LMFDB - Embedded newform 6017.2.a.e.1.5

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:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.64305 q^{2} -0.959171 q^{3} +4.98572 q^{4} -4.09680 q^{5} +2.53514 q^{6} -1.46535 q^{7} -7.89140 q^{8} -2.07999 q^{9} +O(q^{10})$	\(q-2.64305 q^{2} -0.959171 q^{3} +4.98572 q^{4} -4.09680 q^{5} +2.53514 q^{6} -1.46535 q^{7} -7.89140 q^{8} -2.07999 q^{9} +10.8280 q^{10} +1.00000 q^{11} -4.78216 q^{12} +1.41183 q^{13} +3.87299 q^{14} +3.92953 q^{15} +10.8859 q^{16} +6.56764 q^{17} +5.49752 q^{18} +4.78468 q^{19} -20.4255 q^{20} +1.40552 q^{21} -2.64305 q^{22} -4.20047 q^{23} +7.56921 q^{24} +11.7837 q^{25} -3.73154 q^{26} +4.87258 q^{27} -7.30582 q^{28} -6.46403 q^{29} -10.3859 q^{30} +5.73409 q^{31} -12.9893 q^{32} -0.959171 q^{33} -17.3586 q^{34} +6.00324 q^{35} -10.3702 q^{36} +10.3011 q^{37} -12.6461 q^{38} -1.35419 q^{39} +32.3295 q^{40} +0.155456 q^{41} -3.71486 q^{42} +6.15068 q^{43} +4.98572 q^{44} +8.52130 q^{45} +11.1021 q^{46} +9.25976 q^{47} -10.4415 q^{48} -4.85275 q^{49} -31.1450 q^{50} -6.29949 q^{51} +7.03899 q^{52} +4.24431 q^{53} -12.8785 q^{54} -4.09680 q^{55} +11.5637 q^{56} -4.58932 q^{57} +17.0848 q^{58} -6.07767 q^{59} +19.5915 q^{60} +5.73320 q^{61} -15.1555 q^{62} +3.04791 q^{63} +12.5595 q^{64} -5.78398 q^{65} +2.53514 q^{66} -3.39448 q^{67} +32.7444 q^{68} +4.02898 q^{69} -15.8669 q^{70} +10.5457 q^{71} +16.4140 q^{72} -12.7004 q^{73} -27.2264 q^{74} -11.3026 q^{75} +23.8550 q^{76} -1.46535 q^{77} +3.57919 q^{78} -10.9185 q^{79} -44.5975 q^{80} +1.56633 q^{81} -0.410879 q^{82} -17.2373 q^{83} +7.00753 q^{84} -26.9063 q^{85} -16.2566 q^{86} +6.20011 q^{87} -7.89140 q^{88} -4.77635 q^{89} -22.5222 q^{90} -2.06883 q^{91} -20.9424 q^{92} -5.49998 q^{93} -24.4740 q^{94} -19.6018 q^{95} +12.4590 q^{96} +6.32696 q^{97} +12.8261 q^{98} -2.07999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.64305	−1.86892	−0.934460	−	0.356069i	$-0.884117\pi$
$2$	−2.64305	−1.86892	−0.934460	+	0.356069i	$0.884117\pi$
$3$	−0.959171	−0.553778	−0.276889	−	0.960902i	$-0.589303\pi$
$3$	−0.959171	−0.553778	−0.276889	+	0.960902i	$0.589303\pi$
$4$	4.98572	2.49286
$5$	−4.09680	−1.83214	−0.916072	−	0.401015i	$-0.868658\pi$
$5$	−4.09680	−1.83214	−0.916072	+	0.401015i	$0.868658\pi$
$6$	2.53514	1.03497
$7$	−1.46535	−0.553850	−0.276925	−	0.960892i	$-0.589315\pi$
$7$	−1.46535	−0.553850	−0.276925	+	0.960892i	$0.589315\pi$
$8$	−7.89140	−2.79003
$9$	−2.07999	−0.693330
$10$	10.8280	3.42413
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.78216	−1.38049
$13$	1.41183	0.391571	0.195786	−	0.980647i	$-0.437274\pi$
$13$	1.41183	0.391571	0.195786	+	0.980647i	$0.437274\pi$
$14$	3.87299	1.03510
$15$	3.92953	1.01460
$16$	10.8859	2.72149
$17$	6.56764	1.59289	0.796443	−	0.604714i	$-0.206712\pi$
$17$	6.56764	1.59289	0.796443	+	0.604714i	$0.206712\pi$
$18$	5.49752	1.29578
$19$	4.78468	1.09768	0.548840	−	0.835927i	$-0.315070\pi$
$19$	4.78468	1.09768	0.548840	+	0.835927i	$0.315070\pi$
$20$	−20.4255	−4.56727
$21$	1.40552	0.306710
$22$	−2.64305	−0.563500
$23$	−4.20047	−0.875860	−0.437930	−	0.899009i	$-0.644288\pi$
$23$	−4.20047	−0.875860	−0.437930	+	0.899009i	$0.644288\pi$
$24$	7.56921	1.54506
$25$	11.7837	2.35675
$26$	−3.73154	−0.731815
$27$	4.87258	0.937729
$28$	−7.30582	−1.38067
$29$	−6.46403	−1.20034	−0.600170	−	0.799872i	$-0.704900\pi$
$29$	−6.46403	−1.20034	−0.600170	+	0.799872i	$0.704900\pi$
$30$	−10.3859	−1.89621
$31$	5.73409	1.02987	0.514937	−	0.857228i	$-0.327815\pi$
$31$	5.73409	1.02987	0.514937	+	0.857228i	$0.327815\pi$
$32$	−12.9893	−2.29620
$33$	−0.959171	−0.166970
$34$	−17.3586	−2.97698
$35$	6.00324	1.01473
$36$	−10.3702	−1.72837
$37$	10.3011	1.69349	0.846746	−	0.531997i	$-0.178558\pi$
$37$	10.3011	1.69349	0.846746	+	0.531997i	$0.178558\pi$
$38$	−12.6461	−2.05147
$39$	−1.35419	−0.216844
$40$	32.3295	5.11174
$41$	0.155456	0.0242782	0.0121391	−	0.999926i	$-0.496136\pi$
$41$	0.155456	0.0242782	0.0121391	+	0.999926i	$0.496136\pi$
$42$	−3.71486	−0.573216
$43$	6.15068	0.937970	0.468985	−	0.883206i	$-0.344620\pi$
$43$	6.15068	0.937970	0.468985	+	0.883206i	$0.344620\pi$
$44$	4.98572	0.751625
$45$	8.52130	1.27028
$46$	11.1021	1.63691
$47$	9.25976	1.35068	0.675338	−	0.737509i	$-0.263998\pi$
$47$	9.25976	1.35068	0.675338	+	0.737509i	$0.263998\pi$
$48$	−10.4415	−1.50710
$49$	−4.85275	−0.693250
$50$	−31.1450	−4.40457
$51$	−6.29949	−0.882105
$52$	7.03899	0.976132
$53$	4.24431	0.583001	0.291501	−	0.956571i	$-0.405845\pi$
$53$	4.24431	0.583001	0.291501	+	0.956571i	$0.405845\pi$
$54$	−12.8785	−1.75254
$55$	−4.09680	−0.552412
$56$	11.5637	1.54526
$57$	−4.58932	−0.607871
$58$	17.0848	2.24334
$59$	−6.07767	−0.791245	−0.395623	−	0.918413i	$-0.629471\pi$
$59$	−6.07767	−0.791245	−0.395623	+	0.918413i	$0.629471\pi$
$60$	19.5915	2.52926
$61$	5.73320	0.734061	0.367031	−	0.930209i	$-0.380374\pi$
$61$	5.73320	0.734061	0.367031	+	0.930209i	$0.380374\pi$
$62$	−15.1555	−1.92475
$63$	3.04791	0.384001
$64$	12.5595	1.56993
$65$	−5.78398	−0.717415
$66$	2.53514	0.312054
$67$	−3.39448	−0.414702	−0.207351	−	0.978267i	$-0.566484\pi$
$67$	−3.39448	−0.414702	−0.207351	+	0.978267i	$0.566484\pi$
$68$	32.7444	3.97084
$69$	4.02898	0.485032
$70$	−15.8669	−1.89645
$71$	10.5457	1.25155	0.625774	−	0.780004i	$-0.284783\pi$
$71$	10.5457	1.25155	0.625774	+	0.780004i	$0.284783\pi$
$72$	16.4140	1.93441
$73$	−12.7004	−1.48646	−0.743232	−	0.669034i	$-0.766708\pi$
$73$	−12.7004	−1.48646	−0.743232	+	0.669034i	$0.766708\pi$
