LMFDB - Embedded newform 163.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [163,2,Mod(1,163)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(163, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("163.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	163.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:	$1.30156155295$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 19x^{4} - 23x^{2} + 4x + 6 $ x^7 - 3x^6 - 5x^5 + 19x^4 - 23x^2 + 4*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.472573$ of defining polynomial
Character	$\chi$	$=$	163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.472573 q^{2} -2.68646 q^{3} -1.77667 q^{4} +1.65562 q^{5} +1.26955 q^{6} +2.09759 q^{7} +1.78476 q^{8} +4.21705 q^{9} +O(q^{10})$	\(q-0.472573 q^{2} -2.68646 q^{3} -1.77667 q^{4} +1.65562 q^{5} +1.26955 q^{6} +2.09759 q^{7} +1.78476 q^{8} +4.21705 q^{9} -0.782401 q^{10} +0.793490 q^{11} +4.77296 q^{12} +3.06144 q^{13} -0.991265 q^{14} -4.44775 q^{15} +2.70992 q^{16} +1.96545 q^{17} -1.99286 q^{18} +1.29301 q^{19} -2.94150 q^{20} -5.63509 q^{21} -0.374982 q^{22} -0.487146 q^{23} -4.79467 q^{24} -2.25893 q^{25} -1.44675 q^{26} -3.26955 q^{27} -3.72674 q^{28} +6.85444 q^{29} +2.10189 q^{30} -8.44396 q^{31} -4.85015 q^{32} -2.13168 q^{33} -0.928817 q^{34} +3.47281 q^{35} -7.49232 q^{36} +10.2248 q^{37} -0.611043 q^{38} -8.22442 q^{39} +2.95487 q^{40} +6.53014 q^{41} +2.66299 q^{42} -6.03259 q^{43} -1.40977 q^{44} +6.98182 q^{45} +0.230212 q^{46} +12.6082 q^{47} -7.28009 q^{48} -2.60011 q^{49} +1.06751 q^{50} -5.28009 q^{51} -5.43918 q^{52} +3.93372 q^{53} +1.54510 q^{54} +1.31372 q^{55} +3.74369 q^{56} -3.47362 q^{57} -3.23923 q^{58} +4.50300 q^{59} +7.90220 q^{60} -12.9650 q^{61} +3.99039 q^{62} +8.84564 q^{63} -3.12779 q^{64} +5.06857 q^{65} +1.00737 q^{66} +7.79848 q^{67} -3.49196 q^{68} +1.30870 q^{69} -1.64116 q^{70} -16.2605 q^{71} +7.52640 q^{72} +0.906043 q^{73} -4.83199 q^{74} +6.06851 q^{75} -2.29726 q^{76} +1.66442 q^{77} +3.88664 q^{78} -4.87706 q^{79} +4.48660 q^{80} -3.86765 q^{81} -3.08597 q^{82} -2.54346 q^{83} +10.0117 q^{84} +3.25403 q^{85} +2.85084 q^{86} -18.4142 q^{87} +1.41619 q^{88} -2.22829 q^{89} -3.29942 q^{90} +6.42165 q^{91} +0.865501 q^{92} +22.6843 q^{93} -5.95829 q^{94} +2.14074 q^{95} +13.0297 q^{96} +11.5983 q^{97} +1.22874 q^{98} +3.34619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + q^{3} + 5 q^{4} + 11 q^{5} - 3 q^{6} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + q^3 + 5 * q^4 + 11 * q^5 - 3 * q^6 + 3 * q^8 + 2 * q^9	\( 7 q + 3 q^{2} + q^{3} + 5 q^{4} + 11 q^{5} - 3 q^{6} + 3 q^{8} + 2 q^{9} + q^{10} + 2 q^{11} - 4 q^{12} + 10 q^{13} - q^{14} - 4 q^{15} - 3 q^{16} + 13 q^{17} - 4 q^{18} - 5 q^{19} + 4 q^{20} - 5 q^{21} - 11 q^{22} + 2 q^{23} - 7 q^{24} + 4 q^{25} - 9 q^{26} - 11 q^{27} - 18 q^{28} + 7 q^{29} - 13 q^{30} - 11 q^{31} - 6 q^{32} - 6 q^{33} - 6 q^{34} - 9 q^{35} - 24 q^{36} + 3 q^{37} - 5 q^{38} - 13 q^{39} - 12 q^{40} + 17 q^{41} + q^{42} - 10 q^{43} + 8 q^{44} + 12 q^{45} - 24 q^{46} + 11 q^{47} - 8 q^{48} - 7 q^{49} + 13 q^{50} + 6 q^{51} + 23 q^{52} + 18 q^{53} - 4 q^{54} - 6 q^{55} - 2 q^{56} + 20 q^{57} - q^{58} + 11 q^{59} - 27 q^{60} + 4 q^{61} + 25 q^{62} + 7 q^{63} - 21 q^{64} + 34 q^{65} - 10 q^{66} - 18 q^{67} + 23 q^{68} + 8 q^{69} + 6 q^{70} - 3 q^{71} + 22 q^{72} + 2 q^{73} - 9 q^{75} - 24 q^{76} + 25 q^{77} - 10 q^{78} - 8 q^{80} - 13 q^{81} - q^{82} + 18 q^{83} + 16 q^{84} + 12 q^{85} + 15 q^{86} + 19 q^{87} + 3 q^{88} + 18 q^{89} + 37 q^{90} - 36 q^{91} + 23 q^{92} - 15 q^{93} + 51 q^{94} - 25 q^{95} + 28 q^{96} + 21 q^{97} + 6 q^{98} - 13 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + q^3 + 5 * q^4 + 11 * q^5 - 3 * q^6 + 3 * q^8 + 2 * q^9 + q^10 + 2 * q^11 - 4 * q^12 + 10 * q^13 - q^14 - 4 * q^15 - 3 * q^16 + 13 * q^17 - 4 * q^18 - 5 * q^19 + 4 * q^20 - 5 * q^21 - 11 * q^22 + 2 * q^23 - 7 * q^24 + 4 * q^25 - 9 * q^26 - 11 * q^27 - 18 * q^28 + 7 * q^29 - 13 * q^30 - 11 * q^31 - 6 * q^32 - 6 * q^33 - 6 * q^34 - 9 * q^35 - 24 * q^36 + 3 * q^37 - 5 * q^38 - 13 * q^39 - 12 * q^40 + 17 * q^41 + q^42 - 10 * q^43 + 8 * q^44 + 12 * q^45 - 24 * q^46 + 11 * q^47 - 8 * q^48 - 7 * q^49 + 13 * q^50 + 6 * q^51 + 23 * q^52 + 18 * q^53 - 4 * q^54 - 6 * q^55 - 2 * q^56 + 20 * q^57 - q^58 + 11 * q^59 - 27 * q^60 + 4 * q^61 + 25 * q^62 + 7 * q^63 - 21 * q^64 + 34 * q^65 - 10 * q^66 - 18 * q^67 + 23 * q^68 + 8 * q^69 + 6 * q^70 - 3 * q^71 + 22 * q^72 + 2 * q^73 - 9 * q^75 - 24 * q^76 + 25 * q^77 - 10 * q^78 - 8 * q^80 - 13 * q^81 - q^82 + 18 * q^83 + 16 * q^84 + 12 * q^85 + 15 * q^86 + 19 * q^87 + 3 * q^88 + 18 * q^89 + 37 * q^90 - 36 * q^91 + 23 * q^92 - 15 * q^93 + 51 * q^94 - 25 * q^95 + 28 * q^96 + 21 * q^97 + 6 * q^98 - 13 * 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 $

$2$	−0.472573	−0.334160	−0.167080	−	0.985943i	$-0.553434\pi$
$2$	−0.472573	−0.334160	−0.167080	+	0.985943i	$0.553434\pi$
$3$	−2.68646	−1.55103	−0.775513	−	0.631331i	$-0.782509\pi$
$3$	−2.68646	−1.55103	−0.775513	+	0.631331i	$0.782509\pi$
$4$	−1.77667	−0.888337
$5$	1.65562	0.740415	0.370208	−	0.928949i	$-0.379287\pi$
$5$	1.65562	0.740415	0.370208	+	0.928949i	$0.379287\pi$
$6$	1.26955	0.518291
$7$	2.09759	0.792815	0.396407	−	0.918075i	$-0.370257\pi$
$7$	2.09759	0.792815	0.396407	+	0.918075i	$0.370257\pi$
$8$	1.78476	0.631006
$9$	4.21705	1.40568
$10$	−0.782401	−0.247417
$11$	0.793490	0.239246	0.119623	−	0.992819i	$-0.461831\pi$
$11$	0.793490	0.239246	0.119623	+	0.992819i	$0.461831\pi$
$12$	4.77296	1.37783
$13$	3.06144	0.849090	0.424545	−	0.905407i	$-0.360434\pi$
$13$	3.06144	0.849090	0.424545	+	0.905407i	$0.360434\pi$
$14$	−0.991265	−0.264927
$15$	−4.44775	−1.14840
$16$	2.70992	0.677480
$17$	1.96545	0.476691	0.238345	−	0.971180i	$-0.423395\pi$
$17$	1.96545	0.476691	0.238345	+	0.971180i	$0.423395\pi$
$18$	−1.99286	−0.469723
$19$	1.29301	0.296637	0.148319	−	0.988940i	$-0.452614\pi$
$19$	1.29301	0.296637	0.148319	+	0.988940i	$0.452614\pi$
$20$	−2.94150	−0.657738
$21$	−5.63509	−1.22968
$22$	−0.374982	−0.0799465
$23$	−0.487146	−0.101577	−0.0507885	−	0.998709i	$-0.516173\pi$
$23$	−0.487146	−0.101577	−0.0507885	+	0.998709i	$0.516173\pi$
$24$	−4.79467	−0.978707
$25$	−2.25893	−0.451785
