LMFDB - Embedded newform 1997.4.a.a.1.70

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			1.70
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)

$f(q)$	$=$	$q-2.76015 q^{2} -4.70524 q^{3} -0.381583 q^{4} -6.86551 q^{5} +12.9872 q^{6} +2.49796 q^{7} +23.1344 q^{8} -4.86067 q^{9} +O(q^{10})$	\(q-2.76015 q^{2} -4.70524 q^{3} -0.381583 q^{4} -6.86551 q^{5} +12.9872 q^{6} +2.49796 q^{7} +23.1344 q^{8} -4.86067 q^{9} +18.9498 q^{10} -15.4408 q^{11} +1.79544 q^{12} +54.8883 q^{13} -6.89475 q^{14} +32.3039 q^{15} -60.8017 q^{16} -123.147 q^{17} +13.4162 q^{18} -0.288606 q^{19} +2.61976 q^{20} -11.7535 q^{21} +42.6189 q^{22} +33.4262 q^{23} -108.853 q^{24} -77.8647 q^{25} -151.500 q^{26} +149.912 q^{27} -0.953179 q^{28} +31.0383 q^{29} -89.1636 q^{30} +303.690 q^{31} -17.2535 q^{32} +72.6527 q^{33} +339.903 q^{34} -17.1498 q^{35} +1.85475 q^{36} -339.589 q^{37} +0.796596 q^{38} -258.263 q^{39} -158.830 q^{40} -224.364 q^{41} +32.4415 q^{42} -176.107 q^{43} +5.89194 q^{44} +33.3710 q^{45} -92.2611 q^{46} -79.8613 q^{47} +286.087 q^{48} -336.760 q^{49} +214.918 q^{50} +579.435 q^{51} -20.9444 q^{52} +528.358 q^{53} -413.780 q^{54} +106.009 q^{55} +57.7889 q^{56} +1.35796 q^{57} -85.6703 q^{58} -67.2288 q^{59} -12.3266 q^{60} -545.544 q^{61} -838.229 q^{62} -12.1418 q^{63} +534.036 q^{64} -376.836 q^{65} -200.532 q^{66} +422.032 q^{67} +46.9906 q^{68} -157.278 q^{69} +47.3360 q^{70} +948.793 q^{71} -112.449 q^{72} -910.016 q^{73} +937.315 q^{74} +366.373 q^{75} +0.110127 q^{76} -38.5705 q^{77} +712.844 q^{78} +906.898 q^{79} +417.435 q^{80} -574.136 q^{81} +619.278 q^{82} +845.986 q^{83} +4.48494 q^{84} +845.465 q^{85} +486.082 q^{86} -146.043 q^{87} -357.214 q^{88} +592.804 q^{89} -92.1089 q^{90} +137.109 q^{91} -12.7548 q^{92} -1428.94 q^{93} +220.429 q^{94} +1.98143 q^{95} +81.1819 q^{96} -707.759 q^{97} +929.508 q^{98} +75.0526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76015	−0.975860	−0.487930	−	0.872883i	$-0.662248\pi$
$2$	−2.76015	−0.975860	−0.487930	+	0.872883i	$0.662248\pi$
$3$	−4.70524	−0.905525	−0.452762	−	0.891631i	$-0.649561\pi$
$3$	−4.70524	−0.905525	−0.452762	+	0.891631i	$0.649561\pi$
$4$	−0.381583	−0.0476978
$5$	−6.86551	−0.614070	−0.307035	−	0.951698i	$-0.599337\pi$
$5$	−6.86551	−0.614070	−0.307035	+	0.951698i	$0.599337\pi$
$6$	12.9872	0.883665
$7$	2.49796	0.134877	0.0674387	−	0.997723i	$-0.478517\pi$
$7$	2.49796	0.134877	0.0674387	+	0.997723i	$0.478517\pi$
$8$	23.1344	1.02241
$9$	−4.86067	−0.180025
$10$	18.9498	0.599246
$11$	−15.4408	−0.423234	−0.211617	−	0.977353i	$-0.567873\pi$
$11$	−15.4408	−0.423234	−0.211617	+	0.977353i	$0.567873\pi$
$12$	1.79544	0.0431916
$13$	54.8883	1.17102	0.585510	−	0.810665i	$-0.300894\pi$
$13$	54.8883	1.17102	0.585510	+	0.810665i	$0.300894\pi$
$14$	−6.89475	−0.131621
$15$	32.3039	0.556056
$16$	−60.8017	−0.950027
$17$	−123.147	−1.75691	−0.878454	−	0.477826i	$-0.841425\pi$
$17$	−123.147	−1.75691	−0.878454	+	0.477826i	$0.841425\pi$
$18$	13.4162	0.175679
$19$	−0.288606	−0.00348478	−0.00174239	−	0.999998i	$-0.500555\pi$
$19$	−0.288606	−0.00348478	−0.00174239	+	0.999998i	$0.500555\pi$
$20$	2.61976	0.0292898
$21$	−11.7535	−0.122135
$22$	42.6189	0.413017
$23$	33.4262	0.303036	0.151518	−	0.988454i	$-0.451584\pi$
$23$	33.4262	0.303036	0.151518	+	0.988454i	$0.451584\pi$
$24$	−108.853	−0.925814
$25$	−77.8647	−0.622918
$26$	−151.500	−1.14275
$27$	149.912	1.06854
$28$	−0.953179	−0.00643335
$29$	31.0383	0.198747	0.0993736	−	0.995050i	$-0.468316\pi$
$29$	31.0383	0.198747	0.0993736	+	0.995050i	$0.468316\pi$
$30$	−89.1636	−0.542632
$31$	303.690	1.75949	0.879747	−	0.475442i	$-0.157712\pi$
$31$	303.690	1.75949	0.879747	+	0.475442i	$0.157712\pi$
$32$	−17.2535	−0.0953129
$33$	72.6527	0.383249
$34$	339.903	1.71450
$35$	−17.1498	−0.0828241
$36$	1.85475	0.00858679
$37$	−339.589	−1.50887	−0.754433	−	0.656377i	$-0.772088\pi$
$37$	−339.589	−1.50887	−0.754433	+	0.656377i	$0.772088\pi$
$38$	0.796596	0.00340066
$39$	−258.263	−1.06039
$40$	−158.830	−0.627829
$41$	−224.364	−0.854629	−0.427314	−	0.904103i	$-0.640540\pi$
$41$	−224.364	−0.854629	−0.427314	+	0.904103i	$0.640540\pi$
$42$	32.4415	0.119186
$43$	−176.107	−0.624560	−0.312280	−	0.949990i	$-0.601093\pi$
$43$	−176.107	−0.624560	−0.312280	+	0.949990i	$0.601093\pi$
$44$	5.89194	0.0201873
$45$	33.3710	0.110548
$46$	−92.2611	−0.295721
$47$	−79.8613	−0.247851	−0.123925	−	0.992292i	$-0.539548\pi$
$47$	−79.8613	−0.247851	−0.123925	+	0.992292i	$0.539548\pi$
$48$	286.087	0.860273
$49$	−336.760	−0.981808
$50$	214.918	0.607880
$51$	579.435	1.59092
$52$	−20.9444	−0.0558551
$53$	528.358	1.36935	0.684676	−	0.728848i	$-0.259944\pi$
$53$	528.358	1.36935	0.684676	+	0.728848i	$0.259944\pi$
$54$	−413.780	−1.04275
$55$	106.009	0.259895
$56$	57.7889	0.137899
$57$	1.35796	0.00315555
$58$	−85.6703	−0.193949
$59$	−67.2288	−0.148347	−0.0741733	−	0.997245i	$-0.523632\pi$
$59$	−67.2288	−0.148347	−0.0741733	+	0.997245i	$0.523632\pi$
$60$	−12.3266	−0.0265226
$61$	−545.544	−1.14508	−0.572539	−	0.819877i	$-0.694042\pi$
$61$	−545.544	−1.14508	−0.572539	+	0.819877i	$0.694042\pi$
$62$	−838.229	−1.71702
$63$	−12.1418	−0.0242813
$64$	534.036	1.04304
$65$	−376.836	−0.719089
$66$	−200.532	−0.373997
$67$	422.032	0.769544	0.384772	−	0.923012i	$-0.374280\pi$
$67$	422.032	0.769544	0.384772	+	0.923012i	$0.374280\pi$
$68$	46.9906	0.0838007
$69$	−157.278	−0.274407
$70$	47.3360	0.0808247
$71$	948.793	1.58593	0.792965	−	0.609268i	$-0.208536\pi$
$71$	948.793	1.58593	0.792965	+	0.609268i	$0.208536\pi$
$72$	−112.449	−0.184058
$73$	−910.016	−1.45903	−0.729516	−	0.683963i	$-0.760255\pi$