$74$	−27.2264	−3.16500
$75$	−11.3026	−1.30512
$76$	23.8550	2.73636
$77$	−1.46535	−0.166992
$78$	3.57919	0.405263
$79$	−10.9185	−1.22843	−0.614214	−	0.789140i	$-0.710527\pi$
$79$	−10.9185	−1.22843	−0.614214	+	0.789140i	$0.710527\pi$
$80$	−44.5975	−4.98615
$81$	1.56633	0.174037
$82$	−0.410879	−0.0453740
$83$	−17.2373	−1.89204	−0.946022	−	0.324102i	$-0.894938\pi$
$83$	−17.2373	−1.89204	−0.946022	+	0.324102i	$0.894938\pi$
$84$	7.00753	0.764584
$85$	−26.9063	−2.91840
$86$	−16.2566	−1.75299
$87$	6.20011	0.664722
$88$	−7.89140	−0.841226
$89$	−4.77635	−0.506292	−0.253146	−	0.967428i	$-0.581465\pi$
$89$	−4.77635	−0.506292	−0.253146	+	0.967428i	$0.581465\pi$
$90$	−22.5222	−2.37405
$91$	−2.06883	−0.216872
$92$	−20.9424	−2.18339
$93$	−5.49998	−0.570321
$94$	−24.4740	−2.52430
$95$	−19.6018	−2.01111
$96$	12.4590	1.27159
$97$	6.32696	0.642406	0.321203	−	0.947010i	$-0.395913\pi$
$97$	6.32696	0.642406	0.321203	+	0.947010i	$0.395913\pi$
$98$	12.8261	1.29563
$99$	−2.07999	−0.209047
$100$	58.7504	5.87504
$101$	11.7316	1.16734	0.583671	−	0.811990i	$-0.301616\pi$
$101$	11.7316	1.16734	0.583671	+	0.811990i	$0.301616\pi$
$102$	16.6499	1.64858
$103$	−10.9235	−1.07632	−0.538161	−	0.842842i	$-0.680881\pi$
$103$	−10.9235	−1.07632	−0.538161	+	0.842842i	$0.680881\pi$
$104$	−11.1413	−1.09250
$105$	−5.75813	−0.561936
$106$	−11.2179	−1.08958
$107$	1.37581	0.133005	0.0665023	−	0.997786i	$-0.478816\pi$
$107$	1.37581	0.133005	0.0665023	+	0.997786i	$0.478816\pi$
$108$	24.2933	2.33763
$109$	0.359244	0.0344093	0.0172046	−	0.999852i	$-0.494523\pi$
$109$	0.359244	0.0344093	0.0172046	+	0.999852i	$0.494523\pi$
$110$	10.8280	1.03241
$111$	−9.88053	−0.937818
$112$	−15.9517	−1.50729
$113$	−0.608471	−0.0572402	−0.0286201	−	0.999590i	$-0.509111\pi$
$113$	−0.608471	−0.0572402	−0.0286201	+	0.999590i	$0.509111\pi$
$114$	12.1298	1.13606
$115$	17.2085	1.60470
$116$	−32.2278	−2.99228
$117$	−2.93659	−0.271488
$118$	16.0636	1.47877
$119$	−9.62388	−0.882220
$120$	−31.0095	−2.83077
$121$	1.00000	0.0909091
$122$	−15.1531	−1.37190
$123$	−0.149109	−0.0134447
$124$	28.5886	2.56733
$125$	−27.7916	−2.48576
$126$	−8.05579	−0.717667
$127$	13.3798	1.18727	0.593633	−	0.804736i	$-0.297693\pi$
$127$	13.3798	1.18727	0.593633	+	0.804736i	$0.297693\pi$
$128$	−7.21675	−0.637876
$129$	−5.89956	−0.519427
$130$	15.2874	1.34079
$131$	17.4803	1.52726	0.763631	−	0.645653i	$-0.223415\pi$
$131$	17.4803	1.52726	0.763631	+	0.645653i	$0.223415\pi$
$132$	−4.78216	−0.416233
$133$	−7.01122	−0.607950
$134$	8.97178	0.775044
$135$	−19.9620	−1.71805
$136$	−51.8279	−4.44420
$137$	3.98673	0.340609	0.170305	−	0.985391i	$-0.445525\pi$
$137$	3.98673	0.340609	0.170305	+	0.985391i	$0.445525\pi$
$138$	−10.6488	−0.906485
$139$	−10.1990	−0.865071	−0.432536	−	0.901617i	$-0.642381\pi$
$139$	−10.1990	−0.865071	−0.432536	+	0.901617i	$0.642381\pi$
$140$	29.9304	2.52958
$141$	−8.88170	−0.747974
$142$	−27.8729	−2.33904
$143$	1.41183	0.118063
$144$	−22.6427	−1.88689
$145$	26.4818	2.19919
$146$	33.5677	2.77808
$147$	4.65462	0.383907
$148$	51.3584	4.22164
$149$	−12.6776	−1.03859	−0.519295	−	0.854595i	$-0.673805\pi$
$149$	−12.6776	−1.03859	−0.519295	+	0.854595i	$0.673805\pi$
$150$	29.8734	2.43915
$151$	12.5150	1.01845	0.509227	−	0.860632i	$-0.329931\pi$
$151$	12.5150	1.01845	0.509227	+	0.860632i	$0.329931\pi$
$152$	−37.7578	−3.06256
$153$	−13.6606	−1.10440
$154$	3.87299	0.312095
$155$	−23.4914	−1.88688
$156$	−6.75160	−0.540560
$157$	10.0418	0.801426	0.400713	−	0.916204i	$-0.368762\pi$
$157$	10.0418	0.801426	0.400713	+	0.916204i	$0.368762\pi$
$158$	28.8582	2.29583
$159$	−4.07102	−0.322853
$160$	53.2145	4.20698
$161$	6.15516	0.485095
$162$	−4.13989	−0.325261
$163$	21.3596	1.67301	0.836505	−	0.547959i	$-0.184595\pi$
$163$	21.3596	1.67301	0.836505	+	0.547959i	$0.184595\pi$
$164$	0.775062	0.0605222
$165$	3.92953	0.305913
$166$	45.5592	3.53608
$167$	−5.80816	−0.449449	−0.224724	−	0.974422i	$-0.572148\pi$
$167$	−5.80816	−0.449449	−0.224724	+	0.974422i	$0.572148\pi$
$168$	−11.0915	−0.855730
$169$	−11.0067	−0.846672
$170$	71.1147	5.45425
$171$	−9.95208	−0.761054
$172$	30.6656	2.33823
$173$	7.67235	0.583318	0.291659	−	0.956522i	$-0.405793\pi$
$173$	7.67235	0.583318	0.291659	+	0.956522i	$0.405793\pi$
$174$	−16.3872	−1.24231
$175$	−17.2673	−1.30529
$176$	10.8859	0.820559
$177$	5.82953	0.438174
$178$	12.6241	0.946218
$179$	3.22497	0.241046	0.120523	−	0.992711i	$-0.461543\pi$
$179$	3.22497	0.241046	0.120523	+	0.992711i	$0.461543\pi$
$180$	42.4848	3.16663
$181$	−7.42610	−0.551978	−0.275989	−	0.961161i	$-0.589005\pi$
$181$	−7.42610	−0.551978	−0.275989	+	0.961161i	$0.589005\pi$
$182$	5.46801	0.405316
$183$	−5.49912	−0.406507
$184$	33.1476	2.44368
$185$	−42.2016	−3.10272
$186$	14.5367	1.06588
$187$	6.56764	0.480273
$188$	46.1666	3.36704
$189$	−7.14003	−0.519361
$190$	51.8087	3.75860
$191$	−3.63855	−0.263276	−0.131638	−	0.991298i	$-0.542024\pi$
$191$	−3.63855	−0.263276	−0.131638	+	0.991298i	$0.542024\pi$
$192$	−12.0467	−0.869395
$193$	−12.9758	−0.934016	−0.467008	−	0.884253i	$-0.654668\pi$
$193$	−12.9758	−0.934016	−0.467008	+	0.884253i	$0.654668\pi$
$194$	−16.7225	−1.20060
$195$	5.54783	0.397288
$196$	−24.1944	−1.72817
$197$	8.93288	0.636441	0.318221	−	0.948017i	$-0.396915\pi$
$197$	8.93288	0.636441	0.318221	+	0.948017i	$0.396915\pi$
$198$	5.49752	0.390692
$199$	−15.4937	−1.09832	−0.549161	−	0.835717i	$-0.685052\pi$
$199$	−15.4937	−1.09832	−0.549161	+	0.835717i	$0.685052\pi$
$200$	−92.9903	−6.57540
$201$	3.25589	0.229653
$202$	−31.0073	−2.18167
