LMFDB - Embedded newform 667.4.a.b.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.31231 q^{2} -9.27875 q^{3} +10.5960 q^{4} -14.7108 q^{5} -40.0128 q^{6} +19.8161 q^{7} +11.1948 q^{8} +59.0952 q^{9} +O(q^{10})$	\(q+4.31231 q^{2} -9.27875 q^{3} +10.5960 q^{4} -14.7108 q^{5} -40.0128 q^{6} +19.8161 q^{7} +11.1948 q^{8} +59.0952 q^{9} -63.4376 q^{10} +34.2197 q^{11} -98.3176 q^{12} +4.55972 q^{13} +85.4530 q^{14} +136.498 q^{15} -36.4927 q^{16} +76.6889 q^{17} +254.837 q^{18} -118.959 q^{19} -155.876 q^{20} -183.868 q^{21} +147.566 q^{22} -23.0000 q^{23} -103.873 q^{24} +91.4082 q^{25} +19.6629 q^{26} -297.803 q^{27} +209.971 q^{28} +29.0000 q^{29} +588.621 q^{30} +84.2974 q^{31} -246.926 q^{32} -317.516 q^{33} +330.706 q^{34} -291.511 q^{35} +626.173 q^{36} -236.283 q^{37} -512.987 q^{38} -42.3085 q^{39} -164.684 q^{40} -494.690 q^{41} -792.897 q^{42} +210.362 q^{43} +362.592 q^{44} -869.339 q^{45} -99.1831 q^{46} -145.915 q^{47} +338.607 q^{48} +49.6771 q^{49} +394.180 q^{50} -711.577 q^{51} +48.3148 q^{52} +387.134 q^{53} -1284.22 q^{54} -503.400 q^{55} +221.836 q^{56} +1103.79 q^{57} +125.057 q^{58} -366.564 q^{59} +1446.33 q^{60} -921.752 q^{61} +363.517 q^{62} +1171.03 q^{63} -772.879 q^{64} -67.0773 q^{65} -1369.23 q^{66} -323.269 q^{67} +812.596 q^{68} +213.411 q^{69} -1257.08 q^{70} -52.1027 q^{71} +661.557 q^{72} +299.440 q^{73} -1018.92 q^{74} -848.153 q^{75} -1260.49 q^{76} +678.100 q^{77} -182.447 q^{78} -557.695 q^{79} +536.838 q^{80} +1167.67 q^{81} -2133.26 q^{82} -1131.30 q^{83} -1948.27 q^{84} -1128.16 q^{85} +907.146 q^{86} -269.084 q^{87} +383.081 q^{88} +974.752 q^{89} -3748.86 q^{90} +90.3559 q^{91} -243.708 q^{92} -782.175 q^{93} -629.233 q^{94} +1749.98 q^{95} +2291.17 q^{96} +128.922 q^{97} +214.223 q^{98} +2022.22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) $ 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * 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 $

$2$	4.31231	1.52463	0.762316	−	0.647205i	$-0.224062\pi$
$2$	4.31231	1.52463	0.762316	+	0.647205i	$0.224062\pi$
$3$	−9.27875	−1.78570	−0.892848	−	0.450358i	$-0.851296\pi$
$3$	−9.27875	−1.78570	−0.892848	+	0.450358i	$0.851296\pi$
$4$	10.5960	1.32450
$5$	−14.7108	−1.31578	−0.657888	−	0.753116i	$-0.728550\pi$
$5$	−14.7108	−1.31578	−0.657888	+	0.753116i	$0.728550\pi$
$6$	−40.0128	−2.72253
$7$	19.8161	1.06997	0.534984	−	0.844862i	$-0.320318\pi$
$7$	19.8161	1.06997	0.534984	+	0.844862i	$0.320318\pi$
$8$	11.1948	0.494743
$9$	59.0952	2.18871
$10$	−63.4376	−2.00607
$11$	34.2197	0.937966	0.468983	−	0.883207i	$-0.344621\pi$
$11$	34.2197	0.937966	0.468983	+	0.883207i	$0.344621\pi$
$12$	−98.3176	−2.36516
$13$	4.55972	0.0972800	0.0486400	−	0.998816i	$-0.484511\pi$
$13$	4.55972	0.0972800	0.0486400	+	0.998816i	$0.484511\pi$
$14$	85.4530	1.63131
$15$	136.498	2.34958
$16$	−36.4927	−0.570199
$17$	76.6889	1.09411	0.547053	−	0.837098i	$-0.315750\pi$
$17$	76.6889	1.09411	0.547053	+	0.837098i	$0.315750\pi$
$18$	254.837	3.33698
$19$	−118.959	−1.43637	−0.718185	−	0.695853i	$-0.755027\pi$
$19$	−118.959	−1.43637	−0.718185	+	0.695853i	$0.755027\pi$
$20$	−155.876	−1.74275
$21$	−183.868	−1.91064
$22$	147.566	1.43005
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−103.873	−0.883461
$25$	91.4082	0.731265
$26$	19.6629	0.148316
$27$	−297.803	−2.12268
$28$	209.971	1.41717
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	588.621	3.58224
$31$	84.2974	0.488396	0.244198	−	0.969725i	$-0.421475\pi$
$31$	84.2974	0.488396	0.244198	+	0.969725i	$0.421475\pi$
$32$	−246.926	−1.36409
$33$	−317.516	−1.67492
$34$	330.706	1.66811
$35$	−291.511	−1.40784
$36$	626.173	2.89895
$37$	−236.283	−1.04986	−0.524928	−	0.851147i	$-0.675908\pi$
$37$	−236.283	−1.04986	−0.524928	+	0.851147i	$0.675908\pi$
$38$	−512.987	−2.18993
$39$	−42.3085	−0.173712
$40$	−164.684	−0.650971
$41$	−494.690	−1.88433	−0.942167	−	0.335145i	$-0.891215\pi$
$41$	−494.690	−1.88433	−0.942167	+	0.335145i	$0.891215\pi$
$42$	−792.897	−2.91302
$43$	210.362	0.746045	0.373022	−	0.927822i	$-0.378321\pi$
$43$	210.362	0.746045	0.373022	+	0.927822i	$0.378321\pi$
$44$	362.592	1.24234
$45$	−869.339	−2.87985
$46$	−99.1831	−0.317908
$47$	−145.915	−0.452850	−0.226425	−	0.974029i	$-0.572704\pi$
$47$	−145.915	−0.452850	−0.226425	+	0.974029i	$0.572704\pi$
$48$	338.607	1.01820
$49$	49.6771	0.144831
$50$	394.180	1.11491
$51$	−711.577	−1.95374
$52$	48.3148	0.128847
$53$	387.134	1.00334	0.501670	−	0.865059i	$-0.332719\pi$
$53$	387.134	1.00334	0.501670	+	0.865059i	$0.332719\pi$
$54$	−1284.22	−3.23630
$55$	−503.400	−1.23415
$56$	221.836	0.529359
$57$	1103.79	2.56492
$58$	125.057	0.283117
$59$	−366.564	−0.808857	−0.404428	−	0.914570i	$-0.632530\pi$
$59$	−366.564	−0.808857	−0.404428	+	0.914570i	$0.632530\pi$
$60$	1446.33	3.11201
$61$	−921.752	−1.93473	−0.967363	−	0.253396i	$-0.918452\pi$
$61$	−921.752	−1.93473	−0.967363	+	0.253396i	$0.918452\pi$
$62$	363.517	0.744623
$63$	1171.03	2.34185
$64$	−772.879	−1.50953
$65$	−67.0773	−0.127999
$66$	−1369.23	−2.55364
$67$	−323.269	−0.589457	−0.294728	−	0.955581i	$-0.595229\pi$
$67$	−323.269	−0.589457	−0.294728	+	0.955581i	$0.595229\pi$
$68$	812.596	1.44914
$69$	213.411	0.372343
$70$	−1257.08	−2.14643
$71$	−52.1027	−0.0870910	−0.0435455	−	0.999051i	$-0.513865\pi$
$71$	−52.1027	−0.0870910	−0.0435455	+	0.999051i	$0.513865\pi$
$72$	661.557	1.08285
$73$	299.440	0.480094	0.240047	−	0.970761i	$-0.422837\pi$
$73$	299.440	0.480094	0.240047	+	0.970761i	$0.422837\pi$
