LMFDB - Embedded newform 8030.2.a.bc.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 10 x^{9} + 71 x^{8} + 28 x^{7} - 360 x^{6} - 60 x^{5} + 788 x^{4} + 309 x^{3} + \cdots - 95 $ x^11 - 5x^10 - 10x^9 + 71x^8 + 28x^7 - 360x^6 - 60x^5 + 788x^4 + 309x^3 - 632x^2 - 503x - 95
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-2.41966$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.41966 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41966 q^{6} +1.08168 q^{7} -1.00000 q^{8} +2.85477 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.41966 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41966 q^{6} +1.08168 q^{7} -1.00000 q^{8} +2.85477 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.41966 q^{12} -2.32277 q^{13} -1.08168 q^{14} +2.41966 q^{15} +1.00000 q^{16} -2.75813 q^{17} -2.85477 q^{18} -3.19684 q^{19} +1.00000 q^{20} +2.61730 q^{21} -1.00000 q^{22} -4.06828 q^{23} -2.41966 q^{24} +1.00000 q^{25} +2.32277 q^{26} -0.351411 q^{27} +1.08168 q^{28} -2.05113 q^{29} -2.41966 q^{30} -10.6666 q^{31} -1.00000 q^{32} +2.41966 q^{33} +2.75813 q^{34} +1.08168 q^{35} +2.85477 q^{36} -2.44060 q^{37} +3.19684 q^{38} -5.62033 q^{39} -1.00000 q^{40} +4.34412 q^{41} -2.61730 q^{42} +0.193491 q^{43} +1.00000 q^{44} +2.85477 q^{45} +4.06828 q^{46} -3.69487 q^{47} +2.41966 q^{48} -5.82997 q^{49} -1.00000 q^{50} -6.67375 q^{51} -2.32277 q^{52} -6.26157 q^{53} +0.351411 q^{54} +1.00000 q^{55} -1.08168 q^{56} -7.73528 q^{57} +2.05113 q^{58} -4.70462 q^{59} +2.41966 q^{60} +0.633428 q^{61} +10.6666 q^{62} +3.08794 q^{63} +1.00000 q^{64} -2.32277 q^{65} -2.41966 q^{66} -7.64542 q^{67} -2.75813 q^{68} -9.84386 q^{69} -1.08168 q^{70} +2.59553 q^{71} -2.85477 q^{72} -1.00000 q^{73} +2.44060 q^{74} +2.41966 q^{75} -3.19684 q^{76} +1.08168 q^{77} +5.62033 q^{78} +12.6642 q^{79} +1.00000 q^{80} -9.41460 q^{81} -4.34412 q^{82} +3.93782 q^{83} +2.61730 q^{84} -2.75813 q^{85} -0.193491 q^{86} -4.96305 q^{87} -1.00000 q^{88} -9.41090 q^{89} -2.85477 q^{90} -2.51249 q^{91} -4.06828 q^{92} -25.8097 q^{93} +3.69487 q^{94} -3.19684 q^{95} -2.41966 q^{96} +2.02817 q^{97} +5.82997 q^{98} +2.85477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.41966	1.39699	0.698497	−	0.715613i	$-0.253853\pi$
$3$	2.41966	1.39699	0.698497	+	0.715613i	$0.253853\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.41966	−0.987823
$7$	1.08168	0.408836	0.204418	−	0.978884i	$-0.434470\pi$
$7$	1.08168	0.408836	0.204418	+	0.978884i	$0.434470\pi$
$8$	−1.00000	−0.353553
$9$	2.85477	0.951590
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.41966	0.698497
$13$	−2.32277	−0.644221	−0.322111	−	0.946702i	$-0.604392\pi$
$13$	−2.32277	−0.644221	−0.322111	+	0.946702i	$0.604392\pi$
$14$	−1.08168	−0.289091
$15$	2.41966	0.624754
$16$	1.00000	0.250000
$17$	−2.75813	−0.668946	−0.334473	−	0.942405i	$-0.608558\pi$
$17$	−2.75813	−0.668946	−0.334473	+	0.942405i	$0.608558\pi$
$18$	−2.85477	−0.672875
$19$	−3.19684	−0.733406	−0.366703	−	0.930338i	$-0.619513\pi$
$19$	−3.19684	−0.733406	−0.366703	+	0.930338i	$0.619513\pi$
$20$	1.00000	0.223607
$21$	2.61730	0.571141
$22$	−1.00000	−0.213201
$23$	−4.06828	−0.848294	−0.424147	−	0.905593i	$-0.639426\pi$
$23$	−4.06828	−0.848294	−0.424147	+	0.905593i	$0.639426\pi$
$24$	−2.41966	−0.493912
$25$	1.00000	0.200000
$26$	2.32277	0.455533
$27$	−0.351411	−0.0676290
$28$	1.08168	0.204418
$29$	−2.05113	−0.380886	−0.190443	−	0.981698i	$-0.560992\pi$
$29$	−2.05113	−0.380886	−0.190443	+	0.981698i	$0.560992\pi$
$30$	−2.41966	−0.441768
$31$	−10.6666	−1.91578	−0.957892	−	0.287128i	$-0.907299\pi$
$31$	−10.6666	−1.91578	−0.957892	+	0.287128i	$0.907299\pi$
$32$	−1.00000	−0.176777
$33$	2.41966	0.421209
$34$	2.75813	0.473016
$35$	1.08168	0.182837
$36$	2.85477	0.475795
$37$	−2.44060	−0.401233	−0.200616	−	0.979670i	$-0.564294\pi$
$37$	−2.44060	−0.401233	−0.200616	+	0.979670i	$0.564294\pi$
$38$	3.19684	0.518596
$39$	−5.62033	−0.899972
$40$	−1.00000	−0.158114
$41$	4.34412	0.678438	0.339219	−	0.940707i	$-0.389837\pi$
$41$	4.34412	0.678438	0.339219	+	0.940707i	$0.389837\pi$
$42$	−2.61730	−0.403858
$43$	0.193491	0.0295070	0.0147535	−	0.999891i	$-0.495304\pi$
$43$	0.193491	0.0295070	0.0147535	+	0.999891i	$0.495304\pi$
$44$	1.00000	0.150756
$45$	2.85477	0.425564
$46$	4.06828	0.599835
$47$	−3.69487	−0.538952	−0.269476	−	0.963007i	$-0.586851\pi$
$47$	−3.69487	−0.538952	−0.269476	+	0.963007i	$0.586851\pi$
$48$	2.41966	0.349248
$49$	−5.82997	−0.832853
$50$	−1.00000	−0.141421
$51$	−6.67375	−0.934512
$52$	−2.32277	−0.322111
$53$	−6.26157	−0.860093	−0.430046	−	0.902807i	$-0.641503\pi$
$53$	−6.26157	−0.860093	−0.430046	+	0.902807i	$0.641503\pi$
$54$	0.351411	0.0478209
$55$	1.00000	0.134840
$56$	−1.08168	−0.144545
$57$	−7.73528	−1.02456
$58$	2.05113	0.269327
$59$	−4.70462	−0.612490	−0.306245	−	0.951953i	$-0.599073\pi$
$59$	−4.70462	−0.612490	−0.306245	+	0.951953i	$0.599073\pi$
$60$	2.41966	0.312377
$61$	0.633428	0.0811021	0.0405511	−	0.999177i	$-0.487089\pi$
$61$	0.633428	0.0811021	0.0405511	+	0.999177i	$0.487089\pi$
$62$	10.6666	1.35466
$63$	3.08794	0.389044
$64$	1.00000	0.125000
$65$	−2.32277	−0.288104
$66$	−2.41966	−0.297840
$67$	−7.64542	−0.934037	−0.467019	−	0.884247i	$-0.654672\pi$
$67$	−7.64542	−0.934037	−0.467019	+	0.884247i	$0.654672\pi$
$68$	−2.75813	−0.334473
$69$	−9.84386	−1.18506
$70$	−1.08168	−0.129285
$71$	2.59553	0.308033	0.154016	−	0.988068i	$-0.450779\pi$
$71$	2.59553	0.308033	0.154016	+	0.988068i	$0.450779\pi$
$72$	−2.85477	−0.336438
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	2.44060	0.283714
