LMFDB - Embedded newform 8015.2.a.l.1.24

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:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
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)

$f(q)$	$=$	$q-0.737016 q^{2} +0.825255 q^{3} -1.45681 q^{4} -1.00000 q^{5} -0.608226 q^{6} -1.00000 q^{7} +2.54772 q^{8} -2.31895 q^{9} +O(q^{10})$	\(q-0.737016 q^{2} +0.825255 q^{3} -1.45681 q^{4} -1.00000 q^{5} -0.608226 q^{6} -1.00000 q^{7} +2.54772 q^{8} -2.31895 q^{9} +0.737016 q^{10} +0.0628820 q^{11} -1.20224 q^{12} -0.351818 q^{13} +0.737016 q^{14} -0.825255 q^{15} +1.03591 q^{16} -2.54461 q^{17} +1.70911 q^{18} -5.35415 q^{19} +1.45681 q^{20} -0.825255 q^{21} -0.0463450 q^{22} +1.58772 q^{23} +2.10252 q^{24} +1.00000 q^{25} +0.259296 q^{26} -4.38949 q^{27} +1.45681 q^{28} -1.09035 q^{29} +0.608226 q^{30} -7.26184 q^{31} -5.85892 q^{32} +0.0518937 q^{33} +1.87541 q^{34} +1.00000 q^{35} +3.37827 q^{36} -5.46649 q^{37} +3.94609 q^{38} -0.290340 q^{39} -2.54772 q^{40} +1.65375 q^{41} +0.608226 q^{42} +11.9328 q^{43} -0.0916070 q^{44} +2.31895 q^{45} -1.17017 q^{46} -9.00250 q^{47} +0.854886 q^{48} +1.00000 q^{49} -0.737016 q^{50} -2.09995 q^{51} +0.512532 q^{52} -3.24267 q^{53} +3.23512 q^{54} -0.0628820 q^{55} -2.54772 q^{56} -4.41853 q^{57} +0.803602 q^{58} +8.82509 q^{59} +1.20224 q^{60} -3.79486 q^{61} +5.35209 q^{62} +2.31895 q^{63} +2.24631 q^{64} +0.351818 q^{65} -0.0382464 q^{66} +2.20636 q^{67} +3.70700 q^{68} +1.31027 q^{69} -0.737016 q^{70} -13.4509 q^{71} -5.90805 q^{72} -14.4189 q^{73} +4.02889 q^{74} +0.825255 q^{75} +7.79996 q^{76} -0.0628820 q^{77} +0.213985 q^{78} +0.110548 q^{79} -1.03591 q^{80} +3.33441 q^{81} -1.21884 q^{82} +13.1669 q^{83} +1.20224 q^{84} +2.54461 q^{85} -8.79468 q^{86} -0.899813 q^{87} +0.160206 q^{88} +17.4818 q^{89} -1.70911 q^{90} +0.351818 q^{91} -2.31300 q^{92} -5.99287 q^{93} +6.63498 q^{94} +5.35415 q^{95} -4.83510 q^{96} +9.00690 q^{97} -0.737016 q^{98} -0.145820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−0.737016	−0.521149	−0.260574	−	0.965454i	$-0.583912\pi$
$2$	−0.737016	−0.521149	−0.260574	+	0.965454i	$0.583912\pi$
$3$	0.825255	0.476461	0.238231	−	0.971209i	$-0.423433\pi$
$3$	0.825255	0.476461	0.238231	+	0.971209i	$0.423433\pi$
$4$	−1.45681	−0.728404
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.608226	−0.248307
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.54772	0.900756
$9$	−2.31895	−0.772985
$10$	0.737016	0.233065
$11$	0.0628820	0.0189596	0.00947982	−	0.999955i	$-0.496982\pi$
$11$	0.0628820	0.0189596	0.00947982	+	0.999955i	$0.496982\pi$
$12$	−1.20224	−0.347056
$13$	−0.351818	−0.0975768	−0.0487884	−	0.998809i	$-0.515536\pi$
$13$	−0.351818	−0.0975768	−0.0487884	+	0.998809i	$0.515536\pi$
$14$	0.737016	0.196976
$15$	−0.825255	−0.213080
$16$	1.03591	0.258976
$17$	−2.54461	−0.617157	−0.308579	−	0.951199i	$-0.599853\pi$
$17$	−2.54461	−0.617157	−0.308579	+	0.951199i	$0.599853\pi$
$18$	1.70911	0.402840
$19$	−5.35415	−1.22833	−0.614163	−	0.789179i	$-0.710506\pi$
$19$	−5.35415	−1.22833	−0.614163	+	0.789179i	$0.710506\pi$
$20$	1.45681	0.325752
$21$	−0.825255	−0.180085
$22$	−0.0463450	−0.00988079
$23$	1.58772	0.331062	0.165531	−	0.986205i	$-0.447066\pi$
$23$	1.58772	0.331062	0.165531	+	0.986205i	$0.447066\pi$
$24$	2.10252	0.429175
$25$	1.00000	0.200000
$26$	0.259296	0.0508521
$27$	−4.38949	−0.844758
$28$	1.45681	0.275311
$29$	−1.09035	−0.202472	−0.101236	−	0.994862i	$-0.532280\pi$
$29$	−1.09035	−0.202472	−0.101236	+	0.994862i	$0.532280\pi$
$30$	0.608226	0.111046
$31$	−7.26184	−1.30426	−0.652132	−	0.758105i	$-0.726125\pi$
$31$	−7.26184	−1.30426	−0.652132	+	0.758105i	$0.726125\pi$
$32$	−5.85892	−1.03572
$33$	0.0518937	0.00903353
$34$	1.87541	0.321631
$35$	1.00000	0.169031
$36$	3.37827	0.563045
$37$	−5.46649	−0.898686	−0.449343	−	0.893359i	$-0.648342\pi$
$37$	−5.46649	−0.898686	−0.449343	+	0.893359i	$0.648342\pi$
$38$	3.94609	0.640140
$39$	−0.290340	−0.0464916
$40$	−2.54772	−0.402830
$41$	1.65375	0.258272	0.129136	−	0.991627i	$-0.458780\pi$
$41$	1.65375	0.258272	0.129136	+	0.991627i	$0.458780\pi$
$42$	0.608226	0.0938513
$43$	11.9328	1.81974	0.909870	−	0.414894i	$-0.136181\pi$
$43$	11.9328	1.81974	0.909870	+	0.414894i	$0.136181\pi$
$44$	−0.0916070	−0.0138103
$45$	2.31895	0.345689
$46$	−1.17017	−0.172532
$47$	−9.00250	−1.31315	−0.656575	−	0.754261i	$-0.727995\pi$
$47$	−9.00250	−1.31315	−0.656575	+	0.754261i	$0.727995\pi$
$48$	0.854886	0.123392
$49$	1.00000	0.142857
$50$	−0.737016	−0.104230
$51$	−2.09995	−0.294051
$52$	0.512532	0.0710754
$53$	−3.24267	−0.445415	−0.222708	−	0.974885i	$-0.571490\pi$
$53$	−3.24267	−0.445415	−0.222708	+	0.974885i	$0.571490\pi$
$54$	3.23512	0.440245
$55$	−0.0628820	−0.00847901
$56$	−2.54772	−0.340454
$57$	−4.41853	−0.585249
$58$	0.803602	0.105518
$59$	8.82509	1.14893	0.574465	−	0.818529i	$-0.305210\pi$
$59$	8.82509	1.14893	0.574465	+	0.818529i	$0.305210\pi$
$60$	1.20224	0.155208
$61$	−3.79486	−0.485882	−0.242941	−	0.970041i	$-0.578112\pi$
$61$	−3.79486	−0.485882	−0.242941	+	0.970041i	$0.578112\pi$
$62$	5.35209	0.679716
$63$	2.31895	0.292161
$64$	2.24631	0.280788
$65$	0.351818	0.0436377
$66$	−0.0382464	−0.00470781
$67$	2.20636	0.269550	0.134775	−	0.990876i	$-0.456969\pi$
$67$	2.20636	0.269550	0.134775	+	0.990876i	$0.456969\pi$
$68$	3.70700	0.449540
$69$	1.31027	0.157738
$70$	−0.737016	−0.0880902
$71$	−13.4509	−1.59633	−0.798163	−	0.602441i	$-0.794195\pi$
$71$	−13.4509	−1.59633	−0.798163	+	0.602441i	$0.794195\pi$
$72$	−5.90805	−0.696270
$73$	−14.4189	−1.68761	−0.843804	−	0.536652i	$-0.819689\pi$
$73$	−14.4189	−1.68761	−0.843804	+	0.536652i	$0.819689\pi$
