LMFDB - Embedded newform 8030.2.a.bl.1.10

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			1.10
Root			$0.489749$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.510251 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.510251 q^{6} -0.810786 q^{7} +1.00000 q^{8} -2.73964 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.510251 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.510251 q^{6} -0.810786 q^{7} +1.00000 q^{8} -2.73964 q^{9} +1.00000 q^{10} +1.00000 q^{11} +0.510251 q^{12} +5.31023 q^{13} -0.810786 q^{14} +0.510251 q^{15} +1.00000 q^{16} +6.99993 q^{17} -2.73964 q^{18} -0.804839 q^{19} +1.00000 q^{20} -0.413705 q^{21} +1.00000 q^{22} +6.55148 q^{23} +0.510251 q^{24} +1.00000 q^{25} +5.31023 q^{26} -2.92866 q^{27} -0.810786 q^{28} -4.22024 q^{29} +0.510251 q^{30} +1.74797 q^{31} +1.00000 q^{32} +0.510251 q^{33} +6.99993 q^{34} -0.810786 q^{35} -2.73964 q^{36} -5.01890 q^{37} -0.804839 q^{38} +2.70955 q^{39} +1.00000 q^{40} +7.75536 q^{41} -0.413705 q^{42} -11.3526 q^{43} +1.00000 q^{44} -2.73964 q^{45} +6.55148 q^{46} +10.6946 q^{47} +0.510251 q^{48} -6.34263 q^{49} +1.00000 q^{50} +3.57172 q^{51} +5.31023 q^{52} -1.38087 q^{53} -2.92866 q^{54} +1.00000 q^{55} -0.810786 q^{56} -0.410670 q^{57} -4.22024 q^{58} +9.85387 q^{59} +0.510251 q^{60} -7.97495 q^{61} +1.74797 q^{62} +2.22126 q^{63} +1.00000 q^{64} +5.31023 q^{65} +0.510251 q^{66} -5.56945 q^{67} +6.99993 q^{68} +3.34290 q^{69} -0.810786 q^{70} +0.896854 q^{71} -2.73964 q^{72} -1.00000 q^{73} -5.01890 q^{74} +0.510251 q^{75} -0.804839 q^{76} -0.810786 q^{77} +2.70955 q^{78} +1.61988 q^{79} +1.00000 q^{80} +6.72458 q^{81} +7.75536 q^{82} -9.72069 q^{83} -0.413705 q^{84} +6.99993 q^{85} -11.3526 q^{86} -2.15338 q^{87} +1.00000 q^{88} -6.39666 q^{89} -2.73964 q^{90} -4.30546 q^{91} +6.55148 q^{92} +0.891902 q^{93} +10.6946 q^{94} -0.804839 q^{95} +0.510251 q^{96} +3.44367 q^{97} -6.34263 q^{98} -2.73964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.510251	0.294594	0.147297	−	0.989092i	$-0.452943\pi$
$3$	0.510251	0.294594	0.147297	+	0.989092i	$0.452943\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.510251	0.208309
$7$	−0.810786	−0.306448	−0.153224	−	0.988191i	$-0.548966\pi$
$7$	−0.810786	−0.306448	−0.153224	+	0.988191i	$0.548966\pi$
$8$	1.00000	0.353553
$9$	−2.73964	−0.913215
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.510251	0.147297
$13$	5.31023	1.47279	0.736396	−	0.676551i	$-0.236526\pi$
$13$	5.31023	1.47279	0.736396	+	0.676551i	$0.236526\pi$
$14$	−0.810786	−0.216692
$15$	0.510251	0.131746
$16$	1.00000	0.250000
$17$	6.99993	1.69773	0.848866	−	0.528608i	$-0.177286\pi$
$17$	6.99993	1.69773	0.848866	+	0.528608i	$0.177286\pi$
$18$	−2.73964	−0.645740
$19$	−0.804839	−0.184643	−0.0923214	−	0.995729i	$-0.529429\pi$
$19$	−0.804839	−0.184643	−0.0923214	+	0.995729i	$0.529429\pi$
$20$	1.00000	0.223607
$21$	−0.413705	−0.0902777
$22$	1.00000	0.213201
$23$	6.55148	1.36608	0.683039	−	0.730382i	$-0.260658\pi$
$23$	6.55148	1.36608	0.683039	+	0.730382i	$0.260658\pi$
$24$	0.510251	0.104155
$25$	1.00000	0.200000
$26$	5.31023	1.04142
$27$	−2.92866	−0.563621
$28$	−0.810786	−0.153224
$29$	−4.22024	−0.783679	−0.391839	−	0.920034i	$-0.628161\pi$
$29$	−4.22024	−0.783679	−0.391839	+	0.920034i	$0.628161\pi$
$30$	0.510251	0.0931587
$31$	1.74797	0.313944	0.156972	−	0.987603i	$-0.449827\pi$
$31$	1.74797	0.313944	0.156972	+	0.987603i	$0.449827\pi$
$32$	1.00000	0.176777
$33$	0.510251	0.0888233
$34$	6.99993	1.20048
$35$	−0.810786	−0.137048
$36$	−2.73964	−0.456607
$37$	−5.01890	−0.825102	−0.412551	−	0.910935i	$-0.635362\pi$
$37$	−5.01890	−0.825102	−0.412551	+	0.910935i	$0.635362\pi$
$38$	−0.804839	−0.130562
$39$	2.70955	0.433875
$40$	1.00000	0.158114
$41$	7.75536	1.21118	0.605592	−	0.795775i	$-0.292936\pi$
$41$	7.75536	1.21118	0.605592	+	0.795775i	$0.292936\pi$
$42$	−0.413705	−0.0638360
$43$	−11.3526	−1.73125	−0.865624	−	0.500694i	$-0.833078\pi$
$43$	−11.3526	−1.73125	−0.865624	+	0.500694i	$0.833078\pi$
$44$	1.00000	0.150756
$45$	−2.73964	−0.408402
$46$	6.55148	0.965963
$47$	10.6946	1.55996	0.779980	−	0.625804i	$-0.215229\pi$
$47$	10.6946	1.55996	0.779980	+	0.625804i	$0.215229\pi$
$48$	0.510251	0.0736484
$49$	−6.34263	−0.906089
$50$	1.00000	0.141421
$51$	3.57172	0.500141
$52$	5.31023	0.736396
$53$	−1.38087	−0.189678	−0.0948388	−	0.995493i	$-0.530234\pi$
$53$	−1.38087	−0.189678	−0.0948388	+	0.995493i	$0.530234\pi$
$54$	−2.92866	−0.398540
$55$	1.00000	0.134840
$56$	−0.810786	−0.108346
$57$	−0.410670	−0.0543946
$58$	−4.22024	−0.554144
$59$	9.85387	1.28286	0.641432	−	0.767180i	$-0.278341\pi$
$59$	9.85387	1.28286	0.641432	+	0.767180i	$0.278341\pi$
$60$	0.510251	0.0658732
$61$	−7.97495	−1.02109	−0.510544	−	0.859852i	$-0.670556\pi$
$61$	−7.97495	−1.02109	−0.510544	+	0.859852i	$0.670556\pi$
$62$	1.74797	0.221992
$63$	2.22126	0.279853
$64$	1.00000	0.125000
$65$	5.31023	0.658652
$66$	0.510251	0.0628076
$67$	−5.56945	−0.680416	−0.340208	−	0.940350i	$-0.610498\pi$
$67$	−5.56945	−0.680416	−0.340208	+	0.940350i	$0.610498\pi$
$68$	6.99993	0.848866
$69$	3.34290	0.402438
$70$	−0.810786	−0.0969075
$71$	0.896854	0.106437	0.0532185	−	0.998583i	$-0.483052\pi$
$71$	0.896854	0.106437	0.0532185	+	0.998583i	$0.483052\pi$
$72$	−2.73964	−0.322870
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−5.01890	−0.583435
$75$	0.510251	0.0589187
$76$	−0.804839	−0.0923214
$77$	−0.810786	−0.0923976
$78$	2.70955	0.306796
$79$	1.61988	0.182251	0.0911253	−	0.995839i	$-0.470954\pi$
$79$	1.61988	0.182251	0.0911253	+	0.995839i	$0.470954\pi$
