LMFDB - Embedded newform 1997.4.a.a.1.5

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			1.5
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)

$f(q)$	$=$	$q-5.50179 q^{2} +8.24154 q^{3} +22.2697 q^{4} -8.43995 q^{5} -45.3433 q^{6} -6.56247 q^{7} -78.5092 q^{8} +40.9229 q^{9} +O(q^{10})$	\(q-5.50179 q^{2} +8.24154 q^{3} +22.2697 q^{4} -8.43995 q^{5} -45.3433 q^{6} -6.56247 q^{7} -78.5092 q^{8} +40.9229 q^{9} +46.4349 q^{10} +19.5455 q^{11} +183.537 q^{12} -45.7908 q^{13} +36.1053 q^{14} -69.5582 q^{15} +253.784 q^{16} +41.1224 q^{17} -225.150 q^{18} +121.949 q^{19} -187.956 q^{20} -54.0848 q^{21} -107.536 q^{22} +88.0831 q^{23} -647.037 q^{24} -53.7672 q^{25} +251.932 q^{26} +114.747 q^{27} -146.144 q^{28} +38.4431 q^{29} +382.695 q^{30} -201.902 q^{31} -768.192 q^{32} +161.085 q^{33} -226.247 q^{34} +55.3869 q^{35} +911.344 q^{36} -158.773 q^{37} -670.940 q^{38} -377.387 q^{39} +662.614 q^{40} -478.060 q^{41} +297.564 q^{42} -232.214 q^{43} +435.274 q^{44} -345.388 q^{45} -484.615 q^{46} -99.6018 q^{47} +2091.57 q^{48} -299.934 q^{49} +295.816 q^{50} +338.912 q^{51} -1019.75 q^{52} +603.578 q^{53} -631.312 q^{54} -164.963 q^{55} +515.214 q^{56} +1005.05 q^{57} -211.506 q^{58} +24.7330 q^{59} -1549.04 q^{60} +570.240 q^{61} +1110.83 q^{62} -268.555 q^{63} +2196.16 q^{64} +386.472 q^{65} -886.258 q^{66} -265.033 q^{67} +915.785 q^{68} +725.940 q^{69} -304.727 q^{70} +275.513 q^{71} -3212.83 q^{72} +495.989 q^{73} +873.538 q^{74} -443.125 q^{75} +2715.78 q^{76} -128.267 q^{77} +2076.30 q^{78} +207.953 q^{79} -2141.92 q^{80} -159.232 q^{81} +2630.19 q^{82} -119.603 q^{83} -1204.46 q^{84} -347.071 q^{85} +1277.59 q^{86} +316.830 q^{87} -1534.51 q^{88} -535.896 q^{89} +1900.25 q^{90} +300.501 q^{91} +1961.59 q^{92} -1663.99 q^{93} +547.988 q^{94} -1029.25 q^{95} -6331.08 q^{96} -1460.06 q^{97} +1650.18 q^{98} +799.861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.50179	−1.94518	−0.972589	−	0.232531i	$-0.925299\pi$
$2$	−5.50179	−1.94518	−0.972589	+	0.232531i	$0.925299\pi$
$3$	8.24154	1.58608	0.793042	−	0.609166i	$-0.208496\pi$
$3$	8.24154	1.58608	0.793042	+	0.609166i	$0.208496\pi$
$4$	22.2697	2.78372
$5$	−8.43995	−0.754892	−0.377446	−	0.926032i	$-0.623198\pi$
$5$	−8.43995	−0.754892	−0.377446	+	0.926032i	$0.623198\pi$
$6$	−45.3433	−3.08522
$7$	−6.56247	−0.354340	−0.177170	−	0.984180i	$-0.556694\pi$
$7$	−6.56247	−0.354340	−0.177170	+	0.984180i	$0.556694\pi$
$8$	−78.5092	−3.46965
$9$	40.9229	1.51566
$10$	46.4349	1.46840
$11$	19.5455	0.535746	0.267873	−	0.963454i	$-0.413679\pi$
$11$	19.5455	0.535746	0.267873	+	0.963454i	$0.413679\pi$
$12$	183.537	4.41521
$13$	−45.7908	−0.976930	−0.488465	−	0.872583i	$-0.662443\pi$
$13$	−45.7908	−0.976930	−0.488465	+	0.872583i	$0.662443\pi$
$14$	36.1053	0.689254
$15$	−69.5582	−1.19732
$16$	253.784	3.96537
$17$	41.1224	0.586685	0.293343	−	0.956007i	$-0.405232\pi$
$17$	41.1224	0.586685	0.293343	+	0.956007i	$0.405232\pi$
$18$	−225.150	−2.94824
$19$	121.949	1.47248	0.736239	−	0.676721i	$-0.236600\pi$
$19$	121.949	1.47248	0.736239	+	0.676721i	$0.236600\pi$
$20$	−187.956	−2.10141
$21$	−54.0848	−0.562013
$22$	−107.536	−1.04212
$23$	88.0831	0.798548	0.399274	−	0.916832i	$-0.369262\pi$
$23$	88.0831	0.798548	0.399274	+	0.916832i	$0.369262\pi$
$24$	−647.037	−5.50316
$25$	−53.7672	−0.430138
$26$	251.932	1.90030
$27$	114.747	0.817888
$28$	−146.144	−0.986382
$29$	38.4431	0.246162	0.123081	−	0.992397i	$-0.460722\pi$
$29$	38.4431	0.246162	0.123081	+	0.992397i	$0.460722\pi$
$30$	382.695	2.32901
$31$	−201.902	−1.16977	−0.584883	−	0.811118i	$-0.698860\pi$
$31$	−201.902	−1.16977	−0.584883	+	0.811118i	$0.698860\pi$
$32$	−768.192	−4.24370
$33$	161.085	0.849738
$34$	−226.247	−1.14121
$35$	55.3869	0.267488
$36$	911.344	4.21918
$37$	−158.773	−0.705464	−0.352732	−	0.935724i	$-0.614747\pi$
$37$	−158.773	−0.705464	−0.352732	+	0.935724i	$0.614747\pi$
$38$	−670.940	−2.86423
$39$	−377.387	−1.54949
$40$	662.614	2.61921
$41$	−478.060	−1.82098	−0.910492	−	0.413526i	$-0.864297\pi$
$41$	−478.060	−1.82098	−0.910492	+	0.413526i	$0.864297\pi$
$42$	297.564	1.09322
$43$	−232.214	−0.823542	−0.411771	−	0.911287i	$-0.635090\pi$
$43$	−232.214	−0.823542	−0.411771	+	0.911287i	$0.635090\pi$
$44$	435.274	1.49137
$45$	−345.388	−1.14416
$46$	−484.615	−1.55332
$47$	−99.6018	−0.309115	−0.154558	−	0.987984i	$-0.549395\pi$
$47$	−99.6018	−0.309115	−0.154558	+	0.987984i	$0.549395\pi$
$48$	2091.57	6.28941
$49$	−299.934	−0.874443
$50$	295.816	0.836695
$51$	338.912	0.930532
$52$	−1019.75	−2.71950
$53$	603.578	1.56430	0.782149	−	0.623092i	$-0.214124\pi$
$53$	603.578	1.56430	0.782149	+	0.623092i	$0.214124\pi$
$54$	−631.312	−1.59094
$55$	−164.963	−0.404430
$56$	515.214	1.22944
$57$	1005.05	2.33548
$58$	−211.506	−0.478830
$59$	24.7330	0.0545756	0.0272878	−	0.999628i	$-0.491313\pi$
$59$	24.7330	0.0545756	0.0272878	+	0.999628i	$0.491313\pi$
$60$	−1549.04	−3.33301
$61$	570.240	1.19691	0.598457	−	0.801155i	$-0.295781\pi$
$61$	570.240	1.19691	0.598457	+	0.801155i	$0.295781\pi$
$62$	1110.83	2.27540
$63$	−268.555	−0.537060
$64$	2196.16	4.28938
$65$	386.472	0.737477
$66$	−886.258	−1.65289
$67$	−265.033	−0.483267	−0.241633	−	0.970368i	$-0.577683\pi$
$67$	−265.033	−0.483267	−0.241633	+	0.970368i	$0.577683\pi$
$68$	915.785	1.63317
$69$	725.940	1.26656
$70$	−304.727	−0.520313
$71$	275.513	0.460527	0.230263	−	0.973128i	$-0.426041\pi$
$71$	275.513	0.460527	0.230263	+	0.973128i	$0.426041\pi$
$72$	−3212.83	−5.25883
$73$	495.989	0.795221	0.397610	−	0.917554i	$-0.369840\pi$
