LMFDB - Embedded newform 4030.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.4418197.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} - x^{3} + 12x^{2} + 3x - 1 $ x^6 - 7x^4 - x^3 + 12x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.95223$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.58368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.58368 q^{6} -0.667536 q^{7} +1.00000 q^{8} +3.67538 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.58368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.58368 q^{6} -0.667536 q^{7} +1.00000 q^{8} +3.67538 q^{9} -1.00000 q^{10} -2.84568 q^{11} -2.58368 q^{12} +1.00000 q^{13} -0.667536 q^{14} +2.58368 q^{15} +1.00000 q^{16} +1.37374 q^{17} +3.67538 q^{18} +1.12705 q^{19} -1.00000 q^{20} +1.72470 q^{21} -2.84568 q^{22} -0.435841 q^{23} -2.58368 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.74496 q^{27} -0.667536 q^{28} +3.39742 q^{29} +2.58368 q^{30} -1.00000 q^{31} +1.00000 q^{32} +7.35231 q^{33} +1.37374 q^{34} +0.667536 q^{35} +3.67538 q^{36} +6.66636 q^{37} +1.12705 q^{38} -2.58368 q^{39} -1.00000 q^{40} -4.55705 q^{41} +1.72470 q^{42} -8.44112 q^{43} -2.84568 q^{44} -3.67538 q^{45} -0.435841 q^{46} +1.87000 q^{47} -2.58368 q^{48} -6.55440 q^{49} +1.00000 q^{50} -3.54931 q^{51} +1.00000 q^{52} +6.09399 q^{53} -1.74496 q^{54} +2.84568 q^{55} -0.667536 q^{56} -2.91193 q^{57} +3.39742 q^{58} +9.16780 q^{59} +2.58368 q^{60} +0.621446 q^{61} -1.00000 q^{62} -2.45345 q^{63} +1.00000 q^{64} -1.00000 q^{65} +7.35231 q^{66} -15.1922 q^{67} +1.37374 q^{68} +1.12607 q^{69} +0.667536 q^{70} -0.573489 q^{71} +3.67538 q^{72} +15.1539 q^{73} +6.66636 q^{74} -2.58368 q^{75} +1.12705 q^{76} +1.89959 q^{77} -2.58368 q^{78} -8.71493 q^{79} -1.00000 q^{80} -6.51773 q^{81} -4.55705 q^{82} -14.9770 q^{83} +1.72470 q^{84} -1.37374 q^{85} -8.44112 q^{86} -8.77782 q^{87} -2.84568 q^{88} +0.261768 q^{89} -3.67538 q^{90} -0.667536 q^{91} -0.435841 q^{92} +2.58368 q^{93} +1.87000 q^{94} -1.12705 q^{95} -2.58368 q^{96} -14.0327 q^{97} -6.55440 q^{98} -10.4589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 6 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} - 8 q^{17} - q^{18} - 9 q^{19} - 6 q^{20} - 5 q^{21} - 4 q^{22} - 7 q^{23} - 3 q^{24} + 6 q^{25} + 6 q^{26} + 9 q^{27} - 2 q^{28} - 14 q^{29} + 3 q^{30} - 6 q^{31} + 6 q^{32} - 6 q^{33} - 8 q^{34} + 2 q^{35} - q^{36} - 9 q^{38} - 3 q^{39} - 6 q^{40} + 2 q^{41} - 5 q^{42} - 7 q^{43} - 4 q^{44} + q^{45} - 7 q^{46} - 8 q^{47} - 3 q^{48} - 14 q^{49} + 6 q^{50} - 5 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 14 q^{58} - 5 q^{59} + 3 q^{60} - 5 q^{61} - 6 q^{62} - 19 q^{63} + 6 q^{64} - 6 q^{65} - 6 q^{66} - 12 q^{67} - 8 q^{68} + 2 q^{70} - 10 q^{71} - q^{72} + 5 q^{73} - 3 q^{75} - 9 q^{76} - q^{77} - 3 q^{78} - 16 q^{79} - 6 q^{80} - 10 q^{81} + 2 q^{82} - 22 q^{83} - 5 q^{84} + 8 q^{85} - 7 q^{86} - 31 q^{87} - 4 q^{88} + 14 q^{89} + q^{90} - 2 q^{91} - 7 q^{92} + 3 q^{93} - 8 q^{94} + 9 q^{95} - 3 q^{96} - 9 q^{97} - 14 q^{98} - 21 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9 - 6 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 - 8 * q^17 - q^18 - 9 * q^19 - 6 * q^20 - 5 * q^21 - 4 * q^22 - 7 * q^23 - 3 * q^24 + 6 * q^25 + 6 * q^26 + 9 * q^27 - 2 * q^28 - 14 * q^29 + 3 * q^30 - 6 * q^31 + 6 * q^32 - 6 * q^33 - 8 * q^34 + 2 * q^35 - q^36 - 9 * q^38 - 3 * q^39 - 6 * q^40 + 2 * q^41 - 5 * q^42 - 7 * q^43 - 4 * q^44 + q^45 - 7 * q^46 - 8 * q^47 - 3 * q^48 - 14 * q^49 + 6 * q^50 - 5 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 14 * q^58 - 5 * q^59 + 3 * q^60 - 5 * q^61 - 6 * q^62 - 19 * q^63 + 6 * q^64 - 6 * q^65 - 6 * q^66 - 12 * q^67 - 8 * q^68 + 2 * q^70 - 10 * q^71 - q^72 + 5 * q^73 - 3 * q^75 - 9 * q^76 - q^77 - 3 * q^78 - 16 * q^79 - 6 * q^80 - 10 * q^81 + 2 * q^82 - 22 * q^83 - 5 * q^84 + 8 * q^85 - 7 * q^86 - 31 * q^87 - 4 * q^88 + 14 * q^89 + q^90 - 2 * q^91 - 7 * q^92 + 3 * q^93 - 8 * q^94 + 9 * q^95 - 3 * q^96 - 9 * q^97 - 14 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.58368	−1.49169	−0.745843	−	0.666122i	$-0.767953\pi$
$3$	−2.58368	−1.49169	−0.745843	+	0.666122i	$0.767953\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.58368	−1.05478
$7$	−0.667536	−0.252305	−0.126152	−	0.992011i	$-0.540263\pi$
$7$	−0.667536	−0.252305	−0.126152	+	0.992011i	$0.540263\pi$
$8$	1.00000	0.353553
$9$	3.67538	1.22513
$10$	−1.00000	−0.316228
$11$	−2.84568	−0.858004	−0.429002	−	0.903304i	$-0.641135\pi$
$11$	−2.84568	−0.858004	−0.429002	+	0.903304i	$0.641135\pi$
$12$	−2.58368	−0.745843
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.667536	−0.178406
$15$	2.58368	0.667102
$16$	1.00000	0.250000
$17$	1.37374	0.333182	0.166591	−	0.986026i	$-0.446724\pi$
$17$	1.37374	0.333182	0.166591	+	0.986026i	$0.446724\pi$
$18$	3.67538	0.866295
$19$	1.12705	0.258563	0.129282	−	0.991608i	$-0.458733\pi$
$19$	1.12705	0.258563	0.129282	+	0.991608i	$0.458733\pi$
$20$	−1.00000	−0.223607
$21$	1.72470	0.376359
$22$	−2.84568	−0.606700
$23$	−0.435841	−0.0908791	−0.0454396	−	0.998967i	$-0.514469\pi$
$23$	−0.435841	−0.0908791	−0.0454396	+	0.998967i	$0.514469\pi$
$24$	−2.58368	−0.527391
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−1.74496	−0.335817
$28$	−0.667536	−0.126152
$29$	3.39742	0.630885	0.315442	−	0.948945i	$-0.397847\pi$
$29$	3.39742	0.630885	0.315442	+	0.948945i	$0.397847\pi$
$30$	2.58368	0.471712
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	7.35231	1.27987
$34$	1.37374	0.235595
$35$	0.667536	0.112834
$36$	3.67538	0.612563
$37$	6.66636	1.09594	0.547971	−	0.836497i	$-0.315400\pi$
$37$	6.66636	1.09594	0.547971	+	0.836497i	$0.315400\pi$
$38$	1.12705	0.182832
$39$	−2.58368	−0.413719
$40$	−1.00000	−0.158114
$41$	−4.55705	−0.711692	−0.355846	−	0.934545i	$-0.615807\pi$
$41$	−4.55705	−0.711692	−0.355846	+	0.934545i	$0.615807\pi$
$42$	1.72470	0.266126
$43$	−8.44112	−1.28726	−0.643629	−	0.765337i	$-0.722572\pi$
$43$	−8.44112	−1.28726	−0.643629	+	0.765337i	$0.722572\pi$
$44$	−2.84568	−0.429002
$45$	−3.67538	−0.547893
