LMFDB - Embedded newform 2005.2.a.g.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.26463 q^{2} -1.05618 q^{3} +3.12854 q^{4} +1.00000 q^{5} +2.39186 q^{6} +1.78961 q^{7} -2.55571 q^{8} -1.88448 q^{9} +O(q^{10})$	\(q-2.26463 q^{2} -1.05618 q^{3} +3.12854 q^{4} +1.00000 q^{5} +2.39186 q^{6} +1.78961 q^{7} -2.55571 q^{8} -1.88448 q^{9} -2.26463 q^{10} -3.65068 q^{11} -3.30431 q^{12} -3.53094 q^{13} -4.05280 q^{14} -1.05618 q^{15} -0.469334 q^{16} -5.83737 q^{17} +4.26763 q^{18} -4.81744 q^{19} +3.12854 q^{20} -1.89016 q^{21} +8.26743 q^{22} +2.44796 q^{23} +2.69930 q^{24} +1.00000 q^{25} +7.99627 q^{26} +5.15890 q^{27} +5.59886 q^{28} +3.49657 q^{29} +2.39186 q^{30} -5.12210 q^{31} +6.17429 q^{32} +3.85579 q^{33} +13.2195 q^{34} +1.78961 q^{35} -5.89565 q^{36} -0.874894 q^{37} +10.9097 q^{38} +3.72932 q^{39} -2.55571 q^{40} +7.23671 q^{41} +4.28051 q^{42} -5.15282 q^{43} -11.4213 q^{44} -1.88448 q^{45} -5.54371 q^{46} +11.8429 q^{47} +0.495703 q^{48} -3.79729 q^{49} -2.26463 q^{50} +6.16533 q^{51} -11.0467 q^{52} +1.41923 q^{53} -11.6830 q^{54} -3.65068 q^{55} -4.57373 q^{56} +5.08811 q^{57} -7.91843 q^{58} +9.35579 q^{59} -3.30431 q^{60} +2.78859 q^{61} +11.5996 q^{62} -3.37248 q^{63} -13.0438 q^{64} -3.53094 q^{65} -8.73193 q^{66} +0.593079 q^{67} -18.2624 q^{68} -2.58549 q^{69} -4.05280 q^{70} -13.7544 q^{71} +4.81618 q^{72} +13.6038 q^{73} +1.98131 q^{74} -1.05618 q^{75} -15.0715 q^{76} -6.53330 q^{77} -8.44553 q^{78} -14.2999 q^{79} -0.469334 q^{80} +0.204676 q^{81} -16.3884 q^{82} +14.1569 q^{83} -5.91343 q^{84} -5.83737 q^{85} +11.6692 q^{86} -3.69302 q^{87} +9.33009 q^{88} +0.882318 q^{89} +4.26763 q^{90} -6.31902 q^{91} +7.65852 q^{92} +5.40988 q^{93} -26.8197 q^{94} -4.81744 q^{95} -6.52119 q^{96} +10.6921 q^{97} +8.59945 q^{98} +6.87962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.26463	−1.60133	−0.800667	−	0.599110i	$-0.795521\pi$
$2$	−2.26463	−1.60133	−0.800667	+	0.599110i	$0.795521\pi$
$3$	−1.05618	−0.609788	−0.304894	−	0.952386i	$-0.598621\pi$
$3$	−1.05618	−0.609788	−0.304894	+	0.952386i	$0.598621\pi$
$4$	3.12854	1.56427
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.39186	0.976474
$7$	1.78961	0.676410	0.338205	−	0.941073i	$-0.390180\pi$
$7$	1.78961	0.676410	0.338205	+	0.941073i	$0.390180\pi$
$8$	−2.55571	−0.903581
$9$	−1.88448	−0.628159
$10$	−2.26463	−0.716138
$11$	−3.65068	−1.10072	−0.550361	−	0.834927i	$-0.685510\pi$
$11$	−3.65068	−1.10072	−0.550361	+	0.834927i	$0.685510\pi$
$12$	−3.30431	−0.953872
$13$	−3.53094	−0.979307	−0.489654	−	0.871917i	$-0.662877\pi$
$13$	−3.53094	−0.979307	−0.489654	+	0.871917i	$0.662877\pi$
$14$	−4.05280	−1.08316
$15$	−1.05618	−0.272705
$16$	−0.469334	−0.117334
$17$	−5.83737	−1.41577	−0.707885	−	0.706328i	$-0.750350\pi$
$17$	−5.83737	−1.41577	−0.707885	+	0.706328i	$0.750350\pi$
$18$	4.26763	1.00589
$19$	−4.81744	−1.10520	−0.552599	−	0.833447i	$-0.686364\pi$
$19$	−4.81744	−1.10520	−0.552599	+	0.833447i	$0.686364\pi$
$20$	3.12854	0.699562
$21$	−1.89016	−0.412466
$22$	8.26743	1.76262
$23$	2.44796	0.510434	0.255217	−	0.966884i	$-0.417853\pi$
$23$	2.44796	0.510434	0.255217	+	0.966884i	$0.417853\pi$
$24$	2.69930	0.550993
$25$	1.00000	0.200000
$26$	7.99627	1.56820
$27$	5.15890	0.992832
$28$	5.59886	1.05809
$29$	3.49657	0.649297	0.324648	−	0.945835i	$-0.394754\pi$
$29$	3.49657	0.649297	0.324648	+	0.945835i	$0.394754\pi$
$30$	2.39186	0.436692
$31$	−5.12210	−0.919956	−0.459978	−	0.887930i	$-0.652143\pi$
$31$	−5.12210	−0.919956	−0.459978	+	0.887930i	$0.652143\pi$
$32$	6.17429	1.09147
$33$	3.85579	0.671207
$34$	13.2195	2.26712
$35$	1.78961	0.302500
$36$	−5.89565	−0.982608
$37$	−0.874894	−0.143832	−0.0719159	−	0.997411i	$-0.522911\pi$
$37$	−0.874894	−0.143832	−0.0719159	+	0.997411i	$0.522911\pi$
$38$	10.9097	1.76979
$39$	3.72932	0.597170
$40$	−2.55571	−0.404094
$41$	7.23671	1.13018	0.565092	−	0.825028i	$-0.308841\pi$
$41$	7.23671	1.13018	0.565092	+	0.825028i	$0.308841\pi$
$42$	4.28051	0.660496
$43$	−5.15282	−0.785797	−0.392899	−	0.919582i	$-0.628528\pi$
$43$	−5.15282	−0.785797	−0.392899	+	0.919582i	$0.628528\pi$
$44$	−11.4213	−1.72182
$45$	−1.88448	−0.280921
$46$	−5.54371	−0.817375
$47$	11.8429	1.72746	0.863731	−	0.503953i	$-0.168121\pi$
$47$	11.8429	1.72746	0.863731	+	0.503953i	$0.168121\pi$
$48$	0.495703	0.0715486
$49$	−3.79729	−0.542470
$50$	−2.26463	−0.320267
$51$	6.16533	0.863319
$52$	−11.0467	−1.53190
$53$	1.41923	0.194946	0.0974729	−	0.995238i	$-0.468924\pi$
$53$	1.41923	0.194946	0.0974729	+	0.995238i	$0.468924\pi$
$54$	−11.6830	−1.58985
$55$	−3.65068	−0.492258
$56$	−4.57373	−0.611191
$57$	5.08811	0.673936
$58$	−7.91843	−1.03974
$59$	9.35579	1.21802	0.609010	−	0.793163i	$-0.291567\pi$
$59$	9.35579	1.21802	0.609010	+	0.793163i	$0.291567\pi$
$60$	−3.30431	−0.426584
$61$	2.78859	0.357043	0.178521	−	0.983936i	$-0.442869\pi$
$61$	2.78859	0.357043	0.178521	+	0.983936i	$0.442869\pi$
$62$	11.5996	1.47316
$63$	−3.37248	−0.424892
$64$	−13.0438	−1.63048
$65$	−3.53094	−0.437960
$66$	−8.73193	−1.07483
$67$	0.593079	0.0724561	0.0362281	−	0.999344i	$-0.488466\pi$
$67$	0.593079	0.0724561	0.0362281	+	0.999344i	$0.488466\pi$
$68$	−18.2624	−2.21464
$69$	−2.58549	−0.311257
$70$	−4.05280	−0.484403
$71$	−13.7544	−1.63234	−0.816172	−	0.577809i	$-0.803908\pi$
$71$	−13.7544	−1.63234	−0.816172	+	0.577809i	$0.803908\pi$
$72$	4.81618	0.567592
$73$	13.6038	1.59221	0.796103	−	0.605161i	$-0.206891\pi$
$73$	13.6038	1.59221	0.796103	+	0.605161i	$0.206891\pi$
$74$	1.98131	0.230323
$75$	−1.05618	−0.121958