$73$	495.989	0.795221	0.397610	+	0.917554i	$0.369840\pi$
$74$	873.538	1.37225
$75$	−443.125	−0.682235
$76$	2715.78	4.09897
$77$	−128.267	−0.189836
$78$	2076.30	3.01404
$79$	207.953	0.296159	0.148080	−	0.988975i	$-0.452691\pi$
$79$	207.953	0.296159	0.148080	+	0.988975i	$0.452691\pi$
$80$	−2141.92	−2.99343
$81$	−159.232	−0.218425
$82$	2630.19	3.54214
$83$	−119.603	−0.158170	−0.0790850	−	0.996868i	$-0.525200\pi$
$83$	−119.603	−0.158170	−0.0790850	+	0.996868i	$0.525200\pi$
$84$	−1204.46	−1.56449
$85$	−347.071	−0.442884
$86$	1277.59	1.60194
$87$	316.830	0.390434
$88$	−1534.51	−1.85885
$89$	−535.896	−0.638257	−0.319129	−	0.947711i	$-0.603390\pi$
$89$	−535.896	−0.638257	−0.319129	+	0.947711i	$0.603390\pi$
$90$	1900.25	2.22560
$91$	300.501	0.346165
$92$	1961.59	2.22293
$93$	−1663.99	−1.85535
$94$	547.988	0.601284
$95$	−1029.25	−1.11156
$96$	−6331.08	−6.73087
$97$	−1460.06	−1.52831	−0.764157	−	0.645031i	$-0.776845\pi$
$97$	−1460.06	−1.52831	−0.764157	+	0.645031i	$0.776845\pi$
$98$	1650.18	1.70095
$99$	799.861	0.812011
$100$	−1197.38	−1.19738
$101$	−169.363	−0.166854	−0.0834272	−	0.996514i	$-0.526587\pi$
$101$	−169.363	−0.166854	−0.0834272	+	0.996514i	$0.526587\pi$
$102$	−1864.62	−1.81005
$103$	−843.627	−0.807039	−0.403520	−	0.914971i	$-0.632213\pi$
$103$	−843.627	−0.807039	−0.403520	+	0.914971i	$0.632213\pi$
$104$	3595.00	3.38960
$105$	456.473	0.424259
$106$	−3320.76	−3.04284
$107$	370.637	0.334867	0.167434	−	0.985883i	$-0.446452\pi$
$107$	370.637	0.334867	0.167434	+	0.985883i	$0.446452\pi$
$108$	2555.38	2.27677
$109$	813.585	0.714930	0.357465	−	0.933927i	$-0.383641\pi$
$109$	813.585	0.714930	0.357465	+	0.933927i	$0.383641\pi$
$110$	907.595	0.786689
$111$	−1308.54	−1.11893
$112$	−1665.45	−1.40509
$113$	1562.08	1.30042	0.650211	−	0.759753i	$-0.274680\pi$
$113$	1562.08	1.30042	0.650211	+	0.759753i	$0.274680\pi$
$114$	−5529.58	−4.54292
$115$	−743.417	−0.602817
$116$	856.118	0.685247
$117$	−1873.90	−1.48070
$118$	−136.076	−0.106159
$119$	−269.864	−0.207886
$120$	5460.96	4.15429
$121$	−948.972	−0.712977
$122$	−3137.34	−2.32821
$123$	−3939.95	−2.88824
$124$	−4496.31	−3.25630
$125$	1508.79	1.07960
$126$	1477.54	1.04468
$127$	2127.94	1.48681	0.743403	−	0.668844i	$-0.233210\pi$
$127$	2127.94	1.48681	0.743403	+	0.668844i	$0.233210\pi$
$128$	−5937.31	−4.09991
$129$	−1913.80	−1.30621
$130$	−2126.29	−1.43452
$131$	−724.799	−0.483404	−0.241702	−	0.970350i	$-0.577706\pi$
$131$	−724.799	−0.483404	−0.241702	+	0.970350i	$0.577706\pi$
$132$	3587.33	2.36543
$133$	−800.288	−0.521758
$134$	1458.15	0.940040
$135$	−968.455	−0.617417
$136$	−3228.49	−2.03559
$137$	−588.746	−0.367153	−0.183576	−	0.983005i	$-0.558767\pi$
$137$	−588.746	−0.367153	−0.183576	+	0.983005i	$0.558767\pi$
$138$	−3993.97	−2.46369
$139$	71.9117	0.0438811	0.0219406	−	0.999759i	$-0.493016\pi$
$139$	71.9117	0.0438811	0.0219406	+	0.999759i	$0.493016\pi$
$140$	1233.45	0.744612
$141$	−820.872	−0.490283
$142$	−1515.82	−0.895807
$143$	−895.007	−0.523386
$144$	10385.6	6.01017
$145$	−324.458	−0.185826
$146$	−2728.83	−1.54685
$147$	−2471.92	−1.38694
$148$	−3535.84	−1.96381
$149$	455.840	0.250630	0.125315	−	0.992117i	$-0.460006\pi$
$149$	455.840	0.250630	0.125315	+	0.992117i	$0.460006\pi$
$150$	2437.98	1.32707
$151$	−1445.46	−0.779006	−0.389503	−	0.921025i	$-0.627353\pi$
$151$	−1445.46	−0.779006	−0.389503	+	0.921025i	$0.627353\pi$
$152$	−9574.15	−5.10899
$153$	1682.85	0.889218
$154$	705.698	0.369265
$155$	1704.05	0.883047
$156$	−8404.31	−4.31335
$157$	−2997.71	−1.52384	−0.761922	−	0.647669i	$-0.775744\pi$
$157$	−2997.71	−1.52384	−0.761922	+	0.647669i	$0.775744\pi$
$158$	−1144.12	−0.576082
$159$	4974.41	2.48111
$160$	6483.50	3.20353
$161$	−578.042	−0.282957
$162$	876.061	0.424876
$163$	−1926.91	−0.925932	−0.462966	−	0.886376i	$-0.653215\pi$
$163$	−1926.91	−0.925932	−0.462966	+	0.886376i	$0.653215\pi$
$164$	−10646.3	−5.06911
$165$	−1359.55	−0.641461
$166$	658.030	0.307669
$167$	860.921	0.398923	0.199461	−	0.979906i	$-0.436081\pi$
$167$	860.921	0.398923	0.199461	+	0.979906i	$0.436081\pi$
$168$	4246.16	1.94999
$169$	−100.200	−0.0456077
$170$	1909.51	0.861488
$171$	4990.53	2.23178
$172$	−5171.35	−2.29251
$173$	2166.57	0.952148	0.476074	−	0.879405i	$-0.342059\pi$
$173$	2166.57	0.952148	0.476074	+	0.879405i	$0.342059\pi$
$174$	−1743.14	−0.759464
$175$	352.846	0.152415
$176$	4960.34	2.12443
$177$	203.838	0.0865616
$178$	2948.39	1.24152
$179$	2980.07	1.24436	0.622181	−	0.782873i	$-0.286247\pi$
$179$	2980.07	1.24436	0.622181	+	0.782873i	$0.286247\pi$
$180$	−7691.70	−3.18503
$181$	1364.60	0.560386	0.280193	−	0.959944i	$-0.409602\pi$
$181$	1364.60	0.560386	0.280193	+	0.959944i	$0.409602\pi$
$182$	−1653.29	−0.673353
$183$	4699.66	1.89841
$184$	−6915.33	−2.77068
$185$	1340.04	0.532549
$186$	9154.91	3.60898
$187$	803.759	0.314314
$188$	−2218.11	−0.860489
$189$	−753.020	−0.289810
$190$	5662.70	2.16219
$191$	−3542.07	−1.34186	−0.670929	−	0.741521i	$-0.734105\pi$
$191$	−3542.07	−1.34186	−0.670929	+	0.741521i	$0.734105\pi$
$192$	18099.8	6.80332
$193$	−4349.57	−1.62222	−0.811111	−	0.584893i	$-0.801137\pi$
$193$	−4349.57	−1.62222	−0.811111	+	0.584893i	$0.801137\pi$
$194$	8032.94	2.97284
$195$	3185.13	1.16970
$196$	−6679.45	−2.43420
$197$	−741.944	−0.268331	−0.134166	−	0.990959i	$-0.542835\pi$
$197$	−741.944	−0.268331	−0.134166	+	0.990959i	$0.542835\pi$
$198$	−4400.67	−1.57951
$199$	3174.72	1.13090	0.565452	−	0.824781i	$-0.308702\pi$
$199$	3174.72	1.13090	0.565452	+	0.824781i	$0.308702\pi$
$200$	4221.22	1.49243