$74$	4.02889	0.468349
$75$	0.825255	0.0952922
$76$	7.79996	0.894717
$77$	−0.0628820	−0.00716607
$78$	0.213985	0.0242290
$79$	0.110548	0.0124376	0.00621880	−	0.999981i	$-0.498020\pi$
$79$	0.110548	0.0124376	0.00621880	+	0.999981i	$0.498020\pi$
$80$	−1.03591	−0.115818
$81$	3.33441	0.370491
$82$	−1.21884	−0.134598
$83$	13.1669	1.44526	0.722630	−	0.691235i	$-0.242933\pi$
$83$	13.1669	1.44526	0.722630	+	0.691235i	$0.242933\pi$
$84$	1.20224	0.131175
$85$	2.54461	0.276001
$86$	−8.79468	−0.948355
$87$	−0.899813	−0.0964701
$88$	0.160206	0.0170780
$89$	17.4818	1.85307	0.926535	−	0.376210i	$-0.122773\pi$
$89$	17.4818	1.85307	0.926535	+	0.376210i	$0.122773\pi$
$90$	−1.70911	−0.180156
$91$	0.351818	0.0368806
$92$	−2.31300	−0.241147
$93$	−5.99287	−0.621431
$94$	6.63498	0.684346
$95$	5.35415	0.549324
$96$	−4.83510	−0.493481
$97$	9.00690	0.914513	0.457256	−	0.889335i	$-0.348832\pi$
$97$	9.00690	0.914513	0.457256	+	0.889335i	$0.348832\pi$
$98$	−0.737016	−0.0744498
$99$	−0.145820	−0.0146555
$100$	−1.45681	−0.145681
$101$	−6.59130	−0.655859	−0.327930	−	0.944702i	$-0.606351\pi$
$101$	−6.59130	−0.655859	−0.327930	+	0.944702i	$0.606351\pi$
$102$	1.54769	0.153245
$103$	−17.1071	−1.68561	−0.842807	−	0.538215i	$-0.819099\pi$
$103$	−17.1071	−1.68561	−0.842807	+	0.538215i	$0.819099\pi$
$104$	−0.896335	−0.0878929
$105$	0.825255	0.0805366
$106$	2.38990	0.232128
$107$	−1.56299	−0.151100	−0.0755502	−	0.997142i	$-0.524071\pi$
$107$	−1.56299	−0.151100	−0.0755502	+	0.997142i	$0.524071\pi$
$108$	6.39465	0.615325
$109$	−0.349916	−0.0335159	−0.0167579	−	0.999860i	$-0.505334\pi$
$109$	−0.349916	−0.0335159	−0.0167579	+	0.999860i	$0.505334\pi$
$110$	0.0463450	0.00441882
$111$	−4.51125	−0.428189
$112$	−1.03591	−0.0978839
$113$	−4.74995	−0.446837	−0.223419	−	0.974723i	$-0.571722\pi$
$113$	−4.74995	−0.446837	−0.223419	+	0.974723i	$0.571722\pi$
$114$	3.25653	0.305002
$115$	−1.58772	−0.148055
$116$	1.58842	0.147482
$117$	0.815851	0.0754254
$118$	−6.50423	−0.598763
$119$	2.54461	0.233264
$120$	−2.10252	−0.191933
$121$	−10.9960	−0.999641
$122$	2.79687	0.253217
$123$	1.36476	0.123057
$124$	10.5791	0.950032
$125$	−1.00000	−0.0894427
$126$	−1.70911	−0.152259
$127$	−11.5163	−1.02190	−0.510952	−	0.859609i	$-0.670707\pi$
$127$	−11.5163	−1.02190	−0.510952	+	0.859609i	$0.670707\pi$
$128$	10.0623	0.889388
$129$	9.84762	0.867035
$130$	−0.259296	−0.0227417
$131$	−2.69595	−0.235546	−0.117773	−	0.993041i	$-0.537576\pi$
$131$	−2.69595	−0.235546	−0.117773	+	0.993041i	$0.537576\pi$
$132$	−0.0755991	−0.00658006
$133$	5.35415	0.464263
$134$	−1.62612	−0.140476
$135$	4.38949	0.377787
$136$	−6.48295	−0.555908
$137$	−7.22672	−0.617421	−0.308710	−	0.951156i	$-0.599897\pi$
$137$	−7.22672	−0.617421	−0.308710	+	0.951156i	$0.599897\pi$
$138$	−0.965690	−0.0822050
$139$	19.2883	1.63601	0.818005	−	0.575210i	$-0.195080\pi$
$139$	19.2883	1.63601	0.818005	+	0.575210i	$0.195080\pi$
$140$	−1.45681	−0.123123
$141$	−7.42935	−0.625664
$142$	9.91351	0.831924
$143$	−0.0221230	−0.00185002
$144$	−2.40222	−0.200185
$145$	1.09035	0.0905483
$146$	10.6270	0.879495
$147$	0.825255	0.0680659
$148$	7.96363	0.654606
$149$	−4.86869	−0.398859	−0.199429	−	0.979912i	$-0.563909\pi$
$149$	−4.86869	−0.398859	−0.199429	+	0.979912i	$0.563909\pi$
$150$	−0.608226	−0.0496614
$151$	−16.0932	−1.30965	−0.654825	−	0.755781i	$-0.727258\pi$
$151$	−16.0932	−1.30965	−0.654825	+	0.755781i	$0.727258\pi$
$152$	−13.6409	−1.10642
$153$	5.90082	0.477053
$154$	0.0463450	0.00373459
$155$	7.26184	0.583285
$156$	0.422969	0.0338646
$157$	24.2977	1.93916	0.969582	−	0.244765i	$-0.0787109\pi$
$157$	24.2977	1.93916	0.969582	+	0.244765i	$0.0787109\pi$
$158$	−0.0814755	−0.00648184
$159$	−2.67603	−0.212223
$160$	5.85892	0.463188
$161$	−1.58772	−0.125130
$162$	−2.45752	−0.193081
$163$	7.60415	0.595603	0.297802	−	0.954628i	$-0.403747\pi$
$163$	7.60415	0.595603	0.297802	+	0.954628i	$0.403747\pi$
$164$	−2.40919	−0.188126
$165$	−0.0518937	−0.00403992
$166$	−9.70424	−0.753195
$167$	−19.2358	−1.48851	−0.744256	−	0.667895i	$-0.767196\pi$
$167$	−19.2358	−1.48851	−0.744256	+	0.667895i	$0.767196\pi$
$168$	−2.10252	−0.162213
$169$	−12.8762	−0.990479
$170$	−1.87541	−0.143838
$171$	12.4160	0.949477
$172$	−17.3838	−1.32551
$173$	−0.953843	−0.0725194	−0.0362597	−	0.999342i	$-0.511544\pi$
$173$	−0.953843	−0.0725194	−0.0362597	+	0.999342i	$0.511544\pi$
$174$	0.663176	0.0502753
$175$	−1.00000	−0.0755929
$176$	0.0651398	0.00491010
$177$	7.28295	0.547420
$178$	−12.8844	−0.965725
$179$	7.32528	0.547517	0.273758	−	0.961798i	$-0.411733\pi$
$179$	7.32528	0.547517	0.273758	+	0.961798i	$0.411733\pi$
$180$	−3.37827	−0.251802
$181$	18.6102	1.38329	0.691644	−	0.722238i	$-0.256887\pi$
$181$	18.6102	1.38329	0.691644	+	0.722238i	$0.256887\pi$
$182$	−0.259296	−0.0192203
$183$	−3.13173	−0.231504
$184$	4.04506	0.298206
$185$	5.46649	0.401905
$186$	4.41684	0.323858
$187$	−0.160010	−0.0117011
$188$	13.1149	0.956503
$189$	4.38949	0.319289
$190$	−3.94609	−0.286279
$191$	18.3205	1.32563	0.662814	−	0.748784i	$-0.269362\pi$
$191$	18.3205	1.32563	0.662814	+	0.748784i	$0.269362\pi$
$192$	1.85377	0.133785
$193$	−9.41833	−0.677946	−0.338973	−	0.940796i	$-0.610080\pi$
$193$	−9.41833	−0.677946	−0.338973	+	0.940796i	$0.610080\pi$
$194$	−6.63823	−0.476597
$195$	0.290340	0.0207917
$196$	−1.45681	−0.104058
$197$	0.00829155	0.000590749 0	0.000295374	−	1.00000i	$-0.499906\pi$
$197$	0.00829155	0.000590749 0	0.000295374		1.00000i	$0.499906\pi$
$198$	0.107472	0.00763770
$199$	−7.36505	−0.522094	−0.261047	−	0.965326i	$-0.584068\pi$
$199$	−7.36505	−0.522094	−0.261047	+	0.965326i	$0.584068\pi$
$200$	2.54772	0.180151
