LMFDB - Embedded newform 4033.2.a.d.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.32027 q^{2} +1.35424 q^{3} +3.38367 q^{4} +2.79503 q^{5} -3.14221 q^{6} +4.55894 q^{7} -3.21050 q^{8} -1.16603 q^{9} +O(q^{10})$	\(q-2.32027 q^{2} +1.35424 q^{3} +3.38367 q^{4} +2.79503 q^{5} -3.14221 q^{6} +4.55894 q^{7} -3.21050 q^{8} -1.16603 q^{9} -6.48525 q^{10} -4.50751 q^{11} +4.58231 q^{12} -0.542954 q^{13} -10.5780 q^{14} +3.78515 q^{15} +0.681903 q^{16} -5.71836 q^{17} +2.70551 q^{18} -1.76426 q^{19} +9.45749 q^{20} +6.17391 q^{21} +10.4587 q^{22} -3.18066 q^{23} -4.34780 q^{24} +2.81222 q^{25} +1.25980 q^{26} -5.64181 q^{27} +15.4260 q^{28} -7.61112 q^{29} -8.78260 q^{30} -1.83148 q^{31} +4.83881 q^{32} -6.10426 q^{33} +13.2682 q^{34} +12.7424 q^{35} -3.94546 q^{36} -1.00000 q^{37} +4.09356 q^{38} -0.735291 q^{39} -8.97347 q^{40} -9.61850 q^{41} -14.3252 q^{42} +3.29074 q^{43} -15.2520 q^{44} -3.25909 q^{45} +7.38000 q^{46} +7.88287 q^{47} +0.923462 q^{48} +13.7839 q^{49} -6.52512 q^{50} -7.74405 q^{51} -1.83718 q^{52} -3.17321 q^{53} +13.0906 q^{54} -12.5987 q^{55} -14.6365 q^{56} -2.38923 q^{57} +17.6599 q^{58} +1.31889 q^{59} +12.8077 q^{60} +2.66774 q^{61} +4.24954 q^{62} -5.31585 q^{63} -12.5912 q^{64} -1.51758 q^{65} +14.1636 q^{66} -3.57012 q^{67} -19.3491 q^{68} -4.30738 q^{69} -29.5658 q^{70} -8.88574 q^{71} +3.74354 q^{72} +4.02855 q^{73} +2.32027 q^{74} +3.80842 q^{75} -5.96967 q^{76} -20.5495 q^{77} +1.70608 q^{78} -17.5481 q^{79} +1.90594 q^{80} -4.14229 q^{81} +22.3176 q^{82} +8.15290 q^{83} +20.8905 q^{84} -15.9830 q^{85} -7.63541 q^{86} -10.3073 q^{87} +14.4714 q^{88} -13.3217 q^{89} +7.56198 q^{90} -2.47529 q^{91} -10.7623 q^{92} -2.48027 q^{93} -18.2904 q^{94} -4.93116 q^{95} +6.55292 q^{96} +0.623333 q^{97} -31.9825 q^{98} +5.25589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.32027	−1.64068	−0.820341	−	0.571875i	$-0.806216\pi$
$2$	−2.32027	−1.64068	−0.820341	+	0.571875i	$0.806216\pi$
$3$	1.35424	0.781872	0.390936	−	0.920418i	$-0.372151\pi$
$3$	1.35424	0.781872	0.390936	+	0.920418i	$0.372151\pi$
$4$	3.38367	1.69184
$5$	2.79503	1.24998	0.624989	−	0.780634i	$-0.285104\pi$
$5$	2.79503	1.24998	0.624989	+	0.780634i	$0.285104\pi$
$6$	−3.14221	−1.28280
$7$	4.55894	1.72312	0.861558	−	0.507659i	$-0.169489\pi$
$7$	4.55894	1.72312	0.861558	+	0.507659i	$0.169489\pi$
$8$	−3.21050	−1.13508
$9$	−1.16603	−0.388676
$10$	−6.48525	−2.05082
$11$	−4.50751	−1.35907	−0.679533	−	0.733645i	$-0.737818\pi$
$11$	−4.50751	−1.35907	−0.679533	+	0.733645i	$0.737818\pi$
$12$	4.58231	1.32280
$13$	−0.542954	−0.150588	−0.0752942	−	0.997161i	$-0.523990\pi$
$13$	−0.542954	−0.150588	−0.0752942	+	0.997161i	$0.523990\pi$
$14$	−10.5780	−2.82709
$15$	3.78515	0.977323
$16$	0.681903	0.170476
$17$	−5.71836	−1.38691	−0.693453	−	0.720502i	$-0.743912\pi$
$17$	−5.71836	−1.38691	−0.693453	+	0.720502i	$0.743912\pi$
$18$	2.70551	0.637694
$19$	−1.76426	−0.404748	−0.202374	−	0.979308i	$-0.564866\pi$
$19$	−1.76426	−0.404748	−0.202374	+	0.979308i	$0.564866\pi$
$20$	9.45749	2.11476
$21$	6.17391	1.34726
$22$	10.4587	2.22980
$23$	−3.18066	−0.663213	−0.331607	−	0.943418i	$-0.607591\pi$
$23$	−3.18066	−0.663213	−0.331607	+	0.943418i	$0.607591\pi$
$24$	−4.34780	−0.887491
$25$	2.81222	0.562444
$26$	1.25980	0.247068
$27$	−5.64181	−1.08577
$28$	15.4260	2.91523
$29$	−7.61112	−1.41335	−0.706675	−	0.707538i	$-0.749806\pi$
$29$	−7.61112	−1.41335	−0.706675	+	0.707538i	$0.749806\pi$
$30$	−8.78260	−1.60348
$31$	−1.83148	−0.328944	−0.164472	−	0.986382i	$-0.552592\pi$
$31$	−1.83148	−0.328944	−0.164472	+	0.986382i	$0.552592\pi$
$32$	4.83881	0.855388
$33$	−6.10426	−1.06262
$34$	13.2682	2.27547
$35$	12.7424	2.15386
$36$	−3.94546	−0.657577
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	4.09356	0.664063
$39$	−0.735291	−0.117741
$40$	−8.97347	−1.41883
$41$	−9.61850	−1.50216	−0.751079	−	0.660213i	$-0.770466\pi$
$41$	−9.61850	−1.50216	−0.751079	+	0.660213i	$0.770466\pi$
$42$	−14.3252	−2.21042
$43$	3.29074	0.501833	0.250916	−	0.968009i	$-0.419268\pi$
$43$	3.29074	0.501833	0.250916	+	0.968009i	$0.419268\pi$
$44$	−15.2520	−2.29932
$45$	−3.25909	−0.485836
$46$	7.38000	1.08812
$47$	7.88287	1.14984	0.574918	−	0.818211i	$-0.305034\pi$
$47$	7.88287	1.14984	0.574918	+	0.818211i	$0.305034\pi$
$48$	0.923462	0.133290
$49$	13.7839	1.96913
$50$	−6.52512	−0.922791
$51$	−7.74405	−1.08438
$52$	−1.83718	−0.254771
$53$	−3.17321	−0.435874	−0.217937	−	0.975963i	$-0.569933\pi$
$53$	−3.17321	−0.435874	−0.217937	+	0.975963i	$0.569933\pi$
$54$	13.0906	1.78140
$55$	−12.5987	−1.69880
$56$	−14.6365	−1.95588
$57$	−2.38923	−0.316461
$58$	17.6599	2.31886
$59$	1.31889	0.171705	0.0858526	−	0.996308i	$-0.472639\pi$
$59$	1.31889	0.171705	0.0858526	+	0.996308i	$0.472639\pi$
$60$	12.8077	1.65347
$61$	2.66774	0.341569	0.170784	−	0.985308i	$-0.445370\pi$
$61$	2.66774	0.341569	0.170784	+	0.985308i	$0.445370\pi$
$62$	4.24954	0.539692
$63$	−5.31585	−0.669734
$64$	−12.5912	−1.57390
$65$	−1.51758	−0.188232
$66$	14.1636	1.74341
$67$	−3.57012	−0.436160	−0.218080	−	0.975931i	$-0.569979\pi$
$67$	−3.57012	−0.436160	−0.218080	+	0.975931i	$0.569979\pi$
$68$	−19.3491	−2.34642
$69$	−4.30738	−0.518548
$70$	−29.5658	−3.53379
$71$	−8.88574	−1.05454	−0.527272	−	0.849697i	$-0.676785\pi$
$71$	−8.88574	−1.05454	−0.527272	+	0.849697i	$0.676785\pi$
$72$	3.74354	0.441180
$73$	4.02855	0.471506	0.235753	−	0.971813i	$-0.424244\pi$
$73$	4.02855	0.471506	0.235753	+	0.971813i	$0.424244\pi$
$74$	2.32027	0.269726
