LMFDB - Embedded newform 8030.2.a.bf.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:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 4 x^{14} - 23 x^{13} + 99 x^{12} + 191 x^{11} - 922 x^{10} - 702 x^{9} + 4108 x^{8} + 957 x^{7} + \cdots + 8 $ x^15 - 4x^14 - 23x^13 + 99x^12 + 191x^11 - 922x^10 - 702x^9 + 4108x^8 + 957x^7 - 8875x^6 + 479x^5 + 7698x^4 - 1731x^3 - 626x^2 + 46x + 8
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			$0.440451$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.440451 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.440451 q^{6} +3.12770 q^{7} +1.00000 q^{8} -2.80600 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.440451 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.440451 q^{6} +3.12770 q^{7} +1.00000 q^{8} -2.80600 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.440451 q^{12} +5.02637 q^{13} +3.12770 q^{14} +0.440451 q^{15} +1.00000 q^{16} -0.113444 q^{17} -2.80600 q^{18} -6.57951 q^{19} -1.00000 q^{20} -1.37760 q^{21} -1.00000 q^{22} +2.34867 q^{23} -0.440451 q^{24} +1.00000 q^{25} +5.02637 q^{26} +2.55726 q^{27} +3.12770 q^{28} -10.4615 q^{29} +0.440451 q^{30} -1.18438 q^{31} +1.00000 q^{32} +0.440451 q^{33} -0.113444 q^{34} -3.12770 q^{35} -2.80600 q^{36} -9.28017 q^{37} -6.57951 q^{38} -2.21387 q^{39} -1.00000 q^{40} +8.98507 q^{41} -1.37760 q^{42} -12.0082 q^{43} -1.00000 q^{44} +2.80600 q^{45} +2.34867 q^{46} -10.6015 q^{47} -0.440451 q^{48} +2.78251 q^{49} +1.00000 q^{50} +0.0499666 q^{51} +5.02637 q^{52} -4.37406 q^{53} +2.55726 q^{54} +1.00000 q^{55} +3.12770 q^{56} +2.89795 q^{57} -10.4615 q^{58} +4.55112 q^{59} +0.440451 q^{60} -13.4962 q^{61} -1.18438 q^{62} -8.77634 q^{63} +1.00000 q^{64} -5.02637 q^{65} +0.440451 q^{66} +11.8464 q^{67} -0.113444 q^{68} -1.03447 q^{69} -3.12770 q^{70} +6.49746 q^{71} -2.80600 q^{72} +1.00000 q^{73} -9.28017 q^{74} -0.440451 q^{75} -6.57951 q^{76} -3.12770 q^{77} -2.21387 q^{78} -1.20414 q^{79} -1.00000 q^{80} +7.29166 q^{81} +8.98507 q^{82} +0.720781 q^{83} -1.37760 q^{84} +0.113444 q^{85} -12.0082 q^{86} +4.60778 q^{87} -1.00000 q^{88} +17.7332 q^{89} +2.80600 q^{90} +15.7210 q^{91} +2.34867 q^{92} +0.521661 q^{93} -10.6015 q^{94} +6.57951 q^{95} -0.440451 q^{96} +3.30096 q^{97} +2.78251 q^{98} +2.80600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9} - 15 q^{10} - 15 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{14} + 4 q^{15} + 15 q^{16} + 2 q^{17} + 17 q^{18} - 8 q^{19} - 15 q^{20} - 17 q^{21} - 15 q^{22} - 4 q^{23} - 4 q^{24} + 15 q^{25} - 6 q^{26} - 19 q^{27} - 6 q^{28} - 13 q^{29} + 4 q^{30} - 20 q^{31} + 15 q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 17 q^{36} - 15 q^{37} - 8 q^{38} - 11 q^{39} - 15 q^{40} + 2 q^{41} - 17 q^{42} - 26 q^{43} - 15 q^{44} - 17 q^{45} - 4 q^{46} - 14 q^{47} - 4 q^{48} + 11 q^{49} + 15 q^{50} - 39 q^{51} - 6 q^{52} - 21 q^{53} - 19 q^{54} + 15 q^{55} - 6 q^{56} + q^{57} - 13 q^{58} - 14 q^{59} + 4 q^{60} - 45 q^{61} - 20 q^{62} - 17 q^{63} + 15 q^{64} + 6 q^{65} + 4 q^{66} - 10 q^{67} + 2 q^{68} - 23 q^{69} + 6 q^{70} - 9 q^{71} + 17 q^{72} + 15 q^{73} - 15 q^{74} - 4 q^{75} - 8 q^{76} + 6 q^{77} - 11 q^{78} - 26 q^{79} - 15 q^{80} + 15 q^{81} + 2 q^{82} - 30 q^{83} - 17 q^{84} - 2 q^{85} - 26 q^{86} - 14 q^{87} - 15 q^{88} + 10 q^{89} - 17 q^{90} - 17 q^{91} - 4 q^{92} - 8 q^{93} - 14 q^{94} + 8 q^{95} - 4 q^{96} - 27 q^{97} + 11 q^{98} - 17 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9 - 15 * q^10 - 15 * q^11 - 4 * q^12 - 6 * q^13 - 6 * q^14 + 4 * q^15 + 15 * q^16 + 2 * q^17 + 17 * q^18 - 8 * q^19 - 15 * q^20 - 17 * q^21 - 15 * q^22 - 4 * q^23 - 4 * q^24 + 15 * q^25 - 6 * q^26 - 19 * q^27 - 6 * q^28 - 13 * q^29 + 4 * q^30 - 20 * q^31 + 15 * q^32 + 4 * q^33 + 2 * q^34 + 6 * q^35 + 17 * q^36 - 15 * q^37 - 8 * q^38 - 11 * q^39 - 15 * q^40 + 2 * q^41 - 17 * q^42 - 26 * q^43 - 15 * q^44 - 17 * q^45 - 4 * q^46 - 14 * q^47 - 4 * q^48 + 11 * q^49 + 15 * q^50 - 39 * q^51 - 6 * q^52 - 21 * q^53 - 19 * q^54 + 15 * q^55 - 6 * q^56 + q^57 - 13 * q^58 - 14 * q^59 + 4 * q^60 - 45 * q^61 - 20 * q^62 - 17 * q^63 + 15 * q^64 + 6 * q^65 + 4 * q^66 - 10 * q^67 + 2 * q^68 - 23 * q^69 + 6 * q^70 - 9 * q^71 + 17 * q^72 + 15 * q^73 - 15 * q^74 - 4 * q^75 - 8 * q^76 + 6 * q^77 - 11 * q^78 - 26 * q^79 - 15 * q^80 + 15 * q^81 + 2 * q^82 - 30 * q^83 - 17 * q^84 - 2 * q^85 - 26 * q^86 - 14 * q^87 - 15 * q^88 + 10 * q^89 - 17 * q^90 - 17 * q^91 - 4 * q^92 - 8 * q^93 - 14 * q^94 + 8 * q^95 - 4 * q^96 - 27 * q^97 + 11 * q^98 - 17 * 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
$3$	−0.440451	−0.254294	−0.127147	−	0.991884i	$-0.540582\pi$
$3$	−0.440451	−0.254294	−0.127147	+	0.991884i	$0.540582\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.440451	−0.179813
$7$	3.12770	1.18216	0.591080	−	0.806613i	$-0.298702\pi$
$7$	3.12770	1.18216	0.591080	+	0.806613i	$0.298702\pi$
$8$	1.00000	0.353553
$9$	−2.80600	−0.935334
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.440451	−0.127147
$13$	5.02637	1.39406	0.697032	−	0.717040i	$-0.254504\pi$
$13$	5.02637	1.39406	0.697032	+	0.717040i	$0.254504\pi$
$14$	3.12770	0.835913
$15$	0.440451	0.113724
$16$	1.00000	0.250000
$17$	−0.113444	−0.0275143	−0.0137571	−	0.999905i	$-0.504379\pi$
$17$	−0.113444	−0.0275143	−0.0137571	+	0.999905i	$0.504379\pi$
$18$	−2.80600	−0.661381
$19$	−6.57951	−1.50944	−0.754721	−	0.656045i	$-0.772228\pi$
$19$	−6.57951	−1.50944	−0.754721	+	0.656045i	$0.772228\pi$
$20$	−1.00000	−0.223607
$21$	−1.37760	−0.300616
$22$	−1.00000	−0.213201
$23$	2.34867	0.489731	0.244866	−	0.969557i	$-0.421256\pi$
$23$	2.34867	0.489731	0.244866	+	0.969557i	$0.421256\pi$
$24$	−0.440451	−0.0899066
$25$	1.00000	0.200000
$26$	5.02637	0.985752
$27$	2.55726	0.492145
$28$	3.12770	0.591080
$29$	−10.4615	−1.94265	−0.971327	−	0.237747i	$-0.923591\pi$
$29$	−10.4615	−1.94265	−0.971327	+	0.237747i	$0.923591\pi$
$30$	0.440451	0.0804149
$31$	−1.18438	−0.212721	−0.106360	−	0.994328i	$-0.533920\pi$
$31$	−1.18438	−0.212721	−0.106360	+	0.994328i	$0.533920\pi$
$32$	1.00000	0.176777
$33$	0.440451	0.0766726
$34$	−0.113444	−0.0194555
$35$	−3.12770	−0.528678
$36$	−2.80600	−0.467667
