LMFDB - Embedded newform 8005.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, 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("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15149 q^{2} -2.91656 q^{3} +2.62891 q^{4} -1.00000 q^{5} +6.27495 q^{6} +1.67048 q^{7} -1.35310 q^{8} +5.50631 q^{9} +O(q^{10})$	\(q-2.15149 q^{2} -2.91656 q^{3} +2.62891 q^{4} -1.00000 q^{5} +6.27495 q^{6} +1.67048 q^{7} -1.35310 q^{8} +5.50631 q^{9} +2.15149 q^{10} -6.05720 q^{11} -7.66738 q^{12} -5.01581 q^{13} -3.59403 q^{14} +2.91656 q^{15} -2.34664 q^{16} -5.97825 q^{17} -11.8468 q^{18} -6.79041 q^{19} -2.62891 q^{20} -4.87206 q^{21} +13.0320 q^{22} +3.85939 q^{23} +3.94640 q^{24} +1.00000 q^{25} +10.7915 q^{26} -7.30979 q^{27} +4.39156 q^{28} +3.87120 q^{29} -6.27495 q^{30} -0.0634631 q^{31} +7.75498 q^{32} +17.6662 q^{33} +12.8622 q^{34} -1.67048 q^{35} +14.4756 q^{36} -0.0380445 q^{37} +14.6095 q^{38} +14.6289 q^{39} +1.35310 q^{40} -10.3442 q^{41} +10.4822 q^{42} +5.48368 q^{43} -15.9239 q^{44} -5.50631 q^{45} -8.30345 q^{46} -2.26962 q^{47} +6.84411 q^{48} -4.20948 q^{49} -2.15149 q^{50} +17.4359 q^{51} -13.1861 q^{52} +9.89245 q^{53} +15.7270 q^{54} +6.05720 q^{55} -2.26034 q^{56} +19.8046 q^{57} -8.32885 q^{58} -4.87277 q^{59} +7.66738 q^{60} +8.62513 q^{61} +0.136540 q^{62} +9.19820 q^{63} -11.9915 q^{64} +5.01581 q^{65} -38.0086 q^{66} +4.09948 q^{67} -15.7163 q^{68} -11.2561 q^{69} +3.59403 q^{70} -6.38085 q^{71} -7.45060 q^{72} +9.51615 q^{73} +0.0818523 q^{74} -2.91656 q^{75} -17.8514 q^{76} -10.1185 q^{77} -31.4739 q^{78} +12.5084 q^{79} +2.34664 q^{80} +4.80050 q^{81} +22.2555 q^{82} +4.36215 q^{83} -12.8082 q^{84} +5.97825 q^{85} -11.7981 q^{86} -11.2906 q^{87} +8.19602 q^{88} +13.5425 q^{89} +11.8468 q^{90} -8.37883 q^{91} +10.1460 q^{92} +0.185094 q^{93} +4.88307 q^{94} +6.79041 q^{95} -22.6178 q^{96} +11.4629 q^{97} +9.05666 q^{98} -33.3528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) $ 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * 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 $

$2$	−2.15149	−1.52133	−0.760667	−	0.649142i	$-0.775128\pi$
$2$	−2.15149	−1.52133	−0.760667	+	0.649142i	$0.775128\pi$
$3$	−2.91656	−1.68388	−0.841938	−	0.539575i	$-0.818585\pi$
$3$	−2.91656	−1.68388	−0.841938	+	0.539575i	$0.818585\pi$
$4$	2.62891	1.31446
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.27495	2.56174
$7$	1.67048	0.631384	0.315692	−	0.948862i	$-0.397763\pi$
$7$	1.67048	0.631384	0.315692	+	0.948862i	$0.397763\pi$
$8$	−1.35310	−0.478394
$9$	5.50631	1.83544
$10$	2.15149	0.680361
$11$	−6.05720	−1.82631	−0.913157	−	0.407608i	$-0.866363\pi$
$11$	−6.05720	−1.82631	−0.913157	+	0.407608i	$0.866363\pi$
$12$	−7.66738	−2.21338
$13$	−5.01581	−1.39113	−0.695567	−	0.718461i	$-0.744847\pi$
$13$	−5.01581	−1.39113	−0.695567	+	0.718461i	$0.744847\pi$
$14$	−3.59403	−0.960546
$15$	2.91656	0.753052
$16$	−2.34664	−0.586660
$17$	−5.97825	−1.44994	−0.724970	−	0.688781i	$-0.758146\pi$
$17$	−5.97825	−1.44994	−0.724970	+	0.688781i	$0.758146\pi$
$18$	−11.8468	−2.79231
$19$	−6.79041	−1.55783	−0.778914	−	0.627131i	$-0.784229\pi$
$19$	−6.79041	−1.55783	−0.778914	+	0.627131i	$0.784229\pi$
$20$	−2.62891	−0.587843
$21$	−4.87206	−1.06317
$22$	13.0320	2.77843
$23$	3.85939	0.804739	0.402369	−	0.915477i	$-0.368187\pi$
$23$	3.85939	0.804739	0.402369	+	0.915477i	$0.368187\pi$
$24$	3.94640	0.805556
$25$	1.00000	0.200000
$26$	10.7915	2.11638
$27$	−7.30979	−1.40677
$28$	4.39156	0.829927
$29$	3.87120	0.718863	0.359432	−	0.933171i	$-0.382971\pi$
$29$	3.87120	0.718863	0.359432	+	0.933171i	$0.382971\pi$
$30$	−6.27495	−1.14564
$31$	−0.0634631	−0.0113983	−0.00569915	−	0.999984i	$-0.501814\pi$
$31$	−0.0634631	−0.0113983	−0.00569915	+	0.999984i	$0.501814\pi$
$32$	7.75498	1.37090
$33$	17.6662	3.07528
$34$	12.8622	2.20584
$35$	−1.67048	−0.282363
$36$	14.4756	2.41260
$37$	−0.0380445	−0.00625447	−0.00312723	−	0.999995i	$-0.500995\pi$
$37$	−0.0380445	−0.00625447	−0.00312723	+	0.999995i	$0.500995\pi$
$38$	14.6095	2.36998
$39$	14.6289	2.34250
$40$	1.35310	0.213944
$41$	−10.3442	−1.61549	−0.807747	−	0.589530i	$-0.799313\pi$
$41$	−10.3442	−1.61549	−0.807747	+	0.589530i	$0.799313\pi$
$42$	10.4822	1.61744
$43$	5.48368	0.836254	0.418127	−	0.908389i	$-0.362687\pi$
$43$	5.48368	0.836254	0.418127	+	0.908389i	$0.362687\pi$
$44$	−15.9239	−2.40061
$45$	−5.50631	−0.820832
$46$	−8.30345	−1.22428
$47$	−2.26962	−0.331058	−0.165529	−	0.986205i	$-0.552933\pi$
$47$	−2.26962	−0.331058	−0.165529	+	0.986205i	$0.552933\pi$
$48$	6.84411	0.987862
$49$	−4.20948	−0.601355
$50$	−2.15149	−0.304267
$51$	17.4359	2.44152
$52$	−13.1861	−1.82859
$53$	9.89245	1.35883	0.679416	−	0.733753i	$-0.262233\pi$
$53$	9.89245	1.35883	0.679416	+	0.733753i	$0.262233\pi$
$54$	15.7270	2.14017
$55$	6.05720	0.816752
$56$	−2.26034	−0.302050
$57$	19.8046	2.62319
$58$	−8.32885	−1.09363
$59$	−4.87277	−0.634381	−0.317190	−	0.948362i	$-0.602739\pi$
$59$	−4.87277	−0.634381	−0.317190	+	0.948362i	$0.602739\pi$
$60$	7.66738	0.989854
$61$	8.62513	1.10433	0.552167	−	0.833733i	$-0.313801\pi$
$61$	8.62513	1.10433	0.552167	+	0.833733i	$0.313801\pi$
$62$	0.136540	0.0173406
$63$	9.19820	1.15886
$64$	−11.9915	−1.49894
$65$	5.01581	0.622134
$66$	−38.0086	−4.67854
$67$	4.09948	0.500832	0.250416	−	0.968138i	$-0.419433\pi$
$67$	4.09948	0.500832	0.250416	+	0.968138i	$0.419433\pi$
$68$	−15.7163	−1.90588
$69$	−11.2561	−1.35508
$70$	3.59403	0.429569
$71$	−6.38085	−0.757267	−0.378634	−	0.925547i	$-0.623606\pi$
$71$	−6.38085	−0.757267	−0.378634	+	0.925547i	$0.623606\pi$
