LMFDB - Embedded newform 1997.4.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1997,4,Mod(1,1997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1997, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1997.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1997 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1997.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:	$117.826814281$
Analytic rank:	$1$
Dimension:	$239$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1997.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.43887 q^{2} +0.991773 q^{3} +21.5813 q^{4} -3.96164 q^{5} -5.39413 q^{6} -25.9935 q^{7} -73.8672 q^{8} -26.0164 q^{9} +O(q^{10})$	\(q-5.43887 q^{2} +0.991773 q^{3} +21.5813 q^{4} -3.96164 q^{5} -5.39413 q^{6} -25.9935 q^{7} -73.8672 q^{8} -26.0164 q^{9} +21.5469 q^{10} +37.7976 q^{11} +21.4038 q^{12} +19.7928 q^{13} +141.375 q^{14} -3.92905 q^{15} +229.103 q^{16} -37.0725 q^{17} +141.500 q^{18} +73.9079 q^{19} -85.4975 q^{20} -25.7796 q^{21} -205.576 q^{22} -116.968 q^{23} -73.2594 q^{24} -109.305 q^{25} -107.650 q^{26} -52.5802 q^{27} -560.975 q^{28} +63.3102 q^{29} +21.3696 q^{30} +137.894 q^{31} -655.127 q^{32} +37.4866 q^{33} +201.633 q^{34} +102.977 q^{35} -561.468 q^{36} -222.442 q^{37} -401.976 q^{38} +19.6299 q^{39} +292.635 q^{40} +357.172 q^{41} +140.212 q^{42} -134.883 q^{43} +815.722 q^{44} +103.068 q^{45} +636.172 q^{46} +218.858 q^{47} +227.219 q^{48} +332.662 q^{49} +594.498 q^{50} -36.7675 q^{51} +427.154 q^{52} +465.003 q^{53} +285.977 q^{54} -149.740 q^{55} +1920.07 q^{56} +73.2998 q^{57} -344.336 q^{58} -373.622 q^{59} -84.7941 q^{60} -699.310 q^{61} -749.986 q^{62} +676.257 q^{63} +1730.33 q^{64} -78.4118 q^{65} -203.885 q^{66} +320.392 q^{67} -800.074 q^{68} -116.005 q^{69} -560.078 q^{70} +1000.46 q^{71} +1921.76 q^{72} +326.573 q^{73} +1209.83 q^{74} -108.406 q^{75} +1595.03 q^{76} -982.491 q^{77} -106.765 q^{78} +1006.77 q^{79} -907.625 q^{80} +650.295 q^{81} -1942.61 q^{82} -1203.09 q^{83} -556.359 q^{84} +146.868 q^{85} +733.613 q^{86} +62.7894 q^{87} -2792.00 q^{88} +441.824 q^{89} -560.571 q^{90} -514.483 q^{91} -2524.32 q^{92} +136.759 q^{93} -1190.34 q^{94} -292.797 q^{95} -649.737 q^{96} +939.036 q^{97} -1809.31 q^{98} -983.356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) $ 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9} - 273 q^{10} - 294 q^{11} - 864 q^{12} - 797 q^{13} - 220 q^{14} - 580 q^{15} + 2816 q^{16} - 439 q^{17} - 536 q^{18} - 1704 q^{19} - 933 q^{20} - 596 q^{21} - 1046 q^{22} - 829 q^{23} - 1237 q^{24} + 4364 q^{25} - 818 q^{26} - 3670 q^{27} - 3690 q^{28} - 316 q^{29} - 888 q^{30} - 2595 q^{31} - 1881 q^{32} - 2066 q^{33} - 2605 q^{34} - 2450 q^{35} + 5863 q^{36} - 1912 q^{37} - 1709 q^{38} - 914 q^{39} - 3582 q^{40} - 1064 q^{41} - 3228 q^{42} - 5184 q^{43} - 2656 q^{44} - 3967 q^{45} - 2521 q^{46} - 4909 q^{47} - 7461 q^{48} + 7193 q^{49} - 1906 q^{50} - 3240 q^{51} - 9614 q^{52} - 2722 q^{53} - 3754 q^{54} - 6018 q^{55} - 2347 q^{56} - 2032 q^{57} - 6709 q^{58} - 6318 q^{59} - 5821 q^{60} - 2990 q^{61} - 2117 q^{62} - 8738 q^{63} + 6866 q^{64} - 1738 q^{65} - 3080 q^{66} - 14729 q^{67} - 3897 q^{68} - 2080 q^{69} - 7445 q^{70} - 3240 q^{71} - 8263 q^{72} - 8828 q^{73} - 3103 q^{74} - 12716 q^{75} - 14843 q^{76} - 3818 q^{77} - 8029 q^{78} - 4794 q^{79} - 10336 q^{80} + 11899 q^{81} - 13447 q^{82} - 11434 q^{83} - 7957 q^{84} - 8188 q^{85} - 5196 q^{86} - 11266 q^{87} - 11861 q^{88} - 4845 q^{89} - 7759 q^{90} - 12734 q^{91} - 8644 q^{92} - 10130 q^{93} - 6909 q^{94} - 3686 q^{95} - 11958 q^{96} - 16108 q^{97} - 6845 q^{98} - 12372 q^{99}+O(q^{100}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9 - 273 * q^10 - 294 * q^11 - 864 * q^12 - 797 * q^13 - 220 * q^14 - 580 * q^15 + 2816 * q^16 - 439 * q^17 - 536 * q^18 - 1704 * q^19 - 933 * q^20 - 596 * q^21 - 1046 * q^22 - 829 * q^23 - 1237 * q^24 + 4364 * q^25 - 818 * q^26 - 3670 * q^27 - 3690 * q^28 - 316 * q^29 - 888 * q^30 - 2595 * q^31 - 1881 * q^32 - 2066 * q^33 - 2605 * q^34 - 2450 * q^35 + 5863 * q^36 - 1912 * q^37 - 1709 * q^38 - 914 * q^39 - 3582 * q^40 - 1064 * q^41 - 3228 * q^42 - 5184 * q^43 - 2656 * q^44 - 3967 * q^45 - 2521 * q^46 - 4909 * q^47 - 7461 * q^48 + 7193 * q^49 - 1906 * q^50 - 3240 * q^51 - 9614 * q^52 - 2722 * q^53 - 3754 * q^54 - 6018 * q^55 - 2347 * q^56 - 2032 * q^57 - 6709 * q^58 - 6318 * q^59 - 5821 * q^60 - 2990 * q^61 - 2117 * q^62 - 8738 * q^63 + 6866 * q^64 - 1738 * q^65 - 3080 * q^66 - 14729 * q^67 - 3897 * q^68 - 2080 * q^69 - 7445 * q^70 - 3240 * q^71 - 8263 * q^72 - 8828 * q^73 - 3103 * q^74 - 12716 * q^75 - 14843 * q^76 - 3818 * q^77 - 8029 * q^78 - 4794 * q^79 - 10336 * q^80 + 11899 * q^81 - 13447 * q^82 - 11434 * q^83 - 7957 * q^84 - 8188 * q^85 - 5196 * q^86 - 11266 * q^87 - 11861 * q^88 - 4845 * q^89 - 7759 * q^90 - 12734 * q^91 - 8644 * q^92 - 10130 * q^93 - 6909 * q^94 - 3686 * q^95 - 11958 * q^96 - 16108 * q^97 - 6845 * q^98 - 12372 * 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 $

$2$	−5.43887	−1.92293	−0.961466	−	0.274924i	$-0.911347\pi$
$2$	−5.43887	−1.92293	−0.961466	+	0.274924i	$0.911347\pi$
$3$	0.991773	0.190867	0.0954334	−	0.995436i	$-0.469576\pi$
$3$	0.991773	0.190867	0.0954334	+	0.995436i	$0.469576\pi$
$4$	21.5813	2.69767
$5$	−3.96164	−0.354340	−0.177170	−	0.984180i	$-0.556694\pi$
$5$	−3.96164	−0.354340	−0.177170	+	0.984180i	$0.556694\pi$
$6$	−5.39413	−0.367024
$7$	−25.9935	−1.40352	−0.701759	−	0.712415i	$-0.747601\pi$
$7$	−25.9935	−1.40352	−0.701759	+	0.712415i	$0.747601\pi$
$8$	−73.8672	−3.26450
$9$	−26.0164	−0.963570
$10$	21.5469	0.681372
$11$	37.7976	1.03604	0.518018	−	0.855370i	$-0.326670\pi$
$11$	37.7976	1.03604	0.518018	+	0.855370i	$0.326670\pi$
$12$	21.4038	0.514895
$13$	19.7928	0.422271	0.211135	−	0.977457i	$-0.432284\pi$
$13$	19.7928	0.422271	0.211135	+	0.977457i	$0.432284\pi$
$14$	141.375	2.69887
$15$	−3.92905	−0.0676317
$16$	229.103	3.57974
$17$	−37.0725	−0.528906	−0.264453	−	0.964399i	$-0.585191\pi$
$17$	−37.0725	−0.528906	−0.264453	+	0.964399i	$0.585191\pi$
$18$	141.500	1.85288
$19$	73.9079	0.892402	0.446201	−	0.894933i	$-0.352777\pi$
$19$	73.9079	0.892402	0.446201	+	0.894933i	$0.352777\pi$
$20$	−85.4975	−0.955891
$21$	−25.7796	−0.267885
