LMFDB - Embedded newform 2005.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0100056053$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.65420 q^{2} -1.14990 q^{3} +5.04475 q^{4} -1.00000 q^{5} +3.05206 q^{6} +2.92882 q^{7} -8.08137 q^{8} -1.67773 q^{9} +O(q^{10})$	\(q-2.65420 q^{2} -1.14990 q^{3} +5.04475 q^{4} -1.00000 q^{5} +3.05206 q^{6} +2.92882 q^{7} -8.08137 q^{8} -1.67773 q^{9} +2.65420 q^{10} -1.83471 q^{11} -5.80096 q^{12} +2.80189 q^{13} -7.77366 q^{14} +1.14990 q^{15} +11.3600 q^{16} +5.84483 q^{17} +4.45302 q^{18} -4.48755 q^{19} -5.04475 q^{20} -3.36785 q^{21} +4.86967 q^{22} -6.47656 q^{23} +9.29277 q^{24} +1.00000 q^{25} -7.43677 q^{26} +5.37892 q^{27} +14.7752 q^{28} +2.46390 q^{29} -3.05206 q^{30} -6.21921 q^{31} -13.9890 q^{32} +2.10973 q^{33} -15.5133 q^{34} -2.92882 q^{35} -8.46373 q^{36} +6.04534 q^{37} +11.9108 q^{38} -3.22190 q^{39} +8.08137 q^{40} +2.51795 q^{41} +8.93893 q^{42} -5.94597 q^{43} -9.25564 q^{44} +1.67773 q^{45} +17.1901 q^{46} -3.69540 q^{47} -13.0629 q^{48} +1.57799 q^{49} -2.65420 q^{50} -6.72097 q^{51} +14.1349 q^{52} -6.54608 q^{53} -14.2767 q^{54} +1.83471 q^{55} -23.6689 q^{56} +5.16023 q^{57} -6.53968 q^{58} -12.5414 q^{59} +5.80096 q^{60} +1.05280 q^{61} +16.5070 q^{62} -4.91377 q^{63} +14.4095 q^{64} -2.80189 q^{65} -5.59963 q^{66} +5.80793 q^{67} +29.4857 q^{68} +7.44740 q^{69} +7.77366 q^{70} -2.29241 q^{71} +13.5584 q^{72} +13.4813 q^{73} -16.0455 q^{74} -1.14990 q^{75} -22.6386 q^{76} -5.37352 q^{77} +8.55155 q^{78} +11.8228 q^{79} -11.3600 q^{80} -1.15203 q^{81} -6.68312 q^{82} +12.9874 q^{83} -16.9900 q^{84} -5.84483 q^{85} +15.7818 q^{86} -2.83324 q^{87} +14.8269 q^{88} -7.61328 q^{89} -4.45302 q^{90} +8.20624 q^{91} -32.6727 q^{92} +7.15147 q^{93} +9.80830 q^{94} +4.48755 q^{95} +16.0859 q^{96} -4.28227 q^{97} -4.18829 q^{98} +3.07814 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) $ 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * 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 $

$2$	−2.65420	−1.87680	−0.938400	−	0.345552i	$-0.887692\pi$
$2$	−2.65420	−1.87680	−0.938400	+	0.345552i	$0.887692\pi$
$3$	−1.14990	−0.663895	−0.331948	−	0.943298i	$-0.607706\pi$
$3$	−1.14990	−0.663895	−0.331948	+	0.943298i	$0.607706\pi$
$4$	5.04475	2.52238
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.05206	1.24600
$7$	2.92882	1.10699	0.553495	−	0.832852i	$-0.313294\pi$
$7$	2.92882	1.10699	0.553495	+	0.832852i	$0.313294\pi$
$8$	−8.08137	−2.85720
$9$	−1.67773	−0.559243
$10$	2.65420	0.839330
$11$	−1.83471	−0.553185	−0.276592	−	0.960987i	$-0.589205\pi$
$11$	−1.83471	−0.553185	−0.276592	+	0.960987i	$0.589205\pi$
$12$	−5.80096	−1.67459
$13$	2.80189	0.777106	0.388553	−	0.921426i	$-0.372975\pi$
$13$	2.80189	0.777106	0.388553	+	0.921426i	$0.372975\pi$
$14$	−7.77366	−2.07760
$15$	1.14990	0.296903
$16$	11.3600	2.84001
$17$	5.84483	1.41758	0.708790	−	0.705420i	$-0.249242\pi$
$17$	5.84483	1.41758	0.708790	+	0.705420i	$0.249242\pi$
$18$	4.45302	1.04959
$19$	−4.48755	−1.02951	−0.514757	−	0.857336i	$-0.672118\pi$
$19$	−4.48755	−1.02951	−0.514757	+	0.857336i	$0.672118\pi$
$20$	−5.04475	−1.12804
$21$	−3.36785	−0.734925
$22$	4.86967	1.03822
$23$	−6.47656	−1.35046	−0.675228	−	0.737609i	$-0.735955\pi$
$23$	−6.47656	−1.35046	−0.675228	+	0.737609i	$0.735955\pi$
$24$	9.29277	1.89688
$25$	1.00000	0.200000
$26$	−7.43677	−1.45847
$27$	5.37892	1.03517
$28$	14.7752	2.79225
$29$	2.46390	0.457535	0.228768	−	0.973481i	$-0.426530\pi$
$29$	2.46390	0.457535	0.228768	+	0.973481i	$0.426530\pi$
$30$	−3.05206	−0.557227
$31$	−6.21921	−1.11700	−0.558501	−	0.829504i	$-0.688623\pi$
$31$	−6.21921	−1.11700	−0.558501	+	0.829504i	$0.688623\pi$
$32$	−13.9890	−2.47293
$33$	2.10973	0.367257
$34$	−15.5133	−2.66051
$35$	−2.92882	−0.495061
$36$	−8.46373	−1.41062
$37$	6.04534	0.993848	0.496924	−	0.867794i	$-0.334463\pi$
$37$	6.04534	0.993848	0.496924	+	0.867794i	$0.334463\pi$
$38$	11.9108	1.93219
$39$	−3.22190	−0.515917
$40$	8.08137	1.27778
$41$	2.51795	0.393237	0.196618	−	0.980480i	$-0.437004\pi$
$41$	2.51795	0.393237	0.196618	+	0.980480i	$0.437004\pi$
$42$	8.93893	1.37931
$43$	−5.94597	−0.906751	−0.453376	−	0.891320i	$-0.649780\pi$
$43$	−5.94597	−0.906751	−0.453376	+	0.891320i	$0.649780\pi$
$44$	−9.25564	−1.39534
$45$	1.67773	0.250101
$46$	17.1901	2.53454
$47$	−3.69540	−0.539029	−0.269515	−	0.962996i	$-0.586863\pi$
$47$	−3.69540	−0.539029	−0.269515	+	0.962996i	$0.586863\pi$
$48$	−13.0629	−1.88547
$49$	1.57799	0.225427
$50$	−2.65420	−0.375360
$51$	−6.72097	−0.941124
$52$	14.1349	1.96015
$53$	−6.54608	−0.899173	−0.449586	−	0.893237i	$-0.648429\pi$
$53$	−6.54608	−0.899173	−0.449586	+	0.893237i	$0.648429\pi$
$54$	−14.2767	−1.94281
$55$	1.83471	0.247392
$56$	−23.6689	−3.16289
$57$	5.16023	0.683489
$58$	−6.53968	−0.858702
$59$	−12.5414	−1.63275	−0.816376	−	0.577521i	$-0.804020\pi$
$59$	−12.5414	−1.63275	−0.816376	+	0.577521i	$0.804020\pi$
$60$	5.80096	0.748901
$61$	1.05280	0.134797	0.0673985	−	0.997726i	$-0.478530\pi$
$61$	1.05280	0.134797	0.0673985	+	0.997726i	$0.478530\pi$
$62$	16.5070	2.09639
$63$	−4.91377	−0.619077
$64$	14.4095	1.80118
$65$	−2.80189	−0.347532
$66$	−5.59963	−0.689267
$67$	5.80793	0.709551	0.354776	−	0.934951i	$-0.384557\pi$
$67$	5.80793	0.709551	0.354776	+	0.934951i	$0.384557\pi$
$68$	29.4857	3.57567
$69$	7.44740	0.896561
$70$	7.77366	0.929130
$71$	−2.29241	−0.272059	−0.136030	−	0.990705i	$-0.543434\pi$
$71$	−2.29241	−0.272059	−0.136030	+	0.990705i	$0.543434\pi$
$72$	13.5584	1.59787