$72$	−7.45060	−0.878062
$73$	9.51615	1.11378	0.556891	−	0.830586i	$-0.311994\pi$
$73$	9.51615	1.11378	0.556891	+	0.830586i	$0.311994\pi$
$74$	0.0818523	0.00951514
$75$	−2.91656	−0.336775
$76$	−17.8514	−2.04770
$77$	−10.1185	−1.15310
$78$	−31.4739	−3.56372
$79$	12.5084	1.40730	0.703650	−	0.710547i	$-0.251552\pi$
$79$	12.5084	1.40730	0.703650	+	0.710547i	$0.251552\pi$
$80$	2.34664	0.262362
$81$	4.80050	0.533389
$82$	22.2555	2.45771
$83$	4.36215	0.478808	0.239404	−	0.970920i	$-0.423048\pi$
$83$	4.36215	0.478808	0.239404	+	0.970920i	$0.423048\pi$
$84$	−12.8082	−1.39749
$85$	5.97825	0.648433
$86$	−11.7981	−1.27222
$87$	−11.2906	−1.21048
$88$	8.19602	0.873698
$89$	13.5425	1.43551	0.717753	−	0.696298i	$-0.245171\pi$
$89$	13.5425	1.43551	0.717753	+	0.696298i	$0.245171\pi$
$90$	11.8468	1.24876
$91$	−8.37883	−0.878340
$92$	10.1460	1.05779
$93$	0.185094	0.0191933
$94$	4.88307	0.503650
$95$	6.79041	0.696681
$96$	−22.6178	−2.30842
$97$	11.4629	1.16388	0.581938	−	0.813233i	$-0.302295\pi$
$97$	11.4629	1.16388	0.581938	+	0.813233i	$0.302295\pi$
$98$	9.05666	0.914861
$99$	−33.3528	−3.35208
$100$	2.62891	0.262891
$101$	6.94137	0.690692	0.345346	−	0.938475i	$-0.387762\pi$
$101$	6.94137	0.690692	0.345346	+	0.938475i	$0.387762\pi$
$102$	−37.5132	−3.71436
$103$	−12.1451	−1.19669	−0.598347	−	0.801237i	$-0.704175\pi$
$103$	−12.1451	−1.19669	−0.598347	+	0.801237i	$0.704175\pi$
$104$	6.78690	0.665511
$105$	4.87206	0.475465
$106$	−21.2835	−2.06724
$107$	−13.0062	−1.25736	−0.628679	−	0.777665i	$-0.716404\pi$
$107$	−13.0062	−1.25736	−0.628679	+	0.777665i	$0.716404\pi$
$108$	−19.2168	−1.84914
$109$	−20.0986	−1.92509	−0.962547	−	0.271116i	$-0.912607\pi$
$109$	−20.0986	−1.92509	−0.962547	+	0.271116i	$0.912607\pi$
$110$	−13.0320	−1.24255
$111$	0.110959	0.0105317
$112$	−3.92002	−0.370407
$113$	−7.20546	−0.677833	−0.338916	−	0.940816i	$-0.610060\pi$
$113$	−7.20546	−0.677833	−0.338916	+	0.940816i	$0.610060\pi$
$114$	−42.6095	−3.99074
$115$	−3.85939	−0.359890
$116$	10.1770	0.944915
$117$	−27.6186	−2.55334
$118$	10.4837	0.965105
$119$	−9.98658	−0.915468
$120$	−3.94640	−0.360256
$121$	25.6896	2.33542
$122$	−18.5569	−1.68006
$123$	30.1695	2.72029
$124$	−0.166839	−0.0149826
$125$	−1.00000	−0.0894427
$126$	−19.7898	−1.76302
$127$	7.88212	0.699425	0.349713	−	0.936857i	$-0.386279\pi$
$127$	7.88212	0.699425	0.349713	+	0.936857i	$0.386279\pi$
$128$	10.2896	0.909483
$129$	−15.9935	−1.40815
$130$	−10.7915	−0.946474
$131$	−8.54614	−0.746680	−0.373340	−	0.927695i	$-0.621787\pi$
$131$	−8.54614	−0.746680	−0.373340	+	0.927695i	$0.621787\pi$
$132$	46.4428	4.04233
$133$	−11.3433	−0.983587
$134$	−8.82000	−0.761932
$135$	7.30979	0.629127
$136$	8.08919	0.693643
$137$	4.07011	0.347733	0.173867	−	0.984769i	$-0.444374\pi$
$137$	4.07011	0.347733	0.173867	+	0.984769i	$0.444374\pi$
$138$	24.2175	2.06153
$139$	5.01223	0.425132	0.212566	−	0.977147i	$-0.431818\pi$
$139$	5.01223	0.425132	0.212566	+	0.977147i	$0.431818\pi$
$140$	−4.39156	−0.371155
$141$	6.61948	0.557461
$142$	13.7283	1.15206
$143$	30.3817	2.54065
$144$	−12.9213	−1.07678
$145$	−3.87120	−0.321485
$146$	−20.4739	−1.69443
$147$	12.2772	1.01261
$148$	−0.100016	−0.00822123
$149$	−11.6554	−0.954845	−0.477422	−	0.878674i	$-0.658429\pi$
$149$	−11.6554	−0.954845	−0.477422	+	0.878674i	$0.658429\pi$
$150$	6.27495	0.512347
$151$	11.2702	0.917157	0.458579	−	0.888654i	$-0.348359\pi$
$151$	11.2702	0.917157	0.458579	+	0.888654i	$0.348359\pi$
$152$	9.18813	0.745256
$153$	−32.9181	−2.66127
$154$	21.7698	1.75426
$155$	0.0634631	0.00509748
$156$	38.4581	3.07911
$157$	−3.14240	−0.250791	−0.125396	−	0.992107i	$-0.540020\pi$
$157$	−3.14240	−0.250791	−0.125396	+	0.992107i	$0.540020\pi$
$158$	−26.9116	−2.14097
$159$	−28.8519	−2.28810
$160$	−7.75498	−0.613085
$161$	6.44705	0.508099
$162$	−10.3282	−0.811463
$163$	6.70202	0.524943	0.262472	−	0.964940i	$-0.415462\pi$
$163$	6.70202	0.524943	0.262472	+	0.964940i	$0.415462\pi$
$164$	−27.1940	−2.12350
$165$	−17.6662	−1.37531
$166$	−9.38513	−0.728427
$167$	23.4326	1.81327	0.906635	−	0.421915i	$-0.138642\pi$
$167$	23.4326	1.81327	0.906635	+	0.421915i	$0.138642\pi$
$168$	6.59241	0.508615
$169$	12.1583	0.935254
$170$	−12.8622	−0.986483
$171$	−37.3901	−2.85929
$172$	14.4161	1.09922
$173$	−9.16908	−0.697112	−0.348556	−	0.937288i	$-0.613328\pi$
$173$	−9.16908	−0.697112	−0.348556	+	0.937288i	$0.613328\pi$
$174$	24.2916	1.84154
$175$	1.67048	0.126277
$176$	14.2141	1.07142
$177$	14.2117	1.06822
$178$	−29.1366	−2.18388
$179$	−21.7354	−1.62458	−0.812288	−	0.583256i	$-0.801778\pi$
$179$	−21.7354	−1.62458	−0.812288	+	0.583256i	$0.801778\pi$
$180$	−14.4756	−1.07895
$181$	20.4316	1.51867	0.759335	−	0.650699i	$-0.225524\pi$
$181$	20.4316	1.51867	0.759335	+	0.650699i	$0.225524\pi$
$182$	18.0270	1.33625
$183$	−25.1557	−1.85956
$184$	−5.22216	−0.384982
$185$	0.0380445	0.00279708
$186$	−0.398228	−0.0291995
$187$	36.2115	2.64804
$188$	−5.96664	−0.435162
$189$	−12.2109	−0.888212
$190$	−14.6095	−1.05989
$191$	14.4631	1.04651	0.523257	−	0.852175i	$-0.324717\pi$
$191$	14.4631	1.04651	0.523257	+	0.852175i	$0.324717\pi$
$192$	34.9739	2.52402
$193$	9.55938	0.688099	0.344050	−	0.938951i	$-0.388201\pi$
$193$	9.55938	0.688099	0.344050	+	0.938951i	$0.388201\pi$
$194$	−24.6622	−1.77064
$195$	−14.6289	−1.04760
$196$	−11.0664	−0.790455
$197$	−13.5351	−0.964339	−0.482169	−	0.876078i	$-0.660151\pi$
$197$	−13.5351	−0.964339	−0.482169	+	0.876078i	$0.660151\pi$
$198$	71.7582	5.09964
$199$	−21.2865	−1.50896	−0.754481	−	0.656322i	$-0.772111\pi$
