LMFDB - Embedded newform 1441.4.a.c.1.8

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:	$0$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-4.94545 q^{2} -7.30968 q^{3} +16.4575 q^{4} -2.24027 q^{5} +36.1497 q^{6} -13.8801 q^{7} -41.8261 q^{8} +26.4315 q^{9} +O(q^{10})$	\(q-4.94545 q^{2} -7.30968 q^{3} +16.4575 q^{4} -2.24027 q^{5} +36.1497 q^{6} -13.8801 q^{7} -41.8261 q^{8} +26.4315 q^{9} +11.0791 q^{10} -11.0000 q^{11} -120.299 q^{12} +7.54365 q^{13} +68.6432 q^{14} +16.3756 q^{15} +75.1890 q^{16} +24.2821 q^{17} -130.716 q^{18} +74.0115 q^{19} -36.8691 q^{20} +101.459 q^{21} +54.4000 q^{22} -141.181 q^{23} +305.736 q^{24} -119.981 q^{25} -37.3068 q^{26} +4.15564 q^{27} -228.431 q^{28} +152.511 q^{29} -80.9849 q^{30} -214.687 q^{31} -37.2349 q^{32} +80.4065 q^{33} -120.086 q^{34} +31.0950 q^{35} +434.996 q^{36} -3.36104 q^{37} -366.020 q^{38} -55.1417 q^{39} +93.7016 q^{40} +88.8035 q^{41} -501.760 q^{42} +495.121 q^{43} -181.032 q^{44} -59.2135 q^{45} +698.206 q^{46} +183.025 q^{47} -549.608 q^{48} -150.344 q^{49} +593.361 q^{50} -177.494 q^{51} +124.150 q^{52} -335.225 q^{53} -20.5515 q^{54} +24.6429 q^{55} +580.549 q^{56} -541.001 q^{57} -754.234 q^{58} +664.197 q^{59} +269.502 q^{60} +509.666 q^{61} +1061.73 q^{62} -366.871 q^{63} -417.369 q^{64} -16.8998 q^{65} -397.647 q^{66} -164.465 q^{67} +399.622 q^{68} +1031.99 q^{69} -153.779 q^{70} -161.482 q^{71} -1105.53 q^{72} -977.400 q^{73} +16.6218 q^{74} +877.025 q^{75} +1218.04 q^{76} +152.681 q^{77} +272.701 q^{78} +744.724 q^{79} -168.443 q^{80} -744.027 q^{81} -439.174 q^{82} -812.098 q^{83} +1669.76 q^{84} -54.3982 q^{85} -2448.60 q^{86} -1114.80 q^{87} +460.087 q^{88} +885.714 q^{89} +292.838 q^{90} -104.706 q^{91} -2323.49 q^{92} +1569.30 q^{93} -905.140 q^{94} -165.805 q^{95} +272.175 q^{96} -1726.24 q^{97} +743.518 q^{98} -290.746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) $ 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * 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 $

$2$	−4.94545	−1.74848	−0.874241	−	0.485493i	$-0.838640\pi$
$2$	−4.94545	−1.74848	−0.874241	+	0.485493i	$0.838640\pi$
$3$	−7.30968	−1.40675	−0.703375	−	0.710819i	$-0.748324\pi$
$3$	−7.30968	−1.40675	−0.703375	+	0.710819i	$0.748324\pi$
$4$	16.4575	2.05719
$5$	−2.24027	−0.200375	−0.100188	−	0.994969i	$-0.531944\pi$
$5$	−2.24027	−0.200375	−0.100188	+	0.994969i	$0.531944\pi$
$6$	36.1497	2.45967
$7$	−13.8801	−0.749453	−0.374727	−	0.927135i	$-0.622263\pi$
$7$	−13.8801	−0.749453	−0.374727	+	0.927135i	$0.622263\pi$
$8$	−41.8261	−1.84847
$9$	26.4315	0.978944
$10$	11.0791	0.350353
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−120.299	−2.89395
$13$	7.54365	0.160941	0.0804705	−	0.996757i	$-0.474358\pi$
$13$	7.54365	0.160941	0.0804705	+	0.996757i	$0.474358\pi$
$14$	68.6432	1.31040
$15$	16.3756	0.281878
$16$	75.1890	1.17483
$17$	24.2821	0.346427	0.173214	−	0.984884i	$-0.444585\pi$
$17$	24.2821	0.346427	0.173214	+	0.984884i	$0.444585\pi$
$18$	−130.716	−1.71167
$19$	74.0115	0.893653	0.446827	−	0.894621i	$-0.352554\pi$
$19$	74.0115	0.893653	0.446827	+	0.894621i	$0.352554\pi$
$20$	−36.8691	−0.412209
$21$	101.459	1.05429
$22$	54.4000	0.527187
$23$	−141.181	−1.27993	−0.639964	−	0.768405i	$-0.721051\pi$
$23$	−141.181	−1.27993	−0.639964	+	0.768405i	$0.721051\pi$
$24$	305.736	2.60033
$25$	−119.981	−0.959850
$26$	−37.3068	−0.281402
$27$	4.15564	0.0296205
$28$	−228.431	−1.54176
$29$	152.511	0.976569	0.488285	−	0.872684i	$-0.337623\pi$
$29$	152.511	0.976569	0.488285	+	0.872684i	$0.337623\pi$
$30$	−80.9849	−0.492858
$31$	−214.687	−1.24384	−0.621920	−	0.783081i	$-0.713647\pi$
$31$	−214.687	−1.24384	−0.621920	+	0.783081i	$0.713647\pi$
$32$	−37.2349	−0.205696
$33$	80.4065	0.424151
$34$	−120.086	−0.605722
$35$	31.0950	0.150172
$36$	434.996	2.01387
$37$	−3.36104	−0.0149338	−0.00746690	−	0.999972i	$-0.502377\pi$
$37$	−3.36104	−0.0149338	−0.00746690	+	0.999972i	$0.502377\pi$
$38$	−366.020	−1.56254
$39$	−55.1417	−0.226404
$40$	93.7016	0.370388
$41$	88.8035	0.338263	0.169131	−	0.985593i	$-0.445904\pi$
$41$	88.8035	0.338263	0.169131	+	0.985593i	$0.445904\pi$
$42$	−501.760	−1.84341
$43$	495.121	1.75594	0.877968	−	0.478719i	$-0.158899\pi$
$43$	495.121	1.75594	0.877968	+	0.478719i	$0.158899\pi$
$44$	−181.032	−0.620265
$45$	−59.2135	−0.196156
$46$	698.206	2.23793
$47$	183.025	0.568019	0.284009	−	0.958821i	$-0.408335\pi$
$47$	183.025	0.568019	0.284009	+	0.958821i	$0.408335\pi$
$48$	−549.608	−1.65269
$49$	−150.344	−0.438320
$50$	593.361	1.67828
$51$	−177.494	−0.487336
$52$	124.150	0.331085
$53$	−335.225	−0.868806	−0.434403	−	0.900719i	$-0.643041\pi$
$53$	−335.225	−0.868806	−0.434403	+	0.900719i	$0.643041\pi$
$54$	−20.5515	−0.0517908
$55$	24.6429	0.0604155
$56$	580.549	1.38534
$57$	−541.001	−1.25715
$58$	−754.234	−1.70751
$59$	664.197	1.46561	0.732806	−	0.680438i	$-0.238210\pi$
$59$	664.197	1.46561	0.732806	+	0.680438i	$0.238210\pi$
$60$	269.502	0.579875
$61$	509.666	1.06977	0.534885	−	0.844925i	$-0.320355\pi$
$61$	509.666	1.06977	0.534885	+	0.844925i	$0.320355\pi$
$62$	1061.73	2.17483
$63$	−366.871	−0.733673
$64$	−417.369	−0.815174
$65$	−16.8998	−0.0322486
$66$	−397.647	−0.741620
$67$	−164.465	−0.299889	−0.149945	−	0.988694i	$-0.547910\pi$
$67$	−164.465	−0.299889	−0.149945	+	0.988694i	$0.547910\pi$
$68$	399.622	0.712665
$69$	1031.99	1.80054
$70$	−153.779	−0.262573
$71$	−161.482	−0.269921	−0.134961	−	0.990851i	$-0.543091\pi$
$71$	−161.482	−0.269921	−0.134961	+	0.990851i	$0.543091\pi$
$72$	−1105.53	−1.80955