$201$	−2184.28	−0.766502
$202$	931.803	0.324562
$203$	−252.282	−0.0872251
$204$	7547.48	2.59034
$205$	4034.80	1.37465
$206$	4641.46	1.56984
$207$	3604.62	1.21033
$208$	−11621.0	−3.87389
$209$	2383.57	0.788874
$210$	−2511.42	−0.825260
$211$	−2486.78	−0.811360	−0.405680	−	0.914015i	$-0.632965\pi$
$211$	−2486.78	−0.811360	−0.405680	+	0.914015i	$0.632965\pi$
$212$	13441.5	4.35456
$213$	2270.65	0.730435
$214$	−2039.17	−0.651377
$215$	1959.87	0.621685
$216$	−9008.66	−2.83778
$217$	1324.98	0.414495
$218$	−4476.18	−1.39067
$219$	4087.71	1.26129
$220$	−3673.69	−1.12582
$221$	−1883.03	−0.573150
$222$	7199.30	2.17651
$223$	−4318.15	−1.29670	−0.648351	−	0.761342i	$-0.724541\pi$
$223$	−4318.15	−1.29670	−0.648351	+	0.761342i	$0.724541\pi$
$224$	5041.23	1.50371
$225$	−2200.31	−0.651945
$226$	−8594.22	−2.52955
$227$	1200.98	0.351154	0.175577	−	0.984466i	$-0.443821\pi$
$227$	1200.98	0.351154	0.175577	+	0.984466i	$0.443821\pi$
$228$	22382.2	6.50131
$229$	2473.23	0.713693	0.356847	−	0.934163i	$-0.383852\pi$
$229$	2473.23	0.713693	0.356847	+	0.934163i	$0.383852\pi$
$230$	4090.13	1.17259
$231$	−1057.12	−0.301096
$232$	−3018.14	−0.854097
$233$	−341.548	−0.0960325	−0.0480162	−	0.998847i	$-0.515290\pi$
$233$	−341.548	−0.0960325	−0.0480162	+	0.998847i	$0.515290\pi$
$234$	10309.8	2.88022
$235$	840.634	0.233349
$236$	550.797	0.151923
$237$	1713.85	0.469733
$238$	1484.74	0.404375
$239$	5091.95	1.37812	0.689060	−	0.724704i	$-0.258024\pi$
$239$	5091.95	1.37812	0.689060	+	0.724704i	$0.258024\pi$
$240$	−17652.7	−4.74783
$241$	−6151.99	−1.64433	−0.822167	−	0.569246i	$-0.807235\pi$
$241$	−6151.99	−1.64433	−0.822167	+	0.569246i	$0.807235\pi$
$242$	5221.05	1.38687
$243$	−4410.47	−1.16433
$244$	12699.1	3.33187
$245$	2531.43	0.660110
$246$	21676.8	5.61813
$247$	−5584.16	−1.43851
$248$	15851.2	4.05868
$249$	−985.710	−0.250871
$250$	−8301.03	−2.10001
$251$	−2347.33	−0.590288	−0.295144	−	0.955453i	$-0.595368\pi$
$251$	−2347.33	−0.590288	−0.295144	+	0.955453i	$0.595368\pi$
$252$	−5980.66	−1.49502
$253$	1721.63	0.427818
$254$	−11707.5	−2.89210
$255$	−2860.40	−0.702451
$256$	15096.5	3.68568
$257$	−4154.58	−1.00839	−0.504194	−	0.863590i	$-0.668210\pi$
$257$	−4154.58	−1.00839	−0.504194	+	0.863590i	$0.668210\pi$
$258$	10529.3	2.54081
$259$	1041.94	0.249974
$260$	8606.64	2.05293
$261$	1573.21	0.373100
$262$	3987.69	0.940308
$263$	−3930.71	−0.921589	−0.460795	−	0.887507i	$-0.652436\pi$
$263$	−3930.71	−0.921589	−0.460795	+	0.887507i	$0.652436\pi$
$264$	−12646.7	−2.94829
$265$	−5094.16	−1.18088
$266$	4403.02	1.01491
$267$	−4416.61	−1.01233
$268$	−5902.21	−1.34528
$269$	−121.065	−0.0274405	−0.0137202	−	0.999906i	$-0.504367\pi$
$269$	−121.065	−0.0274405	−0.0137202	+	0.999906i	$0.504367\pi$
$270$	5328.24	1.20099
$271$	2456.65	0.550666	0.275333	−	0.961349i	$-0.411212\pi$
$271$	2456.65	0.550666	0.275333	+	0.961349i	$0.411212\pi$
$272$	10436.2	2.32642
$273$	2476.59	0.549047
$274$	3239.16	0.714178
$275$	−1050.91	−0.230444
$276$	16166.5	3.52576
$277$	−5791.64	−1.25627	−0.628134	−	0.778105i	$-0.716181\pi$
$277$	−5791.64	−1.25627	−0.628134	+	0.778105i	$0.716181\pi$
$278$	−395.644	−0.0853566
$279$	−8262.44	−1.77297
$280$	−4348.38	−0.928091
$281$	−616.432	−0.130866	−0.0654328	−	0.997857i	$-0.520843\pi$
$281$	−616.432	−0.130866	−0.0654328	+	0.997857i	$0.520843\pi$
$282$	4516.27	0.953687
$283$	−6359.02	−1.33570	−0.667852	−	0.744294i	$-0.732786\pi$
$283$	−6359.02	−1.33570	−0.667852	+	0.744294i	$0.732786\pi$
$284$	6135.61	1.28198
$285$	−8482.57	−1.76303
$286$	4924.14	1.01808
$287$	3137.25	0.645248
$288$	−31436.7	−6.43202
$289$	−3221.95	−0.655801
$290$	1785.10	0.361465
$291$	−12033.1	−2.42403
$292$	11045.5	2.21367
$293$	−8440.87	−1.68301	−0.841503	−	0.540252i	$-0.818329\pi$
$293$	−8440.87	−1.68301	−0.841503	+	0.540252i	$0.818329\pi$
$294$	13600.0	2.69785
$295$	−208.745	−0.0411987
$296$	12465.2	2.44771
$297$	2242.78	0.438180
$298$	−2507.94	−0.487520
$299$	−4033.40	−0.780125
$300$	−9868.27	−1.89915
$301$	1523.90	0.291814
$302$	7952.63	1.51531
$303$	−1395.82	−0.264645
$304$	30948.7	5.83892
$305$	−4812.80	−0.903541
$306$	−9258.69	−1.72969
$307$	830.065	0.154314	0.0771569	−	0.997019i	$-0.475416\pi$
$307$	830.065	0.154314	0.0771569	+	0.997019i	$0.475416\pi$
$308$	−2856.47	−0.528450
$309$	−6952.79	−1.28003
$310$	−9375.31	−1.71768
$311$	−4209.90	−0.767594	−0.383797	−	0.923417i	$-0.625384\pi$
$311$	−4209.90	−0.767594	−0.383797	+	0.923417i	$0.625384\pi$
$312$	29628.3	5.37620
$313$	−8140.73	−1.47010	−0.735050	−	0.678013i	$-0.762841\pi$
$313$	−8140.73	−1.47010	−0.735050	+	0.678013i	$0.762841\pi$
$314$	16492.8	2.96415
$315$	2266.59	0.405423
$316$	4631.07	0.824424
$317$	−370.432	−0.0656325	−0.0328163	−	0.999461i	$-0.510448\pi$
$317$	−370.432	−0.0656325	−0.0328163	+	0.999461i	$0.510448\pi$
$318$	−27368.2	−4.82620
$319$	751.392	0.131880
$320$	−18535.5	−3.23802
$321$	3054.62	0.531128
$322$	3180.27	0.550402
$323$	5014.85	0.863881
$324$	−3546.05	−0.608034
$325$	2462.05	0.420215
$326$	10601.4	1.80110
$327$	6705.19	1.13394
$328$	37532.1	6.31818
$329$	653.633	0.109532
$330$	7479.98	1.24776
$331$	8048.14	1.33645	0.668226	−	0.743958i	$-0.267054\pi$
$331$	8048.14	1.33645	0.668226	+	0.743958i	$0.267054\pi$
$332$	−2663.52	−0.440300
$333$	−6497.47	−1.06925
$334$	−4736.61	−0.775976
$335$	2236.86	0.364814
$336$	−13725.8	−2.22859
$337$	171.056	0.0276500	0.0138250	−	0.999904i	$-0.495599\pi$
$337$	171.056	0.0276500	0.0138250	+	0.999904i	$0.495599\pi$
$338$	551.280	0.0887150
$339$	12873.9	2.06258
$340$	−7729.18	−1.23286
