LMFDB - Embedded newform 6033.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53542 q^{2} +1.00000 q^{3} +4.42834 q^{4} -3.51748 q^{5} -2.53542 q^{6} -3.36027 q^{7} -6.15684 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.53542 q^{2} +1.00000 q^{3} +4.42834 q^{4} -3.51748 q^{5} -2.53542 q^{6} -3.36027 q^{7} -6.15684 q^{8} +1.00000 q^{9} +8.91826 q^{10} -4.01174 q^{11} +4.42834 q^{12} +6.82384 q^{13} +8.51968 q^{14} -3.51748 q^{15} +6.75349 q^{16} -1.20600 q^{17} -2.53542 q^{18} +3.62861 q^{19} -15.5766 q^{20} -3.36027 q^{21} +10.1714 q^{22} -1.93339 q^{23} -6.15684 q^{24} +7.37263 q^{25} -17.3013 q^{26} +1.00000 q^{27} -14.8804 q^{28} -0.514107 q^{29} +8.91826 q^{30} -3.39123 q^{31} -4.80922 q^{32} -4.01174 q^{33} +3.05772 q^{34} +11.8197 q^{35} +4.42834 q^{36} -0.0398898 q^{37} -9.20004 q^{38} +6.82384 q^{39} +21.6565 q^{40} -6.14508 q^{41} +8.51968 q^{42} -6.78865 q^{43} -17.7653 q^{44} -3.51748 q^{45} +4.90194 q^{46} -7.96789 q^{47} +6.75349 q^{48} +4.29141 q^{49} -18.6927 q^{50} -1.20600 q^{51} +30.2183 q^{52} +5.97634 q^{53} -2.53542 q^{54} +14.1112 q^{55} +20.6887 q^{56} +3.62861 q^{57} +1.30348 q^{58} +11.8051 q^{59} -15.5766 q^{60} -3.31257 q^{61} +8.59817 q^{62} -3.36027 q^{63} -1.31361 q^{64} -24.0027 q^{65} +10.1714 q^{66} -5.06319 q^{67} -5.34059 q^{68} -1.93339 q^{69} -29.9678 q^{70} -0.302256 q^{71} -6.15684 q^{72} -0.626308 q^{73} +0.101137 q^{74} +7.37263 q^{75} +16.0687 q^{76} +13.4805 q^{77} -17.3013 q^{78} -12.5671 q^{79} -23.7552 q^{80} +1.00000 q^{81} +15.5803 q^{82} +5.45996 q^{83} -14.8804 q^{84} +4.24209 q^{85} +17.2121 q^{86} -0.514107 q^{87} +24.6997 q^{88} +4.04225 q^{89} +8.91826 q^{90} -22.9299 q^{91} -8.56169 q^{92} -3.39123 q^{93} +20.2019 q^{94} -12.7636 q^{95} -4.80922 q^{96} -15.4640 q^{97} -10.8805 q^{98} -4.01174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−2.53542	−1.79281	−0.896405	−	0.443236i	$-0.853830\pi$
$2$	−2.53542	−1.79281	−0.896405	+	0.443236i	$0.853830\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.42834	2.21417
$5$	−3.51748	−1.57306	−0.786531	−	0.617550i	$-0.788125\pi$
$5$	−3.51748	−1.57306	−0.786531	+	0.617550i	$0.788125\pi$
$6$	−2.53542	−1.03508
$7$	−3.36027	−1.27006	−0.635031	−	0.772486i	$-0.719013\pi$
$7$	−3.36027	−1.27006	−0.635031	+	0.772486i	$0.719013\pi$
$8$	−6.15684	−2.17677
$9$	1.00000	0.333333
$10$	8.91826	2.82020
$11$	−4.01174	−1.20959	−0.604793	−	0.796383i	$-0.706744\pi$
$11$	−4.01174	−1.20959	−0.604793	+	0.796383i	$0.706744\pi$
$12$	4.42834	1.27835
$13$	6.82384	1.89259	0.946296	−	0.323301i	$-0.104793\pi$
$13$	6.82384	1.89259	0.946296	+	0.323301i	$0.104793\pi$
$14$	8.51968	2.27698
$15$	−3.51748	−0.908208
$16$	6.75349	1.68837
$17$	−1.20600	−0.292499	−0.146249	−	0.989248i	$-0.546720\pi$
$17$	−1.20600	−0.292499	−0.146249	+	0.989248i	$0.546720\pi$
$18$	−2.53542	−0.597603
$19$	3.62861	0.832461	0.416230	−	0.909259i	$-0.363351\pi$
$19$	3.62861	0.832461	0.416230	+	0.909259i	$0.363351\pi$
$20$	−15.5766	−3.48303
$21$	−3.36027	−0.733271
$22$	10.1714	2.16856
$23$	−1.93339	−0.403139	−0.201570	−	0.979474i	$-0.564604\pi$
$23$	−1.93339	−0.403139	−0.201570	+	0.979474i	$0.564604\pi$
$24$	−6.15684	−1.25676
$25$	7.37263	1.47453
$26$	−17.3013	−3.39306
$27$	1.00000	0.192450
$28$	−14.8804	−2.81213
$29$	−0.514107	−0.0954673	−0.0477336	−	0.998860i	$-0.515200\pi$
$29$	−0.514107	−0.0954673	−0.0477336	+	0.998860i	$0.515200\pi$
$30$	8.91826	1.62824
$31$	−3.39123	−0.609082	−0.304541	−	0.952499i	$-0.598503\pi$
$31$	−3.39123	−0.609082	−0.304541	+	0.952499i	$0.598503\pi$
$32$	−4.80922	−0.850158
$33$	−4.01174	−0.698354
$34$	3.05772	0.524395
$35$	11.8197	1.99789
$36$	4.42834	0.738056
$37$	−0.0398898	−0.00655784	−0.00327892	−	0.999995i	$-0.501044\pi$
$37$	−0.0398898	−0.00655784	−0.00327892	+	0.999995i	$0.501044\pi$
$38$	−9.20004	−1.49244
$39$	6.82384	1.09269
$40$	21.6565	3.42420
$41$	−6.14508	−0.959700	−0.479850	−	0.877351i	$-0.659309\pi$
$41$	−6.14508	−0.959700	−0.479850	+	0.877351i	$0.659309\pi$
$42$	8.51968	1.31462
$43$	−6.78865	−1.03526	−0.517630	−	0.855605i	$-0.673186\pi$
$43$	−6.78865	−1.03526	−0.517630	+	0.855605i	$0.673186\pi$
$44$	−17.7653	−2.67822
$45$	−3.51748	−0.524354
$46$	4.90194	0.722752
$47$	−7.96789	−1.16224	−0.581118	−	0.813819i	$-0.697385\pi$
$47$	−7.96789	−1.16224	−0.581118	+	0.813819i	$0.697385\pi$
$48$	6.75349	0.974782
$49$	4.29141	0.613059
$50$	−18.6927	−2.64355
$51$	−1.20600	−0.168874
$52$	30.2183	4.19052
$53$	5.97634	0.820913	0.410457	−	0.911880i	$-0.365369\pi$
$53$	5.97634	0.820913	0.410457	+	0.911880i	$0.365369\pi$
$54$	−2.53542	−0.345026
$55$	14.1112	1.90275
$56$	20.6887	2.76464
$57$	3.62861	0.480622
$58$	1.30348	0.171155
$59$	11.8051	1.53689	0.768445	−	0.639916i	$-0.221031\pi$
$59$	11.8051	1.53689	0.768445	+	0.639916i	$0.221031\pi$
$60$	−15.5766	−2.01093
$61$	−3.31257	−0.424132	−0.212066	−	0.977255i	$-0.568019\pi$
$61$	−3.31257	−0.424132	−0.212066	+	0.977255i	$0.568019\pi$
$62$	8.59817	1.09197
$63$	−3.36027	−0.423354
$64$	−1.31361	−0.164201
$65$	−24.0027	−2.97717
$66$	10.1714	1.25202
$67$	−5.06319	−0.618567	−0.309284	−	0.950970i	$-0.600089\pi$
$67$	−5.06319	−0.618567	−0.309284	+	0.950970i	$0.600089\pi$
$68$	−5.34059	−0.647641
$69$	−1.93339	−0.232753
$70$	−29.9678	−3.58183
$71$	−0.302256	−0.0358712	−0.0179356	−	0.999839i	$-0.505709\pi$
$71$	−0.302256	−0.0358712	−0.0179356	+	0.999839i	$0.505709\pi$
$72$	−6.15684	−0.725591
$73$	−0.626308	−0.0733038	−0.0366519	−	0.999328i	$-0.511669\pi$
$73$	−0.626308	−0.0733038	−0.0366519	+	0.999328i	$0.511669\pi$