$76$	−15.0715	−1.72883
$77$	−6.53330	−0.744539
$78$	−8.44553	−0.956268
$79$	−14.2999	−1.60886	−0.804432	−	0.594045i	$-0.797530\pi$
$79$	−14.2999	−1.60886	−0.804432	+	0.594045i	$0.797530\pi$
$80$	−0.469334	−0.0524732
$81$	0.204676	0.0227417
$82$	−16.3884	−1.80980
$83$	14.1569	1.55392	0.776961	−	0.629548i	$-0.216760\pi$
$83$	14.1569	1.55392	0.776961	+	0.629548i	$0.216760\pi$
$84$	−5.91343	−0.645208
$85$	−5.83737	−0.633151
$86$	11.6692	1.25832
$87$	−3.69302	−0.395933
$88$	9.33009	0.994591
$89$	0.882318	0.0935255	0.0467627	−	0.998906i	$-0.485110\pi$
$89$	0.882318	0.0935255	0.0467627	+	0.998906i	$0.485110\pi$
$90$	4.26763	0.449848
$91$	−6.31902	−0.662413
$92$	7.65852	0.798456
$93$	5.40988	0.560978
$94$	−26.8197	−2.76624
$95$	−4.81744	−0.494259
$96$	−6.52119	−0.665566
$97$	10.6921	1.08562	0.542808	−	0.839857i	$-0.317361\pi$
$97$	10.6921	1.08562	0.542808	+	0.839857i	$0.317361\pi$
$98$	8.59945	0.868675
$99$	6.87962	0.691428
$100$	3.12854	0.312854
$101$	−1.47769	−0.147035	−0.0735176	−	0.997294i	$-0.523423\pi$
$101$	−1.47769	−0.147035	−0.0735176	+	0.997294i	$0.523423\pi$
$102$	−13.9622	−1.38246
$103$	2.64647	0.260765	0.130382	−	0.991464i	$-0.458379\pi$
$103$	2.64647	0.260765	0.130382	+	0.991464i	$0.458379\pi$
$104$	9.02408	0.884884
$105$	−1.89016	−0.184461
$106$	−3.21402	−0.312173
$107$	15.4054	1.48930	0.744650	−	0.667455i	$-0.232616\pi$
$107$	15.4054	1.48930	0.744650	+	0.667455i	$0.232616\pi$
$108$	16.1398	1.55305
$109$	3.12617	0.299433	0.149716	−	0.988729i	$-0.452164\pi$
$109$	3.12617	0.299433	0.149716	+	0.988729i	$0.452164\pi$
$110$	8.26743	0.788268
$111$	0.924049	0.0877069
$112$	−0.839926	−0.0793656
$113$	3.87360	0.364398	0.182199	−	0.983262i	$-0.441679\pi$
$113$	3.87360	0.364398	0.182199	+	0.983262i	$0.441679\pi$
$114$	−11.5227	−1.07920
$115$	2.44796	0.228273
$116$	10.9391	1.01567
$117$	6.65398	0.615160
$118$	−21.1874	−1.95046
$119$	−10.4466	−0.957640
$120$	2.69930	0.246412
$121$	2.32747	0.211588
$122$	−6.31512	−0.571744
$123$	−7.64329	−0.689173
$124$	−16.0247	−1.43906
$125$	1.00000	0.0894427
$126$	7.63741	0.680394
$127$	15.6918	1.39243	0.696213	−	0.717835i	$-0.254867\pi$
$127$	15.6918	1.39243	0.696213	+	0.717835i	$0.254867\pi$
$128$	17.1908	1.51946
$129$	5.44232	0.479170
$130$	7.99627	0.701319
$131$	−19.4374	−1.69826	−0.849128	−	0.528187i	$-0.822872\pi$
$131$	−19.4374	−1.69826	−0.849128	+	0.528187i	$0.822872\pi$
$132$	12.0630	1.04995
$133$	−8.62135	−0.747566
$134$	−1.34310	−0.116026
$135$	5.15890	0.444008
$136$	14.9186	1.27926
$137$	−17.2360	−1.47257	−0.736287	−	0.676669i	$-0.763423\pi$
$137$	−17.2360	−1.47257	−0.736287	+	0.676669i	$0.763423\pi$
$138$	5.85517	0.498426
$139$	17.9496	1.52246	0.761232	−	0.648480i	$-0.224595\pi$
$139$	17.9496	1.52246	0.761232	+	0.648480i	$0.224595\pi$
$140$	5.59886	0.473190
$141$	−12.5083	−1.05339
$142$	31.1485	2.61393
$143$	12.8903	1.07794
$144$	0.884449	0.0737041
$145$	3.49657	0.290374
$146$	−30.8076	−2.54965
$147$	4.01064	0.330792
$148$	−2.73714	−0.224991
$149$	0.733594	0.0600984	0.0300492	−	0.999548i	$-0.490434\pi$
$149$	0.733594	0.0600984	0.0300492	+	0.999548i	$0.490434\pi$
$150$	2.39186	0.195295
$151$	5.40464	0.439823	0.219911	−	0.975520i	$-0.429423\pi$
$151$	5.40464	0.439823	0.219911	+	0.975520i	$0.429423\pi$
$152$	12.3120	0.998636
$153$	11.0004	0.889328
$154$	14.7955	1.19225
$155$	−5.12210	−0.411417
$156$	11.6673	0.934134
$157$	−3.89336	−0.310724	−0.155362	−	0.987858i	$-0.549654\pi$
$157$	−3.89336	−0.310724	−0.155362	+	0.987858i	$0.549654\pi$
$158$	32.3839	2.57633
$159$	−1.49896	−0.118876
$160$	6.17429	0.488121
$161$	4.38089	0.345263
$162$	−0.463514	−0.0364171
$163$	−15.9562	−1.24978	−0.624892	−	0.780711i	$-0.714857\pi$
$163$	−15.9562	−1.24978	−0.624892	+	0.780711i	$0.714857\pi$
$164$	22.6403	1.76791
$165$	3.85579	0.300173
$166$	−32.0601	−2.48835
$167$	−8.42469	−0.651922	−0.325961	−	0.945383i	$-0.605688\pi$
$167$	−8.42469	−0.651922	−0.325961	+	0.945383i	$0.605688\pi$
$168$	4.83070	0.372697
$169$	−0.532445	−0.0409573
$170$	13.2195	1.01389
$171$	9.07836	0.694239
$172$	−16.1208	−1.22920
$173$	5.11641	0.388994	0.194497	−	0.980903i	$-0.437693\pi$
$173$	5.11641	0.388994	0.194497	+	0.980903i	$0.437693\pi$
$174$	8.36331	0.634021
$175$	1.78961	0.135282
$176$	1.71339	0.129152
$177$	−9.88143	−0.742734
$178$	−1.99812	−0.149765
$179$	21.1097	1.57781	0.788906	−	0.614514i	$-0.210648\pi$
$179$	21.1097	1.57781	0.788906	+	0.614514i	$0.210648\pi$
$180$	−5.89565	−0.439436
$181$	6.18337	0.459606	0.229803	−	0.973237i	$-0.426192\pi$
$181$	6.18337	0.459606	0.229803	+	0.973237i	$0.426192\pi$
$182$	14.3102	1.06074
$183$	−2.94527	−0.217720
$184$	−6.25627	−0.461219
$185$	−0.874894	−0.0643235
$186$	−12.2514	−0.898313
$187$	21.3104	1.55837
$188$	37.0509	2.70221
$189$	9.23243	0.671561
$190$	10.9097	0.791474
$191$	−0.442593	−0.0320249	−0.0160125	−	0.999872i	$-0.505097\pi$
$191$	−0.442593	−0.0320249	−0.0160125	+	0.999872i	$0.505097\pi$
$192$	13.7767	0.994245
$193$	−14.7558	−1.06214	−0.531072	−	0.847327i	$-0.678210\pi$
$193$	−14.7558	−1.06214	−0.531072	+	0.847327i	$0.678210\pi$
$194$	−24.2136	−1.73843
$195$	3.72932	0.267062
$196$	−11.8800	−0.848569
$197$	14.9947	1.06833	0.534163	−	0.845381i	$-0.320627\pi$
$197$	14.9947	1.06833	0.534163	+	0.845381i	$0.320627\pi$
$198$	−15.5798	−1.10721
$199$	9.52739	0.675379	0.337689	−	0.941258i	$-0.390355\pi$
$199$	9.52739	0.675379	0.337689	+	0.941258i	$0.390355\pi$
$200$	−2.55571	−0.180716
$201$	−0.626400	−0.0441829
$202$	3.34641	0.235452
$203$	6.25750	0.439190
$204$	19.2885	1.35046
