LMFDB - Embedded newform 8021.2.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36088 q^{2} +0.842254 q^{3} +3.57377 q^{4} -1.49212 q^{5} -1.98846 q^{6} -1.11078 q^{7} -3.71549 q^{8} -2.29061 q^{9} +O(q^{10})$	\(q-2.36088 q^{2} +0.842254 q^{3} +3.57377 q^{4} -1.49212 q^{5} -1.98846 q^{6} -1.11078 q^{7} -3.71549 q^{8} -2.29061 q^{9} +3.52272 q^{10} -4.02952 q^{11} +3.01003 q^{12} +1.00000 q^{13} +2.62242 q^{14} -1.25674 q^{15} +1.62430 q^{16} -0.552282 q^{17} +5.40786 q^{18} +3.31880 q^{19} -5.33250 q^{20} -0.935560 q^{21} +9.51322 q^{22} +6.65139 q^{23} -3.12939 q^{24} -2.77358 q^{25} -2.36088 q^{26} -4.45604 q^{27} -3.96968 q^{28} -4.21363 q^{29} +2.96703 q^{30} +8.36402 q^{31} +3.59619 q^{32} -3.39388 q^{33} +1.30387 q^{34} +1.65742 q^{35} -8.18611 q^{36} -7.94263 q^{37} -7.83530 q^{38} +0.842254 q^{39} +5.54396 q^{40} +10.6180 q^{41} +2.20875 q^{42} -1.90766 q^{43} -14.4006 q^{44} +3.41786 q^{45} -15.7032 q^{46} +6.14413 q^{47} +1.36808 q^{48} -5.76617 q^{49} +6.54809 q^{50} -0.465162 q^{51} +3.57377 q^{52} +6.22973 q^{53} +10.5202 q^{54} +6.01252 q^{55} +4.12710 q^{56} +2.79528 q^{57} +9.94789 q^{58} -1.22581 q^{59} -4.49132 q^{60} -5.39620 q^{61} -19.7465 q^{62} +2.54436 q^{63} -11.7388 q^{64} -1.49212 q^{65} +8.01255 q^{66} +2.00241 q^{67} -1.97373 q^{68} +5.60216 q^{69} -3.91297 q^{70} +0.614736 q^{71} +8.51074 q^{72} -10.5550 q^{73} +18.7516 q^{74} -2.33606 q^{75} +11.8606 q^{76} +4.47591 q^{77} -1.98846 q^{78} -0.421182 q^{79} -2.42366 q^{80} +3.11871 q^{81} -25.0679 q^{82} +4.75340 q^{83} -3.34348 q^{84} +0.824071 q^{85} +4.50375 q^{86} -3.54895 q^{87} +14.9716 q^{88} +10.9624 q^{89} -8.06918 q^{90} -1.11078 q^{91} +23.7706 q^{92} +7.04463 q^{93} -14.5056 q^{94} -4.95205 q^{95} +3.02891 q^{96} +5.73345 q^{97} +13.6133 q^{98} +9.23004 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.36088	−1.66940	−0.834698	−	0.550707i	$-0.814358\pi$
$2$	−2.36088	−1.66940	−0.834698	+	0.550707i	$0.814358\pi$
$3$	0.842254	0.486276	0.243138	−	0.969992i	$-0.421823\pi$
$3$	0.842254	0.486276	0.243138	+	0.969992i	$0.421823\pi$
$4$	3.57377	1.78689
$5$	−1.49212	−0.667297	−0.333648	−	0.942698i	$-0.608280\pi$
$5$	−1.49212	−0.667297	−0.333648	+	0.942698i	$0.608280\pi$
$6$	−1.98846	−0.811787
$7$	−1.11078	−0.419835	−0.209918	−	0.977719i	$-0.567320\pi$
$7$	−1.11078	−0.419835	−0.209918	+	0.977719i	$0.567320\pi$
$8$	−3.71549	−1.31363
$9$	−2.29061	−0.763536
$10$	3.52272	1.11398
$11$	−4.02952	−1.21495	−0.607473	−	0.794341i	$-0.707817\pi$
$11$	−4.02952	−1.21495	−0.607473	+	0.794341i	$0.707817\pi$
$12$	3.01003	0.868919
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.62242	0.700872
$15$	−1.25674	−0.324490
$16$	1.62430	0.406076
$17$	−0.552282	−0.133948	−0.0669740	−	0.997755i	$-0.521334\pi$
$17$	−0.552282	−0.133948	−0.0669740	+	0.997755i	$0.521334\pi$
$18$	5.40786	1.27464
$19$	3.31880	0.761385	0.380693	−	0.924702i	$-0.375686\pi$
$19$	3.31880	0.761385	0.380693	+	0.924702i	$0.375686\pi$
$20$	−5.33250	−1.19238
$21$	−0.935560	−0.204156
$22$	9.51322	2.02823
$23$	6.65139	1.38691	0.693455	−	0.720500i	$-0.256088\pi$
$23$	6.65139	1.38691	0.693455	+	0.720500i	$0.256088\pi$
$24$	−3.12939	−0.638784
$25$	−2.77358	−0.554715
$26$	−2.36088	−0.463007
$27$	−4.45604	−0.857565
$28$	−3.96968	−0.750198
$29$	−4.21363	−0.782451	−0.391226	−	0.920295i	$-0.627949\pi$
$29$	−4.21363	−0.782451	−0.391226	+	0.920295i	$0.627949\pi$
$30$	2.96703	0.541703
$31$	8.36402	1.50222	0.751111	−	0.660175i	$-0.229518\pi$
$31$	8.36402	1.50222	0.751111	+	0.660175i	$0.229518\pi$
$32$	3.59619	0.635723
$33$	−3.39388	−0.590798
$34$	1.30387	0.223612
$35$	1.65742	0.280155
$36$	−8.18611	−1.36435
$37$	−7.94263	−1.30576	−0.652880	−	0.757461i	$-0.726440\pi$
$37$	−7.94263	−1.30576	−0.652880	+	0.757461i	$0.726440\pi$
$38$	−7.83530	−1.27105
$39$	0.842254	0.134869
$40$	5.54396	0.876578
$41$	10.6180	1.65826	0.829129	−	0.559058i	$-0.188837\pi$
$41$	10.6180	1.65826	0.829129	+	0.559058i	$0.188837\pi$
$42$	2.20875	0.340817
$43$	−1.90766	−0.290915	−0.145457	−	0.989365i	$-0.546465\pi$
$43$	−1.90766	−0.290915	−0.145457	+	0.989365i	$0.546465\pi$
$44$	−14.4006	−2.17097
$45$	3.41786	0.509505
$46$	−15.7032	−2.31530
$47$	6.14413	0.896213	0.448107	−	0.893980i	$-0.352098\pi$
$47$	6.14413	0.896213	0.448107	+	0.893980i	$0.352098\pi$
$48$	1.36808	0.197465
$49$	−5.76617	−0.823738
$50$	6.54809	0.926040
$51$	−0.465162	−0.0651357
$52$	3.57377	0.495593
$53$	6.22973	0.855720	0.427860	−	0.903845i	$-0.359268\pi$
$53$	6.22973	0.855720	0.427860	+	0.903845i	$0.359268\pi$
$54$	10.5202	1.43162
$55$	6.01252	0.810729
$56$	4.12710	0.551507
$57$	2.79528	0.370243
$58$	9.94789	1.30622
$59$	−1.22581	−0.159587	−0.0797935	−	0.996811i	$-0.525426\pi$
$59$	−1.22581	−0.159587	−0.0797935	+	0.996811i	$0.525426\pi$
$60$	−4.49132	−0.579827
$61$	−5.39620	−0.690912	−0.345456	−	0.938435i	$-0.612276\pi$
$61$	−5.39620	−0.690912	−0.345456	+	0.938435i	$0.612276\pi$
$62$	−19.7465	−2.50781
$63$	2.54436	0.320559
$64$	−11.7388	−1.46735
$65$	−1.49212	−0.185075
$66$	8.01255	0.986277
$67$	2.00241	0.244633	0.122317	−	0.992491i	$-0.460968\pi$
$67$	2.00241	0.244633	0.122317	+	0.992491i	$0.460968\pi$
$68$	−1.97373	−0.239350
$69$	5.60216	0.674421
$70$	−3.91297	−0.467689
$71$	0.614736	0.0729557	0.0364779	−	0.999334i	$-0.488386\pi$
$71$	0.614736	0.0729557	0.0364779	+	0.999334i	$0.488386\pi$
$72$	8.51074	1.00300
$73$	−10.5550	−1.23537	−0.617686	−	0.786425i	$-0.711930\pi$
$73$	−10.5550	−1.23537	−0.617686	+	0.786425i	$0.711930\pi$
$74$	18.7516	2.17983
$75$	−2.33606	−0.269745
