LMFDB - Embedded newform 6031.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40987 q^{2} -2.85971 q^{3} +3.80748 q^{4} +1.79940 q^{5} +6.89154 q^{6} +2.51983 q^{7} -4.35580 q^{8} +5.17794 q^{9} +O(q^{10})$	\(q-2.40987 q^{2} -2.85971 q^{3} +3.80748 q^{4} +1.79940 q^{5} +6.89154 q^{6} +2.51983 q^{7} -4.35580 q^{8} +5.17794 q^{9} -4.33633 q^{10} -5.37875 q^{11} -10.8883 q^{12} -3.80766 q^{13} -6.07246 q^{14} -5.14577 q^{15} +2.88196 q^{16} -3.07998 q^{17} -12.4782 q^{18} +2.50740 q^{19} +6.85120 q^{20} -7.20597 q^{21} +12.9621 q^{22} -3.21994 q^{23} +12.4563 q^{24} -1.76215 q^{25} +9.17598 q^{26} -6.22828 q^{27} +9.59419 q^{28} +2.35133 q^{29} +12.4007 q^{30} -0.00921845 q^{31} +1.76645 q^{32} +15.3817 q^{33} +7.42235 q^{34} +4.53418 q^{35} +19.7149 q^{36} +1.00000 q^{37} -6.04252 q^{38} +10.8888 q^{39} -7.83785 q^{40} -0.243772 q^{41} +17.3655 q^{42} +9.41105 q^{43} -20.4795 q^{44} +9.31721 q^{45} +7.75963 q^{46} +5.41949 q^{47} -8.24157 q^{48} -0.650480 q^{49} +4.24655 q^{50} +8.80784 q^{51} -14.4976 q^{52} +8.12195 q^{53} +15.0094 q^{54} -9.67855 q^{55} -10.9759 q^{56} -7.17044 q^{57} -5.66641 q^{58} -2.48189 q^{59} -19.5924 q^{60} -4.18194 q^{61} +0.0222153 q^{62} +13.0475 q^{63} -10.0208 q^{64} -6.85152 q^{65} -37.0679 q^{66} +3.24290 q^{67} -11.7270 q^{68} +9.20808 q^{69} -10.9268 q^{70} -4.67680 q^{71} -22.5541 q^{72} +14.4418 q^{73} -2.40987 q^{74} +5.03923 q^{75} +9.54689 q^{76} -13.5535 q^{77} -26.2406 q^{78} +11.0721 q^{79} +5.18581 q^{80} +2.27725 q^{81} +0.587460 q^{82} +7.90144 q^{83} -27.4366 q^{84} -5.54212 q^{85} -22.6794 q^{86} -6.72412 q^{87} +23.4288 q^{88} -14.1789 q^{89} -22.4533 q^{90} -9.59465 q^{91} -12.2598 q^{92} +0.0263621 q^{93} -13.0603 q^{94} +4.51183 q^{95} -5.05153 q^{96} +4.16949 q^{97} +1.56757 q^{98} -27.8509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.40987	−1.70404	−0.852018	−	0.523512i	$-0.824622\pi$
$2$	−2.40987	−1.70404	−0.852018	+	0.523512i	$0.824622\pi$
$3$	−2.85971	−1.65105	−0.825527	−	0.564362i	$-0.809122\pi$
$3$	−2.85971	−1.65105	−0.825527	+	0.564362i	$0.809122\pi$
$4$	3.80748	1.90374
$5$	1.79940	0.804718	0.402359	−	0.915482i	$-0.368190\pi$
$5$	1.79940	0.804718	0.402359	+	0.915482i	$0.368190\pi$
$6$	6.89154	2.81346
$7$	2.51983	0.952404	0.476202	−	0.879336i	$-0.342013\pi$
$7$	2.51983	0.952404	0.476202	+	0.879336i	$0.342013\pi$
$8$	−4.35580	−1.54001
$9$	5.17794	1.72598
$10$	−4.33633	−1.37127
$11$	−5.37875	−1.62176	−0.810878	−	0.585216i	$-0.801010\pi$
$11$	−5.37875	−1.62176	−0.810878	+	0.585216i	$0.801010\pi$
$12$	−10.8883	−3.14318
$13$	−3.80766	−1.05606	−0.528028	−	0.849227i	$-0.677068\pi$
$13$	−3.80766	−1.05606	−0.528028	+	0.849227i	$0.677068\pi$
$14$	−6.07246	−1.62293
$15$	−5.14577	−1.32863
$16$	2.88196	0.720490
$17$	−3.07998	−0.747004	−0.373502	−	0.927629i	$-0.621843\pi$
$17$	−3.07998	−0.747004	−0.373502	+	0.927629i	$0.621843\pi$
$18$	−12.4782	−2.94113
$19$	2.50740	0.575237	0.287619	−	0.957745i	$-0.407136\pi$
$19$	2.50740	0.575237	0.287619	+	0.957745i	$0.407136\pi$
$20$	6.85120	1.53197
$21$	−7.20597	−1.57247
$22$	12.9621	2.76353
$23$	−3.21994	−0.671403	−0.335701	−	0.941968i	$-0.608973\pi$
$23$	−3.21994	−0.671403	−0.335701	+	0.941968i	$0.608973\pi$
$24$	12.4563	2.54264
$25$	−1.76215	−0.352429
$26$	9.17598	1.79956
$27$	−6.22828	−1.19863
$28$	9.59419	1.81313
$29$	2.35133	0.436631	0.218316	−	0.975878i	$-0.429944\pi$
$29$	2.35133	0.436631	0.218316	+	0.975878i	$0.429944\pi$
$30$	12.4007	2.26404
$31$	−0.00921845	−0.00165568	−0.000827842	−	1.00000i	$-0.500264\pi$
$31$	−0.00921845	−0.00165568	−0.000827842		1.00000i	$0.500264\pi$
$32$	1.76645	0.312267
$33$	15.3817	2.67761
$34$	7.42235	1.27292
$35$	4.53418	0.766417
$36$	19.7149	3.28582
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−6.04252	−0.980225
$39$	10.8888	1.74361
$40$	−7.83785	−1.23927
$41$	−0.243772	−0.0380708	−0.0190354	−	0.999819i	$-0.506060\pi$
$41$	−0.243772	−0.0380708	−0.0190354	+	0.999819i	$0.506060\pi$
$42$	17.3655	2.67955
$43$	9.41105	1.43517	0.717586	−	0.696470i	$-0.245247\pi$
$43$	9.41105	1.43517	0.717586	+	0.696470i	$0.245247\pi$
$44$	−20.4795	−3.08740
$45$	9.31721	1.38893
$46$	7.75963	1.14410
$47$	5.41949	0.790513	0.395257	−	0.918571i	$-0.370656\pi$
$47$	5.41949	0.790513	0.395257	+	0.918571i	$0.370656\pi$
$48$	−8.24157	−1.18957
$49$	−0.650480	−0.0929257
$50$	4.24655	0.600553
$51$	8.80784	1.23334
$52$	−14.4976	−2.01046
$53$	8.12195	1.11564	0.557818	−	0.829964i	$-0.311639\pi$
$53$	8.12195	1.11564	0.557818	+	0.829964i	$0.311639\pi$
$54$	15.0094	2.04252
$55$	−9.67855	−1.30506
$56$	−10.9759	−1.46671
$57$	−7.17044	−0.949748
$58$	−5.66641	−0.744036
$59$	−2.48189	−0.323114	−0.161557	−	0.986863i	$-0.551652\pi$
$59$	−2.48189	−0.323114	−0.161557	+	0.986863i	$0.551652\pi$
$60$	−19.5924	−2.52937
$61$	−4.18194	−0.535442	−0.267721	−	0.963496i	$-0.586271\pi$
$61$	−4.18194	−0.535442	−0.267721	+	0.963496i	$0.586271\pi$
$62$	0.0222153	0.00282135
$63$	13.0475	1.64383
$64$	−10.0208	−1.25260
$65$	−6.85152	−0.849827
$66$	−37.0679	−4.56274
$67$	3.24290	0.396184	0.198092	−	0.980183i	$-0.436526\pi$
$67$	3.24290	0.396184	0.198092	+	0.980183i	$0.436526\pi$
$68$	−11.7270	−1.42210
$69$	9.20808	1.10852
$70$	−10.9268	−1.30600
$71$	−4.67680	−0.555034	−0.277517	−	0.960721i	$-0.589511\pi$
$71$	−4.67680	−0.555034	−0.277517	+	0.960721i	$0.589511\pi$
$72$	−22.5541	−2.65803
$73$	14.4418	1.69028	0.845142	−	0.534541i	$-0.179516\pi$
$73$	14.4418	1.69028	0.845142	+	0.534541i	$0.179516\pi$
$74$	−2.40987	−0.280142
$75$	5.03923	0.581880
