LMFDB - Embedded newform 143.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,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, 4, names="a")

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

chi := DirichletCharacter("143.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
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:	$8.43727313082$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 34x^{4} - 26x^{3} + 249x^{2} + 274x - 200 $ x^6 - 34x^4 - 26x^3 + 249x^2 + 274x - 200
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			1.1
Root			$-4.30719$ 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)

$f(q)$	$=$	$q-5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} -24.5072 q^{6} -25.3474 q^{7} -64.5685 q^{8} -5.67656 q^{9} +O(q^{10})$	\(q-5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} -24.5072 q^{6} -25.3474 q^{7} -64.5685 q^{8} -5.67656 q^{9} -27.2453 q^{10} +11.0000 q^{11} +93.1223 q^{12} -13.0000 q^{13} +134.523 q^{14} +23.7058 q^{15} +181.347 q^{16} -33.4620 q^{17} +30.1266 q^{18} -79.5721 q^{19} +103.527 q^{20} -117.047 q^{21} -58.3791 q^{22} +28.3682 q^{23} -298.160 q^{24} -98.6456 q^{25} +68.9934 q^{26} -150.892 q^{27} -511.161 q^{28} +248.189 q^{29} -125.811 q^{30} -104.834 q^{31} -445.897 q^{32} +50.7950 q^{33} +177.589 q^{34} -130.125 q^{35} -114.475 q^{36} -377.610 q^{37} +422.304 q^{38} -60.0305 q^{39} -331.473 q^{40} -263.301 q^{41} +621.192 q^{42} +320.858 q^{43} +221.829 q^{44} -29.1415 q^{45} -150.555 q^{46} -328.795 q^{47} +837.414 q^{48} +299.489 q^{49} +523.531 q^{50} -154.519 q^{51} -262.161 q^{52} -452.030 q^{53} +800.810 q^{54} +56.4702 q^{55} +1636.64 q^{56} -367.442 q^{57} -1317.18 q^{58} +504.608 q^{59} +478.058 q^{60} -61.1162 q^{61} +556.371 q^{62} +143.886 q^{63} +915.677 q^{64} -66.7375 q^{65} -269.579 q^{66} -72.0712 q^{67} -674.804 q^{68} +130.997 q^{69} +690.596 q^{70} +423.212 q^{71} +366.527 q^{72} -623.580 q^{73} +2004.05 q^{74} -455.519 q^{75} -1604.67 q^{76} -278.821 q^{77} +318.593 q^{78} -1325.65 q^{79} +930.975 q^{80} -543.509 q^{81} +1397.39 q^{82} +697.928 q^{83} -2360.41 q^{84} -171.783 q^{85} -1702.85 q^{86} +1146.07 q^{87} -710.254 q^{88} +994.203 q^{89} +154.659 q^{90} +329.516 q^{91} +572.080 q^{92} -484.093 q^{93} +1744.98 q^{94} -408.496 q^{95} -2059.03 q^{96} +1094.12 q^{97} -1589.45 q^{98} -62.4422 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} - 15 q^{6} - 53 q^{7} - 36 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 - 15 * q^6 - 53 * q^7 - 36 * q^8	\( 6 q - 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} - 15 q^{6} - 53 q^{7} - 36 q^{8} - 52 q^{10} + 66 q^{11} - 19 q^{12} - 78 q^{13} - 120 q^{14} - 23 q^{15} + 26 q^{16} - 117 q^{17} - 27 q^{18} - 67 q^{19} + 10 q^{20} + 19 q^{21} - 66 q^{22} - 158 q^{23} - 609 q^{24} - 234 q^{25} + 78 q^{26} - 531 q^{27} - 670 q^{28} - 145 q^{29} - 211 q^{30} - 58 q^{31} - 364 q^{32} - 66 q^{33} + 43 q^{34} - 210 q^{35} + 383 q^{36} - 753 q^{37} + 738 q^{38} + 78 q^{39} + 4 q^{40} - 232 q^{41} + 1593 q^{42} - 390 q^{43} + 286 q^{44} - 107 q^{45} + 5 q^{46} - 205 q^{47} + 1625 q^{48} + 491 q^{49} + 938 q^{50} + 363 q^{51} - 338 q^{52} - 65 q^{53} + 1917 q^{54} - 88 q^{55} + 1816 q^{56} - 1657 q^{57} - 1685 q^{58} + 1735 q^{59} + 871 q^{60} + 421 q^{61} + 3394 q^{62} - 125 q^{63} + 570 q^{64} + 104 q^{65} - 165 q^{66} - 703 q^{67} + 209 q^{68} - 272 q^{69} + 1968 q^{70} + 445 q^{71} + 1035 q^{72} - 2340 q^{73} + 1135 q^{74} + 1941 q^{75} - 1208 q^{76} - 583 q^{77} + 195 q^{78} - 1234 q^{79} + 2766 q^{80} + 606 q^{81} - 897 q^{82} - 1601 q^{83} - 7 q^{84} - 2245 q^{85} - 1146 q^{86} + 2462 q^{87} - 396 q^{88} - 442 q^{89} + 113 q^{90} + 689 q^{91} + 2737 q^{92} - 982 q^{93} + 2733 q^{94} - 504 q^{95} - 1153 q^{96} - 2682 q^{97} + 2036 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 - 15 * q^6 - 53 * q^7 - 36 * q^8 - 52 * q^10 + 66 * q^11 - 19 * q^12 - 78 * q^13 - 120 * q^14 - 23 * q^15 + 26 * q^16 - 117 * q^17 - 27 * q^18 - 67 * q^19 + 10 * q^20 + 19 * q^21 - 66 * q^22 - 158 * q^23 - 609 * q^24 - 234 * q^25 + 78 * q^26 - 531 * q^27 - 670 * q^28 - 145 * q^29 - 211 * q^30 - 58 * q^31 - 364 * q^32 - 66 * q^33 + 43 * q^34 - 210 * q^35 + 383 * q^36 - 753 * q^37 + 738 * q^38 + 78 * q^39 + 4 * q^40 - 232 * q^41 + 1593 * q^42 - 390 * q^43 + 286 * q^44 - 107 * q^45 + 5 * q^46 - 205 * q^47 + 1625 * q^48 + 491 * q^49 + 938 * q^50 + 363 * q^51 - 338 * q^52 - 65 * q^53 + 1917 * q^54 - 88 * q^55 + 1816 * q^56 - 1657 * q^57 - 1685 * q^58 + 1735 * q^59 + 871 * q^60 + 421 * q^61 + 3394 * q^62 - 125 * q^63 + 570 * q^64 + 104 * q^65 - 165 * q^66 - 703 * q^67 + 209 * q^68 - 272 * q^69 + 1968 * q^70 + 445 * q^71 + 1035 * q^72 - 2340 * q^73 + 1135 * q^74 + 1941 * q^75 - 1208 * q^76 - 583 * q^77 + 195 * q^78 - 1234 * q^79 + 2766 * q^80 + 606 * q^81 - 897 * q^82 - 1601 * q^83 - 7 * q^84 - 2245 * q^85 - 1146 * q^86 + 2462 * q^87 - 396 * q^88 - 442 * q^89 + 113 * q^90 + 689 * q^91 + 2737 * q^92 - 982 * q^93 + 2733 * q^94 - 504 * q^95 - 1153 * q^96 - 2682 * q^97 + 2036 * q^98

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 $

$2$	−5.30719	−1.87637	−0.938187	−	0.346128i	$-0.887496\pi$
$2$	−5.30719	−1.87637	−0.938187	+	0.346128i	$0.887496\pi$
$3$	4.61773	0.888683	0.444341	−	0.895858i	$-0.353438\pi$
$3$	4.61773	0.888683	0.444341	+	0.895858i	$0.353438\pi$
$4$	20.1662	2.52078
$5$	5.13365	0.459168	0.229584	−	0.973289i	$-0.426263\pi$
$5$	5.13365	0.459168	0.229584	+	0.973289i	$0.426263\pi$
$6$	−24.5072	−1.66750
$7$	−25.3474	−1.36863	−0.684315	−	0.729187i	$-0.739899\pi$
$7$	−25.3474	−1.36863	−0.684315	+	0.729187i	$0.739899\pi$
$8$	−64.5685	−2.85355
$9$	−5.67656	−0.210243
$10$	−27.2453	−0.861571
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	93.1223	2.24017
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	134.523	2.56806
$15$	23.7058	0.408055
$16$	181.347	2.83355
$17$	−33.4620	−0.477396	−0.238698	−	0.971094i	$-0.576721\pi$
$17$	−33.4620	−0.477396	−0.238698	+	0.971094i	$0.576721\pi$
$18$	30.1266	0.394495
$19$	−79.5721	−0.960794	−0.480397	−	0.877051i	$-0.659507\pi$
$19$	−79.5721	−0.960794	−0.480397	+	0.877051i	$0.659507\pi$
$20$	103.527	1.15746
$21$	−117.047	−1.21628
$22$	−58.3791	−0.565748
$23$	28.3682	0.257182	0.128591	−	0.991698i	$-0.458955\pi$
