LMFDB - Embedded newform 4033.2.a.d.1.75

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.75
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.44610 q^{2} -1.80658 q^{3} +3.98342 q^{4} +1.33911 q^{5} -4.41908 q^{6} -4.17474 q^{7} +4.85164 q^{8} +0.263733 q^{9} +O(q^{10})$	\(q+2.44610 q^{2} -1.80658 q^{3} +3.98342 q^{4} +1.33911 q^{5} -4.41908 q^{6} -4.17474 q^{7} +4.85164 q^{8} +0.263733 q^{9} +3.27560 q^{10} +0.612543 q^{11} -7.19636 q^{12} +2.45119 q^{13} -10.2118 q^{14} -2.41921 q^{15} +3.90078 q^{16} +7.47439 q^{17} +0.645118 q^{18} -6.84398 q^{19} +5.33424 q^{20} +7.54200 q^{21} +1.49834 q^{22} -7.81284 q^{23} -8.76488 q^{24} -3.20678 q^{25} +5.99586 q^{26} +4.94329 q^{27} -16.6297 q^{28} -3.09317 q^{29} -5.91764 q^{30} -4.22281 q^{31} -0.161578 q^{32} -1.10661 q^{33} +18.2831 q^{34} -5.59044 q^{35} +1.05056 q^{36} -1.00000 q^{37} -16.7411 q^{38} -4.42827 q^{39} +6.49689 q^{40} -1.96975 q^{41} +18.4485 q^{42} +3.54798 q^{43} +2.44002 q^{44} +0.353168 q^{45} -19.1110 q^{46} +1.35685 q^{47} -7.04707 q^{48} +10.4284 q^{49} -7.84411 q^{50} -13.5031 q^{51} +9.76412 q^{52} -8.34433 q^{53} +12.0918 q^{54} +0.820264 q^{55} -20.2543 q^{56} +12.3642 q^{57} -7.56621 q^{58} -1.91380 q^{59} -9.63673 q^{60} +3.51702 q^{61} -10.3294 q^{62} -1.10102 q^{63} -8.19680 q^{64} +3.28242 q^{65} -2.70688 q^{66} +4.43376 q^{67} +29.7736 q^{68} +14.1145 q^{69} -13.6748 q^{70} -10.0942 q^{71} +1.27954 q^{72} -5.35784 q^{73} -2.44610 q^{74} +5.79331 q^{75} -27.2624 q^{76} -2.55721 q^{77} -10.8320 q^{78} +2.37682 q^{79} +5.22358 q^{80} -9.72164 q^{81} -4.81822 q^{82} -14.3917 q^{83} +30.0429 q^{84} +10.0090 q^{85} +8.67873 q^{86} +5.58806 q^{87} +2.97184 q^{88} -2.09022 q^{89} +0.863885 q^{90} -10.2331 q^{91} -31.1218 q^{92} +7.62885 q^{93} +3.31900 q^{94} -9.16486 q^{95} +0.291903 q^{96} -5.77977 q^{97} +25.5091 q^{98} +0.161548 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	2.44610	1.72966	0.864828	−	0.502069i	$-0.167427\pi$
$2$	2.44610	1.72966	0.864828	+	0.502069i	$0.167427\pi$
$3$	−1.80658	−1.04303	−0.521515	−	0.853242i	$-0.674633\pi$
$3$	−1.80658	−1.04303	−0.521515	+	0.853242i	$0.674633\pi$
$4$	3.98342	1.99171
$5$	1.33911	0.598869	0.299434	−	0.954117i	$-0.403202\pi$
$5$	1.33911	0.598869	0.299434	+	0.954117i	$0.403202\pi$
$6$	−4.41908	−1.80408
$7$	−4.17474	−1.57790	−0.788952	−	0.614455i	$-0.789376\pi$
$7$	−4.17474	−1.57790	−0.788952	+	0.614455i	$0.789376\pi$
$8$	4.85164	1.71531
$9$	0.263733	0.0879110
$10$	3.27560	1.03584
$11$	0.612543	0.184689	0.0923444	−	0.995727i	$-0.470564\pi$
$11$	0.612543	0.184689	0.0923444	+	0.995727i	$0.470564\pi$
$12$	−7.19636	−2.07741
$13$	2.45119	0.679838	0.339919	−	0.940455i	$-0.389600\pi$
$13$	2.45119	0.679838	0.339919	+	0.940455i	$0.389600\pi$
$14$	−10.2118	−2.72923
$15$	−2.41921	−0.624638
$16$	3.90078	0.975195
$17$	7.47439	1.81280	0.906402	−	0.422415i	$-0.138818\pi$
$17$	7.47439	1.81280	0.906402	+	0.422415i	$0.138818\pi$
$18$	0.645118	0.152056
$19$	−6.84398	−1.57012	−0.785059	−	0.619421i	$-0.787367\pi$
$19$	−6.84398	−1.57012	−0.785059	+	0.619421i	$0.787367\pi$
$20$	5.33424	1.19277
$21$	7.54200	1.64580
$22$	1.49834	0.319448
$23$	−7.81284	−1.62909	−0.814545	−	0.580101i	$-0.803013\pi$
$23$	−7.81284	−1.62909	−0.814545	+	0.580101i	$0.803013\pi$
$24$	−8.76488	−1.78912
$25$	−3.20678	−0.641356
$26$	5.99586	1.17589
$27$	4.94329	0.951336
$28$	−16.6297	−3.14272
$29$	−3.09317	−0.574387	−0.287193	−	0.957873i	$-0.592722\pi$
$29$	−3.09317	−0.574387	−0.287193	+	0.957873i	$0.592722\pi$
$30$	−5.91764	−1.08041
$31$	−4.22281	−0.758440	−0.379220	−	0.925307i	$-0.623808\pi$
$31$	−4.22281	−0.758440	−0.379220	+	0.925307i	$0.623808\pi$
$32$	−0.161578	−0.0285632
$33$	−1.10661	−0.192636
$34$	18.2831	3.13553
$35$	−5.59044	−0.944957
$36$	1.05056	0.175093
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−16.7411	−2.71576
$39$	−4.42827	−0.709091
$40$	6.49689	1.02725
$41$	−1.96975	−0.307624	−0.153812	−	0.988100i	$-0.549155\pi$
$41$	−1.96975	−0.307624	−0.153812	+	0.988100i	$0.549155\pi$
$42$	18.4485	2.84667
$43$	3.54798	0.541062	0.270531	−	0.962711i	$-0.412801\pi$
$43$	3.54798	0.541062	0.270531	+	0.962711i	$0.412801\pi$
$44$	2.44002	0.367846
$45$	0.353168	0.0526472
$46$	−19.1110	−2.81776
$47$	1.35685	0.197917	0.0989585	−	0.995092i	$-0.468449\pi$
$47$	1.35685	0.197917	0.0989585	+	0.995092i	$0.468449\pi$
$48$	−7.04707	−1.01716
$49$	10.4284	1.48978
$50$	−7.84411	−1.10933
$51$	−13.5031	−1.89081
$52$	9.76412	1.35404
$53$	−8.34433	−1.14618	−0.573091	−	0.819492i	$-0.694256\pi$
$53$	−8.34433	−1.14618	−0.573091	+	0.819492i	$0.694256\pi$
$54$	12.0918	1.64548
$55$	0.820264	0.110604
$56$	−20.2543	−2.70660
$57$	12.3642	1.63768
$58$	−7.56621	−0.993492
$59$	−1.91380	−0.249156	−0.124578	−	0.992210i	$-0.539758\pi$
$59$	−1.91380	−0.249156	−0.124578	+	0.992210i	$0.539758\pi$
$60$	−9.63673	−1.24410
$61$	3.51702	0.450308	0.225154	−	0.974323i	$-0.427711\pi$
$61$	3.51702	0.450308	0.225154	+	0.974323i	$0.427711\pi$
$62$	−10.3294	−1.31184
$63$	−1.10102	−0.138715
$64$	−8.19680	−1.02460
$65$	3.28242	0.407134
$66$	−2.70688	−0.333194
$67$	4.43376	0.541669	0.270835	−	0.962626i	$-0.412700\pi$
$67$	4.43376	0.541669	0.270835	+	0.962626i	$0.412700\pi$
$68$	29.7736	3.61058
$69$	14.1145	1.69919
$70$	−13.6748	−1.63445
$71$	−10.0942	−1.19796	−0.598979	−	0.800764i	$-0.704427\pi$
$71$	−10.0942	−1.19796	−0.598979	+	0.800764i	$0.704427\pi$
$72$	1.27954	0.150795
$73$	−5.35784	−0.627087	−0.313544	−	0.949574i	$-0.601516\pi$
$73$	−5.35784	−0.627087	−0.313544	+	0.949574i	$0.601516\pi$
