LMFDB - Embedded newform 6034.2.a.k.1.11

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			1.11
Root			$0.751545$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.751545 q^{3} +1.00000 q^{4} +2.13649 q^{5} -0.751545 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.43518 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.751545 q^{3} +1.00000 q^{4} +2.13649 q^{5} -0.751545 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.43518 q^{9} -2.13649 q^{10} -5.95838 q^{11} +0.751545 q^{12} +3.73145 q^{13} -1.00000 q^{14} +1.60567 q^{15} +1.00000 q^{16} +8.03319 q^{17} +2.43518 q^{18} +0.239104 q^{19} +2.13649 q^{20} +0.751545 q^{21} +5.95838 q^{22} -6.05411 q^{23} -0.751545 q^{24} -0.435405 q^{25} -3.73145 q^{26} -4.08478 q^{27} +1.00000 q^{28} -8.86601 q^{29} -1.60567 q^{30} -0.280533 q^{31} -1.00000 q^{32} -4.47799 q^{33} -8.03319 q^{34} +2.13649 q^{35} -2.43518 q^{36} -5.32148 q^{37} -0.239104 q^{38} +2.80435 q^{39} -2.13649 q^{40} -3.45126 q^{41} -0.751545 q^{42} +0.398393 q^{43} -5.95838 q^{44} -5.20274 q^{45} +6.05411 q^{46} +6.08411 q^{47} +0.751545 q^{48} +1.00000 q^{49} +0.435405 q^{50} +6.03731 q^{51} +3.73145 q^{52} -0.586258 q^{53} +4.08478 q^{54} -12.7300 q^{55} -1.00000 q^{56} +0.179697 q^{57} +8.86601 q^{58} +3.67929 q^{59} +1.60567 q^{60} -3.14385 q^{61} +0.280533 q^{62} -2.43518 q^{63} +1.00000 q^{64} +7.97220 q^{65} +4.47799 q^{66} -3.78879 q^{67} +8.03319 q^{68} -4.54994 q^{69} -2.13649 q^{70} -14.7490 q^{71} +2.43518 q^{72} -9.18079 q^{73} +5.32148 q^{74} -0.327227 q^{75} +0.239104 q^{76} -5.95838 q^{77} -2.80435 q^{78} +4.32894 q^{79} +2.13649 q^{80} +4.23565 q^{81} +3.45126 q^{82} -13.5758 q^{83} +0.751545 q^{84} +17.1629 q^{85} -0.398393 q^{86} -6.66320 q^{87} +5.95838 q^{88} +7.59153 q^{89} +5.20274 q^{90} +3.73145 q^{91} -6.05411 q^{92} -0.210833 q^{93} -6.08411 q^{94} +0.510844 q^{95} -0.751545 q^{96} +5.43259 q^{97} -1.00000 q^{98} +14.5097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.751545	0.433905	0.216952	−	0.976182i	$-0.430388\pi$
$3$	0.751545	0.433905	0.216952	+	0.976182i	$0.430388\pi$
$4$	1.00000	0.500000
$5$	2.13649	0.955468	0.477734	−	0.878505i	$-0.341458\pi$
$5$	2.13649	0.955468	0.477734	+	0.878505i	$0.341458\pi$
$6$	−0.751545	−0.306817
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.43518	−0.811727
$10$	−2.13649	−0.675618
$11$	−5.95838	−1.79652	−0.898259	−	0.439467i	$-0.855167\pi$
$11$	−5.95838	−1.79652	−0.898259	+	0.439467i	$0.855167\pi$
$12$	0.751545	0.216952
$13$	3.73145	1.03492	0.517459	−	0.855708i	$-0.326878\pi$
$13$	3.73145	1.03492	0.517459	+	0.855708i	$0.326878\pi$
$14$	−1.00000	−0.267261
$15$	1.60567	0.414582
$16$	1.00000	0.250000
$17$	8.03319	1.94834	0.974168	−	0.225825i	$-0.0725077\pi$
$17$	8.03319	1.94834	0.974168	+	0.225825i	$0.0725077\pi$
$18$	2.43518	0.573978
$19$	0.239104	0.0548542	0.0274271	−	0.999624i	$-0.491269\pi$
$19$	0.239104	0.0548542	0.0274271	+	0.999624i	$0.491269\pi$
$20$	2.13649	0.477734
$21$	0.751545	0.164001
$22$	5.95838	1.27033
$23$	−6.05411	−1.26237	−0.631185	−	0.775632i	$-0.717431\pi$
$23$	−6.05411	−1.26237	−0.631185	+	0.775632i	$0.717431\pi$
$24$	−0.751545	−0.153408
$25$	−0.435405	−0.0870811
$26$	−3.73145	−0.731797
$27$	−4.08478	−0.786117
$28$	1.00000	0.188982
$29$	−8.86601	−1.64638	−0.823188	−	0.567769i	$-0.807807\pi$
$29$	−8.86601	−1.64638	−0.823188	+	0.567769i	$0.807807\pi$
$30$	−1.60567	−0.293154
$31$	−0.280533	−0.0503852	−0.0251926	−	0.999683i	$-0.508020\pi$
$31$	−0.280533	−0.0503852	−0.0251926	+	0.999683i	$0.508020\pi$
$32$	−1.00000	−0.176777
$33$	−4.47799	−0.779517
$34$	−8.03319	−1.37768
$35$	2.13649	0.361133
$36$	−2.43518	−0.405863
$37$	−5.32148	−0.874846	−0.437423	−	0.899256i	$-0.644109\pi$
$37$	−5.32148	−0.874846	−0.437423	+	0.899256i	$0.644109\pi$
$38$	−0.239104	−0.0387878
$39$	2.80435	0.449055
$40$	−2.13649	−0.337809
$41$	−3.45126	−0.538997	−0.269498	−	0.963001i	$-0.586858\pi$
$41$	−3.45126	−0.538997	−0.269498	+	0.963001i	$0.586858\pi$
$42$	−0.751545	−0.115966
$43$	0.398393	0.0607544	0.0303772	−	0.999539i	$-0.490329\pi$
$43$	0.398393	0.0607544	0.0303772	+	0.999539i	$0.490329\pi$
$44$	−5.95838	−0.898259
$45$	−5.20274	−0.775579
$46$	6.05411	0.892631
$47$	6.08411	0.887458	0.443729	−	0.896161i	$-0.353655\pi$
$47$	6.08411	0.887458	0.443729	+	0.896161i	$0.353655\pi$
$48$	0.751545	0.108476
$49$	1.00000	0.142857
$50$	0.435405	0.0615756
$51$	6.03731	0.845392
$52$	3.73145	0.517459
$53$	−0.586258	−0.0805288	−0.0402644	−	0.999189i	$-0.512820\pi$
$53$	−0.586258	−0.0805288	−0.0402644	+	0.999189i	$0.512820\pi$
$54$	4.08478	0.555868
$55$	−12.7300	−1.71652
$56$	−1.00000	−0.133631
$57$	0.179697	0.0238015
$58$	8.86601	1.16416
$59$	3.67929	0.479003	0.239501	−	0.970896i	$-0.423016\pi$
$59$	3.67929	0.479003	0.239501	+	0.970896i	$0.423016\pi$
$60$	1.60567	0.207291
$61$	−3.14385	−0.402529	−0.201264	−	0.979537i	$-0.564505\pi$
$61$	−3.14385	−0.402529	−0.201264	+	0.979537i	$0.564505\pi$
$62$	0.280533	0.0356277
$63$	−2.43518	−0.306804
$64$	1.00000	0.125000
$65$	7.97220	0.988830
$66$	4.47799	0.551202
$67$	−3.78879	−0.462875	−0.231437	−	0.972850i	$-0.574343\pi$
$67$	−3.78879	−0.462875	−0.231437	+	0.972850i	$0.574343\pi$
$68$	8.03319	0.974168
$69$	−4.54994	−0.547748
$70$	−2.13649	−0.255360
$71$	−14.7490	−1.75039	−0.875195	−	0.483771i	$-0.839267\pi$
$71$	−14.7490	−1.75039	−0.875195	+	0.483771i	$0.839267\pi$
$72$	2.43518	0.286989
$73$	−9.18079	−1.07453	−0.537265	−	0.843414i	$-0.680542\pi$
$73$	−9.18079	−1.07453	−0.537265	+	0.843414i	$0.680542\pi$
$74$	5.32148	0.618610
$75$	−0.327227	−0.0377849
$76$	0.239104	0.0274271
