LMFDB - Embedded newform 1045.4.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.30475 q^{2} +8.78392 q^{3} +10.5309 q^{4} +5.00000 q^{5} +37.8126 q^{6} +4.68368 q^{7} +10.8947 q^{8} +50.1573 q^{9} +O(q^{10})$	\(q+4.30475 q^{2} +8.78392 q^{3} +10.5309 q^{4} +5.00000 q^{5} +37.8126 q^{6} +4.68368 q^{7} +10.8947 q^{8} +50.1573 q^{9} +21.5237 q^{10} +11.0000 q^{11} +92.5022 q^{12} +6.17155 q^{13} +20.1620 q^{14} +43.9196 q^{15} -37.3480 q^{16} +126.733 q^{17} +215.915 q^{18} -19.0000 q^{19} +52.6543 q^{20} +41.1410 q^{21} +47.3522 q^{22} -146.760 q^{23} +95.6980 q^{24} +25.0000 q^{25} +26.5669 q^{26} +203.412 q^{27} +49.3231 q^{28} +6.35386 q^{29} +189.063 q^{30} -81.1155 q^{31} -247.931 q^{32} +96.6232 q^{33} +545.553 q^{34} +23.4184 q^{35} +528.199 q^{36} +309.123 q^{37} -81.7902 q^{38} +54.2104 q^{39} +54.4734 q^{40} -137.662 q^{41} +177.102 q^{42} -496.640 q^{43} +115.839 q^{44} +250.787 q^{45} -631.765 q^{46} -191.678 q^{47} -328.062 q^{48} -321.063 q^{49} +107.619 q^{50} +1113.21 q^{51} +64.9916 q^{52} +219.115 q^{53} +875.637 q^{54} +55.0000 q^{55} +51.0271 q^{56} -166.895 q^{57} +27.3518 q^{58} +617.640 q^{59} +462.511 q^{60} +720.377 q^{61} -349.182 q^{62} +234.921 q^{63} -768.497 q^{64} +30.8577 q^{65} +415.938 q^{66} +172.953 q^{67} +1334.60 q^{68} -1289.13 q^{69} +100.810 q^{70} -164.757 q^{71} +546.448 q^{72} -856.057 q^{73} +1330.70 q^{74} +219.598 q^{75} -200.086 q^{76} +51.5204 q^{77} +233.362 q^{78} +222.948 q^{79} -186.740 q^{80} +432.508 q^{81} -592.602 q^{82} +1018.63 q^{83} +433.250 q^{84} +633.664 q^{85} -2137.91 q^{86} +55.8118 q^{87} +119.841 q^{88} -580.689 q^{89} +1079.57 q^{90} +28.9055 q^{91} -1545.51 q^{92} -712.512 q^{93} -825.125 q^{94} -95.0000 q^{95} -2177.81 q^{96} -202.698 q^{97} -1382.10 q^{98} +551.730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) $ 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * 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 $

$2$	4.30475	1.52196	0.760979	−	0.648776i	$-0.224719\pi$
$2$	4.30475	1.52196	0.760979	+	0.648776i	$0.224719\pi$
$3$	8.78392	1.69047	0.845233	−	0.534397i	$-0.179461\pi$
$3$	8.78392	1.69047	0.845233	+	0.534397i	$0.179461\pi$
$4$	10.5309	1.31636
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	37.8126	2.57282
$7$	4.68368	0.252895	0.126447	−	0.991973i	$-0.459643\pi$
$7$	4.68368	0.252895	0.126447	+	0.991973i	$0.459643\pi$
$8$	10.8947	0.481481
$9$	50.1573	1.85768
$10$	21.5237	0.680640
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	92.5022	2.22526
$13$	6.17155	0.131668	0.0658338	−	0.997831i	$-0.479029\pi$
$13$	6.17155	0.131668	0.0658338	+	0.997831i	$0.479029\pi$
$14$	20.1620	0.384895
$15$	43.9196	0.756000
$16$	−37.3480	−0.583562
$17$	126.733	1.80807	0.904036	−	0.427457i	$-0.140590\pi$
$17$	126.733	1.80807	0.904036	+	0.427457i	$0.140590\pi$
$18$	215.915	2.82731
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	52.6543	0.588692
$21$	41.1410	0.427510
$22$	47.3522	0.458888
$23$	−146.760	−1.33050	−0.665252	−	0.746619i	$-0.731676\pi$
$23$	−146.760	−1.33050	−0.665252	+	0.746619i	$0.731676\pi$
$24$	95.6980	0.813928
$25$	25.0000	0.200000
$26$	26.5669	0.200393
$27$	203.412	1.44988
$28$	49.3231	0.332900
$29$	6.35386	0.0406856	0.0203428	−	0.999793i	$-0.493524\pi$
$29$	6.35386	0.0406856	0.0203428	+	0.999793i	$0.493524\pi$
$30$	189.063	1.15060
$31$	−81.1155	−0.469960	−0.234980	−	0.972000i	$-0.575503\pi$
$31$	−81.1155	−0.469960	−0.234980	+	0.972000i	$0.575503\pi$
$32$	−247.931	−1.36964
$33$	96.6232	0.509695
$34$	545.553	2.75181
$35$	23.4184	0.113098
$36$	528.199	2.44537
$37$	309.123	1.37350	0.686751	−	0.726893i	$-0.259036\pi$
$37$	309.123	1.37350	0.686751	+	0.726893i	$0.259036\pi$
$38$	−81.7902	−0.349161
$39$	54.2104	0.222580
$40$	54.4734	0.215325
$41$	−137.662	−0.524372	−0.262186	−	0.965017i	$-0.584443\pi$
$41$	−137.662	−0.524372	−0.262186	+	0.965017i	$0.584443\pi$
$42$	177.102	0.650652
$43$	−496.640	−1.76132	−0.880661	−	0.473747i	$-0.842901\pi$
$43$	−496.640	−1.76132	−0.880661	+	0.473747i	$0.842901\pi$
$44$	115.839	0.396896
$45$	250.787	0.830779
$46$	−631.765	−2.02497
$47$	−191.678	−0.594875	−0.297437	−	0.954741i	$-0.596132\pi$
$47$	−191.678	−0.594875	−0.297437	+	0.954741i	$0.596132\pi$
$48$	−328.062	−0.986492
$49$	−321.063	−0.936044
$50$	107.619	0.304392
$51$	1113.21	3.05649
$52$	64.9916	0.173321
$53$	219.115	0.567883	0.283942	−	0.958842i	$-0.408358\pi$
$53$	219.115	0.567883	0.283942	+	0.958842i	$0.408358\pi$
$54$	875.637	2.20665
$55$	55.0000	0.134840
$56$	51.0271	0.121764
$57$	−166.895	−0.387820
$58$	27.3518	0.0619218
$59$	617.640	1.36288	0.681440	−	0.731874i	$-0.261354\pi$
$59$	617.640	1.36288	0.681440	+	0.731874i	$0.261354\pi$
$60$	462.511	0.995165
$61$	720.377	1.51205	0.756023	−	0.654545i	$-0.227140\pi$
$61$	720.377	1.51205	0.756023	+	0.654545i	$0.227140\pi$
$62$	−349.182	−0.715260
$63$	234.921	0.469797
$64$	−768.497	−1.50097
$65$	30.8577	0.0588835
$66$	415.938	0.775734
$67$	172.953	0.315367	0.157684	−	0.987490i	$-0.449597\pi$
$67$	172.953	0.315367	0.157684	+	0.987490i	$0.449597\pi$
$68$	1334.60	2.38007
$69$	−1289.13	−2.24917
$70$	100.810	0.172130
$71$	−164.757	−0.275396	−0.137698	−	0.990474i	$-0.543970\pi$
$71$	−164.757	−0.275396	−0.137698	+	0.990474i	$0.543970\pi$
$72$	546.448	0.894437
$73$	−856.057	−1.37252	−0.686260	−	0.727357i	$-0.740749\pi$
$73$	−856.057	−1.37252	−0.686260	+	0.727357i	$0.740749\pi$
$74$	1330.70	2.09041
$75$	219.598	0.338093
$76$	−200.086	−0.301993
$77$	51.5204	0.0762506
$78$	233.362	0.338757
