LMFDB - Embedded newform 2005.2.a.d.1.3

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.39330 q^{2} -3.02965 q^{3} +3.72790 q^{4} +1.00000 q^{5} +7.25088 q^{6} -0.331604 q^{7} -4.13539 q^{8} +6.17880 q^{9} +O(q^{10})$	\(q-2.39330 q^{2} -3.02965 q^{3} +3.72790 q^{4} +1.00000 q^{5} +7.25088 q^{6} -0.331604 q^{7} -4.13539 q^{8} +6.17880 q^{9} -2.39330 q^{10} +3.34531 q^{11} -11.2942 q^{12} +2.55439 q^{13} +0.793629 q^{14} -3.02965 q^{15} +2.44143 q^{16} -2.72568 q^{17} -14.7877 q^{18} -1.24333 q^{19} +3.72790 q^{20} +1.00465 q^{21} -8.00635 q^{22} -4.98647 q^{23} +12.5288 q^{24} +1.00000 q^{25} -6.11343 q^{26} -9.63065 q^{27} -1.23619 q^{28} -1.40243 q^{29} +7.25088 q^{30} -1.02790 q^{31} +2.42768 q^{32} -10.1351 q^{33} +6.52337 q^{34} -0.331604 q^{35} +23.0339 q^{36} +0.323494 q^{37} +2.97567 q^{38} -7.73892 q^{39} -4.13539 q^{40} -2.10421 q^{41} -2.40442 q^{42} -3.26126 q^{43} +12.4710 q^{44} +6.17880 q^{45} +11.9341 q^{46} -8.40823 q^{47} -7.39670 q^{48} -6.89004 q^{49} -2.39330 q^{50} +8.25786 q^{51} +9.52251 q^{52} +6.93175 q^{53} +23.0491 q^{54} +3.34531 q^{55} +1.37131 q^{56} +3.76686 q^{57} +3.35645 q^{58} +0.107798 q^{59} -11.2942 q^{60} +4.38903 q^{61} +2.46008 q^{62} -2.04891 q^{63} -10.6930 q^{64} +2.55439 q^{65} +24.2565 q^{66} +4.22442 q^{67} -10.1611 q^{68} +15.1073 q^{69} +0.793629 q^{70} -9.59127 q^{71} -25.5517 q^{72} +15.4004 q^{73} -0.774220 q^{74} -3.02965 q^{75} -4.63501 q^{76} -1.10932 q^{77} +18.5216 q^{78} +5.43247 q^{79} +2.44143 q^{80} +10.6411 q^{81} +5.03602 q^{82} -5.98552 q^{83} +3.74522 q^{84} -2.72568 q^{85} +7.80518 q^{86} +4.24888 q^{87} -13.8342 q^{88} +3.81768 q^{89} -14.7877 q^{90} -0.847047 q^{91} -18.5891 q^{92} +3.11418 q^{93} +20.1234 q^{94} -1.24333 q^{95} -7.35503 q^{96} +8.23691 q^{97} +16.4899 q^{98} +20.6700 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9}+O(q^{10}) $ 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9} - 5 q^{10} - 30 q^{11} - 29 q^{12} - 18 q^{13} + 6 q^{14} - 10 q^{15} + 21 q^{16} - 18 q^{17} - 30 q^{18} - 17 q^{19} + 25 q^{20} + 6 q^{21} - 2 q^{22} - 44 q^{23} + 11 q^{24} + 25 q^{25} - 14 q^{26} - 25 q^{27} - 50 q^{28} - 9 q^{29} + 2 q^{30} - 13 q^{31} - 45 q^{32} - 21 q^{33} - 21 q^{34} - 31 q^{35} + 5 q^{36} - 28 q^{37} - 32 q^{38} + 9 q^{39} - 30 q^{40} + 28 q^{41} - 67 q^{42} - 61 q^{43} - 49 q^{44} + 17 q^{45} + 18 q^{46} - 53 q^{47} - 44 q^{48} + 28 q^{49} - 5 q^{50} - 30 q^{51} - 3 q^{52} - 36 q^{53} + 17 q^{54} - 30 q^{55} - 3 q^{56} - 13 q^{57} + 2 q^{58} - 39 q^{59} - 29 q^{60} + 10 q^{61} - 30 q^{62} - 44 q^{63} - 4 q^{64} - 18 q^{65} + 33 q^{66} - 10 q^{67} - 18 q^{68} - 6 q^{69} + 6 q^{70} - 7 q^{71} - q^{72} - 26 q^{73} - 3 q^{74} - 10 q^{75} + 12 q^{76} + 29 q^{77} - 5 q^{78} - 6 q^{79} + 21 q^{80} + 13 q^{81} - 30 q^{82} - 35 q^{83} + 117 q^{84} - 18 q^{85} + 14 q^{86} - 104 q^{87} + 53 q^{88} + 7 q^{89} - 30 q^{90} - 25 q^{91} - 31 q^{92} + 2 q^{93} + 68 q^{94} - 17 q^{95} + 92 q^{96} + 6 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9 - 5 * q^10 - 30 * q^11 - 29 * q^12 - 18 * q^13 + 6 * q^14 - 10 * q^15 + 21 * q^16 - 18 * q^17 - 30 * q^18 - 17 * q^19 + 25 * q^20 + 6 * q^21 - 2 * q^22 - 44 * q^23 + 11 * q^24 + 25 * q^25 - 14 * q^26 - 25 * q^27 - 50 * q^28 - 9 * q^29 + 2 * q^30 - 13 * q^31 - 45 * q^32 - 21 * q^33 - 21 * q^34 - 31 * q^35 + 5 * q^36 - 28 * q^37 - 32 * q^38 + 9 * q^39 - 30 * q^40 + 28 * q^41 - 67 * q^42 - 61 * q^43 - 49 * q^44 + 17 * q^45 + 18 * q^46 - 53 * q^47 - 44 * q^48 + 28 * q^49 - 5 * q^50 - 30 * q^51 - 3 * q^52 - 36 * q^53 + 17 * q^54 - 30 * q^55 - 3 * q^56 - 13 * q^57 + 2 * q^58 - 39 * q^59 - 29 * q^60 + 10 * q^61 - 30 * q^62 - 44 * q^63 - 4 * q^64 - 18 * q^65 + 33 * q^66 - 10 * q^67 - 18 * q^68 - 6 * q^69 + 6 * q^70 - 7 * q^71 - q^72 - 26 * q^73 - 3 * q^74 - 10 * q^75 + 12 * q^76 + 29 * q^77 - 5 * q^78 - 6 * q^79 + 21 * q^80 + 13 * q^81 - 30 * q^82 - 35 * q^83 + 117 * q^84 - 18 * q^85 + 14 * q^86 - 104 * q^87 + 53 * q^88 + 7 * q^89 - 30 * q^90 - 25 * q^91 - 31 * q^92 + 2 * q^93 + 68 * q^94 - 17 * q^95 + 92 * q^96 + 6 * q^97 + 15 * q^98 - 36 * 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 $

$2$	−2.39330	−1.69232	−0.846160	−	0.532928i	$-0.821092\pi$
$2$	−2.39330	−1.69232	−0.846160	+	0.532928i	$0.821092\pi$
$3$	−3.02965	−1.74917	−0.874585	−	0.484871i	$-0.838866\pi$
$3$	−3.02965	−1.74917	−0.874585	+	0.484871i	$0.838866\pi$
$4$	3.72790	1.86395
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.25088	2.96016
$7$	−0.331604	−0.125335	−0.0626673	−	0.998034i	$-0.519961\pi$
$7$	−0.331604	−0.125335	−0.0626673	+	0.998034i	$0.519961\pi$
$8$	−4.13539	−1.46208
$9$	6.17880	2.05960
$10$	−2.39330	−0.756829
$11$	3.34531	1.00865	0.504325	−	0.863514i	$-0.331741\pi$
$11$	3.34531	1.00865	0.504325	+	0.863514i	$0.331741\pi$
$12$	−11.2942	−3.26037
$13$	2.55439	0.708461	0.354230	−	0.935158i	$-0.384743\pi$
$13$	2.55439	0.708461	0.354230	+	0.935158i	$0.384743\pi$
$14$	0.793629	0.212106
$15$	−3.02965	−0.782253
$16$	2.44143	0.610358
$17$	−2.72568	−0.661074	−0.330537	−	0.943793i	$-0.607230\pi$
$17$	−2.72568	−0.661074	−0.330537	+	0.943793i	$0.607230\pi$
$18$	−14.7877	−3.48550
$19$	−1.24333	−0.285240	−0.142620	−	0.989778i	$-0.545553\pi$
$19$	−1.24333	−0.285240	−0.142620	+	0.989778i	$0.545553\pi$
$20$	3.72790	0.833584
$21$	1.00465	0.219232
$22$	−8.00635	−1.70696
$23$	−4.98647	−1.03975	−0.519876	−	0.854242i	$-0.674022\pi$
$23$	−4.98647	−1.03975	−0.519876	+	0.854242i	$0.674022\pi$
$24$	12.5288	2.55743
$25$	1.00000	0.200000
$26$	−6.11343	−1.19894
$27$	−9.63065	−1.85342
$28$	−1.23619	−0.233617
$29$	−1.40243	−0.260425	−0.130213	−	0.991486i	$-0.541566\pi$
$29$	−1.40243	−0.260425	−0.130213	+	0.991486i	$0.541566\pi$
$30$	7.25088	1.32382
$31$	−1.02790	−0.184616	−0.0923082	−	0.995730i	$-0.529425\pi$
$31$	−1.02790	−0.184616	−0.0923082	+	0.995730i	$0.529425\pi$
$32$	2.42768	0.429158
$33$	−10.1351	−1.76430
$34$	6.52337	1.11875
$35$	−0.331604	−0.0560513
$36$	23.0339	3.83899
$37$	0.323494	0.0531821	0.0265911	−	0.999646i	$-0.491535\pi$
$37$	0.323494	0.0531821	0.0265911	+	0.999646i	$0.491535\pi$
$38$	2.97567	0.482717
