LMFDB - Embedded newform 6034.2.a.k.1.15

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			1.15
Root			$1.67912$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.67912 q^{3} +1.00000 q^{4} -1.69524 q^{5} -1.67912 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.180554 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.67912 q^{3} +1.00000 q^{4} -1.69524 q^{5} -1.67912 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.180554 q^{9} +1.69524 q^{10} +4.65489 q^{11} +1.67912 q^{12} -0.320498 q^{13} -1.00000 q^{14} -2.84652 q^{15} +1.00000 q^{16} +2.38023 q^{17} +0.180554 q^{18} -4.51393 q^{19} -1.69524 q^{20} +1.67912 q^{21} -4.65489 q^{22} -8.80596 q^{23} -1.67912 q^{24} -2.12616 q^{25} +0.320498 q^{26} -5.34053 q^{27} +1.00000 q^{28} +4.80865 q^{29} +2.84652 q^{30} +3.45359 q^{31} -1.00000 q^{32} +7.81612 q^{33} -2.38023 q^{34} -1.69524 q^{35} -0.180554 q^{36} -0.904135 q^{37} +4.51393 q^{38} -0.538154 q^{39} +1.69524 q^{40} +5.03633 q^{41} -1.67912 q^{42} -7.81603 q^{43} +4.65489 q^{44} +0.306082 q^{45} +8.80596 q^{46} -7.05508 q^{47} +1.67912 q^{48} +1.00000 q^{49} +2.12616 q^{50} +3.99670 q^{51} -0.320498 q^{52} +1.94750 q^{53} +5.34053 q^{54} -7.89116 q^{55} -1.00000 q^{56} -7.57943 q^{57} -4.80865 q^{58} -10.8892 q^{59} -2.84652 q^{60} +5.12583 q^{61} -3.45359 q^{62} -0.180554 q^{63} +1.00000 q^{64} +0.543321 q^{65} -7.81612 q^{66} -3.33775 q^{67} +2.38023 q^{68} -14.7863 q^{69} +1.69524 q^{70} -1.07135 q^{71} +0.180554 q^{72} +10.7129 q^{73} +0.904135 q^{74} -3.57007 q^{75} -4.51393 q^{76} +4.65489 q^{77} +0.538154 q^{78} -14.1319 q^{79} -1.69524 q^{80} -8.42574 q^{81} -5.03633 q^{82} -14.2802 q^{83} +1.67912 q^{84} -4.03507 q^{85} +7.81603 q^{86} +8.07430 q^{87} -4.65489 q^{88} -10.1044 q^{89} -0.306082 q^{90} -0.320498 q^{91} -8.80596 q^{92} +5.79899 q^{93} +7.05508 q^{94} +7.65220 q^{95} -1.67912 q^{96} -6.73224 q^{97} -1.00000 q^{98} -0.840457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.67912	0.969441	0.484720	−	0.874669i	$-0.338921\pi$
$3$	1.67912	0.969441	0.484720	+	0.874669i	$0.338921\pi$
$4$	1.00000	0.500000
$5$	−1.69524	−0.758135	−0.379068	−	0.925369i	$-0.623755\pi$
$5$	−1.69524	−0.758135	−0.379068	+	0.925369i	$0.623755\pi$
$6$	−1.67912	−0.685498
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−0.180554	−0.0601845
$10$	1.69524	0.536082
$11$	4.65489	1.40350	0.701751	−	0.712423i	$-0.252402\pi$
$11$	4.65489	1.40350	0.701751	+	0.712423i	$0.252402\pi$
$12$	1.67912	0.484720
$13$	−0.320498	−0.0888901	−0.0444450	−	0.999012i	$-0.514152\pi$
$13$	−0.320498	−0.0888901	−0.0444450	+	0.999012i	$0.514152\pi$
$14$	−1.00000	−0.267261
$15$	−2.84652	−0.734967
$16$	1.00000	0.250000
$17$	2.38023	0.577292	0.288646	−	0.957436i	$-0.406795\pi$
$17$	2.38023	0.577292	0.288646	+	0.957436i	$0.406795\pi$
$18$	0.180554	0.0425569
$19$	−4.51393	−1.03557	−0.517783	−	0.855512i	$-0.673243\pi$
$19$	−4.51393	−1.03557	−0.517783	+	0.855512i	$0.673243\pi$
$20$	−1.69524	−0.379068
$21$	1.67912	0.366414
$22$	−4.65489	−0.992425
$23$	−8.80596	−1.83617	−0.918084	−	0.396385i	$-0.870265\pi$
$23$	−8.80596	−1.83617	−0.918084	+	0.396385i	$0.870265\pi$
$24$	−1.67912	−0.342749
$25$	−2.12616	−0.425231
$26$	0.320498	0.0628548
$27$	−5.34053	−1.02779
$28$	1.00000	0.188982
$29$	4.80865	0.892944	0.446472	−	0.894798i	$-0.352680\pi$
$29$	4.80865	0.892944	0.446472	+	0.894798i	$0.352680\pi$
$30$	2.84652	0.519700
$31$	3.45359	0.620283	0.310141	−	0.950690i	$-0.399624\pi$
$31$	3.45359	0.620283	0.310141	+	0.950690i	$0.399624\pi$
$32$	−1.00000	−0.176777
$33$	7.81612	1.36061
$34$	−2.38023	−0.408207
$35$	−1.69524	−0.286548
$36$	−0.180554	−0.0300923
$37$	−0.904135	−0.148639	−0.0743194	−	0.997234i	$-0.523678\pi$
$37$	−0.904135	−0.148639	−0.0743194	+	0.997234i	$0.523678\pi$
$38$	4.51393	0.732256
$39$	−0.538154	−0.0861737
$40$	1.69524	0.268041
$41$	5.03633	0.786542	0.393271	−	0.919423i	$-0.371343\pi$
$41$	5.03633	0.786542	0.393271	+	0.919423i	$0.371343\pi$
$42$	−1.67912	−0.259094
$43$	−7.81603	−1.19193	−0.595967	−	0.803009i	$-0.703231\pi$
$43$	−7.81603	−1.19193	−0.595967	+	0.803009i	$0.703231\pi$
$44$	4.65489	0.701751
$45$	0.306082	0.0456280
$46$	8.80596	1.29837
$47$	−7.05508	−1.02909	−0.514544	−	0.857464i	$-0.672039\pi$
$47$	−7.05508	−1.02909	−0.514544	+	0.857464i	$0.672039\pi$
$48$	1.67912	0.242360
$49$	1.00000	0.142857
$50$	2.12616	0.300684
$51$	3.99670	0.559650
$52$	−0.320498	−0.0444450
$53$	1.94750	0.267510	0.133755	−	0.991014i	$-0.457296\pi$
$53$	1.94750	0.267510	0.133755	+	0.991014i	$0.457296\pi$
$54$	5.34053	0.726755
$55$	−7.89116	−1.06404
$56$	−1.00000	−0.133631
$57$	−7.57943	−1.00392
$58$	−4.80865	−0.631407
$59$	−10.8892	−1.41766	−0.708829	−	0.705380i	$-0.750776\pi$
$59$	−10.8892	−1.41766	−0.708829	+	0.705380i	$0.750776\pi$
$60$	−2.84652	−0.367484
$61$	5.12583	0.656296	0.328148	−	0.944626i	$-0.393576\pi$
$61$	5.12583	0.656296	0.328148	+	0.944626i	$0.393576\pi$
$62$	−3.45359	−0.438606
$63$	−0.180554	−0.0227476
$64$	1.00000	0.125000
$65$	0.543321	0.0673907
$66$	−7.81612	−0.962098
$67$	−3.33775	−0.407771	−0.203886	−	0.978995i	$-0.565357\pi$
$67$	−3.33775	−0.407771	−0.203886	+	0.978995i	$0.565357\pi$
$68$	2.38023	0.288646
$69$	−14.7863	−1.78006
$70$	1.69524	0.202620
$71$	−1.07135	−0.127146	−0.0635728	−	0.997977i	$-0.520250\pi$
$71$	−1.07135	−0.127146	−0.0635728	+	0.997977i	$0.520250\pi$
$72$	0.180554	0.0212784
$73$	10.7129	1.25385	0.626927	−	0.779078i	$-0.284312\pi$
$73$	10.7129	1.25385	0.626927	+	0.779078i	$0.284312\pi$
$74$	0.904135	0.105104
$75$	−3.57007	−0.412236
$76$	−4.51393	−0.517783