$205$	7.23671	0.505434
$206$	−5.99328	−0.417571
$207$	−4.61311	−0.320634
$208$	1.65719	0.114906
$209$	17.5869	1.21651
$210$	4.28051	0.295383
$211$	−8.77245	−0.603920	−0.301960	−	0.953321i	$-0.597641\pi$
$211$	−8.77245	−0.603920	−0.301960	+	0.953321i	$0.597641\pi$
$212$	4.44010	0.304947
$213$	14.5271	0.995384
$214$	−34.8876	−2.38487
$215$	−5.15282	−0.351419
$216$	−13.1847	−0.897104
$217$	−9.16657	−0.622267
$218$	−7.07960	−0.479491
$219$	−14.3681	−0.970908
$220$	−11.4213	−0.770023
$221$	20.6114	1.38647
$222$	−2.09263	−0.140448
$223$	8.15929	0.546387	0.273193	−	0.961959i	$-0.411920\pi$
$223$	8.15929	0.546387	0.273193	+	0.961959i	$0.411920\pi$
$224$	11.0496	0.738282
$225$	−1.88448	−0.125632
$226$	−8.77227	−0.583522
$227$	20.9115	1.38794	0.693972	−	0.720002i	$-0.255859\pi$
$227$	20.9115	1.38794	0.693972	+	0.720002i	$0.255859\pi$
$228$	15.9183	1.05422
$229$	10.9207	0.721661	0.360831	−	0.932631i	$-0.382493\pi$
$229$	10.9207	0.721661	0.360831	+	0.932631i	$0.382493\pi$
$230$	−5.54371	−0.365541
$231$	6.90037	0.454011
$232$	−8.93623	−0.586692
$233$	−20.5098	−1.34364	−0.671822	−	0.740712i	$-0.734488\pi$
$233$	−20.5098	−1.34364	−0.671822	+	0.740712i	$0.734488\pi$
$234$	−15.0688	−0.985077
$235$	11.8429	0.772545
$236$	29.2699	1.90531
$237$	15.1033	0.981066
$238$	23.6577	1.53350
$239$	21.8076	1.41062	0.705308	−	0.708901i	$-0.250809\pi$
$239$	21.8076	1.41062	0.705308	+	0.708901i	$0.250809\pi$
$240$	0.495703	0.0319975
$241$	4.00230	0.257811	0.128906	−	0.991657i	$-0.458854\pi$
$241$	4.00230	0.257811	0.128906	+	0.991657i	$0.458854\pi$
$242$	−5.27084	−0.338823
$243$	−15.6929	−1.00670
$244$	8.72421	0.558510
$245$	−3.79729	−0.242600
$246$	17.3092	1.10359
$247$	17.0101	1.08233
$248$	13.0906	0.831255
$249$	−14.9523	−0.947563
$250$	−2.26463	−0.143228
$251$	6.95377	0.438918	0.219459	−	0.975622i	$-0.429571\pi$
$251$	6.95377	0.438918	0.219459	+	0.975622i	$0.429571\pi$
$252$	−10.5509	−0.664646
$253$	−8.93670	−0.561846
$254$	−35.5362	−2.22974
$255$	6.16533	0.386088
$256$	−12.8431	−0.802692
$257$	−23.6395	−1.47459	−0.737296	−	0.675570i	$-0.763898\pi$
$257$	−23.6395	−1.47459	−0.737296	+	0.675570i	$0.763898\pi$
$258$	−12.3248	−0.767310
$259$	−1.56572	−0.0972892
$260$	−11.0467	−0.685086
$261$	−6.58920	−0.407861
$262$	44.0185	2.71947
$263$	27.3871	1.68876	0.844381	−	0.535744i	$-0.179969\pi$
$263$	27.3871	1.68876	0.844381	+	0.535744i	$0.179969\pi$
$264$	−9.85429	−0.606490
$265$	1.41923	0.0871824
$266$	19.5242	1.19710
$267$	−0.931890	−0.0570307
$268$	1.85547	0.113341
$269$	−3.91276	−0.238565	−0.119282	−	0.992860i	$-0.538059\pi$
$269$	−3.91276	−0.238565	−0.119282	+	0.992860i	$0.538059\pi$
$270$	−11.6830	−0.711004
$271$	14.5250	0.882330	0.441165	−	0.897426i	$-0.354565\pi$
$271$	14.5250	0.882330	0.441165	+	0.897426i	$0.354565\pi$
$272$	2.73968	0.166117
$273$	6.67404	0.403931
$274$	39.0332	2.35808
$275$	−3.65068	−0.220144
$276$	−8.08880	−0.486889
$277$	12.8430	0.771660	0.385830	−	0.922570i	$-0.373915\pi$
$277$	12.8430	0.771660	0.385830	+	0.922570i	$0.373915\pi$
$278$	−40.6491	−2.43797
$279$	9.65247	0.577878
$280$	−4.57373	−0.273333
$281$	−2.77451	−0.165513	−0.0827566	−	0.996570i	$-0.526372\pi$
$281$	−2.77451	−0.165513	−0.0827566	+	0.996570i	$0.526372\pi$
$282$	28.3266	1.68682
$283$	−32.3810	−1.92485	−0.962426	−	0.271545i	$-0.912465\pi$
$283$	−32.3810	−1.92485	−0.962426	+	0.271545i	$0.912465\pi$
$284$	−43.0311	−2.55342
$285$	5.08811	0.301393
$286$	−29.1918	−1.72615
$287$	12.9509	0.764467
$288$	−11.6353	−0.685617
$289$	17.0749	1.00440
$290$	−7.91843	−0.464986
$291$	−11.2928	−0.661996
$292$	42.5600	2.49064
$293$	−12.6526	−0.739174	−0.369587	−	0.929196i	$-0.620501\pi$
$293$	−12.6526	−0.739174	−0.369587	+	0.929196i	$0.620501\pi$
$294$	−9.08260	−0.529708
$295$	9.35579	0.544715
$296$	2.23598	0.129964
$297$	−18.8335	−1.09283
$298$	−1.66132	−0.0962375
$299$	−8.64359	−0.499872
$300$	−3.30431	−0.190774
$301$	−9.22154	−0.531521
$302$	−12.2395	−0.704303
$303$	1.56071	0.0896603
$304$	2.26099	0.129677
$305$	2.78859	0.159674
$306$	−24.9118	−1.42411
$307$	0.381868	0.0217944	0.0108972	−	0.999941i	$-0.496531\pi$
$307$	0.381868	0.0217944	0.0108972	+	0.999941i	$0.496531\pi$
$308$	−20.4397	−1.16466
$309$	−2.79516	−0.159011
$310$	11.5996	0.658815
$311$	2.36988	0.134383	0.0671917	−	0.997740i	$-0.478596\pi$
$311$	2.36988	0.134383	0.0671917	+	0.997740i	$0.478596\pi$
$312$	−9.53108	−0.539591
$313$	−18.6449	−1.05387	−0.526936	−	0.849905i	$-0.676659\pi$
$313$	−18.6449	−1.05387	−0.526936	+	0.849905i	$0.676659\pi$
$314$	8.81701	0.497573
$315$	−3.37248	−0.190018
$316$	−44.7377	−2.51669
$317$	28.8461	1.62016	0.810078	−	0.586322i	$-0.199425\pi$
$317$	28.8461	1.62016	0.810078	+	0.586322i	$0.199425\pi$
$318$	3.39459	0.190359
$319$	−12.7649	−0.714695
$320$	−13.0438	−0.729171
$321$	−16.2710	−0.908158
$322$	−9.92108	−0.552880
$323$	28.1212	1.56470
$324$	0.640335	0.0355742
$325$	−3.53094	−0.195861
$326$	36.1348	2.00132
$327$	−3.30181	−0.182590
$328$	−18.4949	−1.02121
$329$	21.1942	1.16847
$330$	−8.73193	−0.480677
$331$	−30.8420	−1.69523	−0.847615	−	0.530611i	$-0.821963\pi$
$331$	−30.8420	−1.69523	−0.847615	+	0.530611i	$0.821963\pi$
$332$	44.2904	2.43075
$333$	1.64872	0.0903491
$334$	19.0788	1.04394
$335$	0.593079	0.0324034
$336$	0.887116	0.0483962
$337$	−2.49853	−0.136104	−0.0680518	−	0.997682i	$-0.521678\pi$
$337$	−2.49853	−0.136104	−0.0680518	+	0.997682i	$0.521678\pi$
$338$	1.20579	0.0655863
$339$	−4.09124	−0.222205
$340$	−18.2624	−0.990418
$341$	18.6991	1.01262
$342$	−20.5591	−1.11171