$80$	1.00000	0.111803
$81$	6.72458	0.747175
$82$	7.75536	0.856437
$83$	−9.72069	−1.06698	−0.533492	−	0.845805i	$-0.679121\pi$
$83$	−9.72069	−1.06698	−0.533492	+	0.845805i	$0.679121\pi$
$84$	−0.413705	−0.0451389
$85$	6.99993	0.759249
$86$	−11.3526	−1.22418
$87$	−2.15338	−0.230867
$88$	1.00000	0.106600
$89$	−6.39666	−0.678044	−0.339022	−	0.940778i	$-0.610096\pi$
$89$	−6.39666	−0.678044	−0.339022	+	0.940778i	$0.610096\pi$
$90$	−2.73964	−0.288784
$91$	−4.30546	−0.451334
$92$	6.55148	0.683039
$93$	0.891902	0.0924859
$94$	10.6946	1.10306
$95$	−0.804839	−0.0825748
$96$	0.510251	0.0520773
$97$	3.44367	0.349652	0.174826	−	0.984599i	$-0.444064\pi$
$97$	3.44367	0.349652	0.174826	+	0.984599i	$0.444064\pi$
$98$	−6.34263	−0.640702
$99$	−2.73964	−0.275345
$100$	1.00000	0.100000
$101$	11.1727	1.11173	0.555864	−	0.831273i	$-0.312387\pi$
$101$	11.1727	1.11173	0.555864	+	0.831273i	$0.312387\pi$
$102$	3.57172	0.353653
$103$	−14.2688	−1.40595	−0.702973	−	0.711216i	$-0.748145\pi$
$103$	−14.2688	−1.40595	−0.702973	+	0.711216i	$0.748145\pi$
$104$	5.31023	0.520710
$105$	−0.413705	−0.0403734
$106$	−1.38087	−0.134122
$107$	18.5421	1.79253	0.896267	−	0.443515i	$-0.146269\pi$
$107$	18.5421	1.79253	0.896267	+	0.443515i	$0.146269\pi$
$108$	−2.92866	−0.281810
$109$	18.0731	1.73109	0.865545	−	0.500832i	$-0.166972\pi$
$109$	18.0731	1.73109	0.865545	+	0.500832i	$0.166972\pi$
$110$	1.00000	0.0953463
$111$	−2.56090	−0.243070
$112$	−0.810786	−0.0766121
$113$	−14.8079	−1.39301	−0.696504	−	0.717553i	$-0.745262\pi$
$113$	−14.8079	−1.39301	−0.696504	+	0.717553i	$0.745262\pi$
$114$	−0.410670	−0.0384628
$115$	6.55148	0.610929
$116$	−4.22024	−0.391839
$117$	−14.5481	−1.34497
$118$	9.85387	0.907122
$119$	−5.67544	−0.520267
$120$	0.510251	0.0465794
$121$	1.00000	0.0909091
$122$	−7.97495	−0.722018
$123$	3.95718	0.356807
$124$	1.74797	0.156972
$125$	1.00000	0.0894427
$126$	2.22126	0.197886
$127$	−11.9058	−1.05647	−0.528236	−	0.849098i	$-0.677146\pi$
$127$	−11.9058	−1.05647	−0.528236	+	0.849098i	$0.677146\pi$
$128$	1.00000	0.0883883
$129$	−5.79266	−0.510015
$130$	5.31023	0.465738
$131$	18.6125	1.62619	0.813093	−	0.582134i	$-0.197782\pi$
$131$	18.6125	1.62619	0.813093	+	0.582134i	$0.197782\pi$
$132$	0.510251	0.0444117
$133$	0.652553	0.0565835
$134$	−5.56945	−0.481127
$135$	−2.92866	−0.252059
$136$	6.99993	0.600239
$137$	18.6958	1.59729	0.798643	−	0.601805i	$-0.205552\pi$
$137$	18.6958	1.59729	0.798643	+	0.601805i	$0.205552\pi$
$138$	3.34290	0.284567
$139$	−8.46049	−0.717609	−0.358805	−	0.933413i	$-0.616816\pi$
$139$	−8.46049	−0.717609	−0.358805	+	0.933413i	$0.616816\pi$
$140$	−0.810786	−0.0685239
$141$	5.45691	0.459555
$142$	0.896854	0.0752623
$143$	5.31023	0.444063
$144$	−2.73964	−0.228304
$145$	−4.22024	−0.350472
$146$	−1.00000	−0.0827606
$147$	−3.23633	−0.266928
$148$	−5.01890	−0.412551
$149$	11.7114	0.959438	0.479719	−	0.877422i	$-0.340739\pi$
$149$	11.7114	0.959438	0.479719	+	0.877422i	$0.340739\pi$
$150$	0.510251	0.0416618
$151$	5.54491	0.451238	0.225619	−	0.974216i	$-0.427560\pi$
$151$	5.54491	0.451238	0.225619	+	0.974216i	$0.427560\pi$
$152$	−0.804839	−0.0652811
$153$	−19.1773	−1.55039
$154$	−0.810786	−0.0653350
$155$	1.74797	0.140400
$156$	2.70955	0.216938
$157$	−4.63911	−0.370241	−0.185121	−	0.982716i	$-0.559268\pi$
$157$	−4.63911	−0.370241	−0.185121	+	0.982716i	$0.559268\pi$
$158$	1.61988	0.128871
$159$	−0.704592	−0.0558778
$160$	1.00000	0.0790569
$161$	−5.31185	−0.418632
$162$	6.72458	0.528333
$163$	15.6880	1.22878	0.614391	−	0.789002i	$-0.289402\pi$
$163$	15.6880	1.22878	0.614391	+	0.789002i	$0.289402\pi$
$164$	7.75536	0.605592
$165$	0.510251	0.0397230
$166$	−9.72069	−0.754472
$167$	21.7580	1.68369	0.841843	−	0.539722i	$-0.181471\pi$
$167$	21.7580	1.68369	0.841843	+	0.539722i	$0.181471\pi$
$168$	−0.413705	−0.0319180
$169$	15.1985	1.16911
$170$	6.99993	0.536870
$171$	2.20497	0.168619
$172$	−11.3526	−0.865624
$173$	−10.2379	−0.778372	−0.389186	−	0.921159i	$-0.627244\pi$
$173$	−10.2379	−0.778372	−0.389186	+	0.921159i	$0.627244\pi$
$174$	−2.15338	−0.163247
$175$	−0.810786	−0.0612897
$176$	1.00000	0.0753778
$177$	5.02795	0.377924
$178$	−6.39666	−0.479450
$179$	6.35158	0.474740	0.237370	−	0.971419i	$-0.423715\pi$
$179$	6.35158	0.474740	0.237370	+	0.971419i	$0.423715\pi$
$180$	−2.73964	−0.204201
$181$	−16.1811	−1.20273	−0.601367	−	0.798973i	$-0.705377\pi$
$181$	−16.1811	−1.20273	−0.601367	+	0.798973i	$0.705377\pi$
$182$	−4.30546	−0.319142
$183$	−4.06923	−0.300806
$184$	6.55148	0.482981
$185$	−5.01890	−0.368997
$186$	0.891902	0.0653974
$187$	6.99993	0.511885
$188$	10.6946	0.779980
$189$	2.37452	0.172721
$190$	−0.804839	−0.0583892
$191$	26.2104	1.89652	0.948258	−	0.317502i	$-0.102844\pi$
$191$	26.2104	1.89652	0.948258	+	0.317502i	$0.102844\pi$
$192$	0.510251	0.0368242
$193$	2.41130	0.173569	0.0867846	−	0.996227i	$-0.472341\pi$
$193$	2.41130	0.173569	0.0867846	+	0.996227i	$0.472341\pi$
$194$	3.44367	0.247241
$195$	2.70955	0.194035
$196$	−6.34263	−0.453045
$197$	7.88127	0.561517	0.280759	−	0.959778i	$-0.409414\pi$
$197$	7.88127	0.561517	0.280759	+	0.959778i	$0.409414\pi$
$198$	−2.73964	−0.194698
$199$	10.1620	0.720363	0.360182	−	0.932882i	$-0.382715\pi$
$199$	10.1620	0.720363	0.360182	+	0.932882i	$0.382715\pi$
$200$	1.00000	0.0707107
$201$	−2.84182	−0.200446
$202$	11.1727	0.786111
$203$	3.42171	0.240157
$204$	3.57172	0.250071
$205$	7.75536	0.541658
$206$	−14.2688	−0.994154
$207$	−17.9487	−1.24752
$208$	5.31023	0.368198
$209$	−0.804839	−0.0556719
$210$	−0.413705	−0.0285483
$211$	10.5678	0.727518	0.363759	−	0.931493i	$-0.381493\pi$