$201$	1.82081	0.128430
$202$	4.85789	0.341800
$203$	1.09035	0.0765273
$204$	3.05922	0.214188
$205$	−1.65375	−0.115503
$206$	12.6082	0.878456
$207$	−3.68184	−0.255906
$208$	−0.364451	−0.0252701
$209$	−0.336679	−0.0232886
$210$	−0.608226	−0.0419716
$211$	7.58022	0.521844	0.260922	−	0.965360i	$-0.415973\pi$
$211$	7.58022	0.521844	0.260922	+	0.965360i	$0.415973\pi$
$212$	4.72395	0.324442
$213$	−11.1004	−0.760587
$214$	1.15195	0.0787457
$215$	−11.9328	−0.813812
$216$	−11.1832	−0.760921
$217$	7.26184	0.492966
$218$	0.257894	0.0174668
$219$	−11.8993	−0.804079
$220$	0.0916070	0.00617614
$221$	0.895239	0.0602203
$222$	3.32486	0.223150
$223$	−14.7494	−0.987696	−0.493848	−	0.869548i	$-0.664410\pi$
$223$	−14.7494	−0.987696	−0.493848	+	0.869548i	$0.664410\pi$
$224$	5.85892	0.391466
$225$	−2.31895	−0.154597
$226$	3.50078	0.232869
$227$	13.9472	0.925711	0.462856	−	0.886434i	$-0.346825\pi$
$227$	13.9472	0.925711	0.462856	+	0.886434i	$0.346825\pi$
$228$	6.43696	0.426298
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	1.17017	0.0771588
$231$	−0.0518937	−0.00341435
$232$	−2.77790	−0.182378
$233$	−12.1414	−0.795407	−0.397704	−	0.917514i	$-0.630193\pi$
$233$	−12.1414	−0.795407	−0.397704	+	0.917514i	$0.630193\pi$
$234$	−0.601295	−0.0393079
$235$	9.00250	0.587258
$236$	−12.8565	−0.836884
$237$	0.0912302	0.00592604
$238$	−1.87541	−0.121565
$239$	15.4988	1.00253	0.501266	−	0.865294i	$-0.332868\pi$
$239$	15.4988	1.00253	0.501266	+	0.865294i	$0.332868\pi$
$240$	−0.854886	−0.0551826
$241$	9.21320	0.593474	0.296737	−	0.954959i	$-0.404101\pi$
$241$	9.21320	0.593474	0.296737	+	0.954959i	$0.404101\pi$
$242$	8.10426	0.520961
$243$	15.9202	1.02128
$244$	5.52838	0.353918
$245$	−1.00000	−0.0638877
$246$	−1.00585	−0.0641308
$247$	1.88369	0.119856
$248$	−18.5011	−1.17482
$249$	10.8661	0.688610
$250$	0.737016	0.0466130
$251$	3.58987	0.226591	0.113295	−	0.993561i	$-0.463859\pi$
$251$	3.58987	0.226591	0.113295	+	0.993561i	$0.463859\pi$
$252$	−3.37827	−0.212811
$253$	0.0998387	0.00627681
$254$	8.48768	0.532564
$255$	2.09995	0.131504
$256$	−11.9087	−0.744292
$257$	20.2690	1.26434	0.632171	−	0.774829i	$-0.282164\pi$
$257$	20.2690	1.26434	0.632171	+	0.774829i	$0.282164\pi$
$258$	−7.25785	−0.451854
$259$	5.46649	0.339671
$260$	−0.512532	−0.0317859
$261$	2.52846	0.156508
$262$	1.98696	0.122755
$263$	7.34119	0.452677	0.226339	−	0.974049i	$-0.427324\pi$
$263$	7.34119	0.452677	0.226339	+	0.974049i	$0.427324\pi$
$264$	0.132211	0.00813700
$265$	3.24267	0.199196
$266$	−3.94609	−0.241950
$267$	14.4270	0.882915
$268$	−3.21425	−0.196341
$269$	−25.1085	−1.53089	−0.765446	−	0.643500i	$-0.777482\pi$
$269$	−25.1085	−1.53089	−0.765446	+	0.643500i	$0.777482\pi$
$270$	−3.23512	−0.196883
$271$	20.4849	1.24437	0.622185	−	0.782870i	$-0.286245\pi$
$271$	20.4849	1.24437	0.622185	+	0.782870i	$0.286245\pi$
$272$	−2.63597	−0.159829
$273$	0.290340	0.0175722
$274$	5.32621	0.321768
$275$	0.0628820	0.00379193
$276$	−1.90881	−0.114897
$277$	2.11864	0.127297	0.0636485	−	0.997972i	$-0.479726\pi$
$277$	2.11864	0.127297	0.0636485	+	0.997972i	$0.479726\pi$
$278$	−14.2158	−0.852605
$279$	16.8399	1.00818
$280$	2.54772	0.152255
$281$	−6.29937	−0.375789	−0.187895	−	0.982189i	$-0.560166\pi$
$281$	−6.29937	−0.375789	−0.187895	+	0.982189i	$0.560166\pi$
$282$	5.47555	0.326064
$283$	−2.33712	−0.138928	−0.0694638	−	0.997584i	$-0.522129\pi$
$283$	−2.33712	−0.138928	−0.0694638	+	0.997584i	$0.522129\pi$
$284$	19.5954	1.16277
$285$	4.41853	0.261731
$286$	0.0163050	0.000964136 0
$287$	−1.65375	−0.0976176
$288$	13.5866	0.800596
$289$	−10.5250	−0.619117
$290$	−0.803602	−0.0471891
$291$	7.43299	0.435730
$292$	21.0056	1.22926
$293$	25.4594	1.48735	0.743676	−	0.668540i	$-0.233081\pi$
$293$	25.4594	1.48735	0.743676	+	0.668540i	$0.233081\pi$
$294$	−0.608226	−0.0354724
$295$	−8.82509	−0.513817
$296$	−13.9271	−0.809496
$297$	−0.276020	−0.0160163
$298$	3.58830	0.207865
$299$	−0.558588	−0.0323040
$300$	−1.20224	−0.0694112
$301$	−11.9328	−0.687797
$302$	11.8610	0.682522
$303$	−5.43951	−0.312491
$304$	−5.54639	−0.318107
$305$	3.79486	0.217293
$306$	−4.34900	−0.248616
$307$	26.6271	1.51969	0.759845	−	0.650104i	$-0.225275\pi$
$307$	26.6271	1.51969	0.759845	+	0.650104i	$0.225275\pi$
$308$	0.0916070	0.00521979
$309$	−14.1177	−0.803130
$310$	−5.35209	−0.303978
$311$	17.3663	0.984752	0.492376	−	0.870382i	$-0.336128\pi$
$311$	17.3663	0.984752	0.492376	+	0.870382i	$0.336128\pi$
$312$	−0.739705	−0.0418775
$313$	10.8130	0.611189	0.305594	−	0.952162i	$-0.401145\pi$
$313$	10.8130	0.611189	0.305594	+	0.952162i	$0.401145\pi$
$314$	−17.9078	−1.01059
$315$	−2.31895	−0.130658
$316$	−0.161047	−0.00905960
$317$	7.42801	0.417199	0.208599	−	0.978001i	$-0.433110\pi$
$317$	7.42801	0.417199	0.208599	+	0.978001i	$0.433110\pi$
$318$	1.97228	0.110600
$319$	−0.0685631	−0.00383880
$320$	−2.24631	−0.125572
$321$	−1.28987	−0.0719934
$322$	1.17017	0.0652111
$323$	13.6242	0.758070
$324$	−4.85760	−0.269867
$325$	−0.351818	−0.0195154
$326$	−5.60438	−0.310398
$327$	−0.288770	−0.0159690
$328$	4.21329	0.232640
$329$	9.00250	0.496324
$330$	0.0382464	0.00210540
$331$	−10.3159	−0.567013	−0.283507	−	0.958970i	$-0.591498\pi$
$331$	−10.3159	−0.567013	−0.283507	+	0.958970i	$0.591498\pi$
$332$	−19.1817	−1.05273
$333$	12.6765	0.694671
$334$	14.1771	0.775736
$335$	−2.20636	−0.120546
$336$	−0.854886	−0.0466378
$337$	−28.3060	−1.54193	−0.770964	−	0.636879i	$-0.780225\pi$
$337$	−28.3060	−1.54193	−0.770964	+	0.636879i	$0.780225\pi$
$338$	9.48998	0.516187
$339$	−3.91992	−0.212901
$340$	−3.70700	−0.201040
$341$	−0.456639	−0.0247284
$342$	−9.15080	−0.494819
$343$	−1.00000	−0.0539949
