LMFDB - Embedded newform 6034.2.a.k.1.17

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			1.17
Root			$2.00937$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.00937 q^{3} +1.00000 q^{4} +2.56029 q^{5} -2.00937 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.03758 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.00937 q^{3} +1.00000 q^{4} +2.56029 q^{5} -2.00937 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.03758 q^{9} -2.56029 q^{10} -2.73376 q^{11} +2.00937 q^{12} -1.28782 q^{13} -1.00000 q^{14} +5.14459 q^{15} +1.00000 q^{16} -3.83902 q^{17} -1.03758 q^{18} -5.83084 q^{19} +2.56029 q^{20} +2.00937 q^{21} +2.73376 q^{22} -4.22796 q^{23} -2.00937 q^{24} +1.55510 q^{25} +1.28782 q^{26} -3.94323 q^{27} +1.00000 q^{28} -7.12917 q^{29} -5.14459 q^{30} +0.0674626 q^{31} -1.00000 q^{32} -5.49315 q^{33} +3.83902 q^{34} +2.56029 q^{35} +1.03758 q^{36} +9.14613 q^{37} +5.83084 q^{38} -2.58771 q^{39} -2.56029 q^{40} +3.90960 q^{41} -2.00937 q^{42} +3.92064 q^{43} -2.73376 q^{44} +2.65652 q^{45} +4.22796 q^{46} -7.32544 q^{47} +2.00937 q^{48} +1.00000 q^{49} -1.55510 q^{50} -7.71403 q^{51} -1.28782 q^{52} -1.13251 q^{53} +3.94323 q^{54} -6.99923 q^{55} -1.00000 q^{56} -11.7163 q^{57} +7.12917 q^{58} -12.2275 q^{59} +5.14459 q^{60} +10.9877 q^{61} -0.0674626 q^{62} +1.03758 q^{63} +1.00000 q^{64} -3.29720 q^{65} +5.49315 q^{66} -10.3770 q^{67} -3.83902 q^{68} -8.49556 q^{69} -2.56029 q^{70} +0.938932 q^{71} -1.03758 q^{72} -5.30972 q^{73} -9.14613 q^{74} +3.12478 q^{75} -5.83084 q^{76} -2.73376 q^{77} +2.58771 q^{78} -5.57474 q^{79} +2.56029 q^{80} -11.0362 q^{81} -3.90960 q^{82} +4.27370 q^{83} +2.00937 q^{84} -9.82902 q^{85} -3.92064 q^{86} -14.3252 q^{87} +2.73376 q^{88} -1.86054 q^{89} -2.65652 q^{90} -1.28782 q^{91} -4.22796 q^{92} +0.135558 q^{93} +7.32544 q^{94} -14.9287 q^{95} -2.00937 q^{96} -0.460859 q^{97} -1.00000 q^{98} -2.83651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.00937	1.16011	0.580056	−	0.814576i	$-0.303031\pi$
$3$	2.00937	1.16011	0.580056	+	0.814576i	$0.303031\pi$
$4$	1.00000	0.500000
$5$	2.56029	1.14500	0.572499	−	0.819905i	$-0.305974\pi$
$5$	2.56029	1.14500	0.572499	+	0.819905i	$0.305974\pi$
$6$	−2.00937	−0.820324
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.03758	0.345861
$10$	−2.56029	−0.809636
$11$	−2.73376	−0.824260	−0.412130	−	0.911125i	$-0.635215\pi$
$11$	−2.73376	−0.824260	−0.412130	+	0.911125i	$0.635215\pi$
$12$	2.00937	0.580056
$13$	−1.28782	−0.357177	−0.178589	−	0.983924i	$-0.557153\pi$
$13$	−1.28782	−0.357177	−0.178589	+	0.983924i	$0.557153\pi$
$14$	−1.00000	−0.267261
$15$	5.14459	1.32833
$16$	1.00000	0.250000
$17$	−3.83902	−0.931100	−0.465550	−	0.885022i	$-0.654143\pi$
$17$	−3.83902	−0.931100	−0.465550	+	0.885022i	$0.654143\pi$
$18$	−1.03758	−0.244561
$19$	−5.83084	−1.33769	−0.668843	−	0.743403i	$-0.733210\pi$
$19$	−5.83084	−1.33769	−0.668843	+	0.743403i	$0.733210\pi$
$20$	2.56029	0.572499
$21$	2.00937	0.438481
$22$	2.73376	0.582840
$23$	−4.22796	−0.881591	−0.440796	−	0.897607i	$-0.645304\pi$
$23$	−4.22796	−0.881591	−0.440796	+	0.897607i	$0.645304\pi$
$24$	−2.00937	−0.410162
$25$	1.55510	0.311020
$26$	1.28782	0.252562
$27$	−3.94323	−0.758875
$28$	1.00000	0.188982
$29$	−7.12917	−1.32385	−0.661927	−	0.749568i	$-0.730261\pi$
$29$	−7.12917	−1.32385	−0.661927	+	0.749568i	$0.730261\pi$
$30$	−5.14459	−0.939269
$31$	0.0674626	0.0121166	0.00605832	−	0.999982i	$-0.498072\pi$
$31$	0.0674626	0.0121166	0.00605832	+	0.999982i	$0.498072\pi$
$32$	−1.00000	−0.176777
$33$	−5.49315	−0.956234
$34$	3.83902	0.658387
$35$	2.56029	0.432769
$36$	1.03758	0.172931
$37$	9.14613	1.50361	0.751807	−	0.659383i	$-0.229182\pi$
$37$	9.14613	1.50361	0.751807	+	0.659383i	$0.229182\pi$
$38$	5.83084	0.945887
$39$	−2.58771	−0.414366
$40$	−2.56029	−0.404818
$41$	3.90960	0.610577	0.305288	−	0.952260i	$-0.401247\pi$
$41$	3.90960	0.610577	0.305288	+	0.952260i	$0.401247\pi$
$42$	−2.00937	−0.310053
$43$	3.92064	0.597892	0.298946	−	0.954270i	$-0.403365\pi$
$43$	3.92064	0.597892	0.298946	+	0.954270i	$0.403365\pi$
$44$	−2.73376	−0.412130
$45$	2.65652	0.396010
$46$	4.22796	0.623379
$47$	−7.32544	−1.06853	−0.534263	−	0.845318i	$-0.679411\pi$
$47$	−7.32544	−1.06853	−0.534263	+	0.845318i	$0.679411\pi$
$48$	2.00937	0.290028
$49$	1.00000	0.142857
$50$	−1.55510	−0.219925
$51$	−7.71403	−1.08018
$52$	−1.28782	−0.178589
$53$	−1.13251	−0.155563	−0.0777813	−	0.996970i	$-0.524784\pi$
$53$	−1.13251	−0.155563	−0.0777813	+	0.996970i	$0.524784\pi$
$54$	3.94323	0.536605
$55$	−6.99923	−0.943776
$56$	−1.00000	−0.133631
$57$	−11.7163	−1.55187
$58$	7.12917	0.936106
$59$	−12.2275	−1.59189	−0.795945	−	0.605370i	$-0.793025\pi$
$59$	−12.2275	−1.59189	−0.795945	+	0.605370i	$0.793025\pi$
$60$	5.14459	0.664163
$61$	10.9877	1.40683	0.703413	−	0.710781i	$-0.251658\pi$
$61$	10.9877	1.40683	0.703413	+	0.710781i	$0.251658\pi$
$62$	−0.0674626	−0.00856775
$63$	1.03758	0.130723
$64$	1.00000	0.125000
$65$	−3.29720	−0.408967
$66$	5.49315	0.676160
$67$	−10.3770	−1.26775	−0.633875	−	0.773436i	$-0.718537\pi$
$67$	−10.3770	−1.26775	−0.633875	+	0.773436i	$0.718537\pi$
$68$	−3.83902	−0.465550
$69$	−8.49556	−1.02275
$70$	−2.56029	−0.306014
$71$	0.938932	0.111431	0.0557153	−	0.998447i	$-0.482256\pi$
$71$	0.938932	0.111431	0.0557153	+	0.998447i	$0.482256\pi$
$72$	−1.03758	−0.122280
$73$	−5.30972	−0.621455	−0.310728	−	0.950499i	$-0.600573\pi$
$73$	−5.30972	−0.621455	−0.310728	+	0.950499i	$0.600573\pi$
$74$	−9.14613	−1.06322
$75$	3.12478	0.360818
$76$	−5.83084	−0.668843
