022	0.0204511	−	0.999791i	$-0.493490\pi$
$157$	0.512503	0.0409022	0.0204511	+	0.999791i	$0.493490\pi$
$158$	−5.47999	−0.435965
$159$	−8.89976	−0.705797
$160$	−4.66553	−0.368842
$161$	−0.247916	−0.0195385
$162$	−5.08746	−0.399709
$163$	−12.5348	−0.981804	−0.490902	−	0.871215i	$-0.663333\pi$
$163$	−12.5348	−0.981804	−0.490902	+	0.871215i	$0.663333\pi$
$164$	−8.35900	−0.652728
$165$	−2.97124	−0.231311
$166$	−15.2339	−1.18238
$167$	6.30347	0.487777	0.243888	−	0.969803i	$-0.421577\pi$
$167$	6.30347	0.487777	0.243888	+	0.969803i	$0.421577\pi$
$168$	1.61737	0.124783
$169$	−11.5200	−0.886156
$170$	3.68918	0.282947
$171$	−15.5065	−1.18581
$172$	−1.08094	−0.0824206
$173$	−12.5296	−0.952608	−0.476304	−	0.879281i	$-0.658024\pi$
$173$	−12.5296	−0.952608	−0.476304	+	0.879281i	$0.658024\pi$
$174$	−4.72754	−0.358394
$175$	1.00000	0.0755929
$176$	−17.3930	−1.31105
$177$	−9.99099	−0.750969
$178$	3.25245	0.243781
$179$	−21.8629	−1.63411	−0.817055	−	0.576559i	$-0.804395\pi$
$179$	−21.8629	−1.63411	−0.817055	+	0.576559i	$0.804395\pi$
$180$	2.00460	0.149414
$181$	10.3707	0.770849	0.385424	−	0.922739i	$-0.374055\pi$
$181$	10.3707	0.770849	0.385424	+	0.922739i	$0.374055\pi$
$182$	−2.06501	−0.153069
$183$	7.06256	0.522079
$184$	−0.470766	−0.0347053
$185$	8.51487	0.626026
$186$	13.4012	0.982622
$187$	7.58164	0.554424
$188$	2.09305	0.152651
$189$	−4.49254	−0.326784
$190$	11.5722	0.839537
$191$	19.5467	1.41435	0.707176	−	0.707038i	$-0.249969\pi$
$191$	19.5467	1.41435	0.707176	+	0.707038i	$0.249969\pi$
$192$	1.74807	0.126156
$193$	−21.0852	−1.51775	−0.758875	−	0.651237i	$-0.774250\pi$
$193$	−21.0852	−1.51775	−0.758875	+	0.651237i	$0.774250\pi$
$194$	−19.9759	−1.43418
$195$	−1.03618	−0.0742021
$196$	0.881321	0.0629515
$197$	−12.4870	−0.889659	−0.444830	−	0.895615i	$-0.646736\pi$
$197$	−12.4870	−0.889659	−0.444830	+	0.895615i	$0.646736\pi$
$198$	13.4685	0.957163
$199$	1.29703	0.0919444	0.0459722	−	0.998943i	$-0.485361\pi$
$199$	1.29703	0.0919444	0.0459722	+	0.998943i	$0.485361\pi$
$200$	1.89890	0.134272
$201$	−2.97987	−0.210184
$202$	13.7807	0.969610
$203$	3.26988	0.229500
$204$	1.63146	0.114225
$205$	9.48462	0.662435
$206$	−9.68173	−0.674558
$207$	0.563894	0.0391933
$208$	−6.06556	−0.420571
$209$	23.7821	1.64504
$210$	1.44578	0.0997686
$211$	22.1160	1.52253	0.761266	−	0.648440i	$-0.224578\pi$
$211$	22.1160	1.52253	0.761266	+	0.648440i	$0.224578\pi$
$212$	−9.20884	−0.632466
$213$	−10.5112	−0.720213
$214$	−20.4958	−1.40107
$215$	1.22649	0.0836462
$216$	−8.53087	−0.580452
$217$	−9.26914	−0.629230
$218$	−3.18511	−0.215723
$219$	−12.8189	−0.866220
$220$	−3.07443	−0.207278
$221$	2.64399	0.177854
$222$	12.3107	0.826238
$223$	−0.933299	−0.0624983	−0.0312492	−	0.999512i	$-0.509949\pi$
$223$	−0.933299	−0.0624983	−0.0312492	+	0.999512i	$0.509949\pi$
$224$	4.66553	0.311729
$225$	−2.27454	−0.151636
$226$	−13.0199	−0.866073
$227$	−2.92684	−0.194261	−0.0971306	−	0.995272i	$-0.530966\pi$
$227$	−2.92684	−0.194261	−0.0971306	+	0.995272i	$0.530966\pi$
$228$	5.11756	0.338919
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−0.420824	−0.0277483
$231$	2.97124	0.195493
$232$	6.20916	0.407651
$233$	10.4711	0.685986	0.342993	−	0.939338i	$-0.388559\pi$
$233$	10.4711	0.685986	0.342993	+	0.939338i	$0.388559\pi$
$234$	4.69694	0.307048
$235$	−2.37490	−0.154921
$236$	−10.3380	−0.672944
$237$	2.74974	0.178615
$238$	−3.68918	−0.239134
$239$	−21.7977	−1.40998	−0.704989	−	0.709219i	$-0.749048\pi$
$239$	−21.7977	−1.40998	−0.704989	+	0.709219i	$0.749048\pi$
$240$	4.24671	0.274124
$241$	−7.43284	−0.478791	−0.239396	−	0.970922i	$-0.576949\pi$
$241$	−7.43284	−0.478791	−0.239396	+	0.970922i	$0.576949\pi$
$242$	−1.98453	−0.127571
$243$	16.0304	1.02835
$244$	7.30783	0.467836
$245$	−1.00000	−0.0638877
$246$	13.7127	0.874291
$247$	8.29368	0.527714
$248$	−17.6011	−1.11767
$249$	7.64405	0.484422
$250$	1.69745	0.107356
$251$	17.7496	1.12034	0.560172	−	0.828377i	$-0.310735\pi$
$251$	17.7496	1.12034	0.560172	+	0.828377i	$0.310735\pi$
$252$	−2.00460	−0.126278
$253$	−0.864836	−0.0543718
$254$	−26.5360	−1.66502
$255$	−1.85115	−0.115923
$256$	17.6477	1.10298
$257$	−13.2264	−0.825039	−0.412520	−	0.910949i	$-0.635351\pi$
$257$	−13.2264	−0.825039	−0.412520	+	0.910949i	$0.635351\pi$
$258$	1.77325	0.110398
$259$	−8.51487	−0.529088
$260$	−1.07216	−0.0664927
$261$	−7.43746	−0.460367
$262$	−9.84060	−0.607954
$263$	−1.09929	−0.0677853	−0.0338926	−	0.999425i	$-0.510790\pi$