$74$	0.101137	0.0117570
$75$	7.37263	0.851318
$76$	16.0687	1.84321
$77$	13.4805	1.53625
$78$	−17.3013	−1.95898
$79$	−12.5671	−1.41391	−0.706953	−	0.707261i	$-0.749931\pi$
$79$	−12.5671	−1.41391	−0.706953	+	0.707261i	$0.749931\pi$
$80$	−23.7552	−2.65592
$81$	1.00000	0.111111
$82$	15.5803	1.72056
$83$	5.45996	0.599308	0.299654	−	0.954048i	$-0.403129\pi$
$83$	5.45996	0.599308	0.299654	+	0.954048i	$0.403129\pi$
$84$	−14.8804	−1.62359
$85$	4.24209	0.460119
$86$	17.2121	1.85602
$87$	−0.514107	−0.0551181
$88$	24.6997	2.63299
$89$	4.04225	0.428478	0.214239	−	0.976781i	$-0.431273\pi$
$89$	4.04225	0.428478	0.214239	+	0.976781i	$0.431273\pi$
$90$	8.91826	0.940068
$91$	−22.9299	−2.40371
$92$	−8.56169	−0.892618
$93$	−3.39123	−0.351654
$94$	20.2019	2.08367
$95$	−12.7636	−1.30951
$96$	−4.80922	−0.490839
$97$	−15.4640	−1.57013	−0.785064	−	0.619415i	$-0.787370\pi$
$97$	−15.4640	−1.57013	−0.785064	+	0.619415i	$0.787370\pi$
$98$	−10.8805	−1.09910
$99$	−4.01174	−0.403195
$100$	32.6485	3.26485
$101$	1.88334	0.187400	0.0936998	−	0.995600i	$-0.470131\pi$
$101$	1.88334	0.187400	0.0936998	+	0.995600i	$0.470131\pi$
$102$	3.05772	0.302759
$103$	0.553164	0.0545049	0.0272524	−	0.999629i	$-0.491324\pi$
$103$	0.553164	0.0545049	0.0272524	+	0.999629i	$0.491324\pi$
$104$	−42.0133	−4.11974
$105$	11.8197	1.15348
$106$	−15.1525	−1.47174
$107$	2.45433	0.237269	0.118635	−	0.992938i	$-0.462148\pi$
$107$	2.45433	0.237269	0.118635	+	0.992938i	$0.462148\pi$
$108$	4.42834	0.426117
$109$	−10.9146	−1.04543	−0.522714	−	0.852508i	$-0.675081\pi$
$109$	−10.9146	−1.04543	−0.522714	+	0.852508i	$0.675081\pi$
$110$	−35.7778	−3.41128
$111$	−0.0398898	−0.00378617
$112$	−22.6935	−2.14434
$113$	−20.7671	−1.95360	−0.976801	−	0.214151i	$-0.931301\pi$
$113$	−20.7671	−1.95360	−0.976801	+	0.214151i	$0.931301\pi$
$114$	−9.20004	−0.861663
$115$	6.80065	0.634164
$116$	−2.27664	−0.211381
$117$	6.82384	0.630864
$118$	−29.9308	−2.75535
$119$	4.05249	0.371492
$120$	21.6565	1.97696
$121$	5.09406	0.463096
$122$	8.39875	0.760387
$123$	−6.14508	−0.554083
$124$	−15.0175	−1.34861
$125$	−8.34568	−0.746460
$126$	8.51968	0.758994
$127$	10.7427	0.953262	0.476631	−	0.879103i	$-0.341858\pi$
$127$	10.7427	0.953262	0.476631	+	0.879103i	$0.341858\pi$
$128$	12.9490	1.14454
$129$	−6.78865	−0.597708
$130$	60.8568	5.33749
$131$	−3.70456	−0.323669	−0.161834	−	0.986818i	$-0.551741\pi$
$131$	−3.70456	−0.323669	−0.161834	+	0.986818i	$0.551741\pi$
$132$	−17.7653	−1.54627
$133$	−12.1931	−1.05728
$134$	12.8373	1.10897
$135$	−3.51748	−0.302736
$136$	7.42517	0.636703
$137$	−22.1954	−1.89628	−0.948142	−	0.317846i	$-0.897040\pi$
$137$	−22.1954	−1.89628	−0.948142	+	0.317846i	$0.897040\pi$
$138$	4.90194	0.417281
$139$	−15.2622	−1.29452	−0.647260	−	0.762269i	$-0.724085\pi$
$139$	−15.2622	−1.29452	−0.647260	+	0.762269i	$0.724085\pi$
$140$	52.3415	4.42366
$141$	−7.96789	−0.671017
$142$	0.766345	0.0643102
$143$	−27.3755	−2.28925
$144$	6.75349	0.562791
$145$	1.80836	0.150176
$146$	1.58795	0.131420
$147$	4.29141	0.353950
$148$	−0.176645	−0.0145202
$149$	−17.2203	−1.41074	−0.705371	−	0.708838i	$-0.749220\pi$
$149$	−17.2203	−1.41074	−0.705371	+	0.708838i	$0.749220\pi$
$150$	−18.6927	−1.52625
$151$	−13.7096	−1.11567	−0.557837	−	0.829950i	$-0.688369\pi$
$151$	−13.7096	−1.11567	−0.557837	+	0.829950i	$0.688369\pi$
$152$	−22.3408	−1.81208
$153$	−1.20600	−0.0974996
$154$	−34.1788	−2.75420
$155$	11.9286	0.958125
$156$	30.2183	2.41940
$157$	15.2208	1.21475	0.607374	−	0.794416i	$-0.292223\pi$
$157$	15.2208	1.21475	0.607374	+	0.794416i	$0.292223\pi$
$158$	31.8628	2.53486
$159$	5.97634	0.473955
$160$	16.9163	1.33735
$161$	6.49671	0.512012
$162$	−2.53542	−0.199201
$163$	−4.75017	−0.372062	−0.186031	−	0.982544i	$-0.559563\pi$
$163$	−4.75017	−0.372062	−0.186031	+	0.982544i	$0.559563\pi$
$164$	−27.2125	−2.12494
$165$	14.1112	1.09856
$166$	−13.8433	−1.07445
$167$	19.5359	1.51174	0.755868	−	0.654724i	$-0.227215\pi$
$167$	19.5359	1.51174	0.755868	+	0.654724i	$0.227215\pi$
$168$	20.6887	1.59616
$169$	33.5648	2.58191
$170$	−10.7555	−0.824906
$171$	3.62861	0.277487
$172$	−30.0624	−2.29224
$173$	−1.15453	−0.0877775	−0.0438888	−	0.999036i	$-0.513975\pi$
$173$	−1.15453	−0.0877775	−0.0438888	+	0.999036i	$0.513975\pi$
$174$	1.30348	0.0988162
$175$	−24.7740	−1.87274
$176$	−27.0932	−2.04223
$177$	11.8051	0.887323
$178$	−10.2488	−0.768180
$179$	18.3716	1.37316	0.686578	−	0.727056i	$-0.259112\pi$
$179$	18.3716	1.37316	0.686578	+	0.727056i	$0.259112\pi$
$180$	−15.5766	−1.16101
$181$	15.1505	1.12613	0.563063	−	0.826414i	$-0.309623\pi$
$181$	15.1505	1.12613	0.563063	+	0.826414i	$0.309623\pi$
$182$	58.1369	4.30940
$183$	−3.31257	−0.244872
$184$	11.9036	0.877543
$185$	0.140311	0.0103159
$186$	8.59817	0.630449
$187$	4.83817	0.353802
$188$	−35.2845	−2.57339
$189$	−3.36027	−0.244424
$190$	32.3609	2.34771
$191$	19.6806	1.42404	0.712019	−	0.702161i	$-0.247781\pi$
$191$	19.6806	1.42404	0.712019	+	0.702161i	$0.247781\pi$
$192$	−1.31361	−0.0948013
$193$	13.9896	1.00699	0.503495	−	0.863998i	$-0.332047\pi$
$193$	13.9896	1.00699	0.503495	+	0.863998i	$0.332047\pi$
$194$	39.2076	2.81494
$195$	−24.0027	−1.71887
$196$	19.0038	1.35742
$197$	27.5635	1.96382	0.981908	−	0.189357i	$-0.0606405\pi$
$197$	27.5635	1.96382	0.981908	+	0.189357i	$0.0606405\pi$
$198$	10.1714	0.722852
$199$	13.5820	0.962801	0.481400	−	0.876501i	$-0.340128\pi$
$199$	13.5820	0.962801	0.481400	+	0.876501i	$0.340128\pi$
$200$	−45.3921	−3.20971
$201$	−5.06319	−0.357130
$202$	−4.77506	−0.335972
$203$	1.72754	0.121249