$199$	−21.2865	−1.50896	−0.754481	+	0.656322i	$0.772111\pi$
$200$	−1.35310	−0.0956789
$201$	−11.9564	−0.843338
$202$	−14.9343	−1.05077
$203$	6.46678	0.453879
$204$	45.8375	3.20927
$205$	10.3442	0.722471
$206$	26.1301	1.82057
$207$	21.2510	1.47705
$208$	11.7703	0.816122
$209$	41.1309	2.84508
$210$	−10.4822	−0.723341
$211$	−6.44288	−0.443546	−0.221773	−	0.975098i	$-0.571184\pi$
$211$	−6.44288	−0.443546	−0.221773	+	0.975098i	$0.571184\pi$
$212$	26.0064	1.78613
$213$	18.6101	1.27514
$214$	27.9828	1.91286
$215$	−5.48368	−0.373984
$216$	9.89090	0.672991
$217$	−0.106014	−0.00719671
$218$	43.2419	2.92871
$219$	−27.7544	−1.87547
$220$	15.9239	1.07359
$221$	29.9858	2.01706
$222$	−0.238727	−0.0160223
$223$	23.6717	1.58518	0.792588	−	0.609758i	$-0.208733\pi$
$223$	23.6717	1.58518	0.792588	+	0.609758i	$0.208733\pi$
$224$	12.9546	0.865564
$225$	5.50631	0.367087
$226$	15.5025	1.03121
$227$	8.88101	0.589453	0.294727	−	0.955582i	$-0.404771\pi$
$227$	8.88101	0.589453	0.294727	+	0.955582i	$0.404771\pi$
$228$	52.0647	3.44807
$229$	28.3720	1.87487	0.937436	−	0.348158i	$-0.113193\pi$
$229$	28.3720	1.87487	0.937436	+	0.348158i	$0.113193\pi$
$230$	8.30345	0.547513
$231$	29.5111	1.94168
$232$	−5.23813	−0.343900
$233$	27.3151	1.78947	0.894735	−	0.446597i	$-0.147364\pi$
$233$	27.3151	1.78947	0.894735	+	0.446597i	$0.147364\pi$
$234$	59.4211	3.88448
$235$	2.26962	0.148054
$236$	−12.8101	−0.833866
$237$	−36.4813	−2.36972
$238$	21.4860	1.39273
$239$	3.48319	0.225309	0.112654	−	0.993634i	$-0.464065\pi$
$239$	3.48319	0.225309	0.112654	+	0.993634i	$0.464065\pi$
$240$	−6.84411	−0.441785
$241$	−12.3051	−0.792644	−0.396322	−	0.918112i	$-0.629714\pi$
$241$	−12.3051	−0.792644	−0.396322	+	0.918112i	$0.629714\pi$
$242$	−55.2710	−3.55296
$243$	7.92843	0.508609
$244$	22.6747	1.45160
$245$	4.20948	0.268934
$246$	−64.9094	−4.13847
$247$	34.0594	2.16715
$248$	0.0858721	0.00545288
$249$	−12.7225	−0.806253
$250$	2.15149	0.136072
$251$	−29.9321	−1.88930	−0.944648	−	0.328086i	$-0.893596\pi$
$251$	−29.9321	−1.88930	−0.944648	+	0.328086i	$0.893596\pi$
$252$	24.1813	1.52328
$253$	−23.3771	−1.46971
$254$	−16.9583	−1.06406
$255$	−17.4359	−1.09188
$256$	1.84493	0.115308
$257$	−1.42393	−0.0888221	−0.0444111	−	0.999013i	$-0.514141\pi$
$257$	−1.42393	−0.0888221	−0.0444111	+	0.999013i	$0.514141\pi$
$258$	34.4098	2.14226
$259$	−0.0635527	−0.00394897
$260$	13.1861	0.817769
$261$	21.3160	1.31943
$262$	18.3869	1.13595
$263$	7.20078	0.444019	0.222009	−	0.975045i	$-0.428738\pi$
$263$	7.20078	0.444019	0.222009	+	0.975045i	$0.428738\pi$
$264$	−23.9042	−1.47120
$265$	−9.89245	−0.607688
$266$	24.4050	1.49636
$267$	−39.4976	−2.41721
$268$	10.7772	0.658322
$269$	4.79376	0.292280	0.146140	−	0.989264i	$-0.453315\pi$
$269$	4.79376	0.292280	0.146140	+	0.989264i	$0.453315\pi$
$270$	−15.7270	−0.957112
$271$	12.8346	0.779646	0.389823	−	0.920890i	$-0.372536\pi$
$271$	12.8346	0.779646	0.389823	+	0.920890i	$0.372536\pi$
$272$	14.0288	0.850621
$273$	24.4373	1.47901
$274$	−8.75681	−0.529018
$275$	−6.05720	−0.365263
$276$	−29.5914	−1.78119
$277$	26.3358	1.58237	0.791184	−	0.611579i	$-0.209465\pi$
$277$	26.3358	1.58237	0.791184	+	0.611579i	$0.209465\pi$
$278$	−10.7838	−0.646768
$279$	−0.349447	−0.0209209
$280$	2.26034	0.135081
$281$	−20.7876	−1.24008	−0.620042	−	0.784569i	$-0.712884\pi$
$281$	−20.7876	−1.24008	−0.620042	+	0.784569i	$0.712884\pi$
$282$	−14.2417	−0.848084
$283$	−2.39439	−0.142331	−0.0711657	−	0.997465i	$-0.522672\pi$
$283$	−2.39439	−0.142331	−0.0711657	+	0.997465i	$0.522672\pi$
$284$	−16.7747	−0.995396
$285$	−19.8046	−1.17312
$286$	−65.3660	−3.86517
$287$	−17.2798	−1.02000
$288$	42.7013	2.51620
$289$	18.7395	1.10232
$290$	8.32885	0.489087
$291$	−33.4321	−1.95982
$292$	25.0172	1.46402
$293$	−22.9333	−1.33978	−0.669888	−	0.742462i	$-0.733658\pi$
$293$	−22.9333	−1.33978	−0.669888	+	0.742462i	$0.733658\pi$
$294$	−26.4143	−1.54051
$295$	4.87277	0.283704
$296$	0.0514781	0.00299210
$297$	44.2768	2.56920
$298$	25.0764	1.45264
$299$	−19.3580	−1.11950
$300$	−7.66738	−0.442676
$301$	9.16041	0.527997
$302$	−24.2478	−1.39530
$303$	−20.2449	−1.16304
$304$	15.9346	0.913914
$305$	−8.62513	−0.493874
$306$	70.8230	4.04868
$307$	9.79481	0.559019	0.279510	−	0.960143i	$-0.409828\pi$
$307$	9.79481	0.559019	0.279510	+	0.960143i	$0.409828\pi$
$308$	−26.6006	−1.51571
$309$	35.4219	2.01508
$310$	−0.136540	−0.00775497
$311$	9.71422	0.550843	0.275421	−	0.961324i	$-0.411183\pi$
$311$	9.71422	0.550843	0.275421	+	0.961324i	$0.411183\pi$
$312$	−19.7944	−1.12064
$313$	5.73224	0.324006	0.162003	−	0.986790i	$-0.448205\pi$
$313$	5.73224	0.324006	0.162003	+	0.986790i	$0.448205\pi$
$314$	6.76085	0.381537
$315$	−9.19820	−0.518260
$316$	32.8834	1.84983
$317$	6.61955	0.371791	0.185896	−	0.982570i	$-0.440481\pi$
$317$	6.61955	0.371791	0.185896	+	0.982570i	$0.440481\pi$
$318$	62.0746	3.48097
$319$	−23.4486	−1.31287
$320$	11.9915	0.670345
$321$	37.9334	2.11724
$322$	−13.8708	−0.772988
$323$	40.5948	2.25875
$324$	12.6201	0.701117
$325$	−5.01581	−0.278227
$326$	−14.4193	−0.798614
$327$	58.6186	3.24162
$328$	13.9968	0.772843
$329$	−3.79137	−0.209025
$330$	38.0086	2.09230
$331$	−3.66452	−0.201420	−0.100710	−	0.994916i	$-0.532111\pi$
$331$	−3.66452	−0.201420	−0.100710	+	0.994916i	$0.532111\pi$
$332$	11.4677	0.629373
$333$	−0.209484	−0.0114797
$334$	−50.4151	−2.75859
$335$	−4.09948	−0.223979
$336$	11.4330	0.623720
$337$	4.03381	0.219736	0.109868	−	0.993946i	$-0.464957\pi$
$337$	4.03381	0.219736	0.109868	+	0.993946i	$0.464957\pi$
$338$	−26.1585	−1.42283
$339$	21.0151	1.14139