$23$	28.3682	0.257182	0.128591	+	0.991698i	$0.458955\pi$
$24$	−298.160	−2.53590
$25$	−98.6456	−0.789165
$26$	68.9934	0.520413
$27$	−150.892	−1.07552
$28$	−511.161	−3.45001
$29$	248.189	1.58922	0.794612	−	0.607117i	$-0.207674\pi$
$29$	248.189	1.58922	0.794612	+	0.607117i	$0.207674\pi$
$30$	−125.811	−0.765663
$31$	−104.834	−0.607376	−0.303688	−	0.952771i	$-0.598218\pi$
$31$	−104.834	−0.607376	−0.303688	+	0.952771i	$0.598218\pi$
$32$	−445.897	−2.46325
$33$	50.7950	0.267948
$34$	177.589	0.895774
$35$	−130.125	−0.628431
$36$	−114.475	−0.529976
$37$	−377.610	−1.67780	−0.838901	−	0.544284i	$-0.816802\pi$
$37$	−377.610	−1.67780	−0.838901	+	0.544284i	$0.816802\pi$
$38$	422.304	1.80281
$39$	−60.0305	−0.246476
$40$	−331.473	−1.31026
$41$	−263.301	−1.00294	−0.501472	−	0.865174i	$-0.667208\pi$
$41$	−263.301	−1.00294	−0.501472	+	0.865174i	$0.667208\pi$
$42$	621.192	2.28219
$43$	320.858	1.13791	0.568957	−	0.822367i	$-0.307347\pi$
$43$	320.858	1.13791	0.568957	+	0.822367i	$0.307347\pi$
$44$	221.829	0.760044
$45$	−29.1415	−0.0965369
$46$	−150.555	−0.482569
$47$	−328.795	−1.02042	−0.510210	−	0.860050i	$-0.670432\pi$
$47$	−328.795	−1.02042	−0.510210	+	0.860050i	$0.670432\pi$
$48$	837.414	2.51813
$49$	299.489	0.873147
$50$	523.531	1.48077
$51$	−154.519	−0.424254
$52$	−262.161	−0.699139
$53$	−452.030	−1.17153	−0.585765	−	0.810481i	$-0.699206\pi$
$53$	−452.030	−1.17153	−0.585765	+	0.810481i	$0.699206\pi$
$54$	800.810	2.01808
$55$	56.4702	0.138444
$56$	1636.64	3.90546
$57$	−367.442	−0.853841
$58$	−1317.18	−2.98198
$59$	504.608	1.11346	0.556732	−	0.830692i	$-0.312055\pi$
$59$	504.608	1.11346	0.556732	+	0.830692i	$0.312055\pi$
$60$	478.058	1.02862
$61$	−61.1162	−0.128281	−0.0641404	−	0.997941i	$-0.520431\pi$
$61$	−61.1162	−0.128281	−0.0641404	+	0.997941i	$0.520431\pi$
$62$	556.371	1.13967
$63$	143.886	0.287745
$64$	915.677	1.78843
$65$	−66.7375	−0.127350
$66$	−269.579	−0.502771
$67$	−72.0712	−0.131416	−0.0657082	−	0.997839i	$-0.520931\pi$
$67$	−72.0712	−0.131416	−0.0657082	+	0.997839i	$0.520931\pi$
$68$	−674.804	−1.20341
$69$	130.997	0.228553
$70$	690.596	1.17917
$71$	423.212	0.707410	0.353705	−	0.935357i	$-0.384922\pi$
$71$	423.212	0.707410	0.353705	+	0.935357i	$0.384922\pi$
$72$	366.527	0.599940
$73$	−623.580	−0.999789	−0.499894	−	0.866086i	$-0.666628\pi$
$73$	−623.580	−0.999789	−0.499894	+	0.866086i	$0.666628\pi$
$74$	2004.05	3.14819
$75$	−455.519	−0.701317
$76$	−1604.67	−2.42195
$77$	−278.821	−0.412657
$78$	318.593	0.462482
$79$	−1325.65	−1.88794	−0.943972	−	0.330026i	$-0.892942\pi$
$79$	−1325.65	−1.88794	−0.943972	+	0.330026i	$0.892942\pi$
$80$	930.975	1.30108
$81$	−543.509	−0.745555
$82$	1397.39	1.88190
$83$	697.928	0.922983	0.461491	−	0.887145i	$-0.347314\pi$
$83$	697.928	0.922983	0.461491	+	0.887145i	$0.347314\pi$
$84$	−2360.41	−3.06597
$85$	−171.783	−0.219205
$86$	−1702.85	−2.13515
$87$	1146.07	1.41232
$88$	−710.254	−0.860379
$89$	994.203	1.18410	0.592052	−	0.805900i	$-0.298318\pi$
$89$	994.203	1.18410	0.592052	+	0.805900i	$0.298318\pi$
$90$	154.659	0.181139
$91$	329.516	0.379590
$92$	572.080	0.648299
$93$	−484.093	−0.539765
$94$	1744.98	1.91469
$95$	−408.496	−0.441166
$96$	−2059.03	−2.18905
$97$	1094.12	1.14526	0.572632	−	0.819812i	$-0.305922\pi$
$97$	1094.12	1.14526	0.572632	+	0.819812i	$0.305922\pi$
$98$	−1589.45	−1.63835
$99$	−62.4422	−0.0633907
$100$	−1989.31	−1.98931
$101$	182.929	0.180219	0.0901093	−	0.995932i	$-0.471278\pi$
$101$	182.929	0.180219	0.0901093	+	0.995932i	$0.471278\pi$
$102$	820.060	0.796059
$103$	229.184	0.219244	0.109622	−	0.993973i	$-0.465036\pi$
$103$	229.184	0.219244	0.109622	+	0.993973i	$0.465036\pi$
$104$	839.391	0.791433
$105$	−600.881	−0.558476
$106$	2399.01	2.19823
$107$	−1673.53	−1.51202	−0.756010	−	0.654560i	$-0.772854\pi$
$107$	−1673.53	−1.51202	−0.756010	+	0.654560i	$0.772854\pi$
$108$	−3042.92	−2.71115
$109$	1049.20	0.921973	0.460986	−	0.887407i	$-0.347496\pi$
$109$	1049.20	0.921973	0.460986	+	0.887407i	$0.347496\pi$
$110$	−299.698	−0.259773
$111$	−1743.70	−1.49103
$112$	−4596.68	−3.87809
$113$	335.067	0.278942	0.139471	−	0.990226i	$-0.455460\pi$
$113$	335.067	0.278942	0.139471	+	0.990226i	$0.455460\pi$
$114$	1950.09	1.60213
$115$	145.633	0.118090
$116$	5005.04	4.00609
$117$	73.7953	0.0583109
$118$	−2678.05	−2.08928
$119$	848.175	0.653379
$120$	−1530.65	−1.16441
$121$	121.000	0.0909091
$122$	324.355	0.240703
$123$	−1215.85	−0.891299
$124$	−2114.10	−1.53106
$125$	−1148.12	−0.821527
$126$	−763.630	−0.539917
$127$	2542.22	1.77627	0.888133	−	0.459586i	$-0.152002\pi$
$127$	2542.22	1.77627	0.888133	+	0.459586i	$0.152002\pi$
$128$	−1292.50	−0.892515
$129$	1481.63	1.01124
$130$	354.189	0.238957
$131$	−512.054	−0.341514	−0.170757	−	0.985313i	$-0.554621\pi$
$131$	−512.054	−0.341514	−0.170757	+	0.985313i	$0.554621\pi$
$132$	1024.35	0.675438
$133$	2016.94	1.31497
$134$	382.495	0.246586
$135$	−774.625	−0.493845
$136$	2160.59	1.36228
$137$	−1139.91	−0.710869	−0.355435	−	0.934701i	$-0.615667\pi$
$137$	−1139.91	−0.710869	−0.355435	+	0.934701i	$0.615667\pi$
$138$	−695.225	−0.428851
$139$	−1154.97	−0.704770	−0.352385	−	0.935855i	$-0.614629\pi$
$139$	−1154.97	−0.704770	−0.352385	+	0.935855i	$0.614629\pi$
$140$	−2624.13	−1.58414
$141$	−1518.29	−0.906829
$142$	−2246.07	−1.32737
$143$	−143.000	−0.0836242
$144$	−1029.43	−0.595735
$145$	1274.12	0.729721
$146$	3309.46	1.87598
$147$	1382.96	0.775951
$148$	−7614.97	−4.22937
$149$	2691.89	1.48006	0.740028	−	0.672576i	$-0.234812\pi$
$149$	2691.89	1.48006	0.740028	+	0.672576i	$0.234812\pi$
$150$	2417.52	1.31593
$151$	3221.34	1.73608	0.868042	−	0.496492i	$-0.165379\pi$
$151$	3221.34	1.73608	0.868042	+	0.496492i	$0.165379\pi$
$152$	5137.85	2.74168
$153$	189.949	0.100369
$154$	1479.76	0.774300
$155$	−538.179	−0.278888
$156$	−1210.59	−0.621312
$157$	1475.65	0.750126	0.375063	−	0.926999i	$-0.377621\pi$
$157$	1475.65	0.750126	0.375063	+	0.926999i	$0.377621\pi$
$158$	7035.49	3.54249
$159$	−2087.35	−1.04112
$160$	−2289.08	−1.13105
$161$	−719.060	−0.351987
$162$	2884.51	1.39894
$163$	−1080.37	−0.519146	−0.259573	−	0.965723i	$-0.583582\pi$
$163$	−1080.37	−0.519146	−0.259573	+	0.965723i	$0.583582\pi$
$164$	−5309.79	−2.52820
$165$	260.764	0.123033
$166$	−3704.04	−1.73186
$167$	4082.38	1.89164	0.945820	−	0.324691i	$-0.105260\pi$
