LMFDB - Embedded newform 1441.4.a.b.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:	$1$
Dimension:	$79$
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)

$f(q)$	$=$	$q-4.92029 q^{2} -10.0554 q^{3} +16.2093 q^{4} +5.77408 q^{5} +49.4755 q^{6} -6.22578 q^{7} -40.3920 q^{8} +74.1112 q^{9} +O(q^{10})$	\(q-4.92029 q^{2} -10.0554 q^{3} +16.2093 q^{4} +5.77408 q^{5} +49.4755 q^{6} -6.22578 q^{7} -40.3920 q^{8} +74.1112 q^{9} -28.4102 q^{10} +11.0000 q^{11} -162.991 q^{12} +80.6561 q^{13} +30.6327 q^{14} -58.0607 q^{15} +69.0662 q^{16} +57.4284 q^{17} -364.649 q^{18} +16.0981 q^{19} +93.5936 q^{20} +62.6028 q^{21} -54.1232 q^{22} +170.329 q^{23} +406.158 q^{24} -91.6600 q^{25} -396.852 q^{26} -473.722 q^{27} -100.915 q^{28} +165.934 q^{29} +285.676 q^{30} -156.511 q^{31} -16.6899 q^{32} -110.609 q^{33} -282.564 q^{34} -35.9482 q^{35} +1201.29 q^{36} +103.019 q^{37} -79.2071 q^{38} -811.030 q^{39} -233.227 q^{40} -459.495 q^{41} -308.024 q^{42} -162.215 q^{43} +178.302 q^{44} +427.924 q^{45} -838.070 q^{46} +127.616 q^{47} -694.489 q^{48} -304.240 q^{49} +450.994 q^{50} -577.466 q^{51} +1307.38 q^{52} -507.013 q^{53} +2330.85 q^{54} +63.5149 q^{55} +251.472 q^{56} -161.873 q^{57} -816.444 q^{58} -558.409 q^{59} -941.122 q^{60} -308.998 q^{61} +770.078 q^{62} -461.400 q^{63} -470.410 q^{64} +465.715 q^{65} +544.231 q^{66} +424.707 q^{67} +930.872 q^{68} -1712.73 q^{69} +176.876 q^{70} -922.290 q^{71} -2993.50 q^{72} +1052.56 q^{73} -506.885 q^{74} +921.678 q^{75} +260.938 q^{76} -68.4836 q^{77} +3990.50 q^{78} +829.287 q^{79} +398.794 q^{80} +2762.47 q^{81} +2260.85 q^{82} -1305.59 q^{83} +1014.75 q^{84} +331.596 q^{85} +798.146 q^{86} -1668.53 q^{87} -444.312 q^{88} -618.588 q^{89} -2105.51 q^{90} -502.148 q^{91} +2760.91 q^{92} +1573.78 q^{93} -627.908 q^{94} +92.9515 q^{95} +167.824 q^{96} -1116.36 q^{97} +1496.95 q^{98} +815.223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) $ 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.92029	−1.73959	−0.869793	−	0.493417i	$-0.835748\pi$
$2$	−4.92029	−1.73959	−0.869793	+	0.493417i	$0.835748\pi$
$3$	−10.0554	−1.93516	−0.967582	−	0.252558i	$-0.918728\pi$
$3$	−10.0554	−1.93516	−0.967582	+	0.252558i	$0.918728\pi$
$4$	16.2093	2.02616
$5$	5.77408	0.516449	0.258225	−	0.966085i	$-0.416862\pi$
$5$	5.77408	0.516449	0.258225	+	0.966085i	$0.416862\pi$
$6$	49.4755	3.36638
$7$	−6.22578	−0.336161	−0.168080	−	0.985773i	$-0.553757\pi$
$7$	−6.22578	−0.336161	−0.168080	+	0.985773i	$0.553757\pi$
$8$	−40.3920	−1.78509
$9$	74.1112	2.74486
$10$	−28.4102	−0.898408
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−162.991	−3.92095
$13$	80.6561	1.72077	0.860384	−	0.509646i	$-0.170224\pi$
$13$	80.6561	1.72077	0.860384	+	0.509646i	$0.170224\pi$
$14$	30.6327	0.584780
$15$	−58.0607	−0.999414
$16$	69.0662	1.07916
$17$	57.4284	0.819320	0.409660	−	0.912238i	$-0.365647\pi$
$17$	57.4284	0.819320	0.409660	+	0.912238i	$0.365647\pi$
$18$	−364.649	−4.77492
$19$	16.0981	0.194376	0.0971881	−	0.995266i	$-0.469015\pi$
$19$	16.0981	0.194376	0.0971881	+	0.995266i	$0.469015\pi$
$20$	93.5936	1.04641
$21$	62.6028	0.650526
$22$	−54.1232	−0.524505
$23$	170.329	1.54418	0.772090	−	0.635514i	$-0.219212\pi$
$23$	170.329	1.54418	0.772090	+	0.635514i	$0.219212\pi$
$24$	406.158	3.45444
$25$	−91.6600	−0.733280
$26$	−396.852	−2.99342
$27$	−473.722	−3.37659
$28$	−100.915	−0.681115
$29$	165.934	1.06252	0.531262	−	0.847208i	$-0.321718\pi$
$29$	165.934	1.06252	0.531262	+	0.847208i	$0.321718\pi$
$30$	285.676	1.73857
$31$	−156.511	−0.906779	−0.453390	−	0.891312i	$-0.649785\pi$
$31$	−156.511	−0.906779	−0.453390	+	0.891312i	$0.649785\pi$
$32$	−16.6899	−0.0921997
$33$	−110.609	−0.583474
$34$	−282.564	−1.42528
$35$	−35.9482	−0.173610
$36$	1201.29	5.56152
$37$	103.019	0.457737	0.228868	−	0.973457i	$-0.426497\pi$
$37$	103.019	0.457737	0.228868	+	0.973457i	$0.426497\pi$
$38$	−79.2071	−0.338134
$39$	−811.030	−3.32997
$40$	−233.227	−0.921909
$41$	−459.495	−1.75027	−0.875135	−	0.483879i	$-0.839227\pi$
$41$	−459.495	−1.75027	−0.875135	+	0.483879i	$0.839227\pi$
$42$	−308.024	−1.13165
$43$	−162.215	−0.575292	−0.287646	−	0.957737i	$-0.592873\pi$
$43$	−162.215	−0.575292	−0.287646	+	0.957737i	$0.592873\pi$
$44$	178.302	0.610910
$45$	427.924	1.41758
$46$	−838.070	−2.68623
$47$	127.616	0.396057	0.198029	−	0.980196i	$-0.436546\pi$
$47$	127.616	0.396057	0.198029	+	0.980196i	$0.436546\pi$
$48$	−694.489	−2.08835
$49$	−304.240	−0.886996
$50$	450.994	1.27560
$51$	−577.466	−1.58552
$52$	1307.38	3.48655
$53$	−507.013	−1.31403	−0.657015	−	0.753878i	$-0.728181\pi$
$53$	−507.013	−1.31403	−0.657015	+	0.753878i	$0.728181\pi$
$54$	2330.85	5.87386
$55$	63.5149	0.155715
$56$	251.472	0.600077
$57$	−161.873	−0.376150
$58$	−816.444	−1.84835
$59$	−558.409	−1.23218	−0.616090	−	0.787676i	$-0.711284\pi$
$59$	−558.409	−1.23218	−0.616090	+	0.787676i	$0.711284\pi$
$60$	−941.122	−2.02497
$61$	−308.998	−0.648577	−0.324288	−	0.945958i	$-0.605125\pi$
$61$	−308.998	−0.648577	−0.324288	+	0.945958i	$0.605125\pi$
$62$	770.078	1.57742
$63$	−461.400	−0.922714
$64$	−470.410	−0.918770
$65$	465.715	0.888690
$66$	544.231	1.01500
$67$	424.707	0.774422	0.387211	−	0.921991i	$-0.373439\pi$
$67$	424.707	0.774422	0.387211	+	0.921991i	$0.373439\pi$
$68$	930.872	1.66007
$69$	−1712.73	−2.98824
$70$	176.876	0.302010
$71$	−922.290	−1.54163	−0.770815	−	0.637059i	$-0.780151\pi$
$71$	−922.290	−1.54163	−0.770815	+	0.637059i	$0.780151\pi$
$72$	−2993.50	−4.89982
$73$	1052.56	1.68758	0.843789	−	0.536675i	$-0.180320\pi$