$263$	−1.09929	−0.0677853	−0.0338926	+	0.999425i	$0.510790\pi$
$264$	5.64207	0.347246
$265$	10.4489	0.641871
$266$	−11.5722	−0.709539
$267$	−1.63201	−0.0998772
$268$	−3.08336	−0.188346
$269$	21.3355	1.30085	0.650425	−	0.759571i	$-0.274591\pi$
$269$	21.3355	1.30085	0.650425	+	0.759571i	$0.274591\pi$
$270$	−7.62584	−0.464094
$271$	−24.9265	−1.51418	−0.757088	−	0.653313i	$-0.773379\pi$
$271$	−24.9265	−1.51418	−0.757088	+	0.653313i	$0.773379\pi$
$272$	−10.8362	−0.657043
$273$	1.03618	0.0627123
$274$	9.15101	0.552833
$275$	3.48843	0.210360
$276$	−0.186100	−0.0112019
$277$	11.5242	0.692421	0.346210	−	0.938157i	$-0.387468\pi$
$277$	11.5242	0.692421	0.346210	+	0.938157i	$0.387468\pi$
$278$	25.3547	1.52067
$279$	21.0830	1.26221
$280$	−1.89890	−0.113481
$281$	26.2826	1.56789	0.783943	−	0.620832i	$-0.213205\pi$
$281$	26.2826	1.56789	0.783943	+	0.620832i	$0.213205\pi$
$282$	−3.43359	−0.204468
$283$	−28.4396	−1.69056	−0.845279	−	0.534325i	$-0.820566\pi$
$283$	−28.4396	−1.69056	−0.845279	+	0.534325i	$0.820566\pi$
$284$	−10.8762	−0.645384
$285$	−5.80669	−0.343959
$286$	−7.20363	−0.425960
$287$	−9.48462	−0.559859
$288$	−10.6119	−0.625313
$289$	−12.2765	−0.722145
$290$	5.55044	0.325933
$291$	10.0235	0.587586
$292$	−13.2641	−0.776221
$293$	24.3664	1.42350	0.711751	−	0.702432i	$-0.247902\pi$
$293$	24.3664	1.42350	0.711751	+	0.702432i	$0.247902\pi$
$294$	−1.44578	−0.0843199
$295$	11.7301	0.682951
$296$	−16.1689	−0.939796
$297$	−15.6719	−0.909376
$298$	−11.5368	−0.668308
$299$	−0.301599	−0.0174419
$300$	0.750658	0.0433393
$301$	−1.22649	−0.0706940
$302$	15.2505	0.877568
$303$	−6.91488	−0.397249
$304$	−33.9912	−1.94953
$305$	−8.29191	−0.474793
$306$	8.39116	0.479691
$307$	−26.0462	−1.48654	−0.743268	−	0.668994i	$-0.766725\pi$
$307$	−26.0462	−1.48654	−0.743268	+	0.668994i	$0.766725\pi$
$308$	3.07443	0.175182
$309$	4.85808	0.276367
$310$	−15.7339	−0.893623
$311$	−17.3977	−0.986535	−0.493268	−	0.869878i	$-0.664198\pi$
$311$	−17.3977	−0.986535	−0.493268	+	0.869878i	$0.664198\pi$
$312$	1.96759	0.111393
$313$	12.1210	0.685118	0.342559	−	0.939496i	$-0.388706\pi$
$313$	12.1210	0.685118	0.342559	+	0.939496i	$0.388706\pi$
$314$	−0.869945	−0.0490939
$315$	2.27454	0.128156
$316$	2.84524	0.160057
$317$	−13.1215	−0.736977	−0.368489	−	0.929632i	$-0.620125\pi$
$317$	−13.1215	−0.736977	−0.368489	+	0.929632i	$0.620125\pi$
$318$	15.1069	0.847150
$319$	11.4067	0.638654
$320$	−2.05235	−0.114730
$321$	10.2844	0.574017
$322$	0.420824	0.0234516
$323$	14.8168	0.824429
$324$	2.64143	0.146746
$325$	1.21654	0.0674814
$326$	21.2772	1.17844
$327$	1.59822	0.0883816
$328$	−18.0103	−0.994453
$329$	2.37490	0.130932
$330$	5.04352	0.277636
$331$	4.47967	0.246225	0.123112	−	0.992393i	$-0.460712\pi$
$331$	4.47967	0.246225	0.123112	+	0.992393i	$0.460712\pi$
$332$	7.90952	0.434091
$333$	19.3674	1.06133
$334$	−10.6998	−0.585467
$335$	3.49856	0.191147
$336$	−4.24671	−0.231677
$337$	−6.72817	−0.366507	−0.183253	−	0.983066i	$-0.558663\pi$
$337$	−6.72817	−0.366507	−0.183253	+	0.983066i	$0.558663\pi$
$338$	19.5546	1.06363
$339$	6.53312	0.354830
$340$	−1.91544	−0.103879
$341$	−32.3347	−1.75102
$342$	26.3215	1.42330
$343$	1.00000	0.0539949
$344$	−2.32899	−0.125570
$345$	0.211160	0.0113685
$346$	21.2683	1.14339
$347$	−16.1235	−0.865556	−0.432778	−	0.901500i	$-0.642467\pi$
$347$	−16.1235	−0.865556	−0.432778	+	0.901500i	$0.642467\pi$
$348$	2.45456	0.131578
$349$	−18.2117	−0.974849	−0.487425	−	0.873165i	$-0.662064\pi$
$349$	−18.2117	−0.974849	−0.487425	+	0.873165i	$0.662064\pi$
$350$	−1.69745	−0.0907323
$351$	−5.46535	−0.291719
$352$	16.2754	0.867480
$353$	−11.9843	−0.637863	−0.318931	−	0.947778i	$-0.603324\pi$
$353$	−11.9843	−0.637863	−0.318931	+	0.947778i	$0.603324\pi$
$354$	16.9592	0.901369
$355$	12.3408	0.654981
$356$	−1.68868	−0.0895001
$357$	1.85115	0.0979731
$358$	37.1111	1.96138
$359$	15.1107	0.797511	0.398755	−	0.917057i	$-0.369442\pi$
$359$	15.1107	0.797511	0.398755	+	0.917057i	$0.369442\pi$
$360$	4.31911	0.227637
$361$	27.4774	1.44618
$362$	−17.6037	−0.925231
$363$	0.995796	0.0522657
$364$	1.07216	0.0561966
$365$	15.0502	0.787764
$366$	−11.9883	−0.626639
$367$	−4.65493	−0.242986	−0.121493	−	0.992592i	$-0.538768\pi$
$367$	−4.65493	−0.242986	−0.121493	+	0.992592i	$0.538768\pi$
$368$	1.23609	0.0644355
$369$	21.5731	1.12305
$370$	−14.4535	−0.751403
$371$	−10.4489	−0.542480
$372$	−6.95795	−0.360753
$373$	−24.0014	−1.24274	−0.621372	−	0.783516i	$-0.713424\pi$