$75$	2.41966	0.279399
$76$	−3.19684	−0.366703
$77$	1.08168	0.123269
$78$	5.62033	0.636377
$79$	12.6642	1.42484	0.712419	−	0.701755i	$-0.247600\pi$
$79$	12.6642	1.42484	0.712419	+	0.701755i	$0.247600\pi$
$80$	1.00000	0.111803
$81$	−9.41460	−1.04607
$82$	−4.34412	−0.479728
$83$	3.93782	0.432232	0.216116	−	0.976368i	$-0.430661\pi$
$83$	3.93782	0.432232	0.216116	+	0.976368i	$0.430661\pi$
$84$	2.61730	0.285570
$85$	−2.75813	−0.299162
$86$	−0.193491	−0.0208646
$87$	−4.96305	−0.532095
$88$	−1.00000	−0.106600
$89$	−9.41090	−0.997553	−0.498776	−	0.866731i	$-0.666217\pi$
$89$	−9.41090	−0.997553	−0.498776	+	0.866731i	$0.666217\pi$
$90$	−2.85477	−0.300919
$91$	−2.51249	−0.263381
$92$	−4.06828	−0.424147
$93$	−25.8097	−2.67634
$94$	3.69487	0.381097
$95$	−3.19684	−0.327989
$96$	−2.41966	−0.246956
$97$	2.02817	0.205929	0.102965	−	0.994685i	$-0.467167\pi$
$97$	2.02817	0.205929	0.102965	+	0.994685i	$0.467167\pi$
$98$	5.82997	0.588916
$99$	2.85477	0.286915
$100$	1.00000	0.100000
$101$	−10.9071	−1.08530	−0.542648	−	0.839960i	$-0.682578\pi$
$101$	−10.9071	−1.08530	−0.542648	+	0.839960i	$0.682578\pi$
$102$	6.67375	0.660800
$103$	−11.3410	−1.11746	−0.558729	−	0.829350i	$-0.688711\pi$
$103$	−11.3410	−1.11746	−0.558729	+	0.829350i	$0.688711\pi$
$104$	2.32277	0.227767
$105$	2.61730	0.255422
$106$	6.26157	0.608177
$107$	−7.52297	−0.727273	−0.363637	−	0.931541i	$-0.618465\pi$
$107$	−7.52297	−0.727273	−0.363637	+	0.931541i	$0.618465\pi$
$108$	−0.351411	−0.0338145
$109$	16.6479	1.59458	0.797289	−	0.603598i	$-0.206267\pi$
$109$	16.6479	1.59458	0.797289	+	0.603598i	$0.206267\pi$
$110$	−1.00000	−0.0953463
$111$	−5.90544	−0.560519
$112$	1.08168	0.102209
$113$	−4.17707	−0.392946	−0.196473	−	0.980509i	$-0.562949\pi$
$113$	−4.17707	−0.392946	−0.196473	+	0.980509i	$0.562949\pi$
$114$	7.73528	0.724476
$115$	−4.06828	−0.379369
$116$	−2.05113	−0.190443
$117$	−6.63098	−0.613034
$118$	4.70462	0.433096
$119$	−2.98341	−0.273489
$120$	−2.41966	−0.220884
$121$	1.00000	0.0909091
$122$	−0.633428	−0.0573479
$123$	10.5113	0.947773
$124$	−10.6666	−0.957892
$125$	1.00000	0.0894427
$126$	−3.08794	−0.275096
$127$	12.0949	1.07325	0.536626	−	0.843820i	$-0.319698\pi$
$127$	12.0949	1.07325	0.536626	+	0.843820i	$0.319698\pi$
$128$	−1.00000	−0.0883883
$129$	0.468182	0.0412211
$130$	2.32277	0.203721
$131$	10.7036	0.935180	0.467590	−	0.883945i	$-0.345122\pi$
$131$	10.7036	0.935180	0.467590	+	0.883945i	$0.345122\pi$
$132$	2.41966	0.210605
$133$	−3.45796	−0.299843
$134$	7.64542	0.660464
$135$	−0.351411	−0.0302446
$136$	2.75813	0.236508
$137$	−3.73647	−0.319228	−0.159614	−	0.987179i	$-0.551025\pi$
$137$	−3.73647	−0.319228	−0.159614	+	0.987179i	$0.551025\pi$
$138$	9.84386	0.837965
$139$	−15.1575	−1.28564	−0.642819	−	0.766018i	$-0.722235\pi$
$139$	−15.1575	−1.28564	−0.642819	+	0.766018i	$0.722235\pi$
$140$	1.08168	0.0914185
$141$	−8.94034	−0.752913
$142$	−2.59553	−0.217812
$143$	−2.32277	−0.194240
$144$	2.85477	0.237897
$145$	−2.05113	−0.170337
$146$	1.00000	0.0827606
$147$	−14.1066	−1.16349
$148$	−2.44060	−0.200616
$149$	−13.6261	−1.11629	−0.558145	−	0.829743i	$-0.688487\pi$
$149$	−13.6261	−1.11629	−0.558145	+	0.829743i	$0.688487\pi$
$150$	−2.41966	−0.197565
$151$	22.8565	1.86003	0.930017	−	0.367517i	$-0.119792\pi$
$151$	22.8565	1.86003	0.930017	+	0.367517i	$0.119792\pi$
$152$	3.19684	0.259298
$153$	−7.87383	−0.636562
$154$	−1.08168	−0.0871641
$155$	−10.6666	−0.856765
$156$	−5.62033	−0.449986
$157$	17.4052	1.38908	0.694542	−	0.719452i	$-0.255607\pi$
$157$	17.4052	1.38908	0.694542	+	0.719452i	$0.255607\pi$
$158$	−12.6642	−1.00751
$159$	−15.1509	−1.20154
$160$	−1.00000	−0.0790569
$161$	−4.40057	−0.346813
$162$	9.41460	0.739681
$163$	21.7568	1.70412	0.852061	−	0.523442i	$-0.175352\pi$
$163$	21.7568	1.70412	0.852061	+	0.523442i	$0.175352\pi$
$164$	4.34412	0.339219
$165$	2.41966	0.188371
$166$	−3.93782	−0.305634
$167$	−1.73575	−0.134317	−0.0671584	−	0.997742i	$-0.521393\pi$
$167$	−1.73575	−0.134317	−0.0671584	+	0.997742i	$0.521393\pi$
$168$	−2.61730	−0.201929
$169$	−7.60473	−0.584979
$170$	2.75813	0.211539
$171$	−9.12625	−0.697902
$172$	0.193491	0.0147535
$173$	−3.35958	−0.255424	−0.127712	−	0.991811i	$-0.540763\pi$
$173$	−3.35958	−0.255424	−0.127712	+	0.991811i	$0.540763\pi$
$174$	4.96305	0.376248
$175$	1.08168	0.0817672
$176$	1.00000	0.0753778
$177$	−11.3836	−0.855644
$178$	9.41090	0.705376
$179$	25.2126	1.88448	0.942239	−	0.334941i	$-0.108717\pi$
$179$	25.2126	1.88448	0.942239	+	0.334941i	$0.108717\pi$
$180$	2.85477	0.212782
$181$	−3.63537	−0.270215	−0.135108	−	0.990831i	$-0.543138\pi$
$181$	−3.63537	−0.270215	−0.135108	+	0.990831i	$0.543138\pi$
$182$	2.51249	0.186238
$183$	1.53268	0.113299
$184$	4.06828	0.299917
$185$	−2.44060	−0.179437
$186$	25.8097	1.89246
$187$	−2.75813	−0.201695
$188$	−3.69487	−0.269476
$189$	−0.380113	−0.0276492
$190$	3.19684	0.231923
$191$	−3.62141	−0.262036	−0.131018	−	0.991380i	$-0.541825\pi$
$191$	−3.62141	−0.262036	−0.131018	+	0.991380i	$0.541825\pi$
$192$	2.41966	0.174624
$193$	−23.5802	−1.69734	−0.848669	−	0.528925i	$-0.822595\pi$
$193$	−23.5802	−1.69734	−0.848669	+	0.528925i	$0.822595\pi$
$194$	−2.02817	−0.145614
$195$	−5.62033	−0.402480
$196$	−5.82997	−0.416427
$197$	18.7532	1.33611	0.668054	−	0.744113i	$-0.267128\pi$
$197$	18.7532	1.33611	0.668054	+	0.744113i	$0.267128\pi$
$198$	−2.85477	−0.202880
$199$	5.82024	0.412586	0.206293	−	0.978490i	$-0.433860\pi$
$199$	5.82024	0.412586	0.206293	+	0.978490i	$0.433860\pi$
$200$	−1.00000	−0.0707107
$201$	−18.4993	−1.30484
$202$	10.9071	0.767420
$203$	−2.21867	−0.155720
$204$	−6.67375	−0.467256
