LMFDB - Embedded newform 8030.2.a.bl.1.7

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:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} - x^{17} + 200 x^{16} - 263 x^{15} - 1900 x^{14} + 3165 x^{13} + 10217 x^{12} + \cdots + 1388 $ x^19 - 9x^18 - x^17 + 200x^16 - 263x^15 - 1900x^14 + 3165x^13 + 10217x^12 - 16393x^11 - 33875x^10 + 44043x^9 + 68537x^8 - 63620x^7 - 79890x^6 + 48388x^5 + 49353x^4 - 17806x^3 - 14287x^2 + 2436*x + 1388
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.26056$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.260557 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.260557 q^{6} -0.332615 q^{7} +1.00000 q^{8} -2.93211 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.260557 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.260557 q^{6} -0.332615 q^{7} +1.00000 q^{8} -2.93211 q^{9} +1.00000 q^{10} +1.00000 q^{11} -0.260557 q^{12} +1.17725 q^{13} -0.332615 q^{14} -0.260557 q^{15} +1.00000 q^{16} -2.26526 q^{17} -2.93211 q^{18} -5.91708 q^{19} +1.00000 q^{20} +0.0866651 q^{21} +1.00000 q^{22} +5.32638 q^{23} -0.260557 q^{24} +1.00000 q^{25} +1.17725 q^{26} +1.54565 q^{27} -0.332615 q^{28} +2.41194 q^{29} -0.260557 q^{30} +3.43615 q^{31} +1.00000 q^{32} -0.260557 q^{33} -2.26526 q^{34} -0.332615 q^{35} -2.93211 q^{36} +10.8505 q^{37} -5.91708 q^{38} -0.306740 q^{39} +1.00000 q^{40} +4.91154 q^{41} +0.0866651 q^{42} +1.16823 q^{43} +1.00000 q^{44} -2.93211 q^{45} +5.32638 q^{46} -7.51930 q^{47} -0.260557 q^{48} -6.88937 q^{49} +1.00000 q^{50} +0.590229 q^{51} +1.17725 q^{52} -13.7653 q^{53} +1.54565 q^{54} +1.00000 q^{55} -0.332615 q^{56} +1.54173 q^{57} +2.41194 q^{58} +1.28536 q^{59} -0.260557 q^{60} +6.94198 q^{61} +3.43615 q^{62} +0.975264 q^{63} +1.00000 q^{64} +1.17725 q^{65} -0.260557 q^{66} +9.48895 q^{67} -2.26526 q^{68} -1.38782 q^{69} -0.332615 q^{70} +9.95746 q^{71} -2.93211 q^{72} -1.00000 q^{73} +10.8505 q^{74} -0.260557 q^{75} -5.91708 q^{76} -0.332615 q^{77} -0.306740 q^{78} +1.75015 q^{79} +1.00000 q^{80} +8.39360 q^{81} +4.91154 q^{82} +11.7551 q^{83} +0.0866651 q^{84} -2.26526 q^{85} +1.16823 q^{86} -0.628447 q^{87} +1.00000 q^{88} +9.25022 q^{89} -2.93211 q^{90} -0.391571 q^{91} +5.32638 q^{92} -0.895311 q^{93} -7.51930 q^{94} -5.91708 q^{95} -0.260557 q^{96} +12.1089 q^{97} -6.88937 q^{98} -2.93211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) $ 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * 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
$3$	−0.260557	−0.150432	−0.0752162	−	0.997167i	$-0.523965\pi$
$3$	−0.260557	−0.150432	−0.0752162	+	0.997167i	$0.523965\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.260557	−0.106372
$7$	−0.332615	−0.125717	−0.0628583	−	0.998022i	$-0.520022\pi$
$7$	−0.332615	−0.125717	−0.0628583	+	0.998022i	$0.520022\pi$
$8$	1.00000	0.353553
$9$	−2.93211	−0.977370
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.260557	−0.0752162
$13$	1.17725	0.326511	0.163255	−	0.986584i	$-0.447801\pi$
$13$	1.17725	0.326511	0.163255	+	0.986584i	$0.447801\pi$
$14$	−0.332615	−0.0888951
$15$	−0.260557	−0.0672754
$16$	1.00000	0.250000
$17$	−2.26526	−0.549407	−0.274703	−	0.961529i	$-0.588580\pi$
$17$	−2.26526	−0.549407	−0.274703	+	0.961529i	$0.588580\pi$
$18$	−2.93211	−0.691105
$19$	−5.91708	−1.35747	−0.678735	−	0.734383i	$-0.737472\pi$
$19$	−5.91708	−1.35747	−0.678735	+	0.734383i	$0.737472\pi$
$20$	1.00000	0.223607
$21$	0.0866651	0.0189119
$22$	1.00000	0.213201
$23$	5.32638	1.11063	0.555313	−	0.831641i	$-0.312598\pi$
$23$	5.32638	1.11063	0.555313	+	0.831641i	$0.312598\pi$
$24$	−0.260557	−0.0531859
$25$	1.00000	0.200000
$26$	1.17725	0.230878
$27$	1.54565	0.297461
$28$	−0.332615	−0.0628583
$29$	2.41194	0.447886	0.223943	−	0.974602i	$-0.428107\pi$
$29$	2.41194	0.447886	0.223943	+	0.974602i	$0.428107\pi$
$30$	−0.260557	−0.0475709
$31$	3.43615	0.617150	0.308575	−	0.951200i	$-0.400148\pi$
$31$	3.43615	0.617150	0.308575	+	0.951200i	$0.400148\pi$
$32$	1.00000	0.176777
$33$	−0.260557	−0.0453571
$34$	−2.26526	−0.388489
$35$	−0.332615	−0.0562222
$36$	−2.93211	−0.488685
$37$	10.8505	1.78381	0.891903	−	0.452228i	$-0.149371\pi$
$37$	10.8505	1.78381	0.891903	+	0.452228i	$0.149371\pi$
$38$	−5.91708	−0.959877
$39$	−0.306740	−0.0491178
$40$	1.00000	0.158114
$41$	4.91154	0.767054	0.383527	−	0.923530i	$-0.374709\pi$
$41$	4.91154	0.767054	0.383527	+	0.923530i	$0.374709\pi$
$42$	0.0866651	0.0133727
$43$	1.16823	0.178154	0.0890769	−	0.996025i	$-0.471608\pi$
$43$	1.16823	0.178154	0.0890769	+	0.996025i	$0.471608\pi$
$44$	1.00000	0.150756
$45$	−2.93211	−0.437093
$46$	5.32638	0.785332
$47$	−7.51930	−1.09680	−0.548401	−	0.836215i	$-0.684763\pi$
$47$	−7.51930	−1.09680	−0.548401	+	0.836215i	$0.684763\pi$
$48$	−0.260557	−0.0376081
$49$	−6.88937	−0.984195
$50$	1.00000	0.141421
$51$	0.590229	0.0826486
$52$	1.17725	0.163255
$53$	−13.7653	−1.89080	−0.945402	−	0.325908i	$-0.894330\pi$
$53$	−13.7653	−1.89080	−0.945402	+	0.325908i	$0.894330\pi$
$54$	1.54565	0.210336
$55$	1.00000	0.134840
$56$	−0.332615	−0.0444476
$57$	1.54173	0.204208
$58$	2.41194	0.316703
$59$	1.28536	0.167340	0.0836700	−	0.996494i	$-0.473336\pi$
$59$	1.28536	0.167340	0.0836700	+	0.996494i	$0.473336\pi$
$60$	−0.260557	−0.0336377
$61$	6.94198	0.888829	0.444415	−	0.895821i	$-0.353412\pi$
$61$	6.94198	0.888829	0.444415	+	0.895821i	$0.353412\pi$
$62$	3.43615	0.436391
$63$	0.975264	0.122872
$64$	1.00000	0.125000
$65$	1.17725	0.146020
$66$	−0.260557	−0.0320723
$67$	9.48895	1.15926	0.579630	−	0.814880i	$-0.303197\pi$
$67$	9.48895	1.15926	0.579630	+	0.814880i	$0.303197\pi$
$68$	−2.26526	−0.274703
$69$	−1.38782	−0.167074
$70$	−0.332615	−0.0397551