$203$	9.47206	0.664808
$204$	−31.4075	−2.19896
$205$	−0.636874	−0.0444812
$206$	28.8713	2.01156
$207$	8.73695	0.607260
$208$	15.3691	1.06566
$209$	4.78468	0.330963
$210$	15.2190	1.05021
$211$	−10.9358	−0.752851	−0.376426	−	0.926447i	$-0.622847\pi$
$211$	−10.9358	−0.752851	−0.376426	+	0.926447i	$0.622847\pi$
$212$	21.1610	1.45334
$213$	−10.1152	−0.693080
$214$	−3.63634	−0.248575
$215$	−25.1981	−1.71850
$216$	−38.4515	−2.61629
$217$	−8.40245	−0.570396
$218$	−0.949499	−0.0643082
$219$	12.1818	0.823171
$220$	−20.4255	−1.37708
$221$	9.27239	0.623729
$222$	26.1147	1.75271
$223$	17.0164	1.13951	0.569753	−	0.821816i	$-0.307039\pi$
$223$	17.0164	1.13951	0.569753	+	0.821816i	$0.307039\pi$
$224$	19.0339	1.27175
$225$	−24.5101	−1.63400
$226$	1.60822	0.106977
$227$	10.7649	0.714489	0.357245	−	0.934011i	$-0.383716\pi$
$227$	10.7649	0.714489	0.357245	+	0.934011i	$0.383716\pi$
$228$	−22.8811	−1.51534
$229$	−6.37355	−0.421176	−0.210588	−	0.977575i	$-0.567538\pi$
$229$	−6.37355	−0.421176	−0.210588	+	0.977575i	$0.567538\pi$
$230$	−45.4829	−2.99905
$231$	1.40552	0.0924765
$232$	51.0102	3.34899
$233$	−14.9215	−0.977540	−0.488770	−	0.872413i	$-0.662554\pi$
$233$	−14.9215	−0.977540	−0.488770	+	0.872413i	$0.662554\pi$
$234$	7.76157	0.507390
$235$	−37.9354	−2.47463
$236$	−30.3015	−1.97246
$237$	10.4727	0.680276
$238$	25.4364	1.64880
$239$	9.07617	0.587089	0.293544	−	0.955945i	$-0.405165\pi$
$239$	9.07617	0.587089	0.293544	+	0.955945i	$0.405165\pi$
$240$	42.7766	2.76122
$241$	11.3934	0.733916	0.366958	−	0.930238i	$-0.380399\pi$
$241$	11.3934	0.733916	0.366958	+	0.930238i	$0.380399\pi$
$242$	−2.64305	−0.169902
$243$	−16.1201	−1.03411
$244$	28.5841	1.82991
$245$	19.8807	1.27013
$246$	0.394104	0.0251271
$247$	6.75515	0.429820
$248$	−45.2500	−2.87338
$249$	16.5336	1.04777
$250$	73.4547	4.64568
$251$	−26.7544	−1.68872	−0.844361	−	0.535775i	$-0.820020\pi$
$251$	−26.7544	−1.68872	−0.844361	+	0.535775i	$0.820020\pi$
$252$	15.1960	0.957260
$253$	−4.20047	−0.264082
$254$	−35.3635	−2.21890
$255$	25.8077	1.61614
$256$	−6.04472	−0.377795
$257$	8.43591	0.526218	0.263109	−	0.964766i	$-0.415252\pi$
$257$	8.43591	0.526218	0.263109	+	0.964766i	$0.415252\pi$
$258$	15.5928	0.970767
$259$	−15.0947	−0.937941
$260$	−28.8373	−1.78841
$261$	13.4451	0.832232
$262$	−46.2013	−2.85433
$263$	5.32086	0.328098	0.164049	−	0.986452i	$-0.447544\pi$
$263$	5.32086	0.328098	0.164049	+	0.986452i	$0.447544\pi$
$264$	7.56921	0.465852
$265$	−17.3881	−1.06814
$266$	18.5310	1.13621
$267$	4.58133	0.280373
$268$	−16.9239	−1.03379
$269$	26.0721	1.58964	0.794822	−	0.606842i	$-0.207564\pi$
$269$	26.0721	1.58964	0.794822	+	0.606842i	$0.207564\pi$
$270$	52.7605	3.21090
$271$	17.6449	1.07185	0.535925	−	0.844265i	$-0.319963\pi$
$271$	17.6449	1.07185	0.535925	+	0.844265i	$0.319963\pi$
$272$	71.4949	4.33502
$273$	1.98436	0.120099
$274$	−10.5371	−0.636571
$275$	11.7837	0.710586
$276$	20.0873	1.20912
$277$	−1.73644	−0.104332	−0.0521661	−	0.998638i	$-0.516613\pi$
$277$	−1.73644	−0.104332	−0.0521661	+	0.998638i	$0.516613\pi$
$278$	26.9566	1.61675
$279$	−11.9269	−0.714043
$280$	−47.3740	−2.83114
$281$	23.4565	1.39930	0.699650	−	0.714486i	$-0.253339\pi$
$281$	23.4565	1.39930	0.699650	+	0.714486i	$0.253339\pi$
$282$	23.4748	1.39790
$283$	5.44881	0.323898	0.161949	−	0.986799i	$-0.448222\pi$
$283$	5.44881	0.323898	0.161949	+	0.986799i	$0.448222\pi$
$284$	52.5780	3.11993
$285$	18.8015	1.11371
$286$	−3.73154	−0.220651
$287$	−0.227798	−0.0134465
$288$	27.0176	1.59203
$289$	26.1339	1.53729
$290$	−69.9928	−4.11012
$291$	−6.06864	−0.355750
$292$	−63.3204	−3.70554
$293$	−19.8969	−1.16239	−0.581196	−	0.813764i	$-0.697415\pi$
$293$	−19.8969	−1.16239	−0.581196	+	0.813764i	$0.697415\pi$
$294$	−12.3024	−0.717490
$295$	24.8990	1.44967
$296$	−81.2902	−4.72490
$297$	4.87258	0.282736
$298$	33.5076	1.94104
$299$	−5.93036	−0.342962
$300$	−56.3517	−3.25347
$301$	−9.01290	−0.519495
$302$	−33.0777	−1.90341
$303$	−11.2527	−0.646448
$304$	52.0857	2.98732
$305$	−23.4878	−1.34491
$306$	36.1057	2.06403
$307$	−7.85309	−0.448200	−0.224100	−	0.974566i	$-0.571944\pi$
$307$	−7.85309	−0.448200	−0.224100	+	0.974566i	$0.571944\pi$
$308$	−7.30582	−0.416288
$309$	10.4775	0.596044
$310$	62.0890	3.52642
$311$	−34.0410	−1.93029	−0.965144	−	0.261719i	$-0.915710\pi$
$311$	−34.0410	−1.93029	−0.965144	+	0.261719i	$0.915710\pi$
$312$	10.6864	0.605000
$313$	7.15460	0.404402	0.202201	−	0.979344i	$-0.435191\pi$
$313$	7.15460	0.404402	0.202201	+	0.979344i	$0.435191\pi$
$314$	−26.5411	−1.49780
$315$	−12.4867	−0.703545
$316$	−54.4366	−3.06230
$317$	23.1410	1.29973	0.649863	−	0.760051i	$-0.274826\pi$
$317$	23.1410	1.29973	0.649863	+	0.760051i	$0.274826\pi$
$318$	10.7599	0.603387
$319$	−6.46403	−0.361916
$320$	−51.4536	−2.87634
$321$	−1.31964	−0.0736550
$322$	−16.2684	−0.906603
$323$	31.4240	1.74848
$324$	7.80928	0.433849
$325$	16.6367	0.922835
$326$	−56.4544	−3.12672
$327$	−0.344576	−0.0190551
$328$	−1.22677	−0.0677370
$329$	−13.5688	−0.748072
$330$	−10.3859	−0.571728
$331$	−16.2979	−0.895816	−0.447908	−	0.894080i	$-0.647831\pi$
$331$	−16.2979	−0.895816	−0.447908	+	0.894080i	$0.647831\pi$
$332$	−85.9405	−4.71660
$333$	−21.4262	−1.17415
$334$	15.3513	0.839984
$335$	13.9065	0.759793
$336$	15.3004	0.834706
$337$	−9.04581	−0.492757	−0.246378	−	0.969174i	$-0.579241\pi$
$337$	−9.04581	−0.492757	−0.246378	+	0.969174i	$0.579241\pi$
$338$	29.0914	1.58236
$339$	0.583628	0.0316983
$340$	−134.147	−7.27515
$341$	5.73409	0.310519
$342$	26.3038	1.42235
