LMFDB - Embedded newform 1343.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1343,2,Mod(1,1343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1343, 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("1343.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1343 = 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1343.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:	$10.7239089915$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 25 x^{18} + 48 x^{17} + 257 x^{16} - 467 x^{15} - 1414 x^{14} + 2385 x^{13} + \cdots + 1 $ x^20 - 2x^19 - 25x^18 + 48x^17 + 257x^16 - 467x^15 - 1414x^14 + 2385x^13 + 4540x^12 - 6927x^11 - 8678x^10 + 11583x^9 + 9611x^8 - 10745x^7 - 5686x^6 + 4961x^5 + 1561x^4 - 847x^3 - 191x^2 + 22*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-1.19164$ of defining polynomial
Character	$\chi$	$=$	1343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.19164 q^{2} +2.55447 q^{3} -0.579984 q^{4} -1.88775 q^{5} +3.04402 q^{6} -3.11778 q^{7} -3.07442 q^{8} +3.52533 q^{9} +O(q^{10})$	\(q+1.19164 q^{2} +2.55447 q^{3} -0.579984 q^{4} -1.88775 q^{5} +3.04402 q^{6} -3.11778 q^{7} -3.07442 q^{8} +3.52533 q^{9} -2.24952 q^{10} -1.60843 q^{11} -1.48155 q^{12} +0.416169 q^{13} -3.71529 q^{14} -4.82220 q^{15} -2.50365 q^{16} -1.00000 q^{17} +4.20094 q^{18} -7.95021 q^{19} +1.09486 q^{20} -7.96429 q^{21} -1.91667 q^{22} -5.69842 q^{23} -7.85353 q^{24} -1.43641 q^{25} +0.495925 q^{26} +1.34194 q^{27} +1.80827 q^{28} +6.04543 q^{29} -5.74635 q^{30} +4.51555 q^{31} +3.16539 q^{32} -4.10868 q^{33} -1.19164 q^{34} +5.88559 q^{35} -2.04464 q^{36} +7.02886 q^{37} -9.47382 q^{38} +1.06309 q^{39} +5.80373 q^{40} +2.60324 q^{41} -9.49060 q^{42} +6.86175 q^{43} +0.932862 q^{44} -6.65493 q^{45} -6.79049 q^{46} +2.71540 q^{47} -6.39550 q^{48} +2.72057 q^{49} -1.71169 q^{50} -2.55447 q^{51} -0.241372 q^{52} -13.1079 q^{53} +1.59912 q^{54} +3.03630 q^{55} +9.58538 q^{56} -20.3086 q^{57} +7.20400 q^{58} +5.64281 q^{59} +2.79680 q^{60} -9.97764 q^{61} +5.38093 q^{62} -10.9912 q^{63} +8.77931 q^{64} -0.785622 q^{65} -4.89608 q^{66} -4.60037 q^{67} +0.579984 q^{68} -14.5565 q^{69} +7.01352 q^{70} +1.58466 q^{71} -10.8384 q^{72} +5.91008 q^{73} +8.37590 q^{74} -3.66927 q^{75} +4.61100 q^{76} +5.01472 q^{77} +1.26683 q^{78} -1.00000 q^{79} +4.72626 q^{80} -7.14804 q^{81} +3.10214 q^{82} -1.99437 q^{83} +4.61916 q^{84} +1.88775 q^{85} +8.17677 q^{86} +15.4429 q^{87} +4.94498 q^{88} -15.2097 q^{89} -7.93031 q^{90} -1.29752 q^{91} +3.30499 q^{92} +11.5349 q^{93} +3.23579 q^{94} +15.0080 q^{95} +8.08590 q^{96} -12.3252 q^{97} +3.24195 q^{98} -5.67023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 4 q^{3} + 14 q^{4} - 7 q^{5} - 4 q^{6} - 11 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 4 * q^3 + 14 * q^4 - 7 * q^5 - 4 * q^6 - 11 * q^7 - 6 * q^8 + 10 * q^9	\( 20 q - 2 q^{2} - 4 q^{3} + 14 q^{4} - 7 q^{5} - 4 q^{6} - 11 q^{7} - 6 q^{8} + 10 q^{9} - 19 q^{10} - 7 q^{11} - 17 q^{12} - 19 q^{13} - 3 q^{14} + 10 q^{16} - 20 q^{17} - 17 q^{18} - 9 q^{19} - 6 q^{20} - 16 q^{21} - 17 q^{22} - 15 q^{23} - 5 q^{24} - 21 q^{25} + 5 q^{26} - 19 q^{27} - 27 q^{28} - 11 q^{29} - 9 q^{30} - 13 q^{31} + q^{32} - 20 q^{33} + 2 q^{34} - 9 q^{35} - 6 q^{36} - 26 q^{37} + 9 q^{38} - 5 q^{39} - 19 q^{40} - 6 q^{41} + 4 q^{42} - 32 q^{43} - 35 q^{44} - 12 q^{45} - 42 q^{46} + 3 q^{47} - 31 q^{48} - 7 q^{49} + 23 q^{50} + 4 q^{51} - 49 q^{52} - 20 q^{53} + 41 q^{54} - 30 q^{55} + 5 q^{56} - 35 q^{57} - 9 q^{58} + 26 q^{59} + 33 q^{60} - 33 q^{61} - 18 q^{62} - 32 q^{63} - 12 q^{64} - 20 q^{65} + 38 q^{66} - 31 q^{67} - 14 q^{68} - 18 q^{69} - 13 q^{70} + 2 q^{71} - 44 q^{72} - 71 q^{73} + 4 q^{74} + 15 q^{75} + 13 q^{76} + 20 q^{77} - 3 q^{78} - 20 q^{79} + 7 q^{80} - 36 q^{81} - 26 q^{82} + 21 q^{83} + 37 q^{84} + 7 q^{85} + q^{86} - 3 q^{87} - 11 q^{88} - 15 q^{89} + 9 q^{90} - 4 q^{91} - 13 q^{92} - 21 q^{93} + 44 q^{94} + 7 q^{95} + q^{96} - 47 q^{97} + 7 q^{98} - 35 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 4 * q^3 + 14 * q^4 - 7 * q^5 - 4 * q^6 - 11 * q^7 - 6 * q^8 + 10 * q^9 - 19 * q^10 - 7 * q^11 - 17 * q^12 - 19 * q^13 - 3 * q^14 + 10 * q^16 - 20 * q^17 - 17 * q^18 - 9 * q^19 - 6 * q^20 - 16 * q^21 - 17 * q^22 - 15 * q^23 - 5 * q^24 - 21 * q^25 + 5 * q^26 - 19 * q^27 - 27 * q^28 - 11 * q^29 - 9 * q^30 - 13 * q^31 + q^32 - 20 * q^33 + 2 * q^34 - 9 * q^35 - 6 * q^36 - 26 * q^37 + 9 * q^38 - 5 * q^39 - 19 * q^40 - 6 * q^41 + 4 * q^42 - 32 * q^43 - 35 * q^44 - 12 * q^45 - 42 * q^46 + 3 * q^47 - 31 * q^48 - 7 * q^49 + 23 * q^50 + 4 * q^51 - 49 * q^52 - 20 * q^53 + 41 * q^54 - 30 * q^55 + 5 * q^56 - 35 * q^57 - 9 * q^58 + 26 * q^59 + 33 * q^60 - 33 * q^61 - 18 * q^62 - 32 * q^63 - 12 * q^64 - 20 * q^65 + 38 * q^66 - 31 * q^67 - 14 * q^68 - 18 * q^69 - 13 * q^70 + 2 * q^71 - 44 * q^72 - 71 * q^73 + 4 * q^74 + 15 * q^75 + 13 * q^76 + 20 * q^77 - 3 * q^78 - 20 * q^79 + 7 * q^80 - 36 * q^81 - 26 * q^82 + 21 * q^83 + 37 * q^84 + 7 * q^85 + q^86 - 3 * q^87 - 11 * q^88 - 15 * q^89 + 9 * q^90 - 4 * q^91 - 13 * q^92 - 21 * q^93 + 44 * q^94 + 7 * q^95 + q^96 - 47 * q^97 + 7 * q^98 - 35 * 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 $

$2$	1.19164	0.842620	0.421310	−	0.906917i	$-0.361571\pi$
$2$	1.19164	0.842620	0.421310	+	0.906917i	$0.361571\pi$
$3$	2.55447	1.47483	0.737413	−	0.675442i	$-0.236047\pi$
$3$	2.55447	1.47483	0.737413	+	0.675442i	$0.236047\pi$
$4$	−0.579984	−0.289992
$5$	−1.88775	−0.844226	−0.422113	−	0.906543i	$-0.638712\pi$
$5$	−1.88775	−0.844226	−0.422113	+	0.906543i	$0.638712\pi$
$6$	3.04402	1.24272
$7$	−3.11778	−1.17841	−0.589206	−	0.807983i	$-0.700559\pi$
$7$	−3.11778	−1.17841	−0.589206	+	0.807983i	$0.700559\pi$
$8$	−3.07442	−1.08697
$9$	3.52533	1.17511
$10$	−2.24952	−0.711362
$11$	−1.60843	−0.484959	−0.242479	−	0.970157i	$-0.577961\pi$
$11$	−1.60843	−0.484959	−0.242479	+	0.970157i	$0.577961\pi$
$12$	−1.48155	−0.427688
$13$	0.416169	0.115424	0.0577122	−	0.998333i	$-0.481619\pi$
$13$	0.416169	0.115424	0.0577122	+	0.998333i	$0.481619\pi$
$14$	−3.71529	−0.992952
$15$	−4.82220	−1.24509
$16$	−2.50365	−0.625912
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.20094	0.990171
$19$	−7.95021	−1.82390	−0.911951	−	0.410299i	$-0.865424\pi$