$46$	−0.435841	−0.0642613
$47$	1.87000	0.272768	0.136384	−	0.990656i	$-0.456452\pi$
$47$	1.87000	0.272768	0.136384	+	0.990656i	$0.456452\pi$
$48$	−2.58368	−0.372921
$49$	−6.55440	−0.936342
$50$	1.00000	0.141421
$51$	−3.54931	−0.497002
$52$	1.00000	0.138675
$53$	6.09399	0.837074	0.418537	−	0.908200i	$-0.362543\pi$
$53$	6.09399	0.837074	0.418537	+	0.908200i	$0.362543\pi$
$54$	−1.74496	−0.237459
$55$	2.84568	0.383711
$56$	−0.667536	−0.0892032
$57$	−2.91193	−0.385695
$58$	3.39742	0.446103
$59$	9.16780	1.19355	0.596773	−	0.802410i	$-0.296449\pi$
$59$	9.16780	1.19355	0.596773	+	0.802410i	$0.296449\pi$
$60$	2.58368	0.333551
$61$	0.621446	0.0795680	0.0397840	−	0.999208i	$-0.487333\pi$
$61$	0.621446	0.0795680	0.0397840	+	0.999208i	$0.487333\pi$
$62$	−1.00000	−0.127000
$63$	−2.45345	−0.309105
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	7.35231	0.905006
$67$	−15.1922	−1.85602	−0.928011	−	0.372553i	$-0.878482\pi$
$67$	−15.1922	−1.85602	−0.928011	+	0.372553i	$0.878482\pi$
$68$	1.37374	0.166591
$69$	1.12607	0.135563
$70$	0.667536	0.0797858
$71$	−0.573489	−0.0680606	−0.0340303	−	0.999421i	$-0.510834\pi$
$71$	−0.573489	−0.0680606	−0.0340303	+	0.999421i	$0.510834\pi$
$72$	3.67538	0.433147
$73$	15.1539	1.77363	0.886815	−	0.462125i	$-0.152913\pi$
$73$	15.1539	1.77363	0.886815	+	0.462125i	$0.152913\pi$
$74$	6.66636	0.774949
$75$	−2.58368	−0.298337
$76$	1.12705	0.129282
$77$	1.89959	0.216479
$78$	−2.58368	−0.292544
$79$	−8.71493	−0.980507	−0.490253	−	0.871580i	$-0.663096\pi$
$79$	−8.71493	−0.980507	−0.490253	+	0.871580i	$0.663096\pi$
$80$	−1.00000	−0.111803
$81$	−6.51773	−0.724192
$82$	−4.55705	−0.503242
$83$	−14.9770	−1.64394	−0.821971	−	0.569529i	$-0.807126\pi$
$83$	−14.9770	−1.64394	−0.821971	+	0.569529i	$0.807126\pi$
$84$	1.72470	0.188180
$85$	−1.37374	−0.149003
$86$	−8.44112	−0.910229
$87$	−8.77782	−0.941081
$88$	−2.84568	−0.303350
$89$	0.261768	0.0277474	0.0138737	−	0.999904i	$-0.495584\pi$
$89$	0.261768	0.0277474	0.0138737	+	0.999904i	$0.495584\pi$
$90$	−3.67538	−0.387419
$91$	−0.667536	−0.0699768
$92$	−0.435841	−0.0454396
$93$	2.58368	0.267915
$94$	1.87000	0.192876
$95$	−1.12705	−0.115633
$96$	−2.58368	−0.263695
$97$	−14.0327	−1.42480	−0.712402	−	0.701772i	$-0.752393\pi$
$97$	−14.0327	−1.42480	−0.712402	+	0.701772i	$0.752393\pi$
$98$	−6.55440	−0.662094
$99$	−10.4589	−1.05116
$100$	1.00000	0.100000
$101$	−6.89933	−0.686509	−0.343254	−	0.939242i	$-0.611529\pi$
$101$	−6.89933	−0.686509	−0.343254	+	0.939242i	$0.611529\pi$
$102$	−3.54931	−0.351434
$103$	19.0139	1.87349	0.936745	−	0.350012i	$-0.113822\pi$
$103$	19.0139	1.87349	0.936745	+	0.350012i	$0.113822\pi$
$104$	1.00000	0.0980581
$105$	−1.72470	−0.168313
$106$	6.09399	0.591900
$107$	5.32124	0.514424	0.257212	−	0.966355i	$-0.417196\pi$
$107$	5.32124	0.514424	0.257212	+	0.966355i	$0.417196\pi$
$108$	−1.74496	−0.167909
$109$	−0.774663	−0.0741992	−0.0370996	−	0.999312i	$-0.511812\pi$
$109$	−0.774663	−0.0741992	−0.0370996	+	0.999312i	$0.511812\pi$
$110$	2.84568	0.271325
$111$	−17.2237	−1.63480
$112$	−0.667536	−0.0630762
$113$	0.172180	0.0161973	0.00809865	−	0.999967i	$-0.497422\pi$
$113$	0.172180	0.0161973	0.00809865	+	0.999967i	$0.497422\pi$
$114$	−2.91193	−0.272727
$115$	0.435841	0.0406424
$116$	3.39742	0.315442
$117$	3.67538	0.339789
$118$	9.16780	0.843965
$119$	−0.917023	−0.0840633
$120$	2.58368	0.235856
$121$	−2.90212	−0.263829
$122$	0.621446	0.0562631
$123$	11.7739	1.06162
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	−2.45345	−0.218570
$127$	9.77114	0.867048	0.433524	−	0.901142i	$-0.357270\pi$
$127$	9.77114	0.867048	0.433524	+	0.901142i	$0.357270\pi$
$128$	1.00000	0.0883883
$129$	21.8091	1.92018
$130$	−1.00000	−0.0877058
$131$	−15.1936	−1.32747	−0.663735	−	0.747968i	$-0.731030\pi$
$131$	−15.1936	−1.32747	−0.663735	+	0.747968i	$0.731030\pi$
$132$	7.35231	0.639936
$133$	−0.752347	−0.0652367
$134$	−15.1922	−1.31241
$135$	1.74496	0.150182
$136$	1.37374	0.117798
$137$	−21.8397	−1.86589	−0.932945	−	0.360019i	$-0.882770\pi$
$137$	−21.8397	−1.86589	−0.932945	+	0.360019i	$0.882770\pi$
$138$	1.12607	0.0958576
$139$	−18.7401	−1.58952	−0.794759	−	0.606926i	$-0.792403\pi$
$139$	−18.7401	−1.58952	−0.794759	+	0.606926i	$0.792403\pi$
$140$	0.667536	0.0564171
$141$	−4.83147	−0.406883
$142$	−0.573489	−0.0481261
$143$	−2.84568	−0.237967
$144$	3.67538	0.306281
$145$	−3.39742	−0.282140
$146$	15.1539	1.25415
$147$	16.9344	1.39673
$148$	6.66636	0.547971
$149$	−1.27180	−0.104190	−0.0520948	−	0.998642i	$-0.516590\pi$
$149$	−1.27180	−0.104190	−0.0520948	+	0.998642i	$0.516590\pi$
$150$	−2.58368	−0.210956
$151$	−3.32959	−0.270958	−0.135479	−	0.990780i	$-0.543257\pi$
$151$	−3.32959	−0.270958	−0.135479	+	0.990780i	$0.543257\pi$
$152$	1.12705	0.0914159
$153$	5.04903	0.408189
$154$	1.89959	0.153073
$155$	1.00000	0.0803219
$156$	−2.58368	−0.206860
$157$	−1.80308	−0.143902	−0.0719508	−	0.997408i	$-0.522922\pi$
$157$	−1.80308	−0.143902	−0.0719508	+	0.997408i	$0.522922\pi$
$158$	−8.71493	−0.693323
$159$	−15.7449	−1.24865
$160$	−1.00000	−0.0790569
$161$	0.290939	0.0229292
$162$	−6.51773	−0.512081
$163$	10.9449	0.857267	0.428633	−	0.903478i	$-0.358995\pi$
$163$	10.9449	0.857267	0.428633	+	0.903478i	$0.358995\pi$
$164$	−4.55705	−0.355846
$165$	−7.35231	−0.572376
$166$	−14.9770	−1.16244
$167$	−7.15082	−0.553347	−0.276674	−	0.960964i	$-0.589232\pi$
$167$	−7.15082	−0.553347	−0.276674	+	0.960964i	$0.589232\pi$
$168$	1.72470	0.133063
$169$	1.00000	0.0769231
$170$	−1.37374	−0.105361
$171$	4.14234	0.316772
$172$	−8.44112	−0.643629
$173$	−14.1002	−1.07202	−0.536011	−	0.844211i	$-0.680069\pi$
$173$	−14.1002	−1.07202	−0.536011	+	0.844211i	$0.680069\pi$
$174$	−8.77782	−0.665445
$175$	−0.667536	−0.0504610
$176$	−2.84568	−0.214501
$177$	−23.6866	−1.78040
$178$	0.261768	0.0196203
$179$	−22.3539	−1.67081	−0.835403	−	0.549638i	$-0.814766\pi$
$179$	−22.3539	−1.67081	−0.835403	+	0.549638i	$0.814766\pi$
$180$	−3.67538	−0.273946
$181$	3.13201	0.232800	0.116400	−	0.993202i	$-0.462865\pi$
$181$	3.13201	0.232800	0.116400	+	0.993202i	$0.462865\pi$