$211$	10.5678	0.727518	0.363759	+	0.931493i	$0.381493\pi$
$212$	−1.38087	−0.0948388
$213$	0.457621	0.0313557
$214$	18.5421	1.26751
$215$	−11.3526	−0.774238
$216$	−2.92866	−0.199270
$217$	−1.41723	−0.0962076
$218$	18.0731	1.22407
$219$	−0.510251	−0.0344796
$220$	1.00000	0.0674200
$221$	37.1712	2.50040
$222$	−2.56090	−0.171876
$223$	−20.5249	−1.37445	−0.687223	−	0.726447i	$-0.741170\pi$
$223$	−20.5249	−1.37445	−0.687223	+	0.726447i	$0.741170\pi$
$224$	−0.810786	−0.0541729
$225$	−2.73964	−0.182643
$226$	−14.8079	−0.985005
$227$	11.6448	0.772895	0.386447	−	0.922311i	$-0.373702\pi$
$227$	11.6448	0.772895	0.386447	+	0.922311i	$0.373702\pi$
$228$	−0.410670	−0.0271973
$229$	19.7273	1.30362	0.651808	−	0.758384i	$-0.274011\pi$
$229$	19.7273	1.30362	0.651808	+	0.758384i	$0.274011\pi$
$230$	6.55148	0.431992
$231$	−0.413705	−0.0272198
$232$	−4.22024	−0.277072
$233$	10.6192	0.695690	0.347845	−	0.937552i	$-0.386914\pi$
$233$	10.6192	0.695690	0.347845	+	0.937552i	$0.386914\pi$
$234$	−14.5481	−0.951041
$235$	10.6946	0.697636
$236$	9.85387	0.641432
$237$	0.826546	0.0536899
$238$	−5.67544	−0.367884
$239$	−23.0295	−1.48965	−0.744827	−	0.667258i	$-0.767468\pi$
$239$	−23.0295	−1.48965	−0.744827	+	0.667258i	$0.767468\pi$
$240$	0.510251	0.0329366
$241$	8.58275	0.552864	0.276432	−	0.961034i	$-0.410848\pi$
$241$	8.58275	0.552864	0.276432	+	0.961034i	$0.410848\pi$
$242$	1.00000	0.0642824
$243$	12.2172	0.783734
$244$	−7.97495	−0.510544
$245$	−6.34263	−0.405216
$246$	3.95718	0.252301
$247$	−4.27388	−0.271940
$248$	1.74797	0.110996
$249$	−4.95999	−0.314327
$250$	1.00000	0.0632456
$251$	12.7944	0.807574	0.403787	−	0.914853i	$-0.367694\pi$
$251$	12.7944	0.807574	0.403787	+	0.914853i	$0.367694\pi$
$252$	2.22126	0.139927
$253$	6.55148	0.411888
$254$	−11.9058	−0.747038
$255$	3.57172	0.223670
$256$	1.00000	0.0625000
$257$	−0.335395	−0.0209214	−0.0104607	−	0.999945i	$-0.503330\pi$
$257$	−0.335395	−0.0209214	−0.0104607	+	0.999945i	$0.503330\pi$
$258$	−5.79266	−0.360635
$259$	4.06925	0.252851
$260$	5.31023	0.329326
$261$	11.5619	0.715667
$262$	18.6125	1.14989
$263$	9.36888	0.577710	0.288855	−	0.957373i	$-0.406725\pi$
$263$	9.36888	0.577710	0.288855	+	0.957373i	$0.406725\pi$
$264$	0.510251	0.0314038
$265$	−1.38087	−0.0848264
$266$	0.652553	0.0400106
$267$	−3.26390	−0.199748
$268$	−5.56945	−0.340208
$269$	0.687750	0.0419329	0.0209664	−	0.999780i	$-0.493326\pi$
$269$	0.687750	0.0419329	0.0209664	+	0.999780i	$0.493326\pi$
$270$	−2.92866	−0.178233
$271$	2.31247	0.140472	0.0702362	−	0.997530i	$-0.477625\pi$
$271$	2.31247	0.140472	0.0702362	+	0.997530i	$0.477625\pi$
$272$	6.99993	0.424433
$273$	−2.19686	−0.132960
$274$	18.6958	1.12945
$275$	1.00000	0.0603023
$276$	3.34290	0.201219
$277$	−19.3862	−1.16480	−0.582401	−	0.812902i	$-0.697887\pi$
$277$	−19.3862	−1.16480	−0.582401	+	0.812902i	$0.697887\pi$
$278$	−8.46049	−0.507427
$279$	−4.78880	−0.286698
$280$	−0.810786	−0.0484537
$281$	−13.6711	−0.815552	−0.407776	−	0.913082i	$-0.633696\pi$
$281$	−13.6711	−0.815552	−0.407776	+	0.913082i	$0.633696\pi$
$282$	5.45691	0.324954
$283$	9.54960	0.567665	0.283832	−	0.958874i	$-0.408394\pi$
$283$	9.54960	0.567665	0.283832	+	0.958874i	$0.408394\pi$
$284$	0.896854	0.0532185
$285$	−0.410670	−0.0243260
$286$	5.31023	0.314000
$287$	−6.28794	−0.371165
$288$	−2.73964	−0.161435
$289$	31.9990	1.88229
$290$	−4.22024	−0.247821
$291$	1.75714	0.103005
$292$	−1.00000	−0.0585206
$293$	−28.0682	−1.63976	−0.819882	−	0.572532i	$-0.805961\pi$
$293$	−28.0682	−1.63976	−0.819882	+	0.572532i	$0.805961\pi$
$294$	−3.23633	−0.188747
$295$	9.85387	0.573714
$296$	−5.01890	−0.291718
$297$	−2.92866	−0.169938
$298$	11.7114	0.678425
$299$	34.7898	2.01195
$300$	0.510251	0.0294594
$301$	9.20449	0.530538
$302$	5.54491	0.319074
$303$	5.70090	0.327508
$304$	−0.804839	−0.0461607
$305$	−7.97495	−0.456645
$306$	−19.1773	−1.09629
$307$	6.68071	0.381288	0.190644	−	0.981659i	$-0.438942\pi$
$307$	6.68071	0.381288	0.190644	+	0.981659i	$0.438942\pi$
$308$	−0.810786	−0.0461988
$309$	−7.28067	−0.414183
$310$	1.74797	0.0992778
$311$	−32.9301	−1.86729	−0.933647	−	0.358194i	$-0.883393\pi$
$311$	−32.9301	−1.86729	−0.933647	+	0.358194i	$0.883393\pi$
$312$	2.70955	0.153398
$313$	−20.6601	−1.16778	−0.583889	−	0.811834i	$-0.698469\pi$
$313$	−20.6601	−1.16778	−0.583889	+	0.811834i	$0.698469\pi$
$314$	−4.63911	−0.261800
$315$	2.22126	0.125154
$316$	1.61988	0.0911253
$317$	−17.4193	−0.978363	−0.489181	−	0.872182i	$-0.662704\pi$
$317$	−17.4193	−0.978363	−0.489181	+	0.872182i	$0.662704\pi$
$318$	−0.704592	−0.0395116
$319$	−4.22024	−0.236288
$320$	1.00000	0.0559017
$321$	9.46114	0.528069
$322$	−5.31185	−0.296018
$323$	−5.63382	−0.313474
$324$	6.72458	0.373588
$325$	5.31023	0.294558
$326$	15.6880	0.868880
$327$	9.22182	0.509968
$328$	7.75536	0.428218
$329$	−8.67099	−0.478047
$330$	0.510251	0.0280884
$331$	17.6045	0.967631	0.483815	−	0.875170i	$-0.339251\pi$
$331$	17.6045	0.967631	0.483815	+	0.875170i	$0.339251\pi$
$332$	−9.72069	−0.533492
$333$	13.7500	0.753495
$334$	21.7580	1.19055
$335$	−5.56945	−0.304291
$336$	−0.413705	−0.0225694
$337$	−10.0622	−0.548124	−0.274062	−	0.961712i	$-0.588367\pi$
$337$	−10.0622	−0.548124	−0.274062	+	0.961712i	$0.588367\pi$
$338$	15.1985	0.826689
$339$	−7.55574	−0.410371
$340$	6.99993	0.379624
$341$	1.74797	0.0946577
$342$	2.20497	0.119231
$343$	10.8180	0.584118
$344$	−11.3526	−0.612089
$345$	3.34290	0.179976
$346$	−10.2379	−0.550392
$347$	6.57974	0.353219	0.176610	−	0.984281i	$-0.443487\pi$
$347$	6.57974	0.353219	0.176610	+	0.984281i	$0.443487\pi$
$348$	−2.15338	−0.115433