$205$	4.34412	0.303407
$206$	11.3410	0.790162
$207$	−11.6140	−0.807228
$208$	−2.32277	−0.161055
$209$	−3.19684	−0.221130
$210$	−2.61730	−0.180611
$211$	−2.98120	−0.205234	−0.102617	−	0.994721i	$-0.532722\pi$
$211$	−2.98120	−0.205234	−0.102617	+	0.994721i	$0.532722\pi$
$212$	−6.26157	−0.430046
$213$	6.28031	0.430320
$214$	7.52297	0.514260
$215$	0.193491	0.0131960
$216$	0.351411	0.0239105
$217$	−11.5379	−0.783241
$218$	−16.6479	−1.12754
$219$	−2.41966	−0.163506
$220$	1.00000	0.0674200
$221$	6.40652	0.430949
$222$	5.90544	0.396347
$223$	−27.5151	−1.84255	−0.921275	−	0.388912i	$-0.872851\pi$
$223$	−27.5151	−1.84255	−0.921275	+	0.388912i	$0.872851\pi$
$224$	−1.08168	−0.0722727
$225$	2.85477	0.190318
$226$	4.17707	0.277855
$227$	−12.9546	−0.859827	−0.429913	−	0.902870i	$-0.641456\pi$
$227$	−12.9546	−0.859827	−0.429913	+	0.902870i	$0.641456\pi$
$228$	−7.73528	−0.512282
$229$	−27.0992	−1.79077	−0.895384	−	0.445294i	$-0.853099\pi$
$229$	−27.0992	−1.79077	−0.895384	+	0.445294i	$0.853099\pi$
$230$	4.06828	0.268254
$231$	2.61730	0.172205
$232$	2.05113	0.134664
$233$	16.5249	1.08258	0.541292	−	0.840835i	$-0.317935\pi$
$233$	16.5249	1.08258	0.541292	+	0.840835i	$0.317935\pi$
$234$	6.63098	0.433481
$235$	−3.69487	−0.241027
$236$	−4.70462	−0.306245
$237$	30.6432	1.99049
$238$	2.98341	0.193386
$239$	30.3524	1.96333	0.981667	−	0.190603i	$-0.0610444\pi$
$239$	30.3524	1.96333	0.981667	+	0.190603i	$0.0610444\pi$
$240$	2.41966	0.156189
$241$	17.2242	1.10951	0.554754	−	0.832015i	$-0.312813\pi$
$241$	17.2242	1.10951	0.554754	+	0.832015i	$0.312813\pi$
$242$	−1.00000	−0.0642824
$243$	−21.7259	−1.39372
$244$	0.633428	0.0405511
$245$	−5.82997	−0.372463
$246$	−10.5113	−0.670177
$247$	7.42554	0.472476
$248$	10.6666	0.677332
$249$	9.52819	0.603825
$250$	−1.00000	−0.0632456
$251$	14.6808	0.926644	0.463322	−	0.886190i	$-0.346657\pi$
$251$	14.6808	0.926644	0.463322	+	0.886190i	$0.346657\pi$
$252$	3.08794	0.194522
$253$	−4.06828	−0.255770
$254$	−12.0949	−0.758904
$255$	−6.67375	−0.417927
$256$	1.00000	0.0625000
$257$	25.4686	1.58869	0.794343	−	0.607469i	$-0.207815\pi$
$257$	25.4686	1.58869	0.794343	+	0.607469i	$0.207815\pi$
$258$	−0.468182	−0.0291477
$259$	−2.63995	−0.164038
$260$	−2.32277	−0.144052
$261$	−5.85551	−0.362447
$262$	−10.7036	−0.661272
$263$	4.95869	0.305766	0.152883	−	0.988244i	$-0.451144\pi$
$263$	4.95869	0.305766	0.152883	+	0.988244i	$0.451144\pi$
$264$	−2.41966	−0.148920
$265$	−6.26157	−0.384645
$266$	3.45796	0.212021
$267$	−22.7712	−1.39357
$268$	−7.64542	−0.467019
$269$	14.5857	0.889305	0.444653	−	0.895703i	$-0.353327\pi$
$269$	14.5857	0.889305	0.444653	+	0.895703i	$0.353327\pi$
$270$	0.351411	0.0213862
$271$	20.5674	1.24938	0.624690	−	0.780872i	$-0.285225\pi$
$271$	20.5674	1.24938	0.624690	+	0.780872i	$0.285225\pi$
$272$	−2.75813	−0.167236
$273$	−6.07939	−0.367941
$274$	3.73647	0.225728
$275$	1.00000	0.0603023
$276$	−9.84386	−0.592531
$277$	19.1121	1.14833	0.574166	−	0.818739i	$-0.305326\pi$
$277$	19.1121	1.14833	0.574166	+	0.818739i	$0.305326\pi$
$278$	15.1575	0.909084
$279$	−30.4508	−1.82304
$280$	−1.08168	−0.0646426
$281$	7.31817	0.436566	0.218283	−	0.975886i	$-0.429954\pi$
$281$	7.31817	0.436566	0.218283	+	0.975886i	$0.429954\pi$
$282$	8.94034	0.532390
$283$	−32.4599	−1.92954	−0.964771	−	0.263093i	$-0.915258\pi$
$283$	−32.4599	−1.92954	−0.964771	+	0.263093i	$0.915258\pi$
$284$	2.59553	0.154016
$285$	−7.73528	−0.458199
$286$	2.32277	0.137348
$287$	4.69894	0.277370
$288$	−2.85477	−0.168219
$289$	−9.39270	−0.552512
$290$	2.05113	0.120447
$291$	4.90748	0.287681
$292$	−1.00000	−0.0585206
$293$	27.8643	1.62785	0.813925	−	0.580970i	$-0.197327\pi$
$293$	27.8643	1.62785	0.813925	+	0.580970i	$0.197327\pi$
$294$	14.1066	0.822712
$295$	−4.70462	−0.273914
$296$	2.44060	0.141857
$297$	−0.351411	−0.0203909
$298$	13.6261	0.789337
$299$	9.44968	0.546489
$300$	2.41966	0.139699
$301$	0.209295	0.0120635
$302$	−22.8565	−1.31524
$303$	−26.3915	−1.51615
$304$	−3.19684	−0.183352
$305$	0.633428	0.0362700
$306$	7.87383	0.450117
$307$	−30.0726	−1.71633	−0.858166	−	0.513372i	$-0.828396\pi$
$307$	−30.0726	−1.71633	−0.858166	+	0.513372i	$0.828396\pi$
$308$	1.08168	0.0616343
$309$	−27.4413	−1.56108
$310$	10.6666	0.605824
$311$	−12.3438	−0.699950	−0.349975	−	0.936759i	$-0.613810\pi$
$311$	−12.3438	−0.699950	−0.349975	+	0.936759i	$0.613810\pi$
$312$	5.62033	0.318188
$313$	−16.3944	−0.926667	−0.463333	−	0.886184i	$-0.653347\pi$
$313$	−16.3944	−0.926667	−0.463333	+	0.886184i	$0.653347\pi$
$314$	−17.4052	−0.982231
$315$	3.08794	0.173986
$316$	12.6642	0.712419
$317$	−25.3604	−1.42438	−0.712192	−	0.701985i	$-0.752297\pi$
$317$	−25.3604	−1.42438	−0.712192	+	0.701985i	$0.752297\pi$
$318$	15.1509	0.849619
$319$	−2.05113	−0.114841
$320$	1.00000	0.0559017
$321$	−18.2031	−1.01600
$322$	4.40057	0.245234
$323$	8.81732	0.490609
$324$	−9.41460	−0.523033
$325$	−2.32277	−0.128844
$326$	−21.7568	−1.20500
$327$	40.2823	2.22761
$328$	−4.34412	−0.239864
$329$	−3.99666	−0.220343
$330$	−2.41966	−0.133198
$331$	7.65058	0.420514	0.210257	−	0.977646i	$-0.432570\pi$
$331$	7.65058	0.420514	0.210257	+	0.977646i	$0.432570\pi$
$332$	3.93782	0.216116
$333$	−6.96736	−0.381809
$334$	1.73575	0.0949763
$335$	−7.64542	−0.417714
$336$	2.61730	0.142785
$337$	−11.6829	−0.636409	−0.318205	−	0.948022i	$-0.603080\pi$
$337$	−11.6829	−0.636409	−0.318205	+	0.948022i	$0.603080\pi$
$338$	7.60473	0.413643
$339$	−10.1071	−0.548943
$340$	−2.75813	−0.149581
$341$	−10.6666	−0.577631
$342$	9.12625	0.493491
$343$	−13.8779	−0.749336
$344$	−0.193491	−0.0104323
$345$	−9.84386	−0.529975