$73$	13.4813	1.57787	0.788934	−	0.614478i	$-0.210633\pi$
$73$	13.4813	1.57787	0.788934	+	0.614478i	$0.210633\pi$
$74$	−16.0455	−1.86525
$75$	−1.14990	−0.132779
$76$	−22.6386	−2.59682
$77$	−5.37352	−0.612370
$78$	8.55155	0.968272
$79$	11.8228	1.33017	0.665086	−	0.746767i	$-0.268395\pi$
$79$	11.8228	1.33017	0.665086	+	0.746767i	$0.268395\pi$
$80$	−11.3600	−1.27009
$81$	−1.15203	−0.128003
$82$	−6.68312	−0.738027
$83$	12.9874	1.42556	0.712778	−	0.701389i	$-0.247437\pi$
$83$	12.9874	1.42556	0.712778	+	0.701389i	$0.247437\pi$
$84$	−16.9900	−1.85376
$85$	−5.84483	−0.633961
$86$	15.7818	1.70179
$87$	−2.83324	−0.303755
$88$	14.8269	1.58056
$89$	−7.61328	−0.807006	−0.403503	−	0.914978i	$-0.632207\pi$
$89$	−7.61328	−0.807006	−0.403503	+	0.914978i	$0.632207\pi$
$90$	−4.45302	−0.469390
$91$	8.20624	0.860248
$92$	−32.6727	−3.40636
$93$	7.15147	0.741573
$94$	9.80830	1.01165
$95$	4.48755	0.460413
$96$	16.0859	1.64176
$97$	−4.28227	−0.434799	−0.217399	−	0.976083i	$-0.569757\pi$
$97$	−4.28227	−0.434799	−0.217399	+	0.976083i	$0.569757\pi$
$98$	−4.18829	−0.423081
$99$	3.07814	0.309365
$100$	5.04475	0.504475
$101$	9.94141	0.989207	0.494603	−	0.869119i	$-0.335313\pi$
$101$	9.94141	0.989207	0.494603	+	0.869119i	$0.335313\pi$
$102$	17.8388	1.76630
$103$	4.60875	0.454114	0.227057	−	0.973881i	$-0.427090\pi$
$103$	4.60875	0.454114	0.227057	+	0.973881i	$0.427090\pi$
$104$	−22.6431	−2.22034
$105$	3.36785	0.328669
$106$	17.3746	1.68757
$107$	−3.63477	−0.351386	−0.175693	−	0.984445i	$-0.556217\pi$
$107$	−3.63477	−0.351386	−0.175693	+	0.984445i	$0.556217\pi$
$108$	27.1353	2.61110
$109$	14.5676	1.39532	0.697662	−	0.716427i	$-0.254224\pi$
$109$	14.5676	1.39532	0.697662	+	0.716427i	$0.254224\pi$
$110$	−4.86967	−0.464305
$111$	−6.95154	−0.659811
$112$	33.2715	3.14386
$113$	−12.3108	−1.15810	−0.579052	−	0.815290i	$-0.696577\pi$
$113$	−12.3108	−1.15810	−0.579052	+	0.815290i	$0.696577\pi$
$114$	−13.6963	−1.28277
$115$	6.47656	0.603942
$116$	12.4298	1.15408
$117$	−4.70082	−0.434591
$118$	33.2873	3.06435
$119$	17.1185	1.56925
$120$	−9.29277	−0.848310
$121$	−7.63385	−0.693987
$122$	−2.79433	−0.252987
$123$	−2.89539	−0.261068
$124$	−31.3744	−2.81750
$125$	−1.00000	−0.0894427
$126$	13.0421	1.16188
$127$	−4.13901	−0.367278	−0.183639	−	0.982994i	$-0.558788\pi$
$127$	−4.13901	−0.367278	−0.183639	+	0.982994i	$0.558788\pi$
$128$	−10.2675	−0.907531
$129$	6.83727	0.601988
$130$	7.43677	0.652248
$131$	−20.0070	−1.74802	−0.874012	−	0.485904i	$-0.838490\pi$
$131$	−20.0070	−1.74802	−0.874012	+	0.485904i	$0.838490\pi$
$132$	10.6431	0.926359
$133$	−13.1432	−1.13966
$134$	−15.4154	−1.33169
$135$	−5.37892	−0.462944
$136$	−47.2342	−4.05030
$137$	10.4563	0.893345	0.446673	−	0.894697i	$-0.352609\pi$
$137$	10.4563	0.893345	0.446673	+	0.894697i	$0.352609\pi$
$138$	−19.7668	−1.68267
$139$	0.595621	0.0505199	0.0252600	−	0.999681i	$-0.491959\pi$
$139$	0.595621	0.0505199	0.0252600	+	0.999681i	$0.491959\pi$
$140$	−14.7752	−1.24873
$141$	4.24934	0.357859
$142$	6.08451	0.510600
$143$	−5.14065	−0.429883
$144$	−19.0591	−1.58825
$145$	−2.46390	−0.204616
$146$	−35.7820	−2.96134
$147$	−1.81453	−0.149660
$148$	30.4973	2.50686
$149$	−8.26598	−0.677176	−0.338588	−	0.940935i	$-0.609949\pi$
$149$	−8.26598	−0.677176	−0.338588	+	0.940935i	$0.609949\pi$
$150$	3.05206	0.249200
$151$	−11.9233	−0.970305	−0.485152	−	0.874430i	$-0.661236\pi$
$151$	−11.9233	−0.970305	−0.485152	+	0.874430i	$0.661236\pi$
$152$	36.2655	2.94152
$153$	−9.80605	−0.792772
$154$	14.2624	1.14930
$155$	6.21921	0.499539
$156$	−16.2537	−1.30134
$157$	−16.7446	−1.33637	−0.668183	−	0.743997i	$-0.732928\pi$
$157$	−16.7446	−1.33637	−0.668183	+	0.743997i	$0.732928\pi$
$158$	−31.3801	−2.49647
$159$	7.52733	0.596956
$160$	13.9890	1.10593
$161$	−18.9687	−1.49494
$162$	3.05772	0.240237
$163$	−2.98684	−0.233947	−0.116974	−	0.993135i	$-0.537319\pi$
$163$	−2.98684	−0.233947	−0.116974	+	0.993135i	$0.537319\pi$
$164$	12.7024	0.991892
$165$	−2.10973	−0.164242
$166$	−34.4712	−2.67548
$167$	10.7306	0.830360	0.415180	−	0.909739i	$-0.363719\pi$
$167$	10.7306	0.830360	0.415180	+	0.909739i	$0.363719\pi$
$168$	27.2168	2.09982
$169$	−5.14939	−0.396107
$170$	15.5133	1.18982
$171$	7.52890	0.575749
$172$	−29.9959	−2.28717
$173$	−2.67862	−0.203651	−0.101826	−	0.994802i	$-0.532468\pi$
$173$	−2.67862	−0.203651	−0.101826	+	0.994802i	$0.532468\pi$
$174$	7.51997	0.570088
$175$	2.92882	0.221398
$176$	−20.8423	−1.57105
$177$	14.4214	1.08398
$178$	20.2071	1.51459
$179$	7.81069	0.583799	0.291899	−	0.956449i	$-0.405713\pi$
$179$	7.81069	0.583799	0.291899	+	0.956449i	$0.405713\pi$
$180$	8.46373	0.630849
$181$	−20.8450	−1.54940	−0.774698	−	0.632332i	$-0.782098\pi$
$181$	−20.8450	−1.54940	−0.774698	+	0.632332i	$0.782098\pi$
$182$	−21.7810	−1.61451
$183$	−1.21061	−0.0894911
$184$	52.3395	3.85852
$185$	−6.04534	−0.444462
$186$	−18.9814	−1.39178
$187$	−10.7235	−0.784183
$188$	−18.6424	−1.35963
$189$	15.7539	1.14593
$190$	−11.9108	−0.864102
$191$	5.34034	0.386413	0.193207	−	0.981158i	$-0.438111\pi$
$191$	5.34034	0.386413	0.193207	+	0.981158i	$0.438111\pi$
$192$	−16.5694	−1.19580
$193$	−3.25338	−0.234184	−0.117092	−	0.993121i	$-0.537357\pi$
$193$	−3.25338	−0.234184	−0.117092	+	0.993121i	$0.537357\pi$
$194$	11.3660	0.816030
$195$	3.22190	0.230725
$196$	7.96056	0.568612
$197$	−12.3689	−0.881247	−0.440624	−	0.897692i	$-0.645243\pi$
$197$	−12.3689	−0.881247	−0.440624	+	0.897692i	$0.645243\pi$
$198$	−8.16999	−0.580616
$199$	−6.04661	−0.428633	−0.214316	−	0.976764i	$-0.568752\pi$