$37$	−9.28017	−1.52565	−0.762825	−	0.646605i	$-0.776188\pi$
$37$	−9.28017	−1.52565	−0.762825	+	0.646605i	$0.776188\pi$
$38$	−6.57951	−1.06734
$39$	−2.21387	−0.354503
$40$	−1.00000	−0.158114
$41$	8.98507	1.40323	0.701616	−	0.712555i	$-0.252462\pi$
$41$	8.98507	1.40323	0.701616	+	0.712555i	$0.252462\pi$
$42$	−1.37760	−0.212568
$43$	−12.0082	−1.83123	−0.915614	−	0.402058i	$-0.868295\pi$
$43$	−12.0082	−1.83123	−0.915614	+	0.402058i	$0.868295\pi$
$44$	−1.00000	−0.150756
$45$	2.80600	0.418294
$46$	2.34867	0.346292
$47$	−10.6015	−1.54639	−0.773194	−	0.634170i	$-0.781342\pi$
$47$	−10.6015	−1.54639	−0.773194	+	0.634170i	$0.781342\pi$
$48$	−0.440451	−0.0635736
$49$	2.78251	0.397501
$50$	1.00000	0.141421
$51$	0.0499666	0.00699672
$52$	5.02637	0.697032
$53$	−4.37406	−0.600823	−0.300412	−	0.953810i	$-0.597124\pi$
$53$	−4.37406	−0.600823	−0.300412	+	0.953810i	$0.597124\pi$
$54$	2.55726	0.347999
$55$	1.00000	0.134840
$56$	3.12770	0.417956
$57$	2.89795	0.383843
$58$	−10.4615	−1.37366
$59$	4.55112	0.592506	0.296253	−	0.955110i	$-0.404263\pi$
$59$	4.55112	0.592506	0.296253	+	0.955110i	$0.404263\pi$
$60$	0.440451	0.0568619
$61$	−13.4962	−1.72801	−0.864006	−	0.503482i	$-0.832052\pi$
$61$	−13.4962	−1.72801	−0.864006	+	0.503482i	$0.832052\pi$
$62$	−1.18438	−0.150416
$63$	−8.77634	−1.10571
$64$	1.00000	0.125000
$65$	−5.02637	−0.623444
$66$	0.440451	0.0542157
$67$	11.8464	1.44727	0.723635	−	0.690183i	$-0.242470\pi$
$67$	11.8464	1.44727	0.723635	+	0.690183i	$0.242470\pi$
$68$	−0.113444	−0.0137571
$69$	−1.03447	−0.124536
$70$	−3.12770	−0.373832
$71$	6.49746	0.771107	0.385554	−	0.922685i	$-0.374010\pi$
$71$	6.49746	0.771107	0.385554	+	0.922685i	$0.374010\pi$
$72$	−2.80600	−0.330691
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−9.28017	−1.07880
$75$	−0.440451	−0.0508589
$76$	−6.57951	−0.754721
$77$	−3.12770	−0.356434
$78$	−2.21387	−0.250671
$79$	−1.20414	−0.135476	−0.0677381	−	0.997703i	$-0.521578\pi$
$79$	−1.20414	−0.135476	−0.0677381	+	0.997703i	$0.521578\pi$
$80$	−1.00000	−0.111803
$81$	7.29166	0.810185
$82$	8.98507	0.992235
$83$	0.720781	0.0791160	0.0395580	−	0.999217i	$-0.487405\pi$
$83$	0.720781	0.0791160	0.0395580	+	0.999217i	$0.487405\pi$
$84$	−1.37760	−0.150308
$85$	0.113444	0.0123048
$86$	−12.0082	−1.29487
$87$	4.60778	0.494006
$88$	−1.00000	−0.106600
$89$	17.7332	1.87971	0.939857	−	0.341569i	$-0.110958\pi$
$89$	17.7332	1.87971	0.939857	+	0.341569i	$0.110958\pi$
$90$	2.80600	0.295779
$91$	15.7210	1.64801
$92$	2.34867	0.244866
$93$	0.521661	0.0540937
$94$	−10.6015	−1.09346
$95$	6.57951	0.675043
$96$	−0.440451	−0.0449533
$97$	3.30096	0.335162	0.167581	−	0.985858i	$-0.446404\pi$
$97$	3.30096	0.335162	0.167581	+	0.985858i	$0.446404\pi$
$98$	2.78251	0.281076
$99$	2.80600	0.282014
$100$	1.00000	0.100000
$101$	0.967449	0.0962648	0.0481324	−	0.998841i	$-0.484673\pi$
$101$	0.967449	0.0962648	0.0481324	+	0.998841i	$0.484673\pi$
$102$	0.0499666	0.00494743
$103$	1.53461	0.151209	0.0756046	−	0.997138i	$-0.475911\pi$
$103$	1.53461	0.151209	0.0756046	+	0.997138i	$0.475911\pi$
$104$	5.02637	0.492876
$105$	1.37760	0.134440
$106$	−4.37406	−0.424846
$107$	−6.42791	−0.621409	−0.310705	−	0.950507i	$-0.600565\pi$
$107$	−6.42791	−0.621409	−0.310705	+	0.950507i	$0.600565\pi$
$108$	2.55726	0.246072
$109$	−2.81863	−0.269976	−0.134988	−	0.990847i	$-0.543100\pi$
$109$	−2.81863	−0.269976	−0.134988	+	0.990847i	$0.543100\pi$
$110$	1.00000	0.0953463
$111$	4.08746	0.387964
$112$	3.12770	0.295540
$113$	−9.62097	−0.905065	−0.452532	−	0.891748i	$-0.649479\pi$
$113$	−9.62097	−0.905065	−0.452532	+	0.891748i	$0.649479\pi$
$114$	2.89795	0.271418
$115$	−2.34867	−0.219015
$116$	−10.4615	−0.971327
$117$	−14.1040	−1.30392
$118$	4.55112	0.418965
$119$	−0.354819	−0.0325262
$120$	0.440451	0.0402075
$121$	1.00000	0.0909091
$122$	−13.4962	−1.22189
$123$	−3.95748	−0.356834
$124$	−1.18438	−0.106360
$125$	−1.00000	−0.0894427
$126$	−8.77634	−0.781858
$127$	−2.52463	−0.224025	−0.112012	−	0.993707i	$-0.535730\pi$
$127$	−2.52463	−0.224025	−0.112012	+	0.993707i	$0.535730\pi$
$128$	1.00000	0.0883883
$129$	5.28901	0.465671
$130$	−5.02637	−0.440842
$131$	−4.07263	−0.355827	−0.177914	−	0.984046i	$-0.556935\pi$
$131$	−4.07263	−0.355827	−0.177914	+	0.984046i	$0.556935\pi$
$132$	0.440451	0.0383363
$133$	−20.5787	−1.78440
$134$	11.8464	1.02337
$135$	−2.55726	−0.220094
$136$	−0.113444	−0.00972776
$137$	17.6873	1.51113	0.755563	−	0.655076i	$-0.227364\pi$
$137$	17.6873	1.51113	0.755563	+	0.655076i	$0.227364\pi$
$138$	−1.03447	−0.0880602
$139$	−13.0453	−1.10649	−0.553246	−	0.833018i	$-0.686611\pi$
$139$	−13.0453	−1.10649	−0.553246	+	0.833018i	$0.686611\pi$
$140$	−3.12770	−0.264339
$141$	4.66944	0.393238
$142$	6.49746	0.545255
$143$	−5.02637	−0.420326
$144$	−2.80600	−0.233834
$145$	10.4615	0.868781
$146$	1.00000	0.0827606
$147$	−1.22556	−0.101082
$148$	−9.28017	−0.762825
$149$	−15.4147	−1.26282	−0.631411	−	0.775449i	$-0.717524\pi$
$149$	−15.4147	−1.26282	−0.631411	+	0.775449i	$0.717524\pi$
$150$	−0.440451	−0.0359627
$151$	0.107193	0.00872326	0.00436163	−	0.999990i	$-0.498612\pi$
$151$	0.107193	0.00872326	0.00436163	+	0.999990i	$0.498612\pi$
$152$	−6.57951	−0.533669
$153$	0.318325	0.0257350
$154$	−3.12770	−0.252037
$155$	1.18438	0.0951316
$156$	−2.21387	−0.177251
$157$	−15.4723	−1.23483	−0.617414	−	0.786639i	$-0.711819\pi$
$157$	−15.4723	−1.23483	−0.617414	+	0.786639i	$0.711819\pi$
$158$	−1.20414	−0.0957961
$159$	1.92656	0.152786
$160$	−1.00000	−0.0790569
$161$	7.34593	0.578941
$162$	7.29166	0.572887
$163$	−16.3412	−1.27995	−0.639973	−	0.768398i	$-0.721054\pi$
$163$	−16.3412	−1.27995	−0.639973	+	0.768398i	$0.721054\pi$
$164$	8.98507	0.701616
$165$	−0.440451	−0.0342890
$166$	0.720781	0.0559435
$167$	−18.4321	−1.42632	−0.713158	−	0.701003i	$-0.752736\pi$
$167$	−18.4321	−1.42632	−0.713158	+	0.701003i	$0.752736\pi$
$168$	−1.37760	−0.106284
$169$	12.2644	0.943413
$170$	0.113444	0.00870077
$171$	18.4621	1.41183
$172$	−12.0082	−0.915614
$173$	0.410955	0.0312444	0.0156222	−	0.999878i	$-0.495027\pi$
$173$	0.410955	0.0312444	0.0156222	+	0.999878i	$0.495027\pi$
$174$	4.60778	0.349315
$175$	3.12770	0.236432
$176$	−1.00000	−0.0753778
$177$	−2.00454	−0.150671