$73$	−910.016	−1.45903	−0.729516	+	0.683963i	$0.760255\pi$
$74$	937.315	1.47244
$75$	366.373	0.564068
$76$	0.110127	0.000166216 0
$77$	−38.5705	−0.0570847
$78$	712.844	1.03479
$79$	906.898	1.29157	0.645785	−	0.763520i	$-0.276530\pi$
$79$	906.898	1.29157	0.645785	+	0.763520i	$0.276530\pi$
$80$	417.435	0.583383
$81$	−574.136	−0.787566
$82$	619.278	0.833998
$83$	845.986	1.11878	0.559392	−	0.828904i	$-0.311035\pi$
$83$	845.986	1.11878	0.559392	+	0.828904i	$0.311035\pi$
$84$	4.48494	0.00582556
$85$	845.465	1.07887
$86$	486.082	0.609483
$87$	−146.043	−0.179971
$88$	−357.214	−0.432717
$89$	592.804	0.706035	0.353018	−	0.935617i	$-0.385156\pi$
$89$	592.804	0.706035	0.353018	+	0.935617i	$0.385156\pi$
$90$	−92.1089	−0.107879
$91$	137.109	0.157944
$92$	−12.7548	−0.0144542
$93$	−1428.94	−1.59327
$94$	220.429	0.241867
$95$	1.98143	0.00213990
$96$	81.1819	0.0863082
$97$	−707.759	−0.740846	−0.370423	−	0.928863i	$-0.620787\pi$
$97$	−707.759	−0.740846	−0.370423	+	0.928863i	$0.620787\pi$
$98$	929.508	0.958107
$99$	75.0526	0.0761926
$100$	29.7118	0.0297118
$101$	880.965	0.867914	0.433957	−	0.900934i	$-0.357117\pi$
$101$	880.965	0.867914	0.433957	+	0.900934i	$0.357117\pi$
$102$	−1599.33	−1.55252
$103$	1152.87	1.10287	0.551437	−	0.834216i	$-0.314080\pi$
$103$	1152.87	1.10287	0.551437	+	0.834216i	$0.314080\pi$
$104$	1269.81	1.19726
$105$	80.6940	0.0749993
$106$	−1458.35	−1.33629
$107$	1262.33	1.14051	0.570253	−	0.821469i	$-0.306845\pi$
$107$	1262.33	1.14051	0.570253	+	0.821469i	$0.306845\pi$
$108$	−57.2039	−0.0509671
$109$	826.942	0.726667	0.363333	−	0.931659i	$-0.381639\pi$
$109$	826.942	0.726667	0.363333	+	0.931659i	$0.381639\pi$
$110$	−292.600	−0.253621
$111$	1597.85	1.36632
$112$	−151.880	−0.128137
$113$	2205.93	1.83643	0.918216	−	0.396079i	$-0.129629\pi$
$113$	2205.93	1.83643	0.918216	+	0.396079i	$0.129629\pi$
$114$	−3.74818	−0.00307938
$115$	−229.488	−0.186086
$116$	−11.8437	−0.00947981
$117$	−266.794	−0.210813
$118$	185.561	0.144765
$119$	−307.616	−0.236967
$120$	747.332	0.568515
$121$	−1092.58	−0.820873
$122$	1505.78	1.11744
$123$	1055.69	0.773888
$124$	−115.883	−0.0839241
$125$	1392.77	0.996585
$126$	33.5131	0.0236951
$127$	1427.88	0.997665	0.498832	−	0.866698i	$-0.333762\pi$
$127$	1427.88	0.997665	0.498832	+	0.866698i	$0.333762\pi$
$128$	−1335.99	−0.922547
$129$	828.627	0.565555
$130$	1040.12	0.701730
$131$	434.209	0.289595	0.144798	−	0.989461i	$-0.453747\pi$
$131$	434.209	0.289595	0.144798	+	0.989461i	$0.453747\pi$
$132$	−27.7230	−0.0182801
$133$	−0.720928	−0.000470018 0
$134$	−1164.87	−0.750967
$135$	−1029.22	−0.656160
$136$	−2848.92	−1.79627
$137$	−2534.82	−1.58076	−0.790382	−	0.612615i	$-0.790118\pi$
$137$	−2534.82	−1.58076	−0.790382	+	0.612615i	$0.790118\pi$
$138$	434.111	0.267783
$139$	−1345.54	−0.821061	−0.410530	−	0.911847i	$-0.634656\pi$
$139$	−1345.54	−0.821061	−0.410530	+	0.911847i	$0.634656\pi$
$140$	6.54406	0.00395053
$141$	375.767	0.224435
$142$	−2618.81	−1.54764
$143$	−847.519	−0.495616
$144$	295.537	0.171028
$145$	−213.094	−0.122045
$146$	2511.78	1.42381
$147$	1584.54	0.889052
$148$	129.581	0.0719696
$149$	−2063.95	−1.13480	−0.567400	−	0.823442i	$-0.692051\pi$
$149$	−2063.95	−1.13480	−0.567400	+	0.823442i	$0.692051\pi$
$150$	−1011.24	−0.550451
$151$	−2.16365	−0.00116606	−0.000583030	−	1.00000i	$-0.500186\pi$
$151$	−2.16365	−0.00116606	−0.000583030		1.00000i	$0.500186\pi$
$152$	−6.67673	−0.00356286
$153$	598.575	0.316287
$154$	106.460	0.0557066
$155$	−2084.99	−1.08045
$156$	98.5486	0.0505782
$157$	427.976	0.217555	0.108778	−	0.994066i	$-0.465306\pi$
$157$	427.976	0.217555	0.108778	+	0.994066i	$0.465306\pi$
$158$	−2503.17	−1.26039
$159$	−2486.06	−1.23998
$160$	118.454	0.0585288
$161$	83.4973	0.0408727
$162$	1584.70	0.768554
$163$	2351.77	1.13009	0.565045	−	0.825060i	$-0.308859\pi$
$163$	2351.77	1.13009	0.565045	+	0.825060i	$0.308859\pi$
$164$	85.6134	0.0407639
$165$	−498.798	−0.235342
$166$	−2335.05	−1.09178
$167$	−2932.07	−1.35863	−0.679313	−	0.733849i	$-0.737722\pi$
$167$	−2932.07	−1.35863	−0.679313	+	0.733849i	$0.737722\pi$
$168$	−271.911	−0.124871
$169$	815.723	0.371290
$170$	−2333.61	−1.05282
$171$	1.40282	0.000627347 0
$172$	67.1994	0.0297901
$173$	3365.39	1.47899	0.739496	−	0.673161i	$-0.235064\pi$
$173$	3365.39	1.47899	0.739496	+	0.673161i	$0.235064\pi$
$174$	403.100	0.175626
$175$	−194.503	−0.0840175
$176$	938.827	0.402084
$177$	316.328	0.134331
$178$	−1636.23	−0.688991
$179$	3263.23	1.36260	0.681300	−	0.732004i	$-0.261415\pi$
$179$	3263.23	1.36260	0.681300	+	0.732004i	$0.261415\pi$
$180$	−12.7338	−0.00527289
$181$	1702.44	0.699125	0.349562	−	0.936913i	$-0.386330\pi$
$181$	1702.44	0.699125	0.349562	+	0.936913i	$0.386330\pi$
$182$	−378.441	−0.154131
$183$	2566.92	1.03690
$184$	773.294	0.309826
$185$	2331.45	0.926549
$186$	3944.07	1.55480
$187$	1901.48	0.743583
$188$	30.4737	0.0118219
$189$	374.475	0.144122
$190$	−5.46904	−0.00208824
$191$	353.912	0.134074	0.0670372	−	0.997750i	$-0.478645\pi$
$191$	353.912	0.134074	0.0670372	+	0.997750i	$0.478645\pi$
$192$	−2512.77	−0.944498
$193$	502.679	0.187480	0.0937399	−	0.995597i	$-0.470118\pi$
$193$	502.679	0.187480	0.0937399	+	0.995597i	$0.470118\pi$
$194$	1953.52	0.722961
$195$	1773.11	0.651153
$196$	128.502	0.0468301
$197$	4482.60	1.62118	0.810589	−	0.585616i	$-0.199147\pi$
$197$	4482.60	1.62118	0.810589	+	0.585616i	$0.199147\pi$
$198$	−207.156	−0.0743533
$199$	−1710.76	−0.609412	−0.304706	−	0.952447i	$-0.598558\pi$
$199$	−1710.76	−0.609412	−0.304706	+	0.952447i	$0.598558\pi$
$200$	−1801.35	−0.636875
$201$	−1985.77	−0.696841
$202$	−2431.60	−0.846963
$203$	77.5326	0.0268065