$74$	−1018.92	−1.60064
$75$	−848.153	−1.30582
$76$	−1260.49	−1.90247
$77$	678.100	1.00359
$78$	−182.447	−0.264847
$79$	−557.695	−0.794248	−0.397124	−	0.917765i	$-0.629992\pi$
$79$	−557.695	−0.794248	−0.397124	+	0.917765i	$0.629992\pi$
$80$	536.838	0.750254
$81$	1167.67	1.60174
$82$	−2133.26	−2.87291
$83$	−1131.30	−1.49610	−0.748048	−	0.663645i	$-0.769009\pi$
$83$	−1131.30	−1.49610	−0.748048	+	0.663645i	$0.769009\pi$
$84$	−1948.27	−2.53064
$85$	−1128.16	−1.43960
$86$	907.146	1.13744
$87$	−269.084	−0.331595
$88$	383.081	0.464053
$89$	974.752	1.16094	0.580469	−	0.814282i	$-0.302869\pi$
$89$	974.752	1.16094	0.580469	+	0.814282i	$0.302869\pi$
$90$	−3748.86	−4.39071
$91$	90.3559	0.104086
$92$	−243.708	−0.276177
$93$	−782.175	−0.872126
$94$	−629.233	−0.690430
$95$	1749.98	1.88994
$96$	2291.17	2.43584
$97$	128.922	0.134949	0.0674744	−	0.997721i	$-0.478506\pi$
$97$	128.922	0.134949	0.0674744	+	0.997721i	$0.478506\pi$
$98$	214.223	0.220814
$99$	2022.22	2.05294
$100$	968.561	0.968561
$101$	−837.175	−0.824773	−0.412386	−	0.911009i	$-0.635305\pi$
$101$	−837.175	−0.824773	−0.412386	+	0.911009i	$0.635305\pi$
$102$	−3068.54	−2.97873
$103$	716.227	0.685164	0.342582	−	0.939488i	$-0.388699\pi$
$103$	716.227	0.685164	0.342582	+	0.939488i	$0.388699\pi$
$104$	51.0450	0.0481286
$105$	2704.86	2.51397
$106$	1669.44	1.52972
$107$	−832.634	−0.752278	−0.376139	−	0.926563i	$-0.622748\pi$
$107$	−832.634	−0.752278	−0.376139	+	0.926563i	$0.622748\pi$
$108$	−3155.52	−2.81148
$109$	819.599	0.720214	0.360107	−	0.932911i	$-0.382740\pi$
$109$	819.599	0.720214	0.360107	+	0.932911i	$0.382740\pi$
$110$	−2170.82	−1.88163
$111$	2192.41	1.87472
$112$	−723.143	−0.610095
$113$	1893.25	1.57612	0.788060	−	0.615598i	$-0.211086\pi$
$113$	1893.25	1.57612	0.788060	+	0.615598i	$0.211086\pi$
$114$	4759.88	3.91056
$115$	338.349	0.274358
$116$	307.284	0.245954
$117$	269.458	0.212918
$118$	−1580.74	−1.23321
$119$	1519.67	1.17066
$120$	1528.06	1.16244
$121$	−160.012	−0.120219
$122$	−3974.88	−2.94974
$123$	4590.11	3.36485
$124$	893.216	0.646880
$125$	494.163	0.353594
$126$	5049.86	3.57046
$127$	561.290	0.392177	0.196088	−	0.980586i	$-0.437176\pi$
$127$	561.290	0.392177	0.196088	+	0.980586i	$0.437176\pi$
$128$	−1357.49	−0.937390
$129$	−1951.90	−1.33221
$130$	−289.258	−0.195151
$131$	−2487.57	−1.65909	−0.829544	−	0.558442i	$-0.811399\pi$
$131$	−2487.57	−1.65909	−0.829544	+	0.558442i	$0.811399\pi$
$132$	−3364.40	−2.21844
$133$	−2357.30	−1.53687
$134$	−1394.04	−0.898704
$135$	4380.93	2.79296
$136$	858.514	0.541301
$137$	−1962.60	−1.22392	−0.611958	−	0.790891i	$-0.709618\pi$
$137$	−1962.60	−1.22392	−0.611958	+	0.790891i	$0.709618\pi$
$138$	920.295	0.567686
$139$	2620.80	1.59923	0.799617	−	0.600511i	$-0.205036\pi$
$139$	2620.80	1.59923	0.799617	+	0.600511i	$0.205036\pi$
$140$	−3088.85	−1.86468
$141$	1353.91	0.808653
$142$	−224.683	−0.132782
$143$	156.032	0.0912453
$144$	−2156.55	−1.24800
$145$	−426.614	−0.244333
$146$	1291.28	0.731966
$147$	−460.941	−0.258624
$148$	−2503.65	−1.39053
$149$	1582.03	0.869834	0.434917	−	0.900470i	$-0.356778\pi$
$149$	1582.03	0.869834	0.434917	+	0.900470i	$0.356778\pi$
$150$	−3657.50	−1.99089
$151$	175.130	0.0943833	0.0471916	−	0.998886i	$-0.484973\pi$
$151$	175.130	0.0943833	0.0471916	+	0.998886i	$0.484973\pi$
$152$	−1331.72	−0.710634
$153$	4531.95	2.39468
$154$	2924.18	1.53011
$155$	−1240.08	−0.642619
$156$	−448.301	−0.230082
$157$	−2468.41	−1.25478	−0.627390	−	0.778705i	$-0.715877\pi$
$157$	−2468.41	−1.25478	−0.627390	+	0.778705i	$0.715877\pi$
$158$	−2404.95	−1.21094
$159$	−3592.12	−1.79166
$160$	3632.48	1.79483
$161$	−455.770	−0.223104
$162$	5035.36	2.44207
$163$	−4007.08	−1.92551	−0.962756	−	0.270372i	$-0.912853\pi$
$163$	−4007.08	−1.92551	−0.962756	+	0.270372i	$0.912853\pi$
$164$	−5241.74	−2.49580
$165$	4670.92	2.20382
$166$	−4878.50	−2.28099
$167$	−746.286	−0.345805	−0.172902	−	0.984939i	$-0.555314\pi$
$167$	−746.286	−0.345805	−0.172902	+	0.984939i	$0.555314\pi$
$168$	−2058.36	−0.945275
$169$	−2176.21	−0.990537
$170$	−4864.96	−2.19486
$171$	−7029.89	−3.14380
$172$	2229.00	0.988137
$173$	−2816.29	−1.23768	−0.618841	−	0.785517i	$-0.712397\pi$
$173$	−2816.29	−1.23768	−0.618841	+	0.785517i	$0.712397\pi$
$174$	−1160.37	−0.505561
$175$	1811.35	0.782430
$176$	−1248.77	−0.534828
$177$	3401.25	1.44437
$178$	4203.43	1.77000
$179$	897.178	0.374627	0.187314	−	0.982300i	$-0.440022\pi$
$179$	897.178	0.374627	0.187314	+	0.982300i	$0.440022\pi$
$180$	−9211.51	−3.81436
$181$	1793.64	0.736575	0.368287	−	0.929712i	$-0.379944\pi$
$181$	1793.64	0.736575	0.368287	+	0.929712i	$0.379944\pi$
$182$	389.642	0.158693
$183$	8552.71	3.45483
$184$	−257.480	−0.103161
$185$	3475.91	1.38137
$186$	−3372.98	−1.32967
$187$	2624.27	1.02623
$188$	−1546.12	−0.599800
$189$	−5901.29	−2.27119
$190$	7546.46	2.88146
$191$	−1511.92	−0.572767	−0.286383	−	0.958115i	$-0.592453\pi$
$191$	−1511.92	−0.572767	−0.286383	+	0.958115i	$0.592453\pi$
$192$	7171.35	2.69556
$193$	570.738	0.212863	0.106432	−	0.994320i	$-0.466057\pi$
$193$	570.738	0.212863	0.106432	+	0.994320i	$0.466057\pi$
$194$	555.951	0.205747
$195$	622.393	0.228567
$196$	526.378	0.191829
$197$	745.927	0.269772	0.134886	−	0.990861i	$-0.456933\pi$
$197$	745.927	0.269772	0.134886	+	0.990861i	$0.456933\pi$
$198$	8720.43	3.12997
$199$	−1431.74	−0.510018	−0.255009	−	0.966939i	$-0.582078\pi$
$199$	−1431.74	−0.510018	−0.255009	+	0.966939i	$0.582078\pi$
$200$	1023.29	0.361789
$201$	2999.53	1.05259
$202$	−3610.16	−1.25747