$77$	4.65489	0.530474
$78$	0.538154	0.0609340
$79$	−14.1319	−1.58996	−0.794982	−	0.606633i	$-0.792520\pi$
$79$	−14.1319	−1.58996	−0.794982	+	0.606633i	$0.792520\pi$
$80$	−1.69524	−0.189534
$81$	−8.42574	−0.936193
$82$	−5.03633	−0.556169
$83$	−14.2802	−1.56746	−0.783728	−	0.621104i	$-0.786684\pi$
$83$	−14.2802	−1.56746	−0.783728	+	0.621104i	$0.786684\pi$
$84$	1.67912	0.183207
$85$	−4.03507	−0.437665
$86$	7.81603	0.842825
$87$	8.07430	0.865656
$88$	−4.65489	−0.496213
$89$	−10.1044	−1.07107	−0.535534	−	0.844514i	$-0.679890\pi$
$89$	−10.1044	−1.07107	−0.535534	+	0.844514i	$0.679890\pi$
$90$	−0.306082	−0.0322639
$91$	−0.320498	−0.0335973
$92$	−8.80596	−0.918084
$93$	5.79899	0.601327
$94$	7.05508	0.727676
$95$	7.65220	0.785099
$96$	−1.67912	−0.171375
$97$	−6.73224	−0.683555	−0.341778	−	0.939781i	$-0.611029\pi$
$97$	−6.73224	−0.683555	−0.341778	+	0.939781i	$0.611029\pi$
$98$	−1.00000	−0.101015
$99$	−0.840457	−0.0844691
$100$	−2.12616	−0.212616
$101$	−9.31507	−0.926885	−0.463442	−	0.886127i	$-0.653386\pi$
$101$	−9.31507	−0.926885	−0.463442	+	0.886127i	$0.653386\pi$
$102$	−3.99670	−0.395732
$103$	15.5693	1.53409	0.767044	−	0.641595i	$-0.221727\pi$
$103$	15.5693	1.53409	0.767044	+	0.641595i	$0.221727\pi$
$104$	0.320498	0.0314274
$105$	−2.84652	−0.277791
$106$	−1.94750	−0.189158
$107$	3.93041	0.379967	0.189983	−	0.981787i	$-0.439157\pi$
$107$	3.93041	0.379967	0.189983	+	0.981787i	$0.439157\pi$
$108$	−5.34053	−0.513893
$109$	8.05728	0.771747	0.385874	−	0.922552i	$-0.373900\pi$
$109$	8.05728	0.771747	0.385874	+	0.922552i	$0.373900\pi$
$110$	7.89116	0.752393
$111$	−1.51815	−0.144097
$112$	1.00000	0.0944911
$113$	20.8811	1.96433	0.982166	−	0.188014i	$-0.0602051\pi$
$113$	20.8811	1.96433	0.982166	+	0.188014i	$0.0602051\pi$
$114$	7.57943	0.709879
$115$	14.9282	1.39206
$116$	4.80865	0.446472
$117$	0.0578670	0.00534981
$118$	10.8892	1.00244
$119$	2.38023	0.218196
$120$	2.84652	0.259850
$121$	10.6680	0.969817
$122$	−5.12583	−0.464071
$123$	8.45660	0.762506
$124$	3.45359	0.310141
$125$	12.0806	1.08052
$126$	0.180554	0.0160850
$127$	−17.0922	−1.51669	−0.758343	−	0.651855i	$-0.773991\pi$
$127$	−17.0922	−1.51669	−0.758343	+	0.651855i	$0.773991\pi$
$128$	−1.00000	−0.0883883
$129$	−13.1241	−1.15551
$130$	−0.543321	−0.0476524
$131$	−11.5798	−1.01173	−0.505867	−	0.862612i	$-0.668827\pi$
$131$	−11.5798	−1.01173	−0.505867	+	0.862612i	$0.668827\pi$
$132$	7.81612	0.680306
$133$	−4.51393	−0.391407
$134$	3.33775	0.288338
$135$	9.05349	0.779201
$136$	−2.38023	−0.204103
$137$	9.68178	0.827170	0.413585	−	0.910465i	$-0.364276\pi$
$137$	9.68178	0.827170	0.413585	+	0.910465i	$0.364276\pi$
$138$	14.7863	1.25869
$139$	3.29751	0.279691	0.139846	−	0.990173i	$-0.455339\pi$
$139$	3.29751	0.279691	0.139846	+	0.990173i	$0.455339\pi$
$140$	−1.69524	−0.143274
$141$	−11.8463	−0.997641
$142$	1.07135	0.0899055
$143$	−1.49188	−0.124757
$144$	−0.180554	−0.0150461
$145$	−8.15182	−0.676972
$146$	−10.7129	−0.886609
$147$	1.67912	0.138492
$148$	−0.904135	−0.0743194
$149$	0.607727	0.0497870	0.0248935	−	0.999690i	$-0.492075\pi$
$149$	0.607727	0.0497870	0.0248935	+	0.999690i	$0.492075\pi$
$150$	3.57007	0.291495
$151$	−16.2823	−1.32503	−0.662516	−	0.749048i	$-0.730511\pi$
$151$	−16.2823	−1.32503	−0.662516	+	0.749048i	$0.730511\pi$
$152$	4.51393	0.366128
$153$	−0.429760	−0.0347440
$154$	−4.65489	−0.375102
$155$	−5.85466	−0.470258
$156$	−0.538154	−0.0430868
$157$	5.49442	0.438502	0.219251	−	0.975668i	$-0.429639\pi$
$157$	5.49442	0.438502	0.219251	+	0.975668i	$0.429639\pi$
$158$	14.1319	1.12427
$159$	3.27010	0.259335
$160$	1.69524	0.134021
$161$	−8.80596	−0.694007
$162$	8.42574	0.661989
$163$	22.0981	1.73086	0.865430	−	0.501029i	$-0.167045\pi$
$163$	22.0981	1.73086	0.865430	+	0.501029i	$0.167045\pi$
$164$	5.03633	0.393271
$165$	−13.2502	−1.03153
$166$	14.2802	1.10836
$167$	−9.33203	−0.722134	−0.361067	−	0.932540i	$-0.617587\pi$
$167$	−9.33203	−0.722134	−0.361067	+	0.932540i	$0.617587\pi$
$168$	−1.67912	−0.129547
$169$	−12.8973	−0.992099
$170$	4.03507	0.309476
$171$	0.815006	0.0623250
$172$	−7.81603	−0.595967
$173$	−11.6432	−0.885213	−0.442606	−	0.896716i	$-0.645946\pi$
$173$	−11.6432	−0.885213	−0.442606	+	0.896716i	$0.645946\pi$
$174$	−8.07430	−0.612111
$175$	−2.12616	−0.160722
$176$	4.65489	0.350875
$177$	−18.2843	−1.37434
$178$	10.1044	0.757360
$179$	−15.1013	−1.12872	−0.564361	−	0.825528i	$-0.690877\pi$
$179$	−15.1013	−1.12872	−0.564361	+	0.825528i	$0.690877\pi$
$180$	0.306082	0.0228140
$181$	9.02565	0.670871	0.335435	−	0.942063i	$-0.391117\pi$
$181$	9.02565	0.670871	0.335435	+	0.942063i	$0.391117\pi$
$182$	0.320498	0.0237569
$183$	8.60689	0.636240
$184$	8.80596	0.649184
$185$	1.53273	0.112688
$186$	−5.79899	−0.425203
$187$	11.0797	0.810230
$188$	−7.05508	−0.514544
$189$	−5.34053	−0.388467
$190$	−7.65220	−0.555149
$191$	−13.2071	−0.955633	−0.477816	−	0.878460i	$-0.658572\pi$
$191$	−13.2071	−0.955633	−0.477816	+	0.878460i	$0.658572\pi$
$192$	1.67912	0.121180
$193$	22.0719	1.58877	0.794384	−	0.607416i	$-0.207794\pi$
$193$	22.0719	1.58877	0.794384	+	0.607416i	$0.207794\pi$
$194$	6.73224	0.483346
$195$	0.912302	0.0653313
$196$	1.00000	0.0714286
$197$	2.31580	0.164994	0.0824968	−	0.996591i	$-0.473711\pi$
$197$	2.31580	0.164994	0.0824968	+	0.996591i	$0.473711\pi$
$198$	0.840457	0.0597286
$199$	−22.5978	−1.60191	−0.800957	−	0.598722i	$-0.795675\pi$
$199$	−22.5978	−1.60191	−0.800957	+	0.598722i	$0.795675\pi$
$200$	2.12616	0.150342
$201$	−5.60449	−0.395310
$202$	9.31507	0.655406
$203$	4.80865	0.337501
$204$	3.99670	0.279825
$205$	−8.53779	−0.596305