$75$	3.80842	0.439759
$76$	−5.96967	−0.684768
$77$	−20.5495	−2.34183
$78$	1.70608	0.193175
$79$	−17.5481	−1.97431	−0.987155	−	0.159763i	$-0.948927\pi$
$79$	−17.5481	−1.97431	−0.987155	+	0.159763i	$0.948927\pi$
$80$	1.90594	0.213091
$81$	−4.14229	−0.460255
$82$	22.3176	2.46456
$83$	8.15290	0.894897	0.447448	−	0.894310i	$-0.352333\pi$
$83$	8.15290	0.894897	0.447448	+	0.894310i	$0.352333\pi$
$84$	20.8905	2.27934
$85$	−15.9830	−1.73360
$86$	−7.63541	−0.823348
$87$	−10.3073	−1.10506
$88$	14.4714	1.54266
$89$	−13.3217	−1.41210	−0.706051	−	0.708161i	$-0.749525\pi$
$89$	−13.3217	−1.41210	−0.706051	+	0.708161i	$0.749525\pi$
$90$	7.56198	0.797103
$91$	−2.47529	−0.259481
$92$	−10.7623	−1.12205
$93$	−2.48027	−0.257192
$94$	−18.2904	−1.88651
$95$	−4.93116	−0.505926
$96$	6.55292	0.668804
$97$	0.623333	0.0632898	0.0316449	−	0.999499i	$-0.489925\pi$
$97$	0.623333	0.0632898	0.0316449	+	0.999499i	$0.489925\pi$
$98$	−31.9825	−3.23072
$99$	5.25589	0.528236
$100$	9.51563	0.951563
$101$	−12.5441	−1.24818	−0.624090	−	0.781352i	$-0.714530\pi$
$101$	−12.5441	−1.24818	−0.624090	+	0.781352i	$0.714530\pi$
$102$	17.9683	1.77913
$103$	−4.75597	−0.468620	−0.234310	−	0.972162i	$-0.575283\pi$
$103$	−4.75597	−0.468620	−0.234310	+	0.972162i	$0.575283\pi$
$104$	1.74316	0.170931
$105$	17.2563	1.68404
$106$	7.36273	0.715131
$107$	4.38886	0.424287	0.212143	−	0.977239i	$-0.431956\pi$
$107$	4.38886	0.424287	0.212143	+	0.977239i	$0.431956\pi$
$108$	−19.0901	−1.83694
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	29.2323	2.78719
$111$	−1.35424	−0.128539
$112$	3.10875	0.293750
$113$	10.6375	1.00069	0.500345	−	0.865826i	$-0.333207\pi$
$113$	10.6375	1.00069	0.500345	+	0.865826i	$0.333207\pi$
$114$	5.54367	0.519212
$115$	−8.89005	−0.829002
$116$	−25.7536	−2.39116
$117$	0.633100	0.0585301
$118$	−3.06019	−0.281714
$119$	−26.0697	−2.38980
$120$	−12.1523	−1.10934
$121$	9.31766	0.847060
$122$	−6.18988	−0.560405
$123$	−13.0258	−1.17449
$124$	−6.19714	−0.556519
$125$	−6.11493	−0.546936
$126$	12.3342	1.09882
$127$	3.28276	0.291298	0.145649	−	0.989336i	$-0.453473\pi$
$127$	3.28276	0.291298	0.145649	+	0.989336i	$0.453473\pi$
$128$	19.5373	1.72687
$129$	4.45646	0.392369
$130$	3.52119	0.308829
$131$	5.19340	0.453749	0.226875	−	0.973924i	$-0.427149\pi$
$131$	5.19340	0.453749	0.226875	+	0.973924i	$0.427149\pi$
$132$	−20.6548	−1.79777
$133$	−8.04313	−0.697428
$134$	8.28367	0.715600
$135$	−15.7691	−1.35718
$136$	18.3588	1.57426
$137$	−2.60966	−0.222959	−0.111479	−	0.993767i	$-0.535559\pi$
$137$	−2.60966	−0.222959	−0.111479	+	0.993767i	$0.535559\pi$
$138$	9.99431	0.850772
$139$	15.8532	1.34465	0.672324	−	0.740257i	$-0.265296\pi$
$139$	15.8532	1.34465	0.672324	+	0.740257i	$0.265296\pi$
$140$	43.1161	3.64397
$141$	10.6753	0.899024
$142$	20.6174	1.73017
$143$	2.44737	0.204660
$144$	−0.795118	−0.0662598
$145$	−21.2733	−1.76666
$146$	−9.34734	−0.773592
$147$	18.6668	1.53961
$148$	−3.38367	−0.278136
$149$	−7.20544	−0.590293	−0.295146	−	0.955452i	$-0.595368\pi$
$149$	−7.20544	−0.590293	−0.295146	+	0.955452i	$0.595368\pi$
$150$	−8.83659	−0.721505
$151$	16.9066	1.37584	0.687920	−	0.725787i	$-0.258524\pi$
$151$	16.9066	1.37584	0.687920	+	0.725787i	$0.258524\pi$
$152$	5.66415	0.459423
$153$	6.66777	0.539057
$154$	47.6804	3.84220
$155$	−5.11905	−0.411172
$156$	−2.48799	−0.199198
$157$	12.4778	0.995835	0.497918	−	0.867224i	$-0.334098\pi$
$157$	12.4778	0.995835	0.497918	+	0.867224i	$0.334098\pi$
$158$	40.7163	3.23922
$159$	−4.29730	−0.340798
$160$	13.5246	1.06922
$161$	−14.5004	−1.14279
$162$	9.61126	0.755132
$163$	−17.6605	−1.38328	−0.691638	−	0.722244i	$-0.743111\pi$
$163$	−17.6605	−1.38328	−0.691638	+	0.722244i	$0.743111\pi$
$164$	−32.5459	−2.54141
$165$	−17.0616	−1.32825
$166$	−18.9170	−1.46824
$167$	18.3737	1.42180	0.710901	−	0.703292i	$-0.248287\pi$
$167$	18.3737	1.42180	0.710901	+	0.703292i	$0.248287\pi$
$168$	−19.8214	−1.52925
$169$	−12.7052	−0.977323
$170$	37.0850	2.84429
$171$	2.05717	0.157316
$172$	11.1348	0.849019
$173$	5.75232	0.437341	0.218671	−	0.975799i	$-0.429828\pi$
$173$	5.75232	0.437341	0.218671	+	0.975799i	$0.429828\pi$
$174$	23.9158	1.81305
$175$	12.8207	0.969156
$176$	−3.07369	−0.231688
$177$	1.78610	0.134251
$178$	30.9101	2.31681
$179$	−20.1054	−1.50275	−0.751375	−	0.659876i	$-0.770609\pi$
$179$	−20.1054	−1.50275	−0.751375	+	0.659876i	$0.770609\pi$
$180$	−11.0277	−0.821956
$181$	−7.62640	−0.566866	−0.283433	−	0.958992i	$-0.591473\pi$
$181$	−7.62640	−0.566866	−0.283433	+	0.958992i	$0.591473\pi$
$182$	5.74336	0.425726
$183$	3.61276	0.267063
$184$	10.2115	0.752803
$185$	−2.79503	−0.205495
$186$	5.75491	0.421970
$187$	25.7756	1.88490
$188$	26.6731	1.94533
$189$	−25.7207	−1.87090
$190$	11.4416	0.830063
$191$	12.2848	0.888897	0.444449	−	0.895804i	$-0.353400\pi$
$191$	12.2848	0.888897	0.444449	+	0.895804i	$0.353400\pi$
$192$	−17.0515	−1.23059
$193$	10.4966	0.755558	0.377779	−	0.925896i	$-0.376688\pi$
$193$	10.4966	0.755558	0.377779	+	0.925896i	$0.376688\pi$
$194$	−1.44630	−0.103838
$195$	−2.05516	−0.147173
$196$	46.6403	3.33145
$197$	20.5025	1.46075	0.730373	−	0.683049i	$-0.239346\pi$
$197$	20.5025	1.46075	0.730373	+	0.683049i	$0.239346\pi$
$198$	−12.1951	−0.866668
$199$	19.8362	1.40615	0.703075	−	0.711116i	$-0.251810\pi$
$199$	19.8362	1.40615	0.703075	+	0.711116i	$0.251810\pi$
$200$	−9.02864	−0.638421
$201$	−4.83481	−0.341021
$202$	29.1057	2.04787
$203$	−34.6986	−2.43537
$204$	−26.2033	−1.83460
$205$	−26.8840	−1.87766
$206$	11.0352	0.768856
$207$	3.70874	0.257775