$204$	−5.34059	−0.373916
$205$	21.6152	1.50967
$206$	−1.40250	−0.0977169
$207$	−1.93339	−0.134380
$208$	46.0847	3.19540
$209$	−14.5571	−1.00693
$210$	−29.9678	−2.06797
$211$	23.3771	1.60934	0.804672	−	0.593719i	$-0.202341\pi$
$211$	23.3771	1.60934	0.804672	+	0.593719i	$0.202341\pi$
$212$	26.4652	1.81764
$213$	−0.302256	−0.0207102
$214$	−6.22275	−0.425379
$215$	23.8789	1.62853
$216$	−6.15684	−0.418920
$217$	11.3954	0.773573
$218$	27.6730	1.87426
$219$	−0.626308	−0.0423219
$220$	62.4891	4.21302
$221$	−8.22957	−0.553581
$222$	0.101137	0.00678789
$223$	−2.58841	−0.173333	−0.0866665	−	0.996237i	$-0.527621\pi$
$223$	−2.58841	−0.173333	−0.0866665	+	0.996237i	$0.527621\pi$
$224$	16.1603	1.07975
$225$	7.37263	0.491509
$226$	52.6532	3.50244
$227$	−7.36852	−0.489066	−0.244533	−	0.969641i	$-0.578635\pi$
$227$	−7.36852	−0.489066	−0.244533	+	0.969641i	$0.578635\pi$
$228$	16.0687	1.06418
$229$	−17.1180	−1.13119	−0.565595	−	0.824683i	$-0.691353\pi$
$229$	−17.1180	−1.13119	−0.565595	+	0.824683i	$0.691353\pi$
$230$	−17.2425	−1.13693
$231$	13.4805	0.886954
$232$	3.16528	0.207811
$233$	−9.77167	−0.640163	−0.320082	−	0.947390i	$-0.603710\pi$
$233$	−9.77167	−0.640163	−0.320082	+	0.947390i	$0.603710\pi$
$234$	−17.3013	−1.13102
$235$	28.0269	1.82827
$236$	52.2768	3.40293
$237$	−12.5671	−0.816319
$238$	−10.2748	−0.666014
$239$	−28.9643	−1.87354	−0.936772	−	0.349941i	$-0.886202\pi$
$239$	−28.9643	−1.87354	−0.936772	+	0.349941i	$0.886202\pi$
$240$	−23.7552	−1.53339
$241$	−28.5089	−1.83642	−0.918209	−	0.396097i	$-0.870364\pi$
$241$	−28.5089	−1.83642	−0.918209	+	0.396097i	$0.870364\pi$
$242$	−12.9156	−0.830244
$243$	1.00000	0.0641500
$244$	−14.6692	−0.939099
$245$	−15.0949	−0.964380
$246$	15.5803	0.993365
$247$	24.7611	1.57551
$248$	20.8793	1.32583
$249$	5.45996	0.346011
$250$	21.1598	1.33826
$251$	9.42270	0.594755	0.297378	−	0.954760i	$-0.403888\pi$
$251$	9.42270	0.594755	0.297378	+	0.954760i	$0.403888\pi$
$252$	−14.8804	−0.937377
$253$	7.75625	0.487631
$254$	−27.2373	−1.70902
$255$	4.24209	0.265650
$256$	−30.2038	−1.88774
$257$	12.2963	0.767022	0.383511	−	0.923536i	$-0.374715\pi$
$257$	12.2963	0.767022	0.383511	+	0.923536i	$0.374715\pi$
$258$	17.2121	1.07158
$259$	0.134040	0.00832887
$260$	−106.292	−6.59195
$261$	−0.514107	−0.0318224
$262$	9.39259	0.580276
$263$	19.7512	1.21791	0.608955	−	0.793205i	$-0.291589\pi$
$263$	19.7512	1.21791	0.608955	+	0.793205i	$0.291589\pi$
$264$	24.6997	1.52016
$265$	−21.0216	−1.29135
$266$	30.9146	1.89550
$267$	4.04225	0.247382
$268$	−22.4215	−1.36961
$269$	5.56143	0.339086	0.169543	−	0.985523i	$-0.445771\pi$
$269$	5.56143	0.339086	0.169543	+	0.985523i	$0.445771\pi$
$270$	8.91826	0.542748
$271$	9.24452	0.561565	0.280782	−	0.959771i	$-0.409406\pi$
$271$	9.24452	0.561565	0.280782	+	0.959771i	$0.409406\pi$
$272$	−8.14473	−0.493847
$273$	−22.9299	−1.38778
$274$	56.2747	3.39968
$275$	−29.5771	−1.78357
$276$	−8.56169	−0.515353
$277$	−1.60736	−0.0965768	−0.0482884	−	0.998833i	$-0.515377\pi$
$277$	−1.60736	−0.0965768	−0.0482884	+	0.998833i	$0.515377\pi$
$278$	38.6960	2.32083
$279$	−3.39123	−0.203027
$280$	−72.7718	−4.34895
$281$	−18.1449	−1.08243	−0.541217	−	0.840883i	$-0.682036\pi$
$281$	−18.1449	−1.08243	−0.541217	+	0.840883i	$0.682036\pi$
$282$	20.2019	1.20301
$283$	17.6483	1.04908	0.524542	−	0.851384i	$-0.324236\pi$
$283$	17.6483	1.04908	0.524542	+	0.851384i	$0.324236\pi$
$284$	−1.33849	−0.0794248
$285$	−12.7636	−0.756048
$286$	69.4082	4.10419
$287$	20.6491	1.21888
$288$	−4.80922	−0.283386
$289$	−15.5456	−0.914445
$290$	−4.58494	−0.269237
$291$	−15.4640	−0.906514
$292$	−2.77350	−0.162307
$293$	−19.9669	−1.16648	−0.583240	−	0.812300i	$-0.698215\pi$
$293$	−19.9669	−1.16648	−0.583240	+	0.812300i	$0.698215\pi$
$294$	−10.8805	−0.634565
$295$	−41.5240	−2.41762
$296$	0.245595	0.0142749
$297$	−4.01174	−0.232785
$298$	43.6607	2.52919
$299$	−13.1931	−0.762978
$300$	32.6485	1.88496
$301$	22.8117	1.31484
$302$	34.7597	2.00019
$303$	1.88334	0.108195
$304$	24.5058	1.40550
$305$	11.6519	0.667186
$306$	3.05772	0.174798
$307$	22.9399	1.30925	0.654624	−	0.755955i	$-0.272827\pi$
$307$	22.9399	1.30925	0.654624	+	0.755955i	$0.272827\pi$
$308$	59.6963	3.40151
$309$	0.553164	0.0314684
$310$	−30.2439	−1.71774
$311$	−2.26730	−0.128567	−0.0642833	−	0.997932i	$-0.520476\pi$
$311$	−2.26730	−0.128567	−0.0642833	+	0.997932i	$0.520476\pi$
$312$	−42.0133	−2.37853
$313$	−4.01474	−0.226926	−0.113463	−	0.993542i	$-0.536194\pi$
$313$	−4.01474	−0.226926	−0.113463	+	0.993542i	$0.536194\pi$
$314$	−38.5910	−2.17781
$315$	11.8197	0.665963
$316$	−55.6512	−3.13062
$317$	−23.4560	−1.31742	−0.658709	−	0.752398i	$-0.728897\pi$
$317$	−23.4560	−1.31742	−0.658709	+	0.752398i	$0.728897\pi$
$318$	−15.1525	−0.849711
$319$	2.06246	0.115476
$320$	4.62057	0.258298
$321$	2.45433	0.136987
$322$	−16.4719	−0.917941
$323$	−4.37612	−0.243494
$324$	4.42834	0.246019
$325$	50.3097	2.79068
$326$	12.0437	0.667037
$327$	−10.9146	−0.603579
$328$	37.8343	2.08905
$329$	26.7743	1.47611
$330$	−35.7778	−1.96950
$331$	29.5244	1.62281	0.811404	−	0.584485i	$-0.198703\pi$
$331$	29.5244	1.62281	0.811404	+	0.584485i	$0.198703\pi$
$332$	24.1785	1.32697
$333$	−0.0398898	−0.00218595
$334$	−49.5317	−2.71026
$335$	17.8097	0.973046
$336$	−22.6935	−1.23803
$337$	−7.70971	−0.419975	−0.209987	−	0.977704i	$-0.567342\pi$
$337$	−7.70971	−0.419975	−0.209987	+	0.977704i	$0.567342\pi$
$338$	−85.1007	−4.62887
$339$	−20.7671	−1.12791
$340$	18.7854	1.01878
$341$	13.6047	0.736737
$342$	−9.20004	−0.497481