$79$	222.948	0.317514	0.158757	−	0.987318i	$-0.449251\pi$
$79$	222.948	0.317514	0.158757	+	0.987318i	$0.449251\pi$
$80$	−186.740	−0.260977
$81$	432.508	0.593289
$82$	−592.602	−0.798072
$83$	1018.63	1.34709	0.673547	−	0.739144i	$-0.264770\pi$
$83$	1018.63	1.34709	0.673547	+	0.739144i	$0.264770\pi$
$84$	433.250	0.562756
$85$	633.664	0.808594
$86$	−2137.91	−2.68066
$87$	55.8118	0.0687776
$88$	119.841	0.145172
$89$	−580.689	−0.691606	−0.345803	−	0.938307i	$-0.612393\pi$
$89$	−580.689	−0.691606	−0.345803	+	0.938307i	$0.612393\pi$
$90$	1079.57	1.26441
$91$	28.9055	0.0332980
$92$	−1545.51	−1.75142
$93$	−712.512	−0.794452
$94$	−825.125	−0.905374
$95$	−95.0000	−0.102598
$96$	−2177.81	−2.31533
$97$	−202.698	−0.212174	−0.106087	−	0.994357i	$-0.533832\pi$
$97$	−202.698	−0.212174	−0.106087	+	0.994357i	$0.533832\pi$
$98$	−1382.10	−1.42462
$99$	551.730	0.560111
$100$	263.271	0.263271
$101$	−1293.42	−1.27426	−0.637132	−	0.770755i	$-0.719879\pi$
$101$	−1293.42	−1.27426	−0.637132	+	0.770755i	$0.719879\pi$
$102$	4792.09	4.65184
$103$	854.415	0.817359	0.408680	−	0.912678i	$-0.365989\pi$
$103$	854.415	0.817359	0.408680	+	0.912678i	$0.365989\pi$
$104$	67.2370	0.0633955
$105$	205.705	0.191188
$106$	943.237	0.864295
$107$	−1257.35	−1.13601	−0.568004	−	0.823026i	$-0.692284\pi$
$107$	−1257.35	−1.13601	−0.568004	+	0.823026i	$0.692284\pi$
$108$	2142.10	1.90855
$109$	229.536	0.201702	0.100851	−	0.994902i	$-0.467843\pi$
$109$	229.536	0.201702	0.100851	+	0.994902i	$0.467843\pi$
$110$	236.761	0.205221
$111$	2715.32	2.32186
$112$	−174.926	−0.147580
$113$	682.731	0.568371	0.284186	−	0.958769i	$-0.408277\pi$
$113$	682.731	0.568371	0.284186	+	0.958769i	$0.408277\pi$
$114$	−718.439	−0.590245
$115$	−733.801	−0.595020
$116$	66.9116	0.0535567
$117$	309.548	0.244596
$118$	2658.79	2.07425
$119$	593.575	0.457252
$120$	478.490	0.364000
$121$	121.000	0.0909091
$122$	3101.04	2.30127
$123$	−1209.22	−0.886433
$124$	−854.215	−0.618635
$125$	125.000	0.0894427
$126$	1011.27	0.715011
$127$	399.082	0.278841	0.139420	−	0.990233i	$-0.455476\pi$
$127$	399.082	0.278841	0.139420	+	0.990233i	$0.455476\pi$
$128$	−1324.74	−0.914775
$129$	−4362.45	−2.97746
$130$	132.835	0.0896183
$131$	−2321.06	−1.54803	−0.774014	−	0.633168i	$-0.781754\pi$
$131$	−2321.06	−1.54803	−0.774014	+	0.633168i	$0.781754\pi$
$132$	1017.52	0.670940
$133$	−88.9898	−0.0580180
$134$	744.520	0.479976
$135$	1017.06	0.648404
$136$	1380.71	0.870553
$137$	396.656	0.247362	0.123681	−	0.992322i	$-0.460530\pi$
$137$	396.656	0.247362	0.123681	+	0.992322i	$0.460530\pi$
$138$	−5549.38	−3.42315
$139$	2270.18	1.38528	0.692640	−	0.721284i	$-0.256448\pi$
$139$	2270.18	1.38528	0.692640	+	0.721284i	$0.256448\pi$
$140$	246.615	0.148877
$141$	−1683.68	−1.00562
$142$	−709.239	−0.419141
$143$	67.8870	0.0396993
$144$	−1873.27	−1.08407
$145$	31.7693	0.0181951
$146$	−3685.11	−2.08892
$147$	−2820.19	−1.58235
$148$	3255.33	1.80802
$149$	−1792.49	−0.985548	−0.492774	−	0.870157i	$-0.664017\pi$
$149$	−1792.49	−0.985548	−0.492774	+	0.870157i	$0.664017\pi$
$150$	945.314	0.514564
$151$	−243.596	−0.131282	−0.0656410	−	0.997843i	$-0.520909\pi$
$151$	−243.596	−0.131282	−0.0656410	+	0.997843i	$0.520909\pi$
$152$	−206.999	−0.110459
$153$	6356.58	3.35881
$154$	221.782	0.116050
$155$	−405.577	−0.210173
$156$	570.881	0.292994
$157$	−2242.64	−1.14001	−0.570007	−	0.821640i	$-0.693060\pi$
$157$	−2242.64	−1.14001	−0.570007	+	0.821640i	$0.693060\pi$
$158$	959.734	0.483243
$159$	1924.69	0.959988
$160$	−1239.66	−0.612521
$161$	−687.377	−0.336478
$162$	1861.84	0.902962
$163$	2794.92	1.34304	0.671520	−	0.740987i	$-0.265642\pi$
$163$	2794.92	1.34304	0.671520	+	0.740987i	$0.265642\pi$
$164$	−1449.70	−0.690260
$165$	483.116	0.227942
$166$	4384.93	2.05022
$167$	−818.726	−0.379371	−0.189685	−	0.981845i	$-0.560747\pi$
$167$	−818.726	−0.379371	−0.189685	+	0.981845i	$0.560747\pi$
$168$	448.218	0.205838
$169$	−2158.91	−0.982664
$170$	2727.76	1.23065
$171$	−952.989	−0.426181
$172$	−5230.04	−2.31853
$173$	−3349.46	−1.47199	−0.735997	−	0.676985i	$-0.763286\pi$
$173$	−3349.46	−1.47199	−0.735997	+	0.676985i	$0.763286\pi$
$174$	240.256	0.104677
$175$	117.092	0.0505789
$176$	−410.828	−0.175951
$177$	5425.31	2.30390
$178$	−2499.72	−1.05259
$179$	−3252.91	−1.35829	−0.679146	−	0.734003i	$-0.737650\pi$
$179$	−3252.91	−1.35829	−0.679146	+	0.734003i	$0.737650\pi$
$180$	2641.00	1.09360
$181$	−937.834	−0.385131	−0.192565	−	0.981284i	$-0.561681\pi$
$181$	−937.834	−0.385131	−0.192565	+	0.981284i	$0.561681\pi$
$182$	124.431	0.0506782
$183$	6327.74	2.55607
$184$	−1598.90	−0.640613
$185$	1545.62	0.614249
$186$	−3067.18	−1.20912
$187$	1394.06	0.545154
$188$	−2018.53	−0.783067
$189$	952.716	0.366666
$190$	−408.951	−0.156150
$191$	2758.30	1.04494	0.522469	−	0.852658i	$-0.325011\pi$
$191$	2758.30	1.04494	0.522469	+	0.852658i	$0.325011\pi$
$192$	−6750.42	−2.53734
$193$	−160.968	−0.0600347	−0.0300174	−	0.999549i	$-0.509556\pi$
$193$	−160.968	−0.0600347	−0.0300174	+	0.999549i	$0.509556\pi$
$194$	−872.563	−0.322919
$195$	271.052	0.0995407
$196$	−3381.07	−1.23217
$197$	−448.749	−0.162294	−0.0811472	−	0.996702i	$-0.525858\pi$
$197$	−448.749	−0.162294	−0.0811472	+	0.996702i	$0.525858\pi$
$198$	2375.06	0.852465
$199$	1055.97	0.376158	0.188079	−	0.982154i	$-0.439774\pi$
$199$	1055.97	0.376158	0.188079	+	0.982154i	$0.439774\pi$
$200$	272.367	0.0962962
$201$	1519.21	0.533118
$202$	−5567.87	−1.93938
$203$	29.7594	0.0102892
$204$	11723.1	4.02342
$205$	−688.312	−0.234506
$206$	3678.04	1.24399
$207$	−7361.09	−2.47165