$208$	−0.370242	−0.0256717
$209$	7.95240	0.550079
$210$	−40.0393	−2.76297
$211$	−9.91613	−0.682654	−0.341327	−	0.939945i	$-0.610876\pi$
$211$	−9.91613	−0.682654	−0.341327	+	0.939945i	$0.610876\pi$
$212$	−10.7371	−0.737428
$213$	−12.0334	−0.824518
$214$	−10.1834	−0.696120
$215$	9.19772	0.627280
$216$	18.1131	1.23244
$217$	−8.34961	−0.566808
$218$	2.32027	0.157149
$219$	5.45563	0.368657
$220$	−42.6297	−2.87410
$221$	3.10481	0.208852
$222$	3.14221	0.210892
$223$	−4.75550	−0.318452	−0.159226	−	0.987242i	$-0.550900\pi$
$223$	−4.75550	−0.318452	−0.159226	+	0.987242i	$0.550900\pi$
$224$	22.0598	1.47393
$225$	−3.27913	−0.218608
$226$	−24.6819	−1.64181
$227$	−11.6726	−0.774740	−0.387370	−	0.921924i	$-0.626616\pi$
$227$	−11.6726	−0.774740	−0.387370	+	0.921924i	$0.626616\pi$
$228$	−8.08437	−0.535401
$229$	−2.28055	−0.150703	−0.0753516	−	0.997157i	$-0.524008\pi$
$229$	−2.28055	−0.150703	−0.0753516	+	0.997157i	$0.524008\pi$
$230$	20.6274	1.36013
$231$	−27.8290	−1.83101
$232$	24.4355	1.60427
$233$	−9.09780	−0.596017	−0.298008	−	0.954563i	$-0.596322\pi$
$233$	−9.09780	−0.596017	−0.298008	+	0.954563i	$0.596322\pi$
$234$	−1.46896	−0.0960292
$235$	22.0329	1.43727
$236$	4.46270	0.290497
$237$	−23.7643	−1.54366
$238$	60.4888	3.92090
$239$	−4.65691	−0.301231	−0.150615	−	0.988592i	$-0.548126\pi$
$239$	−4.65691	−0.301231	−0.150615	+	0.988592i	$0.548126\pi$
$240$	2.58111	0.166610
$241$	−22.8884	−1.47437	−0.737187	−	0.675689i	$-0.763846\pi$
$241$	−22.8884	−1.47437	−0.737187	+	0.675689i	$0.763846\pi$
$242$	−21.6195	−1.38976
$243$	11.3158	0.725907
$244$	9.02675	0.577878
$245$	38.5265	2.46137
$246$	30.2234	1.92697
$247$	0.957910	0.0609503
$248$	5.87998	0.373379
$249$	11.0410	0.699695
$250$	14.1883	0.897347
$251$	13.7361	0.867014	0.433507	−	0.901150i	$-0.357276\pi$
$251$	13.7361	0.867014	0.433507	+	0.901150i	$0.357276\pi$
$252$	−17.9871	−1.13308
$253$	14.3369	0.901351
$254$	−7.61690	−0.477927
$255$	−21.6449	−1.35545
$256$	−20.1497	−1.25936
$257$	12.3695	0.771590	0.385795	−	0.922585i	$-0.373927\pi$
$257$	12.3695	0.771590	0.385795	+	0.922585i	$0.373927\pi$
$258$	−10.3402	−0.643753
$259$	−4.55894	−0.283279
$260$	−5.13498	−0.318458
$261$	8.87478	0.549335
$262$	−12.0501	−0.744458
$263$	30.9483	1.90835	0.954177	−	0.299244i	$-0.0967345\pi$
$263$	30.9483	1.90835	0.954177	+	0.299244i	$0.0967345\pi$
$264$	19.5978	1.20616
$265$	−8.86924	−0.544833
$266$	18.6623	1.14426
$267$	−18.0409	−1.10408
$268$	−12.0801	−0.737912
$269$	5.77611	0.352176	0.176088	−	0.984374i	$-0.443656\pi$
$269$	5.77611	0.352176	0.176088	+	0.984374i	$0.443656\pi$
$270$	36.5885	2.22671
$271$	3.48402	0.211639	0.105819	−	0.994385i	$-0.466253\pi$
$271$	3.48402	0.211639	0.105819	+	0.994385i	$0.466253\pi$
$272$	−3.89937	−0.236434
$273$	−3.35215	−0.202881
$274$	6.05514	0.365804
$275$	−12.6761	−0.764398
$276$	−14.5748	−0.877299
$277$	15.6447	0.940000	0.470000	−	0.882666i	$-0.344254\pi$
$277$	15.6447	0.940000	0.470000	+	0.882666i	$0.344254\pi$
$278$	−36.7837	−2.20614
$279$	2.13556	0.127853
$280$	−40.9095	−2.44481
$281$	−0.0847937	−0.00505837	−0.00252918	−	0.999997i	$-0.500805\pi$
$281$	−0.0847937	−0.00505837	−0.00252918	+	0.999997i	$0.500805\pi$
$282$	−24.7697	−1.47501
$283$	20.0758	1.19338	0.596690	−	0.802472i	$-0.296482\pi$
$283$	20.0758	1.19338	0.596690	+	0.802472i	$0.296482\pi$
$284$	−30.0665	−1.78412
$285$	−6.67798	−0.395569
$286$	−5.67857	−0.335781
$287$	−43.8501	−2.58839
$288$	−5.64218	−0.332469
$289$	15.6997	0.923509
$290$	49.3600	2.89852
$291$	0.844143	0.0494845
$292$	13.6313	0.797712
$293$	5.53254	0.323215	0.161607	−	0.986855i	$-0.448332\pi$
$293$	5.53254	0.323215	0.161607	+	0.986855i	$0.448332\pi$
$294$	−43.3120	−2.52601
$295$	3.68635	0.214628
$296$	3.21050	0.186607
$297$	25.4305	1.47563
$298$	16.7186	0.968483
$299$	1.72695	0.0998722
$300$	12.8865	0.744001
$301$	15.0023	0.864716
$302$	−39.2280	−2.25732
$303$	−16.9877	−0.975917
$304$	−1.20305	−0.0689997
$305$	7.45641	0.426953
$306$	−15.4711	−0.884422
$307$	−9.62765	−0.549479	−0.274740	−	0.961519i	$-0.588592\pi$
$307$	−9.62765	−0.549479	−0.274740	+	0.961519i	$0.588592\pi$
$308$	−69.5327	−3.96199
$309$	−6.44074	−0.366401
$310$	11.8776	0.674603
$311$	−28.3753	−1.60901	−0.804507	−	0.593943i	$-0.797570\pi$
$311$	−28.3753	−1.60901	−0.804507	+	0.593943i	$0.797570\pi$
$312$	2.36066	0.133646
$313$	2.52731	0.142852	0.0714260	−	0.997446i	$-0.477245\pi$
$313$	2.52731	0.142852	0.0714260	+	0.997446i	$0.477245\pi$
$314$	−28.9519	−1.63385
$315$	−14.8580	−0.837152
$316$	−59.3769	−3.34021
$317$	10.9461	0.614792	0.307396	−	0.951582i	$-0.400542\pi$
$317$	10.9461	0.614792	0.307396	+	0.951582i	$0.400542\pi$
$318$	9.97091	0.559141
$319$	34.3072	1.92084
$320$	−35.1927	−1.96733
$321$	5.94358	0.331738
$322$	33.6450	1.87496
$323$	10.0887	0.561348
$324$	−14.0162	−0.778676
$325$	−1.52691	−0.0846975
$326$	40.9772	2.26952
$327$	−1.35424	−0.0748898
$328$	30.8802	1.70508
$329$	35.9375	1.98130
$330$	39.5877	2.17923
$331$	−6.37333	−0.350310	−0.175155	−	0.984541i	$-0.556043\pi$
$331$	−6.37333	−0.350310	−0.175155	+	0.984541i	$0.556043\pi$
$332$	27.5867	1.51402
$333$	1.16603	0.0638979
$334$	−42.6321	−2.33273
$335$	−9.97862	−0.545190
$336$	4.21000	0.229675
$337$	−24.9949	−1.36156	−0.680780	−	0.732488i	$-0.738359\pi$
$337$	−24.9949	−1.36156	−0.680780	+	0.732488i	$0.738359\pi$
$338$	29.4796	1.60348
$339$	14.4057	0.782412
$340$	−54.0813	−2.93297
$341$	8.25542	0.447056
$342$	−4.77320	−0.258105
$343$	30.9274	1.66992
$344$	−10.5649	−0.569623