$344$	30.4015	1.63914
$345$	−1.31027	−0.0705426
$346$	0.702997	0.0377934
$347$	−2.97376	−0.159640	−0.0798199	−	0.996809i	$-0.525435\pi$
$347$	−2.97376	−0.159640	−0.0798199	+	0.996809i	$0.525435\pi$
$348$	1.31085	0.0702692
$349$	13.9312	0.745721	0.372861	−	0.927887i	$-0.378377\pi$
$349$	13.9312	0.745721	0.372861	+	0.927887i	$0.378377\pi$
$350$	0.737016	0.0393951
$351$	1.54430	0.0824288
$352$	−0.368421	−0.0196369
$353$	2.40986	0.128264	0.0641318	−	0.997941i	$-0.479572\pi$
$353$	2.40986	0.128264	0.0641318	+	0.997941i	$0.479572\pi$
$354$	−5.36765	−0.285287
$355$	13.4509	0.713899
$356$	−25.4677	−1.34978
$357$	2.09995	0.111141
$358$	−5.39884	−0.285338
$359$	5.95394	0.314237	0.157119	−	0.987580i	$-0.449780\pi$
$359$	5.95394	0.314237	0.157119	+	0.987580i	$0.449780\pi$
$360$	5.90805	0.311382
$361$	9.66688	0.508783
$362$	−13.7160	−0.720899
$363$	−9.07454	−0.476290
$364$	−0.512532	−0.0268640
$365$	14.4189	0.754721
$366$	2.30813	0.120648
$367$	−36.1088	−1.88486	−0.942431	−	0.334401i	$-0.891466\pi$
$367$	−36.1088	−1.88486	−0.942431	+	0.334401i	$0.891466\pi$
$368$	1.64472	0.0857372
$369$	−3.83497	−0.199640
$370$	−4.02889	−0.209452
$371$	3.24267	0.168351
$372$	8.73046	0.452653
$373$	9.97325	0.516395	0.258198	−	0.966092i	$-0.416871\pi$
$373$	9.97325	0.516395	0.258198	+	0.966092i	$0.416871\pi$
$374$	0.117930	0.00609800
$375$	−0.825255	−0.0426160
$376$	−22.9359	−1.18283
$377$	0.383604	0.0197566
$378$	−3.23512	−0.166397
$379$	11.8304	0.607685	0.303843	−	0.952722i	$-0.401730\pi$
$379$	11.8304	0.607685	0.303843	+	0.952722i	$0.401730\pi$
$380$	−7.79996	−0.400130
$381$	−9.50387	−0.486898
$382$	−13.5025	−0.690849
$383$	−17.8199	−0.910555	−0.455278	−	0.890349i	$-0.650460\pi$
$383$	−17.8199	−0.910555	−0.455278	+	0.890349i	$0.650460\pi$
$384$	8.30394	0.423759
$385$	0.0628820	0.00320476
$386$	6.94146	0.353311
$387$	−27.6717	−1.40663
$388$	−13.1213	−0.666135
$389$	33.3319	1.69000	0.844998	−	0.534770i	$-0.179602\pi$
$389$	33.3319	1.69000	0.844998	+	0.534770i	$0.179602\pi$
$390$	−0.213985	−0.0108355
$391$	−4.04011	−0.204317
$392$	2.54772	0.128679
$393$	−2.22485	−0.112229
$394$	−0.00611100	−0.000307868 0
$395$	−0.110548	−0.00556227
$396$	0.212432	0.0106751
$397$	13.0985	0.657394	0.328697	−	0.944435i	$-0.393390\pi$
$397$	13.0985	0.657394	0.328697	+	0.944435i	$0.393390\pi$
$398$	5.42815	0.272089
$399$	4.41853	0.221203
$400$	1.03591	0.0517953
$401$	28.2307	1.40977	0.704886	−	0.709320i	$-0.250998\pi$
$401$	28.2307	1.40977	0.704886	+	0.709320i	$0.250998\pi$
$402$	−1.34197	−0.0669312
$403$	2.55485	0.127266
$404$	9.60227	0.477731
$405$	−3.33441	−0.165688
$406$	−0.803602	−0.0398821
$407$	−0.343744	−0.0170388
$408$	−5.35008	−0.264869
$409$	21.5002	1.06312	0.531558	−	0.847022i	$-0.321607\pi$
$409$	21.5002	1.06312	0.531558	+	0.847022i	$0.321607\pi$
$410$	1.21884	0.0601941
$411$	−5.96389	−0.294177
$412$	24.9218	1.22781
$413$	−8.82509	−0.434254
$414$	2.71357	0.133365
$415$	−13.1669	−0.646340
$416$	2.06128	0.101062
$417$	15.9177	0.779495
$418$	0.248138	0.0121368
$419$	10.8623	0.530656	0.265328	−	0.964158i	$-0.414520\pi$
$419$	10.8623	0.530656	0.265328	+	0.964158i	$0.414520\pi$
$420$	−1.20224	−0.0586632
$421$	1.14036	0.0555777	0.0277888	−	0.999614i	$-0.491153\pi$
$421$	1.14036	0.0555777	0.0277888	+	0.999614i	$0.491153\pi$
$422$	−5.58674	−0.271958
$423$	20.8764	1.01504
$424$	−8.26143	−0.401210
$425$	−2.54461	−0.123431
$426$	8.18117	0.396379
$427$	3.79486	0.183646
$428$	2.27698	0.110062
$429$	−0.0182571	−0.000881463 0
$430$	8.79468	0.424117
$431$	−7.20406	−0.347008	−0.173504	−	0.984833i	$-0.555509\pi$
$431$	−7.20406	−0.347008	−0.173504	+	0.984833i	$0.555509\pi$
$432$	−4.54710	−0.218772
$433$	33.1616	1.59364	0.796822	−	0.604214i	$-0.206513\pi$
$433$	33.1616	1.59364	0.796822	+	0.604214i	$0.206513\pi$
$434$	−5.35209	−0.256908
$435$	0.899813	0.0431427
$436$	0.509761	0.0244131
$437$	−8.50086	−0.406652
$438$	8.76996	0.419045
$439$	4.96485	0.236959	0.118480	−	0.992956i	$-0.462198\pi$
$439$	4.96485	0.236959	0.118480	+	0.992956i	$0.462198\pi$
$440$	−0.160206	−0.00763751
$441$	−2.31895	−0.110426
$442$	−0.659805	−0.0313837
$443$	16.5571	0.786650	0.393325	−	0.919399i	$-0.371325\pi$
$443$	16.5571	0.786650	0.393325	+	0.919399i	$0.371325\pi$
$444$	6.57202	0.311894
$445$	−17.4818	−0.828718
$446$	10.8706	0.514736
$447$	−4.01791	−0.190041
$448$	−2.24631	−0.106128
$449$	−22.5413	−1.06379	−0.531894	−	0.846811i	$-0.678520\pi$
$449$	−22.5413	−1.06379	−0.531894	+	0.846811i	$0.678520\pi$
$450$	1.70911	0.0805680
$451$	0.103991	0.00489674
$452$	6.91976	0.325478
$453$	−13.2810	−0.623997
$454$	−10.2793	−0.482433
$455$	−0.351818	−0.0164935
$456$	−11.2572	−0.527166
$457$	23.1868	1.08463	0.542316	−	0.840175i	$-0.317548\pi$
$457$	23.1868	1.08463	0.542316	+	0.840175i	$0.317548\pi$
$458$	−0.737016	−0.0344385
$459$	11.1695	0.521349
$460$	2.31300	0.107844
$461$	35.2320	1.64092	0.820458	−	0.571706i	$-0.193718\pi$
$461$	35.2320	1.64092	0.820458	+	0.571706i	$0.193718\pi$
$462$	0.0382464	0.00177939
$463$	24.8805	1.15629	0.578147	−	0.815932i	$-0.303776\pi$
$463$	24.8805	1.15629	0.578147	+	0.815932i	$0.303776\pi$
$464$	−1.12950	−0.0524355
$465$	5.99287	0.277913
$466$	8.94838	0.414526
$467$	−28.7261	−1.32929	−0.664644	−	0.747160i	$-0.731417\pi$
$467$	−28.7261	−1.32929	−0.664644	+	0.747160i	$0.731417\pi$
$468$	−1.18854	−0.0549402
$469$	−2.20636	−0.101880
$470$	−6.63498	−0.306049
$471$	20.0518	0.923936
$472$	22.4839	1.03490
$473$	0.750360	0.0345016
$474$	−0.0672381	−0.00308835
$475$	−5.35415	−0.245665
$476$	−3.70700	−0.169910
$477$	7.51961	0.344299
$478$	−11.4228	−0.522468
$479$	6.99527	0.319622	0.159811	−	0.987148i	$-0.448911\pi$