$182$	−0.667536	−0.0494810
$183$	−1.60561	−0.118690
$184$	−0.435841	−0.0321306
$185$	−6.66636	−0.490121
$186$	2.58368	0.189444
$187$	−3.90923	−0.285871
$188$	1.87000	0.136384
$189$	1.16482	0.0847283
$190$	−1.12705	−0.0817648
$191$	−11.9729	−0.866328	−0.433164	−	0.901315i	$-0.642603\pi$
$191$	−11.9729	−0.866328	−0.433164	+	0.901315i	$0.642603\pi$
$192$	−2.58368	−0.186461
$193$	−3.99866	−0.287830	−0.143915	−	0.989590i	$-0.545969\pi$
$193$	−3.99866	−0.287830	−0.143915	+	0.989590i	$0.545969\pi$
$194$	−14.0327	−1.00749
$195$	2.58368	0.185021
$196$	−6.55440	−0.468171
$197$	13.0147	0.927256	0.463628	−	0.886030i	$-0.346547\pi$
$197$	13.0147	0.927256	0.463628	+	0.886030i	$0.346547\pi$
$198$	−10.4589	−0.743284
$199$	12.8215	0.908893	0.454447	−	0.890774i	$-0.349837\pi$
$199$	12.8215	0.908893	0.454447	+	0.890774i	$0.349837\pi$
$200$	1.00000	0.0707107
$201$	39.2517	2.76860
$202$	−6.89933	−0.485435
$203$	−2.26790	−0.159175
$204$	−3.54931	−0.248501
$205$	4.55705	0.318278
$206$	19.0139	1.32476
$207$	−1.60188	−0.111338
$208$	1.00000	0.0693375
$209$	−3.20722	−0.221848
$210$	−1.72470	−0.119015
$211$	−27.0211	−1.86021	−0.930105	−	0.367292i	$-0.880285\pi$
$211$	−27.0211	−1.86021	−0.930105	+	0.367292i	$0.880285\pi$
$212$	6.09399	0.418537
$213$	1.48171	0.101525
$214$	5.32124	0.363753
$215$	8.44112	0.575679
$216$	−1.74496	−0.118729
$217$	0.667536	0.0453153
$218$	−0.774663	−0.0524668
$219$	−39.1528	−2.64570
$220$	2.84568	0.191856
$221$	1.37374	0.0924080
$222$	−17.2237	−1.15598
$223$	4.99819	0.334704	0.167352	−	0.985897i	$-0.446478\pi$
$223$	4.99819	0.334704	0.167352	+	0.985897i	$0.446478\pi$
$224$	−0.667536	−0.0446016
$225$	3.67538	0.245025
$226$	0.172180	0.0114532
$227$	−10.0209	−0.665112	−0.332556	−	0.943084i	$-0.607911\pi$
$227$	−10.0209	−0.665112	−0.332556	+	0.943084i	$0.607911\pi$
$228$	−2.91193	−0.192847
$229$	−11.8143	−0.780710	−0.390355	−	0.920664i	$-0.627648\pi$
$229$	−11.8143	−0.780710	−0.390355	+	0.920664i	$0.627648\pi$
$230$	0.435841	0.0287385
$231$	−4.90793	−0.322918
$232$	3.39742	0.223051
$233$	18.3641	1.20308	0.601538	−	0.798845i	$-0.294555\pi$
$233$	18.3641	1.20308	0.601538	+	0.798845i	$0.294555\pi$
$234$	3.67538	0.240267
$235$	−1.87000	−0.121985
$236$	9.16780	0.596773
$237$	22.5166	1.46261
$238$	−0.917023	−0.0594417
$239$	−15.7543	−1.01906	−0.509531	−	0.860452i	$-0.670181\pi$
$239$	−15.7543	−1.01906	−0.509531	+	0.860452i	$0.670181\pi$
$240$	2.58368	0.166776
$241$	26.3281	1.69594	0.847970	−	0.530043i	$-0.177824\pi$
$241$	26.3281	1.69594	0.847970	+	0.530043i	$0.177824\pi$
$242$	−2.90212	−0.186555
$243$	22.0746	1.41608
$244$	0.621446	0.0397840
$245$	6.55440	0.418745
$246$	11.7739	0.750679
$247$	1.12705	0.0717125
$248$	−1.00000	−0.0635001
$249$	38.6958	2.45224
$250$	−1.00000	−0.0632456
$251$	−11.4360	−0.721835	−0.360918	−	0.932598i	$-0.617536\pi$
$251$	−11.4360	−0.721835	−0.360918	+	0.932598i	$0.617536\pi$
$252$	−2.45345	−0.154553
$253$	1.24026	0.0779747
$254$	9.77114	0.613096
$255$	3.54931	0.222266
$256$	1.00000	0.0625000
$257$	−26.1966	−1.63410	−0.817051	−	0.576566i	$-0.804392\pi$
$257$	−26.1966	−1.63410	−0.817051	+	0.576566i	$0.804392\pi$
$258$	21.8091	1.35778
$259$	−4.45003	−0.276512
$260$	−1.00000	−0.0620174
$261$	12.4868	0.772913
$262$	−15.1936	−0.938663
$263$	−5.32719	−0.328489	−0.164244	−	0.986420i	$-0.552519\pi$
$263$	−5.32719	−0.328489	−0.164244	+	0.986420i	$0.552519\pi$
$264$	7.35231	0.452503
$265$	−6.09399	−0.374351
$266$	−0.752347	−0.0461293
$267$	−0.676324	−0.0413903
$268$	−15.1922	−0.928011
$269$	−14.8195	−0.903562	−0.451781	−	0.892129i	$-0.649211\pi$
$269$	−14.8195	−0.903562	−0.451781	+	0.892129i	$0.649211\pi$
$270$	1.74496	0.106195
$271$	9.36508	0.568888	0.284444	−	0.958693i	$-0.408191\pi$
$271$	9.36508	0.568888	0.284444	+	0.958693i	$0.408191\pi$
$272$	1.37374	0.0832954
$273$	1.72470	0.104383
$274$	−21.8397	−1.31938
$275$	−2.84568	−0.171601
$276$	1.12607	0.0677815
$277$	−9.53219	−0.572734	−0.286367	−	0.958120i	$-0.592448\pi$
$277$	−9.53219	−0.572734	−0.286367	+	0.958120i	$0.592448\pi$
$278$	−18.7401	−1.12396
$279$	−3.67538	−0.220039
$280$	0.667536	0.0398929
$281$	−16.5401	−0.986701	−0.493350	−	0.869831i	$-0.664228\pi$
$281$	−16.5401	−0.986701	−0.493350	+	0.869831i	$0.664228\pi$
$282$	−4.83147	−0.287710
$283$	−16.8986	−1.00452	−0.502258	−	0.864718i	$-0.667497\pi$
$283$	−16.8986	−1.00452	−0.502258	+	0.864718i	$0.667497\pi$
$284$	−0.573489	−0.0340303
$285$	2.91193	0.172488
$286$	−2.84568	−0.168268
$287$	3.04200	0.179563
$288$	3.67538	0.216574
$289$	−15.1128	−0.888990
$290$	−3.39742	−0.199503
$291$	36.2559	2.12536
$292$	15.1539	0.886815
$293$	−20.1637	−1.17798	−0.588989	−	0.808141i	$-0.700474\pi$
$293$	−20.1637	−1.17798	−0.588989	+	0.808141i	$0.700474\pi$
$294$	16.9344	0.987636
$295$	−9.16780	−0.533770
$296$	6.66636	0.387474
$297$	4.96558	0.288132
$298$	−1.27180	−0.0736732
$299$	−0.435841	−0.0252053
$300$	−2.58368	−0.149169
$301$	5.63475	0.324781
$302$	−3.32959	−0.191597
$303$	17.8256	1.02406
$304$	1.12705	0.0646408
$305$	−0.621446	−0.0355839
$306$	5.04903	0.288634
$307$	1.63537	0.0933357	0.0466678	−	0.998910i	$-0.485140\pi$
$307$	1.63537	0.0933357	0.0466678	+	0.998910i	$0.485140\pi$
$308$	1.89959	0.108239
$309$	−49.1256	−2.79466
$310$	1.00000	0.0567962
$311$	30.0340	1.70307	0.851536	−	0.524296i	$-0.175671\pi$
$311$	30.0340	1.70307	0.851536	+	0.524296i	$0.175671\pi$
$312$	−2.58368	−0.146272
$313$	14.6006	0.825273	0.412637	−	0.910896i	$-0.364608\pi$
$313$	14.6006	0.825273	0.412637	+	0.910896i	$0.364608\pi$
$314$	−1.80308	−0.101754
$315$	2.45345	0.138236
$316$	−8.71493	−0.490253
$317$	1.04173	0.0585095	0.0292547	−	0.999572i	$-0.490687\pi$
$317$	1.04173	0.0585095	0.0292547	+	0.999572i	$0.490687\pi$
$318$	−15.7449	−0.882929
$319$	−9.66795	−0.541301
$320$	−1.00000	−0.0559017
$321$	−13.7484	−0.767359
$322$	0.290939	0.0162134
$323$	1.54828	0.0861485
$324$	−6.51773	−0.362096
$325$	1.00000	0.0554700
$326$	10.9449	0.606179
$327$	2.00148	0.110682
$328$	−4.55705	−0.251621
$329$	−1.24829	−0.0688206
$330$	−7.35231	−0.404731
$331$	−26.6829	−1.46662	−0.733312	−	0.679892i	$-0.762026\pi$