$178$	17.7332	1.32916
$179$	9.01707	0.673967	0.336984	−	0.941510i	$-0.390593\pi$
$179$	9.01707	0.673967	0.336984	+	0.941510i	$0.390593\pi$
$180$	2.80600	0.209147
$181$	15.0411	1.11799	0.558997	−	0.829170i	$-0.311186\pi$
$181$	15.0411	1.11799	0.558997	+	0.829170i	$0.311186\pi$
$182$	15.7210	1.16532
$183$	5.94441	0.439424
$184$	2.34867	0.173146
$185$	9.28017	0.682291
$186$	0.521661	0.0382500
$187$	0.113444	0.00829586
$188$	−10.6015	−0.773194
$189$	7.99834	0.581793
$190$	6.57951	0.477328
$191$	−22.2773	−1.61193	−0.805965	−	0.591963i	$-0.798353\pi$
$191$	−22.2773	−1.61193	−0.805965	+	0.591963i	$0.798353\pi$
$192$	−0.440451	−0.0317868
$193$	7.31154	0.526296	0.263148	−	0.964755i	$-0.415239\pi$
$193$	7.31154	0.526296	0.263148	+	0.964755i	$0.415239\pi$
$194$	3.30096	0.236995
$195$	2.21387	0.158538
$196$	2.78251	0.198751
$197$	−20.1536	−1.43589	−0.717943	−	0.696102i	$-0.754916\pi$
$197$	−20.1536	−1.43589	−0.717943	+	0.696102i	$0.754916\pi$
$198$	2.80600	0.199414
$199$	−7.91178	−0.560851	−0.280425	−	0.959876i	$-0.590476\pi$
$199$	−7.91178	−0.560851	−0.280425	+	0.959876i	$0.590476\pi$
$200$	1.00000	0.0707107
$201$	−5.21776	−0.368033
$202$	0.967449	0.0680695
$203$	−32.7205	−2.29653
$204$	0.0499666	0.00349836
$205$	−8.98507	−0.627545
$206$	1.53461	0.106921
$207$	−6.59037	−0.458063
$208$	5.02637	0.348516
$209$	6.57951	0.455114
$210$	1.37760	0.0950633
$211$	−16.7027	−1.14986	−0.574930	−	0.818203i	$-0.694971\pi$
$211$	−16.7027	−1.14986	−0.574930	+	0.818203i	$0.694971\pi$
$212$	−4.37406	−0.300412
$213$	−2.86181	−0.196088
$214$	−6.42791	−0.439403
$215$	12.0082	0.818950
$216$	2.55726	0.173999
$217$	−3.70438	−0.251470
$218$	−2.81863	−0.190902
$219$	−0.440451	−0.0297629
$220$	1.00000	0.0674200
$221$	−0.570212	−0.0383566
$222$	4.08746	0.274332
$223$	0.929563	0.0622482	0.0311241	−	0.999516i	$-0.490091\pi$
$223$	0.929563	0.0622482	0.0311241	+	0.999516i	$0.490091\pi$
$224$	3.12770	0.208978
$225$	−2.80600	−0.187067
$226$	−9.62097	−0.639977
$227$	−5.60246	−0.371849	−0.185924	−	0.982564i	$-0.559528\pi$
$227$	−5.60246	−0.371849	−0.185924	+	0.982564i	$0.559528\pi$
$228$	2.89795	0.191921
$229$	−16.6788	−1.10217	−0.551084	−	0.834449i	$-0.685786\pi$
$229$	−16.6788	−1.10217	−0.551084	+	0.834449i	$0.685786\pi$
$230$	−2.34867	−0.154867
$231$	1.37760	0.0906393
$232$	−10.4615	−0.686832
$233$	−11.7476	−0.769612	−0.384806	−	0.922997i	$-0.625732\pi$
$233$	−11.7476	−0.769612	−0.384806	+	0.922997i	$0.625732\pi$
$234$	−14.1040	−0.922008
$235$	10.6015	0.691565
$236$	4.55112	0.296253
$237$	0.530364	0.0344508
$238$	−0.354819	−0.0229995
$239$	15.1524	0.980128	0.490064	−	0.871687i	$-0.336973\pi$
$239$	15.1524	0.980128	0.490064	+	0.871687i	$0.336973\pi$
$240$	0.440451	0.0284310
$241$	−1.69646	−0.109279	−0.0546394	−	0.998506i	$-0.517401\pi$
$241$	−1.69646	−0.109279	−0.0546394	+	0.998506i	$0.517401\pi$
$242$	1.00000	0.0642824
$243$	−10.8834	−0.698170
$244$	−13.4962	−0.864006
$245$	−2.78251	−0.177768
$246$	−3.95748	−0.252320
$247$	−33.0710	−2.10426
$248$	−1.18438	−0.0752082
$249$	−0.317469	−0.0201188
$250$	−1.00000	−0.0632456
$251$	20.2187	1.27619	0.638097	−	0.769956i	$-0.279722\pi$
$251$	20.2187	1.27619	0.638097	+	0.769956i	$0.279722\pi$
$252$	−8.77634	−0.552857
$253$	−2.34867	−0.147660
$254$	−2.52463	−0.158410
$255$	−0.0499666	−0.00312903
$256$	1.00000	0.0625000
$257$	−8.82639	−0.550575	−0.275287	−	0.961362i	$-0.588773\pi$
$257$	−8.82639	−0.550575	−0.275287	+	0.961362i	$0.588773\pi$
$258$	5.28901	0.329279
$259$	−29.0256	−1.80356
$260$	−5.02637	−0.311722
$261$	29.3550	1.81703
$262$	−4.07263	−0.251608
$263$	18.5123	1.14152	0.570759	−	0.821118i	$-0.306649\pi$
$263$	18.5123	1.14152	0.570759	+	0.821118i	$0.306649\pi$
$264$	0.440451	0.0271079
$265$	4.37406	0.268696
$266$	−20.5787	−1.26176
$267$	−7.81059	−0.478000
$268$	11.8464	0.723635
$269$	10.9398	0.667010	0.333505	−	0.942748i	$-0.391769\pi$
$269$	10.9398	0.667010	0.333505	+	0.942748i	$0.391769\pi$
$270$	−2.55726	−0.155630
$271$	27.0433	1.64277	0.821383	−	0.570377i	$-0.193203\pi$
$271$	27.0433	1.64277	0.821383	+	0.570377i	$0.193203\pi$
$272$	−0.113444	−0.00687857
$273$	−6.92431	−0.419079
$274$	17.6873	1.06853
$275$	−1.00000	−0.0603023
$276$	−1.03447	−0.0622680
$277$	−14.1580	−0.850673	−0.425336	−	0.905035i	$-0.639844\pi$
$277$	−14.1580	−0.850673	−0.425336	+	0.905035i	$0.639844\pi$
$278$	−13.0453	−0.782408
$279$	3.32337	0.198965
$280$	−3.12770	−0.186916
$281$	3.11267	0.185686	0.0928431	−	0.995681i	$-0.470404\pi$
$281$	3.11267	0.185686	0.0928431	+	0.995681i	$0.470404\pi$
$282$	4.66944	0.278061
$283$	20.3019	1.20682	0.603410	−	0.797431i	$-0.293808\pi$
$283$	20.3019	1.20682	0.603410	+	0.797431i	$0.293808\pi$
$284$	6.49746	0.385554
$285$	−2.89795	−0.171660
$286$	−5.02637	−0.297215
$287$	28.1026	1.65884
$288$	−2.80600	−0.165345
$289$	−16.9871	−0.999243
$290$	10.4615	0.614321
$291$	−1.45391	−0.0852298
$292$	1.00000	0.0585206
$293$	11.7568	0.686839	0.343420	−	0.939182i	$-0.388415\pi$
$293$	11.7568	0.686839	0.343420	+	0.939182i	$0.388415\pi$
$294$	−1.22556	−0.0714760
$295$	−4.55112	−0.264977
$296$	−9.28017	−0.539399
$297$	−2.55726	−0.148387
$298$	−15.4147	−0.892950
$299$	11.8053	0.682717
$300$	−0.440451	−0.0254294
$301$	−37.5579	−2.16480
$302$	0.107193	0.00616827
$303$	−0.426114	−0.0244796
$304$	−6.57951	−0.377361
$305$	13.4962	0.772790
$306$	0.318325	0.0181974
$307$	−10.5648	−0.602965	−0.301482	−	0.953472i	$-0.597481\pi$
$307$	−10.5648	−0.602965	−0.301482	+	0.953472i	$0.597481\pi$
$308$	−3.12770	−0.178217
$309$	−0.675918	−0.0384517
$310$	1.18438	0.0672682
$311$	−1.75781	−0.0996762	−0.0498381	−	0.998757i	$-0.515871\pi$
$311$	−1.75781	−0.0996762	−0.0498381	+	0.998757i	$0.515871\pi$
$312$	−2.21387	−0.125336
$313$	12.0016	0.678371	0.339186	−	0.940719i	$-0.389848\pi$
$313$	12.0016	0.678371	0.339186	+	0.940719i	$0.389848\pi$
$314$	−15.4723	−0.873155
$315$	8.77634	0.494491
$316$	−1.20414	−0.0677381
$317$	−11.8931	−0.667981	−0.333991	−	0.942576i	$-0.608395\pi$
$317$	−11.8931	−0.667981	−0.333991	+	0.942576i	$0.608395\pi$
$318$	1.92656	0.108036
$319$	10.4615	0.585732
$320$	−1.00000	−0.0559017
$321$	2.83118	0.158021
$322$	7.34593	0.409373
$323$	0.746407	0.0415312
$324$	7.29166	0.405092
