LMFDB - Embedded newform 6017.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34564 q^{2} +1.00441 q^{3} +3.50205 q^{4} +3.21165 q^{5} -2.35600 q^{6} +2.32596 q^{7} -3.52327 q^{8} -1.99115 q^{9} +O(q^{10})$	\(q-2.34564 q^{2} +1.00441 q^{3} +3.50205 q^{4} +3.21165 q^{5} -2.35600 q^{6} +2.32596 q^{7} -3.52327 q^{8} -1.99115 q^{9} -7.53339 q^{10} -1.00000 q^{11} +3.51750 q^{12} +0.0597910 q^{13} -5.45587 q^{14} +3.22583 q^{15} +1.26024 q^{16} +2.58155 q^{17} +4.67054 q^{18} -6.50989 q^{19} +11.2473 q^{20} +2.33623 q^{21} +2.34564 q^{22} -5.96032 q^{23} -3.53882 q^{24} +5.31470 q^{25} -0.140248 q^{26} -5.01318 q^{27} +8.14562 q^{28} -7.58769 q^{29} -7.56664 q^{30} -2.30068 q^{31} +4.09046 q^{32} -1.00441 q^{33} -6.05539 q^{34} +7.47017 q^{35} -6.97311 q^{36} -3.47816 q^{37} +15.2699 q^{38} +0.0600549 q^{39} -11.3155 q^{40} -0.683539 q^{41} -5.47996 q^{42} +7.58494 q^{43} -3.50205 q^{44} -6.39489 q^{45} +13.9808 q^{46} +7.54305 q^{47} +1.26580 q^{48} -1.58991 q^{49} -12.4664 q^{50} +2.59294 q^{51} +0.209391 q^{52} -3.37304 q^{53} +11.7591 q^{54} -3.21165 q^{55} -8.19498 q^{56} -6.53862 q^{57} +17.7980 q^{58} -5.00113 q^{59} +11.2970 q^{60} -8.41811 q^{61} +5.39658 q^{62} -4.63134 q^{63} -12.1152 q^{64} +0.192028 q^{65} +2.35600 q^{66} -2.48559 q^{67} +9.04070 q^{68} -5.98663 q^{69} -17.5224 q^{70} -6.98541 q^{71} +7.01536 q^{72} +6.11512 q^{73} +8.15852 q^{74} +5.33815 q^{75} -22.7979 q^{76} -2.32596 q^{77} -0.140867 q^{78} +15.6792 q^{79} +4.04745 q^{80} +0.938147 q^{81} +1.60334 q^{82} +8.19155 q^{83} +8.18157 q^{84} +8.29102 q^{85} -17.7916 q^{86} -7.62118 q^{87} +3.52327 q^{88} -5.95695 q^{89} +15.0001 q^{90} +0.139071 q^{91} -20.8733 q^{92} -2.31084 q^{93} -17.6933 q^{94} -20.9075 q^{95} +4.10852 q^{96} +12.0908 q^{97} +3.72937 q^{98} +1.99115 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * 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 $

$2$	−2.34564	−1.65862	−0.829310	−	0.558788i	$-0.811267\pi$
$2$	−2.34564	−1.65862	−0.829310	+	0.558788i	$0.811267\pi$
$3$	1.00441	0.579899	0.289949	−	0.957042i	$-0.406362\pi$
$3$	1.00441	0.579899	0.289949	+	0.957042i	$0.406362\pi$
$4$	3.50205	1.75102
$5$	3.21165	1.43629	0.718147	−	0.695892i	$-0.244991\pi$
$5$	3.21165	1.43629	0.718147	+	0.695892i	$0.244991\pi$
$6$	−2.35600	−0.961832
$7$	2.32596	0.879130	0.439565	−	0.898211i	$-0.355133\pi$
$7$	2.32596	0.879130	0.439565	+	0.898211i	$0.355133\pi$
$8$	−3.52327	−1.24566
$9$	−1.99115	−0.663718
$10$	−7.53339	−2.38227
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.51750	1.01542
$13$	0.0597910	0.0165830	0.00829152	−	0.999966i	$-0.497361\pi$
$13$	0.0597910	0.0165830	0.00829152	+	0.999966i	$0.497361\pi$
$14$	−5.45587	−1.45814
$15$	3.22583	0.832905
$16$	1.26024	0.315060
$17$	2.58155	0.626117	0.313059	−	0.949734i	$-0.398646\pi$
$17$	2.58155	0.626117	0.313059	+	0.949734i	$0.398646\pi$
$18$	4.67054	1.10086
$19$	−6.50989	−1.49347	−0.746735	−	0.665121i	$-0.768380\pi$
$19$	−6.50989	−1.49347	−0.746735	+	0.665121i	$0.768380\pi$
$20$	11.2473	2.51498
$21$	2.33623	0.509806
$22$	2.34564	0.500093
$23$	−5.96032	−1.24281	−0.621407	−	0.783488i	$-0.713439\pi$
$23$	−5.96032	−1.24281	−0.621407	+	0.783488i	$0.713439\pi$
$24$	−3.53882	−0.722358
$25$	5.31470	1.06294
$26$	−0.140248	−0.0275050
$27$	−5.01318	−0.964788
$28$	8.14562	1.53938
$29$	−7.58769	−1.40900	−0.704499	−	0.709705i	$-0.748828\pi$
$29$	−7.58769	−1.40900	−0.704499	+	0.709705i	$0.748828\pi$
$30$	−7.56664	−1.38147
$31$	−2.30068	−0.413215	−0.206607	−	0.978424i	$-0.566242\pi$
$31$	−2.30068	−0.413215	−0.206607	+	0.978424i	$0.566242\pi$
$32$	4.09046	0.723099
$33$	−1.00441	−0.174846
$34$	−6.05539	−1.03849
$35$	7.47017	1.26269
$36$	−6.97311	−1.16219
$37$	−3.47816	−0.571806	−0.285903	−	0.958259i	$-0.592293\pi$
$37$	−3.47816	−0.571806	−0.285903	+	0.958259i	$0.592293\pi$
$38$	15.2699	2.47710
$39$	0.0600549	0.00961648
$40$	−11.3155	−1.78914
$41$	−0.683539	−0.106751	−0.0533754	−	0.998575i	$-0.516998\pi$
$41$	−0.683539	−0.106751	−0.0533754	+	0.998575i	$0.516998\pi$
$42$	−5.47996	−0.845576
$43$	7.58494	1.15669	0.578346	−	0.815792i	$-0.303698\pi$
$43$	7.58494	1.15669	0.578346	+	0.815792i	$0.303698\pi$
$44$	−3.50205	−0.527953
$45$	−6.39489	−0.953293
$46$	13.9808	2.06136
$47$	7.54305	1.10027	0.550134	−	0.835077i	$-0.314577\pi$
$47$	7.54305	1.10027	0.550134	+	0.835077i	$0.314577\pi$
$48$	1.26580	0.182703
$49$	−1.58991	−0.227130
$50$	−12.4664	−1.76301
$51$	2.59294	0.363084
$52$	0.209391	0.0290373
$53$	−3.37304	−0.463322	−0.231661	−	0.972797i	$-0.574416\pi$
$53$	−3.37304	−0.463322	−0.231661	+	0.972797i	$0.574416\pi$
$54$	11.7591	1.60022
$55$	−3.21165	−0.433059
$56$	−8.19498	−1.09510
$57$	−6.53862	−0.866061
$58$	17.7980	2.33699
$59$	−5.00113	−0.651092	−0.325546	−	0.945526i	$-0.605548\pi$
$59$	−5.00113	−0.651092	−0.325546	+	0.945526i	$0.605548\pi$
$60$	11.2970	1.45844
$61$	−8.41811	−1.07783	−0.538914	−	0.842360i	$-0.681165\pi$
$61$	−8.41811	−1.07783	−0.538914	+	0.842360i	$0.681165\pi$
$62$	5.39658	0.685367
$63$	−4.63134	−0.583494
$64$	−12.1152	−1.51441
$65$	0.192028	0.0238181
$66$	2.35600	0.290003
$67$	−2.48559	−0.303663	−0.151832	−	0.988406i	$-0.548517\pi$
$67$	−2.48559	−0.303663	−0.151832	+	0.988406i	$0.548517\pi$
$68$	9.04070	1.09635
$69$	−5.98663	−0.720706
$70$	−17.5224	−2.09432
$71$	−6.98541	−0.829016	−0.414508	−	0.910046i	$-0.636046\pi$
$71$	−6.98541	−0.829016	−0.414508	+	0.910046i	$0.636046\pi$
$72$	7.01536	0.826769
$73$	6.11512	0.715721	0.357860	−	0.933775i	$-0.383506\pi$
$73$	6.11512	0.715721	0.357860	+	0.933775i	$0.383506\pi$
