LMFDB - Embedded newform 8013.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59970 q^{2} +1.00000 q^{3} +4.75846 q^{4} +1.02648 q^{5} -2.59970 q^{6} -4.07018 q^{7} -7.17119 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.59970 q^{2} +1.00000 q^{3} +4.75846 q^{4} +1.02648 q^{5} -2.59970 q^{6} -4.07018 q^{7} -7.17119 q^{8} +1.00000 q^{9} -2.66854 q^{10} -2.37383 q^{11} +4.75846 q^{12} +4.83564 q^{13} +10.5813 q^{14} +1.02648 q^{15} +9.12606 q^{16} +1.25033 q^{17} -2.59970 q^{18} +6.30041 q^{19} +4.88446 q^{20} -4.07018 q^{21} +6.17125 q^{22} -2.91520 q^{23} -7.17119 q^{24} -3.94634 q^{25} -12.5712 q^{26} +1.00000 q^{27} -19.3678 q^{28} -7.88097 q^{29} -2.66854 q^{30} -1.97118 q^{31} -9.38267 q^{32} -2.37383 q^{33} -3.25050 q^{34} -4.17796 q^{35} +4.75846 q^{36} -0.814054 q^{37} -16.3792 q^{38} +4.83564 q^{39} -7.36107 q^{40} -2.01068 q^{41} +10.5813 q^{42} -3.25216 q^{43} -11.2958 q^{44} +1.02648 q^{45} +7.57865 q^{46} +6.79314 q^{47} +9.12606 q^{48} +9.56640 q^{49} +10.2593 q^{50} +1.25033 q^{51} +23.0102 q^{52} +2.75569 q^{53} -2.59970 q^{54} -2.43668 q^{55} +29.1881 q^{56} +6.30041 q^{57} +20.4882 q^{58} +6.56759 q^{59} +4.88446 q^{60} -0.0575094 q^{61} +5.12447 q^{62} -4.07018 q^{63} +6.14005 q^{64} +4.96367 q^{65} +6.17125 q^{66} +1.04040 q^{67} +5.94967 q^{68} -2.91520 q^{69} +10.8615 q^{70} -3.04806 q^{71} -7.17119 q^{72} +0.895688 q^{73} +2.11630 q^{74} -3.94634 q^{75} +29.9803 q^{76} +9.66192 q^{77} -12.5712 q^{78} +15.4614 q^{79} +9.36770 q^{80} +1.00000 q^{81} +5.22717 q^{82} +2.31992 q^{83} -19.3678 q^{84} +1.28344 q^{85} +8.45467 q^{86} -7.88097 q^{87} +17.0232 q^{88} -7.16653 q^{89} -2.66854 q^{90} -19.6819 q^{91} -13.8719 q^{92} -1.97118 q^{93} -17.6602 q^{94} +6.46723 q^{95} -9.38267 q^{96} -10.0203 q^{97} -24.8698 q^{98} -2.37383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.59970	−1.83827	−0.919134	−	0.393944i	$-0.871110\pi$
$2$	−2.59970	−1.83827	−0.919134	+	0.393944i	$0.871110\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.75846	2.37923
$5$	1.02648	0.459055	0.229528	−	0.973302i	$-0.426282\pi$
$5$	1.02648	0.459055	0.229528	+	0.973302i	$0.426282\pi$
$6$	−2.59970	−1.06133
$7$	−4.07018	−1.53838	−0.769192	−	0.639017i	$-0.779341\pi$
$7$	−4.07018	−1.53838	−0.769192	+	0.639017i	$0.779341\pi$
$8$	−7.17119	−2.53540
$9$	1.00000	0.333333
$10$	−2.66854	−0.843867
$11$	−2.37383	−0.715736	−0.357868	−	0.933772i	$-0.616496\pi$
$11$	−2.37383	−0.715736	−0.357868	+	0.933772i	$0.616496\pi$
$12$	4.75846	1.37365
$13$	4.83564	1.34116	0.670582	−	0.741835i	$-0.266044\pi$
$13$	4.83564	1.34116	0.670582	+	0.741835i	$0.266044\pi$
$14$	10.5813	2.82797
$15$	1.02648	0.265036
$16$	9.12606	2.28151
$17$	1.25033	0.303250	0.151625	−	0.988438i	$-0.451549\pi$
$17$	1.25033	0.303250	0.151625	+	0.988438i	$0.451549\pi$
$18$	−2.59970	−0.612756
$19$	6.30041	1.44541	0.722707	−	0.691155i	$-0.242898\pi$
$19$	6.30041	1.44541	0.722707	+	0.691155i	$0.242898\pi$
$20$	4.88446	1.09220
$21$	−4.07018	−0.888187
$22$	6.17125	1.31572
$23$	−2.91520	−0.607861	−0.303930	−	0.952694i	$-0.598299\pi$
$23$	−2.91520	−0.607861	−0.303930	+	0.952694i	$0.598299\pi$
$24$	−7.17119	−1.46381
$25$	−3.94634	−0.789268
$26$	−12.5712	−2.46542
$27$	1.00000	0.192450
$28$	−19.3678	−3.66018
$29$	−7.88097	−1.46346	−0.731730	−	0.681595i	$-0.761287\pi$
$29$	−7.88097	−1.46346	−0.731730	+	0.681595i	$0.761287\pi$
$30$	−2.66854	−0.487207
$31$	−1.97118	−0.354034	−0.177017	−	0.984208i	$-0.556645\pi$
$31$	−1.97118	−0.354034	−0.177017	+	0.984208i	$0.556645\pi$
$32$	−9.38267	−1.65864
$33$	−2.37383	−0.413231
$34$	−3.25050	−0.557456
$35$	−4.17796	−0.706203
$36$	4.75846	0.793077
$37$	−0.814054	−0.133830	−0.0669148	−	0.997759i	$-0.521316\pi$
$37$	−0.814054	−0.133830	−0.0669148	+	0.997759i	$0.521316\pi$
$38$	−16.3792	−2.65706
$39$	4.83564	0.774321
$40$	−7.36107	−1.16389
$41$	−2.01068	−0.314015	−0.157008	−	0.987597i	$-0.550185\pi$
$41$	−2.01068	−0.314015	−0.157008	+	0.987597i	$0.550185\pi$
$42$	10.5813	1.63273
$43$	−3.25216	−0.495950	−0.247975	−	0.968766i	$-0.579765\pi$
$43$	−3.25216	−0.495950	−0.247975	+	0.968766i	$0.579765\pi$
$44$	−11.2958	−1.70290
$45$	1.02648	0.153018
$46$	7.57865	1.11741
$47$	6.79314	0.990881	0.495441	−	0.868642i	$-0.335007\pi$
$47$	6.79314	0.990881	0.495441	+	0.868642i	$0.335007\pi$
$48$	9.12606	1.31723
$49$	9.56640	1.36663
$50$	10.2593	1.45089
$51$	1.25033	0.175082
$52$	23.0102	3.19094
$53$	2.75569	0.378523	0.189261	−	0.981927i	$-0.439391\pi$
$53$	2.75569	0.378523	0.189261	+	0.981927i	$0.439391\pi$
$54$	−2.59970	−0.353775
$55$	−2.43668	−0.328562
$56$	29.1881	3.90042
$57$	6.30041	0.834510
$58$	20.4882	2.69023
$59$	6.56759	0.855027	0.427514	−	0.904009i	$-0.359390\pi$
$59$	6.56759	0.855027	0.427514	+	0.904009i	$0.359390\pi$
$60$	4.88446	0.630581
$61$	−0.0575094	−0.00736332	−0.00368166	−	0.999993i	$-0.501172\pi$
$61$	−0.0575094	−0.00736332	−0.00368166	+	0.999993i	$0.501172\pi$
$62$	5.12447	0.650809
$63$	−4.07018	−0.512795
$64$	6.14005	0.767506
$65$	4.96367	0.615668
$66$	6.17125	0.759629
$67$	1.04040	0.127105	0.0635523	−	0.997979i	$-0.479757\pi$
$67$	1.04040	0.127105	0.0635523	+	0.997979i	$0.479757\pi$
$68$	5.94967	0.721503
$69$	−2.91520	−0.350948
$70$	10.8615	1.29819
$71$	−3.04806	−0.361738	−0.180869	−	0.983507i	$-0.557891\pi$
$71$	−3.04806	−0.361738	−0.180869	+	0.983507i	$0.557891\pi$
$72$	−7.17119	−0.845133
$73$	0.895688	0.104832	0.0524161	−	0.998625i	$-0.483308\pi$
$73$	0.895688	0.104832	0.0524161	+	0.998625i	$0.483308\pi$
$74$	2.11630	0.246015
$75$	−3.94634	−0.455684