$76$	9.54689	1.09510
$77$	−13.5535	−1.54457
$78$	−26.2406	−2.97117
$79$	11.0721	1.24571	0.622857	−	0.782336i	$-0.285972\pi$
$79$	11.0721	1.24571	0.622857	+	0.782336i	$0.285972\pi$
$80$	5.18581	0.579791
$81$	2.27725	0.253028
$82$	0.587460	0.0648741
$83$	7.90144	0.867296	0.433648	−	0.901082i	$-0.357226\pi$
$83$	7.90144	0.867296	0.433648	+	0.901082i	$0.357226\pi$
$84$	−27.4366	−2.99358
$85$	−5.54212	−0.601127
$86$	−22.6794	−2.44559
$87$	−6.72412	−0.720902
$88$	23.4288	2.49752
$89$	−14.1789	−1.50296	−0.751479	−	0.659756i	$-0.770659\pi$
$89$	−14.1789	−1.50296	−0.751479	+	0.659756i	$0.770659\pi$
$90$	−22.4533	−2.36678
$91$	−9.59465	−1.00579
$92$	−12.2598	−1.27818
$93$	0.0263621	0.00273362
$94$	−13.0603	−1.34706
$95$	4.51183	0.462904
$96$	−5.05153	−0.515570
$97$	4.16949	0.423348	0.211674	−	0.977340i	$-0.432109\pi$
$97$	4.16949	0.423348	0.211674	+	0.977340i	$0.432109\pi$
$98$	1.56757	0.158349
$99$	−27.8509	−2.79912
$100$	−6.70935	−0.670935
$101$	−13.7276	−1.36595	−0.682974	−	0.730443i	$-0.739314\pi$
$101$	−13.7276	−1.36595	−0.682974	+	0.730443i	$0.739314\pi$
$102$	−21.2258	−2.10166
$103$	−7.77715	−0.766305	−0.383153	−	0.923685i	$-0.625162\pi$
$103$	−7.77715	−0.766305	−0.383153	+	0.923685i	$0.625162\pi$
$104$	16.5854	1.62634
$105$	−12.9664	−1.26540
$106$	−19.5729	−1.90108
$107$	1.89211	0.182918	0.0914588	−	0.995809i	$-0.470847\pi$
$107$	1.89211	0.182918	0.0914588	+	0.995809i	$0.470847\pi$
$108$	−23.7141	−2.28189
$109$	14.5329	1.39200	0.696000	−	0.718042i	$-0.254961\pi$
$109$	14.5329	1.39200	0.696000	+	0.718042i	$0.254961\pi$
$110$	23.3241	2.22386
$111$	−2.85971	−0.271432
$112$	7.26204	0.686198
$113$	16.8622	1.58626	0.793130	−	0.609053i	$-0.208450\pi$
$113$	16.8622	1.58626	0.793130	+	0.609053i	$0.208450\pi$
$114$	17.2798	1.61841
$115$	−5.79396	−0.540290
$116$	8.95265	0.831233
$117$	−19.7159	−1.82273
$118$	5.98103	0.550599
$119$	−7.76100	−0.711450
$120$	22.4140	2.04611
$121$	17.9310	1.63009
$122$	10.0779	0.912413
$123$	0.697118	0.0628570
$124$	−0.0350991	−0.00315199
$125$	−12.1678	−1.08832
$126$	−31.4428	−2.80115
$127$	0.787046	0.0698390	0.0349195	−	0.999390i	$-0.488883\pi$
$127$	0.787046	0.0698390	0.0349195	+	0.999390i	$0.488883\pi$
$128$	20.6160	1.82222
$129$	−26.9129	−2.36955
$130$	16.5113	1.44814
$131$	−4.45074	−0.388863	−0.194432	−	0.980916i	$-0.562286\pi$
$131$	−4.45074	−0.388863	−0.194432	+	0.980916i	$0.562286\pi$
$132$	58.5655	5.09747
$133$	6.31821	0.547859
$134$	−7.81498	−0.675112
$135$	−11.2072	−0.964561
$136$	13.4158	1.15039
$137$	−16.3831	−1.39970	−0.699849	−	0.714291i	$-0.746750\pi$
$137$	−16.3831	−1.39970	−0.699849	+	0.714291i	$0.746750\pi$
$138$	−22.1903	−1.88896
$139$	16.3143	1.38376	0.691881	−	0.722012i	$-0.256782\pi$
$139$	16.3143	1.38376	0.691881	+	0.722012i	$0.256782\pi$
$140$	17.2638	1.45906
$141$	−15.4982	−1.30518
$142$	11.2705	0.945798
$143$	20.4805	1.71266
$144$	14.9226	1.24355
$145$	4.23099	0.351365
$146$	−34.8029	−2.88031
$147$	1.86018	0.153425
$148$	3.80748	0.312973
$149$	−0.0850151	−0.00696471	−0.00348235	−	0.999994i	$-0.501108\pi$
$149$	−0.0850151	−0.00696471	−0.00348235	+	0.999994i	$0.501108\pi$
$150$	−12.1439	−0.991545
$151$	−6.45451	−0.525260	−0.262630	−	0.964897i	$-0.584590\pi$
$151$	−6.45451	−0.525260	−0.262630	+	0.964897i	$0.584590\pi$
$152$	−10.9217	−0.885870
$153$	−15.9479	−1.28931
$154$	32.6623	2.63200
$155$	−0.0165877	−0.00133236
$156$	41.4590	3.31937
$157$	0.358397	0.0286032	0.0143016	−	0.999898i	$-0.495448\pi$
$157$	0.358397	0.0286032	0.0143016	+	0.999898i	$0.495448\pi$
$158$	−26.6824	−2.12274
$159$	−23.2264	−1.84197
$160$	3.17855	0.251287
$161$	−8.11367	−0.639447
$162$	−5.48789	−0.431170
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−0.928159	−0.0724770
$165$	27.6778	2.15472
$166$	−19.0415	−1.47790
$167$	7.21051	0.557966	0.278983	−	0.960296i	$-0.410003\pi$
$167$	7.21051	0.557966	0.278983	+	0.960296i	$0.410003\pi$
$168$	31.3878	2.42162
$169$	1.49830	0.115254
$170$	13.3558	1.02434
$171$	12.9832	0.992848
$172$	35.8324	2.73220
$173$	−4.89802	−0.372390	−0.186195	−	0.982513i	$-0.559616\pi$
$173$	−4.89802	−0.372390	−0.186195	+	0.982513i	$0.559616\pi$
$174$	16.2043	1.22844
$175$	−4.44030	−0.335655
$176$	−15.5014	−1.16846
$177$	7.09748	0.533479
$178$	34.1693	2.56110
$179$	−7.99750	−0.597761	−0.298880	−	0.954291i	$-0.596613\pi$
$179$	−7.99750	−0.597761	−0.298880	+	0.954291i	$0.596613\pi$
$180$	35.4751	2.64416
$181$	−4.95154	−0.368045	−0.184023	−	0.982922i	$-0.558912\pi$
$181$	−4.95154	−0.368045	−0.184023	+	0.982922i	$0.558912\pi$
$182$	23.1219	1.71391
$183$	11.9591	0.884044
$184$	14.0254	1.03397
$185$	1.79940	0.132295
$186$	−0.0635293	−0.00465819
$187$	16.5664	1.21146
$188$	20.6346	1.50493
$189$	−15.6942	−1.14158
$190$	−10.8729	−0.788805
$191$	15.8024	1.14342	0.571709	−	0.820456i	$-0.306281\pi$
$191$	15.8024	1.14342	0.571709	+	0.820456i	$0.306281\pi$
$192$	28.6567	2.06812
$193$	−11.9774	−0.862155	−0.431078	−	0.902315i	$-0.641866\pi$
$193$	−11.9774	−0.862155	−0.431078	+	0.902315i	$0.641866\pi$
$194$	−10.0479	−0.721400
$195$	19.5934	1.40311
$196$	−2.47669	−0.176907
$197$	5.98464	0.426388	0.213194	−	0.977010i	$-0.431613\pi$
$197$	5.98464	0.426388	0.213194	+	0.977010i	$0.431613\pi$
$198$	67.1170	4.76980
$199$	−16.8020	−1.19106	−0.595531	−	0.803332i	$-0.703058\pi$
$199$	−16.8020	−1.19106	−0.595531	+	0.803332i	$0.703058\pi$
$200$	7.67557	0.542744
$201$	−9.27376	−0.654121
$202$	33.0818	2.32763
$203$	5.92494	0.415849
$204$	33.5357	2.34797
$205$	−0.438645	−0.0306363
$206$	18.7419	1.30581
$207$	−16.6726	−1.15883