$341$	−3946.29	−0.626697
$342$	−27456.9	−4.34122
$343$	4219.23	0.664190
$344$	18230.9	2.85740
$345$	−6126.90	−0.956119
$346$	−11920.0	−1.85210
$347$	−5402.02	−0.835723	−0.417861	−	0.908511i	$-0.637220\pi$
$347$	−5402.02	−0.835723	−0.417861	+	0.908511i	$0.637220\pi$
$348$	7055.73	1.08686
$349$	10113.6	1.55121	0.775603	−	0.631221i	$-0.217446\pi$
$349$	10113.6	1.55121	0.775603	+	0.631221i	$0.217446\pi$
$350$	−1941.28	−0.296474
$351$	−5254.34	−0.799019
$352$	−15014.7	−2.27354
$353$	−6309.13	−0.951278	−0.475639	−	0.879641i	$-0.657783\pi$
$353$	−6309.13	−0.951278	−0.475639	+	0.879641i	$0.657783\pi$
$354$	−1121.47	−0.168378
$355$	−2325.32	−0.347648
$356$	−11934.3	−1.77673
$357$	−2224.10	−0.329725
$358$	−16395.7	−2.42051
$359$	−4451.93	−0.654495	−0.327247	−	0.944939i	$-0.606121\pi$
$359$	−4451.93	−0.654495	−0.327247	+	0.944939i	$0.606121\pi$
$360$	27116.1	3.96985
$361$	8012.64	1.16819
$362$	−7507.74	−1.09005
$363$	−7820.99	−1.13084
$364$	6692.08	0.963627
$365$	−4186.12	−0.600306
$366$	−25856.5	−3.69274
$367$	−1142.37	−0.162483	−0.0812413	−	0.996694i	$-0.525888\pi$
$367$	−1142.37	−0.162483	−0.0812413	+	0.996694i	$0.525888\pi$
$368$	22354.0	3.16654
$369$	−19563.6	−2.76000
$370$	−7372.62	−1.03590
$371$	−3960.96	−0.554293
$372$	−37056.5	−5.16476
$373$	−2799.07	−0.388553	−0.194276	−	0.980947i	$-0.562236\pi$
$373$	−2799.07	−0.388553	−0.194276	+	0.980947i	$0.562236\pi$
$374$	−4422.12	−0.611397
$375$	12434.7	1.71234
$376$	7819.66	1.07252
$377$	−1760.34	−0.240483
$378$	4142.96	0.563733
$379$	−1945.37	−0.263660	−0.131830	−	0.991272i	$-0.542085\pi$
$379$	−1945.37	−0.263660	−0.131830	+	0.991272i	$0.542085\pi$
$380$	−22921.1	−3.09428
$381$	17537.5	2.35820
$382$	19487.7	2.61015
$383$	−2133.11	−0.284586	−0.142293	−	0.989825i	$-0.545448\pi$
$383$	−2133.11	−0.284586	−0.142293	+	0.989825i	$0.545448\pi$
$384$	−48932.6	−6.50281
$385$	1082.57	0.143306
$386$	23930.4	3.15551
$387$	−9502.88	−1.24821
$388$	−32515.1	−4.25439
$389$	14531.4	1.89402	0.947010	−	0.321205i	$-0.104088\pi$
$389$	14531.4	1.89402	0.947010	+	0.321205i	$0.104088\pi$
$390$	−17523.9	−2.27528
$391$	3622.19	0.468496
$392$	23547.6	3.03401
$393$	−5973.46	−0.766720
$394$	4082.02	0.521953
$395$	−1755.12	−0.223568
$396$	17812.7	2.26041
$397$	−6232.15	−0.787866	−0.393933	−	0.919139i	$-0.628886\pi$
$397$	−6232.15	−0.787866	−0.393933	+	0.919139i	$0.628886\pi$
$398$	−17466.7	−2.19981
$399$	−6595.61	−0.827552
$400$	−13645.2	−1.70565
$401$	6673.47	0.831065	0.415533	−	0.909578i	$-0.363595\pi$
$401$	6673.47	0.831065	0.415533	+	0.909578i	$0.363595\pi$
$402$	12017.4	1.49098
$403$	9245.28	1.14278
$404$	−3771.68	−0.464476
$405$	1343.91	0.164887
$406$	1388.00	0.169668
$407$	−3103.31	−0.377949
$408$	−26607.7	−3.22862
$409$	8687.79	1.05033	0.525163	−	0.851002i	$-0.324004\pi$
$409$	8687.79	1.05033	0.525163	+	0.851002i	$0.324004\pi$
$410$	−22198.6	−2.67393
$411$	−4852.17	−0.582336
$412$	−18787.4	−2.24657
$413$	−162.309	−0.0193383
$414$	−19831.9	−2.35431
$415$	1009.44	0.119401
$416$	35176.1	4.14580
$417$	592.663	0.0695991
$418$	−13113.9	−1.53450
$419$	−11638.3	−1.35696	−0.678481	−	0.734618i	$-0.737361\pi$
$419$	−11638.3	−1.35696	−0.678481	+	0.734618i	$0.737361\pi$
$420$	10165.5	1.18102
$421$	−15043.3	−1.74148	−0.870741	−	0.491741i	$-0.836361\pi$
$421$	−15043.3	−1.74148	−0.870741	+	0.491741i	$0.836361\pi$
$422$	13681.8	1.57824
$423$	−4076.00	−0.468515
$424$	−47386.4	−5.42756
$425$	−2211.04	−0.252355
$426$	−12492.7	−1.42083
$427$	−3742.18	−0.424114
$428$	8253.99	0.932176
$429$	−7376.23	−0.830135
$430$	−10782.8	−1.20929
$431$	9191.65	1.02725	0.513627	−	0.858014i	$-0.328302\pi$
$431$	9191.65	1.02725	0.513627	+	0.858014i	$0.328302\pi$
$432$	29120.8	3.24323
$433$	−17705.0	−1.96500	−0.982502	−	0.186251i	$-0.940366\pi$
$433$	−17705.0	−1.96500	−0.982502	+	0.186251i	$0.940366\pi$
$434$	−7289.75	−0.806266
$435$	−2674.03	−0.294736
$436$	18118.3	1.99016
$437$	10741.7	1.17584
$438$	−22489.7	−2.45343
$439$	−1990.77	−0.216433	−0.108217	−	0.994127i	$-0.534514\pi$
$439$	−1990.77	−0.216433	−0.108217	+	0.994127i	$0.534514\pi$
$440$	12951.1	1.40323
$441$	−12274.2	−1.32536
$442$	10360.0	1.11488
$443$	−1173.54	−0.125861	−0.0629307	−	0.998018i	$-0.520045\pi$
$443$	−1173.54	−0.125861	−0.0629307	+	0.998018i	$0.520045\pi$
$444$	−29140.8	−3.11477
$445$	4522.94	0.481816
$446$	23757.6	2.52232
$447$	3756.83	0.397521
$448$	−14412.2	−1.51990
$449$	−12365.5	−1.29970	−0.649850	−	0.760063i	$-0.725168\pi$
$449$	−12365.5	−1.29970	−0.649850	+	0.760063i	$0.725168\pi$
$450$	12105.7	1.26815
$451$	−9343.94	−0.975585
$452$	34787.0	3.62001
$453$	−11912.8	−1.23557
$454$	−6607.55	−0.683056
$455$	−2536.21	−0.261317
$456$	−78905.7	−8.10328
$457$	−2594.27	−0.265546	−0.132773	−	0.991146i	$-0.542388\pi$
$457$	−2594.27	−0.265546	−0.132773	+	0.991146i	$0.542388\pi$
$458$	−13607.2	−1.38826
$459$	4718.65	0.479843
$460$	−16555.7	−1.67807
$461$	6691.09	0.675998	0.337999	−	0.941147i	$-0.390250\pi$
$461$	6691.09	0.675998	0.337999	+	0.941147i	$0.390250\pi$
$462$	5816.04	0.585686
$463$	−7003.69	−0.703000	−0.351500	−	0.936188i	$-0.614328\pi$
$463$	−7003.69	−0.703000	−0.351500	+	0.936188i	$0.614328\pi$
$464$	9756.23	0.976124
$465$	14044.0	1.40059
$466$	1879.13	0.186800
$467$	19585.0	1.94065	0.970326	−	0.241800i	$-0.0777379\pi$
$467$	19585.0	1.94065	0.970326	+	0.241800i	$0.0777379\pi$
$468$	−41731.2	−4.12185
$469$	1739.27	0.171241
$470$	−4625.00	−0.453905
$471$	−24705.8	−2.41694
$472$	−1941.77	−0.189358
$473$	−4538.75	−0.441209
$474$	−9429.28	−0.913715
$475$	−6556.88	−0.633369