$74$	−2.44610	−0.284354
$75$	5.79331	0.668953
$76$	−27.2624	−3.12722
$77$	−2.55721	−0.291421
$78$	−10.8320	−1.22648
$79$	2.37682	0.267413	0.133707	−	0.991021i	$-0.457312\pi$
$79$	2.37682	0.267413	0.133707	+	0.991021i	$0.457312\pi$
$80$	5.22358	0.584014
$81$	−9.72164	−1.08018
$82$	−4.81822	−0.532083
$83$	−14.3917	−1.57970	−0.789849	−	0.613301i	$-0.789841\pi$
$83$	−14.3917	−1.57970	−0.789849	+	0.613301i	$0.789841\pi$
$84$	30.0429	3.27795
$85$	10.0090	1.08563
$86$	8.67873	0.935851
$87$	5.58806	0.599103
$88$	2.97184	0.316799
$89$	−2.09022	−0.221563	−0.110781	−	0.993845i	$-0.535335\pi$
$89$	−2.09022	−0.221563	−0.110781	+	0.993845i	$0.535335\pi$
$90$	0.863885	0.0910615
$91$	−10.2331	−1.07272
$92$	−31.1218	−3.24467
$93$	7.62885	0.791075
$94$	3.31900	0.342328
$95$	−9.16486	−0.940295
$96$	0.291903	0.0297923
$97$	−5.77977	−0.586847	−0.293423	−	0.955983i	$-0.594795\pi$
$97$	−5.77977	−0.586847	−0.293423	+	0.955983i	$0.594795\pi$
$98$	25.5091	2.57680
$99$	0.161548	0.0162362
$100$	−12.7739	−1.27739
$101$	−4.04191	−0.402185	−0.201093	−	0.979572i	$-0.564449\pi$
$101$	−4.04191	−0.402185	−0.201093	+	0.979572i	$0.564449\pi$
$102$	−33.0299	−3.27045
$103$	2.21723	0.218470	0.109235	−	0.994016i	$-0.465160\pi$
$103$	2.21723	0.218470	0.109235	+	0.994016i	$0.465160\pi$
$104$	11.8923	1.16614
$105$	10.0996	0.985618
$106$	−20.4111	−1.98250
$107$	5.15764	0.498607	0.249304	−	0.968425i	$-0.419798\pi$
$107$	5.15764	0.498607	0.249304	+	0.968425i	$0.419798\pi$
$108$	19.6912	1.89478
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	2.00645	0.191307
$111$	1.80658	0.171473
$112$	−16.2847	−1.53876
$113$	16.9465	1.59419	0.797096	−	0.603853i	$-0.206369\pi$
$113$	16.9465	1.59419	0.797096	+	0.603853i	$0.206369\pi$
$114$	30.2441	2.83262
$115$	−10.4623	−0.975611
$116$	−12.3214	−1.14401
$117$	0.646460	0.0597653
$118$	−4.68135	−0.430953
$119$	−31.2036	−2.86043
$120$	−11.7372	−1.07145
$121$	−10.6248	−0.965890
$122$	8.60299	0.778878
$123$	3.55852	0.320861
$124$	−16.8212	−1.51059
$125$	−10.9898	−0.982957
$126$	−2.69320	−0.239929
$127$	−2.68867	−0.238581	−0.119290	−	0.992859i	$-0.538062\pi$
$127$	−2.68867	−0.238581	−0.119290	+	0.992859i	$0.538062\pi$
$128$	−19.7270	−1.74364
$129$	−6.40972	−0.564344
$130$	8.02913	0.704201
$131$	−13.5543	−1.18424	−0.592121	−	0.805849i	$-0.701709\pi$
$131$	−13.5543	−1.18424	−0.592121	+	0.805849i	$0.701709\pi$
$132$	−4.40808	−0.383675
$133$	28.5718	2.47749
$134$	10.8454	0.936902
$135$	6.61961	0.569725
$136$	36.2630	3.10953
$137$	−11.5652	−0.988081	−0.494041	−	0.869439i	$-0.664481\pi$
$137$	−11.5652	−0.988081	−0.494041	+	0.869439i	$0.664481\pi$
$138$	34.5256	2.93901
$139$	0.0116364	0.000986986 0	0.000493493	−	1.00000i	$-0.499843\pi$
$139$	0.0116364	0.000986986 0	0.000493493		1.00000i	$0.499843\pi$
$140$	−22.2691	−1.88208
$141$	−2.45126	−0.206433
$142$	−24.6914	−2.07206
$143$	1.50146	0.125558
$144$	1.02876	0.0857304
$145$	−4.14210	−0.343982
$146$	−13.1058	−1.08464
$147$	−18.8398	−1.55388
$148$	−3.98342	−0.327435
$149$	22.1706	1.81628	0.908142	−	0.418663i	$-0.137501\pi$
$149$	22.1706	1.81628	0.908142	+	0.418663i	$0.137501\pi$
$150$	14.1710	1.15706
$151$	−8.05237	−0.655293	−0.327646	−	0.944800i	$-0.606255\pi$
$151$	−8.05237	−0.655293	−0.327646	+	0.944800i	$0.606255\pi$
$152$	−33.2046	−2.69325
$153$	1.97124	0.159366
$154$	−6.25519	−0.504058
$155$	−5.65482	−0.454206
$156$	−17.6397	−1.41230
$157$	−20.2601	−1.61693	−0.808465	−	0.588545i	$-0.799701\pi$
$157$	−20.2601	−1.61693	−0.808465	+	0.588545i	$0.799701\pi$
$158$	5.81395	0.462533
$159$	15.0747	1.19550
$160$	−0.216371	−0.0171056
$161$	32.6166	2.57055
$162$	−23.7801	−1.86834
$163$	−14.3993	−1.12784	−0.563920	−	0.825829i	$-0.690707\pi$
$163$	−14.3993	−1.12784	−0.563920	+	0.825829i	$0.690707\pi$
$164$	−7.84635	−0.612697
$165$	−1.48187	−0.115364
$166$	−35.2037	−2.73233
$167$	16.7655	1.29736	0.648679	−	0.761063i	$-0.275322\pi$
$167$	16.7655	1.29736	0.648679	+	0.761063i	$0.275322\pi$
$168$	36.5911	2.82306
$169$	−6.99166	−0.537820
$170$	24.4831	1.87777
$171$	−1.80499	−0.138031
$172$	14.1331	1.07764
$173$	5.72084	0.434947	0.217474	−	0.976066i	$-0.430218\pi$
$173$	5.72084	0.434947	0.217474	+	0.976066i	$0.430218\pi$
$174$	13.6690	1.03624
$175$	13.3875	1.01200
$176$	2.38940	0.180108
$177$	3.45743	0.259877
$178$	−5.11289	−0.383228
$179$	9.91899	0.741380	0.370690	−	0.928757i	$-0.379121\pi$
$179$	9.91899	0.741380	0.370690	+	0.928757i	$0.379121\pi$
$180$	1.40682	0.104858
$181$	12.9823	0.964969	0.482484	−	0.875905i	$-0.339735\pi$
$181$	12.9823	0.964969	0.482484	+	0.875905i	$0.339735\pi$
$182$	−25.0312	−1.85543
$183$	−6.35378	−0.469685
$184$	−37.9051	−2.79440
$185$	−1.33911	−0.0984534
$186$	18.6610	1.36829
$187$	4.57839	0.334805
$188$	5.40490	0.394193
$189$	−20.6369	−1.50112
$190$	−22.4182	−1.62639
$191$	20.7791	1.50352	0.751762	−	0.659435i	$-0.229204\pi$
$191$	20.7791	1.50352	0.751762	+	0.659435i	$0.229204\pi$
$192$	14.8082	1.06869
$193$	18.7307	1.34827	0.674134	−	0.738609i	$-0.264517\pi$
$193$	18.7307	1.34827	0.674134	+	0.738609i	$0.264517\pi$
$194$	−14.1379	−1.01504
$195$	−5.92995	−0.424653
$196$	41.5409	2.96720
$197$	10.0956	0.719284	0.359642	−	0.933090i	$-0.382899\pi$
$197$	10.0956	0.719284	0.359642	+	0.933090i	$0.382899\pi$
$198$	0.395163	0.0280830
$199$	−10.5950	−0.751060	−0.375530	−	0.926810i	$-0.622539\pi$
$199$	−10.5950	−0.751060	−0.375530	+	0.926810i	$0.622539\pi$
$200$	−15.5582	−1.10013
$201$	−8.00994	−0.564977
$202$	−9.88693	−0.695642
$203$	12.9132	0.906327
$204$	−53.7884	−3.76594
