LMFDB - Embedded newform 547.4.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,4,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, 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("547.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	547.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:	$32.2740447731$
Analytic rank:	$1$
Dimension:	$65$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.59199 q^{2} -5.98144 q^{3} +4.90240 q^{4} +5.54311 q^{5} +21.4853 q^{6} -31.4038 q^{7} +11.1265 q^{8} +8.77766 q^{9} +O(q^{10})$	\(q-3.59199 q^{2} -5.98144 q^{3} +4.90240 q^{4} +5.54311 q^{5} +21.4853 q^{6} -31.4038 q^{7} +11.1265 q^{8} +8.77766 q^{9} -19.9108 q^{10} +14.8601 q^{11} -29.3234 q^{12} +10.6067 q^{13} +112.802 q^{14} -33.1558 q^{15} -79.1857 q^{16} -58.1265 q^{17} -31.5293 q^{18} -50.2525 q^{19} +27.1745 q^{20} +187.840 q^{21} -53.3773 q^{22} +180.026 q^{23} -66.5528 q^{24} -94.2740 q^{25} -38.0992 q^{26} +108.996 q^{27} -153.954 q^{28} +104.154 q^{29} +119.095 q^{30} +306.426 q^{31} +195.422 q^{32} -88.8848 q^{33} +208.790 q^{34} -174.074 q^{35} +43.0316 q^{36} -293.470 q^{37} +180.507 q^{38} -63.4434 q^{39} +61.6756 q^{40} +309.457 q^{41} -674.719 q^{42} -306.967 q^{43} +72.8501 q^{44} +48.6555 q^{45} -646.650 q^{46} +457.299 q^{47} +473.645 q^{48} +643.196 q^{49} +338.631 q^{50} +347.680 q^{51} +51.9983 q^{52} +219.046 q^{53} -391.512 q^{54} +82.3711 q^{55} -349.415 q^{56} +300.583 q^{57} -374.121 q^{58} +721.011 q^{59} -162.543 q^{60} +13.9552 q^{61} -1100.68 q^{62} -275.651 q^{63} -68.4683 q^{64} +58.7941 q^{65} +319.273 q^{66} -373.595 q^{67} -284.959 q^{68} -1076.81 q^{69} +625.273 q^{70} -543.871 q^{71} +97.6650 q^{72} +682.773 q^{73} +1054.14 q^{74} +563.894 q^{75} -246.358 q^{76} -466.663 q^{77} +227.888 q^{78} -760.651 q^{79} -438.935 q^{80} -888.949 q^{81} -1111.57 q^{82} -129.826 q^{83} +920.866 q^{84} -322.201 q^{85} +1102.62 q^{86} -622.993 q^{87} +165.342 q^{88} -1032.49 q^{89} -174.770 q^{90} -333.091 q^{91} +882.557 q^{92} -1832.87 q^{93} -1642.61 q^{94} -278.555 q^{95} -1168.90 q^{96} -1683.12 q^{97} -2310.35 q^{98} +130.437 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) $ 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * 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 $

$2$	−3.59199	−1.26996	−0.634980	−	0.772528i	$-0.718992\pi$
$2$	−3.59199	−1.26996	−0.634980	+	0.772528i	$0.718992\pi$
$3$	−5.98144	−1.15113	−0.575565	−	0.817756i	$-0.695218\pi$
$3$	−5.98144	−1.15113	−0.575565	+	0.817756i	$0.695218\pi$
$4$	4.90240	0.612800
$5$	5.54311	0.495790	0.247895	−	0.968787i	$-0.420261\pi$
$5$	5.54311	0.495790	0.247895	+	0.968787i	$0.420261\pi$
$6$	21.4853	1.46189
$7$	−31.4038	−1.69564	−0.847822	−	0.530281i	$-0.822086\pi$
$7$	−31.4038	−1.69564	−0.847822	+	0.530281i	$0.822086\pi$
$8$	11.1265	0.491729
$9$	8.77766	0.325098
$10$	−19.9108	−0.629634
$11$	14.8601	0.407317	0.203658	−	0.979042i	$-0.434717\pi$
$11$	14.8601	0.407317	0.203658	+	0.979042i	$0.434717\pi$
$12$	−29.3234	−0.705412
$13$	10.6067	0.226290	0.113145	−	0.993578i	$-0.463908\pi$
$13$	10.6067	0.226290	0.113145	+	0.993578i	$0.463908\pi$
$14$	112.802	2.15340
$15$	−33.1558	−0.570719
$16$	−79.1857	−1.23728
$17$	−58.1265	−0.829279	−0.414640	−	0.909986i	$-0.636092\pi$
$17$	−58.1265	−0.829279	−0.414640	+	0.909986i	$0.636092\pi$
$18$	−31.5293	−0.412862
$19$	−50.2525	−0.606775	−0.303387	−	0.952867i	$-0.598118\pi$
$19$	−50.2525	−0.606775	−0.303387	+	0.952867i	$0.598118\pi$
$20$	27.1745	0.303820
$21$	187.840	1.95190
$22$	−53.3773	−0.517276
$23$	180.026	1.63208	0.816042	−	0.577993i	$-0.196164\pi$
$23$	180.026	1.63208	0.816042	+	0.577993i	$0.196164\pi$
$24$	−66.5528	−0.566043
$25$	−94.2740	−0.754192
$26$	−38.0992	−0.287380
$27$	108.996	0.776899
$28$	−153.954	−1.03909
$29$	104.154	0.666930	0.333465	−	0.942763i	$-0.391782\pi$
$29$	104.154	0.666930	0.333465	+	0.942763i	$0.391782\pi$
$30$	119.095	0.724790
$31$	306.426	1.77535	0.887674	−	0.460472i	$-0.152320\pi$
$31$	306.426	1.77535	0.887674	+	0.460472i	$0.152320\pi$
$32$	195.422	1.07956
$33$	−88.8848	−0.468874
$34$	208.790	1.05315
$35$	−174.074	−0.840684
$36$	43.0316	0.199220
$37$	−293.470	−1.30395	−0.651974	−	0.758241i	$-0.726059\pi$
$37$	−293.470	−1.30395	−0.651974	+	0.758241i	$0.726059\pi$
$38$	180.507	0.770580
$39$	−63.4434	−0.260489
$40$	61.6756	0.243794
$41$	309.457	1.17876	0.589379	−	0.807856i	$-0.299372\pi$
$41$	309.457	1.17876	0.589379	+	0.807856i	$0.299372\pi$
$42$	−674.719	−2.47884
$43$	−306.967	−1.08865	−0.544326	−	0.838874i	$-0.683214\pi$
$43$	−306.967	−1.08865	−0.544326	+	0.838874i	$0.683214\pi$
$44$	72.8501	0.249604
$45$	48.6555	0.161181
$46$	−646.650	−2.07268
$47$	457.299	1.41923	0.709616	−	0.704588i	$-0.248868\pi$
$47$	457.299	1.41923	0.709616	+	0.704588i	$0.248868\pi$
$48$	473.645	1.42426
$49$	643.196	1.87521
$50$	338.631	0.957794
$51$	347.680	0.954608
$52$	51.9983	0.138671
$53$	219.046	0.567702	0.283851	−	0.958868i	$-0.408388\pi$
$53$	219.046	0.567702	0.283851	+	0.958868i	$0.408388\pi$
$54$	−391.512	−0.986631
$55$	82.3711	0.201944
$56$	−349.415	−0.833796
$57$	300.583	0.698476
$58$	−374.121	−0.846975
$59$	721.011	1.59098	0.795488	−	0.605969i	$-0.207214\pi$
$59$	721.011	1.59098	0.795488	+	0.605969i	$0.207214\pi$
$60$	−162.543	−0.349737
$61$	13.9552	0.0292915	0.0146457	−	0.999893i	$-0.495338\pi$
$61$	13.9552	0.0292915	0.0146457	+	0.999893i	$0.495338\pi$
$62$	−1100.68	−2.25462
$63$	−275.651	−0.551251
$64$	−68.4683	−0.133727
$65$	58.7941	0.112192
$66$	319.273	0.595452
$67$	−373.595	−0.681222	−0.340611	−	0.940204i	$-0.610634\pi$