$26$	−1.44675	−0.283732
$27$	−3.26955	−0.629225
$28$	−3.72674	−0.704287
$29$	6.85444	1.27284	0.636419	−	0.771344i	$-0.280415\pi$
$29$	6.85444	1.27284	0.636419	+	0.771344i	$0.280415\pi$
$30$	2.10189	0.383750
$31$	−8.44396	−1.51658	−0.758290	−	0.651917i	$-0.773965\pi$
$31$	−8.44396	−1.51658	−0.758290	+	0.651917i	$0.773965\pi$
$32$	−4.85015	−0.857393
$33$	−2.13168	−0.371077
$34$	−0.928817	−0.159291
$35$	3.47281	0.587012
$36$	−7.49232	−1.24872
$37$	10.2248	1.68095	0.840477	−	0.541847i	$-0.182275\pi$
$37$	10.2248	1.68095	0.840477	+	0.541847i	$0.182275\pi$
$38$	−0.611043	−0.0991243
$39$	−8.22442	−1.31696
$40$	2.95487	0.467207
$41$	6.53014	1.01984	0.509918	−	0.860223i	$-0.329676\pi$
$41$	6.53014	1.01984	0.509918	+	0.860223i	$0.329676\pi$
$42$	2.66299	0.410909
$43$	−6.03259	−0.919962	−0.459981	−	0.887929i	$-0.652144\pi$
$43$	−6.03259	−0.919962	−0.459981	+	0.887929i	$0.652144\pi$
$44$	−1.40977	−0.212531
$45$	6.98182	1.04079
$46$	0.230212	0.0339430
$47$	12.6082	1.83909	0.919546	−	0.392983i	$-0.128557\pi$
$47$	12.6082	1.83909	0.919546	+	0.392983i	$0.128557\pi$
$48$	−7.28009	−1.05079
$49$	−2.60011	−0.371444
$50$	1.06751	0.150969
$51$	−5.28009	−0.739360
$52$	−5.43918	−0.754279
$53$	3.93372	0.540337	0.270169	−	0.962813i	$-0.412921\pi$
$53$	3.93372	0.540337	0.270169	+	0.962813i	$0.412921\pi$
$54$	1.54510	0.210262
$55$	1.31372	0.177142
$56$	3.74369	0.500271
$57$	−3.47362	−0.460092
$58$	−3.23923	−0.425331
$59$	4.50300	0.586241	0.293120	−	0.956076i	$-0.405306\pi$
$59$	4.50300	0.586241	0.293120	+	0.956076i	$0.405306\pi$
$60$	7.90220	1.02017
$61$	−12.9650	−1.66000	−0.830002	−	0.557760i	$-0.811661\pi$
$61$	−12.9650	−1.66000	−0.830002	+	0.557760i	$0.811661\pi$
$62$	3.99039	0.506780
$63$	8.84564	1.11445
$64$	−3.12779	−0.390974
$65$	5.06857	0.628679
$66$	1.00737	0.123999
$67$	7.79848	0.952736	0.476368	−	0.879246i	$-0.341953\pi$
$67$	7.79848	0.952736	0.476368	+	0.879246i	$0.341953\pi$
$68$	−3.49196	−0.423462
$69$	1.30870	0.157549
$70$	−1.64116	−0.196156
$71$	−16.2605	−1.92976	−0.964882	−	0.262683i	$-0.915393\pi$
$71$	−16.2605	−1.92976	−0.964882	+	0.262683i	$0.915393\pi$
$72$	7.52640	0.886995
$73$	0.906043	0.106044	0.0530221	−	0.998593i	$-0.483115\pi$
$73$	0.906043	0.106044	0.0530221	+	0.998593i	$0.483115\pi$
$74$	−4.83199	−0.561707
$75$	6.06851	0.700731
$76$	−2.29726	−0.263514
$77$	1.66442	0.189678
$78$	3.88664	0.440076
$79$	−4.87706	−0.548713	−0.274356	−	0.961628i	$-0.588465\pi$
$79$	−4.87706	−0.548713	−0.274356	+	0.961628i	$0.588465\pi$
$80$	4.48660	0.501617
$81$	−3.86765	−0.429739
$82$	−3.08597	−0.340788
$83$	−2.54346	−0.279181	−0.139591	−	0.990209i	$-0.544579\pi$
$83$	−2.54346	−0.279181	−0.139591	+	0.990209i	$0.544579\pi$
$84$	10.0117	1.09237
$85$	3.25403	0.352949
$86$	2.85084	0.307414
$87$	−18.4142	−1.97421
$88$	1.41619	0.150966
$89$	−2.22829	−0.236199	−0.118099	−	0.993002i	$-0.537680\pi$
$89$	−2.22829	−0.236199	−0.118099	+	0.993002i	$0.537680\pi$
$90$	−3.29942	−0.347790
$91$	6.42165	0.673171
$92$	0.865501	0.0902347
$93$	22.6843	2.35226
$94$	−5.95829	−0.614550
$95$	2.14074	0.219635
$96$	13.0297	1.32984
$97$	11.5983	1.17763	0.588813	−	0.808270i	$-0.299596\pi$
$97$	11.5983	1.17763	0.588813	+	0.808270i	$0.299596\pi$
$98$	1.22874	0.124122
$99$	3.34619	0.336304
$100$	4.01338	0.401338
$101$	11.8818	1.18228	0.591141	−	0.806568i	$-0.298677\pi$
$101$	11.8818	1.18228	0.591141	+	0.806568i	$0.298677\pi$
$102$	2.49523	0.247064
$103$	−12.1770	−1.19983	−0.599916	−	0.800063i	$-0.704800\pi$
$103$	−12.1770	−1.19983	−0.599916	+	0.800063i	$0.704800\pi$
$104$	5.46392	0.535781
$105$	−9.32955	−0.910471
$106$	−1.85897	−0.180559
$107$	10.9029	1.05403	0.527013	−	0.849857i	$-0.323312\pi$
$107$	10.9029	1.05403	0.527013	+	0.849857i	$0.323312\pi$
$108$	5.80892	0.558964
$109$	−13.8458	−1.32618	−0.663092	−	0.748538i	$-0.730756\pi$
$109$	−13.8458	−1.32618	−0.663092	+	0.748538i	$0.730756\pi$
$110$	−0.620827	−0.0591936
$111$	−27.4686	−2.60720
$112$	5.68431	0.537117
$113$	−3.67690	−0.345894	−0.172947	−	0.984931i	$-0.555329\pi$
$113$	−3.67690	−0.345894	−0.172947	+	0.984931i	$0.555329\pi$
$114$	1.64154	0.153744
$115$	−0.806529	−0.0752092
$116$	−12.1781	−1.13071
$117$	12.9102	1.19355
$118$	−2.12800	−0.195898
$119$	4.12270	0.377928
$120$	−7.93814	−0.724650
$121$	−10.3704	−0.942761
$122$	6.12693	0.554707
$123$	−17.5429	−1.58179
$124$	15.0022	1.34723
$125$	−12.0180	−1.07492
$126$	−4.18021	−0.372403
$127$	−3.05302	−0.270912	−0.135456	−	0.990783i	$-0.543250\pi$
$127$	−3.05302	−0.270912	−0.135456	+	0.990783i	$0.543250\pi$
$128$	11.1784	0.988041
$129$	16.2063	1.42689
$130$	−2.39527	−0.210079
$131$	11.1003	0.969839	0.484919	−	0.874559i	$-0.338849\pi$
$131$	11.1003	0.969839	0.484919	+	0.874559i	$0.338849\pi$
$132$	3.78729	0.329642
$133$	2.71221	0.235179
$134$	−3.68535	−0.318366
$135$	−5.41312	−0.465887
$136$	3.50784	0.300795
$137$	−13.4160	−1.14621	−0.573104	−	0.819482i	$-0.694261\pi$
$137$	−13.4160	−1.14621	−0.573104	+	0.819482i	$0.694261\pi$
$138$	−0.618456	−0.0526464
$139$	5.36155	0.454761	0.227380	−	0.973806i	$-0.426984\pi$
$139$	5.36155	0.454761	0.227380	+	0.973806i	$0.426984\pi$
$140$	−6.17005	−0.521465
$141$	−33.8713	−2.85248
$142$	7.68427	0.644850
$143$	2.42922	0.203142
$144$	11.4279	0.952322
$145$	11.3483	0.942428
$146$	−0.428172	−0.0354357
$147$	6.98509	0.576120
$148$	−18.1662	−1.49325
$149$	−19.0343	−1.55935	−0.779677	−	0.626182i	$-0.784617\pi$
$149$	−19.0343	−1.55935	−0.779677	+	0.626182i	$0.784617\pi$
$150$	−2.86782	−0.234156
$151$	−1.46332	−0.119083	−0.0595414	−	0.998226i	$-0.518964\pi$
$151$	−1.46332	−0.119083	−0.0595414	+	0.998226i	$0.518964\pi$
$152$	2.30771	0.187180
$153$	8.28838	0.670076
$154$	−0.786559	−0.0633827
$155$	−13.9800	−1.12290
$156$	14.6121	1.16991
$157$	−6.37179	−0.508524	−0.254262	−	0.967135i	$-0.581833\pi$
$157$	−6.37179	−0.508524	−0.254262	+	0.967135i	$0.581833\pi$
$158$	2.30477	0.183358
$159$	−10.5678	−0.838078
$160$	−8.02999	−0.634827
$161$	−1.02183	−0.0805318
$162$	1.82775	0.143601
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−11.6019	−0.905959
$165$	−3.52924	−0.274751
$166$	1.20197	0.0932911
$167$	−8.37117	−0.647780	−0.323890	−	0.946095i	$-0.604991\pi$
$167$	−8.37117	−0.647780	−0.323890	+	0.946095i	$0.604991\pi$
$168$	−10.0573	−0.775934
$169$	−3.62759	−0.279046
