LMFDB - Embedded newform 2005.2.a.g.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.20338 q^{2} -1.29534 q^{3} -0.551875 q^{4} +1.00000 q^{5} +1.55878 q^{6} -0.246916 q^{7} +3.07088 q^{8} -1.32210 q^{9} +O(q^{10})$	\(q-1.20338 q^{2} -1.29534 q^{3} -0.551875 q^{4} +1.00000 q^{5} +1.55878 q^{6} -0.246916 q^{7} +3.07088 q^{8} -1.32210 q^{9} -1.20338 q^{10} -1.77301 q^{11} +0.714864 q^{12} -3.33697 q^{13} +0.297134 q^{14} -1.29534 q^{15} -2.59168 q^{16} +1.21423 q^{17} +1.59099 q^{18} +1.20522 q^{19} -0.551875 q^{20} +0.319839 q^{21} +2.13360 q^{22} -3.82717 q^{23} -3.97782 q^{24} +1.00000 q^{25} +4.01564 q^{26} +5.59858 q^{27} +0.136267 q^{28} -0.468831 q^{29} +1.55878 q^{30} +2.07126 q^{31} -3.02297 q^{32} +2.29664 q^{33} -1.46118 q^{34} -0.246916 q^{35} +0.729637 q^{36} +3.22202 q^{37} -1.45033 q^{38} +4.32250 q^{39} +3.07088 q^{40} +2.59051 q^{41} -0.384888 q^{42} -5.47683 q^{43} +0.978478 q^{44} -1.32210 q^{45} +4.60554 q^{46} -7.24468 q^{47} +3.35710 q^{48} -6.93903 q^{49} -1.20338 q^{50} -1.57284 q^{51} +1.84159 q^{52} +0.424116 q^{53} -6.73722 q^{54} -1.77301 q^{55} -0.758248 q^{56} -1.56116 q^{57} +0.564183 q^{58} +1.57346 q^{59} +0.714864 q^{60} -13.6834 q^{61} -2.49251 q^{62} +0.326449 q^{63} +8.82115 q^{64} -3.33697 q^{65} -2.76373 q^{66} +12.1271 q^{67} -0.670104 q^{68} +4.95747 q^{69} +0.297134 q^{70} -5.49687 q^{71} -4.06002 q^{72} +2.36202 q^{73} -3.87732 q^{74} -1.29534 q^{75} -0.665128 q^{76} +0.437783 q^{77} -5.20161 q^{78} +13.3684 q^{79} -2.59168 q^{80} -3.28573 q^{81} -3.11736 q^{82} +2.50356 q^{83} -0.176511 q^{84} +1.21423 q^{85} +6.59071 q^{86} +0.607294 q^{87} -5.44468 q^{88} -12.7853 q^{89} +1.59099 q^{90} +0.823951 q^{91} +2.11212 q^{92} -2.68297 q^{93} +8.71811 q^{94} +1.20522 q^{95} +3.91576 q^{96} +18.8644 q^{97} +8.35030 q^{98} +2.34410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.20338	−0.850919	−0.425459	−	0.904978i	$-0.639887\pi$
$2$	−1.20338	−0.850919	−0.425459	+	0.904978i	$0.639887\pi$
$3$	−1.29534	−0.747863	−0.373931	−	0.927456i	$-0.621990\pi$
$3$	−1.29534	−0.747863	−0.373931	+	0.927456i	$0.621990\pi$
$4$	−0.551875	−0.275938
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.55878	0.636370
$7$	−0.246916	−0.0933254	−0.0466627	−	0.998911i	$-0.514859\pi$
$7$	−0.246916	−0.0933254	−0.0466627	+	0.998911i	$0.514859\pi$
$8$	3.07088	1.08572
$9$	−1.32210	−0.440702
$10$	−1.20338	−0.380542
$11$	−1.77301	−0.534582	−0.267291	−	0.963616i	$-0.586128\pi$
$11$	−1.77301	−0.534582	−0.267291	+	0.963616i	$0.586128\pi$
$12$	0.714864	0.206363
$13$	−3.33697	−0.925509	−0.462754	−	0.886487i	$-0.653139\pi$
$13$	−3.33697	−0.925509	−0.462754	+	0.886487i	$0.653139\pi$
$14$	0.297134	0.0794123
$15$	−1.29534	−0.334454
$16$	−2.59168	−0.647921
$17$	1.21423	0.294495	0.147247	−	0.989100i	$-0.452959\pi$
$17$	1.21423	0.294495	0.147247	+	0.989100i	$0.452959\pi$
$18$	1.59099	0.375001
$19$	1.20522	0.276495	0.138248	−	0.990398i	$-0.455853\pi$
$19$	1.20522	0.276495	0.138248	+	0.990398i	$0.455853\pi$
$20$	−0.551875	−0.123403
$21$	0.319839	0.0697946
$22$	2.13360	0.454885
$23$	−3.82717	−0.798020	−0.399010	−	0.916946i	$-0.630646\pi$
$23$	−3.82717	−0.798020	−0.399010	+	0.916946i	$0.630646\pi$
$24$	−3.97782	−0.811969
$25$	1.00000	0.200000
$26$	4.01564	0.787533
$27$	5.59858	1.07745
$28$	0.136267	0.0257520
$29$	−0.468831	−0.0870598	−0.0435299	−	0.999052i	$-0.513860\pi$
$29$	−0.468831	−0.0870598	−0.0435299	+	0.999052i	$0.513860\pi$
$30$	1.55878	0.284593
$31$	2.07126	0.372009	0.186004	−	0.982549i	$-0.440446\pi$
$31$	2.07126	0.372009	0.186004	+	0.982549i	$0.440446\pi$
$32$	−3.02297	−0.534391
$33$	2.29664	0.399794
$34$	−1.46118	−0.250591
$35$	−0.246916	−0.0417364
$36$	0.729637	0.121606
$37$	3.22202	0.529697	0.264849	−	0.964290i	$-0.414678\pi$
$37$	3.22202	0.529697	0.264849	+	0.964290i	$0.414678\pi$
$38$	−1.45033	−0.235275
$39$	4.32250	0.692153
$40$	3.07088	0.485548
$41$	2.59051	0.404569	0.202285	−	0.979327i	$-0.435163\pi$
$41$	2.59051	0.404569	0.202285	+	0.979327i	$0.435163\pi$
$42$	−0.384888	−0.0593895
$43$	−5.47683	−0.835209	−0.417604	−	0.908629i	$-0.637130\pi$
$43$	−5.47683	−0.835209	−0.417604	+	0.908629i	$0.637130\pi$
$44$	0.978478	0.147511
$45$	−1.32210	−0.197088
$46$	4.60554	0.679050
$47$	−7.24468	−1.05675	−0.528373	−	0.849013i	$-0.677198\pi$
$47$	−7.24468	−1.05675	−0.528373	+	0.849013i	$0.677198\pi$
$48$	3.35710	0.484556
$49$	−6.93903	−0.991290
$50$	−1.20338	−0.170184
$51$	−1.57284	−0.220241
$52$	1.84159	0.255383
$53$	0.424116	0.0582568	0.0291284	−	0.999576i	$-0.490727\pi$
$53$	0.424116	0.0582568	0.0291284	+	0.999576i	$0.490727\pi$
$54$	−6.73722	−0.916820
$55$	−1.77301	−0.239072
$56$	−0.758248	−0.101325
$57$	−1.56116	−0.206781
$58$	0.564183	0.0740808
$59$	1.57346	0.204847	0.102424	−	0.994741i	$-0.467340\pi$
$59$	1.57346	0.204847	0.102424	+	0.994741i	$0.467340\pi$
$60$	0.714864	0.0922885
$61$	−13.6834	−1.75198	−0.875992	−	0.482325i	$-0.839792\pi$
$61$	−13.6834	−1.75198	−0.875992	+	0.482325i	$0.839792\pi$
$62$	−2.49251	−0.316549
$63$	0.326449	0.0411286
$64$	8.82115	1.10264
$65$	−3.33697	−0.413900
$66$	−2.76373	−0.340192
$67$	12.1271	1.48157	0.740783	−	0.671745i	$-0.234455\pi$
$67$	12.1271	1.48157	0.740783	+	0.671745i	$0.234455\pi$
$68$	−0.670104	−0.0812621
$69$	4.95747	0.596810
$70$	0.297134	0.0355143
$71$	−5.49687	−0.652358	−0.326179	−	0.945308i	$-0.605761\pi$
$71$	−5.49687	−0.652358	−0.326179	+	0.945308i	$0.605761\pi$
$72$	−4.06002	−0.478478
$73$	2.36202	0.276454	0.138227	−	0.990401i	$-0.455860\pi$
$73$	2.36202	0.276454	0.138227	+	0.990401i	$0.455860\pi$
$74$	−3.87732	−0.450729