$343$	17.3684	0.937807
$344$	−48.5375	−2.61697
$345$	−16.5059	−0.888647
$346$	−20.2784	−1.09017
$347$	17.2482	0.925931	0.462966	−	0.886376i	$-0.346785\pi$
$347$	17.2482	0.925931	0.462966	+	0.886376i	$0.346785\pi$
$348$	30.9120	1.65706
$349$	−13.1186	−0.702224	−0.351112	−	0.936333i	$-0.614196\pi$
$349$	−13.1186	−0.702224	−0.351112	+	0.936333i	$0.614196\pi$
$350$	45.6384	2.43947
$351$	6.87926	0.367188
$352$	−12.9893	−0.692332
$353$	−13.9608	−0.743060	−0.371530	−	0.928421i	$-0.621167\pi$
$353$	−13.9608	−0.743060	−0.371530	+	0.928421i	$0.621167\pi$
$354$	−15.4077	−0.818912
$355$	−43.2037	−2.29302
$356$	−23.8135	−1.26211
$357$	9.23095	0.488554
$358$	−8.52376	−0.450495
$359$	4.68628	0.247332	0.123666	−	0.992324i	$-0.460535\pi$
$359$	4.68628	0.247332	0.123666	+	0.992324i	$0.460535\pi$
$360$	−67.2450	−3.54412
$361$	3.89312	0.204901
$362$	19.6276	1.03160
$363$	−0.959171	−0.0503434
$364$	−10.3146	−0.540631
$365$	52.0308	2.72341
$366$	14.5345	0.759728
$367$	3.39952	0.177453	0.0887266	−	0.996056i	$-0.471720\pi$
$367$	3.39952	0.177453	0.0887266	+	0.996056i	$0.471720\pi$
$368$	−45.7261	−2.38364
$369$	−0.323348	−0.0168328
$370$	111.541	5.79873
$371$	−6.21940	−0.322895
$372$	−27.4213	−1.42173
$373$	29.6974	1.53767	0.768836	−	0.639446i	$-0.220836\pi$
$373$	29.6974	1.53767	0.768836	+	0.639446i	$0.220836\pi$
$374$	−17.3586	−0.897592
$375$	26.6569	1.37656
$376$	−73.0725	−3.76843
$377$	−9.12611	−0.470019
$378$	18.8715	0.970644
$379$	−26.2936	−1.35061	−0.675306	−	0.737537i	$-0.735989\pi$
$379$	−26.2936	−1.35061	−0.675306	+	0.737537i	$0.735989\pi$
$380$	−97.7292	−5.01340
$381$	−12.8335	−0.657481
$382$	9.61686	0.492041
$383$	9.84900	0.503261	0.251630	−	0.967823i	$-0.419033\pi$
$383$	9.84900	0.503261	0.251630	+	0.967823i	$0.419033\pi$
$384$	6.92210	0.353242
$385$	6.00324	0.305953
$386$	34.2956	1.74560
$387$	−12.7934	−0.650323
$388$	31.5445	1.60143
$389$	−37.6218	−1.90750	−0.953749	−	0.300603i	$-0.902812\pi$
$389$	−37.6218	−1.90750	−0.953749	+	0.300603i	$0.902812\pi$
$390$	−14.6632	−0.742500
$391$	−27.5872	−1.39514
$392$	38.2950	1.93419
$393$	−16.7666	−0.845764
$394$	−23.6100	−1.18946
$395$	44.7309	2.25066
$396$	−10.3702	−0.521124
$397$	9.17208	0.460334	0.230167	−	0.973151i	$-0.426073\pi$
$397$	9.17208	0.460334	0.230167	+	0.973151i	$0.426073\pi$
$398$	40.9507	2.05267
$399$	6.72496	0.336669
$400$	128.277	6.41386
$401$	−31.7076	−1.58340	−0.791701	−	0.610909i	$-0.790804\pi$
$401$	−31.7076	−1.58340	−0.791701	+	0.610909i	$0.790804\pi$
$402$	−8.60547	−0.429202
$403$	8.09557	0.403269
$404$	58.4907	2.91002
$405$	−6.41694	−0.318860
$406$	−25.0351	−1.24247
$407$	10.3011	0.510607
$408$	49.7118	2.46110
$409$	31.4183	1.55353	0.776767	−	0.629788i	$-0.216858\pi$
$409$	31.4183	1.55353	0.776767	+	0.629788i	$0.216858\pi$
$410$	1.68329	0.0831317
$411$	−3.82396	−0.188622
$412$	−54.4614	−2.68312
$413$	8.90591	0.438231
$414$	−23.0922	−1.13492
$415$	70.6179	3.46650
$416$	−18.3387	−0.899128
$417$	9.78263	0.479057
$418$	−12.6461	−0.618543
$419$	−17.8529	−0.872170	−0.436085	−	0.899906i	$-0.643635\pi$
$419$	−17.8529	−0.872170	−0.436085	+	0.899906i	$0.643635\pi$
$420$	−28.7084	−1.40083
$421$	−27.2333	−1.32727	−0.663635	−	0.748057i	$-0.730987\pi$
$421$	−27.2333	−1.32727	−0.663635	+	0.748057i	$0.730987\pi$
$422$	28.9039	1.40702
$423$	−19.2602	−0.936464
$424$	−33.4936	−1.62659
$425$	77.3914	3.75403
$426$	26.7349	1.29531
$427$	−8.40114	−0.406560
$428$	6.85940	0.331562
$429$	−1.35419	−0.0653808
$430$	66.5998	3.21173
$431$	−20.1436	−0.970284	−0.485142	−	0.874435i	$-0.661232\pi$
$431$	−20.1436	−0.970284	−0.485142	+	0.874435i	$0.661232\pi$
$432$	53.0426	2.55202
$433$	10.8171	0.519835	0.259918	−	0.965631i	$-0.416305\pi$
$433$	10.8171	0.519835	0.259918	+	0.965631i	$0.416305\pi$
$434$	22.2081	1.06602
$435$	−25.4006	−1.21787
$436$	1.79109	0.0857775
$437$	−20.0979	−0.961413
$438$	−32.1971	−1.53844
$439$	−39.9270	−1.90561	−0.952807	−	0.303578i	$-0.901819\pi$
$439$	−39.9270	−1.90561	−0.952807	+	0.303578i	$0.901819\pi$
$440$	32.3295	1.54125
$441$	10.0937	0.480651
$442$	−24.5074	−1.16570
$443$	19.2722	0.915649	0.457824	−	0.889043i	$-0.348629\pi$
$443$	19.2722	0.915649	0.457824	+	0.889043i	$0.348629\pi$
$444$	−49.2615	−2.33785
$445$	19.5677	0.927599
$446$	−44.9753	−2.12964
$447$	12.1600	0.575148
$448$	−18.4040	−0.869508
$449$	27.5320	1.29931	0.649657	−	0.760227i	$-0.274912\pi$
$449$	27.5320	1.29931	0.649657	+	0.760227i	$0.274912\pi$
$450$	64.7814	3.05382
$451$	0.155456	0.00732016
$452$	−3.03367	−0.142692
$453$	−12.0040	−0.563997
$454$	−28.4521	−1.33532
$455$	8.47556	0.397340
$456$	36.2162	1.69598
$457$	37.2068	1.74046	0.870231	−	0.492644i	$-0.163970\pi$
$457$	37.2068	1.74046	0.870231	+	0.492644i	$0.163970\pi$
$458$	16.8456	0.787144
$459$	32.0013	1.49369
$460$	85.7967	4.00029
$461$	40.6006	1.89096	0.945479	−	0.325682i	$-0.105594\pi$
$461$	40.6006	1.89096	0.945479	+	0.325682i	$0.105594\pi$
$462$	−3.71486	−0.172831
$463$	37.5797	1.74648	0.873239	−	0.487292i	$-0.162015\pi$
$463$	37.5797	1.74648	0.873239	+	0.487292i	$0.162015\pi$
$464$	−70.3670	−3.26671
$465$	22.5323	1.04491
$466$	39.4383	1.82694
$467$	−26.2621	−1.21526	−0.607632	−	0.794219i	$-0.707881\pi$
$467$	−26.2621	−1.21526	−0.607632	+	0.794219i	$0.707881\pi$
$468$	−14.6410	−0.676782
$469$	4.97410	0.229682
$470$	100.265	4.62488
$471$	−9.63185	−0.443812
$472$	47.9613	2.20760
$473$	6.15068	0.282809
$474$	−27.6799	−1.27138
$475$	56.3814	2.58696
$476$	−47.9820	−2.19925
$477$	−8.82813	−0.404212
$478$	−23.9888	−1.09722
