LMFDB - Embedded newform 2005.2.a.g.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.16173 q^{2} -0.113518 q^{3} +2.67309 q^{4} +1.00000 q^{5} +0.245396 q^{6} -2.73299 q^{7} -1.45504 q^{8} -2.98711 q^{9} +O(q^{10})$	\(q-2.16173 q^{2} -0.113518 q^{3} +2.67309 q^{4} +1.00000 q^{5} +0.245396 q^{6} -2.73299 q^{7} -1.45504 q^{8} -2.98711 q^{9} -2.16173 q^{10} +1.80454 q^{11} -0.303444 q^{12} +6.30786 q^{13} +5.90799 q^{14} -0.113518 q^{15} -2.20077 q^{16} -2.83838 q^{17} +6.45734 q^{18} +0.0940355 q^{19} +2.67309 q^{20} +0.310244 q^{21} -3.90093 q^{22} -0.210148 q^{23} +0.165173 q^{24} +1.00000 q^{25} -13.6359 q^{26} +0.679646 q^{27} -7.30552 q^{28} +2.96624 q^{29} +0.245396 q^{30} -8.04376 q^{31} +7.66756 q^{32} -0.204848 q^{33} +6.13582 q^{34} -2.73299 q^{35} -7.98482 q^{36} +7.48146 q^{37} -0.203280 q^{38} -0.716057 q^{39} -1.45504 q^{40} -10.3971 q^{41} -0.670664 q^{42} +1.86684 q^{43} +4.82369 q^{44} -2.98711 q^{45} +0.454285 q^{46} +7.69074 q^{47} +0.249828 q^{48} +0.469221 q^{49} -2.16173 q^{50} +0.322208 q^{51} +16.8615 q^{52} +0.289822 q^{53} -1.46921 q^{54} +1.80454 q^{55} +3.97660 q^{56} -0.0106747 q^{57} -6.41223 q^{58} +6.22423 q^{59} -0.303444 q^{60} -2.72007 q^{61} +17.3885 q^{62} +8.16374 q^{63} -12.1737 q^{64} +6.30786 q^{65} +0.442827 q^{66} -1.31159 q^{67} -7.58725 q^{68} +0.0238557 q^{69} +5.90799 q^{70} +12.6661 q^{71} +4.34636 q^{72} -9.14309 q^{73} -16.1729 q^{74} -0.113518 q^{75} +0.251365 q^{76} -4.93178 q^{77} +1.54792 q^{78} +13.5768 q^{79} -2.20077 q^{80} +8.88419 q^{81} +22.4758 q^{82} +8.86227 q^{83} +0.829309 q^{84} -2.83838 q^{85} -4.03562 q^{86} -0.336723 q^{87} -2.62567 q^{88} -11.7866 q^{89} +6.45734 q^{90} -17.2393 q^{91} -0.561745 q^{92} +0.913113 q^{93} -16.6253 q^{94} +0.0940355 q^{95} -0.870408 q^{96} -4.00220 q^{97} -1.01433 q^{98} -5.39036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * 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 $

$2$	−2.16173	−1.52858	−0.764288	−	0.644875i	$-0.776909\pi$
$2$	−2.16173	−1.52858	−0.764288	+	0.644875i	$0.776909\pi$
$3$	−0.113518	−0.0655398	−0.0327699	−	0.999463i	$-0.510433\pi$
$3$	−0.113518	−0.0655398	−0.0327699	+	0.999463i	$0.510433\pi$
$4$	2.67309	1.33654
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.245396	0.100183
$7$	−2.73299	−1.03297	−0.516486	−	0.856296i	$-0.672760\pi$
$7$	−2.73299	−1.03297	−0.516486	+	0.856296i	$0.672760\pi$
$8$	−1.45504	−0.514434
$9$	−2.98711	−0.995705
$10$	−2.16173	−0.683600
$11$	1.80454	0.544089	0.272044	−	0.962285i	$-0.412300\pi$
$11$	1.80454	0.544089	0.272044	+	0.962285i	$0.412300\pi$
$12$	−0.303444	−0.0875968
$13$	6.30786	1.74949	0.874743	−	0.484587i	$-0.161030\pi$
$13$	6.30786	1.74949	0.874743	+	0.484587i	$0.161030\pi$
$14$	5.90799	1.57898
$15$	−0.113518	−0.0293103
$16$	−2.20077	−0.550193
$17$	−2.83838	−0.688409	−0.344204	−	0.938895i	$-0.611851\pi$
$17$	−2.83838	−0.688409	−0.344204	+	0.938895i	$0.611851\pi$
$18$	6.45734	1.52201
$19$	0.0940355	0.0215732	0.0107866	−	0.999942i	$-0.496566\pi$
$19$	0.0940355	0.0215732	0.0107866	+	0.999942i	$0.496566\pi$
$20$	2.67309	0.597721
$21$	0.310244	0.0677008
$22$	−3.90093	−0.831681
$23$	−0.210148	−0.0438190	−0.0219095	−	0.999760i	$-0.506975\pi$
$23$	−0.210148	−0.0438190	−0.0219095	+	0.999760i	$0.506975\pi$
$24$	0.165173	0.0337159
$25$	1.00000	0.200000
$26$	−13.6359	−2.67422
$27$	0.679646	0.130798
$28$	−7.30552	−1.38061
$29$	2.96624	0.550818	0.275409	−	0.961327i	$-0.411187\pi$
$29$	2.96624	0.550818	0.275409	+	0.961327i	$0.411187\pi$
$30$	0.245396	0.0448030
$31$	−8.04376	−1.44470	−0.722351	−	0.691527i	$-0.756938\pi$
$31$	−8.04376	−1.44470	−0.722351	+	0.691527i	$0.756938\pi$
$32$	7.66756	1.35545
$33$	−0.204848	−0.0356595
$34$	6.13582	1.05229
$35$	−2.73299	−0.461959
$36$	−7.98482	−1.33080
$37$	7.48146	1.22995	0.614973	−	0.788548i	$-0.289167\pi$
$37$	7.48146	1.22995	0.614973	+	0.788548i	$0.289167\pi$
$38$	−0.203280	−0.0329763
$39$	−0.716057	−0.114661
$40$	−1.45504	−0.230062
$41$	−10.3971	−1.62376	−0.811879	−	0.583825i	$-0.801555\pi$
$41$	−10.3971	−1.62376	−0.811879	+	0.583825i	$0.801555\pi$
$42$	−0.670664	−0.103486
$43$	1.86684	0.284691	0.142346	−	0.989817i	$-0.454536\pi$
$43$	1.86684	0.284691	0.142346	+	0.989817i	$0.454536\pi$
$44$	4.82369	0.727199
$45$	−2.98711	−0.445293
$46$	0.454285	0.0669806
$47$	7.69074	1.12181	0.560905	−	0.827880i	$-0.310453\pi$
$47$	7.69074	1.12181	0.560905	+	0.827880i	$0.310453\pi$
$48$	0.249828	0.0360595
$49$	0.469221	0.0670316
$50$	−2.16173	−0.305715
$51$	0.322208	0.0451181
$52$	16.8615	2.33827
$53$	0.289822	0.0398102	0.0199051	−	0.999802i	$-0.493664\pi$
$53$	0.289822	0.0398102	0.0199051	+	0.999802i	$0.493664\pi$
$54$	−1.46921	−0.199935
$55$	1.80454	0.243324
$56$	3.97660	0.531396
$57$	−0.0106747	−0.00141390
$58$	−6.41223	−0.841967
$59$	6.22423	0.810325	0.405163	−	0.914245i	$-0.367215\pi$
$59$	6.22423	0.810325	0.405163	+	0.914245i	$0.367215\pi$
$60$	−0.303444	−0.0391745
$61$	−2.72007	−0.348269	−0.174135	−	0.984722i	$-0.555713\pi$
$61$	−2.72007	−0.348269	−0.174135	+	0.984722i	$0.555713\pi$
$62$	17.3885	2.20834
$63$	8.16374	1.02854
$64$	−12.1737	−1.52171
$65$	6.30786	0.782394
$66$	0.442827	0.0545082
$67$	−1.31159	−0.160237	−0.0801184	−	0.996785i	$-0.525530\pi$
$67$	−1.31159	−0.160237	−0.0801184	+	0.996785i	$0.525530\pi$
$68$	−7.58725	−0.920089
$69$	0.0238557	0.00287188
$70$	5.90799	0.706140
$71$	12.6661	1.50319	0.751594	−	0.659626i	$-0.229285\pi$
$71$	12.6661	1.50319	0.751594	+	0.659626i	$0.229285\pi$
$72$	4.34636	0.512224
$73$	−9.14309	−1.07012	−0.535059	−	0.844815i	$-0.679710\pi$
$73$	−9.14309	−1.07012	−0.535059	+	0.844815i	$0.679710\pi$