$479$	6.99527	0.319622	0.159811	+	0.987148i	$0.448911\pi$
$480$	4.83510	0.220691
$481$	1.92321	0.0876909
$482$	−6.79027	−0.309288
$483$	−1.31027	−0.0596194
$484$	16.0191	0.728142
$485$	−9.00690	−0.408982
$486$	−11.7334	−0.532240
$487$	−26.2201	−1.18815	−0.594074	−	0.804410i	$-0.702481\pi$
$487$	−26.2201	−1.18815	−0.594074	+	0.804410i	$0.702481\pi$
$488$	−9.66824	−0.437661
$489$	6.27536	0.283782
$490$	0.737016	0.0332950
$491$	5.32237	0.240195	0.120098	−	0.992762i	$-0.461679\pi$
$491$	5.32237	0.240195	0.120098	+	0.992762i	$0.461679\pi$
$492$	−1.98820	−0.0896349
$493$	2.77450	0.124957
$494$	−1.38831	−0.0624629
$495$	0.145820	0.00655414
$496$	−7.52258	−0.337774
$497$	13.4509	0.603355
$498$	−8.00847	−0.358868
$499$	−10.3197	−0.461972	−0.230986	−	0.972957i	$-0.574195\pi$
$499$	−10.3197	−0.461972	−0.230986	+	0.972957i	$0.574195\pi$
$500$	1.45681	0.0651504
$501$	−15.8744	−0.709218
$502$	−2.64579	−0.118087
$503$	13.8698	0.618424	0.309212	−	0.950993i	$-0.399935\pi$
$503$	13.8698	0.618424	0.309212	+	0.950993i	$0.399935\pi$
$504$	5.90805	0.263165
$505$	6.59130	0.293309
$506$	−0.0735827	−0.00327115
$507$	−10.6262	−0.471925
$508$	16.7770	0.744360
$509$	−35.7747	−1.58568	−0.792842	−	0.609427i	$-0.791399\pi$
$509$	−35.7747	−1.58568	−0.792842	+	0.609427i	$0.791399\pi$
$510$	−1.54769	−0.0685330
$511$	14.4189	0.637856
$512$	−11.3477	−0.501502
$513$	23.5020	1.03764
$514$	−14.9385	−0.658911
$515$	17.1071	0.753830
$516$	−14.3461	−0.631552
$517$	−0.566095	−0.0248968
$518$	−4.02889	−0.177019
$519$	−0.787164	−0.0345527
$520$	0.896335	0.0393069
$521$	21.2117	0.929300	0.464650	−	0.885494i	$-0.346180\pi$
$521$	21.2117	0.929300	0.464650	+	0.885494i	$0.346180\pi$
$522$	−1.86352	−0.0815639
$523$	−6.22479	−0.272191	−0.136096	−	0.990696i	$-0.543455\pi$
$523$	−6.22479	−0.272191	−0.136096	+	0.990696i	$0.543455\pi$
$524$	3.92748	0.171573
$525$	−0.825255	−0.0360171
$526$	−5.41057	−0.235912
$527$	18.4785	0.804937
$528$	0.0537569	0.00233947
$529$	−20.4792	−0.890398
$530$	−2.38990	−0.103811
$531$	−20.4650	−0.888105
$532$	−7.79996	−0.338171
$533$	−0.581819	−0.0252014
$534$	−10.6329	−0.460130
$535$	1.56299	0.0675741
$536$	5.62120	0.242799
$537$	6.04522	0.260870
$538$	18.5054	0.797823
$539$	0.0628820	0.00270852
$540$	−6.39465	−0.275182
$541$	−3.39171	−0.145821	−0.0729105	−	0.997338i	$-0.523229\pi$
$541$	−3.39171	−0.145821	−0.0729105	+	0.997338i	$0.523229\pi$
$542$	−15.0977	−0.648502
$543$	15.3582	0.659083
$544$	14.9086	0.639203
$545$	0.349916	0.0149888
$546$	−0.213985	−0.00915771
$547$	10.8320	0.463144	0.231572	−	0.972818i	$-0.425613\pi$
$547$	10.8320	0.463144	0.231572	+	0.972818i	$0.425613\pi$
$548$	10.5279	0.449732
$549$	8.80011	0.375579
$550$	−0.0463450	−0.00197616
$551$	5.83787	0.248702
$552$	3.33820	0.142083
$553$	−0.110548	−0.00470097
$554$	−1.56147	−0.0663406
$555$	4.51125	0.191492
$556$	−28.0993	−1.19168
$557$	41.3939	1.75392	0.876958	−	0.480567i	$-0.159569\pi$
$557$	41.3939	1.75392	0.876958	+	0.480567i	$0.159569\pi$
$558$	−12.4112	−0.525410
$559$	−4.19819	−0.177564
$560$	1.03591	0.0437750
$561$	−0.132049	−0.00557511
$562$	4.64274	0.195842
$563$	18.0979	0.762734	0.381367	−	0.924424i	$-0.375453\pi$
$563$	18.0979	0.762734	0.381367	+	0.924424i	$0.375453\pi$
$564$	10.8231	0.455736
$565$	4.74995	0.199832
$566$	1.72250	0.0724019
$567$	−3.33441	−0.140032
$568$	−34.2691	−1.43790
$569$	15.9517	0.668729	0.334365	−	0.942444i	$-0.391478\pi$
$569$	15.9517	0.668729	0.334365	+	0.942444i	$0.391478\pi$
$570$	−3.25653	−0.136401
$571$	−9.44426	−0.395230	−0.197615	−	0.980280i	$-0.563320\pi$
$571$	−9.44426	−0.395230	−0.197615	+	0.980280i	$0.563320\pi$
$572$	0.0322290	0.00134756
$573$	15.1191	0.631610
$574$	1.21884	0.0508733
$575$	1.58772	0.0662123
$576$	−5.20908	−0.217045
$577$	37.4000	1.55698	0.778491	−	0.627656i	$-0.215985\pi$
$577$	37.4000	1.55698	0.778491	+	0.627656i	$0.215985\pi$
$578$	7.75708	0.322652
$579$	−7.77252	−0.323015
$580$	−1.58842	−0.0659557
$581$	−13.1669	−0.546257
$582$	−5.47823	−0.227080
$583$	−0.203906	−0.00844491
$584$	−36.7354	−1.52012
$585$	−0.815851	−0.0337313
$586$	−18.7639	−0.775132
$587$	9.55110	0.394216	0.197108	−	0.980382i	$-0.436845\pi$
$587$	9.55110	0.394216	0.197108	+	0.980382i	$0.436845\pi$
$588$	−1.20224	−0.0495794
$589$	38.8809	1.60206
$590$	6.50423	0.267775
$591$	0.00684264	0.000281469 0
$592$	−5.66277	−0.232738
$593$	−24.6023	−1.01029	−0.505147	−	0.863034i	$-0.668562\pi$
$593$	−24.6023	−1.01029	−0.505147	+	0.863034i	$0.668562\pi$
$594$	0.203431	0.00834688
$595$	−2.54461	−0.104319
$596$	7.09275	0.290530
$597$	−6.07804	−0.248758
$598$	0.411688	0.0168352
$599$	30.5245	1.24720	0.623598	−	0.781745i	$-0.285670\pi$
$599$	30.5245	1.24720	0.623598	+	0.781745i	$0.285670\pi$
$600$	2.10252	0.0858350
$601$	−16.2353	−0.662251	−0.331126	−	0.943587i	$-0.607428\pi$
$601$	−16.2353	−0.662251	−0.331126	+	0.943587i	$0.607428\pi$
$602$	8.79468	0.358444
$603$	−5.11645	−0.208358
$604$	23.4448	0.953954
$605$	10.9960	0.447053
$606$	4.00900	0.162855
$607$	−8.82351	−0.358135	−0.179068	−	0.983837i	$-0.557308\pi$
$607$	−8.82351	−0.358135	−0.179068	+	0.983837i	$0.557308\pi$
$608$	31.3695	1.27220
$609$	0.899813	0.0364623
$610$	−2.79687	−0.113242
$611$	3.16724	0.128133
$612$	−8.59637	−0.347488
$613$	40.8478	1.64983	0.824913	−	0.565259i	$-0.191224\pi$
$613$	40.8478	1.64983	0.824913	+	0.565259i	$0.191224\pi$
$614$	−19.6246	−0.791985
$615$	−1.36476	−0.0550326
$616$	−0.160206	−0.00645487
$617$	6.65236	0.267814	0.133907	−	0.990994i	$-0.457248\pi$
$617$	6.65236	0.267814	0.133907	+	0.990994i	$0.457248\pi$
$618$	10.4050	0.418550
$619$	45.8466	1.84273	0.921366	−	0.388696i	$-0.127074\pi$