$476$	−6009.81	−0.578696
$477$	24700.2	2.37095
$478$	−28014.8	−2.68069
$479$	−13949.9	−1.33067	−0.665333	−	0.746546i	$-0.731711\pi$
$479$	−13949.9	−1.33067	−0.665333	+	0.746546i	$0.731711\pi$
$480$	53434.0	5.08108
$481$	7270.36	0.689189
$482$	33847.0	3.19852
$483$	−4763.96	−0.448794
$484$	−21133.4	−1.98473
$485$	12322.8	1.15371
$486$	24265.5	2.26483
$487$	−8351.25	−0.777066	−0.388533	−	0.921435i	$-0.627018\pi$
$487$	−8351.25	−0.777066	−0.388533	+	0.921435i	$0.627018\pi$
$488$	−44769.1	−4.15287
$489$	−15880.7	−1.46861
$490$	−13927.4	−1.28403
$491$	−9440.09	−0.867668	−0.433834	−	0.900993i	$-0.642840\pi$
$491$	−9440.09	−0.867668	−0.433834	+	0.900993i	$0.642840\pi$
$492$	−87741.6	−8.04004
$493$	1580.87	0.144420
$494$	30722.9	2.79816
$495$	−6750.79	−0.612981
$496$	−51239.5	−4.63855
$497$	−1808.05	−0.163183
$498$	5423.18	0.487989
$499$	−8405.07	−0.754033	−0.377017	−	0.926206i	$-0.623050\pi$
$499$	−8405.07	−0.754033	−0.377017	+	0.926206i	$0.623050\pi$
$500$	33600.3	3.00530
$501$	7095.32	0.632725
$502$	12914.5	1.14822
$503$	−11789.0	−1.04502	−0.522509	−	0.852634i	$-0.675004\pi$
$503$	−11789.0	−1.04502	−0.522509	+	0.852634i	$0.675004\pi$
$504$	21084.1	1.86341
$505$	1429.42	0.125957
$506$	−9472.06	−0.832183
$507$	−825.802	−0.0723376
$508$	47388.7	4.13885
$509$	7923.97	0.690027	0.345014	−	0.938598i	$-0.387874\pi$
$509$	7923.97	0.690027	0.345014	+	0.938598i	$0.387874\pi$
$510$	15737.3	1.36639
$511$	−3254.91	−0.281778
$512$	−35559.6	−3.06939
$513$	13993.3	1.20432
$514$	22857.7	1.96150
$515$	7120.17	0.609228
$516$	−42619.8	−3.63611
$517$	−1946.77	−0.165607
$518$	−5732.57	−0.486244
$519$	17855.9	1.51019
$520$	−30341.6	−2.55879
$521$	2213.43	0.186127	0.0930634	−	0.995660i	$-0.470334\pi$
$521$	2213.43	0.186127	0.0930634	+	0.995660i	$0.470334\pi$
$522$	−8655.46	−0.725745
$523$	−230.368	−0.0192606	−0.00963031	−	0.999954i	$-0.503065\pi$
$523$	−230.368	−0.0192606	−0.00963031	+	0.999954i	$0.503065\pi$
$524$	−16141.1	−1.34566
$525$	2907.99	0.241743
$526$	21626.0	1.79266
$527$	−8302.71	−0.686284
$528$	40880.8	3.36952
$529$	−4408.37	−0.362322
$530$	28027.0	2.29701
$531$	1012.15	0.0827183
$532$	−17822.2	−1.45243
$533$	21890.7	1.77897
$534$	24299.3	1.96916
$535$	−3128.16	−0.252789
$536$	20807.5	1.67677
$537$	24560.4	1.97366
$538$	666.076	0.0533766
$539$	−5862.37	−0.468479
$540$	−21567.2	−1.71872
$541$	24537.6	1.95001	0.975003	−	0.222193i	$-0.0713214\pi$
$541$	24537.6	1.95001	0.975003	+	0.222193i	$0.0713214\pi$
$542$	−13516.0	−1.07114
$543$	11246.4	0.888820
$544$	−31589.9	−2.48971
$545$	−6866.62	−0.539695
$546$	−13625.7	−1.06800
$547$	−6837.14	−0.534433	−0.267217	−	0.963636i	$-0.586104\pi$
$547$	−6837.14	−0.534433	−0.267217	+	0.963636i	$0.586104\pi$
$548$	−13111.2	−1.02205
$549$	23335.9	1.81412
$550$	5781.89	0.448256
$551$	4688.11	0.362469
$552$	−56993.0	−4.39453
$553$	−1364.69	−0.104941
$554$	31864.4	2.44366
$555$	11044.0	0.844668
$556$	1601.46	0.122153
$557$	934.888	0.0711176	0.0355588	−	0.999368i	$-0.488679\pi$
$557$	934.888	0.0711176	0.0355588	+	0.999368i	$0.488679\pi$
$558$	45458.3	3.44875
$559$	10633.3	0.804543
$560$	14056.3	1.06069
$561$	6624.21	0.498529
$562$	3391.48	0.254557
$563$	8285.16	0.620209	0.310105	−	0.950702i	$-0.399636\pi$
$563$	8285.16	0.620209	0.310105	+	0.950702i	$0.399636\pi$
$564$	−18280.6	−1.36481
$565$	−13183.8	−0.981679
$566$	34986.0	2.59818
$567$	1044.95	0.0773967
$568$	−21630.3	−1.59787
$569$	−6742.89	−0.496795	−0.248398	−	0.968658i	$-0.579904\pi$
$569$	−6742.89	−0.496795	−0.248398	+	0.968658i	$0.579904\pi$
$570$	46669.4	3.42941
$571$	24508.0	1.79619	0.898097	−	0.439797i	$-0.144949\pi$
$571$	24508.0	1.79619	0.898097	+	0.439797i	$0.144949\pi$
$572$	−19931.6	−1.45696
$573$	−29192.1	−2.12830
$574$	−17260.5	−1.25512
$575$	−4735.98	−0.343486
$576$	89873.5	6.50126
$577$	−8210.28	−0.592371	−0.296186	−	0.955130i	$-0.595715\pi$
$577$	−8210.28	−0.592371	−0.296186	+	0.955130i	$0.595715\pi$
$578$	17726.5	1.27565
$579$	−35847.1	−2.57298
$580$	−7225.60	−0.517287
$581$	784.889	0.0560459
$582$	66203.8	4.71518
$583$	11797.3	0.838065
$584$	−38939.7	−2.75914
$585$	15815.6	1.11777
$586$	46439.9	3.27375
$587$	−5316.68	−0.373838	−0.186919	−	0.982375i	$-0.559850\pi$
$587$	−5316.68	−0.373838	−0.186919	+	0.982375i	$0.559850\pi$
$588$	−55049.0	−3.86085
$589$	−24621.9	−1.72246
$590$	1148.47	0.0801388
$591$	−6114.76	−0.425596
$592$	−40294.1	−2.79743
$593$	−16384.3	−1.13461	−0.567303	−	0.823509i	$-0.692013\pi$
$593$	−16384.3	−1.13461	−0.567303	+	0.823509i	$0.692013\pi$
$594$	−12339.3	−0.852338
$595$	2277.64	0.156931
$596$	10151.5	0.697684
$597$	26164.6	1.79371
$598$	22190.9	1.51748
$599$	2797.11	0.190796	0.0953980	−	0.995439i	$-0.469588\pi$
$599$	2797.11	0.190796	0.0953980	+	0.995439i	$0.469588\pi$
$600$	34789.4	2.36712
$601$	9202.97	0.624621	0.312310	−	0.949980i	$-0.398897\pi$
$601$	9202.97	0.624621	0.312310	+	0.949980i	$0.398897\pi$
$602$	−8384.17	−0.567630
$603$	−10845.9	−0.732471
$604$	−32190.0	−2.16853
$605$	8009.28	0.538220
$606$	7679.49	0.514782
$607$	−5840.54	−0.390544	−0.195272	−	0.980749i	$-0.562559\pi$
$607$	−5840.54	−0.390544	−0.195272	+	0.980749i	$0.562559\pi$
$608$	−93680.5	−6.24876
$609$	−2079.19	−0.138346
$610$	26479.0	1.75755
$611$	4560.85	0.301984
$612$	37476.6	2.47533
$613$	−2627.03	−0.173091	−0.0865456	−	0.996248i	$-0.527583\pi$
$613$	−2627.03	−0.173091	−0.0865456	+	0.996248i	$0.527583\pi$
$614$	−4566.85	−0.300168
$615$	33253.0	2.18031
$616$	10070.1	0.658665
$617$	−23003.5	−1.50095	−0.750476	−	0.660897i	$-0.770176\pi$