$73$	1052.56	1.68758	0.843789	+	0.536675i	$0.180320\pi$
$74$	−506.885	−0.796273
$75$	921.678	1.41902
$76$	260.938	0.393837
$77$	−68.4836	−0.101356
$78$	3990.50	5.79277
$79$	829.287	1.18104	0.590520	−	0.807023i	$-0.298923\pi$
$79$	829.287	1.18104	0.590520	+	0.807023i	$0.298923\pi$
$80$	398.794	0.557331
$81$	2762.47	3.78939
$82$	2260.85	3.04474
$83$	−1305.59	−1.72659	−0.863294	−	0.504701i	$-0.831603\pi$
$83$	−1305.59	−1.72659	−0.863294	+	0.504701i	$0.831603\pi$
$84$	1014.75	1.31807
$85$	331.596	0.423137
$86$	798.146	1.00077
$87$	−1668.53	−2.05616
$88$	−444.312	−0.538225
$89$	−618.588	−0.736744	−0.368372	−	0.929678i	$-0.620085\pi$
$89$	−618.588	−0.736744	−0.368372	+	0.929678i	$0.620085\pi$
$90$	−2105.51	−2.46600
$91$	−502.148	−0.578455
$92$	2760.91	3.12875
$93$	1573.78	1.75477
$94$	−627.908	−0.688976
$95$	92.9515	0.100385
$96$	167.824	0.178421
$97$	−1116.36	−1.16855	−0.584275	−	0.811556i	$-0.698621\pi$
$97$	−1116.36	−1.16855	−0.584275	+	0.811556i	$0.698621\pi$
$98$	1496.95	1.54301
$99$	815.223	0.827606
$100$	−1485.74	−1.48574
$101$	1468.54	1.44678	0.723390	−	0.690440i	$-0.242583\pi$
$101$	1468.54	1.44678	0.723390	+	0.690440i	$0.242583\pi$
$102$	2841.30	2.75814
$103$	1223.19	1.17014	0.585068	−	0.810984i	$-0.301068\pi$
$103$	1223.19	1.17014	0.585068	+	0.810984i	$0.301068\pi$
$104$	−3257.86	−3.07173
$105$	361.474	0.335964
$106$	2494.65	2.28587
$107$	−492.899	−0.445331	−0.222665	−	0.974895i	$-0.571476\pi$
$107$	−492.899	−0.445331	−0.222665	+	0.974895i	$0.571476\pi$
$108$	−7678.69	−6.84150
$109$	−1405.28	−1.23487	−0.617437	−	0.786621i	$-0.711829\pi$
$109$	−1405.28	−1.23487	−0.617437	+	0.786621i	$0.711829\pi$
$110$	−312.512	−0.270880
$111$	−1035.90	−0.885796
$112$	−429.991	−0.362771
$113$	2025.63	1.68633	0.843166	−	0.537653i	$-0.180689\pi$
$113$	2025.63	1.68633	0.843166	+	0.537653i	$0.180689\pi$
$114$	796.460	0.654345
$115$	983.495	0.797491
$116$	2689.67	2.15284
$117$	5977.52	4.72327
$118$	2747.53	2.14348
$119$	−357.537	−0.275423
$120$	2345.19	1.78404
$121$	121.000	0.0909091
$122$	1520.36	1.12825
$123$	4620.41	3.38706
$124$	−2536.92	−1.83728
$125$	−1251.01	−0.895152
$126$	2270.22	1.60514
$127$	−1711.99	−1.19618	−0.598090	−	0.801429i	$-0.704073\pi$
$127$	−1711.99	−1.19618	−0.598090	+	0.801429i	$0.704073\pi$
$128$	2448.07	1.69048
$129$	1631.14	1.11328
$130$	−2291.45	−1.54595
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	−1792.90	−1.18221
$133$	−100.223	−0.0653417
$134$	−2089.68	−1.34717
$135$	−2735.31	−1.74384
$136$	−2319.65	−1.46256
$137$	−232.002	−0.144681	−0.0723404	−	0.997380i	$-0.523047\pi$
$137$	−232.002	−0.144681	−0.0723404	+	0.997380i	$0.523047\pi$
$138$	8427.13	5.19830
$139$	1625.90	0.992139	0.496070	−	0.868283i	$-0.334776\pi$
$139$	1625.90	0.992139	0.496070	+	0.868283i	$0.334776\pi$
$140$	−582.694	−0.351761
$141$	−1283.23	−0.766436
$142$	4537.94	2.68180
$143$	887.218	0.518831
$144$	5118.58	2.96214
$145$	958.116	0.548740
$146$	−5178.92	−2.93569
$147$	3059.25	1.71648
$148$	1669.87	0.927447
$149$	−2415.07	−1.32785	−0.663927	−	0.747798i	$-0.731111\pi$
$149$	−2415.07	−1.32785	−0.663927	+	0.747798i	$0.731111\pi$
$150$	−4534.93	−2.46850
$151$	−3225.82	−1.73850	−0.869250	−	0.494373i	$-0.835398\pi$
$151$	−3225.82	−1.73850	−0.869250	+	0.494373i	$0.835398\pi$
$152$	−650.233	−0.346979
$153$	4256.09	2.24892
$154$	336.959	0.176318
$155$	−903.706	−0.468306
$156$	−13146.2	−6.74704
$157$	2169.99	1.10309	0.551543	−	0.834147i	$-0.314039\pi$
$157$	2169.99	1.10309	0.551543	+	0.834147i	$0.314039\pi$
$158$	−4080.34	−2.05452
$159$	5098.22	2.54286
$160$	−96.3690	−0.0476165
$161$	−1060.43	−0.519092
$162$	−13592.1	−6.59197
$163$	−2579.11	−1.23933	−0.619667	−	0.784865i	$-0.712732\pi$
$163$	−2579.11	−1.23933	−0.619667	+	0.784865i	$0.712732\pi$
$164$	−7448.08	−3.54632
$165$	−638.668	−0.301335
$166$	6423.87	3.00355
$167$	−3231.29	−1.49727	−0.748636	−	0.662981i	$-0.769291\pi$
$167$	−3231.29	−1.49727	−0.748636	+	0.662981i	$0.769291\pi$
$168$	−2528.65	−1.16125
$169$	4308.41	1.96104
$170$	−1631.55	−0.736083
$171$	1193.05	0.533535
$172$	−2629.39	−1.16563
$173$	−612.932	−0.269366	−0.134683	−	0.990889i	$-0.543002\pi$
$173$	−612.932	−0.269366	−0.134683	+	0.990889i	$0.543002\pi$
$174$	8209.67	3.57686
$175$	570.655	0.246500
$176$	759.728	0.325379
$177$	5615.03	2.38447
$178$	3043.63	1.28163
$179$	−687.489	−0.287069	−0.143535	−	0.989645i	$-0.545847\pi$
$179$	−687.489	−0.287069	−0.143535	+	0.989645i	$0.545847\pi$
$180$	6936.33	2.87224
$181$	4014.66	1.64866	0.824331	−	0.566109i	$-0.191552\pi$
$181$	4014.66	1.64866	0.824331	+	0.566109i	$0.191552\pi$
$182$	2470.71	1.00627
$183$	3107.10	1.25510
$184$	−6879.94	−2.75650
$185$	594.842	0.236398
$186$	−7743.45	−3.05257
$187$	631.712	0.247034
$188$	2068.56	0.802475
$189$	2949.29	1.13508
$190$	−457.348	−0.174629
$191$	−3007.76	−1.13944	−0.569722	−	0.821838i	$-0.692949\pi$
$191$	−3007.76	−1.13944	−0.569722	+	0.821838i	$0.692949\pi$
$192$	4730.17	1.77797
$193$	2183.70	0.814436	0.407218	−	0.913331i	$-0.366499\pi$
$193$	2183.70	0.814436	0.407218	+	0.913331i	$0.366499\pi$
$194$	5492.82	2.03279
$195$	−4682.95	−1.71976
$196$	−4931.50	−1.79719
$197$	−2638.12	−0.954103	−0.477052	−	0.878875i	$-0.658294\pi$
$197$	−2638.12	−0.954103	−0.477052	+	0.878875i	$0.658294\pi$
$198$	−4011.13	−1.43969
$199$	−1438.95	−0.512585	−0.256293	−	0.966599i	$-0.582501\pi$
$199$	−1438.95	−0.512585	−0.256293	+	0.966599i	$0.582501\pi$
$200$	3702.33	1.30897
$201$	−4270.60	−1.49863
$202$	−7225.62	−2.51680
$203$	−1033.07	−0.357179
