LMFDB - Embedded newform 2005.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, 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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05755 q^{2} +2.25661 q^{3} +2.23350 q^{4} -1.00000 q^{5} -4.64308 q^{6} +1.74407 q^{7} -0.480444 q^{8} +2.09227 q^{9} +O(q^{10})$	\(q-2.05755 q^{2} +2.25661 q^{3} +2.23350 q^{4} -1.00000 q^{5} -4.64308 q^{6} +1.74407 q^{7} -0.480444 q^{8} +2.09227 q^{9} +2.05755 q^{10} +0.110642 q^{11} +5.04014 q^{12} +2.92019 q^{13} -3.58851 q^{14} -2.25661 q^{15} -3.47847 q^{16} +7.82864 q^{17} -4.30495 q^{18} -4.46863 q^{19} -2.23350 q^{20} +3.93568 q^{21} -0.227652 q^{22} +2.62310 q^{23} -1.08417 q^{24} +1.00000 q^{25} -6.00843 q^{26} -2.04838 q^{27} +3.89539 q^{28} +3.33062 q^{29} +4.64308 q^{30} +2.06883 q^{31} +8.11801 q^{32} +0.249676 q^{33} -16.1078 q^{34} -1.74407 q^{35} +4.67310 q^{36} +4.14715 q^{37} +9.19441 q^{38} +6.58971 q^{39} +0.480444 q^{40} -8.52859 q^{41} -8.09785 q^{42} -5.63824 q^{43} +0.247120 q^{44} -2.09227 q^{45} -5.39715 q^{46} +6.50160 q^{47} -7.84954 q^{48} -3.95822 q^{49} -2.05755 q^{50} +17.6662 q^{51} +6.52225 q^{52} -6.26737 q^{53} +4.21465 q^{54} -0.110642 q^{55} -0.837929 q^{56} -10.0839 q^{57} -6.85291 q^{58} +6.25033 q^{59} -5.04014 q^{60} +14.5621 q^{61} -4.25671 q^{62} +3.64907 q^{63} -9.74625 q^{64} -2.92019 q^{65} -0.513721 q^{66} +6.16818 q^{67} +17.4853 q^{68} +5.91930 q^{69} +3.58851 q^{70} +6.43850 q^{71} -1.00522 q^{72} -9.63973 q^{73} -8.53297 q^{74} +2.25661 q^{75} -9.98069 q^{76} +0.192968 q^{77} -13.5587 q^{78} -9.21781 q^{79} +3.47847 q^{80} -10.8992 q^{81} +17.5480 q^{82} -6.15713 q^{83} +8.79035 q^{84} -7.82864 q^{85} +11.6010 q^{86} +7.51590 q^{87} -0.0531575 q^{88} +16.0965 q^{89} +4.30495 q^{90} +5.09301 q^{91} +5.85870 q^{92} +4.66853 q^{93} -13.3774 q^{94} +4.46863 q^{95} +18.3191 q^{96} +4.73013 q^{97} +8.14423 q^{98} +0.231494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) $ 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * 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 $

$2$	−2.05755	−1.45491	−0.727453	−	0.686157i	$-0.759296\pi$
$2$	−2.05755	−1.45491	−0.727453	+	0.686157i	$0.759296\pi$
$3$	2.25661	1.30285	0.651426	−	0.758712i	$-0.274171\pi$
$3$	2.25661	1.30285	0.651426	+	0.758712i	$0.274171\pi$
$4$	2.23350	1.11675
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.64308	−1.89553
$7$	1.74407	0.659196	0.329598	−	0.944121i	$-0.393087\pi$
$7$	1.74407	0.659196	0.329598	+	0.944121i	$0.393087\pi$
$8$	−0.480444	−0.169863
$9$	2.09227	0.697424
$10$	2.05755	0.650654
$11$	0.110642	0.0333599	0.0166800	−	0.999861i	$-0.494690\pi$
$11$	0.110642	0.0333599	0.0166800	+	0.999861i	$0.494690\pi$
$12$	5.04014	1.45496
$13$	2.92019	0.809914	0.404957	−	0.914336i	$-0.367286\pi$
$13$	2.92019	0.809914	0.404957	+	0.914336i	$0.367286\pi$
$14$	−3.58851	−0.959069
$15$	−2.25661	−0.582653
$16$	−3.47847	−0.869617
$17$	7.82864	1.89872	0.949362	−	0.314185i	$-0.101731\pi$
$17$	7.82864	1.89872	0.949362	+	0.314185i	$0.101731\pi$
$18$	−4.30495	−1.01469
$19$	−4.46863	−1.02517	−0.512587	−	0.858636i	$-0.671313\pi$
$19$	−4.46863	−1.02517	−0.512587	+	0.858636i	$0.671313\pi$
$20$	−2.23350	−0.499427
$21$	3.93568	0.858836
$22$	−0.227652	−0.0485356
$23$	2.62310	0.546954	0.273477	−	0.961879i	$-0.411826\pi$
$23$	2.62310	0.546954	0.273477	+	0.961879i	$0.411826\pi$
$24$	−1.08417	−0.221306
$25$	1.00000	0.200000
$26$	−6.00843	−1.17835
$27$	−2.04838	−0.394212
$28$	3.89539	0.736159
$29$	3.33062	0.618481	0.309241	−	0.950984i	$-0.399925\pi$
$29$	3.33062	0.618481	0.309241	+	0.950984i	$0.399925\pi$
$30$	4.64308	0.847706
$31$	2.06883	0.371573	0.185786	−	0.982590i	$-0.440517\pi$
$31$	2.06883	0.371573	0.185786	+	0.982590i	$0.440517\pi$
$32$	8.11801	1.43507
$33$	0.249676	0.0434631
$34$	−16.1078	−2.76246
$35$	−1.74407	−0.294802
$36$	4.67310	0.778849
$37$	4.14715	0.681788	0.340894	−	0.940102i	$-0.389270\pi$
$37$	4.14715	0.681788	0.340894	+	0.940102i	$0.389270\pi$
$38$	9.19441	1.49153
$39$	6.58971	1.05520
$40$	0.480444	0.0759649
$41$	−8.52859	−1.33194	−0.665971	−	0.745978i	$-0.731982\pi$
$41$	−8.52859	−1.33194	−0.665971	+	0.745978i	$0.731982\pi$
$42$	−8.09785	−1.24953
$43$	−5.63824	−0.859824	−0.429912	−	0.902871i	$-0.641455\pi$
$43$	−5.63824	−0.859824	−0.429912	+	0.902871i	$0.641455\pi$
$44$	0.247120	0.0372548
$45$	−2.09227	−0.311898
$46$	−5.39715	−0.795766
$47$	6.50160	0.948356	0.474178	−	0.880429i	$-0.342745\pi$
$47$	6.50160	0.948356	0.474178	+	0.880429i	$0.342745\pi$
$48$	−7.84954	−1.13298
$49$	−3.95822	−0.565460
$50$	−2.05755	−0.290981
$51$	17.6662	2.47376
$52$	6.52225	0.904473
$53$	−6.26737	−0.860889	−0.430445	−	0.902617i	$-0.641643\pi$
$53$	−6.26737	−0.860889	−0.430445	+	0.902617i	$0.641643\pi$
$54$	4.21465	0.573541
$55$	−0.110642	−0.0149190
$56$	−0.837929	−0.111973
$57$	−10.0839	−1.33565
$58$	−6.85291	−0.899832
$59$	6.25033	0.813723	0.406862	−	0.913490i	$-0.366623\pi$
$59$	6.25033	0.813723	0.406862	+	0.913490i	$0.366623\pi$
$60$	−5.04014	−0.650679
$61$	14.5621	1.86449	0.932244	−	0.361831i	$-0.117848\pi$
$61$	14.5621	1.86449	0.932244	+	0.361831i	$0.117848\pi$
$62$	−4.25671	−0.540603
$63$	3.64907	0.459739
$64$	−9.74625	−1.21828
$65$	−2.92019	−0.362205
$66$	−0.513721	−0.0632347
$67$	6.16818	0.753563	0.376781	−	0.926302i	$-0.377031\pi$
$67$	6.16818	0.753563	0.376781	+	0.926302i	$0.377031\pi$
$68$	17.4853	2.12040
$69$	5.91930	0.712600
$70$	3.58851	0.428909
$71$	6.43850	0.764109	0.382054	−	0.924140i	$-0.375217\pi$
$71$	6.43850	0.764109	0.382054	+	0.924140i	$0.375217\pi$