$77$	−2.73376	−0.311541
$78$	2.58771	0.293001
$79$	−5.57474	−0.627207	−0.313604	−	0.949554i	$-0.601536\pi$
$79$	−5.57474	−0.627207	−0.313604	+	0.949554i	$0.601536\pi$
$80$	2.56029	0.286249
$81$	−11.0362	−1.22624
$82$	−3.90960	−0.431743
$83$	4.27370	0.469100	0.234550	−	0.972104i	$-0.424638\pi$
$83$	4.27370	0.469100	0.234550	+	0.972104i	$0.424638\pi$
$84$	2.00937	0.219241
$85$	−9.82902	−1.06611
$86$	−3.92064	−0.422774
$87$	−14.3252	−1.53582
$88$	2.73376	0.291420
$89$	−1.86054	−0.197217	−0.0986084	−	0.995126i	$-0.531439\pi$
$89$	−1.86054	−0.197217	−0.0986084	+	0.995126i	$0.531439\pi$
$90$	−2.65652	−0.280022
$91$	−1.28782	−0.135000
$92$	−4.22796	−0.440796
$93$	0.135558	0.0140567
$94$	7.32544	0.755562
$95$	−14.9287	−1.53165
$96$	−2.00937	−0.205081
$97$	−0.460859	−0.0467931	−0.0233966	−	0.999726i	$-0.507448\pi$
$97$	−0.460859	−0.0467931	−0.0233966	+	0.999726i	$0.507448\pi$
$98$	−1.00000	−0.101015
$99$	−2.83651	−0.285080
$100$	1.55510	0.155510
$101$	9.19912	0.915347	0.457674	−	0.889120i	$-0.348683\pi$
$101$	9.19912	0.915347	0.457674	+	0.889120i	$0.348683\pi$
$102$	7.71403	0.763803
$103$	11.5680	1.13983	0.569915	−	0.821704i	$-0.306976\pi$
$103$	11.5680	1.13983	0.569915	+	0.821704i	$0.306976\pi$
$104$	1.28782	0.126281
$105$	5.14459	0.502060
$106$	1.13251	0.109999
$107$	−11.5512	−1.11669	−0.558347	−	0.829607i	$-0.688564\pi$
$107$	−11.5512	−1.11669	−0.558347	+	0.829607i	$0.688564\pi$
$108$	−3.94323	−0.379437
$109$	9.35472	0.896020	0.448010	−	0.894029i	$-0.352133\pi$
$109$	9.35472	0.896020	0.448010	+	0.894029i	$0.352133\pi$
$110$	6.99923	0.667350
$111$	18.3780	1.74436
$112$	1.00000	0.0944911
$113$	3.65887	0.344198	0.172099	−	0.985080i	$-0.444945\pi$
$113$	3.65887	0.344198	0.172099	+	0.985080i	$0.444945\pi$
$114$	11.7163	1.09734
$115$	−10.8248	−1.00942
$116$	−7.12917	−0.661927
$117$	−1.33622	−0.123534
$118$	12.2275	1.12564
$119$	−3.83902	−0.351923
$120$	−5.14459	−0.469634
$121$	−3.52655	−0.320596
$122$	−10.9877	−0.994777
$123$	7.85584	0.708338
$124$	0.0674626	0.00605832
$125$	−8.81995	−0.788880
$126$	−1.03758	−0.0924353
$127$	13.3824	1.18749	0.593746	−	0.804653i	$-0.297648\pi$
$127$	13.3824	1.18749	0.593746	+	0.804653i	$0.297648\pi$
$128$	−1.00000	−0.0883883
$129$	7.87804	0.693623
$130$	3.29720	0.289184
$131$	16.0989	1.40656	0.703282	−	0.710911i	$-0.251717\pi$
$131$	16.0989	1.40656	0.703282	+	0.710911i	$0.251717\pi$
$132$	−5.49315	−0.478117
$133$	−5.83084	−0.505598
$134$	10.3770	0.896434
$135$	−10.0958	−0.868910
$136$	3.83902	0.329193
$137$	2.03606	0.173952	0.0869762	−	0.996210i	$-0.472280\pi$
$137$	2.03606	0.173952	0.0869762	+	0.996210i	$0.472280\pi$
$138$	8.49556	0.723190
$139$	−21.0187	−1.78278	−0.891392	−	0.453233i	$-0.850271\pi$
$139$	−21.0187	−1.78278	−0.891392	+	0.453233i	$0.850271\pi$
$140$	2.56029	0.216384
$141$	−14.7196	−1.23961
$142$	−0.938932	−0.0787934
$143$	3.52059	0.294407
$144$	1.03758	0.0864653
$145$	−18.2528	−1.51581
$146$	5.30972	0.439435
$147$	2.00937	0.165730
$148$	9.14613	0.751807
$149$	−5.27045	−0.431772	−0.215886	−	0.976419i	$-0.569264\pi$
$149$	−5.27045	−0.431772	−0.215886	+	0.976419i	$0.569264\pi$
$150$	−3.12478	−0.255137
$151$	−8.19236	−0.666685	−0.333343	−	0.942806i	$-0.608177\pi$
$151$	−8.19236	−0.666685	−0.333343	+	0.942806i	$0.608177\pi$
$152$	5.83084	0.472944
$153$	−3.98331	−0.322031
$154$	2.73376	0.220293
$155$	0.172724	0.0138735
$156$	−2.58771	−0.207183
$157$	−8.37185	−0.668147	−0.334073	−	0.942547i	$-0.608423\pi$
$157$	−8.37185	−0.668147	−0.334073	+	0.942547i	$0.608423\pi$
$158$	5.57474	0.443502
$159$	−2.27564	−0.180470
$160$	−2.56029	−0.202409
$161$	−4.22796	−0.333210
$162$	11.0362	0.867084
$163$	−14.0258	−1.09858	−0.549291	−	0.835631i	$-0.685102\pi$
$163$	−14.0258	−1.09858	−0.549291	+	0.835631i	$0.685102\pi$
$164$	3.90960	0.305288
$165$	−14.0641	−1.09489
$166$	−4.27370	−0.331704
$167$	−15.4791	−1.19781	−0.598906	−	0.800819i	$-0.704398\pi$
$167$	−15.4791	−1.19781	−0.598906	+	0.800819i	$0.704398\pi$
$168$	−2.00937	−0.155027
$169$	−11.3415	−0.872424
$170$	9.82902	0.753852
$171$	−6.04999	−0.462654
$172$	3.92064	0.298946
$173$	3.77210	0.286787	0.143394	−	0.989666i	$-0.454199\pi$
$173$	3.77210	0.286787	0.143394	+	0.989666i	$0.454199\pi$
$174$	14.3252	1.08599
$175$	1.55510	0.117555
$176$	−2.73376	−0.206065
$177$	−24.5697	−1.84677
$178$	1.86054	0.139453
$179$	−19.2039	−1.43537	−0.717685	−	0.696368i	$-0.754798\pi$
$179$	−19.2039	−1.43537	−0.717685	+	0.696368i	$0.754798\pi$
$180$	2.65652	0.198005
$181$	−13.5956	−1.01055	−0.505277	−	0.862957i	$-0.668610\pi$
$181$	−13.5956	−1.01055	−0.505277	+	0.862957i	$0.668610\pi$
$182$	1.28782	0.0954596
$183$	22.0783	1.63208
$184$	4.22796	0.311690
$185$	23.4168	1.72164
$186$	−0.135558	−0.00993956
$187$	10.4950	0.767468
$188$	−7.32544	−0.534263
$189$	−3.94323	−0.286828
$190$	14.9287	1.08304
$191$	4.28562	0.310097	0.155048	−	0.987907i	$-0.450447\pi$
$191$	4.28562	0.310097	0.155048	+	0.987907i	$0.450447\pi$
$192$	2.00937	0.145014
$193$	1.49249	0.107432	0.0537160	−	0.998556i	$-0.482893\pi$
$193$	1.49249	0.107432	0.0537160	+	0.998556i	$0.482893\pi$
$194$	0.460859	0.0330877
$195$	−6.62531	−0.474448
$196$	1.00000	0.0714286
$197$	9.97461	0.710661	0.355331	−	0.934741i	$-0.384368\pi$
$197$	9.97461	0.710661	0.355331	+	0.934741i	$0.384368\pi$
$198$	2.83651	0.201582
$199$	15.9927	1.13369	0.566845	−	0.823825i	$-0.308164\pi$
$199$	15.9927	1.13369	0.566845	+	0.823825i	$0.308164\pi$
$200$	−1.55510	−0.109962
$201$	−20.8512	−1.47073
$202$	−9.19912	−0.647248
$203$	−7.12917	−0.500370
$204$	−7.71403	−0.540090
$205$	10.0097	0.699109