$208$	−230.495	−0.0768362
$209$	−209.000	−0.0691714
$210$	885.509	0.290981
$211$	−1473.85	−0.480872	−0.240436	−	0.970665i	$-0.577290\pi$
$211$	−1473.85	−0.480872	−0.240436	+	0.970665i	$0.577290\pi$
$212$	2307.47	0.747537
$213$	−1447.22	−0.465548
$214$	−5412.58	−1.72896
$215$	−2483.20	−0.787687
$216$	2216.11	0.698088
$217$	−379.919	−0.118850
$218$	988.094	0.306983
$219$	−7519.54	−2.32020
$220$	579.197	0.177497
$221$	782.137	0.238064
$222$	11688.8	3.53377
$223$	−5791.12	−1.73902	−0.869511	−	0.493914i	$-0.835566\pi$
$223$	−5791.12	−1.73902	−0.869511	+	0.493914i	$0.835566\pi$
$224$	−1161.23	−0.346374
$225$	1253.93	0.371536
$226$	2938.99	0.865037
$227$	3607.29	1.05473	0.527366	−	0.849638i	$-0.323180\pi$
$227$	3607.29	1.05473	0.527366	+	0.849638i	$0.323180\pi$
$228$	−1757.54	−0.510509
$229$	−3283.62	−0.947545	−0.473772	−	0.880647i	$-0.657108\pi$
$229$	−3283.62	−0.947545	−0.473772	+	0.880647i	$0.657108\pi$
$230$	−3158.83	−0.905595
$231$	452.552	0.128899
$232$	69.2232	0.0195893
$233$	5002.26	1.40648	0.703239	−	0.710954i	$-0.251737\pi$
$233$	5002.26	1.40648	0.703239	+	0.710954i	$0.251737\pi$
$234$	1332.53	0.372265
$235$	−958.390	−0.266036
$236$	6504.28	1.79404
$237$	1958.36	0.536747
$238$	2555.19	0.695918
$239$	3797.96	1.02791	0.513953	−	0.857818i	$-0.328181\pi$
$239$	3797.96	1.02791	0.513953	+	0.857818i	$0.328181\pi$
$240$	−1640.31	−0.441173
$241$	−4015.56	−1.07330	−0.536649	−	0.843805i	$-0.680310\pi$
$241$	−4015.56	−1.07330	−0.536649	+	0.843805i	$0.680310\pi$
$242$	520.874	0.138360
$243$	−1693.01	−0.446940
$244$	7586.19	1.99039
$245$	−1605.32	−0.418612
$246$	−5205.37	−1.34911
$247$	−117.259	−0.0302066
$248$	−883.727	−0.226277
$249$	8947.54	2.27722
$250$	538.093	0.136128
$251$	6162.64	1.54973	0.774865	−	0.632127i	$-0.217818\pi$
$251$	6162.64	1.54973	0.774865	+	0.632127i	$0.217818\pi$
$252$	2473.91	0.618420
$253$	−1614.36	−0.401162
$254$	1717.95	0.424384
$255$	5566.06	1.36690
$256$	445.320	0.108721
$257$	−4793.53	−1.16347	−0.581736	−	0.813378i	$-0.697626\pi$
$257$	−4793.53	−1.16347	−0.581736	+	0.813378i	$0.697626\pi$
$258$	−18779.2	−4.53156
$259$	1447.83	0.347351
$260$	324.958	0.0775117
$261$	318.692	0.0755807
$262$	−9991.57	−2.35603
$263$	−723.581	−0.169650	−0.0848249	−	0.996396i	$-0.527033\pi$
$263$	−723.581	−0.169650	−0.0848249	+	0.996396i	$0.527033\pi$
$264$	1052.68	0.245409
$265$	1095.58	0.253965
$266$	−383.079	−0.0883010
$267$	−5100.73	−1.16914
$268$	1821.34	0.415136
$269$	−1072.46	−0.243083	−0.121542	−	0.992586i	$-0.538784\pi$
$269$	−1072.46	−0.243083	−0.121542	+	0.992586i	$0.538784\pi$
$270$	4378.19	0.986844
$271$	456.082	0.102233	0.0511163	−	0.998693i	$-0.483722\pi$
$271$	456.082	0.102233	0.0511163	+	0.998693i	$0.483722\pi$
$272$	−4733.21	−1.05512
$273$	253.904	0.0562892
$274$	1707.50	0.376475
$275$	275.000	0.0603023
$276$	−13575.6	−2.96071
$277$	−7310.69	−1.58577	−0.792883	−	0.609374i	$-0.791421\pi$
$277$	−7310.69	−1.58577	−0.792883	+	0.609374i	$0.791421\pi$
$278$	9772.53	2.10834
$279$	−4068.53	−0.873035
$280$	255.136	0.0544545
$281$	3250.19	0.690000	0.345000	−	0.938603i	$-0.387879\pi$
$281$	3250.19	0.690000	0.345000	+	0.938603i	$0.387879\pi$
$282$	−7247.84	−1.53051
$283$	8788.79	1.84608	0.923038	−	0.384709i	$-0.125698\pi$
$283$	8788.79	1.84608	0.923038	+	0.384709i	$0.125698\pi$
$284$	−1735.04	−0.362519
$285$	−834.473	−0.173438
$286$	292.236	0.0604206
$287$	−644.766	−0.132611
$288$	−12435.6	−2.54435
$289$	11148.2	2.26912
$290$	136.759	0.0276923
$291$	−1780.48	−0.358672
$292$	−9015.01	−1.80672
$293$	−5847.43	−1.16591	−0.582953	−	0.812506i	$-0.698103\pi$
$293$	−5847.43	−1.16591	−0.582953	+	0.812506i	$0.698103\pi$
$294$	−12140.2	−2.40827
$295$	3088.20	0.609499
$296$	3367.80	0.661316
$297$	2237.53	0.437154
$298$	−7716.23	−1.49996
$299$	−905.737	−0.175184
$300$	2312.55	0.445051
$301$	−2326.10	−0.445429
$302$	−1048.62	−0.199806
$303$	−11361.3	−2.15410
$304$	709.612	0.133878
$305$	3601.89	0.676208
$306$	27363.5	5.11198
$307$	8550.27	1.58954	0.794772	−	0.606909i	$-0.207591\pi$
$307$	8550.27	1.58954	0.794772	+	0.606909i	$0.207591\pi$
$308$	542.554	0.100373
$309$	7505.12	1.38172
$310$	−1745.91	−0.319874
$311$	5221.50	0.952038	0.476019	−	0.879435i	$-0.342079\pi$
$311$	5221.50	0.952038	0.476019	+	0.879435i	$0.342079\pi$
$312$	590.605	0.107168
$313$	−749.643	−0.135375	−0.0676874	−	0.997707i	$-0.521562\pi$
$313$	−749.643	−0.135375	−0.0676874	+	0.997707i	$0.521562\pi$
$314$	−9654.00	−1.73505
$315$	1174.60	0.210100
$316$	2347.83	0.417961
$317$	−7816.99	−1.38500	−0.692501	−	0.721417i	$-0.743491\pi$
$317$	−7816.99	−1.38500	−0.692501	+	0.721417i	$0.743491\pi$
$318$	8285.32	1.46106
$319$	69.8925	0.0122672
$320$	−3842.48	−0.671254
$321$	−11044.5	−1.92038
$322$	−2958.98	−0.512105
$323$	−2407.92	−0.414800
$324$	4554.68	0.780980
$325$	154.289	0.0263335
$326$	12031.4	2.04405
$327$	2016.23	0.340971
$328$	−1499.79	−0.252475
$329$	−897.758	−0.150441
$330$	2079.69	0.346919
$331$	−3859.61	−0.640916	−0.320458	−	0.947263i	$-0.603837\pi$
$331$	−3859.61	−0.640916	−0.320458	+	0.947263i	$0.603837\pi$
$332$	10727.0	1.77326
$333$	15504.8	2.55153
$334$	−3524.41	−0.577386
$335$	864.766	0.141036
$336$	−1536.53	−0.249479
$337$	9685.10	1.56552	0.782762	−	0.622322i	$-0.213810\pi$
$337$	9685.10	1.56552	0.782762	+	0.622322i	$0.213810\pi$
$338$	−9293.57	−1.49557
$339$	5997.06	0.960813
$340$	6673.02	1.06440
$341$	−892.270	−0.141698
$342$	−4102.38	−0.648629
$343$	−3110.26	−0.489615
$344$	−5410.73	−0.848044
$345$	−6445.65	−1.00586
$346$	−14418.6	−2.24031
