LMFDB - Embedded newform 4033.2.a.d.1.53

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			1.53
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)

$f(q)$	$=$	$q+0.917442 q^{2} +1.63863 q^{3} -1.15830 q^{4} -0.712488 q^{5} +1.50335 q^{6} +5.07808 q^{7} -2.89756 q^{8} -0.314887 q^{9} +O(q^{10})$	\(q+0.917442 q^{2} +1.63863 q^{3} -1.15830 q^{4} -0.712488 q^{5} +1.50335 q^{6} +5.07808 q^{7} -2.89756 q^{8} -0.314887 q^{9} -0.653666 q^{10} +1.56092 q^{11} -1.89803 q^{12} -5.06872 q^{13} +4.65885 q^{14} -1.16751 q^{15} -0.341737 q^{16} -4.58341 q^{17} -0.288890 q^{18} -4.27442 q^{19} +0.825276 q^{20} +8.32111 q^{21} +1.43205 q^{22} +0.218924 q^{23} -4.74803 q^{24} -4.49236 q^{25} -4.65026 q^{26} -5.43188 q^{27} -5.88195 q^{28} +1.07787 q^{29} -1.07112 q^{30} -7.36144 q^{31} +5.48159 q^{32} +2.55777 q^{33} -4.20501 q^{34} -3.61808 q^{35} +0.364734 q^{36} -1.00000 q^{37} -3.92153 q^{38} -8.30577 q^{39} +2.06448 q^{40} -7.98086 q^{41} +7.63413 q^{42} -2.18402 q^{43} -1.80801 q^{44} +0.224353 q^{45} +0.200850 q^{46} -6.61918 q^{47} -0.559980 q^{48} +18.7869 q^{49} -4.12148 q^{50} -7.51052 q^{51} +5.87111 q^{52} +10.3484 q^{53} -4.98343 q^{54} -1.11213 q^{55} -14.7140 q^{56} -7.00419 q^{57} +0.988886 q^{58} +0.843542 q^{59} +1.35232 q^{60} -3.82345 q^{61} -6.75369 q^{62} -1.59902 q^{63} +5.71251 q^{64} +3.61141 q^{65} +2.34660 q^{66} -5.92723 q^{67} +5.30897 q^{68} +0.358735 q^{69} -3.31937 q^{70} +11.1525 q^{71} +0.912403 q^{72} +13.8504 q^{73} -0.917442 q^{74} -7.36132 q^{75} +4.95106 q^{76} +7.92647 q^{77} -7.62006 q^{78} -3.77914 q^{79} +0.243483 q^{80} -7.95619 q^{81} -7.32197 q^{82} +10.1900 q^{83} -9.63835 q^{84} +3.26563 q^{85} -2.00371 q^{86} +1.76624 q^{87} -4.52284 q^{88} -15.0610 q^{89} +0.205831 q^{90} -25.7394 q^{91} -0.253580 q^{92} -12.0627 q^{93} -6.07271 q^{94} +3.04547 q^{95} +8.98231 q^{96} -10.9061 q^{97} +17.2359 q^{98} -0.491512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.917442	0.648729	0.324365	−	0.945932i	$-0.394850\pi$
$2$	0.917442	0.648729	0.324365	+	0.945932i	$0.394850\pi$
$3$	1.63863	0.946064	0.473032	−	0.881045i	$-0.343159\pi$
$3$	1.63863	0.946064	0.473032	+	0.881045i	$0.343159\pi$
$4$	−1.15830	−0.579151
$5$	−0.712488	−0.318635	−0.159317	−	0.987227i	$-0.550929\pi$
$5$	−0.712488	−0.318635	−0.159317	+	0.987227i	$0.550929\pi$
$6$	1.50335	0.613739
$7$	5.07808	1.91934	0.959668	−	0.281137i	$-0.0907114\pi$
$7$	5.07808	1.91934	0.959668	+	0.281137i	$0.0907114\pi$
$8$	−2.89756	−1.02444
$9$	−0.314887	−0.104962
$10$	−0.653666	−0.206707
$11$	1.56092	0.470634	0.235317	−	0.971919i	$-0.424387\pi$
$11$	1.56092	0.470634	0.235317	+	0.971919i	$0.424387\pi$
$12$	−1.89803	−0.547914
$13$	−5.06872	−1.40581	−0.702905	−	0.711283i	$-0.748114\pi$
$13$	−5.06872	−1.40581	−0.702905	+	0.711283i	$0.748114\pi$
$14$	4.65885	1.24513
$15$	−1.16751	−0.301449
$16$	−0.341737	−0.0854341
$17$	−4.58341	−1.11164	−0.555820	−	0.831302i	$-0.687596\pi$
$17$	−4.58341	−1.11164	−0.555820	+	0.831302i	$0.687596\pi$
$18$	−0.288890	−0.0680921
$19$	−4.27442	−0.980618	−0.490309	−	0.871549i	$-0.663116\pi$
$19$	−4.27442	−0.980618	−0.490309	+	0.871549i	$0.663116\pi$
$20$	0.825276	0.184537
$21$	8.32111	1.81581
$22$	1.43205	0.305314
$23$	0.218924	0.0456487	0.0228244	−	0.999739i	$-0.492734\pi$
$23$	0.218924	0.0456487	0.0228244	+	0.999739i	$0.492734\pi$
$24$	−4.74803	−0.969187
$25$	−4.49236	−0.898472
$26$	−4.65026	−0.911990
$27$	−5.43188	−1.04537
$28$	−5.88195	−1.11158
$29$	1.07787	0.200156	0.100078	−	0.994980i	$-0.468091\pi$
$29$	1.07787	0.200156	0.100078	+	0.994980i	$0.468091\pi$
$30$	−1.07112	−0.195559
$31$	−7.36144	−1.32215	−0.661077	−	0.750318i	$-0.729900\pi$
$31$	−7.36144	−1.32215	−0.661077	+	0.750318i	$0.729900\pi$
$32$	5.48159	0.969017
$33$	2.55777	0.445250
$34$	−4.20501	−0.721154
$35$	−3.61808	−0.611567
$36$	0.364734	0.0607890
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−3.92153	−0.636156
$39$	−8.30577	−1.32999
$40$	2.06448	0.326422
$41$	−7.98086	−1.24640	−0.623200	−	0.782062i	$-0.714168\pi$
$41$	−7.98086	−1.24640	−0.623200	+	0.782062i	$0.714168\pi$
$42$	7.63413	1.17797
$43$	−2.18402	−0.333060	−0.166530	−	0.986036i	$-0.553256\pi$
$43$	−2.18402	−0.333060	−0.166530	+	0.986036i	$0.553256\pi$
$44$	−1.80801	−0.272568
$45$	0.224353	0.0334446
$46$	0.200850	0.0296137
$47$	−6.61918	−0.965506	−0.482753	−	0.875757i	$-0.660363\pi$
$47$	−6.61918	−0.965506	−0.482753	+	0.875757i	$0.660363\pi$
$48$	−0.559980	−0.0808262
$49$	18.7869	2.68385
$50$	−4.12148	−0.582865
$51$	−7.51052	−1.05168
$52$	5.87111	0.814176
$53$	10.3484	1.42146	0.710732	−	0.703463i	$-0.248364\pi$
$53$	10.3484	1.42146	0.710732	+	0.703463i	$0.248364\pi$
$54$	−4.98343	−0.678159
$55$	−1.11213	−0.149960
$56$	−14.7140	−1.96625
$57$	−7.00419	−0.927728
$58$	0.988886	0.129847
$59$	0.843542	0.109820	0.0549099	−	0.998491i	$-0.482513\pi$
$59$	0.843542	0.109820	0.0549099	+	0.998491i	$0.482513\pi$
$60$	1.35232	0.174584
$61$	−3.82345	−0.489542	−0.244771	−	0.969581i	$-0.578713\pi$
$61$	−3.82345	−0.489542	−0.244771	+	0.969581i	$0.578713\pi$
$62$	−6.75369	−0.857720
$63$	−1.59902	−0.201458
$64$	5.71251	0.714064
$65$	3.61141	0.447940
$66$	2.34660	0.288847
$67$	−5.92723	−0.724126	−0.362063	−	0.932154i	$-0.617927\pi$
$67$	−5.92723	−0.724126	−0.362063	+	0.932154i	$0.617927\pi$
$68$	5.30897	0.643807
$69$	0.358735	0.0431866
$70$	−3.31937	−0.396741
$71$	11.1525	1.32356	0.661781	−	0.749698i	$-0.269801\pi$
$71$	11.1525	1.32356	0.661781	+	0.749698i	$0.269801\pi$
$72$	0.912403	0.107528
$73$	13.8504	1.62107	0.810535	−	0.585690i	$-0.199177\pi$