$75$	−1.29534	−0.149573
$76$	−0.665128	−0.0762955
$77$	0.437783	0.0498900
$78$	−5.20161	−0.588966
$79$	13.3684	1.50406	0.752029	−	0.659130i	$-0.229075\pi$
$79$	13.3684	1.50406	0.752029	+	0.659130i	$0.229075\pi$
$80$	−2.59168	−0.289759
$81$	−3.28573	−0.365081
$82$	−3.11736	−0.344255
$83$	2.50356	0.274802	0.137401	−	0.990516i	$-0.456125\pi$
$83$	2.50356	0.274802	0.137401	+	0.990516i	$0.456125\pi$
$84$	−0.176511	−0.0192589
$85$	1.21423	0.131702
$86$	6.59071	0.710695
$87$	0.607294	0.0651088
$88$	−5.44468	−0.580405
$89$	−12.7853	−1.35524	−0.677618	−	0.735414i	$-0.736988\pi$
$89$	−12.7853	−1.35524	−0.677618	+	0.735414i	$0.736988\pi$
$90$	1.59099	0.167706
$91$	0.823951	0.0863735
$92$	2.11212	0.220204
$93$	−2.68297	−0.278211
$94$	8.71811	0.899204
$95$	1.20522	0.123653
$96$	3.91576	0.399651
$97$	18.8644	1.91539	0.957695	−	0.287784i	$-0.0929186\pi$
$97$	18.8644	1.91539	0.957695	+	0.287784i	$0.0929186\pi$
$98$	8.35030	0.843507
$99$	2.34410	0.235591
$100$	−0.551875	−0.0551875
$101$	−13.1150	−1.30499	−0.652497	−	0.757792i	$-0.726278\pi$
$101$	−13.1150	−1.30499	−0.652497	+	0.757792i	$0.726278\pi$
$102$	1.89272	0.187408
$103$	2.29323	0.225959	0.112979	−	0.993597i	$-0.463961\pi$
$103$	2.29323	0.225959	0.112979	+	0.993597i	$0.463961\pi$
$104$	−10.2474	−1.00484
$105$	0.319839	0.0312131
$106$	−0.510373	−0.0495718
$107$	16.2367	1.56966	0.784829	−	0.619712i	$-0.212751\pi$
$107$	16.2367	1.56966	0.784829	+	0.619712i	$0.212751\pi$
$108$	−3.08972	−0.297308
$109$	−9.19314	−0.880544	−0.440272	−	0.897865i	$-0.645118\pi$
$109$	−9.19314	−0.880544	−0.440272	+	0.897865i	$0.645118\pi$
$110$	2.13360	0.203431
$111$	−4.17360	−0.396141
$112$	0.639928	0.0604675
$113$	17.4716	1.64359	0.821796	−	0.569782i	$-0.192972\pi$
$113$	17.4716	1.64359	0.821796	+	0.569782i	$0.192972\pi$
$114$	1.87867	0.175953
$115$	−3.82717	−0.356886
$116$	0.258736	0.0240231
$117$	4.41182	0.407873
$118$	−1.89347	−0.174308
$119$	−0.299813	−0.0274838
$120$	−3.97782	−0.363123
$121$	−7.85645	−0.714223
$122$	16.4664	1.49080
$123$	−3.35558	−0.302562
$124$	−1.14308	−0.102651
$125$	1.00000	0.0894427
$126$	−0.392842	−0.0349971
$127$	−5.79527	−0.514247	−0.257124	−	0.966379i	$-0.582775\pi$
$127$	−5.79527	−0.514247	−0.257124	+	0.966379i	$0.582775\pi$
$128$	−4.56926	−0.403869
$129$	7.09434	0.624622
$130$	4.01564	0.352195
$131$	21.8842	1.91203	0.956015	−	0.293317i	$-0.0947592\pi$
$131$	21.8842	1.91203	0.956015	+	0.293317i	$0.0947592\pi$
$132$	−1.26746	−0.110318
$133$	−0.297587	−0.0258040
$134$	−14.5936	−1.26069
$135$	5.59858	0.481849
$136$	3.72876	0.319738
$137$	15.4227	1.31765	0.658824	−	0.752297i	$-0.271054\pi$
$137$	15.4227	1.31765	0.658824	+	0.752297i	$0.271054\pi$
$138$	−5.96573	−0.507836
$139$	5.37125	0.455583	0.227792	−	0.973710i	$-0.426849\pi$
$139$	5.37125	0.455583	0.227792	+	0.973710i	$0.426849\pi$
$140$	0.136267	0.0115166
$141$	9.38430	0.790300
$142$	6.61483	0.555104
$143$	5.91647	0.494760
$144$	3.42648	0.285540
$145$	−0.468831	−0.0389343
$146$	−2.84241	−0.235240
$147$	8.98838	0.741349
$148$	−1.77815	−0.146163
$149$	21.1010	1.72866	0.864331	−	0.502924i	$-0.167743\pi$
$149$	21.1010	1.72866	0.864331	+	0.502924i	$0.167743\pi$
$150$	1.55878	0.127274
$151$	9.73933	0.792576	0.396288	−	0.918126i	$-0.370298\pi$
$151$	9.73933	0.792576	0.396288	+	0.918126i	$0.370298\pi$
$152$	3.70107	0.300196
$153$	−1.60534	−0.129784
$154$	−0.526820	−0.0424524
$155$	2.07126	0.166367
$156$	−2.38548	−0.190991
$157$	18.3783	1.46675	0.733375	−	0.679825i	$-0.237944\pi$
$157$	18.3783	1.46675	0.733375	+	0.679825i	$0.237944\pi$
$158$	−16.0872	−1.27983
$159$	−0.549373	−0.0435681
$160$	−3.02297	−0.238987
$161$	0.944989	0.0744756
$162$	3.95398	0.310654
$163$	−2.34694	−0.183827	−0.0919134	−	0.995767i	$-0.529298\pi$
$163$	−2.34694	−0.183827	−0.0919134	+	0.995767i	$0.529298\pi$
$164$	−1.42964	−0.111636
$165$	2.29664	0.178793
$166$	−3.01274	−0.233834
$167$	24.6602	1.90827	0.954133	−	0.299382i	$-0.0967804\pi$
$167$	24.6602	1.90827	0.954133	+	0.299382i	$0.0967804\pi$
$168$	0.982186	0.0757773
$169$	−1.86464	−0.143434
$170$	−1.46118	−0.112068
$171$	−1.59342	−0.121852
$172$	3.02253	0.230465
$173$	5.19622	0.395062	0.197531	−	0.980297i	$-0.436708\pi$
$173$	5.19622	0.395062	0.197531	+	0.980297i	$0.436708\pi$
$174$	−0.730806	−0.0554023
$175$	−0.246916	−0.0186651
$176$	4.59507	0.346367
$177$	−2.03816	−0.153197
$178$	15.3855	1.15319
$179$	−14.6717	−1.09661	−0.548306	−	0.836278i	$-0.684727\pi$
$179$	−14.6717	−1.09661	−0.548306	+	0.836278i	$0.684727\pi$
$180$	0.729637	0.0543839
$181$	−11.0838	−0.823852	−0.411926	−	0.911217i	$-0.635144\pi$
$181$	−11.0838	−0.823852	−0.411926	+	0.911217i	$0.635144\pi$
$182$	−0.991526	−0.0734968
$183$	17.7246	1.31024
$184$	−11.7528	−0.866426
$185$	3.22202	0.236888
$186$	3.22864	0.236735
$187$	−2.15284	−0.157431
$188$	3.99816	0.291596
$189$	−1.38238	−0.100553
$190$	−1.45033	−0.105218
$191$	2.32712	0.168384	0.0841921	−	0.996450i	$-0.473169\pi$
$191$	2.32712	0.168384	0.0841921	+	0.996450i	$0.473169\pi$
$192$	−11.4264	−0.824626
$193$	18.8659	1.35800	0.678998	−	0.734141i	$-0.262415\pi$
$193$	18.8659	1.35800	0.678998	+	0.734141i	$0.262415\pi$
$194$	−22.7011	−1.62984
$195$	4.32250	0.309540
$196$	3.82948	0.273534
$197$	−12.7507	−0.908451	−0.454226	−	0.890887i	$-0.650084\pi$
$197$	−12.7507	−0.908451	−0.454226	+	0.890887i	$0.650084\pi$
$198$	−2.82084	−0.200469
$199$	16.1781	1.14684	0.573419	−	0.819262i	$-0.305617\pi$
$199$	16.1781	1.14684	0.573419	+	0.819262i	$0.305617\pi$
$200$	3.07088	0.217144
$201$	−15.7087	−1.10801
$202$	15.7824	1.11044
$203$	0.115762	0.00812489
$204$	0.868011	0.0607729