$74$	8.15852	0.948409
$75$	5.33815	0.616397
$76$	−22.7979	−2.61510
$77$	−2.32596	−0.265068
$78$	−0.140867	−0.0159501
$79$	15.6792	1.76404	0.882022	−	0.471209i	$-0.156182\pi$
$79$	15.6792	1.76404	0.882022	+	0.471209i	$0.156182\pi$
$80$	4.04745	0.452518
$81$	0.938147	0.104239
$82$	1.60334	0.177059
$83$	8.19155	0.899140	0.449570	−	0.893245i	$-0.351577\pi$
$83$	8.19155	0.899140	0.449570	+	0.893245i	$0.351577\pi$
$84$	8.18157	0.892683
$85$	8.29102	0.899288
$86$	−17.7916	−1.91851
$87$	−7.62118	−0.817076
$88$	3.52327	0.375582
$89$	−5.95695	−0.631435	−0.315718	−	0.948853i	$-0.602245\pi$
$89$	−5.95695	−0.631435	−0.315718	+	0.948853i	$0.602245\pi$
$90$	15.0001	1.58115
$91$	0.139071	0.0145786
$92$	−20.8733	−2.17620
$93$	−2.31084	−0.239623
$94$	−17.6933	−1.82493
$95$	−20.9075	−2.14506
$96$	4.10852	0.419324
$97$	12.0908	1.22763	0.613815	−	0.789450i	$-0.289634\pi$
$97$	12.0908	1.22763	0.613815	+	0.789450i	$0.289634\pi$
$98$	3.72937	0.376723
$99$	1.99115	0.200118
$100$	18.6123	1.86123
$101$	6.28902	0.625781	0.312890	−	0.949789i	$-0.398703\pi$
$101$	6.28902	0.625781	0.312890	+	0.949789i	$0.398703\pi$
$102$	−6.08212	−0.602219
$103$	−17.0409	−1.67909	−0.839546	−	0.543289i	$-0.817179\pi$
$103$	−17.0409	−1.67909	−0.839546	+	0.543289i	$0.817179\pi$
$104$	−0.210660	−0.0206569
$105$	7.50314	0.732232
$106$	7.91194	0.768476
$107$	−11.9369	−1.15399	−0.576993	−	0.816749i	$-0.695774\pi$
$107$	−11.9369	−1.15399	−0.576993	+	0.816749i	$0.695774\pi$
$108$	−17.5564	−1.68937
$109$	−11.3581	−1.08791	−0.543953	−	0.839116i	$-0.683073\pi$
$109$	−11.3581	−1.08791	−0.543953	+	0.839116i	$0.683073\pi$
$110$	7.53339	0.718280
$111$	−3.49351	−0.331589
$112$	2.93126	0.276978
$113$	18.3011	1.72162	0.860811	−	0.508925i	$-0.169957\pi$
$113$	18.3011	1.72162	0.860811	+	0.508925i	$0.169957\pi$
$114$	15.3373	1.43647
$115$	−19.1425	−1.78505
$116$	−26.5724	−2.46719
$117$	−0.119053	−0.0110065
$118$	11.7309	1.07992
$119$	6.00457	0.550438
$120$	−11.3654	−1.03752
$121$	1.00000	0.0909091
$122$	19.7459	1.78771
$123$	−0.686556	−0.0619047
$124$	−8.05710	−0.723549
$125$	1.01069	0.0903989
$126$	10.8635	0.967796
$127$	−10.5486	−0.936038	−0.468019	−	0.883718i	$-0.655032\pi$
$127$	−10.5486	−0.936038	−0.468019	+	0.883718i	$0.655032\pi$
$128$	20.2371	1.78873
$129$	7.61842	0.670764
$130$	−0.450429	−0.0395052
$131$	−13.2835	−1.16059	−0.580293	−	0.814408i	$-0.697062\pi$
$131$	−13.2835	−1.16059	−0.580293	+	0.814408i	$0.697062\pi$
$132$	−3.51750	−0.306159
$133$	−15.1417	−1.31295
$134$	5.83031	0.503662
$135$	−16.1006	−1.38572
$136$	−9.09548	−0.779931
$137$	−19.2917	−1.64821	−0.824103	−	0.566440i	$-0.808320\pi$
$137$	−19.2917	−1.64821	−0.824103	+	0.566440i	$0.808320\pi$
$138$	14.0425	1.19538
$139$	2.43287	0.206353	0.103177	−	0.994663i	$-0.467099\pi$
$139$	2.43287	0.206353	0.103177	+	0.994663i	$0.467099\pi$
$140$	26.1609	2.21100
$141$	7.57635	0.638043
$142$	16.3853	1.37502
$143$	−0.0597910	−0.00499997
$144$	−2.50933	−0.209111
$145$	−24.3690	−2.02374
$146$	−14.3439	−1.18711
$147$	−1.59693	−0.131712
$148$	−12.1807	−1.00124
$149$	−18.1799	−1.48935	−0.744677	−	0.667425i	$-0.767396\pi$
$149$	−18.1799	−1.48935	−0.744677	+	0.667425i	$0.767396\pi$
$150$	−12.5214	−1.02237
$151$	−15.3255	−1.24717	−0.623584	−	0.781756i	$-0.714324\pi$
$151$	−15.3255	−1.24717	−0.623584	+	0.781756i	$0.714324\pi$
$152$	22.9361	1.86036
$153$	−5.14025	−0.415565
$154$	5.45587	0.439647
$155$	−7.38899	−0.593498
$156$	0.210315	0.0168387
$157$	−20.8150	−1.66122	−0.830608	−	0.556858i	$-0.812007\pi$
$157$	−20.8150	−1.66122	−0.830608	+	0.556858i	$0.812007\pi$
$158$	−36.7777	−2.92588
$159$	−3.38792	−0.268680
$160$	13.1371	1.03858
$161$	−13.8635	−1.09259
$162$	−2.20056	−0.172892
$163$	11.9528	0.936219	0.468110	−	0.883670i	$-0.344935\pi$
$163$	11.9528	0.936219	0.468110	+	0.883670i	$0.344935\pi$
$164$	−2.39378	−0.186923
$165$	−3.22583	−0.251130
$166$	−19.2145	−1.49133
$167$	19.8505	1.53608	0.768041	−	0.640401i	$-0.221232\pi$
$167$	19.8505	1.53608	0.768041	+	0.640401i	$0.221232\pi$
$168$	−8.23115	−0.635047
$169$	−12.9964	−0.999725
$170$	−19.4478	−1.49158
$171$	12.9622	0.991243
$172$	26.5628	2.02539
$173$	14.9562	1.13710	0.568548	−	0.822650i	$-0.307505\pi$
$173$	14.9562	1.13710	0.568548	+	0.822650i	$0.307505\pi$
$174$	17.8766	1.35522
$175$	12.3618	0.934462
$176$	−1.26024	−0.0949941
$177$	−5.02321	−0.377567
$178$	13.9729	1.04731
$179$	16.8687	1.26082	0.630412	−	0.776260i	$-0.282886\pi$
$179$	16.8687	1.26082	0.630412	+	0.776260i	$0.282886\pi$
$180$	−22.3952	−1.66924
$181$	−14.8248	−1.10192	−0.550958	−	0.834533i	$-0.685738\pi$
$181$	−14.8248	−1.10192	−0.550958	+	0.834533i	$0.685738\pi$
$182$	−0.326212	−0.0241804
$183$	−8.45527	−0.625032
$184$	20.9998	1.54813
$185$	−11.1706	−0.821281
$186$	5.42040	0.397443
$187$	−2.58155	−0.188781
$188$	26.4161	1.92659
$189$	−11.6605	−0.848174
$190$	49.0415	3.55784
$191$	−21.2600	−1.53832	−0.769160	−	0.639056i	$-0.779325\pi$
$191$	−21.2600	−1.53832	−0.769160	+	0.639056i	$0.779325\pi$
$192$	−12.1687	−0.878202
$193$	15.5256	1.11756	0.558780	−	0.829316i	$-0.311270\pi$
$193$	15.5256	1.11756	0.558780	+	0.829316i	$0.311270\pi$
$194$	−28.3606	−2.03617
$195$	0.192875	0.0138121
$196$	−5.56794	−0.397710
$197$	−5.75073	−0.409722	−0.204861	−	0.978791i	$-0.565674\pi$
$197$	−5.75073	−0.409722	−0.204861	+	0.978791i	$0.565674\pi$
$198$	−4.67054	−0.331921
$199$	−18.2307	−1.29234	−0.646172	−	0.763192i	$-0.723631\pi$
$199$	−18.2307	−1.29234	−0.646172	+	0.763192i	$0.723631\pi$
$200$	−18.7251	−1.32406
$201$	−2.49656	−0.176094