$343$	−19.3230	−1.04334
$344$	13.1691	0.710031
$345$	−2.58549	−0.139198
$346$	−11.5868	−0.622909
$347$	2.00306	0.107530	0.0537651	−	0.998554i	$-0.482878\pi$
$347$	2.00306	0.107530	0.0537651	+	0.998554i	$0.482878\pi$
$348$	−11.5537	−0.619346
$349$	29.2422	1.56530	0.782649	−	0.622463i	$-0.213868\pi$
$349$	29.2422	1.56530	0.782649	+	0.622463i	$0.213868\pi$
$350$	−4.05280	−0.216631
$351$	−18.2158	−0.972287
$352$	−22.5404	−1.20141
$353$	−31.6875	−1.68656	−0.843278	−	0.537478i	$-0.819377\pi$
$353$	−31.6875	−1.68656	−0.843278	+	0.537478i	$0.819377\pi$
$354$	22.3778	1.18936
$355$	−13.7544	−0.730006
$356$	2.76036	0.146299
$357$	11.0336	0.583957
$358$	−47.8056	−2.52660
$359$	25.1393	1.32680	0.663402	−	0.748263i	$-0.269112\pi$
$359$	25.1393	1.32680	0.663402	+	0.748263i	$0.269112\pi$
$360$	4.81618	0.253835
$361$	4.20777	0.221462
$362$	−14.0030	−0.735983
$363$	−2.45823	−0.129024
$364$	−19.7693	−1.03619
$365$	13.6038	0.712056
$366$	6.66993	0.348643
$367$	−6.83122	−0.356587	−0.178293	−	0.983977i	$-0.557058\pi$
$367$	−6.83122	−0.356587	−0.178293	+	0.983977i	$0.557058\pi$
$368$	−1.14891	−0.0598911
$369$	−13.6374	−0.709935
$370$	1.98131	0.103003
$371$	2.53986	0.131863
$372$	16.9250	0.877520
$373$	23.1866	1.20056	0.600279	−	0.799791i	$-0.295056\pi$
$373$	23.1866	1.20056	0.600279	+	0.799791i	$0.295056\pi$
$374$	−48.2600	−2.49547
$375$	−1.05618	−0.0545411
$376$	−30.2670	−1.56090
$377$	−12.3462	−0.635861
$378$	−20.9080	−1.07539
$379$	9.40388	0.483045	0.241522	−	0.970395i	$-0.422353\pi$
$379$	9.40388	0.483045	0.241522	+	0.970395i	$0.422353\pi$
$380$	−15.0715	−0.773154
$381$	−16.5735	−0.849085
$382$	1.00231	0.0512826
$383$	13.3771	0.683535	0.341768	−	0.939784i	$-0.388974\pi$
$383$	13.3771	0.683535	0.341768	+	0.939784i	$0.388974\pi$
$384$	−18.1566	−0.926551
$385$	−6.53330	−0.332968
$386$	33.4163	1.70085
$387$	9.71036	0.493605
$388$	33.4506	1.69819
$389$	−12.4935	−0.633446	−0.316723	−	0.948518i	$-0.602583\pi$
$389$	−12.4935	−0.633446	−0.316723	+	0.948518i	$0.602583\pi$
$390$	−8.44553	−0.427656
$391$	−14.2896	−0.722657
$392$	9.70479	0.490166
$393$	20.5295	1.03558
$394$	−33.9574	−1.71075
$395$	−14.2999	−0.719506
$396$	21.5231	1.08158
$397$	−6.89474	−0.346037	−0.173019	−	0.984919i	$-0.555352\pi$
$397$	−6.89474	−0.346037	−0.173019	+	0.984919i	$0.555352\pi$
$398$	−21.5760	−1.08151
$399$	9.10574	0.455857
$400$	−0.469334	−0.0234667
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	1.41856	0.0707515
$403$	18.0858	0.900920
$404$	−4.62299	−0.230003
$405$	0.204676	0.0101704
$406$	−14.1709	−0.703290
$407$	3.19396	0.158319
$408$	−15.7568	−0.780079
$409$	16.6950	0.825517	0.412758	−	0.910841i	$-0.364565\pi$
$409$	16.6950	0.825517	0.412758	+	0.910841i	$0.364565\pi$
$410$	−16.3884	−0.809368
$411$	18.2044	0.897959
$412$	8.27959	0.407906
$413$	16.7432	0.823880
$414$	10.4470	0.513441
$415$	14.1569	0.694935
$416$	−21.8011	−1.06889
$417$	−18.9581	−0.928380
$418$	−39.8279	−1.94805
$419$	29.1376	1.42346	0.711732	−	0.702451i	$-0.247911\pi$
$419$	29.1376	1.42346	0.711732	+	0.702451i	$0.247911\pi$
$420$	−5.91343	−0.288546
$421$	−11.7245	−0.571419	−0.285709	−	0.958316i	$-0.592229\pi$
$421$	−11.7245	−0.571419	−0.285709	+	0.958316i	$0.592229\pi$
$422$	19.8663	0.967077
$423$	−22.3176	−1.08512
$424$	−3.62714	−0.176149
$425$	−5.83737	−0.283154
$426$	−32.8986	−1.59394
$427$	4.99050	0.241507
$428$	48.1965	2.32967
$429$	−13.6146	−0.657318
$430$	11.6692	0.562739
$431$	−22.0368	−1.06147	−0.530737	−	0.847537i	$-0.678085\pi$
$431$	−22.0368	−1.06147	−0.530737	+	0.847537i	$0.678085\pi$
$432$	−2.42125	−0.116492
$433$	−23.8187	−1.14465	−0.572327	−	0.820025i	$-0.693959\pi$
$433$	−23.8187	−1.14465	−0.572327	+	0.820025i	$0.693959\pi$
$434$	20.7589	0.996457
$435$	−3.69302	−0.177067
$436$	9.78033	0.468393
$437$	−11.7929	−0.564131
$438$	32.5385	1.55475
$439$	21.2217	1.01286	0.506428	−	0.862282i	$-0.330966\pi$
$439$	21.2217	1.01286	0.506428	+	0.862282i	$0.330966\pi$
$440$	9.33009	0.444795
$441$	7.15590	0.340757
$442$	−46.6772	−2.22021
$443$	39.1695	1.86100	0.930500	−	0.366292i	$-0.119373\pi$
$443$	39.1695	1.86100	0.930500	+	0.366292i	$0.119373\pi$
$444$	2.89092	0.137197
$445$	0.882318	0.0418259
$446$	−18.4778	−0.874947
$447$	−0.774810	−0.0366473
$448$	−23.3433	−1.10287
$449$	−16.8041	−0.793037	−0.396518	−	0.918027i	$-0.629782\pi$
$449$	−16.8041	−0.793037	−0.396518	+	0.918027i	$0.629782\pi$
$450$	4.26763	0.201178
$451$	−26.4189	−1.24402
$452$	12.1187	0.570016
$453$	−5.70829	−0.268199
$454$	−47.3567	−2.22256
$455$	−6.31902	−0.296240
$456$	−13.0037	−0.608956
$457$	10.8531	0.507689	0.253844	−	0.967245i	$-0.418305\pi$
$457$	10.8531	0.507689	0.253844	+	0.967245i	$0.418305\pi$
$458$	−24.7313	−1.15562
$459$	−30.1144	−1.40562
$460$	7.65852	0.357080
$461$	−22.8469	−1.06409	−0.532043	−	0.846717i	$-0.678576\pi$
$461$	−22.8469	−1.06409	−0.532043	+	0.846717i	$0.678576\pi$
$462$	−15.6268	−0.727022
$463$	−13.1111	−0.609325	−0.304662	−	0.952460i	$-0.598544\pi$
$463$	−13.1111	−0.609325	−0.304662	+	0.952460i	$0.598544\pi$
$464$	−1.64106	−0.0761843
$465$	5.40988	0.250877
$466$	46.4472	2.15162
$467$	27.6115	1.27771	0.638853	−	0.769329i	$-0.279409\pi$
$467$	27.6115	1.27771	0.638853	+	0.769329i	$0.279409\pi$
$468$	20.8172	0.962275
$469$	1.06138	0.0490100
$470$	−26.8197	−1.23710
$471$	4.11211	0.189476
$472$	−23.9107	−1.10058
$473$	18.8113	0.864944
$474$	−34.2034	−1.57101
$475$	−4.81744	−0.221040
$476$	−32.6826	−1.49801
$477$	−2.67450	−0.122457
$478$	−49.3861	−2.25887
$479$	13.5575	0.619459	0.309729	−	0.950825i	$-0.399762\pi$