$72$	−1.00522	−0.118466
$73$	−9.63973	−1.12825	−0.564123	−	0.825691i	$-0.690785\pi$
$73$	−9.63973	−1.12825	−0.564123	+	0.825691i	$0.690785\pi$
$74$	−8.53297	−0.991938
$75$	2.25661	0.260570
$76$	−9.98069	−1.14486
$77$	0.192968	0.0219908
$78$	−13.5587	−1.53522
$79$	−9.21781	−1.03708	−0.518542	−	0.855052i	$-0.673525\pi$
$79$	−9.21781	−1.03708	−0.518542	+	0.855052i	$0.673525\pi$
$80$	3.47847	0.388905
$81$	−10.8992	−1.21102
$82$	17.5480	1.93785
$83$	−6.15713	−0.675833	−0.337916	−	0.941176i	$-0.609722\pi$
$83$	−6.15713	−0.675833	−0.337916	+	0.941176i	$0.609722\pi$
$84$	8.79035	0.959106
$85$	−7.82864	−0.849135
$86$	11.6010	1.25096
$87$	7.51590	0.805789
$88$	−0.0531575	−0.00566661
$89$	16.0965	1.70622	0.853112	−	0.521727i	$-0.174712\pi$
$89$	16.0965	1.70622	0.853112	+	0.521727i	$0.174712\pi$
$90$	4.30495	0.453782
$91$	5.09301	0.533893
$92$	5.85870	0.610812
$93$	4.66853	0.484104
$94$	−13.3774	−1.37977
$95$	4.46863	0.458471
$96$	18.3191	1.86969
$97$	4.73013	0.480272	0.240136	−	0.970739i	$-0.422808\pi$
$97$	4.73013	0.480272	0.240136	+	0.970739i	$0.422808\pi$
$98$	8.14423	0.822691
$99$	0.231494	0.0232660
$100$	2.23350	0.223350
$101$	17.7577	1.76696	0.883479	−	0.468471i	$-0.155195\pi$
$101$	17.7577	1.76696	0.883479	+	0.468471i	$0.155195\pi$
$102$	−36.3490	−3.59908
$103$	16.1093	1.58729	0.793647	−	0.608378i	$-0.208180\pi$
$103$	16.1093	1.58729	0.793647	+	0.608378i	$0.208180\pi$
$104$	−1.40299	−0.137574
$105$	−3.93568	−0.384083
$106$	12.8954	1.25251
$107$	5.36328	0.518487	0.259244	−	0.965812i	$-0.416527\pi$
$107$	5.36328	0.518487	0.259244	+	0.965812i	$0.416527\pi$
$108$	−4.57507	−0.440237
$109$	−18.0581	−1.72965	−0.864824	−	0.502075i	$-0.832570\pi$
$109$	−18.0581	−1.72965	−0.864824	+	0.502075i	$0.832570\pi$
$110$	0.227652	0.0217058
$111$	9.35850	0.888269
$112$	−6.06669	−0.573249
$113$	2.05174	0.193011	0.0965057	−	0.995332i	$-0.469233\pi$
$113$	2.05174	0.193011	0.0965057	+	0.995332i	$0.469233\pi$
$114$	20.7482	1.94324
$115$	−2.62310	−0.244605
$116$	7.43896	0.690690
$117$	6.10983	0.564854
$118$	−12.8603	−1.18389
$119$	13.6537	1.25163
$120$	1.08417	0.0989711
$121$	−10.9878	−0.998887
$122$	−29.9622	−2.71265
$123$	−19.2457	−1.73532
$124$	4.62074	0.414954
$125$	−1.00000	−0.0894427
$126$	−7.50813	−0.668878
$127$	5.29251	0.469635	0.234817	−	0.972040i	$-0.424551\pi$
$127$	5.29251	0.469635	0.234817	+	0.972040i	$0.424551\pi$
$128$	3.81736	0.337410
$129$	−12.7233	−1.12022
$130$	6.00843	0.526974
$131$	16.8750	1.47438	0.737190	−	0.675686i	$-0.236152\pi$
$131$	16.8750	1.47438	0.737190	+	0.675686i	$0.236152\pi$
$132$	0.557653	0.0485375
$133$	−7.79360	−0.675790
$134$	−12.6913	−1.09636
$135$	2.04838	0.176297
$136$	−3.76123	−0.322522
$137$	−1.62181	−0.138560	−0.0692801	−	0.997597i	$-0.522070\pi$
$137$	−1.62181	−0.138560	−0.0692801	+	0.997597i	$0.522070\pi$
$138$	−12.1792	−1.03677
$139$	−2.66735	−0.226241	−0.113121	−	0.993581i	$-0.536085\pi$
$139$	−2.66735	−0.226241	−0.113121	+	0.993581i	$0.536085\pi$
$140$	−3.89539	−0.329220
$141$	14.6716	1.23557
$142$	−13.2475	−1.11171
$143$	0.323097	0.0270187
$144$	−7.27790	−0.606492
$145$	−3.33062	−0.276593
$146$	19.8342	1.64149
$147$	−8.93214	−0.736711
$148$	9.26268	0.761388
$149$	−13.5340	−1.10875	−0.554375	−	0.832267i	$-0.687043\pi$
$149$	−13.5340	−1.10875	−0.554375	+	0.832267i	$0.687043\pi$
$150$	−4.64308	−0.379106
$151$	−10.1837	−0.828740	−0.414370	−	0.910109i	$-0.635998\pi$
$151$	−10.1837	−0.828740	−0.414370	+	0.910109i	$0.635998\pi$
$152$	2.14693	0.174139
$153$	16.3796	1.32422
$154$	−0.397041	−0.0319945
$155$	−2.06883	−0.166172
$156$	14.7181	1.17840
$157$	−22.8890	−1.82674	−0.913369	−	0.407132i	$-0.866529\pi$
$157$	−22.8890	−1.82674	−0.913369	+	0.407132i	$0.866529\pi$
$158$	18.9661	1.50886
$159$	−14.1430	−1.12161
$160$	−8.11801	−0.641785
$161$	4.57487	0.360550
$162$	22.4257	1.76193
$163$	−13.6533	−1.06941	−0.534704	−	0.845039i	$-0.679577\pi$
$163$	−13.6533	−1.06941	−0.534704	+	0.845039i	$0.679577\pi$
$164$	−19.0486	−1.48745
$165$	−0.249676	−0.0194373
$166$	12.6686	0.983273
$167$	18.1808	1.40687	0.703437	−	0.710758i	$-0.251648\pi$
$167$	18.1808	1.40687	0.703437	+	0.710758i	$0.251648\pi$
$168$	−1.89088	−0.145884
$169$	−4.47250	−0.344039
$170$	16.1078	1.23541
$171$	−9.34958	−0.714980
$172$	−12.5930	−0.960210
$173$	−1.72499	−0.131149	−0.0655743	−	0.997848i	$-0.520888\pi$
$173$	−1.72499	−0.131149	−0.0655743	+	0.997848i	$0.520888\pi$
$174$	−15.4643	−1.17235
$175$	1.74407	0.131839
$176$	−0.384866	−0.0290104
$177$	14.1045	1.06016
$178$	−33.1193	−2.48240
$179$	11.8426	0.885154	0.442577	−	0.896731i	$-0.354064\pi$
$179$	11.8426	0.885154	0.442577	+	0.896731i	$0.354064\pi$
$180$	−4.67310	−0.348312
$181$	6.25342	0.464813	0.232406	−	0.972619i	$-0.425340\pi$
$181$	6.25342	0.464813	0.232406	+	0.972619i	$0.425340\pi$
$182$	−10.4791	−0.776764
$183$	32.8610	2.42915
$184$	−1.26025	−0.0929071
$185$	−4.14715	−0.304905
$186$	−9.60573	−0.704326
$187$	0.866180	0.0633413
$188$	14.5213	1.05908
$189$	−3.57253	−0.259863
$190$	−9.19441	−0.667033
$191$	−15.6548	−1.13274	−0.566372	−	0.824150i	$-0.691653\pi$
$191$	−15.6548	−1.13274	−0.566372	+	0.824150i	$0.691653\pi$
$192$	−21.9934	−1.58724
$193$	16.3325	1.17564	0.587820	−	0.808992i	$-0.299986\pi$
$193$	16.3325	1.17564	0.587820	+	0.808992i	$0.299986\pi$
$194$	−9.73246	−0.698750
$195$	−6.58971	−0.471899
$196$	−8.84070	−0.631478
$197$	−4.55430	−0.324481	−0.162240	−	0.986751i	$-0.551872\pi$
$197$	−4.55430	−0.324481	−0.162240	+	0.986751i	$0.551872\pi$
$198$	−0.476310	−0.0338499
$199$	15.3561	1.08857	0.544284	−	0.838901i	$-0.316801\pi$