$331$	−26.6829	−1.46662	−0.733312	+	0.679892i	$0.762026\pi$
$332$	−14.9770	−0.821971
$333$	24.5014	1.34267
$334$	−7.15082	−0.391275
$335$	15.1922	0.830038
$336$	1.72470	0.0940899
$337$	21.0760	1.14808	0.574042	−	0.818826i	$-0.305375\pi$
$337$	21.0760	1.14808	0.574042	+	0.818826i	$0.305375\pi$
$338$	1.00000	0.0543928
$339$	−0.444857	−0.0241613
$340$	−1.37374	−0.0745017
$341$	2.84568	0.154102
$342$	4.14234	0.223992
$343$	9.04804	0.488548
$344$	−8.44112	−0.455115
$345$	−1.12607	−0.0606257
$346$	−14.1002	−0.758034
$347$	15.1484	0.813210	0.406605	−	0.913604i	$-0.366713\pi$
$347$	15.1484	0.813210	0.406605	+	0.913604i	$0.366713\pi$
$348$	−8.77782	−0.470541
$349$	4.81220	0.257591	0.128796	−	0.991671i	$-0.458889\pi$
$349$	4.81220	0.257591	0.128796	+	0.991671i	$0.458889\pi$
$350$	−0.667536	−0.0356813
$351$	−1.74496	−0.0931389
$352$	−2.84568	−0.151675
$353$	−2.98394	−0.158819	−0.0794096	−	0.996842i	$-0.525304\pi$
$353$	−2.98394	−0.158819	−0.0794096	+	0.996842i	$0.525304\pi$
$354$	−23.6866	−1.25893
$355$	0.573489	0.0304376
$356$	0.261768	0.0138737
$357$	2.36929	0.125396
$358$	−22.3539	−1.18144
$359$	−30.3642	−1.60256	−0.801281	−	0.598289i	$-0.795848\pi$
$359$	−30.3642	−1.60256	−0.801281	+	0.598289i	$0.795848\pi$
$360$	−3.67538	−0.193709
$361$	−17.7298	−0.933145
$362$	3.13201	0.164615
$363$	7.49814	0.393550
$364$	−0.667536	−0.0349884
$365$	−15.1539	−0.793191
$366$	−1.60561	−0.0839268
$367$	15.0688	0.786585	0.393293	−	0.919413i	$-0.371336\pi$
$367$	15.0688	0.786585	0.393293	+	0.919413i	$0.371336\pi$
$368$	−0.435841	−0.0227198
$369$	−16.7489	−0.871912
$370$	−6.66636	−0.346568
$371$	−4.06796	−0.211198
$372$	2.58368	0.133957
$373$	1.32323	0.0685141	0.0342571	−	0.999413i	$-0.489094\pi$
$373$	1.32323	0.0685141	0.0342571	+	0.999413i	$0.489094\pi$
$374$	−3.90923	−0.202141
$375$	2.58368	0.133420
$376$	1.87000	0.0964379
$377$	3.39742	0.174976
$378$	1.16482	0.0599119
$379$	−30.1419	−1.54829	−0.774144	−	0.633010i	$-0.781819\pi$
$379$	−30.1419	−1.54829	−0.774144	+	0.633010i	$0.781819\pi$
$380$	−1.12705	−0.0578165
$381$	−25.2455	−1.29336
$382$	−11.9729	−0.612587
$383$	−14.0592	−0.718394	−0.359197	−	0.933262i	$-0.616949\pi$
$383$	−14.0592	−0.718394	−0.359197	+	0.933262i	$0.616949\pi$
$384$	−2.58368	−0.131848
$385$	−1.89959	−0.0968121
$386$	−3.99866	−0.203526
$387$	−31.0243	−1.57705
$388$	−14.0327	−0.712402
$389$	6.48024	0.328561	0.164281	−	0.986414i	$-0.447470\pi$
$389$	6.48024	0.328561	0.164281	+	0.986414i	$0.447470\pi$
$390$	2.58368	0.130829
$391$	−0.598734	−0.0302793
$392$	−6.55440	−0.331047
$393$	39.2553	1.98017
$394$	13.0147	0.655669
$395$	8.71493	0.438496
$396$	−10.4589	−0.525581
$397$	28.0958	1.41009	0.705043	−	0.709165i	$-0.250928\pi$
$397$	28.0958	1.41009	0.705043	+	0.709165i	$0.250928\pi$
$398$	12.8215	0.642684
$399$	1.94382	0.0973127
$400$	1.00000	0.0500000
$401$	31.9072	1.59337	0.796684	−	0.604396i	$-0.206585\pi$
$401$	31.9072	1.59337	0.796684	+	0.604396i	$0.206585\pi$
$402$	39.2517	1.95770
$403$	−1.00000	−0.0498135
$404$	−6.89933	−0.343254
$405$	6.51773	0.323869
$406$	−2.26790	−0.112554
$407$	−18.9703	−0.940323
$408$	−3.54931	−0.175717
$409$	32.7128	1.61755	0.808773	−	0.588121i	$-0.200132\pi$
$409$	32.7128	1.61755	0.808773	+	0.588121i	$0.200132\pi$
$410$	4.55705	0.225057
$411$	56.4266	2.78332
$412$	19.0139	0.936745
$413$	−6.11984	−0.301137
$414$	−1.60188	−0.0787281
$415$	14.9770	0.735193
$416$	1.00000	0.0490290
$417$	48.4184	2.37106
$418$	−3.20722	−0.156870
$419$	22.4404	1.09628	0.548142	−	0.836385i	$-0.315335\pi$
$419$	22.4404	1.09628	0.548142	+	0.836385i	$0.315335\pi$
$420$	−1.72470	−0.0841565
$421$	9.40354	0.458301	0.229150	−	0.973391i	$-0.426405\pi$
$421$	9.40354	0.458301	0.229150	+	0.973391i	$0.426405\pi$
$422$	−27.0211	−1.31537
$423$	6.87296	0.334175
$424$	6.09399	0.295950
$425$	1.37374	0.0666363
$426$	1.48171	0.0717890
$427$	−0.414837	−0.0200754
$428$	5.32124	0.257212
$429$	7.35231	0.354973
$430$	8.44112	0.407067
$431$	−23.5643	−1.13505	−0.567526	−	0.823356i	$-0.692099\pi$
$431$	−23.5643	−1.13505	−0.567526	+	0.823356i	$0.692099\pi$
$432$	−1.74496	−0.0839543
$433$	11.9152	0.572606	0.286303	−	0.958139i	$-0.407574\pi$
$433$	11.9152	0.572606	0.286303	+	0.958139i	$0.407574\pi$
$434$	0.667536	0.0320427
$435$	8.77782	0.420864
$436$	−0.774663	−0.0370996
$437$	−0.491215	−0.0234980
$438$	−39.1528	−1.87079
$439$	−40.6319	−1.93926	−0.969628	−	0.244583i	$-0.921349\pi$
$439$	−40.6319	−1.93926	−0.969628	+	0.244583i	$0.921349\pi$
$440$	2.84568	0.135662
$441$	−24.0899	−1.14714
$442$	1.37374	0.0653423
$443$	−21.8424	−1.03776	−0.518882	−	0.854846i	$-0.673652\pi$
$443$	−21.8424	−1.03776	−0.518882	+	0.854846i	$0.673652\pi$
$444$	−17.2237	−0.817401
$445$	−0.261768	−0.0124090
$446$	4.99819	0.236671
$447$	3.28591	0.155418
$448$	−0.667536	−0.0315381
$449$	5.96092	0.281313	0.140657	−	0.990058i	$-0.455079\pi$
$449$	5.96092	0.281313	0.140657	+	0.990058i	$0.455079\pi$
$450$	3.67538	0.173259
$451$	12.9679	0.610635
$452$	0.172180	0.00809865
$453$	8.60259	0.404185
$454$	−10.0209	−0.470305
$455$	0.667536	0.0312946
$456$	−2.91193	−0.136364
$457$	28.0231	1.31086	0.655432	−	0.755254i	$-0.272487\pi$
$457$	28.0231	1.31086	0.655432	+	0.755254i	$0.272487\pi$
$458$	−11.8143	−0.552045
$459$	−2.39712	−0.111888
$460$	0.435841	0.0203212
$461$	9.15109	0.426209	0.213104	−	0.977029i	$-0.431643\pi$
$461$	9.15109	0.426209	0.213104	+	0.977029i	$0.431643\pi$
$462$	−4.90793	−0.228337
$463$	16.0997	0.748217	0.374109	−	0.927385i	$-0.377949\pi$
$463$	16.0997	0.748217	0.374109	+	0.927385i	$0.377949\pi$
$464$	3.39742	0.157721
$465$	−2.58368	−0.119815
$466$	18.3641	0.850703
$467$	1.88462	0.0872100	0.0436050	−	0.999049i	$-0.486116\pi$
$467$	1.88462	0.0872100	0.0436050	+	0.999049i	$0.486116\pi$
$468$	3.67538	0.169894
$469$	10.1413	0.468283
$470$	−1.87000	−0.0862567
$471$	4.65858	0.214656
$472$	9.16780	0.421982
$473$	24.0207	1.10447
$474$	22.5166	1.03422
$475$	1.12705	0.0517126
$476$	−0.917023	−0.0420317
$477$	22.3977	1.02552
$478$	−15.7543	−0.720586
$479$	33.4694	1.52926	0.764628	−	0.644472i	$-0.222923\pi$