$19$	−7.95021	−1.82390	−0.911951	+	0.410299i	$0.865424\pi$
$20$	1.09486	0.244819
$21$	−7.96429	−1.73795
$22$	−1.91667	−0.408636
$23$	−5.69842	−1.18820	−0.594101	−	0.804390i	$-0.702492\pi$
$23$	−5.69842	−1.18820	−0.594101	+	0.804390i	$0.702492\pi$
$24$	−7.85353	−1.60310
$25$	−1.43641	−0.287282
$26$	0.495925	0.0972589
$27$	1.34194	0.258257
$28$	1.80827	0.341730
$29$	6.04543	1.12261	0.561304	−	0.827610i	$-0.310300\pi$
$29$	6.04543	1.12261	0.561304	+	0.827610i	$0.310300\pi$
$30$	−5.74635	−1.04913
$31$	4.51555	0.811017	0.405509	−	0.914091i	$-0.367094\pi$
$31$	4.51555	0.811017	0.405509	+	0.914091i	$0.367094\pi$
$32$	3.16539	0.559567
$33$	−4.10868	−0.715229
$34$	−1.19164	−0.204365
$35$	5.88559	0.994846
$36$	−2.04464	−0.340773
$37$	7.02886	1.15554	0.577769	−	0.816200i	$-0.303923\pi$
$37$	7.02886	1.15554	0.577769	+	0.816200i	$0.303923\pi$
$38$	−9.47382	−1.53686
$39$	1.06309	0.170231
$40$	5.80373	0.917651
$41$	2.60324	0.406559	0.203279	−	0.979121i	$-0.434840\pi$
$41$	2.60324	0.406559	0.203279	+	0.979121i	$0.434840\pi$
$42$	−9.49060	−1.46443
$43$	6.86175	1.04641	0.523204	−	0.852208i	$-0.324737\pi$
$43$	6.86175	1.04641	0.523204	+	0.852208i	$0.324737\pi$
$44$	0.932862	0.140634
$45$	−6.65493	−0.992059
$46$	−6.79049	−1.00120
$47$	2.71540	0.396081	0.198041	−	0.980194i	$-0.436542\pi$
$47$	2.71540	0.396081	0.198041	+	0.980194i	$0.436542\pi$
$48$	−6.39550	−0.923111
$49$	2.72057	0.388653
$50$	−1.71169	−0.242069
$51$	−2.55447	−0.357698
$52$	−0.241372	−0.0334722
$53$	−13.1079	−1.80051	−0.900254	−	0.435365i	$-0.856619\pi$
$53$	−13.1079	−1.80051	−0.900254	+	0.435365i	$0.856619\pi$
$54$	1.59912	0.217612
$55$	3.03630	0.409415
$56$	9.58538	1.28090
$57$	−20.3086	−2.68994
$58$	7.20400	0.945931
$59$	5.64281	0.734632	0.367316	−	0.930096i	$-0.380277\pi$
$59$	5.64281	0.734632	0.367316	+	0.930096i	$0.380277\pi$
$60$	2.79680	0.361065
$61$	−9.97764	−1.27751	−0.638753	−	0.769412i	$-0.720550\pi$
$61$	−9.97764	−1.27751	−0.638753	+	0.769412i	$0.720550\pi$
$62$	5.38093	0.683379
$63$	−10.9912	−1.38476
$64$	8.77931	1.09741
$65$	−0.785622	−0.0974444
$66$	−4.89608	−0.602666
$67$	−4.60037	−0.562025	−0.281013	−	0.959704i	$-0.590670\pi$
$67$	−4.60037	−0.562025	−0.281013	+	0.959704i	$0.590670\pi$
$68$	0.579984	0.0703334
$69$	−14.5565	−1.75239
$70$	7.01352	0.838276
$71$	1.58466	0.188064	0.0940321	−	0.995569i	$-0.470024\pi$
$71$	1.58466	0.188064	0.0940321	+	0.995569i	$0.470024\pi$
$72$	−10.8384	−1.27731
$73$	5.91008	0.691722	0.345861	−	0.938286i	$-0.387587\pi$
$73$	5.91008	0.691722	0.345861	+	0.938286i	$0.387587\pi$
$74$	8.37590	0.973679
$75$	−3.66927	−0.423691
$76$	4.61100	0.528918
$77$	5.01472	0.571480
$78$	1.26683	0.143440
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	4.72626	0.528412
$81$	−7.14804	−0.794226
$82$	3.10214	0.342574
$83$	−1.99437	−0.218910	−0.109455	−	0.993992i	$-0.534911\pi$
$83$	−1.99437	−0.218910	−0.109455	+	0.993992i	$0.534911\pi$
$84$	4.61916	0.503992
$85$	1.88775	0.204755
$86$	8.17677	0.881723
$87$	15.4429	1.65565
$88$	4.94498	0.527137
$89$	−15.2097	−1.61222	−0.806111	−	0.591764i	$-0.798432\pi$
$89$	−15.2097	−1.61222	−0.806111	+	0.591764i	$0.798432\pi$
$90$	−7.93031	−0.835928
$91$	−1.29752	−0.136017
$92$	3.30499	0.344569
$93$	11.5349	1.19611
$94$	3.23579	0.333746
$95$	15.0080	1.53979
$96$	8.08590	0.825263
$97$	−12.3252	−1.25143	−0.625716	−	0.780051i	$-0.715193\pi$
$97$	−12.3252	−1.25143	−0.625716	+	0.780051i	$0.715193\pi$
$98$	3.24195	0.327486
$99$	−5.67023	−0.569880
$100$	0.833095	0.0833095
$101$	6.92291	0.688856	0.344428	−	0.938813i	$-0.388073\pi$
$101$	6.92291	0.688856	0.344428	+	0.938813i	$0.388073\pi$
$102$	−3.04402	−0.301403
$103$	12.1513	1.19730	0.598650	−	0.801011i	$-0.295704\pi$
$103$	12.1513	1.19730	0.598650	+	0.801011i	$0.295704\pi$
$104$	−1.27948	−0.125463
$105$	15.0346	1.46722
$106$	−15.6199	−1.51714
$107$	−3.78551	−0.365959	−0.182979	−	0.983117i	$-0.558574\pi$
$107$	−3.78551	−0.365959	−0.182979	+	0.983117i	$0.558574\pi$
$108$	−0.778305	−0.0748925
$109$	−12.2934	−1.17749	−0.588747	−	0.808317i	$-0.700379\pi$
$109$	−12.2934	−1.17749	−0.588747	+	0.808317i	$0.700379\pi$
$110$	3.61819	0.344981
$111$	17.9550	1.70422
$112$	7.80583	0.737582
$113$	−19.2318	−1.80917	−0.904587	−	0.426288i	$-0.859821\pi$
$113$	−19.2318	−1.80917	−0.904587	+	0.426288i	$0.859821\pi$
$114$	−24.2006	−2.26659
$115$	10.7572	1.00311
$116$	−3.50625	−0.325547
$117$	1.46713	0.135636
$118$	6.72423	0.619015
$119$	3.11778	0.285807
$120$	14.8255	1.35338
$121$	−8.41297	−0.764815
$122$	−11.8898	−1.07645
$123$	6.64992	0.599603
$124$	−2.61895	−0.235189
$125$	12.1503	1.08676
$126$	−13.0976	−1.16683
$127$	−12.2930	−1.09082	−0.545412	−	0.838168i	$-0.683627\pi$
$127$	−12.2930	−1.09082	−0.545412	+	0.838168i	$0.683627\pi$
$128$	4.13104	0.365136
$129$	17.5282	1.54327
$130$	−0.936182	−0.0821086
$131$	−0.931969	−0.0814265	−0.0407132	−	0.999171i	$-0.512963\pi$
$131$	−0.931969	−0.0814265	−0.0407132	+	0.999171i	$0.512963\pi$
$132$	2.38297	0.207411
$133$	24.7870	2.14931
$134$	−5.48201	−0.473573
$135$	−2.53325	−0.218027
$136$	3.07442	0.263630
$137$	20.8300	1.77963	0.889814	−	0.456323i	$-0.150834\pi$
$137$	20.8300	1.77963	0.889814	+	0.456323i	$0.150834\pi$
$138$	−17.3461	−1.47660
$139$	−22.7329	−1.92818	−0.964090	−	0.265575i	$-0.914438\pi$
$139$	−22.7329	−1.92818	−0.964090	+	0.265575i	$0.914438\pi$
$140$	−3.41355	−0.288498
$141$	6.93641	0.584151
$142$	1.88835	0.158467
$143$	−0.669377	−0.0559761
$144$	−8.82619	−0.735516
$145$	−11.4122	−0.947735
$146$	7.04271	0.582859
$147$	6.94962	0.573195
$148$	−4.07663	−0.335097
$149$	6.97404	0.571336	0.285668	−	0.958329i	$-0.407785\pi$
$149$	6.97404	0.571336	0.285668	+	0.958329i	$0.407785\pi$
$150$	−4.37246	−0.357010
$151$	22.6881	1.84633	0.923164	−	0.384406i	$-0.125594\pi$
$151$	22.6881	1.84633	0.923164	+	0.384406i	$0.125594\pi$
$152$	24.4423	1.98253
$153$	−3.52533	−0.285006
$154$	5.97576	0.481541
$155$	−8.52423	−0.684682
$156$	−0.616577	−0.0493657
$157$	11.0263	0.879994	0.439997	−	0.897999i	$-0.354979\pi$
$157$	11.0263	0.879994	0.439997	+	0.897999i	$0.354979\pi$
$158$	−1.19164	−0.0948021
$159$	−33.4838	−2.65544
$160$	−5.97545	−0.472401
$161$	17.7664	1.40019
$162$	−8.51792	−0.669231
$163$	15.8100	1.23833	0.619166	−	0.785260i	$-0.287471\pi$
