LMFDB - Embedded newform 8026.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.72230 q^{3} +1.00000 q^{4} -4.08988 q^{5} -1.72230 q^{6} -0.697853 q^{7} +1.00000 q^{8} -0.0336847 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.72230 q^{3} +1.00000 q^{4} -4.08988 q^{5} -1.72230 q^{6} -0.697853 q^{7} +1.00000 q^{8} -0.0336847 q^{9} -4.08988 q^{10} +3.79673 q^{11} -1.72230 q^{12} -3.33057 q^{13} -0.697853 q^{14} +7.04399 q^{15} +1.00000 q^{16} -3.47976 q^{17} -0.0336847 q^{18} -0.539103 q^{19} -4.08988 q^{20} +1.20191 q^{21} +3.79673 q^{22} +2.81729 q^{23} -1.72230 q^{24} +11.7271 q^{25} -3.33057 q^{26} +5.22491 q^{27} -0.697853 q^{28} +7.58186 q^{29} +7.04399 q^{30} -3.46211 q^{31} +1.00000 q^{32} -6.53911 q^{33} -3.47976 q^{34} +2.85413 q^{35} -0.0336847 q^{36} -7.47440 q^{37} -0.539103 q^{38} +5.73624 q^{39} -4.08988 q^{40} +3.13222 q^{41} +1.20191 q^{42} -4.45148 q^{43} +3.79673 q^{44} +0.137766 q^{45} +2.81729 q^{46} +3.03903 q^{47} -1.72230 q^{48} -6.51300 q^{49} +11.7271 q^{50} +5.99320 q^{51} -3.33057 q^{52} +8.90247 q^{53} +5.22491 q^{54} -15.5282 q^{55} -0.697853 q^{56} +0.928497 q^{57} +7.58186 q^{58} -3.63041 q^{59} +7.04399 q^{60} +2.61297 q^{61} -3.46211 q^{62} +0.0235070 q^{63} +1.00000 q^{64} +13.6216 q^{65} -6.53911 q^{66} +13.0722 q^{67} -3.47976 q^{68} -4.85221 q^{69} +2.85413 q^{70} +0.277422 q^{71} -0.0336847 q^{72} +11.7316 q^{73} -7.47440 q^{74} -20.1976 q^{75} -0.539103 q^{76} -2.64956 q^{77} +5.73624 q^{78} -0.856761 q^{79} -4.08988 q^{80} -8.89781 q^{81} +3.13222 q^{82} +2.77582 q^{83} +1.20191 q^{84} +14.2318 q^{85} -4.45148 q^{86} -13.0582 q^{87} +3.79673 q^{88} +15.4820 q^{89} +0.137766 q^{90} +2.32425 q^{91} +2.81729 q^{92} +5.96278 q^{93} +3.03903 q^{94} +2.20487 q^{95} -1.72230 q^{96} +4.58437 q^{97} -6.51300 q^{98} -0.127892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.72230	−0.994370	−0.497185	−	0.867645i	$-0.665633\pi$
$3$	−1.72230	−0.994370	−0.497185	+	0.867645i	$0.665633\pi$
$4$	1.00000	0.500000
$5$	−4.08988	−1.82905	−0.914524	−	0.404532i	$-0.867435\pi$
$5$	−4.08988	−1.82905	−0.914524	+	0.404532i	$0.867435\pi$
$6$	−1.72230	−0.703126
$7$	−0.697853	−0.263764	−0.131882	−	0.991265i	$-0.542102\pi$
$7$	−0.697853	−0.263764	−0.131882	+	0.991265i	$0.542102\pi$
$8$	1.00000	0.353553
$9$	−0.0336847	−0.0112282
$10$	−4.08988	−1.29333
$11$	3.79673	1.14476	0.572379	−	0.819989i	$-0.306021\pi$
$11$	3.79673	1.14476	0.572379	+	0.819989i	$0.306021\pi$
$12$	−1.72230	−0.497185
$13$	−3.33057	−0.923734	−0.461867	−	0.886949i	$-0.652820\pi$
$13$	−3.33057	−0.923734	−0.461867	+	0.886949i	$0.652820\pi$
$14$	−0.697853	−0.186509
$15$	7.04399	1.81875
$16$	1.00000	0.250000
$17$	−3.47976	−0.843967	−0.421983	−	0.906604i	$-0.638666\pi$
$17$	−3.47976	−0.843967	−0.421983	+	0.906604i	$0.638666\pi$
$18$	−0.0336847	−0.00793957
$19$	−0.539103	−0.123679	−0.0618394	−	0.998086i	$-0.519697\pi$
$19$	−0.539103	−0.123679	−0.0618394	+	0.998086i	$0.519697\pi$
$20$	−4.08988	−0.914524
$21$	1.20191	0.262279
$22$	3.79673	0.809466
$23$	2.81729	0.587445	0.293723	−	0.955891i	$-0.405106\pi$
$23$	2.81729	0.587445	0.293723	+	0.955891i	$0.405106\pi$
$24$	−1.72230	−0.351563
$25$	11.7271	2.34542
$26$	−3.33057	−0.653178
$27$	5.22491	1.00554
$28$	−0.697853	−0.131882
$29$	7.58186	1.40792	0.703958	−	0.710242i	$-0.251415\pi$
$29$	7.58186	1.40792	0.703958	+	0.710242i	$0.251415\pi$
$30$	7.04399	1.28605
$31$	−3.46211	−0.621812	−0.310906	−	0.950441i	$-0.600633\pi$
$31$	−3.46211	−0.621812	−0.310906	+	0.950441i	$0.600633\pi$
$32$	1.00000	0.176777
$33$	−6.53911	−1.13831
$34$	−3.47976	−0.596775
$35$	2.85413	0.482437
$36$	−0.0336847	−0.00561412
$37$	−7.47440	−1.22878	−0.614392	−	0.789001i	$-0.710599\pi$
$37$	−7.47440	−1.22878	−0.614392	+	0.789001i	$0.710599\pi$
$38$	−0.539103	−0.0874541
$39$	5.73624	0.918533
$40$	−4.08988	−0.646666
$41$	3.13222	0.489170	0.244585	−	0.969628i	$-0.421348\pi$
$41$	3.13222	0.489170	0.244585	+	0.969628i	$0.421348\pi$
$42$	1.20191	0.185459
$43$	−4.45148	−0.678844	−0.339422	−	0.940634i	$-0.610231\pi$
$43$	−4.45148	−0.678844	−0.339422	+	0.940634i	$0.610231\pi$
$44$	3.79673	0.572379
$45$	0.137766	0.0205370
$46$	2.81729	0.415386
$47$	3.03903	0.443287	0.221644	−	0.975128i	$-0.428858\pi$
$47$	3.03903	0.443287	0.221644	+	0.975128i	$0.428858\pi$
$48$	−1.72230	−0.248593
$49$	−6.51300	−0.930429
$50$	11.7271	1.65846
$51$	5.99320	0.839215
$52$	−3.33057	−0.461867
$53$	8.90247	1.22285	0.611424	−	0.791303i	$-0.290597\pi$
$53$	8.90247	1.22285	0.611424	+	0.791303i	$0.290597\pi$
$54$	5.22491	0.711021
$55$	−15.5282	−2.09382
$56$	−0.697853	−0.0932546
$57$	0.928497	0.122982
$58$	7.58186	0.995546
$59$	−3.63041	−0.472639	−0.236319	−	0.971675i	$-0.575941\pi$
$59$	−3.63041	−0.472639	−0.236319	+	0.971675i	$0.575941\pi$
$60$	7.04399	0.909375
$61$	2.61297	0.334557	0.167278	−	0.985910i	$-0.446502\pi$
$61$	2.61297	0.334557	0.167278	+	0.985910i	$0.446502\pi$
$62$	−3.46211	−0.439688
$63$	0.0235070	0.00296160
$64$	1.00000	0.125000
$65$	13.6216	1.68955
$66$	−6.53911	−0.804909
$67$	13.0722	1.59702	0.798509	−	0.601982i	$-0.205622\pi$
$67$	13.0722	1.59702	0.798509	+	0.601982i	$0.205622\pi$
$68$	−3.47976	−0.421983
$69$	−4.85221	−0.584138
$70$	2.85413	0.341134
$71$	0.277422	0.0329240	0.0164620	−	0.999864i	$-0.494760\pi$
$71$	0.277422	0.0329240	0.0164620	+	0.999864i	$0.494760\pi$
$72$	−0.0336847	−0.00396978
$73$	11.7316	1.37308	0.686541	−	0.727091i	$-0.259128\pi$
$73$	11.7316	1.37308	0.686541	+	0.727091i	$0.259128\pi$
$74$	−7.47440	−0.868881
$75$	−20.1976	−2.33221
$76$	−0.539103	−0.0618394
$77$	−2.64956	−0.301946
$78$	5.73624	0.649501
