LMFDB - Embedded newform 6041.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37296 q^{2} +0.810716 q^{3} +3.63095 q^{4} +0.528258 q^{5} -1.92380 q^{6} -1.00000 q^{7} -3.87017 q^{8} -2.34274 q^{9} +O(q^{10})$	\(q-2.37296 q^{2} +0.810716 q^{3} +3.63095 q^{4} +0.528258 q^{5} -1.92380 q^{6} -1.00000 q^{7} -3.87017 q^{8} -2.34274 q^{9} -1.25354 q^{10} +1.31379 q^{11} +2.94367 q^{12} +5.82315 q^{13} +2.37296 q^{14} +0.428267 q^{15} +1.92188 q^{16} -3.72721 q^{17} +5.55923 q^{18} -1.33377 q^{19} +1.91808 q^{20} -0.810716 q^{21} -3.11758 q^{22} -7.17308 q^{23} -3.13761 q^{24} -4.72094 q^{25} -13.8181 q^{26} -4.33144 q^{27} -3.63095 q^{28} -0.596235 q^{29} -1.01626 q^{30} -4.89459 q^{31} +3.17980 q^{32} +1.06511 q^{33} +8.84453 q^{34} -0.528258 q^{35} -8.50636 q^{36} -4.85801 q^{37} +3.16500 q^{38} +4.72092 q^{39} -2.04445 q^{40} +6.63757 q^{41} +1.92380 q^{42} +2.97069 q^{43} +4.77032 q^{44} -1.23757 q^{45} +17.0215 q^{46} +5.61453 q^{47} +1.55810 q^{48} +1.00000 q^{49} +11.2026 q^{50} -3.02171 q^{51} +21.1435 q^{52} -6.90685 q^{53} +10.2784 q^{54} +0.694022 q^{55} +3.87017 q^{56} -1.08131 q^{57} +1.41484 q^{58} -2.01739 q^{59} +1.55501 q^{60} +8.03211 q^{61} +11.6147 q^{62} +2.34274 q^{63} -11.3893 q^{64} +3.07612 q^{65} -2.52747 q^{66} +9.23706 q^{67} -13.5333 q^{68} -5.81533 q^{69} +1.25354 q^{70} +3.95971 q^{71} +9.06681 q^{72} +6.74904 q^{73} +11.5279 q^{74} -3.82735 q^{75} -4.84286 q^{76} -1.31379 q^{77} -11.2026 q^{78} +13.9843 q^{79} +1.01525 q^{80} +3.51665 q^{81} -15.7507 q^{82} -2.98026 q^{83} -2.94367 q^{84} -1.96893 q^{85} -7.04934 q^{86} -0.483377 q^{87} -5.08461 q^{88} +3.43514 q^{89} +2.93671 q^{90} -5.82315 q^{91} -26.0451 q^{92} -3.96812 q^{93} -13.3231 q^{94} -0.704577 q^{95} +2.57791 q^{96} +1.88621 q^{97} -2.37296 q^{98} -3.07788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.37296	−1.67794	−0.838969	−	0.544180i	$-0.816841\pi$
$2$	−2.37296	−1.67794	−0.838969	+	0.544180i	$0.816841\pi$
$3$	0.810716	0.468067	0.234034	−	0.972229i	$-0.424807\pi$
$3$	0.810716	0.468067	0.234034	+	0.972229i	$0.424807\pi$
$4$	3.63095	1.81547
$5$	0.528258	0.236244	0.118122	−	0.992999i	$-0.462313\pi$
$5$	0.528258	0.236244	0.118122	+	0.992999i	$0.462313\pi$
$6$	−1.92380	−0.785387
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.87017	−1.36831
$9$	−2.34274	−0.780913
$10$	−1.25354	−0.396403
$11$	1.31379	0.396124	0.198062	−	0.980190i	$-0.436535\pi$
$11$	1.31379	0.396124	0.198062	+	0.980190i	$0.436535\pi$
$12$	2.94367	0.849764
$13$	5.82315	1.61505	0.807526	−	0.589833i	$-0.200806\pi$
$13$	5.82315	1.61505	0.807526	+	0.589833i	$0.200806\pi$
$14$	2.37296	0.634201
$15$	0.428267	0.110578
$16$	1.92188	0.480471
$17$	−3.72721	−0.903981	−0.451991	−	0.892023i	$-0.649286\pi$
$17$	−3.72721	−0.903981	−0.451991	+	0.892023i	$0.649286\pi$
$18$	5.55923	1.31032
$19$	−1.33377	−0.305989	−0.152994	−	0.988227i	$-0.548892\pi$
$19$	−1.33377	−0.305989	−0.152994	+	0.988227i	$0.548892\pi$
$20$	1.91808	0.428895
$21$	−0.810716	−0.176913
$22$	−3.11758	−0.664671
$23$	−7.17308	−1.49569	−0.747846	−	0.663873i	$-0.768912\pi$
$23$	−7.17308	−1.49569	−0.747846	+	0.663873i	$0.768912\pi$
$24$	−3.13761	−0.640463
$25$	−4.72094	−0.944189
$26$	−13.8181	−2.70995
$27$	−4.33144	−0.833587
$28$	−3.63095	−0.686184
$29$	−0.596235	−0.110718	−0.0553590	−	0.998467i	$-0.517630\pi$
$29$	−0.596235	−0.110718	−0.0553590	+	0.998467i	$0.517630\pi$
$30$	−1.01626	−0.185543
$31$	−4.89459	−0.879094	−0.439547	−	0.898220i	$-0.644861\pi$
$31$	−4.89459	−0.879094	−0.439547	+	0.898220i	$0.644861\pi$
$32$	3.17980	0.562114
$33$	1.06511	0.185412
$34$	8.84453	1.51682
$35$	−0.528258	−0.0892918
$36$	−8.50636	−1.41773
$37$	−4.85801	−0.798652	−0.399326	−	0.916809i	$-0.630756\pi$
$37$	−4.85801	−0.798652	−0.399326	+	0.916809i	$0.630756\pi$
$38$	3.16500	0.513430
$39$	4.72092	0.755952
$40$	−2.04445	−0.323256
$41$	6.63757	1.03661	0.518307	−	0.855195i	$-0.326562\pi$
$41$	6.63757	1.03661	0.518307	+	0.855195i	$0.326562\pi$
$42$	1.92380	0.296849
$43$	2.97069	0.453027	0.226513	−	0.974008i	$-0.427267\pi$
$43$	2.97069	0.453027	0.226513	+	0.974008i	$0.427267\pi$
$44$	4.77032	0.719152
$45$	−1.23757	−0.184486
$46$	17.0215	2.50968
$47$	5.61453	0.818964	0.409482	−	0.912318i	$-0.365710\pi$
$47$	5.61453	0.818964	0.409482	+	0.912318i	$0.365710\pi$
$48$	1.55810	0.224892
$49$	1.00000	0.142857
$50$	11.2026	1.58429
$51$	−3.02171	−0.423124
$52$	21.1435	2.93208
$53$	−6.90685	−0.948728	−0.474364	−	0.880329i	$-0.657322\pi$
$53$	−6.90685	−0.948728	−0.474364	+	0.880329i	$0.657322\pi$
$54$	10.2784	1.39871
$55$	0.694022	0.0935818
$56$	3.87017	0.517174
$57$	−1.08131	−0.143223
$58$	1.41484	0.185778
$59$	−2.01739	−0.262642	−0.131321	−	0.991340i	$-0.541922\pi$
$59$	−2.01739	−0.262642	−0.131321	+	0.991340i	$0.541922\pi$
$60$	1.55501	0.200752
$61$	8.03211	1.02841	0.514203	−	0.857669i	$-0.328088\pi$
$61$	8.03211	1.02841	0.514203	+	0.857669i	$0.328088\pi$
$62$	11.6147	1.47506
$63$	2.34274	0.295157
$64$	−11.3893	−1.42366
$65$	3.07612	0.381546
$66$	−2.52747	−0.311111
$67$	9.23706	1.12849	0.564243	−	0.825609i	$-0.309168\pi$
$67$	9.23706	1.12849	0.564243	+	0.825609i	$0.309168\pi$
$68$	−13.5333	−1.64115
$69$	−5.81533	−0.700084
$70$	1.25354	0.149826
$71$	3.95971	0.469931	0.234965	−	0.972004i	$-0.424502\pi$
$71$	3.95971	0.469931	0.234965	+	0.972004i	$0.424502\pi$
$72$	9.06681	1.06853
$73$	6.74904	0.789916	0.394958	−	0.918699i	$-0.370759\pi$
$73$	6.74904	0.789916	0.394958	+	0.918699i	$0.370759\pi$
$74$	11.5279	1.34009
$75$	−3.82735	−0.441944