$325$	5.02637	0.278813
$326$	−16.3412	−0.905058
$327$	1.24147	0.0686534
$328$	8.98507	0.496118
$329$	−33.1583	−1.82808
$330$	−0.440451	−0.0242460
$331$	17.6909	0.972380	0.486190	−	0.873853i	$-0.338386\pi$
$331$	17.6909	0.972380	0.486190	+	0.873853i	$0.338386\pi$
$332$	0.720781	0.0395580
$333$	26.0402	1.42699
$334$	−18.4321	−1.00856
$335$	−11.8464	−0.647239
$336$	−1.37760	−0.0751541
$337$	−32.5066	−1.77075	−0.885374	−	0.464880i	$-0.846097\pi$
$337$	−32.5066	−1.77075	−0.885374	+	0.464880i	$0.846097\pi$
$338$	12.2644	0.667094
$339$	4.23756	0.230153
$340$	0.113444	0.00615238
$341$	1.18438	0.0641377
$342$	18.4621	0.998317
$343$	−13.1911	−0.712250
$344$	−12.0082	−0.647437
$345$	1.03447	0.0556942
$346$	0.410955	0.0220931
$347$	25.3720	1.36204	0.681020	−	0.732265i	$-0.261537\pi$
$347$	25.3720	1.36204	0.681020	+	0.732265i	$0.261537\pi$
$348$	4.60778	0.247003
$349$	26.5585	1.42164	0.710821	−	0.703373i	$-0.248323\pi$
$349$	26.5585	1.42164	0.710821	+	0.703373i	$0.248323\pi$
$350$	3.12770	0.167183
$351$	12.8537	0.686081
$352$	−1.00000	−0.0533002
$353$	−7.98969	−0.425248	−0.212624	−	0.977134i	$-0.568201\pi$
$353$	−7.98969	−0.425248	−0.212624	+	0.977134i	$0.568201\pi$
$354$	−2.00454	−0.106540
$355$	−6.49746	−0.344850
$356$	17.7332	0.939857
$357$	0.156280	0.00827124
$358$	9.01707	0.476567
$359$	−22.4490	−1.18481	−0.592407	−	0.805639i	$-0.701822\pi$
$359$	−22.4490	−1.18481	−0.592407	+	0.805639i	$0.701822\pi$
$360$	2.80600	0.147889
$361$	24.2899	1.27842
$362$	15.0411	0.790541
$363$	−0.440451	−0.0231177
$364$	15.7210	0.824003
$365$	−1.00000	−0.0523424
$366$	5.94441	0.310719
$367$	−6.10653	−0.318758	−0.159379	−	0.987217i	$-0.550949\pi$
$367$	−6.10653	−0.318758	−0.159379	+	0.987217i	$0.550949\pi$
$368$	2.34867	0.122433
$369$	−25.2121	−1.31249
$370$	9.28017	0.482453
$371$	−13.6807	−0.710269
$372$	0.521661	0.0270469
$373$	1.22041	0.0631905	0.0315953	−	0.999501i	$-0.489941\pi$
$373$	1.22041	0.0631905	0.0315953	+	0.999501i	$0.489941\pi$
$374$	0.113444	0.00586606
$375$	0.440451	0.0227448
$376$	−10.6015	−0.546730
$377$	−52.5834	−2.70818
$378$	7.99834	0.411390
$379$	−22.2039	−1.14054	−0.570268	−	0.821459i	$-0.693160\pi$
$379$	−22.2039	−1.14054	−0.570268	+	0.821459i	$0.693160\pi$
$380$	6.57951	0.337522
$381$	1.11198	0.0569683
$382$	−22.2773	−1.13981
$383$	1.59647	0.0815757	0.0407878	−	0.999168i	$-0.487013\pi$
$383$	1.59647	0.0815757	0.0407878	+	0.999168i	$0.487013\pi$
$384$	−0.440451	−0.0224767
$385$	3.12770	0.159402
$386$	7.31154	0.372147
$387$	33.6950	1.71281
$388$	3.30096	0.167581
$389$	−19.8663	−1.00726	−0.503631	−	0.863919i	$-0.668003\pi$
$389$	−19.8663	−1.00726	−0.503631	+	0.863919i	$0.668003\pi$
$390$	2.21387	0.112104
$391$	−0.266443	−0.0134746
$392$	2.78251	0.140538
$393$	1.79379	0.0904849
$394$	−20.1536	−1.01532
$395$	1.20414	0.0605868
$396$	2.80600	0.141007
$397$	2.18391	0.109607	0.0548035	−	0.998497i	$-0.482547\pi$
$397$	2.18391	0.109607	0.0548035	+	0.998497i	$0.482547\pi$
$398$	−7.91178	−0.396581
$399$	9.06392	0.453763
$400$	1.00000	0.0500000
$401$	16.9886	0.848369	0.424185	−	0.905576i	$-0.360561\pi$
$401$	16.9886	0.848369	0.424185	+	0.905576i	$0.360561\pi$
$402$	−5.21776	−0.260238
$403$	−5.95313	−0.296546
$404$	0.967449	0.0481324
$405$	−7.29166	−0.362326
$406$	−32.7205	−1.62389
$407$	9.28017	0.460001
$408$	0.0499666	0.00247371
$409$	−32.9763	−1.63057	−0.815287	−	0.579057i	$-0.803421\pi$
$409$	−32.9763	−1.63057	−0.815287	+	0.579057i	$0.803421\pi$
$410$	−8.98507	−0.443741
$411$	−7.79037	−0.384271
$412$	1.53461	0.0756046
$413$	14.2345	0.700436
$414$	−6.59037	−0.323899
$415$	−0.720781	−0.0353818
$416$	5.02637	0.246438
$417$	5.74583	0.281375
$418$	6.57951	0.321814
$419$	−20.4603	−0.999550	−0.499775	−	0.866155i	$-0.666584\pi$
$419$	−20.4603	−0.999550	−0.499775	+	0.866155i	$0.666584\pi$
$420$	1.37760	0.0672199
$421$	−6.02189	−0.293489	−0.146745	−	0.989174i	$-0.546880\pi$
$421$	−6.02189	−0.293489	−0.146745	+	0.989174i	$0.546880\pi$
$422$	−16.7027	−0.813074
$423$	29.7478	1.44639
$424$	−4.37406	−0.212423
$425$	−0.113444	−0.00550285
$426$	−2.86181	−0.138655
$427$	−42.2121	−2.04279
$428$	−6.42791	−0.310705
$429$	2.21387	0.106887
$430$	12.0082	0.579085
$431$	−0.346511	−0.0166908	−0.00834542	−	0.999965i	$-0.502656\pi$
$431$	−0.346511	−0.0166908	−0.00834542	+	0.999965i	$0.502656\pi$
$432$	2.55726	0.123036
$433$	9.46825	0.455015	0.227508	−	0.973776i	$-0.426942\pi$
$433$	9.46825	0.455015	0.227508	+	0.973776i	$0.426942\pi$
$434$	−3.70438	−0.177816
$435$	−4.60778	−0.220926
$436$	−2.81863	−0.134988
$437$	−15.4531	−0.739221
$438$	−0.440451	−0.0210456
$439$	−25.9363	−1.23787	−0.618935	−	0.785442i	$-0.712436\pi$
$439$	−25.9363	−1.23787	−0.618935	+	0.785442i	$0.712436\pi$
$440$	1.00000	0.0476731
$441$	−7.80772	−0.371796
$442$	−0.570212	−0.0271222
$443$	−16.2080	−0.770065	−0.385033	−	0.922903i	$-0.625810\pi$
$443$	−16.2080	−0.770065	−0.385033	+	0.922903i	$0.625810\pi$
$444$	4.08746	0.193982
$445$	−17.7332	−0.840633
$446$	0.929563	0.0440161
$447$	6.78942	0.321128
$448$	3.12770	0.147770
$449$	16.0901	0.759341	0.379670	−	0.925122i	$-0.376037\pi$
$449$	16.0901	0.759341	0.379670	+	0.925122i	$0.376037\pi$
$450$	−2.80600	−0.132276
$451$	−8.98507	−0.423091
$452$	−9.62097	−0.452532
$453$	−0.0472133	−0.00221827
$454$	−5.60246	−0.262937
$455$	−15.7210	−0.737010
$456$	2.89795	0.135709
$457$	3.80781	0.178122	0.0890608	−	0.996026i	$-0.471613\pi$
$457$	3.80781	0.178122	0.0890608	+	0.996026i	$0.471613\pi$
$458$	−16.6788	−0.779351
$459$	−0.290106	−0.0135410
$460$	−2.34867	−0.109507
$461$	−40.0911	−1.86723	−0.933613	−	0.358282i	$-0.883363\pi$
$461$	−40.0911	−1.86723	−0.933613	+	0.358282i	$0.883363\pi$
$462$	1.37760	0.0640917
$463$	6.94308	0.322672	0.161336	−	0.986900i	$-0.448420\pi$
$463$	6.94308	0.322672	0.161336	+	0.986900i	$0.448420\pi$
$464$	−10.4615	−0.485664
$465$	−0.521661	−0.0241914
$466$	−11.7476	−0.544198
$467$	36.7955	1.70269	0.851346	−	0.524604i	$-0.175787\pi$
$467$	36.7955	1.70269	0.851346	+	0.524604i	$0.175787\pi$
$468$	−14.1040	−0.651958
$469$	37.0520	1.71090
$470$	10.6015	0.489011
$471$	6.81480	0.314010
$472$	4.55112	0.209482
$473$	12.0082	0.552136
$474$	0.530364	0.0243604
$475$	−6.57951	−0.301889
$476$	−0.354819	−0.0162631