$22$	−205.576	−1.99223
$23$	−116.968	−1.06041	−0.530205	−	0.847870i	$-0.677885\pi$
$23$	−116.968	−1.06041	−0.530205	+	0.847870i	$0.677885\pi$
$24$	−73.2594	−0.623084
$25$	−109.305	−0.874443
$26$	−107.650	−0.811998
$27$	−52.5802	−0.374780
$28$	−560.975	−3.78622
$29$	63.3102	0.405394	0.202697	−	0.979242i	$-0.435029\pi$
$29$	63.3102	0.405394	0.202697	+	0.979242i	$0.435029\pi$
$30$	21.3696	0.130051
$31$	137.894	0.798917	0.399458	−	0.916751i	$-0.369198\pi$
$31$	137.894	0.798917	0.399458	+	0.916751i	$0.369198\pi$
$32$	−655.127	−3.61910
$33$	37.4866	0.197745
$34$	201.633	1.01705
$35$	102.977	0.497322
$36$	−561.468	−2.59939
$37$	−222.442	−0.988357	−0.494178	−	0.869360i	$-0.664531\pi$
$37$	−222.442	−0.988357	−0.494178	+	0.869360i	$0.664531\pi$
$38$	−401.976	−1.71603
$39$	19.6299	0.0805975
$40$	292.635	1.15674
$41$	357.172	1.36051	0.680255	−	0.732976i	$-0.261869\pi$
$41$	357.172	1.36051	0.680255	+	0.732976i	$0.261869\pi$
$42$	140.212	0.515124
$43$	−134.883	−0.478361	−0.239180	−	0.970975i	$-0.576879\pi$
$43$	−134.883	−0.478361	−0.239180	+	0.970975i	$0.576879\pi$
$44$	815.722	2.79488
$45$	103.068	0.341431
$46$	636.172	2.03910
$47$	218.858	0.679228	0.339614	−	0.940565i	$-0.389704\pi$
$47$	218.858	0.679228	0.339614	+	0.940565i	$0.389704\pi$
$48$	227.219	0.683254
$49$	332.662	0.969861
$50$	594.498	1.68149
$51$	−36.7675	−0.100951
$52$	427.154	1.13915
$53$	465.003	1.20515	0.602576	−	0.798061i	$-0.294141\pi$
$53$	465.003	1.20515	0.602576	+	0.798061i	$0.294141\pi$
$54$	285.977	0.720677
$55$	−149.740	−0.367109
$56$	1920.07	4.58178
$57$	73.2998	0.170330
$58$	−344.336	−0.779544
$59$	−373.622	−0.824431	−0.412215	−	0.911086i	$-0.635245\pi$
$59$	−373.622	−0.824431	−0.412215	+	0.911086i	$0.635245\pi$
$60$	−84.7941	−0.182448
$61$	−699.310	−1.46783	−0.733914	−	0.679243i	$-0.762308\pi$
$61$	−699.310	−1.46783	−0.733914	+	0.679243i	$0.762308\pi$
$62$	−749.986	−1.53626
$63$	676.257	1.35239
$64$	1730.33	3.37954
$65$	−78.4118	−0.149627
$66$	−203.885	−0.380250
$67$	320.392	0.584210	0.292105	−	0.956386i	$-0.405644\pi$
$67$	320.392	0.584210	0.292105	+	0.956386i	$0.405644\pi$
$68$	−800.074	−1.42681
$69$	−116.005	−0.202397
$70$	−560.078	−0.956317
$71$	1000.46	1.67230	0.836148	−	0.548504i	$-0.184802\pi$
$71$	1000.46	1.67230	0.836148	+	0.548504i	$0.184802\pi$
$72$	1921.76	3.14557
$73$	326.573	0.523596	0.261798	−	0.965123i	$-0.415685\pi$
$73$	326.573	0.523596	0.261798	+	0.965123i	$0.415685\pi$
$74$	1209.83	1.90054
$75$	−108.406	−0.166902
$76$	1595.03	2.40740
$77$	−982.491	−1.45409
$78$	−106.765	−0.154983
$79$	1006.77	1.43380	0.716899	−	0.697177i	$-0.245561\pi$
$79$	1006.77	1.43380	0.716899	+	0.697177i	$0.245561\pi$
$80$	−907.625	−1.26845
$81$	650.295	0.892037
$82$	−1942.61	−2.61617
$83$	−1203.09	−1.59103	−0.795517	−	0.605931i	$-0.792801\pi$
$83$	−1203.09	−1.59103	−0.795517	+	0.605931i	$0.792801\pi$
$84$	−556.359	−0.722664
$85$	146.868	0.187413
$86$	733.613	0.919855
$87$	62.7894	0.0773762
$88$	−2792.00	−3.38214
$89$	441.824	0.526216	0.263108	−	0.964766i	$-0.415252\pi$
$89$	441.824	0.526216	0.263108	+	0.964766i	$0.415252\pi$
$90$	−560.571	−0.656549
$91$	−514.483	−0.592665
$92$	−2524.32	−2.86063
$93$	136.759	0.152487
$94$	−1190.34	−1.30611
$95$	−292.797	−0.316214
$96$	−649.737	−0.690766
$97$	939.036	0.982935	0.491467	−	0.870896i	$-0.336461\pi$
$97$	939.036	0.982935	0.491467	+	0.870896i	$0.336461\pi$
$98$	−1809.31	−1.86498
$99$	−983.356	−0.998293
$100$	−2358.96	−2.35896
$101$	122.719	0.120901	0.0604507	−	0.998171i	$-0.480746\pi$
$101$	122.719	0.120901	0.0604507	+	0.998171i	$0.480746\pi$
$102$	199.974	0.194121
$103$	−983.627	−0.940967	−0.470484	−	0.882409i	$-0.655921\pi$
$103$	−983.627	−0.940967	−0.470484	+	0.882409i	$0.655921\pi$
$104$	−1462.03	−1.37850
$105$	102.130	0.0949223
$106$	−2529.09	−2.31743
$107$	21.6332	0.0195454	0.00977271	−	0.999952i	$-0.496889\pi$
$107$	21.6332	0.0195454	0.00977271	+	0.999952i	$0.496889\pi$
$108$	−1134.75	−1.01103
$109$	−1815.64	−1.59547	−0.797737	−	0.603005i	$-0.793970\pi$
$109$	−1815.64	−1.59547	−0.797737	+	0.603005i	$0.793970\pi$
$110$	814.419	0.705925
$111$	−220.612	−0.188644
$112$	−5955.20	−5.02423
$113$	633.390	0.527295	0.263647	−	0.964619i	$-0.415074\pi$
$113$	633.390	0.527295	0.263647	+	0.964619i	$0.415074\pi$
$114$	−398.668	−0.327533
$115$	463.384	0.375746
$116$	1366.32	1.09362
$117$	−514.936	−0.406888
$118$	2032.08	1.58532
$119$	963.644	0.742329
$120$	290.228	0.220784
$121$	97.6561	0.0733705
$122$	3803.46	2.82253
$123$	354.233	0.259676
$124$	2975.93	2.15521
$125$	928.234	0.664190
$126$	−3678.08	−2.60055
$127$	711.711	0.497276	0.248638	−	0.968596i	$-0.420017\pi$
$127$	711.711	0.497276	0.248638	+	0.968596i	$0.420017\pi$
$128$	−4170.00	−2.87953
$129$	−133.774	−0.0913032
$130$	426.472	0.287723
$131$	1191.57	0.794715	0.397357	−	0.917664i	$-0.369927\pi$
$131$	1191.57	0.794715	0.397357	+	0.917664i	$0.369927\pi$
$132$	809.011	0.533450
$133$	−1921.13	−1.25250
$134$	−1742.57	−1.12340
$135$	208.304	0.132800
$136$	2738.44	1.72661
$137$	378.900	0.236289	0.118144	−	0.992996i	$-0.462305\pi$
$137$	378.900	0.236289	0.118144	+	0.992996i	$0.462305\pi$
$138$	630.938	0.389196
$139$	598.563	0.365248	0.182624	−	0.983183i	$-0.441541\pi$
$139$	598.563	0.365248	0.182624	+	0.983183i	$0.441541\pi$
$140$	2222.38	1.34161
$141$	217.057	0.129642
$142$	−5441.39	−3.21571
$143$	748.118	0.437488
$144$	−5960.44	−3.44933
$145$	−250.812	−0.143647
$146$	−1776.19	−1.00684
$147$	329.925	0.185114
$148$	−4800.59	−2.66626
$149$	1185.59	0.651862	0.325931	−	0.945394i	$-0.394322\pi$
$149$	1185.59	0.651862	0.325931	+	0.945394i	$0.394322\pi$
$150$	589.607	0.320941
$151$	2386.82	1.28634	0.643168	−	0.765725i	$-0.277620\pi$
$151$	2386.82	1.28634	0.643168	+	0.765725i	$0.277620\pi$
$152$	−5459.37	−2.91324
$153$	964.493	0.509638
$154$	5343.64	2.79612
$155$	−546.285	−0.283088
$156$	423.640	0.217425
$157$	143.805	0.0731012	0.0365506	−	0.999332i	$-0.488363\pi$
$157$	143.805	0.0731012	0.0365506	+	0.999332i	$0.488363\pi$
$158$	−5475.67	−2.75710
$159$	461.177	0.230024
$160$	2595.38	1.28239
$161$	3040.40	1.48830
$162$	−3536.87	−1.71533
$163$	2334.50	1.12179	0.560896	−	0.827887i	$-0.310457\pi$
$163$	2334.50	1.12179	0.560896	+	0.827887i	$0.310457\pi$
$164$	7708.25	3.67020
$165$	−148.508	−0.0700689
$166$	6543.43	3.05945