$206$	−15.5693	−1.08476
$207$	1.58995	0.110509
$208$	−0.320498	−0.0222225
$209$	−21.0118	−1.45342
$210$	2.84652	0.196428
$211$	−10.1175	−0.696520	−0.348260	−	0.937398i	$-0.613227\pi$
$211$	−10.1175	−0.696520	−0.348260	+	0.937398i	$0.613227\pi$
$212$	1.94750	0.133755
$213$	−1.79892	−0.123260
$214$	−3.93041	−0.268677
$215$	13.2501	0.903647
$216$	5.34053	0.363377
$217$	3.45359	0.234445
$218$	−8.05728	−0.545708
$219$	17.9883	1.21554
$220$	−7.89116	−0.532022
$221$	−0.762860	−0.0513155
$222$	1.51815	0.101892
$223$	−2.00505	−0.134268	−0.0671340	−	0.997744i	$-0.521385\pi$
$223$	−2.00505	−0.134268	−0.0671340	+	0.997744i	$0.521385\pi$
$224$	−1.00000	−0.0668153
$225$	0.383885	0.0255923
$226$	−20.8811	−1.38899
$227$	17.4811	1.16026	0.580130	−	0.814524i	$-0.303002\pi$
$227$	17.4811	1.16026	0.580130	+	0.814524i	$0.303002\pi$
$228$	−7.57943	−0.501960
$229$	9.89158	0.653654	0.326827	−	0.945084i	$-0.394021\pi$
$229$	9.89158	0.653654	0.326827	+	0.945084i	$0.394021\pi$
$230$	−14.9282	−0.984338
$231$	7.81612	0.514263
$232$	−4.80865	−0.315703
$233$	−22.6361	−1.48294	−0.741469	−	0.670987i	$-0.765871\pi$
$233$	−22.6361	−1.48294	−0.741469	+	0.670987i	$0.765871\pi$
$234$	−0.0578670	−0.00378288
$235$	11.9601	0.780188
$236$	−10.8892	−0.708829
$237$	−23.7292	−1.54138
$238$	−2.38023	−0.154288
$239$	−14.9512	−0.967112	−0.483556	−	0.875313i	$-0.660655\pi$
$239$	−14.9512	−0.967112	−0.483556	+	0.875313i	$0.660655\pi$
$240$	−2.84652	−0.183742
$241$	6.92521	0.446092	0.223046	−	0.974808i	$-0.428400\pi$
$241$	6.92521	0.446092	0.223046	+	0.974808i	$0.428400\pi$
$242$	−10.6680	−0.685764
$243$	1.87377	0.120202
$244$	5.12583	0.328148
$245$	−1.69524	−0.108305
$246$	−8.45660	−0.539173
$247$	1.44670	0.0920515
$248$	−3.45359	−0.219303
$249$	−23.9782	−1.51956
$250$	−12.0806	−0.764041
$251$	−16.3274	−1.03058	−0.515288	−	0.857017i	$-0.672315\pi$
$251$	−16.3274	−1.03058	−0.515288	+	0.857017i	$0.672315\pi$
$252$	−0.180554	−0.0113738
$253$	−40.9907	−2.57707
$254$	17.0922	1.07246
$255$	−6.77537	−0.424290
$256$	1.00000	0.0625000
$257$	−3.16381	−0.197353	−0.0986765	−	0.995120i	$-0.531461\pi$
$257$	−3.16381	−0.197353	−0.0986765	+	0.995120i	$0.531461\pi$
$258$	13.1241	0.817069
$259$	−0.904135	−0.0561802
$260$	0.543321	0.0336953
$261$	−0.868219	−0.0537414
$262$	11.5798	0.715404
$263$	30.9705	1.90972	0.954862	−	0.297051i	$-0.0960030\pi$
$263$	30.9705	1.90972	0.954862	+	0.297051i	$0.0960030\pi$
$264$	−7.81612	−0.481049
$265$	−3.30149	−0.202809
$266$	4.51393	0.276767
$267$	−16.9666	−1.03834
$268$	−3.33775	−0.203886
$269$	−8.76749	−0.534563	−0.267282	−	0.963618i	$-0.586125\pi$
$269$	−8.76749	−0.534563	−0.267282	+	0.963618i	$0.586125\pi$
$270$	−9.05349	−0.550978
$271$	−6.85765	−0.416573	−0.208286	−	0.978068i	$-0.566789\pi$
$271$	−6.85765	−0.416573	−0.208286	+	0.978068i	$0.566789\pi$
$272$	2.38023	0.144323
$273$	−0.538154	−0.0325706
$274$	−9.68178	−0.584898
$275$	−9.89702	−0.596813
$276$	−14.7863	−0.890028
$277$	−5.83536	−0.350613	−0.175306	−	0.984514i	$-0.556092\pi$
$277$	−5.83536	−0.350613	−0.175306	+	0.984514i	$0.556092\pi$
$278$	−3.29751	−0.197771
$279$	−0.623557	−0.0373314
$280$	1.69524	0.101310
$281$	−11.9693	−0.714026	−0.357013	−	0.934099i	$-0.616205\pi$
$281$	−11.9693	−0.714026	−0.357013	+	0.934099i	$0.616205\pi$
$282$	11.8463	0.705439
$283$	14.5373	0.864155	0.432077	−	0.901837i	$-0.357781\pi$
$283$	14.5373	0.864155	0.432077	+	0.901837i	$0.357781\pi$
$284$	−1.07135	−0.0635728
$285$	12.8490	0.761107
$286$	1.49188	0.0882168
$287$	5.03633	0.297285
$288$	0.180554	0.0106392
$289$	−11.3345	−0.666734
$290$	8.15182	0.478692
$291$	−11.3042	−0.662666
$292$	10.7129	0.626927
$293$	−3.47046	−0.202747	−0.101373	−	0.994848i	$-0.532324\pi$
$293$	−3.47046	−0.202747	−0.101373	+	0.994848i	$0.532324\pi$
$294$	−1.67912	−0.0979283
$295$	18.4599	1.07478
$296$	0.904135	0.0525518
$297$	−24.8596	−1.44250
$298$	−0.607727	−0.0352047
$299$	2.82229	0.163217
$300$	−3.57007	−0.206118
$301$	−7.81603	−0.450509
$302$	16.2823	0.936939
$303$	−15.6411	−0.898560
$304$	−4.51393	−0.258892
$305$	−8.68953	−0.497561
$306$	0.429760	0.0245677
$307$	−32.8909	−1.87718	−0.938592	−	0.345029i	$-0.887869\pi$
$307$	−32.8909	−1.87718	−0.938592	+	0.345029i	$0.887869\pi$
$308$	4.65489	0.265237
$309$	26.1427	1.48721
$310$	5.85466	0.332523
$311$	−7.67360	−0.435130	−0.217565	−	0.976046i	$-0.569811\pi$
$311$	−7.67360	−0.435130	−0.217565	+	0.976046i	$0.569811\pi$
$312$	0.538154	0.0304670
$313$	24.1768	1.36655	0.683276	−	0.730160i	$-0.260555\pi$
$313$	24.1768	1.36655	0.683276	+	0.730160i	$0.260555\pi$
$314$	−5.49442	−0.310068
$315$	0.306082	0.0172458
$316$	−14.1319	−0.794982
$317$	−19.8711	−1.11607	−0.558035	−	0.829817i	$-0.688445\pi$
$317$	−19.8711	−1.11607	−0.558035	+	0.829817i	$0.688445\pi$
$318$	−3.27010	−0.183378
$319$	22.3837	1.25325
$320$	−1.69524	−0.0947669
$321$	6.59963	0.368355
$322$	8.80596	0.490737
$323$	−10.7442	−0.597824
$324$	−8.42574	−0.468097
$325$	0.681428	0.0377988
$326$	−22.0981	−1.22390
$327$	13.5291	0.748163
$328$	−5.03633	−0.278085
$329$	−7.05508	−0.388959
$330$	13.2502	0.729400
$331$	25.5262	1.40305	0.701525	−	0.712645i	$-0.252503\pi$
$331$	25.5262	1.40305	0.701525	+	0.712645i	$0.252503\pi$
$332$	−14.2802	−0.783728
$333$	0.163245	0.00894576
$334$	9.33203	0.510626
$335$	5.65829	0.309146
$336$	1.67912	0.0916035
$337$	−4.93092	−0.268604	−0.134302	−	0.990940i	$-0.542879\pi$
$337$	−4.93092	−0.268604	−0.134302	+	0.990940i	$0.542879\pi$
$338$	12.8973	0.701520
$339$	35.0620	1.90430
$340$	−4.03507	−0.218833
$341$	16.0761	0.870568
$342$	−0.815006	−0.0440705