$373$	−24.0014	−1.24274	−0.621372	+	0.783516i	$0.713424\pi$
$374$	−12.8694	−0.665462
$375$	−0.851741	−0.0439837
$376$	4.50969	0.232569
$377$	3.97793	0.204874
$378$	7.62584	0.392231
$379$	−13.4017	−0.688400	−0.344200	−	0.938896i	$-0.611850\pi$
$379$	−13.4017	−0.688400	−0.344200	+	0.938896i	$0.611850\pi$
$380$	−6.00835	−0.308222
$381$	13.3152	0.682158
$382$	−33.1795	−1.69761
$383$	−28.1668	−1.43926	−0.719629	−	0.694359i	$-0.755688\pi$
$383$	−28.1668	−1.43926	−0.719629	+	0.694359i	$0.755688\pi$
$384$	−10.9149	−0.556999
$385$	−3.48843	−0.177787
$386$	35.7911	1.82172
$387$	2.78971	0.141809
$388$	10.3716	0.526537
$389$	34.7631	1.76256	0.881281	−	0.472593i	$-0.156682\pi$
$389$	34.7631	1.76256	0.881281	+	0.472593i	$0.156682\pi$
$390$	1.75885	0.0890630
$391$	−0.538812	−0.0272489
$392$	1.89890	0.0959087
$393$	4.93780	0.249079
$394$	21.1959	1.06784
$395$	−3.22838	−0.162437
$396$	−6.99290	−0.351406
$397$	−3.99664	−0.200586	−0.100293	−	0.994958i	$-0.531978\pi$
$397$	−3.99664	−0.200586	−0.100293	+	0.994958i	$0.531978\pi$
$398$	−2.20165	−0.110359
$399$	5.80669	0.290698
$400$	−4.98592	−0.249296
$401$	11.6503	0.581788	0.290894	−	0.956755i	$-0.406047\pi$
$401$	11.6503	0.581788	0.290894	+	0.956755i	$0.406047\pi$
$402$	5.05817	0.252279
$403$	−11.2763	−0.561711
$404$	−7.15502	−0.355976
$405$	−2.99713	−0.148928
$406$	−5.55044	−0.275464
$407$	−29.7035	−1.47235
$408$	3.51514	0.174025
$409$	−20.1996	−0.998804	−0.499402	−	0.866370i	$-0.666447\pi$
$409$	−20.1996	−0.998804	−0.499402	+	0.866370i	$0.666447\pi$
$410$	−16.0996	−0.795104
$411$	−4.59178	−0.226496
$412$	5.02680	0.247653
$413$	−11.7301	−0.577199
$414$	−0.957179	−0.0470428
$415$	−8.97461	−0.440546
$416$	5.67580	0.278279
$417$	−12.7224	−0.623019
$418$	−40.3689	−1.97451
$419$	−3.73287	−0.182363	−0.0911813	−	0.995834i	$-0.529064\pi$
$419$	−3.73287	−0.182363	−0.0911813	+	0.995834i	$0.529064\pi$
$420$	−0.750658	−0.0366284
$421$	−32.0257	−1.56084	−0.780419	−	0.625256i	$-0.784994\pi$
$421$	−32.0257	−1.56084	−0.780419	+	0.625256i	$0.784994\pi$
$422$	−37.5408	−1.82746
$423$	−5.40180	−0.262644
$424$	−19.8414	−0.963582
$425$	2.17337	0.105424
$426$	17.8421	0.864454
$427$	8.29191	0.401273
$428$	10.6415	0.514377
$429$	3.61463	0.174516
$430$	−2.08191	−0.100399
$431$	−0.581676	−0.0280183	−0.0140092	−	0.999902i	$-0.504459\pi$
$431$	−0.581676	−0.0280183	−0.0140092	+	0.999902i	$0.504459\pi$
$432$	22.3994	1.07769
$433$	−33.3111	−1.60083	−0.800414	−	0.599447i	$-0.795387\pi$
$433$	−33.3111	−1.60083	−0.800414	+	0.599447i	$0.795387\pi$
$434$	15.7339	0.755250
$435$	−2.78509	−0.133535
$436$	1.65372	0.0791989
$437$	−1.69015	−0.0808508
$438$	21.7594	1.03970
$439$	−20.0871	−0.958706	−0.479353	−	0.877622i	$-0.659129\pi$
$439$	−20.0871	−0.958706	−0.479353	+	0.877622i	$0.659129\pi$
$440$	−6.62416	−0.315795
$441$	−2.27454	−0.108311
$442$	−4.48803	−0.213474
$443$	8.82021	0.419061	0.209530	−	0.977802i	$-0.432806\pi$
$443$	8.82021	0.419061	0.209530	+	0.977802i	$0.432806\pi$
$444$	−6.39176	−0.303339
$445$	1.91608	0.0908310
$446$	1.58422	0.0750152
$447$	5.78891	0.273806
$448$	2.05235	0.0969645
$449$	−9.71626	−0.458538	−0.229269	−	0.973363i	$-0.573634\pi$
$449$	−9.71626	−0.458538	−0.229269	+	0.973363i	$0.573634\pi$
$450$	3.86090	0.182005
$451$	−33.0864	−1.55798
$452$	6.76001	0.317964
$453$	−7.65237	−0.359540
$454$	4.96815	0.233167
$455$	−1.21654	−0.0570322
$456$	11.0263	0.516354
$457$	9.60835	0.449460	0.224730	−	0.974421i	$-0.427850\pi$
$457$	9.60835	0.449460	0.224730	+	0.974421i	$0.427850\pi$
$458$	−1.69745	−0.0793164
$459$	−9.76395	−0.455742
$460$	0.218493	0.0101873
$461$	10.5890	0.493180	0.246590	−	0.969120i	$-0.420690\pi$
$461$	10.5890	0.493180	0.246590	+	0.969120i	$0.420690\pi$
$462$	−5.04352	−0.234646
$463$	−18.1482	−0.843418	−0.421709	−	0.906731i	$-0.638570\pi$
$463$	−18.1482	−0.843418	−0.421709	+	0.906731i	$0.638570\pi$
$464$	−16.3033	−0.756863
$465$	7.89491	0.366118
$466$	−17.7742	−0.823372
$467$	3.22762	0.149356	0.0746782	−	0.997208i	$-0.476207\pi$
$467$	3.22762	0.149356	0.0746782	+	0.997208i	$0.476207\pi$
$468$	−2.43867	−0.112728
$469$	−3.49856	−0.161549
$470$	4.03126	0.185948
$471$	0.436520	0.0201138
$472$	−22.2742	−1.02525
$473$	−4.27854	−0.196727
$474$	−4.66754	−0.214387
$475$	6.81744	0.312805
$476$	1.91544	0.0877939
$477$	23.7664	1.08819
$478$	37.0004	1.69236
$479$	34.8867	1.59401	0.797007	−	0.603970i	$-0.206416\pi$
$479$	34.8867	1.59401	0.797007	+	0.603970i	$0.206416\pi$
