LMFDB - Embedded newform 4015.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64676 q^{2} -3.26170 q^{3} +5.00536 q^{4} +1.00000 q^{5} +8.63297 q^{6} +0.334745 q^{7} -7.95449 q^{8} +7.63872 q^{9} +O(q^{10})$	\(q-2.64676 q^{2} -3.26170 q^{3} +5.00536 q^{4} +1.00000 q^{5} +8.63297 q^{6} +0.334745 q^{7} -7.95449 q^{8} +7.63872 q^{9} -2.64676 q^{10} -1.00000 q^{11} -16.3260 q^{12} +1.71876 q^{13} -0.885992 q^{14} -3.26170 q^{15} +11.0429 q^{16} -2.47153 q^{17} -20.2179 q^{18} -8.31191 q^{19} +5.00536 q^{20} -1.09184 q^{21} +2.64676 q^{22} -7.20192 q^{23} +25.9452 q^{24} +1.00000 q^{25} -4.54917 q^{26} -15.1301 q^{27} +1.67552 q^{28} +5.37978 q^{29} +8.63297 q^{30} -6.67599 q^{31} -13.3191 q^{32} +3.26170 q^{33} +6.54156 q^{34} +0.334745 q^{35} +38.2346 q^{36} -10.6409 q^{37} +21.9997 q^{38} -5.60610 q^{39} -7.95449 q^{40} +6.65088 q^{41} +2.88984 q^{42} -10.7929 q^{43} -5.00536 q^{44} +7.63872 q^{45} +19.0618 q^{46} +5.79001 q^{47} -36.0188 q^{48} -6.88795 q^{49} -2.64676 q^{50} +8.06140 q^{51} +8.60304 q^{52} +5.13950 q^{53} +40.0459 q^{54} -1.00000 q^{55} -2.66273 q^{56} +27.1110 q^{57} -14.2390 q^{58} -0.128618 q^{59} -16.3260 q^{60} -0.465246 q^{61} +17.6698 q^{62} +2.55702 q^{63} +13.1666 q^{64} +1.71876 q^{65} -8.63297 q^{66} +1.92942 q^{67} -12.3709 q^{68} +23.4905 q^{69} -0.885992 q^{70} -1.39231 q^{71} -60.7621 q^{72} -1.00000 q^{73} +28.1640 q^{74} -3.26170 q^{75} -41.6041 q^{76} -0.334745 q^{77} +14.8380 q^{78} -1.15788 q^{79} +11.0429 q^{80} +26.4339 q^{81} -17.6033 q^{82} +12.0680 q^{83} -5.46506 q^{84} -2.47153 q^{85} +28.5662 q^{86} -17.5473 q^{87} +7.95449 q^{88} +16.4990 q^{89} -20.2179 q^{90} +0.575348 q^{91} -36.0482 q^{92} +21.7751 q^{93} -15.3248 q^{94} -8.31191 q^{95} +43.4429 q^{96} +12.3470 q^{97} +18.2308 q^{98} -7.63872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) $ 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * 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 $

$2$	−2.64676	−1.87155	−0.935773	−	0.352604i	$-0.885296\pi$
$2$	−2.64676	−1.87155	−0.935773	+	0.352604i	$0.885296\pi$
$3$	−3.26170	−1.88315	−0.941573	−	0.336809i	$-0.890652\pi$
$3$	−3.26170	−1.88315	−0.941573	+	0.336809i	$0.890652\pi$
$4$	5.00536	2.50268
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	8.63297	3.52439
$7$	0.334745	0.126522	0.0632609	−	0.997997i	$-0.479850\pi$
$7$	0.334745	0.126522	0.0632609	+	0.997997i	$0.479850\pi$
$8$	−7.95449	−2.81234
$9$	7.63872	2.54624
$10$	−2.64676	−0.836980
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−16.3260	−4.71292
$13$	1.71876	0.476700	0.238350	−	0.971179i	$-0.423394\pi$
$13$	1.71876	0.476700	0.238350	+	0.971179i	$0.423394\pi$
$14$	−0.885992	−0.236791
$15$	−3.26170	−0.842169
$16$	11.0429	2.76073
$17$	−2.47153	−0.599434	−0.299717	−	0.954028i	$-0.596892\pi$
$17$	−2.47153	−0.599434	−0.299717	+	0.954028i	$0.596892\pi$
$18$	−20.2179	−4.76540
$19$	−8.31191	−1.90688	−0.953441	−	0.301579i	$-0.902486\pi$
$19$	−8.31191	−1.90688	−0.953441	+	0.301579i	$0.902486\pi$
$20$	5.00536	1.11923
$21$	−1.09184	−0.238259
$22$	2.64676	0.564292
$23$	−7.20192	−1.50170	−0.750852	−	0.660470i	$-0.770357\pi$
$23$	−7.20192	−1.50170	−0.750852	+	0.660470i	$0.770357\pi$
$24$	25.9452	5.29604
$25$	1.00000	0.200000
$26$	−4.54917	−0.892165
$27$	−15.1301	−2.91179
$28$	1.67552	0.316644
$29$	5.37978	0.999000	0.499500	−	0.866314i	$-0.333517\pi$
$29$	5.37978	0.999000	0.499500	+	0.866314i	$0.333517\pi$
$30$	8.63297	1.57616
$31$	−6.67599	−1.19904	−0.599521	−	0.800359i	$-0.704642\pi$
$31$	−6.67599	−1.19904	−0.599521	+	0.800359i	$0.704642\pi$
$32$	−13.3191	−2.35450
$33$	3.26170	0.567790
$34$	6.54156	1.12187
$35$	0.334745	0.0565823
$36$	38.2346	6.37243
$37$	−10.6409	−1.74936	−0.874679	−	0.484702i	$-0.838928\pi$
$37$	−10.6409	−1.74936	−0.874679	+	0.484702i	$0.838928\pi$
$38$	21.9997	3.56882
$39$	−5.60610	−0.897695
$40$	−7.95449	−1.25772
$41$	6.65088	1.03869	0.519346	−	0.854564i	$-0.326176\pi$
$41$	6.65088	1.03869	0.519346	+	0.854564i	$0.326176\pi$
$42$	2.88984	0.445913
$43$	−10.7929	−1.64590	−0.822950	−	0.568114i	$-0.807673\pi$
$43$	−10.7929	−1.64590	−0.822950	+	0.568114i	$0.807673\pi$
$44$	−5.00536	−0.754587
$45$	7.63872	1.13871
$46$	19.0618	2.81051
$47$	5.79001	0.844560	0.422280	−	0.906465i	$-0.361230\pi$
$47$	5.79001	0.844560	0.422280	+	0.906465i	$0.361230\pi$
$48$	−36.0188	−5.19887
$49$	−6.88795	−0.983992
$50$	−2.64676	−0.374309
$51$	8.06140	1.12882
$52$	8.60304	1.19303
$53$	5.13950	0.705965	0.352982	−	0.935630i	$-0.385168\pi$
$53$	5.13950	0.705965	0.352982	+	0.935630i	$0.385168\pi$
$54$	40.0459	5.44956
$55$	−1.00000	−0.134840
$56$	−2.66273	−0.355822
$57$	27.1110	3.59094
$58$	−14.2390	−1.86967
$59$	−0.128618	−0.0167446	−0.00837232	−	0.999965i	$-0.502665\pi$
$59$	−0.128618	−0.0167446	−0.00837232	+	0.999965i	$0.502665\pi$
$60$	−16.3260	−2.10768
$61$	−0.465246	−0.0595687	−0.0297843	−	0.999556i	$-0.509482\pi$
$61$	−0.465246	−0.0595687	−0.0297843	+	0.999556i	$0.509482\pi$
$62$	17.6698	2.24406
$63$	2.55702	0.322155
$64$	13.1666	1.64582
$65$	1.71876	0.213187
$66$	−8.63297	−1.06264
$67$	1.92942	0.235717	0.117858	−	0.993030i	$-0.462397\pi$
$67$	1.92942	0.235717	0.117858	+	0.993030i	$0.462397\pi$
$68$	−12.3709	−1.50019
$69$	23.4905	2.82793
$70$	−0.885992	−0.105896
$71$	−1.39231	−0.165237	−0.0826183	−	0.996581i	$-0.526328\pi$
$71$	−1.39231	−0.165237	−0.0826183	+	0.996581i	$0.526328\pi$
$72$	−60.7621	−7.16088
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	28.1640	3.27400
$75$	−3.26170	−0.376629
$76$	−41.6041	−4.77232