$199$	−6.04661	−0.428633	−0.214316	+	0.976764i	$0.568752\pi$
$200$	−8.08137	−0.571439
$201$	−6.67854	−0.471068
$202$	−26.3864	−1.85654
$203$	7.21633	0.506487
$204$	−33.9056	−2.37387
$205$	−2.51795	−0.175861
$206$	−12.2325	−0.852281
$207$	10.8659	0.755234
$208$	31.8296	2.20699
$209$	8.23333	0.569512
$210$	−8.93893	−0.616845
$211$	−5.56057	−0.382806	−0.191403	−	0.981512i	$-0.561304\pi$
$211$	−5.56057	−0.382806	−0.191403	+	0.981512i	$0.561304\pi$
$212$	−33.0233	−2.26805
$213$	2.63604	0.180619
$214$	9.64739	0.659482
$215$	5.94597	0.405512
$216$	−43.4691	−2.95769
$217$	−18.2149	−1.23651
$218$	−38.6653	−2.61874
$219$	−15.5022	−1.04754
$220$	9.25564	0.624015
$221$	16.3766	1.10161
$222$	18.4507	1.23833
$223$	−24.3344	−1.62956	−0.814778	−	0.579774i	$-0.803141\pi$
$223$	−24.3344	−1.62956	−0.814778	+	0.579774i	$0.803141\pi$
$224$	−40.9712	−2.73751
$225$	−1.67773	−0.111849
$226$	32.6753	2.17353
$227$	−26.2692	−1.74355	−0.871775	−	0.489906i	$-0.837031\pi$
$227$	−26.2692	−1.74355	−0.871775	+	0.489906i	$0.837031\pi$
$228$	26.0321	1.72402
$229$	−25.4311	−1.68053	−0.840266	−	0.542175i	$-0.817601\pi$
$229$	−25.4311	−1.68053	−0.840266	+	0.542175i	$0.817601\pi$
$230$	−17.1901	−1.13348
$231$	6.17902	0.406549
$232$	−19.9117	−1.30727
$233$	−14.8137	−0.970479	−0.485239	−	0.874381i	$-0.661268\pi$
$233$	−14.8137	−0.970479	−0.485239	+	0.874381i	$0.661268\pi$
$234$	12.4769	0.815641
$235$	3.69540	0.241061
$236$	−63.2683	−4.11841
$237$	−13.5951	−0.883095
$238$	−45.4357	−2.94516
$239$	23.3386	1.50965	0.754824	−	0.655928i	$-0.227722\pi$
$239$	23.3386	1.50965	0.754824	+	0.655928i	$0.227722\pi$
$240$	13.0629	0.843206
$241$	25.4022	1.63630	0.818149	−	0.575007i	$-0.195000\pi$
$241$	25.4022	1.63630	0.818149	+	0.575007i	$0.195000\pi$
$242$	20.2617	1.30247
$243$	−14.8120	−0.950193
$244$	5.31111	0.340009
$245$	−1.57799	−0.100814
$246$	7.68492	0.489972
$247$	−12.5736	−0.800041
$248$	50.2597	3.19149
$249$	−14.9343	−0.946420
$250$	2.65420	0.167866
$251$	−19.6555	−1.24064	−0.620321	−	0.784348i	$-0.712998\pi$
$251$	−19.6555	−1.24064	−0.620321	+	0.784348i	$0.712998\pi$
$252$	−24.7888	−1.56154
$253$	11.8826	0.747052
$254$	10.9858	0.689307
$255$	6.72097	0.420883
$256$	−1.56686	−0.0979285
$257$	8.49355	0.529813	0.264906	−	0.964274i	$-0.414659\pi$
$257$	8.49355	0.529813	0.264906	+	0.964274i	$0.414659\pi$
$258$	−18.1474	−1.12981
$259$	17.7057	1.10018
$260$	−14.1349	−0.876607
$261$	−4.13376	−0.255873
$262$	53.1026	3.28069
$263$	2.24561	0.138470	0.0692351	−	0.997600i	$-0.477944\pi$
$263$	2.24561	0.138470	0.0692351	+	0.997600i	$0.477944\pi$
$264$	−17.0495	−1.04932
$265$	6.54608	0.402122
$266$	34.8847	2.13892
$267$	8.75451	0.535767
$268$	29.2996	1.78976
$269$	−4.09952	−0.249952	−0.124976	−	0.992160i	$-0.539885\pi$
$269$	−4.09952	−0.249952	−0.124976	+	0.992160i	$0.539885\pi$
$270$	14.2767	0.868853
$271$	−3.78887	−0.230157	−0.115079	−	0.993356i	$-0.536712\pi$
$271$	−3.78887	−0.230157	−0.115079	+	0.993356i	$0.536712\pi$
$272$	66.3974	4.02593
$273$	−9.43636	−0.571115
$274$	−27.7532	−1.67663
$275$	−1.83471	−0.110637
$276$	37.5703	2.26147
$277$	−25.5146	−1.53302	−0.766512	−	0.642230i	$-0.778009\pi$
$277$	−25.5146	−1.53302	−0.766512	+	0.642230i	$0.778009\pi$
$278$	−1.58090	−0.0948158
$279$	10.4342	0.624676
$280$	23.6689	1.41449
$281$	−6.81978	−0.406834	−0.203417	−	0.979092i	$-0.565205\pi$
$281$	−6.81978	−0.406834	−0.203417	+	0.979092i	$0.565205\pi$
$282$	−11.2786	−0.671629
$283$	−8.21621	−0.488403	−0.244202	−	0.969724i	$-0.578526\pi$
$283$	−8.21621	−0.488403	−0.244202	+	0.969724i	$0.578526\pi$
$284$	−11.5646	−0.686235
$285$	−5.16023	−0.305666
$286$	13.6443	0.806804
$287$	7.37461	0.435309
$288$	23.4698	1.38297
$289$	17.1620	1.00953
$290$	6.53968	0.384023
$291$	4.92418	0.288661
$292$	68.0099	3.97998
$293$	22.9920	1.34321	0.671603	−	0.740911i	$-0.265606\pi$
$293$	22.9920	1.34321	0.671603	+	0.740911i	$0.265606\pi$
$294$	4.81611	0.280881
$295$	12.5414	0.730189
$296$	−48.8546	−2.83962
$297$	−9.86874	−0.572642
$298$	21.9395	1.27092
$299$	−18.1466	−1.04945
$300$	−5.80096	−0.334919
$301$	−17.4147	−1.00376
$302$	31.6468	1.82107
$303$	−11.4316	−0.656729
$304$	−50.9787	−2.92383
$305$	−1.05280	−0.0602831
$306$	26.0272	1.48787
$307$	−23.7229	−1.35394	−0.676968	−	0.736012i	$-0.736707\pi$
$307$	−23.7229	−1.35394	−0.676968	+	0.736012i	$0.736707\pi$
$308$	−27.1081	−1.54463
$309$	−5.29961	−0.301484
$310$	−16.5070	−0.937534
$311$	−13.2894	−0.753571	−0.376785	−	0.926301i	$-0.622971\pi$
$311$	−13.2894	−0.753571	−0.376785	+	0.926301i	$0.622971\pi$
$312$	26.0373	1.47407
$313$	−26.6710	−1.50753	−0.753766	−	0.657143i	$-0.771765\pi$
$313$	−26.6710	−1.50753	−0.753766	+	0.657143i	$0.771765\pi$
$314$	44.4435	2.50809
$315$	4.91377	0.276860
$316$	59.6433	3.35520
$317$	−0.737242	−0.0414076	−0.0207038	−	0.999786i	$-0.506591\pi$
$317$	−0.737242	−0.0414076	−0.0207038	+	0.999786i	$0.506591\pi$
$318$	−19.9790	−1.12037
$319$	−4.52054	−0.253101
$320$	−14.4095	−0.805513
$321$	4.17962	0.233284
$322$	50.3466	2.80571
$323$	−26.2290	−1.45942
$324$	−5.81171	−0.322873
$325$	2.80189	0.155421
$326$	7.92765	0.439072
$327$	−16.7513	−0.926349
$328$	−20.3484	−1.12355
$329$	−10.8232	−0.596700
$330$	5.59963	0.308250
$331$	−1.62058	−0.0890749	−0.0445374	−	0.999008i	$-0.514181\pi$
$331$	−1.62058	−0.0890749	−0.0445374	+	0.999008i	$0.514181\pi$
$332$	65.5184	3.59579
$333$	−10.1425	−0.555803
$334$	−28.4812	−1.55842
$335$	−5.80793	−0.317321
$336$	−38.2589	−2.08719
$337$	20.3139	1.10657	0.553283	−	0.832993i	$-0.313375\pi$
$337$	20.3139	1.10657	0.553283	+	0.832993i	$0.313375\pi$