$479$	2.00317	0.0915270	0.0457635	−	0.998952i	$-0.485428\pi$
$479$	2.00317	0.0915270	0.0457635	+	0.998952i	$0.485428\pi$
$480$	−51.0418	−2.32973
$481$	14.5434	0.663123
$482$	−30.1134	−1.37163
$483$	−5.90386	−0.268635
$484$	4.98572	0.226624
$485$	−25.9203	−1.17698
$486$	42.6063	1.93266
$487$	13.8573	0.627933	0.313967	−	0.949434i	$-0.398342\pi$
$487$	13.8573	0.627933	0.313967	+	0.949434i	$0.398342\pi$
$488$	−45.2430	−2.04805
$489$	−20.4875	−0.926476
$490$	−52.5458	−2.37378
$491$	−10.5300	−0.475213	−0.237606	−	0.971362i	$-0.576363\pi$
$491$	−10.5300	−0.475213	−0.237606	+	0.971362i	$0.576363\pi$
$492$	−0.743417	−0.0335158
$493$	−42.4534	−1.91200
$494$	−17.8542	−0.803299
$495$	8.52130	0.383004
$496$	62.4210	2.80279
$497$	−15.4532	−0.693170
$498$	−43.6991	−1.95820
$499$	9.08591	0.406741	0.203371	−	0.979102i	$-0.434810\pi$
$499$	9.08591	0.406741	0.203371	+	0.979102i	$0.434810\pi$
$500$	−138.561	−6.19664
$501$	5.57102	0.248895
$502$	70.7132	3.15609
$503$	10.1231	0.451367	0.225683	−	0.974201i	$-0.427539\pi$
$503$	10.1231	0.451367	0.225683	+	0.974201i	$0.427539\pi$
$504$	−24.0523	−1.07137
$505$	−48.0622	−2.13874
$506$	11.1021	0.493547
$507$	10.5573	0.468868
$508$	66.7079	2.95968
$509$	−30.9824	−1.37327	−0.686636	−	0.727001i	$-0.740913\pi$
$509$	−30.9824	−1.37327	−0.686636	+	0.727001i	$0.740913\pi$
$510$	−68.2111	−3.02044
$511$	18.6105	0.823278
$512$	30.4100	1.34394
$513$	23.3137	1.02933
$514$	−22.2965	−0.983458
$515$	44.7513	1.97198
$516$	−29.4135	−1.29486
$517$	9.25976	0.407244
$518$	39.8961	1.75294
$519$	−7.35909	−0.323028
$520$	45.6437	2.00161
$521$	−39.6703	−1.73799	−0.868995	−	0.494821i	$-0.835234\pi$
$521$	−39.6703	−1.73799	−0.868995	+	0.494821i	$0.835234\pi$
$522$	−35.5361	−1.55537
$523$	−37.8780	−1.65629	−0.828146	−	0.560513i	$-0.810604\pi$
$523$	−37.8780	−1.65629	−0.828146	+	0.560513i	$0.810604\pi$
$524$	87.1519	3.80725
$525$	16.5623	0.722838
$526$	−14.0633	−0.613189
$527$	37.6595	1.64047
$528$	−10.4415	−0.454407
$529$	−5.35601	−0.232870
$530$	45.9576	1.99627
$531$	12.6415	0.548594
$532$	−34.9560	−1.51553
$533$	0.219478	0.00950666
$534$	−12.1087	−0.523995
$535$	−5.63641	−0.243683
$536$	26.7872	1.15703
$537$	−3.09330	−0.133486
$538$	−68.9099	−2.97092
$539$	−4.85275	−0.209023
$540$	−99.5248	−4.28286
$541$	−1.55429	−0.0668242	−0.0334121	−	0.999442i	$-0.510637\pi$
$541$	−1.55429	−0.0668242	−0.0334121	+	0.999442i	$0.510637\pi$
$542$	−46.6363	−2.00320
$543$	7.12290	0.305673
$544$	−85.3090	−3.65759
$545$	−1.47175	−0.0630427
$546$	−5.24476	−0.224455
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	19.8767	0.849091
$549$	−11.9250	−0.508947
$550$	−31.1450	−1.32803
$551$	−30.9283	−1.31759
$552$	−31.7943	−1.35325
$553$	15.9994	0.680365
$554$	4.58949	0.194989
$555$	40.4785	1.71822
$556$	−50.8495	−2.15650
$557$	1.81947	0.0770932	0.0385466	−	0.999257i	$-0.487727\pi$
$557$	1.81947	0.0770932	0.0385466	+	0.999257i	$0.487727\pi$
$558$	31.5233	1.33449
$559$	8.68372	0.367282
$560$	65.3509	2.76158
$561$	−6.29949	−0.265965
$562$	−61.9969	−2.61518
$563$	−21.7908	−0.918371	−0.459186	−	0.888340i	$-0.651859\pi$
$563$	−21.7908	−0.918371	−0.459186	+	0.888340i	$0.651859\pi$
$564$	−44.2816	−1.86459
$565$	2.49278	0.104872
$566$	−14.4015	−0.605340
$567$	−2.29522	−0.0963903
$568$	−83.2206	−3.49186
$569$	40.2845	1.68881	0.844407	−	0.535703i	$-0.179953\pi$
$569$	40.2845	1.68881	0.844407	+	0.535703i	$0.179953\pi$
$570$	−49.6934	−2.08143
$571$	13.4832	0.564254	0.282127	−	0.959377i	$-0.408960\pi$
$571$	13.4832	0.564254	0.282127	+	0.959377i	$0.408960\pi$
$572$	7.03899	0.294315
$573$	3.48999	0.145796
$574$	0.602082	0.0251304
$575$	−49.4973	−2.06418
$576$	−26.1236	−1.08848
$577$	15.7592	0.656066	0.328033	−	0.944666i	$-0.393614\pi$
$577$	15.7592	0.656066	0.328033	+	0.944666i	$0.393614\pi$
$578$	−69.0731	−2.87306
$579$	12.4460	0.517237
$580$	132.031	5.48228
$581$	25.2587	1.04791
$582$	16.0397	0.664868
$583$	4.24431	0.175782
$584$	100.224	4.14728
$585$	12.0306	0.497405
$586$	52.5886	2.17242
$587$	35.3955	1.46093	0.730464	−	0.682952i	$-0.239304\pi$
$587$	35.3955	1.46093	0.730464	+	0.682952i	$0.239304\pi$
$588$	23.2066	0.957025
$589$	27.4358	1.13047
$590$	−65.8093	−2.70932
$591$	−8.56816	−0.352447
$592$	112.137	4.60881
$593$	38.3290	1.57398	0.786992	−	0.616963i	$-0.211637\pi$
$593$	38.3290	1.57398	0.786992	+	0.616963i	$0.211637\pi$
$594$	−12.8785	−0.528410
$595$	39.4271	1.61635
$596$	−63.2070	−2.58906
$597$	14.8611	0.608226
$598$	15.6742	0.640967
$599$	−15.0811	−0.616195	−0.308098	−	0.951355i	$-0.599692\pi$
$599$	−15.0811	−0.616195	−0.308098	+	0.951355i	$0.599692\pi$
$600$	89.1936	3.64131
$601$	43.4772	1.77347	0.886735	−	0.462277i	$-0.152968\pi$
$601$	43.4772	1.77347	0.886735	+	0.462277i	$0.152968\pi$
$602$	23.8215	0.970894
$603$	7.06048	0.287525
$604$	62.3961	2.53886
$605$	−4.09680	−0.166558
$606$	29.7413	1.20816
$607$	19.4987	0.791427	0.395713	−	0.918374i	$-0.370497\pi$
$607$	19.4987	0.791427	0.395713	+	0.918374i	$0.370497\pi$
$608$	−62.1495	−2.52050
$609$	−9.08533	−0.368156
$610$	62.0794	2.51352
$611$	13.0732	0.528886
$612$	−68.1080	−2.75310
$613$	−41.0380	−1.65751	−0.828754	−	0.559613i	$-0.810950\pi$
$613$	−41.0380	−1.65751	−0.828754	+	0.559613i	$0.810950\pi$
$614$	20.7561	0.837649
$615$	0.610871	0.0246327
$616$	11.5637	0.465913
$617$	−46.5089	−1.87238	−0.936188	−	0.351498i	$-0.885672\pi$
$617$	−46.5089	−1.87238	−0.936188	+	0.351498i	$0.885672\pi$
$618$	−27.6925	−1.11396
$619$	14.4763	0.581850	0.290925	−	0.956746i	$-0.406037\pi$
$619$	14.4763	0.581850	0.290925	+	0.956746i	$0.406037\pi$