$343$	1.00000	0.0539949
$344$	7.81603	0.421412
$345$	25.0663	1.34952
$346$	11.6432	0.625940
$347$	−23.5333	−1.26333	−0.631667	−	0.775240i	$-0.717629\pi$
$347$	−23.5333	−1.26333	−0.631667	+	0.775240i	$0.717629\pi$
$348$	8.07430	0.432828
$349$	−21.5736	−1.15481	−0.577403	−	0.816459i	$-0.695934\pi$
$349$	−21.5736	−1.15481	−0.577403	+	0.816459i	$0.695934\pi$
$350$	2.12616	0.113648
$351$	1.71163	0.0913600
$352$	−4.65489	−0.248106
$353$	15.8953	0.846020	0.423010	−	0.906125i	$-0.360973\pi$
$353$	15.8953	0.846020	0.423010	+	0.906125i	$0.360973\pi$
$354$	18.2843	0.971802
$355$	1.81619	0.0963935
$356$	−10.1044	−0.535534
$357$	3.99670	0.211528
$358$	15.1013	0.798127
$359$	−19.8503	−1.04766	−0.523828	−	0.851824i	$-0.675497\pi$
$359$	−19.8503	−1.04766	−0.523828	+	0.851824i	$0.675497\pi$
$360$	−0.306082	−0.0161319
$361$	1.37554	0.0723970
$362$	−9.02565	−0.474377
$363$	17.9128	0.940180
$364$	−0.320498	−0.0167986
$365$	−18.1610	−0.950591
$366$	−8.60689	−0.449890
$367$	7.59621	0.396519	0.198260	−	0.980150i	$-0.436471\pi$
$367$	7.59621	0.396519	0.198260	+	0.980150i	$0.436471\pi$
$368$	−8.80596	−0.459042
$369$	−0.909327	−0.0473377
$370$	−1.53273	−0.0796827
$371$	1.94750	0.101109
$372$	5.79899	0.300664
$373$	−21.1480	−1.09500	−0.547502	−	0.836805i	$-0.684421\pi$
$373$	−21.1480	−1.09500	−0.547502	+	0.836805i	$0.684421\pi$
$374$	−11.0797	−0.572919
$375$	20.2847	1.04750
$376$	7.05508	0.363838
$377$	−1.54116	−0.0793738
$378$	5.34053	0.274687
$379$	20.9551	1.07639	0.538196	−	0.842820i	$-0.319106\pi$
$379$	20.9551	1.07639	0.538196	+	0.842820i	$0.319106\pi$
$380$	7.65220	0.392549
$381$	−28.6999	−1.47034
$382$	13.2071	0.675734
$383$	−7.98102	−0.407811	−0.203906	−	0.978991i	$-0.565364\pi$
$383$	−7.98102	−0.407811	−0.203906	+	0.978991i	$0.565364\pi$
$384$	−1.67912	−0.0856873
$385$	−7.89116	−0.402171
$386$	−22.0719	−1.12343
$387$	1.41121	0.0717360
$388$	−6.73224	−0.341778
$389$	−2.61899	−0.132788	−0.0663941	−	0.997793i	$-0.521149\pi$
$389$	−2.61899	−0.132788	−0.0663941	+	0.997793i	$0.521149\pi$
$390$	−0.912302	−0.0461962
$391$	−20.9602	−1.06000
$392$	−1.00000	−0.0505076
$393$	−19.4439	−0.980816
$394$	−2.31580	−0.116668
$395$	23.9570	1.20541
$396$	−0.840457	−0.0422345
$397$	−16.5937	−0.832813	−0.416407	−	0.909178i	$-0.636711\pi$
$397$	−16.5937	−0.832813	−0.416407	+	0.909178i	$0.636711\pi$
$398$	22.5978	1.13272
$399$	−7.57943	−0.379446
$400$	−2.12616	−0.106308
$401$	−29.3423	−1.46528	−0.732642	−	0.680614i	$-0.761713\pi$
$401$	−29.3423	−1.46528	−0.732642	+	0.680614i	$0.761713\pi$
$402$	5.60449	0.279526
$403$	−1.10687	−0.0551370
$404$	−9.31507	−0.463442
$405$	14.2837	0.709761
$406$	−4.80865	−0.238649
$407$	−4.20865	−0.208615
$408$	−3.99670	−0.197866
$409$	−16.3535	−0.808629	−0.404315	−	0.914620i	$-0.632490\pi$
$409$	−16.3535	−0.808629	−0.404315	+	0.914620i	$0.632490\pi$
$410$	8.53779	0.421651
$411$	16.2569	0.801892
$412$	15.5693	0.767044
$413$	−10.8892	−0.535824
$414$	−1.58995	−0.0781416
$415$	24.2084	1.18834
$416$	0.320498	0.0157137
$417$	5.53692	0.271144
$418$	21.0118	1.02772
$419$	16.4889	0.805534	0.402767	−	0.915302i	$-0.368048\pi$
$419$	16.4889	0.805534	0.402767	+	0.915302i	$0.368048\pi$
$420$	−2.84652	−0.138896
$421$	34.3247	1.67288	0.836441	−	0.548057i	$-0.184632\pi$
$421$	34.3247	1.67288	0.836441	+	0.548057i	$0.184632\pi$
$422$	10.1175	0.492514
$423$	1.27382	0.0619352
$424$	−1.94750	−0.0945792
$425$	−5.06075	−0.245482
$426$	1.79892	0.0871581
$427$	5.12583	0.248056
$428$	3.93041	0.189983
$429$	−2.50505	−0.120945
$430$	−13.2501	−0.638975
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.34053	−0.256947
$433$	34.7377	1.66939	0.834694	−	0.550715i	$-0.185645\pi$
$433$	34.7377	1.66939	0.834694	+	0.550715i	$0.185645\pi$
$434$	−3.45359	−0.165777
$435$	−13.6879	−0.656284
$436$	8.05728	0.385874
$437$	39.7494	1.90147
$438$	−17.9883	−0.859515
$439$	16.7314	0.798545	0.399273	−	0.916832i	$-0.369263\pi$
$439$	16.7314	0.798545	0.399273	+	0.916832i	$0.369263\pi$
$440$	7.89116	0.376196
$441$	−0.180554	−0.00859779
$442$	0.762860	0.0362855
$443$	−19.8474	−0.942979	−0.471489	−	0.881872i	$-0.656283\pi$
$443$	−19.8474	−0.942979	−0.471489	+	0.881872i	$0.656283\pi$
$444$	−1.51815	−0.0720483
$445$	17.1295	0.812015
$446$	2.00505	0.0949418
$447$	1.02045	0.0482655
$448$	1.00000	0.0472456
$449$	29.5772	1.39583	0.697917	−	0.716179i	$-0.254111\pi$
$449$	29.5772	1.39583	0.697917	+	0.716179i	$0.254111\pi$
$450$	−0.383885	−0.0180965
$451$	23.4435	1.10391
$452$	20.8811	0.982166
$453$	−27.3399	−1.28454
$454$	−17.4811	−0.820428
$455$	0.543321	0.0254713
$456$	7.57943	0.354939
$457$	8.54237	0.399595	0.199798	−	0.979837i	$-0.435972\pi$
$457$	8.54237	0.399595	0.199798	+	0.979837i	$0.435972\pi$
$458$	−9.89158	−0.462203
$459$	−12.7117	−0.593332
$460$	14.9282	0.696032
$461$	18.1465	0.845168	0.422584	−	0.906324i	$-0.361123\pi$
$461$	18.1465	0.845168	0.422584	+	0.906324i	$0.361123\pi$
$462$	−7.81612	−0.363639
$463$	−17.4189	−0.809524	−0.404762	−	0.914422i	$-0.632646\pi$
$463$	−17.4189	−0.809524	−0.404762	+	0.914422i	$0.632646\pi$
$464$	4.80865	0.223236
$465$	−9.83069	−0.455887
$466$	22.6361	1.04860
$467$	0.511382	0.0236640	0.0118320	−	0.999930i	$-0.496234\pi$
$467$	0.511382	0.0236640	0.0118320	+	0.999930i	$0.496234\pi$
$468$	0.0578670	0.00267490
$469$	−3.33775	−0.154123
$470$	−11.9601	−0.551677
$471$	9.22579	0.425102
$472$	10.8892	0.501218
$473$	−36.3828	−1.67288
$474$	23.7292	1.08992
$475$	9.59731	0.440355
$476$	2.38023	0.109098
$477$	−0.351629	−0.0161000
$478$	14.9512	0.683852
$479$	−16.6965	−0.762881	−0.381441	−	0.924393i	$-0.624572\pi$