$349$	−1.41558	−0.0757744	−0.0378872	−	0.999282i	$-0.512063\pi$
$349$	−1.41558	−0.0757744	−0.0378872	+	0.999282i	$0.512063\pi$
$350$	−0.810786	−0.0433383
$351$	−15.5518	−0.830096
$352$	1.00000	0.0533002
$353$	−10.0151	−0.533052	−0.266526	−	0.963828i	$-0.585876\pi$
$353$	−10.0151	−0.533052	−0.266526	+	0.963828i	$0.585876\pi$
$354$	5.02795	0.267232
$355$	0.896854	0.0476001
$356$	−6.39666	−0.339022
$357$	−2.89590	−0.153267
$358$	6.35158	0.335692
$359$	12.8191	0.676566	0.338283	−	0.941044i	$-0.390154\pi$
$359$	12.8191	0.676566	0.338283	+	0.941044i	$0.390154\pi$
$360$	−2.73964	−0.144392
$361$	−18.3522	−0.965907
$362$	−16.1811	−0.850462
$363$	0.510251	0.0267812
$364$	−4.30546	−0.225667
$365$	−1.00000	−0.0523424
$366$	−4.06923	−0.212702
$367$	9.65585	0.504031	0.252016	−	0.967723i	$-0.418907\pi$
$367$	9.65585	0.504031	0.252016	+	0.967723i	$0.418907\pi$
$368$	6.55148	0.341519
$369$	−21.2469	−1.10607
$370$	−5.01890	−0.260920
$371$	1.11959	0.0581263
$372$	0.891902	0.0462430
$373$	−11.7454	−0.608152	−0.304076	−	0.952648i	$-0.598348\pi$
$373$	−11.7454	−0.608152	−0.304076	+	0.952648i	$0.598348\pi$
$374$	6.99993	0.361958
$375$	0.510251	0.0263493
$376$	10.6946	0.551529
$377$	−22.4104	−1.15420
$378$	2.37452	0.122132
$379$	−37.2307	−1.91241	−0.956205	−	0.292697i	$-0.905447\pi$
$379$	−37.2307	−1.91241	−0.956205	+	0.292697i	$0.905447\pi$
$380$	−0.804839	−0.0412874
$381$	−6.07496	−0.311230
$382$	26.2104	1.34104
$383$	14.1879	0.724966	0.362483	−	0.931990i	$-0.381929\pi$
$383$	14.1879	0.724966	0.362483	+	0.931990i	$0.381929\pi$
$384$	0.510251	0.0260387
$385$	−0.810786	−0.0413215
$386$	2.41130	0.122732
$387$	31.1020	1.58100
$388$	3.44367	0.174826
$389$	−1.01260	−0.0513408	−0.0256704	−	0.999670i	$-0.508172\pi$
$389$	−1.01260	−0.0513408	−0.0256704	+	0.999670i	$0.508172\pi$
$390$	2.70955	0.137203
$391$	45.8599	2.31923
$392$	−6.34263	−0.320351
$393$	9.49707	0.479064
$394$	7.88127	0.397052
$395$	1.61988	0.0815050
$396$	−2.73964	−0.137672
$397$	−0.258839	−0.0129908	−0.00649538	−	0.999979i	$-0.502068\pi$
$397$	−0.258839	−0.0129908	−0.00649538	+	0.999979i	$0.502068\pi$
$398$	10.1620	0.509374
$399$	0.332966	0.0166691
$400$	1.00000	0.0500000
$401$	−31.6204	−1.57905	−0.789523	−	0.613721i	$-0.789672\pi$
$401$	−31.6204	−1.57905	−0.789523	+	0.613721i	$0.789672\pi$
$402$	−2.84182	−0.141737
$403$	9.28209	0.462374
$404$	11.1727	0.555864
$405$	6.72458	0.334147
$406$	3.42171	0.169817
$407$	−5.01890	−0.248778
$408$	3.57172	0.176827
$409$	−27.1953	−1.34472	−0.672361	−	0.740223i	$-0.734720\pi$
$409$	−27.1953	−1.34472	−0.672361	+	0.740223i	$0.734720\pi$
$410$	7.75536	0.383010
$411$	9.53953	0.470550
$412$	−14.2688	−0.702973
$413$	−7.98938	−0.393132
$414$	−17.9487	−0.882131
$415$	−9.72069	−0.477170
$416$	5.31023	0.260355
$417$	−4.31698	−0.211403
$418$	−0.804839	−0.0393660
$419$	17.7259	0.865965	0.432982	−	0.901402i	$-0.357461\pi$
$419$	17.7259	0.865965	0.432982	+	0.901402i	$0.357461\pi$
$420$	−0.413705	−0.0201867
$421$	10.0618	0.490382	0.245191	−	0.969475i	$-0.421149\pi$
$421$	10.0618	0.490382	0.245191	+	0.969475i	$0.421149\pi$
$422$	10.5678	0.514433
$423$	−29.2993	−1.42458
$424$	−1.38087	−0.0670611
$425$	6.99993	0.339546
$426$	0.457621	0.0221718
$427$	6.46598	0.312911
$428$	18.5421	0.896267
$429$	2.70955	0.130818
$430$	−11.3526	−0.547469
$431$	−27.7608	−1.33719	−0.668594	−	0.743627i	$-0.733104\pi$
$431$	−27.7608	−1.33719	−0.668594	+	0.743627i	$0.733104\pi$
$432$	−2.92866	−0.140905
$433$	−15.4418	−0.742087	−0.371044	−	0.928615i	$-0.621000\pi$
$433$	−15.4418	−0.742087	−0.371044	+	0.928615i	$0.621000\pi$
$434$	−1.41723	−0.0680290
$435$	−2.15338	−0.103247
$436$	18.0731	0.865545
$437$	−5.27289	−0.252236
$438$	−0.510251	−0.0243807
$439$	−23.6585	−1.12916	−0.564579	−	0.825379i	$-0.690961\pi$
$439$	−23.6585	−1.12916	−0.564579	+	0.825379i	$0.690961\pi$
$440$	1.00000	0.0476731
$441$	17.3765	0.827454
$442$	37.1712	1.76805
$443$	−12.7659	−0.606525	−0.303263	−	0.952907i	$-0.598076\pi$
$443$	−12.7659	−0.606525	−0.303263	+	0.952907i	$0.598076\pi$
$444$	−2.56090	−0.121535
$445$	−6.39666	−0.303231
$446$	−20.5249	−0.971880
$447$	5.97577	0.282644
$448$	−0.810786	−0.0383060
$449$	−1.77394	−0.0837175	−0.0418588	−	0.999124i	$-0.513328\pi$
$449$	−1.77394	−0.0837175	−0.0418588	+	0.999124i	$0.513328\pi$
$450$	−2.73964	−0.129148
$451$	7.75536	0.365186
$452$	−14.8079	−0.696504
$453$	2.82930	0.132932
$454$	11.6448	0.546519
$455$	−4.30546	−0.201843
$456$	−0.410670	−0.0192314
$457$	21.3320	0.997870	0.498935	−	0.866639i	$-0.333725\pi$
$457$	21.3320	0.997870	0.498935	+	0.866639i	$0.333725\pi$
$458$	19.7273	0.921795
$459$	−20.5004	−0.956877
$460$	6.55148	0.305464
$461$	−35.6159	−1.65880	−0.829399	−	0.558657i	$-0.811317\pi$
$461$	−35.6159	−1.65880	−0.829399	+	0.558657i	$0.811317\pi$
$462$	−0.413705	−0.0192473
$463$	40.4686	1.88074	0.940368	−	0.340160i	$-0.110481\pi$
$463$	40.4686	1.88074	0.940368	+	0.340160i	$0.110481\pi$
$464$	−4.22024	−0.195920
$465$	0.891902	0.0413610
$466$	10.6192	0.491927
$467$	11.1785	0.517281	0.258640	−	0.965974i	$-0.416726\pi$
$467$	11.1785	0.517281	0.258640	+	0.965974i	$0.416726\pi$
$468$	−14.5481	−0.672487
$469$	4.51563	0.208512
$470$	10.6946	0.493303
$471$	−2.36711	−0.109071
$472$	9.85387	0.453561
$473$	−11.3526	−0.521991
$474$	0.826546	0.0379645
$475$	−0.804839	−0.0369286
$476$	−5.67544	−0.260134
$477$	3.78310	0.173216
$478$	−23.0295	−1.05334
$479$	−33.0816	−1.51154	−0.755768	−	0.654840i	$-0.772736\pi$
$479$	−33.0816	−1.51154	−0.755768	+	0.654840i	$0.772736\pi$
$480$	0.510251	0.0232897
$481$	−26.6515	−1.21520
$482$	8.58275	0.390934