$170$	−1.53777	−0.117941
$171$	5.45270	0.416978
$172$	10.7180	0.817236
$173$	−10.0361	−0.763028	−0.381514	−	0.924363i	$-0.624597\pi$
$173$	−10.0361	−0.763028	−0.381514	+	0.924363i	$0.624597\pi$
$174$	8.70204	0.659700
$175$	−4.73831	−0.358182
$176$	2.15030	0.162085
$177$	−12.0971	−0.909275
$178$	1.05303	0.0789281
$179$	15.8458	1.18437	0.592186	−	0.805801i	$-0.298265\pi$
$179$	15.8458	1.18437	0.592186	+	0.805801i	$0.298265\pi$
$180$	−12.4044	−0.924571
$181$	25.7435	1.91350	0.956750	−	0.290910i	$-0.0939580\pi$
$181$	25.7435	1.91350	0.956750	+	0.290910i	$0.0939580\pi$
$182$	−3.03470	−0.224947
$183$	34.8300	2.57471
$184$	−0.869437	−0.0640958
$185$	16.9284	1.24460
$186$	−10.7200	−0.786029
$187$	1.55956	0.114046
$188$	−22.4006	−1.63373
$189$	−6.85817	−0.498859
$190$	−1.01165	−0.0733931
$191$	15.3714	1.11224	0.556118	−	0.831103i	$-0.312290\pi$
$191$	15.3714	1.11224	0.556118	+	0.831103i	$0.312290\pi$
$192$	8.40268	0.606411
$193$	−4.92874	−0.354778	−0.177389	−	0.984141i	$-0.556765\pi$
$193$	−4.92874	−0.354778	−0.177389	+	0.984141i	$0.556765\pi$
$194$	−5.48103	−0.393515
$195$	−13.6165	−0.975098
$196$	4.61955	0.329968
$197$	−14.2564	−1.01572	−0.507862	−	0.861439i	$-0.669564\pi$
$197$	−14.2564	−1.01572	−0.507862	+	0.861439i	$0.669564\pi$
$198$	−1.58132	−0.112379
$199$	13.0754	0.926891	0.463446	−	0.886125i	$-0.346613\pi$
$199$	13.0754	0.926891	0.463446	+	0.886125i	$0.346613\pi$
$200$	−4.03163	−0.285079
$201$	−20.9503	−1.47772
$202$	−5.61502	−0.395071
$203$	14.3778	1.00912
$204$	9.38099	0.656801
$205$	10.8114	0.755102
$206$	5.75451	0.400936
$207$	−2.05432	−0.142785
$208$	8.29626	0.575242
$209$	1.02599	0.0709694
$210$	4.40890	0.304243
$211$	−16.3100	−1.12283	−0.561414	−	0.827535i	$-0.689742\pi$
$211$	−16.3100	−1.12283	−0.561414	+	0.827535i	$0.689742\pi$
$212$	−6.98893	−0.480002
$213$	43.6831	2.99312
$214$	−5.15243	−0.352213
$215$	−9.98767	−0.681154
$216$	−5.83534	−0.397045
$217$	−17.7120	−1.20237
$218$	6.54314	0.443157
$219$	−2.43404	−0.164477
$220$	−2.33405	−0.157361
$221$	6.01709	0.404753
$222$	12.9809	0.871223
$223$	28.7884	1.92781	0.963907	−	0.266240i	$-0.0857815\pi$
$223$	28.7884	1.92781	0.963907	+	0.266240i	$0.0857815\pi$
$224$	−10.1736	−0.679754
$225$	−9.52601	−0.635067
$226$	1.73761	0.115584
$227$	5.62241	0.373172	0.186586	−	0.982439i	$-0.440258\pi$
$227$	5.62241	0.373172	0.186586	+	0.982439i	$0.440258\pi$
$228$	6.17149	0.408717
$229$	−1.58039	−0.104435	−0.0522174	−	0.998636i	$-0.516629\pi$
$229$	−1.58039	−0.104435	−0.0522174	+	0.998636i	$0.516629\pi$
$230$	0.381144	0.0251319
$231$	−4.47138	−0.294196
$232$	12.2335	0.803169
$233$	16.5788	1.08611	0.543056	−	0.839696i	$-0.317267\pi$
$233$	16.5788	1.08611	0.543056	+	0.839696i	$0.317267\pi$
$234$	−6.10103	−0.398837
$235$	20.8743	1.36169
$236$	−8.00036	−0.520779
$237$	13.1020	0.851068
$238$	−1.94828	−0.126288
$239$	−17.5348	−1.13423	−0.567116	−	0.823638i	$-0.691941\pi$
$239$	−17.5348	−1.13423	−0.567116	+	0.823638i	$0.691941\pi$
$240$	−12.0530	−0.778021
$241$	3.50493	0.225772	0.112886	−	0.993608i	$-0.463990\pi$
$241$	3.50493	0.225772	0.112886	+	0.993608i	$0.463990\pi$
$242$	4.90076	0.315033
$243$	20.1989	1.29576
$244$	23.0347	1.47464
$245$	−4.30479	−0.275023
$246$	8.29032	0.528572
$247$	3.95848	0.251872
$248$	−15.0704	−0.956972
$249$	6.83289	0.433017
$250$	5.67939	0.359196
$251$	−7.76204	−0.489936	−0.244968	−	0.969531i	$-0.578777\pi$
$251$	−7.76204	−0.489936	−0.244968	+	0.969531i	$0.578777\pi$
$252$	−15.7158	−0.990004
$253$	−0.386546	−0.0243019
$254$	1.44278	0.0905279
$255$	−8.74181	−0.547433
$256$	0.972970	0.0608106
$257$	−16.0116	−0.998776	−0.499388	−	0.866378i	$-0.666442\pi$
$257$	−16.0116	−0.998776	−0.499388	+	0.866378i	$0.666442\pi$
$258$	−7.65866	−0.476808
$259$	21.4475	1.33269
$260$	−9.00521	−0.558479
$261$	28.9055	1.78921
$262$	−5.24571	−0.324081
$263$	0.500086	0.0308366	0.0154183	−	0.999881i	$-0.495092\pi$
$263$	0.500086	0.0308366	0.0154183	+	0.999881i	$0.495092\pi$
$264$	−3.80452	−0.234152
$265$	6.51273	0.400074
$266$	−1.28172	−0.0785872
$267$	5.98622	0.366350
$268$	−13.8554	−0.846351
$269$	−0.286026	−0.0174393	−0.00871967	−	0.999962i	$-0.502776\pi$
$269$	−0.286026	−0.0174393	−0.00871967	+	0.999962i	$0.502776\pi$
$270$	2.55810	0.155681
$271$	−14.7895	−0.898398	−0.449199	−	0.893432i	$-0.648291\pi$
$271$	−14.7895	−0.898398	−0.449199	+	0.893432i	$0.648291\pi$
$272$	5.32620	0.322949
$273$	−17.2515	−1.04411
$274$	6.34006	0.383017
$275$	−1.79244	−0.108088
$276$	−2.32513	−0.139956
$277$	−15.5133	−0.932103	−0.466051	−	0.884758i	$-0.654324\pi$
$277$	−15.5133	−0.932103	−0.466051	+	0.884758i	$0.654324\pi$
$278$	−2.53373	−0.151963
$279$	−35.6086	−2.13183
$280$	6.19812	0.370408
$281$	28.7512	1.71515	0.857577	−	0.514356i	$-0.171969\pi$
$281$	28.7512	1.71515	0.857577	+	0.514356i	$0.171969\pi$
$282$	16.0067	0.953184
$283$	−23.8801	−1.41953	−0.709764	−	0.704440i	$-0.751198\pi$
$283$	−23.8801	−1.41953	−0.709764	+	0.704440i	$0.751198\pi$
$284$	28.8896	1.71428
$285$	−5.75099	−0.340659
$286$	−1.14798	−0.0678818
$287$	13.6976	0.808541
$288$	−20.4533	−1.20522
$289$	−13.1370	−0.772766
$290$	−5.36292	−0.314922
$291$	−31.1582	−1.82653
$292$	−1.60974	−0.0942031
$293$	18.6220	1.08791	0.543954	−	0.839115i	$-0.316927\pi$
$293$	18.6220	1.08791	0.543954	+	0.839115i	$0.316927\pi$
$294$	−3.30096	−0.192516
$295$	7.45525	0.434061
$296$	18.2488	1.06069
$297$	−2.59435	−0.150540
$298$	8.99512	0.521073
$299$	−1.49137	−0.0862481
$300$	−10.7818	−0.622486
$301$	−12.6539	−0.729360
$302$	0.691524	0.0397927
$303$	−31.9199	−1.83375
$304$	3.50396	0.200966
$305$	−21.4652	−1.22909
$306$	−3.91687	−0.223912
$307$	−3.07227	−0.175344	−0.0876718	−	0.996149i	$-0.527943\pi$
$307$	−3.07227	−0.175344	−0.0876718	+	0.996149i	$0.527943\pi$
$308$	−2.95713	−0.168498
$309$	32.7129	1.86097
$310$	6.60656	0.375228
$311$	9.87087	0.559725	0.279863	−	0.960040i	$-0.409711\pi$
$311$	9.87087	0.559725	0.279863	+	0.960040i	$0.409711\pi$
$312$	−14.6786	−0.831011
$313$	−1.33231	−0.0753069	−0.0376534	−	0.999291i	$-0.511988\pi$
$313$	−1.33231	−0.0753069	−0.0376534	+	0.999291i	$0.511988\pi$
$314$	3.01114	0.169928
$315$	14.6450	0.825153
$316$	8.66496	0.487442
$317$	−17.9779	−1.00974	−0.504871	−	0.863195i	$-0.668460\pi$
$317$	−17.9779	−1.00974	−0.504871	+	0.863195i	$0.668460\pi$