$479$	−16.6965	−0.762881	−0.381441	+	0.924393i	$0.624572\pi$
$480$	2.84652	0.129925
$481$	0.289773	0.0132125
$482$	−6.92521	−0.315435
$483$	−14.7863	−0.672798
$484$	10.6680	0.484908
$485$	11.4128	0.518227
$486$	−1.87377	−0.0849957
$487$	−22.3050	−1.01073	−0.505367	−	0.862905i	$-0.668643\pi$
$487$	−22.3050	−1.01073	−0.505367	+	0.862905i	$0.668643\pi$
$488$	−5.12583	−0.232036
$489$	37.1055	1.67797
$490$	1.69524	0.0765832
$491$	−4.56334	−0.205941	−0.102970	−	0.994684i	$-0.532835\pi$
$491$	−4.56334	−0.205941	−0.102970	+	0.994684i	$0.532835\pi$
$492$	8.45660	0.381253
$493$	11.4457	0.515489
$494$	−1.44670	−0.0650903
$495$	1.42478	0.0640390
$496$	3.45359	0.155071
$497$	−1.07135	−0.0480565
$498$	23.9782	1.07449
$499$	18.7300	0.838468	0.419234	−	0.907878i	$-0.362299\pi$
$499$	18.7300	0.838468	0.419234	+	0.907878i	$0.362299\pi$
$500$	12.0806	0.540259
$501$	−15.6696	−0.700066
$502$	16.3274	0.728728
$503$	−30.9273	−1.37898	−0.689491	−	0.724294i	$-0.742166\pi$
$503$	−30.9273	−1.37898	−0.689491	+	0.724294i	$0.742166\pi$
$504$	0.180554	0.00804249
$505$	15.7913	0.702704
$506$	40.9907	1.82226
$507$	−21.6561	−0.961781
$508$	−17.0922	−0.758343
$509$	−26.5905	−1.17860	−0.589302	−	0.807913i	$-0.700597\pi$
$509$	−26.5905	−1.17860	−0.589302	+	0.807913i	$0.700597\pi$
$510$	6.77537	0.300019
$511$	10.7129	0.473912
$512$	−1.00000	−0.0441942
$513$	24.1068	1.06434
$514$	3.16381	0.139550
$515$	−26.3937	−1.16305
$516$	−13.1241	−0.577755
$517$	−32.8406	−1.44433
$518$	0.904135	0.0397254
$519$	−19.5503	−0.858161
$520$	−0.543321	−0.0238262
$521$	−6.49701	−0.284639	−0.142320	−	0.989821i	$-0.545456\pi$
$521$	−6.49701	−0.284639	−0.142320	+	0.989821i	$0.545456\pi$
$522$	0.868219	0.0380009
$523$	32.9020	1.43870	0.719352	−	0.694646i	$-0.244439\pi$
$523$	32.9020	1.43870	0.719352	+	0.694646i	$0.244439\pi$
$524$	−11.5798	−0.505867
$525$	−3.57007	−0.155811
$526$	−30.9705	−1.35038
$527$	8.22035	0.358084
$528$	7.81612	0.340153
$529$	54.5449	2.37152
$530$	3.30149	0.143408
$531$	1.96609	0.0853211
$532$	−4.51393	−0.195704
$533$	−1.61413	−0.0699158
$534$	16.9666	0.734216
$535$	−6.66299	−0.288066
$536$	3.33775	0.144169
$537$	−25.3569	−1.09423
$538$	8.76749	0.377993
$539$	4.65489	0.200500
$540$	9.05349	0.389600
$541$	−25.2935	−1.08745	−0.543726	−	0.839262i	$-0.682987\pi$
$541$	−25.2935	−1.08745	−0.543726	+	0.839262i	$0.682987\pi$
$542$	6.85765	0.294561
$543$	15.1551	0.650370
$544$	−2.38023	−0.102052
$545$	−13.6590	−0.585089
$546$	0.538154	0.0230309
$547$	−35.4016	−1.51366	−0.756832	−	0.653609i	$-0.773254\pi$
$547$	−35.4016	−1.51366	−0.756832	+	0.653609i	$0.773254\pi$
$548$	9.68178	0.413585
$549$	−0.925487	−0.0394988
$550$	9.89702	0.422010
$551$	−21.7059	−0.924702
$552$	14.7863	0.629345
$553$	−14.1319	−0.600950
$554$	5.83536	0.247921
$555$	2.57363	0.109245
$556$	3.29751	0.139846
$557$	−21.9621	−0.930564	−0.465282	−	0.885163i	$-0.654047\pi$
$557$	−21.9621	−0.930564	−0.465282	+	0.885163i	$0.654047\pi$
$558$	0.623557	0.0263973
$559$	2.50502	0.105951
$560$	−1.69524	−0.0716370
$561$	18.6042	0.785470
$562$	11.9693	0.504892
$563$	2.56426	0.108070	0.0540352	−	0.998539i	$-0.482792\pi$
$563$	2.56426	0.108070	0.0540352	+	0.998539i	$0.482792\pi$
$564$	−11.8463	−0.498820
$565$	−35.3986	−1.48923
$566$	−14.5373	−0.611050
$567$	−8.42574	−0.353848
$568$	1.07135	0.0449527
$569$	−29.9862	−1.25709	−0.628544	−	0.777774i	$-0.716349\pi$
$569$	−29.9862	−1.25709	−0.628544	+	0.777774i	$0.716349\pi$
$570$	−12.8490	−0.538184
$571$	−21.4041	−0.895735	−0.447868	−	0.894100i	$-0.647816\pi$
$571$	−21.4041	−0.895735	−0.447868	+	0.894100i	$0.647816\pi$
$572$	−1.49188	−0.0623787
$573$	−22.1763	−0.926429
$574$	−5.03633	−0.210212
$575$	18.7228	0.780796
$576$	−0.180554	−0.00752306
$577$	20.3302	0.846356	0.423178	−	0.906047i	$-0.360915\pi$
$577$	20.3302	0.846356	0.423178	+	0.906047i	$0.360915\pi$
$578$	11.3345	0.471452
$579$	37.0613	1.54022
$580$	−8.15182	−0.338486
$581$	−14.2802	−0.592443
$582$	11.3042	0.468576
$583$	9.06542	0.375451
$584$	−10.7129	−0.443304
$585$	−0.0980985	−0.00405588
$586$	3.47046	0.143363
$587$	25.9845	1.07250	0.536248	−	0.844061i	$-0.319841\pi$
$587$	25.9845	1.07250	0.536248	+	0.844061i	$0.319841\pi$
$588$	1.67912	0.0692458
$589$	−15.5892	−0.642344
$590$	−18.4599	−0.759982
$591$	3.88850	0.159952
$592$	−0.904135	−0.0371597
$593$	16.3280	0.670509	0.335255	−	0.942128i	$-0.391178\pi$
$593$	16.3280	0.670509	0.335255	+	0.942128i	$0.391178\pi$
$594$	24.8596	1.02000
$595$	−4.03507	−0.165422
$596$	0.607727	0.0248935
$597$	−37.9444	−1.55296
$598$	−2.82229	−0.115412
$599$	−33.2897	−1.36018	−0.680089	−	0.733129i	$-0.738059\pi$
$599$	−33.2897	−1.36018	−0.680089	+	0.733129i	$0.738059\pi$
$600$	3.57007	0.145748
$601$	−15.6808	−0.639634	−0.319817	−	0.947479i	$-0.603621\pi$
$601$	−15.6808	−0.639634	−0.319817	+	0.947479i	$0.603621\pi$
$602$	7.81603	0.318558
$603$	0.602643	0.0245415
$604$	−16.2823	−0.662516
$605$	−18.0848	−0.735252
$606$	15.6411	0.635378
$607$	25.5853	1.03848	0.519238	−	0.854630i	$-0.326216\pi$
$607$	25.5853	1.03848	0.519238	+	0.854630i	$0.326216\pi$
$608$	4.51393	0.183064
$609$	8.07430	0.327187
$610$	8.68953	0.351829
$611$	2.26114	0.0914758
$612$	−0.429760	−0.0173720
$613$	−6.66315	−0.269122	−0.134561	−	0.990905i	$-0.542962\pi$
$613$	−6.66315	−0.269122	−0.134561	+	0.990905i	$0.542962\pi$
$614$	32.8909	1.32737
$615$	−14.3360	−0.578083
$616$	−4.65489	−0.187551
$617$	−11.7456	−0.472861	−0.236430	−	0.971648i	$-0.575978\pi$
$617$	−11.7456	−0.472861	−0.236430	+	0.971648i	$0.575978\pi$
$618$	−26.1427	−1.05161
$619$	−9.60722	−0.386147	−0.193073	−	0.981184i	$-0.561846\pi$