$204$	−9360.30	−3.21251
$205$	−2653.16	−0.903926
$206$	−6018.43	−2.03555
$207$	12623.3	4.23855
$208$	5570.61	1.85698
$209$	177.079	0.0586066
$210$	−1778.56	−0.584438
$211$	−3755.92	−1.22544	−0.612721	−	0.790300i	$-0.709925\pi$
$211$	−3755.92	−1.22544	−0.612721	+	0.790300i	$0.709925\pi$
$212$	−8218.31	−2.66243
$213$	9274.00	2.98331
$214$	2425.21	0.774691
$215$	−936.643	−0.297109
$216$	19134.6	6.02751
$217$	974.402	0.304824
$218$	6914.38	2.14817
$219$	−10583.9	−3.26574
$220$	1029.53	0.315504
$221$	4631.95	1.40986
$222$	5096.93	1.54092
$223$	1562.94	0.469338	0.234669	−	0.972075i	$-0.424599\pi$
$223$	1562.94	0.469338	0.234669	+	0.972075i	$0.424599\pi$
$224$	103.908	0.0309939
$225$	−6793.03	−2.01275
$226$	−9966.70	−2.93352
$227$	−5532.44	−1.61763	−0.808813	−	0.588066i	$-0.799889\pi$
$227$	−5532.44	−1.61763	−0.808813	+	0.588066i	$0.799889\pi$
$228$	−2623.83	−0.762139
$229$	−2346.41	−0.677097	−0.338549	−	0.940949i	$-0.609936\pi$
$229$	−2346.41	−0.677097	−0.338549	+	0.940949i	$0.609936\pi$
$230$	−4839.08	−1.38730
$231$	688.631	0.196141
$232$	−6702.40	−1.89670
$233$	−1061.31	−0.298407	−0.149203	−	0.988807i	$-0.547671\pi$
$233$	−1061.31	−0.298407	−0.149203	+	0.988807i	$0.547671\pi$
$234$	−29411.1	−8.21653
$235$	736.865	0.204544
$236$	−9051.40	−2.49659
$237$	−8338.82	−2.28550
$238$	1759.19	0.479122
$239$	−2245.48	−0.607733	−0.303867	−	0.952715i	$-0.598278\pi$
$239$	−2245.48	−0.607733	−0.303867	+	0.952715i	$0.598278\pi$
$240$	−4010.03	−1.07853
$241$	5882.26	1.57224	0.786119	−	0.618075i	$-0.212087\pi$
$241$	5882.26	1.57224	0.786119	+	0.618075i	$0.212087\pi$
$242$	−595.355	−0.158144
$243$	−14987.2	−3.95650
$244$	−5008.64	−1.31412
$245$	−1756.70	−0.458089
$246$	−22733.8	−5.89208
$247$	1298.41	0.334476
$248$	6321.78	1.61868
$249$	13128.2	3.34123
$250$	6155.34	1.55719
$251$	820.882	0.206429	0.103214	−	0.994659i	$-0.467087\pi$
$251$	820.882	0.206429	0.103214	+	0.994659i	$0.467087\pi$
$252$	−7478.96	−1.86956
$253$	1873.62	0.465588
$254$	8423.50	2.08086
$255$	−3334.33	−0.818840
$256$	−8281.96	−2.02196
$257$	−5544.14	−1.34566	−0.672829	−	0.739798i	$-0.734921\pi$
$257$	−5544.14	−1.34566	−0.672829	+	0.739798i	$0.734921\pi$
$258$	−8025.68	−1.93665
$259$	−641.376	−0.153873
$260$	7548.90	1.80063
$261$	12297.6	2.91648
$262$	644.558	0.151988
$263$	3201.12	0.750531	0.375266	−	0.926917i	$-0.377552\pi$
$263$	3201.12	0.750531	0.375266	+	0.926917i	$0.377552\pi$
$264$	4467.74	1.04155
$265$	−2927.53	−0.678630
$266$	493.127	0.113667
$267$	6220.16	1.42572
$268$	6884.19	1.56910
$269$	1537.51	0.348489	0.174245	−	0.984702i	$-0.444252\pi$
$269$	1537.51	0.348489	0.174245	+	0.984702i	$0.444252\pi$
$270$	13458.5	3.03355
$271$	−5139.83	−1.15211	−0.576056	−	0.817410i	$-0.695409\pi$
$271$	−5139.83	−1.15211	−0.576056	+	0.817410i	$0.695409\pi$
$272$	3966.36	0.884176
$273$	5049.30	1.11940
$274$	1141.52	0.251684
$275$	−1008.26	−0.221092
$276$	−27762.1	−6.05465
$277$	−7365.99	−1.59776	−0.798880	−	0.601490i	$-0.794574\pi$
$277$	−7365.99	−1.59776	−0.798880	+	0.601490i	$0.794574\pi$
$278$	−7999.92	−1.72591
$279$	−11599.2	−2.48898
$280$	1452.02	0.309910
$281$	−2350.11	−0.498917	−0.249458	−	0.968386i	$-0.580253\pi$
$281$	−2350.11	−0.498917	−0.249458	+	0.968386i	$0.580253\pi$
$282$	6313.87	1.33328
$283$	−681.428	−0.143133	−0.0715666	−	0.997436i	$-0.522800\pi$
$283$	−681.428	−0.143133	−0.0715666	+	0.997436i	$0.522800\pi$
$284$	−14949.6	−3.12359
$285$	−934.665	−0.194262
$286$	−4365.37	−0.902551
$287$	2860.72	0.588372
$288$	−1236.91	−0.253075
$289$	−1614.98	−0.328715
$290$	−4714.21	−0.954579
$291$	11225.5	2.26133
$292$	17061.3	3.41930
$293$	−838.221	−0.167131	−0.0835655	−	0.996502i	$-0.526631\pi$
$293$	−838.221	−0.167131	−0.0835655	+	0.996502i	$0.526631\pi$
$294$	−15052.4	−2.98597
$295$	−3224.30	−0.636359
$296$	−4161.15	−0.817102
$297$	−5210.94	−1.01808
$298$	11882.8	2.30992
$299$	13738.1	2.65717
$300$	14939.7	2.87515
$301$	1009.92	0.193391
$302$	15872.0	3.02427
$303$	−14766.7	−2.79976
$304$	1111.83	0.209763
$305$	−1784.18	−0.334957
$306$	−20941.2	−3.91218
$307$	−1642.16	−0.305288	−0.152644	−	0.988281i	$-0.548779\pi$
$307$	−1642.16	−0.305288	−0.152644	+	0.988281i	$0.548779\pi$
$308$	−1110.07	−0.205364
$309$	−12299.6	−2.26441
$310$	4446.50	0.814658
$311$	−311.453	−0.0567874	−0.0283937	−	0.999597i	$-0.509039\pi$
$311$	−311.453	−0.0567874	−0.0283937	+	0.999597i	$0.509039\pi$
$312$	32759.1	5.94429
$313$	−229.708	−0.0414820	−0.0207410	−	0.999785i	$-0.506603\pi$
$313$	−229.708	−0.0414820	−0.0207410	+	0.999785i	$0.506603\pi$
$314$	−10677.0	−1.91891
$315$	−2664.16	−0.476535
$316$	13442.1	2.39297
$317$	−1938.27	−0.343419	−0.171710	−	0.985148i	$-0.554929\pi$
$317$	−1938.27	−0.343419	−0.171710	+	0.985148i	$0.554929\pi$
$318$	−25084.7	−4.42353
$319$	1825.27	0.320363
$320$	−2716.19	−0.474498
$321$	4956.30	0.861788
$322$	5217.64	0.903006
$323$	924.486	0.159256
$324$	44777.5	7.67790
$325$	−7392.94	−1.26180
$326$	12690.0	2.15593
$327$	14130.6	2.38968
$328$	18559.9	3.12439
$329$	−794.509	−0.133139
$330$	3142.43	0.524198
$331$	907.685	0.150728	0.0753639	−	0.997156i	$-0.475988\pi$
$331$	907.685	0.150728	0.0753639	+	0.997156i	$0.475988\pi$
$332$	−21162.6	−3.49834
$333$	7634.88	1.25642
$334$	15898.9	2.60463
$335$	2452.29	0.399950
$336$	4323.74	0.702021
$337$	−2827.65	−0.457068	−0.228534	−	0.973536i	$-0.573393\pi$
$337$	−2827.65	−0.457068	−0.228534	+	0.973536i	$0.573393\pi$
$338$	−21198.6	−3.41140
$339$	−20368.6	−3.26333
$340$	5374.93	0.857343
$341$	−1721.62	−0.273404
$342$	−5870.13	−0.928130