$338$	13.6675	0.743413
$339$	14.1562	0.768860
$340$	−29.4857	−1.59909
$341$	11.4104	0.617909
$342$	−19.9832	−1.08057
$343$	−15.8801	−0.857445
$344$	48.0515	2.59077
$345$	−7.44740	−0.400954
$346$	7.10957	0.382213
$347$	32.3521	1.73675	0.868376	−	0.495906i	$-0.165164\pi$
$347$	32.3521	1.73675	0.868376	+	0.495906i	$0.165164\pi$
$348$	−14.2930	−0.766185
$349$	−14.7244	−0.788180	−0.394090	−	0.919072i	$-0.628940\pi$
$349$	−14.7244	−0.788180	−0.394090	+	0.919072i	$0.628940\pi$
$350$	−7.77366	−0.415520
$351$	15.0712	0.804440
$352$	25.6657	1.36799
$353$	32.5701	1.73353	0.866767	−	0.498714i	$-0.166194\pi$
$353$	32.5701	1.73353	0.866767	+	0.498714i	$0.166194\pi$
$354$	−38.2771	−2.03440
$355$	2.29241	0.121669
$356$	−38.4071	−2.03557
$357$	−19.6845	−1.04181
$358$	−20.7311	−1.09567
$359$	−1.04087	−0.0549352	−0.0274676	−	0.999623i	$-0.508744\pi$
$359$	−1.04087	−0.0549352	−0.0274676	+	0.999623i	$0.508744\pi$
$360$	−13.5584	−0.714588
$361$	1.13809	0.0598995
$362$	55.3267	2.90790
$363$	8.77817	0.460734
$364$	41.3985	2.16987
$365$	−13.4813	−0.705644
$366$	3.21320	0.167957
$367$	−33.5632	−1.75198	−0.875992	−	0.482326i	$-0.839792\pi$
$367$	−33.5632	−1.75198	−0.875992	+	0.482326i	$0.839792\pi$
$368$	−73.5739	−3.83531
$369$	−4.22443	−0.219915
$370$	16.0455	0.834167
$371$	−19.1723	−0.995375
$372$	36.0774	1.87053
$373$	−23.7743	−1.23098	−0.615492	−	0.788143i	$-0.711043\pi$
$373$	−23.7743	−1.23098	−0.615492	+	0.788143i	$0.711043\pi$
$374$	28.4624	1.47175
$375$	1.14990	0.0593806
$376$	29.8639	1.54011
$377$	6.90359	0.355553
$378$	−41.8139	−2.15068
$379$	−12.5559	−0.644951	−0.322476	−	0.946578i	$-0.604515\pi$
$379$	−12.5559	−0.644951	−0.322476	+	0.946578i	$0.604515\pi$
$380$	22.6386	1.16133
$381$	4.75945	0.243834
$382$	−14.1743	−0.725221
$383$	−17.8828	−0.913770	−0.456885	−	0.889526i	$-0.651035\pi$
$383$	−17.8828	−0.913770	−0.456885	+	0.889526i	$0.651035\pi$
$384$	11.8066	0.602505
$385$	5.37352	0.273860
$386$	8.63512	0.439516
$387$	9.97573	0.507095
$388$	−21.6030	−1.09673
$389$	9.86945	0.500401	0.250200	−	0.968194i	$-0.419503\pi$
$389$	9.86945	0.500401	0.250200	+	0.968194i	$0.419503\pi$
$390$	−8.55155	−0.433024
$391$	−37.8544	−1.91438
$392$	−12.7523	−0.644089
$393$	23.0061	1.16050
$394$	32.8295	1.65392
$395$	−11.8228	−0.594871
$396$	15.5285	0.780335
$397$	8.42215	0.422695	0.211348	−	0.977411i	$-0.432215\pi$
$397$	8.42215	0.422695	0.211348	+	0.977411i	$0.432215\pi$
$398$	16.0489	0.804458
$399$	15.1134	0.756616
$400$	11.3600	0.568001
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	17.7261	0.884100
$403$	−17.4256	−0.868029
$404$	50.1519	2.49515
$405$	1.15203	0.0572449
$406$	−19.1535	−0.950574
$407$	−11.0914	−0.549782
$408$	54.3146	2.68897
$409$	27.0517	1.33762	0.668811	−	0.743433i	$-0.266804\pi$
$409$	27.0517	1.33762	0.668811	+	0.743433i	$0.266804\pi$
$410$	6.68312	0.330056
$411$	−12.0237	−0.593087
$412$	23.2500	1.14545
$413$	−36.7315	−1.80744
$414$	−28.8403	−1.41742
$415$	−12.9874	−0.637528
$416$	−39.1957	−1.92173
$417$	−0.684905	−0.0335399
$418$	−21.8529	−1.06886
$419$	−17.5840	−0.859033	−0.429517	−	0.903059i	$-0.641316\pi$
$419$	−17.5840	−0.859033	−0.429517	+	0.903059i	$0.641316\pi$
$420$	16.9900	0.829026
$421$	23.8796	1.16382	0.581909	−	0.813254i	$-0.302306\pi$
$421$	23.8796	1.16382	0.581909	+	0.813254i	$0.302306\pi$
$422$	14.7589	0.718450
$423$	6.19988	0.301448
$424$	52.9013	2.56911
$425$	5.84483	0.283516
$426$	−6.99657	−0.338985
$427$	3.08346	0.149219
$428$	−18.3365	−0.886329
$429$	5.91124	0.285397
$430$	−15.7818	−0.761064
$431$	−3.44546	−0.165962	−0.0829810	−	0.996551i	$-0.526444\pi$
$431$	−3.44546	−0.165962	−0.0829810	+	0.996551i	$0.526444\pi$
$432$	61.1047	2.93990
$433$	−25.9792	−1.24848	−0.624241	−	0.781232i	$-0.714592\pi$
$433$	−25.9792	−1.24848	−0.624241	+	0.781232i	$0.714592\pi$
$434$	48.3460	2.32068
$435$	2.83324	0.135843
$436$	73.4900	3.51953
$437$	29.0639	1.39031
$438$	41.1457	1.96602
$439$	31.7480	1.51525	0.757626	−	0.652689i	$-0.226359\pi$
$439$	31.7480	1.51525	0.757626	+	0.652689i	$0.226359\pi$
$440$	−14.8269	−0.706847
$441$	−2.64744	−0.126069
$442$	−43.4667	−2.06750
$443$	−23.7452	−1.12817	−0.564084	−	0.825718i	$-0.690771\pi$
$443$	−23.7452	−1.12817	−0.564084	+	0.825718i	$0.690771\pi$
$444$	−35.0688	−1.66429
$445$	7.61328	0.360904
$446$	64.5884	3.05835
$447$	9.50505	0.449574
$448$	42.2027	1.99389
$449$	−27.1548	−1.28151	−0.640757	−	0.767744i	$-0.721379\pi$
$449$	−27.1548	−1.28151	−0.640757	+	0.767744i	$0.721379\pi$
$450$	4.45302	0.209918
$451$	−4.61969	−0.217533
$452$	−62.1051	−2.92118
$453$	13.7106	0.644181
$454$	69.7237	3.27230
$455$	−8.20624	−0.384715
$456$	−41.7017	−1.95286
$457$	26.0654	1.21929	0.609644	−	0.792675i	$-0.291312\pi$
$457$	26.0654	1.21929	0.609644	+	0.792675i	$0.291312\pi$
$458$	67.4990	3.15402
$459$	31.4389	1.46744
$460$	32.6727	1.52337
$461$	−16.1490	−0.752132	−0.376066	−	0.926593i	$-0.622723\pi$
$461$	−16.1490	−0.752132	−0.376066	+	0.926593i	$0.622723\pi$
$462$	−16.4003	−0.763012
$463$	15.2689	0.709607	0.354804	−	0.934941i	$-0.384548\pi$
$463$	15.2689	0.709607	0.354804	+	0.934941i	$0.384548\pi$
$464$	27.9900	1.29940
$465$	−7.15147	−0.331641
$466$	39.3185	1.82139
$467$	34.7323	1.60722	0.803611	−	0.595155i	$-0.202910\pi$
$467$	34.7323	1.60722	0.803611	+	0.595155i	$0.202910\pi$
$468$	−23.7145	−1.09620
$469$	17.0104	0.785466
$470$	−9.80830	−0.452423
$471$	19.2546	0.887207
$472$	101.352	4.66509
$473$	10.9091	0.501601
$474$	36.0840	1.65739
$475$	−4.48755	−0.205903
$476$	86.3584	3.95823
$477$	10.9825	0.502856