$318$	4.99404	0.280052
$319$	5.43893	0.304522
$320$	−5.17843	−0.289483
$321$	−29.2903	−1.63482
$322$	0.482891	0.0269105
$323$	2.54135	0.141404
$324$	6.87155	0.381753
$325$	−6.91557	−0.383607
$326$	−0.472573	−0.0261734
$327$	37.1961	2.05695
$328$	11.6547	0.643523
$329$	26.4468	1.45806
$330$	1.66783	0.0918108
$331$	20.8720	1.14723	0.573615	−	0.819125i	$-0.305541\pi$
$331$	20.8720	1.14723	0.573615	+	0.819125i	$0.305541\pi$
$332$	4.51890	0.248007
$333$	43.1187	2.36289
$334$	3.95599	0.216462
$335$	12.9113	0.705420
$336$	−15.2706	−0.833082
$337$	−4.07020	−0.221718	−0.110859	−	0.993836i	$-0.535360\pi$
$337$	−4.07020	−0.221718	−0.110859	+	0.993836i	$0.535360\pi$
$338$	1.71430	0.0932458
$339$	9.87784	0.536490
$340$	−5.78135	−0.313538
$341$	−6.70020	−0.362836
$342$	−2.57680	−0.139337
$343$	−20.1371	−1.08730
$344$	−10.7667	−0.580502
$345$	2.16670	0.116651
$346$	4.74278	0.254973
$347$	−30.4008	−1.63200	−0.816000	−	0.578053i	$-0.803813\pi$
$347$	−30.4008	−1.63200	−0.816000	+	0.578053i	$0.803813\pi$
$348$	32.7160	1.75376
$349$	−27.6387	−1.47947	−0.739734	−	0.672900i	$-0.765049\pi$
$349$	−27.6387	−1.47947	−0.739734	+	0.672900i	$0.765049\pi$
$350$	2.23920	0.119690
$351$	−10.0095	−0.534269
$352$	−3.84854	−0.205128
$353$	−13.8099	−0.735028	−0.367514	−	0.930018i	$-0.619791\pi$
$353$	−13.8099	−0.735028	−0.367514	+	0.930018i	$0.619791\pi$
$354$	5.71677	0.303843
$355$	−26.9212	−1.42883
$356$	3.95895	0.209824
$357$	−11.0755	−0.586176
$358$	−7.48831	−0.395769
$359$	−31.0350	−1.63796	−0.818982	−	0.573819i	$-0.805461\pi$
$359$	−31.0350	−1.63796	−0.818982	+	0.573819i	$0.805461\pi$
$360$	12.4608	0.656744
$361$	−17.3281	−0.912006
$362$	−12.1657	−0.639415
$363$	27.8596	1.46225
$364$	−11.4092	−0.598003
$365$	1.50006	0.0785168
$366$	−16.4597	−0.860365
$367$	31.0379	1.62017	0.810083	−	0.586316i	$-0.199422\pi$
$367$	31.0379	1.62017	0.810083	+	0.586316i	$0.199422\pi$
$368$	−1.32013	−0.0688165
$369$	27.5379	1.43357
$370$	−7.99993	−0.415896
$371$	8.25133	0.428388
$372$	−40.3027	−2.08960
$373$	−7.17530	−0.371523	−0.185762	−	0.982595i	$-0.559475\pi$
$373$	−7.17530	−0.371523	−0.185762	+	0.982595i	$0.559475\pi$
$374$	−0.737007	−0.0381097
$375$	32.2859	1.66724
$376$	22.5025	1.16048
$377$	20.9845	1.08075
$378$	3.24099	0.166699
$379$	9.78902	0.502828	0.251414	−	0.967880i	$-0.419104\pi$
$379$	9.78902	0.502828	0.251414	+	0.967880i	$0.419104\pi$
$380$	−3.80339	−0.195110
$381$	8.20181	0.420192
$382$	−7.26411	−0.371664
$383$	−21.1853	−1.08252	−0.541258	−	0.840857i	$-0.682052\pi$
$383$	−21.1853	−1.08252	−0.541258	+	0.840857i	$0.682052\pi$
$384$	−30.0303	−1.53248
$385$	2.75564	0.140440
$386$	2.32919	0.118553
$387$	−25.4397	−1.29317
$388$	−20.6063	−1.04613
$389$	25.9447	1.31545	0.657724	−	0.753259i	$-0.271519\pi$
$389$	25.9447	1.31545	0.657724	+	0.753259i	$0.271519\pi$
$390$	6.43480	0.325839
$391$	−0.957460	−0.0484208
$392$	−4.64056	−0.234384
$393$	−29.8205	−1.50425
$394$	6.73717	0.339414
$395$	−8.07456	−0.406275
$396$	−5.94508	−0.298752
$397$	8.41231	0.422202	0.211101	−	0.977464i	$-0.432295\pi$
$397$	8.41231	0.422202	0.211101	+	0.977464i	$0.432295\pi$
$398$	−6.17909	−0.309730
$399$	−7.28624	−0.364768
$400$	−6.12152	−0.306076
$401$	−32.5919	−1.62756	−0.813780	−	0.581173i	$-0.802594\pi$
$401$	−32.5919	−1.62756	−0.813780	+	0.581173i	$0.802594\pi$
$402$	9.90054	0.493794
$403$	−25.8507	−1.28771
$404$	−21.1101	−1.05027
$405$	−6.40335	−0.318185
$406$	−6.79457	−0.337209
$407$	8.11331	0.402162
$408$	−9.42366	−0.466541
$409$	2.58910	0.128023	0.0640113	−	0.997949i	$-0.479611\pi$
$409$	2.58910	0.128023	0.0640113	+	0.997949i	$0.479611\pi$
$410$	−5.10919	−0.252325
$411$	36.0416	1.77780
$412$	21.6345	1.06586
$413$	9.44545	0.464780
$414$	0.970817	0.0477130
$415$	−4.21100	−0.206710
$416$	−14.8484	−0.728004
$417$	−14.4036	−0.705346
$418$	−0.484857	−0.0237151
$419$	−6.80035	−0.332219	−0.166109	−	0.986107i	$-0.553121\pi$
$419$	−6.80035	−0.332219	−0.166109	+	0.986107i	$0.553121\pi$
$420$	16.5756	0.808806
$421$	−4.45495	−0.217121	−0.108561	−	0.994090i	$-0.534624\pi$
$421$	−4.45495	−0.217121	−0.108561	+	0.994090i	$0.534624\pi$
$422$	7.70768	0.375204
$423$	53.1693	2.58518
$424$	7.02072	0.340956
$425$	−4.43980	−0.215362
$426$	−20.6435	−1.00018
$427$	−27.1954	−1.31608
$428$	−19.3710	−0.936331
$429$	−6.52600	−0.315078
$430$	4.71991	0.227614
$431$	−22.9198	−1.10401	−0.552003	−	0.833842i	$-0.686136\pi$
$431$	−22.9198	−1.10401	−0.552003	+	0.833842i	$0.686136\pi$
$432$	−8.86022	−0.426287
$433$	3.94037	0.189362	0.0946810	−	0.995508i	$-0.469817\pi$
$433$	3.94037	0.189362	0.0946810	+	0.995508i	$0.469817\pi$
$434$	8.37021	0.401783
$435$	−30.4868	−1.46173
$436$	24.5994	1.17810
$437$	−0.629886	−0.0301316
$438$	1.15026	0.0549618
$439$	13.5306	0.645781	0.322891	−	0.946436i	$-0.395345\pi$
$439$	13.5306	0.645781	0.322891	+	0.946436i	$0.395345\pi$
$440$	2.34466	0.111777
$441$	−10.9648	−0.522133
$442$	−2.84352	−0.135252
$443$	−9.13855	−0.434186	−0.217093	−	0.976151i	$-0.569657\pi$
$443$	−9.13855	−0.434186	−0.217093	+	0.976151i	$0.569657\pi$
$444$	48.8028	2.31608
$445$	−3.68921	−0.174885
$446$	−13.6046	−0.644198
$447$	51.1349	2.41860
$448$	−6.56083	−0.309970
$449$	−0.361869	−0.0170777	−0.00853883	−	0.999964i	$-0.502718\pi$
$449$	−0.361869	−0.0170777	−0.00853883	+	0.999964i	$0.502718\pi$
$450$	4.50174	0.212214
$451$	5.18160	0.243992
$452$	6.53266	0.307270
$453$	3.93113	0.184701
$454$	−2.65700	−0.124699
$455$	10.6318	0.498426
$456$	−6.19956	−0.290321
$457$	42.2793	1.97774	0.988870	−	0.148782i	$-0.0475354\pi$
$457$	42.2793	1.97774	0.988870	+	0.148782i	$0.0475354\pi$
$458$	0.746848	0.0348979
$459$	−6.42612	−0.299946
$460$	1.43294	0.0668111
$461$	24.8822	1.15888	0.579439	−	0.815016i	$-0.303272\pi$
$461$	24.8822	1.15888	0.579439	+	0.815016i	$0.303272\pi$
$462$	2.11306	0.0983083
$463$	−25.8093	−1.19946	−0.599731	−	0.800202i	$-0.704726\pi$
$463$	−25.8093	−1.19946	−0.599731	+	0.800202i	$0.704726\pi$
$464$	18.5750	0.862323
$465$	37.5566	1.74165
$466$	−7.83469	−0.362935
$467$	−20.9198	−0.968054	−0.484027	−	0.875053i	$-0.660826\pi$
$467$	−20.9198	−0.968054	−0.484027	+	0.875053i	$0.660826\pi$
$468$	−22.9373	−1.06028
$469$	16.3580	0.755344
$470$	−9.86465	−0.455022
$471$	17.1175	0.788735
$472$	8.03675	0.369922
$473$	−4.78680	−0.220097
$474$	−6.19166	−0.284393