$199$	15.3561	1.08857	0.544284	+	0.838901i	$0.316801\pi$
$200$	−0.480444	−0.0339725
$201$	13.9191	0.981781
$202$	−36.5373	−2.57076
$203$	5.80884	0.407701
$204$	39.4574	2.76257
$205$	8.52859	0.595662
$206$	−33.1456	−2.30936
$207$	5.48823	0.381459
$208$	−10.1578	−0.704316
$209$	−0.494420	−0.0341997
$210$	8.09785	0.558805
$211$	22.9656	1.58102	0.790509	−	0.612450i	$-0.209816\pi$
$211$	22.9656	1.58102	0.790509	+	0.612450i	$0.209816\pi$
$212$	−13.9982	−0.961399
$213$	14.5292	0.995521
$214$	−11.0352	−0.754351
$215$	5.63824	0.384525
$216$	0.984135	0.0669619
$217$	3.60818	0.244939
$218$	37.1553	2.51648
$219$	−21.7531	−1.46994
$220$	−0.247120	−0.0166608
$221$	22.8611	1.53780
$222$	−19.2556	−1.29235
$223$	−17.0960	−1.14483	−0.572417	−	0.819963i	$-0.693994\pi$
$223$	−17.0960	−1.14483	−0.572417	+	0.819963i	$0.693994\pi$
$224$	14.1584	0.945996
$225$	2.09227	0.139485
$226$	−4.22155	−0.280813
$227$	27.4819	1.82403	0.912017	−	0.410151i	$-0.134524\pi$
$227$	27.4819	1.82403	0.912017	+	0.410151i	$0.134524\pi$
$228$	−22.5225	−1.49159
$229$	24.3486	1.60900	0.804499	−	0.593954i	$-0.202434\pi$
$229$	24.3486	1.60900	0.804499	+	0.593954i	$0.202434\pi$
$230$	5.39715	0.355878
$231$	0.435453	0.0286507
$232$	−1.60018	−0.105057
$233$	26.1099	1.71052	0.855258	−	0.518202i	$-0.173399\pi$
$233$	26.1099	1.71052	0.855258	+	0.518202i	$0.173399\pi$
$234$	−12.5713	−0.821809
$235$	−6.50160	−0.424118
$236$	13.9601	0.908727
$237$	−20.8010	−1.35117
$238$	−28.0931	−1.82101
$239$	−12.8221	−0.829390	−0.414695	−	0.909960i	$-0.636112\pi$
$239$	−12.8221	−0.829390	−0.414695	+	0.909960i	$0.636112\pi$
$240$	7.84954	0.506685
$241$	13.9124	0.896179	0.448089	−	0.893989i	$-0.352105\pi$
$241$	13.9124	0.896179	0.448089	+	0.893989i	$0.352105\pi$
$242$	22.6078	1.45329
$243$	−18.4501	−1.18357
$244$	32.5245	2.08217
$245$	3.95822	0.252881
$246$	39.5989	2.52473
$247$	−13.0492	−0.830302
$248$	−0.993957	−0.0631163
$249$	−13.8942	−0.880510
$250$	2.05755	0.130131
$251$	15.2633	0.963409	0.481704	−	0.876334i	$-0.340018\pi$
$251$	15.2633	0.963409	0.481704	+	0.876334i	$0.340018\pi$
$252$	8.15021	0.513415
$253$	0.290226	0.0182463
$254$	−10.8896	−0.683274
$255$	−17.6662	−1.10630
$256$	11.6381	0.727381
$257$	−13.3060	−0.830005	−0.415002	−	0.909820i	$-0.636219\pi$
$257$	−13.3060	−0.830005	−0.415002	+	0.909820i	$0.636219\pi$
$258$	26.1788	1.62982
$259$	7.23293	0.449432
$260$	−6.52225	−0.404493
$261$	6.96857	0.431344
$262$	−34.7212	−2.14508
$263$	−18.2302	−1.12412	−0.562060	−	0.827096i	$-0.689991\pi$
$263$	−18.2302	−1.12412	−0.562060	+	0.827096i	$0.689991\pi$
$264$	−0.119956	−0.00738276
$265$	6.26737	0.385001
$266$	16.0357	0.983212
$267$	36.3234	2.22296
$268$	13.7766	0.841542
$269$	−1.24060	−0.0756406	−0.0378203	−	0.999285i	$-0.512041\pi$
$269$	−1.24060	−0.0756406	−0.0378203	+	0.999285i	$0.512041\pi$
$270$	−4.21465	−0.256495
$271$	−4.38394	−0.266306	−0.133153	−	0.991096i	$-0.542510\pi$
$271$	−4.38394	−0.266306	−0.133153	+	0.991096i	$0.542510\pi$
$272$	−27.2317	−1.65116
$273$	11.4929	0.695583
$274$	3.33694	0.201592
$275$	0.110642	0.00667199
$276$	13.2208	0.795797
$277$	0.361576	0.0217250	0.0108625	−	0.999941i	$-0.496542\pi$
$277$	0.361576	0.0217250	0.0108625	+	0.999941i	$0.496542\pi$
$278$	5.48819	0.329160
$279$	4.32855	0.259144
$280$	0.837929	0.0500758
$281$	−4.78840	−0.285652	−0.142826	−	0.989748i	$-0.545619\pi$
$281$	−4.78840	−0.285652	−0.142826	+	0.989748i	$0.545619\pi$
$282$	−30.1874	−1.79763
$283$	24.7687	1.47235	0.736173	−	0.676793i	$-0.236631\pi$
$283$	24.7687	1.47235	0.736173	+	0.676793i	$0.236631\pi$
$284$	14.3804	0.853320
$285$	10.0839	0.597320
$286$	−0.664787	−0.0393097
$287$	−14.8745	−0.878011
$288$	16.9851	1.00086
$289$	44.2876	2.60515
$290$	6.85291	0.402417
$291$	10.6740	0.625723
$292$	−21.5304	−1.25997
$293$	−23.7776	−1.38910	−0.694551	−	0.719443i	$-0.744397\pi$
$293$	−23.7776	−1.38910	−0.694551	+	0.719443i	$0.744397\pi$
$294$	18.3783	1.07185
$295$	−6.25033	−0.363908
$296$	−1.99248	−0.115810
$297$	−0.226638	−0.0131509
$298$	27.8469	1.61313
$299$	7.65994	0.442986
$300$	5.04014	0.290992
$301$	−9.83349	−0.566793
$302$	20.9535	1.20574
$303$	40.0722	2.30208
$304$	15.5440	0.891508
$305$	−14.5621	−0.833824
$306$	−33.7019	−1.92661
$307$	−6.92603	−0.395289	−0.197645	−	0.980274i	$-0.563329\pi$
$307$	−6.92603	−0.395289	−0.197645	+	0.980274i	$0.563329\pi$
$308$	0.430995	0.0245582
$309$	36.3523	2.06801
$310$	4.25671	0.241765
$311$	−1.58296	−0.0897615	−0.0448808	−	0.998992i	$-0.514291\pi$
$311$	−1.58296	−0.0897615	−0.0448808	+	0.998992i	$0.514291\pi$
$312$	−3.16599	−0.179239
$313$	7.82229	0.442142	0.221071	−	0.975258i	$-0.429045\pi$
$313$	7.82229	0.442142	0.221071	+	0.975258i	$0.429045\pi$
$314$	47.0952	2.65773
$315$	−3.64907	−0.205602
$316$	−20.5880	−1.15817
$317$	31.4187	1.76465	0.882326	−	0.470639i	$-0.155976\pi$
$317$	31.4187	1.76465	0.882326	+	0.470639i	$0.155976\pi$
$318$	29.0999	1.63184
$319$	0.368508	0.0206325
$320$	9.74625	0.544832
$321$	12.1028	0.675513
$322$	−9.41301	−0.524566
$323$	−34.9833	−1.94652
$324$	−24.3434	−1.35241
$325$	2.92019	0.161983
$326$	28.0923	1.55589
$327$	−40.7499	−2.25348
$328$	4.09751	0.226247
$329$	11.3392	0.625153
$330$	0.513721	0.0282794
$331$	−18.3471	−1.00845	−0.504223	−	0.863573i	$-0.668221\pi$
$331$	−18.3471	−1.00845	−0.504223	+	0.863573i	$0.668221\pi$
$332$	−13.7520	−0.754737
$333$	8.67698	0.475495
$334$	−37.4079	−2.04687
$335$	−6.16818	−0.337003
$336$	−13.6901	−0.746858
$337$	14.1291	0.769661	0.384831	−	0.922987i	$-0.374260\pi$
$337$	14.1291	0.769661	0.384831	+	0.922987i	$0.374260\pi$
$338$	9.20239	0.500544
$339$	4.62997	0.251465
