LMFDB - Embedded newform 143.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(1,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, 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("143.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.194616205.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 10x^{4} - 2x^{3} + 24x^{2} + 7x - 12 $ x^6 - 10x^4 - 2x^3 + 24x^2 + 7x - 12
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			$0.633036$ of defining polynomial
Character	$\chi$	$=$	143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.633036 q^{2} +2.27944 q^{3} -1.59927 q^{4} +4.04223 q^{5} -1.44297 q^{6} -3.23808 q^{7} +2.27847 q^{8} +2.19585 q^{9} +O(q^{10})$	\(q-0.633036 q^{2} +2.27944 q^{3} -1.59927 q^{4} +4.04223 q^{5} -1.44297 q^{6} -3.23808 q^{7} +2.27847 q^{8} +2.19585 q^{9} -2.55888 q^{10} -1.00000 q^{11} -3.64543 q^{12} +1.00000 q^{13} +2.04982 q^{14} +9.21403 q^{15} +1.75618 q^{16} +1.26607 q^{17} -1.39005 q^{18} -3.76279 q^{19} -6.46460 q^{20} -7.38101 q^{21} +0.633036 q^{22} -4.00268 q^{23} +5.19362 q^{24} +11.3396 q^{25} -0.633036 q^{26} -1.83302 q^{27} +5.17855 q^{28} +2.63965 q^{29} -5.83281 q^{30} -3.14112 q^{31} -5.66866 q^{32} -2.27944 q^{33} -0.801470 q^{34} -13.0891 q^{35} -3.51174 q^{36} -8.50684 q^{37} +2.38198 q^{38} +2.27944 q^{39} +9.21009 q^{40} -10.4366 q^{41} +4.67245 q^{42} +5.18335 q^{43} +1.59927 q^{44} +8.87613 q^{45} +2.53384 q^{46} -3.82495 q^{47} +4.00311 q^{48} +3.48516 q^{49} -7.17841 q^{50} +2.88594 q^{51} -1.59927 q^{52} +0.485163 q^{53} +1.16037 q^{54} -4.04223 q^{55} -7.37785 q^{56} -8.57706 q^{57} -1.67099 q^{58} +12.8985 q^{59} -14.7357 q^{60} +13.9902 q^{61} +1.98844 q^{62} -7.11033 q^{63} +0.0761058 q^{64} +4.04223 q^{65} +1.44297 q^{66} +11.2408 q^{67} -2.02479 q^{68} -9.12388 q^{69} +8.28586 q^{70} -3.39103 q^{71} +5.00316 q^{72} -1.58775 q^{73} +5.38514 q^{74} +25.8481 q^{75} +6.01770 q^{76} +3.23808 q^{77} -1.44297 q^{78} +4.63965 q^{79} +7.09889 q^{80} -10.7658 q^{81} +6.60675 q^{82} +9.85469 q^{83} +11.8042 q^{84} +5.11776 q^{85} -3.28125 q^{86} +6.01692 q^{87} -2.27847 q^{88} -6.51470 q^{89} -5.61891 q^{90} -3.23808 q^{91} +6.40135 q^{92} -7.15999 q^{93} +2.42133 q^{94} -15.2101 q^{95} -12.9214 q^{96} +9.70000 q^{97} -2.20623 q^{98} -2.19585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9	\( 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 12 q^{14} + 3 q^{15} + 8 q^{16} + 6 q^{18} - 10 q^{19} + 4 q^{20} - 12 q^{21} + 11 q^{23} - 38 q^{24} + 23 q^{25} + 9 q^{27} + 9 q^{28} + 2 q^{29} - 56 q^{30} - 9 q^{31} - 17 q^{32} - 3 q^{33} - 40 q^{34} - 24 q^{35} + 11 q^{36} + 15 q^{37} - 9 q^{38} + 3 q^{39} + 16 q^{40} - 4 q^{41} + 19 q^{42} - 2 q^{43} - 8 q^{44} - 26 q^{45} - 6 q^{46} + 6 q^{47} + 19 q^{48} + 20 q^{49} - 4 q^{50} + 6 q^{51} + 8 q^{52} + 2 q^{53} + 37 q^{54} - q^{55} - 39 q^{56} + 22 q^{57} + 18 q^{58} + 11 q^{59} - 24 q^{60} + 16 q^{61} + 16 q^{62} - 26 q^{63} + 36 q^{64} + q^{65} + 3 q^{66} + 9 q^{67} + 12 q^{68} - 3 q^{69} + 32 q^{70} - 15 q^{71} + 5 q^{72} + 32 q^{73} + 22 q^{74} + 4 q^{75} - 26 q^{76} - 4 q^{77} - 3 q^{78} + 14 q^{79} + 56 q^{80} - 2 q^{81} - 24 q^{82} - 26 q^{83} + 43 q^{84} - 12 q^{85} - 10 q^{86} - 38 q^{87} + 6 q^{88} - 23 q^{89} - 10 q^{90} + 4 q^{91} + 83 q^{92} + 23 q^{93} + 46 q^{94} - 52 q^{95} - 56 q^{96} + 27 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 12 * q^14 + 3 * q^15 + 8 * q^16 + 6 * q^18 - 10 * q^19 + 4 * q^20 - 12 * q^21 + 11 * q^23 - 38 * q^24 + 23 * q^25 + 9 * q^27 + 9 * q^28 + 2 * q^29 - 56 * q^30 - 9 * q^31 - 17 * q^32 - 3 * q^33 - 40 * q^34 - 24 * q^35 + 11 * q^36 + 15 * q^37 - 9 * q^38 + 3 * q^39 + 16 * q^40 - 4 * q^41 + 19 * q^42 - 2 * q^43 - 8 * q^44 - 26 * q^45 - 6 * q^46 + 6 * q^47 + 19 * q^48 + 20 * q^49 - 4 * q^50 + 6 * q^51 + 8 * q^52 + 2 * q^53 + 37 * q^54 - q^55 - 39 * q^56 + 22 * q^57 + 18 * q^58 + 11 * q^59 - 24 * q^60 + 16 * q^61 + 16 * q^62 - 26 * q^63 + 36 * q^64 + q^65 + 3 * q^66 + 9 * q^67 + 12 * q^68 - 3 * q^69 + 32 * q^70 - 15 * q^71 + 5 * q^72 + 32 * q^73 + 22 * q^74 + 4 * q^75 - 26 * q^76 - 4 * q^77 - 3 * q^78 + 14 * q^79 + 56 * q^80 - 2 * q^81 - 24 * q^82 - 26 * q^83 + 43 * q^84 - 12 * q^85 - 10 * q^86 - 38 * q^87 + 6 * q^88 - 23 * q^89 - 10 * q^90 + 4 * q^91 + 83 * q^92 + 23 * q^93 + 46 * q^94 - 52 * q^95 - 56 * q^96 + 27 * q^97 - 3 * 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 $

$2$	−0.633036	−0.447624	−0.223812	−	0.974632i	$-0.571850\pi$
$2$	−0.633036	−0.447624	−0.223812	+	0.974632i	$0.571850\pi$
$3$	2.27944	1.31604	0.658018	−	0.753002i	$-0.271395\pi$
$3$	2.27944	1.31604	0.658018	+	0.753002i	$0.271395\pi$
$4$	−1.59927	−0.799633
$5$	4.04223	1.80774	0.903871	−	0.427805i	$-0.140713\pi$
$5$	4.04223	1.80774	0.903871	+	0.427805i	$0.140713\pi$
$6$	−1.44297	−0.589089
$7$	−3.23808	−1.22388	−0.611940	−	0.790904i	$-0.709610\pi$
$7$	−3.23808	−1.22388	−0.611940	+	0.790904i	$0.709610\pi$
$8$	2.27847	0.805559
$9$	2.19585	0.731949
$10$	−2.55888	−0.809189
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.64543	−1.05234
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.04982	0.547838
$15$	9.21403	2.37905
$16$	1.75618	0.439045
$17$	1.26607	0.307068	0.153534	−	0.988143i	$-0.450935\pi$
$17$	1.26607	0.307068	0.153534	+	0.988143i	$0.450935\pi$
$18$	−1.39005	−0.327638
$19$	−3.76279	−0.863244	−0.431622	−	0.902055i	$-0.642059\pi$
$19$	−3.76279	−0.863244	−0.431622	+	0.902055i	$0.642059\pi$
$20$	−6.46460	−1.44553
$21$	−7.38101	−1.61067
$22$	0.633036	0.134964
$23$	−4.00268	−0.834617	−0.417309	−	0.908765i	$-0.637027\pi$
$23$	−4.00268	−0.834617	−0.417309	+	0.908765i	$0.637027\pi$
$24$	5.19362	1.06014
$25$	11.3396	2.26793
$26$	−0.633036	−0.124149
$27$	−1.83302	−0.352765
$28$	5.17855	0.978654
$29$	2.63965	0.490171	0.245085	−	0.969502i	$-0.421184\pi$
$29$	2.63965	0.490171	0.245085	+	0.969502i	$0.421184\pi$
$30$	−5.83281	−1.06492
$31$	−3.14112	−0.564162	−0.282081	−	0.959391i	$-0.591025\pi$
$31$	−3.14112	−0.564162	−0.282081	+	0.959391i	$0.591025\pi$
$32$	−5.66866	−1.00209
$33$	−2.27944	−0.396800
$34$	−0.801470	−0.137451
$35$	−13.0891	−2.21246
$36$	−3.51174	−0.585290
$37$	−8.50684	−1.39852	−0.699258	−	0.714870i	$-0.746486\pi$