$76$	11.8606	1.36051
$77$	4.47591	0.510077
$78$	−1.98846	−0.225149
$79$	−0.421182	−0.0473866	−0.0236933	−	0.999719i	$-0.507543\pi$
$79$	−0.421182	−0.0473866	−0.0236933	+	0.999719i	$0.507543\pi$
$80$	−2.42366	−0.270973
$81$	3.11871	0.346523
$82$	−25.0679	−2.76829
$83$	4.75340	0.521753	0.260877	−	0.965372i	$-0.415988\pi$
$83$	4.75340	0.521753	0.260877	+	0.965372i	$0.415988\pi$
$84$	−3.34348	−0.364803
$85$	0.824071	0.0893831
$86$	4.50375	0.485652
$87$	−3.54895	−0.380487
$88$	14.9716	1.59598
$89$	10.9624	1.16201	0.581007	−	0.813899i	$-0.302659\pi$
$89$	10.9624	1.16201	0.581007	+	0.813899i	$0.302659\pi$
$90$	−8.06918	−0.850566
$91$	−1.11078	−0.116441
$92$	23.7706	2.47825
$93$	7.04463	0.730495
$94$	−14.5056	−1.49614
$95$	−4.95205	−0.508070
$96$	3.02891	0.309137
$97$	5.73345	0.582144	0.291072	−	0.956701i	$-0.405988\pi$
$97$	5.73345	0.582144	0.291072	+	0.956701i	$0.405988\pi$
$98$	13.6133	1.37515
$99$	9.23004	0.927654
$100$	−9.91213	−0.991213
$101$	9.25237	0.920645	0.460323	−	0.887752i	$-0.347734\pi$
$101$	9.25237	0.920645	0.460323	+	0.887752i	$0.347734\pi$
$102$	1.09819	0.108737
$103$	0.522737	0.0515068	0.0257534	−	0.999668i	$-0.491802\pi$
$103$	0.522737	0.0515068	0.0257534	+	0.999668i	$0.491802\pi$
$104$	−3.71549	−0.364334
$105$	1.39597	0.136232
$106$	−14.7077	−1.42854
$107$	13.3705	1.29257	0.646287	−	0.763095i	$-0.276321\pi$
$107$	13.3705	1.29257	0.646287	+	0.763095i	$0.276321\pi$
$108$	−15.9249	−1.53237
$109$	−4.35596	−0.417226	−0.208613	−	0.977998i	$-0.566895\pi$
$109$	−4.35596	−0.417226	−0.208613	+	0.977998i	$0.566895\pi$
$110$	−14.1949	−1.35343
$111$	−6.68972	−0.634960
$112$	−1.80424	−0.170485
$113$	−6.53192	−0.614471	−0.307236	−	0.951633i	$-0.599404\pi$
$113$	−6.53192	−0.614471	−0.307236	+	0.951633i	$0.599404\pi$
$114$	−6.59932	−0.618083
$115$	−9.92467	−0.925481
$116$	−15.0586	−1.39815
$117$	−2.29061	−0.211767
$118$	2.89400	0.266414
$119$	0.613464	0.0562361
$120$	4.66943	0.426258
$121$	5.23701	0.476092
$122$	12.7398	1.15341
$123$	8.94308	0.806371
$124$	29.8911	2.68430
$125$	11.5991	1.03746
$126$	−6.00694	−0.535141
$127$	6.42505	0.570131	0.285066	−	0.958508i	$-0.407985\pi$
$127$	6.42505	0.570131	0.285066	+	0.958508i	$0.407985\pi$
$128$	20.5216	1.81387
$129$	−1.60673	−0.141465
$130$	3.52272	0.308963
$131$	11.5028	1.00500	0.502501	−	0.864576i	$-0.332413\pi$
$131$	11.5028	1.00500	0.502501	+	0.864576i	$0.332413\pi$
$132$	−12.1289	−1.05569
$133$	−3.68646	−0.319657
$134$	−4.72746	−0.408390
$135$	6.64894	0.572250
$136$	2.05200	0.175958
$137$	4.21690	0.360274	0.180137	−	0.983642i	$-0.442346\pi$
$137$	4.21690	0.360274	0.180137	+	0.983642i	$0.442346\pi$
$138$	−13.2261	−1.12588
$139$	−1.06118	−0.0900079	−0.0450039	−	0.998987i	$-0.514330\pi$
$139$	−1.06118	−0.0900079	−0.0450039	+	0.998987i	$0.514330\pi$
$140$	5.92323	0.500605
$141$	5.17492	0.435807
$142$	−1.45132	−0.121792
$143$	−4.02952	−0.336965
$144$	−3.72064	−0.310054
$145$	6.28724	0.522127
$146$	24.9192	2.06233
$147$	−4.85658	−0.400564
$148$	−28.3852	−2.33325
$149$	15.4857	1.26864	0.634320	−	0.773070i	$-0.281280\pi$
$149$	15.4857	1.26864	0.634320	+	0.773070i	$0.281280\pi$
$150$	5.51516	0.450311
$151$	−5.34591	−0.435044	−0.217522	−	0.976055i	$-0.569797\pi$
$151$	−5.34591	−0.435044	−0.217522	+	0.976055i	$0.569797\pi$
$152$	−12.3310	−1.00018
$153$	1.26506	0.102274
$154$	−10.5671	−0.851521
$155$	−12.4801	−1.00243
$156$	3.01003	0.240995
$157$	−23.8554	−1.90387	−0.951936	−	0.306298i	$-0.900910\pi$
$157$	−23.8554	−1.90387	−0.951936	+	0.306298i	$0.900910\pi$
$158$	0.994361	0.0791071
$159$	5.24702	0.416116
$160$	−5.36595	−0.424216
$161$	−7.38823	−0.582274
$162$	−7.36290	−0.578484
$163$	3.26411	0.255665	0.127832	−	0.991796i	$-0.459198\pi$
$163$	3.26411	0.255665	0.127832	+	0.991796i	$0.459198\pi$
$164$	37.9464	2.96312
$165$	5.06407	0.394238
$166$	−11.2222	−0.871013
$167$	−9.45268	−0.731470	−0.365735	−	0.930719i	$-0.619182\pi$
$167$	−9.45268	−0.731470	−0.365735	+	0.930719i	$0.619182\pi$
$168$	3.47607	0.268184
$169$	1.00000	0.0769231
$170$	−1.94554	−0.149216
$171$	−7.60207	−0.581345
$172$	−6.81752	−0.519831
$173$	−25.7126	−1.95489	−0.977447	−	0.211183i	$-0.932268\pi$
$173$	−25.7126	−1.95489	−0.977447	+	0.211183i	$0.932268\pi$
$174$	8.37865	0.635184
$175$	3.08083	0.232889
$176$	−6.54516	−0.493360
$177$	−1.03244	−0.0776033
$178$	−25.8810	−1.93986
$179$	4.60035	0.343846	0.171923	−	0.985110i	$-0.445002\pi$
$179$	4.60035	0.343846	0.171923	+	0.985110i	$0.445002\pi$
$180$	12.2147	0.910427
$181$	−24.1233	−1.79307	−0.896536	−	0.442971i	$-0.853925\pi$
$181$	−24.1233	−1.79307	−0.896536	+	0.442971i	$0.853925\pi$
$182$	2.62242	0.194387
$183$	−4.54497	−0.335974
$184$	−24.7132	−1.82188
$185$	11.8514	0.871330
$186$	−16.6316	−1.21949
$187$	2.22543	0.162740
$188$	21.9577	1.60143
$189$	4.94968	0.360036
$190$	11.6912	0.848170
$191$	11.3389	0.820456	0.410228	−	0.911983i	$-0.365449\pi$
$191$	11.3389	0.820456	0.410228	+	0.911983i	$0.365449\pi$
$192$	−9.88706	−0.713537
$193$	−9.79782	−0.705263	−0.352631	−	0.935762i	$-0.614713\pi$
$193$	−9.79782	−0.705263	−0.352631	+	0.935762i	$0.614713\pi$
$194$	−13.5360	−0.971829
$195$	−1.25674	−0.0899974
$196$	−20.6070	−1.47193
$197$	−7.46261	−0.531689	−0.265844	−	0.964016i	$-0.585651\pi$
$197$	−7.46261	−0.531689	−0.265844	+	0.964016i	$0.585651\pi$
$198$	−21.7911	−1.54862
$199$	8.02015	0.568533	0.284267	−	0.958745i	$-0.408250\pi$
$199$	8.02015	0.568533	0.284267	+	0.958745i	$0.408250\pi$
$200$	10.3052	0.728688
$201$	1.68654	0.118959
$202$	−21.8438	−1.53692
$203$	4.68042	0.328501
$204$	−1.66238	−0.116390