$620$	−117.122	−4.70372
$621$	−20.4672	−0.821319
$622$	89.9721	3.60755
$623$	6.99901	0.280410
$624$	−14.7416	−0.590137
$625$	54.9379	2.19752
$626$	−18.9100	−0.755794
$627$	−4.58932	−0.183280
$628$	50.0658	1.99784
$629$	67.6540	2.69754
$630$	33.0029	1.31487
$631$	18.9829	0.755699	0.377849	−	0.925867i	$-0.376664\pi$
$631$	18.9829	0.755699	0.377849	+	0.925867i	$0.376664\pi$
$632$	86.1623	3.42735
$633$	10.4893	0.416912
$634$	−61.1628	−2.42908
$635$	−54.8143	−2.17524
$636$	−20.2970	−0.804828
$637$	−6.85126	−0.271457
$638$	17.0848	0.676392
$639$	−21.9350	−0.867736
$640$	29.5655	1.16868
$641$	−5.36794	−0.212021	−0.106010	−	0.994365i	$-0.533808\pi$
$641$	−5.36794	−0.212021	−0.106010	+	0.994365i	$0.533808\pi$
$642$	3.48787	0.137655
$643$	−31.1762	−1.22947	−0.614735	−	0.788733i	$-0.710737\pi$
$643$	−31.1762	−1.22947	−0.614735	+	0.788733i	$0.710737\pi$
$644$	30.6879	1.20927
$645$	24.1693	0.951665
$646$	−83.0553	−3.26777
$647$	−0.103863	−0.00408327	−0.00204164	−	0.999998i	$-0.500650\pi$
$647$	−0.103863	−0.00408327	−0.00204164	+	0.999998i	$0.500650\pi$
$648$	−12.3605	−0.485568
$649$	−6.07767	−0.238569
$650$	−43.9715	−1.72470
$651$	8.05939	0.315872
$652$	106.493	4.17058
$653$	12.8199	0.501680	0.250840	−	0.968029i	$-0.419293\pi$
$653$	12.8199	0.501680	0.250840	+	0.968029i	$0.419293\pi$
$654$	0.910732	0.0356124
$655$	−71.6133	−2.79816
$656$	1.69229	0.0660728
$657$	26.4166	1.03061
$658$	35.8630	1.39809
$659$	−11.7643	−0.458271	−0.229136	−	0.973395i	$-0.573590\pi$
$659$	−11.7643	−0.458271	−0.229136	+	0.973395i	$0.573590\pi$
$660$	19.5915	0.762599
$661$	−1.40748	−0.0547447	−0.0273724	−	0.999625i	$-0.508714\pi$
$661$	−1.40748	−0.0547447	−0.0273724	+	0.999625i	$0.508714\pi$
$662$	43.0763	1.67421
$663$	−8.89381	−0.345407
$664$	136.027	5.27886
$665$	28.7235	1.11385
$666$	56.6306	2.19439
$667$	27.1520	1.05133
$668$	−28.9578	−1.12041
$669$	−16.3217	−0.631033
$670$	−36.7556	−1.41999
$671$	5.73320	0.221328
$672$	−18.2567	−0.704268
$673$	−26.8925	−1.03663	−0.518316	−	0.855189i	$-0.673441\pi$
$673$	−26.8925	−1.03663	−0.518316	+	0.855189i	$0.673441\pi$
$674$	23.9085	0.920923
$675$	57.4172	2.20999
$676$	−54.8765	−2.11063
$677$	−0.365495	−0.0140471	−0.00702356	−	0.999975i	$-0.502236\pi$
$677$	−0.365495	−0.0140471	−0.00702356	+	0.999975i	$0.502236\pi$
$678$	−1.54256	−0.0592416
$679$	−9.27121	−0.355796
$680$	212.328	8.14242
$681$	−10.3254	−0.395668
$682$	−15.1555	−0.580334
$683$	19.3545	0.740580	0.370290	−	0.928916i	$-0.379258\pi$
$683$	19.3545	0.740580	0.370290	+	0.928916i	$0.379258\pi$
$684$	−49.6182	−1.89720
$685$	−16.3328	−0.624045
$686$	−45.9056	−1.75268
$687$	6.11333	0.233238
$688$	66.9560	2.55267
$689$	5.99225	0.228287
$690$	43.6259	1.66081
$691$	15.3261	0.583032	0.291516	−	0.956566i	$-0.405840\pi$
$691$	15.3261	0.583032	0.291516	+	0.956566i	$0.405840\pi$
$692$	38.2522	1.45413
$693$	3.04791	0.115781
$694$	−45.5878	−1.73049
$695$	41.7834	1.58493
$696$	−48.9276	−1.85459
$697$	1.02098	0.0386724
$698$	34.6732	1.31240
$699$	14.3123	0.541340
$700$	−86.0899	−3.25389
$701$	−6.47388	−0.244515	−0.122257	−	0.992498i	$-0.539013\pi$
$701$	−6.47388	−0.244515	−0.122257	+	0.992498i	$0.539013\pi$
$702$	−18.1822	−0.686244
$703$	49.2875	1.85891
$704$	12.5595	0.473353
$705$	36.3865	1.37040
$706$	36.8992	1.38872
$707$	−17.1910	−0.646533
$708$	29.0644	1.09231
$709$	−0.517412	−0.0194318	−0.00971591	−	0.999953i	$-0.503093\pi$
$709$	−0.517412	−0.0194318	−0.00971591	+	0.999953i	$0.503093\pi$
$710$	114.190	4.28546
$711$	22.7104	0.851706
$712$	37.6921	1.41257
$713$	−24.0859	−0.902025
$714$	−24.3979	−0.913068
$715$	−5.78398	−0.216309
$716$	16.0788	0.600893
$717$	−8.70561	−0.325117
$718$	−12.3861	−0.462244
$719$	12.5457	0.467875	0.233938	−	0.972252i	$-0.424839\pi$
$719$	12.5457	0.467875	0.233938	+	0.972252i	$0.424839\pi$
$720$	92.7624	3.45705
$721$	16.0067	0.596121
$722$	−10.2897	−0.382943
$723$	−10.9283	−0.406426
$724$	−37.0244	−1.37600
$725$	−76.1705	−2.82890
$726$	2.53514	0.0940878
$727$	−18.9874	−0.704203	−0.352102	−	0.935962i	$-0.614533\pi$
$727$	−18.9874	−0.704203	−0.352102	+	0.935962i	$0.614533\pi$
$728$	16.3259	0.605079
$729$	10.7630	0.398628
$730$	−137.520	−5.08984
$731$	40.3954	1.49408
$732$	−27.4171	−1.01336
$733$	10.7163	0.395815	0.197908	−	0.980221i	$-0.436585\pi$
$733$	10.7163	0.395815	0.197908	+	0.980221i	$0.436585\pi$
$734$	−8.98509	−0.331646
$735$	−19.0690	−0.703372
$736$	54.5612	2.01115
$737$	−3.39448	−0.125037
$738$	0.854625	0.0314592
$739$	19.1580	0.704740	0.352370	−	0.935861i	$-0.385376\pi$
$739$	19.1580	0.704740	0.352370	+	0.935861i	$0.385376\pi$
$740$	−210.405	−7.73464
$741$	−6.47935	−0.238025
$742$	16.4382	0.603465
$743$	25.1466	0.922541	0.461270	−	0.887260i	$-0.347394\pi$
$743$	25.1466	0.922541	0.461270	+	0.887260i	$0.347394\pi$
$744$	43.4025	1.59121
$745$	51.9376	1.90285
$746$	−78.4916	−2.87378
$747$	35.8535	1.31181
$748$	32.7444	1.19725
$749$	−2.01604	−0.0736646
$750$	−70.4556	−2.57267
$751$	22.1575	0.808539	0.404269	−	0.914640i	$-0.367526\pi$
$751$	22.1575	0.808539	0.404269	+	0.914640i	$0.367526\pi$
$752$	100.801	3.67584
$753$	25.6620	0.935177
$754$	24.1208	0.878427
$755$	−51.2713	−1.86595
$756$	−35.5982	−1.29469
$757$	25.5394	0.928244	0.464122	−	0.885771i	$-0.346370\pi$
$757$	25.5394	0.928244	0.464122	+	0.885771i	$0.346370\pi$
$758$	69.4954	2.52419
$759$	4.02898	0.146243
$760$	154.686	5.61105
$761$	−29.9811	−1.08681	−0.543407	−	0.839470i	$-0.682866\pi$
$761$	−29.9811	−1.08681	−0.543407	+	0.839470i	$0.682866\pi$