$77$	−0.334745	−0.0381478
$78$	14.8380	1.68008
$79$	−1.15788	−0.130272	−0.0651361	−	0.997876i	$-0.520748\pi$
$79$	−1.15788	−0.130272	−0.0651361	+	0.997876i	$0.520748\pi$
$80$	11.0429	1.23464
$81$	26.4339	2.93710
$82$	−17.6033	−1.94396
$83$	12.0680	1.32463	0.662316	−	0.749225i	$-0.269574\pi$
$83$	12.0680	1.32463	0.662316	+	0.749225i	$0.269574\pi$
$84$	−5.46506	−0.596287
$85$	−2.47153	−0.268075
$86$	28.5662	3.08038
$87$	−17.5473	−1.88126
$88$	7.95449	0.847951
$89$	16.4990	1.74889	0.874447	−	0.485121i	$-0.161225\pi$
$89$	16.4990	1.74889	0.874447	+	0.485121i	$0.161225\pi$
$90$	−20.2179	−2.13115
$91$	0.575348	0.0603129
$92$	−36.0482	−3.75829
$93$	21.7751	2.25797
$94$	−15.3248	−1.58063
$95$	−8.31191	−0.852784
$96$	43.4429	4.43387
$97$	12.3470	1.25365	0.626826	−	0.779159i	$-0.284354\pi$
$97$	12.3470	1.25365	0.626826	+	0.779159i	$0.284354\pi$
$98$	18.2308	1.84159
$99$	−7.63872	−0.767720
$100$	5.00536	0.500536
$101$	−16.8821	−1.67983	−0.839916	−	0.542716i	$-0.817396\pi$
$101$	−16.8821	−1.67983	−0.839916	+	0.542716i	$0.817396\pi$
$102$	−21.3366	−2.11264
$103$	−5.23963	−0.516277	−0.258138	−	0.966108i	$-0.583109\pi$
$103$	−5.23963	−0.516277	−0.258138	+	0.966108i	$0.583109\pi$
$104$	−13.6719	−1.34064
$105$	−1.09184	−0.106553
$106$	−13.6030	−1.32124
$107$	−2.74598	−0.265464	−0.132732	−	0.991152i	$-0.542375\pi$
$107$	−2.74598	−0.265464	−0.132732	+	0.991152i	$0.542375\pi$
$108$	−75.7318	−7.28730
$109$	−14.6169	−1.40005	−0.700023	−	0.714120i	$-0.746827\pi$
$109$	−14.6169	−1.40005	−0.700023	+	0.714120i	$0.746827\pi$
$110$	2.64676	0.252359
$111$	34.7076	3.29430
$112$	3.69657	0.349293
$113$	15.0235	1.41330	0.706648	−	0.707566i	$-0.250207\pi$
$113$	15.0235	1.41330	0.706648	+	0.707566i	$0.250207\pi$
$114$	−71.7564	−6.72060
$115$	−7.20192	−0.671583
$116$	26.9278	2.50018
$117$	13.1292	1.21379
$118$	0.340422	0.0313384
$119$	−0.827333	−0.0758415
$120$	25.9452	2.36846
$121$	1.00000	0.0909091
$122$	1.23140	0.111486
$123$	−21.6932	−1.95601
$124$	−33.4157	−3.00082
$125$	1.00000	0.0894427
$126$	−6.76784	−0.602927
$127$	−1.60143	−0.142104	−0.0710520	−	0.997473i	$-0.522636\pi$
$127$	−1.60143	−0.142104	−0.0710520	+	0.997473i	$0.522636\pi$
$128$	−8.21070	−0.725730
$129$	35.2032	3.09947
$130$	−4.54917	−0.398988
$131$	−13.0807	−1.14286	−0.571432	−	0.820649i	$-0.693612\pi$
$131$	−13.0807	−1.14286	−0.571432	+	0.820649i	$0.693612\pi$
$132$	16.3260	1.42100
$133$	−2.78237	−0.241262
$134$	−5.10673	−0.441155
$135$	−15.1301	−1.30219
$136$	19.6598	1.68581
$137$	−12.4420	−1.06300	−0.531498	−	0.847060i	$-0.678371\pi$
$137$	−12.4420	−1.06300	−0.531498	+	0.847060i	$0.678371\pi$
$138$	−62.1739	−5.29260
$139$	5.67569	0.481405	0.240703	−	0.970599i	$-0.422622\pi$
$139$	5.67569	0.481405	0.240703	+	0.970599i	$0.422622\pi$
$140$	1.67552	0.141607
$141$	−18.8853	−1.59043
$142$	3.68511	0.309248
$143$	−1.71876	−0.143730
$144$	84.3539	7.02949
$145$	5.37978	0.446767
$146$	2.64676	0.219048
$147$	22.4664	1.85300
$148$	−53.2617	−4.37809
$149$	−15.4095	−1.26240	−0.631198	−	0.775622i	$-0.717436\pi$
$149$	−15.4095	−1.26240	−0.631198	+	0.775622i	$0.717436\pi$
$150$	8.63297	0.704879
$151$	2.28735	0.186142	0.0930709	−	0.995659i	$-0.470332\pi$
$151$	2.28735	0.186142	0.0930709	+	0.995659i	$0.470332\pi$
$152$	66.1170	5.36280
$153$	−18.8793	−1.52630
$154$	0.885992	0.0713953
$155$	−6.67599	−0.536228
$156$	−28.0606	−2.24665
$157$	−9.90240	−0.790298	−0.395149	−	0.918617i	$-0.629307\pi$
$157$	−9.90240	−0.790298	−0.395149	+	0.918617i	$0.629307\pi$
$158$	3.06465	0.243810
$159$	−16.7635	−1.32943
$160$	−13.3191	−1.05297
$161$	−2.41081	−0.189998
$162$	−69.9642	−5.49691
$163$	25.3132	1.98268	0.991341	−	0.131316i	$-0.0419203\pi$
$163$	25.3132	1.98268	0.991341	+	0.131316i	$0.0419203\pi$
$164$	33.2901	2.59952
$165$	3.26170	0.253923
$166$	−31.9411	−2.47911
$167$	−17.4632	−1.35134	−0.675670	−	0.737204i	$-0.736146\pi$
$167$	−17.4632	−1.35134	−0.675670	+	0.737204i	$0.736146\pi$
$168$	8.68503	0.670065
$169$	−10.0458	−0.772757
$170$	6.54156	0.501715
$171$	−63.4923	−4.85538
$172$	−54.0223	−4.11916
$173$	−8.46565	−0.643632	−0.321816	−	0.946802i	$-0.604293\pi$
$173$	−8.46565	−0.643632	−0.321816	+	0.946802i	$0.604293\pi$
$174$	46.4435	3.52087
$175$	0.334745	0.0253044
$176$	−11.0429	−0.832393
$177$	0.419514	0.0315326
$178$	−43.6690	−3.27313
$179$	22.9150	1.71274	0.856372	−	0.516359i	$-0.172713\pi$
$179$	22.9150	1.71274	0.856372	+	0.516359i	$0.172713\pi$
$180$	38.2346	2.84984
$181$	8.10616	0.602526	0.301263	−	0.953541i	$-0.402592\pi$
$181$	8.10616	0.602526	0.301263	+	0.953541i	$0.402592\pi$
$182$	−1.52281	−0.112878
$183$	1.51750	0.112177
$184$	57.2876	4.22330
$185$	−10.6409	−0.782337
$186$	−57.6336	−4.22590
$187$	2.47153	0.180736
$188$	28.9811	2.11366
$189$	−5.06474	−0.368406
$190$	21.9997	1.59602
$191$	20.0445	1.45037	0.725184	−	0.688555i	$-0.241755\pi$
$191$	20.0445	1.45037	0.725184	+	0.688555i	$0.241755\pi$
$192$	−42.9455	−3.09933
$193$	10.1571	0.731124	0.365562	−	0.930787i	$-0.380877\pi$
$193$	10.1571	0.731124	0.365562	+	0.930787i	$0.380877\pi$
$194$	−32.6797	−2.34627
$195$	−5.60610	−0.401461
$196$	−34.4767	−2.46262
$197$	−12.4534	−0.887270	−0.443635	−	0.896207i	$-0.646311\pi$
$197$	−12.4534	−0.887270	−0.443635	+	0.896207i	$0.646311\pi$
$198$	20.2179	1.43682
$199$	−0.484852	−0.0343703	−0.0171851	−	0.999852i	$-0.505470\pi$
$199$	−0.484852	−0.0343703	−0.0171851	+	0.999852i	$0.505470\pi$
$200$	−7.95449	−0.562467
$201$	−6.29321	−0.443889
$202$	44.6830	3.14388
$203$	1.80086	0.126395
$204$	40.3502	2.82508
$205$	6.65088	0.464517