$346$	3.35958	0.180612
$347$	0.216678	0.0116319	0.00581594	−	0.999983i	$-0.498149\pi$
$347$	0.216678	0.0116319	0.00581594	+	0.999983i	$0.498149\pi$
$348$	−4.96305	−0.266048
$349$	−22.4242	−1.20034	−0.600170	−	0.799872i	$-0.704900\pi$
$349$	−22.4242	−1.20034	−0.600170	+	0.799872i	$0.704900\pi$
$350$	−1.08168	−0.0578181
$351$	0.816247	0.0435681
$352$	−1.00000	−0.0533002
$353$	19.2782	1.02607	0.513037	−	0.858366i	$-0.328520\pi$
$353$	19.2782	1.02607	0.513037	+	0.858366i	$0.328520\pi$
$354$	11.3836	0.605032
$355$	2.59553	0.137757
$356$	−9.41090	−0.498776
$357$	−7.21885	−0.382062
$358$	−25.2126	−1.33253
$359$	−10.2885	−0.543006	−0.271503	−	0.962438i	$-0.587521\pi$
$359$	−10.2885	−0.543006	−0.271503	+	0.962438i	$0.587521\pi$
$360$	−2.85477	−0.150460
$361$	−8.78020	−0.462116
$362$	3.63537	0.191071
$363$	2.41966	0.126999
$364$	−2.51249	−0.131690
$365$	−1.00000	−0.0523424
$366$	−1.53268	−0.0801146
$367$	−10.5989	−0.553258	−0.276629	−	0.960977i	$-0.589217\pi$
$367$	−10.5989	−0.553258	−0.276629	+	0.960977i	$0.589217\pi$
$368$	−4.06828	−0.212074
$369$	12.4015	0.645595
$370$	2.44060	0.126881
$371$	−6.77300	−0.351637
$372$	−25.8097	−1.33817
$373$	35.8985	1.85875	0.929376	−	0.369135i	$-0.120346\pi$
$373$	35.8985	1.85875	0.929376	+	0.369135i	$0.120346\pi$
$374$	2.75813	0.142620
$375$	2.41966	0.124951
$376$	3.69487	0.190548
$377$	4.76432	0.245375
$378$	0.380113	0.0195509
$379$	−29.3821	−1.50926	−0.754629	−	0.656151i	$-0.772183\pi$
$379$	−29.3821	−1.50926	−0.754629	+	0.656151i	$0.772183\pi$
$380$	−3.19684	−0.163995
$381$	29.2657	1.49933
$382$	3.62141	0.185287
$383$	19.3946	0.991019	0.495509	−	0.868603i	$-0.334981\pi$
$383$	19.3946	0.991019	0.495509	+	0.868603i	$0.334981\pi$
$384$	−2.41966	−0.123478
$385$	1.08168	0.0551274
$386$	23.5802	1.20020
$387$	0.552371	0.0280786
$388$	2.02817	0.102965
$389$	19.9052	1.00923	0.504616	−	0.863344i	$-0.331634\pi$
$389$	19.9052	1.00923	0.504616	+	0.863344i	$0.331634\pi$
$390$	5.62033	0.284596
$391$	11.2208	0.567463
$392$	5.82997	0.294458
$393$	25.8992	1.30644
$394$	−18.7532	−0.944771
$395$	12.6642	0.637207
$396$	2.85477	0.143458
$397$	28.7073	1.44078	0.720388	−	0.693571i	$-0.243964\pi$
$397$	28.7073	1.44078	0.720388	+	0.693571i	$0.243964\pi$
$398$	−5.82024	−0.291742
$399$	−8.36709	−0.418878
$400$	1.00000	0.0500000
$401$	−1.46219	−0.0730180	−0.0365090	−	0.999333i	$-0.511624\pi$
$401$	−1.46219	−0.0730180	−0.0365090	+	0.999333i	$0.511624\pi$
$402$	18.4993	0.922664
$403$	24.7762	1.23419
$404$	−10.9071	−0.542648
$405$	−9.41460	−0.467815
$406$	2.21867	0.110111
$407$	−2.44060	−0.120976
$408$	6.67375	0.330400
$409$	−3.26767	−0.161576	−0.0807879	−	0.996731i	$-0.525744\pi$
$409$	−3.26767	−0.161576	−0.0807879	+	0.996731i	$0.525744\pi$
$410$	−4.34412	−0.214541
$411$	−9.04100	−0.445960
$412$	−11.3410	−0.558729
$413$	−5.08889	−0.250408
$414$	11.6140	0.570796
$415$	3.93782	0.193300
$416$	2.32277	0.113883
$417$	−36.6759	−1.79603
$418$	3.19684	0.156363
$419$	12.7661	0.623667	0.311833	−	0.950137i	$-0.399057\pi$
$419$	12.7661	0.623667	0.311833	+	0.950137i	$0.399057\pi$
$420$	2.61730	0.127711
$421$	4.53611	0.221077	0.110538	−	0.993872i	$-0.464743\pi$
$421$	4.53611	0.221077	0.110538	+	0.993872i	$0.464743\pi$
$422$	2.98120	0.145122
$423$	−10.5480	−0.512861
$424$	6.26157	0.304089
$425$	−2.75813	−0.133789
$426$	−6.28031	−0.304282
$427$	0.685165	0.0331575
$428$	−7.52297	−0.363637
$429$	−5.62033	−0.271352
$430$	−0.193491	−0.00933095
$431$	9.09018	0.437858	0.218929	−	0.975741i	$-0.429744\pi$
$431$	9.09018	0.437858	0.218929	+	0.975741i	$0.429744\pi$
$432$	−0.351411	−0.0169073
$433$	37.0153	1.77884	0.889420	−	0.457091i	$-0.151109\pi$
$433$	37.0153	1.77884	0.889420	+	0.457091i	$0.151109\pi$
$434$	11.5379	0.553835
$435$	−4.96305	−0.237960
$436$	16.6479	0.797289
$437$	13.0056	0.622144
$438$	2.41966	0.115616
$439$	−21.4954	−1.02592	−0.512959	−	0.858413i	$-0.671451\pi$
$439$	−21.4954	−1.02592	−0.512959	+	0.858413i	$0.671451\pi$
$440$	−1.00000	−0.0476731
$441$	−16.6432	−0.792534
$442$	−6.40652	−0.304727
$443$	−15.3961	−0.731491	−0.365745	−	0.930715i	$-0.619186\pi$
$443$	−15.3961	−0.731491	−0.365745	+	0.930715i	$0.619186\pi$
$444$	−5.90544	−0.280260
$445$	−9.41090	−0.446119
$446$	27.5151	1.30288
$447$	−32.9705	−1.55945
$448$	1.08168	0.0511045
$449$	−16.6062	−0.783694	−0.391847	−	0.920030i	$-0.628164\pi$
$449$	−16.6062	−0.783694	−0.391847	+	0.920030i	$0.628164\pi$
$450$	−2.85477	−0.134575
$451$	4.34412	0.204557
$452$	−4.17707	−0.196473
$453$	55.3050	2.59845
$454$	12.9546	0.607989
$455$	−2.51249	−0.117787
$456$	7.73528	0.362238
$457$	17.9591	0.840091	0.420045	−	0.907503i	$-0.362014\pi$
$457$	17.9591	0.840091	0.420045	+	0.907503i	$0.362014\pi$
$458$	27.0992	1.26626
$459$	0.969238	0.0452401
$460$	−4.06828	−0.189684
$461$	−27.6692	−1.28868	−0.644341	−	0.764739i	$-0.722868\pi$
$461$	−27.6692	−1.28868	−0.644341	+	0.764739i	$0.722868\pi$
$462$	−2.61730	−0.121768
$463$	−0.286392	−0.0133098	−0.00665488	−	0.999978i	$-0.502118\pi$
$463$	−0.286392	−0.0133098	−0.00665488	+	0.999978i	$0.502118\pi$
$464$	−2.05113	−0.0952215
$465$	−25.8097	−1.19689
$466$	−16.5249	−0.765502
$467$	6.01091	0.278152	0.139076	−	0.990282i	$-0.455587\pi$
$467$	6.01091	0.278152	0.139076	+	0.990282i	$0.455587\pi$
$468$	−6.63098	−0.306517
$469$	−8.26989	−0.381868
$470$	3.69487	0.170432
$471$	42.1147	1.94054
$472$	4.70462	0.216548
$473$	0.193491	0.00889671
$474$	−30.6432	−1.40749
$475$	−3.19684	−0.146681
$476$	−2.98341	−0.136745
$477$	−17.8753	−0.818455
$478$	−30.3524	−1.38829
$479$	−41.7598	−1.90805	−0.954027	−	0.299721i	$-0.903106\pi$