$347$	12251.3	1.89534	0.947669	−	0.319254i	$-0.103432\pi$
$347$	12251.3	1.89534	0.947669	+	0.319254i	$0.103432\pi$
$348$	587.746	0.0905359
$349$	7584.53	1.16330	0.581648	−	0.813441i	$-0.302408\pi$
$349$	7584.53	1.16330	0.581648	+	0.813441i	$0.302408\pi$
$350$	504.051	0.0769790
$351$	1255.37	0.190902
$352$	−2727.24	−0.412962
$353$	−2890.53	−0.435829	−0.217914	−	0.975968i	$-0.569925\pi$
$353$	−2890.53	−0.435829	−0.217914	+	0.975968i	$0.569925\pi$
$354$	23354.6	3.50645
$355$	−823.787	−0.123161
$356$	−6115.15	−0.910400
$357$	5213.92	0.772969
$358$	−14003.0	−2.06726
$359$	10914.9	1.60465	0.802324	−	0.596889i	$-0.203597\pi$
$359$	10914.9	1.60465	0.802324	+	0.596889i	$0.203597\pi$
$360$	2732.24	0.400004
$361$	361.000	0.0526316
$362$	−4037.14	−0.586153
$363$	1062.85	0.153679
$364$	304.400	0.0438321
$365$	−4280.29	−0.613809
$366$	27239.3	3.89022
$367$	4172.52	0.593471	0.296736	−	0.954960i	$-0.404102\pi$
$367$	4172.52	0.593471	0.296736	+	0.954960i	$0.404102\pi$
$368$	5481.20	0.776432
$369$	−6904.77	−0.974114
$370$	6653.49	0.934861
$371$	1026.27	0.143615
$372$	−7503.36	−1.04578
$373$	6232.05	0.865103	0.432551	−	0.901609i	$-0.357613\pi$
$373$	6232.05	0.865103	0.432551	+	0.901609i	$0.357613\pi$
$374$	6001.08	0.829702
$375$	1097.99	0.151200
$376$	−2088.27	−0.286421
$377$	39.2131	0.00535697
$378$	4101.20	0.558050
$379$	−2918.69	−0.395575	−0.197788	−	0.980245i	$-0.563376\pi$
$379$	−2918.69	−0.395575	−0.197788	+	0.980245i	$0.563376\pi$
$380$	−1000.43	−0.135055
$381$	3505.50	0.471371
$382$	11873.8	1.59035
$383$	−4774.73	−0.637016	−0.318508	−	0.947920i	$-0.603182\pi$
$383$	−4774.73	−0.637016	−0.318508	+	0.947920i	$0.603182\pi$
$384$	−11636.4	−1.54640
$385$	257.602	0.0341003
$386$	−692.925	−0.0913704
$387$	−24910.1	−3.27197
$388$	−2134.58	−0.279296
$389$	−993.242	−0.129459	−0.0647293	−	0.997903i	$-0.520618\pi$
$389$	−993.242	−0.129459	−0.0647293	+	0.997903i	$0.520618\pi$
$390$	1166.81	0.151497
$391$	−18599.3	−2.40565
$392$	−3497.88	−0.450688
$393$	−20388.0	−2.61689
$394$	−1931.75	−0.247005
$395$	1114.74	0.141997
$396$	5810.19	0.737306
$397$	−7834.36	−0.990416	−0.495208	−	0.868774i	$-0.664908\pi$
$397$	−7834.36	−0.990416	−0.495208	+	0.868774i	$0.664908\pi$
$398$	4545.67	0.572497
$399$	−781.680	−0.0980775
$400$	−933.699	−0.116712
$401$	−5076.37	−0.632174	−0.316087	−	0.948730i	$-0.602369\pi$
$401$	−5076.37	−0.632174	−0.316087	+	0.948730i	$0.602369\pi$
$402$	6539.81	0.811383
$403$	−500.608	−0.0618785
$404$	−13620.9	−1.67738
$405$	2162.54	0.265327
$406$	128.107	0.0156597
$407$	3400.36	0.414127
$408$	12128.1	1.47164
$409$	10076.7	1.21824	0.609121	−	0.793077i	$-0.291522\pi$
$409$	10076.7	1.21824	0.609121	+	0.793077i	$0.291522\pi$
$410$	−2963.01	−0.356909
$411$	3484.19	0.418157
$412$	8997.72	1.07594
$413$	2892.83	0.344665
$414$	−31687.6	−3.76175
$415$	5093.13	0.602439
$416$	−1530.12	−0.180337
$417$	19941.1	2.34177
$418$	−899.692	−0.105276
$419$	8149.33	0.950168	0.475084	−	0.879940i	$-0.342418\pi$
$419$	8149.33	0.950168	0.475084	+	0.879940i	$0.342418\pi$
$420$	2166.25	0.251672
$421$	4539.57	0.525522	0.262761	−	0.964861i	$-0.415367\pi$
$421$	4539.57	0.525522	0.262761	+	0.964861i	$0.415367\pi$
$422$	−6344.55	−0.731867
$423$	−9614.05	−1.10509
$424$	2387.19	0.273425
$425$	3168.32	0.361614
$426$	−6229.90	−0.708544
$427$	3374.01	0.382389
$428$	−13241.0	−1.49539
$429$	596.314	0.0671103
$430$	−10689.5	−1.19883
$431$	2688.84	0.300503	0.150251	−	0.988648i	$-0.451992\pi$
$431$	2688.84	0.300503	0.150251	+	0.988648i	$0.451992\pi$
$432$	−7597.03	−0.846093
$433$	2614.93	0.290220	0.145110	−	0.989416i	$-0.453646\pi$
$433$	2614.93	0.290220	0.145110	+	0.989416i	$0.453646\pi$
$434$	−1635.45	−0.180885
$435$	279.059	0.0307583
$436$	2417.21	0.265512
$437$	2788.44	0.305239
$438$	−32369.7	−3.53124
$439$	17674.1	1.92150	0.960751	−	0.277413i	$-0.0894771\pi$
$439$	17674.1	1.92150	0.960751	+	0.277413i	$0.0894771\pi$
$440$	599.207	0.0649229
$441$	−16103.7	−1.73887
$442$	3366.90	0.362324
$443$	5236.19	0.561578	0.280789	−	0.959770i	$-0.409404\pi$
$443$	5236.19	0.561578	0.280789	+	0.959770i	$0.409404\pi$
$444$	28594.6	3.05640
$445$	−2903.44	−0.309295
$446$	−24929.3	−2.64672
$447$	−15745.1	−1.66604
$448$	−3599.39	−0.379587
$449$	−2280.49	−0.239695	−0.119847	−	0.992792i	$-0.538241\pi$
$449$	−2280.49	−0.239695	−0.119847	+	0.992792i	$0.538241\pi$
$450$	5397.86	0.565462
$451$	−1514.29	−0.158104
$452$	7189.74	0.748179
$453$	−2139.73	−0.221928
$454$	15528.5	1.60526
$455$	144.528	0.0148913
$456$	−1818.26	−0.186728
$457$	−4540.35	−0.464745	−0.232373	−	0.972627i	$-0.574649\pi$
$457$	−4540.35	−0.464745	−0.232373	+	0.972627i	$0.574649\pi$
$458$	−14135.2	−1.44212
$459$	25779.0	2.62148
$460$	−7727.55	−0.783258
$461$	−9006.70	−0.909944	−0.454972	−	0.890506i	$-0.650351\pi$
$461$	−9006.70	−0.909944	−0.454972	+	0.890506i	$0.650351\pi$
$462$	1948.12	0.196179
$463$	−9573.01	−0.960898	−0.480449	−	0.877023i	$-0.659526\pi$
$463$	−9573.01	−0.960898	−0.480449	+	0.877023i	$0.659526\pi$
$464$	−237.304	−0.0237426
$465$	−3562.56	−0.355290
$466$	21533.5	2.14060
$467$	−9167.96	−0.908443	−0.454221	−	0.890889i	$-0.650082\pi$
$467$	−9167.96	−0.908443	−0.454221	+	0.890889i	$0.650082\pi$
$468$	3259.80	0.321975
$469$	810.057	0.0797547
$470$	−4125.63	−0.404896
$471$	−19699.2	−1.92716
$472$	6728.99	0.656201
$473$	−5463.04	−0.531059
$474$	8430.23	0.816906
$475$	−475.000	−0.0458831
$476$	6250.85	0.601906
$477$	10990.2	1.05494
$478$	16349.3	1.56443
$479$	19130.4	1.82482	0.912410	−	0.409278i	$-0.134219\pi$