$167$	4082.38	1.89164	0.945820	+	0.324691i	$0.105260\pi$
$168$	7557.58	3.47071
$169$	169.000	0.0769231
$170$	911.682	0.411311
$171$	451.696	0.202000
$172$	6470.49	2.86843
$173$	−2979.93	−1.30959	−0.654797	−	0.755805i	$-0.727246\pi$
$173$	−2979.93	−1.30959	−0.654797	+	0.755805i	$0.727246\pi$
$174$	−6082.40	−2.65003
$175$	2500.41	1.08007
$176$	1994.82	0.854349
$177$	2330.15	0.989517
$178$	−5276.42	−2.22182
$179$	469.115	0.195884	0.0979422	−	0.995192i	$-0.468774\pi$
$179$	469.115	0.195884	0.0979422	+	0.995192i	$0.468774\pi$
$180$	−587.675	−0.243348
$181$	−1155.75	−0.474620	−0.237310	−	0.971434i	$-0.576266\pi$
$181$	−1155.75	−0.474620	−0.237310	+	0.971434i	$0.576266\pi$
$182$	−1748.80	−0.712252
$183$	−282.218	−0.114001
$184$	−1831.69	−0.733882
$185$	−1938.52	−0.770393
$186$	2569.17	1.01280
$187$	−368.082	−0.143940
$188$	−6630.56	−2.57225
$189$	3824.71	1.47199
$190$	2167.96	0.827792
$191$	−2968.67	−1.12464	−0.562318	−	0.826921i	$-0.690090\pi$
$191$	−2968.67	−1.12464	−0.562318	+	0.826921i	$0.690090\pi$
$192$	4228.35	1.58935
$193$	−5282.89	−1.97031	−0.985157	−	0.171655i	$-0.945088\pi$
$193$	−5282.89	−1.97031	−0.985157	+	0.171655i	$0.945088\pi$
$194$	−5806.68	−2.14895
$195$	−308.176	−0.113174
$196$	6039.58	2.20101
$197$	−2152.73	−0.778558	−0.389279	−	0.921120i	$-0.627276\pi$
$197$	−2152.73	−0.778558	−0.389279	+	0.921120i	$0.627276\pi$
$198$	331.392	0.118945
$199$	4790.13	1.70635	0.853174	−	0.521626i	$-0.174674\pi$
$199$	4790.13	1.70635	0.853174	+	0.521626i	$0.174674\pi$
$200$	6369.40	2.25192
$201$	−332.805	−0.116787
$202$	−970.836	−0.338157
$203$	−6290.93	−2.17506
$204$	−3116.06	−1.06945
$205$	−1351.70	−0.460520
$206$	−1216.32	−0.411384
$207$	−161.034	−0.0540707
$208$	−2357.52	−0.785886
$209$	−875.293	−0.289690
$210$	3188.99	1.04791
$211$	−4741.30	−1.54694	−0.773471	−	0.633832i	$-0.781481\pi$
$211$	−4741.30	−1.54694	−0.773471	+	0.633832i	$0.781481\pi$
$212$	−9115.74	−2.95317
$213$	1954.28	0.628663
$214$	8881.73	2.83711
$215$	1647.17	0.522494
$216$	9742.85	3.06906
$217$	2657.26	0.831273
$218$	−5568.30	−1.72997
$219$	−2879.53	−0.888495
$220$	1138.79	0.348988
$221$	435.006	0.132406
$222$	9254.15	2.79774
$223$	2279.21	0.684426	0.342213	−	0.939622i	$-0.388824\pi$
$223$	2279.21	0.684426	0.342213	+	0.939622i	$0.388824\pi$
$224$	11302.3	3.37128
$225$	559.968	0.165916
$226$	−1778.26	−0.523399
$227$	−5286.81	−1.54581	−0.772903	−	0.634524i	$-0.781196\pi$
$227$	−5286.81	−1.54581	−0.772903	+	0.634524i	$0.781196\pi$
$228$	−7409.93	−2.15235
$229$	−906.243	−0.261512	−0.130756	−	0.991415i	$-0.541740\pi$
$229$	−906.243	−0.261512	−0.130756	+	0.991415i	$0.541740\pi$
$230$	−772.900	−0.221580
$231$	−1287.52	−0.366721
$232$	−16025.2	−4.53494
$233$	960.037	0.269932	0.134966	−	0.990850i	$-0.456908\pi$
$233$	960.037	0.269932	0.134966	+	0.990850i	$0.456908\pi$
$234$	−391.646	−0.109413
$235$	−1687.92	−0.468544
$236$	10176.1	2.80680
$237$	−6121.51	−1.67778
$238$	−4501.42	−1.22598
$239$	−1475.35	−0.399299	−0.199650	−	0.979867i	$-0.563980\pi$
$239$	−1475.35	−0.399299	−0.199650	+	0.979867i	$0.563980\pi$
$240$	4298.99	1.15624
$241$	−4054.32	−1.08366	−0.541829	−	0.840489i	$-0.682268\pi$
$241$	−4054.32	−1.08366	−0.541829	+	0.840489i	$0.682268\pi$
$242$	−642.170	−0.170579
$243$	1564.29	0.412960
$244$	−1232.48	−0.323368
$245$	1537.48	0.400921
$246$	6452.76	1.67241
$247$	1034.44	0.266476
$248$	6768.95	1.73318
$249$	3222.85	0.820239
$250$	6093.28	1.54149
$251$	5951.50	1.49663	0.748317	−	0.663341i	$-0.230862\pi$
$251$	5951.50	1.49663	0.748317	+	0.663341i	$0.230862\pi$
$252$	2901.64	0.725342
$253$	312.050	0.0775432
$254$	−13492.1	−3.33294
$255$	−793.246	−0.194804
$256$	−465.882	−0.113741
$257$	1199.56	0.291153	0.145577	−	0.989347i	$-0.453496\pi$
$257$	1199.56	0.291153	0.145577	+	0.989347i	$0.453496\pi$
$258$	−7863.31	−1.89747
$259$	9571.42	2.29629
$260$	−1345.84	−0.321022
$261$	−1408.86	−0.334123
$262$	2717.57	0.640809
$263$	4206.58	0.986270	0.493135	−	0.869953i	$-0.335851\pi$
$263$	4206.58	0.986270	0.493135	+	0.869953i	$0.335851\pi$
$264$	−3279.76	−0.764604
$265$	−2320.56	−0.537929
$266$	−10704.3	−2.46738
$267$	4590.96	1.05229
$268$	−1453.41	−0.331272
$269$	−2482.72	−0.562728	−0.281364	−	0.959601i	$-0.590787\pi$
$269$	−2482.72	−0.562728	−0.281364	+	0.959601i	$0.590787\pi$
$270$	4111.08	0.926639
$271$	8757.29	1.96298	0.981489	−	0.191516i	$-0.0613404\pi$
$271$	8757.29	1.96298	0.981489	+	0.191516i	$0.0613404\pi$
$272$	−6068.25	−1.35273
$273$	1521.62	0.337335
$274$	6049.72	1.33386
$275$	−1085.10	−0.237942
$276$	2641.71	0.576132
$277$	−3877.23	−0.841012	−0.420506	−	0.907290i	$-0.638147\pi$
$277$	−3877.23	−0.841012	−0.420506	+	0.907290i	$0.638147\pi$
$278$	6129.63	1.32241
$279$	595.094	0.127697
$280$	8401.96	1.79326
$281$	5016.86	1.06506	0.532528	−	0.846412i	$-0.321242\pi$
$281$	5016.86	1.06506	0.532528	+	0.846412i	$0.321242\pi$
$282$	8057.84	1.70155
$283$	5498.11	1.15487	0.577436	−	0.816436i	$-0.304053\pi$
$283$	5498.11	1.15487	0.577436	+	0.816436i	$0.304053\pi$
$284$	8534.60	1.78322
$285$	−1886.32	−0.392057
$286$	758.928	0.156910
$287$	6673.99	1.37266
$288$	2531.16	0.517882
$289$	−3793.29	−0.772093
$290$	−6761.97	−1.36923
$291$	5052.34	1.01778
$292$	−12575.3	−2.52025
$293$	−5050.99	−1.00711	−0.503553	−	0.863965i	$-0.667974\pi$
$293$	−5050.99	−1.00711	−0.503553	+	0.863965i	$0.667974\pi$
$294$	−7339.64	−1.45597
$295$	2590.49	0.511267
$296$	24381.7	4.78770
$297$	−1659.81	−0.324282
$298$	−14286.4	−2.77714
$299$	−368.787	−0.0713294
$300$	−9186.10	−1.76787
$301$	−8132.90	−1.55738
$302$	−17096.2	−3.25754
$303$	844.715	0.160157
$304$	−14430.2	−2.72246
$305$	−313.749	−0.0589024
$306$	−1008.10	−0.188330
$307$	−4499.69	−0.836518	−0.418259	−	0.908328i	$-0.637359\pi$
$307$	−4499.69	−0.836518	−0.418259	+	0.908328i	$0.637359\pi$
$308$	−5622.77	−1.04022
$309$	1058.31	0.194839
$310$	2856.22	0.523298
$311$	−3800.20	−0.692893	−0.346446	−	0.938070i	$-0.612612\pi$
$311$	−3800.20	−0.692893	−0.346446	+	0.938070i	$0.612612\pi$
$312$	3876.08	0.703333
$313$	−6595.05	−1.19097	−0.595486	−	0.803366i	$-0.703040\pi$
$313$	−6595.05	−1.19097	−0.595486	+	0.803366i	$0.703040\pi$
$314$	−7831.56	−1.40752
$315$	738.661	0.132123
$316$	−26733.4	−4.75909
$317$	−1941.46	−0.343984	−0.171992	−	0.985098i	$-0.555020\pi$