$76$	29.9803	3.43897
$77$	9.66192	1.10108
$78$	−12.5712	−1.42341
$79$	15.4614	1.73954	0.869771	−	0.493455i	$-0.164266\pi$
$79$	15.4614	1.73954	0.869771	+	0.493455i	$0.164266\pi$
$80$	9.36770	1.04734
$81$	1.00000	0.111111
$82$	5.22717	0.577245
$83$	2.31992	0.254644	0.127322	−	0.991861i	$-0.459362\pi$
$83$	2.31992	0.254644	0.127322	+	0.991861i	$0.459362\pi$
$84$	−19.3678	−2.11320
$85$	1.28344	0.139209
$86$	8.45467	0.911690
$87$	−7.88097	−0.844929
$88$	17.0232	1.81468
$89$	−7.16653	−0.759650	−0.379825	−	0.925058i	$-0.624016\pi$
$89$	−7.16653	−0.759650	−0.379825	+	0.925058i	$0.624016\pi$
$90$	−2.66854	−0.281289
$91$	−19.6819	−2.06323
$92$	−13.8719	−1.44624
$93$	−1.97118	−0.204401
$94$	−17.6602	−1.82151
$95$	6.46723	0.663524
$96$	−9.38267	−0.957615
$97$	−10.0203	−1.01741	−0.508706	−	0.860941i	$-0.669876\pi$
$97$	−10.0203	−1.01741	−0.508706	+	0.860941i	$0.669876\pi$
$98$	−24.8698	−2.51223
$99$	−2.37383	−0.238579
$100$	−18.7785	−1.87785
$101$	−17.6323	−1.75448	−0.877239	−	0.480053i	$-0.840617\pi$
$101$	−17.6323	−1.75448	−0.877239	+	0.480053i	$0.840617\pi$
$102$	−3.25050	−0.321847
$103$	7.03561	0.693239	0.346620	−	0.938006i	$-0.387330\pi$
$103$	7.03561	0.693239	0.346620	+	0.938006i	$0.387330\pi$
$104$	−34.6773	−3.40039
$105$	−4.17796	−0.407727
$106$	−7.16397	−0.695826
$107$	7.73840	0.748100	0.374050	−	0.927409i	$-0.377969\pi$
$107$	7.73840	0.748100	0.374050	+	0.927409i	$0.377969\pi$
$108$	4.75846	0.457883
$109$	17.0334	1.63151	0.815753	−	0.578400i	$-0.196323\pi$
$109$	17.0334	1.63151	0.815753	+	0.578400i	$0.196323\pi$
$110$	6.33466	0.603986
$111$	−0.814054	−0.0772666
$112$	−37.1447	−3.50985
$113$	8.90159	0.837391	0.418696	−	0.908127i	$-0.362487\pi$
$113$	8.90159	0.837391	0.418696	+	0.908127i	$0.362487\pi$
$114$	−16.3792	−1.53405
$115$	−2.99239	−0.279041
$116$	−37.5013	−3.48191
$117$	4.83564	0.447055
$118$	−17.0738	−1.57177
$119$	−5.08909	−0.466516
$120$	−7.36107	−0.671971
$121$	−5.36494	−0.487722
$122$	0.149507	0.0135358
$123$	−2.01068	−0.181297
$124$	−9.37977	−0.842328
$125$	−9.18323	−0.821373
$126$	10.5813	0.942655
$127$	16.9662	1.50551	0.752756	−	0.658300i	$-0.228724\pi$
$127$	16.9662	1.50551	0.752756	+	0.658300i	$0.228724\pi$
$128$	2.80302	0.247754
$129$	−3.25216	−0.286337
$130$	−12.9041	−1.13176
$131$	−7.94817	−0.694435	−0.347218	−	0.937785i	$-0.612873\pi$
$131$	−7.94817	−0.694435	−0.347218	+	0.937785i	$0.612873\pi$
$132$	−11.2958	−0.983172
$133$	−25.6438	−2.22360
$134$	−2.70472	−0.233653
$135$	1.02648	0.0883452
$136$	−8.96638	−0.768861
$137$	−3.80116	−0.324755	−0.162378	−	0.986729i	$-0.551916\pi$
$137$	−3.80116	−0.324755	−0.162378	+	0.986729i	$0.551916\pi$
$138$	7.57865	0.645138
$139$	9.84042	0.834654	0.417327	−	0.908756i	$-0.362967\pi$
$139$	9.84042	0.834654	0.417327	+	0.908756i	$0.362967\pi$
$140$	−19.8807	−1.68022
$141$	6.79314	0.572086
$142$	7.92406	0.664972
$143$	−11.4790	−0.959920
$144$	9.12606	0.760505
$145$	−8.08964	−0.671808
$146$	−2.32852	−0.192710
$147$	9.56640	0.789023
$148$	−3.87365	−0.318412
$149$	11.7342	0.961306	0.480653	−	0.876911i	$-0.340400\pi$
$149$	11.7342	0.961306	0.480653	+	0.876911i	$0.340400\pi$
$150$	10.2593	0.837670
$151$	−10.1801	−0.828446	−0.414223	−	0.910175i	$-0.635947\pi$
$151$	−10.1801	−0.828446	−0.414223	+	0.910175i	$0.635947\pi$
$152$	−45.1815	−3.66470
$153$	1.25033	0.101083
$154$	−25.1181	−2.02408
$155$	−2.02337	−0.162521
$156$	23.0102	1.84229
$157$	20.9789	1.67430	0.837151	−	0.546972i	$-0.184220\pi$
$157$	20.9789	1.67430	0.837151	+	0.546972i	$0.184220\pi$
$158$	−40.1950	−3.19775
$159$	2.75569	0.218540
$160$	−9.63110	−0.761406
$161$	11.8654	0.935124
$162$	−2.59970	−0.204252
$163$	−4.64229	−0.363613	−0.181806	−	0.983334i	$-0.558194\pi$
$163$	−4.64229	−0.363613	−0.181806	+	0.983334i	$0.558194\pi$
$164$	−9.56774	−0.747115
$165$	−2.43668	−0.189696
$166$	−6.03110	−0.468104
$167$	−1.28107	−0.0991319	−0.0495659	−	0.998771i	$-0.515784\pi$
$167$	−1.28107	−0.0991319	−0.0495659	+	0.998771i	$0.515784\pi$
$168$	29.1881	2.25191
$169$	10.3834	0.798721
$170$	−3.33657	−0.255903
$171$	6.30041	0.481804
$172$	−15.4753	−1.17998
$173$	3.18117	0.241860	0.120930	−	0.992661i	$-0.461412\pi$
$173$	3.18117	0.241860	0.120930	+	0.992661i	$0.461412\pi$
$174$	20.4882	1.55321
$175$	16.0623	1.21420
$176$	−21.6637	−1.63296
$177$	6.56759	0.493650
$178$	18.6309	1.39644
$179$	5.58298	0.417292	0.208646	−	0.977991i	$-0.433094\pi$
$179$	5.58298	0.417292	0.208646	+	0.977991i	$0.433094\pi$
$180$	4.88446	0.364066
$181$	−2.59246	−0.192696	−0.0963481	−	0.995348i	$-0.530716\pi$
$181$	−2.59246	−0.192696	−0.0963481	+	0.995348i	$0.530716\pi$
$182$	51.1672	3.79277
$183$	−0.0575094	−0.00425122
$184$	20.9054	1.54117
$185$	−0.835609	−0.0614352
$186$	5.12447	0.375745
$187$	−2.96808	−0.217047
$188$	32.3249	2.35754
$189$	−4.07018	−0.296062
$190$	−16.8129	−1.21974
$191$	−20.7352	−1.50035	−0.750173	−	0.661242i	$-0.770030\pi$
$191$	−20.7352	−1.50035	−0.750173	+	0.661242i	$0.770030\pi$
$192$	6.14005	0.443120
$193$	6.42548	0.462516	0.231258	−	0.972892i	$-0.425716\pi$
$193$	6.42548	0.462516	0.231258	+	0.972892i	$0.425716\pi$
$194$	26.0499	1.87028
$195$	4.96367	0.355456
$196$	45.5214	3.25153
$197$	−10.8247	−0.771229	−0.385614	−	0.922660i	$-0.626011\pi$
$197$	−10.8247	−0.771229	−0.385614	+	0.922660i	$0.626011\pi$
$198$	6.17125	0.438572
$199$	9.39737	0.666162	0.333081	−	0.942898i	$-0.391912\pi$
$199$	9.39737	0.666162	0.333081	+	0.942898i	$0.391912\pi$
$200$	28.3000	2.00111
$201$	1.04040	0.0733839
$202$	45.8387	3.22520
$203$	32.0770	2.25136