$477$	12.2736	0.561971
$478$	15.1524	0.693055
$479$	2.93437	0.134075	0.0670375	−	0.997750i	$-0.478645\pi$
$479$	2.93437	0.134075	0.0670375	+	0.997750i	$0.478645\pi$
$480$	0.440451	0.0201037
$481$	−46.6455	−2.12685
$482$	−1.69646	−0.0772718
$483$	−3.23552	−0.147221
$484$	1.00000	0.0454545
$485$	−3.30096	−0.149889
$486$	−10.8834	−0.493681
$487$	−2.43422	−0.110305	−0.0551526	−	0.998478i	$-0.517565\pi$
$487$	−2.43422	−0.110305	−0.0551526	+	0.998478i	$0.517565\pi$
$488$	−13.4962	−0.610944
$489$	7.19751	0.325483
$490$	−2.78251	−0.125701
$491$	27.2109	1.22801	0.614005	−	0.789302i	$-0.289558\pi$
$491$	27.2109	1.22801	0.614005	+	0.789302i	$0.289558\pi$
$492$	−3.95748	−0.178417
$493$	1.18680	0.0534507
$494$	−33.0710	−1.48794
$495$	−2.80600	−0.126120
$496$	−1.18438	−0.0531802
$497$	20.3221	0.911572
$498$	−0.317469	−0.0142261
$499$	−14.8520	−0.664868	−0.332434	−	0.943126i	$-0.607870\pi$
$499$	−14.8520	−0.664868	−0.332434	+	0.943126i	$0.607870\pi$
$500$	−1.00000	−0.0447214
$501$	8.11842	0.362704
$502$	20.2187	0.902406
$503$	3.48322	0.155309	0.0776546	−	0.996980i	$-0.475257\pi$
$503$	3.48322	0.155309	0.0776546	+	0.996980i	$0.475257\pi$
$504$	−8.77634	−0.390929
$505$	−0.967449	−0.0430509
$506$	−2.34867	−0.104411
$507$	−5.40185	−0.239905
$508$	−2.52463	−0.112012
$509$	−0.0607539	−0.00269287	−0.00134644	−	0.999999i	$-0.500429\pi$
$509$	−0.0607539	−0.00269287	−0.00134644	+	0.999999i	$0.500429\pi$
$510$	−0.0499666	−0.00221256
$511$	3.12770	0.138361
$512$	1.00000	0.0441942
$513$	−16.8255	−0.742864
$514$	−8.82639	−0.389315
$515$	−1.53461	−0.0676228
$516$	5.28901	0.232835
$517$	10.6015	0.466253
$518$	−29.0256	−1.27531
$519$	−0.181006	−0.00794526
$520$	−5.02637	−0.220421
$521$	37.4202	1.63941	0.819704	−	0.572788i	$-0.194138\pi$
$521$	37.4202	1.63941	0.819704	+	0.572788i	$0.194138\pi$
$522$	29.3550	1.28484
$523$	26.5157	1.15945	0.579725	−	0.814812i	$-0.303160\pi$
$523$	26.5157	1.15945	0.579725	+	0.814812i	$0.303160\pi$
$524$	−4.07263	−0.177914
$525$	−1.37760	−0.0601233
$526$	18.5123	0.807175
$527$	0.134361	0.00585286
$528$	0.440451	0.0191682
$529$	−17.4838	−0.760163
$530$	4.37406	0.189997
$531$	−12.7705	−0.554191
$532$	−20.5787	−0.892201
$533$	45.1623	1.95620
$534$	−7.81059	−0.337997
$535$	6.42791	0.277903
$536$	11.8464	0.511687
$537$	−3.97158	−0.171386
$538$	10.9398	0.471647
$539$	−2.78251	−0.119851
$540$	−2.55726	−0.110047
$541$	−37.2867	−1.60308	−0.801540	−	0.597942i	$-0.795985\pi$
$541$	−37.2867	−1.60308	−0.801540	+	0.597942i	$0.795985\pi$
$542$	27.0433	1.16161
$543$	−6.62485	−0.284299
$544$	−0.113444	−0.00486388
$545$	2.81863	0.120737
$546$	−6.92431	−0.296333
$547$	33.9029	1.44958	0.724792	−	0.688968i	$-0.241936\pi$
$547$	33.9029	1.44958	0.724792	+	0.688968i	$0.241936\pi$
$548$	17.6873	0.755563
$549$	37.8704	1.61627
$550$	−1.00000	−0.0426401
$551$	68.8316	2.93233
$552$	−1.03447	−0.0440301
$553$	−3.76618	−0.160154
$554$	−14.1580	−0.601517
$555$	−4.08746	−0.173503
$556$	−13.0453	−0.553246
$557$	12.1127	0.513233	0.256616	−	0.966513i	$-0.417392\pi$
$557$	12.1127	0.513233	0.256616	+	0.966513i	$0.417392\pi$
$558$	3.32337	0.140690
$559$	−60.3575	−2.55285
$560$	−3.12770	−0.132169
$561$	−0.0499666	−0.00210959
$562$	3.11267	0.131300
$563$	−30.2314	−1.27410	−0.637052	−	0.770821i	$-0.719846\pi$
$563$	−30.2314	−1.27410	−0.637052	+	0.770821i	$0.719846\pi$
$564$	4.66944	0.196619
$565$	9.62097	0.404757
$566$	20.3019	0.853351
$567$	22.8061	0.957768
$568$	6.49746	0.272628
$569$	24.1987	1.01446	0.507231	−	0.861810i	$-0.330669\pi$
$569$	24.1987	1.01446	0.507231	+	0.861810i	$0.330669\pi$
$570$	−2.89795	−0.121382
$571$	8.57190	0.358723	0.179361	−	0.983783i	$-0.442597\pi$
$571$	8.57190	0.358723	0.179361	+	0.983783i	$0.442597\pi$
$572$	−5.02637	−0.210163
$573$	9.81207	0.409905
$574$	28.1026	1.17298
$575$	2.34867	0.0979463
$576$	−2.80600	−0.116917
$577$	−1.11939	−0.0466007	−0.0233003	−	0.999729i	$-0.507417\pi$
$577$	−1.11939	−0.0466007	−0.0233003	+	0.999729i	$0.507417\pi$
$578$	−16.9871	−0.706571
$579$	−3.22037	−0.133834
$580$	10.4615	0.434391
$581$	2.25439	0.0935277
$582$	−1.45391	−0.0602666
$583$	4.37406	0.181155
$584$	1.00000	0.0413803
$585$	14.1040	0.583129
$586$	11.7568	0.485669
$587$	−9.41117	−0.388441	−0.194220	−	0.980958i	$-0.562218\pi$
$587$	−9.41117	−0.388441	−0.194220	+	0.980958i	$0.562218\pi$
$588$	−1.22556	−0.0505411
$589$	7.79264	0.321090
$590$	−4.55112	−0.187367
$591$	8.87667	0.365138
$592$	−9.28017	−0.381413
$593$	13.7656	0.565284	0.282642	−	0.959225i	$-0.408789\pi$
$593$	13.7656	0.565284	0.282642	+	0.959225i	$0.408789\pi$
$594$	−2.55726	−0.104926
$595$	0.354819	0.0145462
$596$	−15.4147	−0.631411
$597$	3.48475	0.142621
$598$	11.8053	0.482754
$599$	39.9525	1.63242	0.816208	−	0.577758i	$-0.196072\pi$
$599$	39.9525	1.63242	0.816208	+	0.577758i	$0.196072\pi$
$600$	−0.440451	−0.0179813
$601$	−4.48364	−0.182892	−0.0914458	−	0.995810i	$-0.529149\pi$
$601$	−4.48364	−0.182892	−0.0914458	+	0.995810i	$0.529149\pi$
$602$	−37.5579	−1.53075
$603$	−33.2411	−1.35368
$604$	0.107193	0.00436163
$605$	−1.00000	−0.0406558
$606$	−0.426114	−0.0173097
$607$	−12.9173	−0.524296	−0.262148	−	0.965028i	$-0.584431\pi$
$607$	−12.9173	−0.524296	−0.262148	+	0.965028i	$0.584431\pi$
$608$	−6.57951	−0.266834
$609$	14.4118	0.583994
$610$	13.4962	0.546445
$611$	−53.2870	−2.15576
$612$	0.318325	0.0128675
$613$	−26.7765	−1.08149	−0.540746	−	0.841186i	$-0.681858\pi$
$613$	−26.7765	−1.08149	−0.540746	+	0.841186i	$0.681858\pi$
$614$	−10.5648	−0.426360
$615$	3.95748	0.159581
$616$	−3.12770	−0.126019
$617$	12.1055	0.487348	0.243674	−	0.969857i	$-0.421647\pi$
$617$	12.1055	0.487348	0.243674	+	0.969857i	$0.421647\pi$
$618$	−0.675918	−0.0271894
$619$	15.8955	0.638893	0.319446	−	0.947604i	$-0.396503\pi$
$619$	15.8955	0.638893	0.319446	+	0.947604i	$0.396503\pi$
$620$	1.18438	0.0475658
$621$	6.00615	0.241019
$622$	−1.75781	−0.0704817
$623$	55.4641	2.22212
$624$	−2.21387	−0.0886256
$625$	1.00000	0.0400000
$626$	12.0016	0.479681
$627$	−2.89795	−0.115733
$628$	−15.4723	−0.617414
$629$	1.05278	0.0419771
$630$	8.77634	0.349658
$631$	8.28418	0.329788	0.164894	−	0.986311i	$-0.447272\pi$
$631$	8.28418	0.329788	0.164894	+	0.986311i	$0.447272\pi$