$67$	−373.595	−0.681222	−0.340611	+	0.940204i	$0.610634\pi$
$68$	−284.959	−0.508182
$69$	−1076.81	−1.87874
$70$	625.273	1.06764
$71$	−543.871	−0.909093	−0.454546	−	0.890723i	$-0.650199\pi$
$71$	−543.871	−0.909093	−0.454546	+	0.890723i	$0.650199\pi$
$72$	97.6650	0.159860
$73$	682.773	1.09469	0.547346	−	0.836907i	$-0.315638\pi$
$73$	682.773	1.09469	0.547346	+	0.836907i	$0.315638\pi$
$74$	1054.14	1.65596
$75$	563.894	0.868172
$76$	−246.358	−0.371832
$77$	−466.663	−0.690664
$78$	227.888	0.330811
$79$	−760.651	−1.08329	−0.541645	−	0.840607i	$-0.682198\pi$
$79$	−760.651	−1.08329	−0.541645	+	0.840607i	$0.682198\pi$
$80$	−438.935	−0.613430
$81$	−888.949	−1.21941
$82$	−1111.57	−1.49698
$83$	−129.826	−0.171690	−0.0858448	−	0.996309i	$-0.527359\pi$
$83$	−129.826	−0.171690	−0.0858448	+	0.996309i	$0.527359\pi$
$84$	920.866	1.19613
$85$	−322.201	−0.411149
$86$	1102.62	1.38254
$87$	−622.993	−0.767722
$88$	165.342	0.200289
$89$	−1032.49	−1.22971	−0.614855	−	0.788641i	$-0.710785\pi$
$89$	−1032.49	−1.22971	−0.614855	+	0.788641i	$0.710785\pi$
$90$	−174.770	−0.204693
$91$	−333.091	−0.383707
$92$	882.557	1.00014
$93$	−1832.87	−2.04366
$94$	−1642.61	−1.80237
$95$	−278.555	−0.300833
$96$	−1168.90	−1.24272
$97$	−1683.12	−1.76180	−0.880902	−	0.473299i	$-0.843063\pi$
$97$	−1683.12	−1.76180	−0.880902	+	0.473299i	$0.843063\pi$
$98$	−2310.35	−2.38144
$99$	130.437	0.132418
$100$	−462.169	−0.462169
$101$	93.8042	0.0924146	0.0462073	−	0.998932i	$-0.485287\pi$
$101$	93.8042	0.0924146	0.0462073	+	0.998932i	$0.485287\pi$
$102$	−1248.86	−1.21231
$103$	−482.474	−0.461549	−0.230775	−	0.973007i	$-0.574126\pi$
$103$	−482.474	−0.461549	−0.230775	+	0.973007i	$0.574126\pi$
$104$	118.016	0.111273
$105$	1041.22	0.967736
$106$	−786.810	−0.720959
$107$	−1397.60	−1.26272	−0.631361	−	0.775489i	$-0.717503\pi$
$107$	−1397.60	−1.26272	−0.631361	+	0.775489i	$0.717503\pi$
$108$	534.342	0.476084
$109$	562.557	0.494341	0.247170	−	0.968972i	$-0.420499\pi$
$109$	562.557	0.494341	0.247170	+	0.968972i	$0.420499\pi$
$110$	−295.876	−0.256461
$111$	1755.37	1.50101
$112$	2486.73	2.09798
$113$	137.633	0.114579	0.0572896	−	0.998358i	$-0.481754\pi$
$113$	137.633	0.114579	0.0572896	+	0.998358i	$0.481754\pi$
$114$	−1079.69	−0.887037
$115$	997.901	0.809171
$116$	510.606	0.408695
$117$	93.1021	0.0735666
$118$	−2589.86	−2.02048
$119$	1825.39	1.40616
$120$	−368.909	−0.280639
$121$	−1110.18	−0.834093
$122$	−50.1270	−0.0371990
$123$	−1851.00	−1.35690
$124$	1502.23	1.08793
$125$	−1215.46	−0.869712
$126$	990.138	0.700067
$127$	−844.632	−0.590150	−0.295075	−	0.955474i	$-0.595345\pi$
$127$	−844.632	−0.590150	−0.295075	+	0.955474i	$0.595345\pi$
$128$	−1317.44	−0.909735
$129$	1836.10	1.25318
$130$	−211.188	−0.142480
$131$	2792.60	1.86252	0.931261	−	0.364353i	$-0.118710\pi$
$131$	2792.60	1.86252	0.931261	+	0.364353i	$0.118710\pi$
$132$	−435.749	−0.287326
$133$	1578.12	1.02887
$134$	1341.95	0.865126
$135$	604.176	0.385179
$136$	−646.747	−0.407780
$137$	−2944.36	−1.83616	−0.918080	−	0.396396i	$-0.870261\pi$
$137$	−2944.36	−1.83616	−0.918080	+	0.396396i	$0.870261\pi$
$138$	3867.90	2.38592
$139$	1439.49	0.878391	0.439195	−	0.898392i	$-0.355264\pi$
$139$	1439.49	0.878391	0.439195	+	0.898392i	$0.355264\pi$
$140$	−853.382	−0.515171
$141$	−2735.31	−1.63372
$142$	1953.58	1.15451
$143$	157.617	0.0921718
$144$	−695.065	−0.402237
$145$	577.338	0.330657
$146$	−2452.51	−1.39022
$147$	−3847.24	−2.15861
$148$	−1438.71	−0.799060
$149$	−2720.57	−1.49582	−0.747912	−	0.663798i	$-0.768944\pi$
$149$	−2720.57	−1.49582	−0.747912	+	0.663798i	$0.768944\pi$
$150$	−2025.50	−1.10254
$151$	3568.35	1.92310	0.961550	−	0.274631i	$-0.0885558\pi$
$151$	3568.35	1.92310	0.961550	+	0.274631i	$0.0885558\pi$
$152$	−559.137	−0.298368
$153$	−510.215	−0.269597
$154$	1676.25	0.877116
$155$	1698.55	0.880201
$156$	−311.025	−0.159628
$157$	894.897	0.454908	0.227454	−	0.973789i	$-0.426960\pi$
$157$	894.897	0.454908	0.227454	+	0.973789i	$0.426960\pi$
$158$	2732.25	1.37574
$159$	−1310.21	−0.653499
$160$	1083.24	0.535237
$161$	−5653.48	−2.76743
$162$	3193.10	1.54860
$163$	−749.199	−0.360011	−0.180005	−	0.983666i	$-0.557612\pi$
$163$	−749.199	−0.360011	−0.180005	+	0.983666i	$0.557612\pi$
$164$	1517.08	0.722344
$165$	−492.698	−0.232463
$166$	466.333	0.218039
$167$	219.533	0.101725	0.0508623	−	0.998706i	$-0.483803\pi$
$167$	219.533	0.101725	0.0508623	+	0.998706i	$0.483803\pi$
$168$	2090.01	0.959807
$169$	−2084.50	−0.948793
$170$	1157.34	0.522143
$171$	−441.100	−0.197262
$172$	−1504.87	−0.667126
$173$	3529.32	1.55104	0.775518	−	0.631325i	$-0.217489\pi$
$173$	3529.32	1.55104	0.775518	+	0.631325i	$0.217489\pi$
$174$	2237.78	0.974977
$175$	2960.56	1.27884
$176$	−1176.71	−0.503963
$177$	−4312.69	−1.83142
$178$	3708.71	1.56168
$179$	−953.982	−0.398346	−0.199173	−	0.979964i	$-0.563826\pi$
$179$	−953.982	−0.398346	−0.199173	+	0.979964i	$0.563826\pi$
$180$	238.529	0.0987716
$181$	303.708	0.124721	0.0623604	−	0.998054i	$-0.480137\pi$
$181$	303.708	0.124721	0.0623604	+	0.998054i	$0.480137\pi$
$182$	1196.46	0.487293
$183$	−83.4723	−0.0337183
$184$	2003.06	0.802542
$185$	−1626.73	−0.646485
$186$	6583.66	2.59536
$187$	−863.765	−0.337779
$188$	2241.86	0.869706
$189$	−3422.88	−1.31734
$190$	1000.57	0.382046
$191$	3565.20	1.35062	0.675310	−	0.737534i	$-0.264010\pi$
$191$	3565.20	1.35062	0.675310	+	0.737534i	$0.264010\pi$
$192$	409.539	0.153937
$193$	4221.02	1.57428	0.787139	−	0.616776i	$-0.211561\pi$
$193$	4221.02	1.57428	0.787139	+	0.616776i	$0.211561\pi$
$194$	6045.75	2.23742
$195$	−351.674	−0.129148
$196$	3153.20	1.14913