$39$	−7.73892	−1.23922
$40$	−4.13539	−0.653862
$41$	−2.10421	−0.328623	−0.164311	−	0.986409i	$-0.552540\pi$
$41$	−2.10421	−0.328623	−0.164311	+	0.986409i	$0.552540\pi$
$42$	−2.40442	−0.371010
$43$	−3.26126	−0.497337	−0.248669	−	0.968589i	$-0.579993\pi$
$43$	−3.26126	−0.497337	−0.248669	+	0.968589i	$0.579993\pi$
$44$	12.4710	1.88007
$45$	6.17880	0.921081
$46$	11.9341	1.75959
$47$	−8.40823	−1.22647	−0.613233	−	0.789902i	$-0.710131\pi$
$47$	−8.40823	−1.22647	−0.613233	+	0.789902i	$0.710131\pi$
$48$	−7.39670	−1.06762
$49$	−6.89004	−0.984291
$50$	−2.39330	−0.338464
$51$	8.25786	1.15633
$52$	9.52251	1.32053
$53$	6.93175	0.952150	0.476075	−	0.879405i	$-0.342059\pi$
$53$	6.93175	0.952150	0.476075	+	0.879405i	$0.342059\pi$
$54$	23.0491	3.13658
$55$	3.34531	0.451082
$56$	1.37131	0.183249
$57$	3.76686	0.498933
$58$	3.35645	0.440723
$59$	0.107798	0.0140341	0.00701703	−	0.999975i	$-0.497766\pi$
$59$	0.107798	0.0140341	0.00701703	+	0.999975i	$0.497766\pi$
$60$	−11.2942	−1.45808
$61$	4.38903	0.561957	0.280979	−	0.959714i	$-0.409341\pi$
$61$	4.38903	0.561957	0.280979	+	0.959714i	$0.409341\pi$
$62$	2.46008	0.312430
$63$	−2.04891	−0.258139
$64$	−10.6930	−1.33663
$65$	2.55439	0.316833
$66$	24.2565	2.98576
$67$	4.22442	0.516095	0.258047	−	0.966132i	$-0.416921\pi$
$67$	4.22442	0.516095	0.258047	+	0.966132i	$0.416921\pi$
$68$	−10.1611	−1.23221
$69$	15.1073	1.81870
$70$	0.793629	0.0948568
$71$	−9.59127	−1.13827	−0.569137	−	0.822243i	$-0.692723\pi$
$71$	−9.59127	−1.13827	−0.569137	+	0.822243i	$0.692723\pi$
$72$	−25.5517	−3.01130
$73$	15.4004	1.80248	0.901238	−	0.433324i	$-0.142659\pi$
$73$	15.4004	1.80248	0.901238	+	0.433324i	$0.142659\pi$
$74$	−0.774220	−0.0900012
$75$	−3.02965	−0.349834
$76$	−4.63501	−0.531672
$77$	−1.10932	−0.126419
$78$	18.5216	2.09716
$79$	5.43247	0.611200	0.305600	−	0.952160i	$-0.401143\pi$
$79$	5.43247	0.611200	0.305600	+	0.952160i	$0.401143\pi$
$80$	2.44143	0.272961
$81$	10.6411	1.18235
$82$	5.03602	0.556135
$83$	−5.98552	−0.656996	−0.328498	−	0.944505i	$-0.606542\pi$
$83$	−5.98552	−0.656996	−0.328498	+	0.944505i	$0.606542\pi$
$84$	3.74522	0.408637
$85$	−2.72568	−0.295641
$86$	7.80518	0.841654
$87$	4.24888	0.455528
$88$	−13.8342	−1.47473
$89$	3.81768	0.404673	0.202337	−	0.979316i	$-0.435146\pi$
$89$	3.81768	0.404673	0.202337	+	0.979316i	$0.435146\pi$
$90$	−14.7877	−1.55876
$91$	−0.847047	−0.0887946
$92$	−18.5891	−1.93804
$93$	3.11418	0.322926
$94$	20.1234	2.07558
$95$	−1.24333	−0.127563
$96$	−7.35503	−0.750670
$97$	8.23691	0.836332	0.418166	−	0.908371i	$-0.362673\pi$
$97$	8.23691	0.836332	0.418166	+	0.908371i	$0.362673\pi$
$98$	16.4899	1.66574
$99$	20.6700	2.07742
$100$	3.72790	0.372790
$101$	−0.829076	−0.0824962	−0.0412481	−	0.999149i	$-0.513133\pi$
$101$	−0.829076	−0.0824962	−0.0412481	+	0.999149i	$0.513133\pi$
$102$	−19.7636	−1.95688
$103$	7.44573	0.733649	0.366825	−	0.930290i	$-0.380445\pi$
$103$	7.44573	0.733649	0.366825	+	0.930290i	$0.380445\pi$
$104$	−10.5634	−1.03583
$105$	1.00465	0.0980434
$106$	−16.5898	−1.61134
$107$	−1.93088	−0.186665	−0.0933325	−	0.995635i	$-0.529752\pi$
$107$	−1.93088	−0.186665	−0.0933325	+	0.995635i	$0.529752\pi$
$108$	−35.9021	−3.45468
$109$	−2.06321	−0.197619	−0.0988097	−	0.995106i	$-0.531504\pi$
$109$	−2.06321	−0.197619	−0.0988097	+	0.995106i	$0.531504\pi$
$110$	−8.00635	−0.763376
$111$	−0.980075	−0.0930246
$112$	−0.809590	−0.0764990
$113$	−10.6903	−1.00566	−0.502828	−	0.864386i	$-0.667707\pi$
$113$	−10.6903	−1.00566	−0.502828	+	0.864386i	$0.667707\pi$
$114$	−9.01524	−0.844354
$115$	−4.98647	−0.464991
$116$	−5.22813	−0.485419
$117$	15.7831	1.45914
$118$	−0.257993	−0.0237501
$119$	0.903846	0.0828554
$120$	12.5288	1.14372
$121$	0.191132	0.0173756
$122$	−10.5043	−0.951012
$123$	6.37504	0.574818
$124$	−3.83191	−0.344116
$125$	1.00000	0.0894427
$126$	4.90367	0.436854
$127$	1.73315	0.153792	0.0768960	−	0.997039i	$-0.475499\pi$
$127$	1.73315	0.153792	0.0768960	+	0.997039i	$0.475499\pi$
$128$	20.7363	1.83285
$129$	9.88048	0.869928
$130$	−6.11343	−0.536183
$131$	−1.18444	−0.103485	−0.0517425	−	0.998660i	$-0.516478\pi$
$131$	−1.18444	−0.103485	−0.0517425	+	0.998660i	$0.516478\pi$
$132$	−37.7828	−3.28857
$133$	0.412294	0.0357504
$134$	−10.1103	−0.873397
$135$	−9.63065	−0.828874
$136$	11.2717	0.966543
$137$	−17.9566	−1.53414	−0.767069	−	0.641564i	$-0.778286\pi$
$137$	−17.9566	−1.53414	−0.767069	+	0.641564i	$0.778286\pi$
$138$	−36.1563	−3.07783
$139$	9.52227	0.807668	0.403834	−	0.914832i	$-0.367677\pi$
$139$	9.52227	0.807668	0.403834	+	0.914832i	$0.367677\pi$
$140$	−1.23619	−0.104477
$141$	25.4740	2.14530
$142$	22.9548	1.92633
$143$	8.54524	0.714589
$144$	15.0851	1.25709
$145$	−1.40243	−0.116466
$146$	−36.8577	−3.05037
$147$	20.8744	1.72169
$148$	1.20595	0.0991288
$149$	5.37079	0.439992	0.219996	−	0.975501i	$-0.429396\pi$
$149$	5.37079	0.439992	0.219996	+	0.975501i	$0.429396\pi$
$150$	7.25088	0.592032
$151$	−14.7287	−1.19861	−0.599303	−	0.800522i	$-0.704556\pi$
$151$	−14.7287	−1.19861	−0.599303	+	0.800522i	$0.704556\pi$
$152$	5.14165	0.417043
$153$	−16.8414	−1.36155
$154$	2.65494	0.213941
$155$	−1.02790	−0.0825630
$156$	−28.8499	−2.30984
$157$	−12.1907	−0.972927	−0.486463	−	0.873701i	$-0.661713\pi$
$157$	−12.1907	−0.972927	−0.486463	+	0.873701i	$0.661713\pi$
$158$	−13.0015	−1.03435
$159$	−21.0008	−1.66547
$160$	2.42768	0.191925
$161$	1.65354	0.130317
$162$	−25.4675	−2.00091
$163$	0.0411445	0.00322269	0.00161134	−	0.999999i	$-0.499487\pi$
$163$	0.0411445	0.00322269	0.00161134	+	0.999999i	$0.499487\pi$
$164$	−7.84429	−0.612536
$165$	−10.1351	−0.789020
$166$	14.3252	1.11185
$167$	−13.4454	−1.04044	−0.520218	−	0.854034i	$-0.674149\pi$
$167$	−13.4454	−1.04044	−0.520218	+	0.854034i	$0.674149\pi$
$168$	−4.15460	−0.320534
$169$	−6.47509	−0.498083
$170$	6.52337	0.500320
$171$	−7.68229	−0.587479
$172$	−12.1576	−0.927011
$173$	−3.86963	−0.294202	−0.147101	−	0.989121i	$-0.546994\pi$
$173$	−3.86963	−0.294202	−0.147101	+	0.989121i	$0.546994\pi$
$174$	−10.1689	−0.770900
$175$	−0.331604	−0.0250669
$176$	8.16736	0.615638
$177$	−0.326590	−0.0245480
$178$	−9.13687	−0.684837