$205$	2.59051	0.180929
$206$	−2.75963	−0.192272
$207$	5.05992	0.351689
$208$	8.64837	0.599657
$209$	−2.13685	−0.147809
$210$	−0.384888	−0.0265598
$211$	13.1029	0.902038	0.451019	−	0.892514i	$-0.351061\pi$
$211$	13.1029	0.902038	0.451019	+	0.892514i	$0.351061\pi$
$212$	−0.234059	−0.0160752
$213$	7.12029	0.487874
$214$	−19.5389	−1.33565
$215$	−5.47683	−0.373517
$216$	17.1925	1.16980
$217$	−0.511426	−0.0347179
$218$	11.0629	0.749271
$219$	−3.05961	−0.206750
$220$	0.978478	0.0659690
$221$	−4.05186	−0.272557
$222$	5.02243	0.337083
$223$	−22.0276	−1.47508	−0.737539	−	0.675304i	$-0.764012\pi$
$223$	−22.0276	−1.47508	−0.737539	+	0.675304i	$0.764012\pi$
$224$	0.746420	0.0498723
$225$	−1.32210	−0.0881403
$226$	−21.0250	−1.39856
$227$	21.0192	1.39510	0.697548	−	0.716538i	$-0.254274\pi$
$227$	21.0192	1.39510	0.697548	+	0.716538i	$0.254274\pi$
$228$	0.861565	0.0570585
$229$	2.14538	0.141771	0.0708853	−	0.997484i	$-0.477418\pi$
$229$	2.14538	0.141771	0.0708853	+	0.997484i	$0.477418\pi$
$230$	4.60554	0.303681
$231$	−0.567076	−0.0373109
$232$	−1.43972	−0.0945225
$233$	−6.87277	−0.450250	−0.225125	−	0.974330i	$-0.572279\pi$
$233$	−6.87277	−0.450250	−0.225125	+	0.974330i	$0.572279\pi$
$234$	−5.30910	−0.347067
$235$	−7.24468	−0.472591
$236$	−0.868353	−0.0565250
$237$	−17.3165	−1.12483
$238$	0.360789	0.0233865
$239$	−6.60373	−0.427160	−0.213580	−	0.976926i	$-0.568512\pi$
$239$	−6.60373	−0.427160	−0.213580	+	0.976926i	$0.568512\pi$
$240$	3.35710	0.216700
$241$	21.7381	1.40027	0.700136	−	0.714010i	$-0.253123\pi$
$241$	21.7381	1.40027	0.700136	+	0.714010i	$0.253123\pi$
$242$	9.45430	0.607745
$243$	−12.5396	−0.804417
$244$	7.55155	0.483438
$245$	−6.93903	−0.443319
$246$	4.03803	0.257456
$247$	−4.02177	−0.255899
$248$	6.36058	0.403897
$249$	−3.24295	−0.205514
$250$	−1.20338	−0.0761085
$251$	−20.7269	−1.30827	−0.654134	−	0.756379i	$-0.726967\pi$
$251$	−20.7269	−1.30827	−0.654134	+	0.756379i	$0.726967\pi$
$252$	−0.180159	−0.0113489
$253$	6.78560	0.426607
$254$	6.97392	0.437583
$255$	−1.57284	−0.0984950
$256$	−12.1437	−0.758984
$257$	9.09208	0.567148	0.283574	−	0.958950i	$-0.408480\pi$
$257$	9.09208	0.567148	0.283574	+	0.958950i	$0.408480\pi$
$258$	−8.53719	−0.531502
$259$	−0.795568	−0.0494342
$260$	1.84159	0.114211
$261$	0.619844	0.0383674
$262$	−26.3350	−1.62698
$263$	−20.9695	−1.29303	−0.646517	−	0.762900i	$-0.723775\pi$
$263$	−20.9695	−1.29303	−0.646517	+	0.762900i	$0.723775\pi$
$264$	7.05270	0.434063
$265$	0.424116	0.0260532
$266$	0.358110	0.0219571
$267$	16.5612	1.01353
$268$	−6.69266	−0.408820
$269$	25.0733	1.52875	0.764373	−	0.644774i	$-0.223049\pi$
$269$	25.0733	1.52875	0.764373	+	0.644774i	$0.223049\pi$
$270$	−6.73722	−0.410014
$271$	−14.1812	−0.861449	−0.430725	−	0.902483i	$-0.641742\pi$
$271$	−14.1812	−0.861449	−0.430725	+	0.902483i	$0.641742\pi$
$272$	−3.14691	−0.190809
$273$	−1.06729	−0.0645955
$274$	−18.5593	−1.12121
$275$	−1.77301	−0.106916
$276$	−2.73591	−0.164682
$277$	−19.2087	−1.15414	−0.577070	−	0.816695i	$-0.695804\pi$
$277$	−19.2087	−1.15414	−0.577070	+	0.816695i	$0.695804\pi$
$278$	−6.46366	−0.387664
$279$	−2.73842	−0.163945
$280$	−0.758248	−0.0453140
$281$	22.9648	1.36996	0.684982	−	0.728560i	$-0.259810\pi$
$281$	22.9648	1.36996	0.684982	+	0.728560i	$0.259810\pi$
$282$	−11.2929	−0.672481
$283$	22.1431	1.31627	0.658134	−	0.752901i	$-0.271346\pi$
$283$	22.1431	1.31627	0.658134	+	0.752901i	$0.271346\pi$
$284$	3.03359	0.180010
$285$	−1.56116	−0.0924751
$286$	−7.11976	−0.421000
$287$	−0.639637	−0.0377566
$288$	3.99668	0.235507
$289$	−15.5256	−0.913273
$290$	0.564183	0.0331299
$291$	−24.4357	−1.43245
$292$	−1.30354	−0.0762840
$293$	5.64426	0.329741	0.164871	−	0.986315i	$-0.447279\pi$
$293$	5.64426	0.329741	0.164871	+	0.986315i	$0.447279\pi$
$294$	−10.8164	−0.630828
$295$	1.57346	0.0916104
$296$	9.89443	0.575102
$297$	−9.92631	−0.575983
$298$	−25.3925	−1.47095
$299$	12.7712	0.738575
$300$	0.714864	0.0412727
$301$	1.35232	0.0779462
$302$	−11.7201	−0.674417
$303$	16.9884	0.975956
$304$	−3.12354	−0.179147
$305$	−13.6834	−0.783511
$306$	1.93184	0.110436
$307$	17.5302	1.00050	0.500250	−	0.865881i	$-0.333241\pi$
$307$	17.5302	1.00050	0.500250	+	0.865881i	$0.333241\pi$
$308$	−0.241602	−0.0137665
$309$	−2.97050	−0.168986
$310$	−2.49251	−0.141565
$311$	27.3541	1.55111	0.775554	−	0.631282i	$-0.217471\pi$
$311$	27.3541	1.55111	0.775554	+	0.631282i	$0.217471\pi$
$312$	13.2739	0.751484
$313$	−26.0997	−1.47524	−0.737622	−	0.675214i	$-0.764051\pi$
$313$	−26.0997	−1.47524	−0.737622	+	0.675214i	$0.764051\pi$
$314$	−22.1161	−1.24808
$315$	0.326449	0.0183933
$316$	−7.37767	−0.415026
$317$	14.4197	0.809893	0.404947	−	0.914340i	$-0.367290\pi$
$317$	14.4197	0.809893	0.404947	+	0.914340i	$0.367290\pi$
$318$	0.661104	0.0370729
$319$	0.831241	0.0465406
$320$	8.82115	0.493117
$321$	−21.0320	−1.17389
$322$	−1.13718	−0.0633727
$323$	1.46341	0.0814264
$324$	1.81331	0.100739
$325$	−3.33697	−0.185102
$326$	2.82427	0.156422
$327$	11.9082	0.658526
$328$	7.95512	0.439248
$329$	1.78883	0.0986212
$330$	−2.76373	−0.152138
$331$	9.19427	0.505363	0.252681	−	0.967550i	$-0.418688\pi$
$331$	9.19427	0.505363	0.252681	+	0.967550i	$0.418688\pi$
$332$	−1.38165	−0.0758281
$333$	−4.25985	−0.233438
$334$	−29.6757	−1.62378
$335$	12.1271	0.662576
$336$	−0.828921	−0.0452214
$337$	−13.7098	−0.746820	−0.373410	−	0.927666i	$-0.621811\pi$
$337$	−13.7098	−0.746820	−0.373410	+	0.927666i	$0.621811\pi$
$338$	2.24387	0.122050
$339$	−22.6316	−1.22918
$340$	−0.670104	−0.0363415
$341$	−3.67235	−0.198869
$342$	1.91749	0.103686
$343$	3.44177	0.185838
