LMFDB - Embedded newform 6034.2.a.k.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Root			$3.22416$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.22416 q^{3} +1.00000 q^{4} -3.48974 q^{5} -3.22416 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.39519 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.22416 q^{3} +1.00000 q^{4} -3.48974 q^{5} -3.22416 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.39519 q^{9} +3.48974 q^{10} -4.14566 q^{11} +3.22416 q^{12} +3.72278 q^{13} -1.00000 q^{14} -11.2515 q^{15} +1.00000 q^{16} +3.53638 q^{17} -7.39519 q^{18} -6.23343 q^{19} -3.48974 q^{20} +3.22416 q^{21} +4.14566 q^{22} -1.88248 q^{23} -3.22416 q^{24} +7.17825 q^{25} -3.72278 q^{26} +14.1708 q^{27} +1.00000 q^{28} -9.33944 q^{29} +11.2515 q^{30} -3.46997 q^{31} -1.00000 q^{32} -13.3663 q^{33} -3.53638 q^{34} -3.48974 q^{35} +7.39519 q^{36} -3.08522 q^{37} +6.23343 q^{38} +12.0028 q^{39} +3.48974 q^{40} -10.1002 q^{41} -3.22416 q^{42} +7.78000 q^{43} -4.14566 q^{44} -25.8073 q^{45} +1.88248 q^{46} -4.01738 q^{47} +3.22416 q^{48} +1.00000 q^{49} -7.17825 q^{50} +11.4018 q^{51} +3.72278 q^{52} -0.104233 q^{53} -14.1708 q^{54} +14.4673 q^{55} -1.00000 q^{56} -20.0975 q^{57} +9.33944 q^{58} -8.27180 q^{59} -11.2515 q^{60} +10.3390 q^{61} +3.46997 q^{62} +7.39519 q^{63} +1.00000 q^{64} -12.9915 q^{65} +13.3663 q^{66} -8.34891 q^{67} +3.53638 q^{68} -6.06941 q^{69} +3.48974 q^{70} +6.81433 q^{71} -7.39519 q^{72} +3.97477 q^{73} +3.08522 q^{74} +23.1438 q^{75} -6.23343 q^{76} -4.14566 q^{77} -12.0028 q^{78} -16.3625 q^{79} -3.48974 q^{80} +23.5032 q^{81} +10.1002 q^{82} +7.42416 q^{83} +3.22416 q^{84} -12.3410 q^{85} -7.78000 q^{86} -30.1118 q^{87} +4.14566 q^{88} -5.13768 q^{89} +25.8073 q^{90} +3.72278 q^{91} -1.88248 q^{92} -11.1877 q^{93} +4.01738 q^{94} +21.7530 q^{95} -3.22416 q^{96} +7.89549 q^{97} -1.00000 q^{98} -30.6580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * 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
$3$	3.22416	1.86147	0.930734	−	0.365697i	$-0.119169\pi$
$3$	3.22416	1.86147	0.930734	+	0.365697i	$0.119169\pi$
$4$	1.00000	0.500000
$5$	−3.48974	−1.56066	−0.780329	−	0.625370i	$-0.784948\pi$
$5$	−3.48974	−1.56066	−0.780329	+	0.625370i	$0.784948\pi$
$6$	−3.22416	−1.31626
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	7.39519	2.46506
$10$	3.48974	1.10355
$11$	−4.14566	−1.24996	−0.624982	−	0.780639i	$-0.714894\pi$
$11$	−4.14566	−1.24996	−0.624982	+	0.780639i	$0.714894\pi$
$12$	3.22416	0.930734
$13$	3.72278	1.03251	0.516257	−	0.856434i	$-0.327325\pi$
$13$	3.72278	1.03251	0.516257	+	0.856434i	$0.327325\pi$
$14$	−1.00000	−0.267261
$15$	−11.2515	−2.90511
$16$	1.00000	0.250000
$17$	3.53638	0.857698	0.428849	−	0.903376i	$-0.358919\pi$
$17$	3.53638	0.857698	0.428849	+	0.903376i	$0.358919\pi$
$18$	−7.39519	−1.74306
$19$	−6.23343	−1.43005	−0.715023	−	0.699101i	$-0.753584\pi$
$19$	−6.23343	−1.43005	−0.715023	+	0.699101i	$0.753584\pi$
$20$	−3.48974	−0.780329
$21$	3.22416	0.703569
$22$	4.14566	0.883858
$23$	−1.88248	−0.392524	−0.196262	−	0.980551i	$-0.562880\pi$
$23$	−1.88248	−0.392524	−0.196262	+	0.980551i	$0.562880\pi$
$24$	−3.22416	−0.658128
$25$	7.17825	1.43565
$26$	−3.72278	−0.730097
$27$	14.1708	2.72717
$28$	1.00000	0.188982
$29$	−9.33944	−1.73429	−0.867145	−	0.498055i	$-0.834048\pi$
$29$	−9.33944	−1.73429	−0.867145	+	0.498055i	$0.834048\pi$
$30$	11.2515	2.05423
$31$	−3.46997	−0.623225	−0.311612	−	0.950209i	$-0.600869\pi$
$31$	−3.46997	−0.623225	−0.311612	+	0.950209i	$0.600869\pi$
$32$	−1.00000	−0.176777
$33$	−13.3663	−2.32677
$34$	−3.53638	−0.606484
$35$	−3.48974	−0.589873
$36$	7.39519	1.23253
$37$	−3.08522	−0.507207	−0.253603	−	0.967308i	$-0.581616\pi$
$37$	−3.08522	−0.507207	−0.253603	+	0.967308i	$0.581616\pi$
$38$	6.23343	1.01120
$39$	12.0028	1.92199
$40$	3.48974	0.551776
$41$	−10.1002	−1.57739	−0.788695	−	0.614784i	$-0.789243\pi$
$41$	−10.1002	−1.57739	−0.788695	+	0.614784i	$0.789243\pi$
$42$	−3.22416	−0.497498
$43$	7.78000	1.18644	0.593219	−	0.805041i	$-0.297857\pi$
$43$	7.78000	1.18644	0.593219	+	0.805041i	$0.297857\pi$
$44$	−4.14566	−0.624982
$45$	−25.8073	−3.84712
$46$	1.88248	0.277557
$47$	−4.01738	−0.585996	−0.292998	−	0.956113i	$-0.594653\pi$
$47$	−4.01738	−0.585996	−0.292998	+	0.956113i	$0.594653\pi$
$48$	3.22416	0.465367
$49$	1.00000	0.142857
$50$	−7.17825	−1.01516
$51$	11.4018	1.59658
$52$	3.72278	0.516257
$53$	−0.104233	−0.0143176	−0.00715879	−	0.999974i	$-0.502279\pi$
$53$	−0.104233	−0.0143176	−0.00715879	+	0.999974i	$0.502279\pi$
$54$	−14.1708	−1.92840
$55$	14.4673	1.95077
$56$	−1.00000	−0.133631
$57$	−20.0975	−2.66198
$58$	9.33944	1.22633
$59$	−8.27180	−1.07690	−0.538448	−	0.842659i	$-0.680989\pi$
$59$	−8.27180	−1.07690	−0.538448	+	0.842659i	$0.680989\pi$
$60$	−11.2515	−1.45256
$61$	10.3390	1.32377	0.661887	−	0.749604i	$-0.269756\pi$
$61$	10.3390	1.32377	0.661887	+	0.749604i	$0.269756\pi$
$62$	3.46997	0.440686
$63$	7.39519	0.931706
$64$	1.00000	0.125000
$65$	−12.9915	−1.61140
$66$	13.3663	1.64527
$67$	−8.34891	−1.01998	−0.509991	−	0.860180i	$-0.670351\pi$
$67$	−8.34891	−1.01998	−0.509991	+	0.860180i	$0.670351\pi$
$68$	3.53638	0.428849
$69$	−6.06941	−0.730671
$70$	3.48974	0.417103
$71$	6.81433	0.808712	0.404356	−	0.914602i	$-0.367496\pi$
$71$	6.81433	0.808712	0.404356	+	0.914602i	$0.367496\pi$
$72$	−7.39519	−0.871531
$73$	3.97477	0.465212	0.232606	−	0.972571i	$-0.425275\pi$
$73$	3.97477	0.465212	0.232606	+	0.972571i	$0.425275\pi$
$74$	3.08522	0.358649