$167$	−914.885	−0.423928	−0.211964	−	0.977278i	$-0.567986\pi$
$167$	−914.885	−0.423928	−0.211964	+	0.977278i	$0.567986\pi$
$168$	1904.27	0.874509
$169$	−1805.25	−0.821687
$170$	−798.796	−0.360382
$171$	−1922.82	−0.859892
$172$	−2910.96	−1.29046
$173$	−558.289	−0.245352	−0.122676	−	0.992447i	$-0.539148\pi$
$173$	−558.289	−0.245352	−0.122676	+	0.992447i	$0.539148\pi$
$174$	−341.503	−0.148789
$175$	2841.23	1.22730
$176$	8659.55	3.70874
$177$	−370.548	−0.157356
$178$	−2403.02	−1.01188
$179$	−558.240	−0.233099	−0.116550	−	0.993185i	$-0.537183\pi$
$179$	−558.240	−0.233099	−0.116550	+	0.993185i	$0.537183\pi$
$180$	2224.34	0.921068
$181$	−1228.69	−0.504573	−0.252287	−	0.967653i	$-0.581183\pi$
$181$	−1228.69	−0.504573	−0.252287	+	0.967653i	$0.581183\pi$
$182$	2798.21	1.13965
$183$	−693.557	−0.280159
$184$	8640.06	3.46171
$185$	881.234	0.350214
$186$	−743.815	−0.293221
$187$	−1401.25	−0.547966
$188$	4723.25	1.83233
$189$	1366.74	0.526010
$190$	1592.48	0.608057
$191$	−1350.45	−0.511596	−0.255798	−	0.966730i	$-0.582338\pi$
$191$	−1350.45	−0.511596	−0.255798	+	0.966730i	$0.582338\pi$
$192$	1716.09	0.645042
$193$	−1735.90	−0.647425	−0.323713	−	0.946155i	$-0.604931\pi$
$193$	−1735.90	−0.647425	−0.323713	+	0.946155i	$0.604931\pi$
$194$	−5107.30	−1.89012
$195$	−77.7667	−0.0285589
$196$	7179.30	2.61636
$197$	1272.60	0.460248	0.230124	−	0.973161i	$-0.426087\pi$
$197$	1272.60	0.460248	0.230124	+	0.973161i	$0.426087\pi$
$198$	5348.35	1.91965
$199$	−81.3076	−0.0289635	−0.0144818	−	0.999895i	$-0.504610\pi$
$199$	−81.3076	−0.0289635	−0.0144818	+	0.999895i	$0.504610\pi$
$200$	8074.08	2.85462
$201$	317.756	0.111506
$202$	−667.456	−0.232485
$203$	−1645.66	−0.568977
$204$	−793.492	−0.272331
$205$	−1414.99	−0.482083
$206$	5349.82	1.80942
$207$	3043.07	1.02178
$208$	4534.59	1.51162
$209$	2793.54	0.924560
$210$	−555.470	−0.182529
$211$	−3524.86	−1.15005	−0.575027	−	0.818135i	$-0.695008\pi$
$211$	−3524.86	−1.15005	−0.575027	+	0.818135i	$0.695008\pi$
$212$	10035.4	3.25110
$213$	992.231	0.319186
$214$	−117.660	−0.0375845
$215$	534.359	0.169502
$216$	3883.95	1.22347
$217$	−3584.34	−1.12129
$218$	9875.03	3.06799
$219$	323.887	0.0999371
$220$	−3231.60	−0.990338
$221$	−733.767	−0.223342
$222$	1199.88	0.362750
$223$	2053.64	0.616691	0.308346	−	0.951274i	$-0.400225\pi$
$223$	2053.64	0.616691	0.308346	+	0.951274i	$0.400225\pi$
$224$	17029.0	5.07947
$225$	2843.73	0.842587
$226$	−3444.93	−1.01395
$227$	−5840.56	−1.70771	−0.853857	−	0.520507i	$-0.825743\pi$
$227$	−5840.56	−1.70771	−0.853857	+	0.520507i	$0.825743\pi$
$228$	1581.91	0.459493
$229$	−4580.17	−1.32169	−0.660843	−	0.750524i	$-0.729801\pi$
$229$	−4580.17	−1.32169	−0.660843	+	0.750524i	$0.729801\pi$
$230$	−2520.28	−0.722533
$231$	−974.408	−0.277538
$232$	−4676.55	−1.32341
$233$	−1088.34	−0.306005	−0.153003	−	0.988226i	$-0.548894\pi$
$233$	−1088.34	−0.306005	−0.153003	+	0.988226i	$0.548894\pi$
$234$	2800.67	0.782417
$235$	−867.037	−0.240678
$236$	−8063.26	−2.22404
$237$	998.483	0.273664
$238$	−5241.14	−1.42745
$239$	6495.47	1.75798	0.878990	−	0.476841i	$-0.158218\pi$
$239$	6495.47	1.75798	0.878990	+	0.476841i	$0.158218\pi$
$240$	−900.158	−0.242104
$241$	1531.23	0.409275	0.204637	−	0.978838i	$-0.434398\pi$
$241$	1531.23	0.409275	0.204637	+	0.978838i	$0.434398\pi$
$242$	−531.139	−0.141086
$243$	2064.61	0.545040
$244$	−15092.0	−3.95971
$245$	−1317.89	−0.343660
$246$	−1926.63	−0.499339
$247$	1462.84	0.376835
$248$	−10185.8	−2.60806
$249$	−1193.19	−0.303675
$250$	−5048.55	−1.27719
$251$	3519.35	0.885017	0.442508	−	0.896764i	$-0.354089\pi$
$251$	3519.35	0.885017	0.442508	+	0.896764i	$0.354089\pi$
$252$	14594.5	3.64829
$253$	−4421.09	−1.09862
$254$	−3870.90	−0.956229
$255$	145.660	0.0357708
$256$	8837.52	2.15760
$257$	−1944.07	−0.471860	−0.235930	−	0.971770i	$-0.575814\pi$
$257$	−1944.07	−0.471860	−0.235930	+	0.971770i	$0.575814\pi$
$258$	727.578	0.175570
$259$	5782.04	1.38718
$260$	−1692.23	−0.403645
$261$	−1647.10	−0.390625
$262$	−6480.78	−1.52818
$263$	3344.39	0.784121	0.392061	−	0.919939i	$-0.371762\pi$
$263$	3344.39	0.784121	0.392061	+	0.919939i	$0.371762\pi$
$264$	−2769.03	−0.645538
$265$	−1842.17	−0.427034
$266$	10448.8	2.40848
$267$	438.189	0.100437
$268$	6914.48	1.57600
$269$	−2630.12	−0.596140	−0.298070	−	0.954544i	$-0.596343\pi$
$269$	−2630.12	−0.596140	−0.298070	+	0.954544i	$0.596343\pi$
$270$	−1132.94	−0.255365
$271$	−3971.49	−0.890224	−0.445112	−	0.895475i	$-0.646836\pi$
$271$	−3971.49	−0.890224	−0.445112	+	0.895475i	$0.646836\pi$
$272$	−8493.44	−1.89335
$273$	−510.250	−0.113120
$274$	−2060.79	−0.454368
$275$	−4131.48	−0.905955
$276$	−2503.55	−0.546000
$277$	4257.99	0.923601	0.461801	−	0.886984i	$-0.347204\pi$
$277$	4257.99	0.923601	0.461801	+	0.886984i	$0.347204\pi$
$278$	−3255.51	−0.702347
$279$	−3587.49	−0.769812
$280$	−7606.61	−1.62351
$281$	5105.51	1.08388	0.541938	−	0.840419i	$-0.317691\pi$
$281$	5105.51	1.08388	0.541938	+	0.840419i	$0.317691\pi$
$282$	−1180.55	−0.249293
$283$	−481.534	−0.101146	−0.0505728	−	0.998720i	$-0.516105\pi$
$283$	−481.534	−0.101146	−0.0505728	+	0.998720i	$0.516105\pi$
$284$	21591.3	4.51130
$285$	−290.388	−0.0603547
$286$	−4068.92	−0.841259
$287$	−9284.15	−1.90950
$288$	17044.0	3.48726
$289$	−3538.63	−0.720258
$290$	1364.14	0.276224
$291$	931.310	0.187610
$292$	7047.89	1.41249
$293$	−3679.63	−0.733673	−0.366837	−	0.930285i	$-0.619559\pi$
$293$	−3679.63	−0.733673	−0.366837	+	0.930285i	$0.619559\pi$
$294$	−1794.42	−0.355962
$295$	1480.16	0.292129
$296$	16431.1	3.22649
$297$	−1987.40	−0.388286
$298$	−6448.28	−1.25349
$299$	−2315.11	−0.447780
$300$	−2339.55	−0.450246
$301$	3506.09	0.671388
$302$	−12981.6	−2.47354
$303$	121.710	0.0230761
$304$	16932.6	3.19457
$305$	2770.41	0.520110
$306$	−5245.75	−0.979999
$307$	−3489.00	−0.648625	−0.324312	−	0.945950i	$-0.605133\pi$
$307$	−3489.00	−0.648625	−0.324312	+	0.945950i	$0.605133\pi$
$308$	−21203.5	−3.92266
$309$	−975.534	−0.179599
$310$	2971.17	0.544359
$311$	3240.03	0.590756	0.295378	−	0.955380i	$-0.404554\pi$
$311$	3240.03	0.590756	0.295378	+	0.955380i	$0.404554\pi$
$312$	−1450.01	−0.263110
$313$	−365.084	−0.0659290	−0.0329645	−	0.999457i	$-0.510495\pi$
$313$	−365.084	−0.0659290	−0.0329645	+	0.999457i	$0.510495\pi$
$314$	−782.137	−0.140569
$315$	−2679.09	−0.479205