$345$	−12.0393	−0.648173
$346$	−13.3470	−0.717538
$347$	−21.9289	−1.17720	−0.588601	−	0.808423i	$-0.700321\pi$
$347$	−21.9289	−1.17720	−0.588601	+	0.808423i	$0.700321\pi$
$348$	−34.8766	−1.86958
$349$	2.11353	0.113135	0.0565675	−	0.998399i	$-0.481984\pi$
$349$	2.11353	0.113135	0.0565675	+	0.998399i	$0.481984\pi$
$350$	−29.7476	−1.59008
$351$	3.06324	0.163504
$352$	−21.8110	−1.16253
$353$	13.5606	0.721759	0.360879	−	0.932613i	$-0.382477\pi$
$353$	13.5606	0.721759	0.360879	+	0.932613i	$0.382477\pi$
$354$	−4.14424	−0.220264
$355$	−24.8360	−1.31816
$356$	−45.0764	−2.38905
$357$	−35.3046	−1.86852
$358$	46.6501	2.46553
$359$	−8.79154	−0.464000	−0.232000	−	0.972716i	$-0.574527\pi$
$359$	−8.79154	−0.464000	−0.232000	+	0.972716i	$0.574527\pi$
$360$	10.4633	0.551465
$361$	−15.8874	−0.836179
$362$	17.6953	0.930046
$363$	12.6184	0.662293
$364$	−8.37559	−0.439000
$365$	11.2599	0.589372
$366$	−8.38260	−0.438165
$367$	19.6485	1.02564	0.512821	−	0.858496i	$-0.328601\pi$
$367$	19.6485	1.02564	0.512821	+	0.858496i	$0.328601\pi$
$368$	−2.16890	−0.113062
$369$	11.2154	0.583853
$370$	6.48525	0.337152
$371$	−14.4665	−0.751062
$372$	−8.39242	−0.435127
$373$	−21.0622	−1.09056	−0.545280	−	0.838254i	$-0.683577\pi$
$373$	−21.0622	−1.09056	−0.545280	+	0.838254i	$0.683577\pi$
$374$	−59.8064	−3.09252
$375$	−8.28109	−0.427634
$376$	−25.3080	−1.30516
$377$	4.13249	0.212834
$378$	59.6790	3.06956
$379$	−29.5015	−1.51539	−0.757696	−	0.652608i	$-0.773675\pi$
$379$	−29.5015	−1.51539	−0.757696	+	0.652608i	$0.773675\pi$
$380$	−16.6854	−0.855944
$381$	4.44565	0.227758
$382$	−28.5041	−1.45840
$383$	−1.80978	−0.0924754	−0.0462377	−	0.998930i	$-0.514723\pi$
$383$	−1.80978	−0.0924754	−0.0462377	+	0.998930i	$0.514723\pi$
$384$	26.4583	1.35019
$385$	−57.4365	−2.92723
$386$	−24.3549	−1.23963
$387$	−3.83709	−0.195050
$388$	2.10915	0.107076
$389$	11.9716	0.606984	0.303492	−	0.952834i	$-0.401847\pi$
$389$	11.9716	0.606984	0.303492	+	0.952834i	$0.401847\pi$
$390$	4.76855	0.241465
$391$	18.1882	0.919815
$392$	−44.2533	−2.23513
$393$	7.03312	0.354774
$394$	−47.5715	−2.39662
$395$	−49.0474	−2.46784
$396$	17.7842	0.893690
$397$	16.7828	0.842305	0.421152	−	0.906990i	$-0.361626\pi$
$397$	16.7828	0.842305	0.421152	+	0.906990i	$0.361626\pi$
$398$	−46.0254	−2.30704
$399$	−10.8923	−0.545299
$400$	1.91766	0.0958830
$401$	−6.20959	−0.310092	−0.155046	−	0.987907i	$-0.549553\pi$
$401$	−6.20959	−0.310092	−0.155046	+	0.987907i	$0.549553\pi$
$402$	11.2181	0.559508
$403$	0.994410	0.0495351
$404$	−42.4450	−2.11172
$405$	−11.5779	−0.575308
$406$	80.5103	3.99566
$407$	4.50751	0.223429
$408$	24.8623	1.23087
$409$	26.2955	1.30023	0.650115	−	0.759836i	$-0.274721\pi$
$409$	26.2955	1.30023	0.650115	+	0.759836i	$0.274721\pi$
$410$	62.3784	3.08065
$411$	−3.53412	−0.174325
$412$	−16.0927	−0.792828
$413$	6.01275	0.295868
$414$	−8.60529	−0.422927
$415$	22.7876	1.11860
$416$	−2.62725	−0.128811
$417$	21.4690	1.05134
$418$	−18.4518	−0.902505
$419$	20.8439	1.01829	0.509145	−	0.860681i	$-0.329962\pi$
$419$	20.8439	1.01829	0.509145	+	0.860681i	$0.329962\pi$
$420$	58.3896	2.84912
$421$	−18.8063	−0.916564	−0.458282	−	0.888807i	$-0.651535\pi$
$421$	−18.8063	−0.916564	−0.458282	+	0.888807i	$0.651535\pi$
$422$	23.0081	1.12002
$423$	−9.19165	−0.446913
$424$	10.1876	0.494754
$425$	−16.0813	−0.780057
$426$	27.9209	1.35277
$427$	12.1620	0.588562
$428$	14.8505	0.717824
$429$	3.31433	0.160018
$430$	−21.3412	−1.02917
$431$	−14.2075	−0.684352	−0.342176	−	0.939636i	$-0.611164\pi$
$431$	−14.2075	−0.684352	−0.342176	+	0.939636i	$0.611164\pi$
$432$	−3.84717	−0.185097
$433$	35.2815	1.69552	0.847760	−	0.530379i	$-0.177951\pi$
$433$	35.2815	1.69552	0.847760	+	0.530379i	$0.177951\pi$
$434$	19.3734	0.929952
$435$	−28.8093	−1.38130
$436$	−3.38367	−0.162049
$437$	5.61150	0.268434
$438$	−12.6586	−0.604850
$439$	4.61054	0.220049	0.110025	−	0.993929i	$-0.464907\pi$
$439$	4.61054	0.220049	0.110025	+	0.993929i	$0.464907\pi$
$440$	40.4480	1.92828
$441$	−16.0724	−0.765354
$442$	−7.20401	−0.342660
$443$	20.1239	0.956114	0.478057	−	0.878329i	$-0.341341\pi$
$443$	20.1239	0.956114	0.478057	+	0.878329i	$0.341341\pi$
$444$	−4.58231	−0.217467
$445$	−37.2347	−1.76510
$446$	11.0341	0.522478
$447$	−9.75791	−0.461533
$448$	−57.4023	−2.71201
$449$	7.15537	0.337683	0.168841	−	0.985643i	$-0.445997\pi$
$449$	7.15537	0.337683	0.168841	+	0.985643i	$0.445997\pi$
$450$	7.60847	0.358667
$451$	43.3555	2.04153
$452$	35.9938	1.69300
$453$	22.8956	1.07573
$454$	27.0837	1.27110
$455$	−6.91853	−0.324346
$456$	7.67063	0.359210
$457$	−2.31265	−0.108181	−0.0540907	−	0.998536i	$-0.517226\pi$
$457$	−2.31265	−0.108181	−0.0540907	+	0.998536i	$0.517226\pi$
$458$	5.29151	0.247256
$459$	32.2619	1.50586
$460$	−30.0810	−1.40254
$461$	−7.36287	−0.342923	−0.171462	−	0.985191i	$-0.554849\pi$
$461$	−7.36287	−0.342923	−0.171462	+	0.985191i	$0.554849\pi$
$462$	64.5708	3.00411
$463$	−7.39672	−0.343755	−0.171877	−	0.985118i	$-0.554983\pi$
$463$	−7.39672	−0.343755	−0.171877	+	0.985118i	$0.554983\pi$
$464$	−5.19005	−0.240942
$465$	−6.93244	−0.321484
$466$	21.1094	0.977874
$467$	−34.1617	−1.58082	−0.790408	−	0.612580i	$-0.790132\pi$
$467$	−34.1617	−1.58082	−0.790408	+	0.612580i	$0.790132\pi$
$468$	2.14220	0.0990234
$469$	−16.2760	−0.751555
$470$	−51.1224	−2.35810
$471$	16.8979	0.778616
$472$	−4.23431	−0.194900
$473$	−14.8330	−0.682024
$474$	55.1397	2.53265
$475$	−4.96147	−0.227648
$476$	−88.2112	−4.04315
$477$	3.70006	0.169414
$478$	10.8053	0.494224