$479$	33.4694	1.52926	0.764628	+	0.644472i	$0.222923\pi$
$480$	2.58368	0.117928
$481$	6.66636	0.303960
$482$	26.3281	1.19921
$483$	−0.751693	−0.0342032
$484$	−2.90212	−0.131915
$485$	14.0327	0.637191
$486$	22.0746	1.00132
$487$	26.8466	1.21654	0.608268	−	0.793732i	$-0.291865\pi$
$487$	26.8466	1.21654	0.608268	+	0.793732i	$0.291865\pi$
$488$	0.621446	0.0281315
$489$	−28.2779	−1.27877
$490$	6.55440	0.296097
$491$	18.1787	0.820393	0.410196	−	0.911997i	$-0.365460\pi$
$491$	18.1787	0.820393	0.410196	+	0.911997i	$0.365460\pi$
$492$	11.7739	0.530810
$493$	4.66718	0.210199
$494$	1.12705	0.0507084
$495$	10.4589	0.470094
$496$	−1.00000	−0.0449013
$497$	0.382824	0.0171720
$498$	38.6958	1.73400
$499$	−2.88109	−0.128975	−0.0644877	−	0.997919i	$-0.520541\pi$
$499$	−2.88109	−0.128975	−0.0644877	+	0.997919i	$0.520541\pi$
$500$	−1.00000	−0.0447214
$501$	18.4754	0.825420
$502$	−11.4360	−0.510414
$503$	27.4648	1.22460	0.612298	−	0.790627i	$-0.290245\pi$
$503$	27.4648	1.22460	0.612298	+	0.790627i	$0.290245\pi$
$504$	−2.45345	−0.109285
$505$	6.89933	0.307016
$506$	1.24026	0.0551364
$507$	−2.58368	−0.114745
$508$	9.77114	0.433524
$509$	−23.1987	−1.02826	−0.514132	−	0.857711i	$-0.671886\pi$
$509$	−23.1987	−1.02826	−0.514132	+	0.857711i	$0.671886\pi$
$510$	3.54931	0.157166
$511$	−10.1158	−0.447495
$512$	1.00000	0.0441942
$513$	−1.96665	−0.0868299
$514$	−26.1966	−1.15548
$515$	−19.0139	−0.837851
$516$	21.8091	0.960092
$517$	−5.32142	−0.234036
$518$	−4.45003	−0.195523
$519$	36.4305	1.59912
$520$	−1.00000	−0.0438529
$521$	−13.7819	−0.603797	−0.301899	−	0.953340i	$-0.597620\pi$
$521$	−13.7819	−0.603797	−0.301899	+	0.953340i	$0.597620\pi$
$522$	12.4868	0.546532
$523$	−23.4117	−1.02372	−0.511861	−	0.859068i	$-0.671044\pi$
$523$	−23.4117	−1.02372	−0.511861	+	0.859068i	$0.671044\pi$
$524$	−15.1936	−0.663735
$525$	1.72470	0.0752719
$526$	−5.32719	−0.232276
$527$	−1.37374	−0.0598412
$528$	7.35231	0.319968
$529$	−22.8100	−0.991741
$530$	−6.09399	−0.264706
$531$	33.6951	1.46224
$532$	−0.752347	−0.0326184
$533$	−4.55705	−0.197388
$534$	−0.676324	−0.0292674
$535$	−5.32124	−0.230057
$536$	−15.1922	−0.656203
$537$	57.7551	2.49232
$538$	−14.8195	−0.638915
$539$	18.6517	0.803385
$540$	1.74496	0.0750910
$541$	−7.63228	−0.328137	−0.164069	−	0.986449i	$-0.552462\pi$
$541$	−7.63228	−0.328137	−0.164069	+	0.986449i	$0.552462\pi$
$542$	9.36508	0.402265
$543$	−8.09209	−0.347265
$544$	1.37374	0.0588988
$545$	0.774663	0.0331829
$546$	1.72470	0.0738102
$547$	−8.05877	−0.344568	−0.172284	−	0.985047i	$-0.555115\pi$
$547$	−8.05877	−0.344568	−0.172284	+	0.985047i	$0.555115\pi$
$548$	−21.8397	−0.932945
$549$	2.28405	0.0974808
$550$	−2.84568	−0.121340
$551$	3.82906	0.163123
$552$	1.12607	0.0479288
$553$	5.81753	0.247386
$554$	−9.53219	−0.404984
$555$	17.2237	0.731106
$556$	−18.7401	−0.794759
$557$	−9.73541	−0.412503	−0.206251	−	0.978499i	$-0.566126\pi$
$557$	−9.73541	−0.412503	−0.206251	+	0.978499i	$0.566126\pi$
$558$	−3.67538	−0.155591
$559$	−8.44112	−0.357021
$560$	0.667536	0.0282085
$561$	10.1002	0.426430
$562$	−16.5401	−0.697703
$563$	−26.7207	−1.12614	−0.563072	−	0.826408i	$-0.690381\pi$
$563$	−26.7207	−1.12614	−0.563072	+	0.826408i	$0.690381\pi$
$564$	−4.83147	−0.203442
$565$	−0.172180	−0.00724366
$566$	−16.8986	−0.710300
$567$	4.35082	0.182717
$568$	−0.573489	−0.0240630
$569$	−24.1738	−1.01342	−0.506710	−	0.862117i	$-0.669138\pi$
$569$	−24.1738	−1.01342	−0.506710	+	0.862117i	$0.669138\pi$
$570$	2.91193	0.121967
$571$	−11.2901	−0.472475	−0.236238	−	0.971695i	$-0.575914\pi$
$571$	−11.2901	−0.472475	−0.236238	+	0.971695i	$0.575914\pi$
$572$	−2.84568	−0.118984
$573$	30.9341	1.29229
$574$	3.04200	0.126970
$575$	−0.435841	−0.0181758
$576$	3.67538	0.153141
$577$	26.3661	1.09764	0.548818	−	0.835942i	$-0.315078\pi$
$577$	26.3661	1.09764	0.548818	+	0.835942i	$0.315078\pi$
$578$	−15.1128	−0.628611
$579$	10.3312	0.429351
$580$	−3.39742	−0.141070
$581$	9.99770	0.414774
$582$	36.2559	1.50286
$583$	−17.3415	−0.718213
$584$	15.1539	0.627073
$585$	−3.67538	−0.151958
$586$	−20.1637	−0.832956
$587$	−6.94172	−0.286515	−0.143258	−	0.989685i	$-0.545758\pi$
$587$	−6.94172	−0.286515	−0.143258	+	0.989685i	$0.545758\pi$
$588$	16.9344	0.698364
$589$	−1.12705	−0.0464393
$590$	−9.16780	−0.377432
$591$	−33.6256	−1.38317
$592$	6.66636	0.273986
$593$	20.0038	0.821458	0.410729	−	0.911757i	$-0.365274\pi$
$593$	20.0038	0.821458	0.410729	+	0.911757i	$0.365274\pi$
$594$	4.96558	0.203740
$595$	0.917023	0.0375943
$596$	−1.27180	−0.0520948
$597$	−33.1266	−1.35578
$598$	−0.435841	−0.0178229
$599$	−34.0007	−1.38923	−0.694615	−	0.719382i	$-0.744425\pi$
$599$	−34.0007	−1.38923	−0.694615	+	0.719382i	$0.744425\pi$
$600$	−2.58368	−0.105478
$601$	45.0090	1.83595	0.917977	−	0.396634i	$-0.129822\pi$
$601$	45.0090	1.83595	0.917977	+	0.396634i	$0.129822\pi$
$602$	5.63475	0.229655
$603$	−55.8370	−2.27386
$604$	−3.32959	−0.135479
$605$	2.90212	0.117988
$606$	17.8256	0.724117
$607$	−25.3651	−1.02954	−0.514768	−	0.857330i	$-0.672122\pi$
$607$	−25.3651	−1.02954	−0.514768	+	0.857330i	$0.672122\pi$
$608$	1.12705	0.0457079
$609$	5.85951	0.237439
$610$	−0.621446	−0.0251616
$611$	1.87000	0.0756521
$612$	5.04903	0.204095
$613$	−3.70474	−0.149633	−0.0748166	−	0.997197i	$-0.523837\pi$
$613$	−3.70474	−0.149633	−0.0748166	+	0.997197i	$0.523837\pi$
$614$	1.63537	0.0659983
$615$	−11.7739	−0.474771
$616$	1.89959	0.0765367
$617$	−14.0120	−0.564101	−0.282051	−	0.959400i	$-0.591015\pi$
$617$	−14.0120	−0.564101	−0.282051	+	0.959400i	$0.591015\pi$
$618$	−49.1256	−1.97612
$619$	29.1480	1.17156	0.585778	−	0.810472i	$-0.300789\pi$
$619$	29.1480	1.17156	0.585778	+	0.810472i	$0.300789\pi$
$620$	1.00000	0.0401610
$621$	0.760524	0.0305188
$622$	30.0340	1.20425
$623$	−0.174740	−0.00700079
$624$	−2.58368	−0.103430
$625$	1.00000	0.0400000
$626$	14.6006	0.583556
$627$	8.28642	0.330928
$628$	−1.80308	−0.0719508
$629$	9.15787	0.365148
$630$	2.45345	0.0977476
$631$	39.1209	1.55738	0.778689	−	0.627411i	$-0.215885\pi$
$631$	39.1209	1.55738	0.778689	+	0.627411i	$0.215885\pi$