$475$	−2.92082	−0.134016
$476$	−7.32470	−0.335727
$477$	16.5887	0.759543
$478$	8.28648	0.379015
$479$	34.0610	1.55629	0.778143	−	0.628087i	$-0.216162\pi$
$479$	34.0610	1.55629	0.778143	+	0.628087i	$0.216162\pi$
$480$	21.5722	0.984633
$481$	31.3027	1.42728
$482$	−1.65634	−0.0754441
$483$	2.74511	0.124907
$484$	18.4248	0.837490
$485$	19.2023	0.871932
$486$	−9.54547	−0.432991
$487$	−12.5759	−0.569868	−0.284934	−	0.958547i	$-0.591972\pi$
$487$	−12.5759	−0.569868	−0.284934	+	0.958547i	$0.591972\pi$
$488$	−23.1394	−1.04747
$489$	−2.68646	−0.121486
$490$	2.03433	0.0919017
$491$	26.7878	1.20892	0.604459	−	0.796636i	$-0.293389\pi$
$491$	26.7878	1.20892	0.604459	+	0.796636i	$0.293389\pi$
$492$	31.1681	1.40517
$493$	13.4720	0.606750
$494$	−1.87067	−0.0841655
$495$	5.54001	0.249005
$496$	−22.8825	−1.02745
$497$	−34.1078	−1.52995
$498$	−3.22904	−0.144697
$499$	−11.2847	−0.505172	−0.252586	−	0.967574i	$-0.581281\pi$
$499$	−11.2847	−0.505172	−0.252586	+	0.967574i	$0.581281\pi$
$500$	21.3521	0.954895
$501$	22.4888	1.00472
$502$	3.66813	0.163717
$503$	22.3473	0.996416	0.498208	−	0.867057i	$-0.333992\pi$
$503$	22.3473	0.996416	0.498208	+	0.867057i	$0.333992\pi$
$504$	15.7873	0.703223
$505$	19.6717	0.875380
$506$	0.182671	0.00812073
$507$	9.74537	0.432807
$508$	5.42423	0.240661
$509$	10.6891	0.473784	0.236892	−	0.971536i	$-0.423871\pi$
$509$	10.6891	0.473784	0.236892	+	0.971536i	$0.423871\pi$
$510$	4.13114	0.182930
$511$	1.90051	0.0840735
$512$	−22.8166	−1.00836
$513$	−4.22757	−0.186652
$514$	7.56666	0.333751
$515$	−20.1604	−0.888374
$516$	−28.7933	−1.26756
$517$	10.0045	0.439996
$518$	−10.1355	−0.445330
$519$	26.9615	1.18348
$520$	9.04617	0.396701
$521$	9.34165	0.409265	0.204633	−	0.978839i	$-0.434400\pi$
$521$	9.34165	0.409265	0.204633	+	0.978839i	$0.434400\pi$
$522$	−13.6600	−0.597881
$523$	−2.73329	−0.119518	−0.0597592	−	0.998213i	$-0.519033\pi$
$523$	−2.73329	−0.119518	−0.0597592	+	0.998213i	$0.519033\pi$
$524$	−19.7216	−0.861544
$525$	12.7293	0.555550
$526$	−0.236327	−0.0103044
$527$	−16.5962	−0.722940
$528$	−5.77667	−0.251397
$529$	−22.7627	−0.989682
$530$	−3.07774	−0.133689
$531$	18.9894	0.824068
$532$	−4.81872	−0.208918
$533$	19.9916	0.865933
$534$	−2.82893	−0.122420
$535$	18.0511	0.780417
$536$	13.9184	0.601183
$537$	−42.5691	−1.83699
$538$	0.135168	0.00582752
$539$	−2.06316	−0.0888667
$540$	9.61736	0.413865
$541$	−27.9720	−1.20261	−0.601305	−	0.799020i	$-0.705352\pi$
$541$	−27.9720	−1.20261	−0.601305	+	0.799020i	$0.705352\pi$
$542$	6.98912	0.300209
$543$	−69.1588	−2.96789
$544$	−9.53270	−0.408711
$545$	−22.9233	−0.981927
$546$	8.15259	0.348898
$547$	46.1378	1.97271	0.986356	−	0.164629i	$-0.0526426\pi$
$547$	46.1378	1.97271	0.986356	+	0.164629i	$0.0526426\pi$
$548$	23.8359	1.01822
$549$	−54.6742	−2.33344
$550$	0.847057	0.0361186
$551$	8.86288	0.377571
$552$	2.33571	0.0994142
$553$	−10.2301	−0.435028
$554$	7.33116	0.311471
$555$	−45.4775	−1.93041
$556$	−9.52573	−0.403981
$557$	−10.6105	−0.449581	−0.224790	−	0.974407i	$-0.572170\pi$
$557$	−10.6105	−0.449581	−0.224790	+	0.974407i	$0.572170\pi$
$558$	16.8277	0.712372
$559$	−18.4684	−0.781131
$560$	9.41104	0.397689
$561$	−4.18969	−0.176889
$562$	−13.5871	−0.573135
$563$	0.657381	0.0277053	0.0138526	−	0.999904i	$-0.495590\pi$
$563$	0.657381	0.0277053	0.0138526	+	0.999904i	$0.495590\pi$
$564$	60.1783	2.53396
$565$	−6.08755	−0.256105
$566$	11.2851	0.474349
$567$	−8.11274	−0.340703
$568$	−29.0210	−1.21769
$569$	−33.5273	−1.40554	−0.702769	−	0.711418i	$-0.748053\pi$
$569$	−33.5273	−1.40554	−0.702769	+	0.711418i	$0.748053\pi$
$570$	2.71776	0.113835
$571$	−10.9584	−0.458596	−0.229298	−	0.973356i	$-0.573643\pi$
$571$	−10.9584	−0.458596	−0.229298	+	0.973356i	$0.573643\pi$
$572$	−4.31593	−0.180458
$573$	−41.2946	−1.72511
$574$	−6.47310	−0.270182
$575$	1.10043	0.0458910
$576$	−13.1901	−0.549586
$577$	−29.0892	−1.21100	−0.605499	−	0.795846i	$-0.707026\pi$
$577$	−29.0892	−1.21100	−0.605499	+	0.795846i	$0.707026\pi$
$578$	6.20820	0.258227
$579$	13.2408	0.550271
$580$	−20.1623	−0.837194
$581$	−5.33514	−0.221339
$582$	14.7245	0.610352
$583$	3.12136	0.129274
$584$	1.61706	0.0669146
$585$	21.3744	0.883724
$586$	−8.80025	−0.363535
$587$	22.5317	0.929982	0.464991	−	0.885315i	$-0.346057\pi$
$587$	22.5317	0.929982	0.464991	+	0.885315i	$0.346057\pi$
$588$	−12.4102	−0.511789
$589$	−10.9181	−0.449874
$590$	−3.52315	−0.145046
$591$	38.2991	1.57541
$592$	27.7085	1.13881
$593$	−14.7940	−0.607518	−0.303759	−	0.952749i	$-0.598242\pi$
$593$	−14.7940	−0.607518	−0.303759	+	0.952749i	$0.598242\pi$
$594$	1.22602	0.0503043
$595$	6.82562	0.279823
$596$	33.8178	1.38523
$597$	−35.1265	−1.43763
$598$	0.704781	0.0288206
$599$	−22.6870	−0.926967	−0.463484	−	0.886105i	$-0.653401\pi$
$599$	−22.6870	−0.926967	−0.463484	+	0.886105i	$0.653401\pi$
$600$	10.8308	0.442166
$601$	−34.1974	−1.39494	−0.697471	−	0.716613i	$-0.745692\pi$
$601$	−34.1974	−1.39494	−0.697471	+	0.716613i	$0.745692\pi$
$602$	5.97990	0.243723
$603$	32.8866	1.33924
$604$	2.59983	0.105786
$605$	−17.1694	−0.698035
$606$	15.0845	0.612766
$607$	24.4533	0.992530	0.496265	−	0.868171i	$-0.334704\pi$
$607$	24.4533	0.992530	0.496265	+	0.868171i	$0.334704\pi$
$608$	−6.27130	−0.254335
$609$	−38.6254	−1.56518
$610$	10.1439	0.410713
$611$	38.5992	1.56155
$612$	−14.7258	−0.595253
$613$	17.1361	0.692122	0.346061	−	0.938212i	$-0.387519\pi$
$613$	17.1361	0.692122	0.346061	+	0.938212i	$0.387519\pi$
$614$	1.45187	0.0585928
$615$	−29.0444	−1.17118
$616$	2.97058	0.119688
$617$	−30.1120	−1.21227	−0.606133	−	0.795364i	$-0.707280\pi$
$617$	−30.1120	−1.21227	−0.606133	+	0.795364i	$0.707280\pi$
$618$	−15.4592	−0.621862
$619$	−31.3567	−1.26033	−0.630166	−	0.776460i	$-0.717013\pi$
$619$	−31.3567	−1.26033	−0.630166	+	0.776460i	$0.717013\pi$
$620$	24.8379	0.997513
$621$	1.59275	0.0639148
$622$	−4.66471	−0.187038
$623$	−4.67405	−0.187262
$624$	−22.2875	−0.892215
$625$	−8.60261	−0.344104
$626$	0.629616	0.0251645
$627$	−2.75628	−0.110075
$628$	11.3206	0.451741
$629$	20.0964	0.801295
$630$	−6.92084	−0.275733
$631$	23.7334	0.944811	0.472406	−	0.881381i	$-0.343386\pi$
$631$	23.7334	0.944811	0.472406	+	0.881381i	$0.343386\pi$
$632$	−8.70437	−0.346241
$633$	43.8161	1.74154
$634$	8.49590	0.337415
$635$	−5.05464	−0.200587