$73$	13.8504	1.62107	0.810535	+	0.585690i	$0.199177\pi$
$74$	−0.917442	−0.106650
$75$	−7.36132	−0.850012
$76$	4.95106	0.567926
$77$	7.92647	0.903305
$78$	−7.62006	−0.862802
$79$	−3.77914	−0.425187	−0.212593	−	0.977141i	$-0.568191\pi$
$79$	−3.77914	−0.425187	−0.212593	+	0.977141i	$0.568191\pi$
$80$	0.243483	0.0272223
$81$	−7.95619	−0.884021
$82$	−7.32197	−0.808576
$83$	10.1900	1.11850	0.559248	−	0.829000i	$-0.311090\pi$
$83$	10.1900	1.11850	0.559248	+	0.829000i	$0.311090\pi$
$84$	−9.63835	−1.05163
$85$	3.26563	0.354207
$86$	−2.00371	−0.216065
$87$	1.76624	0.189361
$88$	−4.52284	−0.482137
$89$	−15.0610	−1.59647	−0.798234	−	0.602347i	$-0.794232\pi$
$89$	−15.0610	−1.59647	−0.798234	+	0.602347i	$0.794232\pi$
$90$	0.205831	0.0216965
$91$	−25.7394	−2.69822
$92$	−0.253580	−0.0264375
$93$	−12.0627	−1.25084
$94$	−6.07271	−0.626352
$95$	3.04547	0.312459
$96$	8.98231	0.916753
$97$	−10.9061	−1.10735	−0.553673	−	0.832734i	$-0.686774\pi$
$97$	−10.9061	−1.10735	−0.553673	+	0.832734i	$0.686774\pi$
$98$	17.2359	1.74109
$99$	−0.491512	−0.0493988
$100$	5.20351	0.520351
$101$	9.56139	0.951394	0.475697	−	0.879609i	$-0.342196\pi$
$101$	9.56139	0.951394	0.475697	+	0.879609i	$0.342196\pi$
$102$	−6.89047	−0.682258
$103$	8.46577	0.834157	0.417078	−	0.908870i	$-0.363054\pi$
$103$	8.46577	0.834157	0.417078	+	0.908870i	$0.363054\pi$
$104$	14.6869	1.44017
$105$	−5.92869	−0.578581
$106$	9.49407	0.922146
$107$	1.56998	0.151776	0.0758878	−	0.997116i	$-0.475821\pi$
$107$	1.56998	0.151776	0.0758878	+	0.997116i	$0.475821\pi$
$108$	6.29175	0.605424
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−1.02032	−0.0972836
$111$	−1.63863	−0.155532
$112$	−1.73537	−0.163977
$113$	−2.99902	−0.282124	−0.141062	−	0.990001i	$-0.545052\pi$
$113$	−2.99902	−0.282124	−0.141062	+	0.990001i	$0.545052\pi$
$114$	−6.42594	−0.601844
$115$	−0.155981	−0.0145453
$116$	−1.24850	−0.115921
$117$	1.59607	0.147557
$118$	0.773901	0.0712434
$119$	−23.2750	−2.13361
$120$	3.38291	0.308816
$121$	−8.56354	−0.778504
$122$	−3.50779	−0.317580
$123$	−13.0777	−1.17918
$124$	8.52677	0.765726
$125$	6.76320	0.604919
$126$	−1.46701	−0.130692
$127$	4.39429	0.389931	0.194965	−	0.980810i	$-0.437541\pi$
$127$	4.39429	0.389931	0.194965	+	0.980810i	$0.437541\pi$
$128$	−5.72228	−0.505783
$129$	−3.57880	−0.315096
$130$	3.31325	0.290592
$131$	−19.2786	−1.68438	−0.842191	−	0.539179i	$-0.818735\pi$
$131$	−19.2786	−1.68438	−0.842191	+	0.539179i	$0.818735\pi$
$132$	−2.96266	−0.257867
$133$	−21.7058	−1.88214
$134$	−5.43788	−0.469762
$135$	3.87015	0.333089
$136$	13.2807	1.13881
$137$	0.991154	0.0846800	0.0423400	−	0.999103i	$-0.486519\pi$
$137$	0.991154	0.0846800	0.0423400	+	0.999103i	$0.486519\pi$
$138$	0.329119	0.0280164
$139$	−8.55460	−0.725591	−0.362796	−	0.931869i	$-0.618178\pi$
$139$	−8.55460	−0.725591	−0.362796	+	0.931869i	$0.618178\pi$
$140$	4.19082	0.354189
$141$	−10.8464	−0.913431
$142$	10.2318	0.858633
$143$	−7.91185	−0.661622
$144$	0.107608	0.00896736
$145$	−0.767973	−0.0637767
$146$	12.7070	1.05164
$147$	30.7849	2.53909
$148$	1.15830	0.0952118
$149$	−12.4871	−1.02298	−0.511491	−	0.859289i	$-0.670907\pi$
$149$	−12.4871	−1.02298	−0.511491	+	0.859289i	$0.670907\pi$
$150$	−6.75358	−0.551428
$151$	7.23804	0.589023	0.294512	−	0.955648i	$-0.404843\pi$
$151$	7.23804	0.589023	0.294512	+	0.955648i	$0.404843\pi$
$152$	12.3854	1.00459
$153$	1.44326	0.116680
$154$	7.27207	0.586000
$155$	5.24494	0.421284
$156$	9.62058	0.770263
$157$	−11.4422	−0.913185	−0.456593	−	0.889676i	$-0.650930\pi$
$157$	−11.4422	−0.913185	−0.456593	+	0.889676i	$0.650930\pi$
$158$	−3.46714	−0.275831
$159$	16.9572	1.34480
$160$	−3.90557	−0.308762
$161$	1.11171	0.0876152
$162$	−7.29933	−0.573490
$163$	14.7512	1.15541	0.577703	−	0.816247i	$-0.303949\pi$
$163$	14.7512	1.15541	0.577703	+	0.816247i	$0.303949\pi$
$164$	9.24424	0.721854
$165$	−1.82238	−0.141872
$166$	9.34872	0.725601
$167$	−9.41207	−0.728328	−0.364164	−	0.931335i	$-0.618645\pi$
$167$	−9.41207	−0.728328	−0.364164	+	0.931335i	$0.618645\pi$
$168$	−24.1109	−1.86020
$169$	12.6920	0.976304
$170$	2.99602	0.229784
$171$	1.34596	0.102928
$172$	2.52975	0.192892
$173$	−6.47579	−0.492345	−0.246173	−	0.969226i	$-0.579173\pi$
$173$	−6.47579	−0.492345	−0.246173	+	0.969226i	$0.579173\pi$
$174$	1.62042	0.122844
$175$	−22.8126	−1.72447
$176$	−0.533422	−0.0402082
$177$	1.38226	0.103897
$178$	−13.8176	−1.03568
$179$	16.6571	1.24501	0.622505	−	0.782616i	$-0.286115\pi$
$179$	16.6571	1.24501	0.622505	+	0.782616i	$0.286115\pi$
$180$	−0.259869	−0.0193695
$181$	4.01008	0.298067	0.149034	−	0.988832i	$-0.452384\pi$
$181$	4.01008	0.298067	0.149034	+	0.988832i	$0.452384\pi$
$182$	−23.6144	−1.75042
$183$	−6.26522	−0.463138
$184$	−0.634344	−0.0467644
$185$	0.712488	0.0523832
$186$	−11.0668	−0.811458
$187$	−7.15432	−0.523176
$188$	7.66700	0.559173
$189$	−27.5835	−2.00641
$190$	2.79404	0.202701
$191$	−0.886902	−0.0641740	−0.0320870	−	0.999485i	$-0.510215\pi$
$191$	−0.886902	−0.0641740	−0.0320870	+	0.999485i	$0.510215\pi$
$192$	9.36070	0.675550
$193$	4.76312	0.342857	0.171428	−	0.985197i	$-0.445162\pi$
$193$	4.76312	0.342857	0.171428	+	0.985197i	$0.445162\pi$
$194$	−10.0057	−0.718368
$195$	5.91776	0.423780
$196$	−21.7609	−1.55435
$197$	5.29850	0.377503	0.188751	−	0.982025i	$-0.439556\pi$
$197$	5.29850	0.377503	0.188751	+	0.982025i	$0.439556\pi$
$198$	−0.450934	−0.0320465
$199$	−3.54326	−0.251175	−0.125588	−	0.992083i	$-0.540082\pi$
$199$	−3.54326	−0.251175	−0.125588	+	0.992083i	$0.540082\pi$
$200$	13.0169	0.920432
$201$	−9.71254	−0.685070
$202$	8.77202	0.617197
$203$	5.47353	0.384167
