LMFDB - Embedded newform 1441.4.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-4.62908 q^{2} -6.73541 q^{3} +13.4284 q^{4} -11.7563 q^{5} +31.1787 q^{6} +27.0401 q^{7} -25.1283 q^{8} +18.3657 q^{9} +O(q^{10})$	\(q-4.62908 q^{2} -6.73541 q^{3} +13.4284 q^{4} -11.7563 q^{5} +31.1787 q^{6} +27.0401 q^{7} -25.1283 q^{8} +18.3657 q^{9} +54.4209 q^{10} -11.0000 q^{11} -90.4455 q^{12} -43.8094 q^{13} -125.171 q^{14} +79.1835 q^{15} +8.89397 q^{16} -44.6836 q^{17} -85.0162 q^{18} -123.721 q^{19} -157.868 q^{20} -182.126 q^{21} +50.9199 q^{22} +124.236 q^{23} +169.249 q^{24} +13.2108 q^{25} +202.797 q^{26} +58.1555 q^{27} +363.104 q^{28} +203.254 q^{29} -366.547 q^{30} -21.3886 q^{31} +159.856 q^{32} +74.0895 q^{33} +206.844 q^{34} -317.891 q^{35} +246.621 q^{36} +45.4643 q^{37} +572.712 q^{38} +295.074 q^{39} +295.416 q^{40} -243.062 q^{41} +843.075 q^{42} -136.258 q^{43} -147.712 q^{44} -215.913 q^{45} -575.096 q^{46} +498.085 q^{47} -59.9045 q^{48} +388.166 q^{49} -61.1538 q^{50} +300.962 q^{51} -588.288 q^{52} +322.808 q^{53} -269.207 q^{54} +129.319 q^{55} -679.471 q^{56} +833.308 q^{57} -940.877 q^{58} -584.979 q^{59} +1063.30 q^{60} -676.674 q^{61} +99.0096 q^{62} +496.610 q^{63} -811.135 q^{64} +515.037 q^{65} -342.966 q^{66} -973.369 q^{67} -600.027 q^{68} -836.777 q^{69} +1471.54 q^{70} -5.17174 q^{71} -461.499 q^{72} -776.717 q^{73} -210.458 q^{74} -88.9800 q^{75} -1661.36 q^{76} -297.441 q^{77} -1365.92 q^{78} +843.364 q^{79} -104.560 q^{80} -887.575 q^{81} +1125.15 q^{82} -863.577 q^{83} -2445.65 q^{84} +525.314 q^{85} +630.750 q^{86} -1369.00 q^{87} +276.411 q^{88} +638.508 q^{89} +999.477 q^{90} -1184.61 q^{91} +1668.28 q^{92} +144.061 q^{93} -2305.68 q^{94} +1454.50 q^{95} -1076.69 q^{96} +184.708 q^{97} -1796.85 q^{98} -202.023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.62908	−1.63663	−0.818313	−	0.574773i	$-0.805090\pi$
$2$	−4.62908	−1.63663	−0.818313	+	0.574773i	$0.805090\pi$
$3$	−6.73541	−1.29623	−0.648115	−	0.761543i	$-0.724442\pi$
$3$	−6.73541	−1.29623	−0.648115	+	0.761543i	$0.724442\pi$
$4$	13.4284	1.67854
$5$	−11.7563	−1.05152	−0.525758	−	0.850634i	$-0.676218\pi$
$5$	−11.7563	−1.05152	−0.525758	+	0.850634i	$0.676218\pi$
$6$	31.1787	2.12144
$7$	27.0401	1.46003	0.730013	−	0.683433i	$-0.239514\pi$
$7$	27.0401	1.46003	0.730013	+	0.683433i	$0.239514\pi$
$8$	−25.1283	−1.11052
$9$	18.3657	0.680211
$10$	54.4209	1.72094
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−90.4455	−2.17578
$13$	−43.8094	−0.934657	−0.467328	−	0.884084i	$-0.654783\pi$
$13$	−43.8094	−0.934657	−0.467328	+	0.884084i	$0.654783\pi$
$14$	−125.171	−2.38952
$15$	79.1835	1.36301
$16$	8.89397	0.138968
$17$	−44.6836	−0.637492	−0.318746	−	0.947840i	$-0.603262\pi$
$17$	−44.6836	−0.637492	−0.318746	+	0.947840i	$0.603262\pi$
$18$	−85.0162	−1.11325
$19$	−123.721	−1.49387	−0.746933	−	0.664900i	$-0.768474\pi$
$19$	−123.721	−1.49387	−0.746933	+	0.664900i	$0.768474\pi$
$20$	−157.868	−1.76502
$21$	−182.126	−1.89253
$22$	50.9199	0.493461
$23$	124.236	1.12630	0.563150	−	0.826354i	$-0.309589\pi$
$23$	124.236	1.12630	0.563150	+	0.826354i	$0.309589\pi$
$24$	169.249	1.43949
$25$	13.2108	0.105686
$26$	202.797	1.52968
$27$	58.1555	0.414520
$28$	363.104	2.45072
$29$	203.254	1.30149	0.650746	−	0.759295i	$-0.274456\pi$
$29$	203.254	1.30149	0.650746	+	0.759295i	$0.274456\pi$
$30$	−366.547	−2.23073
$31$	−21.3886	−0.123920	−0.0619598	−	0.998079i	$-0.519735\pi$
$31$	−21.3886	−0.123920	−0.0619598	+	0.998079i	$0.519735\pi$
$32$	159.856	0.883085
$33$	74.0895	0.390828
$34$	206.844	1.04334
$35$	−317.891	−1.53524
$36$	246.621	1.14176
$37$	45.4643	0.202008	0.101004	−	0.994886i	$-0.467795\pi$
$37$	45.4643	0.202008	0.101004	+	0.994886i	$0.467795\pi$
$38$	572.712	2.44490
$39$	295.074	1.21153
$40$	295.416	1.16773
$41$	−243.062	−0.925851	−0.462925	−	0.886397i	$-0.653200\pi$
$41$	−243.062	−0.925851	−0.462925	+	0.886397i	$0.653200\pi$
$42$	843.075	3.09736
$43$	−136.258	−0.483237	−0.241618	−	0.970371i	$-0.577678\pi$
$43$	−136.258	−0.483237	−0.241618	+	0.970371i	$0.577678\pi$
$44$	−147.712	−0.506100
$45$	−215.913	−0.715253
$46$	−575.096	−1.84333
$47$	498.085	1.54581	0.772906	−	0.634520i	$-0.218802\pi$
$47$	498.085	1.54581	0.772906	+	0.634520i	$0.218802\pi$
$48$	−59.9045	−0.180135
$49$	388.166	1.13168
$50$	−61.1538	−0.172969
$51$	300.962	0.826336
$52$	−588.288	−1.56886
$53$	322.808	0.836624	0.418312	−	0.908303i	$-0.362622\pi$
$53$	322.808	0.836624	0.418312	+	0.908303i	$0.362622\pi$
$54$	−269.207	−0.678414
$55$	129.319	0.317044
$56$	−679.471	−1.62140
$57$	833.308	1.93639
$58$	−940.877	−2.13006
$59$	−584.979	−1.29081	−0.645404	−	0.763841i	$-0.723311\pi$
$59$	−584.979	−1.29081	−0.645404	+	0.763841i	$0.723311\pi$
$60$	1063.30	2.28787
$61$	−676.674	−1.42032	−0.710158	−	0.704042i	$-0.751377\pi$
$61$	−676.674	−1.42032	−0.710158	+	0.704042i	$0.751377\pi$
$62$	99.0096	0.202810
$63$	496.610	0.993126
$64$	−811.135	−1.58425
$65$	515.037	0.982807
$66$	−342.966	−0.639639
$67$	−973.369	−1.77487	−0.887433	−	0.460937i	$-0.847513\pi$
$67$	−973.369	−1.77487	−0.887433	+	0.460937i	$0.847513\pi$
$68$	−600.027	−1.07006
$69$	−836.777	−1.45994
$70$	1471.54	2.51262
$71$	−5.17174	−0.00864469	−0.00432235	−	0.999991i	$-0.501376\pi$
$71$	−5.17174	−0.00864469	−0.00432235	+	0.999991i	$0.501376\pi$
$72$	−461.499	−0.755391
$73$	−776.717	−1.24531	−0.622656	−	0.782495i	$-0.713947\pi$
$73$	−776.717	−1.24531	−0.622656	+	0.782495i	$0.713947\pi$
$74$	−210.458	−0.330611