$317$	−1941.46	−0.343984	−0.171992	+	0.985098i	$0.555020\pi$
$318$	11078.0	1.95353
$319$	2730.08	0.479169
$320$	4700.77	0.821191
$321$	−7727.90	−1.34371
$322$	3816.19	0.660459
$323$	2662.64	0.458679
$324$	−10960.5	−1.87938
$325$	1282.39	0.218875
$326$	5733.71	0.974112
$327$	4844.92	0.819341
$328$	17001.0	2.86195
$329$	8334.09	1.39658
$330$	−1383.92	−0.230856
$331$	1.93737	0.000321715 0	0.000160857	−	1.00000i	$-0.499949\pi$
$331$	1.93737	0.000321715 0	0.000160857		1.00000i	$0.499949\pi$
$332$	14074.6	2.32664
$333$	2143.53	0.352746
$334$	−21665.9	−3.54943
$335$	−369.989	−0.0603422
$336$	−21226.2	−3.44639
$337$	−1488.93	−0.240674	−0.120337	−	0.992733i	$-0.538398\pi$
$337$	−1488.93	−0.240674	−0.120337	+	0.992733i	$0.538398\pi$
$338$	−896.915	−0.144336
$339$	1547.25	0.247891
$340$	−3464.21	−0.552568
$341$	−1153.17	−0.183131
$342$	−2397.23	−0.379028
$343$	1102.88	0.173615
$344$	−20717.3	−3.24710
$345$	672.492	0.104944
$346$	15815.0	2.45729
$347$	−5329.54	−0.824509	−0.412254	−	0.911069i	$-0.635259\pi$
$347$	−5329.54	−0.824509	−0.412254	+	0.911069i	$0.635259\pi$
$348$	23111.9	3.56014
$349$	5077.47	0.778770	0.389385	−	0.921075i	$-0.372688\pi$
$349$	5077.47	0.778770	0.389385	+	0.921075i	$0.372688\pi$
$350$	−13270.1	−2.02662
$351$	1961.59	0.298296
$352$	−4904.86	−0.742699
$353$	1385.36	0.208881	0.104441	−	0.994531i	$-0.466695\pi$
$353$	1385.36	0.208881	0.104441	+	0.994531i	$0.466695\pi$
$354$	−12366.5	−1.85670
$355$	2172.63	0.324820
$356$	20049.3	2.98487
$357$	3916.64	0.580646
$358$	−2489.68	−0.367552
$359$	−672.605	−0.0988822	−0.0494411	−	0.998777i	$-0.515744\pi$
$359$	−672.605	−0.0988822	−0.0494411	+	0.998777i	$0.515744\pi$
$360$	1881.62	0.275473
$361$	−527.283	−0.0768746
$362$	6133.78	0.890564
$363$	558.745	0.0807893
$364$	6645.10	0.956862
$365$	−3201.25	−0.459071
$366$	1497.78	0.213908
$367$	−3226.94	−0.458978	−0.229489	−	0.973311i	$-0.573705\pi$
$367$	−3226.94	−0.458978	−0.229489	+	0.973311i	$0.573705\pi$
$368$	5144.50	0.728738
$369$	1494.64	0.210862
$370$	10288.1	1.44555
$371$	11457.8	1.60339
$372$	−9762.34	−1.36063
$373$	−7233.83	−1.00416	−0.502082	−	0.864820i	$-0.667432\pi$
$373$	−7233.83	−1.00416	−0.502082	+	0.864820i	$0.667432\pi$
$374$	1953.48	0.270086
$375$	−5301.71	−0.730077
$376$	21229.8	2.91182
$377$	−3226.45	−0.440771
$378$	−20298.4	−2.76201
$379$	−2271.87	−0.307911	−0.153956	−	0.988078i	$-0.549201\pi$
$379$	−2271.87	−0.307911	−0.153956	+	0.988078i	$0.549201\pi$
$380$	−8237.82	−1.11208
$381$	11739.3	1.57854
$382$	15755.3	2.11024
$383$	630.510	0.0841190	0.0420595	−	0.999115i	$-0.486608\pi$
$383$	630.510	0.0841190	0.0420595	+	0.999115i	$0.486608\pi$
$384$	−5968.41	−0.793162
$385$	−1431.37	−0.189479
$386$	28037.3	3.69705
$387$	−1821.37	−0.239239
$388$	22064.2	2.88696
$389$	−2027.27	−0.264233	−0.132117	−	0.991234i	$-0.542177\pi$
$389$	−2027.27	−0.264233	−0.132117	+	0.991234i	$0.542177\pi$
$390$	1635.55	0.212357
$391$	−949.258	−0.122778
$392$	−19337.6	−2.49157
$393$	−2364.53	−0.303498
$394$	11425.0	1.46087
$395$	−6805.44	−0.866883
$396$	−1259.22	−0.159794
$397$	12483.4	1.57814	0.789072	−	0.614301i	$-0.210562\pi$
$397$	12483.4	1.57814	0.789072	+	0.614301i	$0.210562\pi$
$398$	−25422.1	−3.20175
$399$	9313.70	1.16859
$400$	−17889.1	−2.23614
$401$	−8877.78	−1.10557	−0.552787	−	0.833323i	$-0.686436\pi$
$401$	−8877.78	−1.10557	−0.552787	+	0.833323i	$0.686436\pi$
$402$	1766.26	0.219137
$403$	1362.84	0.168456
$404$	3688.98	0.454291
$405$	−2790.19	−0.342335
$406$	33387.2	4.08123
$407$	−4153.71	−0.505876
$408$	9977.04	1.21063
$409$	−12566.8	−1.51928	−0.759642	−	0.650342i	$-0.774626\pi$
$409$	−12566.8	−1.51928	−0.759642	+	0.650342i	$0.774626\pi$
$410$	7173.71	0.864107
$411$	−5263.80	−0.631737
$412$	4621.78	0.552667
$413$	−12790.5	−1.52392
$414$	854.637	0.101457
$415$	3582.92	0.423804
$416$	5796.65	0.683184
$417$	−5333.33	−0.626317
$418$	4645.34	0.543567
$419$	−5389.40	−0.628376	−0.314188	−	0.949361i	$-0.601732\pi$
$419$	−5389.40	−0.628376	−0.314188	+	0.949361i	$0.601732\pi$
$420$	−12117.5	−1.40779
$421$	−1450.59	−0.167927	−0.0839636	−	0.996469i	$-0.526758\pi$
$421$	−1450.59	−0.167927	−0.0839636	+	0.996469i	$0.526758\pi$
$422$	25163.0	2.90264
$423$	1866.43	0.214536
$424$	29186.9	3.34302
$425$	3300.88	0.376744
$426$	−10371.7	−1.17961
$427$	1549.13	0.175569
$428$	−33748.8	−3.81147
$429$	−660.336	−0.0743154
$430$	−8741.85	−0.980394
$431$	10952.4	1.22404	0.612019	−	0.790843i	$-0.290358\pi$
$431$	10952.4	1.22404	0.612019	+	0.790843i	$0.290358\pi$
$432$	−27363.8	−3.04755
$433$	−3961.80	−0.439705	−0.219852	−	0.975533i	$-0.570558\pi$
$433$	−3961.80	−0.439705	−0.219852	+	0.975533i	$0.570558\pi$
$434$	−14102.6	−1.55978
$435$	5883.52	0.648490
$436$	21158.4	2.32409
$437$	−2257.32	−0.247099
$438$	15282.2	1.66715
$439$	−1137.14	−0.123628	−0.0618139	−	0.998088i	$-0.519689\pi$
$439$	−1137.14	−0.123628	−0.0618139	+	0.998088i	$0.519689\pi$
$440$	−3646.20	−0.395058
$441$	−1700.07	−0.183573
$442$	−2308.66	−0.248443
$443$	12242.6	1.31301	0.656507	−	0.754320i	$-0.272033\pi$
$443$	12242.6	1.31301	0.656507	+	0.754320i	$0.272033\pi$
$444$	−35163.9	−3.75857
$445$	5103.89	0.543703
$446$	−12096.2	−1.28424
$447$	12430.4	1.31530
$448$	−23210.0	−2.44770
$449$	4360.33	0.458300	0.229150	−	0.973391i	$-0.426405\pi$
$449$	4360.33	0.458300	0.229150	+	0.973391i	$0.426405\pi$
$450$	−2971.85	−0.311321
$451$	−2896.31	−0.302399
$452$	6757.03	0.703151
$453$	14875.3	1.54283
$454$	28058.1	2.90051
$455$	1691.62	0.174295
$456$	23725.2	2.43648
$457$	−2779.55	−0.284511	−0.142256	−	0.989830i	$-0.545436\pi$
$457$	−2779.55	−0.284511	−0.142256	+	0.989830i	$0.545436\pi$
$458$	4809.60	0.490694
$459$	5049.14	0.513450
$460$	2936.86	0.297678
$461$	−11722.8	−1.18435	−0.592176	−	0.805808i	$-0.701731\pi$
$461$	−11722.8	−1.18435	−0.592176	+	0.805808i	$0.701731\pi$
$462$	6833.12	0.688107
$463$	−13289.6	−1.33395	−0.666976	−	0.745080i	$-0.732411\pi$
$463$	−13289.6	−1.33395	−0.666976	+	0.745080i	$0.732411\pi$
$464$	45008.4	4.50315
$465$	−2485.17	−0.247843
$466$	−5095.10	−0.506493
$467$	−12299.9	−1.21878	−0.609391	−	0.792870i	$-0.708586\pi$
$467$	−12299.9	−1.21878	−0.609391	+	0.792870i	$0.708586\pi$
$468$	1488.17	0.146989
$469$	1826.82	0.179860
$470$	8958.11	0.879164
$471$	6814.16	0.666624
$472$	−32581.8	−3.17733
$473$	3529.43	0.343094