$163$	15.8100	1.23833	0.619166	+	0.785260i	$0.287471\pi$
$164$	−1.50984	−0.117899
$165$	7.75615	0.603815
$166$	−2.37657	−0.184458
$167$	10.6177	0.821624	0.410812	−	0.911720i	$-0.365245\pi$
$167$	10.6177	0.821624	0.410812	+	0.911720i	$0.365245\pi$
$168$	24.4856	1.88910
$169$	−12.8268	−0.986677
$170$	2.24952	0.172531
$171$	−28.0271	−2.14329
$172$	−3.97971	−0.303450
$173$	3.65984	0.278252	0.139126	−	0.990275i	$-0.455571\pi$
$173$	3.65984	0.278252	0.139126	+	0.990275i	$0.455571\pi$
$174$	18.4024	1.39508
$175$	4.47841	0.338536
$176$	4.02693	0.303541
$177$	14.4144	1.08345
$178$	−18.1245	−1.35849
$179$	−1.08895	−0.0813922	−0.0406961	−	0.999172i	$-0.512958\pi$
$179$	−1.08895	−0.0813922	−0.0406961	+	0.999172i	$0.512958\pi$
$180$	3.85976	0.287689
$181$	−5.86637	−0.436044	−0.218022	−	0.975944i	$-0.569960\pi$
$181$	−5.86637	−0.436044	−0.218022	+	0.975944i	$0.569960\pi$
$182$	−1.54619	−0.114611
$183$	−25.4876	−1.88410
$184$	17.5193	1.29154
$185$	−13.2687	−0.975535
$186$	13.7454	1.00787
$187$	1.60843	0.117620
$188$	−1.57489	−0.114861
$189$	−4.18388	−0.304333
$190$	17.8842	1.29745
$191$	16.2306	1.17440	0.587202	−	0.809440i	$-0.300229\pi$
$191$	16.2306	1.17440	0.587202	+	0.809440i	$0.300229\pi$
$192$	22.4265	1.61849
$193$	−18.1009	−1.30293	−0.651466	−	0.758678i	$-0.725845\pi$
$193$	−18.1009	−1.30293	−0.651466	+	0.758678i	$0.725845\pi$
$194$	−14.6872	−1.05448
$195$	−2.00685	−0.143713
$196$	−1.57789	−0.112706
$197$	−14.0565	−1.00149	−0.500743	−	0.865596i	$-0.666940\pi$
$197$	−14.0565	−1.00149	−0.500743	+	0.865596i	$0.666940\pi$
$198$	−6.75690	−0.480192
$199$	12.2576	0.868920	0.434460	−	0.900691i	$-0.356939\pi$
$199$	12.2576	0.868920	0.434460	+	0.900691i	$0.356939\pi$
$200$	4.41613	0.312268
$201$	−11.7515	−0.828889
$202$	8.24965	0.580443
$203$	−18.8483	−1.32289
$204$	1.48155	0.103730
$205$	−4.91427	−0.343227
$206$	14.4800	1.00887
$207$	−20.0888	−1.39627
$208$	−1.04194	−0.0722456
$209$	12.7873	0.884517
$210$	17.9159	1.23631
$211$	20.5272	1.41315	0.706574	−	0.707639i	$-0.250240\pi$
$211$	20.5272	1.41315	0.706574	+	0.707639i	$0.250240\pi$
$212$	7.60238	0.522133
$213$	4.04796	0.277362
$214$	−4.51098	−0.308364
$215$	−12.9533	−0.883405
$216$	−4.12570	−0.280718
$217$	−14.0785	−0.955712
$218$	−14.6494	−0.992179
$219$	15.0971	1.02017
$220$	−1.76101	−0.118727
$221$	−0.416169	−0.0279946
$222$	21.3960	1.43601
$223$	3.84359	0.257386	0.128693	−	0.991684i	$-0.458922\pi$
$223$	3.84359	0.257386	0.128693	+	0.991684i	$0.458922\pi$
$224$	−9.86899	−0.659400
$225$	−5.06382	−0.337588
$226$	−22.9174	−1.52445
$227$	−16.3274	−1.08369	−0.541843	−	0.840480i	$-0.682273\pi$
$227$	−16.3274	−1.08369	−0.541843	+	0.840480i	$0.682273\pi$
$228$	11.7787	0.780061
$229$	−27.9666	−1.84808	−0.924042	−	0.382291i	$-0.875135\pi$
$229$	−27.9666	−1.84808	−0.924042	+	0.382291i	$0.875135\pi$
$230$	12.8187	0.845242
$231$	12.8100	0.842834
$232$	−18.5862	−1.22024
$233$	−25.3247	−1.65908	−0.829540	−	0.558448i	$-0.811397\pi$
$233$	−25.3247	−1.65908	−0.829540	+	0.558448i	$0.811397\pi$
$234$	1.74830	0.114290
$235$	−5.12598	−0.334382
$236$	−3.27274	−0.213038
$237$	−2.55447	−0.165931
$238$	3.71529	0.240826
$239$	2.26924	0.146785	0.0733923	−	0.997303i	$-0.476617\pi$
$239$	2.26924	0.146785	0.0733923	+	0.997303i	$0.476617\pi$
$240$	12.0731	0.779315
$241$	14.0186	0.903018	0.451509	−	0.892267i	$-0.350886\pi$
$241$	14.0186	0.903018	0.451509	+	0.892267i	$0.350886\pi$
$242$	−10.0253	−0.644448
$243$	−22.2853	−1.42960
$244$	5.78688	0.370467
$245$	−5.13574	−0.328111
$246$	7.92433	0.505237
$247$	−3.30863	−0.210523
$248$	−13.8827	−0.881554
$249$	−5.09455	−0.322854
$250$	14.4789	0.915723
$251$	−10.8877	−0.687226	−0.343613	−	0.939111i	$-0.611651\pi$
$251$	−10.8877	−0.687226	−0.343613	+	0.939111i	$0.611651\pi$
$252$	6.37473	0.401570
$253$	9.16548	0.576229
$254$	−14.6488	−0.919149
$255$	4.82220	0.301978
$256$	−12.6359	−0.789744
$257$	−4.49526	−0.280407	−0.140203	−	0.990123i	$-0.544776\pi$
$257$	−4.49526	−0.280407	−0.140203	+	0.990123i	$0.544776\pi$
$258$	20.8873	1.30039
$259$	−21.9145	−1.36170
$260$	0.455649	0.0282581
$261$	21.3121	1.31919
$262$	−1.11058	−0.0686116
$263$	−3.78322	−0.233284	−0.116642	−	0.993174i	$-0.537213\pi$
$263$	−3.78322	−0.233284	−0.116642	+	0.993174i	$0.537213\pi$
$264$	12.6318	0.777435
$265$	24.7444	1.52004
$266$	29.5373	1.81105
$267$	−38.8527	−2.37775
$268$	2.66815	0.162983
$269$	19.3224	1.17811	0.589053	−	0.808094i	$-0.299501\pi$
$269$	19.3224	1.17811	0.589053	+	0.808094i	$0.299501\pi$
$270$	−3.01873	−0.183714
$271$	9.13689	0.555027	0.277513	−	0.960722i	$-0.410490\pi$
$271$	9.13689	0.555027	0.277513	+	0.960722i	$0.410490\pi$
$272$	2.50365	0.151806
$273$	−3.31449	−0.200602
$274$	24.8220	1.49955
$275$	2.31036	0.139320
$276$	8.44252	0.508180
$277$	−4.53621	−0.272554	−0.136277	−	0.990671i	$-0.543514\pi$
$277$	−4.53621	−0.272554	−0.136277	+	0.990671i	$0.543514\pi$
$278$	−27.0895	−1.62472
$279$	15.9188	0.953035
$280$	−18.0948	−1.08137
$281$	13.2004	0.787471	0.393736	−	0.919224i	$-0.371183\pi$
$281$	13.2004	0.787471	0.393736	+	0.919224i	$0.371183\pi$
$282$	8.26573	0.492217
$283$	5.01264	0.297971	0.148985	−	0.988839i	$-0.452399\pi$
$283$	5.01264	0.297971	0.148985	+	0.988839i	$0.452399\pi$
$284$	−0.919076	−0.0545371
$285$	38.3375	2.27092
$286$	−0.797659	−0.0471666
$287$	−8.11635	−0.479093
$288$	11.1590	0.657553
$289$	1.00000	0.0588235
$290$	−13.5993	−0.798580
$291$	−31.4843	−1.84564
$292$	−3.42775	−0.200594
$293$	10.7698	0.629176	0.314588	−	0.949228i	$-0.398134\pi$
$293$	10.7698	0.629176	0.314588	+	0.949228i	$0.398134\pi$
$294$	8.28147	0.482985
$295$	−10.6522	−0.620196
$296$	−21.6097	−1.25604
$297$	−2.15841	−0.125244
$298$	8.31057	0.481419
$299$	−2.37150	−0.137148
$300$	2.12812	0.122867
$301$	−21.3935	−1.23310
$302$	27.0361	1.55575
$303$	17.6844	1.01594
$304$	19.9045	1.14160
$305$	18.8353	1.07850
$306$	−4.20094	−0.240152
$307$	18.7658	1.07102	0.535511	−	0.844528i	$-0.320119\pi$
$307$	18.7658	1.07102	0.535511	+	0.844528i	$0.320119\pi$
$308$	−2.90846	−0.165725
$309$	31.0401	1.76581
$310$	−10.1578	−0.576927
$311$	−11.6767	−0.662126	−0.331063	−	0.943609i	$-0.607407\pi$
$311$	−11.6767	−0.662126	−0.331063	+	0.943609i	$0.607407\pi$
$312$	−3.26840	−0.185036
$313$	−28.2556	−1.59710	−0.798549	−	0.601929i	$-0.794399\pi$
$313$	−28.2556	−1.59710	−0.798549	+	0.601929i	$0.794399\pi$