$340$	15.7163	0.852337
$341$	0.384408	0.0208169
$342$	80.4445	4.34994
$343$	−18.7253	−1.01107
$344$	−7.41999	−0.400059
$345$	11.2561	0.606010
$346$	19.7272	1.06054
$347$	−16.2086	−0.870123	−0.435062	−	0.900401i	$-0.643273\pi$
$347$	−16.2086	−0.870123	−0.435062	+	0.900401i	$0.643273\pi$
$348$	−29.6819	−1.59112
$349$	−31.3955	−1.68056	−0.840282	−	0.542150i	$-0.817610\pi$
$349$	−31.3955	−1.68056	−0.840282	+	0.542150i	$0.817610\pi$
$350$	−3.59403	−0.192109
$351$	36.6645	1.95701
$352$	−46.9734	−2.50369
$353$	−29.2777	−1.55830	−0.779149	−	0.626839i	$-0.784348\pi$
$353$	−29.2777	−1.55830	−0.779149	+	0.626839i	$0.784348\pi$
$354$	−30.5764	−1.62512
$355$	6.38085	0.338660
$356$	35.6022	1.88691
$357$	29.1264	1.54153
$358$	46.7634	2.47152
$359$	6.07908	0.320841	0.160421	−	0.987049i	$-0.448715\pi$
$359$	6.07908	0.320841	0.160421	+	0.987049i	$0.448715\pi$
$360$	7.45060	0.392681
$361$	27.1097	1.42683
$362$	−43.9585	−2.31041
$363$	−74.9253	−3.93256
$364$	−22.0272	−1.15454
$365$	−9.51615	−0.498098
$366$	54.1222	2.82902
$367$	−18.9130	−0.987249	−0.493624	−	0.869675i	$-0.664328\pi$
$367$	−18.9130	−0.987249	−0.493624	+	0.869675i	$0.664328\pi$
$368$	−9.05660	−0.472108
$369$	−56.9584	−2.96514
$370$	−0.0818523	−0.00425530
$371$	16.5252	0.857945
$372$	0.486596	0.0252288
$373$	22.8665	1.18398	0.591992	−	0.805944i	$-0.298342\pi$
$373$	22.8665	1.18398	0.591992	+	0.805944i	$0.298342\pi$
$374$	−77.9086	−4.02856
$375$	2.91656	0.150610
$376$	3.07103	0.158376
$377$	−19.4172	−1.00004
$378$	26.2716	1.35127
$379$	3.01300	0.154768	0.0773838	−	0.997001i	$-0.475343\pi$
$379$	3.01300	0.154768	0.0773838	+	0.997001i	$0.475343\pi$
$380$	17.8514	0.915758
$381$	−22.9887	−1.17774
$382$	−31.1173	−1.59210
$383$	−13.2334	−0.676194	−0.338097	−	0.941111i	$-0.609783\pi$
$383$	−13.2334	−0.676194	−0.338097	+	0.941111i	$0.609783\pi$
$384$	−30.0103	−1.53146
$385$	10.1185	0.515684
$386$	−20.5669	−1.04683
$387$	30.1949	1.53489
$388$	30.1349	1.52987
$389$	7.64126	0.387427	0.193714	−	0.981058i	$-0.437947\pi$
$389$	7.64126	0.387427	0.193714	+	0.981058i	$0.437947\pi$
$390$	31.4739	1.59374
$391$	−23.0724	−1.16682
$392$	5.69586	0.287685
$393$	24.9253	1.25732
$394$	29.1207	1.46708
$395$	−12.5084	−0.629363
$396$	−87.6816	−4.40617
$397$	7.44555	0.373681	0.186841	−	0.982390i	$-0.440175\pi$
$397$	7.44555	0.373681	0.186841	+	0.982390i	$0.440175\pi$
$398$	45.7978	2.29564
$399$	33.0833	1.65624
$400$	−2.34664	−0.117332
$401$	−28.0498	−1.40074	−0.700370	−	0.713780i	$-0.746982\pi$
$401$	−28.0498	−1.40074	−0.700370	+	0.713780i	$0.746982\pi$
$402$	25.7240	1.28300
$403$	0.318318	0.0158566
$404$	18.2483	0.907885
$405$	−4.80050	−0.238539
$406$	−13.9132	−0.690501
$407$	0.230443	0.0114226
$408$	−23.5926	−1.16801
$409$	27.3909	1.35439	0.677197	−	0.735801i	$-0.263194\pi$
$409$	27.3909	1.35439	0.677197	+	0.735801i	$0.263194\pi$
$410$	−22.2555	−1.09912
$411$	−11.8707	−0.585539
$412$	−31.9285	−1.57300
$413$	−8.13989	−0.400538
$414$	−45.7213	−2.24708
$415$	−4.36215	−0.214129
$416$	−38.8975	−1.90711
$417$	−14.6185	−0.715869
$418$	−88.4927	−4.32832
$419$	−14.6850	−0.717408	−0.358704	−	0.933451i	$-0.616781\pi$
$419$	−14.6850	−0.717408	−0.358704	+	0.933451i	$0.616781\pi$
$420$	12.8082	0.624978
$421$	15.0569	0.733828	0.366914	−	0.930255i	$-0.380414\pi$
$421$	15.0569	0.733828	0.366914	+	0.930255i	$0.380414\pi$
$422$	13.8618	0.674782
$423$	−12.4972	−0.607636
$424$	−13.3855	−0.650058
$425$	−5.97825	−0.289988
$426$	−40.0395	−1.93992
$427$	14.4081	0.697259
$428$	−34.1922	−1.65274
$429$	−88.6101	−4.27813
$430$	11.7981	0.568955
$431$	7.67338	0.369614	0.184807	−	0.982775i	$-0.440834\pi$
$431$	7.67338	0.369614	0.184807	+	0.982775i	$0.440834\pi$
$432$	17.1534	0.825295
$433$	−28.7603	−1.38213	−0.691065	−	0.722793i	$-0.742858\pi$
$433$	−28.7603	−1.38213	−0.691065	+	0.722793i	$0.742858\pi$
$434$	0.228088	0.0109486
$435$	11.2906	0.541341
$436$	−52.8374	−2.53045
$437$	−26.2069	−1.25364
$438$	59.7134	2.85322
$439$	16.4357	0.784433	0.392216	−	0.919873i	$-0.371708\pi$
$439$	16.4357	0.784433	0.392216	+	0.919873i	$0.371708\pi$
$440$	−8.19602	−0.390730
$441$	−23.1787	−1.10375
$442$	−64.5141	−3.06862
$443$	1.63950	0.0778951	0.0389476	−	0.999241i	$-0.487599\pi$
$443$	1.63950	0.0778951	0.0389476	+	0.999241i	$0.487599\pi$
$444$	0.291701	0.0138435
$445$	−13.5425	−0.641978
$446$	−50.9295	−2.41158
$447$	33.9935	1.60784
$448$	−20.0316	−0.946404
$449$	24.3765	1.15040	0.575199	−	0.818013i	$-0.304925\pi$
$449$	24.3765	1.15040	0.575199	+	0.818013i	$0.304925\pi$
$450$	−11.8468	−0.558462
$451$	62.6569	2.95040
$452$	−18.9425	−0.890982
$453$	−32.8702	−1.54438
$454$	−19.1074	−0.896755
$455$	8.37883	0.392805
$456$	−26.7977	−1.25492
$457$	−8.62087	−0.403267	−0.201634	−	0.979461i	$-0.564625\pi$
$457$	−8.62087	−0.403267	−0.201634	+	0.979461i	$0.564625\pi$
$458$	−61.0420	−2.85231
$459$	43.6998	2.03973
$460$	−10.1460	−0.473060
$461$	−8.74752	−0.407413	−0.203706	−	0.979032i	$-0.565299\pi$
$461$	−8.74752	−0.407413	−0.203706	+	0.979032i	$0.565299\pi$
$462$	−63.4928	−2.95395
$463$	27.0746	1.25826	0.629131	−	0.777299i	$-0.283411\pi$
$463$	27.0746	1.25826	0.629131	+	0.777299i	$0.283411\pi$
$464$	−9.08430	−0.421728
$465$	−0.185094	−0.00858352
$466$	−58.7682	−2.72238
$467$	−2.20220	−0.101906	−0.0509529	−	0.998701i	$-0.516226\pi$
$467$	−2.20220	−0.101906	−0.0509529	+	0.998701i	$0.516226\pi$
$468$	−72.6069	−3.35625
$469$	6.84812	0.316217
$470$	−4.88307	−0.225239
$471$	9.16500	0.422301
$472$	6.59336	0.303484
$473$	−33.2158	−1.52726
$474$	78.4892	3.60513
$475$	−6.79041	−0.311565