$77$	−5.95838	−0.679020
$78$	−2.80435	−0.317530
$79$	4.32894	0.487044	0.243522	−	0.969895i	$-0.421697\pi$
$79$	4.32894	0.487044	0.243522	+	0.969895i	$0.421697\pi$
$80$	2.13649	0.238867
$81$	4.23565	0.470627
$82$	3.45126	0.381128
$83$	−13.5758	−1.49014	−0.745071	−	0.666985i	$-0.767584\pi$
$83$	−13.5758	−1.49014	−0.745071	+	0.666985i	$0.767584\pi$
$84$	0.751545	0.0820003
$85$	17.1629	1.86157
$86$	−0.398393	−0.0429599
$87$	−6.66320	−0.714370
$88$	5.95838	0.635165
$89$	7.59153	0.804701	0.402350	−	0.915486i	$-0.368193\pi$
$89$	7.59153	0.804701	0.402350	+	0.915486i	$0.368193\pi$
$90$	5.20274	0.548417
$91$	3.73145	0.391162
$92$	−6.05411	−0.631185
$93$	−0.210833	−0.0218624
$94$	−6.08411	−0.627528
$95$	0.510844	0.0524115
$96$	−0.751545	−0.0767042
$97$	5.43259	0.551596	0.275798	−	0.961216i	$-0.411058\pi$
$97$	5.43259	0.551596	0.275798	+	0.961216i	$0.411058\pi$
$98$	−1.00000	−0.101015
$99$	14.5097	1.45828
$100$	−0.435405	−0.0435405
$101$	−12.2321	−1.21714	−0.608572	−	0.793499i	$-0.708257\pi$
$101$	−12.2321	−1.21714	−0.608572	+	0.793499i	$0.708257\pi$
$102$	−6.03731	−0.597782
$103$	−3.50846	−0.345699	−0.172849	−	0.984948i	$-0.555297\pi$
$103$	−3.50846	−0.345699	−0.172849	+	0.984948i	$0.555297\pi$
$104$	−3.73145	−0.365899
$105$	1.60567	0.156697
$106$	0.586258	0.0569425
$107$	7.91026	0.764714	0.382357	−	0.924015i	$-0.375113\pi$
$107$	7.91026	0.764714	0.382357	+	0.924015i	$0.375113\pi$
$108$	−4.08478	−0.393058
$109$	9.97730	0.955652	0.477826	−	0.878454i	$-0.341425\pi$
$109$	9.97730	0.955652	0.477826	+	0.878454i	$0.341425\pi$
$110$	12.7300	1.21376
$111$	−3.99933	−0.379600
$112$	1.00000	0.0944911
$113$	12.7463	1.19907	0.599536	−	0.800348i	$-0.295352\pi$
$113$	12.7463	1.19907	0.599536	+	0.800348i	$0.295352\pi$
$114$	−0.179697	−0.0168302
$115$	−12.9346	−1.20615
$116$	−8.86601	−0.823188
$117$	−9.08675	−0.840070
$118$	−3.67929	−0.338706
$119$	8.03319	0.736402
$120$	−1.60567	−0.146577
$121$	24.5022	2.22748
$122$	3.14385	0.284631
$123$	−2.59378	−0.233873
$124$	−0.280533	−0.0251926
$125$	−11.6127	−1.03867
$126$	2.43518	0.216943
$127$	4.36573	0.387396	0.193698	−	0.981061i	$-0.437952\pi$
$127$	4.36573	0.387396	0.193698	+	0.981061i	$0.437952\pi$
$128$	−1.00000	−0.0883883
$129$	0.299411	0.0263616
$130$	−7.97220	−0.699209
$131$	−4.36546	−0.381412	−0.190706	−	0.981647i	$-0.561078\pi$
$131$	−4.36546	−0.381412	−0.190706	+	0.981647i	$0.561078\pi$
$132$	−4.47799	−0.389759
$133$	0.239104	0.0207329
$134$	3.78879	0.327302
$135$	−8.72710	−0.751109
$136$	−8.03319	−0.688841
$137$	−20.4144	−1.74412	−0.872061	−	0.489397i	$-0.837217\pi$
$137$	−20.4144	−1.74412	−0.872061	+	0.489397i	$0.837217\pi$
$138$	4.54994	0.387316
$139$	7.10028	0.602238	0.301119	−	0.953587i	$-0.402640\pi$
$139$	7.10028	0.602238	0.301119	+	0.953587i	$0.402640\pi$
$140$	2.13649	0.180566
$141$	4.57248	0.385072
$142$	14.7490	1.23771
$143$	−22.2334	−1.85925
$144$	−2.43518	−0.202932
$145$	−18.9421	−1.57306
$146$	9.18079	0.759807
$147$	0.751545	0.0619864
$148$	−5.32148	−0.437423
$149$	−14.4488	−1.18369	−0.591847	−	0.806051i	$-0.701601\pi$
$149$	−14.4488	−1.18369	−0.591847	+	0.806051i	$0.701601\pi$
$150$	0.327227	0.0267179
$151$	−18.5716	−1.51133	−0.755666	−	0.654957i	$-0.772687\pi$
$151$	−18.5716	−1.51133	−0.755666	+	0.654957i	$0.772687\pi$
$152$	−0.239104	−0.0193939
$153$	−19.5623	−1.58152
$154$	5.95838	0.480140
$155$	−0.599356	−0.0481415
$156$	2.80435	0.224528
$157$	−6.40053	−0.510818	−0.255409	−	0.966833i	$-0.582210\pi$
$157$	−6.40053	−0.510818	−0.255409	+	0.966833i	$0.582210\pi$
$158$	−4.32894	−0.344392
$159$	−0.440599	−0.0349418
$160$	−2.13649	−0.168904
$161$	−6.05411	−0.477131
$162$	−4.23565	−0.332784
$163$	−17.2311	−1.34964	−0.674820	−	0.737982i	$-0.735779\pi$
$163$	−17.2311	−1.34964	−0.674820	+	0.737982i	$0.735779\pi$
$164$	−3.45126	−0.269498
$165$	−9.56718	−0.744804
$166$	13.5758	1.05369
$167$	−24.2808	−1.87891	−0.939453	−	0.342677i	$-0.888666\pi$
$167$	−24.2808	−1.87891	−0.939453	+	0.342677i	$0.888666\pi$
$168$	−0.751545	−0.0579829
$169$	0.923699	0.0710538
$170$	−17.1629	−1.31633
$171$	−0.582261	−0.0445266
$172$	0.398393	0.0303772
$173$	14.0397	1.06742	0.533709	−	0.845668i	$-0.320798\pi$
$173$	14.0397	1.06742	0.533709	+	0.845668i	$0.320798\pi$
$174$	6.66320	0.505136
$175$	−0.435405	−0.0329135
$176$	−5.95838	−0.449129
$177$	2.76515	0.207841
$178$	−7.59153	−0.569009
$179$	12.5258	0.936223	0.468111	−	0.883670i	$-0.344935\pi$
$179$	12.5258	0.936223	0.468111	+	0.883670i	$0.344935\pi$
$180$	−5.20274	−0.387789
$181$	14.3003	1.06293	0.531466	−	0.847080i	$-0.321641\pi$
$181$	14.3003	1.06293	0.531466	+	0.847080i	$0.321641\pi$
$182$	−3.73145	−0.276593
$183$	−2.36274	−0.174659
$184$	6.05411	0.446315
$185$	−11.3693	−0.835888
$186$	0.210833	0.0154590
$187$	−47.8648	−3.50022
$188$	6.08411	0.443729
$189$	−4.08478	−0.297124
$190$	−0.510844	−0.0370605
$191$	−14.2729	−1.03275	−0.516374	−	0.856363i	$-0.672719\pi$
$191$	−14.2729	−1.03275	−0.516374	+	0.856363i	$0.672719\pi$
$192$	0.751545	0.0542381
$193$	−0.0222935	−0.00160472	−0.000802359	−	1.00000i	$-0.500255\pi$
$193$	−0.0222935	−0.00160472	−0.000802359		1.00000i	$0.500255\pi$
$194$	−5.43259	−0.390037
$195$	5.99147	0.429058
$196$	1.00000	0.0714286
$197$	0.543063	0.0386917	0.0193458	−	0.999813i	$-0.493842\pi$
$197$	0.543063	0.0386917	0.0193458	+	0.999813i	$0.493842\pi$
$198$	−14.5097	−1.03116
$199$	−3.20340	−0.227083	−0.113542	−	0.993533i	$-0.536220\pi$
$199$	−3.20340	−0.227083	−0.113542	+	0.993533i	$0.536220\pi$
$200$	0.435405	0.0307878
$201$	−2.84745	−0.200844
$202$	12.2321	0.860651
$203$	−8.86601	−0.622272
$204$	6.03731	0.422696