$203$	574.666	0.198688
$204$	−7539.87	−2.58773
$205$	7277.30	2.47936
$206$	3088.59	1.04462
$207$	−1359.19	−0.456378
$208$	−166.397	−0.0554690
$209$	−4070.73	−1.34727
$210$	11664.2	3.83288
$211$	2836.86	0.925579	0.462790	−	0.886468i	$-0.346848\pi$
$211$	2836.86	0.925579	0.462790	+	0.886468i	$0.346848\pi$
$212$	4102.08	1.32892
$213$	483.448	0.155518
$214$	−3590.57	−1.14695
$215$	−3094.60	−0.981627
$216$	−3333.84	−1.05018
$217$	1670.44	0.522568
$218$	3534.36	1.09806
$219$	−2778.43	−0.857301
$220$	−5334.03	−1.63464
$221$	349.680	0.106435
$222$	9454.34	2.85826
$223$	4261.37	1.27965	0.639826	−	0.768519i	$-0.279006\pi$
$223$	4261.37	1.27965	0.639826	+	0.768519i	$0.279006\pi$
$224$	−4893.11	−1.45953
$225$	5401.78	1.60053
$226$	8164.26	2.40300
$227$	−3116.68	−0.911283	−0.455641	−	0.890163i	$-0.650590\pi$
$227$	−3116.68	−0.911283	−0.455641	+	0.890163i	$0.650590\pi$
$228$	11695.7	3.39724
$229$	2068.10	0.596785	0.298393	−	0.954443i	$-0.403550\pi$
$229$	2068.10	0.596785	0.298393	+	0.954443i	$0.403550\pi$
$230$	1459.06	0.418295
$231$	−6291.92	−1.79211
$232$	324.648	0.0918715
$233$	−5212.95	−1.46572	−0.732858	−	0.680381i	$-0.761814\pi$
$233$	−5212.95	−1.46572	−0.732858	+	0.680381i	$0.761814\pi$
$234$	1161.98	0.324621
$235$	2146.54	0.595849
$236$	−3884.11	−1.07133
$237$	5174.71	1.41829
$238$	6553.30	1.78482
$239$	−2254.88	−0.610276	−0.305138	−	0.952308i	$-0.598703\pi$
$239$	−2254.88	−0.610276	−0.305138	+	0.952308i	$0.598703\pi$
$240$	−4981.19	−1.33973
$241$	−5291.70	−1.41439	−0.707195	−	0.707018i	$-0.750040\pi$
$241$	−5291.70	−1.41439	−0.707195	+	0.707018i	$0.750040\pi$
$242$	−690.021	−0.183290
$243$	−2793.84	−0.737551
$244$	−9766.89	−2.56254
$245$	−730.790	−0.190565
$246$	19794.0	5.13015
$247$	−542.419	−0.139730
$248$	943.690	0.241631
$249$	10497.0	2.67157
$250$	2130.98	0.539101
$251$	3699.60	0.930346	0.465173	−	0.885220i	$-0.345992\pi$
$251$	3699.60	0.930346	0.465173	+	0.885220i	$0.345992\pi$
$252$	12408.3	3.10178
$253$	−787.053	−0.195579
$254$	2420.46	0.597925
$255$	10467.9	2.57068
$256$	329.139	0.0803562
$257$	−3280.10	−0.796136	−0.398068	−	0.917356i	$-0.630319\pi$
$257$	−3280.10	−0.796136	−0.398068	+	0.917356i	$0.630319\pi$
$258$	−8417.18	−2.03113
$259$	−4682.20	−1.12331
$260$	−710.751	−0.169534
$261$	1713.76	0.406433
$262$	−10727.2	−2.52950
$263$	2366.07	0.554746	0.277373	−	0.960762i	$-0.410536\pi$
$263$	2366.07	0.554746	0.277373	+	0.960762i	$0.410536\pi$
$264$	−3554.52	−0.828657
$265$	−5695.06	−1.32017
$266$	−10165.4	−2.34316
$267$	−9044.48	−2.07308
$268$	−3425.36	−0.780735
$269$	−3886.83	−0.880983	−0.440491	−	0.897757i	$-0.645196\pi$
$269$	−3886.83	−0.880983	−0.440491	+	0.897757i	$0.645196\pi$
$270$	18891.9	4.25824
$271$	2134.04	0.478353	0.239177	−	0.970976i	$-0.423123\pi$
$271$	2134.04	0.478353	0.239177	+	0.970976i	$0.423123\pi$
$272$	−2798.59	−0.623858
$273$	−838.389	−0.185867
$274$	−8463.34	−1.86602
$275$	3127.96	0.685902
$276$	2261.31	0.493169
$277$	−3723.74	−0.807718	−0.403859	−	0.914821i	$-0.632331\pi$
$277$	−3723.74	−0.807718	−0.403859	+	0.914821i	$0.632331\pi$
$278$	11301.7	2.43824
$279$	4981.57	1.06896
$280$	−3263.39	−0.696518
$281$	−3650.10	−0.774900	−0.387450	−	0.921891i	$-0.626644\pi$
$281$	−3650.10	−0.774900	−0.387450	+	0.921891i	$0.626644\pi$
$282$	5838.49	1.23290
$283$	5724.45	1.20242	0.601208	−	0.799093i	$-0.294686\pi$
$283$	5724.45	1.20242	0.601208	+	0.799093i	$0.294686\pi$
$284$	−552.081	−0.115352
$285$	−16237.6	−3.37486
$286$	672.860	0.139115
$287$	−9802.82	−2.01618
$288$	−14592.1	−2.98559
$289$	968.190	0.197067
$290$	−1839.69	−0.372518
$291$	−1196.23	−0.240977
$292$	3172.87	0.635884
$293$	−8877.06	−1.76998	−0.884989	−	0.465612i	$-0.845834\pi$
$293$	−8877.06	−1.76998	−0.884989	+	0.465612i	$0.845834\pi$
$294$	−1987.72	−0.394307
$295$	5392.45	1.06427
$296$	−2645.13	−0.519409
$297$	−10190.7	−1.99100
$298$	6822.22	1.32618
$299$	−104.874	−0.0202843
$300$	−8987.04	−1.72956
$301$	4168.55	0.798244
$302$	755.214	0.143900
$303$	7767.94	1.47279
$304$	4341.13	0.819017
$305$	13559.7	2.54566
$306$	19543.1	3.65100
$307$	−10080.3	−1.87398	−0.936992	−	0.349351i	$-0.886402\pi$
$307$	−10080.3	−1.87398	−0.936992	+	0.349351i	$0.886402\pi$
$308$	7185.15	1.32926
$309$	−6645.69	−1.22349
$310$	−5347.63	−0.979757
$311$	6038.77	1.10105	0.550526	−	0.834818i	$-0.314427\pi$
$311$	6038.77	1.10105	0.550526	+	0.834818i	$0.314427\pi$
$312$	−473.634	−0.0859431
$313$	3189.51	0.575980	0.287990	−	0.957633i	$-0.407013\pi$
$313$	3189.51	0.575980	0.287990	+	0.957633i	$0.407013\pi$
$314$	−10644.5	−1.91308
$315$	−17226.9	−3.08135
$316$	−5909.34	−1.05198
$317$	8734.68	1.54760	0.773799	−	0.633432i	$-0.218354\pi$
$317$	8734.68	1.54760	0.773799	+	0.633432i	$0.218354\pi$
$318$	−15490.3	−2.73162
$319$	992.371	0.174176
$320$	11369.7	1.98620
$321$	7725.80	1.34334
$322$	−1965.42	−0.340151
$323$	−9122.82	−1.57154
$324$	12372.6	2.12151
$325$	416.796	0.0711375
$326$	−17279.7	−2.93570
$327$	−7604.85	−1.28608
$328$	−5537.94	−0.932261
$329$	−2891.47	−0.484535
$330$	20142.4	3.36002
$331$	10793.9	1.79241	0.896207	−	0.443637i	$-0.146312\pi$
$331$	10793.9	1.79241	0.896207	+	0.443637i	$0.146312\pi$
$332$	−11987.2	−1.98158
$333$	−13963.2	−2.29783
$334$	−3218.22	−0.527224
$335$	4755.55	0.775593
$336$	6709.86	1.08944
$337$	2191.48	0.354236	0.177118	−	0.984190i	$-0.443323\pi$
$337$	2191.48	0.354236	0.177118	+	0.984190i	$0.443323\pi$
$338$	−9384.48	−1.51020
$339$	−17567.0	−2.81447
$340$	−11954.0	−1.90675
$341$	2884.63	0.458099
$342$	−30315.1	−4.79313