$479$	−36.8577	−1.68407	−0.842036	−	0.539421i	$-0.818643\pi$
$479$	−36.8577	−1.68407	−0.842036	+	0.539421i	$0.818643\pi$
$480$	18.3156	0.835990
$481$	0.542954	0.0247566
$482$	53.1074	2.41898
$483$	−19.6371	−0.893518
$484$	31.5279	1.43309
$485$	1.74224	0.0791109
$486$	−26.2557	−1.19098
$487$	24.7483	1.12145	0.560727	−	0.828001i	$-0.310522\pi$
$487$	24.7483	1.12145	0.560727	+	0.828001i	$0.310522\pi$
$488$	−8.56478	−0.387709
$489$	−23.9166	−1.08154
$490$	−89.3921	−4.03832
$491$	5.94814	0.268436	0.134218	−	0.990952i	$-0.457148\pi$
$491$	5.94814	0.268436	0.134218	+	0.990952i	$0.457148\pi$
$492$	−44.0750	−1.98705
$493$	43.5231	1.96018
$494$	−2.22261	−0.100000
$495$	14.6904	0.660284
$496$	−1.24889	−0.0560769
$497$	−40.5095	−1.81710
$498$	−25.6181	−1.14798
$499$	9.74237	0.436128	0.218064	−	0.975934i	$-0.430026\pi$
$499$	9.74237	0.436128	0.218064	+	0.975934i	$0.430026\pi$
$500$	−20.6909	−0.925326
$501$	24.8825	1.11167
$502$	−31.8715	−1.42249
$503$	−23.3427	−1.04080	−0.520400	−	0.853923i	$-0.674217\pi$
$503$	−23.3427	−1.04080	−0.520400	+	0.853923i	$0.674217\pi$
$504$	17.0666	0.760205
$505$	−35.0611	−1.56020
$506$	−33.2654	−1.47883
$507$	−17.2059	−0.764142
$508$	11.1078	0.492828
$509$	16.0759	0.712551	0.356275	−	0.934381i	$-0.384046\pi$
$509$	16.0759	0.712551	0.356275	+	0.934381i	$0.384046\pi$
$510$	50.2221	2.22387
$511$	18.3659	0.812460
$512$	7.67810	0.339327
$513$	9.95360	0.439462
$514$	−28.7007	−1.26593
$515$	−13.2931	−0.585764
$516$	15.0792	0.663824
$517$	−35.5322	−1.56270
$518$	10.5780	0.464770
$519$	7.79004	0.341945
$520$	4.87218	0.213659
$521$	−34.9058	−1.52925	−0.764625	−	0.644476i	$-0.777076\pi$
$521$	−34.9058	−1.52925	−0.764625	+	0.644476i	$0.777076\pi$
$522$	−20.5919	−0.901284
$523$	39.8219	1.74129	0.870646	−	0.491911i	$-0.163701\pi$
$523$	39.8219	1.74129	0.870646	+	0.491911i	$0.163701\pi$
$524$	17.5728	0.767670
$525$	17.3624	0.757756
$526$	−71.8085	−3.13100
$527$	10.4731	0.456214
$528$	−4.16252	−0.181150
$529$	−12.8834	−0.560148
$530$	20.5791	0.893898
$531$	−1.53787	−0.0667377
$532$	−27.2153	−1.17993
$533$	5.22240	0.226207
$534$	41.8598	1.81145
$535$	12.2670	0.530349
$536$	11.4619	0.495079
$537$	−27.2276	−1.17496
$538$	−13.4022	−0.577808
$539$	−62.1311	−2.67618
$540$	−53.3574	−2.29613
$541$	−31.8027	−1.36731	−0.683653	−	0.729807i	$-0.739610\pi$
$541$	−31.8027	−1.36731	−0.683653	+	0.729807i	$0.739610\pi$
$542$	−8.08387	−0.347232
$543$	−10.3280	−0.443216
$544$	−27.6700	−1.18634
$545$	−2.79503	−0.119726
$546$	7.77790	0.332863
$547$	0.572452	0.0244763	0.0122381	−	0.999925i	$-0.496104\pi$
$547$	0.572452	0.0244763	0.0122381	+	0.999925i	$0.496104\pi$
$548$	−8.83025	−0.377210
$549$	−3.11065	−0.132760
$550$	29.4121	1.25413
$551$	13.4280	0.572050
$552$	13.8289	0.588596
$553$	−80.0005	−3.40197
$554$	−36.3000	−1.54224
$555$	−3.78515	−0.160671
$556$	53.6419	2.27492
$557$	−17.8864	−0.757872	−0.378936	−	0.925423i	$-0.623710\pi$
$557$	−17.8864	−0.757872	−0.378936	+	0.925423i	$0.623710\pi$
$558$	−4.95508	−0.209765
$559$	−1.78672	−0.0755702
$560$	8.68907	0.367180
$561$	34.9064	1.47375
$562$	0.196745	0.00829917
$563$	−19.1333	−0.806371	−0.403186	−	0.915118i	$-0.632097\pi$
$563$	−19.1333	−0.806371	−0.403186	+	0.915118i	$0.632097\pi$
$564$	36.1218	1.52100
$565$	29.7321	1.25084
$566$	−46.5813	−1.95796
$567$	−18.8845	−0.793073
$568$	28.5277	1.19700
$569$	−29.5091	−1.23708	−0.618542	−	0.785751i	$-0.712277\pi$
$569$	−29.5091	−1.23708	−0.618542	+	0.785751i	$0.712277\pi$
$570$	15.4947	0.649003
$571$	6.93007	0.290014	0.145007	−	0.989431i	$-0.453679\pi$
$571$	6.93007	0.290014	0.145007	+	0.989431i	$0.453679\pi$
$572$	8.28111	0.346251
$573$	16.6366	0.695004
$574$	101.744	4.24673
$575$	−8.94471	−0.373020
$576$	14.6817	0.611736
$577$	−25.9680	−1.08106	−0.540531	−	0.841324i	$-0.681777\pi$
$577$	−25.9680	−1.08106	−0.540531	+	0.841324i	$0.681777\pi$
$578$	−36.4275	−1.51519
$579$	14.2149	0.590750
$580$	−71.9821	−2.98889
$581$	37.1685	1.54201
$582$	−1.95864	−0.0811884
$583$	14.3033	0.592382
$584$	−12.9337	−0.535199
$585$	1.76954	0.0731613
$586$	−12.8370	−0.530292
$587$	−30.4304	−1.25600	−0.627999	−	0.778214i	$-0.716126\pi$
$587$	−30.4304	−1.25600	−0.627999	+	0.778214i	$0.716126\pi$
$588$	63.1622	2.60477
$589$	3.23120	0.133139
$590$	−8.55334	−0.352136
$591$	27.7654	1.14212
$592$	−0.681903	−0.0280260
$593$	4.03002	0.165493	0.0827466	−	0.996571i	$-0.473631\pi$
$593$	4.03002	0.165493	0.0827466	+	0.996571i	$0.473631\pi$
$594$	−59.0058	−2.42104
$595$	−72.8656	−2.98720
$596$	−24.3809	−0.998679
$597$	26.8630	1.09943
$598$	−4.00700	−0.163858
$599$	47.9874	1.96071	0.980355	−	0.197239i	$-0.0631975\pi$
$599$	47.9874	1.96071	0.980355	+	0.197239i	$0.0631975\pi$
$600$	−12.2270	−0.499164
$601$	12.5769	0.513022	0.256511	−	0.966541i	$-0.417427\pi$
$601$	12.5769	0.513022	0.256511	+	0.966541i	$0.417427\pi$
$602$	−34.8094	−1.41872
$603$	4.16287	0.169525
$604$	57.2064	2.32770
$605$	26.0432	1.05881
$606$	39.4161	1.60117
$607$	3.74591	0.152042	0.0760208	−	0.997106i	$-0.475778\pi$
$607$	3.74591	0.152042	0.0760208	+	0.997106i	$0.475778\pi$
$608$	−8.53689	−0.346217
$609$	−46.9903	−1.90414
$610$	−17.3009	−0.700494
$611$	−4.28004	−0.173152
$612$	22.5616	0.911997
$613$	16.5359	0.667880	0.333940	−	0.942594i	$-0.391622\pi$
$613$	16.5359	0.667880	0.333940	+	0.942594i	$0.391622\pi$
$614$	22.3388	0.901520
$615$	−36.4075	−1.46809
$616$	65.9741	2.65817
$617$	−17.3833	−0.699824	−0.349912	−	0.936783i	$-0.613789\pi$
$617$	−17.3833	−0.699824	−0.349912	+	0.936783i	$0.613789\pi$
$618$	14.9443	0.601147