$344$	−16.8187	−0.906802
$345$	4.95747	0.266901
$346$	−6.25304	−0.336165
$347$	3.37776	0.181328	0.0906639	−	0.995882i	$-0.471101\pi$
$347$	3.37776	0.181328	0.0906639	+	0.995882i	$0.471101\pi$
$348$	−0.335151	−0.0179660
$349$	−24.4587	−1.30924	−0.654621	−	0.755957i	$-0.727172\pi$
$349$	−24.4587	−1.30924	−0.654621	+	0.755957i	$0.727172\pi$
$350$	0.297134	0.0158825
$351$	−18.6823	−0.997186
$352$	5.35975	0.285676
$353$	26.3329	1.40156	0.700781	−	0.713377i	$-0.252835\pi$
$353$	26.3329	1.40156	0.700781	+	0.713377i	$0.252835\pi$
$354$	2.45268	0.130359
$355$	−5.49687	−0.291744
$356$	7.05587	0.373960
$357$	0.388359	0.0205541
$358$	17.6556	0.933128
$359$	−2.55869	−0.135042	−0.0675211	−	0.997718i	$-0.521509\pi$
$359$	−2.55869	−0.135042	−0.0675211	+	0.997718i	$0.521509\pi$
$360$	−4.06002	−0.213982
$361$	−17.5475	−0.923550
$362$	13.3380	0.701031
$363$	10.1767	0.534140
$364$	−0.454718	−0.0238337
$365$	2.36202	0.123634
$366$	−21.3295	−1.11491
$367$	19.5809	1.02212	0.511058	−	0.859546i	$-0.329254\pi$
$367$	19.5809	1.02212	0.511058	+	0.859546i	$0.329254\pi$
$368$	9.91882	0.517054
$369$	−3.42492	−0.178294
$370$	−3.87732	−0.201572
$371$	−0.104721	−0.00543684
$372$	1.48067	0.0767690
$373$	−10.0578	−0.520774	−0.260387	−	0.965504i	$-0.583850\pi$
$373$	−10.0578	−0.520774	−0.260387	+	0.965504i	$0.583850\pi$
$374$	2.59069	0.133961
$375$	−1.29534	−0.0668909
$376$	−22.2475	−1.14733
$377$	1.56448	0.0805746
$378$	1.66353	0.0855626
$379$	26.9081	1.38217	0.691087	−	0.722772i	$-0.257132\pi$
$379$	26.9081	1.38217	0.691087	+	0.722772i	$0.257132\pi$
$380$	−0.665128	−0.0341204
$381$	7.50682	0.384586
$382$	−2.80041	−0.143281
$383$	15.1377	0.773500	0.386750	−	0.922185i	$-0.373598\pi$
$383$	15.1377	0.773500	0.386750	+	0.922185i	$0.373598\pi$
$384$	5.91873	0.302039
$385$	0.437783	0.0223115
$386$	−22.7028	−1.15554
$387$	7.24094	0.368078
$388$	−10.4108	−0.528528
$389$	20.1383	1.02105	0.510526	−	0.859862i	$-0.329451\pi$
$389$	20.1383	1.02105	0.510526	+	0.859862i	$0.329451\pi$
$390$	−5.20161	−0.263394
$391$	−4.64708	−0.235013
$392$	−21.3089	−1.07626
$393$	−28.3474	−1.42994
$394$	15.3440	0.773018
$395$	13.3684	0.672636
$396$	−1.29365	−0.0650084
$397$	−2.66517	−0.133761	−0.0668804	−	0.997761i	$-0.521305\pi$
$397$	−2.66517	−0.133761	−0.0668804	+	0.997761i	$0.521305\pi$
$398$	−19.4685	−0.975866
$399$	0.385475	0.0192979
$400$	−2.59168	−0.129584
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	18.9036	0.942824
$403$	−6.91172	−0.344297
$404$	7.23785	0.360097
$405$	−3.28573	−0.163269
$406$	−0.139306	−0.00691362
$407$	−5.71266	−0.283166
$408$	−4.82999	−0.239120
$409$	−31.5330	−1.55920	−0.779602	−	0.626275i	$-0.784579\pi$
$409$	−31.5330	−1.55920	−0.779602	+	0.626275i	$0.784579\pi$
$410$	−3.11736	−0.153956
$411$	−19.9775	−0.985419
$412$	−1.26558	−0.0623505
$413$	−0.388512	−0.0191174
$414$	−6.08901	−0.299259
$415$	2.50356	0.122895
$416$	10.0876	0.494584
$417$	−6.95757	−0.340714
$418$	2.57145	0.125774
$419$	−1.17848	−0.0575723	−0.0287862	−	0.999586i	$-0.509164\pi$
$419$	−1.17848	−0.0575723	−0.0287862	+	0.999586i	$0.509164\pi$
$420$	−0.176511	−0.00861286
$421$	−27.5108	−1.34079	−0.670397	−	0.742002i	$-0.733876\pi$
$421$	−27.5108	−1.34079	−0.670397	+	0.742002i	$0.733876\pi$
$422$	−15.7677	−0.767561
$423$	9.57822	0.465709
$424$	1.30241	0.0632505
$425$	1.21423	0.0588989
$426$	−8.56842	−0.415141
$427$	3.37866	0.163505
$428$	−8.96062	−0.433128
$429$	−7.66381	−0.370012
$430$	6.59071	0.317832
$431$	17.4490	0.840489	0.420244	−	0.907411i	$-0.361944\pi$
$431$	17.4490	0.840489	0.420244	+	0.907411i	$0.361944\pi$
$432$	−14.5097	−0.698100
$433$	10.9375	0.525621	0.262810	−	0.964848i	$-0.415351\pi$
$433$	10.9375	0.525621	0.262810	+	0.964848i	$0.415351\pi$
$434$	0.615440	0.0295421
$435$	0.607294	0.0291175
$436$	5.07347	0.242975
$437$	−4.61257	−0.220649
$438$	3.68188	0.175927
$439$	−8.17818	−0.390323	−0.195162	−	0.980771i	$-0.562523\pi$
$439$	−8.17818	−0.390323	−0.195162	+	0.980771i	$0.562523\pi$
$440$	−5.44468	−0.259565
$441$	9.17413	0.436863
$442$	4.87592	0.231924
$443$	0.374384	0.0177875	0.00889377	−	0.999960i	$-0.497169\pi$
$443$	0.374384	0.0177875	0.00889377	+	0.999960i	$0.497169\pi$
$444$	2.30331	0.109310
$445$	−12.7853	−0.606080
$446$	26.5076	1.25517
$447$	−27.3329	−1.29280
$448$	−2.17808	−0.102905
$449$	−6.06628	−0.286286	−0.143143	−	0.989702i	$-0.545721\pi$
$449$	−6.06628	−0.286286	−0.143143	+	0.989702i	$0.545721\pi$
$450$	1.59099	0.0750002
$451$	−4.59298	−0.216275
$452$	−9.64215	−0.453529
$453$	−12.6157	−0.592738
$454$	−25.2941	−1.18711
$455$	0.823951	0.0386274
$456$	−4.79413	−0.224506
$457$	−30.0029	−1.40348	−0.701739	−	0.712434i	$-0.747593\pi$
$457$	−30.0029	−1.40348	−0.701739	+	0.712434i	$0.747593\pi$
$458$	−2.58171	−0.120635
$459$	6.79797	0.317302
$460$	2.11212	0.0984781
$461$	6.27133	0.292085	0.146042	−	0.989278i	$-0.453346\pi$
$461$	6.27133	0.292085	0.146042	+	0.989278i	$0.453346\pi$
$462$	0.682409	0.0317485
$463$	11.0444	0.513277	0.256639	−	0.966507i	$-0.417385\pi$
$463$	11.0444	0.513277	0.256639	+	0.966507i	$0.417385\pi$
$464$	1.21506	0.0564079
$465$	−2.68297	−0.124420
$466$	8.27056	0.383126
$467$	−11.3593	−0.525643	−0.262822	−	0.964844i	$-0.584653\pi$
$467$	−11.3593	−0.525643	−0.262822	+	0.964844i	$0.584653\pi$
$468$	−2.43477	−0.112547
$469$	−2.99438	−0.138268
$470$	8.71811	0.402136
$471$	−23.8061	−1.09693
$472$	4.83190	0.222406
$473$	9.71046	0.446487
$474$	20.8384	0.957138
$475$	1.20522	0.0552991
$476$	0.165459	0.00758382
$477$	−0.560726	−0.0256739
$478$	7.94680	0.363478
$479$	−1.01453	−0.0463550	−0.0231775	−	0.999731i	$-0.507378\pi$