$476$	−26.2539	−1.20334
$477$	54.4709	2.49405
$478$	−7.49406	−0.342770
$479$	−2.09497	−0.0957214	−0.0478607	−	0.998854i	$-0.515240\pi$
$479$	−2.09497	−0.0957214	−0.0478607	+	0.998854i	$0.515240\pi$
$480$	22.6178	1.03236
$481$	0.190824	0.00870081
$482$	26.4744	1.20588
$483$	−18.8032	−0.855575
$484$	67.5359	3.06981
$485$	−11.4629	−0.520501
$486$	−17.0580	−0.773764
$487$	−2.87989	−0.130500	−0.0652501	−	0.997869i	$-0.520785\pi$
$487$	−2.87989	−0.130500	−0.0652501	+	0.997869i	$0.520785\pi$
$488$	−11.6707	−0.528307
$489$	−19.5468	−0.883939
$490$	−9.05666	−0.409138
$491$	12.4891	0.563626	0.281813	−	0.959469i	$-0.409064\pi$
$491$	12.4891	0.563626	0.281813	+	0.959469i	$0.409064\pi$
$492$	79.3130	3.57570
$493$	−23.1430	−1.04231
$494$	−73.2785	−3.29695
$495$	33.3528	1.49910
$496$	0.148925	0.00668693
$497$	−10.6591	−0.478126
$498$	27.3723	1.22658
$499$	−15.6421	−0.700239	−0.350119	−	0.936705i	$-0.613859\pi$
$499$	−15.6421	−0.700239	−0.350119	+	0.936705i	$0.613859\pi$
$500$	−2.62891	−0.117569
$501$	−68.3426	−3.05332
$502$	64.3986	2.87425
$503$	5.42596	0.241932	0.120966	−	0.992657i	$-0.461401\pi$
$503$	5.42596	0.241932	0.120966	+	0.992657i	$0.461401\pi$
$504$	−12.4461	−0.554394
$505$	−6.94137	−0.308887
$506$	50.2956	2.23591
$507$	−35.4604	−1.57485
$508$	20.7214	0.919364
$509$	39.0023	1.72874	0.864372	−	0.502852i	$-0.167716\pi$
$509$	39.0023	1.72874	0.864372	+	0.502852i	$0.167716\pi$
$510$	37.5132	1.66111
$511$	15.8966	0.703224
$512$	−24.5486	−1.08491
$513$	49.6365	2.19150
$514$	3.06357	0.135128
$515$	12.1451	0.535177
$516$	−42.0455	−1.85095
$517$	13.7475	0.604616
$518$	0.136733	0.00600770
$519$	26.7422	1.17385
$520$	−6.78690	−0.297625
$521$	8.75810	0.383699	0.191850	−	0.981424i	$-0.438551\pi$
$521$	8.75810	0.383699	0.191850	+	0.981424i	$0.438551\pi$
$522$	−45.8612	−2.00729
$523$	−11.8070	−0.516286	−0.258143	−	0.966107i	$-0.583111\pi$
$523$	−11.8070	−0.516286	−0.258143	+	0.966107i	$0.583111\pi$
$524$	−22.4671	−0.981479
$525$	−4.87206	−0.212634
$526$	−15.4924	−0.675501
$527$	0.379398	0.0165269
$528$	−41.4561	−1.80415
$529$	−8.10509	−0.352395
$530$	21.2835	0.924497
$531$	−26.8310	−1.16437
$532$	−29.8205	−1.29288
$533$	51.8845	2.24737
$534$	84.9787	3.67739
$535$	13.0062	0.562308
$536$	−5.54702	−0.239595
$537$	63.3924	2.73558
$538$	−10.3137	−0.444656
$539$	25.4977	1.09826
$540$	19.2168	0.826960
$541$	32.0939	1.37982	0.689911	−	0.723894i	$-0.257650\pi$
$541$	32.0939	1.37982	0.689911	+	0.723894i	$0.257650\pi$
$542$	−27.6135	−1.18610
$543$	−59.5900	−2.55725
$544$	−46.3612	−1.98772
$545$	20.0986	0.860928
$546$	−52.5767	−2.25007
$547$	−35.7384	−1.52806	−0.764032	−	0.645178i	$-0.776783\pi$
$547$	−35.7384	−1.52806	−0.764032	+	0.645178i	$0.776783\pi$
$548$	10.7000	0.457080
$549$	47.4926	2.02694
$550$	13.0320	0.555687
$551$	−26.2870	−1.11986
$552$	15.2307	0.648262
$553$	20.8950	0.888546
$554$	−56.6613	−2.40731
$555$	−0.110959	−0.00470994
$556$	13.1767	0.558818
$557$	8.96337	0.379790	0.189895	−	0.981804i	$-0.439185\pi$
$557$	8.96337	0.379790	0.189895	+	0.981804i	$0.439185\pi$
$558$	0.751833	0.0318276
$559$	−27.5051	−1.16334
$560$	3.92002	0.165651
$561$	−105.613	−4.45898
$562$	44.7243	1.88658
$563$	−9.13013	−0.384789	−0.192394	−	0.981318i	$-0.561625\pi$
$563$	−9.13013	−0.384789	−0.192394	+	0.981318i	$0.561625\pi$
$564$	17.4020	0.732758
$565$	7.20546	0.303136
$566$	5.15150	0.216534
$567$	8.01916	0.336773
$568$	8.63395	0.362272
$569$	28.2548	1.18450	0.592251	−	0.805754i	$-0.298240\pi$
$569$	28.2548	1.18450	0.592251	+	0.805754i	$0.298240\pi$
$570$	42.6095	1.78471
$571$	−25.4354	−1.06444	−0.532219	−	0.846607i	$-0.678642\pi$
$571$	−25.4354	−1.06444	−0.532219	+	0.846607i	$0.678642\pi$
$572$	79.8710	3.33957
$573$	−42.1825	−1.76220
$574$	37.1774	1.55176
$575$	3.85939	0.160948
$576$	−66.0288	−2.75120
$577$	42.9514	1.78809	0.894045	−	0.447976i	$-0.147855\pi$
$577$	42.9514	1.78809	0.894045	+	0.447976i	$0.147855\pi$
$578$	−40.3179	−1.67700
$579$	−27.8805	−1.15867
$580$	−10.1770	−0.422579
$581$	7.28690	0.302312
$582$	71.9288	2.98155
$583$	−59.9205	−2.48165
$584$	−12.8763	−0.532827
$585$	27.6186	1.14189
$586$	49.3407	2.03825
$587$	17.3018	0.714123	0.357062	−	0.934081i	$-0.383779\pi$
$587$	17.3018	0.714123	0.357062	+	0.934081i	$0.383779\pi$
$588$	32.2757	1.33103
$589$	0.430940	0.0177566
$590$	−10.4837	−0.431608
$591$	39.4760	1.62383
$592$	0.0892766	0.00366924
$593$	−28.2574	−1.16039	−0.580197	−	0.814476i	$-0.697024\pi$
$593$	−28.2574	−1.16039	−0.580197	+	0.814476i	$0.697024\pi$
$594$	−95.2612	−3.90862
$595$	9.98658	0.409410
$596$	−30.6410	−1.25510
$597$	62.0834	2.54090
$598$	41.6485	1.70313
$599$	−12.7542	−0.521122	−0.260561	−	0.965457i	$-0.583908\pi$
$599$	−12.7542	−0.521122	−0.260561	+	0.965457i	$0.583908\pi$
$600$	3.94640	0.161111
$601$	−6.46335	−0.263645	−0.131823	−	0.991273i	$-0.542083\pi$
$601$	−6.46335	−0.263645	−0.131823	+	0.991273i	$0.542083\pi$
$602$	−19.7085	−0.803260
$603$	22.5730	0.919244
$604$	29.6284	1.20556
$605$	−25.6896	−1.04443
$606$	43.5567	1.76937
$607$	25.2720	1.02576	0.512879	−	0.858461i	$-0.328579\pi$
$607$	25.2720	1.02576	0.512879	+	0.858461i	$0.328579\pi$
$608$	−52.6595	−2.13562
$609$	−18.8607	−0.764275
$610$	18.5569	0.751347
$611$	11.3840	0.460546
$612$	−86.5389	−3.49813
$613$	−2.97309	−0.120082	−0.0600410	−	0.998196i	$-0.519123\pi$
$613$	−2.97309	−0.120082	−0.0600410	+	0.998196i	$0.519123\pi$
$614$	−21.0734	−0.850455
$615$	−30.1695	−1.21655
$616$	13.6913	0.551639
$617$	36.9193	1.48632	0.743158	−	0.669116i	$-0.233327\pi$
$617$	36.9193	1.48632	0.743158	+	0.669116i	$0.233327\pi$