$343$	−5812.51	−0.915003
$344$	2354.95	0.369101
$345$	−3139.45	−0.489920
$346$	−12144.7	−1.88701
$347$	6056.10	0.936913	0.468456	−	0.883487i	$-0.344810\pi$
$347$	6056.10	0.936913	0.468456	+	0.883487i	$0.344810\pi$
$348$	−2851.21	−0.439198
$349$	8150.31	1.25007	0.625037	−	0.780595i	$-0.285084\pi$
$349$	8150.31	1.25007	0.625037	+	0.780595i	$0.285084\pi$
$350$	7811.11	1.19292
$351$	−1357.90	−0.206494
$352$	−8449.74	−1.27947
$353$	−3887.05	−0.586082	−0.293041	−	0.956100i	$-0.594667\pi$
$353$	−3887.05	−0.586082	−0.293041	+	0.956100i	$0.594667\pi$
$354$	14667.3	2.20214
$355$	766.474	0.114592
$356$	10328.5	1.53766
$357$	−14100.7	−2.09044
$358$	3868.91	0.571168
$359$	−9646.84	−1.41822	−0.709110	−	0.705098i	$-0.750903\pi$
$359$	−9646.84	−1.41822	−0.709110	+	0.705098i	$0.750903\pi$
$360$	−9732.04	−1.42479
$361$	7292.19	1.06316
$362$	7734.72	1.12300
$363$	1484.71	0.214675
$364$	957.411	0.137863
$365$	−4405.01	−0.631695
$366$	36881.9	5.26734
$367$	8106.57	1.15302	0.576511	−	0.817089i	$-0.304414\pi$
$367$	8106.57	1.15302	0.576511	+	0.817089i	$0.304414\pi$
$368$	839.333	0.118895
$369$	−29233.8	−4.12426
$370$	14989.2	2.10609
$371$	7671.48	1.07354
$372$	−8287.93	−1.15513
$373$	−13673.5	−1.89808	−0.949042	−	0.315150i	$-0.897945\pi$
$373$	−13673.5	−1.89808	−0.949042	+	0.315150i	$0.897945\pi$
$374$	11316.7	1.56463
$375$	−4585.22	−0.631412
$376$	−1633.49	−0.224045
$377$	132.232	0.0180644
$378$	−25448.2	−3.46273
$379$	−1308.91	−0.177399	−0.0886996	−	0.996058i	$-0.528271\pi$
$379$	−1308.91	−0.177399	−0.0886996	+	0.996058i	$0.528271\pi$
$380$	18542.8	2.50323
$381$	−5208.07	−0.700309
$382$	−6519.85	−0.873258
$383$	−1171.38	−0.156279	−0.0781394	−	0.996942i	$-0.524898\pi$
$383$	−1171.38	−0.156279	−0.0781394	+	0.996942i	$0.524898\pi$
$384$	12595.8	1.67389
$385$	−9975.41	−1.32050
$386$	2461.20	0.324538
$387$	12431.4	1.63288
$388$	1366.06	0.178740
$389$	−7729.15	−1.00741	−0.503706	−	0.863875i	$-0.668031\pi$
$389$	−7729.15	−1.00741	−0.503706	+	0.863875i	$0.668031\pi$
$390$	2683.95	0.348480
$391$	−1763.85	−0.228137
$392$	556.123	0.0716542
$393$	23081.6	2.96263
$394$	3216.67	0.411303
$395$	8204.15	1.04505
$396$	21427.4	2.71912
$397$	2928.50	0.370220	0.185110	−	0.982718i	$-0.440736\pi$
$397$	2928.50	0.370220	0.185110	+	0.982718i	$0.440736\pi$
$398$	−6174.11	−0.777589
$399$	21872.8	2.74438
$400$	−3335.74	−0.416967
$401$	−5441.40	−0.677632	−0.338816	−	0.940853i	$-0.610026\pi$
$401$	−5441.40	−0.677632	−0.338816	+	0.940853i	$0.610026\pi$
$402$	12934.9	1.60481
$403$	384.373	0.0475111
$404$	−8870.71	−1.09241
$405$	−17177.4	−2.10753
$406$	2478.14	0.302926
$407$	−8085.53	−0.984729
$408$	−7965.94	−0.966600
$409$	5366.66	0.648812	0.324406	−	0.945918i	$-0.394836\pi$
$409$	5366.66	0.648812	0.324406	+	0.945918i	$0.394836\pi$
$410$	31382.0	3.78011
$411$	18210.5	2.18554
$412$	7589.14	0.907500
$413$	−7263.86	−0.865451
$414$	−5861.24	−0.695808
$415$	16642.3	1.96853
$416$	−1125.91	−0.132698
$417$	−24317.8	−2.85574
$418$	−17554.3	−2.05408
$419$	2740.68	0.319549	0.159775	−	0.987154i	$-0.448923\pi$
$419$	2740.68	0.319549	0.159775	+	0.987154i	$0.448923\pi$
$420$	28660.7	3.32975
$421$	7698.34	0.891198	0.445599	−	0.895233i	$-0.352991\pi$
$421$	7698.34	0.891198	0.445599	+	0.895233i	$0.352991\pi$
$422$	12233.4	1.41117
$423$	−8622.90	−0.991158
$424$	4333.88	0.496395
$425$	7009.99	0.800081
$426$	2084.78	0.237108
$427$	−18265.5	−2.07009
$428$	−8822.59	−0.996392
$429$	−1447.79	−0.162936
$430$	−13344.9	−1.49662
$431$	5157.03	0.576346	0.288173	−	0.957578i	$-0.406952\pi$
$431$	5157.03	0.576346	0.288173	+	0.957578i	$0.406952\pi$
$432$	10867.7	1.21035
$433$	1178.83	0.130833	0.0654166	−	0.997858i	$-0.479162\pi$
$433$	1178.83	0.130833	0.0654166	+	0.997858i	$0.479162\pi$
$434$	7203.47	0.796723
$435$	3958.44	0.436305
$436$	8684.47	0.953924
$437$	2736.05	0.299504
$438$	−11981.5	−1.30707
$439$	9978.75	1.08487	0.542437	−	0.840097i	$-0.317502\pi$
$439$	9978.75	1.08487	0.542437	+	0.840097i	$0.317502\pi$
$440$	−5635.44	−0.610589
$441$	2935.67	0.316993
$442$	1507.93	0.162273
$443$	−5919.49	−0.634861	−0.317431	−	0.948281i	$-0.602820\pi$
$443$	−5919.49	−0.634861	−0.317431	+	0.948281i	$0.602820\pi$
$444$	23230.8	2.48307
$445$	−14339.4	−1.52753
$446$	18376.3	1.95100
$447$	−14679.3	−1.55326
$448$	−15315.4	−1.61515
$449$	−1802.60	−0.189466	−0.0947328	−	0.995503i	$-0.530200\pi$
$449$	−1802.60	−0.189466	−0.0947328	+	0.995503i	$0.530200\pi$
$450$	23294.2	2.44022
$451$	−16928.2	−1.76744
$452$	20060.8	2.08757
$453$	−1624.99	−0.168540
$454$	−13440.1	−1.38937
$455$	−1329.21	−0.136954
$456$	12356.7	1.26898
$457$	6794.03	0.695430	0.347715	−	0.937600i	$-0.386958\pi$
$457$	6794.03	0.695430	0.347715	+	0.937600i	$0.386958\pi$
$458$	8918.28	0.909877
$459$	−22838.2	−2.32243
$460$	3585.14	0.363387
$461$	−7439.41	−0.751600	−0.375800	−	0.926701i	$-0.622632\pi$
$461$	−7439.41	−0.751600	−0.375800	+	0.926701i	$0.622632\pi$
$462$	−27132.7	−2.73231
$463$	8122.70	0.815322	0.407661	−	0.913133i	$-0.366345\pi$
$463$	8122.70	0.815322	0.407661	+	0.913133i	$0.366345\pi$
$464$	−1058.29	−0.105883
$465$	11506.4	1.14752
$466$	−22479.9	−2.23468
$467$	16806.0	1.66529	0.832644	−	0.553808i	$-0.186826\pi$
$467$	16806.0	1.66529	0.832644	+	0.553808i	$0.186826\pi$
$468$	2855.17	0.282010
$469$	−6405.92	−0.630700
$470$	9256.53	0.908450
$471$	22903.7	2.24065
$472$	−4103.60	−0.400177
$473$	7198.53	0.699765
$474$	22315.0	2.16236
$475$	−10873.8	−1.05037
$476$	16102.5	1.55054
$477$	22877.8	2.19602
$478$	−9723.74	−0.930446