$343$	9.10159	0.491440
$344$	41.7967	2.25353
$345$	6.80065	0.366134
$346$	2.92722	0.157368
$347$	30.8214	1.65458	0.827290	−	0.561774i	$-0.189881\pi$
$347$	30.8214	1.65458	0.827290	+	0.561774i	$0.189881\pi$
$348$	−2.27664	−0.122041
$349$	13.3250	0.713269	0.356635	−	0.934244i	$-0.383924\pi$
$349$	13.3250	0.713269	0.356635	+	0.934244i	$0.383924\pi$
$350$	62.8125	3.35747
$351$	6.82384	0.364230
$352$	19.2933	1.02834
$353$	19.4183	1.03353	0.516765	−	0.856127i	$-0.327136\pi$
$353$	19.4183	1.03353	0.516765	+	0.856127i	$0.327136\pi$
$354$	−29.9308	−1.59080
$355$	1.06318	0.0564276
$356$	17.9005	0.948722
$357$	4.05249	0.214481
$358$	−46.5796	−2.46181
$359$	22.8061	1.20366	0.601830	−	0.798624i	$-0.294439\pi$
$359$	22.8061	1.20366	0.601830	+	0.798624i	$0.294439\pi$
$360$	21.6565	1.14140
$361$	−5.83317	−0.307009
$362$	−38.4127	−2.01893
$363$	5.09406	0.267369
$364$	−101.541	−5.32222
$365$	2.20302	0.115311
$366$	8.39875	0.439010
$367$	18.5056	0.965983	0.482992	−	0.875625i	$-0.339550\pi$
$367$	18.5056	0.965983	0.482992	+	0.875625i	$0.339550\pi$
$368$	−13.0571	−0.680649
$369$	−6.14508	−0.319900
$370$	−0.355748	−0.0184944
$371$	−20.0821	−1.04261
$372$	−15.0175	−0.778621
$373$	20.1991	1.04587	0.522935	−	0.852372i	$-0.324837\pi$
$373$	20.1991	1.04587	0.522935	+	0.852372i	$0.324837\pi$
$374$	−12.2668	−0.634300
$375$	−8.34568	−0.430969
$376$	49.0570	2.52992
$377$	−3.50818	−0.180681
$378$	8.51968	0.438205
$379$	−9.24886	−0.475082	−0.237541	−	0.971378i	$-0.576341\pi$
$379$	−9.24886	−0.475082	−0.237541	+	0.971378i	$0.576341\pi$
$380$	−56.5213	−2.89948
$381$	10.7427	0.550366
$382$	−49.8985	−2.55303
$383$	13.0098	0.664772	0.332386	−	0.943143i	$-0.392146\pi$
$383$	13.0098	0.664772	0.332386	+	0.943143i	$0.392146\pi$
$384$	12.9490	0.660800
$385$	−47.4174	−2.41662
$386$	−35.4694	−1.80534
$387$	−6.78865	−0.345087
$388$	−68.4796	−3.47653
$389$	−5.57048	−0.282435	−0.141217	−	0.989979i	$-0.545102\pi$
$389$	−5.57048	−0.282435	−0.141217	+	0.989979i	$0.545102\pi$
$390$	60.8568	3.08160
$391$	2.33167	0.117918
$392$	−26.4215	−1.33449
$393$	−3.70456	−0.186870
$394$	−69.8849	−3.52075
$395$	44.2044	2.22416
$396$	−17.7653	−0.892742
$397$	4.64551	0.233151	0.116576	−	0.993182i	$-0.462808\pi$
$397$	4.64551	0.233151	0.116576	+	0.993182i	$0.462808\pi$
$398$	−34.4360	−1.72612
$399$	−12.1931	−0.610419
$400$	49.7910	2.48955
$401$	−7.26387	−0.362740	−0.181370	−	0.983415i	$-0.558053\pi$
$401$	−7.26387	−0.362740	−0.181370	+	0.983415i	$0.558053\pi$
$402$	12.8373	0.640266
$403$	−23.1412	−1.15274
$404$	8.34008	0.414934
$405$	−3.51748	−0.174785
$406$	−4.38003	−0.217377
$407$	0.160028	0.00793227
$408$	7.42517	0.367601
$409$	−19.5731	−0.967829	−0.483915	−	0.875115i	$-0.660785\pi$
$409$	−19.5731	−0.967829	−0.483915	+	0.875115i	$0.660785\pi$
$410$	−54.8034	−2.70655
$411$	−22.1954	−1.09482
$412$	2.44960	0.120683
$413$	−39.6682	−1.95195
$414$	4.90194	0.240917
$415$	−19.2053	−0.942750
$416$	−32.8173	−1.60900
$417$	−15.2622	−0.747392
$418$	36.9082	1.80524
$419$	7.90993	0.386425	0.193213	−	0.981157i	$-0.438109\pi$
$419$	7.90993	0.386425	0.193213	+	0.981157i	$0.438109\pi$
$420$	52.3415	2.55400
$421$	−4.12684	−0.201130	−0.100565	−	0.994931i	$-0.532065\pi$
$421$	−4.12684	−0.201130	−0.100565	+	0.994931i	$0.532065\pi$
$422$	−59.2706	−2.88525
$423$	−7.96789	−0.387412
$424$	−36.7954	−1.78694
$425$	−8.89142	−0.431297
$426$	0.766345	0.0371295
$427$	11.1311	0.538674
$428$	10.8686	0.525354
$429$	−27.3755	−1.32170
$430$	−60.5430	−2.91964
$431$	0.336856	0.0162258	0.00811290	−	0.999967i	$-0.497418\pi$
$431$	0.336856	0.0162258	0.00811290	+	0.999967i	$0.497418\pi$
$432$	6.75349	0.324927
$433$	−20.7620	−0.997758	−0.498879	−	0.866672i	$-0.666255\pi$
$433$	−20.7620	−0.997758	−0.498879	+	0.866672i	$0.666255\pi$
$434$	−28.8922	−1.38687
$435$	1.80836	0.0867042
$436$	−48.3335	−2.31475
$437$	−7.01552	−0.335598
$438$	1.58795	0.0758752
$439$	−7.71167	−0.368058	−0.184029	−	0.982921i	$-0.558914\pi$
$439$	−7.71167	−0.368058	−0.184029	+	0.982921i	$0.558914\pi$
$440$	−86.8804	−4.14186
$441$	4.29141	0.204353
$442$	20.8654	0.992465
$443$	2.60908	0.123961	0.0619805	−	0.998077i	$-0.480258\pi$
$443$	2.60908	0.123961	0.0619805	+	0.998077i	$0.480258\pi$
$444$	−0.176645	−0.00838322
$445$	−14.2185	−0.674023
$446$	6.56271	0.310753
$447$	−17.2203	−0.814493
$448$	4.41407	0.208545
$449$	−24.3552	−1.14939	−0.574696	−	0.818367i	$-0.694880\pi$
$449$	−24.3552	−1.14939	−0.574696	+	0.818367i	$0.694880\pi$
$450$	−18.6927	−0.881182
$451$	24.6524	1.16084
$452$	−91.9635	−4.32560
$453$	−13.7096	−0.644135
$454$	18.6823	0.876802
$455$	80.6555	3.78119
$456$	−22.3408	−1.04620
$457$	3.74866	0.175355	0.0876776	−	0.996149i	$-0.472055\pi$
$457$	3.74866	0.175355	0.0876776	+	0.996149i	$0.472055\pi$
$458$	43.4013	2.02801
$459$	−1.20600	−0.0562914
$460$	30.1155	1.40414
$461$	28.3194	1.31897	0.659483	−	0.751719i	$-0.270775\pi$
$461$	28.3194	1.31897	0.659483	+	0.751719i	$0.270775\pi$
$462$	−34.1788	−1.59014
$463$	9.01529	0.418976	0.209488	−	0.977811i	$-0.432820\pi$
$463$	9.01529	0.418976	0.209488	+	0.977811i	$0.432820\pi$
$464$	−3.47202	−0.161184
$465$	11.9286	0.553174
$466$	24.7753	1.14769
$467$	−19.7299	−0.912991	−0.456495	−	0.889726i	$-0.650895\pi$
$467$	−19.7299	−0.912991	−0.456495	+	0.889726i	$0.650895\pi$
$468$	30.2183	1.39684
$469$	17.0137	0.785619
$470$	−71.0597	−3.27774
$471$	15.2208	0.701336
$472$	−72.6820	−3.34546
$473$	27.2343	1.25224
$474$	31.8628	1.46350
$475$	26.7524	1.22749
$476$	17.9458	0.822545
$477$	5.97634	0.273638
$478$	73.4365	3.35891