$205$	−7.37360	−0.514994
$206$	3.50846	0.244446
$207$	14.7429	1.02470
$208$	3.73145	0.258729
$209$	−1.42467	−0.0985466
$210$	−1.60567	−0.110802
$211$	26.9749	1.85703	0.928514	−	0.371297i	$-0.121087\pi$
$211$	26.9749	1.85703	0.928514	+	0.371297i	$0.121087\pi$
$212$	−0.586258	−0.0402644
$213$	−11.0846	−0.759502
$214$	−7.91026	−0.540734
$215$	0.851164	0.0580489
$216$	4.08478	0.277934
$217$	−0.280533	−0.0190438
$218$	−9.97730	−0.675748
$219$	−6.89977	−0.466243
$220$	−12.7300	−0.858258
$221$	29.9754	2.01637
$222$	3.99933	0.268418
$223$	−7.21962	−0.483461	−0.241731	−	0.970343i	$-0.577715\pi$
$223$	−7.21962	−0.483461	−0.241731	+	0.970343i	$0.577715\pi$
$224$	−1.00000	−0.0668153
$225$	1.06029	0.0706860
$226$	−12.7463	−0.847872
$227$	−5.16301	−0.342681	−0.171340	−	0.985212i	$-0.554810\pi$
$227$	−5.16301	−0.342681	−0.171340	+	0.985212i	$0.554810\pi$
$228$	0.179697	0.0119007
$229$	15.5335	1.02649	0.513243	−	0.858244i	$-0.328444\pi$
$229$	15.5335	1.02649	0.513243	+	0.858244i	$0.328444\pi$
$230$	12.9346	0.852880
$231$	−4.47799	−0.294630
$232$	8.86601	0.582082
$233$	11.1312	0.729227	0.364614	−	0.931159i	$-0.381201\pi$
$233$	11.1312	0.729227	0.364614	+	0.931159i	$0.381201\pi$
$234$	9.08675	0.594019
$235$	12.9986	0.847938
$236$	3.67929	0.239501
$237$	3.25339	0.211331
$238$	−8.03319	−0.520715
$239$	−12.4535	−0.805548	−0.402774	−	0.915299i	$-0.631954\pi$
$239$	−12.4535	−0.805548	−0.402774	+	0.915299i	$0.631954\pi$
$240$	1.60567	0.103645
$241$	5.84369	0.376425	0.188213	−	0.982128i	$-0.439731\pi$
$241$	5.84369	0.376425	0.188213	+	0.982128i	$0.439731\pi$
$242$	−24.5022	−1.57506
$243$	15.4376	0.990324
$244$	−3.14385	−0.201264
$245$	2.13649	0.136495
$246$	2.59378	0.165373
$247$	0.892204	0.0567696
$248$	0.280533	0.0178139
$249$	−10.2029	−0.646579
$250$	11.6127	0.734451
$251$	−3.35870	−0.211999	−0.106000	−	0.994366i	$-0.533804\pi$
$251$	−3.35870	−0.211999	−0.106000	+	0.994366i	$0.533804\pi$
$252$	−2.43518	−0.153402
$253$	36.0727	2.26787
$254$	−4.36573	−0.273930
$255$	12.8986	0.807745
$256$	1.00000	0.0625000
$257$	1.27714	0.0796655	0.0398328	−	0.999206i	$-0.487317\pi$
$257$	1.27714	0.0796655	0.0398328	+	0.999206i	$0.487317\pi$
$258$	−0.299411	−0.0186405
$259$	−5.32148	−0.330661
$260$	7.97220	0.494415
$261$	21.5903	1.33641
$262$	4.36546	0.269699
$263$	−17.9080	−1.10425	−0.552126	−	0.833761i	$-0.686183\pi$
$263$	−17.9080	−1.10425	−0.552126	+	0.833761i	$0.686183\pi$
$264$	4.47799	0.275601
$265$	−1.25254	−0.0769427
$266$	−0.239104	−0.0146604
$267$	5.70537	0.349163
$268$	−3.78879	−0.231437
$269$	27.3611	1.66824	0.834118	−	0.551587i	$-0.185977\pi$
$269$	27.3611	1.66824	0.834118	+	0.551587i	$0.185977\pi$
$270$	8.72710	0.531114
$271$	−14.1221	−0.857855	−0.428927	−	0.903339i	$-0.641108\pi$
$271$	−14.1221	−0.857855	−0.428927	+	0.903339i	$0.641108\pi$
$272$	8.03319	0.487084
$273$	2.80435	0.169727
$274$	20.4144	1.23328
$275$	2.59431	0.156443
$276$	−4.54994	−0.273874
$277$	−11.4750	−0.689467	−0.344734	−	0.938701i	$-0.612031\pi$
$277$	−11.4750	−0.689467	−0.344734	+	0.938701i	$0.612031\pi$
$278$	−7.10028	−0.425847
$279$	0.683149	0.0408990
$280$	−2.13649	−0.127680
$281$	2.22138	0.132516	0.0662581	−	0.997803i	$-0.478894\pi$
$281$	2.22138	0.132516	0.0662581	+	0.997803i	$0.478894\pi$
$282$	−4.57248	−0.272287
$283$	18.2905	1.08726	0.543629	−	0.839326i	$-0.317050\pi$
$283$	18.2905	1.08726	0.543629	+	0.839326i	$0.317050\pi$
$284$	−14.7490	−0.875195
$285$	0.383922	0.0227416
$286$	22.2334	1.31469
$287$	−3.45126	−0.203722
$288$	2.43518	0.143494
$289$	47.5322	2.79601
$290$	18.9421	1.11232
$291$	4.08283	0.239340
$292$	−9.18079	−0.537265
$293$	−11.3050	−0.660445	−0.330223	−	0.943903i	$-0.607124\pi$
$293$	−11.3050	−0.660445	−0.330223	+	0.943903i	$0.607124\pi$
$294$	−0.751545	−0.0438310
$295$	7.86077	0.457672
$296$	5.32148	0.309305
$297$	24.3387	1.41227
$298$	14.4488	0.836997
$299$	−22.5906	−1.30645
$300$	−0.327227	−0.0188924
$301$	0.398393	0.0229630
$302$	18.5716	1.06867
$303$	−9.19300	−0.528124
$304$	0.239104	0.0137136
$305$	−6.71681	−0.384603
$306$	19.5623	1.11830
$307$	−29.0124	−1.65582	−0.827911	−	0.560859i	$-0.810471\pi$
$307$	−29.0124	−1.65582	−0.827911	+	0.560859i	$0.810471\pi$
$308$	−5.95838	−0.339510
$309$	−2.63676	−0.150000
$310$	0.599356	0.0340412
$311$	−29.8301	−1.69151	−0.845755	−	0.533571i	$-0.820850\pi$
$311$	−29.8301	−1.69151	−0.845755	+	0.533571i	$0.820850\pi$
$312$	−2.80435	−0.158765
$313$	2.14928	0.121485	0.0607423	−	0.998153i	$-0.480653\pi$
$313$	2.14928	0.121485	0.0607423	+	0.998153i	$0.480653\pi$
$314$	6.40053	0.361203
$315$	−5.20274	−0.293141
$316$	4.32894	0.243522
$317$	18.3808	1.03237	0.516186	−	0.856477i	$-0.327351\pi$
$317$	18.3808	1.03237	0.516186	+	0.856477i	$0.327351\pi$
$318$	0.440599	0.0247076
$319$	52.8270	2.95774
$320$	2.13649	0.119433
$321$	5.94491	0.331813
$322$	6.05411	0.337383
$323$	1.92077	0.106874
$324$	4.23565	0.235314
$325$	−1.62469	−0.0901217
$326$	17.2311	0.954340
$327$	7.49839	0.414662
$328$	3.45126	0.190564
$329$	6.08411	0.335428
$330$	9.56718	0.526656
$331$	−15.5805	−0.856384	−0.428192	−	0.903688i	$-0.640849\pi$
$331$	−15.5805	−0.856384	−0.428192	+	0.903688i	$0.640849\pi$
$332$	−13.5758	−0.745071
$333$	12.9588	0.710136
$334$	24.2808	1.32859
$335$	−8.09473	−0.442262
$336$	0.751545	0.0410001
$337$	−18.3002	−0.996873	−0.498436	−	0.866926i	$-0.666092\pi$
$337$	−18.3002	−0.996873	−0.498436	+	0.866926i	$0.666092\pi$
$338$	−0.923699	−0.0502426
$339$	9.57942	0.520283
$340$	17.1629	0.930786
$341$	1.67152	0.0905180
$342$	0.582261	0.0314851
$343$	1.00000	0.0539949
$344$	−0.398393	−0.0214799