$79$	−0.856761	−0.0963932	−0.0481966	−	0.998838i	$-0.515347\pi$
$79$	−0.856761	−0.0963932	−0.0481966	+	0.998838i	$0.515347\pi$
$80$	−4.08988	−0.457262
$81$	−8.89781	−0.988646
$82$	3.13222	0.345896
$83$	2.77582	0.304686	0.152343	−	0.988328i	$-0.451318\pi$
$83$	2.77582	0.304686	0.152343	+	0.988328i	$0.451318\pi$
$84$	1.20191	0.131139
$85$	14.2318	1.54366
$86$	−4.45148	−0.480015
$87$	−13.0582	−1.39999
$88$	3.79673	0.404733
$89$	15.4820	1.64109	0.820543	−	0.571585i	$-0.193671\pi$
$89$	15.4820	1.64109	0.820543	+	0.571585i	$0.193671\pi$
$90$	0.137766	0.0145218
$91$	2.32425	0.243647
$92$	2.81729	0.293723
$93$	5.96278	0.618312
$94$	3.03903	0.313451
$95$	2.20487	0.226214
$96$	−1.72230	−0.175781
$97$	4.58437	0.465472	0.232736	−	0.972540i	$-0.425232\pi$
$97$	4.58437	0.465472	0.232736	+	0.972540i	$0.425232\pi$
$98$	−6.51300	−0.657912
$99$	−0.127892	−0.0128536
$100$	11.7271	1.17271
$101$	2.92681	0.291229	0.145614	−	0.989341i	$-0.453484\pi$
$101$	2.92681	0.291229	0.145614	+	0.989341i	$0.453484\pi$
$102$	5.99320	0.593415
$103$	−11.7746	−1.16019	−0.580093	−	0.814550i	$-0.696984\pi$
$103$	−11.7746	−1.16019	−0.580093	+	0.814550i	$0.696984\pi$
$104$	−3.33057	−0.326589
$105$	−4.91567	−0.479721
$106$	8.90247	0.864684
$107$	−0.706436	−0.0682937	−0.0341469	−	0.999417i	$-0.510871\pi$
$107$	−0.706436	−0.0682937	−0.0341469	+	0.999417i	$0.510871\pi$
$108$	5.22491	0.502768
$109$	−12.6187	−1.20865	−0.604325	−	0.796738i	$-0.706557\pi$
$109$	−12.6187	−1.20865	−0.604325	+	0.796738i	$0.706557\pi$
$110$	−15.5282	−1.48055
$111$	12.8732	1.22187
$112$	−0.697853	−0.0659409
$113$	−10.7340	−1.00977	−0.504884	−	0.863187i	$-0.668465\pi$
$113$	−10.7340	−1.00977	−0.504884	+	0.863187i	$0.668465\pi$
$114$	0.928497	0.0869617
$115$	−11.5224	−1.07447
$116$	7.58186	0.703958
$117$	0.112189	0.0103719
$118$	−3.63041	−0.334206
$119$	2.42836	0.222608
$120$	7.04399	0.643025
$121$	3.41518	0.310471
$122$	2.61297	0.236567
$123$	−5.39462	−0.486416
$124$	−3.46211	−0.310906
$125$	−27.5129	−2.46083
$126$	0.0235070	0.00209417
$127$	12.8809	1.14300	0.571500	−	0.820602i	$-0.306362\pi$
$127$	12.8809	1.14300	0.571500	+	0.820602i	$0.306362\pi$
$128$	1.00000	0.0883883
$129$	7.66677	0.675022
$130$	13.6216	1.19469
$131$	11.0264	0.963381	0.481690	−	0.876341i	$-0.340023\pi$
$131$	11.0264	0.963381	0.481690	+	0.876341i	$0.340023\pi$
$132$	−6.53911	−0.569156
$133$	0.376215	0.0326220
$134$	13.0722	1.12926
$135$	−21.3692	−1.83917
$136$	−3.47976	−0.298387
$137$	0.0980447	0.00837653	0.00418826	−	0.999991i	$-0.498667\pi$
$137$	0.0980447	0.00837653	0.00418826	+	0.999991i	$0.498667\pi$
$138$	−4.85221	−0.413048
$139$	−13.2183	−1.12116	−0.560579	−	0.828101i	$-0.689421\pi$
$139$	−13.2183	−1.12116	−0.560579	+	0.828101i	$0.689421\pi$
$140$	2.85413	0.241218
$141$	−5.23411	−0.440792
$142$	0.277422	0.0232808
$143$	−12.6453	−1.05745
$144$	−0.0336847	−0.00280706
$145$	−31.0088	−2.57514
$146$	11.7316	0.970915
$147$	11.2173	0.925190
$148$	−7.47440	−0.614392
$149$	6.24766	0.511828	0.255914	−	0.966700i	$-0.417624\pi$
$149$	6.24766	0.511828	0.255914	+	0.966700i	$0.417624\pi$
$150$	−20.1976	−1.64912
$151$	−17.9741	−1.46271	−0.731356	−	0.681996i	$-0.761112\pi$
$151$	−17.9741	−1.46271	−0.731356	+	0.681996i	$0.761112\pi$
$152$	−0.539103	−0.0437271
$153$	0.117215	0.00947626
$154$	−2.64956	−0.213508
$155$	14.1596	1.13732
$156$	5.73624	0.459267
$157$	−4.34098	−0.346448	−0.173224	−	0.984882i	$-0.555418\pi$
$157$	−4.34098	−0.346448	−0.173224	+	0.984882i	$0.555418\pi$
$158$	−0.856761	−0.0681603
$159$	−15.3327	−1.21596
$160$	−4.08988	−0.323333
$161$	−1.96605	−0.154947
$162$	−8.89781	−0.699078
$163$	22.1431	1.73438	0.867189	−	0.497979i	$-0.165925\pi$
$163$	22.1431	1.73438	0.867189	+	0.497979i	$0.165925\pi$
$164$	3.13222	0.244585
$165$	26.7441	2.08203
$166$	2.77582	0.215446
$167$	−7.68325	−0.594547	−0.297274	−	0.954792i	$-0.596077\pi$
$167$	−7.68325	−0.594547	−0.297274	+	0.954792i	$0.596077\pi$
$168$	1.20191	0.0927296
$169$	−1.90731	−0.146716
$170$	14.2318	1.09153
$171$	0.0181595	0.00138870
$172$	−4.45148	−0.339422
$173$	−14.7267	−1.11965	−0.559825	−	0.828611i	$-0.689132\pi$
$173$	−14.7267	−1.11965	−0.559825	+	0.828611i	$0.689132\pi$
$174$	−13.0582	−0.989941
$175$	−8.18379	−0.618636
$176$	3.79673	0.286189
$177$	6.25265	0.469978
$178$	15.4820	1.16042
$179$	−14.7065	−1.09922	−0.549609	−	0.835422i	$-0.685223\pi$
$179$	−14.7065	−1.09922	−0.549609	+	0.835422i	$0.685223\pi$
$180$	0.137766	0.0102685
$181$	−16.6764	−1.23955	−0.619774	−	0.784780i	$-0.712776\pi$
$181$	−16.6764	−1.23955	−0.619774	+	0.784780i	$0.712776\pi$
$182$	2.32425	0.172285
$183$	−4.50032	−0.332673
$184$	2.81729	0.207693
$185$	30.5694	2.24750
$186$	5.96278	0.437212
$187$	−13.2117	−0.966138
$188$	3.03903	0.221644
$189$	−3.64622	−0.265224
$190$	2.20487	0.159958
$191$	−14.1756	−1.02571	−0.512856	−	0.858475i	$-0.671413\pi$
$191$	−14.1756	−1.02571	−0.512856	+	0.858475i	$0.671413\pi$
$192$	−1.72230	−0.124296
$193$	25.1614	1.81116	0.905578	−	0.424179i	$-0.139437\pi$
$193$	25.1614	1.81116	0.905578	+	0.424179i	$0.139437\pi$
$194$	4.58437	0.329139
$195$	−23.4605	−1.68004
$196$	−6.51300	−0.465214
$197$	−21.1061	−1.50375	−0.751875	−	0.659306i	$-0.770850\pi$
$197$	−21.1061	−1.50375	−0.751875	+	0.659306i	$0.770850\pi$
$198$	−0.127892	−0.00908888
$199$	−27.7254	−1.96540	−0.982700	−	0.185203i	$-0.940706\pi$
$199$	−27.7254	−1.96540	−0.982700	+	0.185203i	$0.940706\pi$
$200$	11.7271	0.829230
$201$	−22.5142	−1.58803
$202$	2.92681	0.205930
$203$	−5.29102	−0.371357
$204$	5.99320	0.419608
$205$	−12.8104	−0.894716
$206$	−11.7746	−0.820376