$74$	−16.1729	−1.88006
$75$	−0.113518	−0.0131080
$76$	0.251365	0.0288336
$77$	−4.93178	−0.562029
$78$	1.54792	0.175268
$79$	13.5768	1.52751	0.763755	−	0.645507i	$-0.223354\pi$
$79$	13.5768	1.52751	0.763755	+	0.645507i	$0.223354\pi$
$80$	−2.20077	−0.246054
$81$	8.88419	0.987132
$82$	22.4758	2.48204
$83$	8.86227	0.972760	0.486380	−	0.873747i	$-0.338317\pi$
$83$	8.86227	0.972760	0.486380	+	0.873747i	$0.338317\pi$
$84$	0.829309	0.0904851
$85$	−2.83838	−0.307866
$86$	−4.03562	−0.435172
$87$	−0.336723	−0.0361005
$88$	−2.62567	−0.279898
$89$	−11.7866	−1.24937	−0.624687	−	0.780876i	$-0.714773\pi$
$89$	−11.7866	−1.24937	−0.624687	+	0.780876i	$0.714773\pi$
$90$	6.45734	0.680664
$91$	−17.2393	−1.80717
$92$	−0.561745	−0.0585660
$93$	0.913113	0.0946854
$94$	−16.6253	−1.71477
$95$	0.0940355	0.00964784
$96$	−0.870408	−0.0888356
$97$	−4.00220	−0.406362	−0.203181	−	0.979141i	$-0.565128\pi$
$97$	−4.00220	−0.406362	−0.203181	+	0.979141i	$0.565128\pi$
$98$	−1.01433	−0.102463
$99$	−5.39036	−0.541752
$100$	2.67309	0.267309
$101$	−17.0997	−1.70149	−0.850743	−	0.525582i	$-0.823848\pi$
$101$	−17.0997	−1.70149	−0.850743	+	0.525582i	$0.823848\pi$
$102$	−0.696528	−0.0689665
$103$	12.2990	1.21186	0.605928	−	0.795520i	$-0.292802\pi$
$103$	12.2990	1.21186	0.605928	+	0.795520i	$0.292802\pi$
$104$	−9.17818	−0.899995
$105$	0.310244	0.0302767
$106$	−0.626519	−0.0608529
$107$	7.39667	0.715063	0.357532	−	0.933901i	$-0.383618\pi$
$107$	7.39667	0.715063	0.357532	+	0.933901i	$0.383618\pi$
$108$	1.81676	0.174817
$109$	7.38006	0.706881	0.353441	−	0.935457i	$-0.385012\pi$
$109$	7.38006	0.706881	0.353441	+	0.935457i	$0.385012\pi$
$110$	−3.90093	−0.371939
$111$	−0.849282	−0.0806103
$112$	6.01469	0.568335
$113$	0.475014	0.0446855	0.0223428	−	0.999750i	$-0.492887\pi$
$113$	0.475014	0.0446855	0.0223428	+	0.999750i	$0.492887\pi$
$114$	0.0230759	0.00216126
$115$	−0.210148	−0.0195964
$116$	7.92904	0.736193
$117$	−18.8423	−1.74197
$118$	−13.4551	−1.23864
$119$	7.75726	0.711107
$120$	0.165173	0.0150782
$121$	−7.74364	−0.703967
$122$	5.88007	0.532356
$123$	1.18026	0.106421
$124$	−21.5017	−1.93091
$125$	1.00000	0.0894427
$126$	−17.6478	−1.57219
$127$	−5.45565	−0.484111	−0.242055	−	0.970262i	$-0.577822\pi$
$127$	−5.45565	−0.484111	−0.242055	+	0.970262i	$0.577822\pi$
$128$	10.9811	0.970602
$129$	−0.211921	−0.0186586
$130$	−13.6359	−1.19595
$131$	4.34979	0.380043	0.190021	−	0.981780i	$-0.439144\pi$
$131$	4.34979	0.380043	0.190021	+	0.981780i	$0.439144\pi$
$132$	−0.547577	−0.0476604
$133$	−0.256998	−0.0222845
$134$	2.83532	0.244934
$135$	0.679646	0.0584946
$136$	4.12995	0.354141
$137$	4.43063	0.378534	0.189267	−	0.981926i	$-0.439389\pi$
$137$	4.43063	0.378534	0.189267	+	0.981926i	$0.439389\pi$
$138$	−0.0515696	−0.00438989
$139$	−13.8224	−1.17240	−0.586202	−	0.810165i	$-0.699377\pi$
$139$	−13.8224	−1.17240	−0.586202	+	0.810165i	$0.699377\pi$
$140$	−7.30552	−0.617429
$141$	−0.873038	−0.0735231
$142$	−27.3807	−2.29774
$143$	11.3828	0.951876
$144$	6.57396	0.547830
$145$	2.96624	0.246333
$146$	19.7649	1.63576
$147$	−0.0532652	−0.00439324
$148$	19.9986	1.64388
$149$	17.2463	1.41287	0.706435	−	0.707778i	$-0.250302\pi$
$149$	17.2463	1.41287	0.706435	+	0.707778i	$0.250302\pi$
$150$	0.245396	0.0200365
$151$	0.881924	0.0717700	0.0358850	−	0.999356i	$-0.488575\pi$
$151$	0.881924	0.0717700	0.0358850	+	0.999356i	$0.488575\pi$
$152$	−0.136825	−0.0110980
$153$	8.47857	0.685452
$154$	10.6612	0.859104
$155$	−8.04376	−0.646090
$156$	−1.91408	−0.153249
$157$	−11.9350	−0.952518	−0.476259	−	0.879305i	$-0.658008\pi$
$157$	−11.9350	−0.952518	−0.476259	+	0.879305i	$0.658008\pi$
$158$	−29.3494	−2.33491
$159$	−0.0329001	−0.00260915
$160$	7.66756	0.606174
$161$	0.574333	0.0452638
$162$	−19.2052	−1.50891
$163$	5.97131	0.467709	0.233855	−	0.972272i	$-0.424866\pi$
$163$	5.97131	0.467709	0.233855	+	0.972272i	$0.424866\pi$
$164$	−27.7924	−2.17023
$165$	−0.204848	−0.0159474
$166$	−19.1579	−1.48694
$167$	20.7342	1.60446	0.802230	−	0.597015i	$-0.203647\pi$
$167$	20.7342	1.60446	0.802230	+	0.597015i	$0.203647\pi$
$168$	−0.451417	−0.0348275
$169$	26.7891	2.06070
$170$	6.13582	0.470596
$171$	−0.280895	−0.0214806
$172$	4.99024	0.380502
$173$	13.6394	1.03699	0.518493	−	0.855082i	$-0.326493\pi$
$173$	13.6394	1.03699	0.518493	+	0.855082i	$0.326493\pi$
$174$	0.727905	0.0551823
$175$	−2.73299	−0.206594
$176$	−3.97138	−0.299354
$177$	−0.706563	−0.0531085
$178$	25.4794	1.90976
$179$	10.8802	0.813227	0.406613	−	0.913600i	$-0.366710\pi$
$179$	10.8802	0.813227	0.406613	+	0.913600i	$0.366710\pi$
$180$	−7.98482	−0.595153
$181$	21.5019	1.59822	0.799110	−	0.601185i	$-0.205304\pi$
$181$	21.5019	1.59822	0.799110	+	0.601185i	$0.205304\pi$
$182$	37.2668	2.76240
$183$	0.308778	0.0228255
$184$	0.305774	0.0225420
$185$	7.48146	0.550048
$186$	−1.97391	−0.144734
$187$	−5.12197	−0.374556
$188$	20.5580	1.49935
$189$	−1.85747	−0.135111
$190$	−0.203280	−0.0147475
$191$	16.1195	1.16637	0.583183	−	0.812341i	$-0.301807\pi$
$191$	16.1195	1.16637	0.583183	+	0.812341i	$0.301807\pi$
$192$	1.38193	0.0997324
$193$	19.3992	1.39639	0.698193	−	0.715909i	$-0.253988\pi$
$193$	19.3992	1.39639	0.698193	+	0.715909i	$0.253988\pi$
$194$	8.65169	0.621155
$195$	−0.716057	−0.0512779
$196$	1.25427	0.0895907
$197$	19.2581	1.37208	0.686040	−	0.727564i	$-0.259347\pi$
$197$	19.2581	1.37208	0.686040	+	0.727564i	$0.259347\pi$
$198$	11.6525	0.828109
$199$	8.10050	0.574229	0.287115	−	0.957896i	$-0.407304\pi$
$199$	8.10050	0.574229	0.287115	+	0.957896i	$0.407304\pi$
$200$	−1.45504	−0.102887
$201$	0.148890	0.0105019
$202$	36.9650	2.60085