$206$	13.8681	0.966235
$207$	−55.0135	−3.82370
$208$	18.9802	1.31604
$209$	8.31191	0.574947
$210$	2.88984	0.199418
$211$	17.9238	1.23393	0.616964	−	0.786991i	$-0.288362\pi$
$211$	17.9238	1.23393	0.616964	+	0.786991i	$0.288362\pi$
$212$	25.7251	1.76680
$213$	4.54130	0.311165
$214$	7.26797	0.496828
$215$	−10.7929	−0.736069
$216$	120.352	8.18895
$217$	−2.23476	−0.151705
$218$	38.6875	2.62025
$219$	3.26170	0.220406
$220$	−5.00536	−0.337462
$221$	−4.24798	−0.285750
$222$	−91.8628	−6.16543
$223$	9.84726	0.659421	0.329711	−	0.944082i	$-0.393049\pi$
$223$	9.84726	0.659421	0.329711	+	0.944082i	$0.393049\pi$
$224$	−4.45850	−0.297896
$225$	7.63872	0.509248
$226$	−39.7638	−2.64505
$227$	9.05477	0.600986	0.300493	−	0.953784i	$-0.402849\pi$
$227$	9.05477	0.600986	0.300493	+	0.953784i	$0.402849\pi$
$228$	135.700	8.98698
$229$	−27.4692	−1.81522	−0.907609	−	0.419817i	$-0.862094\pi$
$229$	−27.4692	−1.81522	−0.907609	+	0.419817i	$0.862094\pi$
$230$	19.0618	1.25690
$231$	1.09184	0.0718378
$232$	−42.7934	−2.80953
$233$	−14.7856	−0.968636	−0.484318	−	0.874892i	$-0.660932\pi$
$233$	−14.7856	−0.968636	−0.484318	+	0.874892i	$0.660932\pi$
$234$	−34.7498	−2.27167
$235$	5.79001	0.377699
$236$	−0.643780	−0.0419065
$237$	3.77668	0.245321
$238$	2.18976	0.141941
$239$	−14.0158	−0.906609	−0.453304	−	0.891356i	$-0.649755\pi$
$239$	−14.0158	−0.906609	−0.453304	+	0.891356i	$0.649755\pi$
$240$	−36.0188	−2.32500
$241$	−5.85756	−0.377318	−0.188659	−	0.982043i	$-0.560414\pi$
$241$	−5.85756	−0.377318	−0.188659	+	0.982043i	$0.560414\pi$
$242$	−2.64676	−0.170140
$243$	−40.8291	−2.61919
$244$	−2.32873	−0.149081
$245$	−6.88795	−0.440055
$246$	57.4168	3.66076
$247$	−14.2862	−0.909010
$248$	53.1041	3.37211
$249$	−39.3621	−2.49447
$250$	−2.64676	−0.167396
$251$	4.49149	0.283501	0.141750	−	0.989902i	$-0.454727\pi$
$251$	4.49149	0.283501	0.141750	+	0.989902i	$0.454727\pi$
$252$	12.7988	0.806251
$253$	7.20192	0.452781
$254$	4.23861	0.265954
$255$	8.06140	0.504825
$256$	−4.60138	−0.287586
$257$	9.64660	0.601738	0.300869	−	0.953665i	$-0.402723\pi$
$257$	9.64660	0.601738	0.300869	+	0.953665i	$0.402723\pi$
$258$	−93.1746	−5.80080
$259$	−3.56200	−0.221332
$260$	8.60304	0.533538
$261$	41.0946	2.54369
$262$	34.6215	2.13892
$263$	9.88946	0.609810	0.304905	−	0.952383i	$-0.401375\pi$
$263$	9.88946	0.609810	0.304905	+	0.952383i	$0.401375\pi$
$264$	−25.9452	−1.59682
$265$	5.13950	0.315717
$266$	7.36428	0.451533
$267$	−53.8150	−3.29342
$268$	9.65747	0.589924
$269$	6.39410	0.389855	0.194927	−	0.980818i	$-0.437553\pi$
$269$	6.39410	0.389855	0.194927	+	0.980818i	$0.437553\pi$
$270$	40.0459	2.43712
$271$	0.268608	0.0163168	0.00815840	−	0.999967i	$-0.497403\pi$
$271$	0.268608	0.0163168	0.00815840	+	0.999967i	$0.497403\pi$
$272$	−27.2930	−1.65488
$273$	−1.87662	−0.113578
$274$	32.9312	1.98944
$275$	−1.00000	−0.0603023
$276$	117.579	7.07741
$277$	30.7863	1.84977	0.924883	−	0.380251i	$-0.124162\pi$
$277$	30.7863	1.84977	0.924883	+	0.380251i	$0.124162\pi$
$278$	−15.0222	−0.900972
$279$	−50.9960	−3.05305
$280$	−2.66273	−0.159128
$281$	−17.5451	−1.04665	−0.523327	−	0.852132i	$-0.675309\pi$
$281$	−17.5451	−1.04665	−0.523327	+	0.852132i	$0.675309\pi$
$282$	49.9850	2.97656
$283$	14.6953	0.873546	0.436773	−	0.899572i	$-0.356121\pi$
$283$	14.6953	0.873546	0.436773	+	0.899572i	$0.356121\pi$
$284$	−6.96901	−0.413535
$285$	27.1110	1.60592
$286$	4.54917	0.268998
$287$	2.22635	0.131417
$288$	−101.741	−5.99513
$289$	−10.8915	−0.640679
$290$	−14.2390	−0.836144
$291$	−40.2724	−2.36081
$292$	−5.00536	−0.292917
$293$	−8.07714	−0.471872	−0.235936	−	0.971769i	$-0.575816\pi$
$293$	−8.07714	−0.471872	−0.235936	+	0.971769i	$0.575816\pi$
$294$	−59.4634	−3.46798
$295$	−0.128618	−0.00748843
$296$	84.6432	4.91979
$297$	15.1301	0.877939
$298$	40.7853	2.36263
$299$	−12.3784	−0.715862
$300$	−16.3260	−0.942583
$301$	−3.61287	−0.208242
$302$	−6.05407	−0.348373
$303$	55.0644	3.16337
$304$	−91.7879	−5.26440
$305$	−0.465246	−0.0266399
$306$	49.9691	2.85654
$307$	−4.77495	−0.272521	−0.136260	−	0.990673i	$-0.543508\pi$
$307$	−4.77495	−0.272521	−0.136260	+	0.990673i	$0.543508\pi$
$308$	−1.67552	−0.0954717
$309$	17.0901	0.972224
$310$	17.6698	1.00358
$311$	24.6462	1.39756	0.698779	−	0.715338i	$-0.253727\pi$
$311$	24.6462	1.39756	0.698779	+	0.715338i	$0.253727\pi$
$312$	44.5937	2.52462
$313$	5.04098	0.284933	0.142466	−	0.989800i	$-0.454497\pi$
$313$	5.04098	0.284933	0.142466	+	0.989800i	$0.454497\pi$
$314$	26.2093	1.47908
$315$	2.55702	0.144072
$316$	−5.79563	−0.326030
$317$	−12.3122	−0.691522	−0.345761	−	0.938323i	$-0.612379\pi$
$317$	−12.3122	−0.691522	−0.345761	+	0.938323i	$0.612379\pi$
$318$	44.3691	2.48810
$319$	−5.37978	−0.301210
$320$	13.1666	0.736034
$321$	8.95659	0.499908
$322$	6.38085	0.355591
$323$	20.5431	1.14305
$324$	132.311	7.35062
$325$	1.71876	0.0953399
$326$	−66.9980	−3.71068
$327$	47.6760	2.63649
$328$	−52.9043	−2.92115
$329$	1.93818	0.106855
$330$	−8.63297	−0.475229
$331$	20.7475	1.14038	0.570192	−	0.821511i	$-0.306869\pi$
$331$	20.7475	1.14038	0.570192	+	0.821511i	$0.306869\pi$
$332$	60.4046	3.31513
$333$	−81.2831	−4.45429
$334$	46.2209	2.52909
$335$	1.92942	0.105416
$336$	−12.0571	−0.657770
$337$	19.0649	1.03853	0.519266	−	0.854612i	$-0.326205\pi$
$337$	19.0649	1.03853	0.519266	+	0.854612i	$0.326205\pi$
$338$	26.5890	1.44625
$339$	−49.0023	−2.66144
$340$	−12.3709	−0.670907
$341$	6.67599	0.361525
$342$	168.049	9.08706
$343$	−4.64892	−0.251018
$344$	85.8519	4.62882
$345$	23.4905	1.26469
$346$	22.4066	1.20459