$479$	−7118.80	−0.679053	−0.339527	−	0.940596i	$-0.610267\pi$
$479$	−7118.80	−0.679053	−0.339527	+	0.940596i	$0.610267\pi$
$480$	−33704.9	−3.20502
$481$	−1077.38	−0.102130
$482$	−22819.4	−2.15642
$483$	4228.97	0.398395
$484$	−1695.49	−0.159231
$485$	−1896.55	−0.177562
$486$	−12047.9	−1.12449
$487$	1137.50	0.105842	0.0529211	−	0.998599i	$-0.483147\pi$
$487$	1137.50	0.105842	0.0529211	+	0.998599i	$0.483147\pi$
$488$	−10318.8	−0.957192
$489$	37180.7	3.43838
$490$	−3151.39	−0.290542
$491$	7306.16	0.671533	0.335766	−	0.941945i	$-0.391005\pi$
$491$	7306.16	0.671533	0.335766	+	0.941945i	$0.391005\pi$
$492$	48636.8	4.45674
$493$	2223.98	0.203170
$494$	−2339.08	−0.213037
$495$	−29748.5	−2.70120
$496$	−3076.25	−0.278483
$497$	−1032.47	−0.0931845
$498$	45266.4	4.07316
$499$	17608.0	1.57964	0.789822	−	0.613336i	$-0.210173\pi$
$499$	17608.0	1.57964	0.789822	+	0.613336i	$0.210173\pi$
$500$	5236.16	0.468336
$501$	6924.60	0.617502
$502$	15953.8	1.41843
$503$	18070.1	1.60180	0.800901	−	0.598796i	$-0.204354\pi$
$503$	18070.1	1.60180	0.800901	+	0.598796i	$0.204354\pi$
$504$	13109.5	1.15861
$505$	12315.5	1.08522
$506$	−3394.02	−0.298187
$507$	20192.5	1.76880
$508$	5947.43	0.519438
$509$	−19550.1	−1.70244	−0.851220	−	0.524809i	$-0.824137\pi$
$509$	−19550.1	−1.70244	−0.851220	+	0.524809i	$0.824137\pi$
$510$	45140.7	3.91934
$511$	5933.73	0.513685
$512$	12279.2	1.05990
$513$	35426.3	3.04895
$514$	−14144.8	−1.21381
$515$	−10536.3	−0.901522
$516$	−20682.3	−1.76451
$517$	−4993.18	−0.424758
$518$	−20191.1	−1.71264
$519$	26131.7	2.21012
$520$	−750.914	−0.0633265
$521$	21358.5	1.79603	0.898017	−	0.439961i	$-0.145008\pi$
$521$	21358.5	1.79603	0.898017	+	0.439961i	$0.145008\pi$
$522$	7390.26	0.619661
$523$	−4748.61	−0.397022	−0.198511	−	0.980099i	$-0.563610\pi$
$523$	−4748.61	−0.397022	−0.198511	+	0.980099i	$0.563610\pi$
$524$	−26358.3	−2.19746
$525$	−16807.1	−1.39718
$526$	10203.2	0.845783
$527$	6464.68	0.534356
$528$	11587.0	0.955040
$529$	529.000	0.0434783
$530$	−24558.9	−2.01277
$531$	−21662.2	−1.77035
$532$	−24977.9	−2.03558
$533$	−2255.65	−0.183308
$534$	−39002.6	−3.16069
$535$	12248.7	0.989829
$536$	−3618.92	−0.291630
$537$	−8324.69	−0.668970
$538$	−16761.2	−1.34317
$539$	1699.93	0.135847
$540$	46420.3	3.69928
$541$	10258.6	0.815251	0.407626	−	0.913149i	$-0.366357\pi$
$541$	10258.6	0.815251	0.407626	+	0.913149i	$0.366357\pi$
$542$	9202.64	0.729312
$543$	−16642.7	−1.31530
$544$	−18936.5	−1.49245
$545$	−12057.0	−0.947640
$546$	−3615.39	−0.283378
$547$	−9122.14	−0.713043	−0.356521	−	0.934287i	$-0.616037\pi$
$547$	−9122.14	−0.713043	−0.356521	+	0.934287i	$0.616037\pi$
$548$	−20795.7	−1.62108
$549$	−54471.1	−4.23455
$550$	13488.7	1.04575
$551$	−3449.80	−0.266727
$552$	2389.09	0.184214
$553$	−11051.3	−0.849820
$554$	−16057.9	−1.23147
$555$	−32252.1	−2.46671
$556$	27770.0	2.11818
$557$	20030.0	1.52370	0.761848	−	0.647756i	$-0.224292\pi$
$557$	20030.0	1.52370	0.761848	+	0.647756i	$0.224292\pi$
$558$	21482.1	1.62976
$559$	959.193	0.0725752
$560$	10638.0	0.802748
$561$	−24350.0	−1.83254
$562$	−15740.4	−1.18144
$563$	−24214.3	−1.81263	−0.906315	−	0.422602i	$-0.861117\pi$
$563$	−24214.3	−1.81263	−0.906315	+	0.422602i	$0.861117\pi$
$564$	14346.1	1.07106
$565$	−27851.2	−2.07382
$566$	24685.6	1.83324
$567$	23138.7	1.71381
$568$	−583.278	−0.0430877
$569$	3119.60	0.229843	0.114921	−	0.993375i	$-0.463338\pi$
$569$	3119.60	0.229843	0.114921	+	0.993375i	$0.463338\pi$
$570$	−70021.7	−5.14541
$571$	239.040	0.0175193	0.00875963	−	0.999962i	$-0.497212\pi$
$571$	239.040	0.0175193	0.00875963	+	0.999962i	$0.497212\pi$
$572$	1653.32	0.120854
$573$	14028.7	1.02279
$574$	−42272.8	−3.07392
$575$	−2102.39	−0.152479
$576$	−45673.5	−3.30392
$577$	−3348.64	−0.241604	−0.120802	−	0.992677i	$-0.538547\pi$
$577$	−3348.64	−0.241604	−0.120802	+	0.992677i	$0.538547\pi$
$578$	4175.13	0.300454
$579$	−5295.73	−0.380109
$580$	−4520.40	−0.323620
$581$	−22417.9	−1.60077
$582$	−5158.53	−0.367402
$583$	13247.6	0.941098
$584$	3352.16	0.237523
$585$	−3963.94	−0.280152
$586$	−38280.6	−2.69856
$587$	8527.45	0.599600	0.299800	−	0.954002i	$-0.403080\pi$
$587$	8527.45	0.599600	0.299800	+	0.954002i	$0.403080\pi$
$588$	−4884.13	−0.342548
$589$	−10027.9	−0.701517
$590$	23253.9	1.62263
$591$	−6921.27	−0.481731
$592$	8622.61	0.598627
$593$	8053.68	0.557715	0.278857	−	0.960333i	$-0.410044\pi$
$593$	8053.68	0.557715	0.278857	+	0.960333i	$0.410044\pi$
$594$	−43945.6	−3.03554
$595$	−22355.6	−1.54032
$596$	16763.2	1.15210
$597$	13284.8	0.910736
$598$	−452.247	−0.0309260
$599$	2509.39	0.171170	0.0855850	−	0.996331i	$-0.472724\pi$
$599$	2509.39	0.171170	0.0855850	+	0.996331i	$0.472724\pi$
$600$	−9494.88	−0.646045
$601$	21767.6	1.47740	0.738700	−	0.674034i	$-0.235440\pi$
$601$	21767.6	1.47740	0.738700	+	0.674034i	$0.235440\pi$
$602$	17976.1	1.21703
$603$	−19103.6	−1.29015
$604$	1855.68	0.125011
$605$	2353.91	0.158182
$606$	33497.7	2.24547
$607$	−20474.2	−1.36907	−0.684533	−	0.728982i	$-0.739994\pi$
$607$	−20474.2	−1.36907	−0.684533	+	0.728982i	$0.739994\pi$
$608$	29374.0	1.95933
$609$	−5332.18	−0.354796
$610$	58473.7	3.88120
$611$	−665.334	−0.0440533
$612$	48020.5	3.17175
$613$	6060.22	0.399298	0.199649	−	0.979867i	$-0.436020\pi$
$613$	6060.22	0.399298	0.199649	+	0.979867i	$0.436020\pi$
$614$	−43469.4	−2.85713
$615$	−67524.2	−4.42738
$616$	7591.17	0.496521
$617$	−26878.9	−1.75382	−0.876908	−	0.480658i	$-0.840398\pi$
$617$	−26878.9	−1.75382	−0.876908	+	0.480658i	$0.840398\pi$
$618$	−28658.2	−1.86538