$345$	−9.72090	−0.523356
$346$	−14.0397	−0.754779
$347$	−20.8812	−1.12096	−0.560480	−	0.828168i	$-0.689383\pi$
$347$	−20.8812	−1.12096	−0.560480	+	0.828168i	$0.689383\pi$
$348$	−6.66320	−0.357185
$349$	−19.6121	−1.04981	−0.524907	−	0.851160i	$-0.675900\pi$
$349$	−19.6121	−1.04981	−0.524907	+	0.851160i	$0.675900\pi$
$350$	0.435405	0.0232734
$351$	−15.2421	−0.813566
$352$	5.95838	0.317582
$353$	12.6577	0.673701	0.336850	−	0.941558i	$-0.390638\pi$
$353$	12.6577	0.673701	0.336850	+	0.941558i	$0.390638\pi$
$354$	−2.76515	−0.146966
$355$	−31.5112	−1.67244
$356$	7.59153	0.402350
$357$	6.03731	0.319528
$358$	−12.5258	−0.662009
$359$	25.5997	1.35110	0.675549	−	0.737315i	$-0.263907\pi$
$359$	25.5997	1.35110	0.675549	+	0.737315i	$0.263907\pi$
$360$	5.20274	0.274209
$361$	−18.9428	−0.996991
$362$	−14.3003	−0.751606
$363$	18.4145	0.966512
$364$	3.73145	0.195581
$365$	−19.6147	−1.02668
$366$	2.36274	0.123503
$367$	6.29401	0.328545	0.164272	−	0.986415i	$-0.447472\pi$
$367$	6.29401	0.328545	0.164272	+	0.986415i	$0.447472\pi$
$368$	−6.05411	−0.315593
$369$	8.40445	0.437518
$370$	11.3693	0.591062
$371$	−0.586258	−0.0304370
$372$	−0.210833	−0.0109312
$373$	−3.95632	−0.204851	−0.102425	−	0.994741i	$-0.532660\pi$
$373$	−3.95632	−0.204851	−0.102425	+	0.994741i	$0.532660\pi$
$374$	47.8648	2.47503
$375$	−8.72746	−0.450684
$376$	−6.08411	−0.313764
$377$	−33.0830	−1.70386
$378$	4.08478	0.210098
$379$	19.6394	1.00881	0.504403	−	0.863468i	$-0.331713\pi$
$379$	19.6394	1.00881	0.504403	+	0.863468i	$0.331713\pi$
$380$	0.510844	0.0262057
$381$	3.28104	0.168093
$382$	14.2729	0.730263
$383$	38.0383	1.94367	0.971834	−	0.235667i	$-0.0757276\pi$
$383$	38.0383	1.94367	0.971834	+	0.235667i	$0.0757276\pi$
$384$	−0.751545	−0.0383521
$385$	−12.7300	−0.648782
$386$	0.0222935	0.00113471
$387$	−0.970160	−0.0493160
$388$	5.43259	0.275798
$389$	−12.2258	−0.619871	−0.309935	−	0.950758i	$-0.600307\pi$
$389$	−12.2258	−0.619871	−0.309935	+	0.950758i	$0.600307\pi$
$390$	−5.99147	−0.303390
$391$	−48.6339	−2.45952
$392$	−1.00000	−0.0505076
$393$	−3.28084	−0.165496
$394$	−0.543063	−0.0273591
$395$	9.24875	0.465355
$396$	14.5097	0.729141
$397$	−4.75623	−0.238708	−0.119354	−	0.992852i	$-0.538082\pi$
$397$	−4.75623	−0.238708	−0.119354	+	0.992852i	$0.538082\pi$
$398$	3.20340	0.160572
$399$	0.179697	0.00899612
$400$	−0.435405	−0.0217703
$401$	−1.11675	−0.0557676	−0.0278838	−	0.999611i	$-0.508877\pi$
$401$	−1.11675	−0.0557676	−0.0278838	+	0.999611i	$0.508877\pi$
$402$	2.84745	0.142018
$403$	−1.04679	−0.0521445
$404$	−12.2321	−0.608572
$405$	9.04942	0.449669
$406$	8.86601	0.440013
$407$	31.7074	1.57168
$408$	−6.03731	−0.298891
$409$	−0.0593532	−0.00293483	−0.00146741	−	0.999999i	$-0.500467\pi$
$409$	−0.0593532	−0.00293483	−0.00146741	+	0.999999i	$0.500467\pi$
$410$	7.37360	0.364156
$411$	−15.3424	−0.756783
$412$	−3.50846	−0.172849
$413$	3.67929	0.181046
$414$	−14.7429	−0.724572
$415$	−29.0047	−1.42378
$416$	−3.73145	−0.182949
$417$	5.33618	0.261314
$418$	1.42467	0.0696830
$419$	19.4694	0.951142	0.475571	−	0.879677i	$-0.342241\pi$
$419$	19.4694	0.951142	0.475571	+	0.879677i	$0.342241\pi$
$420$	1.60567	0.0783486
$421$	34.4887	1.68088	0.840438	−	0.541908i	$-0.182298\pi$
$421$	34.4887	1.68088	0.840438	+	0.541908i	$0.182298\pi$
$422$	−26.9749	−1.31312
$423$	−14.8159	−0.720373
$424$	0.586258	0.0284712
$425$	−3.49770	−0.169663
$426$	11.0846	0.537049
$427$	−3.14385	−0.152142
$428$	7.91026	0.382357
$429$	−16.7094	−0.806736
$430$	−0.851164	−0.0410468
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−4.08478	−0.196529
$433$	−14.6256	−0.702864	−0.351432	−	0.936213i	$-0.614305\pi$
$433$	−14.6256	−0.702864	−0.351432	+	0.936213i	$0.614305\pi$
$434$	0.280533	0.0134660
$435$	−14.2359	−0.682558
$436$	9.97730	0.477826
$437$	−1.44756	−0.0692463
$438$	6.89977	0.329684
$439$	9.84609	0.469928	0.234964	−	0.972004i	$-0.424503\pi$
$439$	9.84609	0.469928	0.234964	+	0.972004i	$0.424503\pi$
$440$	12.7300	0.606880
$441$	−2.43518	−0.115961
$442$	−29.9754	−1.42579
$443$	−34.7697	−1.65196	−0.825979	−	0.563700i	$-0.809377\pi$
$443$	−34.7697	−1.65196	−0.825979	+	0.563700i	$0.809377\pi$
$444$	−3.99933	−0.189800
$445$	16.2192	0.768866
$446$	7.21962	0.341859
$447$	−10.8589	−0.513610
$448$	1.00000	0.0472456
$449$	−19.3907	−0.915103	−0.457551	−	0.889183i	$-0.651273\pi$
$449$	−19.3907	−0.915103	−0.457551	+	0.889183i	$0.651273\pi$
$450$	−1.06029	−0.0499826
$451$	20.5639	0.968318
$452$	12.7463	0.599536
$453$	−13.9574	−0.655774
$454$	5.16301	0.242312
$455$	7.97220	0.373743
$456$	−0.179697	−0.00841510
$457$	−3.57656	−0.167305	−0.0836523	−	0.996495i	$-0.526658\pi$
$457$	−3.57656	−0.167305	−0.0836523	+	0.996495i	$0.526658\pi$
$458$	−15.5335	−0.725835
$459$	−32.8138	−1.53162
$460$	−12.9346	−0.603077
$461$	27.0939	1.26189	0.630945	−	0.775827i	$-0.282667\pi$
$461$	27.0939	1.26189	0.630945	+	0.775827i	$0.282667\pi$
$462$	4.47799	0.208335
$463$	32.3681	1.50428	0.752138	−	0.659006i	$-0.229023\pi$
$463$	32.3681	1.50428	0.752138	+	0.659006i	$0.229023\pi$
$464$	−8.86601	−0.411594
$465$	−0.450443	−0.0208888
$466$	−11.1312	−0.515642
$467$	20.9327	0.968652	0.484326	−	0.874888i	$-0.339065\pi$
$467$	20.9327	0.968652	0.484326	+	0.874888i	$0.339065\pi$
$468$	−9.08675	−0.420035
$469$	−3.78879	−0.174950
$470$	−12.9986	−0.599582
$471$	−4.81029	−0.221646
$472$	−3.67929	−0.169353
$473$	−2.37378	−0.109146
$474$	−3.25339	−0.149433
$475$	−0.104107	−0.00477676
$476$	8.03319	0.368201
$477$	1.42765	0.0653674
$478$	12.4535	0.569608
$479$	−7.66558	−0.350249	−0.175125	−	0.984546i	$-0.556033\pi$
$479$	−7.66558	−0.350249	−0.175125	+	0.984546i	$0.556033\pi$