$202$	−14.7518	−1.03793
$203$	−17.6487	−1.23869
$204$	9.08060	0.635769
$205$	−2.19529	−0.153326
$206$	39.9719	2.78498
$207$	11.8679	0.824877
$208$	0.0753509	0.00522464
$209$	6.50989	0.450298
$210$	−17.5997	−1.21449
$211$	−23.6805	−1.63023	−0.815116	−	0.579298i	$-0.803327\pi$
$211$	−23.6805	−1.63023	−0.815116	+	0.579298i	$0.803327\pi$
$212$	−11.8125	−0.811288
$213$	−7.01624	−0.480745
$214$	27.9998	1.91403
$215$	24.3602	1.66135
$216$	17.6628	1.20180
$217$	−5.35129	−0.363270
$218$	26.6420	1.80442
$219$	6.14211	0.415046
$220$	−11.2473	−0.758296
$221$	0.154353	0.0103829
$222$	8.19453	0.549981
$223$	−11.3122	−0.757518	−0.378759	−	0.925495i	$-0.623649\pi$
$223$	−11.3122	−0.757518	−0.378759	+	0.925495i	$0.623649\pi$
$224$	9.51425	0.635698
$225$	−10.5824	−0.705491
$226$	−42.9278	−2.85552
$227$	9.04480	0.600325	0.300162	−	0.953888i	$-0.402959\pi$
$227$	9.04480	0.600325	0.300162	+	0.953888i	$0.402959\pi$
$228$	−22.8986	−1.51649
$229$	−8.67252	−0.573096	−0.286548	−	0.958066i	$-0.592508\pi$
$229$	−8.67252	−0.573096	−0.286548	+	0.958066i	$0.592508\pi$
$230$	44.9014	2.96071
$231$	−2.33623	−0.153712
$232$	26.7335	1.75514
$233$	−1.48547	−0.0973163	−0.0486582	−	0.998815i	$-0.515494\pi$
$233$	−1.48547	−0.0973163	−0.0486582	+	0.998815i	$0.515494\pi$
$234$	0.279256	0.0182555
$235$	24.2256	1.58031
$236$	−17.5142	−1.14008
$237$	15.7484	1.02297
$238$	−14.0846	−0.912969
$239$	−3.32573	−0.215123	−0.107562	−	0.994198i	$-0.534304\pi$
$239$	−3.32573	−0.215123	−0.107562	+	0.994198i	$0.534304\pi$
$240$	4.06531	0.262415
$241$	18.5834	1.19706	0.598532	−	0.801099i	$-0.295751\pi$
$241$	18.5834	1.19706	0.598532	+	0.801099i	$0.295751\pi$
$242$	−2.34564	−0.150784
$243$	15.9818	1.02524
$244$	−29.4806	−1.88730
$245$	−5.10624	−0.326226
$246$	1.61042	0.102676
$247$	−0.389232	−0.0247663
$248$	8.10592	0.514726
$249$	8.22771	0.521410
$250$	−2.37072	−0.149938
$251$	−8.33336	−0.525997	−0.262999	−	0.964796i	$-0.584711\pi$
$251$	−8.33336	−0.525997	−0.262999	+	0.964796i	$0.584711\pi$
$252$	−16.2192	−1.02171
$253$	5.96032	0.374722
$254$	24.7433	1.55253
$255$	8.32762	0.521496
$256$	−23.2386	−1.45241
$257$	13.9391	0.869500	0.434750	−	0.900551i	$-0.356837\pi$
$257$	13.9391	0.869500	0.434750	+	0.900551i	$0.356837\pi$
$258$	−17.8701	−1.11254
$259$	−8.09005	−0.502691
$260$	0.672490	0.0417061
$261$	15.1082	0.935177
$262$	31.1584	1.92497
$263$	8.46427	0.521930	0.260965	−	0.965348i	$-0.415959\pi$
$263$	8.46427	0.521930	0.260965	+	0.965348i	$0.415959\pi$
$264$	3.53882	0.217799
$265$	−10.8330	−0.665466
$266$	35.5171	2.17769
$267$	−5.98324	−0.366169
$268$	−8.70465	−0.531721
$269$	15.5692	0.949271	0.474635	−	0.880183i	$-0.342580\pi$
$269$	15.5692	0.949271	0.474635	+	0.880183i	$0.342580\pi$
$270$	37.7663	2.29838
$271$	−31.9823	−1.94279	−0.971394	−	0.237473i	$-0.923681\pi$
$271$	−31.9823	−1.94279	−0.971394	+	0.237473i	$0.923681\pi$
$272$	3.25337	0.197264
$273$	0.139685	0.00845414
$274$	45.2516	2.73375
$275$	−5.31470	−0.320488
$276$	−20.9655	−1.26197
$277$	29.1827	1.75342	0.876708	−	0.481022i	$-0.159734\pi$
$277$	29.1827	1.75342	0.876708	+	0.481022i	$0.159734\pi$
$278$	−5.70665	−0.342262
$279$	4.58101	0.274258
$280$	−26.3194	−1.57289
$281$	18.5073	1.10405	0.552026	−	0.833827i	$-0.313855\pi$
$281$	18.5073	1.10405	0.552026	+	0.833827i	$0.313855\pi$
$282$	−17.7714	−1.05827
$283$	19.3562	1.15061	0.575303	−	0.817940i	$-0.304884\pi$
$283$	19.3562	1.15061	0.575303	+	0.817940i	$0.304884\pi$
$284$	−24.4632	−1.45163
$285$	−20.9998	−1.24392
$286$	0.140248	0.00829306
$287$	−1.58988	−0.0938479
$288$	−8.14474	−0.479933
$289$	−10.3356	−0.607977
$290$	57.1610	3.35661
$291$	12.1441	0.711901
$292$	21.4154	1.25324
$293$	23.6430	1.38124	0.690620	−	0.723218i	$-0.257338\pi$
$293$	23.6430	1.38124	0.690620	+	0.723218i	$0.257338\pi$
$294$	3.74583	0.218461
$295$	−16.0619	−0.935160
$296$	12.2545	0.712277
$297$	5.01318	0.290894
$298$	42.6435	2.47027
$299$	−0.356374	−0.0206096
$300$	18.6945	1.07933
$301$	17.6423	1.01688
$302$	35.9481	2.06858
$303$	6.31678	0.362889
$304$	−8.20401	−0.470532
$305$	−27.0360	−1.54808
$306$	12.0572	0.689265
$307$	20.0819	1.14613	0.573067	−	0.819509i	$-0.305754\pi$
$307$	20.0819	1.14613	0.573067	+	0.819509i	$0.305754\pi$
$308$	−8.14562	−0.464140
$309$	−17.1161	−0.973703
$310$	17.3319	0.984388
$311$	2.33082	0.132169	0.0660844	−	0.997814i	$-0.478949\pi$
$311$	2.33082	0.132169	0.0660844	+	0.997814i	$0.478949\pi$
$312$	−0.211589	−0.0119789
$313$	−2.00636	−0.113406	−0.0567030	−	0.998391i	$-0.518059\pi$
$313$	−2.00636	−0.113406	−0.0567030	+	0.998391i	$0.518059\pi$
$314$	48.8245	2.75533
$315$	−14.8742	−0.838069
$316$	54.9091	3.08888
$317$	17.3652	0.975328	0.487664	−	0.873031i	$-0.337849\pi$
$317$	17.3652	0.975328	0.487664	+	0.873031i	$0.337849\pi$
$318$	7.94686	0.445638
$319$	7.58769	0.424829
$320$	−38.9099	−2.17513
$321$	−11.9896	−0.669195
$322$	32.5188	1.81220
$323$	−16.8056	−0.935087
$324$	3.28544	0.182524
$325$	0.317771	0.0176268
$326$	−28.0371	−1.55283
$327$	−11.4082	−0.630875
$328$	2.40829	0.132976
$329$	17.5448	0.967278
$330$	7.56664	0.416530
$331$	18.6456	1.02486	0.512428	−	0.858730i	$-0.328746\pi$
$331$	18.6456	1.02486	0.512428	+	0.858730i	$0.328746\pi$
$332$	28.6872	1.57441
$333$	6.92554	0.379517
$334$	−46.5623	−2.54778
$335$	−7.98284	−0.436149
$336$	2.94420	0.160619
$337$	−35.2312	−1.91916	−0.959582	−	0.281428i	$-0.909192\pi$
$337$	−35.2312	−1.91916	−0.959582	+	0.281428i	$0.909192\pi$
$338$	30.4850	1.65816
$339$	18.3819	0.998366
$340$	29.0356	1.57467
$341$	2.30068	0.124589
$342$	−30.4047	−1.64410