$479$	−1.01453	−0.0463550	−0.0231775	+	0.999731i	$0.507378\pi$
$480$	3.91576	0.178729
$481$	−10.7518	−0.490239
$482$	−26.1592	−1.19152
$483$	−1.22408	−0.0556975
$484$	4.33578	0.197081
$485$	18.8644	0.856589
$486$	15.0899	0.684493
$487$	−12.9307	−0.585946	−0.292973	−	0.956121i	$-0.594645\pi$
$487$	−12.9307	−0.585946	−0.292973	+	0.956121i	$0.594645\pi$
$488$	−42.0202	−1.90216
$489$	3.04008	0.137477
$490$	8.35030	0.377228
$491$	9.81842	0.443099	0.221550	−	0.975149i	$-0.428889\pi$
$491$	9.81842	0.443099	0.221550	+	0.975149i	$0.428889\pi$
$492$	1.85186	0.0834882
$493$	−0.569270	−0.0256386
$494$	4.83972	0.217749
$495$	2.34410	0.105359
$496$	−5.36804	−0.241032
$497$	1.35726	0.0608816
$498$	3.90251	0.174876
$499$	4.22049	0.188935	0.0944675	−	0.995528i	$-0.469885\pi$
$499$	4.22049	0.188935	0.0944675	+	0.995528i	$0.469885\pi$
$500$	−0.551875	−0.0246806
$501$	−31.9433	−1.42712
$502$	24.9423	1.11323
$503$	−34.5008	−1.53831	−0.769156	−	0.639061i	$-0.779323\pi$
$503$	−34.5008	−1.53831	−0.769156	+	0.639061i	$0.779323\pi$
$504$	1.00248	0.0446542
$505$	−13.1150	−0.583611
$506$	−8.16566	−0.363008
$507$	2.41533	0.107269
$508$	3.19827	0.141900
$509$	26.9860	1.19613	0.598066	−	0.801447i	$-0.295936\pi$
$509$	26.9860	1.19613	0.598066	+	0.801447i	$0.295936\pi$
$510$	1.89272	0.0838112
$511$	−0.583221	−0.0258002
$512$	23.7521	1.04970
$513$	6.74749	0.297909
$514$	−10.9412	−0.482597
$515$	2.29323	0.101052
$516$	−3.91519	−0.172357
$517$	12.8449	0.564916
$518$	0.957371	0.0420645
$519$	−6.73086	−0.295452
$520$	−10.2474	−0.449379
$521$	28.3733	1.24306	0.621528	−	0.783392i	$-0.286512\pi$
$521$	28.3733	1.24306	0.621528	+	0.783392i	$0.286512\pi$
$522$	−0.745908	−0.0326475
$523$	−17.2953	−0.756269	−0.378134	−	0.925751i	$-0.623434\pi$
$523$	−17.2953	−0.756269	−0.378134	+	0.925751i	$0.623434\pi$
$524$	−12.0773	−0.527601
$525$	0.319839	0.0139589
$526$	25.2343	1.10027
$527$	2.51499	0.109555
$528$	−5.95216	−0.259035
$529$	−8.35276	−0.363163
$530$	−0.510373	−0.0221692
$531$	−2.08028	−0.0902764
$532$	0.164231	0.00712031
$533$	−8.64444	−0.374432
$534$	−19.9294	−0.862431
$535$	16.2367	0.701973
$536$	37.2409	1.60856
$537$	19.0047	0.820115
$538$	−30.1727	−1.30084
$539$	12.3029	0.529925
$540$	−3.08972	−0.132960
$541$	−10.8939	−0.468365	−0.234183	−	0.972193i	$-0.575241\pi$
$541$	−10.8939	−0.468365	−0.234183	+	0.972193i	$0.575241\pi$
$542$	17.0654	0.733023
$543$	14.3572	0.616128
$544$	−3.67059	−0.157375
$545$	−9.19314	−0.393791
$546$	1.28436	0.0549655
$547$	19.4646	0.832246	0.416123	−	0.909308i	$-0.363389\pi$
$547$	19.4646	0.832246	0.416123	+	0.909308i	$0.363389\pi$
$548$	−8.51138	−0.363588
$549$	18.0909	0.772102
$550$	2.13360	0.0909771
$551$	−0.565043	−0.0240716
$552$	15.2238	0.647968
$553$	−3.30086	−0.140367
$554$	23.1154	0.982079
$555$	−4.17360	−0.177159
$556$	−2.96426	−0.125713
$557$	5.84825	0.247798	0.123899	−	0.992295i	$-0.460460\pi$
$557$	5.84825	0.247798	0.123899	+	0.992295i	$0.460460\pi$
$558$	3.29536	0.139504
$559$	18.2760	0.772993
$560$	0.639928	0.0270419
$561$	2.78865	0.117737
$562$	−27.6354	−1.16573
$563$	10.8364	0.456702	0.228351	−	0.973579i	$-0.426667\pi$
$563$	10.8364	0.456702	0.228351	+	0.973579i	$0.426667\pi$
$564$	−5.17896	−0.218074
$565$	17.4716	0.735037
$566$	−26.6465	−1.12004
$567$	0.811298	0.0340713
$568$	−16.8802	−0.708278
$569$	−36.0314	−1.51051	−0.755257	−	0.655429i	$-0.772488\pi$
$569$	−36.0314	−1.51051	−0.755257	+	0.655429i	$0.772488\pi$
$570$	1.87867	0.0786888
$571$	−8.53761	−0.357288	−0.178644	−	0.983914i	$-0.557171\pi$
$571$	−8.53761	−0.357288	−0.178644	+	0.983914i	$0.557171\pi$
$572$	−3.26515	−0.136523
$573$	−3.01440	−0.125928
$574$	0.769727	0.0321278
$575$	−3.82717	−0.159604
$576$	−11.6625	−0.485937
$577$	36.6914	1.52748	0.763741	−	0.645522i	$-0.223360\pi$
$577$	36.6914	1.52748	0.763741	+	0.645522i	$0.223360\pi$
$578$	18.6833	0.777121
$579$	−24.4376	−1.01559
$580$	0.258736	0.0107434
$581$	−0.618169	−0.0256460
$582$	29.4055	1.21890
$583$	−0.751960	−0.0311430
$584$	7.25348	0.300151
$585$	4.41182	0.182406
$586$	−6.79220	−0.280583
$587$	38.6064	1.59346	0.796728	−	0.604339i	$-0.206563\pi$
$587$	38.6064	1.59346	0.796728	+	0.604339i	$0.206563\pi$
$588$	−4.96046	−0.204566
$589$	2.49631	0.102859
$590$	−1.89347	−0.0779530
$591$	16.5165	0.679397
$592$	−8.35046	−0.343202
$593$	−37.1379	−1.52507	−0.762534	−	0.646948i	$-0.776045\pi$
$593$	−37.1379	−1.52507	−0.762534	+	0.646948i	$0.776045\pi$
$594$	11.9451	0.490115
$595$	−0.299813	−0.0122911
$596$	−11.6451	−0.477002
$597$	−20.9561	−0.857677
$598$	−15.3686	−0.628467
$599$	5.62387	0.229785	0.114893	−	0.993378i	$-0.463348\pi$
$599$	5.62387	0.229785	0.114893	+	0.993378i	$0.463348\pi$
$600$	−3.97782	−0.162394
$601$	−3.02948	−0.123575	−0.0617876	−	0.998089i	$-0.519680\pi$
$601$	−3.02948	−0.123575	−0.0617876	+	0.998089i	$0.519680\pi$
$602$	−1.62735	−0.0663259
$603$	−16.0333	−0.652928
$604$	−5.37490	−0.218701
$605$	−7.85645	−0.319410
$606$	−20.4435	−0.830459
$607$	−1.69755	−0.0689013	−0.0344507	−	0.999406i	$-0.510968\pi$
$607$	−1.69755	−0.0689013	−0.0344507	+	0.999406i	$0.510968\pi$
$608$	−3.64333	−0.147757
$609$	−0.149951	−0.00607630
$610$	16.4664	0.666704
$611$	24.1753	0.978027
$612$	0.885948	0.0358123
$613$	−47.2427	−1.90811	−0.954057	−	0.299625i	$-0.903138\pi$
$613$	−47.2427	−1.90811	−0.954057	+	0.299625i	$0.903138\pi$
$614$	−21.0955	−0.851344
$615$	−3.35558	−0.135310
$616$	1.34438	0.0541666
$617$	−8.34190	−0.335832	−0.167916	−	0.985801i	$-0.553704\pi$
$617$	−8.34190	−0.335832	−0.167916	+	0.985801i	$0.553704\pi$
$618$	3.57465	0.143793