$340$	−17.4853	−0.948273
$341$	0.228900	0.0123956
$342$	19.2372	1.04023
$343$	−19.1119	−1.03195
$344$	2.70886	0.146052
$345$	−5.91930	−0.318684
$346$	3.54925	0.190809
$347$	−16.2290	−0.871216	−0.435608	−	0.900136i	$-0.643467\pi$
$347$	−16.2290	−0.871216	−0.435608	+	0.900136i	$0.643467\pi$
$348$	16.7868	0.899867
$349$	−11.1627	−0.597526	−0.298763	−	0.954327i	$-0.596574\pi$
$349$	−11.1627	−0.597526	−0.298763	+	0.954327i	$0.596574\pi$
$350$	−3.58851	−0.191814
$351$	−5.98167	−0.319278
$352$	0.898196	0.0478740
$353$	−8.59736	−0.457591	−0.228796	−	0.973475i	$-0.573479\pi$
$353$	−8.59736	−0.457591	−0.228796	+	0.973475i	$0.573479\pi$
$354$	−29.0207	−1.54243
$355$	−6.43850	−0.341720
$356$	35.9516	1.90543
$357$	30.8110	1.63069
$358$	−24.3666	−1.28782
$359$	−6.94667	−0.366631	−0.183315	−	0.983054i	$-0.558683\pi$
$359$	−6.94667	−0.366631	−0.183315	+	0.983054i	$0.558683\pi$
$360$	1.00522	0.0529798
$361$	0.968616	0.0509798
$362$	−12.8667	−0.676259
$363$	−24.7950	−1.30140
$364$	11.3753	0.596226
$365$	9.63973	0.504567
$366$	−67.6130	−3.53419
$367$	−35.0879	−1.83158	−0.915788	−	0.401663i	$-0.868432\pi$
$367$	−35.0879	−1.83158	−0.915788	+	0.401663i	$0.868432\pi$
$368$	−9.12437	−0.475640
$369$	−17.8441	−0.928928
$370$	8.53297	0.443608
$371$	−10.9307	−0.567495
$372$	10.4272	0.540624
$373$	20.1235	1.04196	0.520978	−	0.853570i	$-0.325567\pi$
$373$	20.1235	1.04196	0.520978	+	0.853570i	$0.325567\pi$
$374$	−1.78221	−0.0921557
$375$	−2.25661	−0.116531
$376$	−3.12366	−0.161090
$377$	9.72604	0.500917
$378$	7.35064	0.378076
$379$	15.6445	0.803602	0.401801	−	0.915727i	$-0.368384\pi$
$379$	15.6445	0.803602	0.401801	+	0.915727i	$0.368384\pi$
$380$	9.98069	0.511999
$381$	11.9431	0.611865
$382$	32.2106	1.64804
$383$	−28.9427	−1.47890	−0.739451	−	0.673211i	$-0.764915\pi$
$383$	−28.9427	−1.47890	−0.739451	+	0.673211i	$0.764915\pi$
$384$	8.61428	0.439596
$385$	−0.192968	−0.00983457
$386$	−33.6049	−1.71044
$387$	−11.7967	−0.599662
$388$	10.5648	0.536344
$389$	−6.27767	−0.318290	−0.159145	−	0.987255i	$-0.550874\pi$
$389$	−6.27767	−0.318290	−0.159145	+	0.987255i	$0.550874\pi$
$390$	13.5587	0.686569
$391$	20.5353	1.03851
$392$	1.90170	0.0960506
$393$	38.0803	1.92090
$394$	9.37070	0.472089
$395$	9.21781	0.463798
$396$	0.517043	0.0259824
$397$	−3.91953	−0.196716	−0.0983578	−	0.995151i	$-0.531359\pi$
$397$	−3.91953	−0.196716	−0.0983578	+	0.995151i	$0.531359\pi$
$398$	−31.5960	−1.58376
$399$	−17.5871	−0.880455
$400$	−3.47847	−0.173923
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−28.6393	−1.42840
$403$	6.04137	0.300942
$404$	39.6619	1.97325
$405$	10.8992	0.541586
$406$	−11.9520	−0.593166
$407$	0.458851	0.0227444
$408$	−8.48761	−0.420199
$409$	−10.9654	−0.542204	−0.271102	−	0.962551i	$-0.587388\pi$
$409$	−10.9654	−0.542204	−0.271102	+	0.962551i	$0.587388\pi$
$410$	−17.5480	−0.866633
$411$	−3.65978	−0.180524
$412$	35.9801	1.77261
$413$	10.9010	0.536403
$414$	−11.2923	−0.554987
$415$	6.15713	0.302242
$416$	23.7061	1.16229
$417$	−6.01915	−0.294759
$418$	1.01729	0.0497574
$419$	10.4993	0.512923	0.256461	−	0.966555i	$-0.417443\pi$
$419$	10.4993	0.512923	0.256461	+	0.966555i	$0.417443\pi$
$420$	−8.79035	−0.428925
$421$	−33.6310	−1.63907	−0.819537	−	0.573026i	$-0.805769\pi$
$421$	−33.6310	−1.63907	−0.819537	+	0.573026i	$0.805769\pi$
$422$	−47.2529	−2.30023
$423$	13.6031	0.661406
$424$	3.01112	0.146233
$425$	7.82864	0.379745
$426$	−29.8944	−1.44839
$427$	25.3973	1.22906
$428$	11.9789	0.579022
$429$	0.729102	0.0352014
$430$	−11.6010	−0.559448
$431$	−3.41863	−0.164670	−0.0823348	−	0.996605i	$-0.526238\pi$
$431$	−3.41863	−0.164670	−0.0823348	+	0.996605i	$0.526238\pi$
$432$	7.12524	0.342813
$433$	−12.7067	−0.610643	−0.305321	−	0.952249i	$-0.598764\pi$
$433$	−12.7067	−0.610643	−0.305321	+	0.952249i	$0.598764\pi$
$434$	−7.42401	−0.356364
$435$	−7.51590	−0.360360
$436$	−40.3327	−1.93159
$437$	−11.7216	−0.560722
$438$	44.7580	2.13862
$439$	−2.31137	−0.110316	−0.0551579	−	0.998478i	$-0.517566\pi$
$439$	−2.31137	−0.110316	−0.0551579	+	0.998478i	$0.517566\pi$
$440$	0.0531575	0.00253419
$441$	−8.28167	−0.394365
$442$	−47.0378	−2.23736
$443$	21.1390	1.00434	0.502172	−	0.864768i	$-0.332534\pi$
$443$	21.1390	1.00434	0.502172	+	0.864768i	$0.332534\pi$
$444$	20.9022	0.991976
$445$	−16.0965	−0.763047
$446$	35.1758	1.66562
$447$	−30.5409	−1.44454
$448$	−16.9981	−0.803087
$449$	−27.9970	−1.32126	−0.660630	−	0.750712i	$-0.729711\pi$
$449$	−27.9970	−1.32126	−0.660630	+	0.750712i	$0.729711\pi$
$450$	−4.30495	−0.202937
$451$	−0.943623	−0.0444335
$452$	4.58257	0.215546
$453$	−22.9807	−1.07973
$454$	−56.5452	−2.65380
$455$	−5.09301	−0.238764
$456$	4.84477	0.226877
$457$	−40.3178	−1.88599	−0.942993	−	0.332813i	$-0.892002\pi$
$457$	−40.3178	−1.88599	−0.942993	+	0.332813i	$0.892002\pi$
$458$	−50.0983	−2.34094
$459$	−16.0361	−0.748499
$460$	−5.85870	−0.273163
$461$	12.5864	0.586208	0.293104	−	0.956081i	$-0.405312\pi$
$461$	12.5864	0.586208	0.293104	+	0.956081i	$0.405312\pi$
$462$	−0.895966	−0.0416841
$463$	−18.7673	−0.872190	−0.436095	−	0.899901i	$-0.643639\pi$
$463$	−18.7673	−0.872190	−0.436095	+	0.899901i	$0.643639\pi$
$464$	−11.5855	−0.537842
$465$	−4.66853	−0.216498
$466$	−53.7224	−2.48864
$467$	7.67407	0.355113	0.177557	−	0.984111i	$-0.443181\pi$
$467$	7.67407	0.355113	0.177557	+	0.984111i	$0.443181\pi$
$468$	13.6463	0.630801
$469$	10.7577	0.496746
$470$	13.3774	0.617051
$471$	−51.6514	−2.37997
$472$	−3.00293	−0.138221
$473$	−0.623829	−0.0286837
$474$	42.7990	1.96582
$475$	−4.46863	−0.205035
$476$	30.4956	1.39776
$477$	−13.1130	−0.600405