$480$	−3.97382	−0.181379
$481$	−10.3587	−0.472315
$482$	12.6168	0.574681
$483$	−0.211160	−0.00960812
$484$	1.03038	0.0468354
$485$	−11.7682	−0.534367
$486$	−27.2107	−1.23430
$487$	−4.00597	−0.181528	−0.0907640	−	0.995872i	$-0.528931\pi$
$487$	−4.00597	−0.181528	−0.0907640	+	0.995872i	$0.528931\pi$
$488$	15.7455	0.712764
$489$	−10.6764	−0.482805
$490$	1.69745	0.0766828
$491$	0.126069	0.00568943	0.00284472	−	0.999996i	$-0.499094\pi$
$491$	0.126069	0.00568943	0.00284472	+	0.999996i	$0.499094\pi$
$492$	−7.11971	−0.320981
$493$	7.10665	0.320067
$494$	−14.0781	−0.633402
$495$	7.93456	0.356632
$496$	46.2152	2.07512
$497$	−12.3408	−0.553560
$498$	−12.9754	−0.581439
$499$	4.21404	0.188646	0.0943232	−	0.995542i	$-0.469931\pi$
$499$	4.21404	0.188646	0.0943232	+	0.995542i	$0.469931\pi$
$500$	−0.881321	−0.0394139
$501$	5.36892	0.239866
$502$	−30.1289	−1.34472
$503$	−15.8955	−0.708746	−0.354373	−	0.935104i	$-0.615306\pi$
$503$	−15.8955	−0.708746	−0.354373	+	0.935104i	$0.615306\pi$
$504$	−4.31911	−0.192388
$505$	8.11852	0.361269
$506$	1.46801	0.0652611
$507$	−9.81209	−0.435770
$508$	13.7776	0.611283
$509$	29.8404	1.32265	0.661327	−	0.750098i	$-0.269994\pi$
$509$	29.8404	1.32265	0.661327	+	0.750098i	$0.269994\pi$
$510$	3.14222	0.139140
$511$	−15.0502	−0.665782
$512$	−4.32646	−0.191204
$513$	−30.6276	−1.35224
$514$	22.4511	0.990274
$515$	−5.70371	−0.251335
$516$	−0.920678	−0.0405306
$517$	8.28467	0.364359
$518$	14.4535	0.635052
$519$	−10.6720	−0.468448
$520$	−2.31008	−0.101304
$521$	37.7808	1.65521	0.827603	−	0.561314i	$-0.189704\pi$
$521$	37.7808	1.65521	0.827603	+	0.561314i	$0.189704\pi$
$522$	12.6247	0.552567
$523$	−24.4519	−1.06921	−0.534604	−	0.845103i	$-0.679539\pi$
$523$	−24.4519	−1.06921	−0.534604	+	0.845103i	$0.679539\pi$
$524$	5.10928	0.223200
$525$	0.851741	0.0371730
$526$	1.86599	0.0813610
$527$	−20.1453	−0.877541
$528$	−14.8143	−0.644712
$529$	−22.9385	−0.997328
$530$	−17.7364	−0.770421
$531$	26.6805	1.15783
$532$	6.00835	0.260495
$533$	−11.5384	−0.499784
$534$	2.77024	0.119880
$535$	−12.0745	−0.522026
$536$	−6.64341	−0.286952
$537$	−18.6215	−0.803579
$538$	−36.2159	−1.56138
$539$	3.48843	0.150257
$540$	3.95937	0.170384
$541$	24.6169	1.05836	0.529182	−	0.848508i	$-0.322499\pi$
$541$	24.6169	1.05836	0.529182	+	0.848508i	$0.322499\pi$
$542$	42.3113	1.81743
$543$	8.83316	0.379067
$544$	10.1399	0.434745
$545$	−1.87641	−0.0803766
$546$	−1.75885	−0.0752720
$547$	22.8286	0.976080	0.488040	−	0.872821i	$-0.337712\pi$
$547$	22.8286	0.976080	0.488040	+	0.872821i	$0.337712\pi$
$548$	−4.75125	−0.202963
$549$	−18.8602	−0.804936
$550$	−5.92142	−0.252490
$551$	22.2922	0.949679
$552$	−0.400971	−0.0170665
$553$	3.22838	0.137285
$554$	−19.5617	−0.831095
$555$	7.25247	0.307850
$556$	−13.1643	−0.558289
$557$	−6.75431	−0.286189	−0.143095	−	0.989709i	$-0.545705\pi$
$557$	−6.75431	−0.286189	−0.143095	+	0.989709i	$0.545705\pi$
$558$	−35.7872	−1.51500
$559$	−1.49208	−0.0631082
$560$	4.98592	0.210693
$561$	6.45760	0.272640
$562$	−44.6132	−1.88190
$563$	−27.7070	−1.16771	−0.583856	−	0.811858i	$-0.698457\pi$
$563$	−27.7070	−1.16771	−0.583856	+	0.811858i	$0.698457\pi$
$564$	1.78274	0.0750668
$565$	−7.67031	−0.322692
$566$	48.2746	2.02913
$567$	2.99713	0.125868
$568$	−23.4339	−0.983264
$569$	37.4051	1.56810	0.784051	−	0.620696i	$-0.213150\pi$
$569$	37.4051	1.56810	0.784051	+	0.620696i	$0.213150\pi$
$570$	9.85654	0.412845
$571$	−19.5011	−0.816097	−0.408049	−	0.912960i	$-0.633791\pi$
$571$	−19.5011	−0.816097	−0.408049	+	0.912960i	$0.633791\pi$
$572$	3.74016	0.156384
$573$	16.6488	0.695512
$574$	16.0996	0.671985
$575$	−0.247916	−0.0103388
$576$	−4.66815	−0.194506
$577$	35.2889	1.46910	0.734548	−	0.678557i	$-0.237394\pi$
$577$	35.2889	1.46910	0.734548	+	0.678557i	$0.237394\pi$
$578$	20.8386	0.866773
$579$	−17.9592	−0.746358
$580$	−2.88181	−0.119661
$581$	8.97461	0.372330
$582$	−17.0143	−0.705265
$583$	−36.4502	−1.50961
$584$	−28.5788	−1.18260
$585$	2.76706	0.114404
$586$	−41.3607	−1.70859
$587$	−14.8618	−0.613413	−0.306706	−	0.951804i	$-0.599227\pi$
$587$	−14.8618	−0.613413	−0.306706	+	0.951804i	$0.599227\pi$
$588$	0.750658	0.0309566
$589$	−63.1918	−2.60377
$590$	−19.9112	−0.819730
$591$	−10.6357	−0.437493
$592$	42.4544	1.74487
$593$	−8.87802	−0.364577	−0.182288	−	0.983245i	$-0.558350\pi$
$593$	−8.87802	−0.364577	−0.182288	+	0.983245i	$0.558350\pi$
$594$	26.6022	1.09150
$595$	−2.17337	−0.0890994