$618$	−76.2099	−3.06561
$619$	2.55725	0.102785	0.0513923	−	0.998679i	$-0.483634\pi$
$619$	2.55725	0.102785	0.0513923	+	0.998679i	$0.483634\pi$
$620$	0.166839	0.00670042
$621$	−28.2113	−1.13208
$622$	−20.9001	−0.838016
$623$	22.6226	0.906355
$624$	−34.3287	−1.37425
$625$	1.00000	0.0400000
$626$	−12.3329	−0.492921
$627$	−119.961	−4.79076
$628$	−8.26111	−0.329654
$629$	0.227439	0.00906860
$630$	19.7898	0.788446
$631$	−15.5502	−0.619042	−0.309521	−	0.950893i	$-0.600169\pi$
$631$	−15.5502	−0.619042	−0.309521	+	0.950893i	$0.600169\pi$
$632$	−16.9251	−0.673244
$633$	18.7910	0.746876
$634$	−14.2419	−0.565618
$635$	−7.88212	−0.312792
$636$	−75.8492	−3.00762
$637$	21.1139	0.836565
$638$	50.4495	1.99731
$639$	−35.1349	−1.38992
$640$	−10.2896	−0.406733
$641$	1.16830	0.0461452	0.0230726	−	0.999734i	$-0.492655\pi$
$641$	1.16830	0.0461452	0.0230726	+	0.999734i	$0.492655\pi$
$642$	−81.6133	−3.22102
$643$	−1.32675	−0.0523220	−0.0261610	−	0.999658i	$-0.508328\pi$
$643$	−1.32675	−0.0523220	−0.0261610	+	0.999658i	$0.508328\pi$
$644$	16.9488	0.667874
$645$	15.9935	0.629743
$646$	−87.3393	−3.43632
$647$	−50.1369	−1.97108	−0.985542	−	0.169430i	$-0.945807\pi$
$647$	−50.1369	−1.97108	−0.985542	+	0.169430i	$0.945807\pi$
$648$	−6.49558	−0.255170
$649$	29.5153	1.15858
$650$	10.7915	0.423276
$651$	0.309196	0.0121184
$652$	17.6190	0.690015
$653$	4.67839	0.183080	0.0915398	−	0.995801i	$-0.470821\pi$
$653$	4.67839	0.183080	0.0915398	+	0.995801i	$0.470821\pi$
$654$	−126.117	−4.93158
$655$	8.54614	0.333925
$656$	24.2741	0.947745
$657$	52.3989	2.04427
$658$	8.15709	0.317996
$659$	−25.5446	−0.995075	−0.497538	−	0.867442i	$-0.665762\pi$
$659$	−25.5446	−0.995075	−0.497538	+	0.867442i	$0.665762\pi$
$660$	−46.4428	−1.80778
$661$	−23.8208	−0.926520	−0.463260	−	0.886222i	$-0.653320\pi$
$661$	−23.8208	−0.926520	−0.463260	+	0.886222i	$0.653320\pi$
$662$	7.88419	0.306428
$663$	−87.4552	−3.39648
$664$	−5.90244	−0.229059
$665$	11.3433	0.439873
$666$	0.450704	0.0174644
$667$	14.9405	0.578497
$668$	61.6023	2.38347
$669$	−69.0399	−2.66924
$670$	8.82000	0.340746
$671$	−52.2441	−2.01686
$672$	−37.7828	−1.45750
$673$	30.6603	1.18187	0.590934	−	0.806720i	$-0.298759\pi$
$673$	30.6603	1.18187	0.590934	+	0.806720i	$0.298759\pi$
$674$	−8.67870	−0.334291
$675$	−7.30979	−0.281354
$676$	31.9631	1.22935
$677$	−30.0200	−1.15376	−0.576881	−	0.816829i	$-0.695730\pi$
$677$	−30.0200	−1.15376	−0.576881	+	0.816829i	$0.695730\pi$
$678$	−45.2139	−1.73643
$679$	19.1485	0.734853
$680$	−8.08919	−0.310206
$681$	−25.9020	−0.992565
$682$	−0.827051	−0.0316694
$683$	−15.0443	−0.575656	−0.287828	−	0.957682i	$-0.592933\pi$
$683$	−15.0443	−0.575656	−0.287828	+	0.957682i	$0.592933\pi$
$684$	−98.2953	−3.75842
$685$	−4.07011	−0.155511
$686$	40.2872	1.53817
$687$	−82.7485	−3.15705
$688$	−12.8682	−0.490596
$689$	−49.6186	−1.89032
$690$	−24.2175	−0.921944
$691$	22.4190	0.852859	0.426430	−	0.904521i	$-0.359771\pi$
$691$	22.4190	0.852859	0.426430	+	0.904521i	$0.359771\pi$
$692$	−24.1047	−0.916324
$693$	−55.7153	−2.11645
$694$	34.8727	1.32375
$695$	−5.01223	−0.190125
$696$	15.2773	0.579085
$697$	61.8403	2.34237
$698$	67.5472	2.55670
$699$	−79.6660	−3.01325
$700$	4.39156	0.165985
$701$	28.3584	1.07108	0.535541	−	0.844509i	$-0.320108\pi$
$701$	28.3584	1.07108	0.535541	+	0.844509i	$0.320108\pi$
$702$	−78.8833	−2.97726
$703$	0.258337	0.00974338
$704$	72.6348	2.73753
$705$	−6.61948	−0.249304
$706$	62.9908	2.37069
$707$	11.5955	0.436092
$708$	37.3614	1.40413
$709$	28.3295	1.06394	0.531969	−	0.846764i	$-0.321452\pi$
$709$	28.3295	1.06394	0.531969	+	0.846764i	$0.321452\pi$
$710$	−13.7283	−0.515215
$711$	68.8748	2.58301
$712$	−18.3244	−0.686738
$713$	−0.244929	−0.00917266
$714$	−62.6653	−2.34519
$715$	−30.3817	−1.13621
$716$	−57.1404	−2.13544
$717$	−10.1589	−0.379392
$718$	−13.0791	−0.488107
$719$	−9.12605	−0.340344	−0.170172	−	0.985414i	$-0.554432\pi$
$719$	−9.12605	−0.340344	−0.170172	+	0.985414i	$0.554432\pi$
$720$	12.9213	0.481549
$721$	−20.2882	−0.755573
$722$	−58.3262	−2.17068
$723$	35.8887	1.33471
$724$	53.7130	1.99623
$725$	3.87120	0.143773
$726$	161.201	5.98274
$727$	−36.8143	−1.36537	−0.682684	−	0.730714i	$-0.739187\pi$
$727$	−36.8143	−1.36537	−0.682684	+	0.730714i	$0.739187\pi$
$728$	11.3374	0.420193
$729$	−37.5252	−1.38982
$730$	20.4739	0.757774
$731$	−32.7829	−1.21252
$732$	−66.1322	−2.44431
$733$	−9.76046	−0.360511	−0.180255	−	0.983620i	$-0.557692\pi$
$733$	−9.76046	−0.360511	−0.180255	+	0.983620i	$0.557692\pi$
$734$	40.6911	1.50194
$735$	−12.2772	−0.452851
$736$	29.9295	1.10322
$737$	−24.8314	−0.914676
$738$	122.545	4.51096
$739$	14.8821	0.547449	0.273724	−	0.961808i	$-0.411744\pi$
$739$	14.8821	0.547449	0.273724	+	0.961808i	$0.411744\pi$
$740$	0.100016	0.00367665
$741$	−99.3362	−3.64920
$742$	−35.5538	−1.30522
$743$	−41.3806	−1.51811	−0.759054	−	0.651028i	$-0.774338\pi$
$743$	−41.3806	−1.51811	−0.759054	+	0.651028i	$0.774338\pi$
$744$	−0.250451	−0.00918198
$745$	11.6554	0.427020
$746$	−49.1971	−1.80124
$747$	24.0193	0.878822
$748$	95.1968	3.48074
$749$	−21.7267	−0.793876
$750$	−6.27495	−0.229129
$751$	−17.5012	−0.638628	−0.319314	−	0.947649i	$-0.603453\pi$
$751$	−17.5012	−0.638628	−0.319314	+	0.947649i	$0.603453\pi$
$752$	5.32598	0.194218
$753$	87.2986	3.18134
$754$	41.7759	1.52139
$755$	−11.2702	−0.410165
$756$	−32.1014	−1.16752
$757$	6.70801	0.243807	0.121903	−	0.992542i	$-0.461100\pi$
$757$	6.70801	0.243807	0.121903	+	0.992542i	$0.461100\pi$
$758$	−6.48245	−0.235453
$759$	68.1807	2.47480
$760$	−9.18813	−0.333288