$71$	9.95746	1.18173	0.590866	−	0.806769i	$-0.298786\pi$
$71$	9.95746	1.18173	0.590866	+	0.806769i	$0.298786\pi$
$72$	−2.93211	−0.345553
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	10.8505	1.26134
$75$	−0.260557	−0.0300865
$76$	−5.91708	−0.678735
$77$	−0.332615	−0.0379050
$78$	−0.306740	−0.0347315
$79$	1.75015	0.196907	0.0984536	−	0.995142i	$-0.468610\pi$
$79$	1.75015	0.196907	0.0984536	+	0.995142i	$0.468610\pi$
$80$	1.00000	0.111803
$81$	8.39360	0.932622
$82$	4.91154	0.542389
$83$	11.7551	1.29029	0.645147	−	0.764058i	$-0.276796\pi$
$83$	11.7551	1.29029	0.645147	+	0.764058i	$0.276796\pi$
$84$	0.0866651	0.00945593
$85$	−2.26526	−0.245702
$86$	1.16823	0.125974
$87$	−0.628447	−0.0673766
$88$	1.00000	0.106600
$89$	9.25022	0.980521	0.490261	−	0.871576i	$-0.336902\pi$
$89$	9.25022	0.980521	0.490261	+	0.871576i	$0.336902\pi$
$90$	−2.93211	−0.309072
$91$	−0.391571	−0.0410478
$92$	5.32638	0.555313
$93$	−0.895311	−0.0928394
$94$	−7.51930	−0.775556
$95$	−5.91708	−0.607079
$96$	−0.260557	−0.0265930
$97$	12.1089	1.22947	0.614737	−	0.788732i	$-0.289262\pi$
$97$	12.1089	1.22947	0.614737	+	0.788732i	$0.289262\pi$
$98$	−6.88937	−0.695931
$99$	−2.93211	−0.294688
$100$	1.00000	0.100000
$101$	0.968776	0.0963968	0.0481984	−	0.998838i	$-0.484652\pi$
$101$	0.968776	0.0963968	0.0481984	+	0.998838i	$0.484652\pi$
$102$	0.590229	0.0584414
$103$	−5.98452	−0.589673	−0.294836	−	0.955548i	$-0.595265\pi$
$103$	−5.98452	−0.589673	−0.294836	+	0.955548i	$0.595265\pi$
$104$	1.17725	0.115439
$105$	0.0866651	0.00845764
$106$	−13.7653	−1.33700
$107$	−13.9436	−1.34798	−0.673988	−	0.738743i	$-0.735420\pi$
$107$	−13.9436	−1.34798	−0.673988	+	0.738743i	$0.735420\pi$
$108$	1.54565	0.148730
$109$	0.223252	0.0213837	0.0106918	−	0.999943i	$-0.496597\pi$
$109$	0.223252	0.0213837	0.0106918	+	0.999943i	$0.496597\pi$
$110$	1.00000	0.0953463
$111$	−2.82716	−0.268342
$112$	−0.332615	−0.0314292
$113$	−2.23612	−0.210356	−0.105178	−	0.994453i	$-0.533541\pi$
$113$	−2.23612	−0.210356	−0.105178	+	0.994453i	$0.533541\pi$
$114$	1.54173	0.144397
$115$	5.32638	0.496687
$116$	2.41194	0.223943
$117$	−3.45183	−0.319122
$118$	1.28536	0.118327
$119$	0.753460	0.0690696
$120$	−0.260557	−0.0237855
$121$	1.00000	0.0909091
$122$	6.94198	0.628497
$123$	−1.27974	−0.115390
$124$	3.43615	0.308575
$125$	1.00000	0.0894427
$126$	0.975264	0.0868834
$127$	19.0214	1.68788	0.843938	−	0.536440i	$-0.180231\pi$
$127$	19.0214	1.68788	0.843938	+	0.536440i	$0.180231\pi$
$128$	1.00000	0.0883883
$129$	−0.304391	−0.0268001
$130$	1.17725	0.103252
$131$	1.91115	0.166978	0.0834888	−	0.996509i	$-0.473394\pi$
$131$	1.91115	0.166978	0.0834888	+	0.996509i	$0.473394\pi$
$132$	−0.260557	−0.0226785
$133$	1.96811	0.170657
$134$	9.48895	0.819721
$135$	1.54565	0.133028
$136$	−2.26526	−0.194245
$137$	9.22351	0.788018	0.394009	−	0.919107i	$-0.371088\pi$
$137$	9.22351	0.788018	0.394009	+	0.919107i	$0.371088\pi$
$138$	−1.38782	−0.118139
$139$	9.63361	0.817112	0.408556	−	0.912733i	$-0.366032\pi$
$139$	9.63361	0.817112	0.408556	+	0.912733i	$0.366032\pi$
$140$	−0.332615	−0.0281111
$141$	1.95920	0.164995
$142$	9.95746	0.835611
$143$	1.17725	0.0984466
$144$	−2.93211	−0.244343
$145$	2.41194	0.200301
$146$	−1.00000	−0.0827606
$147$	1.79507	0.148055
$148$	10.8505	0.891903
$149$	16.2654	1.33251	0.666257	−	0.745722i	$-0.267895\pi$
$149$	16.2654	1.33251	0.666257	+	0.745722i	$0.267895\pi$
$150$	−0.260557	−0.0212744
$151$	4.76758	0.387980	0.193990	−	0.981004i	$-0.437857\pi$
$151$	4.76758	0.387980	0.193990	+	0.981004i	$0.437857\pi$
$152$	−5.91708	−0.479938
$153$	6.64200	0.536974
$154$	−0.332615	−0.0268029
$155$	3.43615	0.275998
$156$	−0.306740	−0.0245589
$157$	−6.23831	−0.497872	−0.248936	−	0.968520i	$-0.580081\pi$
$157$	−6.23831	−0.497872	−0.248936	+	0.968520i	$0.580081\pi$
$158$	1.75015	0.139234
$159$	3.58663	0.284438
$160$	1.00000	0.0790569
$161$	−1.77163	−0.139624
$162$	8.39360	0.659464
$163$	−9.39199	−0.735637	−0.367819	−	0.929898i	$-0.619895\pi$
$163$	−9.39199	−0.735637	−0.367819	+	0.929898i	$0.619895\pi$
$164$	4.91154	0.383527
$165$	−0.260557	−0.0202843
$166$	11.7551	0.912376
$167$	0.0778547	0.00602458	0.00301229	−	0.999995i	$-0.499041\pi$
$167$	0.0778547	0.00602458	0.00301229	+	0.999995i	$0.499041\pi$
$168$	0.0866651	0.00668635
$169$	−11.6141	−0.893391
$170$	−2.26526	−0.173738
$171$	17.3495	1.32675
$172$	1.16823	0.0890769
$173$	4.74454	0.360721	0.180360	−	0.983601i	$-0.442274\pi$
$173$	4.74454	0.360721	0.180360	+	0.983601i	$0.442274\pi$
$174$	−0.628447	−0.0476424
$175$	−0.332615	−0.0251433
$176$	1.00000	0.0753778
$177$	−0.334910	−0.0251734
$178$	9.25022	0.693333
$179$	10.0883	0.754031	0.377016	−	0.926207i	$-0.376950\pi$
$179$	10.0883	0.754031	0.377016	+	0.926207i	$0.376950\pi$
$180$	−2.93211	−0.218547
$181$	26.5403	1.97272	0.986361	−	0.164594i	$-0.0526315\pi$
$181$	26.5403	1.97272	0.986361	+	0.164594i	$0.0526315\pi$
$182$	−0.391571	−0.0290252
$183$	−1.80878	−0.133709
$184$	5.32638	0.392666
$185$	10.8505	0.797742
$186$	−0.895311	−0.0656474
$187$	−2.26526	−0.165652
$188$	−7.51930	−0.548401
$189$	−0.514107	−0.0373958
$190$	−5.91708	−0.429270
$191$	5.16957	0.374057	0.187028	−	0.982355i	$-0.440114\pi$
$191$	5.16957	0.374057	0.187028	+	0.982355i	$0.440114\pi$
$192$	−0.260557	−0.0188041
$193$	−10.1350	−0.729533	−0.364767	−	0.931099i	$-0.618851\pi$
$193$	−10.1350	−0.729533	−0.364767	+	0.931099i	$0.618851\pi$
$194$	12.1089	0.869370
$195$	−0.306740	−0.0219661
$196$	−6.88937	−0.492098
$197$	−15.3042	−1.09038	−0.545188	−	0.838314i	$-0.683542\pi$
$197$	−15.3042	−1.09038	−0.545188	+	0.838314i	$0.683542\pi$
$198$	−2.93211	−0.208376
$199$	12.2135	0.865791	0.432895	−	0.901444i	$-0.357492\pi$