$204$	8.69945	0.609083
$205$	5.68627	0.397146
$206$	7.76685	0.541142
$207$	−0.0689362	−0.00479140
$208$	1.73217	0.120104
$209$	−6.67201	−0.461512
$210$	−5.43923	−0.375343
$211$	8.54364	0.588169	0.294084	−	0.955779i	$-0.404985\pi$
$211$	8.54364	0.588169	0.294084	+	0.955779i	$0.404985\pi$
$212$	−11.9866	−0.823242
$213$	18.2749	1.25217
$214$	1.44036	0.0984612
$215$	1.55609	0.106124
$216$	15.7392	1.07092
$217$	−37.3820	−2.53766
$218$	−0.917442	−0.0621370
$219$	22.6957	1.53364
$220$	1.28819	0.0868496
$221$	23.2320	1.56276
$222$	−1.50335	−0.100898
$223$	21.2116	1.42043	0.710217	−	0.703983i	$-0.248597\pi$
$223$	21.2116	1.42043	0.710217	+	0.703983i	$0.248597\pi$
$224$	27.8360	1.85987
$225$	1.41459	0.0943057
$226$	−2.75142	−0.183022
$227$	−9.57186	−0.635307	−0.317653	−	0.948207i	$-0.602895\pi$
$227$	−9.57186	−0.635307	−0.317653	+	0.948207i	$0.602895\pi$
$228$	8.11296	0.537294
$229$	−19.5616	−1.29266	−0.646332	−	0.763056i	$-0.723698\pi$
$229$	−19.5616	−1.29266	−0.646332	+	0.763056i	$0.723698\pi$
$230$	−0.143103	−0.00943594
$231$	12.9886	0.854584
$232$	−3.12320	−0.205048
$233$	11.7728	0.771260	0.385630	−	0.922654i	$-0.373984\pi$
$233$	11.7728	0.771260	0.385630	+	0.922654i	$0.373984\pi$
$234$	1.46431	0.0957246
$235$	4.71609	0.307644
$236$	−0.977076	−0.0636022
$237$	−6.19262	−0.402254
$238$	−21.3534	−1.38414
$239$	15.9813	1.03375	0.516873	−	0.856062i	$-0.327096\pi$
$239$	15.9813	1.03375	0.516873	+	0.856062i	$0.327096\pi$
$240$	0.398979	0.0257540
$241$	−21.1575	−1.36287	−0.681436	−	0.731877i	$-0.738644\pi$
$241$	−21.1575	−1.36287	−0.681436	+	0.731877i	$0.738644\pi$
$242$	−7.85655	−0.505038
$243$	3.25838	0.209025
$244$	4.42870	0.283519
$245$	−13.3855	−0.855167
$246$	−11.9980	−0.764965
$247$	21.6658	1.37856
$248$	21.3302	1.35447
$249$	16.6976	1.05817
$250$	6.20484	0.392428
$251$	−10.0710	−0.635673	−0.317836	−	0.948146i	$-0.602956\pi$
$251$	−10.0710	−0.635673	−0.317836	+	0.948146i	$0.602956\pi$
$252$	1.85215	0.116674
$253$	0.341722	0.0214839
$254$	4.03151	0.252959
$255$	5.35116	0.335103
$256$	−16.6749	−1.04218
$257$	−18.8008	−1.17276	−0.586380	−	0.810036i	$-0.699448\pi$
$257$	−18.8008	−1.17276	−0.586380	+	0.810036i	$0.699448\pi$
$258$	−3.28334	−0.204412
$259$	−5.07808	−0.315537
$260$	−4.18310	−0.259425
$261$	−0.339408	−0.0210088
$262$	−17.6870	−1.09271
$263$	−0.323523	−0.0199493	−0.00997464	−	0.999950i	$-0.503175\pi$
$263$	−0.323523	−0.0199493	−0.00997464	+	0.999950i	$0.503175\pi$
$264$	−7.41127	−0.456132
$265$	−7.37313	−0.452928
$266$	−19.9138	−1.22100
$267$	−24.6795	−1.51036
$268$	6.86551	0.419378
$269$	−20.0436	−1.22208	−0.611040	−	0.791600i	$-0.709248\pi$
$269$	−20.0436	−1.22208	−0.611040	+	0.791600i	$0.709248\pi$
$270$	3.55064	0.216085
$271$	17.6720	1.07350	0.536749	−	0.843742i	$-0.319652\pi$
$271$	17.6720	1.07350	0.536749	+	0.843742i	$0.319652\pi$
$272$	1.56632	0.0949720
$273$	−42.1774	−2.55269
$274$	0.909326	0.0549344
$275$	−7.01220	−0.422852
$276$	−0.415523	−0.0250116
$277$	16.4136	0.986196	0.493098	−	0.869974i	$-0.335864\pi$
$277$	16.4136	0.986196	0.493098	+	0.869974i	$0.335864\pi$
$278$	−7.84834	−0.470712
$279$	2.31802	0.138776
$280$	10.4836	0.626514
$281$	−9.83011	−0.586415	−0.293208	−	0.956049i	$-0.594723\pi$
$281$	−9.83011	−0.586415	−0.293208	+	0.956049i	$0.594723\pi$
$282$	−9.95093	−0.592569
$283$	0.684725	0.0407027	0.0203513	−	0.999793i	$-0.493522\pi$
$283$	0.684725	0.0407027	0.0203513	+	0.999793i	$0.493522\pi$
$284$	−12.9180	−0.766541
$285$	4.99041	0.295606
$286$	−7.25866	−0.429214
$287$	−40.5275	−2.39226
$288$	−1.72608	−0.101710
$289$	4.00766	0.235745
$290$	−0.704570	−0.0413738
$291$	−17.8711	−1.04762
$292$	−16.0430	−0.938843
$293$	−32.6795	−1.90916	−0.954580	−	0.297956i	$-0.903695\pi$
$293$	−32.6795	−1.90916	−0.954580	+	0.297956i	$0.903695\pi$
$294$	28.2433	1.64718
$295$	−0.601014	−0.0349924
$296$	2.89756	0.168417
$297$	−8.47871	−0.491985
$298$	−11.4562	−0.663638
$299$	−1.10966	−0.0641735
$300$	8.52663	0.492285
$301$	−11.0906	−0.639253
$302$	6.64048	0.382116
$303$	15.6676	0.900080
$304$	1.46072	0.0837783
$305$	2.72416	0.155985
$306$	1.32410	0.0756939
$307$	−16.5153	−0.942578	−0.471289	−	0.881979i	$-0.656211\pi$
$307$	−16.5153	−0.942578	−0.471289	+	0.881979i	$0.656211\pi$
$308$	−9.18123	−0.523149
$309$	13.8723	0.789166
$310$	4.81193	0.273299
$311$	14.3696	0.814828	0.407414	−	0.913244i	$-0.366431\pi$
$311$	14.3696	0.814828	0.407414	+	0.913244i	$0.366431\pi$
$312$	24.0664	1.36249
$313$	18.1336	1.02497	0.512486	−	0.858696i	$-0.328725\pi$
$313$	18.1336	1.02497	0.512486	+	0.858696i	$0.328725\pi$
$314$	−10.4975	−0.592410
$315$	1.13928	0.0641914
$316$	4.37739	0.246247
$317$	6.62002	0.371818	0.185909	−	0.982567i	$-0.440477\pi$
$317$	6.62002	0.371818	0.185909	+	0.982567i	$0.440477\pi$
$318$	15.5573	0.872409
$319$	1.68247	0.0942003
$320$	−4.07010	−0.227525
$321$	2.57262	0.143589
$322$	1.01993	0.0568386
$323$	19.5914	1.09010
$324$	9.21566	0.511981
$325$	22.7705	1.26308
$326$	13.5334	0.749546
$327$	−1.63863	−0.0906165
$328$	23.1250	1.27686
$329$	−33.6127	−1.85313
$330$	−1.67193	−0.0920365
$331$	27.1236	1.49085	0.745423	−	0.666591i	$-0.232247\pi$
$331$	27.1236	1.49085	0.745423	+	0.666591i	$0.232247\pi$
$332$	−11.8031	−0.647778
$333$	0.314887	0.0172557
$334$	−8.63502	−0.472488
$335$	4.22308	0.230731
$336$	−2.84363	−0.155133
$337$	−1.91085	−0.104090	−0.0520452	−	0.998645i	$-0.516574\pi$
$337$	−1.91085	−0.104090	−0.0520452	+	0.998645i	$0.516574\pi$
$338$	11.6441	0.633357
$339$	−4.91428	−0.266907
$340$	−3.78258	−0.205139
$341$	−11.4906	−0.622251
$342$	1.23484	0.0667724
$343$	59.8551	3.23187