$636$	18.7755	0.744496
$637$	−7.96008	−0.315390
$638$	−2.57029	−0.101759
$639$	−68.5712	−2.71264
$640$	18.5072	0.731560
$641$	−13.7755	−0.544098	−0.272049	−	0.962283i	$-0.587701\pi$
$641$	−13.7755	−0.544098	−0.272049	+	0.962283i	$0.587701\pi$
$642$	13.8418	0.546292
$643$	−21.2462	−0.837869	−0.418935	−	0.908016i	$-0.637596\pi$
$643$	−21.2462	−0.837869	−0.418935	+	0.908016i	$0.637596\pi$
$644$	1.81547	0.0715394
$645$	26.8315	1.05649
$646$	−1.20097	−0.0472516
$647$	−17.6319	−0.693183	−0.346591	−	0.938016i	$-0.612661\pi$
$647$	−17.6319	−0.693183	−0.346591	+	0.938016i	$0.612661\pi$
$648$	−6.90281	−0.271168
$649$	3.57308	0.140256
$650$	3.26811	0.128186
$651$	47.5825	1.86490
$652$	−1.77667	−0.0695799
$653$	41.2213	1.61312	0.806558	−	0.591155i	$-0.201328\pi$
$653$	41.2213	1.61312	0.806558	+	0.591155i	$0.201328\pi$
$654$	−17.5779	−0.687349
$655$	18.3779	0.718083
$656$	17.6962	0.690919
$657$	3.82083	0.149065
$658$	−12.4980	−0.487225
$659$	−31.9854	−1.24597	−0.622987	−	0.782232i	$-0.714081\pi$
$659$	−31.9854	−1.24597	−0.622987	+	0.782232i	$0.714081\pi$
$660$	6.27031	0.244072
$661$	−4.80318	−0.186822	−0.0934111	−	0.995628i	$-0.529777\pi$
$661$	−4.80318	−0.186822	−0.0934111	+	0.995628i	$0.529777\pi$
$662$	−9.86355	−0.383358
$663$	−16.1647	−0.627783
$664$	−4.53945	−0.176165
$665$	4.49039	0.174130
$666$	−20.3767	−0.789582
$667$	−3.33912	−0.129291
$668$	14.8728	0.575447
$669$	−77.3388	−2.99009
$670$	−6.10154	−0.235723
$671$	−10.2876	−0.397150
$672$	27.3310	1.05432
$673$	−4.64292	−0.178971	−0.0894857	−	0.995988i	$-0.528522\pi$
$673$	−4.64292	−0.178971	−0.0894857	+	0.995988i	$0.528522\pi$
$674$	1.92347	0.0740892
$675$	7.38567	0.284275
$676$	6.44505	0.247887
$677$	25.6521	0.985891	0.492945	−	0.870060i	$-0.335920\pi$
$677$	25.6521	0.985891	0.492945	+	0.870060i	$0.335920\pi$
$678$	−4.66800	−0.179274
$679$	24.3284	0.933639
$680$	5.80765	0.222713
$681$	−15.1044	−0.578800
$682$	3.16633	0.121245
$683$	26.9137	1.02982	0.514911	−	0.857243i	$-0.327825\pi$
$683$	26.9137	1.02982	0.514911	+	0.857243i	$0.327825\pi$
$684$	−9.68767	−0.370417
$685$	−22.2118	−0.848670
$686$	9.51626	0.363332
$687$	4.24564	0.161981
$688$	−16.3479	−0.623256
$689$	12.0428	0.458795
$690$	−1.02393	−0.0389802
$691$	1.83777	0.0699122	0.0349561	−	0.999389i	$-0.488871\pi$
$691$	1.83777	0.0699122	0.0349561	+	0.999389i	$0.488871\pi$
$692$	17.8308	0.677826
$693$	7.01893	0.266627
$694$	14.3666	0.545348
$695$	8.87669	0.336712
$696$	−32.8648	−1.24574
$697$	12.8346	0.486147
$698$	13.0613	0.494379
$699$	−44.5382	−1.68459
$700$	8.41843	0.318187
$701$	24.8552	0.938767	0.469383	−	0.882994i	$-0.344476\pi$
$701$	24.8552	0.938767	0.469383	+	0.882994i	$0.344476\pi$
$702$	4.73023	0.178531
$703$	13.2208	0.498634
$704$	−2.48187	−0.0935391
$705$	−56.0780	−2.11202
$706$	6.52620	0.245617
$707$	24.9232	0.937332
$708$	21.4926	0.807742
$709$	26.3674	0.990249	0.495124	−	0.868822i	$-0.335123\pi$
$709$	26.3674	0.990249	0.495124	+	0.868822i	$0.335123\pi$
$710$	12.7222	0.477456
$711$	−20.5668	−0.771316
$712$	−3.97696	−0.149043
$713$	4.11345	0.154050
$714$	5.23397	0.195876
$715$	4.02186	0.150409
$716$	−28.1529	−1.05212
$717$	47.1065	1.75922
$718$	14.6663	0.547342
$719$	15.4425	0.575907	0.287954	−	0.957644i	$-0.407025\pi$
$719$	15.4425	0.575907	0.287954	+	0.957644i	$0.407025\pi$
$720$	18.9202	0.705114
$721$	−25.5423	−0.951245
$722$	8.18881	0.304756
$723$	−9.41585	−0.350179
$724$	−45.7379	−1.69983
$725$	−15.4837	−0.575050
$726$	−13.1657	−0.488624
$727$	9.34159	0.346460	0.173230	−	0.984881i	$-0.444580\pi$
$727$	9.34159	0.346460	0.173230	+	0.984881i	$0.444580\pi$
$728$	11.4611	0.424775
$729$	−42.6606	−1.58002
$730$	−0.708889	−0.0262372
$731$	−11.8567	−0.438537
$732$	−61.8816	−2.28721
$733$	3.83480	0.141641	0.0708207	−	0.997489i	$-0.477438\pi$
$733$	3.83480	0.141641	0.0708207	+	0.997489i	$0.477438\pi$
$734$	−14.6677	−0.541394
$735$	11.5646	0.426568
$736$	2.36273	0.0870915
$737$	6.18802	0.227939
$738$	−13.0137	−0.479040
$739$	9.82730	0.361503	0.180752	−	0.983529i	$-0.442147\pi$
$739$	9.82730	0.361503	0.180752	+	0.983529i	$0.442147\pi$
$740$	−30.0763	−1.10563
$741$	−10.6343	−0.390660
$742$	−3.89936	−0.143150
$743$	17.9973	0.660256	0.330128	−	0.943936i	$-0.392908\pi$
$743$	17.9973	0.660256	0.330128	+	0.943936i	$0.392908\pi$
$744$	40.4860	1.48429
$745$	−31.5136	−1.15457
$746$	3.39086	0.124148
$747$	−10.7259	−0.392440
$748$	−2.77083	−0.101312
$749$	22.8699	0.835648
$750$	−15.2574	−0.557123
$751$	25.7472	0.939527	0.469764	−	0.882792i	$-0.344339\pi$
$751$	25.7472	0.939527	0.469764	+	0.882792i	$0.344339\pi$
$752$	34.1672	1.24595
$753$	20.8524	0.759903
$754$	−9.91669	−0.361145
$755$	−2.42269	−0.0881708
$756$	12.1847	0.443155
$757$	6.33193	0.230138	0.115069	−	0.993358i	$-0.463291\pi$
$757$	6.33193	0.230138	0.115069	+	0.993358i	$0.463291\pi$
$758$	−4.62603	−0.168025
$759$	1.03844	0.0376929
$760$	3.82069	0.138591
$761$	9.71353	0.352115	0.176058	−	0.984380i	$-0.443665\pi$
$761$	9.71353	0.352115	0.176058	+	0.984380i	$0.443665\pi$
$762$	−3.87596	−0.140411
$763$	−29.0428	−1.05142
$764$	−27.3100	−0.988040
$765$	13.7224	0.496134
$766$	10.0116	0.361733
$767$	13.7857	0.497771
$768$	−2.61384	−0.0943189
$769$	−13.6464	−0.492103	−0.246052	−	0.969257i	$-0.579133\pi$
$769$	−13.6464	−0.492103	−0.246052	+	0.969257i	$0.579133\pi$
$770$	−1.30224	−0.0469295
$771$	43.0145	1.54913
$772$	8.75676	0.315163
$773$	−10.8734	−0.391088	−0.195544	−	0.980695i	$-0.562647\pi$
$773$	−10.8734	−0.391088	−0.195544	+	0.980695i	$0.562647\pi$
$774$	12.0221	0.432127
$775$	19.0743	0.685169
$776$	20.7001	0.743089
$777$	−57.6179	−2.06703
$778$	−12.2608	−0.439570
$779$	8.44355	0.302522
$780$	24.1921	0.866216
$781$	−12.9025	−0.461689
$782$	0.452470	0.0161803
$783$	−22.4109	−0.800901
$784$	−7.04610	−0.251646
$785$	−10.5493	−0.376519
$786$	14.0924	0.502658
$787$	11.5097	0.410276	0.205138	−	0.978733i	$-0.434236\pi$
$787$	11.5097	0.410276	0.205138	+	0.978733i	$0.434236\pi$
$788$	25.3289	0.902305
$789$	−1.34346	−0.0478284
$790$	3.81582	0.135761
$791$	−7.71264	−0.274230
$792$	5.97212	0.212210
$793$	−39.6917	−1.40949
$794$	−3.97543	−0.141083
$795$	−17.4962	−0.620525
$796$	−23.2308	−0.823392
$797$	19.0707	0.675518	0.337759	−	0.941233i	$-0.390331\pi$
$797$	19.0707	0.675518	0.337759	+	0.941233i	$0.390331\pi$