$619$	−13.9649	−0.561295	−0.280648	−	0.959811i	$-0.590549\pi$
$619$	−13.9649	−0.561295	−0.280648	+	0.959811i	$0.590549\pi$
$620$	−1.14308	−0.0459070
$621$	−21.4267	−0.859825
$622$	−32.9174	−1.31987
$623$	3.15688	0.126478
$624$	−11.2025	−0.448461
$625$	1.00000	0.0400000
$626$	31.4079	1.25531
$627$	2.76795	0.110541
$628$	−10.1425	−0.404731
$629$	3.91228	0.155993
$630$	−0.392842	−0.0156512
$631$	4.53765	0.180641	0.0903204	−	0.995913i	$-0.471211\pi$
$631$	4.53765	0.180641	0.0903204	+	0.995913i	$0.471211\pi$
$632$	41.0526	1.63299
$633$	−16.9726	−0.674601
$634$	−17.3524	−0.689153
$635$	−5.79527	−0.229978
$636$	0.303185	0.0120221
$637$	23.1553	0.917448
$638$	−1.00030	−0.0396022
$639$	7.26744	0.287495
$640$	−4.56926	−0.180616
$641$	3.11502	0.123036	0.0615180	−	0.998106i	$-0.480406\pi$
$641$	3.11502	0.123036	0.0615180	+	0.998106i	$0.480406\pi$
$642$	25.3094	0.998884
$643$	−22.4530	−0.885461	−0.442731	−	0.896655i	$-0.645990\pi$
$643$	−22.4530	−0.885461	−0.442731	+	0.896655i	$0.645990\pi$
$644$	−0.521516	−0.0205506
$645$	7.09434	0.279339
$646$	−1.76104	−0.0692872
$647$	−37.0175	−1.45531	−0.727655	−	0.685944i	$-0.759390\pi$
$647$	−37.0175	−1.45531	−0.727655	+	0.685944i	$0.759390\pi$
$648$	−10.0901	−0.396375
$649$	−2.78975	−0.109507
$650$	4.01564	0.157507
$651$	0.662469	0.0259642
$652$	1.29522	0.0507247
$653$	−2.82872	−0.110697	−0.0553483	−	0.998467i	$-0.517627\pi$
$653$	−2.82872	−0.110697	−0.0553483	+	0.998467i	$0.517627\pi$
$654$	−14.3301	−0.560352
$655$	21.8842	0.855086
$656$	−6.71377	−0.262129
$657$	−3.12284	−0.121834
$658$	−2.15264	−0.0839186
$659$	9.62339	0.374874	0.187437	−	0.982277i	$-0.439982\pi$
$659$	9.62339	0.374874	0.187437	+	0.982277i	$0.439982\pi$
$660$	−1.26746	−0.0493357
$661$	−33.2928	−1.29494	−0.647470	−	0.762091i	$-0.724173\pi$
$661$	−33.2928	−1.29494	−0.647470	+	0.762091i	$0.724173\pi$
$662$	−11.0642	−0.430022
$663$	5.24851	0.203835
$664$	7.68813	0.298357
$665$	−0.297587	−0.0115399
$666$	5.12622	0.198637
$667$	1.79430	0.0694755
$668$	−13.6094	−0.526562
$669$	28.5332	1.10316
$670$	−14.5936	−0.563798
$671$	24.2608	0.936579
$672$	−0.966864	−0.0372976
$673$	16.8618	0.649974	0.324987	−	0.945718i	$-0.394640\pi$
$673$	16.8618	0.649974	0.324987	+	0.945718i	$0.394640\pi$
$674$	16.4981	0.635483
$675$	5.59858	0.215489
$676$	1.02905	0.0395787
$677$	−30.2478	−1.16252	−0.581258	−	0.813719i	$-0.697439\pi$
$677$	−30.2478	−1.16252	−0.581258	+	0.813719i	$0.697439\pi$
$678$	27.2345	1.04593
$679$	−4.65792	−0.178755
$680$	3.72876	0.142991
$681$	−27.2270	−1.04334
$682$	4.41924	0.169221
$683$	41.3265	1.58131	0.790657	−	0.612260i	$-0.209739\pi$
$683$	41.3265	1.58131	0.790657	+	0.612260i	$0.209739\pi$
$684$	0.879369	0.0336235
$685$	15.4227	0.589270
$686$	−4.14176	−0.158133
$687$	−2.77899	−0.106025
$688$	14.1942	0.541149
$689$	−1.41526	−0.0539172
$690$	−5.96573	−0.227111
$691$	23.3528	0.888384	0.444192	−	0.895932i	$-0.353491\pi$
$691$	23.3528	0.888384	0.444192	+	0.895932i	$0.353491\pi$
$692$	−2.86767	−0.109012
$693$	−0.578795	−0.0219866
$694$	−4.06474	−0.154295
$695$	5.37125	0.203743
$696$	1.86493	0.0706898
$697$	3.14548	0.119143
$698$	29.4331	1.11406
$699$	8.90255	0.336725
$700$	0.136267	0.00515040
$701$	49.9632	1.88708	0.943542	−	0.331253i	$-0.107471\pi$
$701$	49.9632	1.88708	0.943542	+	0.331253i	$0.107471\pi$
$702$	22.4819	0.848524
$703$	3.88323	0.146459
$704$	−15.6400	−0.589453
$705$	9.38430	0.353433
$706$	−31.6886	−1.19261
$707$	3.23831	0.121789
$708$	1.12481	0.0422729
$709$	−4.37718	−0.164389	−0.0821943	−	0.996616i	$-0.526193\pi$
$709$	−4.37718	−0.164389	−0.0821943	+	0.996616i	$0.526193\pi$
$710$	6.61483	0.248250
$711$	−17.6744	−0.662841
$712$	−39.2620	−1.47140
$713$	−7.92706	−0.296871
$714$	−0.467343	−0.0174899
$715$	5.91647	0.221263
$716$	8.09693	0.302596
$717$	8.55405	0.319457
$718$	3.07907	0.114910
$719$	−20.8370	−0.777091	−0.388545	−	0.921430i	$-0.627022\pi$
$719$	−20.8370	−0.777091	−0.388545	+	0.921430i	$0.627022\pi$
$720$	3.42648	0.127697
$721$	−0.566235	−0.0210877
$722$	21.1163	0.785866
$723$	−28.1581	−1.04721
$724$	6.11687	0.227332
$725$	−0.468831	−0.0174120
$726$	−12.2465	−0.454510
$727$	26.2060	0.971925	0.485963	−	0.873980i	$-0.338469\pi$
$727$	26.2060	0.971925	0.485963	+	0.873980i	$0.338469\pi$
$728$	2.53025	0.0937773
$729$	26.1002	0.966674
$730$	−2.84241	−0.105202
$731$	−6.65015	−0.245965
$732$	−9.78179	−0.361545
$733$	−36.6382	−1.35326	−0.676632	−	0.736321i	$-0.736561\pi$
$733$	−36.6382	−1.35326	−0.676632	+	0.736321i	$0.736561\pi$
$734$	−23.5633	−0.869737
$735$	8.98838	0.331541
$736$	11.5694	0.426455
$737$	−21.5015	−0.792018
$738$	4.12148	0.151714
$739$	43.8226	1.61204	0.806020	−	0.591889i	$-0.201617\pi$
$739$	43.8226	1.61204	0.806020	+	0.591889i	$0.201617\pi$
$740$	−1.77815	−0.0653662
$741$	5.20954	0.191377
$742$	0.126019	0.00462631
$743$	−1.85861	−0.0681860	−0.0340930	−	0.999419i	$-0.510854\pi$
$743$	−1.85861	−0.0681860	−0.0340930	+	0.999419i	$0.510854\pi$
$744$	−8.23908	−0.302059
$745$	21.1010	0.773081
$746$	12.1034	0.443136
$747$	−3.30997	−0.121105
$748$	1.18810	0.0434412
$749$	−4.00909	−0.146489
$750$	1.55878	0.0569187
$751$	−33.0239	−1.20506	−0.602530	−	0.798096i	$-0.705841\pi$
$751$	−33.0239	−1.20506	−0.602530	+	0.798096i	$0.705841\pi$
$752$	18.7759	0.684687
$753$	26.8482	0.978405
$754$	−1.88266	−0.0685624
$755$	9.73933	0.354451
$756$	0.762900	0.0277464
$757$	4.38682	0.159442	0.0797208	−	0.996817i	$-0.474597\pi$
$757$	4.38682	0.159442	0.0797208	+	0.996817i	$0.474597\pi$
$758$	−32.3806	−1.17612
$759$	−8.78963	−0.319043
$760$	3.70107	0.134252
$761$	−22.4794	−0.814878	−0.407439	−	0.913232i	$-0.633578\pi$