$343$	4029.57	0.634334
$344$	6552.19	1.02695
$345$	−9889.44	−1.54327
$346$	3015.80	0.468585
$347$	3520.16	0.544588	0.272294	−	0.962214i	$-0.412218\pi$
$347$	3520.16	0.544588	0.272294	+	0.962214i	$0.412218\pi$
$348$	−27045.7	−4.16610
$349$	12586.9	1.93055	0.965276	−	0.261233i	$-0.0841291\pi$
$349$	12586.9	1.93055	0.965276	+	0.261233i	$0.0841291\pi$
$350$	−2807.79	−0.428808
$351$	−38208.6	−5.81032
$352$	−183.589	−0.0277993
$353$	5900.82	0.889714	0.444857	−	0.895602i	$-0.353255\pi$
$353$	5900.82	0.889714	0.444857	+	0.895602i	$0.353255\pi$
$354$	−27627.6	−4.14799
$355$	−5325.38	−0.796174
$356$	−10026.9	−1.49276
$357$	3595.18	0.532989
$358$	3382.65	0.499381
$359$	3095.92	0.455143	0.227572	−	0.973761i	$-0.426921\pi$
$359$	3095.92	0.455143	0.227572	+	0.973761i	$0.426921\pi$
$360$	−17284.7	−2.53051
$361$	−6599.85	−0.962218
$362$	−19753.3	−2.86799
$363$	−1216.70	−0.175924
$364$	−8139.45	−1.17204
$365$	6077.58	0.871549
$366$	−15287.9	−2.18336
$367$	3064.99	0.435944	0.217972	−	0.975955i	$-0.430056\pi$
$367$	3064.99	0.435944	0.217972	+	0.975955i	$0.430056\pi$
$368$	11764.0	1.66642
$369$	−34053.7	−4.80424
$370$	−2926.79	−0.411235
$371$	3156.55	0.441725
$372$	25509.8	3.55543
$373$	12584.7	1.74695	0.873475	−	0.486869i	$-0.161861\pi$
$373$	12584.7	1.74695	0.873475	+	0.486869i	$0.161861\pi$
$374$	−3108.21	−0.429737
$375$	12579.4	1.73226
$376$	−5154.66	−0.706998
$377$	13383.6	1.82836
$378$	−14511.4	−1.97456
$379$	555.797	0.0753281	0.0376641	−	0.999290i	$-0.488008\pi$
$379$	555.797	0.0753281	0.0376641	+	0.999290i	$0.488008\pi$
$380$	1506.68	0.203397
$381$	17214.8	2.31480
$382$	14799.0	1.98216
$383$	2435.71	0.324958	0.162479	−	0.986712i	$-0.448051\pi$
$383$	2435.71	0.324958	0.162479	+	0.986712i	$0.448051\pi$
$384$	−24616.4	−3.27135
$385$	−395.430	−0.0523454
$386$	−10744.4	−1.41678
$387$	−12022.0	−1.57910
$388$	−18095.4	−2.36767
$389$	14461.3	1.88488	0.942439	−	0.334377i	$-0.108526\pi$
$389$	14461.3	1.88488	0.942439	+	0.334377i	$0.108526\pi$
$390$	23041.5	2.99167
$391$	9781.74	1.26518
$392$	12288.8	1.58337
$393$	1317.26	0.169076
$394$	12980.3	1.65974
$395$	4788.37	0.609947
$396$	13214.2	1.67686
$397$	−242.408	−0.0306450	−0.0153225	−	0.999883i	$-0.504878\pi$
$397$	−242.408	−0.0306450	−0.0153225	+	0.999883i	$0.504878\pi$
$398$	7080.06	0.891686
$399$	1007.78	0.126447
$400$	−6330.61	−0.791326
$401$	−9914.23	−1.23465	−0.617323	−	0.786710i	$-0.711783\pi$
$401$	−9914.23	−1.23465	−0.617323	+	0.786710i	$0.711783\pi$
$402$	21012.6	2.60700
$403$	−12623.6	−1.56036
$404$	23803.9	2.93140
$405$	15950.7	1.95703
$406$	5083.00	0.621343
$407$	1133.21	0.138013
$408$	23325.0	2.83029
$409$	−1191.93	−0.144101	−0.0720503	−	0.997401i	$-0.522954\pi$
$409$	−1191.93	−0.144101	−0.0720503	+	0.997401i	$0.522954\pi$
$410$	13054.3	1.57246
$411$	2332.87	0.279981
$412$	19826.9	2.37088
$413$	3476.53	0.414211
$414$	−62110.3	−7.37333
$415$	−7538.57	−0.891696
$416$	−1346.15	−0.158654
$417$	−16349.1	−1.91995
$418$	−871.279	−0.101951
$419$	−5184.48	−0.604483	−0.302241	−	0.953231i	$-0.597735\pi$
$419$	−5184.48	−0.604483	−0.302241	+	0.953231i	$0.597735\pi$
$420$	5859.22	0.680716
$421$	984.146	0.113930	0.0569648	−	0.998376i	$-0.481858\pi$
$421$	984.146	0.113930	0.0569648	+	0.998376i	$0.481858\pi$
$422$	18480.2	2.13176
$423$	9457.77	1.08712
$424$	20479.3	2.34566
$425$	−5263.89	−0.600791
$426$	−45630.8	−5.18972
$427$	1923.76	0.218026
$428$	−7989.54	−0.902310
$429$	−8921.33	−1.00402
$430$	4608.56	0.516847
$431$	−10225.2	−1.14277	−0.571383	−	0.820683i	$-0.693593\pi$
$431$	−10225.2	−1.14277	−0.571383	+	0.820683i	$0.693593\pi$
$432$	−32718.2	−3.64388
$433$	4391.00	0.487339	0.243669	−	0.969858i	$-0.421649\pi$
$433$	4391.00	0.487339	0.243669	+	0.969858i	$0.421649\pi$
$434$	−4794.34	−0.530267
$435$	−9634.25	−1.06190
$436$	−22778.5	−2.50205
$437$	2741.97	0.300152
$438$	52076.1	5.68103
$439$	7204.02	0.783210	0.391605	−	0.920133i	$-0.371920\pi$
$439$	7204.02	0.783210	0.391605	+	0.920133i	$0.371920\pi$
$440$	−2565.49	−0.277966
$441$	−22547.6	−2.43468
$442$	−22790.6	−2.45257
$443$	3754.52	0.402670	0.201335	−	0.979522i	$-0.435472\pi$
$443$	3754.52	0.402670	0.201335	+	0.979522i	$0.435472\pi$
$444$	−16791.2	−1.79476
$445$	−3571.78	−0.380491
$446$	−7690.14	−0.816454
$447$	24284.5	2.56961
$448$	2928.67	0.308854
$449$	3714.96	0.390468	0.195234	−	0.980757i	$-0.437453\pi$
$449$	3714.96	0.390468	0.195234	+	0.980757i	$0.437453\pi$
$450$	33423.7	3.50135
$451$	−5054.44	−0.527726
$452$	32834.0	3.41678
$453$	32436.9	3.36428
$454$	27221.2	2.81400
$455$	−2899.44	−0.298743
$456$	6538.35	0.671461
$457$	−704.074	−0.0720683	−0.0360341	−	0.999351i	$-0.511473\pi$
$457$	−704.074	−0.0720683	−0.0360341	+	0.999351i	$0.511473\pi$
$458$	11545.0	1.17787
$459$	−27205.1	−2.76650
$460$	15941.7	1.61584
$461$	−8832.26	−0.892319	−0.446160	−	0.894953i	$-0.647209\pi$
$461$	−8832.26	−0.892319	−0.446160	+	0.894953i	$0.647209\pi$
$462$	−3388.26	−0.341204
$463$	9763.81	0.980050	0.490025	−	0.871708i	$-0.336988\pi$
$463$	9763.81	0.980050	0.490025	+	0.871708i	$0.336988\pi$
$464$	11460.4	1.14663
$465$	9087.13	0.906248
$466$	5221.96	0.519104
$467$	−13383.9	−1.32619	−0.663095	−	0.748535i	$-0.730758\pi$
$467$	−13383.9	−1.32619	−0.663095	+	0.748535i	$0.730758\pi$
$468$	96891.2	9.57008
$469$	−2644.14	−0.260330
$470$	−3625.59	−0.355821
$471$	−21820.2	−2.13465
$472$	22555.2	2.19955
$473$	−1784.37	−0.173457
$474$	41029.4	3.97583
$475$	−1475.55	−0.142532
$476$	−5795.41	−0.558051
$477$	−37575.3	−3.60683
$478$	11048.4	1.05720