$205$	−2.63772	−0.184226
$206$	5.42357	0.377878
$207$	−2.06050	−0.143215
$208$	9.56156	0.662975
$209$	−4.19224	−0.289983
$210$	24.7046	1.70478
$211$	−11.5143	−0.792676	−0.396338	−	0.918105i	$-0.629719\pi$
$211$	−11.5143	−0.792676	−0.396338	+	0.918105i	$0.629719\pi$
$212$	−33.2390	−2.28286
$213$	18.2360	1.24951
$214$	12.6161	0.862419
$215$	4.75114	0.324025
$216$	23.9831	1.63184
$217$	17.6292	1.19674
$218$	−2.44610	−0.165671
$219$	9.67936	0.654071
$220$	3.26745	0.220292
$221$	18.3211	1.23241
$222$	4.41908	0.296589
$223$	−9.92779	−0.664814	−0.332407	−	0.943136i	$-0.607861\pi$
$223$	−9.92779	−0.664814	−0.332407	+	0.943136i	$0.607861\pi$
$224$	0.674546	0.0450700
$225$	−0.845734	−0.0563823
$226$	41.4528	2.75740
$227$	29.3932	1.95090	0.975448	−	0.220231i	$-0.0706811\pi$
$227$	29.3932	1.95090	0.975448	+	0.220231i	$0.0706811\pi$
$228$	49.2518	3.26178
$229$	2.23538	0.147718	0.0738590	−	0.997269i	$-0.476469\pi$
$229$	2.23538	0.147718	0.0738590	+	0.997269i	$0.476469\pi$
$230$	−25.5918	−1.68747
$231$	4.61980	0.303961
$232$	−15.0069	−0.985254
$233$	28.3189	1.85524	0.927618	−	0.373531i	$-0.121853\pi$
$233$	28.3189	1.85524	0.927618	+	0.373531i	$0.121853\pi$
$234$	1.58131	0.103373
$235$	1.81697	0.118526
$236$	−7.62346	−0.496245
$237$	−4.29392	−0.278920
$238$	−76.3272	−4.94756
$239$	−1.59945	−0.103460	−0.0517299	−	0.998661i	$-0.516473\pi$
$239$	−1.59945	−0.103460	−0.0517299	+	0.998661i	$0.516473\pi$
$240$	−9.43682	−0.609144
$241$	6.35498	0.409360	0.204680	−	0.978829i	$-0.434385\pi$
$241$	6.35498	0.409360	0.204680	+	0.978829i	$0.434385\pi$
$242$	−25.9893	−1.67066
$243$	2.73307	0.175327
$244$	14.0098	0.896883
$245$	13.9649	0.892182
$246$	8.70450	0.554979
$247$	−16.7759	−1.06743
$248$	−20.4876	−1.30096
$249$	25.9998	1.64767
$250$	−26.8822	−1.70018
$251$	−2.31711	−0.146255	−0.0731273	−	0.997323i	$-0.523298\pi$
$251$	−2.31711	−0.146255	−0.0731273	+	0.997323i	$0.523298\pi$
$252$	−4.38581	−0.276280
$253$	−4.78570	−0.300874
$254$	−6.57676	−0.412663
$255$	−18.0821	−1.13235
$256$	−31.8608	−1.99130
$257$	7.14336	0.445590	0.222795	−	0.974865i	$-0.428482\pi$
$257$	7.14336	0.445590	0.222795	+	0.974865i	$0.428482\pi$
$258$	−15.6788	−0.976121
$259$	4.17474	0.259406
$260$	13.0752	0.810892
$261$	−0.815771	−0.0504950
$262$	−33.1552	−2.04833
$263$	6.94540	0.428272	0.214136	−	0.976804i	$-0.431306\pi$
$263$	6.94540	0.428272	0.214136	+	0.976804i	$0.431306\pi$
$264$	−5.36887	−0.330431
$265$	−11.1740	−0.686413
$266$	69.8897	4.28521
$267$	3.77615	0.231097
$268$	17.6615	1.07885
$269$	9.79250	0.597059	0.298530	−	0.954400i	$-0.403504\pi$
$269$	9.79250	0.597059	0.298530	+	0.954400i	$0.403504\pi$
$270$	16.1922	0.985429
$271$	−9.69305	−0.588811	−0.294405	−	0.955681i	$-0.595122\pi$
$271$	−9.69305	−0.588811	−0.294405	+	0.955681i	$0.595122\pi$
$272$	29.1559	1.76784
$273$	18.4869	1.11888
$274$	−28.2897	−1.70904
$275$	−1.96429	−0.118451
$276$	56.2240	3.38429
$277$	−12.1845	−0.732096	−0.366048	−	0.930596i	$-0.619289\pi$
$277$	−12.1845	−0.732096	−0.366048	+	0.930596i	$0.619289\pi$
$278$	0.0284638	0.00170715
$279$	−1.11370	−0.0666752
$280$	−27.1228	−1.62090
$281$	−6.10319	−0.364086	−0.182043	−	0.983291i	$-0.558271\pi$
$281$	−6.10319	−0.364086	−0.182043	+	0.983291i	$0.558271\pi$
$282$	−5.99603	−0.357059
$283$	−14.3797	−0.854786	−0.427393	−	0.904066i	$-0.640568\pi$
$283$	−14.3797	−0.854786	−0.427393	+	0.904066i	$0.640568\pi$
$284$	−40.2093	−2.38599
$285$	16.5571	0.980755
$286$	3.67273	0.217173
$287$	8.22321	0.485401
$288$	−0.0426134	−0.00251102
$289$	38.8664	2.28626
$290$	−10.1320	−0.594971
$291$	10.4416	0.612099
$292$	−21.3425	−1.24897
$293$	−33.4377	−1.95345	−0.976726	−	0.214489i	$-0.931191\pi$
$293$	−33.4377	−1.95345	−0.976726	+	0.214489i	$0.931191\pi$
$294$	−46.0842	−2.68768
$295$	−2.56279	−0.149211
$296$	−4.85164	−0.281996
$297$	3.02798	0.175701
$298$	54.2315	3.14155
$299$	−19.1508	−1.10752
$300$	23.0772	1.33236
$301$	−14.8119	−0.853744
$302$	−19.6969	−1.13343
$303$	7.30204	0.419491
$304$	−26.6969	−1.53117
$305$	4.70968	0.269676
$306$	4.82186	0.275648
$307$	−9.90932	−0.565555	−0.282777	−	0.959186i	$-0.591256\pi$
$307$	−9.90932	−0.565555	−0.282777	+	0.959186i	$0.591256\pi$
$308$	−10.1864	−0.580426
$309$	−4.00560	−0.227871
$310$	−13.8323	−0.785620
$311$	−8.80217	−0.499125	−0.249563	−	0.968359i	$-0.580287\pi$
$311$	−8.80217	−0.499125	−0.249563	+	0.968359i	$0.580287\pi$
$312$	−21.4844	−1.21631
$313$	24.2161	1.36878	0.684388	−	0.729118i	$-0.260070\pi$
$313$	24.2161	1.36878	0.684388	+	0.729118i	$0.260070\pi$
$314$	−49.5582	−2.79673
$315$	−1.47438	−0.0830722
$316$	9.46787	0.532609
$317$	6.56845	0.368921	0.184460	−	0.982840i	$-0.440946\pi$
$317$	6.56845	0.368921	0.184460	+	0.982840i	$0.440946\pi$
$318$	36.8743	2.06781
$319$	−1.89470	−0.106083
$320$	−10.9764	−0.613601
$321$	−9.31768	−0.520062
$322$	79.7835	4.44616
$323$	−51.1546	−2.84632
$324$	−38.7254	−2.15141
$325$	−7.86043	−0.436018
$326$	−35.2222	−1.95077
$327$	1.80658	0.0999041
$328$	−9.55654	−0.527672
$329$	−5.66450	−0.312294
$330$	−3.62481	−0.199539
$331$	13.5879	0.746858	0.373429	−	0.927659i	$-0.378182\pi$
$331$	13.5879	0.746858	0.373429	+	0.927659i	$0.378182\pi$
$332$	−57.3283	−3.14630
$333$	−0.263733	−0.0144525
$334$	41.0102	2.24398
$335$	5.93729	0.324389
$336$	29.4197	1.60498
$337$	−20.8660	−1.13664	−0.568321	−	0.822807i	$-0.692407\pi$
$337$	−20.8660	−1.13664	−0.568321	+	0.822807i	$0.692407\pi$
$338$	−17.1023	−0.930244
$339$	−30.6152	−1.66279
$340$	39.8702	2.16226
$341$	−2.58666	−0.140075
$342$	−4.41518	−0.238746
$343$	−14.3129	−0.772823