$75$	23.1438	2.67242
$76$	−6.23343	−0.715023
$77$	−4.14566	−0.472442
$78$	−12.0028	−1.35905
$79$	−16.3625	−1.84093	−0.920463	−	0.390829i	$-0.872188\pi$
$79$	−16.3625	−1.84093	−0.920463	+	0.390829i	$0.872188\pi$
$80$	−3.48974	−0.390164
$81$	23.5032	2.61147
$82$	10.1002	1.11538
$83$	7.42416	0.814907	0.407454	−	0.913226i	$-0.366417\pi$
$83$	7.42416	0.814907	0.407454	+	0.913226i	$0.366417\pi$
$84$	3.22416	0.351784
$85$	−12.3410	−1.33857
$86$	−7.78000	−0.838939
$87$	−30.1118	−3.22833
$88$	4.14566	0.441929
$89$	−5.13768	−0.544593	−0.272296	−	0.962213i	$-0.587783\pi$
$89$	−5.13768	−0.544593	−0.272296	+	0.962213i	$0.587783\pi$
$90$	25.8073	2.72032
$91$	3.72278	0.390253
$92$	−1.88248	−0.196262
$93$	−11.1877	−1.16011
$94$	4.01738	0.414362
$95$	21.7530	2.23181
$96$	−3.22416	−0.329064
$97$	7.89549	0.801665	0.400833	−	0.916151i	$-0.368721\pi$
$97$	7.89549	0.801665	0.400833	+	0.916151i	$0.368721\pi$
$98$	−1.00000	−0.101015
$99$	−30.6580	−3.08124
$100$	7.17825	0.717825
$101$	−14.9853	−1.49109	−0.745545	−	0.666456i	$-0.767811\pi$
$101$	−14.9853	−1.49109	−0.745545	+	0.666456i	$0.767811\pi$
$102$	−11.4018	−1.12895
$103$	−12.5004	−1.23170	−0.615848	−	0.787865i	$-0.711187\pi$
$103$	−12.5004	−1.23170	−0.615848	+	0.787865i	$0.711187\pi$
$104$	−3.72278	−0.365049
$105$	−11.2515	−1.09803
$106$	0.104233	0.0101241
$107$	−2.67499	−0.258601	−0.129300	−	0.991605i	$-0.541273\pi$
$107$	−2.67499	−0.258601	−0.129300	+	0.991605i	$0.541273\pi$
$108$	14.1708	1.36358
$109$	13.1554	1.26006	0.630028	−	0.776573i	$-0.283044\pi$
$109$	13.1554	1.26006	0.630028	+	0.776573i	$0.283044\pi$
$110$	−14.4673	−1.37940
$111$	−9.94722	−0.944149
$112$	1.00000	0.0944911
$113$	−7.68133	−0.722599	−0.361299	−	0.932450i	$-0.617667\pi$
$113$	−7.68133	−0.722599	−0.361299	+	0.932450i	$0.617667\pi$
$114$	20.0975	1.88231
$115$	6.56936	0.612596
$116$	−9.33944	−0.867145
$117$	27.5307	2.54521
$118$	8.27180	0.761481
$119$	3.53638	0.324179
$120$	11.2515	1.02711
$121$	6.18653	0.562412
$122$	−10.3390	−0.936049
$123$	−32.5647	−2.93626
$124$	−3.46997	−0.311612
$125$	−7.60153	−0.679901
$126$	−7.39519	−0.658816
$127$	−22.2794	−1.97698	−0.988488	−	0.151296i	$-0.951655\pi$
$127$	−22.2794	−1.97698	−0.988488	+	0.151296i	$0.951655\pi$
$128$	−1.00000	−0.0883883
$129$	25.0839	2.20852
$130$	12.9915	1.13943
$131$	2.02630	0.177039	0.0885193	−	0.996074i	$-0.471787\pi$
$131$	2.02630	0.177039	0.0885193	+	0.996074i	$0.471787\pi$
$132$	−13.3663	−1.16338
$133$	−6.23343	−0.540507
$134$	8.34891	0.721236
$135$	−49.4523	−4.25617
$136$	−3.53638	−0.303242
$137$	6.05258	0.517107	0.258553	−	0.965997i	$-0.416754\pi$
$137$	6.05258	0.517107	0.258553	+	0.965997i	$0.416754\pi$
$138$	6.06941	0.516663
$139$	7.52313	0.638104	0.319052	−	0.947737i	$-0.396636\pi$
$139$	7.52313	0.638104	0.319052	+	0.947737i	$0.396636\pi$
$140$	−3.48974	−0.294936
$141$	−12.9527	−1.09081
$142$	−6.81433	−0.571846
$143$	−15.4334	−1.29061
$144$	7.39519	0.616266
$145$	32.5922	2.70663
$146$	−3.97477	−0.328955
$147$	3.22416	0.265924
$148$	−3.08522	−0.253603
$149$	12.8892	1.05593	0.527964	−	0.849267i	$-0.322956\pi$
$149$	12.8892	1.05593	0.527964	+	0.849267i	$0.322956\pi$
$150$	−23.1438	−1.88968
$151$	8.76175	0.713021	0.356511	−	0.934291i	$-0.383966\pi$
$151$	8.76175	0.713021	0.356511	+	0.934291i	$0.383966\pi$
$152$	6.23343	0.505598
$153$	26.1522	2.11428
$154$	4.14566	0.334067
$155$	12.1093	0.972640
$156$	12.0028	0.960995
$157$	17.5830	1.40328	0.701638	−	0.712534i	$-0.252453\pi$
$157$	17.5830	1.40328	0.701638	+	0.712534i	$0.252453\pi$
$158$	16.3625	1.30173
$159$	−0.336065	−0.0266517
$160$	3.48974	0.275888
$161$	−1.88248	−0.148360
$162$	−23.5032	−1.84659
$163$	−0.928501	−0.0727258	−0.0363629	−	0.999339i	$-0.511577\pi$
$163$	−0.928501	−0.0727258	−0.0363629	+	0.999339i	$0.511577\pi$
$164$	−10.1002	−0.788695
$165$	46.6447	3.63129
$166$	−7.42416	−0.576226
$167$	−11.1798	−0.865119	−0.432560	−	0.901605i	$-0.642389\pi$
$167$	−11.1798	−0.865119	−0.432560	+	0.901605i	$0.642389\pi$
$168$	−3.22416	−0.248749
$169$	0.859091	0.0660839
$170$	12.3410	0.946514
$171$	−46.0974	−3.52515
$172$	7.78000	0.593219
$173$	−1.82547	−0.138788	−0.0693938	−	0.997589i	$-0.522106\pi$
$173$	−1.82547	−0.138788	−0.0693938	+	0.997589i	$0.522106\pi$
$174$	30.1118	2.28277
$175$	7.17825	0.542625
$176$	−4.14566	−0.312491
$177$	−26.6696	−2.00461
$178$	5.13768	0.385085
$179$	19.3511	1.44637	0.723186	−	0.690653i	$-0.242677\pi$
$179$	19.3511	1.44637	0.723186	+	0.690653i	$0.242677\pi$
$180$	−25.8073	−1.92356
$181$	−24.3180	−1.80754	−0.903771	−	0.428016i	$-0.859213\pi$
$181$	−24.3180	−1.80754	−0.903771	+	0.428016i	$0.859213\pi$
$182$	−3.72278	−0.275951
$183$	33.3346	2.46416
$184$	1.88248	0.138778
$185$	10.7666	0.791576
$186$	11.1877	0.820324
$187$	−14.6606	−1.07209
$188$	−4.01738	−0.292998
$189$	14.1708	1.03077
$190$	−21.7530	−1.57813
$191$	18.0451	1.30570	0.652849	−	0.757488i	$-0.273574\pi$
$191$	18.0451	1.30570	0.652849	+	0.757488i	$0.273574\pi$
$192$	3.22416	0.232683
$193$	−5.99571	−0.431581	−0.215790	−	0.976440i	$-0.569233\pi$
$193$	−5.99571	−0.431581	−0.215790	+	0.976440i	$0.569233\pi$
$194$	−7.89549	−0.566863
$195$	−41.8867	−2.99957
$196$	1.00000	0.0714286
$197$	−8.19177	−0.583639	−0.291820	−	0.956473i	$-0.594261\pi$
$197$	−8.19177	−0.583639	−0.291820	+	0.956473i	$0.594261\pi$
$198$	30.6580	2.17877
$199$	−10.3582	−0.734270	−0.367135	−	0.930168i	$-0.619661\pi$
$199$	−10.3582	−0.734270	−0.367135	+	0.930168i	$0.619661\pi$
$200$	−7.17825	−0.507579
$201$	−26.9182	−1.89866
$202$	14.9853	1.05436
$203$	−9.33944	−0.655500