$197$	−1172.57	−0.424073	−0.212036	−	0.977262i	$-0.568010\pi$
$197$	−1172.57	−0.424073	−0.212036	+	0.977262i	$0.568010\pi$
$198$	−468.528	−0.168166
$199$	2306.31	0.821558	0.410779	−	0.911735i	$-0.365257\pi$
$199$	2306.31	0.821558	0.410779	+	0.911735i	$0.365257\pi$
$200$	−1048.94	−0.370858
$201$	2234.64	0.784175
$202$	−336.944	−0.117363
$203$	−3270.84	−1.13088
$204$	1704.47	0.584984
$205$	1715.35	0.584417
$206$	1733.04	0.586150
$207$	1580.20	0.530588
$208$	−839.899	−0.279983
$209$	−746.757	−0.247150
$210$	−3740.04	−1.22899
$211$	−1722.62	−0.562038	−0.281019	−	0.959702i	$-0.590672\pi$
$211$	−1722.62	−0.562038	−0.281019	+	0.959702i	$0.590672\pi$
$212$	1073.85	0.347888
$213$	3253.13	1.04648
$214$	5020.17	1.60361
$215$	−1701.55	−0.539743
$216$	1212.75	0.382023
$217$	−9622.94	−3.01036
$218$	−2020.70	−0.627794
$219$	−4083.97	−1.26013
$220$	403.816	0.123751
$221$	−616.531	−0.187658
$222$	−6305.28	−1.90623
$223$	−3867.74	−1.16145	−0.580724	−	0.814100i	$-0.697231\pi$
$223$	−3867.74	−1.16145	−0.580724	+	0.814100i	$0.697231\pi$
$224$	−6136.98	−1.83055
$225$	−827.505	−0.245187
$226$	−494.378	−0.145511
$227$	−781.627	−0.228539	−0.114270	−	0.993450i	$-0.536453\pi$
$227$	−781.627	−0.228539	−0.114270	+	0.993450i	$0.536453\pi$
$228$	1473.58	0.428026
$229$	−2549.52	−0.735707	−0.367854	−	0.929884i	$-0.619907\pi$
$229$	−2549.52	−0.735707	−0.367854	+	0.929884i	$0.619907\pi$
$230$	−3584.45	−1.02762
$231$	2791.32	0.795044
$232$	1158.88	0.327948
$233$	1508.87	0.424247	0.212123	−	0.977243i	$-0.431962\pi$
$233$	1508.87	0.424247	0.212123	+	0.977243i	$0.431962\pi$
$234$	−334.422	−0.0934267
$235$	2534.86	0.703642
$236$	3534.68	0.974951
$237$	4549.79	1.24701
$238$	−6556.79	−1.78577
$239$	2018.10	0.546191	0.273096	−	0.961987i	$-0.411952\pi$
$239$	2018.10	0.546191	0.273096	+	0.961987i	$0.411952\pi$
$240$	2625.46	0.706137
$241$	−2465.80	−0.659071	−0.329536	−	0.944143i	$-0.606892\pi$
$241$	−2465.80	−0.659071	−0.329536	+	0.944143i	$0.606892\pi$
$242$	3987.75	1.05927
$243$	2374.31	0.626799
$244$	68.4140	0.0179498
$245$	3565.30	0.929710
$246$	6648.78	1.72321
$247$	−533.014	−0.137307
$248$	3409.47	0.872990
$249$	776.545	0.197637
$250$	4365.92	1.10450
$251$	−5867.94	−1.47562	−0.737811	−	0.675007i	$-0.764141\pi$
$251$	−5867.94	−1.47562	−0.737811	+	0.675007i	$0.764141\pi$
$252$	−1351.35	−0.337807
$253$	2675.20	0.664775
$254$	3033.91	0.749467
$255$	1927.23	0.473285
$256$	5279.97	1.28906
$257$	−7597.02	−1.84393	−0.921963	−	0.387279i	$-0.873415\pi$
$257$	−7597.02	−1.84393	−0.921963	+	0.387279i	$0.873415\pi$
$258$	−6595.27	−1.59149
$259$	9216.05	2.21103
$260$	288.232	0.0687516
$261$	914.231	0.216818
$262$	−10031.0	−2.36533
$263$	−3907.36	−0.916114	−0.458057	−	0.888923i	$-0.651454\pi$
$263$	−3907.36	−0.916114	−0.458057	+	0.888923i	$0.651454\pi$
$264$	−988.981	−0.230559
$265$	1214.19	0.281461
$266$	−5668.59	−1.30663
$267$	6175.80	1.41555
$268$	−1831.51	−0.417453
$269$	−682.392	−0.154670	−0.0773350	−	0.997005i	$-0.524641\pi$
$269$	−682.392	−0.154670	−0.0773350	+	0.997005i	$0.524641\pi$
$270$	−2170.19	−0.489162
$271$	6982.41	1.56513	0.782567	−	0.622567i	$-0.213910\pi$
$271$	6982.41	1.56513	0.782567	+	0.622567i	$0.213910\pi$
$272$	4602.79	1.02605
$273$	1992.36	0.441697
$274$	10576.1	2.33185
$275$	−1400.92	−0.307195
$276$	−5278.97	−1.15129
$277$	−512.924	−0.111259	−0.0556293	−	0.998451i	$-0.517716\pi$
$277$	−512.924	−0.111259	−0.0556293	+	0.998451i	$0.517716\pi$
$278$	−5170.65	−1.11552
$279$	2689.71	0.577163
$280$	−1936.85	−0.413388
$281$	318.248	0.0675626	0.0337813	−	0.999429i	$-0.489245\pi$
$281$	318.248	0.0675626	0.0337813	+	0.999429i	$0.489245\pi$
$282$	9825.21	2.07476
$283$	−2417.09	−0.507708	−0.253854	−	0.967243i	$-0.581698\pi$
$283$	−2417.09	−0.507708	−0.253854	+	0.967243i	$0.581698\pi$
$284$	−2666.27	−0.557092
$285$	1666.16	0.346298
$286$	−566.158	−0.117055
$287$	−9718.12	−1.99875
$288$	1715.35	0.350964
$289$	−1534.31	−0.312296
$290$	−2073.79	−0.419922
$291$	10067.5	2.02806
$292$	3347.23	0.670827
$293$	−93.7827	−0.0186991	−0.00934957	−	0.999956i	$-0.502976\pi$
$293$	−93.7827	−0.0186991	−0.00934957	+	0.999956i	$0.502976\pi$
$294$	13819.3	2.74134
$295$	3996.64	0.788791
$296$	−3265.30	−0.641189
$297$	1619.69	0.316444
$298$	9772.26	1.89964
$299$	1909.48	0.369324
$300$	2764.44	0.532016
$301$	9639.91	1.84596
$302$	−12817.5	−2.44226
$303$	−561.085	−0.106381
$304$	3979.28	0.750748
$305$	77.3552	0.0145224
$306$	1832.69	0.342378
$307$	−5242.23	−0.974561	−0.487280	−	0.873246i	$-0.662011\pi$
$307$	−5242.23	−0.974561	−0.487280	+	0.873246i	$0.662011\pi$
$308$	−2287.77	−0.423239
$309$	2885.89	0.531303
$310$	−6101.19	−1.11782
$311$	2479.37	0.452065	0.226032	−	0.974120i	$-0.427425\pi$
$311$	2479.37	0.452065	0.226032	+	0.974120i	$0.427425\pi$
$312$	−705.906	−0.128090
$313$	−5975.42	−1.07908	−0.539538	−	0.841961i	$-0.681401\pi$
$313$	−5975.42	−1.07908	−0.539538	+	0.841961i	$0.681401\pi$
$314$	−3214.46	−0.577715
$315$	−1527.96	−0.273305
$316$	−3729.02	−0.663841
$317$	−5051.44	−0.895007	−0.447504	−	0.894282i	$-0.647687\pi$
$317$	−5051.44	−0.895007	−0.447504	+	0.894282i	$0.647687\pi$
$318$	4706.26	0.829918
$319$	1547.74	0.271652
$320$	−379.527	−0.0663006
$321$	8359.68	1.45356
$322$	20307.2	3.51453
$323$	2921.00	0.503186
$324$	−4357.99	−0.747254
$325$	−999.937	−0.170666
$326$	2691.12	0.457200
$327$	−3364.90	−0.569050
$328$	3443.19	0.579629
$329$	−14360.9	−2.40651
$330$	1769.77	0.295219
$331$	−2940.58	−0.488305	−0.244152	−	0.969737i	$-0.578510\pi$
$331$	−2940.58	−0.488305	−0.244152	+	0.969737i	$0.578510\pi$
$332$	−636.458	−0.105211
$333$	−2575.98	−0.423912
$334$	−788.562	−0.129186