$347$	−1.62562	−0.0872681	−0.0436340	−	0.999048i	$-0.513894\pi$
$347$	−1.62562	−0.0872681	−0.0436340	+	0.999048i	$0.513894\pi$
$348$	−87.8304	−4.70820
$349$	36.5227	1.95501	0.977507	−	0.210901i	$-0.0676397\pi$
$349$	36.5227	1.95501	0.977507	+	0.210901i	$0.0676397\pi$
$350$	−0.885992	−0.0473583
$351$	−26.0051	−1.38805
$352$	13.3191	0.709909
$353$	18.0654	0.961523	0.480762	−	0.876851i	$-0.340360\pi$
$353$	18.0654	0.961523	0.480762	+	0.876851i	$0.340360\pi$
$354$	−1.11036	−0.0590147
$355$	−1.39231	−0.0738961
$356$	82.5836	4.37692
$357$	2.69852	0.142821
$358$	−60.6505	−3.20548
$359$	3.76416	0.198665	0.0993325	−	0.995054i	$-0.468329\pi$
$359$	3.76416	0.198665	0.0993325	+	0.995054i	$0.468329\pi$
$360$	−60.7621	−3.20244
$361$	50.0878	2.63620
$362$	−21.4551	−1.12766
$363$	−3.26170	−0.171195
$364$	2.87983	0.150944
$365$	−1.00000	−0.0523424
$366$	−4.01646	−0.209943
$367$	−3.16598	−0.165263	−0.0826314	−	0.996580i	$-0.526332\pi$
$367$	−3.16598	−0.165263	−0.0826314	+	0.996580i	$0.526332\pi$
$368$	−79.5304	−4.14581
$369$	50.8042	2.64476
$370$	28.1640	1.46418
$371$	1.72042	0.0893199
$372$	108.992	5.65099
$373$	−17.7715	−0.920174	−0.460087	−	0.887874i	$-0.652182\pi$
$373$	−17.7715	−0.920174	−0.460087	+	0.887874i	$0.652182\pi$
$374$	−6.54156	−0.338256
$375$	−3.26170	−0.168434
$376$	−46.0566	−2.37519
$377$	9.24658	0.476223
$378$	13.4052	0.689488
$379$	−4.38417	−0.225200	−0.112600	−	0.993640i	$-0.535918\pi$
$379$	−4.38417	−0.225200	−0.112600	+	0.993640i	$0.535918\pi$
$380$	−41.6041	−2.13425
$381$	5.22340	0.267603
$382$	−53.0530	−2.71443
$383$	−5.56508	−0.284362	−0.142181	−	0.989841i	$-0.545412\pi$
$383$	−5.56508	−0.284362	−0.142181	+	0.989841i	$0.545412\pi$
$384$	26.7809	1.36666
$385$	−0.334745	−0.0170602
$386$	−26.8834	−1.36833
$387$	−82.4438	−4.19085
$388$	61.8014	3.13749
$389$	−35.7927	−1.81476	−0.907382	−	0.420308i	$-0.861922\pi$
$389$	−35.7927	−1.81476	−0.907382	+	0.420308i	$0.861922\pi$
$390$	14.8380	0.751353
$391$	17.7998	0.900173
$392$	54.7901	2.76732
$393$	42.6653	2.15218
$394$	32.9613	1.66057
$395$	−1.15788	−0.0582595
$396$	−38.2346	−1.92136
$397$	1.95043	0.0978894	0.0489447	−	0.998801i	$-0.484414\pi$
$397$	1.95043	0.0978894	0.0489447	+	0.998801i	$0.484414\pi$
$398$	1.28329	0.0643255
$399$	9.07528	0.454332
$400$	11.0429	0.552147
$401$	29.1660	1.45648	0.728240	−	0.685322i	$-0.240339\pi$
$401$	29.1660	1.45648	0.728240	+	0.685322i	$0.240339\pi$
$402$	16.6567	0.830759
$403$	−11.4745	−0.571583
$404$	−84.5011	−4.20409
$405$	26.4339	1.31351
$406$	−4.76644	−0.236555
$407$	10.6409	0.527451
$408$	−64.1243	−3.17463
$409$	6.95766	0.344034	0.172017	−	0.985094i	$-0.444972\pi$
$409$	6.95766	0.344034	0.172017	+	0.985094i	$0.444972\pi$
$410$	−17.6033	−0.869365
$411$	40.5823	2.00178
$412$	−26.2263	−1.29208
$413$	−0.0430543	−0.00211856
$414$	145.608	7.15623
$415$	12.0680	0.592393
$416$	−22.8924	−1.12239
$417$	−18.5124	−0.906557
$418$	−21.9997	−1.07604
$419$	26.9646	1.31731	0.658654	−	0.752446i	$-0.271126\pi$
$419$	26.9646	1.31731	0.658654	+	0.752446i	$0.271126\pi$
$420$	−5.46506	−0.266668
$421$	−14.7233	−0.717571	−0.358786	−	0.933420i	$-0.616809\pi$
$421$	−14.7233	−0.717571	−0.358786	+	0.933420i	$0.616809\pi$
$422$	−47.4402	−2.30935
$423$	44.2283	2.15045
$424$	−40.8821	−1.98541
$425$	−2.47153	−0.119887
$426$	−12.0197	−0.582359
$427$	−0.155739	−0.00753674
$428$	−13.7446	−0.664373
$429$	5.60610	0.270665
$430$	28.5662	1.37759
$431$	17.5033	0.843105	0.421552	−	0.906804i	$-0.361485\pi$
$431$	17.5033	0.843105	0.421552	+	0.906804i	$0.361485\pi$
$432$	−167.081	−8.03869
$433$	−6.09273	−0.292798	−0.146399	−	0.989226i	$-0.546768\pi$
$433$	−6.09273	−0.292798	−0.146399	+	0.989226i	$0.546768\pi$
$434$	5.91487	0.283923
$435$	−17.5473	−0.841327
$436$	−73.1629	−3.50387
$437$	59.8617	2.86357
$438$	−8.63297	−0.412499
$439$	−37.5919	−1.79416	−0.897081	−	0.441866i	$-0.854317\pi$
$439$	−37.5919	−1.79416	−0.897081	+	0.441866i	$0.854317\pi$
$440$	7.95449	0.379215
$441$	−52.6151	−2.50548
$442$	11.2434	0.534794
$443$	−18.7883	−0.892660	−0.446330	−	0.894868i	$-0.647269\pi$
$443$	−18.7883	−0.892660	−0.446330	+	0.894868i	$0.647269\pi$
$444$	173.724	8.24458
$445$	16.4990	0.782129
$446$	−26.0634	−1.23414
$447$	50.2613	2.37728
$448$	4.40745	0.208233
$449$	13.6314	0.643304	0.321652	−	0.946858i	$-0.395762\pi$
$449$	13.6314	0.643304	0.321652	+	0.946858i	$0.395762\pi$
$450$	−20.2179	−0.953080
$451$	−6.65088	−0.313178
$452$	75.1982	3.53703
$453$	−7.46065	−0.350532
$454$	−23.9658	−1.12477
$455$	0.575348	0.0269728
$456$	−215.654	−10.0989
$457$	19.8713	0.929540	0.464770	−	0.885432i	$-0.346137\pi$
$457$	19.8713	0.929540	0.464770	+	0.885432i	$0.346137\pi$
$458$	72.7046	3.39726
$459$	37.3946	1.74543
$460$	−36.0482	−1.68076
$461$	−6.82164	−0.317715	−0.158858	−	0.987301i	$-0.550781\pi$
$461$	−6.82164	−0.317715	−0.158858	+	0.987301i	$0.550781\pi$
$462$	−2.88984	−0.134448
$463$	−29.0493	−1.35004	−0.675019	−	0.737800i	$-0.735865\pi$
$463$	−29.0493	−1.35004	−0.675019	+	0.737800i	$0.735865\pi$
$464$	59.4086	2.75797
$465$	21.7751	1.00980
$466$	39.1340	1.81285
$467$	15.3123	0.708569	0.354284	−	0.935138i	$-0.384724\pi$
$467$	15.3123	0.708569	0.354284	+	0.935138i	$0.384724\pi$
$468$	65.7162	3.03773
$469$	0.645866	0.0298233
$470$	−15.3248	−0.706880
$471$	32.2987	1.48825
$472$	1.02309	0.0470916
$473$	10.7929	0.496257
$474$	−9.99597	−0.459130
$475$	−8.31191	−0.381377
$476$	−4.14110	−0.189807
$477$	39.2592	1.79755
$478$	37.0966	1.69676
$479$	−21.9822	−1.00439	−0.502195	−	0.864754i	$-0.667474\pi$