$73$	−977.400	−1.56707	−0.783534	−	0.621348i	$-0.786585\pi$
$73$	−977.400	−1.56707	−0.783534	+	0.621348i	$0.786585\pi$
$74$	16.6218	0.0261115
$75$	877.025	1.35027
$76$	1218.04	1.83841
$77$	152.681	0.225969
$78$	272.701	0.395862
$79$	744.724	1.06061	0.530304	−	0.847808i	$-0.322078\pi$
$79$	744.724	1.06061	0.530304	+	0.847808i	$0.322078\pi$
$80$	−168.443	−0.235407
$81$	−744.027	−1.02061
$82$	−439.174	−0.591446
$83$	−812.098	−1.07397	−0.536984	−	0.843592i	$-0.680436\pi$
$83$	−812.098	−1.07397	−0.536984	+	0.843592i	$0.680436\pi$
$84$	1669.76	2.16888
$85$	−54.3982	−0.0694155
$86$	−2448.60	−3.07022
$87$	−1114.80	−1.37379
$88$	460.087	0.557335
$89$	885.714	1.05489	0.527447	−	0.849588i	$-0.323150\pi$
$89$	885.714	1.05489	0.527447	+	0.849588i	$0.323150\pi$
$90$	292.838	0.342976
$91$	−104.706	−0.120618
$92$	−2323.49	−2.63305
$93$	1569.30	1.74977
$94$	−905.140	−0.993170
$95$	−165.805	−0.179066
$96$	272.175	0.289362
$97$	−1726.24	−1.80694	−0.903469	−	0.428654i	$-0.858988\pi$
$97$	−1726.24	−1.80694	−0.903469	+	0.428654i	$0.858988\pi$
$98$	743.518	0.766394
$99$	−290.746	−0.295163
$100$	−1974.59	−1.97459
$101$	−1792.62	−1.76607	−0.883034	−	0.469309i	$-0.844503\pi$
$101$	−1792.62	−1.76607	−0.883034	+	0.469309i	$0.844503\pi$
$102$	877.789	0.852099
$103$	−606.553	−0.580247	−0.290123	−	0.956989i	$-0.593696\pi$
$103$	−606.553	−0.580247	−0.290123	+	0.956989i	$0.593696\pi$
$104$	−315.521	−0.297494
$105$	−227.295	−0.211254
$106$	1657.84	1.51909
$107$	−1311.38	−1.18482	−0.592410	−	0.805637i	$-0.701823\pi$
$107$	−1311.38	−1.18482	−0.592410	+	0.805637i	$0.701823\pi$
$108$	68.3914	0.0609348
$109$	−1616.27	−1.42028	−0.710142	−	0.704059i	$-0.751369\pi$
$109$	−1616.27	−1.42028	−0.710142	+	0.704059i	$0.751369\pi$
$110$	−121.870	−0.105635
$111$	24.5681	0.0210081
$112$	−1043.63	−0.880479
$113$	−602.160	−0.501296	−0.250648	−	0.968078i	$-0.580644\pi$
$113$	−602.160	−0.501296	−0.250648	+	0.968078i	$0.580644\pi$
$114$	2675.49	2.19810
$115$	316.284	0.256466
$116$	2509.94	2.00899
$117$	199.390	0.157552
$118$	−3284.75	−2.56259
$119$	−337.037	−0.259631
$120$	−684.929	−0.521043
$121$	121.000	0.0909091
$122$	−2520.53	−1.87047
$123$	−649.126	−0.475851
$124$	−3533.22	−2.55881
$125$	548.823	0.392706
$126$	1814.34	1.28281
$127$	−703.497	−0.491537	−0.245769	−	0.969329i	$-0.579040\pi$
$127$	−703.497	−0.491537	−0.245769	+	0.969329i	$0.579040\pi$
$128$	2361.96	1.63101
$129$	−3619.18	−2.47016
$130$	83.5770	0.0563861
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	1323.29	0.872557
$133$	−1027.29	−0.669751
$134$	813.352	0.524350
$135$	−9.30973	−0.00593521
$136$	−1015.62	−0.640360
$137$	1571.19	0.979826	0.489913	−	0.871771i	$-0.337028\pi$
$137$	1571.19	0.979826	0.489913	+	0.871771i	$0.337028\pi$
$138$	−5103.66	−3.14821
$139$	996.291	0.607945	0.303972	−	0.952681i	$-0.401687\pi$
$139$	996.291	0.607945	0.303972	+	0.952681i	$0.401687\pi$
$140$	511.746	0.308932
$141$	−1337.85	−0.799060
$142$	798.602	0.471952
$143$	−82.9801	−0.0485255
$144$	1987.36	1.15009
$145$	−341.664	−0.195680
$146$	4833.68	2.73999
$147$	1098.97	0.616606
$148$	−55.3142	−0.0307216
$149$	2576.52	1.41662	0.708311	−	0.705901i	$-0.249457\pi$
$149$	2576.52	1.41662	0.708311	+	0.705901i	$0.249457\pi$
$150$	−4337.28	−2.36092
$151$	−3173.16	−1.71012	−0.855059	−	0.518530i	$-0.826479\pi$
$151$	−3173.16	−1.71012	−0.855059	+	0.518530i	$0.826479\pi$
$152$	−3095.61	−1.65189
$153$	641.811	0.339133
$154$	−755.075	−0.395102
$155$	480.957	0.249235
$156$	−907.494	−0.465754
$157$	−666.394	−0.338752	−0.169376	−	0.985552i	$-0.554175\pi$
$157$	−666.394	−0.338752	−0.169376	+	0.985552i	$0.554175\pi$
$158$	−3683.00	−1.85445
$159$	2450.39	1.22219
$160$	83.4160	0.0412163
$161$	1959.61	0.959246
$162$	3679.55	1.78452
$163$	528.641	0.254027	0.127013	−	0.991901i	$-0.459461\pi$
$163$	528.641	0.254027	0.127013	+	0.991901i	$0.459461\pi$
$164$	1461.48	0.695870
$165$	−180.132	−0.0849894
$166$	4016.19	1.87781
$167$	−1803.37	−0.835622	−0.417811	−	0.908534i	$-0.637203\pi$
$167$	−1803.37	−0.835622	−0.417811	+	0.908534i	$0.637203\pi$
$168$	−4243.63	−1.94883
$169$	−2140.09	−0.974098
$170$	269.024	0.121372
$171$	1956.24	0.874837
$172$	8148.45	3.61229
$173$	−3638.28	−1.59892	−0.799461	−	0.600719i	$-0.794881\pi$
$173$	−3638.28	−1.59892	−0.799461	+	0.600719i	$0.794881\pi$
$174$	5513.21	2.40204
$175$	1665.35	0.719362
$176$	−827.079	−0.354224
$177$	−4855.07	−2.06175
$178$	−4380.25	−1.84446
$179$	3110.23	1.29871	0.649356	−	0.760484i	$-0.275038\pi$
$179$	3110.23	1.29871	0.649356	+	0.760484i	$0.275038\pi$
$180$	−974.506	−0.403530
$181$	−3019.07	−1.23981	−0.619906	−	0.784676i	$-0.712829\pi$
$181$	−3019.07	−1.23981	−0.619906	+	0.784676i	$0.712829\pi$
$182$	517.820	0.210898
$183$	−3725.50	−1.50490
$184$	5905.07	2.36591
$185$	7.52961	0.00299237
$186$	−7760.89	−3.05944
$187$	−267.103	−0.104452
$188$	3012.13	1.16852
$189$	−57.6805	−0.0221992
$190$	819.983	0.313094
$191$	720.088	0.272794	0.136397	−	0.990654i	$-0.456448\pi$
$191$	720.088	0.272794	0.136397	+	0.990654i	$0.456448\pi$
$192$	3050.84	1.14675
$193$	−4954.19	−1.84772	−0.923862	−	0.382726i	$-0.874985\pi$
$193$	−4954.19	−1.84772	−0.923862	+	0.382726i	$0.874985\pi$
$194$	8537.03	3.15940
$195$	123.532	0.0453657
$196$	−2474.28	−0.901706
$197$	−1865.06	−0.674518	−0.337259	−	0.941412i	$-0.609500\pi$
$197$	−1865.06	−0.674518	−0.337259	+	0.941412i	$0.609500\pi$
$198$	1437.87	0.516086
$199$	4786.77	1.70515	0.852577	−	0.522602i	$-0.175039\pi$
$199$	4786.77	1.70515	0.852577	+	0.522602i	$0.175039\pi$
$200$	5018.35	1.77425
$201$	1202.19	0.421869