$204$	−221.102	−0.0758836
$205$	1540.37	0.524802
$206$	−3182.10	−1.07625
$207$	−162.474	−0.0545541
$208$	−3337.30	−1.11250
$209$	4.45631	0.00147488
$210$	−222.727	−0.0731888
$211$	−2833.39	−0.924447	−0.462224	−	0.886763i	$-0.652948\pi$
$211$	−2833.39	−0.924447	−0.462224	+	0.886763i	$0.652948\pi$
$212$	−201.612	−0.0653151
$213$	−4464.30	−1.43610
$214$	−3484.22	−1.11297
$215$	1209.07	0.383524
$216$	3468.13	1.09248
$217$	758.606	0.237316
$218$	−2282.48	−0.709125
$219$	4281.85	1.32119
$220$	−40.4512	−0.0123964
$221$	−6759.31	−2.05738
$222$	−4410.30	−1.33333
$223$	1655.34	0.497084	0.248542	−	0.968621i	$-0.420049\pi$
$223$	1655.34	0.497084	0.248542	+	0.968621i	$0.420049\pi$
$224$	−43.0986	−0.0128556
$225$	378.475	0.112141
$226$	−6088.71	−1.79210
$227$	−3305.13	−0.966384	−0.483192	−	0.875514i	$-0.660523\pi$
$227$	−3305.13	−0.966384	−0.483192	+	0.875514i	$0.660523\pi$
$228$	−0.518175	−0.000150513 0
$229$	−1705.88	−0.492261	−0.246130	−	0.969237i	$-0.579159\pi$
$229$	−1705.88	−0.492261	−0.246130	+	0.969237i	$0.579159\pi$
$230$	633.420	0.181593
$231$	181.484	0.0516916
$232$	718.053	0.203200
$233$	4341.32	1.22064	0.610320	−	0.792155i	$-0.291041\pi$
$233$	4341.32	1.22064	0.610320	+	0.792155i	$0.291041\pi$
$234$	736.390	0.205724
$235$	548.289	0.152198
$236$	25.6533	0.00707581
$237$	−4267.18	−1.16955
$238$	849.065	0.231247
$239$	−4440.74	−1.20187	−0.600936	−	0.799297i	$-0.705205\pi$
$239$	−4440.74	−1.20187	−0.600936	+	0.799297i	$0.705205\pi$
$240$	−1964.13	−0.528268
$241$	−4698.94	−1.25596	−0.627978	−	0.778231i	$-0.716117\pi$
$241$	−4698.94	−1.25596	−0.627978	+	0.778231i	$0.716117\pi$
$242$	3015.69	0.801057
$243$	−1346.18	−0.355381
$244$	208.170	0.0546177
$245$	2312.03	0.602899
$246$	−2913.86	−0.755206
$247$	−15.8411	−0.00408075
$248$	7025.69	1.79892
$249$	−3980.57	−1.01309
$250$	−3844.25	−0.972528
$251$	1012.06	0.254505	0.127253	−	0.991870i	$-0.459384\pi$
$251$	1012.06	0.254505	0.127253	+	0.991870i	$0.459384\pi$
$252$	4.63309	0.00115816
$253$	−516.126	−0.128255
$254$	−3941.15	−0.973581
$255$	−3978.12	−0.976939
$256$	−584.756	−0.142763
$257$	3706.37	0.899599	0.449799	−	0.893130i	$-0.351495\pi$
$257$	3706.37	0.899599	0.449799	+	0.893130i	$0.351495\pi$
$258$	−2287.13	−0.551902
$259$	−848.280	−0.203512
$260$	143.794	0.0342990
$261$	−150.867	−0.0357794
$262$	−1198.48	−0.282604
$263$	−4699.05	−1.10173	−0.550866	−	0.834594i	$-0.685702\pi$
$263$	−4699.05	−1.10173	−0.550866	+	0.834594i	$0.685702\pi$
$264$	1680.78	0.391836
$265$	−3627.45	−0.840878
$266$	1.98987	0.000458671 0
$267$	−2789.29	−0.639332
$268$	−161.040	−0.0367056
$269$	−3287.91	−0.745231	−0.372615	−	0.927986i	$-0.621539\pi$
$269$	−3287.91	−0.745231	−0.372615	+	0.927986i	$0.621539\pi$
$270$	2840.81	0.640320
$271$	−6931.62	−1.55375	−0.776874	−	0.629656i	$-0.783196\pi$
$271$	−6931.62	−1.55375	−0.776874	+	0.629656i	$0.783196\pi$
$272$	7487.53	1.66911
$273$	−645.131	−0.143022
$274$	6996.49	1.54260
$275$	1202.29	0.263640
$276$	60.0146	0.0130886
$277$	1539.28	0.333887	0.166943	−	0.985966i	$-0.446610\pi$
$277$	1539.28	0.333887	0.166943	+	0.985966i	$0.446610\pi$
$278$	3713.90	0.801240
$279$	−1476.14	−0.316753
$280$	−396.750	−0.0846799
$281$	−312.911	−0.0664295	−0.0332147	−	0.999448i	$-0.510575\pi$
$281$	−312.911	−0.0664295	−0.0332147	+	0.999448i	$0.510575\pi$
$282$	−1037.17	−0.219017
$283$	5483.72	1.15185	0.575925	−	0.817503i	$-0.304642\pi$
$283$	5483.72	1.15185	0.575925	+	0.817503i	$0.304642\pi$
$284$	−362.043	−0.0756454
$285$	−9.32311	−0.00193773
$286$	2339.28	0.483652
$287$	−560.453	−0.115270
$288$	83.8635	0.0171587
$289$	10252.1	2.08673
$290$	588.171	0.119099
$291$	3330.18	0.670854
$292$	347.246	0.0695927
$293$	−6967.04	−1.38914	−0.694572	−	0.719424i	$-0.744406\pi$
$293$	−6967.04	−1.38914	−0.694572	+	0.719424i	$0.744406\pi$
$294$	−4373.56	−0.867590
$295$	461.560	0.0910952
$296$	−7856.18	−1.54267
$297$	−2314.76	−0.452243
$298$	5696.80	1.10741
$299$	1834.70	0.354862
$300$	−139.801	−0.0269048
$301$	−439.909	−0.0842390
$302$	5.97199	0.00113791
$303$	−4145.16	−0.785918
$304$	17.5478	0.00331063
$305$	3745.44	0.703158
$306$	−1652.16	−0.308652
$307$	3302.11	0.613882	0.306941	−	0.951729i	$-0.400695\pi$
$307$	3302.11	0.613882	0.306941	+	0.951729i	$0.400695\pi$
$308$	14.7178	0.00272281
$309$	−5424.55	−0.998680
$310$	5754.87	1.05437
$311$	6004.63	1.09483	0.547414	−	0.836862i	$-0.315612\pi$
$311$	6004.63	1.09483	0.547414	+	0.836862i	$0.315612\pi$
$312$	−5974.76	−1.08415
$313$	−6848.58	−1.23676	−0.618378	−	0.785881i	$-0.712210\pi$
$313$	−6848.58	−1.23676	−0.618378	+	0.785881i	$0.712210\pi$
$314$	−1181.28	−0.212303
$315$	83.3595	0.0149104
$316$	−346.056	−0.0616050
$317$	−5421.07	−0.960498	−0.480249	−	0.877132i	$-0.659454\pi$
$317$	−5421.07	−0.960498	−0.480249	+	0.877132i	$0.659454\pi$
$318$	6861.88	1.21005
$319$	−479.256	−0.0841166
$320$	−3666.43	−0.640499
$321$	−5939.58	−1.03276
$322$	−230.465	−0.0398860
$323$	35.5409	0.00612244
$324$	219.080	0.0375652
$325$	−4273.86	−0.729450
$326$	−6491.22	−1.10281
$327$	−3890.96	−0.658015
$328$	−5190.53	−0.873778
$329$	−199.491	−0.0334294
$330$	1376.76	0.229661
$331$	8371.05	1.39007	0.695037	−	0.718974i	$-0.255388\pi$
$331$	8371.05	1.39007	0.695037	+	0.718974i	$0.255388\pi$
$332$	−322.813	−0.0533635
$333$	1650.63	0.271633
$334$	8092.95	1.32583
$335$	−2897.47	−0.472554
$336$	714.635	0.116031
$337$	−2467.18	−0.398801	−0.199400	−	0.979918i	$-0.563899\pi$
$337$	−2467.18	−0.398801	−0.199400	+	0.979918i	$0.563899\pi$
$338$	−2251.52	−0.362327
$339$	−10379.5	−1.66294
$340$	−322.615	−0.0514595
$341$	−4689.21	−0.744678
$342$	−3.87199	−0.000612202 0