$203$	−8.10671	−0.568980
$204$	0.861291	0.0603024
$205$	−10.3971	−0.726167
$206$	−26.5871	−1.85241
$207$	0.627737	0.0436307
$208$	−13.8822	−0.962556
$209$	0.169691	0.0117378
$210$	−0.670664	−0.0462802
$211$	−3.93598	−0.270964	−0.135482	−	0.990780i	$-0.543258\pi$
$211$	−3.93598	−0.270964	−0.135482	+	0.990780i	$0.543258\pi$
$212$	0.774721	0.0532081
$213$	−1.43783	−0.0985186
$214$	−15.9896	−1.09303
$215$	1.86684	0.127318
$216$	−0.988911	−0.0672869
$217$	21.9835	1.49234
$218$	−15.9537	−1.08052
$219$	1.03791	0.0701352
$220$	4.82369	0.325213
$221$	−17.9041	−1.20436
$222$	1.83592	0.123219
$223$	14.2465	0.954013	0.477007	−	0.878900i	$-0.341722\pi$
$223$	14.2465	0.954013	0.477007	+	0.878900i	$0.341722\pi$
$224$	−20.9554	−1.40014
$225$	−2.98711	−0.199141
$226$	−1.02685	−0.0683052
$227$	−4.92773	−0.327065	−0.163533	−	0.986538i	$-0.552289\pi$
$227$	−4.92773	−0.327065	−0.163533	+	0.986538i	$0.552289\pi$
$228$	−0.0285345	−0.00188975
$229$	−21.7309	−1.43602	−0.718010	−	0.696033i	$-0.754947\pi$
$229$	−21.7309	−1.43602	−0.718010	+	0.696033i	$0.754947\pi$
$230$	0.454285	0.0299546
$231$	0.559847	0.0368352
$232$	−4.31600	−0.283359
$233$	24.3442	1.59484	0.797420	−	0.603424i	$-0.206198\pi$
$233$	24.3442	1.59484	0.797420	+	0.603424i	$0.206198\pi$
$234$	40.7320	2.66274
$235$	7.69074	0.501688
$236$	16.6379	1.08304
$237$	−1.54121	−0.100113
$238$	−16.7691	−1.08698
$239$	23.9706	1.55053	0.775265	−	0.631636i	$-0.217616\pi$
$239$	23.9706	1.55053	0.775265	+	0.631636i	$0.217616\pi$
$240$	0.249828	0.0161263
$241$	10.7133	0.690107	0.345053	−	0.938583i	$-0.387861\pi$
$241$	10.7133	0.690107	0.345053	+	0.938583i	$0.387861\pi$
$242$	16.7397	1.07607
$243$	−3.04746	−0.195494
$244$	−7.27099	−0.465478
$245$	0.469221	0.0299775
$246$	−2.55141	−0.162672
$247$	0.593163	0.0377421
$248$	11.7040	0.743203
$249$	−1.00603	−0.0637545
$250$	−2.16173	−0.136720
$251$	29.9214	1.88862	0.944311	−	0.329055i	$-0.106730\pi$
$251$	29.9214	1.88862	0.944311	+	0.329055i	$0.106730\pi$
$252$	21.8224	1.37468
$253$	−0.379221	−0.0238414
$254$	11.7937	0.740000
$255$	0.322208	0.0201774
$256$	0.609133	0.0380708
$257$	7.73866	0.482724	0.241362	−	0.970435i	$-0.422406\pi$
$257$	7.73866	0.482724	0.241362	+	0.970435i	$0.422406\pi$
$258$	0.458116	0.0285211
$259$	−20.4468	−1.27050
$260$	16.8615	1.04570
$261$	−8.86051	−0.548452
$262$	−9.40307	−0.580924
$263$	−6.74704	−0.416041	−0.208020	−	0.978125i	$-0.566702\pi$
$263$	−6.74704	−0.416041	−0.208020	+	0.978125i	$0.566702\pi$
$264$	0.298062	0.0183444
$265$	0.289822	0.0178036
$266$	0.555561	0.0340636
$267$	1.33799	0.0818836
$268$	−3.50601	−0.214163
$269$	0.590177	0.0359838	0.0179919	−	0.999838i	$-0.494273\pi$
$269$	0.590177	0.0359838	0.0179919	+	0.999838i	$0.494273\pi$
$270$	−1.46921	−0.0894135
$271$	−19.1341	−1.16232	−0.581158	−	0.813791i	$-0.697400\pi$
$271$	−19.1341	−1.16232	−0.581158	+	0.813791i	$0.697400\pi$
$272$	6.24664	0.378758
$273$	1.95698	0.118442
$274$	−9.57784	−0.578618
$275$	1.80454	0.108818
$276$	0.0637683	0.00383840
$277$	10.0921	0.606375	0.303187	−	0.952931i	$-0.401949\pi$
$277$	10.0921	0.606375	0.303187	+	0.952931i	$0.401949\pi$
$278$	29.8804	1.79211
$279$	24.0276	1.43850
$280$	3.97660	0.237647
$281$	−8.15704	−0.486608	−0.243304	−	0.969950i	$-0.578231\pi$
$281$	−8.15704	−0.486608	−0.243304	+	0.969950i	$0.578231\pi$
$282$	1.88728	0.112386
$283$	−29.8510	−1.77446	−0.887229	−	0.461330i	$-0.847372\pi$
$283$	−29.8510	−1.77446	−0.887229	+	0.461330i	$0.847372\pi$
$284$	33.8576	2.00908
$285$	−0.0106747	−0.000632317 0
$286$	−24.6065	−1.45502
$287$	28.4152	1.67730
$288$	−22.9039	−1.34962
$289$	−8.94359	−0.526093
$290$	−6.41223	−0.376539
$291$	0.454323	0.0266329
$292$	−24.4403	−1.43026
$293$	30.9580	1.80859	0.904293	−	0.426912i	$-0.140399\pi$
$293$	30.9580	1.80859	0.904293	+	0.426912i	$0.140399\pi$
$294$	0.115145	0.00671540
$295$	6.22423	0.362388
$296$	−10.8858	−0.632725
$297$	1.22645	0.0711657
$298$	−37.2819	−2.15968
$299$	−1.32559	−0.0766607
$300$	−0.303444	−0.0175194
$301$	−5.10206	−0.294078
$302$	−1.90648	−0.109706
$303$	1.94113	0.111515
$304$	−0.206951	−0.0118695
$305$	−2.72007	−0.155751
$306$	−18.3284	−1.04776
$307$	−12.1569	−0.693829	−0.346915	−	0.937897i	$-0.612771\pi$
$307$	−12.1569	−0.693829	−0.346915	+	0.937897i	$0.612771\pi$
$308$	−13.1831	−0.751176
$309$	−1.39616	−0.0794247
$310$	17.3885	0.987598
$311$	−8.08693	−0.458568	−0.229284	−	0.973360i	$-0.573638\pi$
$311$	−8.08693	−0.458568	−0.229284	+	0.973360i	$0.573638\pi$
$312$	1.04189	0.0589854
$313$	−0.507912	−0.0287089	−0.0143544	−	0.999897i	$-0.504569\pi$
$313$	−0.507912	−0.0287089	−0.0143544	+	0.999897i	$0.504569\pi$
$314$	25.8003	1.45600
$315$	8.16374	0.459975
$316$	36.2920	2.04158
$317$	6.69877	0.376240	0.188120	−	0.982146i	$-0.439761\pi$
$317$	6.69877	0.376240	0.188120	+	0.982146i	$0.439761\pi$
$318$	0.0711213	0.00398828
$319$	5.35270	0.299694
$320$	−12.1737	−0.680529
$321$	−0.839657	−0.0468651
$322$	−1.24155	−0.0691891
$323$	−0.266909	−0.0148512
$324$	23.7482	1.31935
$325$	6.30786	0.349897
$326$	−12.9084	−0.714929
$327$	−0.837771	−0.0463288
$328$	15.1282	0.835316
$329$	−21.0187	−1.15880
$330$	0.442827	0.0243768
$331$	0.790853	0.0434692	0.0217346	−	0.999764i	$-0.493081\pi$
$331$	0.790853	0.0434692	0.0217346	+	0.999764i	$0.493081\pi$
$332$	23.6896	1.30014
$333$	−22.3480	−1.22466
$334$	−44.8218	−2.45254
$335$	−1.31159	−0.0716600
$336$	−0.682776	−0.0372485
$337$	12.1130	0.659839	0.329920	−	0.944009i	$-0.392978\pi$
$337$	12.1130	0.659839	0.329920	+	0.944009i	$0.392978\pi$
$338$	−57.9110	−3.14994
$339$	−0.0539227	−0.00292868
$340$	−7.58725	−0.411476
$341$	−14.5153	−0.786046