$479$	−21.9822	−1.00439	−0.502195	+	0.864754i	$0.667474\pi$
$480$	43.4429	1.98289
$481$	−18.2893	−0.833919
$482$	15.5036	0.706168
$483$	7.86335	0.357795
$484$	5.00536	0.227517
$485$	12.3470	0.560650
$486$	108.065	4.90192
$487$	36.3465	1.64702	0.823509	−	0.567303i	$-0.192013\pi$
$487$	36.3465	1.64702	0.823509	+	0.567303i	$0.192013\pi$
$488$	3.70080	0.167527
$489$	−82.5641	−3.73368
$490$	18.2308	0.823582
$491$	−0.663774	−0.0299557	−0.0149779	−	0.999888i	$-0.504768\pi$
$491$	−0.663774	−0.0299557	−0.0149779	+	0.999888i	$0.504768\pi$
$492$	−108.582	−4.89527
$493$	−13.2963	−0.598835
$494$	37.8123	1.70125
$495$	−7.63872	−0.343335
$496$	−73.7225	−3.31024
$497$	−0.466069	−0.0209060
$498$	104.182	4.66852
$499$	1.63492	0.0731892	0.0365946	−	0.999330i	$-0.488349\pi$
$499$	1.63492	0.0731892	0.0365946	+	0.999330i	$0.488349\pi$
$500$	5.00536	0.223847
$501$	56.9597	2.54477
$502$	−11.8879	−0.530584
$503$	−7.70067	−0.343356	−0.171678	−	0.985153i	$-0.554919\pi$
$503$	−7.70067	−0.343356	−0.171678	+	0.985153i	$0.554919\pi$
$504$	−20.3398	−0.906008
$505$	−16.8821	−0.751244
$506$	−19.0618	−0.847400
$507$	32.7666	1.45522
$508$	−8.01575	−0.355641
$509$	21.1338	0.936740	0.468370	−	0.883532i	$-0.344841\pi$
$509$	21.1338	0.936740	0.468370	+	0.883532i	$0.344841\pi$
$510$	−21.3366	−0.944802
$511$	−0.334745	−0.0148083
$512$	28.6002	1.26396
$513$	125.760	5.55245
$514$	−25.5323	−1.12618
$515$	−5.23963	−0.230886
$516$	176.205	7.75699
$517$	−5.79001	−0.254644
$518$	9.42778	0.414233
$519$	27.6125	1.21205
$520$	−13.6719	−0.599552
$521$	−4.84763	−0.212378	−0.106189	−	0.994346i	$-0.533865\pi$
$521$	−4.84763	−0.212378	−0.106189	+	0.994346i	$0.533865\pi$
$522$	−108.768	−4.76064
$523$	−2.56462	−0.112143	−0.0560714	−	0.998427i	$-0.517857\pi$
$523$	−2.56462	−0.112143	−0.0560714	+	0.998427i	$0.517857\pi$
$524$	−65.4735	−2.86022
$525$	−1.09184	−0.0476518
$526$	−26.1751	−1.14129
$527$	16.4999	0.718747
$528$	36.0188	1.56752
$529$	28.8677	1.25512
$530$	−13.6030	−0.590879
$531$	−0.982477	−0.0426359
$532$	−13.9268	−0.603803
$533$	11.4313	0.495144
$534$	142.436	6.16379
$535$	−2.74598	−0.118719
$536$	−15.3476	−0.662915
$537$	−74.7418	−3.22535
$538$	−16.9237	−0.729631
$539$	6.88795	0.296685
$540$	−75.7318	−3.25898
$541$	−33.4125	−1.43652	−0.718258	−	0.695776i	$-0.755060\pi$
$541$	−33.4125	−1.43652	−0.718258	+	0.695776i	$0.755060\pi$
$542$	−0.710943	−0.0305376
$543$	−26.4399	−1.13464
$544$	32.9185	1.41137
$545$	−14.6169	−0.626119
$546$	4.96696	0.212566
$547$	12.8060	0.547545	0.273772	−	0.961795i	$-0.411729\pi$
$547$	12.8060	0.547545	0.273772	+	0.961795i	$0.411729\pi$
$548$	−62.2769	−2.66034
$549$	−3.55389	−0.151676
$550$	2.64676	0.112858
$551$	−44.7163	−1.90498
$552$	−186.855	−7.95309
$553$	−0.387596	−0.0164823
$554$	−81.4840	−3.46192
$555$	34.7076	1.47325
$556$	28.4089	1.20480
$557$	21.7255	0.920538	0.460269	−	0.887779i	$-0.347753\pi$
$557$	21.7255	0.920538	0.460269	+	0.887779i	$0.347753\pi$
$558$	134.974	5.71392
$559$	−18.5504	−0.784600
$560$	3.69657	0.156209
$561$	−8.06140	−0.340353
$562$	46.4378	1.95886
$563$	11.2224	0.472970	0.236485	−	0.971635i	$-0.424005\pi$
$563$	11.2224	0.472970	0.236485	+	0.971635i	$0.424005\pi$
$564$	−94.5278	−3.98034
$565$	15.0235	0.632045
$566$	−38.8951	−1.63488
$567$	8.84861	0.371607
$568$	11.0751	0.464701
$569$	−27.2901	−1.14406	−0.572031	−	0.820232i	$-0.693844\pi$
$569$	−27.2901	−1.14406	−0.572031	+	0.820232i	$0.693844\pi$
$570$	−71.7564	−3.00555
$571$	1.50617	0.0630314	0.0315157	−	0.999503i	$-0.489967\pi$
$571$	1.50617	0.0630314	0.0315157	+	0.999503i	$0.489967\pi$
$572$	−8.60304	−0.359711
$573$	−65.3792	−2.73126
$574$	−5.89262	−0.245953
$575$	−7.20192	−0.300341
$576$	100.576	4.19066
$577$	28.2542	1.17624	0.588120	−	0.808774i	$-0.299868\pi$
$577$	28.2542	1.17624	0.588120	+	0.808774i	$0.299868\pi$
$578$	28.8273	1.19906
$579$	−33.1295	−1.37681
$580$	26.9278	1.11811
$581$	4.03969	0.167595
$582$	106.592	4.41836
$583$	−5.13950	−0.212856
$584$	7.95449	0.329159
$585$	13.1292	0.542824
$586$	21.3783	0.883129
$587$	28.4770	1.17537	0.587686	−	0.809089i	$-0.300039\pi$
$587$	28.4770	1.17537	0.587686	+	0.809089i	$0.300039\pi$
$588$	112.453	4.63747
$589$	55.4902	2.28643
$590$	0.340422	0.0140149
$591$	40.6194	1.67086
$592$	−117.507	−4.82951
$593$	−4.42824	−0.181846	−0.0909230	−	0.995858i	$-0.528982\pi$
$593$	−4.42824	−0.181846	−0.0909230	+	0.995858i	$0.528982\pi$
$594$	−40.0459	−1.64310
$595$	−0.827333	−0.0339173
$596$	−77.1302	−3.15938
$597$	1.58145	0.0647242
$598$	32.7627	1.33977
$599$	2.64882	0.108228	0.0541139	−	0.998535i	$-0.482767\pi$
$599$	2.64882	0.108228	0.0541139	+	0.998535i	$0.482767\pi$
$600$	25.9452	1.05921
$601$	−23.6802	−0.965937	−0.482969	−	0.875638i	$-0.660441\pi$
$601$	−23.6802	−0.965937	−0.482969	+	0.875638i	$0.660441\pi$
$602$	9.56241	0.389735
$603$	14.7383	0.600191
$604$	11.4490	0.465854
$605$	1.00000	0.0406558
$606$	−145.743	−5.92039
$607$	−14.0861	−0.571736	−0.285868	−	0.958269i	$-0.592282\pi$
$607$	−14.0861	−0.571736	−0.285868	+	0.958269i	$0.592282\pi$
$608$	110.707	4.48976
$609$	−5.87386	−0.238021
$610$	1.23140	0.0498578
$611$	9.95167	0.402601
$612$	−94.4979	−3.81985
$613$	−0.00679129	−0.000274298 0	−0.000137149	−	1.00000i	$-0.500044\pi$
$613$	−0.00679129	−0.000274298 0	−0.000137149		1.00000i	$0.500044\pi$
$614$	12.6382	0.510035
$615$	−21.6932	−0.874754
$616$	2.66273	0.107284
$617$	−26.3041	−1.05896	−0.529482	−	0.848321i	$-0.677614\pi$
$617$	−26.3041	−1.05896	−0.529482	+	0.848321i	$0.677614\pi$
$618$	−45.2336	−1.81956
$619$	2.39916	0.0964304	0.0482152	−	0.998837i	$-0.484647\pi$