$343$	−19.9798	−1.07881
$344$	−26.7238	−1.44085
$345$	−19.2270	−1.03515
$346$	−35.0818	−1.88601
$347$	10.4718	0.562155	0.281077	−	0.959685i	$-0.409308\pi$
$347$	10.4718	0.562155	0.281077	+	0.959685i	$0.409308\pi$
$348$	−26.6897	−1.43072
$349$	24.6923	1.32175	0.660876	−	0.750496i	$-0.270185\pi$
$349$	24.6923	1.32175	0.660876	+	0.750496i	$0.270185\pi$
$350$	−28.9963	−1.54992
$351$	−0.299743	−0.0159991
$352$	−4.09046	−0.218022
$353$	−1.68402	−0.0896315	−0.0448158	−	0.998995i	$-0.514270\pi$
$353$	−1.68402	−0.0896315	−0.0448158	+	0.998995i	$0.514270\pi$
$354$	11.7827	0.626241
$355$	−22.4347	−1.19071
$356$	−20.8615	−1.10566
$357$	6.03108	0.319198
$358$	−39.5679	−2.09123
$359$	0.393018	0.0207427	0.0103713	−	0.999946i	$-0.496699\pi$
$359$	0.393018	0.0207427	0.0103713	+	0.999946i	$0.496699\pi$
$360$	22.5309	1.18748
$361$	23.3786	1.23045
$362$	34.7736	1.82766
$363$	1.00441	0.0527181
$364$	0.487035	0.0255275
$365$	19.6396	1.02799
$366$	19.8331	1.03669
$367$	−18.4746	−0.964366	−0.482183	−	0.876071i	$-0.660156\pi$
$367$	−18.4746	−0.964366	−0.482183	+	0.876071i	$0.660156\pi$
$368$	−7.51143	−0.391560
$369$	1.36103	0.0708524
$370$	26.2023	1.36219
$371$	−7.84554	−0.407320
$372$	−8.09266	−0.419585
$373$	7.21396	0.373525	0.186762	−	0.982405i	$-0.440201\pi$
$373$	7.21396	0.373525	0.186762	+	0.982405i	$0.440201\pi$
$374$	6.05539	0.313117
$375$	1.01515	0.0524222
$376$	−26.5762	−1.37056
$377$	−0.453675	−0.0233655
$378$	27.3513	1.40680
$379$	5.88974	0.302536	0.151268	−	0.988493i	$-0.451664\pi$
$379$	5.88974	0.302536	0.151268	+	0.988493i	$0.451664\pi$
$380$	−73.2190	−3.75605
$381$	−10.5952	−0.542807
$382$	49.8684	2.55149
$383$	−23.4113	−1.19626	−0.598131	−	0.801398i	$-0.704090\pi$
$383$	−23.4113	−1.19626	−0.598131	+	0.801398i	$0.704090\pi$
$384$	20.3265	1.03728
$385$	−7.47017	−0.380715
$386$	−36.4176	−1.85361
$387$	−15.1028	−0.767717
$388$	42.3424	2.14961
$389$	−29.5657	−1.49904	−0.749520	−	0.661982i	$-0.769716\pi$
$389$	−29.5657	−1.49904	−0.749520	+	0.661982i	$0.769716\pi$
$390$	−0.452417	−0.0229090
$391$	−15.3869	−0.778147
$392$	5.60168	0.282928
$393$	−13.3421	−0.673022
$394$	13.4892	0.679574
$395$	50.3560	2.53368
$396$	6.97311	0.350412
$397$	−34.9856	−1.75588	−0.877939	−	0.478772i	$-0.841082\pi$
$397$	−34.9856	−1.75588	−0.877939	+	0.478772i	$0.841082\pi$
$398$	42.7628	2.14351
$399$	−15.2086	−0.761381
$400$	6.69778	0.334889
$401$	31.0529	1.55071	0.775353	−	0.631528i	$-0.217572\pi$
$401$	31.0529	1.55071	0.775353	+	0.631528i	$0.217572\pi$
$402$	5.85604	0.292073
$403$	−0.137560	−0.00685235
$404$	22.0244	1.09576
$405$	3.01300	0.149717
$406$	41.3975	2.05452
$407$	3.47816	0.172406
$408$	−9.13563	−0.452281
$409$	0.681539	0.0337000	0.0168500	−	0.999858i	$-0.494636\pi$
$409$	0.681539	0.0337000	0.0168500	+	0.999858i	$0.494636\pi$
$410$	5.14936	0.254309
$411$	−19.3769	−0.955792
$412$	−59.6781	−2.94013
$413$	−11.6324	−0.572395
$414$	−27.8379	−1.36816
$415$	26.3084	1.29143
$416$	0.244573	0.0119912
$417$	2.44361	0.119664
$418$	−15.2699	−0.746874
$419$	30.7013	1.49986	0.749928	−	0.661519i	$-0.230088\pi$
$419$	30.7013	1.49986	0.749928	+	0.661519i	$0.230088\pi$
$420$	26.2764	1.28215
$421$	−13.6026	−0.662949	−0.331475	−	0.943464i	$-0.607546\pi$
$421$	−13.6026	−0.662949	−0.331475	+	0.943464i	$0.607546\pi$
$422$	55.5460	2.70394
$423$	−15.0194	−0.730267
$424$	11.8841	0.577143
$425$	13.7201	0.665524
$426$	16.4576	0.797374
$427$	−19.5802	−0.947552
$428$	−41.8037	−2.02066
$429$	−0.0600549	−0.00289948
$430$	−57.1403	−2.75555
$431$	−27.4374	−1.32161	−0.660807	−	0.750556i	$-0.729786\pi$
$431$	−27.4374	−1.32161	−0.660807	+	0.750556i	$0.729786\pi$
$432$	−6.31781	−0.303966
$433$	21.3917	1.02802	0.514010	−	0.857784i	$-0.328159\pi$
$433$	21.3917	1.02802	0.514010	+	0.857784i	$0.328159\pi$
$434$	12.5522	0.602526
$435$	−24.4766	−1.17356
$436$	−39.7765	−1.90495
$437$	38.8010	1.85611
$438$	−14.4072	−0.688403
$439$	−8.51216	−0.406263	−0.203132	−	0.979151i	$-0.565112\pi$
$439$	−8.51216	−0.406263	−0.203132	+	0.979151i	$0.565112\pi$
$440$	11.3155	0.539445
$441$	3.16576	0.150750
$442$	−0.362058	−0.0172213
$443$	27.0491	1.28514	0.642570	−	0.766227i	$-0.277868\pi$
$443$	27.0491	1.28514	0.642570	+	0.766227i	$0.277868\pi$
$444$	−12.2344	−0.580621
$445$	−19.1316	−0.906927
$446$	26.5343	1.25644
$447$	−18.2601	−0.863674
$448$	−28.1796	−1.33136
$449$	14.7855	0.697769	0.348885	−	0.937166i	$-0.386561\pi$
$449$	14.7855	0.697769	0.348885	+	0.937166i	$0.386561\pi$
$450$	24.8225	1.17014
$451$	0.683539	0.0321866
$452$	64.0913	3.01460
$453$	−15.3931	−0.723231
$454$	−21.2159	−0.995711
$455$	0.446649	0.0209392
$456$	23.0373	1.07882
$457$	10.0967	0.472304	0.236152	−	0.971716i	$-0.424114\pi$
$457$	10.0967	0.472304	0.236152	+	0.971716i	$0.424114\pi$
$458$	20.3427	0.950550
$459$	−12.9418	−0.604070
$460$	−67.0379	−3.12566
$461$	−1.50264	−0.0699847	−0.0349923	−	0.999388i	$-0.511141\pi$
$461$	−1.50264	−0.0699847	−0.0349923	+	0.999388i	$0.511141\pi$
$462$	5.47996	0.254951
$463$	−28.6276	−1.33044	−0.665218	−	0.746649i	$-0.731661\pi$
$463$	−28.6276	−1.33044	−0.665218	+	0.746649i	$0.731661\pi$
$464$	−9.56230	−0.443919
$465$	−7.42160	−0.344168
$466$	3.48438	0.161411
$467$	−27.8149	−1.28712	−0.643560	−	0.765396i	$-0.722543\pi$
$467$	−27.8149	−1.28712	−0.643560	+	0.765396i	$0.722543\pi$
$468$	−0.416929	−0.0192726
$469$	−5.78138	−0.266959
$470$	−56.8247	−2.62113
$471$	−20.9069	−0.963337
$472$	17.6203	0.811042
$473$	−7.58494	−0.348756
$474$	−36.9401	−1.69671
$475$	−34.5981	−1.58747
$476$	21.0283	0.963831
$477$	6.71623	0.307515
$478$	7.80097	0.356808