$619$	−582.357	−0.0378140	−0.0189070	−	0.999821i	$-0.506019\pi$
$619$	−582.357	−0.0378140	−0.0189070	+	0.999821i	$0.506019\pi$
$620$	−13139.9	−0.851149
$621$	6849.47	0.442608
$622$	26041.0	1.67870
$623$	19315.8	1.24217
$624$	1543.95	0.0990507
$625$	−18695.6	−1.19652
$626$	13754.2	0.878158
$627$	37771.3	2.40581
$628$	−26155.3	−1.66196
$629$	−18120.3	−1.14865
$630$	−74287.6	−4.69792
$631$	22205.3	1.40092	0.700460	−	0.713692i	$-0.252978\pi$
$631$	22205.3	1.40092	0.700460	+	0.713692i	$0.252978\pi$
$632$	−6243.26	−0.392949
$633$	−26322.5	−1.65280
$634$	37666.6	2.35952
$635$	−8257.04	−0.516017
$636$	−38062.1	−2.37305
$637$	226.514	0.0140892
$638$	4279.41	0.265554
$639$	−3079.02	−0.190617
$640$	19969.7	1.23339
$641$	18355.6	1.13105	0.565525	−	0.824731i	$-0.308674\pi$
$641$	18355.6	1.13105	0.565525	+	0.824731i	$0.308674\pi$
$642$	33316.0	2.04810
$643$	6162.94	0.377982	0.188991	−	0.981979i	$-0.439478\pi$
$643$	6162.94	0.377982	0.188991	+	0.981979i	$0.439478\pi$
$644$	−4829.34	−0.295501
$645$	28714.0	1.75289
$646$	−39340.4	−2.39602
$647$	−2592.08	−0.157504	−0.0787521	−	0.996894i	$-0.525094\pi$
$647$	−2592.08	−0.157504	−0.0787521	+	0.996894i	$0.525094\pi$
$648$	13071.8	0.792452
$649$	−12543.7	−0.758680
$650$	1797.35	0.108458
$651$	−15499.6	−0.933147
$652$	−42459.0	−2.55034
$653$	−22348.3	−1.33929	−0.669645	−	0.742682i	$-0.733554\pi$
$653$	−22348.3	−1.33929	−0.669645	+	0.742682i	$0.733554\pi$
$654$	−32794.5	−1.96080
$655$	36594.3	2.18299
$656$	18052.6	1.07445
$657$	17695.5	1.05079
$658$	−12468.9	−0.738737
$659$	−3432.16	−0.202880	−0.101440	−	0.994842i	$-0.532345\pi$
$659$	−3432.16	−0.202880	−0.101440	+	0.994842i	$0.532345\pi$
$660$	49493.1	2.91896
$661$	4471.31	0.263107	0.131554	−	0.991309i	$-0.458003\pi$
$661$	4471.31	0.263107	0.131554	+	0.991309i	$0.458003\pi$
$662$	46546.8	2.73277
$663$	−3244.60	−0.190060
$664$	−12664.6	−0.740183
$665$	34677.8	2.02217
$666$	−60213.5	−3.50334
$667$	−667.000	−0.0387202
$668$	−7907.65	−0.458018
$669$	−39540.2	−2.28507
$670$	20507.4	1.18249
$671$	−31542.1	−1.81471
$672$	45401.9	2.60628
$673$	12897.5	0.738725	0.369362	−	0.929285i	$-0.379576\pi$
$673$	12897.5	0.738725	0.369362	+	0.929285i	$0.379576\pi$
$674$	9450.34	0.540080
$675$	−27221.6	−1.55224
$676$	−23059.1	−1.31197
$677$	−6925.22	−0.393143	−0.196572	−	0.980489i	$-0.562981\pi$
$677$	−6925.22	−0.393143	−0.196572	+	0.980489i	$0.562981\pi$
$678$	−75754.1	−4.29103
$679$	2554.73	0.144391
$680$	−12629.4	−0.712231
$681$	28918.9	1.62727
$682$	12439.4	0.698432
$683$	22335.8	1.25133	0.625663	−	0.780093i	$-0.284829\pi$
$683$	22335.8	1.25133	0.625663	+	0.780093i	$0.284829\pi$
$684$	−74488.7	−4.16396
$685$	28871.5	1.61040
$686$	−25065.3	−1.39504
$687$	−19189.4	−1.06568
$688$	−7676.69	−0.425394
$689$	1765.23	0.0976048
$690$	−13538.3	−0.746948
$691$	−1658.37	−0.0912989	−0.0456495	−	0.998958i	$-0.514536\pi$
$691$	−1658.37	−0.0912989	−0.0456495	+	0.998958i	$0.514536\pi$
$692$	−29841.5	−1.63931
$693$	40072.5	2.19658
$694$	26115.8	1.42845
$695$	−38554.1	−2.10423
$696$	−3012.33	−0.164055
$697$	−37937.3	−2.06166
$698$	35146.6	1.90590
$699$	48369.7	2.61732
$700$	19193.1	1.03633
$701$	−34092.2	−1.83687	−0.918433	−	0.395577i	$-0.870545\pi$
$701$	−34092.2	−1.83687	−0.918433	+	0.395577i	$0.870545\pi$
$702$	−5855.68	−0.314827
$703$	28107.9	1.50798
$704$	−26447.7	−1.41589
$705$	−19917.2	−1.06401
$706$	−16762.2	−0.893559
$707$	−16589.5	−0.882480
$708$	36039.7	1.91307
$709$	18791.8	0.995405	0.497703	−	0.867348i	$-0.334177\pi$
$709$	18791.8	0.995405	0.497703	+	0.867348i	$0.334177\pi$
$710$	3305.27	0.174711
$711$	−32957.1	−1.73838
$712$	10912.1	0.574366
$713$	−1938.84	−0.101838
$714$	−60806.4	−3.18715
$715$	−2295.36	−0.120058
$716$	9506.50	0.496194
$717$	20922.5	1.08977
$718$	−41600.2	−2.16226
$719$	24708.5	1.28160	0.640801	−	0.767707i	$-0.278602\pi$
$719$	24708.5	1.28160	0.640801	+	0.767707i	$0.278602\pi$
$720$	31724.6	1.64209
$721$	14192.8	0.733103
$722$	31446.2	1.62092
$723$	49100.3	2.52567
$724$	19005.4	0.975593
$725$	2650.84	0.135793
$726$	6402.53	0.327301
$727$	−19944.9	−1.01749	−0.508745	−	0.860917i	$-0.669890\pi$
$727$	−19944.9	−1.01749	−0.508745	+	0.860917i	$0.669890\pi$
$728$	1011.51	0.0514961
$729$	−5603.78	−0.284702
$730$	−18995.8	−0.963103
$731$	16132.4	0.816252
$732$	90624.5	4.57593
$733$	−16796.0	−0.846350	−0.423175	−	0.906048i	$-0.639084\pi$
$733$	−16796.0	−0.846350	−0.423175	+	0.906048i	$0.639084\pi$
$734$	34958.0	1.75793
$735$	6780.82	0.340291
$736$	5679.30	0.284432
$737$	−11062.2	−0.552890
$738$	−126065.	−6.28797
$739$	−2626.04	−0.130718	−0.0653589	−	0.997862i	$-0.520819\pi$
$739$	−2626.04	−0.130718	−0.0653589	+	0.997862i	$0.520819\pi$
$740$	36830.8	1.82963
$741$	5032.97	0.249515
$742$	33081.8	1.63675
$743$	13564.3	0.669752	0.334876	−	0.942262i	$-0.391306\pi$
$743$	13564.3	0.669752	0.334876	+	0.942262i	$0.391306\pi$
$744$	−8756.26	−0.431479
$745$	−23273.0	−1.14451
$746$	−58964.2	−2.89388
$747$	−66854.2	−3.27452
$748$	27806.8	1.35925
$749$	−16499.5	−0.804913
$750$	−19772.9	−0.962671
$751$	4869.70	0.236615	0.118308	−	0.992977i	$-0.462253\pi$
$751$	4869.70	0.236615	0.118308	+	0.992977i	$0.462253\pi$
$752$	5324.86	0.258215
$753$	−34327.7	−1.66132
$754$	570.225	0.0275416
$755$	−2576.30	−0.124187
$756$	−62530.1	−3.00820
$757$	−4279.30	−0.205461	−0.102730	−	0.994709i	$-0.532758\pi$
$757$	−4279.30	−0.205461	−0.102730	+	0.994709i	$0.532758\pi$
$758$	−5644.43	−0.270468
$759$	7302.87	0.349246
$760$	19590.6	0.935035
$761$	−30664.2	−1.46068	−0.730339	−	0.683085i	$-0.760638\pi$