$474$	32488.0	3.14815
$475$	7849.44	0.758225
$476$	17104.5	1.64702
$477$	2565.97	0.246306
$478$	7829.97	0.749235
$479$	−4120.96	−0.393093	−0.196547	−	0.980494i	$-0.562973\pi$
$479$	−4120.96	−0.393093	−0.196547	+	0.980494i	$0.562973\pi$
$480$	−10570.3	−1.00514
$481$	4908.93	0.465339
$482$	21517.0	2.03335
$483$	−3320.42	−0.312804
$484$	2440.12	0.229162
$485$	5616.82	0.525869
$486$	−8301.99	−0.774868
$487$	−11817.4	−1.09959	−0.549793	−	0.835301i	$-0.685293\pi$
$487$	−11817.4	−1.09959	−0.549793	+	0.835301i	$0.685293\pi$
$488$	3946.18	0.366056
$489$	−4988.84	−0.461356
$490$	−8159.67	−0.752278
$491$	4311.90	0.396320	0.198160	−	0.980170i	$-0.436503\pi$
$491$	4311.90	0.396320	0.198160	+	0.980170i	$0.436503\pi$
$492$	−24519.2	−2.24677
$493$	−8304.90	−0.758690
$494$	−5489.95	−0.500009
$495$	−320.557	−0.0291070
$496$	−19011.3	−1.72103
$497$	−10727.3	−0.968182
$498$	−17104.2	−1.53908
$499$	−4441.37	−0.398443	−0.199222	−	0.979954i	$-0.563841\pi$
$499$	−4441.37	−0.398443	−0.199222	+	0.979954i	$0.563841\pi$
$500$	−23153.3	−2.07089
$501$	18851.3	1.68107
$502$	−31585.7	−2.80825
$503$	−26.9872	−0.00239225	−0.00119612	−	0.999999i	$-0.500381\pi$
$503$	−26.9872	−0.00239225	−0.00119612	+	0.999999i	$0.500381\pi$
$504$	−9290.50	−0.821095
$505$	939.092	0.0827506
$506$	−1656.11	−0.145500
$507$	780.397	0.0683602
$508$	51267.1	4.47758
$509$	−9236.28	−0.804304	−0.402152	−	0.915573i	$-0.631738\pi$
$509$	−9236.28	−0.804304	−0.402152	+	0.915573i	$0.631738\pi$
$510$	4209.90	0.365525
$511$	15806.1	1.36834
$512$	12812.5	1.10593
$513$	12006.8	1.03336
$514$	−6366.28	−0.546312
$515$	1176.55	0.100670
$516$	29879.0	2.54913
$517$	−3616.75	−0.307668
$518$	−50797.3	−4.30870
$519$	−13760.5	−1.16381
$520$	4309.14	0.363401
$521$	−11817.5	−0.993735	−0.496867	−	0.867827i	$-0.665516\pi$
$521$	−11817.5	−0.993735	−0.496867	+	0.867827i	$0.665516\pi$
$522$	7477.08	0.626940
$523$	16935.2	1.41591	0.707957	−	0.706256i	$-0.249617\pi$
$523$	16935.2	1.41591	0.707957	+	0.706256i	$0.249617\pi$
$524$	−10326.2	−0.860883
$525$	11546.2	0.959843
$526$	−22325.1	−1.85061
$527$	3507.94	0.289959
$528$	9211.55	0.759245
$529$	−11362.2	−0.933858
$530$	12315.7	1.00936
$531$	−2864.44	−0.234098
$532$	40674.2	3.31475
$533$	3422.91	0.278167
$534$	−24365.1	−1.97450
$535$	−8591.32	−0.694271
$536$	4653.53	0.375004
$537$	2166.25	0.174079
$538$	13176.2	1.05589
$539$	3294.38	0.263264
$540$	−15621.3	−1.24488
$541$	−13506.6	−1.07337	−0.536686	−	0.843782i	$-0.680324\pi$
$541$	−13506.6	−1.07337	−0.536686	+	0.843782i	$0.680324\pi$
$542$	−46476.6	−3.68328
$543$	−5336.94	−0.421786
$544$	14920.6	1.17595
$545$	5386.23	0.423340
$546$	−8075.50	−0.632966
$547$	1981.49	0.154886	0.0774428	−	0.996997i	$-0.475324\pi$
$547$	1981.49	0.154886	0.0774428	+	0.996997i	$0.475324\pi$
$548$	−22987.7	−1.79195
$549$	346.930	0.0269701
$550$	5758.84	0.446468
$551$	−19748.9	−1.52692
$552$	−8458.27	−0.652188
$553$	33601.8	2.58390
$554$	20577.2	1.57805
$555$	−8951.56	−0.684635
$556$	−23291.3	−1.77657
$557$	−4004.82	−0.304649	−0.152325	−	0.988331i	$-0.548676\pi$
$557$	−4004.82	−0.304649	−0.152325	+	0.988331i	$0.548676\pi$
$558$	−3158.28	−0.239607
$559$	−4171.15	−0.315601
$560$	−23597.8	−1.78069
$561$	−1699.71	−0.127917
$562$	−26625.4	−1.99845
$563$	−15066.8	−1.12787	−0.563935	−	0.825819i	$-0.690713\pi$
$563$	−15066.8	−1.12787	−0.563935	+	0.825819i	$0.690713\pi$
$564$	−30618.2	−2.28592
$565$	1720.12	0.128081
$566$	−29179.5	−2.16697
$567$	13776.5	1.02039
$568$	−27326.2	−2.01863
$569$	−2037.33	−0.150104	−0.0750522	−	0.997180i	$-0.523912\pi$
$569$	−2037.33	−0.150104	−0.0750522	+	0.997180i	$0.523912\pi$
$570$	10011.1	0.735645
$571$	−17246.9	−1.26403	−0.632015	−	0.774956i	$-0.717772\pi$
$571$	−17246.9	−1.26403	−0.632015	+	0.774956i	$0.717772\pi$
$572$	−2883.77	−0.210798
$573$	−13708.5	−0.999444
$574$	−35420.1	−2.57562
$575$	−2798.40	−0.202959
$576$	−5197.90	−0.376005
$577$	−24835.2	−1.79186	−0.895928	−	0.444199i	$-0.853488\pi$
$577$	−24835.2	−1.79186	−0.895928	+	0.444199i	$0.853488\pi$
$578$	20131.7	1.44874
$579$	−24395.0	−1.75098
$580$	25694.1	1.83947
$581$	−17690.7	−1.26322
$582$	−26813.7	−1.90973
$583$	−4972.33	−0.353229
$584$	40263.7	2.85295
$585$	378.840	0.0267745
$586$	26806.5	1.88971
$587$	16695.4	1.17392	0.586961	−	0.809615i	$-0.300324\pi$
$587$	16695.4	1.17392	0.586961	+	0.809615i	$0.300324\pi$
$588$	27889.1	1.95600
$589$	8341.83	0.583564
$590$	−13748.2	−0.959329
$591$	−9940.74	−0.691891
$592$	−68478.6	−4.75414
$593$	−15968.5	−1.10581	−0.552907	−	0.833243i	$-0.686482\pi$
$593$	−15968.5	−1.10581	−0.552907	+	0.833243i	$0.686482\pi$
$594$	8808.91	0.608475
$595$	4354.24	0.300011
$596$	54285.4	3.73090
$597$	22119.5	1.51640
$598$	1957.22	0.133841
$599$	17197.9	1.17310	0.586549	−	0.809914i	$-0.300486\pi$
$599$	17197.9	1.17310	0.586549	+	0.809914i	$0.300486\pi$
$600$	29412.2	2.00125
$601$	−18775.2	−1.27430	−0.637152	−	0.770738i	$-0.719888\pi$
$601$	−18775.2	−1.27430	−0.637152	+	0.770738i	$0.719888\pi$
$602$	43162.8	2.92223
$603$	409.117	0.0276294
$604$	64962.2	4.37628
$605$	621.172	0.0417425
$606$	−4483.06	−0.300515
$607$	16839.7	1.12603	0.563016	−	0.826446i	$-0.309641\pi$
$607$	16839.7	1.12603	0.563016	+	0.826446i	$0.309641\pi$
$608$	35480.9	2.36668
$609$	−29049.8	−1.93294
$610$	1665.13	0.110523
$611$	4274.34	0.283013
$612$	3830.56	0.253009
$613$	23364.9	1.53948	0.769739	−	0.638358i	$-0.220386\pi$
$613$	23364.9	1.53948	0.769739	+	0.638358i	$0.220386\pi$
$614$	23880.7	1.56962
$615$	−6241.77	−0.409256
$616$	18003.1	1.17754
$617$	27460.3	1.79175	0.895876	−	0.444304i	$-0.146549\pi$
$617$	27460.3	1.79175	0.895876	+	0.444304i	$0.146549\pi$
$618$	−5616.65	−0.365590
$619$	−13032.5	−0.846234	−0.423117	−	0.906075i	$-0.639064\pi$
$619$	−13032.5	−0.846234	−0.423117	+	0.906075i	$0.639064\pi$
$620$	−10853.1	−0.703015
$621$	−4280.52	−0.276605
$622$	20168.4	1.30013
$623$	−25200.4	−1.62060
$624$	−10886.4	−0.698404
$625$	6436.65	0.411946
$626$	35001.2	2.23471
$627$	−4041.87	−0.257443
$628$	29758.4	1.89090
$629$	12635.6	0.800977
$630$	−3920.21	−0.247913
$631$	−17203.7	−1.08537	−0.542686	−	0.839936i	$-0.682593\pi$
$631$	−17203.7	−1.08537	−0.542686	+	0.839936i	$0.682593\pi$
$632$	85595.4	5.38735
$633$	−21894.1	−1.37474
$634$	10303.7	0.645443
$635$	13050.9	0.815605
$636$	−42094.0	−2.62443
$637$	−3893.36	−0.242167
