LMFDB - Embedded newform 1441.4.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.36465 q^{2} -2.69161 q^{3} +20.7795 q^{4} -8.89356 q^{5} +14.4395 q^{6} -3.71000 q^{7} -68.5575 q^{8} -19.7553 q^{9} +O(q^{10})$	\(q-5.36465 q^{2} -2.69161 q^{3} +20.7795 q^{4} -8.89356 q^{5} +14.4395 q^{6} -3.71000 q^{7} -68.5575 q^{8} -19.7553 q^{9} +47.7108 q^{10} +11.0000 q^{11} -55.9302 q^{12} -61.1954 q^{13} +19.9028 q^{14} +23.9379 q^{15} +201.551 q^{16} +46.3108 q^{17} +105.980 q^{18} -127.362 q^{19} -184.804 q^{20} +9.98585 q^{21} -59.0112 q^{22} +38.6057 q^{23} +184.530 q^{24} -45.9046 q^{25} +328.292 q^{26} +125.847 q^{27} -77.0918 q^{28} -28.4560 q^{29} -128.419 q^{30} +307.734 q^{31} -532.793 q^{32} -29.6077 q^{33} -248.441 q^{34} +32.9951 q^{35} -410.504 q^{36} +360.498 q^{37} +683.251 q^{38} +164.714 q^{39} +609.720 q^{40} -398.403 q^{41} -53.5706 q^{42} +319.421 q^{43} +228.574 q^{44} +175.695 q^{45} -207.106 q^{46} -15.2566 q^{47} -542.497 q^{48} -329.236 q^{49} +246.262 q^{50} -124.650 q^{51} -1271.61 q^{52} -305.332 q^{53} -675.124 q^{54} -97.8291 q^{55} +254.348 q^{56} +342.807 q^{57} +152.657 q^{58} +557.736 q^{59} +497.418 q^{60} +578.256 q^{61} -1650.89 q^{62} +73.2920 q^{63} +1245.84 q^{64} +544.244 q^{65} +158.835 q^{66} -236.773 q^{67} +962.315 q^{68} -103.911 q^{69} -177.007 q^{70} -465.470 q^{71} +1354.37 q^{72} -389.818 q^{73} -1933.95 q^{74} +123.557 q^{75} -2646.51 q^{76} -40.8100 q^{77} -883.632 q^{78} +1277.78 q^{79} -1792.51 q^{80} +194.662 q^{81} +2137.29 q^{82} -1176.30 q^{83} +207.501 q^{84} -411.868 q^{85} -1713.58 q^{86} +76.5924 q^{87} -754.133 q^{88} -677.400 q^{89} -942.540 q^{90} +227.035 q^{91} +802.206 q^{92} -828.298 q^{93} +81.8465 q^{94} +1132.70 q^{95} +1434.07 q^{96} +4.85026 q^{97} +1766.24 q^{98} -217.308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) $ 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.36465	−1.89669	−0.948345	−	0.317239i	$-0.897244\pi$
$2$	−5.36465	−1.89669	−0.948345	+	0.317239i	$0.897244\pi$
$3$	−2.69161	−0.518000	−0.259000	−	0.965877i	$-0.583393\pi$
$3$	−2.69161	−0.518000	−0.259000	+	0.965877i	$0.583393\pi$
$4$	20.7795	2.59744
$5$	−8.89356	−0.795464	−0.397732	−	0.917502i	$-0.630203\pi$
$5$	−8.89356	−0.795464	−0.397732	+	0.917502i	$0.630203\pi$
$6$	14.4395	0.982485
$7$	−3.71000	−0.200321	−0.100160	−	0.994971i	$-0.531936\pi$
$7$	−3.71000	−0.200321	−0.100160	+	0.994971i	$0.531936\pi$
$8$	−68.5575	−3.02984
$9$	−19.7553	−0.731676
$10$	47.7108	1.50875
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−55.9302	−1.34547
$13$	−61.1954	−1.30558	−0.652790	−	0.757539i	$-0.726402\pi$
$13$	−61.1954	−1.30558	−0.652790	+	0.757539i	$0.726402\pi$
$14$	19.9028	0.379947
$15$	23.9379	0.412050
$16$	201.551	3.14924
$17$	46.3108	0.660707	0.330354	−	0.943857i	$-0.392832\pi$
$17$	46.3108	0.660707	0.330354	+	0.943857i	$0.392832\pi$
$18$	105.980	1.38776
$19$	−127.362	−1.53783	−0.768915	−	0.639351i	$-0.779203\pi$
$19$	−127.362	−1.53783	−0.768915	+	0.639351i	$0.779203\pi$
$20$	−184.804	−2.06617
$21$	9.98585	0.103766
$22$	−59.0112	−0.571874
$23$	38.6057	0.349993	0.174997	−	0.984569i	$-0.444009\pi$
$23$	38.6057	0.349993	0.174997	+	0.984569i	$0.444009\pi$
$24$	184.530	1.56946
$25$	−45.9046	−0.367237
$26$	328.292	2.47628
$27$	125.847	0.897008
$28$	−77.0918	−0.520321
$29$	−28.4560	−0.182212	−0.0911061	−	0.995841i	$-0.529040\pi$
$29$	−28.4560	−0.182212	−0.0911061	+	0.995841i	$0.529040\pi$
$30$	−128.419	−0.781532
$31$	307.734	1.78292	0.891462	−	0.453096i	$-0.149680\pi$
$31$	307.734	1.78292	0.891462	+	0.453096i	$0.149680\pi$
$32$	−532.793	−2.94329
$33$	−29.6077	−0.156183
$34$	−248.441	−1.25316
$35$	32.9951	0.159348
$36$	−410.504	−1.90048
$37$	360.498	1.60177	0.800885	−	0.598818i	$-0.204363\pi$
$37$	360.498	1.60177	0.800885	+	0.598818i	$0.204363\pi$
$38$	683.251	2.91679
$39$	164.714	0.676290
$40$	609.720	2.41013
$41$	−398.403	−1.51756	−0.758781	−	0.651346i	$-0.774205\pi$
$41$	−398.403	−1.51756	−0.758781	+	0.651346i	$0.774205\pi$
$42$	−53.5706	−0.196812
$43$	319.421	1.13282	0.566409	−	0.824124i	$-0.308332\pi$
$43$	319.421	1.13282	0.566409	+	0.824124i	$0.308332\pi$
$44$	228.574	0.783157
$45$	175.695	0.582022
$46$	−207.106	−0.663829
$47$	−15.2566	−0.0473491	−0.0236745	−	0.999720i	$-0.507537\pi$
$47$	−15.2566	−0.0473491	−0.0236745	+	0.999720i	$0.507537\pi$
$48$	−542.497	−1.63130
$49$	−329.236	−0.959872
$50$	246.262	0.696535
$51$	−124.650	−0.342246
$52$	−1271.61	−3.39116
$53$	−305.332	−0.791332	−0.395666	−	0.918395i	$-0.629486\pi$
$53$	−305.332	−0.791332	−0.395666	+	0.918395i	$0.629486\pi$
$54$	−675.124	−1.70135
$55$	−97.8291	−0.239841
$56$	254.348	0.606941
$57$	342.807	0.796595
$58$	152.657	0.345600
$59$	557.736	1.23070	0.615348	−	0.788256i	$-0.289016\pi$
$59$	557.736	1.23070	0.615348	+	0.788256i	$0.289016\pi$
$60$	497.418	1.07027
$61$	578.256	1.21374	0.606869	−	0.794802i	$-0.292425\pi$
$61$	578.256	1.21374	0.606869	+	0.794802i	$0.292425\pi$
$62$	−1650.89	−3.38166
$63$	73.2920	0.146570
$64$	1245.84	2.43327
$65$	544.244	1.03854
$66$	158.835	0.296230
$67$	−236.773	−0.431737	−0.215868	−	0.976422i	$-0.569258\pi$
$67$	−236.773	−0.431737	−0.215868	+	0.976422i	$0.569258\pi$
$68$	962.315	1.71614
$69$	−103.911	−0.181296
$70$	−177.007	−0.302234
$71$	−465.470	−0.778045	−0.389022	−	0.921228i	$-0.627187\pi$
$71$	−465.470	−0.778045	−0.389022	+	0.921228i	$0.627187\pi$
$72$	1354.37	2.21686
$73$	−389.818	−0.624997	−0.312499	−	0.949918i	$-0.601166\pi$
$73$	−389.818	−0.624997	−0.312499	+	0.949918i	$0.601166\pi$