$478$	−61.9452	−2.83331
$479$	11.3872	0.520294	0.260147	−	0.965569i	$-0.416229\pi$
$479$	11.3872	0.520294	0.260147	+	0.965569i	$0.416229\pi$
$480$	−16.0859	−0.734219
$481$	16.9384	0.772325
$482$	−67.4223	−3.07100
$483$	21.8121	0.992484
$484$	−38.5109	−1.75050
$485$	4.28227	0.194448
$486$	39.3141	1.78332
$487$	5.36013	0.242891	0.121445	−	0.992598i	$-0.461247\pi$
$487$	5.36013	0.242891	0.121445	+	0.992598i	$0.461247\pi$
$488$	−8.50805	−0.385141
$489$	3.43456	0.155316
$490$	4.18829	0.189208
$491$	−9.84998	−0.444523	−0.222262	−	0.974987i	$-0.571344\pi$
$491$	−9.84998	−0.444523	−0.222262	+	0.974987i	$0.571344\pi$
$492$	−14.6065	−0.658512
$493$	14.4011	0.648592
$494$	33.3729	1.50152
$495$	−3.07814	−0.138352
$496$	−70.6504	−3.17229
$497$	−6.71406	−0.301167
$498$	39.6384	1.77624
$499$	−7.03606	−0.314977	−0.157489	−	0.987521i	$-0.550340\pi$
$499$	−7.03606	−0.314977	−0.157489	+	0.987521i	$0.550340\pi$
$500$	−5.04475	−0.225608
$501$	−12.3391	−0.551272
$502$	52.1695	2.32844
$503$	12.0360	0.536657	0.268329	−	0.963327i	$-0.413529\pi$
$503$	12.0360	0.536657	0.268329	+	0.963327i	$0.413529\pi$
$504$	39.7100	1.76882
$505$	−9.94141	−0.442387
$506$	−31.5387	−1.40207
$507$	5.92128	0.262973
$508$	−20.8803	−0.926414
$509$	2.19794	0.0974222	0.0487111	−	0.998813i	$-0.484489\pi$
$509$	2.19794	0.0974222	0.0487111	+	0.998813i	$0.484489\pi$
$510$	−17.8388	−0.789914
$511$	39.4843	1.74668
$512$	24.6938	1.09132
$513$	−24.1382	−1.06573
$514$	−22.5435	−0.994353
$515$	−4.60875	−0.203086
$516$	34.4923	1.51844
$517$	6.77997	0.298183
$518$	−46.9944	−2.06482
$519$	3.08014	0.135203
$520$	22.6431	0.992967
$521$	−1.39104	−0.0609428	−0.0304714	−	0.999536i	$-0.509701\pi$
$521$	−1.39104	−0.0609428	−0.0304714	+	0.999536i	$0.509701\pi$
$522$	10.9718	0.480223
$523$	−34.4323	−1.50562	−0.752809	−	0.658239i	$-0.771302\pi$
$523$	−34.4323	−1.50562	−0.752809	+	0.658239i	$0.771302\pi$
$524$	−100.931	−4.40917
$525$	−3.36785	−0.146985
$526$	−5.96029	−0.259881
$527$	−36.3502	−1.58344
$528$	23.9666	1.04301
$529$	18.9458	0.823733
$530$	−17.3746	−0.754703
$531$	21.0411	0.913105
$532$	−66.3043	−2.87466
$533$	7.05502	0.305587
$534$	−23.2362	−1.00553
$535$	3.63477	0.157145
$536$	−46.9360	−2.02733
$537$	−8.98152	−0.387581
$538$	10.8809	0.469110
$539$	−2.89515	−0.124703
$540$	−27.1353	−1.16772
$541$	−36.4741	−1.56814	−0.784072	−	0.620670i	$-0.786861\pi$
$541$	−36.4741	−1.56814	−0.784072	+	0.620670i	$0.786861\pi$
$542$	10.0564	0.431959
$543$	23.9696	1.02864
$544$	−81.7633	−3.50557
$545$	−14.5676	−0.624008
$546$	25.0459	1.07187
$547$	18.7078	0.799887	0.399943	−	0.916540i	$-0.369030\pi$
$547$	18.7078	0.799887	0.399943	+	0.916540i	$0.369030\pi$
$548$	52.7496	2.25335
$549$	−1.76631	−0.0753843
$550$	4.86967	0.207643
$551$	−11.0569	−0.471039
$552$	−60.1852	−2.56165
$553$	34.6270	1.47249
$554$	67.7207	2.87718
$555$	6.95154	0.295076
$556$	3.00476	0.127430
$557$	−35.4329	−1.50134	−0.750669	−	0.660678i	$-0.770269\pi$
$557$	−35.4329	−1.50134	−0.750669	+	0.660678i	$0.770269\pi$
$558$	−27.6943	−1.17239
$559$	−16.6600	−0.704642
$560$	−33.2715	−1.40598
$561$	12.3310	0.520615
$562$	18.1010	0.763545
$563$	39.7148	1.67378	0.836891	−	0.547370i	$-0.184371\pi$
$563$	39.7148	1.67378	0.836891	+	0.547370i	$0.184371\pi$
$564$	21.4369	0.902654
$565$	12.3108	0.517920
$566$	21.8074	0.916635
$567$	−3.37409	−0.141699
$568$	18.5258	0.777326
$569$	−17.4451	−0.731335	−0.365668	−	0.930745i	$-0.619159\pi$
$569$	−17.4451	−0.731335	−0.365668	+	0.930745i	$0.619159\pi$
$570$	13.6963	0.573673
$571$	−9.56425	−0.400251	−0.200126	−	0.979770i	$-0.564135\pi$
$571$	−9.56425	−0.400251	−0.200126	+	0.979770i	$0.564135\pi$
$572$	−25.9333	−1.08433
$573$	−6.14086	−0.256538
$574$	−19.5737	−0.816989
$575$	−6.47656	−0.270091
$576$	−24.1752	−1.00730
$577$	18.7684	0.781339	0.390669	−	0.920531i	$-0.372244\pi$
$577$	18.7684	0.781339	0.390669	+	0.920531i	$0.372244\pi$
$578$	−45.5514	−1.89469
$579$	3.74107	0.155473
$580$	−12.4298	−0.516118
$581$	38.0379	1.57808
$582$	−13.0697	−0.541758
$583$	12.0101	0.497409
$584$	−108.947	−4.50828
$585$	4.70082	0.194355
$586$	−61.0252	−2.52093
$587$	8.94177	0.369066	0.184533	−	0.982826i	$-0.440923\pi$
$587$	8.94177	0.369066	0.184533	+	0.982826i	$0.440923\pi$
$588$	−9.15385	−0.377498
$589$	27.9090	1.14997
$590$	−33.2873	−1.37042
$591$	14.2230	0.585056
$592$	68.6753	2.82254
$593$	20.7986	0.854094	0.427047	−	0.904229i	$-0.359554\pi$
$593$	20.7986	0.854094	0.427047	+	0.904229i	$0.359554\pi$
$594$	26.1936	1.07474
$595$	−17.1185	−0.701788
$596$	−41.6998	−1.70809
$597$	6.95299	0.284567
$598$	48.1647	1.96960
$599$	−5.30140	−0.216609	−0.108305	−	0.994118i	$-0.534542\pi$
$599$	−5.30140	−0.216609	−0.108305	+	0.994118i	$0.534542\pi$
$600$	9.29277	0.379376
$601$	−45.2331	−1.84510	−0.922549	−	0.385880i	$-0.873898\pi$
$601$	−45.2331	−1.84510	−0.922549	+	0.385880i	$0.873898\pi$
$602$	46.2219	1.88387
$603$	−9.74414	−0.396812
$604$	−60.1501	−2.44747
$605$	7.63385	0.310360
$606$	30.3418	1.23255
$607$	28.2818	1.14792	0.573961	−	0.818883i	$-0.305406\pi$
$607$	28.2818	1.14792	0.573961	+	0.818883i	$0.305406\pi$
$608$	62.7763	2.54591
$609$	−8.29805	−0.336254
$610$	2.79433	0.113139
$611$	−10.3541	−0.418882
$612$	−49.4691	−1.99967
$613$	−6.40526	−0.258706	−0.129353	−	0.991599i	$-0.541290\pi$
$613$	−6.40526	−0.258706	−0.129353	+	0.991599i	$0.541290\pi$
$614$	62.9652	2.54107
$615$	2.89539	0.116753
$616$	43.4254	1.74966
$617$	15.3964	0.619836	0.309918	−	0.950763i	$-0.399698\pi$
$617$	15.3964	0.619836	0.309918	+	0.950763i	$0.399698\pi$
$618$	14.0662	0.565825