$617$	−23003.5	−1.50095	−0.750476	+	0.660897i	$0.770176\pi$
$618$	38252.8	2.48989
$619$	5826.36	0.378322	0.189161	−	0.981946i	$-0.439423\pi$
$619$	5826.36	0.378322	0.189161	+	0.981946i	$0.439423\pi$
$620$	37948.7	2.45815
$621$	10107.2	0.653122
$622$	23162.0	1.49311
$623$	3516.80	0.226160
$624$	−95774.6	−6.14431
$625$	−6013.18	−0.384844
$626$	44788.6	2.85961
$627$	19644.2	1.25122
$628$	−66758.3	−4.24195
$629$	−6529.14	−0.413885
$630$	−12470.3	−0.788619
$631$	−21318.2	−1.34495	−0.672476	−	0.740119i	$-0.734769\pi$
$631$	−21318.2	−1.34495	−0.672476	+	0.740119i	$0.734769\pi$
$632$	−16326.2	−1.02757
$633$	−20494.9	−1.28689
$634$	2038.04	0.127667
$635$	−17959.7	−1.12238
$636$	110779.	6.90671
$637$	13734.2	0.854270
$638$	−4134.00	−0.256531
$639$	11274.8	0.698004
$640$	50110.6	3.09499
$641$	−28156.0	−1.73494	−0.867470	−	0.497490i	$-0.834255\pi$
$641$	−28156.0	−1.73494	−0.867470	+	0.497490i	$0.834255\pi$
$642$	−16805.9	−1.03314
$643$	27921.3	1.71246	0.856229	−	0.516597i	$-0.172801\pi$
$643$	27921.3	1.71246	0.856229	+	0.516597i	$0.172801\pi$
$644$	−12872.9	−0.787673
$645$	16152.4	0.986046
$646$	−27590.7	−1.68040
$647$	−26342.5	−1.60066	−0.800332	−	0.599557i	$-0.795343\pi$
$647$	−26342.5	−1.60066	−0.800332	+	0.599557i	$0.795343\pi$
$648$	12501.2	0.757859
$649$	483.420	0.0292387
$650$	−13545.7	−0.817392
$651$	10919.9	0.657424
$652$	−42911.7	−2.57753
$653$	2966.46	0.177774	0.0888870	−	0.996042i	$-0.471669\pi$
$653$	2966.46	0.177774	0.0888870	+	0.996042i	$0.471669\pi$
$654$	−36890.6	−2.20571
$655$	6117.27	0.364918
$656$	−121324.	−7.22088
$657$	20297.3	1.20529
$658$	−3596.16	−0.213059
$659$	29407.2	1.73830	0.869152	−	0.494545i	$-0.164665\pi$
$659$	29407.2	1.73830	0.869152	+	0.494545i	$0.164665\pi$
$660$	−30276.9	−1.78565
$661$	−33331.0	−1.96131	−0.980655	−	0.195743i	$-0.937288\pi$
$661$	−33331.0	−1.96131	−0.980655	+	0.195743i	$0.937288\pi$
$662$	−44279.2	−2.59964
$663$	−15519.1	−0.909065
$664$	9389.91	0.548794
$665$	6754.40	0.393871
$666$	35747.8	2.07988
$667$	3386.19	0.196572
$668$	19172.5	1.11049
$669$	−35588.2	−2.05668
$670$	−12306.8	−0.709629
$671$	11145.7	0.641242
$672$	41547.5	2.38501
$673$	19205.0	1.10000	0.549999	−	0.835165i	$-0.314628\pi$
$673$	19205.0	1.10000	0.549999	+	0.835165i	$0.314628\pi$
$674$	−941.117	−0.0537841
$675$	−6169.60	−0.351805
$676$	−2231.43	−0.126959
$677$	−2381.44	−0.135194	−0.0675969	−	0.997713i	$-0.521533\pi$
$677$	−2381.44	−0.135194	−0.0675969	+	0.997713i	$0.521533\pi$
$678$	−70829.6	−4.01209
$679$	9581.58	0.541542
$680$	27248.3	1.53665
$681$	9897.93	0.556959
$682$	21711.7	1.21904
$683$	26633.9	1.49212	0.746060	−	0.665879i	$-0.231943\pi$
$683$	26633.9	1.49212	0.746060	+	0.665879i	$0.231943\pi$
$684$	111138.	6.21266
$685$	4968.99	0.277161
$686$	−23213.4	−1.29197
$687$	20383.2	1.13198
$688$	−58932.1	−3.26565
$689$	−27638.3	−1.52821
$690$	33708.9	1.85982
$691$	−16933.8	−0.932263	−0.466132	−	0.884715i	$-0.654353\pi$
$691$	−16933.8	−0.932263	−0.466132	+	0.884715i	$0.654353\pi$
$692$	48249.0	2.65051
$693$	−5249.06	−0.287728
$694$	29720.8	1.62563
$695$	−606.931	−0.0331255
$696$	−24874.1	−1.35467
$697$	−19659.0	−1.06834
$698$	−55643.2	−3.01737
$699$	−2814.88	−0.152316
$700$	7857.78	0.424280
$701$	17515.8	0.943740	0.471870	−	0.881668i	$-0.343579\pi$
$701$	17515.8	0.943740	0.471870	+	0.881668i	$0.343579\pi$
$702$	28908.3	1.55424
$703$	−19362.3	−1.03878
$704$	42925.2	2.29802
$705$	6928.12	0.370111
$706$	34711.5	1.85040
$707$	1111.44	0.0591232
$708$	4539.42	0.240963
$709$	11393.9	0.603538	0.301769	−	0.953381i	$-0.402423\pi$
$709$	11393.9	0.603538	0.301769	+	0.953381i	$0.402423\pi$
$710$	12793.4	0.676238
$711$	8510.06	0.448878
$712$	42072.8	2.21453
$713$	−17784.2	−0.934114
$714$	12236.5	0.641373
$715$	7553.81	0.395100
$716$	66365.4	3.46395
$717$	41965.5	2.18581
$718$	24493.6	1.27311
$719$	6558.16	0.340164	0.170082	−	0.985430i	$-0.445597\pi$
$719$	6558.16	0.340164	0.170082	+	0.985430i	$0.445597\pi$
$720$	−87653.7	−4.53703
$721$	5536.27	0.285966
$722$	−44083.9	−2.27235
$723$	−50701.9	−2.60805
$724$	30389.3	1.55996
$725$	−2066.98	−0.105884
$726$	43029.5	2.19969
$727$	−10636.4	−0.542617	−0.271309	−	0.962492i	$-0.587456\pi$
$727$	−10636.4	−0.542617	−0.271309	+	0.962492i	$0.587456\pi$
$728$	−23592.1	−1.20107
$729$	−32049.8	−1.62830
$730$	23031.2	1.16770
$731$	−9549.20	−0.483160
$732$	104660.	5.28463
$733$	−18958.9	−0.955340	−0.477670	−	0.878539i	$-0.658519\pi$
$733$	−18958.9	−0.955340	−0.477670	+	0.878539i	$0.658519\pi$
$734$	6285.07	0.316058
$735$	20862.9	1.04699
$736$	−67664.7	−3.38880
$737$	−5180.21	−0.258908
$738$	107635.	5.36870
$739$	−13792.3	−0.686545	−0.343272	−	0.939236i	$-0.611535\pi$
$739$	−13792.3	−0.686545	−0.343272	+	0.939236i	$0.611535\pi$
$740$	29842.3	1.48247
$741$	−46022.1	−2.28160
$742$	21792.4	1.07820
$743$	30766.4	1.51913	0.759563	−	0.650433i	$-0.225413\pi$
$743$	30766.4	1.51913	0.759563	+	0.650433i	$0.225413\pi$
$744$	130638.	6.43741
$745$	−3847.27	−0.189199
$746$	15399.9	0.755805
$747$	−4894.50	−0.239733
$748$	17899.5	0.874962
$749$	−2432.29	−0.118657
$750$	−68413.3	−3.33080
$751$	31745.9	1.54251	0.771255	−	0.636526i	$-0.219629\pi$
$751$	31745.9	1.54251	0.771255	+	0.636526i	$0.219629\pi$
$752$	−25277.3	−1.22576
$753$	−19345.6	−0.936247
$754$	9685.04	0.467783
$755$	12199.6	0.588066
$756$	−16769.6	−0.806750
$757$	25961.3	1.24647	0.623236	−	0.782034i	$-0.285818\pi$
$757$	25961.3	1.24647	0.623236	+	0.782034i	$0.285818\pi$
$758$	10703.0	0.512865
$759$	14188.9	0.678556
$760$	80805.3	3.85673
$761$	31779.4	1.51380	0.756901	−	0.653529i	$-0.226712\pi$