$207$	−0.0948996	−0.00659598
$208$	−3.33057	−0.230933
$209$	−2.04683	−0.141582
$210$	−4.91567	−0.339214
$211$	−10.0302	−0.690505	−0.345253	−	0.938510i	$-0.612207\pi$
$211$	−10.0302	−0.690505	−0.345253	+	0.938510i	$0.612207\pi$
$212$	8.90247	0.611424
$213$	−0.477804	−0.0327386
$214$	−0.706436	−0.0482909
$215$	18.2060	1.24164
$216$	5.22491	0.355510
$217$	2.41604	0.164012
$218$	−12.6187	−0.854645
$219$	−20.2054	−1.36535
$220$	−15.5282	−1.04691
$221$	11.5896	0.779600
$222$	12.8732	0.863989
$223$	−4.41506	−0.295654	−0.147827	−	0.989013i	$-0.547228\pi$
$223$	−4.41506	−0.295654	−0.147827	+	0.989013i	$0.547228\pi$
$224$	−0.697853	−0.0466273
$225$	−0.395024	−0.0263349
$226$	−10.7340	−0.714014
$227$	−19.0498	−1.26438	−0.632189	−	0.774814i	$-0.717843\pi$
$227$	−19.0498	−1.26438	−0.632189	+	0.774814i	$0.717843\pi$
$228$	0.928497	0.0614912
$229$	6.37302	0.421141	0.210571	−	0.977579i	$-0.432468\pi$
$229$	6.37302	0.421141	0.210571	+	0.977579i	$0.432468\pi$
$230$	−11.5224	−0.759762
$231$	4.56334	0.300246
$232$	7.58186	0.497773
$233$	−9.76373	−0.639643	−0.319822	−	0.947478i	$-0.603623\pi$
$233$	−9.76373	−0.639643	−0.319822	+	0.947478i	$0.603623\pi$
$234$	0.112189	0.00733404
$235$	−12.4292	−0.810794
$236$	−3.63041	−0.236319
$237$	1.47560	0.0958505
$238$	2.42836	0.157408
$239$	−15.3464	−0.992678	−0.496339	−	0.868129i	$-0.665323\pi$
$239$	−15.3464	−0.992678	−0.496339	+	0.868129i	$0.665323\pi$
$240$	7.04399	0.454688
$241$	−4.30794	−0.277499	−0.138749	−	0.990328i	$-0.544308\pi$
$241$	−4.30794	−0.277499	−0.138749	+	0.990328i	$0.544308\pi$
$242$	3.41518	0.219536
$243$	−0.350045	−0.0224554
$244$	2.61297	0.167278
$245$	26.6374	1.70180
$246$	−5.39462	−0.343948
$247$	1.79552	0.114246
$248$	−3.46211	−0.219844
$249$	−4.78080	−0.302971
$250$	−27.5129	−1.74007
$251$	−19.2747	−1.21661	−0.608305	−	0.793704i	$-0.708150\pi$
$251$	−19.2747	−1.21661	−0.608305	+	0.793704i	$0.708150\pi$
$252$	0.0235070	0.00148080
$253$	10.6965	0.672482
$254$	12.8809	0.808223
$255$	−24.5114	−1.53496
$256$	1.00000	0.0625000
$257$	2.22914	0.139050	0.0695250	−	0.997580i	$-0.477852\pi$
$257$	2.22914	0.139050	0.0695250	+	0.997580i	$0.477852\pi$
$258$	7.66677	0.477313
$259$	5.21603	0.324109
$260$	13.6216	0.844777
$261$	−0.255393	−0.0158084
$262$	11.0264	0.681213
$263$	−13.8337	−0.853025	−0.426512	−	0.904482i	$-0.640258\pi$
$263$	−13.8337	−0.853025	−0.426512	+	0.904482i	$0.640258\pi$
$264$	−6.53911	−0.402454
$265$	−36.4100	−2.23665
$266$	0.376215	0.0230672
$267$	−26.6646	−1.63185
$268$	13.0722	0.798509
$269$	−12.6021	−0.768363	−0.384182	−	0.923258i	$-0.625516\pi$
$269$	−12.6021	−0.768363	−0.384182	+	0.923258i	$0.625516\pi$
$270$	−21.3692	−1.30049
$271$	23.2395	1.41170	0.705849	−	0.708363i	$-0.250566\pi$
$271$	23.2395	1.41170	0.705849	+	0.708363i	$0.250566\pi$
$272$	−3.47976	−0.210992
$273$	−4.00305	−0.242276
$274$	0.0980447	0.00592310
$275$	44.5246	2.68493
$276$	−4.85221	−0.292069
$277$	32.9484	1.97968	0.989839	−	0.142193i	$-0.0454153\pi$
$277$	32.9484	1.97968	0.989839	+	0.142193i	$0.0454153\pi$
$278$	−13.2183	−0.792778
$279$	0.116620	0.00698186
$280$	2.85413	0.170567
$281$	25.3185	1.51037	0.755187	−	0.655509i	$-0.227546\pi$
$281$	25.3185	1.51037	0.755187	+	0.655509i	$0.227546\pi$
$282$	−5.23411	−0.311687
$283$	31.5423	1.87500	0.937498	−	0.347992i	$-0.113136\pi$
$283$	31.5423	1.87500	0.937498	+	0.347992i	$0.113136\pi$
$284$	0.277422	0.0164620
$285$	−3.79744	−0.224941
$286$	−12.6453	−0.747731
$287$	−2.18583	−0.129025
$288$	−0.0336847	−0.00198489
$289$	−4.89124	−0.287720
$290$	−31.0088	−1.82090
$291$	−7.89566	−0.462852
$292$	11.7316	0.686541
$293$	32.9242	1.92345	0.961727	−	0.274009i	$-0.0883497\pi$
$293$	32.9242	1.92345	0.961727	+	0.274009i	$0.0883497\pi$
$294$	11.2173	0.654208
$295$	14.8479	0.864479
$296$	−7.47440	−0.434441
$297$	19.8376	1.15109
$298$	6.24766	0.361917
$299$	−9.38317	−0.542643
$300$	−20.1976	−1.16611
$301$	3.10648	0.179054
$302$	−17.9741	−1.03429
$303$	−5.04084	−0.289589
$304$	−0.539103	−0.0309197
$305$	−10.6867	−0.611920
$306$	0.117215	0.00670073
$307$	−27.7989	−1.58657	−0.793284	−	0.608852i	$-0.791630\pi$
$307$	−27.7989	−1.58657	−0.793284	+	0.608852i	$0.791630\pi$
$308$	−2.64956	−0.150973
$309$	20.2794	1.15365
$310$	14.1596	0.804210
$311$	−30.2900	−1.71759	−0.858793	−	0.512323i	$-0.828785\pi$
$311$	−30.2900	−1.71759	−0.858793	+	0.512323i	$0.828785\pi$
$312$	5.73624	0.324750
$313$	11.1620	0.630915	0.315458	−	0.948940i	$-0.397842\pi$
$313$	11.1620	0.630915	0.315458	+	0.948940i	$0.397842\pi$
$314$	−4.34098	−0.244976
$315$	−0.0961407	−0.00541692
$316$	−0.856761	−0.0481966
$317$	4.92796	0.276782	0.138391	−	0.990378i	$-0.455807\pi$
$317$	4.92796	0.276782	0.138391	+	0.990378i	$0.455807\pi$
$318$	−15.3327	−0.859816
$319$	28.7863	1.61172
$320$	−4.08988	−0.228631
$321$	1.21669	0.0679092
$322$	−1.96605	−0.109564
$323$	1.87595	0.104381
$324$	−8.89781	−0.494323
$325$	−39.0579	−2.16654
$326$	22.1431	1.22639
$327$	21.7331	1.20185
$328$	3.13222	0.172948
$329$	−2.12079	−0.116923
$330$	26.7441	1.47222
$331$	23.6037	1.29738	0.648688	−	0.761054i	$-0.275318\pi$
$331$	23.6037	1.29738	0.648688	+	0.761054i	$0.275318\pi$
$332$	2.77582	0.152343
$333$	0.251773	0.0137971
$334$	−7.68325	−0.420409
$335$	−53.4635	−2.92102
$336$	1.20191	0.0655697
$337$	−3.05950	−0.166661	−0.0833307	−	0.996522i	$-0.526556\pi$
$337$	−3.05950	−0.166661	−0.0833307	+	0.996522i	$0.526556\pi$
$338$	−1.90731	−0.103744
$339$	18.4871	1.00408
$340$	14.2318	0.771828
$341$	−13.1447	−0.711825
$342$	0.0181595	0.000981956 0
$343$	9.43009	0.509177
$344$	−4.45148	−0.240008
$345$	19.8449	1.06842