$208$	−10.9735	−0.760878
$209$	−13.4867	−0.932894
$210$	31.2475	2.15628
$211$	10.2708	0.707068	0.353534	−	0.935422i	$-0.384980\pi$
$211$	10.2708	0.707068	0.353534	+	0.935422i	$0.384980\pi$
$212$	30.9242	2.12388
$213$	13.3743	0.916391
$214$	−4.55975	−0.311698
$215$	16.9343	1.15491
$216$	27.1292	1.84591
$217$	−0.0232289	−0.00157688
$218$	−35.0224	−2.37202
$219$	−41.2994	−2.79075
$220$	−36.8509	−2.48449
$221$	11.7275	0.788878
$222$	6.89154	0.462530
$223$	−4.28261	−0.286785	−0.143392	−	0.989666i	$-0.545801\pi$
$223$	−4.28261	−0.286785	−0.143392	+	0.989666i	$0.545801\pi$
$224$	4.45114	0.297405
$225$	−9.12430	−0.608286
$226$	−40.6357	−2.70304
$227$	−12.3199	−0.817698	−0.408849	−	0.912602i	$-0.634070\pi$
$227$	−12.3199	−0.817698	−0.408849	+	0.912602i	$0.634070\pi$
$228$	−27.3013	−1.80807
$229$	21.6810	1.43272	0.716361	−	0.697730i	$-0.245806\pi$
$229$	21.6810	1.43272	0.716361	+	0.697730i	$0.245806\pi$
$230$	13.9627	0.920674
$231$	38.7591	2.55016
$232$	−10.2419	−0.672416
$233$	−10.9655	−0.718372	−0.359186	−	0.933266i	$-0.616946\pi$
$233$	−10.9655	−0.718372	−0.359186	+	0.933266i	$0.616946\pi$
$234$	47.5127	3.10600
$235$	9.75184	0.636140
$236$	−9.44975	−0.615126
$237$	−31.6631	−2.05674
$238$	18.7030	1.21234
$239$	−18.0729	−1.16904	−0.584519	−	0.811380i	$-0.698717\pi$
$239$	−18.0729	−1.16904	−0.584519	+	0.811380i	$0.698717\pi$
$240$	−14.8299	−0.957267
$241$	1.31066	0.0844270	0.0422135	−	0.999109i	$-0.486559\pi$
$241$	1.31066	0.0844270	0.0422135	+	0.999109i	$0.486559\pi$
$242$	−43.2114	−2.77773
$243$	12.1726	0.780870
$244$	−15.9227	−1.01934
$245$	−1.17048	−0.0747790
$246$	−1.67996	−0.107111
$247$	−9.54734	−0.607483
$248$	0.0401538	0.00254977
$249$	−22.5958	−1.43195
$250$	29.3229	1.85454
$251$	13.7224	0.866153	0.433077	−	0.901357i	$-0.357428\pi$
$251$	13.7224	0.866153	0.433077	+	0.901357i	$0.357428\pi$
$252$	49.6782	3.12943
$253$	17.3192	1.08885
$254$	−1.89668	−0.119008
$255$	15.8489	0.992494
$256$	−29.6403	−1.85252
$257$	−8.15472	−0.508678	−0.254339	−	0.967115i	$-0.581858\pi$
$257$	−8.15472	−0.508678	−0.254339	+	0.967115i	$0.581858\pi$
$258$	64.8566	4.03780
$259$	2.51983	0.156574
$260$	−26.0871	−1.61785
$261$	12.1751	0.753617
$262$	10.7257	0.662637
$263$	12.7140	0.783977	0.391989	−	0.919970i	$-0.371787\pi$
$263$	12.7140	0.783977	0.391989	+	0.919970i	$0.371787\pi$
$264$	−66.9995	−4.12354
$265$	14.6147	0.897771
$266$	−15.2261	−0.933571
$267$	40.5475	2.48147
$268$	12.3473	0.754231
$269$	−26.1102	−1.59197	−0.795984	−	0.605318i	$-0.793046\pi$
$269$	−26.1102	−1.59197	−0.795984	+	0.605318i	$0.793046\pi$
$270$	27.0079	1.64365
$271$	26.3061	1.59798	0.798992	−	0.601341i	$-0.205367\pi$
$271$	26.3061	1.59798	0.798992	+	0.601341i	$0.205367\pi$
$272$	−8.87637	−0.538209
$273$	27.4379	1.66062
$274$	39.4811	2.38514
$275$	9.47816	0.571554
$276$	35.0596	2.11034
$277$	8.71772	0.523797	0.261898	−	0.965095i	$-0.415651\pi$
$277$	8.71772	0.523797	0.261898	+	0.965095i	$0.415651\pi$
$278$	−39.3154	−2.35798
$279$	−0.0477326	−0.00285768
$280$	−19.7500	−1.18029
$281$	14.2650	0.850977	0.425489	−	0.904964i	$-0.360102\pi$
$281$	14.2650	0.850977	0.425489	+	0.904964i	$0.360102\pi$
$282$	37.3486	2.22408
$283$	−29.4969	−1.75341	−0.876704	−	0.481030i	$-0.840263\pi$
$283$	−29.4969	−1.75341	−0.876704	+	0.481030i	$0.840263\pi$
$284$	−17.8068	−1.05664
$285$	−12.9025	−0.764279
$286$	−49.3553	−2.91844
$287$	−0.614263	−0.0362588
$288$	9.14657	0.538967
$289$	−7.51375	−0.441985
$290$	−10.1962	−0.598739
$291$	−11.9235	−0.698970
$292$	54.9869	3.21786
$293$	−19.6795	−1.14969	−0.574843	−	0.818264i	$-0.694937\pi$
$293$	−19.6795	−1.14969	−0.574843	+	0.818264i	$0.694937\pi$
$294$	−4.48281	−0.261443
$295$	−4.46592	−0.260016
$296$	−4.35580	−0.253176
$297$	33.5004	1.94389
$298$	0.204875	0.0118681
$299$	12.2604	0.709039
$300$	19.1868	1.10775
$301$	23.7142	1.36686
$302$	15.5545	0.895063
$303$	39.2570	2.25525
$304$	7.22623	0.414453
$305$	−7.52499	−0.430880
$306$	38.4325	2.19704
$307$	−7.99067	−0.456052	−0.228026	−	0.973655i	$-0.573227\pi$
$307$	−7.99067	−0.456052	−0.228026	+	0.973655i	$0.573227\pi$
$308$	−51.6048	−2.94046
$309$	22.2404	1.26521
$310$	0.0399743	0.00227039
$311$	−28.8766	−1.63744	−0.818722	−	0.574190i	$-0.805317\pi$
$311$	−28.8766	−1.63744	−0.818722	+	0.574190i	$0.805317\pi$
$312$	−47.4295	−2.68517
$313$	1.21105	0.0684528	0.0342264	−	0.999414i	$-0.489103\pi$
$313$	1.21105	0.0684528	0.0342264	+	0.999414i	$0.489103\pi$
$314$	−0.863691	−0.0487409
$315$	23.4777	1.32282
$316$	42.1570	2.37152
$317$	3.76236	0.211315	0.105658	−	0.994403i	$-0.466305\pi$
$317$	3.76236	0.211315	0.105658	+	0.994403i	$0.466305\pi$
$318$	55.9727	3.13879
$319$	−12.6472	−0.708109
$320$	−18.0315	−1.00799
$321$	−5.41090	−0.302007
$322$	19.5529	1.08964
$323$	−7.72273	−0.429704
$324$	8.67061	0.481701
$325$	6.70966	0.372185
$326$	−2.40987	−0.133470
$327$	−41.5599	−2.29827
$328$	1.06182	0.0586294
$329$	13.6562	0.752889
$330$	−66.7001	−3.67172
$331$	5.38465	0.295967	0.147984	−	0.988990i	$-0.452722\pi$
$331$	5.38465	0.295967	0.147984	+	0.988990i	$0.452722\pi$
$332$	30.0846	1.65111
$333$	5.17794	0.283749
$334$	−17.3764	−0.950795
$335$	5.83529	0.318816
$336$	−20.7673	−1.13295
$337$	−31.3190	−1.70605	−0.853026	−	0.521868i	$-0.825235\pi$
$337$	−31.3190	−1.70605	−0.853026	+	0.521868i	$0.825235\pi$
$338$	−3.61071	−0.196396
$339$	−48.2209	−2.61900
$340$	−21.1015	−1.14439
$341$	0.0495838	0.00268511
$342$	−31.2878	−1.69185
$343$	−19.2779	−1.04091
$344$	−40.9927	−2.21018
$345$	16.5691	0.892048
$346$	11.8036	0.634566