$206$	−11.5680	−0.805982
$207$	−4.38687	−0.304908
$208$	−1.28782	−0.0892943
$209$	15.9401	1.10260
$210$	−5.14459	−0.355010
$211$	9.57810	0.659384	0.329692	−	0.944089i	$-0.393055\pi$
$211$	9.57810	0.659384	0.329692	+	0.944089i	$0.393055\pi$
$212$	−1.13251	−0.0777813
$213$	1.88666	0.129272
$214$	11.5512	0.789623
$215$	10.0380	0.684586
$216$	3.94323	0.268303
$217$	0.0674626	0.00457966
$218$	−9.35472	−0.633582
$219$	−10.6692	−0.720958
$220$	−6.99923	−0.471888
$221$	4.94397	0.332568
$222$	−18.3780	−1.23345
$223$	−11.4917	−0.769542	−0.384771	−	0.923012i	$-0.625720\pi$
$223$	−11.4917	−0.769542	−0.384771	+	0.923012i	$0.625720\pi$
$224$	−1.00000	−0.0668153
$225$	1.61355	0.107570
$226$	−3.65887	−0.243385
$227$	18.5420	1.23068	0.615338	−	0.788263i	$-0.289020\pi$
$227$	18.5420	1.23068	0.615338	+	0.788263i	$0.289020\pi$
$228$	−11.7163	−0.775934
$229$	−5.39454	−0.356481	−0.178241	−	0.983987i	$-0.557041\pi$
$229$	−5.39454	−0.356481	−0.178241	+	0.983987i	$0.557041\pi$
$230$	10.8248	0.713768
$231$	−5.49315	−0.361423
$232$	7.12917	0.468053
$233$	−7.49450	−0.490981	−0.245490	−	0.969399i	$-0.578949\pi$
$233$	−7.49450	−0.490981	−0.245490	+	0.969399i	$0.578949\pi$
$234$	1.33622	0.0873516
$235$	−18.7553	−1.22346
$236$	−12.2275	−0.795945
$237$	−11.2017	−0.727631
$238$	3.83902	0.248847
$239$	10.4339	0.674914	0.337457	−	0.941341i	$-0.390433\pi$
$239$	10.4339	0.674914	0.337457	+	0.941341i	$0.390433\pi$
$240$	5.14459	0.332082
$241$	15.7691	1.01578	0.507888	−	0.861423i	$-0.330426\pi$
$241$	15.7691	1.01578	0.507888	+	0.861423i	$0.330426\pi$
$242$	3.52655	0.226695
$243$	−10.3461	−0.663703
$244$	10.9877	0.703413
$245$	2.56029	0.163571
$246$	−7.85584	−0.500870
$247$	7.50908	0.477791
$248$	−0.0674626	−0.00428388
$249$	8.58747	0.544209
$250$	8.81995	0.557823
$251$	13.0514	0.823795	0.411897	−	0.911230i	$-0.364866\pi$
$251$	13.0514	0.823795	0.411897	+	0.911230i	$0.364866\pi$
$252$	1.03758	0.0653616
$253$	11.5582	0.726660
$254$	−13.3824	−0.839684
$255$	−19.7502	−1.23680
$256$	1.00000	0.0625000
$257$	−13.9287	−0.868846	−0.434423	−	0.900709i	$-0.643048\pi$
$257$	−13.9287	−0.868846	−0.434423	+	0.900709i	$0.643048\pi$
$258$	−7.87804	−0.490465
$259$	9.14613	0.568313
$260$	−3.29720	−0.204484
$261$	−7.39711	−0.457870
$262$	−16.0989	−0.994591
$263$	−9.27319	−0.571809	−0.285905	−	0.958258i	$-0.592294\pi$
$263$	−9.27319	−0.571809	−0.285905	+	0.958258i	$0.592294\pi$
$264$	5.49315	0.338080
$265$	−2.89957	−0.178119
$266$	5.83084	0.357512
$267$	−3.73852	−0.228794
$268$	−10.3770	−0.633875
$269$	−10.2253	−0.623446	−0.311723	−	0.950173i	$-0.600906\pi$
$269$	−10.2253	−0.623446	−0.311723	+	0.950173i	$0.600906\pi$
$270$	10.0958	0.614412
$271$	27.4023	1.66457	0.832285	−	0.554348i	$-0.187032\pi$
$271$	27.4023	1.66457	0.832285	+	0.554348i	$0.187032\pi$
$272$	−3.83902	−0.232775
$273$	−2.58771	−0.156616
$274$	−2.03606	−0.123003
$275$	−4.25127	−0.256361
$276$	−8.49556	−0.511373
$277$	29.2936	1.76008	0.880042	−	0.474897i	$-0.157515\pi$
$277$	29.2936	1.76008	0.880042	+	0.474897i	$0.157515\pi$
$278$	21.0187	1.26062
$279$	0.0699981	0.00419067
$280$	−2.56029	−0.153007
$281$	7.02284	0.418948	0.209474	−	0.977814i	$-0.432825\pi$
$281$	7.02284	0.418948	0.209474	+	0.977814i	$0.432825\pi$
$282$	14.7196	0.876537
$283$	−5.83587	−0.346906	−0.173453	−	0.984842i	$-0.555493\pi$
$283$	−5.83587	−0.346906	−0.173453	+	0.984842i	$0.555493\pi$
$284$	0.938932	0.0557153
$285$	−29.9973	−1.77689
$286$	−3.52059	−0.208177
$287$	3.90960	0.230776
$288$	−1.03758	−0.0611402
$289$	−2.26191	−0.133054
$290$	18.2528	1.07184
$291$	−0.926038	−0.0542853
$292$	−5.30972	−0.310728
$293$	3.89651	0.227637	0.113818	−	0.993502i	$-0.463692\pi$
$293$	3.89651	0.227637	0.113818	+	0.993502i	$0.463692\pi$
$294$	−2.00937	−0.117189
$295$	−31.3061	−1.82271
$296$	−9.14613	−0.531608
$297$	10.7798	0.625510
$298$	5.27045	0.305309
$299$	5.44486	0.314884
$300$	3.12478	0.180409
$301$	3.92064	0.225982
$302$	8.19236	0.471418
$303$	18.4845	1.06191
$304$	−5.83084	−0.334422
$305$	28.1317	1.61081
$306$	3.98331	0.227711
$307$	−13.5338	−0.772415	−0.386207	−	0.922412i	$-0.626215\pi$
$307$	−13.5338	−0.772415	−0.386207	+	0.922412i	$0.626215\pi$
$308$	−2.73376	−0.155770
$309$	23.2445	1.32233
$310$	−0.172724	−0.00981006
$311$	6.55082	0.371463	0.185732	−	0.982601i	$-0.440535\pi$
$311$	6.55082	0.371463	0.185732	+	0.982601i	$0.440535\pi$
$312$	2.58771	0.146500
$313$	−6.33301	−0.357963	−0.178981	−	0.983852i	$-0.557280\pi$
$313$	−6.33301	−0.357963	−0.178981	+	0.983852i	$0.557280\pi$
$314$	8.37185	0.472451
$315$	2.65652	0.149678
$316$	−5.57474	−0.313604
$317$	−24.1536	−1.35660	−0.678301	−	0.734784i	$-0.737283\pi$
$317$	−24.1536	−1.35660	−0.678301	+	0.734784i	$0.737283\pi$
$318$	2.27564	0.127612
$319$	19.4894	1.09120
$320$	2.56029	0.143125
$321$	−23.2106	−1.29549
$322$	4.22796	0.235615
$323$	22.3847	1.24552
$324$	−11.0362	−0.613121
$325$	−2.00269	−0.111089
$326$	14.0258	0.776815
$327$	18.7971	1.03948
$328$	−3.90960	−0.215871
$329$	−7.32544	−0.403865
$330$	14.0641	0.774201
$331$	−5.23730	−0.287868	−0.143934	−	0.989587i	$-0.545975\pi$
$331$	−5.23730	−0.287868	−0.143934	+	0.989587i	$0.545975\pi$
$332$	4.27370	0.234550
$333$	9.48988	0.520042
$334$	15.4791	0.846981
$335$	−26.5681	−1.45157
$336$	2.00937	0.109620
$337$	23.4134	1.27541	0.637705	−	0.770280i	$-0.279884\pi$
$337$	23.4134	1.27541	0.637705	+	0.770280i	$0.279884\pi$
$338$	11.3415	0.616897
$339$	7.35204	0.399308
$340$	−9.82902	−0.533054
$341$	−0.184426	−0.00998725
$342$	6.04999	0.327146
$343$	1.00000	0.0539949
$344$	−3.92064	−0.211387
$345$	−21.7511	−1.17104