$335$	−2070.88	−0.337744
$336$	−14874.2	−2.41505
$337$	−1516.34	−0.245105	−0.122552	−	0.992462i	$-0.539108\pi$
$337$	−1516.34	−0.245105	−0.122552	+	0.992462i	$0.539108\pi$
$338$	7487.50	1.20493
$339$	−823.246	−0.131896
$340$	−1579.56	−0.251952
$341$	4553.52	0.723130
$342$	1584.43	0.250514
$343$	−9427.28	−1.48404
$344$	−3415.48	−0.535321
$345$	−5968.88	−0.931461
$346$	−12677.3	−1.96976
$347$	4626.59	0.715760	0.357880	−	0.933768i	$-0.383500\pi$
$347$	4626.59	0.715760	0.357880	+	0.933768i	$0.383500\pi$
$348$	−3054.16	−0.470460
$349$	−6859.57	−1.05210	−0.526052	−	0.850452i	$-0.676328\pi$
$349$	−6859.57	−1.05210	−0.526052	+	0.850452i	$0.676328\pi$
$350$	−10634.3	−1.62408
$351$	1156.09	0.175805
$352$	2903.99	0.439724
$353$	−5179.80	−0.781000	−0.390500	−	0.920603i	$-0.627698\pi$
$353$	−5179.80	−0.781000	−0.390500	+	0.920603i	$0.627698\pi$
$354$	15491.1	2.32583
$355$	−3014.73	−0.450720
$356$	−5061.70	−0.753566
$357$	−10918.5	−1.61867
$358$	3426.69	0.505884
$359$	10398.0	1.52865	0.764325	−	0.644831i	$-0.223072\pi$
$359$	10398.0	1.52865	0.764325	+	0.644831i	$0.223072\pi$
$360$	541.368	0.0792571
$361$	−4333.68	−0.631824
$362$	−1090.92	−0.158391
$363$	6640.46	0.960149
$364$	−1632.94	−0.235136
$365$	3784.68	0.542738
$366$	299.832	0.0428209
$367$	2875.58	0.409003	0.204501	−	0.978866i	$-0.434443\pi$
$367$	2875.58	0.409003	0.204501	+	0.978866i	$0.434443\pi$
$368$	−14255.4	−2.01934
$369$	2716.31	0.383213
$370$	5843.21	0.821011
$371$	−6878.85	−0.962621
$372$	−8985.48	−1.25235
$373$	7687.95	1.06720	0.533602	−	0.845736i	$-0.320838\pi$
$373$	7687.95	1.06720	0.533602	+	0.845736i	$0.320838\pi$
$374$	3102.64	0.428967
$375$	7270.20	1.00115
$376$	5088.16	0.697877
$377$	1104.73	0.150920
$378$	12295.0	1.67297
$379$	13452.8	1.82329	0.911643	−	0.410984i	$-0.134815\pi$
$379$	13452.8	1.82329	0.911643	+	0.410984i	$0.134815\pi$
$380$	−1365.59	−0.184351
$381$	5052.12	0.679339
$382$	−12806.2	−1.71524
$383$	−12720.0	−1.69703	−0.848515	−	0.529171i	$-0.822503\pi$
$383$	−12720.0	−1.69703	−0.848515	+	0.529171i	$0.822503\pi$
$384$	7880.18	1.04722
$385$	−2586.76	−0.342425
$386$	−15161.9	−1.99927
$387$	−2694.45	−0.353919
$388$	−8251.33	−1.07963
$389$	9756.15	1.27161	0.635805	−	0.771849i	$-0.280668\pi$
$389$	9756.15	1.27161	0.635805	+	0.771849i	$0.280668\pi$
$390$	1263.21	0.164013
$391$	−10464.3	−1.35345
$392$	7156.55	0.922093
$393$	−16703.8	−2.14400
$394$	4211.87	0.538556
$395$	−4216.37	−0.537085
$396$	639.454	0.0811458
$397$	6840.98	0.864833	0.432417	−	0.901674i	$-0.357661\pi$
$397$	6840.98	0.864833	0.432417	+	0.901674i	$0.357661\pi$
$398$	−8284.25	−1.04335
$399$	−9439.42	−1.18437
$400$	7465.15	0.933144
$401$	7502.79	0.934343	0.467171	−	0.884167i	$-0.345273\pi$
$401$	7502.79	0.934343	0.467171	+	0.884167i	$0.345273\pi$
$402$	−8026.80	−0.995871
$403$	3250.18	0.401744
$404$	459.866	0.0566317
$405$	−4927.54	−0.604572
$406$	11748.8	1.43617
$407$	−4360.99	−0.531120
$408$	3868.48	0.469408
$409$	−12369.8	−1.49548	−0.747738	−	0.663994i	$-0.768860\pi$
$409$	−12369.8	−1.49548	−0.747738	+	0.663994i	$0.768860\pi$
$410$	−6161.54	−0.742187
$411$	17611.5	2.11366
$412$	−2365.28	−0.282838
$413$	−22642.5	−2.69773
$414$	−5676.07	−0.673826
$415$	−719.638	−0.0851220
$416$	2072.78	0.244295
$417$	−8610.25	−1.01114
$418$	2682.35	0.313870
$419$	15318.8	1.78609	0.893046	−	0.449965i	$-0.148564\pi$
$419$	15318.8	1.78609	0.893046	+	0.449965i	$0.148564\pi$
$420$	5104.46	0.593029
$421$	−3514.95	−0.406907	−0.203454	−	0.979085i	$-0.565217\pi$
$421$	−3514.95	−0.406907	−0.203454	+	0.979085i	$0.565217\pi$
$422$	6187.63	0.713766
$423$	4014.02	0.461390
$424$	2437.22	0.279155
$425$	5479.82	0.625436
$426$	−11685.2	−1.32899
$427$	−438.246	−0.0496679
$428$	−6851.61	−0.773796
$429$	−942.775	−0.106102
$430$	6111.95	0.685452
$431$	−5176.82	−0.578558	−0.289279	−	0.957245i	$-0.593416\pi$
$431$	−5176.82	−0.578558	−0.289279	+	0.957245i	$0.593416\pi$
$432$	−8630.91	−0.961238
$433$	−2759.51	−0.306266	−0.153133	−	0.988206i	$-0.548936\pi$
$433$	−2759.51	−0.306266	−0.153133	+	0.988206i	$0.548936\pi$
$434$	34565.5	3.82304
$435$	−3453.32	−0.380629
$436$	2757.88	0.302932
$437$	−9046.74	−0.990307
$438$	14669.6	1.60032
$439$	−15360.8	−1.67000	−0.835002	−	0.550247i	$-0.814533\pi$
$439$	−15360.8	−1.67000	−0.835002	+	0.550247i	$0.814533\pi$
$440$	916.505	0.0993015
$441$	5645.75	0.609627
$442$	2214.57	0.238318
$443$	−15674.2	−1.68104	−0.840522	−	0.541778i	$-0.817751\pi$
$443$	−15674.2	−1.68104	−0.840522	+	0.541778i	$0.817751\pi$
$444$	8605.54	0.919821
$445$	−5723.22	−0.609678
$446$	13892.9	1.47499
$447$	16272.9	1.72189
$448$	2150.16	0.226753
$449$	−6596.55	−0.693342	−0.346671	−	0.937987i	$-0.612688\pi$
$449$	−6596.55	−0.693342	−0.346671	+	0.937987i	$0.612688\pi$
$450$	2972.39	0.311377
$451$	4598.56	0.480128
$452$	674.734	0.0702142
$453$	−21343.9	−2.21374
$454$	2807.60	0.290236
$455$	−1846.36	−0.190238
$456$	3344.45	0.343461
$457$	4505.74	0.461203	0.230602	−	0.973048i	$-0.425931\pi$
$457$	4505.74	0.461203	0.230602	+	0.973048i	$0.425931\pi$
$458$	9157.85	0.934320
$459$	−6335.55	−0.644266
$460$	4892.11	0.495860
$461$	−8288.80	−0.837414	−0.418707	−	0.908121i	$-0.637517\pi$
$461$	−8288.80	−0.837414	−0.418707	+	0.908121i	$0.637517\pi$
$462$	−10026.4	−1.00967
$463$	−16690.6	−1.67534	−0.837668	−	0.546180i	$-0.816081\pi$
$463$	−16690.6	−1.67534	−0.837668	+	0.546180i	$0.816081\pi$
$464$	−8247.53	−0.825176
$465$	−10159.8	−1.01323
$466$	−5419.85	−0.538777
$467$	−3505.08	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$467$	−3505.08	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$468$	456.424	0.0450816