$75$	−88.9800	−0.136994
$76$	−1661.36	−2.50752
$77$	−297.441	−0.440215
$78$	−1365.92	−1.98282
$79$	843.364	1.20109	0.600543	−	0.799592i	$-0.294951\pi$
$79$	843.364	1.20109	0.600543	+	0.799592i	$0.294951\pi$
$80$	−104.560	−0.146127
$81$	−887.575	−1.21752
$82$	1125.15	1.51527
$83$	−863.577	−1.14205	−0.571023	−	0.820934i	$-0.693453\pi$
$83$	−863.577	−1.14205	−0.571023	+	0.820934i	$0.693453\pi$
$84$	−2445.65	−3.17670
$85$	525.314	0.670333
$86$	630.750	0.790878
$87$	−1369.00	−1.68703
$88$	276.411	0.334836
$89$	638.508	0.760469	0.380235	−	0.924890i	$-0.375843\pi$
$89$	638.508	0.760469	0.380235	+	0.924890i	$0.375843\pi$
$90$	999.477	1.17060
$91$	−1184.61	−1.36462
$92$	1668.28	1.89055
$93$	144.061	0.160628
$94$	−2305.68	−2.52992
$95$	1454.50	1.57082
$96$	−1076.69	−1.14468
$97$	184.708	0.193343	0.0966713	−	0.995316i	$-0.469180\pi$
$97$	184.708	0.193343	0.0966713	+	0.995316i	$0.469180\pi$
$98$	−1796.85	−1.85213
$99$	−202.023	−0.205091
$100$	177.399	0.177399
$101$	1128.66	1.11194	0.555970	−	0.831203i	$-0.312347\pi$
$101$	1128.66	1.11194	0.555970	+	0.831203i	$0.312347\pi$
$102$	−1393.18	−1.35240
$103$	−504.521	−0.482640	−0.241320	−	0.970446i	$-0.577580\pi$
$103$	−504.521	−0.482640	−0.241320	+	0.970446i	$0.577580\pi$
$104$	1100.86	1.03796
$105$	2141.13	1.99003
$106$	−1494.30	−1.36924
$107$	−1122.65	−1.01430	−0.507151	−	0.861857i	$-0.669301\pi$
$107$	−1122.65	−1.01430	−0.507151	+	0.861857i	$0.669301\pi$
$108$	780.934	0.695790
$109$	1049.34	0.922093	0.461047	−	0.887376i	$-0.347474\pi$
$109$	1049.34	0.922093	0.461047	+	0.887376i	$0.347474\pi$
$110$	−598.630	−0.518883
$111$	−306.221	−0.261849
$112$	240.494	0.202897
$113$	−2129.01	−1.77239	−0.886195	−	0.463312i	$-0.846661\pi$
$113$	−2129.01	−1.77239	−0.886195	+	0.463312i	$0.846661\pi$
$114$	−3857.45	−3.16915
$115$	−1460.55	−1.18432
$116$	2729.36	2.18461
$117$	−804.590	−0.635764
$118$	2707.91	2.11257
$119$	−1208.25	−0.930755
$120$	−1989.75	−1.51365
$121$	121.000	0.0909091
$122$	3132.38	2.32453
$123$	1637.12	1.20011
$124$	−287.214	−0.208005
$125$	1314.23	0.940385
$126$	−2298.85	−1.62538
$127$	686.003	0.479315	0.239657	−	0.970858i	$-0.422965\pi$
$127$	686.003	0.479315	0.239657	+	0.970858i	$0.422965\pi$
$128$	2475.96	1.70974
$129$	917.754	0.626386
$130$	−2384.15	−1.60849
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	994.900	0.656022
$133$	−3345.41	−2.18108
$134$	4505.80	2.90479
$135$	−683.695	−0.435875
$136$	1122.82	0.707950
$137$	3065.14	1.91148	0.955740	−	0.294213i	$-0.0950575\pi$
$137$	3065.14	1.91148	0.955740	+	0.294213i	$0.0950575\pi$
$138$	3873.51	2.38938
$139$	905.291	0.552416	0.276208	−	0.961098i	$-0.410922\pi$
$139$	905.291	0.552416	0.276208	+	0.961098i	$0.410922\pi$
$140$	−4268.76	−2.57697
$141$	−3354.81	−2.00373
$142$	23.9404	0.0141481
$143$	481.903	0.281810
$144$	163.344	0.0945277
$145$	−2389.51	−1.36854
$146$	3595.48	2.03811
$147$	−2614.45	−1.46691
$148$	610.511	0.339079
$149$	−591.697	−0.325327	−0.162664	−	0.986682i	$-0.552009\pi$
$149$	−591.697	−0.325327	−0.162664	+	0.986682i	$0.552009\pi$
$150$	411.896	0.224208
$151$	−2698.55	−1.45433	−0.727167	−	0.686460i	$-0.759164\pi$
$151$	−2698.55	−1.45433	−0.727167	+	0.686460i	$0.759164\pi$
$152$	3108.89	1.65897
$153$	−820.645	−0.433629
$154$	1376.88	0.720467
$155$	251.451	0.130304
$156$	3962.36	2.03361
$157$	−3823.39	−1.94356	−0.971782	−	0.235879i	$-0.924203\pi$
$157$	−3823.39	−1.94356	−0.971782	+	0.235879i	$0.924203\pi$
$158$	−3904.00	−1.96573
$159$	−2174.24	−1.08446
$160$	−1879.31	−0.928579
$161$	3359.34	1.64443
$162$	4108.65	1.99263
$163$	−1755.02	−0.843335	−0.421668	−	0.906750i	$-0.638555\pi$
$163$	−1755.02	−0.843335	−0.421668	+	0.906750i	$0.638555\pi$
$164$	−3263.92	−1.55408
$165$	−871.019	−0.410962
$166$	3997.56	1.86910
$167$	−3731.60	−1.72910	−0.864551	−	0.502545i	$-0.832397\pi$
$167$	−3731.60	−1.72910	−0.864551	+	0.502545i	$0.832397\pi$
$168$	4576.51	2.10170
$169$	−277.737	−0.126416
$170$	−2431.72	−1.09708
$171$	−2272.21	−1.01614
$172$	−1829.72	−0.811134
$173$	−3938.60	−1.73090	−0.865451	−	0.500994i	$-0.832968\pi$
$173$	−3938.60	−1.73090	−0.865451	+	0.500994i	$0.832968\pi$
$174$	6337.19	2.76104
$175$	357.221	0.154305
$176$	−97.8337	−0.0419005
$177$	3940.07	1.67318
$178$	−2955.71	−1.24460
$179$	413.813	0.172792	0.0863962	−	0.996261i	$-0.472465\pi$
$179$	413.813	0.172792	0.0863962	+	0.996261i	$0.472465\pi$
$180$	−2899.35	−1.20058
$181$	−307.486	−0.126272	−0.0631360	−	0.998005i	$-0.520110\pi$
$181$	−307.486	−0.126272	−0.0631360	+	0.998005i	$0.520110\pi$
$182$	5483.65	2.23338
$183$	4557.68	1.84106
$184$	−3121.83	−1.25078
$185$	−534.493	−0.212415
$186$	−666.870	−0.262889
$187$	491.519	0.192211
$188$	6688.47	2.59472
$189$	1572.53	0.605210
$190$	−6732.98	−2.57085
$191$	−620.707	−0.235146	−0.117573	−	0.993064i	$-0.537511\pi$
$191$	−620.707	−0.235146	−0.117573	+	0.993064i	$0.537511\pi$
$192$	5463.33	2.05355
$193$	1775.81	0.662311	0.331155	−	0.943576i	$-0.392562\pi$
$193$	1775.81	0.662311	0.331155	+	0.943576i	$0.392562\pi$
$194$	−855.027	−0.316430
$195$	−3468.98	−1.27394
$196$	5212.43	1.89957
$197$	−512.146	−0.185223	−0.0926115	−	0.995702i	$-0.529521\pi$
$197$	−512.146	−0.185223	−0.0926115	+	0.995702i	$0.529521\pi$
$198$	935.179	0.335658
$199$	−2346.75	−0.835964	−0.417982	−	0.908455i	$-0.637262\pi$
$199$	−2346.75	−0.835964	−0.417982	+	0.908455i	$0.637262\pi$
$200$	−331.965	−0.117367
$201$	6556.04	2.30063
$202$	−5224.65	−1.81983
$203$	5496.00	1.90021
$204$	4041.43	1.38704
$205$	2857.51	0.973547