$479$	−25.8535	−0.00246613	−0.00123307	−	0.999999i	$-0.500392\pi$
$479$	−25.8535	−0.00246613	−0.00123307	+	0.999999i	$0.500392\pi$
$480$	969.029	0.0921457
$481$	8309.14	0.787659
$482$	−28942.4	−2.73504
$483$	10663.1	1.00453
$484$	1961.32	0.184196
$485$	−6445.96	−0.603497
$486$	73741.5	6.88268
$487$	−14052.2	−1.30752	−0.653762	−	0.756700i	$-0.726810\pi$
$487$	−14052.2	−1.30752	−0.653762	+	0.756700i	$0.726810\pi$
$488$	12481.1	1.15777
$489$	25934.0	2.39832
$490$	8643.50	0.796884
$491$	3728.63	0.342710	0.171355	−	0.985209i	$-0.445186\pi$
$491$	3728.63	0.342710	0.171355	+	0.985209i	$0.445186\pi$
$492$	74893.4	6.86272
$493$	9529.32	0.870546
$494$	−6388.54	−0.581850
$495$	4707.16	0.427417
$496$	−10809.6	−0.978559
$497$	5741.98	0.518235
$498$	−64594.6	−5.81236
$499$	13941.4	1.25070	0.625352	−	0.780343i	$-0.284956\pi$
$499$	13941.4	1.25070	0.625352	+	0.780343i	$0.284956\pi$
$500$	−20278.0	−1.81372
$501$	32491.9	2.89747
$502$	−4038.98	−0.359101
$503$	9232.37	0.818392	0.409196	−	0.912447i	$-0.365809\pi$
$503$	9232.37	0.818392	0.409196	+	0.912447i	$0.365809\pi$
$504$	18636.9	1.64713
$505$	8479.44	0.747189
$506$	−9218.77	−0.809929
$507$	−43322.8	−3.79494
$508$	−27750.1	−2.42365
$509$	−1056.24	−0.0919781	−0.0459891	−	0.998942i	$-0.514644\pi$
$509$	−1056.24	−0.0919781	−0.0459891	+	0.998942i	$0.514644\pi$
$510$	16405.9	1.42444
$511$	−6553.03	−0.567297
$512$	21165.1	1.82690
$513$	−7626.01	−0.656328
$514$	27278.8	2.34089
$515$	7062.78	0.604317
$516$	26439.6	2.25569
$517$	1403.78	0.119416
$518$	3155.76	0.267676
$519$	6163.28	0.521267
$520$	−18811.2	−1.58639
$521$	−15041.2	−1.26481	−0.632405	−	0.774638i	$-0.717932\pi$
$521$	−15041.2	−1.26481	−0.632405	+	0.774638i	$0.717932\pi$
$522$	−60507.6	−5.07346
$523$	−5401.66	−0.451622	−0.225811	−	0.974171i	$-0.572503\pi$
$523$	−5401.66	−0.451622	−0.225811	+	0.974171i	$0.572503\pi$
$524$	−2123.41	−0.177026
$525$	−5738.17	−0.477018
$526$	−15750.5	−1.30561
$527$	−8988.16	−0.742942
$528$	−7639.37	−0.629661
$529$	16845.1	1.38449
$530$	14404.3	1.18053
$531$	−41384.3	−3.38216
$532$	−1624.54	−0.132393
$533$	−37061.1	−3.01181
$534$	−30605.0	−2.48016
$535$	−2846.04	−0.229991
$536$	−17154.8	−1.38241
$537$	6912.98	0.555526
$538$	−7564.99	−0.606227
$539$	−3346.64	−0.267439
$540$	−44337.4	−3.53329
$541$	3264.02	0.259393	0.129696	−	0.991554i	$-0.458600\pi$
$541$	3264.02	0.259393	0.129696	+	0.991554i	$0.458600\pi$
$542$	25289.5	2.00420
$543$	−40369.1	−3.19043
$544$	−958.476	−0.0755410
$545$	−8114.19	−0.637750
$546$	−24844.0	−1.94730
$547$	−21769.0	−1.70160	−0.850801	−	0.525488i	$-0.823883\pi$
$547$	−21769.0	−1.70160	−0.850801	+	0.525488i	$0.823883\pi$
$548$	−3760.58	−0.293146
$549$	−22900.2	−1.78025
$550$	4960.93	0.384609
$551$	2671.22	0.206529
$552$	69180.6	5.33428
$553$	−5162.96	−0.397019
$554$	36242.8	2.77944
$555$	−5981.37	−0.457469
$556$	26354.7	2.01023
$557$	3452.64	0.262645	0.131322	−	0.991340i	$-0.458078\pi$
$557$	3452.64	0.262645	0.131322	+	0.991340i	$0.458078\pi$
$558$	57071.4	4.32980
$559$	−13083.6	−0.989945
$560$	−2482.80	−0.187353
$561$	−6352.12	−0.478052
$562$	11563.2	0.867909
$563$	−12192.9	−0.912738	−0.456369	−	0.889791i	$-0.650850\pi$
$563$	−12192.9	−0.912738	−0.456369	+	0.889791i	$0.650850\pi$
$564$	−20800.2	−1.55292
$565$	11696.2	0.870905
$566$	3352.82	0.248992
$567$	−17198.5	−1.27384
$568$	37253.1	2.75195
$569$	−2449.25	−0.180453	−0.0902266	−	0.995921i	$-0.528759\pi$
$569$	−2449.25	−0.180453	−0.0902266	+	0.995921i	$0.528759\pi$
$570$	4598.82	0.337936
$571$	−24740.5	−1.81323	−0.906617	−	0.421954i	$-0.861344\pi$
$571$	−24740.5	−1.81323	−0.906617	+	0.421954i	$0.861344\pi$
$572$	14381.1	1.05123
$573$	30244.2	2.20501
$574$	−14075.6	−1.02352
$575$	−15612.4	−1.13232
$576$	−34862.7	−2.52189
$577$	−16723.9	−1.20663	−0.603315	−	0.797503i	$-0.706154\pi$
$577$	−16723.9	−1.20663	−0.603315	+	0.797503i	$0.706154\pi$
$578$	7946.17	0.571829
$579$	−21958.0	−1.57607
$580$	15530.4	1.11183
$581$	8128.31	0.580411
$582$	−55232.6	−3.93379
$583$	−5577.14	−0.396195
$584$	−42515.1	−3.01248
$585$	34514.7	2.43933
$586$	4124.29	0.290739
$587$	−22178.0	−1.55943	−0.779714	−	0.626136i	$-0.784636\pi$
$587$	−22178.0	−1.55943	−0.779714	+	0.626136i	$0.784636\pi$
$588$	49588.2	3.47787
$589$	−2519.52	−0.176256
$590$	15864.5	1.10700
$591$	26527.4	1.84635
$592$	7115.15	0.493971
$593$	−3692.37	−0.255696	−0.127848	−	0.991794i	$-0.540807\pi$
$593$	−3692.37	−0.255696	−0.127848	+	0.991794i	$0.540807\pi$
$594$	25639.4	1.77104
$595$	−2064.45	−0.142242
$596$	−39146.5	−2.69044
$597$	14469.2	0.991937
$598$	−67595.5	−4.62238
$599$	328.623	0.0224160	0.0112080	−	0.999937i	$-0.496432\pi$
$599$	328.623	0.0224160	0.0112080	+	0.999937i	$0.496432\pi$
$600$	−37228.4	−2.53307
$601$	−2215.65	−0.150380	−0.0751898	−	0.997169i	$-0.523956\pi$
$601$	−2215.65	−0.150380	−0.0751898	+	0.997169i	$0.523956\pi$
$602$	−4969.08	−0.336420
$603$	31475.6	2.12568
$604$	−52288.2	−3.52248
$605$	698.664	0.0469500
$606$	72656.6	4.87041
$607$	12750.6	0.852607	0.426304	−	0.904580i	$-0.359816\pi$
$607$	12750.6	0.852607	0.426304	+	0.904580i	$0.359816\pi$
$608$	−268.675	−0.0179214
$609$	10387.9	0.691199
$610$	8778.69	0.582687
$611$	10293.0	0.681523
$612$	68988.0	4.55666
$613$	−9826.63	−0.647462	−0.323731	−	0.946149i	$-0.604937\pi$
$613$	−9826.63	−0.647462	−0.323731	+	0.946149i	$0.604937\pi$
$614$	8079.93	0.531074
$615$	26678.6	1.74924
$616$	2766.19	0.180930
$617$	−18781.2	−1.22545	−0.612726	−	0.790295i	$-0.709927\pi$
$617$	−18781.2	−1.22545	−0.612726	+	0.790295i	$0.709927\pi$
$618$	60517.8	3.93913