$204$	5.94967	0.416560
$205$	−2.06392	−0.144150
$206$	−18.2905	−1.27436
$207$	−2.91520	−0.202620
$208$	44.1303	3.05989
$209$	−14.9561	−1.03453
$210$	10.8615	0.749511
$211$	−0.579477	−0.0398929	−0.0199464	−	0.999801i	$-0.506350\pi$
$211$	−0.579477	−0.0398929	−0.0199464	+	0.999801i	$0.506350\pi$
$212$	13.1128	0.900593
$213$	−3.04806	−0.208850
$214$	−20.1176	−1.37521
$215$	−3.33828	−0.227668
$216$	−7.17119	−0.487938
$217$	8.02305	0.544640
$218$	−44.2819	−2.99915
$219$	0.895688	0.0605250
$220$	−11.5949	−0.781726
$221$	6.04616	0.406709
$222$	2.11630	0.142037
$223$	−5.76932	−0.386342	−0.193171	−	0.981165i	$-0.561877\pi$
$223$	−5.76932	−0.386342	−0.193171	+	0.981165i	$0.561877\pi$
$224$	38.1892	2.55162
$225$	−3.94634	−0.263089
$226$	−23.1415	−1.53935
$227$	20.6353	1.36961	0.684807	−	0.728725i	$-0.259887\pi$
$227$	20.6353	1.36961	0.684807	+	0.728725i	$0.259887\pi$
$228$	29.9803	1.98549
$229$	−9.06771	−0.599211	−0.299606	−	0.954063i	$-0.596855\pi$
$229$	−9.06771	−0.599211	−0.299606	+	0.954063i	$0.596855\pi$
$230$	7.77932	0.512953
$231$	9.66192	0.635708
$232$	56.5160	3.71045
$233$	−4.05467	−0.265630	−0.132815	−	0.991141i	$-0.542402\pi$
$233$	−4.05467	−0.265630	−0.132815	+	0.991141i	$0.542402\pi$
$234$	−12.5712	−0.821807
$235$	6.97301	0.454869
$236$	31.2516	2.03431
$237$	15.4614	1.00433
$238$	13.2301	0.857582
$239$	−13.1040	−0.847627	−0.423813	−	0.905750i	$-0.639309\pi$
$239$	−13.1040	−0.847627	−0.423813	+	0.905750i	$0.639309\pi$
$240$	9.36770	0.604682
$241$	24.8821	1.60279	0.801397	−	0.598133i	$-0.204090\pi$
$241$	24.8821	1.60279	0.801397	+	0.598133i	$0.204090\pi$
$242$	13.9473	0.896563
$243$	1.00000	0.0641500
$244$	−0.273656	−0.0175191
$245$	9.81970	0.627358
$246$	5.22717	0.333272
$247$	30.4665	1.93854
$248$	14.1357	0.897617
$249$	2.31992	0.147019
$250$	23.8737	1.50990
$251$	−21.8411	−1.37860	−0.689299	−	0.724477i	$-0.742081\pi$
$251$	−21.8411	−1.37860	−0.689299	+	0.724477i	$0.742081\pi$
$252$	−19.3678	−1.22006
$253$	6.92018	0.435068
$254$	−44.1072	−2.76753
$255$	1.28344	0.0803721
$256$	−19.5671	−1.22294
$257$	−6.78537	−0.423260	−0.211630	−	0.977350i	$-0.567877\pi$
$257$	−6.78537	−0.423260	−0.211630	+	0.977350i	$0.567877\pi$
$258$	8.45467	0.526364
$259$	3.31335	0.205882
$260$	23.6195	1.46482
$261$	−7.88097	−0.487820
$262$	20.6629	1.27656
$263$	−2.57516	−0.158791	−0.0793956	−	0.996843i	$-0.525299\pi$
$263$	−2.57516	−0.158791	−0.0793956	+	0.996843i	$0.525299\pi$
$264$	17.0232	1.04770
$265$	2.82865	0.173763
$266$	66.6664	4.08758
$267$	−7.16653	−0.438584
$268$	4.95069	0.302412
$269$	9.47293	0.577575	0.288787	−	0.957393i	$-0.406748\pi$
$269$	9.47293	0.577575	0.288787	+	0.957393i	$0.406748\pi$
$270$	−2.66854	−0.162402
$271$	5.88575	0.357534	0.178767	−	0.983891i	$-0.442789\pi$
$271$	5.88575	0.357534	0.178767	+	0.983891i	$0.442789\pi$
$272$	11.4106	0.691870
$273$	−19.6819	−1.19120
$274$	9.88190	0.596988
$275$	9.36794	0.564908
$276$	−13.8719	−0.834988
$277$	7.51482	0.451522	0.225761	−	0.974183i	$-0.427513\pi$
$277$	7.51482	0.451522	0.225761	+	0.974183i	$0.427513\pi$
$278$	−25.5822	−1.53432
$279$	−1.97118	−0.118011
$280$	29.9609	1.79051
$281$	3.51751	0.209837	0.104918	−	0.994481i	$-0.466542\pi$
$281$	3.51751	0.209837	0.104918	+	0.994481i	$0.466542\pi$
$282$	−17.6602	−1.05165
$283$	−7.39641	−0.439671	−0.219835	−	0.975537i	$-0.570552\pi$
$283$	−7.39641	−0.439671	−0.219835	+	0.975537i	$0.570552\pi$
$284$	−14.5041	−0.860660
$285$	6.46723	0.383086
$286$	29.8419	1.76459
$287$	8.18383	0.483076
$288$	−9.38267	−0.552879
$289$	−15.4367	−0.908039
$290$	21.0307	1.23496
$291$	−10.0203	−0.587403
$292$	4.26210	0.249420
$293$	−6.89255	−0.402667	−0.201334	−	0.979523i	$-0.564528\pi$
$293$	−6.89255	−0.402667	−0.201334	+	0.979523i	$0.564528\pi$
$294$	−24.8698	−1.45044
$295$	6.74149	0.392505
$296$	5.83774	0.339312
$297$	−2.37383	−0.137744
$298$	−30.5055	−1.76714
$299$	−14.0968	−0.815241
$300$	−18.7785	−1.08418
$301$	13.2369	0.762963
$302$	26.4653	1.52291
$303$	−17.6323	−1.01295
$304$	57.4979	3.29773
$305$	−0.0590321	−0.00338017
$306$	−3.25050	−0.185819
$307$	9.83725	0.561442	0.280721	−	0.959789i	$-0.409427\pi$
$307$	9.83725	0.561442	0.280721	+	0.959789i	$0.409427\pi$
$308$	45.9759	2.61972
$309$	7.03561	0.400242
$310$	5.26016	0.298757
$311$	4.49528	0.254904	0.127452	−	0.991845i	$-0.459320\pi$
$311$	4.49528	0.254904	0.127452	+	0.991845i	$0.459320\pi$
$312$	−34.6773	−1.96321
$313$	−4.03795	−0.228238	−0.114119	−	0.993467i	$-0.536405\pi$
$313$	−4.03795	−0.228238	−0.114119	+	0.993467i	$0.536405\pi$
$314$	−54.5391	−3.07782
$315$	−4.17796	−0.235401
$316$	73.5725	4.13878
$317$	33.1515	1.86197	0.930986	−	0.365055i	$-0.118950\pi$
$317$	33.1515	1.86197	0.930986	+	0.365055i	$0.118950\pi$
$318$	−7.16397	−0.401736
$319$	18.7081	1.04745
$320$	6.30263	0.352328
$321$	7.73840	0.431916
$322$	−30.8465	−1.71901
$323$	7.87761	0.438322
$324$	4.75846	0.264359
$325$	−19.0831	−1.05854
$326$	12.0686	0.668418
$327$	17.0334	0.941951
$328$	14.4190	0.796154
$329$	−27.6493	−1.52436
$330$	6.33466	0.348711
$331$	13.0377	0.716618	0.358309	−	0.933603i	$-0.383354\pi$
$331$	13.0377	0.716618	0.358309	+	0.933603i	$0.383354\pi$
$332$	11.0393	0.605858
$333$	−0.814054	−0.0446099
$334$	3.33039	0.182231
$335$	1.06794	0.0583480
$336$	−37.1447	−2.02641
$337$	5.81223	0.316613	0.158306	−	0.987390i	$-0.449397\pi$
$337$	5.81223	0.316613	0.158306	+	0.987390i	$0.449397\pi$
$338$	−26.9937	−1.46826
$339$	8.90159	0.483468
$340$	6.10721	0.331210
$341$	4.67923	0.253395
$342$	−16.3792	−0.885686
$343$	−10.4457	−0.564016
$344$	23.3219	1.25743