$346$	−3.77210	−0.202789
$347$	−13.1613	−0.706536	−0.353268	−	0.935522i	$-0.614930\pi$
$347$	−13.1613	−0.706536	−0.353268	+	0.935522i	$0.614930\pi$
$348$	−14.3252	−0.767910
$349$	32.3423	1.73124	0.865622	−	0.500697i	$-0.166923\pi$
$349$	32.3423	1.73124	0.865622	+	0.500697i	$0.166923\pi$
$350$	−1.55510	−0.0831236
$351$	5.07817	0.271053
$352$	2.73376	0.145710
$353$	9.34573	0.497423	0.248712	−	0.968578i	$-0.419993\pi$
$353$	9.34573	0.497423	0.248712	+	0.968578i	$0.419993\pi$
$354$	24.5697	1.30586
$355$	2.40394	0.127588
$356$	−1.86054	−0.0986084
$357$	−7.71403	−0.408270
$358$	19.2039	1.01496
$359$	10.5980	0.559342	0.279671	−	0.960096i	$-0.409775\pi$
$359$	10.5980	0.559342	0.279671	+	0.960096i	$0.409775\pi$
$360$	−2.65652	−0.140011
$361$	14.9987	0.789406
$362$	13.5956	0.714569
$363$	−7.08616	−0.371927
$364$	−1.28782	−0.0675002
$365$	−13.5944	−0.711565
$366$	−22.0783	−1.15405
$367$	18.5157	0.966509	0.483255	−	0.875480i	$-0.339455\pi$
$367$	18.5157	0.966509	0.483255	+	0.875480i	$0.339455\pi$
$368$	−4.22796	−0.220398
$369$	4.05654	0.211175
$370$	−23.4168	−1.21738
$371$	−1.13251	−0.0587972
$372$	0.135558	0.00702833
$373$	18.1847	0.941569	0.470785	−	0.882248i	$-0.343971\pi$
$373$	18.1847	0.941569	0.470785	+	0.882248i	$0.343971\pi$
$374$	−10.4950	−0.542682
$375$	−17.7226	−0.915190
$376$	7.32544	0.377781
$377$	9.18110	0.472850
$378$	3.94323	0.202818
$379$	17.2183	0.884445	0.442222	−	0.896905i	$-0.354190\pi$
$379$	17.2183	0.884445	0.442222	+	0.896905i	$0.354190\pi$
$380$	−14.9287	−0.765824
$381$	26.8902	1.37762
$382$	−4.28562	−0.219271
$383$	9.67040	0.494134	0.247067	−	0.968998i	$-0.420533\pi$
$383$	9.67040	0.494134	0.247067	+	0.968998i	$0.420533\pi$
$384$	−2.00937	−0.102540
$385$	−6.99923	−0.356714
$386$	−1.49249	−0.0759659
$387$	4.06800	0.206788
$388$	−0.460859	−0.0233966
$389$	37.3431	1.89337	0.946686	−	0.322159i	$-0.104408\pi$
$389$	37.3431	1.89337	0.946686	+	0.322159i	$0.104408\pi$
$390$	6.62531	0.335485
$391$	16.2312	0.820849
$392$	−1.00000	−0.0505076
$393$	32.3486	1.63177
$394$	−9.97461	−0.502514
$395$	−14.2730	−0.718151
$396$	−2.83651	−0.142540
$397$	30.5706	1.53429	0.767146	−	0.641472i	$-0.221676\pi$
$397$	30.5706	1.53429	0.767146	+	0.641472i	$0.221676\pi$
$398$	−15.9927	−0.801639
$399$	−11.7163	−0.586551
$400$	1.55510	0.0777551
$401$	−13.9888	−0.698565	−0.349283	−	0.937017i	$-0.613575\pi$
$401$	−13.9888	−0.698565	−0.349283	+	0.937017i	$0.613575\pi$
$402$	20.8512	1.03996
$403$	−0.0868797	−0.00432779
$404$	9.19912	0.457674
$405$	−28.2558	−1.40404
$406$	7.12917	0.353815
$407$	−25.0033	−1.23937
$408$	7.71403	0.381901
$409$	−23.1937	−1.14686	−0.573428	−	0.819256i	$-0.694387\pi$
$409$	−23.1937	−1.14686	−0.573428	+	0.819256i	$0.694387\pi$
$410$	−10.0097	−0.494345
$411$	4.09121	0.201804
$412$	11.5680	0.569915
$413$	−12.2275	−0.601678
$414$	4.38687	0.215603
$415$	10.9419	0.537118
$416$	1.28782	0.0631406
$417$	−42.2345	−2.06823
$418$	−15.9401	−0.779657
$419$	−0.876876	−0.0428382	−0.0214191	−	0.999771i	$-0.506818\pi$
$419$	−0.876876	−0.0428382	−0.0214191	+	0.999771i	$0.506818\pi$
$420$	5.14459	0.251030
$421$	−32.6519	−1.59136	−0.795679	−	0.605718i	$-0.792886\pi$
$421$	−32.6519	−1.59136	−0.795679	+	0.605718i	$0.792886\pi$
$422$	−9.57810	−0.466255
$423$	−7.60076	−0.369562
$424$	1.13251	0.0549997
$425$	−5.97007	−0.289591
$426$	−1.88666	−0.0914092
$427$	10.9877	0.531731
$428$	−11.5512	−0.558347
$429$	7.07419	0.341545
$430$	−10.0380	−0.484075
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−3.94323	−0.189719
$433$	−31.8938	−1.53272	−0.766360	−	0.642412i	$-0.777934\pi$
$433$	−31.8938	−1.53272	−0.766360	+	0.642412i	$0.777934\pi$
$434$	−0.0674626	−0.00323831
$435$	−36.6766	−1.75851
$436$	9.35472	0.448010
$437$	24.6526	1.17929
$438$	10.6692	0.509794
$439$	−32.6388	−1.55777	−0.778883	−	0.627169i	$-0.784214\pi$
$439$	−32.6388	−1.55777	−0.778883	+	0.627169i	$0.784214\pi$
$440$	6.99923	0.333675
$441$	1.03758	0.0494088
$442$	−4.94397	−0.235161
$443$	1.81043	0.0860160	0.0430080	−	0.999075i	$-0.486306\pi$
$443$	1.81043	0.0860160	0.0430080	+	0.999075i	$0.486306\pi$
$444$	18.3780	0.872181
$445$	−4.76353	−0.225813
$446$	11.4917	0.544148
$447$	−10.5903	−0.500904
$448$	1.00000	0.0472456
$449$	−3.82872	−0.180688	−0.0903442	−	0.995911i	$-0.528797\pi$
$449$	−3.82872	−0.180688	−0.0903442	+	0.995911i	$0.528797\pi$
$450$	−1.61355	−0.0760634
$451$	−10.6879	−0.503274
$452$	3.65887	0.172099
$453$	−16.4615	−0.773430
$454$	−18.5420	−0.870219
$455$	−3.29720	−0.154575
$456$	11.7163	0.548668
$457$	24.6700	1.15401	0.577006	−	0.816740i	$-0.304221\pi$
$457$	24.6700	1.15401	0.577006	+	0.816740i	$0.304221\pi$
$458$	5.39454	0.252070
$459$	15.1381	0.706588
$460$	−10.8248	−0.504710
$461$	−28.4793	−1.32641	−0.663206	−	0.748437i	$-0.730805\pi$
$461$	−28.4793	−1.32641	−0.663206	+	0.748437i	$0.730805\pi$
$462$	5.49315	0.255564
$463$	−39.2676	−1.82492	−0.912461	−	0.409164i	$-0.865820\pi$
$463$	−39.2676	−1.82492	−0.912461	+	0.409164i	$0.865820\pi$
$464$	−7.12917	−0.330963
$465$	0.347067	0.0160948
$466$	7.49450	0.347176
$467$	27.5142	1.27320	0.636602	−	0.771192i	$-0.280339\pi$
$467$	27.5142	1.27320	0.636602	+	0.771192i	$0.280339\pi$
$468$	−1.33622	−0.0617669
$469$	−10.3770	−0.479164
$470$	18.7553	0.865117
$471$	−16.8222	−0.775125
$472$	12.2275	0.562818
$473$	−10.7181	−0.492819
$474$	11.2017	0.514513
$475$	−9.06755	−0.416048
$476$	−3.83902	−0.175961
$477$	−1.17508	−0.0538031
$478$	−10.4339	−0.477236
$479$	21.8637	0.998980	0.499490	−	0.866320i	$-0.333521\pi$
$479$	21.8637	0.998980	0.499490	+	0.866320i	$0.333521\pi$