$619$	7754.20	0.503502	0.251751	−	0.967792i	$-0.418994\pi$
$619$	7754.20	0.503502	0.251751	+	0.967792i	$0.418994\pi$
$620$	−14648.4	−0.948862
$621$	−80688.8	−5.21405
$622$	1532.44	0.0987865
$623$	3851.20	0.247664
$624$	−56014.8	−3.59357
$625$	4234.05	0.270979
$626$	1130.23	0.0721614
$627$	−1780.60	−0.113413
$628$	35174.0	2.23503
$629$	5916.23	0.375033
$630$	13108.5	0.828974
$631$	11811.1	0.745154	0.372577	−	0.928001i	$-0.378474\pi$
$631$	11811.1	0.745154	0.372577	+	0.928001i	$0.378474\pi$
$632$	−33496.6	−2.10826
$633$	37767.3	2.37143
$634$	9536.84	0.597408
$635$	−9885.18	−0.617766
$636$	82638.4	5.15224
$637$	−24538.8	−1.52631
$638$	−8980.88	−0.557299
$639$	−68352.0	−4.23156
$640$	14135.4	0.873047
$641$	22331.0	1.37601	0.688005	−	0.725706i	$-0.258487\pi$
$641$	22331.0	1.37601	0.688005	+	0.725706i	$0.258487\pi$
$642$	−24386.5	−1.49915
$643$	7244.97	0.444345	0.222172	−	0.975007i	$-0.428685\pi$
$643$	7244.97	0.444345	0.222172	+	0.975007i	$0.428685\pi$
$644$	−17188.9	−1.05176
$645$	9418.33	0.574955
$646$	−4548.74	−0.277040
$647$	30479.1	1.85202	0.926009	−	0.377501i	$-0.123216\pi$
$647$	30479.1	1.85202	0.926009	+	0.377501i	$0.123216\pi$
$648$	−111581.	−6.76440
$649$	−6142.50	−0.371516
$650$	36375.4	2.19502
$651$	−9798.01	−0.589884
$652$	−41805.5	−2.51109
$653$	−4512.51	−0.270426	−0.135213	−	0.990817i	$-0.543172\pi$
$653$	−4512.51	−0.270426	−0.135213	+	0.990817i	$0.543172\pi$
$654$	−69526.9	−4.15706
$655$	−756.405	−0.0451224
$656$	−31735.6	−1.88882
$657$	78006.7	4.63216
$658$	3909.22	0.231607
$659$	2540.98	0.150201	0.0751005	−	0.997176i	$-0.476072\pi$
$659$	2540.98	0.150201	0.0751005	+	0.997176i	$0.476072\pi$
$660$	−10352.3	−0.610552
$661$	7265.43	0.427523	0.213761	−	0.976886i	$-0.431429\pi$
$661$	7265.43	0.427523	0.213761	+	0.976886i	$0.431429\pi$
$662$	−4466.08	−0.262204
$663$	−46576.2	−2.72831
$664$	52735.3	3.08212
$665$	−578.696	−0.0337457
$666$	−37565.8	−2.18566
$667$	28263.4	1.64073
$668$	−52376.8	−3.03371
$669$	−15716.0	−0.908247
$670$	−12066.0	−0.695747
$671$	−3398.98	−0.195553
$672$	−1044.84	−0.0599783
$673$	7327.75	0.419709	0.209854	−	0.977733i	$-0.432701\pi$
$673$	7327.75	0.419709	0.209854	+	0.977733i	$0.432701\pi$
$674$	13912.9	0.795110
$675$	43421.4	2.47598
$676$	69836.2	3.97338
$677$	−9844.19	−0.558852	−0.279426	−	0.960167i	$-0.590144\pi$
$677$	−9844.19	−0.558852	−0.279426	+	0.960167i	$0.590144\pi$
$678$	100219.	5.67684
$679$	6950.22	0.392821
$680$	−13393.8	−0.755338
$681$	55630.9	3.13037
$682$	8470.86	0.475610
$683$	4179.29	0.234138	0.117069	−	0.993124i	$-0.462650\pi$
$683$	4179.29	0.234138	0.117069	+	0.993124i	$0.462650\pi$
$684$	19338.4	1.08103
$685$	−1339.60	−0.0747203
$686$	−19826.7	−1.10348
$687$	23594.1	1.31029
$688$	−11203.6	−0.620832
$689$	−40893.7	−2.26114
$690$	48658.9	2.68466
$691$	6555.90	0.360924	0.180462	−	0.983582i	$-0.442241\pi$
$691$	6555.90	0.360924	0.180462	+	0.983582i	$0.442241\pi$
$692$	−9935.17	−0.545778
$693$	−5075.40	−0.278209
$694$	−17320.2	−0.947357
$695$	9388.10	0.512390
$696$	67395.4	3.67042
$697$	−26388.1	−1.43403
$698$	−61931.3	−3.35836
$699$	10671.9	0.577466
$700$	9249.90	0.499448
$701$	−4204.47	−0.226534	−0.113267	−	0.993565i	$-0.536132\pi$
$701$	−4204.47	−0.226534	−0.113267	+	0.993565i	$0.536132\pi$
$702$	187997.	10.1076
$703$	1658.41	0.0889732
$704$	−5174.51	−0.277020
$705$	−7409.47	−0.395825
$706$	−29033.7	−1.54773
$707$	−9142.78	−0.486351
$708$	91015.5	4.83132
$709$	−25800.9	−1.36667	−0.683337	−	0.730103i	$-0.739472\pi$
$709$	−25800.9	−1.36667	−0.683337	+	0.730103i	$0.739472\pi$
$710$	26202.4	1.38501
$711$	61459.5	3.24179
$712$	24986.0	1.31515
$713$	−26658.4	−1.40023
$714$	−17689.3	−0.927180
$715$	5122.87	0.267950
$716$	−11143.7	−0.581647
$717$	22579.3	1.17606
$718$	−15232.8	−0.791761
$719$	8735.20	0.453085	0.226542	−	0.974001i	$-0.427258\pi$
$719$	8735.20	0.453085	0.226542	+	0.974001i	$0.427258\pi$
$720$	29555.1	1.52980
$721$	−7615.29	−0.393354
$722$	32473.2	1.67386
$723$	−59148.5	−3.04254
$724$	65074.8	3.34045
$725$	−15209.5	−0.779127
$726$	5986.54	0.306035
$727$	420.954	0.0214750	0.0107375	−	0.999942i	$-0.496582\pi$
$727$	420.954	0.0214750	0.0107375	+	0.999942i	$0.496582\pi$
$728$	20282.7	1.03259
$729$	76115.9	3.86709
$730$	−29903.5	−1.51613
$731$	−9315.75	−0.471348
$732$	50363.9	2.54304
$733$	31893.9	1.60713	0.803567	−	0.595215i	$-0.202933\pi$
$733$	31893.9	1.60713	0.803567	+	0.595215i	$0.202933\pi$
$734$	−15080.7	−0.758361
$735$	17664.4	0.886476
$736$	−2842.78	−0.142373
$737$	4671.78	0.233497
$738$	167554.	8.35739
$739$	1264.46	0.0629416	0.0314708	−	0.999505i	$-0.489981\pi$
$739$	1264.46	0.0629416	0.0314708	+	0.999505i	$0.489981\pi$
$740$	9641.95	0.478980
$741$	−13056.0	−0.647267
$742$	−15531.2	−0.768419
$743$	−7481.78	−0.369421	−0.184711	−	0.982793i	$-0.559135\pi$
$743$	−7481.78	−0.369421	−0.184711	+	0.982793i	$0.559135\pi$
$744$	−63568.1	−3.13242
$745$	−13944.8	−0.685769
$746$	−61920.5	−3.03897
$747$	−96758.6	−4.73924
$748$	10239.6	0.500530
$749$	3068.69	0.149703
$750$	−61894.5	−3.01342
$751$	24688.5	1.19959	0.599797	−	0.800152i	$-0.295248\pi$
$751$	24688.5	1.19959	0.599797	+	0.800152i	$0.295248\pi$
$752$	8813.95	0.427409
$753$	−8254.30	−0.399474
$754$	−65851.2	−3.18058
$755$	−18626.1	−0.897847
$756$	47805.8	2.29984
$757$	8475.08	0.406912	0.203456	−	0.979084i	$-0.434783\pi$
$757$	8475.08	0.406912	0.203456	+	0.979084i	$0.434783\pi$
$758$	−2734.68	−0.131040
$759$	−18840.0	−0.900988
$760$	−3754.50	−0.179197
$761$	−10123.3	−0.482222	−0.241111	−	0.970498i	$-0.577512\pi$