$619$	45.8466	1.84273	0.921366	+	0.388696i	$0.127074\pi$
$620$	−10.5791	−0.424867
$621$	−6.96927	−0.279667
$622$	−12.7992	−0.513202
$623$	−17.4818	−0.700394
$624$	−0.300765	−0.0120402
$625$	1.00000	0.0400000
$626$	−7.96937	−0.318520
$627$	−0.277846	−0.0110961
$628$	−35.3970	−1.41250
$629$	13.9101	0.554631
$630$	1.70911	0.0680924
$631$	25.3598	1.00956	0.504778	−	0.863249i	$-0.331574\pi$
$631$	25.3598	1.00956	0.504778	+	0.863249i	$0.331574\pi$
$632$	0.281645	0.0112032
$633$	6.25561	0.248638
$634$	−5.47456	−0.217422
$635$	11.5163	0.457010
$636$	3.89846	0.154584
$637$	−0.351818	−0.0139395
$638$	0.0505321	0.00200058
$639$	31.1920	1.23394
$640$	−10.0623	−0.397747
$641$	−15.0457	−0.594271	−0.297135	−	0.954835i	$-0.596031\pi$
$641$	−15.0457	−0.594271	−0.297135	+	0.954835i	$0.596031\pi$
$642$	0.950653	0.0375193
$643$	24.0676	0.949135	0.474567	−	0.880219i	$-0.342605\pi$
$643$	24.0676	0.949135	0.474567	+	0.880219i	$0.342605\pi$
$644$	2.31300	0.0911449
$645$	−9.84762	−0.387750
$646$	−10.0412	−0.395067
$647$	−37.5254	−1.47528	−0.737638	−	0.675196i	$-0.764059\pi$
$647$	−37.5254	−1.47528	−0.737638	+	0.675196i	$0.764059\pi$
$648$	8.49516	0.333721
$649$	0.554939	0.0217833
$650$	0.259296	0.0101704
$651$	5.99287	0.234879
$652$	−11.0778	−0.433840
$653$	−35.7378	−1.39853	−0.699264	−	0.714864i	$-0.746489\pi$
$653$	−35.7378	−1.39853	−0.699264	+	0.714864i	$0.746489\pi$
$654$	0.212828	0.00832223
$655$	2.69595	0.105340
$656$	1.71313	0.0668863
$657$	33.4368	1.30450
$658$	−6.63498	−0.258659
$659$	−5.85681	−0.228149	−0.114074	−	0.993472i	$-0.536390\pi$
$659$	−5.85681	−0.228149	−0.114074	+	0.993472i	$0.536390\pi$
$660$	0.0755991	0.00294269
$661$	−42.2086	−1.64172	−0.820862	−	0.571127i	$-0.806507\pi$
$661$	−42.2086	−1.64172	−0.820862	+	0.571127i	$0.806507\pi$
$662$	7.60298	0.295498
$663$	0.738800	0.0286926
$664$	33.5457	1.30183
$665$	−5.35415	−0.207625
$666$	−9.34281	−0.362027
$667$	−1.73116	−0.0670308
$668$	28.0229	1.08424
$669$	−12.1720	−0.470598
$670$	1.62612	0.0628226
$671$	−0.238628	−0.00921214
$672$	4.83510	0.186518
$673$	−24.1384	−0.930466	−0.465233	−	0.885188i	$-0.654030\pi$
$673$	−24.1384	−0.930466	−0.465233	+	0.885188i	$0.654030\pi$
$674$	20.8620	0.803574
$675$	−4.38949	−0.168952
$676$	18.7582	0.721469
$677$	−7.57912	−0.291289	−0.145645	−	0.989337i	$-0.546526\pi$
$677$	−7.57912	−0.291289	−0.145645	+	0.989337i	$0.546526\pi$
$678$	2.88904	0.110953
$679$	−9.00690	−0.345653
$680$	6.48295	0.248610
$681$	11.5100	0.441065
$682$	0.336550	0.0128872
$683$	−23.8489	−0.912554	−0.456277	−	0.889838i	$-0.650817\pi$
$683$	−23.8489	−0.912554	−0.456277	+	0.889838i	$0.650817\pi$
$684$	−18.0878	−0.691603
$685$	7.22672	0.276119
$686$	0.737016	0.0281394
$687$	0.825255	0.0314854
$688$	12.3613	0.471270
$689$	1.14083	0.0434622
$690$	0.965690	0.0367632
$691$	−6.56434	−0.249719	−0.124860	−	0.992174i	$-0.539848\pi$
$691$	−6.56434	−0.249719	−0.124860	+	0.992174i	$0.539848\pi$
$692$	1.38957	0.0528234
$693$	0.145820	0.00553926
$694$	2.19171	0.0831961
$695$	−19.2883	−0.731646
$696$	−2.29247	−0.0868960
$697$	−4.20814	−0.159394
$698$	−10.2675	−0.388632
$699$	−10.0197	−0.378981
$700$	1.45681	0.0550622
$701$	−42.9343	−1.62161	−0.810803	−	0.585319i	$-0.800969\pi$
$701$	−42.9343	−1.62161	−0.810803	+	0.585319i	$0.800969\pi$
$702$	−1.13818	−0.0429577
$703$	29.2684	1.10388
$704$	0.141252	0.00532364
$705$	7.42935	0.279806
$706$	−1.77610	−0.0668445
$707$	6.59130	0.247892
$708$	−10.6099	−0.398743
$709$	−31.6571	−1.18891	−0.594454	−	0.804130i	$-0.702632\pi$
$709$	−31.6571	−1.18891	−0.594454	+	0.804130i	$0.702632\pi$
$710$	−9.91351	−0.372048
$711$	−0.256356	−0.00961408
$712$	44.5388	1.66916
$713$	−11.5297	−0.431792
$714$	−1.54769	−0.0579210
$715$	0.0221230	0.000827355 0
$716$	−10.6715	−0.398813
$717$	12.7904	0.477667
$718$	−4.38815	−0.163764
$719$	−14.3345	−0.534585	−0.267293	−	0.963615i	$-0.586129\pi$
$719$	−14.3345	−0.534585	−0.267293	+	0.963615i	$0.586129\pi$
$720$	2.40222	0.0895254
$721$	17.1071	0.637102
$722$	−7.12464	−0.265152
$723$	7.60324	0.282767
$724$	−27.1115	−1.00759
$725$	−1.09035	−0.0404944
$726$	6.68808	0.248218
$727$	26.6864	0.989743	0.494871	−	0.868966i	$-0.335215\pi$
$727$	26.6864	0.989743	0.494871	+	0.868966i	$0.335215\pi$
$728$	0.896335	0.0332204
$729$	3.13499	0.116111
$730$	−10.6270	−0.393322
$731$	−30.3643	−1.12307
$732$	4.56232	0.168628
$733$	16.3915	0.605433	0.302717	−	0.953081i	$-0.402106\pi$
$733$	16.3915	0.605433	0.302717	+	0.953081i	$0.402106\pi$
$734$	26.6127	0.982293
$735$	−0.825255	−0.0304400
$736$	−9.30230	−0.342887
$737$	0.138740	0.00511057
$738$	2.82643	0.104042
$739$	6.08143	0.223709	0.111854	−	0.993725i	$-0.464321\pi$
$739$	6.08143	0.223709	0.111854	+	0.993725i	$0.464321\pi$
$740$	−7.96363	−0.292749
$741$	1.55452	0.0571068
$742$	−2.38990	−0.0877360
$743$	−0.353465	−0.0129674	−0.00648369	−	0.999979i	$-0.502064\pi$
$743$	−0.353465	−0.0129674	−0.00648369	+	0.999979i	$0.502064\pi$
$744$	−15.2682	−0.559758
$745$	4.86869	0.178375
$746$	−7.35044	−0.269119
$747$	−30.5335	−1.11716
$748$	0.233104	0.00852311
$749$	1.56299	0.0571106
$750$	0.608226	0.0222093
$751$	−5.07656	−0.185246	−0.0926232	−	0.995701i	$-0.529525\pi$
$751$	−5.07656	−0.185246	−0.0926232	+	0.995701i	$0.529525\pi$
$752$	−9.32574	−0.340075
$753$	2.96256	0.107962
$754$	−0.282722	−0.0102961
$755$	16.0932	0.585693
$756$	−6.39465	−0.232571
$757$	−36.9443	−1.34276	−0.671382	−	0.741111i	$-0.734299\pi$
$757$	−36.9443	−1.34276	−0.671382	+	0.741111i	$0.734299\pi$
$758$	−8.71917	−0.316694
$759$	0.0823924	0.00299065
$760$	13.6409	0.494806
$761$	28.1062	1.01885	0.509424	−	0.860516i	$-0.329858\pi$