$596$	5.98995	0.245358
$597$	1.10474	0.0452139
$598$	0.511948	0.0209351
$599$	25.8209	1.05501	0.527507	−	0.849551i	$-0.323127\pi$
$599$	25.8209	1.05501	0.527507	+	0.849551i	$0.323127\pi$
$600$	1.61737	0.0660288
$601$	−10.6795	−0.435624	−0.217812	−	0.975991i	$-0.569892\pi$
$601$	−10.6795	−0.435624	−0.217812	+	0.975991i	$0.569892\pi$
$602$	2.08191	0.0848522
$603$	7.95761	0.324059
$604$	−7.91813	−0.322184
$605$	−1.16913	−0.0475319
$606$	11.7376	0.476808
$607$	45.7215	1.85578	0.927889	−	0.372858i	$-0.121622\pi$
$607$	45.7215	1.85578	0.927889	+	0.372858i	$0.121622\pi$
$608$	31.8069	1.28994
$609$	2.78509	0.112858
$610$	14.0751	0.569882
$611$	2.88916	0.116883
$612$	−4.35673	−0.176110
$613$	24.7463	0.999494	0.499747	−	0.866171i	$-0.333426\pi$
$613$	24.7463	0.999494	0.499747	+	0.866171i	$0.333426\pi$
$614$	44.2120	1.78425
$615$	8.07844	0.325754
$616$	6.62416	0.266895
$617$	−17.1179	−0.689139	−0.344570	−	0.938761i	$-0.611975\pi$
$617$	−17.1179	−0.689139	−0.344570	+	0.938761i	$0.611975\pi$
$618$	−8.24633	−0.331716
$619$	−18.8215	−0.756499	−0.378249	−	0.925704i	$-0.623474\pi$
$619$	−18.8215	−0.756499	−0.378249	+	0.925704i	$0.623474\pi$
$620$	8.16909	0.328079
$621$	1.11377	0.0446941
$622$	29.5317	1.18411
$623$	−1.91608	−0.0767662
$624$	−5.16629	−0.206817
$625$	1.00000	0.0400000
$626$	−20.5747	−0.822330
$627$	20.2562	0.808956
$628$	0.451680	0.0180240
$629$	−18.5060	−0.737881
$630$	−3.86090	−0.153822
$631$	45.1918	1.79906	0.899529	−	0.436862i	$-0.143910\pi$
$631$	45.1918	1.79906	0.899529	+	0.436862i	$0.143910\pi$
$632$	6.13035	0.243852
$633$	18.8372	0.748710
$634$	22.2730	0.884576
$635$	−15.6329	−0.620373
$636$	−7.84355	−0.311017
$637$	1.21654	0.0482010
$638$	−19.3623	−0.766561
$639$	28.0696	1.11042
$640$	12.8148	0.506550
$641$	−23.1585	−0.914706	−0.457353	−	0.889285i	$-0.651202\pi$
$641$	−23.1585	−0.914706	−0.457353	+	0.889285i	$0.651202\pi$
$642$	−17.4571	−0.688978
$643$	−16.3154	−0.643415	−0.321707	−	0.946839i	$-0.604257\pi$
$643$	−16.3154	−0.643415	−0.321707	+	0.946839i	$0.604257\pi$
$644$	−0.218493	−0.00860985
$645$	1.04466	0.0411333
$646$	−25.1507	−0.989542
$647$	38.4094	1.51003	0.755014	−	0.655709i	$-0.227630\pi$
$647$	38.4094	1.51003	0.755014	+	0.655709i	$0.227630\pi$
$648$	5.69123	0.223573
$649$	−40.9195	−1.60623
$650$	−2.06501	−0.0809963
$651$	−7.89491	−0.309426
$652$	−11.0472	−0.432642
$653$	−5.58318	−0.218487	−0.109243	−	0.994015i	$-0.534843\pi$
$653$	−5.58318	−0.218487	−0.109243	+	0.994015i	$0.534843\pi$
$654$	−2.71289	−0.106082
$655$	−5.79730	−0.226519
$656$	47.2895	1.84635
$657$	34.2323	1.33553
$658$	−4.03126	−0.157155
$659$	−42.0384	−1.63758	−0.818791	−	0.574091i	$-0.805356\pi$
$659$	−42.0384	−1.63758	−0.818791	+	0.574091i	$0.805356\pi$
$660$	−2.61862	−0.101929
$661$	41.1090	1.59895	0.799477	−	0.600697i	$-0.205110\pi$
$661$	41.1090	1.59895	0.799477	+	0.600697i	$0.205110\pi$
$662$	−7.60400	−0.295538
$663$	2.25199	0.0874602
$664$	17.0419	0.661352
$665$	−6.81744	−0.264369
$666$	−32.8751	−1.27388
$667$	−0.810654	−0.0313887
$668$	5.55538	0.214944
$669$	−0.794929	−0.0307337
$670$	−5.93862	−0.229429
$671$	28.9257	1.11666
$672$	3.97382	0.153294
$673$	45.9410	1.77090	0.885448	−	0.464738i	$-0.153851\pi$
$673$	45.9410	1.77090	0.885448	+	0.464738i	$0.153851\pi$
$674$	11.4207	0.439909
$675$	−4.49254	−0.172918
$676$	−10.1529	−0.390494
$677$	17.3204	0.665676	0.332838	−	0.942984i	$-0.391994\pi$
$677$	17.3204	0.665676	0.332838	+	0.942984i	$0.391994\pi$
$678$	−11.0896	−0.425894
$679$	11.7682	0.451622
$680$	−4.12700	−0.158263
$681$	−2.49291	−0.0955285
$682$	54.8864	2.10171
$683$	−50.1678	−1.91962	−0.959810	−	0.280652i	$-0.909449\pi$
$683$	−50.1678	−1.91962	−0.959810	+	0.280652i	$0.909449\pi$
$684$	−13.6662	−0.522541
$685$	5.39105	0.205981
$686$	−1.69745	−0.0648088
$687$	0.851741	0.0324960
$688$	6.11520	0.233140
$689$	−12.7115	−0.484269
$690$	−0.358433	−0.0136453
$691$	−25.9839	−0.988475	−0.494237	−	0.869327i	$-0.664553\pi$
$691$	−25.9839	−0.988475	−0.494237	+	0.869327i	$0.664553\pi$
$692$	−11.0426	−0.419777
$693$	−7.93456	−0.301409
$694$	27.3688	1.03891
$695$	14.9369	0.566591
$696$	5.28860	0.200464
$697$	−20.6136	−0.780795
$698$	30.9133	1.17009
$699$	8.91869	0.337336
$700$	0.881321	0.0333108
$701$	5.57264	0.210476	0.105238	−	0.994447i	$-0.466440\pi$
$701$	5.57264	0.210476	0.105238	+	0.994447i	$0.466440\pi$
$702$	9.27714	0.350143
$703$	−58.0496	−2.18938
$704$	7.15948	0.269833
$705$	−2.02280	−0.0761831