$761$	−10123.3	−0.482222	−0.241111	+	0.970498i	$0.577512\pi$
$762$	−84701.7	−4.02680
$763$	8748.96	0.415116
$764$	−48753.5	−2.30869
$765$	24575.0	1.16145
$766$	−11984.4	−0.565292
$767$	−45039.1	−2.12030
$768$	83278.5	3.91283
$769$	−20519.7	−0.962237	−0.481118	−	0.876656i	$-0.659769\pi$
$769$	−20519.7	−0.962237	−0.481118	+	0.876656i	$0.659769\pi$
$770$	1945.63	0.0910593
$771$	55748.6	2.60407
$772$	35396.2	1.65018
$773$	1598.12	0.0743600	0.0371800	−	0.999309i	$-0.488163\pi$
$773$	1598.12	0.0743600	0.0371800	+	0.999309i	$0.488163\pi$
$774$	59151.5	2.74697
$775$	14345.8	0.664923
$776$	45092.0	2.08597
$777$	6449.29	0.297770
$778$	−71153.9	−3.27891
$779$	−7396.98	−0.340211
$780$	−75907.2	−3.48451
$781$	−10145.2	−0.464819
$782$	−48129.0	−2.20088
$783$	−78606.6	−3.58770
$784$	−21012.7	−0.957210
$785$	12529.7	0.569688
$786$	−6481.29	−0.294122
$787$	18552.3	0.840301	0.420150	−	0.907454i	$-0.361977\pi$
$787$	18552.3	0.840301	0.420150	+	0.907454i	$0.361977\pi$
$788$	−42762.0	−1.93316
$789$	−32188.6	−1.45240
$790$	−23560.2	−1.06106
$791$	−12611.2	−0.566879
$792$	−32928.5	−1.47735
$793$	−24922.6	−1.11605
$794$	1192.72	0.0533097
$795$	29437.5	1.31326
$796$	−23324.3	−1.03858
$797$	14922.9	0.663234	0.331617	−	0.943414i	$-0.392406\pi$
$797$	14922.9	0.663234	0.331617	+	0.943414i	$0.392406\pi$
$798$	−4958.59	−0.219965
$799$	7328.78	0.324498
$800$	1529.80	0.0676082
$801$	−45844.3	−2.02226
$802$	48780.9	2.14777
$803$	11578.2	0.508824
$804$	−69223.4	−3.03647
$805$	−6123.03	−0.268085
$806$	62111.6	2.71437
$807$	−15460.3	−0.674384
$808$	−59317.1	−2.58263
$809$	9865.03	0.428722	0.214361	−	0.976755i	$-0.431233\pi$
$809$	9865.03	0.428722	0.214361	+	0.976755i	$0.431233\pi$
$810$	−78482.1	−3.40442
$811$	19967.3	0.864547	0.432273	−	0.901743i	$-0.357712\pi$
$811$	19967.3	0.864547	0.432273	+	0.901743i	$0.357712\pi$
$812$	−16745.3	−0.723700
$813$	51683.1	2.22953
$814$	−5575.73	−0.240085
$815$	−14892.0	−0.640054
$816$	−39883.4	−1.71103
$817$	−2611.35	−0.111823
$818$	5864.65	0.250675
$819$	−37214.8	−1.58778
$820$	−43005.8	−1.83150
$821$	−15391.4	−0.654280	−0.327140	−	0.944976i	$-0.606085\pi$
$821$	−15391.4	−0.654280	−0.327140	+	0.944976i	$0.606085\pi$
$822$	−11478.4	−0.487051
$823$	−10754.5	−0.455502	−0.227751	−	0.973719i	$-0.573137\pi$
$823$	−10754.5	−0.455502	−0.227751	+	0.973719i	$0.573137\pi$
$824$	−49406.9	−2.08880
$825$	10138.5	0.427850
$826$	−17105.6	−0.720555
$827$	−883.724	−0.0371585	−0.0185793	−	0.999827i	$-0.505914\pi$
$827$	−883.724	−0.0371585	−0.0185793	+	0.999827i	$0.505914\pi$
$828$	204615.	8.58798
$829$	−1705.82	−0.0714663	−0.0357332	−	0.999361i	$-0.511377\pi$
$829$	−1705.82	−0.0714663	−0.0357332	+	0.999361i	$0.511377\pi$
$830$	37091.9	1.55118
$831$	74068.0	3.09193
$832$	−37941.5	−1.58099
$833$	−17472.0	−0.726733
$834$	80442.4	3.33992
$835$	−18657.7	−0.773265
$836$	2870.32	0.118746
$837$	74142.6	3.06182
$838$	25509.1	1.05155
$839$	−23406.9	−0.963166	−0.481583	−	0.876401i	$-0.659938\pi$
$839$	−23406.9	−0.963166	−0.481583	+	0.876401i	$0.659938\pi$
$840$	−14600.6	−0.599726
$841$	3145.09	0.128955
$842$	−4842.28	−0.198190
$843$	23631.3	0.965486
$844$	−60880.7	−2.48294
$845$	24877.1	1.01278
$846$	−46535.0	−1.89114
$847$	−753.320	−0.0305601
$848$	−35017.4	−1.41805
$849$	6852.03	0.276986
$850$	25899.9	1.04513
$851$	17547.2	0.706828
$852$	150325.	6.04465
$853$	19546.3	0.784588	0.392294	−	0.919840i	$-0.371682\pi$
$853$	19546.3	0.784588	0.392294	+	0.919840i	$0.371682\pi$
$854$	−9465.45	−0.379275
$855$	6888.74	0.275544
$856$	19909.2	0.794955
$857$	7157.94	0.285310	0.142655	−	0.989772i	$-0.454436\pi$
$857$	7157.94	0.285310	0.142655	+	0.989772i	$0.454436\pi$
$858$	43895.6	1.74658
$859$	−30769.6	−1.22217	−0.611085	−	0.791565i	$-0.709267\pi$
$859$	−30769.6	−1.22217	−0.611085	+	0.791565i	$0.709267\pi$
$860$	−15182.3	−0.601991
$861$	−28765.7	−1.13860
$862$	50311.1	1.98794
$863$	5932.37	0.233998	0.116999	−	0.993132i	$-0.462673\pi$
$863$	5932.37	0.233998	0.116999	+	0.993132i	$0.462673\pi$
$864$	7906.39	0.311320
$865$	−3539.12	−0.139114
$866$	−21605.0	−0.847768
$867$	16239.3	0.636118
$868$	15794.3	0.617621
$869$	9122.16	0.356097
$870$	47403.3	1.84727
$871$	34255.2	1.33260
$872$	56762.0	2.20436
$873$	−82734.8	−3.20750
$874$	−13491.3	−0.522140
$875$	7788.53	0.300915
$876$	−171558.	−6.61690
$877$	−15249.3	−0.587151	−0.293575	−	0.955936i	$-0.594845\pi$
$877$	−15249.3	−0.587151	−0.293575	+	0.955936i	$0.594845\pi$
$878$	−35445.9	−1.36246
$879$	8428.65	0.323426
$880$	4386.73	0.168042
$881$	34840.5	1.33236	0.666178	−	0.745792i	$-0.267929\pi$
$881$	34840.5	1.33236	0.666178	+	0.745792i	$0.267929\pi$
$882$	110941.	4.23533
$883$	41228.1	1.57127	0.785637	−	0.618688i	$-0.212335\pi$
$883$	41228.1	1.57127	0.785637	+	0.618688i	$0.212335\pi$
$884$	75080.6	2.85660
$885$	32421.6	1.23146
$886$	−18473.3	−0.700479
$887$	−689.598	−0.0261042	−0.0130521	−	0.999915i	$-0.504155\pi$
$887$	−689.598	−0.0261042	−0.0130521	+	0.999915i	$0.504155\pi$
$888$	41842.1	1.58123
$889$	10658.5	0.402109
$890$	17574.2	0.661897
$891$	30387.1	1.14254
$892$	25334.2	0.950954
$893$	2054.37	0.0769841
$894$	−119487.	−4.47006
$895$	−3969.62	−0.148257
$896$	−15241.2	−0.568273
$897$	−138142.	−5.14207
$898$	−18278.7	−0.679252
$899$	−25970.5	−0.963474
$900$	−110110.	−4.07815
$901$	−29116.9	−1.07661
$902$	24869.3	0.918025
$903$	−10155.1	−0.374243
$904$	−81819.3	−3.01026
$905$	23181.0	0.851450
$906$	−159599.	−5.85246
$907$	21309.8	0.780134	0.390067	−	0.920786i	$-0.372452\pi$
$907$	21309.8	0.780134	0.390067	+	0.920786i	$0.372452\pi$