$344$	6.32831	0.341200
$345$	−0.255595	−0.0137608
$346$	−5.94116	−0.319399
$347$	−25.9173	−1.39132	−0.695658	−	0.718373i	$-0.744887\pi$
$347$	−25.9173	−1.39132	−0.695658	+	0.718373i	$0.744887\pi$
$348$	−2.04584	−0.109668
$349$	−16.0223	−0.857652	−0.428826	−	0.903387i	$-0.641073\pi$
$349$	−16.0223	−0.857652	−0.428826	+	0.903387i	$0.641073\pi$
$350$	−20.9292	−1.11871
$351$	27.5327	1.46959
$352$	8.55630	0.456053
$353$	−18.5352	−0.986529	−0.493264	−	0.869879i	$-0.664196\pi$
$353$	−18.5352	−0.986529	−0.493264	+	0.869879i	$0.664196\pi$
$354$	1.26814	0.0674008
$355$	−7.94605	−0.421732
$356$	17.4452	0.924595
$357$	−38.1391	−2.01853
$358$	15.2819	0.807674
$359$	−19.1610	−1.01128	−0.505640	−	0.862744i	$-0.668744\pi$
$359$	−19.1610	−1.01128	−0.505640	+	0.862744i	$0.668744\pi$
$360$	−0.650076	−0.0342620
$361$	−0.729368	−0.0383878
$362$	3.67902	0.193365
$363$	−14.0325	−0.736514
$364$	29.8140	1.56268
$365$	−9.86827	−0.516529
$366$	−5.74797	−0.300451
$367$	−34.4884	−1.80028	−0.900140	−	0.435600i	$-0.856536\pi$
$367$	−34.4884	−1.80028	−0.900140	+	0.435600i	$0.856536\pi$
$368$	−0.0748142	−0.00389996
$369$	2.51307	0.130825
$370$	0.653666	0.0339825
$371$	52.5501	2.72827
$372$	13.9722	0.724426
$373$	23.4353	1.21343	0.606717	−	0.794918i	$-0.292486\pi$
$373$	23.4353	1.21343	0.606717	+	0.794918i	$0.292486\pi$
$374$	−6.56367	−0.339399
$375$	11.0824	0.572292
$376$	19.1794	0.989104
$377$	−5.46344	−0.281382
$378$	−25.3063	−1.30161
$379$	36.4741	1.87355	0.936775	−	0.349932i	$-0.113795\pi$
$379$	36.4741	1.87355	0.936775	+	0.349932i	$0.113795\pi$
$380$	−3.52757	−0.180961
$381$	7.20063	0.368899
$382$	−0.813681	−0.0416315
$383$	5.12910	0.262085	0.131042	−	0.991377i	$-0.458168\pi$
$383$	5.12910	0.262085	0.131042	+	0.991377i	$0.458168\pi$
$384$	−9.37672	−0.478504
$385$	−5.64751	−0.287824
$386$	4.36988	0.222421
$387$	0.687719	0.0349587
$388$	12.6325	0.641320
$389$	−4.06469	−0.206088	−0.103044	−	0.994677i	$-0.532858\pi$
$389$	−4.06469	−0.206088	−0.103044	+	0.994677i	$0.532858\pi$
$390$	5.42920	0.274918
$391$	−1.00342	−0.0507450
$392$	−54.4362	−2.74944
$393$	−31.5906	−1.59353
$394$	4.86107	0.244897
$395$	2.69260	0.135479
$396$	0.569319	0.0286094
$397$	11.9338	0.598939	0.299469	−	0.954106i	$-0.403190\pi$
$397$	11.9338	0.598939	0.299469	+	0.954106i	$0.403190\pi$
$398$	−3.25073	−0.162945
$399$	−35.5679	−1.78062
$400$	1.53520	0.0767602
$401$	−39.1960	−1.95736	−0.978678	−	0.205401i	$-0.934150\pi$
$401$	−39.1960	−1.95736	−0.978678	+	0.205401i	$0.934150\pi$
$402$	−8.91069	−0.444425
$403$	37.3131	1.85870
$404$	−11.0750	−0.551001
$405$	5.66869	0.281679
$406$	5.02165	0.249220
$407$	−1.56092	−0.0773718
$408$	21.7622	1.07739
$409$	5.09688	0.252024	0.126012	−	0.992029i	$-0.459782\pi$
$409$	5.09688	0.252024	0.126012	+	0.992029i	$0.459782\pi$
$410$	5.21682	0.257640
$411$	1.62414	0.0801128
$412$	−9.80591	−0.483102
$413$	4.28358	0.210781
$414$	−0.0632449	−0.00310832
$415$	−7.26025	−0.356392
$416$	−27.7847	−1.36226
$417$	−14.0178	−0.686456
$418$	−6.12118	−0.299396
$419$	−24.0684	−1.17582	−0.587910	−	0.808926i	$-0.700049\pi$
$419$	−24.0684	−1.17582	−0.587910	+	0.808926i	$0.700049\pi$
$420$	6.86721	0.335086
$421$	25.2040	1.22837	0.614184	−	0.789163i	$-0.289485\pi$
$421$	25.2040	1.22837	0.614184	+	0.789163i	$0.289485\pi$
$422$	7.83829	0.381562
$423$	2.08429	0.101342
$424$	−29.9851	−1.45621
$425$	20.5903	0.998778
$426$	16.7661	0.812322
$427$	−19.4158	−0.939596
$428$	−1.81851	−0.0879009
$429$	−12.9646	−0.625937
$430$	1.42762	0.0688459
$431$	32.9757	1.58839	0.794193	−	0.607666i	$-0.207894\pi$
$431$	32.9757	1.58839	0.794193	+	0.607666i	$0.207894\pi$
$432$	1.85627	0.0893099
$433$	16.9997	0.816956	0.408478	−	0.912768i	$-0.366060\pi$
$433$	16.9997	0.816956	0.408478	+	0.912768i	$0.366060\pi$
$434$	−34.2958	−1.64625
$435$	−1.25842	−0.0603368
$436$	1.15830	0.0554726
$437$	−0.935771	−0.0447640
$438$	20.8220	0.994914
$439$	36.4265	1.73854	0.869271	−	0.494336i	$-0.164589\pi$
$439$	36.4265	1.73854	0.869271	+	0.494336i	$0.164589\pi$
$440$	3.22247	0.153625
$441$	−5.91576	−0.281703
$442$	21.3140	1.01381
$443$	−28.4441	−1.35142	−0.675709	−	0.737169i	$-0.736162\pi$
$443$	−28.4441	−1.35142	−0.675709	+	0.737169i	$0.736162\pi$
$444$	1.89803	0.0900765
$445$	10.7308	0.508690
$446$	19.4604	0.921477
$447$	−20.4617	−0.967807
$448$	29.0086	1.37053
$449$	24.2492	1.14439	0.572195	−	0.820117i	$-0.306092\pi$
$449$	24.2492	1.14439	0.572195	+	0.820117i	$0.306092\pi$
$450$	1.29780	0.0611789
$451$	−12.4575	−0.586599
$452$	3.47377	0.163392
$453$	11.8605	0.557254
$454$	−8.78163	−0.412142
$455$	18.3390	0.859747
$456$	20.2950	0.950403
$457$	−5.61315	−0.262572	−0.131286	−	0.991345i	$-0.541911\pi$
$457$	−5.61315	−0.262572	−0.131286	+	0.991345i	$0.541911\pi$
$458$	−17.9466	−0.838589
$459$	24.8965	1.16207
$460$	0.180672	0.00842390
$461$	12.0059	0.559169	0.279585	−	0.960121i	$-0.409803\pi$
$461$	12.0059	0.559169	0.279585	+	0.960121i	$0.409803\pi$
$462$	11.9162	0.554394
$463$	36.5663	1.69938	0.849691	−	0.527282i	$-0.176789\pi$
$463$	36.5663	1.69938	0.849691	+	0.527282i	$0.176789\pi$
$464$	−0.368349	−0.0171002
$465$	8.59453	0.398562
$466$	10.8008	0.500339
$467$	18.9848	0.878511	0.439255	−	0.898362i	$-0.355242\pi$
$467$	18.9848	0.878511	0.439255	+	0.898362i	$0.355242\pi$
$468$	−1.84873	−0.0854578
$469$	−30.0990	−1.38984
$470$	4.32673	0.199577
$471$	−18.7495	−0.863932
$472$	−2.44421	−0.112504
$473$	−3.40907	−0.156749
$474$	−5.68137	−0.260954
$475$	19.2022	0.881058
$476$	26.9594	1.23568
$477$	−3.25858	−0.149200
$478$	14.6619	0.670621
$479$	23.9454	1.09409	0.547047	−	0.837102i	$-0.315752\pi$