$469$	11732.3	1.15511
$470$	−9105.19	−0.893598
$471$	−5352.77	−0.523658
$472$	8022.36	0.782329
$473$	−4561.55	−0.443426
$474$	−16342.8	−1.58365
$475$	4737.51	0.457625
$476$	8948.80	0.861696
$477$	1922.71	0.184559
$478$	−7248.98	−0.693641
$479$	2785.87	0.265740	0.132870	−	0.991133i	$-0.457581\pi$
$479$	2785.87	0.265740	0.132870	+	0.991133i	$0.457581\pi$
$480$	−6479.36	−0.616127
$481$	−3112.75	−0.295071
$482$	8857.14	0.836995
$483$	33816.0	3.18567
$484$	−5442.54	−0.511132
$485$	−9329.71	−0.873485
$486$	−8528.51	−0.796010
$487$	20864.4	1.94139	0.970696	−	0.240310i	$-0.0772492\pi$
$487$	20864.4	1.94139	0.970696	+	0.240310i	$0.0772492\pi$
$488$	155.273	0.0144035
$489$	4481.29	0.414419
$490$	−12806.5	−1.18069
$491$	12504.9	1.14936	0.574682	−	0.818377i	$-0.305126\pi$
$491$	12504.9	1.14936	0.574682	+	0.818377i	$0.305126\pi$
$492$	−9074.35	−0.831511
$493$	−6054.12	−0.553071
$494$	1914.58	0.174375
$495$	723.025	0.0656516
$496$	−24264.6	−2.19660
$497$	17079.6	1.54150
$498$	−2789.34	−0.250991
$499$	−6108.91	−0.548041	−0.274020	−	0.961724i	$-0.588354\pi$
$499$	−6108.91	−0.548041	−0.274020	+	0.961724i	$0.588354\pi$
$500$	−5958.67	−0.532959
$501$	−1313.13	−0.117098
$502$	21077.6	1.87398
$503$	8344.52	0.739689	0.369845	−	0.929094i	$-0.379411\pi$
$503$	8344.52	0.739689	0.369845	+	0.929094i	$0.379411\pi$
$504$	−3067.05	−0.271066
$505$	519.967	0.0458183
$506$	−9609.28	−0.844238
$507$	12468.3	1.09218
$508$	−4140.73	−0.361644
$509$	17689.5	1.54042	0.770208	−	0.637793i	$-0.220152\pi$
$509$	17689.5	1.54042	0.770208	+	0.637793i	$0.220152\pi$
$510$	−6922.59	−0.601054
$511$	−21441.6	−1.85621
$512$	−8426.11	−0.727314
$513$	−5477.32	−0.471403
$514$	27288.4	2.34171
$515$	−2674.41	−0.228832
$516$	9001.32	0.767948
$517$	6795.51	0.578077
$518$	−33104.0	−2.80792
$519$	−21110.4	−1.78544
$520$	654.175	0.0551683
$521$	−15219.4	−1.27980	−0.639899	−	0.768459i	$-0.721024\pi$
$521$	−15219.4	−1.27980	−0.639899	+	0.768459i	$0.721024\pi$
$522$	−3283.91	−0.275350
$523$	−2527.03	−0.211280	−0.105640	−	0.994404i	$-0.533689\pi$
$523$	−2527.03	−0.211280	−0.105640	+	0.994404i	$0.533689\pi$
$524$	13690.4	1.14135
$525$	−17708.4	−1.47211
$526$	14035.2	1.16343
$527$	−17811.5	−1.47226
$528$	7038.40	0.580127
$529$	20242.2	1.66370
$530$	−4361.37	−0.357445
$531$	6328.79	0.517224
$532$	7736.57	0.630494
$533$	3282.32	0.266742
$534$	−22183.4	−1.79770
$535$	−7747.05	−0.626046
$536$	−4156.82	−0.334976
$537$	5706.19	0.458548
$538$	2451.15	0.196425
$539$	9557.95	0.763803
$540$	2961.91	0.236038
$541$	5714.76	0.454153	0.227077	−	0.973877i	$-0.427083\pi$
$541$	5714.76	0.454153	0.227077	+	0.973877i	$0.427083\pi$
$542$	−25080.7	−1.98766
$543$	−1816.61	−0.143570
$544$	−11359.2	−0.895260
$545$	3118.31	0.245090
$546$	−7156.55	−0.560938
$547$	547.000	0.0427569
$547$	547.000	0.0427569
$548$	−14434.4	−1.12520
$549$	122.494	0.00952262
$550$	5032.09	0.390126
$551$	−5234.02	−0.404676
$552$	−11981.2	−0.923830
$553$	23887.3	1.83687
$554$	1842.42	0.141294
$555$	9730.21	0.744188
$556$	7056.98	0.538278
$557$	19405.8	1.47621	0.738105	−	0.674686i	$-0.235721\pi$
$557$	19405.8	1.47621	0.738105	+	0.674686i	$0.235721\pi$
$558$	−9661.40	−0.732975
$559$	−3255.91	−0.246351
$560$	13784.2	1.04016
$561$	5166.56	0.388828
$562$	−1143.14	−0.0858018
$563$	24975.8	1.86963	0.934816	−	0.355131i	$-0.115564\pi$
$563$	24975.8	1.86963	0.934816	+	0.355131i	$0.115564\pi$
$564$	−13409.6	−1.00114
$565$	762.916	0.0568073
$566$	8682.18	0.644769
$567$	27916.4	2.06768
$568$	−6051.40	−0.447027
$569$	−16995.0	−1.25214	−0.626072	−	0.779766i	$-0.715338\pi$
$569$	−16995.0	−1.25214	−0.626072	+	0.779766i	$0.715338\pi$
$570$	−5984.84	−0.439785
$571$	275.809	0.0202141	0.0101070	−	0.999949i	$-0.496783\pi$
$571$	275.809	0.0202141	0.0101070	+	0.999949i	$0.496783\pi$
$572$	772.700	0.0564829
$573$	−21325.0	−1.55474
$574$	34907.4	2.53834
$575$	−16971.7	−1.23090
$576$	−600.991	−0.0434745
$577$	1319.39	0.0951941	0.0475970	−	0.998867i	$-0.484844\pi$
$577$	1319.39	0.0951941	0.0475970	+	0.998867i	$0.484844\pi$
$578$	5511.23	0.396604
$579$	−25247.8	−1.81220
$580$	2830.34	0.202627
$581$	4077.02	0.291124
$582$	−36162.3	−2.57556
$583$	3255.04	0.231235
$584$	7596.90	0.538291
$585$	516.075	0.0364736
$586$	336.867	0.0237472
$587$	−16816.1	−1.18241	−0.591206	−	0.806521i	$-0.701348\pi$
$587$	−16816.1	−1.18241	−0.591206	+	0.806521i	$0.701348\pi$
$588$	−18860.7	−1.32279
$589$	−15398.7	−1.07724
$590$	−14355.9	−1.00173
$591$	7013.67	0.488162
$592$	23238.6	1.61334
$593$	16460.8	1.13991	0.569953	−	0.821677i	$-0.306961\pi$
$593$	16460.8	1.13991	0.569953	+	0.821677i	$0.306961\pi$
$594$	−5817.91	−0.401872
$595$	10118.3	0.697162
$596$	−13337.3	−0.916641
$597$	−13795.1	−0.945719
$598$	−6858.83	−0.469027
$599$	−5020.11	−0.342431	−0.171215	−	0.985234i	$-0.554769\pi$
$599$	−5020.11	−0.342431	−0.171215	+	0.985234i	$0.554769\pi$
$600$	6274.20	0.426905
$601$	−21375.4	−1.45078	−0.725392	−	0.688337i	$-0.758341\pi$
$601$	−21375.4	−1.45078	−0.725392	+	0.688337i	$0.758341\pi$
$602$	−34626.5	−2.34430
$603$	−3279.29	−0.221464
$604$	17493.5	1.17848
$605$	−6153.83	−0.413535
$606$	2015.41	0.135100
$607$	−14067.0	−0.940631	−0.470316	−	0.882498i	$-0.655860\pi$
$607$	−14067.0	−0.940631	−0.470316	+	0.882498i	$0.655860\pi$
$608$	−9820.44	−0.655052
$609$	19564.3	1.30178
$610$	−277.859	−0.0184429
$611$	4850.44	0.321158
$612$	−2501.28	−0.165209
$613$	17281.4	1.13864	0.569322	−	0.822114i	$-0.307206\pi$
$613$	17281.4	1.13864	0.569322	+	0.822114i	$0.307206\pi$
$614$	18830.1	1.23765
$615$	−10260.3	−0.672740
$616$	−5192.34	−0.339619