$479$	7.67845	0.350837	0.175419	−	0.984494i	$-0.443872\pi$
$479$	7.67845	0.350837	0.175419	+	0.984494i	$0.443872\pi$
$480$	16.9163	0.772120
$481$	−0.272202	−0.0124113
$482$	72.2818	3.29235
$483$	6.49671	0.295610
$484$	22.5582	1.02537
$485$	54.3941	2.46991
$486$	−2.53542	−0.115009
$487$	11.4616	0.519377	0.259688	−	0.965693i	$-0.416380\pi$
$487$	11.4616	0.519377	0.259688	+	0.965693i	$0.416380\pi$
$488$	20.3950	0.923238
$489$	−4.75017	−0.214810
$490$	38.2719	1.72895
$491$	10.9627	0.494742	0.247371	−	0.968921i	$-0.420433\pi$
$491$	10.9627	0.494742	0.247371	+	0.968921i	$0.420433\pi$
$492$	−27.2125	−1.22683
$493$	0.620015	0.0279241
$494$	−62.7796	−2.82459
$495$	14.1112	0.634251
$496$	−22.9026	−1.02836
$497$	1.01566	0.0455586
$498$	−13.8433	−0.620332
$499$	20.0623	0.898112	0.449056	−	0.893504i	$-0.351760\pi$
$499$	20.0623	0.898112	0.449056	+	0.893504i	$0.351760\pi$
$500$	−36.9575	−1.65279
$501$	19.5359	0.872801
$502$	−23.8905	−1.06628
$503$	−25.0786	−1.11820	−0.559100	−	0.829100i	$-0.688853\pi$
$503$	−25.0786	−1.11820	−0.559100	+	0.829100i	$0.688853\pi$
$504$	20.6887	0.921546
$505$	−6.62461	−0.294791
$506$	−19.6653	−0.874230
$507$	33.5648	1.49066
$508$	47.5724	2.11068
$509$	5.34801	0.237046	0.118523	−	0.992951i	$-0.462184\pi$
$509$	5.34801	0.237046	0.118523	+	0.992951i	$0.462184\pi$
$510$	−10.7555	−0.476259
$511$	2.10456	0.0931003
$512$	50.6813	2.23982
$513$	3.62861	0.160207
$514$	−31.1763	−1.37513
$515$	−1.94574	−0.0857396
$516$	−30.0624	−1.32343
$517$	31.9651	1.40582
$518$	−0.339848	−0.0149321
$519$	−1.15453	−0.0506784
$520$	147.781	6.48062
$521$	14.0294	0.614639	0.307319	−	0.951606i	$-0.400568\pi$
$521$	14.0294	0.614639	0.307319	+	0.951606i	$0.400568\pi$
$522$	1.30348	0.0570516
$523$	19.1041	0.835363	0.417682	−	0.908594i	$-0.362843\pi$
$523$	19.1041	0.835363	0.417682	+	0.908594i	$0.362843\pi$
$524$	−16.4050	−0.716657
$525$	−24.7740	−1.08123
$526$	−50.0774	−2.18348
$527$	4.08983	0.178156
$528$	−27.0932	−1.17908
$529$	−19.2620	−0.837479
$530$	53.2986	2.31514
$531$	11.8051	0.512296
$532$	−53.9952	−2.34099
$533$	−41.9330	−1.81632
$534$	−10.2488	−0.443509
$535$	−8.63305	−0.373239
$536$	31.1733	1.34648
$537$	18.3716	0.792792
$538$	−14.1005	−0.607917
$539$	−17.2160	−0.741547
$540$	−15.5766	−0.670309
$541$	6.92603	0.297773	0.148887	−	0.988854i	$-0.452431\pi$
$541$	6.92603	0.297773	0.148887	+	0.988854i	$0.452431\pi$
$542$	−23.4387	−1.00678
$543$	15.1505	0.650169
$544$	5.79993	0.248670
$545$	38.3918	1.64452
$546$	58.1369	2.48803
$547$	−5.00941	−0.214187	−0.107093	−	0.994249i	$-0.534154\pi$
$547$	−5.00941	−0.214187	−0.107093	+	0.994249i	$0.534154\pi$
$548$	−98.2889	−4.19869
$549$	−3.31257	−0.141377
$550$	74.9902	3.19759
$551$	−1.86550	−0.0794728
$552$	11.9036	0.506650
$553$	42.2287	1.79575
$554$	4.07532	0.173144
$555$	0.140311	0.00595589
$556$	−67.5860	−2.86629
$557$	−24.7818	−1.05004	−0.525018	−	0.851091i	$-0.675942\pi$
$557$	−24.7818	−1.05004	−0.525018	+	0.851091i	$0.675942\pi$
$558$	8.59817	0.363990
$559$	−46.3247	−1.95933
$560$	79.8240	3.37318
$561$	4.83817	0.204268
$562$	46.0048	1.94060
$563$	35.1596	1.48180	0.740900	−	0.671615i	$-0.234399\pi$
$563$	35.1596	1.48180	0.740900	+	0.671615i	$0.234399\pi$
$564$	−35.2845	−1.48575
$565$	73.0476	3.07314
$566$	−44.7459	−1.88081
$567$	−3.36027	−0.141118
$568$	1.86094	0.0780834
$569$	−33.8795	−1.42030	−0.710152	−	0.704049i	$-0.751374\pi$
$569$	−33.8795	−1.42030	−0.710152	+	0.704049i	$0.751374\pi$
$570$	32.3609	1.35545
$571$	23.2422	0.972657	0.486328	−	0.873776i	$-0.338336\pi$
$571$	23.2422	0.972657	0.486328	+	0.873776i	$0.338336\pi$
$572$	−121.228	−5.06879
$573$	19.6806	0.822168
$574$	−52.3541	−2.18522
$575$	−14.2542	−0.594440
$576$	−1.31361	−0.0547336
$577$	45.6999	1.90251	0.951257	−	0.308400i	$-0.0997936\pi$
$577$	45.6999	1.90251	0.951257	+	0.308400i	$0.0997936\pi$
$578$	39.4145	1.63943
$579$	13.9896	0.581386
$580$	8.00802	0.332515
$581$	−18.3469	−0.761159
$582$	39.2076	1.62521
$583$	−23.9755	−0.992965
$584$	3.85608	0.159566
$585$	−24.0027	−0.992389
$586$	50.6244	2.09128
$587$	5.98176	0.246894	0.123447	−	0.992351i	$-0.460605\pi$
$587$	5.98176	0.246894	0.123447	+	0.992351i	$0.460605\pi$
$588$	19.0038	0.783704
$589$	−12.3054	−0.507037
$590$	105.281	4.33434
$591$	27.5635	1.13381
$592$	−0.269395	−0.0110721
$593$	−9.53971	−0.391749	−0.195874	−	0.980629i	$-0.562755\pi$
$593$	−9.53971	−0.391749	−0.195874	+	0.980629i	$0.562755\pi$
$594$	10.1714	0.417339
$595$	−14.2546	−0.584380
$596$	−76.2573	−3.12362
$597$	13.5820	0.555873
$598$	33.4501	1.36788
$599$	−11.1188	−0.454301	−0.227151	−	0.973860i	$-0.572941\pi$
$599$	−11.1188	−0.454301	−0.227151	+	0.973860i	$0.572941\pi$
$600$	−45.3921	−1.85313
$601$	4.22825	0.172474	0.0862370	−	0.996275i	$-0.472516\pi$
$601$	4.22825	0.172474	0.0862370	+	0.996275i	$0.472516\pi$
$602$	−57.8372	−2.35727
$603$	−5.06319	−0.206189
$604$	−60.7109	−2.47029
$605$	−17.9182	−0.728480
$606$	−4.77506	−0.193974
$607$	31.4149	1.27509	0.637546	−	0.770413i	$-0.279950\pi$
$607$	31.4149	1.27509	0.637546	+	0.770413i	$0.279950\pi$
$608$	−17.4508	−0.707723
$609$	1.72754	0.0700034
$610$	−29.5424	−1.19614
$611$	−54.3716	−2.19964
$612$	−5.34059	−0.215880
$613$	−18.8508	−0.761377	−0.380689	−	0.924703i	$-0.624313\pi$
$613$	−18.8508	−0.761377	−0.380689	+	0.924703i	$0.624313\pi$
$614$	−58.1621	−2.34723
$615$	21.6152	0.871607
$616$	−82.9975	−3.34406
$617$	25.3035	1.01868	0.509340	−	0.860565i	$-0.329889\pi$
$617$	25.3035	1.01868	0.509340	+	0.860565i	$0.329889\pi$
$618$	−1.40250	−0.0564169