$346$	−14.7267	−0.791712
$347$	−35.4170	−1.90129	−0.950643	−	0.310286i	$-0.899575\pi$
$347$	−35.4170	−1.90129	−0.950643	+	0.310286i	$0.899575\pi$
$348$	−13.0582	−0.699994
$349$	9.48433	0.507685	0.253842	−	0.967246i	$-0.418306\pi$
$349$	9.48433	0.507685	0.253842	+	0.967246i	$0.418306\pi$
$350$	−8.18379	−0.437442
$351$	−17.4019	−0.928847
$352$	3.79673	0.202367
$353$	−0.962893	−0.0512496	−0.0256248	−	0.999672i	$-0.508158\pi$
$353$	−0.962893	−0.0512496	−0.0256248	+	0.999672i	$0.508158\pi$
$354$	6.25265	0.332325
$355$	−1.13462	−0.0602195
$356$	15.4820	0.820543
$357$	−4.18237	−0.221355
$358$	−14.7065	−0.777264
$359$	10.7913	0.569541	0.284771	−	0.958596i	$-0.408083\pi$
$359$	10.7913	0.569541	0.284771	+	0.958596i	$0.408083\pi$
$360$	0.137766	0.00726092
$361$	−18.7094	−0.984704
$362$	−16.6764	−0.876493
$363$	−5.88196	−0.308723
$364$	2.32425	0.121824
$365$	−47.9809	−2.51143
$366$	−4.50032	−0.235235
$367$	33.3516	1.74094	0.870468	−	0.492224i	$-0.163816\pi$
$367$	33.3516	1.74094	0.870468	+	0.492224i	$0.163816\pi$
$368$	2.81729	0.146861
$369$	−0.105508	−0.00549252
$370$	30.5694	1.58923
$371$	−6.21262	−0.322543
$372$	5.96278	0.309156
$373$	15.6000	0.807738	0.403869	−	0.914817i	$-0.367665\pi$
$373$	15.6000	0.807738	0.403869	+	0.914817i	$0.367665\pi$
$374$	−13.2117	−0.683162
$375$	47.3855	2.44698
$376$	3.03903	0.156726
$377$	−25.2519	−1.30054
$378$	−3.64622	−0.187541
$379$	2.40637	0.123607	0.0618034	−	0.998088i	$-0.480315\pi$
$379$	2.40637	0.123607	0.0618034	+	0.998088i	$0.480315\pi$
$380$	2.20487	0.113107
$381$	−22.1848	−1.13656
$382$	−14.1756	−0.725288
$383$	−7.38963	−0.377593	−0.188796	−	0.982016i	$-0.560459\pi$
$383$	−7.38963	−0.377593	−0.188796	+	0.982016i	$0.560459\pi$
$384$	−1.72230	−0.0878907
$385$	10.8364	0.552273
$386$	25.1614	1.28068
$387$	0.149947	0.00762222
$388$	4.58437	0.232736
$389$	−18.5609	−0.941074	−0.470537	−	0.882380i	$-0.655940\pi$
$389$	−18.5609	−0.941074	−0.470537	+	0.882380i	$0.655940\pi$
$390$	−23.4605	−1.18797
$391$	−9.80350	−0.495784
$392$	−6.51300	−0.328956
$393$	−18.9908	−0.957957
$394$	−21.1061	−1.06331
$395$	3.50405	0.176308
$396$	−0.127892	−0.00642681
$397$	−2.78047	−0.139548	−0.0697738	−	0.997563i	$-0.522228\pi$
$397$	−2.78047	−0.139548	−0.0697738	+	0.997563i	$0.522228\pi$
$398$	−27.7254	−1.38975
$399$	−0.647955	−0.0324383
$400$	11.7271	0.586354
$401$	21.3202	1.06468	0.532339	−	0.846531i	$-0.321313\pi$
$401$	21.3202	1.06468	0.532339	+	0.846531i	$0.321313\pi$
$402$	−22.5142	−1.12291
$403$	11.5308	0.574389
$404$	2.92681	0.145614
$405$	36.3909	1.80828
$406$	−5.29102	−0.262589
$407$	−28.3783	−1.40666
$408$	5.99320	0.296707
$409$	−32.9705	−1.63028	−0.815142	−	0.579261i	$-0.803341\pi$
$409$	−32.9705	−1.63028	−0.815142	+	0.579261i	$0.803341\pi$
$410$	−12.8104	−0.632660
$411$	−0.168862	−0.00832937
$412$	−11.7746	−0.580093
$413$	2.53349	0.124665
$414$	−0.0948996	−0.00466406
$415$	−11.3528	−0.557286
$416$	−3.33057	−0.163295
$417$	22.7658	1.11485
$418$	−2.04683	−0.100114
$419$	−5.85953	−0.286257	−0.143129	−	0.989704i	$-0.545716\pi$
$419$	−5.85953	−0.286257	−0.143129	+	0.989704i	$0.545716\pi$
$420$	−4.91567	−0.239860
$421$	7.72562	0.376524	0.188262	−	0.982119i	$-0.439715\pi$
$421$	7.72562	0.376524	0.188262	+	0.982119i	$0.439715\pi$
$422$	−10.0302	−0.488261
$423$	−0.102369	−0.00497734
$424$	8.90247	0.432342
$425$	−40.8075	−1.97945
$426$	−0.477804	−0.0231497
$427$	−1.82347	−0.0882439
$428$	−0.706436	−0.0341469
$429$	21.7790	1.05150
$430$	18.2060	0.877971
$431$	−27.0825	−1.30452	−0.652260	−	0.757995i	$-0.726179\pi$
$431$	−27.0825	−1.30452	−0.652260	+	0.757995i	$0.726179\pi$
$432$	5.22491	0.251384
$433$	−24.3769	−1.17148	−0.585740	−	0.810499i	$-0.699196\pi$
$433$	−24.3769	−1.17148	−0.585740	+	0.810499i	$0.699196\pi$
$434$	2.41604	0.115974
$435$	53.4065	2.56065
$436$	−12.6187	−0.604325
$437$	−1.51881	−0.0726545
$438$	−20.2054	−0.965449
$439$	1.69644	0.0809669	0.0404834	−	0.999180i	$-0.487110\pi$
$439$	1.69644	0.0809669	0.0404834	+	0.999180i	$0.487110\pi$
$440$	−15.5282	−0.740276
$441$	0.219389	0.0104471
$442$	11.5896	0.551261
$443$	21.1039	1.00267	0.501337	−	0.865252i	$-0.332842\pi$
$443$	21.1039	1.00267	0.501337	+	0.865252i	$0.332842\pi$
$444$	12.8732	0.610933
$445$	−63.3194	−3.00163
$446$	−4.41506	−0.209059
$447$	−10.7603	−0.508947
$448$	−0.697853	−0.0329705
$449$	27.1669	1.28208	0.641042	−	0.767506i	$-0.278503\pi$
$449$	27.1669	1.28208	0.641042	+	0.767506i	$0.278503\pi$
$450$	−0.395024	−0.0186216
$451$	11.8922	0.559981
$452$	−10.7340	−0.504884
$453$	30.9568	1.45448
$454$	−19.0498	−0.894050
$455$	−9.50589	−0.445643
$456$	0.928497	0.0434809
$457$	−7.22184	−0.337824	−0.168912	−	0.985631i	$-0.554025\pi$
$457$	−7.22184	−0.337824	−0.168912	+	0.985631i	$0.554025\pi$
$458$	6.37302	0.297792
$459$	−18.1815	−0.848638
$460$	−11.5224	−0.537233
$461$	−5.26355	−0.245148	−0.122574	−	0.992459i	$-0.539115\pi$
$461$	−5.26355	−0.245148	−0.122574	+	0.992459i	$0.539115\pi$
$462$	4.56334	0.212306
$463$	−23.9862	−1.11474	−0.557368	−	0.830266i	$-0.688189\pi$
$463$	−23.9862	−1.11474	−0.557368	+	0.830266i	$0.688189\pi$
$464$	7.58186	0.351979
$465$	−24.3870	−1.13092
$466$	−9.76373	−0.452296
$467$	−14.4996	−0.670960	−0.335480	−	0.942047i	$-0.608899\pi$
$467$	−14.4996	−0.670960	−0.335480	+	0.942047i	$0.608899\pi$
$468$	0.112189	0.00518595
$469$	−9.12245	−0.421236
$470$	−12.4292	−0.573318
$471$	7.47646	0.344497
$472$	−3.63041	−0.167103
$473$	−16.9011	−0.777112
$474$	1.47560	0.0677765
$475$	−6.32211	−0.290078
$476$	2.42836	0.111304
$477$	−0.299877	−0.0137304
$478$	−15.3464	−0.701929
$479$	−21.1087	−0.964483	−0.482242	−	0.876038i	$-0.660177\pi$