$344$	17.2135	0.928092
$345$	18.9009	1.01759
$346$	13.9938	0.752309
$347$	3.37993	0.181444	0.0907222	−	0.995876i	$-0.471082\pi$
$347$	3.37993	0.181444	0.0907222	+	0.995876i	$0.471082\pi$
$348$	22.2596	1.19324
$349$	−19.5431	−1.04612	−0.523060	−	0.852296i	$-0.675210\pi$
$349$	−19.5431	−1.04612	−0.523060	+	0.852296i	$0.675210\pi$
$350$	32.7471	1.75041
$351$	12.1169	0.646754
$352$	−0.0989735	−0.00527530
$353$	−29.0837	−1.54797	−0.773986	−	0.633203i	$-0.781740\pi$
$353$	−29.0837	−1.54797	−0.773986	+	0.633203i	$0.781740\pi$
$354$	8.45724	0.449497
$355$	−13.5172	−0.717420
$356$	−8.32622	−0.441289
$357$	56.3718	2.98351
$358$	24.2629	1.28233
$359$	28.0570	1.48079	0.740396	−	0.672171i	$-0.234638\pi$
$359$	28.0570	1.48079	0.740396	+	0.672171i	$0.234638\pi$
$360$	1.71345	0.0903065
$361$	27.8401	1.46527
$362$	31.7561	1.66906
$363$	19.1945	1.00745
$364$	−40.7626	−2.13654
$365$	−7.17474	−0.375543
$366$	−15.5420	−0.812393
$367$	24.2984	1.26837	0.634183	−	0.773183i	$-0.281337\pi$
$367$	24.2984	1.26837	0.634183	+	0.773183i	$0.281337\pi$
$368$	−30.4762	−1.58868
$369$	−0.519489	−0.0270435
$370$	−3.27560	−0.170291
$371$	34.8354	1.80856
$372$	30.3889	1.57559
$373$	22.0973	1.14416	0.572078	−	0.820199i	$-0.306137\pi$
$373$	22.0973	1.14416	0.572078	+	0.820199i	$0.306137\pi$
$374$	11.1992	0.579097
$375$	19.8539	1.02525
$376$	6.58296	0.339490
$377$	−7.58195	−0.390490
$378$	−50.4801	−2.59641
$379$	21.3235	1.09532	0.547658	−	0.836702i	$-0.315519\pi$
$379$	21.3235	1.09532	0.547658	+	0.836702i	$0.315519\pi$
$380$	−36.5075	−1.87279
$381$	4.85730	0.248847
$382$	50.8278	2.60058
$383$	−4.24228	−0.216770	−0.108385	−	0.994109i	$-0.534568\pi$
$383$	−4.24228	−0.216770	−0.108385	+	0.994109i	$0.534568\pi$
$384$	35.6385	1.81867
$385$	−3.42439	−0.174523
$386$	45.8173	2.33204
$387$	0.935720	0.0475653
$388$	−23.0232	−1.16883
$389$	−13.1112	−0.664765	−0.332382	−	0.943145i	$-0.607852\pi$
$389$	−13.1112	−0.664765	−0.332382	+	0.943145i	$0.607852\pi$
$390$	−14.5053	−0.734503
$391$	−58.3962	−2.95322
$392$	50.5951	2.55544
$393$	24.4869	1.23520
$394$	24.6949	1.24411
$395$	3.18283	0.160145
$396$	0.643513	0.0323377
$397$	2.57927	0.129450	0.0647249	−	0.997903i	$-0.479383\pi$
$397$	2.57927	0.129450	0.0647249	+	0.997903i	$0.479383\pi$
$398$	−25.9165	−1.29908
$399$	−51.6173	−2.58410
$400$	−12.5089	−0.625447
$401$	34.8985	1.74275	0.871373	−	0.490621i	$-0.163230\pi$
$401$	34.8985	1.74275	0.871373	+	0.490621i	$0.163230\pi$
$402$	−19.5931	−0.977216
$403$	−10.3509	−0.515616
$404$	−16.1006	−0.801036
$405$	−13.0184	−0.646888
$406$	31.5869	1.56763
$407$	−0.612543	−0.0303626
$408$	−65.5121	−3.24333
$409$	18.7501	0.927131	0.463565	−	0.886063i	$-0.346570\pi$
$409$	18.7501	0.927131	0.463565	+	0.886063i	$0.346570\pi$
$410$	−6.45213	−0.318648
$411$	20.8935	1.03060
$412$	8.83215	0.435129
$413$	7.98962	0.393143
$414$	−5.04020	−0.247713
$415$	−19.2721	−0.946032
$416$	−0.396058	−0.0194184
$417$	−0.0210221	−0.00102946
$418$	−10.2546	−0.501571
$419$	9.75134	0.476384	0.238192	−	0.971218i	$-0.423445\pi$
$419$	9.75134	0.476384	0.238192	+	0.971218i	$0.423445\pi$
$420$	40.2309	1.96306
$421$	2.17943	0.106219	0.0531095	−	0.998589i	$-0.483087\pi$
$421$	2.17943	0.106219	0.0531095	+	0.998589i	$0.483087\pi$
$422$	−28.1651	−1.37106
$423$	0.357847	0.0173991
$424$	−40.4837	−1.96606
$425$	−23.9687	−1.16265
$426$	44.6070	2.16122
$427$	−14.6826	−0.710543
$428$	20.5450	0.993081
$429$	−2.71251	−0.130961
$430$	11.6218	0.560452
$431$	23.3967	1.12698	0.563491	−	0.826122i	$-0.309458\pi$
$431$	23.3967	1.12698	0.563491	+	0.826122i	$0.309458\pi$
$432$	19.2827	0.927738
$433$	−3.79452	−0.182353	−0.0911764	−	0.995835i	$-0.529063\pi$
$433$	−3.79452	−0.182353	−0.0911764	+	0.995835i	$0.529063\pi$
$434$	43.1227	2.06996
$435$	7.48303	0.358784
$436$	−3.98342	−0.190771
$437$	53.4709	2.55786
$438$	23.6767	1.13132
$439$	−27.8340	−1.32844	−0.664222	−	0.747535i	$-0.731237\pi$
$439$	−27.8340	−1.32844	−0.664222	+	0.747535i	$0.731237\pi$
$440$	3.97963	0.189721
$441$	2.75033	0.130968
$442$	44.8154	2.13165
$443$	−13.6949	−0.650665	−0.325332	−	0.945600i	$-0.605476\pi$
$443$	−13.6949	−0.650665	−0.325332	+	0.945600i	$0.605476\pi$
$444$	7.19636	0.341524
$445$	−2.79904	−0.132687
$446$	−24.2844	−1.14990
$447$	−40.0529	−1.89444
$448$	34.2195	1.61672
$449$	13.7459	0.648707	0.324354	−	0.945936i	$-0.394853\pi$
$449$	13.7459	0.648707	0.324354	+	0.945936i	$0.394853\pi$
$450$	−2.06875	−0.0975219
$451$	−1.20656	−0.0568147
$452$	67.5049	3.17517
$453$	14.5473	0.683490
$454$	71.8988	3.37438
$455$	−13.7032	−0.642418
$456$	59.9867	2.80914
$457$	−38.5346	−1.80257	−0.901286	−	0.433225i	$-0.857375\pi$
$457$	−38.5346	−1.80257	−0.901286	+	0.433225i	$0.857375\pi$
$458$	5.46796	0.255501
$459$	36.9480	1.72459
$460$	−41.6756	−1.94313
$461$	−21.2497	−0.989696	−0.494848	−	0.868980i	$-0.664776\pi$
$461$	−21.2497	−0.989696	−0.494848	+	0.868980i	$0.664776\pi$
$462$	11.3005	0.525747
$463$	−12.8583	−0.597576	−0.298788	−	0.954319i	$-0.596582\pi$
$463$	−12.8583	−0.597576	−0.298788	+	0.954319i	$0.596582\pi$
$464$	−12.0658	−0.560139
$465$	10.2159	0.473750
$466$	69.2710	3.20892
$467$	28.2193	1.30583	0.652917	−	0.757430i	$-0.273545\pi$
$467$	28.2193	1.30583	0.652917	+	0.757430i	$0.273545\pi$
$468$	2.57512	0.119035
$469$	−18.5098	−0.854702
$470$	4.44451	0.205010
$471$	36.6014	1.68651
$472$	−9.28507	−0.427380
$473$	2.17329	0.0999281
$474$	−10.5034	−0.482435
$475$	21.9472	1.00700
$476$	−124.297	−5.69714
$477$	−2.20068	−0.100762
$478$	−3.91241	−0.178950
$479$	7.23890	0.330754	0.165377	−	0.986230i	$-0.447116\pi$