$619$	25.9256	1.04204	0.521018	−	0.853546i	$-0.325552\pi$
$619$	25.9256	1.04204	0.521018	+	0.853546i	$0.325552\pi$
$620$	52.8237	2.12145
$621$	−1.93339	−0.0775842
$622$	5.74855	0.230496
$623$	−13.5831	−0.544194
$624$	46.0847	1.84487
$625$	−7.50745	−0.300298
$626$	10.1790	0.406836
$627$	−14.5571	−0.581353
$628$	67.4026	2.68966
$629$	0.0481072	0.00191816
$630$	−29.9678	−1.19394
$631$	12.5198	0.498406	0.249203	−	0.968451i	$-0.419831\pi$
$631$	12.5198	0.498406	0.249203	+	0.968451i	$0.419831\pi$
$632$	77.3735	3.07775
$633$	23.3771	0.929155
$634$	59.4706	2.36188
$635$	−37.7872	−1.49954
$636$	26.4652	1.04942
$637$	29.2839	1.16027
$638$	−5.22921	−0.207026
$639$	−0.302256	−0.0119571
$640$	−45.5477	−1.80043
$641$	−8.26508	−0.326451	−0.163226	−	0.986589i	$-0.552190\pi$
$641$	−8.26508	−0.326451	−0.163226	+	0.986589i	$0.552190\pi$
$642$	−6.22275	−0.245592
$643$	7.38544	0.291253	0.145627	−	0.989340i	$-0.453480\pi$
$643$	7.38544	0.291253	0.145627	+	0.989340i	$0.453480\pi$
$644$	28.7696	1.13368
$645$	23.8789	0.940232
$646$	11.0953	0.436538
$647$	13.0663	0.513688	0.256844	−	0.966453i	$-0.417317\pi$
$647$	13.0663	0.513688	0.256844	+	0.966453i	$0.417317\pi$
$648$	−6.15684	−0.241864
$649$	−47.3589	−1.85900
$650$	−127.556	−5.00316
$651$	11.3954	0.446622
$652$	−21.0354	−0.823808
$653$	−15.1098	−0.591292	−0.295646	−	0.955298i	$-0.595535\pi$
$653$	−15.1098	−0.591292	−0.295646	+	0.955298i	$0.595535\pi$
$654$	27.6730	1.08210
$655$	13.0307	0.509151
$656$	−41.5007	−1.62033
$657$	−0.626308	−0.0244346
$658$	−67.8839	−2.64639
$659$	50.2221	1.95637	0.978187	−	0.207726i	$-0.0666063\pi$
$659$	50.2221	1.95637	0.978187	+	0.207726i	$0.0666063\pi$
$660$	62.4891	2.43239
$661$	18.8610	0.733607	0.366803	−	0.930298i	$-0.380452\pi$
$661$	18.8610	0.733607	0.366803	+	0.930298i	$0.380452\pi$
$662$	−74.8567	−2.90939
$663$	−8.22957	−0.319610
$664$	−33.6161	−1.30456
$665$	42.8890	1.66316
$666$	0.101137	0.00391899
$667$	0.993969	0.0384866
$668$	86.5117	3.34724
$669$	−2.58841	−0.100074
$670$	−45.1549	−1.74449
$671$	13.2892	0.513023
$672$	16.1603	0.623396
$673$	18.6239	0.717898	0.358949	−	0.933357i	$-0.383135\pi$
$673$	18.6239	0.717898	0.358949	+	0.933357i	$0.383135\pi$
$674$	19.5473	0.752935
$675$	7.37263	0.283773
$676$	148.636	5.71677
$677$	28.5218	1.09618	0.548090	−	0.836419i	$-0.315355\pi$
$677$	28.5218	1.09618	0.548090	+	0.836419i	$0.315355\pi$
$678$	52.6532	2.02213
$679$	51.9631	1.99416
$680$	−26.1179	−1.00157
$681$	−7.36852	−0.282362
$682$	−34.4936	−1.32083
$683$	8.71290	0.333390	0.166695	−	0.986009i	$-0.446690\pi$
$683$	8.71290	0.333390	0.166695	+	0.986009i	$0.446690\pi$
$684$	16.0687	0.614403
$685$	78.0719	2.98297
$686$	−23.0763	−0.881058
$687$	−17.1180	−0.653093
$688$	−45.8471	−1.74790
$689$	40.7816	1.55365
$690$	−17.2425	−0.656410
$691$	−0.563817	−0.0214486	−0.0107243	−	0.999942i	$-0.503414\pi$
$691$	−0.563817	−0.0214486	−0.0107243	+	0.999942i	$0.503414\pi$
$692$	−5.11266	−0.194354
$693$	13.4805	0.512083
$694$	−78.1451	−2.96635
$695$	53.6843	2.03636
$696$	3.16528	0.119980
$697$	7.41098	0.280711
$698$	−33.7843	−1.27876
$699$	−9.77167	−0.369599
$700$	−109.708	−4.14656
$701$	−26.6816	−1.00775	−0.503875	−	0.863776i	$-0.668093\pi$
$701$	−26.6816	−1.00775	−0.503875	+	0.863776i	$0.668093\pi$
$702$	−17.3013	−0.652994
$703$	−0.144745	−0.00545915
$704$	5.26984	0.198615
$705$	28.0269	1.05555
$706$	−49.2334	−1.85292
$707$	−6.32854	−0.238009
$708$	52.2768	1.96468
$709$	0.604368	0.0226975	0.0113488	−	0.999936i	$-0.496387\pi$
$709$	0.604368	0.0226975	0.0113488	+	0.999936i	$0.496387\pi$
$710$	−2.69560	−0.101164
$711$	−12.5671	−0.471302
$712$	−24.8875	−0.932699
$713$	6.55656	0.245545
$714$	−10.2748	−0.384523
$715$	96.2925	3.60114
$716$	81.3555	3.04040
$717$	−28.9643	−1.08169
$718$	−57.8229	−2.15793
$719$	−1.40483	−0.0523915	−0.0261957	−	0.999657i	$-0.508339\pi$
$719$	−1.40483	−0.0523915	−0.0261957	+	0.999657i	$0.508339\pi$
$720$	−23.7552	−0.885305
$721$	−1.85878	−0.0692246
$722$	14.7895	0.550409
$723$	−28.5089	−1.06026
$724$	67.0914	2.49343
$725$	−3.79032	−0.140769
$726$	−12.9156	−0.479342
$727$	−37.3115	−1.38381	−0.691904	−	0.721990i	$-0.743228\pi$
$727$	−37.3115	−1.38381	−0.691904	+	0.721990i	$0.743228\pi$
$728$	141.176	5.23233
$729$	1.00000	0.0370370
$730$	−5.58558	−0.206731
$731$	8.18714	0.302812
$732$	−14.6692	−0.542189
$733$	−32.2654	−1.19175	−0.595874	−	0.803078i	$-0.703194\pi$
$733$	−32.2654	−1.19175	−0.595874	+	0.803078i	$0.703194\pi$
$734$	−46.9193	−1.73182
$735$	−15.0949	−0.556785
$736$	9.29809	0.342732
$737$	20.3122	0.748210
$738$	15.5803	0.573520
$739$	−33.8011	−1.24339	−0.621696	−	0.783258i	$-0.713556\pi$
$739$	−33.8011	−1.24339	−0.621696	+	0.783258i	$0.713556\pi$
$740$	0.621346	0.0228411
$741$	24.7611	0.909621
$742$	50.9165	1.86920
$743$	15.2149	0.558179	0.279090	−	0.960265i	$-0.409967\pi$
$743$	15.2149	0.558179	0.279090	+	0.960265i	$0.409967\pi$
$744$	20.8793	0.765470
$745$	60.5720	2.21919
$746$	−51.2132	−1.87505
$747$	5.45996	0.199769
$748$	21.4250	0.783377
$749$	−8.24722	−0.301347
$750$	21.1598	0.772645
$751$	−8.95061	−0.326612	−0.163306	−	0.986575i	$-0.552216\pi$
$751$	−8.95061	−0.326612	−0.163306	+	0.986575i	$0.552216\pi$
$752$	−53.8110	−1.96229
$753$	9.42270	0.343382
$754$	8.89471	0.323926
$755$	48.2233	1.75503
$756$	−14.8804	−0.541195
$757$	−35.4130	−1.28711	−0.643554	−	0.765401i	$-0.722541\pi$
$757$	−35.4130	−1.28711	−0.643554	+	0.765401i	$0.722541\pi$
$758$	23.4497	0.851732
$759$	7.75625	0.281534
$760$	78.5832	2.85051
$761$	−53.3775	−1.93493	−0.967466	−	0.253002i	$-0.918582\pi$