$479$	25.3597	1.15871	0.579356	−	0.815074i	$-0.303304\pi$
$479$	25.3597	1.15871	0.579356	+	0.815074i	$0.303304\pi$
$480$	13.1951	0.602272
$481$	−0.207962	−0.00948227
$482$	−43.5901	−1.98547
$483$	−13.9247	−0.633594
$484$	3.50205	0.159184
$485$	38.8313	1.76324
$486$	−37.4877	−1.70048
$487$	33.2217	1.50542	0.752709	−	0.658353i	$-0.228747\pi$
$487$	33.2217	1.50542	0.752709	+	0.658353i	$0.228747\pi$
$488$	29.6593	1.34261
$489$	12.0056	0.542912
$490$	11.9774	0.541085
$491$	−27.7606	−1.25282	−0.626410	−	0.779494i	$-0.715476\pi$
$491$	−27.7606	−1.25282	−0.626410	+	0.779494i	$0.715476\pi$
$492$	−2.40435	−0.108396
$493$	−19.5880	−0.882198
$494$	0.913001	0.0410779
$495$	6.39489	0.287429
$496$	−2.89941	−0.130187
$497$	−16.2478	−0.728813
$498$	−19.2993	−0.864821
$499$	−37.0535	−1.65874	−0.829371	−	0.558699i	$-0.811301\pi$
$499$	−37.0535	−1.65874	−0.829371	+	0.558699i	$0.811301\pi$
$500$	3.53949	0.158291
$501$	19.9382	0.890771
$502$	19.5471	0.872430
$503$	−34.2656	−1.52783	−0.763915	−	0.645317i	$-0.776725\pi$
$503$	−34.2656	−1.52783	−0.763915	+	0.645317i	$0.776725\pi$
$504$	16.3175	0.726837
$505$	20.1981	0.898805
$506$	−13.9808	−0.621522
$507$	−13.0538	−0.579739
$508$	−36.9417	−1.63902
$509$	−13.0236	−0.577261	−0.288631	−	0.957441i	$-0.593200\pi$
$509$	−13.0236	−0.577261	−0.288631	+	0.957441i	$0.593200\pi$
$510$	−19.5336	−0.864964
$511$	14.2235	0.629212
$512$	14.0353	0.620277
$513$	32.6353	1.44088
$514$	−32.6963	−1.44217
$515$	−54.7295	−2.41167
$516$	26.6800	1.17452
$517$	−7.54305	−0.331743
$518$	18.9764	0.833775
$519$	15.0222	0.659401
$520$	−0.676565	−0.0296693
$521$	20.9208	0.916555	0.458278	−	0.888809i	$-0.348467\pi$
$521$	20.9208	0.916555	0.458278	+	0.888809i	$0.348467\pi$
$522$	−35.4386	−1.55110
$523$	17.8069	0.778643	0.389321	−	0.921102i	$-0.372710\pi$
$523$	17.8069	0.778643	0.389321	+	0.921102i	$0.372710\pi$
$524$	−46.5195	−2.03221
$525$	12.4163	0.541893
$526$	−19.8542	−0.865683
$527$	−5.93932	−0.258721
$528$	−1.26580	−0.0550869
$529$	12.5255	0.544586
$530$	25.4104	1.10376
$531$	9.95802	0.432141
$532$	−53.0271	−2.29901
$533$	−0.0408694	−0.00177025
$534$	14.0346	0.607335
$535$	−38.3372	−1.65746
$536$	8.75740	0.378262
$537$	16.9431	0.731151
$538$	−36.5198	−1.57448
$539$	1.58991	0.0684823
$540$	−56.3850	−2.42642
$541$	−0.997898	−0.0429030	−0.0214515	−	0.999770i	$-0.506829\pi$
$541$	−0.997898	−0.0429030	−0.0214515	+	0.999770i	$0.506829\pi$
$542$	75.0192	3.22235
$543$	−14.8902	−0.639000
$544$	10.5597	0.452744
$545$	−36.4781	−1.56255
$546$	−0.327652	−0.0140222
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−67.5606	−2.88605
$549$	16.7617	0.715374
$550$	12.4664	0.531568
$551$	49.3950	2.10430
$552$	21.0925	0.897757
$553$	36.4691	1.55082
$554$	−68.4522	−2.90825
$555$	−11.2199	−0.476259
$556$	8.52003	0.361330
$557$	6.31476	0.267565	0.133783	−	0.991011i	$-0.457288\pi$
$557$	6.31476	0.267565	0.133783	+	0.991011i	$0.457288\pi$
$558$	−10.7454	−0.454890
$559$	0.453511	0.0191815
$560$	9.41420	0.397822
$561$	−2.59294	−0.109474
$562$	−43.4115	−1.83120
$563$	−13.8395	−0.583266	−0.291633	−	0.956530i	$-0.594199\pi$
$563$	−13.8395	−0.583266	−0.291633	+	0.956530i	$0.594199\pi$
$564$	26.5327	1.11723
$565$	58.7767	2.47275
$566$	−45.4027	−1.90842
$567$	2.18209	0.0916393
$568$	24.6115	1.03267
$569$	17.7706	0.744983	0.372491	−	0.928036i	$-0.378504\pi$
$569$	17.7706	0.744983	0.372491	+	0.928036i	$0.378504\pi$
$570$	49.2580	2.06319
$571$	−15.4352	−0.645944	−0.322972	−	0.946408i	$-0.604682\pi$
$571$	−15.4352	−0.645944	−0.322972	+	0.946408i	$0.604682\pi$
$572$	−0.209391	−0.00875507
$573$	−21.3538	−0.892070
$574$	3.72930	0.155658
$575$	−31.6773	−1.32104
$576$	24.1233	1.00514
$577$	−26.7688	−1.11440	−0.557200	−	0.830379i	$-0.688124\pi$
$577$	−26.7688	−1.11440	−0.557200	+	0.830379i	$0.688124\pi$
$578$	24.2437	1.00840
$579$	15.5942	0.648071
$580$	−85.3414	−3.54361
$581$	19.0532	0.790461
$582$	−28.4858	−1.18077
$583$	3.37304	0.139697
$584$	−21.5452	−0.891547
$585$	−0.382356	−0.0158085
$586$	−55.4581	−2.29095
$587$	10.8974	0.449782	0.224891	−	0.974384i	$-0.427797\pi$
$587$	10.8974	0.449782	0.224891	+	0.974384i	$0.427797\pi$
$588$	−5.59252	−0.230632
$589$	14.9772	0.617124
$590$	37.6755	1.55108
$591$	−5.77611	−0.237597
$592$	−4.38331	−0.180153
$593$	−32.0419	−1.31580	−0.657902	−	0.753103i	$-0.728556\pi$
$593$	−32.0419	−1.31580	−0.657902	+	0.753103i	$0.728556\pi$
$594$	−11.7591	−0.482484
$595$	19.2846	0.790591
$596$	−63.6668	−2.60789
$597$	−18.3112	−0.749428
$598$	0.835926	0.0341835
$599$	40.4659	1.65339	0.826695	−	0.562650i	$-0.190218\pi$
$599$	40.4659	1.65339	0.826695	+	0.562650i	$0.190218\pi$
$600$	−18.8077	−0.767823
$601$	31.4218	1.28172	0.640860	−	0.767658i	$-0.278578\pi$
$601$	31.4218	1.28172	0.640860	+	0.767658i	$0.278578\pi$
$602$	−41.3825	−1.68662
$603$	4.94919	0.201547
$604$	−53.6705	−2.18382
$605$	3.21165	0.130572
$606$	−14.8169	−0.601896
$607$	−25.6647	−1.04170	−0.520849	−	0.853649i	$-0.674385\pi$
$607$	−25.6647	−1.04170	−0.520849	+	0.853649i	$0.674385\pi$
$608$	−26.6285	−1.07993
$609$	−17.7266	−0.718316
$610$	63.4169	2.56768
$611$	0.451006	0.0182458
$612$	−18.0014	−0.727664
$613$	39.1963	1.58312	0.791561	−	0.611090i	$-0.209269\pi$
$613$	39.1963	1.58312	0.791561	+	0.611090i	$0.209269\pi$
$614$	−47.1050	−1.90100
$615$	−2.20498	−0.0889132
$616$	8.19498	0.330185
$617$	17.1780	0.691559	0.345779	−	0.938316i	$-0.387615\pi$
$617$	17.1780	0.691559	0.345779	+	0.938316i	$0.387615\pi$
$618$	40.1484	1.61500
$619$	0.110168	0.00442802	0.00221401	−	0.999998i	$-0.499295\pi$