$76$	−4.84286	−0.555515
$77$	−1.31379	−0.149721
$78$	−11.2026	−1.26844
$79$	13.9843	1.57335	0.786676	−	0.617366i	$-0.211800\pi$
$79$	13.9843	1.57335	0.786676	+	0.617366i	$0.211800\pi$
$80$	1.01525	0.113508
$81$	3.51665	0.390738
$82$	−15.7507	−1.73937
$83$	−2.98026	−0.327126	−0.163563	−	0.986533i	$-0.552299\pi$
$83$	−2.98026	−0.327126	−0.163563	+	0.986533i	$0.552299\pi$
$84$	−2.94367	−0.321180
$85$	−1.96893	−0.213560
$86$	−7.04934	−0.760150
$87$	−0.483377	−0.0518235
$88$	−5.08461	−0.542021
$89$	3.43514	0.364124	0.182062	−	0.983287i	$-0.441723\pi$
$89$	3.43514	0.364124	0.182062	+	0.983287i	$0.441723\pi$
$90$	2.93671	0.309556
$91$	−5.82315	−0.610432
$92$	−26.0451	−2.71539
$93$	−3.96812	−0.411475
$94$	−13.3231	−1.37417
$95$	−0.704577	−0.0722880
$96$	2.57791	0.263107
$97$	1.88621	0.191516	0.0957580	−	0.995405i	$-0.469473\pi$
$97$	1.88621	0.191516	0.0957580	+	0.995405i	$0.469473\pi$
$98$	−2.37296	−0.239705
$99$	−3.07788	−0.309338
$100$	−17.1415	−1.71415
$101$	−10.5996	−1.05470	−0.527348	−	0.849649i	$-0.676814\pi$
$101$	−10.5996	−1.05470	−0.527348	+	0.849649i	$0.676814\pi$
$102$	7.17040	0.709976
$103$	−0.733789	−0.0723023	−0.0361512	−	0.999346i	$-0.511510\pi$
$103$	−0.733789	−0.0723023	−0.0361512	+	0.999346i	$0.511510\pi$
$104$	−22.5366	−2.20990
$105$	−0.428267	−0.0417946
$106$	16.3897	1.59191
$107$	0.878854	0.0849620	0.0424810	−	0.999097i	$-0.486474\pi$
$107$	0.878854	0.0849620	0.0424810	+	0.999097i	$0.486474\pi$
$108$	−15.7272	−1.51335
$109$	12.9340	1.23885	0.619425	−	0.785056i	$-0.287366\pi$
$109$	12.9340	1.23885	0.619425	+	0.785056i	$0.287366\pi$
$110$	−1.64689	−0.157024
$111$	−3.93847	−0.373823
$112$	−1.92188	−0.181601
$113$	−3.25096	−0.305824	−0.152912	−	0.988240i	$-0.548865\pi$
$113$	−3.25096	−0.305824	−0.152912	+	0.988240i	$0.548865\pi$
$114$	2.56591	0.240320
$115$	−3.78924	−0.353348
$116$	−2.16490	−0.201006
$117$	−13.6421	−1.26121
$118$	4.78719	0.440697
$119$	3.72721	0.341673
$120$	−1.65747	−0.151305
$121$	−9.27395	−0.843086
$122$	−19.0599	−1.72560
$123$	5.38118	0.485205
$124$	−17.7720	−1.59597
$125$	−5.13516	−0.459303
$126$	−5.55923	−0.495256
$127$	12.0022	1.06503	0.532513	−	0.846422i	$-0.321248\pi$
$127$	12.0022	1.06503	0.532513	+	0.846422i	$0.321248\pi$
$128$	20.6668	1.82670
$129$	2.40839	0.212047
$130$	−7.29952	−0.640210
$131$	6.88101	0.601197	0.300598	−	0.953751i	$-0.402814\pi$
$131$	6.88101	0.601197	0.300598	+	0.953751i	$0.402814\pi$
$132$	3.86737	0.336611
$133$	1.33377	0.115653
$134$	−21.9192	−1.89353
$135$	−2.28812	−0.196930
$136$	14.4250	1.23693
$137$	17.3551	1.48274	0.741372	−	0.671094i	$-0.234176\pi$
$137$	17.3551	1.48274	0.741372	+	0.671094i	$0.234176\pi$
$138$	13.7996	1.17470
$139$	5.25832	0.446004	0.223002	−	0.974818i	$-0.428414\pi$
$139$	5.25832	0.446004	0.223002	+	0.974818i	$0.428414\pi$
$140$	−1.91808	−0.162107
$141$	4.55179	0.383330
$142$	−9.39623	−0.788514
$143$	7.65042	0.639760
$144$	−4.50247	−0.375206
$145$	−0.314966	−0.0261565
$146$	−16.0152	−1.32543
$147$	0.810716	0.0668667
$148$	−17.6392	−1.44993
$149$	12.7714	1.04627	0.523136	−	0.852249i	$-0.324762\pi$
$149$	12.7714	1.04627	0.523136	+	0.852249i	$0.324762\pi$
$150$	9.08214	0.741554
$151$	4.16362	0.338831	0.169415	−	0.985545i	$-0.445812\pi$
$151$	4.16362	0.338831	0.169415	+	0.985545i	$0.445812\pi$
$152$	5.16194	0.418689
$153$	8.73188	0.705931
$154$	3.11758	0.251222
$155$	−2.58560	−0.207681
$156$	17.1414	1.37241
$157$	15.0677	1.20253	0.601265	−	0.799049i	$-0.294663\pi$
$157$	15.0677	1.20253	0.601265	+	0.799049i	$0.294663\pi$
$158$	−33.1841	−2.63999
$159$	−5.59949	−0.444069
$160$	1.67975	0.132796
$161$	7.17308	0.565318
$162$	−8.34487	−0.655635
$163$	−15.5008	−1.21411	−0.607057	−	0.794658i	$-0.707650\pi$
$163$	−15.5008	−1.21411	−0.607057	+	0.794658i	$0.707650\pi$
$164$	24.1007	1.88195
$165$	0.562654	0.0438026
$166$	7.07205	0.548897
$167$	10.2354	0.792036	0.396018	−	0.918243i	$-0.370392\pi$
$167$	10.2354	0.792036	0.396018	+	0.918243i	$0.370392\pi$
$168$	3.13761	0.242072
$169$	20.9091	1.60839
$170$	4.67219	0.358341
$171$	3.12469	0.238951
$172$	10.7864	0.822458
$173$	−12.7020	−0.965712	−0.482856	−	0.875700i	$-0.660401\pi$
$173$	−12.7020	−0.965712	−0.482856	+	0.875700i	$0.660401\pi$
$174$	1.14704	0.0869566
$175$	4.72094	0.356870
$176$	2.52496	0.190326
$177$	−1.63553	−0.122934
$178$	−8.15145	−0.610977
$179$	−23.1340	−1.72912	−0.864558	−	0.502533i	$-0.832401\pi$
$179$	−23.1340	−1.72912	−0.864558	+	0.502533i	$0.832401\pi$
$180$	−4.49355	−0.334930
$181$	13.6785	1.01671	0.508357	−	0.861146i	$-0.330253\pi$
$181$	13.6785	1.01671	0.508357	+	0.861146i	$0.330253\pi$
$182$	13.8181	1.02427
$183$	6.51176	0.481363
$184$	27.7611	2.04657
$185$	−2.56628	−0.188677
$186$	9.41620	0.690429
$187$	−4.89679	−0.358088
$188$	20.3861	1.48681
$189$	4.33144	0.315066
$190$	1.67193	0.121295
$191$	−4.68911	−0.339292	−0.169646	−	0.985505i	$-0.554262\pi$
$191$	−4.68911	−0.339292	−0.169646	+	0.985505i	$0.554262\pi$
$192$	−9.23349	−0.666370
$193$	11.0094	0.792476	0.396238	−	0.918148i	$-0.370315\pi$
$193$	11.0094	0.792476	0.396238	+	0.918148i	$0.370315\pi$
$194$	−4.47591	−0.321352
$195$	2.49386	0.178589
$196$	3.63095	0.259353
$197$	5.58283	0.397760	0.198880	−	0.980024i	$-0.436270\pi$
$197$	5.58283	0.397760	0.198880	+	0.980024i	$0.436270\pi$
$198$	7.30368	0.519050
$199$	−4.43985	−0.314733	−0.157366	−	0.987540i	$-0.550300\pi$
$199$	−4.43985	−0.314733	−0.157366	+	0.987540i	$0.550300\pi$
$200$	18.2709	1.29195
$201$	7.48863	0.528207
$202$	25.1524	1.76972
$203$	0.596235	0.0418475
$204$	−10.9717	−0.768170