$342$	0.607220	0.0328347
$343$	17.8485	0.963730
$344$	−2.71633	−0.146455
$345$	0.0238557	0.00128435
$346$	−29.4848	−1.58511
$347$	6.50517	0.349216	0.174608	−	0.984638i	$-0.444134\pi$
$347$	6.50517	0.349216	0.174608	+	0.984638i	$0.444134\pi$
$348$	−0.900090	−0.0482499
$349$	−20.6280	−1.10419	−0.552096	−	0.833781i	$-0.686172\pi$
$349$	−20.6280	−1.10419	−0.552096	+	0.833781i	$0.686172\pi$
$350$	5.90799	0.315795
$351$	4.28712	0.228829
$352$	13.8364	0.737483
$353$	−13.4042	−0.713436	−0.356718	−	0.934212i	$-0.616104\pi$
$353$	−13.4042	−0.713436	−0.356718	+	0.934212i	$0.616104\pi$
$354$	1.52740	0.0811804
$355$	12.6661	0.672246
$356$	−31.5065	−1.66984
$357$	−0.880590	−0.0466058
$358$	−23.5202	−1.24308
$359$	6.97758	0.368262	0.184131	−	0.982902i	$-0.441053\pi$
$359$	6.97758	0.368262	0.184131	+	0.982902i	$0.441053\pi$
$360$	4.34636	0.229074
$361$	−18.9912	−0.999535
$362$	−46.4813	−2.44300
$363$	0.879044	0.0461378
$364$	−46.0822	−2.41536
$365$	−9.14309	−0.478571
$366$	−0.667495	−0.0348905
$367$	−33.6834	−1.75826	−0.879129	−	0.476584i	$-0.841875\pi$
$367$	−33.6834	−1.75826	−0.879129	+	0.476584i	$0.841875\pi$
$368$	0.462489	0.0241089
$369$	31.0574	1.61678
$370$	−16.1729	−0.840790
$371$	−0.792081	−0.0411228
$372$	2.44083	0.126551
$373$	9.54308	0.494122	0.247061	−	0.969000i	$-0.420535\pi$
$373$	9.54308	0.494122	0.247061	+	0.969000i	$0.420535\pi$
$374$	11.0723	0.572537
$375$	−0.113518	−0.00586205
$376$	−11.1903	−0.577096
$377$	18.7107	0.963648
$378$	4.01534	0.206527
$379$	25.0328	1.28585	0.642925	−	0.765930i	$-0.277721\pi$
$379$	25.0328	1.28585	0.642925	+	0.765930i	$0.277721\pi$
$380$	0.251365	0.0128948
$381$	0.619316	0.0317285
$382$	−34.8460	−1.78288
$383$	−24.4002	−1.24679	−0.623397	−	0.781906i	$-0.714248\pi$
$383$	−24.4002	−1.24679	−0.623397	+	0.781906i	$0.714248\pi$
$384$	−1.24656	−0.0636130
$385$	−4.93178	−0.251347
$386$	−41.9359	−2.13448
$387$	−5.57648	−0.283468
$388$	−10.6982	−0.543121
$389$	0.105586	0.00535342	0.00267671	−	0.999996i	$-0.499148\pi$
$389$	0.105586	0.00535342	0.00267671	+	0.999996i	$0.499148\pi$
$390$	1.54792	0.0783822
$391$	0.596481	0.0301654
$392$	−0.682735	−0.0344833
$393$	−0.493780	−0.0249079
$394$	−41.6308	−2.09733
$395$	13.5768	0.683123
$396$	−14.4089	−0.724075
$397$	−33.6137	−1.68702	−0.843512	−	0.537110i	$-0.819516\pi$
$397$	−33.6137	−1.68702	−0.843512	+	0.537110i	$0.819516\pi$
$398$	−17.5111	−0.877753
$399$	0.0291739	0.00146052
$400$	−2.20077	−0.110039
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−0.321860	−0.0160529
$403$	−50.7389	−2.52749
$404$	−45.7091	−2.27411
$405$	8.88419	0.441459
$406$	17.5245	0.869728
$407$	13.5006	0.669200
$408$	−0.468825	−0.0232103
$409$	3.71918	0.183901	0.0919507	−	0.995764i	$-0.470690\pi$
$409$	3.71918	0.183901	0.0919507	+	0.995764i	$0.470690\pi$
$410$	22.4758	1.11000
$411$	−0.502957	−0.0248090
$412$	32.8763	1.61970
$413$	−17.0107	−0.837043
$414$	−1.35700	−0.0666929
$415$	8.86227	0.435032
$416$	48.3659	2.37133
$417$	1.56910	0.0768390
$418$	−0.366826	−0.0179421
$419$	−16.9146	−0.826334	−0.413167	−	0.910655i	$-0.635577\pi$
$419$	−16.9146	−0.826334	−0.413167	+	0.910655i	$0.635577\pi$
$420$	0.829309	0.0404662
$421$	9.68021	0.471785	0.235892	−	0.971779i	$-0.424199\pi$
$421$	9.68021	0.471785	0.235892	+	0.971779i	$0.424199\pi$
$422$	8.50854	0.414189
$423$	−22.9731	−1.11699
$424$	−0.421703	−0.0204797
$425$	−2.83838	−0.137682
$426$	3.10821	0.150593
$427$	7.43392	0.359753
$428$	19.7720	0.955714
$429$	−1.29215	−0.0623857
$430$	−4.03562	−0.194615
$431$	26.3369	1.26860	0.634302	−	0.773086i	$-0.281288\pi$
$431$	26.3369	1.26860	0.634302	+	0.773086i	$0.281288\pi$
$432$	−1.49575	−0.0719642
$433$	8.50660	0.408801	0.204401	−	0.978887i	$-0.434475\pi$
$433$	8.50660	0.408801	0.204401	+	0.978887i	$0.434475\pi$
$434$	−47.5225	−2.28115
$435$	−0.336723	−0.0161446
$436$	19.7275	0.944778
$437$	−0.0197614	−0.000945317 0
$438$	−2.24368	−0.107207
$439$	28.0720	1.33980	0.669901	−	0.742451i	$-0.266337\pi$
$439$	28.0720	1.33980	0.669901	+	0.742451i	$0.266337\pi$
$440$	−2.62567	−0.125174
$441$	−1.40162	−0.0667437
$442$	38.7039	1.84096
$443$	26.5835	1.26302	0.631510	−	0.775368i	$-0.282435\pi$
$443$	26.5835	1.26302	0.631510	+	0.775368i	$0.282435\pi$
$444$	−2.27021	−0.107739
$445$	−11.7866	−0.558737
$446$	−30.7970	−1.45828
$447$	−1.95777	−0.0925992
$448$	33.2705	1.57188
$449$	6.88282	0.324820	0.162410	−	0.986723i	$-0.448073\pi$
$449$	6.88282	0.324820	0.162410	+	0.986723i	$0.448073\pi$
$450$	6.45734	0.304402
$451$	−18.7620	−0.883469
$452$	1.26975	0.0597242
$453$	−0.100114	−0.00470379
$454$	10.6524	0.499944
$455$	−17.2393	−0.808191
$456$	0.0155322	0.000727360 0
$457$	−2.97546	−0.139186	−0.0695930	−	0.997575i	$-0.522170\pi$
$457$	−2.97546	−0.139186	−0.0695930	+	0.997575i	$0.522170\pi$
$458$	46.9764	2.19506
$459$	−1.92910	−0.0900425
$460$	−0.561745	−0.0261915
$461$	−15.6626	−0.729482	−0.364741	−	0.931109i	$-0.618842\pi$
$461$	−15.6626	−0.729482	−0.364741	+	0.931109i	$0.618842\pi$
$462$	−1.21024	−0.0563054
$463$	6.45766	0.300113	0.150056	−	0.988677i	$-0.452054\pi$
$463$	6.45766	0.300113	0.150056	+	0.988677i	$0.452054\pi$
$464$	−6.52803	−0.303056
$465$	0.913113	0.0423446
$466$	−52.6256	−2.43783
$467$	7.85709	0.363583	0.181791	−	0.983337i	$-0.441810\pi$
$467$	7.85709	0.363583	0.181791	+	0.983337i	$0.441810\pi$
$468$	−50.3672	−2.32822
$469$	3.58457	0.165520
$470$	−16.6253	−0.766869
$471$	1.35484	0.0624278
$472$	−9.05649	−0.416859
$473$	3.36879	0.154897
$474$	3.33169	0.153030
$475$	0.0940355	0.00431465
$476$	20.7359	0.950426
$477$	−0.865732	−0.0396392
$478$	−51.8180	−2.37010