$206$	2335.47	0.789902
$207$	2281.67	0.766122
$208$	−389.639	−0.129888
$209$	1360.93	0.450417
$210$	−9911.45	−3.25693
$211$	2251.92	0.734733	0.367366	−	0.930076i	$-0.380260\pi$
$211$	2251.92	0.734733	0.367366	+	0.930076i	$0.380260\pi$
$212$	4334.78	1.40431
$213$	34.8338	0.0112055
$214$	5196.82	1.66003
$215$	1601.89	0.508131
$216$	−1461.35	−0.460335
$217$	−578.350	−0.180926
$218$	−4857.46	−1.50912
$219$	5231.50	1.61421
$220$	1736.55	0.532173
$221$	1957.56	0.595836
$222$	1417.52	0.428548
$223$	−3773.27	−1.13308	−0.566540	−	0.824035i	$-0.691718\pi$
$223$	−3773.27	−1.13308	−0.566540	+	0.824035i	$0.691718\pi$
$224$	4322.51	1.28933
$225$	242.625	0.0718890
$226$	9855.34	2.90074
$227$	−3192.85	−0.933555	−0.466778	−	0.884375i	$-0.654585\pi$
$227$	−3192.85	−0.933555	−0.466778	+	0.884375i	$0.654585\pi$
$228$	11190.0	3.25032
$229$	−4499.62	−1.29844	−0.649222	−	0.760599i	$-0.724905\pi$
$229$	−4499.62	−1.29844	−0.649222	+	0.760599i	$0.724905\pi$
$230$	6761.01	1.93829
$231$	2003.38	0.570619
$232$	−5107.42	−1.44534
$233$	4162.38	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$233$	4162.38	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$234$	3724.51	1.04051
$235$	−5855.64	−1.62545
$236$	−7855.30	−2.16668
$237$	−5680.40	−1.55688
$238$	5593.07	1.52330
$239$	3221.78	0.871965	0.435982	−	0.899955i	$-0.356401\pi$
$239$	3221.78	0.871965	0.435982	+	0.899955i	$0.356401\pi$
$240$	704.256	0.189415
$241$	6802.95	1.81833	0.909164	−	0.416439i	$-0.136722\pi$
$241$	6802.95	1.81833	0.909164	+	0.416439i	$0.136722\pi$
$242$	−560.118	−0.148784
$243$	4407.98	1.16367
$244$	−9086.63	−2.38406
$245$	−4563.39	−1.18998
$246$	−7578.35	−1.96414
$247$	5420.12	1.39625
$248$	537.460	0.137616
$249$	5816.54	1.48035
$250$	−6083.67	−1.53906
$251$	−1847.25	−0.464532	−0.232266	−	0.972652i	$-0.574614\pi$
$251$	−1847.25	−0.464532	−0.232266	+	0.972652i	$0.574614\pi$
$252$	6668.65	1.66701
$253$	−1366.59	−0.339592
$254$	−3175.56	−0.784459
$255$	−3538.20	−0.868905
$256$	−4972.35	−1.21395
$257$	−1758.35	−0.426780	−0.213390	−	0.976967i	$-0.568451\pi$
$257$	−1758.35	−0.426780	−0.213390	+	0.976967i	$0.568451\pi$
$258$	−4248.35	−1.02516
$259$	1229.36	0.294937
$260$	6916.10	1.64969
$261$	3732.90	0.885289
$262$	606.409	0.142993
$263$	−1857.20	−0.435436	−0.217718	−	0.976012i	$-0.569861\pi$
$263$	−1857.20	−0.435436	−0.217718	+	0.976012i	$0.569861\pi$
$264$	−1861.74	−0.434024
$265$	−3795.03	−0.879724
$266$	15486.2	3.56962
$267$	−4300.61	−0.985743
$268$	−13070.8	−2.97919
$269$	5725.94	1.29783	0.648915	−	0.760860i	$-0.275223\pi$
$269$	5725.94	1.29783	0.648915	+	0.760860i	$0.275223\pi$
$270$	3164.88	0.713364
$271$	4166.27	0.933885	0.466943	−	0.884288i	$-0.345355\pi$
$271$	4166.27	0.933885	0.466943	+	0.884288i	$0.345355\pi$
$272$	−397.414	−0.0885911
$273$	7978.83	1.76887
$274$	−14188.8	−3.12838
$275$	−145.319	−0.0318656
$276$	−11236.5	−2.45058
$277$	258.437	0.0560576	0.0280288	−	0.999607i	$-0.491077\pi$
$277$	258.437	0.0560576	0.0280288	+	0.999607i	$0.491077\pi$
$278$	−4190.66	−0.904098
$279$	−392.817	−0.0842915
$280$	7988.07	1.70492
$281$	−8165.36	−1.73347	−0.866734	−	0.498770i	$-0.833785\pi$
$281$	−8165.36	−1.73347	−0.866734	+	0.498770i	$0.833785\pi$
$282$	15529.7	3.27935
$283$	−2271.83	−0.477195	−0.238598	−	0.971118i	$-0.576688\pi$
$283$	−2271.83	−0.477195	−0.238598	+	0.971118i	$0.576688\pi$
$284$	−69.4481	−0.0145105
$285$	−9796.63	−2.03615
$286$	−2230.77	−0.461217
$287$	−6572.41	−1.35177
$288$	2935.86	0.600684
$289$	−2916.38	−0.593604
$290$	11061.2	2.23979
$291$	−1244.08	−0.250616
$292$	−10430.0	−2.09031
$293$	−1813.88	−0.361665	−0.180832	−	0.983514i	$-0.557879\pi$
$293$	−1813.88	−0.361665	−0.180832	+	0.983514i	$0.557879\pi$
$294$	12102.5	2.40079
$295$	6877.19	1.35731
$296$	−1142.44	−0.224335
$297$	−639.711	−0.124982
$298$	2739.01	0.532439
$299$	−5442.69	−1.05270
$300$	−1194.86	−0.229950
$301$	−3684.43	−0.705538
$302$	12491.8	2.38020
$303$	−7601.98	−1.44133
$304$	−1100.37	−0.207600
$305$	7955.19	1.49349
$306$	3798.83	0.709688
$307$	1602.65	0.297941	0.148971	−	0.988842i	$-0.452404\pi$
$307$	1602.65	0.297941	0.148971	+	0.988842i	$0.452404\pi$
$308$	−3994.14	−0.738920
$309$	3398.15	0.625613
$310$	−1163.99	−0.213258
$311$	−5104.17	−0.930646	−0.465323	−	0.885141i	$-0.654062\pi$
$311$	−5104.17	−0.930646	−0.465323	+	0.885141i	$0.654062\pi$
$312$	−7414.71	−1.34543
$313$	5240.32	0.946328	0.473164	−	0.880974i	$-0.343112\pi$
$313$	5240.32	0.946328	0.473164	+	0.880974i	$0.343112\pi$
$314$	17698.8	3.18089
$315$	−5838.30	−1.04429
$316$	11325.0	2.01608
$317$	7647.78	1.35502	0.677511	−	0.735513i	$-0.263059\pi$
$317$	7647.78	1.35502	0.677511	+	0.735513i	$0.263059\pi$
$318$	10064.7	1.77485
$319$	−2235.79	−0.392415
$320$	9535.96	1.66586
$321$	7561.48	1.31477
$322$	−15550.6	−2.69132
$323$	5528.28	0.952327
$324$	−11918.7	−2.04367
$325$	−578.757	−0.0987805
$326$	8124.12	1.38022
$327$	−7067.71	−1.19524
$328$	6107.73	1.02818
$329$	13468.3	2.25693
$330$	4032.01	0.672591
$331$	6321.03	1.04965	0.524827	−	0.851209i	$-0.324130\pi$
$331$	6321.03	1.04965	0.524827	+	0.851209i	$0.324130\pi$
$332$	−11596.4	−1.91698
$333$	834.984	0.137408
$334$	17273.9	2.82989
$335$	11443.2	1.86630
$336$	−1619.82	−0.263002
$337$	−8552.05	−1.38237	−0.691186	−	0.722677i	$-0.742912\pi$
$337$	−8552.05	−1.38237	−0.691186	+	0.722677i	$0.742912\pi$
$338$	1285.66	0.206896
$339$	14339.7	2.29743
$340$	7054.11	1.12518
$341$	235.275	0.0373632
$342$	10518.3	1.66305
$343$	1221.28	0.192254
$344$	3423.94	0.536646