$343$	−1698.02	−0.267301
$344$	−4074.13	−0.638554
$345$	1079.80	0.168505
$346$	−9288.97	−1.44329
$347$	−6834.38	−1.05732	−0.528658	−	0.848835i	$-0.677305\pi$
$347$	−6834.38	−1.05732	−0.528658	+	0.848835i	$0.677305\pi$
$348$	55.7274	0.00858420
$349$	1956.01	0.300008	0.150004	−	0.988685i	$-0.452071\pi$
$349$	1956.01	0.300008	0.150004	+	0.988685i	$0.452071\pi$
$350$	536.858	0.0819893
$351$	8228.43	1.25128
$352$	266.407	0.0403397
$353$	1914.47	0.288660	0.144330	−	0.989530i	$-0.453897\pi$
$353$	1914.47	0.288660	0.144330	+	0.989530i	$0.453897\pi$
$354$	−873.112	−0.131089
$355$	−6513.95	−0.973872
$356$	−226.204	−0.0336763
$357$	1447.41	0.214580
$358$	−9007.01	−1.32971
$359$	2456.04	0.361072	0.180536	−	0.983568i	$-0.442217\pi$
$359$	2456.04	0.361072	0.180536	+	0.983568i	$0.442217\pi$
$360$	772.018	0.113025
$361$	−6858.92	−0.999988
$362$	−4699.00	−0.682248
$363$	5140.87	0.743321
$364$	−52.3184	−0.00753359
$365$	6247.73	0.895948
$366$	−7085.08	−1.01187
$367$	6636.29	0.943901	0.471951	−	0.881625i	$-0.343550\pi$
$367$	6636.29	0.943901	0.471951	+	0.881625i	$0.343550\pi$
$368$	−2032.37	−0.287893
$369$	1090.56	0.153854
$370$	−6435.15	−0.904182
$371$	1319.82	0.184694
$372$	545.257	0.0759953
$373$	4512.98	0.626470	0.313235	−	0.949676i	$-0.398587\pi$
$373$	4512.98	0.626470	0.313235	+	0.949676i	$0.398587\pi$
$374$	−5248.37	−0.725633
$375$	−6553.33	−0.902433
$376$	−1847.54	−0.253404
$377$	1703.64	0.232737
$378$	−1033.61	−0.140643
$379$	−9951.42	−1.34873	−0.674367	−	0.738396i	$-0.735583\pi$
$379$	−9951.42	−1.34873	−0.674367	+	0.738396i	$0.735583\pi$
$380$	−0.756079	−0.000102068 0
$381$	−6718.50	−0.903410
$382$	−976.851	−0.130838
$383$	5502.85	0.734158	0.367079	−	0.930190i	$-0.380358\pi$
$383$	5502.85	0.734158	0.367079	+	0.930190i	$0.380358\pi$
$384$	6286.16	0.835389
$385$	264.807	0.0350540
$386$	−1387.47	−0.182954
$387$	855.998	0.112436
$388$	270.068	0.0353367
$389$	−3833.91	−0.499710	−0.249855	−	0.968283i	$-0.580383\pi$
$389$	−3833.91	−0.499710	−0.249855	+	0.968283i	$0.580383\pi$
$390$	−4894.04	−0.635434
$391$	−4116.32	−0.532407
$392$	−7790.75	−1.00381
$393$	−2043.06	−0.262236
$394$	−12372.6	−1.58204
$395$	−6226.32	−0.793114
$396$	−28.6388	−0.00363422
$397$	−14440.3	−1.82554	−0.912771	−	0.408472i	$-0.866062\pi$
$397$	−14440.3	−1.82554	−0.912771	+	0.408472i	$0.866062\pi$
$398$	4721.96	0.594700
$399$	3.39214	0.000425613 0
$400$	4734.31	0.591789
$401$	−4805.51	−0.598444	−0.299222	−	0.954184i	$-0.596727\pi$
$401$	−4805.51	−0.598444	−0.299222	+	0.954184i	$0.596727\pi$
$402$	5481.01	0.680020
$403$	16669.0	2.06040
$404$	−336.161	−0.0413976
$405$	3941.74	0.483621
$406$	−214.001	−0.0261594
$407$	5243.52	0.638603
$408$	13404.9	1.62657
$409$	−6112.32	−0.738961	−0.369480	−	0.929239i	$-0.620464\pi$
$409$	−6112.32	−0.738961	−0.369480	+	0.929239i	$0.620464\pi$
$410$	−4251.66	−0.512133
$411$	11927.0	1.43142
$412$	−439.917	−0.0526047
$413$	−167.935	−0.0200086
$414$	448.451	0.0532371
$415$	−5808.13	−0.687011
$416$	−947.014	−0.111613
$417$	6331.11	0.743491
$418$	−12.3001	−0.00143927
$419$	−14627.9	−1.70554	−0.852768	−	0.522290i	$-0.825078\pi$
$419$	−14627.9	−1.70554	−0.852768	+	0.522290i	$0.825078\pi$
$420$	−30.7914	−0.00357730
$421$	16469.9	1.90664	0.953320	−	0.301963i	$-0.0976419\pi$
$421$	16469.9	1.90664	0.953320	+	0.301963i	$0.0976419\pi$
$422$	7820.57	0.902131
$423$	388.180	0.0446192
$424$	12223.3	1.40003
$425$	9588.78	1.09441
$426$	12322.1	1.40143
$427$	−1362.75	−0.154445
$428$	−481.684	−0.0543997
$429$	3987.78	0.448792
$430$	−3337.20	−0.374265
$431$	1203.13	0.134461	0.0672305	−	0.997737i	$-0.478584\pi$
$431$	1203.13	0.134461	0.0672305	+	0.997737i	$0.478584\pi$
$432$	−9114.93	−1.01514
$433$	4300.84	0.477333	0.238666	−	0.971102i	$-0.423290\pi$
$433$	4300.84	0.477333	0.238666	+	0.971102i	$0.423290\pi$
$434$	−2093.87	−0.231587
$435$	1002.66	0.110515
$436$	−315.547	−0.0346604
$437$	−9.64699	−0.00105601
$438$	−11818.5	−1.28930
$439$	1859.26	0.202136	0.101068	−	0.994880i	$-0.467774\pi$
$439$	1859.26	0.202136	0.101068	+	0.994880i	$0.467774\pi$
$440$	2452.45	0.265719
$441$	1636.88	0.176750
$442$	18656.7	2.00771
$443$	−2786.13	−0.298810	−0.149405	−	0.988776i	$-0.547736\pi$
$443$	−2786.13	−0.298810	−0.149405	+	0.988776i	$0.547736\pi$
$444$	−609.711	−0.0651703
$445$	−4069.91	−0.433555
$446$	−4568.98	−0.485084
$447$	9711.38	1.02759
$448$	1334.00	0.140682
$449$	2409.64	0.253270	0.126635	−	0.991949i	$-0.459582\pi$
$449$	2409.64	0.253270	0.126635	+	0.991949i	$0.459582\pi$
$450$	−1044.65	−0.109434
$451$	3464.36	0.361708
$452$	−841.746	−0.0875938
$453$	10.1805	0.00105590
$454$	9122.65	0.943055
$455$	−941.323	−0.0969888
$456$	31.4157	0.00322626
$457$	−5589.61	−0.572147	−0.286073	−	0.958208i	$-0.592350\pi$
$457$	−5589.61	−0.572147	−0.286073	+	0.958208i	$0.592350\pi$
$458$	4708.48	0.480377
$459$	−18461.2	−1.87733
$460$	87.5685	0.00887587
$461$	13715.7	1.38569	0.692845	−	0.721087i	$-0.256357\pi$
$461$	13715.7	1.38569	0.692845	+	0.721087i	$0.256357\pi$
$462$	−500.922	−0.0504437
$463$	−9049.10	−0.908309	−0.454155	−	0.890923i	$-0.650059\pi$
$463$	−9049.10	−0.908309	−0.454155	+	0.890923i	$0.650059\pi$
$464$	−1887.18	−0.188815
$465$	9810.38	0.978377
$466$	−11982.7	−1.19117
$467$	−18246.6	−1.80803	−0.904017	−	0.427497i	$-0.859395\pi$
$467$	−18246.6	−1.80803	−0.904017	+	0.427497i	$0.859395\pi$
$468$	101.804	0.0100553
$469$	1054.22	0.103794
$470$	−1513.36	−0.148524
$471$	−2013.73	−0.197002
$472$	−1555.30	−0.151670
$473$	2719.23	0.264335
$474$	11778.0	1.14131
$475$	22.4722	0.00217073
$476$	117.381	0.0113028
$477$	−2568.18	−0.246517
$478$	12257.1	1.17286
$479$	13703.0	1.30711	0.653554	−	0.756880i	$-0.273277\pi$