$202$	8865.34	3.08794
$203$	−2116.86	−0.731893
$204$	−2921.11	−1.00254
$205$	−198.943	−0.0677796
$206$	2999.68	1.01455
$207$	−3731.63	−1.25298
$208$	567.200	0.189078
$209$	−814.127	−0.269447
$210$	1124.08	0.369374
$211$	657.964	0.214674	0.107337	−	0.994223i	$-0.465768\pi$
$211$	657.964	0.214674	0.107337	+	0.994223i	$0.465768\pi$
$212$	−5516.96	−1.78730
$213$	1180.38	0.379711
$214$	6485.35	2.07163
$215$	−1109.20	−0.351846
$216$	−173.814	−0.0547525
$217$	2979.88	0.932199
$218$	7993.20	2.48334
$219$	7144.49	2.20447
$220$	405.561	0.124286
$221$	183.175	0.0557543
$222$	−121.500	−0.0367323
$223$	395.370	0.118726	0.0593631	−	0.998236i	$-0.481093\pi$
$223$	395.370	0.118726	0.0593631	+	0.998236i	$0.481093\pi$
$224$	516.822	0.154159
$225$	−3171.28	−0.939639
$226$	2977.95	0.876506
$227$	4688.17	1.37077	0.685385	−	0.728181i	$-0.259634\pi$
$227$	4688.17	1.37077	0.685385	+	0.728181i	$0.259634\pi$
$228$	−8903.52	−2.58618
$229$	5727.32	1.65272	0.826359	−	0.563144i	$-0.190408\pi$
$229$	5727.32	1.65272	0.826359	+	0.563144i	$0.190408\pi$
$230$	−1564.17	−0.448426
$231$	−1116.05	−0.317881
$232$	−6378.92	−1.80516
$233$	641.003	0.180230	0.0901148	−	0.995931i	$-0.471277\pi$
$233$	641.003	0.180230	0.0901148	+	0.995931i	$0.471277\pi$
$234$	−986.073	−0.275477
$235$	−410.024	−0.113817
$236$	10931.0	3.01504
$237$	−5443.70	−1.49201
$238$	1666.80	0.453960
$239$	−2556.85	−0.692005	−0.346002	−	0.938234i	$-0.612461\pi$
$239$	−2556.85	−0.692005	−0.346002	+	0.938234i	$0.612461\pi$
$240$	1231.27	0.331158
$241$	−7194.22	−1.92291	−0.961453	−	0.274970i	$-0.911332\pi$
$241$	−7194.22	−1.92291	−0.961453	+	0.274970i	$0.911332\pi$
$242$	−598.400	−0.158953
$243$	5326.40	1.40613
$244$	8387.82	2.20072
$245$	336.810	0.0878285
$246$	3210.22	0.832017
$247$	558.317	0.143825
$248$	8979.54	2.29920
$249$	5936.18	1.51080
$250$	−2714.18	−0.686638
$251$	1486.96	0.373929	0.186964	−	0.982367i	$-0.440135\pi$
$251$	1486.96	0.373929	0.186964	+	0.982367i	$0.440135\pi$
$252$	−6037.77	−1.50930
$253$	1553.00	0.385913
$254$	3479.11	0.859444
$255$	397.634	0.0976502
$256$	−8341.99	−2.03662
$257$	4508.64	1.09432	0.547162	−	0.837027i	$-0.315708\pi$
$257$	4508.64	1.09432	0.547162	+	0.837027i	$0.315708\pi$
$258$	17898.5	4.31903
$259$	46.6514	0.0111922
$260$	−278.128	−0.0663414
$261$	4031.08	0.956007
$262$	647.854	0.152766
$263$	−5327.65	−1.24911	−0.624557	−	0.780979i	$-0.714720\pi$
$263$	−5327.65	−1.24911	−0.624557	+	0.780979i	$0.714720\pi$
$264$	−3363.09	−0.784030
$265$	750.993	0.174087
$266$	5080.39	1.17105
$267$	−6474.29	−1.48397
$268$	−2706.68	−0.616928
$269$	213.634	0.0484218	0.0242109	−	0.999707i	$-0.492293\pi$
$269$	213.634	0.0484218	0.0242109	+	0.999707i	$0.492293\pi$
$270$	46.0408	0.0103776
$271$	5304.54	1.18903	0.594516	−	0.804084i	$-0.297344\pi$
$271$	5304.54	1.18903	0.594516	+	0.804084i	$0.297344\pi$
$272$	1825.74	0.406993
$273$	765.370	0.169679
$274$	−7770.27	−1.71321
$275$	1319.79	0.289406
$276$	16984.0	3.70404
$277$	1906.81	0.413606	0.206803	−	0.978383i	$-0.433694\pi$
$277$	1906.81	0.413606	0.206803	+	0.978383i	$0.433694\pi$
$278$	−4927.11	−1.06298
$279$	−5674.51	−1.21765
$280$	−1300.58	−0.277588
$281$	2728.80	0.579311	0.289655	−	0.957131i	$-0.406459\pi$
$281$	2728.80	0.579311	0.289655	+	0.957131i	$0.406459\pi$
$282$	6616.28	1.39714
$283$	2559.42	0.537603	0.268801	−	0.963196i	$-0.413372\pi$
$283$	2559.42	0.537603	0.268801	+	0.963196i	$0.413372\pi$
$284$	−2657.59	−0.555278
$285$	1211.99	0.251901
$286$	410.374	0.0848459
$287$	−1232.60	−0.253512
$288$	−984.173	−0.201364
$289$	−4323.38	−0.879988
$290$	1689.68	0.342144
$291$	12618.3	2.54191
$292$	−16085.6	−3.22375
$293$	4886.21	0.974250	0.487125	−	0.873332i	$-0.338046\pi$
$293$	4886.21	0.974250	0.487125	+	0.873332i	$0.338046\pi$
$294$	−5434.88	−1.07812
$295$	−1487.98	−0.293673
$296$	140.579	0.0276047
$297$	−45.7120	−0.00893091
$298$	−12742.0	−2.47694
$299$	−1065.02	−0.205993
$300$	14433.6	2.77775
$301$	−6872.31	−1.31599
$302$	15692.7	2.99011
$303$	13103.5	2.48441
$304$	5564.86	1.04989
$305$	−1141.79	−0.214356
$306$	−3174.04	−0.592968
$307$	−5221.13	−0.970637	−0.485318	−	0.874337i	$-0.661296\pi$
$307$	−5221.13	−0.970637	−0.485318	+	0.874337i	$0.661296\pi$
$308$	2512.74	0.464860
$309$	4433.71	0.816262
$310$	−2378.55	−0.435782
$311$	2503.11	0.456394	0.228197	−	0.973615i	$-0.426717\pi$
$311$	2503.11	0.456394	0.228197	+	0.973615i	$0.426717\pi$
$312$	2306.36	0.418500
$313$	−7662.91	−1.38381	−0.691906	−	0.721988i	$-0.743229\pi$
$313$	−7662.91	−1.38381	−0.691906	+	0.721988i	$0.743229\pi$
$314$	3295.62	0.592301
$315$	821.888	0.147010
$316$	12256.3	2.18187
$317$	7457.77	1.32136	0.660679	−	0.750669i	$-0.270269\pi$
$317$	7457.77	1.32136	0.660679	+	0.750669i	$0.270269\pi$
$318$	−12118.3	−2.13698
$319$	−1677.62	−0.294447
$320$	935.017	0.163341
$321$	9585.76	1.66674
$322$	−9691.14	−1.67722
$323$	1797.15	0.309586
$324$	−12244.8	−2.09959
$325$	−905.096	−0.154479
$326$	−2614.37	−0.444161
$327$	11814.5	1.99798
$328$	−3714.31	−0.625269
$329$	−2540.39	−0.425704
$330$	890.834	0.148602
$331$	−5560.28	−0.923326	−0.461663	−	0.887055i	$-0.652747\pi$
$331$	−5560.28	−0.923326	−0.461663	+	0.887055i	$0.652747\pi$
$332$	−13365.1	−2.20935
$333$	−88.8372	−0.0146194
$334$	8918.47	1.46107
$335$	368.445	0.0600904
$336$	7628.60	1.23861
$337$	−5746.79	−0.928925	−0.464463	−	0.885593i	$-0.653753\pi$
$337$	−5746.79	−0.928925	−0.464463	+	0.885593i	$0.653753\pi$
$338$	10583.7	1.70319
$339$	4401.60	0.705197
$340$	−895.259	−0.142801
$341$	2361.56	0.375032
$342$	−9674.47	−1.52964
$343$	6847.64	1.07795