$638$	−14489.0	−0.899101
$639$	−2402.39	−0.148728
$640$	−6635.24	−0.409814
$641$	21794.3	1.34294	0.671470	−	0.741032i	$-0.265663\pi$
$641$	21794.3	1.34294	0.671470	+	0.741032i	$0.265663\pi$
$642$	41013.4	2.52130
$643$	−20959.7	−1.28549	−0.642746	−	0.766080i	$-0.722205\pi$
$643$	−20959.7	−1.28549	−0.642746	+	0.766080i	$0.722205\pi$
$644$	−14500.7	−0.887281
$645$	7606.20	0.464331
$646$	−14131.2	−0.860654
$647$	7163.17	0.435260	0.217630	−	0.976031i	$-0.430167\pi$
$647$	7163.17	0.435260	0.217630	+	0.976031i	$0.430167\pi$
$648$	35093.6	2.12748
$649$	5550.69	0.335722
$650$	−6805.90	−0.410691
$651$	12270.5	0.738738
$652$	−21786.9	−1.30865
$653$	10701.5	0.641320	0.320660	−	0.947194i	$-0.396095\pi$
$653$	10701.5	0.641320	0.320660	+	0.947194i	$0.396095\pi$
$654$	−25712.9	−1.53739
$655$	−2628.71	−0.156812
$656$	−47748.9	−2.84190
$657$	3539.79	0.210199
$658$	−44230.6	−2.62050
$659$	−1643.84	−0.0971697	−0.0485848	−	0.998819i	$-0.515471\pi$
$659$	−1643.84	−0.0971697	−0.0485848	+	0.998819i	$0.515471\pi$
$660$	5258.63	0.310139
$661$	11036.9	0.649451	0.324726	−	0.945808i	$-0.394728\pi$
$661$	11036.9	0.649451	0.324726	+	0.945808i	$0.394728\pi$
$662$	−10.2820	−0.000603657 0
$663$	2008.74	0.117667
$664$	−45064.2	−2.63378
$665$	10354.3	0.603793
$666$	−11376.1	−0.661884
$667$	7040.67	0.408720
$668$	82326.2	4.76841
$669$	10524.8	0.608237
$670$	1963.60	0.113225
$671$	−672.278	−0.0386781
$672$	52191.0	2.99600
$673$	−13422.4	−0.768792	−0.384396	−	0.923168i	$-0.625590\pi$
$673$	−13422.4	−0.768792	−0.384396	+	0.923168i	$0.625590\pi$
$674$	7902.03	0.451594
$675$	14884.8	0.848764
$676$	3408.10	0.193906
$677$	8927.32	0.506802	0.253401	−	0.967361i	$-0.418451\pi$
$677$	8927.32	0.506802	0.253401	+	0.967361i	$0.418451\pi$
$678$	−8211.53	−0.465136
$679$	−27733.0	−1.56744
$680$	11091.7	0.625513
$681$	−24413.1	−1.37373
$682$	6120.09	0.343622
$683$	1189.95	0.0666647	0.0333324	−	0.999444i	$-0.489388\pi$
$683$	1189.95	0.0666647	0.0333324	+	0.999444i	$0.489388\pi$
$684$	9109.01	0.509198
$685$	−5851.91	−0.326408
$686$	−5853.18	−0.325766
$687$	−4184.79	−0.232401
$688$	58186.7	3.22434
$689$	5876.39	0.324924
$690$	−3569.04	−0.196915
$691$	853.797	0.0470043	0.0235022	−	0.999724i	$-0.492518\pi$
$691$	853.797	0.0470043	0.0235022	+	0.999724i	$0.492518\pi$
$692$	−60094.0	−3.30120
$693$	1582.75	0.0867583
$694$	28284.9	1.54709
$695$	−5929.20	−0.323608
$696$	−74000.0	−4.03012
$697$	8810.59	0.478802
$698$	−26947.1	−1.46126
$699$	4433.19	0.239884
$700$	50423.8	2.72263
$701$	−28917.3	−1.55805	−0.779023	−	0.626995i	$-0.784285\pi$
$701$	−28917.3	−1.55805	−0.779023	+	0.626995i	$0.784285\pi$
$702$	−10410.5	−0.559715
$703$	30047.2	1.61202
$704$	10072.5	0.539233
$705$	−7794.36	−0.416387
$706$	−7352.35	−0.391939
$707$	−4636.76	−0.246652
$708$	46990.3	2.49436
$709$	−23256.4	−1.23189	−0.615947	−	0.787787i	$-0.711227\pi$
$709$	−23256.4	−1.23189	−0.615947	+	0.787787i	$0.711227\pi$
$710$	−11530.5	−0.609484
$711$	7525.15	0.396927
$712$	−64194.2	−3.37890
$713$	−2973.94	−0.156206
$714$	−20786.4	−1.08951
$715$	−734.113	−0.0383976
$716$	9460.29	0.493781
$717$	−6812.78	−0.354851
$718$	3569.64	0.185540
$719$	−3093.49	−0.160456	−0.0802278	−	0.996777i	$-0.525565\pi$
$719$	−3093.49	−0.160456	−0.0802278	+	0.996777i	$0.525565\pi$
$720$	−5284.74	−0.273542
$721$	−5809.21	−0.300064
$722$	2798.39	0.144246
$723$	−18721.8	−0.963028
$724$	−23307.1	−1.19641
$725$	−24482.7	−1.25416
$726$	−2965.37	−0.151591
$727$	30538.0	1.55790	0.778949	−	0.627088i	$-0.215753\pi$
$727$	30538.0	1.55790	0.778949	+	0.627088i	$0.215753\pi$
$728$	−21276.4	−1.08318
$729$	21898.2	1.11255
$730$	16989.6	0.861389
$731$	−10736.5	−0.543236
$732$	−5691.28	−0.287371
$733$	−33455.3	−1.68581	−0.842906	−	0.538061i	$-0.819157\pi$
$733$	−33455.3	−1.68581	−0.842906	+	0.538061i	$0.819157\pi$
$734$	17126.0	0.861214
$735$	7099.65	0.356292
$736$	−12649.3	−0.633504
$737$	−792.783	−0.0396235
$738$	−7932.36	−0.395656
$739$	−1598.95	−0.0795920	−0.0397960	−	0.999208i	$-0.512671\pi$
$739$	−1598.95	−0.0795920	−0.0397960	+	0.999208i	$0.512671\pi$
$740$	−39092.6	−1.94199
$741$	4776.75	0.236813
$742$	−60808.5	−3.00856
$743$	36061.5	1.78058	0.890288	−	0.455398i	$-0.150503\pi$
$743$	36061.5	1.78058	0.890288	+	0.455398i	$0.150503\pi$
$744$	31257.2	1.54025
$745$	13819.2	0.679595
$746$	38391.3	1.88419
$747$	−3961.83	−0.194051
$748$	−7422.84	−0.362842
$749$	42419.6	2.06940
$750$	28137.1	1.36990
$751$	10315.2	0.501206	0.250603	−	0.968090i	$-0.419371\pi$
$751$	10315.2	0.501206	0.250603	+	0.968090i	$0.419371\pi$
$752$	−59626.2	−2.89141
$753$	27482.4	1.33003
$754$	17123.4	0.827052
$755$	16537.2	0.797154
$756$	77129.9	3.71057
$757$	−4875.63	−0.234092	−0.117046	−	0.993126i	$-0.537343\pi$
$757$	−4875.63	−0.234092	−0.117046	+	0.993126i	$0.537343\pi$
$758$	12057.3	0.577757
$759$	1440.96	0.0689113
$760$	26376.0	1.25889
$761$	−36160.3	−1.72248	−0.861241	−	0.508197i	$-0.830312\pi$
$761$	−36160.3	−1.72248	−0.861241	+	0.508197i	$0.830312\pi$
$762$	−62302.7	−2.96193
$763$	−26594.4	−1.26184
$764$	−59866.9	−2.83496
$765$	975.134	0.0460863
$766$	−3346.24	−0.157839
$767$	−6559.91	−0.308820
$768$	−2151.32	−0.101080
$769$	1446.71	0.0678409	0.0339204	−	0.999425i	$-0.489201\pi$
$769$	1446.71	0.0678409	0.0339204	+	0.999425i	$0.489201\pi$
$770$	7596.56	0.355534
$771$	5539.23	0.258743
$772$	−106536.	−4.96673
$773$	23535.3	1.09509	0.547545	−	0.836776i	$-0.315562\pi$
$773$	23535.3	1.09509	0.547545	+	0.836776i	$0.315562\pi$
$774$	9666.34	0.448901
$775$	10341.4	0.479320
$776$	−70645.5	−3.26807
$777$	44198.2	2.04067
$778$	10759.1	0.495801
$779$	20951.4	0.963623
$780$	−6214.75	−0.285287
$781$	4655.34	0.213292
$782$	5037.89	0.230377
$783$	−37449.6	−1.70925
$784$	54311.6	2.47411
$785$	7575.49	0.344434
$786$	12549.0	0.569476
$787$	19738.9	0.894046	0.447023	−	0.894522i	$-0.352484\pi$
$787$	19738.9	0.894046	0.447023	+	0.894522i	$0.352484\pi$
$788$	−43412.5	−1.96257
$789$	19424.9	0.876481
$790$	36117.8	1.62660
$791$	−8493.06	−0.381768
$792$	4031.80	0.180889
$793$	794.510	0.0355787
$794$	−66251.7	−2.96119
$795$	−10715.7	−0.478048
$796$	96599.0	4.30133
$797$	15133.5	0.672592	0.336296	−	0.941756i	$-0.390826\pi$
$797$	15133.5	0.672592	0.336296	+	0.941756i	$0.390826\pi$
$798$	−49429.6	−2.19272
$799$	11002.2	0.487144
$800$	43985.7	1.94391