$483$	−2.71038	−0.123326
$484$	1.00000	0.0454545
$485$	3.44367	0.156369
$486$	12.2172	0.554184
$487$	−0.245965	−0.0111457	−0.00557287	−	0.999984i	$-0.501774\pi$
$487$	−0.245965	−0.0111457	−0.00557287	+	0.999984i	$0.501774\pi$
$488$	−7.97495	−0.361009
$489$	8.00484	0.361991
$490$	−6.34263	−0.286531
$491$	15.0234	0.677996	0.338998	−	0.940787i	$-0.389912\pi$
$491$	15.0234	0.677996	0.338998	+	0.940787i	$0.389912\pi$
$492$	3.95718	0.178404
$493$	−29.5414	−1.33048
$494$	−4.27388	−0.192291
$495$	−2.73964	−0.123138
$496$	1.74797	0.0784860
$497$	−0.727157	−0.0326174
$498$	−4.95999	−0.222263
$499$	−41.9420	−1.87758	−0.938792	−	0.344484i	$-0.888054\pi$
$499$	−41.9420	−1.87758	−0.938792	+	0.344484i	$0.888054\pi$
$500$	1.00000	0.0447214
$501$	11.1021	0.496004
$502$	12.7944	0.571041
$503$	−11.1691	−0.498005	−0.249003	−	0.968503i	$-0.580103\pi$
$503$	−11.1691	−0.498005	−0.249003	+	0.968503i	$0.580103\pi$
$504$	2.22126	0.0989430
$505$	11.1727	0.497180
$506$	6.55148	0.291249
$507$	7.75505	0.344414
$508$	−11.9058	−0.528236
$509$	−31.4287	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$509$	−31.4287	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$510$	3.57172	0.158159
$511$	0.810786	0.0358671
$512$	1.00000	0.0441942
$513$	2.35710	0.104069
$514$	−0.335395	−0.0147936
$515$	−14.2688	−0.628758
$516$	−5.79266	−0.255007
$517$	10.6946	0.470346
$518$	4.06925	0.178793
$519$	−5.22389	−0.229303
$520$	5.31023	0.232869
$521$	−30.9873	−1.35758	−0.678789	−	0.734333i	$-0.737495\pi$
$521$	−30.9873	−1.35758	−0.678789	+	0.734333i	$0.737495\pi$
$522$	11.5619	0.506053
$523$	−3.22433	−0.140990	−0.0704951	−	0.997512i	$-0.522458\pi$
$523$	−3.22433	−0.140990	−0.0704951	+	0.997512i	$0.522458\pi$
$524$	18.6125	0.813093
$525$	−0.413705	−0.0180555
$526$	9.36888	0.408503
$527$	12.2356	0.532993
$528$	0.510251	0.0222058
$529$	19.9219	0.866168
$530$	−1.38087	−0.0599813
$531$	−26.9961	−1.17153
$532$	0.652553	0.0282917
$533$	41.1827	1.78382
$534$	−3.26390	−0.141243
$535$	18.5421	0.801645
$536$	−5.56945	−0.240564
$537$	3.24090	0.139855
$538$	0.687750	0.0296510
$539$	−6.34263	−0.273196
$540$	−2.92866	−0.126029
$541$	24.0496	1.03397	0.516985	−	0.855994i	$-0.327054\pi$
$541$	24.0496	1.03397	0.516985	+	0.855994i	$0.327054\pi$
$542$	2.31247	0.0993289
$543$	−8.25644	−0.354318
$544$	6.99993	0.300119
$545$	18.0731	0.774167
$546$	−2.19686	−0.0940171
$547$	−40.6554	−1.73830	−0.869150	−	0.494549i	$-0.835333\pi$
$547$	−40.6554	−1.73830	−0.869150	+	0.494549i	$0.835333\pi$
$548$	18.6958	0.798643
$549$	21.8485	0.932473
$550$	1.00000	0.0426401
$551$	3.39661	0.144701
$552$	3.34290	0.142283
$553$	−1.31338	−0.0558504
$554$	−19.3862	−0.823639
$555$	−2.56090	−0.108704
$556$	−8.46049	−0.358805
$557$	13.1865	0.558731	0.279365	−	0.960185i	$-0.409876\pi$
$557$	13.1865	0.558731	0.279365	+	0.960185i	$0.409876\pi$
$558$	−4.78880	−0.202726
$559$	−60.2846	−2.54977
$560$	−0.810786	−0.0342620
$561$	3.57172	0.150798
$562$	−13.6711	−0.576682
$563$	2.89448	0.121988	0.0609938	−	0.998138i	$-0.480573\pi$
$563$	2.89448	0.121988	0.0609938	+	0.998138i	$0.480573\pi$
$564$	5.45691	0.229777
$565$	−14.8079	−0.622972
$566$	9.54960	0.401400
$567$	−5.45219	−0.228971
$568$	0.896854	0.0376312
$569$	22.8191	0.956628	0.478314	−	0.878189i	$-0.341248\pi$
$569$	22.8191	0.956628	0.478314	+	0.878189i	$0.341248\pi$
$570$	−0.410670	−0.0172011
$571$	−12.9170	−0.540561	−0.270281	−	0.962782i	$-0.587117\pi$
$571$	−12.9170	−0.540561	−0.270281	+	0.962782i	$0.587117\pi$
$572$	5.31023	0.222032
$573$	13.3739	0.558701
$574$	−6.28794	−0.262454
$575$	6.55148	0.273216
$576$	−2.73964	−0.114152
$577$	23.0755	0.960645	0.480322	−	0.877092i	$-0.340520\pi$
$577$	23.0755	0.960645	0.480322	+	0.877092i	$0.340520\pi$
$578$	31.9990	1.33098
$579$	1.23037	0.0511324
$580$	−4.22024	−0.175236
$581$	7.88140	0.326975
$582$	1.75714	0.0728357
$583$	−1.38087	−0.0571899
$584$	−1.00000	−0.0413803
$585$	−14.5481	−0.601491
$586$	−28.0682	−1.15949
$587$	−2.82031	−0.116407	−0.0582033	−	0.998305i	$-0.518537\pi$
$587$	−2.82031	−0.116407	−0.0582033	+	0.998305i	$0.518537\pi$
$588$	−3.23633	−0.133464
$589$	−1.40683	−0.0579675
$590$	9.85387	0.405677
$591$	4.02143	0.165419
$592$	−5.01890	−0.206275
$593$	−46.2790	−1.90045	−0.950226	−	0.311562i	$-0.899148\pi$
$593$	−46.2790	−1.90045	−0.950226	+	0.311562i	$0.899148\pi$
$594$	−2.92866	−0.120164
$595$	−5.67544	−0.232670
$596$	11.7114	0.479719
$597$	5.18516	0.212214
$598$	34.7898	1.42266
$599$	−14.5785	−0.595660	−0.297830	−	0.954619i	$-0.596263\pi$
$599$	−14.5785	−0.595660	−0.297830	+	0.954619i	$0.596263\pi$
$600$	0.510251	0.0208309
$601$	−31.2817	−1.27601	−0.638004	−	0.770033i	$-0.720240\pi$
$601$	−31.2817	−1.27601	−0.638004	+	0.770033i	$0.720240\pi$
$602$	9.20449	0.375147
$603$	15.2583	0.621366
$604$	5.54491	0.225619
$605$	1.00000	0.0406558
$606$	5.70090	0.231583
$607$	−30.9647	−1.25682	−0.628408	−	0.777884i	$-0.716293\pi$
$607$	−30.9647	−1.25682	−0.628408	+	0.777884i	$0.716293\pi$
$608$	−0.804839	−0.0326405
$609$	1.74593	0.0707487
$610$	−7.97495	−0.322896
$611$	56.7905	2.29750
$612$	−19.1773	−0.775197
$613$	36.5461	1.47608	0.738041	−	0.674756i	$-0.235751\pi$
$613$	36.5461	1.47608	0.738041	+	0.674756i	$0.235751\pi$
$614$	6.68071	0.269612
$615$	3.95718	0.159569
$616$	−0.810786	−0.0326675
$617$	27.5181	1.10784	0.553918	−	0.832571i	$-0.313132\pi$
$617$	27.5181	1.10784	0.553918	+	0.832571i	$0.313132\pi$
$618$	−7.28067	−0.292872
$619$	2.70008	0.108525	0.0542627	−	0.998527i	$-0.482719\pi$
$619$	2.70008	0.108525	0.0542627	+	0.998527i	$0.482719\pi$
$620$	1.74797	0.0702000
$621$	−19.1871	−0.769950