$619$	−10.8398	−0.435690	−0.217845	−	0.975983i	$-0.569903\pi$
$619$	−10.8398	−0.435690	−0.217845	+	0.975983i	$0.569903\pi$
$620$	31.3744	1.26002
$621$	−34.8369	−1.39796
$622$	35.2726	1.41430
$623$	−22.2979	−0.893347
$624$	−36.6008	−1.46521
$625$	1.00000	0.0400000
$626$	70.7900	2.82934
$627$	−9.46751	−0.378096
$628$	−84.4725	−3.37082
$629$	35.3340	1.40886
$630$	−13.0421	−0.519610
$631$	6.18688	0.246296	0.123148	−	0.992388i	$-0.460701\pi$
$631$	6.18688	0.246296	0.123148	+	0.992388i	$0.460701\pi$
$632$	−95.5447	−3.80056
$633$	6.39410	0.254143
$634$	1.95678	0.0777138
$635$	4.13901	0.164252
$636$	37.9735	1.50575
$637$	4.42136	0.175181
$638$	11.9984	0.475021
$639$	3.84605	0.152147
$640$	10.2675	0.405860
$641$	23.2063	0.916592	0.458296	−	0.888800i	$-0.348460\pi$
$641$	23.2063	0.916592	0.458296	+	0.888800i	$0.348460\pi$
$642$	−11.0935	−0.437827
$643$	−6.54325	−0.258040	−0.129020	−	0.991642i	$-0.541183\pi$
$643$	−6.54325	−0.258040	−0.129020	+	0.991642i	$0.541183\pi$
$644$	−95.6923	−3.77081
$645$	−6.83727	−0.269217
$646$	69.6168	2.73903
$647$	−33.5048	−1.31721	−0.658604	−	0.752490i	$-0.728853\pi$
$647$	−33.5048	−1.31721	−0.658604	+	0.752490i	$0.728853\pi$
$648$	9.30999	0.365731
$649$	23.0098	0.903213
$650$	−7.43677	−0.291694
$651$	20.9454	0.820913
$652$	−15.0678	−0.590102
$653$	−24.5732	−0.961625	−0.480813	−	0.876823i	$-0.659658\pi$
$653$	−24.5732	−0.961625	−0.480813	+	0.876823i	$0.659658\pi$
$654$	44.4612	1.73857
$655$	20.0070	0.781740
$656$	28.6039	1.11680
$657$	−22.6180	−0.882412
$658$	28.7268	1.11989
$659$	40.5517	1.57967	0.789835	−	0.613320i	$-0.210166\pi$
$659$	40.5517	1.57967	0.789835	+	0.613320i	$0.210166\pi$
$660$	−10.6431	−0.414281
$661$	0.690433	0.0268547	0.0134274	−	0.999910i	$-0.495726\pi$
$661$	0.690433	0.0268547	0.0134274	+	0.999910i	$0.495726\pi$
$662$	4.30132	0.167176
$663$	−18.8314	−0.731353
$664$	−104.956	−4.07309
$665$	13.1432	0.509672
$666$	26.9201	1.04313
$667$	−15.9576	−0.617881
$668$	54.1333	2.09448
$669$	27.9822	1.08185
$670$	15.4154	0.595548
$671$	−1.93158	−0.0745677
$672$	47.1128	1.81742
$673$	22.1979	0.855666	0.427833	−	0.903858i	$-0.359277\pi$
$673$	22.1979	0.855666	0.427833	+	0.903858i	$0.359277\pi$
$674$	−53.9169	−2.07680
$675$	5.37892	0.207035
$676$	−25.9774	−0.999130
$677$	−49.9580	−1.92004	−0.960022	−	0.279926i	$-0.909690\pi$
$677$	−49.9580	−1.92004	−0.960022	+	0.279926i	$0.909690\pi$
$678$	−37.5734	−1.44300
$679$	−12.5420	−0.481318
$680$	47.2342	1.81135
$681$	30.2070	1.15753
$682$	−30.2855	−1.15969
$683$	−19.4799	−0.745377	−0.372688	−	0.927957i	$-0.621564\pi$
$683$	−19.4799	−0.745377	−0.372688	+	0.927957i	$0.621564\pi$
$684$	37.9814	1.45226
$685$	−10.4563	−0.399516
$686$	42.1489	1.60925
$687$	29.2432	1.11570
$688$	−67.5463	−2.57518
$689$	−18.3414	−0.698752
$690$	19.7668	0.752511
$691$	−21.2330	−0.807740	−0.403870	−	0.914816i	$-0.632335\pi$
$691$	−21.2330	−0.807740	−0.403870	+	0.914816i	$0.632335\pi$
$692$	−13.5130	−0.513685
$693$	9.01532	0.342464
$694$	−85.8688	−3.25954
$695$	−0.595621	−0.0225932
$696$	22.8965	0.867888
$697$	14.7170	0.557445
$698$	39.0815	1.47926
$699$	17.0343	0.644296
$700$	14.7752	0.558449
$701$	12.6421	0.477484	0.238742	−	0.971083i	$-0.423265\pi$
$701$	12.6421	0.477484	0.238742	+	0.971083i	$0.423265\pi$
$702$	−40.0018	−1.50977
$703$	−27.1288	−1.02318
$704$	−26.4371	−0.996387
$705$	−4.24934	−0.160039
$706$	−86.4475	−3.25349
$707$	29.1166	1.09504
$708$	72.7522	2.73419
$709$	−40.1759	−1.50884	−0.754418	−	0.656394i	$-0.772081\pi$
$709$	−40.1759	−1.50884	−0.754418	+	0.656394i	$0.772081\pi$
$710$	−6.08451	−0.228347
$711$	−19.8355	−0.743890
$712$	61.5257	2.30577
$713$	40.2791	1.50846
$714$	52.2465	1.95528
$715$	5.14065	0.192250
$716$	39.4030	1.47256
$717$	−26.8370	−1.00225
$718$	2.76268	0.103102
$719$	−22.8803	−0.853291	−0.426646	−	0.904419i	$-0.640305\pi$
$719$	−22.8803	−0.853291	−0.426646	+	0.904419i	$0.640305\pi$
$720$	19.0591	0.710289
$721$	13.4982	0.502700
$722$	−3.02071	−0.112419
$723$	−29.2100	−1.08633
$724$	−105.158	−3.90816
$725$	2.46390	0.0915070
$726$	−23.2990	−0.864706
$727$	−6.14050	−0.227739	−0.113869	−	0.993496i	$-0.536325\pi$
$727$	−6.14050	−0.227739	−0.113869	+	0.993496i	$0.536325\pi$
$728$	−66.3177	−2.45790
$729$	20.4885	0.758832
$730$	35.7820	1.32435
$731$	−34.7532	−1.28539
$732$	−6.10724	−0.225730
$733$	30.3283	1.12020	0.560101	−	0.828425i	$-0.310762\pi$
$733$	30.3283	1.12020	0.560101	+	0.828425i	$0.310762\pi$
$734$	89.0832	3.28812
$735$	1.81453	0.0669299
$736$	90.6006	3.33958
$737$	−10.6558	−0.392513
$738$	11.2125	0.412737
$739$	−24.1451	−0.888194	−0.444097	−	0.895979i	$-0.646475\pi$
$739$	−24.1451	−0.888194	−0.444097	+	0.895979i	$0.646475\pi$
$740$	−30.4973	−1.12110
$741$	14.4584	0.531143
$742$	50.8870	1.86812
$743$	13.9121	0.510385	0.255192	−	0.966890i	$-0.417861\pi$
$743$	13.9121	0.510385	0.255192	+	0.966890i	$0.417861\pi$
$744$	−57.7936	−2.11882
$745$	8.26598	0.302842
$746$	63.1015	2.31031
$747$	−21.7894	−0.797233
$748$	−54.0976	−1.97801
$749$	−10.6456	−0.388981
$750$	−3.05206	−0.111445
$751$	−43.2179	−1.57704	−0.788522	−	0.615006i	$-0.789153\pi$
$751$	−43.2179	−1.57704	−0.788522	+	0.615006i	$0.789153\pi$
$752$	−41.9798	−1.53085
$753$	22.6018	0.823657
$754$	−18.3235	−0.667302
$755$	11.9233	0.433933
$756$	79.4745	2.89046
$757$	−15.8863	−0.577397	−0.288698	−	0.957420i	$-0.593222\pi$
$757$	−15.8863	−0.577397	−0.288698	+	0.957420i	$0.593222\pi$
$758$	33.3257	1.21044
$759$	−13.6638	−0.495964
$760$	−36.2655	−1.31549
$761$	7.09656	0.257250	0.128625	−	0.991693i	$-0.458944\pi$