$345$	9837.41	1.53516
$346$	18232.1	2.83284
$347$	−3811.23	−0.589618	−0.294809	−	0.955556i	$-0.595256\pi$
$347$	−3811.23	−0.589618	−0.294809	+	0.955556i	$0.595256\pi$
$348$	−18383.4	−2.83176
$349$	−1760.72	−0.270056	−0.135028	−	0.990842i	$-0.543112\pi$
$349$	−1760.72	−0.270056	−0.135028	+	0.990842i	$0.543112\pi$
$350$	−1653.60	−0.252539
$351$	−2547.76	−0.387434
$352$	−1758.41	−0.266260
$353$	9169.13	1.38250	0.691252	−	0.722614i	$-0.257060\pi$
$353$	9169.13	1.38250	0.691252	+	0.722614i	$0.257060\pi$
$354$	−18238.9	−2.73838
$355$	60.8006	0.00909003
$356$	8574.12	1.27648
$357$	8138.04	1.20647
$358$	−1915.57	−0.282797
$359$	10751.3	1.58059	0.790294	−	0.612728i	$-0.209928\pi$
$359$	10751.3	1.58059	0.790294	+	0.612728i	$0.209928\pi$
$360$	5425.52	0.794306
$361$	8447.77	1.23163
$362$	1423.38	0.206660
$363$	−814.984	−0.117839
$364$	−15907.4	−2.29058
$365$	9131.32	1.30947
$366$	−21097.8	−3.01312
$367$	−1208.85	−0.171939	−0.0859693	−	0.996298i	$-0.527399\pi$
$367$	−1208.85	−0.171939	−0.0859693	+	0.996298i	$0.527399\pi$
$368$	1104.95	0.156520
$369$	−4464.00	−0.629774
$370$	2474.21	0.347643
$371$	8728.75	1.22149
$372$	1934.50	0.269622
$373$	7431.26	1.03157	0.515785	−	0.856718i	$-0.327500\pi$
$373$	7431.26	1.03157	0.515785	+	0.856718i	$0.327500\pi$
$374$	−2275.28	−0.314578
$375$	−8851.86	−1.21896
$376$	−12516.0	−1.71666
$377$	−8904.42	−1.21645
$378$	−7279.36	−0.990503
$379$	−7372.94	−0.999267	−0.499634	−	0.866237i	$-0.666532\pi$
$379$	−7372.94	−0.999267	−0.499634	+	0.866237i	$0.666532\pi$
$380$	19531.5	2.63670
$381$	−4620.51	−0.621302
$382$	2873.30	0.384845
$383$	3188.92	0.425446	0.212723	−	0.977112i	$-0.431767\pi$
$383$	3188.92	0.425446	0.212723	+	0.977112i	$0.431767\pi$
$384$	−16676.6	−2.21621
$385$	3496.81	0.462893
$386$	−8220.39	−1.08395
$387$	−2502.48	−0.328703
$388$	2480.32	0.324534
$389$	−13800.9	−1.79880	−0.899401	−	0.437126i	$-0.855997\pi$
$389$	−13800.9	−1.79880	−0.899401	+	0.437126i	$0.855997\pi$
$390$	16058.2	2.08497
$391$	−5551.29	−0.718008
$392$	−9753.94	−1.25676
$393$	882.338	0.113252
$394$	2370.77	0.303141
$395$	−9914.84	−1.26296
$396$	−2712.83	−0.344255
$397$	10719.6	1.35516	0.677582	−	0.735447i	$-0.263028\pi$
$397$	10719.6	1.35516	0.677582	+	0.735447i	$0.263028\pi$
$398$	10863.3	1.36816
$399$	22532.7	2.82718
$400$	117.496	0.0146870
$401$	7460.09	0.929025	0.464512	−	0.885567i	$-0.346230\pi$
$401$	7460.09	0.929025	0.464512	+	0.885567i	$0.346230\pi$
$402$	−30348.4	−3.76528
$403$	937.023	0.115822
$404$	15156.0	1.86644
$405$	10434.6	1.28025
$406$	−25441.4	−3.10994
$407$	−500.108	−0.0609077
$408$	−7562.67	−0.917666
$409$	9708.47	1.17372	0.586862	−	0.809687i	$-0.300363\pi$
$409$	9708.47	1.17372	0.586862	+	0.809687i	$0.300363\pi$
$410$	−13227.6	−1.59333
$411$	−20645.0	−2.47772
$412$	−6774.89	−0.810133
$413$	−15817.9	−1.88462
$414$	−10562.0	−1.25386
$415$	10152.5	1.20088
$416$	−7003.17	−0.825382
$417$	−6097.50	−0.716057
$418$	−6299.83	−0.737165
$419$	13511.2	1.57534	0.787670	−	0.616097i	$-0.211287\pi$
$419$	13511.2	1.57534	0.787670	+	0.616097i	$0.211287\pi$
$420$	28751.8	3.34035
$421$	−2295.95	−0.265790	−0.132895	−	0.991130i	$-0.542427\pi$
$421$	−2295.95	−0.265790	−0.132895	+	0.991130i	$0.542427\pi$
$422$	−10424.3	−1.20248
$423$	9147.68	1.05148
$424$	−8111.62	−0.929092
$425$	−590.305	−0.0673742
$426$	−161.248	−0.0183392
$427$	−18297.3	−2.07370
$428$	−15075.3	−1.70255
$429$	−3245.81	−0.365290
$430$	−7415.29	−0.831621
$431$	−615.981	−0.0688417	−0.0344208	−	0.999407i	$-0.510959\pi$
$431$	−615.981	−0.0688417	−0.0344208	+	0.999407i	$0.510959\pi$
$432$	517.234	0.0576051
$433$	6660.59	0.739232	0.369616	−	0.929185i	$-0.379489\pi$
$433$	6660.59	0.739232	0.369616	+	0.929185i	$0.379489\pi$
$434$	2677.23	0.296108
$435$	16094.3	1.77394
$436$	14090.9	1.54778
$437$	−15370.5	−1.68254
$438$	−24217.0	−2.64186
$439$	8373.75	0.910381	0.455190	−	0.890394i	$-0.349571\pi$
$439$	8373.75	0.910381	0.455190	+	0.890394i	$0.349571\pi$
$440$	−3249.58	−0.352085
$441$	7128.93	0.769780
$442$	−9061.70	−0.975161
$443$	−9868.88	−1.05843	−0.529215	−	0.848488i	$-0.677514\pi$
$443$	−9868.88	−1.05843	−0.529215	+	0.848488i	$0.677514\pi$
$444$	−4112.04	−0.439525
$445$	−7506.50	−0.799646
$446$	17466.7	1.85443
$447$	3985.32	0.421699
$448$	−21933.2	−2.31305
$449$	11073.7	1.16392	0.581960	−	0.813218i	$-0.302286\pi$
$449$	11073.7	1.16392	0.581960	+	0.813218i	$0.302286\pi$
$450$	−1123.13	−0.117655
$451$	2673.68	0.279154
$452$	−28589.1	−2.97504
$453$	18175.8	1.88515
$454$	14780.0	1.52788
$455$	13926.6	1.43492
$456$	−20939.6	−2.15041
$457$	4354.01	0.445672	0.222836	−	0.974856i	$-0.428469\pi$
$457$	4354.01	0.445672	0.222836	+	0.974856i	$0.428469\pi$
$458$	20829.1	2.12507
$459$	−2598.60	−0.264253
$460$	−19612.8	−1.98794
$461$	−12110.5	−1.22352	−0.611760	−	0.791043i	$-0.709538\pi$
$461$	−12110.5	−1.22352	−0.611760	+	0.791043i	$0.709538\pi$
$462$	−9273.82	−0.933890
$463$	−13976.3	−1.40288	−0.701441	−	0.712727i	$-0.747460\pi$
$463$	−13976.3	−1.40288	−0.701441	+	0.712727i	$0.747460\pi$
$464$	1807.73	0.180866
$465$	−1693.63	−0.168903
$466$	−19268.0	−1.91539
$467$	15202.7	1.50642	0.753208	−	0.657783i	$-0.228505\pi$
$467$	15202.7	1.50642	0.753208	+	0.657783i	$0.228505\pi$
$468$	−10804.3	−1.06716
$469$	−26320.0	−2.59135
$470$	27106.2	2.66025
$471$	25752.1	2.51931
$472$	14699.5	1.43347
$473$	1498.84	0.145701
$474$	26295.0	2.54804
$475$	−1634.45	−0.157881
$476$	−16224.8	−1.56231
$477$	5928.59	0.569081
$478$	−14913.9	−1.42708