$761$	31779.4	1.51380	0.756901	+	0.653529i	$0.226712\pi$
$762$	−96487.8	−4.58712
$763$	−5339.13	−0.253328
$764$	−78880.9	−3.73536
$765$	−14203.2	−0.671264
$766$	11735.9	0.553571
$767$	−1132.54	−0.0533166
$768$	124419.	5.84580
$769$	24019.1	1.12633	0.563167	−	0.826343i	$-0.309583\pi$
$769$	24019.1	1.12633	0.563167	+	0.826343i	$0.309583\pi$
$770$	−5956.06	−0.278755
$771$	−34240.2	−1.59939
$772$	−96863.8	−4.51581
$773$	−27907.0	−1.29850	−0.649252	−	0.760573i	$-0.724918\pi$
$773$	−27907.0	−1.29850	−0.649252	+	0.760573i	$0.724918\pi$
$774$	52282.9	2.42800
$775$	10855.7	0.503160
$776$	114628.	5.30271
$777$	8587.23	0.396480
$778$	−79949.0	−3.68421
$779$	−58299.1	−2.68136
$780$	70932.0	3.25612
$781$	5385.06	0.246725
$782$	−19928.5	−0.911308
$783$	4411.21	0.201333
$784$	−76118.3	−3.46749
$785$	25300.5	1.15034
$786$	32864.7	1.49141
$787$	16371.8	0.741538	0.370769	−	0.928725i	$-0.379094\pi$
$787$	16371.8	0.741538	0.370769	+	0.928725i	$0.379094\pi$
$788$	−16522.9	−0.746959
$789$	−32395.1	−1.46172
$790$	9656.28	0.434880
$791$	−10251.1	−0.460792
$792$	−62796.5	−2.81739
$793$	−26111.8	−1.16930
$794$	34288.0	1.53254
$795$	−41983.8	−1.87297
$796$	70700.2	3.14812
$797$	−20704.7	−0.920200	−0.460100	−	0.887867i	$-0.652186\pi$
$797$	−20704.7	−0.920200	−0.460100	+	0.887867i	$0.652186\pi$
$798$	36287.7	1.60974
$799$	−4095.86	−0.181353
$800$	41303.5	1.82538
$801$	−21930.5	−0.967384
$802$	−36716.1	−1.61657
$803$	9694.37	0.426036
$804$	−48643.3	−2.13373
$805$	4878.65	0.213602
$806$	−50865.6	−2.22291
$807$	−997.764	−0.0435229
$808$	13296.6	0.578926
$809$	9491.38	0.412484	0.206242	−	0.978501i	$-0.433877\pi$
$809$	9491.38	0.412484	0.206242	+	0.978501i	$0.433877\pi$
$810$	−7393.91	−0.320735
$811$	−16134.0	−0.698572	−0.349286	−	0.937016i	$-0.613576\pi$
$811$	−16134.0	−0.698572	−0.349286	+	0.937016i	$0.613576\pi$
$812$	−5618.25	−0.242810
$813$	20246.5	0.873404
$814$	17073.8	0.735179
$815$	16263.0	0.698979
$816$	86010.2	3.68990
$817$	−28318.3	−1.21265
$818$	−47798.4	−2.04307
$819$	12297.4	0.524670
$820$	89854.0	3.82663
$821$	−10160.5	−0.431918	−0.215959	−	0.976402i	$-0.569288\pi$
$821$	−10160.5	−0.431918	−0.215959	+	0.976402i	$0.569288\pi$
$822$	26695.6	1.13275
$823$	24540.9	1.03942	0.519710	−	0.854343i	$-0.326040\pi$
$823$	24540.9	1.03942	0.519710	+	0.854343i	$0.326040\pi$
$824$	66232.5	2.80014
$825$	−8661.11	−0.365504
$826$	892.993	0.0376165
$827$	19858.4	0.834998	0.417499	−	0.908677i	$-0.362907\pi$
$827$	19858.4	0.834998	0.417499	+	0.908677i	$0.362907\pi$
$828$	80274.0	3.36922
$829$	19787.6	0.829015	0.414507	−	0.910046i	$-0.363954\pi$
$829$	19787.6	0.829015	0.414507	+	0.910046i	$0.363954\pi$
$830$	−5553.74	−0.232257
$831$	−47732.1	−1.99255
$832$	−100564.	−4.19043
$833$	−12334.0	−0.513023
$834$	−3260.71	−0.135383
$835$	−7266.13	−0.301144
$836$	53081.4	2.19600
$837$	−23167.6	−0.956737
$838$	64031.4	2.63953
$839$	24386.6	1.00348	0.501739	−	0.865019i	$-0.332694\pi$
$839$	24386.6	1.00348	0.501739	+	0.865019i	$0.332694\pi$
$840$	−35837.3	−1.47203
$841$	−22911.1	−0.939404
$842$	82765.0	3.38749
$843$	−5080.34	−0.207564
$844$	−55380.0	−2.25860
$845$	845.683	0.0344289
$846$	22425.3	0.911345
$847$	6227.60	0.252636
$848$	153178.	6.20301
$849$	−52408.1	−2.11854
$850$	12164.7	0.490876
$851$	−13985.2	−0.563347
$852$	50566.9	2.03332
$853$	−10132.6	−0.406721	−0.203360	−	0.979104i	$-0.565186\pi$
$853$	−10132.6	−0.406721	−0.203360	+	0.979104i	$0.565186\pi$
$854$	20588.7	0.824978
$855$	−42119.8	−1.68476
$856$	−29098.4	−1.16187
$857$	14901.8	0.593974	0.296987	−	0.954882i	$-0.404018\pi$
$857$	14901.8	0.593974	0.296987	+	0.954882i	$0.404018\pi$
$858$	40582.5	1.61476
$859$	33359.7	1.32505	0.662525	−	0.749040i	$-0.269485\pi$
$859$	33359.7	1.32505	0.662525	+	0.749040i	$0.269485\pi$
$860$	43645.9	1.73060
$861$	25855.8	1.02342
$862$	−50570.6	−1.99819
$863$	30919.4	1.21959	0.609797	−	0.792557i	$-0.291251\pi$
$863$	30919.4	1.21959	0.609797	+	0.792557i	$0.291251\pi$
$864$	−88147.3	−3.47087
$865$	−18285.8	−0.718769
$866$	97409.2	3.82228
$867$	−26553.8	−1.04016
$868$	29506.9	1.15384
$869$	4064.56	0.158666
$870$	14712.0	0.573314
$871$	12136.1	0.472118
$872$	−63873.9	−2.48056
$873$	−59749.9	−2.31641
$874$	−59098.5	−2.28723
$875$	−9901.36	−0.382545
$876$	91032.3	3.51107
$877$	−9703.73	−0.373628	−0.186814	−	0.982395i	$-0.559816\pi$
$877$	−9703.73	−0.373628	−0.186814	+	0.982395i	$0.559816\pi$
$878$	10952.8	0.421002
$879$	−69565.7	−2.66939
$880$	−41865.0	−1.60371
$881$	11131.7	0.425694	0.212847	−	0.977085i	$-0.431726\pi$
$881$	11131.7	0.425694	0.212847	+	0.977085i	$0.431726\pi$
$882$	67530.0	2.57807
$883$	5161.15	0.196700	0.0983502	−	0.995152i	$-0.468643\pi$
$883$	5161.15	0.196700	0.0983502	+	0.995152i	$0.468643\pi$
$884$	−41934.6	−1.59549
$885$	−1720.38	−0.0653446
$886$	6456.58	0.244823
$887$	19838.7	0.750980	0.375490	−	0.926826i	$-0.377474\pi$
$887$	19838.7	0.750980	0.375490	+	0.926826i	$0.377474\pi$
$888$	102732.	3.88228
$889$	−13964.6	−0.526835
$890$	−24884.3	−0.937217
$891$	−3112.27	−0.117020
$892$	−96164.0	−3.60965
$893$	−12146.4	−0.455165
$894$	−20669.3	−0.773249
$895$	−25151.6	−0.939359
$896$	38963.4	1.45276
$897$	−33241.4	−1.23734
$898$	68032.6	2.52815
$899$	−7761.76	−0.287952
$900$	−49000.4	−1.81483
$901$	24820.6	0.917750
$902$	51408.4	1.89769
$903$	12559.3	0.462841
$904$	−122637.	−4.51201
$905$	−11517.2	−0.423031
$906$	65541.9	2.40340
$907$	28713.1	1.05116	0.525580	−	0.850744i	$-0.323848\pi$
$907$	28713.1	1.05116	0.525580	+	0.850744i	$0.323848\pi$
$908$	26745.5	0.977513