$619$	2.39916	0.0964304	0.0482152	+	0.998837i	$0.484647\pi$
$620$	−33.4157	−1.34201
$621$	108.966	4.37266
$622$	−65.2327	−2.61559
$623$	5.52297	0.221273
$624$	−61.9078	−2.47830
$625$	1.00000	0.0400000
$626$	−13.3423	−0.533265
$627$	−27.1110	−1.08271
$628$	−49.5651	−1.97786
$629$	26.2994	1.04863
$630$	−6.76784	−0.269637
$631$	−25.0261	−0.996272	−0.498136	−	0.867099i	$-0.665982\pi$
$631$	−25.0261	−0.996272	−0.498136	+	0.867099i	$0.665982\pi$
$632$	9.21038	0.366369
$633$	−58.4623	−2.32367
$634$	32.5875	1.29422
$635$	−1.60143	−0.0635509
$636$	−83.9076	−3.32715
$637$	−11.8388	−0.469069
$638$	14.2390	0.563728
$639$	−10.6355	−0.420732
$640$	−8.21070	−0.324556
$641$	1.95724	0.0773062	0.0386531	−	0.999253i	$-0.487693\pi$
$641$	1.95724	0.0773062	0.0386531	+	0.999253i	$0.487693\pi$
$642$	−23.7060	−0.935601
$643$	25.2246	0.994761	0.497380	−	0.867533i	$-0.334295\pi$
$643$	25.2246	0.994761	0.497380	+	0.867533i	$0.334295\pi$
$644$	−12.0670	−0.475506
$645$	35.2032	1.38612
$646$	−54.3728	−2.13927
$647$	21.5198	0.846029	0.423014	−	0.906123i	$-0.360972\pi$
$647$	21.5198	0.846029	0.423014	+	0.906123i	$0.360972\pi$
$648$	−210.268	−8.26010
$649$	0.128618	0.00504870
$650$	−4.54917	−0.178433
$651$	7.28911	0.285683
$652$	126.702	4.96202
$653$	−38.0535	−1.48915	−0.744574	−	0.667540i	$-0.767347\pi$
$653$	−38.0535	−1.48915	−0.744574	+	0.667540i	$0.767347\pi$
$654$	−126.187	−4.93431
$655$	−13.0807	−0.511104
$656$	73.4452	2.86755
$657$	−7.63872	−0.298015
$658$	−5.12990	−0.199984
$659$	−9.57911	−0.373149	−0.186575	−	0.982441i	$-0.559739\pi$
$659$	−9.57911	−0.373149	−0.186575	+	0.982441i	$0.559739\pi$
$660$	16.3260	0.635489
$661$	−19.5043	−0.758629	−0.379314	−	0.925268i	$-0.623840\pi$
$661$	−19.5043	−0.758629	−0.379314	+	0.925268i	$0.623840\pi$
$662$	−54.9137	−2.13428
$663$	13.8557	0.538109
$664$	−95.9945	−3.72531
$665$	−2.78237	−0.107896
$666$	215.137	8.33640
$667$	−38.7448	−1.50020
$668$	−87.4095	−3.38197
$669$	−32.1188	−1.24179
$670$	−5.10673	−0.197290
$671$	0.465246	0.0179606
$672$	14.5423	0.560981
$673$	−27.6566	−1.06608	−0.533041	−	0.846089i	$-0.678951\pi$
$673$	−27.6566	−1.06608	−0.533041	+	0.846089i	$0.678951\pi$
$674$	−50.4604	−1.94366
$675$	−15.1301	−0.582359
$676$	−50.2831	−1.93397
$677$	5.03543	0.193527	0.0967636	−	0.995307i	$-0.469151\pi$
$677$	5.03543	0.193527	0.0967636	+	0.995307i	$0.469151\pi$
$678$	129.698	4.98101
$679$	4.13311	0.158614
$680$	19.6598	0.753917
$681$	−29.5340	−1.13174
$682$	−17.6698	−0.676610
$683$	−42.2581	−1.61696	−0.808480	−	0.588523i	$-0.799710\pi$
$683$	−42.2581	−1.61696	−0.808480	+	0.588523i	$0.799710\pi$
$684$	−317.802	−12.1515
$685$	−12.4420	−0.475386
$686$	12.3046	0.469792
$687$	89.5965	3.41832
$688$	−119.185	−4.54389
$689$	8.83359	0.336533
$690$	−62.1739	−2.36692
$691$	1.16349	0.0442614	0.0221307	−	0.999755i	$-0.492955\pi$
$691$	1.16349	0.0442614	0.0221307	+	0.999755i	$0.492955\pi$
$692$	−42.3737	−1.61080
$693$	−2.55702	−0.0971333
$694$	4.30265	0.163326
$695$	5.67569	0.215291
$696$	139.580	5.29075
$697$	−16.4378	−0.622628
$698$	−96.6670	−3.65890
$699$	48.2262	1.82408
$700$	1.67552	0.0633288
$701$	14.8862	0.562244	0.281122	−	0.959672i	$-0.409293\pi$
$701$	14.8862	0.562244	0.281122	+	0.959672i	$0.409293\pi$
$702$	68.8295	2.59780
$703$	88.4465	3.33582
$704$	−13.1666	−0.496234
$705$	−18.8853	−0.711262
$706$	−47.8148	−1.79953
$707$	−5.65121	−0.212535
$708$	2.09982	0.0789161
$709$	−7.58108	−0.284713	−0.142357	−	0.989815i	$-0.545468\pi$
$709$	−7.58108	−0.284713	−0.142357	+	0.989815i	$0.545468\pi$
$710$	3.68511	0.138300
$711$	−8.84475	−0.331704
$712$	−131.241	−4.91848
$713$	48.0799	1.80061
$714$	−7.14234	−0.267295
$715$	−1.71876	−0.0642782
$716$	114.698	4.28646
$717$	45.7155	1.70728
$718$	−9.96286	−0.371810
$719$	−26.8099	−0.999839	−0.499920	−	0.866072i	$-0.666637\pi$
$719$	−26.8099	−0.999839	−0.499920	+	0.866072i	$0.666637\pi$
$720$	84.3539	3.14368
$721$	−1.75394	−0.0653203
$722$	−132.571	−4.93377
$723$	19.1056	0.710546
$724$	40.5743	1.50793
$725$	5.37978	0.199800
$726$	8.63297	0.320399
$727$	45.2248	1.67729	0.838647	−	0.544676i	$-0.183347\pi$
$727$	45.2248	1.67729	0.838647	+	0.544676i	$0.183347\pi$
$728$	−4.57660	−0.169620
$729$	53.8708	1.99521
$730$	2.64676	0.0979612
$731$	26.6749	0.986608
$732$	7.59562	0.280742
$733$	26.6688	0.985033	0.492517	−	0.870303i	$-0.336077\pi$
$733$	26.6688	0.985033	0.492517	+	0.870303i	$0.336077\pi$
$734$	8.37960	0.309297
$735$	22.4664	0.828687
$736$	95.9229	3.53577
$737$	−1.92942	−0.0710713
$738$	−134.467	−4.94979
$739$	−25.8810	−0.952047	−0.476023	−	0.879433i	$-0.657922\pi$
$739$	−25.8810	−0.952047	−0.476023	+	0.879433i	$0.657922\pi$
$740$	−53.2617	−1.95794
$741$	46.5974	1.71180
$742$	−4.55356	−0.167166
$743$	18.9865	0.696547	0.348273	−	0.937393i	$-0.386768\pi$
$743$	18.9865	0.696547	0.348273	+	0.937393i	$0.386768\pi$
$744$	−173.210	−6.35018
$745$	−15.4095	−0.564561
$746$	47.0370	1.72215
$747$	92.1838	3.37283
$748$	12.3709	0.452325
$749$	−0.919205	−0.0335870
$750$	8.63297	0.315231
$751$	13.4004	0.488987	0.244494	−	0.969651i	$-0.421378\pi$
$751$	13.4004	0.488987	0.244494	+	0.969651i	$0.421378\pi$
$752$	63.9387	2.33161
$753$	−14.6499	−0.533873
$754$	−24.4735	−0.891273
$755$	2.28735	0.0832451
$756$	−25.3509	−0.922002
$757$	19.2242	0.698716	0.349358	−	0.936989i	$-0.386400\pi$
$757$	19.2242	0.698716	0.349358	+	0.936989i	$0.386400\pi$
$758$	11.6039	0.421471
$759$	−23.4905	−0.852653
$760$	66.1170	2.39832
$761$	14.9800	0.543025	0.271513	−	0.962435i	$-0.412476\pi$