$204$	11.4018	0.798289
$205$	35.2471	2.46177
$206$	12.5004	0.870941
$207$	−13.9213	−0.967597
$208$	3.72278	0.258128
$209$	25.8417	1.78751
$210$	11.2515	0.776424
$211$	−4.98230	−0.342996	−0.171498	−	0.985184i	$-0.554861\pi$
$211$	−4.98230	−0.342996	−0.171498	+	0.985184i	$0.554861\pi$
$212$	−0.104233	−0.00715879
$213$	21.9705	1.50539
$214$	2.67499	0.182858
$215$	−27.1501	−1.85162
$216$	−14.1708	−0.964199
$217$	−3.46997	−0.235557
$218$	−13.1554	−0.890994
$219$	12.8153	0.865977
$220$	14.4673	0.975383
$221$	13.1652	0.885585
$222$	9.94722	0.667614
$223$	−25.2002	−1.68753	−0.843764	−	0.536714i	$-0.819666\pi$
$223$	−25.2002	−1.68753	−0.843764	+	0.536714i	$0.819666\pi$
$224$	−1.00000	−0.0668153
$225$	53.0845	3.53897
$226$	7.68133	0.510954
$227$	4.55258	0.302165	0.151083	−	0.988521i	$-0.451724\pi$
$227$	4.55258	0.302165	0.151083	+	0.988521i	$0.451724\pi$
$228$	−20.0975	−1.33099
$229$	−15.8423	−1.04689	−0.523446	−	0.852059i	$-0.675354\pi$
$229$	−15.8423	−1.04689	−0.523446	+	0.852059i	$0.675354\pi$
$230$	−6.56936	−0.433171
$231$	−13.3663	−0.879436
$232$	9.33944	0.613164
$233$	−20.3230	−1.33140	−0.665701	−	0.746219i	$-0.731867\pi$
$233$	−20.3230	−1.33140	−0.665701	+	0.746219i	$0.731867\pi$
$234$	−27.5307	−1.79974
$235$	14.0196	0.914539
$236$	−8.27180	−0.538448
$237$	−52.7553	−3.42683
$238$	−3.53638	−0.229229
$239$	−18.9143	−1.22346	−0.611731	−	0.791066i	$-0.709527\pi$
$239$	−18.9143	−1.22346	−0.611731	+	0.791066i	$0.709527\pi$
$240$	−11.2515	−0.726278
$241$	14.7686	0.951331	0.475665	−	0.879626i	$-0.342207\pi$
$241$	14.7686	0.951331	0.475665	+	0.879626i	$0.342207\pi$
$242$	−6.18653	−0.397685
$243$	33.2658	2.13400
$244$	10.3390	0.661887
$245$	−3.48974	−0.222951
$246$	32.5647	2.07625
$247$	−23.2057	−1.47654
$248$	3.46997	0.220343
$249$	23.9367	1.51692
$250$	7.60153	0.480763
$251$	−28.0143	−1.76824	−0.884122	−	0.467255i	$-0.845243\pi$
$251$	−28.0143	−1.76824	−0.884122	+	0.467255i	$0.845243\pi$
$252$	7.39519	0.465853
$253$	7.80413	0.490642
$254$	22.2794	1.39793
$255$	−39.7894	−2.49171
$256$	1.00000	0.0625000
$257$	23.5510	1.46907	0.734535	−	0.678570i	$-0.237400\pi$
$257$	23.5510	1.46907	0.734535	+	0.678570i	$0.237400\pi$
$258$	−25.0839	−1.56166
$259$	−3.08522	−0.191706
$260$	−12.9915	−0.805700
$261$	−69.0669	−4.27513
$262$	−2.02630	−0.125185
$263$	−17.2789	−1.06546	−0.532732	−	0.846284i	$-0.678835\pi$
$263$	−17.2789	−1.06546	−0.532732	+	0.846284i	$0.678835\pi$
$264$	13.3663	0.822637
$265$	0.363747	0.0223448
$266$	6.23343	0.382196
$267$	−16.5647	−1.01374
$268$	−8.34891	−0.509991
$269$	15.3522	0.936038	0.468019	−	0.883718i	$-0.344968\pi$
$269$	15.3522	0.936038	0.468019	+	0.883718i	$0.344968\pi$
$270$	49.4523	3.00957
$271$	−25.8166	−1.56824	−0.784122	−	0.620606i	$-0.786886\pi$
$271$	−25.8166	−1.56824	−0.784122	+	0.620606i	$0.786886\pi$
$272$	3.53638	0.214424
$273$	12.0028	0.726444
$274$	−6.05258	−0.365650
$275$	−29.7586	−1.79451
$276$	−6.06941	−0.365336
$277$	0.456807	0.0274469	0.0137234	−	0.999906i	$-0.495632\pi$
$277$	0.456807	0.0274469	0.0137234	+	0.999906i	$0.495632\pi$
$278$	−7.52313	−0.451208
$279$	−25.6611	−1.53629
$280$	3.48974	0.208552
$281$	−4.04721	−0.241436	−0.120718	−	0.992687i	$-0.538520\pi$
$281$	−4.04721	−0.241436	−0.120718	+	0.992687i	$0.538520\pi$
$282$	12.9527	0.771321
$283$	−11.7380	−0.697751	−0.348875	−	0.937169i	$-0.613436\pi$
$283$	−11.7380	−0.697751	−0.348875	+	0.937169i	$0.613436\pi$
$284$	6.81433	0.404356
$285$	70.1351	4.15445
$286$	15.4334	0.912596
$287$	−10.1002	−0.596198
$288$	−7.39519	−0.435766
$289$	−4.49402	−0.264354
$290$	−32.5922	−1.91388
$291$	25.4563	1.49227
$292$	3.97477	0.232606
$293$	−16.6689	−0.973805	−0.486902	−	0.873456i	$-0.661873\pi$
$293$	−16.6689	−0.973805	−0.486902	+	0.873456i	$0.661873\pi$
$294$	−3.22416	−0.188037
$295$	28.8664	1.68067
$296$	3.08522	0.179325
$297$	−58.7473	−3.40886
$298$	−12.8892	−0.746654
$299$	−7.00806	−0.405287
$300$	23.1438	1.33621
$301$	7.78000	0.448432
$302$	−8.76175	−0.504182
$303$	−48.3148	−2.77561
$304$	−6.23343	−0.357512
$305$	−36.0804	−2.06596
$306$	−26.1522	−1.49502
$307$	−18.5756	−1.06017	−0.530083	−	0.847946i	$-0.677839\pi$
$307$	−18.5756	−1.06017	−0.530083	+	0.847946i	$0.677839\pi$
$308$	−4.14566	−0.236221
$309$	−40.3031	−2.29276
$310$	−12.1093	−0.687760
$311$	33.2068	1.88299	0.941493	−	0.337034i	$-0.109424\pi$
$311$	33.2068	1.88299	0.941493	+	0.337034i	$0.109424\pi$
$312$	−12.0028	−0.679526
$313$	−8.45699	−0.478017	−0.239009	−	0.971017i	$-0.576822\pi$
$313$	−8.45699	−0.478017	−0.239009	+	0.971017i	$0.576822\pi$
$314$	−17.5830	−0.992266
$315$	−25.8073	−1.45407
$316$	−16.3625	−0.920463
$317$	11.1732	0.627552	0.313776	−	0.949497i	$-0.398406\pi$
$317$	11.1732	0.627552	0.313776	+	0.949497i	$0.398406\pi$
$318$	0.336065	0.0188456
$319$	38.7182	2.16780
$320$	−3.48974	−0.195082
$321$	−8.62458	−0.481377
$322$	1.88248	0.104907
$323$	−22.0438	−1.22655
$324$	23.5032	1.30574
$325$	26.7231	1.48233
$326$	0.928501	0.0514249
$327$	42.4150	2.34555
$328$	10.1002	0.557692
$329$	−4.01738	−0.221486
$330$	−46.6447	−2.56771
$331$	27.2743	1.49913	0.749565	−	0.661931i	$-0.230263\pi$
$331$	27.2743	1.49913	0.749565	+	0.661931i	$0.230263\pi$
$332$	7.42416	0.407454
$333$	−22.8158	−1.25030
$334$	11.1798	0.611732
$335$	29.1355	1.59184
$336$	3.22416	0.175892
$337$	0.393486	0.0214345	0.0107173	−	0.999943i	$-0.496589\pi$
$337$	0.393486	0.0214345	0.0107173	+	0.999943i	$0.496589\pi$
$338$	−0.859091	−0.0467284
$339$	−24.7658	−1.34509
$340$	−12.3410	−0.669286
$341$	14.3853	0.779009