$205$	3.50635	0.244894
$206$	1.74125	0.121319
$207$	16.8047	1.16800
$208$	11.1914	0.775984
$209$	−1.75230	−0.121209
$210$	1.01626	0.0701287
$211$	19.5836	1.34819	0.674094	−	0.738646i	$-0.264534\pi$
$211$	19.5836	1.34819	0.674094	+	0.738646i	$0.264534\pi$
$212$	−25.0784	−1.72239
$213$	3.21020	0.219959
$214$	−2.08549	−0.142561
$215$	1.56929	0.107025
$216$	16.7634	1.14061
$217$	4.89459	0.332266
$218$	−30.6918	−2.07871
$219$	5.47156	0.369734
$220$	2.51996	0.169895
$221$	−21.7041	−1.45998
$222$	9.34584	0.627252
$223$	18.7373	1.25474	0.627370	−	0.778721i	$-0.284131\pi$
$223$	18.7373	1.25474	0.627370	+	0.778721i	$0.284131\pi$
$224$	−3.17980	−0.212459
$225$	11.0599	0.737329
$226$	7.71439	0.513154
$227$	8.35981	0.554860	0.277430	−	0.960746i	$-0.410517\pi$
$227$	8.35981	0.554860	0.277430	+	0.960746i	$0.410517\pi$
$228$	−3.92619	−0.260018
$229$	−18.8169	−1.24345	−0.621727	−	0.783234i	$-0.713569\pi$
$229$	−18.8169	−1.24345	−0.621727	+	0.783234i	$0.713569\pi$
$230$	8.99171	0.592896
$231$	−1.06511	−0.0700793
$232$	2.30753	0.151497
$233$	−6.87686	−0.450518	−0.225259	−	0.974299i	$-0.572323\pi$
$233$	−6.87686	−0.450518	−0.225259	+	0.974299i	$0.572323\pi$
$234$	32.3722	2.11624
$235$	2.96592	0.193475
$236$	−7.32505	−0.476820
$237$	11.3373	0.736434
$238$	−8.84453	−0.573306
$239$	3.41128	0.220658	0.110329	−	0.993895i	$-0.464810\pi$
$239$	3.41128	0.220658	0.110329	+	0.993895i	$0.464810\pi$
$240$	0.823079	0.0531295
$241$	−11.8687	−0.764531	−0.382266	−	0.924052i	$-0.624856\pi$
$241$	−11.8687	−0.764531	−0.382266	+	0.924052i	$0.624856\pi$
$242$	22.0067	1.41465
$243$	15.8453	1.01648
$244$	29.1642	1.86704
$245$	0.528258	0.0337491
$246$	−12.7693	−0.814144
$247$	−7.76677	−0.494188
$248$	18.9429	1.20288
$249$	−2.41615	−0.153117
$250$	12.1855	0.770682
$251$	17.5957	1.11063	0.555315	−	0.831640i	$-0.312598\pi$
$251$	17.5957	1.11063	0.555315	+	0.831640i	$0.312598\pi$
$252$	8.50636	0.535850
$253$	−9.42395	−0.592479
$254$	−28.4808	−1.78705
$255$	−1.59624	−0.0999605
$256$	−26.2629	−1.64143
$257$	−18.0150	−1.12375	−0.561873	−	0.827224i	$-0.689919\pi$
$257$	−18.0150	−1.12375	−0.561873	+	0.827224i	$0.689919\pi$
$258$	−5.71501	−0.355801
$259$	4.85801	0.301862
$260$	11.1692	0.692687
$261$	1.39682	0.0864612
$262$	−16.3284	−1.00877
$263$	21.1272	1.30276	0.651380	−	0.758752i	$-0.274190\pi$
$263$	21.1272	1.30276	0.651380	+	0.758752i	$0.274190\pi$
$264$	−4.12218	−0.253702
$265$	−3.64859	−0.224131
$266$	−3.16500	−0.194058
$267$	2.78492	0.170434
$268$	33.5393	2.04874
$269$	−0.375330	−0.0228842	−0.0114421	−	0.999935i	$-0.503642\pi$
$269$	−0.375330	−0.0228842	−0.0114421	+	0.999935i	$0.503642\pi$
$270$	5.42962	0.330436
$271$	−15.9546	−0.969174	−0.484587	−	0.874743i	$-0.661030\pi$
$271$	−15.9546	−0.969174	−0.484587	+	0.874743i	$0.661030\pi$
$272$	−7.16326	−0.434336
$273$	−4.72092	−0.285723
$274$	−41.1829	−2.48795
$275$	−6.20235	−0.374016
$276$	−21.1152	−1.27098
$277$	11.9911	0.720475	0.360238	−	0.932861i	$-0.382696\pi$
$277$	11.9911	0.720475	0.360238	+	0.932861i	$0.382696\pi$
$278$	−12.4778	−0.748368
$279$	11.4667	0.686496
$280$	2.04445	0.122179
$281$	14.8835	0.887873	0.443936	−	0.896058i	$-0.353582\pi$
$281$	14.8835	0.887873	0.443936	+	0.896058i	$0.353582\pi$
$282$	−10.8012	−0.643204
$283$	−1.47150	−0.0874715	−0.0437357	−	0.999043i	$-0.513926\pi$
$283$	−1.47150	−0.0874715	−0.0437357	+	0.999043i	$0.513926\pi$
$284$	14.3775	0.853147
$285$	−0.571211	−0.0338356
$286$	−18.1541	−1.07348
$287$	−6.63757	−0.391803
$288$	−7.44944	−0.438962
$289$	−3.10790	−0.182818
$290$	0.747402	0.0438889
$291$	1.52918	0.0896423
$292$	24.5054	1.43407
$293$	−19.4228	−1.13469	−0.567345	−	0.823480i	$-0.692030\pi$
$293$	−19.4228	−1.13469	−0.567345	+	0.823480i	$0.692030\pi$
$294$	−1.92380	−0.112198
$295$	−1.06570	−0.0620476
$296$	18.8014	1.09281
$297$	−5.69062	−0.330204
$298$	−30.3060	−1.75558
$299$	−41.7699	−2.41562
$300$	−13.8969	−0.802337
$301$	−2.97069	−0.171228
$302$	−9.88012	−0.568537
$303$	−8.59324	−0.493669
$304$	−2.56336	−0.147019
$305$	4.24302	0.242955
$306$	−20.7204	−1.18451
$307$	18.9263	1.08018	0.540091	−	0.841607i	$-0.318390\pi$
$307$	18.9263	1.08018	0.540091	+	0.841607i	$0.318390\pi$
$308$	−4.77032	−0.271814
$309$	−0.594894	−0.0338423
$310$	6.13554	0.348475
$311$	−17.7414	−1.00602	−0.503012	−	0.864279i	$-0.667775\pi$
$311$	−17.7414	−1.00602	−0.503012	+	0.864279i	$0.667775\pi$
$312$	−18.2708	−1.03438
$313$	−15.0345	−0.849797	−0.424899	−	0.905241i	$-0.639690\pi$
$313$	−15.0345	−0.849797	−0.424899	+	0.905241i	$0.639690\pi$
$314$	−35.7550	−2.01777
$315$	1.23757	0.0697292
$316$	50.7761	2.85638
$317$	14.9488	0.839607	0.419803	−	0.907615i	$-0.362099\pi$
$317$	14.9488	0.839607	0.419803	+	0.907615i	$0.362099\pi$
$318$	13.2874	0.745119
$319$	−0.783330	−0.0438580
$320$	−6.01649	−0.336332
$321$	0.712501	0.0397679
$322$	−17.0215	−0.948568
$323$	4.97126	0.276608
$324$	12.7688	0.709375
$325$	−27.4908	−1.52491
$326$	36.7828	2.03721
$327$	10.4858	0.579865
$328$	−25.6886	−1.41841
$329$	−5.61453	−0.309539
$330$	−1.33516	−0.0734980
$331$	25.6546	1.41011	0.705053	−	0.709154i	$-0.250923\pi$
$331$	25.6546	1.41011	0.705053	+	0.709154i	$0.250923\pi$
$332$	−10.8212	−0.593889
$333$	11.3811	0.623678
$334$	−24.2881	−1.32899
$335$	4.87955	0.266598
$336$	−1.55810	−0.0850014
$337$	−10.9287	−0.595324	−0.297662	−	0.954671i	$-0.596207\pi$
$337$	−10.9287	−0.595324	−0.297662	+	0.954671i	$0.596207\pi$
$338$	−49.6164	−2.69878
$339$	−2.63560	−0.143146
$340$	−7.14907	−0.387713
$341$	−6.43048	−0.348230
$342$	−7.41476	−0.400944