$632$	−8.71493	−0.346661
$633$	69.8138	2.77485
$634$	1.04173	0.0413724
$635$	−9.77114	−0.387756
$636$	−15.7449	−0.624325
$637$	−6.55440	−0.259695
$638$	−9.66795	−0.382758
$639$	−2.10779	−0.0833828
$640$	−1.00000	−0.0395285
$641$	24.1876	0.955351	0.477675	−	0.878536i	$-0.341480\pi$
$641$	24.1876	0.955351	0.477675	+	0.878536i	$0.341480\pi$
$642$	−13.7484	−0.542605
$643$	35.0258	1.38128	0.690642	−	0.723197i	$-0.257328\pi$
$643$	35.0258	1.38128	0.690642	+	0.723197i	$0.257328\pi$
$644$	0.290939	0.0114646
$645$	−21.8091	−0.858733
$646$	1.54828	0.0609162
$647$	8.28752	0.325816	0.162908	−	0.986641i	$-0.447913\pi$
$647$	8.28752	0.325816	0.162908	+	0.986641i	$0.447913\pi$
$648$	−6.51773	−0.256041
$649$	−26.0886	−1.02407
$650$	1.00000	0.0392232
$651$	−1.72470	−0.0675961
$652$	10.9449	0.428633
$653$	−14.5057	−0.567650	−0.283825	−	0.958876i	$-0.591603\pi$
$653$	−14.5057	−0.567650	−0.283825	+	0.958876i	$0.591603\pi$
$654$	2.00148	0.0782639
$655$	15.1936	0.593663
$656$	−4.55705	−0.177923
$657$	55.6963	2.17292
$658$	−1.24829	−0.0486635
$659$	−26.9167	−1.04853	−0.524263	−	0.851556i	$-0.675659\pi$
$659$	−26.9167	−1.04853	−0.524263	+	0.851556i	$0.675659\pi$
$660$	−7.35231	−0.286188
$661$	6.37499	0.247958	0.123979	−	0.992285i	$-0.460434\pi$
$661$	6.37499	0.247958	0.123979	+	0.992285i	$0.460434\pi$
$662$	−26.6829	−1.03706
$663$	−3.54931	−0.137844
$664$	−14.9770	−0.581221
$665$	0.752347	0.0291747
$666$	24.5014	0.949410
$667$	−1.48073	−0.0573342
$668$	−7.15082	−0.276674
$669$	−12.9137	−0.499273
$670$	15.1922	0.586926
$671$	−1.76843	−0.0682696
$672$	1.72470	0.0665316
$673$	−36.2686	−1.39805	−0.699027	−	0.715096i	$-0.746383\pi$
$673$	−36.2686	−1.39805	−0.699027	+	0.715096i	$0.746383\pi$
$674$	21.0760	0.811817
$675$	−1.74496	−0.0671634
$676$	1.00000	0.0384615
$677$	−1.21930	−0.0468617	−0.0234308	−	0.999725i	$-0.507459\pi$
$677$	−1.21930	−0.0468617	−0.0234308	+	0.999725i	$0.507459\pi$
$678$	−0.444857	−0.0170846
$679$	9.36732	0.359485
$680$	−1.37374	−0.0526806
$681$	25.8908	0.992138
$682$	2.84568	0.108967
$683$	14.6388	0.560138	0.280069	−	0.959980i	$-0.409643\pi$
$683$	14.6388	0.560138	0.280069	+	0.959980i	$0.409643\pi$
$684$	4.14234	0.158386
$685$	21.8397	0.834451
$686$	9.04804	0.345456
$687$	30.5243	1.16457
$688$	−8.44112	−0.321815
$689$	6.09399	0.232162
$690$	−1.12607	−0.0428688
$691$	40.2830	1.53244	0.766218	−	0.642580i	$-0.222136\pi$
$691$	40.2830	1.53244	0.766218	+	0.642580i	$0.222136\pi$
$692$	−14.1002	−0.536011
$693$	6.98172	0.265213
$694$	15.1484	0.575026
$695$	18.7401	0.710854
$696$	−8.77782	−0.332722
$697$	−6.26022	−0.237123
$698$	4.81220	0.182144
$699$	−47.4470	−1.79461
$700$	−0.667536	−0.0252305
$701$	48.5761	1.83470	0.917348	−	0.398087i	$-0.130326\pi$
$701$	48.5761	1.83470	0.917348	+	0.398087i	$0.130326\pi$
$702$	−1.74496	−0.0658592
$703$	7.51333	0.283370
$704$	−2.84568	−0.107250
$705$	4.83147	0.181964
$706$	−2.98394	−0.112302
$707$	4.60555	0.173209
$708$	−23.6866	−0.890198
$709$	−43.4382	−1.63136	−0.815679	−	0.578505i	$-0.803636\pi$
$709$	−43.4382	−1.63136	−0.815679	+	0.578505i	$0.803636\pi$
$710$	0.573489	0.0215226
$711$	−32.0307	−1.20124
$712$	0.261768	0.00981017
$713$	0.435841	0.0163224
$714$	2.36929	0.0886684
$715$	2.84568	0.106422
$716$	−22.3539	−0.835403
$717$	40.7041	1.52012
$718$	−30.3642	−1.13318
$719$	0.909886	0.0339330	0.0169665	−	0.999856i	$-0.494599\pi$
$719$	0.909886	0.0339330	0.0169665	+	0.999856i	$0.494599\pi$
$720$	−3.67538	−0.136973
$721$	−12.6924	−0.472691
$722$	−17.7298	−0.659833
$723$	−68.0232	−2.52981
$724$	3.13201	0.116400
$725$	3.39742	0.126177
$726$	7.49814	0.278282
$727$	12.8509	0.476612	0.238306	−	0.971190i	$-0.423408\pi$
$727$	12.8509	0.476612	0.238306	+	0.971190i	$0.423408\pi$
$728$	−0.667536	−0.0247405
$729$	−37.4803	−1.38816
$730$	−15.1539	−0.560871
$731$	−11.5959	−0.428891
$732$	−1.60561	−0.0593452
$733$	46.8785	1.73150	0.865748	−	0.500480i	$-0.166843\pi$
$733$	46.8785	1.73150	0.865748	+	0.500480i	$0.166843\pi$
$734$	15.0688	0.556200
$735$	−16.9344	−0.624636
$736$	−0.435841	−0.0160653
$737$	43.2321	1.59247
$738$	−16.7489	−0.616535
$739$	−32.3595	−1.19036	−0.595181	−	0.803591i	$-0.702920\pi$
$739$	−32.3595	−1.19036	−0.595181	+	0.803591i	$0.702920\pi$
$740$	−6.66636	−0.245060
$741$	−2.91193	−0.106973
$742$	−4.06796	−0.149339
$743$	34.3768	1.26116	0.630582	−	0.776123i	$-0.282816\pi$
$743$	34.3768	1.26116	0.630582	+	0.776123i	$0.282816\pi$
$744$	2.58368	0.0947221
$745$	1.27180	0.0465950
$746$	1.32323	0.0484468
$747$	−55.0462	−2.01404
$748$	−3.90923	−0.142936
$749$	−3.55212	−0.129792
$750$	2.58368	0.0943425
$751$	4.71021	0.171878	0.0859390	−	0.996300i	$-0.472611\pi$
$751$	4.71021	0.171878	0.0859390	+	0.996300i	$0.472611\pi$
$752$	1.87000	0.0681919
$753$	29.5470	1.07675
$754$	3.39742	0.123727
$755$	3.32959	0.121176
$756$	1.16482	0.0423641
$757$	−42.1212	−1.53092	−0.765461	−	0.643483i	$-0.777489\pi$
$757$	−42.1212	−1.53092	−0.765461	+	0.643483i	$0.777489\pi$
$758$	−30.1419	−1.09480
$759$	−3.20444	−0.116314
$760$	−1.12705	−0.0408824
$761$	−16.0350	−0.581269	−0.290635	−	0.956834i	$-0.593866\pi$
$761$	−16.0350	−0.581269	−0.290635	+	0.956834i	$0.593866\pi$
$762$	−25.2455	−0.914546
$763$	0.517115	0.0187208
$764$	−11.9729	−0.433164
$765$	−5.04903	−0.182548
$766$	−14.0592	−0.507981
$767$	9.16780	0.331030
$768$	−2.58368	−0.0932304
$769$	18.5000	0.667128	0.333564	−	0.942727i	$-0.391749\pi$
$769$	18.5000	0.667128	0.333564	+	0.942727i	$0.391749\pi$
$770$	−1.89959	−0.0684565
$771$	67.6836	2.43757
$772$	−3.99866	−0.143915
$773$	37.4399	1.34662	0.673309	−	0.739361i	$-0.264872\pi$
$773$	37.4399	1.34662	0.673309	+	0.739361i	$0.264872\pi$
$774$	−31.0243	−1.11515
$775$	−1.00000	−0.0359211
$776$	−14.0327	−0.503744
$777$	11.4974	0.412468
$778$	6.48024	0.232328
$779$	−5.13603	−0.184017
$780$	2.58368	0.0925104
$781$	1.63196	0.0583962
$782$	−0.598734	−0.0214107
$783$	−5.92835	−0.211862
$784$	−6.55440	−0.234086
$785$	1.80308	0.0643548
$786$	39.2553	1.40019
$787$	−31.8429	−1.13508	−0.567538	−	0.823347i	$-0.692104\pi$
$787$	−31.8429	−1.13508	−0.567538	+	0.823347i	$0.692104\pi$