$342$	46.0974	2.49266
$343$	1.00000	0.0539949
$344$	−7.78000	−0.419469
$345$	21.1806	1.14033
$346$	1.82547	0.0981376
$347$	22.1462	1.18887	0.594436	−	0.804143i	$-0.297375\pi$
$347$	22.1462	1.18887	0.594436	+	0.804143i	$0.297375\pi$
$348$	−30.1118	−1.61416
$349$	25.7685	1.37936	0.689679	−	0.724115i	$-0.257752\pi$
$349$	25.7685	1.37936	0.689679	+	0.724115i	$0.257752\pi$
$350$	−7.17825	−0.383694
$351$	52.7547	2.81584
$352$	4.14566	0.220965
$353$	−20.6010	−1.09648	−0.548241	−	0.836320i	$-0.684702\pi$
$353$	−20.6010	−1.09648	−0.548241	+	0.836320i	$0.684702\pi$
$354$	26.6696	1.41747
$355$	−23.7802	−1.26212
$356$	−5.13768	−0.272296
$357$	11.4018	0.603449
$358$	−19.3511	−1.02274
$359$	−18.5082	−0.976828	−0.488414	−	0.872612i	$-0.662424\pi$
$359$	−18.5082	−0.976828	−0.488414	+	0.872612i	$0.662424\pi$
$360$	25.8073	1.36016
$361$	19.8556	1.04503
$362$	24.3180	1.27813
$363$	19.9463	1.04691
$364$	3.72278	0.195127
$365$	−13.8709	−0.726037
$366$	−33.3346	−1.74243
$367$	−27.9377	−1.45834	−0.729168	−	0.684335i	$-0.760093\pi$
$367$	−27.9377	−1.45834	−0.729168	+	0.684335i	$0.760093\pi$
$368$	−1.88248	−0.0981311
$369$	−74.6931	−3.88837
$370$	−10.7666	−0.559728
$371$	−0.104233	−0.00541153
$372$	−11.1877	−0.580056
$373$	−30.4042	−1.57427	−0.787136	−	0.616779i	$-0.788437\pi$
$373$	−30.4042	−1.57427	−0.787136	+	0.616779i	$0.788437\pi$
$374$	14.6606	0.758084
$375$	−24.5085	−1.26561
$376$	4.01738	0.207181
$377$	−34.7687	−1.79068
$378$	−14.1708	−0.728866
$379$	−26.2869	−1.35026	−0.675132	−	0.737697i	$-0.735914\pi$
$379$	−26.2869	−1.35026	−0.675132	+	0.737697i	$0.735914\pi$
$380$	21.7530	1.11591
$381$	−71.8323	−3.68008
$382$	−18.0451	−0.923268
$383$	−12.9465	−0.661533	−0.330767	−	0.943713i	$-0.607307\pi$
$383$	−12.9465	−0.661533	−0.330767	+	0.943713i	$0.607307\pi$
$384$	−3.22416	−0.164532
$385$	14.4673	0.737320
$386$	5.99571	0.305174
$387$	57.5346	2.92465
$388$	7.89549	0.400833
$389$	−16.5509	−0.839163	−0.419581	−	0.907718i	$-0.637823\pi$
$389$	−16.5509	−0.839163	−0.419581	+	0.907718i	$0.637823\pi$
$390$	41.8867	2.12102
$391$	−6.65717	−0.336667
$392$	−1.00000	−0.0505076
$393$	6.53311	0.329552
$394$	8.19177	0.412695
$395$	57.1008	2.87305
$396$	−30.6580	−1.54062
$397$	−2.22410	−0.111625	−0.0558123	−	0.998441i	$-0.517775\pi$
$397$	−2.22410	−0.111625	−0.0558123	+	0.998441i	$0.517775\pi$
$398$	10.3582	0.519207
$399$	−20.0975	−1.00614
$400$	7.17825	0.358913
$401$	5.19681	0.259516	0.129758	−	0.991546i	$-0.458580\pi$
$401$	5.19681	0.259516	0.129758	+	0.991546i	$0.458580\pi$
$402$	26.9182	1.34256
$403$	−12.9179	−0.643488
$404$	−14.9853	−0.745545
$405$	−82.0201	−4.07561
$406$	9.33944	0.463509
$407$	12.7903	0.633990
$408$	−11.4018	−0.564475
$409$	35.2966	1.74530	0.872652	−	0.488342i	$-0.162398\pi$
$409$	35.2966	1.74530	0.872652	+	0.488342i	$0.162398\pi$
$410$	−35.2471	−1.74073
$411$	19.5145	0.962577
$412$	−12.5004	−0.615848
$413$	−8.27180	−0.407029
$414$	13.9213	0.684195
$415$	−25.9083	−1.27179
$416$	−3.72278	−0.182524
$417$	24.2558	1.18781
$418$	−25.8417	−1.26396
$419$	0.515179	0.0251681	0.0125841	−	0.999921i	$-0.495994\pi$
$419$	0.515179	0.0251681	0.0125841	+	0.999921i	$0.495994\pi$
$420$	−11.2515	−0.549015
$421$	−0.373477	−0.0182022	−0.00910108	−	0.999959i	$-0.502897\pi$
$421$	−0.373477	−0.0182022	−0.00910108	+	0.999959i	$0.502897\pi$
$422$	4.98230	0.242535
$423$	−29.7093	−1.44452
$424$	0.104233	0.00506203
$425$	25.3850	1.23135
$426$	−21.9705	−1.06447
$427$	10.3390	0.500339
$428$	−2.67499	−0.129300
$429$	−49.7597	−2.40242
$430$	27.1501	1.30930
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	14.1708	0.681792
$433$	−2.01155	−0.0966691	−0.0483346	−	0.998831i	$-0.515391\pi$
$433$	−2.01155	−0.0966691	−0.0483346	+	0.998831i	$0.515391\pi$
$434$	3.46997	0.166564
$435$	105.082	5.03831
$436$	13.1554	0.630028
$437$	11.7343	0.561328
$438$	−12.8153	−0.612338
$439$	20.8844	0.996760	0.498380	−	0.866959i	$-0.333928\pi$
$439$	20.8844	0.996760	0.498380	+	0.866959i	$0.333928\pi$
$440$	−14.4673	−0.689700
$441$	7.39519	0.352152
$442$	−13.1652	−0.626203
$443$	37.3861	1.77627	0.888134	−	0.459584i	$-0.152001\pi$
$443$	37.3861	1.77627	0.888134	+	0.459584i	$0.152001\pi$
$444$	−9.94722	−0.472074
$445$	17.9291	0.849923
$446$	25.2002	1.19326
$447$	41.5570	1.96558
$448$	1.00000	0.0472456
$449$	−0.950254	−0.0448453	−0.0224226	−	0.999749i	$-0.507138\pi$
$449$	−0.950254	−0.0448453	−0.0224226	+	0.999749i	$0.507138\pi$
$450$	−53.0845	−2.50243
$451$	41.8722	1.97168
$452$	−7.68133	−0.361299
$453$	28.2493	1.32727
$454$	−4.55258	−0.213663
$455$	−12.9915	−0.609052
$456$	20.0975	0.941154
$457$	1.71503	0.0802258	0.0401129	−	0.999195i	$-0.487228\pi$
$457$	1.71503	0.0802258	0.0401129	+	0.999195i	$0.487228\pi$
$458$	15.8423	0.740264
$459$	50.1132	2.33909
$460$	6.56936	0.306298
$461$	38.5168	1.79391	0.896953	−	0.442126i	$-0.145776\pi$
$461$	38.5168	1.79391	0.896953	+	0.442126i	$0.145776\pi$
$462$	13.3663	0.621855
$463$	15.6597	0.727768	0.363884	−	0.931444i	$-0.381450\pi$
$463$	15.6597	0.727768	0.363884	+	0.931444i	$0.381450\pi$
$464$	−9.33944	−0.433573
$465$	39.0422	1.81054
$466$	20.3230	0.941443
$467$	−37.6936	−1.74425	−0.872125	−	0.489283i	$-0.837259\pi$
$467$	−37.6936	−1.74425	−0.872125	+	0.489283i	$0.837259\pi$
$468$	27.5307	1.27261
$469$	−8.34891	−0.385517
$470$	−14.0196	−0.646676
$471$	56.6903	2.61215
$472$	8.27180	0.380740
$473$	−32.2533	−1.48301
$474$	52.7553	2.42313
$475$	−44.7451	−2.05305
$476$	3.53638	0.162090
$477$	−0.770826	−0.0352937
$478$	18.9143	0.865119