$479$	23.9454	1.09409	0.547047	+	0.837102i	$0.315752\pi$
$480$	−6.39979	−0.292109
$481$	5.06872	0.231114
$482$	−19.4107	−0.884135
$483$	1.82169	0.0828897
$484$	9.91916	0.450871
$485$	7.77046	0.352839
$486$	2.98937	0.135601
$487$	−23.8814	−1.08217	−0.541086	−	0.840967i	$-0.681987\pi$
$487$	−23.8814	−1.08217	−0.541086	+	0.840967i	$0.681987\pi$
$488$	11.0787	0.501507
$489$	24.1719	1.09309
$490$	−12.2804	−0.554772
$491$	−28.0447	−1.26564	−0.632821	−	0.774298i	$-0.718103\pi$
$491$	−28.0447	−1.26564	−0.632821	+	0.774298i	$0.718103\pi$
$492$	15.1479	0.682920
$493$	−4.94034	−0.222502
$494$	19.8771	0.894315
$495$	0.350197	0.0157402
$496$	2.51567	0.112957
$497$	56.6335	2.54036
$498$	15.3191	0.686466
$499$	28.1203	1.25884	0.629418	−	0.777067i	$-0.283293\pi$
$499$	28.1203	1.25884	0.629418	+	0.777067i	$0.283293\pi$
$500$	−7.83382	−0.350339
$501$	−15.4229	−0.689045
$502$	−9.23951	−0.412380
$503$	−9.74175	−0.434363	−0.217181	−	0.976131i	$-0.569686\pi$
$503$	−9.74175	−0.434363	−0.217181	+	0.976131i	$0.569686\pi$
$504$	4.63326	0.206382
$505$	−6.81238	−0.303147
$506$	0.313510	0.0139372
$507$	20.7974	0.923647
$508$	−5.08991	−0.225828
$509$	−28.7252	−1.27322	−0.636610	−	0.771186i	$-0.719664\pi$
$509$	−28.7252	−1.27322	−0.636610	+	0.771186i	$0.719664\pi$
$510$	4.90938	0.217391
$511$	70.3336	3.11138
$512$	−3.85366	−0.170309
$513$	23.2181	1.02510
$514$	−17.2486	−0.760804
$515$	−6.03176	−0.265791
$516$	4.14533	0.182488
$517$	−10.3320	−0.454400
$518$	−4.65885	−0.204698
$519$	−10.6114	−0.465791
$520$	−10.4643	−0.458888
$521$	−17.4584	−0.764868	−0.382434	−	0.923983i	$-0.624914\pi$
$521$	−17.4584	−0.764868	−0.382434	+	0.923983i	$0.624914\pi$
$522$	−0.311387	−0.0136291
$523$	−13.4561	−0.588396	−0.294198	−	0.955744i	$-0.595053\pi$
$523$	−13.4561	−0.588396	−0.294198	+	0.955744i	$0.595053\pi$
$524$	22.3305	0.975511
$525$	−37.3814	−1.63146
$526$	−0.296813	−0.0129417
$527$	33.7405	1.46976
$528$	−0.874082	−0.0380396
$529$	−22.9521	−0.997916
$530$	−6.76441	−0.293827
$531$	−0.265620	−0.0115269
$532$	25.1419	1.09004
$533$	40.4528	1.75220
$534$	−22.6420	−0.979815
$535$	−1.11859	−0.0483609
$536$	17.1745	0.741824
$537$	27.2948	1.17786
$538$	−18.3888	−0.792798
$539$	29.3248	1.26311
$540$	−4.48280	−0.192909
$541$	−19.3068	−0.830063	−0.415031	−	0.909807i	$-0.636229\pi$
$541$	−19.3068	−0.830063	−0.415031	+	0.909807i	$0.636229\pi$
$542$	16.2130	0.696410
$543$	6.57105	0.281991
$544$	−25.1244	−1.07720
$545$	0.712488	0.0305197
$546$	−38.6953	−1.65601
$547$	8.10310	0.346464	0.173232	−	0.984881i	$-0.444579\pi$
$547$	8.10310	0.346464	0.173232	+	0.984881i	$0.444579\pi$
$548$	−1.14806	−0.0490425
$549$	1.20395	0.0513835
$550$	−6.43328	−0.274316
$551$	−4.60728	−0.196277
$552$	−1.03946	−0.0442422
$553$	−19.1908	−0.816076
$554$	15.0585	0.639774
$555$	1.16751	0.0495579
$556$	9.90880	0.420227
$557$	−10.6965	−0.453227	−0.226613	−	0.973985i	$-0.572765\pi$
$557$	−10.6965	−0.453227	−0.226613	+	0.973985i	$0.572765\pi$
$558$	2.12665	0.0900283
$559$	11.0702	0.468219
$560$	1.23643	0.0522486
$561$	−11.7233	−0.494958
$562$	−9.01855	−0.380425
$563$	−29.2313	−1.23195	−0.615977	−	0.787764i	$-0.711239\pi$
$563$	−29.2313	−1.23195	−0.615977	+	0.787764i	$0.711239\pi$
$564$	12.5634	0.529014
$565$	2.13677	0.0898944
$566$	0.628195	0.0264050
$567$	−40.4022	−1.69673
$568$	−32.3151	−1.35591
$569$	2.82667	0.118500	0.0592500	−	0.998243i	$-0.481129\pi$
$569$	2.82667	0.118500	0.0592500	+	0.998243i	$0.481129\pi$
$570$	4.57841	0.191768
$571$	−13.0262	−0.545129	−0.272564	−	0.962138i	$-0.587872\pi$
$571$	−13.0262	−0.545129	−0.272564	+	0.962138i	$0.587872\pi$
$572$	9.16431	0.383179
$573$	−1.45331	−0.0607127
$574$	−37.1816	−1.55193
$575$	−0.983484	−0.0410141
$576$	−1.79879	−0.0749498
$577$	−14.6852	−0.611353	−0.305677	−	0.952135i	$-0.598883\pi$
$577$	−14.6852	−0.611353	−0.305677	+	0.952135i	$0.598883\pi$
$578$	3.67680	0.152935
$579$	7.80500	0.324365
$580$	0.889543	0.0369363
$581$	51.7456	2.14677
$582$	−16.3957	−0.679622
$583$	16.1530	0.668990
$584$	−40.1324	−1.66069
$585$	−1.13718	−0.0470168
$586$	−29.9816	−1.23853
$587$	−18.2836	−0.754647	−0.377323	−	0.926082i	$-0.623156\pi$
$587$	−18.2836	−0.754647	−0.377323	+	0.926082i	$0.623156\pi$
$588$	−35.6581	−1.47052
$589$	31.4659	1.29653
$590$	−0.551395	−0.0227006
$591$	8.68230	0.357142
$592$	0.341737	0.0140453
$593$	14.0030	0.575034	0.287517	−	0.957775i	$-0.407170\pi$
$593$	14.0030	0.575034	0.287517	+	0.957775i	$0.407170\pi$
$594$	−7.77872	−0.319165
$595$	16.5831	0.679842
$596$	14.4638	0.592461
$597$	−5.80610	−0.237628
$598$	−1.01805	−0.0416312
$599$	28.9501	1.18287	0.591434	−	0.806353i	$-0.298562\pi$
$599$	28.9501	1.18287	0.591434	+	0.806353i	$0.298562\pi$
$600$	21.3298	0.870787
$601$	3.10519	0.126664	0.0633318	−	0.997993i	$-0.479827\pi$
$601$	3.10519	0.126664	0.0633318	+	0.997993i	$0.479827\pi$
$602$	−10.1750	−0.414702
$603$	1.86641	0.0760059
$604$	−8.38383	−0.341133
$605$	6.10142	0.248058
$606$	14.3741	0.583908
$607$	46.4406	1.88497	0.942483	−	0.334254i	$-0.108484\pi$
$607$	46.4406	1.88497	0.942483	+	0.334254i	$0.108484\pi$
$608$	−23.4306	−0.950236
$609$	8.96911	0.363446
$610$	2.49926	0.101192
$611$	33.5508	1.35732
$612$	−1.67173	−0.0675755
$613$	29.3270	1.18451	0.592253	−	0.805752i	$-0.298239\pi$
$613$	29.3270	1.18451	0.592253	+	0.805752i	$0.298239\pi$
$614$	−15.1518	−0.611478
$615$	9.31770	0.375726
$616$	−22.9674	−0.925382
$617$	−20.0409	−0.806816	−0.403408	−	0.915020i	$-0.632175\pi$
$617$	−20.0409	−0.806816	−0.403408	+	0.915020i	$0.632175\pi$
$618$	12.7270	0.511955