$479$	19130.4	1.82482	0.912410	+	0.409278i	$0.134219\pi$
$480$	−10889.0	−1.03545
$481$	1907.77	0.180846
$482$	−17286.0	−1.63352
$483$	−6037.87	−0.568804
$484$	1274.23	0.119669
$485$	−1013.49	−0.0948869
$486$	−7287.97	−0.680224
$487$	10829.1	1.00762	0.503810	−	0.863814i	$-0.331931\pi$
$487$	10829.1	1.00762	0.503810	+	0.863814i	$0.331931\pi$
$488$	7848.28	0.728022
$489$	24550.4	2.27036
$490$	−6910.48	−0.637109
$491$	3632.34	0.333860	0.166930	−	0.985969i	$-0.446615\pi$
$491$	3632.34	0.333860	0.166930	+	0.985969i	$0.446615\pi$
$492$	−12734.1	−1.16686
$493$	805.242	0.0735625
$494$	−504.772	−0.0459732
$495$	2758.65	0.250489
$496$	3029.50	0.274251
$497$	−771.670	−0.0696462
$498$	38516.9	3.46583
$499$	−4674.57	−0.419363	−0.209682	−	0.977770i	$-0.567243\pi$
$499$	−4674.57	−0.419363	−0.209682	+	0.977770i	$0.567243\pi$
$500$	1316.36	0.117738
$501$	−7191.62	−0.641313
$502$	26528.6	2.35862
$503$	−16676.2	−1.47824	−0.739119	−	0.673575i	$-0.764758\pi$
$503$	−16676.2	−1.47824	−0.739119	+	0.673575i	$0.764758\pi$
$504$	2559.38	0.226198
$505$	−6467.12	−0.569868
$506$	−6949.42	−0.610552
$507$	−18963.7	−1.66116
$508$	4202.67	0.367054
$509$	−8951.24	−0.779483	−0.389741	−	0.920924i	$-0.627436\pi$
$509$	−8951.24	−0.779483	−0.389741	+	0.920924i	$0.627436\pi$
$510$	23960.5	2.08037
$511$	−4009.49	−0.347103
$512$	12514.9	1.08024
$513$	−3864.83	−0.332624
$514$	−20634.9	−1.77076
$515$	4272.08	0.365534
$516$	−45940.3	−3.91939
$517$	−2108.46	−0.179361
$518$	6232.56	0.528654
$519$	−29421.4	−2.48836
$520$	336.185	0.0283513
$521$	−51.6687	−0.00434481	−0.00217240	−	0.999998i	$-0.500691\pi$
$521$	−51.6687	−0.00434481	−0.00217240	+	0.999998i	$0.500691\pi$
$522$	1371.89	0.115031
$523$	12631.0	1.05605	0.528025	−	0.849229i	$-0.322933\pi$
$523$	12631.0	1.05605	0.528025	+	0.849229i	$0.322933\pi$
$524$	−24442.7	−2.03776
$525$	1028.53	0.0855020
$526$	−3114.83	−0.258200
$527$	−10280.0	−0.849722
$528$	−3608.68	−0.297439
$529$	9371.54	0.770243
$530$	4716.18	0.386524
$531$	30979.2	2.53179
$532$	−937.139	−0.0763724
$533$	−849.590	−0.0690428
$534$	−21957.3	−1.77938
$535$	−6286.76	−0.508038
$536$	1884.27	0.151843
$537$	−28573.4	−2.29615
$538$	−4616.69	−0.369962
$539$	−3531.70	−0.282228
$540$	10710.5	0.853531
$541$	−9709.97	−0.771653	−0.385826	−	0.922571i	$-0.626084\pi$
$541$	−9709.97	−0.771653	−0.385826	+	0.922571i	$0.626084\pi$
$542$	1963.32	0.155594
$543$	−8237.87	−0.651051
$544$	−31421.0	−2.47640
$545$	1147.68	0.0902040
$546$	1092.99	0.0856698
$547$	−12854.9	−1.00482	−0.502410	−	0.864629i	$-0.667553\pi$
$547$	−12854.9	−1.00482	−0.502410	+	0.864629i	$0.667553\pi$
$548$	4177.12	0.325617
$549$	36132.2	2.80890
$550$	1183.81	0.0917775
$551$	−120.723	−0.00933391
$552$	−14044.7	−1.08293
$553$	1044.22	0.0802976
$554$	−31470.7	−2.41347
$555$	13576.6	1.03837
$556$	23906.9	1.82352
$557$	2517.65	0.191519	0.0957595	−	0.995405i	$-0.469472\pi$
$557$	2517.65	0.191519	0.0957595	+	0.995405i	$0.469472\pi$
$558$	−17514.0	−1.32872
$559$	−3065.03	−0.231909
$560$	−874.629	−0.0659997
$561$	12245.3	0.921565
$562$	13991.2	1.05015
$563$	−3062.74	−0.229270	−0.114635	−	0.993408i	$-0.536570\pi$
$563$	−3062.74	−0.229270	−0.114635	+	0.993408i	$0.536570\pi$
$564$	−17730.6	−1.32375
$565$	3413.66	0.254183
$566$	37833.5	2.80965
$567$	2025.73	0.150040
$568$	−1794.98	−0.132598
$569$	24517.2	1.80635	0.903175	−	0.429273i	$-0.141230\pi$
$569$	24517.2	1.80635	0.903175	+	0.429273i	$0.141230\pi$
$570$	−3592.19	−0.263966
$571$	−2571.12	−0.188438	−0.0942190	−	0.995551i	$-0.530035\pi$
$571$	−2571.12	−0.188438	−0.0942190	+	0.995551i	$0.530035\pi$
$572$	714.908	0.0522584
$573$	24228.7	1.76643
$574$	−2775.55	−0.201828
$575$	−3669.00	−0.266101
$576$	−38545.7	−2.78832
$577$	−23847.9	−1.72062	−0.860311	−	0.509769i	$-0.829731\pi$
$577$	−23847.9	−1.72062	−0.860311	+	0.509769i	$0.829731\pi$
$578$	47990.2	3.45351
$579$	−1413.93	−0.101487
$580$	334.558	0.0239513
$581$	4770.92	0.340673
$582$	−7664.52	−0.545884
$583$	2410.27	0.171223
$584$	−9326.46	−0.660842
$585$	1547.74	0.109387
$586$	−25171.7	−1.77446
$587$	−2936.59	−0.206484	−0.103242	−	0.994656i	$-0.532922\pi$
$587$	−2936.59	−0.206484	−0.103242	+	0.994656i	$0.532922\pi$
$588$	−29699.0	−2.08294
$589$	1541.19	0.107816
$590$	13293.9	0.927631
$591$	−3941.77	−0.274353
$592$	−11545.1	−0.801524
$593$	17357.9	1.20203	0.601015	−	0.799238i	$-0.294763\pi$
$593$	17357.9	1.20203	0.601015	+	0.799238i	$0.294763\pi$
$594$	9632.01	0.665330
$595$	2967.88	0.204489
$596$	−18876.5	−1.29733
$597$	9275.53	0.635883
$598$	−3898.97	−0.266623
$599$	−13909.2	−0.948771	−0.474386	−	0.880317i	$-0.657330\pi$
$599$	−13909.2	−0.948771	−0.474386	+	0.880317i	$0.657330\pi$
$600$	2392.45	0.162786
$601$	3708.45	0.251699	0.125849	−	0.992049i	$-0.459834\pi$
$601$	3708.45	0.251699	0.125849	+	0.992049i	$0.459834\pi$
$602$	−10013.3	−0.677924
$603$	8674.87	0.585851
$604$	−2565.27	−0.172814
$605$	605.000	0.0406558
$606$	−48907.7	−3.27845
$607$	2409.33	0.161106	0.0805532	−	0.996750i	$-0.474331\pi$
$607$	2409.33	0.161106	0.0805532	+	0.996750i	$0.474331\pi$
$608$	4710.69	0.314217
$609$	261.404	0.0173935
$610$	15505.2	1.02916
$611$	−1182.95	−0.0783257
$612$	66940.2	4.42140
$613$	21919.4	1.44424	0.722118	−	0.691770i	$-0.243169\pi$
$613$	21919.4	1.44424	0.722118	+	0.691770i	$0.243169\pi$
$614$	36806.8	2.41922
$615$	−6046.08	−0.396425
$616$	561.298	0.0367132
$617$	−8187.70	−0.534238	−0.267119	−	0.963664i	$-0.586072\pi$
$617$	−8187.70	−0.534238	−0.267119	+	0.963664i	$0.586072\pi$
$618$	32307.6	2.10292
$619$	−7073.39	−0.459295	−0.229648	−	0.973274i	$-0.573757\pi$