$314$	13.1394	0.741501
$315$	20.7486	1.16905
$316$	0.579984	0.0326267
$317$	−7.28851	−0.409363	−0.204682	−	0.978829i	$-0.565616\pi$
$317$	−7.28851	−0.409363	−0.204682	+	0.978829i	$0.565616\pi$
$318$	−39.9007	−2.23752
$319$	−9.72362	−0.544418
$320$	−16.5731	−0.926466
$321$	−9.66997	−0.539725
$322$	21.1713	1.17983
$323$	7.95021	0.442361
$324$	4.14575	0.230319
$325$	−0.597789	−0.0331594
$326$	18.8398	1.04344
$327$	−31.4031	−1.73660
$328$	−8.00348	−0.441918
$329$	−8.46602	−0.466747
$330$	9.24257	0.508787
$331$	−15.3062	−0.841306	−0.420653	−	0.907222i	$-0.638199\pi$
$331$	−15.3062	−0.841306	−0.420653	+	0.907222i	$0.638199\pi$
$332$	1.15670	0.0634822
$333$	24.7791	1.35788
$334$	12.6525	0.692316
$335$	8.68435	0.474476
$336$	19.9398	1.08780
$337$	2.96436	0.161479	0.0807396	−	0.996735i	$-0.474272\pi$
$337$	2.96436	0.161479	0.0807396	+	0.996735i	$0.474272\pi$
$338$	−15.2850	−0.831394
$339$	−49.1271	−2.66822
$340$	−1.09486	−0.0593774
$341$	−7.26293	−0.393310
$342$	−33.3983	−1.80597
$343$	13.3423	0.720419
$344$	−21.0959	−1.13742
$345$	27.4789	1.47941
$346$	4.36122	0.234461
$347$	−4.30320	−0.231008	−0.115504	−	0.993307i	$-0.536848\pi$
$347$	−4.30320	−0.231008	−0.115504	+	0.993307i	$0.536848\pi$
$348$	−8.95663	−0.480126
$349$	−12.0475	−0.644889	−0.322444	−	0.946588i	$-0.604504\pi$
$349$	−12.0475	−0.644889	−0.322444	+	0.946588i	$0.604504\pi$
$350$	5.33667	0.285257
$351$	0.558474	0.0298092
$352$	−5.09129	−0.271367
$353$	−8.01673	−0.426687	−0.213344	−	0.976977i	$-0.568435\pi$
$353$	−8.01673	−0.426687	−0.213344	+	0.976977i	$0.568435\pi$
$354$	17.1769	0.912939
$355$	−2.99143	−0.158769
$356$	8.82137	0.467532
$357$	7.96429	0.421515
$358$	−1.29765	−0.0685827
$359$	−5.87803	−0.310231	−0.155115	−	0.987896i	$-0.549575\pi$
$359$	−5.87803	−0.310231	−0.155115	+	0.987896i	$0.549575\pi$
$360$	20.4601	1.07834
$361$	44.2058	2.32662
$362$	−6.99063	−0.367419
$363$	−21.4907	−1.12797
$364$	0.752544	0.0394440
$365$	−11.1567	−0.583970
$366$	−30.3722	−1.58758
$367$	−29.6675	−1.54863	−0.774316	−	0.632799i	$-0.781906\pi$
$367$	−29.6675	−1.54863	−0.774316	+	0.632799i	$0.781906\pi$
$368$	14.2668	0.743710
$369$	9.17730	0.477751
$370$	−15.8116	−0.822005
$371$	40.8676	2.12174
$372$	−6.69004	−0.346862
$373$	−23.5728	−1.22055	−0.610276	−	0.792189i	$-0.708941\pi$
$373$	−23.5728	−1.22055	−0.610276	+	0.792189i	$0.708941\pi$
$374$	1.91667	0.0991087
$375$	31.0376	1.60278
$376$	−8.34828	−0.430530
$377$	2.51592	0.129576
$378$	−4.98570	−0.256437
$379$	−8.15518	−0.418904	−0.209452	−	0.977819i	$-0.567168\pi$
$379$	−8.15518	−0.418904	−0.209452	+	0.977819i	$0.567168\pi$
$380$	−8.70440	−0.446526
$381$	−31.4020	−1.60877
$382$	19.3411	0.989576
$383$	−22.6409	−1.15690	−0.578448	−	0.815719i	$-0.696342\pi$
$383$	−22.6409	−1.15690	−0.578448	+	0.815719i	$0.696342\pi$
$384$	10.5526	0.538512
$385$	−9.46653	−0.482459
$386$	−21.5698	−1.09788
$387$	24.1899	1.22964
$388$	7.14841	0.362906
$389$	1.46248	0.0741505	0.0370752	−	0.999312i	$-0.488196\pi$
$389$	1.46248	0.0741505	0.0370752	+	0.999312i	$0.488196\pi$
$390$	−2.39145	−0.121096
$391$	5.69842	0.288181
$392$	−8.36418	−0.422455
$393$	−2.38069	−0.120090
$394$	−16.7504	−0.843872
$395$	1.88775	0.0949829
$396$	3.28865	0.165261
$397$	5.26490	0.264238	0.132119	−	0.991234i	$-0.457822\pi$
$397$	5.26490	0.264238	0.132119	+	0.991234i	$0.457822\pi$
$398$	14.6067	0.732169
$399$	63.3177	3.16985
$400$	3.59626	0.179813
$401$	18.4815	0.922921	0.461460	−	0.887161i	$-0.347326\pi$
$401$	18.4815	0.922921	0.461460	+	0.887161i	$0.347326\pi$
$402$	−14.0036	−0.698438
$403$	1.87923	0.0936113
$404$	−4.01518	−0.199763
$405$	13.4937	0.670507
$406$	−22.4605	−1.11470
$407$	−11.3054	−0.560388
$408$	7.85353	0.388808
$409$	−17.4777	−0.864215	−0.432108	−	0.901822i	$-0.642230\pi$
$409$	−17.4777	−0.864215	−0.432108	+	0.901822i	$0.642230\pi$
$410$	−5.85606	−0.289210
$411$	53.2097	2.62464
$412$	−7.04755	−0.347208
$413$	−17.5931	−0.865698
$414$	−23.9387	−1.17652
$415$	3.76486	0.184810
$416$	1.31734	0.0645877
$417$	−58.0706	−2.84373
$418$	15.2379	0.745311
$419$	−1.06659	−0.0521065	−0.0260533	−	0.999661i	$-0.508294\pi$
$419$	−1.06659	−0.0521065	−0.0260533	+	0.999661i	$0.508294\pi$
$420$	−8.71982	−0.425483
$421$	18.5683	0.904963	0.452482	−	0.891774i	$-0.350539\pi$
$421$	18.5683	0.904963	0.452482	+	0.891774i	$0.350539\pi$
$422$	24.4611	1.19075
$423$	9.57267	0.465439
$424$	40.2992	1.95710
$425$	1.43641	0.0696761
$426$	4.82373	0.233710
$427$	31.1081	1.50543
$428$	2.19554	0.106125
$429$	−1.70990	−0.0825550
$430$	−15.4357	−0.744374
$431$	15.7187	0.757144	0.378572	−	0.925572i	$-0.376415\pi$
$431$	15.7187	0.757144	0.378572	+	0.925572i	$0.376415\pi$
$432$	−3.35975	−0.161646
$433$	15.3514	0.737739	0.368869	−	0.929481i	$-0.379745\pi$
$433$	15.3514	0.737739	0.368869	+	0.929481i	$0.379745\pi$
$434$	−16.7766	−0.805302
$435$	−29.1523	−1.39774
$436$	7.12998	0.341464
$437$	45.3036	2.16717
$438$	17.9904	0.859615
$439$	−36.0685	−1.72145	−0.860727	−	0.509067i	$-0.829991\pi$
$439$	−36.0685	−1.72145	−0.860727	+	0.509067i	$0.829991\pi$
$440$	−9.33487	−0.445023
$441$	9.59090	0.456709
$442$	−0.495925	−0.0235888
$443$	28.8986	1.37302	0.686508	−	0.727122i	$-0.259143\pi$
$443$	28.8986	1.37302	0.686508	+	0.727122i	$0.259143\pi$
$444$	−10.4136	−0.494210
$445$	28.7120	1.36108
$446$	4.58019	0.216878
$447$	17.8150	0.842620
$448$	−27.3720	−1.29320
$449$	29.1362	1.37502	0.687512	−	0.726173i	$-0.258703\pi$
$449$	29.1362	1.37502	0.687512	+	0.726173i	$0.258703\pi$
$450$	−6.03427	−0.284458
$451$	−4.18713	−0.197164
$452$	11.1541	0.524647
$453$	57.9560	2.72301
$454$	−19.4564	−0.913135
$455$	2.44940	0.114830
$456$	62.4372	2.92389
$457$	−13.1776	−0.616421	−0.308210	−	0.951318i	$-0.599730\pi$
$457$	−13.1776	−0.616421	−0.308210	+	0.951318i	$0.599730\pi$
$458$	−33.3262	−1.55723
$459$	−1.34194	−0.0626365
$460$	−6.23899	−0.290895
$461$	−18.8669	−0.878721	−0.439360	−	0.898311i	$-0.644795\pi$
$461$	−18.8669	−0.878721	−0.439360	+	0.898311i	$0.644795\pi$
$462$	15.2649	0.710188
$463$	−9.26615	−0.430634	−0.215317	−	0.976544i	$-0.569079\pi$
$463$	−9.26615	−0.430634	−0.215317	+	0.976544i	$0.569079\pi$
$464$	−15.1356	−0.702654
$465$	−21.7749	−1.00979
$466$	−30.1781	−1.39797
$467$	23.3143	1.07886	0.539428	−	0.842032i	$-0.318640\pi$