$479$	−21.1087	−0.964483	−0.482242	+	0.876038i	$0.660177\pi$
$480$	7.04399	0.321513
$481$	24.8940	1.13507
$482$	−4.30794	−0.196221
$483$	3.38613	0.154074
$484$	3.41518	0.155235
$485$	−18.7495	−0.851371
$486$	−0.350045	−0.0158784
$487$	11.4472	0.518723	0.259362	−	0.965780i	$-0.416488\pi$
$487$	11.4472	0.518723	0.259362	+	0.965780i	$0.416488\pi$
$488$	2.61297	0.118284
$489$	−38.1370	−1.72461
$490$	26.6374	1.20335
$491$	3.85467	0.173959	0.0869794	−	0.996210i	$-0.472279\pi$
$491$	3.85467	0.173959	0.0869794	+	0.996210i	$0.472279\pi$
$492$	−5.39462	−0.243208
$493$	−26.3831	−1.18823
$494$	1.79552	0.0807843
$495$	0.523062	0.0235099
$496$	−3.46211	−0.155453
$497$	−0.193600	−0.00868415
$498$	−4.78080	−0.214233
$499$	25.6387	1.14774	0.573872	−	0.818945i	$-0.305441\pi$
$499$	25.6387	1.14774	0.573872	+	0.818945i	$0.305441\pi$
$500$	−27.5129	−1.23042
$501$	13.2329	0.591200
$502$	−19.2747	−0.860273
$503$	13.2450	0.590565	0.295283	−	0.955410i	$-0.404586\pi$
$503$	13.2450	0.590565	0.295283	+	0.955410i	$0.404586\pi$
$504$	0.0235070	0.00104708
$505$	−11.9703	−0.532671
$506$	10.6965	0.475517
$507$	3.28496	0.145890
$508$	12.8809	0.571500
$509$	−18.5263	−0.821164	−0.410582	−	0.911824i	$-0.634674\pi$
$509$	−18.5263	−0.821164	−0.410582	+	0.911824i	$0.634674\pi$
$510$	−24.5114	−1.08538
$511$	−8.18695	−0.362169
$512$	1.00000	0.0441942
$513$	−2.81677	−0.124363
$514$	2.22914	0.0983232
$515$	48.1567	2.12204
$516$	7.66677	0.337511
$517$	11.5384	0.507457
$518$	5.21603	0.229179
$519$	25.3638	1.11335
$520$	13.6216	0.597347
$521$	−14.7607	−0.646678	−0.323339	−	0.946283i	$-0.604805\pi$
$521$	−14.7607	−0.646678	−0.323339	+	0.946283i	$0.604805\pi$
$522$	−0.255393	−0.0111782
$523$	13.7481	0.601163	0.300581	−	0.953756i	$-0.402819\pi$
$523$	13.7481	0.601163	0.300581	+	0.953756i	$0.402819\pi$
$524$	11.0264	0.481690
$525$	14.0949	0.615153
$526$	−13.8337	−0.603180
$527$	12.0473	0.524789
$528$	−6.53911	−0.284578
$529$	−15.0629	−0.654908
$530$	−36.4100	−1.58155
$531$	0.122289	0.00530690
$532$	0.376215	0.0163110
$533$	−10.4321	−0.451863
$534$	−26.6646	−1.15389
$535$	2.88923	0.124912
$536$	13.0722	0.564631
$537$	25.3291	1.09303
$538$	−12.6021	−0.543315
$539$	−24.7281	−1.06512
$540$	−21.3692	−0.919586
$541$	−24.1348	−1.03764	−0.518818	−	0.854885i	$-0.673628\pi$
$541$	−24.1348	−1.03764	−0.518818	+	0.854885i	$0.673628\pi$
$542$	23.2395	0.998221
$543$	28.7218	1.23257
$544$	−3.47976	−0.149194
$545$	51.6088	2.21068
$546$	−4.00305	−0.171315
$547$	2.41644	0.103320	0.0516598	−	0.998665i	$-0.483549\pi$
$547$	2.41644	0.103320	0.0516598	+	0.998665i	$0.483549\pi$
$548$	0.0980447	0.00418826
$549$	−0.0880172	−0.00375648
$550$	44.5246	1.89854
$551$	−4.08740	−0.174129
$552$	−4.85221	−0.206524
$553$	0.597894	0.0254250
$554$	32.9484	1.39984
$555$	−52.6496	−2.23485
$556$	−13.2183	−0.560579
$557$	8.35157	0.353867	0.176934	−	0.984223i	$-0.443382\pi$
$557$	8.35157	0.353867	0.176934	+	0.984223i	$0.443382\pi$
$558$	0.116620	0.00493692
$559$	14.8259	0.627071
$560$	2.85413	0.120609
$561$	22.7546	0.960698
$562$	25.3185	1.06800
$563$	12.2687	0.517062	0.258531	−	0.966003i	$-0.416762\pi$
$563$	12.2687	0.517062	0.258531	+	0.966003i	$0.416762\pi$
$564$	−5.23411	−0.220396
$565$	43.9007	1.84692
$566$	31.5423	1.32582
$567$	6.20937	0.260769
$568$	0.277422	0.0116404
$569$	−34.0919	−1.42921	−0.714603	−	0.699530i	$-0.753393\pi$
$569$	−34.0919	−1.42921	−0.714603	+	0.699530i	$0.753393\pi$
$570$	−3.79744	−0.159057
$571$	−10.0401	−0.420164	−0.210082	−	0.977684i	$-0.567373\pi$
$571$	−10.0401	−0.420164	−0.210082	+	0.977684i	$0.567373\pi$
$572$	−12.6453	−0.528726
$573$	24.4147	1.01994
$574$	−2.18583	−0.0912347
$575$	33.0386	1.37780
$576$	−0.0336847	−0.00140353
$577$	45.9443	1.91268	0.956342	−	0.292249i	$-0.0944036\pi$
$577$	45.9443	1.91268	0.956342	+	0.292249i	$0.0944036\pi$
$578$	−4.89124	−0.203449
$579$	−43.3354	−1.80096
$580$	−31.0088	−1.28757
$581$	−1.93712	−0.0803652
$582$	−7.89566	−0.327286
$583$	33.8003	1.39986
$584$	11.7316	0.485458
$585$	−0.458840	−0.0189707
$586$	32.9242	1.36009
$587$	−0.109519	−0.00452035	−0.00226017	−	0.999997i	$-0.500719\pi$
$587$	−0.109519	−0.00452035	−0.00226017	+	0.999997i	$0.500719\pi$
$588$	11.2173	0.462595
$589$	1.86643	0.0769050
$590$	14.8479	0.611279
$591$	36.3511	1.49528
$592$	−7.47440	−0.307196
$593$	−31.4911	−1.29318	−0.646592	−	0.762836i	$-0.723806\pi$
$593$	−31.4911	−1.29318	−0.646592	+	0.762836i	$0.723806\pi$
$594$	19.8376	0.813947
$595$	−9.93171	−0.407160
$596$	6.24766	0.255914
$597$	47.7514	1.95434
$598$	−9.38317	−0.383706
$599$	−25.6157	−1.04663	−0.523315	−	0.852139i	$-0.675305\pi$
$599$	−25.6157	−1.04663	−0.523315	+	0.852139i	$0.675305\pi$
$600$	−20.1976	−0.824562
$601$	−45.9327	−1.87363	−0.936816	−	0.349822i	$-0.886242\pi$
$601$	−45.9327	−1.87363	−0.936816	+	0.349822i	$0.886242\pi$
$602$	3.10648	0.126611
$603$	−0.440332	−0.0179317
$604$	−17.9741	−0.731356
$605$	−13.9676	−0.567866
$606$	−5.04084	−0.204770
$607$	−10.0517	−0.407986	−0.203993	−	0.978972i	$-0.565392\pi$
$607$	−10.0517	−0.407986	−0.203993	+	0.978972i	$0.565392\pi$
$608$	−0.539103	−0.0218635
$609$	9.11273	0.369266
$610$	−10.6867	−0.432693
$611$	−10.1217	−0.409479
$612$	0.117215	0.00473813
$613$	−41.4124	−1.67263	−0.836316	−	0.548247i	$-0.815295\pi$
$613$	−41.4124	−1.67263	−0.836316	+	0.548247i	$0.815295\pi$
$614$	−27.7989	−1.12187
$615$	22.0633	0.889679
$616$	−2.64956	−0.106754
$617$	−34.5669	−1.39161	−0.695805	−	0.718230i	$-0.744952\pi$
$617$	−34.5669	−1.39161	−0.695805	+	0.718230i	$0.744952\pi$
$618$	20.2794	0.815757
$619$	−6.60739	−0.265574	−0.132787	−	0.991145i	$-0.542393\pi$