$179$	−22.5778	−1.68755	−0.843773	−	0.536700i	$-0.819671\pi$
$179$	−22.5778	−1.68755	−0.843773	+	0.536700i	$0.819671\pi$
$180$	23.0339	1.71685
$181$	6.76573	0.502893	0.251446	−	0.967871i	$-0.419094\pi$
$181$	6.76573	0.502893	0.251446	+	0.967871i	$0.419094\pi$
$182$	2.02724	0.150269
$183$	−13.2972	−0.982960
$184$	20.6210	1.52020
$185$	0.323494	0.0237838
$186$	−7.45318	−0.546494
$187$	−9.11825	−0.666793
$188$	−31.3450	−2.28607
$189$	3.19356	0.232298
$190$	2.97567	0.215878
$191$	26.5726	1.92272	0.961361	−	0.275290i	$-0.0887737\pi$
$191$	26.5726	1.92272	0.961361	+	0.275290i	$0.0887737\pi$
$192$	32.3962	2.33800
$193$	15.4012	1.10860	0.554301	−	0.832316i	$-0.312986\pi$
$193$	15.4012	1.10860	0.554301	+	0.832316i	$0.312986\pi$
$194$	−19.7134	−1.41534
$195$	−7.73892	−0.554196
$196$	−25.6854	−1.83467
$197$	−23.6270	−1.68336	−0.841679	−	0.539979i	$-0.818432\pi$
$197$	−23.6270	−1.68336	−0.841679	+	0.539979i	$0.818432\pi$
$198$	−49.4696	−3.51565
$199$	−13.7701	−0.976136	−0.488068	−	0.872806i	$-0.662298\pi$
$199$	−13.7701	−0.976136	−0.488068	+	0.872806i	$0.662298\pi$
$200$	−4.13539	−0.292416
$201$	−12.7985	−0.902738
$202$	1.98423	0.139610
$203$	0.465052	0.0326403
$204$	30.7845	2.15534
$205$	−2.10421	−0.146965
$206$	−17.8199	−1.24157
$207$	−30.8104	−2.14147
$208$	6.23638	0.432415
$209$	−4.15933	−0.287707
$210$	−2.40442	−0.165921
$211$	−8.99217	−0.619046	−0.309523	−	0.950892i	$-0.600169\pi$
$211$	−8.99217	−0.619046	−0.309523	+	0.950892i	$0.600169\pi$
$212$	25.8409	1.77476
$213$	29.0582	1.99104
$214$	4.62118	0.315897
$215$	−3.26126	−0.222416
$216$	39.8265	2.70985
$217$	0.340856	0.0231388
$218$	4.93788	0.334436
$219$	−46.6578	−3.15284
$220$	12.4710	0.840794
$221$	−6.96245	−0.468345
$222$	2.34562	0.157427
$223$	−7.82975	−0.524319	−0.262160	−	0.965025i	$-0.584435\pi$
$223$	−7.82975	−0.524319	−0.262160	+	0.965025i	$0.584435\pi$
$224$	−0.805030	−0.0537883
$225$	6.17880	0.411920
$226$	25.5851	1.70189
$227$	−4.42878	−0.293949	−0.146974	−	0.989140i	$-0.546953\pi$
$227$	−4.42878	−0.293949	−0.146974	+	0.989140i	$0.546953\pi$
$228$	14.0425	0.929986
$229$	12.9983	0.858951	0.429475	−	0.903079i	$-0.358698\pi$
$229$	12.9983	0.858951	0.429475	+	0.903079i	$0.358698\pi$
$230$	11.9341	0.786914
$231$	3.36086	0.221128
$232$	5.79960	0.380762
$233$	8.34965	0.547004	0.273502	−	0.961871i	$-0.411818\pi$
$233$	8.34965	0.547004	0.273502	+	0.961871i	$0.411818\pi$
$234$	−37.7737	−2.46934
$235$	−8.40823	−0.548493
$236$	0.401859	0.0261588
$237$	−16.4585	−1.06909
$238$	−2.16318	−0.140218
$239$	−10.0406	−0.649474	−0.324737	−	0.945804i	$-0.605276\pi$
$239$	−10.0406	−0.649474	−0.324737	+	0.945804i	$0.605276\pi$
$240$	−7.39670	−0.477455
$241$	−1.70966	−0.110129	−0.0550644	−	0.998483i	$-0.517536\pi$
$241$	−1.70966	−0.110129	−0.0550644	+	0.998483i	$0.517536\pi$
$242$	−0.457436	−0.0294051
$243$	−3.34701	−0.214711
$244$	16.3619	1.04746
$245$	−6.89004	−0.440188
$246$	−15.2574	−0.972776
$247$	−3.17595	−0.202081
$248$	4.25077	0.269924
$249$	18.1341	1.14920
$250$	−2.39330	−0.151366
$251$	−30.9842	−1.95570	−0.977852	−	0.209297i	$-0.932882\pi$
$251$	−30.9842	−1.95570	−0.977852	+	0.209297i	$0.932882\pi$
$252$	−7.63815	−0.481158
$253$	−16.6813	−1.04875
$254$	−4.14795	−0.260265
$255$	8.25786	0.517127
$256$	−28.2422	−1.76514
$257$	21.0823	1.31508	0.657539	−	0.753421i	$-0.271598\pi$
$257$	21.0823	1.31508	0.657539	+	0.753421i	$0.271598\pi$
$258$	−23.6470	−1.47220
$259$	−0.107272	−0.00666556
$260$	9.52251	0.590561
$261$	−8.66534	−0.536371
$262$	2.83472	0.175130
$263$	−6.44516	−0.397426	−0.198713	−	0.980058i	$-0.563676\pi$
$263$	−6.44516	−0.397426	−0.198713	+	0.980058i	$0.563676\pi$
$264$	41.9127	2.57955
$265$	6.93175	0.425814
$266$	−0.986744	−0.0605011
$267$	−11.5662	−0.707843
$268$	15.7482	0.961974
$269$	5.94651	0.362565	0.181282	−	0.983431i	$-0.441975\pi$
$269$	5.94651	0.362565	0.181282	+	0.983431i	$0.441975\pi$
$270$	23.0491	1.40272
$271$	0.573130	0.0348152	0.0174076	−	0.999848i	$-0.494459\pi$
$271$	0.573130	0.0348152	0.0174076	+	0.999848i	$0.494459\pi$
$272$	−6.65456	−0.403492
$273$	2.56626	0.155317
$274$	42.9757	2.59625
$275$	3.34531	0.201730
$276$	56.3184	3.38997
$277$	−8.98034	−0.539576	−0.269788	−	0.962920i	$-0.586954\pi$
$277$	−8.98034	−0.539576	−0.269788	+	0.962920i	$0.586954\pi$
$278$	−22.7897	−1.36683
$279$	−6.35119	−0.380236
$280$	1.37131	0.0819515
$281$	5.50486	0.328392	0.164196	−	0.986428i	$-0.447497\pi$
$281$	5.50486	0.328392	0.164196	+	0.986428i	$0.447497\pi$
$282$	−60.9671	−3.63054
$283$	−5.88283	−0.349698	−0.174849	−	0.984595i	$-0.555944\pi$
$283$	−5.88283	−0.349698	−0.174849	+	0.984595i	$0.555944\pi$
$284$	−35.7553	−2.12169
$285$	3.76686	0.223130
$286$	−20.4514	−1.20931
$287$	0.697766	0.0411878
$288$	15.0002	0.883893
$289$	−9.57068	−0.562981
$290$	3.35645	0.197097
$291$	−24.9550	−1.46289
$292$	57.4110	3.35973
$293$	−15.0504	−0.879255	−0.439628	−	0.898180i	$-0.644890\pi$
$293$	−15.0504	−0.879255	−0.439628	+	0.898180i	$0.644890\pi$
$294$	−49.9588	−2.91366
$295$	0.107798	0.00627622
$296$	−1.33777	−0.0777565
$297$	−32.2176	−1.86945
$298$	−12.8539	−0.744608
$299$	−12.7374	−0.736623
$300$	−11.2942	−0.652073
$301$	1.08145	0.0623336
$302$	35.2503	2.02843
$303$	2.51181	0.144300
$304$	−3.03551	−0.174098
$305$	4.38903	0.251315
$306$	40.3066	2.30417
$307$	30.7023	1.75227	0.876136	−	0.482065i	$-0.160113\pi$
$307$	30.7023	1.75227	0.876136	+	0.482065i	$0.160113\pi$
$308$	−4.13543	−0.235638
$309$	−22.5580	−1.28328
$310$	2.46008	0.139723
$311$	27.4616	1.55720	0.778602	−	0.627518i	$-0.215929\pi$
$311$	27.4616	1.55720	0.778602	+	0.627518i	$0.215929\pi$
$312$	32.0034	1.81184
$313$	21.4306	1.21133	0.605665	−	0.795720i	$-0.292907\pi$
$313$	21.4306	1.21133	0.605665	+	0.795720i	$0.292907\pi$
$314$	29.1761	1.64650
$315$	−2.04891	−0.115443
$316$	20.2517	1.13925
$317$	−6.04751	−0.339662	−0.169831	−	0.985473i	$-0.554322\pi$
$317$	−6.04751	−0.339662	−0.169831	+	0.985473i	$0.554322\pi$
$318$	50.2613	2.81851
$319$	−4.69158	−0.262678
$320$	−10.6930	−0.597759
$321$	5.84989	0.326509
$322$	−3.95741	−0.220538
$323$	3.38892	0.188565
$324$	39.6691	2.20384
$325$	2.55439	0.141692
$326$	−0.0984714	−0.00545382