$467$	23.3143	1.07886	0.539428	+	0.842032i	$0.318640\pi$
$468$	−0.850914	−0.0393335
$469$	14.3430	0.662297
$470$	−6.10835	−0.281757
$471$	28.1664	1.29784
$472$	−17.3484	−0.798525
$473$	−11.0366	−0.507464
$474$	−3.04402	−0.139817
$475$	11.4198	0.523974
$476$	−1.80827	−0.0828817
$477$	−46.2097	−2.11580
$478$	2.70412	0.123684
$479$	−10.9781	−0.501602	−0.250801	−	0.968039i	$-0.580694\pi$
$479$	−10.9781	−0.501602	−0.250801	+	0.968039i	$0.580694\pi$
$480$	−15.2641	−0.696709
$481$	2.92519	0.133377
$482$	16.7052	0.760901
$483$	45.3839	2.06504
$484$	4.87939	0.221790
$485$	23.2668	1.05649
$486$	−26.5561	−1.20461
$487$	−31.7620	−1.43928	−0.719638	−	0.694350i	$-0.755692\pi$
$487$	−31.7620	−1.43928	−0.719638	+	0.694350i	$0.755692\pi$
$488$	30.6755	1.38861
$489$	40.3861	1.82632
$490$	−6.11998	−0.276472
$491$	2.64698	0.119456	0.0597282	−	0.998215i	$-0.480977\pi$
$491$	2.64698	0.119456	0.0597282	+	0.998215i	$0.480977\pi$
$492$	−3.85685	−0.173880
$493$	−6.04543	−0.272272
$494$	−3.94271	−0.177391
$495$	10.7040	0.481107
$496$	−11.3054	−0.507626
$497$	−4.94061	−0.221617
$498$	−6.07089	−0.272043
$499$	24.6914	1.10534	0.552669	−	0.833401i	$-0.313610\pi$
$499$	24.6914	1.10534	0.552669	+	0.833401i	$0.313610\pi$
$500$	−7.04699	−0.315151
$501$	27.1227	1.21175
$502$	−12.9743	−0.579070
$503$	13.1113	0.584606	0.292303	−	0.956326i	$-0.405578\pi$
$503$	13.1113	0.584606	0.292303	+	0.956326i	$0.405578\pi$
$504$	33.7916	1.50520
$505$	−13.0687	−0.581550
$506$	10.9220	0.485542
$507$	−32.7657	−1.45518
$508$	7.12973	0.316330
$509$	11.9549	0.529893	0.264946	−	0.964263i	$-0.414646\pi$
$509$	11.9549	0.529893	0.264946	+	0.964263i	$0.414646\pi$
$510$	5.74635	0.254452
$511$	−18.4263	−0.815133
$512$	−23.3196	−1.03059
$513$	−10.6687	−0.471035
$514$	−5.35676	−0.236276
$515$	−22.9385	−1.01079
$516$	−10.1661	−0.447536
$517$	−4.36751	−0.192083
$518$	−26.1142	−1.14739
$519$	9.34895	0.410373
$520$	2.41533	0.105919
$521$	0.305681	0.0133921	0.00669607	−	0.999978i	$-0.497869\pi$
$521$	0.305681	0.0133921	0.00669607	+	0.999978i	$0.497869\pi$
$522$	25.3965	1.11157
$523$	−28.8281	−1.26057	−0.630283	−	0.776365i	$-0.717061\pi$
$523$	−28.8281	−1.26057	−0.630283	+	0.776365i	$0.717061\pi$
$524$	0.540527	0.0236131
$525$	11.4400	0.499282
$526$	−4.50826	−0.196569
$527$	−4.51555	−0.196701
$528$	10.2867	0.447671
$529$	9.47197	0.411825
$530$	29.4865	1.28081
$531$	19.8928	0.863273
$532$	−14.3761	−0.623282
$533$	1.08339	0.0469268
$534$	−46.2986	−2.00354
$535$	7.14608	0.308952
$536$	14.1435	0.610906
$537$	−2.78170	−0.120039
$538$	23.0254	0.992695
$539$	−4.37583	−0.188480
$540$	1.46924	0.0632262
$541$	−39.7842	−1.71045	−0.855227	−	0.518253i	$-0.826583\pi$
$541$	−39.7842	−1.71045	−0.855227	+	0.518253i	$0.826583\pi$
$542$	10.8879	0.467676
$543$	−14.9855	−0.643089
$544$	−3.16539	−0.135715
$545$	23.2068	0.994071
$546$	−3.94969	−0.169031
$547$	−0.430334	−0.0183998	−0.00919988	−	0.999958i	$-0.502928\pi$
$547$	−0.430334	−0.0183998	−0.00919988	+	0.999958i	$0.502928\pi$
$548$	−12.0811	−0.516078
$549$	−35.1745	−1.50121
$550$	2.75312	0.117394
$551$	−48.0624	−2.04753
$552$	44.7527	1.90480
$553$	3.11778	0.132582
$554$	−5.40554	−0.229659
$555$	−33.8946	−1.43874
$556$	13.1847	0.559157
$557$	−8.32316	−0.352664	−0.176332	−	0.984331i	$-0.556423\pi$
$557$	−8.32316	−0.352664	−0.176332	+	0.984331i	$0.556423\pi$
$558$	18.9696	0.803046
$559$	2.85565	0.120781
$560$	−14.7354	−0.622686
$561$	4.10868	0.173469
$562$	15.7302	0.663539
$563$	20.3214	0.856444	0.428222	−	0.903673i	$-0.359140\pi$
$563$	20.3214	0.856444	0.428222	+	0.903673i	$0.359140\pi$
$564$	−4.02301	−0.169399
$565$	36.3048	1.52735
$566$	5.97329	0.251076
$567$	22.2860	0.935925
$568$	−4.87190	−0.204421
$569$	−11.5759	−0.485285	−0.242642	−	0.970116i	$-0.578014\pi$
$569$	−11.5759	−0.485285	−0.242642	+	0.970116i	$0.578014\pi$
$570$	45.6846	1.91352
$571$	−33.6932	−1.41002	−0.705008	−	0.709199i	$-0.749057\pi$
$571$	−33.6932	−1.41002	−0.705008	+	0.709199i	$0.749057\pi$
$572$	0.388228	0.0162326
$573$	41.4606	1.73204
$574$	−9.67180	−0.403693
$575$	8.18526	0.341349
$576$	30.9500	1.28958
$577$	32.4730	1.35187	0.675934	−	0.736962i	$-0.263740\pi$
$577$	32.4730	1.35187	0.675934	+	0.736962i	$0.263740\pi$
$578$	1.19164	0.0495659
$579$	−46.2382	−1.92160
$580$	6.61892	0.274836
$581$	6.21800	0.257966
$582$	−37.5181	−1.55518
$583$	21.0831	0.873172
$584$	−18.1701	−0.751883
$585$	−2.76958	−0.114508
$586$	12.8337	0.530156
$587$	−37.7372	−1.55758	−0.778790	−	0.627285i	$-0.784166\pi$
$587$	−37.7372	−1.55758	−0.778790	+	0.627285i	$0.784166\pi$
$588$	−4.03067	−0.166222
$589$	−35.8996	−1.47922
$590$	−12.6936	−0.522589
$591$	−35.9070	−1.47702
$592$	−17.5978	−0.723265
$593$	−0.138913	−0.00570448	−0.00285224	−	0.999996i	$-0.500908\pi$
$593$	−0.138913	−0.00570448	−0.00285224	+	0.999996i	$0.500908\pi$
$594$	−2.57206	−0.105533
$595$	−5.88559	−0.241286
$596$	−4.04484	−0.165683
$597$	31.3118	1.28151
$598$	−2.82599	−0.115563
$599$	7.00726	0.286309	0.143154	−	0.989700i	$-0.454275\pi$
$599$	7.00726	0.286309	0.143154	+	0.989700i	$0.454275\pi$
$600$	11.2809	0.460540
$601$	−46.4802	−1.89597	−0.947984	−	0.318317i	$-0.896882\pi$
$601$	−46.4802	−1.89597	−0.947984	+	0.318317i	$0.896882\pi$
$602$	−25.4934	−1.03903
$603$	−16.2178	−0.660441
$604$	−13.1587	−0.535421
$605$	15.8816	0.645677
$606$	21.0735	0.856053
$607$	12.5480	0.509308	0.254654	−	0.967032i	$-0.418038\pi$
$607$	12.5480	0.509308	0.254654	+	0.967032i	$0.418038\pi$
$608$	−25.1655	−1.02060
$609$	−48.1475	−1.95104
$610$	22.4449	0.908769
$611$	1.13006	0.0457175
$612$	2.04464	0.0826495
$613$	2.52411	0.101948	0.0509739	−	0.998700i	$-0.483767\pi$
$613$	2.52411	0.101948	0.0509739	+	0.998700i	$0.483767\pi$
$614$	22.3622	0.902464
$615$	−12.5534	−0.506201
$616$	−15.4174	−0.621184
$617$	−29.0217	−1.16837	−0.584185	−	0.811620i	$-0.698586\pi$
$617$	−29.0217	−1.16837	−0.584185	+	0.811620i	$0.698586\pi$
$618$	36.9887	1.48791
$619$	−24.6709	−0.991606	−0.495803	−	0.868435i	$-0.665126\pi$
$619$	−24.6709	−0.991606	−0.495803	+	0.868435i	$0.665126\pi$
$620$	4.94392	0.198553
$621$	−7.64694	−0.306861
$622$	−13.9145	−0.557920
$623$	47.4205	1.89986
$624$	−2.66161	−0.106550
$625$	−15.7547	−0.630187
$626$	−33.6706	−1.34575
$627$	32.6648	1.30451
$628$	−6.39508	−0.255192
$629$	−7.02886	−0.280259