$479$	−30.3757	−1.38790	−0.693951	−	0.720023i	$-0.744131\pi$
$479$	−30.3757	−1.38790	−0.693951	+	0.720023i	$0.744131\pi$
$480$	11.2515	0.513556
$481$	−11.4856	−0.523698
$482$	−14.7686	−0.672692
$483$	−6.06941	−0.276168
$484$	6.18653	0.281206
$485$	−27.5532	−1.25112
$486$	−33.2658	−1.50897
$487$	−6.79874	−0.308080	−0.154040	−	0.988065i	$-0.549229\pi$
$487$	−6.79874	−0.308080	−0.154040	+	0.988065i	$0.549229\pi$
$488$	−10.3390	−0.468025
$489$	−2.99363	−0.135377
$490$	3.48974	0.157650
$491$	−14.6502	−0.661153	−0.330577	−	0.943779i	$-0.607243\pi$
$491$	−14.6502	−0.661153	−0.330577	+	0.943779i	$0.607243\pi$
$492$	−32.5647	−1.46813
$493$	−33.0278	−1.48750
$494$	23.2057	1.04407
$495$	106.988	4.80876
$496$	−3.46997	−0.155806
$497$	6.81433	0.305665
$498$	−23.9367	−1.07263
$499$	13.0311	0.583350	0.291675	−	0.956517i	$-0.405787\pi$
$499$	13.0311	0.583350	0.291675	+	0.956517i	$0.405787\pi$
$500$	−7.60153	−0.339951
$501$	−36.0454	−1.61039
$502$	28.0143	1.25034
$503$	20.8676	0.930440	0.465220	−	0.885195i	$-0.345975\pi$
$503$	20.8676	0.930440	0.465220	+	0.885195i	$0.345975\pi$
$504$	−7.39519	−0.329408
$505$	52.2946	2.32708
$506$	−7.80413	−0.346936
$507$	2.76984	0.123013
$508$	−22.2794	−0.988488
$509$	12.7009	0.562959	0.281480	−	0.959567i	$-0.409175\pi$
$509$	12.7009	0.562959	0.281480	+	0.959567i	$0.409175\pi$
$510$	39.7894	1.76190
$511$	3.97477	0.175834
$512$	−1.00000	−0.0441942
$513$	−88.3325	−3.89998
$514$	−23.5510	−1.03879
$515$	43.6229	1.92226
$516$	25.0839	1.10426
$517$	16.6547	0.732474
$518$	3.08522	0.135557
$519$	−5.88559	−0.258349
$520$	12.9915	0.569716
$521$	20.5229	0.899125	0.449563	−	0.893249i	$-0.351580\pi$
$521$	20.5229	0.899125	0.449563	+	0.893249i	$0.351580\pi$
$522$	69.0669	3.02298
$523$	23.2294	1.01575	0.507874	−	0.861431i	$-0.330431\pi$
$523$	23.2294	1.01575	0.507874	+	0.861431i	$0.330431\pi$
$524$	2.02630	0.0885193
$525$	23.1438	1.01008
$526$	17.2789	0.753396
$527$	−12.2711	−0.534539
$528$	−13.3663	−0.581692
$529$	−19.4563	−0.845925
$530$	−0.363747	−0.0158002
$531$	−61.1715	−2.65462
$532$	−6.23343	−0.270253
$533$	−37.6009	−1.62868
$534$	16.5647	0.716824
$535$	9.33500	0.403587
$536$	8.34891	0.360618
$537$	62.3911	2.69238
$538$	−15.3522	−0.661879
$539$	−4.14566	−0.178566
$540$	−49.4523	−2.12809
$541$	14.5699	0.626411	0.313205	−	0.949685i	$-0.398597\pi$
$541$	14.5699	0.626411	0.313205	+	0.949685i	$0.398597\pi$
$542$	25.8166	1.10892
$543$	−78.4050	−3.36468
$544$	−3.53638	−0.151621
$545$	−45.9087	−1.96651
$546$	−12.0028	−0.513674
$547$	42.5890	1.82097	0.910487	−	0.413539i	$-0.135707\pi$
$547$	42.5890	1.82097	0.910487	+	0.413539i	$0.135707\pi$
$548$	6.05258	0.258553
$549$	76.4589	3.26319
$550$	29.7586	1.26891
$551$	58.2167	2.48012
$552$	6.06941	0.258331
$553$	−16.3625	−0.695805
$554$	−0.456807	−0.0194079
$555$	34.7132	1.47349
$556$	7.52313	0.319052
$557$	22.7072	0.962136	0.481068	−	0.876683i	$-0.340249\pi$
$557$	22.7072	0.962136	0.481068	+	0.876683i	$0.340249\pi$
$558$	25.6611	1.08632
$559$	28.9632	1.22501
$560$	−3.48974	−0.147468
$561$	−47.2682	−1.99566
$562$	4.04721	0.170721
$563$	−18.4220	−0.776396	−0.388198	−	0.921576i	$-0.626902\pi$
$563$	−18.4220	−0.776396	−0.388198	+	0.921576i	$0.626902\pi$
$564$	−12.9527	−0.545406
$565$	26.8058	1.12773
$566$	11.7380	0.493384
$567$	23.5032	0.987044
$568$	−6.81433	−0.285923
$569$	5.43151	0.227701	0.113850	−	0.993498i	$-0.463682\pi$
$569$	5.43151	0.227701	0.113850	+	0.993498i	$0.463682\pi$
$570$	−70.1351	−2.93764
$571$	41.0634	1.71845	0.859225	−	0.511598i	$-0.170946\pi$
$571$	41.0634	1.71845	0.859225	+	0.511598i	$0.170946\pi$
$572$	−15.4334	−0.645303
$573$	58.1803	2.43052
$574$	10.1002	0.421575
$575$	−13.5129	−0.563528
$576$	7.39519	0.308133
$577$	14.6791	0.611101	0.305550	−	0.952176i	$-0.401160\pi$
$577$	14.6791	0.611101	0.305550	+	0.952176i	$0.401160\pi$
$578$	4.49402	0.186927
$579$	−19.3311	−0.803373
$580$	32.5922	1.35332
$581$	7.42416	0.308006
$582$	−25.4563	−1.05520
$583$	0.432117	0.0178965
$584$	−3.97477	−0.164477
$585$	−96.0747	−3.97220
$586$	16.6689	0.688584
$587$	20.5914	0.849900	0.424950	−	0.905217i	$-0.360292\pi$
$587$	20.5914	0.849900	0.424950	+	0.905217i	$0.360292\pi$
$588$	3.22416	0.132962
$589$	21.6298	0.891240
$590$	−28.8664	−1.18841
$591$	−26.4116	−1.08643
$592$	−3.08522	−0.126802
$593$	−9.58035	−0.393418	−0.196709	−	0.980462i	$-0.563025\pi$
$593$	−9.58035	−0.393418	−0.196709	+	0.980462i	$0.563025\pi$
$594$	58.7473	2.41043
$595$	−12.3410	−0.505933
$596$	12.8892	0.527964
$597$	−33.3963	−1.36682
$598$	7.00806	0.286581
$599$	−3.08572	−0.126079	−0.0630395	−	0.998011i	$-0.520079\pi$
$599$	−3.08572	−0.126079	−0.0630395	+	0.998011i	$0.520079\pi$
$600$	−23.1438	−0.944842
$601$	12.4595	0.508234	0.254117	−	0.967173i	$-0.418215\pi$
$601$	12.4595	0.508234	0.254117	+	0.967173i	$0.418215\pi$
$602$	−7.78000	−0.317089
$603$	−61.7417	−2.51432
$604$	8.76175	0.356511
$605$	−21.5893	−0.877732
$606$	48.3148	1.96266
$607$	28.6561	1.16312	0.581559	−	0.813505i	$-0.302443\pi$
$607$	28.6561	1.16312	0.581559	+	0.813505i	$0.302443\pi$
$608$	6.23343	0.252799
$609$	−30.1118	−1.22019
$610$	36.0804	1.46085
$611$	−14.9558	−0.605049
$612$	26.1522	1.05714
$613$	22.9248	0.925924	0.462962	−	0.886378i	$-0.346787\pi$
$613$	22.9248	0.925924	0.462962	+	0.886378i	$0.346787\pi$
$614$	18.5756	0.749651
$615$	113.642	4.58250
$616$	4.14566	0.167034
$617$	−8.94386	−0.360066	−0.180033	−	0.983661i	$-0.557620\pi$
$617$	−8.94386	−0.360066	−0.180033	+	0.983661i	$0.557620\pi$
$618$	40.3031	1.62123
$619$	24.5182	0.985470	0.492735	−	0.870179i	$-0.335997\pi$