$37$	−8.50684	−1.39852	−0.699258	+	0.714870i	$0.746486\pi$
$38$	2.38198	0.386409
$39$	2.27944	0.365003
$40$	9.21009	1.45624
$41$	−10.4366	−1.62992	−0.814962	−	0.579514i	$-0.803242\pi$
$41$	−10.4366	−1.62992	−0.814962	+	0.579514i	$0.803242\pi$
$42$	4.67245	0.720974
$43$	5.18335	0.790454	0.395227	−	0.918584i	$-0.370666\pi$
$43$	5.18335	0.790454	0.395227	+	0.918584i	$0.370666\pi$
$44$	1.59927	0.241098
$45$	8.87613	1.32317
$46$	2.53384	0.373595
$47$	−3.82495	−0.557927	−0.278963	−	0.960302i	$-0.589991\pi$
$47$	−3.82495	−0.557927	−0.278963	+	0.960302i	$0.589991\pi$
$48$	4.00311	0.577798
$49$	3.48516	0.497880
$50$	−7.17841	−1.01518
$51$	2.88594	0.404112
$52$	−1.59927	−0.221778
$53$	0.485163	0.0666423	0.0333211	−	0.999445i	$-0.489392\pi$
$53$	0.485163	0.0666423	0.0333211	+	0.999445i	$0.489392\pi$
$54$	1.16037	0.157906
$55$	−4.04223	−0.545055
$56$	−7.37785	−0.985907
$57$	−8.57706	−1.13606
$58$	−1.67099	−0.219412
$59$	12.8985	1.67925	0.839623	−	0.543170i	$-0.182776\pi$
$59$	12.8985	1.67925	0.839623	+	0.543170i	$0.182776\pi$
$60$	−14.7357	−1.90237
$61$	13.9902	1.79126	0.895630	−	0.444800i	$-0.146725\pi$
$61$	13.9902	1.79126	0.895630	+	0.444800i	$0.146725\pi$
$62$	1.98844	0.252532
$63$	−7.11033	−0.895817
$64$	0.0761058	0.00951322
$65$	4.04223	0.501377
$66$	1.44297	0.177617
$67$	11.2408	1.37328	0.686639	−	0.726999i	$-0.259085\pi$
$67$	11.2408	1.37328	0.686639	+	0.726999i	$0.259085\pi$
$68$	−2.02479	−0.245541
$69$	−9.12388	−1.09839
$70$	8.28586	0.990350
$71$	−3.39103	−0.402441	−0.201220	−	0.979546i	$-0.564491\pi$
$71$	−3.39103	−0.402441	−0.201220	+	0.979546i	$0.564491\pi$
$72$	5.00316	0.589628
$73$	−1.58775	−0.185832	−0.0929158	−	0.995674i	$-0.529619\pi$
$73$	−1.58775	−0.185832	−0.0929158	+	0.995674i	$0.529619\pi$
$74$	5.38514	0.626009
$75$	25.8481	2.98468
$76$	6.01770	0.690278
$77$	3.23808	0.369013
$78$	−1.44297	−0.163384
$79$	4.63965	0.522001	0.261001	−	0.965339i	$-0.415948\pi$
$79$	4.63965	0.522001	0.261001	+	0.965339i	$0.415948\pi$
$80$	7.09889	0.793680
$81$	−10.7658	−1.19620
$82$	6.60675	0.729594
$83$	9.85469	1.08169	0.540846	−	0.841121i	$-0.318104\pi$
$83$	9.85469	1.08169	0.540846	+	0.841121i	$0.318104\pi$
$84$	11.8042	1.28794
$85$	5.11776	0.555099
$86$	−3.28125	−0.353826
$87$	6.01692	0.645082
$88$	−2.27847	−0.242885
$89$	−6.51470	−0.690557	−0.345278	−	0.938500i	$-0.612215\pi$
$89$	−6.51470	−0.690557	−0.345278	+	0.938500i	$0.612215\pi$
$90$	−5.61891	−0.592285
$91$	−3.23808	−0.339443
$92$	6.40135	0.667387
$93$	−7.15999	−0.742457
$94$	2.42133	0.249741
$95$	−15.2101	−1.56052
$96$	−12.9214	−1.31878
$97$	9.70000	0.984886	0.492443	−	0.870345i	$-0.336104\pi$
$97$	9.70000	0.984886	0.492443	+	0.870345i	$0.336104\pi$
$98$	−2.20623	−0.222863
$99$	−2.19585	−0.220691
$100$	−18.1351	−1.81351
$101$	15.6480	1.55703	0.778515	−	0.627626i	$-0.215973\pi$
$101$	15.6480	1.55703	0.778515	+	0.627626i	$0.215973\pi$
$102$	−1.82690	−0.180890
$103$	−6.86911	−0.676834	−0.338417	−	0.940996i	$-0.609891\pi$
$103$	−6.86911	−0.676834	−0.338417	+	0.940996i	$0.609891\pi$
$104$	2.27847	0.223422
$105$	−29.8358	−2.91167
$106$	−0.307126	−0.0298307
$107$	−0.828205	−0.0800656	−0.0400328	−	0.999198i	$-0.512746\pi$
$107$	−0.828205	−0.0800656	−0.0400328	+	0.999198i	$0.512746\pi$
$108$	2.93148	0.282082
$109$	−13.1133	−1.25603	−0.628015	−	0.778201i	$-0.716132\pi$
$109$	−13.1133	−1.25603	−0.628015	+	0.778201i	$0.716132\pi$
$110$	2.55888	0.243980
$111$	−19.3908	−1.84050
$112$	−5.68665	−0.537338
$113$	3.46105	0.325588	0.162794	−	0.986660i	$-0.447949\pi$
$113$	3.46105	0.325588	0.162794	+	0.986660i	$0.447949\pi$
$114$	5.42959	0.508528
$115$	−16.1798	−1.50877
$116$	−4.22150	−0.391956
$117$	2.19585	0.203006
$118$	−8.16524	−0.751671
$119$	−4.09964	−0.375814
$120$	20.9938	1.91647
$121$	1.00000	0.0909091
$122$	−8.85630	−0.801811
$123$	−23.7896	−2.14504
$124$	5.02348	0.451122
$125$	25.6263	2.29209
$126$	4.50110	0.400989
$127$	−3.17180	−0.281451	−0.140726	−	0.990049i	$-0.544944\pi$
$127$	−3.17180	−0.281451	−0.140726	+	0.990049i	$0.544944\pi$
$128$	11.2891	0.997828
$129$	11.8151	1.04027
$130$	−2.55888	−0.224429
$131$	−1.84799	−0.161460	−0.0807299	−	0.996736i	$-0.525725\pi$
$131$	−1.84799	−0.161460	−0.0807299	+	0.996736i	$0.525725\pi$
$132$	3.64543	0.317294
$133$	12.1842	1.05651
$134$	−7.11581	−0.614712
$135$	−7.40949	−0.637707
$136$	2.88470	0.247361
$137$	10.2094	0.872250	0.436125	−	0.899886i	$-0.356351\pi$
$137$	10.2094	0.872250	0.436125	+	0.899886i	$0.356351\pi$
$138$	5.77574	0.491664
$139$	4.68911	0.397725	0.198863	−	0.980027i	$-0.436275\pi$
$139$	4.68911	0.397725	0.198863	+	0.980027i	$0.436275\pi$
$140$	20.9329	1.76915
$141$	−8.71875	−0.734251
$142$	2.14664	0.180142
$143$	−1.00000	−0.0836242
$144$	3.85630	0.321358
$145$	10.6701	0.886102
$146$	1.00510	0.0831827
$147$	7.94422	0.655228
$148$	13.6047	1.11830
$149$	−20.9128	−1.71324	−0.856620	−	0.515947i	$-0.827440\pi$
$149$	−20.9128	−1.71324	−0.856620	+	0.515947i	$0.827440\pi$
$150$	−16.3628	−1.33601
$151$	−16.9292	−1.37768	−0.688840	−	0.724914i	$-0.741880\pi$
$151$	−16.9292	−1.37768	−0.688840	+	0.724914i	$0.741880\pi$
$152$	−8.57339	−0.695394
$153$	2.78010	0.224758
$154$	−2.04982	−0.165179
$155$	−12.6971	−1.01986
$156$	−3.64543	−0.291868
$157$	13.8125	1.10235	0.551177	−	0.834388i	$-0.314179\pi$
$157$	13.8125	1.10235	0.551177	+	0.834388i	$0.314179\pi$
$158$	−2.93707	−0.233660
$159$	1.10590	0.0877036
$160$	−22.9140	−1.81151
$161$	12.9610	1.02147
$162$	6.81514	0.535448
$163$	20.1801	1.58063	0.790314	−	0.612702i	$-0.209918\pi$
$163$	20.1801	1.58063	0.790314	+	0.612702i	$0.209918\pi$
$164$	16.6909	1.30334
$165$	−9.21403	−0.717311
$166$	−6.23838	−0.484192
$167$	8.91651	0.689980	0.344990	−	0.938606i	$-0.387882\pi$
$167$	8.91651	0.689980	0.344990	+	0.938606i	$0.387882\pi$
$168$	−16.8174	−1.29749
$169$	1.00000	0.0769231
$170$	−3.23973	−0.248476
$171$	−8.26252	−0.631851
$172$	−8.28956	−0.632073
$173$	1.34517	0.102272	0.0511358	−	0.998692i	$-0.483716\pi$
$173$	1.34517	0.102272	0.0511358	+	0.998692i	$0.483716\pi$
$174$	−3.80893	−0.288754
$175$	−36.7187	−2.77567
$176$	−1.75618	−0.132377
$177$	29.4014	2.20995
$178$	4.12404	0.309110