$479$	6768.73	0.645660	0.322830	−	0.946457i	$-0.395366\pi$
$479$	6768.73	0.645660	0.322830	+	0.946457i	$0.395366\pi$
$480$	12657.9	1.20365
$481$	−1991.76	−0.188808
$482$	−31491.4	−2.97592
$483$	−22626.5	−2.13156
$484$	1624.83	0.152595
$485$	−2171.48	−0.203303
$486$	−20404.9	−1.90449
$487$	18926.3	1.76105	0.880525	−	0.474000i	$-0.157190\pi$
$487$	18926.3	1.76105	0.880525	+	0.474000i	$0.157190\pi$
$488$	17003.7	1.57730
$489$	11820.8	1.09316
$490$	21124.3	1.94755
$491$	−11449.1	−1.05232	−0.526162	−	0.850384i	$-0.676369\pi$
$491$	−11449.1	−1.05232	−0.526162	+	0.850384i	$0.676369\pi$
$492$	21983.8	2.01445
$493$	−9082.11	−0.829691
$494$	−25090.2	−2.28514
$495$	2375.04	0.215657
$496$	−190.230	−0.0172209
$497$	−139.844	−0.0126215
$498$	−26925.2	−2.42279
$499$	19382.9	1.73888	0.869438	−	0.494042i	$-0.164481\pi$
$499$	19382.9	1.73888	0.869438	+	0.494042i	$0.164481\pi$
$500$	17647.9	1.57848
$501$	25133.9	2.24131
$502$	8551.08	0.760266
$503$	−18634.2	−1.65180	−0.825900	−	0.563816i	$-0.809333\pi$
$503$	−18634.2	−1.65180	−0.825900	+	0.563816i	$0.809333\pi$
$504$	−12479.0	−1.10289
$505$	−13268.9	−1.16922
$506$	6326.06	0.555786
$507$	1870.67	0.163865
$508$	9211.90	0.804551
$509$	−5785.64	−0.503819	−0.251910	−	0.967751i	$-0.581059\pi$
$509$	−5785.64	−0.503819	−0.251910	+	0.967751i	$0.581059\pi$
$510$	16378.6	1.42207
$511$	−21002.5	−1.81819
$512$	3209.67	0.277049
$513$	−7195.04	−0.619237
$514$	8139.52	0.698480
$515$	5931.31	0.507504
$516$	12323.9	1.05142
$517$	−5478.94	−0.466080
$518$	−5690.80	−0.482701
$519$	26528.0	2.24365
$520$	−12942.0	−1.09143
$521$	−14559.4	−1.22429	−0.612147	−	0.790744i	$-0.709694\pi$
$521$	−14559.4	−1.22429	−0.612147	+	0.790744i	$0.709694\pi$
$522$	−17279.9	−1.44889
$523$	−6339.09	−0.529998	−0.264999	−	0.964249i	$-0.585372\pi$
$523$	−6339.09	−0.529998	−0.264999	+	0.964249i	$0.585372\pi$
$524$	−1759.12	−0.146655
$525$	−2406.03	−0.200015
$526$	8597.12	0.712646
$527$	955.720	0.0789978
$528$	658.950	0.0543127
$529$	3267.49	0.268553
$530$	17567.5	1.43978
$531$	−10743.5	−0.878022
$532$	−44923.4	−3.66105
$533$	10648.4	0.865353
$534$	19907.9	1.61329
$535$	13198.2	1.06656
$536$	24459.1	1.97103
$537$	−2787.20	−0.223979
$538$	−26505.8	−2.12406
$539$	−4269.82	−0.341214
$540$	−9180.90	−0.731635
$541$	3143.16	0.249787	0.124894	−	0.992170i	$-0.460141\pi$
$541$	3143.16	0.249787	0.124894	+	0.992170i	$0.460141\pi$
$542$	−19286.0	−1.52842
$543$	2071.04	0.163678
$544$	−7142.92	−0.562960
$545$	−12336.3	−0.969596
$546$	−36934.6	−2.89497
$547$	22521.3	1.76040	0.880202	−	0.474598i	$-0.157407\pi$
$547$	22521.3	1.76040	0.880202	+	0.474598i	$0.157407\pi$
$548$	41159.8	3.20850
$549$	−12427.6	−0.966115
$550$	672.692	0.0521521
$551$	−25146.7	−1.94425
$552$	21026.8	1.62130
$553$	22804.6	1.75362
$554$	−1196.32	−0.0917453
$555$	3600.03	0.275338
$556$	12156.6	0.927254
$557$	−10537.0	−0.801558	−0.400779	−	0.916175i	$-0.631260\pi$
$557$	−10537.0	−0.801558	−0.400779	+	0.916175i	$0.631260\pi$
$558$	1818.38	0.137954
$559$	5969.39	0.451660
$560$	−2827.32	−0.213350
$561$	−3310.58	−0.249150
$562$	37798.1	2.83704
$563$	18952.3	1.41873	0.709363	−	0.704843i	$-0.248983\pi$
$563$	18952.3	1.41873	0.709363	+	0.704843i	$0.248983\pi$
$564$	−45049.6	−3.36335
$565$	25029.3	1.86370
$566$	10516.5	0.780990
$567$	−24000.1	−1.77762
$568$	129.957	0.00960014
$569$	−8028.02	−0.591480	−0.295740	−	0.955269i	$-0.595566\pi$
$569$	−8028.02	−0.591480	−0.295740	+	0.955269i	$0.595566\pi$
$570$	45349.3	3.33241
$571$	18088.1	1.32568	0.662839	−	0.748762i	$-0.269351\pi$
$571$	18088.1	1.32568	0.662839	+	0.748762i	$0.269351\pi$
$572$	6471.17	0.473030
$573$	4180.72	0.304803
$574$	30424.2	2.21234
$575$	1641.25	0.119035
$576$	−14897.1	−1.07762
$577$	−8695.85	−0.627405	−0.313703	−	0.949521i	$-0.601570\pi$
$577$	−8695.85	−0.627405	−0.313703	+	0.949521i	$0.601570\pi$
$578$	13500.1	0.971508
$579$	−11960.8	−0.858507
$580$	−32087.3	−2.29716
$581$	−23351.2	−1.66742
$582$	5758.95	0.410165
$583$	−3550.89	−0.252252
$584$	19517.6	1.38295
$585$	9459.01	0.668516
$586$	8396.58	0.591910
$587$	−223.978	−0.0157489	−0.00787443	−	0.999969i	$-0.502507\pi$
$587$	−223.978	−0.0157489	−0.00787443	+	0.999969i	$0.502507\pi$
$588$	−35107.8	−2.46228
$589$	2646.21	0.185119
$590$	−31835.0	−2.22140
$591$	3449.51	0.240091
$592$	404.358	0.0280727
$593$	22039.5	1.52623	0.763116	−	0.646261i	$-0.223668\pi$
$593$	22039.5	1.52623	0.763116	+	0.646261i	$0.223668\pi$
$594$	2961.27	0.204550
$595$	14204.5	0.978704
$596$	−7945.53	−0.546076
$597$	15806.3	1.08360
$598$	25194.6	1.72288
$599$	−12172.4	−0.830299	−0.415149	−	0.909753i	$-0.636271\pi$
$599$	−12172.4	−0.830299	−0.415149	+	0.909753i	$0.636271\pi$
$600$	2235.92	0.152135
$601$	3419.51	0.232088	0.116044	−	0.993244i	$-0.462979\pi$
$601$	3419.51	0.232088	0.116044	+	0.993244i	$0.462979\pi$
$602$	17055.5	1.15470
$603$	−17876.6	−1.20728
$604$	−36237.0	−2.44117
$605$	−1422.51	−0.0955924
$606$	35190.2	2.35892
$607$	−28412.5	−1.89988	−0.949939	−	0.312435i	$-0.898855\pi$
$607$	−28412.5	−1.89988	−0.949939	+	0.312435i	$0.898855\pi$
$608$	−19777.4	−1.31921
$609$	−37017.8	−2.46311
$610$	−36825.2	−2.44428
$611$	−21820.8	−1.44480
$612$	−11019.9	−0.727866
$613$	5768.37	0.380069	0.190035	−	0.981777i	$-0.439140\pi$
$613$	5768.37	0.380069	0.190035	+	0.981777i	$0.439140\pi$
$614$	−7418.78	−0.487618
$615$	−19246.5	−1.26194
$616$	7474.18	0.488869
$617$	−10310.0	−0.672716	−0.336358	−	0.941734i	$-0.609195\pi$
$617$	−10310.0	−0.672716	−0.336358	+	0.941734i	$0.609195\pi$
$618$	−15730.3	−1.02389