$344$	−20709.0	−3.24580
$345$	−2311.93	−0.360784
$346$	17992.9	2.79568
$347$	4793.44	0.741572	0.370786	−	0.928718i	$-0.379088\pi$
$347$	4793.44	0.741572	0.370786	+	0.928718i	$0.379088\pi$
$348$	−18346.9	−2.82614
$349$	10776.6	1.65289	0.826443	−	0.563020i	$-0.190361\pi$
$349$	10776.6	1.65289	0.826443	+	0.563020i	$0.190361\pi$
$350$	−8235.89	−1.25779
$351$	31.3487	0.00476715
$352$	409.584	0.0620195
$353$	1227.55	0.185088	0.0925439	−	0.995709i	$-0.470500\pi$
$353$	1227.55	0.185088	0.0925439	+	0.995709i	$0.470500\pi$
$354$	24010.5	3.60493
$355$	361.763	0.0540856
$356$	14576.6	2.17011
$357$	2463.63	0.365236
$358$	−15381.5	−2.27078
$359$	−50.1996	−0.00738003	−0.00369002	−	0.999993i	$-0.501175\pi$
$359$	−50.1996	−0.00738003	−0.00369002	+	0.999993i	$0.501175\pi$
$360$	2476.67	0.362589
$361$	−1381.29	−0.201384
$362$	14930.7	2.16779
$363$	−884.472	−0.127886
$364$	−1723.20	−0.248133
$365$	2189.64	0.314002
$366$	18424.3	2.63129
$367$	3848.36	0.547364	0.273682	−	0.961820i	$-0.411758\pi$
$367$	3848.36	0.547364	0.273682	+	0.961820i	$0.411758\pi$
$368$	−10615.3	−1.50370
$369$	2347.21	0.331141
$370$	−37.2373	−0.00523210
$371$	4652.95	0.651129
$372$	25826.7	3.59960
$373$	6563.45	0.911106	0.455553	−	0.890209i	$-0.349442\pi$
$373$	6563.45	0.911106	0.455553	+	0.890209i	$0.349442\pi$
$374$	1320.94	0.182632
$375$	−4011.72	−0.552438
$376$	−7655.21	−1.04997
$377$	1150.49	0.157170
$378$	285.256	0.0388148
$379$	5046.83	0.684005	0.342003	−	0.939699i	$-0.388895\pi$
$379$	5046.83	0.684005	0.342003	+	0.939699i	$0.388895\pi$
$380$	−2728.74	−0.368372
$381$	5142.34	0.691470
$382$	−3561.16	−0.476976
$383$	−9454.05	−1.26130	−0.630652	−	0.776066i	$-0.717212\pi$
$383$	−9454.05	−1.26130	−0.630652	+	0.776066i	$0.717212\pi$
$384$	−17265.2	−2.29442
$385$	−342.045	−0.0452786
$386$	24500.7	3.23071
$387$	13086.8	1.71896
$388$	−28409.5	−3.71721
$389$	−2656.38	−0.346231	−0.173116	−	0.984901i	$-0.555383\pi$
$389$	−2656.38	−0.346231	−0.173116	+	0.984901i	$0.555383\pi$
$390$	−610.922	−0.0793211
$391$	−3428.17	−0.443402
$392$	6288.29	0.810221
$393$	957.569	0.122908
$394$	9223.57	1.17938
$395$	−1668.38	−0.212520
$396$	−4784.96	−0.607205
$397$	374.629	0.0473604	0.0236802	−	0.999720i	$-0.492462\pi$
$397$	374.629	0.0473604	0.0236802	+	0.999720i	$0.492462\pi$
$398$	−23672.8	−2.98143
$399$	7509.13	0.942172
$400$	−9021.27	−1.12766
$401$	−5235.14	−0.651946	−0.325973	−	0.945379i	$-0.605692\pi$
$401$	−5235.14	−0.651946	−0.325973	+	0.945379i	$0.605692\pi$
$402$	−5945.35	−0.737630
$403$	−1619.53	−0.200185
$404$	−29502.1	−3.63313
$405$	1666.82	0.204506
$406$	10468.8	1.27970
$407$	36.9714	0.00450271
$408$	7423.89	0.900827
$409$	14755.9	1.78394	0.891969	−	0.452097i	$-0.149324\pi$
$409$	14755.9	1.78394	0.891969	+	0.452097i	$0.149324\pi$
$410$	983.865	0.118511
$411$	−11484.9	−1.37837
$412$	−9982.34	−1.19368
$413$	−9219.10	−1.09841
$414$	18454.6	2.19081
$415$	1819.32	0.215197
$416$	−280.887	−0.0331048
$417$	−7282.58	−0.855226
$418$	4026.23	0.471122
$419$	−14549.6	−1.69641	−0.848204	−	0.529670i	$-0.822316\pi$
$419$	−14549.6	−1.69641	−0.848204	+	0.529670i	$0.822316\pi$
$420$	−3740.70	−0.434589
$421$	12742.0	1.47508	0.737540	−	0.675304i	$-0.235987\pi$
$421$	12742.0	1.47508	0.737540	+	0.675304i	$0.235987\pi$
$422$	−3253.93	−0.375353
$423$	4837.61	0.556059
$424$	14021.2	1.60596
$425$	−2913.39	−0.332518
$426$	−5837.53	−0.663918
$427$	−7074.19	−0.801743
$428$	−21582.0	−2.43739
$429$	606.559	0.0682632
$430$	5485.51	0.615197
$431$	−1894.76	−0.211757	−0.105879	−	0.994379i	$-0.533766\pi$
$431$	−1894.76	−0.211757	−0.105879	+	0.994379i	$0.533766\pi$
$432$	312.458	0.0347990
$433$	−15989.6	−1.77462	−0.887311	−	0.461171i	$-0.847429\pi$
$433$	−15989.6	−1.77462	−0.887311	+	0.461171i	$0.847429\pi$
$434$	−14736.8	−1.62993
$435$	2497.46	0.275273
$436$	−26599.8	−2.92179
$437$	−10449.1	−1.14381
$438$	−35332.7	−3.85448
$439$	−934.358	−0.101582	−0.0507910	−	0.998709i	$-0.516174\pi$
$439$	−934.358	−0.101582	−0.0507910	+	0.998709i	$0.516174\pi$
$440$	−1030.72	−0.111676
$441$	−3973.81	−0.429091
$442$	−905.885	−0.0974854
$443$	9473.11	1.01598	0.507992	−	0.861362i	$-0.330388\pi$
$443$	9473.11	1.01598	0.507992	+	0.861362i	$0.330388\pi$
$444$	404.329	0.0432176
$445$	−1984.23	−0.211375
$446$	−1955.28	−0.207591
$447$	−18833.5	−1.99283
$448$	5793.11	0.610935
$449$	6033.93	0.634207	0.317103	−	0.948391i	$-0.397290\pi$
$449$	6033.93	0.634207	0.317103	+	0.948391i	$0.397290\pi$
$450$	15683.4	1.64294
$451$	−976.839	−0.101990
$452$	−9910.04	−1.03126
$453$	23194.8	2.40571
$454$	−23185.1	−2.39676
$455$	234.570	0.0241688
$456$	22628.0	2.32380
$457$	−13102.1	−1.34111	−0.670557	−	0.741858i	$-0.733945\pi$
$457$	−13102.1	−1.34111	−0.670557	+	0.741858i	$0.733945\pi$
$458$	−28324.2	−2.88974
$459$	100.907	0.0102613
$460$	5205.24	0.527599
$461$	7642.24	0.772092	0.386046	−	0.922479i	$-0.373841\pi$
$461$	7642.24	0.772092	0.386046	+	0.922479i	$0.373841\pi$
$462$	5519.36	0.555809
$463$	−3954.28	−0.396913	−0.198457	−	0.980110i	$-0.563593\pi$
$463$	−3954.28	−0.396913	−0.198457	+	0.980110i	$0.563593\pi$
$464$	11467.1	1.14730
$465$	−3515.64	−0.350611
$466$	−3170.05	−0.315128
$467$	18024.1	1.78599	0.892995	−	0.450066i	$-0.148600\pi$
$467$	18024.1	1.78599	0.892995	+	0.450066i	$0.148600\pi$
$468$	3281.46	0.324114
$469$	2282.78	0.224753
$470$	2027.75	0.199007
$471$	4871.13	0.476539
$472$	−27780.8	−2.70914
$473$	−5446.33	−0.529435
$474$	26921.5	2.60875
$475$	−8879.99	−0.857773
$476$	−5546.78	−0.534109
$477$	−8860.50	−0.850512
$478$	12644.8	1.20996