$480$	−1.60567	−0.0732884
$481$	−19.8568	−0.905394
$482$	−5.84369	−0.266173
$483$	−4.54994	−0.207029
$484$	24.5022	1.11374
$485$	11.6067	0.527032
$486$	−15.4376	−0.700265
$487$	−4.27810	−0.193859	−0.0969296	−	0.995291i	$-0.530902\pi$
$487$	−4.27810	−0.193859	−0.0969296	+	0.995291i	$0.530902\pi$
$488$	3.14385	0.142315
$489$	−12.9499	−0.585615
$490$	−2.13649	−0.0965168
$491$	−26.6413	−1.20230	−0.601152	−	0.799135i	$-0.705291\pi$
$491$	−26.6413	−1.20230	−0.601152	+	0.799135i	$0.705291\pi$
$492$	−2.59378	−0.116937
$493$	−71.2224	−3.20769
$494$	−0.892204	−0.0401422
$495$	30.9999	1.39334
$496$	−0.280533	−0.0125963
$497$	−14.7490	−0.661585
$498$	10.2029	0.457201
$499$	−28.2000	−1.26241	−0.631203	−	0.775618i	$-0.717439\pi$
$499$	−28.2000	−1.26241	−0.631203	+	0.775618i	$0.717439\pi$
$500$	−11.6127	−0.519336
$501$	−18.2481	−0.815266
$502$	3.35870	0.149906
$503$	−10.9255	−0.487144	−0.243572	−	0.969883i	$-0.578319\pi$
$503$	−10.9255	−0.487144	−0.243572	+	0.969883i	$0.578319\pi$
$504$	2.43518	0.108472
$505$	−26.1339	−1.16294
$506$	−36.0727	−1.60363
$507$	0.694201	0.0308306
$508$	4.36573	0.193698
$509$	−22.8155	−1.01128	−0.505640	−	0.862745i	$-0.668744\pi$
$509$	−22.8155	−1.01128	−0.505640	+	0.862745i	$0.668744\pi$
$510$	−12.8986	−0.571162
$511$	−9.18079	−0.406134
$512$	−1.00000	−0.0441942
$513$	−0.976688	−0.0431218
$514$	−1.27714	−0.0563320
$515$	−7.49579	−0.330304
$516$	0.299411	0.0131808
$517$	−36.2514	−1.59433
$518$	5.32148	0.233813
$519$	10.5515	0.463158
$520$	−7.97220	−0.349604
$521$	4.37991	0.191887	0.0959436	−	0.995387i	$-0.469413\pi$
$521$	4.37991	0.191887	0.0959436	+	0.995387i	$0.469413\pi$
$522$	−21.5903	−0.944983
$523$	17.6497	0.771768	0.385884	−	0.922547i	$-0.373897\pi$
$523$	17.6497	0.771768	0.385884	+	0.922547i	$0.373897\pi$
$524$	−4.36546	−0.190706
$525$	−0.327227	−0.0142813
$526$	17.9080	0.780824
$527$	−2.25358	−0.0981673
$528$	−4.47799	−0.194879
$529$	13.6523	0.593579
$530$	1.25254	0.0544067
$531$	−8.95973	−0.388819
$532$	0.239104	0.0103665
$533$	−12.8782	−0.557817
$534$	−5.70537	−0.246896
$535$	16.9002	0.730659
$536$	3.78879	0.163651
$537$	9.41370	0.406231
$538$	−27.3611	−1.17962
$539$	−5.95838	−0.256645
$540$	−8.72710	−0.375555
$541$	17.6395	0.758381	0.379190	−	0.925319i	$-0.376203\pi$
$541$	17.6395	0.758381	0.379190	+	0.925319i	$0.376203\pi$
$542$	14.1221	0.606595
$543$	10.7473	0.461211
$544$	−8.03319	−0.344420
$545$	21.3164	0.913095
$546$	−2.80435	−0.120015
$547$	−19.1732	−0.819785	−0.409892	−	0.912134i	$-0.634434\pi$
$547$	−19.1732	−0.819785	−0.409892	+	0.912134i	$0.634434\pi$
$548$	−20.4144	−0.872061
$549$	7.65584	0.326743
$550$	−2.59431	−0.110622
$551$	−2.11990	−0.0903107
$552$	4.54994	0.193658
$553$	4.32894	0.184085
$554$	11.4750	0.487527
$555$	−8.54454	−0.362695
$556$	7.10028	0.301119
$557$	−8.13637	−0.344749	−0.172375	−	0.985031i	$-0.555144\pi$
$557$	−8.13637	−0.344749	−0.172375	+	0.985031i	$0.555144\pi$
$558$	−0.683149	−0.0289200
$559$	1.48658	0.0628758
$560$	2.13649	0.0902832
$561$	−35.9725	−1.51876
$562$	−2.22138	−0.0937031
$563$	28.2661	1.19127	0.595637	−	0.803253i	$-0.296900\pi$
$563$	28.2661	1.19127	0.595637	+	0.803253i	$0.296900\pi$
$564$	4.57248	0.192536
$565$	27.2324	1.14567
$566$	−18.2905	−0.768807
$567$	4.23565	0.177880
$568$	14.7490	0.618856
$569$	22.9055	0.960248	0.480124	−	0.877201i	$-0.340592\pi$
$569$	22.9055	0.960248	0.480124	+	0.877201i	$0.340592\pi$
$570$	−0.383922	−0.0160807
$571$	−13.3359	−0.558091	−0.279045	−	0.960278i	$-0.590018\pi$
$571$	−13.3359	−0.558091	−0.279045	+	0.960278i	$0.590018\pi$
$572$	−22.2334	−0.929624
$573$	−10.7267	−0.448114
$574$	3.45126	0.144053
$575$	2.63599	0.109929
$576$	−2.43518	−0.101466
$577$	−8.97507	−0.373637	−0.186818	−	0.982394i	$-0.559818\pi$
$577$	−8.97507	−0.373637	−0.186818	+	0.982394i	$0.559818\pi$
$578$	−47.5322	−1.97708
$579$	−0.0167545	−0.000696295 0
$580$	−18.9421	−0.786530
$581$	−13.5758	−0.563221
$582$	−4.08283	−0.169239
$583$	3.49315	0.144671
$584$	9.18079	0.379904
$585$	−19.4138	−0.802660
$586$	11.3050	0.467005
$587$	19.5807	0.808182	0.404091	−	0.914719i	$-0.367588\pi$
$587$	19.5807	0.808182	0.404091	+	0.914719i	$0.367588\pi$
$588$	0.751545	0.0309932
$589$	−0.0670766	−0.00276384
$590$	−7.86077	−0.323623
$591$	0.408136	0.0167885
$592$	−5.32148	−0.218712
$593$	−34.7956	−1.42888	−0.714442	−	0.699694i	$-0.753320\pi$
$593$	−34.7956	−1.42888	−0.714442	+	0.699694i	$0.753320\pi$
$594$	−24.3387	−0.998627
$595$	17.1629	0.703608
$596$	−14.4488	−0.591847
$597$	−2.40750	−0.0985324
$598$	22.5906	0.923799
$599$	−36.7040	−1.49969	−0.749843	−	0.661616i	$-0.769871\pi$
$599$	−36.7040	−1.49969	−0.749843	+	0.661616i	$0.769871\pi$
$600$	0.327227	0.0133590
$601$	−37.0335	−1.51063	−0.755315	−	0.655362i	$-0.772516\pi$
$601$	−37.0335	−1.51063	−0.755315	+	0.655362i	$0.772516\pi$
$602$	−0.398393	−0.0162373
$603$	9.22640	0.375728
$604$	−18.5716	−0.755666
$605$	52.3488	2.12828
$606$	9.19300	0.373440
$607$	2.04004	0.0828028	0.0414014	−	0.999143i	$-0.486818\pi$
$607$	2.04004	0.0828028	0.0414014	+	0.999143i	$0.486818\pi$
$608$	−0.239104	−0.00969695
$609$	−6.66320	−0.270007
$610$	6.71681	0.271956
$611$	22.7025	0.918446
$612$	−19.5623	−0.790758
$613$	−43.1396	−1.74239	−0.871196	−	0.490935i	$-0.836655\pi$
$613$	−43.1396	−1.74239	−0.871196	+	0.490935i	$0.836655\pi$
$614$	29.0124	1.17084
$615$	−5.54159	−0.223458
$616$	5.95838	0.240070
$617$	28.2316	1.13656	0.568280	−	0.822835i	$-0.307609\pi$
$617$	28.2316	1.13656	0.568280	+	0.822835i	$0.307609\pi$
$618$	2.63676	0.106066
$619$	−6.02010	−0.241968	−0.120984	−	0.992654i	$-0.538605\pi$