$343$	−1.00000	−0.0539949
$344$	−11.4971	−0.619882
$345$	−3.07199	−0.165391
$346$	30.1413	1.62040
$347$	−11.2755	−0.605301	−0.302650	−	0.953102i	$-0.597871\pi$
$347$	−11.2755	−0.605301	−0.302650	+	0.953102i	$0.597871\pi$
$348$	−1.75512	−0.0940842
$349$	−28.8349	−1.54350	−0.771748	−	0.635929i	$-0.780617\pi$
$349$	−28.8349	−1.54350	−0.771748	+	0.635929i	$0.780617\pi$
$350$	−11.2026	−0.598805
$351$	−25.2226	−1.34629
$352$	4.17760	0.222667
$353$	−1.68156	−0.0895002	−0.0447501	−	0.998998i	$-0.514249\pi$
$353$	−1.68156	−0.0895002	−0.0447501	+	0.998998i	$0.514249\pi$
$354$	3.88106	0.206276
$355$	2.09175	0.111018
$356$	12.4728	0.661057
$357$	3.02171	0.159926
$358$	54.8961	2.90135
$359$	10.8475	0.572510	0.286255	−	0.958154i	$-0.407590\pi$
$359$	10.8475	0.572510	0.286255	+	0.958154i	$0.407590\pi$
$360$	4.78961	0.252435
$361$	−17.2210	−0.906371
$362$	−32.4586	−1.70598
$363$	−7.51854	−0.394621
$364$	−21.1435	−1.10822
$365$	3.56523	0.186613
$366$	−15.4522	−0.807697
$367$	8.13030	0.424398	0.212199	−	0.977226i	$-0.431937\pi$
$367$	8.13030	0.424398	0.212199	+	0.977226i	$0.431937\pi$
$368$	−13.7858	−0.718636
$369$	−15.5501	−0.809506
$370$	6.08969	0.316588
$371$	6.90685	0.358586
$372$	−14.4080	−0.747022
$373$	−20.6285	−1.06810	−0.534052	−	0.845451i	$-0.679331\pi$
$373$	−20.6285	−1.06810	−0.534052	+	0.845451i	$0.679331\pi$
$374$	11.6199	0.600850
$375$	−4.16316	−0.214985
$376$	−21.7292	−1.12060
$377$	−3.47197	−0.178815
$378$	−10.2784	−0.528661
$379$	37.7789	1.94057	0.970285	−	0.241966i	$-0.0777921\pi$
$379$	37.7789	1.94057	0.970285	+	0.241966i	$0.0777921\pi$
$380$	−2.55828	−0.131237
$381$	9.73040	0.498503
$382$	11.1271	0.569311
$383$	13.5235	0.691018	0.345509	−	0.938415i	$-0.387706\pi$
$383$	13.5235	0.691018	0.345509	+	0.938415i	$0.387706\pi$
$384$	16.7549	0.855019
$385$	−0.694022	−0.0353706
$386$	−26.1250	−1.32973
$387$	−6.95956	−0.353774
$388$	6.84874	0.347692
$389$	−24.4198	−1.23813	−0.619066	−	0.785339i	$-0.712489\pi$
$389$	−24.4198	−1.23813	−0.619066	+	0.785339i	$0.712489\pi$
$390$	−5.91784	−0.299661
$391$	26.7356	1.35208
$392$	−3.87017	−0.195473
$393$	5.57855	0.281401
$394$	−13.2479	−0.667417
$395$	7.38729	0.371695
$396$	−11.1756	−0.561595
$397$	6.47703	0.325073	0.162536	−	0.986703i	$-0.448033\pi$
$397$	6.47703	0.325073	0.162536	+	0.986703i	$0.448033\pi$
$398$	10.5356	0.528101
$399$	1.08131	0.0541333
$400$	−9.07310	−0.453655
$401$	−5.48903	−0.274109	−0.137054	−	0.990564i	$-0.543764\pi$
$401$	−5.48903	−0.274109	−0.137054	+	0.990564i	$0.543764\pi$
$402$	−17.7702	−0.886299
$403$	−28.5019	−1.41978
$404$	−38.4865	−1.91477
$405$	1.85770	0.0923096
$406$	−1.41484	−0.0702175
$407$	−6.38243	−0.316365
$408$	11.6945	0.578966
$409$	13.0029	0.642951	0.321475	−	0.946918i	$-0.395821\pi$
$409$	13.0029	0.642951	0.321475	+	0.946918i	$0.395821\pi$
$410$	−8.32043	−0.410917
$411$	14.0700	0.694024
$412$	−2.66435	−0.131263
$413$	2.01739	0.0992694
$414$	−39.8768	−1.95984
$415$	−1.57435	−0.0772816
$416$	18.5164	0.907843
$417$	4.26300	0.208760
$418$	4.15815	0.203382
$419$	3.38607	0.165420	0.0827101	−	0.996574i	$-0.473642\pi$
$419$	3.38607	0.165420	0.0827101	+	0.996574i	$0.473642\pi$
$420$	−1.55501	−0.0758769
$421$	36.6588	1.78664	0.893319	−	0.449423i	$-0.148370\pi$
$421$	36.6588	1.78664	0.893319	+	0.449423i	$0.148370\pi$
$422$	−46.4710	−2.26217
$423$	−13.1534	−0.639539
$424$	26.7307	1.29816
$425$	17.5960	0.853529
$426$	−7.61768	−0.369078
$427$	−8.03211	−0.388701
$428$	3.19107	0.154246
$429$	6.20232	0.299451
$430$	−3.72387	−0.179581
$431$	−33.8703	−1.63147	−0.815737	−	0.578423i	$-0.803668\pi$
$431$	−33.8703	−1.63147	−0.815737	+	0.578423i	$0.803668\pi$
$432$	−8.32453	−0.400514
$433$	6.43032	0.309021	0.154511	−	0.987991i	$-0.450620\pi$
$433$	6.43032	0.309021	0.154511	+	0.987991i	$0.450620\pi$
$434$	−11.6147	−0.557522
$435$	−0.255348	−0.0122430
$436$	46.9626	2.24910
$437$	9.56727	0.457665
$438$	−12.9838	−0.620390
$439$	29.7684	1.42077	0.710383	−	0.703815i	$-0.248522\pi$
$439$	29.7684	1.42077	0.710383	+	0.703815i	$0.248522\pi$
$440$	−2.68598	−0.128049
$441$	−2.34274	−0.111559
$442$	51.5030	2.44975
$443$	−9.97528	−0.473940	−0.236970	−	0.971517i	$-0.576154\pi$
$443$	−9.97528	−0.473940	−0.236970	+	0.971517i	$0.576154\pi$
$444$	−14.3004	−0.678666
$445$	1.81464	0.0860221
$446$	−44.4628	−2.10537
$447$	10.3540	0.489726
$448$	11.3893	0.538094
$449$	24.1720	1.14075	0.570373	−	0.821386i	$-0.306799\pi$
$449$	24.1720	1.14075	0.570373	+	0.821386i	$0.306799\pi$
$450$	−26.2448	−1.23719
$451$	8.72040	0.410627
$452$	−11.8040	−0.555216
$453$	3.37552	0.158596
$454$	−19.8375	−0.931021
$455$	−3.07612	−0.144211
$456$	4.18487	0.195974
$457$	36.4234	1.70382	0.851908	−	0.523692i	$-0.175446\pi$
$457$	36.4234	1.70382	0.851908	+	0.523692i	$0.175446\pi$
$458$	44.6517	2.08644
$459$	16.1442	0.753547
$460$	−13.7585	−0.641494
$461$	13.1537	0.612631	0.306315	−	0.951930i	$-0.400904\pi$
$461$	13.1537	0.612631	0.306315	+	0.951930i	$0.400904\pi$
$462$	2.52747	0.117589
$463$	−30.4915	−1.41706	−0.708531	−	0.705680i	$-0.750642\pi$
$463$	−30.4915	−1.41706	−0.708531	+	0.705680i	$0.750642\pi$
$464$	−1.14589	−0.0531968
$465$	−2.09619	−0.0972085
$466$	16.3185	0.755941
$467$	−16.8753	−0.780894	−0.390447	−	0.920625i	$-0.627680\pi$
$467$	−16.8753	−0.780894	−0.390447	+	0.920625i	$0.627680\pi$
$468$	−49.5338	−2.28970
$469$	−9.23706	−0.426528
$470$	−7.03801	−0.324639
$471$	12.2156	0.562865
$472$	7.80766	0.359377
$473$	3.90288	0.179455
$474$	−26.9029	−1.23569
$475$	6.29667	0.288911
$476$	13.5333	0.620298
$477$	16.1809	0.740874