$179$	−2.02706	−0.151509	−0.0757546	−	0.997126i	$-0.524137\pi$
$179$	−2.02706	−0.151509	−0.0757546	+	0.997126i	$0.524137\pi$
$180$	−14.1953	−1.05805
$181$	−2.79808	−0.207979	−0.103990	−	0.994578i	$-0.533161\pi$
$181$	−2.79808	−0.207979	−0.103990	+	0.994578i	$0.533161\pi$
$182$	2.04982	0.151943
$183$	31.8898	2.35736
$184$	−9.11997	−0.672333
$185$	−34.3866	−2.52815
$186$	4.53254	0.332342
$187$	−1.26607	−0.0925844
$188$	6.11711	0.446136
$189$	5.93546	0.431741
$190$	9.62854	0.698527
$191$	−25.3198	−1.83208	−0.916040	−	0.401087i	$-0.868632\pi$
$191$	−25.3198	−1.83208	−0.916040	+	0.401087i	$0.868632\pi$
$192$	0.173479	0.0125197
$193$	23.9355	1.72291	0.861456	−	0.507832i	$-0.169553\pi$
$193$	23.9355	1.72291	0.861456	+	0.507832i	$0.169553\pi$
$194$	−6.14045	−0.440859
$195$	9.21403	0.659830
$196$	−5.57370	−0.398121
$197$	9.36819	0.667456	0.333728	−	0.942669i	$-0.391693\pi$
$197$	9.36819	0.667456	0.333728	+	0.942669i	$0.391693\pi$
$198$	1.39005	0.0987866
$199$	−11.7368	−0.832003	−0.416002	−	0.909364i	$-0.636569\pi$
$199$	−11.7368	−0.832003	−0.416002	+	0.909364i	$0.636569\pi$
$200$	25.8370	1.82695
$201$	25.6226	1.80728
$202$	−9.90572	−0.696964
$203$	−8.54740	−0.599910
$204$	−4.61538	−0.323141
$205$	−42.1872	−2.94648
$206$	4.34840	0.302967
$207$	−8.78928	−0.610897
$208$	1.75618	0.121769
$209$	3.76279	0.260278
$210$	18.8871	1.30333
$211$	25.9263	1.78484	0.892422	−	0.451203i	$-0.149005\pi$
$211$	25.9263	1.78484	0.892422	+	0.451203i	$0.149005\pi$
$212$	−0.775905	−0.0532893
$213$	−7.72964	−0.529626
$214$	0.524284	0.0358393
$215$	20.9523	1.42894
$216$	−4.17647	−0.284173
$217$	10.1712	0.690466
$218$	8.30121	0.562229
$219$	−3.61917	−0.244561
$220$	6.46460	0.435843
$221$	1.26607	0.0851652
$222$	12.2751	0.823850
$223$	13.2177	0.885124	0.442562	−	0.896738i	$-0.354070\pi$
$223$	13.2177	0.885124	0.442562	+	0.896738i	$0.354070\pi$
$224$	18.3556	1.22643
$225$	24.9001	1.66001
$226$	−2.19097	−0.145741
$227$	−2.23359	−0.148248	−0.0741242	−	0.997249i	$-0.523616\pi$
$227$	−2.23359	−0.148248	−0.0741242	+	0.997249i	$0.523616\pi$
$228$	13.7170	0.908430
$229$	−16.9253	−1.11845	−0.559226	−	0.829015i	$-0.688902\pi$
$229$	−16.9253	−1.11845	−0.559226	+	0.829015i	$0.688902\pi$
$230$	10.2424	0.675363
$231$	7.38101	0.485635
$232$	6.01435	0.394861
$233$	−16.1422	−1.05751	−0.528755	−	0.848774i	$-0.677341\pi$
$233$	−16.1422	−1.05751	−0.528755	+	0.848774i	$0.677341\pi$
$234$	−1.39005	−0.0908705
$235$	−15.4614	−1.00859
$236$	−20.6282	−1.34278
$237$	10.5758	0.686972
$238$	2.59522	0.168223
$239$	−16.4061	−1.06122	−0.530612	−	0.847615i	$-0.678038\pi$
$239$	−16.4061	−1.06122	−0.530612	+	0.847615i	$0.678038\pi$
$240$	16.1815	1.04451
$241$	1.10384	0.0711046	0.0355523	−	0.999368i	$-0.488681\pi$
$241$	1.10384	0.0711046	0.0355523	+	0.999368i	$0.488681\pi$
$242$	−0.633036	−0.0406931
$243$	−19.0409	−1.22148
$244$	−22.3740	−1.43235
$245$	14.0878	0.900039
$246$	15.0597	0.960171
$247$	−3.76279	−0.239421
$248$	−7.15693	−0.454466
$249$	22.4632	1.42355
$250$	−16.2224	−1.02599
$251$	1.49617	0.0944373	0.0472186	−	0.998885i	$-0.484964\pi$
$251$	1.49617	0.0944373	0.0472186	+	0.998885i	$0.484964\pi$
$252$	11.3713	0.716325
$253$	4.00268	0.251647
$254$	2.00786	0.125984
$255$	11.6656	0.730530
$256$	−7.29864	−0.456165
$257$	−22.2056	−1.38515	−0.692573	−	0.721348i	$-0.743523\pi$
$257$	−22.2056	−1.38515	−0.692573	+	0.721348i	$0.743523\pi$
$258$	−7.47941	−0.465648
$259$	27.5458	1.71161
$260$	−6.46460	−0.400918
$261$	5.79627	0.358780
$262$	1.16985	0.0722733
$263$	−20.8494	−1.28563	−0.642814	−	0.766022i	$-0.722233\pi$
$263$	−20.8494	−1.28563	−0.642814	+	0.766022i	$0.722233\pi$
$264$	−5.19362	−0.319646
$265$	1.96114	0.120472
$266$	−7.71306	−0.472918
$267$	−14.8499	−0.908797
$268$	−17.9770	−1.09812
$269$	−1.19979	−0.0731523	−0.0365762	−	0.999331i	$-0.511645\pi$
$269$	−1.19979	−0.0731523	−0.0365762	+	0.999331i	$0.511645\pi$
$270$	4.69048	0.285453
$271$	−3.32823	−0.202176	−0.101088	−	0.994878i	$-0.532232\pi$
$271$	−3.32823	−0.202176	−0.101088	+	0.994878i	$0.532232\pi$
$272$	2.22345	0.134816
$273$	−7.38101	−0.446719
$274$	−6.46293	−0.390440
$275$	−11.3396	−0.683807
$276$	14.5915	0.878305
$277$	13.2157	0.794052	0.397026	−	0.917807i	$-0.370042\pi$
$277$	13.2157	0.794052	0.397026	+	0.917807i	$0.370042\pi$
$278$	−2.96838	−0.178031
$279$	−6.89742	−0.412938
$280$	−29.8230	−1.78227
$281$	−7.86998	−0.469484	−0.234742	−	0.972058i	$-0.575425\pi$
$281$	−7.86998	−0.469484	−0.234742	+	0.972058i	$0.575425\pi$
$282$	5.51928	0.328669
$283$	−4.82988	−0.287106	−0.143553	−	0.989643i	$-0.545853\pi$
$283$	−4.82988	−0.287106	−0.143553	+	0.989643i	$0.545853\pi$
$284$	5.42315	0.321805
$285$	−34.6705	−2.05370
$286$	0.633036	0.0374322
$287$	33.7946	1.99483
$288$	−12.4475	−0.733476
$289$	−15.3971	−0.905709
$290$	−6.75455	−0.396641
$291$	22.1106	1.29614
$292$	2.53923	0.148597
$293$	−2.76027	−0.161257	−0.0806284	−	0.996744i	$-0.525693\pi$
$293$	−2.76027	−0.161257	−0.0806284	+	0.996744i	$0.525693\pi$
$294$	−5.02898	−0.293296
$295$	52.1389	3.03564
$296$	−19.3825	−1.12659
$297$	1.83302	0.106363
$298$	13.2385	0.766888
$299$	−4.00268	−0.231481
$300$	−41.3379	−2.38664
$301$	−16.7841	−0.967420
$302$	10.7168	0.616683
$303$	35.6686	2.04911
$304$	−6.60814	−0.379003
$305$	56.5516	3.23814
$306$	−1.75990	−0.100607
$307$	3.81145	0.217531	0.108765	−	0.994067i	$-0.465310\pi$
$307$	3.81145	0.217531	0.108765	+	0.994067i	$0.465310\pi$
$308$	−5.17855	−0.295075
$309$	−15.6577	−0.890737
$310$	8.03775	0.456513
$311$	−2.61909	−0.148515	−0.0742575	−	0.997239i	$-0.523659\pi$
$311$	−2.61909	−0.148515	−0.0742575	+	0.997239i	$0.523659\pi$
$312$	5.19362	0.294031
$313$	7.25183	0.409898	0.204949	−	0.978773i	$-0.434297\pi$
$313$	7.25183	0.409898	0.204949	+	0.978773i	$0.434297\pi$
$314$	−8.74379	−0.493440
$315$	−28.7416	−1.61941
$316$	−7.42003	−0.417409
$317$	−13.2991	−0.746951	−0.373476	−	0.927640i	$-0.621834\pi$
$317$	−13.2991	−0.746951	−0.373476	+	0.927640i	$0.621834\pi$
$318$	−0.700075	−0.0392583
$319$	−2.63965	−0.147792
$320$	0.307637	0.0171975
$321$	−1.88784	−0.105369
$322$	−8.20479	−0.457235
$323$	−4.76397	−0.265074
$324$	17.2174	0.956520
$325$	11.3396	0.629011
$326$	−12.7747	−0.707527
$327$	−29.8911	−1.65298