$619$	−6.02010	−0.241968	−0.120984	+	0.992654i	$0.538605\pi$
$620$	−0.599356	−0.0240707
$621$	24.7297	0.992370
$622$	29.8301	1.19608
$623$	7.59153	0.304148
$624$	2.80435	0.112264
$625$	−22.6334	−0.905336
$626$	−2.14928	−0.0859026
$627$	−1.07070	−0.0427598
$628$	−6.40053	−0.255409
$629$	−42.7485	−1.70449
$630$	5.20274	0.207282
$631$	36.4923	1.45273	0.726367	−	0.687307i	$-0.241207\pi$
$631$	36.4923	1.45273	0.726367	+	0.687307i	$0.241207\pi$
$632$	−4.32894	−0.172196
$633$	20.2728	0.805773
$634$	−18.3808	−0.729997
$635$	9.32734	0.370144
$636$	−0.440599	−0.0174709
$637$	3.73145	0.147845
$638$	−52.8270	−2.09144
$639$	35.9166	1.42084
$640$	−2.13649	−0.0844522
$641$	−27.2005	−1.07436	−0.537178	−	0.843469i	$-0.680510\pi$
$641$	−27.2005	−1.07436	−0.537178	+	0.843469i	$0.680510\pi$
$642$	−5.94491	−0.234627
$643$	12.4240	0.489953	0.244977	−	0.969529i	$-0.421220\pi$
$643$	12.4240	0.489953	0.244977	+	0.969529i	$0.421220\pi$
$644$	−6.05411	−0.238566
$645$	0.639688	0.0251877
$646$	−1.92077	−0.0755717
$647$	23.3945	0.919734	0.459867	−	0.887988i	$-0.347897\pi$
$647$	23.3945	0.919734	0.459867	+	0.887988i	$0.347897\pi$
$648$	−4.23565	−0.166392
$649$	−21.9226	−0.860537
$650$	1.62469	0.0637257
$651$	−0.210833	−0.00826320
$652$	−17.2311	−0.674820
$653$	−0.656647	−0.0256966	−0.0128483	−	0.999917i	$-0.504090\pi$
$653$	−0.656647	−0.0256966	−0.0128483	+	0.999917i	$0.504090\pi$
$654$	−7.49839	−0.293210
$655$	−9.32677	−0.364427
$656$	−3.45126	−0.134749
$657$	22.3569	0.872225
$658$	−6.08411	−0.237183
$659$	−32.2478	−1.25620	−0.628098	−	0.778134i	$-0.716167\pi$
$659$	−32.2478	−1.25620	−0.628098	+	0.778134i	$0.716167\pi$
$660$	−9.56718	−0.372402
$661$	23.2211	0.903197	0.451598	−	0.892221i	$-0.350854\pi$
$661$	23.2211	0.903197	0.451598	+	0.892221i	$0.350854\pi$
$662$	15.5805	0.605555
$663$	22.5279	0.874911
$664$	13.5758	0.526845
$665$	0.510844	0.0198097
$666$	−12.9588	−0.502142
$667$	53.6758	2.07834
$668$	−24.2808	−0.939453
$669$	−5.42586	−0.209776
$670$	8.09473	0.312727
$671$	18.7322	0.723150
$672$	−0.751545	−0.0289915
$673$	−39.4086	−1.51909	−0.759544	−	0.650456i	$-0.774578\pi$
$673$	−39.4086	−1.51909	−0.759544	+	0.650456i	$0.774578\pi$
$674$	18.3002	0.704896
$675$	1.77854	0.0684559
$676$	0.923699	0.0355269
$677$	−13.7045	−0.526707	−0.263354	−	0.964699i	$-0.584829\pi$
$677$	−13.7045	−0.526707	−0.263354	+	0.964699i	$0.584829\pi$
$678$	−9.57942	−0.367895
$679$	5.43259	0.208484
$680$	−17.1629	−0.658165
$681$	−3.88023	−0.148691
$682$	−1.67152	−0.0640059
$683$	−28.7529	−1.10020	−0.550100	−	0.835099i	$-0.685410\pi$
$683$	−28.7529	−1.10020	−0.550100	+	0.835099i	$0.685410\pi$
$684$	−0.582261	−0.0222633
$685$	−43.6153	−1.66645
$686$	−1.00000	−0.0381802
$687$	11.6742	0.445397
$688$	0.398393	0.0151886
$689$	−2.18759	−0.0833406
$690$	9.72090	0.370068
$691$	30.5945	1.16387	0.581935	−	0.813235i	$-0.302296\pi$
$691$	30.5945	1.16387	0.581935	+	0.813235i	$0.302296\pi$
$692$	14.0397	0.533709
$693$	14.5097	0.551179
$694$	20.8812	0.792638
$695$	15.1697	0.575419
$696$	6.66320	0.252568
$697$	−27.7247	−1.05015
$698$	19.6121	0.742330
$699$	8.36557	0.316415
$700$	−0.435405	−0.0164568
$701$	40.3038	1.52225	0.761127	−	0.648603i	$-0.224646\pi$
$701$	40.3038	1.52225	0.761127	+	0.648603i	$0.224646\pi$
$702$	15.2421	0.575278
$703$	−1.27239	−0.0479890
$704$	−5.95838	−0.224565
$705$	9.76906	0.367924
$706$	−12.6577	−0.476379
$707$	−12.2321	−0.460037
$708$	2.76515	0.103921
$709$	−0.750826	−0.0281979	−0.0140989	−	0.999901i	$-0.504488\pi$
$709$	−0.750826	−0.0281979	−0.0140989	+	0.999901i	$0.504488\pi$
$710$	31.5112	1.18259
$711$	−10.5418	−0.395347
$712$	−7.59153	−0.284505
$713$	1.69838	0.0636048
$714$	−6.03731	−0.225940
$715$	−47.5014	−1.77645
$716$	12.5258	0.468111
$717$	−9.35934	−0.349531
$718$	−25.5997	−0.955371
$719$	−41.8923	−1.56232	−0.781160	−	0.624331i	$-0.785372\pi$
$719$	−41.8923	−1.56232	−0.781160	+	0.624331i	$0.785372\pi$
$720$	−5.20274	−0.193895
$721$	−3.50846	−0.130662
$722$	18.9428	0.704979
$723$	4.39180	0.163333
$724$	14.3003	0.531466
$725$	3.86031	0.143368
$726$	−18.4145	−0.683427
$727$	−26.5391	−0.984280	−0.492140	−	0.870516i	$-0.663785\pi$
$727$	−26.5391	−0.984280	−0.492140	+	0.870516i	$0.663785\pi$
$728$	−3.73145	−0.138297
$729$	−1.10488	−0.0409213
$730$	19.6147	0.725972
$731$	3.20037	0.118370
$732$	−2.36274	−0.0873295
$733$	48.7406	1.80028	0.900138	−	0.435605i	$-0.143466\pi$
$733$	48.7406	1.80028	0.900138	+	0.435605i	$0.143466\pi$
$734$	−6.29401	−0.232316
$735$	1.60567	0.0592260
$736$	6.05411	0.223158
$737$	22.5751	0.831563
$738$	−8.40445	−0.309372
$739$	−12.5522	−0.461739	−0.230870	−	0.972985i	$-0.574157\pi$
$739$	−12.5522	−0.461739	−0.230870	+	0.972985i	$0.574157\pi$
$740$	−11.3693	−0.417944
$741$	0.670531	0.0246326
$742$	0.586258	0.0215222
$743$	−12.5667	−0.461027	−0.230513	−	0.973069i	$-0.574041\pi$
$743$	−12.5667	−0.461027	−0.230513	+	0.973069i	$0.574041\pi$
$744$	0.210833	0.00772952
$745$	−30.8698	−1.13098
$746$	3.95632	0.144851
$747$	33.0596	1.20959
$748$	−47.8648	−1.75011
$749$	7.91026	0.289035
$750$	8.72746	0.318682
$751$	−24.8391	−0.906391	−0.453195	−	0.891411i	$-0.649716\pi$
$751$	−24.8391	−0.906391	−0.453195	+	0.891411i	$0.649716\pi$
$752$	6.08411	0.221864
$753$	−2.52421	−0.0919874
$754$	33.0830	1.20481
$755$	−39.6780	−1.44403
$756$	−4.08478	−0.148562
$757$	34.4707	1.25286	0.626430	−	0.779478i	$-0.284515\pi$
$757$	34.4707	1.25286	0.626430	+	0.779478i	$0.284515\pi$
$758$	−19.6394	−0.713334
$759$	27.1102	0.984039
$760$	−0.510844	−0.0185302
$761$	30.2863	1.09788	0.548939	−	0.835863i	$-0.315032\pi$