$479$	−9.15838	−0.418457	−0.209229	−	0.977867i	$-0.567095\pi$
$479$	−9.15838	−0.418457	−0.209229	+	0.977867i	$0.567095\pi$
$480$	−0.870408	−0.0397285
$481$	47.1921	2.15177
$482$	−23.1594	−1.05488
$483$	−0.0651972	−0.00296658
$484$	−20.6994	−0.940884
$485$	−4.00220	−0.181731
$486$	6.58779	0.298828
$487$	22.5269	1.02079	0.510396	−	0.859940i	$-0.329499\pi$
$487$	22.5269	1.02079	0.510396	+	0.859940i	$0.329499\pi$
$488$	3.95781	0.179162
$489$	−0.677852	−0.0306535
$490$	−1.01433	−0.0458228
$491$	−8.07553	−0.364444	−0.182222	−	0.983257i	$-0.558329\pi$
$491$	−8.07553	−0.364444	−0.182222	+	0.983257i	$0.558329\pi$
$492$	3.15495	0.142236
$493$	−8.41934	−0.379188
$494$	−1.28226	−0.0576916
$495$	−5.39036	−0.242279
$496$	17.7025	0.794866
$497$	−34.6163	−1.55275
$498$	2.17477	0.0974536
$499$	35.5514	1.59150	0.795750	−	0.605625i	$-0.207077\pi$
$499$	35.5514	1.59150	0.795750	+	0.605625i	$0.207077\pi$
$500$	2.67309	0.119544
$501$	−2.35371	−0.105156
$502$	−64.6821	−2.88690
$503$	5.83396	0.260124	0.130062	−	0.991506i	$-0.458482\pi$
$503$	5.83396	0.260124	0.130062	+	0.991506i	$0.458482\pi$
$504$	−11.8786	−0.529113
$505$	−17.0997	−0.760927
$506$	0.819774	0.0364434
$507$	−3.04105	−0.135058
$508$	−14.5834	−0.647035
$509$	−19.8419	−0.879479	−0.439739	−	0.898125i	$-0.644929\pi$
$509$	−19.8419	−0.879479	−0.439739	+	0.898125i	$0.644929\pi$
$510$	−0.696528	−0.0308428
$511$	24.9879	1.10540
$512$	−23.2790	−1.02880
$513$	0.0639109	0.00282174
$514$	−16.7289	−0.737881
$515$	12.2990	0.541958
$516$	−0.566483	−0.0249380
$517$	13.8782	0.610364
$518$	44.2004	1.94205
$519$	−1.54832	−0.0679638
$520$	−9.17818	−0.402490
$521$	42.7866	1.87452	0.937258	−	0.348637i	$-0.113355\pi$
$521$	42.7866	1.87452	0.937258	+	0.348637i	$0.113355\pi$
$522$	19.1541	0.838350
$523$	−23.6959	−1.03615	−0.518075	−	0.855335i	$-0.673351\pi$
$523$	−23.6959	−1.03615	−0.518075	+	0.855335i	$0.673351\pi$
$524$	11.6274	0.507944
$525$	0.310244	0.0135402
$526$	14.5853	0.635950
$527$	22.8313	0.994546
$528$	0.450824	0.0196196
$529$	−22.9558	−0.998080
$530$	−0.626519	−0.0272142
$531$	−18.5925	−0.806845
$532$	−0.686978	−0.0297843
$533$	−65.5837	−2.84074
$534$	−2.89238	−0.125165
$535$	7.39667	0.319786
$536$	1.90842	0.0824312
$537$	−1.23510	−0.0532987
$538$	−1.27581	−0.0550039
$539$	0.846728	0.0364712
$540$	1.81676	0.0781807
$541$	16.8452	0.724232	0.362116	−	0.932133i	$-0.382054\pi$
$541$	16.8452	0.724232	0.362116	+	0.932133i	$0.382054\pi$
$542$	41.3629	1.77669
$543$	−2.44085	−0.104747
$544$	−21.7635	−0.933101
$545$	7.38006	0.316127
$546$	−4.23046	−0.181047
$547$	25.2619	1.08012	0.540061	−	0.841626i	$-0.318401\pi$
$547$	25.2619	1.08012	0.540061	+	0.841626i	$0.318401\pi$
$548$	11.8435	0.505928
$549$	8.12516	0.346773
$550$	−3.90093	−0.166336
$551$	0.278932	0.0118829
$552$	−0.0347109	−0.00147739
$553$	−37.1052	−1.57787
$554$	−21.8164	−0.926890
$555$	−0.849282	−0.0360500
$556$	−36.9486	−1.56697
$557$	−9.45318	−0.400544	−0.200272	−	0.979740i	$-0.564183\pi$
$557$	−9.45318	−0.400544	−0.200272	+	0.979740i	$0.564183\pi$
$558$	−51.9413	−2.19885
$559$	11.7758	0.498063
$560$	6.01469	0.254167
$561$	0.581437	0.0245483
$562$	17.6333	0.743818
$563$	−1.81964	−0.0766888	−0.0383444	−	0.999265i	$-0.512208\pi$
$563$	−1.81964	−0.0766888	−0.0383444	+	0.999265i	$0.512208\pi$
$564$	−2.33371	−0.0982669
$565$	0.475014	0.0199840
$566$	64.5299	2.71239
$567$	−24.2804	−1.01968
$568$	−18.4297	−0.773291
$569$	−30.1199	−1.26269	−0.631346	−	0.775502i	$-0.717497\pi$
$569$	−30.1199	−1.26269	−0.631346	+	0.775502i	$0.717497\pi$
$570$	0.0230759	0.000966545 0
$571$	−31.1872	−1.30515	−0.652573	−	0.757726i	$-0.726310\pi$
$571$	−31.1872	−1.30515	−0.652573	+	0.757726i	$0.726310\pi$
$572$	30.4272	1.27222
$573$	−1.82986	−0.0764433
$574$	−61.4261	−2.56388
$575$	−0.210148	−0.00876379
$576$	36.3641	1.51517
$577$	−30.7792	−1.28135	−0.640677	−	0.767811i	$-0.721346\pi$
$577$	−30.7792	−1.28135	−0.640677	+	0.767811i	$0.721346\pi$
$578$	19.3336	0.804174
$579$	−2.20216	−0.0915189
$580$	7.92904	0.329235
$581$	−24.2205	−1.00483
$582$	−0.982125	−0.0407104
$583$	0.522996	0.0216603
$584$	13.3035	0.550504
$585$	−18.8423	−0.779033
$586$	−66.9229	−2.76456
$587$	−28.2615	−1.16648	−0.583239	−	0.812301i	$-0.698215\pi$
$587$	−28.2615	−1.16648	−0.583239	+	0.812301i	$0.698215\pi$
$588$	−0.142383	−0.00587176
$589$	−0.756399	−0.0311669
$590$	−13.4551	−0.553938
$591$	−2.18614	−0.0899258
$592$	−16.4650	−0.676708
$593$	45.0539	1.85014	0.925072	−	0.379792i	$-0.124004\pi$
$593$	45.0539	1.85014	0.925072	+	0.379792i	$0.124004\pi$
$594$	−2.65125	−0.108782
$595$	7.75726	0.318017
$596$	46.1008	1.88836
$597$	−0.919554	−0.0376348
$598$	2.86557	0.117182
$599$	22.3587	0.913550	0.456775	−	0.889582i	$-0.349004\pi$
$599$	22.3587	0.913550	0.456775	+	0.889582i	$0.349004\pi$
$600$	0.165173	0.00674317
$601$	−25.3246	−1.03301	−0.516506	−	0.856284i	$-0.672768\pi$
$601$	−25.3246	−1.03301	−0.516506	+	0.856284i	$0.672768\pi$
$602$	11.0293	0.449521
$603$	3.91788	0.159548
$604$	2.35746	0.0959238
$605$	−7.74364	−0.314824
$606$	−4.19620	−0.170459
$607$	12.7847	0.518915	0.259458	−	0.965755i	$-0.416456\pi$
$607$	12.7847	0.518915	0.259458	+	0.965755i	$0.416456\pi$
$608$	0.721023	0.0292414
$609$	0.920259	0.0372908
$610$	5.88007	0.238077
$611$	48.5121	1.96259
$612$	22.6640	0.916137
$613$	−22.6988	−0.916797	−0.458399	−	0.888747i	$-0.651577\pi$
$613$	−22.6988	−0.916797	−0.458399	+	0.888747i	$0.651577\pi$
$614$	26.2799	1.06057
$615$	1.18026	0.0475928
$616$	7.17593	0.289127
$617$	−11.8055	−0.475271	−0.237635	−	0.971354i	$-0.576372\pi$
$617$	−11.8055	−0.475271	−0.237635	+	0.971354i	$0.576372\pi$
$618$	3.01812	0.121407