$630$	24.7250	0.985067
$631$	−10.1525	−0.404165	−0.202082	−	0.979369i	$-0.564771\pi$
$631$	−10.1525	−0.404165	−0.202082	+	0.979369i	$0.564771\pi$
$632$	3.07442	0.122294
$633$	52.4361	2.08415
$634$	−8.68531	−0.344938
$635$	23.2060	0.920902
$636$	19.4201	0.770056
$637$	1.13222	0.0448600
$638$	−11.5871	−0.458737
$639$	5.58644	0.220996
$640$	−7.79836	−0.308257
$641$	12.8929	0.509237	0.254619	−	0.967042i	$-0.418050\pi$
$641$	12.8929	0.509237	0.254619	+	0.967042i	$0.418050\pi$
$642$	−11.5232	−0.454783
$643$	15.1617	0.597917	0.298959	−	0.954266i	$-0.403361\pi$
$643$	15.1617	0.597917	0.298959	+	0.954266i	$0.403361\pi$
$644$	−10.3043	−0.406044
$645$	−33.0887	−1.30287
$646$	9.47382	0.372742
$647$	15.5883	0.612841	0.306421	−	0.951896i	$-0.400869\pi$
$647$	15.5883	0.612841	0.306421	+	0.951896i	$0.400869\pi$
$648$	21.9761	0.863302
$649$	−9.07605	−0.356266
$650$	−0.712352	−0.0279407
$651$	−35.9632	−1.40951
$652$	−9.16953	−0.359106
$653$	−13.3218	−0.521322	−0.260661	−	0.965430i	$-0.583941\pi$
$653$	−13.3218	−0.521322	−0.260661	+	0.965430i	$0.583941\pi$
$654$	−37.4214	−1.46329
$655$	1.75932	0.0687424
$656$	−6.51761	−0.254470
$657$	20.8350	0.812850
$658$	−10.0885	−0.393290
$659$	−23.6521	−0.921356	−0.460678	−	0.887567i	$-0.652394\pi$
$659$	−23.6521	−0.921356	−0.460678	+	0.887567i	$0.652394\pi$
$660$	−4.49845	−0.175102
$661$	38.5131	1.49798	0.748992	−	0.662579i	$-0.230538\pi$
$661$	38.5131	1.49798	0.748992	+	0.662579i	$0.230538\pi$
$662$	−18.2396	−0.708901
$663$	−1.06309	−0.0412871
$664$	6.13152	0.237949
$665$	−46.7916	−1.81450
$666$	29.5278	1.14418
$667$	−34.4494	−1.33388
$668$	−6.15811	−0.238265
$669$	9.81835	0.379599
$670$	10.3486	0.399803
$671$	16.0483	0.619538
$672$	−25.2101	−0.972499
$673$	−37.8791	−1.46013	−0.730066	−	0.683377i	$-0.760511\pi$
$673$	−37.8791	−1.46013	−0.730066	+	0.683377i	$0.760511\pi$
$674$	3.53247	0.136066
$675$	−1.92758	−0.0741925
$676$	7.43935	0.286129
$677$	−7.30935	−0.280921	−0.140461	−	0.990086i	$-0.544858\pi$
$677$	−7.30935	−0.280921	−0.140461	+	0.990086i	$0.544858\pi$
$678$	−58.5420	−2.24829
$679$	38.4272	1.47470
$680$	−5.80373	−0.222563
$681$	−41.7078	−1.59825
$682$	−8.65483	−0.331411
$683$	37.9926	1.45375	0.726873	−	0.686772i	$-0.240973\pi$
$683$	37.9926	1.45375	0.726873	+	0.686772i	$0.240973\pi$
$684$	16.2553	0.621536
$685$	−39.3218	−1.50241
$686$	15.8993	0.607039
$687$	−71.4399	−2.72560
$688$	−17.1794	−0.654959
$689$	−5.45510	−0.207823
$690$	32.7451	1.24658
$691$	41.3456	1.57286	0.786429	−	0.617680i	$-0.211927\pi$
$691$	41.3456	1.57286	0.786429	+	0.617680i	$0.211927\pi$
$692$	−2.12265	−0.0806910
$693$	17.6785	0.671552
$694$	−5.12789	−0.194652
$695$	42.9140	1.62782
$696$	−47.4779	−1.79965
$697$	−2.60324	−0.0986049
$698$	−14.3563	−0.543396
$699$	−64.6914	−2.44685
$700$	−2.59741	−0.0981728
$701$	46.8345	1.76891	0.884457	−	0.466622i	$-0.154529\pi$
$701$	46.8345	1.76891	0.884457	+	0.466622i	$0.154529\pi$
$702$	0.665503	0.0251178
$703$	−55.8809	−2.10759
$704$	−14.1209	−0.532200
$705$	−13.0942	−0.493155
$706$	−9.55309	−0.359535
$707$	−21.5841	−0.811755
$708$	−8.36014	−0.314193
$709$	15.7667	0.592130	0.296065	−	0.955168i	$-0.404325\pi$
$709$	15.7667	0.592130	0.296065	+	0.955168i	$0.404325\pi$
$710$	−3.56472	−0.133782
$711$	−3.52533	−0.132210
$712$	46.7610	1.75244
$713$	−25.7315	−0.963653
$714$	9.49060	0.355177
$715$	1.26361	0.0472565
$716$	0.631576	0.0236031
$717$	5.79670	0.216482
$718$	−7.00452	−0.261406
$719$	−25.0276	−0.933374	−0.466687	−	0.884423i	$-0.654552\pi$
$719$	−25.0276	−0.933374	−0.466687	+	0.884423i	$0.654552\pi$
$720$	16.6616	0.620942
$721$	−37.8850	−1.41091
$722$	52.6776	1.96046
$723$	35.8101	1.33179
$724$	3.40241	0.126449
$725$	−8.68371	−0.322505
$726$	−25.6093	−0.950449
$727$	24.6621	0.914668	0.457334	−	0.889295i	$-0.348804\pi$
$727$	24.6621	0.914668	0.457334	+	0.889295i	$0.348804\pi$
$728$	3.98914	0.147847
$729$	−35.4831	−1.31419
$730$	−13.2949	−0.492065
$731$	−6.86175	−0.253791
$732$	14.7824	0.546374
$733$	28.5892	1.05597	0.527983	−	0.849255i	$-0.322949\pi$
$733$	28.5892	1.05597	0.527983	+	0.849255i	$0.322949\pi$
$734$	−35.3531	−1.30491
$735$	−13.1191	−0.483906
$736$	−18.0377	−0.664879
$737$	7.39936	0.272559
$738$	10.9361	0.402562
$739$	−51.3044	−1.88726	−0.943631	−	0.330998i	$-0.892615\pi$
$739$	−51.3044	−1.88726	−0.943631	+	0.330998i	$0.892615\pi$
$740$	7.69565	0.282898
$741$	−8.45180	−0.310485
$742$	48.6996	1.78782
$743$	19.7513	0.724604	0.362302	−	0.932061i	$-0.381991\pi$
$743$	19.7513	0.724604	0.362302	+	0.932061i	$0.381991\pi$
$744$	−35.4630	−1.30014
$745$	−13.1652	−0.482337
$746$	−28.0903	−1.02846
$747$	−7.03080	−0.257243
$748$	−0.932862	−0.0341088
$749$	11.8024	0.431250
$750$	36.9858	1.35053
$751$	12.4653	0.454865	0.227433	−	0.973794i	$-0.426967\pi$
$751$	12.4653	0.454865	0.227433	+	0.973794i	$0.426967\pi$
$752$	−6.79840	−0.247912
$753$	−27.8124	−1.01354
$754$	2.99808	0.109184
$755$	−42.8293	−1.55872
$756$	2.42659	0.0882541
$757$	5.24282	0.190554	0.0952768	−	0.995451i	$-0.469626\pi$
$757$	5.24282	0.190554	0.0952768	+	0.995451i	$0.469626\pi$
$758$	−9.71808	−0.352976
$759$	23.4130	0.849837
$760$	−46.1409	−1.67371
$761$	24.2050	0.877432	0.438716	−	0.898626i	$-0.355433\pi$
$761$	24.2050	0.877432	0.438716	+	0.898626i	$0.355433\pi$
$762$	−37.4200	−1.35558
$763$	38.3281	1.38757
$764$	−9.41349	−0.340568
$765$	6.65493	0.240610
$766$	−26.9799	−0.974824
$767$	2.34836	0.0847945
$768$	−32.2781	−1.16473
$769$	−5.88174	−0.212101	−0.106050	−	0.994361i	$-0.533820\pi$
$769$	−5.88174	−0.212101	−0.106050	+	0.994361i	$0.533820\pi$
$770$	−11.2807	−0.406529
$771$	−11.4830	−0.413551
$772$	10.4982	0.377840
$773$	5.69591	0.204868	0.102434	−	0.994740i	$-0.467337\pi$
$773$	5.69591	0.204868	0.102434	+	0.994740i	$0.467337\pi$
$774$	28.8258	1.03612
$775$	−6.48618	−0.232991
$776$	37.8928	1.36027
$777$	−55.9799	−2.00827
$778$	1.74275	0.0624807
$779$	−20.6963	−0.741523
$780$	1.16394	0.0416758
$781$	−2.54880	−0.0912033
$782$	6.79049	0.242827
$783$	8.11261	0.289921
$784$	−6.81135	−0.243262
$785$	−20.8149	−0.742915
$786$	−2.83693	−0.101190
$787$	−26.5180	−0.945265	−0.472633	−	0.881260i	$-0.656696\pi$
$787$	−26.5180	−0.945265	−0.472633	+	0.881260i	$0.656696\pi$
$788$	8.15257	0.290423
$789$	−9.66414	−0.344053
$790$	2.24952	0.0800344
$791$	59.9605	2.13195