$706$	20.3428	0.765611
$707$	−8.11852	−0.305328
$708$	−8.80527	−0.330922
$709$	1.26359	0.0474551	0.0237275	−	0.999718i	$-0.492447\pi$
$709$	1.26359	0.0474551	0.0237275	+	0.999718i	$0.492447\pi$
$710$	−20.9478	−0.786158
$711$	−7.34306	−0.275386
$712$	−3.63844	−0.136356
$713$	2.29797	0.0860595
$714$	−3.14222	−0.117595
$715$	−4.24381	−0.158709
$716$	−19.2683	−0.720089
$717$	−18.5660	−0.693361
$718$	−25.6495	−0.957232
$719$	32.3105	1.20498	0.602489	−	0.798127i	$-0.294176\pi$
$719$	32.3105	1.20498	0.602489	+	0.798127i	$0.294176\pi$
$720$	−11.3406	−0.422641
$721$	5.70371	0.212417
$722$	−46.6414	−1.73581
$723$	−6.33085	−0.235447
$724$	9.13993	0.339683
$725$	3.26988	0.121440
$726$	−1.69031	−0.0627333
$727$	19.9198	0.738783	0.369392	−	0.929274i	$-0.379566\pi$
$727$	19.9198	0.738783	0.369392	+	0.929274i	$0.379566\pi$
$728$	2.31008	0.0856173
$729$	4.66237	0.172681
$730$	−25.5469	−0.945534
$731$	−2.66562	−0.0985917
$732$	6.22438	0.230060
$733$	−27.4807	−1.01502	−0.507512	−	0.861645i	$-0.669435\pi$
$733$	−27.4807	−1.01502	−0.507512	+	0.861645i	$0.669435\pi$
$734$	7.90150	0.291650
$735$	−0.851741	−0.0314170
$736$	−1.15666	−0.0426350
$737$	−12.2045	−0.449558
$738$	−36.6192	−1.34797
$739$	23.6569	0.870232	0.435116	−	0.900374i	$-0.356707\pi$
$739$	23.6569	0.870232	0.435116	+	0.900374i	$0.356707\pi$
$740$	7.50434	0.275865
$741$	7.06407	0.259505
$742$	17.7364	0.651125
$743$	−17.2806	−0.633963	−0.316981	−	0.948432i	$-0.602669\pi$
$743$	−17.2806	−0.633963	−0.316981	+	0.948432i	$0.602669\pi$
$744$	−14.9916	−0.549619
$745$	−6.79656	−0.249007
$746$	40.7410	1.49163
$747$	−20.4131	−0.746876
$748$	6.68186	0.244313
$749$	12.0745	0.441193
$750$	1.44578	0.0527926
$751$	−49.3515	−1.80086	−0.900431	−	0.434999i	$-0.856749\pi$
$751$	−49.3515	−1.80086	−0.900431	+	0.434999i	$0.856749\pi$
$752$	−11.8410	−0.431799
$753$	15.1180	0.550932
$754$	−6.75233	−0.245905
$755$	8.98439	0.326975
$756$	−3.95937	−0.144001
$757$	−30.9193	−1.12378	−0.561891	−	0.827211i	$-0.689926\pi$
$757$	−30.9193	−1.12378	−0.561891	+	0.827211i	$0.689926\pi$
$758$	22.7487	0.826269
$759$	−0.736617	−0.0267375
$760$	−12.9456	−0.469586
$761$	−30.7932	−1.11625	−0.558126	−	0.829756i	$-0.688479\pi$
$761$	−30.7932	−1.11625	−0.558126	+	0.829756i	$0.688479\pi$
$762$	−22.6018	−0.818778
$763$	1.87641	0.0679307
$764$	17.2270	0.623249
$765$	4.94341	0.178729
$766$	47.8116	1.72751
$767$	−14.2701	−0.515263
$768$	15.0313	0.542396
$769$	42.1370	1.51950	0.759749	−	0.650216i	$-0.225322\pi$
$769$	42.1370	1.51950	0.759749	+	0.650216i	$0.225322\pi$
$770$	5.92142	0.213393
$771$	−11.2655	−0.405716
$772$	−18.5829	−0.668812
$773$	−27.9856	−1.00657	−0.503286	−	0.864120i	$-0.667876\pi$
$773$	−27.9856	−1.00657	−0.503286	+	0.864120i	$0.667876\pi$
$774$	−4.73538	−0.170210
$775$	−9.26914	−0.332957
$776$	22.3466	0.802196
$777$	−7.25247	−0.260181
$778$	−59.0086	−2.11556
$779$	−64.6608	−2.31671
$780$	−0.913205	−0.0326980
$781$	−43.0500	−1.54045
$782$	0.914605	0.0327062
$783$	−14.6901	−0.524980
$784$	−4.98592	−0.178068
$785$	−0.512503	−0.0182920
$786$	−8.38164	−0.298963
$787$	6.03216	0.215023	0.107512	−	0.994204i	$-0.465712\pi$
$787$	6.03216	0.215023	0.107512	+	0.994204i	$0.465712\pi$
$788$	−11.0050	−0.392038
$789$	−0.936313	−0.0333336
$790$	5.47999	0.194969
$791$	7.67031	0.272725
$792$	−15.0669	−0.535379
$793$	10.0874	0.358215
$794$	6.78409	0.240758
$795$	8.89976	0.315642
$796$	1.14310	0.0405163
$797$	33.3451	1.18114	0.590572	−	0.806985i	$-0.298902\pi$
$797$	33.3451	1.18114	0.590572	+	0.806985i	$0.298902\pi$
$798$	−9.85654	−0.348918
$799$	5.16153	0.182602
$800$	4.66553	0.164951
$801$	4.35820	0.153989
$802$	−19.7758	−0.698306
$803$	−52.5016	−1.85274
$804$	−2.62623	−0.0926198
$805$	0.247916	0.00873788
$806$	19.1409	0.674208
$807$	18.1723	0.639697
$808$	−15.4162	−0.542341
$809$	−37.8010	−1.32901	−0.664505	−	0.747283i	$-0.731358\pi$
$809$	−37.8010	−1.32901	−0.664505	+	0.747283i	$0.731358\pi$
$810$	5.08746	0.178755
$811$	−47.3513	−1.66273	−0.831365	−	0.555727i	$-0.812440\pi$
$811$	−47.3513	−1.66273	−0.831365	+	0.555727i	$0.812440\pi$
$812$	2.88181	0.101132
$813$	−21.2309	−0.744601
$814$	50.4201	1.76722
$815$	12.5348	0.439076
$816$	−9.22967	−0.323103
$817$	−8.36155	−0.292533
$818$	34.2876	1.19884
$819$	−2.76706	−0.0966890
$820$	8.35900	0.291909
$821$	15.6577	0.546458	0.273229	−	0.961949i	$-0.411908\pi$
$821$	15.6577	0.546458	0.273229	+	0.961949i	$0.411908\pi$
$822$	7.79430	0.271857