$327$	6.25080	0.345670
$328$	8.70173	0.480473
$329$	2.78821	0.153719
$330$	24.2565	1.33527
$331$	16.0135	0.880180	0.440090	−	0.897954i	$-0.354947\pi$
$331$	16.0135	0.880180	0.440090	+	0.897954i	$0.354947\pi$
$332$	−22.3134	−1.22461
$333$	1.99880	0.109534
$334$	32.1789	1.76075
$335$	4.22442	0.230804
$336$	2.45278	0.133810
$337$	−2.40622	−0.131075	−0.0655376	−	0.997850i	$-0.520876\pi$
$337$	−2.40622	−0.131075	−0.0655376	+	0.997850i	$0.520876\pi$
$338$	15.4968	0.842917
$339$	32.3878	1.75907
$340$	−10.1611	−0.551060
$341$	−3.43865	−0.186213
$342$	18.3860	0.994203
$343$	4.60599	0.248700
$344$	13.4866	0.727147
$345$	15.1073	0.813349
$346$	9.26119	0.497885
$347$	−25.8996	−1.39037	−0.695183	−	0.718833i	$-0.744677\pi$
$347$	−25.8996	−1.39037	−0.695183	+	0.718833i	$0.744677\pi$
$348$	15.8394	0.849081
$349$	6.82325	0.365240	0.182620	−	0.983184i	$-0.441542\pi$
$349$	6.82325	0.365240	0.182620	+	0.983184i	$0.441542\pi$
$350$	0.793629	0.0424213
$351$	−24.6005	−1.31307
$352$	8.12136	0.432870
$353$	10.5863	0.563454	0.281727	−	0.959495i	$-0.409093\pi$
$353$	10.5863	0.563454	0.281727	+	0.959495i	$0.409093\pi$
$354$	0.781628	0.0415430
$355$	−9.59127	−0.509052
$356$	14.2319	0.754291
$357$	−2.73834	−0.144928
$358$	54.0356	2.85587
$359$	−23.3719	−1.23352	−0.616761	−	0.787150i	$-0.711556\pi$
$359$	−23.3719	−1.23352	−0.616761	+	0.787150i	$0.711556\pi$
$360$	−25.5517	−1.34669
$361$	−17.4541	−0.918638
$362$	−16.1924	−0.851056
$363$	−0.579063	−0.0303929
$364$	−3.15771	−0.165509
$365$	15.4004	0.806092
$366$	31.8243	1.66348
$367$	2.50758	0.130895	0.0654473	−	0.997856i	$-0.479153\pi$
$367$	2.50758	0.130895	0.0654473	+	0.997856i	$0.479153\pi$
$368$	−12.1741	−0.634621
$369$	−13.0015	−0.676831
$370$	−0.774220	−0.0402498
$371$	−2.29860	−0.119337
$372$	11.6094	0.601917
$373$	33.8498	1.75268	0.876339	−	0.481695i	$-0.159979\pi$
$373$	33.8498	1.75268	0.876339	+	0.481695i	$0.159979\pi$
$374$	21.8227	1.12843
$375$	−3.02965	−0.156451
$376$	34.7713	1.79319
$377$	−3.58236	−0.184501
$378$	−7.64317	−0.393122
$379$	−22.8431	−1.17337	−0.586685	−	0.809815i	$-0.699567\pi$
$379$	−22.8431	−1.17337	−0.586685	+	0.809815i	$0.699567\pi$
$380$	−4.63501	−0.237771
$381$	−5.25083	−0.269008
$382$	−63.5962	−3.25386
$383$	11.1794	0.571241	0.285621	−	0.958343i	$-0.407800\pi$
$383$	11.1794	0.571241	0.285621	+	0.958343i	$0.407800\pi$
$384$	−62.8239	−3.20597
$385$	−1.10932	−0.0565362
$386$	−36.8597	−1.87611
$387$	−20.1507	−1.02432
$388$	30.7064	1.55888
$389$	−10.4884	−0.531784	−0.265892	−	0.964003i	$-0.585666\pi$
$389$	−10.4884	−0.531784	−0.265892	+	0.964003i	$0.585666\pi$
$390$	18.5216	0.937877
$391$	13.5915	0.687353
$392$	28.4930	1.43911
$393$	3.58844	0.181013
$394$	56.5467	2.84878
$395$	5.43247	0.273337
$396$	77.0558	3.87220
$397$	−30.8529	−1.54846	−0.774230	−	0.632904i	$-0.781863\pi$
$397$	−30.8529	−1.54846	−0.774230	+	0.632904i	$0.781863\pi$
$398$	32.9560	1.65193
$399$	−1.24911	−0.0625336
$400$	2.44143	0.122072
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	30.6307	1.52772
$403$	−2.62566	−0.130793
$404$	−3.09071	−0.153769
$405$	10.6411	0.528762
$406$	−1.11301	−0.0552378
$407$	1.08219	0.0536422
$408$	−34.1494	−1.69065
$409$	18.4903	0.914289	0.457144	−	0.889393i	$-0.348872\pi$
$409$	18.4903	0.914289	0.457144	+	0.889393i	$0.348872\pi$
$410$	5.03602	0.248711
$411$	54.4024	2.68347
$412$	27.7569	1.36749
$413$	−0.0357462	−0.00175895
$414$	73.7387	3.62406
$415$	−5.98552	−0.293818
$416$	6.20125	0.304041
$417$	−28.8492	−1.41275
$418$	9.95454	0.486893
$419$	−18.1868	−0.888481	−0.444241	−	0.895907i	$-0.646526\pi$
$419$	−18.1868	−0.888481	−0.444241	+	0.895907i	$0.646526\pi$
$420$	3.74522	0.182748
$421$	28.1241	1.37069	0.685343	−	0.728220i	$-0.259652\pi$
$421$	28.1241	1.37069	0.685343	+	0.728220i	$0.259652\pi$
$422$	21.5210	1.04763
$423$	−51.9528	−2.52603
$424$	−28.6655	−1.39212
$425$	−2.72568	−0.132215
$426$	−69.5451	−3.36947
$427$	−1.45542	−0.0704327
$428$	−7.19812	−0.347934
$429$	−25.8891	−1.24994
$430$	7.80518	0.376399
$431$	−28.9740	−1.39563	−0.697814	−	0.716279i	$-0.745844\pi$
$431$	−28.9740	−1.39563	−0.697814	+	0.716279i	$0.745844\pi$
$432$	−23.5126	−1.13125
$433$	37.6577	1.80971	0.904857	−	0.425715i	$-0.139977\pi$
$433$	37.6577	1.80971	0.904857	+	0.425715i	$0.139977\pi$
$434$	−0.815772	−0.0391583
$435$	4.24888	0.203718
$436$	−7.69143	−0.368353
$437$	6.19984	0.296578
$438$	111.666	5.33562
$439$	−37.4464	−1.78722	−0.893609	−	0.448846i	$-0.851835\pi$
$439$	−37.4464	−1.78722	−0.893609	+	0.448846i	$0.851835\pi$
$440$	−13.8342	−0.659518
$441$	−42.5721	−2.02725
$442$	16.6632	0.792590
$443$	9.75010	0.463241	0.231621	−	0.972806i	$-0.425597\pi$
$443$	9.75010	0.463241	0.231621	+	0.972806i	$0.425597\pi$
$444$	−3.65362	−0.173393
$445$	3.81768	0.180975
$446$	18.7390	0.887316
$447$	−16.2716	−0.769622
$448$	3.54586	0.167526
$449$	−24.2521	−1.14453	−0.572264	−	0.820070i	$-0.693935\pi$
$449$	−24.2521	−1.14453	−0.572264	+	0.820070i	$0.693935\pi$
$450$	−14.7877	−0.697100
$451$	−7.03926	−0.331466
$452$	−39.8523	−1.87449
$453$	44.6229	2.09657
$454$	10.5994	0.497455
$455$	−0.847047	−0.0397102
$456$	−15.5774	−0.729480
$457$	−37.5732	−1.75760	−0.878799	−	0.477192i	$-0.841655\pi$
$457$	−37.5732	−1.75760	−0.878799	+	0.477192i	$0.841655\pi$
$458$	−31.1088	−1.45362
$459$	26.2501	1.22525
$460$	−18.5891	−0.866720
$461$	0.0295914	0.00137821	0.000689104	−	1.00000i	$-0.499781\pi$
$461$	0.0295914	0.00137821	0.000689104		1.00000i	$0.499781\pi$
$462$	−8.04355	−0.374220
$463$	16.6437	0.773498	0.386749	−	0.922185i	$-0.373598\pi$
$463$	16.6437	0.773498	0.386749	+	0.922185i	$0.373598\pi$
$464$	−3.42395	−0.158953
$465$	3.11418	0.144417
$466$	−19.9833	−0.925706
$467$	−5.48734	−0.253924	−0.126962	−	0.991908i	$-0.540523\pi$
$467$	−5.48734	−0.253924	−0.126962	+	0.991908i	$0.540523\pi$
$468$	58.8377	2.71977
$469$	−1.40083	−0.0646845
$470$	20.1234	0.928225
$471$	36.9337	1.70182
$472$	−0.445785	−0.0205189
$473$	−10.9099	−0.501639
$474$	39.3901	1.80925
$475$	−1.24333	−0.0570479
$476$	3.36945	0.154438
$477$	42.8299	1.96105
$478$	24.0303	1.09912
$479$	−14.6979	−0.671563	−0.335782	−	0.941940i	$-0.609000\pi$