$316$	21727.4	3.86791
$317$	−9163.69	−1.62361	−0.811804	−	0.583930i	$-0.801514\pi$
$317$	−9163.69	−1.62361	−0.811804	+	0.583930i	$0.801514\pi$
$318$	−2508.28	−0.442320
$319$	2392.97	0.420002
$320$	−6854.93	−1.19751
$321$	21.4552	0.00373057
$322$	−16536.3	−2.86191
$323$	−2739.95	−0.471997
$324$	14034.2	2.40642
$325$	−2163.45	−0.369252
$326$	−12697.0	−2.15713
$327$	−1800.70	−0.304523
$328$	−26383.3	−4.44138
$329$	−5688.89	−0.953308
$330$	807.718	0.134738
$331$	−5468.57	−0.908096	−0.454048	−	0.890977i	$-0.650021\pi$
$331$	−5468.57	−0.908096	−0.454048	+	0.890977i	$0.650021\pi$
$332$	−25964.2	−4.29208
$333$	5787.13	0.952351
$334$	4975.94	0.815184
$335$	−1269.28	−0.207009
$336$	−5906.21	−0.958958
$337$	3704.59	0.598818	0.299409	−	0.954125i	$-0.403210\pi$
$337$	3704.59	0.598818	0.299409	+	0.954125i	$0.403210\pi$
$338$	9818.51	1.58005
$339$	628.179	0.100643
$340$	3169.61	0.505577
$341$	5212.04	0.827707
$342$	10458.0	1.65351
$343$	268.715	0.0423011
$344$	9963.45	1.56161
$345$	459.571	0.0717173
$346$	3036.46	0.471795
$347$	7687.00	1.18922	0.594611	−	0.804014i	$-0.297306\pi$
$347$	7687.00	1.18922	0.594611	+	0.804014i	$0.297306\pi$
$348$	1355.08	0.208735
$349$	−6296.45	−0.965735	−0.482867	−	0.875693i	$-0.660405\pi$
$349$	−6296.45	−0.965735	−0.482867	+	0.875693i	$0.660405\pi$
$350$	−15453.1	−2.36001
$351$	−1040.71	−0.158259
$352$	−24762.2	−3.74952
$353$	5819.38	0.877434	0.438717	−	0.898625i	$-0.355433\pi$
$353$	5819.38	0.877434	0.438717	+	0.898625i	$0.355433\pi$
$354$	2015.36	0.302586
$355$	−3963.47	−0.592561
$356$	9535.15	1.41956
$357$	955.716	0.141686
$358$	3036.20	0.448234
$359$	11144.6	1.63841	0.819207	−	0.573499i	$-0.194414\pi$
$359$	11144.6	1.63841	0.819207	+	0.573499i	$0.194414\pi$
$360$	−7613.31	−1.11460
$361$	−1396.62	−0.203619
$362$	6682.68	0.970260
$363$	96.8526	0.0140040
$364$	−11103.2	−1.59881
$365$	−1293.77	−0.185531
$366$	3772.17	0.538727
$367$	12586.8	1.79027	0.895133	−	0.445799i	$-0.147080\pi$
$367$	12586.8	1.79027	0.895133	+	0.445799i	$0.147080\pi$
$368$	−26797.7	−3.79599
$369$	−9292.32	−1.31095
$370$	−4792.92	−0.673438
$371$	−12087.1	−1.69145
$372$	2951.44	0.411358
$373$	−6176.62	−0.857408	−0.428704	−	0.903445i	$-0.641030\pi$
$373$	−6176.62	−0.857408	−0.428704	+	0.903445i	$0.641030\pi$
$374$	7621.22	1.05370
$375$	920.597	0.126772
$376$	−16166.4	−2.21734
$377$	1253.08	0.171186
$378$	−7433.54	−1.01148
$379$	−4967.32	−0.673229	−0.336615	−	0.941642i	$-0.609282\pi$
$379$	−4967.32	−0.673229	−0.336615	+	0.941642i	$0.609282\pi$
$380$	−6318.94	−0.853039
$381$	705.855	0.0949135
$382$	7344.91	0.983765
$383$	−4735.70	−0.631810	−0.315905	−	0.948791i	$-0.602308\pi$
$383$	−4735.70	−0.631810	−0.315905	+	0.948791i	$0.602308\pi$
$384$	−4135.70	−0.549606
$385$	3892.28	0.515244
$386$	9441.36	1.24495
$387$	3509.18	0.460934
$388$	20265.7	2.65163
$389$	434.175	0.0565900	0.0282950	−	0.999600i	$-0.490992\pi$
$389$	434.175	0.0565900	0.0282950	+	0.999600i	$0.490992\pi$
$390$	422.963	0.0549168
$391$	4336.28	0.560857
$392$	−24572.8	−3.16611
$393$	1181.76	0.151685
$394$	−6921.50	−0.885025
$395$	−3988.45	−0.508052
$396$	−21222.1	−2.69306
$397$	−6092.92	−0.770265	−0.385132	−	0.922861i	$-0.625844\pi$
$397$	−6092.92	−0.770265	−0.385132	+	0.922861i	$0.625844\pi$
$398$	442.222	0.0556949
$399$	−1905.32	−0.239061
$400$	−25042.2	−3.13028
$401$	2499.36	0.311252	0.155626	−	0.987816i	$-0.450261\pi$
$401$	2499.36	0.311252	0.155626	+	0.987816i	$0.450261\pi$
$402$	−1728.23	−0.214419
$403$	2729.29	0.337359
$404$	2648.45	0.326152
$405$	−2576.23	−0.316084
$406$	8950.51	1.09410
$407$	−8407.76	−1.02397
$408$	2715.91	0.329553
$409$	−192.953	−0.0233274	−0.0116637	−	0.999932i	$-0.503713\pi$
$409$	−192.953	−0.0233274	−0.0116637	+	0.999932i	$0.503713\pi$
$410$	7695.93	0.927012
$411$	375.782	0.0450997
$412$	−21228.0	−2.53842
$413$	9711.74	1.15710
$414$	−16550.9	−1.96481
$415$	4766.19	0.563767
$416$	−12966.8	−1.52824
$417$	593.638	0.0697136
$418$	−15193.7	−1.77787
$419$	−16208.9	−1.88988	−0.944938	−	0.327251i	$-0.893878\pi$
$419$	−16208.9	−1.88988	−0.944938	+	0.327251i	$0.893878\pi$
$420$	2204.10	0.256069
$421$	−9802.17	−1.13475	−0.567373	−	0.823461i	$-0.692040\pi$
$421$	−9802.17	−1.13475	−0.567373	+	0.823461i	$0.692040\pi$
$422$	19171.3	2.21147
$423$	−5693.89	−0.654484
$424$	−34348.5	−3.93422
$425$	4052.23	0.462498
$426$	−5396.62	−0.613772
$427$	18177.5	2.06012
$428$	466.873	0.0527270
$429$	741.963	0.0835019
$430$	−2906.31	−0.325942
$431$	−3420.98	−0.382326	−0.191163	−	0.981558i	$-0.561226\pi$
$431$	−3420.98	−0.382326	−0.191163	+	0.981558i	$0.561226\pi$
$432$	−12046.3	−1.34162
$433$	−6351.29	−0.704904	−0.352452	−	0.935830i	$-0.614652\pi$
$433$	−6351.29	−0.704904	−0.352452	+	0.935830i	$0.614652\pi$
$434$	19494.8	2.15617
$435$	−248.749	−0.0274175
$436$	−39183.9	−4.30406
$437$	−8644.83	−0.946312
$438$	−1761.58	−0.192172
$439$	−6822.29	−0.741709	−0.370854	−	0.928691i	$-0.620935\pi$
$439$	−6822.29	−0.741709	−0.370854	+	0.928691i	$0.620935\pi$
$440$	11060.9	1.19843
$441$	−8654.67	−0.934529
$442$	3990.87	0.429471
$443$	10626.0	1.13963	0.569814	−	0.821774i	$-0.307015\pi$
$443$	10626.0	1.13963	0.569814	+	0.821774i	$0.307015\pi$
$444$	−4761.10	−0.508900
$445$	−1750.35	−0.186459
$446$	−11169.5	−1.18586
$447$	1175.84	0.124419
$448$	−44977.2	−4.74325
$449$	−12008.7	−1.26220	−0.631098	−	0.775703i	$-0.717396\pi$
$449$	−12008.7	−1.26220	−0.631098	+	0.775703i	$0.717396\pi$
$450$	−15466.7	−1.62024
$451$	13500.2	1.40954
$452$	13669.4	1.42247
$453$	2367.18	0.245519
$454$	31766.0	3.28382
$455$	2038.20	0.210005
$456$	−5414.45	−0.556041
$457$	11159.5	1.14228	0.571138	−	0.820854i	$-0.306502\pi$
$457$	11159.5	1.14228	0.571138	+	0.820854i	$0.306502\pi$
$458$	24911.0	2.54151
$459$	1949.28	0.198224
$460$	10000.4	1.01364
$461$	−4443.84	−0.448959	−0.224480	−	0.974479i	$-0.572068\pi$
$461$	−4443.84	−0.448959	−0.224480	+	0.974479i	$0.572068\pi$
$462$	5299.68	0.533687
$463$	−12584.1	−1.26313	−0.631567	−	0.775321i	$-0.717588\pi$
$463$	−12584.1	−1.26313	−0.631567	+	0.775321i	$0.717588\pi$
$464$	14504.6	1.45120
$465$	−541.790	−0.0540321
$466$	5919.32	0.588427
$467$	−2003.46	−0.198521	−0.0992605	−	0.995061i	$-0.531648\pi$
$467$	−2003.46	−0.198521	−0.0992605	+	0.995061i	$0.531648\pi$
$468$	−11113.0	−1.09765
$469$	−8328.10	−0.819949
$470$	4715.70	0.462807