$619$	24.5182	0.985470	0.492735	+	0.870179i	$0.335997\pi$
$620$	12.1093	0.486320
$621$	−26.6762	−1.07048
$622$	−33.2068	−1.33147
$623$	−5.13768	−0.205837
$624$	12.0028	0.480498
$625$	−9.36395	−0.374558
$626$	8.45699	0.338009
$627$	83.3177	3.32739
$628$	17.5830	0.701638
$629$	−10.9105	−0.435030
$630$	25.8073	1.02819
$631$	−4.20240	−0.167295	−0.0836475	−	0.996495i	$-0.526657\pi$
$631$	−4.20240	−0.167295	−0.0836475	+	0.996495i	$0.526657\pi$
$632$	16.3625	0.650866
$633$	−16.0637	−0.638476
$634$	−11.1732	−0.443746
$635$	77.7492	3.08538
$636$	−0.336065	−0.0133258
$637$	3.72278	0.147502
$638$	−38.7182	−1.53287
$639$	50.3933	1.99353
$640$	3.48974	0.137944
$641$	−20.2787	−0.800962	−0.400481	−	0.916305i	$-0.631157\pi$
$641$	−20.2787	−0.800962	−0.400481	+	0.916305i	$0.631157\pi$
$642$	8.62458	0.340385
$643$	−10.5632	−0.416572	−0.208286	−	0.978068i	$-0.566788\pi$
$643$	−10.5632	−0.416572	−0.208286	+	0.978068i	$0.566788\pi$
$644$	−1.88248	−0.0741801
$645$	−87.5363	−3.44674
$646$	22.0438	0.867300
$647$	27.9064	1.09711	0.548557	−	0.836113i	$-0.315177\pi$
$647$	27.9064	1.09711	0.548557	+	0.836113i	$0.315177\pi$
$648$	−23.5032	−0.923295
$649$	34.2921	1.34608
$650$	−26.7231	−1.04816
$651$	−11.1877	−0.438481
$652$	−0.928501	−0.0363629
$653$	12.8183	0.501618	0.250809	−	0.968037i	$-0.419303\pi$
$653$	12.8183	0.501618	0.250809	+	0.968037i	$0.419303\pi$
$654$	−42.4150	−1.65856
$655$	−7.07125	−0.276297
$656$	−10.1002	−0.394348
$657$	29.3942	1.14678
$658$	4.01738	0.156614
$659$	−26.2091	−1.02096	−0.510481	−	0.859889i	$-0.670533\pi$
$659$	−26.2091	−1.02096	−0.510481	+	0.859889i	$0.670533\pi$
$660$	46.6447	1.81564
$661$	−19.7583	−0.768507	−0.384254	−	0.923228i	$-0.625541\pi$
$661$	−19.7583	−0.768507	−0.384254	+	0.923228i	$0.625541\pi$
$662$	−27.2743	−1.06005
$663$	42.4465	1.64849
$664$	−7.42416	−0.288113
$665$	21.7530	0.843546
$666$	22.8158	0.884093
$667$	17.5813	0.680751
$668$	−11.1798	−0.432560
$669$	−81.2493	−3.14128
$670$	−29.1355	−1.12560
$671$	−42.8620	−1.65467
$672$	−3.22416	−0.124375
$673$	17.9770	0.692963	0.346481	−	0.938057i	$-0.387376\pi$
$673$	17.9770	0.692963	0.346481	+	0.938057i	$0.387376\pi$
$674$	−0.393486	−0.0151565
$675$	101.721	3.91526
$676$	0.859091	0.0330420
$677$	3.98328	0.153090	0.0765450	−	0.997066i	$-0.475611\pi$
$677$	3.98328	0.153090	0.0765450	+	0.997066i	$0.475611\pi$
$678$	24.7658	0.951125
$679$	7.89549	0.303001
$680$	12.3410	0.473257
$681$	14.6782	0.562471
$682$	−14.3853	−0.550842
$683$	−40.2490	−1.54009	−0.770043	−	0.637992i	$-0.779765\pi$
$683$	−40.2490	−1.54009	−0.770043	+	0.637992i	$0.779765\pi$
$684$	−46.0974	−1.76258
$685$	−21.1219	−0.807026
$686$	−1.00000	−0.0381802
$687$	−51.0782	−1.94876
$688$	7.78000	0.296610
$689$	−0.388038	−0.0147831
$690$	−21.1806	−0.806333
$691$	−39.2587	−1.49347	−0.746736	−	0.665121i	$-0.768380\pi$
$691$	−39.2587	−1.49347	−0.746736	+	0.665121i	$0.768380\pi$
$692$	−1.82547	−0.0693938
$693$	−30.6580	−1.16460
$694$	−22.1462	−0.840660
$695$	−26.2537	−0.995861
$696$	30.1118	1.14139
$697$	−35.7182	−1.35292
$698$	−25.7685	−0.975353
$699$	−65.5244	−2.47836
$700$	7.17825	0.271312
$701$	−49.0480	−1.85252	−0.926260	−	0.376886i	$-0.876995\pi$
$701$	−49.0480	−1.85252	−0.926260	+	0.376886i	$0.876995\pi$
$702$	−52.7547	−1.99110
$703$	19.2315	0.725329
$704$	−4.14566	−0.156246
$705$	45.2014	1.70238
$706$	20.6010	0.775330
$707$	−14.9853	−0.563579
$708$	−26.6696	−1.00230
$709$	6.96874	0.261717	0.130858	−	0.991401i	$-0.458227\pi$
$709$	6.96874	0.261717	0.130858	+	0.991401i	$0.458227\pi$
$710$	23.7802	0.892455
$711$	−121.004	−4.53800
$712$	5.13768	0.192543
$713$	6.53215	0.244631
$714$	−11.4018	−0.426703
$715$	53.8585	2.01419
$716$	19.3511	0.723186
$717$	−60.9826	−2.27744
$718$	18.5082	0.690721
$719$	41.2874	1.53976	0.769880	−	0.638188i	$-0.220316\pi$
$719$	41.2874	1.53976	0.769880	+	0.638188i	$0.220316\pi$
$720$	−25.8073	−0.961779
$721$	−12.5004	−0.465537
$722$	−19.8556	−0.738949
$723$	47.6164	1.77087
$724$	−24.3180	−0.903771
$725$	−67.0409	−2.48984
$726$	−19.9463	−0.740278
$727$	−32.1656	−1.19296	−0.596479	−	0.802629i	$-0.703434\pi$
$727$	−32.1656	−1.19296	−0.596479	+	0.802629i	$0.703434\pi$
$728$	−3.72278	−0.137975
$729$	36.7445	1.36091
$730$	13.8709	0.513385
$731$	27.5130	1.01761
$732$	33.3346	1.23208
$733$	10.3448	0.382093	0.191047	−	0.981581i	$-0.438812\pi$
$733$	10.3448	0.382093	0.191047	+	0.981581i	$0.438812\pi$
$734$	27.9377	1.03120
$735$	−11.2515	−0.415016
$736$	1.88248	0.0693892
$737$	34.6118	1.27494
$738$	74.6931	2.74949
$739$	15.7791	0.580442	0.290221	−	0.956960i	$-0.406271\pi$
$739$	15.7791	0.580442	0.290221	+	0.956960i	$0.406271\pi$
$740$	10.7666	0.395788
$741$	−74.8187	−2.74854
$742$	0.104233	0.00382653
$743$	−40.2801	−1.47774	−0.738868	−	0.673851i	$-0.764639\pi$
$743$	−40.2801	−1.47774	−0.738868	+	0.673851i	$0.764639\pi$
$744$	11.1877	0.410162
$745$	−44.9801	−1.64794
$746$	30.4042	1.11318
$747$	54.9030	2.00880
$748$	−14.6606	−0.536046
$749$	−2.67499	−0.0977419
$750$	24.5085	0.894924
$751$	−23.9107	−0.872514	−0.436257	−	0.899822i	$-0.643696\pi$
$751$	−23.9107	−0.872514	−0.436257	+	0.899822i	$0.643696\pi$
$752$	−4.01738	−0.146499
$753$	−90.3224	−3.29153
$754$	34.7687	1.26620
$755$	−30.5762	−1.11278
$756$	14.1708	0.515386
$757$	39.8886	1.44977	0.724887	−	0.688868i	$-0.241892\pi$
$757$	39.8886	1.44977	0.724887	+	0.688868i	$0.241892\pi$
$758$	26.2869	0.954781
$759$	25.1617	0.913314
$760$	−21.7530	−0.789065
$761$	13.8840	0.503296	0.251648	−	0.967819i	$-0.419028\pi$