$205$	−15.8434	−1.10655
$206$	−1.23412	−0.0859853
$207$	−15.2357	−1.05896
$208$	1.62430	0.112625
$209$	−13.3732	−0.925041
$210$	−3.29572	−0.227426
$211$	19.6889	1.35544	0.677719	−	0.735321i	$-0.262969\pi$
$211$	19.6889	1.35544	0.677719	+	0.735321i	$0.262969\pi$
$212$	22.2637	1.52907
$213$	0.517764	0.0354766
$214$	−31.5662	−2.15782
$215$	2.84645	0.194126
$216$	16.5564	1.12652
$217$	−9.29059	−0.630686
$218$	10.2839	0.696515
$219$	−8.89002	−0.600732
$220$	21.4874	1.44868
$221$	−0.552282	−0.0371505
$222$	15.7936	1.06000
$223$	17.1920	1.15126	0.575630	−	0.817710i	$-0.304757\pi$
$223$	17.1920	1.15126	0.575630	+	0.817710i	$0.304757\pi$
$224$	−3.99458	−0.266899
$225$	6.35318	0.423545
$226$	15.4211	1.02580
$227$	−7.58483	−0.503423	−0.251711	−	0.967802i	$-0.580993\pi$
$227$	−7.58483	−0.503423	−0.251711	+	0.967802i	$0.580993\pi$
$228$	9.98968	0.661583
$229$	5.18139	0.342396	0.171198	−	0.985237i	$-0.445236\pi$
$229$	5.18139	0.342396	0.171198	+	0.985237i	$0.445236\pi$
$230$	23.4310	1.54499
$231$	3.76985	0.248038
$232$	15.6557	1.02785
$233$	−23.9444	−1.56865	−0.784325	−	0.620350i	$-0.786991\pi$
$233$	−23.9444	−1.56865	−0.784325	+	0.620350i	$0.786991\pi$
$234$	5.40786	0.353523
$235$	−9.16778	−0.598040
$236$	−4.38077	−0.285164
$237$	−0.354742	−0.0230430
$238$	−1.44832	−0.0938805
$239$	−3.80470	−0.246105	−0.123053	−	0.992400i	$-0.539268\pi$
$239$	−3.80470	−0.246105	−0.123053	+	0.992400i	$0.539268\pi$
$240$	−2.04134	−0.131768
$241$	19.5047	1.25641	0.628204	−	0.778048i	$-0.283790\pi$
$241$	19.5047	1.25641	0.628204	+	0.778048i	$0.283790\pi$
$242$	−12.3640	−0.794786
$243$	15.9949	1.02607
$244$	−19.2848	−1.23458
$245$	8.60382	0.549678
$246$	−21.1136	−1.34615
$247$	3.31880	0.211170
$248$	−31.0765	−1.97336
$249$	4.00357	0.253716
$250$	−27.3842	−1.73193
$251$	−27.7486	−1.75148	−0.875738	−	0.482786i	$-0.839625\pi$
$251$	−27.7486	−1.75148	−0.875738	+	0.482786i	$0.839625\pi$
$252$	9.09297	0.572803
$253$	−26.8019	−1.68502
$254$	−15.1688	−0.951775
$255$	0.694078	0.0434648
$256$	−24.9714	−1.56071
$257$	4.37896	0.273152	0.136576	−	0.990630i	$-0.456390\pi$
$257$	4.37896	0.273152	0.136576	+	0.990630i	$0.456390\pi$
$258$	3.79330	0.236161
$259$	8.82252	0.548205
$260$	−5.33250	−0.330708
$261$	9.65177	0.597430
$262$	−27.1567	−1.67775
$263$	5.94176	0.366384	0.183192	−	0.983077i	$-0.441357\pi$
$263$	5.94176	0.366384	0.183192	+	0.983077i	$0.441357\pi$
$264$	12.6099	0.776088
$265$	−9.29551	−0.571019
$266$	8.70330	0.533634
$267$	9.23315	0.565059
$268$	7.15616	0.437132
$269$	1.03525	0.0631200	0.0315600	−	0.999502i	$-0.489952\pi$
$269$	1.03525	0.0631200	0.0315600	+	0.999502i	$0.489952\pi$
$270$	−15.6974	−0.955312
$271$	−1.49617	−0.0908862	−0.0454431	−	0.998967i	$-0.514470\pi$
$271$	−1.49617	−0.0908862	−0.0454431	+	0.998967i	$0.514470\pi$
$272$	−0.897074	−0.0543931
$273$	−0.935560	−0.0566226
$274$	−9.95561	−0.601441
$275$	11.1762	0.673949
$276$	20.0209	1.20511
$277$	−21.0065	−1.26216	−0.631081	−	0.775717i	$-0.717388\pi$
$277$	−21.0065	−1.26216	−0.631081	+	0.775717i	$0.717388\pi$
$278$	2.50532	0.150259
$279$	−19.1587	−1.14700
$280$	−6.15813	−0.368018
$281$	−19.9178	−1.18819	−0.594097	−	0.804393i	$-0.702491\pi$
$281$	−19.9178	−1.18819	−0.594097	+	0.804393i	$0.702491\pi$
$282$	−12.2174	−0.727535
$283$	4.44783	0.264396	0.132198	−	0.991223i	$-0.457797\pi$
$283$	4.44783	0.264396	0.132198	+	0.991223i	$0.457797\pi$
$284$	2.19693	0.130364
$285$	−4.17089	−0.247062
$286$	9.51322	0.562529
$287$	−11.7943	−0.696195
$288$	−8.23747	−0.485398
$289$	−16.6950	−0.982058
$290$	−14.8434	−0.871637
$291$	4.82902	0.283082
$292$	−37.7213	−2.20747
$293$	−18.3831	−1.07395	−0.536975	−	0.843598i	$-0.680433\pi$
$293$	−18.3831	−1.07395	−0.536975	+	0.843598i	$0.680433\pi$
$294$	11.4658	0.668700
$295$	1.82906	0.106492
$296$	29.5108	1.71528
$297$	17.9557	1.04189
$298$	−36.5600	−2.11787
$299$	6.65139	0.384660
$300$	−8.34854	−0.482003
$301$	2.11899	0.122136
$302$	12.6211	0.726262
$303$	7.79285	0.447687
$304$	5.39074	0.309180
$305$	8.05177	0.461043
$306$	−2.98666	−0.170736
$307$	29.2624	1.67009	0.835047	−	0.550179i	$-0.185441\pi$
$307$	29.2624	1.67009	0.835047	+	0.550179i	$0.185441\pi$
$308$	15.9959	0.911450
$309$	0.440278	0.0250465
$310$	29.4641	1.67345
$311$	−2.48545	−0.140937	−0.0704684	−	0.997514i	$-0.522449\pi$
$311$	−2.48545	−0.140937	−0.0704684	+	0.997514i	$0.522449\pi$
$312$	−3.12939	−0.177167
$313$	−10.6710	−0.603161	−0.301580	−	0.953441i	$-0.597514\pi$
$313$	−10.6710	−0.603161	−0.301580	+	0.953441i	$0.597514\pi$
$314$	56.3199	3.17832
$315$	−3.79649	−0.213908
$316$	−1.50521	−0.0846745
$317$	−2.28107	−0.128118	−0.0640589	−	0.997946i	$-0.520405\pi$
$317$	−2.28107	−0.128118	−0.0640589	+	0.997946i	$0.520405\pi$
$318$	−12.3876	−0.694662
$319$	16.9789	0.950635
$320$	17.5157	0.979158
$321$	11.2614	0.628547
$322$	17.4428	0.972047
$323$	−1.83291	−0.101986
$324$	11.1455	0.619197
$325$	−2.77358	−0.153850
$326$	−7.70617	−0.426806
$327$	−3.66883	−0.202887
$328$	−39.4512	−2.17833
$329$	−6.82478	−0.376262
$330$	−11.9557	−0.658139
$331$	−6.30428	−0.346514	−0.173257	−	0.984877i	$-0.555429\pi$
$331$	−6.30428	−0.346514	−0.173257	+	0.984877i	$0.555429\pi$
$332$	16.9876	0.932314
$333$	18.1935	0.996995
$334$	22.3167	1.22111
$335$	−2.98784	−0.163243
$336$	−1.51963	−0.0829028
$337$	7.27617	0.396358	0.198179	−	0.980166i	$-0.436497\pi$
$337$	7.27617	0.396358	0.198179	+	0.980166i	$0.436497\pi$
$338$	−2.36088	−0.128415
$339$	−5.50154	−0.298802
$340$	2.94504	0.159717
$341$	−33.7030	−1.82512
$342$	17.9476	0.970496
$343$	14.1804	0.765670