$908$	−89676.8	−3.27757
$909$	108835.	3.97121
$910$	14266.1	0.519688
$911$	−3313.09	−0.120491	−0.0602457	−	0.998184i	$-0.519188\pi$
$911$	−3313.09	−0.120491	−0.0602457	+	0.998184i	$0.519188\pi$
$912$	−11179.9	−0.405926
$913$	−14361.5	−0.520586
$914$	3464.25	0.125369
$915$	17940.7	0.648197
$916$	−38033.6	−1.37191
$917$	815.578	0.0293705
$918$	133857.	4.81257
$919$	39652.0	1.42329	0.711643	−	0.702541i	$-0.247951\pi$
$919$	39652.0	1.42329	0.711643	+	0.702541i	$0.247951\pi$
$920$	−39725.3	−1.42359
$921$	16512.6	0.590781
$922$	43457.3	1.55227
$923$	−74388.4	−2.65279
$924$	11162.2	0.397413
$925$	−9442.75	−0.335649
$926$	−48040.8	−1.70488
$927$	90651.8	3.21186
$928$	−2769.43	−0.0979643
$929$	−34685.7	−1.22497	−0.612487	−	0.790481i	$-0.709831\pi$
$929$	−34685.7	−1.22497	−0.612487	+	0.790481i	$0.709831\pi$
$930$	−44711.3	−1.57650
$931$	−4897.67	−0.172411
$932$	−17203.1	−0.604620
$933$	3131.79	0.109893
$934$	65852.5	2.30702
$935$	3647.56	0.127581
$936$	−241444.	−8.43146
$937$	−11993.9	−0.418169	−0.209085	−	0.977898i	$-0.567048\pi$
$937$	−11993.9	−0.418169	−0.209085	+	0.977898i	$0.567048\pi$
$938$	13009.9	0.452867
$939$	2309.81	0.0802744
$940$	11944.0	0.414438
$941$	−45808.6	−1.58695	−0.793474	−	0.608604i	$-0.791730\pi$
$941$	−45808.6	−1.58695	−0.793474	+	0.608604i	$0.791730\pi$
$942$	107362.	3.71341
$943$	−78265.5	−2.70273
$944$	−38567.2	−1.32972
$945$	17029.4	0.586209
$946$	8779.60	0.301744
$947$	−14114.4	−0.484326	−0.242163	−	0.970236i	$-0.577857\pi$
$947$	−14114.4	−0.484326	−0.242163	+	0.970236i	$0.577857\pi$
$948$	−135166.	−4.63079
$949$	84895.7	2.90393
$950$	7260.13	0.247947
$951$	19490.1	0.664573
$952$	14441.6	0.491655
$953$	−23904.2	−0.812520	−0.406260	−	0.913758i	$-0.633167\pi$
$953$	−23904.2	−0.812520	−0.406260	+	0.913758i	$0.633167\pi$
$954$	184882.	6.27438
$955$	−17367.0	−0.588465
$956$	−36397.7	−1.23136
$957$	−18353.9	−0.619954
$958$	127.207	0.00429005
$959$	1444.39	0.0486360
$960$	27312.4	0.918232
$961$	−5295.39	−0.177751
$962$	−40883.4	−1.37020
$963$	−36529.4	−1.22237
$964$	95347.0	3.18560
$965$	12608.9	0.420615
$966$	−52465.5	−1.74746
$967$	19443.6	0.646602	0.323301	−	0.946296i	$-0.395207\pi$
$967$	19443.6	0.646602	0.323301	+	0.946296i	$0.395207\pi$
$968$	−4887.43	−0.162281
$969$	−9296.08	−0.308187
$970$	31716.0	1.04983
$971$	−9757.16	−0.322474	−0.161237	−	0.986916i	$-0.551548\pi$
$971$	−9757.16	−0.322474	−0.161237	+	0.986916i	$0.551548\pi$
$972$	−242932.	−8.01650
$973$	−10122.5	−0.333518
$974$	69140.8	2.27455
$975$	74339.0	2.44180
$976$	−21341.3	−0.699918
$977$	−43247.6	−1.41619	−0.708093	−	0.706119i	$-0.750444\pi$
$977$	−43247.6	−1.41619	−0.708093	+	0.706119i	$0.750444\pi$
$978$	−127603.	−4.17207
$979$	−6804.47	−0.222137
$980$	−28474.9	−0.928160
$981$	−104147.	−3.38955
$982$	−18345.9	−0.596173
$983$	−4627.58	−0.150149	−0.0750747	−	0.997178i	$-0.523920\pi$
$983$	−4627.58	−0.150149	−0.0750747	+	0.997178i	$0.523920\pi$
$984$	−186627.	−6.04621
$985$	−15232.7	−0.492746
$986$	−46887.1	−1.51439
$987$	7989.11	0.257646
$988$	21046.2	0.677702
$989$	−27630.0	−0.888354
$990$	−23160.6	−0.743528
$991$	19392.9	0.621631	0.310815	−	0.950470i	$-0.399398\pi$
$991$	19392.9	0.621631	0.310815	+	0.950470i	$0.399398\pi$
$992$	2612.15	0.0836048
$993$	−9127.14	−0.291683
$994$	−28252.2	−0.901515
$995$	−8308.62	−0.264725
$996$	212799.	6.76986
$997$	37649.9	1.19597	0.597987	−	0.801506i	$-0.295968\pi$
$997$	37649.9	1.19597	0.597987	+	0.801506i	$0.295968\pi$
$998$	−68595.5	−2.17571
$999$	−48802.5	−1.54559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.8	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.8	✓	79	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-4.92029 q^{2} -10.0554 q^{3} +16.2093 q^{4} +5.77408 q^{5} +49.4755 q^{6} -6.22578 q^{7} -40.3920 q^{8} +74.1112 q^{9} +O(q^{10})\)	\(q-4.92029 q^{2} -10.0554 q^{3} +16.2093 q^{4} +5.77408 q^{5} +49.4755 q^{6} -6.22578 q^{7} -40.3920 q^{8} +74.1112 q^{9} -28.4102 q^{10} +11.0000 q^{11} -162.991 q^{12} +80.6561 q^{13} +30.6327 q^{14} -58.0607 q^{15} +69.0662 q^{16} +57.4284 q^{17} -364.649 q^{18} +16.0981 q^{19} +93.5936 q^{20} +62.6028 q^{21} -54.1232 q^{22} +170.329 q^{23} +406.158 q^{24} -91.6600 q^{25} -396.852 q^{26} -473.722 q^{27} -100.915 q^{28} +165.934 q^{29} +285.676 q^{30} -156.511 q^{31} -16.6899 q^{32} -110.609 q^{33} -282.564 q^{34} -35.9482 q^{35} +1201.29 q^{36} +103.019 q^{37} -79.2071 q^{38} -811.030 q^{39} -233.227 q^{40} -459.495 q^{41} -308.024 q^{42} -162.215 q^{43} +178.302 q^{44} +427.924 q^{45} -838.070 q^{46} +127.616 q^{47} -694.489 q^{48} -304.240 q^{49} +450.994 q^{50} -577.466 q^{51} +1307.38 q^{52} -507.013 q^{53} +2330.85 q^{54} +63.5149 q^{55} +251.472 q^{56} -161.873 q^{57} -816.444 q^{58} -558.409 q^{59} -941.122 q^{60} -308.998 q^{61} +770.078 q^{62} -461.400 q^{63} -470.410 q^{64} +465.715 q^{65} +544.231 q^{66} +424.707 q^{67} +930.872 q^{68} -1712.73 q^{69} +176.876 q^{70} -922.290 q^{71} -2993.50 q^{72} +1052.56 q^{73} -506.885 q^{74} +921.678 q^{75} +260.938 q^{76} -68.4836 q^{77} +3990.50 q^{78} +829.287 q^{79} +398.794 q^{80} +2762.47 q^{81} +2260.85 q^{82} -1305.59 q^{83} +1014.75 q^{84} +331.596 q^{85} +798.146 q^{86} -1668.53 q^{87} -444.312 q^{88} -618.588 q^{89} -2105.51 q^{90} -502.148 q^{91} +2760.91 q^{92} +1573.78 q^{93} -627.908 q^{94} +92.9515 q^{95} +167.824 q^{96} -1116.36 q^{97} +1496.95 q^{98} +815.223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * q^99

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