$199$	12.2135	0.865791	0.432895	+	0.901444i	$0.357492\pi$
$200$	1.00000	0.0707107
$201$	−2.47241	−0.174390
$202$	0.968776	0.0681628
$203$	−0.802247	−0.0563067
$204$	0.590229	0.0413243
$205$	4.91154	0.343037
$206$	−5.98452	−0.416961
$207$	−15.6175	−1.08549
$208$	1.17725	0.0816276
$209$	−5.91708	−0.409293
$210$	0.0866651	0.00598046
$211$	−16.9948	−1.16997	−0.584985	−	0.811044i	$-0.698900\pi$
$211$	−16.9948	−1.16997	−0.584985	+	0.811044i	$0.698900\pi$
$212$	−13.7653	−0.945402
$213$	−2.59448	−0.177771
$214$	−13.9436	−0.953163
$215$	1.16823	0.0796728
$216$	1.54565	0.105168
$217$	−1.14291	−0.0775861
$218$	0.223252	0.0151205
$219$	0.260557	0.0176068
$220$	1.00000	0.0674200
$221$	−2.66678	−0.179387
$222$	−2.82716	−0.189747
$223$	9.71287	0.650422	0.325211	−	0.945642i	$-0.394565\pi$
$223$	9.71287	0.650422	0.325211	+	0.945642i	$0.394565\pi$
$224$	−0.332615	−0.0222238
$225$	−2.93211	−0.195474
$226$	−2.23612	−0.148744
$227$	12.2368	0.812183	0.406091	−	0.913832i	$-0.366891\pi$
$227$	12.2368	0.812183	0.406091	+	0.913832i	$0.366891\pi$
$228$	1.54173	0.102104
$229$	−10.2708	−0.678715	−0.339358	−	0.940657i	$-0.610210\pi$
$229$	−10.2708	−0.678715	−0.339358	+	0.940657i	$0.610210\pi$
$230$	5.32638	0.351211
$231$	0.0866651	0.00570214
$232$	2.41194	0.158352
$233$	−2.15740	−0.141336	−0.0706678	−	0.997500i	$-0.522513\pi$
$233$	−2.15740	−0.141336	−0.0706678	+	0.997500i	$0.522513\pi$
$234$	−3.45183	−0.225653
$235$	−7.51930	−0.490505
$236$	1.28536	0.0836700
$237$	−0.456013	−0.0296212
$238$	0.753460	0.0488396
$239$	−2.81891	−0.182340	−0.0911699	−	0.995835i	$-0.529061\pi$
$239$	−2.81891	−0.182340	−0.0911699	+	0.995835i	$0.529061\pi$
$240$	−0.260557	−0.0168189
$241$	−17.0797	−1.10020	−0.550099	−	0.835100i	$-0.685410\pi$
$241$	−17.0797	−1.10020	−0.550099	+	0.835100i	$0.685410\pi$
$242$	1.00000	0.0642824
$243$	−6.82396	−0.437757
$244$	6.94198	0.444415
$245$	−6.88937	−0.440146
$246$	−1.27974	−0.0815930
$247$	−6.96588	−0.443228
$248$	3.43615	0.218196
$249$	−3.06288	−0.194102
$250$	1.00000	0.0632456
$251$	14.7912	0.933614	0.466807	−	0.884359i	$-0.345404\pi$
$251$	14.7912	0.933614	0.466807	+	0.884359i	$0.345404\pi$
$252$	0.975264	0.0614358
$253$	5.32638	0.334867
$254$	19.0214	1.19351
$255$	0.590229	0.0369616
$256$	1.00000	0.0625000
$257$	15.2818	0.953254	0.476627	−	0.879106i	$-0.341859\pi$
$257$	15.2818	0.953254	0.476627	+	0.879106i	$0.341859\pi$
$258$	−0.304391	−0.0189505
$259$	−3.60903	−0.224254
$260$	1.17725	0.0730100
$261$	−7.07207	−0.437750
$262$	1.91115	0.118071
$263$	−29.8849	−1.84278	−0.921392	−	0.388634i	$-0.872947\pi$
$263$	−29.8849	−1.84278	−0.921392	+	0.388634i	$0.872947\pi$
$264$	−0.260557	−0.0160362
$265$	−13.7653	−0.845593
$266$	1.96811	0.120672
$267$	−2.41021	−0.147502
$268$	9.48895	0.579630
$269$	−7.46797	−0.455330	−0.227665	−	0.973740i	$-0.573109\pi$
$269$	−7.46797	−0.455330	−0.227665	+	0.973740i	$0.573109\pi$
$270$	1.54565	0.0940653
$271$	−1.56931	−0.0953286	−0.0476643	−	0.998863i	$-0.515178\pi$
$271$	−1.56931	−0.0953286	−0.0476643	+	0.998863i	$0.515178\pi$
$272$	−2.26526	−0.137352
$273$	0.102026	0.00617492
$274$	9.22351	0.557213
$275$	1.00000	0.0603023
$276$	−1.38782	−0.0835372
$277$	10.0070	0.601265	0.300632	−	0.953740i	$-0.402802\pi$
$277$	10.0070	0.601265	0.300632	+	0.953740i	$0.402802\pi$
$278$	9.63361	0.577786
$279$	−10.0752	−0.603184
$280$	−0.332615	−0.0198775
$281$	−27.4293	−1.63629	−0.818146	−	0.575010i	$-0.804998\pi$
$281$	−27.4293	−1.63629	−0.818146	+	0.575010i	$0.804998\pi$
$282$	1.95920	0.116669
$283$	12.6151	0.749890	0.374945	−	0.927047i	$-0.377662\pi$
$283$	12.6151	0.749890	0.374945	+	0.927047i	$0.377662\pi$
$284$	9.95746	0.590866
$285$	1.54173	0.0913244
$286$	1.17725	0.0696123
$287$	−1.63365	−0.0964315
$288$	−2.93211	−0.172776
$289$	−11.8686	−0.698152
$290$	2.41194	0.141634
$291$	−3.15506	−0.184953
$292$	−1.00000	−0.0585206
$293$	8.75296	0.511353	0.255677	−	0.966762i	$-0.417702\pi$
$293$	8.75296	0.511353	0.255677	+	0.966762i	$0.417702\pi$
$294$	1.79507	0.104691
$295$	1.28536	0.0748368
$296$	10.8505	0.630670
$297$	1.54565	0.0896878
$298$	16.2654	0.942230
$299$	6.27048	0.362631
$300$	−0.260557	−0.0150432
$301$	−0.388571	−0.0223969
$302$	4.76758	0.274343
$303$	−0.252421	−0.0145012
$304$	−5.91708	−0.339368
$305$	6.94198	0.397497
$306$	6.64200	0.379698
$307$	5.32008	0.303633	0.151816	−	0.988409i	$-0.451488\pi$
$307$	5.32008	0.303633	0.151816	+	0.988409i	$0.451488\pi$
$308$	−0.332615	−0.0189525
$309$	1.55931	0.0887059
$310$	3.43615	0.195160
$311$	−2.75887	−0.156441	−0.0782206	−	0.996936i	$-0.524924\pi$
$311$	−2.75887	−0.156441	−0.0782206	+	0.996936i	$0.524924\pi$
$312$	−0.306740	−0.0173658
$313$	−8.66972	−0.490041	−0.245021	−	0.969518i	$-0.578795\pi$
$313$	−8.66972	−0.490041	−0.245021	+	0.969518i	$0.578795\pi$
$314$	−6.23831	−0.352048
$315$	0.975264	0.0549499
$316$	1.75015	0.0984536
$317$	28.8481	1.62027	0.810135	−	0.586243i	$-0.199394\pi$
$317$	28.8481	1.62027	0.810135	+	0.586243i	$0.199394\pi$
$318$	3.58663	0.201128
$319$	2.41194	0.135043
$320$	1.00000	0.0559017
$321$	3.63309	0.202779
$322$	−1.77163	−0.0987293
$323$	13.4037	0.745804
$324$	8.39360	0.466311
$325$	1.17725	0.0653021
$326$	−9.39199	−0.520174
$327$	−0.0581698	−0.00321680
$328$	4.91154	0.271195
$329$	2.50103	0.137886
$330$	−0.260557	−0.0143432
$331$	14.7297	0.809619	0.404810	−	0.914401i	$-0.367338\pi$
$331$	14.7297	0.809619	0.404810	+	0.914401i	$0.367338\pi$
$332$	11.7551	0.645147
$333$	−31.8148	−1.74344
$334$	0.0778547	0.00426002
$335$	9.48895	0.518437
$336$	0.0866651	0.00472797
$337$	18.4412	1.00455	0.502277	−	0.864707i	$-0.332496\pi$
$337$	18.4412	1.00455	0.502277	+	0.864707i	$0.332496\pi$