$480$	−5.14459	−0.234817
$481$	−11.7786	−0.537057
$482$	−15.7691	−0.718262
$483$	−8.49556	−0.386561
$484$	−3.52655	−0.160298
$485$	−1.17993	−0.0535780
$486$	10.3461	0.469309
$487$	33.2084	1.50482	0.752409	−	0.658696i	$-0.228892\pi$
$487$	33.2084	1.50482	0.752409	+	0.658696i	$0.228892\pi$
$488$	−10.9877	−0.497388
$489$	−28.1830	−1.27448
$490$	−2.56029	−0.115662
$491$	13.5131	0.609837	0.304918	−	0.952378i	$-0.401371\pi$
$491$	13.5131	0.609837	0.304918	+	0.952378i	$0.401371\pi$
$492$	7.85584	0.354169
$493$	27.3690	1.23264
$494$	−7.50908	−0.337850
$495$	−7.26229	−0.326416
$496$	0.0674626	0.00302916
$497$	0.938932	0.0421168
$498$	−8.58747	−0.384814
$499$	6.14002	0.274865	0.137433	−	0.990511i	$-0.456115\pi$
$499$	6.14002	0.274865	0.137433	+	0.990511i	$0.456115\pi$
$500$	−8.81995	−0.394440
$501$	−31.1034	−1.38960
$502$	−13.0514	−0.582511
$503$	−18.0371	−0.804236	−0.402118	−	0.915588i	$-0.631726\pi$
$503$	−18.0371	−0.804236	−0.402118	+	0.915588i	$0.631726\pi$
$504$	−1.03758	−0.0462177
$505$	23.5525	1.04807
$506$	−11.5582	−0.513827
$507$	−22.7893	−1.01211
$508$	13.3824	0.593746
$509$	23.1195	1.02475	0.512376	−	0.858761i	$-0.328765\pi$
$509$	23.1195	1.02475	0.512376	+	0.858761i	$0.328765\pi$
$510$	19.7502	0.874553
$511$	−5.30972	−0.234888
$512$	−1.00000	−0.0441942
$513$	22.9923	1.01514
$514$	13.9287	0.614367
$515$	29.6175	1.30510
$516$	7.87804	0.346811
$517$	20.0260	0.880743
$518$	−9.14613	−0.401858
$519$	7.57955	0.332705
$520$	3.29720	0.144592
$521$	−19.5992	−0.858657	−0.429329	−	0.903148i	$-0.641250\pi$
$521$	−19.5992	−0.858657	−0.429329	+	0.903148i	$0.641250\pi$
$522$	7.39711	0.323763
$523$	−19.0030	−0.830941	−0.415471	−	0.909607i	$-0.636383\pi$
$523$	−19.0030	−0.830941	−0.415471	+	0.909607i	$0.636383\pi$
$524$	16.0989	0.703282
$525$	3.12478	0.136377
$526$	9.27319	0.404330
$527$	−0.258990	−0.0112818
$528$	−5.49315	−0.239059
$529$	−5.12432	−0.222797
$530$	2.89957	0.125949
$531$	−12.6871	−0.550573
$532$	−5.83084	−0.252799
$533$	−5.03486	−0.218084
$534$	3.73852	0.161782
$535$	−29.5744	−1.27861
$536$	10.3770	0.448217
$537$	−38.5879	−1.66519
$538$	10.2253	0.440843
$539$	−2.73376	−0.117751
$540$	−10.0958	−0.434455
$541$	12.9839	0.558223	0.279111	−	0.960259i	$-0.409960\pi$
$541$	12.9839	0.558223	0.279111	+	0.960259i	$0.409960\pi$
$542$	−27.4023	−1.17703
$543$	−27.3187	−1.17236
$544$	3.83902	0.164597
$545$	23.9508	1.02594
$546$	2.58771	0.110744
$547$	−7.84307	−0.335346	−0.167673	−	0.985843i	$-0.553625\pi$
$547$	−7.84307	−0.335346	−0.167673	+	0.985843i	$0.553625\pi$
$548$	2.03606	0.0869762
$549$	11.4006	0.486567
$550$	4.25127	0.181275
$551$	41.5691	1.77090
$552$	8.49556	0.361595
$553$	−5.57474	−0.237062
$554$	−29.2936	−1.24457
$555$	47.0531	1.99729
$556$	−21.0187	−0.891392
$557$	−36.6035	−1.55094	−0.775471	−	0.631384i	$-0.782487\pi$
$557$	−36.6035	−1.55094	−0.775471	+	0.631384i	$0.782487\pi$
$558$	−0.0699981	−0.00296325
$559$	−5.04909	−0.213554
$560$	2.56029	0.108192
$561$	21.0883	0.890349
$562$	−7.02284	−0.296241
$563$	−41.4355	−1.74630	−0.873150	−	0.487451i	$-0.837927\pi$
$563$	−41.4355	−1.74630	−0.873150	+	0.487451i	$0.837927\pi$
$564$	−14.7196	−0.619805
$565$	9.36778	0.394106
$566$	5.83587	0.245300
$567$	−11.0362	−0.463476
$568$	−0.938932	−0.0393967
$569$	24.9946	1.04783	0.523913	−	0.851772i	$-0.324472\pi$
$569$	24.9946	1.04783	0.523913	+	0.851772i	$0.324472\pi$
$570$	29.9973	1.25645
$571$	15.1538	0.634167	0.317083	−	0.948398i	$-0.397297\pi$
$571$	15.1538	0.634167	0.317083	+	0.948398i	$0.397297\pi$
$572$	3.52059	0.147203
$573$	8.61141	0.359747
$574$	−3.90960	−0.163183
$575$	−6.57491	−0.274193
$576$	1.03758	0.0432327
$577$	−1.30180	−0.0541945	−0.0270972	−	0.999633i	$-0.508626\pi$
$577$	−1.30180	−0.0541945	−0.0270972	+	0.999633i	$0.508626\pi$
$578$	2.26191	0.0940831
$579$	2.99898	0.124633
$580$	−18.2528	−0.757905
$581$	4.27370	0.177303
$582$	0.926038	0.0383855
$583$	3.09602	0.128224
$584$	5.30972	0.219718
$585$	−3.42112	−0.141446
$586$	−3.89651	−0.160964
$587$	−32.4549	−1.33956	−0.669779	−	0.742561i	$-0.733611\pi$
$587$	−32.4549	−1.33956	−0.669779	+	0.742561i	$0.733611\pi$
$588$	2.00937	0.0828652
$589$	−0.393364	−0.0162083
$590$	31.3061	1.28885
$591$	20.0427	0.824447
$592$	9.14613	0.375904
$593$	−6.18747	−0.254089	−0.127044	−	0.991897i	$-0.540549\pi$
$593$	−6.18747	−0.254089	−0.127044	+	0.991897i	$0.540549\pi$
$594$	−10.7798	−0.442302
$595$	−9.82902	−0.402951
$596$	−5.27045	−0.215886
$597$	32.1352	1.31521
$598$	−5.44486	−0.222657
$599$	−4.82091	−0.196977	−0.0984885	−	0.995138i	$-0.531401\pi$
$599$	−4.82091	−0.196977	−0.0984885	+	0.995138i	$0.531401\pi$
$600$	−3.12478	−0.127569
$601$	4.94048	0.201527	0.100763	−	0.994910i	$-0.467872\pi$
$601$	4.94048	0.201527	0.100763	+	0.994910i	$0.467872\pi$
$602$	−3.92064	−0.159793
$603$	−10.7670	−0.438466
$604$	−8.19236	−0.333343
$605$	−9.02901	−0.367081
$606$	−18.4845	−0.750881
$607$	−7.31202	−0.296786	−0.148393	−	0.988928i	$-0.547410\pi$
$607$	−7.31202	−0.296786	−0.148393	+	0.988928i	$0.547410\pi$
$608$	5.83084	0.236472
$609$	−14.3252	−0.580485
$610$	−28.1317	−1.13902
$611$	9.43386	0.381653
$612$	−3.98331	−0.161016
$613$	32.0443	1.29426	0.647129	−	0.762380i	$-0.275969\pi$
$613$	32.0443	1.29426	0.647129	+	0.762380i	$0.275969\pi$
$614$	13.5338	0.546180
$615$	20.1133	0.811045
$616$	2.73376	0.110146
$617$	0.0275544	0.00110930	0.000554649	−	1.00000i	$-0.499823\pi$
$617$	0.0275544	0.00110930	0.000554649		1.00000i	$0.499823\pi$
$618$	−23.2445	−0.935030
$619$	−46.9983	−1.88902	−0.944510	−	0.328483i	$-0.893463\pi$