$619$	0.110168	0.00442802	0.00221401	+	0.999998i	$0.499295\pi$
$620$	−25.8766	−1.03923
$621$	29.8802	1.19905
$622$	−5.46728	−0.219218
$623$	−13.8556	−0.555114
$624$	0.0756835	0.00302976
$625$	−23.3275	−0.933100
$626$	4.70620	0.188098
$627$	6.53862	0.261127
$628$	−72.8950	−2.90883
$629$	−8.97903	−0.358017
$630$	34.8897	1.39004
$631$	34.6786	1.38053	0.690266	−	0.723555i	$-0.257493\pi$
$631$	34.6786	1.38053	0.690266	+	0.723555i	$0.257493\pi$
$632$	−55.2419	−2.19740
$633$	−23.7850	−0.945369
$634$	−40.7326	−1.61770
$635$	−33.8784	−1.34443
$636$	−11.8647	−0.470465
$637$	−0.0950624	−0.00376651
$638$	−17.7980	−0.704630
$639$	13.9090	0.550232
$640$	64.9946	2.56914
$641$	−17.4992	−0.691176	−0.345588	−	0.938386i	$-0.612320\pi$
$641$	−17.4992	−0.691176	−0.345588	+	0.938386i	$0.612320\pi$
$642$	28.1234	1.10994
$643$	31.8070	1.25434	0.627172	−	0.778880i	$-0.284212\pi$
$643$	31.8070	1.25434	0.627172	+	0.778880i	$0.284212\pi$
$644$	−48.5505	−1.91316
$645$	24.4677	0.963414
$646$	39.4199	1.55096
$647$	3.14492	0.123640	0.0618198	−	0.998087i	$-0.480310\pi$
$647$	3.14492	0.123640	0.0618198	+	0.998087i	$0.480310\pi$
$648$	−3.30534	−0.129846
$649$	5.00113	0.196312
$650$	−0.745377	−0.0292361
$651$	−5.37491	−0.210660
$652$	41.8594	1.63934
$653$	2.70996	0.106049	0.0530245	−	0.998593i	$-0.483114\pi$
$653$	2.70996	0.106049	0.0530245	+	0.998593i	$0.483114\pi$
$654$	26.7596	1.04638
$655$	−42.6620	−1.66694
$656$	−0.861422	−0.0336329
$657$	−12.1761	−0.475036
$658$	−41.1539	−1.60435
$659$	−14.2929	−0.556774	−0.278387	−	0.960469i	$-0.589800\pi$
$659$	−14.2929	−0.556774	−0.278387	+	0.960469i	$0.589800\pi$
$660$	−11.2970	−0.439735
$661$	6.88505	0.267797	0.133899	−	0.990995i	$-0.457250\pi$
$661$	6.88505	0.267797	0.133899	+	0.990995i	$0.457250\pi$
$662$	−43.7360	−1.69985
$663$	0.155035	0.00602104
$664$	−28.8610	−1.12003
$665$	−48.6299	−1.88579
$666$	−16.2449	−0.629475
$667$	45.2251	1.75112
$668$	69.5175	2.68971
$669$	−11.3621	−0.439284
$670$	18.7249	0.723406
$671$	8.41811	0.324978
$672$	9.55625	0.368640
$673$	−20.9436	−0.807317	−0.403658	−	0.914910i	$-0.632262\pi$
$673$	−20.9436	−0.807317	−0.403658	+	0.914910i	$0.632262\pi$
$674$	82.6398	3.18317
$675$	−26.6435	−1.02551
$676$	−45.5141	−1.75054
$677$	19.8783	0.763987	0.381993	−	0.924165i	$-0.375238\pi$
$677$	19.8783	0.763987	0.381993	+	0.924165i	$0.375238\pi$
$678$	−43.1173	−1.65591
$679$	28.1226	1.07925
$680$	−29.2115	−1.12021
$681$	9.08472	0.348127
$682$	−5.39658	−0.206646
$683$	25.5402	0.977270	0.488635	−	0.872488i	$-0.337495\pi$
$683$	25.5402	0.977270	0.488635	+	0.872488i	$0.337495\pi$
$684$	45.3942	1.73569
$685$	−61.9583	−2.36731
$686$	46.8655	1.78933
$687$	−8.71080	−0.332338
$688$	9.55883	0.364427
$689$	−0.201677	−0.00768328
$690$	45.0996	1.71691
$691$	13.9932	0.532326	0.266163	−	0.963928i	$-0.414244\pi$
$691$	13.9932	0.532326	0.266163	+	0.963928i	$0.414244\pi$
$692$	52.3772	1.99108
$693$	4.63134	0.175930
$694$	−24.5631	−0.932402
$695$	7.81353	0.296384
$696$	26.8515	1.01780
$697$	−1.76459	−0.0668385
$698$	−57.9195	−2.19228
$699$	−1.49203	−0.0564336
$700$	43.2915	1.63626
$701$	15.9283	0.601604	0.300802	−	0.953687i	$-0.402746\pi$
$701$	15.9283	0.601604	0.300802	+	0.953687i	$0.402746\pi$
$702$	0.703091	0.0265364
$703$	22.6424	0.853975
$704$	12.1152	0.456611
$705$	24.3326	0.916418
$706$	3.95012	0.148665
$707$	14.6280	0.550143
$708$	−17.5915	−0.661130
$709$	−31.0394	−1.16571	−0.582855	−	0.812576i	$-0.698064\pi$
$709$	−31.0394	−1.16571	−0.582855	+	0.812576i	$0.698064\pi$
$710$	52.6238	1.97494
$711$	−31.2196	−1.17083
$712$	20.9879	0.786556
$713$	13.7128	0.513549
$714$	−14.1468	−0.529429
$715$	−0.192028	−0.00718143
$716$	59.0749	2.20773
$717$	−3.34040	−0.124750
$718$	−0.921880	−0.0344043
$719$	−31.3532	−1.16928	−0.584638	−	0.811295i	$-0.698763\pi$
$719$	−31.3532	−1.16928	−0.584638	+	0.811295i	$0.698763\pi$
$720$	−8.05908	−0.300344
$721$	−39.6365	−1.47614
$722$	−54.8379	−2.04086
$723$	18.6654	0.694175
$724$	−51.9170	−1.92948
$725$	−40.3263	−1.49768
$726$	−2.35600	−0.0874393
$727$	−26.2810	−0.974709	−0.487355	−	0.873204i	$-0.662038\pi$
$727$	−26.2810	−0.974709	−0.487355	+	0.873204i	$0.662038\pi$
$728$	−0.489986	−0.0181601
$729$	13.2379	0.490294
$730$	−46.0676	−1.70504
$731$	19.5809	0.724225
$732$	−29.6108	−1.09444
$733$	−49.7810	−1.83870	−0.919351	−	0.393437i	$-0.871286\pi$
$733$	−49.7810	−1.83870	−0.919351	+	0.393437i	$0.871286\pi$
$734$	43.3348	1.59952
$735$	−5.12878	−0.189178
$736$	−24.3805	−0.898677
$737$	2.48559	0.0915579
$738$	−3.19249	−0.117517
$739$	−14.2583	−0.524500	−0.262250	−	0.965000i	$-0.584464\pi$
$739$	−14.2583	−0.524500	−0.262250	+	0.965000i	$0.584464\pi$
$740$	−39.1200	−1.43808
$741$	−0.390951	−0.0143619
$742$	18.4029	0.675590
$743$	44.6230	1.63706	0.818529	−	0.574466i	$-0.194790\pi$
$743$	44.6230	1.63706	0.818529	+	0.574466i	$0.194790\pi$
$744$	8.14170	0.298489
$745$	−58.3874	−2.13915
$746$	−16.9214	−0.619536
$747$	−16.3106	−0.596775
$748$	−9.04070	−0.330561
$749$	−27.7648	−1.01450
$750$	−2.38119	−0.0869486
$751$	−52.2101	−1.90517	−0.952587	−	0.304267i	$-0.901588\pi$
$751$	−52.2101	−1.90517	−0.952587	+	0.304267i	$0.901588\pi$
$752$	9.50605	0.346650
$753$	−8.37014	−0.305025
$754$	1.06416	0.0387545
$755$	−49.2200	−1.79130
$756$	−40.8355	−1.48517
$757$	−28.3389	−1.03000	−0.514998	−	0.857192i	$-0.672207\pi$
$757$	−28.3389	−1.03000	−0.514998	+	0.857192i	$0.672207\pi$
$758$	−13.8152	−0.501792
$759$	5.98663	0.217301
$760$	73.6626	2.67202
$761$	13.1113	0.475284	0.237642	−	0.971353i	$-0.423626\pi$