$479$	13.5575	0.619459	0.309729	+	0.950825i	$0.399762\pi$
$480$	−6.52119	−0.297650
$481$	3.08920	0.140855
$482$	−9.06373	−0.412841
$483$	−4.62703	−0.210537
$484$	7.28156	0.330980
$485$	10.6921	0.485502
$486$	35.5385	1.61206
$487$	8.33895	0.377874	0.188937	−	0.981989i	$-0.439496\pi$
$487$	8.33895	0.377874	0.188937	+	0.981989i	$0.439496\pi$
$488$	−7.12684	−0.322617
$489$	16.8527	0.762104
$490$	8.59945	0.388483
$491$	13.7558	0.620791	0.310395	−	0.950608i	$-0.399539\pi$
$491$	13.7558	0.620791	0.310395	+	0.950608i	$0.399539\pi$
$492$	−23.9123	−1.07805
$493$	−20.4108	−0.919254
$494$	−38.5216	−1.73317
$495$	6.87962	0.309216
$496$	2.40398	0.107942
$497$	−24.6150	−1.10413
$498$	33.8614	1.51736
$499$	−4.28987	−0.192041	−0.0960204	−	0.995379i	$-0.530611\pi$
$499$	−4.28987	−0.192041	−0.0960204	+	0.995379i	$0.530611\pi$
$500$	3.12854	0.139912
$501$	8.89802	0.397534
$502$	−15.7477	−0.702854
$503$	19.9275	0.888522	0.444261	−	0.895897i	$-0.353466\pi$
$503$	19.9275	0.888522	0.444261	+	0.895897i	$0.353466\pi$
$504$	8.61909	0.383925
$505$	−1.47769	−0.0657562
$506$	20.2383	0.899702
$507$	0.562360	0.0249753
$508$	49.0925	2.17813
$509$	22.2056	0.984246	0.492123	−	0.870526i	$-0.336221\pi$
$509$	22.2056	0.984246	0.492123	+	0.870526i	$0.336221\pi$
$510$	−13.9622	−0.618256
$511$	24.3455	1.07698
$512$	−5.29678	−0.234087
$513$	−24.8527	−1.09728
$514$	53.5347	2.36131
$515$	2.64647	0.116618
$516$	17.0265	0.749550
$517$	−43.2346	−1.90145
$518$	3.54577	0.155792
$519$	−5.40387	−0.237204
$520$	9.02408	0.395732
$521$	−26.6107	−1.16584	−0.582918	−	0.812531i	$-0.698089\pi$
$521$	−26.6107	−1.16584	−0.582918	+	0.812531i	$0.698089\pi$
$522$	14.9221	0.653122
$523$	−9.76063	−0.426803	−0.213401	−	0.976965i	$-0.568454\pi$
$523$	−9.76063	−0.426803	−0.213401	+	0.976965i	$0.568454\pi$
$524$	−60.8107	−2.65653
$525$	−1.89016	−0.0824933
$526$	−62.0216	−2.70427
$527$	29.8996	1.30245
$528$	−1.80965	−0.0787551
$529$	−17.0075	−0.739457
$530$	−3.21402	−0.139608
$531$	−17.6308	−0.765110
$532$	−26.9722	−1.16939
$533$	−25.5524	−1.10680
$534$	2.11038	0.0913252
$535$	15.4054	0.666036
$536$	−1.51574	−0.0654700
$537$	−22.2957	−0.962131
$538$	8.86093	0.382022
$539$	13.8627	0.597108
$540$	16.1398	0.694547
$541$	10.1602	0.436820	0.218410	−	0.975857i	$-0.429913\pi$
$541$	10.1602	0.436820	0.218410	+	0.975857i	$0.429913\pi$
$542$	−32.8937	−1.41290
$543$	−6.53077	−0.280262
$544$	−36.0416	−1.54527
$545$	3.12617	0.133910
$546$	−15.1142	−0.646829
$547$	40.4681	1.73029	0.865145	−	0.501522i	$-0.167226\pi$
$547$	40.4681	1.73029	0.865145	+	0.501522i	$0.167226\pi$
$548$	−53.9236	−2.30350
$549$	−5.25503	−0.224279
$550$	8.26743	0.352524
$551$	−16.8445	−0.717601
$552$	6.60778	0.281246
$553$	−25.5913	−1.08825
$554$	−29.0846	−1.23568
$555$	0.924049	0.0392237
$556$	56.1559	2.38154
$557$	2.27526	0.0964058	0.0482029	−	0.998838i	$-0.484651\pi$
$557$	2.27526	0.0964058	0.0482029	+	0.998838i	$0.484651\pi$
$558$	−21.8592	−0.925376
$559$	18.1943	0.769537
$560$	−0.839926	−0.0354934
$561$	−22.5077	−0.950274
$562$	6.28322	0.265042
$563$	−30.4162	−1.28189	−0.640945	−	0.767587i	$-0.721457\pi$
$563$	−30.4162	−1.28189	−0.640945	+	0.767587i	$0.721457\pi$
$564$	−39.1326	−1.64778
$565$	3.87360	0.162964
$566$	73.3309	3.08233
$567$	0.366290	0.0153827
$568$	35.1522	1.47496
$569$	9.42623	0.395168	0.197584	−	0.980286i	$-0.436690\pi$
$569$	9.42623	0.395168	0.197584	+	0.980286i	$0.436690\pi$
$570$	−11.5227	−0.482631
$571$	6.76535	0.283121	0.141561	−	0.989930i	$-0.454788\pi$
$571$	6.76535	0.283121	0.141561	+	0.989930i	$0.454788\pi$
$572$	40.3279	1.68619
$573$	0.467460	0.0195284
$574$	−29.3289	−1.22417
$575$	2.44796	0.102087
$576$	24.5807	1.02420
$577$	30.3830	1.26486	0.632430	−	0.774618i	$-0.282058\pi$
$577$	30.3830	1.26486	0.632430	+	0.774618i	$0.282058\pi$
$578$	−38.6682	−1.60838
$579$	15.5848	0.647682
$580$	10.9391	0.454223
$581$	25.3354	1.05109
$582$	25.5740	1.06008
$583$	−5.18114	−0.214581
$584$	−34.7674	−1.43869
$585$	6.65398	0.275108
$586$	28.6535	1.18366
$587$	35.8504	1.47970	0.739852	−	0.672770i	$-0.234896\pi$
$587$	35.8504	1.47970	0.739852	+	0.672770i	$0.234896\pi$
$588$	12.5474	0.517447
$589$	24.6754	1.01673
$590$	−21.1874	−0.872270
$591$	−15.8371	−0.651453
$592$	0.410618	0.0168763
$593$	−43.0888	−1.76945	−0.884723	−	0.466117i	$-0.845653\pi$
$593$	−43.0888	−1.76945	−0.884723	+	0.466117i	$0.845653\pi$
$594$	42.6509	1.74999
$595$	−10.4466	−0.428270
$596$	2.29508	0.0940100
$597$	−10.0627	−0.411838
$598$	19.5745	0.800461
$599$	3.78967	0.154842	0.0774208	−	0.996999i	$-0.475332\pi$
$599$	3.78967	0.154842	0.0774208	+	0.996999i	$0.475332\pi$
$600$	2.69930	0.110199
$601$	−1.31440	−0.0536154	−0.0268077	−	0.999641i	$-0.508534\pi$
$601$	−1.31440	−0.0536154	−0.0268077	+	0.999641i	$0.508534\pi$
$602$	20.8833	0.851142
$603$	−1.11764	−0.0455139
$604$	16.9086	0.688001
$605$	2.32747	0.0946250
$606$	−3.53442	−0.143576
$607$	−48.7895	−1.98030	−0.990151	−	0.140001i	$-0.955289\pi$
$607$	−48.7895	−1.98030	−0.990151	+	0.140001i	$0.955289\pi$
$608$	−29.7443	−1.20629
$609$	−6.60907	−0.267813
$610$	−6.31512	−0.255692
$611$	−41.8165	−1.69172
$612$	34.4151	1.39115
$613$	−35.6668	−1.44057	−0.720285	−	0.693679i	$-0.755989\pi$
$613$	−35.6668	−1.44057	−0.720285	+	0.693679i	$0.755989\pi$
$614$	−0.864789	−0.0349001
$615$	−7.64329	−0.308207
$616$	16.6972	0.672751
$617$	38.1998	1.53787	0.768934	−	0.639329i	$-0.220788\pi$
$617$	38.1998	1.53787	0.768934	+	0.639329i	$0.220788\pi$
$618$	6.33000	0.254630
$619$	−41.3271	−1.66108	−0.830539	−	0.556961i	$-0.811967\pi$