$619$	−46.9983	−1.88902	−0.944510	+	0.328483i	$0.893463\pi$
$620$	0.172724	0.00693676
$621$	16.6718	0.669017
$622$	−6.55082	−0.262664
$623$	−1.86054	−0.0745410
$624$	−2.58771	−0.103591
$625$	−30.3572	−1.21429
$626$	6.33301	0.253118
$627$	32.0297	1.27914
$628$	−8.37185	−0.334073
$629$	−35.1122	−1.40001
$630$	−2.65652	−0.105838
$631$	19.1870	0.763824	0.381912	−	0.924199i	$-0.375266\pi$
$631$	19.1870	0.763824	0.381912	+	0.924199i	$0.375266\pi$
$632$	5.57474	0.221751
$633$	19.2460	0.764960
$634$	24.1536	0.959262
$635$	34.2628	1.35968
$636$	−2.27564	−0.0902351
$637$	−1.28782	−0.0510253
$638$	−19.4894	−0.771594
$639$	0.974220	0.0385396
$640$	−2.56029	−0.101204
$641$	−13.5633	−0.535719	−0.267860	−	0.963458i	$-0.586316\pi$
$641$	−13.5633	−0.535719	−0.267860	+	0.963458i	$0.586316\pi$
$642$	23.2106	0.916051
$643$	−24.2615	−0.956779	−0.478389	−	0.878148i	$-0.658779\pi$
$643$	−24.2615	−0.956779	−0.478389	+	0.878148i	$0.658779\pi$
$644$	−4.22796	−0.166605
$645$	20.1701	0.794196
$646$	−22.3847	−0.880715
$647$	−18.0273	−0.708728	−0.354364	−	0.935108i	$-0.615303\pi$
$647$	−18.0273	−0.708728	−0.354364	+	0.935108i	$0.615303\pi$
$648$	11.0362	0.433542
$649$	33.4271	1.31213
$650$	2.00269	0.0785520
$651$	0.135558	0.00531292
$652$	−14.0258	−0.549291
$653$	24.2865	0.950405	0.475202	−	0.879877i	$-0.342375\pi$
$653$	24.2865	0.950405	0.475202	+	0.879877i	$0.342375\pi$
$654$	−18.7971	−0.735026
$655$	41.2178	1.61051
$656$	3.90960	0.152644
$657$	−5.50928	−0.214937
$658$	7.32544	0.285575
$659$	14.9230	0.581316	0.290658	−	0.956827i	$-0.406126\pi$
$659$	14.9230	0.581316	0.290658	+	0.956827i	$0.406126\pi$
$660$	−14.0641	−0.547443
$661$	29.1107	1.13228	0.566138	−	0.824310i	$-0.308437\pi$
$661$	29.1107	1.13228	0.566138	+	0.824310i	$0.308437\pi$
$662$	5.23730	0.203554
$663$	9.93429	0.385816
$664$	−4.27370	−0.165852
$665$	−14.9287	−0.578909
$666$	−9.48988	−0.367725
$667$	30.1419	1.16710
$668$	−15.4791	−0.598906
$669$	−23.0911	−0.892755
$670$	26.5681	1.02642
$671$	−30.0377	−1.15959
$672$	−2.00937	−0.0775133
$673$	−5.81118	−0.224005	−0.112002	−	0.993708i	$-0.535726\pi$
$673$	−5.81118	−0.224005	−0.112002	+	0.993708i	$0.535726\pi$
$674$	−23.4134	−0.901852
$675$	−6.13212	−0.236025
$676$	−11.3415	−0.436212
$677$	4.13855	0.159057	0.0795287	−	0.996833i	$-0.474658\pi$
$677$	4.13855	0.159057	0.0795287	+	0.996833i	$0.474658\pi$
$678$	−7.35204	−0.282353
$679$	−0.460859	−0.0176861
$680$	9.82902	0.376926
$681$	37.2578	1.42772
$682$	0.184426	0.00706206
$683$	−33.7905	−1.29296	−0.646480	−	0.762931i	$-0.723759\pi$
$683$	−33.7905	−1.29296	−0.646480	+	0.762931i	$0.723759\pi$
$684$	−6.04999	−0.231327
$685$	5.21291	0.199175
$686$	−1.00000	−0.0381802
$687$	−10.8397	−0.413559
$688$	3.92064	0.149473
$689$	1.45847	0.0555634
$690$	21.7511	0.828051
$691$	12.7127	0.483614	0.241807	−	0.970324i	$-0.422260\pi$
$691$	12.7127	0.483614	0.241807	+	0.970324i	$0.422260\pi$
$692$	3.77210	0.143394
$693$	−2.83651	−0.107750
$694$	13.1613	0.499596
$695$	−53.8141	−2.04128
$696$	14.3252	0.542994
$697$	−15.0090	−0.568508
$698$	−32.3423	−1.22417
$699$	−15.0592	−0.569593
$700$	1.55510	0.0587773
$701$	−42.5775	−1.60813	−0.804066	−	0.594541i	$-0.797334\pi$
$701$	−42.5775	−1.60813	−0.804066	+	0.594541i	$0.797334\pi$
$702$	−5.07817	−0.191663
$703$	−53.3296	−2.01137
$704$	−2.73376	−0.103032
$705$	−37.6864	−1.41935
$706$	−9.34573	−0.351731
$707$	9.19912	0.345969
$708$	−24.5697	−0.923385
$709$	30.7462	1.15470	0.577349	−	0.816498i	$-0.304087\pi$
$709$	30.7462	1.15470	0.577349	+	0.816498i	$0.304087\pi$
$710$	−2.40394	−0.0902183
$711$	−5.78426	−0.216927
$712$	1.86054	0.0697267
$713$	−0.285229	−0.0106819
$714$	7.71403	0.288690
$715$	9.01375	0.337095
$716$	−19.2039	−0.717685
$717$	20.9656	0.782976
$718$	−10.5980	−0.395515
$719$	−48.4876	−1.80828	−0.904142	−	0.427233i	$-0.859489\pi$
$719$	−48.4876	−1.80828	−0.904142	+	0.427233i	$0.859489\pi$
$720$	2.65652	0.0990026
$721$	11.5680	0.430815
$722$	−14.9987	−0.558195
$723$	31.6860	1.17841
$724$	−13.5956	−0.505277
$725$	−11.0866	−0.411745
$726$	7.08616	0.262992
$727$	−27.6153	−1.02420	−0.512098	−	0.858927i	$-0.671132\pi$
$727$	−27.6153	−1.02420	−0.512098	+	0.858927i	$0.671132\pi$
$728$	1.28782	0.0477298
$729$	12.3193	0.456271
$730$	13.5944	0.503152
$731$	−15.0514	−0.556697
$732$	22.0783	0.816039
$733$	26.7149	0.986736	0.493368	−	0.869821i	$-0.335766\pi$
$733$	26.7149	0.986736	0.493368	+	0.869821i	$0.335766\pi$
$734$	−18.5157	−0.683425
$735$	5.14459	0.189761
$736$	4.22796	0.155845
$737$	28.3682	1.04496
$738$	−4.05654	−0.149323
$739$	11.4055	0.419558	0.209779	−	0.977749i	$-0.432726\pi$
$739$	11.4055	0.419558	0.209779	+	0.977749i	$0.432726\pi$
$740$	23.4168	0.860818
$741$	15.0886	0.554292
$742$	1.13251	0.0415759
$743$	10.6891	0.392146	0.196073	−	0.980589i	$-0.437181\pi$
$743$	10.6891	0.392146	0.196073	+	0.980589i	$0.437181\pi$
$744$	−0.135558	−0.00496978
$745$	−13.4939	−0.494378
$746$	−18.1847	−0.665790
$747$	4.43432	0.162243
$748$	10.4950	0.383734
$749$	−11.5512	−0.422071
$750$	17.7226	0.647137
$751$	8.99374	0.328186	0.164093	−	0.986445i	$-0.447530\pi$
$751$	8.99374	0.328186	0.164093	+	0.986445i	$0.447530\pi$
$752$	−7.32544	−0.267131
$753$	26.2251	0.955695
$754$	−9.18110	−0.334356
$755$	−20.9749	−0.763353
$756$	−3.94323	−0.143414
$757$	−27.7377	−1.00814	−0.504072	−	0.863661i	$-0.668166\pi$
$757$	−27.7377	−1.00814	−0.504072	+	0.863661i	$0.668166\pi$
$758$	−17.2183	−0.625397
$759$	23.2248	0.843008
$760$	14.9287	0.541520
$761$	−38.2729	−1.38739	−0.693696	−	0.720268i	$-0.744019\pi$
$761$	−38.2729	−1.38739	−0.693696	+	0.720268i	$0.744019\pi$