$909$	−6930.85	−0.252895
$910$	13953.7	0.508309
$911$	17310.9	0.629566	0.314783	−	0.949164i	$-0.398068\pi$
$911$	17310.9	0.629566	0.314783	+	0.949164i	$0.398068\pi$
$912$	255065.	9.26102
$913$	−2337.70	−0.0847388
$914$	14273.1	0.516535
$915$	−39664.9	−1.43309
$916$	55078.2	1.98672
$917$	4756.47	0.171289
$918$	−25961.0	−0.933379
$919$	−4490.47	−0.161183	−0.0805914	−	0.996747i	$-0.525681\pi$
$919$	−4490.47	−0.161183	−0.0805914	+	0.996747i	$0.525681\pi$
$920$	58365.1	2.09156
$921$	6841.01	0.244755
$922$	−36813.0	−1.31494
$923$	−12616.0	−0.449903
$924$	−23541.7	−0.838167
$925$	8536.80	0.303447
$926$	38532.8	1.36746
$927$	−34523.7	−1.22320
$928$	−29531.7	−1.04464
$929$	−48213.1	−1.70271	−0.851356	−	0.524588i	$-0.824220\pi$
$929$	−48213.1	−1.70271	−0.851356	+	0.524588i	$0.824220\pi$
$930$	−77267.0	−2.72439
$931$	−36576.8	−1.28760
$932$	−7606.19	−0.267327
$933$	−34696.1	−1.21747
$934$	−107753.	−3.77491
$935$	−6783.69	−0.237273
$936$	147118.	5.13750
$937$	4845.10	0.168925	0.0844625	−	0.996427i	$-0.473083\pi$
$937$	4845.10	0.168925	0.0844625	+	0.996427i	$0.473083\pi$
$938$	−9569.09	−0.333094
$939$	−67092.1	−2.33170
$940$	18720.7	0.649577
$941$	−46123.2	−1.59785	−0.798924	−	0.601432i	$-0.794597\pi$
$941$	−46123.2	−1.59785	−0.798924	+	0.601432i	$0.794597\pi$
$942$	135926.	4.70139
$943$	−42109.0	−1.45414
$944$	6276.83	0.216412
$945$	6355.45	0.218776
$946$	24971.3	0.858230
$947$	1197.97	0.0411075	0.0205538	−	0.999789i	$-0.493457\pi$
$947$	1197.97	0.0411075	0.0205538	+	0.999789i	$0.493457\pi$
$948$	38167.1	1.30761
$949$	−22711.7	−0.776875
$950$	36074.6	1.23202
$951$	−3052.93	−0.104099
$952$	21186.8	0.721291
$953$	−51008.7	−1.73382	−0.866912	−	0.498462i	$-0.833898\pi$
$953$	−51008.7	−1.73382	−0.866912	+	0.498462i	$0.833898\pi$
$954$	−135895.	−4.61192
$955$	29894.9	1.01296
$956$	113396.	3.83630
$957$	6192.62	0.209174
$958$	76749.7	2.58838
$959$	3863.62	0.130097
$960$	−152761.	−5.13578
$961$	10973.6	0.368352
$962$	−40000.0	−1.34060
$963$	15167.5	0.507547
$964$	−137003.	−4.57736
$965$	36710.1	1.22460
$966$	26210.3	0.872985
$967$	12683.3	0.421788	0.210894	−	0.977509i	$-0.432363\pi$
$967$	12683.3	0.421788	0.210894	+	0.977509i	$0.432363\pi$
$968$	74503.0	2.47378
$969$	41330.1	1.37019
$970$	−67797.6	−2.24418
$971$	−52143.4	−1.72334	−0.861668	−	0.507472i	$-0.830580\pi$
$971$	−52143.4	−1.72334	−0.861668	+	0.507472i	$0.830580\pi$
$972$	−98220.1	−3.24116
$973$	−471.918	−0.0155488
$974$	45946.8	1.51153
$975$	20291.0	0.666496
$976$	144718.	4.74621
$977$	54119.7	1.77220	0.886102	−	0.463490i	$-0.153403\pi$
$977$	54119.7	1.77220	0.886102	+	0.463490i	$0.153403\pi$
$978$	87372.1	2.85670
$979$	−10474.4	−0.341944
$980$	56374.3	1.83756
$981$	33294.3	1.08359
$982$	51937.4	1.68777
$983$	34780.2	1.12850	0.564250	−	0.825604i	$-0.309165\pi$
$983$	34780.2	1.12850	0.564250	+	0.825604i	$0.309165\pi$
$984$	309322.	10.0212
$985$	6261.97	0.202561
$986$	−8697.64	−0.280922
$987$	5386.94	0.173727
$988$	−124358.	−4.00440
$989$	−20454.1	−0.657637
$990$	37141.5	1.19236
$991$	−29106.5	−0.932996	−0.466498	−	0.884522i	$-0.654485\pi$
$991$	−29106.5	−0.932996	−0.466498	+	0.884522i	$0.654485\pi$
$992$	155100.	4.96413
$993$	66329.1	2.11973
$994$	9947.50	0.317420
$995$	−26794.5	−0.853711
$996$	−21951.5	−0.698354
$997$	49823.2	1.58266	0.791332	−	0.611386i	$-0.209388\pi$
$997$	49823.2	1.58266	0.791332	+	0.611386i	$0.209388\pi$
$998$	46243.0	1.46673
$999$	−18218.7	−0.576991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1997.4.a.a.1.5	✓	239

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1997.4.a.a.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-5.50179 q^{2} +8.24154 q^{3} +22.2697 q^{4} -8.43995 q^{5} -45.3433 q^{6} -6.56247 q^{7} -78.5092 q^{8} +40.9229 q^{9} +O(q^{10})\)	\(q-5.50179 q^{2} +8.24154 q^{3} +22.2697 q^{4} -8.43995 q^{5} -45.3433 q^{6} -6.56247 q^{7} -78.5092 q^{8} +40.9229 q^{9} +46.4349 q^{10} +19.5455 q^{11} +183.537 q^{12} -45.7908 q^{13} +36.1053 q^{14} -69.5582 q^{15} +253.784 q^{16} +41.1224 q^{17} -225.150 q^{18} +121.949 q^{19} -187.956 q^{20} -54.0848 q^{21} -107.536 q^{22} +88.0831 q^{23} -647.037 q^{24} -53.7672 q^{25} +251.932 q^{26} +114.747 q^{27} -146.144 q^{28} +38.4431 q^{29} +382.695 q^{30} -201.902 q^{31} -768.192 q^{32} +161.085 q^{33} -226.247 q^{34} +55.3869 q^{35} +911.344 q^{36} -158.773 q^{37} -670.940 q^{38} -377.387 q^{39} +662.614 q^{40} -478.060 q^{41} +297.564 q^{42} -232.214 q^{43} +435.274 q^{44} -345.388 q^{45} -484.615 q^{46} -99.6018 q^{47} +2091.57 q^{48} -299.934 q^{49} +295.816 q^{50} +338.912 q^{51} -1019.75 q^{52} +603.578 q^{53} -631.312 q^{54} -164.963 q^{55} +515.214 q^{56} +1005.05 q^{57} -211.506 q^{58} +24.7330 q^{59} -1549.04 q^{60} +570.240 q^{61} +1110.83 q^{62} -268.555 q^{63} +2196.16 q^{64} +386.472 q^{65} -886.258 q^{66} -265.033 q^{67} +915.785 q^{68} +725.940 q^{69} -304.727 q^{70} +275.513 q^{71} -3212.83 q^{72} +495.989 q^{73} +873.538 q^{74} -443.125 q^{75} +2715.78 q^{76} -128.267 q^{77} +2076.30 q^{78} +207.953 q^{79} -2141.92 q^{80} -159.232 q^{81} +2630.19 q^{82} -119.603 q^{83} -1204.46 q^{84} -347.071 q^{85} +1277.59 q^{86} +316.830 q^{87} -1534.51 q^{88} -535.896 q^{89} +1900.25 q^{90} +300.501 q^{91} +1961.59 q^{92} -1663.99 q^{93} +547.988 q^{94} -1029.25 q^{95} -6331.08 q^{96} -1460.06 q^{97} +1650.18 q^{98} +799.861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) \) 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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