$619$	1.70912	0.0686953	0.0343476	−	0.999410i	$-0.489065\pi$
$619$	1.70912	0.0686953	0.0343476	+	0.999410i	$0.489065\pi$
$620$	−6.07522	−0.243987
$621$	−1.18917	−0.0477196
$622$	13.1833	0.528602
$623$	−76.4813	−3.06416
$624$	2.83838	0.113626
$625$	17.6431	0.705724
$626$	16.6365	0.664929
$627$	−10.9330	−0.436620
$628$	13.2535	0.528872
$629$	4.58341	0.182753
$630$	1.04523	0.0416428
$631$	−34.6618	−1.37987	−0.689933	−	0.723874i	$-0.742360\pi$
$631$	−34.6618	−1.37987	−0.689933	+	0.723874i	$0.742360\pi$
$632$	10.9503	0.435579
$633$	13.9999	0.556445
$634$	6.07349	0.241209
$635$	−3.13088	−0.124245
$636$	−19.6416	−0.778840
$637$	−95.2258	−3.77298
$638$	1.54357	0.0611105
$639$	−3.51178	−0.138924
$640$	4.07706	0.161160
$641$	7.83183	0.309339	0.154669	−	0.987966i	$-0.450569\pi$
$641$	7.83183	0.309339	0.154669	+	0.987966i	$0.450569\pi$
$642$	2.36022	0.0931506
$643$	18.4736	0.728529	0.364265	−	0.931296i	$-0.381320\pi$
$643$	18.4736	0.728529	0.364265	+	0.931296i	$0.381320\pi$
$644$	−1.28770	−0.0507424
$645$	2.54985	0.100400
$646$	17.9740	0.707176
$647$	28.8096	1.13262	0.566311	−	0.824192i	$-0.308370\pi$
$647$	28.8096	1.13262	0.566311	+	0.824192i	$0.308370\pi$
$648$	23.0535	0.905627
$649$	1.31670	0.0516850
$650$	20.8906	0.819398
$651$	−61.2554	−2.40079
$652$	−17.0864	−0.669154
$653$	13.6773	0.535235	0.267618	−	0.963525i	$-0.413764\pi$
$653$	13.6773	0.535235	0.267618	+	0.963525i	$0.413764\pi$
$654$	−1.50335	−0.0587856
$655$	13.7358	0.536702
$656$	2.72735	0.106485
$657$	−4.36132	−0.170151
$658$	−30.8377	−1.20218
$659$	12.2662	0.477822	0.238911	−	0.971041i	$-0.423210\pi$
$659$	12.2662	0.477822	0.238911	+	0.971041i	$0.423210\pi$
$660$	2.11086	0.0821653
$661$	47.3255	1.84075	0.920374	−	0.391040i	$-0.127885\pi$
$661$	47.3255	1.84075	0.920374	+	0.391040i	$0.127885\pi$
$662$	24.8843	0.967156
$663$	38.0688	1.47847
$664$	−29.5261	−1.14583
$665$	15.4652	0.599713
$666$	0.288890	0.0111943
$667$	0.235972	0.00913688
$668$	10.9020	0.421812
$669$	34.7580	1.34382
$670$	3.87443	0.149682
$671$	−5.96808	−0.230395
$672$	45.6129	1.75956
$673$	8.28482	0.319356	0.159678	−	0.987169i	$-0.448954\pi$
$673$	8.28482	0.319356	0.159678	+	0.987169i	$0.448954\pi$
$674$	−1.75309	−0.0675265
$675$	24.4020	0.939232
$676$	−14.7011	−0.565427
$677$	13.9577	0.536438	0.268219	−	0.963358i	$-0.413565\pi$
$677$	13.9577	0.536438	0.268219	+	0.963358i	$0.413565\pi$
$678$	−4.50857	−0.173151
$679$	−55.3821	−2.12537
$680$	−9.46234	−0.362864
$681$	−15.6848	−0.601041
$682$	−10.5420	−0.403672
$683$	2.15249	0.0823628	0.0411814	−	0.999152i	$-0.486888\pi$
$683$	2.15249	0.0823628	0.0411814	+	0.999152i	$0.486888\pi$
$684$	−1.55902	−0.0596108
$685$	−0.706186	−0.0269820
$686$	54.9135	2.09661
$687$	−32.0542	−1.22294
$688$	0.746359	0.0284547
$689$	−52.4533	−1.99831
$690$	−0.234493	−0.00892700
$691$	−2.96643	−0.112848	−0.0564242	−	0.998407i	$-0.517970\pi$
$691$	−2.96643	−0.112848	−0.0564242	+	0.998407i	$0.517970\pi$
$692$	7.50092	0.285142
$693$	−2.49594	−0.0948129
$694$	−23.7776	−0.902587
$695$	6.09505	0.231198
$696$	−5.11777	−0.193989
$697$	36.5796	1.38555
$698$	−14.6995	−0.556384
$699$	19.2912	0.729661
$700$	26.4238	0.998727
$701$	−29.7821	−1.12485	−0.562426	−	0.826847i	$-0.690132\pi$
$701$	−29.7821	−1.12485	−0.562426	+	0.826847i	$0.690132\pi$
$702$	25.2596	0.953363
$703$	4.27442	0.161213
$704$	8.91675	0.336063
$705$	7.72793	0.291051
$706$	−17.0050	−0.639990
$707$	48.5536	1.82604
$708$	−1.60107	−0.0601718
$709$	−5.05832	−0.189969	−0.0949845	−	0.995479i	$-0.530280\pi$
$709$	−5.05832	−0.189969	−0.0949845	+	0.995479i	$0.530280\pi$
$710$	−7.29003	−0.273590
$711$	1.19000	0.0446286
$712$	43.6402	1.63549
$713$	−1.61159	−0.0603547
$714$	−34.9904	−1.30948
$715$	5.63710	0.210816
$716$	−19.2939	−0.721048
$717$	26.1875	0.977990
$718$	−17.5791	−0.656047
$719$	5.05168	0.188396	0.0941978	−	0.995553i	$-0.469971\pi$
$719$	5.05168	0.188396	0.0941978	+	0.995553i	$0.469971\pi$
$720$	−0.0766697	−0.00285731
$721$	42.9899	1.60103
$722$	−0.669152	−0.0249033
$723$	−34.6693	−1.28937
$724$	−4.64488	−0.172626
$725$	−4.84220	−0.179835
$726$	−12.8740	−0.477798
$727$	−10.8210	−0.401329	−0.200664	−	0.979660i	$-0.564310\pi$
$727$	−10.8210	−0.401329	−0.200664	+	0.979660i	$0.564310\pi$
$728$	74.5814	2.76417
$729$	29.2078	1.08177
$730$	−9.05356	−0.335087
$731$	10.0103	0.370243
$732$	7.25701	0.268227
$733$	−46.9080	−1.73259	−0.866294	−	0.499535i	$-0.833504\pi$
$733$	−46.9080	−1.73259	−0.866294	+	0.499535i	$0.833504\pi$
$734$	−31.6411	−1.16789
$735$	−21.9339	−0.809043
$736$	1.20005	0.0442344
$737$	−9.25190	−0.340798
$738$	2.30559	0.0848700
$739$	−12.2853	−0.451923	−0.225961	−	0.974136i	$-0.572552\pi$
$739$	−12.2853	−0.451923	−0.225961	+	0.974136i	$0.572552\pi$
$740$	−0.825276	−0.0303378
$741$	35.5023	1.30421
$742$	48.2117	1.76991
$743$	−32.5017	−1.19237	−0.596186	−	0.802846i	$-0.703318\pi$
$743$	−32.5017	−1.19237	−0.596186	+	0.802846i	$0.703318\pi$
$744$	34.9523	1.28141
$745$	8.89691	0.325957
$746$	21.5005	0.787190
$747$	−3.20869	−0.117400
$748$	8.28686	0.302998
$749$	7.97248	0.291308
$750$	10.1674	0.371262
$751$	−7.11673	−0.259693	−0.129847	−	0.991534i	$-0.541448\pi$
$751$	−7.11673	−0.259693	−0.129847	+	0.991534i	$0.541448\pi$
$752$	2.26201	0.0824872
$753$	−16.5026	−0.601387
$754$	−5.01239	−0.182540
$755$	−5.15702	−0.187683
$756$	31.9500	1.16201
$757$	−37.6086	−1.36691	−0.683453	−	0.729994i	$-0.739523\pi$
$757$	−37.6086	−1.36691	−0.683453	+	0.729994i	$0.739523\pi$
$758$	33.4629	1.21543
$759$	0.559956	0.0203251
$760$	−8.82443	−0.320096
$761$	2.22221	0.0805552	0.0402776	−	0.999189i	$-0.487176\pi$