$479$	7869.09	0.750622	0.375311	−	0.926899i	$-0.377536\pi$
$479$	7869.09	0.750622	0.375311	+	0.926899i	$0.377536\pi$
$480$	−609.745	−0.0579810
$481$	−25.3545	−0.00240346
$482$	35578.6	3.36216
$483$	−14324.1	−1.34942
$484$	1991.36	0.187017
$485$	3867.23	0.362066
$486$	−26341.4	−2.45858
$487$	−7144.97	−0.664825	−0.332412	−	0.943134i	$-0.607863\pi$
$487$	−7144.97	−0.664825	−0.332412	+	0.943134i	$0.607863\pi$
$488$	−21317.3	−1.97744
$489$	−3864.20	−0.357352
$490$	−1665.68	−0.153567
$491$	−5014.21	−0.460872	−0.230436	−	0.973087i	$-0.574015\pi$
$491$	−5014.21	−0.460872	−0.230436	+	0.973087i	$0.574015\pi$
$492$	−10683.0	−0.978915
$493$	3703.27	0.338310
$494$	−2761.13	−0.251476
$495$	651.349	0.0591434
$496$	−16142.1	−1.46130
$497$	2241.38	0.202293
$498$	−29357.1	−2.64161
$499$	−10862.7	−0.974509	−0.487254	−	0.873260i	$-0.662002\pi$
$499$	−10862.7	−0.974509	−0.487254	+	0.873260i	$0.662002\pi$
$500$	9032.25	0.807869
$501$	13182.1	1.17551
$502$	−7353.69	−0.653808
$503$	−11834.1	−1.04902	−0.524509	−	0.851405i	$-0.675751\pi$
$503$	−11834.1	−1.04902	−0.524509	+	0.851405i	$0.675751\pi$
$504$	15344.8	1.35617
$505$	4015.95	0.353877
$506$	−7680.26	−0.674761
$507$	15643.4	1.37031
$508$	−11577.8	−1.01118
$509$	−7151.09	−0.622724	−0.311362	−	0.950291i	$-0.600785\pi$
$509$	−7151.09	−0.622724	−0.311362	+	0.950291i	$0.600785\pi$
$510$	−1966.48	−0.170740
$511$	13566.4	1.17444
$512$	22359.3	1.92998
$513$	307.565	0.0264704
$514$	−22297.3	−1.91341
$515$	1358.84	0.116267
$516$	−59562.6	−5.08158
$517$	−2013.27	−0.171264
$518$	−230.712	−0.0195693
$519$	26594.7	2.24928
$520$	706.852	0.0596106
$521$	21340.7	1.79454	0.897268	−	0.441486i	$-0.145549\pi$
$521$	21340.7	1.79454	0.897268	+	0.441486i	$0.145549\pi$
$522$	−19935.5	−1.67156
$523$	13489.6	1.12784	0.563918	−	0.825831i	$-0.309293\pi$
$523$	13489.6	1.12784	0.563918	+	0.825831i	$0.309293\pi$
$524$	−2155.93	−0.179737
$525$	−12173.2	−1.01196
$526$	26347.6	2.18405
$527$	−5213.05	−0.430900
$528$	6045.69	0.498305
$529$	7765.18	0.638216
$530$	−3714.00	−0.304388
$531$	17555.7	1.43475
$532$	−16906.5	−1.37780
$533$	669.903	0.0544403
$534$	32018.3	2.59469
$535$	2937.83	0.237409
$536$	6878.92	0.554336
$537$	−22734.8	−1.82696
$538$	−1056.51	−0.0846647
$539$	1653.78	0.132158
$540$	−153.215	−0.0122098
$541$	−3538.57	−0.281211	−0.140606	−	0.990066i	$-0.544905\pi$
$541$	−3538.57	−0.281211	−0.140606	+	0.990066i	$0.544905\pi$
$542$	−26233.3	−2.07900
$543$	22068.5	1.74410
$544$	−904.139	−0.0712586
$545$	3620.88	0.284590
$546$	−3785.10	−0.296680
$547$	−5744.28	−0.449008	−0.224504	−	0.974473i	$-0.572076\pi$
$547$	−5744.28	−0.449008	−0.224504	+	0.974473i	$0.572076\pi$
$548$	25857.9	2.01569
$549$	13471.2	1.04725
$550$	−6526.97	−0.506020
$551$	11287.5	0.872714
$552$	−43164.2	−3.32824
$553$	−10336.8	−0.794876
$554$	−9430.02	−0.723182
$555$	−55.0391	−0.00420951
$556$	16396.5	1.25066
$557$	21658.0	1.64754	0.823768	−	0.566927i	$-0.191868\pi$
$557$	21658.0	1.64754	0.823768	+	0.566927i	$0.191868\pi$
$558$	28063.0	2.12904
$559$	3735.02	0.282602
$560$	2338.00	0.176426
$561$	1952.44	0.146937
$562$	−13495.1	−1.01291
$563$	20210.5	1.51291	0.756456	−	0.654044i	$-0.226929\pi$
$563$	20210.5	1.51291	0.756456	+	0.654044i	$0.226929\pi$
$564$	−22017.7	−1.64382
$565$	1349.00	0.100447
$566$	−12657.5	−0.939989
$567$	10327.1	0.764901
$568$	6754.17	0.498941
$569$	2135.84	0.157362	0.0786811	−	0.996900i	$-0.474929\pi$
$569$	2135.84	0.157362	0.0786811	+	0.996900i	$0.474929\pi$
$570$	−5993.82	−0.440444
$571$	−16811.5	−1.23212	−0.616059	−	0.787700i	$-0.711272\pi$
$571$	−16811.5	−1.23212	−0.616059	+	0.787700i	$0.711272\pi$
$572$	−1365.64	−0.0998260
$573$	−5263.61	−0.383753
$574$	6095.76	0.443261
$575$	16939.1	1.22854
$576$	−11031.7	−0.798009
$577$	−736.875	−0.0531655	−0.0265827	−	0.999647i	$-0.508463\pi$
$577$	−736.875	−0.0531655	−0.0265827	+	0.999647i	$0.508463\pi$
$578$	21381.1	1.53864
$579$	36213.6	2.59928
$580$	−5622.94	−0.402551
$581$	11272.0	0.804889
$582$	−62403.0	−4.44448
$583$	3687.48	0.261955
$584$	40880.8	2.89668
$585$	−446.686	−0.0315696
$586$	−24164.5	−1.70346
$587$	−7792.25	−0.547905	−0.273953	−	0.961743i	$-0.588331\pi$
$587$	−7792.25	−0.547905	−0.273953	+	0.961743i	$0.588331\pi$
$588$	18086.2	1.26847
$589$	−15889.4	−1.11156
$590$	7358.72	0.513481
$591$	13633.0	0.948878
$592$	−252.713	−0.0175447
$593$	−16000.6	−1.10804	−0.554019	−	0.832504i	$-0.686906\pi$
$593$	−16000.6	−1.10804	−0.554019	+	0.832504i	$0.686906\pi$
$594$	226.067	0.0156155
$595$	755.051	0.0520237
$596$	42403.0	2.91425
$597$	−34989.8	−2.39872
$598$	5267.02	0.360175
$599$	−44.8483	−0.00305919	−0.00152959	−	0.999999i	$-0.500487\pi$
$599$	−44.8483	−0.00305919	−0.00152959	+	0.999999i	$0.500487\pi$
$600$	−36682.5	−2.49593
$601$	9248.06	0.627681	0.313840	−	0.949476i	$-0.398384\pi$
$601$	9248.06	0.627681	0.313840	+	0.949476i	$0.398384\pi$
$602$	33986.7	2.30099
$603$	−4347.05	−0.293575
$604$	−52222.2	−3.51803
$605$	−271.072	−0.0182159
$606$	−64802.8	−4.34395
$607$	29386.6	1.96502	0.982510	−	0.186209i	$-0.0596203\pi$
$607$	29386.6	1.96502	0.982510	+	0.186209i	$0.0596203\pi$
$608$	−2755.81	−0.183821
$609$	15473.6	1.02959
$610$	5646.65	0.374797
$611$	1380.67	0.0914175
$612$	10562.6	0.697660
$613$	−4271.35	−0.281433	−0.140716	−	0.990050i	$-0.544941\pi$
$613$	−4271.35	−0.281433	−0.140716	+	0.990050i	$0.544941\pi$
$614$	25820.8	1.69714
$615$	1454.21	0.0953489
$616$	−6386.04	−0.417696
$617$	20742.6	1.35343	0.676714	−	0.736246i	$-0.263403\pi$
$617$	20742.6	1.35343	0.676714	+	0.736246i	$0.263403\pi$
$618$	−21926.7	−1.42722