$761$	28.1062	1.01885	0.509424	+	0.860516i	$0.329858\pi$
$762$	7.00450	0.253746
$763$	0.349916	0.0126678
$764$	−26.6895	−0.965593
$765$	−5.90082	−0.213345
$766$	13.1336	0.474535
$767$	−3.10483	−0.112109
$768$	−9.82769	−0.354626
$769$	4.42874	0.159704	0.0798522	−	0.996807i	$-0.474555\pi$
$769$	4.42874	0.159704	0.0798522	+	0.996807i	$0.474555\pi$
$770$	−0.0463450	−0.00167016
$771$	16.7271	0.602410
$772$	13.7207	0.493819
$773$	−20.7809	−0.747436	−0.373718	−	0.927542i	$-0.621917\pi$
$773$	−20.7809	−0.747436	−0.373718	+	0.927542i	$0.621917\pi$
$774$	20.3945	0.733064
$775$	−7.26184	−0.260853
$776$	22.9471	0.823752
$777$	4.51125	0.161840
$778$	−24.5661	−0.880739
$779$	−8.85441	−0.317242
$780$	−0.422969	−0.0151447
$781$	−0.845819	−0.0302658
$782$	2.97762	0.106480
$783$	4.78606	0.171040
$784$	1.03591	0.0369966
$785$	−24.2977	−0.867221
$786$	1.63975	0.0584878
$787$	23.6529	0.843136	0.421568	−	0.906797i	$-0.361480\pi$
$787$	23.6529	0.843136	0.421568	+	0.906797i	$0.361480\pi$
$788$	−0.0120792	−0.000430304 0
$789$	6.05835	0.215683
$790$	0.0814755	0.00289877
$791$	4.74995	0.168889
$792$	−0.371510	−0.0132010
$793$	1.33510	0.0474108
$794$	−9.65379	−0.342600
$795$	2.67603	0.0949090
$796$	10.7295	0.380295
$797$	−27.6194	−0.978330	−0.489165	−	0.872191i	$-0.662698\pi$
$797$	−27.6194	−0.978330	−0.489165	+	0.872191i	$0.662698\pi$
$798$	−3.25653	−0.115280
$799$	22.9078	0.810420
$800$	−5.85892	−0.207144
$801$	−40.5395	−1.43239
$802$	−20.8064	−0.734701
$803$	−0.906691	−0.0319964
$804$	−2.65257	−0.0935490
$805$	1.58772	0.0559596
$806$	−1.88296	−0.0663245
$807$	−20.7209	−0.729411
$808$	−16.7928	−0.590769
$809$	−41.1231	−1.44581	−0.722905	−	0.690947i	$-0.757194\pi$
$809$	−41.1231	−1.44581	−0.722905	+	0.690947i	$0.757194\pi$
$810$	2.45752	0.0863483
$811$	15.8233	0.555630	0.277815	−	0.960635i	$-0.410390\pi$
$811$	15.8233	0.555630	0.277815	+	0.960635i	$0.410390\pi$
$812$	−1.58842	−0.0557428
$813$	16.9053	0.592894
$814$	0.253345	0.00887972
$815$	−7.60415	−0.266362
$816$	−2.17535	−0.0761524
$817$	−63.8901	−2.23523
$818$	−15.8460	−0.554041
$819$	−0.815851	−0.0285081
$820$	2.40919	0.0841327
$821$	−39.7137	−1.38602	−0.693010	−	0.720928i	$-0.743716\pi$
$821$	−39.7137	−1.38602	−0.693010	+	0.720928i	$0.743716\pi$
$822$	4.39548	0.153310
$823$	12.9518	0.451470	0.225735	−	0.974189i	$-0.427522\pi$
$823$	12.9518	0.451470	0.225735	+	0.974189i	$0.427522\pi$
$824$	−43.5842	−1.51833
$825$	0.0518937	0.00180671
$826$	6.50423	0.226311
$827$	−48.6843	−1.69292	−0.846459	−	0.532454i	$-0.821270\pi$
$827$	−48.6843	−1.69292	−0.846459	+	0.532454i	$0.821270\pi$
$828$	5.36374	0.186403
$829$	−25.3416	−0.880149	−0.440075	−	0.897961i	$-0.645048\pi$
$829$	−25.3416	−0.880149	−0.440075	+	0.897961i	$0.645048\pi$
$830$	9.70424	0.336839
$831$	1.74842	0.0606520
$832$	−0.790291	−0.0273984
$833$	−2.54461	−0.0881654
$834$	−11.7316	−0.406233
$835$	19.2358	0.665683
$836$	0.490477	0.0169635
$837$	31.8758	1.10179
$838$	−8.00566	−0.276551
$839$	−16.6907	−0.576226	−0.288113	−	0.957596i	$-0.593028\pi$
$839$	−16.6907	−0.576226	−0.288113	+	0.957596i	$0.593028\pi$
$840$	2.10252	0.0725438
$841$	−27.8111	−0.959005
$842$	−0.840462	−0.0289642
$843$	−5.19859	−0.179049
$844$	−11.0429	−0.380113
$845$	12.8762	0.442956
$846$	−15.3862	−0.528989
$847$	10.9960	0.377829
$848$	−3.35910	−0.115352
$849$	−1.92872	−0.0661936
$850$	1.87541	0.0643262
$851$	−8.67924	−0.297520
$852$	16.1712	0.554015
$853$	47.1905	1.61577	0.807886	−	0.589338i	$-0.200612\pi$
$853$	47.1905	1.61577	0.807886	+	0.589338i	$0.200612\pi$
$854$	−2.79687	−0.0957069
$855$	−12.4160	−0.424619
$856$	−3.98207	−0.136104
$857$	−32.8874	−1.12341	−0.561707	−	0.827336i	$-0.689855\pi$
$857$	−32.8874	−1.12341	−0.561707	+	0.827336i	$0.689855\pi$
$858$	0.0134558	0.000459373 0
$859$	−23.8617	−0.814152	−0.407076	−	0.913394i	$-0.633452\pi$
$859$	−23.8617	−0.814152	−0.407076	+	0.913394i	$0.633452\pi$
$860$	17.3838	0.592784
$861$	−1.36476	−0.0465110
$862$	5.30951	0.180843
$863$	21.9990	0.748854	0.374427	−	0.927256i	$-0.377840\pi$
$863$	21.9990	0.748854	0.374427	+	0.927256i	$0.377840\pi$
$864$	25.7177	0.874934
$865$	0.953843	0.0324316
$866$	−24.4406	−0.830526
$867$	−8.68579	−0.294985
$868$	−10.5791	−0.359078
$869$	0.00695147	0.000235812 0
$870$	−0.663176	−0.0224838
$871$	−0.776239	−0.0263018
$872$	−0.891489	−0.0301896
$873$	−20.8866	−0.706904
$874$	6.26527	0.211926
$875$	1.00000	0.0338062
$876$	17.3350	0.585695
$877$	49.0339	1.65576	0.827878	−	0.560908i	$-0.189548\pi$
$877$	49.0339	1.65576	0.827878	+	0.560908i	$0.189548\pi$
$878$	−3.65917	−0.123491
$879$	21.0105	0.708665
$880$	−0.0651398	−0.00219586
$881$	−1.35979	−0.0458125	−0.0229063	−	0.999738i	$-0.507292\pi$
$881$	−1.35979	−0.0458125	−0.0229063	+	0.999738i	$0.507292\pi$
$882$	1.70911	0.0575486
$883$	28.7971	0.969099	0.484550	−	0.874764i	$-0.338983\pi$
$883$	28.7971	0.969099	0.484550	+	0.874764i	$0.338983\pi$
$884$	−1.30419	−0.0438647
$885$	−7.28295	−0.244814
$886$	−12.2028	−0.409962
$887$	34.1659	1.14718	0.573590	−	0.819142i	$-0.305550\pi$
$887$	34.1659	1.14718	0.573590	+	0.819142i	$0.305550\pi$
$888$	−11.4934	−0.385693
$889$	11.5163	0.386244
$890$	12.8844	0.431885
$891$	0.209675	0.00702436
$892$	21.4871	0.719441
$893$	48.2007	1.61297
$894$	2.96126	0.0990394
$895$	−7.32528	−0.244857
$896$	−10.0623	−0.336157
$897$	−0.460977	−0.0153916
$898$	16.6133	0.554392
$899$	7.91791	0.264077
$900$	3.37827	0.112609
$901$	8.25132	0.274891
$902$	−0.0766429	−0.00255193
$903$	−9.84762	−0.327708
$904$	−12.1015	−0.402491
$905$	−18.6102	−0.618625
$906$	9.78832	0.325195
$907$	15.1748	0.503870	0.251935	−	0.967744i	$-0.418933\pi$