$792$	17.4327	0.619444
$793$	−4.15239	−0.147456
$794$	6.27388	0.222652
$795$	63.2089	2.24179
$796$	−7.10923	−0.251980
$797$	6.45423	0.228620	0.114310	−	0.993445i	$-0.463534\pi$
$797$	6.45423	0.228620	0.114310	+	0.993445i	$0.463534\pi$
$798$	75.4522	2.67098
$799$	−2.71540	−0.0960638
$800$	−4.54679	−0.160753
$801$	−53.6191	−1.89454
$802$	22.0233	0.777671
$803$	−9.50592	−0.335457
$804$	6.81571	0.240371
$805$	−33.5385	−1.18208
$806$	2.23938	0.0788787
$807$	49.3585	1.73750
$808$	−21.2840	−0.748767
$809$	50.2516	1.76675	0.883376	−	0.468665i	$-0.155265\pi$
$809$	50.2516	1.76675	0.883376	+	0.468665i	$0.155265\pi$
$810$	16.0797	0.564982
$811$	22.5687	0.792494	0.396247	−	0.918144i	$-0.370312\pi$
$811$	22.5687	0.792494	0.396247	+	0.918144i	$0.370312\pi$
$812$	10.9317	0.383629
$813$	23.3399	0.818568
$814$	−13.4720	−0.472194
$815$	−29.8452	−1.04543
$816$	6.39550	0.223887
$817$	−54.5523	−1.90855
$818$	−20.8272	−0.728205
$819$	−4.57420	−0.159836
$820$	2.85020	0.0995333
$821$	−41.1965	−1.43777	−0.718884	−	0.695130i	$-0.755347\pi$
$821$	−41.1965	−1.43777	−0.718884	+	0.695130i	$0.755347\pi$
$822$	63.4070	2.21157
$823$	24.2232	0.844367	0.422184	−	0.906510i	$-0.361264\pi$
$823$	24.2232	0.844367	0.422184	+	0.906510i	$0.361264\pi$
$824$	−37.3581	−1.30143
$825$	5.90174	0.205472
$826$	−20.9647	−0.729454
$827$	−24.6004	−0.855438	−0.427719	−	0.903912i	$-0.640683\pi$
$827$	−24.6004	−0.855438	−0.427719	+	0.903912i	$0.640683\pi$
$828$	11.6512	0.404907
$829$	−30.4388	−1.05718	−0.528592	−	0.848876i	$-0.677280\pi$
$829$	−30.4388	−1.05718	−0.528592	+	0.848876i	$0.677280\pi$
$830$	4.48637	0.155724
$831$	−11.5876	−0.401970
$832$	3.65368	0.126668
$833$	−2.72057	−0.0942621
$834$	−69.1995	−2.39618
$835$	−20.0436	−0.693637
$836$	−7.41644	−0.256503
$837$	6.05961	0.209451
$838$	−1.27100	−0.0439060
$839$	37.5970	1.29799	0.648997	−	0.760791i	$-0.275189\pi$
$839$	37.5970	1.29799	0.648997	+	0.760791i	$0.275189\pi$
$840$	−46.2226	−1.59483
$841$	7.54719	0.260248
$842$	22.1268	0.762540
$843$	33.7201	1.16138
$844$	−11.9054	−0.409802
$845$	24.2138	0.832979
$846$	11.4072	0.392188
$847$	26.2298	0.901267
$848$	32.8176	1.12696
$849$	12.8047	0.439455
$850$	1.71169	0.0587104
$851$	−40.0534	−1.37301
$852$	−2.34775	−0.0804328
$853$	−45.0202	−1.54146	−0.770730	−	0.637161i	$-0.780108\pi$
$853$	−45.0202	−1.54146	−0.770730	+	0.637161i	$0.780108\pi$
$854$	37.0698	1.26850
$855$	52.9081	1.80942
$856$	11.6382	0.397787
$857$	3.05242	0.104269	0.0521344	−	0.998640i	$-0.483398\pi$
$857$	3.05242	0.104269	0.0521344	+	0.998640i	$0.483398\pi$
$858$	−2.03760	−0.0695624
$859$	52.2573	1.78300	0.891498	−	0.453024i	$-0.149655\pi$
$859$	52.2573	1.78300	0.891498	+	0.453024i	$0.149655\pi$
$860$	7.51269	0.256181
$861$	−20.7330	−0.706579
$862$	18.7311	0.637984
$863$	44.3268	1.50890	0.754451	−	0.656356i	$-0.227903\pi$
$863$	44.3268	1.50890	0.754451	+	0.656356i	$0.227903\pi$
$864$	4.24777	0.144512
$865$	−6.90885	−0.234908
$866$	18.2933	0.621633
$867$	2.55447	0.0867544
$868$	8.16532	0.277149
$869$	1.60843	0.0545621
$870$	−34.7391	−1.17777
$871$	−1.91453	−0.0648715
$872$	37.7951	1.27990
$873$	−43.4503	−1.47057
$874$	53.9858	1.82610
$875$	−37.8820	−1.28065
$876$	−8.75610	−0.295841
$877$	−37.9347	−1.28096	−0.640482	−	0.767973i	$-0.721265\pi$
$877$	−37.9347	−1.28096	−0.640482	+	0.767973i	$0.721265\pi$
$878$	−42.9808	−1.45053
$879$	27.5110	0.927925
$880$	−7.60183	−0.256258
$881$	−48.7823	−1.64352	−0.821758	−	0.569836i	$-0.807007\pi$
$881$	−48.7823	−1.64352	−0.821758	+	0.569836i	$0.807007\pi$
$882$	11.4289	0.384832
$883$	42.4893	1.42988	0.714939	−	0.699186i	$-0.246454\pi$
$883$	42.4893	1.42988	0.714939	+	0.699186i	$0.246454\pi$
$884$	0.241372	0.00811820
$885$	−27.2108	−0.914680
$886$	34.4369	1.15693
$887$	13.1651	0.442041	0.221021	−	0.975269i	$-0.429061\pi$
$887$	13.1651	0.442041	0.221021	+	0.975269i	$0.429061\pi$
$888$	−55.2014	−1.85244
$889$	38.3268	1.28544
$890$	34.2145	1.14687
$891$	11.4971	0.385167
$892$	−2.22922	−0.0746399
$893$	−21.5880	−0.722414
$894$	21.2291	0.710008
$895$	2.05567	0.0687135
$896$	−12.8797	−0.430280
$897$	−6.05794	−0.202269
$898$	34.7200	1.15862
$899$	27.2985	0.910454
$900$	2.93694	0.0978978
$901$	13.1079	0.436687
$902$	−4.98956	−0.166134
$903$	−54.6490	−1.81860
$904$	59.1267	1.96652
$905$	11.0742	0.368120
$906$	69.0630	2.29446
$907$	−19.6870	−0.653695	−0.326848	−	0.945077i	$-0.605986\pi$
$907$	−19.6870	−0.653695	−0.326848	+	0.945077i	$0.605986\pi$
$908$	9.46963	0.314261
$909$	24.4056	0.809481
$910$	2.91881	0.0967576
$911$	46.8071	1.55079	0.775395	−	0.631477i	$-0.217551\pi$
$911$	46.8071	1.55079	0.775395	+	0.631477i	$0.217551\pi$
$912$	50.8456	1.68367
$913$	3.20779	0.106162
$914$	−15.7030	−0.519408
$915$	48.1142	1.59061
$916$	16.2202	0.535930
$917$	2.90568	0.0959539
$918$	−1.59912	−0.0527787
$919$	−30.4286	−1.00375	−0.501874	−	0.864941i	$-0.667356\pi$
$919$	−30.4286	−1.00375	−0.501874	+	0.864941i	$0.667356\pi$
$920$	−33.0721	−1.09036
$921$	47.9368	1.57957
$922$	−22.4827	−0.740427
$923$	0.659485	0.0217072
$924$	−7.42958	−0.244415
$925$	−10.0963	−0.331965
$926$	−11.0419	−0.362861
$927$	42.8372	1.40696
$928$	19.1361	0.628174
$929$	4.91861	0.161374	0.0806872	−	0.996739i	$-0.474289\pi$
$929$	4.91861	0.161374	0.0806872	+	0.996739i	$0.474289\pi$
$930$	−25.9479	−0.850866
$931$	−21.6291	−0.708864
$932$	14.6880	0.481120
$933$	−29.8279	−0.976520
$934$	27.7823	0.909066
$935$	−3.03630	−0.0992977
$936$	−4.51059	−0.147433
$937$	18.3635	0.599910	0.299955	−	0.953953i	$-0.403028\pi$
$937$	18.3635	0.599910	0.299955	+	0.953953i	$0.403028\pi$
$938$	17.0917	0.558064
$939$	−72.1781	−2.35544
$940$	2.97299	0.0969683
$941$	40.7059	1.32697	0.663487	−	0.748188i	$-0.269076\pi$
$941$	40.7059	1.32697	0.663487	+	0.748188i	$0.269076\pi$
$942$	33.5643	1.09358
$943$	−14.8344	−0.483074
$944$	−14.1276	−0.459815
$945$	7.89811	0.256926
$946$	−13.1517	−0.427599
$947$	3.31771	0.107811	0.0539055	−	0.998546i	$-0.482833\pi$
$947$	3.31771	0.107811	0.0539055	+	0.998546i	$0.482833\pi$
$948$	1.48155	0.0481187
$949$	2.45959	0.0798417
$950$	13.6083	0.441511
$951$	−18.6183	−0.603739
$952$	−9.58538	−0.310664
$953$	58.9454	1.90943	0.954714	−	0.297525i	$-0.0961610\pi$
$953$	58.9454	1.90943	0.954714	+	0.297525i	$0.0961610\pi$
$954$	−55.0655	−1.78281