$762$	−26.8902	−0.974128
$763$	9.35472	0.338664
$764$	4.28562	0.155048
$765$	−10.1984	−0.368725
$766$	−9.67040	−0.349406
$767$	15.7469	0.568587
$768$	2.00937	0.0725070
$769$	−29.2609	−1.05517	−0.527587	−	0.849501i	$-0.676903\pi$
$769$	−29.2609	−1.05517	−0.527587	+	0.849501i	$0.676903\pi$
$770$	6.99923	0.252235
$771$	−27.9879	−1.00796
$772$	1.49249	0.0537160
$773$	−13.2765	−0.477524	−0.238762	−	0.971078i	$-0.576742\pi$
$773$	−13.2765	−0.477524	−0.238762	+	0.971078i	$0.576742\pi$
$774$	−4.06800	−0.146221
$775$	0.104911	0.00376852
$776$	0.460859	0.0165439
$777$	18.3780	0.659307
$778$	−37.3431	−1.33882
$779$	−22.7962	−0.816760
$780$	−6.62531	−0.237224
$781$	−2.56681	−0.0918478
$782$	−16.2312	−0.580428
$783$	28.1119	1.00464
$784$	1.00000	0.0357143
$785$	−21.4344	−0.765026
$786$	−32.3486	−1.15384
$787$	30.2090	1.07683	0.538417	−	0.842679i	$-0.319023\pi$
$787$	30.2090	1.07683	0.538417	+	0.842679i	$0.319023\pi$
$788$	9.97461	0.355331
$789$	−18.6333	−0.663363
$790$	14.2730	0.507809
$791$	3.65887	0.130095
$792$	2.83651	0.100791
$793$	−14.1502	−0.502487
$794$	−30.5706	−1.08491
$795$	−5.82631	−0.206638
$796$	15.9927	0.566845
$797$	−34.8573	−1.23471	−0.617354	−	0.786685i	$-0.711796\pi$
$797$	−34.8573	−1.23471	−0.617354	+	0.786685i	$0.711796\pi$
$798$	11.7163	0.414754
$799$	28.1225	0.994904
$800$	−1.55510	−0.0549811
$801$	−1.93047	−0.0682097
$802$	13.9888	0.493960
$803$	14.5155	0.512241
$804$	−20.8512	−0.735366
$805$	−10.8248	−0.381525
$806$	0.0868797	0.00306021
$807$	−20.5464	−0.723267
$808$	−9.19912	−0.323624
$809$	−35.2031	−1.23767	−0.618837	−	0.785519i	$-0.712396\pi$
$809$	−35.2031	−1.23767	−0.618837	+	0.785519i	$0.712396\pi$
$810$	28.2558	0.992809
$811$	2.55991	0.0898907	0.0449454	−	0.998989i	$-0.485689\pi$
$811$	2.55991	0.0898907	0.0449454	+	0.998989i	$0.485689\pi$
$812$	−7.12917	−0.250185
$813$	55.0614	1.93109
$814$	25.0033	0.876366
$815$	−35.9100	−1.25787
$816$	−7.71403	−0.270045
$817$	−22.8606	−0.799793
$818$	23.1937	0.810949
$819$	−1.33622	−0.0466914
$820$	10.0097	0.349554
$821$	−5.05198	−0.176315	−0.0881577	−	0.996107i	$-0.528098\pi$
$821$	−5.05198	−0.176315	−0.0881577	+	0.996107i	$0.528098\pi$
$822$	−4.09121	−0.142697
$823$	−50.3639	−1.75557	−0.877787	−	0.479052i	$-0.840981\pi$
$823$	−50.3639	−1.75557	−0.877787	+	0.479052i	$0.840981\pi$
$824$	−11.5680	−0.402991
$825$	−8.54240	−0.297408
$826$	12.2275	0.425450
$827$	−8.39325	−0.291862	−0.145931	−	0.989295i	$-0.546618\pi$
$827$	−8.39325	−0.291862	−0.145931	+	0.989295i	$0.546618\pi$
$828$	−4.38687	−0.152454
$829$	−43.8114	−1.52163	−0.760816	−	0.648968i	$-0.775201\pi$
$829$	−43.8114	−1.52163	−0.760816	+	0.648968i	$0.775201\pi$
$830$	−10.9419	−0.379800
$831$	58.8618	2.04189
$832$	−1.28782	−0.0446472
$833$	−3.83902	−0.133014
$834$	42.2345	1.46246
$835$	−39.6311	−1.37149
$836$	15.9401	0.551301
$837$	−0.266020	−0.00919500
$838$	0.876876	0.0302912
$839$	28.7226	0.991614	0.495807	−	0.868433i	$-0.334872\pi$
$839$	28.7226	0.991614	0.495807	+	0.868433i	$0.334872\pi$
$840$	−5.14459	−0.177505
$841$	21.8251	0.752588
$842$	32.6519	1.12526
$843$	14.1115	0.486026
$844$	9.57810	0.329692
$845$	−29.0376	−0.998924
$846$	7.60076	0.261320
$847$	−3.52655	−0.121174
$848$	−1.13251	−0.0388907
$849$	−11.7264	−0.402451
$850$	5.97007	0.204772
$851$	−38.6695	−1.32557
$852$	1.88666	0.0646361
$853$	9.79581	0.335402	0.167701	−	0.985838i	$-0.446366\pi$
$853$	9.79581	0.335402	0.167701	+	0.985838i	$0.446366\pi$
$854$	−10.9877	−0.375990
$855$	−15.4897	−0.529738
$856$	11.5512	0.394811
$857$	3.58257	0.122378	0.0611891	−	0.998126i	$-0.480511\pi$
$857$	3.58257	0.122378	0.0611891	+	0.998126i	$0.480511\pi$
$858$	−7.07419	−0.241509
$859$	−0.145163	−0.00495290	−0.00247645	−	0.999997i	$-0.500788\pi$
$859$	−0.145163	−0.00495290	−0.00247645	+	0.999997i	$0.500788\pi$
$860$	10.0380	0.342293
$861$	7.85584	0.267726
$862$	−1.00000	−0.0340601
$863$	−2.40421	−0.0818404	−0.0409202	−	0.999162i	$-0.513029\pi$
$863$	−2.40421	−0.0818404	−0.0409202	+	0.999162i	$0.513029\pi$
$864$	3.94323	0.134151
$865$	9.65767	0.328371
$866$	31.8938	1.08380
$867$	−4.54503	−0.154357
$868$	0.0674626	0.00228983
$869$	15.2400	0.516982
$870$	36.6766	1.24345
$871$	13.3637	0.452811
$872$	−9.35472	−0.316791
$873$	−0.478180	−0.0161839
$874$	−24.6526	−0.833886
$875$	−8.81995	−0.298169
$876$	−10.6692	−0.360479
$877$	8.88430	0.300001	0.150001	−	0.988686i	$-0.452072\pi$
$877$	8.88430	0.300001	0.150001	+	0.988686i	$0.452072\pi$
$878$	32.6388	1.10151
$879$	7.82955	0.264084
$880$	−6.99923	−0.235944
$881$	−11.1434	−0.375429	−0.187715	−	0.982224i	$-0.560108\pi$
$881$	−11.1434	−0.375429	−0.187715	+	0.982224i	$0.560108\pi$
$882$	−1.03758	−0.0349373
$883$	28.8267	0.970097	0.485049	−	0.874487i	$-0.338802\pi$
$883$	28.8267	0.970097	0.485049	+	0.874487i	$0.338802\pi$
$884$	4.94397	0.166284
$885$	−62.9056	−2.11455
$886$	−1.81043	−0.0608225
$887$	37.6634	1.26461	0.632307	−	0.774718i	$-0.282108\pi$
$887$	37.6634	1.26461	0.632307	+	0.774718i	$0.282108\pi$
$888$	−18.3780	−0.616725
$889$	13.3824	0.448830
$890$	4.76353	0.159674
$891$	30.1703	1.01074
$892$	−11.4917	−0.384771
$893$	42.7135	1.42935
$894$	10.5903	0.354193
$895$	−49.1677	−1.64350
$896$	−1.00000	−0.0334077
$897$	10.9408	0.365301
$898$	3.82872	0.127766
$899$	−0.480952	−0.0160406
$900$	1.61355	0.0537849
$901$	4.34774	0.144844
$902$	10.6879	0.355868
$903$	7.87804	0.262165
$904$	−3.65887	−0.121692
$905$	−34.8087	−1.15708
$906$	16.4615	0.546897
$907$	−18.1603	−0.603002	−0.301501	−	0.953466i	$-0.597488\pi$
$907$	−18.1603	−0.603002	−0.301501	+	0.953466i	$0.597488\pi$