$619$	17702.3	1.14946	0.574731	−	0.818343i	$-0.305107\pi$
$619$	17702.3	1.14946	0.574731	+	0.818343i	$0.305107\pi$
$620$	7915.34	0.512722
$621$	−586.699	−0.0379121
$622$	−12379.0	−0.797996
$623$	−12293.8	−0.790593
$624$	−4146.05	−0.265985
$625$	13768.1	0.881161
$626$	37896.5	2.41957
$627$	5951.01	0.379044
$628$	−10967.2	−0.696875
$629$	−81.6129	−0.00517348
$630$	−4064.61	−0.257044
$631$	18690.9	1.17919	0.589597	−	0.807697i	$-0.299286\pi$
$631$	18690.9	1.17919	0.589597	+	0.807697i	$0.299286\pi$
$632$	−31148.9	−1.96050
$633$	−4809.51	−0.301992
$634$	−36882.0	−2.31037
$635$	1576.02	0.0984920
$636$	40327.3	2.51428
$637$	−1134.14	−0.0705436
$638$	8296.57	0.514835
$639$	−4268.21	−0.264238
$640$	−5291.41	−0.326815
$641$	9924.58	0.611540	0.305770	−	0.952105i	$-0.401086\pi$
$641$	9924.58	0.611540	0.305770	+	0.952105i	$0.401086\pi$
$642$	−47405.9	−2.91427
$643$	−13321.3	−0.817015	−0.408507	−	0.912755i	$-0.633951\pi$
$643$	−13321.3	−0.817015	−0.408507	+	0.912755i	$0.633951\pi$
$644$	32250.2	1.97335
$645$	8107.92	0.494960
$646$	−8887.73	−0.541305
$647$	−11917.0	−0.724119	−0.362059	−	0.932155i	$-0.617926\pi$
$647$	−11917.0	−0.724119	−0.362059	+	0.932155i	$0.617926\pi$
$648$	31119.7	1.88657
$649$	−7306.17	−0.441899
$650$	4476.11	0.270104
$651$	−21782.0	−1.31137
$652$	8700.10	0.522580
$653$	−2202.96	−0.132019	−0.0660096	−	0.997819i	$-0.521027\pi$
$653$	−2202.96	−0.132019	−0.0660096	+	0.997819i	$0.521027\pi$
$654$	−58427.8	−3.49344
$655$	293.475	0.0175069
$656$	6677.05	0.397401
$657$	−25834.1	−1.53407
$658$	12563.4	0.744335
$659$	4900.46	0.289673	0.144837	−	0.989456i	$-0.453734\pi$
$659$	4900.46	0.289673	0.144837	+	0.989456i	$0.453734\pi$
$660$	−2964.52	−0.174839
$661$	−11178.1	−0.657756	−0.328878	−	0.944372i	$-0.606670\pi$
$661$	−11178.1	−0.657756	−0.328878	+	0.944372i	$0.606670\pi$
$662$	27498.1	1.61442
$663$	−1338.95	−0.0784324
$664$	33966.9	1.98520
$665$	2301.39	0.134202
$666$	439.340	0.0255617
$667$	−21531.7	−1.24994
$668$	−29678.9	−1.71903
$669$	−2890.03	−0.167018
$670$	−1822.13	−0.105067
$671$	−5606.32	−0.322548
$672$	−3777.81	−0.216863
$673$	−24078.8	−1.37915	−0.689576	−	0.724213i	$-0.742203\pi$
$673$	−24078.8	−1.37915	−0.689576	+	0.724213i	$0.742203\pi$
$674$	28420.5	1.62421
$675$	−498.598	−0.0284312
$676$	−35220.6	−2.00390
$677$	3578.22	0.203135	0.101567	−	0.994829i	$-0.467614\pi$
$677$	3578.22	0.203135	0.101567	+	0.994829i	$0.467614\pi$
$678$	−21767.9	−1.23302
$679$	23960.3	1.35421
$680$	2275.27	0.128312
$681$	−34269.0	−1.92833
$682$	−11679.0	−0.655736
$683$	11339.2	0.635260	0.317630	−	0.948215i	$-0.397113\pi$
$683$	11339.2	0.635260	0.317630	+	0.948215i	$0.397113\pi$
$684$	32194.7	1.79970
$685$	−3519.89	−0.196333
$686$	−33864.7	−1.88478
$687$	−41864.9	−2.32496
$688$	37227.7	2.06292
$689$	−2528.82	−0.139826
$690$	11433.6	0.630823
$691$	−23994.4	−1.32097	−0.660485	−	0.750839i	$-0.729649\pi$
$691$	−23994.4	−1.32097	−0.660485	+	0.750839i	$0.729649\pi$
$692$	−59877.0	−3.28928
$693$	4035.58	0.221211
$694$	−23705.7	−1.29662
$695$	−2231.96	−0.121817
$696$	46627.9	2.53941
$697$	2156.33	0.117184
$698$	−53295.1	−2.89004
$699$	−4685.53	−0.253538
$700$	27407.4	1.47986
$701$	−34598.6	−1.86415	−0.932076	−	0.362263i	$-0.882004\pi$
$701$	−34598.6	−1.86415	−0.932076	+	0.362263i	$0.882004\pi$
$702$	−155.033	−0.00833526
$703$	−248.755	−0.0133456
$704$	4591.06	0.245784
$705$	2997.14	0.160112
$706$	−6070.80	−0.323623
$707$	24881.8	1.32358
$708$	−79902.3	−4.24140
$709$	−34436.3	−1.82409	−0.912047	−	0.410086i	$-0.865499\pi$
$709$	−34436.3	−1.82409	−0.912047	+	0.410086i	$0.865499\pi$
$710$	−1789.08	−0.0945676
$711$	19684.2	1.03828
$712$	−37046.0	−1.94994
$713$	30309.9	1.59202
$714$	−12183.8	−0.638608
$715$	185.898	0.00972332
$716$	51186.6	2.67169
$717$	18689.8	0.973477
$718$	248.259	0.0129038
$719$	21957.9	1.13893	0.569466	−	0.822015i	$-0.307150\pi$
$719$	21957.9	1.13893	0.569466	+	0.822015i	$0.307150\pi$
$720$	−4452.21	−0.230450
$721$	8418.99	0.434868
$722$	6831.11	0.352116
$723$	52587.4	2.70505
$724$	−49686.4	−2.55052
$725$	−18298.4	−0.937360
$726$	4374.11	0.223607
$727$	−6036.98	−0.307977	−0.153988	−	0.988073i	$-0.549212\pi$
$727$	−6036.98	−0.307977	−0.153988	+	0.988073i	$0.549212\pi$
$728$	4379.46	0.222958
$729$	−18845.6	−0.957454
$730$	−10828.7	−0.549027
$731$	12022.6	0.608304
$732$	−61312.3	−3.09586
$733$	11982.5	0.603796	0.301898	−	0.953340i	$-0.402380\pi$
$733$	11982.5	0.603796	0.301898	+	0.953340i	$0.402380\pi$
$734$	−19031.9	−0.957056
$735$	−2461.97	−0.123553
$736$	5256.87	0.263276
$737$	1809.11	0.0904200
$738$	−11608.0	−0.578993
$739$	15588.5	0.775956	0.387978	−	0.921669i	$-0.373174\pi$
$739$	15588.5	0.775956	0.387978	+	0.921669i	$0.373174\pi$
$740$	123.919	0.00615586
$741$	−4081.12	−0.202326
$742$	−23010.9	−1.13849
$743$	16736.4	0.826379	0.413190	−	0.910645i	$-0.364415\pi$
$743$	16736.4	0.826379	0.413190	+	0.910645i	$0.364415\pi$
$744$	−65637.6	−3.23440
$745$	−5772.09	−0.283856
$746$	−32459.2	−1.59305
$747$	−21465.0	−1.05135
$748$	−4395.84	−0.214877
$749$	18202.0	0.887966
$750$	19839.8	0.965928
$751$	−33499.9	−1.62774	−0.813868	−	0.581050i	$-0.802642\pi$
$751$	−33499.9	−1.62774	−0.813868	+	0.581050i	$0.802642\pi$
$752$	13761.4	0.667325
$753$	−10869.2	−0.526024
$754$	−5689.68	−0.274809
$755$	7108.71	0.342666
$756$	−949.276	−0.0456678
$757$	−13014.6	−0.624864	−0.312432	−	0.949940i	$-0.601144\pi$
$757$	−13014.6	−0.624864	−0.312432	+	0.949940i	$0.601144\pi$
$758$	−24958.8	−1.19597
$759$	−11351.9	−0.542883
$760$	6935.00	0.330998
$761$	−31719.1	−1.51093	−0.755463	−	0.655191i	$-0.772588\pi$