$478$	−8.09485	−0.370250
$479$	1.33491	0.0609934	0.0304967	−	0.999535i	$-0.490291\pi$
$479$	1.33491	0.0609934	0.0304967	+	0.999535i	$0.490291\pi$
$480$	1.36180	0.0621575
$481$	−28.2889	−1.28986
$482$	28.1640	1.28284
$483$	5.81533	0.264607
$484$	−33.6732	−1.53060
$485$	0.996406	0.0452445
$486$	−37.6004	−1.70559
$487$	−10.8195	−0.490278	−0.245139	−	0.969488i	$-0.578834\pi$
$487$	−10.8195	−0.490278	−0.245139	+	0.969488i	$0.578834\pi$
$488$	−31.0857	−1.40718
$489$	−12.5667	−0.568287
$490$	−1.25354	−0.0566289
$491$	3.95994	0.178710	0.0893548	−	0.996000i	$-0.471520\pi$
$491$	3.95994	0.178710	0.0893548	+	0.996000i	$0.471520\pi$
$492$	19.5388	0.880877
$493$	2.22229	0.100087
$494$	18.4302	0.829216
$495$	−1.62591	−0.0730793
$496$	−9.40682	−0.422379
$497$	−3.95971	−0.177617
$498$	5.73342	0.256921
$499$	17.3326	0.775915	0.387958	−	0.921677i	$-0.373181\pi$
$499$	17.3326	0.775915	0.387958	+	0.921677i	$0.373181\pi$
$500$	−18.6455	−0.833852
$501$	8.29797	0.370726
$502$	−41.7539	−1.86357
$503$	−12.7606	−0.568968	−0.284484	−	0.958681i	$-0.591822\pi$
$503$	−12.7606	−0.568968	−0.284484	+	0.958681i	$0.591822\pi$
$504$	−9.06681	−0.403868
$505$	−5.59930	−0.249166
$506$	22.3627	0.994142
$507$	16.9513	0.752834
$508$	43.5795	1.93353
$509$	13.2278	0.586313	0.293156	−	0.956064i	$-0.405294\pi$
$509$	13.2278	0.586313	0.293156	+	0.956064i	$0.405294\pi$
$510$	3.78782	0.167727
$511$	−6.74904	−0.298560
$512$	20.9872	0.927513
$513$	5.77717	0.255068
$514$	42.7489	1.88557
$515$	−0.387629	−0.0170810
$516$	8.74473	0.384965
$517$	7.37634	0.324411
$518$	−11.5279	−0.506506
$519$	−10.2977	−0.452018
$520$	−11.9051	−0.522075
$521$	20.6664	0.905410	0.452705	−	0.891660i	$-0.350459\pi$
$521$	20.6664	0.905410	0.452705	+	0.891660i	$0.350459\pi$
$522$	−3.31461	−0.145076
$523$	22.4571	0.981981	0.490991	−	0.871165i	$-0.336635\pi$
$523$	22.4571	0.981981	0.490991	+	0.871165i	$0.336635\pi$
$524$	24.9846	1.09146
$525$	3.82735	0.167039
$526$	−50.1341	−2.18595
$527$	18.2432	0.794685
$528$	2.04702	0.0890852
$529$	28.4531	1.23709
$530$	8.65797	0.376078
$531$	4.72622	0.205101
$532$	4.84286	0.209965
$533$	38.6516	1.67418
$534$	−6.60851	−0.285978
$535$	0.464261	0.0200718
$536$	−35.7490	−1.54412
$537$	−18.7551	−0.809342
$538$	0.890643	0.0383983
$539$	1.31379	0.0565891
$540$	−8.30804	−0.357521
$541$	36.9286	1.58768	0.793842	−	0.608124i	$-0.208077\pi$
$541$	36.9286	1.58768	0.793842	+	0.608124i	$0.208077\pi$
$542$	37.8597	1.62621
$543$	11.0894	0.475891
$544$	−11.8518	−0.508141
$545$	6.83247	0.292671
$546$	11.2026	0.479425
$547$	−32.1209	−1.37339	−0.686696	−	0.726945i	$-0.740940\pi$
$547$	−32.1209	−1.37339	−0.686696	+	0.726945i	$0.740940\pi$
$548$	63.0153	2.69188
$549$	−18.8171	−0.803096
$550$	14.7179	0.627575
$551$	0.795243	0.0338785
$552$	22.5064	0.957934
$553$	−13.9843	−0.594671
$554$	−28.4544	−1.20891
$555$	−2.08053	−0.0883134
$556$	19.0927	0.809709
$557$	23.0927	0.978471	0.489235	−	0.872152i	$-0.337276\pi$
$557$	23.0927	0.978471	0.489235	+	0.872152i	$0.337276\pi$
$558$	−27.2101	−1.15190
$559$	17.2988	0.731661
$560$	−1.01525	−0.0429021
$561$	−3.96990	−0.167609
$562$	−35.3179	−1.48980
$563$	−12.6754	−0.534203	−0.267102	−	0.963668i	$-0.586066\pi$
$563$	−12.6754	−0.534203	−0.267102	+	0.963668i	$0.586066\pi$
$564$	16.5273	0.695925
$565$	−1.71734	−0.0722491
$566$	3.49181	0.146772
$567$	−3.51665	−0.147685
$568$	−15.3248	−0.643012
$569$	−4.07032	−0.170637	−0.0853184	−	0.996354i	$-0.527191\pi$
$569$	−4.07032	−0.170637	−0.0853184	+	0.996354i	$0.527191\pi$
$570$	1.35546	0.0567741
$571$	41.4919	1.73638	0.868191	−	0.496231i	$-0.165283\pi$
$571$	41.4919	1.73638	0.868191	+	0.496231i	$0.165283\pi$
$572$	27.7783	1.16147
$573$	−3.80154	−0.158812
$574$	15.7507	0.657421
$575$	33.8637	1.41221
$576$	26.6822	1.11176
$577$	27.9903	1.16525	0.582626	−	0.812740i	$-0.302025\pi$
$577$	27.9903	1.16525	0.582626	+	0.812740i	$0.302025\pi$
$578$	7.37492	0.306756
$579$	8.92552	0.370932
$580$	−1.14362	−0.0474864
$581$	2.98026	0.123642
$582$	−3.62869	−0.150414
$583$	−9.07417	−0.375814
$584$	−26.1200	−1.08085
$585$	−7.20656	−0.297954
$586$	46.0895	1.90394
$587$	−15.0208	−0.619976	−0.309988	−	0.950740i	$-0.600325\pi$
$587$	−15.0208	−0.619976	−0.309988	+	0.950740i	$0.600325\pi$
$588$	2.94367	0.121395
$589$	6.52828	0.268993
$590$	2.52887	0.104112
$591$	4.52609	0.186179
$592$	−9.33653	−0.383729
$593$	−28.7065	−1.17884	−0.589418	−	0.807828i	$-0.700643\pi$
$593$	−28.7065	−1.17884	−0.589418	+	0.807828i	$0.700643\pi$
$594$	13.5036	0.554061
$595$	1.96893	0.0807182
$596$	46.3722	1.89948
$597$	−3.59946	−0.147316
$598$	99.1185	4.05325
$599$	28.8854	1.18022	0.590112	−	0.807321i	$-0.299084\pi$
$599$	28.8854	1.18022	0.590112	+	0.807321i	$0.299084\pi$
$600$	14.8125	0.604718
$601$	−5.25547	−0.214375	−0.107188	−	0.994239i	$-0.534185\pi$
$601$	−5.25547	−0.214375	−0.107188	+	0.994239i	$0.534185\pi$
$602$	7.04934	0.287310
$603$	−21.6400	−0.881250
$604$	15.1179	0.615139
$605$	−4.89903	−0.199174
$606$	20.3914	0.828345
$607$	−26.3996	−1.07153	−0.535763	−	0.844368i	$-0.679976\pi$
$607$	−26.3996	−1.07153	−0.535763	+	0.844368i	$0.679976\pi$
$608$	−4.24113	−0.172001
$609$	0.483377	0.0195874
$610$	−10.0685	−0.407663
$611$	32.6943	1.32267
$612$	31.7050	1.28160
$613$	8.20135	0.331249	0.165625	−	0.986189i	$-0.447036\pi$
$613$	8.20135	0.331249	0.165625	+	0.986189i	$0.447036\pi$
$614$	−44.9114	−1.81248
$615$	2.84265	0.114627
$616$	5.08461	0.204865
$617$	−33.1451	−1.33437	−0.667185	−	0.744892i	$-0.732501\pi$
$617$	−33.1451	−1.33437	−0.667185	+	0.744892i	$0.732501\pi$