$619$	−41.3271	−1.66108	−0.830539	+	0.556961i	$0.811967\pi$
$620$	−16.0247	−0.643566
$621$	12.6288	0.506775
$622$	−5.36689	−0.215193
$623$	1.57901	0.0632615
$624$	−1.75030	−0.0700681
$625$	1.00000	0.0400000
$626$	42.2237	1.68760
$627$	−18.5751	−0.741816
$628$	−12.1805	−0.486056
$629$	5.10708	0.203633
$630$	7.63741	0.304282
$631$	41.8874	1.66751	0.833755	−	0.552134i	$-0.186186\pi$
$631$	41.8874	1.66751	0.833755	+	0.552134i	$0.186186\pi$
$632$	36.5464	1.45374
$633$	9.26531	0.368263
$634$	−65.3256	−2.59441
$635$	15.6918	0.622712
$636$	−4.68956	−0.185953
$637$	13.4080	0.531245
$638$	28.9076	1.14446
$639$	25.9198	1.02537
$640$	17.1908	0.679525
$641$	11.5416	0.455866	0.227933	−	0.973677i	$-0.426803\pi$
$641$	11.5416	0.455866	0.227933	+	0.973677i	$0.426803\pi$
$642$	36.8477	1.45426
$643$	36.8689	1.45397	0.726983	−	0.686656i	$-0.240922\pi$
$643$	36.8689	1.45397	0.726983	+	0.686656i	$0.240922\pi$
$644$	13.7058	0.540083
$645$	5.44232	0.214291
$646$	−63.6840	−2.50561
$647$	−45.7568	−1.79888	−0.899442	−	0.437040i	$-0.856027\pi$
$647$	−45.7568	−1.79888	−0.899442	+	0.437040i	$0.856027\pi$
$648$	−0.523092	−0.0205490
$649$	−34.1550	−1.34070
$650$	7.99627	0.313639
$651$	9.68158	0.379451
$652$	−49.9195	−1.95500
$653$	35.6996	1.39703	0.698517	−	0.715594i	$-0.253844\pi$
$653$	35.6996	1.39703	0.698517	+	0.715594i	$0.253844\pi$
$654$	7.47736	0.292388
$655$	−19.4374	−0.759483
$656$	−3.39644	−0.132609
$657$	−25.6361	−1.00016
$658$	−47.9969	−1.87111
$659$	−27.9487	−1.08873	−0.544363	−	0.838850i	$-0.683229\pi$
$659$	−27.9487	−1.08873	−0.544363	+	0.838850i	$0.683229\pi$
$660$	12.0630	0.469551
$661$	−0.985155	−0.0383181	−0.0191590	−	0.999816i	$-0.506099\pi$
$661$	−0.985155	−0.0383181	−0.0191590	+	0.999816i	$0.506099\pi$
$662$	69.8457	2.71463
$663$	−21.7694	−0.845455
$664$	−36.1810	−1.40409
$665$	−8.62135	−0.334322
$666$	−3.73373	−0.144679
$667$	8.55945	0.331423
$668$	−26.3570	−1.01978
$669$	−8.61771	−0.333180
$670$	−1.34310	−0.0518886
$671$	−10.1803	−0.393004
$672$	−11.6704	−0.450195
$673$	−16.0856	−0.620056	−0.310028	−	0.950727i	$-0.600338\pi$
$673$	−16.0856	−0.620056	−0.310028	+	0.950727i	$0.600338\pi$
$674$	5.65824	0.217947
$675$	5.15890	0.198566
$676$	−1.66577	−0.0640682
$677$	−35.6189	−1.36895	−0.684473	−	0.729038i	$-0.739968\pi$
$677$	−35.6189	−1.36895	−0.684473	+	0.729038i	$0.739968\pi$
$678$	9.26513	0.355825
$679$	19.1347	0.734321
$680$	14.9186	0.572104
$681$	−22.0864	−0.846351
$682$	−42.3466	−1.62153
$683$	−5.14564	−0.196893	−0.0984463	−	0.995142i	$-0.531387\pi$
$683$	−5.14564	−0.196893	−0.0984463	+	0.995142i	$0.531387\pi$
$684$	28.4020	1.08598
$685$	−17.2360	−0.658555
$686$	43.7593	1.67074
$687$	−11.5343	−0.440060
$688$	2.41839	0.0922004
$689$	−5.01121	−0.190912
$690$	5.85517	0.222903
$691$	23.4606	0.892482	0.446241	−	0.894913i	$-0.352762\pi$
$691$	23.4606	0.892482	0.446241	+	0.894913i	$0.352762\pi$
$692$	16.0069	0.608491
$693$	12.3118	0.467688
$694$	−4.53619	−0.172192
$695$	17.9496	0.680867
$696$	9.43830	0.357758
$697$	−42.2433	−1.60008
$698$	−66.2226	−2.50656
$699$	21.6622	0.819339
$700$	5.59886	0.211617
$701$	−6.05538	−0.228709	−0.114354	−	0.993440i	$-0.536480\pi$
$701$	−6.05538	−0.228709	−0.114354	+	0.993440i	$0.536480\pi$
$702$	41.2520	1.55696
$703$	4.21475	0.158962
$704$	47.6188	1.79470
$705$	−12.5083	−0.471088
$706$	71.7604	2.70074
$707$	−2.64448	−0.0994561
$708$	−30.9144	−1.16183
$709$	−27.5592	−1.03501	−0.517504	−	0.855681i	$-0.673139\pi$
$709$	−27.5592	−1.03501	−0.517504	+	0.855681i	$0.673139\pi$
$710$	31.1485	1.16898
$711$	26.9478	1.01062
$712$	−2.25495	−0.0845079
$713$	−12.5387	−0.469577
$714$	−24.9869	−0.935110
$715$	12.8903	0.482071
$716$	66.0424	2.46812
$717$	−23.0328	−0.860177
$718$	−56.9313	−2.12466
$719$	−22.7681	−0.849108	−0.424554	−	0.905403i	$-0.639569\pi$
$719$	−22.7681	−0.849108	−0.424554	+	0.905403i	$0.639569\pi$
$720$	0.884449	0.0329615
$721$	4.73616	0.176384
$722$	−9.52903	−0.354634
$723$	−4.22717	−0.157210
$724$	19.3449	0.718947
$725$	3.49657	0.129859
$726$	5.56698	0.206610
$727$	29.0943	1.07905	0.539524	−	0.841970i	$-0.318604\pi$
$727$	29.0943	1.07905	0.539524	+	0.841970i	$0.318604\pi$
$728$	16.1496	0.598544
$729$	15.9605	0.591131
$730$	−30.8076	−1.14024
$731$	30.0789	1.11251
$732$	−9.21437	−0.340573
$733$	37.4954	1.38492	0.692461	−	0.721455i	$-0.256526\pi$
$733$	37.4954	1.38492	0.692461	+	0.721455i	$0.256526\pi$
$734$	15.4702	0.571014
$735$	4.01064	0.147935
$736$	15.1144	0.557124
$737$	−2.16514	−0.0797540
$738$	30.8836	1.13684
$739$	38.6118	1.42036	0.710179	−	0.704022i	$-0.248614\pi$
$739$	38.6118	1.42036	0.710179	+	0.704022i	$0.248614\pi$
$740$	−2.73714	−0.100619
$741$	−17.9658	−0.659991
$742$	−5.75184	−0.211157
$743$	35.8391	1.31481	0.657404	−	0.753538i	$-0.271654\pi$
$743$	35.8391	1.31481	0.657404	+	0.753538i	$0.271654\pi$
$744$	−13.8261	−0.506889
$745$	0.733594	0.0268768
$746$	−52.5091	−1.92249
$747$	−26.6783	−0.976110
$748$	66.6702	2.43771
$749$	27.5698	1.00738
$750$	2.39186	0.0873385
$751$	32.6254	1.19052	0.595258	−	0.803535i	$-0.297050\pi$
$751$	32.6254	1.19052	0.595258	+	0.803535i	$0.297050\pi$
$752$	−5.55827	−0.202689
$753$	−7.34446	−0.267647
$754$	27.9595	1.01823
$755$	5.40464	0.196695
$756$	28.8840	1.05050
$757$	21.7714	0.791295	0.395648	−	0.918402i	$-0.370520\pi$
$757$	21.7714	0.791295	0.395648	+	0.918402i	$0.370520\pi$
$758$	−21.2963	−0.773515
$759$	9.43880	0.342607
$760$	12.3120	0.446603
$761$	5.67152	0.205593	0.102796	−	0.994702i	$-0.467221\pi$