$74$	−1933.95	−3.03806
$75$	123.557	0.190229
$76$	−2646.51	−3.99441
$77$	−40.8100	−0.0603990
$78$	−883.632	−1.28271
$79$	1277.78	1.81976	0.909881	−	0.414869i	$-0.136173\pi$
$79$	1277.78	1.81976	0.909881	+	0.414869i	$0.136173\pi$
$80$	−1792.51	−2.50511
$81$	194.662	0.267027
$82$	2137.29	2.87835
$83$	−1176.30	−1.55562	−0.777808	−	0.628502i	$-0.783668\pi$
$83$	−1176.30	−1.55562	−0.777808	+	0.628502i	$0.783668\pi$
$84$	207.501	0.269526
$85$	−411.868	−0.525569
$86$	−1713.58	−2.14861
$87$	76.5924	0.0943859
$88$	−754.133	−0.913532
$89$	−677.400	−0.806789	−0.403395	−	0.915026i	$-0.632170\pi$
$89$	−677.400	−0.806789	−0.403395	+	0.915026i	$0.632170\pi$
$90$	−942.540	−1.10392
$91$	227.035	0.261535
$92$	802.206	0.909085
$93$	−828.298	−0.923554
$94$	81.8465	0.0898066
$95$	1132.70	1.22329
$96$	1434.07	1.52462
$97$	4.85026	0.00507701	0.00253850	−	0.999997i	$-0.499192\pi$
$97$	4.85026	0.00507701	0.00253850	+	0.999997i	$0.499192\pi$
$98$	1766.24	1.82058
$99$	−217.308	−0.220609
$100$	−953.875	−0.953875
$101$	−1352.23	−1.33220	−0.666099	−	0.745863i	$-0.732037\pi$
$101$	−1352.23	−1.33220	−0.666099	+	0.745863i	$0.732037\pi$
$102$	668.706	0.649135
$103$	1456.59	1.39341	0.696707	−	0.717355i	$-0.254648\pi$
$103$	1456.59	1.39341	0.696707	+	0.717355i	$0.254648\pi$
$104$	4195.40	3.95570
$105$	−88.8097	−0.0825423
$106$	1638.00	1.50091
$107$	1729.79	1.56285	0.781425	−	0.623999i	$-0.214493\pi$
$107$	1729.79	1.56285	0.781425	+	0.623999i	$0.214493\pi$
$108$	2615.03	2.32992
$109$	1004.46	0.882657	0.441329	−	0.897346i	$-0.354507\pi$
$109$	1004.46	0.882657	0.441329	+	0.897346i	$0.354507\pi$
$110$	524.819	0.454905
$111$	−970.318	−0.829716
$112$	−747.755	−0.630859
$113$	1558.99	1.29785	0.648926	−	0.760852i	$-0.275218\pi$
$113$	1558.99	1.29785	0.648926	+	0.760852i	$0.275218\pi$
$114$	−1839.04	−1.51089
$115$	−343.342	−0.278407
$116$	−591.302	−0.473285
$117$	1208.93	0.955262
$118$	−2992.06	−2.33425
$119$	−171.813	−0.132353
$120$	−1641.13	−1.24845
$121$	121.000	0.0909091
$122$	−3102.14	−2.30209
$123$	1072.34	0.786097
$124$	6394.55	4.63103
$125$	1519.95	1.08759
$126$	−393.186	−0.277998
$127$	1827.63	1.27698	0.638488	−	0.769632i	$-0.279560\pi$
$127$	1827.63	1.27698	0.638488	+	0.769632i	$0.279560\pi$
$128$	−2421.14	−1.67188
$129$	−859.754	−0.586800
$130$	−2919.68	−1.96979
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	−615.232	−0.405675
$133$	472.511	0.308060
$134$	1270.20	0.818871
$135$	−1119.22	−0.713537
$136$	−3174.95	−2.00184
$137$	−20.0477	−0.0125021	−0.00625106	−	0.999980i	$-0.501990\pi$
$137$	−20.0477	−0.0125021	−0.00625106	+	0.999980i	$0.501990\pi$
$138$	557.448	0.343863
$139$	630.122	0.384505	0.192253	−	0.981345i	$-0.438421\pi$
$139$	630.122	0.384505	0.192253	+	0.981345i	$0.438421\pi$
$140$	685.621	0.413897
$141$	41.0648	0.0245268
$142$	2497.09	1.47571
$143$	−673.149	−0.393647
$144$	−3981.70	−2.30422
$145$	253.075	0.144943
$146$	2091.24	1.18543
$147$	886.173	0.497213
$148$	7490.96	4.16050
$149$	−1584.98	−0.871452	−0.435726	−	0.900079i	$-0.643508\pi$
$149$	−1584.98	−0.871452	−0.435726	+	0.900079i	$0.643508\pi$
$150$	−662.841	−0.360805
$151$	897.320	0.483595	0.241798	−	0.970327i	$-0.422263\pi$
$151$	897.320	0.483595	0.241798	+	0.970327i	$0.422263\pi$
$152$	8731.60	4.65938
$153$	−914.882	−0.483424
$154$	218.931	0.114558
$155$	−2736.85	−1.41825
$156$	3422.67	1.75662
$157$	2315.98	1.17729	0.588647	−	0.808391i	$-0.299661\pi$
$157$	2315.98	1.17729	0.588647	+	0.808391i	$0.299661\pi$
$158$	−6854.83	−3.45153
$159$	821.833	0.409909
$160$	4738.42	2.34128
$161$	−143.227	−0.0701109
$162$	−1044.30	−0.506467
$163$	932.635	0.448157	0.224079	−	0.974571i	$-0.428063\pi$
$163$	932.635	0.448157	0.224079	+	0.974571i	$0.428063\pi$
$164$	−8278.61	−3.94177
$165$	263.317	0.124238
$166$	6310.46	2.95052
$167$	2907.07	1.34704	0.673521	−	0.739168i	$-0.264781\pi$
$167$	2907.07	1.34704	0.673521	+	0.739168i	$0.264781\pi$
$168$	−684.605	−0.314395
$169$	1547.87	0.704539
$170$	2209.53	0.996841
$171$	2516.06	1.12519
$172$	6637.40	2.94242
$173$	1087.37	0.477870	0.238935	−	0.971036i	$-0.423202\pi$
$173$	1087.37	0.477870	0.238935	+	0.971036i	$0.423202\pi$
$174$	−410.892	−0.179021
$175$	170.306	0.0735653
$176$	2217.06	0.949531
$177$	−1501.20	−0.637500
$178$	3634.01	1.53023
$179$	−1850.96	−0.772888	−0.386444	−	0.922313i	$-0.626297\pi$
$179$	−1850.96	−0.772888	−0.386444	+	0.922313i	$0.626297\pi$
$180$	3650.84	1.51177
$181$	−2144.35	−0.880598	−0.440299	−	0.897851i	$-0.645128\pi$
$181$	−2144.35	−0.880598	−0.440299	+	0.897851i	$0.645128\pi$
$182$	−1217.96	−0.496051
$183$	−1556.44	−0.628716
$184$	−2646.71	−1.06042
$185$	−3206.11	−1.27415
$186$	4443.53	1.75170
$187$	509.419	0.199211
$188$	−317.025	−0.122986
$189$	−466.891	−0.179689
$190$	−6076.53	−2.32020
$191$	−3622.23	−1.37223	−0.686113	−	0.727495i	$-0.740685\pi$
$191$	−3622.23	−1.37223	−0.686113	+	0.727495i	$0.740685\pi$
$192$	−3353.30	−1.26043
$193$	−3735.98	−1.39338	−0.696689	−	0.717373i	$-0.745344\pi$
$193$	−3735.98	−1.39338	−0.696689	+	0.717373i	$0.745344\pi$
$194$	−26.0200	−0.00962951
$195$	−1464.89	−0.537964
$196$	−6841.36	−2.49321
$197$	−1348.41	−0.487668	−0.243834	−	0.969817i	$-0.578405\pi$
$197$	−1348.41	−0.487668	−0.243834	+	0.969817i	$0.578405\pi$
$198$	1165.78	0.418427
$199$	3488.20	1.24257	0.621286	−	0.783584i	$-0.286611\pi$
$199$	3488.20	1.24257	0.621286	+	0.783584i	$0.286611\pi$
$200$	3147.11	1.11267
$201$	637.298	0.223640
$202$	7254.25	2.52677
$203$	105.572	0.0365009
$204$	−2590.17	−0.888962
$205$	3543.22	1.20717
$206$	−7814.08	−2.64288