$479$	−14.6979	−0.671563	−0.335782	+	0.941940i	$0.609000\pi$
$480$	−7.35503	−0.335710
$481$	0.826331	0.0376774
$482$	4.09173	0.186373
$483$	−5.00964	−0.227947
$484$	0.712520	0.0323873
$485$	8.23691	0.374019
$486$	8.01040	0.363359
$487$	10.4180	0.472086	0.236043	−	0.971743i	$-0.424149\pi$
$487$	10.4180	0.472086	0.236043	+	0.971743i	$0.424149\pi$
$488$	−18.1503	−0.821627
$489$	−0.124654	−0.00563703
$490$	16.4899	0.744940
$491$	29.2696	1.32092	0.660460	−	0.750861i	$-0.270361\pi$
$491$	29.2696	1.32092	0.660460	+	0.750861i	$0.270361\pi$
$492$	23.7655	1.07143
$493$	3.82258	0.172160
$494$	7.60102	0.341986
$495$	20.6700	0.929048
$496$	−2.50955	−0.112682
$497$	3.18050	0.142665
$498$	−43.4003	−1.94481
$499$	−26.6959	−1.19507	−0.597537	−	0.801841i	$-0.703854\pi$
$499$	−26.6959	−1.19507	−0.597537	+	0.801841i	$0.703854\pi$
$500$	3.72790	0.166717
$501$	40.7348	1.81990
$502$	74.1545	3.30968
$503$	−0.155859	−0.00694941	−0.00347470	−	0.999994i	$-0.501106\pi$
$503$	−0.155859	−0.00694941	−0.00347470	+	0.999994i	$0.501106\pi$
$504$	8.47305	0.377420
$505$	−0.829076	−0.0368934
$506$	39.9235	1.77481
$507$	19.6173	0.871233
$508$	6.46100	0.286660
$509$	−15.1742	−0.672583	−0.336292	−	0.941758i	$-0.609173\pi$
$509$	−15.1742	−0.672583	−0.336292	+	0.941758i	$0.609173\pi$
$510$	−19.7636	−0.875145
$511$	−5.10683	−0.225913
$512$	26.1196	1.15433
$513$	11.9741	0.528669
$514$	−50.4563	−2.22553
$515$	7.44573	0.328098
$516$	36.8334	1.62150
$517$	−28.1282	−1.23708
$518$	0.256734	0.0112803
$519$	11.7236	0.514610
$520$	−10.5634	−0.463235
$521$	3.44651	0.150994	0.0754972	−	0.997146i	$-0.475946\pi$
$521$	3.44651	0.150994	0.0754972	+	0.997146i	$0.475946\pi$
$522$	20.7388	0.907712
$523$	5.49375	0.240225	0.120113	−	0.992760i	$-0.461674\pi$
$523$	5.49375	0.240225	0.120113	+	0.992760i	$0.461674\pi$
$524$	−4.41547	−0.192891
$525$	1.00465	0.0438463
$526$	15.4252	0.672572
$527$	2.80173	0.122045
$528$	−24.7443	−1.07686
$529$	1.86493	0.0810839
$530$	−16.5898	−0.720614
$531$	0.666060	0.0289045
$532$	1.53699	0.0666369
$533$	−5.37498	−0.232816
$534$	27.6815	1.19790
$535$	−1.93088	−0.0834791
$536$	−17.4696	−0.754571
$537$	68.4030	2.95181
$538$	−14.2318	−0.613576
$539$	−23.0493	−0.992806
$540$	−35.9021	−1.54498
$541$	−33.2268	−1.42853	−0.714267	−	0.699874i	$-0.753240\pi$
$541$	−33.2268	−1.42853	−0.714267	+	0.699874i	$0.753240\pi$
$542$	−1.37167	−0.0589184
$543$	−20.4978	−0.879645
$544$	−6.61708	−0.283705
$545$	−2.06321	−0.0883781
$546$	−6.14183	−0.262846
$547$	−20.1644	−0.862168	−0.431084	−	0.902312i	$-0.641869\pi$
$547$	−20.1644	−0.862168	−0.431084	+	0.902312i	$0.641869\pi$
$548$	−66.9405	−2.85956
$549$	27.1189	1.15741
$550$	−8.00635	−0.341392
$551$	1.74369	0.0742836
$552$	−62.4745	−2.65909
$553$	−1.80143	−0.0766045
$554$	21.4927	0.913136
$555$	−0.980075	−0.0416019
$556$	35.4981	1.50545
$557$	−32.8877	−1.39350	−0.696749	−	0.717315i	$-0.745371\pi$
$557$	−32.8877	−1.39350	−0.696749	+	0.717315i	$0.745371\pi$
$558$	15.2003	0.643481
$559$	−8.33053	−0.352344
$560$	−0.809590	−0.0342114
$561$	27.6251	1.16633
$562$	−13.1748	−0.555745
$563$	−36.7566	−1.54911	−0.774553	−	0.632509i	$-0.782025\pi$
$563$	−36.7566	−1.54911	−0.774553	+	0.632509i	$0.782025\pi$
$564$	94.9646	3.99873
$565$	−10.6903	−0.449743
$566$	14.0794	0.591802
$567$	−3.52865	−0.148189
$568$	39.6636	1.66425
$569$	−25.5909	−1.07283	−0.536414	−	0.843955i	$-0.680221\pi$
$569$	−25.5909	−1.07283	−0.536414	+	0.843955i	$0.680221\pi$
$570$	−9.01524	−0.377607
$571$	−22.8209	−0.955023	−0.477511	−	0.878626i	$-0.658461\pi$
$571$	−22.8209	−0.955023	−0.477511	+	0.878626i	$0.658461\pi$
$572$	31.8558	1.33196
$573$	−80.5056	−3.36317
$574$	−1.66997	−0.0697030
$575$	−4.98647	−0.207950
$576$	−66.0702	−2.75292
$577$	−30.6968	−1.27792	−0.638962	−	0.769238i	$-0.720636\pi$
$577$	−30.6968	−1.27792	−0.638962	+	0.769238i	$0.720636\pi$
$578$	22.9055	0.952745
$579$	−46.6602	−1.93913
$580$	−5.22813	−0.217086
$581$	1.98482	0.0823444
$582$	59.7248	2.47567
$583$	23.1889	0.960386
$584$	−63.6865	−2.63536
$585$	15.7831	0.652549
$586$	36.0202	1.48798
$587$	−36.5343	−1.50793	−0.753967	−	0.656912i	$-0.771862\pi$
$587$	−36.5343	−1.50793	−0.753967	+	0.656912i	$0.771862\pi$
$588$	77.8178	3.20915
$589$	1.27802	0.0526599
$590$	−0.257993	−0.0106214
$591$	71.5817	2.94448
$592$	0.789789	0.0324601
$593$	35.0188	1.43805	0.719025	−	0.694984i	$-0.244589\pi$
$593$	35.0188	1.43805	0.719025	+	0.694984i	$0.244589\pi$
$594$	77.1064	3.16371
$595$	0.903846	0.0370541
$596$	20.0218	0.820123
$597$	41.7186	1.70743
$598$	30.4845	1.24660
$599$	37.0439	1.51357	0.756787	−	0.653662i	$-0.226768\pi$
$599$	37.0439	1.51357	0.756787	+	0.653662i	$0.226768\pi$
$600$	12.5288	0.511485
$601$	−37.9997	−1.55004	−0.775019	−	0.631938i	$-0.782260\pi$
$601$	−37.9997	−1.55004	−0.775019	+	0.631938i	$0.782260\pi$
$602$	−2.58823	−0.105488
$603$	26.1018	1.06295
$604$	−54.9072	−2.23414
$605$	0.191132	0.00777061
$606$	−6.01153	−0.244202
$607$	8.16456	0.331389	0.165695	−	0.986177i	$-0.447013\pi$
$607$	8.16456	0.331389	0.165695	+	0.986177i	$0.447013\pi$
$608$	−3.01841	−0.122413
$609$	−1.40895	−0.0570934
$610$	−10.5043	−0.425306
$611$	−21.4779	−0.868904
$612$	−62.7831	−2.53786
$613$	−8.20913	−0.331564	−0.165782	−	0.986162i	$-0.553015\pi$
$613$	−8.20913	−0.331564	−0.165782	+	0.986162i	$0.553015\pi$
$614$	−73.4798	−2.96541
$615$	6.37504	0.257066
$616$	4.58747	0.184834
$617$	−25.5649	−1.02920	−0.514602	−	0.857429i	$-0.672060\pi$
$617$	−25.5649	−1.02920	−0.514602	+	0.857429i	$0.672060\pi$
$618$	53.9881	2.17172
$619$	−17.1587	−0.689665	−0.344832	−	0.938664i	$-0.612064\pi$
$619$	−17.1587	−0.689665	−0.344832	+	0.938664i	$0.612064\pi$
$620$	−3.83191	−0.153893
$621$	48.0230	1.92710
$622$	−65.7239	−2.63529
$623$	−1.26596	−0.0507196
$624$	−18.8941	−0.756368
$625$	1.00000	0.0400000
$626$	−51.2899	−2.04996
$627$	12.6013	0.503249
$628$	−45.4458	−1.81349
$629$	−0.881741	−0.0351573
$630$	4.90367	0.195367
$631$	−36.9593	−1.47133	−0.735663	−	0.677348i	$-0.763129\pi$
$631$	−36.9593	−1.47133	−0.735663	+	0.677348i	$0.763129\pi$
$632$	−22.4653	−0.893623
$633$	27.2432	1.08282
$634$	14.4735	0.574817