$328$	−23.7795	−1.31300
$329$	12.3855	0.682835
$330$	5.83281	0.321086
$331$	0.905054	0.0497463	0.0248731	−	0.999691i	$-0.492082\pi$
$331$	0.905054	0.0497463	0.0248731	+	0.999691i	$0.492082\pi$
$332$	−15.7603	−0.864957
$333$	−18.6797	−1.02364
$334$	−5.64447	−0.308852
$335$	45.4378	2.48253
$336$	−12.9624	−0.707156
$337$	11.3871	0.620294	0.310147	−	0.950689i	$-0.399622\pi$
$337$	11.3871	0.620294	0.310147	+	0.950689i	$0.399622\pi$
$338$	−0.633036	−0.0344326
$339$	7.88925	0.428485
$340$	−8.18466	−0.443875
$341$	3.14112	0.170101
$342$	5.23047	0.282832
$343$	11.3813	0.614534
$344$	11.8101	0.636757
$345$	−36.8808	−1.98560
$346$	−0.851543	−0.0457792
$347$	−12.5454	−0.673471	−0.336735	−	0.941599i	$-0.609323\pi$
$347$	−12.5454	−0.673471	−0.336735	+	0.941599i	$0.609323\pi$
$348$	−9.62266	−0.515829
$349$	19.1719	1.02625	0.513124	−	0.858314i	$-0.328488\pi$
$349$	19.1719	1.02625	0.513124	+	0.858314i	$0.328488\pi$
$350$	23.2443	1.24246
$351$	−1.83302	−0.0978393
$352$	5.66866	0.302140
$353$	−13.8801	−0.738763	−0.369382	−	0.929278i	$-0.620430\pi$
$353$	−13.8801	−0.738763	−0.369382	+	0.929278i	$0.620430\pi$
$354$	−18.6122	−0.989226
$355$	−13.7073	−0.727509
$356$	10.4187	0.552191
$357$	−9.34489	−0.494584
$358$	1.28320	0.0678192
$359$	−5.09239	−0.268766	−0.134383	−	0.990929i	$-0.542905\pi$
$359$	−5.09239	−0.268766	−0.134383	+	0.990929i	$0.542905\pi$
$360$	20.2239	1.06590
$361$	−4.84139	−0.254810
$362$	1.77128	0.0930966
$363$	2.27944	0.119640
$364$	5.17855	0.271430
$365$	−6.41804	−0.335935
$366$	−20.1874	−1.05521
$367$	−11.3127	−0.590520	−0.295260	−	0.955417i	$-0.595406\pi$
$367$	−11.3127	−0.590520	−0.295260	+	0.955417i	$0.595406\pi$
$368$	−7.02943	−0.366434
$369$	−22.9172	−1.19302
$370$	21.7680	1.13166
$371$	−1.57100	−0.0815621
$372$	11.4507	0.593693
$373$	−4.17679	−0.216266	−0.108133	−	0.994136i	$-0.534487\pi$
$373$	−4.17679	−0.216266	−0.108133	+	0.994136i	$0.534487\pi$
$374$	0.801470	0.0414430
$375$	58.4137	3.01647
$376$	−8.71502	−0.449443
$377$	2.63965	0.135949
$378$	−3.75736	−0.193258
$379$	−15.4158	−0.791857	−0.395929	−	0.918281i	$-0.629577\pi$
$379$	−15.4158	−0.791857	−0.395929	+	0.918281i	$0.629577\pi$
$380$	24.3250	1.24784
$381$	−7.22992	−0.370400
$382$	16.0284	0.820083
$383$	−13.3291	−0.681084	−0.340542	−	0.940229i	$-0.610611\pi$
$383$	−13.3291	−0.681084	−0.340542	+	0.940229i	$0.610611\pi$
$384$	25.7329	1.31318
$385$	13.0891	0.667081
$386$	−15.1520	−0.771217
$387$	11.3818	0.578572
$388$	−15.5129	−0.787547
$389$	8.75270	0.443779	0.221890	−	0.975072i	$-0.428778\pi$
$389$	8.75270	0.443779	0.221890	+	0.975072i	$0.428778\pi$
$390$	−5.83281	−0.295356
$391$	−5.06769	−0.256284
$392$	7.94082	0.401072
$393$	−4.21239	−0.212487
$394$	−5.93041	−0.298770
$395$	18.7545	0.943644
$396$	3.51174	0.176472
$397$	1.93051	0.0968894	0.0484447	−	0.998826i	$-0.484574\pi$
$397$	1.93051	0.0968894	0.0484447	+	0.998826i	$0.484574\pi$
$398$	7.42985	0.372425
$399$	27.7732	1.39040
$400$	19.9145	0.995723
$401$	12.9543	0.646905	0.323453	−	0.946244i	$-0.395156\pi$
$401$	12.9543	0.646905	0.323453	+	0.946244i	$0.395156\pi$
$402$	−16.2201	−0.808983
$403$	−3.14112	−0.156470
$404$	−25.0252	−1.24505
$405$	−43.5179	−2.16242
$406$	5.41081	0.268534
$407$	8.50684	0.421668
$408$	6.57551	0.325536
$409$	−23.3170	−1.15295	−0.576477	−	0.817113i	$-0.695573\pi$
$409$	−23.3170	−1.15295	−0.576477	+	0.817113i	$0.695573\pi$
$410$	26.7060	1.31892
$411$	23.2718	1.14791
$412$	10.9855	0.541218
$413$	−41.7665	−2.05519
$414$	5.56393	0.273452
$415$	39.8350	1.95542
$416$	−5.66866	−0.277929
$417$	10.6885	0.523420
$418$	−2.38198	−0.116507
$419$	2.86911	0.140165	0.0700826	−	0.997541i	$-0.477674\pi$
$419$	2.86911	0.140165	0.0700826	+	0.997541i	$0.477674\pi$
$420$	47.7153	2.32827
$421$	−3.50286	−0.170719	−0.0853595	−	0.996350i	$-0.527204\pi$
$421$	−3.50286	−0.170719	−0.0853595	+	0.996350i	$0.527204\pi$
$422$	−16.4123	−0.798939
$423$	−8.39901	−0.408374
$424$	1.10543	0.0536843
$425$	14.3568	0.696408
$426$	4.89314	0.237073
$427$	−45.3014	−2.19229
$428$	1.32452	0.0640231
$429$	−2.27944	−0.110052
$430$	−13.2636	−0.639627
$431$	33.6141	1.61913	0.809566	−	0.587029i	$-0.199703\pi$
$431$	33.6141	1.61913	0.809566	+	0.587029i	$0.199703\pi$
$432$	−3.21911	−0.154879
$433$	19.8185	0.952418	0.476209	−	0.879332i	$-0.342011\pi$
$433$	19.8185	0.952418	0.476209	+	0.879332i	$0.342011\pi$
$434$	−6.43874	−0.309069
$435$	24.3218	1.16614
$436$	20.9717	1.00436
$437$	15.0613	0.720478
$438$	2.29107	0.109471
$439$	−4.49550	−0.214559	−0.107279	−	0.994229i	$-0.534214\pi$
$439$	−4.49550	−0.214559	−0.107279	+	0.994229i	$0.534214\pi$
$440$	−9.21009	−0.439074
$441$	7.65288	0.364423
$442$	−0.801470	−0.0381220
$443$	32.8455	1.56054	0.780270	−	0.625443i	$-0.215082\pi$
$443$	32.8455	1.56054	0.780270	+	0.625443i	$0.215082\pi$
$444$	31.0111	1.47172
$445$	−26.3339	−1.24835
$446$	−8.36730	−0.396203
$447$	−47.6694	−2.25469
$448$	−0.246437	−0.0116430
$449$	−20.3887	−0.962204	−0.481102	−	0.876665i	$-0.659763\pi$
$449$	−20.3887	−0.962204	−0.481102	+	0.876665i	$0.659763\pi$
$450$	−15.7627	−0.743060
$451$	10.4366	0.491441
$452$	−5.53513	−0.260351
$453$	−38.5891	−1.81307
$454$	1.41394	0.0663596
$455$	−13.0891	−0.613625
$456$	−19.5425	−0.915163
$457$	−9.78703	−0.457818	−0.228909	−	0.973448i	$-0.573516\pi$
$457$	−9.78703	−0.457818	−0.228909	+	0.973448i	$0.573516\pi$
$458$	10.7143	0.500647
$459$	−2.32073	−0.108323
$460$	25.8758	1.20646
$461$	−22.8980	−1.06647	−0.533234	−	0.845968i	$-0.679023\pi$
$461$	−22.8980	−1.06647	−0.533234	+	0.845968i	$0.679023\pi$
$462$	−4.67245	−0.217382
$463$	−2.93739	−0.136512	−0.0682560	−	0.997668i	$-0.521743\pi$
$463$	−2.93739	−0.136512	−0.0682560	+	0.997668i	$0.521743\pi$
$464$	4.63570	0.215207
$465$	−28.9424	−1.34217
$466$	10.2186	0.473367
$467$	16.9403	0.783903	0.391952	−	0.919986i	$-0.371800\pi$
$467$	16.9403	0.783903	0.391952	+	0.919986i	$0.371800\pi$
$468$	−3.51174	−0.162330
$469$	−36.3985	−1.68073
$470$	9.78759	0.451468
$471$	31.4847	1.45074
$472$	29.3889	1.35273
$473$	−5.18335	−0.238331
$474$	−6.69487	−0.307505
$475$	−42.6688	−1.95778
$476$	6.55642	0.300513
$477$	1.06534	0.0487788
$478$	10.3857	0.475030
$479$	−3.12698	−0.142875	−0.0714376	−	0.997445i	$-0.522759\pi$