$761$	−30664.2	−1.46068	−0.730339	+	0.683085i	$0.760638\pi$
$762$	−22458.8	−1.06771
$763$	16241.2	0.770606
$764$	−16020.3	−0.758630
$765$	−66668.6	−3.15086
$766$	−5051.36	−0.238267
$767$	−1671.43	−0.0786856
$768$	−3054.00	−0.143492
$769$	−36485.0	−1.71090	−0.855449	−	0.517886i	$-0.826719\pi$
$769$	−36485.0	−1.71090	−0.855449	+	0.517886i	$0.826719\pi$
$770$	−43017.0	−2.01328
$771$	30435.2	1.42166
$772$	6047.54	0.281938
$773$	−35311.2	−1.64302	−0.821511	−	0.570193i	$-0.806868\pi$
$773$	−35311.2	−1.64302	−0.821511	+	0.570193i	$0.806868\pi$
$774$	53608.0	2.48953
$775$	7705.47	0.357147
$776$	1443.25	0.0667650
$777$	43444.9	2.00589
$778$	−33330.5	−1.53593
$779$	58847.8	2.70660
$780$	6594.88	0.302737
$781$	−1782.94	−0.0816884
$782$	−7606.24	−0.347824
$783$	−8636.29	−0.394171
$784$	−1812.85	−0.0825826
$785$	36312.3	1.65101
$786$	99534.9	4.51691
$787$	7604.69	0.344445	0.172222	−	0.985058i	$-0.444905\pi$
$787$	7604.69	0.344445	0.172222	+	0.985058i	$0.444905\pi$
$788$	7903.84	0.357313
$789$	−21954.2	−0.990608
$790$	35378.8	1.59332
$791$	37516.7	1.68640
$792$	22638.3	1.01568
$793$	−4202.93	−0.188210
$794$	12628.6	0.564449
$795$	52843.0	2.35742
$796$	−15170.7	−0.675519
$797$	−32479.3	−1.44351	−0.721754	−	0.692150i	$-0.756664\pi$
$797$	−32479.3	−1.44351	−0.721754	+	0.692150i	$0.756664\pi$
$798$	94322.1	4.18417
$799$	−11190.1	−0.495466
$800$	−22571.1	−0.997509
$801$	57603.1	2.54096
$802$	−23465.0	−1.03314
$803$	10246.8	0.450312
$804$	31783.0	1.39416
$805$	6704.75	0.293554
$806$	1657.53	0.0724369
$807$	36064.9	1.57317
$808$	−9371.98	−0.408051
$809$	−346.319	−0.0150506	−0.00752529	−	0.999972i	$-0.502395\pi$
$809$	−346.319	−0.0150506	−0.00752529	+	0.999972i	$0.502395\pi$
$810$	−74074.2	−3.21321
$811$	34644.8	1.50005	0.750026	−	0.661408i	$-0.230041\pi$
$811$	34644.8	1.50005	0.750026	+	0.661408i	$0.230041\pi$
$812$	6089.17	0.263162
$813$	−19801.2	−0.854193
$814$	−34867.3	−1.50135
$815$	58947.4	2.53354
$816$	25967.4	1.11402
$817$	−25024.4	−1.07160
$818$	23142.7	0.989199
$819$	5339.60	0.227815
$820$	77110.3	3.28391
$821$	−25328.3	−1.07669	−0.538347	−	0.842724i	$-0.680951\pi$
$821$	−25328.3	−1.07669	−0.538347	+	0.842724i	$0.680951\pi$
$822$	78529.3	3.33214
$823$	−14533.2	−0.615546	−0.307773	−	0.951460i	$-0.599584\pi$
$823$	−14533.2	−0.615546	−0.307773	+	0.951460i	$0.599584\pi$
$824$	8017.99	0.338980
$825$	−29023.6	−1.22481
$826$	−31324.0	−1.31949
$827$	19737.4	0.829909	0.414955	−	0.909842i	$-0.363797\pi$
$827$	19737.4	0.829909	0.414955	+	0.909842i	$0.363797\pi$
$828$	−14402.0	−0.604472
$829$	−37980.5	−1.59121	−0.795607	−	0.605813i	$-0.792848\pi$
$829$	−37980.5	−1.59121	−0.795607	+	0.605813i	$0.792848\pi$
$830$	71766.7	3.00128
$831$	34551.7	1.44234
$832$	−3524.12	−0.146847
$833$	3809.68	0.158460
$834$	−104866.	−4.35396
$835$	10978.5	0.455001
$836$	−43133.5	−1.78445
$837$	−25104.0	−1.03671
$838$	11818.7	0.487195
$839$	28240.5	1.16206	0.581031	−	0.813882i	$-0.302650\pi$
$839$	28240.5	1.16206	0.581031	+	0.813882i	$0.302650\pi$
$840$	30280.2	1.24377
$841$	841.000	0.0344828
$842$	33197.6	1.35875
$843$	33868.4	1.38374
$844$	30059.3	1.22593
$845$	32013.8	1.30332
$846$	−37184.6	−1.51115
$847$	−3170.81	−0.128631
$848$	−14127.6	−0.572103
$849$	−53115.8	−2.14715
$850$	30229.3	1.21983
$851$	5434.50	0.218910
$852$	5122.62	0.205984
$853$	12473.8	0.500698	0.250349	−	0.968156i	$-0.419455\pi$
$853$	12473.8	0.500698	0.250349	+	0.968156i	$0.419455\pi$
$854$	−78766.5	−3.15613
$855$	103415.	4.13653
$856$	−9321.14	−0.372184
$857$	3825.65	0.152488	0.0762438	−	0.997089i	$-0.475707\pi$
$857$	3825.65	0.152488	0.0762438	+	0.997089i	$0.475707\pi$
$858$	−6243.30	−0.248418
$859$	29600.6	1.17574	0.587869	−	0.808956i	$-0.299967\pi$
$859$	29600.6	1.17574	0.587869	+	0.808956i	$0.299967\pi$
$860$	−32790.4	−1.30017
$861$	90957.9	3.60028
$862$	22238.7	0.878716
$863$	−39710.0	−1.56633	−0.783165	−	0.621814i	$-0.786396\pi$
$863$	−39710.0	−1.56633	−0.783165	+	0.621814i	$0.786396\pi$
$864$	73535.4	2.89551
$865$	41430.0	1.62851
$866$	5083.46	0.199472
$867$	−8983.59	−0.351902
$868$	17700.0	0.692141
$869$	−19084.2	−0.744978
$870$	17070.0	0.665204
$871$	−1474.02	−0.0573423
$872$	9175.22	0.356321
$873$	7618.66	0.295364
$874$	11798.7	0.456633
$875$	9792.38	0.378335
$876$	−29440.3	−1.13550
$877$	21260.3	0.818596	0.409298	−	0.912401i	$-0.365774\pi$
$877$	21260.3	0.818596	0.409298	+	0.912401i	$0.365774\pi$
$878$	43031.4	1.65403
$879$	82368.0	3.16064
$880$	18370.4	0.703713
$881$	24518.6	0.937629	0.468815	−	0.883297i	$-0.344681\pi$
$881$	24518.6	0.937629	0.468815	+	0.883297i	$0.344681\pi$
$882$	12659.5	0.483298
$883$	4979.94	0.189794	0.0948972	−	0.995487i	$-0.469748\pi$
$883$	4979.94	0.189794	0.0948972	+	0.995487i	$0.469748\pi$
$884$	3705.21	0.140973
$885$	−50035.2	−1.90047
$886$	−25526.7	−0.967930
$887$	19571.7	0.740871	0.370435	−	0.928858i	$-0.379209\pi$
$887$	19571.7	0.740871	0.370435	+	0.928858i	$0.379209\pi$
$888$	24543.5	0.927506
$889$	11122.6	0.419617
$890$	−61835.9	−2.32893
$891$	39957.3	1.50238
$892$	45153.5	1.69490
$893$	17357.9	0.650460
$894$	−63301.7	−2.36815
$895$	−13198.2	−0.492925
$896$	−26900.0	−1.00298
$897$	973.096	0.0362216
$898$	−7773.38	−0.288865
$899$	2444.63	0.0906928
$900$	57237.3	2.11990
$901$	29688.9	1.09776
$902$	−72999.4	−2.69470
$903$	−38679.0	−1.42542
$904$	21194.4	0.779775
$905$	−26385.9	−0.969167
$906$	−7007.44	−0.256961
$907$	−48623.3	−1.78006	−0.890028	−	0.455906i	$-0.849315\pi$
$907$	−48623.3	−1.78006	−0.890028	+	0.455906i	$0.849315\pi$