$955$	−30.6393	−0.991463
$956$	−1.31612	−0.0425664
$957$	−24.8387	−0.802922
$958$	−13.0820	−0.422659
$959$	−64.9435	−2.09713
$960$	−42.3356	−1.36638
$961$	−10.6098	−0.342251
$962$	3.48579	0.112386
$963$	−13.3452	−0.430042
$964$	−8.13057	−0.261868
$965$	34.1699	1.09997
$966$	54.0814	1.74004
$967$	46.7344	1.50288	0.751438	−	0.659804i	$-0.229360\pi$
$967$	46.7344	1.50288	0.751438	+	0.659804i	$0.229360\pi$
$968$	25.8650	0.831333
$969$	20.3086	0.652406
$970$	27.7258	0.890221
$971$	32.9500	1.05742	0.528708	−	0.848804i	$-0.322677\pi$
$971$	32.9500	1.05742	0.528708	+	0.848804i	$0.322677\pi$
$972$	12.9251	0.414574
$973$	70.8763	2.27219
$974$	−37.8490	−1.21276
$975$	−1.52704	−0.0489043
$976$	24.9805	0.799607
$977$	22.1354	0.708173	0.354087	−	0.935213i	$-0.384792\pi$
$977$	22.1354	0.708173	0.354087	+	0.935213i	$0.384792\pi$
$978$	48.1259	1.53890
$979$	24.4636	0.781861
$980$	2.97865	0.0951496
$981$	−43.3383	−1.38368
$982$	3.15425	0.100656
$983$	−6.60585	−0.210694	−0.105347	−	0.994436i	$-0.533595\pi$
$983$	−6.60585	−0.210694	−0.105347	+	0.994436i	$0.533595\pi$
$984$	−20.4447	−0.651752
$985$	26.5352	0.845481
$986$	−7.20400	−0.229422
$987$	−21.6262	−0.688370
$988$	1.91895	0.0610500
$989$	−39.1011	−1.24334
$990$	12.7553	0.405391
$991$	−7.67612	−0.243840	−0.121920	−	0.992540i	$-0.538905\pi$
$991$	−7.67612	−0.243840	−0.121920	+	0.992540i	$0.538905\pi$
$992$	14.2935	0.453818
$993$	−39.0993	−1.24078
$994$	−5.88745	−0.186739
$995$	−23.1393	−0.733565
$996$	2.95476	0.0936252
$997$	15.5315	0.491887	0.245944	−	0.969284i	$-0.420902\pi$
$997$	15.5315	0.491887	0.245944	+	0.969284i	$0.420902\pi$
$998$	29.4233	0.931379
$999$	9.43232	0.298425

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1343.2.a.c.1.15	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1343.2.a.c.1.15	✓	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1343 = 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1343.a (trivial)

\(f(q)\)	\(=\)	\(q+1.19164 q^{2} +2.55447 q^{3} -0.579984 q^{4} -1.88775 q^{5} +3.04402 q^{6} -3.11778 q^{7} -3.07442 q^{8} +3.52533 q^{9} +O(q^{10})\)	\(q+1.19164 q^{2} +2.55447 q^{3} -0.579984 q^{4} -1.88775 q^{5} +3.04402 q^{6} -3.11778 q^{7} -3.07442 q^{8} +3.52533 q^{9} -2.24952 q^{10} -1.60843 q^{11} -1.48155 q^{12} +0.416169 q^{13} -3.71529 q^{14} -4.82220 q^{15} -2.50365 q^{16} -1.00000 q^{17} +4.20094 q^{18} -7.95021 q^{19} +1.09486 q^{20} -7.96429 q^{21} -1.91667 q^{22} -5.69842 q^{23} -7.85353 q^{24} -1.43641 q^{25} +0.495925 q^{26} +1.34194 q^{27} +1.80827 q^{28} +6.04543 q^{29} -5.74635 q^{30} +4.51555 q^{31} +3.16539 q^{32} -4.10868 q^{33} -1.19164 q^{34} +5.88559 q^{35} -2.04464 q^{36} +7.02886 q^{37} -9.47382 q^{38} +1.06309 q^{39} +5.80373 q^{40} +2.60324 q^{41} -9.49060 q^{42} +6.86175 q^{43} +0.932862 q^{44} -6.65493 q^{45} -6.79049 q^{46} +2.71540 q^{47} -6.39550 q^{48} +2.72057 q^{49} -1.71169 q^{50} -2.55447 q^{51} -0.241372 q^{52} -13.1079 q^{53} +1.59912 q^{54} +3.03630 q^{55} +9.58538 q^{56} -20.3086 q^{57} +7.20400 q^{58} +5.64281 q^{59} +2.79680 q^{60} -9.97764 q^{61} +5.38093 q^{62} -10.9912 q^{63} +8.77931 q^{64} -0.785622 q^{65} -4.89608 q^{66} -4.60037 q^{67} +0.579984 q^{68} -14.5565 q^{69} +7.01352 q^{70} +1.58466 q^{71} -10.8384 q^{72} +5.91008 q^{73} +8.37590 q^{74} -3.66927 q^{75} +4.61100 q^{76} +5.01472 q^{77} +1.26683 q^{78} -1.00000 q^{79} +4.72626 q^{80} -7.14804 q^{81} +3.10214 q^{82} -1.99437 q^{83} +4.61916 q^{84} +1.88775 q^{85} +8.17677 q^{86} +15.4429 q^{87} +4.94498 q^{88} -15.2097 q^{89} -7.93031 q^{90} -1.29752 q^{91} +3.30499 q^{92} +11.5349 q^{93} +3.23579 q^{94} +15.0080 q^{95} +8.08590 q^{96} -12.3252 q^{97} +3.24195 q^{98} -5.67023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 4 q^{3} + 14 q^{4} - 7 q^{5} - 4 q^{6} - 11 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 4 * q^3 + 14 * q^4 - 7 * q^5 - 4 * q^6 - 11 * q^7 - 6 * q^8 + 10 * q^9	\( 20 q - 2 q^{2} - 4 q^{3} + 14 q^{4} - 7 q^{5} - 4 q^{6} - 11 q^{7} - 6 q^{8} + 10 q^{9} - 19 q^{10} - 7 q^{11} - 17 q^{12} - 19 q^{13} - 3 q^{14} + 10 q^{16} - 20 q^{17} - 17 q^{18} - 9 q^{19} - 6 q^{20} - 16 q^{21} - 17 q^{22} - 15 q^{23} - 5 q^{24} - 21 q^{25} + 5 q^{26} - 19 q^{27} - 27 q^{28} - 11 q^{29} - 9 q^{30} - 13 q^{31} + q^{32} - 20 q^{33} + 2 q^{34} - 9 q^{35} - 6 q^{36} - 26 q^{37} + 9 q^{38} - 5 q^{39} - 19 q^{40} - 6 q^{41} + 4 q^{42} - 32 q^{43} - 35 q^{44} - 12 q^{45} - 42 q^{46} + 3 q^{47} - 31 q^{48} - 7 q^{49} + 23 q^{50} + 4 q^{51} - 49 q^{52} - 20 q^{53} + 41 q^{54} - 30 q^{55} + 5 q^{56} - 35 q^{57} - 9 q^{58} + 26 q^{59} + 33 q^{60} - 33 q^{61} - 18 q^{62} - 32 q^{63} - 12 q^{64} - 20 q^{65} + 38 q^{66} - 31 q^{67} - 14 q^{68} - 18 q^{69} - 13 q^{70} + 2 q^{71} - 44 q^{72} - 71 q^{73} + 4 q^{74} + 15 q^{75} + 13 q^{76} + 20 q^{77} - 3 q^{78} - 20 q^{79} + 7 q^{80} - 36 q^{81} - 26 q^{82} + 21 q^{83} + 37 q^{84} + 7 q^{85} + q^{86} - 3 q^{87} - 11 q^{88} - 15 q^{89} + 9 q^{90} - 4 q^{91} - 13 q^{92} - 21 q^{93} + 44 q^{94} + 7 q^{95} + q^{96} - 47 q^{97} + 7 q^{98} - 35 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 4 * q^3 + 14 * q^4 - 7 * q^5 - 4 * q^6 - 11 * q^7 - 6 * q^8 + 10 * q^9 - 19 * q^10 - 7 * q^11 - 17 * q^12 - 19 * q^13 - 3 * q^14 + 10 * q^16 - 20 * q^17 - 17 * q^18 - 9 * q^19 - 6 * q^20 - 16 * q^21 - 17 * q^22 - 15 * q^23 - 5 * q^24 - 21 * q^25 + 5 * q^26 - 19 * q^27 - 27 * q^28 - 11 * q^29 - 9 * q^30 - 13 * q^31 + q^32 - 20 * q^33 + 2 * q^34 - 9 * q^35 - 6 * q^36 - 26 * q^37 + 9 * q^38 - 5 * q^39 - 19 * q^40 - 6 * q^41 + 4 * q^42 - 32 * q^43 - 35 * q^44 - 12 * q^45 - 42 * q^46 + 3 * q^47 - 31 * q^48 - 7 * q^49 + 23 * q^50 + 4 * q^51 - 49 * q^52 - 20 * q^53 + 41 * q^54 - 30 * q^55 + 5 * q^56 - 35 * q^57 - 9 * q^58 + 26 * q^59 + 33 * q^60 - 33 * q^61 - 18 * q^62 - 32 * q^63 - 12 * q^64 - 20 * q^65 + 38 * q^66 - 31 * q^67 - 14 * q^68 - 18 * q^69 - 13 * q^70 + 2 * q^71 - 44 * q^72 - 71 * q^73 + 4 * q^74 + 15 * q^75 + 13 * q^76 + 20 * q^77 - 3 * q^78 - 20 * q^79 + 7 * q^80 - 36 * q^81 - 26 * q^82 + 21 * q^83 + 37 * q^84 + 7 * q^85 + q^86 - 3 * q^87 - 11 * q^88 - 15 * q^89 + 9 * q^90 - 4 * q^91 - 13 * q^92 - 21 * q^93 + 44 * q^94 + 7 * q^95 + q^96 - 47 * q^97 + 7 * q^98 - 35 * q^99

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