$619$	−7073.39	−0.459295	−0.229648	+	0.973274i	$0.573757\pi$
$620$	−4271.08	−0.276662
$621$	−29852.8	−1.92907
$622$	22477.2	1.44896
$623$	−2719.76	−0.174903
$624$	−2024.65	−0.129889
$625$	625.000	0.0400000
$626$	−3227.02	−0.206035
$627$	−1835.84	−0.116932
$628$	−23616.9	−1.50067
$629$	39176.1	2.48339
$630$	5056.37	0.319763
$631$	−2683.92	−0.169327	−0.0846633	−	0.996410i	$-0.526981\pi$
$631$	−2683.92	−0.169327	−0.0846633	+	0.996410i	$0.526981\pi$
$632$	2428.94	0.152877
$633$	−12946.2	−0.812898
$634$	−33650.1	−2.10792
$635$	1995.41	0.124701
$636$	20268.7	1.26369
$637$	−1981.46	−0.123247
$638$	300.869	0.0186701
$639$	−8263.79	−0.511597
$640$	−6623.68	−0.409100
$641$	21057.6	1.29754	0.648772	−	0.760983i	$-0.275283\pi$
$641$	21057.6	1.29754	0.648772	+	0.760983i	$0.275283\pi$
$642$	−47543.7	−2.92274
$643$	2594.60	0.159131	0.0795654	−	0.996830i	$-0.474647\pi$
$643$	2594.60	0.159131	0.0795654	+	0.996830i	$0.474647\pi$
$644$	−7238.66	−0.442924
$645$	−21812.2	−1.33156
$646$	−10365.5	−0.631308
$647$	−6453.04	−0.392110	−0.196055	−	0.980593i	$-0.562813\pi$
$647$	−6453.04	−0.392110	−0.196055	+	0.980593i	$0.562813\pi$
$648$	4712.03	0.285658
$649$	6794.04	0.410924
$650$	664.174	0.0400785
$651$	−3337.18	−0.200913
$652$	29432.9	1.76792
$653$	−22492.3	−1.34792	−0.673959	−	0.738769i	$-0.735408\pi$
$653$	−22492.3	−1.34792	−0.673959	+	0.738769i	$0.735408\pi$
$654$	8679.34	0.518944
$655$	−11605.3	−0.692300
$656$	5141.41	0.306004
$657$	−42937.5	−2.54970
$658$	−3864.62	−0.228964
$659$	−7255.34	−0.428874	−0.214437	−	0.976738i	$-0.568792\pi$
$659$	−7255.34	−0.428874	−0.214437	+	0.976738i	$0.568792\pi$
$660$	5087.62	0.300054
$661$	−13053.6	−0.768121	−0.384061	−	0.923308i	$-0.625475\pi$
$661$	−13053.6	−0.768121	−0.384061	+	0.923308i	$0.625475\pi$
$662$	−16614.6	−0.975447
$663$	6870.23	0.402440
$664$	11097.6	0.648600
$665$	−444.949	−0.0259464
$666$	66744.3	3.88331
$667$	−932.493	−0.0541324
$668$	−8621.88	−0.499387
$669$	−50868.7	−2.93976
$670$	3722.60	0.214652
$671$	7924.15	0.455899
$672$	−10200.1	−0.585534
$673$	11971.2	0.685667	0.342834	−	0.939396i	$-0.388613\pi$
$673$	11971.2	0.685667	0.342834	+	0.939396i	$0.388613\pi$
$674$	41691.9	2.38266
$675$	5085.30	0.289975
$676$	−22735.2	−1.29354
$677$	−17741.9	−1.00720	−0.503602	−	0.863936i	$-0.667992\pi$
$677$	−17741.9	−1.00720	−0.503602	+	0.863936i	$0.667992\pi$
$678$	25815.8	1.46232
$679$	−949.371	−0.0536576
$680$	6903.56	0.389323
$681$	31686.2	1.78299
$682$	−3841.00	−0.215659
$683$	−17884.6	−1.00195	−0.500976	−	0.865461i	$-0.667026\pi$
$683$	−17884.6	−1.00195	−0.500976	+	0.865461i	$0.667026\pi$
$684$	−10035.8	−0.561006
$685$	1983.28	0.110624
$686$	−13388.9	−0.745174
$687$	−28843.1	−1.60179
$688$	18548.5	1.02784
$689$	1352.28	0.0747719
$690$	−27746.9	−1.53088
$691$	33109.2	1.82277	0.911384	−	0.411558i	$-0.135015\pi$
$691$	33109.2	1.82277	0.911384	+	0.411558i	$0.135015\pi$
$692$	−35272.7	−1.93767
$693$	2584.13	0.141649
$694$	52738.6	2.88463
$695$	11350.9	0.619516
$696$	608.052	0.0331151
$697$	−17446.3	−0.948102
$698$	32649.5	1.77049
$699$	43939.5	2.37760
$700$	1233.08	0.0665799
$701$	4550.03	0.245153	0.122577	−	0.992459i	$-0.460884\pi$
$701$	4550.03	0.245153	0.122577	+	0.992459i	$0.460884\pi$
$702$	5404.03	0.290544
$703$	−5873.35	−0.315103
$704$	−8453.46	−0.452560
$705$	−8418.42	−0.449725
$706$	−12443.0	−0.663313
$707$	−6057.98	−0.322254
$708$	57133.1	3.03276
$709$	31584.0	1.67301	0.836503	−	0.547962i	$-0.184596\pi$
$709$	31584.0	1.67301	0.836503	+	0.547962i	$0.184596\pi$
$710$	−3546.20	−0.187446
$711$	11182.5	0.589838
$712$	−6326.42	−0.332995
$713$	11904.5	0.625284
$714$	22444.6	1.17643
$715$	339.435	0.0177541
$716$	−34256.0	−1.78800
$717$	33361.0	1.73764
$718$	46986.1	2.44221
$719$	22215.6	1.15230	0.576150	−	0.817344i	$-0.304554\pi$
$719$	22215.6	1.15230	0.576150	+	0.817344i	$0.304554\pi$
$720$	−9366.37	−0.484811
$721$	4001.80	0.206706
$722$	1554.01	0.0801031
$723$	−35272.4	−1.81438
$724$	−9876.20	−0.506970
$725$	158.846	0.00813712
$726$	4575.32	0.233893
$727$	−28812.4	−1.46986	−0.734932	−	0.678141i	$-0.762786\pi$
$727$	−28812.4	−1.46986	−0.734932	+	0.678141i	$0.762786\pi$
$728$	314.916	0.0160324
$729$	−26549.0	−1.34883
$730$	−18425.5	−0.934192
$731$	−62940.5	−3.18460
$732$	66636.5	3.36469
$733$	−11268.7	−0.567828	−0.283914	−	0.958850i	$-0.591633\pi$
$733$	−11268.7	−0.567828	−0.283914	+	0.958850i	$0.591633\pi$
$734$	17961.7	0.903238
$735$	−14101.0	−0.707649
$736$	36386.4	1.82231
$737$	1902.49	0.0950868
$738$	−29723.3	−1.48256
$739$	31262.6	1.55617	0.778086	−	0.628157i	$-0.216191\pi$
$739$	31262.6	1.55617	0.778086	+	0.628157i	$0.216191\pi$
$740$	16276.7	0.808571
$741$	−1030.00	−0.0510633
$742$	4417.82	0.218576
$743$	37448.5	1.84906	0.924529	−	0.381111i	$-0.124458\pi$
$743$	37448.5	1.84906	0.924529	+	0.381111i	$0.124458\pi$
$744$	−7762.59	−0.382514
$745$	−8962.46	−0.440751
$746$	26827.4	1.31665
$747$	51091.6	2.50247
$748$	14680.6	0.717617
$749$	−5889.03	−0.287290
$750$	4726.57	0.230120
$751$	−35791.0	−1.73906	−0.869528	−	0.493884i	$-0.835577\pi$
$751$	−35791.0	−1.73906	−0.869528	+	0.493884i	$0.835577\pi$
$752$	7158.79	0.347146
$753$	54132.1	2.61977
$754$	168.803	0.00815309
$755$	−1217.98	−0.0587111
$756$	10032.9	0.482663
$757$	7190.49	0.345235	0.172617	−	0.984989i	$-0.444778\pi$
$757$	7190.49	0.345235	0.172617	+	0.984989i	$0.444778\pi$
$758$	−12564.2	−0.602049
$759$	−14180.4	−0.678151
$760$	−1034.99	−0.0493989
$761$	−23493.5	−1.11910	−0.559552	−	0.828796i	$-0.689027\pi$