$788$	13.0147	0.463628
$789$	13.7637	0.490002
$790$	8.71493	0.310063
$791$	−0.114936	−0.00408666
$792$	−10.4589	−0.371642
$793$	0.621446	0.0220682
$794$	28.0958	0.997081
$795$	15.7449	0.558414
$796$	12.8215	0.454447
$797$	−26.5286	−0.939692	−0.469846	−	0.882748i	$-0.655691\pi$
$797$	−26.5286	−0.939692	−0.469846	+	0.882748i	$0.655691\pi$
$798$	1.94382	0.0688105
$799$	2.56890	0.0908812
$800$	1.00000	0.0353553
$801$	0.962097	0.0339940
$802$	31.9072	1.12668
$803$	−43.1231	−1.52178
$804$	39.2517	1.38430
$805$	−0.290939	−0.0102543
$806$	−1.00000	−0.0352235
$807$	38.2888	1.34783
$808$	−6.89933	−0.242718
$809$	−39.7194	−1.39646	−0.698229	−	0.715874i	$-0.746028\pi$
$809$	−39.7194	−1.39646	−0.698229	+	0.715874i	$0.746028\pi$
$810$	6.51773	0.229010
$811$	−16.4908	−0.579071	−0.289536	−	0.957167i	$-0.593501\pi$
$811$	−16.4908	−0.579071	−0.289536	+	0.957167i	$0.593501\pi$
$812$	−2.26790	−0.0795876
$813$	−24.1963	−0.848602
$814$	−18.9703	−0.664909
$815$	−10.9449	−0.383381
$816$	−3.54931	−0.124251
$817$	−9.51357	−0.332838
$818$	32.7128	1.14378
$819$	−2.45345	−0.0857303
$820$	4.55705	0.159139
$821$	−51.5885	−1.80045	−0.900226	−	0.435423i	$-0.856599\pi$
$821$	−51.5885	−1.80045	−0.900226	+	0.435423i	$0.856599\pi$
$822$	56.4266	1.96811
$823$	24.9637	0.870179	0.435089	−	0.900387i	$-0.356717\pi$
$823$	24.9637	0.870179	0.435089	+	0.900387i	$0.356717\pi$
$824$	19.0139	0.662379
$825$	7.35231	0.255974
$826$	−6.11984	−0.212936
$827$	13.0834	0.454954	0.227477	−	0.973783i	$-0.426952\pi$
$827$	13.0834	0.454954	0.227477	+	0.973783i	$0.426952\pi$
$828$	−1.60188	−0.0556692
$829$	−3.65472	−0.126934	−0.0634669	−	0.997984i	$-0.520216\pi$
$829$	−3.65472	−0.126934	−0.0634669	+	0.997984i	$0.520216\pi$
$830$	14.9770	0.519860
$831$	24.6281	0.854339
$832$	1.00000	0.0346688
$833$	−9.00406	−0.311972
$834$	48.4184	1.67659
$835$	7.15082	0.247464
$836$	−3.20722	−0.110924
$837$	1.74496	0.0603145
$838$	22.4404	0.775190
$839$	−6.68690	−0.230857	−0.115429	−	0.993316i	$-0.536824\pi$
$839$	−6.68690	−0.230857	−0.115429	+	0.993316i	$0.536824\pi$
$840$	−1.72470	−0.0595077
$841$	−17.4576	−0.601985
$842$	9.40354	0.324067
$843$	42.7343	1.47185
$844$	−27.0211	−0.930105
$845$	−1.00000	−0.0344010
$846$	6.87296	0.236297
$847$	1.93727	0.0665654
$848$	6.09399	0.209268
$849$	43.6604	1.49842
$850$	1.37374	0.0471190
$851$	−2.90547	−0.0995983
$852$	1.48171	0.0507625
$853$	−29.7239	−1.01773	−0.508864	−	0.860847i	$-0.669934\pi$
$853$	−29.7239	−1.01773	−0.508864	+	0.860847i	$0.669934\pi$
$854$	−0.414837	−0.0141954
$855$	−4.14234	−0.141665
$856$	5.32124	0.181876
$857$	−16.5202	−0.564320	−0.282160	−	0.959367i	$-0.591051\pi$
$857$	−16.5202	−0.564320	−0.282160	+	0.959367i	$0.591051\pi$
$858$	7.35231	0.251004
$859$	27.6703	0.944099	0.472049	−	0.881572i	$-0.343514\pi$
$859$	27.6703	0.944099	0.472049	+	0.881572i	$0.343514\pi$
$860$	8.44112	0.287840
$861$	−7.85953	−0.267852
$862$	−23.5643	−0.802603
$863$	15.7292	0.535427	0.267713	−	0.963499i	$-0.413732\pi$
$863$	15.7292	0.535427	0.267713	+	0.963499i	$0.413732\pi$
$864$	−1.74496	−0.0593646
$865$	14.1002	0.479423
$866$	11.9152	0.404893
$867$	39.0466	1.32609
$868$	0.667536	0.0226576
$869$	24.7999	0.841279
$870$	8.77782	0.297596
$871$	−15.1922	−0.514768
$872$	−0.774663	−0.0262334
$873$	−51.5754	−1.74556
$874$	−0.491215	−0.0166156
$875$	0.667536	0.0225668
$876$	−39.1528	−1.32285
$877$	−25.8797	−0.873896	−0.436948	−	0.899487i	$-0.643941\pi$
$877$	−25.8797	−0.873896	−0.436948	+	0.899487i	$0.643941\pi$
$878$	−40.6319	−1.37126
$879$	52.0965	1.75717
$880$	2.84568	0.0959278
$881$	−5.80538	−0.195588	−0.0977941	−	0.995207i	$-0.531179\pi$
$881$	−5.80538	−0.195588	−0.0977941	+	0.995207i	$0.531179\pi$
$882$	−24.0899	−0.811149
$883$	0.215006	0.00723552	0.00361776	−	0.999993i	$-0.498848\pi$
$883$	0.215006	0.00723552	0.00361776	+	0.999993i	$0.498848\pi$
$884$	1.37374	0.0462040
$885$	23.6866	0.796217
$886$	−21.8424	−0.733811
$887$	49.7454	1.67029	0.835144	−	0.550031i	$-0.185384\pi$
$887$	49.7454	1.67029	0.835144	+	0.550031i	$0.185384\pi$
$888$	−17.2237	−0.577990
$889$	−6.52258	−0.218760
$890$	−0.261768	−0.00877449
$891$	18.5474	0.621360
$892$	4.99819	0.167352
$893$	2.10759	0.0705276
$894$	3.28591	0.109897
$895$	22.3539	0.747207
$896$	−0.667536	−0.0223008
$897$	1.12607	0.0375984
$898$	5.96092	0.198919
$899$	−3.39742	−0.113310
$900$	3.67538	0.122513
$901$	8.37157	0.278898
$902$	12.9679	0.431784
$903$	−14.5584	−0.484472
$904$	0.172180	0.00572661
$905$	−3.13201	−0.104111
$906$	8.60259	0.285802
$907$	8.64404	0.287021	0.143510	−	0.989649i	$-0.454161\pi$
$907$	8.64404	0.287021	0.143510	+	0.989649i	$0.454161\pi$
$908$	−10.0209	−0.332556
$909$	−25.3576	−0.841060
$910$	0.667536	0.0221286
$911$	−18.2160	−0.603524	−0.301762	−	0.953383i	$-0.597575\pi$
$911$	−18.2160	−0.603524	−0.301762	+	0.953383i	$0.597575\pi$
$912$	−2.91193	−0.0964237
$913$	42.6198	1.41051
$914$	28.0231	0.926920
$915$	1.60561	0.0530800
$916$	−11.8143	−0.390355
$917$	10.1423	0.334927
$918$	−2.39712	−0.0791168
$919$	0.0211494	0.000697654 0	0.000348827	−	1.00000i	$-0.499889\pi$
$919$	0.0211494	0.000697654 0	0.000348827		1.00000i	$0.499889\pi$
$920$	0.435841	0.0143693
$921$	−4.22527	−0.139227
$922$	9.15109	0.301375
$923$	−0.573489	−0.0188766
$924$	−4.90793	−0.161459
$925$	6.66636	0.219189
$926$	16.0997	0.529069
$927$	69.8831	2.29526
$928$	3.39742	0.111526
$929$	33.7466	1.10719	0.553596	−	0.832785i	$-0.313255\pi$
$929$	33.7466	1.10719	0.553596	+	0.832785i	$0.313255\pi$
$930$	−2.58368	−0.0847220
$931$	−7.38714	−0.242104
$932$	18.3641	0.601538
$933$	−77.5981	−2.54045
$934$	1.88462	0.0616668
$935$	3.90923	0.127845
$936$	3.67538	0.120133
$937$	6.07998	0.198624	0.0993122	−	0.995056i	$-0.468336\pi$
$937$	6.07998	0.198624	0.0993122	+	0.995056i	$0.468336\pi$
$938$	10.1413	0.331126
$939$	−37.7232	−1.23105
$940$	−1.87000	−0.0609927
$941$	−20.2623	−0.660531	−0.330266	−	0.943888i	$-0.607138\pi$
$941$	−20.2623	−0.660531	−0.330266	+	0.943888i	$0.607138\pi$
$942$	4.65858	0.151785
$943$	1.98615	0.0646780
$944$	9.16780	0.298387
$945$	−1.16482	−0.0378916