$207$	−762.665	−0.256082
$208$	−12334.0	−4.11158
$209$	−1400.98	−0.463673
$210$	476.433	0.156557
$211$	−3054.60	−0.996624	−0.498312	−	0.866998i	$-0.666047\pi$
$211$	−3054.60	−0.996624	−0.498312	+	0.866998i	$0.666047\pi$
$212$	−6344.64	−2.05543
$213$	1252.86	0.403027
$214$	−9279.71	−2.96424
$215$	−2840.79	−0.901116
$216$	−8627.74	−2.71779
$217$	−1141.69	−0.357157
$218$	−5388.57	−1.67413
$219$	1049.24	0.323748
$220$	−2032.84	−0.622973
$221$	−2834.01	−0.862606
$222$	5205.42	1.57372
$223$	634.231	0.190454	0.0952270	−	0.995456i	$-0.469642\pi$
$223$	634.231	0.190454	0.0952270	+	0.995456i	$0.469642\pi$
$224$	1976.66	0.589603
$225$	906.858	0.268699
$226$	−8363.43	−2.46162
$227$	2206.77	0.645235	0.322617	−	0.946529i	$-0.395437\pi$
$227$	2206.77	0.645235	0.322617	+	0.946529i	$0.395437\pi$
$228$	7123.36	2.06911
$229$	517.151	0.149233	0.0746164	−	0.997212i	$-0.476227\pi$
$229$	517.151	0.149233	0.0746164	+	0.997212i	$0.476227\pi$
$230$	1841.91	0.528052
$231$	109.844	0.0312867
$232$	1950.88	0.552074
$233$	−6665.16	−1.87403	−0.937015	−	0.349288i	$-0.886423\pi$
$233$	−6665.16	−1.87403	−0.937015	+	0.349288i	$0.886423\pi$
$234$	−6485.49	−1.81184
$235$	135.686	0.0376645
$236$	11589.5	3.19665
$237$	−3439.27	−0.942636
$238$	921.716	0.251034
$239$	2952.84	0.799178	0.399589	−	0.916694i	$-0.369153\pi$
$239$	2952.84	0.799178	0.399589	+	0.916694i	$0.369153\pi$
$240$	4824.72	1.29764
$241$	6119.77	1.63572	0.817862	−	0.575415i	$-0.195159\pi$
$241$	6119.77	1.63572	0.817862	+	0.575415i	$0.195159\pi$
$242$	−649.123	−0.172426
$243$	−3921.82	−1.03533
$244$	12015.9	3.15261
$245$	2928.08	0.763543
$246$	−5752.75	−1.49098
$247$	7793.94	2.00776
$248$	−21097.5	−5.40198
$249$	3166.14	0.805808
$250$	−8154.00	−2.06282
$251$	6060.08	1.52394	0.761970	−	0.647612i	$-0.224232\pi$
$251$	6060.08	1.52394	0.761970	+	0.647612i	$0.224232\pi$
$252$	1522.97	0.380707
$253$	424.662	0.105527
$254$	−9804.60	−2.42203
$255$	1108.59	0.272244
$256$	3021.86	0.737760
$257$	924.929	0.224496	0.112248	−	0.993680i	$-0.464195\pi$
$257$	924.929	0.224496	0.112248	+	0.993680i	$0.464195\pi$
$258$	4612.28	1.11298
$259$	−1337.45	−0.320868
$260$	11309.1	2.69755
$261$	562.157	0.133320
$262$	702.769	0.165715
$263$	−2565.22	−0.601438	−0.300719	−	0.953713i	$-0.597227\pi$
$263$	−2565.22	−0.601438	−0.300719	+	0.953713i	$0.597227\pi$
$264$	2029.83	0.473209
$265$	2715.49	0.629476
$266$	−2534.86	−0.584294
$267$	1823.29	0.417916
$268$	−4920.01	−1.12141
$269$	−111.895	−0.0253620	−0.0126810	−	0.999920i	$-0.504037\pi$
$269$	−111.895	−0.0253620	−0.0126810	+	0.999920i	$0.504037\pi$
$270$	6004.25	1.35336
$271$	−6579.52	−1.47482	−0.737412	−	0.675443i	$-0.763953\pi$
$271$	−6579.52	−1.47482	−0.737412	+	0.675443i	$0.763953\pi$
$272$	9334.00	2.08072
$273$	−611.087	−0.135475
$274$	107.549	0.0237126
$275$	−504.951	−0.110726
$276$	−2159.22	−0.470906
$277$	−204.464	−0.0443504	−0.0221752	−	0.999754i	$-0.507059\pi$
$277$	−204.464	−0.0443504	−0.0221752	+	0.999754i	$0.507059\pi$
$278$	−3380.38	−0.729287
$279$	−6079.36	−1.30452
$280$	−2262.06	−0.482800
$281$	−5749.61	−1.22062	−0.610308	−	0.792164i	$-0.708954\pi$
$281$	−5749.61	−1.22062	−0.610308	+	0.792164i	$0.708954\pi$
$282$	−220.298	−0.0465198
$283$	−761.294	−0.159909	−0.0799544	−	0.996799i	$-0.525477\pi$
$283$	−761.294	−0.159909	−0.0799544	+	0.996799i	$0.525477\pi$
$284$	−9672.24	−2.02092
$285$	−3048.78	−0.633663
$286$	3611.21	0.746627
$287$	1478.07	0.304000
$288$	10525.5	2.15354
$289$	−2768.31	−0.563466
$290$	−1357.66	−0.274913
$291$	−13.0550	−0.00262989
$292$	−8100.23	−1.62339
$293$	3278.25	0.653642	0.326821	−	0.945086i	$-0.394023\pi$
$293$	3278.25	0.653642	0.326821	+	0.945086i	$0.394023\pi$
$294$	−4754.01	−0.943060
$295$	−4960.26	−0.978974
$296$	−24714.8	−4.85311
$297$	1384.31	0.270458
$298$	8502.84	1.65287
$299$	−2362.49	−0.456944
$300$	2567.45	0.494107
$301$	−1185.05	−0.226927
$302$	−4813.81	−0.917231
$303$	3639.67	0.690078
$304$	−25669.9	−4.84299
$305$	−5142.75	−0.965485
$306$	4908.02	0.916905
$307$	197.986	0.0368067	0.0184033	−	0.999831i	$-0.494142\pi$
$307$	197.986	0.0368067	0.0184033	+	0.999831i	$0.494142\pi$
$308$	−848.010	−0.156883
$309$	−3920.55	−0.721788
$310$	14682.2	2.68999
$311$	−7687.02	−1.40158	−0.700789	−	0.713368i	$-0.747169\pi$
$311$	−7687.02	−1.40158	−0.700789	+	0.713368i	$0.747169\pi$
$312$	−11292.4	−2.04905
$313$	9709.39	1.75338	0.876688	−	0.481059i	$-0.159748\pi$
$313$	9709.39	1.75338	0.876688	+	0.481059i	$0.159748\pi$
$314$	−12424.4	−2.23296
$315$	−651.826	−0.116591
$316$	26551.6	4.72672
$317$	−226.869	−0.0401963	−0.0200981	−	0.999798i	$-0.506398\pi$
$317$	−226.869	−0.0401963	−0.0200981	+	0.999798i	$0.506398\pi$
$318$	−4408.85	−0.777472
$319$	−313.016	−0.0549391
$320$	−11079.9	−1.93558
$321$	−4655.91	−0.809556
$322$	768.363	0.132979
$323$	−5898.22	−1.01605
$324$	4044.99	0.693585
$325$	2809.15	0.479457
$326$	−5003.26	−0.850016
$327$	−2703.61	−0.457216
$328$	27313.5	4.59798
$329$	56.6020	0.00948502
$330$	−1412.61	−0.235641
$331$	−9139.88	−1.51774	−0.758872	−	0.651240i	$-0.774249\pi$
$331$	−9139.88	−1.51774	−0.758872	+	0.651240i	$0.774249\pi$
$332$	−24443.0	−4.04061
$333$	−7121.73	−1.17198
$334$	−15595.4	−2.55492
$335$	2105.75	0.343431
$336$	2012.66	0.326785
$337$	−11587.9	−1.87310	−0.936551	−	0.350531i	$-0.886001\pi$
$337$	−11587.9	−1.87310	−0.936551	+	0.350531i	$0.886001\pi$
$338$	−8303.79	−1.33629
$339$	−4196.18	−0.672287
$340$	−8558.40	−1.36513
$341$	3385.07	0.537572
$342$	−13497.8	−2.13414
$343$	2493.99	0.392603
$344$	−21898.7	−3.43226