$338$	−11.6141	−0.631723
$339$	0.582635	0.0316444
$340$	−2.26526	−0.122851
$341$	3.43615	0.186078
$342$	17.3495	0.938155
$343$	4.61981	0.249446
$344$	1.16823	0.0629868
$345$	−1.38782	−0.0747179
$346$	4.74454	0.255068
$347$	−12.7480	−0.684349	−0.342175	−	0.939636i	$-0.611163\pi$
$347$	−12.7480	−0.684349	−0.342175	+	0.939636i	$0.611163\pi$
$348$	−0.628447	−0.0336883
$349$	−21.9251	−1.17362	−0.586812	−	0.809723i	$-0.699617\pi$
$349$	−21.9251	−1.17362	−0.586812	+	0.809723i	$0.699617\pi$
$350$	−0.332615	−0.0177790
$351$	1.81962	0.0971240
$352$	1.00000	0.0533002
$353$	19.0382	1.01330	0.506651	−	0.862151i	$-0.330883\pi$
$353$	19.0382	1.01330	0.506651	+	0.862151i	$0.330883\pi$
$354$	−0.334910	−0.0178003
$355$	9.95746	0.528487
$356$	9.25022	0.490261
$357$	−0.196319	−0.0103903
$358$	10.0883	0.533181
$359$	−4.83347	−0.255101	−0.127550	−	0.991832i	$-0.540711\pi$
$359$	−4.83347	−0.255101	−0.127550	+	0.991832i	$0.540711\pi$
$360$	−2.93211	−0.154536
$361$	16.0118	0.842726
$362$	26.5403	1.39493
$363$	−0.260557	−0.0136757
$364$	−0.391571	−0.0205239
$365$	−1.00000	−0.0523424
$366$	−1.80878	−0.0945464
$367$	−25.2313	−1.31706	−0.658531	−	0.752554i	$-0.728822\pi$
$367$	−25.2313	−1.31706	−0.658531	+	0.752554i	$0.728822\pi$
$368$	5.32638	0.277657
$369$	−14.4012	−0.749696
$370$	10.8505	0.564089
$371$	4.57853	0.237705
$372$	−0.895311	−0.0464197
$373$	−23.1066	−1.19641	−0.598206	−	0.801342i	$-0.704120\pi$
$373$	−23.1066	−1.19641	−0.598206	+	0.801342i	$0.704120\pi$
$374$	−2.26526	−0.117134
$375$	−0.260557	−0.0134551
$376$	−7.51930	−0.387778
$377$	2.83946	0.146239
$378$	−0.514107	−0.0264428
$379$	−26.2151	−1.34658	−0.673289	−	0.739379i	$-0.735119\pi$
$379$	−26.2151	−1.34658	−0.673289	+	0.739379i	$0.735119\pi$
$380$	−5.91708	−0.303540
$381$	−4.95615	−0.253911
$382$	5.16957	0.264498
$383$	14.9183	0.762288	0.381144	−	0.924516i	$-0.375530\pi$
$383$	14.9183	0.762288	0.381144	+	0.924516i	$0.375530\pi$
$384$	−0.260557	−0.0132965
$385$	−0.332615	−0.0169516
$386$	−10.1350	−0.515858
$387$	−3.42538	−0.174122
$388$	12.1089	0.614737
$389$	−6.03899	−0.306189	−0.153094	−	0.988212i	$-0.548924\pi$
$389$	−6.03899	−0.306189	−0.153094	+	0.988212i	$0.548924\pi$
$390$	−0.306740	−0.0155324
$391$	−12.0656	−0.610186
$392$	−6.88937	−0.347966
$393$	−0.497962	−0.0251188
$394$	−15.3042	−0.771012
$395$	1.75015	0.0880596
$396$	−2.93211	−0.147344
$397$	5.29629	0.265813	0.132907	−	0.991129i	$-0.457569\pi$
$397$	5.29629	0.265813	0.132907	+	0.991129i	$0.457569\pi$
$398$	12.2135	0.612207
$399$	−0.512804	−0.0256723
$400$	1.00000	0.0500000
$401$	9.15753	0.457305	0.228653	−	0.973508i	$-0.426568\pi$
$401$	9.15753	0.457305	0.228653	+	0.973508i	$0.426568\pi$
$402$	−2.47241	−0.123313
$403$	4.04521	0.201506
$404$	0.968776	0.0481984
$405$	8.39360	0.417081
$406$	−0.802247	−0.0398148
$407$	10.8505	0.537837
$408$	0.590229	0.0292207
$409$	−4.33916	−0.214558	−0.107279	−	0.994229i	$-0.534214\pi$
$409$	−4.33916	−0.214558	−0.107279	+	0.994229i	$0.534214\pi$
$410$	4.91154	0.242564
$411$	−2.40325	−0.118543
$412$	−5.98452	−0.294836
$413$	−0.427531	−0.0210374
$414$	−15.6175	−0.767560
$415$	11.7551	0.577037
$416$	1.17725	0.0577194
$417$	−2.51010	−0.122920
$418$	−5.91708	−0.289414
$419$	29.3931	1.43595	0.717973	−	0.696071i	$-0.245070\pi$
$419$	29.3931	1.43595	0.717973	+	0.696071i	$0.245070\pi$
$420$	0.0866651	0.00422882
$421$	8.59419	0.418855	0.209428	−	0.977824i	$-0.432840\pi$
$421$	8.59419	0.418855	0.209428	+	0.977824i	$0.432840\pi$
$422$	−16.9948	−0.827294
$423$	22.0474	1.07198
$424$	−13.7653	−0.668500
$425$	−2.26526	−0.109881
$426$	−2.59448	−0.125703
$427$	−2.30901	−0.111741
$428$	−13.9436	−0.673988
$429$	−0.306740	−0.0148096
$430$	1.16823	0.0563371
$431$	13.6654	0.658241	0.329120	−	0.944288i	$-0.393248\pi$
$431$	13.6654	0.658241	0.329120	+	0.944288i	$0.393248\pi$
$432$	1.54565	0.0743652
$433$	15.0239	0.722004	0.361002	−	0.932565i	$-0.382435\pi$
$433$	15.0239	0.722004	0.361002	+	0.932565i	$0.382435\pi$
$434$	−1.14291	−0.0548616
$435$	−0.628447	−0.0301317
$436$	0.223252	0.0106918
$437$	−31.5166	−1.50764
$438$	0.260557	0.0124499
$439$	7.19529	0.343412	0.171706	−	0.985148i	$-0.445072\pi$
$439$	7.19529	0.343412	0.171706	+	0.985148i	$0.445072\pi$
$440$	1.00000	0.0476731
$441$	20.2004	0.961923
$442$	−2.66678	−0.126846
$443$	20.9682	0.996227	0.498113	−	0.867112i	$-0.334026\pi$
$443$	20.9682	0.996227	0.498113	+	0.867112i	$0.334026\pi$
$444$	−2.82716	−0.134171
$445$	9.25022	0.438503
$446$	9.71287	0.459918
$447$	−4.23806	−0.200453
$448$	−0.332615	−0.0157146
$449$	28.4268	1.34154	0.670771	−	0.741664i	$-0.265963\pi$
$449$	28.4268	1.34154	0.670771	+	0.741664i	$0.265963\pi$
$450$	−2.93211	−0.138221
$451$	4.91154	0.231276
$452$	−2.23612	−0.105178
$453$	−1.24222	−0.0583648
$454$	12.2368	0.574300
$455$	−0.391571	−0.0183571
$456$	1.54173	0.0721983
$457$	22.2848	1.04244	0.521220	−	0.853422i	$-0.325477\pi$
$457$	22.2848	1.04244	0.521220	+	0.853422i	$0.325477\pi$
$458$	−10.2708	−0.479924
$459$	−3.50131	−0.163427
$460$	5.32638	0.248344
$461$	−5.04953	−0.235180	−0.117590	−	0.993062i	$-0.537517\pi$
$461$	−5.04953	−0.235180	−0.117590	+	0.993062i	$0.537517\pi$
$462$	0.0866651	0.00403202
$463$	8.61311	0.400285	0.200143	−	0.979767i	$-0.435859\pi$
$463$	8.61311	0.400285	0.200143	+	0.979767i	$0.435859\pi$
$464$	2.41194	0.111971
$465$	−0.895311	−0.0415191
$466$	−2.15740	−0.0999394
$467$	−12.4849	−0.577731	−0.288865	−	0.957370i	$-0.593278\pi$
$467$	−12.4849	−0.577731	−0.288865	+	0.957370i	$0.593278\pi$
$468$	−3.45183	−0.159561
$469$	−3.15617	−0.145738
$470$	−7.51930	−0.346839
$471$	1.62543	0.0748961
$472$	1.28536	0.0591636
$473$	1.16823	0.0537154
$474$	−0.456013	−0.0209454
$475$	−5.91708	−0.271494