$479$	−3.12698	−0.142875	−0.0714376	+	0.997445i	$0.522759\pi$
$480$	−52.2312	−2.38402
$481$	−8.50684	−0.387878
$482$	−0.698771	−0.0318281
$483$	29.5438	1.34429
$484$	−1.59927	−0.0726939
$485$	39.2097	1.78042
$486$	12.0536	0.546762
$487$	−14.5780	−0.660592	−0.330296	−	0.943877i	$-0.607149\pi$
$487$	−14.5780	−0.660592	−0.330296	+	0.943877i	$0.607149\pi$
$488$	31.8762	1.44297
$489$	45.9993	2.08016
$490$	−8.91811	−0.402879
$491$	32.1836	1.45243	0.726213	−	0.687470i	$-0.241279\pi$
$491$	32.1836	1.45243	0.726213	+	0.687470i	$0.241279\pi$
$492$	38.0459	1.71524
$493$	3.34199	0.150516
$494$	2.38198	0.107171
$495$	−8.87613	−0.398952
$496$	−5.51637	−0.247692
$497$	10.9804	0.492539
$498$	−14.2200	−0.637214
$499$	40.4681	1.81160	0.905800	−	0.423705i	$-0.139271\pi$
$499$	40.4681	1.81160	0.905800	+	0.423705i	$0.139271\pi$
$500$	−40.9833	−1.83283
$501$	20.3246	0.908038
$502$	−0.947128	−0.0422724
$503$	−2.52066	−0.112391	−0.0561954	−	0.998420i	$-0.517897\pi$
$503$	−2.52066	−0.112391	−0.0561954	+	0.998420i	$0.517897\pi$
$504$	−16.2006	−0.721634
$505$	63.2527	2.81471
$506$	−2.53384	−0.112643
$507$	2.27944	0.101233
$508$	5.07254	0.225058
$509$	17.6993	0.784506	0.392253	−	0.919857i	$-0.371696\pi$
$509$	17.6993	0.784506	0.392253	+	0.919857i	$0.371696\pi$
$510$	−7.38476	−0.327003
$511$	5.14125	0.227435
$512$	−17.9580	−0.793637
$513$	6.89727	0.304522
$514$	14.0569	0.620025
$515$	−27.7665	−1.22354
$516$	−18.8955	−0.831830
$517$	3.82495	0.168221
$518$	−17.4375	−0.766160
$519$	3.06624	0.134593
$520$	9.21009	0.403889
$521$	−12.7271	−0.557583	−0.278792	−	0.960352i	$-0.589934\pi$
$521$	−12.7271	−0.557583	−0.278792	+	0.960352i	$0.589934\pi$
$522$	−3.66925	−0.160599
$523$	−27.5965	−1.20671	−0.603356	−	0.797472i	$-0.706170\pi$
$523$	−27.5965	−1.20671	−0.603356	+	0.797472i	$0.706170\pi$
$524$	2.95543	0.129108
$525$	−83.6981	−3.65288
$526$	13.1984	0.575478
$527$	−3.97688	−0.173236
$528$	−4.00311	−0.174213
$529$	−6.97853	−0.303414
$530$	−1.24147	−0.0539262
$531$	28.3232	1.22912
$532$	−19.4858	−0.844817
$533$	−10.4366	−0.452060
$534$	9.40050	0.406799
$535$	−3.34780	−0.144738
$536$	25.6117	1.10626
$537$	−4.62055	−0.199392
$538$	0.759509	0.0327448
$539$	−3.48516	−0.150117
$540$	11.8497	0.509932
$541$	−12.6575	−0.544188	−0.272094	−	0.962271i	$-0.587716\pi$
$541$	−12.6575	−0.544188	−0.272094	+	0.962271i	$0.587716\pi$
$542$	2.10689	0.0904987
$543$	−6.37805	−0.273708
$544$	−7.17693	−0.307708
$545$	−53.0071	−2.27058
$546$	4.67245	0.199962
$547$	−12.4758	−0.533425	−0.266713	−	0.963776i	$-0.585937\pi$
$547$	−12.4758	−0.533425	−0.266713	+	0.963776i	$0.585937\pi$
$548$	−16.3276	−0.697479
$549$	30.7203	1.31111
$550$	7.17841	0.306088
$551$	−9.93246	−0.423137
$552$	−20.7884	−0.884815
$553$	−15.0236	−0.638867
$554$	−8.36599	−0.355437
$555$	−78.3822	−3.32714
$556$	−7.49913	−0.318034
$557$	−28.3431	−1.20094	−0.600468	−	0.799649i	$-0.705019\pi$
$557$	−28.3431	−1.20094	−0.600468	+	0.799649i	$0.705019\pi$
$558$	4.36632	0.184841
$559$	5.18335	0.219232
$560$	−22.9868	−0.971368
$561$	−2.88594	−0.121844
$562$	4.98199	0.210152
$563$	16.2889	0.686497	0.343249	−	0.939245i	$-0.388473\pi$
$563$	16.2889	0.686497	0.343249	+	0.939245i	$0.388473\pi$
$564$	13.9436	0.587131
$565$	13.9904	0.588579
$566$	3.05749	0.128516
$567$	34.8605	1.46400
$568$	−7.72633	−0.324190
$569$	−10.6037	−0.444530	−0.222265	−	0.974986i	$-0.571345\pi$
$569$	−10.6037	−0.444530	−0.222265	+	0.974986i	$0.571345\pi$
$570$	21.9477	0.919287
$571$	3.03397	0.126968	0.0634838	−	0.997983i	$-0.479779\pi$
$571$	3.03397	0.126968	0.0634838	+	0.997983i	$0.479779\pi$
$572$	1.59927	0.0668686
$573$	−57.7151	−2.41108
$574$	−21.3932	−0.892935
$575$	−45.3890	−1.89285
$576$	0.167117	0.00696319
$577$	25.1234	1.04590	0.522950	−	0.852363i	$-0.324832\pi$
$577$	25.1234	1.04590	0.522950	+	0.852363i	$0.324832\pi$
$578$	9.74690	0.405417
$579$	54.5594	2.26741
$580$	−17.0643	−0.708556
$581$	−31.9103	−1.32386
$582$	−13.9968	−0.580186
$583$	−0.485163	−0.0200934
$584$	−3.61762	−0.149698
$585$	8.87613	0.366983
$586$	1.74735	0.0721825
$587$	2.39957	0.0990410	0.0495205	−	0.998773i	$-0.484231\pi$
$587$	2.39957	0.0990410	0.0495205	+	0.998773i	$0.484231\pi$
$588$	−12.7049	−0.523942
$589$	11.8194	0.487009
$590$	−33.0058	−1.35883
$591$	21.3542	0.878396
$592$	−14.9395	−0.614011
$593$	18.9205	0.776973	0.388486	−	0.921454i	$-0.372998\pi$
$593$	18.9205	0.776973	0.388486	+	0.921454i	$0.372998\pi$
$594$	−1.16037	−0.0476104
$595$	−16.5717	−0.679374
$596$	33.4451	1.36996
$597$	−26.7534	−1.09495
$598$	2.53384	0.103617
$599$	14.5110	0.592904	0.296452	−	0.955048i	$-0.404196\pi$
$599$	14.5110	0.592904	0.296452	+	0.955048i	$0.404196\pi$
$600$	58.8939	2.40433
$601$	37.1364	1.51482	0.757412	−	0.652938i	$-0.226464\pi$
$601$	37.1364	1.51482	0.757412	+	0.652938i	$0.226464\pi$
$602$	10.6250	0.433041
$603$	24.6830	1.00517
$604$	27.0743	1.10164
$605$	4.04223	0.164340
$606$	−22.5795	−0.917230
$607$	−46.7172	−1.89619	−0.948096	−	0.317985i	$-0.896994\pi$
$607$	−46.7172	−1.89619	−0.948096	+	0.317985i	$0.896994\pi$
$608$	21.3300	0.865045
$609$	−19.4833	−0.789502
$610$	−35.7992	−1.44947
$611$	−3.82495	−0.154741
$612$	−4.44612	−0.179724
$613$	26.1805	1.05742	0.528710	−	0.848803i	$-0.322676\pi$
$613$	26.1805	1.05742	0.528710	+	0.848803i	$0.322676\pi$
$614$	−2.41278	−0.0973720
$615$	−96.1632	−3.87768
$616$	7.37785	0.297262
$617$	−19.7378	−0.794613	−0.397307	−	0.917686i	$-0.630055\pi$
$617$	−19.7378	−0.794613	−0.397307	+	0.917686i	$0.630055\pi$
$618$	9.91191	0.398715
$619$	21.8572	0.878514	0.439257	−	0.898361i	$-0.355242\pi$
$619$	21.8572	0.878514	0.439257	+	0.898361i	$0.355242\pi$
$620$	20.3061	0.815512
$621$	7.33699	0.294423
$622$	1.65798	0.0664789
$623$	21.0951	0.845158
$624$	4.00311	0.160252
$625$	46.8894	1.87558
$626$	−4.59067	−0.183480
$627$	8.57706	0.342535
$628$	−22.0898	−0.881478
$629$	−10.7703	−0.429439
$630$	18.1945	0.724885
$631$	−7.09864	−0.282592	−0.141296	−	0.989967i	$-0.545127\pi$
$631$	−7.09864	−0.282592	−0.141296	+	0.989967i	$0.545127\pi$
$632$	10.5713	0.420503
$633$	59.0975	2.34892
$634$	8.41880	0.334353
$635$	−12.8211	−0.508791
$636$	−1.76863	−0.0701307
$637$	3.48516	0.138087