$347$	27.9872	1.50243	0.751216	−	0.660056i	$-0.229468\pi$
$347$	27.9872	1.50243	0.751216	+	0.660056i	$0.229468\pi$
$348$	−25.6020	−1.37241
$349$	−1.85099	−0.0990811	−0.0495405	−	0.998772i	$-0.515776\pi$
$349$	−1.85099	−0.0990811	−0.0495405	+	0.998772i	$0.515776\pi$
$350$	10.7006	0.571969
$351$	23.7152	1.26582
$352$	−9.50130	−0.506421
$353$	−10.9726	−0.584014	−0.292007	−	0.956416i	$-0.594323\pi$
$353$	−10.9726	−0.584014	−0.292007	+	0.956416i	$0.594323\pi$
$354$	−17.1040	−0.909069
$355$	−8.41544	−0.446645
$356$	−53.9859	−2.86125
$357$	22.1942	1.17464
$358$	19.2729	1.01861
$359$	6.01893	0.317667	0.158833	−	0.987305i	$-0.449227\pi$
$359$	6.01893	0.317667	0.158833	+	0.987305i	$0.449227\pi$
$360$	−40.5839	−2.13896
$361$	−12.7129	−0.669102
$362$	11.9326	0.627162
$363$	−51.2775	−2.69137
$364$	−36.5314	−1.91477
$365$	25.9866	1.36020
$366$	−28.8200	−1.50644
$367$	20.3369	1.06158	0.530788	−	0.847505i	$-0.321896\pi$
$367$	20.3369	1.06158	0.530788	+	0.847505i	$0.321896\pi$
$368$	−9.27973	−0.483739
$369$	−1.26224	−0.0657095
$370$	−4.33633	−0.225435
$371$	20.4659	1.06254
$372$	0.100373	0.00520411
$373$	11.1293	0.576255	0.288128	−	0.957592i	$-0.406967\pi$
$373$	11.1293	0.576255	0.288128	+	0.957592i	$0.406967\pi$
$374$	−39.9230	−2.06437
$375$	34.7965	1.79688
$376$	−23.6062	−1.21740
$377$	−8.95308	−0.461107
$378$	37.8210	1.94530
$379$	3.21947	0.165373	0.0826864	−	0.996576i	$-0.473650\pi$
$379$	3.21947	0.165373	0.0826864	+	0.996576i	$0.473650\pi$
$380$	17.1787	0.881249
$381$	−2.25072	−0.115308
$382$	−38.0817	−1.94843
$383$	22.8839	1.16931	0.584656	−	0.811281i	$-0.301229\pi$
$383$	22.8839	1.16931	0.584656	+	0.811281i	$0.301229\pi$
$384$	−58.9559	−3.00858
$385$	−24.3883	−1.24294
$386$	28.8641	1.46914
$387$	48.7299	2.47708
$388$	15.8753	0.805944
$389$	−27.2186	−1.38004	−0.690020	−	0.723791i	$-0.742398\pi$
$389$	−27.2186	−1.38004	−0.690020	+	0.723791i	$0.742398\pi$
$390$	−47.2175	−2.39095
$391$	9.91732	0.501541
$392$	2.83336	0.143106
$393$	12.7278	0.642034
$394$	−14.4222	−0.726580
$395$	19.9232	1.00245
$396$	−106.042	−5.32880
$397$	−14.7313	−0.739344	−0.369672	−	0.929162i	$-0.620530\pi$
$397$	−14.7313	−0.739344	−0.369672	+	0.929162i	$0.620530\pi$
$398$	40.4907	2.02961
$399$	−18.0683	−0.904544
$400$	−5.07844	−0.253922
$401$	−8.53938	−0.426436	−0.213218	−	0.977005i	$-0.568395\pi$
$401$	−8.53938	−0.426436	−0.213218	+	0.977005i	$0.568395\pi$
$402$	22.3486	1.11465
$403$	0.0351008	0.00174849
$404$	−52.2676	−2.60041
$405$	4.09770	0.203616
$406$	−14.2784	−0.708623
$407$	−5.37875	−0.266615
$408$	−38.3652	−1.89936
$409$	−20.6637	−1.02175	−0.510877	−	0.859654i	$-0.670679\pi$
$409$	−20.6637	−1.02175	−0.510877	+	0.859654i	$0.670679\pi$
$410$	1.05708	0.0522053
$411$	46.8508	2.31098
$412$	−29.6114	−1.45885
$413$	−6.25393	−0.307736
$414$	40.1789	1.97469
$415$	14.2179	0.697928
$416$	−6.72604	−0.329771
$417$	−46.6542	−2.28466
$418$	32.5012	1.58969
$419$	−37.4095	−1.82758	−0.913788	−	0.406192i	$-0.866856\pi$
$419$	−37.4095	−1.82758	−0.913788	+	0.406192i	$0.866856\pi$
$420$	−49.3695	−2.40899
$421$	−12.9057	−0.628985	−0.314493	−	0.949260i	$-0.601834\pi$
$421$	−12.9057	−0.628985	−0.314493	+	0.949260i	$0.601834\pi$
$422$	−24.7512	−1.20487
$423$	28.0618	1.36441
$424$	−35.3776	−1.71809
$425$	5.42737	0.263266
$426$	−32.2303	−1.56156
$427$	−10.5378	−0.509958
$428$	7.20420	0.348228
$429$	−58.5682	−2.82770
$430$	−40.8094	−1.96801
$431$	11.6445	0.560897	0.280449	−	0.959869i	$-0.409517\pi$
$431$	11.6445	0.560897	0.280449	+	0.959869i	$0.409517\pi$
$432$	−17.9497	−0.863603
$433$	30.0561	1.44440	0.722202	−	0.691682i	$-0.243130\pi$
$433$	30.0561	1.44440	0.722202	+	0.691682i	$0.243130\pi$
$434$	0.0559787	0.00268706
$435$	−12.0994	−0.580122
$436$	55.3338	2.65001
$437$	−8.07367	−0.386216
$438$	99.5262	4.75554
$439$	10.8358	0.517163	0.258581	−	0.965989i	$-0.416745\pi$
$439$	10.8358	0.517163	0.258581	+	0.965989i	$0.416745\pi$
$440$	42.1578	2.00980
$441$	−3.36815	−0.160388
$442$	−28.2618	−1.34428
$443$	−37.9460	−1.80287	−0.901435	−	0.432914i	$-0.857485\pi$
$443$	−37.9460	−1.80287	−0.901435	+	0.432914i	$0.857485\pi$
$444$	−10.8883	−0.516736
$445$	−25.5135	−1.20946
$446$	10.3205	0.488692
$447$	0.243118	0.0114991
$448$	−25.2508	−1.19299
$449$	−17.5880	−0.830031	−0.415016	−	0.909814i	$-0.636224\pi$
$449$	−17.5880	−0.830031	−0.415016	+	0.909814i	$0.636224\pi$
$450$	21.9884	1.03654
$451$	1.31119	0.0617416
$452$	64.2024	3.01983
$453$	18.4580	0.867234
$454$	29.6893	1.39339
$455$	−17.2646	−0.809379
$456$	31.2330	1.46262
$457$	−32.7450	−1.53175	−0.765874	−	0.642991i	$-0.777693\pi$
$457$	−32.7450	−1.53175	−0.765874	+	0.642991i	$0.777693\pi$
$458$	−52.2485	−2.44141
$459$	19.1830	0.895384
$460$	−22.0604	−1.02857
$461$	−17.4842	−0.814318	−0.407159	−	0.913357i	$-0.633481\pi$
$461$	−17.4842	−0.814318	−0.407159	+	0.913357i	$0.633481\pi$
$462$	−93.4046	−4.34557
$463$	−18.9357	−0.880019	−0.440009	−	0.897993i	$-0.645025\pi$
$463$	−18.9357	−0.880019	−0.440009	+	0.897993i	$0.645025\pi$
$464$	6.77644	0.314588
$465$	0.0474361	0.00219979
$466$	26.4254	1.22413
$467$	19.3014	0.893163	0.446581	−	0.894743i	$-0.352641\pi$
$467$	19.3014	0.893163	0.446581	+	0.894743i	$0.352641\pi$
$468$	−75.0678	−3.47001
$469$	8.17155	0.377327
$470$	−23.5007	−1.08401
$471$	−1.02491	−0.0472255
$472$	10.8106	0.497599
$473$	−50.6197	−2.32750
$474$	76.3041	3.50476
$475$	−4.41841	−0.202731
$476$	−29.5499	−1.35442
$477$	42.0550	1.92556
$478$	43.5533	1.99208
$479$	−17.8610	−0.816089	−0.408044	−	0.912962i	$-0.633789\pi$