$908$	18.5420	0.615338
$909$	9.54486	0.316583
$910$	3.29720	0.109301
$911$	−13.1677	−0.436266	−0.218133	−	0.975919i	$-0.569997\pi$
$911$	−13.1677	−0.436266	−0.218133	+	0.975919i	$0.569997\pi$
$912$	−11.7163	−0.387967
$913$	−11.6833	−0.386660
$914$	−24.6700	−0.816010
$915$	56.5270	1.86873
$916$	−5.39454	−0.178241
$917$	16.0989	0.531631
$918$	−15.1381	−0.499633
$919$	9.38970	0.309738	0.154869	−	0.987935i	$-0.450504\pi$
$919$	9.38970	0.309738	0.154869	+	0.987935i	$0.450504\pi$
$920$	10.8248	0.356884
$921$	−27.1945	−0.896088
$922$	28.4793	0.937915
$923$	−1.20918	−0.0398005
$924$	−5.49315	−0.180711
$925$	14.2232	0.467654
$926$	39.2676	1.29041
$927$	12.0028	0.394223
$928$	7.12917	0.234026
$929$	19.4941	0.639580	0.319790	−	0.947488i	$-0.396388\pi$
$929$	19.4941	0.639580	0.319790	+	0.947488i	$0.396388\pi$
$930$	−0.347067	−0.0113808
$931$	−5.83084	−0.191098
$932$	−7.49450	−0.245490
$933$	13.1631	0.430939
$934$	−27.5142	−0.900292
$935$	26.8702	0.878749
$936$	1.33622	0.0436758
$937$	54.8540	1.79200	0.896002	−	0.444051i	$-0.146459\pi$
$937$	54.8540	1.79200	0.896002	+	0.444051i	$0.146459\pi$
$938$	10.3770	0.338820
$939$	−12.7254	−0.415277
$940$	−18.7553	−0.611730
$941$	44.2301	1.44186	0.720930	−	0.693008i	$-0.243715\pi$
$941$	44.2301	1.44186	0.720930	+	0.693008i	$0.243715\pi$
$942$	16.8222	0.548096
$943$	−16.5296	−0.538279
$944$	−12.2275	−0.397972
$945$	−10.0958	−0.328417
$946$	10.7181	0.348475
$947$	−0.478604	−0.0155525	−0.00777627	−	0.999970i	$-0.502475\pi$
$947$	−0.478604	−0.0155525	−0.00777627	+	0.999970i	$0.502475\pi$
$948$	−11.2017	−0.363815
$949$	6.83796	0.221970
$950$	9.06755	0.294190
$951$	−48.5336	−1.57381
$952$	3.83902	0.124423
$953$	0.607468	0.0196778	0.00983891	−	0.999952i	$-0.496868\pi$
$953$	0.607468	0.0196778	0.00983891	+	0.999952i	$0.496868\pi$
$954$	1.17508	0.0380445
$955$	10.9724	0.355060
$956$	10.4339	0.337457
$957$	39.1616	1.26591
$958$	−21.8637	−0.706385
$959$	2.03606	0.0657478
$960$	5.14459	0.166041
$961$	−30.9954	−0.999853
$962$	11.7786	0.379757
$963$	−11.9853	−0.386222
$964$	15.7691	0.507888
$965$	3.82122	0.123009
$966$	8.49556	0.273340
$967$	8.68534	0.279302	0.139651	−	0.990201i	$-0.455402\pi$
$967$	8.68534	0.279302	0.139651	+	0.990201i	$0.455402\pi$
$968$	3.52655	0.113348
$969$	44.9793	1.44494
$970$	1.17993	0.0378854
$971$	8.31256	0.266763	0.133381	−	0.991065i	$-0.457416\pi$
$971$	8.31256	0.266763	0.133381	+	0.991065i	$0.457416\pi$
$972$	−10.3461	−0.331852
$973$	−21.0187	−0.673829
$974$	−33.2084	−1.06407
$975$	−4.02416	−0.128876
$976$	10.9877	0.351707
$977$	11.2907	0.361223	0.180611	−	0.983555i	$-0.442192\pi$
$977$	11.2907	0.361223	0.180611	+	0.983555i	$0.442192\pi$
$978$	28.1830	0.901192
$979$	5.08627	0.162558
$980$	2.56029	0.0817856
$981$	9.70631	0.309899
$982$	−13.5131	−0.431220
$983$	−1.83995	−0.0586853	−0.0293427	−	0.999569i	$-0.509341\pi$
$983$	−1.83995	−0.0586853	−0.0293427	+	0.999569i	$0.509341\pi$
$984$	−7.85584	−0.250435
$985$	25.5379	0.813706
$986$	−27.3690	−0.871608
$987$	−14.7196	−0.468529
$988$	7.50908	0.238896
$989$	−16.5763	−0.527097
$990$	7.26229	0.230811
$991$	11.1906	0.355481	0.177741	−	0.984077i	$-0.443121\pi$
$991$	11.1906	0.355481	0.177741	+	0.984077i	$0.443121\pi$
$992$	−0.0674626	−0.00214194
$993$	−10.5237	−0.333960
$994$	−0.938932	−0.0297811
$995$	40.9459	1.29807
$996$	8.58747	0.272104
$997$	−35.6504	−1.12906	−0.564530	−	0.825412i	$-0.690943\pi$
$997$	−35.6504	−1.12906	−0.564530	+	0.825412i	$0.690943\pi$
$998$	−6.14002	−0.194359
$999$	−36.0653	−1.14105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.17	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.00937 q^{3} +1.00000 q^{4} +2.56029 q^{5} -2.00937 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.03758 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.00937 q^{3} +1.00000 q^{4} +2.56029 q^{5} -2.00937 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.03758 q^{9} -2.56029 q^{10} -2.73376 q^{11} +2.00937 q^{12} -1.28782 q^{13} -1.00000 q^{14} +5.14459 q^{15} +1.00000 q^{16} -3.83902 q^{17} -1.03758 q^{18} -5.83084 q^{19} +2.56029 q^{20} +2.00937 q^{21} +2.73376 q^{22} -4.22796 q^{23} -2.00937 q^{24} +1.55510 q^{25} +1.28782 q^{26} -3.94323 q^{27} +1.00000 q^{28} -7.12917 q^{29} -5.14459 q^{30} +0.0674626 q^{31} -1.00000 q^{32} -5.49315 q^{33} +3.83902 q^{34} +2.56029 q^{35} +1.03758 q^{36} +9.14613 q^{37} +5.83084 q^{38} -2.58771 q^{39} -2.56029 q^{40} +3.90960 q^{41} -2.00937 q^{42} +3.92064 q^{43} -2.73376 q^{44} +2.65652 q^{45} +4.22796 q^{46} -7.32544 q^{47} +2.00937 q^{48} +1.00000 q^{49} -1.55510 q^{50} -7.71403 q^{51} -1.28782 q^{52} -1.13251 q^{53} +3.94323 q^{54} -6.99923 q^{55} -1.00000 q^{56} -11.7163 q^{57} +7.12917 q^{58} -12.2275 q^{59} +5.14459 q^{60} +10.9877 q^{61} -0.0674626 q^{62} +1.03758 q^{63} +1.00000 q^{64} -3.29720 q^{65} +5.49315 q^{66} -10.3770 q^{67} -3.83902 q^{68} -8.49556 q^{69} -2.56029 q^{70} +0.938932 q^{71} -1.03758 q^{72} -5.30972 q^{73} -9.14613 q^{74} +3.12478 q^{75} -5.83084 q^{76} -2.73376 q^{77} +2.58771 q^{78} -5.57474 q^{79} +2.56029 q^{80} -11.0362 q^{81} -3.90960 q^{82} +4.27370 q^{83} +2.00937 q^{84} -9.82902 q^{85} -3.92064 q^{86} -14.3252 q^{87} +2.73376 q^{88} -1.86054 q^{89} -2.65652 q^{90} -1.28782 q^{91} -4.22796 q^{92} +0.135558 q^{93} +7.32544 q^{94} -14.9287 q^{95} -2.00937 q^{96} -0.460859 q^{97} -1.00000 q^{98} -2.83651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 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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