$761$	2.22221	0.0805552	0.0402776	+	0.999189i	$0.487176\pi$
$762$	6.60615	0.239316
$763$	−5.07808	−0.183839
$764$	1.02730	0.0371664
$765$	−1.02830	−0.0371784
$766$	4.70565	0.170022
$767$	−4.27568	−0.154386
$768$	−27.3240	−0.985970
$769$	8.15943	0.294237	0.147118	−	0.989119i	$-0.453000\pi$
$769$	8.15943	0.294237	0.147118	+	0.989119i	$0.453000\pi$
$770$	−5.18126	−0.186720
$771$	−30.8076	−1.10951
$772$	−5.51712	−0.198566
$773$	19.9669	0.718158	0.359079	−	0.933307i	$-0.383091\pi$
$773$	19.9669	0.718158	0.359079	+	0.933307i	$0.383091\pi$
$774$	0.630942	0.0226787
$775$	33.0703	1.18792
$776$	31.6010	1.13441
$777$	−8.32111	−0.298518
$778$	−3.72912	−0.133695
$779$	34.1135	1.22224
$780$	−6.85455	−0.245432
$781$	17.4082	0.622913
$782$	−0.920577	−0.0329198
$783$	−5.85488	−0.209236
$784$	−6.42018	−0.229292
$785$	8.15242	0.290972
$786$	−28.9825	−1.03377
$787$	27.1058	0.966217	0.483108	−	0.875561i	$-0.339508\pi$
$787$	27.1058	0.966217	0.483108	+	0.875561i	$0.339508\pi$
$788$	−6.13726	−0.218631
$789$	−0.530135	−0.0188733
$790$	2.47030	0.0878893
$791$	−15.2293	−0.541490
$792$	1.42418	0.0506062
$793$	19.3800	0.688204
$794$	10.9485	0.388549
$795$	−12.0818	−0.428499
$796$	4.10416	0.145468
$797$	25.3949	0.899532	0.449766	−	0.893146i	$-0.351507\pi$
$797$	25.3949	0.899532	0.449766	+	0.893146i	$0.351507\pi$
$798$	−32.6315	−1.15514
$799$	30.3384	1.07330
$800$	−24.6253	−0.870635
$801$	4.74253	0.167569
$802$	−35.9601	−1.26979
$803$	21.6194	0.762931
$804$	11.2500	0.396758
$805$	−0.792083	−0.0279172
$806$	34.2326	1.20579
$807$	−32.8441	−1.15617
$808$	−27.7047	−0.974647
$809$	49.3128	1.73374	0.866872	−	0.498531i	$-0.166127\pi$
$809$	49.3128	1.73374	0.866872	+	0.498531i	$0.166127\pi$
$810$	5.20069	0.182734
$811$	47.3471	1.66258	0.831291	−	0.555837i	$-0.187602\pi$
$811$	47.3471	1.66258	0.831291	+	0.555837i	$0.187602\pi$
$812$	−6.34000	−0.222490
$813$	28.9579	1.01560
$814$	−1.43205	−0.0501933
$815$	−10.5101	−0.368152
$816$	2.56662	0.0898497
$817$	9.33540	0.326604
$818$	4.67609	0.163496
$819$	8.10500	0.283212
$820$	−6.58641	−0.230007
$821$	−31.4883	−1.09895	−0.549475	−	0.835510i	$-0.685172\pi$
$821$	−31.4883	−1.09895	−0.549475	+	0.835510i	$0.685172\pi$
$822$	1.49005	0.0519715
$823$	−41.6174	−1.45069	−0.725346	−	0.688385i	$-0.758320\pi$
$823$	−41.6174	−1.45069	−0.725346	+	0.688385i	$0.758320\pi$
$824$	−24.5300	−0.854544
$825$	−11.4904	−0.400045
$826$	3.92993	0.136740
$827$	8.66570	0.301336	0.150668	−	0.988584i	$-0.451858\pi$
$827$	8.66570	0.301336	0.150668	+	0.988584i	$0.451858\pi$
$828$	0.0798489	0.00277494
$829$	−39.9907	−1.38893	−0.694467	−	0.719524i	$-0.744360\pi$
$829$	−39.9907	−1.38893	−0.694467	+	0.719524i	$0.744360\pi$
$830$	−6.66085	−0.231202
$831$	26.8958	0.933005
$832$	−28.9551	−1.00384
$833$	−86.1083	−2.98348
$834$	−12.8605	−0.445324
$835$	6.70599	0.232070
$836$	7.72819	0.267285
$837$	39.9865	1.38213
$838$	−22.0814	−0.762789
$839$	−20.1318	−0.695026	−0.347513	−	0.937675i	$-0.612974\pi$
$839$	−20.1318	−0.695026	−0.347513	+	0.937675i	$0.612974\pi$
$840$	17.1787	0.592722
$841$	−27.8382	−0.959938
$842$	23.1232	0.796878
$843$	−16.1079	−0.554787
$844$	−9.89611	−0.340638
$845$	−9.04287	−0.311084
$846$	1.91222	0.0657433
$847$	−43.4864	−1.49421
$848$	−3.53643	−0.121442
$849$	1.12201	0.0385074
$850$	18.8904	0.647936
$851$	−0.218924	−0.00750461
$852$	−21.1678	−0.725197
$853$	−9.87869	−0.338240	−0.169120	−	0.985595i	$-0.554093\pi$
$853$	−9.87869	−0.338240	−0.169120	+	0.985595i	$0.554093\pi$
$854$	−17.8128	−0.609543
$855$	−0.958979	−0.0327964
$856$	−4.54910	−0.155485
$857$	−17.2445	−0.589061	−0.294531	−	0.955642i	$-0.595163\pi$
$857$	−17.2445	−0.589061	−0.294531	+	0.955642i	$0.595163\pi$
$858$	−11.8943	−0.406064
$859$	−30.8048	−1.05105	−0.525523	−	0.850779i	$-0.676130\pi$
$859$	−30.8048	−1.05105	−0.525523	+	0.850779i	$0.676130\pi$
$860$	−1.80242	−0.0614619
$861$	−66.4096	−2.26323
$862$	30.2533	1.03043
$863$	−37.4821	−1.27591	−0.637953	−	0.770075i	$-0.720219\pi$
$863$	−37.4821	−1.27591	−0.637953	+	0.770075i	$0.720219\pi$
$864$	−29.7753	−1.01298
$865$	4.61393	0.156878
$866$	15.5963	0.529983
$867$	6.56708	0.223030
$868$	43.2996	1.46969
$869$	−5.89893	−0.200107
$870$	−1.15453	−0.0391422
$871$	30.0435	1.01798
$872$	2.89756	0.0981236
$873$	3.43419	0.116230
$874$	−0.858515	−0.0290397
$875$	34.3441	1.16104
$876$	−26.2885	−0.888206
$877$	−6.02415	−0.203421	−0.101711	−	0.994814i	$-0.532432\pi$
$877$	−6.02415	−0.203421	−0.101711	+	0.994814i	$0.532432\pi$
$878$	33.4192	1.12784
$879$	−53.5497	−1.80619
$880$	0.380057	0.0128117
$881$	−10.7550	−0.362344	−0.181172	−	0.983451i	$-0.557989\pi$
$881$	−10.7550	−0.362344	−0.181172	+	0.983451i	$0.557989\pi$
$882$	−5.42737	−0.182749
$883$	13.2178	0.444813	0.222407	−	0.974954i	$-0.428609\pi$
$883$	13.2178	0.444813	0.222407	+	0.974954i	$0.428609\pi$
$884$	−26.9097	−0.905071
$885$	−0.984841	−0.0331051
$886$	−26.0958	−0.876704
$887$	−10.5877	−0.355499	−0.177749	−	0.984076i	$-0.556882\pi$
$887$	−10.5877	−0.355499	−0.177749	+	0.984076i	$0.556882\pi$
$888$	4.74803	0.159333
$889$	22.3146	0.748407
$890$	9.84490	0.330002
$891$	−12.4189	−0.416050
$892$	−24.5694	−0.822645
$893$	28.2931	0.946793
$894$	−18.7724	−0.627845
$895$	−11.8680	−0.396703
$896$	−29.0582	−0.970768
$897$	−1.81833	−0.0607123
$898$	22.2472	0.742400
$899$	−7.93471	−0.264637
$900$	−1.63852	−0.0546172
$901$	−47.4311	−1.58016
$902$	−11.4290	−0.380544
$903$	−18.1734	−0.604774
$904$	8.68982	0.289019
$905$	−2.85714	−0.0949745
$906$	10.8813	0.361507
$907$	−24.2342	−0.804684	−0.402342	−	0.915489i	$-0.631804\pi$
$907$	−24.2342	−0.804684	−0.402342	+	0.915489i	$0.631804\pi$