$761$	13.8840	0.503296	0.251648	+	0.967819i	$0.419028\pi$
$762$	71.8323	2.60221
$763$	13.1554	0.476256
$764$	18.0451	0.652849
$765$	−91.2642	−3.29967
$766$	12.9465	0.467775
$767$	−30.7941	−1.11191
$768$	3.22416	0.116342
$769$	15.2844	0.551168	0.275584	−	0.961277i	$-0.411129\pi$
$769$	15.2844	0.551168	0.275584	+	0.961277i	$0.411129\pi$
$770$	−14.4673	−0.521364
$771$	75.9321	2.73463
$772$	−5.99571	−0.215790
$773$	2.52128	0.0906843	0.0453421	−	0.998972i	$-0.485562\pi$
$773$	2.52128	0.0906843	0.0453421	+	0.998972i	$0.485562\pi$
$774$	−57.5346	−2.06804
$775$	−24.9083	−0.894733
$776$	−7.89549	−0.283431
$777$	−9.94722	−0.356855
$778$	16.5509	0.593378
$779$	62.9590	2.25574
$780$	−41.8867	−1.49978
$781$	−28.2499	−1.01086
$782$	6.65717	0.238060
$783$	−132.347	−4.72970
$784$	1.00000	0.0357143
$785$	−61.3600	−2.19003
$786$	−6.53311	−0.233028
$787$	55.5988	1.98188	0.990942	−	0.134288i	$-0.0428748\pi$
$787$	55.5988	1.98188	0.990942	+	0.134288i	$0.0428748\pi$
$788$	−8.19177	−0.291820
$789$	−55.7099	−1.98333
$790$	−57.1008	−2.03156
$791$	−7.68133	−0.273117
$792$	30.6580	1.08938
$793$	38.4898	1.36681
$794$	2.22410	0.0789305
$795$	1.17278	0.0415942
$796$	−10.3582	−0.367135
$797$	19.5623	0.692932	0.346466	−	0.938063i	$-0.387382\pi$
$797$	19.5623	0.692932	0.346466	+	0.938063i	$0.387382\pi$
$798$	20.0975	0.711445
$799$	−14.2070	−0.502607
$800$	−7.17825	−0.253790
$801$	−37.9941	−1.34246
$802$	−5.19681	−0.183506
$803$	−16.4781	−0.581499
$804$	−26.9182	−0.949331
$805$	6.56936	0.231539
$806$	12.9179	0.455015
$807$	49.4978	1.74240
$808$	14.9853	0.527180
$809$	6.93768	0.243916	0.121958	−	0.992535i	$-0.461083\pi$
$809$	6.93768	0.243916	0.121958	+	0.992535i	$0.461083\pi$
$810$	82.0201	2.88189
$811$	31.3686	1.10150	0.550749	−	0.834671i	$-0.314342\pi$
$811$	31.3686	1.10150	0.550749	+	0.834671i	$0.314342\pi$
$812$	−9.33944	−0.327750
$813$	−83.2366	−2.91924
$814$	−12.7903	−0.448299
$815$	3.24022	0.113500
$816$	11.4018	0.399144
$817$	−48.4961	−1.69666
$818$	−35.2966	−1.23412
$819$	27.5307	0.961999
$820$	35.2471	1.23088
$821$	21.1915	0.739588	0.369794	−	0.929114i	$-0.379428\pi$
$821$	21.1915	0.739588	0.369794	+	0.929114i	$0.379428\pi$
$822$	−19.5145	−0.680645
$823$	−14.1757	−0.494135	−0.247068	−	0.968998i	$-0.579467\pi$
$823$	−14.1757	−0.494135	−0.247068	+	0.968998i	$0.579467\pi$
$824$	12.5004	0.435470
$825$	−95.9465	−3.34043
$826$	8.27180	0.287813
$827$	−28.3687	−0.986475	−0.493237	−	0.869895i	$-0.664187\pi$
$827$	−28.3687	−0.986475	−0.493237	+	0.869895i	$0.664187\pi$
$828$	−13.9213	−0.483799
$829$	−42.6541	−1.48144	−0.740719	−	0.671815i	$-0.765515\pi$
$829$	−42.6541	−1.48144	−0.740719	+	0.671815i	$0.765515\pi$
$830$	25.9083	0.899292
$831$	1.47282	0.0510915
$832$	3.72278	0.129064
$833$	3.53638	0.122528
$834$	−24.2558	−0.839908
$835$	39.0146	1.35015
$836$	25.8417	0.893754
$837$	−49.1722	−1.69964
$838$	−0.515179	−0.0177966
$839$	−22.0249	−0.760385	−0.380193	−	0.924907i	$-0.624142\pi$
$839$	−22.0249	−0.760385	−0.380193	+	0.924907i	$0.624142\pi$
$840$	11.2515	0.388212
$841$	58.2251	2.00776
$842$	0.373477	0.0128709
$843$	−13.0488	−0.449426
$844$	−4.98230	−0.171498
$845$	−2.99800	−0.103134
$846$	29.7093	1.02143
$847$	6.18653	0.212572
$848$	−0.104233	−0.00357939
$849$	−37.8451	−1.29884
$850$	−25.3850	−0.870699
$851$	5.80786	0.199091
$852$	21.9705	0.752696
$853$	−9.87765	−0.338204	−0.169102	−	0.985599i	$-0.554087\pi$
$853$	−9.87765	−0.338204	−0.169102	+	0.985599i	$0.554087\pi$
$854$	−10.3390	−0.353793
$855$	160.868	5.50156
$856$	2.67499	0.0914292
$857$	28.2963	0.966582	0.483291	−	0.875460i	$-0.339441\pi$
$857$	28.2963	0.966582	0.483291	+	0.875460i	$0.339441\pi$
$858$	49.7597	1.69877
$859$	17.7979	0.607257	0.303629	−	0.952790i	$-0.401802\pi$
$859$	17.7979	0.607257	0.303629	+	0.952790i	$0.401802\pi$
$860$	−27.1501	−0.925812
$861$	−32.5647	−1.10980
$862$	−1.00000	−0.0340601
$863$	−29.8641	−1.01658	−0.508292	−	0.861185i	$-0.669723\pi$
$863$	−29.8641	−1.01658	−0.508292	+	0.861185i	$0.669723\pi$
$864$	−14.1708	−0.482100
$865$	6.37039	0.216600
$866$	2.01155	0.0683554
$867$	−14.4894	−0.492087
$868$	−3.46997	−0.117778
$869$	67.8335	2.30109
$870$	−105.082	−3.56262
$871$	−31.0811	−1.05314
$872$	−13.1554	−0.445497
$873$	58.3886	1.97616
$874$	−11.7343	−0.396919
$875$	−7.60153	−0.256979
$876$	12.8153	0.432989
$877$	24.4703	0.826304	0.413152	−	0.910662i	$-0.364428\pi$
$877$	24.4703	0.826304	0.413152	+	0.910662i	$0.364428\pi$
$878$	−20.8844	−0.704816
$879$	−53.7430	−1.81271
$880$	14.4673	0.487692
$881$	12.5913	0.424212	0.212106	−	0.977247i	$-0.431968\pi$
$881$	12.5913	0.424212	0.212106	+	0.977247i	$0.431968\pi$
$882$	−7.39519	−0.249009
$883$	41.6723	1.40238	0.701192	−	0.712973i	$-0.252652\pi$
$883$	41.6723	1.40238	0.701192	+	0.712973i	$0.252652\pi$
$884$	13.1652	0.442792
$885$	93.0698	3.12851
$886$	−37.3861	−1.25601
$887$	24.5675	0.824897	0.412448	−	0.910981i	$-0.364674\pi$
$887$	24.5675	0.824897	0.412448	+	0.910981i	$0.364674\pi$
$888$	9.94722	0.333807
$889$	−22.2794	−0.747227
$890$	−17.9291	−0.600986
$891$	−97.4366	−3.26425
$892$	−25.2002	−0.843764
$893$	25.0421	0.838001
$894$	−41.5570	−1.38987
$895$	−67.5304	−2.25729
$896$	−1.00000	−0.0334077
$897$	−22.5951	−0.754428
$898$	0.950254	0.0317104
$899$	32.4076	1.08085
$900$	53.0845	1.76948
$901$	−0.368609	−0.0122802
$902$	−41.8722	−1.39419
$903$	25.0839	0.834741
$904$	7.68133	0.255477
$905$	84.8634	2.82095
$906$	−28.2493	−0.938519
$907$	29.6260	0.983715	0.491857	−	0.870676i	$-0.336318\pi$
$907$	29.6260	0.983715	0.491857	+	0.870676i	$0.336318\pi$