$618$	1.41166	0.0567853
$619$	5.57497	0.224077	0.112039	−	0.993704i	$-0.464262\pi$
$619$	5.57497	0.224077	0.112039	+	0.993704i	$0.464262\pi$
$620$	−9.38819	−0.377039
$621$	31.0698	1.24679
$622$	42.0997	1.68805
$623$	−3.43514	−0.137626
$624$	9.07305	0.363213
$625$	20.8920	0.835681
$626$	35.6762	1.42591
$627$	−1.42062	−0.0567341
$628$	54.7099	2.18316
$629$	18.1068	0.721967
$630$	−2.93671	−0.117001
$631$	5.72633	0.227962	0.113981	−	0.993483i	$-0.463640\pi$
$631$	5.72633	0.227962	0.113981	+	0.993483i	$0.463640\pi$
$632$	−54.1215	−2.15284
$633$	15.8767	0.631042
$634$	−35.4729	−1.40881
$635$	6.34027	0.251606
$636$	−20.3315	−0.806195
$637$	5.82315	0.230722
$638$	1.85881	0.0735910
$639$	−9.27656	−0.366975
$640$	10.9174	0.431548
$641$	35.2220	1.39119	0.695593	−	0.718436i	$-0.255142\pi$
$641$	35.2220	1.39119	0.695593	+	0.718436i	$0.255142\pi$
$642$	−1.69074	−0.0667281
$643$	11.5107	0.453936	0.226968	−	0.973902i	$-0.427119\pi$
$643$	11.5107	0.453936	0.226968	+	0.973902i	$0.427119\pi$
$644$	26.0451	1.02632
$645$	1.27225	0.0500948
$646$	−11.7966	−0.464131
$647$	−38.2417	−1.50344	−0.751719	−	0.659484i	$-0.770775\pi$
$647$	−38.2417	−1.50344	−0.751719	+	0.659484i	$0.770775\pi$
$648$	−13.6100	−0.534653
$649$	−2.65044	−0.104039
$650$	65.2345	2.55871
$651$	3.96812	0.155523
$652$	−56.2825	−2.20419
$653$	−14.1551	−0.553933	−0.276967	−	0.960880i	$-0.589329\pi$
$653$	−14.1551	−0.553933	−0.276967	+	0.960880i	$0.589329\pi$
$654$	−24.8824	−0.972977
$655$	3.63495	0.142029
$656$	12.7566	0.498063
$657$	−15.8112	−0.616856
$658$	13.3231	0.519387
$659$	−8.97130	−0.349472	−0.174736	−	0.984615i	$-0.555907\pi$
$659$	−8.97130	−0.349472	−0.174736	+	0.984615i	$0.555907\pi$
$660$	2.04297	0.0795224
$661$	26.7412	1.04011	0.520055	−	0.854133i	$-0.325911\pi$
$661$	26.7412	1.04011	0.520055	+	0.854133i	$0.325911\pi$
$662$	−60.8775	−2.36607
$663$	−17.5959	−0.683367
$664$	11.5341	0.447611
$665$	0.704577	0.0273223
$666$	−27.0068	−1.04649
$667$	4.27684	0.165600
$668$	37.1641	1.43792
$669$	15.1906	0.587302
$670$	−11.5790	−0.447335
$671$	10.5525	0.407376
$672$	−2.57791	−0.0994451
$673$	−33.0700	−1.27476	−0.637378	−	0.770551i	$-0.719981\pi$
$673$	−33.0700	−1.27476	−0.637378	+	0.770551i	$0.719981\pi$
$674$	25.9334	0.998916
$675$	20.4485	0.787063
$676$	75.9197	2.91999
$677$	−50.6531	−1.94676	−0.973378	−	0.229204i	$-0.926388\pi$
$677$	−50.6531	−1.94676	−0.973378	+	0.229204i	$0.926388\pi$
$678$	6.25418	0.240190
$679$	−1.88621	−0.0723862
$680$	7.62009	0.292217
$681$	6.77743	0.259712
$682$	15.2593	0.584308
$683$	−7.49552	−0.286808	−0.143404	−	0.989664i	$-0.545805\pi$
$683$	−7.49552	−0.286808	−0.143404	+	0.989664i	$0.545805\pi$
$684$	11.3456	0.433809
$685$	9.16795	0.350289
$686$	2.37296	0.0906001
$687$	−15.2551	−0.582020
$688$	5.70932	0.217666
$689$	−40.2196	−1.53224
$690$	7.28973	0.277515
$691$	29.4449	1.12014	0.560069	−	0.828446i	$-0.310775\pi$
$691$	29.4449	1.12014	0.560069	+	0.828446i	$0.310775\pi$
$692$	−46.1201	−1.75322
$693$	3.07788	0.116919
$694$	26.7563	1.01566
$695$	2.77775	0.105366
$696$	1.87075	0.0709108
$697$	−24.7396	−0.937080
$698$	68.4240	2.58989
$699$	−5.57518	−0.210873
$700$	17.1415	0.647888
$701$	−22.1278	−0.835756	−0.417878	−	0.908503i	$-0.637226\pi$
$701$	−22.1278	−0.835756	−0.417878	+	0.908503i	$0.637226\pi$
$702$	59.8524	2.25898
$703$	6.47949	0.244379
$704$	−14.9632	−0.563946
$705$	2.40452	0.0905594
$706$	3.99027	0.150176
$707$	10.5996	0.398638
$708$	−5.93853	−0.223184
$709$	−43.5125	−1.63415	−0.817074	−	0.576533i	$-0.804405\pi$
$709$	−43.5125	−1.63415	−0.817074	+	0.576533i	$0.804405\pi$
$710$	−4.96363	−0.186282
$711$	−32.7615	−1.22865
$712$	−13.2946	−0.498236
$713$	35.1093	1.31485
$714$	−7.17040	−0.268346
$715$	4.04139	0.151139
$716$	−83.9983	−3.13916
$717$	2.76558	0.103283
$718$	−25.7407	−0.960635
$719$	13.4547	0.501775	0.250887	−	0.968016i	$-0.419278\pi$
$719$	13.4547	0.501775	0.250887	+	0.968016i	$0.419278\pi$
$720$	−2.37846	−0.0886401
$721$	0.733789	0.0273277
$722$	40.8649	1.52083
$723$	−9.62216	−0.357852
$724$	49.6659	1.84582
$725$	2.81479	0.104539
$726$	17.8412	0.662149
$727$	−8.85417	−0.328383	−0.164192	−	0.986428i	$-0.552502\pi$
$727$	−8.85417	−0.328383	−0.164192	+	0.986428i	$0.552502\pi$
$728$	22.5366	0.835262
$729$	2.29613	0.0850418
$730$	−8.46016	−0.313125
$731$	−11.0724	−0.409528
$732$	23.6438	0.873902
$733$	−4.77397	−0.176331	−0.0881654	−	0.996106i	$-0.528100\pi$
$733$	−4.77397	−0.176331	−0.0881654	+	0.996106i	$0.528100\pi$
$734$	−19.2929	−0.712114
$735$	0.428267	0.0157969
$736$	−22.8089	−0.840749
$737$	12.1356	0.447020
$738$	36.8998	1.35830
$739$	−42.4909	−1.56305	−0.781526	−	0.623873i	$-0.785558\pi$
$739$	−42.4909	−1.56305	−0.781526	+	0.623873i	$0.785558\pi$
$740$	−9.31804	−0.342538
$741$	−6.29664	−0.231313
$742$	−16.3897	−0.601684
$743$	−8.49438	−0.311629	−0.155814	−	0.987786i	$-0.549800\pi$
$743$	−8.49438	−0.311629	−0.155814	+	0.987786i	$0.549800\pi$
$744$	15.3573	0.563027
$745$	6.74658	0.247176
$746$	48.9507	1.79221
$747$	6.98198	0.255457
$748$	−17.7800	−0.650100
$749$	−0.878854	−0.0321126
$750$	9.87902	0.360731
$751$	26.6002	0.970657	0.485328	−	0.874332i	$-0.338700\pi$
$751$	26.6002	0.970657	0.485328	+	0.874332i	$0.338700\pi$
$752$	10.7905	0.393488
$753$	14.2651	0.519850
$754$	8.23884	0.300041
$755$	2.19947	0.0800468
$756$	15.7272	0.571994
$757$	32.7722	1.19113	0.595563	−	0.803309i	$-0.296929\pi$
$757$	32.7722	1.19113	0.595563	+	0.803309i	$0.296929\pi$
$758$	−89.6478	−3.25615
$759$	−7.64015	−0.277320
$760$	2.72683	0.0989127