$619$	−9.60722	−0.386147	−0.193073	+	0.981184i	$0.561846\pi$
$620$	−5.85466	−0.235129
$621$	47.0285	1.88719
$622$	7.67360	0.307683
$623$	−10.1044	−0.404826
$624$	−0.538154	−0.0215434
$625$	−9.84868	−0.393947
$626$	−24.1768	−0.966298
$627$	−35.2814	−1.40900
$628$	5.49442	0.219251
$629$	−2.15205	−0.0858080
$630$	−0.306082	−0.0121946
$631$	6.53168	0.260022	0.130011	−	0.991513i	$-0.458499\pi$
$631$	6.53168	0.260022	0.130011	+	0.991513i	$0.458499\pi$
$632$	14.1319	0.562137
$633$	−16.9886	−0.675235
$634$	19.8711	0.789181
$635$	28.9754	1.14985
$636$	3.27010	0.129668
$637$	−0.320498	−0.0126986
$638$	−22.3837	−0.886180
$639$	0.193436	0.00765219
$640$	1.69524	0.0670103
$641$	40.3329	1.59306	0.796528	−	0.604602i	$-0.206668\pi$
$641$	40.3329	1.59306	0.796528	+	0.604602i	$0.206668\pi$
$642$	−6.59963	−0.260467
$643$	2.35536	0.0928864	0.0464432	−	0.998921i	$-0.485211\pi$
$643$	2.35536	0.0928864	0.0464432	+	0.998921i	$0.485211\pi$
$644$	−8.80596	−0.347003
$645$	22.2485	0.876032
$646$	10.7442	0.422725
$647$	25.7299	1.01155	0.505774	−	0.862666i	$-0.331207\pi$
$647$	25.7299	1.01155	0.505774	+	0.862666i	$0.331207\pi$
$648$	8.42574	0.330994
$649$	−50.6882	−1.98969
$650$	−0.681428	−0.0267278
$651$	5.79899	0.227280
$652$	22.0981	0.865430
$653$	−40.5859	−1.58825	−0.794124	−	0.607756i	$-0.792070\pi$
$653$	−40.5859	−1.58825	−0.794124	+	0.607756i	$0.792070\pi$
$654$	−13.5291	−0.529031
$655$	19.6306	0.767031
$656$	5.03633	0.196636
$657$	−1.93426	−0.0754626
$658$	7.05508	0.275036
$659$	−14.9948	−0.584113	−0.292057	−	0.956401i	$-0.594340\pi$
$659$	−14.9948	−0.584113	−0.292057	+	0.956401i	$0.594340\pi$
$660$	−13.2502	−0.515764
$661$	−47.6644	−1.85393	−0.926965	−	0.375148i	$-0.877592\pi$
$661$	−47.6644	−1.85393	−0.926965	+	0.375148i	$0.877592\pi$
$662$	−25.5262	−0.992106
$663$	−1.28093	−0.0497473
$664$	14.2802	0.554179
$665$	7.65220	0.296740
$666$	−0.163245	−0.00632561
$667$	−42.3448	−1.63960
$668$	−9.33203	−0.361067
$669$	−3.36672	−0.130165
$670$	−5.65829	−0.218599
$671$	23.8602	0.921112
$672$	−1.67912	−0.0647735
$673$	41.1642	1.58676	0.793382	−	0.608724i	$-0.208319\pi$
$673$	41.1642	1.58676	0.793382	+	0.608724i	$0.208319\pi$
$674$	4.93092	0.189932
$675$	11.3548	0.437047
$676$	−12.8973	−0.496049
$677$	37.7514	1.45090	0.725451	−	0.688274i	$-0.241631\pi$
$677$	37.7514	1.45090	0.725451	+	0.688274i	$0.241631\pi$
$678$	−35.0620	−1.34655
$679$	−6.73224	−0.258360
$680$	4.03507	0.154738
$681$	29.3529	1.12480
$682$	−16.0761	−0.615584
$683$	17.9234	0.685819	0.342910	−	0.939368i	$-0.388588\pi$
$683$	17.9234	0.685819	0.342910	+	0.939368i	$0.388588\pi$
$684$	0.815006	0.0311625
$685$	−16.4130	−0.627107
$686$	−1.00000	−0.0381802
$687$	16.6092	0.633679
$688$	−7.81603	−0.297983
$689$	−0.624171	−0.0237790
$690$	−25.0663	−0.954257
$691$	14.2468	0.541972	0.270986	−	0.962583i	$-0.412650\pi$
$691$	14.2468	0.541972	0.270986	+	0.962583i	$0.412650\pi$
$692$	−11.6432	−0.442606
$693$	−0.840457	−0.0319263
$694$	23.5333	0.893313
$695$	−5.59007	−0.212044
$696$	−8.07430	−0.306056
$697$	11.9876	0.454064
$698$	21.5736	0.816572
$699$	−38.0087	−1.43762
$700$	−2.12616	−0.0803611
$701$	40.9890	1.54813	0.774066	−	0.633105i	$-0.218220\pi$
$701$	40.9890	1.54813	0.774066	+	0.633105i	$0.218220\pi$
$702$	−1.71163	−0.0646013
$703$	4.08120	0.153925
$704$	4.65489	0.175438
$705$	20.0824	0.756347
$706$	−15.8953	−0.598227
$707$	−9.31507	−0.350329
$708$	−18.2843	−0.687168
$709$	15.6231	0.586738	0.293369	−	0.955999i	$-0.405224\pi$
$709$	15.6231	0.586738	0.293369	+	0.955999i	$0.405224\pi$
$710$	−1.81619	−0.0681605
$711$	2.55157	0.0956912
$712$	10.1044	0.378680
$713$	−30.4121	−1.13894
$714$	−3.99670	−0.149573
$715$	2.52910	0.0945829
$716$	−15.1013	−0.564361
$717$	−25.1049	−0.937558
$718$	19.8503	0.740805
$719$	−16.7725	−0.625508	−0.312754	−	0.949834i	$-0.601251\pi$
$719$	−16.7725	−0.625508	−0.312754	+	0.949834i	$0.601251\pi$
$720$	0.306082	0.0114070
$721$	15.5693	0.579831
$722$	−1.37554	−0.0511924
$723$	11.6283	0.432460
$724$	9.02565	0.335435
$725$	−10.2239	−0.379708
$726$	−17.9128	−0.664808
$727$	−18.6491	−0.691658	−0.345829	−	0.938298i	$-0.612402\pi$
$727$	−18.6491	−0.691658	−0.345829	+	0.938298i	$0.612402\pi$
$728$	0.320498	0.0118784
$729$	28.4235	1.05272
$730$	18.1610	0.672169
$731$	−18.6040	−0.688093
$732$	8.60689	0.318120
$733$	4.15458	0.153453	0.0767264	−	0.997052i	$-0.475553\pi$
$733$	4.15458	0.153453	0.0767264	+	0.997052i	$0.475553\pi$
$734$	−7.59621	−0.280381
$735$	−2.84652	−0.104995
$736$	8.80596	0.324592
$737$	−15.5369	−0.572308
$738$	0.909327	0.0334728
$739$	24.9210	0.916733	0.458367	−	0.888763i	$-0.348435\pi$
$739$	24.9210	0.916733	0.458367	+	0.888763i	$0.348435\pi$
$740$	1.53273	0.0563442
$741$	2.42919	0.0892385
$742$	−1.94750	−0.0714951
$743$	−27.6902	−1.01586	−0.507928	−	0.861400i	$-0.669588\pi$
$743$	−27.6902	−1.01586	−0.507928	+	0.861400i	$0.669588\pi$
$744$	−5.79899	−0.212601
$745$	−1.03024	−0.0377452
$746$	21.1480	0.774284
$747$	2.57834	0.0943366
$748$	11.0797	0.405115
$749$	3.93041	0.143614
$750$	−20.2847	−0.740693
$751$	41.8437	1.52690	0.763449	−	0.645868i	$-0.223504\pi$
$751$	41.8437	1.52690	0.763449	+	0.645868i	$0.223504\pi$
$752$	−7.05508	−0.257272
$753$	−27.4157	−0.999083
$754$	1.54116	0.0561258
$755$	27.6024	1.00455
$756$	−5.34053	−0.194233
$757$	35.6636	1.29621	0.648107	−	0.761549i	$-0.275561\pi$
$757$	35.6636	1.29621	0.648107	+	0.761549i	$0.275561\pi$
$758$	−20.9551	−0.761124
$759$	−68.8284	−2.49831
$760$	−7.65220	−0.277574
$761$	39.5746	1.43458	0.717289	−	0.696775i	$-0.245383\pi$
$761$	39.5746	1.43458	0.717289	+	0.696775i	$0.245383\pi$