$762$	33.9196	1.22878
$763$	−0.526417	−0.0190576
$764$	−18.1408	−0.656310
$765$	55.9648	2.02341
$766$	−26.0314	−0.940553
$767$	−8.58064	−0.309829
$768$	5.79792	0.209215
$769$	20.2719	0.731022	0.365511	−	0.930807i	$-0.380894\pi$
$769$	20.2719	0.731022	0.365511	+	0.930807i	$0.380894\pi$
$770$	−15.8669	−0.571802
$771$	−8.09148	−0.291408
$772$	−64.6935	−2.32837
$773$	2.50139	0.0899688	0.0449844	−	0.998988i	$-0.485676\pi$
$773$	2.50139	0.0899688	0.0449844	+	0.998988i	$0.485676\pi$
$774$	33.8135	1.21540
$775$	67.5691	2.42715
$776$	−49.9286	−1.79233
$777$	14.4784	0.519411
$778$	99.4362	3.56496
$779$	0.743809	0.0266497
$780$	27.6599	0.990384
$781$	10.5457	0.377356
$782$	72.9144	2.60741
$783$	−31.4965	−1.12559
$784$	−52.8268	−1.88667
$785$	−41.1394	−1.46833
$786$	44.3150	1.58066
$787$	10.2368	0.364903	0.182452	−	0.983215i	$-0.441597\pi$
$787$	10.2368	0.364903	0.182452	+	0.983215i	$0.441597\pi$
$788$	44.5368	1.58656
$789$	−5.10362	−0.181694
$790$	−118.226	−4.20629
$791$	0.891623	0.0317025
$792$	16.4140	0.583248
$793$	8.09431	0.287437
$794$	−24.2423	−0.860326
$795$	16.6782	0.591513
$796$	−77.2473	−2.73796
$797$	9.77537	0.346261	0.173131	−	0.984899i	$-0.444612\pi$
$797$	9.77537	0.346261	0.173131	+	0.984899i	$0.444612\pi$
$798$	−17.7744	−0.629207
$799$	60.8148	2.15147
$800$	−153.062	−5.41158
$801$	9.93475	0.351027
$802$	83.8048	2.95925
$803$	−12.7004	−0.448186
$804$	16.2329	0.572491
$805$	−25.2165	−0.888763
$806$	−21.3970	−0.753677
$807$	−25.0076	−0.880310
$808$	−92.5791	−3.25692
$809$	−0.432418	−0.0152030	−0.00760150	−	0.999971i	$-0.502420\pi$
$809$	−0.432418	−0.0152030	−0.00760150	+	0.999971i	$0.502420\pi$
$810$	16.9603	0.595924
$811$	8.59158	0.301691	0.150846	−	0.988557i	$-0.451800\pi$
$811$	8.59158	0.301691	0.150846	+	0.988557i	$0.451800\pi$
$812$	47.2250	1.65727
$813$	−16.9245	−0.593567
$814$	−27.2264	−0.954283
$815$	−87.5058	−3.06520
$816$	−68.5759	−2.40064
$817$	29.4290	1.02959
$818$	−83.0402	−2.90343
$819$	4.30314	0.150364
$820$	−3.17527	−0.110885
$821$	18.1393	0.633067	0.316534	−	0.948581i	$-0.397481\pi$
$821$	18.1393	0.633067	0.316534	+	0.948581i	$0.397481\pi$
$822$	10.1069	0.352519
$823$	46.0517	1.60526	0.802631	−	0.596476i	$-0.203433\pi$
$823$	46.0517	1.60526	0.802631	+	0.596476i	$0.203433\pi$
$824$	86.2016	3.00298
$825$	−11.3026	−0.393507
$826$	−23.5388	−0.819019
$827$	−8.55936	−0.297638	−0.148819	−	0.988864i	$-0.547547\pi$
$827$	−8.55936	−0.297638	−0.148819	+	0.988864i	$0.547547\pi$
$828$	43.5599	1.51381
$829$	−1.80425	−0.0626642	−0.0313321	−	0.999509i	$-0.509975\pi$
$829$	−1.80425	−0.0626642	−0.0313321	+	0.999509i	$0.509975\pi$
$830$	−186.647	−6.47860
$831$	1.66554	0.0577769
$832$	17.7319	0.614741
$833$	−31.8711	−1.10427
$834$	−25.8560	−0.895319
$835$	23.7949	0.823455
$836$	23.8550	0.825044
$837$	27.9398	0.965742
$838$	47.1860	1.63001
$839$	−24.9138	−0.860119	−0.430059	−	0.902801i	$-0.641507\pi$
$839$	−24.9138	−0.860119	−0.430059	+	0.902801i	$0.641507\pi$
$840$	45.4398	1.56782
$841$	12.7837	0.440816
$842$	71.9790	2.48056
$843$	−22.4989	−0.774902
$844$	−54.5228	−1.87675
$845$	45.0924	1.55122
$846$	50.9057	1.75018
$847$	−1.46535	−0.0503500
$848$	46.2034	1.58663
$849$	−5.22634	−0.179368
$850$	−204.549	−7.01598
$851$	−43.2696	−1.48326
$852$	−50.4314	−1.72775
$853$	53.4922	1.83154	0.915768	−	0.401707i	$-0.131583\pi$
$853$	53.4922	1.83154	0.915768	+	0.401707i	$0.131583\pi$
$854$	22.2046	0.759827
$855$	40.7716	1.39436
$856$	−10.8571	−0.371087
$857$	15.5865	0.532426	0.266213	−	0.963914i	$-0.414228\pi$
$857$	15.5865	0.532426	0.266213	+	0.963914i	$0.414228\pi$
$858$	3.57919	0.122191
$859$	5.76923	0.196844	0.0984218	−	0.995145i	$-0.468621\pi$
$859$	5.76923	0.196844	0.0984218	+	0.995145i	$0.468621\pi$
$860$	−125.631	−4.28397
$861$	0.218497	0.00744637
$862$	53.2406	1.81338
$863$	36.7776	1.25192	0.625962	−	0.779854i	$-0.284707\pi$
$863$	36.7776	1.25192	0.625962	+	0.779854i	$0.284707\pi$
$864$	−63.2914	−2.15322
$865$	−31.4320	−1.06872
$866$	−28.5901	−0.971530
$867$	−25.0669	−0.851315
$868$	−41.8922	−1.42192
$869$	−10.9185	−0.370385
$870$	67.1351	2.27609
$871$	−4.79243	−0.162385
$872$	−2.83494	−0.0960030
$873$	−13.1600	−0.445399
$874$	53.1198	1.79680
$875$	40.7244	1.37674
$876$	60.7351	2.05205
$877$	−4.31870	−0.145832	−0.0729161	−	0.997338i	$-0.523231\pi$
$877$	−4.31870	−0.145832	−0.0729161	+	0.997338i	$0.523231\pi$
$878$	105.529	3.56144
$879$	19.0846	0.643707
$880$	−44.5975	−1.50338
$881$	23.7564	0.800374	0.400187	−	0.916434i	$-0.368945\pi$
$881$	23.7564	0.800374	0.400187	+	0.916434i	$0.368945\pi$
$882$	−26.6781	−0.898298
$883$	−9.24534	−0.311130	−0.155565	−	0.987826i	$-0.549720\pi$
$883$	−9.24534	−0.311130	−0.155565	+	0.987826i	$0.549720\pi$
$884$	46.2295	1.55487
$885$	−23.8824	−0.802798
$886$	−50.9373	−1.71127
$887$	−31.8997	−1.07109	−0.535543	−	0.844508i	$-0.679893\pi$
$887$	−31.8997	−1.07109	−0.535543	+	0.844508i	$0.679893\pi$
$888$	77.9712	2.61654
$889$	−19.6061	−0.657567
$890$	−51.7185	−1.73361
$891$	1.56633	0.0524741
$892$	84.8392	2.84063
$893$	44.3050	1.48261
$894$	−32.1395	−1.07491
$895$	−13.2121	−0.441630
$896$	10.5751	0.353288
$897$	5.68823	0.189925
$898$	−72.7684	−2.42831
$899$	−37.0654	−1.23620
$900$	−122.200	−4.07334
$901$	27.8751	0.928655
$902$	−0.410879	−0.0136808
$903$	8.64491	0.287685
$904$	4.80169	0.159702
$905$	30.4232	1.01130
$906$	31.7272	1.05407
$907$	−51.8491	−1.72162	−0.860811	−	0.508926i	$-0.830043\pi$
$907$	−51.8491	−1.72162	−0.860811	+	0.508926i	$0.830043\pi$
$908$	53.6706	1.78112