$479$	−17.8610	−0.816089	−0.408044	+	0.912962i	$0.633789\pi$
$480$	−9.08975	−0.414888
$481$	−3.80766	−0.173614
$482$	−3.15852	−0.143867
$483$	23.2028	1.05576
$484$	68.2720	3.10327
$485$	7.50259	0.340675
$486$	−29.3343	−1.33063
$487$	−7.32931	−0.332123	−0.166061	−	0.986115i	$-0.553105\pi$
$487$	−7.32931	−0.332123	−0.166061	+	0.986115i	$0.553105\pi$
$488$	18.2157	0.824586
$489$	−2.85971	−0.129321
$490$	2.82070	0.127426
$491$	−1.76335	−0.0795788	−0.0397894	−	0.999208i	$-0.512669\pi$
$491$	−1.76335	−0.0795788	−0.0397894	+	0.999208i	$0.512669\pi$
$492$	2.65426	0.119663
$493$	−7.24204	−0.326165
$494$	23.0079	1.03517
$495$	−50.1150	−2.25250
$496$	−0.0265672	−0.00119290
$497$	−11.7847	−0.528616
$498$	54.4530	2.44010
$499$	30.4689	1.36398	0.681988	−	0.731363i	$-0.261115\pi$
$499$	30.4689	1.36398	0.681988	+	0.731363i	$0.261115\pi$
$500$	−46.3288	−2.07189
$501$	−20.6200	−0.921233
$502$	−33.0693	−1.47596
$503$	4.31284	0.192300	0.0961500	−	0.995367i	$-0.469347\pi$
$503$	4.31284	0.192300	0.0961500	+	0.995367i	$0.469347\pi$
$504$	−56.8324	−2.53151
$505$	−24.7015	−1.09920
$506$	−41.7372	−1.85544
$507$	−4.28470	−0.190290
$508$	2.99666	0.132955
$509$	29.1014	1.28990	0.644949	−	0.764226i	$-0.276879\pi$
$509$	29.1014	1.28990	0.644949	+	0.764226i	$0.276879\pi$
$510$	−38.1937	−1.69125
$511$	36.3908	1.60983
$512$	30.1973	1.33455
$513$	−15.6168	−0.689499
$514$	19.6518	0.866806
$515$	−13.9942	−0.616659
$516$	−102.470	−4.51101
$517$	−29.1501	−1.28202
$518$	−6.07246	−0.266808
$519$	14.0069	0.614836
$520$	29.8439	1.30874
$521$	−35.4308	−1.55225	−0.776126	−	0.630577i	$-0.782818\pi$
$521$	−35.4308	−1.55225	−0.776126	+	0.630577i	$0.782818\pi$
$522$	−29.3403	−1.28419
$523$	30.5937	1.33777	0.668884	−	0.743367i	$-0.266772\pi$
$523$	30.5937	1.33777	0.668884	+	0.743367i	$0.266772\pi$
$524$	−16.9461	−0.740295
$525$	12.6980	0.554185
$526$	−30.6391	−1.33593
$527$	0.0283926	0.00123680
$528$	44.3294	1.92919
$529$	−12.6320	−0.549218
$530$	−35.2195	−1.52984
$531$	−12.8511	−0.557689
$532$	24.0565	1.04298
$533$	0.928203	0.0402049
$534$	−97.7143	−4.22851
$535$	3.40468	0.147197
$536$	−14.1254	−0.610126
$537$	22.8705	0.986936
$538$	62.9223	2.71277
$539$	3.49877	0.150703
$540$	−42.6712	−1.83628
$541$	−33.6027	−1.44469	−0.722346	−	0.691532i	$-0.756936\pi$
$541$	−33.6027	−1.44469	−0.722346	+	0.691532i	$0.756936\pi$
$542$	−63.3944	−2.72302
$543$	14.1600	0.607662
$544$	−5.44062	−0.233265
$545$	26.1506	1.12017
$546$	−66.1218	−2.82975
$547$	−4.41528	−0.188784	−0.0943919	−	0.995535i	$-0.530091\pi$
$547$	−4.41528	−0.188784	−0.0943919	+	0.995535i	$0.530091\pi$
$548$	−62.3782	−2.66466
$549$	−21.6538	−0.924163
$550$	−22.8411	−0.973950
$551$	5.89573	0.251167
$552$	−40.1086	−1.70713
$553$	27.8999	1.18642
$554$	−21.0086	−0.892569
$555$	−5.14577	−0.218426
$556$	62.1164	2.63432
$557$	−40.8815	−1.73221	−0.866103	−	0.499865i	$-0.833383\pi$
$557$	−40.8815	−1.73221	−0.866103	+	0.499865i	$0.833383\pi$
$558$	0.115029	0.00486959
$559$	−35.8341	−1.51562
$560$	13.0673	0.552196
$561$	−47.3752	−2.00018
$562$	−34.3768	−1.45010
$563$	11.4231	0.481427	0.240713	−	0.970596i	$-0.422619\pi$
$563$	11.4231	0.481427	0.240713	+	0.970596i	$0.422619\pi$
$564$	−59.0090	−2.48473
$565$	30.3418	1.27649
$566$	71.0837	2.98787
$567$	5.73828	0.240985
$568$	20.3712	0.854757
$569$	30.7263	1.28811	0.644057	−	0.764977i	$-0.277250\pi$
$569$	30.7263	1.28811	0.644057	+	0.764977i	$0.277250\pi$
$570$	31.0934	1.30236
$571$	28.9672	1.21224	0.606119	−	0.795374i	$-0.292726\pi$
$571$	28.9672	1.21224	0.606119	+	0.795374i	$0.292726\pi$
$572$	77.9791	3.26047
$573$	−45.1902	−1.88785
$574$	1.48030	0.0617864
$575$	5.67400	0.236622
$576$	−51.8873	−2.16197
$577$	41.4974	1.72756	0.863779	−	0.503871i	$-0.168091\pi$
$577$	41.4974	1.72756	0.863779	+	0.503871i	$0.168091\pi$
$578$	18.1072	0.753159
$579$	34.2520	1.42346
$580$	16.1094	0.668908
$581$	19.9102	0.826016
$582$	28.7342	1.19107
$583$	−43.6860	−1.80929
$584$	−62.9056	−2.60305
$585$	−35.4768	−1.46678
$586$	47.4250	1.95911
$587$	39.4394	1.62784	0.813919	−	0.580978i	$-0.197330\pi$
$587$	39.4394	1.62784	0.813919	+	0.580978i	$0.197330\pi$
$588$	7.08262	0.292082
$589$	−0.0231144	−0.000952411 0
$590$	10.7623	0.443077
$591$	−17.1143	−0.703989
$592$	2.88196	0.118448
$593$	4.95010	0.203276	0.101638	−	0.994821i	$-0.467592\pi$
$593$	4.95010	0.203276	0.101638	+	0.994821i	$0.467592\pi$
$594$	−80.7317	−3.31246
$595$	−13.9652	−0.572516
$596$	−0.323693	−0.0132590
$597$	48.0488	1.96651
$598$	−29.5461	−1.20823
$599$	−7.18494	−0.293569	−0.146784	−	0.989169i	$-0.546892\pi$
$599$	−7.18494	−0.293569	−0.146784	+	0.989169i	$0.546892\pi$
$600$	−21.9499	−0.896101
$601$	33.0869	1.34964	0.674821	−	0.737981i	$-0.264221\pi$
$601$	33.0869	1.34964	0.674821	+	0.737981i	$0.264221\pi$
$602$	−57.1482	−2.32919
$603$	16.7916	0.683805
$604$	−24.5754	−0.999960
$605$	32.2651	1.31176
$606$	−94.6043	−3.84304
$607$	24.9282	1.01181	0.505903	−	0.862591i	$-0.331160\pi$
$607$	24.9282	1.01181	0.505903	+	0.862591i	$0.331160\pi$
$608$	4.42920	0.179628
$609$	−16.9436	−0.686590
$610$	18.1343	0.734235
$611$	−20.6356	−0.834826
$612$	−60.7215	−2.45452
$613$	−6.72409	−0.271583	−0.135792	−	0.990737i	$-0.543358\pi$
$613$	−6.72409	−0.271583	−0.135792	+	0.990737i	$0.543358\pi$
$614$	19.2565	0.777129
$615$	1.25440	0.0505821
$616$	59.0365	2.37865
$617$	0.406331	0.0163583	0.00817913	−	0.999967i	$-0.497396\pi$
$617$	0.406331	0.0163583	0.00817913	+	0.999967i	$0.497396\pi$
$618$	−53.5965	−2.15597
$619$	−33.2313	−1.33568	−0.667839	−	0.744306i	$-0.732780\pi$