$479$	−41.7598	−1.90805	−0.954027	+	0.299721i	$0.903106\pi$
$480$	−2.41966	−0.110442
$481$	5.66897	0.258483
$482$	−17.2242	−0.784540
$483$	−10.6479	−0.484496
$484$	1.00000	0.0454545
$485$	2.02817	0.0920943
$486$	21.7259	0.985508
$487$	10.8533	0.491808	0.245904	−	0.969294i	$-0.420915\pi$
$487$	10.8533	0.491808	0.245904	+	0.969294i	$0.420915\pi$
$488$	−0.633428	−0.0286739
$489$	52.6441	2.38065
$490$	5.82997	0.263371
$491$	−2.49014	−0.112378	−0.0561892	−	0.998420i	$-0.517895\pi$
$491$	−2.49014	−0.112378	−0.0561892	+	0.998420i	$0.517895\pi$
$492$	10.5113	0.473887
$493$	5.65730	0.254792
$494$	−7.42554	−0.334091
$495$	2.85477	0.128312
$496$	−10.6666	−0.478946
$497$	2.80753	0.125935
$498$	−9.52819	−0.426968
$499$	18.6269	0.833854	0.416927	−	0.908940i	$-0.363107\pi$
$499$	18.6269	0.833854	0.416927	+	0.908940i	$0.363107\pi$
$500$	1.00000	0.0447214
$501$	−4.19994	−0.187640
$502$	−14.6808	−0.655236
$503$	2.26274	0.100891	0.0504454	−	0.998727i	$-0.483936\pi$
$503$	2.26274	0.100891	0.0504454	+	0.998727i	$0.483936\pi$
$504$	−3.08794	−0.137548
$505$	−10.9071	−0.485359
$506$	4.06828	0.180857
$507$	−18.4009	−0.817212
$508$	12.0949	0.536626
$509$	12.0614	0.534611	0.267305	−	0.963612i	$-0.413867\pi$
$509$	12.0614	0.534611	0.267305	+	0.963612i	$0.413867\pi$
$510$	6.67375	0.295519
$511$	−1.08168	−0.0478506
$512$	−1.00000	−0.0441942
$513$	1.12340	0.0495995
$514$	−25.4686	−1.12337
$515$	−11.3410	−0.499742
$516$	0.468182	0.0206106
$517$	−3.69487	−0.162500
$518$	2.63995	0.115993
$519$	−8.12905	−0.356826
$520$	2.32277	0.101860
$521$	16.9427	0.742275	0.371137	−	0.928578i	$-0.378968\pi$
$521$	16.9427	0.742275	0.371137	+	0.928578i	$0.378968\pi$
$522$	5.85551	0.256289
$523$	−9.98261	−0.436509	−0.218255	−	0.975892i	$-0.570036\pi$
$523$	−9.98261	−0.436509	−0.218255	+	0.975892i	$0.570036\pi$
$524$	10.7036	0.467590
$525$	2.61730	0.114228
$526$	−4.95869	−0.216209
$527$	29.4200	1.28156
$528$	2.41966	0.105302
$529$	−6.44913	−0.280397
$530$	6.26157	0.271985
$531$	−13.4306	−0.582839
$532$	−3.45796	−0.149921
$533$	−10.0904	−0.437064
$534$	22.7712	0.985406
$535$	−7.52297	−0.325246
$536$	7.64542	0.330232
$537$	61.0060	2.63260
$538$	−14.5857	−0.628834
$539$	−5.82997	−0.251115
$540$	−0.351411	−0.0151223
$541$	35.0460	1.50675	0.753373	−	0.657593i	$-0.228425\pi$
$541$	35.0460	1.50675	0.753373	+	0.657593i	$0.228425\pi$
$542$	−20.5674	−0.883446
$543$	−8.79637	−0.377489
$544$	2.75813	0.118254
$545$	16.6479	0.713117
$546$	6.07939	0.260174
$547$	−6.39400	−0.273388	−0.136694	−	0.990613i	$-0.543648\pi$
$547$	−6.39400	−0.273388	−0.136694	+	0.990613i	$0.543648\pi$
$548$	−3.73647	−0.159614
$549$	1.80829	0.0771760
$550$	−1.00000	−0.0426401
$551$	6.55715	0.279344
$552$	9.84386	0.418982
$553$	13.6986	0.582525
$554$	−19.1121	−0.811994
$555$	−5.90544	−0.250672
$556$	−15.1575	−0.642819
$557$	−18.2693	−0.774093	−0.387047	−	0.922060i	$-0.626505\pi$
$557$	−18.2693	−0.774093	−0.387047	+	0.922060i	$0.626505\pi$
$558$	30.4508	1.28908
$559$	−0.449435	−0.0190091
$560$	1.08168	0.0457093
$561$	−6.67375	−0.281766
$562$	−7.31817	−0.308698
$563$	−3.63579	−0.153230	−0.0766152	−	0.997061i	$-0.524411\pi$
$563$	−3.63579	−0.153230	−0.0766152	+	0.997061i	$0.524411\pi$
$564$	−8.94034	−0.376456
$565$	−4.17707	−0.175731
$566$	32.4599	1.36439
$567$	−10.1836	−0.427670
$568$	−2.59553	−0.108906
$569$	−9.73785	−0.408232	−0.204116	−	0.978947i	$-0.565432\pi$
$569$	−9.73785	−0.408232	−0.204116	+	0.978947i	$0.565432\pi$
$570$	7.73528	0.323995
$571$	−31.2127	−1.30621	−0.653106	−	0.757266i	$-0.726534\pi$
$571$	−31.2127	−1.30621	−0.653106	+	0.757266i	$0.726534\pi$
$572$	−2.32277	−0.0971200
$573$	−8.76259	−0.366062
$574$	−4.69894	−0.196130
$575$	−4.06828	−0.169659
$576$	2.85477	0.118949
$577$	−22.1093	−0.920423	−0.460212	−	0.887809i	$-0.652227\pi$
$577$	−22.1093	−0.920423	−0.460212	+	0.887809i	$0.652227\pi$
$578$	9.39270	0.390685
$579$	−57.0560	−2.37117
$580$	−2.05113	−0.0851687
$581$	4.25945	0.176712
$582$	−4.90748	−0.203422
$583$	−6.26157	−0.259328
$584$	1.00000	0.0413803
$585$	−6.63098	−0.274157
$586$	−27.8643	−1.15106
$587$	42.7625	1.76500	0.882498	−	0.470317i	$-0.155860\pi$
$587$	42.7625	1.76500	0.882498	+	0.470317i	$0.155860\pi$
$588$	−14.1066	−0.581745
$589$	34.0996	1.40505
$590$	4.70462	0.193686
$591$	45.3763	1.86653
$592$	−2.44060	−0.100308
$593$	−19.4293	−0.797865	−0.398932	−	0.916980i	$-0.630619\pi$
$593$	−19.4293	−0.797865	−0.398932	+	0.916980i	$0.630619\pi$
$594$	0.351411	0.0144186
$595$	−2.98341	−0.122308
$596$	−13.6261	−0.558145
$597$	14.0830	0.576380
$598$	−9.44968	−0.386426
$599$	−23.1854	−0.947328	−0.473664	−	0.880706i	$-0.657069\pi$
$599$	−23.1854	−0.947328	−0.473664	+	0.880706i	$0.657069\pi$
$600$	−2.41966	−0.0987823
$601$	−1.17508	−0.0479326	−0.0239663	−	0.999713i	$-0.507629\pi$
$601$	−1.17508	−0.0479326	−0.0239663	+	0.999713i	$0.507629\pi$
$602$	−0.209295	−0.00853021
$603$	−21.8259	−0.888820
$604$	22.8565	0.930017
$605$	1.00000	0.0406558
$606$	26.3915	1.07208
$607$	−15.8557	−0.643563	−0.321782	−	0.946814i	$-0.604282\pi$
$607$	−15.8557	−0.643563	−0.321782	+	0.946814i	$0.604282\pi$
$608$	3.19684	0.129649
$609$	−5.36843	−0.217540
$610$	−0.633428	−0.0256468
$611$	8.58234	0.347204
$612$	−7.87383	−0.318281
$613$	−9.74108	−0.393439	−0.196719	−	0.980460i	$-0.563029\pi$
$613$	−9.74108	−0.393439	−0.196719	+	0.980460i	$0.563029\pi$
$614$	30.0726	1.21363
$615$	10.5113	0.423857
$616$	−1.08168	−0.0435821
$617$	−16.2185	−0.652932	−0.326466	−	0.945209i	$-0.605858\pi$
$617$	−16.2185	−0.652932	−0.326466	+	0.945209i	$0.605858\pi$
$618$	27.4413	1.10385
$619$	−31.8257	−1.27918	−0.639592	−	0.768714i	$-0.720897\pi$