$479$	7.23890	0.330754	0.165377	+	0.986230i	$0.447116\pi$
$480$	0.390891	0.0178417
$481$	−2.45119	−0.111765
$482$	15.5449	0.708052
$483$	−58.9244	−2.68116
$484$	−42.3230	−1.92377
$485$	−7.73976	−0.351444
$486$	6.68538	0.303255
$487$	3.94333	0.178689	0.0893447	−	0.996001i	$-0.471523\pi$
$487$	3.94333	0.178689	0.0893447	+	0.996001i	$0.471523\pi$
$488$	17.0633	0.772420
$489$	26.0135	1.17637
$490$	34.1595	1.54317
$491$	17.3093	0.781160	0.390580	−	0.920569i	$-0.372275\pi$
$491$	17.3093	0.781160	0.390580	+	0.920569i	$0.372275\pi$
$492$	14.1751	0.639061
$493$	−23.1195	−1.04125
$494$	−41.0356	−1.84628
$495$	0.216331	0.00972334
$496$	−16.4723	−0.739627
$497$	42.1406	1.89026
$498$	63.5983	2.84991
$499$	−19.8744	−0.889703	−0.444851	−	0.895604i	$-0.646743\pi$
$499$	−19.8744	−0.889703	−0.444851	+	0.895604i	$0.646743\pi$
$500$	−43.7769	−1.95776
$501$	−30.2883	−1.35318
$502$	−5.66789	−0.252970
$503$	−8.95719	−0.399381	−0.199691	−	0.979859i	$-0.563994\pi$
$503$	−8.95719	−0.399381	−0.199691	+	0.979859i	$0.563994\pi$
$504$	−5.34174	−0.237940
$505$	−5.41257	−0.240856
$506$	−11.7063	−0.520409
$507$	12.6310	0.560962
$508$	−10.7101	−0.475184
$509$	20.7281	0.918757	0.459379	−	0.888240i	$-0.348072\pi$
$509$	20.7281	0.918757	0.459379	+	0.888240i	$0.348072\pi$
$510$	−44.2307	−1.95857
$511$	22.3676	0.989483
$512$	−38.4807	−1.70062
$513$	−33.8318	−1.49371
$514$	17.4734	0.770718
$515$	2.96912	0.130835
$516$	−25.5326	−1.12401
$517$	0.831130	0.0365531
$518$	10.2118	0.448683
$519$	−10.3352	−0.453663
$520$	15.9251	0.698363
$521$	−2.73828	−0.119966	−0.0599830	−	0.998199i	$-0.519105\pi$
$521$	−2.73828	−0.119966	−0.0599830	+	0.998199i	$0.519105\pi$
$522$	−1.99546	−0.0873389
$523$	5.93211	0.259393	0.129697	−	0.991554i	$-0.458600\pi$
$523$	5.93211	0.259393	0.129697	+	0.991554i	$0.458600\pi$
$524$	−53.9924	−2.35867
$525$	−24.1855	−1.05554
$526$	16.9892	0.740763
$527$	−31.5629	−1.37490
$528$	−4.31664	−0.187858
$529$	38.0404	1.65393
$530$	−27.3327	−1.18726
$531$	−0.504732	−0.0219035
$532$	113.814	4.93445
$533$	−4.82824	−0.209134
$534$	9.23686	0.399718
$535$	6.90665	0.298600
$536$	21.5110	0.929134
$537$	−17.9195	−0.773282
$538$	23.9535	1.03271
$539$	6.38788	0.275145
$540$	26.3687	1.13473
$541$	−20.1065	−0.864448	−0.432224	−	0.901766i	$-0.642271\pi$
$541$	−20.1065	−0.864448	−0.432224	+	0.901766i	$0.642271\pi$
$542$	−23.7102	−1.01844
$543$	−23.4536	−1.00649
$544$	−1.20770	−0.0517795
$545$	−1.33911	−0.0573612
$546$	45.2208	1.93527
$547$	30.1825	1.29051	0.645255	−	0.763968i	$-0.276751\pi$
$547$	30.1825	1.29051	0.645255	+	0.763968i	$0.276751\pi$
$548$	−46.0690	−1.96797
$549$	0.927555	0.0395871
$550$	−4.80486	−0.204880
$551$	21.1696	0.901855
$552$	68.4786	2.91464
$553$	−9.92260	−0.421952
$554$	−29.8045	−1.26627
$555$	2.41921	0.102690
$556$	0.0463526	0.00196579
$557$	−17.2221	−0.729722	−0.364861	−	0.931062i	$-0.618883\pi$
$557$	−17.2221	−0.729722	−0.364861	+	0.931062i	$0.618883\pi$
$558$	−2.72422	−0.115325
$559$	8.69678	0.367835
$560$	−21.8071	−0.921517
$561$	−8.27122	−0.349211
$562$	−14.9290	−0.629743
$563$	−39.8295	−1.67861	−0.839307	−	0.543657i	$-0.817039\pi$
$563$	−39.8295	−1.67861	−0.839307	+	0.543657i	$0.817039\pi$
$564$	−9.76439	−0.411155
$565$	22.6932	0.954712
$566$	−35.1743	−1.47849
$567$	40.5853	1.70442
$568$	−48.9734	−2.05488
$569$	0.0684185	0.00286825	0.00143413	−	0.999999i	$-0.499544\pi$
$569$	0.0684185	0.00286825	0.00143413	+	0.999999i	$0.499544\pi$
$570$	40.5002	1.69637
$571$	−13.9562	−0.584047	−0.292023	−	0.956411i	$-0.594329\pi$
$571$	−13.9562	−0.584047	−0.292023	+	0.956411i	$0.594329\pi$
$572$	5.98094	0.250076
$573$	−37.5391	−1.56822
$574$	20.1148	0.839576
$575$	25.0541	1.04483
$576$	−2.16177	−0.0900736
$577$	13.7855	0.573897	0.286949	−	0.957946i	$-0.407359\pi$
$577$	13.7855	0.573897	0.286949	+	0.957946i	$0.407359\pi$
$578$	95.0713	3.95444
$579$	−33.8386	−1.40628
$580$	−16.4997	−0.685113
$581$	60.0818	2.49261
$582$	25.5413	1.05872
$583$	−5.11127	−0.211687
$584$	−25.9943	−1.07565
$585$	0.865682	0.0357916
$586$	−81.7921	−3.37880
$587$	11.9315	0.492468	0.246234	−	0.969210i	$-0.420807\pi$
$587$	11.9315	0.492468	0.246234	+	0.969210i	$0.420807\pi$
$588$	−75.0469	−3.09488
$589$	28.9009	1.19084
$590$	−6.26885	−0.258084
$591$	−18.2386	−0.750235
$592$	−3.90078	−0.160321
$593$	27.5900	1.13299	0.566493	−	0.824067i	$-0.308300\pi$
$593$	27.5900	1.13299	0.566493	+	0.824067i	$0.308300\pi$
$594$	7.40674	0.303902
$595$	−41.7851	−1.71302
$596$	88.3146	3.61751
$597$	19.1407	0.783378
$598$	−46.8447	−1.91562
$599$	21.9317	0.896106	0.448053	−	0.894007i	$-0.352118\pi$
$599$	21.9317	0.896106	0.448053	+	0.894007i	$0.352118\pi$
$600$	28.1071	1.14747
$601$	−35.6798	−1.45541	−0.727704	−	0.685891i	$-0.759413\pi$
$601$	−35.6798	−1.45541	−0.727704	+	0.685891i	$0.759413\pi$
$602$	−36.2314	−1.47668
$603$	1.16933	0.0476187
$604$	−32.0760	−1.30515
$605$	−14.2278	−0.578441
$606$	17.8615	0.725575
$607$	−25.9983	−1.05524	−0.527619	−	0.849481i	$-0.676915\pi$
$607$	−25.9983	−1.05524	−0.527619	+	0.849481i	$0.676915\pi$
$608$	1.10584	0.0448476
$609$	−23.3287	−0.945326
$610$	11.5204	0.466446
$611$	3.32590	0.134552
$612$	7.85228	0.317410
$613$	−33.7273	−1.36223	−0.681115	−	0.732176i	$-0.738505\pi$
$613$	−33.7273	−1.36223	−0.681115	+	0.732176i	$0.738505\pi$
$614$	−24.2392	−0.978215
$615$	4.76525	0.192154
$616$	−12.4067	−0.499879
$617$	26.2707	1.05762	0.528810	−	0.848740i	$-0.322639\pi$
$617$	26.2707	1.05762	0.528810	+	0.848740i	$0.322639\pi$
$618$	−9.79812	−0.394138