$798$	3.44328	0.121891
$799$	24.7807	0.876678
$800$	10.9561	0.387358
$801$	−9.39683	−0.332020
$802$	15.4020	0.543865
$803$	0.718936	0.0253707
$804$	37.2218	1.31271
$805$	−1.69177	−0.0596270
$806$	12.2163	0.430302
$807$	0.768397	0.0270489
$808$	21.2061	0.746028
$809$	33.6431	1.18283	0.591414	−	0.806368i	$-0.298570\pi$
$809$	33.6431	1.18283	0.591414	+	0.806368i	$0.298570\pi$
$810$	3.02605	0.106325
$811$	10.5954	0.372055	0.186027	−	0.982545i	$-0.440439\pi$
$811$	10.5954	0.372055	0.186027	+	0.982545i	$0.440439\pi$
$812$	−25.5447	−0.896443
$813$	39.7314	1.39344
$814$	−3.83413	−0.134386
$815$	1.65562	0.0579938
$816$	−14.3086	−0.500902
$817$	−7.80022	−0.272895
$818$	−1.22354	−0.0427800
$819$	27.0804	0.946266
$820$	−19.2084	−0.670785
$821$	50.5054	1.76265	0.881325	−	0.472510i	$-0.156652\pi$
$821$	50.5054	1.76265	0.881325	+	0.472510i	$0.156652\pi$
$822$	−17.0323	−0.594069
$823$	42.1635	1.46973	0.734864	−	0.678215i	$-0.237246\pi$
$823$	42.1635	1.46973	0.734864	+	0.678215i	$0.237246\pi$
$824$	−21.7329	−0.757102
$825$	4.81530	0.167647
$826$	−4.46367	−0.155311
$827$	−7.68387	−0.267194	−0.133597	−	0.991036i	$-0.542653\pi$
$827$	−7.68387	−0.267194	−0.133597	+	0.991036i	$0.542653\pi$
$828$	3.64986	0.126841
$829$	11.2333	0.390150	0.195075	−	0.980788i	$-0.437505\pi$
$829$	11.2333	0.390150	0.195075	+	0.980788i	$0.437505\pi$
$830$	1.99001	0.0690741
$831$	41.6758	1.44572
$832$	−9.57555	−0.331972
$833$	−5.11038	−0.177064
$834$	6.80675	0.235698
$835$	−13.8595	−0.479626
$836$	−1.82285	−0.0630447
$837$	27.6079	0.954270
$838$	3.21366	0.111014
$839$	−24.5967	−0.849173	−0.424587	−	0.905387i	$-0.639581\pi$
$839$	−24.5967	−0.849173	−0.424587	+	0.905387i	$0.639581\pi$
$840$	−16.6510	−0.574513
$841$	17.9834	0.620117
$842$	2.10529	0.0725532
$843$	−77.2389	−2.66025
$844$	28.9776	0.997450
$845$	−6.00591	−0.206610
$846$	−25.1264	−0.863863
$847$	−21.7528	−0.747435
$848$	10.6601	0.366068
$849$	64.1530	2.20172
$850$	2.09813	0.0719653
$851$	−4.98100	−0.170746
$852$	−77.6106	−2.65890
$853$	−32.5459	−1.11435	−0.557175	−	0.830395i	$-0.688115\pi$
$853$	−32.5459	−1.11435	−0.557175	+	0.830395i	$0.688115\pi$
$854$	12.8518	0.439780
$855$	9.02758	0.308737
$856$	19.4591	0.665097
$857$	49.5863	1.69383	0.846917	−	0.531724i	$-0.178456\pi$
$857$	49.5863	1.69383	0.846917	+	0.531724i	$0.178456\pi$
$858$	3.08401	0.105286
$859$	4.41762	0.150727	0.0753636	−	0.997156i	$-0.475988\pi$
$859$	4.41762	0.150727	0.0753636	+	0.997156i	$0.475988\pi$
$860$	17.7448	0.605094
$861$	−36.7979	−1.25407
$862$	10.8313	0.368914
$863$	−15.3706	−0.523222	−0.261611	−	0.965173i	$-0.584254\pi$
$863$	−15.3706	−0.523222	−0.261611	+	0.965173i	$0.584254\pi$
$864$	15.8578	0.539493
$865$	−16.6159	−0.564958
$866$	−1.86211	−0.0632771
$867$	35.2920	1.19858
$868$	31.4684	1.06811
$869$	−3.86990	−0.131277
$870$	14.4073	0.488452
$871$	23.8746	0.808959
$872$	−24.7113	−0.836831
$873$	48.9104	1.65537
$874$	0.297667	0.0100688
$875$	−25.2089	−0.852216
$876$	4.32451	0.146111
$877$	−3.79809	−0.128252	−0.0641261	−	0.997942i	$-0.520426\pi$
$877$	−3.79809	−0.128252	−0.0641261	+	0.997942i	$0.520426\pi$
$878$	−6.39421	−0.215794
$879$	−50.0271	−1.68737
$880$	3.56007	0.120010
$881$	41.0985	1.38464	0.692322	−	0.721589i	$-0.256588\pi$
$881$	41.0985	1.38464	0.692322	+	0.721589i	$0.256588\pi$
$882$	5.18167	0.174476
$883$	8.85164	0.297881	0.148941	−	0.988846i	$-0.452414\pi$
$883$	8.85164	0.297881	0.148941	+	0.988846i	$0.452414\pi$
$884$	−10.6904	−0.359558
$885$	−20.0282	−0.673241
$886$	4.31863	0.145087
$887$	36.3201	1.21951	0.609756	−	0.792590i	$-0.291268\pi$
$887$	36.3201	1.21951	0.609756	+	0.792590i	$0.291268\pi$
$888$	−49.0247	−1.64516
$889$	−6.40399	−0.214783
$890$	1.74342	0.0584396
$891$	−3.06894	−0.102813
$892$	−51.1476	−1.71255
$893$	16.3025	0.545543
$894$	−24.1650	−0.808199
$895$	26.2346	0.876927
$896$	23.4477	0.783333
$897$	4.00650	0.133773
$898$	0.171010	0.00570667
$899$	−57.8786	−1.93036
$900$	16.9246	0.564154
$901$	7.73151	0.257574
$902$	−2.44869	−0.0815323
$903$	33.9942	1.13126
$904$	−6.56237	−0.218261
$905$	42.6214	1.41678
$906$	−1.85775	−0.0617195
$907$	12.9446	0.429817	0.214908	−	0.976634i	$-0.431055\pi$
$907$	12.9446	0.429817	0.214908	+	0.976634i	$0.431055\pi$
$908$	−9.98919	−0.331503
$909$	50.1061	1.66191
$910$	−5.02430	−0.166554
$911$	−3.81424	−0.126371	−0.0631857	−	0.998002i	$-0.520126\pi$
$911$	−3.81424	−0.126371	−0.0631857	+	0.998002i	$0.520126\pi$
$912$	−9.41324	−0.311704
$913$	−2.01821	−0.0667930
$914$	−19.9800	−0.660881
$915$	57.6652	1.90635
$916$	2.80783	0.0927733
$917$	23.2839	0.768902
$918$	3.03681	0.100230
$919$	12.7492	0.420559	0.210279	−	0.977641i	$-0.432563\pi$
$919$	12.7492	0.420559	0.210279	+	0.977641i	$0.432563\pi$
$920$	−1.43946	−0.0474575
$921$	8.25351	0.271963
$922$	−11.7586	−0.387250
$923$	−49.7805	−1.63854
$924$	7.94420	0.261345
$925$	−23.0972	−0.759431
$926$	12.1968	0.400812
$927$	−51.3509	−1.68658
$928$	−33.2451	−1.09132
$929$	−56.0099	−1.83762	−0.918812	−	0.394696i	$-0.870850\pi$
$929$	−56.0099	−1.83762	−0.918812	+	0.394696i	$0.870850\pi$
$930$	−17.7482	−0.581988
$931$	−3.36198	−0.110184
$932$	−29.4551	−0.964834
$933$	−26.5177	−0.868149
$934$	9.88615	0.323485
$935$	2.58204	0.0844417
$936$	23.0416	0.753139
$937$	36.4510	1.19080	0.595401	−	0.803429i	$-0.296993\pi$
$937$	36.4510	1.19080	0.595401	+	0.803429i	$0.296993\pi$
$938$	−7.73037	−0.252405
$939$	3.57920	0.116803
$940$	−37.0869	−1.20964
$941$	−13.4969	−0.439986	−0.219993	−	0.975501i	$-0.570603\pi$
$941$	−13.4969	−0.439986	−0.219993	+	0.975501i	$0.570603\pi$
$942$	−8.08929	−0.263563
$943$	−3.18113	−0.103592
$944$	12.2028	0.397166
$945$	−11.3545	−0.369363
$946$	2.26211	0.0735477
$947$	−9.33729	−0.303421	−0.151711	−	0.988425i	$-0.548478\pi$
$947$	−9.33729	−0.303421	−0.151711	+	0.988425i	$0.548478\pi$
$948$	−23.2780	−0.756035
$949$	2.77379	0.0900412
$950$	1.38030	0.0447829
$951$	48.2970	1.56614
$952$	7.35802	0.238475
$953$	−30.9211	−1.00163	−0.500817	−	0.865553i	$-0.666967\pi$
$953$	−30.9211	−1.00163	−0.500817	+	0.865553i	$0.666967\pi$
$954$	−7.83936	−0.253809
$955$	25.4492	0.823516
$956$	31.1537	1.00758
$957$	−14.6115	−0.472321
$958$	−16.0963	−0.520048
$959$	−28.1413	−0.908731
$960$	13.9116	0.448996
$961$	40.3005	1.30002
$962$	−14.7928	−0.476940