$622$	−32.9301	−1.32038
$623$	5.18632	0.207786
$624$	2.70955	0.108469
$625$	1.00000	0.0400000
$626$	−20.6601	−0.825743
$627$	−0.410670	−0.0164006
$628$	−4.63911	−0.185121
$629$	−35.1319	−1.40080
$630$	2.22126	0.0884973
$631$	−18.2468	−0.726393	−0.363196	−	0.931713i	$-0.618315\pi$
$631$	−18.2468	−0.726393	−0.363196	+	0.931713i	$0.618315\pi$
$632$	1.61988	0.0644353
$633$	5.39224	0.214322
$634$	−17.4193	−0.691807
$635$	−11.9058	−0.472468
$636$	−0.704592	−0.0279389
$637$	−33.6808	−1.33448
$638$	−4.22024	−0.167081
$639$	−2.45706	−0.0971998
$640$	1.00000	0.0395285
$641$	−29.1983	−1.15327	−0.576633	−	0.817004i	$-0.695634\pi$
$641$	−29.1983	−1.15327	−0.576633	+	0.817004i	$0.695634\pi$
$642$	9.46114	0.373401
$643$	38.1772	1.50556	0.752781	−	0.658271i	$-0.228712\pi$
$643$	38.1772	1.50556	0.752781	+	0.658271i	$0.228712\pi$
$644$	−5.31185	−0.209316
$645$	−5.79266	−0.228086
$646$	−5.63382	−0.221660
$647$	−4.42346	−0.173904	−0.0869521	−	0.996212i	$-0.527713\pi$
$647$	−4.42346	−0.173904	−0.0869521	+	0.996212i	$0.527713\pi$
$648$	6.72458	0.264166
$649$	9.85387	0.386798
$650$	5.31023	0.208284
$651$	−0.723142	−0.0283422
$652$	15.6880	0.614391
$653$	32.6973	1.27954	0.639771	−	0.768565i	$-0.279029\pi$
$653$	32.6973	1.27954	0.639771	+	0.768565i	$0.279029\pi$
$654$	9.22182	0.360602
$655$	18.6125	0.727252
$656$	7.75536	0.302796
$657$	2.73964	0.106884
$658$	−8.67099	−0.338030
$659$	−4.48782	−0.174820	−0.0874102	−	0.996172i	$-0.527859\pi$
$659$	−4.48782	−0.174820	−0.0874102	+	0.996172i	$0.527859\pi$
$660$	0.510251	0.0198615
$661$	1.94360	0.0755971	0.0377986	−	0.999285i	$-0.487965\pi$
$661$	1.94360	0.0755971	0.0377986	+	0.999285i	$0.487965\pi$
$662$	17.6045	0.684218
$663$	18.9666	0.736604
$664$	−9.72069	−0.377236
$665$	0.652553	0.0253049
$666$	13.7500	0.532801
$667$	−27.6488	−1.07057
$668$	21.7580	0.841843
$669$	−10.4728	−0.404903
$670$	−5.56945	−0.215167
$671$	−7.97495	−0.307870
$672$	−0.413705	−0.0159590
$673$	−24.7060	−0.952348	−0.476174	−	0.879351i	$-0.657977\pi$
$673$	−24.7060	−0.952348	−0.476174	+	0.879351i	$0.657977\pi$
$674$	−10.0622	−0.387582
$675$	−2.92866	−0.112724
$676$	15.1985	0.584557
$677$	−45.2114	−1.73761	−0.868807	−	0.495151i	$-0.835113\pi$
$677$	−45.2114	−1.73761	−0.868807	+	0.495151i	$0.835113\pi$
$678$	−7.55574	−0.290176
$679$	−2.79208	−0.107150
$680$	6.99993	0.268435
$681$	5.94179	0.227690
$682$	1.74797	0.0669331
$683$	−3.94685	−0.151022	−0.0755110	−	0.997145i	$-0.524059\pi$
$683$	−3.94685	−0.151022	−0.0755110	+	0.997145i	$0.524059\pi$
$684$	2.20497	0.0843093
$685$	18.6958	0.714328
$686$	10.8180	0.413034
$687$	10.0659	0.384037
$688$	−11.3526	−0.432812
$689$	−7.33275	−0.279355
$690$	3.34290	0.127262
$691$	−46.6065	−1.77299	−0.886497	−	0.462734i	$-0.846868\pi$
$691$	−46.6065	−1.77299	−0.886497	+	0.462734i	$0.846868\pi$
$692$	−10.2379	−0.389186
$693$	2.22126	0.0843789
$694$	6.57974	0.249764
$695$	−8.46049	−0.320925
$696$	−2.15338	−0.0816237
$697$	54.2870	2.05627
$698$	−1.41558	−0.0535806
$699$	5.41848	0.204946
$700$	−0.810786	−0.0306448
$701$	25.6114	0.967330	0.483665	−	0.875253i	$-0.339305\pi$
$701$	25.6114	0.967330	0.483665	+	0.875253i	$0.339305\pi$
$702$	−15.5518	−0.586967
$703$	4.03941	0.152349
$704$	1.00000	0.0376889
$705$	5.45691	0.205519
$706$	−10.0151	−0.376925
$707$	−9.05870	−0.340687
$708$	5.02795	0.188962
$709$	45.4627	1.70739	0.853694	−	0.520774i	$-0.174357\pi$
$709$	45.4627	1.70739	0.853694	+	0.520774i	$0.174357\pi$
$710$	0.896854	0.0336583
$711$	−4.43789	−0.166434
$712$	−6.39666	−0.239725
$713$	11.4518	0.428872
$714$	−2.89590	−0.108376
$715$	5.31023	0.198591
$716$	6.35158	0.237370
$717$	−11.7508	−0.438843
$718$	12.8191	0.478405
$719$	−28.4997	−1.06286	−0.531430	−	0.847102i	$-0.678345\pi$
$719$	−28.4997	−1.06286	−0.531430	+	0.847102i	$0.678345\pi$
$720$	−2.73964	−0.102100
$721$	11.5689	0.430850
$722$	−18.3522	−0.682999
$723$	4.37936	0.162870
$724$	−16.1811	−0.601367
$725$	−4.22024	−0.156736
$726$	0.510251	0.0189372
$727$	−37.4103	−1.38747	−0.693736	−	0.720229i	$-0.744037\pi$
$727$	−37.4103	−1.38747	−0.693736	+	0.720229i	$0.744037\pi$
$728$	−4.30546	−0.159571
$729$	−13.9399	−0.516292
$730$	−1.00000	−0.0370117
$731$	−79.4671	−2.93920
$732$	−4.06923	−0.150403
$733$	−20.1036	−0.742543	−0.371271	−	0.928524i	$-0.621078\pi$
$733$	−20.1036	−0.742543	−0.371271	+	0.928524i	$0.621078\pi$
$734$	9.65585	0.356404
$735$	−3.23633	−0.119374
$736$	6.55148	0.241491
$737$	−5.56945	−0.205153
$738$	−21.2469	−0.782110
$739$	−12.1761	−0.447905	−0.223953	−	0.974600i	$-0.571896\pi$
$739$	−12.1761	−0.447905	−0.223953	+	0.974600i	$0.571896\pi$
$740$	−5.01890	−0.184498
$741$	−2.18075	−0.0801119
$742$	1.11959	0.0411015
$743$	9.97790	0.366053	0.183027	−	0.983108i	$-0.441411\pi$
$743$	9.97790	0.366053	0.183027	+	0.983108i	$0.441411\pi$
$744$	0.891902	0.0326987
$745$	11.7114	0.429074
$746$	−11.7454	−0.430029
$747$	26.6312	0.974385
$748$	6.99993	0.255943
$749$	−15.0337	−0.549319
$750$	0.510251	0.0186317
$751$	−13.1699	−0.480575	−0.240288	−	0.970702i	$-0.577242\pi$
$751$	−13.1699	−0.480575	−0.240288	+	0.970702i	$0.577242\pi$
$752$	10.6946	0.389990
$753$	6.52835	0.237906
$754$	−22.4104	−0.816139
$755$	5.54491	0.201800
$756$	2.37452	0.0863603
$757$	−9.43271	−0.342838	−0.171419	−	0.985198i	$-0.554835\pi$
$757$	−9.43271	−0.342838	−0.171419	+	0.985198i	$0.554835\pi$
$758$	−37.2307	−1.35228
$759$	3.34290	0.121340
$760$	−0.804839	−0.0291946
$761$	43.4499	1.57506	0.787529	−	0.616277i	$-0.211360\pi$
$761$	43.4499	1.57506	0.787529	+	0.616277i	$0.211360\pi$
$762$	−6.07496	−0.220073
$763$	−14.6534	−0.530489
$764$	26.2104	0.948258