$761$	14.9800	0.543025	0.271513	+	0.962435i	$0.412476\pi$
$762$	−13.8251	−0.500831
$763$	−4.89294	−0.177136
$764$	100.330	3.62981
$765$	−18.8793	−0.682583
$766$	14.7295	0.532197
$767$	−0.221064	−0.00798217
$768$	15.0083	0.541567
$769$	−25.2964	−0.912211	−0.456105	−	0.889926i	$-0.650756\pi$
$769$	−25.2964	−0.912211	−0.456105	+	0.889926i	$0.650756\pi$
$770$	0.885992	0.0319289
$771$	−31.4644	−1.13316
$772$	50.8400	1.82977
$773$	−19.6640	−0.707263	−0.353632	−	0.935385i	$-0.615053\pi$
$773$	−19.6640	−0.707263	−0.353632	+	0.935385i	$0.615053\pi$
$774$	218.209	7.84337
$775$	−6.67599	−0.239809
$776$	−98.2144	−3.52569
$777$	11.6182	0.416801
$778$	94.7349	3.39641
$779$	−55.2815	−1.98066
$780$	−28.0606	−1.00473
$781$	1.39231	0.0498207
$782$	−47.1118	−1.68471
$783$	−81.3968	−2.90888
$784$	−76.0631	−2.71654
$785$	−9.90240	−0.353432
$786$	−112.925	−4.02790
$787$	25.4131	0.905878	0.452939	−	0.891542i	$-0.350376\pi$
$787$	25.4131	0.905878	0.452939	+	0.891542i	$0.350376\pi$
$788$	−62.3340	−2.22056
$789$	−32.2565	−1.14836
$790$	3.06465	0.109035
$791$	5.02906	0.178813
$792$	60.7621	2.15909
$793$	−0.799649	−0.0283964
$794$	−5.16233	−0.183204
$795$	−16.7635	−0.594541
$796$	−2.42686	−0.0860179
$797$	14.1725	0.502016	0.251008	−	0.967985i	$-0.419238\pi$
$797$	14.1725	0.502016	0.251008	+	0.967985i	$0.419238\pi$
$798$	−24.0201	−0.850303
$799$	−14.3102	−0.506258
$800$	−13.3191	−0.470900
$801$	126.031	4.45310
$802$	−77.1955	−2.72587
$803$	1.00000	0.0352892
$804$	−31.4998	−1.11091
$805$	−2.41081	−0.0849699
$806$	30.3702	1.06974
$807$	−20.8557	−0.734154
$808$	134.289	4.72425
$809$	−17.0521	−0.599521	−0.299761	−	0.954014i	$-0.596907\pi$
$809$	−17.0521	−0.599521	−0.299761	+	0.954014i	$0.596907\pi$
$810$	−69.9642	−2.45829
$811$	−33.5906	−1.17952	−0.589762	−	0.807577i	$-0.700779\pi$
$811$	−33.5906	−1.17952	−0.589762	+	0.807577i	$0.700779\pi$
$812$	9.01394	0.316327
$813$	−0.876121	−0.0307269
$814$	−28.1640	−0.987149
$815$	25.3132	0.886682
$816$	89.0215	3.11638
$817$	89.7095	3.13854
$818$	−18.4153	−0.643876
$819$	4.39492	0.153571
$820$	33.2901	1.16254
$821$	15.5307	0.542025	0.271012	−	0.962576i	$-0.412642\pi$
$821$	15.5307	0.542025	0.271012	+	0.962576i	$0.412642\pi$
$822$	−107.412	−3.74641
$823$	−1.24848	−0.0435194	−0.0217597	−	0.999763i	$-0.506927\pi$
$823$	−1.24848	−0.0435194	−0.0217597	+	0.999763i	$0.506927\pi$
$824$	41.6786	1.45194
$825$	3.26170	0.113558
$826$	0.113955	0.00396499
$827$	0.266475	0.00926626	0.00463313	−	0.999989i	$-0.498525\pi$
$827$	0.266475	0.00926626	0.00463313	+	0.999989i	$0.498525\pi$
$828$	−275.362	−9.56950
$829$	−17.6959	−0.614604	−0.307302	−	0.951612i	$-0.599426\pi$
$829$	−17.6959	−0.614604	−0.307302	+	0.951612i	$0.599426\pi$
$830$	−31.9411	−1.10869
$831$	−100.416	−3.48338
$832$	22.6303	0.784563
$833$	17.0238	0.589839
$834$	48.9980	1.69666
$835$	−17.4632	−0.604338
$836$	41.6041	1.43891
$837$	101.009	3.49137
$838$	−71.3690	−2.46540
$839$	18.2172	0.628928	0.314464	−	0.949269i	$-0.398175\pi$
$839$	18.2172	0.628928	0.314464	+	0.949269i	$0.398175\pi$
$840$	8.68503	0.299662
$841$	−0.0579452	−0.00199811
$842$	38.9692	1.34297
$843$	57.2270	1.97100
$844$	89.7153	3.08813
$845$	−10.0458	−0.345588
$846$	−117.062	−4.02467
$847$	0.334745	0.0115020
$848$	56.7552	1.94898
$849$	−47.9318	−1.64502
$850$	6.54156	0.224374
$851$	76.6352	2.62702
$852$	22.7309	0.778746
$853$	−29.0535	−0.994773	−0.497386	−	0.867529i	$-0.665707\pi$
$853$	−29.0535	−0.994773	−0.497386	+	0.867529i	$0.665707\pi$
$854$	0.412205	0.0141053
$855$	−63.4923	−2.17139
$856$	21.8429	0.746575
$857$	−3.20507	−0.109483	−0.0547415	−	0.998501i	$-0.517433\pi$
$857$	−3.20507	−0.109483	−0.0547415	+	0.998501i	$0.517433\pi$
$858$	−14.8380	−0.506562
$859$	13.1704	0.449369	0.224684	−	0.974432i	$-0.427865\pi$
$859$	13.1704	0.449369	0.224684	+	0.974432i	$0.427865\pi$
$860$	−54.0223	−1.84215
$861$	−7.26170	−0.247478
$862$	−46.3271	−1.57791
$863$	23.4449	0.798074	0.399037	−	0.916935i	$-0.369345\pi$
$863$	23.4449	0.798074	0.399037	+	0.916935i	$0.369345\pi$
$864$	201.519	6.85583
$865$	−8.46565	−0.287841
$866$	16.1260	0.547985
$867$	35.5250	1.20649
$868$	−11.1858	−0.379670
$869$	1.15788	0.0392785
$870$	46.4435	1.57458
$871$	3.31623	0.112366
$872$	116.270	3.93740
$873$	94.3155	3.19210
$874$	−158.440	−5.35931
$875$	0.334745	0.0113165
$876$	16.3260	0.551605
$877$	12.7701	0.431217	0.215608	−	0.976480i	$-0.430827\pi$
$877$	12.7701	0.431217	0.215608	+	0.976480i	$0.430827\pi$
$878$	99.4968	3.35786
$879$	26.3453	0.888603
$880$	−11.0429	−0.372257
$881$	51.2281	1.72592	0.862960	−	0.505272i	$-0.168608\pi$
$881$	51.2281	1.72592	0.862960	+	0.505272i	$0.168608\pi$
$882$	139.260	4.68912
$883$	−29.4888	−0.992378	−0.496189	−	0.868215i	$-0.665268\pi$
$883$	−29.4888	−0.992378	−0.496189	+	0.868215i	$0.665268\pi$
$884$	−21.2627	−0.715141
$885$	0.419514	0.0141018
$886$	49.7283	1.67065
$887$	0.886536	0.0297670	0.0148835	−	0.999889i	$-0.495262\pi$
$887$	0.886536	0.0297670	0.0148835	+	0.999889i	$0.495262\pi$
$888$	−276.081	−9.26468
$889$	−0.536072	−0.0179793
$890$	−43.6690	−1.46379
$891$	−26.4339	−0.885568
$892$	49.2891	1.65032
$893$	−48.1260	−1.61048
$894$	−133.030	−4.44918
$895$	22.9150	0.765963
$896$	−2.74849	−0.0918207
$897$	40.3747	1.34807
$898$	−36.0790	−1.20397
$899$	−35.9154	−1.19784
$900$	38.2346	1.27449
$901$	−12.7024	−0.423179
$902$	17.6033	0.586126
$903$	11.7841	0.392151
$904$	−119.505	−3.97466
$905$	8.10616	0.269458
$906$	19.7466	0.656037
$907$	−22.1774	−0.736387	−0.368194	−	0.929749i	$-0.620024\pi$
$907$	−22.1774	−0.736387	−0.368194	+	0.929749i	$0.620024\pi$