$476$	0.753460	0.0345348
$477$	40.3612	1.84801
$478$	−2.81891	−0.128934
$479$	9.34841	0.427140	0.213570	−	0.976928i	$-0.431491\pi$
$479$	9.34841	0.427140	0.213570	+	0.976928i	$0.431491\pi$
$480$	−0.260557	−0.0118927
$481$	12.7737	0.582431
$482$	−17.0797	−0.777957
$483$	0.461611	0.0210040
$484$	1.00000	0.0454545
$485$	12.1089	0.549838
$486$	−6.82396	−0.309541
$487$	−12.0903	−0.547865	−0.273932	−	0.961749i	$-0.588324\pi$
$487$	−12.0903	−0.547865	−0.273932	+	0.961749i	$0.588324\pi$
$488$	6.94198	0.314249
$489$	2.44715	0.110664
$490$	−6.88937	−0.311230
$491$	−10.0638	−0.454174	−0.227087	−	0.973875i	$-0.572920\pi$
$491$	−10.0638	−0.454174	−0.227087	+	0.973875i	$0.572920\pi$
$492$	−1.27974	−0.0576949
$493$	−5.46367	−0.246072
$494$	−6.96588	−0.313410
$495$	−2.93211	−0.131789
$496$	3.43615	0.154288
$497$	−3.31200	−0.148563
$498$	−3.06288	−0.137251
$499$	−32.0322	−1.43396	−0.716980	−	0.697094i	$-0.754476\pi$
$499$	−32.0322	−1.43396	−0.716980	+	0.697094i	$0.754476\pi$
$500$	1.00000	0.0447214
$501$	−0.0202856	−0.000906293 0
$502$	14.7912	0.660165
$503$	20.8452	0.929442	0.464721	−	0.885457i	$-0.346155\pi$
$503$	20.8452	0.929442	0.464721	+	0.885457i	$0.346155\pi$
$504$	0.975264	0.0434417
$505$	0.968776	0.0431099
$506$	5.32638	0.236786
$507$	3.02613	0.134395
$508$	19.0214	0.843938
$509$	−20.2456	−0.897370	−0.448685	−	0.893690i	$-0.648107\pi$
$509$	−20.2456	−0.897370	−0.448685	+	0.893690i	$0.648107\pi$
$510$	0.590229	0.0261358
$511$	0.332615	0.0147140
$512$	1.00000	0.0441942
$513$	−9.14573	−0.403794
$514$	15.2818	0.674052
$515$	−5.98452	−0.263710
$516$	−0.304391	−0.0134001
$517$	−7.51930	−0.330698
$518$	−3.60903	−0.158572
$519$	−1.23622	−0.0542641
$520$	1.17725	0.0516258
$521$	33.0234	1.44678	0.723390	−	0.690439i	$-0.242583\pi$
$521$	33.0234	1.44678	0.723390	+	0.690439i	$0.242583\pi$
$522$	−7.07207	−0.309536
$523$	−28.3693	−1.24050	−0.620251	−	0.784404i	$-0.712969\pi$
$523$	−28.3693	−1.24050	−0.620251	+	0.784404i	$0.712969\pi$
$524$	1.91115	0.0834888
$525$	0.0866651	0.00378237
$526$	−29.8849	−1.30305
$527$	−7.78378	−0.339067
$528$	−0.260557	−0.0113393
$529$	5.37032	0.233492
$530$	−13.7653	−0.597924
$531$	−3.76883	−0.163553
$532$	1.96811	0.0853283
$533$	5.78212	0.250451
$534$	−2.41021	−0.104300
$535$	−13.9436	−0.602833
$536$	9.48895	0.409860
$537$	−2.62856	−0.113431
$538$	−7.46797	−0.321967
$539$	−6.88937	−0.296746
$540$	1.54565	0.0665142
$541$	6.58426	0.283079	0.141540	−	0.989933i	$-0.454795\pi$
$541$	6.58426	0.283079	0.141540	+	0.989933i	$0.454795\pi$
$542$	−1.56931	−0.0674075
$543$	−6.91524	−0.296762
$544$	−2.26526	−0.0971223
$545$	0.223252	0.00956306
$546$	0.102026	0.00436633
$547$	2.45817	0.105104	0.0525520	−	0.998618i	$-0.483264\pi$
$547$	2.45817	0.105104	0.0525520	+	0.998618i	$0.483264\pi$
$548$	9.22351	0.394009
$549$	−20.3546	−0.868715
$550$	1.00000	0.0426401
$551$	−14.2716	−0.607992
$552$	−1.38782	−0.0590697
$553$	−0.582126	−0.0247545
$554$	10.0070	0.425158
$555$	−2.82716	−0.120006
$556$	9.63361	0.408556
$557$	−34.4063	−1.45784	−0.728920	−	0.684599i	$-0.759978\pi$
$557$	−34.4063	−1.45784	−0.728920	+	0.684599i	$0.759978\pi$
$558$	−10.0752	−0.426516
$559$	1.37530	0.0581691
$560$	−0.332615	−0.0140555
$561$	0.590229	0.0249195
$562$	−27.4293	−1.15703
$563$	29.6635	1.25017	0.625084	−	0.780558i	$-0.285065\pi$
$563$	29.6635	1.25017	0.625084	+	0.780558i	$0.285065\pi$
$564$	1.95920	0.0824974
$565$	−2.23612	−0.0940741
$566$	12.6151	0.530252
$567$	−2.79184	−0.117246
$568$	9.95746	0.417806
$569$	−30.2799	−1.26940	−0.634699	−	0.772759i	$-0.718876\pi$
$569$	−30.2799	−1.26940	−0.634699	+	0.772759i	$0.718876\pi$
$570$	1.54173	0.0645761
$571$	−12.0304	−0.503455	−0.251727	−	0.967798i	$-0.580999\pi$
$571$	−12.0304	−0.503455	−0.251727	+	0.967798i	$0.580999\pi$
$572$	1.17725	0.0492233
$573$	−1.34696	−0.0562703
$574$	−1.63365	−0.0681874
$575$	5.32638	0.222125
$576$	−2.93211	−0.122171
$577$	8.94810	0.372514	0.186257	−	0.982501i	$-0.440364\pi$
$577$	8.94810	0.372514	0.186257	+	0.982501i	$0.440364\pi$
$578$	−11.8686	−0.493668
$579$	2.64074	0.109745
$580$	2.41194	0.100150
$581$	−3.90994	−0.162211
$582$	−3.15506	−0.130781
$583$	−13.7653	−0.570099
$584$	−1.00000	−0.0413803
$585$	−3.45183	−0.142716
$586$	8.75296	0.361582
$587$	29.5703	1.22050	0.610248	−	0.792210i	$-0.291070\pi$
$587$	29.5703	1.22050	0.610248	+	0.792210i	$0.291070\pi$
$588$	1.79507	0.0740275
$589$	−20.3319	−0.837763
$590$	1.28536	0.0529176
$591$	3.98760	0.164028
$592$	10.8505	0.445951
$593$	27.7740	1.14054	0.570270	−	0.821457i	$-0.306838\pi$
$593$	27.7740	1.14054	0.570270	+	0.821457i	$0.306838\pi$
$594$	1.54565	0.0634188
$595$	0.753460	0.0308889
$596$	16.2654	0.666257
$597$	−3.18230	−0.130243
$598$	6.27048	0.256419
$599$	−0.226147	−0.00924012	−0.00462006	−	0.999989i	$-0.501471\pi$
$599$	−0.226147	−0.00924012	−0.00462006	+	0.999989i	$0.501471\pi$
$600$	−0.260557	−0.0106372
$601$	22.6971	0.925834	0.462917	−	0.886402i	$-0.346803\pi$
$601$	22.6971	0.925834	0.462917	+	0.886402i	$0.346803\pi$
$602$	−0.388571	−0.0158370
$603$	−27.8227	−1.13303
$604$	4.76758	0.193990
$605$	1.00000	0.0406558
$606$	−0.252421	−0.0102539
$607$	8.95933	0.363648	0.181824	−	0.983331i	$-0.441800\pi$
$607$	8.95933	0.363648	0.181824	+	0.983331i	$0.441800\pi$
$608$	−5.91708	−0.239969
$609$	0.209031	0.00847036
$610$	6.94198	0.281073
$611$	−8.85210	−0.358118
$612$	6.64200	0.268487
$613$	7.82965	0.316237	0.158118	−	0.987420i	$-0.449457\pi$
$613$	7.82965	0.316237	0.158118	+	0.987420i	$0.449457\pi$
$614$	5.32008	0.214701
$615$	−1.27974	−0.0516039
$616$	−0.332615	−0.0134014
$617$	−8.05006	−0.324083	−0.162042	−	0.986784i	$-0.551808\pi$
$617$	−8.05006	−0.324083	−0.162042	+	0.986784i	$0.551808\pi$