$761$	30.0527	1.08941	0.544705	−	0.838628i	$-0.316642\pi$
$761$	30.0527	1.08941	0.544705	+	0.838628i	$0.316642\pi$
$762$	49.4599	1.79174
$763$	−33.5743	−1.21547
$764$	38.0223	1.37560
$765$	32.9181	1.19016
$766$	28.4715	1.02872
$767$	24.4409	0.882509
$768$	−5.38086	−0.194165
$769$	18.3584	0.662021	0.331011	−	0.943627i	$-0.392610\pi$
$769$	18.3584	0.662021	0.331011	+	0.943627i	$0.392610\pi$
$770$	−21.7698	−0.784528
$771$	4.15297	0.149565
$772$	25.1308	0.904477
$773$	21.1357	0.760199	0.380100	−	0.924946i	$-0.375890\pi$
$773$	21.1357	0.760199	0.380100	+	0.924946i	$0.375890\pi$
$774$	−64.9640	−2.33508
$775$	−0.0634631	−0.00227966
$776$	−15.5104	−0.556792
$777$	0.185355	0.00664957
$778$	−16.4401	−0.589406
$779$	70.2414	2.51666
$780$	−38.4581	−1.37702
$781$	38.6501	1.38301
$782$	49.6401	1.77513
$783$	−28.2976	−1.01128
$784$	9.87813	0.352790
$785$	3.14240	0.112157
$786$	−53.6266	−1.91280
$787$	18.1996	0.648746	0.324373	−	0.945929i	$-0.394847\pi$
$787$	18.1996	0.648746	0.324373	+	0.945929i	$0.394847\pi$
$788$	−35.5827	−1.26758
$789$	−21.0015	−0.747672
$790$	26.9116	0.957472
$791$	−12.0366	−0.427973
$792$	45.1298	1.60362
$793$	−43.2620	−1.53628
$794$	−16.0190	−0.568494
$795$	28.8519	1.02327
$796$	−55.9605	−1.98347
$797$	−29.6048	−1.04866	−0.524328	−	0.851516i	$-0.675683\pi$
$797$	−29.6048	−1.04866	−0.524328	+	0.851516i	$0.675683\pi$
$798$	−71.1785	−2.51969
$799$	13.5684	0.480014
$800$	7.75498	0.274180
$801$	74.5693	2.63478
$802$	60.3489	2.13099
$803$	−57.6412	−2.03411
$804$	−31.4323	−1.10853
$805$	−6.44705	−0.227229
$806$	−0.684859	−0.0241231
$807$	−13.9813	−0.492164
$808$	−9.39239	−0.330423
$809$	−33.9139	−1.19235	−0.596175	−	0.802854i	$-0.703314\pi$
$809$	−33.9139	−1.19235	−0.596175	+	0.802854i	$0.703314\pi$
$810$	10.3282	0.362897
$811$	−26.6537	−0.935939	−0.467969	−	0.883745i	$-0.655014\pi$
$811$	−26.6537	−0.935939	−0.467969	+	0.883745i	$0.655014\pi$
$812$	17.0006	0.596604
$813$	−37.4328	−1.31283
$814$	−0.495796	−0.0173776
$815$	−6.70202	−0.234762
$816$	−40.9158	−1.43234
$817$	−37.2365	−1.30274
$818$	−58.9314	−2.06049
$819$	−46.1364	−1.61214
$820$	27.1940	0.949657
$821$	43.4502	1.51642	0.758212	−	0.652009i	$-0.226073\pi$
$821$	43.4502	1.51642	0.758212	+	0.652009i	$0.226073\pi$
$822$	25.5397	0.890801
$823$	−28.6681	−0.999308	−0.499654	−	0.866225i	$-0.666539\pi$
$823$	−28.6681	−0.999308	−0.499654	+	0.866225i	$0.666539\pi$
$824$	16.4336	0.572491
$825$	17.6662	0.615057
$826$	17.5129	0.609352
$827$	3.49450	0.121516	0.0607578	−	0.998153i	$-0.480648\pi$
$827$	3.49450	0.121516	0.0607578	+	0.998153i	$0.480648\pi$
$828$	55.8671	1.94151
$829$	−5.74252	−0.199446	−0.0997229	−	0.995015i	$-0.531796\pi$
$829$	−5.74252	−0.199446	−0.0997229	+	0.995015i	$0.531796\pi$
$830$	9.38513	0.325762
$831$	−76.8100	−2.66451
$832$	60.1470	2.08522
$833$	25.1653	0.871928
$834$	31.4515	1.08908
$835$	−23.4326	−0.810919
$836$	108.130	3.73974
$837$	0.463902	0.0160348
$838$	31.5946	1.09142
$839$	−3.85833	−0.133204	−0.0666021	−	0.997780i	$-0.521216\pi$
$839$	−3.85833	−0.133204	−0.0666021	+	0.997780i	$0.521216\pi$
$840$	−6.59241	−0.227460
$841$	−14.0138	−0.483236
$842$	−32.3948	−1.11640
$843$	60.6282	2.08815
$844$	−16.9378	−0.583022
$845$	−12.1583	−0.418259
$846$	26.8877	0.924417
$847$	42.9142	1.47455
$848$	−23.2140	−0.797172
$849$	6.98336	0.239668
$850$	12.8622	0.441168
$851$	−0.146828	−0.00503321
$852$	48.9244	1.67612
$853$	−30.3746	−1.04001	−0.520004	−	0.854164i	$-0.674070\pi$
$853$	−30.3746	−1.04001	−0.520004	+	0.854164i	$0.674070\pi$
$854$	−30.9990	−1.06076
$855$	37.3901	1.27871
$856$	17.5988	0.601513
$857$	19.7099	0.673279	0.336639	−	0.941634i	$-0.390710\pi$
$857$	19.7099	0.673279	0.336639	+	0.941634i	$0.390710\pi$
$858$	190.644	6.50847
$859$	−31.3744	−1.07048	−0.535240	−	0.844700i	$-0.679779\pi$
$859$	−31.3744	−1.07048	−0.535240	+	0.844700i	$0.679779\pi$
$860$	−14.4161	−0.491586
$861$	50.3976	1.71755
$862$	−16.5092	−0.562306
$863$	53.7201	1.82865	0.914326	−	0.404979i	$-0.132721\pi$
$863$	53.7201	1.82865	0.914326	+	0.404979i	$0.132721\pi$
$864$	−56.6873	−1.92854
$865$	9.16908	0.311758
$866$	61.8774	2.10268
$867$	−54.6549	−1.85618
$868$	−0.278702	−0.00945976
$869$	−75.7656	−2.57017
$870$	−24.2916	−0.823561
$871$	−20.5622	−0.696724
$872$	27.1954	0.920954
$873$	63.1180	2.13622
$874$	56.3838	1.90721
$875$	−1.67048	−0.0564727
$876$	−72.9640	−2.46522
$877$	44.0814	1.48852	0.744262	−	0.667888i	$-0.232802\pi$
$877$	44.0814	1.48852	0.744262	+	0.667888i	$0.232802\pi$
$878$	−35.3613	−1.19338
$879$	66.8862	2.25602
$880$	−14.2141	−0.479156
$881$	−19.2089	−0.647164	−0.323582	−	0.946200i	$-0.604887\pi$
$881$	−19.2089	−0.647164	−0.323582	+	0.946200i	$0.604887\pi$
$882$	49.8688	1.67917
$883$	−8.81540	−0.296662	−0.148331	−	0.988938i	$-0.547390\pi$
$883$	−8.81540	−0.296662	−0.148331	+	0.988938i	$0.547390\pi$
$884$	78.8300	2.65134
$885$	−14.2117	−0.477722
$886$	−3.52738	−0.118505
$887$	23.0178	0.772864	0.386432	−	0.922318i	$-0.373707\pi$
$887$	23.0178	0.772864	0.386432	+	0.922318i	$0.373707\pi$
$888$	−0.150139	−0.00503833
$889$	13.1670	0.441606
$890$	29.1366	0.976662
$891$	−29.0776	−0.974136
$892$	62.2309	2.08364
$893$	15.4117	0.515731
$894$	−73.1368	−2.44606
$895$	21.7354	0.726533
$896$	17.1887	0.574233
$897$	56.4586	1.88510
$898$	−52.4458	−1.75014
$899$	−0.245678	−0.00819382
$900$	14.4756	0.482520
$901$	−59.1396	−1.97022
$902$	−134.806	−4.48854
$903$	−26.7169	−0.889082
$904$	9.74973	0.324271
$905$	−20.4316	−0.679170
$906$	70.7200	2.34952
$907$	−25.3174	−0.840650	−0.420325	−	0.907374i	$-0.638084\pi$