$761$	5.67152	0.205593	0.102796	+	0.994702i	$0.467221\pi$
$762$	37.5327	1.35967
$763$	5.59463	0.202539
$764$	−1.38467	−0.0500955
$765$	11.0004	0.397719
$766$	−30.2940	−1.09457
$767$	−33.0347	−1.19282
$768$	13.5646	0.489472
$769$	−24.0262	−0.866407	−0.433203	−	0.901296i	$-0.642617\pi$
$769$	−24.0262	−0.866407	−0.433203	+	0.901296i	$0.642617\pi$
$770$	14.7955	0.533192
$771$	24.9677	0.899189
$772$	−46.1639	−1.66148
$773$	3.50777	0.126166	0.0630829	−	0.998008i	$-0.479907\pi$
$773$	3.50777	0.126166	0.0630829	+	0.998008i	$0.479907\pi$
$774$	−21.9903	−0.790426
$775$	−5.12210	−0.183991
$776$	−27.3259	−0.980942
$777$	1.65369	0.0593258
$778$	28.2932	1.01436
$779$	−34.8624	−1.24908
$780$	11.6673	0.417757
$781$	50.2128	1.79676
$782$	32.3607	1.15721
$783$	18.0385	0.644642
$784$	1.78220	0.0636500
$785$	−3.89336	−0.138960
$786$	−46.4917	−1.65830
$787$	36.7549	1.31017	0.655086	−	0.755554i	$-0.272632\pi$
$787$	36.7549	1.31017	0.655086	+	0.755554i	$0.272632\pi$
$788$	46.9114	1.67115
$789$	−28.9258	−1.02979
$790$	32.3839	1.15217
$791$	6.93224	0.246482
$792$	−17.5823	−0.624761
$793$	−9.84636	−0.349654
$794$	15.6140	0.554121
$795$	−1.49896	−0.0531628
$796$	29.8068	1.05647
$797$	−33.3523	−1.18140	−0.590700	−	0.806891i	$-0.701148\pi$
$797$	−33.3523	−1.18140	−0.590700	+	0.806891i	$0.701148\pi$
$798$	−20.6211	−0.729979
$799$	−69.1313	−2.44569
$800$	6.17429	0.218294
$801$	−1.66271	−0.0587488
$802$	2.26463	0.0799668
$803$	−49.6632	−1.75258
$804$	−1.95972	−0.0691138
$805$	4.38089	0.154406
$806$	−40.9577	−1.44267
$807$	4.13259	0.145474
$808$	3.77654	0.132858
$809$	37.0169	1.30144	0.650722	−	0.759316i	$-0.274466\pi$
$809$	37.0169	1.30144	0.650722	+	0.759316i	$0.274466\pi$
$810$	−0.463514	−0.0162862
$811$	−6.95096	−0.244081	−0.122041	−	0.992525i	$-0.538944\pi$
$811$	−6.95096	−0.244081	−0.122041	+	0.992525i	$0.538944\pi$
$812$	19.5768	0.687012
$813$	−15.3411	−0.538034
$814$	−7.23313	−0.253521
$815$	−15.9562	−0.558921
$816$	−2.89360	−0.101296
$817$	24.8234	0.868461
$818$	−37.8080	−1.32193
$819$	11.9080	0.416100
$820$	22.6403	0.790634
$821$	16.7017	0.582894	0.291447	−	0.956587i	$-0.405863\pi$
$821$	16.7017	0.582894	0.291447	+	0.956587i	$0.405863\pi$
$822$	−41.2263	−1.43793
$823$	7.61888	0.265577	0.132789	−	0.991144i	$-0.457607\pi$
$823$	7.61888	0.265577	0.132789	+	0.991144i	$0.457607\pi$
$824$	−6.76363	−0.235622
$825$	3.85579	0.134241
$826$	−37.9172	−1.31931
$827$	1.41081	0.0490588	0.0245294	−	0.999699i	$-0.492191\pi$
$827$	1.41081	0.0490588	0.0245294	+	0.999699i	$0.492191\pi$
$828$	−14.4323	−0.501557
$829$	−9.76399	−0.339118	−0.169559	−	0.985520i	$-0.554234\pi$
$829$	−9.76399	−0.339118	−0.169559	+	0.985520i	$0.554234\pi$
$830$	−32.0601	−1.11282
$831$	−13.5645	−0.470549
$832$	46.0569	1.59674
$833$	22.1662	0.768013
$834$	42.9329	1.48665
$835$	−8.42469	−0.291548
$836$	55.0214	1.90296
$837$	−26.4244	−0.913361
$838$	−65.9858	−2.27944
$839$	−25.9765	−0.896808	−0.448404	−	0.893831i	$-0.648007\pi$
$839$	−25.9765	−0.896808	−0.448404	+	0.893831i	$0.648007\pi$
$840$	4.83070	0.166675
$841$	−16.7740	−0.578414
$842$	26.5517	0.915032
$843$	2.93039	0.100928
$844$	−27.4449	−0.944693
$845$	−0.532445	−0.0183167
$846$	50.5411	1.73764
$847$	4.16526	0.143120
$848$	−0.666092	−0.0228737
$849$	34.2003	1.17375
$850$	13.2195	0.453424
$851$	−2.14170	−0.0734166
$852$	45.4487	1.55705
$853$	24.9713	0.855002	0.427501	−	0.904015i	$-0.359394\pi$
$853$	24.9713	0.855002	0.427501	+	0.904015i	$0.359394\pi$
$854$	−11.3016	−0.386733
$855$	9.07836	0.310473
$856$	−39.3719	−1.34570
$857$	18.9962	0.648898	0.324449	−	0.945903i	$-0.394821\pi$
$857$	18.9962	0.648898	0.324449	+	0.945903i	$0.394821\pi$
$858$	30.8319	1.05258
$859$	−26.1042	−0.890663	−0.445331	−	0.895366i	$-0.646914\pi$
$859$	−26.1042	−0.890663	−0.445331	+	0.895366i	$0.646914\pi$
$860$	−16.1208	−0.549714
$861$	−13.6785	−0.466163
$862$	49.9051	1.69977
$863$	28.7271	0.977883	0.488942	−	0.872317i	$-0.337383\pi$
$863$	28.7271	0.977883	0.488942	+	0.872317i	$0.337383\pi$
$864$	31.8526	1.08365
$865$	5.11641	0.173963
$866$	53.9405	1.83297
$867$	−18.0342	−0.612473
$868$	−28.6779	−0.973392
$869$	52.2043	1.77091
$870$	8.36331	0.283543
$871$	−2.09413	−0.0709568
$872$	−7.98959	−0.270562
$873$	−20.1490	−0.681939
$874$	26.7065	0.903361
$875$	1.78961	0.0604999
$876$	−44.9512	−1.51876
$877$	−11.4610	−0.387011	−0.193506	−	0.981099i	$-0.561986\pi$
$877$	−11.4610	−0.387011	−0.193506	+	0.981099i	$0.561986\pi$
$878$	−48.0592	−1.62192
$879$	13.3635	0.450739
$880$	1.71339	0.0577583
$881$	50.1210	1.68862	0.844310	−	0.535855i	$-0.180011\pi$
$881$	50.1210	1.68862	0.844310	+	0.535855i	$0.180011\pi$
$882$	−16.2054	−0.545666
$883$	30.1912	1.01601	0.508007	−	0.861353i	$-0.330382\pi$
$883$	30.1912	1.01601	0.508007	+	0.861353i	$0.330382\pi$
$884$	64.4835	2.16882
$885$	−9.88143	−0.332161
$886$	−88.7043	−2.98008
$887$	16.4216	0.551384	0.275692	−	0.961246i	$-0.411093\pi$
$887$	16.4216	0.551384	0.275692	+	0.961246i	$0.411093\pi$
$888$	−2.36160	−0.0792503
$889$	28.0823	0.941850
$890$	−1.99812	−0.0669771
$891$	−0.747206	−0.0250323
$892$	25.5266	0.854695
$893$	−57.0524	−1.90919
$894$	1.75466	0.0586845
$895$	21.1097	0.705619
$896$	30.7648	1.02778
$897$	9.12922	0.304816
$898$	38.0551	1.26992
$899$	−17.9098	−0.597324
$900$	−5.89565	−0.196522
$901$	−8.28455	−0.275998
$902$	59.8290	1.99209
$903$	9.73964	0.324115
$904$	−9.89982	−0.329263
$905$	6.18337	0.205542
$906$	12.9271	0.429476
$907$	19.0735	0.633325	0.316663	−	0.948538i	$-0.397438\pi$
$907$	19.0735	0.633325	0.316663	+	0.948538i	$0.397438\pi$