$619$	−30.4908	−1.22553	−0.612764	−	0.790266i	$-0.709942\pi$
$619$	−30.4908	−1.22553	−0.612764	+	0.790266i	$0.709942\pi$
$620$	−21.5017	−0.863529
$621$	−0.142827	−0.00573143
$622$	17.4818	0.700956
$623$	32.2125	1.29057
$624$	1.57588	0.0630857
$625$	1.00000	0.0400000
$626$	1.09797	0.0438837
$627$	−0.0192630	−0.000769290 0
$628$	−31.9034	−1.27308
$629$	−21.2353	−0.846705
$630$	−17.6478	−0.703107
$631$	−22.2375	−0.885262	−0.442631	−	0.896704i	$-0.645955\pi$
$631$	−22.2375	−0.885262	−0.442631	+	0.896704i	$0.645955\pi$
$632$	−19.7548	−0.785802
$633$	0.446806	0.0177589
$634$	−14.4810	−0.575112
$635$	−5.45565	−0.216501
$636$	−0.0879449	−0.00348724
$637$	2.95978	0.117271
$638$	−11.5711	−0.458105
$639$	−37.8351	−1.49673
$640$	10.9811	0.434066
$641$	−38.8251	−1.53350	−0.766750	−	0.641945i	$-0.778128\pi$
$641$	−38.8251	−1.53350	−0.766750	+	0.641945i	$0.778128\pi$
$642$	1.81511	0.0716368
$643$	−26.0172	−1.02602	−0.513008	−	0.858384i	$-0.671469\pi$
$643$	−26.0172	−1.02602	−0.513008	+	0.858384i	$0.671469\pi$
$644$	1.53524	0.0604970
$645$	−0.211921	−0.00834437
$646$	0.576985	0.0227012
$647$	3.60439	0.141703	0.0708516	−	0.997487i	$-0.477428\pi$
$647$	3.60439	0.141703	0.0708516	+	0.997487i	$0.477428\pi$
$648$	−12.9268	−0.507814
$649$	11.2319	0.440889
$650$	−13.6359	−0.534845
$651$	−2.49553	−0.0978074
$652$	15.9618	0.625114
$653$	−42.1132	−1.64802	−0.824008	−	0.566577i	$-0.808267\pi$
$653$	−42.1132	−1.64802	−0.824008	+	0.566577i	$0.808267\pi$
$654$	1.81104	0.0708171
$655$	4.34979	0.169960
$656$	22.8817	0.893381
$657$	27.3114	1.06552
$658$	45.4368	1.77131
$659$	−0.352507	−0.0137317	−0.00686586	−	0.999976i	$-0.502185\pi$
$659$	−0.352507	−0.0137317	−0.00686586	+	0.999976i	$0.502185\pi$
$660$	−0.547577	−0.0213144
$661$	36.7004	1.42748	0.713740	−	0.700411i	$-0.247000\pi$
$661$	36.7004	1.42748	0.713740	+	0.700411i	$0.247000\pi$
$662$	−1.70961	−0.0664460
$663$	2.03244	0.0789336
$664$	−12.8949	−0.500421
$665$	−0.256998	−0.00996595
$666$	48.3104	1.87199
$667$	−0.623351	−0.0241363
$668$	55.4243	2.14443
$669$	−1.61723	−0.0625258
$670$	2.83532	0.109538
$671$	−4.90847	−0.189490
$672$	2.37881	0.0917647
$673$	−18.7737	−0.723673	−0.361836	−	0.932242i	$-0.617850\pi$
$673$	−18.7737	−0.723673	−0.361836	+	0.932242i	$0.617850\pi$
$674$	−26.1852	−1.00861
$675$	0.679646	0.0261596
$676$	71.6097	2.75422
$677$	29.2636	1.12469	0.562345	−	0.826902i	$-0.309899\pi$
$677$	29.2636	1.12469	0.562345	+	0.826902i	$0.309899\pi$
$678$	0.116566	0.00447671
$679$	10.9380	0.419761
$680$	4.12995	0.158377
$681$	0.559387	0.0214358
$682$	31.3782	1.20153
$683$	−39.4108	−1.50801	−0.754006	−	0.656867i	$-0.771881\pi$
$683$	−39.4108	−1.50801	−0.754006	+	0.656867i	$0.771881\pi$
$684$	−0.750857	−0.0287097
$685$	4.43063	0.169286
$686$	−38.5838	−1.47314
$687$	2.46685	0.0941163
$688$	−4.10850	−0.156635
$689$	1.82816	0.0696474
$690$	−0.0515696	−0.00196322
$691$	−1.04191	−0.0396362	−0.0198181	−	0.999804i	$-0.506309\pi$
$691$	−1.04191	−0.0396362	−0.0198181	+	0.999804i	$0.506309\pi$
$692$	36.4594	1.38598
$693$	14.7318	0.559615
$694$	−14.0624	−0.533803
$695$	−13.8224	−0.524315
$696$	0.489945	0.0185713
$697$	29.5110	1.11781
$698$	44.5922	1.68784
$699$	−2.76351	−0.104525
$700$	−7.30552	−0.276123
$701$	−24.9121	−0.940918	−0.470459	−	0.882422i	$-0.655912\pi$
$701$	−24.9121	−0.940918	−0.470459	+	0.882422i	$0.655912\pi$
$702$	−9.26760	−0.349783
$703$	0.703524	0.0265339
$704$	−21.9679	−0.827945
$705$	−0.873038	−0.0328805
$706$	28.9764	1.09054
$707$	46.7333	1.75759
$708$	−1.88871	−0.0709819
$709$	−2.43546	−0.0914656	−0.0457328	−	0.998954i	$-0.514562\pi$
$709$	−2.43546	−0.0914656	−0.0457328	+	0.998954i	$0.514562\pi$
$710$	−27.3807	−1.02758
$711$	−40.5554	−1.52095
$712$	17.1499	0.642720
$713$	1.69038	0.0633053
$714$	1.90360	0.0712405
$715$	11.3828	0.425692
$716$	29.0838	1.08691
$717$	−2.72110	−0.101621
$718$	−15.0837	−0.562917
$719$	31.1338	1.16110	0.580548	−	0.814226i	$-0.302838\pi$
$719$	31.1338	1.16110	0.580548	+	0.814226i	$0.302838\pi$
$720$	6.57396	0.244997
$721$	−33.6130	−1.25181
$722$	41.0538	1.52786
$723$	−1.21616	−0.0452294
$724$	57.4764	2.13609
$725$	2.96624	0.110164
$726$	−1.90026	−0.0705252
$727$	−45.8322	−1.69982	−0.849912	−	0.526925i	$-0.823345\pi$
$727$	−45.8322	−1.69982	−0.849912	+	0.526925i	$0.823345\pi$
$728$	25.0839	0.929670
$729$	−26.3066	−0.974319
$730$	19.7649	0.731532
$731$	−5.29882	−0.195984
$732$	0.825390	0.0305073
$733$	12.3446	0.455959	0.227980	−	0.973666i	$-0.426788\pi$
$733$	12.3446	0.455959	0.227980	+	0.973666i	$0.426788\pi$
$734$	72.8145	2.68763
$735$	−0.0532652	−0.00196472
$736$	−1.61133	−0.0593942
$737$	−2.36682	−0.0871830
$738$	−67.1378	−2.47138
$739$	10.7070	0.393864	0.196932	−	0.980417i	$-0.436902\pi$
$739$	10.7070	0.393864	0.196932	+	0.980417i	$0.436902\pi$
$740$	19.9986	0.735164
$741$	−0.0673348	−0.00247361
$742$	1.71227	0.0628593
$743$	−26.3348	−0.966129	−0.483065	−	0.875585i	$-0.660476\pi$
$743$	−26.3348	−0.966129	−0.483065	+	0.875585i	$0.660476\pi$
$744$	−1.32861	−0.0487094
$745$	17.2463	0.631855
$746$	−20.6296	−0.755303
$747$	−26.4726	−0.968582
$748$	−13.6915	−0.500610
$749$	−20.2150	−0.738641
$750$	0.245396	0.00896060
$751$	9.90407	0.361405	0.180702	−	0.983538i	$-0.442163\pi$
$751$	9.90407	0.361405	0.180702	+	0.983538i	$0.442163\pi$
$752$	−16.9256	−0.617212
$753$	−3.39662	−0.123780
$754$	−40.4475	−1.47301
$755$	0.881924	0.0320965
$756$	−4.96517	−0.180581
$757$	−9.40566	−0.341854	−0.170927	−	0.985284i	$-0.554676\pi$
$757$	−9.40566	−0.341854	−0.170927	+	0.985284i	$0.554676\pi$
$758$	−54.1142	−1.96552
$759$	0.0430485	0.00156256
$760$	−0.136825	−0.00496318