$765$	−19.1773	−0.693357
$766$	14.1879	0.512628
$767$	52.3263	1.88939
$768$	0.510251	0.0184121
$769$	12.1349	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$769$	12.1349	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$770$	−0.810786	−0.0292187
$771$	−0.171136	−0.00616330
$772$	2.41130	0.0867846
$773$	11.1455	0.400877	0.200439	−	0.979706i	$-0.435763\pi$
$773$	11.1455	0.400877	0.200439	+	0.979706i	$0.435763\pi$
$774$	31.1020	1.11794
$775$	1.74797	0.0627888
$776$	3.44367	0.123621
$777$	2.07634	0.0744883
$778$	−1.01260	−0.0363034
$779$	−6.24182	−0.223636
$780$	2.70955	0.0970174
$781$	0.896854	0.0320920
$782$	45.8599	1.63995
$783$	12.3596	0.441698
$784$	−6.34263	−0.226522
$785$	−4.63911	−0.165577
$786$	9.49707	0.338749
$787$	12.1614	0.433506	0.216753	−	0.976227i	$-0.430453\pi$
$787$	12.1614	0.433506	0.216753	+	0.976227i	$0.430453\pi$
$788$	7.88127	0.280759
$789$	4.78048	0.170190
$790$	1.61988	0.0576327
$791$	12.0060	0.426885
$792$	−2.73964	−0.0973490
$793$	−42.3488	−1.50385
$794$	−0.258839	−0.00918585
$795$	−0.704592	−0.0249893
$796$	10.1620	0.360182
$797$	24.8963	0.881873	0.440937	−	0.897538i	$-0.354646\pi$
$797$	24.8963	0.881873	0.440937	+	0.897538i	$0.354646\pi$
$798$	0.332966	0.0117869
$799$	74.8611	2.64839
$800$	1.00000	0.0353553
$801$	17.5246	0.619200
$802$	−31.6204	−1.11655
$803$	−1.00000	−0.0352892
$804$	−2.84182	−0.100223
$805$	−5.31185	−0.187218
$806$	9.28209	0.326948
$807$	0.350925	0.0123532
$808$	11.1727	0.393055
$809$	−13.3627	−0.469809	−0.234904	−	0.972018i	$-0.575478\pi$
$809$	−13.3627	−0.469809	−0.234904	+	0.972018i	$0.575478\pi$
$810$	6.72458	0.236278
$811$	35.1165	1.23311	0.616554	−	0.787313i	$-0.288528\pi$
$811$	35.1165	1.23311	0.616554	+	0.787313i	$0.288528\pi$
$812$	3.42171	0.120078
$813$	1.17994	0.0413823
$814$	−5.01890	−0.175912
$815$	15.6880	0.549528
$816$	3.57172	0.125035
$817$	9.13698	0.319663
$818$	−27.1953	−0.950862
$819$	11.7954	0.412165
$820$	7.75536	0.270829
$821$	2.08108	0.0726302	0.0363151	−	0.999340i	$-0.488438\pi$
$821$	2.08108	0.0726302	0.0363151	+	0.999340i	$0.488438\pi$
$822$	9.53953	0.332729
$823$	−17.1857	−0.599056	−0.299528	−	0.954088i	$-0.596829\pi$
$823$	−17.1857	−0.599056	−0.299528	+	0.954088i	$0.596829\pi$
$824$	−14.2688	−0.497077
$825$	0.510251	0.0177647
$826$	−7.98938	−0.277986
$827$	−0.637920	−0.0221827	−0.0110913	−	0.999938i	$-0.503531\pi$
$827$	−0.637920	−0.0221827	−0.0110913	+	0.999938i	$0.503531\pi$
$828$	−17.9487	−0.623761
$829$	−27.4098	−0.951983	−0.475992	−	0.879450i	$-0.657911\pi$
$829$	−27.4098	−0.951983	−0.475992	+	0.879450i	$0.657911\pi$
$830$	−9.72069	−0.337410
$831$	−9.89182	−0.343143
$832$	5.31023	0.184099
$833$	−44.3979	−1.53830
$834$	−4.31698	−0.149485
$835$	21.7580	0.752968
$836$	−0.804839	−0.0278360
$837$	−5.11920	−0.176945
$838$	17.7259	0.612329
$839$	−0.514914	−0.0177768	−0.00888840	−	0.999960i	$-0.502829\pi$
$839$	−0.514914	−0.0177768	−0.00888840	+	0.999960i	$0.502829\pi$
$840$	−0.413705	−0.0142742
$841$	−11.1896	−0.385848
$842$	10.0618	0.346752
$843$	−6.97572	−0.240257
$844$	10.5678	0.363759
$845$	15.1985	0.522844
$846$	−29.2993	−1.00733
$847$	−0.810786	−0.0278589
$848$	−1.38087	−0.0474194
$849$	4.87270	0.167230
$850$	6.99993	0.240096
$851$	−32.8812	−1.12715
$852$	0.457621	0.0156778
$853$	−1.40592	−0.0481376	−0.0240688	−	0.999710i	$-0.507662\pi$
$853$	−1.40592	−0.0481376	−0.0240688	+	0.999710i	$0.507662\pi$
$854$	6.46598	0.221261
$855$	2.20497	0.0754085
$856$	18.5421	0.633756
$857$	21.5196	0.735097	0.367548	−	0.930004i	$-0.380197\pi$
$857$	21.5196	0.735097	0.367548	+	0.930004i	$0.380197\pi$
$858$	2.70955	0.0925025
$859$	49.7901	1.69882	0.849409	−	0.527735i	$-0.176959\pi$
$859$	49.7901	1.69882	0.849409	+	0.527735i	$0.176959\pi$
$860$	−11.3526	−0.387119
$861$	−3.20843	−0.109343
$862$	−27.7608	−0.945535
$863$	8.68358	0.295592	0.147796	−	0.989018i	$-0.452782\pi$
$863$	8.68358	0.295592	0.147796	+	0.989018i	$0.452782\pi$
$864$	−2.92866	−0.0996351
$865$	−10.2379	−0.348098
$866$	−15.4418	−0.524735
$867$	16.3275	0.554512
$868$	−1.41723	−0.0481038
$869$	1.61988	0.0549506
$870$	−2.15338	−0.0730065
$871$	−29.5750	−1.00211
$872$	18.0731	0.612033
$873$	−9.43444	−0.319307
$874$	−5.27289	−0.178358
$875$	−0.810786	−0.0274096
$876$	−0.510251	−0.0172398
$877$	15.1158	0.510424	0.255212	−	0.966885i	$-0.417855\pi$
$877$	15.1158	0.510424	0.255212	+	0.966885i	$0.417855\pi$
$878$	−23.6585	−0.798435
$879$	−14.3219	−0.483064
$880$	1.00000	0.0337100
$881$	59.1595	1.99314	0.996568	−	0.0827789i	$-0.0263795\pi$
$881$	59.1595	1.99314	0.996568	+	0.0827789i	$0.0263795\pi$
$882$	17.3765	0.585098
$883$	10.5218	0.354086	0.177043	−	0.984203i	$-0.443347\pi$
$883$	10.5218	0.354086	0.177043	+	0.984203i	$0.443347\pi$
$884$	37.1712	1.25020
$885$	5.02795	0.169013
$886$	−12.7659	−0.428878
$887$	4.13230	0.138749	0.0693745	−	0.997591i	$-0.477900\pi$
$887$	4.13230	0.138749	0.0693745	+	0.997591i	$0.477900\pi$
$888$	−2.56090	−0.0859382
$889$	9.65308	0.323754
$890$	−6.39666	−0.214416
$891$	6.72458	0.225282
$892$	−20.5249	−0.687223
$893$	−8.60740	−0.288036
$894$	5.97577	0.199860
$895$	6.35158	0.212310
$896$	−0.810786	−0.0270865
$897$	17.7516	0.592707
$898$	−1.77394	−0.0591972
$899$	−7.37683	−0.246031
$900$	−2.73964	−0.0913215
$901$	−9.66601	−0.322022
$902$	7.75536	0.258225
$903$	4.69660	0.156293
$904$	−14.8079	−0.492502
$905$	−16.1811	−0.537879
$906$	2.82930	0.0939971
$907$	20.2879	0.673648	0.336824	−	0.941568i	$-0.390647\pi$
$907$	20.2879	0.673648	0.336824	+	0.941568i	$0.390647\pi$
$908$	11.6448	0.386447
$909$	−30.6093	−1.01525
$910$	−4.30546	−0.142724