$761$	−31719.1	−1.51093	−0.755463	+	0.655191i	$0.772588\pi$
$762$	−25431.2	−1.20902
$763$	22434.0	1.06444
$764$	11850.8	0.561189
$765$	−1437.83	−0.0679539
$766$	46754.5	2.20537
$767$	5010.47	0.235877
$768$	60977.3	2.86501
$769$	22194.3	1.04076	0.520382	−	0.853934i	$-0.325790\pi$
$769$	22194.3	1.04076	0.520382	+	0.853934i	$0.325790\pi$
$770$	1691.57	0.0791687
$771$	−32956.8	−1.53944
$772$	−81533.6	−3.80111
$773$	22082.8	1.02751	0.513754	−	0.857937i	$-0.328254\pi$
$773$	22082.8	1.02751	0.513754	+	0.857937i	$0.328254\pi$
$774$	−64720.1	−3.00558
$775$	25758.5	1.19390
$776$	72201.8	3.34007
$777$	−341.007	−0.0157446
$778$	13137.0	0.605379
$779$	6572.49	0.302290
$780$	2033.03	0.0933257
$781$	1776.30	0.0813843
$782$	16953.9	0.775280
$783$	633.779	0.0289264
$784$	−11304.2	−0.514951
$785$	1492.90	0.0678775
$786$	−4735.61	−0.214903
$787$	42167.6	1.90993	0.954963	−	0.296726i	$-0.0958949\pi$
$787$	42167.6	1.90993	0.954963	+	0.296726i	$0.0958949\pi$
$788$	−30694.2	−1.38761
$789$	38943.4	1.75719
$790$	8250.89	0.371587
$791$	8358.02	0.375698
$792$	12160.8	0.545599
$793$	3844.74	0.172170
$794$	−1852.71	−0.0828087
$795$	−5489.52	−0.244897
$796$	78778.3	3.50782
$797$	33672.4	1.49654	0.748268	−	0.663397i	$-0.230886\pi$
$797$	33672.4	1.49654	0.748268	+	0.663397i	$0.230886\pi$
$798$	−37136.0	−1.64737
$799$	4444.22	0.196777
$800$	4467.48	0.197437
$801$	23410.7	1.03268
$802$	25890.1	1.13992
$803$	10751.4	0.472489
$804$	19785.0	0.867863
$805$	−4390.04	−0.192209
$806$	8009.29	0.350019
$807$	−1561.59	−0.0681174
$808$	74978.5	3.26452
$809$	−1719.77	−0.0747390	−0.0373695	−	0.999302i	$-0.511898\pi$
$809$	−1719.77	−0.0747390	−0.0373695	+	0.999302i	$0.511898\pi$
$810$	−8243.16	−0.357574
$811$	−34653.6	−1.50044	−0.750218	−	0.661191i	$-0.770051\pi$
$811$	−34653.6	−1.50044	−0.750218	+	0.661191i	$0.770051\pi$
$812$	−34838.2	−1.50564
$813$	−38774.5	−1.67267
$814$	−182.840	−0.00787291
$815$	−1184.30	−0.0509007
$816$	−13345.6	−0.572537
$817$	36644.7	1.56920
$818$	−72974.4	−3.11918
$819$	−2767.54	−0.118078
$820$	−3274.11	−0.139435
$821$	27117.4	1.15274	0.576372	−	0.817188i	$-0.304468\pi$
$821$	27117.4	1.15274	0.576372	+	0.817188i	$0.304468\pi$
$822$	56798.2	2.41005
$823$	42893.7	1.81674	0.908372	−	0.418164i	$-0.137326\pi$
$823$	42893.7	1.81674	0.908372	+	0.418164i	$0.137326\pi$
$824$	25369.7	1.07257
$825$	−9647.27	−0.407121
$826$	45592.6	1.92054
$827$	−17272.5	−0.726269	−0.363134	−	0.931737i	$-0.618293\pi$
$827$	−17272.5	−0.726269	−0.363134	+	0.931737i	$0.618293\pi$
$828$	−61413.3	−2.57761
$829$	8907.01	0.373164	0.186582	−	0.982439i	$-0.440259\pi$
$829$	8907.01	0.373164	0.186582	+	0.982439i	$0.440259\pi$
$830$	−8997.33	−0.376268
$831$	−13938.2	−0.581840
$832$	−3148.48	−0.131195
$833$	−3650.66	−0.151846
$834$	36015.6	1.49535
$835$	4040.02	0.167438
$836$	−13398.5	−0.554302
$837$	−892.163	−0.0368431
$838$	71954.4	2.96614
$839$	−17266.1	−0.710479	−0.355240	−	0.934775i	$-0.615601\pi$
$839$	−17266.1	−0.710479	−0.355240	+	0.934775i	$0.615601\pi$
$840$	9506.86	0.390497
$841$	−1129.51	−0.0463121
$842$	−63015.1	−2.57915
$843$	−19946.6	−0.814945
$844$	10828.4	0.441624
$845$	4794.38	0.195185
$846$	−23924.2	−0.972258
$847$	−1679.49	−0.0681321
$848$	−25205.2	−1.02070
$849$	−18708.5	−0.756273
$850$	14408.0	0.581402
$851$	474.516	0.0191142
$852$	19426.1	0.781137
$853$	−38427.5	−1.54248	−0.771238	−	0.636547i	$-0.780362\pi$
$853$	−38427.5	−1.54248	−0.771238	+	0.636547i	$0.780362\pi$
$854$	34985.1	1.40183
$855$	−4382.49	−0.175296
$856$	54849.8	2.19010
$857$	−36373.5	−1.44982	−0.724910	−	0.688843i	$-0.758119\pi$
$857$	−36373.5	−1.44982	−0.724910	+	0.688843i	$0.758119\pi$
$858$	−2999.71	−0.119357
$859$	−22342.8	−0.887457	−0.443729	−	0.896161i	$-0.646345\pi$
$859$	−22342.8	−0.887457	−0.443729	+	0.896161i	$0.646345\pi$
$860$	−18254.7	−0.723814
$861$	9009.91	0.356628
$862$	9370.45	0.370254
$863$	13259.9	0.523026	0.261513	−	0.965200i	$-0.415779\pi$
$863$	13259.9	0.523026	0.261513	+	0.965200i	$0.415779\pi$
$864$	−154.735	−0.00609280
$865$	8150.71	0.320384
$866$	79075.8	3.10289
$867$	31602.6	1.23792
$868$	49041.3	1.91771
$869$	−8191.96	−0.319785
$870$	−12351.1	−0.481310
$871$	−1240.66	−0.0482644
$872$	67602.4	2.62535
$873$	−45627.0	−1.76889
$874$	51675.3	1.99993
$875$	−7617.70	−0.294314
$876$	117580.	4.53501
$877$	12316.4	0.474226	0.237113	−	0.971482i	$-0.423799\pi$
$877$	12316.4	0.474226	0.237113	+	0.971482i	$0.423799\pi$
$878$	4620.82	0.177614
$879$	−35716.6	−1.37053
$880$	1852.88	0.0709778
$881$	−16361.2	−0.625679	−0.312840	−	0.949806i	$-0.601280\pi$
$881$	−16361.2	−0.625679	−0.312840	+	0.949806i	$0.601280\pi$
$882$	19652.3	0.750257
$883$	52337.6	1.99468	0.997339	−	0.0729101i	$-0.0232286\pi$
$883$	52337.6	1.99468	0.997339	+	0.0729101i	$0.0232286\pi$
$884$	3014.61	0.114697
$885$	10876.6	0.413124
$886$	−46848.8	−1.77643
$887$	37866.3	1.43340	0.716700	−	0.697381i	$-0.245652\pi$
$887$	37866.3	1.43340	0.716700	+	0.697381i	$0.245652\pi$
$888$	−1027.59	−0.0388329
$889$	9764.58	0.368384
$890$	9812.93	0.369585
$891$	8184.29	0.307726
$892$	6506.80	0.244242
$893$	13545.9	0.507612
$894$	93140.4	3.48443
$895$	−6967.74	−0.260230
$896$	−32784.1	−1.22237
$897$	7784.98	0.289780
$898$	−29840.5	−1.10890
$899$	−32742.1	−1.21470
$900$	−52191.3	−1.93301
$901$	−8139.96	−0.300978
$902$	4830.91	0.178328
$903$	50234.5	1.85127
$904$	25186.0	0.926630
$905$	6763.52	0.248428
$906$	−114709.	−4.20633
$907$	−7067.35	−0.258729	−0.129365	−	0.991597i	$-0.541294\pi$
$907$	−7067.35	−0.258729	−0.129365	+	0.991597i	$0.541294\pi$