$619$	−11.5692	−0.465005	−0.232503	−	0.972596i	$-0.574691\pi$
$619$	−11.5692	−0.465005	−0.232503	+	0.972596i	$0.574691\pi$
$620$	−17.3212	−0.695637
$621$	17.9447	0.720095
$622$	65.8384	2.63988
$623$	−60.7330	−2.43322
$624$	−0.501397	−0.0200720
$625$	−31.1525	−1.24610
$626$	−5.86406	−0.234375
$627$	10.7695	0.430092
$628$	42.2207	1.68479
$629$	5.71836	0.228006
$630$	34.4746	1.37350
$631$	28.6251	1.13955	0.569774	−	0.821801i	$-0.307031\pi$
$631$	28.6251	1.13955	0.569774	+	0.821801i	$0.307031\pi$
$632$	56.3381	2.24101
$633$	−13.4288	−0.533748
$634$	−25.3979	−1.00868
$635$	9.17542	0.364116
$636$	−14.5407	−0.576575
$637$	−7.48403	−0.296528
$638$	−79.6022	−3.15148
$639$	10.3610	0.409876
$640$	54.6076	2.15855
$641$	5.31302	0.209852	0.104926	−	0.994480i	$-0.466539\pi$
$641$	5.31302	0.209852	0.104926	+	0.994480i	$0.466539\pi$
$642$	−13.7907	−0.544277
$643$	−31.1406	−1.22806	−0.614032	−	0.789281i	$-0.710453\pi$
$643$	−31.1406	−1.22806	−0.614032	+	0.789281i	$0.710453\pi$
$644$	−49.0647	−1.93342
$645$	12.4559	0.490452
$646$	−23.4084	−0.920993
$647$	5.32709	0.209430	0.104715	−	0.994502i	$-0.466607\pi$
$647$	5.32709	0.209430	0.104715	+	0.994502i	$0.466607\pi$
$648$	13.2989	0.522428
$649$	−5.94492	−0.233359
$650$	3.54284	0.138962
$651$	−11.3074	−0.443172
$652$	−59.7573	−2.34028
$653$	−40.5221	−1.58575	−0.792877	−	0.609382i	$-0.791417\pi$
$653$	−40.5221	−1.58575	−0.792877	+	0.609382i	$0.791417\pi$
$654$	3.14221	0.122870
$655$	14.5157	0.567176
$656$	−6.55888	−0.256081
$657$	−4.69740	−0.183263
$658$	−83.3849	−3.25068
$659$	45.0757	1.75590	0.877950	−	0.478752i	$-0.158911\pi$
$659$	45.0757	1.75590	0.877950	+	0.478752i	$0.158911\pi$
$660$	−57.7310	−2.24718
$661$	27.7112	1.07784	0.538921	−	0.842356i	$-0.318832\pi$
$661$	27.7112	1.07784	0.538921	+	0.842356i	$0.318832\pi$
$662$	14.7879	0.574747
$663$	4.20466	0.163296
$664$	−26.1749	−1.01578
$665$	−22.4808	−0.871769
$666$	−2.70551	−0.104836
$667$	24.2084	0.937352
$668$	62.1707	2.40546
$669$	−6.44009	−0.248988
$670$	23.1531	0.894484
$671$	−12.0249	−0.464214
$672$	29.8743	1.15243
$673$	28.4810	1.09786	0.548930	−	0.835868i	$-0.315035\pi$
$673$	28.4810	1.09786	0.548930	+	0.835868i	$0.315035\pi$
$674$	57.9951	2.23389
$675$	−15.8660	−0.610683
$676$	−42.9903	−1.65347
$677$	−16.5157	−0.634750	−0.317375	−	0.948300i	$-0.602801\pi$
$677$	−16.5157	−0.634750	−0.317375	+	0.948300i	$0.602801\pi$
$678$	−33.4252	−1.28369
$679$	2.84173	0.109056
$680$	51.3135	1.96778
$681$	−15.8076	−0.605748
$682$	−19.1549	−0.733477
$683$	−15.6304	−0.598082	−0.299041	−	0.954240i	$-0.596667\pi$
$683$	−15.6304	−0.598082	−0.299041	+	0.954240i	$0.596667\pi$
$684$	6.96080	0.266153
$685$	−7.29410	−0.278693
$686$	−71.7601	−2.73981
$687$	−3.08842	−0.117831
$688$	2.24396	0.0855503
$689$	1.72291	0.0656376
$690$	27.9344	1.06345
$691$	−36.1910	−1.37677	−0.688385	−	0.725346i	$-0.741680\pi$
$691$	−36.1910	−1.37677	−0.688385	+	0.725346i	$0.741680\pi$
$692$	19.4640	0.739910
$693$	23.9613	0.910213
$694$	50.8810	1.93142
$695$	44.3101	1.68078
$696$	33.0916	1.25434
$697$	55.0021	2.08335
$698$	−4.90398	−0.185618
$699$	−12.3206	−0.466009
$700$	43.3812	1.63965
$701$	3.47540	0.131264	0.0656320	−	0.997844i	$-0.479094\pi$
$701$	3.47540	0.131264	0.0656320	+	0.997844i	$0.479094\pi$
$702$	−7.10757	−0.268258
$703$	1.76426	0.0665402
$704$	56.7548	2.13903
$705$	29.8379	1.12376
$706$	−31.4643	−1.18418
$707$	−57.1876	−2.15076
$708$	6.04358	0.227132
$709$	1.15906	0.0435295	0.0217647	−	0.999763i	$-0.493072\pi$
$709$	1.15906	0.0435295	0.0217647	+	0.999763i	$0.493072\pi$
$710$	57.6262	2.16267
$711$	20.4615	0.767367
$712$	42.7695	1.60286
$713$	5.82532	0.218160
$714$	81.9164	3.06565
$715$	6.84049	0.255820
$716$	−68.0302	−2.54241
$717$	−6.30659	−0.235524
$718$	20.3988	0.761276
$719$	−5.92839	−0.221092	−0.110546	−	0.993871i	$-0.535260\pi$
$719$	−5.92839	−0.221092	−0.110546	+	0.993871i	$0.535260\pi$
$720$	−2.22238	−0.0828233
$721$	−21.6822	−0.807487
$722$	36.8631	1.37190
$723$	−30.9965	−1.15277
$724$	−25.8052	−0.959044
$725$	−21.4041	−0.794930
$726$	−29.2781	−1.08661
$727$	4.15447	0.154081	0.0770404	−	0.997028i	$-0.475453\pi$
$727$	4.15447	0.154081	0.0770404	+	0.997028i	$0.475453\pi$
$728$	7.94694	0.294533
$729$	27.7512	1.02782
$730$	−26.1261	−0.966972
$731$	−18.8176	−0.695995
$732$	12.2244	0.451827
$733$	45.0288	1.66318	0.831589	−	0.555391i	$-0.187431\pi$
$733$	45.0288	1.66318	0.831589	+	0.555391i	$0.187431\pi$
$734$	−45.5898	−1.68275
$735$	52.1742	1.92448
$736$	−15.3906	−0.567305
$737$	16.0924	0.592770
$738$	−26.0229	−0.957916
$739$	−14.9696	−0.550667	−0.275334	−	0.961349i	$-0.588788\pi$
$739$	−14.9696	−0.550667	−0.275334	+	0.961349i	$0.588788\pi$
$740$	−9.45749	−0.347664
$741$	1.29724	0.0476554
$742$	33.5662	1.23225
$743$	38.8332	1.42465	0.712327	−	0.701848i	$-0.247641\pi$
$743$	38.8332	1.42465	0.712327	+	0.701848i	$0.247641\pi$
$744$	7.96292	0.291935
$745$	−20.1395	−0.737853
$746$	48.8701	1.78926
$747$	−9.50651	−0.347825
$748$	87.2162	3.18894
$749$	20.0085	0.731096
$750$	19.2144	0.701611
$751$	6.56896	0.239705	0.119852	−	0.992792i	$-0.461758\pi$
$751$	6.56896	0.239705	0.119852	+	0.992792i	$0.461758\pi$
$752$	5.37536	0.196019
$753$	18.6020	0.677894
$754$	−9.58851	−0.349193
$755$	47.2545	1.71977
$756$	−87.0303	−3.16526
$757$	−30.2955	−1.10111	−0.550555	−	0.834799i	$-0.685584\pi$
$757$	−30.2955	−1.10111	−0.550555	+	0.834799i	$0.685584\pi$
$758$	68.4517	2.48628
$759$	19.4156	0.704741
$760$	15.8315	0.574269
$761$	39.6992	1.43910	0.719548	−	0.694443i	$-0.244349\pi$