$761$	−23493.5	−1.11910	−0.559552	+	0.828796i	$0.689027\pi$
$762$	15090.3	0.717407
$763$	1075.07	0.0510095
$764$	29047.2	1.37551
$765$	31782.9	1.50211
$766$	−20554.0	−0.969512
$767$	3811.80	0.179447
$768$	3911.65	0.183789
$769$	23342.0	1.09458	0.547291	−	0.836942i	$-0.315659\pi$
$769$	23342.0	1.09458	0.547291	+	0.836942i	$0.315659\pi$
$770$	1108.91	0.0518993
$771$	−42106.0	−1.96681
$772$	−1695.13	−0.0790271
$773$	−10655.8	−0.495811	−0.247906	−	0.968784i	$-0.579742\pi$
$773$	−10655.8	−0.495811	−0.247906	+	0.968784i	$0.579742\pi$
$774$	−107232.	−4.97980
$775$	−2027.89	−0.0939921
$776$	−2208.33	−0.102158
$777$	12717.7	0.587186
$778$	−4275.66	−0.197031
$779$	2615.59	0.120299
$780$	2854.41	0.131031
$781$	−1812.33	−0.0830350
$782$	−80065.4	−3.66129
$783$	1292.45	0.0589891
$784$	11991.1	0.546240
$785$	−11213.2	−0.509830
$786$	−87765.2	−3.98280
$787$	14282.9	0.646926	0.323463	−	0.946241i	$-0.395153\pi$
$787$	14282.9	0.646926	0.323463	+	0.946241i	$0.395153\pi$
$788$	−4725.70	−0.213637
$789$	−6355.88	−0.286788
$790$	4798.67	0.216113
$791$	3197.69	0.143738
$792$	6010.92	0.269683
$793$	4445.84	0.199088
$794$	−33724.9	−1.50737
$795$	9623.47	0.429320
$796$	11120.2	0.495158
$797$	−12984.9	−0.577099	−0.288549	−	0.957465i	$-0.593173\pi$
$797$	−12984.9	−0.577099	−0.288549	+	0.957465i	$0.593173\pi$
$798$	−3364.93	−0.149270
$799$	−24291.9	−1.07558
$800$	−6198.28	−0.273928
$801$	−29125.8	−1.28478
$802$	−21852.5	−0.962142
$803$	−9416.63	−0.413830
$804$	15998.6	0.701773
$805$	−3436.88	−0.150477
$806$	−2154.99	−0.0941765
$807$	−9420.45	−0.410924
$808$	−14091.4	−0.613534
$809$	30016.9	1.30450	0.652249	−	0.758005i	$-0.273826\pi$
$809$	30016.9	1.30450	0.652249	+	0.758005i	$0.273826\pi$
$810$	9309.19	0.403817
$811$	−26297.0	−1.13861	−0.569306	−	0.822126i	$-0.692788\pi$
$811$	−26297.0	−1.13861	−0.569306	+	0.822126i	$0.692788\pi$
$812$	313.392	0.0135442
$813$	4006.19	0.172821
$814$	14637.7	0.630283
$815$	13974.6	0.600625
$816$	−41576.2	−1.78365
$817$	9436.16	0.404075
$818$	43377.7	1.85411
$819$	1449.82	0.0618570
$820$	−7248.51	−0.308694
$821$	−26166.9	−1.11234	−0.556169	−	0.831069i	$-0.687729\pi$
$821$	−26166.9	−1.11234	−0.556169	+	0.831069i	$0.687729\pi$
$822$	14998.6	0.636418
$823$	38569.5	1.63359	0.816797	−	0.576925i	$-0.195748\pi$
$823$	38569.5	1.63359	0.816797	+	0.576925i	$0.195748\pi$
$824$	9308.58	0.393543
$825$	2415.58	0.101939
$826$	12452.9	0.524566
$827$	42634.0	1.79266	0.896329	−	0.443390i	$-0.146224\pi$
$827$	42634.0	1.79266	0.896329	+	0.443390i	$0.146224\pi$
$828$	−77518.6	−3.25357
$829$	−17082.2	−0.715667	−0.357833	−	0.933785i	$-0.616484\pi$
$829$	−17082.2	−0.715667	−0.357833	+	0.933785i	$0.616484\pi$
$830$	21924.7	0.916886
$831$	−64216.6	−2.68068
$832$	−4742.81	−0.197629
$833$	−40689.2	−1.69244
$834$	85841.2	3.56407
$835$	−4093.63	−0.169660
$836$	−2200.95	−0.0910543
$837$	−16499.9	−0.681384
$838$	35080.8	1.44612
$839$	−35235.6	−1.44990	−0.724950	−	0.688801i	$-0.758137\pi$
$839$	−35235.6	−1.44990	−0.724950	+	0.688801i	$0.758137\pi$
$840$	2241.09	0.0920536
$841$	−24348.6	−0.998345
$842$	19541.7	0.799823
$843$	28549.4	1.16642
$844$	−15520.9	−0.632999
$845$	−10794.6	−0.439461
$846$	−41386.1	−1.68189
$847$	566.725	0.0229904
$848$	−8183.52	−0.331395
$849$	77200.1	3.12073
$850$	13638.8	0.550362
$851$	−45367.0	−1.82745
$852$	−15240.4	−0.612827
$853$	7943.70	0.318859	0.159430	−	0.987209i	$-0.449034\pi$
$853$	7943.70	0.318859	0.159430	+	0.987209i	$0.449034\pi$
$854$	14524.3	0.581980
$855$	−4764.94	−0.190594
$856$	−13698.4	−0.546966
$857$	27154.4	1.08235	0.541176	−	0.840910i	$-0.317979\pi$
$857$	27154.4	1.08235	0.541176	+	0.840910i	$0.317979\pi$
$858$	2566.98	0.102139
$859$	42280.1	1.67937	0.839684	−	0.543075i	$-0.182740\pi$
$859$	42280.1	1.67937	0.839684	+	0.543075i	$0.182740\pi$
$860$	−26150.2	−1.03688
$861$	−5663.57	−0.224174
$862$	11574.8	0.457353
$863$	6323.18	0.249413	0.124707	−	0.992194i	$-0.460201\pi$
$863$	6323.18	0.249413	0.124707	+	0.992194i	$0.460201\pi$
$864$	−50432.1	−1.98581
$865$	−16747.3	−0.658296
$866$	11256.6	0.441703
$867$	97924.9	3.83588
$868$	−4000.87	−0.156450
$869$	2452.43	0.0957340
$870$	1201.28	0.0468128
$871$	1067.39	0.0415236
$872$	2500.72	0.0971159
$873$	−10166.8	−0.394150
$874$	12003.5	0.464561
$875$	585.459	0.0226196
$876$	−79187.1	−3.05421
$877$	−44653.3	−1.71931	−0.859656	−	0.510873i	$-0.829322\pi$
$877$	−44653.3	−1.71931	−0.859656	+	0.510873i	$0.829322\pi$
$878$	76082.6	2.92444
$879$	−51363.3	−1.97092
$880$	−2054.14	−0.0786875
$881$	3861.10	0.147655	0.0738274	−	0.997271i	$-0.476479\pi$
$881$	3861.10	0.147655	0.0738274	+	0.997271i	$0.476479\pi$
$882$	−69322.2	−2.64649
$883$	−217.863	−0.00830315	−0.00415157	−	0.999991i	$-0.501321\pi$
$883$	−217.863	−0.00830315	−0.00415157	+	0.999991i	$0.501321\pi$
$884$	8236.57	0.313378
$885$	27126.5	1.03034
$886$	22540.5	0.854698
$887$	18542.4	0.701909	0.350955	−	0.936393i	$-0.385857\pi$
$887$	18542.4	0.701909	0.350955	+	0.936393i	$0.385857\pi$
$888$	29582.5	1.11793
$889$	1869.17	0.0705174
$890$	−12498.6	−0.470735
$891$	4757.59	0.178883
$892$	−60985.4	−2.28917
$893$	3641.88	0.136474
$894$	−67778.8	−2.53564
$895$	−16264.6	−0.607447
$896$	−6204.63	−0.231342
$897$	−7955.92	−0.296143
$898$	−9816.93	−0.364805
$899$	−515.396	−0.0191206
$900$	13205.0	0.489073
$901$	27769.1	1.02677
$902$	−6518.62	−0.240628
$903$	−20432.3	−0.752983
$904$	7438.13	0.273660
$905$	−4689.17	−0.172236
$906$	−9211.00	−0.337765
$907$	52209.6	1.91134	0.955672	−	0.294432i	$-0.0951304\pi$
$907$	52209.6	1.91134	0.955672	+	0.294432i	$0.0951304\pi$