$761$	−22.4794	−0.814878	−0.407439	+	0.913232i	$0.633578\pi$
$762$	−9.03357	−0.327252
$763$	2.26993	0.0821771
$764$	−1.28428	−0.0464635
$765$	−1.60534	−0.0580413
$766$	−18.2164	−0.658186
$767$	−5.25059	−0.189588
$768$	15.7302	0.567616
$769$	48.2872	1.74128	0.870640	−	0.491920i	$-0.163705\pi$
$769$	48.2872	1.74128	0.870640	+	0.491920i	$0.163705\pi$
$770$	−0.526820	−0.0189853
$771$	−11.7773	−0.424149
$772$	−10.4116	−0.374722
$773$	−22.0194	−0.791983	−0.395992	−	0.918254i	$-0.629599\pi$
$773$	−22.0194	−0.791983	−0.395992	+	0.918254i	$0.629599\pi$
$774$	−8.71361	−0.313204
$775$	2.07126	0.0744018
$776$	57.9303	2.07958
$777$	1.03053	0.0369700
$778$	−24.2340	−0.868832
$779$	3.12212	0.111861
$780$	−2.38548	−0.0854138
$781$	9.74598	0.348739
$782$	5.59220	0.199977
$783$	−2.62479	−0.0938023
$784$	17.9838	0.642278
$785$	18.3783	0.655950
$786$	34.1127	1.21676
$787$	23.8587	0.850470	0.425235	−	0.905083i	$-0.360191\pi$
$787$	23.8587	0.850470	0.425235	+	0.905083i	$0.360191\pi$
$788$	7.03681	0.250676
$789$	27.1625	0.967012
$790$	−16.0872	−0.572358
$791$	−4.31402	−0.153389
$792$	7.19844	0.255785
$793$	45.6612	1.62148
$794$	3.20721	0.113820
$795$	−0.549373	−0.0194842
$796$	−8.92831	−0.316456
$797$	17.8993	0.634027	0.317014	−	0.948421i	$-0.397320\pi$
$797$	17.8993	0.634027	0.317014	+	0.948421i	$0.397320\pi$
$798$	−0.463873	−0.0164209
$799$	−8.79672	−0.311206
$800$	−3.02297	−0.106878
$801$	16.9035	0.597254
$802$	1.20338	0.0424928
$803$	−4.18788	−0.147787
$804$	8.66925	0.305741
$805$	0.944989	0.0333065
$806$	8.31743	0.292969
$807$	−32.4783	−1.14329
$808$	−40.2746	−1.41686
$809$	37.0308	1.30193	0.650966	−	0.759107i	$-0.274364\pi$
$809$	37.0308	1.30193	0.650966	+	0.759107i	$0.274364\pi$
$810$	3.95398	0.138929
$811$	39.9392	1.40246	0.701228	−	0.712937i	$-0.252636\pi$
$811$	39.9392	1.40246	0.701228	+	0.712937i	$0.252636\pi$
$812$	−0.0638861	−0.00224196
$813$	18.3695	0.644246
$814$	6.87451	0.240951
$815$	−2.34694	−0.0822099
$816$	4.07630	0.142699
$817$	−6.60076	−0.230931
$818$	37.9461	1.32676
$819$	−1.08935	−0.0380649
$820$	−1.42964	−0.0499250
$821$	−42.9822	−1.50009	−0.750045	−	0.661387i	$-0.769968\pi$
$821$	−42.9822	−1.50009	−0.750045	+	0.661387i	$0.769968\pi$
$822$	24.0406	0.838511
$823$	30.3835	1.05910	0.529551	−	0.848278i	$-0.322360\pi$
$823$	30.3835	1.05910	0.529551	+	0.848278i	$0.322360\pi$
$824$	7.04223	0.245328
$825$	2.29664	0.0799587
$826$	0.467528	0.0162674
$827$	16.9065	0.587896	0.293948	−	0.955821i	$-0.405031\pi$
$827$	16.9065	0.587896	0.293948	+	0.955821i	$0.405031\pi$
$828$	−2.79244	−0.0970441
$829$	−30.2378	−1.05020	−0.525100	−	0.851040i	$-0.675972\pi$
$829$	−30.2378	−1.05020	−0.525100	+	0.851040i	$0.675972\pi$
$830$	−3.01274	−0.104574
$831$	24.8817	0.863138
$832$	−29.4359	−1.02051
$833$	−8.42560	−0.291930
$834$	8.37261	0.289920
$835$	24.6602	0.853403
$836$	1.17928	0.0407861
$837$	11.5961	0.400820
$838$	1.41816	0.0489894
$839$	−17.3311	−0.598336	−0.299168	−	0.954200i	$-0.596709\pi$
$839$	−17.3311	−0.598336	−0.299168	+	0.954200i	$0.596709\pi$
$840$	0.982186	0.0338886
$841$	−28.7802	−0.992421
$842$	33.1060	1.14091
$843$	−29.7471	−1.02454
$844$	−7.23114	−0.248906
$845$	−1.86464	−0.0641454
$846$	−11.5262	−0.396281
$847$	1.93988	0.0666551
$848$	−1.09917	−0.0377458
$849$	−28.6827	−0.984388
$850$	−1.46118	−0.0501182
$851$	−12.3312	−0.422709
$852$	−3.92951	−0.134623
$853$	39.5536	1.35429	0.677145	−	0.735850i	$-0.263217\pi$
$853$	39.5536	1.35429	0.677145	+	0.735850i	$0.263217\pi$
$854$	−4.06581	−0.139129
$855$	−1.59342	−0.0544938
$856$	49.8608	1.70421
$857$	−9.04225	−0.308878	−0.154439	−	0.988002i	$-0.549357\pi$
$857$	−9.04225	−0.308878	−0.154439	+	0.988002i	$0.549357\pi$
$858$	9.22248	0.314850
$859$	−23.2269	−0.792491	−0.396246	−	0.918145i	$-0.629687\pi$
$859$	−23.2269	−0.792491	−0.396246	+	0.918145i	$0.629687\pi$
$860$	3.02253	0.103067
$861$	0.828545	0.0282367
$862$	−20.9978	−0.715187
$863$	33.8355	1.15177	0.575886	−	0.817530i	$-0.304657\pi$
$863$	33.8355	1.15177	0.575886	+	0.817530i	$0.304657\pi$
$864$	−16.9243	−0.575778
$865$	5.19622	0.176677
$866$	−13.1619	−0.447260
$867$	20.1109	0.683003
$868$	0.282243	0.00957996
$869$	−23.7022	−0.804042
$870$	−0.730806	−0.0247766
$871$	−40.4679	−1.37120
$872$	−28.2310	−0.956023
$873$	−24.9407	−0.844116
$874$	5.55067	0.187754
$875$	−0.246916	−0.00834728
$876$	1.68852	0.0570500
$877$	−45.1881	−1.52589	−0.762946	−	0.646462i	$-0.776248\pi$
$877$	−45.1881	−1.52589	−0.762946	+	0.646462i	$0.776248\pi$
$878$	9.84146	0.332133
$879$	−7.31122	−0.246601
$880$	4.59507	0.154900
$881$	−31.1331	−1.04890	−0.524450	−	0.851441i	$-0.675729\pi$
$881$	−31.1331	−1.04890	−0.524450	+	0.851441i	$0.675729\pi$
$882$	−11.0400	−0.371735
$883$	−33.9661	−1.14305	−0.571524	−	0.820585i	$-0.693648\pi$
$883$	−33.9661	−1.14305	−0.571524	+	0.820585i	$0.693648\pi$
$884$	2.23612	0.0752088
$885$	−2.03816	−0.0685120
$886$	−0.450527	−0.0151357
$887$	32.8048	1.10148	0.550738	−	0.834678i	$-0.314346\pi$
$887$	32.8048	1.10148	0.550738	+	0.834678i	$0.314346\pi$
$888$	−12.8166	−0.430097
$889$	1.43094	0.0479923
$890$	15.3855	0.515724
$891$	5.82561	0.195165
$892$	12.1565	0.407030
$893$	−8.73140	−0.292185
$894$	32.8919	1.10007
$895$	−14.6717	−0.490420
$896$	1.12822	0.0376913
$897$	−16.5429	−0.552353
$898$	7.30005	0.243606
$899$	−0.971070	−0.0323870
$900$	0.729637	0.0243212
$901$	0.514975	0.0171563
$902$	5.52711	0.184033
$903$	−1.75170	−0.0582931
$904$	53.6532	1.78448
$905$	−11.0838	−0.368438
$906$	15.1815	0.504372
$907$	−18.2928	−0.607403	−0.303701	−	0.952767i	$-0.598222\pi$