$345$	924.141	0.144215
$346$	−5833.38	−0.906372
$347$	−3475.97	−0.537751	−0.268875	−	0.963175i	$-0.586652\pi$
$347$	−3475.97	−0.537751	−0.268875	+	0.963175i	$0.586652\pi$
$348$	1591.55	0.245161
$349$	−5065.73	−0.776969	−0.388485	−	0.921455i	$-0.627001\pi$
$349$	−5065.73	−0.776969	−0.388485	+	0.921455i	$0.627001\pi$
$350$	−913.633	−0.139531
$351$	−7701.23	−1.17112
$352$	−5860.72	−0.887436
$353$	−8900.12	−1.34194	−0.670971	−	0.741483i	$-0.734123\pi$
$353$	−8900.12	−1.34194	−0.670971	+	0.741483i	$0.734123\pi$
$354$	8053.44	1.20914
$355$	4139.69	0.618907
$356$	−14076.0	−2.09558
$357$	462.453	0.0685591
$358$	9929.73	1.46593
$359$	−2385.66	−0.350726	−0.175363	−	0.984504i	$-0.556110\pi$
$359$	−2385.66	−0.350726	−0.175363	+	0.984504i	$0.556110\pi$
$360$	−12045.2	−1.76344
$361$	9361.99	1.36492
$362$	11503.7	1.67022
$363$	−325.684	−0.0470909
$364$	4717.66	0.679321
$365$	3466.87	0.497163
$366$	8349.74	1.19248
$367$	13402.0	1.90621	0.953106	−	0.302636i	$-0.0978666\pi$
$367$	13402.0	1.90621	0.953106	+	0.302636i	$0.0978666\pi$
$368$	7781.03	1.10221
$369$	7870.55	1.11036
$370$	17199.7	2.41667
$371$	1132.78	0.158520
$372$	−17211.6	−2.39887
$373$	−3673.92	−0.509995	−0.254998	−	0.966942i	$-0.582075\pi$
$373$	−3673.92	−0.509995	−0.254998	+	0.966942i	$0.582075\pi$
$374$	−2732.85	−0.377841
$375$	−4091.11	−0.563370
$376$	1045.96	0.143460
$377$	1741.38	0.237893
$378$	2504.71	0.340815
$379$	−233.478	−0.0316436	−0.0158218	−	0.999875i	$-0.505036\pi$
$379$	−233.478	−0.0316436	−0.0158218	+	0.999875i	$0.505036\pi$
$380$	23536.9	3.17741
$381$	−4919.26	−0.661473
$382$	19432.0	2.60269
$383$	4143.65	0.552821	0.276411	−	0.961040i	$-0.410855\pi$
$383$	4143.65	0.552821	0.276411	+	0.961040i	$0.410855\pi$
$384$	6516.74	0.866032
$385$	362.946	0.0480453
$386$	20042.3	2.64281
$387$	−6310.24	−0.828857
$388$	100.786	0.0131872
$389$	2769.06	0.360917	0.180458	−	0.983583i	$-0.442242\pi$
$389$	2769.06	0.360917	0.180458	+	0.983583i	$0.442242\pi$
$390$	7858.63	1.02035
$391$	1787.86	0.231243
$392$	22571.6	2.90826
$393$	352.600	0.0452578
$394$	7233.77	0.924955
$395$	−11364.0	−1.44756
$396$	−4515.55	−0.573017
$397$	5717.80	0.722842	0.361421	−	0.932403i	$-0.382292\pi$
$397$	5717.80	0.722842	0.361421	+	0.932403i	$0.382292\pi$
$398$	−18713.0	−2.35677
$399$	−1271.81	−0.159575
$400$	−9252.14	−1.15652
$401$	−2361.70	−0.294109	−0.147054	−	0.989128i	$-0.546979\pi$
$401$	−2361.70	−0.294109	−0.147054	+	0.989128i	$0.546979\pi$
$402$	−3418.88	−0.424175
$403$	−18831.9	−2.32775
$404$	−28098.7	−3.46030
$405$	−1731.24	−0.212410
$406$	−566.356	−0.0692310
$407$	3965.48	0.482952
$408$	8545.72	1.03695
$409$	−3073.93	−0.371629	−0.185814	−	0.982585i	$-0.559492\pi$
$409$	−3073.93	−0.371629	−0.185814	+	0.982585i	$0.559492\pi$
$410$	−19008.1	−2.28962
$411$	53.9605	0.00647609
$412$	30267.1	3.61931
$413$	−2069.20	−0.246534
$414$	4091.43	0.485708
$415$	10461.5	1.23744
$416$	32604.4	3.84270
$417$	−1696.04	−0.199174
$418$	7515.76	0.879445
$419$	48.4053	0.00564380	0.00282190	−	0.999996i	$-0.499102\pi$
$419$	48.4053	0.00564380	0.00282190	+	0.999996i	$0.499102\pi$
$420$	−1845.42	−0.214398
$421$	−8744.73	−1.01233	−0.506166	−	0.862436i	$-0.668938\pi$
$421$	−8744.73	−1.01233	−0.506166	+	0.862436i	$0.668938\pi$
$422$	16386.9	1.89029
$423$	301.399	0.0346442
$424$	20932.8	2.39761
$425$	−2125.88	−0.242636
$426$	−6721.17	−0.764417
$427$	−2145.33	−0.243137
$428$	35944.1	4.05940
$429$	1811.85	0.203909
$430$	15239.8	1.70914
$431$	2168.82	0.242386	0.121193	−	0.992629i	$-0.461328\pi$
$431$	2168.82	0.242386	0.121193	+	0.992629i	$0.461328\pi$
$432$	25364.6	2.82489
$433$	−13185.5	−1.46340	−0.731701	−	0.681626i	$-0.761273\pi$
$433$	−13185.5	−1.46340	−0.731701	+	0.681626i	$0.761273\pi$
$434$	6124.78	0.677417
$435$	−681.179	−0.0750806
$436$	20872.1	2.29265
$437$	−4916.88	−0.538230
$438$	−5628.79	−0.614050
$439$	−15272.4	−1.66039	−0.830193	−	0.557476i	$-0.811770\pi$
$439$	−15272.4	−1.66039	−0.830193	+	0.557476i	$0.811770\pi$
$440$	6706.92	0.726682
$441$	6504.14	0.702315
$442$	15203.5	1.63610
$443$	5598.63	0.600449	0.300224	−	0.953869i	$-0.402938\pi$
$443$	5598.63	0.600449	0.300224	+	0.953869i	$0.402938\pi$
$444$	−20162.7	−2.15514
$445$	6024.49	0.641772
$446$	−3402.43	−0.361232
$447$	4266.13	0.451412
$448$	−4622.05	−0.487436
$449$	−8306.33	−0.873051	−0.436526	−	0.899692i	$-0.643791\pi$
$449$	−8306.33	−0.873051	−0.436526	+	0.899692i	$0.643791\pi$
$450$	−4864.98	−0.509638
$451$	−4382.43	−0.457562
$452$	32395.0	3.37109
$453$	−2415.23	−0.250502
$454$	−11838.5	−1.22381
$455$	−2019.14	−0.208042
$456$	−23502.0	−2.41356
$457$	−2533.35	−0.259311	−0.129655	−	0.991559i	$-0.541387\pi$
$457$	−2533.35	−0.259311	−0.129655	+	0.991559i	$0.541387\pi$
$458$	−2774.34	−0.283049
$459$	5828.06	0.592659
$460$	−7134.47	−0.723144
$461$	−16446.5	−1.66159	−0.830794	−	0.556580i	$-0.812113\pi$
$461$	−16446.5	−1.66159	−0.830794	+	0.556580i	$0.812113\pi$
$462$	−589.276	−0.0593412
$463$	18906.4	1.89774	0.948871	−	0.315663i	$-0.102227\pi$
$463$	18906.4	1.89774	0.948871	+	0.315663i	$0.102227\pi$
$464$	−5735.35	−0.573830
$465$	7366.52	0.734654
$466$	35756.3	3.55446
$467$	18235.3	1.80692	0.903458	−	0.428678i	$-0.141020\pi$
$467$	18235.3	1.80692	0.903458	+	0.428678i	$0.141020\pi$
$468$	25121.0	2.48123
$469$	878.425	0.0864859
$470$	−727.906	−0.0714379
$471$	−6233.69	−0.609837
$472$	−38237.0	−3.72881
$473$	3513.63	0.341558
$474$	18450.5	1.78789
$475$	5846.49	0.564748
$476$	−3570.18	−0.343780
$477$	6031.91	0.578999
$478$	−15841.0	−1.51579