$619$	−31.8257	−1.27918	−0.639592	+	0.768714i	$0.720897\pi$
$620$	−10.6666	−0.428382
$621$	1.42964	0.0573693
$622$	12.3438	0.494939
$623$	−10.1796	−0.407836
$624$	−5.62033	−0.224993
$625$	1.00000	0.0400000
$626$	16.3944	0.655252
$627$	−7.73528	−0.308917
$628$	17.4052	0.694542
$629$	6.73151	0.268403
$630$	−3.08794	−0.123027
$631$	40.7805	1.62345	0.811724	−	0.584041i	$-0.198529\pi$
$631$	40.7805	1.62345	0.811724	+	0.584041i	$0.198529\pi$
$632$	−12.6642	−0.503756
$633$	−7.21350	−0.286711
$634$	25.3604	1.00719
$635$	12.0949	0.479973
$636$	−15.1509	−0.600772
$637$	13.5417	0.536542
$638$	2.05113	0.0812052
$639$	7.40964	0.293121
$640$	−1.00000	−0.0395285
$641$	30.4843	1.20406	0.602029	−	0.798474i	$-0.294359\pi$
$641$	30.4843	1.20406	0.602029	+	0.798474i	$0.294359\pi$
$642$	18.2031	0.718417
$643$	−12.0546	−0.475389	−0.237694	−	0.971340i	$-0.576392\pi$
$643$	−12.0546	−0.475389	−0.237694	+	0.971340i	$0.576392\pi$
$644$	−4.40057	−0.173407
$645$	0.468182	0.0184347
$646$	−8.81732	−0.346913
$647$	27.5885	1.08461	0.542307	−	0.840180i	$-0.317551\pi$
$647$	27.5885	1.08461	0.542307	+	0.840180i	$0.317551\pi$
$648$	9.41460	0.369840
$649$	−4.70462	−0.184673
$650$	2.32277	0.0911066
$651$	−27.9178	−1.09418
$652$	21.7568	0.852061
$653$	−43.6586	−1.70849	−0.854246	−	0.519868i	$-0.825981\pi$
$653$	−43.6586	−1.70849	−0.854246	+	0.519868i	$0.825981\pi$
$654$	−40.2823	−1.57516
$655$	10.7036	0.418225
$656$	4.34412	0.169609
$657$	−2.85477	−0.111375
$658$	3.99666	0.155806
$659$	20.1204	0.783779	0.391890	−	0.920012i	$-0.371822\pi$
$659$	20.1204	0.783779	0.391890	+	0.920012i	$0.371822\pi$
$660$	2.41966	0.0941853
$661$	28.6099	1.11280	0.556398	−	0.830916i	$-0.312183\pi$
$661$	28.6099	1.11280	0.556398	+	0.830916i	$0.312183\pi$
$662$	−7.65058	−0.297348
$663$	15.5016	0.602033
$664$	−3.93782	−0.152817
$665$	−3.45796	−0.134094
$666$	6.96736	0.269980
$667$	8.34458	0.323103
$668$	−1.73575	−0.0671584
$669$	−66.5774	−2.57403
$670$	7.64542	0.295368
$671$	0.633428	0.0244532
$672$	−2.61730	−0.100964
$673$	−0.774220	−0.0298440	−0.0149220	−	0.999889i	$-0.504750\pi$
$673$	−0.774220	−0.0298440	−0.0149220	+	0.999889i	$0.504750\pi$
$674$	11.6829	0.450009
$675$	−0.351411	−0.0135258
$676$	−7.60473	−0.292490
$677$	−22.2160	−0.853830	−0.426915	−	0.904292i	$-0.640400\pi$
$677$	−22.2160	−0.853830	−0.426915	+	0.904292i	$0.640400\pi$
$678$	10.1071	0.388161
$679$	2.19382	0.0841912
$680$	2.75813	0.105770
$681$	−31.3458	−1.20117
$682$	10.6666	0.408447
$683$	40.2481	1.54005	0.770025	−	0.638014i	$-0.220244\pi$
$683$	40.2481	1.54005	0.770025	+	0.638014i	$0.220244\pi$
$684$	−9.12625	−0.348951
$685$	−3.73647	−0.142763
$686$	13.8779	0.529861
$687$	−65.5710	−2.50169
$688$	0.193491	0.00737676
$689$	14.5442	0.554090
$690$	9.84386	0.374749
$691$	14.9148	0.567384	0.283692	−	0.958915i	$-0.408441\pi$
$691$	14.9148	0.567384	0.283692	+	0.958915i	$0.408441\pi$
$692$	−3.35958	−0.127712
$693$	3.08794	0.117301
$694$	−0.216678	−0.00822498
$695$	−15.1575	−0.574955
$696$	4.96305	0.188124
$697$	−11.9817	−0.453838
$698$	22.4242	0.848769
$699$	39.9847	1.51236
$700$	1.08168	0.0408836
$701$	21.2619	0.803051	0.401526	−	0.915848i	$-0.368480\pi$
$701$	21.2619	0.803051	0.401526	+	0.915848i	$0.368480\pi$
$702$	−0.816247	−0.0308073
$703$	7.80222	0.294266
$704$	1.00000	0.0376889
$705$	−8.94034	−0.336713
$706$	−19.2782	−0.725544
$707$	−11.7980	−0.443708
$708$	−11.3836	−0.427822
$709$	−23.5684	−0.885131	−0.442565	−	0.896736i	$-0.645932\pi$
$709$	−23.5684	−0.885131	−0.442565	+	0.896736i	$0.645932\pi$
$710$	−2.59553	−0.0974086
$711$	36.1535	1.35586
$712$	9.41090	0.352688
$713$	43.3948	1.62515
$714$	7.21885	0.270159
$715$	−2.32277	−0.0868668
$716$	25.2126	0.942239
$717$	73.4426	2.74276
$718$	10.2885	0.383963
$719$	−25.6724	−0.957420	−0.478710	−	0.877973i	$-0.658896\pi$
$719$	−25.6724	−0.957420	−0.478710	+	0.877973i	$0.658896\pi$
$720$	2.85477	0.106391
$721$	−12.2673	−0.456857
$722$	8.78020	0.326765
$723$	41.6767	1.54997
$724$	−3.63537	−0.135108
$725$	−2.05113	−0.0761772
$726$	−2.41966	−0.0898021
$727$	−8.13512	−0.301715	−0.150857	−	0.988556i	$-0.548203\pi$
$727$	−8.13512	−0.301715	−0.150857	+	0.988556i	$0.548203\pi$
$728$	2.51249	0.0931192
$729$	−24.3256	−0.900949
$730$	1.00000	0.0370117
$731$	−0.533673	−0.0197386
$732$	1.53268	0.0566496
$733$	−48.0339	−1.77417	−0.887087	−	0.461602i	$-0.847275\pi$
$733$	−48.0339	−1.77417	−0.887087	+	0.461602i	$0.847275\pi$
$734$	10.5989	0.391213
$735$	−14.1066	−0.520329
$736$	4.06828	0.149959
$737$	−7.64542	−0.281623
$738$	−12.4015	−0.456504
$739$	26.5872	0.978024	0.489012	−	0.872277i	$-0.337357\pi$
$739$	26.5872	0.978024	0.489012	+	0.872277i	$0.337357\pi$
$740$	−2.44060	−0.0897183
$741$	17.9673	0.660045
$742$	6.77300	0.248645
$743$	−22.6769	−0.831934	−0.415967	−	0.909380i	$-0.636557\pi$
$743$	−22.6769	−0.831934	−0.415967	+	0.909380i	$0.636557\pi$
$744$	25.8097	0.946228
$745$	−13.6261	−0.499220
$746$	−35.8985	−1.31434
$747$	11.2416	0.411307
$748$	−2.75813	−0.100847
$749$	−8.13743	−0.297335
$750$	−2.41966	−0.0883536
$751$	−21.7492	−0.793640	−0.396820	−	0.917896i	$-0.629886\pi$
$751$	−21.7492	−0.793640	−0.396820	+	0.917896i	$0.629886\pi$
$752$	−3.69487	−0.134738
$753$	35.5226	1.29452
$754$	−4.76432	−0.173506
$755$	22.8565	0.831832
$756$	−0.380113	−0.0138246
$757$	−52.9038	−1.92282	−0.961410	−	0.275121i	$-0.911282\pi$
$757$	−52.9038	−1.92282	−0.961410	+	0.275121i	$0.911282\pi$
$758$	29.3821	1.06721
$759$	−9.84386	−0.357309
$760$	3.19684	0.115962
$761$	30.0982	1.09106	0.545529	−	0.838092i	$-0.316329\pi$
$761$	30.0982	1.09106	0.545529	+	0.838092i	$0.316329\pi$