$908$	77155.5	2.81993
$909$	−47381.7	−1.72888
$910$	−1160.05	−0.0422587
$911$	38096.9	1.38552	0.692759	−	0.721169i	$-0.256395\pi$
$911$	38096.9	1.38552	0.692759	+	0.721169i	$0.256395\pi$
$912$	−40677.3	−1.47693
$913$	8933.08	0.323814
$914$	64795.7	2.34491
$915$	8346.10	0.301545
$916$	94257.4	3.39995
$917$	1818.29	0.0654800
$918$	−499.033	−0.0179418
$919$	−16221.9	−0.582274	−0.291137	−	0.956681i	$-0.594034\pi$
$919$	−16221.9	−0.582274	−0.291137	+	0.956681i	$0.594034\pi$
$920$	−13228.9	−0.474070
$921$	38164.8	1.36544
$922$	−37794.3	−1.34999
$923$	−1218.16	−0.0434414
$924$	−18367.3	−0.653941
$925$	403.261	0.0143342
$926$	19555.7	0.693995
$927$	−16032.1	−0.568029
$928$	−5678.71	−0.200876
$929$	48111.7	1.69913	0.849565	−	0.527483i	$-0.176864\pi$
$929$	48111.7	1.69913	0.849565	+	0.527483i	$0.176864\pi$
$930$	17386.4	0.613036
$931$	−11127.2	−0.391706
$932$	10549.3	0.370766
$933$	−18297.0	−0.642032
$934$	−89137.5	−3.12277
$935$	598.381	0.0209296
$936$	−8339.70	−0.291230
$937$	−27264.2	−0.950569	−0.475284	−	0.879832i	$-0.657655\pi$
$937$	−27264.2	−0.950569	−0.475284	+	0.879832i	$0.657655\pi$
$938$	−11289.4	−0.392976
$939$	56013.4	1.94668
$940$	−6747.96	−0.234143
$941$	35897.3	1.24359	0.621795	−	0.783180i	$-0.286404\pi$
$941$	35897.3	1.24359	0.621795	+	0.783180i	$0.286404\pi$
$942$	−24089.9	−0.833219
$943$	−12537.4	−0.432952
$944$	49940.3	1.72184
$945$	129.220	0.00444816
$946$	26934.6	0.925707
$947$	−28166.0	−0.966495	−0.483247	−	0.875484i	$-0.660543\pi$
$947$	−28166.0	−0.966495	−0.483247	+	0.875484i	$0.660543\pi$
$948$	−89589.6	−3.06934
$949$	−7373.16	−0.252205
$950$	43915.6	1.49980
$951$	−54514.0	−1.85882
$952$	14096.9	0.479920
$953$	−6991.34	−0.237641	−0.118820	−	0.992916i	$-0.537911\pi$
$953$	−6991.34	−0.237641	−0.118820	+	0.992916i	$0.537911\pi$
$954$	43819.2	1.48710
$955$	−1613.19	−0.0546613
$956$	−42079.4	−1.42358
$957$	12262.9	0.414213
$958$	−38916.2	−1.31245
$959$	−21808.3	−0.734334
$960$	−6834.68	−0.229780
$961$	16299.7	0.547136
$962$	125.389	0.00420241
$963$	−34661.7	−1.15987
$964$	−118399.	−3.95577
$965$	11098.7	0.370238
$966$	70839.2	2.35943
$967$	26728.7	0.888870	0.444435	−	0.895811i	$-0.353404\pi$
$967$	26728.7	0.888870	0.444435	+	0.895811i	$0.353404\pi$
$968$	−5060.96	−0.168043
$969$	−13136.6	−0.435510
$970$	−19125.2	−0.633065
$971$	53900.1	1.78140	0.890699	−	0.454593i	$-0.150215\pi$
$971$	53900.1	1.78140	0.890699	+	0.454593i	$0.150215\pi$
$972$	87659.1	2.89266
$973$	−13828.6	−0.455626
$974$	35335.1	1.16243
$975$	6615.97	0.217313
$976$	38321.3	1.25680
$977$	−45.6419	−0.00149459	−0.000747294	−	1.00000i	$-0.500238\pi$
$977$	−45.6419	−0.00149459	−0.000747294		1.00000i	$0.500238\pi$
$978$	19110.2	0.624823
$979$	−9742.85	−0.318062
$980$	5543.04	0.180680
$981$	−42720.5	−1.39038
$982$	24797.5	0.805826
$983$	−13959.8	−0.452950	−0.226475	−	0.974017i	$-0.572720\pi$
$983$	−13959.8	−0.452950	−0.226475	+	0.974017i	$0.572720\pi$
$984$	27150.4	0.879597
$985$	4178.23	0.135157
$986$	−18314.4	−0.591529
$987$	18569.5	0.598858
$988$	9188.50	0.295876
$989$	−69901.9	−2.24747
$990$	−3221.21	−0.103411
$991$	−527.755	−0.0169169	−0.00845847	−	0.999964i	$-0.502692\pi$
$991$	−527.755	−0.0169169	−0.00845847	+	0.999964i	$0.502692\pi$
$992$	7993.86	0.255852
$993$	40643.9	1.29889
$994$	−11084.6	−0.353706
$995$	−10723.6	−0.341671
$996$	97694.6	3.10801
$997$	37173.1	1.18083	0.590413	−	0.807101i	$-0.298965\pi$
$997$	37173.1	1.18083	0.590413	+	0.807101i	$0.298965\pi$
$998$	53720.8	1.70391
$999$	−13.9672	−0.000442346 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.8	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.8	✓	84	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)

\(f(q)\)	\(=\)	\(q-4.94545 q^{2} -7.30968 q^{3} +16.4575 q^{4} -2.24027 q^{5} +36.1497 q^{6} -13.8801 q^{7} -41.8261 q^{8} +26.4315 q^{9} +O(q^{10})\)	\(q-4.94545 q^{2} -7.30968 q^{3} +16.4575 q^{4} -2.24027 q^{5} +36.1497 q^{6} -13.8801 q^{7} -41.8261 q^{8} +26.4315 q^{9} +11.0791 q^{10} -11.0000 q^{11} -120.299 q^{12} +7.54365 q^{13} +68.6432 q^{14} +16.3756 q^{15} +75.1890 q^{16} +24.2821 q^{17} -130.716 q^{18} +74.0115 q^{19} -36.8691 q^{20} +101.459 q^{21} +54.4000 q^{22} -141.181 q^{23} +305.736 q^{24} -119.981 q^{25} -37.3068 q^{26} +4.15564 q^{27} -228.431 q^{28} +152.511 q^{29} -80.9849 q^{30} -214.687 q^{31} -37.2349 q^{32} +80.4065 q^{33} -120.086 q^{34} +31.0950 q^{35} +434.996 q^{36} -3.36104 q^{37} -366.020 q^{38} -55.1417 q^{39} +93.7016 q^{40} +88.8035 q^{41} -501.760 q^{42} +495.121 q^{43} -181.032 q^{44} -59.2135 q^{45} +698.206 q^{46} +183.025 q^{47} -549.608 q^{48} -150.344 q^{49} +593.361 q^{50} -177.494 q^{51} +124.150 q^{52} -335.225 q^{53} -20.5515 q^{54} +24.6429 q^{55} +580.549 q^{56} -541.001 q^{57} -754.234 q^{58} +664.197 q^{59} +269.502 q^{60} +509.666 q^{61} +1061.73 q^{62} -366.871 q^{63} -417.369 q^{64} -16.8998 q^{65} -397.647 q^{66} -164.465 q^{67} +399.622 q^{68} +1031.99 q^{69} -153.779 q^{70} -161.482 q^{71} -1105.53 q^{72} -977.400 q^{73} +16.6218 q^{74} +877.025 q^{75} +1218.04 q^{76} +152.681 q^{77} +272.701 q^{78} +744.724 q^{79} -168.443 q^{80} -744.027 q^{81} -439.174 q^{82} -812.098 q^{83} +1669.76 q^{84} -54.3982 q^{85} -2448.60 q^{86} -1114.80 q^{87} +460.087 q^{88} +885.714 q^{89} +292.838 q^{90} -104.706 q^{91} -2323.49 q^{92} +1569.30 q^{93} -905.140 q^{94} -165.805 q^{95} +272.175 q^{96} -1726.24 q^{97} +743.518 q^{98} -290.746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * q^99

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