$479$	9730.93	0.928220	0.464110	−	0.885778i	$-0.346374\pi$
$479$	9730.93	0.928220	0.464110	+	0.885778i	$0.346374\pi$
$480$	−12754.0	−1.21278
$481$	−22060.8	−2.09124
$482$	−32830.5	−3.10246
$483$	385.510	0.0363174
$484$	2514.32	0.236131
$485$	−43.1361	−0.00403858
$486$	21039.2	1.96370
$487$	654.448	0.0608950	0.0304475	−	0.999536i	$-0.490307\pi$
$487$	654.448	0.0608950	0.0304475	+	0.999536i	$0.490307\pi$
$488$	−39643.8	−3.67744
$489$	−2510.29	−0.232145
$490$	−15708.1	−1.44821
$491$	7447.55	0.684528	0.342264	−	0.939604i	$-0.388806\pi$
$491$	7447.55	0.684528	0.342264	+	0.939604i	$0.388806\pi$
$492$	22282.7	2.04184
$493$	−1317.82	−0.120389
$494$	−41811.8	−3.80810
$495$	1932.64	0.175486
$496$	62024.2	5.61485
$497$	1726.89	0.155859
$498$	−16985.3	−1.52837
$499$	2293.86	0.205786	0.102893	−	0.994692i	$-0.467190\pi$
$499$	2293.86	0.205786	0.102893	+	0.994692i	$0.467190\pi$
$500$	31583.8	2.82494
$501$	−7824.69	−0.697767
$502$	−32510.2	−2.89044
$503$	−1.93276	−0.000171327 0	−8.56634e−5	−	1.00000i	$-0.500027\pi$
$503$	−1.93276	−0.000171327 0	−8.56634e−5		1.00000i	$0.500027\pi$
$504$	−5024.71	−0.444084
$505$	12026.1	1.05972
$506$	−2278.17	−0.200152
$507$	−4166.26	−0.364951
$508$	37977.2	3.31686
$509$	20876.7	1.81796	0.908982	−	0.416836i	$-0.136861\pi$
$509$	20876.7	1.81796	0.908982	+	0.416836i	$0.136861\pi$
$510$	−5947.17	−0.516363
$511$	1446.22	0.125200
$512$	3157.84	0.272574
$513$	−16028.0	−1.37945
$514$	−4961.92	−0.425800
$515$	−12954.2	−1.10841
$516$	−17865.3	−1.52417
$517$	−167.823	−0.0142763
$518$	7174.93	0.608588
$519$	−2926.78	−0.247537
$520$	−37312.0	−3.14662
$521$	−15158.2	−1.27465	−0.637325	−	0.770596i	$-0.719959\pi$
$521$	−15158.2	−1.27465	−0.637325	+	0.770596i	$0.719959\pi$
$522$	−3015.77	−0.252868
$523$	6523.13	0.545385	0.272693	−	0.962101i	$-0.412086\pi$
$523$	6523.13	0.545385	0.272693	+	0.962101i	$0.412086\pi$
$524$	−2722.11	−0.226939
$525$	−458.397	−0.0381068
$526$	13761.5	1.14074
$527$	14251.4	1.17799
$528$	−5967.46	−0.491857
$529$	−10676.6	−0.877505
$530$	−14567.6	−1.19392
$531$	−11018.2	−0.900471
$532$	9818.54	0.800165
$533$	24380.4	1.98130
$534$	−9781.33	−0.792658
$535$	−15384.0	−1.24319
$536$	16232.5	1.30809
$537$	4982.04	0.400356
$538$	600.280	0.0481039
$539$	−3621.60	−0.289412
$540$	−23256.9	−1.85337
$541$	−6552.39	−0.520720	−0.260360	−	0.965512i	$-0.583841\pi$
$541$	−6552.39	−0.520720	−0.260360	+	0.965512i	$0.583841\pi$
$542$	35296.9	2.79729
$543$	5771.74	0.456149
$544$	−24674.0	−1.94465
$545$	−8933.21	−0.702122
$546$	3278.27	0.256954
$547$	−9193.27	−0.718603	−0.359301	−	0.933222i	$-0.616985\pi$
$547$	−9193.27	−0.718603	−0.359301	+	0.933222i	$0.616985\pi$
$548$	−416.581	−0.0324734
$549$	−11423.6	−0.888064
$550$	2708.89	0.210013
$551$	3624.21	0.280211
$552$	7123.90	0.549299
$553$	−4740.55	−0.364537
$554$	1096.88	0.0841190
$555$	8629.58	0.660009
$556$	13093.6	0.998728
$557$	−13482.5	−1.02562	−0.512811	−	0.858502i	$-0.671396\pi$
$557$	−13482.5	−1.02562	−0.512811	+	0.858502i	$0.671396\pi$
$558$	32613.7	2.47428
$559$	−19547.1	−1.47899
$560$	6650.20	0.501825
$561$	−1371.15	−0.103191
$562$	30844.7	2.31513
$563$	−4145.17	−0.310299	−0.155149	−	0.987891i	$-0.549586\pi$
$563$	−4145.17	−0.310299	−0.155149	+	0.987891i	$0.549586\pi$
$564$	853.306	0.0637068
$565$	−13865.0	−1.03239
$566$	4084.08	0.303298
$567$	−722.197	−0.0534911
$568$	31911.5	2.35735
$569$	−19406.3	−1.42980	−0.714900	−	0.699227i	$-0.753528\pi$
$569$	−19406.3	−1.42980	−0.714900	+	0.699227i	$0.753528\pi$
$570$	16355.6	1.20186
$571$	458.432	0.0335985	0.0167993	−	0.999859i	$-0.494652\pi$
$571$	458.432	0.0335985	0.0167993	+	0.999859i	$0.494652\pi$
$572$	−13987.7	−1.02247
$573$	9749.61	0.710813
$574$	−7929.35	−0.576593
$575$	−1772.18	−0.128530
$576$	−24611.8	−1.78037
$577$	−17442.1	−1.25844	−0.629222	−	0.777225i	$-0.716627\pi$
$577$	−17442.1	−1.25844	−0.629222	+	0.777225i	$0.716627\pi$
$578$	14851.0	1.06872
$579$	10055.8	0.721770
$580$	5258.78	0.376481
$581$	4364.08	0.311622
$582$	70.0355	0.00498808
$583$	−3358.65	−0.238595
$584$	26725.0	1.89364
$585$	−10751.7	−0.759876
$586$	−17586.7	−1.23976
$587$	17104.5	1.20269	0.601345	−	0.798990i	$-0.294632\pi$
$587$	17104.5	1.20269	0.601345	+	0.798990i	$0.294632\pi$
$588$	18414.2	1.29148
$589$	−39193.5	−2.74183
$590$	26610.0	1.85681
$591$	3629.40	0.252612
$592$	72658.8	5.04436
$593$	4077.96	0.282397	0.141199	−	0.989981i	$-0.454904\pi$
$593$	4077.96	0.282397	0.141199	+	0.989981i	$0.454904\pi$
$594$	−7426.36	−0.512975
$595$	1528.03	0.105282
$596$	−32935.0	−2.26354
$597$	−9388.85	−0.643652
$598$	12673.9	0.866681
$599$	15288.4	1.04285	0.521425	−	0.853297i	$-0.325401\pi$
$599$	15288.4	1.04285	0.521425	+	0.853297i	$0.325401\pi$
$600$	−8470.77	−0.576363
$601$	8420.43	0.571508	0.285754	−	0.958303i	$-0.407756\pi$
$601$	8420.43	0.571508	0.285754	+	0.958303i	$0.407756\pi$
$602$	6357.38	0.430411
$603$	4677.50	0.315892
$604$	18645.9	1.25611
$605$	−1076.12	−0.0723149
$606$	−19525.6	−1.30886
$607$	−27112.7	−1.81296	−0.906482	−	0.422245i	$-0.861242\pi$
$607$	−27112.7	−1.81296	−0.906482	+	0.422245i	$0.861242\pi$
$608$	67857.3	4.52628
$609$	−284.158	−0.0189075
$610$	27589.1	1.83123
$611$	933.634	0.0618180
$612$	−19010.8	−1.25566
$613$	−15693.5	−1.03402	−0.517010	−	0.855979i	$-0.672955\pi$
$613$	−15693.5	−1.03402	−0.517010	+	0.855979i	$0.672955\pi$
$614$	−1062.12	−0.0698108
$615$	−9536.94	−0.625312
$616$	2797.83	0.183000
$617$	23953.0	1.56290	0.781452	−	0.623965i	$-0.214479\pi$
$617$	23953.0	1.56290	0.781452	+	0.623965i	$0.214479\pi$
$618$	21032.4	1.36901