$907$	−18.2928	−0.607403	−0.303701	+	0.952767i	$0.598222\pi$
$908$	−11.6000	−0.384959
$909$	17.3394	0.575112
$910$	−0.991526	−0.0328688
$911$	25.6422	0.849563	0.424781	−	0.905296i	$-0.360351\pi$
$911$	25.6422	0.849563	0.424781	+	0.905296i	$0.360351\pi$
$912$	4.04603	0.133977
$913$	−4.43883	−0.146904
$914$	36.1050	1.19425
$915$	17.7246	0.585959
$916$	−1.18398	−0.0391198
$917$	−5.40355	−0.178441
$918$	−8.18055	−0.269998
$919$	24.3112	0.801953	0.400976	−	0.916088i	$-0.368671\pi$
$919$	24.3112	0.801953	0.400976	+	0.916088i	$0.368671\pi$
$920$	−11.7528	−0.387477
$921$	−22.7075	−0.748237
$922$	−7.54679	−0.248540
$923$	18.3429	0.603763
$924$	0.312955	0.0102955
$925$	3.22202	0.105939
$926$	−13.2906	−0.436757
$927$	−3.03189	−0.0995803
$928$	1.41726	0.0465240
$929$	−51.2662	−1.68199	−0.840994	−	0.541044i	$-0.818029\pi$
$929$	−51.2662	−1.68199	−0.840994	+	0.541044i	$0.818029\pi$
$930$	3.22864	0.105871
$931$	−8.36303	−0.274087
$932$	3.79291	0.124241
$933$	−35.4327	−1.16002
$934$	13.6695	0.447280
$935$	−2.15284	−0.0704054
$936$	13.5482	0.442836
$937$	−23.3885	−0.764070	−0.382035	−	0.924148i	$-0.624777\pi$
$937$	−23.3885	−0.764070	−0.382035	+	0.924148i	$0.624777\pi$
$938$	3.60338	0.117655
$939$	33.8079	1.10328
$940$	3.99816	0.130406
$941$	51.1535	1.66756	0.833778	−	0.552101i	$-0.186174\pi$
$941$	51.1535	1.66756	0.833778	+	0.552101i	$0.186174\pi$
$942$	28.6478	0.933396
$943$	−9.91431	−0.322854
$944$	−4.07791	−0.132725
$945$	−1.38238	−0.0449687
$946$	−11.6854	−0.379924
$947$	58.6733	1.90663	0.953313	−	0.301982i	$-0.0976484\pi$
$947$	58.6733	1.90663	0.953313	+	0.301982i	$0.0976484\pi$
$948$	9.55656	0.310383
$949$	−7.88200	−0.255861
$950$	−1.45033	−0.0470550
$951$	−18.6784	−0.605689
$952$	−0.920689	−0.0298397
$953$	33.5094	1.08548	0.542738	−	0.839902i	$-0.317388\pi$
$953$	33.5094	1.08548	0.542738	+	0.839902i	$0.317388\pi$
$954$	0.674766	0.0218464
$955$	2.32712	0.0753037
$956$	3.64443	0.117869
$957$	−1.07674	−0.0348059
$958$	1.22087	0.0394444
$959$	−3.80810	−0.122970
$960$	−11.4264	−0.368784
$961$	−26.7099	−0.861609
$962$	12.9385	0.417154
$963$	−21.4666	−0.691751
$964$	−11.9967	−0.386387
$965$	18.8659	0.607314
$966$	1.47303	0.0473940
$967$	34.0433	1.09476	0.547380	−	0.836885i	$-0.315625\pi$
$967$	34.0433	1.09476	0.547380	+	0.836885i	$0.315625\pi$
$968$	−24.1262	−0.775445
$969$	−1.89561	−0.0608958
$970$	−22.7011	−0.728887
$971$	−27.9091	−0.895646	−0.447823	−	0.894122i	$-0.647800\pi$
$971$	−27.9091	−0.895646	−0.447823	+	0.894122i	$0.647800\pi$
$972$	6.92030	0.221969
$973$	−1.32625	−0.0425175
$974$	15.5606	0.498593
$975$	4.32250	0.138431
$976$	35.4631	1.13515
$977$	17.9500	0.574272	0.287136	−	0.957890i	$-0.407297\pi$
$977$	17.9500	0.574272	0.287136	+	0.957890i	$0.407297\pi$
$978$	−3.65838	−0.116982
$979$	22.6684	0.724484
$980$	3.82948	0.122328
$981$	12.1543	0.388057
$982$	−11.8153	−0.377041
$983$	−30.9957	−0.988610	−0.494305	−	0.869289i	$-0.664577\pi$
$983$	−30.9957	−0.988610	−0.494305	+	0.869289i	$0.664577\pi$
$984$	−10.3046	−0.328497
$985$	−12.7507	−0.406272
$986$	0.685049	0.0218164
$987$	−2.31713	−0.0737551
$988$	2.21951	0.0706121
$989$	20.9608	0.666514
$990$	−2.82084	−0.0896523
$991$	7.55582	0.240019	0.120009	−	0.992773i	$-0.461708\pi$
$991$	7.55582	0.240019	0.120009	+	0.992773i	$0.461708\pi$
$992$	−6.26135	−0.198798
$993$	−11.9097	−0.377942
$994$	−1.63331	−0.0518053
$995$	16.1781	0.512882
$996$	1.78970	0.0567090
$997$	2.12604	0.0673323	0.0336662	−	0.999433i	$-0.489282\pi$
$997$	2.12604	0.0673323	0.0336662	+	0.999433i	$0.489282\pi$
$998$	−5.07885	−0.160768
$999$	18.0387	0.570720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.10	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.20338 q^{2} -1.29534 q^{3} -0.551875 q^{4} +1.00000 q^{5} +1.55878 q^{6} -0.246916 q^{7} +3.07088 q^{8} -1.32210 q^{9} +O(q^{10})\)	\(q-1.20338 q^{2} -1.29534 q^{3} -0.551875 q^{4} +1.00000 q^{5} +1.55878 q^{6} -0.246916 q^{7} +3.07088 q^{8} -1.32210 q^{9} -1.20338 q^{10} -1.77301 q^{11} +0.714864 q^{12} -3.33697 q^{13} +0.297134 q^{14} -1.29534 q^{15} -2.59168 q^{16} +1.21423 q^{17} +1.59099 q^{18} +1.20522 q^{19} -0.551875 q^{20} +0.319839 q^{21} +2.13360 q^{22} -3.82717 q^{23} -3.97782 q^{24} +1.00000 q^{25} +4.01564 q^{26} +5.59858 q^{27} +0.136267 q^{28} -0.468831 q^{29} +1.55878 q^{30} +2.07126 q^{31} -3.02297 q^{32} +2.29664 q^{33} -1.46118 q^{34} -0.246916 q^{35} +0.729637 q^{36} +3.22202 q^{37} -1.45033 q^{38} +4.32250 q^{39} +3.07088 q^{40} +2.59051 q^{41} -0.384888 q^{42} -5.47683 q^{43} +0.978478 q^{44} -1.32210 q^{45} +4.60554 q^{46} -7.24468 q^{47} +3.35710 q^{48} -6.93903 q^{49} -1.20338 q^{50} -1.57284 q^{51} +1.84159 q^{52} +0.424116 q^{53} -6.73722 q^{54} -1.77301 q^{55} -0.758248 q^{56} -1.56116 q^{57} +0.564183 q^{58} +1.57346 q^{59} +0.714864 q^{60} -13.6834 q^{61} -2.49251 q^{62} +0.326449 q^{63} +8.82115 q^{64} -3.33697 q^{65} -2.76373 q^{66} +12.1271 q^{67} -0.670104 q^{68} +4.95747 q^{69} +0.297134 q^{70} -5.49687 q^{71} -4.06002 q^{72} +2.36202 q^{73} -3.87732 q^{74} -1.29534 q^{75} -0.665128 q^{76} +0.437783 q^{77} -5.20161 q^{78} +13.3684 q^{79} -2.59168 q^{80} -3.28573 q^{81} -3.11736 q^{82} +2.50356 q^{83} -0.176511 q^{84} +1.21423 q^{85} +6.59071 q^{86} +0.607294 q^{87} -5.44468 q^{88} -12.7853 q^{89} +1.59099 q^{90} +0.823951 q^{91} +2.11212 q^{92} -2.68297 q^{93} +8.71811 q^{94} +1.20522 q^{95} +3.91576 q^{96} +18.8644 q^{97} +8.35030 q^{98} +2.34410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 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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