$344$	7.08788	0.382153
$345$	−8.35910	−0.450039
$346$	60.7045	3.26349
$347$	−31.9767	−1.71660	−0.858299	−	0.513150i	$-0.828478\pi$
$347$	−31.9767	−1.71660	−0.858299	+	0.513150i	$0.828478\pi$
$348$	−12.6831	−0.679887
$349$	−12.8206	−0.686273	−0.343137	−	0.939285i	$-0.611489\pi$
$349$	−12.8206	−0.686273	−0.343137	+	0.939285i	$0.611489\pi$
$350$	−7.27349	−0.388784
$351$	−4.45604	−0.237846
$352$	−14.4909	−0.772369
$353$	25.9102	1.37906	0.689530	−	0.724257i	$-0.257817\pi$
$353$	25.9102	1.37906	0.689530	+	0.724257i	$0.257817\pi$
$354$	2.43748	0.129551
$355$	−0.917260	−0.0486831
$356$	39.1772	2.07639
$357$	0.516693	0.0273463
$358$	−10.8609	−0.574016
$359$	−31.6273	−1.66922	−0.834612	−	0.550839i	$-0.814308\pi$
$359$	−31.6273	−1.66922	−0.834612	+	0.550839i	$0.814308\pi$
$360$	−12.6990	−0.669298
$361$	−7.98556	−0.420292
$362$	56.9524	2.99335
$363$	4.41089	0.231512
$364$	−3.96968	−0.208068
$365$	15.7494	0.824360
$366$	10.7301	0.560874
$367$	−3.51495	−0.183479	−0.0917393	−	0.995783i	$-0.529243\pi$
$367$	−3.51495	−0.183479	−0.0917393	+	0.995783i	$0.529243\pi$
$368$	10.8039	0.563191
$369$	−24.3217	−1.26614
$370$	−27.9797	−1.45459
$371$	−6.91987	−0.359261
$372$	25.1759	1.30531
$373$	10.2744	0.531987	0.265993	−	0.963975i	$-0.414300\pi$
$373$	10.2744	0.531987	0.265993	+	0.963975i	$0.414300\pi$
$374$	−5.25398	−0.271677
$375$	9.76940	0.504490
$376$	−22.8285	−1.17729
$377$	−4.21363	−0.217013
$378$	−11.6856	−0.601043
$379$	−25.4144	−1.30545	−0.652725	−	0.757595i	$-0.726374\pi$
$379$	−25.4144	−1.30545	−0.652725	+	0.757595i	$0.726374\pi$
$380$	−17.6975	−0.907863
$381$	5.41153	0.277241
$382$	−26.7699	−1.36967
$383$	23.8061	1.21643	0.608217	−	0.793771i	$-0.291885\pi$
$383$	23.8061	1.21643	0.608217	+	0.793771i	$0.291885\pi$
$384$	17.2844	0.882040
$385$	−6.67859	−0.340373
$386$	23.1315	1.17736
$387$	4.36969	0.222124
$388$	20.4901	1.04022
$389$	8.82168	0.447277	0.223639	−	0.974672i	$-0.428206\pi$
$389$	8.82168	0.447277	0.223639	+	0.974672i	$0.428206\pi$
$390$	2.96703	0.150241
$391$	−3.67344	−0.185774
$392$	21.4242	1.08208
$393$	9.68827	0.488708
$394$	17.6183	0.887599
$395$	0.628454	0.0316209
$396$	32.9861	1.65761
$397$	−38.5941	−1.93698	−0.968491	−	0.249047i	$-0.919883\pi$
$397$	−38.5941	−1.93698	−0.968491	+	0.249047i	$0.919883\pi$
$398$	−18.9346	−0.949108
$399$	−3.10494	−0.155441
$400$	−4.50513	−0.225257
$401$	−7.47951	−0.373509	−0.186755	−	0.982407i	$-0.559797\pi$
$401$	−7.47951	−0.373509	−0.186755	+	0.982407i	$0.559797\pi$
$402$	−3.98172	−0.198590
$403$	8.36402	0.416642
$404$	33.0659	1.64509
$405$	−4.65348	−0.231233
$406$	−11.0499	−0.548398
$407$	32.0050	1.58643
$408$	1.72831	0.0855639
$409$	18.6152	0.920461	0.460231	−	0.887799i	$-0.347767\pi$
$409$	18.6152	0.920461	0.460231	+	0.887799i	$0.347767\pi$
$410$	37.4044	1.84727
$411$	3.55170	0.175193
$412$	1.86814	0.0920368
$413$	1.36161	0.0670003
$414$	35.9698	1.76782
$415$	−7.09264	−0.348164
$416$	3.59619	0.176318
$417$	−0.893781	−0.0437686
$418$	31.5725	1.54426
$419$	−29.4583	−1.43913	−0.719565	−	0.694425i	$-0.755659\pi$
$419$	−29.4583	−1.43913	−0.719565	+	0.694425i	$0.755659\pi$
$420$	4.98887	0.243432
$421$	−14.8376	−0.723141	−0.361571	−	0.932345i	$-0.617759\pi$
$421$	−14.8376	−0.723141	−0.361571	+	0.932345i	$0.617759\pi$
$422$	−46.4831	−2.26276
$423$	−14.0738	−0.684291
$424$	−23.1465	−1.12410
$425$	1.53180	0.0743031
$426$	−1.22238	−0.0592245
$427$	5.99399	0.290069
$428$	47.7831	2.30968
$429$	−3.39388	−0.163858
$430$	−6.72014	−0.324074
$431$	−7.67219	−0.369556	−0.184778	−	0.982780i	$-0.559157\pi$
$431$	−7.67219	−0.369556	−0.184778	+	0.982780i	$0.559157\pi$
$432$	−7.23796	−0.348237
$433$	5.51644	0.265103	0.132552	−	0.991176i	$-0.457683\pi$
$433$	5.51644	0.265103	0.132552	+	0.991176i	$0.457683\pi$
$434$	21.9340	1.05287
$435$	5.29546	0.253898
$436$	−15.5672	−0.745535
$437$	22.0746	1.05597
$438$	20.9883	1.00286
$439$	−24.2182	−1.15587	−0.577937	−	0.816081i	$-0.696142\pi$
$439$	−24.2182	−1.15587	−0.577937	+	0.816081i	$0.696142\pi$
$440$	−22.3395	−1.06499
$441$	13.2080	0.628954
$442$	1.30387	0.0620189
$443$	−31.1350	−1.47927	−0.739634	−	0.673009i	$-0.765002\pi$
$443$	−31.1350	−1.47927	−0.739634	+	0.673009i	$0.765002\pi$
$444$	−23.9075	−1.13460
$445$	−16.3572	−0.775408
$446$	−40.5883	−1.92191
$447$	13.0429	0.616909
$448$	13.0392	0.616046
$449$	−23.6827	−1.11765	−0.558827	−	0.829284i	$-0.688749\pi$
$449$	−23.6827	−1.11765	−0.558827	+	0.829284i	$0.688749\pi$
$450$	−14.9991	−0.707065
$451$	−42.7855	−2.01469
$452$	−23.3436	−1.09799
$453$	−4.50262	−0.211551
$454$	17.9069	0.840412
$455$	1.65742	0.0777009
$456$	−10.3858	−0.486361
$457$	−23.2451	−1.08736	−0.543680	−	0.839292i	$-0.682970\pi$
$457$	−23.2451	−1.08736	−0.543680	+	0.839292i	$0.682970\pi$
$458$	−12.2327	−0.571595
$459$	2.46099	0.114869
$460$	−35.4685	−1.65373
$461$	39.8332	1.85522	0.927608	−	0.373554i	$-0.121861\pi$
$461$	39.8332	1.85522	0.927608	+	0.373554i	$0.121861\pi$
$462$	−8.90018	−0.414074
$463$	40.0564	1.86158	0.930790	−	0.365553i	$-0.119120\pi$
$463$	40.0564	1.86158	0.930790	+	0.365553i	$0.119120\pi$
$464$	−6.84422	−0.317735
$465$	−10.5114	−0.487456
$466$	56.5300	2.61870
$467$	29.4700	1.36371	0.681854	−	0.731489i	$-0.261174\pi$
$467$	29.4700	1.36371	0.681854	+	0.731489i	$0.261174\pi$
$468$	−8.18611	−0.378403
$469$	−2.22424	−0.102706
$470$	21.6441	0.998366
$471$	−20.0924	−0.925807
$472$	4.55449	0.209637
$473$	7.68693	0.353445
$474$	0.837505	0.0384679
$475$	−9.20495	−0.422352
$476$	2.19238	0.100488
$477$	−14.2699	−0.653373
$478$	8.98245	0.410848