$638$	1.67099	0.0661553
$639$	−7.44617	−0.294566
$640$	45.6333	1.80381
$641$	13.0904	0.517041	0.258520	−	0.966006i	$-0.416765\pi$
$641$	13.0904	0.517041	0.258520	+	0.966006i	$0.416765\pi$
$642$	1.19507	0.0471658
$643$	8.44394	0.332996	0.166498	−	0.986042i	$-0.446754\pi$
$643$	8.44394	0.332996	0.166498	+	0.986042i	$0.446754\pi$
$644$	−20.7281	−0.816801
$645$	47.7596	1.88053
$646$	3.01576	0.118654
$647$	9.27154	0.364502	0.182251	−	0.983252i	$-0.441662\pi$
$647$	9.27154	0.364502	0.182251	+	0.983252i	$0.441662\pi$
$648$	−24.5295	−0.963610
$649$	−12.8985	−0.506312
$650$	−7.17841	−0.281560
$651$	23.1846	0.908677
$652$	−32.2733	−1.26392
$653$	−21.5511	−0.843359	−0.421680	−	0.906745i	$-0.638559\pi$
$653$	−21.5511	−0.843359	−0.421680	+	0.906745i	$0.638559\pi$
$654$	18.9221	0.739913
$655$	−7.47001	−0.291878
$656$	−18.3286	−0.715610
$657$	−3.48645	−0.136019
$658$	−7.84047	−0.305653
$659$	−44.1938	−1.72155	−0.860773	−	0.508989i	$-0.830019\pi$
$659$	−44.1938	−1.72155	−0.860773	+	0.508989i	$0.830019\pi$
$660$	14.7357	0.573585
$661$	−8.41372	−0.327256	−0.163628	−	0.986522i	$-0.552320\pi$
$661$	−8.41372	−0.327256	−0.163628	+	0.986522i	$0.552320\pi$
$662$	−0.572932	−0.0222676
$663$	2.88594	0.112080
$664$	22.4536	0.871368
$665$	49.2515	1.90989
$666$	11.8249	0.458207
$667$	−10.5657	−0.409105
$668$	−14.2599	−0.551730
$669$	30.1290	1.16485
$670$	−28.7638	−1.11124
$671$	−13.9902	−0.540085
$672$	41.8404	1.61403
$673$	40.7928	1.57245	0.786224	−	0.617942i	$-0.212033\pi$
$673$	40.7928	1.57245	0.786224	+	0.617942i	$0.212033\pi$
$674$	−7.20844	−0.277659
$675$	−20.7858	−0.800045
$676$	−1.59927	−0.0615102
$677$	6.58736	0.253173	0.126586	−	0.991956i	$-0.459598\pi$
$677$	6.58736	0.253173	0.126586	+	0.991956i	$0.459598\pi$
$678$	−4.99418	−0.191800
$679$	−31.4094	−1.20538
$680$	11.6606	0.447165
$681$	−5.09133	−0.195100
$682$	−1.98844	−0.0761414
$683$	13.7216	0.525041	0.262521	−	0.964926i	$-0.415446\pi$
$683$	13.7216	0.525041	0.262521	+	0.964926i	$0.415446\pi$
$684$	13.2140	0.505248
$685$	41.2689	1.57680
$686$	−7.20479	−0.275080
$687$	−38.5801	−1.47192
$688$	9.10290	0.347045
$689$	0.485163	0.0184832
$690$	23.3469	0.888802
$691$	32.4678	1.23513	0.617566	−	0.786519i	$-0.288119\pi$
$691$	32.4678	1.23513	0.617566	+	0.786519i	$0.288119\pi$
$692$	−2.15129	−0.0817797
$693$	7.11033	0.270099
$694$	7.94168	0.301462
$695$	18.9545	0.718984
$696$	13.7094	0.519652
$697$	−13.2135	−0.500497
$698$	−12.1365	−0.459373
$699$	−36.7952	−1.39172
$700$	58.7229	2.21952
$701$	−19.1385	−0.722853	−0.361426	−	0.932401i	$-0.617710\pi$
$701$	−19.1385	−0.722853	−0.361426	+	0.932401i	$0.617710\pi$
$702$	1.16037	0.0437952
$703$	32.0095	1.20726
$704$	−0.0761058	−0.00286834
$705$	−35.2432	−1.32734
$706$	8.78661	0.330688
$707$	−50.6693	−1.90562
$708$	−47.0207	−1.76715
$709$	−4.53349	−0.170259	−0.0851295	−	0.996370i	$-0.527130\pi$
$709$	−4.53349	−0.170259	−0.0851295	+	0.996370i	$0.527130\pi$
$710$	8.67723	0.325651
$711$	10.1880	0.382078
$712$	−14.8435	−0.556284
$713$	12.5729	0.470859
$714$	5.91566	0.221388
$715$	−4.04223	−0.151171
$716$	3.24180	0.121152
$717$	−37.3968	−1.39661
$718$	3.22367	0.120306
$719$	12.1524	0.453207	0.226603	−	0.973987i	$-0.427238\pi$
$719$	12.1524	0.453207	0.226603	+	0.973987i	$0.427238\pi$
$720$	15.5881	0.580933
$721$	22.2427	0.828363
$722$	3.06477	0.114059
$723$	2.51614	0.0935761
$724$	4.47487	0.166307
$725$	29.9327	1.11167
$726$	−1.44297	−0.0535536
$727$	47.4062	1.75820	0.879099	−	0.476639i	$-0.158145\pi$
$727$	47.4062	1.75820	0.879099	+	0.476639i	$0.158145\pi$
$728$	−7.37785	−0.273441
$729$	−11.1053	−0.411306
$730$	4.06285	0.150373
$731$	6.56250	0.242723
$732$	−51.0002	−1.88502
$733$	21.5972	0.797712	0.398856	−	0.917014i	$-0.369407\pi$
$733$	21.5972	0.797712	0.398856	+	0.917014i	$0.369407\pi$
$734$	7.16137	0.264331
$735$	32.1124	1.18448
$736$	22.6898	0.836358
$737$	−11.2408	−0.414059
$738$	14.5074	0.534025
$739$	−16.1417	−0.593780	−0.296890	−	0.954912i	$-0.595950\pi$
$739$	−16.1417	−0.593780	−0.296890	+	0.954912i	$0.595950\pi$
$740$	54.9933	2.02159
$741$	−8.57706	−0.315086
$742$	0.994498	0.0365092
$743$	33.5096	1.22935	0.614674	−	0.788781i	$-0.289288\pi$
$743$	33.5096	1.22935	0.614674	+	0.788781i	$0.289288\pi$
$744$	−16.3138	−0.598093
$745$	−84.5343	−3.09710
$746$	2.64406	0.0968060
$747$	21.6394	0.791744
$748$	2.02479	0.0740335
$749$	2.68179	0.0979906
$750$	−36.9780	−1.35025
$751$	−11.7062	−0.427164	−0.213582	−	0.976925i	$-0.568513\pi$
$751$	−11.7062	−0.427164	−0.213582	+	0.976925i	$0.568513\pi$
$752$	−6.71730	−0.244955
$753$	3.41042	0.124283
$754$	−1.67099	−0.0608540
$755$	−68.4318	−2.49049
$756$	−9.49238	−0.345234
$757$	−4.68425	−0.170252	−0.0851260	−	0.996370i	$-0.527129\pi$
$757$	−4.68425	−0.170252	−0.0851260	+	0.996370i	$0.527129\pi$
$758$	9.75877	0.354454
$759$	9.12388	0.331176
$760$	−34.6557	−1.25709
$761$	−46.3345	−1.67963	−0.839813	−	0.542876i	$-0.817335\pi$
$761$	−46.3345	−1.67963	−0.839813	+	0.542876i	$0.817335\pi$
$762$	4.57680	0.165800
$763$	42.4620	1.53723
$764$	40.4931	1.46499
$765$	11.2378	0.406304
$766$	8.43779	0.304870
$767$	12.8985	0.465739
$768$	−16.6368	−0.600329
$769$	−36.6201	−1.32056	−0.660278	−	0.751021i	$-0.729561\pi$
$769$	−36.6201	−1.32056	−0.660278	+	0.751021i	$0.729561\pi$
$770$	−8.28586	−0.298602
$771$	−50.6163	−1.82290
$772$	−38.2791	−1.37770
$773$	0.613229	0.0220563	0.0110282	−	0.999939i	$-0.496490\pi$
$773$	0.613229	0.0220563	0.0110282	+	0.999939i	$0.496490\pi$
$774$	−7.20512	−0.258983
$775$	−35.6192	−1.27948
$776$	22.1011	0.793384
$777$	62.7890	2.25254
$778$	−5.54077	−0.198646
$779$	39.2708	1.40702
$780$	−14.7357	−0.527622
$781$	3.39103	0.121340
$782$	3.20803	0.114719
$783$	−4.83853	−0.172915
$784$	6.12057	0.218592
$785$	55.8332	1.99277
$786$	2.66659	0.0951142
$787$	−35.4355	−1.26314	−0.631569	−	0.775319i	$-0.717589\pi$
$787$	−35.4355	−1.26314	−0.631569	+	0.775319i	$0.717589\pi$
$788$	−14.9822	−0.533720
$789$	−47.5249	−1.69193
$790$	−11.8723	−0.422398
$791$	−11.2071	−0.398480
$792$	−5.00316	−0.177780
$793$	13.9902	0.496806
$794$	−1.22208	−0.0433701
$795$	4.47031	0.158545
$796$	18.7703	0.665297
$797$	48.0913	1.70348	0.851740	−	0.523965i	$-0.175548\pi$