$908$	−33024.3	−1.20699
$909$	−49473.0	−1.80519
$910$	−5731.96	−0.208805
$911$	−44881.7	−1.63227	−0.816134	−	0.577863i	$-0.803887\pi$
$911$	−44881.7	−1.63227	−0.816134	+	0.577863i	$0.803887\pi$
$912$	−40280.3	−1.46251
$913$	−38712.6	−1.40329
$914$	29298.0	1.06027
$915$	−125817.	−4.54578
$916$	21913.6	0.790442
$917$	−49294.0	−1.77517
$918$	−98485.4	−3.54085
$919$	−24842.1	−0.891692	−0.445846	−	0.895110i	$-0.647097\pi$
$919$	−24842.1	−0.891692	−0.445846	+	0.895110i	$0.647097\pi$
$920$	3787.73	0.135737
$921$	93532.6	3.34637
$922$	−32081.0	−1.14591
$923$	−237.574	−0.00847221
$924$	−66669.2	−2.37365
$925$	−21598.2	−0.767723
$926$	35027.6	1.24307
$927$	42325.5	1.49963
$928$	−7160.86	−0.253305
$929$	45309.4	1.60016	0.800082	−	0.599891i	$-0.204789\pi$
$929$	45309.4	1.60016	0.800082	+	0.599891i	$0.204789\pi$
$930$	49619.3	1.74955
$931$	−5909.52	−0.208031
$932$	−55236.5	−1.94134
$933$	−56032.2	−1.96615
$934$	72472.7	2.53895
$935$	−38605.2	−1.35029
$936$	3016.52	0.105340
$937$	5732.36	0.199859	0.0999296	−	0.994995i	$-0.468138\pi$
$937$	5732.36	0.199859	0.0999296	+	0.994995i	$0.468138\pi$
$938$	−27624.3	−0.961584
$939$	−29594.7	−1.02853
$940$	22744.7	0.789203
$941$	39778.8	1.37806	0.689029	−	0.724734i	$-0.258037\pi$
$941$	39778.8	1.37806	0.689029	+	0.724734i	$0.258037\pi$
$942$	98768.0	3.41617
$943$	11377.9	0.392911
$944$	13376.9	0.461210
$945$	86812.8	2.98838
$946$	31042.3	1.06688
$947$	3727.05	0.127891	0.0639456	−	0.997953i	$-0.479632\pi$
$947$	3727.05	0.127891	0.0639456	+	0.997953i	$0.479632\pi$
$948$	54831.3	1.87852
$949$	1365.36	0.0467035
$950$	−46891.2	−1.60142
$951$	−81046.9	−2.76354
$952$	17012.4	0.579175
$953$	−56143.9	−1.90837	−0.954187	−	0.299211i	$-0.903276\pi$
$953$	−56143.9	−1.90837	−0.954187	+	0.299211i	$0.903276\pi$
$954$	98656.0	3.34812
$955$	22241.5	0.753632
$956$	−23892.7	−0.808311
$957$	−9207.96	−0.311025
$958$	−30698.5	−1.03531
$959$	−38891.1	−1.30955
$960$	−105496.	−3.54675
$961$	−22684.9	−0.761470
$962$	−4646.01	−0.155710
$963$	−49204.6	−1.64652
$964$	−56070.8	−1.87336
$965$	−8396.02	−0.280080
$966$	18236.6	0.607406
$967$	17500.1	0.581970	0.290985	−	0.956728i	$-0.406017\pi$
$967$	17500.1	0.581970	0.290985	+	0.956728i	$0.406017\pi$
$968$	−1791.30	−0.0594777
$969$	84648.4	2.80629
$970$	−8178.49	−0.270717
$971$	−24205.4	−0.799987	−0.399994	−	0.916518i	$-0.630988\pi$
$971$	−24205.4	−0.799987	−0.399994	+	0.916518i	$0.630988\pi$
$972$	−29603.5	−0.976886
$973$	51934.0	1.71113
$974$	4905.26	0.161370
$975$	−3867.35	−0.127030
$976$	33637.3	1.10318
$977$	−27501.8	−0.900573	−0.450286	−	0.892884i	$-0.648678\pi$
$977$	−27501.8	−0.900573	−0.450286	+	0.892884i	$0.648678\pi$
$978$	160334.	5.24226
$979$	33355.7	1.08892
$980$	−7743.45	−0.252404
$981$	48434.4	1.57634
$982$	31506.4	1.02384
$983$	48667.7	1.57910	0.789552	−	0.613683i	$-0.210313\pi$
$983$	48667.7	1.57910	0.789552	+	0.613683i	$0.210313\pi$
$984$	51385.2	1.66474
$985$	−10973.2	−0.354959
$986$	9590.48	0.309760
$987$	26829.3	0.865233
$988$	−5747.48	−0.185072
$989$	−4838.33	−0.155561
$990$	−128285.	−4.11834
$991$	28177.2	0.903208	0.451604	−	0.892218i	$-0.350852\pi$
$991$	28177.2	0.903208	0.451604	+	0.892218i	$0.350852\pi$
$992$	−20815.2	−0.666214
$993$	−100154.	−3.20071
$994$	−4452.34	−0.142072
$995$	21062.1	0.671069
$996$	111226.	3.53850
$997$	11687.9	0.371273	0.185636	−	0.982619i	$-0.440565\pi$
$997$	11687.9	0.371273	0.185636	+	0.982619i	$0.440565\pi$
$998$	75931.1	2.40837
$999$	70365.8	2.22850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.34	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.34	✓	38	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+4.31231 q^{2} -9.27875 q^{3} +10.5960 q^{4} -14.7108 q^{5} -40.0128 q^{6} +19.8161 q^{7} +11.1948 q^{8} +59.0952 q^{9} +O(q^{10})\)	\(q+4.31231 q^{2} -9.27875 q^{3} +10.5960 q^{4} -14.7108 q^{5} -40.0128 q^{6} +19.8161 q^{7} +11.1948 q^{8} +59.0952 q^{9} -63.4376 q^{10} +34.2197 q^{11} -98.3176 q^{12} +4.55972 q^{13} +85.4530 q^{14} +136.498 q^{15} -36.4927 q^{16} +76.6889 q^{17} +254.837 q^{18} -118.959 q^{19} -155.876 q^{20} -183.868 q^{21} +147.566 q^{22} -23.0000 q^{23} -103.873 q^{24} +91.4082 q^{25} +19.6629 q^{26} -297.803 q^{27} +209.971 q^{28} +29.0000 q^{29} +588.621 q^{30} +84.2974 q^{31} -246.926 q^{32} -317.516 q^{33} +330.706 q^{34} -291.511 q^{35} +626.173 q^{36} -236.283 q^{37} -512.987 q^{38} -42.3085 q^{39} -164.684 q^{40} -494.690 q^{41} -792.897 q^{42} +210.362 q^{43} +362.592 q^{44} -869.339 q^{45} -99.1831 q^{46} -145.915 q^{47} +338.607 q^{48} +49.6771 q^{49} +394.180 q^{50} -711.577 q^{51} +48.3148 q^{52} +387.134 q^{53} -1284.22 q^{54} -503.400 q^{55} +221.836 q^{56} +1103.79 q^{57} +125.057 q^{58} -366.564 q^{59} +1446.33 q^{60} -921.752 q^{61} +363.517 q^{62} +1171.03 q^{63} -772.879 q^{64} -67.0773 q^{65} -1369.23 q^{66} -323.269 q^{67} +812.596 q^{68} +213.411 q^{69} -1257.08 q^{70} -52.1027 q^{71} +661.557 q^{72} +299.440 q^{73} -1018.92 q^{74} -848.153 q^{75} -1260.49 q^{76} +678.100 q^{77} -182.447 q^{78} -557.695 q^{79} +536.838 q^{80} +1167.67 q^{81} -2133.26 q^{82} -1131.30 q^{83} -1948.27 q^{84} -1128.16 q^{85} +907.146 q^{86} -269.084 q^{87} +383.081 q^{88} +974.752 q^{89} -3748.86 q^{90} +90.3559 q^{91} -243.708 q^{92} -782.175 q^{93} -629.233 q^{94} +1749.98 q^{95} +2291.17 q^{96} +128.922 q^{97} +214.223 q^{98} +2022.22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * q^99

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