$635$	1.73315	0.0687779
$636$	−78.2889	−3.10436
$637$	−17.5999	−0.697332
$638$	11.2284	0.444535
$639$	−59.2625	−2.34439
$640$	20.7363	0.819676
$641$	11.5921	0.457861	0.228930	−	0.973443i	$-0.426477\pi$
$641$	11.5921	0.457861	0.228930	+	0.973443i	$0.426477\pi$
$642$	−14.0006	−0.552558
$643$	−39.7141	−1.56617	−0.783086	−	0.621913i	$-0.786356\pi$
$643$	−39.7141	−1.56617	−0.783086	+	0.621913i	$0.786356\pi$
$644$	6.16421	0.242904
$645$	9.88048	0.389044
$646$	−8.11071	−0.319112
$647$	−26.3876	−1.03740	−0.518701	−	0.854955i	$-0.673584\pi$
$647$	−26.3876	−1.03740	−0.518701	+	0.854955i	$0.673584\pi$
$648$	−44.0052	−1.72869
$649$	0.360617	0.0141555
$650$	−6.11343	−0.239789
$651$	−1.03268	−0.0404738
$652$	0.153383	0.00600693
$653$	1.19285	0.0466799	0.0233399	−	0.999728i	$-0.492570\pi$
$653$	1.19285	0.0466799	0.0233399	+	0.999728i	$0.492570\pi$
$654$	−14.9601	−0.584985
$655$	−1.18444	−0.0462799
$656$	−5.13730	−0.200578
$657$	95.1558	3.71238
$658$	−6.67302	−0.260141
$659$	−1.91763	−0.0747004	−0.0373502	−	0.999302i	$-0.511892\pi$
$659$	−1.91763	−0.0747004	−0.0373502	+	0.999302i	$0.511892\pi$
$660$	−37.7828	−1.47069
$661$	2.19213	0.0852638	0.0426319	−	0.999091i	$-0.486426\pi$
$661$	2.19213	0.0852638	0.0426319	+	0.999091i	$0.486426\pi$
$662$	−38.3251	−1.48955
$663$	21.0938	0.819215
$664$	24.7524	0.960581
$665$	0.412294	0.0159881
$666$	−4.78375	−0.185366
$667$	6.99319	0.270778
$668$	−50.1230	−1.93932
$669$	23.7214	0.917124
$670$	−10.1103	−0.390595
$671$	14.6827	0.566819
$672$	2.43896	0.0940849
$673$	−20.4067	−0.786620	−0.393310	−	0.919406i	$-0.628670\pi$
$673$	−20.4067	−0.786620	−0.393310	+	0.919406i	$0.628670\pi$
$674$	5.75881	0.221821
$675$	−9.63065	−0.370684
$676$	−24.1385	−0.928402
$677$	13.3981	0.514930	0.257465	−	0.966288i	$-0.417113\pi$
$677$	13.3981	0.514930	0.257465	+	0.966288i	$0.417113\pi$
$678$	−77.5139	−2.97690
$679$	−2.73139	−0.104821
$680$	11.2717	0.432251
$681$	13.4177	0.514166
$682$	8.22973	0.315133
$683$	−31.6388	−1.21063	−0.605313	−	0.795987i	$-0.706952\pi$
$683$	−31.6388	−1.21063	−0.605313	+	0.795987i	$0.706952\pi$
$684$	−28.6388	−1.09503
$685$	−17.9566	−0.686088
$686$	−11.0235	−0.420881
$687$	−39.3803	−1.50245
$688$	−7.96214	−0.303554
$689$	17.7064	0.674561
$690$	−36.1563	−1.37645
$691$	19.2671	0.732954	0.366477	−	0.930427i	$-0.380564\pi$
$691$	19.2671	0.732954	0.366477	+	0.930427i	$0.380564\pi$
$692$	−14.4256	−0.548378
$693$	−6.85427	−0.260372
$694$	61.9857	2.35295
$695$	9.52227	0.361200
$696$	−17.5708	−0.666018
$697$	5.73541	0.217244
$698$	−16.3301	−0.618103
$699$	−25.2966	−0.956804
$700$	−1.23619	−0.0467235
$701$	28.4923	1.07614	0.538070	−	0.842900i	$-0.319154\pi$
$701$	28.4923	1.07614	0.538070	+	0.842900i	$0.319154\pi$
$702$	58.8763	2.22214
$703$	−0.402210	−0.0151696
$704$	−35.7716	−1.34819
$705$	25.4740	0.959407
$706$	−25.3363	−0.953544
$707$	0.274925	0.0103396
$708$	−1.21749	−0.0457562
$709$	25.3571	0.952307	0.476154	−	0.879362i	$-0.342031\pi$
$709$	25.3571	0.952307	0.476154	+	0.879362i	$0.342031\pi$
$710$	22.9548	0.861479
$711$	33.5661	1.25883
$712$	−15.7876	−0.591665
$713$	5.12560	0.191955
$714$	6.55368	0.245265
$715$	8.54524	0.319574
$716$	−84.1679	−3.14550
$717$	30.4196	1.13604
$718$	55.9361	2.08752
$719$	51.2236	1.91032	0.955159	−	0.296092i	$-0.0956836\pi$
$719$	51.2236	1.91032	0.955159	+	0.296092i	$0.0956836\pi$
$720$	15.0851	0.562189
$721$	−2.46903	−0.0919516
$722$	41.7730	1.55463
$723$	5.17967	0.192634
$724$	25.2220	0.937367
$725$	−1.40243	−0.0520850
$726$	1.38587	0.0514346
$727$	5.35862	0.198740	0.0993702	−	0.995051i	$-0.468317\pi$
$727$	5.35862	0.198740	0.0993702	+	0.995051i	$0.468317\pi$
$728$	3.50287	0.129825
$729$	−21.7831	−0.806783
$730$	−36.8577	−1.36417
$731$	8.88914	0.328777
$732$	−49.5707	−1.83219
$733$	−33.2647	−1.22866	−0.614330	−	0.789049i	$-0.710574\pi$
$733$	−33.2647	−1.22866	−0.614330	+	0.789049i	$0.710574\pi$
$734$	−6.00140	−0.221516
$735$	20.8744	0.769965
$736$	−12.1056	−0.446217
$737$	14.1320	0.520559
$738$	31.1165	1.14542
$739$	38.8374	1.42866	0.714328	−	0.699811i	$-0.246732\pi$
$739$	38.8374	1.42866	0.714328	+	0.699811i	$0.246732\pi$
$740$	1.20595	0.0443317
$741$	9.62204	0.353474
$742$	5.50124	0.201957
$743$	23.8578	0.875257	0.437629	−	0.899156i	$-0.355818\pi$
$743$	23.8578	0.875257	0.437629	+	0.899156i	$0.355818\pi$
$744$	−12.8783	−0.472143
$745$	5.37079	0.196771
$746$	−81.0129	−2.96609
$747$	−36.9833	−1.35315
$748$	−33.9919	−1.24287
$749$	0.640287	0.0233956
$750$	7.25088	0.264765
$751$	38.2148	1.39448	0.697239	−	0.716839i	$-0.254412\pi$
$751$	38.2148	1.39448	0.697239	+	0.716839i	$0.254412\pi$
$752$	−20.5281	−0.748584
$753$	93.8713	3.42086
$754$	8.57367	0.312235
$755$	−14.7287	−0.536033
$756$	11.9053	0.432991
$757$	−16.6848	−0.606421	−0.303211	−	0.952924i	$-0.598059\pi$
$757$	−16.6848	−0.606421	−0.303211	+	0.952924i	$0.598059\pi$
$758$	54.6704	1.98572
$759$	50.5386	1.83444
$760$	5.14165	0.186507
$761$	52.8271	1.91498	0.957491	−	0.288464i	$-0.0931444\pi$
$761$	52.8271	1.91498	0.957491	+	0.288464i	$0.0931444\pi$
$762$	12.5668	0.455249
$763$	0.684168	0.0247686
$764$	99.0598	3.58386
$765$	−16.8414	−0.608902
$766$	−26.7557	−0.966724
$767$	0.275357	0.00994258
$768$	85.5642	3.08753
$769$	−41.7491	−1.50551	−0.752756	−	0.658300i	$-0.771276\pi$
$769$	−41.7491	−1.50551	−0.752756	+	0.658300i	$0.771276\pi$
$770$	2.65494	0.0956774
$771$	−63.8720	−2.30030
$772$	57.4141	2.06638
$773$	−17.0840	−0.614469	−0.307234	−	0.951634i	$-0.599404\pi$
$773$	−17.0840	−0.614469	−0.307234	+	0.951634i	$0.599404\pi$
$774$	48.2266	1.73347
$775$	−1.02790	−0.0369233
$776$	−34.0628	−1.22278
$777$	0.324997	0.0116592
$778$	25.1020	0.899949
$779$	2.61623	0.0937363
$780$	−28.8499	−1.03299
$781$	−32.0858	−1.14812
$782$	−32.5286	−1.16322
$783$	13.5063	0.482677
$784$	−16.8216	−0.600770
$785$	−12.1907	−0.435106
$786$	−8.58823	−0.306332
$787$	−16.1246	−0.574779	−0.287390	−	0.957814i	$-0.592787\pi$
$787$	−16.1246	−0.574779	−0.287390	+	0.957814i	$0.592787\pi$
$788$	−88.0792	−3.13769
$789$	19.5266	0.695165
$790$	−13.0015	−0.462574
$791$	3.54494	0.126044
$792$	−85.4785	−3.03735
$793$	11.2113	0.398125
$794$	73.8402	2.62049