$761$	39.6992	1.43910	0.719548	+	0.694443i	$0.244349\pi$
$762$	−10.3151	−0.373678
$763$	−4.55894	−0.165045
$764$	41.5678	1.50387
$765$	18.6366	0.673809
$766$	4.19919	0.151723
$767$	−0.716098	−0.0258568
$768$	−27.2876	−0.984655
$769$	−28.0237	−1.01056	−0.505280	−	0.862955i	$-0.668611\pi$
$769$	−28.0237	−1.01056	−0.505280	+	0.862955i	$0.668611\pi$
$770$	133.268	4.80266
$771$	16.7513	0.603285
$772$	35.5169	1.27828
$773$	27.1559	0.976730	0.488365	−	0.872639i	$-0.337593\pi$
$773$	27.1559	0.976730	0.488365	+	0.872639i	$0.337593\pi$
$774$	8.90311	0.320016
$775$	−5.15053	−0.185012
$776$	−2.00121	−0.0718393
$777$	−6.17391	−0.221488
$778$	−27.7774	−0.995867
$779$	16.9695	0.607995
$780$	−6.95401	−0.248993
$781$	40.0526	1.43319
$782$	−42.2015	−1.50912
$783$	42.9405	1.53457
$784$	9.39929	0.335689
$785$	34.8758	1.24477
$786$	−16.3188	−0.582071
$787$	9.59642	0.342075	0.171038	−	0.985264i	$-0.445288\pi$
$787$	9.59642	0.342075	0.171038	+	0.985264i	$0.445288\pi$
$788$	69.3739	2.47134
$789$	41.9115	1.49209
$790$	113.804	4.04895
$791$	48.4956	1.72431
$792$	−16.8740	−0.599593
$793$	−1.44846	−0.0514362
$794$	−38.9407	−1.38195
$795$	−12.0111	−0.425990
$796$	67.1192	2.37898
$797$	6.74808	0.239029	0.119515	−	0.992832i	$-0.461866\pi$
$797$	6.74808	0.239029	0.119515	+	0.992832i	$0.461866\pi$
$798$	25.2732	0.894663
$799$	−45.0771	−1.59471
$800$	13.6078	0.481108
$801$	15.5335	0.548850
$802$	14.4080	0.508763
$803$	−18.1587	−0.640808
$804$	−16.3594	−0.576953
$805$	−40.5292	−1.42847
$806$	−2.30730	−0.0812713
$807$	7.82226	0.275356
$808$	40.2727	1.41679
$809$	−35.2446	−1.23913	−0.619567	−	0.784944i	$-0.712692\pi$
$809$	−35.2446	−1.23913	−0.619567	+	0.784944i	$0.712692\pi$
$810$	26.8638	0.943898
$811$	−45.9002	−1.61177	−0.805886	−	0.592070i	$-0.798311\pi$
$811$	−45.9002	−1.61177	−0.805886	+	0.592070i	$0.798311\pi$
$812$	−117.409	−4.12024
$813$	4.71820	0.165475
$814$	−10.4587	−0.366576
$815$	−49.3617	−1.72906
$816$	−5.28069	−0.184861
$817$	−5.80570	−0.203116
$818$	−61.0128	−2.13326
$819$	2.88626	0.100854
$820$	−90.9668	−3.17670
$821$	18.1215	0.632445	0.316223	−	0.948685i	$-0.397585\pi$
$821$	18.1215	0.632445	0.316223	+	0.948685i	$0.397585\pi$
$822$	8.20012	0.286012
$823$	−52.8759	−1.84314	−0.921568	−	0.388216i	$-0.873091\pi$
$823$	−52.8759	−1.84314	−0.921568	+	0.388216i	$0.873091\pi$
$824$	15.2691	0.531923
$825$	−17.1665	−0.597662
$826$	−13.9512	−0.485425
$827$	−39.5266	−1.37448	−0.687238	−	0.726432i	$-0.741177\pi$
$827$	−39.5266	−1.37448	−0.687238	+	0.726432i	$0.741177\pi$
$828$	12.5492	0.436113
$829$	−6.48153	−0.225113	−0.112556	−	0.993645i	$-0.535904\pi$
$829$	−6.48153	−0.225113	−0.112556	+	0.993645i	$0.535904\pi$
$830$	−52.8736	−1.83527
$831$	21.1867	0.734960
$832$	6.83642	0.237010
$833$	−78.8214	−2.73100
$834$	−49.8140	−1.72492
$835$	51.3552	1.77722
$836$	26.9083	0.930645
$837$	10.3329	0.357156
$838$	−48.3635	−1.67069
$839$	19.2899	0.665961	0.332980	−	0.942934i	$-0.391946\pi$
$839$	19.2899	0.665961	0.332980	+	0.942934i	$0.391946\pi$
$840$	−55.4014	−1.91153
$841$	28.9292	0.997557
$842$	43.6358	1.50379
$843$	−0.114831	−0.00395500
$844$	−33.5529	−1.15494
$845$	−35.5115	−1.22163
$846$	21.3272	0.733243
$847$	42.4787	1.45958
$848$	−2.16382	−0.0743060
$849$	27.1874	0.933071
$850$	37.3130	1.27982
$851$	3.18066	0.109032
$852$	−40.7173	−1.39495
$853$	57.7687	1.97796	0.988981	−	0.148041i	$-0.0472966\pi$
$853$	57.7687	1.97796	0.988981	+	0.148041i	$0.0472966\pi$
$854$	−28.2193	−0.965644
$855$	5.74987	0.196641
$856$	−14.0904	−0.481602
$857$	−18.4445	−0.630051	−0.315026	−	0.949083i	$-0.602013\pi$
$857$	−18.4445	−0.630051	−0.315026	+	0.949083i	$0.602013\pi$
$858$	−7.69016	−0.262538
$859$	−5.57626	−0.190260	−0.0951298	−	0.995465i	$-0.530327\pi$
$859$	−5.57626	−0.190260	−0.0951298	+	0.995465i	$0.530327\pi$
$860$	31.1221	1.06125
$861$	−59.3837	−2.02379
$862$	32.9653	1.12280
$863$	−4.39475	−0.149599	−0.0747996	−	0.997199i	$-0.523832\pi$
$863$	−4.39475	−0.149599	−0.0747996	+	0.997199i	$0.523832\pi$
$864$	−27.2996	−0.928752
$865$	16.0779	0.546666
$866$	−81.8628	−2.78181
$867$	21.2611	0.722066
$868$	−28.2524	−0.958948
$869$	79.0981	2.68322
$870$	66.8454	2.26627
$871$	1.93841	0.0656806
$872$	3.21050	0.108721
$873$	−0.726823	−0.0245992
$874$	−13.0202	−0.440415
$875$	−27.8776	−0.942434
$876$	18.4601	0.623708
$877$	22.8025	0.769986	0.384993	−	0.922920i	$-0.374204\pi$
$877$	22.8025	0.769986	0.384993	+	0.922920i	$0.374204\pi$
$878$	−10.6977	−0.361031
$879$	7.49240	0.252713
$880$	−8.59106	−0.289605
$881$	−43.2800	−1.45814	−0.729070	−	0.684439i	$-0.760047\pi$
$881$	−43.2800	−1.45814	−0.729070	+	0.684439i	$0.760047\pi$
$882$	37.2924	1.25570
$883$	−54.9047	−1.84769	−0.923845	−	0.382767i	$-0.874971\pi$
$883$	−54.9047	−1.84769	−0.923845	+	0.382767i	$0.874971\pi$
$884$	10.5057	0.353343
$885$	4.99221	0.167811
$886$	−46.6929	−1.56868
$887$	−34.8669	−1.17072	−0.585358	−	0.810775i	$-0.699046\pi$
$887$	−34.8669	−1.17072	−0.585358	+	0.810775i	$0.699046\pi$
$888$	4.34780	0.145903
$889$	14.9659	0.501940
$890$	86.3948	2.89596
$891$	18.6714	0.625517
$892$	−16.0911	−0.538768
$893$	−13.9074	−0.465394
$894$	22.6410	0.757229
$895$	−56.1953	−1.87840
$896$	89.0696	2.97560
$897$	2.33871	0.0780873
$898$	−16.6024	−0.554030
$899$	13.9396	0.464913
$900$	−11.0955	−0.369850
$901$	18.1456	0.604517
$902$	−100.597	−3.34950
$903$	20.3167	0.676097
$904$	−34.1517	−1.13587
$905$	−21.3160	−0.708569
$906$	−53.1242	−1.76493
$907$	55.4376	1.84077	0.920387	−	0.391008i	$-0.127874\pi$