$632$	−1.20414	−0.0478980
$633$	7.35671	0.292403
$634$	−11.8931	−0.472334
$635$	2.52463	0.100187
$636$	1.92656	0.0763930
$637$	13.9859	0.554142
$638$	10.4615	0.414175
$639$	−18.2319	−0.721243
$640$	−1.00000	−0.0395285
$641$	−38.5327	−1.52195	−0.760975	−	0.648781i	$-0.775279\pi$
$641$	−38.5327	−1.52195	−0.760975	+	0.648781i	$0.775279\pi$
$642$	2.83118	0.111738
$643$	−37.2234	−1.46795	−0.733973	−	0.679178i	$-0.762336\pi$
$643$	−37.2234	−1.46795	−0.733973	+	0.679178i	$0.762336\pi$
$644$	7.34593	0.289470
$645$	−5.28901	−0.208254
$646$	0.746407	0.0293670
$647$	−10.1892	−0.400577	−0.200289	−	0.979737i	$-0.564188\pi$
$647$	−10.1892	−0.400577	−0.200289	+	0.979737i	$0.564188\pi$
$648$	7.29166	0.286444
$649$	−4.55112	−0.178647
$650$	5.02637	0.197150
$651$	1.63160	0.0639474
$652$	−16.3412	−0.639973
$653$	21.8523	0.855148	0.427574	−	0.903980i	$-0.359368\pi$
$653$	21.8523	0.855148	0.427574	+	0.903980i	$0.359368\pi$
$654$	1.24147	0.0485453
$655$	4.07263	0.159131
$656$	8.98507	0.350808
$657$	−2.80600	−0.109473
$658$	−33.1583	−1.29264
$659$	−3.35485	−0.130686	−0.0653432	−	0.997863i	$-0.520814\pi$
$659$	−3.35485	−0.130686	−0.0653432	+	0.997863i	$0.520814\pi$
$660$	−0.440451	−0.0171445
$661$	−23.7728	−0.924656	−0.462328	−	0.886709i	$-0.652986\pi$
$661$	−23.7728	−0.924656	−0.462328	+	0.886709i	$0.652986\pi$
$662$	17.6909	0.687576
$663$	0.251150	0.00975388
$664$	0.720781	0.0279717
$665$	20.5787	0.798009
$666$	26.0402	1.00904
$667$	−24.5706	−0.951379
$668$	−18.4321	−0.713158
$669$	−0.409427	−0.0158294
$670$	−11.8464	−0.457667
$671$	13.4962	0.521015
$672$	−1.37760	−0.0531420
$673$	−0.947538	−0.0365249	−0.0182625	−	0.999833i	$-0.505813\pi$
$673$	−0.947538	−0.0365249	−0.0182625	+	0.999833i	$0.505813\pi$
$674$	−32.5066	−1.25211
$675$	2.55726	0.0984289
$676$	12.2644	0.471707
$677$	51.3238	1.97253	0.986266	−	0.165163i	$-0.0528149\pi$
$677$	51.3238	1.97253	0.986266	+	0.165163i	$0.0528149\pi$
$678$	4.23756	0.162743
$679$	10.3244	0.396215
$680$	0.113444	0.00435039
$681$	2.46761	0.0945590
$682$	1.18438	0.0453522
$683$	7.51594	0.287589	0.143795	−	0.989608i	$-0.454070\pi$
$683$	7.51594	0.287589	0.143795	+	0.989608i	$0.454070\pi$
$684$	18.4621	0.705917
$685$	−17.6873	−0.675796
$686$	−13.1911	−0.503637
$687$	7.34621	0.280275
$688$	−12.0082	−0.457807
$689$	−21.9856	−0.837586
$690$	1.03447	0.0393817
$691$	37.7617	1.43652	0.718261	−	0.695774i	$-0.244938\pi$
$691$	37.7617	1.43652	0.718261	+	0.695774i	$0.244938\pi$
$692$	0.410955	0.0156222
$693$	8.77634	0.333385
$694$	25.3720	0.963108
$695$	13.0453	0.494838
$696$	4.60778	0.174657
$697$	−1.01930	−0.0386089
$698$	26.5585	1.00525
$699$	5.17425	0.195708
$700$	3.12770	0.118216
$701$	1.36912	0.0517109	0.0258554	−	0.999666i	$-0.491769\pi$
$701$	1.36912	0.0517109	0.0258554	+	0.999666i	$0.491769\pi$
$702$	12.8537	0.485132
$703$	61.0589	2.30288
$704$	−1.00000	−0.0376889
$705$	−4.66944	−0.175861
$706$	−7.98969	−0.300696
$707$	3.02589	0.113800
$708$	−2.00454	−0.0753354
$709$	41.8284	1.57090	0.785449	−	0.618927i	$-0.212432\pi$
$709$	41.8284	1.57090	0.785449	+	0.618927i	$0.212432\pi$
$710$	−6.49746	−0.243846
$711$	3.37882	0.126715
$712$	17.7332	0.664579
$713$	−2.78172	−0.104176
$714$	0.156280	0.00584865
$715$	5.02637	0.187975
$716$	9.01707	0.336984
$717$	−6.67389	−0.249241
$718$	−22.4490	−0.837791
$719$	−31.9264	−1.19065	−0.595327	−	0.803483i	$-0.702978\pi$
$719$	−31.9264	−1.19065	−0.595327	+	0.803483i	$0.702978\pi$
$720$	2.80600	0.104574
$721$	4.79979	0.178753
$722$	24.2899	0.903978
$723$	0.747209	0.0277890
$724$	15.0411	0.558997
$725$	−10.4615	−0.388531
$726$	−0.440451	−0.0163467
$727$	36.1548	1.34091	0.670453	−	0.741952i	$-0.266100\pi$
$727$	36.1548	1.34091	0.670453	+	0.741952i	$0.266100\pi$
$728$	15.7210	0.582658
$729$	−17.0814	−0.632644
$730$	−1.00000	−0.0370117
$731$	1.36226	0.0503849
$732$	5.94441	0.219712
$733$	−19.9762	−0.737839	−0.368920	−	0.929461i	$-0.620272\pi$
$733$	−19.9762	−0.737839	−0.368920	+	0.929461i	$0.620272\pi$
$734$	−6.10653	−0.225396
$735$	1.22556	0.0452054
$736$	2.34867	0.0865731
$737$	−11.8464	−0.436368
$738$	−25.2121	−0.928072
$739$	21.9692	0.808151	0.404075	−	0.914726i	$-0.367593\pi$
$739$	21.9692	0.808151	0.404075	+	0.914726i	$0.367593\pi$
$740$	9.28017	0.341146
$741$	14.5662	0.535101
$742$	−13.6807	−0.502236
$743$	−25.9328	−0.951381	−0.475691	−	0.879613i	$-0.657802\pi$
$743$	−25.9328	−0.951381	−0.475691	+	0.879613i	$0.657802\pi$
$744$	0.521661	0.0191250
$745$	15.4147	0.564751
$746$	1.22041	0.0446824
$747$	−2.02251	−0.0739999
$748$	0.113444	0.00414793
$749$	−20.1046	−0.734605
$750$	0.440451	0.0160830
$751$	−17.1904	−0.627285	−0.313642	−	0.949541i	$-0.601549\pi$
$751$	−17.1904	−0.627285	−0.313642	+	0.949541i	$0.601549\pi$
$752$	−10.6015	−0.386597
$753$	−8.90535	−0.324529
$754$	−52.5834	−1.91497
$755$	−0.107193	−0.00390116
$756$	7.99834	0.290897
$757$	2.95340	0.107343	0.0536715	−	0.998559i	$-0.482908\pi$
$757$	2.95340	0.107343	0.0536715	+	0.998559i	$0.482908\pi$
$758$	−22.2039	−0.806480
$759$	1.03447	0.0375490
$760$	6.57951	0.238664
$761$	33.3787	1.20998	0.604988	−	0.796234i	$-0.293178\pi$
$761$	33.3787	1.20998	0.604988	+	0.796234i	$0.293178\pi$
$762$	1.11198	0.0402826
$763$	−8.81584	−0.319155
$764$	−22.2773	−0.805965
$765$	−0.318325	−0.0115091
$766$	1.59647	0.0576827
$767$	22.8756	0.825990
$768$	−0.440451	−0.0158934
$769$	−5.41342	−0.195213	−0.0976065	−	0.995225i	$-0.531119\pi$
$769$	−5.41342	−0.195213	−0.0976065	+	0.995225i	$0.531119\pi$
$770$	3.12770	0.112714
$771$	3.88759	0.140008
$772$	7.31154	0.263148
$773$	4.83400	0.173867	0.0869335	−	0.996214i	$-0.472293\pi$
$773$	4.83400	0.173867	0.0869335	+	0.996214i	$0.472293\pi$
$774$	33.6950	1.21114
$775$	−1.18438	−0.0425442
$776$	3.30096	0.118498
$777$	12.7843	0.458636
$778$	−19.8663	−0.712241
$779$	−59.1174	−2.11810
$780$	2.21387	0.0792692
$781$	−6.49746	−0.232498
$782$	−0.266443	−0.00952798
$783$	−26.7528	−0.956067
$784$	2.78251	0.0993753
$785$	15.4723	0.552231
$786$	1.79379	0.0639825
$787$	−48.6394	−1.73381	−0.866904	−	0.498476i	$-0.833893\pi$
$787$	−48.6394	−1.73381	−0.866904	+	0.498476i	$0.833893\pi$
$788$	−20.1536	−0.717943
$789$	−8.15376	−0.290281
$790$	1.20414	0.0428413
$791$	−30.0915	−1.06993