$619$	20338.6	1.32064	0.660321	−	0.750983i	$-0.270420\pi$
$619$	20338.6	1.32064	0.660321	+	0.750983i	$0.270420\pi$
$620$	3376.58	0.218720
$621$	7224.99	0.466874
$622$	23627.6	1.52312
$623$	17265.3	1.11031
$624$	2624.38	0.168364
$625$	−17101.8	−1.09452
$626$	−24257.9	−1.54878
$627$	−9166.39	−0.583844
$628$	−51341.8	−3.26236
$629$	−2031.51	−0.128778
$630$	27025.9	1.70911
$631$	8447.22	0.532929	0.266465	−	0.963845i	$-0.414144\pi$
$631$	8447.22	0.532929	0.266465	+	0.963845i	$0.414144\pi$
$632$	−21192.3	−1.33384
$633$	−15167.6	−0.952382
$634$	−35402.2	−2.21766
$635$	−8064.87	−0.504007
$636$	−29196.5	−1.82031
$637$	−17005.3	−1.05773
$638$	10349.7	0.642236
$639$	−94.9827	−0.00588021
$640$	−29108.2	−1.79782
$641$	−6900.61	−0.425207	−0.212604	−	0.977139i	$-0.568194\pi$
$641$	−6900.61	−0.425207	−0.212604	+	0.977139i	$0.568194\pi$
$642$	−35002.7	−2.15178
$643$	−22745.8	−1.39504	−0.697518	−	0.716567i	$-0.745712\pi$
$643$	−22745.8	−1.39504	−0.697518	+	0.716567i	$0.745712\pi$
$644$	45110.4	2.76025
$645$	−10789.4	−0.658655
$646$	−25590.8	−1.55860
$647$	5511.34	0.334889	0.167445	−	0.985881i	$-0.446448\pi$
$647$	5511.34	0.334889	0.167445	+	0.985881i	$0.446448\pi$
$648$	22303.3	1.35209
$649$	6434.76	0.389194
$650$	2679.11	0.161667
$651$	3895.42	0.234522
$652$	−23567.0	−1.41558
$653$	22928.3	1.37405	0.687025	−	0.726634i	$-0.258916\pi$
$653$	22928.3	1.37405	0.687025	+	0.726634i	$0.258916\pi$
$654$	32717.0	1.95617
$655$	1540.08	0.0918714
$656$	−2161.78	−0.128664
$657$	−14264.9	−0.847075
$658$	−62345.6	−3.69375
$659$	14422.0	0.852507	0.426253	−	0.904604i	$-0.359833\pi$
$659$	14422.0	0.852507	0.426253	+	0.904604i	$0.359833\pi$
$660$	−11696.4	−0.689818
$661$	8132.50	0.478544	0.239272	−	0.970953i	$-0.423091\pi$
$661$	8132.50	0.478544	0.239272	+	0.970953i	$0.423091\pi$
$662$	−29260.5	−1.71789
$663$	−13185.0	−0.772340
$664$	21700.2	1.26827
$665$	39329.7	2.29344
$666$	−3865.21	−0.224885
$667$	25251.4	1.46587
$668$	−50109.3	−2.90238
$669$	25414.5	1.46873
$670$	−52971.6	−3.05444
$671$	7443.42	0.428241
$672$	−29113.8	−1.67127
$673$	11983.4	0.686368	0.343184	−	0.939268i	$-0.388495\pi$
$673$	11983.4	0.686368	0.343184	+	0.939268i	$0.388495\pi$
$674$	39588.1	2.26243
$675$	768.281	0.0438091
$676$	−3729.55	−0.212195
$677$	14011.0	0.795400	0.397700	−	0.917516i	$-0.369809\pi$
$677$	14011.0	0.795400	0.397700	+	0.917516i	$0.369809\pi$
$678$	−66379.7	−3.76003
$679$	4994.51	0.282285
$680$	−13200.2	−0.744421
$681$	21505.2	1.21010
$682$	−1089.11	−0.0611496
$683$	6554.75	0.367219	0.183610	−	0.982999i	$-0.441222\pi$
$683$	6554.75	0.367219	0.183610	+	0.982999i	$0.441222\pi$
$684$	−30512.1	−1.70564
$685$	−36034.8	−2.00995
$686$	−5653.41	−0.314647
$687$	30306.8	1.68308
$688$	−1211.88	−0.0671546
$689$	−14142.0	−0.781957
$690$	−45538.1	−2.51247
$691$	10215.2	0.562383	0.281191	−	0.959652i	$-0.409270\pi$
$691$	10215.2	0.562383	0.281191	+	0.959652i	$0.409270\pi$
$692$	−52888.9	−2.90540
$693$	−5462.71	−0.299439
$694$	17642.5	0.964985
$695$	−10642.9	−0.580874
$696$	34400.6	1.87349
$697$	10860.9	0.590222
$698$	8150.53	0.441980
$699$	−28035.3	−1.51701
$700$	4796.89	0.259008
$701$	24229.7	1.30548	0.652741	−	0.757581i	$-0.273619\pi$
$701$	24229.7	1.30548	0.652741	+	0.757581i	$0.273619\pi$
$702$	11793.8	0.634085
$703$	−5624.87	−0.301772
$704$	8922.49	0.477669
$705$	39440.1	2.10695
$706$	−42444.6	−2.26264
$707$	30519.0	1.62346
$708$	52908.7	2.80852
$709$	8671.82	0.459347	0.229673	−	0.973268i	$-0.426234\pi$
$709$	8671.82	0.459347	0.229673	+	0.973268i	$0.426234\pi$
$710$	−281.451	−0.0148770
$711$	15489.0	0.816992
$712$	−16044.6	−0.844520
$713$	−2657.23	−0.139571
$714$	−37671.6	−1.97454
$715$	−5665.40	−0.296327
$716$	5556.83	0.290040
$717$	−21700.0	−1.13027
$718$	−49768.5	−2.58683
$719$	24385.9	1.26487	0.632434	−	0.774614i	$-0.282056\pi$
$719$	24385.9	1.26487	0.632434	+	0.774614i	$0.282056\pi$
$720$	−1920.32	−0.0993975
$721$	−13642.3	−0.704668
$722$	−39105.4	−2.01572
$723$	−45820.7	−2.35697
$724$	−4129.03	−0.211953
$725$	2685.14	0.137550
$726$	3772.62	0.192858
$727$	23998.1	1.22426	0.612132	−	0.790755i	$-0.290312\pi$
$727$	23998.1	1.22426	0.612132	+	0.790755i	$0.290312\pi$
$728$	29767.2	1.51545
$729$	−5725.00	−0.290860
$730$	−42269.6	−2.14311
$731$	6088.50	0.308059
$732$	61202.1	3.09029
$733$	17518.7	0.882766	0.441383	−	0.897319i	$-0.354488\pi$
$733$	17518.7	0.882766	0.441383	+	0.897319i	$0.354488\pi$
$734$	5595.86	0.281399
$735$	30736.3	1.54248
$736$	19859.7	0.994620
$737$	10707.1	0.535142
$738$	20664.2	1.03070
$739$	63.2867	0.00315026	0.00157513	−	0.999999i	$-0.499499\pi$
$739$	63.2867	0.00315026	0.00157513	+	0.999999i	$0.499499\pi$
$740$	−7177.36	−0.356547
$741$	−36506.7	−1.80986
$742$	−40406.1	−1.99913
$743$	−27121.8	−1.33917	−0.669585	−	0.742735i	$-0.733528\pi$
$743$	−27121.8	−1.33917	−0.669585	+	0.742735i	$0.733528\pi$
$744$	−3620.01	−0.178382
$745$	6956.18	0.342087
$746$	−34399.9	−1.68830
$747$	−15860.2	−0.776832
$748$	6600.30	0.322635
$749$	−30356.4	−1.48091
$750$	40976.0	1.99497
$751$	10300.3	0.500485	0.250243	−	0.968183i	$-0.419490\pi$
$751$	10300.3	0.500485	0.250243	+	0.968183i	$0.419490\pi$
$752$	4429.96	0.214819
$753$	12442.0	0.602140
$754$	41219.3	1.99087
$755$	31724.9	1.52926
$756$	21116.5	1.01587
$757$	669.992	0.0321681	0.0160841	−	0.999871i	$-0.494880\pi$
$757$	669.992	0.0321681	0.0160841	+	0.999871i	$0.494880\pi$
$758$	34129.9	1.63543
$759$	9204.55	0.440190
$760$	−36549.0	−1.74444
$761$	464.656	0.0221337	0.0110669	−	0.999939i	$-0.496477\pi$