$617$	22886.4	1.49331	0.746654	−	0.665212i	$-0.231659\pi$
$617$	22886.4	1.49331	0.746654	+	0.665212i	$0.231659\pi$
$618$	−10366.1	−0.674734
$619$	−24312.6	−1.57868	−0.789342	−	0.613954i	$-0.789578\pi$
$619$	−24312.6	−1.57868	−0.789342	+	0.613954i	$0.789578\pi$
$620$	8326.99	0.539387
$621$	19622.0	1.26796
$622$	−8905.87	−0.574104
$623$	32424.2	2.08515
$624$	5023.81	0.322297
$625$	5046.83	0.322997
$626$	21463.7	1.37038
$627$	4466.69	0.284501
$628$	4387.14	0.278768
$629$	17058.4	1.08134
$630$	5488.44	0.347087
$631$	−11427.2	−0.720933	−0.360466	−	0.932772i	$-0.617382\pi$
$631$	−11427.2	−0.720933	−0.360466	+	0.932772i	$0.617382\pi$
$632$	−8463.42	−0.532685
$633$	10303.7	0.646978
$634$	18144.7	1.13662
$635$	−4681.89	−0.292591
$636$	−6423.17	−0.400464
$637$	6822.19	0.424341
$638$	−5559.48	−0.344987
$639$	−4773.91	−0.295545
$640$	−7302.70	−0.451038
$641$	29531.7	1.81971	0.909853	−	0.414931i	$-0.136194\pi$
$641$	29531.7	1.81971	0.909853	+	0.414931i	$0.136194\pi$
$642$	−30027.9	−1.84596
$643$	−27117.6	−1.66316	−0.831580	−	0.555405i	$-0.812563\pi$
$643$	−27117.6	−1.66316	−0.831580	+	0.555405i	$0.812563\pi$
$644$	−27715.6	−1.69588
$645$	10177.7	0.621314
$646$	−10492.2	−0.639026
$647$	9632.54	0.585308	0.292654	−	0.956218i	$-0.405462\pi$
$647$	9632.54	0.585308	0.292654	+	0.956218i	$0.405462\pi$
$648$	−9890.94	−0.599618
$649$	10714.3	0.648032
$650$	3591.76	0.216739
$651$	57559.1	3.46531
$652$	−3672.87	−0.220615
$653$	−19340.2	−1.15902	−0.579511	−	0.814964i	$-0.696756\pi$
$653$	−19340.2	−1.15902	−0.579511	+	0.814964i	$0.696756\pi$
$654$	12086.7	0.722672
$655$	15479.7	0.923420
$656$	−24504.6	−1.45845
$657$	5993.14	0.355883
$658$	51584.3	3.05618
$659$	−9878.47	−0.583931	−0.291965	−	0.956429i	$-0.594309\pi$
$659$	−9878.47	−0.583931	−0.291965	+	0.956429i	$0.594309\pi$
$660$	−2415.40	−0.142454
$661$	−20737.2	−1.22025	−0.610124	−	0.792306i	$-0.708880\pi$
$661$	−20737.2	−1.22025	−0.610124	+	0.792306i	$0.708880\pi$
$662$	10562.5	0.620128
$663$	3687.74	0.216018
$664$	−1444.51	−0.0844246
$665$	8747.68	0.510106
$666$	9252.88	0.538351
$667$	18750.4	1.08849
$668$	1076.24	0.0623368
$669$	23134.7	1.33698
$670$	7438.57	0.428921
$671$	207.376	0.0119309
$672$	36708.0	2.10721
$673$	10365.1	0.593678	0.296839	−	0.954928i	$-0.404067\pi$
$673$	10365.1	0.593678	0.296839	+	0.954928i	$0.404067\pi$
$674$	5446.68	0.311274
$675$	−10275.5	−0.585931
$676$	−10219.0	−0.581420
$677$	−12804.2	−0.726890	−0.363445	−	0.931616i	$-0.618400\pi$
$677$	−12804.2	−0.726890	−0.363445	+	0.931616i	$0.618400\pi$
$678$	2957.09	0.167502
$679$	52856.3	2.98739
$680$	−3584.99	−0.202174
$681$	4675.25	0.263078
$682$	−16356.2	−0.918346
$683$	5357.61	0.300151	0.150075	−	0.988675i	$-0.452048\pi$
$683$	5357.61	0.300151	0.150075	+	0.988675i	$0.452048\pi$
$684$	−2162.45	−0.120882
$685$	−16320.9	−0.910350
$686$	33862.7	1.88467
$687$	15249.8	0.846894
$688$	24307.4	1.34696
$689$	2323.35	0.128465
$690$	21440.2	1.18292
$691$	1368.48	0.0753394	0.0376697	−	0.999290i	$-0.488007\pi$
$691$	1368.48	0.0753394	0.0376697	+	0.999290i	$0.488007\pi$
$692$	17302.1	0.950475
$693$	−4096.21	−0.224534
$694$	−16618.7	−0.908987
$695$	7979.27	0.435498
$696$	−6931.76	−0.377511
$697$	−17987.7	−0.977520
$698$	24639.5	1.33613
$699$	−9025.23	−0.488363
$700$	14513.8	0.783674
$701$	23322.4	1.25660	0.628300	−	0.777971i	$-0.283751\pi$
$701$	23322.4	1.25660	0.628300	+	0.777971i	$0.283751\pi$
$702$	−4152.66	−0.223265
$703$	14747.6	0.791203
$704$	−1017.44	−0.0544693
$705$	−15162.1	−0.809983
$706$	18605.8	0.991839
$707$	−2945.81	−0.156702
$708$	−21142.5	−1.12229
$709$	−8674.93	−0.459512	−0.229756	−	0.973248i	$-0.573793\pi$
$709$	−8674.93	−0.459512	−0.229756	+	0.973248i	$0.573793\pi$
$710$	10828.9	0.572396
$711$	−6676.74	−0.352176
$712$	−11488.1	−0.604683
$713$	55164.6	2.89752
$714$	39219.0	2.05565
$715$	873.686	0.0456979
$716$	−4676.80	−0.244107
$717$	−12071.1	−0.628737
$718$	−37349.5	−1.94133
$719$	32085.8	1.66426	0.832128	−	0.554584i	$-0.187123\pi$
$719$	32085.8	1.66426	0.832128	+	0.554584i	$0.187123\pi$
$720$	−3852.82	−0.199425
$721$	15151.5	0.782623
$722$	15566.6	0.802392
$723$	14749.0	0.758676
$724$	1488.90	0.0764289
$725$	−9819.04	−0.502993
$726$	−23852.5	−1.21935
$727$	13099.7	0.668280	0.334140	−	0.942524i	$-0.391554\pi$
$727$	13099.7	0.668280	0.334140	+	0.942524i	$0.391554\pi$
$728$	−3706.15	−0.188680
$729$	9799.83	0.497883
$730$	−13594.5	−0.689255
$731$	17842.9	0.902796
$732$	−409.215	−0.0206626
$733$	11088.5	0.558752	0.279376	−	0.960182i	$-0.409872\pi$
$733$	11088.5	0.558752	0.279376	+	0.960182i	$0.409872\pi$
$734$	−10329.1	−0.519417
$735$	−21325.7	−1.07022
$736$	35180.9	1.76194
$737$	−5551.66	−0.277473
$738$	−9756.96	−0.486665
$739$	−21744.5	−1.08239	−0.541195	−	0.840897i	$-0.682028\pi$
$739$	−21744.5	−1.08239	−0.541195	+	0.840897i	$0.682028\pi$
$740$	−7974.90	−0.396166
$741$	3188.19	0.158058
$742$	24708.8	1.22249
$743$	−12178.7	−0.601338	−0.300669	−	0.953729i	$-0.597210\pi$
$743$	−12178.7	−0.601338	−0.300669	+	0.953729i	$0.597210\pi$
$744$	−20393.5	−1.00492
$745$	−15080.4	−0.741615
$746$	−27615.1	−1.35531
$747$	−1139.57	−0.0558160
$748$	−4234.52	−0.206991
$749$	43889.9	2.14113
$750$	−26114.5	−1.27142
$751$	−22376.5	−1.08726	−0.543629	−	0.839326i	$-0.682950\pi$
$751$	−22376.5	−1.08726	−0.543629	+	0.839326i	$0.682950\pi$
$752$	−36211.5	−1.75598
$753$	35098.8	1.69863
$754$	−3968.20	−0.191662
$755$	19779.7	0.953454
$756$	−16780.3	−0.807268
$757$	−22367.5	−1.07392	−0.536961	−	0.843607i	$-0.680428\pi$
$757$	−22367.5	−1.07392	−0.536961	+	0.843607i	$0.680428\pi$
$758$	−48322.4	−2.31550
$759$	−16001.5	−0.765242