$761$	13.1113	0.475284	0.237642	+	0.971353i	$0.423626\pi$
$762$	24.8525	0.900311
$763$	−26.4184	−0.956411
$764$	−74.4535	−2.69363
$765$	−16.5087	−0.596873
$766$	54.9146	1.98414
$767$	−0.299023	−0.0107971
$768$	−23.3412	−0.842253
$769$	54.7971	1.97603	0.988017	−	0.154347i	$-0.0493275\pi$
$769$	54.7971	1.97603	0.988017	+	0.154347i	$0.0493275\pi$
$770$	17.5224	0.631462
$771$	14.0007	0.504222
$772$	54.3715	1.95687
$773$	−34.1550	−1.22847	−0.614235	−	0.789123i	$-0.710535\pi$
$773$	−34.1550	−1.22847	−0.614235	+	0.789123i	$0.710535\pi$
$774$	35.4257	1.27335
$775$	−12.2274	−0.439222
$776$	−42.5990	−1.52921
$777$	−8.12576	−0.291510
$778$	69.3506	2.48634
$779$	4.44976	0.159429
$780$	0.675458	0.0241853
$781$	6.98541	0.249958
$782$	36.0921	1.29065
$783$	38.0385	1.35938
$784$	−2.00367	−0.0715596
$785$	−66.8504	−2.38599
$786$	31.2959	1.11629
$787$	−36.7486	−1.30994	−0.654972	−	0.755653i	$-0.727320\pi$
$787$	−36.7486	−1.30994	−0.654972	+	0.755653i	$0.727320\pi$
$788$	−20.1393	−0.717434
$789$	8.50163	0.302666
$790$	−118.117	−4.20242
$791$	42.5676	1.51353
$792$	−7.01536	−0.249280
$793$	−0.503327	−0.0178737
$794$	82.0638	2.91234
$795$	−10.8808	−0.385903
$796$	−63.8449	−2.26292
$797$	17.9050	0.634228	0.317114	−	0.948387i	$-0.397286\pi$
$797$	17.9050	0.634228	0.317114	+	0.948387i	$0.397286\pi$
$798$	35.6739	1.26284
$799$	19.4727	0.688896
$800$	21.7396	0.768610
$801$	11.8612	0.419095
$802$	−72.8390	−2.57203
$803$	−6.11512	−0.215798
$804$	−8.74307	−0.308344
$805$	−44.5246	−1.56929
$806$	0.322667	0.0113655
$807$	15.6379	0.550481
$808$	−22.1579	−0.779512
$809$	−34.0989	−1.19885	−0.599427	−	0.800429i	$-0.704605\pi$
$809$	−34.0989	−1.19885	−0.599427	+	0.800429i	$0.704605\pi$
$810$	−7.06743	−0.248324
$811$	−47.9475	−1.68366	−0.841832	−	0.539740i	$-0.818523\pi$
$811$	−47.9475	−1.68366	−0.841832	+	0.539740i	$0.818523\pi$
$812$	−61.8064	−2.16898
$813$	−32.1235	−1.12662
$814$	−8.15852	−0.285956
$815$	38.3884	1.34469
$816$	3.26773	0.114393
$817$	−49.3771	−1.72749
$818$	−1.59865	−0.0558954
$819$	−0.276912	−0.00967610
$820$	−7.68800	−0.268477
$821$	−14.6487	−0.511244	−0.255622	−	0.966777i	$-0.582280\pi$
$821$	−14.6487	−0.511244	−0.255622	+	0.966777i	$0.582280\pi$
$822$	45.4513	1.58530
$823$	−3.81811	−0.133091	−0.0665455	−	0.997783i	$-0.521198\pi$
$823$	−3.81811	−0.133091	−0.0665455	+	0.997783i	$0.521198\pi$
$824$	60.0397	2.09158
$825$	−5.33815	−0.185851
$826$	27.2856	0.949386
$827$	45.1867	1.57130	0.785648	−	0.618674i	$-0.212330\pi$
$827$	45.1867	1.57130	0.785648	+	0.618674i	$0.212330\pi$
$828$	41.5620	1.44438
$829$	26.5865	0.923386	0.461693	−	0.887040i	$-0.347242\pi$
$829$	26.5865	0.923386	0.461693	+	0.887040i	$0.347242\pi$
$830$	−61.7101	−2.14199
$831$	29.3115	1.01680
$832$	−0.724383	−0.0251134
$833$	−4.10443	−0.142210
$834$	−5.73184	−0.198477
$835$	63.7530	2.20626
$836$	22.7979	0.788483
$837$	11.5337	0.398664
$838$	−72.0143	−2.48769
$839$	50.3801	1.73931	0.869657	−	0.493656i	$-0.164340\pi$
$839$	50.3801	1.73931	0.869657	+	0.493656i	$0.164340\pi$
$840$	−26.4356	−0.912114
$841$	28.5730	0.985276
$842$	31.9068	1.09958
$843$	18.5890	0.640238
$844$	−82.9302	−2.85457
$845$	−41.7400	−1.43590
$846$	35.2301	1.21124
$847$	2.32596	0.0799209
$848$	−4.25083	−0.145974
$849$	19.4416	0.667235
$850$	−32.1826	−1.10385
$851$	20.7309	0.710648
$852$	−24.5712	−0.841796
$853$	37.3736	1.27965	0.639824	−	0.768521i	$-0.279007\pi$
$853$	37.3736	1.27965	0.639824	+	0.768521i	$0.279007\pi$
$854$	45.9282	1.57163
$855$	41.6300	1.42372
$856$	42.0570	1.43748
$857$	−48.9885	−1.67342	−0.836708	−	0.547649i	$-0.815523\pi$
$857$	−48.9885	−1.67342	−0.836708	+	0.547649i	$0.815523\pi$
$858$	0.140867	0.00480913
$859$	20.1162	0.686354	0.343177	−	0.939271i	$-0.388497\pi$
$859$	20.1162	0.686354	0.343177	+	0.939271i	$0.388497\pi$
$860$	85.3104	2.90906
$861$	−1.59690	−0.0544222
$862$	64.3584	2.19206
$863$	−50.2341	−1.70999	−0.854995	−	0.518636i	$-0.826440\pi$
$863$	−50.2341	−1.70999	−0.854995	+	0.518636i	$0.826440\pi$
$864$	−20.5062	−0.697637
$865$	48.0340	1.63320
$866$	−50.1774	−1.70510
$867$	−10.3812	−0.352565
$868$	−18.7405	−0.636094
$869$	−15.6792	−0.531879
$870$	57.4133	1.94649
$871$	−0.148616	−0.00503566
$872$	40.0175	1.35516
$873$	−24.0745	−0.814800
$874$	−91.0134	−3.07858
$875$	2.35083	0.0794724
$876$	21.5100	0.726754
$877$	−8.12995	−0.274529	−0.137264	−	0.990534i	$-0.543831\pi$
$877$	−8.12995	−0.274529	−0.137264	+	0.990534i	$0.543831\pi$
$878$	19.9665	0.673836
$879$	23.7474	0.800979
$880$	−4.04745	−0.136439
$881$	−27.9838	−0.942798	−0.471399	−	0.881920i	$-0.656251\pi$
$881$	−27.9838	−0.942798	−0.471399	+	0.881920i	$0.656251\pi$
$882$	−7.42574	−0.250038
$883$	12.8421	0.432170	0.216085	−	0.976375i	$-0.430671\pi$
$883$	12.8421	0.432170	0.216085	+	0.976375i	$0.430671\pi$
$884$	0.540552	0.0181807
$885$	−16.1328	−0.542298
$886$	−63.4475	−2.13156
$887$	−35.4929	−1.19173	−0.595867	−	0.803083i	$-0.703191\pi$
$887$	−35.4929	−1.19173	−0.595867	+	0.803083i	$0.703191\pi$
$888$	12.3086	0.413049
$889$	−24.5356	−0.822899
$890$	44.8760	1.50425
$891$	−0.938147	−0.0314291
$892$	−39.6157	−1.32643
$893$	−49.1044	−1.64322
$894$	42.8317	1.43251
$895$	54.1763	1.81091
$896$	47.0708	1.57252
$897$	−0.357947	−0.0119515
$898$	−34.6814	−1.15733
$899$	17.4569	0.582219
$900$	−37.0600	−1.23533
$901$	−8.70765	−0.290094
$902$	−1.60334	−0.0533853
$903$	17.7201	0.589689
$904$	−64.4796	−2.14456
$905$	−47.6120	−1.58268
$906$	36.1067	1.19957
$907$	−29.9950	−0.995967	−0.497983	−	0.867187i	$-0.665926\pi$
$907$	−29.9950	−0.995967	−0.497983	+	0.867187i	$0.665926\pi$