$345$	−2.99239	−0.161105
$346$	−8.27009	−0.444603
$347$	35.6214	1.91226	0.956128	−	0.292951i	$-0.0946372\pi$
$347$	35.6214	1.91226	0.956128	+	0.292951i	$0.0946372\pi$
$348$	−37.5013	−2.01028
$349$	9.83278	0.526337	0.263168	−	0.964750i	$-0.415233\pi$
$349$	9.83278	0.526337	0.263168	+	0.964750i	$0.415233\pi$
$350$	−41.7573	−2.23202
$351$	4.83564	0.258107
$352$	22.2728	1.18715
$353$	−17.2384	−0.917508	−0.458754	−	0.888563i	$-0.651704\pi$
$353$	−17.2384	−0.917508	−0.458754	+	0.888563i	$0.651704\pi$
$354$	−17.0738	−0.907462
$355$	−3.12877	−0.166058
$356$	−34.1017	−1.80738
$357$	−5.08909	−0.269343
$358$	−14.5141	−0.767095
$359$	6.84798	0.361423	0.180711	−	0.983536i	$-0.442160\pi$
$359$	6.84798	0.361423	0.180711	+	0.983536i	$0.442160\pi$
$360$	−7.36107	−0.387963
$361$	20.6952	1.08922
$362$	6.73964	0.354228
$363$	−5.36494	−0.281586
$364$	−93.6558	−4.90890
$365$	0.919404	0.0481238
$366$	0.149507	0.00781488
$367$	−10.6940	−0.558225	−0.279112	−	0.960258i	$-0.590040\pi$
$367$	−10.6940	−0.558225	−0.279112	+	0.960258i	$0.590040\pi$
$368$	−26.6043	−1.38684
$369$	−2.01068	−0.104672
$370$	2.17234	0.112934
$371$	−11.2162	−0.582314
$372$	−9.37977	−0.486318
$373$	−10.0366	−0.519674	−0.259837	−	0.965652i	$-0.583669\pi$
$373$	−10.0366	−0.519674	−0.259837	+	0.965652i	$0.583669\pi$
$374$	7.71613	0.398991
$375$	−9.18323	−0.474220
$376$	−48.7149	−2.51228
$377$	−38.1095	−1.96274
$378$	10.5813	0.544242
$379$	−2.48673	−0.127735	−0.0638673	−	0.997958i	$-0.520343\pi$
$379$	−2.48673	−0.127735	−0.0638673	+	0.997958i	$0.520343\pi$
$380$	30.7741	1.57868
$381$	16.9662	0.869207
$382$	53.9054	2.75804
$383$	−17.4184	−0.890041	−0.445021	−	0.895520i	$-0.646804\pi$
$383$	−17.4184	−0.890041	−0.445021	+	0.895520i	$0.646804\pi$
$384$	2.80302	0.143041
$385$	9.91775	0.505455
$386$	−16.7043	−0.850229
$387$	−3.25216	−0.165317
$388$	−47.6814	−2.42066
$389$	−28.8224	−1.46135	−0.730677	−	0.682723i	$-0.760796\pi$
$389$	−28.8224	−1.46135	−0.730677	+	0.682723i	$0.760796\pi$
$390$	−12.9041	−0.653424
$391$	−3.64497	−0.184334
$392$	−68.6025	−3.46495
$393$	−7.94817	−0.400932
$394$	28.1411	1.41773
$395$	15.8708	0.798546
$396$	−11.2958	−0.567634
$397$	37.2030	1.86716	0.933582	−	0.358363i	$-0.116665\pi$
$397$	37.2030	1.86716	0.933582	+	0.358363i	$0.116665\pi$
$398$	−24.4304	−1.22458
$399$	−25.6438	−1.28380
$400$	−36.0145	−1.80073
$401$	11.9679	0.597650	0.298825	−	0.954308i	$-0.403405\pi$
$401$	11.9679	0.597650	0.298825	+	0.954308i	$0.403405\pi$
$402$	−2.70472	−0.134899
$403$	−9.53189	−0.474817
$404$	−83.9026	−4.17431
$405$	1.02648	0.0510061
$406$	−83.3907	−4.13861
$407$	1.93243	0.0957868
$408$	−8.96638	−0.443902
$409$	14.4765	0.715816	0.357908	−	0.933757i	$-0.383490\pi$
$409$	14.4765	0.715816	0.357908	+	0.933757i	$0.383490\pi$
$410$	5.36558	0.264987
$411$	−3.80116	−0.187498
$412$	33.4787	1.64938
$413$	−26.7313	−1.31536
$414$	7.57865	0.372470
$415$	2.38135	0.116896
$416$	−45.3712	−2.22450
$417$	9.84042	0.481887
$418$	38.8814	1.90175
$419$	0.843042	0.0411853	0.0205926	−	0.999788i	$-0.493445\pi$
$419$	0.843042	0.0411853	0.0205926	+	0.999788i	$0.493445\pi$
$420$	−19.8807	−0.970077
$421$	−8.52732	−0.415596	−0.207798	−	0.978172i	$-0.566630\pi$
$421$	−8.52732	−0.415596	−0.207798	+	0.978172i	$0.566630\pi$
$422$	1.50647	0.0733338
$423$	6.79314	0.330294
$424$	−19.7616	−0.959706
$425$	−4.93424	−0.239346
$426$	7.92406	0.383922
$427$	0.234074	0.0113276
$428$	36.8229	1.77990
$429$	−11.4790	−0.554210
$430$	8.67853	0.418516
$431$	−15.9995	−0.770670	−0.385335	−	0.922777i	$-0.625914\pi$
$431$	−15.9995	−0.770670	−0.385335	+	0.922777i	$0.625914\pi$
$432$	9.12606	0.439078
$433$	38.0094	1.82662	0.913309	−	0.407268i	$-0.133518\pi$
$433$	38.0094	1.82662	0.913309	+	0.407268i	$0.133518\pi$
$434$	−20.8576	−1.00119
$435$	−8.08964	−0.387869
$436$	81.0530	3.88173
$437$	−18.3669	−0.878610
$438$	−2.32852	−0.111261
$439$	−6.54202	−0.312233	−0.156117	−	0.987739i	$-0.549898\pi$
$439$	−6.54202	−0.312233	−0.156117	+	0.987739i	$0.549898\pi$
$440$	17.4739	0.833037
$441$	9.56640	0.455543
$442$	−15.7182	−0.747640
$443$	21.5203	1.02246	0.511229	−	0.859445i	$-0.329190\pi$
$443$	21.5203	1.02246	0.511229	+	0.859445i	$0.329190\pi$
$444$	−3.87365	−0.183835
$445$	−7.35628	−0.348721
$446$	14.9985	0.710200
$447$	11.7342	0.555010
$448$	−24.9911	−1.18072
$449$	24.3737	1.15027	0.575134	−	0.818059i	$-0.304950\pi$
$449$	24.3737	1.15027	0.575134	+	0.818059i	$0.304950\pi$
$450$	10.2593	0.483629
$451$	4.77301	0.224752
$452$	42.3579	1.99235
$453$	−10.1801	−0.478304
$454$	−53.6457	−2.51772
$455$	−20.2031	−0.947135
$456$	−45.1815	−2.11582
$457$	14.7107	0.688138	0.344069	−	0.938944i	$-0.388195\pi$
$457$	14.7107	0.688138	0.344069	+	0.938944i	$0.388195\pi$
$458$	23.5734	1.10151
$459$	1.25033	0.0583606
$460$	−14.2392	−0.663904
$461$	11.1049	0.517208	0.258604	−	0.965983i	$-0.416738\pi$
$461$	11.1049	0.517208	0.258604	+	0.965983i	$0.416738\pi$
$462$	−25.1181	−1.16860
$463$	31.5632	1.46686	0.733432	−	0.679763i	$-0.237917\pi$
$463$	31.5632	1.46686	0.733432	+	0.679763i	$0.237917\pi$
$464$	−71.9222	−3.33890
$465$	−2.02337	−0.0938315
$466$	10.5409	0.488300
$467$	0.242139	0.0112049	0.00560243	−	0.999984i	$-0.498217\pi$
$467$	0.242139	0.0112049	0.00560243	+	0.999984i	$0.498217\pi$
$468$	23.0102	1.06365
$469$	−4.23461	−0.195536
$470$	−18.1278	−0.836172
$471$	20.9789	0.966659
$472$	−47.0975	−2.16784
$473$	7.72008	0.354970
$474$	−40.1950	−1.84622
$475$	−24.8636	−1.14082
$476$	−24.2162	−1.10995
$477$	2.75569	0.126174
$478$	34.0665	1.55817