$619$	25328.6	1.64465	0.822327	−	0.569015i	$-0.192675\pi$
$619$	25328.6	1.64465	0.822327	+	0.569015i	$0.192675\pi$
$620$	−56870.3	−3.68382
$621$	4858.40	0.313946
$622$	41238.2	2.65836
$623$	2513.15	0.161617
$624$	33198.3	2.12980
$625$	−7779.69	−0.497900
$626$	−52087.5	−3.32561
$627$	3770.88	0.240183
$628$	48124.8	3.05794
$629$	16694.9	1.05830
$630$	3496.82	0.221138
$631$	7447.86	0.469881	0.234940	−	0.972010i	$-0.424511\pi$
$631$	7447.86	0.469881	0.234940	+	0.972010i	$0.424511\pi$
$632$	−87601.3	−5.51359
$633$	8221.79	0.516251
$634$	1217.07	0.0762399
$635$	−16254.1	−1.01579
$636$	17077.3	1.06471
$637$	20147.7	1.25319
$638$	1679.22	0.104202
$639$	9195.49	0.569277
$640$	21532.5	1.32992
$641$	−21219.2	−1.30750	−0.653752	−	0.756709i	$-0.726806\pi$
$641$	−21219.2	−1.30750	−0.653752	+	0.756709i	$0.726806\pi$
$642$	24977.3	1.53548
$643$	−16505.9	−1.01233	−0.506167	−	0.862435i	$-0.668938\pi$
$643$	−16505.9	−1.01233	−0.506167	+	0.862435i	$0.668938\pi$
$644$	−2976.18	−0.182109
$645$	7646.27	0.466778
$646$	31641.9	1.92714
$647$	26398.4	1.60406	0.802032	−	0.597281i	$-0.203752\pi$
$647$	26398.4	1.60406	0.802032	+	0.597281i	$0.203752\pi$
$648$	−13345.6	−0.809049
$649$	6135.09	0.371069
$650$	−15070.1	−0.909382
$651$	3072.98	0.185007
$652$	19379.7	1.16406
$653$	9466.70	0.567321	0.283661	−	0.958925i	$-0.408451\pi$
$653$	9466.70	0.567321	0.283661	+	0.958925i	$0.408451\pi$
$654$	14503.9	0.867198
$655$	1165.06	0.0695000
$656$	−80298.6	−4.77917
$657$	7700.96	0.457296
$658$	−303.650	−0.0179901
$659$	−29970.9	−1.77163	−0.885813	−	0.464043i	$-0.846398\pi$
$659$	−29970.9	−1.77163	−0.885813	+	0.464043i	$0.846398\pi$
$660$	5471.60	0.322700
$661$	−24658.2	−1.45097	−0.725486	−	0.688237i	$-0.758385\pi$
$661$	−24658.2	−1.45097	−0.725486	+	0.688237i	$0.758385\pi$
$662$	49032.3	2.87869
$663$	7628.02	0.446829
$664$	80644.5	4.71327
$665$	−4202.31	−0.245050
$666$	38205.6	2.22288
$667$	−1098.56	−0.0637730
$668$	60407.4	3.49885
$669$	−1707.10	−0.0986551
$670$	−11296.6	−0.651383
$671$	6360.81	0.365956
$672$	−5320.38	−0.305414
$673$	30809.8	1.76468	0.882340	−	0.470613i	$-0.155967\pi$
$673$	30809.8	1.76468	0.882340	+	0.470613i	$0.155967\pi$
$674$	62165.3	3.55270
$675$	−5776.95	−0.329414
$676$	32164.0	1.82999
$677$	10337.9	0.586878	0.293439	−	0.955978i	$-0.405200\pi$
$677$	10337.9	0.586878	0.293439	+	0.955978i	$0.405200\pi$
$678$	22511.0	1.27512
$679$	−17.9945	−0.00101703
$680$	28236.6	1.59239
$681$	−5939.75	−0.334231
$682$	−18159.7	−1.01961
$683$	−24398.7	−1.36690	−0.683450	−	0.729998i	$-0.739521\pi$
$683$	−24398.7	−1.36690	−0.683450	+	0.729998i	$0.739521\pi$
$684$	52282.5	2.92262
$685$	178.295	0.00994498
$686$	−13379.4	−0.744647
$687$	−1391.97	−0.0773026
$688$	64379.7	3.56752
$689$	18684.9	1.03315
$690$	−4957.69	−0.273531
$691$	−34538.9	−1.90148	−0.950740	−	0.309989i	$-0.899675\pi$
$691$	−34538.9	−1.90148	−0.950740	+	0.309989i	$0.899675\pi$
$692$	22595.1	1.24124
$693$	806.211	0.0441926
$694$	18647.3	1.01995
$695$	−5604.02	−0.305860
$696$	−5250.99	−0.285974
$697$	−18450.3	−1.00266
$698$	27175.9	1.47367
$699$	17940.0	0.970747
$700$	3538.87	0.191081
$701$	36083.0	1.94413	0.972067	−	0.234705i	$-0.0754123\pi$
$701$	36083.0	1.94413	0.972067	+	0.234705i	$0.0754123\pi$
$702$	41314.4	2.22124
$703$	−45913.6	−2.46325
$704$	13704.2	0.733660
$705$	−365.212	−0.0195102
$706$	47746.1	2.54525
$707$	5016.77	0.266867
$708$	−31194.3	−1.65586
$709$	−653.048	−0.0345920	−0.0172960	−	0.999850i	$-0.505506\pi$
$709$	−653.048	−0.0345920	−0.0172960	+	0.999850i	$0.505506\pi$
$710$	−22208.0	−1.17387
$711$	−25242.8	−1.33148
$712$	46440.8	2.44444
$713$	11880.3	0.624011
$714$	−2480.90	−0.130035
$715$	5986.69	0.313132
$716$	−38461.9	−2.00753
$717$	−7947.89	−0.413974
$718$	12798.3	0.665218
$719$	−24599.1	−1.27593	−0.637964	−	0.770066i	$-0.720223\pi$
$719$	−24599.1	−1.27593	−0.637964	+	0.770066i	$0.720223\pi$
$720$	35411.5	1.83293
$721$	−5403.93	−0.279130
$722$	−50223.8	−2.58883
$723$	−16472.0	−0.847304
$724$	−44558.5	−2.28730
$725$	1306.26	0.0669151
$726$	1747.18	0.0893168
$727$	−6130.42	−0.312744	−0.156372	−	0.987698i	$-0.549980\pi$
$727$	−6130.42	−0.312744	−0.156372	+	0.987698i	$0.549980\pi$
$728$	−15564.9	−0.792410
$729$	5300.09	0.269273
$730$	−18598.6	−0.942964
$731$	14792.6	0.748461
$732$	−32341.9	−1.63305
$733$	−9681.65	−0.487858	−0.243929	−	0.969793i	$-0.578436\pi$
$733$	−9681.65	−0.487858	−0.243929	+	0.969793i	$0.578436\pi$
$734$	−71897.2	−3.61550
$735$	−7881.23	−0.395515
$736$	−20568.8	−1.03013
$737$	−2604.50	−0.130174
$738$	−42222.8	−2.10602
$739$	13614.6	0.677703	0.338852	−	0.940840i	$-0.389962\pi$
$739$	13614.6	0.677703	0.338852	+	0.940840i	$0.389962\pi$
$740$	−66621.3	−3.30952
$741$	−20978.2	−1.04002
$742$	−6076.97	−0.300664
$743$	13988.6	0.690700	0.345350	−	0.938474i	$-0.387760\pi$
$743$	13988.6	0.690700	0.345350	+	0.938474i	$0.387760\pi$
$744$	56786.1	2.79822
$745$	14096.1	0.693208
$746$	19709.3	0.967303
$747$	23238.2	1.13821
$748$	10585.5	0.517437
$749$	−6417.51	−0.313072
$750$	21947.4	1.06854
$751$	3300.71	0.160379	0.0801894	−	0.996780i	$-0.474447\pi$
$751$	3300.71	0.160379	0.0801894	+	0.996780i	$0.474447\pi$
$752$	−3074.99	−0.149114
$753$	−16311.4	−0.789401
$754$	−9341.89	−0.451209
$755$	−7980.37	−0.384683
$756$	−9701.75	−0.466732
$757$	−24165.4	−1.16024	−0.580122	−	0.814530i	$-0.696995\pi$
$757$	−24165.4	−1.16024	−0.580122	+	0.814530i	$0.696995\pi$
$758$	1252.53	0.0600182
$759$	−1143.02	−0.0546629
$760$	−77655.0	−3.70637
$761$	16264.6	0.774758	0.387379	−	0.921920i	$-0.373380\pi$