$619$	5.96593	0.239791	0.119895	−	0.992787i	$-0.461744\pi$
$619$	5.96593	0.239791	0.119895	+	0.992787i	$0.461744\pi$
$620$	−22.5255	−0.904646
$621$	−38.6211	−1.54981
$622$	−21.5310	−0.863315
$623$	8.72613	0.349605
$624$	−17.2737	−0.691502
$625$	1.31734	0.0526937
$626$	59.2351	2.36751
$627$	7.57361	0.302461
$628$	−80.7043	−3.22045
$629$	−7.47439	−0.298023
$630$	−3.60650	−0.143686
$631$	−4.24233	−0.168885	−0.0844423	−	0.996428i	$-0.526911\pi$
$631$	−4.24233	−0.168885	−0.0844423	+	0.996428i	$0.526911\pi$
$632$	11.5315	0.458698
$633$	20.8015	0.826784
$634$	16.0671	0.638106
$635$	−3.60043	−0.142879
$636$	60.0489	2.38109
$637$	25.5621	1.01281
$638$	−4.63463	−0.183487
$639$	−2.66217	−0.105314
$640$	−26.4167	−1.04421
$641$	−40.5235	−1.60058	−0.800290	−	0.599613i	$-0.795321\pi$
$641$	−40.5235	−1.60058	−0.800290	+	0.599613i	$0.795321\pi$
$642$	−22.7920	−0.899529
$643$	41.2101	1.62517	0.812583	−	0.582845i	$-0.198061\pi$
$643$	41.2101	1.62517	0.812583	+	0.582845i	$0.198061\pi$
$644$	129.925	5.11978
$645$	−8.58332	−0.337968
$646$	−125.129	−4.92315
$647$	−42.7367	−1.68015	−0.840076	−	0.542469i	$-0.817490\pi$
$647$	−42.7367	−1.68015	−0.840076	+	0.542469i	$0.817490\pi$
$648$	−47.1659	−1.85285
$649$	−1.17229	−0.0460162
$650$	−19.2274	−0.754161
$651$	−31.8485	−1.24824
$652$	−57.3584	−2.24633
$653$	−41.0743	−1.60736	−0.803680	−	0.595061i	$-0.797128\pi$
$653$	−41.0743	−1.60736	−0.803680	+	0.595061i	$0.797128\pi$
$654$	4.41908	0.172800
$655$	−18.1507	−0.709206
$656$	−7.68358	−0.299993
$657$	−1.41304	−0.0551279
$658$	−13.8559	−0.540161
$659$	−33.3395	−1.29872	−0.649362	−	0.760479i	$-0.724964\pi$
$659$	−33.3395	−1.29872	−0.649362	+	0.760479i	$0.724964\pi$
$660$	−5.90292	−0.229771
$661$	15.5442	0.604598	0.302299	−	0.953213i	$-0.402246\pi$
$661$	15.5442	0.604598	0.302299	+	0.953213i	$0.402246\pi$
$662$	33.2374	1.29181
$663$	−33.0986	−1.28544
$664$	−69.8236	−2.70968
$665$	38.2609	1.48369
$666$	−0.645118	−0.0249978
$667$	24.1664	0.935728
$668$	66.7842	2.58396
$669$	17.9354	0.693421
$670$	14.5232	0.561081
$671$	2.15433	0.0831669
$672$	−1.21862	−0.0470093
$673$	−1.03649	−0.0399536	−0.0199768	−	0.999800i	$-0.506359\pi$
$673$	−1.03649	−0.0399536	−0.0199768	+	0.999800i	$0.506359\pi$
$674$	−51.0403	−1.96600
$675$	−15.8520	−0.610145
$676$	−27.8507	−1.07118
$677$	−34.5332	−1.32722	−0.663610	−	0.748079i	$-0.730977\pi$
$677$	−34.5332	−1.32722	−0.663610	+	0.748079i	$0.730977\pi$
$678$	−74.8879	−2.87605
$679$	24.1290	0.925988
$680$	48.5603	1.86220
$681$	−53.1012	−2.03484
$682$	−6.32723	−0.242282
$683$	23.2550	0.889828	0.444914	−	0.895573i	$-0.353234\pi$
$683$	23.2550	0.889828	0.444914	+	0.895573i	$0.353234\pi$
$684$	−7.19001	−0.274917
$685$	−15.4871	−0.591731
$686$	−35.0108	−1.33672
$687$	−4.03839	−0.154074
$688$	13.8399	0.527641
$689$	−20.4536	−0.779218
$690$	46.2336	1.76008
$691$	5.34749	0.203428	0.101714	−	0.994814i	$-0.467567\pi$
$691$	5.34749	0.203428	0.101714	+	0.994814i	$0.467567\pi$
$692$	22.7885	0.866288
$693$	−0.674421	−0.0256191
$694$	8.26767	0.313836
$695$	0.0155824	0.000591075 0
$696$	27.1113	1.02765
$697$	−14.7227	−0.557662
$698$	−47.8045	−1.80943
$699$	−51.1604	−1.93507
$700$	53.3279	2.01560
$701$	18.7435	0.707933	0.353967	−	0.935258i	$-0.384833\pi$
$701$	18.7435	0.707933	0.353967	+	0.935258i	$0.384833\pi$
$702$	29.6393	1.11866
$703$	6.84398	0.258126
$704$	−5.02089	−0.189232
$705$	−3.28251	−0.123627
$706$	−71.1418	−2.67746
$707$	16.8739	0.634609
$708$	13.7724	0.517598
$709$	−32.8463	−1.23357	−0.616785	−	0.787132i	$-0.711565\pi$
$709$	−32.8463	−1.23357	−0.616785	+	0.787132i	$0.711565\pi$
$710$	−33.0645	−1.24089
$711$	0.626846	0.0235086
$712$	−10.1410	−0.380050
$713$	32.9922	1.23557
$714$	137.891	5.16045
$715$	2.01062	0.0751930
$716$	39.5115	1.47661
$717$	2.88953	0.107912
$718$	68.6303	2.56126
$719$	6.23042	0.232356	0.116178	−	0.993228i	$-0.462936\pi$
$719$	6.23042	0.232356	0.116178	+	0.993228i	$0.462936\pi$
$720$	1.37763	0.0513413
$721$	−9.25635	−0.344725
$722$	68.0998	2.53441
$723$	−11.4808	−0.426975
$724$	51.7140	1.92194
$725$	9.91911	0.368387
$726$	46.9518	1.74255
$727$	−51.6898	−1.91707	−0.958533	−	0.284980i	$-0.908013\pi$
$727$	−51.6898	−1.91707	−0.958533	+	0.284980i	$0.908013\pi$
$728$	−49.6473	−1.84005
$729$	24.2274	0.897312
$730$	−17.5501	−0.649560
$731$	26.5190	0.980840
$732$	−25.3098	−0.935475
$733$	53.6854	1.98292	0.991458	−	0.130429i	$-0.0416356\pi$
$733$	53.6854	1.98292	0.991458	+	0.130429i	$0.0416356\pi$
$734$	59.4363	2.19383
$735$	−25.2286	−0.930572
$736$	1.26238	0.0465320
$737$	2.71587	0.100040
$738$	−1.27072	−0.0467760
$739$	2.76233	0.101614	0.0508071	−	0.998708i	$-0.483821\pi$
$739$	2.76233	0.101614	0.0508071	+	0.998708i	$0.483821\pi$
$740$	−5.33424	−0.196091
$741$	30.3070	1.11336
$742$	85.2110	3.12819
$743$	−5.91035	−0.216830	−0.108415	−	0.994106i	$-0.534577\pi$
$743$	−5.91035	−0.216830	−0.108415	+	0.994106i	$0.534577\pi$
$744$	37.0125	1.35694
$745$	29.6889	1.08772
$746$	54.0523	1.97900
$747$	−3.79558	−0.138873
$748$	18.2376	0.666833
$749$	−21.5318	−0.786754
$750$	48.5648	1.77334
$751$	−1.23506	−0.0450680	−0.0225340	−	0.999746i	$-0.507173\pi$
$751$	−1.23506	−0.0450680	−0.0225340	+	0.999746i	$0.507173\pi$
$752$	5.29278	0.193008
$753$	4.18604	0.152548
$754$	−18.5462	−0.675413
$755$	−10.7830	−0.392435
$756$	−82.2055	−2.98979
$757$	−27.7336	−1.00800	−0.503998	−	0.863705i	$-0.668138\pi$
$757$	−27.7336	−1.00800	−0.503998	+	0.863705i	$0.668138\pi$
$758$	52.1596	1.89452
$759$	8.64576	0.313821
$760$	−44.4646	−1.61290
$761$	25.5091	0.924703	0.462352	−	0.886697i	$-0.347006\pi$