$797$	48.0913	1.70348	0.851740	+	0.523965i	$0.175548\pi$
$798$	−17.5814	−0.622377
$799$	−4.84267	−0.171321
$800$	−64.2806	−2.27266
$801$	−14.3053	−0.505452
$802$	−8.20052	−0.289571
$803$	1.58775	0.0560303
$804$	−40.9774	−1.44516
$805$	52.3914	1.84656
$806$	1.98844	0.0700399
$807$	−2.73484	−0.0962710
$808$	35.6533	1.25428
$809$	−43.4857	−1.52887	−0.764437	−	0.644698i	$-0.776983\pi$
$809$	−43.4857	−1.52887	−0.764437	+	0.644698i	$0.776983\pi$
$810$	27.5484	0.967952
$811$	16.7443	0.587973	0.293986	−	0.955810i	$-0.405018\pi$
$811$	16.7443	0.587973	0.293986	+	0.955810i	$0.405018\pi$
$812$	13.6696	0.479707
$813$	−7.58650	−0.266070
$814$	−5.38514	−0.188749
$815$	81.5727	2.85737
$816$	5.06822	0.177423
$817$	−19.5039	−0.682355
$818$	14.7605	0.516090
$819$	−7.11033	−0.248455
$820$	67.4685	2.35610
$821$	−30.1941	−1.05378	−0.526891	−	0.849933i	$-0.676642\pi$
$821$	−30.1941	−1.05378	−0.526891	+	0.849933i	$0.676642\pi$
$822$	−14.7319	−0.513833
$823$	31.7930	1.10824	0.554118	−	0.832438i	$-0.313056\pi$
$823$	31.7930	1.10824	0.554118	+	0.832438i	$0.313056\pi$
$824$	−15.6510	−0.545230
$825$	−25.8481	−0.899914
$826$	26.4397	0.919954
$827$	−26.3699	−0.916972	−0.458486	−	0.888702i	$-0.651608\pi$
$827$	−26.3699	−0.916972	−0.458486	+	0.888702i	$0.651608\pi$
$828$	14.0564	0.488493
$829$	−19.8541	−0.689560	−0.344780	−	0.938684i	$-0.612046\pi$
$829$	−19.8541	−0.689560	−0.344780	+	0.938684i	$0.612046\pi$
$830$	−25.2170	−0.875294
$831$	30.1243	1.04500
$832$	0.0761058	0.00263849
$833$	4.41247	0.152883
$834$	−6.76624	−0.234296
$835$	36.0426	1.24731
$836$	−6.01770	−0.208127
$837$	5.75773	0.199016
$838$	−1.81625	−0.0627414
$839$	31.3544	1.08248	0.541238	−	0.840870i	$-0.317956\pi$
$839$	31.3544	1.08248	0.541238	+	0.840870i	$0.317956\pi$
$840$	−67.9797	−2.34552
$841$	−22.0322	−0.759733
$842$	2.21744	0.0764180
$843$	−17.9392	−0.617857
$844$	−41.4631	−1.42722
$845$	4.04223	0.139057
$846$	5.31688	0.182798
$847$	−3.23808	−0.111262
$848$	0.852033	0.0292589
$849$	−11.0094	−0.377842
$850$	−9.08839	−0.311729
$851$	34.0502	1.16722
$852$	12.3617	0.423506
$853$	4.99851	0.171146	0.0855729	−	0.996332i	$-0.472728\pi$
$853$	4.99851	0.171146	0.0855729	+	0.996332i	$0.472728\pi$
$854$	28.6774	0.981320
$855$	−33.3990	−1.14222
$856$	−1.88704	−0.0644976
$857$	−25.1930	−0.860576	−0.430288	−	0.902692i	$-0.641588\pi$
$857$	−25.1930	−0.860576	−0.430288	+	0.902692i	$0.641588\pi$
$858$	1.44297	0.0492621
$859$	23.3650	0.797204	0.398602	−	0.917124i	$-0.369495\pi$
$859$	23.3650	0.797204	0.398602	+	0.917124i	$0.369495\pi$
$860$	−33.5083	−1.14262
$861$	77.0327	2.62527
$862$	−21.2789	−0.724763
$863$	30.7426	1.04649	0.523245	−	0.852182i	$-0.324721\pi$
$863$	30.7426	1.04649	0.523245	+	0.852182i	$0.324721\pi$
$864$	10.3908	0.353501
$865$	5.43750	0.184881
$866$	−12.5458	−0.426325
$867$	−35.0967	−1.19195
$868$	−16.2664	−0.552119
$869$	−4.63965	−0.157389
$870$	−15.3966	−0.521993
$871$	11.2408	0.380879
$872$	−29.8783	−1.01181
$873$	21.2997	0.720886
$874$	−9.53433	−0.322504
$875$	−82.9802	−2.80524
$876$	5.78801	0.195559
$877$	41.0801	1.38718	0.693588	−	0.720372i	$-0.256029\pi$
$877$	41.0801	1.38718	0.693588	+	0.720372i	$0.256029\pi$
$878$	2.84582	0.0960416
$879$	−6.29188	−0.212220
$880$	−7.09889	−0.239303
$881$	41.6538	1.40335	0.701677	−	0.712496i	$-0.252435\pi$
$881$	41.6538	1.40335	0.701677	+	0.712496i	$0.252435\pi$
$882$	−4.84455	−0.163125
$883$	−29.2559	−0.984540	−0.492270	−	0.870442i	$-0.663833\pi$
$883$	−29.2559	−0.984540	−0.492270	+	0.870442i	$0.663833\pi$
$884$	−2.02479	−0.0681009
$885$	118.847	3.99501
$886$	−20.7924	−0.698535
$887$	−6.36925	−0.213858	−0.106929	−	0.994267i	$-0.534102\pi$
$887$	−6.36925	−0.213858	−0.106929	+	0.994267i	$0.534102\pi$
$888$	−44.1813	−1.48263
$889$	10.2705	0.344462
$890$	16.6703	0.558791
$891$	10.7658	0.360668
$892$	−21.1386	−0.707774
$893$	14.3925	0.481627
$894$	30.1765	1.00925
$895$	−8.19383	−0.273890
$896$	−36.5551	−1.22122
$897$	−9.12388	−0.304637
$898$	12.9068	0.430706
$899$	−8.29146	−0.276536
$900$	−39.8219	−1.32740
$901$	0.614252	0.0204637
$902$	−6.60675	−0.219981
$903$	−38.2584	−1.27316
$904$	7.88587	0.262280
$905$	−11.3105	−0.375973
$906$	24.4283	0.811576
$907$	−44.1922	−1.46738	−0.733688	−	0.679486i	$-0.762203\pi$
$907$	−44.1922	−1.46738	−0.733688	+	0.679486i	$0.762203\pi$
$908$	3.57210	0.118544
$909$	34.3605	1.13967
$910$	8.28586	0.274674
$911$	−23.7227	−0.785968	−0.392984	−	0.919545i	$-0.628557\pi$
$911$	−23.7227	−0.785968	−0.392984	+	0.919545i	$0.628557\pi$
$912$	−15.0629	−0.498781
$913$	−9.85469	−0.326143
$914$	6.19555	0.204930
$915$	128.906	4.26150
$916$	27.0680	0.894351
$917$	5.98394	0.197607
$918$	1.46911	0.0484878
$919$	−27.5851	−0.909947	−0.454974	−	0.890505i	$-0.650351\pi$
$919$	−27.5851	−0.909947	−0.454974	+	0.890505i	$0.650351\pi$
$920$	−36.8651	−1.21541
$921$	8.68796	0.286278
$922$	14.4953	0.477377
$923$	−3.39103	−0.111617
$924$	−11.8042	−0.388329
$925$	−96.4645	−3.17173
$926$	1.85947	0.0611061
$927$	−15.0835	−0.495408
$928$	−14.9633	−0.491193
$929$	−32.2047	−1.05660	−0.528301	−	0.849057i	$-0.677171\pi$
$929$	−32.2047	−1.05660	−0.528301	+	0.849057i	$0.677171\pi$
$930$	18.3216	0.600788
$931$	−13.1139	−0.429792
$932$	25.8157	0.845620
$933$	−5.97006	−0.195451
$934$	−10.7238	−0.350894
$935$	−5.11776	−0.167369
$936$	5.00316	0.163533
$937$	13.9883	0.456978	0.228489	−	0.973546i	$-0.426621\pi$
$937$	13.9883	0.456978	0.228489	+	0.973546i	$0.426621\pi$
$938$	23.0416	0.752334
$939$	16.5301	0.539440
$940$	24.7268	0.806499
$941$	−5.96820	−0.194558	−0.0972788	−	0.995257i	$-0.531014\pi$
$941$	−5.96820	−0.194558	−0.0972788	+	0.995257i	$0.531014\pi$
$942$	−19.9309	−0.649385
$943$	41.7744	1.36036
$944$	22.6521	0.737264
$945$	23.9925	0.780477
$946$	3.28125	0.106683
$947$	5.42913	0.176423	0.0882115	−	0.996102i	$-0.471885\pi$
$947$	5.42913	0.176423	0.0882115	+	0.996102i	$0.471885\pi$
$948$	−16.9135	−0.549325
$949$	−1.58775	−0.0515404
$950$	27.0109	0.876348
$951$	−30.3145	−0.983014
$952$	−9.34090	−0.302740
$953$	−54.1920	−1.75545	−0.877725	−	0.479164i	$-0.840940\pi$
$953$	−54.1920	−1.75545	−0.877725	+	0.479164i	$0.840940\pi$
$954$	−0.674401	−0.0218346
$955$	−102.349	−3.31193
$956$	26.2378	0.848590