$908$	31.6753	1.05118
$909$	−12.5224	−0.415342
$910$	−1.04768	−0.0347302
$911$	−2.18104	−0.0722612	−0.0361306	−	0.999347i	$-0.511503\pi$
$911$	−2.18104	−0.0722612	−0.0361306	+	0.999347i	$0.511503\pi$
$912$	−8.24022	−0.272861
$913$	−8.19155	−0.271101
$914$	−23.6833	−0.783373
$915$	−27.1554	−0.897729
$916$	−30.3716	−1.00351
$917$	−30.8969	−1.02031
$918$	30.3568	1.00192
$919$	−23.8855	−0.787910	−0.393955	−	0.919130i	$-0.628893\pi$
$919$	−23.8855	−0.787910	−0.393955	+	0.919130i	$0.628893\pi$
$920$	67.4441	2.22357
$921$	20.1705	0.664641
$922$	3.52465	0.116078
$923$	−0.417665	−0.0137476
$924$	−8.18157	−0.269154
$925$	−18.4853	−0.607794
$926$	67.1501	2.20669
$927$	33.9311	1.11444
$928$	−31.0372	−1.01884
$929$	11.4279	0.374936	0.187468	−	0.982271i	$-0.439972\pi$
$929$	11.4279	0.374936	0.187468	+	0.982271i	$0.439972\pi$
$930$	17.4084	0.570845
$931$	10.3501	0.339212
$932$	−5.20218	−0.170403
$933$	2.34111	0.0766445
$934$	65.2438	2.13484
$935$	−8.29102	−0.271145
$936$	0.419455	0.0137103
$937$	−6.35090	−0.207475	−0.103737	−	0.994605i	$-0.533080\pi$
$937$	−6.35090	−0.207475	−0.103737	+	0.994605i	$0.533080\pi$
$938$	13.5611	0.442784
$939$	−2.01521	−0.0657640
$940$	84.8393	2.76715
$941$	52.8939	1.72429	0.862146	−	0.506660i	$-0.169120\pi$
$941$	52.8939	1.72429	0.862146	+	0.506660i	$0.169120\pi$
$942$	49.0400	1.59781
$943$	4.07411	0.132671
$944$	−6.30262	−0.205133
$945$	−37.4493	−1.21823
$946$	17.7916	0.578454
$947$	−7.91125	−0.257081	−0.128540	−	0.991704i	$-0.541029\pi$
$947$	−7.91125	−0.257081	−0.128540	+	0.991704i	$0.541029\pi$
$948$	55.1515	1.79124
$949$	0.365629	0.0118688
$950$	81.1547	2.63301
$951$	17.4419	0.565591
$952$	−21.1557	−0.685661
$953$	15.4743	0.501263	0.250632	−	0.968083i	$-0.419362\pi$
$953$	15.4743	0.501263	0.250632	+	0.968083i	$0.419362\pi$
$954$	−15.7539	−0.510051
$955$	−68.2797	−2.20948
$956$	−11.6468	−0.376686
$957$	7.62118	0.246358
$958$	−59.4848	−1.92187
$959$	−44.8718	−1.44899
$960$	−39.0817	−1.26136
$961$	−25.7069	−0.829254
$962$	0.487806	0.0157275
$963$	23.7682	0.765921
$964$	65.0800	2.09609
$965$	49.8629	1.60514
$966$	32.6623	1.05089
$967$	−18.1409	−0.583373	−0.291686	−	0.956514i	$-0.594216\pi$
$967$	−18.1409	−0.583373	−0.291686	+	0.956514i	$0.594216\pi$
$968$	−3.52327	−0.113242
$969$	−16.8798	−0.542256
$970$	−91.0843	−2.92454
$971$	29.8036	0.956444	0.478222	−	0.878239i	$-0.341281\pi$
$971$	29.8036	0.956444	0.478222	+	0.878239i	$0.341281\pi$
$972$	55.9691	1.79521
$973$	5.65876	0.181411
$974$	−77.9262	−2.49692
$975$	0.319173	0.0102217
$976$	−10.6088	−0.339580
$977$	−5.18777	−0.165971	−0.0829857	−	0.996551i	$-0.526446\pi$
$977$	−5.18777	−0.165971	−0.0829857	+	0.996551i	$0.526446\pi$
$978$	−28.1609	−0.900485
$979$	5.95695	0.190385
$980$	−17.8823	−0.571229
$981$	22.6157	0.722062
$982$	65.1165	2.07795
$983$	−29.3998	−0.937708	−0.468854	−	0.883276i	$-0.655333\pi$
$983$	−29.3998	−0.937708	−0.468854	+	0.883276i	$0.655333\pi$
$984$	2.41892	0.0771123
$985$	−18.4693	−0.588482
$986$	45.9464	1.46323
$987$	17.6223	0.560923
$988$	−1.36311	−0.0433663
$989$	−45.2087	−1.43755
$990$	−15.0001	−0.476735
$991$	−5.74799	−0.182591	−0.0912955	−	0.995824i	$-0.529101\pi$
$991$	−5.74799	−0.182591	−0.0912955	+	0.995824i	$0.529101\pi$
$992$	−9.41086	−0.298795
$993$	18.7279	0.594312
$994$	38.1115	1.20882
$995$	−58.5508	−1.85618
$996$	28.8138	0.913001
$997$	−7.58689	−0.240279	−0.120140	−	0.992757i	$-0.538334\pi$
$997$	−7.58689	−0.240279	−0.120140	+	0.992757i	$0.538334\pi$
$998$	86.9143	2.75122
$999$	17.4366	0.551671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.11	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.11	✓	107	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34564 q^{2} +1.00441 q^{3} +3.50205 q^{4} +3.21165 q^{5} -2.35600 q^{6} +2.32596 q^{7} -3.52327 q^{8} -1.99115 q^{9} +O(q^{10})\)	\(q-2.34564 q^{2} +1.00441 q^{3} +3.50205 q^{4} +3.21165 q^{5} -2.35600 q^{6} +2.32596 q^{7} -3.52327 q^{8} -1.99115 q^{9} -7.53339 q^{10} -1.00000 q^{11} +3.51750 q^{12} +0.0597910 q^{13} -5.45587 q^{14} +3.22583 q^{15} +1.26024 q^{16} +2.58155 q^{17} +4.67054 q^{18} -6.50989 q^{19} +11.2473 q^{20} +2.33623 q^{21} +2.34564 q^{22} -5.96032 q^{23} -3.53882 q^{24} +5.31470 q^{25} -0.140248 q^{26} -5.01318 q^{27} +8.14562 q^{28} -7.58769 q^{29} -7.56664 q^{30} -2.30068 q^{31} +4.09046 q^{32} -1.00441 q^{33} -6.05539 q^{34} +7.47017 q^{35} -6.97311 q^{36} -3.47816 q^{37} +15.2699 q^{38} +0.0600549 q^{39} -11.3155 q^{40} -0.683539 q^{41} -5.47996 q^{42} +7.58494 q^{43} -3.50205 q^{44} -6.39489 q^{45} +13.9808 q^{46} +7.54305 q^{47} +1.26580 q^{48} -1.58991 q^{49} -12.4664 q^{50} +2.59294 q^{51} +0.209391 q^{52} -3.37304 q^{53} +11.7591 q^{54} -3.21165 q^{55} -8.19498 q^{56} -6.53862 q^{57} +17.7980 q^{58} -5.00113 q^{59} +11.2970 q^{60} -8.41811 q^{61} +5.39658 q^{62} -4.63134 q^{63} -12.1152 q^{64} +0.192028 q^{65} +2.35600 q^{66} -2.48559 q^{67} +9.04070 q^{68} -5.98663 q^{69} -17.5224 q^{70} -6.98541 q^{71} +7.01536 q^{72} +6.11512 q^{73} +8.15852 q^{74} +5.33815 q^{75} -22.7979 q^{76} -2.32596 q^{77} -0.140867 q^{78} +15.6792 q^{79} +4.04745 q^{80} +0.938147 q^{81} +1.60334 q^{82} +8.19155 q^{83} +8.18157 q^{84} +8.29102 q^{85} -17.7916 q^{86} -7.62118 q^{87} +3.52327 q^{88} -5.95695 q^{89} +15.0001 q^{90} +0.139071 q^{91} -20.8733 q^{92} -2.31084 q^{93} -17.6933 q^{94} -20.9075 q^{95} +4.10852 q^{96} +12.0908 q^{97} +3.72937 q^{98} +1.99115 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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