$762$	−29.2657	−1.06018
$763$	18.0077	0.651921
$764$	−3.62141	−0.131018
$765$	−7.87383	−0.284679
$766$	−19.3946	−0.700756
$767$	10.9278	0.394579
$768$	2.41966	0.0873121
$769$	33.0988	1.19357	0.596787	−	0.802400i	$-0.296444\pi$
$769$	33.0988	1.19357	0.596787	+	0.802400i	$0.296444\pi$
$770$	−1.08168	−0.0389810
$771$	61.6254	2.21938
$772$	−23.5802	−0.848669
$773$	−45.0172	−1.61916	−0.809579	−	0.587012i	$-0.800304\pi$
$773$	−45.0172	−1.61916	−0.809579	+	0.587012i	$0.800304\pi$
$774$	−0.552371	−0.0198546
$775$	−10.6666	−0.383157
$776$	−2.02817	−0.0728069
$777$	−6.38778	−0.229160
$778$	−19.9052	−0.713634
$779$	−13.8875	−0.497571
$780$	−5.62033	−0.201240
$781$	2.59553	0.0928754
$782$	−11.2208	−0.401257
$783$	0.720791	0.0257590
$784$	−5.82997	−0.208213
$785$	17.4052	0.621217
$786$	−25.8992	−0.923793
$787$	−9.93984	−0.354317	−0.177159	−	0.984182i	$-0.556691\pi$
$787$	−9.93984	−0.354317	−0.177159	+	0.984182i	$0.556691\pi$
$788$	18.7532	0.668054
$789$	11.9984	0.427153
$790$	−12.6642	−0.450573
$791$	−4.51825	−0.160650
$792$	−2.85477	−0.101440
$793$	−1.47131	−0.0522477
$794$	−28.7073	−1.01878
$795$	−15.1509	−0.537347
$796$	5.82024	0.206293
$797$	5.98991	0.212174	0.106087	−	0.994357i	$-0.466168\pi$
$797$	5.98991	0.212174	0.106087	+	0.994357i	$0.466168\pi$
$798$	8.36709	0.296192
$799$	10.1909	0.360530
$800$	−1.00000	−0.0353553
$801$	−26.8659	−0.949261
$802$	1.46219	0.0516316
$803$	−1.00000	−0.0352892
$804$	−18.4993	−0.652422
$805$	−4.40057	−0.155100
$806$	−24.7762	−0.872703
$807$	35.2925	1.24235
$808$	10.9071	0.383710
$809$	−15.1961	−0.534268	−0.267134	−	0.963659i	$-0.586077\pi$
$809$	−15.1961	−0.534268	−0.267134	+	0.963659i	$0.586077\pi$
$810$	9.41460	0.330795
$811$	20.2870	0.712371	0.356186	−	0.934415i	$-0.384077\pi$
$811$	20.2870	0.712371	0.356186	+	0.934415i	$0.384077\pi$
$812$	−2.21867	−0.0778600
$813$	49.7662	1.74538
$814$	2.44060	0.0855431
$815$	21.7568	0.762107
$816$	−6.67375	−0.233628
$817$	−0.618559	−0.0216406
$818$	3.26767	0.114251
$819$	−7.17259	−0.250630
$820$	4.34412	0.151703
$821$	−24.0385	−0.838949	−0.419475	−	0.907767i	$-0.637786\pi$
$821$	−24.0385	−0.838949	−0.419475	+	0.907767i	$0.637786\pi$
$822$	9.04100	0.315341
$823$	23.2203	0.809409	0.404705	−	0.914447i	$-0.367374\pi$
$823$	23.2203	0.809409	0.404705	+	0.914447i	$0.367374\pi$
$824$	11.3410	0.395081
$825$	2.41966	0.0842419
$826$	5.08889	0.177065
$827$	−16.1626	−0.562030	−0.281015	−	0.959703i	$-0.590671\pi$
$827$	−16.1626	−0.562030	−0.281015	+	0.959703i	$0.590671\pi$
$828$	−11.6140	−0.403614
$829$	−7.35470	−0.255439	−0.127720	−	0.991810i	$-0.540766\pi$
$829$	−7.35470	−0.255439	−0.127720	+	0.991810i	$0.540766\pi$
$830$	−3.93782	−0.136684
$831$	46.2448	1.60421
$832$	−2.32277	−0.0805276
$833$	16.0798	0.557134
$834$	36.6759	1.26998
$835$	−1.73575	−0.0600683
$836$	−3.19684	−0.110565
$837$	3.74837	0.129563
$838$	−12.7661	−0.440999
$839$	11.9654	0.413093	0.206546	−	0.978437i	$-0.433778\pi$
$839$	11.9654	0.413093	0.206546	+	0.978437i	$0.433778\pi$
$840$	−2.61730	−0.0903053
$841$	−24.7928	−0.854926
$842$	−4.53611	−0.156325
$843$	17.7075	0.609879
$844$	−2.98120	−0.102617
$845$	−7.60473	−0.261611
$846$	10.5480	0.362648
$847$	1.08168	0.0371669
$848$	−6.26157	−0.215023
$849$	−78.5420	−2.69556
$850$	2.75813	0.0946032
$851$	9.92905	0.340363
$852$	6.28031	0.215160
$853$	20.5757	0.704499	0.352250	−	0.935906i	$-0.385417\pi$
$853$	20.5757	0.704499	0.352250	+	0.935906i	$0.385417\pi$
$854$	−0.685165	−0.0234459
$855$	−9.12625	−0.312111
$856$	7.52297	0.257130
$857$	−5.10602	−0.174418	−0.0872092	−	0.996190i	$-0.527795\pi$
$857$	−5.10602	−0.174418	−0.0872092	+	0.996190i	$0.527795\pi$
$858$	5.62033	0.191875
$859$	−21.8064	−0.744025	−0.372013	−	0.928228i	$-0.621332\pi$
$859$	−21.8064	−0.744025	−0.372013	+	0.928228i	$0.621332\pi$
$860$	0.193491	0.00659798
$861$	11.3699	0.387484
$862$	−9.09018	−0.309613
$863$	52.3340	1.78147	0.890736	−	0.454522i	$-0.150190\pi$
$863$	52.3340	1.78147	0.890736	+	0.454522i	$0.150190\pi$
$864$	0.351411	0.0119552
$865$	−3.35958	−0.114229
$866$	−37.0153	−1.25783
$867$	−22.7272	−0.771855
$868$	−11.5379	−0.391621
$869$	12.6642	0.429605
$870$	4.96305	0.168263
$871$	17.7586	0.601727
$872$	−16.6479	−0.563769
$873$	5.78994	0.195960
$874$	−13.0056	−0.439922
$875$	1.08168	0.0365674
$876$	−2.41966	−0.0817528
$877$	−43.4954	−1.46873	−0.734367	−	0.678752i	$-0.762521\pi$
$877$	−43.4954	−1.46873	−0.734367	+	0.678752i	$0.762521\pi$
$878$	21.4954	0.725434
$879$	67.4222	2.27410
$880$	1.00000	0.0337100
$881$	−23.2559	−0.783510	−0.391755	−	0.920070i	$-0.628132\pi$
$881$	−23.2559	−0.783510	−0.391755	+	0.920070i	$0.628132\pi$
$882$	16.6432	0.560406
$883$	−58.4986	−1.96864	−0.984318	−	0.176405i	$-0.943553\pi$
$883$	−58.4986	−1.96864	−0.984318	+	0.176405i	$0.943553\pi$
$884$	6.40652	0.215474
$885$	−11.3836	−0.382656
$886$	15.3961	0.517242
$887$	−14.6127	−0.490646	−0.245323	−	0.969441i	$-0.578894\pi$
$887$	−14.6127	−0.490646	−0.245323	+	0.969441i	$0.578894\pi$
$888$	5.90544	0.198173
$889$	13.0828	0.438784
$890$	9.41090	0.315454
$891$	−9.41460	−0.315401
$892$	−27.5151	−0.921275
$893$	11.8119	0.395271
$894$	32.9705	1.10270
$895$	25.2126	0.842764
$896$	−1.08168	−0.0361363
$897$	22.8650	0.763441
$898$	16.6062	0.554155
$899$	21.8787	0.729695
$900$	2.85477	0.0951590
$901$	17.2702	0.575355
$902$	−4.34412	−0.144643
$903$	0.506422	0.0168527
$904$	4.17707	0.138927
$905$	−3.63537	−0.120844
$906$	−55.3050	−1.83738
$907$	−3.85606	−0.128038	−0.0640191	−	0.997949i	$-0.520392\pi$
$907$	−3.85606	−0.128038	−0.0640191	+	0.997949i	$0.520392\pi$
$908$	−12.9546	−0.429913