$479$	−38.7881	−1.77228	−0.886138	−	0.463422i	$-0.846621\pi$
$479$	−38.7881	−1.77228	−0.886138	+	0.463422i	$0.846621\pi$
$480$	−4.51950	−0.206286
$481$	−7.94263	−0.362153
$482$	−46.0483	−2.09744
$483$	−6.22277	−0.283146
$484$	18.7159	0.850721
$485$	−8.55500	−0.388463
$486$	−37.7620	−1.71292
$487$	25.3558	1.14898	0.574490	−	0.818512i	$-0.305201\pi$
$487$	25.3558	1.14898	0.574490	+	0.818512i	$0.305201\pi$
$488$	20.0495	0.907600
$489$	2.74921	0.124323
$490$	−20.3126	−0.917630
$491$	13.1626	0.594021	0.297010	−	0.954874i	$-0.404010\pi$
$491$	13.1626	0.594021	0.297010	+	0.954874i	$0.404010\pi$
$492$	31.9605	1.44089
$493$	2.32711	0.104808
$494$	−7.83530	−0.352527
$495$	−13.7723	−0.619020
$496$	13.5857	0.610017
$497$	−0.682836	−0.0306294
$498$	−9.45196	−0.423553
$499$	5.54956	0.248432	0.124216	−	0.992255i	$-0.460358\pi$
$499$	5.54956	0.248432	0.124216	+	0.992255i	$0.460358\pi$
$500$	41.4526	1.85382
$501$	−7.96156	−0.355696
$502$	65.5112	2.92391
$503$	10.3359	0.460854	0.230427	−	0.973090i	$-0.425988\pi$
$503$	10.3359	0.460854	0.230427	+	0.973090i	$0.425988\pi$
$504$	−9.45356	−0.421095
$505$	−13.8057	−0.614343
$506$	63.2761	2.81297
$507$	0.842254	0.0374058
$508$	22.9617	1.01876
$509$	16.9481	0.751213	0.375606	−	0.926779i	$-0.377434\pi$
$509$	16.9481	0.751213	0.375606	+	0.926779i	$0.377434\pi$
$510$	−1.63864	−0.0725600
$511$	11.7243	0.518653
$512$	17.9115	0.791584
$513$	−14.7887	−0.652937
$514$	−10.3382	−0.455999
$515$	−0.779987	−0.0343703
$516$	−5.74209	−0.252781
$517$	−24.7579	−1.08885
$518$	−20.8289	−0.915171
$519$	−21.6566	−0.950617
$520$	5.54396	0.243119
$521$	1.07030	0.0468908	0.0234454	−	0.999725i	$-0.492536\pi$
$521$	1.07030	0.0468908	0.0234454	+	0.999725i	$0.492536\pi$
$522$	−22.7867	−0.997347
$523$	24.0357	1.05101	0.525504	−	0.850791i	$-0.323877\pi$
$523$	24.0357	1.05101	0.525504	+	0.850791i	$0.323877\pi$
$524$	41.1083	1.79583
$525$	2.59485	0.113248
$526$	−14.0278	−0.611641
$527$	−4.61930	−0.201220
$528$	−5.51269	−0.239909
$529$	21.2410	0.923521
$530$	21.9456	0.953257
$531$	2.80785	0.121850
$532$	−13.1746	−0.571190
$533$	10.6180	0.459918
$534$	−21.7984	−0.943308
$535$	−19.9504	−0.862530
$536$	−7.43995	−0.321357
$537$	3.87466	0.167204
$538$	−2.44409	−0.105372
$539$	23.2349	1.00080
$540$	23.7618	1.02255
$541$	−10.4810	−0.450614	−0.225307	−	0.974288i	$-0.572338\pi$
$541$	−10.4810	−0.450614	−0.225307	+	0.974288i	$0.572338\pi$
$542$	3.53230	0.151725
$543$	−20.3180	−0.871928
$544$	−1.98611	−0.0851539
$545$	6.49962	0.278413
$546$	2.20875	0.0945257
$547$	−29.8181	−1.27493	−0.637465	−	0.770479i	$-0.720017\pi$
$547$	−29.8181	−1.27493	−0.637465	+	0.770479i	$0.720017\pi$
$548$	15.0702	0.643769
$549$	12.3606	0.527536
$550$	−26.3857	−1.12509
$551$	−13.9842	−0.595747
$552$	−20.8148	−0.885937
$553$	0.467840	0.0198946
$554$	49.5940	2.10705
$555$	9.98186	0.423706
$556$	−3.79241	−0.160834
$557$	−1.00405	−0.0425431	−0.0212716	−	0.999774i	$-0.506771\pi$
$557$	−1.00405	−0.0425431	−0.0212716	+	0.999774i	$0.506771\pi$
$558$	45.2314	1.91480
$559$	−1.90766	−0.0806852
$560$	2.69215	0.113764
$561$	1.87438	0.0791363
$562$	47.0235	1.98357
$563$	30.6111	1.29010	0.645052	−	0.764139i	$-0.276836\pi$
$563$	30.6111	1.29010	0.645052	+	0.764139i	$0.276836\pi$
$564$	18.4940	0.778737
$565$	9.74641	0.410035
$566$	−10.5008	−0.441382
$567$	−3.46420	−0.145483
$568$	−2.28405	−0.0958365
$569$	17.1696	0.719788	0.359894	−	0.932993i	$-0.382813\pi$
$569$	17.1696	0.719788	0.359894	+	0.932993i	$0.382813\pi$
$570$	9.84698	0.412445
$571$	−32.6019	−1.36435	−0.682174	−	0.731190i	$-0.738966\pi$
$571$	−32.6019	−1.36435	−0.682174	+	0.731190i	$0.738966\pi$
$572$	−14.4006	−0.602118
$573$	9.55026	0.398968
$574$	27.8450	1.16223
$575$	−18.4481	−0.769341
$576$	26.8890	1.12037
$577$	42.5497	1.77137	0.885683	−	0.464291i	$-0.153691\pi$
$577$	42.5497	1.77137	0.885683	+	0.464291i	$0.153691\pi$
$578$	39.4149	1.63944
$579$	−8.25226	−0.342952
$580$	22.4692	0.932982
$581$	−5.27998	−0.219050
$582$	−11.4008	−0.472577
$583$	−25.1028	−1.03965
$584$	39.2171	1.62282
$585$	3.41786	0.141311
$586$	43.4003	1.79285
$587$	18.4839	0.762912	0.381456	−	0.924387i	$-0.375423\pi$
$587$	18.4839	0.762912	0.381456	+	0.924387i	$0.375423\pi$
$588$	−17.3563	−0.715762
$589$	27.7585	1.14377
$590$	−4.31819	−0.177777
$591$	−6.28541	−0.258547
$592$	−12.9013	−0.530238
$593$	−1.55593	−0.0638945	−0.0319473	−	0.999490i	$-0.510171\pi$
$593$	−1.55593	−0.0638945	−0.0319473	+	0.999490i	$0.510171\pi$
$594$	−42.3913	−1.73933
$595$	−0.915362	−0.0375262
$596$	55.3425	2.26692
$597$	6.75501	0.276464
$598$	−15.7032	−0.642150
$599$	−21.7797	−0.889895	−0.444947	−	0.895557i	$-0.646778\pi$
$599$	−21.7797	−0.889895	−0.444947	+	0.895557i	$0.646778\pi$
$600$	8.67961	0.354343
$601$	−9.74175	−0.397374	−0.198687	−	0.980063i	$-0.563668\pi$
$601$	−9.74175	−0.397374	−0.198687	+	0.980063i	$0.563668\pi$
$602$	−5.00268	−0.203894
$603$	−4.58674	−0.186786
$604$	−19.1051	−0.777375
$605$	−7.81424	−0.317694
$606$	−18.3980	−0.747368
$607$	21.5635	0.875236	0.437618	−	0.899161i	$-0.355822\pi$
$607$	21.5635	0.875236	0.437618	+	0.899161i	$0.355822\pi$
$608$	11.9351	0.484030
$609$	3.94210	0.159742
$610$	−19.0093	−0.769664
$611$	6.14413	0.248565
$612$	4.52104	0.182752
$613$	30.3385	1.22536	0.612681	−	0.790331i	$-0.290091\pi$
$613$	30.3385	1.22536	0.612681	+	0.790331i	$0.290091\pi$
$614$	−69.0851	−2.78805
$615$	−13.3442	−0.538088
$616$	−16.6302	−0.670050
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−1.03944	−0.0418126
$619$	19.7686	0.794567	0.397284	−	0.917696i	$-0.369953\pi$