$761$	−19.0584	−0.690867	−0.345434	−	0.938443i	$-0.612268\pi$
$761$	−19.0584	−0.690867	−0.345434	+	0.938443i	$0.612268\pi$
$762$	−23.0899	−0.836457
$763$	−12.9340	−0.468241
$764$	−17.0259	−0.615976
$765$	4.61268	0.166772
$766$	−32.0907	−1.15949
$767$	−11.7476	−0.424180
$768$	−21.2917	−0.768299
$769$	−18.7282	−0.675356	−0.337678	−	0.941262i	$-0.609641\pi$
$769$	−18.7282	−0.675356	−0.337678	+	0.941262i	$0.609641\pi$
$770$	1.64689	0.0593497
$771$	−14.6051	−0.525988
$772$	39.9747	1.43872
$773$	30.1914	1.08591	0.542954	−	0.839762i	$-0.317306\pi$
$773$	30.1914	1.08591	0.542954	+	0.839762i	$0.317306\pi$
$774$	16.5148	0.593611
$775$	23.1071	0.830031
$776$	−7.29997	−0.262054
$777$	3.93847	0.141292
$778$	57.9472	2.07751
$779$	−8.85302	−0.317192
$780$	9.05508	0.324224
$781$	5.20224	0.186151
$782$	−63.4425	−2.26870
$783$	2.58256	0.0922931
$784$	1.92188	0.0686387
$785$	7.95961	0.284091
$786$	−13.2377	−0.472172
$787$	44.8157	1.59751	0.798754	−	0.601657i	$-0.205493\pi$
$787$	44.8157	1.59751	0.798754	+	0.601657i	$0.205493\pi$
$788$	20.2710	0.722124
$789$	17.1282	0.609779
$790$	−17.5298	−0.623681
$791$	3.25096	0.115591
$792$	11.9119	0.423272
$793$	46.7722	1.66093
$794$	−15.3697	−0.545452
$795$	−2.95797	−0.104909
$796$	−16.1209	−0.571389
$797$	32.3298	1.14518	0.572589	−	0.819842i	$-0.305939\pi$
$797$	32.3298	1.14518	0.572589	+	0.819842i	$0.305939\pi$
$798$	−2.56591	−0.0908323
$799$	−20.9265	−0.740328
$800$	−15.0116	−0.530742
$801$	−8.04764	−0.284349
$802$	13.0253	0.459938
$803$	8.86685	0.312904
$804$	27.1908	0.958946
$805$	3.78924	0.133553
$806$	67.6340	2.38230
$807$	−0.304286	−0.0107114
$808$	41.0222	1.44316
$809$	36.9338	1.29852	0.649261	−	0.760566i	$-0.275078\pi$
$809$	36.9338	1.29852	0.649261	+	0.760566i	$0.275078\pi$
$810$	−4.40824	−0.154890
$811$	10.6176	0.372834	0.186417	−	0.982471i	$-0.440312\pi$
$811$	10.6176	0.372834	0.186417	+	0.982471i	$0.440312\pi$
$812$	2.16490	0.0759730
$813$	−12.9347	−0.453638
$814$	15.1453	0.530841
$815$	−8.18841	−0.286827
$816$	−5.80737	−0.203299
$817$	−3.96223	−0.138621
$818$	−30.8553	−1.07883
$819$	13.6421	0.476694
$820$	12.7314	0.444598
$821$	24.3811	0.850905	0.425453	−	0.904981i	$-0.360115\pi$
$821$	24.3811	0.850905	0.425453	+	0.904981i	$0.360115\pi$
$822$	−33.3877	−1.16453
$823$	1.10014	0.0383485	0.0191742	−	0.999816i	$-0.493896\pi$
$823$	1.10014	0.0383485	0.0191742	+	0.999816i	$0.493896\pi$
$824$	2.83989	0.0989323
$825$	−5.02834	−0.175064
$826$	−4.78719	−0.166568
$827$	34.7704	1.20909	0.604543	−	0.796573i	$-0.293356\pi$
$827$	34.7704	1.20909	0.604543	+	0.796573i	$0.293356\pi$
$828$	61.0168	2.12048
$829$	17.7730	0.617282	0.308641	−	0.951179i	$-0.400126\pi$
$829$	17.7730	0.617282	0.308641	+	0.951179i	$0.400126\pi$
$830$	3.73586	0.129674
$831$	9.72138	0.337231
$832$	−66.3216	−2.29929
$833$	−3.72721	−0.129140
$834$	−10.1159	−0.350286
$835$	5.40691	0.187114
$836$	−6.36252	−0.220052
$837$	21.2006	0.732801
$838$	−8.03501	−0.277565
$839$	44.0035	1.51917	0.759584	−	0.650409i	$-0.225403\pi$
$839$	44.0035	1.51917	0.759584	+	0.650409i	$0.225403\pi$
$840$	1.65747	0.0571881
$841$	−28.6445	−0.987742
$842$	−86.9898	−2.99787
$843$	12.0663	0.415584
$844$	71.1069	2.44760
$845$	11.0454	0.379972
$846$	31.2125	1.07311
$847$	9.27395	0.318657
$848$	−13.2741	−0.455836
$849$	−1.19297	−0.0409425
$850$	−41.7545	−1.43217
$851$	34.8469	1.19454
$852$	11.6561	0.399330
$853$	−52.3922	−1.79387	−0.896937	−	0.442159i	$-0.854213\pi$
$853$	−52.3922	−1.79387	−0.896937	+	0.442159i	$0.854213\pi$
$854$	19.0599	0.652216
$855$	1.65064	0.0564507
$856$	−3.40132	−0.116255
$857$	45.1903	1.54367	0.771836	−	0.635822i	$-0.219339\pi$
$857$	45.1903	1.54367	0.771836	+	0.635822i	$0.219339\pi$
$858$	−14.7179	−0.502459
$859$	11.7311	0.400259	0.200130	−	0.979769i	$-0.435864\pi$
$859$	11.7311	0.400259	0.200130	+	0.979769i	$0.435864\pi$
$860$	5.69801	0.194301
$861$	−5.38118	−0.183390
$862$	80.3729	2.73751
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−13.7731	−0.468571
$865$	−6.70991	−0.228144
$866$	−15.2589	−0.518518
$867$	−2.51962	−0.0855709
$868$	17.7720	0.603221
$869$	18.3724	0.623242
$870$	0.605930	0.0205430
$871$	53.7888	1.82256
$872$	−50.0568	−1.69514
$873$	−4.41891	−0.149557
$874$	−22.7028	−0.767933
$875$	5.13516	0.173600
$876$	19.8669	0.671242
$877$	3.55664	0.120099	0.0600497	−	0.998195i	$-0.480874\pi$
$877$	3.55664	0.120099	0.0600497	+	0.998195i	$0.480874\pi$
$878$	−70.6392	−2.38396
$879$	−15.7464	−0.531111
$880$	1.33383	0.0449633
$881$	−18.1235	−0.610598	−0.305299	−	0.952257i	$-0.598756\pi$
$881$	−18.1235	−0.610598	−0.305299	+	0.952257i	$0.598756\pi$
$882$	5.55923	0.187189
$883$	32.9109	1.10754	0.553770	−	0.832670i	$-0.313189\pi$
$883$	32.9109	1.10754	0.553770	+	0.832670i	$0.313189\pi$
$884$	−78.8065	−2.65055
$885$	−0.863983	−0.0290425
$886$	23.6710	0.795242
$887$	13.8184	0.463975	0.231987	−	0.972719i	$-0.425477\pi$
$887$	13.8184	0.463975	0.231987	+	0.972719i	$0.425477\pi$
$888$	15.2426	0.511507
$889$	−12.0022	−0.402542
$890$	−4.30607	−0.144340
$891$	4.62015	0.154781
$892$	68.0340	2.27795
$893$	−7.48852	−0.250594
$894$	−24.5696	−0.821729
$895$	−12.2207	−0.408493
$896$	−20.6668	−0.690429
$897$	−33.8636	−1.13067
$898$	−57.3591	−1.91410
$899$	2.91833	0.0973316
$900$	40.1581	1.33860
$901$	25.7433	0.857633
$902$	−20.6932	−0.689007
$903$	−2.40839	−0.0801462
$904$	12.5818	0.418463
$905$	7.22577	0.240193
$906$	−8.00997	−0.266114
$907$	26.1129	0.867065	0.433532	−	0.901138i	$-0.357267\pi$
$907$	26.1129	0.867065	0.433532	+	0.901138i	$0.357267\pi$
$908$	30.3540	1.00733