$479$	32.3970	1.48026	0.740129	−	0.672465i	$-0.234765\pi$
$479$	32.3970	1.48026	0.740129	+	0.672465i	$0.234765\pi$
$480$	−9.63110	−0.439598
$481$	−3.93647	−0.179488
$482$	−64.6860	−2.94637
$483$	11.8654	0.539894
$484$	−25.5289	−1.16040
$485$	−10.2857	−0.467048
$486$	−2.59970	−0.117925
$487$	16.7196	0.757636	0.378818	−	0.925471i	$-0.376331\pi$
$487$	16.7196	0.757636	0.378818	+	0.925471i	$0.376331\pi$
$488$	0.412411	0.0186690
$489$	−4.64229	−0.209932
$490$	−25.5283	−1.15325
$491$	9.07243	0.409433	0.204716	−	0.978821i	$-0.434373\pi$
$491$	9.07243	0.409433	0.204716	+	0.978821i	$0.434373\pi$
$492$	−9.56774	−0.431347
$493$	−9.85384	−0.443795
$494$	−79.2039	−3.56355
$495$	−2.43668	−0.109521
$496$	−17.9891	−0.807733
$497$	12.4062	0.556493
$498$	−6.03110	−0.270260
$499$	41.4678	1.85635	0.928177	−	0.372138i	$-0.121375\pi$
$499$	41.4678	1.85635	0.928177	+	0.372138i	$0.121375\pi$
$500$	−43.6981	−1.95424
$501$	−1.28107	−0.0572338
$502$	56.7804	2.53423
$503$	7.89599	0.352065	0.176032	−	0.984384i	$-0.443674\pi$
$503$	7.89599	0.352065	0.176032	+	0.984384i	$0.443674\pi$
$504$	29.1881	1.30014
$505$	−18.0992	−0.805402
$506$	−17.9904	−0.799772
$507$	10.3834	0.461142
$508$	80.7333	3.58196
$509$	−6.09805	−0.270291	−0.135146	−	0.990826i	$-0.543150\pi$
$509$	−6.09805	−0.270291	−0.135146	+	0.990826i	$0.543150\pi$
$510$	−3.33657	−0.147746
$511$	−3.64561	−0.161272
$512$	45.2627	2.00035
$513$	6.30041	0.278170
$514$	17.6400	0.778066
$515$	7.22190	0.318235
$516$	−15.4753	−0.681262
$517$	−16.1258	−0.709210
$518$	−8.61373	−0.378466
$519$	3.18117	0.139638
$520$	−35.5955	−1.56096
$521$	−6.33909	−0.277721	−0.138860	−	0.990312i	$-0.544344\pi$
$521$	−6.33909	−0.277721	−0.138860	+	0.990312i	$0.544344\pi$
$522$	20.4882	0.896744
$523$	−22.7979	−0.996883	−0.498442	−	0.866923i	$-0.666094\pi$
$523$	−22.7979	−0.996883	−0.498442	+	0.866923i	$0.666094\pi$
$524$	−37.8211	−1.65222
$525$	16.0623	0.701018
$526$	6.69466	0.291901
$527$	−2.46463	−0.107361
$528$	−21.6637	−0.942792
$529$	−14.5016	−0.630506
$530$	−7.35366	−0.319423
$531$	6.56759	0.285009
$532$	−122.025	−5.29047
$533$	−9.72291	−0.421146
$534$	18.6309	0.806236
$535$	7.94330	0.343419
$536$	−7.46089	−0.322261
$537$	5.58298	0.240924
$538$	−24.6268	−1.06174
$539$	−22.7090	−0.978146
$540$	4.88446	0.210194
$541$	19.9653	0.858376	0.429188	−	0.903215i	$-0.358800\pi$
$541$	19.9653	0.858376	0.429188	+	0.903215i	$0.358800\pi$
$542$	−15.3012	−0.657244
$543$	−2.59246	−0.111253
$544$	−11.7315	−0.502982
$545$	17.4844	0.748951
$546$	51.1672	2.18975
$547$	−5.36865	−0.229547	−0.114773	−	0.993392i	$-0.536614\pi$
$547$	−5.36865	−0.229547	−0.114773	+	0.993392i	$0.536614\pi$
$548$	−18.0877	−0.772668
$549$	−0.0575094	−0.00245444
$550$	−24.3539	−1.03845
$551$	−49.6533	−2.11530
$552$	20.9054	0.889795
$553$	−62.9307	−2.67609
$554$	−19.5363	−0.830018
$555$	−0.835609	−0.0354696
$556$	46.8253	1.98583
$557$	−15.8883	−0.673208	−0.336604	−	0.941646i	$-0.609278\pi$
$557$	−15.8883	−0.673208	−0.336604	+	0.941646i	$0.609278\pi$
$558$	5.12447	0.216936
$559$	−15.7263	−0.665151
$560$	−38.1283	−1.61121
$561$	−2.96808	−0.125312
$562$	−9.14448	−0.385736
$563$	7.67544	0.323481	0.161741	−	0.986833i	$-0.448289\pi$
$563$	7.67544	0.323481	0.161741	+	0.986833i	$0.448289\pi$
$564$	32.3249	1.36112
$565$	9.13729	0.384409
$566$	19.2285	0.808233
$567$	−4.07018	−0.170932
$568$	21.8582	0.917152
$569$	13.8353	0.580006	0.290003	−	0.957026i	$-0.406344\pi$
$569$	13.8353	0.580006	0.290003	+	0.957026i	$0.406344\pi$
$570$	−16.8129	−0.704215
$571$	9.21485	0.385630	0.192815	−	0.981235i	$-0.438238\pi$
$571$	9.21485	0.385630	0.192815	+	0.981235i	$0.438238\pi$
$572$	−54.6223	−2.28387
$573$	−20.7352	−0.866225
$574$	−21.2755	−0.888024
$575$	11.5044	0.479765
$576$	6.14005	0.255835
$577$	−17.4636	−0.727018	−0.363509	−	0.931591i	$-0.618421\pi$
$577$	−17.4636	−0.727018	−0.363509	+	0.931591i	$0.618421\pi$
$578$	40.1308	1.66922
$579$	6.42548	0.267034
$580$	−38.4943	−1.59839
$581$	−9.44250	−0.391741
$582$	26.0499	1.07980
$583$	−6.54153	−0.270922
$584$	−6.42315	−0.265792
$585$	4.96367	0.205223
$586$	17.9186	0.740211
$587$	29.2954	1.20915	0.604576	−	0.796548i	$-0.293343\pi$
$587$	29.2954	1.20915	0.604576	+	0.796548i	$0.293343\pi$
$588$	45.5214	1.87727
$589$	−12.4192	−0.511725
$590$	−17.5259	−0.721529
$591$	−10.8247	−0.445269
$592$	−7.42911	−0.305334
$593$	25.5900	1.05086	0.525429	−	0.850838i	$-0.323905\pi$
$593$	25.5900	1.05086	0.525429	+	0.850838i	$0.323905\pi$
$594$	6.17125	0.253210
$595$	−5.22384	−0.214156
$596$	55.8369	2.28717
$597$	9.39737	0.384609
$598$	36.6476	1.49863
$599$	12.8508	0.525070	0.262535	−	0.964923i	$-0.415442\pi$
$599$	12.8508	0.525070	0.262535	+	0.964923i	$0.415442\pi$
$600$	28.3000	1.15534
$601$	−6.57908	−0.268366	−0.134183	−	0.990957i	$-0.542841\pi$
$601$	−6.57908	−0.268366	−0.134183	+	0.990957i	$0.542841\pi$
$602$	−34.4120	−1.40253
$603$	1.04040	0.0423682
$604$	−48.4417	−1.97107
$605$	−5.50699	−0.223891
$606$	45.8387	1.86207
$607$	−3.67511	−0.149168	−0.0745841	−	0.997215i	$-0.523763\pi$
$607$	−3.67511	−0.149168	−0.0745841	+	0.997215i	$0.523763\pi$
$608$	−59.1147	−2.39742
$609$	32.0770	1.29983
$610$	0.153466	0.00621366
$611$	32.8492	1.32893
$612$	5.94967	0.240501
$613$	−9.58731	−0.387228	−0.193614	−	0.981078i	$-0.562021\pi$
$613$	−9.58731	−0.387228	−0.193614	+	0.981078i	$0.562021\pi$
$614$	−25.5739	−1.03208
$615$	−2.06392	−0.0832252
$616$	−69.2875	−2.79167
$617$	−48.5144	−1.95312	−0.976558	−	0.215254i	$-0.930942\pi$
$617$	−48.5144	−1.95312	−0.976558	+	0.215254i	$0.930942\pi$