$911$	−2.94228	−0.0974821	−0.0487411	−	0.998811i	$-0.515521\pi$
$911$	−2.94228	−0.0974821	−0.0487411	+	0.998811i	$0.515521\pi$
$912$	−0.410670	−0.0135987
$913$	−9.72069	−0.321708
$914$	21.3320	0.705601
$915$	−4.06923	−0.134525
$916$	19.7273	0.651808
$917$	−15.0908	−0.498342
$918$	−20.5004	−0.676614
$919$	15.5394	0.512598	0.256299	−	0.966598i	$-0.417497\pi$
$919$	15.5394	0.512598	0.256299	+	0.966598i	$0.417497\pi$
$920$	6.55148	0.215996
$921$	3.40884	0.112325
$922$	−35.6159	−1.17295
$923$	4.76250	0.156760
$924$	−0.413705	−0.0136099
$925$	−5.01890	−0.165020
$926$	40.4686	1.32988
$927$	39.0914	1.28393
$928$	−4.22024	−0.138536
$929$	−0.567043	−0.0186041	−0.00930203	−	0.999957i	$-0.502961\pi$
$929$	−0.567043	−0.0186041	−0.00930203	+	0.999957i	$0.502961\pi$
$930$	0.891902	0.0292466
$931$	5.10480	0.167303
$932$	10.6192	0.347845
$933$	−16.8026	−0.550093
$934$	11.1785	0.365773
$935$	6.99993	0.228922
$936$	−14.5481	−0.475520
$937$	−36.6022	−1.19574	−0.597870	−	0.801593i	$-0.703986\pi$
$937$	−36.6022	−1.19574	−0.597870	+	0.801593i	$0.703986\pi$
$938$	4.51563	0.147441
$939$	−10.5418	−0.344020
$940$	10.6946	0.348818
$941$	45.8677	1.49524	0.747622	−	0.664124i	$-0.231195\pi$
$941$	45.8677	1.49524	0.747622	+	0.664124i	$0.231195\pi$
$942$	−2.36711	−0.0771246
$943$	50.8091	1.65457
$944$	9.85387	0.320716
$945$	2.37452	0.0772430
$946$	−11.3526	−0.369103
$947$	−56.2444	−1.82770	−0.913848	−	0.406056i	$-0.866904\pi$
$947$	−56.2444	−1.82770	−0.913848	+	0.406056i	$0.866904\pi$
$948$	0.826546	0.0268450
$949$	−5.31023	−0.172377
$950$	−0.804839	−0.0261124
$951$	−8.88820	−0.288220
$952$	−5.67544	−0.183942
$953$	17.4050	0.563803	0.281902	−	0.959443i	$-0.409035\pi$
$953$	17.4050	0.563803	0.281902	+	0.959443i	$0.409035\pi$
$954$	3.78310	0.122482
$955$	26.2104	0.848147
$956$	−23.0295	−0.744827
$957$	−2.15338	−0.0696089
$958$	−33.0816	−1.06882
$959$	−15.1583	−0.489486
$960$	0.510251	0.0164683
$961$	−27.9446	−0.901439
$962$	−26.6515	−0.859278
$963$	−50.7988	−1.63697
$964$	8.58275	0.276432
$965$	2.41130	0.0776225
$966$	−2.71038	−0.0872049
$967$	9.97862	0.320891	0.160445	−	0.987045i	$-0.448707\pi$
$967$	9.97862	0.320891	0.160445	+	0.987045i	$0.448707\pi$
$968$	1.00000	0.0321412
$969$	−2.87466	−0.0923475
$970$	3.44367	0.110570
$971$	32.9690	1.05802	0.529012	−	0.848614i	$-0.322562\pi$
$971$	32.9690	1.05802	0.529012	+	0.848614i	$0.322562\pi$
$972$	12.2172	0.391867
$973$	6.85965	0.219910
$974$	−0.245965	−0.00788123
$975$	2.70955	0.0867750
$976$	−7.97495	−0.255272
$977$	48.5157	1.55216	0.776078	−	0.630637i	$-0.217206\pi$
$977$	48.5157	1.55216	0.776078	+	0.630637i	$0.217206\pi$
$978$	8.00484	0.255966
$979$	−6.39666	−0.204438
$980$	−6.34263	−0.202608
$981$	−49.5139	−1.58086
$982$	15.0234	0.479415
$983$	11.8261	0.377195	0.188598	−	0.982054i	$-0.439606\pi$
$983$	11.8261	0.377195	0.188598	+	0.982054i	$0.439606\pi$
$984$	3.95718	0.126150
$985$	7.88127	0.251118
$986$	−29.5414	−0.940789
$987$	−4.42438	−0.140830
$988$	−4.27388	−0.135970
$989$	−74.3760	−2.36502
$990$	−2.73964	−0.0870716
$991$	−56.2036	−1.78537	−0.892684	−	0.450684i	$-0.851180\pi$
$991$	−56.2036	−1.78537	−0.892684	+	0.450684i	$0.851180\pi$
$992$	1.74797	0.0554980
$993$	8.98272	0.285058
$994$	−0.727157	−0.0230640
$995$	10.1620	0.322156
$996$	−4.95999	−0.157163
$997$	−38.3707	−1.21521	−0.607606	−	0.794239i	$-0.707870\pi$
$997$	−38.3707	−1.21521	−0.607606	+	0.794239i	$0.707870\pi$
$998$	−41.9420	−1.32765
$999$	14.6987	0.465045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bl.1.10	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bl.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.510251 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.510251 q^{6} -0.810786 q^{7} +1.00000 q^{8} -2.73964 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.510251 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.510251 q^{6} -0.810786 q^{7} +1.00000 q^{8} -2.73964 q^{9} +1.00000 q^{10} +1.00000 q^{11} +0.510251 q^{12} +5.31023 q^{13} -0.810786 q^{14} +0.510251 q^{15} +1.00000 q^{16} +6.99993 q^{17} -2.73964 q^{18} -0.804839 q^{19} +1.00000 q^{20} -0.413705 q^{21} +1.00000 q^{22} +6.55148 q^{23} +0.510251 q^{24} +1.00000 q^{25} +5.31023 q^{26} -2.92866 q^{27} -0.810786 q^{28} -4.22024 q^{29} +0.510251 q^{30} +1.74797 q^{31} +1.00000 q^{32} +0.510251 q^{33} +6.99993 q^{34} -0.810786 q^{35} -2.73964 q^{36} -5.01890 q^{37} -0.804839 q^{38} +2.70955 q^{39} +1.00000 q^{40} +7.75536 q^{41} -0.413705 q^{42} -11.3526 q^{43} +1.00000 q^{44} -2.73964 q^{45} +6.55148 q^{46} +10.6946 q^{47} +0.510251 q^{48} -6.34263 q^{49} +1.00000 q^{50} +3.57172 q^{51} +5.31023 q^{52} -1.38087 q^{53} -2.92866 q^{54} +1.00000 q^{55} -0.810786 q^{56} -0.410670 q^{57} -4.22024 q^{58} +9.85387 q^{59} +0.510251 q^{60} -7.97495 q^{61} +1.74797 q^{62} +2.22126 q^{63} +1.00000 q^{64} +5.31023 q^{65} +0.510251 q^{66} -5.56945 q^{67} +6.99993 q^{68} +3.34290 q^{69} -0.810786 q^{70} +0.896854 q^{71} -2.73964 q^{72} -1.00000 q^{73} -5.01890 q^{74} +0.510251 q^{75} -0.804839 q^{76} -0.810786 q^{77} +2.70955 q^{78} +1.61988 q^{79} +1.00000 q^{80} +6.72458 q^{81} +7.75536 q^{82} -9.72069 q^{83} -0.413705 q^{84} +6.99993 q^{85} -11.3526 q^{86} -2.15338 q^{87} +1.00000 q^{88} -6.39666 q^{89} -2.73964 q^{90} -4.30546 q^{91} +6.55148 q^{92} +0.891902 q^{93} +10.6946 q^{94} -0.804839 q^{95} +0.510251 q^{96} +3.44367 q^{97} -6.34263 q^{98} -2.73964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) \) 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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