$795$	−21.0008	−0.744822
$796$	−51.3335	−1.81947
$797$	−36.8101	−1.30388	−0.651941	−	0.758270i	$-0.726045\pi$
$797$	−36.8101	−1.30388	−0.651941	+	0.758270i	$0.726045\pi$
$798$	2.98949	0.105827
$799$	22.9181	0.810785
$800$	2.42768	0.0858315
$801$	23.5887	0.833465
$802$	−2.39330	−0.0845105
$803$	51.5191	1.81807
$804$	−47.7116	−1.68266
$805$	1.65354	0.0582795
$806$	6.28400	0.221345
$807$	−18.0158	−0.634188
$808$	3.42855	0.120616
$809$	30.5250	1.07320	0.536600	−	0.843836i	$-0.319708\pi$
$809$	30.5250	1.07320	0.536600	+	0.843836i	$0.319708\pi$
$810$	−25.4675	−0.894836
$811$	−35.1323	−1.23366	−0.616831	−	0.787095i	$-0.711584\pi$
$811$	−35.1323	−1.23366	−0.616831	+	0.787095i	$0.711584\pi$
$812$	1.73367	0.0608398
$813$	−1.73638	−0.0608977
$814$	−2.59001	−0.0907797
$815$	0.0411445	0.00144123
$816$	20.1610	0.705777
$817$	4.05482	0.141860
$818$	−44.2530	−1.54727
$819$	−5.23373	−0.182881
$820$	−7.84429	−0.273935
$821$	−1.64618	−0.0574521	−0.0287261	−	0.999587i	$-0.509145\pi$
$821$	−1.64618	−0.0574521	−0.0287261	+	0.999587i	$0.509145\pi$
$822$	−130.201	−4.54129
$823$	1.62713	0.0567181	0.0283591	−	0.999598i	$-0.490972\pi$
$823$	1.62713	0.0567181	0.0283591	+	0.999598i	$0.490972\pi$
$824$	−30.7910	−1.07265
$825$	−10.1351	−0.352860
$826$	0.0855514	0.00297671
$827$	6.22167	0.216349	0.108174	−	0.994132i	$-0.465500\pi$
$827$	6.22167	0.216349	0.108174	+	0.994132i	$0.465500\pi$
$828$	−114.858	−3.99160
$829$	27.2789	0.947436	0.473718	−	0.880677i	$-0.342912\pi$
$829$	27.2789	0.947436	0.473718	+	0.880677i	$0.342912\pi$
$830$	14.3252	0.497234
$831$	27.2073	0.943811
$832$	−27.3142	−0.946950
$833$	18.7800	0.650689
$834$	69.0448	2.39083
$835$	−13.4454	−0.465297
$836$	−15.5056	−0.536271
$837$	9.89935	0.342172
$838$	43.5264	1.50360
$839$	24.4834	0.845262	0.422631	−	0.906302i	$-0.361107\pi$
$839$	24.4834	0.845262	0.422631	+	0.906302i	$0.361107\pi$
$840$	−4.15460	−0.143347
$841$	−27.0332	−0.932179
$842$	−67.3096	−2.31964
$843$	−16.6778	−0.574414
$844$	−33.5219	−1.15387
$845$	−6.47509	−0.222750
$846$	124.339	4.27485
$847$	−0.0633801	−0.00217777
$848$	16.9234	0.581152
$849$	17.8229	0.611682
$850$	6.52337	0.223750
$851$	−1.61310	−0.0552962
$852$	108.326	3.71119
$853$	24.6597	0.844331	0.422166	−	0.906519i	$-0.361270\pi$
$853$	24.6597	0.844331	0.422166	+	0.906519i	$0.361270\pi$
$854$	3.48326	0.119195
$855$	−7.68229	−0.262729
$856$	7.98493	0.272919
$857$	0.731066	0.0249727	0.0124864	−	0.999922i	$-0.496025\pi$
$857$	0.731066	0.0249727	0.0124864	+	0.999922i	$0.496025\pi$
$858$	61.9605	2.11530
$859$	−27.5525	−0.940079	−0.470040	−	0.882645i	$-0.655760\pi$
$859$	−27.5525	−0.940079	−0.470040	+	0.882645i	$0.655760\pi$
$860$	−12.1576	−0.414572
$861$	−2.11399	−0.0720445
$862$	69.3435	2.36185
$863$	1.10400	0.0375807	0.0187903	−	0.999823i	$-0.494018\pi$
$863$	1.10400	0.0375807	0.0187903	+	0.999823i	$0.494018\pi$
$864$	−23.3802	−0.795409
$865$	−3.86963	−0.131571
$866$	−90.1263	−3.06262
$867$	28.9958	0.984750
$868$	1.27068	0.0431296
$869$	18.1733	0.616487
$870$	−10.1689	−0.344757
$871$	10.7908	0.365633
$872$	8.53216	0.288935
$873$	50.8942	1.72251
$874$	−14.8381	−0.501906
$875$	−0.331604	−0.0112103
$876$	−173.935	−5.87673
$877$	24.5746	0.829824	0.414912	−	0.909862i	$-0.363812\pi$
$877$	24.5746	0.829824	0.414912	+	0.909862i	$0.363812\pi$
$878$	89.6205	3.02455
$879$	45.5976	1.53797
$880$	8.16736	0.275322
$881$	−4.87630	−0.164287	−0.0821433	−	0.996621i	$-0.526177\pi$
$881$	−4.87630	−0.164287	−0.0821433	+	0.996621i	$0.526177\pi$
$882$	101.888	3.43075
$883$	34.7120	1.16815	0.584076	−	0.811699i	$-0.301457\pi$
$883$	34.7120	1.16815	0.584076	+	0.811699i	$0.301457\pi$
$884$	−25.9553	−0.872971
$885$	−0.326590	−0.0109782
$886$	−23.3349	−0.783953
$887$	−29.6879	−0.996822	−0.498411	−	0.866941i	$-0.666083\pi$
$887$	−29.6879	−0.996822	−0.498411	+	0.866941i	$0.666083\pi$
$888$	4.05299	0.136009
$889$	−0.574719	−0.0192755
$890$	−9.13687	−0.306268
$891$	35.5980	1.19258
$892$	−29.1885	−0.977304
$893$	10.4542	0.349837
$894$	38.9429	1.30245
$895$	−22.5778	−0.754694
$896$	−6.87626	−0.229720
$897$	38.5899	1.28848
$898$	58.0426	1.93691
$899$	1.44156	0.0480788
$900$	23.0339	0.767798
$901$	−18.8937	−0.629441
$902$	16.8471	0.560946
$903$	−3.27641	−0.109032
$904$	44.2084	1.47035
$905$	6.76573	0.224900
$906$	−106.796	−3.54806
$907$	44.2553	1.46947	0.734737	−	0.678352i	$-0.237305\pi$
$907$	44.2553	1.46947	0.734737	+	0.678352i	$0.237305\pi$
$908$	−16.5100	−0.547905
$909$	−5.12269	−0.169909
$910$	2.02724	0.0672023
$911$	−24.5287	−0.812671	−0.406335	−	0.913724i	$-0.633194\pi$
$911$	−24.5287	−0.812671	−0.406335	+	0.913724i	$0.633194\pi$
$912$	9.19654	0.304528
$913$	−20.0235	−0.662680
$914$	89.9239	2.97442
$915$	−13.2972	−0.439593
$916$	48.4563	1.60104
$917$	0.392765	0.0129703
$918$	−62.8243	−2.07351
$919$	−36.9428	−1.21863	−0.609315	−	0.792928i	$-0.708556\pi$
$919$	−36.9428	−1.21863	−0.609315	+	0.792928i	$0.708556\pi$
$920$	20.6210	0.679854
$921$	−93.0172	−3.06502
$922$	−0.0708212	−0.00233237
$923$	−24.4999	−0.806423
$924$	12.5289	0.412172
$925$	0.323494	0.0106364
$926$	−39.8334	−1.30901
$927$	46.0056	1.51102
$928$	−3.40466	−0.111763
$929$	51.3508	1.68477	0.842383	−	0.538880i	$-0.181152\pi$
$929$	51.3508	1.68477	0.842383	+	0.538880i	$0.181152\pi$
$930$	−7.45318	−0.244399
$931$	8.56660	0.280759
$932$	31.1267	1.01959
$933$	−83.1991	−2.72382
$934$	13.1329	0.429721
$935$	−9.11825	−0.298199
$936$	−65.2691	−2.13339
$937$	−39.1684	−1.27958	−0.639788	−	0.768552i	$-0.720978\pi$
$937$	−39.1684	−1.27958	−0.639788	+	0.768552i	$0.720978\pi$
$938$	3.35262	0.109467
$939$	−64.9273	−2.11882
$940$	−31.3450	−1.02236
$941$	−1.68582	−0.0549563	−0.0274782	−	0.999622i	$-0.508748\pi$
$941$	−1.68582	−0.0549563	−0.0274782	+	0.999622i	$0.508748\pi$
$942$	−88.3936	−2.88002
$943$	10.4926	0.341686
$944$	0.263181	0.00856581
$945$	3.19356	0.103887
$946$	26.1108	0.848935
$947$	11.4965	0.373585	0.186792	−	0.982399i	$-0.440191\pi$
$947$	11.4965	0.373585	0.186792	+	0.982399i	$0.440191\pi$
$948$	−61.3556	−1.99274
$949$	39.3386	1.27698
$950$	2.97567	0.0965434
$951$	18.3219	0.594127
$952$	−3.73775	−0.121141