$762$	28.6999	1.03969
$763$	8.05728	0.291693
$764$	−13.2071	−0.477816
$765$	0.728547	0.0263407
$766$	7.98102	0.288366
$767$	3.48998	0.126016
$768$	1.67912	0.0605901
$769$	45.1389	1.62775	0.813876	−	0.581039i	$-0.197354\pi$
$769$	45.1389	1.62775	0.813876	+	0.581039i	$0.197354\pi$
$770$	7.89116	0.284378
$771$	−5.31242	−0.191322
$772$	22.0719	0.794384
$773$	−22.2821	−0.801432	−0.400716	−	0.916202i	$-0.631239\pi$
$773$	−22.2821	−0.801432	−0.400716	+	0.916202i	$0.631239\pi$
$774$	−1.41121	−0.0507250
$775$	−7.34286	−0.263763
$776$	6.73224	0.241673
$777$	−1.51815	−0.0544634
$778$	2.61899	0.0938955
$779$	−22.7336	−0.814516
$780$	0.912302	0.0326656
$781$	−4.98700	−0.178449
$782$	20.9602	0.749537
$783$	−25.6808	−0.917755
$784$	1.00000	0.0357143
$785$	−9.31437	−0.332444
$786$	19.4439	0.693542
$787$	16.6883	0.594875	0.297437	−	0.954741i	$-0.403868\pi$
$787$	16.6883	0.594875	0.297437	+	0.954741i	$0.403868\pi$
$788$	2.31580	0.0824968
$789$	52.0032	1.85136
$790$	−23.9570	−0.852352
$791$	20.8811	0.742448
$792$	0.840457	0.0298643
$793$	−1.64282	−0.0583382
$794$	16.5937	0.588888
$795$	−5.54360	−0.196611
$796$	−22.5978	−0.800957
$797$	−21.9933	−0.779041	−0.389521	−	0.921018i	$-0.627359\pi$
$797$	−21.9933	−0.779041	−0.389521	+	0.921018i	$0.627359\pi$
$798$	7.57943	0.268309
$799$	−16.7927	−0.594084
$800$	2.12616	0.0751710
$801$	1.82439	0.0644617
$802$	29.3423	1.03611
$803$	49.8675	1.75979
$804$	−5.60449	−0.197655
$805$	14.9282	0.526151
$806$	1.10687	0.0389877
$807$	−14.7217	−0.518227
$808$	9.31507	0.327703
$809$	19.4768	0.684767	0.342384	−	0.939560i	$-0.388766\pi$
$809$	19.4768	0.684767	0.342384	+	0.939560i	$0.388766\pi$
$810$	−14.2837	−0.501877
$811$	−14.6955	−0.516030	−0.258015	−	0.966141i	$-0.583068\pi$
$811$	−14.6955	−0.516030	−0.258015	+	0.966141i	$0.583068\pi$
$812$	4.80865	0.168751
$813$	−11.5148	−0.403843
$814$	4.20865	0.147513
$815$	−37.4617	−1.31223
$816$	3.99670	0.139913
$817$	35.2810	1.23433
$818$	16.3535	0.571787
$819$	0.0578670	0.00202204
$820$	−8.53779	−0.298153
$821$	−36.1838	−1.26282	−0.631411	−	0.775448i	$-0.717524\pi$
$821$	−36.1838	−1.26282	−0.631411	+	0.775448i	$0.717524\pi$
$822$	−16.2569	−0.567024
$823$	53.9031	1.87895	0.939473	−	0.342624i	$-0.111316\pi$
$823$	53.9031	1.87895	0.939473	+	0.342624i	$0.111316\pi$
$824$	−15.5693	−0.542382
$825$	−16.6183	−0.578575
$826$	10.8892	0.378885
$827$	14.9178	0.518743	0.259371	−	0.965778i	$-0.416485\pi$
$827$	14.9178	0.518743	0.259371	+	0.965778i	$0.416485\pi$
$828$	1.58995	0.0552545
$829$	−16.9196	−0.587642	−0.293821	−	0.955861i	$-0.594927\pi$
$829$	−16.9196	−0.587642	−0.293821	+	0.955861i	$0.594927\pi$
$830$	−24.2084	−0.840286
$831$	−9.79827	−0.339898
$832$	−0.320498	−0.0111113
$833$	2.38023	0.0824702
$834$	−5.53692	−0.191728
$835$	15.8200	0.547475
$836$	−21.0118	−0.726709
$837$	−18.4440	−0.637518
$838$	−16.4889	−0.569599
$839$	1.18319	0.0408482	0.0204241	−	0.999791i	$-0.493498\pi$
$839$	1.18319	0.0408482	0.0204241	+	0.999791i	$0.493498\pi$
$840$	2.84652	0.0982141
$841$	−5.87689	−0.202651
$842$	−34.3247	−1.18291
$843$	−20.0978	−0.692206
$844$	−10.1175	−0.348260
$845$	21.8640	0.752145
$846$	−1.27382	−0.0437948
$847$	10.6680	0.366556
$848$	1.94750	0.0668776
$849$	24.4099	0.837747
$850$	5.06075	0.173582
$851$	7.96177	0.272926
$852$	−1.79892	−0.0616301
$853$	−6.17733	−0.211508	−0.105754	−	0.994392i	$-0.533726\pi$
$853$	−6.17733	−0.211508	−0.105754	+	0.994392i	$0.533726\pi$
$854$	−5.12583	−0.175402
$855$	−1.38163	−0.0472508
$856$	−3.93041	−0.134339
$857$	5.80041	0.198138	0.0990691	−	0.995081i	$-0.468414\pi$
$857$	5.80041	0.198138	0.0990691	+	0.995081i	$0.468414\pi$
$858$	2.50505	0.0855209
$859$	20.6426	0.704316	0.352158	−	0.935941i	$-0.385448\pi$
$859$	20.6426	0.704316	0.352158	+	0.935941i	$0.385448\pi$
$860$	13.2501	0.451823
$861$	8.45660	0.288200
$862$	−1.00000	−0.0340601
$863$	−28.4197	−0.967419	−0.483709	−	0.875229i	$-0.660711\pi$
$863$	−28.4197	−0.967419	−0.483709	+	0.875229i	$0.660711\pi$
$864$	5.34053	0.181689
$865$	19.7380	0.671111
$866$	−34.7377	−1.18043
$867$	−19.0320	−0.646360
$868$	3.45359	0.117222
$869$	−65.7825	−2.23152
$870$	13.6879	0.464063
$871$	1.06974	0.0362468
$872$	−8.05728	−0.272854
$873$	1.21553	0.0411394
$874$	−39.7494	−1.34455
$875$	12.0806	0.408397
$876$	17.9883	0.607769
$877$	−13.5017	−0.455920	−0.227960	−	0.973670i	$-0.573206\pi$
$877$	−13.5017	−0.455920	−0.227960	+	0.973670i	$0.573206\pi$
$878$	−16.7314	−0.564657
$879$	−5.82732	−0.196551
$880$	−7.89116	−0.266011
$881$	−55.2816	−1.86249	−0.931243	−	0.364399i	$-0.881274\pi$
$881$	−55.2816	−1.86249	−0.931243	+	0.364399i	$0.881274\pi$
$882$	0.180554	0.00607955
$883$	−16.0483	−0.540067	−0.270034	−	0.962851i	$-0.587035\pi$
$883$	−16.0483	−0.540067	−0.270034	+	0.962851i	$0.587035\pi$
$884$	−0.762860	−0.0256577
$885$	30.9964	1.04193
$886$	19.8474	0.666787
$887$	−5.26273	−0.176705	−0.0883525	−	0.996089i	$-0.528160\pi$
$887$	−5.26273	−0.176705	−0.0883525	+	0.996089i	$0.528160\pi$
$888$	1.51815	0.0509458
$889$	−17.0922	−0.573254
$890$	−17.1295	−0.574181
$891$	−39.2209	−1.31395
$892$	−2.00505	−0.0671340
$893$	31.8461	1.06569
$894$	−1.02045	−0.0341289
$895$	25.6003	0.855724
$896$	−1.00000	−0.0334077
$897$	4.73896	0.158229
$898$	−29.5772	−0.987003
$899$	16.6071	0.553877
$900$	0.383885	0.0127962
$901$	4.63552	0.154431
$902$	−23.4435	−0.780584
$903$	−13.1241	−0.436742
$904$	−20.8811	−0.694496
$905$	−15.3007	−0.508611
$906$	27.3399	0.908306
$907$	−52.3032	−1.73670	−0.868350	−	0.495952i	$-0.834819\pi$
$907$	−52.3032	−1.73670	−0.868350	+	0.495952i	$0.834819\pi$