$761$	7.09656	0.257250	0.128625	+	0.991693i	$0.458944\pi$
$762$	−12.6325	−0.457628
$763$	42.6659	1.54461
$764$	26.9407	0.974680
$765$	9.80605	0.354538
$766$	47.4645	1.71496
$767$	−35.1397	−1.26882
$768$	1.80173	0.0650143
$769$	−1.13572	−0.0409550	−0.0204775	−	0.999790i	$-0.506519\pi$
$769$	−1.13572	−0.0409550	−0.0204775	+	0.999790i	$0.506519\pi$
$770$	−14.2624	−0.513981
$771$	−9.76673	−0.351740
$772$	−16.4125	−0.590699
$773$	12.5696	0.452099	0.226049	−	0.974116i	$-0.427419\pi$
$773$	12.5696	0.452099	0.226049	+	0.974116i	$0.427419\pi$
$774$	−26.4775	−0.951715
$775$	−6.21921	−0.223401
$776$	34.6066	1.24230
$777$	−20.3598	−0.730404
$778$	−26.1954	−0.939152
$779$	−11.2994	−0.404843
$780$	16.2537	0.581975
$781$	4.20590	0.150499
$782$	100.473	3.59291
$783$	13.2531	0.473628
$784$	17.9260	0.640214
$785$	16.7446	0.597641
$786$	−61.0627	−2.17803
$787$	−34.4106	−1.22661	−0.613303	−	0.789848i	$-0.710159\pi$
$787$	−34.4106	−1.22661	−0.613303	+	0.789848i	$0.710159\pi$
$788$	−62.3980	−2.22284
$789$	−2.58223	−0.0919297
$790$	31.3801	1.11645
$791$	−36.0562	−1.28201
$792$	−24.8756	−0.883916
$793$	2.94983	0.104752
$794$	−22.3540	−0.793314
$795$	−7.52733	−0.266967
$796$	−30.5036	−1.08117
$797$	25.1869	0.892166	0.446083	−	0.894992i	$-0.352819\pi$
$797$	25.1869	0.892166	0.446083	+	0.894992i	$0.352819\pi$
$798$	−40.1139	−1.42002
$799$	−21.5990	−0.764116
$800$	−13.9890	−0.494585
$801$	12.7730	0.451313
$802$	2.65420	0.0937229
$803$	−24.7342	−0.872852
$804$	−33.6916	−1.18821
$805$	18.9687	0.668558
$806$	46.2508	1.62912
$807$	4.71404	0.165942
$808$	−80.3402	−2.82636
$809$	−1.04526	−0.0367495	−0.0183747	−	0.999831i	$-0.505849\pi$
$809$	−1.04526	−0.0367495	−0.0183747	+	0.999831i	$0.505849\pi$
$810$	−3.05772	−0.107437
$811$	23.2192	0.815337	0.407668	−	0.913130i	$-0.366342\pi$
$811$	23.2192	0.815337	0.407668	+	0.913130i	$0.366342\pi$
$812$	36.4046	1.27755
$813$	4.35682	0.152800
$814$	29.4388	1.03183
$815$	2.98684	0.104624
$816$	−76.3504	−2.67280
$817$	26.6828	0.933513
$818$	−71.8005	−2.51045
$819$	−13.7679	−0.481088
$820$	−12.7024	−0.443587
$821$	−41.8034	−1.45895	−0.729474	−	0.684009i	$-0.760235\pi$
$821$	−41.8034	−1.45895	−0.729474	+	0.684009i	$0.760235\pi$
$822$	31.9134	1.11311
$823$	16.6018	0.578701	0.289350	−	0.957223i	$-0.406561\pi$
$823$	16.6018	0.578701	0.289350	+	0.957223i	$0.406561\pi$
$824$	−37.2450	−1.29749
$825$	2.10973	0.0734513
$826$	97.4926	3.39220
$827$	33.1786	1.15373	0.576866	−	0.816839i	$-0.304276\pi$
$827$	33.1786	1.15373	0.576866	+	0.816839i	$0.304276\pi$
$828$	54.8159	1.90498
$829$	33.5286	1.16450	0.582248	−	0.813011i	$-0.302173\pi$
$829$	33.5286	1.16450	0.582248	+	0.813011i	$0.302173\pi$
$830$	34.4712	1.19651
$831$	29.3392	1.01777
$832$	40.3738	1.39971
$833$	9.22307	0.319561
$834$	1.81787	0.0629477
$835$	−10.7306	−0.371348
$836$	41.5351	1.43652
$837$	−33.4526	−1.15629
$838$	46.6713	1.61223
$839$	28.8829	0.997147	0.498573	−	0.866847i	$-0.333857\pi$
$839$	28.8829	0.997147	0.498573	+	0.866847i	$0.333857\pi$
$840$	−27.2168	−0.939070
$841$	−22.9292	−0.790662
$842$	−63.3810	−2.18425
$843$	7.84206	0.270095
$844$	−28.0517	−0.965580
$845$	5.14939	0.177144
$846$	−16.4557	−0.565758
$847$	−22.3582	−0.768236
$848$	−74.3636	−2.55366
$849$	9.44782	0.324248
$850$	−15.5133	−0.532102
$851$	−39.1530	−1.34215
$852$	13.2982	0.455588
$853$	−25.2091	−0.863142	−0.431571	−	0.902079i	$-0.642040\pi$
$853$	−25.2091	−0.863142	−0.431571	+	0.902079i	$0.642040\pi$
$854$	−8.18410	−0.280054
$855$	−7.52890	−0.257483
$856$	29.3739	1.00398
$857$	52.4288	1.79093	0.895467	−	0.445127i	$-0.146842\pi$
$857$	52.4288	1.79093	0.895467	+	0.445127i	$0.146842\pi$
$858$	−15.6896	−0.535633
$859$	36.2711	1.23755	0.618777	−	0.785567i	$-0.287628\pi$
$859$	36.2711	1.23755	0.618777	+	0.785567i	$0.287628\pi$
$860$	29.9959	1.02285
$861$	−8.48006	−0.289000
$862$	9.14492	0.311477
$863$	−27.0081	−0.919365	−0.459683	−	0.888083i	$-0.652037\pi$
$863$	−27.0081	−0.919365	−0.459683	+	0.888083i	$0.652037\pi$
$864$	−75.2457	−2.55991
$865$	2.67862	0.0910757
$866$	68.9539	2.34315
$867$	−19.7346	−0.670223
$868$	−91.8899	−3.11895
$869$	−21.6914	−0.735831
$870$	−7.51997	−0.254951
$871$	16.2732	0.551396
$872$	−117.726	−3.98672
$873$	7.18449	0.243158
$874$	−77.1412	−2.60934
$875$	−2.92882	−0.0990122
$876$	−78.2045	−2.64229
$877$	41.0219	1.38521	0.692605	−	0.721317i	$-0.256463\pi$
$877$	41.0219	1.38521	0.692605	+	0.721317i	$0.256463\pi$
$878$	−84.2655	−2.84382
$879$	−26.4385	−0.891748
$880$	20.8423	0.702594
$881$	21.0997	0.710869	0.355434	−	0.934701i	$-0.384333\pi$
$881$	21.0997	0.710869	0.355434	+	0.934701i	$0.384333\pi$
$882$	7.02682	0.236605
$883$	−56.1545	−1.88975	−0.944876	−	0.327430i	$-0.893818\pi$
$883$	−56.1545	−1.88975	−0.944876	+	0.327430i	$0.893818\pi$
$884$	82.6159	2.77867
$885$	−14.4214	−0.484769
$886$	63.0244	2.11734
$887$	−16.8308	−0.565122	−0.282561	−	0.959249i	$-0.591184\pi$
$887$	−16.8308	−0.565122	−0.282561	+	0.959249i	$0.591184\pi$
$888$	56.1780	1.88521
$889$	−12.1224	−0.406573
$890$	−20.2071	−0.677344
$891$	2.11364	0.0708096
$892$	−122.761	−4.11035
$893$	16.5833	0.554938
$894$	−25.2283	−0.843759
$895$	−7.81069	−0.261083
$896$	−30.0718	−1.00463
$897$	20.8668	0.696723
$898$	72.0741	2.40515
$899$	−15.3235	−0.511068
$900$	−8.46373	−0.282124
$901$	−38.2607	−1.27465
$902$	12.2616	0.408265
$903$	20.0251	0.666394
$904$	99.4883	3.30893
$905$	20.8450	0.692911
$906$	−36.3906	−1.20900
$907$	54.3297	1.80399	0.901995	−	0.431747i	$-0.142103\pi$
$907$	54.3297	1.80399	0.901995	+	0.431747i	$0.142103\pi$