$619$	−33.2313	−1.33568	−0.667839	+	0.744306i	$0.732780\pi$
$620$	−0.0631574	−0.00253646
$621$	20.0547	0.804766
$622$	69.5890	2.79027
$623$	−35.7283	−1.43142
$624$	31.3811	1.25625
$625$	−13.0841	−0.523364
$626$	−2.91849	−0.116646
$627$	38.5680	1.54026
$628$	1.36459	0.0544531
$629$	−3.07998	−0.122807
$630$	−56.5783	−2.25413
$631$	6.94615	0.276522	0.138261	−	0.990396i	$-0.455849\pi$
$631$	6.94615	0.276522	0.138261	+	0.990396i	$0.455849\pi$
$632$	−48.2281	−1.91841
$633$	−29.3714	−1.16741
$634$	−9.06681	−0.360089
$635$	1.41621	0.0562007
$636$	−88.4342	−3.50664
$637$	2.47681	0.0981348
$638$	30.4782	1.20664
$639$	−24.2162	−0.957977
$640$	37.0966	1.46637
$641$	44.8846	1.77283	0.886417	−	0.462888i	$-0.153187\pi$
$641$	44.8846	1.77283	0.886417	+	0.462888i	$0.153187\pi$
$642$	13.0396	0.514631
$643$	−20.8377	−0.821757	−0.410879	−	0.911690i	$-0.634778\pi$
$643$	−20.8377	−0.821757	−0.410879	+	0.911690i	$0.634778\pi$
$644$	−30.8927	−1.21734
$645$	−48.4271	−1.90682
$646$	18.6108	0.732232
$647$	−32.9148	−1.29402	−0.647008	−	0.762483i	$-0.723980\pi$
$647$	−32.9148	−1.29402	−0.647008	+	0.762483i	$0.723980\pi$
$648$	−9.91927	−0.389666
$649$	13.3495	0.524012
$650$	−16.1694	−0.634217
$651$	0.0664279	0.00260351
$652$	3.80748	0.149113
$653$	37.5796	1.47060	0.735301	−	0.677741i	$-0.237041\pi$
$653$	37.5796	1.47060	0.735301	+	0.677741i	$0.237041\pi$
$654$	100.154	3.91633
$655$	−8.00868	−0.312925
$656$	−0.702542	−0.0274297
$657$	74.7788	2.91740
$658$	−32.9096	−1.28295
$659$	9.66158	0.376362	0.188181	−	0.982134i	$-0.439741\pi$
$659$	9.66158	0.376362	0.188181	+	0.982134i	$0.439741\pi$
$660$	105.383	4.10202
$661$	−18.7858	−0.730684	−0.365342	−	0.930873i	$-0.619048\pi$
$661$	−18.7858	−0.730684	−0.365342	+	0.930873i	$0.619048\pi$
$662$	−12.9763	−0.504339
$663$	−33.5373	−1.30248
$664$	−34.4171	−1.33564
$665$	11.3690	0.440871
$666$	−12.4782	−0.483520
$667$	−7.57113	−0.293155
$668$	27.4539	1.06222
$669$	12.2470	0.473498
$670$	−14.0623	−0.543274
$671$	22.4936	0.868357
$672$	−12.7290	−0.491031
$673$	−24.5819	−0.947562	−0.473781	−	0.880643i	$-0.657111\pi$
$673$	−24.5819	−0.947562	−0.473781	+	0.880643i	$0.657111\pi$
$674$	75.4747	2.90718
$675$	10.9752	0.422434
$676$	5.70474	0.219413
$677$	1.70273	0.0654413	0.0327206	−	0.999465i	$-0.489583\pi$
$677$	1.70273	0.0654413	0.0327206	+	0.999465i	$0.489583\pi$
$678$	116.206	4.46287
$679$	10.5064	0.403198
$680$	24.1404	0.925741
$681$	35.2312	1.35006
$682$	−0.119491	−0.00457553
$683$	9.44909	0.361559	0.180780	−	0.983524i	$-0.442138\pi$
$683$	9.44909	0.361559	0.180780	+	0.983524i	$0.442138\pi$
$684$	49.4332	1.89013
$685$	−29.4797	−1.12636
$686$	46.4572	1.77374
$687$	−62.0014	−2.36550
$688$	27.1223	1.03403
$689$	−30.9256	−1.17817
$690$	−39.9293	−1.52008
$691$	13.5363	0.514946	0.257473	−	0.966285i	$-0.417110\pi$
$691$	13.5363	0.514946	0.257473	+	0.966285i	$0.417110\pi$
$692$	−18.6491	−0.708934
$693$	−70.1793	−2.66589
$694$	−67.4456	−2.56020
$695$	29.3560	1.11354
$696$	29.2890	1.11020
$697$	0.750812	0.0284391
$698$	4.46064	0.168838
$699$	31.3581	1.18607
$700$	−16.9064	−0.639001
$701$	−6.80046	−0.256850	−0.128425	−	0.991719i	$-0.540992\pi$
$701$	−6.80046	−0.256850	−0.128425	+	0.991719i	$0.540992\pi$
$702$	−57.1506	−2.15701
$703$	2.50740	0.0945684
$704$	53.8996	2.03142
$705$	−27.8874	−1.05030
$706$	26.4426	0.995182
$707$	−34.5912	−1.30094
$708$	27.0235	1.01561
$709$	11.3553	0.426456	0.213228	−	0.977003i	$-0.431602\pi$
$709$	11.3553	0.426456	0.213228	+	0.977003i	$0.431602\pi$
$710$	20.2801	0.761100
$711$	57.3309	2.15008
$712$	61.7604	2.31457
$713$	0.0296828	0.00111163
$714$	−53.4852	−2.00163
$715$	36.8527	1.37821
$716$	−30.4503	−1.13798
$717$	51.6832	1.93015
$718$	−14.5048	−0.541316
$719$	−40.7063	−1.51809	−0.759045	−	0.651038i	$-0.774334\pi$
$719$	−40.7063	−1.51809	−0.759045	+	0.651038i	$0.774334\pi$
$720$	26.8518	1.00071
$721$	−19.5971	−0.729833
$722$	30.6366	1.14017
$723$	−3.74811	−0.139394
$724$	−18.8529	−0.700663
$725$	−4.14339	−0.153882
$726$	123.572	4.58619
$727$	−25.5539	−0.947741	−0.473870	−	0.880595i	$-0.657143\pi$
$727$	−25.5539	−0.947741	−0.473870	+	0.880595i	$0.657143\pi$
$728$	41.7924	1.54893
$729$	−41.6417	−1.54229
$730$	−62.6244	−2.31783
$731$	−28.9858	−1.07208
$732$	45.5342	1.68299
$733$	−11.1404	−0.411478	−0.205739	−	0.978607i	$-0.565960\pi$
$733$	−11.1404	−0.411478	−0.205739	+	0.978607i	$0.565960\pi$
$734$	−49.0092	−1.80896
$735$	3.34722	0.123464
$736$	−5.68785	−0.209657
$737$	−17.4428	−0.642513
$738$	3.04183	0.111971
$739$	−23.4019	−0.860853	−0.430426	−	0.902626i	$-0.641637\pi$
$739$	−23.4019	−0.860853	−0.430426	+	0.902626i	$0.641637\pi$
$740$	6.85120	0.251855
$741$	27.3026	1.00299
$742$	−49.3202	−1.81060
$743$	31.8637	1.16896	0.584482	−	0.811407i	$-0.301298\pi$
$743$	31.8637	1.16896	0.584482	+	0.811407i	$0.301298\pi$
$744$	−0.114828	−0.00420980
$745$	−0.152976	−0.00560462
$746$	−26.8203	−0.981960
$747$	40.9132	1.49694
$748$	63.0764	2.30630
$749$	4.76780	0.174212
$750$	−83.8550	−3.06195
$751$	−7.67744	−0.280154	−0.140077	−	0.990141i	$-0.544735\pi$
$751$	−7.67744	−0.280154	−0.140077	+	0.990141i	$0.544735\pi$
$752$	15.6187	0.569557
$753$	−39.2422	−1.43007
$754$	21.5758	0.785743
$755$	−11.6143	−0.422686
$756$	−59.7553	−2.17328
$757$	−1.17473	−0.0426964	−0.0213482	−	0.999772i	$-0.506796\pi$
$757$	−1.17473	−0.0426964	−0.0213482	+	0.999772i	$0.506796\pi$
$758$	−7.75850	−0.281801
$759$	−49.5280	−1.79775
$760$	−19.6526	−0.712876
$761$	−1.38261	−0.0501197	−0.0250598	−	0.999686i	$-0.507978\pi$
$761$	−1.38261	−0.0501197	−0.0250598	+	0.999686i	$0.507978\pi$