$619$	19.7686	0.794567	0.397284	+	0.917696i	$0.369953\pi$
$620$	−44.6011	−1.79122
$621$	−29.6388	−1.18937
$622$	5.86785	0.235279
$623$	−12.1768	−0.487855
$624$	1.36808	0.0547669
$625$	−3.43939	−0.137575
$626$	25.1930	1.00691
$627$	−11.2636	−0.449825
$628$	−85.2539	−3.40200
$629$	4.38657	0.174904
$630$	8.96308	0.357098
$631$	7.69381	0.306286	0.153143	−	0.988204i	$-0.451061\pi$
$631$	7.69381	0.306286	0.153143	+	0.988204i	$0.451061\pi$
$632$	1.56490	0.0622483
$633$	16.5830	0.659116
$634$	5.38535	0.213880
$635$	−9.58695	−0.380447
$636$	18.7517	0.743552
$637$	−5.76617	−0.228464
$638$	−40.0852	−1.58699
$639$	−1.40812	−0.0557043
$640$	−30.6206	−1.21039
$641$	−34.7073	−1.37086	−0.685428	−	0.728140i	$-0.740385\pi$
$641$	−34.7073	−1.37086	−0.685428	+	0.728140i	$0.740385\pi$
$642$	−26.5867	−1.04929
$643$	−4.10986	−0.162077	−0.0810385	−	0.996711i	$-0.525824\pi$
$643$	−4.10986	−0.162077	−0.0810385	+	0.996711i	$0.525824\pi$
$644$	−26.4039	−1.04046
$645$	2.39744	0.0943989
$646$	4.32730	0.170255
$647$	−50.6102	−1.98969	−0.994846	−	0.101401i	$-0.967668\pi$
$647$	−50.6102	−1.98969	−0.994846	+	0.101401i	$0.967668\pi$
$648$	−11.5875	−0.455201
$649$	4.93943	0.193889
$650$	6.54809	0.256837
$651$	−7.82504	−0.306688
$652$	11.6652	0.456843
$653$	−9.56040	−0.374127	−0.187064	−	0.982348i	$-0.559897\pi$
$653$	−9.56040	−0.374127	−0.187064	+	0.982348i	$0.559897\pi$
$654$	8.66168	0.338699
$655$	−17.1635	−0.670635
$656$	17.2469	0.673379
$657$	24.1774	0.943251
$658$	16.1125	0.628131
$659$	46.4542	1.80960	0.904799	−	0.425838i	$-0.140021\pi$
$659$	46.4542	1.80960	0.904799	+	0.425838i	$0.140021\pi$
$660$	18.0979	0.704458
$661$	−21.4062	−0.832605	−0.416303	−	0.909226i	$-0.636674\pi$
$661$	−21.4062	−0.832605	−0.416303	+	0.909226i	$0.636674\pi$
$662$	14.8837	0.578470
$663$	−0.465162	−0.0180654
$664$	−17.6612	−0.685388
$665$	5.50064	0.213306
$666$	−42.9526	−1.66438
$667$	−28.0265	−1.08519
$668$	−33.7817	−1.30705
$669$	14.4800	0.559830
$670$	7.05394	0.272517
$671$	21.7441	0.839420
$672$	−3.36445	−0.129787
$673$	51.0194	1.96665	0.983326	−	0.181849i	$-0.0582082\pi$
$673$	51.0194	1.96665	0.983326	+	0.181849i	$0.0582082\pi$
$674$	−17.1782	−0.661680
$675$	12.3592	0.475704
$676$	3.57377	0.137453
$677$	−39.8547	−1.53174	−0.765870	−	0.642996i	$-0.777691\pi$
$677$	−39.8547	−1.53174	−0.765870	+	0.642996i	$0.777691\pi$
$678$	12.9885	0.498820
$679$	−6.36860	−0.244405
$680$	−3.06183	−0.117416
$681$	−6.38835	−0.244802
$682$	79.5688	3.04685
$683$	−19.5118	−0.746598	−0.373299	−	0.927711i	$-0.621773\pi$
$683$	−19.5118	−0.746598	−0.373299	+	0.927711i	$0.621773\pi$
$684$	−27.1681	−1.03880
$685$	−6.29212	−0.240410
$686$	−33.4783	−1.27821
$687$	4.36405	0.166499
$688$	−3.09861	−0.118133
$689$	6.22973	0.237334
$690$	19.7349	0.751293
$691$	−20.5940	−0.783433	−0.391717	−	0.920086i	$-0.628119\pi$
$691$	−20.5940	−0.783433	−0.391717	+	0.920086i	$0.628119\pi$
$692$	−91.8910	−3.49317
$693$	−10.2525	−0.389462
$694$	75.4932	2.86568
$695$	1.58340	0.0600619
$696$	13.1861	0.499818
$697$	−5.86415	−0.222120
$698$	30.2680	1.14566
$699$	−20.1673	−0.762797
$700$	11.0102	0.416146
$701$	−29.9768	−1.13221	−0.566104	−	0.824334i	$-0.691550\pi$
$701$	−29.9768	−1.13221	−0.566104	+	0.824334i	$0.691550\pi$
$702$	10.5202	0.397059
$703$	−26.3600	−0.994187
$704$	47.3017	1.78275
$705$	−7.72160	−0.290812
$706$	−61.1709	−2.30220
$707$	−10.2773	−0.386520
$708$	−3.68972	−0.138668
$709$	5.18527	0.194737	0.0973685	−	0.995248i	$-0.468957\pi$
$709$	5.18527	0.194737	0.0973685	+	0.995248i	$0.468957\pi$
$710$	2.16554	0.0812714
$711$	0.964762	0.0361814
$712$	−40.7308	−1.52645
$713$	55.6324	2.08345
$714$	−1.21985	−0.0456518
$715$	6.01252	0.224856
$716$	16.4406	0.614414
$717$	−3.20452	−0.119675
$718$	74.6683	2.78660
$719$	20.7096	0.772338	0.386169	−	0.922428i	$-0.373798\pi$
$719$	20.7096	0.772338	0.386169	+	0.922428i	$0.373798\pi$
$720$	5.55165	0.206898
$721$	−0.580646	−0.0216244
$722$	18.8530	0.701635
$723$	16.4279	0.610961
$724$	−86.2112	−3.20402
$725$	11.6868	0.434038
$726$	−10.4136	−0.386485
$727$	13.6661	0.506849	0.253425	−	0.967355i	$-0.418443\pi$
$727$	13.6661	0.506849	0.253425	+	0.967355i	$0.418443\pi$
$728$	4.12710	0.152960
$729$	4.11562	0.152430
$730$	−37.1824	−1.37618
$731$	1.05356	0.0389675
$732$	−16.2427	−0.600347
$733$	−35.2869	−1.30335	−0.651676	−	0.758497i	$-0.725934\pi$
$733$	−35.2869	−1.30335	−0.651676	+	0.758497i	$0.725934\pi$
$734$	8.29838	0.306299
$735$	7.24660	0.267295
$736$	23.9197	0.881691
$737$	−8.06875	−0.297216
$738$	57.4208	2.11369
$739$	−24.4833	−0.900633	−0.450316	−	0.892869i	$-0.648689\pi$
$739$	−24.4833	−0.900633	−0.450316	+	0.892869i	$0.648689\pi$
$740$	42.3541	1.55697
$741$	2.79528	0.102687
$742$	16.3370	0.599750
$743$	−33.1324	−1.21551	−0.607756	−	0.794124i	$-0.707930\pi$
$743$	−33.1324	−1.21551	−0.607756	+	0.794124i	$0.707930\pi$
$744$	−26.1743	−0.959596
$745$	−23.1066	−0.846560
$746$	−24.2566	−0.888097
$747$	−10.8882	−0.398377
$748$	7.95318	0.290797
$749$	−14.8517	−0.542668
$750$	−23.0644	−0.842194
$751$	35.6218	1.29986	0.649930	−	0.759994i	$-0.274798\pi$
$751$	35.6218	1.29986	0.649930	+	0.759994i	$0.274798\pi$
$752$	9.97994	0.363931
$753$	−23.3714	−0.851700
$754$	9.94789	0.362281
$755$	7.97675	0.290303
$756$	17.6890	0.643344
$757$	7.19443	0.261486	0.130743	−	0.991416i	$-0.458264\pi$
$757$	7.19443	0.261486	0.130743	+	0.991416i	$0.458264\pi$
$758$	60.0004	2.17931
$759$	−22.5740	−0.819384
$760$	18.3993	0.667413
$761$	38.7127	1.40333	0.701667	−	0.712505i	$-0.252439\pi$
$761$	38.7127	1.40333	0.701667	+	0.712505i	$0.252439\pi$