$761$	16264.6	0.774758	0.387379	+	0.921920i	$0.373380\pi$
$762$	26390.1	1.25461
$763$	−3726.54	−0.176815
$764$	−75268.1	−3.56427
$765$	8136.56	0.384546
$766$	−22229.2	−1.04853
$767$	−34130.8	−1.60677
$768$	−8133.67	−0.382159
$769$	18011.6	0.844621	0.422311	−	0.906451i	$-0.361219\pi$
$769$	18011.6	0.844621	0.422311	+	0.906451i	$0.361219\pi$
$770$	−1947.08	−0.0911270
$771$	−2489.54	−0.116289
$772$	−77631.9	−3.61921
$773$	13592.3	0.632448	0.316224	−	0.948685i	$-0.397585\pi$
$773$	13592.3	0.632448	0.316224	+	0.948685i	$0.397585\pi$
$774$	33852.2	1.57208
$775$	−14126.4	−0.654756
$776$	−332.522	−0.0153825
$777$	3599.88	0.166210
$778$	−14855.0	−0.684548
$779$	50741.2	2.33375
$780$	−30439.7	−1.39733
$781$	−5120.17	−0.234589
$782$	−9591.25	−0.438596
$783$	−3581.10	−0.163446
$784$	−66357.9	−3.02287
$785$	−20597.3	−0.936494
$786$	−1891.58	−0.0858401
$787$	−14192.6	−0.642833	−0.321417	−	0.946938i	$-0.604159\pi$
$787$	−14192.6	−0.642833	−0.321417	+	0.946938i	$0.604159\pi$
$788$	−28019.4	−1.26669
$789$	6904.55	0.311545
$790$	60963.8	2.74556
$791$	−5783.84	−0.259987
$792$	14898.1	0.668410
$793$	−35386.6	−1.58463
$794$	−30674.0	−1.37101
$795$	−7309.02	−0.326068
$796$	72483.0	3.22750
$797$	49.7515	0.00221115	0.00110558	−	0.999999i	$-0.499648\pi$
$797$	49.7515	0.00221115	0.00110558	+	0.999999i	$0.499648\pi$
$798$	6822.84	0.302664
$799$	−706.546	−0.0312839
$800$	24457.6	1.08089
$801$	13382.2	0.590308
$802$	12669.7	0.557834
$803$	−4288.00	−0.188444
$804$	13242.7	0.580889
$805$	1273.80	0.0557707
$806$	101027.	4.41502
$807$	301.178	0.0131375
$808$	92705.6	4.03635
$809$	2653.34	0.115311	0.0576554	−	0.998337i	$-0.481638\pi$
$809$	2653.34	0.115311	0.0576554	+	0.998337i	$0.481638\pi$
$810$	9287.51	0.402876
$811$	35759.1	1.54830	0.774151	−	0.633001i	$-0.218177\pi$
$811$	35759.1	1.54830	0.774151	+	0.633001i	$0.218177\pi$
$812$	2193.73	0.0948089
$813$	17709.5	0.763959
$814$	−21273.4	−0.916010
$815$	−8294.45	−0.356493
$816$	−25123.5	−1.07781
$817$	−40681.9	−1.74208
$818$	16490.6	0.704865
$819$	−4485.13	−0.191359
$820$	73626.3	3.13554
$821$	15333.4	0.651812	0.325906	−	0.945402i	$-0.394331\pi$
$821$	15333.4	0.651812	0.325906	+	0.945402i	$0.394331\pi$
$822$	−289.479	−0.0122831
$823$	−8840.22	−0.374424	−0.187212	−	0.982320i	$-0.559945\pi$
$823$	−8840.22	−0.374424	−0.187212	+	0.982320i	$0.559945\pi$
$824$	−99859.9	−4.22183
$825$	1359.13	0.0573561
$826$	11100.5	0.467599
$827$	−36282.5	−1.52559	−0.762797	−	0.646638i	$-0.776175\pi$
$827$	−36282.5	−1.52559	−0.762797	+	0.646638i	$0.776175\pi$
$828$	−15847.8	−0.665156
$829$	5084.92	0.213036	0.106518	−	0.994311i	$-0.466030\pi$
$829$	5084.92	0.213036	0.106518	+	0.994311i	$0.466030\pi$
$830$	−56122.4	−2.34703
$831$	550.337	0.0229735
$832$	−76239.4	−3.17683
$833$	−15247.2	−0.634194
$834$	9098.66	0.377771
$835$	−25854.2	−1.07152
$836$	−29111.6	−1.20436
$837$	38727.3	1.59930
$838$	−259.678	−0.0107045
$839$	−24837.7	−1.02204	−0.511021	−	0.859568i	$-0.670733\pi$
$839$	−24837.7	−1.02204	−0.511021	+	0.859568i	$0.670733\pi$
$840$	6088.57	0.250090
$841$	−23579.3	−0.966799
$842$	46912.4	1.92008
$843$	15475.7	0.632279
$844$	−63473.1	−2.58867
$845$	−13766.1	−0.560435
$846$	−1616.90	−0.0657094
$847$	−448.910	−0.0182110
$848$	−61540.1	−2.49209
$849$	2049.10	0.0828327
$850$	11404.6	0.460206
$851$	13917.3	0.560608
$852$	26033.8	1.04684
$853$	22688.5	0.910713	0.455356	−	0.890309i	$-0.349512\pi$
$853$	22688.5	0.910713	0.455356	+	0.890309i	$0.349512\pi$
$854$	11508.9	0.461156
$855$	−22376.7	−0.895051
$856$	−118590.	−4.73519
$857$	−23337.9	−0.930229	−0.465115	−	0.885250i	$-0.653987\pi$
$857$	−23337.9	−0.930229	−0.465115	+	0.885250i	$0.653987\pi$
$858$	−9719.95	−0.386752
$859$	7953.03	0.315895	0.157948	−	0.987448i	$-0.449512\pi$
$859$	7953.03	0.315895	0.157948	+	0.987448i	$0.449512\pi$
$860$	−59030.1	−2.34059
$861$	−3978.39	−0.157472
$862$	−11635.0	−0.459731
$863$	−23823.7	−0.939706	−0.469853	−	0.882745i	$-0.655693\pi$
$863$	−23823.7	−0.939706	−0.469853	+	0.882745i	$0.655693\pi$
$864$	−67050.2	−2.64015
$865$	−9670.62	−0.380128
$866$	70735.4	2.77562
$867$	7451.20	0.291875
$868$	−23723.8	−0.927693
$869$	14055.6	0.548679
$870$	3654.29	0.142405
$871$	14489.4	0.563667
$872$	−68863.2	−2.67431
$873$	−95.8182	−0.00371473
$874$	26377.4	1.02086
$875$	−5639.01	−0.217867
$876$	21802.6	0.840915
$877$	42936.0	1.65319	0.826595	−	0.562798i	$-0.190275\pi$
$877$	42936.0	1.65319	0.826595	+	0.562798i	$0.190275\pi$
$878$	81930.8	3.14924
$879$	−8823.75	−0.338587
$880$	−19717.6	−0.755318
$881$	−11460.0	−0.438250	−0.219125	−	0.975697i	$-0.570320\pi$
$881$	−11460.0	−0.438250	−0.219125	+	0.975697i	$0.570320\pi$
$882$	−34892.5	−1.33208
$883$	18699.2	0.712658	0.356329	−	0.934361i	$-0.384028\pi$
$883$	18699.2	0.712658	0.356329	+	0.934361i	$0.384028\pi$
$884$	−58889.2	−2.24056
$885$	13351.0	0.507108
$886$	−30034.7	−1.13887
$887$	−26739.1	−1.01219	−0.506095	−	0.862478i	$-0.668911\pi$
$887$	−26739.1	−1.01219	−0.506095	+	0.862478i	$0.668911\pi$
$888$	66522.6	2.51391
$889$	−6780.50	−0.255805
$890$	−32319.3	−1.21724
$891$	2141.29	0.0805116
$892$	13179.0	0.494692
$893$	1943.11	0.0728148
$894$	−22886.3	−0.856188
$895$	16461.6	0.614805
$896$	8982.41	0.334912
$897$	6358.88	0.236697
$898$	44560.6	1.65591
$899$	−8756.89	−0.324871
$900$	18844.0	0.697928
$901$	−14140.2	−0.522838
$902$	23510.2	0.867854
$903$	3189.69	0.117548
$904$	−106880.	−3.93229
$905$	19070.9	0.700484
$906$	12956.9	0.475125
$907$	−5938.59	−0.217407	−0.108703	−	0.994074i	$-0.534670\pi$
$907$	−5938.59	−0.217407	−0.108703	+	0.994074i	$0.534670\pi$