$907$	55.4376	1.84077	0.920387	+	0.391008i	$0.127874\pi$
$908$	−39.4964	−1.31073
$909$	14.6267	0.485138
$910$	16.0529	0.532148
$911$	−5.96738	−0.197708	−0.0988541	−	0.995102i	$-0.531518\pi$
$911$	−5.96738	−0.197708	−0.0988541	+	0.995102i	$0.531518\pi$
$912$	−1.62922	−0.0539490
$913$	−36.7493	−1.21622
$914$	5.36599	0.177491
$915$	10.0978	0.333823
$916$	−7.71665	−0.254965
$917$	23.6764	0.781863
$918$	−74.8565	−2.47063
$919$	26.2471	0.865812	0.432906	−	0.901439i	$-0.357488\pi$
$919$	26.2471	0.865812	0.432906	+	0.901439i	$0.357488\pi$
$920$	28.5416	0.940987
$921$	−13.0382	−0.429622
$922$	17.0839	0.562628
$923$	4.82455	0.158802
$924$	−94.1641	−3.09777
$925$	−2.81222	−0.0924652
$926$	17.1624	0.563992
$927$	5.54560	0.182141
$928$	−36.8287	−1.20896
$929$	−13.2520	−0.434785	−0.217392	−	0.976084i	$-0.569755\pi$
$929$	−13.2520	−0.434785	−0.217392	+	0.976084i	$0.569755\pi$
$930$	16.0852	0.527453
$931$	−24.3183	−0.797001
$932$	−30.7840	−1.00836
$933$	−38.4270	−1.25804
$934$	79.2646	2.59362
$935$	72.0436	2.35608
$936$	−2.03257	−0.0664366
$937$	56.5819	1.84845	0.924225	−	0.381849i	$-0.124713\pi$
$937$	56.5819	1.84845	0.924225	+	0.381849i	$0.124713\pi$
$938$	37.7647	1.23306
$939$	3.42259	0.111692
$940$	74.5522	2.43162
$941$	−23.2216	−0.757001	−0.378501	−	0.925601i	$-0.623560\pi$
$941$	−23.2216	−0.757001	−0.378501	+	0.925601i	$0.623560\pi$
$942$	−39.2078	−1.27746
$943$	30.5932	0.996251
$944$	0.899357	0.0292716
$945$	−71.8901	−2.33859
$946$	34.4167	1.11898
$947$	48.0255	1.56062	0.780310	−	0.625393i	$-0.215061\pi$
$947$	48.0255	1.56062	0.780310	+	0.625393i	$0.215061\pi$
$948$	−80.4107	−2.61162
$949$	−2.18732	−0.0710033
$950$	11.5120	0.373498
$951$	14.8236	0.480689
$952$	83.6967	2.71263
$953$	−12.6050	−0.408316	−0.204158	−	0.978938i	$-0.565446\pi$
$953$	−12.6050	−0.408316	−0.204158	+	0.978938i	$0.565446\pi$
$954$	−8.58515	−0.277954
$955$	34.3365	1.11110
$956$	−15.7575	−0.509633
$957$	46.4603	1.50185
$958$	85.5200	2.76303
$959$	−11.8973	−0.384184
$960$	−47.6595	−1.53820
$961$	−27.6457	−0.891796
$962$	−1.25980	−0.0406177
$963$	−5.11753	−0.164910
$964$	−77.4470	−2.49440
$965$	29.3382	0.944431
$966$	45.5634	1.46598
$967$	13.1586	0.423153	0.211577	−	0.977361i	$-0.432140\pi$
$967$	13.1586	0.423153	0.211577	+	0.977361i	$0.432140\pi$
$968$	−29.9144	−0.961485
$969$	13.6625	0.438902
$970$	−4.04247	−0.129796
$971$	−10.0381	−0.322138	−0.161069	−	0.986943i	$-0.551494\pi$
$971$	−10.0381	−0.322138	−0.161069	+	0.986943i	$0.551494\pi$
$972$	38.2889	1.22812
$973$	72.2736	2.31698
$974$	−57.4229	−1.83995
$975$	−2.06780	−0.0662226
$976$	1.81914	0.0582292
$977$	−33.9704	−1.08681	−0.543404	−	0.839471i	$-0.682865\pi$
$977$	−33.9704	−1.08681	−0.543404	+	0.839471i	$0.682865\pi$
$978$	55.4930	1.77447
$979$	60.0479	1.91914
$980$	130.361	4.16423
$981$	1.16603	0.0372284
$982$	−13.8013	−0.440418
$983$	−23.0476	−0.735105	−0.367553	−	0.930003i	$-0.619804\pi$
$983$	−23.0476	−0.735105	−0.367553	+	0.930003i	$0.619804\pi$
$984$	41.8193	1.33315
$985$	57.3053	1.82590
$986$	−100.986	−3.21604
$987$	48.6681	1.54912
$988$	3.24125	0.103118
$989$	−10.4667	−0.332822
$990$	−34.0857	−1.08332
$991$	49.0958	1.55958	0.779790	−	0.626041i	$-0.215326\pi$
$991$	49.0958	1.55958	0.779790	+	0.626041i	$0.215326\pi$
$992$	−8.86218	−0.281375
$993$	−8.63103	−0.273897
$994$	93.9933	2.98129
$995$	55.4428	1.75765
$996$	37.3591	1.18377
$997$	−4.09217	−0.129600	−0.0648001	−	0.997898i	$-0.520641\pi$
$997$	−4.09217	−0.129600	−0.0648001	+	0.997898i	$0.520641\pi$
$998$	−22.6050	−0.715548
$999$	5.64181	0.178499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.10	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.32027 q^{2} +1.35424 q^{3} +3.38367 q^{4} +2.79503 q^{5} -3.14221 q^{6} +4.55894 q^{7} -3.21050 q^{8} -1.16603 q^{9} +O(q^{10})\)	\(q-2.32027 q^{2} +1.35424 q^{3} +3.38367 q^{4} +2.79503 q^{5} -3.14221 q^{6} +4.55894 q^{7} -3.21050 q^{8} -1.16603 q^{9} -6.48525 q^{10} -4.50751 q^{11} +4.58231 q^{12} -0.542954 q^{13} -10.5780 q^{14} +3.78515 q^{15} +0.681903 q^{16} -5.71836 q^{17} +2.70551 q^{18} -1.76426 q^{19} +9.45749 q^{20} +6.17391 q^{21} +10.4587 q^{22} -3.18066 q^{23} -4.34780 q^{24} +2.81222 q^{25} +1.25980 q^{26} -5.64181 q^{27} +15.4260 q^{28} -7.61112 q^{29} -8.78260 q^{30} -1.83148 q^{31} +4.83881 q^{32} -6.10426 q^{33} +13.2682 q^{34} +12.7424 q^{35} -3.94546 q^{36} -1.00000 q^{37} +4.09356 q^{38} -0.735291 q^{39} -8.97347 q^{40} -9.61850 q^{41} -14.3252 q^{42} +3.29074 q^{43} -15.2520 q^{44} -3.25909 q^{45} +7.38000 q^{46} +7.88287 q^{47} +0.923462 q^{48} +13.7839 q^{49} -6.52512 q^{50} -7.74405 q^{51} -1.83718 q^{52} -3.17321 q^{53} +13.0906 q^{54} -12.5987 q^{55} -14.6365 q^{56} -2.38923 q^{57} +17.6599 q^{58} +1.31889 q^{59} +12.8077 q^{60} +2.66774 q^{61} +4.24954 q^{62} -5.31585 q^{63} -12.5912 q^{64} -1.51758 q^{65} +14.1636 q^{66} -3.57012 q^{67} -19.3491 q^{68} -4.30738 q^{69} -29.5658 q^{70} -8.88574 q^{71} +3.74354 q^{72} +4.02855 q^{73} +2.32027 q^{74} +3.80842 q^{75} -5.96967 q^{76} -20.5495 q^{77} +1.70608 q^{78} -17.5481 q^{79} +1.90594 q^{80} -4.14229 q^{81} +22.3176 q^{82} +8.15290 q^{83} +20.8905 q^{84} -15.9830 q^{85} -7.63541 q^{86} -10.3073 q^{87} +14.4714 q^{88} -13.3217 q^{89} +7.56198 q^{90} -2.47529 q^{91} -10.7623 q^{92} -2.48027 q^{93} -18.2904 q^{94} -4.93116 q^{95} +6.55292 q^{96} +0.623333 q^{97} -31.9825 q^{98} +5.25589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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