$823$	30.7445	1.07169	0.535844	−	0.844317i	$-0.319994\pi$
$823$	30.7445	1.07169	0.535844	+	0.844317i	$0.319994\pi$
$824$	10.8307	0.377307
$825$	2.97124	0.103445
$826$	19.9112	0.692798
$827$	−38.2915	−1.33153	−0.665763	−	0.746163i	$-0.731894\pi$
$827$	−38.2915	−1.33153	−0.665763	+	0.746163i	$0.731894\pi$
$828$	0.496971	0.0172710
$829$	14.4330	0.501277	0.250639	−	0.968081i	$-0.419359\pi$
$829$	14.4330	0.501277	0.250639	+	0.968081i	$0.419359\pi$
$830$	15.2339	0.528777
$831$	9.81562	0.340500
$832$	2.49676	0.0865597
$833$	2.17337	0.0753028
$834$	21.5956	0.747795
$835$	−6.30347	−0.218140
$836$	20.9597	0.724906
$837$	41.6420	1.43936
$838$	6.33634	0.218885
$839$	21.8221	0.753381	0.376690	−	0.926339i	$-0.377062\pi$
$839$	21.8221	0.753381	0.376690	+	0.926339i	$0.377062\pi$
$840$	−1.61737	−0.0558045
$841$	−18.3079	−0.631307
$842$	54.3619	1.87344
$843$	22.3860	0.771013
$844$	19.4913	0.670920
$845$	11.5200	0.396301
$846$	9.16926	0.315246
$847$	1.16913	0.0401718
$848$	52.0973	1.78903
$849$	−24.2232	−0.831337
$850$	−3.68918	−0.126538
$851$	2.11097	0.0723632
$852$	−9.26371	−0.317370
$853$	−51.9073	−1.77727	−0.888636	−	0.458612i	$-0.848347\pi$
$853$	−51.9073	−1.77727	−0.888636	+	0.458612i	$0.848347\pi$
$854$	−14.0751	−0.481639
$855$	15.5065	0.530311
$856$	22.9282	0.783671
$857$	9.71037	0.331700	0.165850	−	0.986151i	$-0.446963\pi$
$857$	9.71037	0.331700	0.165850	+	0.986151i	$0.446963\pi$
$858$	−6.13563	−0.209467
$859$	24.3525	0.830896	0.415448	−	0.909617i	$-0.363625\pi$
$859$	24.3525	0.830896	0.415448	+	0.909617i	$0.363625\pi$
$860$	1.08094	0.0368596
$861$	−8.07844	−0.275313
$862$	0.987363	0.0336297
$863$	−44.9241	−1.52923	−0.764617	−	0.644484i	$-0.777072\pi$
$863$	−44.9241	−1.52923	−0.764617	+	0.644484i	$0.777072\pi$
$864$	−20.9601	−0.713076
$865$	12.5296	0.426019
$866$	56.5437	1.92143
$867$	−10.4564	−0.355117
$868$	−8.16909	−0.277277
$869$	11.2620	0.382036
$870$	4.72754	0.160279
$871$	−4.25614	−0.144214
$872$	3.56311	0.120662
$873$	−26.7672	−0.905933
$874$	2.86894	0.0970432
$875$	−1.00000	−0.0338062
$876$	−11.2976	−0.381709
$877$	−20.0660	−0.677580	−0.338790	−	0.940862i	$-0.610018\pi$
$877$	−20.0660	−0.677580	−0.338790	+	0.940862i	$0.610018\pi$
$878$	34.0968	1.15071
$879$	20.7539	0.700012
$880$	17.3930	0.586318
$881$	24.4871	0.824990	0.412495	−	0.910960i	$-0.364657\pi$
$881$	24.4871	0.824990	0.412495	+	0.910960i	$0.364657\pi$
$882$	3.86090	0.130003
$883$	−27.2737	−0.917835	−0.458917	−	0.888479i	$-0.651763\pi$
$883$	−27.2737	−0.917835	−0.458917	+	0.888479i	$0.651763\pi$
$884$	2.33020	0.0783732
$885$	9.99099	0.335843
$886$	−14.9718	−0.502988
$887$	42.0634	1.41235	0.706176	−	0.708037i	$-0.250419\pi$
$887$	42.0634	1.41235	0.706176	+	0.708037i	$0.250419\pi$
$888$	−13.7717	−0.462147
$889$	15.6329	0.524311
$890$	−3.25245	−0.109022
$891$	10.4553	0.350264
$892$	−0.822536	−0.0275406
$893$	16.1907	0.541802
$894$	−9.82636	−0.328643
$895$	21.8629	0.730797
$896$	−12.8148	−0.428113
$897$	−0.256885	−0.00857712
$898$	16.4928	0.550372
$899$	−30.3090	−1.01086
$900$	−2.00460	−0.0668199
$901$	−22.7093	−0.756557
$902$	56.1624	1.87000
$903$	−1.04466	−0.0347640
$904$	14.5651	0.484429
$905$	−10.3707	−0.344734
$906$	12.9895	0.431547
$907$	−15.6796	−0.520633	−0.260316	−	0.965523i	$-0.583827\pi$
$907$	−15.6796	−0.520633	−0.260316	+	0.965523i	$0.583827\pi$
$908$	−2.57949	−0.0856033
$909$	18.4659	0.612474
$910$	2.06501	0.0684544
$911$	−4.80572	−0.159221	−0.0796103	−	0.996826i	$-0.525368\pi$
$911$	−4.80572	−0.159221	−0.0796103	+	0.996826i	$0.525368\pi$
$912$	−28.9517	−0.958686
$913$	31.3073	1.03612
$914$	−16.3097	−0.539475
$915$	−7.06256	−0.233481
$916$	0.881321	0.0291197
$917$	5.79730	0.191444
$918$	16.5738	0.547016
$919$	−44.2794	−1.46064	−0.730322	−	0.683103i	$-0.760630\pi$
$919$	−44.2794	−1.46064	−0.730322	+	0.683103i	$0.760630\pi$
$920$	0.470766	0.0155207
$921$	−22.1846	−0.731009
$922$	−17.9743	−0.591952
$923$	−15.0131	−0.494161
$924$	2.61862	0.0861461
$925$	−8.51487	−0.279967
$926$	30.8055	1.01233
$927$	−12.9733	−0.426099
$928$	15.2557	0.500793
$929$	−37.1811	−1.21987	−0.609936	−	0.792450i	$-0.708805\pi$
$929$	−37.1811	−1.21987	−0.609936	+	0.792450i	$0.708805\pi$
$930$	−13.4012	−0.439442
$931$	6.81744	0.223432
$932$	9.22842	0.302287
$933$	−14.8184	−0.485132
$934$	−5.47871	−0.179269
$935$	−7.58164	−0.247946
$936$	−5.25436	−0.171744
$937$	−32.3856	−1.05799	−0.528995	−	0.848625i	$-0.677431\pi$
$937$	−32.3856	−1.05799	−0.528995	+	0.848625i	$0.677431\pi$