$762$	5.42395	0.196489
$763$	36.6204	1.32575
$764$	60.1672	2.17677
$765$	−28.6968	−1.03753
$766$	−55.1473	−1.99255
$767$	9.45020	0.341227
$768$	84.7628	3.05861
$769$	−36.4346	−1.31386	−0.656932	−	0.753950i	$-0.728146\pi$
$769$	−36.4346	−1.31386	−0.656932	+	0.753950i	$0.728146\pi$
$770$	58.7726	2.11802
$771$	23.3201	0.839855
$772$	−45.6039	−1.64132
$773$	42.9604	1.54518	0.772589	−	0.634907i	$-0.218962\pi$
$773$	42.9604	1.54518	0.772589	+	0.634907i	$0.218962\pi$
$774$	−117.433	−4.22103
$775$	0.0162443	0.000583512 0
$776$	−18.1615	−0.651959
$777$	−7.20597	−0.258513
$778$	65.5934	2.35164
$779$	−0.611235	−0.0218998
$780$	74.6014	2.67116
$781$	25.1553	0.900129
$782$	−23.8995	−0.854643
$783$	−14.6448	−0.523361
$784$	−1.87466	−0.0669521
$785$	0.644901	0.0230175
$786$	−30.6724	−1.09405
$787$	−8.17750	−0.291496	−0.145748	−	0.989322i	$-0.546559\pi$
$787$	−8.17750	−0.291496	−0.145748	+	0.989322i	$0.546559\pi$
$788$	22.7864	0.811732
$789$	−36.3583	−1.29439
$790$	−48.0125	−1.70821
$791$	42.4897	1.51076
$792$	121.313	4.31067
$793$	15.9234	0.565457
$794$	35.5006	1.25987
$795$	−41.7937	−1.48227
$796$	−63.9733	−2.26747
$797$	38.1930	1.35286	0.676432	−	0.736505i	$-0.263525\pi$
$797$	38.1930	1.35286	0.676432	+	0.736505i	$0.263525\pi$
$798$	43.5422	1.54138
$799$	−16.6919	−0.590517
$800$	−3.11274	−0.110052
$801$	−73.4174	−2.59408
$802$	20.5788	0.726663
$803$	−77.6789	−2.74123
$804$	−35.3097	−1.24528
$805$	−14.5998	−0.514574
$806$	−0.0845884	−0.00297950
$807$	74.6676	2.62842
$808$	59.7948	2.10357
$809$	−16.5988	−0.583583	−0.291792	−	0.956482i	$-0.594251\pi$
$809$	−16.5988	−0.583583	−0.291792	+	0.956482i	$0.594251\pi$
$810$	−9.87493	−0.346970
$811$	2.83335	0.0994923	0.0497461	−	0.998762i	$-0.484159\pi$
$811$	2.83335	0.0994923	0.0497461	+	0.998762i	$0.484159\pi$
$812$	22.5591	0.791670
$813$	−75.2280	−2.63836
$814$	12.9621	0.454322
$815$	1.79940	0.0630304
$816$	25.3838	0.888612
$817$	23.5973	0.825564
$818$	49.7969	1.74111
$819$	−49.6805	−1.73598
$820$	−1.67013	−0.0583235
$821$	−15.8251	−0.552301	−0.276151	−	0.961114i	$-0.589059\pi$
$821$	−15.8251	−0.552301	−0.276151	+	0.961114i	$0.589059\pi$
$822$	−112.904	−3.93799
$823$	−7.47479	−0.260555	−0.130277	−	0.991478i	$-0.541587\pi$
$823$	−7.47479	−0.260555	−0.130277	+	0.991478i	$0.541587\pi$
$824$	33.8757	1.18012
$825$	−27.1048	−0.943667
$826$	15.0712	0.524393
$827$	−35.5144	−1.23496	−0.617479	−	0.786588i	$-0.711846\pi$
$827$	−35.5144	−1.23496	−0.617479	+	0.786588i	$0.711846\pi$
$828$	−63.4808	−2.20611
$829$	23.3500	0.810980	0.405490	−	0.914100i	$-0.367101\pi$
$829$	23.3500	0.810980	0.405490	+	0.914100i	$0.367101\pi$
$830$	−34.2633	−1.18930
$831$	−24.9301	−0.864817
$832$	38.1560	1.32282
$833$	2.00346	0.0694159
$834$	112.431	3.89315
$835$	12.9746	0.449005
$836$	−51.3504	−1.77599
$837$	0.0574151	0.00198456
$838$	90.1522	3.11426
$839$	−56.9569	−1.96637	−0.983185	−	0.182611i	$-0.941545\pi$
$839$	−56.9569	−1.96637	−0.983185	+	0.182611i	$0.941545\pi$
$840$	56.4793	1.94872
$841$	−23.4712	−0.809353
$842$	31.1011	1.07181
$843$	−40.7937	−1.40501
$844$	39.1057	1.34607
$845$	2.69604	0.0927467
$846$	−67.6253	−2.32501
$847$	45.1830	1.55251
$848$	23.4071	0.803804
$849$	84.3525	2.89497
$850$	−13.0793	−0.448615
$851$	−3.21994	−0.110378
$852$	50.9223	1.74457
$853$	0.971674	0.0332695	0.0166347	−	0.999862i	$-0.494705\pi$
$853$	0.971674	0.0332695	0.0166347	+	0.999862i	$0.494705\pi$
$854$	25.3946	0.868987
$855$	23.3620	0.798963
$856$	−8.24168	−0.281695
$857$	−41.5445	−1.41913	−0.709567	−	0.704638i	$-0.751109\pi$
$857$	−41.5445	−1.41913	−0.709567	+	0.704638i	$0.751109\pi$
$858$	141.142	4.81851
$859$	21.1893	0.722968	0.361484	−	0.932378i	$-0.382270\pi$
$859$	21.1893	0.722968	0.361484	+	0.932378i	$0.382270\pi$
$860$	64.4770	2.19865
$861$	1.75662	0.0598653
$862$	−28.0618	−0.955789
$863$	38.2214	1.30107	0.650536	−	0.759475i	$-0.274544\pi$
$863$	38.2214	1.30107	0.650536	+	0.759475i	$0.274544\pi$
$864$	−11.0019	−0.374294
$865$	−8.81352	−0.299669
$866$	−72.4314	−2.46132
$867$	21.4872	0.729742
$868$	−0.0884436	−0.00300197
$869$	−59.5543	−2.02024
$870$	29.1580	0.988550
$871$	−12.3479	−0.418392
$872$	−63.3024	−2.14369
$873$	21.5894	0.730690
$874$	19.4565	0.658126
$875$	−30.6608	−1.03652
$876$	−157.247	−5.31287
$877$	−9.51939	−0.321447	−0.160724	−	0.986999i	$-0.551383\pi$
$877$	−9.51939	−0.321447	−0.160724	+	0.986999i	$0.551383\pi$
$878$	−26.1128	−0.881264
$879$	56.2775	1.89819
$880$	−27.8932	−0.940279
$881$	−9.81383	−0.330636	−0.165318	−	0.986240i	$-0.552865\pi$
$881$	−9.81383	−0.330636	−0.165318	+	0.986240i	$0.552865\pi$
$882$	8.11681	0.273307
$883$	−4.08846	−0.137588	−0.0687938	−	0.997631i	$-0.521915\pi$
$883$	−4.08846	−0.137588	−0.0687938	+	0.997631i	$0.521915\pi$
$884$	44.6523	1.50182
$885$	12.7712	0.429300
$886$	91.4451	3.07216
$887$	2.80261	0.0941023	0.0470512	−	0.998892i	$-0.485018\pi$
$887$	2.80261	0.0941023	0.0470512	+	0.998892i	$0.485018\pi$
$888$	12.4563	0.418007
$889$	1.98322	0.0665150
$890$	61.4844	2.06096
$891$	−12.2488	−0.410350
$892$	−16.3060	−0.545964
$893$	13.5888	0.454733
$894$	−0.585884	−0.0195949
$895$	−14.3907	−0.481029
$896$	51.9488	1.73549
$897$	−35.0613	−1.17066
$898$	42.3849	1.41440
$899$	−0.0216756	−0.000722923 0
$900$	−34.7406	−1.15802
$901$	−25.0154	−0.833384
$902$	−3.15980	−0.105210
$903$	−67.8158	−2.25677
$904$	−73.4483	−2.44285
$905$	−8.90982	−0.296172
$906$	−44.4815	−1.47780
$907$	10.2671	0.340912	0.170456	−	0.985365i	$-0.445476\pi$
$907$	10.2671	0.340912	0.170456	+	0.985365i	$0.445476\pi$