$761$	−53.3775	−1.93493	−0.967466	+	0.253002i	$0.918582\pi$
$762$	−27.2373	−0.986702
$763$	36.6760	1.32776
$764$	87.1522	3.15306
$765$	4.24209	0.153373
$766$	−32.9854	−1.19181
$767$	80.5559	2.90870
$768$	−30.2038	−1.08989
$769$	−48.1959	−1.73799	−0.868995	−	0.494822i	$-0.835233\pi$
$769$	−48.1959	−1.73799	−0.868995	+	0.494822i	$0.835233\pi$
$770$	120.223	4.33253
$771$	12.2963	0.442841
$772$	61.9505	2.22965
$773$	35.2945	1.26945	0.634727	−	0.772736i	$-0.281112\pi$
$773$	35.2945	1.26945	0.634727	+	0.772736i	$0.281112\pi$
$774$	17.2121	0.618675
$775$	−25.0023	−0.898108
$776$	95.2092	3.41781
$777$	0.134040	0.00480868
$778$	14.1235	0.506352
$779$	−22.2981	−0.798912
$780$	−106.292	−3.80586
$781$	1.21257	0.0433892
$782$	−5.91176	−0.211404
$783$	−0.514107	−0.0183727
$784$	28.9820	1.03507
$785$	−53.5386	−1.91088
$786$	9.39259	0.335023
$787$	25.9011	0.923274	0.461637	−	0.887069i	$-0.347262\pi$
$787$	25.9011	0.923274	0.461637	+	0.887069i	$0.347262\pi$
$788$	122.060	4.34822
$789$	19.7512	0.703160
$790$	−112.076	−3.98750
$791$	69.7829	2.48120
$792$	24.6997	0.877664
$793$	−22.6045	−0.802708
$794$	−11.7783	−0.417996
$795$	−21.0216	−0.745560
$796$	60.1456	2.13180
$797$	28.2723	1.00146	0.500728	−	0.865605i	$-0.333066\pi$
$797$	28.2723	1.00146	0.500728	+	0.865605i	$0.333066\pi$
$798$	30.9146	1.09437
$799$	9.60930	0.339952
$800$	−35.4566	−1.25358
$801$	4.04225	0.142826
$802$	18.4169	0.650324
$803$	2.51258	0.0886671
$804$	−22.4215	−0.790746
$805$	−22.8520	−0.805427
$806$	58.6725	2.06665
$807$	5.56143	0.195772
$808$	−11.5954	−0.407926
$809$	6.33873	0.222858	0.111429	−	0.993772i	$-0.464457\pi$
$809$	6.33873	0.222858	0.111429	+	0.993772i	$0.464457\pi$
$810$	8.91826	0.313356
$811$	21.5035	0.755090	0.377545	−	0.925991i	$-0.376768\pi$
$811$	21.5035	0.755090	0.377545	+	0.925991i	$0.376768\pi$
$812$	7.65012	0.268467
$813$	9.24452	0.324220
$814$	−0.405736	−0.0142211
$815$	16.7086	0.585277
$816$	−8.14473	−0.285122
$817$	−24.6334	−0.861814
$818$	49.6261	1.73513
$819$	−22.9299	−0.801237
$820$	95.7192	3.34266
$821$	11.9305	0.416379	0.208189	−	0.978089i	$-0.433243\pi$
$821$	11.9305	0.416379	0.208189	+	0.978089i	$0.433243\pi$
$822$	56.2747	1.96280
$823$	11.1403	0.388327	0.194164	−	0.980969i	$-0.437801\pi$
$823$	11.1403	0.388327	0.194164	+	0.980969i	$0.437801\pi$
$824$	−3.40574	−0.118645
$825$	−29.5771	−1.02974
$826$	100.575	3.49947
$827$	6.61153	0.229905	0.114953	−	0.993371i	$-0.463328\pi$
$827$	6.61153	0.229905	0.114953	+	0.993371i	$0.463328\pi$
$828$	−8.56169	−0.297539
$829$	13.6895	0.475457	0.237728	−	0.971332i	$-0.423597\pi$
$829$	13.6895	0.475457	0.237728	+	0.971332i	$0.423597\pi$
$830$	48.6934	1.69017
$831$	−1.60736	−0.0557586
$832$	−8.96383	−0.310765
$833$	−5.17545	−0.179319
$834$	38.6960	1.33993
$835$	−68.7172	−2.37806
$836$	−64.4635	−2.22952
$837$	−3.39123	−0.117218
$838$	−20.0550	−0.692787
$839$	30.2023	1.04270	0.521349	−	0.853344i	$-0.325429\pi$
$839$	30.2023	1.04270	0.521349	+	0.853344i	$0.325429\pi$
$840$	−72.7718	−2.51087
$841$	−28.7357	−0.990886
$842$	10.4633	0.360587
$843$	−18.1449	−0.624943
$844$	103.522	3.56336
$845$	−118.063	−4.06150
$846$	20.2019	0.694556
$847$	−17.1174	−0.588161
$848$	40.3611	1.38601
$849$	17.6483	0.605689
$850$	22.5434	0.773234
$851$	0.0771225	0.00264372
$852$	−1.33849	−0.0458559
$853$	−6.35526	−0.217600	−0.108800	−	0.994064i	$-0.534701\pi$
$853$	−6.35526	−0.217600	−0.108800	+	0.994064i	$0.534701\pi$
$854$	−28.2221	−0.965740
$855$	−12.7636	−0.436504
$856$	−15.1109	−0.516481
$857$	41.5343	1.41878	0.709392	−	0.704815i	$-0.248970\pi$
$857$	41.5343	1.41878	0.709392	+	0.704815i	$0.248970\pi$
$858$	69.4082	2.36956
$859$	−56.5325	−1.92887	−0.964433	−	0.264328i	$-0.914850\pi$
$859$	−56.5325	−1.92887	−0.964433	+	0.264328i	$0.914850\pi$
$860$	105.744	3.60584
$861$	20.6491	0.703720
$862$	−0.854071	−0.0290898
$863$	33.0734	1.12583	0.562917	−	0.826514i	$-0.309679\pi$
$863$	33.0734	1.12583	0.562917	+	0.826514i	$0.309679\pi$
$864$	−4.80922	−0.163613
$865$	4.06104	0.138080
$866$	52.6403	1.78879
$867$	−15.5456	−0.527955
$868$	50.4628	1.71282
$869$	50.4158	1.71024
$870$	−4.58494	−0.155444
$871$	−34.5504	−1.17070
$872$	67.1995	2.27566
$873$	−15.4640	−0.523376
$874$	17.7873	0.601663
$875$	28.0437	0.948051
$876$	−2.77350	−0.0937079
$877$	28.6151	0.966263	0.483131	−	0.875548i	$-0.339499\pi$
$877$	28.6151	0.966263	0.483131	+	0.875548i	$0.339499\pi$
$878$	19.5523	0.659858
$879$	−19.9669	−0.673467
$880$	95.2998	3.21256
$881$	22.4935	0.757824	0.378912	−	0.925433i	$-0.376298\pi$
$881$	22.4935	0.757824	0.378912	+	0.925433i	$0.376298\pi$
$882$	−10.8805	−0.366366
$883$	−18.2723	−0.614913	−0.307457	−	0.951562i	$-0.599478\pi$
$883$	−18.2723	−0.614913	−0.307457	+	0.951562i	$0.599478\pi$
$884$	−36.4433	−1.22572
$885$	−41.5240	−1.39582
$886$	−6.61509	−0.222238
$887$	21.3562	0.717070	0.358535	−	0.933516i	$-0.383276\pi$
$887$	21.3562	0.717070	0.358535	+	0.933516i	$0.383276\pi$
$888$	0.245595	0.00824164
$889$	−36.0984	−1.21070
$890$	36.0499	1.20839
$891$	−4.01174	−0.134398
$892$	−11.4624	−0.383789
$893$	−28.9124	−0.967516
$894$	43.6607	1.46023
$895$	−64.6216	−2.16006
$896$	−43.5120	−1.45364
$897$	−13.1931	−0.440506
$898$	61.7506	2.06064
$899$	1.74345	0.0581474
$900$	32.6485	1.08828
$901$	−7.20748	−0.240116
$902$	−62.5042	−2.08116
$903$	22.8117	0.759126
$904$	127.860	4.25255
$905$	−53.2914	−1.77147
$906$	34.7597	1.15481
$907$	52.0349	1.72779	0.863895	−	0.503672i	$-0.168018\pi$
$907$	52.0349	1.72779	0.863895	+	0.503672i	$0.168018\pi$