$908$	4.55258	0.151083
$909$	−110.819	−3.67563
$910$	12.9915	0.430665
$911$	−14.6832	−0.486476	−0.243238	−	0.969967i	$-0.578210\pi$
$911$	−14.6832	−0.486476	−0.243238	+	0.969967i	$0.578210\pi$
$912$	−20.0975	−0.665496
$913$	−30.7781	−1.01861
$914$	−1.71503	−0.0567282
$915$	−116.329	−3.84571
$916$	−15.8423	−0.523446
$917$	2.02630	0.0669143
$918$	−50.1132	−1.65398
$919$	5.21985	0.172187	0.0860935	−	0.996287i	$-0.472562\pi$
$919$	5.21985	0.172187	0.0860935	+	0.996287i	$0.472562\pi$
$920$	−6.56936	−0.216585
$921$	−59.8907	−1.97347
$922$	−38.5168	−1.26848
$923$	25.3683	0.835006
$924$	−13.3663	−0.439718
$925$	−22.1465	−0.728171
$926$	−15.6597	−0.514610
$927$	−92.4425	−3.03621
$928$	9.33944	0.306582
$929$	−6.81845	−0.223706	−0.111853	−	0.993725i	$-0.535679\pi$
$929$	−6.81845	−0.223706	−0.111853	+	0.993725i	$0.535679\pi$
$930$	−39.0422	−1.28024
$931$	−6.23343	−0.204292
$932$	−20.3230	−0.665701
$933$	107.064	3.50512
$934$	37.6936	1.23337
$935$	51.1617	1.67317
$936$	−27.5307	−0.899868
$937$	21.9257	0.716283	0.358141	−	0.933667i	$-0.383411\pi$
$937$	21.9257	0.716283	0.358141	+	0.933667i	$0.383411\pi$
$938$	8.34891	0.272601
$939$	−27.2667	−0.889814
$940$	14.0196	0.457269
$941$	−1.79969	−0.0586681	−0.0293341	−	0.999570i	$-0.509339\pi$
$941$	−1.79969	−0.0586681	−0.0293341	+	0.999570i	$0.509339\pi$
$942$	−56.6903	−1.84707
$943$	19.0135	0.619164
$944$	−8.27180	−0.269224
$945$	−49.4523	−1.60868
$946$	32.2533	1.04864
$947$	30.5214	0.991812	0.495906	−	0.868376i	$-0.334836\pi$
$947$	30.5214	0.991812	0.495906	+	0.868376i	$0.334836\pi$
$948$	−52.7553	−1.71341
$949$	14.7972	0.480338
$950$	44.7451	1.45172
$951$	36.0243	1.16817
$952$	−3.53638	−0.114615
$953$	−2.25010	−0.0728879	−0.0364440	−	0.999336i	$-0.511603\pi$
$953$	−2.25010	−0.0728879	−0.0364440	+	0.999336i	$0.511603\pi$
$954$	0.770826	0.0249564
$955$	−62.9727	−2.03775
$956$	−18.9143	−0.611731
$957$	124.833	4.03529
$958$	30.3757	0.981394
$959$	6.05258	0.195448
$960$	−11.2515	−0.363139
$961$	−18.9593	−0.611591
$962$	11.4856	0.370310
$963$	−19.7820	−0.637467
$964$	14.7686	0.475665
$965$	20.9234	0.673549
$966$	6.06941	0.195280
$967$	−43.6644	−1.40415	−0.702076	−	0.712102i	$-0.747743\pi$
$967$	−43.6644	−1.40415	−0.702076	+	0.712102i	$0.747743\pi$
$968$	−6.18653	−0.198842
$969$	−71.0725	−2.28318
$970$	27.5532	0.884679
$971$	−43.6095	−1.39950	−0.699748	−	0.714390i	$-0.746704\pi$
$971$	−43.6095	−1.39950	−0.699748	+	0.714390i	$0.746704\pi$
$972$	33.2658	1.06700
$973$	7.52313	0.241181
$974$	6.79874	0.217846
$975$	86.1593	2.75931
$976$	10.3390	0.330943
$977$	38.2701	1.22437	0.612185	−	0.790715i	$-0.290291\pi$
$977$	38.2701	1.22437	0.612185	+	0.790715i	$0.290291\pi$
$978$	2.99363	0.0957258
$979$	21.2991	0.680722
$980$	−3.48974	−0.111476
$981$	97.2864	3.10612
$982$	14.6502	0.467506
$983$	5.19612	0.165730	0.0828652	−	0.996561i	$-0.473593\pi$
$983$	5.19612	0.165730	0.0828652	+	0.996561i	$0.473593\pi$
$984$	32.5647	1.03813
$985$	28.5871	0.910861
$986$	33.0278	1.05182
$987$	−12.9527	−0.412288
$988$	−23.2057	−0.738271
$989$	−14.6457	−0.465706
$990$	−106.988	−3.40031
$991$	49.7486	1.58032	0.790158	−	0.612903i	$-0.209999\pi$
$991$	49.7486	1.58032	0.790158	+	0.612903i	$0.209999\pi$
$992$	3.46997	0.110172
$993$	87.9366	2.79058
$994$	−6.81433	−0.216137
$995$	36.1472	1.14594
$996$	23.9367	0.758462
$997$	−38.7397	−1.22690	−0.613450	−	0.789734i	$-0.710219\pi$
$997$	−38.7397	−1.22690	−0.613450	+	0.789734i	$0.710219\pi$
$998$	−13.0311	−0.412491
$999$	−43.7199	−1.38324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.20	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.20	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.22416 q^{3} +1.00000 q^{4} -3.48974 q^{5} -3.22416 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.39519 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.22416 q^{3} +1.00000 q^{4} -3.48974 q^{5} -3.22416 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.39519 q^{9} +3.48974 q^{10} -4.14566 q^{11} +3.22416 q^{12} +3.72278 q^{13} -1.00000 q^{14} -11.2515 q^{15} +1.00000 q^{16} +3.53638 q^{17} -7.39519 q^{18} -6.23343 q^{19} -3.48974 q^{20} +3.22416 q^{21} +4.14566 q^{22} -1.88248 q^{23} -3.22416 q^{24} +7.17825 q^{25} -3.72278 q^{26} +14.1708 q^{27} +1.00000 q^{28} -9.33944 q^{29} +11.2515 q^{30} -3.46997 q^{31} -1.00000 q^{32} -13.3663 q^{33} -3.53638 q^{34} -3.48974 q^{35} +7.39519 q^{36} -3.08522 q^{37} +6.23343 q^{38} +12.0028 q^{39} +3.48974 q^{40} -10.1002 q^{41} -3.22416 q^{42} +7.78000 q^{43} -4.14566 q^{44} -25.8073 q^{45} +1.88248 q^{46} -4.01738 q^{47} +3.22416 q^{48} +1.00000 q^{49} -7.17825 q^{50} +11.4018 q^{51} +3.72278 q^{52} -0.104233 q^{53} -14.1708 q^{54} +14.4673 q^{55} -1.00000 q^{56} -20.0975 q^{57} +9.33944 q^{58} -8.27180 q^{59} -11.2515 q^{60} +10.3390 q^{61} +3.46997 q^{62} +7.39519 q^{63} +1.00000 q^{64} -12.9915 q^{65} +13.3663 q^{66} -8.34891 q^{67} +3.53638 q^{68} -6.06941 q^{69} +3.48974 q^{70} +6.81433 q^{71} -7.39519 q^{72} +3.97477 q^{73} +3.08522 q^{74} +23.1438 q^{75} -6.23343 q^{76} -4.14566 q^{77} -12.0028 q^{78} -16.3625 q^{79} -3.48974 q^{80} +23.5032 q^{81} +10.1002 q^{82} +7.42416 q^{83} +3.22416 q^{84} -12.3410 q^{85} -7.78000 q^{86} -30.1118 q^{87} +4.14566 q^{88} -5.13768 q^{89} +25.8073 q^{90} +3.72278 q^{91} -1.88248 q^{92} -11.1877 q^{93} +4.01738 q^{94} +21.7530 q^{95} -3.22416 q^{96} +7.89549 q^{97} -1.00000 q^{98} -30.6580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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