$619$	−6.60739	−0.265574	−0.132787	+	0.991145i	$0.542393\pi$
$620$	14.1596	0.568662
$621$	14.7201	0.590697
$622$	−30.2900	−1.21452
$623$	−10.8041	−0.432859
$624$	5.73624	0.229633
$625$	53.8891	2.15556
$626$	11.1620	0.446125
$627$	3.52526	0.140785
$628$	−4.34098	−0.173224
$629$	26.0091	1.03705
$630$	−0.0961407	−0.00383034
$631$	32.7359	1.30320	0.651598	−	0.758565i	$-0.274099\pi$
$631$	32.7359	1.30320	0.651598	+	0.758565i	$0.274099\pi$
$632$	−0.856761	−0.0340801
$633$	17.2750	0.686618
$634$	4.92796	0.195714
$635$	−52.6815	−2.09060
$636$	−15.3327	−0.607982
$637$	21.6920	0.859468
$638$	28.7863	1.13966
$639$	−0.00934489	−0.000369678 0
$640$	−4.08988	−0.161667
$641$	−24.4602	−0.966118	−0.483059	−	0.875588i	$-0.660474\pi$
$641$	−24.4602	−0.966118	−0.483059	+	0.875588i	$0.660474\pi$
$642$	1.21669	0.0480191
$643$	25.9478	1.02328	0.511641	−	0.859199i	$-0.329038\pi$
$643$	25.9478	1.02328	0.511641	+	0.859199i	$0.329038\pi$
$644$	−1.96605	−0.0774734
$645$	−31.3562	−1.23465
$646$	1.87595	0.0738084
$647$	−11.1304	−0.437582	−0.218791	−	0.975772i	$-0.570211\pi$
$647$	−11.1304	−0.437582	−0.218791	+	0.975772i	$0.570211\pi$
$648$	−8.89781	−0.349539
$649$	−13.7837	−0.541057
$650$	−39.0579	−1.53198
$651$	−4.16115	−0.163088
$652$	22.1431	0.867189
$653$	5.06477	0.198200	0.0990999	−	0.995077i	$-0.468404\pi$
$653$	5.06477	0.198200	0.0990999	+	0.995077i	$0.468404\pi$
$654$	21.7331	0.849833
$655$	−45.0966	−1.76207
$656$	3.13222	0.122293
$657$	−0.395176	−0.0154173
$658$	−2.12079	−0.0826772
$659$	14.4303	0.562125	0.281062	−	0.959690i	$-0.409313\pi$
$659$	14.4303	0.562125	0.281062	+	0.959690i	$0.409313\pi$
$660$	26.7441	1.04101
$661$	−11.6502	−0.453139	−0.226569	−	0.973995i	$-0.572751\pi$
$661$	−11.6502	−0.453139	−0.226569	+	0.973995i	$0.572751\pi$
$662$	23.6037	0.917384
$663$	−19.9608	−0.775211
$664$	2.77582	0.107723
$665$	−1.53867	−0.0596672
$666$	0.251773	0.00975601
$667$	21.3603	0.827073
$668$	−7.68325	−0.297274
$669$	7.60405	0.293990
$670$	−53.4635	−2.06548
$671$	9.92075	0.382986
$672$	1.20191	0.0463648
$673$	−16.3164	−0.628950	−0.314475	−	0.949266i	$-0.601828\pi$
$673$	−16.3164	−0.628950	−0.314475	+	0.949266i	$0.601828\pi$
$674$	−3.05950	−0.117847
$675$	61.2730	2.35840
$676$	−1.90731	−0.0733580
$677$	−10.4589	−0.401969	−0.200985	−	0.979594i	$-0.564414\pi$
$677$	−10.4589	−0.401969	−0.200985	+	0.979594i	$0.564414\pi$
$678$	18.4871	0.709995
$679$	−3.19922	−0.122775
$680$	14.2318	0.545765
$681$	32.8094	1.25726
$682$	−13.1447	−0.503336
$683$	13.6757	0.523286	0.261643	−	0.965165i	$-0.415736\pi$
$683$	13.6757	0.523286	0.261643	+	0.965165i	$0.415736\pi$
$684$	0.0181595	0.000694348 0
$685$	−0.400991	−0.0153211
$686$	9.43009	0.360043
$687$	−10.9763	−0.418770
$688$	−4.45148	−0.169711
$689$	−29.6503	−1.12959
$690$	19.8449	0.755484
$691$	−16.4731	−0.626666	−0.313333	−	0.949643i	$-0.601446\pi$
$691$	−16.4731	−0.626666	−0.313333	+	0.949643i	$0.601446\pi$
$692$	−14.7267	−0.559825
$693$	0.0892498	0.00339032
$694$	−35.4170	−1.34441
$695$	54.0610	2.05065
$696$	−13.0582	−0.494971
$697$	−10.8994	−0.412843
$698$	9.48433	0.358987
$699$	16.8161	0.636042
$700$	−8.18379	−0.309318
$701$	41.6309	1.57238	0.786189	−	0.617986i	$-0.212051\pi$
$701$	41.6309	1.57238	0.786189	+	0.617986i	$0.212051\pi$
$702$	−17.4019	−0.656794
$703$	4.02947	0.151974
$704$	3.79673	0.143095
$705$	21.4069	0.806229
$706$	−0.962893	−0.0362390
$707$	−2.04248	−0.0768155
$708$	6.25265	0.234989
$709$	39.3799	1.47894	0.739471	−	0.673188i	$-0.235075\pi$
$709$	39.3799	1.47894	0.739471	+	0.673188i	$0.235075\pi$
$710$	−1.13462	−0.0425816
$711$	0.0288598	0.00108233
$712$	15.4820	0.580212
$713$	−9.75375	−0.365281
$714$	−4.18237	−0.156521
$715$	51.7176	1.93413
$716$	−14.7065	−0.549609
$717$	26.4311	0.987089
$718$	10.7913	0.402727
$719$	−7.57939	−0.282664	−0.141332	−	0.989962i	$-0.545138\pi$
$719$	−7.57939	−0.282664	−0.141332	+	0.989962i	$0.545138\pi$
$720$	0.137766	0.00513425
$721$	8.21695	0.306015
$722$	−18.7094	−0.696291
$723$	7.41955	0.275936
$724$	−16.6764	−0.619774
$725$	88.9131	3.30215
$726$	−5.88196	−0.218300
$727$	−49.7246	−1.84418	−0.922092	−	0.386970i	$-0.873522\pi$
$727$	−49.7246	−1.84418	−0.922092	+	0.386970i	$0.873522\pi$
$728$	2.32425	0.0861424
$729$	27.2963	1.01097
$730$	−47.9809	−1.77585
$731$	15.4901	0.572922
$732$	−4.50032	−0.166337
$733$	2.82268	0.104258	0.0521291	−	0.998640i	$-0.483399\pi$
$733$	2.82268	0.104258	0.0521291	+	0.998640i	$0.483399\pi$
$734$	33.3516	1.23103
$735$	−45.8775	−1.69222
$736$	2.81729	0.103847
$737$	49.6315	1.82820
$738$	−0.105508	−0.00388380
$739$	−28.9582	−1.06525	−0.532623	−	0.846353i	$-0.678794\pi$
$739$	−28.9582	−1.06525	−0.532623	+	0.846353i	$0.678794\pi$
$740$	30.5694	1.12375
$741$	−3.09242	−0.113603
$742$	−6.21262	−0.228072
$743$	−2.34313	−0.0859611	−0.0429805	−	0.999076i	$-0.513685\pi$
$743$	−2.34313	−0.0859611	−0.0429805	+	0.999076i	$0.513685\pi$
$744$	5.96278	0.218606
$745$	−25.5521	−0.936158
$746$	15.6000	0.571157
$747$	−0.0935028	−0.00342109
$748$	−13.2117	−0.483069
$749$	0.492988	0.0180134
$750$	47.3855	1.73027
$751$	34.4967	1.25880	0.629401	−	0.777081i	$-0.283300\pi$
$751$	34.4967	1.25880	0.629401	+	0.777081i	$0.283300\pi$
$752$	3.03903	0.110822
$753$	33.1968	1.20976
$754$	−25.2519	−0.919620
$755$	73.5119	2.67537
$756$	−3.64622	−0.132612
$757$	12.7966	0.465101	0.232550	−	0.972584i	$-0.425293\pi$
$757$	12.7966	0.465101	0.232550	+	0.972584i	$0.425293\pi$
$758$	2.40637	0.0874032
$759$	−18.4226	−0.668696
$760$	2.20487	0.0799789
$761$	−13.2582	−0.480609	−0.240305	−	0.970698i	$-0.577247\pi$