$618$	1.55931	0.0627245
$619$	15.7563	0.633297	0.316649	−	0.948543i	$-0.397442\pi$
$619$	15.7563	0.633297	0.316649	+	0.948543i	$0.397442\pi$
$620$	3.43615	0.137999
$621$	8.23272	0.330368
$622$	−2.75887	−0.110621
$623$	−3.07676	−0.123268
$624$	−0.306740	−0.0122794
$625$	1.00000	0.0400000
$626$	−8.66972	−0.346512
$627$	1.54173	0.0615709
$628$	−6.23831	−0.248936
$629$	−24.5791	−0.980035
$630$	0.975264	0.0388554
$631$	1.16888	0.0465324	0.0232662	−	0.999729i	$-0.492593\pi$
$631$	1.16888	0.0465324	0.0232662	+	0.999729i	$0.492593\pi$
$632$	1.75015	0.0696172
$633$	4.42811	0.176002
$634$	28.8481	1.14570
$635$	19.0214	0.754841
$636$	3.58663	0.142219
$637$	−8.11051	−0.321350
$638$	2.41194	0.0954896
$639$	−29.1964	−1.15499
$640$	1.00000	0.0395285
$641$	−29.0694	−1.14817	−0.574086	−	0.818795i	$-0.694642\pi$
$641$	−29.0694	−1.14817	−0.574086	+	0.818795i	$0.694642\pi$
$642$	3.63309	0.143387
$643$	35.2383	1.38966	0.694832	−	0.719173i	$-0.255479\pi$
$643$	35.2383	1.38966	0.694832	+	0.719173i	$0.255479\pi$
$644$	−1.77163	−0.0698121
$645$	−0.304391	−0.0119854
$646$	13.4037	0.527363
$647$	−29.5441	−1.16150	−0.580749	−	0.814083i	$-0.697240\pi$
$647$	−29.5441	−1.16150	−0.580749	+	0.814083i	$0.697240\pi$
$648$	8.39360	0.329732
$649$	1.28536	0.0504549
$650$	1.17725	0.0461756
$651$	0.297794	0.0116715
$652$	−9.39199	−0.367819
$653$	−23.6922	−0.927149	−0.463574	−	0.886058i	$-0.653433\pi$
$653$	−23.6922	−0.927149	−0.463574	+	0.886058i	$0.653433\pi$
$654$	−0.0581698	−0.00227462
$655$	1.91115	0.0746746
$656$	4.91154	0.191764
$657$	2.93211	0.114393
$658$	2.50103	0.0975004
$659$	−20.8813	−0.813419	−0.406710	−	0.913557i	$-0.633324\pi$
$659$	−20.8813	−0.813419	−0.406710	+	0.913557i	$0.633324\pi$
$660$	−0.260557	−0.0101422
$661$	−5.14803	−0.200235	−0.100118	−	0.994976i	$-0.531922\pi$
$661$	−5.14803	−0.200235	−0.100118	+	0.994976i	$0.531922\pi$
$662$	14.7297	0.572487
$663$	0.694848	0.0269856
$664$	11.7551	0.456188
$665$	1.96811	0.0763200
$666$	−31.8148	−1.23280
$667$	12.8469	0.497434
$668$	0.0778547	0.00301229
$669$	−2.53075	−0.0978446
$670$	9.48895	0.366590
$671$	6.94198	0.267992
$672$	0.0866651	0.00334318
$673$	9.72935	0.375039	0.187519	−	0.982261i	$-0.439955\pi$
$673$	9.72935	0.375039	0.187519	+	0.982261i	$0.439955\pi$
$674$	18.4412	0.710327
$675$	1.54565	0.0594921
$676$	−11.6141	−0.446695
$677$	−24.5563	−0.943775	−0.471887	−	0.881659i	$-0.656427\pi$
$677$	−24.5563	−0.943775	−0.471887	+	0.881659i	$0.656427\pi$
$678$	0.582635	0.0223760
$679$	−4.02761	−0.154565
$680$	−2.26526	−0.0868689
$681$	−3.18837	−0.122179
$682$	3.43615	0.131577
$683$	16.1614	0.618399	0.309200	−	0.950997i	$-0.399939\pi$
$683$	16.1614	0.618399	0.309200	+	0.950997i	$0.399939\pi$
$684$	17.3495	0.663375
$685$	9.22351	0.352412
$686$	4.61981	0.176385
$687$	2.67613	0.102101
$688$	1.16823	0.0445384
$689$	−16.2052	−0.617367
$690$	−1.38782	−0.0528335
$691$	−25.7843	−0.980881	−0.490441	−	0.871475i	$-0.663164\pi$
$691$	−25.7843	−0.980881	−0.490441	+	0.871475i	$0.663164\pi$
$692$	4.74454	0.180360
$693$	0.975264	0.0370472
$694$	−12.7480	−0.483908
$695$	9.63361	0.365424
$696$	−0.628447	−0.0238212
$697$	−11.1259	−0.421425
$698$	−21.9251	−0.829877
$699$	0.562124	0.0212615
$700$	−0.332615	−0.0125717
$701$	−32.4760	−1.22660	−0.613300	−	0.789850i	$-0.710158\pi$
$701$	−32.4760	−1.22660	−0.613300	+	0.789850i	$0.710158\pi$
$702$	1.81962	0.0686771
$703$	−64.2030	−2.42146
$704$	1.00000	0.0376889
$705$	1.95920	0.0737879
$706$	19.0382	0.716512
$707$	−0.322229	−0.0121187
$708$	−0.334910	−0.0125867
$709$	−31.4787	−1.18221	−0.591104	−	0.806595i	$-0.701308\pi$
$709$	−31.4787	−1.18221	−0.591104	+	0.806595i	$0.701308\pi$
$710$	9.95746	0.373697
$711$	−5.13163	−0.192451
$712$	9.25022	0.346667
$713$	18.3022	0.685424
$714$	−0.196319	−0.00734706
$715$	1.17725	0.0440267
$716$	10.0883	0.377016
$717$	0.734485	0.0274298
$718$	−4.83347	−0.180384
$719$	−48.3934	−1.80477	−0.902384	−	0.430933i	$-0.858184\pi$
$719$	−48.3934	−1.80477	−0.902384	+	0.430933i	$0.858184\pi$
$720$	−2.93211	−0.109273
$721$	1.99054	0.0741317
$722$	16.0118	0.595897
$723$	4.45022	0.165505
$724$	26.5403	0.986361
$725$	2.41194	0.0895771
$726$	−0.260557	−0.00967017
$727$	24.8963	0.923352	0.461676	−	0.887049i	$-0.347248\pi$
$727$	24.8963	0.923352	0.461676	+	0.887049i	$0.347248\pi$
$728$	−0.391571	−0.0145126
$729$	−23.4028	−0.866769
$730$	−1.00000	−0.0370117
$731$	−2.64635	−0.0978789
$732$	−1.80878	−0.0668544
$733$	32.5026	1.20051	0.600255	−	0.799809i	$-0.295066\pi$
$733$	32.5026	1.20051	0.600255	+	0.799809i	$0.295066\pi$
$734$	−25.2313	−0.931304
$735$	1.79507	0.0662122
$736$	5.32638	0.196333
$737$	9.48895	0.349530
$738$	−14.4012	−0.530115
$739$	13.6645	0.502657	0.251328	−	0.967902i	$-0.419133\pi$
$739$	13.6645	0.502657	0.251328	+	0.967902i	$0.419133\pi$
$740$	10.8505	0.398871
$741$	1.81501	0.0666759
$742$	4.57853	0.168083
$743$	37.1255	1.36200	0.681001	−	0.732283i	$-0.261545\pi$
$743$	37.1255	1.36200	0.681001	+	0.732283i	$0.261545\pi$
$744$	−0.895311	−0.0328237
$745$	16.2654	0.595918
$746$	−23.1066	−0.845991
$747$	−34.4674	−1.26109
$748$	−2.26526	−0.0828262
$749$	4.63784	0.169463
$750$	−0.260557	−0.00951418
$751$	−4.16727	−0.152066	−0.0760330	−	0.997105i	$-0.524225\pi$
$751$	−4.16727	−0.152066	−0.0760330	+	0.997105i	$0.524225\pi$
$752$	−7.51930	−0.274201
$753$	−3.85395	−0.140446
$754$	2.83946	0.103407
$755$	4.76758	0.173510
$756$	−0.514107	−0.0186979
$757$	−46.9485	−1.70637	−0.853187	−	0.521605i	$-0.825333\pi$
$757$	−46.9485	−1.70637	−0.853187	+	0.521605i	$0.825333\pi$
$758$	−26.2151	−0.952175
$759$	−1.38782	−0.0503748
$760$	−5.91708	−0.214635
$761$	−1.19212	−0.0432142	−0.0216071	−	0.999767i	$-0.506878\pi$