$618$	−18.2905	−0.735752
$619$	32.7471	1.31622	0.658109	−	0.752923i	$-0.271357\pi$
$619$	32.7471	1.31622	0.658109	+	0.752923i	$0.271357\pi$
$620$	−9.62813	−0.386675
$621$	−2.91520	−0.116983
$622$	−11.6864	−0.468582
$623$	29.1691	1.16863
$624$	44.1303	1.76663
$625$	10.3053	0.412213
$626$	10.4975	0.419563
$627$	−14.9561	−0.597289
$628$	99.8276	3.98355
$629$	−1.01784	−0.0405839
$630$	10.8615	0.432731
$631$	−29.9006	−1.19032	−0.595161	−	0.803606i	$-0.702912\pi$
$631$	−29.9006	−1.19032	−0.595161	+	0.803606i	$0.702912\pi$
$632$	−110.877	−4.41044
$633$	−0.579477	−0.0230322
$634$	−86.1840	−3.42280
$635$	17.4155	0.691112
$636$	13.1128	0.519958
$637$	46.2596	1.83287
$638$	−48.6355	−1.92550
$639$	−3.04806	−0.120579
$640$	2.87724	0.113733
$641$	7.08309	0.279765	0.139883	−	0.990168i	$-0.455327\pi$
$641$	7.08309	0.279765	0.139883	+	0.990168i	$0.455327\pi$
$642$	−20.1176	−0.793977
$643$	2.45035	0.0966322	0.0483161	−	0.998832i	$-0.484615\pi$
$643$	2.45035	0.0966322	0.0483161	+	0.998832i	$0.484615\pi$
$644$	56.4610	2.22488
$645$	−3.33828	−0.131444
$646$	−20.4795	−0.805754
$647$	−10.9253	−0.429516	−0.214758	−	0.976667i	$-0.568896\pi$
$647$	−10.9253	−0.429516	−0.214758	+	0.976667i	$0.568896\pi$
$648$	−7.17119	−0.281711
$649$	−15.5903	−0.611974
$650$	49.6104	1.94588
$651$	8.02305	0.314448
$652$	−22.0902	−0.865119
$653$	23.1792	0.907073	0.453536	−	0.891238i	$-0.350162\pi$
$653$	23.1792	0.907073	0.453536	+	0.891238i	$0.350162\pi$
$654$	−44.2819	−1.73156
$655$	−8.15863	−0.318784
$656$	−18.3496	−0.716430
$657$	0.895688	0.0349441
$658$	71.8801	2.80218
$659$	−45.1554	−1.75900	−0.879502	−	0.475895i	$-0.842124\pi$
$659$	−45.1554	−1.75900	−0.879502	+	0.475895i	$0.842124\pi$
$660$	−11.5949	−0.451330
$661$	−0.573851	−0.0223202	−0.0111601	−	0.999938i	$-0.503552\pi$
$661$	−0.573851	−0.0223202	−0.0111601	+	0.999938i	$0.503552\pi$
$662$	−33.8942	−1.31734
$663$	6.04616	0.234813
$664$	−16.6366	−0.645625
$665$	−26.3228	−1.02076
$666$	2.11630	0.0820050
$667$	22.9746	0.889579
$668$	−6.09591	−0.235858
$669$	−5.76932	−0.223055
$670$	−2.77634	−0.107259
$671$	0.136517	0.00527020
$672$	38.1892	1.47318
$673$	32.1480	1.23921	0.619607	−	0.784912i	$-0.287292\pi$
$673$	32.1480	1.23921	0.619607	+	0.784912i	$0.287292\pi$
$674$	−15.1101	−0.582019
$675$	−3.94634	−0.151895
$676$	49.4089	1.90034
$677$	35.7059	1.37229	0.686145	−	0.727465i	$-0.259301\pi$
$677$	35.7059	1.37229	0.686145	+	0.727465i	$0.259301\pi$
$678$	−23.1415	−0.888744
$679$	40.7846	1.56517
$680$	−9.20380	−0.352950
$681$	20.6353	0.790747
$682$	−12.1646	−0.465808
$683$	10.9963	0.420761	0.210380	−	0.977620i	$-0.432530\pi$
$683$	10.9963	0.420761	0.210380	+	0.977620i	$0.432530\pi$
$684$	29.9803	1.14632
$685$	−3.90181	−0.149081
$686$	27.1558	1.03681
$687$	−9.06771	−0.345955
$688$	−29.6794	−1.13152
$689$	13.3255	0.507661
$690$	7.77932	0.296154
$691$	27.2872	1.03806	0.519028	−	0.854758i	$-0.326294\pi$
$691$	27.2872	1.03806	0.519028	+	0.854758i	$0.326294\pi$
$692$	15.1375	0.575440
$693$	9.66192	0.367026
$694$	−92.6050	−3.51524
$695$	10.1010	0.383152
$696$	56.5160	2.14223
$697$	−2.51402	−0.0952253
$698$	−25.5623	−0.967548
$699$	−4.05467	−0.153362
$700$	76.4321	2.88886
$701$	−23.3289	−0.881120	−0.440560	−	0.897723i	$-0.645220\pi$
$701$	−23.3289	−0.881120	−0.440560	+	0.897723i	$0.645220\pi$
$702$	−12.5712	−0.474470
$703$	−5.12888	−0.193439
$704$	−14.5754	−0.549332
$705$	6.97301	0.262619
$706$	44.8148	1.68663
$707$	71.7667	2.69906
$708$	31.2516	1.17451
$709$	16.6842	0.626588	0.313294	−	0.949656i	$-0.398567\pi$
$709$	16.6842	0.626588	0.313294	+	0.949656i	$0.398567\pi$
$710$	8.13388	0.305259
$711$	15.4614	0.579847
$712$	51.3926	1.92602
$713$	5.74636	0.215203
$714$	13.2301	0.495125
$715$	−11.7829	−0.440656
$716$	26.5664	0.992834
$717$	−13.1040	−0.489378
$718$	−17.8027	−0.664392
$719$	20.1339	0.750866	0.375433	−	0.926849i	$-0.377494\pi$
$719$	20.1339	0.750866	0.375433	+	0.926849i	$0.377494\pi$
$720$	9.36770	0.349114
$721$	−28.6362	−1.06647
$722$	−53.8013	−2.00228
$723$	24.8821	0.925374
$724$	−12.3361	−0.458469
$725$	31.1010	1.15506
$726$	13.9473	0.517631
$727$	15.7036	0.582414	0.291207	−	0.956660i	$-0.405943\pi$
$727$	15.7036	0.582414	0.291207	+	0.956660i	$0.405943\pi$
$728$	141.143	5.23110
$729$	1.00000	0.0370370
$730$	−2.39018	−0.0884645
$731$	−4.06629	−0.150397
$732$	−0.273656	−0.0101146
$733$	44.7785	1.65393	0.826965	−	0.562253i	$-0.190065\pi$
$733$	44.7785	1.65393	0.826965	+	0.562253i	$0.190065\pi$
$734$	27.8014	1.02617
$735$	9.81970	0.362205
$736$	27.3523	1.00822
$737$	−2.46972	−0.0909734
$738$	5.22717	0.192415
$739$	16.7201	0.615058	0.307529	−	0.951539i	$-0.400498\pi$
$739$	16.7201	0.615058	0.307529	+	0.951539i	$0.400498\pi$
$740$	−3.97622	−0.146169
$741$	30.4665	1.11921
$742$	29.1587	1.07045
$743$	23.2226	0.851956	0.425978	−	0.904734i	$-0.359930\pi$
$743$	23.2226	0.851956	0.425978	+	0.904734i	$0.359930\pi$
$744$	14.1357	0.518239
$745$	12.0449	0.441292
$746$	26.0921	0.955301
$747$	2.31992	0.0848814
$748$	−14.1235	−0.516406
$749$	−31.4967	−1.15087
$750$	23.8737	0.871743
$751$	−37.9132	−1.38347	−0.691735	−	0.722151i	$-0.743154\pi$
$751$	−37.9132	−1.38347	−0.691735	+	0.722151i	$0.743154\pi$
$752$	61.9946	2.26071
$753$	−21.8411	−0.795934
$754$	99.0734	3.60804
$755$	−10.4497	−0.380302
$756$	−19.3678	−0.704401
$757$	−50.1984	−1.82449	−0.912245	−	0.409645i	$-0.865653\pi$
$757$	−50.1984	−1.82449	−0.912245	+	0.409645i	$0.865653\pi$
$758$	6.46476	0.234811
$759$	6.92018	0.251187
$760$	−46.3778	−1.68230
$761$	23.5439	0.853466	0.426733	−	0.904378i	$-0.359664\pi$