$761$	−13.2582	−0.480609	−0.240305	+	0.970698i	$0.577247\pi$
$762$	−22.1848	−0.803672
$763$	8.80599	0.318798
$764$	−14.1756	−0.512856
$765$	−0.479394	−0.0173325
$766$	−7.38963	−0.266998
$767$	12.0913	0.436592
$768$	−1.72230	−0.0621481
$769$	10.6699	0.384766	0.192383	−	0.981320i	$-0.438378\pi$
$769$	10.6699	0.384766	0.192383	+	0.981320i	$0.438378\pi$
$770$	10.8364	0.390516
$771$	−3.83925	−0.138267
$772$	25.1614	0.905578
$773$	−10.9549	−0.394020	−0.197010	−	0.980401i	$-0.563123\pi$
$773$	−10.9549	−0.394020	−0.197010	+	0.980401i	$0.563123\pi$
$774$	0.149947	0.00538972
$775$	−40.6004	−1.45841
$776$	4.58437	0.164569
$777$	−8.98357	−0.322284
$778$	−18.5609	−0.665440
$779$	−1.68859	−0.0605000
$780$	−23.4605	−0.840021
$781$	1.05330	0.0376900
$782$	−9.80350	−0.350572
$783$	39.6145	1.41571
$784$	−6.51300	−0.232607
$785$	17.7541	0.633670
$786$	−18.9908	−0.677378
$787$	35.2019	1.25481	0.627405	−	0.778693i	$-0.284117\pi$
$787$	35.2019	1.25481	0.627405	+	0.778693i	$0.284117\pi$
$788$	−21.1061	−0.751875
$789$	23.8258	0.848222
$790$	3.50405	0.124668
$791$	7.49075	0.266340
$792$	−0.127892	−0.00454444
$793$	−8.70268	−0.309041
$794$	−2.78047	−0.0986751
$795$	62.7089	2.22406
$796$	−27.7254	−0.982700
$797$	32.3921	1.14739	0.573693	−	0.819070i	$-0.305510\pi$
$797$	32.3921	1.14739	0.573693	+	0.819070i	$0.305510\pi$
$798$	−0.647955	−0.0229374
$799$	−10.5751	−0.374120
$800$	11.7271	0.414615
$801$	−0.521506	−0.0184265
$802$	21.3202	0.752842
$803$	44.5418	1.57185
$804$	−22.5142	−0.794014
$805$	8.04092	0.283405
$806$	11.5308	0.406154
$807$	21.7046	0.764037
$808$	2.92681	0.102965
$809$	26.4710	0.930670	0.465335	−	0.885135i	$-0.345934\pi$
$809$	26.4710	0.930670	0.465335	+	0.885135i	$0.345934\pi$
$810$	36.3909	1.27865
$811$	1.06790	0.0374989	0.0187495	−	0.999824i	$-0.494032\pi$
$811$	1.06790	0.0374989	0.0187495	+	0.999824i	$0.494032\pi$
$812$	−5.29102	−0.185679
$813$	−40.0253	−1.40375
$814$	−28.3783	−0.994658
$815$	−90.5623	−3.17226
$816$	5.99320	0.209804
$817$	2.39981	0.0839586
$818$	−32.9705	−1.15279
$819$	−0.0782917	−0.00273573
$820$	−12.8104	−0.447358
$821$	−32.5795	−1.13703	−0.568516	−	0.822672i	$-0.692482\pi$
$821$	−32.5795	−1.13703	−0.568516	+	0.822672i	$0.692482\pi$
$822$	−0.168862	−0.00588975
$823$	40.9384	1.42702	0.713511	−	0.700644i	$-0.247104\pi$
$823$	40.9384	1.42702	0.713511	+	0.700644i	$0.247104\pi$
$824$	−11.7746	−0.410188
$825$	−76.6847	−2.66982
$826$	2.53349	0.0881515
$827$	15.5677	0.541344	0.270672	−	0.962672i	$-0.412754\pi$
$827$	15.5677	0.541344	0.270672	+	0.962672i	$0.412754\pi$
$828$	−0.0948996	−0.00329799
$829$	−20.9907	−0.729038	−0.364519	−	0.931196i	$-0.618767\pi$
$829$	−20.9907	−0.729038	−0.364519	+	0.931196i	$0.618767\pi$
$830$	−11.3528	−0.394060
$831$	−56.7470	−1.96853
$832$	−3.33057	−0.115467
$833$	22.6637	0.785251
$834$	22.7658	0.788315
$835$	31.4235	1.08746
$836$	−2.04683	−0.0707911
$837$	−18.0892	−0.625254
$838$	−5.85953	−0.202414
$839$	3.29172	0.113643	0.0568213	−	0.998384i	$-0.481903\pi$
$839$	3.29172	0.113643	0.0568213	+	0.998384i	$0.481903\pi$
$840$	−4.91567	−0.169607
$841$	28.4845	0.982225
$842$	7.72562	0.266243
$843$	−43.6060	−1.50187
$844$	−10.0302	−0.345253
$845$	7.80066	0.268351
$846$	−0.102369	−0.00351951
$847$	−2.38329	−0.0818909
$848$	8.90247	0.305712
$849$	−54.3253	−1.86444
$850$	−40.8075	−1.39969
$851$	−21.0575	−0.721843
$852$	−0.477804	−0.0163693
$853$	−17.2822	−0.591730	−0.295865	−	0.955230i	$-0.595608\pi$
$853$	−17.2822	−0.591730	−0.295865	+	0.955230i	$0.595608\pi$
$854$	−1.82347	−0.0623979
$855$	−0.0742703	−0.00253999
$856$	−0.706436	−0.0241455
$857$	22.4749	0.767730	0.383865	−	0.923389i	$-0.374593\pi$
$857$	22.4749	0.767730	0.383865	+	0.923389i	$0.374593\pi$
$858$	21.7790	0.743521
$859$	−13.4857	−0.460126	−0.230063	−	0.973176i	$-0.573893\pi$
$859$	−13.4857	−0.460126	−0.230063	+	0.973176i	$0.573893\pi$
$860$	18.2060	0.620819
$861$	3.76465	0.128299
$862$	−27.0825	−0.922435
$863$	48.2080	1.64102	0.820510	−	0.571632i	$-0.193690\pi$
$863$	48.2080	1.64102	0.820510	+	0.571632i	$0.193690\pi$
$864$	5.22491	0.177755
$865$	60.2303	2.04789
$866$	−24.3769	−0.828361
$867$	8.42419	0.286100
$868$	2.41604	0.0820058
$869$	−3.25289	−0.110347
$870$	53.4065	1.81065
$871$	−43.5377	−1.47522
$872$	−12.6187	−0.427322
$873$	−0.154423	−0.00522644
$874$	−1.51881	−0.0513745
$875$	19.2000	0.649078
$876$	−20.2054	−0.682676
$877$	14.3666	0.485127	0.242564	−	0.970136i	$-0.422012\pi$
$877$	14.3666	0.485127	0.242564	+	0.970136i	$0.422012\pi$
$878$	1.69644	0.0572522
$879$	−56.7054	−1.91263
$880$	−15.5282	−0.523454
$881$	−34.2350	−1.15341	−0.576703	−	0.816954i	$-0.695661\pi$
$881$	−34.2350	−1.15341	−0.576703	+	0.816954i	$0.695661\pi$
$882$	0.219389	0.00738720
$883$	16.9059	0.568927	0.284464	−	0.958687i	$-0.408184\pi$
$883$	16.9059	0.568927	0.284464	+	0.958687i	$0.408184\pi$
$884$	11.5896	0.389800
$885$	−25.5726	−0.859612
$886$	21.1039	0.708998
$887$	32.6395	1.09593	0.547964	−	0.836502i	$-0.315403\pi$
$887$	32.6395	1.09593	0.547964	+	0.836502i	$0.315403\pi$
$888$	12.8732	0.431995
$889$	−8.98901	−0.301482
$890$	−63.3194	−2.12247
$891$	−33.7826	−1.13176
$892$	−4.41506	−0.147827
$893$	−1.63835	−0.0548252
$894$	−10.7603	−0.359880
$895$	60.1479	2.01052
$896$	−0.697853	−0.0233136
$897$	16.1606	0.539588
$898$	27.1669	0.906570
$899$	−26.2492	−0.875459
$900$	−0.395024	−0.0131675
$901$	−30.9785	−1.03204
$902$	11.8922	0.395967
$903$	−5.35028	−0.178046
$904$	−10.7340	−0.357007
$905$	68.2045	2.26719
$906$	30.9568	1.02847
$907$	−37.8930	−1.25822	−0.629108	−	0.777318i	$-0.716580\pi$
$907$	−37.8930	−1.25822	−0.629108	+	0.777318i	$0.716580\pi$