$479$	13703.0	1.30711	0.653554	+	0.756880i	$0.273277\pi$
$480$	−557.355	−0.0529993
$481$	−18639.4	−1.76691
$482$	12969.8	1.22564
$483$	−392.875	−0.0370113
$484$	416.910	0.0391538
$485$	4859.13	0.454931
$486$	3715.66	0.346802
$487$	−20567.6	−1.91377	−0.956884	−	0.290471i	$-0.906188\pi$
$487$	−20567.6	−1.91377	−0.956884	+	0.290471i	$0.906188\pi$
$488$	−12620.8	−1.17073
$489$	−11065.6	−1.02332
$490$	−6381.55	−0.588345
$491$	14643.4	1.34592	0.672961	−	0.739678i	$-0.265022\pi$
$491$	14643.4	1.34592	0.672961	+	0.739678i	$0.265022\pi$
$492$	−402.832	−0.0369128
$493$	−3822.26	−0.349181
$494$	43.7238	0.00398224
$495$	−515.275	−0.0467876
$496$	−18464.9	−1.67157
$497$	2370.05	0.213906
$498$	10987.0	0.988630
$499$	8198.31	0.735484	0.367742	−	0.929928i	$-0.380131\pi$
$499$	8198.31	0.735484	0.367742	+	0.929928i	$0.380131\pi$
$500$	−531.457	−0.0475350
$501$	13796.1	1.23027
$502$	−2793.44	−0.248361
$503$	16387.4	1.45264	0.726318	−	0.687359i	$-0.241230\pi$
$503$	16387.4	1.45264	0.726318	+	0.687359i	$0.241230\pi$
$504$	−280.893	−0.0248253
$505$	−6048.28	−0.532960
$506$	1424.59	0.125159
$507$	−3838.18	−0.336212
$508$	−544.852	−0.0475864
$509$	8403.79	0.731810	0.365905	−	0.930652i	$-0.380759\pi$
$509$	8403.79	0.731810	0.365905	+	0.930652i	$0.380759\pi$
$510$	10980.2	0.953356
$511$	−2273.19	−0.196790
$512$	12301.9	1.06186
$513$	−43.2656	−0.00372363
$514$	−10230.1	−0.877882
$515$	−7915.07	−0.677242
$516$	−316.190	−0.0269757
$517$	1233.12	0.104899
$518$	2341.38	0.198599
$519$	−15835.0	−1.33926
$520$	−8717.88	−0.735201
$521$	11215.8	0.943133	0.471567	−	0.881830i	$-0.343689\pi$
$521$	11215.8	0.943133	0.471567	+	0.881830i	$0.343689\pi$
$522$	416.415	0.0349157
$523$	11281.6	0.943228	0.471614	−	0.881805i	$-0.343672\pi$
$523$	11281.6	0.943228	0.471614	+	0.881805i	$0.343672\pi$
$524$	−165.686	−0.0138131
$525$	915.185	0.0760799
$526$	12970.1	1.07514
$527$	−37398.4	−3.09127
$528$	−4417.41	−0.364097
$529$	−11049.7	−0.908169
$530$	10012.3	0.820579
$531$	326.777	0.0267061
$532$	0.275093	2.24188e−5 0
$533$	−12315.0	−1.00079
$534$	7698.85	0.623899
$535$	−8666.55	−0.700351
$536$	9763.47	0.786787
$537$	−15354.3	−1.23387
$538$	9075.10	0.727241
$539$	5199.84	0.415535
$540$	392.734	0.0312974
$541$	−15586.5	−1.23866	−0.619331	−	0.785130i	$-0.712596\pi$
$541$	−15586.5	−1.23866	−0.619331	+	0.785130i	$0.712596\pi$
$542$	19132.3	1.51624
$543$	−8010.41	−0.633075
$544$	2124.71	0.167456
$545$	−5677.38	−0.446224
$546$	1780.66	0.139570
$547$	6735.76	0.526508	0.263254	−	0.964726i	$-0.415204\pi$
$547$	6735.76	0.526508	0.263254	+	0.964726i	$0.415204\pi$
$548$	967.244	0.0753990
$549$	2651.71	0.206142
$550$	−3318.51	−0.257276
$551$	−8.95785	−0.000692590 0
$552$	−3638.54	−0.280555
$553$	2265.40	0.174203
$554$	−4248.65	−0.325827
$555$	−10970.0	−0.839013
$556$	513.436	0.0391628
$557$	−8407.74	−0.639583	−0.319791	−	0.947488i	$-0.603613\pi$
$557$	−8407.74	−0.639583	−0.319791	+	0.947488i	$0.603613\pi$
$558$	4074.36	0.309106
$559$	−9666.21	−0.731373
$560$	1042.74	0.0786852
$561$	−8946.94	−0.673333
$562$	863.679	0.0648258
$563$	−8223.62	−0.615603	−0.307801	−	0.951451i	$-0.599593\pi$
$563$	−8223.62	−0.615603	−0.307801	+	0.951451i	$0.599593\pi$
$564$	−143.386	−0.0107050
$565$	−15144.9	−1.12770
$566$	−15135.9	−1.12404
$567$	−1434.17	−0.106225
$568$	21949.8	1.62146
$569$	−9408.91	−0.693219	−0.346610	−	0.938009i	$-0.612667\pi$
$569$	−9408.91	−0.693219	−0.346610	+	0.938009i	$0.612667\pi$
$570$	25.7332	0.00189095
$571$	−6287.40	−0.460805	−0.230402	−	0.973095i	$-0.574004\pi$
$571$	−6287.40	−0.460805	−0.230402	+	0.973095i	$0.574004\pi$
$572$	323.398	0.0236398
$573$	−1665.24	−0.121408
$574$	1546.93	0.112487
$575$	−2602.72	−0.188767
$576$	−2595.77	−0.187773
$577$	−13940.6	−1.00582	−0.502908	−	0.864340i	$-0.667736\pi$
$577$	−13940.6	−1.00582	−0.502908	+	0.864340i	$0.667736\pi$
$578$	−28297.3	−2.03635
$579$	−2365.23	−0.169768
$580$	81.3129	0.00582127
$581$	2113.24	0.150898
$582$	−9191.79	−0.654660
$583$	−8158.27	−0.579556
$584$	−21052.7	−1.49172
$585$	1831.68	0.129454
$586$	19230.1	1.35561
$587$	4803.36	0.337744	0.168872	−	0.985638i	$-0.445988\pi$
$587$	4803.36	0.337744	0.168872	+	0.985638i	$0.445988\pi$
$588$	−604.632	−0.0424058
$589$	−87.6468	−0.00613145
$590$	−1273.97	−0.0888961
$591$	−21091.7	−1.46802
$592$	20647.6	1.43346
$593$	4097.31	0.283737	0.141869	−	0.989885i	$-0.454689\pi$
$593$	4097.31	0.283737	0.141869	+	0.989885i	$0.454689\pi$
$594$	6389.09	0.441326
$595$	2111.94	0.145514
$596$	787.567	0.0541275
$597$	8049.57	0.551837
$598$	−5064.06	−0.346295
$599$	−7088.01	−0.483486	−0.241743	−	0.970340i	$-0.577719\pi$
$599$	−7088.01	−0.483486	−0.241743	+	0.970340i	$0.577719\pi$
$600$	8475.81	0.576706
$601$	21025.9	1.42706	0.713529	−	0.700625i	$-0.247095\pi$
$601$	21025.9	1.42706	0.713529	+	0.700625i	$0.247095\pi$
$602$	1214.21	0.0822054
$603$	−2051.36	−0.138537
$604$	0.825610	5.56186e−5 0
$605$	7501.14	0.504074
$606$	11441.3	0.766946
$607$	−10388.6	−0.694660	−0.347330	−	0.937743i	$-0.612912\pi$
$607$	−10388.6	−0.694660	−0.347330	+	0.937743i	$0.612912\pi$
$608$	4.97946	0.000332144 0
$609$	−364.810	−0.0242739
$610$	−10338.0	−0.686184
$611$	−4383.45	−0.290238
$612$	−228.406	−0.0150862
$613$	−7598.74	−0.500669	−0.250335	−	0.968159i	$-0.580541\pi$
$613$	−7598.74	−0.500669	−0.250335	+	0.968159i	$0.580541\pi$
$614$	−9114.33	−0.599062
$615$	−7247.84	−0.475221
$616$	−892.306	−0.0583637
$617$	−7419.80	−0.484132	−0.242066	−	0.970260i	$-0.577825\pi$
$617$	−7419.80	−0.484132	−0.242066	+	0.970260i	$0.577825\pi$
$618$	14972.6	0.974571
$619$	12600.2	0.818163	0.409082	−	0.912498i	$-0.365849\pi$