$761$	23.5439	0.853466	0.426733	+	0.904378i	$0.359664\pi$
$762$	−44.1072	−1.59784
$763$	−69.3292	−2.50989
$764$	−98.6677	−3.56967
$765$	1.28344	0.0464029
$766$	45.2828	1.63613
$767$	31.7585	1.14673
$768$	−19.5671	−0.706068
$769$	5.44001	0.196172	0.0980859	−	0.995178i	$-0.468728\pi$
$769$	5.44001	0.196172	0.0980859	+	0.995178i	$0.468728\pi$
$770$	−25.7832	−0.929163
$771$	−6.78537	−0.244369
$772$	30.5754	1.10043
$773$	−7.70465	−0.277117	−0.138559	−	0.990354i	$-0.544247\pi$
$773$	−7.70465	−0.277117	−0.138559	+	0.990354i	$0.544247\pi$
$774$	8.45467	0.303897
$775$	7.77893	0.279428
$776$	71.8578	2.57954
$777$	3.31335	0.118866
$778$	74.9298	2.68636
$779$	−12.6681	−0.453882
$780$	23.6195	0.845713
$781$	7.23558	0.258909
$782$	9.47584	0.338855
$783$	−7.88097	−0.281643
$784$	87.3035	3.11798
$785$	21.5344	0.768597
$786$	20.6629	0.737021
$787$	11.1301	0.396744	0.198372	−	0.980127i	$-0.436435\pi$
$787$	11.1301	0.396744	0.198372	+	0.980127i	$0.436435\pi$
$788$	−51.5090	−1.83493
$789$	−2.57516	−0.0916782
$790$	−41.2593	−1.46794
$791$	−36.2311	−1.28823
$792$	17.0232	0.604893
$793$	−0.278095	−0.00987543
$794$	−96.7168	−3.43235
$795$	2.82865	0.100322
$796$	44.7170	1.58495
$797$	−22.6263	−0.801465	−0.400733	−	0.916195i	$-0.631244\pi$
$797$	−22.6263	−0.801465	−0.400733	+	0.916195i	$0.631244\pi$
$798$	66.6664	2.35996
$799$	8.49369	0.300485
$800$	37.0272	1.30911
$801$	−7.16653	−0.253217
$802$	−31.1131	−1.09864
$803$	−2.12621	−0.0750323
$804$	4.95069	0.174597
$805$	12.1796	0.429273
$806$	24.7801	0.872841
$807$	9.47293	0.333463
$808$	126.445	4.44830
$809$	−7.66768	−0.269581	−0.134791	−	0.990874i	$-0.543036\pi$
$809$	−7.66768	−0.269581	−0.134791	+	0.990874i	$0.543036\pi$
$810$	−2.66854	−0.0937629
$811$	38.3699	1.34735	0.673674	−	0.739028i	$-0.264715\pi$
$811$	38.3699	1.34735	0.673674	+	0.739028i	$0.264715\pi$
$812$	152.637	5.35652
$813$	5.88575	0.206422
$814$	−5.02374	−0.176082
$815$	−4.76521	−0.166918
$816$	11.4106	0.399451
$817$	−20.4900	−0.716853
$818$	−37.6346	−1.31586
$819$	−19.6819	−0.687742
$820$	−9.82108	−0.342967
$821$	−46.7528	−1.63168	−0.815842	−	0.578275i	$-0.803726\pi$
$821$	−46.7528	−1.63168	−0.815842	+	0.578275i	$0.803726\pi$
$822$	9.88190	0.344671
$823$	−47.1983	−1.64523	−0.822614	−	0.568600i	$-0.807485\pi$
$823$	−47.1983	−1.64523	−0.822614	+	0.568600i	$0.807485\pi$
$824$	−50.4537	−1.75764
$825$	9.36794	0.326150
$826$	69.4935	2.41799
$827$	31.2545	1.08683	0.543413	−	0.839465i	$-0.317132\pi$
$827$	31.2545	1.08683	0.543413	+	0.839465i	$0.317132\pi$
$828$	−13.8719	−0.482081
$829$	−4.85338	−0.168565	−0.0842825	−	0.996442i	$-0.526860\pi$
$829$	−4.85338	−0.168565	−0.0842825	+	0.996442i	$0.526860\pi$
$830$	−6.19080	−0.214886
$831$	7.51482	0.260686
$832$	29.6910	1.02935
$833$	11.9612	0.414431
$834$	−25.5822	−0.885839
$835$	−1.31499	−0.0455070
$836$	−71.1681	−2.46140
$837$	−1.97118	−0.0681338
$838$	−2.19166	−0.0757096
$839$	28.1752	0.972716	0.486358	−	0.873760i	$-0.338325\pi$
$839$	28.1752	0.972716	0.486358	+	0.873760i	$0.338325\pi$
$840$	29.9609	1.03375
$841$	33.1097	1.14171
$842$	22.1685	0.763978
$843$	3.51751	0.121149
$844$	−2.75742	−0.0949144
$845$	10.6583	0.366657
$846$	−17.6602	−0.607169
$847$	21.8363	0.750303
$848$	25.1486	0.863605
$849$	−7.39641	−0.253844
$850$	12.8276	0.439982
$851$	2.37313	0.0813498
$852$	−14.5041	−0.496902
$853$	−3.61354	−0.123725	−0.0618626	−	0.998085i	$-0.519704\pi$
$853$	−3.61354	−0.123725	−0.0618626	+	0.998085i	$0.519704\pi$
$854$	−0.608523	−0.0208232
$855$	6.46723	0.221175
$856$	−55.4936	−1.89673
$857$	−28.1944	−0.963103	−0.481551	−	0.876418i	$-0.659927\pi$
$857$	−28.1944	−0.963103	−0.481551	+	0.876418i	$0.659927\pi$
$858$	29.8419	1.01879
$859$	−31.4098	−1.07169	−0.535843	−	0.844317i	$-0.680006\pi$
$859$	−31.4098	−1.07169	−0.535843	+	0.844317i	$0.680006\pi$
$860$	−15.8851	−0.541676
$861$	8.18383	0.278904
$862$	41.5940	1.41670
$863$	33.4840	1.13981	0.569904	−	0.821711i	$-0.306980\pi$
$863$	33.4840	1.13981	0.569904	+	0.821711i	$0.306980\pi$
$864$	−9.38267	−0.319205
$865$	3.26540	0.111027
$866$	−98.8133	−3.35781
$867$	−15.4367	−0.524257
$868$	38.1774	1.29582
$869$	−36.7027	−1.24505
$870$	21.0307	0.713007
$871$	5.03098	0.170468
$872$	−122.150	−4.13652
$873$	−10.0203	−0.339137
$874$	47.7486	1.61512
$875$	37.3774	1.26359
$876$	4.26210	0.144003
$877$	−48.3169	−1.63155	−0.815773	−	0.578372i	$-0.803688\pi$
$877$	−48.3169	−1.63155	−0.815773	+	0.578372i	$0.803688\pi$
$878$	17.0073	0.573969
$879$	−6.89255	−0.232480
$880$	−22.2373	−0.749620
$881$	−53.5836	−1.80528	−0.902639	−	0.430399i	$-0.858373\pi$
$881$	−53.5836	−1.80528	−0.902639	+	0.430399i	$0.858373\pi$
$882$	−24.8698	−0.837410
$883$	3.09441	0.104135	0.0520676	−	0.998644i	$-0.483419\pi$
$883$	3.09441	0.104135	0.0520676	+	0.998644i	$0.483419\pi$
$884$	28.7704	0.967654
$885$	6.74149	0.226613
$886$	−55.9463	−1.87955
$887$	37.5967	1.26237	0.631187	−	0.775631i	$-0.282568\pi$
$887$	37.5967	1.26237	0.631187	+	0.775631i	$0.282568\pi$
$888$	5.83774	0.195902
$889$	−69.0558	−2.31606
$890$	19.1242	0.641043
$891$	−2.37383	−0.0795263
$892$	−27.4531	−0.919197
$893$	42.7996	1.43223
$894$	−30.5055	−1.02026
$895$	5.73081	0.191560
$896$	−11.4088	−0.381141
$897$	−14.0968	−0.470679
$898$	−63.3645	−2.11450
$899$	15.5348	0.518114
$900$	−18.7785	−0.625951
$901$	3.44553	0.114787
$902$	−12.4084	−0.413155
$903$	13.2369	0.440497
$904$	−63.8350	−2.12312
$905$	−2.66111	−0.0884582
$906$	26.4653	0.879251
$907$	34.2699	1.13791	0.568956	−	0.822368i	$-0.307347\pi$