$478$	26.3820	1.20668
$479$	−12.0412	−0.550178	−0.275089	−	0.961419i	$-0.588707\pi$
$479$	−12.0412	−0.550178	−0.275089	+	0.961419i	$0.588707\pi$
$480$	−18.3191	−0.836151
$481$	12.1105	0.552190
$482$	−28.6255	−1.30386
$483$	10.3237	0.469743
$484$	−24.5412	−1.11551
$485$	−4.73013	−0.214784
$486$	37.9619	1.72199
$487$	−33.8822	−1.53535	−0.767674	−	0.640841i	$-0.778586\pi$
$487$	−33.8822	−1.53535	−0.767674	+	0.640841i	$0.778586\pi$
$488$	−6.99629	−0.316707
$489$	−30.8101	−1.39328
$490$	−8.14423	−0.367919
$491$	28.7802	1.29883	0.649417	−	0.760433i	$-0.275013\pi$
$491$	28.7802	1.29883	0.649417	+	0.760433i	$0.275013\pi$
$492$	−42.9853	−1.93792
$493$	26.0742	1.17432
$494$	26.8494	1.20801
$495$	−0.231494	−0.0104049
$496$	−7.19636	−0.323126
$497$	11.2292	0.503698
$498$	28.5880	1.28106
$499$	3.44769	0.154340	0.0771700	−	0.997018i	$-0.475412\pi$
$499$	3.44769	0.154340	0.0771700	+	0.997018i	$0.475412\pi$
$500$	−2.23350	−0.0998853
$501$	41.0269	1.83295
$502$	−31.4049	−1.40167
$503$	19.0585	0.849776	0.424888	−	0.905246i	$-0.360314\pi$
$503$	19.0585	0.849776	0.424888	+	0.905246i	$0.360314\pi$
$504$	−1.75317	−0.0780926
$505$	−17.7577	−0.790208
$506$	−0.597154	−0.0265467
$507$	−10.0927	−0.448232
$508$	11.8208	0.524465
$509$	−28.0395	−1.24283	−0.621414	−	0.783482i	$-0.713442\pi$
$509$	−28.0395	−1.24283	−0.621414	+	0.783482i	$0.713442\pi$
$510$	36.3490	1.60956
$511$	−16.8124	−0.743735
$512$	−31.5807	−1.39568
$513$	9.15346	0.404135
$514$	27.3777	1.20758
$515$	−16.1093	−0.709860
$516$	−28.4175	−1.25101
$517$	0.719353	0.0316371
$518$	−14.8821	−0.653882
$519$	−3.89263	−0.170867
$520$	1.40299	0.0615251
$521$	−31.6635	−1.38720	−0.693602	−	0.720358i	$-0.743977\pi$
$521$	−31.6635	−1.38720	−0.693602	+	0.720358i	$0.743977\pi$
$522$	−14.3382	−0.627564
$523$	−3.77292	−0.164978	−0.0824891	−	0.996592i	$-0.526287\pi$
$523$	−3.77292	−0.164978	−0.0824891	+	0.996592i	$0.526287\pi$
$524$	37.6905	1.64652
$525$	3.93568	0.171767
$526$	37.5095	1.63549
$527$	16.1961	0.705514
$528$	−0.868492	−0.0377962
$529$	−16.1194	−0.700842
$530$	−12.8954	−0.560141
$531$	13.0774	0.567510
$532$	−17.4070	−0.754690
$533$	−24.9051	−1.07876
$534$	−74.7372	−3.23420
$535$	−5.36328	−0.231875
$536$	−2.96347	−0.128002
$537$	26.7240	1.15322
$538$	2.55259	0.110050
$539$	−0.437947	−0.0188637
$540$	4.57507	0.196880
$541$	32.4080	1.39333	0.696664	−	0.717398i	$-0.254667\pi$
$541$	32.4080	1.39333	0.696664	+	0.717398i	$0.254667\pi$
$542$	9.02018	0.387450
$543$	14.1115	0.605582
$544$	63.5529	2.72481
$545$	18.0581	0.773522
$546$	−23.6472	−1.01201
$547$	−21.4597	−0.917548	−0.458774	−	0.888553i	$-0.651711\pi$
$547$	−21.4597	−0.917548	−0.458774	+	0.888553i	$0.651711\pi$
$548$	−3.62231	−0.154737
$549$	30.4679	1.30034
$550$	−0.227652	−0.00970712
$551$	−14.8833	−0.634050
$552$	−2.84389	−0.121044
$553$	−16.0765	−0.683642
$554$	−0.743961	−0.0316079
$555$	−9.35850	−0.397246
$556$	−5.95753	−0.252655
$557$	−28.6277	−1.21300	−0.606498	−	0.795085i	$-0.707426\pi$
$557$	−28.6277	−1.21300	−0.606498	+	0.795085i	$0.707426\pi$
$558$	−8.90620	−0.377030
$559$	−16.4647	−0.696384
$560$	6.06669	0.256365
$561$	1.95463	0.0825244
$562$	9.85237	0.415597
$563$	−17.2558	−0.727247	−0.363623	−	0.931546i	$-0.618460\pi$
$563$	−17.2558	−0.727247	−0.363623	+	0.931546i	$0.618460\pi$
$564$	32.7690	1.37982
$565$	−2.05174	−0.0863173
$566$	−50.9628	−2.14213
$567$	−19.0090	−0.798303
$568$	−3.09334	−0.129794
$569$	1.67484	0.0702128	0.0351064	−	0.999384i	$-0.488823\pi$
$569$	1.67484	0.0702128	0.0351064	+	0.999384i	$0.488823\pi$
$570$	−20.7482	−0.869045
$571$	13.1291	0.549434	0.274717	−	0.961525i	$-0.411416\pi$
$571$	13.1291	0.549434	0.274717	+	0.961525i	$0.411416\pi$
$572$	0.721637	0.0301732
$573$	−35.3268	−1.47580
$574$	30.6049	1.27742
$575$	2.62310	0.109391
$576$	−20.3918	−0.849658
$577$	26.2818	1.09413	0.547063	−	0.837091i	$-0.315746\pi$
$577$	26.2818	1.09413	0.547063	+	0.837091i	$0.315746\pi$
$578$	−91.1238	−3.79025
$579$	36.8560	1.53168
$580$	−7.43896	−0.308886
$581$	−10.7385	−0.445507
$582$	−21.9623	−0.910368
$583$	−0.693437	−0.0287192
$584$	4.63136	0.191647
$585$	−6.10983	−0.252610
$586$	48.9236	2.02101
$587$	18.2512	0.753309	0.376654	−	0.926354i	$-0.377074\pi$
$587$	18.2512	0.753309	0.376654	+	0.926354i	$0.377074\pi$
$588$	−19.9500	−0.822723
$589$	−9.24482	−0.380926
$590$	12.8603	0.529452
$591$	−10.2773	−0.422750
$592$	−14.4258	−0.592895
$593$	−46.7814	−1.92108	−0.960542	−	0.278136i	$-0.910283\pi$
$593$	−46.7814	−1.92108	−0.960542	+	0.278136i	$0.910283\pi$
$594$	0.466319	0.0191333
$595$	−13.6537	−0.559747
$596$	−30.2283	−1.23820
$597$	34.6528	1.41824
$598$	−15.7607	−0.644503
$599$	3.01280	0.123100	0.0615499	−	0.998104i	$-0.480396\pi$
$599$	3.01280	0.123100	0.0615499	+	0.998104i	$0.480396\pi$
$600$	−1.08417	−0.0442612
$601$	−33.8184	−1.37948	−0.689740	−	0.724057i	$-0.742275\pi$
$601$	−33.8184	−1.37948	−0.689740	+	0.724057i	$0.742275\pi$
$602$	20.2329	0.824630
$603$	12.9055	0.525553
$604$	−22.7454	−0.925496
$605$	10.9878	0.446716
$606$	−82.4504	−3.34932
$607$	6.55730	0.266152	0.133076	−	0.991106i	$-0.457514\pi$
$607$	6.55730	0.266152	0.133076	+	0.991106i	$0.457514\pi$
$608$	−36.2763	−1.47120
$609$	13.1083	0.531174
$610$	29.9622	1.21314
$611$	18.9859	0.768087
$612$	36.5840	1.47882
$613$	−25.4995	−1.02992	−0.514958	−	0.857216i	$-0.672192\pi$
$613$	−25.4995	−1.02992	−0.514958	+	0.857216i	$0.672192\pi$
$614$	14.2506	0.575109
$615$	19.2457	0.776060
$616$	−0.0927104	−0.00373541
$617$	0.489412	0.0197030	0.00985150	−	0.999951i	$-0.496864\pi$
$617$	0.489412	0.0197030	0.00985150	+	0.999951i	$0.496864\pi$