$801$	−5643.65	−0.248950
$802$	47116.0	2.07447
$803$	−6859.39	−0.301448
$804$	−6711.43	−0.294396
$805$	−3691.40	−0.161621
$806$	−7232.83	−0.316086
$807$	−11464.5	−0.500087
$808$	−11811.4	−0.514263
$809$	−23565.6	−1.02413	−0.512065	−	0.858947i	$-0.671119\pi$
$809$	−23565.6	−1.02413	−0.512065	+	0.858947i	$0.671119\pi$
$810$	14808.1	0.642349
$811$	−9896.86	−0.428515	−0.214258	−	0.976777i	$-0.568733\pi$
$811$	−9896.86	−0.428515	−0.214258	+	0.976777i	$0.568733\pi$
$812$	−126865.	−5.48285
$813$	40438.8	1.74447
$814$	22044.5	0.949214
$815$	−5546.23	−0.238375
$816$	−28021.6	−1.20215
$817$	−25531.3	−1.09330
$818$	66694.2	2.85074
$819$	−1870.52	−0.0798061
$820$	−27258.6	−1.16087
$821$	33812.2	1.43734	0.718669	−	0.695352i	$-0.244751\pi$
$821$	33812.2	1.43734	0.718669	+	0.695352i	$0.244751\pi$
$822$	27936.0	1.18538
$823$	−8303.91	−0.351708	−0.175854	−	0.984416i	$-0.556269\pi$
$823$	−8303.91	−0.351708	−0.175854	+	0.984416i	$0.556269\pi$
$824$	−14798.1	−0.625625
$825$	−5010.71	−0.211455
$826$	67881.6	2.85945
$827$	−6445.69	−0.271026	−0.135513	−	0.990776i	$-0.543268\pi$
$827$	−6445.69	−0.271026	−0.135513	+	0.990776i	$0.543268\pi$
$828$	−3247.45	−0.136300
$829$	4568.94	0.191419	0.0957093	−	0.995409i	$-0.469488\pi$
$829$	4568.94	0.191419	0.0957093	+	0.995409i	$0.469488\pi$
$830$	−19015.2	−0.795215
$831$	−17904.0	−0.747393
$832$	−11903.8	−0.496022
$833$	−10021.5	−0.416837
$834$	28305.0	1.17520
$835$	20957.5	0.868581
$836$	−17651.4	−0.730246
$837$	15818.5	0.653247
$838$	28602.6	1.17907
$839$	18726.7	0.770581	0.385290	−	0.922795i	$-0.374101\pi$
$839$	18726.7	0.770581	0.385290	+	0.922795i	$0.374101\pi$
$840$	38798.0	1.59364
$841$	37208.7	1.52563
$842$	7698.55	0.315094
$843$	23166.5	0.946498
$844$	−95614.3	−3.89950
$845$	867.588	0.0353206
$846$	−9905.47	−0.402550
$847$	−3067.03	−0.124421
$848$	−81974.4	−3.31959
$849$	25388.8	1.02632
$850$	−17518.4	−0.706913
$851$	−10712.1	−0.431500
$852$	39410.5	1.58472
$853$	5700.90	0.228834	0.114417	−	0.993433i	$-0.463500\pi$
$853$	5700.90	0.228834	0.114417	+	0.993433i	$0.463500\pi$
$854$	−8221.55	−0.329433
$855$	2318.85	0.0927521
$856$	108057.	4.31463
$857$	34915.4	1.39170	0.695851	−	0.718186i	$-0.255028\pi$
$857$	34915.4	1.39170	0.695851	+	0.718186i	$0.255028\pi$
$858$	3504.52	0.139443
$859$	−12387.9	−0.492048	−0.246024	−	0.969264i	$-0.579124\pi$
$859$	−12387.9	−0.492048	−0.246024	+	0.969264i	$0.579124\pi$
$860$	33217.3	1.31709
$861$	30818.7	1.21986
$862$	−58126.6	−2.29675
$863$	9285.36	0.366254	0.183127	−	0.983089i	$-0.441378\pi$
$863$	9285.36	0.366254	0.183127	+	0.983089i	$0.441378\pi$
$864$	67282.0	2.64928
$865$	−15297.9	−0.601324
$866$	21026.0	0.825051
$867$	−17516.4	−0.686146
$868$	53586.9	2.09546
$869$	−14582.2	−0.569236
$870$	−31225.0	−1.21681
$871$	936.925	0.0364483
$872$	−67745.3	−2.63090
$873$	−6210.82	−0.240784
$874$	11980.0	0.463650
$875$	29101.8	1.12437
$876$	−58069.2	−2.23970
$877$	7761.34	0.298839	0.149419	−	0.988774i	$-0.452260\pi$
$877$	7761.34	0.298839	0.149419	+	0.988774i	$0.452260\pi$
$878$	6035.00	0.231972
$879$	−23324.1	−0.894997
$880$	10240.7	0.392290
$881$	−24308.1	−0.929581	−0.464790	−	0.885421i	$-0.653870\pi$
$881$	−24308.1	−0.929581	−0.464790	+	0.885421i	$0.653870\pi$
$882$	9022.59	0.344452
$883$	3876.23	0.147730	0.0738649	−	0.997268i	$-0.476467\pi$
$883$	3876.23	0.147730	0.0738649	+	0.997268i	$0.476467\pi$
$884$	8772.45	0.333766
$885$	11962.2	0.454355
$886$	−64974.0	−2.46371
$887$	−11107.2	−0.420455	−0.210228	−	0.977652i	$-0.567421\pi$
$887$	−11107.2	−0.420455	−0.210228	+	0.977652i	$0.567421\pi$
$888$	112588.	4.25474
$889$	−64438.7	−2.43105
$890$	−27087.3	−1.02019
$891$	−5978.60	−0.224793
$892$	45963.0	1.72529
$893$	26162.9	0.980413
$894$	−65970.7	−2.46800
$895$	2408.27	0.0899438
$896$	32761.5	1.22152
$897$	−1702.96	−0.0633892
$898$	−23141.1	−0.859942
$899$	−26018.5	−0.965257
$900$	11292.4	0.418239
$901$	15125.8	0.559284
$902$	15371.3	0.567414
$903$	−37555.5	−1.38402
$904$	−21634.8	−0.795975
$905$	−5933.22	−0.217930
$906$	−78945.8	−2.89492
$907$	38754.9	1.41878	0.709391	−	0.704815i	$-0.248970\pi$
$907$	38754.9	1.41878	0.709391	+	0.704815i	$0.248970\pi$
$908$	−106615.	−3.89664
$909$	−1038.41	−0.0378897
$910$	−8977.75	−0.327043
$911$	37191.3	1.35258	0.676291	−	0.736635i	$-0.263586\pi$
$911$	37191.3	1.35258	0.676291	+	0.736635i	$0.263586\pi$
$912$	−66634.7	−2.41940
$913$	7677.21	0.278290
$914$	14751.6	0.533850
$915$	−1448.81	−0.0523456
$916$	−18275.5	−0.659214
$917$	12979.2	0.467407
$918$	−26796.7	−0.963425
$919$	23959.9	0.860025	0.430012	−	0.902823i	$-0.358509\pi$
$919$	23959.9	0.860025	0.430012	+	0.902823i	$0.358509\pi$
$920$	−9403.29	−0.336975
$921$	−20778.4	−0.743399
$922$	62215.3	2.22229
$923$	−5501.76	−0.196200
$924$	−25964.5	−0.924424
$925$	37249.6	1.32406
$926$	70530.3	2.50299
$927$	−1300.98	−0.0460946
$928$	−110667.	−3.91466
$929$	3622.70	0.127941	0.0639704	−	0.997952i	$-0.479624\pi$
$929$	3622.70	0.127941	0.0639704	+	0.997952i	$0.479624\pi$
$930$	13189.3	0.465046
$931$	−23831.0	−0.838915
$932$	19360.3	0.680439
$933$	−17548.3	−0.615762
$934$	65277.9	2.28689
$935$	−1889.61	−0.0660928
$936$	−4764.85	−0.166393
$937$	23974.0	0.835855	0.417928	−	0.908480i	$-0.362757\pi$
$937$	23974.0	0.835855	0.417928	+	0.908480i	$0.362757\pi$
$938$	−9695.25	−0.337485
$939$	−30454.2	−1.05840
$940$	−34039.0	−1.18110
$941$	30208.2	1.04650	0.523251	−	0.852179i	$-0.324719\pi$
$941$	30208.2	1.04650	0.523251	+	0.852179i	$0.324719\pi$
$942$	−36164.0	−1.25084
$943$	−7469.38	−0.257939
$944$	91509.4	3.15506
$945$	19634.7	0.675891
$946$	−18731.4	−0.643773
$947$	−21182.8	−0.726872	−0.363436	−	0.931619i	$-0.618396\pi$
$947$	−21182.8	−0.726872	−0.363436	+	0.931619i	$0.618396\pi$
$948$	−123448.	−4.22932
$949$	8106.55	0.277291
$950$	−41658.4	−1.42271
$951$	−8965.12	−0.305693
$952$	−54765.4	−1.86445
$953$	18371.4	0.624458	0.312229	−	0.950007i	$-0.398924\pi$
$953$	18371.4	0.624458	0.312229	+	0.950007i	$0.398924\pi$
$954$	−13618.1	−0.462162
$955$	−15240.1	−0.516397
$956$	−29752.3	−1.00655
$957$	12606.8	0.425829
$958$	21870.7	0.737590
$959$	28893.7	0.972917
$960$	21706.9	0.729778
$961$	−18800.9	−0.631094
$962$	−26052.6	−0.873149
$963$	9499.89	0.317892
$964$	−81760.4	−2.73166
$965$	−27120.5	−0.904705
$966$	17622.1	0.586938