$761$	464.656	0.0221337	0.0110669	+	0.999939i	$0.496477\pi$
$762$	21388.7	1.01684
$763$	28374.1	1.34628
$764$	−8335.08	−0.394702
$765$	9647.76	0.455968
$766$	−14761.7	−0.696297
$767$	25627.6	1.20646
$768$	33490.8	1.57356
$769$	−28439.2	−1.33361	−0.666805	−	0.745233i	$-0.732338\pi$
$769$	−28439.2	−1.33361	−0.666805	+	0.745233i	$0.732338\pi$
$770$	−16187.0	−0.757582
$771$	11843.2	0.553205
$772$	23846.3	1.11172
$773$	6119.71	0.284749	0.142374	−	0.989813i	$-0.454526\pi$
$773$	6119.71	0.284749	0.142374	+	0.989813i	$0.454526\pi$
$774$	11584.2	0.537964
$775$	−282.561	−0.0130966
$776$	−4641.39	−0.214712
$777$	−8280.23	−0.382306
$778$	63885.5	2.94396
$779$	30071.7	1.38310
$780$	−46582.7	−2.13837
$781$	56.8892	0.00260647
$782$	25697.4	1.17511
$783$	11820.3	0.539495
$784$	3452.33	0.157267
$785$	44948.9	2.04369
$786$	−4084.41	−0.185351
$787$	−6671.76	−0.302189	−0.151094	−	0.988519i	$-0.548280\pi$
$787$	−6671.76	−0.302189	−0.151094	+	0.988519i	$0.548280\pi$
$788$	−6877.29	−0.310905
$789$	12509.0	0.564425
$790$	45896.6	2.06700
$791$	−57568.5	−2.58774
$792$	5076.49	0.227759
$793$	29644.7	1.32751
$794$	−49621.7	−2.21790
$795$	25561.1	1.14032
$796$	−31513.0	−1.40320
$797$	−34668.9	−1.54082	−0.770412	−	0.637547i	$-0.779949\pi$
$797$	−34668.9	−1.54082	−0.770412	+	0.637547i	$0.779949\pi$
$798$	−104306.	−4.62704
$799$	−22256.2	−0.985443
$800$	2111.82	0.0933300
$801$	11726.7	0.517280
$802$	−34533.3	−1.52047
$803$	8543.89	0.375476
$804$	88036.8	3.86172
$805$	−39493.4	−1.72914
$806$	−4337.55	−0.189558
$807$	−38566.5	−1.68229
$808$	−28361.3	−1.23484
$809$	25451.4	1.10608	0.553042	−	0.833153i	$-0.313467\pi$
$809$	25451.4	1.10608	0.553042	+	0.833153i	$0.313467\pi$
$810$	−48302.6	−2.09528
$811$	18965.0	0.821150	0.410575	−	0.911827i	$-0.365328\pi$
$811$	18965.0	0.821150	0.410575	+	0.911827i	$0.365328\pi$
$812$	73802.2	3.18959
$813$	−28061.5	−1.21053
$814$	2315.04	0.0996831
$815$	20632.5	0.886781
$816$	2676.75	0.114834
$817$	16857.9	0.721890
$818$	−44941.3	−1.92095
$819$	−21756.2	−0.928232
$820$	38371.7	1.63414
$821$	−11636.5	−0.494662	−0.247331	−	0.968931i	$-0.579554\pi$
$821$	−11636.5	−0.494662	−0.247331	+	0.968931i	$0.579554\pi$
$822$	95567.2	4.05510
$823$	−1356.11	−0.0574375	−0.0287187	−	0.999588i	$-0.509143\pi$
$823$	−1356.11	−0.0574375	−0.0287187	+	0.999588i	$0.509143\pi$
$824$	12677.8	0.535984
$825$	978.780	0.0413052
$826$	73222.1	3.08441
$827$	−28299.3	−1.18992	−0.594960	−	0.803755i	$-0.702832\pi$
$827$	−28299.3	−1.18992	−0.594960	+	0.803755i	$0.702832\pi$
$828$	30639.1	1.28597
$829$	23063.8	0.966270	0.483135	−	0.875546i	$-0.339498\pi$
$829$	23063.8	0.966270	0.483135	+	0.875546i	$0.339498\pi$
$830$	−46996.6	−1.96539
$831$	−1740.68	−0.0726635
$832$	35535.4	1.48073
$833$	−17344.6	−0.721436
$834$	28225.8	1.17192
$835$	43869.9	1.81818
$836$	18275.0	0.756046
$837$	−1243.87	−0.0513672
$838$	−62544.6	−2.57824
$839$	44017.4	1.81126	0.905631	−	0.424067i	$-0.139398\pi$
$839$	44017.4	1.81126	0.905631	+	0.424067i	$0.139398\pi$
$840$	−53802.9	−2.20997
$841$	16923.1	0.693882
$842$	10628.1	0.434999
$843$	54997.0	2.24697
$844$	30239.6	1.23328
$845$	3265.16	0.132929
$846$	−42345.3	−1.72088
$847$	3271.85	0.132730
$848$	2871.04	0.116264
$849$	15301.7	0.618555
$850$	2732.57	0.110266
$851$	5648.29	0.227522
$852$	467.761	0.0188089
$853$	−10302.3	−0.413535	−0.206768	−	0.978390i	$-0.566294\pi$
$853$	−10302.3	−0.413535	−0.206768	+	0.978390i	$0.566294\pi$
$854$	84699.7	3.39387
$855$	26712.8	1.06849
$856$	28210.2	1.12641
$857$	−6834.46	−0.272416	−0.136208	−	0.990680i	$-0.543492\pi$
$857$	−6834.46	−0.272416	−0.136208	+	0.990680i	$0.543492\pi$
$858$	15025.1	0.597843
$859$	−24870.9	−0.987873	−0.493936	−	0.869498i	$-0.664442\pi$
$859$	−24870.9	−0.987873	−0.493936	+	0.869498i	$0.664442\pi$
$860$	21510.8	0.852921
$861$	44267.8	1.75220
$862$	2851.42	0.112668
$863$	28145.9	1.11019	0.555097	−	0.831785i	$-0.312681\pi$
$863$	28145.9	1.11019	0.555097	+	0.831785i	$0.312681\pi$
$864$	9296.49	0.366057
$865$	46303.3	1.82007
$866$	−30832.4	−1.20985
$867$	19643.0	0.769447
$868$	−7766.29	−0.303693
$869$	−9277.00	−0.362141
$870$	−74502.0	−2.90328
$871$	42642.7	1.65889
$872$	−26368.0	−1.02401
$873$	3392.29	0.131514
$874$	71151.2	2.75369
$875$	35536.8	1.37299
$876$	70250.5	2.70953
$877$	−32808.2	−1.26323	−0.631616	−	0.775281i	$-0.717608\pi$
$877$	−32808.2	−1.26323	−0.631616	+	0.775281i	$0.717608\pi$
$878$	−38762.7	−1.48995
$879$	12217.2	0.468801
$880$	1150.16	0.0440591
$881$	−25455.8	−0.973470	−0.486735	−	0.873550i	$-0.661812\pi$
$881$	−25455.8	−0.973470	−0.486735	+	0.873550i	$0.661812\pi$
$882$	−33000.4	−1.25984
$883$	23160.2	0.882677	0.441338	−	0.897341i	$-0.354504\pi$
$883$	23160.2	0.882677	0.441338	+	0.897341i	$0.354504\pi$
$884$	26286.8	1.00014
$885$	−46320.7	−1.75938
$886$	45683.8	1.73225
$887$	−1342.49	−0.0508188	−0.0254094	−	0.999677i	$-0.508089\pi$
$887$	−1342.49	−0.0508188	−0.0254094	+	0.999677i	$0.508089\pi$
$888$	7694.81	0.290789
$889$	18549.6	0.699812
$890$	34748.2	1.30872
$891$	9763.33	0.367097
$892$	−50668.8	−1.90192
$893$	−61623.4	−2.30924
$894$	−18448.4	−0.690163
$895$	−4864.91	−0.181694
$896$	66950.3	2.49626
$897$	36658.7	1.36455
$898$	−51261.0	−1.90490
$899$	−4347.32	−0.161281
$900$	3258.06	0.120669
$901$	−14424.2	−0.533341
$902$	−12376.7	−0.456871
$903$	24816.1	0.914540
$904$	53498.3	1.96828
$905$	3614.90	0.132777
$906$	−84137.2	−3.08529
$907$	20929.7	0.766217	0.383108	−	0.923703i	$-0.374854\pi$
$907$	20929.7	0.766217	0.383108	+	0.923703i	$0.374854\pi$