$760$	−3099.36	−0.147928
$761$	−2882.06	−0.137286	−0.0686429	−	0.997641i	$-0.521867\pi$
$761$	−2882.06	−0.137286	−0.0686429	+	0.997641i	$0.521867\pi$
$762$	−18147.2	−0.862733
$763$	−17666.4	−0.838226
$764$	17478.0	0.827661
$765$	−2828.17	−0.133664
$766$	45690.2	2.15516
$767$	7647.55	0.360022
$768$	−31581.8	−1.48387
$769$	−36853.7	−1.72819	−0.864095	−	0.503330i	$-0.832108\pi$
$769$	−36853.7	−1.72819	−0.864095	+	0.503330i	$0.832108\pi$
$770$	9291.62	0.434866
$771$	45441.1	2.12260
$772$	20693.1	0.964718
$773$	−22444.6	−1.04434	−0.522170	−	0.852841i	$-0.674878\pi$
$773$	−22444.6	−1.04434	−0.522170	+	0.852841i	$0.674878\pi$
$774$	9678.44	0.449463
$775$	−28888.0	−1.33895
$776$	−18727.3	−0.866329
$777$	−55125.3	−2.54518
$778$	−35044.0	−1.61490
$779$	−15551.0	−0.715241
$780$	−1724.05	−0.0791419
$781$	−8081.97	−0.370289
$782$	37587.5	1.71883
$783$	11352.4	0.518137
$784$	−50931.9	−2.32015
$785$	4960.51	0.225539
$786$	59999.8	2.72280
$787$	6297.39	0.285232	0.142616	−	0.989778i	$-0.454449\pi$
$787$	6297.39	0.285232	0.142616	+	0.989778i	$0.454449\pi$
$788$	−5748.42	−0.259872
$789$	23371.6	1.05457
$790$	15145.2	0.682077
$791$	−4322.20	−0.194286
$792$	1451.31	0.0651138
$793$	148.019	0.00662838
$794$	−24572.7	−1.09830
$795$	−7262.62	−0.323998
$796$	11306.5	0.503451
$797$	−22192.3	−0.986313	−0.493156	−	0.869941i	$-0.664157\pi$
$797$	−22192.3	−0.986313	−0.493156	+	0.869941i	$0.664157\pi$
$798$	33906.3	1.50410
$799$	−26581.2	−1.17694
$800$	−18423.2	−0.814198
$801$	−9062.88	−0.399777
$802$	−26950.0	−1.18658
$803$	10146.1	0.445886
$804$	10955.1	0.480543
$805$	−31337.8	−1.37207
$806$	−11674.6	−0.510199
$807$	4081.69	0.178045
$808$	1043.72	0.0454429
$809$	−22874.4	−0.994094	−0.497047	−	0.867724i	$-0.665582\pi$
$809$	−22874.4	−0.994094	−0.497047	+	0.867724i	$0.665582\pi$
$810$	17699.7	0.767782
$811$	90.5246	0.00391954	0.00195977	−	0.999998i	$-0.499376\pi$
$811$	90.5246	0.00391954	0.00195977	+	0.999998i	$0.499376\pi$
$812$	−16034.9	−0.693001
$813$	−41764.9	−1.80167
$814$	15664.6	0.674502
$815$	−4152.89	−0.178490
$816$	−27531.3	−1.18111
$817$	15425.9	0.660566
$818$	44432.4	1.89920
$819$	−2923.75	−0.124743
$820$	8409.36	0.358131
$821$	−18922.1	−0.804369	−0.402185	−	0.915559i	$-0.631749\pi$
$821$	−18922.1	−0.804369	−0.402185	+	0.915559i	$0.631749\pi$
$822$	−63260.5	−2.68426
$823$	−13210.3	−0.559516	−0.279758	−	0.960071i	$-0.590254\pi$
$823$	−13210.3	−0.559516	−0.279758	+	0.960071i	$0.590254\pi$
$824$	−5368.27	−0.226957
$825$	8379.52	0.353621
$826$	81331.5	3.42601
$827$	−33212.7	−1.39652	−0.698258	−	0.715846i	$-0.746041\pi$
$827$	−33212.7	−1.39652	−0.698258	+	0.715846i	$0.746041\pi$
$828$	7746.79	0.325144
$829$	4758.50	0.199360	0.0996801	−	0.995020i	$-0.468218\pi$
$829$	4758.50	0.199360	0.0996801	+	0.995020i	$0.468218\pi$
$830$	2584.93	0.108102
$831$	3068.03	0.128073
$832$	−726.223	−0.0302611
$833$	−37386.7	−1.55507
$834$	30928.0	1.28411
$835$	1216.90	0.0504340
$836$	−3660.90	−0.151453
$837$	33399.2	1.37927
$838$	−55025.0	−2.26827
$839$	24747.3	1.01832	0.509161	−	0.860671i	$-0.329956\pi$
$839$	24747.3	1.01832	0.509161	+	0.860671i	$0.329956\pi$
$840$	11585.1	0.475863
$841$	−13540.9	−0.555205
$842$	12625.7	0.516756
$843$	−1903.58	−0.0777732
$844$	−8444.97	−0.344417
$845$	−11554.6	−0.470402
$846$	−14418.3	−0.585948
$847$	34863.8	1.41432
$848$	−17345.3	−0.702404
$849$	14457.7	0.584437
$850$	−19683.5	−0.794279
$851$	−52832.0	−2.12815
$852$	15948.2	0.641285
$853$	−8924.04	−0.358210	−0.179105	−	0.983830i	$-0.557320\pi$
$853$	−8924.04	−0.358210	−0.179105	+	0.983830i	$0.557320\pi$
$854$	1574.18	0.0630763
$855$	−2445.06	−0.0978004
$856$	−15550.5	−0.620917
$857$	−38841.0	−1.54817	−0.774086	−	0.633081i	$-0.781790\pi$
$857$	−38841.0	−1.54817	−0.774086	+	0.633081i	$0.781790\pi$
$858$	3386.44	0.134745
$859$	5735.81	0.227827	0.113914	−	0.993491i	$-0.463661\pi$
$859$	5735.81	0.227827	0.113914	+	0.993491i	$0.463661\pi$
$860$	−8341.68	−0.330755
$861$	58128.4	2.30082
$862$	18595.1	0.734746
$863$	2131.26	0.0840659	0.0420330	−	0.999116i	$-0.486617\pi$
$863$	2131.26	0.0840659	0.0420330	+	0.999116i	$0.486617\pi$
$864$	21300.2	0.838712
$865$	19563.4	0.768989
$866$	9912.12	0.388946
$867$	9177.39	0.359493
$868$	−47175.5	−1.84475
$869$	−11303.3	−0.441243
$870$	12404.3	0.483384
$871$	−3962.61	−0.154154
$872$	6259.31	0.243082
$873$	−14773.9	−0.572760
$874$	32495.8	1.25765
$875$	38170.0	1.47472
$876$	−20021.2	−0.772209
$877$	47738.5	1.83810	0.919051	−	0.394138i	$-0.128957\pi$
$877$	47738.5	1.83810	0.919051	+	0.394138i	$0.128957\pi$
$878$	55175.9	2.12084
$879$	560.956	0.0215251
$880$	−6522.61	−0.249860
$881$	−17656.0	−0.675193	−0.337597	−	0.941291i	$-0.609614\pi$
$881$	−17656.0	−0.675193	−0.337597	+	0.941291i	$0.609614\pi$
$882$	−20279.5	−0.774202
$883$	−6247.72	−0.238112	−0.119056	−	0.992888i	$-0.537987\pi$
$883$	−6247.72	−0.238112	−0.119056	+	0.992888i	$0.537987\pi$
$884$	−3022.48	−0.114997
$885$	−23905.7	−0.908000
$886$	56301.5	2.13486
$887$	−2538.40	−0.0960894	−0.0480447	−	0.998845i	$-0.515299\pi$
$887$	−2538.40	−0.0960894	−0.0480447	+	0.998845i	$0.515299\pi$
$888$	19531.2	0.738091
$889$	26524.6	1.00068
$890$	20557.8	0.774267
$891$	−13209.9	−0.496686
$892$	−18961.2	−0.711736
$893$	−22980.4	−0.861155
$894$	−58452.2	−2.18673
$895$	−5288.02	−0.197496
$896$	41372.5	1.54259
$897$	−11421.4	−0.425140
$898$	23694.8	0.880517
$899$	31915.6	1.18403
$900$	−4056.76	−0.150250
$901$	−12732.3	−0.470784
$902$	−16518.0	−0.609744
$903$	−57660.6	−2.12494
$904$	1531.38	0.0563419
$905$	1683.49	0.0618354
$906$	76667.0	2.81136
$907$	17624.0	0.645198	0.322599	−	0.946536i	$-0.395443\pi$