$471$	142.622	0.0139526
$472$	27598.4	2.69135
$473$	−5098.26	−0.495599
$474$	−5430.62	−0.526238
$475$	−8078.53	−0.780355
$476$	20796.7	2.00256
$477$	−12097.7	−1.16125
$478$	−35328.0	−3.38047
$479$	3068.78	0.292726	0.146363	−	0.989231i	$-0.453243\pi$
$479$	3068.78	0.292726	0.146363	+	0.989231i	$0.453243\pi$
$480$	2574.03	0.244766
$481$	−4402.74	−0.417354
$482$	−8328.17	−0.787007
$483$	3015.38	0.284068
$484$	2107.55	0.197929
$485$	−3720.12	−0.348293
$486$	−11229.2	−1.04808
$487$	−4583.61	−0.426496	−0.213248	−	0.976998i	$-0.568404\pi$
$487$	−4583.61	−0.426496	−0.213248	+	0.976998i	$0.568404\pi$
$488$	51656.0	4.79172
$489$	2315.29	0.214113
$490$	7167.83	0.660835
$491$	11412.2	1.04893	0.524466	−	0.851432i	$-0.324265\pi$
$491$	11412.2	1.04893	0.524466	+	0.851432i	$0.324265\pi$
$492$	7644.83	0.700519
$493$	−2347.07	−0.214415
$494$	−7956.21	−0.724629
$495$	3895.70	0.353735
$496$	31591.9	2.85992
$497$	−26005.5	−2.34710
$498$	6489.60	0.583947
$499$	−5894.40	−0.528797	−0.264398	−	0.964414i	$-0.585173\pi$
$499$	−5894.40	−0.528797	−0.264398	+	0.964414i	$0.585173\pi$
$500$	20032.5	1.79176
$501$	−907.358	−0.0809137
$502$	−19141.3	−1.70183
$503$	−13736.2	−1.21763	−0.608814	−	0.793313i	$-0.708355\pi$
$503$	−13736.2	−1.21763	−0.608814	+	0.793313i	$0.708355\pi$
$504$	−49953.2	−4.41487
$505$	−486.170	−0.0428402
$506$	24045.7	2.11258
$507$	−1790.39	−0.156833
$508$	15359.7	1.34149
$509$	−17492.7	−1.52328	−0.761640	−	0.648000i	$-0.775606\pi$
$509$	−17492.7	−1.52328	−0.761640	+	0.648000i	$0.775606\pi$
$510$	−792.224	−0.0687848
$511$	−8488.79	−0.734877
$512$	−14706.1	−1.26938
$513$	−3886.09	−0.334455
$514$	10573.6	0.907354
$515$	3896.78	0.333422
$516$	−2887.01	−0.246306
$517$	8272.30	0.703705
$518$	−31447.8	−2.66745
$519$	−553.695	−0.0468295
$520$	5792.06	0.488459
$521$	−26.9179	−0.00226352	−0.00113176	−	0.999999i	$-0.500360\pi$
$521$	−26.9179	−0.00226352	−0.00113176	+	0.999999i	$0.500360\pi$
$522$	8958.39	0.751146
$523$	−8630.72	−0.721597	−0.360798	−	0.932644i	$-0.617496\pi$
$523$	−8630.72	−0.721597	−0.360798	+	0.932644i	$0.617496\pi$
$524$	25715.6	2.14388
$525$	2817.85	0.234250
$526$	−18189.7	−1.50781
$527$	−5112.06	−0.422552
$528$	8588.31	0.707875
$529$	1514.42	0.124469
$530$	10019.4	0.821157
$531$	9720.29	0.794397
$532$	−41460.5	−3.37883
$533$	7069.42	0.574504
$534$	−2383.25	−0.193134
$535$	−85.7029	−0.00692572
$536$	−23666.4	−1.90715
$537$	−553.647	−0.0444909
$538$	14304.9	1.14634
$539$	12573.8	1.00481
$540$	4495.48	0.358249
$541$	−6294.93	−0.500259	−0.250130	−	0.968212i	$-0.580473\pi$
$541$	−6294.93	−0.500259	−0.250130	+	0.968212i	$0.580473\pi$
$542$	21600.4	1.71184
$543$	−1218.58	−0.0963062
$544$	24287.2	1.91416
$545$	7192.91	0.565340
$546$	2775.19	0.217522
$547$	−11134.1	−0.870310	−0.435155	−	0.900356i	$-0.643306\pi$
$547$	−11134.1	−0.870310	−0.435155	+	0.900356i	$0.643306\pi$
$548$	8177.16	0.637429
$549$	18193.5	1.41435
$550$	22470.6	1.74209
$551$	4679.13	0.361774
$552$	8568.98	0.660725
$553$	−26169.4	−2.01236
$554$	−23158.6	−1.77602
$555$	873.984	0.0668443
$556$	12917.8	0.985317
$557$	8327.87	0.633507	0.316753	−	0.948508i	$-0.397407\pi$
$557$	8327.87	0.633507	0.316753	+	0.948508i	$0.397407\pi$
$558$	19511.9	1.48030
$559$	−2669.71	−0.201998
$560$	23592.4	1.78028
$561$	−1389.72	−0.104588
$562$	−27768.2	−2.08422
$563$	−1095.38	−0.0819976	−0.0409988	−	0.999159i	$-0.513054\pi$
$563$	−1095.38	−0.0819976	−0.0409988	+	0.999159i	$0.513054\pi$
$564$	4684.39	0.349731
$565$	−2509.26	−0.186842
$566$	2619.00	0.194496
$567$	−16903.4	−1.25199
$568$	−73901.3	−5.45921
$569$	6438.73	0.474386	0.237193	−	0.971463i	$-0.423773\pi$
$569$	6438.73	0.474386	0.237193	+	0.971463i	$0.423773\pi$
$570$	1579.38	0.116058
$571$	−24007.1	−1.75948	−0.879742	−	0.475451i	$-0.842285\pi$
$571$	−24007.1	−1.75948	−0.879742	+	0.475451i	$0.842285\pi$
$572$	16145.4	1.18020
$573$	−1339.34	−0.0976467
$574$	50495.3	3.67184
$575$	12785.2	0.927268
$576$	−45016.8	−3.25642
$577$	6839.25	0.493452	0.246726	−	0.969085i	$-0.420645\pi$
$577$	6839.25	0.493452	0.246726	+	0.969085i	$0.420645\pi$
$578$	19246.2	1.38501
$579$	−1721.62	−0.123572
$580$	−5412.87	−0.387512
$581$	31272.4	2.23304
$582$	−5065.28	−0.360760
$583$	17576.0	1.24858
$584$	−24123.1	−1.70928
$585$	2039.99	0.144176
$586$	20013.0	1.41080
$587$	17136.1	1.20491	0.602454	−	0.798153i	$-0.294189\pi$
$587$	17136.1	1.20491	0.602454	+	0.798153i	$0.294189\pi$
$588$	7120.23	0.499376
$589$	10191.4	0.712955
$590$	−8050.38	−0.561744
$591$	1262.13	0.0878460
$592$	−50962.2	−3.53806
$593$	18389.4	1.27346	0.636731	−	0.771086i	$-0.280286\pi$
$593$	18389.4	1.27346	0.636731	+	0.771086i	$0.280286\pi$
$594$	10809.2	0.746647
$595$	−3817.61	−0.263037
$596$	25586.7	1.75851
$597$	−80.6386	−0.00552817
$598$	12591.6	0.861051
$599$	−9936.94	−0.677817	−0.338909	−	0.940819i	$-0.610058\pi$
$599$	−9936.94	−0.677817	−0.338909	+	0.940819i	$0.610058\pi$
$600$	8007.65	0.544852
$601$	−20008.6	−1.35802	−0.679008	−	0.734130i	$-0.737590\pi$
$601$	−20008.6	−1.35802	−0.679008	+	0.734130i	$0.737590\pi$
$602$	−19069.2	−1.29103
$603$	−8335.43	−0.562927
$604$	51510.8	3.47011
$605$	−386.878	−0.0259981
$606$	−661.964	−0.0443737
$607$	3479.78	0.232685	0.116343	−	0.993209i	$-0.462883\pi$
$607$	3479.78	0.232685	0.116343	+	0.993209i	$0.462883\pi$
$608$	−48419.1	−3.22969
$609$	−1632.12	−0.108599
$610$	−15067.9	−1.00014
$611$	4331.80	0.286818
$612$	20815.0	1.37483
$613$	−19963.2	−1.31534	−0.657672	−	0.753305i	$-0.728459\pi$
$613$	−19963.2	−1.31534	−0.657672	+	0.753305i	$0.728459\pi$
$614$	18976.2	1.24726
$615$	−1403.35	−0.0920136
$616$	72573.8	4.74689
$617$	−6041.08	−0.394173	−0.197086	−	0.980386i	$-0.563148\pi$
$617$	−6041.08	−0.394173	−0.197086	+	0.980386i	$0.563148\pi$
$618$	5305.81	0.345357
$619$	9765.04	0.634071	0.317036	−	0.948414i	$-0.397313\pi$
$619$	9765.04	0.634071	0.317036	+	0.948414i	$0.397313\pi$
$620$	−11789.6	−0.763677
$621$	6150.18	0.397421
$622$	−17622.1	−1.13598
$623$	−11484.6	−0.738554
$624$	4497.28	0.288518
$625$	9985.85	0.639094
$626$	1985.65	0.126777
$627$	2770.56	0.176468
$628$	3103.50	0.197203
$629$	8246.48	0.522748
$630$	14571.2	0.921478
$631$	−14498.9	−0.914728	−0.457364	−	0.889280i	$-0.651206\pi$
$631$	−14498.9	−0.914728	−0.457364	+	0.889280i	$0.651206\pi$
$632$	−74367.0	−4.68063