$946$	24.0207	0.780980
$947$	−39.3941	−1.28014	−0.640069	−	0.768318i	$-0.721094\pi$
$947$	−39.3941	−1.28014	−0.640069	+	0.768318i	$0.721094\pi$
$948$	22.5166	0.731304
$949$	15.1539	0.491916
$950$	1.12705	0.0365664
$951$	−2.69150	−0.0872777
$952$	−0.917023	−0.0297209
$953$	−0.213052	−0.00690142	−0.00345071	−	0.999994i	$-0.501098\pi$
$953$	−0.213052	−0.00690142	−0.00345071	+	0.999994i	$0.501098\pi$
$954$	22.3977	0.725153
$955$	11.9729	0.387434
$956$	−15.7543	−0.509531
$957$	24.9788	0.807452
$958$	33.4694	1.08135
$959$	14.5788	0.470773
$960$	2.58368	0.0833878
$961$	1.00000	0.0322581
$962$	6.66636	0.214932
$963$	19.5576	0.630234
$964$	26.3281	0.847970
$965$	3.99866	0.128721
$966$	−0.751693	−0.0241853
$967$	−46.6253	−1.49937	−0.749685	−	0.661795i	$-0.769795\pi$
$967$	−46.6253	−1.49937	−0.749685	+	0.661795i	$0.769795\pi$
$968$	−2.90212	−0.0932777
$969$	−4.00025	−0.128506
$970$	14.0327	0.450562
$971$	26.2579	0.842657	0.421328	−	0.906908i	$-0.361564\pi$
$971$	26.2579	0.842657	0.421328	+	0.906908i	$0.361564\pi$
$972$	22.0746	0.708042
$973$	12.5097	0.401043
$974$	26.8466	0.860220
$975$	−2.58368	−0.0827438
$976$	0.621446	0.0198920
$977$	7.45597	0.238538	0.119269	−	0.992862i	$-0.461945\pi$
$977$	7.45597	0.238538	0.119269	+	0.992862i	$0.461945\pi$
$978$	−28.2779	−0.904229
$979$	−0.744908	−0.0238073
$980$	6.55440	0.209373
$981$	−2.84718	−0.0909034
$982$	18.1787	0.580105
$983$	−16.0620	−0.512298	−0.256149	−	0.966637i	$-0.582454\pi$
$983$	−16.0620	−0.512298	−0.256149	+	0.966637i	$0.582454\pi$
$984$	11.7739	0.375340
$985$	−13.0147	−0.414681
$986$	4.66718	0.148633
$987$	3.22518	0.102659
$988$	1.12705	0.0358563
$989$	3.67899	0.116985
$990$	10.4589	0.332407
$991$	35.1127	1.11539	0.557696	−	0.830045i	$-0.311686\pi$
$991$	35.1127	1.11539	0.557696	+	0.830045i	$0.311686\pi$
$992$	−1.00000	−0.0317500
$993$	68.9399	2.18774
$994$	0.382824	0.0121424
$995$	−12.8215	−0.406469
$996$	38.6958	1.22612
$997$	6.23411	0.197436	0.0987181	−	0.995115i	$-0.468526\pi$
$997$	6.23411	0.197436	0.0987181	+	0.995115i	$0.468526\pi$
$998$	−2.88109	−0.0911994
$999$	−11.6325	−0.368036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.f.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.f.1.1	✓	6	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.58368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.58368 q^{6} -0.667536 q^{7} +1.00000 q^{8} +3.67538 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.58368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.58368 q^{6} -0.667536 q^{7} +1.00000 q^{8} +3.67538 q^{9} -1.00000 q^{10} -2.84568 q^{11} -2.58368 q^{12} +1.00000 q^{13} -0.667536 q^{14} +2.58368 q^{15} +1.00000 q^{16} +1.37374 q^{17} +3.67538 q^{18} +1.12705 q^{19} -1.00000 q^{20} +1.72470 q^{21} -2.84568 q^{22} -0.435841 q^{23} -2.58368 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.74496 q^{27} -0.667536 q^{28} +3.39742 q^{29} +2.58368 q^{30} -1.00000 q^{31} +1.00000 q^{32} +7.35231 q^{33} +1.37374 q^{34} +0.667536 q^{35} +3.67538 q^{36} +6.66636 q^{37} +1.12705 q^{38} -2.58368 q^{39} -1.00000 q^{40} -4.55705 q^{41} +1.72470 q^{42} -8.44112 q^{43} -2.84568 q^{44} -3.67538 q^{45} -0.435841 q^{46} +1.87000 q^{47} -2.58368 q^{48} -6.55440 q^{49} +1.00000 q^{50} -3.54931 q^{51} +1.00000 q^{52} +6.09399 q^{53} -1.74496 q^{54} +2.84568 q^{55} -0.667536 q^{56} -2.91193 q^{57} +3.39742 q^{58} +9.16780 q^{59} +2.58368 q^{60} +0.621446 q^{61} -1.00000 q^{62} -2.45345 q^{63} +1.00000 q^{64} -1.00000 q^{65} +7.35231 q^{66} -15.1922 q^{67} +1.37374 q^{68} +1.12607 q^{69} +0.667536 q^{70} -0.573489 q^{71} +3.67538 q^{72} +15.1539 q^{73} +6.66636 q^{74} -2.58368 q^{75} +1.12705 q^{76} +1.89959 q^{77} -2.58368 q^{78} -8.71493 q^{79} -1.00000 q^{80} -6.51773 q^{81} -4.55705 q^{82} -14.9770 q^{83} +1.72470 q^{84} -1.37374 q^{85} -8.44112 q^{86} -8.77782 q^{87} -2.84568 q^{88} +0.261768 q^{89} -3.67538 q^{90} -0.667536 q^{91} -0.435841 q^{92} +2.58368 q^{93} +1.87000 q^{94} -1.12705 q^{95} -2.58368 q^{96} -14.0327 q^{97} -6.55440 q^{98} -10.4589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 6 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} - 8 q^{17} - q^{18} - 9 q^{19} - 6 q^{20} - 5 q^{21} - 4 q^{22} - 7 q^{23} - 3 q^{24} + 6 q^{25} + 6 q^{26} + 9 q^{27} - 2 q^{28} - 14 q^{29} + 3 q^{30} - 6 q^{31} + 6 q^{32} - 6 q^{33} - 8 q^{34} + 2 q^{35} - q^{36} - 9 q^{38} - 3 q^{39} - 6 q^{40} + 2 q^{41} - 5 q^{42} - 7 q^{43} - 4 q^{44} + q^{45} - 7 q^{46} - 8 q^{47} - 3 q^{48} - 14 q^{49} + 6 q^{50} - 5 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 14 q^{58} - 5 q^{59} + 3 q^{60} - 5 q^{61} - 6 q^{62} - 19 q^{63} + 6 q^{64} - 6 q^{65} - 6 q^{66} - 12 q^{67} - 8 q^{68} + 2 q^{70} - 10 q^{71} - q^{72} + 5 q^{73} - 3 q^{75} - 9 q^{76} - q^{77} - 3 q^{78} - 16 q^{79} - 6 q^{80} - 10 q^{81} + 2 q^{82} - 22 q^{83} - 5 q^{84} + 8 q^{85} - 7 q^{86} - 31 q^{87} - 4 q^{88} + 14 q^{89} + q^{90} - 2 q^{91} - 7 q^{92} + 3 q^{93} - 8 q^{94} + 9 q^{95} - 3 q^{96} - 9 q^{97} - 14 q^{98} - 21 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9 - 6 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 - 8 * q^17 - q^18 - 9 * q^19 - 6 * q^20 - 5 * q^21 - 4 * q^22 - 7 * q^23 - 3 * q^24 + 6 * q^25 + 6 * q^26 + 9 * q^27 - 2 * q^28 - 14 * q^29 + 3 * q^30 - 6 * q^31 + 6 * q^32 - 6 * q^33 - 8 * q^34 + 2 * q^35 - q^36 - 9 * q^38 - 3 * q^39 - 6 * q^40 + 2 * q^41 - 5 * q^42 - 7 * q^43 - 4 * q^44 + q^45 - 7 * q^46 - 8 * q^47 - 3 * q^48 - 14 * q^49 + 6 * q^50 - 5 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 14 * q^58 - 5 * q^59 + 3 * q^60 - 5 * q^61 - 6 * q^62 - 19 * q^63 + 6 * q^64 - 6 * q^65 - 6 * q^66 - 12 * q^67 - 8 * q^68 + 2 * q^70 - 10 * q^71 - q^72 + 5 * q^73 - 3 * q^75 - 9 * q^76 - q^77 - 3 * q^78 - 16 * q^79 - 6 * q^80 - 10 * q^81 + 2 * q^82 - 22 * q^83 - 5 * q^84 + 8 * q^85 - 7 * q^86 - 31 * q^87 - 4 * q^88 + 14 * q^89 + q^90 - 2 * q^91 - 7 * q^92 + 3 * q^93 - 8 * q^94 + 9 * q^95 - 3 * q^96 - 9 * q^97 - 14 * q^98 - 21 * q^99

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