$908$	17.4811	0.580130
$909$	1.68187	0.0557841
$910$	−0.543321	−0.0180109
$911$	29.2091	0.967740	0.483870	−	0.875140i	$-0.339231\pi$
$911$	29.2091	0.967740	0.483870	+	0.875140i	$0.339231\pi$
$912$	−7.57943	−0.250980
$913$	−66.4727	−2.19993
$914$	−8.54237	−0.282556
$915$	−14.5908	−0.482356
$916$	9.89158	0.326827
$917$	−11.5798	−0.382399
$918$	12.7117	0.419549
$919$	7.85800	0.259212	0.129606	−	0.991566i	$-0.458629\pi$
$919$	7.85800	0.259212	0.129606	+	0.991566i	$0.458629\pi$
$920$	−14.9282	−0.492169
$921$	−55.2278	−1.81982
$922$	−18.1465	−0.597624
$923$	0.343364	0.0113020
$924$	7.81612	0.257131
$925$	1.92233	0.0632059
$926$	17.4189	0.572420
$927$	−2.81109	−0.0923283
$928$	−4.80865	−0.157852
$929$	33.3330	1.09362	0.546810	−	0.837257i	$-0.315842\pi$
$929$	33.3330	1.09362	0.546810	+	0.837257i	$0.315842\pi$
$930$	9.83069	0.322361
$931$	−4.51393	−0.147938
$932$	−22.6361	−0.741469
$933$	−12.8849	−0.421833
$934$	−0.511382	−0.0167329
$935$	−18.7828	−0.614264
$936$	−0.0578670	−0.00189144
$937$	21.4008	0.699134	0.349567	−	0.936911i	$-0.386329\pi$
$937$	21.4008	0.699134	0.349567	+	0.936911i	$0.386329\pi$
$938$	3.33775	0.108981
$939$	40.5957	1.32479
$940$	11.9601	0.390094
$941$	−47.8628	−1.56028	−0.780141	−	0.625604i	$-0.784853\pi$
$941$	−47.8628	−1.56028	−0.780141	+	0.625604i	$0.784853\pi$
$942$	−9.22579	−0.300593
$943$	−44.3497	−1.44422
$944$	−10.8892	−0.354415
$945$	9.05349	0.294510
$946$	36.3828	1.18291
$947$	−32.0873	−1.04270	−0.521348	−	0.853344i	$-0.674571\pi$
$947$	−32.0873	−1.04270	−0.521348	+	0.853344i	$0.674571\pi$
$948$	−23.7292	−0.770688
$949$	−3.43347	−0.111455
$950$	−9.59731	−0.311378
$951$	−33.3659	−1.08196
$952$	−2.38023	−0.0771438
$953$	19.3039	0.625314	0.312657	−	0.949866i	$-0.398781\pi$
$953$	19.3039	0.625314	0.312657	+	0.949866i	$0.398781\pi$
$954$	0.351629	0.0113844
$955$	22.3892	0.724499
$956$	−14.9512	−0.483556
$957$	37.5850	1.21495
$958$	16.6965	0.539439
$959$	9.68178	0.312641
$960$	−2.84652	−0.0918709
$961$	−19.0727	−0.615250
$962$	−0.289773	−0.00934266
$963$	−0.709649	−0.0228681
$964$	6.92521	0.223046
$965$	−37.4172	−1.20450
$966$	14.7863	0.475740
$967$	44.6870	1.43704	0.718519	−	0.695508i	$-0.244821\pi$
$967$	44.6870	1.43704	0.718519	+	0.695508i	$0.244821\pi$
$968$	−10.6680	−0.342882
$969$	−18.0408	−0.579555
$970$	−11.4128	−0.366442
$971$	−27.5301	−0.883482	−0.441741	−	0.897143i	$-0.645639\pi$
$971$	−27.5301	−0.883482	−0.441741	+	0.897143i	$0.645639\pi$
$972$	1.87377	0.0601011
$973$	3.29751	0.105713
$974$	22.3050	0.714697
$975$	1.14420	0.0366437
$976$	5.12583	0.164074
$977$	−10.9831	−0.351379	−0.175690	−	0.984446i	$-0.556216\pi$
$977$	−10.9831	−0.351379	−0.175690	+	0.984446i	$0.556216\pi$
$978$	−37.1055	−1.18650
$979$	−47.0350	−1.50325
$980$	−1.69524	−0.0541525
$981$	−1.45477	−0.0464472
$982$	4.56334	0.145622
$983$	11.4059	0.363793	0.181897	−	0.983318i	$-0.441776\pi$
$983$	11.4059	0.363793	0.181897	+	0.983318i	$0.441776\pi$
$984$	−8.45660	−0.269587
$985$	−3.92583	−0.125087
$986$	−11.4457	−0.364506
$987$	−11.8463	−0.377073
$988$	1.44670	0.0460258
$989$	68.8276	2.18859
$990$	−1.42478	−0.0452824
$991$	−32.6072	−1.03580	−0.517901	−	0.855441i	$-0.673286\pi$
$991$	−32.6072	−1.03580	−0.517901	+	0.855441i	$0.673286\pi$
$992$	−3.45359	−0.109651
$993$	42.8616	1.36017
$994$	1.07135	0.0339811
$995$	38.3087	1.21447
$996$	−23.9782	−0.759778
$997$	44.6125	1.41289	0.706446	−	0.707767i	$-0.250297\pi$
$997$	44.6125	1.41289	0.706446	+	0.707767i	$0.250297\pi$
$998$	−18.7300	−0.592887
$999$	4.82856	0.152769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.15	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.67912 q^{3} +1.00000 q^{4} -1.69524 q^{5} -1.67912 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.180554 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.67912 q^{3} +1.00000 q^{4} -1.69524 q^{5} -1.67912 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.180554 q^{9} +1.69524 q^{10} +4.65489 q^{11} +1.67912 q^{12} -0.320498 q^{13} -1.00000 q^{14} -2.84652 q^{15} +1.00000 q^{16} +2.38023 q^{17} +0.180554 q^{18} -4.51393 q^{19} -1.69524 q^{20} +1.67912 q^{21} -4.65489 q^{22} -8.80596 q^{23} -1.67912 q^{24} -2.12616 q^{25} +0.320498 q^{26} -5.34053 q^{27} +1.00000 q^{28} +4.80865 q^{29} +2.84652 q^{30} +3.45359 q^{31} -1.00000 q^{32} +7.81612 q^{33} -2.38023 q^{34} -1.69524 q^{35} -0.180554 q^{36} -0.904135 q^{37} +4.51393 q^{38} -0.538154 q^{39} +1.69524 q^{40} +5.03633 q^{41} -1.67912 q^{42} -7.81603 q^{43} +4.65489 q^{44} +0.306082 q^{45} +8.80596 q^{46} -7.05508 q^{47} +1.67912 q^{48} +1.00000 q^{49} +2.12616 q^{50} +3.99670 q^{51} -0.320498 q^{52} +1.94750 q^{53} +5.34053 q^{54} -7.89116 q^{55} -1.00000 q^{56} -7.57943 q^{57} -4.80865 q^{58} -10.8892 q^{59} -2.84652 q^{60} +5.12583 q^{61} -3.45359 q^{62} -0.180554 q^{63} +1.00000 q^{64} +0.543321 q^{65} -7.81612 q^{66} -3.33775 q^{67} +2.38023 q^{68} -14.7863 q^{69} +1.69524 q^{70} -1.07135 q^{71} +0.180554 q^{72} +10.7129 q^{73} +0.904135 q^{74} -3.57007 q^{75} -4.51393 q^{76} +4.65489 q^{77} +0.538154 q^{78} -14.1319 q^{79} -1.69524 q^{80} -8.42574 q^{81} -5.03633 q^{82} -14.2802 q^{83} +1.67912 q^{84} -4.03507 q^{85} +7.81603 q^{86} +8.07430 q^{87} -4.65489 q^{88} -10.1044 q^{89} -0.306082 q^{90} -0.320498 q^{91} -8.80596 q^{92} +5.79899 q^{93} +7.05508 q^{94} +7.65220 q^{95} -1.67912 q^{96} -6.73224 q^{97} -1.00000 q^{98} -0.840457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 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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