$907$	15.1748	0.503870	0.251935	+	0.967744i	$0.418933\pi$
$908$	−20.3185	−0.674292
$909$	15.2849	0.506969
$910$	0.259296	0.00859557
$911$	25.5108	0.845212	0.422606	−	0.906314i	$-0.361115\pi$
$911$	25.5108	0.845212	0.422606	+	0.906314i	$0.361115\pi$
$912$	−4.57718	−0.151566
$913$	0.827963	0.0274016
$914$	−17.0890	−0.565254
$915$	3.13173	0.103532
$916$	−1.45681	−0.0481343
$917$	2.69595	0.0890282
$918$	−8.23212	−0.271700
$919$	−30.9660	−1.02147	−0.510737	−	0.859737i	$-0.670627\pi$
$919$	−30.9660	−1.02147	−0.510737	+	0.859737i	$0.670627\pi$
$920$	−4.04506	−0.133362
$921$	21.9742	0.724073
$922$	−25.9665	−0.855162
$923$	4.73227	0.155765
$924$	0.0755991	0.00248703
$925$	−5.46649	−0.179737
$926$	−18.3373	−0.602602
$927$	39.6706	1.30295
$928$	6.38825	0.209705
$929$	40.0507	1.31402	0.657010	−	0.753881i	$-0.271821\pi$
$929$	40.0507	1.31402	0.657010	+	0.753881i	$0.271821\pi$
$930$	−4.41684	−0.144834
$931$	−5.35415	−0.175475
$932$	17.6876	0.579378
$933$	14.3316	0.469196
$934$	21.1716	0.692756
$935$	0.160010	0.00523288
$936$	2.07856	0.0679399
$937$	−15.2995	−0.499813	−0.249907	−	0.968270i	$-0.580400\pi$
$937$	−15.2995	−0.499813	−0.249907	+	0.968270i	$0.580400\pi$
$938$	1.62612	0.0530948
$939$	8.92350	0.291208
$940$	−13.1149	−0.427761
$941$	56.2127	1.83248	0.916241	−	0.400628i	$-0.131208\pi$
$941$	56.2127	1.83248	0.916241	+	0.400628i	$0.131208\pi$
$942$	−14.7785	−0.481508
$943$	2.62568	0.0855040
$944$	9.14196	0.297545
$945$	−4.38949	−0.142790
$946$	−0.553027	−0.0179805
$947$	−13.0122	−0.422838	−0.211419	−	0.977395i	$-0.567809\pi$
$947$	−13.0122	−0.422838	−0.211419	+	0.977395i	$0.567809\pi$
$948$	−0.132905	−0.00431655
$949$	5.07284	0.164671
$950$	3.94609	0.128028
$951$	6.13000	0.198779
$952$	6.48295	0.210113
$953$	43.7835	1.41829	0.709144	−	0.705064i	$-0.249082\pi$
$953$	43.7835	1.41829	0.709144	+	0.705064i	$0.249082\pi$
$954$	−5.54207	−0.179431
$955$	−18.3205	−0.592839
$956$	−22.5787	−0.730248
$957$	−0.0565820	−0.00182904
$958$	−5.15562	−0.166571
$959$	7.22672	0.233363
$960$	−1.85377	−0.0598303
$961$	21.7343	0.701106
$962$	−1.41744	−0.0457000
$963$	3.62451	0.116798
$964$	−13.4219	−0.432289
$965$	9.41833	0.303187
$966$	0.965690	0.0310706
$967$	23.7562	0.763948	0.381974	−	0.924173i	$-0.375244\pi$
$967$	23.7562	0.763948	0.381974	+	0.924173i	$0.375244\pi$
$968$	−28.0149	−0.900432
$969$	11.2434	0.361191
$970$	6.63823	0.213141
$971$	14.3197	0.459542	0.229771	−	0.973245i	$-0.426202\pi$
$971$	14.3197	0.459542	0.229771	+	0.973245i	$0.426202\pi$
$972$	−23.1927	−0.743906
$973$	−19.2883	−0.618354
$974$	19.3247	0.619202
$975$	−0.290340	−0.00929831
$976$	−3.93112	−0.125832
$977$	28.4418	0.909934	0.454967	−	0.890508i	$-0.349651\pi$
$977$	28.4418	0.909934	0.454967	+	0.890508i	$0.349651\pi$
$978$	−4.62504	−0.147892
$979$	1.09929	0.0351335
$980$	1.45681	0.0465360
$981$	0.811440	0.0259073
$982$	−3.92267	−0.125177
$983$	−31.1926	−0.994888	−0.497444	−	0.867496i	$-0.665728\pi$
$983$	−31.1926	−0.994888	−0.497444	+	0.867496i	$0.665728\pi$
$984$	3.47704	0.110844
$985$	−0.00829155	−0.000264191 0
$986$	−2.04485	−0.0651213
$987$	7.42935	0.236479
$988$	−2.74417	−0.0873037
$989$	18.9459	0.602446
$990$	−0.107472	−0.00341568
$991$	43.1418	1.37044	0.685222	−	0.728335i	$-0.259705\pi$
$991$	43.1418	1.37044	0.685222	+	0.728335i	$0.259705\pi$
$992$	42.5465	1.35085
$993$	−8.51325	−0.270160
$994$	−9.91351	−0.314438
$995$	7.36505	0.233488
$996$	−15.8298	−0.501586
$997$	25.4690	0.806611	0.403306	−	0.915065i	$-0.367861\pi$
$997$	25.4690	0.806611	0.403306	+	0.915065i	$0.367861\pi$
$998$	7.60576	0.240756
$999$	23.9951	0.759172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.24	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.24	✓	62	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)

\(f(q)\)	\(=\)	\(q-0.737016 q^{2} +0.825255 q^{3} -1.45681 q^{4} -1.00000 q^{5} -0.608226 q^{6} -1.00000 q^{7} +2.54772 q^{8} -2.31895 q^{9} +O(q^{10})\)	\(q-0.737016 q^{2} +0.825255 q^{3} -1.45681 q^{4} -1.00000 q^{5} -0.608226 q^{6} -1.00000 q^{7} +2.54772 q^{8} -2.31895 q^{9} +0.737016 q^{10} +0.0628820 q^{11} -1.20224 q^{12} -0.351818 q^{13} +0.737016 q^{14} -0.825255 q^{15} +1.03591 q^{16} -2.54461 q^{17} +1.70911 q^{18} -5.35415 q^{19} +1.45681 q^{20} -0.825255 q^{21} -0.0463450 q^{22} +1.58772 q^{23} +2.10252 q^{24} +1.00000 q^{25} +0.259296 q^{26} -4.38949 q^{27} +1.45681 q^{28} -1.09035 q^{29} +0.608226 q^{30} -7.26184 q^{31} -5.85892 q^{32} +0.0518937 q^{33} +1.87541 q^{34} +1.00000 q^{35} +3.37827 q^{36} -5.46649 q^{37} +3.94609 q^{38} -0.290340 q^{39} -2.54772 q^{40} +1.65375 q^{41} +0.608226 q^{42} +11.9328 q^{43} -0.0916070 q^{44} +2.31895 q^{45} -1.17017 q^{46} -9.00250 q^{47} +0.854886 q^{48} +1.00000 q^{49} -0.737016 q^{50} -2.09995 q^{51} +0.512532 q^{52} -3.24267 q^{53} +3.23512 q^{54} -0.0628820 q^{55} -2.54772 q^{56} -4.41853 q^{57} +0.803602 q^{58} +8.82509 q^{59} +1.20224 q^{60} -3.79486 q^{61} +5.35209 q^{62} +2.31895 q^{63} +2.24631 q^{64} +0.351818 q^{65} -0.0382464 q^{66} +2.20636 q^{67} +3.70700 q^{68} +1.31027 q^{69} -0.737016 q^{70} -13.4509 q^{71} -5.90805 q^{72} -14.4189 q^{73} +4.02889 q^{74} +0.825255 q^{75} +7.79996 q^{76} -0.0628820 q^{77} +0.213985 q^{78} +0.110548 q^{79} -1.03591 q^{80} +3.33441 q^{81} -1.21884 q^{82} +13.1669 q^{83} +1.20224 q^{84} +2.54461 q^{85} -8.79468 q^{86} -0.899813 q^{87} +0.160206 q^{88} +17.4818 q^{89} -1.70911 q^{90} +0.351818 q^{91} -2.31300 q^{92} -5.99287 q^{93} +6.63498 q^{94} +5.35415 q^{95} -4.83510 q^{96} +9.00690 q^{97} -0.737016 q^{98} -0.145820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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