$907$	17624.0	0.645198	0.322599	+	0.946536i	$0.395443\pi$
$908$	−3831.85	−0.140049
$909$	823.382	0.0300438
$910$	6632.09	0.241595
$911$	13312.7	0.484158	0.242079	−	0.970257i	$-0.422171\pi$
$911$	13312.7	0.484158	0.242079	+	0.970257i	$0.422171\pi$
$912$	−23801.8	−0.864208
$913$	−1929.22	−0.0699320
$914$	−16184.6	−0.585710
$915$	−462.696	−0.0167172
$916$	−12498.8	−0.450842
$917$	−87698.0	−3.15817
$918$	22757.2	0.818193
$919$	−29307.6	−1.05198	−0.525990	−	0.850491i	$-0.676305\pi$
$919$	−29307.6	−1.05198	−0.525990	+	0.850491i	$0.676305\pi$
$920$	11103.2	0.397893
$921$	31356.1	1.12185
$922$	29773.3	1.06348
$923$	−5768.68	−0.205719
$924$	13684.2	0.487203
$925$	27666.5	0.983428
$926$	59952.7	2.12761
$927$	−4234.99	−0.150049
$928$	20354.0	0.719993
$929$	−5331.25	−0.188281	−0.0941403	−	0.995559i	$-0.530010\pi$
$929$	−5331.25	−0.188281	−0.0941403	+	0.995559i	$0.530010\pi$
$930$	36493.9	1.28676
$931$	−32322.2	−1.13783
$932$	7397.09	0.259978
$933$	−14830.2	−0.520385
$934$	12590.2	0.441075
$935$	−4787.94	−0.167468
$936$	1035.90	0.0361748
$937$	−29917.9	−1.04309	−0.521545	−	0.853224i	$-0.674644\pi$
$937$	−29917.9	−1.04309	−0.521545	+	0.853224i	$0.674644\pi$
$938$	−42142.3	−1.46694
$939$	35741.6	1.24216
$940$	12426.9	0.431192
$941$	−15256.2	−0.528520	−0.264260	−	0.964451i	$-0.585128\pi$
$941$	−15256.2	−0.528520	−0.264260	+	0.964451i	$0.585128\pi$
$942$	19227.1	0.665025
$943$	55710.2	1.92383
$944$	−57093.7	−1.96848
$945$	−18973.4	−0.653126
$946$	16385.1	0.563134
$947$	−10180.3	−0.349331	−0.174665	−	0.984628i	$-0.555884\pi$
$947$	−10180.3	−0.349331	−0.174665	+	0.984628i	$0.555884\pi$
$948$	22304.9	0.764166
$949$	7241.97	0.247718
$950$	−17017.1	−0.581165
$951$	30214.9	1.03027
$952$	20310.3	0.691450
$953$	23545.2	0.800320	0.400160	−	0.916445i	$-0.368955\pi$
$953$	23545.2	0.800320	0.400160	+	0.916445i	$0.368955\pi$
$954$	−6906.35	−0.234383
$955$	19762.3	0.669625
$956$	9893.51	0.334706
$957$	−9257.73	−0.312706
$958$	−10006.8	−0.337479
$959$	92464.0	3.11347
$960$	2270.12	0.0763206
$961$	64106.2	2.15186
$962$	11181.0	0.374728
$963$	−12267.7	−0.410509
$964$	−12088.3	−0.403879
$965$	23397.6	0.780512
$966$	−121467.	−4.04568
$967$	−27152.8	−0.902972	−0.451486	−	0.892278i	$-0.649106\pi$
$967$	−27152.8	−0.902972	−0.451486	+	0.892278i	$0.649106\pi$
$968$	−12352.4	−0.410147
$969$	−17471.8	−0.579232
$970$	33512.2	1.10929
$971$	−12837.8	−0.424287	−0.212144	−	0.977238i	$-0.568044\pi$
$971$	−12837.8	−0.424287	−0.212144	+	0.977238i	$0.568044\pi$
$972$	11639.8	0.384102
$973$	−45205.5	−1.48944
$974$	−74944.9	−2.46549
$975$	5981.06	0.196459
$976$	−1105.05	−0.0362417
$977$	12540.6	0.410654	0.205327	−	0.978693i	$-0.434174\pi$
$977$	12540.6	0.410654	0.205327	+	0.978693i	$0.434174\pi$
$978$	−16096.8	−0.526296
$979$	−15343.0	−0.500881
$980$	17478.5	0.569726
$981$	4937.93	0.160709
$982$	−44917.4	−1.45965
$983$	−16234.0	−0.526739	−0.263369	−	0.964695i	$-0.584834\pi$
$983$	−16234.0	−0.526739	−0.263369	+	0.964695i	$0.584834\pi$
$984$	−20595.3	−0.667228
$985$	−6499.69	−0.210251
$986$	21746.4	0.702379
$987$	85899.0	2.77021
$988$	−2613.05	−0.0841419
$989$	−55261.9	−1.77677
$990$	−2597.10	−0.0833750
$991$	7368.83	0.236205	0.118102	−	0.993001i	$-0.462319\pi$
$991$	7368.83	0.236205	0.118102	+	0.993001i	$0.462319\pi$
$992$	59882.4	1.91660
$993$	17588.9	0.562102
$994$	−61349.7	−1.95764
$995$	12784.1	0.407321
$996$	3806.94	0.121112
$997$	39649.1	1.25948	0.629739	−	0.776806i	$-0.283162\pi$
$997$	39649.1	1.25948	0.629739	+	0.776806i	$0.283162\pi$
$998$	21943.2	0.695990
$999$	−31987.0	−1.01304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.a.1.14	✓	65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.a.1.14	✓	65	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-3.59199 q^{2} -5.98144 q^{3} +4.90240 q^{4} +5.54311 q^{5} +21.4853 q^{6} -31.4038 q^{7} +11.1265 q^{8} +8.77766 q^{9} +O(q^{10})\)	\(q-3.59199 q^{2} -5.98144 q^{3} +4.90240 q^{4} +5.54311 q^{5} +21.4853 q^{6} -31.4038 q^{7} +11.1265 q^{8} +8.77766 q^{9} -19.9108 q^{10} +14.8601 q^{11} -29.3234 q^{12} +10.6067 q^{13} +112.802 q^{14} -33.1558 q^{15} -79.1857 q^{16} -58.1265 q^{17} -31.5293 q^{18} -50.2525 q^{19} +27.1745 q^{20} +187.840 q^{21} -53.3773 q^{22} +180.026 q^{23} -66.5528 q^{24} -94.2740 q^{25} -38.0992 q^{26} +108.996 q^{27} -153.954 q^{28} +104.154 q^{29} +119.095 q^{30} +306.426 q^{31} +195.422 q^{32} -88.8848 q^{33} +208.790 q^{34} -174.074 q^{35} +43.0316 q^{36} -293.470 q^{37} +180.507 q^{38} -63.4434 q^{39} +61.6756 q^{40} +309.457 q^{41} -674.719 q^{42} -306.967 q^{43} +72.8501 q^{44} +48.6555 q^{45} -646.650 q^{46} +457.299 q^{47} +473.645 q^{48} +643.196 q^{49} +338.631 q^{50} +347.680 q^{51} +51.9983 q^{52} +219.046 q^{53} -391.512 q^{54} +82.3711 q^{55} -349.415 q^{56} +300.583 q^{57} -374.121 q^{58} +721.011 q^{59} -162.543 q^{60} +13.9552 q^{61} -1100.68 q^{62} -275.651 q^{63} -68.4683 q^{64} +58.7941 q^{65} +319.273 q^{66} -373.595 q^{67} -284.959 q^{68} -1076.81 q^{69} +625.273 q^{70} -543.871 q^{71} +97.6650 q^{72} +682.773 q^{73} +1054.14 q^{74} +563.894 q^{75} -246.358 q^{76} -466.663 q^{77} +227.888 q^{78} -760.651 q^{79} -438.935 q^{80} -888.949 q^{81} -1111.57 q^{82} -129.826 q^{83} +920.866 q^{84} -322.201 q^{85} +1102.62 q^{86} -622.993 q^{87} +165.342 q^{88} -1032.49 q^{89} -174.770 q^{90} -333.091 q^{91} +882.557 q^{92} -1832.87 q^{93} -1642.61 q^{94} -278.555 q^{95} -1168.90 q^{96} -1683.12 q^{97} -2310.35 q^{98} +130.437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * q^99

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