$762$	−12.7760	−0.462825
$763$	4.83852	0.175166
$764$	40.5228	1.46606
$765$	−1.88762	−0.0682472
$766$	−56.2034	−2.03071
$767$	−1.22581	−0.0442615
$768$	−21.0323	−0.758937
$769$	16.6572	0.600674	0.300337	−	0.953833i	$-0.402901\pi$
$769$	16.6572	0.600674	0.300337	+	0.953833i	$0.402901\pi$
$770$	15.7674	0.568217
$771$	3.68820	0.132827
$772$	−35.0152	−1.26022
$773$	−45.2249	−1.62663	−0.813313	−	0.581826i	$-0.802338\pi$
$773$	−45.2249	−1.62663	−0.813313	+	0.581826i	$0.802338\pi$
$774$	−10.3163	−0.370813
$775$	−23.1983	−0.833306
$776$	−21.3026	−0.764719
$777$	7.43080	0.266579
$778$	−20.8270	−0.746683
$779$	35.2391	1.26257
$780$	−4.49132	−0.160815
$781$	−2.47709	−0.0886372
$782$	8.67257	0.310131
$783$	18.7761	0.671003
$784$	−9.36601	−0.334500
$785$	35.5952	1.27045
$786$	−22.8729	−0.815848
$787$	−45.4763	−1.62105	−0.810527	−	0.585701i	$-0.800819\pi$
$787$	−45.4763	−1.62105	−0.810527	+	0.585701i	$0.800819\pi$
$788$	−26.6697	−0.950067
$789$	5.00447	0.178164
$790$	−1.48371	−0.0527879
$791$	7.25553	0.257977
$792$	−34.2942	−1.21859
$793$	−5.39620	−0.191625
$794$	91.1162	3.23359
$795$	−7.82919	−0.277673
$796$	28.6622	1.01590
$797$	−40.4312	−1.43215	−0.716073	−	0.698026i	$-0.754062\pi$
$797$	−40.4312	−1.43215	−0.716073	+	0.698026i	$0.754062\pi$
$798$	7.33039	0.259493
$799$	−3.39329	−0.120046
$800$	−9.97432	−0.352645
$801$	−25.1106	−0.887239
$802$	17.6583	0.623535
$803$	42.5317	1.50091
$804$	6.02731	0.212567
$805$	11.0241	0.388550
$806$	−19.7465	−0.695540
$807$	0.871940	0.0306937
$808$	−34.3771	−1.20938
$809$	13.6723	0.480693	0.240346	−	0.970687i	$-0.422739\pi$
$809$	13.6723	0.480693	0.240346	+	0.970687i	$0.422739\pi$
$810$	10.9863	0.386020
$811$	−51.7356	−1.81668	−0.908342	−	0.418228i	$-0.862651\pi$
$811$	−51.7356	−1.81668	−0.908342	+	0.418228i	$0.862651\pi$
$812$	16.7267	0.586994
$813$	−1.26016	−0.0441957
$814$	−75.5600	−2.64838
$815$	−4.87044	−0.170604
$816$	−0.755565	−0.0264500
$817$	−6.33113	−0.221498
$818$	−43.9483	−1.53661
$819$	2.54436	0.0889072
$820$	−56.6206	−1.97728
$821$	36.9186	1.28847	0.644234	−	0.764828i	$-0.277176\pi$
$821$	36.9186	1.28847	0.644234	+	0.764828i	$0.277176\pi$
$822$	−8.38516	−0.292466
$823$	−11.5662	−0.403171	−0.201586	−	0.979471i	$-0.564609\pi$
$823$	−11.5662	−0.403171	−0.201586	+	0.979471i	$0.564609\pi$
$824$	−1.94223	−0.0676607
$825$	9.41318	0.327725
$826$	−3.21459	−0.111850
$827$	25.0866	0.872345	0.436173	−	0.899863i	$-0.356334\pi$
$827$	25.0866	0.872345	0.436173	+	0.899863i	$0.356334\pi$
$828$	−54.4490	−1.89223
$829$	−38.7695	−1.34652	−0.673261	−	0.739405i	$-0.735107\pi$
$829$	−38.7695	−1.34652	−0.673261	+	0.739405i	$0.735107\pi$
$830$	16.7449	0.581224
$831$	−17.6929	−0.613758
$832$	−11.7388	−0.406970
$833$	3.18455	0.110338
$834$	2.11011	0.0730672
$835$	14.1045	0.488108
$836$	−47.7927	−1.65294
$837$	−37.2704	−1.28825
$838$	69.5475	2.40248
$839$	−42.1311	−1.45453	−0.727263	−	0.686359i	$-0.759208\pi$
$839$	−42.1311	−1.45453	−0.727263	+	0.686359i	$0.759208\pi$
$840$	−5.18671	−0.178958
$841$	−11.2453	−0.387770
$842$	35.0299	1.20721
$843$	−16.7758	−0.577790
$844$	70.3635	2.42201
$845$	−1.49212	−0.0513305
$846$	33.2266	1.14235
$847$	−5.81716	−0.199880
$848$	10.1190	0.347487
$849$	3.74621	0.128569
$850$	−3.61639	−0.124041
$851$	−52.8295	−1.81097
$852$	1.85037	0.0633926
$853$	−5.68866	−0.194776	−0.0973881	−	0.995246i	$-0.531049\pi$
$853$	−5.68866	−0.194776	−0.0973881	+	0.995246i	$0.531049\pi$
$854$	−14.1511	−0.484241
$855$	11.3432	0.387929
$856$	−49.6780	−1.69796
$857$	−46.4025	−1.58508	−0.792540	−	0.609820i	$-0.791242\pi$
$857$	−46.4025	−1.58508	−0.792540	+	0.609820i	$0.791242\pi$
$858$	8.01255	0.273544
$859$	−38.4765	−1.31280	−0.656400	−	0.754413i	$-0.727922\pi$
$859$	−38.4765	−1.31280	−0.656400	+	0.754413i	$0.727922\pi$
$860$	10.1726	0.346882
$861$	−9.93380	−0.338543
$862$	18.1131	0.616936
$863$	−9.08228	−0.309165	−0.154582	−	0.987980i	$-0.549403\pi$
$863$	−9.08228	−0.309165	−0.154582	+	0.987980i	$0.549403\pi$
$864$	−16.0248	−0.545174
$865$	38.3663	1.30449
$866$	−13.0237	−0.442563
$867$	−14.0614	−0.477551
$868$	−33.2025	−1.12696
$869$	1.69716	0.0575722
$870$	−12.5020	−0.423856
$871$	2.00241	0.0678491
$872$	16.1846	0.548078
$873$	−13.1331	−0.444488
$874$	−52.1157	−1.76284
$875$	−12.8841	−0.435561
$876$	−31.7709	−1.07344
$877$	−48.8374	−1.64912	−0.824561	−	0.565774i	$-0.808578\pi$
$877$	−48.8374	−1.64912	−0.824561	+	0.565774i	$0.808578\pi$
$878$	57.1765	1.92961
$879$	−15.4832	−0.522236
$880$	9.76617	0.329217
$881$	7.14183	0.240614	0.120307	−	0.992737i	$-0.461612\pi$
$881$	7.14183	0.240614	0.120307	+	0.992737i	$0.461612\pi$
$882$	−31.1826	−1.04997
$883$	27.8030	0.935645	0.467823	−	0.883822i	$-0.345039\pi$
$883$	27.8030	0.935645	0.467823	+	0.883822i	$0.345039\pi$
$884$	−1.97373	−0.0663837
$885$	1.54053	0.0517844
$886$	73.5061	2.46949
$887$	−8.89410	−0.298635	−0.149317	−	0.988789i	$-0.547708\pi$
$887$	−8.89410	−0.298635	−0.149317	+	0.988789i	$0.547708\pi$
$888$	24.8556	0.834099
$889$	−7.13682	−0.239361
$890$	38.6176	1.29446
$891$	−12.5669	−0.421006
$892$	61.4402	2.05717
$893$	20.3911	0.682364
$894$	−30.7928	−1.02987
$895$	−6.86428	−0.229447
$896$	−22.7949	−0.761526
$897$	5.60216	0.187051
$898$	55.9120	1.86581
$899$	−35.2429	−1.17542
$900$	22.7048	0.756827
$901$	−3.44057	−0.114622
$902$	101.012	3.36332
$903$	1.78472	0.0593919
$904$	24.2693	0.807185
$905$	35.9949	1.19651
$906$	10.6302	0.353163
$907$	2.26215	0.0751136	0.0375568	−	0.999294i	$-0.488042\pi$
$907$	2.26215	0.0751136	0.0375568	+	0.999294i	$0.488042\pi$