$761$	30.2863	1.09788	0.548939	+	0.835863i	$0.315032\pi$
$762$	−3.28104	−0.118860
$763$	9.97730	0.361203
$764$	−14.2729	−0.516374
$765$	−41.7946	−1.51109
$766$	−38.0383	−1.37438
$767$	13.7291	0.495728
$768$	0.751545	0.0271190
$769$	−5.58928	−0.201555	−0.100777	−	0.994909i	$-0.532133\pi$
$769$	−5.58928	−0.201555	−0.100777	+	0.994909i	$0.532133\pi$
$770$	12.7300	0.458758
$771$	0.959825	0.0345672
$772$	−0.0222935	−0.000802359 0
$773$	−36.6093	−1.31674	−0.658372	−	0.752692i	$-0.728755\pi$
$773$	−36.6093	−1.31674	−0.658372	+	0.752692i	$0.728755\pi$
$774$	0.970160	0.0348717
$775$	0.122146	0.00438760
$776$	−5.43259	−0.195018
$777$	−3.99933	−0.143475
$778$	12.2258	0.438315
$779$	−0.825211	−0.0295663
$780$	5.99147	0.214529
$781$	87.8803	3.14461
$782$	48.6339	1.73914
$783$	36.2157	1.29424
$784$	1.00000	0.0357143
$785$	−13.6747	−0.488070
$786$	3.28084	0.117024
$787$	−4.22892	−0.150745	−0.0753723	−	0.997155i	$-0.524015\pi$
$787$	−4.22892	−0.150745	−0.0753723	+	0.997155i	$0.524015\pi$
$788$	0.543063	0.0193458
$789$	−13.4586	−0.479140
$790$	−9.24875	−0.329056
$791$	12.7463	0.453207
$792$	−14.5097	−0.515580
$793$	−11.7311	−0.416584
$794$	4.75623	0.168792
$795$	−0.941337	−0.0333858
$796$	−3.20340	−0.113542
$797$	−12.8117	−0.453813	−0.226907	−	0.973917i	$-0.572861\pi$
$797$	−12.8117	−0.453813	−0.226907	+	0.973917i	$0.572861\pi$
$798$	−0.179697	−0.00636122
$799$	48.8748	1.72907
$800$	0.435405	0.0153939
$801$	−18.4867	−0.653197
$802$	1.11675	0.0394336
$803$	54.7026	1.93041
$804$	−2.84745	−0.100422
$805$	−12.9346	−0.455883
$806$	1.04679	0.0368718
$807$	20.5631	0.723855
$808$	12.2321	0.430325
$809$	2.79622	0.0983100	0.0491550	−	0.998791i	$-0.484347\pi$
$809$	2.79622	0.0983100	0.0491550	+	0.998791i	$0.484347\pi$
$810$	−9.04942	−0.317964
$811$	21.8374	0.766816	0.383408	−	0.923579i	$-0.374750\pi$
$811$	21.8374	0.766816	0.383408	+	0.923579i	$0.374750\pi$
$812$	−8.86601	−0.311136
$813$	−10.6134	−0.372227
$814$	−31.7074	−1.11134
$815$	−36.8140	−1.28954
$816$	6.03731	0.211348
$817$	0.0952575	0.00333264
$818$	0.0593532	0.00207524
$819$	−9.08675	−0.317517
$820$	−7.37360	−0.257497
$821$	48.0696	1.67764	0.838821	−	0.544407i	$-0.183245\pi$
$821$	48.0696	1.67764	0.838821	+	0.544407i	$0.183245\pi$
$822$	15.3424	0.535126
$823$	0.0840996	0.00293153	0.00146576	−	0.999999i	$-0.499533\pi$
$823$	0.0840996	0.00293153	0.00146576	+	0.999999i	$0.499533\pi$
$824$	3.50846	0.122223
$825$	1.94974	0.0678812
$826$	−3.67929	−0.128019
$827$	−24.9999	−0.869331	−0.434665	−	0.900592i	$-0.643133\pi$
$827$	−24.9999	−0.869331	−0.434665	+	0.900592i	$0.643133\pi$
$828$	14.7429	0.512350
$829$	13.6323	0.473471	0.236735	−	0.971574i	$-0.423923\pi$
$829$	13.6323	0.473471	0.236735	+	0.971574i	$0.423923\pi$
$830$	29.0047	1.00677
$831$	−8.62399	−0.299163
$832$	3.73145	0.129365
$833$	8.03319	0.278334
$834$	−5.33618	−0.184777
$835$	−51.8758	−1.79523
$836$	−1.42467	−0.0492733
$837$	1.14592	0.0396087
$838$	−19.4694	−0.672559
$839$	−21.9651	−0.758318	−0.379159	−	0.925332i	$-0.623787\pi$
$839$	−21.9651	−0.758318	−0.379159	+	0.925332i	$0.623787\pi$
$840$	−1.60567	−0.0554008
$841$	49.6061	1.71055
$842$	−34.4887	−1.18856
$843$	1.66946	0.0574994
$844$	26.9749	0.928514
$845$	1.97347	0.0678896
$846$	14.8159	0.509381
$847$	24.5022	0.841907
$848$	−0.586258	−0.0201322
$849$	13.7461	0.471766
$850$	3.49770	0.119970
$851$	32.2169	1.10438
$852$	−11.0846	−0.379751
$853$	1.88183	0.0644325	0.0322163	−	0.999481i	$-0.489743\pi$
$853$	1.88183	0.0644325	0.0322163	+	0.999481i	$0.489743\pi$
$854$	3.14385	0.107580
$855$	−1.24400	−0.0425438
$856$	−7.91026	−0.270367
$857$	11.2088	0.382885	0.191443	−	0.981504i	$-0.438683\pi$
$857$	11.2088	0.382885	0.191443	+	0.981504i	$0.438683\pi$
$858$	16.7094	0.570448
$859$	18.7653	0.640265	0.320132	−	0.947373i	$-0.396273\pi$
$859$	18.7653	0.640265	0.320132	+	0.947373i	$0.396273\pi$
$860$	0.851164	0.0290245
$861$	−2.59378	−0.0883958
$862$	−1.00000	−0.0340601
$863$	−43.6799	−1.48688	−0.743440	−	0.668802i	$-0.766807\pi$
$863$	−43.6799	−1.48688	−0.743440	+	0.668802i	$0.766807\pi$
$864$	4.08478	0.138967
$865$	29.9957	1.01988
$866$	14.6256	0.497000
$867$	35.7226	1.21320
$868$	−0.280533	−0.00952191
$869$	−25.7935	−0.874983
$870$	14.2359	0.482641
$871$	−14.1377	−0.479037
$872$	−9.97730	−0.337874
$873$	−13.2293	−0.447745
$874$	1.44756	0.0489646
$875$	−11.6127	−0.392581
$876$	−6.89977	−0.233122
$877$	49.3798	1.66744	0.833718	−	0.552190i	$-0.186208\pi$
$877$	49.3798	1.66744	0.833718	+	0.552190i	$0.186208\pi$
$878$	−9.84609	−0.332290
$879$	−8.49622	−0.286570
$880$	−12.7300	−0.429129
$881$	−11.7577	−0.396126	−0.198063	−	0.980189i	$-0.563465\pi$
$881$	−11.7577	−0.396126	−0.198063	+	0.980189i	$0.563465\pi$
$882$	2.43518	0.0819968
$883$	21.6621	0.728987	0.364494	−	0.931206i	$-0.381242\pi$
$883$	21.6621	0.728987	0.364494	+	0.931206i	$0.381242\pi$
$884$	29.9754	1.00818
$885$	5.90772	0.198586
$886$	34.7697	1.16811
$887$	−14.8905	−0.499975	−0.249988	−	0.968249i	$-0.580427\pi$
$887$	−14.8905	−0.499975	−0.249988	+	0.968249i	$0.580427\pi$
$888$	3.99933	0.134209
$889$	4.36573	0.146422
$890$	−16.2192	−0.543670
$891$	−25.2376	−0.845490
$892$	−7.21962	−0.241731
$893$	1.45473	0.0486808
$894$	10.8589	0.363177
$895$	26.7613	0.894531
$896$	−1.00000	−0.0334077
$897$	−16.9779	−0.566874
$898$	19.3907	0.647075
$899$	2.48721	0.0829530
$900$	1.06029	0.0353430
$901$	−4.70953	−0.156897
$902$	−20.5639	−0.684704
$903$	0.299411	0.00996376
$904$	−12.7463	−0.423936
$905$	30.5524	1.01560
$906$	13.9574	0.463702
$907$	10.8388	0.359896	0.179948	−	0.983676i	$-0.442407\pi$
$907$	10.8388	0.359896	0.179948	+	0.983676i	$0.442407\pi$