$619$	12600.2	0.818163	0.409082	+	0.912498i	$0.365849\pi$
$620$	795.595	0.0515353
$621$	5010.99	0.323807
$622$	−16573.7	−1.06840
$623$	1480.80	0.0952281
$624$	15702.8	1.00740
$625$	171.007	0.0109444
$626$	18903.1	1.20690
$627$	−20.9680	−0.00133554
$628$	−163.308	−0.0103769
$629$	41819.2	2.65094
$630$	−230.085	−0.0145505
$631$	−13569.1	−0.856067	−0.428033	−	0.903763i	$-0.640793\pi$
$631$	−13569.1	−0.856067	−0.428033	+	0.903763i	$0.640793\pi$
$632$	20980.5	1.32051
$633$	13331.8	0.837110
$634$	14963.0	0.937311
$635$	−9803.10	−0.612636
$636$	948.635	0.0591444
$637$	−18484.2	−1.14972
$638$	1322.82	0.0820860
$639$	−4611.77	−0.285507
$640$	9172.26	0.566509
$641$	3038.65	0.187238	0.0936188	−	0.995608i	$-0.470157\pi$
$641$	3038.65	0.187238	0.0936188	+	0.995608i	$0.470157\pi$
$642$	16394.1	1.00783
$643$	−19815.3	−1.21530	−0.607650	−	0.794205i	$-0.707888\pi$
$643$	−19815.3	−1.21530	−0.607650	+	0.794205i	$0.707888\pi$
$644$	−31.8611	−0.00194954
$645$	−5688.95	−0.347290
$646$	−98.0981	−0.00597464
$647$	−7858.37	−0.477503	−0.238751	−	0.971081i	$-0.576738\pi$
$647$	−7858.37	−0.477503	−0.238751	+	0.971081i	$0.576738\pi$
$648$	−13282.3	−0.805213
$649$	1038.07	0.0627853
$650$	11796.5	0.711841
$651$	−3569.43	−0.214895
$652$	−897.393	−0.0539028
$653$	−18560.8	−1.11232	−0.556158	−	0.831077i	$-0.687725\pi$
$653$	−18560.8	−1.11232	−0.556158	+	0.831077i	$0.687725\pi$
$654$	10739.6	0.642130
$655$	−2981.07	−0.177832
$656$	13641.7	0.811921
$657$	4423.29	0.262662
$658$	550.624	0.0326224
$659$	14576.9	0.861662	0.430831	−	0.902433i	$-0.358221\pi$
$659$	14576.9	0.861662	0.430831	+	0.902433i	$0.358221\pi$
$660$	190.333	0.0112253
$661$	−21960.2	−1.29221	−0.646106	−	0.763248i	$-0.723604\pi$
$661$	−21960.2	−1.29221	−0.646106	+	0.763248i	$0.723604\pi$
$662$	−23105.3	−1.35652
$663$	31804.2	1.86301
$664$	19571.4	1.14385
$665$	4.94954	0.000288624 0
$666$	−4555.98	−0.265076
$667$	1037.49	0.0602276
$668$	1118.83	0.0648035
$669$	−7788.78	−0.450122
$670$	7997.44	0.461147
$671$	8423.63	0.484636
$672$	202.789	0.0116410
$673$	−5475.58	−0.313623	−0.156811	−	0.987629i	$-0.550121\pi$
$673$	−5475.58	−0.313623	−0.156811	+	0.987629i	$0.550121\pi$
$674$	6809.78	0.389173
$675$	−11672.9	−0.665614
$676$	−311.266	−0.0177097
$677$	−581.517	−0.0330126	−0.0165063	−	0.999864i	$-0.505254\pi$
$677$	−581.517	−0.0330126	−0.0165063	+	0.999864i	$0.505254\pi$
$678$	28648.9	1.62279
$679$	−1767.96	−0.0999233
$680$	19559.3	1.10304
$681$	15551.4	0.875084
$682$	12942.9	0.726701
$683$	−13721.9	−0.768749	−0.384374	−	0.923177i	$-0.625583\pi$
$683$	−13721.9	−0.768749	−0.384374	+	0.923177i	$0.625583\pi$
$684$	−0.535291	−2.99231e−5 0
$685$	17402.9	0.970700
$686$	4686.78	0.260848
$687$	8026.58	0.445754
$688$	10707.6	0.593349
$689$	29000.7	1.60354
$690$	−2980.40	−0.164437
$691$	−13268.5	−0.730476	−0.365238	−	0.930914i	$-0.619012\pi$
$691$	−13268.5	−0.730476	−0.365238	+	0.930914i	$0.619012\pi$
$692$	−1284.17	−0.0705447
$693$	187.479	0.0102767
$694$	18863.9	1.03179
$695$	9237.84	0.504189
$696$	−3378.62	−0.184003
$697$	27629.7	1.50150
$698$	−5398.87	−0.292766
$699$	−20427.0	−1.10532
$700$	74.2190	0.00400745
$701$	−8331.99	−0.448923	−0.224461	−	0.974483i	$-0.572062\pi$
$701$	−8331.99	−0.448923	−0.224461	+	0.974483i	$0.572062\pi$
$702$	−22711.7	−1.22108
$703$	98.0074	0.00525806
$704$	−8245.94	−0.441450
$705$	−2579.83	−0.137819
$706$	−5284.22	−0.281691
$707$	2200.62	0.117062
$708$	−120.705	−0.00640732
$709$	−16348.8	−0.865996	−0.432998	−	0.901395i	$-0.642544\pi$
$709$	−16348.8	−0.865996	−0.432998	+	0.901395i	$0.642544\pi$
$710$	17979.5	0.950362
$711$	−4408.13	−0.232514
$712$	13714.2	0.721855
$713$	10151.2	0.533191
$714$	−3995.06	−0.209400
$715$	5818.65	0.304343
$716$	−1245.19	−0.0649931
$717$	20894.8	1.08832
$718$	−6779.03	−0.352355
$719$	−12172.3	−0.631365	−0.315682	−	0.948865i	$-0.602233\pi$
$719$	−12172.3	−0.631365	−0.315682	+	0.948865i	$0.602233\pi$
$720$	−2029.01	−0.105023
$721$	2879.84	0.148753
$722$	18931.6	0.975848
$723$	22109.7	1.13730
$724$	−649.623	−0.0333467
$725$	−2416.79	−0.123803
$726$	−14189.5	−0.725377
$727$	29252.9	1.49234	0.746168	−	0.665757i	$-0.231891\pi$
$727$	29252.9	1.49234	0.746168	+	0.665757i	$0.231891\pi$
$728$	3171.93	0.161483
$729$	21835.8	1.10937
$730$	−17244.7	−0.874320
$731$	21687.0	1.09729
$732$	−979.491	−0.0494577
$733$	37664.4	1.89791	0.948955	−	0.315412i	$-0.102143\pi$
$733$	37664.4	1.89791	0.948955	+	0.315412i	$0.102143\pi$
$734$	−18317.2	−0.921115
$735$	−10878.7	−0.545940
$736$	−576.718	−0.0288833
$737$	−6516.52	−0.325697
$738$	−3010.11	−0.150140
$739$	−3929.89	−0.195620	−0.0978102	−	0.995205i	$-0.531184\pi$
$739$	−3929.89	−0.195620	−0.0978102	+	0.995205i	$0.531184\pi$
$740$	−889.641	−0.0441944
$741$	74.5362	0.00369522
$742$	−3642.90	−0.180236
$743$	11460.5	0.565877	0.282938	−	0.959138i	$-0.408691\pi$
$743$	11460.5	0.565877	0.282938	+	0.959138i	$0.408691\pi$
$744$	−33057.6	−1.62896
$745$	14170.1	0.696847
$746$	−12456.5	−0.611347
$747$	−4112.06	−0.201409
$748$	−725.572	−0.0354673
$749$	3153.26	0.153828
$750$	18088.2	0.880648
$751$	−15877.5	−0.771477	−0.385738	−	0.922608i	$-0.626053\pi$
$751$	−15877.5	−0.771477	−0.385738	+	0.922608i	$0.626053\pi$
$752$	4855.71	0.235465
$753$	−4762.00	−0.230461
$754$	−4702.30	−0.227119
$755$	14.8546	0.000716043 0
$756$	−142.893	−0.00687431
$757$	−20218.6	−0.970750	−0.485375	−	0.874306i	$-0.661317\pi$
$757$	−20218.6	−0.970750	−0.485375	+	0.874306i	$0.661317\pi$
$758$	27467.4	1.31617
$759$	2428.50	0.116138
$760$	45.8392	0.00218785
$761$	23499.8	1.11940	0.559702	−	0.828694i	$-0.310915\pi$
$761$	23499.8	1.11940	0.559702	+	0.828694i	$0.310915\pi$