$908$	65.4223	2.17111
$909$	2.78466	0.0923615
$910$	14.3102	0.474379
$911$	−26.8805	−0.890591	−0.445296	−	0.895384i	$-0.646901\pi$
$911$	−26.8805	−0.890591	−0.445296	+	0.895384i	$0.646901\pi$
$912$	−2.38802	−0.0790753
$913$	−51.6823	−1.71044
$914$	−24.5783	−0.812979
$915$	−2.94527	−0.0973675
$916$	34.1658	1.12887
$917$	−34.7855	−1.14872
$918$	68.1979	2.25087
$919$	29.0078	0.956880	0.478440	−	0.878120i	$-0.341202\pi$
$919$	29.0078	0.956880	0.478440	+	0.878120i	$0.341202\pi$
$920$	−6.25627	−0.206263
$921$	−0.403323	−0.0132900
$922$	51.7397	1.70396
$923$	48.5659	1.59857
$924$	21.5880	0.710194
$925$	−0.874894	−0.0287663
$926$	29.6918	0.975732
$927$	−4.98722	−0.163802
$928$	21.5888	0.708689
$929$	33.6923	1.10541	0.552704	−	0.833378i	$-0.313596\pi$
$929$	33.6923	1.10541	0.552704	+	0.833378i	$0.313596\pi$
$930$	−12.2514	−0.401738
$931$	18.2932	0.599537
$932$	−64.1658	−2.10182
$933$	−2.50303	−0.0819454
$934$	−62.5296	−2.04603
$935$	21.3104	0.696923
$936$	−17.0057	−0.555847
$937$	55.6416	1.81773	0.908866	−	0.417088i	$-0.136949\pi$
$937$	55.6416	1.81773	0.908866	+	0.417088i	$0.136949\pi$
$938$	−2.40363	−0.0784813
$939$	19.6924	0.642638
$940$	37.0509	1.20847
$941$	17.8816	0.582923	0.291462	−	0.956582i	$-0.405858\pi$
$941$	17.8816	0.582923	0.291462	+	0.956582i	$0.405858\pi$
$942$	−9.31239	−0.303414
$943$	17.7151	0.576884
$944$	−4.39099	−0.142915
$945$	9.23243	0.300331
$946$	−42.6005	−1.38506
$947$	−5.74132	−0.186568	−0.0932839	−	0.995640i	$-0.529736\pi$
$947$	−5.74132	−0.186568	−0.0932839	+	0.995640i	$0.529736\pi$
$948$	47.2513	1.53465
$949$	−48.0343	−1.55926
$950$	10.9097	0.353958
$951$	−30.4668	−0.987952
$952$	26.6986	0.865306
$953$	−8.07530	−0.261585	−0.130792	−	0.991410i	$-0.541752\pi$
$953$	−8.07530	−0.261585	−0.130792	+	0.991410i	$0.541752\pi$
$954$	6.05674	0.196094
$955$	−0.442593	−0.0143220
$956$	68.2259	2.20658
$957$	13.4820	0.435812
$958$	−30.7027	−0.991960
$959$	−30.8458	−0.996064
$960$	13.7767	0.444640
$961$	−4.76411	−0.153681
$962$	−6.99589	−0.225557
$963$	−29.0312	−0.935517
$964$	12.5214	0.403286
$965$	−14.7558	−0.475005
$966$	10.4785	0.337140
$967$	18.6044	0.598279	0.299139	−	0.954209i	$-0.403300\pi$
$967$	18.6044	0.598279	0.299139	+	0.954209i	$0.403300\pi$
$968$	−5.94834	−0.191187
$969$	−29.7011	−0.954138
$970$	−24.2136	−0.777451
$971$	−29.7205	−0.953775	−0.476888	−	0.878964i	$-0.658235\pi$
$971$	−29.7205	−0.953775	−0.476888	+	0.878964i	$0.658235\pi$
$972$	−49.0958	−1.57475
$973$	32.1228	1.02981
$974$	−18.8846	−0.605102
$975$	3.72932	0.119434
$976$	−1.30878	−0.0418931
$977$	−17.0126	−0.544282	−0.272141	−	0.962257i	$-0.587732\pi$
$977$	−17.0126	−0.544282	−0.272141	+	0.962257i	$0.587732\pi$
$978$	−38.1650	−1.22038
$979$	−3.22106	−0.102945
$980$	−11.8800	−0.379491
$981$	−5.89119	−0.188091
$982$	−31.1518	−0.994093
$983$	−5.53874	−0.176659	−0.0883293	−	0.996091i	$-0.528153\pi$
$983$	−5.53874	−0.176659	−0.0883293	+	0.996091i	$0.528153\pi$
$984$	19.5341	0.622723
$985$	14.9947	0.477770
$986$	46.2228	1.47203
$987$	−22.3849	−0.712520
$988$	53.2168	1.69305
$989$	−12.6139	−0.401098
$990$	−15.5798	−0.495158
$991$	−13.5488	−0.430390	−0.215195	−	0.976571i	$-0.569039\pi$
$991$	−13.5488	−0.430390	−0.215195	+	0.976571i	$0.569039\pi$
$992$	−31.6253	−1.00411
$993$	32.5748	1.03373
$994$	55.7438	1.76808
$995$	9.52739	0.302039
$996$	−46.7788	−1.48224
$997$	0.592665	0.0187699	0.00938495	−	0.999956i	$-0.497013\pi$
$997$	0.592665	0.0187699	0.00938495	+	0.999956i	$0.497013\pi$
$998$	9.71495	0.307521
$999$	−4.51350	−0.142801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.4	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.26463 q^{2} -1.05618 q^{3} +3.12854 q^{4} +1.00000 q^{5} +2.39186 q^{6} +1.78961 q^{7} -2.55571 q^{8} -1.88448 q^{9} +O(q^{10})\)	\(q-2.26463 q^{2} -1.05618 q^{3} +3.12854 q^{4} +1.00000 q^{5} +2.39186 q^{6} +1.78961 q^{7} -2.55571 q^{8} -1.88448 q^{9} -2.26463 q^{10} -3.65068 q^{11} -3.30431 q^{12} -3.53094 q^{13} -4.05280 q^{14} -1.05618 q^{15} -0.469334 q^{16} -5.83737 q^{17} +4.26763 q^{18} -4.81744 q^{19} +3.12854 q^{20} -1.89016 q^{21} +8.26743 q^{22} +2.44796 q^{23} +2.69930 q^{24} +1.00000 q^{25} +7.99627 q^{26} +5.15890 q^{27} +5.59886 q^{28} +3.49657 q^{29} +2.39186 q^{30} -5.12210 q^{31} +6.17429 q^{32} +3.85579 q^{33} +13.2195 q^{34} +1.78961 q^{35} -5.89565 q^{36} -0.874894 q^{37} +10.9097 q^{38} +3.72932 q^{39} -2.55571 q^{40} +7.23671 q^{41} +4.28051 q^{42} -5.15282 q^{43} -11.4213 q^{44} -1.88448 q^{45} -5.54371 q^{46} +11.8429 q^{47} +0.495703 q^{48} -3.79729 q^{49} -2.26463 q^{50} +6.16533 q^{51} -11.0467 q^{52} +1.41923 q^{53} -11.6830 q^{54} -3.65068 q^{55} -4.57373 q^{56} +5.08811 q^{57} -7.91843 q^{58} +9.35579 q^{59} -3.30431 q^{60} +2.78859 q^{61} +11.5996 q^{62} -3.37248 q^{63} -13.0438 q^{64} -3.53094 q^{65} -8.73193 q^{66} +0.593079 q^{67} -18.2624 q^{68} -2.58549 q^{69} -4.05280 q^{70} -13.7544 q^{71} +4.81618 q^{72} +13.6038 q^{73} +1.98131 q^{74} -1.05618 q^{75} -15.0715 q^{76} -6.53330 q^{77} -8.44553 q^{78} -14.2999 q^{79} -0.469334 q^{80} +0.204676 q^{81} -16.3884 q^{82} +14.1569 q^{83} -5.91343 q^{84} -5.83737 q^{85} +11.6692 q^{86} -3.69302 q^{87} +9.33009 q^{88} +0.882318 q^{89} +4.26763 q^{90} -6.31902 q^{91} +7.65852 q^{92} +5.40988 q^{93} -26.8197 q^{94} -4.81744 q^{95} -6.52119 q^{96} +10.6921 q^{97} +8.59945 q^{98} +6.87962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 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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