$908$	−42874.8	−1.56701
$909$	20728.6	0.756353
$910$	−64467.5	−2.34843
$911$	5183.81	0.188526	0.0942631	−	0.995547i	$-0.469951\pi$
$911$	5183.81	0.188526	0.0942631	+	0.995547i	$0.469951\pi$
$912$	7411.42	0.269097
$913$	9499.34	0.344340
$914$	−20155.1	−0.729398
$915$	−53581.5	−1.93590
$916$	−60422.6	−2.17950
$917$	−3542.25	−0.127563
$918$	12029.1	0.432484
$919$	−29458.7	−1.05740	−0.528702	−	0.848808i	$-0.677321\pi$
$919$	−29458.7	−1.05740	−0.528702	+	0.848808i	$0.677321\pi$
$920$	36701.2	1.31522
$921$	−10794.5	−0.386200
$922$	56060.5	2.00244
$923$	226.571	0.00807982
$924$	26902.2	0.957810
$925$	600.620	0.0213495
$926$	64697.5	2.29599
$927$	−9265.88	−0.328297
$928$	32491.2	1.14933
$929$	14266.5	0.503842	0.251921	−	0.967748i	$-0.418938\pi$
$929$	14266.5	0.503842	0.251921	+	0.967748i	$0.418938\pi$
$930$	7839.93	0.276432
$931$	−48024.1	−1.69057
$932$	55893.9	1.96445
$933$	34378.7	1.20633
$934$	−70374.4	−2.46544
$935$	−5778.45	−0.202113
$936$	20218.0	0.706031
$937$	−45991.0	−1.60348	−0.801740	−	0.597674i	$-0.796092\pi$
$937$	−45991.0	−1.60348	−0.801740	+	0.597674i	$0.796092\pi$
$938$	121837.	4.24107
$939$	−35295.7	−1.22666
$940$	−78631.7	−2.72839
$941$	19521.2	0.676272	0.338136	−	0.941097i	$-0.390204\pi$
$941$	19521.2	0.676272	0.338136	+	0.941097i	$0.390204\pi$
$942$	−119208.	−4.12316
$943$	−30196.9	−1.04279
$944$	−5202.78	−0.179381
$945$	−18487.2	−0.636388
$946$	−6938.25	−0.238459
$947$	47182.3	1.61903	0.809514	−	0.587100i	$-0.199731\pi$
$947$	47182.3	1.61903	0.809514	+	0.587100i	$0.199731\pi$
$948$	−76278.4	−2.61330
$949$	34027.5	1.16394
$950$	7565.98	0.258392
$951$	−51510.9	−1.75642
$952$	30361.2	1.03363
$953$	8424.73	0.286363	0.143181	−	0.989696i	$-0.454267\pi$
$953$	8424.73	0.286363	0.143181	+	0.989696i	$0.454267\pi$
$954$	−27443.9	−0.931373
$955$	7297.23	0.247259
$956$	43263.2	1.46363
$957$	15059.0	0.508659
$958$	−31333.0	−1.05670
$959$	82881.7	2.79081
$960$	−64228.5	−2.15934
$961$	−29333.5	−0.984644
$962$	9220.03	0.309008
$963$	−20618.2	−0.689939
$964$	91352.5	3.05214
$965$	−20877.0	−0.696430
$966$	104740.	3.48856
$967$	−22756.6	−0.756778	−0.378389	−	0.925647i	$-0.623522\pi$
$967$	−22756.6	−0.756778	−0.378389	+	0.925647i	$0.623522\pi$
$968$	−3040.52	−0.100957
$969$	−37235.2	−1.23443
$970$	10052.0	0.332731
$971$	−9735.96	−0.321773	−0.160887	−	0.986973i	$-0.551435\pi$
$971$	−9735.96	−0.321773	−0.160887	+	0.986973i	$0.551435\pi$
$972$	59191.9	1.95327
$973$	24479.1	0.806542
$974$	−87611.2	−2.88218
$975$	3898.16	0.128042
$976$	−6018.32	−0.197379
$977$	35110.6	1.14973	0.574866	−	0.818248i	$-0.305054\pi$
$977$	35110.6	1.14973	0.574866	+	0.818248i	$0.305054\pi$
$978$	−54719.2	−1.78909
$979$	−7023.59	−0.229290
$980$	−61278.9	−1.99743
$981$	19271.8	0.627218
$982$	52998.8	1.72226
$983$	7022.92	0.227870	0.113935	−	0.993488i	$-0.463654\pi$
$983$	7022.92	0.227870	0.113935	+	0.993488i	$0.463654\pi$
$984$	−41138.0	−1.33276
$985$	6020.95	0.194765
$986$	42041.8	1.35789
$987$	−90714.2	−2.92550
$988$	72783.4	2.34367
$989$	−16928.1	−0.544270
$990$	−10994.2	−0.352950
$991$	30264.3	0.970107	0.485054	−	0.874484i	$-0.338800\pi$
$991$	30264.3	0.970107	0.485054	+	0.874484i	$0.338800\pi$
$992$	−3419.09	−0.109432
$993$	−42574.7	−1.36059
$994$	647.350	0.0206566
$995$	27589.1	0.879030
$996$	78106.6	2.48484
$997$	6598.82	0.209616	0.104808	−	0.994492i	$-0.466577\pi$
$997$	6598.82	0.209616	0.104808	+	0.994492i	$0.466577\pi$
$998$	−89725.1	−2.84589
$999$	2644.00	0.0837363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.10	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-4.62908 q^{2} -6.73541 q^{3} +13.4284 q^{4} -11.7563 q^{5} +31.1787 q^{6} +27.0401 q^{7} -25.1283 q^{8} +18.3657 q^{9} +O(q^{10})\)	\(q-4.62908 q^{2} -6.73541 q^{3} +13.4284 q^{4} -11.7563 q^{5} +31.1787 q^{6} +27.0401 q^{7} -25.1283 q^{8} +18.3657 q^{9} +54.4209 q^{10} -11.0000 q^{11} -90.4455 q^{12} -43.8094 q^{13} -125.171 q^{14} +79.1835 q^{15} +8.89397 q^{16} -44.6836 q^{17} -85.0162 q^{18} -123.721 q^{19} -157.868 q^{20} -182.126 q^{21} +50.9199 q^{22} +124.236 q^{23} +169.249 q^{24} +13.2108 q^{25} +202.797 q^{26} +58.1555 q^{27} +363.104 q^{28} +203.254 q^{29} -366.547 q^{30} -21.3886 q^{31} +159.856 q^{32} +74.0895 q^{33} +206.844 q^{34} -317.891 q^{35} +246.621 q^{36} +45.4643 q^{37} +572.712 q^{38} +295.074 q^{39} +295.416 q^{40} -243.062 q^{41} +843.075 q^{42} -136.258 q^{43} -147.712 q^{44} -215.913 q^{45} -575.096 q^{46} +498.085 q^{47} -59.9045 q^{48} +388.166 q^{49} -61.1538 q^{50} +300.962 q^{51} -588.288 q^{52} +322.808 q^{53} -269.207 q^{54} +129.319 q^{55} -679.471 q^{56} +833.308 q^{57} -940.877 q^{58} -584.979 q^{59} +1063.30 q^{60} -676.674 q^{61} +99.0096 q^{62} +496.610 q^{63} -811.135 q^{64} +515.037 q^{65} -342.966 q^{66} -973.369 q^{67} -600.027 q^{68} -836.777 q^{69} +1471.54 q^{70} -5.17174 q^{71} -461.499 q^{72} -776.717 q^{73} -210.458 q^{74} -88.9800 q^{75} -1661.36 q^{76} -297.441 q^{77} -1365.92 q^{78} +843.364 q^{79} -104.560 q^{80} -887.575 q^{81} +1125.15 q^{82} -863.577 q^{83} -2445.65 q^{84} +525.314 q^{85} +630.750 q^{86} -1369.00 q^{87} +276.411 q^{88} +638.508 q^{89} +999.477 q^{90} -1184.61 q^{91} +1668.28 q^{92} +144.061 q^{93} -2305.68 q^{94} +1454.50 q^{95} -1076.69 q^{96} +184.708 q^{97} -1796.85 q^{98} -202.023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 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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