$762$	18544.1	0.881602
$763$	2065.67	0.0980109
$764$	−135.047	−0.00639505
$765$	−4109.53	−0.194223
$766$	−15188.7	−0.716436
$767$	−3690.07	−0.173717
$768$	2751.42	0.129275
$769$	29600.4	1.38806	0.694029	−	0.719947i	$-0.255834\pi$
$769$	29600.4	1.38806	0.694029	+	0.719947i	$0.255834\pi$
$770$	−730.905	−0.0342078
$771$	−17439.4	−0.814609
$772$	−191.813	−0.00894238
$773$	−27577.5	−1.28317	−0.641587	−	0.767050i	$-0.721724\pi$
$773$	−27577.5	−1.28317	−0.641587	+	0.767050i	$0.721724\pi$
$774$	−2362.68	−0.109722
$775$	−23646.7	−1.09602
$776$	−16373.6	−0.757445
$777$	3991.36	0.184285
$778$	10582.2	0.487647
$779$	64.7529	0.00297819
$780$	−676.587	−0.0310586
$781$	−14650.1	−0.671219
$782$	11361.6	0.519555
$783$	4653.02	0.212370
$784$	20475.6	0.932744
$785$	−2938.27	−0.133594
$786$	5639.14	0.255905
$787$	11651.2	0.527726	0.263863	−	0.964560i	$-0.415003\pi$
$787$	11651.2	0.527726	0.263863	+	0.964560i	$0.415003\pi$
$788$	−1710.48	−0.0773266
$789$	22110.2	0.997646
$790$	17185.6	0.773968
$791$	5510.34	0.247693
$792$	1736.30	0.0778998
$793$	−29944.0	−1.34091
$794$	39857.5	1.78147
$795$	17068.0	0.761436
$796$	652.798	0.0290676
$797$	31387.4	1.39498	0.697490	−	0.716595i	$-0.254300\pi$
$797$	31387.4	1.39498	0.697490	+	0.716595i	$0.254300\pi$
$798$	−9.36281	−0.000415338 0
$799$	9834.66	0.435451
$800$	1343.44	0.0593721
$801$	−2881.43	−0.127104
$802$	13263.9	0.583997
$803$	14051.4	0.617512
$804$	757.734	0.0332378
$805$	−573.252	−0.0250987
$806$	−46009.0	−2.01067
$807$	15470.4	0.674825
$808$	20380.6	0.887361
$809$	−10893.6	−0.473422	−0.236711	−	0.971580i	$-0.576069\pi$
$809$	−10893.6	−0.473422	−0.236711	+	0.971580i	$0.576069\pi$
$810$	−10879.8	−0.471946
$811$	29519.7	1.27815	0.639073	−	0.769146i	$-0.279318\pi$
$811$	29519.7	1.27815	0.639073	+	0.769146i	$0.279318\pi$
$812$	−29.5851	−0.00127861
$813$	32615.0	1.40696
$814$	−14472.9	−0.623187
$815$	−16146.1	−0.693954
$816$	−35230.7	−1.51142
$817$	50.8256	0.00217645
$818$	16870.9	0.721122
$819$	−666.441	−0.0284339
$820$	−587.780	−0.0250319
$821$	−12375.9	−0.526092	−0.263046	−	0.964783i	$-0.584727\pi$
$821$	−12375.9	−0.526092	−0.263046	+	0.964783i	$0.584727\pi$
$822$	−32920.2	−1.39687
$823$	269.809	0.0114276	0.00571382	−	0.999984i	$-0.498181\pi$
$823$	269.809	0.0114276	0.00571382	+	0.999984i	$0.498181\pi$
$824$	26671.1	1.12759
$825$	−5657.08	−0.238733
$826$	463.526	0.0195256
$827$	31788.0	1.33661	0.668306	−	0.743887i	$-0.267020\pi$
$827$	31788.0	1.33661	0.668306	+	0.743887i	$0.267020\pi$
$828$	61.9971	0.00260211
$829$	16429.8	0.688336	0.344168	−	0.938908i	$-0.388161\pi$
$829$	16429.8	0.688336	0.344168	+	0.938908i	$0.388161\pi$
$830$	16031.3	0.670427
$831$	−7242.71	−0.302343
$832$	29312.3	1.22142
$833$	41470.9	1.72495
$834$	−17474.8	−0.725543
$835$	20130.2	0.834291
$836$	−1.70045	−7.03484e−5 0
$837$	45526.9	1.88009
$838$	40375.2	1.66436
$839$	−2939.79	−0.120969	−0.0604843	−	0.998169i	$-0.519265\pi$
$839$	−2939.79	−0.120969	−0.0604843	+	0.998169i	$0.519265\pi$
$840$	1866.81	0.0766798
$841$	−23425.6	−0.960500
$842$	−45459.4	−1.86061
$843$	1472.32	0.0601535
$844$	1081.17	0.0440941
$845$	−5600.36	−0.227998
$846$	−1071.43	−0.0435421
$847$	−2729.23	−0.110717
$848$	−32125.1	−1.30092
$849$	−25802.3	−1.04303
$850$	−26466.4	−1.06799
$851$	−11351.1	−0.457241
$852$	1703.50	0.0684988
$853$	16894.9	0.678160	0.339080	−	0.940758i	$-0.389884\pi$
$853$	16894.9	0.678160	0.339080	+	0.940758i	$0.389884\pi$
$854$	3761.39	0.150717
$855$	−9.63108	−0.000385235 0
$856$	29203.3	1.16606
$857$	−27783.0	−1.10741	−0.553705	−	0.832713i	$-0.686786\pi$
$857$	−27783.0	−1.10741	−0.553705	+	0.832713i	$0.686786\pi$
$858$	−11006.9	−0.437958
$859$	−5869.41	−0.233134	−0.116567	−	0.993183i	$-0.537189\pi$
$859$	−5869.41	−0.233134	−0.116567	+	0.993183i	$0.537189\pi$
$860$	−461.358	−0.0182932
$861$	2637.07	0.104380
$862$	−3320.81	−0.131215
$863$	−10920.8	−0.430763	−0.215381	−	0.976530i	$-0.569099\pi$
$863$	−10920.8	−0.430763	−0.215381	+	0.976530i	$0.569099\pi$
$864$	−2586.51	−0.101846
$865$	−23105.1	−0.908205
$866$	−11870.9	−0.465810
$867$	−48238.6	−1.88958
$868$	−289.471	−0.0113195
$869$	−14003.2	−0.546636
$870$	−2767.49	−0.107847
$871$	23164.6	0.901152
$872$	19130.8	0.742949
$873$	3440.18	0.133371
$874$	26.6271	0.00103052
$875$	3479.09	0.134417
$876$	−1633.88	−0.0630179
$877$	−21819.5	−0.840127	−0.420063	−	0.907495i	$-0.637992\pi$
$877$	−21819.5	−0.840127	−0.420063	+	0.907495i	$0.637992\pi$
$878$	−5131.82	−0.197256
$879$	32781.6	1.25790
$880$	−6445.53	−0.246908
$881$	9861.42	0.377117	0.188558	−	0.982062i	$-0.439619\pi$
$881$	9861.42	0.377117	0.188558	+	0.982062i	$0.439619\pi$
$882$	−4518.03	−0.172483
$883$	−18010.0	−0.686393	−0.343197	−	0.939264i	$-0.611510\pi$
$883$	−18010.0	−0.686393	−0.343197	+	0.939264i	$0.611510\pi$
$884$	2579.23	0.0981324
$885$	−2171.75	−0.0824889
$886$	7690.12	0.291597
$887$	−11959.5	−0.452719	−0.226360	−	0.974044i	$-0.572682\pi$
$887$	−11959.5	−0.452719	−0.226360	+	0.974044i	$0.572682\pi$
$888$	36965.3	1.39693
$889$	3566.78	0.134562
$890$	11233.5	0.423089
$891$	8865.11	0.333325
$892$	−631.648	−0.0237098
$893$	23.0485	0.000863704 0
$894$	−26804.9	−1.00278
$895$	−22403.8	−0.836732
$896$	−3337.26	−0.124431
$897$	−8632.73	−0.321336
$898$	−6650.97	−0.247156
$899$	9426.03	0.349695
$900$	−144.419	−0.00534886
$901$	−65065.6	−2.40582
$902$	−9562.15	−0.352976
$903$	2069.88	0.0762805
$904$	51033.0	1.87758
$905$	−11688.1	−0.429312
$906$	−28.0997	−0.00103041
$907$	24963.8	0.913902	0.456951	−	0.889492i	$-0.348941\pi$
$907$	24963.8	0.913902	0.456951	+	0.889492i	$0.348941\pi$
$908$	1261.18	0.0460944