$761$	25.5091	0.924703	0.462352	+	0.886697i	$0.347006\pi$
$762$	11.8815	0.430420
$763$	4.17474	0.151136
$764$	82.7719	2.99458
$765$	2.63971	0.0954391
$766$	−10.3770	−0.374938
$767$	−4.69109	−0.169385
$768$	57.5591	2.07698
$769$	−13.4603	−0.485391	−0.242695	−	0.970103i	$-0.578032\pi$
$769$	−13.4603	−0.485391	−0.242695	+	0.970103i	$0.578032\pi$
$770$	−8.37640	−0.301865
$771$	−12.9050	−0.464764
$772$	74.6123	2.68536
$773$	−25.8672	−0.930377	−0.465189	−	0.885212i	$-0.654014\pi$
$773$	−25.8672	−0.930377	−0.465189	+	0.885212i	$0.654014\pi$
$774$	2.28887	0.0822717
$775$	13.5416	0.486430
$776$	−28.0414	−1.00663
$777$	−7.54200	−0.270568
$778$	−32.0714	−1.14981
$779$	13.4810	0.483006
$780$	−23.6215	−0.845785
$781$	−6.18312	−0.221250
$782$	−142.843	−5.10806
$783$	−15.2904	−0.546435
$784$	40.6791	1.45282
$785$	−27.1305	−0.968328
$786$	59.8975	2.13647
$787$	−34.6146	−1.23388	−0.616938	−	0.787012i	$-0.711627\pi$
$787$	−34.6146	−1.23388	−0.616938	+	0.787012i	$0.711627\pi$
$788$	40.2151	1.43260
$789$	−12.5474	−0.446700
$790$	7.78552	0.276996
$791$	−70.7472	−2.51548
$792$	0.783773	0.0278502
$793$	8.62089	0.306137
$794$	6.30916	0.223904
$795$	20.1867	0.715949
$796$	−42.2044	−1.49589
$797$	43.6997	1.54792	0.773961	−	0.633233i	$-0.218272\pi$
$797$	43.6997	1.54792	0.773961	+	0.633233i	$0.218272\pi$
$798$	−126.261	−4.46960
$799$	10.1416	0.358785
$800$	0.518145	0.0183192
$801$	−0.551261	−0.0194778
$802$	85.3652	3.01435
$803$	−3.28191	−0.115816
$804$	−31.9069	−1.12527
$805$	43.6772	1.53942
$806$	−25.3194	−0.891839
$807$	−17.6909	−0.622751
$808$	−19.6099	−0.689874
$809$	−52.7616	−1.85500	−0.927500	−	0.373824i	$-0.878046\pi$
$809$	−52.7616	−1.85500	−0.927500	+	0.373824i	$0.878046\pi$
$810$	−31.8443	−1.11889
$811$	−3.02752	−0.106311	−0.0531553	−	0.998586i	$-0.516928\pi$
$811$	−3.02752	−0.106311	−0.0531553	+	0.998586i	$0.516928\pi$
$812$	51.4386	1.80514
$813$	17.5113	0.614147
$814$	−1.49834	−0.0525169
$815$	−19.2823	−0.675428
$816$	−52.6725	−1.84391
$817$	−24.2823	−0.849531
$818$	45.8646	1.60362
$819$	−2.69880	−0.0943038
$820$	−10.5071	−0.366925
$821$	0.502349	0.0175321	0.00876606	−	0.999962i	$-0.497210\pi$
$821$	0.502349	0.0175321	0.00876606	+	0.999962i	$0.497210\pi$
$822$	51.1075	1.78258
$823$	8.01340	0.279330	0.139665	−	0.990199i	$-0.455398\pi$
$823$	8.01340	0.279330	0.139665	+	0.990199i	$0.455398\pi$
$824$	10.7572	0.374745
$825$	3.54865	0.123548
$826$	19.5434	0.680002
$827$	−4.00780	−0.139365	−0.0696824	−	0.997569i	$-0.522199\pi$
$827$	−4.00780	−0.139365	−0.0696824	+	0.997569i	$0.522199\pi$
$828$	−8.20785	−0.285242
$829$	34.4246	1.19561	0.597807	−	0.801640i	$-0.296039\pi$
$829$	34.4246	1.19561	0.597807	+	0.801640i	$0.296039\pi$
$830$	−47.1416	−1.63631
$831$	22.0123	0.763598
$832$	−20.0919	−0.696562
$833$	77.9463	2.70068
$834$	−0.0514222	−0.00178060
$835$	22.4509	0.776947
$836$	−16.6994	−0.577562
$837$	−20.8746	−0.721531
$838$	23.8528	0.823980
$839$	38.1691	1.31774	0.658872	−	0.752255i	$-0.271034\pi$
$839$	38.1691	1.31774	0.658872	+	0.752255i	$0.271034\pi$
$840$	48.9996	1.69065
$841$	−19.4323	−0.670080
$842$	5.33111	0.183722
$843$	11.0259	0.379753
$844$	−45.8662	−1.57878
$845$	−9.36262	−0.322084
$846$	0.875329	0.0300944
$847$	44.3557	1.52408
$848$	−32.5494	−1.11775
$849$	25.9781	0.891568
$850$	−58.6299	−2.01099
$851$	7.81284	0.267821
$852$	72.6414	2.48865
$853$	0.853508	0.0292235	0.0146118	−	0.999893i	$-0.495349\pi$
$853$	0.853508	0.0292235	0.0146118	+	0.999893i	$0.495349\pi$
$854$	−35.9152	−1.22899
$855$	−2.41708	−0.0826623
$856$	25.0230	0.855269
$857$	−27.9044	−0.953197	−0.476598	−	0.879121i	$-0.658130\pi$
$857$	−27.9044	−0.953197	−0.476598	+	0.879121i	$0.658130\pi$
$858$	−6.63508	−0.226518
$859$	4.99476	0.170419	0.0852095	−	0.996363i	$-0.472844\pi$
$859$	4.99476	0.170419	0.0852095	+	0.996363i	$0.472844\pi$
$860$	18.9258	0.645364
$861$	−14.8559	−0.506287
$862$	57.2308	1.94929
$863$	9.23352	0.314313	0.157156	−	0.987574i	$-0.449767\pi$
$863$	9.23352	0.314313	0.157156	+	0.987574i	$0.449767\pi$
$864$	−0.798726	−0.0271732
$865$	7.66084	0.260476
$866$	−9.28178	−0.315408
$867$	−70.2154	−2.38464
$868$	70.2243	2.38357
$869$	1.45591	0.0493882
$870$	18.3043	0.620573
$871$	10.8680	0.368248
$872$	−4.85164	−0.164297
$873$	−1.52432	−0.0515903
$874$	130.795	4.42422
$875$	45.8795	1.55101
$876$	38.5569	1.30272
$877$	13.7236	0.463412	0.231706	−	0.972786i	$-0.425569\pi$
$877$	13.7236	0.463412	0.231706	+	0.972786i	$0.425569\pi$
$878$	−68.0848	−2.29775
$879$	60.4079	2.03751
$880$	3.19967	0.107861
$881$	−29.0341	−0.978183	−0.489092	−	0.872232i	$-0.662672\pi$
$881$	−29.0341	−0.978183	−0.489092	+	0.872232i	$0.662672\pi$
$882$	6.72758	0.226530
$883$	44.7996	1.50762	0.753812	−	0.657090i	$-0.228213\pi$
$883$	44.7996	1.50762	0.753812	+	0.657090i	$0.228213\pi$
$884$	72.9808	2.45461
$885$	4.62989	0.155632
$886$	−33.4992	−1.12543
$887$	−45.3833	−1.52382	−0.761912	−	0.647681i	$-0.775739\pi$
$887$	−45.3833	−1.52382	−0.761912	+	0.647681i	$0.775739\pi$
$888$	8.76488	0.294130
$889$	11.2245	0.376458
$890$	−6.84674	−0.229503
$891$	−5.95493	−0.199498
$892$	−39.5466	−1.32412
$893$	−9.28627	−0.310753
$894$	−97.9735	−3.27673
$895$	13.2826	0.443990
$896$	82.3553	2.75130
$897$	34.5974	1.15517
$898$	33.6238	1.12204
$899$	13.0619	0.435638
$900$	−3.36891	−0.112297
$901$	−62.3688	−2.07781
$902$	−2.95137	−0.0982698
$903$	26.7589	0.890480
$904$	82.2183	2.73454
$905$	17.3848	0.577890
$906$	35.5841	1.18220
$907$	38.2967	1.27162	0.635810	−	0.771845i	$-0.280666\pi$