$618$	−74.7966	−3.00876
$619$	−15.6424	−0.628722	−0.314361	−	0.949303i	$-0.601790\pi$
$619$	−15.6424	−0.628722	−0.314361	+	0.949303i	$0.601790\pi$
$620$	−4.62074	−0.185573
$621$	−5.37311	−0.215616
$622$	3.25702	0.130595
$623$	28.0734	1.12474
$624$	−22.9221	−0.917619
$625$	1.00000	0.0400000
$626$	−16.0947	−0.643275
$627$	−1.11571	−0.0445572
$628$	−51.1226	−2.04001
$629$	32.4666	1.29453
$630$	7.50813	0.299131
$631$	−19.1287	−0.761502	−0.380751	−	0.924678i	$-0.624334\pi$
$631$	−19.1287	−0.761502	−0.380751	+	0.924678i	$0.624334\pi$
$632$	4.42864	0.176162
$633$	51.8244	2.05983
$634$	−64.6456	−2.56740
$635$	−5.29251	−0.210027
$636$	−31.5884	−1.25256
$637$	−11.5587	−0.457974
$638$	−0.758223	−0.0300183
$639$	13.4711	0.532908
$640$	−3.81736	−0.150894
$641$	−34.0967	−1.34674	−0.673369	−	0.739306i	$-0.735153\pi$
$641$	−34.0967	−1.34674	−0.673369	+	0.739306i	$0.735153\pi$
$642$	−24.9021	−0.982807
$643$	15.8945	0.626820	0.313410	−	0.949618i	$-0.398529\pi$
$643$	15.8945	0.626820	0.313410	+	0.949618i	$0.398529\pi$
$644$	10.2180	0.402645
$645$	12.7233	0.500979
$646$	71.9797	2.83200
$647$	0.773402	0.0304056	0.0152028	−	0.999884i	$-0.495161\pi$
$647$	0.773402	0.0304056	0.0152028	+	0.999884i	$0.495161\pi$
$648$	5.23647	0.205708
$649$	0.691551	0.0271458
$650$	−6.00843	−0.235670
$651$	8.14225	0.319120
$652$	−30.4947	−1.19426
$653$	−28.8113	−1.12747	−0.563736	−	0.825955i	$-0.690636\pi$
$653$	−28.8113	−1.12747	−0.563736	+	0.825955i	$0.690636\pi$
$654$	83.8450	3.27860
$655$	−16.8750	−0.659362
$656$	29.6664	1.15828
$657$	−20.1689	−0.786865
$658$	−23.3310	−0.909539
$659$	3.94941	0.153847	0.0769236	−	0.997037i	$-0.475490\pi$
$659$	3.94941	0.153847	0.0769236	+	0.997037i	$0.475490\pi$
$660$	−0.557653	−0.0217066
$661$	5.85556	0.227755	0.113877	−	0.993495i	$-0.463673\pi$
$661$	5.85556	0.227755	0.113877	+	0.993495i	$0.463673\pi$
$662$	37.7500	1.46719
$663$	51.5885	2.00353
$664$	2.95816	0.114799
$665$	7.79360	0.302223
$666$	−17.8533	−0.691801
$667$	8.73655	0.338281
$668$	40.6069	1.57113
$669$	−38.5790	−1.49155
$670$	12.6913	0.490308
$671$	1.61119	0.0621992
$672$	31.9499	1.23249
$673$	−5.15756	−0.198809	−0.0994046	−	0.995047i	$-0.531694\pi$
$673$	−5.15756	−0.198809	−0.0994046	+	0.995047i	$0.531694\pi$
$674$	−29.0713	−1.11979
$675$	−2.04838	−0.0788424
$676$	−9.98935	−0.384206
$677$	−16.5217	−0.634979	−0.317490	−	0.948262i	$-0.602840\pi$
$677$	−16.5217	−0.634979	−0.317490	+	0.948262i	$0.602840\pi$
$678$	−9.52638	−0.365858
$679$	8.24967	0.316593
$680$	3.76123	0.144236
$681$	62.0157	2.37645
$682$	−0.470973	−0.0180345
$683$	−14.6475	−0.560470	−0.280235	−	0.959931i	$-0.590412\pi$
$683$	−14.6475	−0.560470	−0.280235	+	0.959931i	$0.590412\pi$
$684$	−20.8823	−0.798456
$685$	1.62181	0.0619660
$686$	39.3237	1.50138
$687$	54.9451	2.09629
$688$	19.6125	0.747718
$689$	−18.3019	−0.697246
$690$	12.1792	0.463656
$691$	15.3252	0.582998	0.291499	−	0.956571i	$-0.405846\pi$
$691$	15.3252	0.582998	0.291499	+	0.956571i	$0.405846\pi$
$692$	−3.85277	−0.146460
$693$	0.403742	0.0153369
$694$	33.3919	1.26754
$695$	2.66735	0.101178
$696$	−3.61097	−0.136874
$697$	−66.7672	−2.52899
$698$	22.9678	0.869345
$699$	58.9198	2.22855
$700$	3.89539	0.147232
$701$	−32.8409	−1.24038	−0.620192	−	0.784450i	$-0.712946\pi$
$701$	−32.8409	−1.24038	−0.620192	+	0.784450i	$0.712946\pi$
$702$	12.3076	0.464519
$703$	−18.5321	−0.698951
$704$	−1.07835	−0.0406418
$705$	−14.6716	−0.552563
$706$	17.6895	0.665752
$707$	30.9707	1.16477
$708$	31.5025	1.18394
$709$	−25.3498	−0.952032	−0.476016	−	0.879437i	$-0.657920\pi$
$709$	−25.3498	−0.952032	−0.476016	+	0.879437i	$0.657920\pi$
$710$	13.2475	0.497170
$711$	−19.2862	−0.723287
$712$	−7.73347	−0.289824
$713$	5.42674	0.203233
$714$	−63.3951	−2.37250
$715$	−0.323097	−0.0120831
$716$	26.4504	0.988497
$717$	−28.9343	−1.08057
$718$	14.2931	0.533414
$719$	3.82068	0.142487	0.0712436	−	0.997459i	$-0.477303\pi$
$719$	3.82068	0.142487	0.0712436	+	0.997459i	$0.477303\pi$
$720$	7.27790	0.271231
$721$	28.0957	1.04634
$722$	−1.99297	−0.0741708
$723$	31.3949	1.16759
$724$	13.9670	0.519081
$725$	3.33062	0.123696
$726$	51.0170	1.89342
$727$	−38.9823	−1.44577	−0.722887	−	0.690966i	$-0.757185\pi$
$727$	−38.9823	−1.44577	−0.722887	+	0.690966i	$0.757185\pi$
$728$	−2.44691	−0.0906885
$729$	−8.93693	−0.330997
$730$	−19.8342	−0.734097
$731$	−44.1398	−1.63257
$732$	73.3951	2.71276
$733$	−5.23475	−0.193350	−0.0966749	−	0.995316i	$-0.530821\pi$
$733$	−5.23475	−0.193350	−0.0966749	+	0.995316i	$0.530821\pi$
$734$	72.1951	2.66477
$735$	8.93214	0.329467
$736$	21.2943	0.784919
$737$	0.682462	0.0251388
$738$	36.7151	1.35150
$739$	−5.44132	−0.200162	−0.100081	−	0.994979i	$-0.531910\pi$
$739$	−5.44132	−0.200162	−0.100081	+	0.994979i	$0.531910\pi$
$740$	−9.26268	−0.340503
$741$	−29.4470	−1.08176
$742$	22.4905	0.825652
$743$	−28.2350	−1.03584	−0.517922	−	0.855428i	$-0.673294\pi$
$743$	−28.2350	−1.03584	−0.517922	+	0.855428i	$0.673294\pi$
$744$	−2.24297	−0.0822313
$745$	13.5340	0.495848
$746$	−41.4051	−1.51595
$747$	−12.8824	−0.471342
$748$	1.93461	0.0707365
$749$	9.35393	0.341785
$750$	4.64308	0.169541
$751$	1.29740	0.0473429	0.0236715	−	0.999720i	$-0.492464\pi$
$751$	1.29740	0.0473429	0.0236715	+	0.999720i	$0.492464\pi$
$752$	−22.6156	−0.824707
$753$	34.4432	1.25518
$754$	−20.0118	−0.728787
$755$	10.1837	0.370624
$756$	−7.97925	−0.290202
$757$	47.7292	1.73475	0.867374	−	0.497656i	$-0.165806\pi$
$757$	47.7292	1.73475	0.867374	+	0.497656i	$0.165806\pi$
$758$	−32.1892	−1.16917
$759$	0.654926	0.0237723
$760$	−2.14693	−0.0778772