$761$	−50.7885	−1.84108	−0.920541	−	0.390646i	$-0.872252\pi$
$761$	−50.7885	−1.84108	−0.920541	+	0.390646i	$0.872252\pi$
$762$	−1.33879	−0.0484994
$763$	−20.1696	−0.730189
$764$	43.0888	1.55890
$765$	8.47857	0.306543
$766$	52.7468	1.90582
$767$	39.2616	1.41765
$768$	−0.0691477	−0.00249515
$769$	38.0893	1.37354	0.686768	−	0.726877i	$-0.259029\pi$
$769$	38.0893	1.37354	0.686768	+	0.726877i	$0.259029\pi$
$770$	10.6612	0.384203
$771$	−0.878479	−0.0316376
$772$	51.8558	1.86633
$773$	54.4317	1.95777	0.978886	−	0.204407i	$-0.0655266\pi$
$773$	54.4317	1.95777	0.978886	+	0.204407i	$0.0655266\pi$
$774$	12.0549	0.433303
$775$	−8.04376	−0.288940
$776$	5.82336	0.209046
$777$	2.32108	0.0832682
$778$	−0.228248	−0.00818310
$779$	−0.977699	−0.0350297
$780$	−1.91408	−0.0685352
$781$	22.8565	0.817868
$782$	−1.28943	−0.0461100
$783$	2.01600	0.0720459
$784$	−1.03265	−0.0368804
$785$	−11.9350	−0.425979
$786$	1.06742	0.0380736
$787$	52.6742	1.87763	0.938816	−	0.344419i	$-0.111924\pi$
$787$	52.6742	1.87763	0.938816	+	0.344419i	$0.111924\pi$
$788$	51.4785	1.83385
$789$	0.765912	0.0272672
$790$	−29.3494	−1.04421
$791$	−1.29821	−0.0461589
$792$	7.84318	0.278695
$793$	−17.1578	−0.609293
$794$	72.6639	2.57875
$795$	−0.0329001	−0.00116685
$796$	21.6534	0.767483
$797$	3.94514	0.139744	0.0698720	−	0.997556i	$-0.477741\pi$
$797$	3.94514	0.139744	0.0698720	+	0.997556i	$0.477741\pi$
$798$	−0.0630663	−0.00223252
$799$	−21.8292	−0.772263
$800$	7.66756	0.271089
$801$	35.2078	1.24401
$802$	2.16173	0.0763334
$803$	−16.4991	−0.582239
$804$	0.397996	0.0140362
$805$	0.574333	0.0202426
$806$	109.684	3.86346
$807$	−0.0669959	−0.00235837
$808$	24.8807	0.875302
$809$	6.89457	0.242400	0.121200	−	0.992628i	$-0.461326\pi$
$809$	6.89457	0.242400	0.121200	+	0.992628i	$0.461326\pi$
$810$	−19.2052	−0.674803
$811$	31.2052	1.09576	0.547881	−	0.836557i	$-0.315435\pi$
$811$	31.2052	1.09576	0.547881	+	0.836557i	$0.315435\pi$
$812$	−21.6700	−0.760466
$813$	2.17207	0.0761779
$814$	−29.1847	−1.02292
$815$	5.97131	0.209166
$816$	−0.709107	−0.0248237
$817$	0.175550	0.00614171
$818$	−8.03986	−0.281107
$819$	51.4958	1.79941
$820$	−27.7924	−0.970554
$821$	−27.1289	−0.946805	−0.473403	−	0.880846i	$-0.656974\pi$
$821$	−27.1289	−0.946805	−0.473403	+	0.880846i	$0.656974\pi$
$822$	1.08726	0.0379225
$823$	3.98305	0.138840	0.0694201	−	0.997588i	$-0.477885\pi$
$823$	3.98305	0.138840	0.0694201	+	0.997588i	$0.477885\pi$
$824$	−17.8955	−0.623419
$825$	−0.204848	−0.00713189
$826$	36.7727	1.27948
$827$	−27.5716	−0.958760	−0.479380	−	0.877607i	$-0.659138\pi$
$827$	−27.5716	−0.958760	−0.479380	+	0.877607i	$0.659138\pi$
$828$	1.67800	0.0583144
$829$	14.6968	0.510440	0.255220	−	0.966883i	$-0.417852\pi$
$829$	14.6968	0.510440	0.255220	+	0.966883i	$0.417852\pi$
$830$	−19.1579	−0.664979
$831$	−1.14564	−0.0397416
$832$	−76.7899	−2.66221
$833$	−1.33183	−0.0461452
$834$	−3.39197	−0.117454
$835$	20.7342	0.717536
$836$	0.453598	0.0156880
$837$	−5.46691	−0.188964
$838$	36.5649	1.26311
$839$	−21.3763	−0.737992	−0.368996	−	0.929431i	$-0.620298\pi$
$839$	−21.3763	−0.737992	−0.368996	+	0.929431i	$0.620298\pi$
$840$	−0.451417	−0.0155754
$841$	−20.2014	−0.696600
$842$	−20.9260	−0.721159
$843$	0.925972	0.0318922
$844$	−10.5212	−0.362156
$845$	26.7891	0.921574
$846$	49.6617	1.70740
$847$	21.1633	0.727179
$848$	−0.637834	−0.0219033
$849$	3.38863	0.116297
$850$	6.13582	0.210457
$851$	−1.57222	−0.0538949
$852$	−3.84345	−0.131675
$853$	4.47023	0.153058	0.0765288	−	0.997067i	$-0.475616\pi$
$853$	4.47023	0.153058	0.0765288	+	0.997067i	$0.475616\pi$
$854$	−16.0702	−0.549909
$855$	−0.280895	−0.00960640
$856$	−10.7624	−0.367853
$857$	−35.1594	−1.20102	−0.600511	−	0.799616i	$-0.705036\pi$
$857$	−35.1594	−1.20102	−0.600511	+	0.799616i	$0.705036\pi$
$858$	2.79329	0.0953613
$859$	15.8393	0.540430	0.270215	−	0.962800i	$-0.412905\pi$
$859$	15.8393	0.540430	0.270215	+	0.962800i	$0.412905\pi$
$860$	4.99024	0.170166
$861$	−3.22564	−0.109930
$862$	−56.9333	−1.93916
$863$	14.2659	0.485618	0.242809	−	0.970074i	$-0.421931\pi$
$863$	14.2659	0.485618	0.242809	+	0.970074i	$0.421931\pi$
$864$	5.21123	0.177290
$865$	13.6394	0.463754
$866$	−18.3890	−0.624884
$867$	1.01526	0.0344800
$868$	58.7638	1.99457
$869$	24.4999	0.831101
$870$	0.727905	0.0246783
$871$	−8.27336	−0.280332
$872$	−10.7383	−0.363643
$873$	11.9550	0.404617
$874$	0.0427189	0.00144499
$875$	−2.73299	−0.0923918
$876$	2.77442	0.0937388
$877$	−28.9468	−0.977464	−0.488732	−	0.872434i	$-0.662540\pi$
$877$	−28.9468	−0.977464	−0.488732	+	0.872434i	$0.662540\pi$
$878$	−60.6841	−2.04799
$879$	−3.51430	−0.118534
$880$	−3.97138	−0.133875
$881$	10.6987	0.360449	0.180224	−	0.983626i	$-0.442318\pi$
$881$	10.6987	0.360449	0.180224	+	0.983626i	$0.442318\pi$
$882$	3.02992	0.102023
$883$	24.0322	0.808749	0.404374	−	0.914594i	$-0.367489\pi$
$883$	24.0322	0.808749	0.404374	+	0.914594i	$0.367489\pi$
$884$	−47.8593	−1.60968
$885$	−0.706563	−0.0237509
$886$	−57.4664	−1.93062
$887$	34.1529	1.14674	0.573371	−	0.819296i	$-0.305635\pi$
$887$	34.1529	1.14674	0.573371	+	0.819296i	$0.305635\pi$
$888$	1.23574	0.0414687
$889$	14.9102	0.500073
$890$	25.4794	0.854071
$891$	16.0319	0.537088
$892$	38.0820	1.27508
$893$	0.723202	0.0242010
$894$	4.23217	0.141545
$895$	10.8802	0.363686
$896$	−30.0112	−1.00260
$897$	0.150478	0.00502432
$898$	−14.8788	−0.496513
$899$	−23.8598	−0.795768
$900$	−7.98482	−0.266161
$901$	−0.822627	−0.0274057
$902$	40.5585	1.35045
$903$	0.579177	0.0192738
$904$	−0.691163	−0.0229877
$905$	21.5019	0.714746
$906$	0.216421	0.00719010
$907$	−10.8690	−0.360899	−0.180450	−	0.983584i	$-0.557755\pi$