$633$	−3495.86	−0.219507
$634$	49840.1	3.12209
$635$	−2819.54	−0.176205
$636$	9952.82	0.620527
$637$	6584.30	0.409544
$638$	−13015.1	−0.807636
$639$	−26028.4	−1.61137
$640$	16520.1	1.02033
$641$	10261.0	0.632272	0.316136	−	0.948714i	$-0.397614\pi$
$641$	10261.0	0.632272	0.316136	+	0.948714i	$0.397614\pi$
$642$	−116.692	−0.00717363
$643$	−20503.2	−1.25749	−0.628746	−	0.777610i	$-0.716432\pi$
$643$	−20503.2	−1.25749	−0.628746	+	0.777610i	$0.716432\pi$
$644$	65615.8	4.01495
$645$	529.963	0.0323524
$646$	14902.2	0.907618
$647$	31730.9	1.92809	0.964043	−	0.265746i	$-0.0856184\pi$
$647$	31730.9	1.92809	0.964043	+	0.265746i	$0.0856184\pi$
$648$	−48035.4	−2.91205
$649$	−14122.0	−0.854140
$650$	11766.8	0.710046
$651$	−3554.85	−0.214018
$652$	50381.6	3.02622
$653$	16095.3	0.964559	0.482279	−	0.876017i	$-0.339809\pi$
$653$	16095.3	0.964559	0.482279	+	0.876017i	$0.339809\pi$
$654$	9793.79	0.585577
$655$	−4720.56	−0.281599
$656$	81829.3	4.87027
$657$	−8496.26	−0.504522
$658$	30941.1	1.83315
$659$	−18422.5	−1.08898	−0.544491	−	0.838767i	$-0.683277\pi$
$659$	−18422.5	−1.08898	−0.544491	+	0.838767i	$0.683277\pi$
$660$	−3205.01	−0.189022
$661$	9263.63	0.545104	0.272552	−	0.962141i	$-0.412132\pi$
$661$	9263.63	0.545104	0.272552	+	0.962141i	$0.412132\pi$
$662$	29742.9	1.74621
$663$	−727.730	−0.0426285
$664$	88868.5	5.19393
$665$	7610.81	0.443811
$666$	−31475.5	−1.83131
$667$	−7405.25	−0.429884
$668$	−19744.4	−1.14362
$669$	2036.75	0.117706
$670$	6903.44	0.398064
$671$	−26432.2	−1.52072
$672$	16888.9	0.969502
$673$	2047.08	0.117250	0.0586250	−	0.998280i	$-0.481328\pi$
$673$	2047.08	0.117250	0.0586250	+	0.998280i	$0.481328\pi$
$674$	−20148.8	−1.15149
$675$	5747.30	0.327724
$676$	−38959.6	−2.21664
$677$	−7597.45	−0.431305	−0.215653	−	0.976470i	$-0.569188\pi$
$677$	−7597.45	−0.431305	−0.215653	+	0.976470i	$0.569188\pi$
$678$	−3416.58	−0.193530
$679$	−24408.8	−1.37957
$680$	−10848.7	−0.611808
$681$	−5792.50	−0.325946
$682$	−28347.6	−1.59162
$683$	−28731.2	−1.60962	−0.804810	−	0.593533i	$-0.797733\pi$
$683$	−28731.2	−1.60962	−0.804810	+	0.593533i	$0.797733\pi$
$684$	−41497.0	−2.31970
$685$	−1501.06	−0.0837266
$686$	−1461.51	−0.0813421
$687$	−4542.49	−0.252266
$688$	−30902.2	−1.71241
$689$	9203.69	0.508901
$690$	−2499.55	−0.137908
$691$	−9947.07	−0.547618	−0.273809	−	0.961784i	$-0.588284\pi$
$691$	−9947.07	−0.547618	−0.273809	+	0.961784i	$0.588284\pi$
$692$	−12048.6	−0.661878
$693$	25560.9	1.40112
$694$	−41808.6	−2.28679
$695$	−2371.29	−0.129422
$696$	−4638.07	−0.252594
$697$	−13241.3	−0.719582
$698$	34245.6	1.85704
$699$	−1079.38	−0.0584062
$700$	61317.6	3.31084
$701$	2040.94	0.109965	0.0549823	−	0.998487i	$-0.482490\pi$
$701$	2040.94	0.109965	0.0549823	+	0.998487i	$0.482490\pi$
$702$	5660.27	0.304321
$703$	−16440.2	−0.882012
$704$	65402.1	3.50133
$705$	−859.903	−0.0459373
$706$	−31650.8	−1.68725
$707$	−3189.91	−0.169687
$708$	−7996.92	−0.424495
$709$	7681.16	0.406872	0.203436	−	0.979088i	$-0.434789\pi$
$709$	7681.16	0.406872	0.203436	+	0.979088i	$0.434789\pi$
$710$	21556.8	1.13945
$711$	−26192.4	−1.38156
$712$	−32636.3	−1.71783
$713$	−16129.1	−0.847179
$714$	−5198.02	−0.272452
$715$	−2963.77	−0.155019
$716$	−12047.6	−0.628825
$717$	6442.03	0.335540
$718$	−60614.1	−3.15056
$719$	18285.1	0.948428	0.474214	−	0.880410i	$-0.342732\pi$
$719$	18285.1	0.948428	0.474214	+	0.880410i	$0.342732\pi$
$720$	23613.1	1.22224
$721$	25567.9	1.32066
$722$	7596.05	0.391545
$723$	1518.63	0.0781169
$724$	−26516.7	−1.36117
$725$	−6920.15	−0.354494
$726$	−526.769	−0.0269287
$727$	−11983.6	−0.611346	−0.305673	−	0.952137i	$-0.598881\pi$
$727$	−11983.6	−0.611346	−0.305673	+	0.952137i	$0.598881\pi$
$728$	38003.4	1.93475
$729$	−15510.3	−0.788007
$730$	7036.63	0.356764
$731$	5000.46	0.253008
$732$	−14967.9	−0.755777
$733$	−178.095	−0.00897421	−0.00448711	−	0.999990i	$-0.501428\pi$
$733$	−178.095	−0.00897421	−0.00448711	+	0.999990i	$0.501428\pi$
$734$	−68458.2	−3.44256
$735$	−1307.05	−0.0655933
$736$	76628.6	3.83773
$737$	12110.0	0.605263
$738$	50539.8	2.52086
$739$	−34673.7	−1.72597	−0.862985	−	0.505230i	$-0.831408\pi$
$739$	−34673.7	−1.72597	−0.862985	+	0.505230i	$0.831408\pi$
$740$	19018.2	0.944762
$741$	1450.81	0.0719253
$742$	65740.0	3.25255
$743$	−39729.0	−1.96166	−0.980831	−	0.194860i	$-0.937575\pi$
$743$	−39729.0	−1.96166	−0.980831	+	0.194860i	$0.937575\pi$
$744$	−10102.0	−0.497792
$745$	−4696.89	−0.230981
$746$	33593.9	1.64874
$747$	31299.9	1.53307
$748$	−30240.9	−1.47823
$749$	−562.322	−0.0274323
$750$	−5007.01	−0.243774
$751$	21515.0	1.04540	0.522698	−	0.852518i	$-0.324925\pi$
$751$	21515.0	1.04540	0.522698	+	0.852518i	$0.324925\pi$
$752$	50141.1	2.43146
$753$	3490.39	0.168920
$754$	−6815.36	−0.329179
$755$	−9455.73	−0.455800
$756$	29496.2	1.41900
$757$	−19808.1	−0.951041	−0.475521	−	0.879705i	$-0.657740\pi$
$757$	−19808.1	−0.951041	−0.475521	+	0.879705i	$0.657740\pi$
$758$	27016.6	1.29457
$759$	−4384.72	−0.209691
$760$	21628.1	1.03228
$761$	−29328.7	−1.39706	−0.698531	−	0.715580i	$-0.746162\pi$
$761$	−29328.7	−1.39706	−0.698531	+	0.715580i	$0.746162\pi$
$762$	−3839.06	−0.182512
$763$	47194.8	2.23928
$764$	−29144.4	−1.38012
$765$	−3820.97	−0.180585
$766$	25756.9	1.21493
$767$	−7395.01	−0.348133
$768$	8764.81	0.411813
$769$	−25720.3	−1.20611	−0.603055	−	0.797699i	$-0.706050\pi$
$769$	−25720.3	−1.20611	−0.603055	+	0.797699i	$0.706050\pi$
$770$	−21169.6	−0.990778
$771$	−1928.08	−0.0900623
$772$	−37463.1	−1.74654
$773$	−17314.6	−0.805643	−0.402821	−	0.915279i	$-0.631970\pi$
$773$	−17314.6	−0.805643	−0.402821	+	0.915279i	$0.631970\pi$
$774$	−19086.0	−0.886345
$775$	−15072.5	−0.698607
$776$	−69363.9	−3.20879
$777$	5734.47	0.264766
$778$	−2361.42	−0.108819
$779$	26397.8	1.21412
$780$	−1678.31	−0.0770424
$781$	37815.0	1.73256
$782$	−23584.5	−1.07849
$783$	−3328.87	−0.151934
$784$	76214.1	3.47185
$785$	−569.704	−0.0259027
$786$	−6427.46	−0.291679
$787$	−8130.23	−0.368248	−0.184124	−	0.982903i	$-0.558945\pi$
$787$	−8130.23	−0.368248	−0.184124	+	0.982903i	$0.558945\pi$
$788$	27464.4	1.24160
$789$	3316.87	0.149663
$790$	21692.6	0.976949
$791$	−16464.0	−0.740067
$792$	72637.7	3.25893
$793$	−13841.3	−0.619821
$794$	33138.6	1.48117
$795$	−1827.02	−0.0815065
$796$	−1754.73	−0.0781340
$797$	−21591.3	−0.959604	−0.479802	−	0.877377i	$-0.659292\pi$