$909$	−31.1372	−1.03276
$910$	2.51249	0.0832883
$911$	39.7421	1.31671	0.658357	−	0.752705i	$-0.271252\pi$
$911$	39.7421	1.31671	0.658357	+	0.752705i	$0.271252\pi$
$912$	−7.73528	−0.256141
$913$	3.93782	0.130323
$914$	−17.9591	−0.594034
$915$	1.53268	0.0506689
$916$	−27.0992	−0.895384
$917$	11.5779	0.382335
$918$	−0.969238	−0.0319896
$919$	17.5185	0.577882	0.288941	−	0.957347i	$-0.406697\pi$
$919$	17.5185	0.577882	0.288941	+	0.957347i	$0.406697\pi$
$920$	4.06828	0.134127
$921$	−72.7655	−2.39771
$922$	27.6692	0.911235
$923$	−6.02883	−0.198441
$924$	2.61730	0.0861027
$925$	−2.44060	−0.0802465
$926$	0.286392	0.00941143
$927$	−32.3758	−1.06336
$928$	2.05113	0.0673318
$929$	−46.9531	−1.54048	−0.770240	−	0.637754i	$-0.779864\pi$
$929$	−46.9531	−1.54048	−0.770240	+	0.637754i	$0.779864\pi$
$930$	25.8097	0.846332
$931$	18.6375	0.610820
$932$	16.5249	0.541292
$933$	−29.8677	−0.977825
$934$	−6.01091	−0.196683
$935$	−2.75813	−0.0902006
$936$	6.63098	0.216740
$937$	−60.8677	−1.98846	−0.994230	−	0.107266i	$-0.965790\pi$
$937$	−60.8677	−1.98846	−0.994230	+	0.107266i	$0.965790\pi$
$938$	8.26989	0.270021
$939$	−39.6689	−1.29455
$940$	−3.69487	−0.120513
$941$	4.37954	0.142769	0.0713845	−	0.997449i	$-0.477258\pi$
$941$	4.37954	0.142769	0.0713845	+	0.997449i	$0.477258\pi$
$942$	−42.1147	−1.37217
$943$	−17.6731	−0.575515
$944$	−4.70462	−0.153122
$945$	−0.380113	−0.0123651
$946$	−0.193491	−0.00629092
$947$	−27.6288	−0.897815	−0.448907	−	0.893578i	$-0.648187\pi$
$947$	−27.6288	−0.897815	−0.448907	+	0.893578i	$0.648187\pi$
$948$	30.6432	0.995244
$949$	2.32277	0.0754004
$950$	3.19684	0.103719
$951$	−61.3637	−1.98985
$952$	2.98341	0.0966930
$953$	30.4251	0.985567	0.492784	−	0.870152i	$-0.335979\pi$
$953$	30.4251	0.985567	0.492784	+	0.870152i	$0.335979\pi$
$954$	17.8753	0.578735
$955$	−3.62141	−0.117186
$956$	30.3524	0.981667
$957$	−4.96305	−0.160433
$958$	41.7598	1.34920
$959$	−4.04166	−0.130512
$960$	2.41966	0.0780943
$961$	82.7771	2.67023
$962$	−5.66897	−0.182775
$963$	−21.4763	−0.692065
$964$	17.2242	0.554754
$965$	−23.5802	−0.759072
$966$	10.6479	0.342590
$967$	−26.9313	−0.866052	−0.433026	−	0.901381i	$-0.642554\pi$
$967$	−26.9313	−0.866052	−0.433026	+	0.901381i	$0.642554\pi$
$968$	−1.00000	−0.0321412
$969$	21.3349	0.685377
$970$	−2.02817	−0.0651205
$971$	−4.02097	−0.129039	−0.0645196	−	0.997916i	$-0.520551\pi$
$971$	−4.02097	−0.129039	−0.0645196	+	0.997916i	$0.520551\pi$
$972$	−21.7259	−0.696860
$973$	−16.3955	−0.525615
$974$	−10.8533	−0.347761
$975$	−5.62033	−0.179994
$976$	0.633428	0.0202755
$977$	−20.2355	−0.647392	−0.323696	−	0.946161i	$-0.604926\pi$
$977$	−20.2355	−0.647392	−0.323696	+	0.946161i	$0.604926\pi$
$978$	−52.6441	−1.68337
$979$	−9.41090	−0.300774
$980$	−5.82997	−0.186232
$981$	47.5259	1.51738
$982$	2.49014	0.0794635
$983$	−0.330364	−0.0105370	−0.00526848	−	0.999986i	$-0.501677\pi$
$983$	−0.330364	−0.0105370	−0.00526848	+	0.999986i	$0.501677\pi$
$984$	−10.5113	−0.335088
$985$	18.7532	0.597526
$986$	−5.65730	−0.180165
$987$	−9.67057	−0.307818
$988$	7.42554	0.236238
$989$	−0.787173	−0.0250307
$990$	−2.85477	−0.0907305
$991$	35.2932	1.12112	0.560562	−	0.828112i	$-0.310585\pi$
$991$	35.2932	1.12112	0.560562	+	0.828112i	$0.310585\pi$
$992$	10.6666	0.338666
$993$	18.5118	0.587455
$994$	−2.80753	−0.0890494
$995$	5.82024	0.184514
$996$	9.52819	0.301912
$997$	5.89045	0.186552	0.0932762	−	0.995640i	$-0.470266\pi$
$997$	5.89045	0.186552	0.0932762	+	0.995640i	$0.470266\pi$
$998$	−18.6269	−0.589624
$999$	0.857654	0.0271350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bc.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bc.1.11	✓	11	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.41966 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41966 q^{6} +1.08168 q^{7} -1.00000 q^{8} +2.85477 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.41966 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41966 q^{6} +1.08168 q^{7} -1.00000 q^{8} +2.85477 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.41966 q^{12} -2.32277 q^{13} -1.08168 q^{14} +2.41966 q^{15} +1.00000 q^{16} -2.75813 q^{17} -2.85477 q^{18} -3.19684 q^{19} +1.00000 q^{20} +2.61730 q^{21} -1.00000 q^{22} -4.06828 q^{23} -2.41966 q^{24} +1.00000 q^{25} +2.32277 q^{26} -0.351411 q^{27} +1.08168 q^{28} -2.05113 q^{29} -2.41966 q^{30} -10.6666 q^{31} -1.00000 q^{32} +2.41966 q^{33} +2.75813 q^{34} +1.08168 q^{35} +2.85477 q^{36} -2.44060 q^{37} +3.19684 q^{38} -5.62033 q^{39} -1.00000 q^{40} +4.34412 q^{41} -2.61730 q^{42} +0.193491 q^{43} +1.00000 q^{44} +2.85477 q^{45} +4.06828 q^{46} -3.69487 q^{47} +2.41966 q^{48} -5.82997 q^{49} -1.00000 q^{50} -6.67375 q^{51} -2.32277 q^{52} -6.26157 q^{53} +0.351411 q^{54} +1.00000 q^{55} -1.08168 q^{56} -7.73528 q^{57} +2.05113 q^{58} -4.70462 q^{59} +2.41966 q^{60} +0.633428 q^{61} +10.6666 q^{62} +3.08794 q^{63} +1.00000 q^{64} -2.32277 q^{65} -2.41966 q^{66} -7.64542 q^{67} -2.75813 q^{68} -9.84386 q^{69} -1.08168 q^{70} +2.59553 q^{71} -2.85477 q^{72} -1.00000 q^{73} +2.44060 q^{74} +2.41966 q^{75} -3.19684 q^{76} +1.08168 q^{77} +5.62033 q^{78} +12.6642 q^{79} +1.00000 q^{80} -9.41460 q^{81} -4.34412 q^{82} +3.93782 q^{83} +2.61730 q^{84} -2.75813 q^{85} -0.193491 q^{86} -4.96305 q^{87} -1.00000 q^{88} -9.41090 q^{89} -2.85477 q^{90} -2.51249 q^{91} -4.06828 q^{92} -25.8097 q^{93} +3.69487 q^{94} -3.19684 q^{95} -2.41966 q^{96} +2.02817 q^{97} +5.82997 q^{98} +2.85477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

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