$908$	−132.522	−4.39789
$909$	−16.6790	−0.553207
$910$	21.7810	0.722032
$911$	−31.1857	−1.03323	−0.516614	−	0.856218i	$-0.672808\pi$
$911$	−31.1857	−1.03323	−0.516614	+	0.856218i	$0.672808\pi$
$912$	58.6204	1.94111
$913$	−23.8281	−0.788596
$914$	−69.1827	−2.28836
$915$	1.21061	0.0400216
$916$	−128.293	−4.23893
$917$	−58.5971	−1.93505
$918$	−83.4449	−2.75409
$919$	8.18626	0.270040	0.135020	−	0.990843i	$-0.456890\pi$
$919$	8.18626	0.270040	0.135020	+	0.990843i	$0.456890\pi$
$920$	−52.3395	−1.72558
$921$	27.2789	0.898872
$922$	42.8625	1.41160
$923$	−6.42309	−0.211419
$924$	31.1716	1.02547
$925$	6.04534	0.198770
$926$	−40.5267	−1.33179
$927$	−7.73225	−0.253960
$928$	−34.4675	−1.13145
$929$	−14.3612	−0.471175	−0.235588	−	0.971853i	$-0.575701\pi$
$929$	−14.3612	−0.471175	−0.235588	+	0.971853i	$0.575701\pi$
$930$	18.9814	0.622424
$931$	−7.08130	−0.232080
$932$	−74.7315	−2.44791
$933$	15.2814	0.500292
$934$	−92.1864	−3.01643
$935$	10.7235	0.350697
$936$	37.9891	1.24171
$937$	−30.3184	−0.990460	−0.495230	−	0.868762i	$-0.664916\pi$
$937$	−30.3184	−0.990460	−0.495230	+	0.868762i	$0.664916\pi$
$938$	−45.1489	−1.47416
$939$	30.6689	1.00084
$940$	18.6424	0.608047
$941$	−10.7891	−0.351715	−0.175857	−	0.984416i	$-0.556270\pi$
$941$	−10.7891	−0.351715	−0.175857	+	0.984416i	$0.556270\pi$
$942$	−51.1056	−1.66511
$943$	−16.3076	−0.531049
$944$	−142.471	−4.63702
$945$	−15.7539	−0.512474
$946$	−28.9549	−0.941405
$947$	−23.6696	−0.769160	−0.384580	−	0.923092i	$-0.625654\pi$
$947$	−23.6696	−0.769160	−0.384580	+	0.923092i	$0.625654\pi$
$948$	−68.5838	−2.22750
$949$	37.7732	1.22617
$950$	11.9108	0.386438
$951$	0.847755	0.0274903
$952$	−138.341	−4.48364
$953$	56.3300	1.82471	0.912354	−	0.409402i	$-0.134263\pi$
$953$	56.3300	1.82471	0.912354	+	0.409402i	$0.134263\pi$
$954$	−29.1498	−0.943761
$955$	−5.34034	−0.172809
$956$	117.737	3.80790
$957$	5.19816	0.168033
$958$	−30.2238	−0.976487
$959$	30.6247	0.988924
$960$	16.5694	0.534776
$961$	7.67854	0.247695
$962$	−44.9579	−1.44950
$963$	6.09816	0.196510
$964$	128.148	4.12736
$965$	3.25338	0.104730
$966$	−57.8935	−1.86269
$967$	28.4297	0.914238	0.457119	−	0.889405i	$-0.348881\pi$
$967$	28.4297	0.914238	0.457119	+	0.889405i	$0.348881\pi$
$968$	61.6920	1.98286
$969$	30.1607	0.968900
$970$	−11.3660	−0.364940
$971$	35.5731	1.14159	0.570797	−	0.821091i	$-0.306634\pi$
$971$	35.5731	1.14159	0.570797	+	0.821091i	$0.306634\pi$
$972$	−74.7231	−2.39674
$973$	1.74447	0.0559251
$974$	−14.2268	−0.455857
$975$	−3.22190	−0.103183
$976$	11.9598	0.382824
$977$	42.8164	1.36982	0.684910	−	0.728628i	$-0.259842\pi$
$977$	42.8164	1.36982	0.684910	+	0.728628i	$0.259842\pi$
$978$	−9.11600	−0.291497
$979$	13.9681	0.446423
$980$	−7.96056	−0.254291
$981$	−24.4405	−0.780326
$982$	26.1438	0.834281
$983$	46.7001	1.48950	0.744751	−	0.667342i	$-0.232568\pi$
$983$	46.7001	1.48950	0.744751	+	0.667342i	$0.232568\pi$
$984$	23.3987	0.745923
$985$	12.3689	0.394106
$986$	−38.2233	−1.21728
$987$	12.4455	0.396146
$988$	−63.4309	−2.01801
$989$	38.5094	1.22453
$990$	8.16999	0.259659
$991$	−1.05090	−0.0333829	−0.0166914	−	0.999861i	$-0.505313\pi$
$991$	−1.05090	−0.0333829	−0.0166914	+	0.999861i	$0.505313\pi$
$992$	87.0004	2.76227
$993$	1.86350	0.0591364
$994$	17.8204	0.565230
$995$	6.04661	0.191690
$996$	−75.3396	−2.38723
$997$	6.50690	0.206075	0.103038	−	0.994677i	$-0.467144\pi$
$997$	6.50690	0.206075	0.103038	+	0.994677i	$0.467144\pi$
$998$	18.6751	0.591149
$999$	32.5174	1.02881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.e.1.2	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.e.1.2	✓	29	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)

\(f(q)\)	\(=\)	\(q-2.65420 q^{2} -1.14990 q^{3} +5.04475 q^{4} -1.00000 q^{5} +3.05206 q^{6} +2.92882 q^{7} -8.08137 q^{8} -1.67773 q^{9} +O(q^{10})\)	\(q-2.65420 q^{2} -1.14990 q^{3} +5.04475 q^{4} -1.00000 q^{5} +3.05206 q^{6} +2.92882 q^{7} -8.08137 q^{8} -1.67773 q^{9} +2.65420 q^{10} -1.83471 q^{11} -5.80096 q^{12} +2.80189 q^{13} -7.77366 q^{14} +1.14990 q^{15} +11.3600 q^{16} +5.84483 q^{17} +4.45302 q^{18} -4.48755 q^{19} -5.04475 q^{20} -3.36785 q^{21} +4.86967 q^{22} -6.47656 q^{23} +9.29277 q^{24} +1.00000 q^{25} -7.43677 q^{26} +5.37892 q^{27} +14.7752 q^{28} +2.46390 q^{29} -3.05206 q^{30} -6.21921 q^{31} -13.9890 q^{32} +2.10973 q^{33} -15.5133 q^{34} -2.92882 q^{35} -8.46373 q^{36} +6.04534 q^{37} +11.9108 q^{38} -3.22190 q^{39} +8.08137 q^{40} +2.51795 q^{41} +8.93893 q^{42} -5.94597 q^{43} -9.25564 q^{44} +1.67773 q^{45} +17.1901 q^{46} -3.69540 q^{47} -13.0629 q^{48} +1.57799 q^{49} -2.65420 q^{50} -6.72097 q^{51} +14.1349 q^{52} -6.54608 q^{53} -14.2767 q^{54} +1.83471 q^{55} -23.6689 q^{56} +5.16023 q^{57} -6.53968 q^{58} -12.5414 q^{59} +5.80096 q^{60} +1.05280 q^{61} +16.5070 q^{62} -4.91377 q^{63} +14.4095 q^{64} -2.80189 q^{65} -5.59963 q^{66} +5.80793 q^{67} +29.4857 q^{68} +7.44740 q^{69} +7.77366 q^{70} -2.29241 q^{71} +13.5584 q^{72} +13.4813 q^{73} -16.0455 q^{74} -1.14990 q^{75} -22.6386 q^{76} -5.37352 q^{77} +8.55155 q^{78} +11.8228 q^{79} -11.3600 q^{80} -1.15203 q^{81} -6.68312 q^{82} +12.9874 q^{83} -16.9900 q^{84} -5.84483 q^{85} +15.7818 q^{86} -2.83324 q^{87} +14.8269 q^{88} -7.61328 q^{89} -4.45302 q^{90} +8.20624 q^{91} -32.6727 q^{92} +7.15147 q^{93} +9.80830 q^{94} +4.48755 q^{95} +16.0859 q^{96} -4.28227 q^{97} -4.18829 q^{98} +3.07814 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * q^99

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