$907$	34.2699	1.13791	0.568956	+	0.822368i	$0.307347\pi$
$908$	98.1924	3.25863
$909$	−17.6323	−0.584826
$910$	52.5220	1.74109
$911$	35.6531	1.18124	0.590620	−	0.806950i	$-0.298883\pi$
$911$	35.6531	1.18124	0.590620	+	0.806950i	$0.298883\pi$
$912$	57.4979	1.90395
$913$	−5.50709	−0.182258
$914$	−38.2435	−1.26498
$915$	−0.0590321	−0.00195154
$916$	−43.1484	−1.42566
$917$	32.3505	1.06831
$918$	−3.25050	−0.107282
$919$	12.2073	0.402682	0.201341	−	0.979521i	$-0.435470\pi$
$919$	12.2073	0.402682	0.201341	+	0.979521i	$0.435470\pi$
$920$	21.4590	0.707482
$921$	9.83725	0.324148
$922$	−28.8695	−0.950767
$923$	−14.7393	−0.485151
$924$	45.9759	1.51250
$925$	3.21254	0.105628
$926$	−82.0549	−2.69649
$927$	7.03561	0.231080
$928$	73.9445	2.42735
$929$	3.15561	0.103532	0.0517662	−	0.998659i	$-0.483515\pi$
$929$	3.15561	0.103532	0.0517662	+	0.998659i	$0.483515\pi$
$930$	5.26016	0.172487
$931$	60.2722	1.97534
$932$	−19.2940	−0.631996
$933$	4.49528	0.147169
$934$	−0.629490	−0.0205976
$935$	−3.04667	−0.0996367
$936$	−34.6773	−1.13346
$937$	22.8448	0.746305	0.373153	−	0.927770i	$-0.378277\pi$
$937$	22.8448	0.746305	0.373153	+	0.927770i	$0.378277\pi$
$938$	11.0087	0.359448
$939$	−4.03795	−0.131773
$940$	33.1808	1.08224
$941$	1.51666	0.0494418	0.0247209	−	0.999694i	$-0.492130\pi$
$941$	1.51666	0.0494418	0.0247209	+	0.999694i	$0.492130\pi$
$942$	−54.5391	−1.77698
$943$	5.86152	0.190878
$944$	59.9362	1.95076
$945$	−4.17796	−0.135909
$946$	−20.0699	−0.652530
$947$	20.7148	0.673141	0.336570	−	0.941658i	$-0.390733\pi$
$947$	20.7148	0.673141	0.336570	+	0.941658i	$0.390733\pi$
$948$	73.5725	2.38952
$949$	4.33122	0.140597
$950$	64.6380	2.09713
$951$	33.1515	1.07501
$952$	36.4948	1.18280
$953$	59.7534	1.93560	0.967800	−	0.251719i	$-0.0809958\pi$
$953$	59.7534	1.93560	0.967800	+	0.251719i	$0.0809958\pi$
$954$	−7.16397	−0.231942
$955$	−21.2842	−0.688741
$956$	−62.3549	−2.01670
$957$	18.7081	0.604746
$958$	−84.2227	−2.72111
$959$	15.4714	0.499599
$960$	6.30263	0.203416
$961$	−27.1145	−0.874660
$962$	10.2337	0.329946
$963$	7.73840	0.249367
$964$	118.400	3.81342
$965$	6.59561	0.212320
$966$	−30.8465	−0.992470
$967$	14.3287	0.460780	0.230390	−	0.973098i	$-0.426000\pi$
$967$	14.3287	0.460780	0.230390	+	0.973098i	$0.426000\pi$
$968$	38.4730	1.23657
$969$	7.87761	0.253065
$970$	26.7397	0.858559
$971$	−34.0186	−1.09171	−0.545855	−	0.837880i	$-0.683795\pi$
$971$	−34.0186	−1.09171	−0.545855	+	0.837880i	$0.683795\pi$
$972$	4.75846	0.152628
$973$	−40.0523	−1.28402
$974$	−43.4660	−1.39274
$975$	−19.0831	−0.611147
$976$	−0.524834	−0.0167995
$977$	22.5677	0.722004	0.361002	−	0.932565i	$-0.382435\pi$
$977$	22.5677	0.722004	0.361002	+	0.932565i	$0.382435\pi$
$978$	12.0686	0.385911
$979$	17.0121	0.543709
$980$	46.7267	1.49263
$981$	17.0334	0.543836
$982$	−23.5856	−0.752648
$983$	15.6439	0.498961	0.249481	−	0.968380i	$-0.419740\pi$
$983$	15.6439	0.498961	0.249481	+	0.968380i	$0.419740\pi$
$984$	14.4190	0.459660
$985$	−11.1113	−0.354037
$986$	25.6171	0.815814
$987$	−27.6493	−0.880088
$988$	144.974	4.61223
$989$	9.48070	0.301469
$990$	6.33466	0.201329
$991$	−8.79260	−0.279306	−0.139653	−	0.990200i	$-0.544599\pi$
$991$	−8.79260	−0.279306	−0.139653	+	0.990200i	$0.544599\pi$
$992$	18.4949	0.587213
$993$	13.0377	0.413739
$994$	−32.2524	−1.02298
$995$	9.64619	0.305805
$996$	11.0393	0.349792
$997$	−45.2410	−1.43280	−0.716399	−	0.697691i	$-0.754211\pi$
$997$	−45.2410	−1.43280	−0.716399	+	0.697691i	$0.754211\pi$
$998$	−107.804	−3.41248
$999$	−0.814054	−0.0257555

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.6	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.6	✓	129	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59970 q^{2} +1.00000 q^{3} +4.75846 q^{4} +1.02648 q^{5} -2.59970 q^{6} -4.07018 q^{7} -7.17119 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.59970 q^{2} +1.00000 q^{3} +4.75846 q^{4} +1.02648 q^{5} -2.59970 q^{6} -4.07018 q^{7} -7.17119 q^{8} +1.00000 q^{9} -2.66854 q^{10} -2.37383 q^{11} +4.75846 q^{12} +4.83564 q^{13} +10.5813 q^{14} +1.02648 q^{15} +9.12606 q^{16} +1.25033 q^{17} -2.59970 q^{18} +6.30041 q^{19} +4.88446 q^{20} -4.07018 q^{21} +6.17125 q^{22} -2.91520 q^{23} -7.17119 q^{24} -3.94634 q^{25} -12.5712 q^{26} +1.00000 q^{27} -19.3678 q^{28} -7.88097 q^{29} -2.66854 q^{30} -1.97118 q^{31} -9.38267 q^{32} -2.37383 q^{33} -3.25050 q^{34} -4.17796 q^{35} +4.75846 q^{36} -0.814054 q^{37} -16.3792 q^{38} +4.83564 q^{39} -7.36107 q^{40} -2.01068 q^{41} +10.5813 q^{42} -3.25216 q^{43} -11.2958 q^{44} +1.02648 q^{45} +7.57865 q^{46} +6.79314 q^{47} +9.12606 q^{48} +9.56640 q^{49} +10.2593 q^{50} +1.25033 q^{51} +23.0102 q^{52} +2.75569 q^{53} -2.59970 q^{54} -2.43668 q^{55} +29.1881 q^{56} +6.30041 q^{57} +20.4882 q^{58} +6.56759 q^{59} +4.88446 q^{60} -0.0575094 q^{61} +5.12447 q^{62} -4.07018 q^{63} +6.14005 q^{64} +4.96367 q^{65} +6.17125 q^{66} +1.04040 q^{67} +5.94967 q^{68} -2.91520 q^{69} +10.8615 q^{70} -3.04806 q^{71} -7.17119 q^{72} +0.895688 q^{73} +2.11630 q^{74} -3.94634 q^{75} +29.9803 q^{76} +9.66192 q^{77} -12.5712 q^{78} +15.4614 q^{79} +9.36770 q^{80} +1.00000 q^{81} +5.22717 q^{82} +2.31992 q^{83} -19.3678 q^{84} +1.28344 q^{85} +8.45467 q^{86} -7.88097 q^{87} +17.0232 q^{88} -7.16653 q^{89} -2.66854 q^{90} -19.6819 q^{91} -13.8719 q^{92} -1.97118 q^{93} -17.6602 q^{94} +6.46723 q^{95} -9.38267 q^{96} -10.0203 q^{97} -24.8698 q^{98} -2.37383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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