$907$	38.2967	1.27162	0.635810	+	0.771845i	$0.280666\pi$
$908$	117.085	3.88562
$909$	−1.06599	−0.0353565
$910$	−33.5195	−1.11116
$911$	51.7376	1.71414	0.857071	−	0.515198i	$-0.172282\pi$
$911$	51.7376	1.71414	0.857071	+	0.515198i	$0.172282\pi$
$912$	48.2300	1.59706
$913$	−8.81556	−0.291753
$914$	−94.2595	−3.11783
$915$	−8.50842	−0.281280
$916$	8.90444	0.294211
$917$	56.5856	1.86862
$918$	90.3787	2.98294
$919$	−32.7621	−1.08072	−0.540360	−	0.841434i	$-0.681712\pi$
$919$	−32.7621	−1.08072	−0.540360	+	0.841434i	$0.681712\pi$
$920$	−50.7591	−1.67348
$921$	17.9020	0.589890
$922$	−51.9789	−1.71183
$923$	−24.7428	−0.814418
$924$	18.4026	0.605401
$925$	3.20678	0.105438
$926$	−31.4527	−1.03360
$927$	0.584757	0.0192059
$928$	0.499788	0.0164063
$929$	9.60337	0.315076	0.157538	−	0.987513i	$-0.449644\pi$
$929$	9.60337	0.315076	0.157538	+	0.987513i	$0.449644\pi$
$930$	24.9891	0.819425
$931$	−71.3721	−2.33913
$932$	112.806	3.69509
$933$	15.9018	0.520602
$934$	69.0273	2.25864
$935$	6.13097	0.200504
$936$	3.13639	0.102516
$937$	35.7119	1.16666	0.583328	−	0.812236i	$-0.301750\pi$
$937$	35.7119	1.16666	0.583328	+	0.812236i	$0.301750\pi$
$938$	−45.2768	−1.47834
$939$	−43.7484	−1.42767
$940$	7.23777	0.236070
$941$	−23.7039	−0.772726	−0.386363	−	0.922347i	$-0.626269\pi$
$941$	−23.7039	−0.772726	−0.386363	+	0.922347i	$0.626269\pi$
$942$	89.5309	2.91707
$943$	15.3894	0.501147
$944$	−7.46531	−0.242975
$945$	−27.6352	−0.898972
$946$	5.31610	0.172841
$947$	50.8866	1.65359	0.826796	−	0.562502i	$-0.190161\pi$
$947$	50.8866	1.65359	0.826796	+	0.562502i	$0.190161\pi$
$948$	−17.1045	−0.555527
$949$	−13.1331	−0.426318
$950$	53.6850	1.74177
$951$	−11.8664	−0.384795
$952$	−151.389	−4.90654
$953$	−33.5992	−1.08838	−0.544192	−	0.838961i	$-0.683164\pi$
$953$	−33.5992	−1.08838	−0.544192	+	0.838961i	$0.683164\pi$
$954$	−5.38308	−0.174284
$955$	27.8256	0.900414
$956$	−6.37127	−0.206062
$957$	3.42293	0.110648
$958$	17.7071	0.572090
$959$	48.2817	1.55910
$960$	19.8298	0.640004
$961$	−13.1678	−0.424769
$962$	−5.99586	−0.193314
$963$	1.36024	0.0438331
$964$	25.3145	0.815326
$965$	25.0825	0.807436
$966$	−144.135	−4.63748
$967$	40.9164	1.31578	0.657891	−	0.753113i	$-0.271449\pi$
$967$	40.9164	1.31578	0.657891	+	0.753113i	$0.271449\pi$
$968$	−51.5477	−1.65681
$969$	92.4149	2.96879
$970$	−18.9322	−0.607878
$971$	−52.9467	−1.69914	−0.849569	−	0.527477i	$-0.823138\pi$
$971$	−52.9467	−1.69914	−0.849569	+	0.527477i	$0.823138\pi$
$972$	10.8870	0.349200
$973$	−0.0485789	−0.00155737
$974$	9.64580	0.309071
$975$	14.2005	0.454780
$976$	13.7191	0.439138
$977$	−30.4169	−0.973124	−0.486562	−	0.873646i	$-0.661749\pi$
$977$	−30.4169	−0.973124	−0.486562	+	0.873646i	$0.661749\pi$
$978$	63.6317	2.03472
$979$	−1.28035	−0.0409202
$980$	55.6279	1.77697
$981$	−0.263733	−0.00842035
$982$	42.3404	1.35114
$983$	27.9762	0.892302	0.446151	−	0.894958i	$-0.352794\pi$
$983$	27.9762	0.892302	0.446151	+	0.894958i	$0.352794\pi$
$984$	17.2647	0.550377
$985$	13.5192	0.430757
$986$	−56.5528	−1.80101
$987$	10.2334	0.325732
$988$	−66.8255	−2.12600
$989$	−27.7198	−0.881439
$990$	0.529167	0.0168180
$991$	33.7883	1.07332	0.536661	−	0.843798i	$-0.319685\pi$
$991$	33.7883	1.07332	0.536661	+	0.843798i	$0.319685\pi$
$992$	0.682314	0.0216635
$993$	−24.5476	−0.778996
$994$	103.080	3.26950
$995$	−14.1879	−0.449787
$996$	103.568	3.28168
$997$	−53.2334	−1.68592	−0.842960	−	0.537976i	$-0.819189\pi$
$997$	−53.2334	−1.68592	−0.842960	+	0.537976i	$0.819189\pi$
$998$	−48.6149	−1.53888
$999$	−4.94329	−0.156399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.75	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.75	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+2.44610 q^{2} -1.80658 q^{3} +3.98342 q^{4} +1.33911 q^{5} -4.41908 q^{6} -4.17474 q^{7} +4.85164 q^{8} +0.263733 q^{9} +O(q^{10})\)	\(q+2.44610 q^{2} -1.80658 q^{3} +3.98342 q^{4} +1.33911 q^{5} -4.41908 q^{6} -4.17474 q^{7} +4.85164 q^{8} +0.263733 q^{9} +3.27560 q^{10} +0.612543 q^{11} -7.19636 q^{12} +2.45119 q^{13} -10.2118 q^{14} -2.41921 q^{15} +3.90078 q^{16} +7.47439 q^{17} +0.645118 q^{18} -6.84398 q^{19} +5.33424 q^{20} +7.54200 q^{21} +1.49834 q^{22} -7.81284 q^{23} -8.76488 q^{24} -3.20678 q^{25} +5.99586 q^{26} +4.94329 q^{27} -16.6297 q^{28} -3.09317 q^{29} -5.91764 q^{30} -4.22281 q^{31} -0.161578 q^{32} -1.10661 q^{33} +18.2831 q^{34} -5.59044 q^{35} +1.05056 q^{36} -1.00000 q^{37} -16.7411 q^{38} -4.42827 q^{39} +6.49689 q^{40} -1.96975 q^{41} +18.4485 q^{42} +3.54798 q^{43} +2.44002 q^{44} +0.353168 q^{45} -19.1110 q^{46} +1.35685 q^{47} -7.04707 q^{48} +10.4284 q^{49} -7.84411 q^{50} -13.5031 q^{51} +9.76412 q^{52} -8.34433 q^{53} +12.0918 q^{54} +0.820264 q^{55} -20.2543 q^{56} +12.3642 q^{57} -7.56621 q^{58} -1.91380 q^{59} -9.63673 q^{60} +3.51702 q^{61} -10.3294 q^{62} -1.10102 q^{63} -8.19680 q^{64} +3.28242 q^{65} -2.70688 q^{66} +4.43376 q^{67} +29.7736 q^{68} +14.1145 q^{69} -13.6748 q^{70} -10.0942 q^{71} +1.27954 q^{72} -5.35784 q^{73} -2.44610 q^{74} +5.79331 q^{75} -27.2624 q^{76} -2.55721 q^{77} -10.8320 q^{78} +2.37682 q^{79} +5.22358 q^{80} -9.72164 q^{81} -4.81822 q^{82} -14.3917 q^{83} +30.0429 q^{84} +10.0090 q^{85} +8.67873 q^{86} +5.58806 q^{87} +2.97184 q^{88} -2.09022 q^{89} +0.863885 q^{90} -10.2331 q^{91} -31.1218 q^{92} +7.62885 q^{93} +3.31900 q^{94} -9.16486 q^{95} +0.291903 q^{96} -5.77977 q^{97} +25.5091 q^{98} +0.161548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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