$761$	24.4145	0.885025	0.442513	−	0.896762i	$-0.354087\pi$
$761$	24.4145	0.885025	0.442513	+	0.896762i	$0.354087\pi$
$762$	−24.5735	−0.890205
$763$	−31.4945	−1.14018
$764$	−34.9651	−1.26499
$765$	−16.3796	−0.592207
$766$	59.5509	2.15166
$767$	18.2521	0.659046
$768$	26.2626	0.947670
$769$	2.55962	0.0923023	0.0461511	−	0.998934i	$-0.485304\pi$
$769$	2.55962	0.0923023	0.0461511	+	0.998934i	$0.485304\pi$
$770$	0.397041	0.0143084
$771$	−30.0264	−1.08137
$772$	36.4787	1.31290
$773$	40.5639	1.45898	0.729492	−	0.683990i	$-0.239757\pi$
$773$	40.5639	1.45898	0.729492	+	0.683990i	$0.239757\pi$
$774$	24.2724	0.872452
$775$	2.06883	0.0743145
$776$	−2.27256	−0.0815803
$777$	16.3219	0.585544
$778$	12.9166	0.463083
$779$	38.1111	1.36547
$780$	−14.7181	−0.526994
$781$	0.712371	0.0254906
$782$	−42.2523	−1.51094
$783$	−6.82239	−0.243813
$784$	13.7685	0.491734
$785$	22.8890	0.816942
$786$	−78.3521	−2.79473
$787$	14.8553	0.529533	0.264766	−	0.964313i	$-0.414705\pi$
$787$	14.8553	0.529533	0.264766	+	0.964313i	$0.414705\pi$
$788$	−10.1721	−0.362364
$789$	−41.1383	−1.46456
$790$	−18.9661	−0.674783
$791$	3.57838	0.127232
$792$	−0.111220	−0.00395203
$793$	42.5241	1.51008
$794$	8.06462	0.286203
$795$	14.1430	0.501600
$796$	34.2980	1.21566
$797$	−15.1577	−0.536912	−0.268456	−	0.963292i	$-0.586513\pi$
$797$	−15.1577	−0.536912	−0.268456	+	0.963292i	$0.586513\pi$
$798$	36.1863	1.28098
$799$	50.8987	1.80067
$800$	8.11801	0.287015
$801$	33.6782	1.18996
$802$	−2.05755	−0.0726545
$803$	−1.06656	−0.0376382
$804$	31.0885	1.09641
$805$	−4.57487	−0.161243
$806$	−12.4304	−0.437842
$807$	−2.79954	−0.0985485
$808$	−8.53159	−0.300140
$809$	39.5317	1.38986	0.694931	−	0.719077i	$-0.255435\pi$
$809$	39.5317	1.38986	0.694931	+	0.719077i	$0.255435\pi$
$810$	−22.4257	−0.787957
$811$	−2.22459	−0.0781160	−0.0390580	−	0.999237i	$-0.512436\pi$
$811$	−2.22459	−0.0781160	−0.0390580	+	0.999237i	$0.512436\pi$
$812$	12.9741	0.455300
$813$	−9.89284	−0.346957
$814$	−0.944108	−0.0330910
$815$	13.6533	0.478254
$816$	−61.4512	−2.15122
$817$	25.1952	0.881468
$818$	22.5618	0.788855
$819$	10.6560	0.372350
$820$	19.0486	0.665207
$821$	−18.4270	−0.643107	−0.321553	−	0.946891i	$-0.604205\pi$
$821$	−18.4270	−0.643107	−0.321553	+	0.946891i	$0.604205\pi$
$822$	7.53017	0.262645
$823$	−42.9756	−1.49803	−0.749017	−	0.662551i	$-0.769474\pi$
$823$	−42.9756	−1.49803	−0.749017	+	0.662551i	$0.769474\pi$
$824$	−7.73961	−0.269622
$825$	0.249676	0.00869262
$826$	−22.4293	−0.780416
$827$	−18.1086	−0.629698	−0.314849	−	0.949142i	$-0.601954\pi$
$827$	−18.1086	−0.629698	−0.314849	+	0.949142i	$0.601954\pi$
$828$	12.2580	0.425995
$829$	−25.1471	−0.873395	−0.436698	−	0.899608i	$-0.643852\pi$
$829$	−25.1471	−0.873395	−0.436698	+	0.899608i	$0.643852\pi$
$830$	−12.6686	−0.439733
$831$	0.815935	0.0283045
$832$	−28.4609	−0.986703
$833$	−30.9875	−1.07365
$834$	12.3847	0.428847
$835$	−18.1808	−0.629173
$836$	−1.10429	−0.0381926
$837$	−4.23776	−0.146478
$838$	−21.6027	−0.746254
$839$	16.2053	0.559471	0.279735	−	0.960077i	$-0.409753\pi$
$839$	16.2053	0.559471	0.279735	+	0.960077i	$0.409753\pi$
$840$	1.89088	0.0652414
$841$	−17.9070	−0.617481
$842$	69.1974	2.38470
$843$	−10.8055	−0.372163
$844$	51.2938	1.76561
$845$	4.47250	0.153859
$846$	−27.9891	−0.962284
$847$	−19.1634	−0.658463
$848$	21.8008	0.748644
$849$	55.8932	1.91825
$850$	−16.1078	−0.552493
$851$	10.8784	0.372907
$852$	32.4509	1.11175
$853$	49.3716	1.69045	0.845225	−	0.534411i	$-0.179466\pi$
$853$	49.3716	1.69045	0.845225	+	0.534411i	$0.179466\pi$
$854$	−52.2563	−1.78817
$855$	9.34958	0.319749
$856$	−2.57676	−0.0880717
$857$	12.1925	0.416488	0.208244	−	0.978077i	$-0.433225\pi$
$857$	12.1925	0.416488	0.208244	+	0.978077i	$0.433225\pi$
$858$	−1.50016	−0.0512147
$859$	−0.0488364	−0.00166628	−0.000833139	−	1.00000i	$-0.500265\pi$
$859$	−0.0488364	−0.00166628	−0.000833139		1.00000i	$0.500265\pi$
$860$	12.5930	0.429419
$861$	−33.5658	−1.14392
$862$	7.03400	0.239579
$863$	−51.2943	−1.74608	−0.873039	−	0.487651i	$-0.837854\pi$
$863$	−51.2943	−1.74608	−0.873039	+	0.487651i	$0.837854\pi$
$864$	−16.6288	−0.565723
$865$	1.72499	0.0586515
$866$	26.1446	0.888428
$867$	99.9396	3.39413
$868$	8.05889	0.273536
$869$	−1.01988	−0.0345971
$870$	15.4643	0.524290
$871$	18.0122	0.610321
$872$	8.67590	0.293803
$873$	9.89671	0.334953
$874$	24.1178	0.815798
$875$	−1.74407	−0.0589603
$876$	−48.5856	−1.64155
$877$	23.0733	0.779131	0.389566	−	0.920999i	$-0.372625\pi$
$877$	23.0733	0.779131	0.389566	+	0.920999i	$0.372625\pi$
$878$	4.75576	0.160499
$879$	−53.6567	−1.80980
$880$	0.384866	0.0129738
$881$	6.84384	0.230575	0.115287	−	0.993332i	$-0.463221\pi$
$881$	6.84384	0.230575	0.115287	+	0.993332i	$0.463221\pi$
$882$	17.0399	0.573765
$883$	−51.9033	−1.74669	−0.873343	−	0.487105i	$-0.838053\pi$
$883$	−51.9033	−1.74669	−0.873343	+	0.487105i	$0.838053\pi$
$884$	51.0603	1.71734
$885$	−14.1045	−0.474118
$886$	−43.4945	−1.46123
$887$	11.3815	0.382153	0.191077	−	0.981575i	$-0.438802\pi$
$887$	11.3815	0.382153	0.191077	+	0.981575i	$0.438802\pi$
$888$	−4.49624	−0.150884
$889$	9.23051	0.309582
$890$	33.1193	1.11016
$891$	−1.20592	−0.0403997
$892$	−38.1840	−1.27849
$893$	−29.0532	−0.972229
$894$	62.8394	2.10167
$895$	−11.8426	−0.395853
$896$	6.65774	0.222420
$897$	17.2855	0.577145
$898$	57.6051	1.92231
$899$	6.89049	0.229811
$900$	4.67310	0.155770
$901$	−49.0650	−1.63459
$902$	1.94155	0.0646466
$903$	−22.1903	−0.738447
$904$	−0.985747	−0.0327854
$905$	−6.25342	−0.207871
$906$	47.2838	1.57090
$907$	43.6637	1.44983	0.724914	−	0.688839i	$-0.241879\pi$