$908$	45855.5	1.67596
$909$	26713.7	0.974738
$910$	10832.0	0.394591
$911$	−17530.7	−0.637562	−0.318781	−	0.947828i	$-0.603273\pi$
$911$	−17530.7	−0.637562	−0.318781	+	0.947828i	$0.603273\pi$
$912$	69093.3	2.50867
$913$	−12939.3	−0.469036
$914$	13590.5	0.491833
$915$	13842.3	0.500121
$916$	10746.1	0.387623
$917$	486.010	0.0175021
$918$	−31265.5	−1.12409
$919$	7154.79	0.256817	0.128408	−	0.991721i	$-0.459013\pi$
$919$	7154.79	0.256817	0.128408	+	0.991721i	$0.459013\pi$
$920$	23538.7	0.843529
$921$	−532.899	−0.0190658
$922$	88230.0	3.15152
$923$	28484.6	1.01580
$924$	2282.51	0.0812652
$925$	−16548.5	−0.588229
$926$	−101426.	−3.59943
$927$	−28775.2	−1.01953
$928$	15161.2	0.536304
$929$	12086.1	0.426839	0.213419	−	0.976961i	$-0.431540\pi$
$929$	12086.1	0.426839	0.213419	+	0.976961i	$0.431540\pi$
$930$	−39518.8	−1.39341
$931$	41932.0	1.47612
$932$	−138499.	−4.86768
$933$	20690.4	0.726017
$934$	−97826.1	−3.42716
$935$	−4530.55	−0.158465
$936$	−82881.3	−2.89429
$937$	−51893.0	−1.80925	−0.904627	−	0.426204i	$-0.859851\pi$
$937$	−51893.0	−1.80925	−0.904627	+	0.426204i	$0.859851\pi$
$938$	−4712.45	−0.164037
$939$	−26133.8	−0.908249
$940$	2819.48	0.0978311
$941$	−54707.5	−1.89523	−0.947616	−	0.319411i	$-0.896515\pi$
$941$	−54707.5	−1.89523	−0.947616	+	0.319411i	$0.896515\pi$
$942$	33441.6	1.15667
$943$	−15380.6	−0.531136
$944$	112412.	3.87575
$945$	4152.32	0.142936
$946$	−18849.4	−0.647829
$947$	12072.0	0.414242	0.207121	−	0.978315i	$-0.433591\pi$
$947$	12072.0	0.414242	0.207121	+	0.978315i	$0.433591\pi$
$948$	−71466.3	−2.44844
$949$	23855.1	0.815984
$950$	−31364.4	−1.07115
$951$	610.641	0.0208216
$952$	11779.1	0.401010
$953$	−25989.5	−0.883401	−0.441701	−	0.897163i	$-0.645625\pi$
$953$	−25989.5	−0.883401	−0.441701	+	0.897163i	$0.645625\pi$
$954$	−32359.1	−1.09818
$955$	32214.5	1.09156
$956$	61358.6	2.07581
$957$	842.517	0.0284584
$958$	−52203.0	−1.76055
$959$	74.3768	0.00250444
$960$	29822.8	1.00263
$961$	64909.2	2.17882
$962$	118349.	3.96643
$963$	−34172.4	−1.14350
$964$	127166.	4.24869
$965$	33226.2	1.10838
$966$	−2068.13	−0.0688830
$967$	−55068.4	−1.83131	−0.915656	−	0.401962i	$-0.868328\pi$
$967$	−55068.4	−1.83131	−0.915656	+	0.401962i	$0.868328\pi$
$968$	−8295.46	−0.275440
$969$	15875.7	0.526316
$970$	231.410	0.00765993
$971$	14616.9	0.483088	0.241544	−	0.970390i	$-0.422346\pi$
$971$	14616.9	0.483088	0.241544	+	0.970390i	$0.422346\pi$
$972$	−81493.3	−2.68920
$973$	−2337.75	−0.0770244
$974$	−3510.89	−0.115499
$975$	−7561.12	−0.248359
$976$	116548.	3.82235
$977$	−37510.1	−1.22831	−0.614153	−	0.789187i	$-0.710502\pi$
$977$	−37510.1	−1.22831	−0.614153	+	0.789187i	$0.710502\pi$
$978$	13466.8	0.440308
$979$	−7451.40	−0.243256
$980$	60844.0	1.98325
$981$	−19843.3	−0.645820
$982$	−39953.5	−1.29834
$983$	7527.57	0.244244	0.122122	−	0.992515i	$-0.461030\pi$
$983$	7527.57	0.244244	0.122122	+	0.992515i	$0.461030\pi$
$984$	−73517.2	−2.38175
$985$	11992.2	0.387922
$986$	7069.66	0.228341
$987$	−152.350	−0.00491323
$988$	161954.	5.21503
$989$	12331.5	0.396479
$990$	−10367.9	−0.332843
$991$	4605.76	0.147635	0.0738177	−	0.997272i	$-0.476482\pi$
$991$	4605.76	0.147635	0.0738177	+	0.997272i	$0.476482\pi$
$992$	−163958.	−5.24766
$993$	24600.9	0.786191
$994$	−9264.18	−0.295616
$995$	−31022.5	−0.988421
$996$	65790.9	2.09304
$997$	968.506	0.0307652	0.0153826	−	0.999882i	$-0.495103\pi$
$997$	968.506	0.0307652	0.0153826	+	0.999882i	$0.495103\pi$
$998$	−12305.8	−0.390313
$999$	45367.5	1.43680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.4	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.4	✓	79	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-5.36465 q^{2} -2.69161 q^{3} +20.7795 q^{4} -8.89356 q^{5} +14.4395 q^{6} -3.71000 q^{7} -68.5575 q^{8} -19.7553 q^{9} +O(q^{10})\)	\(q-5.36465 q^{2} -2.69161 q^{3} +20.7795 q^{4} -8.89356 q^{5} +14.4395 q^{6} -3.71000 q^{7} -68.5575 q^{8} -19.7553 q^{9} +47.7108 q^{10} +11.0000 q^{11} -55.9302 q^{12} -61.1954 q^{13} +19.9028 q^{14} +23.9379 q^{15} +201.551 q^{16} +46.3108 q^{17} +105.980 q^{18} -127.362 q^{19} -184.804 q^{20} +9.98585 q^{21} -59.0112 q^{22} +38.6057 q^{23} +184.530 q^{24} -45.9046 q^{25} +328.292 q^{26} +125.847 q^{27} -77.0918 q^{28} -28.4560 q^{29} -128.419 q^{30} +307.734 q^{31} -532.793 q^{32} -29.6077 q^{33} -248.441 q^{34} +32.9951 q^{35} -410.504 q^{36} +360.498 q^{37} +683.251 q^{38} +164.714 q^{39} +609.720 q^{40} -398.403 q^{41} -53.5706 q^{42} +319.421 q^{43} +228.574 q^{44} +175.695 q^{45} -207.106 q^{46} -15.2566 q^{47} -542.497 q^{48} -329.236 q^{49} +246.262 q^{50} -124.650 q^{51} -1271.61 q^{52} -305.332 q^{53} -675.124 q^{54} -97.8291 q^{55} +254.348 q^{56} +342.807 q^{57} +152.657 q^{58} +557.736 q^{59} +497.418 q^{60} +578.256 q^{61} -1650.89 q^{62} +73.2920 q^{63} +1245.84 q^{64} +544.244 q^{65} +158.835 q^{66} -236.773 q^{67} +962.315 q^{68} -103.911 q^{69} -177.007 q^{70} -465.470 q^{71} +1354.37 q^{72} -389.818 q^{73} -1933.95 q^{74} +123.557 q^{75} -2646.51 q^{76} -40.8100 q^{77} -883.632 q^{78} +1277.78 q^{79} -1792.51 q^{80} +194.662 q^{81} +2137.29 q^{82} -1176.30 q^{83} +207.501 q^{84} -411.868 q^{85} -1713.58 q^{86} +76.5924 q^{87} -754.133 q^{88} -677.400 q^{89} -942.540 q^{90} +227.035 q^{91} +802.206 q^{92} -828.298 q^{93} +81.8465 q^{94} +1132.70 q^{95} +1434.07 q^{96} +4.85026 q^{97} +1766.24 q^{98} -217.308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * q^99

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