$908$	−46.9076	−1.55668
$909$	−71.0808	−2.35760
$910$	41.6056	1.37921
$911$	−4.18168	−0.138545	−0.0692727	−	0.997598i	$-0.522068\pi$
$911$	−4.18168	−0.138545	−0.0692727	+	0.997598i	$0.522068\pi$
$912$	−20.6649	−0.684284
$913$	−42.4999	−1.40654
$914$	78.9113	2.61015
$915$	21.5193	0.711406
$916$	82.5501	2.72753
$917$	−11.2151	−0.370355
$918$	−46.2285	−1.52577
$919$	25.6838	0.847232	0.423616	−	0.905842i	$-0.360761\pi$
$919$	25.6838	0.847232	0.423616	+	0.905842i	$0.360761\pi$
$920$	25.2374	0.832051
$921$	22.8510	0.752966
$922$	42.1346	1.38763
$923$	17.8077	0.586146
$924$	147.575	4.85485
$925$	−1.76215	−0.0579391
$926$	45.6327	1.49958
$927$	−40.2696	−1.32263
$928$	4.15351	0.136346
$929$	−24.3406	−0.798588	−0.399294	−	0.916823i	$-0.630745\pi$
$929$	−24.3406	−0.798588	−0.399294	+	0.916823i	$0.630745\pi$
$930$	−0.114315	−0.00374853
$931$	−1.63101	−0.0534543
$932$	−41.7509	−1.36759
$933$	82.5788	2.70351
$934$	−46.5139	−1.52198
$935$	29.8097	0.974881
$936$	85.8784	2.80702
$937$	11.2665	0.368060	0.184030	−	0.982921i	$-0.441086\pi$
$937$	11.2665	0.368060	0.184030	+	0.982921i	$0.441086\pi$
$938$	−19.6924	−0.642979
$939$	−3.46326	−0.113019
$940$	37.1300	1.21105
$941$	−36.6303	−1.19411	−0.597057	−	0.802199i	$-0.703663\pi$
$941$	−36.6303	−1.19411	−0.597057	+	0.802199i	$0.703663\pi$
$942$	2.46991	0.0804739
$943$	0.784931	0.0255609
$944$	−7.15270	−0.232801
$945$	−28.2402	−0.918653
$946$	121.987	3.96614
$947$	−12.1983	−0.396391	−0.198195	−	0.980163i	$-0.563508\pi$
$947$	−12.1983	−0.396391	−0.198195	+	0.980163i	$0.563508\pi$
$948$	−120.557	−3.91550
$949$	−54.9895	−1.78503
$950$	10.6478	0.345460
$951$	−10.7593	−0.348893
$952$	33.8054	1.09564
$953$	−36.5841	−1.18508	−0.592538	−	0.805542i	$-0.701874\pi$
$953$	−36.5841	−1.18508	−0.592538	+	0.805542i	$0.701874\pi$
$954$	−101.347	−3.28123
$955$	28.4348	0.920129
$956$	−68.8122	−2.22555
$957$	36.1674	1.16913
$958$	43.0427	1.39065
$959$	−41.2824	−1.33308
$960$	51.5649	1.66425
$961$	−30.9999	−0.999997
$962$	9.17598	0.295845
$963$	9.79726	0.315712
$964$	4.99031	0.160727
$965$	−21.5522	−0.693791
$966$	−55.9157	−1.79906
$967$	5.17421	0.166391	0.0831957	−	0.996533i	$-0.473487\pi$
$967$	5.17421	0.166391	0.0831957	+	0.996533i	$0.473487\pi$
$968$	−78.1039	−2.51035
$969$	22.0848	0.709465
$970$	−18.0803	−0.580523
$971$	−47.5943	−1.52737	−0.763687	−	0.645587i	$-0.776613\pi$
$971$	−47.5943	−1.52737	−0.763687	+	0.645587i	$0.776613\pi$
$972$	46.3468	1.48657
$973$	41.1092	1.31790
$974$	17.6627	0.565949
$975$	−19.1877	−0.614498
$976$	−12.0522	−0.385781
$977$	−11.6780	−0.373612	−0.186806	−	0.982397i	$-0.559814\pi$
$977$	−11.6780	−0.373612	−0.186806	+	0.982397i	$0.559814\pi$
$978$	6.89154	0.220367
$979$	76.2647	2.43743
$980$	−4.45657	−0.142360
$981$	75.2505	2.40256
$982$	4.24944	0.135605
$983$	38.8305	1.23850	0.619250	−	0.785194i	$-0.287437\pi$
$983$	38.8305	1.23850	0.619250	+	0.785194i	$0.287437\pi$
$984$	−3.03651	−0.0968003
$985$	10.7688	0.343122
$986$	17.4524	0.555797
$987$	−39.0527	−1.24306
$988$	−36.3513	−1.15649
$989$	−30.3030	−0.963579
$990$	120.771	3.83834
$991$	13.9417	0.442872	0.221436	−	0.975175i	$-0.428926\pi$
$991$	13.9417	0.442872	0.221436	+	0.975175i	$0.428926\pi$
$992$	−0.0162839	−0.000517015 0
$993$	−15.3985	−0.488658
$994$	28.3996	0.900782
$995$	−30.2336	−0.958469
$996$	−86.0332	−2.72607
$997$	−8.49991	−0.269195	−0.134597	−	0.990900i	$-0.542974\pi$
$997$	−8.49991	−0.269195	−0.134597	+	0.990900i	$0.542974\pi$
$998$	−73.4262	−2.32427
$999$	−6.22828	−0.197054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.11	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.11	✓	109	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40987 q^{2} -2.85971 q^{3} +3.80748 q^{4} +1.79940 q^{5} +6.89154 q^{6} +2.51983 q^{7} -4.35580 q^{8} +5.17794 q^{9} +O(q^{10})\)	\(q-2.40987 q^{2} -2.85971 q^{3} +3.80748 q^{4} +1.79940 q^{5} +6.89154 q^{6} +2.51983 q^{7} -4.35580 q^{8} +5.17794 q^{9} -4.33633 q^{10} -5.37875 q^{11} -10.8883 q^{12} -3.80766 q^{13} -6.07246 q^{14} -5.14577 q^{15} +2.88196 q^{16} -3.07998 q^{17} -12.4782 q^{18} +2.50740 q^{19} +6.85120 q^{20} -7.20597 q^{21} +12.9621 q^{22} -3.21994 q^{23} +12.4563 q^{24} -1.76215 q^{25} +9.17598 q^{26} -6.22828 q^{27} +9.59419 q^{28} +2.35133 q^{29} +12.4007 q^{30} -0.00921845 q^{31} +1.76645 q^{32} +15.3817 q^{33} +7.42235 q^{34} +4.53418 q^{35} +19.7149 q^{36} +1.00000 q^{37} -6.04252 q^{38} +10.8888 q^{39} -7.83785 q^{40} -0.243772 q^{41} +17.3655 q^{42} +9.41105 q^{43} -20.4795 q^{44} +9.31721 q^{45} +7.75963 q^{46} +5.41949 q^{47} -8.24157 q^{48} -0.650480 q^{49} +4.24655 q^{50} +8.80784 q^{51} -14.4976 q^{52} +8.12195 q^{53} +15.0094 q^{54} -9.67855 q^{55} -10.9759 q^{56} -7.17044 q^{57} -5.66641 q^{58} -2.48189 q^{59} -19.5924 q^{60} -4.18194 q^{61} +0.0222153 q^{62} +13.0475 q^{63} -10.0208 q^{64} -6.85152 q^{65} -37.0679 q^{66} +3.24290 q^{67} -11.7270 q^{68} +9.20808 q^{69} -10.9268 q^{70} -4.67680 q^{71} -22.5541 q^{72} +14.4418 q^{73} -2.40987 q^{74} +5.03923 q^{75} +9.54689 q^{76} -13.5535 q^{77} -26.2406 q^{78} +11.0721 q^{79} +5.18581 q^{80} +2.27725 q^{81} +0.587460 q^{82} +7.90144 q^{83} -27.4366 q^{84} -5.54212 q^{85} -22.6794 q^{86} -6.72412 q^{87} +23.4288 q^{88} -14.1789 q^{89} -22.4533 q^{90} -9.59465 q^{91} -12.2598 q^{92} +0.0263621 q^{93} -13.0603 q^{94} +4.51183 q^{95} -5.05153 q^{96} +4.16949 q^{97} +1.56757 q^{98} -27.8509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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