$938$	5.93862	0.193903
$939$	10.3239	0.336909
$940$	−2.09305	−0.0682678
$941$	−19.9462	−0.650227	−0.325114	−	0.945675i	$-0.605403\pi$
$941$	−19.9462	−0.650227	−0.325114	+	0.945675i	$0.605403\pi$
$942$	−0.740968	−0.0241421
$943$	2.35139	0.0765717
$944$	58.4852	1.90353
$945$	4.49254	0.146142
$946$	7.26259	0.236127
$947$	−5.09592	−0.165595	−0.0827975	−	0.996566i	$-0.526385\pi$
$947$	−5.09592	−0.165595	−0.0827975	+	0.996566i	$0.526385\pi$
$948$	2.42341	0.0787086
$949$	−18.3092	−0.594341
$950$	−11.5722	−0.375453
$951$	−11.1761	−0.362411
$952$	4.12700	0.133757
$953$	−25.4519	−0.824468	−0.412234	−	0.911078i	$-0.635251\pi$
$953$	−25.4519	−0.824468	−0.412234	+	0.911078i	$0.635251\pi$
$954$	−40.3422	−1.30613
$955$	−19.5467	−0.632517
$956$	−19.2108	−0.621322
$957$	9.71559	0.314060
$958$	−59.2183	−1.91325
$959$	−5.39105	−0.174086
$960$	−1.74807	−0.0564188
$961$	54.9170	1.77152
$962$	17.5833	0.566908
$963$	−27.4639	−0.885012
$964$	−6.55072	−0.210984
$965$	21.0852	0.678758
$966$	0.358433	0.0115324
$967$	10.9115	0.350891	0.175445	−	0.984489i	$-0.443863\pi$
$967$	10.9115	0.350891	0.175445	+	0.984489i	$0.443863\pi$
$968$	2.22006	0.0713553
$969$	12.6201	0.405415
$970$	19.9759	0.641387
$971$	52.9001	1.69764	0.848822	−	0.528679i	$-0.177312\pi$
$971$	52.9001	1.69764	0.848822	+	0.528679i	$0.177312\pi$
$972$	14.1279	0.453154
$973$	−14.9369	−0.478857
$974$	6.79992	0.217884
$975$	1.03618	0.0331842
$976$	−41.3427	−1.32335
$977$	23.1315	0.740043	0.370022	−	0.929023i	$-0.379350\pi$
$977$	23.1315	0.740043	0.370022	+	0.929023i	$0.379350\pi$
$978$	18.1227	0.579499
$979$	−6.68412	−0.213625
$980$	−0.881321	−0.0281528
$981$	−4.26797	−0.136266
$982$	−0.213996	−0.00682888
$983$	−34.5113	−1.10074	−0.550370	−	0.834921i	$-0.685513\pi$
$983$	−34.5113	−1.10074	−0.550370	+	0.834921i	$0.685513\pi$
$984$	−15.3401	−0.489025
$985$	12.4870	0.397868
$986$	−12.0632	−0.384169
$987$	2.02280	0.0643864
$988$	7.30939	0.232543
$989$	0.304067	0.00966878
$990$	−13.4685	−0.428056
$991$	−40.4959	−1.28639	−0.643197	−	0.765701i	$-0.722392\pi$
$991$	−40.4959	−1.28639	−0.643197	+	0.765701i	$0.722392\pi$
$992$	−43.2454	−1.37304
$993$	3.81552	0.121082
$994$	20.9478	0.664425
$995$	−1.29703	−0.0411188
$996$	6.73686	0.213466
$997$	−12.9114	−0.408907	−0.204453	−	0.978876i	$-0.565542\pi$
$997$	−12.9114	−0.408907	−0.204453	+	0.978876i	$0.565542\pi$
$998$	−7.15310	−0.226428
$999$	38.2534	1.21028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.10	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.69745 q^{2} +0.851741 q^{3} +0.881321 q^{4} -1.00000 q^{5} -1.44578 q^{6} +1.00000 q^{7} +1.89890 q^{8} -2.27454 q^{9} +O(q^{10})\)	\(q-1.69745 q^{2} +0.851741 q^{3} +0.881321 q^{4} -1.00000 q^{5} -1.44578 q^{6} +1.00000 q^{7} +1.89890 q^{8} -2.27454 q^{9} +1.69745 q^{10} +3.48843 q^{11} +0.750658 q^{12} +1.21654 q^{13} -1.69745 q^{14} -0.851741 q^{15} -4.98592 q^{16} +2.17337 q^{17} +3.86090 q^{18} +6.81744 q^{19} -0.881321 q^{20} +0.851741 q^{21} -5.92142 q^{22} -0.247916 q^{23} +1.61737 q^{24} +1.00000 q^{25} -2.06501 q^{26} -4.49254 q^{27} +0.881321 q^{28} +3.26988 q^{29} +1.44578 q^{30} -9.26914 q^{31} +4.66553 q^{32} +2.97124 q^{33} -3.68918 q^{34} -1.00000 q^{35} -2.00460 q^{36} -8.51487 q^{37} -11.5722 q^{38} +1.03618 q^{39} -1.89890 q^{40} -9.48462 q^{41} -1.44578 q^{42} -1.22649 q^{43} +3.07443 q^{44} +2.27454 q^{45} +0.420824 q^{46} +2.37490 q^{47} -4.24671 q^{48} +1.00000 q^{49} -1.69745 q^{50} +1.85115 q^{51} +1.07216 q^{52} -10.4489 q^{53} +7.62584 q^{54} -3.48843 q^{55} +1.89890 q^{56} +5.80669 q^{57} -5.55044 q^{58} -11.7301 q^{59} -0.750658 q^{60} +8.29191 q^{61} +15.7339 q^{62} -2.27454 q^{63} +2.05235 q^{64} -1.21654 q^{65} -5.04352 q^{66} -3.49856 q^{67} +1.91544 q^{68} -0.211160 q^{69} +1.69745 q^{70} -12.3408 q^{71} -4.31911 q^{72} -15.0502 q^{73} +14.4535 q^{74} +0.851741 q^{75} +6.00835 q^{76} +3.48843 q^{77} -1.75885 q^{78} +3.22838 q^{79} +4.98592 q^{80} +2.99713 q^{81} +16.0996 q^{82} +8.97461 q^{83} +0.750658 q^{84} -2.17337 q^{85} +2.08191 q^{86} +2.78509 q^{87} +6.62416 q^{88} -1.91608 q^{89} -3.86090 q^{90} +1.21654 q^{91} -0.218493 q^{92} -7.89491 q^{93} -4.03126 q^{94} -6.81744 q^{95} +3.97382 q^{96} +11.7682 q^{97} -1.69745 q^{98} -7.93456 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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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