$967$	−14257.5	−0.474137	−0.237069	−	0.971493i	$-0.576187\pi$
$967$	−14257.5	−0.474137	−0.237069	+	0.971493i	$0.576187\pi$
$968$	−7812.79	−0.259414
$969$	12295.4	0.407621
$970$	−29809.5	−0.986727
$971$	−5160.59	−0.170557	−0.0852787	−	0.996357i	$-0.527178\pi$
$971$	−5160.59	−0.170557	−0.0852787	+	0.996357i	$0.527178\pi$
$972$	31545.9	1.04098
$973$	29275.4	0.964569
$974$	62717.3	2.06324
$975$	5921.74	0.194510
$976$	−11083.3	−0.363490
$977$	−18922.9	−0.619650	−0.309825	−	0.950794i	$-0.600271\pi$
$977$	−18922.9	−0.619650	−0.309825	+	0.950794i	$0.600271\pi$
$978$	26476.7	0.865677
$979$	10936.2	0.357021
$980$	31005.1	1.01063
$981$	−5955.84	−0.193838
$982$	−22884.1	−0.743645
$983$	−13472.7	−0.437144	−0.218572	−	0.975821i	$-0.570140\pi$
$983$	−13472.7	−0.437144	−0.218572	+	0.975821i	$0.570140\pi$
$984$	78505.8	2.54337
$985$	−11051.4	−0.357489
$986$	44075.7	1.42359
$987$	38484.6	1.24111
$988$	20860.7	0.671728
$989$	9102.16	0.292651
$990$	1701.25	0.0546156
$991$	30136.5	0.966011	0.483005	−	0.875617i	$-0.339545\pi$
$991$	30136.5	0.966011	0.483005	+	0.875617i	$0.339545\pi$
$992$	46744.9	1.49612
$993$	8.94626	0.000285902 0
$994$	56931.9	1.81667
$995$	24590.9	0.783501
$996$	64992.7	2.06764
$997$	−18832.5	−0.598226	−0.299113	−	0.954218i	$-0.596691\pi$
$997$	−18832.5	−0.598226	−0.299113	+	0.954218i	$0.596691\pi$
$998$	23571.2	0.747629
$999$	56978.2	1.80451

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.a.b.1.1	✓	6
3.2	odd	2		1287.4.a.f.1.6		6
4.3	odd	2		2288.4.a.m.1.1		6
11.10	odd	2		1573.4.a.d.1.6		6
13.12	even	2		1859.4.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.b.1.1	✓	6	1.1	even	1	trivial
1287.4.a.f.1.6		6	3.2	odd	2
1573.4.a.d.1.6		6	11.10	odd	2
1859.4.a.c.1.6		6	13.12	even	2
2288.4.a.m.1.1		6	4.3	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q-5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} -24.5072 q^{6} -25.3474 q^{7} -64.5685 q^{8} -5.67656 q^{9} +O(q^{10})\)	\(q-5.30719 q^{2} +4.61773 q^{3} +20.1662 q^{4} +5.13365 q^{5} -24.5072 q^{6} -25.3474 q^{7} -64.5685 q^{8} -5.67656 q^{9} -27.2453 q^{10} +11.0000 q^{11} +93.1223 q^{12} -13.0000 q^{13} +134.523 q^{14} +23.7058 q^{15} +181.347 q^{16} -33.4620 q^{17} +30.1266 q^{18} -79.5721 q^{19} +103.527 q^{20} -117.047 q^{21} -58.3791 q^{22} +28.3682 q^{23} -298.160 q^{24} -98.6456 q^{25} +68.9934 q^{26} -150.892 q^{27} -511.161 q^{28} +248.189 q^{29} -125.811 q^{30} -104.834 q^{31} -445.897 q^{32} +50.7950 q^{33} +177.589 q^{34} -130.125 q^{35} -114.475 q^{36} -377.610 q^{37} +422.304 q^{38} -60.0305 q^{39} -331.473 q^{40} -263.301 q^{41} +621.192 q^{42} +320.858 q^{43} +221.829 q^{44} -29.1415 q^{45} -150.555 q^{46} -328.795 q^{47} +837.414 q^{48} +299.489 q^{49} +523.531 q^{50} -154.519 q^{51} -262.161 q^{52} -452.030 q^{53} +800.810 q^{54} +56.4702 q^{55} +1636.64 q^{56} -367.442 q^{57} -1317.18 q^{58} +504.608 q^{59} +478.058 q^{60} -61.1162 q^{61} +556.371 q^{62} +143.886 q^{63} +915.677 q^{64} -66.7375 q^{65} -269.579 q^{66} -72.0712 q^{67} -674.804 q^{68} +130.997 q^{69} +690.596 q^{70} +423.212 q^{71} +366.527 q^{72} -623.580 q^{73} +2004.05 q^{74} -455.519 q^{75} -1604.67 q^{76} -278.821 q^{77} +318.593 q^{78} -1325.65 q^{79} +930.975 q^{80} -543.509 q^{81} +1397.39 q^{82} +697.928 q^{83} -2360.41 q^{84} -171.783 q^{85} -1702.85 q^{86} +1146.07 q^{87} -710.254 q^{88} +994.203 q^{89} +154.659 q^{90} +329.516 q^{91} +572.080 q^{92} -484.093 q^{93} +1744.98 q^{94} -408.496 q^{95} -2059.03 q^{96} +1094.12 q^{97} -1589.45 q^{98} -62.4422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} - 15 q^{6} - 53 q^{7} - 36 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 - 15 * q^6 - 53 * q^7 - 36 * q^8	\( 6 q - 6 q^{2} - 6 q^{3} + 26 q^{4} - 8 q^{5} - 15 q^{6} - 53 q^{7} - 36 q^{8} - 52 q^{10} + 66 q^{11} - 19 q^{12} - 78 q^{13} - 120 q^{14} - 23 q^{15} + 26 q^{16} - 117 q^{17} - 27 q^{18} - 67 q^{19} + 10 q^{20} + 19 q^{21} - 66 q^{22} - 158 q^{23} - 609 q^{24} - 234 q^{25} + 78 q^{26} - 531 q^{27} - 670 q^{28} - 145 q^{29} - 211 q^{30} - 58 q^{31} - 364 q^{32} - 66 q^{33} + 43 q^{34} - 210 q^{35} + 383 q^{36} - 753 q^{37} + 738 q^{38} + 78 q^{39} + 4 q^{40} - 232 q^{41} + 1593 q^{42} - 390 q^{43} + 286 q^{44} - 107 q^{45} + 5 q^{46} - 205 q^{47} + 1625 q^{48} + 491 q^{49} + 938 q^{50} + 363 q^{51} - 338 q^{52} - 65 q^{53} + 1917 q^{54} - 88 q^{55} + 1816 q^{56} - 1657 q^{57} - 1685 q^{58} + 1735 q^{59} + 871 q^{60} + 421 q^{61} + 3394 q^{62} - 125 q^{63} + 570 q^{64} + 104 q^{65} - 165 q^{66} - 703 q^{67} + 209 q^{68} - 272 q^{69} + 1968 q^{70} + 445 q^{71} + 1035 q^{72} - 2340 q^{73} + 1135 q^{74} + 1941 q^{75} - 1208 q^{76} - 583 q^{77} + 195 q^{78} - 1234 q^{79} + 2766 q^{80} + 606 q^{81} - 897 q^{82} - 1601 q^{83} - 7 q^{84} - 2245 q^{85} - 1146 q^{86} + 2462 q^{87} - 396 q^{88} - 442 q^{89} + 113 q^{90} + 689 q^{91} + 2737 q^{92} - 982 q^{93} + 2733 q^{94} - 504 q^{95} - 1153 q^{96} - 2682 q^{97} + 2036 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 26 * q^4 - 8 * q^5 - 15 * q^6 - 53 * q^7 - 36 * q^8 - 52 * q^10 + 66 * q^11 - 19 * q^12 - 78 * q^13 - 120 * q^14 - 23 * q^15 + 26 * q^16 - 117 * q^17 - 27 * q^18 - 67 * q^19 + 10 * q^20 + 19 * q^21 - 66 * q^22 - 158 * q^23 - 609 * q^24 - 234 * q^25 + 78 * q^26 - 531 * q^27 - 670 * q^28 - 145 * q^29 - 211 * q^30 - 58 * q^31 - 364 * q^32 - 66 * q^33 + 43 * q^34 - 210 * q^35 + 383 * q^36 - 753 * q^37 + 738 * q^38 + 78 * q^39 + 4 * q^40 - 232 * q^41 + 1593 * q^42 - 390 * q^43 + 286 * q^44 - 107 * q^45 + 5 * q^46 - 205 * q^47 + 1625 * q^48 + 491 * q^49 + 938 * q^50 + 363 * q^51 - 338 * q^52 - 65 * q^53 + 1917 * q^54 - 88 * q^55 + 1816 * q^56 - 1657 * q^57 - 1685 * q^58 + 1735 * q^59 + 871 * q^60 + 421 * q^61 + 3394 * q^62 - 125 * q^63 + 570 * q^64 + 104 * q^65 - 165 * q^66 - 703 * q^67 + 209 * q^68 - 272 * q^69 + 1968 * q^70 + 445 * q^71 + 1035 * q^72 - 2340 * q^73 + 1135 * q^74 + 1941 * q^75 - 1208 * q^76 - 583 * q^77 + 195 * q^78 - 1234 * q^79 + 2766 * q^80 + 606 * q^81 - 897 * q^82 - 1601 * q^83 - 7 * q^84 - 2245 * q^85 - 1146 * q^86 + 2462 * q^87 - 396 * q^88 - 442 * q^89 + 113 * q^90 + 689 * q^91 + 2737 * q^92 - 982 * q^93 + 2733 * q^94 - 504 * q^95 - 1153 * q^96 - 2682 * q^97 + 2036 * q^98

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