$907$	43.6637	1.44983	0.724914	+	0.688839i	$0.241879\pi$
$908$	61.3808	2.03699
$909$	37.1540	1.23232
$910$	10.4791	0.347379
$911$	52.4126	1.73651	0.868253	−	0.496121i	$-0.165243\pi$
$911$	52.4126	1.73651	0.868253	+	0.496121i	$0.165243\pi$
$912$	35.0766	1.16150
$913$	−0.681240	−0.0225457
$914$	82.9557	2.74393
$915$	−32.8610	−1.08635
$916$	54.3826	1.79685
$917$	29.4312	0.971905
$918$	32.9950	1.08900
$919$	36.6652	1.20947	0.604736	−	0.796426i	$-0.293279\pi$
$919$	36.6652	1.20947	0.604736	+	0.796426i	$0.293279\pi$
$920$	1.26025	0.0415493
$921$	−15.6293	−0.515004
$922$	−25.8971	−0.852877
$923$	18.8016	0.618863
$924$	0.972586	0.0319957
$925$	4.14715	0.136358
$926$	38.6146	1.26895
$927$	33.7050	1.10702
$928$	27.0380	0.887566
$929$	−7.20115	−0.236262	−0.118131	−	0.992998i	$-0.537690\pi$
$929$	−7.20115	−0.236262	−0.118131	+	0.992998i	$0.537690\pi$
$930$	9.60573	0.314984
$931$	17.6878	0.579694
$932$	58.3165	1.91022
$933$	−3.57212	−0.116946
$934$	−15.7898	−0.516657
$935$	−0.866180	−0.0283271
$936$	−2.93543	−0.0959476
$937$	9.80729	0.320390	0.160195	−	0.987085i	$-0.448788\pi$
$937$	9.80729	0.320390	0.160195	+	0.987085i	$0.448788\pi$
$938$	−22.1345	−0.722719
$939$	17.6518	0.576046
$940$	−14.5213	−0.473634
$941$	−11.9740	−0.390342	−0.195171	−	0.980769i	$-0.562526\pi$
$941$	−11.9740	−0.390342	−0.195171	+	0.980769i	$0.562526\pi$
$942$	106.275	3.46263
$943$	−22.3713	−0.728510
$944$	−21.7416	−0.707628
$945$	3.57253	0.116214
$946$	1.28356	0.0417321
$947$	−44.4176	−1.44338	−0.721690	−	0.692217i	$-0.756634\pi$
$947$	−44.4176	−1.44338	−0.721690	+	0.692217i	$0.756634\pi$
$948$	−46.4590	−1.50892
$949$	−28.1498	−0.913782
$950$	9.19441	0.298306
$951$	70.8997	2.29908
$952$	−6.55984	−0.212606
$953$	3.11428	0.100881	0.0504407	−	0.998727i	$-0.483937\pi$
$953$	3.11428	0.100881	0.0504407	+	0.998727i	$0.483937\pi$
$954$	26.9807	0.873533
$955$	15.6548	0.506579
$956$	−28.6381	−0.926223
$957$	0.831578	0.0268811
$958$	24.7754	0.800457
$959$	−2.82854	−0.0913384
$960$	21.9934	0.709835
$961$	−26.7199	−0.861934
$962$	−24.9179	−0.803384
$963$	11.2214	0.361606
$964$	31.0735	1.00081
$965$	−16.3325	−0.525762
$966$	−21.2415	−0.683432
$967$	11.6157	0.373535	0.186768	−	0.982404i	$-0.440199\pi$
$967$	11.6157	0.373535	0.186768	+	0.982404i	$0.440199\pi$
$968$	5.27901	0.169674
$969$	−78.9434	−2.53603
$970$	9.73246	0.312491
$971$	−37.9544	−1.21802	−0.609008	−	0.793164i	$-0.708432\pi$
$971$	−37.9544	−1.21802	−0.609008	+	0.793164i	$0.708432\pi$
$972$	−41.2083	−1.32176
$973$	−4.65204	−0.149138
$974$	69.7142	2.23379
$975$	6.58971	0.211040
$976$	−50.6539	−1.62139
$977$	39.7155	1.27061	0.635306	−	0.772260i	$-0.280874\pi$
$977$	39.7155	1.27061	0.635306	+	0.772260i	$0.280874\pi$
$978$	63.3932	2.02709
$979$	1.78095	0.0569196
$980$	8.84070	0.282406
$981$	−37.7824	−1.20630
$982$	−59.2167	−1.88968
$983$	21.4957	0.685606	0.342803	−	0.939407i	$-0.388624\pi$
$983$	21.4957	0.685606	0.342803	+	0.939407i	$0.388624\pi$
$984$	9.24647	0.294767
$985$	4.55430	0.145112
$986$	−53.6490	−1.70853
$987$	25.5882	0.814482
$988$	−29.1455	−0.927242
$989$	−14.7897	−0.470284
$990$	0.476310	0.0151381
$991$	−47.7292	−1.51617	−0.758085	−	0.652156i	$-0.773865\pi$
$991$	−47.7292	−1.51617	−0.758085	+	0.652156i	$0.773865\pi$
$992$	16.7948	0.533234
$993$	−41.4021	−1.31386
$994$	−23.1046	−0.732833
$995$	−15.3561	−0.486823
$996$	−31.0328	−0.983311
$997$	−35.7169	−1.13117	−0.565583	−	0.824691i	$-0.691349\pi$
$997$	−35.7169	−1.13117	−0.565583	+	0.824691i	$0.691349\pi$
$998$	−7.09379	−0.224550
$999$	−8.49497	−0.268769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.f.1.6	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.f.1.6	✓	37	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05755 q^{2} +2.25661 q^{3} +2.23350 q^{4} -1.00000 q^{5} -4.64308 q^{6} +1.74407 q^{7} -0.480444 q^{8} +2.09227 q^{9} +O(q^{10})\)	\(q-2.05755 q^{2} +2.25661 q^{3} +2.23350 q^{4} -1.00000 q^{5} -4.64308 q^{6} +1.74407 q^{7} -0.480444 q^{8} +2.09227 q^{9} +2.05755 q^{10} +0.110642 q^{11} +5.04014 q^{12} +2.92019 q^{13} -3.58851 q^{14} -2.25661 q^{15} -3.47847 q^{16} +7.82864 q^{17} -4.30495 q^{18} -4.46863 q^{19} -2.23350 q^{20} +3.93568 q^{21} -0.227652 q^{22} +2.62310 q^{23} -1.08417 q^{24} +1.00000 q^{25} -6.00843 q^{26} -2.04838 q^{27} +3.89539 q^{28} +3.33062 q^{29} +4.64308 q^{30} +2.06883 q^{31} +8.11801 q^{32} +0.249676 q^{33} -16.1078 q^{34} -1.74407 q^{35} +4.67310 q^{36} +4.14715 q^{37} +9.19441 q^{38} +6.58971 q^{39} +0.480444 q^{40} -8.52859 q^{41} -8.09785 q^{42} -5.63824 q^{43} +0.247120 q^{44} -2.09227 q^{45} -5.39715 q^{46} +6.50160 q^{47} -7.84954 q^{48} -3.95822 q^{49} -2.05755 q^{50} +17.6662 q^{51} +6.52225 q^{52} -6.26737 q^{53} +4.21465 q^{54} -0.110642 q^{55} -0.837929 q^{56} -10.0839 q^{57} -6.85291 q^{58} +6.25033 q^{59} -5.04014 q^{60} +14.5621 q^{61} -4.25671 q^{62} +3.64907 q^{63} -9.74625 q^{64} -2.92019 q^{65} -0.513721 q^{66} +6.16818 q^{67} +17.4853 q^{68} +5.91930 q^{69} +3.58851 q^{70} +6.43850 q^{71} -1.00522 q^{72} -9.63973 q^{73} -8.53297 q^{74} +2.25661 q^{75} -9.98069 q^{76} +0.192968 q^{77} -13.5587 q^{78} -9.21781 q^{79} +3.47847 q^{80} -10.8992 q^{81} +17.5480 q^{82} -6.15713 q^{83} +8.79035 q^{84} -7.82864 q^{85} +11.6010 q^{86} +7.51590 q^{87} -0.0531575 q^{88} +16.0965 q^{89} +4.30495 q^{90} +5.09301 q^{91} +5.85870 q^{92} +4.66853 q^{93} -13.3774 q^{94} +4.46863 q^{95} +18.3191 q^{96} +4.73013 q^{97} +8.14423 q^{98} +0.231494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * q^99

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