$909$	−4282.08	−0.156246
$910$	2598.19	0.0946475
$911$	51520.2	1.87370	0.936851	−	0.349730i	$-0.113727\pi$
$911$	51520.2	1.87370	0.936851	+	0.349730i	$0.113727\pi$
$912$	−82.5665	−0.00299786
$913$	−13062.7	−0.473507
$914$	15428.2	0.558335
$915$	−17623.2	−0.636727
$916$	650.934	0.0234798
$917$	1084.64	0.0390598
$918$	50955.6	1.83201
$919$	4232.26	0.151914	0.0759572	−	0.997111i	$-0.475799\pi$
$919$	4232.26	0.151914	0.0759572	+	0.997111i	$0.475799\pi$
$920$	−5309.06	−0.190255
$921$	−15537.3	−0.555885
$922$	−37857.3	−1.35224
$923$	52077.6	1.85716
$924$	−69.2511	−0.00246558
$925$	26442.0	0.939899
$926$	24976.8	0.886382
$927$	−5603.74	−0.198545
$928$	−535.519	−0.0189432
$929$	−33324.8	−1.17691	−0.588456	−	0.808529i	$-0.700264\pi$
$929$	−33324.8	−1.17691	−0.588456	+	0.808529i	$0.700264\pi$
$930$	−27078.1	−0.954759
$931$	97.1911	0.00342138
$932$	−1656.57	−0.0582218
$933$	−28253.3	−0.991393
$934$	50363.3	1.76439
$935$	−13054.6	−0.456612
$936$	−6172.12	−0.215536
$937$	8530.17	0.297405	0.148703	−	0.988882i	$-0.452490\pi$
$937$	8530.17	0.297405	0.148703	+	0.988882i	$0.452490\pi$
$938$	−2909.81	−0.101288
$939$	32224.3	1.11991
$940$	−209.218	−0.00725949
$941$	20764.3	0.719339	0.359669	−	0.933080i	$-0.382890\pi$
$941$	20764.3	0.719339	0.359669	+	0.933080i	$0.382890\pi$
$942$	5558.19	0.192246
$943$	−7499.63	−0.258984
$944$	4087.63	0.140933
$945$	−2570.97	−0.0885011
$946$	−7505.49	−0.257954
$947$	−11879.1	−0.407622	−0.203811	−	0.979010i	$-0.565333\pi$
$947$	−11879.1	−0.407622	−0.203811	+	0.979010i	$0.565333\pi$
$948$	1628.28	0.0557849
$949$	−49949.2	−1.70856
$950$	−62.0267	−0.00211833
$951$	25507.5	0.869755
$952$	−7116.51	−0.242277
$953$	−40654.8	−1.38189	−0.690943	−	0.722909i	$-0.742805\pi$
$953$	−40654.8	−1.38189	−0.690943	+	0.722909i	$0.742805\pi$
$954$	7088.55	0.240566
$955$	−2429.79	−0.0823311
$956$	1694.51	0.0573267
$957$	2255.02	0.0761697
$958$	−37822.2	−1.27555
$959$	−6331.89	−0.213209
$960$	17251.5	0.579988
$961$	62436.6	2.09582
$962$	51447.6	1.72426
$963$	−6135.78	−0.205319
$964$	1793.03	0.0599063
$965$	−3451.15	−0.115126
$966$	1084.39	0.0361178
$967$	−29182.9	−0.970486	−0.485243	−	0.874379i	$-0.661269\pi$
$967$	−29182.9	−0.970486	−0.485243	+	0.874379i	$0.661269\pi$
$968$	−25276.2	−0.839266
$969$	−167.229	−0.00554402
$970$	−13411.9	−0.443949
$971$	21283.8	0.703430	0.351715	−	0.936107i	$-0.385599\pi$
$971$	21283.8	0.703430	0.351715	+	0.936107i	$0.385599\pi$
$972$	513.679	0.0169509
$973$	−3361.12	−0.110742
$974$	56769.5	1.86757
$975$	20109.6	0.660535
$976$	33170.0	1.08786
$977$	40886.1	1.33886	0.669428	−	0.742877i	$-0.266539\pi$
$977$	40886.1	1.33886	0.669428	+	0.742877i	$0.266539\pi$
$978$	30542.8	0.998621
$979$	−9153.37	−0.298818
$980$	−882.231	−0.0287570
$981$	−4019.49	−0.130818
$982$	−40418.0	−1.31343
$983$	8436.41	0.273733	0.136867	−	0.990589i	$-0.456297\pi$
$983$	8436.41	0.273733	0.136867	+	0.990589i	$0.456297\pi$
$984$	24422.7	0.791227
$985$	−30775.3	−0.995516
$986$	10550.0	0.340751
$987$	938.653	0.0302712
$988$	6.04469	0.000194643 0
$989$	−5886.58	−0.189264
$990$	1422.23	0.0456582
$991$	−4587.60	−0.147053	−0.0735267	−	0.997293i	$-0.523425\pi$
$991$	−4587.60	−0.147053	−0.0735267	+	0.997293i	$0.523425\pi$
$992$	−5239.71	−0.167703
$993$	−39387.8	−1.25875
$994$	−6541.69	−0.208742
$995$	11745.3	0.374222
$996$	1518.92	0.0483220
$997$	1524.36	0.0484221	0.0242111	−	0.999707i	$-0.492293\pi$
$997$	1524.36	0.0484221	0.0242111	+	0.999707i	$0.492293\pi$
$998$	−22628.5	−0.717730
$999$	−50908.5	−1.61229

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1997.4.a.a.1.70	✓	239

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1997.4.a.a.1.70	✓	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)

\(f(q)\)	\(=\)	\(q-2.76015 q^{2} -4.70524 q^{3} -0.381583 q^{4} -6.86551 q^{5} +12.9872 q^{6} +2.49796 q^{7} +23.1344 q^{8} -4.86067 q^{9} +O(q^{10})\)	\(q-2.76015 q^{2} -4.70524 q^{3} -0.381583 q^{4} -6.86551 q^{5} +12.9872 q^{6} +2.49796 q^{7} +23.1344 q^{8} -4.86067 q^{9} +18.9498 q^{10} -15.4408 q^{11} +1.79544 q^{12} +54.8883 q^{13} -6.89475 q^{14} +32.3039 q^{15} -60.8017 q^{16} -123.147 q^{17} +13.4162 q^{18} -0.288606 q^{19} +2.61976 q^{20} -11.7535 q^{21} +42.6189 q^{22} +33.4262 q^{23} -108.853 q^{24} -77.8647 q^{25} -151.500 q^{26} +149.912 q^{27} -0.953179 q^{28} +31.0383 q^{29} -89.1636 q^{30} +303.690 q^{31} -17.2535 q^{32} +72.6527 q^{33} +339.903 q^{34} -17.1498 q^{35} +1.85475 q^{36} -339.589 q^{37} +0.796596 q^{38} -258.263 q^{39} -158.830 q^{40} -224.364 q^{41} +32.4415 q^{42} -176.107 q^{43} +5.89194 q^{44} +33.3710 q^{45} -92.2611 q^{46} -79.8613 q^{47} +286.087 q^{48} -336.760 q^{49} +214.918 q^{50} +579.435 q^{51} -20.9444 q^{52} +528.358 q^{53} -413.780 q^{54} +106.009 q^{55} +57.7889 q^{56} +1.35796 q^{57} -85.6703 q^{58} -67.2288 q^{59} -12.3266 q^{60} -545.544 q^{61} -838.229 q^{62} -12.1418 q^{63} +534.036 q^{64} -376.836 q^{65} -200.532 q^{66} +422.032 q^{67} +46.9906 q^{68} -157.278 q^{69} +47.3360 q^{70} +948.793 q^{71} -112.449 q^{72} -910.016 q^{73} +937.315 q^{74} +366.373 q^{75} +0.110127 q^{76} -38.5705 q^{77} +712.844 q^{78} +906.898 q^{79} +417.435 q^{80} -574.136 q^{81} +619.278 q^{82} +845.986 q^{83} +4.48494 q^{84} +845.465 q^{85} +486.082 q^{86} -146.043 q^{87} -357.214 q^{88} +592.804 q^{89} -92.1089 q^{90} +137.109 q^{91} -12.7548 q^{92} -1428.94 q^{93} +220.429 q^{94} +1.98143 q^{95} +81.1819 q^{96} -707.759 q^{97} +929.508 q^{98} +75.0526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) \) 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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