$792$	2.80600	0.0997070
$793$	−67.8369	−2.40896
$794$	2.18391	0.0775039
$795$	−1.92656	−0.0683279
$796$	−7.91178	−0.280425
$797$	−26.1669	−0.926880	−0.463440	−	0.886128i	$-0.653385\pi$
$797$	−26.1669	−0.926880	−0.463440	+	0.886128i	$0.653385\pi$
$798$	9.06392	0.320859
$799$	1.20268	0.0425477
$800$	1.00000	0.0353553
$801$	−49.7594	−1.75816
$802$	16.9886	0.599888
$803$	−1.00000	−0.0352892
$804$	−5.21776	−0.184016
$805$	−7.34593	−0.258910
$806$	−5.95313	−0.209690
$807$	−4.81844	−0.169617
$808$	0.967449	0.0340347
$809$	40.0953	1.40968	0.704839	−	0.709368i	$-0.251019\pi$
$809$	40.0953	1.40968	0.704839	+	0.709368i	$0.251019\pi$
$810$	−7.29166	−0.256203
$811$	−14.3157	−0.502692	−0.251346	−	0.967897i	$-0.580873\pi$
$811$	−14.3157	−0.502692	−0.251346	+	0.967897i	$0.580873\pi$
$812$	−32.7205	−1.14826
$813$	−11.9113	−0.417746
$814$	9.28017	0.325270
$815$	16.3412	0.572409
$816$	0.0499666	0.00174918
$817$	79.0078	2.76413
$818$	−32.9763	−1.15299
$819$	−44.1131	−1.54144
$820$	−8.98507	−0.313772
$821$	34.2320	1.19471	0.597353	−	0.801979i	$-0.296219\pi$
$821$	34.2320	1.19471	0.597353	+	0.801979i	$0.296219\pi$
$822$	−7.79037	−0.271720
$823$	−33.7551	−1.17663	−0.588314	−	0.808632i	$-0.700208\pi$
$823$	−33.7551	−1.17663	−0.588314	+	0.808632i	$0.700208\pi$
$824$	1.53461	0.0534605
$825$	0.440451	0.0153345
$826$	14.2345	0.495283
$827$	22.0388	0.766366	0.383183	−	0.923673i	$-0.374828\pi$
$827$	22.0388	0.766366	0.383183	+	0.923673i	$0.374828\pi$
$828$	−6.59037	−0.229031
$829$	−27.8751	−0.968142	−0.484071	−	0.875029i	$-0.660842\pi$
$829$	−27.8751	−0.968142	−0.484071	+	0.875029i	$0.660842\pi$
$830$	−0.720781	−0.0250187
$831$	6.23591	0.216321
$832$	5.02637	0.174258
$833$	−0.315659	−0.0109369
$834$	5.74583	0.198962
$835$	18.4321	0.637868
$836$	6.57951	0.227557
$837$	−3.02876	−0.104689
$838$	−20.4603	−0.706789
$839$	−30.7489	−1.06157	−0.530785	−	0.847507i	$-0.678103\pi$
$839$	−30.7489	−1.06157	−0.530785	+	0.847507i	$0.678103\pi$
$840$	1.37760	0.0475316
$841$	80.4432	2.77390
$842$	−6.02189	−0.207528
$843$	−1.37098	−0.0472190
$844$	−16.7027	−0.574930
$845$	−12.2644	−0.421907
$846$	29.7478	1.02275
$847$	3.12770	0.107469
$848$	−4.37406	−0.150206
$849$	−8.94197	−0.306888
$850$	−0.113444	−0.00389110
$851$	−21.7960	−0.747159
$852$	−2.86181	−0.0980441
$853$	46.1831	1.58128	0.790639	−	0.612282i	$-0.209748\pi$
$853$	46.1831	1.58128	0.790639	+	0.612282i	$0.209748\pi$
$854$	−42.2121	−1.44447
$855$	−18.4621	−0.631391
$856$	−6.42791	−0.219701
$857$	−18.0742	−0.617401	−0.308701	−	0.951159i	$-0.599894\pi$
$857$	−18.0742	−0.617401	−0.308701	+	0.951159i	$0.599894\pi$
$858$	2.21387	0.0755802
$859$	−38.2978	−1.30670	−0.653352	−	0.757055i	$-0.726638\pi$
$859$	−38.2978	−1.30670	−0.653352	+	0.757055i	$0.726638\pi$
$860$	12.0082	0.409475
$861$	−12.3778	−0.421835
$862$	−0.346511	−0.0118022
$863$	−31.0798	−1.05797	−0.528984	−	0.848632i	$-0.677427\pi$
$863$	−31.0798	−1.05797	−0.528984	+	0.848632i	$0.677427\pi$
$864$	2.55726	0.0869997
$865$	−0.410955	−0.0139729
$866$	9.46825	0.321744
$867$	7.48199	0.254102
$868$	−3.70438	−0.125735
$869$	1.20414	0.0408476
$870$	−4.60778	−0.156218
$871$	59.5444	2.01759
$872$	−2.81863	−0.0954510
$873$	−9.26251	−0.313488
$874$	−15.4531	−0.522709
$875$	−3.12770	−0.105736
$876$	−0.440451	−0.0148815
$877$	−58.6254	−1.97964	−0.989820	−	0.142327i	$-0.954542\pi$
$877$	−58.6254	−1.97964	−0.989820	+	0.142327i	$0.954542\pi$
$878$	−25.9363	−0.875306
$879$	−5.17829	−0.174659
$880$	1.00000	0.0337100
$881$	44.8988	1.51268	0.756340	−	0.654179i	$-0.226986\pi$
$881$	44.8988	1.51268	0.756340	+	0.654179i	$0.226986\pi$
$882$	−7.80772	−0.262900
$883$	45.8879	1.54425	0.772125	−	0.635471i	$-0.219194\pi$
$883$	45.8879	1.54425	0.772125	+	0.635471i	$0.219194\pi$
$884$	−0.570212	−0.0191783
$885$	2.00454	0.0673820
$886$	−16.2080	−0.544519
$887$	−0.580319	−0.0194852	−0.00974261	−	0.999953i	$-0.503101\pi$
$887$	−0.580319	−0.0194852	−0.00974261	+	0.999953i	$0.503101\pi$
$888$	4.08746	0.137166
$889$	−7.89629	−0.264833
$890$	−17.7332	−0.594417
$891$	−7.29166	−0.244280
$892$	0.929563	0.0311241
$893$	69.7526	2.33418
$894$	6.78942	0.227072
$895$	−9.01707	−0.301407
$896$	3.12770	0.104489
$897$	−5.19964	−0.173611
$898$	16.0901	0.536935
$899$	12.3904	0.413243
$900$	−2.80600	−0.0935334
$901$	0.496212	0.0165312
$902$	−8.98507	−0.299170
$903$	16.5424	0.550497
$904$	−9.62097	−0.319989
$905$	−15.0411	−0.499982
$906$	−0.0472133	−0.00156856
$907$	32.8519	1.09083	0.545415	−	0.838166i	$-0.316372\pi$
$907$	32.8519	1.09083	0.545415	+	0.838166i	$0.316372\pi$
$908$	−5.60246	−0.185924
$909$	−2.71466	−0.0900397
$910$	−15.7210	−0.521145
$911$	−21.8824	−0.724997	−0.362498	−	0.931984i	$-0.618076\pi$
$911$	−21.8824	−0.724997	−0.362498	+	0.931984i	$0.618076\pi$
$912$	2.89795	0.0959607
$913$	−0.720781	−0.0238544
$914$	3.80781	0.125951
$915$	−5.94441	−0.196516
$916$	−16.6788	−0.551084
$917$	−12.7380	−0.420645
$918$	−0.290106	−0.00957493
$919$	60.0196	1.97987	0.989933	−	0.141539i	$-0.0452050\pi$
$919$	60.0196	1.97987	0.989933	+	0.141539i	$0.0452050\pi$
$920$	−2.34867	−0.0774333
$921$	4.65327	0.153331
$922$	−40.0911	−1.32033
$923$	32.6586	1.07497
$924$	1.37760	0.0453196
$925$	−9.28017	−0.305130
$926$	6.94308	0.228164
$927$	−4.30611	−0.141431
$928$	−10.4615	−0.343416
$929$	21.0806	0.691633	0.345816	−	0.938302i	$-0.387602\pi$
$929$	21.0806	0.691633	0.345816	+	0.938302i	$0.387602\pi$
$930$	−0.521661	−0.0171059
$931$	−18.3075	−0.600005
$932$	−11.7476	−0.384806
$933$	0.774228	0.0253471
$934$	36.7955	1.20399
$935$	−0.113444	−0.00371002
$936$	−14.1040	−0.461004
$937$	−24.5005	−0.800398	−0.400199	−	0.916428i	$-0.631059\pi$
$937$	−24.5005	−0.800398	−0.400199	+	0.916428i	$0.631059\pi$
$938$	37.0520	1.20979
$939$	−5.28612	−0.172506
$940$	10.6015	0.345783
$941$	3.35933	0.109511	0.0547554	−	0.998500i	$-0.482562\pi$
$941$	3.35933	0.109511	0.0547554	+	0.998500i	$0.482562\pi$
$942$	6.81480	0.222038
$943$	21.1030	0.687207
$944$	4.55112	0.148126
$945$	−7.99834	−0.260186
$946$	12.0082	0.390419
$947$	−35.1926	−1.14361	−0.571804	−	0.820391i	$-0.693756\pi$
$947$	−35.1926	−1.14361	−0.571804	+	0.820391i	$0.693756\pi$
$948$	0.530364	0.0172254
$949$	5.02637	0.163163