$797$	−21591.3	−0.959604	−0.479802	+	0.877377i	$0.659292\pi$
$798$	10362.8	0.459698
$799$	−8113.61	−0.359248
$800$	71608.9	3.16470
$801$	−11494.7	−0.507046
$802$	−13593.7	−0.598517
$803$	12343.7	0.542465
$804$	6857.59	0.300807
$805$	−12045.0	−0.527365
$806$	−14844.3	−0.648719
$807$	−2608.49	−0.113783
$808$	−9064.94	−0.394682
$809$	−11941.5	−0.518961	−0.259480	−	0.965748i	$-0.583551\pi$
$809$	−11941.5	−0.518961	−0.259480	+	0.965748i	$0.583551\pi$
$810$	14011.8	0.607808
$811$	−27890.8	−1.20762	−0.603810	−	0.797128i	$-0.706351\pi$
$811$	−27890.8	−1.20762	−0.603810	+	0.797128i	$0.706351\pi$
$812$	−35515.4	−1.53491
$813$	−3938.81	−0.169914
$814$	45728.7	1.96903
$815$	−9248.44	−0.397495
$816$	−8423.56	−0.361377
$817$	−9968.95	−0.426890
$818$	1049.45	0.0448570
$819$	13385.0	0.571074
$820$	−30537.3	−1.30050
$821$	−2757.45	−0.117218	−0.0586088	−	0.998281i	$-0.518666\pi$
$821$	−2757.45	−0.117218	−0.0586088	+	0.998281i	$0.518666\pi$
$822$	−2043.83	−0.0867237
$823$	−10621.9	−0.449885	−0.224943	−	0.974372i	$-0.572219\pi$
$823$	−10621.9	−0.449885	−0.224943	+	0.974372i	$0.572219\pi$
$824$	72657.7	3.07179
$825$	−4097.49	−0.172917
$826$	−52820.9	−2.22503
$827$	2918.86	0.122731	0.0613657	−	0.998115i	$-0.480454\pi$
$827$	2918.86	0.122731	0.0613657	+	0.998115i	$0.480454\pi$
$828$	65673.6	2.75642
$829$	−28933.4	−1.21218	−0.606091	−	0.795396i	$-0.707263\pi$
$829$	−28933.4	−1.21218	−0.606091	+	0.795396i	$0.707263\pi$
$830$	−25922.7	−1.08409
$831$	4222.95	0.176285
$832$	34247.9	1.42708
$833$	−12332.6	−0.512965
$834$	−3228.72	−0.134055
$835$	3624.44	0.150214
$836$	60288.3	2.49416
$837$	−7250.47	−0.299418
$838$	88158.3	3.63410
$839$	34172.8	1.40617	0.703084	−	0.711107i	$-0.251806\pi$
$839$	34172.8	1.40617	0.703084	+	0.711107i	$0.251806\pi$
$840$	−7544.03	−0.309874
$841$	−20380.8	−0.835656
$842$	53312.7	2.18204
$843$	5063.50	0.206876
$844$	−76071.2	−3.10246
$845$	7151.74	0.291157
$846$	30968.4	1.25853
$847$	−2538.42	−0.102977
$848$	106534.	4.31413
$849$	−477.572	−0.0193053
$850$	−22039.5	−0.889353
$851$	26018.5	1.04806
$852$	21413.7	0.861057
$853$	23197.7	0.931154	0.465577	−	0.885007i	$-0.345847\pi$
$853$	23197.7	0.931154	0.465577	+	0.885007i	$0.345847\pi$
$854$	−98865.2	−3.96147
$855$	7617.51	0.304694
$856$	−1597.98	−0.0638060
$857$	38007.4	1.51495	0.757473	−	0.652866i	$-0.226434\pi$
$857$	38007.4	1.51495	0.757473	+	0.652866i	$0.226434\pi$
$858$	−4035.44	−0.160568
$859$	36028.7	1.43107	0.715533	−	0.698579i	$-0.246184\pi$
$859$	36028.7	1.43107	0.715533	+	0.698579i	$0.246184\pi$
$860$	11532.2	0.457261
$861$	−9207.77	−0.364460
$862$	18606.3	0.735187
$863$	−2976.99	−0.117425	−0.0587126	−	0.998275i	$-0.518700\pi$
$863$	−2976.99	−0.117425	−0.0587126	+	0.998275i	$0.518700\pi$
$864$	34446.7	1.35637
$865$	2211.74	0.0869380
$866$	34543.8	1.35548
$867$	−3509.52	−0.137473
$868$	−77354.8	−3.02488
$869$	38053.3	1.48547
$870$	1352.91	0.0527219
$871$	6341.43	0.246695
$872$	134116.	5.20843
$873$	−24430.3	−0.947126
$874$	47018.1	1.81969
$875$	−24128.0	−0.932202
$876$	6989.91	0.269597
$877$	36093.2	1.38972	0.694859	−	0.719146i	$-0.255467\pi$
$877$	36093.2	1.38972	0.694859	+	0.719146i	$0.255467\pi$
$878$	37105.6	1.42626
$879$	−3649.36	−0.140034
$880$	−34306.0	−1.31415
$881$	19482.8	0.745055	0.372527	−	0.928021i	$-0.378491\pi$
$881$	19482.8	0.745055	0.372527	+	0.928021i	$0.378491\pi$
$882$	47071.6	1.79703
$883$	−16351.6	−0.623190	−0.311595	−	0.950215i	$-0.600863\pi$
$883$	−16351.6	−0.623190	−0.311595	+	0.950215i	$0.600863\pi$
$884$	−15835.7	−0.602501
$885$	1467.98	0.0557577
$886$	−57793.3	−2.19143
$887$	−10969.7	−0.415250	−0.207625	−	0.978209i	$-0.566573\pi$
$887$	−10969.7	−0.415250	−0.207625	+	0.978209i	$0.566573\pi$
$888$	16296.0	0.615830
$889$	−18499.8	−0.697936
$890$	9519.92	0.358549
$891$	24579.6	0.924182
$892$	44320.4	1.66363
$893$	16175.3	0.606144
$894$	−6395.23	−0.239249
$895$	2211.55	0.0825964
$896$	108393.	4.04147
$897$	−2296.06	−0.0854664
$898$	65313.9	2.42712
$899$	8730.08	0.323876
$900$	61371.5	2.27302
$901$	−17238.8	−0.637412
$902$	−73426.0	−2.71044
$903$	3477.25	0.128146
$904$	−46786.7	−1.72135
$905$	4867.62	0.178790
$906$	−12874.8	−0.472116
$907$	−13226.0	−0.484192	−0.242096	−	0.970252i	$-0.577835\pi$
$907$	−13226.0	−0.484192	−0.242096	+	0.970252i	$0.577835\pi$
$908$	−126047.	−4.60685
$909$	−3192.72	−0.116497
$910$	−11085.5	−0.403825
$911$	23316.9	0.847993	0.423997	−	0.905664i	$-0.360627\pi$
$911$	23316.9	0.847993	0.423997	+	0.905664i	$0.360627\pi$
$912$	16793.2	0.609737
$913$	−45473.7	−1.64837
$914$	−60695.2	−2.19652
$915$	2747.62	0.0992717
$916$	−98846.2	−3.56547
$917$	−30973.0	−1.11540
$918$	−10601.9	−0.381170
$919$	−14311.1	−0.513689	−0.256844	−	0.966453i	$-0.582683\pi$
$919$	−14311.1	−0.513689	−0.256844	+	0.966453i	$0.582683\pi$
$920$	−34228.8	−1.22662
$921$	−3460.29	−0.123801
$922$	24169.5	0.863318
$923$	19801.9	0.706162
$924$	−21029.0	−0.748706
$925$	24314.1	0.864262
$926$	68443.1	2.42892
$927$	25590.4	0.906688
$928$	−41476.3	−1.46716
$929$	−36471.7	−1.28805	−0.644025	−	0.765004i	$-0.722737\pi$
$929$	−36471.7	−1.28805	−0.644025	+	0.765004i	$0.722737\pi$
$930$	2946.73	0.103900
$931$	24586.4	0.865505
$932$	−23487.7	−0.825500
$933$	3213.37	0.112756
$934$	10896.6	0.381742
$935$	5551.25	0.194166
$936$	38036.9	1.32828
$937$	12677.0	0.441986	0.220993	−	0.975275i	$-0.429070\pi$
$937$	12677.0	0.441986	0.220993	+	0.975275i	$0.429070\pi$
$938$	45295.5	1.57671
$939$	−362.080	−0.0125837
$940$	−18711.8	−0.649268
$941$	49899.3	1.72866	0.864332	−	0.502922i	$-0.167742\pi$
$941$	49899.3	1.72866	0.864332	+	0.502922i	$0.167742\pi$
$942$	−775.702	−0.0268299
$943$	−41777.5	−1.44270
$944$	−85598.1	−2.95125
$945$	−5414.55	−0.186386
$946$	27728.8	0.953003
$947$	−55179.7	−1.89345	−0.946726	−	0.322041i	$-0.895631\pi$
$947$	−55179.7	−1.89345	−0.946726	+	0.322041i	$0.895631\pi$
$948$	21548.6	0.738255
$949$	6463.79	0.221100
$950$	43938.1	1.50057
$951$	−9088.29	−0.309893
$952$	−71181.7	−2.42333
$953$	9335.51	0.317321	0.158660	−	0.987333i	$-0.449282\pi$
$953$	9335.51	0.317321	0.158660	+	0.987333i	$0.449282\pi$
$954$	65797.8	2.23300
$955$	5349.98	0.181279
$956$	140181.	4.74244
$957$	2373.29	0.0801645
$958$	−16690.7	−0.562893
$959$	−9848.93	−0.331636
$960$	−6798.53	−0.228564
$961$	−10776.4	−0.361732