$908$	−32.6303	−1.08287
$909$	1.88334	0.0624665
$910$	−204.495	−6.77895
$911$	−16.6628	−0.552063	−0.276032	−	0.961149i	$-0.589019\pi$
$911$	−16.6628	−0.552063	−0.276032	+	0.961149i	$0.589019\pi$
$912$	24.5058	0.811468
$913$	−21.9039	−0.724915
$914$	−9.50442	−0.314378
$915$	11.6519	0.385200
$916$	−75.8043	−2.50464
$917$	12.4483	0.411079
$918$	3.05772	0.100920
$919$	−31.9758	−1.05478	−0.527392	−	0.849622i	$-0.676830\pi$
$919$	−31.9758	−1.05478	−0.527392	+	0.849622i	$0.676830\pi$
$920$	−41.8705	−1.38043
$921$	22.9399	0.755894
$922$	−71.8015	−2.36466
$923$	−2.06255	−0.0678895
$924$	59.6963	1.96386
$925$	−0.294093	−0.00966971
$926$	−22.8575	−0.751144
$927$	0.553164	0.0181683
$928$	2.47245	0.0811623
$929$	−22.2640	−0.730459	−0.365230	−	0.930917i	$-0.619010\pi$
$929$	−22.2640	−0.730459	−0.365230	+	0.930917i	$0.619010\pi$
$930$	−30.2439	−0.991735
$931$	15.5719	0.510347
$932$	−43.2722	−1.41743
$933$	−2.26730	−0.0742280
$934$	50.0235	1.63682
$935$	−17.0181	−0.556553
$936$	−42.0133	−1.37325
$937$	21.9146	0.715919	0.357959	−	0.933737i	$-0.383473\pi$
$937$	21.9146	0.715919	0.357959	+	0.933737i	$0.383473\pi$
$938$	−43.1368	−1.40847
$939$	−4.01474	−0.131016
$940$	124.112	4.04810
$941$	20.1951	0.658343	0.329171	−	0.944270i	$-0.393231\pi$
$941$	20.1951	0.658343	0.329171	+	0.944270i	$0.393231\pi$
$942$	−38.5910	−1.25736
$943$	11.8808	0.386893
$944$	79.7254	2.59484
$945$	11.8197	0.384494
$946$	−69.0503	−2.24502
$947$	−40.5441	−1.31751	−0.658753	−	0.752359i	$-0.728916\pi$
$947$	−40.5441	−1.31751	−0.658753	+	0.752359i	$0.728916\pi$
$948$	−55.6512	−1.80747
$949$	−4.27382	−0.138734
$950$	−67.8286	−2.20065
$951$	−23.4560	−0.760612
$952$	−24.9506	−0.808653
$953$	53.2995	1.72654	0.863271	−	0.504742i	$-0.168412\pi$
$953$	53.2995	1.72654	0.863271	+	0.504742i	$0.168412\pi$
$954$	−15.1525	−0.490581
$955$	−69.2260	−2.24010
$956$	−128.264	−4.14834
$957$	2.06246	0.0666700
$958$	−19.4681	−0.628985
$959$	74.5827	2.40840
$960$	4.62057	0.149128
$961$	−19.4996	−0.629019
$962$	0.690144	0.0222511
$963$	2.45433	0.0790897
$964$	−126.247	−4.06614
$965$	−49.2079	−1.58406
$966$	−16.4719	−0.529973
$967$	0.354858	0.0114115	0.00570573	−	0.999984i	$-0.498184\pi$
$967$	0.354858	0.0114115	0.00570573	+	0.999984i	$0.498184\pi$
$968$	−31.3633	−1.00806
$969$	−4.37612	−0.140581
$970$	−137.912	−4.42808
$971$	−53.4749	−1.71609	−0.858046	−	0.513572i	$-0.828322\pi$
$971$	−53.4749	−1.71609	−0.858046	+	0.513572i	$0.828322\pi$
$972$	4.42834	0.142039
$973$	51.2850	1.64412
$974$	−29.0600	−0.931143
$975$	50.3097	1.61120
$976$	−22.3714	−0.716092
$977$	−49.0093	−1.56795	−0.783973	−	0.620795i	$-0.786810\pi$
$977$	−49.0093	−1.56795	−0.783973	+	0.620795i	$0.786810\pi$
$978$	12.0437	0.385114
$979$	−16.2165	−0.518281
$980$	−66.8454	−2.13530
$981$	−10.9146	−0.348476
$982$	−27.7951	−0.886978
$983$	13.1857	0.420558	0.210279	−	0.977641i	$-0.432563\pi$
$983$	13.1857	0.420558	0.210279	+	0.977641i	$0.432563\pi$
$984$	37.8343	1.20611
$985$	−96.9539	−3.08921
$986$	−1.57200	−0.0500625
$987$	26.7743	0.852234
$988$	109.650	3.48844
$989$	13.1251	0.417354
$990$	−35.7778	−1.13709
$991$	44.0472	1.39921	0.699603	−	0.714532i	$-0.253360\pi$
$991$	44.0472	1.39921	0.699603	+	0.714532i	$0.253360\pi$
$992$	16.3092	0.517816
$993$	29.5244	0.936929
$994$	−2.57512	−0.0816780
$995$	−47.7743	−1.51455
$996$	24.1785	0.766126
$997$	43.9505	1.39193	0.695964	−	0.718077i	$-0.254977\pi$
$997$	43.9505	1.39193	0.695964	+	0.718077i	$0.254977\pi$
$998$	−50.8663	−1.61014
$999$	−0.0398898	−0.00126206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.7	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.7	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53542 q^{2} +1.00000 q^{3} +4.42834 q^{4} -3.51748 q^{5} -2.53542 q^{6} -3.36027 q^{7} -6.15684 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.53542 q^{2} +1.00000 q^{3} +4.42834 q^{4} -3.51748 q^{5} -2.53542 q^{6} -3.36027 q^{7} -6.15684 q^{8} +1.00000 q^{9} +8.91826 q^{10} -4.01174 q^{11} +4.42834 q^{12} +6.82384 q^{13} +8.51968 q^{14} -3.51748 q^{15} +6.75349 q^{16} -1.20600 q^{17} -2.53542 q^{18} +3.62861 q^{19} -15.5766 q^{20} -3.36027 q^{21} +10.1714 q^{22} -1.93339 q^{23} -6.15684 q^{24} +7.37263 q^{25} -17.3013 q^{26} +1.00000 q^{27} -14.8804 q^{28} -0.514107 q^{29} +8.91826 q^{30} -3.39123 q^{31} -4.80922 q^{32} -4.01174 q^{33} +3.05772 q^{34} +11.8197 q^{35} +4.42834 q^{36} -0.0398898 q^{37} -9.20004 q^{38} +6.82384 q^{39} +21.6565 q^{40} -6.14508 q^{41} +8.51968 q^{42} -6.78865 q^{43} -17.7653 q^{44} -3.51748 q^{45} +4.90194 q^{46} -7.96789 q^{47} +6.75349 q^{48} +4.29141 q^{49} -18.6927 q^{50} -1.20600 q^{51} +30.2183 q^{52} +5.97634 q^{53} -2.53542 q^{54} +14.1112 q^{55} +20.6887 q^{56} +3.62861 q^{57} +1.30348 q^{58} +11.8051 q^{59} -15.5766 q^{60} -3.31257 q^{61} +8.59817 q^{62} -3.36027 q^{63} -1.31361 q^{64} -24.0027 q^{65} +10.1714 q^{66} -5.06319 q^{67} -5.34059 q^{68} -1.93339 q^{69} -29.9678 q^{70} -0.302256 q^{71} -6.15684 q^{72} -0.626308 q^{73} +0.101137 q^{74} +7.37263 q^{75} +16.0687 q^{76} +13.4805 q^{77} -17.3013 q^{78} -12.5671 q^{79} -23.7552 q^{80} +1.00000 q^{81} +15.5803 q^{82} +5.45996 q^{83} -14.8804 q^{84} +4.24209 q^{85} +17.2121 q^{86} -0.514107 q^{87} +24.6997 q^{88} +4.04225 q^{89} +8.91826 q^{90} -22.9299 q^{91} -8.56169 q^{92} -3.39123 q^{93} +20.2019 q^{94} -12.7636 q^{95} -4.80922 q^{96} -15.4640 q^{97} -10.8805 q^{98} -4.01174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

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