$953$	−1.04301	−0.0337863	−0.0168932	−	0.999857i	$-0.505378\pi$
$953$	−1.04301	−0.0337863	−0.0168932	+	0.999857i	$0.505378\pi$
$954$	−102.505	−3.31872
$955$	26.5726	0.859868
$956$	−37.4304	−1.21059
$957$	14.2139	0.459469
$958$	35.1765	1.13650
$959$	5.95449	0.192281
$960$	32.3962	1.04558
$961$	−29.9434	−0.965917
$962$	−1.97766	−0.0637623
$963$	−11.9305	−0.384455
$964$	−6.37343	−0.205274
$965$	15.4012	0.495782
$966$	11.9896	0.385759
$967$	−7.91575	−0.254553	−0.127277	−	0.991867i	$-0.540624\pi$
$967$	−7.91575	−0.254553	−0.127277	+	0.991867i	$0.540624\pi$
$968$	−0.790404	−0.0254045
$969$	−10.2672	−0.329832
$970$	−19.7134	−0.632960
$971$	−26.5220	−0.851133	−0.425566	−	0.904927i	$-0.639925\pi$
$971$	−26.5220	−0.851133	−0.425566	+	0.904927i	$0.639925\pi$
$972$	−12.4773	−0.400210
$973$	−3.15762	−0.101229
$974$	−24.9335	−0.798921
$975$	−7.73892	−0.247844
$976$	10.7155	0.342995
$977$	39.4815	1.26313	0.631563	−	0.775325i	$-0.282414\pi$
$977$	39.4815	1.26313	0.631563	+	0.775325i	$0.282414\pi$
$978$	0.298334	0.00953967
$979$	12.7713	0.408174
$980$	−25.6854	−0.820489
$981$	−12.7481	−0.407017
$982$	−70.0511	−2.23542
$983$	−15.9212	−0.507807	−0.253904	−	0.967230i	$-0.581715\pi$
$983$	−15.9212	−0.507807	−0.253904	+	0.967230i	$0.581715\pi$
$984$	−26.3632	−0.840429
$985$	−23.6270	−0.752820
$986$	−9.14859	−0.291350
$987$	−8.44729	−0.268880
$988$	−11.8396	−0.376669
$989$	16.2622	0.517107
$990$	−49.4696	−1.57225
$991$	17.8845	0.568119	0.284060	−	0.958807i	$-0.408319\pi$
$991$	17.8845	0.568119	0.284060	+	0.958807i	$0.408319\pi$
$992$	−2.49542	−0.0792295
$993$	−48.5152	−1.53958
$994$	−7.61191	−0.241435
$995$	−13.7701	−0.436541
$996$	67.6019	2.14205
$997$	16.1203	0.510536	0.255268	−	0.966870i	$-0.417836\pi$
$997$	16.1203	0.510536	0.255268	+	0.966870i	$0.417836\pi$
$998$	63.8915	2.02245
$999$	−3.11546	−0.0985688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.d.1.3	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.d.1.3	✓	25	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)

\(f(q)\)	\(=\)	\(q-2.39330 q^{2} -3.02965 q^{3} +3.72790 q^{4} +1.00000 q^{5} +7.25088 q^{6} -0.331604 q^{7} -4.13539 q^{8} +6.17880 q^{9} +O(q^{10})\)	\(q-2.39330 q^{2} -3.02965 q^{3} +3.72790 q^{4} +1.00000 q^{5} +7.25088 q^{6} -0.331604 q^{7} -4.13539 q^{8} +6.17880 q^{9} -2.39330 q^{10} +3.34531 q^{11} -11.2942 q^{12} +2.55439 q^{13} +0.793629 q^{14} -3.02965 q^{15} +2.44143 q^{16} -2.72568 q^{17} -14.7877 q^{18} -1.24333 q^{19} +3.72790 q^{20} +1.00465 q^{21} -8.00635 q^{22} -4.98647 q^{23} +12.5288 q^{24} +1.00000 q^{25} -6.11343 q^{26} -9.63065 q^{27} -1.23619 q^{28} -1.40243 q^{29} +7.25088 q^{30} -1.02790 q^{31} +2.42768 q^{32} -10.1351 q^{33} +6.52337 q^{34} -0.331604 q^{35} +23.0339 q^{36} +0.323494 q^{37} +2.97567 q^{38} -7.73892 q^{39} -4.13539 q^{40} -2.10421 q^{41} -2.40442 q^{42} -3.26126 q^{43} +12.4710 q^{44} +6.17880 q^{45} +11.9341 q^{46} -8.40823 q^{47} -7.39670 q^{48} -6.89004 q^{49} -2.39330 q^{50} +8.25786 q^{51} +9.52251 q^{52} +6.93175 q^{53} +23.0491 q^{54} +3.34531 q^{55} +1.37131 q^{56} +3.76686 q^{57} +3.35645 q^{58} +0.107798 q^{59} -11.2942 q^{60} +4.38903 q^{61} +2.46008 q^{62} -2.04891 q^{63} -10.6930 q^{64} +2.55439 q^{65} +24.2565 q^{66} +4.22442 q^{67} -10.1611 q^{68} +15.1073 q^{69} +0.793629 q^{70} -9.59127 q^{71} -25.5517 q^{72} +15.4004 q^{73} -0.774220 q^{74} -3.02965 q^{75} -4.63501 q^{76} -1.10932 q^{77} +18.5216 q^{78} +5.43247 q^{79} +2.44143 q^{80} +10.6411 q^{81} +5.03602 q^{82} -5.98552 q^{83} +3.74522 q^{84} -2.72568 q^{85} +7.80518 q^{86} +4.24888 q^{87} -13.8342 q^{88} +3.81768 q^{89} -14.7877 q^{90} -0.847047 q^{91} -18.5891 q^{92} +3.11418 q^{93} +20.1234 q^{94} -1.24333 q^{95} -7.35503 q^{96} +8.23691 q^{97} +16.4899 q^{98} +20.6700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9}+O(q^{10}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9} - 5 q^{10} - 30 q^{11} - 29 q^{12} - 18 q^{13} + 6 q^{14} - 10 q^{15} + 21 q^{16} - 18 q^{17} - 30 q^{18} - 17 q^{19} + 25 q^{20} + 6 q^{21} - 2 q^{22} - 44 q^{23} + 11 q^{24} + 25 q^{25} - 14 q^{26} - 25 q^{27} - 50 q^{28} - 9 q^{29} + 2 q^{30} - 13 q^{31} - 45 q^{32} - 21 q^{33} - 21 q^{34} - 31 q^{35} + 5 q^{36} - 28 q^{37} - 32 q^{38} + 9 q^{39} - 30 q^{40} + 28 q^{41} - 67 q^{42} - 61 q^{43} - 49 q^{44} + 17 q^{45} + 18 q^{46} - 53 q^{47} - 44 q^{48} + 28 q^{49} - 5 q^{50} - 30 q^{51} - 3 q^{52} - 36 q^{53} + 17 q^{54} - 30 q^{55} - 3 q^{56} - 13 q^{57} + 2 q^{58} - 39 q^{59} - 29 q^{60} + 10 q^{61} - 30 q^{62} - 44 q^{63} - 4 q^{64} - 18 q^{65} + 33 q^{66} - 10 q^{67} - 18 q^{68} - 6 q^{69} + 6 q^{70} - 7 q^{71} - q^{72} - 26 q^{73} - 3 q^{74} - 10 q^{75} + 12 q^{76} + 29 q^{77} - 5 q^{78} - 6 q^{79} + 21 q^{80} + 13 q^{81} - 30 q^{82} - 35 q^{83} + 117 q^{84} - 18 q^{85} + 14 q^{86} - 104 q^{87} + 53 q^{88} + 7 q^{89} - 30 q^{90} - 25 q^{91} - 31 q^{92} + 2 q^{93} + 68 q^{94} - 17 q^{95} + 92 q^{96} + 6 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9 - 5 * q^10 - 30 * q^11 - 29 * q^12 - 18 * q^13 + 6 * q^14 - 10 * q^15 + 21 * q^16 - 18 * q^17 - 30 * q^18 - 17 * q^19 + 25 * q^20 + 6 * q^21 - 2 * q^22 - 44 * q^23 + 11 * q^24 + 25 * q^25 - 14 * q^26 - 25 * q^27 - 50 * q^28 - 9 * q^29 + 2 * q^30 - 13 * q^31 - 45 * q^32 - 21 * q^33 - 21 * q^34 - 31 * q^35 + 5 * q^36 - 28 * q^37 - 32 * q^38 + 9 * q^39 - 30 * q^40 + 28 * q^41 - 67 * q^42 - 61 * q^43 - 49 * q^44 + 17 * q^45 + 18 * q^46 - 53 * q^47 - 44 * q^48 + 28 * q^49 - 5 * q^50 - 30 * q^51 - 3 * q^52 - 36 * q^53 + 17 * q^54 - 30 * q^55 - 3 * q^56 - 13 * q^57 + 2 * q^58 - 39 * q^59 - 29 * q^60 + 10 * q^61 - 30 * q^62 - 44 * q^63 - 4 * q^64 - 18 * q^65 + 33 * q^66 - 10 * q^67 - 18 * q^68 - 6 * q^69 + 6 * q^70 - 7 * q^71 - q^72 - 26 * q^73 - 3 * q^74 - 10 * q^75 + 12 * q^76 + 29 * q^77 - 5 * q^78 - 6 * q^79 + 21 * q^80 + 13 * q^81 - 30 * q^82 - 35 * q^83 + 117 * q^84 - 18 * q^85 + 14 * q^86 - 104 * q^87 + 53 * q^88 + 7 * q^89 - 30 * q^90 - 25 * q^91 - 31 * q^92 + 2 * q^93 + 68 * q^94 - 17 * q^95 + 92 * q^96 + 6 * q^97 + 15 * q^98 - 36 * q^99

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