$761$	−1.19212	−0.0432142	−0.0216071	+	0.999767i	$0.506878\pi$
$762$	−4.95615	−0.179542
$763$	−0.0742569	−0.00268828
$764$	5.16957	0.187028
$765$	6.64200	0.240142
$766$	14.9183	0.539019
$767$	1.51319	0.0546383
$768$	−0.260557	−0.00940203
$769$	41.3233	1.49016	0.745079	−	0.666977i	$-0.232412\pi$
$769$	41.3233	1.49016	0.745079	+	0.666977i	$0.232412\pi$
$770$	−0.332615	−0.0119866
$771$	−3.98178	−0.143400
$772$	−10.1350	−0.364767
$773$	−52.7372	−1.89683	−0.948413	−	0.317038i	$-0.897312\pi$
$773$	−52.7372	−1.89683	−0.948413	+	0.317038i	$0.897312\pi$
$774$	−3.42538	−0.123123
$775$	3.43615	0.123430
$776$	12.1089	0.434685
$777$	0.940356	0.0337351
$778$	−6.03899	−0.216508
$779$	−29.0620	−1.04125
$780$	−0.306740	−0.0109831
$781$	9.95746	0.356306
$782$	−12.0656	−0.431467
$783$	3.72801	0.133228
$784$	−6.88937	−0.246049
$785$	−6.23831	−0.222655
$786$	−0.497962	−0.0177617
$787$	19.2454	0.686026	0.343013	−	0.939331i	$-0.388553\pi$
$787$	19.2454	0.686026	0.343013	+	0.939331i	$0.388553\pi$
$788$	−15.3042	−0.545188
$789$	7.78672	0.277215
$790$	1.75015	0.0622675
$791$	0.743766	0.0264453
$792$	−2.93211	−0.104188
$793$	8.17245	0.290212
$794$	5.29629	0.187958
$795$	3.58663	0.127205
$796$	12.2135	0.432895
$797$	−46.1519	−1.63478	−0.817391	−	0.576083i	$-0.804581\pi$
$797$	−46.1519	−1.63478	−0.817391	+	0.576083i	$0.804581\pi$
$798$	−0.512804	−0.0181531
$799$	17.0332	0.602591
$800$	1.00000	0.0353553
$801$	−27.1227	−0.958332
$802$	9.15753	0.323364
$803$	−1.00000	−0.0352892
$804$	−2.47241	−0.0871952
$805$	−1.77163	−0.0624419
$806$	4.04521	0.142486
$807$	1.94583	0.0684964
$808$	0.968776	0.0340814
$809$	12.3130	0.432903	0.216452	−	0.976293i	$-0.430552\pi$
$809$	12.3130	0.432903	0.216452	+	0.976293i	$0.430552\pi$
$810$	8.39360	0.294921
$811$	27.2617	0.957287	0.478643	−	0.878009i	$-0.341129\pi$
$811$	27.2617	0.957287	0.478643	+	0.878009i	$0.341129\pi$
$812$	−0.802247	−0.0281533
$813$	0.408893	0.0143405
$814$	10.8505	0.380309
$815$	−9.39199	−0.328987
$816$	0.590229	0.0206622
$817$	−6.91252	−0.241838
$818$	−4.33916	−0.151715
$819$	1.14813	0.0401189
$820$	4.91154	0.171519
$821$	−18.4270	−0.643106	−0.321553	−	0.946892i	$-0.604205\pi$
$821$	−18.4270	−0.643106	−0.321553	+	0.946892i	$0.604205\pi$
$822$	−2.40325	−0.0838229
$823$	−32.5313	−1.13397	−0.566984	−	0.823729i	$-0.691890\pi$
$823$	−32.5313	−1.13397	−0.566984	+	0.823729i	$0.691890\pi$
$824$	−5.98452	−0.208481
$825$	−0.260557	−0.00907142
$826$	−0.427531	−0.0148757
$827$	26.7452	0.930021	0.465011	−	0.885305i	$-0.346051\pi$
$827$	26.7452	0.930021	0.465011	+	0.885305i	$0.346051\pi$
$828$	−15.6175	−0.542747
$829$	33.8206	1.17464	0.587319	−	0.809355i	$-0.300183\pi$
$829$	33.8206	1.17464	0.587319	+	0.809355i	$0.300183\pi$
$830$	11.7551	0.408027
$831$	−2.60740	−0.0904497
$832$	1.17725	0.0408138
$833$	15.6062	0.540724
$834$	−2.51010	−0.0869177
$835$	0.0778547	0.00269427
$836$	−5.91708	−0.204646
$837$	5.31108	0.183578
$838$	29.3931	1.01537
$839$	−56.0821	−1.93617	−0.968084	−	0.250627i	$-0.919363\pi$
$839$	−56.0821	−1.93617	−0.968084	+	0.250627i	$0.919363\pi$
$840$	0.0866651	0.00299023
$841$	−23.1826	−0.799398
$842$	8.59419	0.296175
$843$	7.14688	0.246151
$844$	−16.9948	−0.584985
$845$	−11.6141	−0.399537
$846$	22.0474	0.758006
$847$	−0.332615	−0.0114288
$848$	−13.7653	−0.472701
$849$	−3.28695	−0.112808
$850$	−2.26526	−0.0776979
$851$	57.7937	1.98114
$852$	−2.59448	−0.0888855
$853$	−15.0789	−0.516293	−0.258146	−	0.966106i	$-0.583112\pi$
$853$	−15.0789	−0.516293	−0.258146	+	0.966106i	$0.583112\pi$
$854$	−2.30901	−0.0790126
$855$	17.3495	0.593341
$856$	−13.9436	−0.476581
$857$	−16.3960	−0.560076	−0.280038	−	0.959989i	$-0.590347\pi$
$857$	−16.3960	−0.560076	−0.280038	+	0.959989i	$0.590347\pi$
$858$	−0.306740	−0.0104719
$859$	−10.5700	−0.360645	−0.180323	−	0.983608i	$-0.557714\pi$
$859$	−10.5700	−0.360645	−0.180323	+	0.983608i	$0.557714\pi$
$860$	1.16823	0.0398364
$861$	0.425659	0.0145064
$862$	13.6654	0.465447
$863$	24.2424	0.825221	0.412611	−	0.910908i	$-0.364617\pi$
$863$	24.2424	0.825221	0.412611	+	0.910908i	$0.364617\pi$
$864$	1.54565	0.0525841
$865$	4.74454	0.161319
$866$	15.0239	0.510534
$867$	3.09244	0.105025
$868$	−1.14291	−0.0387930
$869$	1.75015	0.0593698
$870$	−0.628447	−0.0213063
$871$	11.1709	0.378511
$872$	0.223252	0.00756026
$873$	−35.5047	−1.20165
$874$	−31.5166	−1.06606
$875$	−0.332615	−0.0112444
$876$	0.260557	0.00880339
$877$	−12.8881	−0.435200	−0.217600	−	0.976038i	$-0.569823\pi$
$877$	−12.8881	−0.435200	−0.217600	+	0.976038i	$0.569823\pi$
$878$	7.19529	0.242829
$879$	−2.28064	−0.0769242
$880$	1.00000	0.0337100
$881$	−40.4472	−1.36270	−0.681350	−	0.731957i	$-0.738607\pi$
$881$	−40.4472	−1.36270	−0.681350	+	0.731957i	$0.738607\pi$
$882$	20.2004	0.680182
$883$	20.7825	0.699388	0.349694	−	0.936864i	$-0.386285\pi$
$883$	20.7825	0.699388	0.349694	+	0.936864i	$0.386285\pi$
$884$	−2.66678	−0.0896936
$885$	−0.334910	−0.0112579
$886$	20.9682	0.704439
$887$	−50.5367	−1.69686	−0.848429	−	0.529309i	$-0.822451\pi$
$887$	−50.5367	−1.69686	−0.848429	+	0.529309i	$0.822451\pi$
$888$	−2.82716	−0.0948733
$889$	−6.32680	−0.212194
$890$	9.25022	0.310068
$891$	8.39360	0.281196
$892$	9.71287	0.325211
$893$	44.4923	1.48888
$894$	−4.23806	−0.141742
$895$	10.0883	0.337213
$896$	−0.332615	−0.0111119
$897$	−1.63382	−0.0545515
$898$	28.4268	0.948614
$899$	8.28777	0.276413
$900$	−2.93211	−0.0977370
$901$	31.1819	1.03882
$902$	4.91154	0.163537
$903$	0.101245	0.00336922
$904$	−2.23612	−0.0743721
$905$	26.5403	0.882228
$906$	−1.24222	−0.0412701
$907$	1.03081	0.0342274	0.0171137	−	0.999854i	$-0.494552\pi$
$907$	1.03081	0.0342274	0.0171137	+	0.999854i	$0.494552\pi$