$962$	23945.9	0.802544
$963$	−562.817	−0.0188334
$964$	33046.0	1.10409
$965$	6877.03	0.229409
$966$	−16400.3	−0.546243
$967$	−4987.96	−0.165876	−0.0829379	−	0.996555i	$-0.526430\pi$
$967$	−4987.96	−0.165876	−0.0829379	+	0.996555i	$0.526430\pi$
$968$	−7213.58	−0.239518
$969$	−2717.41	−0.0900885
$970$	20233.3	0.669744
$971$	−25594.5	−0.845898	−0.422949	−	0.906153i	$-0.639005\pi$
$971$	−25594.5	−0.845898	−0.422949	+	0.906153i	$0.639005\pi$
$972$	44557.0	1.47034
$973$	−15558.7	−0.512632
$974$	24929.7	0.820122
$975$	−2145.66	−0.0704779
$976$	−160214.	−5.25444
$977$	−36341.6	−1.19004	−0.595020	−	0.803711i	$-0.702856\pi$
$977$	−36341.6	−1.19004	−0.595020	+	0.803711i	$0.702856\pi$
$978$	−12592.6	−0.411724
$979$	16699.9	0.545179
$980$	−28441.8	−0.927081
$981$	47236.4	1.53735
$982$	−62069.5	−2.01702
$983$	28724.8	0.932023	0.466011	−	0.884779i	$-0.345691\pi$
$983$	28724.8	0.932023	0.466011	+	0.884779i	$0.345691\pi$
$984$	−26166.2	−0.847712
$985$	−5041.58	−0.163084
$986$	12765.4	0.412306
$987$	−5642.08	−0.181955
$988$	31570.1	1.01658
$989$	15777.0	0.507259
$990$	−21188.2	−0.680208
$991$	6723.12	0.215507	0.107753	−	0.994178i	$-0.465634\pi$
$991$	6723.12	0.215507	0.107753	+	0.994178i	$0.465634\pi$
$992$	−90337.8	−2.89136
$993$	−5423.58	−0.173325
$994$	141441.	4.51331
$995$	322.111	0.0102629
$996$	−25750.6	−0.819215
$997$	53452.5	1.69795	0.848975	−	0.528433i	$-0.177220\pi$
$997$	53452.5	1.69795	0.848975	+	0.528433i	$0.177220\pi$
$998$	32058.9	1.01684
$999$	11696.0	0.370417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1997.4.a.a.1.6	✓	239

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1997.4.a.a.1.6	✓	239	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:	\( N \)	\(=\)	\( 1997 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1997.a (trivial)

\(f(q)\)	\(=\)	\(q-5.43887 q^{2} +0.991773 q^{3} +21.5813 q^{4} -3.96164 q^{5} -5.39413 q^{6} -25.9935 q^{7} -73.8672 q^{8} -26.0164 q^{9} +O(q^{10})\)	\(q-5.43887 q^{2} +0.991773 q^{3} +21.5813 q^{4} -3.96164 q^{5} -5.39413 q^{6} -25.9935 q^{7} -73.8672 q^{8} -26.0164 q^{9} +21.5469 q^{10} +37.7976 q^{11} +21.4038 q^{12} +19.7928 q^{13} +141.375 q^{14} -3.92905 q^{15} +229.103 q^{16} -37.0725 q^{17} +141.500 q^{18} +73.9079 q^{19} -85.4975 q^{20} -25.7796 q^{21} -205.576 q^{22} -116.968 q^{23} -73.2594 q^{24} -109.305 q^{25} -107.650 q^{26} -52.5802 q^{27} -560.975 q^{28} +63.3102 q^{29} +21.3696 q^{30} +137.894 q^{31} -655.127 q^{32} +37.4866 q^{33} +201.633 q^{34} +102.977 q^{35} -561.468 q^{36} -222.442 q^{37} -401.976 q^{38} +19.6299 q^{39} +292.635 q^{40} +357.172 q^{41} +140.212 q^{42} -134.883 q^{43} +815.722 q^{44} +103.068 q^{45} +636.172 q^{46} +218.858 q^{47} +227.219 q^{48} +332.662 q^{49} +594.498 q^{50} -36.7675 q^{51} +427.154 q^{52} +465.003 q^{53} +285.977 q^{54} -149.740 q^{55} +1920.07 q^{56} +73.2998 q^{57} -344.336 q^{58} -373.622 q^{59} -84.7941 q^{60} -699.310 q^{61} -749.986 q^{62} +676.257 q^{63} +1730.33 q^{64} -78.4118 q^{65} -203.885 q^{66} +320.392 q^{67} -800.074 q^{68} -116.005 q^{69} -560.078 q^{70} +1000.46 q^{71} +1921.76 q^{72} +326.573 q^{73} +1209.83 q^{74} -108.406 q^{75} +1595.03 q^{76} -982.491 q^{77} -106.765 q^{78} +1006.77 q^{79} -907.625 q^{80} +650.295 q^{81} -1942.61 q^{82} -1203.09 q^{83} -556.359 q^{84} +146.868 q^{85} +733.613 q^{86} +62.7894 q^{87} -2792.00 q^{88} +441.824 q^{89} -560.571 q^{90} -514.483 q^{91} -2524.32 q^{92} +136.759 q^{93} -1190.34 q^{94} -292.797 q^{95} -649.737 q^{96} +939.036 q^{97} -1809.31 q^{98} -983.356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9} - 273 q^{10} - 294 q^{11} - 864 q^{12} - 797 q^{13} - 220 q^{14} - 580 q^{15} + 2816 q^{16} - 439 q^{17} - 536 q^{18} - 1704 q^{19} - 933 q^{20} - 596 q^{21} - 1046 q^{22} - 829 q^{23} - 1237 q^{24} + 4364 q^{25} - 818 q^{26} - 3670 q^{27} - 3690 q^{28} - 316 q^{29} - 888 q^{30} - 2595 q^{31} - 1881 q^{32} - 2066 q^{33} - 2605 q^{34} - 2450 q^{35} + 5863 q^{36} - 1912 q^{37} - 1709 q^{38} - 914 q^{39} - 3582 q^{40} - 1064 q^{41} - 3228 q^{42} - 5184 q^{43} - 2656 q^{44} - 3967 q^{45} - 2521 q^{46} - 4909 q^{47} - 7461 q^{48} + 7193 q^{49} - 1906 q^{50} - 3240 q^{51} - 9614 q^{52} - 2722 q^{53} - 3754 q^{54} - 6018 q^{55} - 2347 q^{56} - 2032 q^{57} - 6709 q^{58} - 6318 q^{59} - 5821 q^{60} - 2990 q^{61} - 2117 q^{62} - 8738 q^{63} + 6866 q^{64} - 1738 q^{65} - 3080 q^{66} - 14729 q^{67} - 3897 q^{68} - 2080 q^{69} - 7445 q^{70} - 3240 q^{71} - 8263 q^{72} - 8828 q^{73} - 3103 q^{74} - 12716 q^{75} - 14843 q^{76} - 3818 q^{77} - 8029 q^{78} - 4794 q^{79} - 10336 q^{80} + 11899 q^{81} - 13447 q^{82} - 11434 q^{83} - 7957 q^{84} - 8188 q^{85} - 5196 q^{86} - 11266 q^{87} - 11861 q^{88} - 4845 q^{89} - 7759 q^{90} - 12734 q^{91} - 8644 q^{92} - 10130 q^{93} - 6909 q^{94} - 3686 q^{95} - 11958 q^{96} - 16108 q^{97} - 6845 q^{98} - 12372 q^{99}+O(q^{100}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9 - 273 * q^10 - 294 * q^11 - 864 * q^12 - 797 * q^13 - 220 * q^14 - 580 * q^15 + 2816 * q^16 - 439 * q^17 - 536 * q^18 - 1704 * q^19 - 933 * q^20 - 596 * q^21 - 1046 * q^22 - 829 * q^23 - 1237 * q^24 + 4364 * q^25 - 818 * q^26 - 3670 * q^27 - 3690 * q^28 - 316 * q^29 - 888 * q^30 - 2595 * q^31 - 1881 * q^32 - 2066 * q^33 - 2605 * q^34 - 2450 * q^35 + 5863 * q^36 - 1912 * q^37 - 1709 * q^38 - 914 * q^39 - 3582 * q^40 - 1064 * q^41 - 3228 * q^42 - 5184 * q^43 - 2656 * q^44 - 3967 * q^45 - 2521 * q^46 - 4909 * q^47 - 7461 * q^48 + 7193 * q^49 - 1906 * q^50 - 3240 * q^51 - 9614 * q^52 - 2722 * q^53 - 3754 * q^54 - 6018 * q^55 - 2347 * q^56 - 2032 * q^57 - 6709 * q^58 - 6318 * q^59 - 5821 * q^60 - 2990 * q^61 - 2117 * q^62 - 8738 * q^63 + 6866 * q^64 - 1738 * q^65 - 3080 * q^66 - 14729 * q^67 - 3897 * q^68 - 2080 * q^69 - 7445 * q^70 - 3240 * q^71 - 8263 * q^72 - 8828 * q^73 - 3103 * q^74 - 12716 * q^75 - 14843 * q^76 - 3818 * q^77 - 8029 * q^78 - 4794 * q^79 - 10336 * q^80 + 11899 * q^81 - 13447 * q^82 - 11434 * q^83 - 7957 * q^84 - 8188 * q^85 - 5196 * q^86 - 11266 * q^87 - 11861 * q^88 - 4845 * q^89 - 7759 * q^90 - 12734 * q^91 - 8644 * q^92 - 10130 * q^93 - 6909 * q^94 - 3686 * q^95 - 11958 * q^96 - 16108 * q^97 - 6845 * q^98 - 12372 * q^99

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