$950$	−6.57951	−0.213467
$951$	5.23831	0.169864
$952$	−0.354819	−0.0114998
$953$	−6.05657	−0.196192	−0.0980958	−	0.995177i	$-0.531275\pi$
$953$	−6.05657	−0.196192	−0.0980958	+	0.995177i	$0.531275\pi$
$954$	12.2736	0.397373
$955$	22.2773	0.720877
$956$	15.1524	0.490064
$957$	−4.60778	−0.148948
$958$	2.93437	0.0948053
$959$	55.3205	1.78639
$960$	0.440451	0.0142155
$961$	−29.5972	−0.954750
$962$	−46.6455	−1.50391
$963$	18.0367	0.581225
$964$	−1.69646	−0.0546394
$965$	−7.31154	−0.235367
$966$	−3.23552	−0.104101
$967$	−36.0381	−1.15891	−0.579453	−	0.815005i	$-0.696734\pi$
$967$	−36.0381	−1.15891	−0.579453	+	0.815005i	$0.696734\pi$
$968$	1.00000	0.0321412
$969$	−0.328756	−0.0105612
$970$	−3.30096	−0.105987
$971$	25.7937	0.827759	0.413879	−	0.910332i	$-0.364174\pi$
$971$	25.7937	0.827759	0.413879	+	0.910332i	$0.364174\pi$
$972$	−10.8834	−0.349085
$973$	−40.8019	−1.30805
$974$	−2.43422	−0.0779975
$975$	−2.21387	−0.0709005
$976$	−13.4962	−0.432003
$977$	−16.8142	−0.537932	−0.268966	−	0.963150i	$-0.586682\pi$
$977$	−16.8142	−0.537932	−0.268966	+	0.963150i	$0.586682\pi$
$978$	7.19751	0.230151
$979$	−17.7332	−0.566755
$980$	−2.78251	−0.0888839
$981$	7.90909	0.252518
$982$	27.2109	0.868334
$983$	29.4877	0.940512	0.470256	−	0.882530i	$-0.344162\pi$
$983$	29.4877	0.940512	0.470256	+	0.882530i	$0.344162\pi$
$984$	−3.95748	−0.126160
$985$	20.1536	0.642147
$986$	1.18680	0.0377953
$987$	14.6046	0.464869
$988$	−33.0710	−1.05213
$989$	−28.2032	−0.896810
$990$	−2.80600	−0.0891806
$991$	−51.2420	−1.62776	−0.813879	−	0.581035i	$-0.802648\pi$
$991$	−51.2420	−1.62776	−0.813879	+	0.581035i	$0.802648\pi$
$992$	−1.18438	−0.0376041
$993$	−7.79197	−0.247271
$994$	20.3221	0.644579
$995$	7.91178	0.250820
$996$	−0.317469	−0.0100594
$997$	50.9696	1.61422	0.807111	−	0.590399i	$-0.201030\pi$
$997$	50.9696	1.61422	0.807111	+	0.590399i	$0.201030\pi$
$998$	−14.8520	−0.470133
$999$	−23.7318	−0.750840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bf.1.7	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bf.1.7	✓	15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.440451 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.440451 q^{6} +3.12770 q^{7} +1.00000 q^{8} -2.80600 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.440451 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.440451 q^{6} +3.12770 q^{7} +1.00000 q^{8} -2.80600 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.440451 q^{12} +5.02637 q^{13} +3.12770 q^{14} +0.440451 q^{15} +1.00000 q^{16} -0.113444 q^{17} -2.80600 q^{18} -6.57951 q^{19} -1.00000 q^{20} -1.37760 q^{21} -1.00000 q^{22} +2.34867 q^{23} -0.440451 q^{24} +1.00000 q^{25} +5.02637 q^{26} +2.55726 q^{27} +3.12770 q^{28} -10.4615 q^{29} +0.440451 q^{30} -1.18438 q^{31} +1.00000 q^{32} +0.440451 q^{33} -0.113444 q^{34} -3.12770 q^{35} -2.80600 q^{36} -9.28017 q^{37} -6.57951 q^{38} -2.21387 q^{39} -1.00000 q^{40} +8.98507 q^{41} -1.37760 q^{42} -12.0082 q^{43} -1.00000 q^{44} +2.80600 q^{45} +2.34867 q^{46} -10.6015 q^{47} -0.440451 q^{48} +2.78251 q^{49} +1.00000 q^{50} +0.0499666 q^{51} +5.02637 q^{52} -4.37406 q^{53} +2.55726 q^{54} +1.00000 q^{55} +3.12770 q^{56} +2.89795 q^{57} -10.4615 q^{58} +4.55112 q^{59} +0.440451 q^{60} -13.4962 q^{61} -1.18438 q^{62} -8.77634 q^{63} +1.00000 q^{64} -5.02637 q^{65} +0.440451 q^{66} +11.8464 q^{67} -0.113444 q^{68} -1.03447 q^{69} -3.12770 q^{70} +6.49746 q^{71} -2.80600 q^{72} +1.00000 q^{73} -9.28017 q^{74} -0.440451 q^{75} -6.57951 q^{76} -3.12770 q^{77} -2.21387 q^{78} -1.20414 q^{79} -1.00000 q^{80} +7.29166 q^{81} +8.98507 q^{82} +0.720781 q^{83} -1.37760 q^{84} +0.113444 q^{85} -12.0082 q^{86} +4.60778 q^{87} -1.00000 q^{88} +17.7332 q^{89} +2.80600 q^{90} +15.7210 q^{91} +2.34867 q^{92} +0.521661 q^{93} -10.6015 q^{94} +6.57951 q^{95} -0.440451 q^{96} +3.30096 q^{97} +2.78251 q^{98} +2.80600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9} - 15 q^{10} - 15 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{14} + 4 q^{15} + 15 q^{16} + 2 q^{17} + 17 q^{18} - 8 q^{19} - 15 q^{20} - 17 q^{21} - 15 q^{22} - 4 q^{23} - 4 q^{24} + 15 q^{25} - 6 q^{26} - 19 q^{27} - 6 q^{28} - 13 q^{29} + 4 q^{30} - 20 q^{31} + 15 q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 17 q^{36} - 15 q^{37} - 8 q^{38} - 11 q^{39} - 15 q^{40} + 2 q^{41} - 17 q^{42} - 26 q^{43} - 15 q^{44} - 17 q^{45} - 4 q^{46} - 14 q^{47} - 4 q^{48} + 11 q^{49} + 15 q^{50} - 39 q^{51} - 6 q^{52} - 21 q^{53} - 19 q^{54} + 15 q^{55} - 6 q^{56} + q^{57} - 13 q^{58} - 14 q^{59} + 4 q^{60} - 45 q^{61} - 20 q^{62} - 17 q^{63} + 15 q^{64} + 6 q^{65} + 4 q^{66} - 10 q^{67} + 2 q^{68} - 23 q^{69} + 6 q^{70} - 9 q^{71} + 17 q^{72} + 15 q^{73} - 15 q^{74} - 4 q^{75} - 8 q^{76} + 6 q^{77} - 11 q^{78} - 26 q^{79} - 15 q^{80} + 15 q^{81} + 2 q^{82} - 30 q^{83} - 17 q^{84} - 2 q^{85} - 26 q^{86} - 14 q^{87} - 15 q^{88} + 10 q^{89} - 17 q^{90} - 17 q^{91} - 4 q^{92} - 8 q^{93} - 14 q^{94} + 8 q^{95} - 4 q^{96} - 27 q^{97} + 11 q^{98} - 17 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9 - 15 * q^10 - 15 * q^11 - 4 * q^12 - 6 * q^13 - 6 * q^14 + 4 * q^15 + 15 * q^16 + 2 * q^17 + 17 * q^18 - 8 * q^19 - 15 * q^20 - 17 * q^21 - 15 * q^22 - 4 * q^23 - 4 * q^24 + 15 * q^25 - 6 * q^26 - 19 * q^27 - 6 * q^28 - 13 * q^29 + 4 * q^30 - 20 * q^31 + 15 * q^32 + 4 * q^33 + 2 * q^34 + 6 * q^35 + 17 * q^36 - 15 * q^37 - 8 * q^38 - 11 * q^39 - 15 * q^40 + 2 * q^41 - 17 * q^42 - 26 * q^43 - 15 * q^44 - 17 * q^45 - 4 * q^46 - 14 * q^47 - 4 * q^48 + 11 * q^49 + 15 * q^50 - 39 * q^51 - 6 * q^52 - 21 * q^53 - 19 * q^54 + 15 * q^55 - 6 * q^56 + q^57 - 13 * q^58 - 14 * q^59 + 4 * q^60 - 45 * q^61 - 20 * q^62 - 17 * q^63 + 15 * q^64 + 6 * q^65 + 4 * q^66 - 10 * q^67 + 2 * q^68 - 23 * q^69 + 6 * q^70 - 9 * q^71 + 17 * q^72 + 15 * q^73 - 15 * q^74 - 4 * q^75 - 8 * q^76 + 6 * q^77 - 11 * q^78 - 26 * q^79 - 15 * q^80 + 15 * q^81 + 2 * q^82 - 30 * q^83 - 17 * q^84 - 2 * q^85 - 26 * q^86 - 14 * q^87 - 15 * q^88 + 10 * q^89 - 17 * q^90 - 17 * q^91 - 4 * q^92 - 8 * q^93 - 14 * q^94 + 8 * q^95 - 4 * q^96 - 27 * q^97 + 11 * q^98 - 17 * q^99

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