$908$	11.0871	0.367938
$909$	−3.01076	−0.0998605
$910$	16.8250	0.557743
$911$	−48.0597	−1.59229	−0.796145	−	0.605106i	$-0.793131\pi$
$911$	−48.0597	−1.59229	−0.796145	+	0.605106i	$0.793131\pi$
$912$	2.39359	0.0792596
$913$	15.9057	0.526403
$914$	−5.14974	−0.170338
$915$	4.46390	0.147572
$916$	22.6582	0.748648
$917$	−97.8986	−3.23290
$918$	22.8411	0.753869
$919$	30.9954	1.02244	0.511222	−	0.859449i	$-0.329193\pi$
$919$	30.9954	1.02244	0.511222	+	0.859449i	$0.329193\pi$
$920$	0.451963	0.0149008
$921$	−27.0625	−0.891739
$922$	11.0147	0.362749
$923$	−56.5291	−1.86068
$924$	−15.0447	−0.494933
$925$	4.49236	0.147708
$926$	33.5475	1.10244
$927$	−2.66576	−0.0875550
$928$	5.90846	0.193955
$929$	28.1553	0.923746	0.461873	−	0.886946i	$-0.347178\pi$
$929$	28.1553	0.923746	0.461873	+	0.886946i	$0.347178\pi$
$930$	7.88498	0.258559
$931$	−80.3032	−2.63183
$932$	−13.6364	−0.446676
$933$	23.5465	0.770879
$934$	17.4174	0.569915
$935$	5.09737	0.166702
$936$	−4.62472	−0.151164
$937$	−28.0815	−0.917383	−0.458692	−	0.888596i	$-0.651682\pi$
$937$	−28.0815	−0.917383	−0.458692	+	0.888596i	$0.651682\pi$
$938$	−27.6140	−0.901630
$939$	29.7143	0.969689
$940$	−5.46265	−0.178172
$941$	−47.8562	−1.56007	−0.780034	−	0.625737i	$-0.784798\pi$
$941$	−47.8562	−1.56007	−0.780034	+	0.625737i	$0.784798\pi$
$942$	−17.2016	−0.560458
$943$	−1.74720	−0.0568966
$944$	−0.288269	−0.00938237
$945$	19.6529	0.639310
$946$	−3.12762	−0.101688
$947$	−26.1602	−0.850093	−0.425047	−	0.905171i	$-0.639742\pi$
$947$	−26.1602	−0.850093	−0.425047	+	0.905171i	$0.639742\pi$
$948$	7.17292	0.232966
$949$	−70.2040	−2.27892
$950$	17.6169	0.571568
$951$	10.8478	0.351763
$952$	67.4405	2.18576
$953$	54.4868	1.76500	0.882500	−	0.470313i	$-0.155859\pi$
$953$	54.4868	1.76500	0.882500	+	0.470313i	$0.155859\pi$
$954$	−2.98956	−0.0967905
$955$	0.631908	0.0204480
$956$	−18.5112	−0.598694
$957$	2.75695	0.0891195
$958$	21.9685	0.709771
$959$	5.03317	0.162529
$960$	−6.66939	−0.215254
$961$	23.1908	0.748092
$962$	4.65026	0.149930
$963$	−0.494366	−0.0159307
$964$	24.5067	0.789308
$965$	−3.39367	−0.109246
$966$	1.67129	0.0537729
$967$	35.3839	1.13787	0.568935	−	0.822383i	$-0.307356\pi$
$967$	35.3839	1.13787	0.568935	+	0.822383i	$0.307356\pi$
$968$	24.8133	0.797531
$969$	32.1031	1.03130
$970$	7.12895	0.228897
$971$	32.6169	1.04673	0.523363	−	0.852110i	$-0.324677\pi$
$971$	32.6169	1.04673	0.523363	+	0.852110i	$0.324677\pi$
$972$	−3.77418	−0.121057
$973$	−43.4410	−1.39265
$974$	−21.9098	−0.702036
$975$	37.3125	1.19496
$976$	1.30661	0.0418236
$977$	−46.2049	−1.47823	−0.739113	−	0.673582i	$-0.764755\pi$
$977$	−46.2049	−1.47823	−0.739113	+	0.673582i	$0.764755\pi$
$978$	22.1763	0.709119
$979$	−23.5090	−0.751352
$980$	15.5044	0.495270
$981$	0.314887	0.0100536
$982$	−25.7294	−0.821059
$983$	6.28046	0.200315	0.100158	−	0.994972i	$-0.468065\pi$
$983$	6.28046	0.200315	0.100158	+	0.994972i	$0.468065\pi$
$984$	37.8933	1.20800
$985$	−3.77512	−0.120285
$986$	−4.53247	−0.144343
$987$	−55.0789	−1.75318
$988$	−25.0956	−0.798396
$989$	−0.478133	−0.0152037
$990$	0.321285	0.0102111
$991$	−25.5369	−0.811206	−0.405603	−	0.914049i	$-0.632938\pi$
$991$	−25.5369	−0.811206	−0.405603	+	0.914049i	$0.632938\pi$
$992$	−40.3524	−1.28119
$993$	44.4455	1.41044
$994$	51.9579	1.64800
$995$	2.52453	0.0800330
$996$	−19.3409	−0.612840
$997$	34.7888	1.10177	0.550886	−	0.834580i	$-0.314290\pi$
$997$	34.7888	1.10177	0.550886	+	0.834580i	$0.314290\pi$
$998$	25.7987	0.816644
$999$	5.43188	0.171857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.53	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.53	✓	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)

\(f(q)\)	\(=\)	\(q+0.917442 q^{2} +1.63863 q^{3} -1.15830 q^{4} -0.712488 q^{5} +1.50335 q^{6} +5.07808 q^{7} -2.89756 q^{8} -0.314887 q^{9} +O(q^{10})\)	\(q+0.917442 q^{2} +1.63863 q^{3} -1.15830 q^{4} -0.712488 q^{5} +1.50335 q^{6} +5.07808 q^{7} -2.89756 q^{8} -0.314887 q^{9} -0.653666 q^{10} +1.56092 q^{11} -1.89803 q^{12} -5.06872 q^{13} +4.65885 q^{14} -1.16751 q^{15} -0.341737 q^{16} -4.58341 q^{17} -0.288890 q^{18} -4.27442 q^{19} +0.825276 q^{20} +8.32111 q^{21} +1.43205 q^{22} +0.218924 q^{23} -4.74803 q^{24} -4.49236 q^{25} -4.65026 q^{26} -5.43188 q^{27} -5.88195 q^{28} +1.07787 q^{29} -1.07112 q^{30} -7.36144 q^{31} +5.48159 q^{32} +2.55777 q^{33} -4.20501 q^{34} -3.61808 q^{35} +0.364734 q^{36} -1.00000 q^{37} -3.92153 q^{38} -8.30577 q^{39} +2.06448 q^{40} -7.98086 q^{41} +7.63413 q^{42} -2.18402 q^{43} -1.80801 q^{44} +0.224353 q^{45} +0.200850 q^{46} -6.61918 q^{47} -0.559980 q^{48} +18.7869 q^{49} -4.12148 q^{50} -7.51052 q^{51} +5.87111 q^{52} +10.3484 q^{53} -4.98343 q^{54} -1.11213 q^{55} -14.7140 q^{56} -7.00419 q^{57} +0.988886 q^{58} +0.843542 q^{59} +1.35232 q^{60} -3.82345 q^{61} -6.75369 q^{62} -1.59902 q^{63} +5.71251 q^{64} +3.61141 q^{65} +2.34660 q^{66} -5.92723 q^{67} +5.30897 q^{68} +0.358735 q^{69} -3.31937 q^{70} +11.1525 q^{71} +0.912403 q^{72} +13.8504 q^{73} -0.917442 q^{74} -7.36132 q^{75} +4.95106 q^{76} +7.92647 q^{77} -7.62006 q^{78} -3.77914 q^{79} +0.243483 q^{80} -7.95619 q^{81} -7.32197 q^{82} +10.1900 q^{83} -9.63835 q^{84} +3.26563 q^{85} -2.00371 q^{86} +1.76624 q^{87} -4.52284 q^{88} -15.0610 q^{89} +0.205831 q^{90} -25.7394 q^{91} -0.253580 q^{92} -12.0627 q^{93} -6.07271 q^{94} +3.04547 q^{95} +8.98231 q^{96} -10.9061 q^{97} +17.2359 q^{98} -0.491512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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