$907$	−10.8690	−0.360899	−0.180450	+	0.983584i	$0.557755\pi$
$908$	−13.1723	−0.437137
$909$	51.0788	1.69418
$910$	37.2668	1.23538
$911$	13.7055	0.454083	0.227041	−	0.973885i	$-0.427095\pi$
$911$	13.7055	0.454083	0.227041	+	0.973885i	$0.427095\pi$
$912$	0.0234927	0.000777921 0
$913$	15.9923	0.529268
$914$	6.43215	0.212756
$915$	0.308778	0.0102079
$916$	−58.0887	−1.91930
$917$	−11.8879	−0.392573
$918$	4.17019	0.137637
$919$	−44.9581	−1.48303	−0.741516	−	0.670935i	$-0.765893\pi$
$919$	−44.9581	−1.48303	−0.741516	+	0.670935i	$0.765893\pi$
$920$	0.305774	0.0100811
$921$	1.38003	0.0454734
$922$	33.8584	1.11507
$923$	79.8960	2.62981
$924$	1.49652	0.0492319
$925$	7.48146	0.245989
$926$	−13.9597	−0.458745
$927$	−36.7385	−1.20665
$928$	22.7439	0.746604
$929$	−34.2134	−1.12250	−0.561252	−	0.827645i	$-0.689680\pi$
$929$	−34.2134	−1.12250	−0.561252	+	0.827645i	$0.689680\pi$
$930$	−1.97391	−0.0647270
$931$	0.0441235	0.00144609
$932$	65.0742	2.13157
$933$	0.918014	0.0300544
$934$	−16.9849	−0.555764
$935$	−5.12197	−0.167506
$936$	27.4163	0.896129
$937$	−3.61916	−0.118233	−0.0591164	−	0.998251i	$-0.518828\pi$
$937$	−3.61916	−0.118233	−0.0591164	+	0.998251i	$0.518828\pi$
$938$	−7.74888	−0.253010
$939$	0.0576573	0.00188157
$940$	20.5580	0.670529
$941$	−36.4838	−1.18934	−0.594669	−	0.803971i	$-0.702717\pi$
$941$	−36.4838	−1.18934	−0.594669	+	0.803971i	$0.702717\pi$
$942$	−2.92881	−0.0954257
$943$	2.18494	0.0711514
$944$	−13.6981	−0.445836
$945$	−1.85747	−0.0604233
$946$	−7.28243	−0.236772
$947$	−41.2707	−1.34112	−0.670559	−	0.741856i	$-0.733946\pi$
$947$	−41.2707	−1.34112	−0.670559	+	0.741856i	$0.733946\pi$
$948$	−4.11980	−0.133805
$949$	−57.6733	−1.87216
$950$	−0.203280	−0.00659526
$951$	−0.760432	−0.0246587
$952$	−11.2871	−0.365817
$953$	46.1504	1.49496	0.747479	−	0.664286i	$-0.231264\pi$
$953$	46.1504	1.49496	0.747479	+	0.664286i	$0.231264\pi$
$954$	1.87148	0.0605915
$955$	16.1195	0.521615
$956$	64.0756	2.07235
$957$	−0.607629	−0.0196419
$958$	19.7980	0.639644
$959$	−12.1089	−0.391015
$960$	1.38193	0.0446017
$961$	33.7021	1.08716
$962$	−102.017	−3.28915
$963$	−22.0947	−0.711992
$964$	28.6377	0.922358
$965$	19.3992	0.624483
$966$	0.140939	0.00453464
$967$	6.58087	0.211627	0.105813	−	0.994386i	$-0.466255\pi$
$967$	6.58087	0.211627	0.105813	+	0.994386i	$0.466255\pi$
$968$	11.2673	0.362144
$969$	0.0302990	0.000973344 0
$970$	8.65169	0.277789
$971$	16.0235	0.514220	0.257110	−	0.966382i	$-0.417230\pi$
$971$	16.0235	0.514220	0.257110	+	0.966382i	$0.417230\pi$
$972$	−8.14612	−0.261287
$973$	37.7765	1.21106
$974$	−48.6971	−1.56036
$975$	−0.716057	−0.0229322
$976$	5.98626	0.191616
$977$	−1.70544	−0.0545617	−0.0272809	−	0.999628i	$-0.508685\pi$
$977$	−1.70544	−0.0545617	−0.0272809	+	0.999628i	$0.508685\pi$
$978$	1.46534	0.0468563
$979$	−21.2693	−0.679770
$980$	1.25427	0.0400662
$981$	−22.0451	−0.703845
$982$	17.4571	0.557080
$983$	−47.7858	−1.52413	−0.762065	−	0.647501i	$-0.775814\pi$
$983$	−47.7858	−1.52413	−0.762065	+	0.647501i	$0.775814\pi$
$984$	−1.71733	−0.0547464
$985$	19.2581	0.613613
$986$	18.2004	0.579617
$987$	2.38600	0.0759473
$988$	1.58558	0.0504440
$989$	−0.392314	−0.0124749
$990$	11.6525	0.370341
$991$	−3.12812	−0.0993681	−0.0496840	−	0.998765i	$-0.515821\pi$
$991$	−3.12812	−0.0993681	−0.0496840	+	0.998765i	$0.515821\pi$
$992$	−61.6760	−1.95822
$993$	−0.0897762	−0.00284896
$994$	74.8311	2.37350
$995$	8.10050	0.256803
$996$	−2.68920	−0.0852107
$997$	33.4663	1.05989	0.529944	−	0.848033i	$-0.322213\pi$
$997$	33.4663	1.05989	0.529944	+	0.848033i	$0.322213\pi$
$998$	−76.8527	−2.43273
$999$	5.08475	0.160874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.5	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.16173 q^{2} -0.113518 q^{3} +2.67309 q^{4} +1.00000 q^{5} +0.245396 q^{6} -2.73299 q^{7} -1.45504 q^{8} -2.98711 q^{9} +O(q^{10})\)	\(q-2.16173 q^{2} -0.113518 q^{3} +2.67309 q^{4} +1.00000 q^{5} +0.245396 q^{6} -2.73299 q^{7} -1.45504 q^{8} -2.98711 q^{9} -2.16173 q^{10} +1.80454 q^{11} -0.303444 q^{12} +6.30786 q^{13} +5.90799 q^{14} -0.113518 q^{15} -2.20077 q^{16} -2.83838 q^{17} +6.45734 q^{18} +0.0940355 q^{19} +2.67309 q^{20} +0.310244 q^{21} -3.90093 q^{22} -0.210148 q^{23} +0.165173 q^{24} +1.00000 q^{25} -13.6359 q^{26} +0.679646 q^{27} -7.30552 q^{28} +2.96624 q^{29} +0.245396 q^{30} -8.04376 q^{31} +7.66756 q^{32} -0.204848 q^{33} +6.13582 q^{34} -2.73299 q^{35} -7.98482 q^{36} +7.48146 q^{37} -0.203280 q^{38} -0.716057 q^{39} -1.45504 q^{40} -10.3971 q^{41} -0.670664 q^{42} +1.86684 q^{43} +4.82369 q^{44} -2.98711 q^{45} +0.454285 q^{46} +7.69074 q^{47} +0.249828 q^{48} +0.469221 q^{49} -2.16173 q^{50} +0.322208 q^{51} +16.8615 q^{52} +0.289822 q^{53} -1.46921 q^{54} +1.80454 q^{55} +3.97660 q^{56} -0.0106747 q^{57} -6.41223 q^{58} +6.22423 q^{59} -0.303444 q^{60} -2.72007 q^{61} +17.3885 q^{62} +8.16374 q^{63} -12.1737 q^{64} +6.30786 q^{65} +0.442827 q^{66} -1.31159 q^{67} -7.58725 q^{68} +0.0238557 q^{69} +5.90799 q^{70} +12.6661 q^{71} +4.34636 q^{72} -9.14309 q^{73} -16.1729 q^{74} -0.113518 q^{75} +0.251365 q^{76} -4.93178 q^{77} +1.54792 q^{78} +13.5768 q^{79} -2.20077 q^{80} +8.88419 q^{81} +22.4758 q^{82} +8.86227 q^{83} +0.829309 q^{84} -2.83838 q^{85} -4.03562 q^{86} -0.336723 q^{87} -2.62567 q^{88} -11.7866 q^{89} +6.45734 q^{90} -17.2393 q^{91} -0.561745 q^{92} +0.913113 q^{93} -16.6253 q^{94} +0.0940355 q^{95} -0.870408 q^{96} -4.00220 q^{97} -1.01433 q^{98} -5.39036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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