$907$	−25.3174	−0.840650	−0.420325	+	0.907374i	$0.638084\pi$
$908$	23.3474	0.774811
$909$	38.2213	1.26772
$910$	−18.0270	−0.597588
$911$	6.09125	0.201812	0.100906	−	0.994896i	$-0.467826\pi$
$911$	6.09125	0.201812	0.100906	+	0.994896i	$0.467826\pi$
$912$	−46.4743	−1.53892
$913$	−26.4224	−0.874454
$914$	18.5477	0.613504
$915$	25.1557	0.831621
$916$	74.5875	2.46444
$917$	−14.2762	−0.471442
$918$	−94.0197	−3.10311
$919$	43.9496	1.44976	0.724882	−	0.688873i	$-0.241894\pi$
$919$	43.9496	1.44976	0.724882	+	0.688873i	$0.241894\pi$
$920$	5.22216	0.172169
$921$	−28.5671	−0.941319
$922$	18.8202	0.619811
$923$	32.0051	1.05346
$924$	77.5820	2.55226
$925$	−0.0380445	−0.00125089
$926$	−58.2507	−1.91424
$927$	−66.8747	−2.19645
$928$	30.0211	0.985489
$929$	37.3273	1.22467	0.612334	−	0.790599i	$-0.290231\pi$
$929$	37.3273	1.22467	0.612334	+	0.790599i	$0.290231\pi$
$930$	0.398228	0.0130584
$931$	28.5841	0.936806
$932$	71.8090	2.35218
$933$	−28.3321	−0.927551
$934$	4.73802	0.155033
$935$	−36.2115	−1.18424
$936$	37.3708	1.22150
$937$	−4.08274	−0.133377	−0.0666887	−	0.997774i	$-0.521243\pi$
$937$	−4.08274	−0.133377	−0.0666887	+	0.997774i	$0.521243\pi$
$938$	−14.7337	−0.481072
$939$	−16.7184	−0.545585
$940$	5.96664	0.194610
$941$	27.3355	0.891111	0.445556	−	0.895254i	$-0.353006\pi$
$941$	27.3355	0.891111	0.445556	+	0.895254i	$0.353006\pi$
$942$	−19.7184	−0.642461
$943$	−39.9223	−1.30005
$944$	11.4346	0.372166
$945$	12.2109	0.397220
$946$	71.4634	2.32348
$947$	59.6197	1.93738	0.968690	−	0.248273i	$-0.0798630\pi$
$947$	59.6197	1.93738	0.968690	+	0.248273i	$0.0798630\pi$
$948$	−95.9063	−3.11489
$949$	−47.7312	−1.54942
$950$	14.6095	0.473995
$951$	−19.3063	−0.626050
$952$	13.5129	0.437955
$953$	20.6824	0.669969	0.334984	−	0.942224i	$-0.391269\pi$
$953$	20.6824	0.669969	0.334984	+	0.942224i	$0.391269\pi$
$954$	−117.194	−3.79428
$955$	−14.4631	−0.468015
$956$	9.15701	0.296159
$957$	68.3892	2.21071
$958$	4.50730	0.145624
$959$	6.79906	0.219553
$960$	−34.9739	−1.12878
$961$	−30.9960	−0.999870
$962$	−0.410555	−0.0132368
$963$	−71.6162	−2.30780
$964$	−32.3492	−1.04190
$965$	−9.55938	−0.307727
$966$	40.4549	1.30162
$967$	14.7652	0.474818	0.237409	−	0.971410i	$-0.423702\pi$
$967$	14.7652	0.474818	0.237409	+	0.971410i	$0.423702\pi$
$968$	−34.7607	−1.11725
$969$	−118.397	−3.80346
$970$	24.6622	0.791856
$971$	−7.50683	−0.240906	−0.120453	−	0.992719i	$-0.538435\pi$
$971$	−7.50683	−0.240906	−0.120453	+	0.992719i	$0.538435\pi$
$972$	20.8432	0.668545
$973$	8.37286	0.268421
$974$	6.19606	0.198535
$975$	14.6289	0.468499
$976$	−20.2401	−0.647869
$977$	−22.7641	−0.728287	−0.364144	−	0.931343i	$-0.618638\pi$
$977$	−22.7641	−0.728287	−0.364144	+	0.931343i	$0.618638\pi$
$978$	42.0549	1.34477
$979$	−82.0298	−2.62168
$980$	11.0664	0.353502
$981$	−110.669	−3.53339
$982$	−26.8702	−0.857463
$983$	−33.8791	−1.08058	−0.540288	−	0.841480i	$-0.681685\pi$
$983$	−33.8791	−1.08058	−0.540288	+	0.841480i	$0.681685\pi$
$984$	−40.8224	−1.30137
$985$	13.5351	0.431265
$986$	49.7920	1.58570
$987$	11.0577	0.351972
$988$	89.5392	2.84862
$989$	21.1637	0.672966
$990$	−71.7582	−2.28063
$991$	−48.6451	−1.54526	−0.772632	−	0.634855i	$-0.781060\pi$
$991$	−48.6451	−1.54526	−0.772632	+	0.634855i	$0.781060\pi$
$992$	−0.492155	−0.0156259
$993$	10.6878	0.339167
$994$	22.9330	0.727390
$995$	21.2865	0.674829
$996$	−33.4463	−1.05979
$997$	−54.7753	−1.73475	−0.867376	−	0.497654i	$-0.834195\pi$
$997$	−54.7753	−1.73475	−0.867376	+	0.497654i	$0.834195\pi$
$998$	33.6539	1.06530
$999$	0.278097	0.00879860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.f.1.17	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.f.1.17	✓	127	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15149 q^{2} -2.91656 q^{3} +2.62891 q^{4} -1.00000 q^{5} +6.27495 q^{6} +1.67048 q^{7} -1.35310 q^{8} +5.50631 q^{9} +O(q^{10})\)	\(q-2.15149 q^{2} -2.91656 q^{3} +2.62891 q^{4} -1.00000 q^{5} +6.27495 q^{6} +1.67048 q^{7} -1.35310 q^{8} +5.50631 q^{9} +2.15149 q^{10} -6.05720 q^{11} -7.66738 q^{12} -5.01581 q^{13} -3.59403 q^{14} +2.91656 q^{15} -2.34664 q^{16} -5.97825 q^{17} -11.8468 q^{18} -6.79041 q^{19} -2.62891 q^{20} -4.87206 q^{21} +13.0320 q^{22} +3.85939 q^{23} +3.94640 q^{24} +1.00000 q^{25} +10.7915 q^{26} -7.30979 q^{27} +4.39156 q^{28} +3.87120 q^{29} -6.27495 q^{30} -0.0634631 q^{31} +7.75498 q^{32} +17.6662 q^{33} +12.8622 q^{34} -1.67048 q^{35} +14.4756 q^{36} -0.0380445 q^{37} +14.6095 q^{38} +14.6289 q^{39} +1.35310 q^{40} -10.3442 q^{41} +10.4822 q^{42} +5.48368 q^{43} -15.9239 q^{44} -5.50631 q^{45} -8.30345 q^{46} -2.26962 q^{47} +6.84411 q^{48} -4.20948 q^{49} -2.15149 q^{50} +17.4359 q^{51} -13.1861 q^{52} +9.89245 q^{53} +15.7270 q^{54} +6.05720 q^{55} -2.26034 q^{56} +19.8046 q^{57} -8.32885 q^{58} -4.87277 q^{59} +7.66738 q^{60} +8.62513 q^{61} +0.136540 q^{62} +9.19820 q^{63} -11.9915 q^{64} +5.01581 q^{65} -38.0086 q^{66} +4.09948 q^{67} -15.7163 q^{68} -11.2561 q^{69} +3.59403 q^{70} -6.38085 q^{71} -7.45060 q^{72} +9.51615 q^{73} +0.0818523 q^{74} -2.91656 q^{75} -17.8514 q^{76} -10.1185 q^{77} -31.4739 q^{78} +12.5084 q^{79} +2.34664 q^{80} +4.80050 q^{81} +22.2555 q^{82} +4.36215 q^{83} -12.8082 q^{84} +5.97825 q^{85} -11.7981 q^{86} -11.2906 q^{87} +8.19602 q^{88} +13.5425 q^{89} +11.8468 q^{90} -8.37883 q^{91} +10.1460 q^{92} +0.185094 q^{93} +4.88307 q^{94} +6.79041 q^{95} -22.6178 q^{96} +11.4629 q^{97} +9.05666 q^{98} -33.3528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * q^99

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