$908$	37987.8	1.38840
$909$	−64874.7	−2.36717
$910$	622.155	0.0226640
$911$	−16134.1	−0.586770	−0.293385	−	0.955994i	$-0.594782\pi$
$911$	−16134.1	−0.586770	−0.293385	+	0.955994i	$0.594782\pi$
$912$	6233.17	0.226317
$913$	11204.9	0.406164
$914$	−19545.1	−0.707323
$915$	31638.7	1.14311
$916$	−34579.3	−1.24731
$917$	−10871.1	−0.391488
$918$	110972.	3.98978
$919$	23946.6	0.859548	0.429774	−	0.902937i	$-0.358593\pi$
$919$	23946.6	0.859548	0.429774	+	0.902937i	$0.358593\pi$
$920$	−7994.52	−0.286491
$921$	75104.9	2.68707
$922$	−38771.6	−1.38490
$923$	−1016.81	−0.0362607
$924$	4765.75	0.169677
$925$	7728.09	0.274700
$926$	−41209.4	−1.46245
$927$	42855.2	1.51839
$928$	−1575.32	−0.0557245
$929$	−16780.4	−0.592623	−0.296312	−	0.955091i	$-0.595757\pi$
$929$	−16780.4	−0.592623	−0.296312	+	0.955091i	$0.595757\pi$
$930$	−15335.9	−0.540736
$931$	6100.20	0.214743
$932$	52678.1	1.85143
$933$	45865.2	1.60939
$934$	−39465.8	−1.38261
$935$	6970.30	0.243800
$936$	3372.43	0.117768
$937$	31361.5	1.09342	0.546711	−	0.837321i	$-0.315880\pi$
$937$	31361.5	1.09342	0.546711	+	0.837321i	$0.315880\pi$
$938$	3487.09	0.121383
$939$	−6584.81	−0.228847
$940$	−10092.7	−0.350198
$941$	44405.0	1.53832	0.769162	−	0.639054i	$-0.220674\pi$
$941$	44405.0	1.53832	0.769162	+	0.639054i	$0.220674\pi$
$942$	−84800.0	−2.93305
$943$	20203.4	0.697679
$944$	−23067.6	−0.795325
$945$	4763.58	0.163978
$946$	−23517.0	−0.808249
$947$	6620.15	0.227166	0.113583	−	0.993529i	$-0.463767\pi$
$947$	6620.15	0.227166	0.113583	+	0.993529i	$0.463767\pi$
$948$	20623.2	0.706550
$949$	−5283.19	−0.180716
$950$	−2044.76	−0.0698322
$951$	−68663.8	−2.34130
$952$	6466.81	0.220158
$953$	−6723.89	−0.228550	−0.114275	−	0.993449i	$-0.536455\pi$
$953$	−6723.89	−0.228550	−0.114275	+	0.993449i	$0.536455\pi$
$954$	47310.2	1.60558
$955$	13791.5	0.467311
$956$	39995.7	1.35309
$957$	613.930	0.0207372
$958$	82351.4	2.77730
$959$	1857.81	0.0625565
$960$	−33752.1	−1.13473
$961$	−23211.3	−0.779137
$962$	8212.47	0.275240
$963$	−63065.4	−2.11034
$964$	−42287.3	−1.41284
$965$	−804.838	−0.0268484
$966$	−25991.5	−0.865696
$967$	25040.0	0.832712	0.416356	−	0.909202i	$-0.363307\pi$
$967$	25040.0	0.832712	0.416356	+	0.909202i	$0.363307\pi$
$968$	1318.26	0.0437710
$969$	−21151.0	−0.701206
$970$	−4362.81	−0.144414
$971$	43748.9	1.44590	0.722950	−	0.690900i	$-0.242786\pi$
$971$	43748.9	1.44590	0.722950	+	0.690900i	$0.242786\pi$
$972$	−17828.8	−0.588332
$973$	10632.8	0.350330
$974$	46616.3	1.53356
$975$	1355.26	0.0445159
$976$	−26904.6	−0.882373
$977$	25141.1	0.823271	0.411636	−	0.911349i	$-0.364958\pi$
$977$	25141.1	0.823271	0.411636	+	0.911349i	$0.364958\pi$
$978$	105683.	3.45540
$979$	−6387.58	−0.208527
$980$	−16905.3	−0.551042
$981$	11512.9	0.374698
$982$	15636.3	0.508121
$983$	16640.1	0.539917	0.269958	−	0.962872i	$-0.412990\pi$
$983$	16640.1	0.539917	0.269958	+	0.962872i	$0.412990\pi$
$984$	−13174.0	−0.426801
$985$	−2243.74	−0.0725803
$986$	3466.37	0.111959
$987$	−7885.83	−0.254315
$988$	−1234.84	−0.0397627
$989$	72886.9	2.34345
$990$	11875.3	0.381234
$991$	20228.0	0.648400	0.324200	−	0.945989i	$-0.394905\pi$
$991$	20228.0	0.648400	0.324200	+	0.945989i	$0.394905\pi$
$992$	20111.0	0.643676
$993$	−33902.5	−1.08345
$994$	−3321.85	−0.105999
$995$	5279.83	0.168223
$996$	94225.2	2.99763
$997$	−42387.7	−1.34647	−0.673235	−	0.739428i	$-0.735096\pi$
$997$	−42387.7	−1.34647	−0.673235	+	0.739428i	$0.735096\pi$
$998$	−20122.8	−0.638253
$999$	62879.4	1.99141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.e.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.e.1.18	✓	22	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+4.30475 q^{2} +8.78392 q^{3} +10.5309 q^{4} +5.00000 q^{5} +37.8126 q^{6} +4.68368 q^{7} +10.8947 q^{8} +50.1573 q^{9} +O(q^{10})\)	\(q+4.30475 q^{2} +8.78392 q^{3} +10.5309 q^{4} +5.00000 q^{5} +37.8126 q^{6} +4.68368 q^{7} +10.8947 q^{8} +50.1573 q^{9} +21.5237 q^{10} +11.0000 q^{11} +92.5022 q^{12} +6.17155 q^{13} +20.1620 q^{14} +43.9196 q^{15} -37.3480 q^{16} +126.733 q^{17} +215.915 q^{18} -19.0000 q^{19} +52.6543 q^{20} +41.1410 q^{21} +47.3522 q^{22} -146.760 q^{23} +95.6980 q^{24} +25.0000 q^{25} +26.5669 q^{26} +203.412 q^{27} +49.3231 q^{28} +6.35386 q^{29} +189.063 q^{30} -81.1155 q^{31} -247.931 q^{32} +96.6232 q^{33} +545.553 q^{34} +23.4184 q^{35} +528.199 q^{36} +309.123 q^{37} -81.7902 q^{38} +54.2104 q^{39} +54.4734 q^{40} -137.662 q^{41} +177.102 q^{42} -496.640 q^{43} +115.839 q^{44} +250.787 q^{45} -631.765 q^{46} -191.678 q^{47} -328.062 q^{48} -321.063 q^{49} +107.619 q^{50} +1113.21 q^{51} +64.9916 q^{52} +219.115 q^{53} +875.637 q^{54} +55.0000 q^{55} +51.0271 q^{56} -166.895 q^{57} +27.3518 q^{58} +617.640 q^{59} +462.511 q^{60} +720.377 q^{61} -349.182 q^{62} +234.921 q^{63} -768.497 q^{64} +30.8577 q^{65} +415.938 q^{66} +172.953 q^{67} +1334.60 q^{68} -1289.13 q^{69} +100.810 q^{70} -164.757 q^{71} +546.448 q^{72} -856.057 q^{73} +1330.70 q^{74} +219.598 q^{75} -200.086 q^{76} +51.5204 q^{77} +233.362 q^{78} +222.948 q^{79} -186.740 q^{80} +432.508 q^{81} -592.602 q^{82} +1018.63 q^{83} +433.250 q^{84} +633.664 q^{85} -2137.91 q^{86} +55.8118 q^{87} +119.841 q^{88} -580.689 q^{89} +1079.57 q^{90} +28.9055 q^{91} -1545.51 q^{92} -712.512 q^{93} -825.125 q^{94} -95.0000 q^{95} -2177.81 q^{96} -202.698 q^{97} -1382.10 q^{98} +551.730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * q^99

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