$908$	−5.16301	−0.171340
$909$	29.7875	0.987988
$910$	−7.97220	−0.264276
$911$	2.55314	0.0845894	0.0422947	−	0.999105i	$-0.486533\pi$
$911$	2.55314	0.0845894	0.0422947	+	0.999105i	$0.486533\pi$
$912$	0.179697	0.00595037
$913$	80.8899	2.67707
$914$	3.57656	0.118302
$915$	−5.04798	−0.166881
$916$	15.5335	0.513243
$917$	−4.36546	−0.144160
$918$	32.8138	1.08302
$919$	12.8712	0.424583	0.212292	−	0.977206i	$-0.431907\pi$
$919$	12.8712	0.424583	0.212292	+	0.977206i	$0.431907\pi$
$920$	12.9346	0.426440
$921$	−21.8041	−0.718469
$922$	−27.0939	−0.892291
$923$	−55.0353	−1.81151
$924$	−4.47799	−0.147315
$925$	2.31700	0.0761825
$926$	−32.3681	−1.06368
$927$	8.54373	0.280613
$928$	8.86601	0.291041
$929$	−28.1398	−0.923237	−0.461618	−	0.887079i	$-0.652731\pi$
$929$	−28.1398	−0.923237	−0.461618	+	0.887079i	$0.652731\pi$
$930$	0.450443	0.0147706
$931$	0.239104	0.00783632
$932$	11.1312	0.364614
$933$	−22.4187	−0.733954
$934$	−20.9327	−0.684940
$935$	−102.263	−3.34435
$936$	9.08675	0.297010
$937$	−42.8376	−1.39944	−0.699721	−	0.714416i	$-0.746693\pi$
$937$	−42.8376	−1.39944	−0.699721	+	0.714416i	$0.746693\pi$
$938$	3.78879	0.123709
$939$	1.61528	0.0527127
$940$	12.9986	0.423969
$941$	−11.1519	−0.363541	−0.181770	−	0.983341i	$-0.558183\pi$
$941$	−11.1519	−0.363541	−0.181770	+	0.983341i	$0.558183\pi$
$942$	4.81029	0.156728
$943$	20.8944	0.680414
$944$	3.67929	0.119751
$945$	−8.72710	−0.283893
$946$	2.37378	0.0771782
$947$	23.6739	0.769298	0.384649	−	0.923063i	$-0.374323\pi$
$947$	23.6739	0.769298	0.384649	+	0.923063i	$0.374323\pi$
$948$	3.25339	0.105665
$949$	−34.2576	−1.11205
$950$	0.104107	0.00337768
$951$	13.8140	0.447951
$952$	−8.03319	−0.260357
$953$	21.1774	0.686002	0.343001	−	0.939335i	$-0.388557\pi$
$953$	21.1774	0.686002	0.343001	+	0.939335i	$0.388557\pi$
$954$	−1.42765	−0.0462217
$955$	−30.4939	−0.986758
$956$	−12.4535	−0.402774
$957$	39.7018	1.28338
$958$	7.66558	0.247664
$959$	−20.4144	−0.659216
$960$	1.60567	0.0518227
$961$	−30.9213	−0.997461
$962$	19.8568	0.640210
$963$	−19.2629	−0.620739
$964$	5.84369	0.188213
$965$	−0.0476298	−0.00153326
$966$	4.54994	0.146392
$967$	−32.4736	−1.04428	−0.522141	−	0.852859i	$-0.674867\pi$
$967$	−32.4736	−1.04428	−0.522141	+	0.852859i	$0.674867\pi$
$968$	−24.5022	−0.787532
$969$	1.44354	0.0463733
$970$	−11.6067	−0.372668
$971$	8.81755	0.282968	0.141484	−	0.989941i	$-0.454813\pi$
$971$	8.81755	0.282968	0.141484	+	0.989941i	$0.454813\pi$
$972$	15.4376	0.495162
$973$	7.10028	0.227625
$974$	4.27810	0.137079
$975$	−1.22103	−0.0391042
$976$	−3.14385	−0.100632
$977$	−27.2832	−0.872868	−0.436434	−	0.899736i	$-0.643759\pi$
$977$	−27.2832	−0.872868	−0.436434	+	0.899736i	$0.643759\pi$
$978$	12.9499	0.414093
$979$	−45.2332	−1.44566
$980$	2.13649	0.0682477
$981$	−24.2965	−0.775728
$982$	26.6413	0.850157
$983$	−28.9916	−0.924687	−0.462344	−	0.886701i	$-0.652991\pi$
$983$	−28.9916	−0.924687	−0.462344	+	0.886701i	$0.652991\pi$
$984$	2.59378	0.0826867
$985$	1.16025	0.0369686
$986$	71.2224	2.26818
$987$	4.57248	0.145544
$988$	0.892204	0.0283848
$989$	−2.41192	−0.0766946
$990$	−30.9999	−0.985241
$991$	10.8232	0.343810	0.171905	−	0.985114i	$-0.445008\pi$
$991$	10.8232	0.343810	0.171905	+	0.985114i	$0.445008\pi$
$992$	0.280533	0.00890693
$993$	−11.7095	−0.371589
$994$	14.7490	0.467811
$995$	−6.84404	−0.216971
$996$	−10.2029	−0.323290
$997$	−11.4596	−0.362929	−0.181465	−	0.983397i	$-0.558084\pi$
$997$	−11.4596	−0.362929	−0.181465	+	0.983397i	$0.558084\pi$
$998$	28.2000	0.892656
$999$	21.7371	0.687731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.11	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.751545 q^{3} +1.00000 q^{4} +2.13649 q^{5} -0.751545 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.43518 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.751545 q^{3} +1.00000 q^{4} +2.13649 q^{5} -0.751545 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.43518 q^{9} -2.13649 q^{10} -5.95838 q^{11} +0.751545 q^{12} +3.73145 q^{13} -1.00000 q^{14} +1.60567 q^{15} +1.00000 q^{16} +8.03319 q^{17} +2.43518 q^{18} +0.239104 q^{19} +2.13649 q^{20} +0.751545 q^{21} +5.95838 q^{22} -6.05411 q^{23} -0.751545 q^{24} -0.435405 q^{25} -3.73145 q^{26} -4.08478 q^{27} +1.00000 q^{28} -8.86601 q^{29} -1.60567 q^{30} -0.280533 q^{31} -1.00000 q^{32} -4.47799 q^{33} -8.03319 q^{34} +2.13649 q^{35} -2.43518 q^{36} -5.32148 q^{37} -0.239104 q^{38} +2.80435 q^{39} -2.13649 q^{40} -3.45126 q^{41} -0.751545 q^{42} +0.398393 q^{43} -5.95838 q^{44} -5.20274 q^{45} +6.05411 q^{46} +6.08411 q^{47} +0.751545 q^{48} +1.00000 q^{49} +0.435405 q^{50} +6.03731 q^{51} +3.73145 q^{52} -0.586258 q^{53} +4.08478 q^{54} -12.7300 q^{55} -1.00000 q^{56} +0.179697 q^{57} +8.86601 q^{58} +3.67929 q^{59} +1.60567 q^{60} -3.14385 q^{61} +0.280533 q^{62} -2.43518 q^{63} +1.00000 q^{64} +7.97220 q^{65} +4.47799 q^{66} -3.78879 q^{67} +8.03319 q^{68} -4.54994 q^{69} -2.13649 q^{70} -14.7490 q^{71} +2.43518 q^{72} -9.18079 q^{73} +5.32148 q^{74} -0.327227 q^{75} +0.239104 q^{76} -5.95838 q^{77} -2.80435 q^{78} +4.32894 q^{79} +2.13649 q^{80} +4.23565 q^{81} +3.45126 q^{82} -13.5758 q^{83} +0.751545 q^{84} +17.1629 q^{85} -0.398393 q^{86} -6.66320 q^{87} +5.95838 q^{88} +7.59153 q^{89} +5.20274 q^{90} +3.73145 q^{91} -6.05411 q^{92} -0.210833 q^{93} -6.08411 q^{94} +0.510844 q^{95} -0.751545 q^{96} +5.43259 q^{97} -1.00000 q^{98} +14.5097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 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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