$908$	−27.1064	−0.899559
$909$	−21.1935	−0.702946
$910$	−3.91297	−0.129714
$911$	53.1420	1.76067	0.880336	−	0.474351i	$-0.157317\pi$
$911$	53.1420	1.76067	0.880336	+	0.474351i	$0.157317\pi$
$912$	4.54038	0.150347
$913$	−19.1539	−0.633901
$914$	54.8790	1.81524
$915$	6.78164	0.224194
$916$	18.5171	0.611823
$917$	−12.7771	−0.421936
$918$	−5.81011	−0.191762
$919$	−35.7339	−1.17875	−0.589376	−	0.807859i	$-0.700626\pi$
$919$	−35.7339	−1.17875	−0.589376	+	0.807859i	$0.700626\pi$
$920$	36.8751	1.21573
$921$	24.6464	0.812126
$922$	−94.0415	−3.09709
$923$	0.614736	0.0202343
$924$	13.4726	0.443216
$925$	22.0295	0.724325
$926$	−94.5686	−3.10772
$927$	−1.19739	−0.0393273
$928$	−15.1530	−0.497423
$929$	0.271820	0.00891812	0.00445906	−	0.999990i	$-0.498581\pi$
$929$	0.271820	0.00891812	0.00445906	+	0.999990i	$0.498581\pi$
$930$	24.8163	0.813758
$931$	−19.1368	−0.627182
$932$	−85.5719	−2.80300
$933$	−2.09338	−0.0685342
$934$	−69.5752	−2.27657
$935$	−3.32061	−0.108596
$936$	8.51074	0.278182
$937$	−47.7399	−1.55959	−0.779797	−	0.626033i	$-0.784678\pi$
$937$	−47.7399	−1.55959	−0.779797	+	0.626033i	$0.784678\pi$
$938$	5.25117	0.171457
$939$	−8.98770	−0.293302
$940$	−32.7636	−1.06863
$941$	−58.8941	−1.91989	−0.959946	−	0.280186i	$-0.909604\pi$
$941$	−58.8941	−1.91989	−0.959946	+	0.280186i	$0.909604\pi$
$942$	47.4357	1.54554
$943$	70.6246	2.29985
$944$	−1.99109	−0.0648044
$945$	−7.38552	−0.240251
$946$	−18.1479	−0.590041
$947$	−31.7238	−1.03088	−0.515442	−	0.856924i	$-0.672372\pi$
$947$	−31.7238	−1.03088	−0.515442	+	0.856924i	$0.672372\pi$
$948$	−1.26777	−0.0411752
$949$	−10.5550	−0.342631
$950$	21.7318	0.705073
$951$	−1.92124	−0.0623006
$952$	−2.27932	−0.0738732
$953$	−12.1670	−0.394127	−0.197063	−	0.980391i	$-0.563140\pi$
$953$	−12.1670	−0.394127	−0.197063	+	0.980391i	$0.563140\pi$
$954$	33.6895	1.09074
$955$	−16.9190	−0.547488
$956$	−13.5971	−0.439762
$957$	14.3005	0.462271
$958$	91.5743	2.95863
$959$	−4.68405	−0.151256
$960$	14.7527	0.476141
$961$	38.9569	1.25667
$962$	18.7516	0.604577
$963$	−30.6265	−0.986926
$964$	69.7054	2.24506
$965$	14.6195	0.470619
$966$	14.6912	0.472683
$967$	2.43370	0.0782624	0.0391312	−	0.999234i	$-0.487541\pi$
$967$	2.43370	0.0782624	0.0391312	+	0.999234i	$0.487541\pi$
$968$	−19.4581	−0.625406
$969$	−1.54378	−0.0495934
$970$	20.1974	0.648498
$971$	19.2160	0.616670	0.308335	−	0.951278i	$-0.400228\pi$
$971$	19.2160	0.616670	0.308335	+	0.951278i	$0.400228\pi$
$972$	57.1620	1.83347
$973$	1.17873	0.0377885
$974$	−59.8620	−1.91810
$975$	−2.33606	−0.0748137
$976$	−8.76506	−0.280563
$977$	14.0784	0.450408	0.225204	−	0.974312i	$-0.427695\pi$
$977$	14.0784	0.450408	0.225204	+	0.974312i	$0.427695\pi$
$978$	−6.49056	−0.207545
$979$	−44.1733	−1.41178
$980$	30.7481	0.982211
$981$	9.97781	0.318567
$982$	−31.0754	−0.991656
$983$	14.2794	0.455443	0.227722	−	0.973726i	$-0.426872\pi$
$983$	14.2794	0.455443	0.227722	+	0.973726i	$0.426872\pi$
$984$	−33.2280	−1.05927
$985$	11.1351	0.354794
$986$	−5.49404	−0.174966
$987$	−5.74820	−0.182967
$988$	11.8606	0.377337
$989$	−12.6886	−0.403473
$990$	32.5149	1.03339
$991$	−14.6386	−0.465010	−0.232505	−	0.972595i	$-0.574692\pi$
$991$	−14.6386	−0.465010	−0.232505	+	0.972595i	$0.574692\pi$
$992$	30.0786	0.954998
$993$	−5.30981	−0.168502
$994$	1.61210	0.0511326
$995$	−11.9670	−0.379380
$996$	14.3078	0.453362
$997$	13.2009	0.418076	0.209038	−	0.977907i	$-0.432967\pi$
$997$	13.2009	0.418076	0.209038	+	0.977907i	$0.432967\pi$
$998$	−13.1019	−0.414732
$999$	35.3927	1.11977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.13	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.13	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36088 q^{2} +0.842254 q^{3} +3.57377 q^{4} -1.49212 q^{5} -1.98846 q^{6} -1.11078 q^{7} -3.71549 q^{8} -2.29061 q^{9} +O(q^{10})\)	\(q-2.36088 q^{2} +0.842254 q^{3} +3.57377 q^{4} -1.49212 q^{5} -1.98846 q^{6} -1.11078 q^{7} -3.71549 q^{8} -2.29061 q^{9} +3.52272 q^{10} -4.02952 q^{11} +3.01003 q^{12} +1.00000 q^{13} +2.62242 q^{14} -1.25674 q^{15} +1.62430 q^{16} -0.552282 q^{17} +5.40786 q^{18} +3.31880 q^{19} -5.33250 q^{20} -0.935560 q^{21} +9.51322 q^{22} +6.65139 q^{23} -3.12939 q^{24} -2.77358 q^{25} -2.36088 q^{26} -4.45604 q^{27} -3.96968 q^{28} -4.21363 q^{29} +2.96703 q^{30} +8.36402 q^{31} +3.59619 q^{32} -3.39388 q^{33} +1.30387 q^{34} +1.65742 q^{35} -8.18611 q^{36} -7.94263 q^{37} -7.83530 q^{38} +0.842254 q^{39} +5.54396 q^{40} +10.6180 q^{41} +2.20875 q^{42} -1.90766 q^{43} -14.4006 q^{44} +3.41786 q^{45} -15.7032 q^{46} +6.14413 q^{47} +1.36808 q^{48} -5.76617 q^{49} +6.54809 q^{50} -0.465162 q^{51} +3.57377 q^{52} +6.22973 q^{53} +10.5202 q^{54} +6.01252 q^{55} +4.12710 q^{56} +2.79528 q^{57} +9.94789 q^{58} -1.22581 q^{59} -4.49132 q^{60} -5.39620 q^{61} -19.7465 q^{62} +2.54436 q^{63} -11.7388 q^{64} -1.49212 q^{65} +8.01255 q^{66} +2.00241 q^{67} -1.97373 q^{68} +5.60216 q^{69} -3.91297 q^{70} +0.614736 q^{71} +8.51074 q^{72} -10.5550 q^{73} +18.7516 q^{74} -2.33606 q^{75} +11.8606 q^{76} +4.47591 q^{77} -1.98846 q^{78} -0.421182 q^{79} -2.42366 q^{80} +3.11871 q^{81} -25.0679 q^{82} +4.75340 q^{83} -3.34348 q^{84} +0.824071 q^{85} +4.50375 q^{86} -3.54895 q^{87} +14.9716 q^{88} +10.9624 q^{89} -8.06918 q^{90} -1.11078 q^{91} +23.7706 q^{92} +7.04463 q^{93} -14.5056 q^{94} -4.95205 q^{95} +3.02891 q^{96} +5.73345 q^{97} +13.6133 q^{98} +9.23004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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