$908$	−19.0498	−0.632189
$909$	−0.0985888	−0.00326998
$910$	−9.50589	−0.315117
$911$	−12.0431	−0.399004	−0.199502	−	0.979897i	$-0.563932\pi$
$911$	−12.0431	−0.399004	−0.199502	+	0.979897i	$0.563932\pi$
$912$	0.928497	0.0307456
$913$	10.5391	0.348792
$914$	−7.22184	−0.238877
$915$	18.4057	0.608475
$916$	6.37302	0.210571
$917$	−7.69481	−0.254105
$918$	−18.1815	−0.600078
$919$	−28.4676	−0.939060	−0.469530	−	0.882916i	$-0.655577\pi$
$919$	−28.4676	−0.939060	−0.469530	+	0.882916i	$0.655577\pi$
$920$	−11.5224	−0.379881
$921$	47.8780	1.57763
$922$	−5.26355	−0.173346
$923$	−0.923974	−0.0304130
$924$	4.56334	0.150123
$925$	−87.6529	−2.88201
$926$	−23.9862	−0.788237
$927$	0.396624	0.0130269
$928$	7.58186	0.248887
$929$	−10.2023	−0.334726	−0.167363	−	0.985895i	$-0.553525\pi$
$929$	−10.2023	−0.334726	−0.167363	+	0.985895i	$0.553525\pi$
$930$	−24.3870	−0.799682
$931$	3.51118	0.115074
$932$	−9.76373	−0.319822
$933$	52.1684	1.70792
$934$	−14.4996	−0.474441
$935$	54.0343	1.76711
$936$	0.112189	0.00366702
$937$	34.1936	1.11706	0.558528	−	0.829486i	$-0.311366\pi$
$937$	34.1936	1.11706	0.558528	+	0.829486i	$0.311366\pi$
$938$	−9.12245	−0.297859
$939$	−19.2244	−0.627363
$940$	−12.4292	−0.405397
$941$	16.2047	0.528259	0.264130	−	0.964487i	$-0.414915\pi$
$941$	16.2047	0.528259	0.264130	+	0.964487i	$0.414915\pi$
$942$	7.47646	0.243596
$943$	8.82436	0.287361
$944$	−3.63041	−0.118160
$945$	14.9126	0.485107
$946$	−16.9011	−0.549501
$947$	−7.85714	−0.255323	−0.127661	−	0.991818i	$-0.540747\pi$
$947$	−7.85714	−0.255323	−0.127661	+	0.991818i	$0.540747\pi$
$948$	1.47560	0.0479252
$949$	−39.0730	−1.26836
$950$	−6.32211	−0.205116
$951$	−8.48742	−0.275223
$952$	2.42836	0.0787038
$953$	−5.22928	−0.169393	−0.0846965	−	0.996407i	$-0.526992\pi$
$953$	−5.22928	−0.169393	−0.0846965	+	0.996407i	$0.526992\pi$
$954$	−0.299877	−0.00970888
$955$	57.9765	1.87608
$956$	−15.3464	−0.496339
$957$	−49.5786	−1.60265
$958$	−21.1087	−0.681993
$959$	−0.0684208	−0.00220942
$960$	7.04399	0.227344
$961$	−19.0138	−0.613349
$962$	24.8940	0.802615
$963$	0.0237961	0.000766818 0
$964$	−4.30794	−0.138749
$965$	−102.907	−3.31269
$966$	3.38613	0.108947
$967$	−41.9475	−1.34894	−0.674470	−	0.738302i	$-0.735628\pi$
$967$	−41.9475	−1.34894	−0.674470	+	0.738302i	$0.735628\pi$
$968$	3.41518	0.109768
$969$	−3.23095	−0.103793
$970$	−18.7495	−0.602010
$971$	15.8591	0.508943	0.254471	−	0.967080i	$-0.418099\pi$
$971$	15.8591	0.508943	0.254471	+	0.967080i	$0.418099\pi$
$972$	−0.350045	−0.0112277
$973$	9.22440	0.295721
$974$	11.4472	0.366793
$975$	67.2693	2.15434
$976$	2.61297	0.0836391
$977$	−52.8507	−1.69085	−0.845423	−	0.534098i	$-0.820651\pi$
$977$	−52.8507	−1.69085	−0.845423	+	0.534098i	$0.820651\pi$
$978$	−38.1370	−1.21949
$979$	58.7809	1.87865
$980$	26.6374	0.850899
$981$	0.425057	0.0135710
$982$	3.85467	0.123007
$983$	11.0984	0.353985	0.176992	−	0.984212i	$-0.443363\pi$
$983$	11.0984	0.353985	0.176992	+	0.984212i	$0.443363\pi$
$984$	−5.39462	−0.171974
$985$	86.3214	2.75043
$986$	−26.3831	−0.840208
$987$	3.65264	0.116265
$988$	1.79552	0.0571231
$989$	−12.5411	−0.398783
$990$	0.523062	0.0166240
$991$	28.5127	0.905737	0.452868	−	0.891577i	$-0.350401\pi$
$991$	28.5127	0.905737	0.452868	+	0.891577i	$0.350401\pi$
$992$	−3.46211	−0.109922
$993$	−40.6526	−1.29007
$994$	−0.193600	−0.00614062
$995$	113.393	3.59481
$996$	−4.78080	−0.151485
$997$	48.9412	1.54998	0.774992	−	0.631971i	$-0.217754\pi$
$997$	48.9412	1.54998	0.774992	+	0.631971i	$0.217754\pi$
$998$	25.6387	0.811578
$999$	−39.0531	−1.23558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.19	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.19	✓	71	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.72230 q^{3} +1.00000 q^{4} -4.08988 q^{5} -1.72230 q^{6} -0.697853 q^{7} +1.00000 q^{8} -0.0336847 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.72230 q^{3} +1.00000 q^{4} -4.08988 q^{5} -1.72230 q^{6} -0.697853 q^{7} +1.00000 q^{8} -0.0336847 q^{9} -4.08988 q^{10} +3.79673 q^{11} -1.72230 q^{12} -3.33057 q^{13} -0.697853 q^{14} +7.04399 q^{15} +1.00000 q^{16} -3.47976 q^{17} -0.0336847 q^{18} -0.539103 q^{19} -4.08988 q^{20} +1.20191 q^{21} +3.79673 q^{22} +2.81729 q^{23} -1.72230 q^{24} +11.7271 q^{25} -3.33057 q^{26} +5.22491 q^{27} -0.697853 q^{28} +7.58186 q^{29} +7.04399 q^{30} -3.46211 q^{31} +1.00000 q^{32} -6.53911 q^{33} -3.47976 q^{34} +2.85413 q^{35} -0.0336847 q^{36} -7.47440 q^{37} -0.539103 q^{38} +5.73624 q^{39} -4.08988 q^{40} +3.13222 q^{41} +1.20191 q^{42} -4.45148 q^{43} +3.79673 q^{44} +0.137766 q^{45} +2.81729 q^{46} +3.03903 q^{47} -1.72230 q^{48} -6.51300 q^{49} +11.7271 q^{50} +5.99320 q^{51} -3.33057 q^{52} +8.90247 q^{53} +5.22491 q^{54} -15.5282 q^{55} -0.697853 q^{56} +0.928497 q^{57} +7.58186 q^{58} -3.63041 q^{59} +7.04399 q^{60} +2.61297 q^{61} -3.46211 q^{62} +0.0235070 q^{63} +1.00000 q^{64} +13.6216 q^{65} -6.53911 q^{66} +13.0722 q^{67} -3.47976 q^{68} -4.85221 q^{69} +2.85413 q^{70} +0.277422 q^{71} -0.0336847 q^{72} +11.7316 q^{73} -7.47440 q^{74} -20.1976 q^{75} -0.539103 q^{76} -2.64956 q^{77} +5.73624 q^{78} -0.856761 q^{79} -4.08988 q^{80} -8.89781 q^{81} +3.13222 q^{82} +2.77582 q^{83} +1.20191 q^{84} +14.2318 q^{85} -4.45148 q^{86} -13.0582 q^{87} +3.79673 q^{88} +15.4820 q^{89} +0.137766 q^{90} +2.32425 q^{91} +2.81729 q^{92} +5.96278 q^{93} +3.03903 q^{94} +2.20487 q^{95} -1.72230 q^{96} +4.58437 q^{97} -6.51300 q^{98} -0.127892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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