$909$	24.8320	0.823627
$910$	7.29952	0.241977
$911$	−38.2317	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$911$	−38.2317	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$912$	−2.07815	−0.0688146
$913$	−3.91545	−0.129582
$914$	−86.4314	−2.85890
$915$	3.43989	0.113719
$916$	−68.3231	−2.25746
$917$	−6.88101	−0.227231
$918$	−38.3096	−1.26440
$919$	8.97020	0.295900	0.147950	−	0.988995i	$-0.452733\pi$
$919$	8.97020	0.295900	0.147950	+	0.988995i	$0.452733\pi$
$920$	14.6650	0.483491
$921$	15.3439	0.505598
$922$	−31.2133	−1.02796
$923$	23.0580	0.758962
$924$	−3.86737	−0.127227
$925$	22.9344	0.754079
$926$	72.3553	2.37774
$927$	1.71908	0.0564618
$928$	−1.89591	−0.0622362
$929$	−8.80591	−0.288913	−0.144456	−	0.989511i	$-0.546143\pi$
$929$	−8.80591	−0.288913	−0.144456	+	0.989511i	$0.546143\pi$
$930$	4.97418	0.163110
$931$	−1.33377	−0.0437127
$932$	−24.9695	−0.817903
$933$	−14.3833	−0.470887
$934$	40.0444	1.31029
$935$	−2.58676	−0.0845963
$936$	52.7974	1.72574
$937$	−1.80918	−0.0591034	−0.0295517	−	0.999563i	$-0.509408\pi$
$937$	−1.80918	−0.0591034	−0.0295517	+	0.999563i	$0.509408\pi$
$938$	21.9192	0.715687
$939$	−12.1887	−0.397762
$940$	10.7691	0.351249
$941$	−8.07296	−0.263171	−0.131586	−	0.991305i	$-0.542007\pi$
$941$	−8.07296	−0.263171	−0.131586	+	0.991305i	$0.542007\pi$
$942$	−28.9872	−0.944453
$943$	−47.6118	−1.55045
$944$	−3.87719	−0.126192
$945$	2.28812	0.0744325
$946$	−9.26138	−0.301113
$947$	14.4014	0.467982	0.233991	−	0.972239i	$-0.424821\pi$
$947$	14.4014	0.467982	0.233991	+	0.972239i	$0.424821\pi$
$948$	41.1650	1.33698
$949$	39.3007	1.27575
$950$	−14.9418	−0.484775
$951$	12.1192	0.392992
$952$	−14.4250	−0.467516
$953$	−9.33833	−0.302498	−0.151249	−	0.988496i	$-0.548330\pi$
$953$	−9.33833	−0.302498	−0.151249	+	0.988496i	$0.548330\pi$
$954$	−38.3967	−1.24314
$955$	−2.47706	−0.0801558
$956$	12.3862	0.400598
$957$	−0.635058	−0.0205285
$958$	−3.16768	−0.102343
$959$	−17.3551	−0.560424
$960$	−4.87766	−0.157426
$961$	−7.04300	−0.227194
$962$	67.1286	2.16431
$963$	−2.05893	−0.0663480
$964$	−43.0947	−1.38799
$965$	5.81582	0.187218
$966$	−13.7996	−0.443994
$967$	33.0827	1.06387	0.531935	−	0.846785i	$-0.321465\pi$
$967$	33.0827	1.06387	0.531935	+	0.846785i	$0.321465\pi$
$968$	35.8918	1.15361
$969$	4.03028	0.129471
$970$	−2.36443	−0.0759174
$971$	24.8244	0.796652	0.398326	−	0.917244i	$-0.369591\pi$
$971$	24.8244	0.796652	0.398326	+	0.917244i	$0.369591\pi$
$972$	57.5336	1.84539
$973$	−5.25832	−0.168574
$974$	25.6743	0.822656
$975$	−22.2872	−0.713762
$976$	15.4368	0.494119
$977$	−13.9912	−0.447618	−0.223809	−	0.974633i	$-0.571849\pi$
$977$	−13.9912	−0.447618	−0.223809	+	0.974633i	$0.571849\pi$
$978$	29.8204	0.953550
$979$	4.51306	0.144238
$980$	1.91808	0.0612707
$981$	−30.3009	−0.967435
$982$	−9.39678	−0.299863
$983$	24.5505	0.783039	0.391519	−	0.920170i	$-0.371950\pi$
$983$	24.5505	0.783039	0.391519	+	0.920170i	$0.371950\pi$
$984$	−20.8261	−0.663913
$985$	2.94917	0.0939685
$986$	−5.27342	−0.167940
$987$	−4.55179	−0.144885
$988$	−28.2007	−0.897184
$989$	−21.3090	−0.677588
$990$	3.85823	0.122622
$991$	−18.7755	−0.596424	−0.298212	−	0.954500i	$-0.596390\pi$
$991$	−18.7755	−0.596424	−0.298212	+	0.954500i	$0.596390\pi$
$992$	−15.5638	−0.494151
$993$	20.7986	0.660025
$994$	9.39623	0.298030
$995$	−2.34538	−0.0743537
$996$	−8.77290	−0.277980
$997$	42.9994	1.36181	0.680903	−	0.732374i	$-0.261588\pi$
$997$	42.9994	1.36181	0.680903	+	0.732374i	$0.261588\pi$
$998$	−41.1297	−1.30194
$999$	21.0422	0.665746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.14	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.14	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37296 q^{2} +0.810716 q^{3} +3.63095 q^{4} +0.528258 q^{5} -1.92380 q^{6} -1.00000 q^{7} -3.87017 q^{8} -2.34274 q^{9} +O(q^{10})\)	\(q-2.37296 q^{2} +0.810716 q^{3} +3.63095 q^{4} +0.528258 q^{5} -1.92380 q^{6} -1.00000 q^{7} -3.87017 q^{8} -2.34274 q^{9} -1.25354 q^{10} +1.31379 q^{11} +2.94367 q^{12} +5.82315 q^{13} +2.37296 q^{14} +0.428267 q^{15} +1.92188 q^{16} -3.72721 q^{17} +5.55923 q^{18} -1.33377 q^{19} +1.91808 q^{20} -0.810716 q^{21} -3.11758 q^{22} -7.17308 q^{23} -3.13761 q^{24} -4.72094 q^{25} -13.8181 q^{26} -4.33144 q^{27} -3.63095 q^{28} -0.596235 q^{29} -1.01626 q^{30} -4.89459 q^{31} +3.17980 q^{32} +1.06511 q^{33} +8.84453 q^{34} -0.528258 q^{35} -8.50636 q^{36} -4.85801 q^{37} +3.16500 q^{38} +4.72092 q^{39} -2.04445 q^{40} +6.63757 q^{41} +1.92380 q^{42} +2.97069 q^{43} +4.77032 q^{44} -1.23757 q^{45} +17.0215 q^{46} +5.61453 q^{47} +1.55810 q^{48} +1.00000 q^{49} +11.2026 q^{50} -3.02171 q^{51} +21.1435 q^{52} -6.90685 q^{53} +10.2784 q^{54} +0.694022 q^{55} +3.87017 q^{56} -1.08131 q^{57} +1.41484 q^{58} -2.01739 q^{59} +1.55501 q^{60} +8.03211 q^{61} +11.6147 q^{62} +2.34274 q^{63} -11.3893 q^{64} +3.07612 q^{65} -2.52747 q^{66} +9.23706 q^{67} -13.5333 q^{68} -5.81533 q^{69} +1.25354 q^{70} +3.95971 q^{71} +9.06681 q^{72} +6.74904 q^{73} +11.5279 q^{74} -3.82735 q^{75} -4.84286 q^{76} -1.31379 q^{77} -11.2026 q^{78} +13.9843 q^{79} +1.01525 q^{80} +3.51665 q^{81} -15.7507 q^{82} -2.98026 q^{83} -2.94367 q^{84} -1.96893 q^{85} -7.04934 q^{86} -0.483377 q^{87} -5.08461 q^{88} +3.43514 q^{89} +2.93671 q^{90} -5.82315 q^{91} -26.0451 q^{92} -3.96812 q^{93} -13.3231 q^{94} -0.704577 q^{95} +2.57791 q^{96} +1.88621 q^{97} -2.37296 q^{98} -3.07788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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