$957$	−6.01692	−0.194500
$958$	1.97949	0.0639544
$959$	−33.0589	−1.06753
$960$	0.701241	0.0226325
$961$	−21.1334	−0.681722
$962$	5.38514	0.173624
$963$	−1.81861	−0.0586039
$964$	−1.76533	−0.0568575
$965$	96.7527	3.11458
$966$	−18.7023	−0.601737
$967$	−31.9305	−1.02681	−0.513407	−	0.858145i	$-0.671617\pi$
$967$	−31.9305	−1.02681	−0.513407	+	0.858145i	$0.671617\pi$
$968$	2.27847	0.0732326
$969$	−10.8592	−0.348847
$970$	−24.8211	−0.796959
$971$	14.5692	0.467548	0.233774	−	0.972291i	$-0.424892\pi$
$971$	14.5692	0.467548	0.233774	+	0.972291i	$0.424892\pi$
$972$	30.4515	0.976732
$973$	−15.1837	−0.486768
$974$	9.22840	0.295697
$975$	25.8481	0.827800
$976$	24.5693	0.786443
$977$	37.1394	1.18820	0.594098	−	0.804393i	$-0.297509\pi$
$977$	37.1394	1.18820	0.594098	+	0.804393i	$0.297509\pi$
$978$	−29.1192	−0.931131
$979$	6.51470	0.208211
$980$	−22.5302	−0.719701
$981$	−28.7949	−0.919349
$982$	−20.3734	−0.650141
$983$	14.2909	0.455808	0.227904	−	0.973684i	$-0.426813\pi$
$983$	14.2909	0.455808	0.227904	+	0.973684i	$0.426813\pi$
$984$	−54.2038	−1.72796
$985$	37.8684	1.20659
$986$	−2.11560	−0.0673744
$987$	28.2320	0.898635
$988$	6.01770	0.191449
$989$	−20.7473	−0.659726
$990$	5.61891	0.178581
$991$	28.0370	0.890624	0.445312	−	0.895376i	$-0.353093\pi$
$991$	28.0370	0.890624	0.445312	+	0.895376i	$0.353093\pi$
$992$	17.8059	0.565339
$993$	2.06302	0.0654679
$994$	−6.95100	−0.220472
$995$	−47.4431	−1.50405
$996$	−35.9246	−1.13831
$997$	23.4580	0.742924	0.371462	−	0.928448i	$-0.378857\pi$
$997$	23.4580	0.742924	0.371462	+	0.928448i	$0.378857\pi$
$998$	−25.6178	−0.810916
$999$	15.5932	0.493347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.a.c.1.3	✓	6
3.2	odd	2		1287.2.a.q.1.4		6
4.3	odd	2		2288.2.a.z.1.2		6
5.4	even	2		3575.2.a.p.1.4		6
7.6	odd	2		7007.2.a.r.1.3		6
8.3	odd	2		9152.2.a.cs.1.5		6
8.5	even	2		9152.2.a.cm.1.2		6
11.10	odd	2		1573.2.a.m.1.4		6
13.12	even	2		1859.2.a.m.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.a.c.1.3	✓	6	1.1	even	1	trivial
1287.2.a.q.1.4		6	3.2	odd	2
1573.2.a.m.1.4		6	11.10	odd	2
1859.2.a.m.1.4		6	13.12	even	2
2288.2.a.z.1.2		6	4.3	odd	2
3575.2.a.p.1.4		6	5.4	even	2
7007.2.a.r.1.3		6	7.6	odd	2
9152.2.a.cm.1.2		6	8.5	even	2
9152.2.a.cs.1.5		6	8.3	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q-0.633036 q^{2} +2.27944 q^{3} -1.59927 q^{4} +4.04223 q^{5} -1.44297 q^{6} -3.23808 q^{7} +2.27847 q^{8} +2.19585 q^{9} +O(q^{10})\)	\(q-0.633036 q^{2} +2.27944 q^{3} -1.59927 q^{4} +4.04223 q^{5} -1.44297 q^{6} -3.23808 q^{7} +2.27847 q^{8} +2.19585 q^{9} -2.55888 q^{10} -1.00000 q^{11} -3.64543 q^{12} +1.00000 q^{13} +2.04982 q^{14} +9.21403 q^{15} +1.75618 q^{16} +1.26607 q^{17} -1.39005 q^{18} -3.76279 q^{19} -6.46460 q^{20} -7.38101 q^{21} +0.633036 q^{22} -4.00268 q^{23} +5.19362 q^{24} +11.3396 q^{25} -0.633036 q^{26} -1.83302 q^{27} +5.17855 q^{28} +2.63965 q^{29} -5.83281 q^{30} -3.14112 q^{31} -5.66866 q^{32} -2.27944 q^{33} -0.801470 q^{34} -13.0891 q^{35} -3.51174 q^{36} -8.50684 q^{37} +2.38198 q^{38} +2.27944 q^{39} +9.21009 q^{40} -10.4366 q^{41} +4.67245 q^{42} +5.18335 q^{43} +1.59927 q^{44} +8.87613 q^{45} +2.53384 q^{46} -3.82495 q^{47} +4.00311 q^{48} +3.48516 q^{49} -7.17841 q^{50} +2.88594 q^{51} -1.59927 q^{52} +0.485163 q^{53} +1.16037 q^{54} -4.04223 q^{55} -7.37785 q^{56} -8.57706 q^{57} -1.67099 q^{58} +12.8985 q^{59} -14.7357 q^{60} +13.9902 q^{61} +1.98844 q^{62} -7.11033 q^{63} +0.0761058 q^{64} +4.04223 q^{65} +1.44297 q^{66} +11.2408 q^{67} -2.02479 q^{68} -9.12388 q^{69} +8.28586 q^{70} -3.39103 q^{71} +5.00316 q^{72} -1.58775 q^{73} +5.38514 q^{74} +25.8481 q^{75} +6.01770 q^{76} +3.23808 q^{77} -1.44297 q^{78} +4.63965 q^{79} +7.09889 q^{80} -10.7658 q^{81} +6.60675 q^{82} +9.85469 q^{83} +11.8042 q^{84} +5.11776 q^{85} -3.28125 q^{86} +6.01692 q^{87} -2.27847 q^{88} -6.51470 q^{89} -5.61891 q^{90} -3.23808 q^{91} +6.40135 q^{92} -7.15999 q^{93} +2.42133 q^{94} -15.2101 q^{95} -12.9214 q^{96} +9.70000 q^{97} -2.20623 q^{98} -2.19585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9	\( 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 12 q^{14} + 3 q^{15} + 8 q^{16} + 6 q^{18} - 10 q^{19} + 4 q^{20} - 12 q^{21} + 11 q^{23} - 38 q^{24} + 23 q^{25} + 9 q^{27} + 9 q^{28} + 2 q^{29} - 56 q^{30} - 9 q^{31} - 17 q^{32} - 3 q^{33} - 40 q^{34} - 24 q^{35} + 11 q^{36} + 15 q^{37} - 9 q^{38} + 3 q^{39} + 16 q^{40} - 4 q^{41} + 19 q^{42} - 2 q^{43} - 8 q^{44} - 26 q^{45} - 6 q^{46} + 6 q^{47} + 19 q^{48} + 20 q^{49} - 4 q^{50} + 6 q^{51} + 8 q^{52} + 2 q^{53} + 37 q^{54} - q^{55} - 39 q^{56} + 22 q^{57} + 18 q^{58} + 11 q^{59} - 24 q^{60} + 16 q^{61} + 16 q^{62} - 26 q^{63} + 36 q^{64} + q^{65} + 3 q^{66} + 9 q^{67} + 12 q^{68} - 3 q^{69} + 32 q^{70} - 15 q^{71} + 5 q^{72} + 32 q^{73} + 22 q^{74} + 4 q^{75} - 26 q^{76} - 4 q^{77} - 3 q^{78} + 14 q^{79} + 56 q^{80} - 2 q^{81} - 24 q^{82} - 26 q^{83} + 43 q^{84} - 12 q^{85} - 10 q^{86} - 38 q^{87} + 6 q^{88} - 23 q^{89} - 10 q^{90} + 4 q^{91} + 83 q^{92} + 23 q^{93} + 46 q^{94} - 52 q^{95} - 56 q^{96} + 27 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 12 * q^14 + 3 * q^15 + 8 * q^16 + 6 * q^18 - 10 * q^19 + 4 * q^20 - 12 * q^21 + 11 * q^23 - 38 * q^24 + 23 * q^25 + 9 * q^27 + 9 * q^28 + 2 * q^29 - 56 * q^30 - 9 * q^31 - 17 * q^32 - 3 * q^33 - 40 * q^34 - 24 * q^35 + 11 * q^36 + 15 * q^37 - 9 * q^38 + 3 * q^39 + 16 * q^40 - 4 * q^41 + 19 * q^42 - 2 * q^43 - 8 * q^44 - 26 * q^45 - 6 * q^46 + 6 * q^47 + 19 * q^48 + 20 * q^49 - 4 * q^50 + 6 * q^51 + 8 * q^52 + 2 * q^53 + 37 * q^54 - q^55 - 39 * q^56 + 22 * q^57 + 18 * q^58 + 11 * q^59 - 24 * q^60 + 16 * q^61 + 16 * q^62 - 26 * q^63 + 36 * q^64 + q^65 + 3 * q^66 + 9 * q^67 + 12 * q^68 - 3 * q^69 + 32 * q^70 - 15 * q^71 + 5 * q^72 + 32 * q^73 + 22 * q^74 + 4 * q^75 - 26 * q^76 - 4 * q^77 - 3 * q^78 + 14 * q^79 + 56 * q^80 - 2 * q^81 - 24 * q^82 - 26 * q^83 + 43 * q^84 - 12 * q^85 - 10 * q^86 - 38 * q^87 + 6 * q^88 - 23 * q^89 - 10 * q^90 + 4 * q^91 + 83 * q^92 + 23 * q^93 + 46 * q^94 - 52 * q^95 - 56 * q^96 + 27 * q^97 - 3 * q^98 - 13 * q^99

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