$908$	12.2368	0.406091
$909$	−2.84056	−0.0942153
$910$	−0.391571	−0.0129805
$911$	−11.1925	−0.370825	−0.185413	−	0.982661i	$-0.559362\pi$
$911$	−11.1925	−0.370825	−0.185413	+	0.982661i	$0.559362\pi$
$912$	1.54173	0.0510519
$913$	11.7551	0.389038
$914$	22.2848	0.737117
$915$	−1.80878	−0.0597964
$916$	−10.2708	−0.339358
$917$	−0.635676	−0.0209919
$918$	−3.50131	−0.115560
$919$	31.9094	1.05259	0.526297	−	0.850301i	$-0.323580\pi$
$919$	31.9094	1.05259	0.526297	+	0.850301i	$0.323580\pi$
$920$	5.32638	0.175606
$921$	−1.38618	−0.0456762
$922$	−5.04953	−0.166298
$923$	11.7224	0.385848
$924$	0.0866651	0.00285107
$925$	10.8505	0.356761
$926$	8.61311	0.283044
$927$	17.5473	0.576328
$928$	2.41194	0.0791758
$929$	−1.87426	−0.0614924	−0.0307462	−	0.999527i	$-0.509788\pi$
$929$	−1.87426	−0.0614924	−0.0307462	+	0.999527i	$0.509788\pi$
$930$	−0.895311	−0.0293584
$931$	40.7649	1.33602
$932$	−2.15740	−0.0706678
$933$	0.718842	0.0235338
$934$	−12.4849	−0.408517
$935$	−2.26526	−0.0740820
$936$	−3.45183	−0.112827
$937$	−14.8637	−0.485575	−0.242787	−	0.970080i	$-0.578062\pi$
$937$	−14.8637	−0.485575	−0.242787	+	0.970080i	$0.578062\pi$
$938$	−3.15617	−0.103053
$939$	2.25895	0.0737181
$940$	−7.51930	−0.245252
$941$	−38.0794	−1.24135	−0.620677	−	0.784067i	$-0.713142\pi$
$941$	−38.0794	−1.24135	−0.620677	+	0.784067i	$0.713142\pi$
$942$	1.62543	0.0529595
$943$	26.1607	0.851911
$944$	1.28536	0.0418350
$945$	−0.514107	−0.0167239
$946$	1.16823	0.0379825
$947$	24.4497	0.794508	0.397254	−	0.917709i	$-0.369963\pi$
$947$	24.4497	0.794508	0.397254	+	0.917709i	$0.369963\pi$
$948$	−0.456013	−0.0148106
$949$	−1.17725	−0.0382152
$950$	−5.91708	−0.191975
$951$	−7.51656	−0.243741
$952$	0.753460	0.0244198
$953$	0.752683	0.0243818	0.0121909	−	0.999926i	$-0.496119\pi$
$953$	0.752683	0.0243818	0.0121909	+	0.999926i	$0.496119\pi$
$954$	40.3612	1.30674
$955$	5.16957	0.167283
$956$	−2.81891	−0.0911699
$957$	−0.628447	−0.0203148
$958$	9.34841	0.302033
$959$	−3.06788	−0.0990669
$960$	−0.260557	−0.00840943
$961$	−19.1929	−0.619126
$962$	12.7737	0.411841
$963$	40.8841	1.31747
$964$	−17.0797	−0.550099
$965$	−10.1350	−0.326257
$966$	0.461611	0.0148521
$967$	47.4574	1.52613	0.763063	−	0.646324i	$-0.223695\pi$
$967$	47.4574	1.52613	0.763063	+	0.646324i	$0.223695\pi$
$968$	1.00000	0.0321412
$969$	−3.49243	−0.112193
$970$	12.1089	0.388794
$971$	10.8257	0.347413	0.173706	−	0.984797i	$-0.444426\pi$
$971$	10.8257	0.347413	0.173706	+	0.984797i	$0.444426\pi$
$972$	−6.82396	−0.218879
$973$	−3.20428	−0.102725
$974$	−12.0903	−0.387399
$975$	−0.306740	−0.00982356
$976$	6.94198	0.222207
$977$	37.4359	1.19768	0.598840	−	0.800869i	$-0.295628\pi$
$977$	37.4359	1.19768	0.598840	+	0.800869i	$0.295628\pi$
$978$	2.44715	0.0782511
$979$	9.25022	0.295638
$980$	−6.88937	−0.220073
$981$	−0.654599	−0.0208997
$982$	−10.0638	−0.321149
$983$	−24.7291	−0.788735	−0.394368	−	0.918953i	$-0.629036\pi$
$983$	−24.7291	−0.788735	−0.394368	+	0.918953i	$0.629036\pi$
$984$	−1.27974	−0.0407965
$985$	−15.3042	−0.487631
$986$	−5.46367	−0.173999
$987$	−0.651661	−0.0207426
$988$	−6.96588	−0.221614
$989$	6.22245	0.197862
$990$	−2.93211	−0.0931886
$991$	−15.6657	−0.497637	−0.248819	−	0.968550i	$-0.580042\pi$
$991$	−15.6657	−0.497637	−0.248819	+	0.968550i	$0.580042\pi$
$992$	3.43615	0.109098
$993$	−3.83793	−0.121793
$994$	−3.31200	−0.105050
$995$	12.2135	0.387193
$996$	−3.06288	−0.0970511
$997$	−14.5785	−0.461707	−0.230854	−	0.972988i	$-0.574152\pi$
$997$	−14.5785	−0.461707	−0.230854	+	0.972988i	$0.574152\pi$
$998$	−32.0322	−1.01396
$999$	16.7710	0.530612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bl.1.7	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bl.1.7	✓	19	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.260557 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.260557 q^{6} -0.332615 q^{7} +1.00000 q^{8} -2.93211 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.260557 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.260557 q^{6} -0.332615 q^{7} +1.00000 q^{8} -2.93211 q^{9} +1.00000 q^{10} +1.00000 q^{11} -0.260557 q^{12} +1.17725 q^{13} -0.332615 q^{14} -0.260557 q^{15} +1.00000 q^{16} -2.26526 q^{17} -2.93211 q^{18} -5.91708 q^{19} +1.00000 q^{20} +0.0866651 q^{21} +1.00000 q^{22} +5.32638 q^{23} -0.260557 q^{24} +1.00000 q^{25} +1.17725 q^{26} +1.54565 q^{27} -0.332615 q^{28} +2.41194 q^{29} -0.260557 q^{30} +3.43615 q^{31} +1.00000 q^{32} -0.260557 q^{33} -2.26526 q^{34} -0.332615 q^{35} -2.93211 q^{36} +10.8505 q^{37} -5.91708 q^{38} -0.306740 q^{39} +1.00000 q^{40} +4.91154 q^{41} +0.0866651 q^{42} +1.16823 q^{43} +1.00000 q^{44} -2.93211 q^{45} +5.32638 q^{46} -7.51930 q^{47} -0.260557 q^{48} -6.88937 q^{49} +1.00000 q^{50} +0.590229 q^{51} +1.17725 q^{52} -13.7653 q^{53} +1.54565 q^{54} +1.00000 q^{55} -0.332615 q^{56} +1.54173 q^{57} +2.41194 q^{58} +1.28536 q^{59} -0.260557 q^{60} +6.94198 q^{61} +3.43615 q^{62} +0.975264 q^{63} +1.00000 q^{64} +1.17725 q^{65} -0.260557 q^{66} +9.48895 q^{67} -2.26526 q^{68} -1.38782 q^{69} -0.332615 q^{70} +9.95746 q^{71} -2.93211 q^{72} -1.00000 q^{73} +10.8505 q^{74} -0.260557 q^{75} -5.91708 q^{76} -0.332615 q^{77} -0.306740 q^{78} +1.75015 q^{79} +1.00000 q^{80} +8.39360 q^{81} +4.91154 q^{82} +11.7551 q^{83} +0.0866651 q^{84} -2.26526 q^{85} +1.16823 q^{86} -0.628447 q^{87} +1.00000 q^{88} +9.25022 q^{89} -2.93211 q^{90} -0.391571 q^{91} +5.32638 q^{92} -0.895311 q^{93} -7.51930 q^{94} -5.91708 q^{95} -0.260557 q^{96} +12.1089 q^{97} -6.88937 q^{98} -2.93211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * q^99

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