$963$	45.9782	1.48163
$964$	−6.22712	−0.200562
$965$	−8.16011	−0.262683
$966$	−1.29727	−0.0417389
$967$	−26.2898	−0.845422	−0.422711	−	0.906265i	$-0.638921\pi$
$967$	−26.2898	−0.845422	−0.422711	+	0.906265i	$0.638921\pi$
$968$	−18.5086	−0.594888
$969$	−6.82722	−0.219322
$970$	−9.07449	−0.291364
$971$	−56.4957	−1.81303	−0.906516	−	0.422171i	$-0.861268\pi$
$971$	−56.4957	−1.81303	−0.906516	+	0.422171i	$0.861268\pi$
$972$	−35.8869	−1.15107
$973$	11.2463	0.360541
$974$	5.94303	0.190427
$975$	18.5784	0.594984
$976$	−35.1343	−1.12462
$977$	−5.53002	−0.176921	−0.0884604	−	0.996080i	$-0.528195\pi$
$977$	−5.53002	−0.176921	−0.0884604	+	0.996080i	$0.528195\pi$
$978$	1.26955	0.0405957
$979$	−1.76813	−0.0565097
$980$	7.64821	0.244313
$981$	−58.3883	−1.86419
$982$	−12.6592	−0.403972
$983$	46.6297	1.48726	0.743628	−	0.668594i	$-0.233104\pi$
$983$	46.6297	1.48726	0.743628	+	0.668594i	$0.233104\pi$
$984$	−31.3098	−0.998121
$985$	−23.6031	−0.752057
$986$	−6.36652	−0.202751
$987$	−71.0482	−2.26149
$988$	−7.03293	−0.223747
$989$	2.93876	0.0934470
$990$	−2.61806	−0.0832074
$991$	−0.545477	−0.0173277	−0.00866383	−	0.999962i	$-0.502758\pi$
$991$	−0.545477	−0.0173277	−0.00866383	+	0.999962i	$0.502758\pi$
$992$	40.9545	1.30031
$993$	−56.0717	−1.77938
$994$	16.1185	0.511246
$995$	21.6479	0.686284
$996$	−12.1398	−0.384665
$997$	−41.9099	−1.32730	−0.663650	−	0.748043i	$-0.730994\pi$
$997$	−41.9099	−1.32730	−0.663650	+	0.748043i	$0.730994\pi$
$998$	5.33285	0.168808
$999$	−33.4306	−1.05770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	163.2.a.c.1.3	✓	7
3.2	odd	2		1467.2.a.f.1.5		7
4.3	odd	2		2608.2.a.n.1.7		7
5.4	even	2		4075.2.a.f.1.5		7
7.6	odd	2		7987.2.a.h.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
163.2.a.c.1.3	✓	7	1.1	even	1	trivial
1467.2.a.f.1.5		7	3.2	odd	2
2608.2.a.n.1.7		7	4.3	odd	2
4075.2.a.f.1.5		7	5.4	even	2
7987.2.a.h.1.3		7	7.6	odd	2

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:	\( N \)	\(=\)	\( 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	163.a (trivial)

\(f(q)\)	\(=\)	\(q-0.472573 q^{2} -2.68646 q^{3} -1.77667 q^{4} +1.65562 q^{5} +1.26955 q^{6} +2.09759 q^{7} +1.78476 q^{8} +4.21705 q^{9} +O(q^{10})\)	\(q-0.472573 q^{2} -2.68646 q^{3} -1.77667 q^{4} +1.65562 q^{5} +1.26955 q^{6} +2.09759 q^{7} +1.78476 q^{8} +4.21705 q^{9} -0.782401 q^{10} +0.793490 q^{11} +4.77296 q^{12} +3.06144 q^{13} -0.991265 q^{14} -4.44775 q^{15} +2.70992 q^{16} +1.96545 q^{17} -1.99286 q^{18} +1.29301 q^{19} -2.94150 q^{20} -5.63509 q^{21} -0.374982 q^{22} -0.487146 q^{23} -4.79467 q^{24} -2.25893 q^{25} -1.44675 q^{26} -3.26955 q^{27} -3.72674 q^{28} +6.85444 q^{29} +2.10189 q^{30} -8.44396 q^{31} -4.85015 q^{32} -2.13168 q^{33} -0.928817 q^{34} +3.47281 q^{35} -7.49232 q^{36} +10.2248 q^{37} -0.611043 q^{38} -8.22442 q^{39} +2.95487 q^{40} +6.53014 q^{41} +2.66299 q^{42} -6.03259 q^{43} -1.40977 q^{44} +6.98182 q^{45} +0.230212 q^{46} +12.6082 q^{47} -7.28009 q^{48} -2.60011 q^{49} +1.06751 q^{50} -5.28009 q^{51} -5.43918 q^{52} +3.93372 q^{53} +1.54510 q^{54} +1.31372 q^{55} +3.74369 q^{56} -3.47362 q^{57} -3.23923 q^{58} +4.50300 q^{59} +7.90220 q^{60} -12.9650 q^{61} +3.99039 q^{62} +8.84564 q^{63} -3.12779 q^{64} +5.06857 q^{65} +1.00737 q^{66} +7.79848 q^{67} -3.49196 q^{68} +1.30870 q^{69} -1.64116 q^{70} -16.2605 q^{71} +7.52640 q^{72} +0.906043 q^{73} -4.83199 q^{74} +6.06851 q^{75} -2.29726 q^{76} +1.66442 q^{77} +3.88664 q^{78} -4.87706 q^{79} +4.48660 q^{80} -3.86765 q^{81} -3.08597 q^{82} -2.54346 q^{83} +10.0117 q^{84} +3.25403 q^{85} +2.85084 q^{86} -18.4142 q^{87} +1.41619 q^{88} -2.22829 q^{89} -3.29942 q^{90} +6.42165 q^{91} +0.865501 q^{92} +22.6843 q^{93} -5.95829 q^{94} +2.14074 q^{95} +13.0297 q^{96} +11.5983 q^{97} +1.22874 q^{98} +3.34619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + q^{3} + 5 q^{4} + 11 q^{5} - 3 q^{6} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + q^3 + 5 * q^4 + 11 * q^5 - 3 * q^6 + 3 * q^8 + 2 * q^9	\( 7 q + 3 q^{2} + q^{3} + 5 q^{4} + 11 q^{5} - 3 q^{6} + 3 q^{8} + 2 q^{9} + q^{10} + 2 q^{11} - 4 q^{12} + 10 q^{13} - q^{14} - 4 q^{15} - 3 q^{16} + 13 q^{17} - 4 q^{18} - 5 q^{19} + 4 q^{20} - 5 q^{21} - 11 q^{22} + 2 q^{23} - 7 q^{24} + 4 q^{25} - 9 q^{26} - 11 q^{27} - 18 q^{28} + 7 q^{29} - 13 q^{30} - 11 q^{31} - 6 q^{32} - 6 q^{33} - 6 q^{34} - 9 q^{35} - 24 q^{36} + 3 q^{37} - 5 q^{38} - 13 q^{39} - 12 q^{40} + 17 q^{41} + q^{42} - 10 q^{43} + 8 q^{44} + 12 q^{45} - 24 q^{46} + 11 q^{47} - 8 q^{48} - 7 q^{49} + 13 q^{50} + 6 q^{51} + 23 q^{52} + 18 q^{53} - 4 q^{54} - 6 q^{55} - 2 q^{56} + 20 q^{57} - q^{58} + 11 q^{59} - 27 q^{60} + 4 q^{61} + 25 q^{62} + 7 q^{63} - 21 q^{64} + 34 q^{65} - 10 q^{66} - 18 q^{67} + 23 q^{68} + 8 q^{69} + 6 q^{70} - 3 q^{71} + 22 q^{72} + 2 q^{73} - 9 q^{75} - 24 q^{76} + 25 q^{77} - 10 q^{78} - 8 q^{80} - 13 q^{81} - q^{82} + 18 q^{83} + 16 q^{84} + 12 q^{85} + 15 q^{86} + 19 q^{87} + 3 q^{88} + 18 q^{89} + 37 q^{90} - 36 q^{91} + 23 q^{92} - 15 q^{93} + 51 q^{94} - 25 q^{95} + 28 q^{96} + 21 q^{97} + 6 q^{98} - 13 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + q^3 + 5 * q^4 + 11 * q^5 - 3 * q^6 + 3 * q^8 + 2 * q^9 + q^10 + 2 * q^11 - 4 * q^12 + 10 * q^13 - q^14 - 4 * q^15 - 3 * q^16 + 13 * q^17 - 4 * q^18 - 5 * q^19 + 4 * q^20 - 5 * q^21 - 11 * q^22 + 2 * q^23 - 7 * q^24 + 4 * q^25 - 9 * q^26 - 11 * q^27 - 18 * q^28 + 7 * q^29 - 13 * q^30 - 11 * q^31 - 6 * q^32 - 6 * q^33 - 6 * q^34 - 9 * q^35 - 24 * q^36 + 3 * q^37 - 5 * q^38 - 13 * q^39 - 12 * q^40 + 17 * q^41 + q^42 - 10 * q^43 + 8 * q^44 + 12 * q^45 - 24 * q^46 + 11 * q^47 - 8 * q^48 - 7 * q^49 + 13 * q^50 + 6 * q^51 + 23 * q^52 + 18 * q^53 - 4 * q^54 - 6 * q^55 - 2 * q^56 + 20 * q^57 - q^58 + 11 * q^59 - 27 * q^60 + 4 * q^61 + 25 * q^62 + 7 * q^63 - 21 * q^64 + 34 * q^65 - 10 * q^66 - 18 * q^67 + 23 * q^68 + 8 * q^69 + 6 * q^70 - 3 * q^71 + 22 * q^72 + 2 * q^73 - 9 * q^75 - 24 * q^76 + 25 * q^77 - 10 * q^78 - 8 * q^80 - 13 * q^81 - q^82 + 18 * q^83 + 16 * q^84 + 12 * q^85 + 15 * q^86 + 19 * q^87 + 3 * q^88 + 18 * q^89 + 37 * q^90 - 36 * q^91 + 23 * q^92 - 15 * q^93 + 51 * q^94 - 25 * q^95 + 28 * q^96 + 21 * q^97 + 6 * q^98 - 13 * q^99

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