$909$	−24.4017	−0.809354
$910$	−22.4013	−0.742597
$911$	59.0585	1.95670	0.978348	−	0.206966i	$-0.0663590\pi$
$911$	59.0585	1.95670	0.978348	+	0.206966i	$0.0663590\pi$
$912$	−49.9591	−1.65431
$913$	−17.2373	−0.570473
$914$	−98.3395	−3.25278
$915$	22.5288	0.744779
$916$	−31.7767	−1.04993
$917$	−25.6148	−0.845874
$918$	−84.5812	−2.79160
$919$	1.20346	0.0396986	0.0198493	−	0.999803i	$-0.493681\pi$
$919$	1.20346	0.0396986	0.0198493	+	0.999803i	$0.493681\pi$
$920$	−135.799	−4.47716
$921$	7.53246	0.248203
$922$	−107.309	−3.53405
$923$	14.8888	0.490071
$924$	7.00753	0.230531
$925$	121.386	3.99114
$926$	−99.3251	−3.26403
$927$	22.7207	0.746247
$928$	83.9632	2.75623
$929$	−11.0052	−0.361070	−0.180535	−	0.983569i	$-0.557783\pi$
$929$	−11.0052	−0.361070	−0.180535	+	0.983569i	$0.557783\pi$
$930$	−59.5540	−1.95285
$931$	−23.2188	−0.760967
$932$	−74.3944	−2.43687
$933$	32.6512	1.06895
$934$	69.4120	2.27123
$935$	−26.9063	−0.879929
$936$	23.1738	0.757461
$937$	−60.1264	−1.96425	−0.982123	−	0.188242i	$-0.939721\pi$
$937$	−60.1264	−1.96425	−0.982123	+	0.188242i	$0.939721\pi$
$938$	−13.1468	−0.429258
$939$	−6.86248	−0.223949
$940$	−189.135	−6.16890
$941$	−49.3455	−1.60862	−0.804308	−	0.594213i	$-0.797464\pi$
$941$	−49.3455	−1.60862	−0.804308	+	0.594213i	$0.797464\pi$
$942$	25.4575	0.829449
$943$	−0.652991	−0.0212643
$944$	−66.1612	−2.15336
$945$	29.2513	0.951544
$946$	−16.2566	−0.528546
$947$	−33.4653	−1.08748	−0.543738	−	0.839255i	$-0.682991\pi$
$947$	−33.4653	−1.08748	−0.543738	+	0.839255i	$0.682991\pi$
$948$	52.2140	1.69583
$949$	−17.9307	−0.582057
$950$	−149.019	−4.83481
$951$	−22.1962	−0.719760
$952$	75.9459	2.46142
$953$	−0.186588	−0.00604418	−0.00302209	−	0.999995i	$-0.500962\pi$
$953$	−0.186588	−0.00604418	−0.00302209	+	0.999995i	$0.500962\pi$
$954$	23.3332	0.755440
$955$	14.9064	0.482359
$956$	45.2512	1.46353
$957$	6.20011	0.200421
$958$	−5.29447	−0.171057
$959$	−5.84195	−0.188646
$960$	49.3528	1.59286
$961$	1.87984	0.0606400
$962$	−38.4390	−1.23932
$963$	−2.86167	−0.0922161
$964$	56.8045	1.82955
$965$	53.1591	1.71125
$966$	15.6042	0.502057
$967$	−23.6663	−0.761057	−0.380529	−	0.924769i	$-0.624258\pi$
$967$	−23.6663	−0.761057	−0.380529	+	0.924769i	$0.624258\pi$
$968$	−7.89140	−0.253639
$969$	−30.1410	−0.968269
$970$	68.5086	2.19968
$971$	−32.3918	−1.03950	−0.519750	−	0.854318i	$-0.673975\pi$
$971$	−32.3918	−1.03950	−0.519750	+	0.854318i	$0.673975\pi$
$972$	−80.3704	−2.57788
$973$	14.9452	0.479120
$974$	−36.6255	−1.17356
$975$	−15.9574	−0.511046
$976$	62.4113	1.99774
$977$	28.6647	0.917065	0.458533	−	0.888678i	$-0.348375\pi$
$977$	28.6647	0.917065	0.458533	+	0.888678i	$0.348375\pi$
$978$	54.1495	1.73151
$979$	−4.77635	−0.152653
$980$	99.1197	3.16626
$981$	−0.747223	−0.0238570
$982$	27.8313	0.888134
$983$	19.5479	0.623482	0.311741	−	0.950167i	$-0.399088\pi$
$983$	19.5479	0.623482	0.311741	+	0.950167i	$0.399088\pi$
$984$	1.17668	0.0375113
$985$	−36.5962	−1.16605
$986$	112.206	3.57338
$987$	13.0148	0.414265
$988$	33.6793	1.07148
$989$	−25.8358	−0.821530
$990$	−22.5222	−0.715803
$991$	−19.1972	−0.609819	−0.304909	−	0.952381i	$-0.598626\pi$
$991$	−19.1972	−0.609819	−0.304909	+	0.952381i	$0.598626\pi$
$992$	−74.4818	−2.36480
$993$	15.6325	0.496083
$994$	40.8435	1.29548
$995$	63.4747	2.01228
$996$	82.4317	2.61195
$997$	−24.6801	−0.781627	−0.390813	−	0.920470i	$-0.627806\pi$
$997$	−24.6801	−0.781627	−0.390813	+	0.920470i	$0.627806\pi$
$998$	−24.0145	−0.760166
$999$	50.1930	1.58804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.5	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.5	✓	119	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)

\(f(q)\)	\(=\)	\(q-2.64305 q^{2} -0.959171 q^{3} +4.98572 q^{4} -4.09680 q^{5} +2.53514 q^{6} -1.46535 q^{7} -7.89140 q^{8} -2.07999 q^{9} +O(q^{10})\)	\(q-2.64305 q^{2} -0.959171 q^{3} +4.98572 q^{4} -4.09680 q^{5} +2.53514 q^{6} -1.46535 q^{7} -7.89140 q^{8} -2.07999 q^{9} +10.8280 q^{10} +1.00000 q^{11} -4.78216 q^{12} +1.41183 q^{13} +3.87299 q^{14} +3.92953 q^{15} +10.8859 q^{16} +6.56764 q^{17} +5.49752 q^{18} +4.78468 q^{19} -20.4255 q^{20} +1.40552 q^{21} -2.64305 q^{22} -4.20047 q^{23} +7.56921 q^{24} +11.7837 q^{25} -3.73154 q^{26} +4.87258 q^{27} -7.30582 q^{28} -6.46403 q^{29} -10.3859 q^{30} +5.73409 q^{31} -12.9893 q^{32} -0.959171 q^{33} -17.3586 q^{34} +6.00324 q^{35} -10.3702 q^{36} +10.3011 q^{37} -12.6461 q^{38} -1.35419 q^{39} +32.3295 q^{40} +0.155456 q^{41} -3.71486 q^{42} +6.15068 q^{43} +4.98572 q^{44} +8.52130 q^{45} +11.1021 q^{46} +9.25976 q^{47} -10.4415 q^{48} -4.85275 q^{49} -31.1450 q^{50} -6.29949 q^{51} +7.03899 q^{52} +4.24431 q^{53} -12.8785 q^{54} -4.09680 q^{55} +11.5637 q^{56} -4.58932 q^{57} +17.0848 q^{58} -6.07767 q^{59} +19.5915 q^{60} +5.73320 q^{61} -15.1555 q^{62} +3.04791 q^{63} +12.5595 q^{64} -5.78398 q^{65} +2.53514 q^{66} -3.39448 q^{67} +32.7444 q^{68} +4.02898 q^{69} -15.8669 q^{70} +10.5457 q^{71} +16.4140 q^{72} -12.7004 q^{73} -27.2264 q^{74} -11.3026 q^{75} +23.8550 q^{76} -1.46535 q^{77} +3.57919 q^{78} -10.9185 q^{79} -44.5975 q^{80} +1.56633 q^{81} -0.410879 q^{82} -17.2373 q^{83} +7.00753 q^{84} -26.9063 q^{85} -16.2566 q^{86} +6.20011 q^{87} -7.89140 q^{88} -4.77635 q^{89} -22.5222 q^{90} -2.06883 q^{91} -20.9424 q^{92} -5.49998 q^{93} -24.4740 q^{94} -19.6018 q^{95} +12.4590 q^{96} +6.32696 q^{97} +12.8261 q^{98} -2.07999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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