$908$	45.3224	1.50408
$909$	−128.958	−4.27726
$910$	−1.52281	−0.0504807
$911$	34.6983	1.14961	0.574803	−	0.818292i	$-0.305079\pi$
$911$	34.6983	1.14961	0.574803	+	0.818292i	$0.305079\pi$
$912$	299.385	9.91363
$913$	−12.0680	−0.399391
$914$	−52.5946	−1.73968
$915$	1.51750	0.0501669
$916$	−137.493	−4.54291
$917$	−4.37869	−0.144597
$918$	−98.9746	−3.26665
$919$	−30.2059	−0.996401	−0.498200	−	0.867062i	$-0.666006\pi$
$919$	−30.2059	−0.996401	−0.498200	+	0.867062i	$0.666006\pi$
$920$	57.2876	1.88872
$921$	15.5745	0.513196
$922$	18.0553	0.594619
$923$	−2.39305	−0.0787682
$924$	5.46506	0.179787
$925$	−10.6409	−0.349872
$926$	76.8868	2.52666
$927$	−40.0241	−1.31456
$928$	−71.6537	−2.35215
$929$	22.4826	0.737630	0.368815	−	0.929503i	$-0.379764\pi$
$929$	22.4826	0.737630	0.368815	+	0.929503i	$0.379764\pi$
$930$	−57.6336	−1.88988
$931$	57.2520	1.87636
$932$	−74.0072	−2.42419
$933$	−80.3886	−2.63180
$934$	−40.5281	−1.32612
$935$	2.47153	0.0808277
$936$	−104.436	−3.41359
$937$	26.0566	0.851233	0.425617	−	0.904904i	$-0.360057\pi$
$937$	26.0566	0.851233	0.425617	+	0.904904i	$0.360057\pi$
$938$	−1.70945	−0.0558157
$939$	−16.4422	−0.536570
$940$	28.9811	0.945259
$941$	34.3392	1.11943	0.559713	−	0.828687i	$-0.310912\pi$
$941$	34.3392	1.11943	0.559713	+	0.828687i	$0.310912\pi$
$942$	−85.4871	−2.78532
$943$	−47.8991	−1.55981
$944$	−1.42032	−0.0462275
$945$	−5.06474	−0.164756
$946$	−28.5662	−0.928768
$947$	−20.7420	−0.674024	−0.337012	−	0.941500i	$-0.609416\pi$
$947$	−20.7420	−0.674024	−0.337012	+	0.941500i	$0.609416\pi$
$948$	18.9036	0.613961
$949$	−1.71876	−0.0557935
$950$	21.9997	0.713763
$951$	40.1588	1.30224
$952$	6.58101	0.213292
$953$	40.9982	1.32806	0.664031	−	0.747705i	$-0.268844\pi$
$953$	40.9982	1.32806	0.664031	+	0.747705i	$0.268844\pi$
$954$	−103.910	−3.36421
$955$	20.0445	0.648624
$956$	−70.1543	−2.26895
$957$	17.5473	0.567222
$958$	58.1816	1.87976
$959$	−4.16491	−0.134492
$960$	−42.9455	−1.38606
$961$	13.5688	0.437703
$962$	48.4074	1.56072
$963$	−20.9758	−0.675936
$964$	−29.3192	−0.944308
$965$	10.1571	0.326969
$966$	−20.8124	−0.669629
$967$	−10.9519	−0.352190	−0.176095	−	0.984373i	$-0.556347\pi$
$967$	−10.9519	−0.352190	−0.176095	+	0.984373i	$0.556347\pi$
$968$	−7.95449	−0.255667
$969$	−67.0056	−2.15253
$970$	−32.6797	−1.04928
$971$	44.0613	1.41399	0.706997	−	0.707216i	$-0.250049\pi$
$971$	44.0613	1.41399	0.706997	+	0.707216i	$0.250049\pi$
$972$	−204.364	−6.55499
$973$	1.89991	0.0609083
$974$	−96.2007	−3.08247
$975$	−5.60610	−0.179539
$976$	−5.13769	−0.164453
$977$	−9.16631	−0.293256	−0.146628	−	0.989192i	$-0.546842\pi$
$977$	−9.16631	−0.293256	−0.146628	+	0.989192i	$0.546842\pi$
$978$	218.528	6.98775
$979$	−16.4990	−0.527311
$980$	−34.4767	−1.10132
$981$	−111.654	−3.56485
$982$	1.75685	0.0560635
$983$	2.53497	0.0808531	0.0404266	−	0.999183i	$-0.487128\pi$
$983$	2.53497	0.0808531	0.0404266	+	0.999183i	$0.487128\pi$
$984$	172.558	5.50096
$985$	−12.4534	−0.396799
$986$	35.1922	1.12075
$987$	−6.32177	−0.201224
$988$	−71.5077	−2.27496
$989$	77.7295	2.47165
$990$	20.2179	0.642567
$991$	56.4794	1.79413	0.897063	−	0.441902i	$-0.145696\pi$
$991$	56.4794	1.79413	0.897063	+	0.441902i	$0.145696\pi$
$992$	88.9180	2.82315
$993$	−67.6721	−2.14751
$994$	1.23357	0.0391266
$995$	−0.484852	−0.0153709
$996$	−197.022	−6.24288
$997$	−59.2415	−1.87620	−0.938098	−	0.346370i	$-0.887414\pi$
$997$	−59.2415	−1.87620	−0.938098	+	0.346370i	$0.887414\pi$
$998$	−4.32725	−0.136977
$999$	160.999	5.09377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.i.1.2	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.i.1.2	✓	38	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64676 q^{2} -3.26170 q^{3} +5.00536 q^{4} +1.00000 q^{5} +8.63297 q^{6} +0.334745 q^{7} -7.95449 q^{8} +7.63872 q^{9} +O(q^{10})\)	\(q-2.64676 q^{2} -3.26170 q^{3} +5.00536 q^{4} +1.00000 q^{5} +8.63297 q^{6} +0.334745 q^{7} -7.95449 q^{8} +7.63872 q^{9} -2.64676 q^{10} -1.00000 q^{11} -16.3260 q^{12} +1.71876 q^{13} -0.885992 q^{14} -3.26170 q^{15} +11.0429 q^{16} -2.47153 q^{17} -20.2179 q^{18} -8.31191 q^{19} +5.00536 q^{20} -1.09184 q^{21} +2.64676 q^{22} -7.20192 q^{23} +25.9452 q^{24} +1.00000 q^{25} -4.54917 q^{26} -15.1301 q^{27} +1.67552 q^{28} +5.37978 q^{29} +8.63297 q^{30} -6.67599 q^{31} -13.3191 q^{32} +3.26170 q^{33} +6.54156 q^{34} +0.334745 q^{35} +38.2346 q^{36} -10.6409 q^{37} +21.9997 q^{38} -5.60610 q^{39} -7.95449 q^{40} +6.65088 q^{41} +2.88984 q^{42} -10.7929 q^{43} -5.00536 q^{44} +7.63872 q^{45} +19.0618 q^{46} +5.79001 q^{47} -36.0188 q^{48} -6.88795 q^{49} -2.64676 q^{50} +8.06140 q^{51} +8.60304 q^{52} +5.13950 q^{53} +40.0459 q^{54} -1.00000 q^{55} -2.66273 q^{56} +27.1110 q^{57} -14.2390 q^{58} -0.128618 q^{59} -16.3260 q^{60} -0.465246 q^{61} +17.6698 q^{62} +2.55702 q^{63} +13.1666 q^{64} +1.71876 q^{65} -8.63297 q^{66} +1.92942 q^{67} -12.3709 q^{68} +23.4905 q^{69} -0.885992 q^{70} -1.39231 q^{71} -60.7621 q^{72} -1.00000 q^{73} +28.1640 q^{74} -3.26170 q^{75} -41.6041 q^{76} -0.334745 q^{77} +14.8380 q^{78} -1.15788 q^{79} +11.0429 q^{80} +26.4339 q^{81} -17.6033 q^{82} +12.0680 q^{83} -5.46506 q^{84} -2.47153 q^{85} +28.5662 q^{86} -17.5473 q^{87} +7.95449 q^{88} +16.4990 q^{89} -20.2179 q^{90} +0.575348 q^{91} -36.0482 q^{92} +21.7751 q^{93} -15.3248 q^{94} -8.31191 q^{95} +43.4429 q^{96} +12.3470 q^{97} +18.2308 q^{98} -7.63872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * q^99

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