LMFDB - Embedded newform 1441.4.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-4.33328 q^{2} +7.87388 q^{3} +10.7773 q^{4} +11.6477 q^{5} -34.1197 q^{6} -12.9990 q^{7} -12.0350 q^{8} +34.9979 q^{9} +O(q^{10})$	\(q-4.33328 q^{2} +7.87388 q^{3} +10.7773 q^{4} +11.6477 q^{5} -34.1197 q^{6} -12.9990 q^{7} -12.0350 q^{8} +34.9979 q^{9} -50.4726 q^{10} +11.0000 q^{11} +84.8594 q^{12} -11.0592 q^{13} +56.3283 q^{14} +91.7122 q^{15} -34.0677 q^{16} +48.7429 q^{17} -151.656 q^{18} -100.524 q^{19} +125.531 q^{20} -102.353 q^{21} -47.6661 q^{22} -103.028 q^{23} -94.7619 q^{24} +10.6679 q^{25} +47.9227 q^{26} +62.9748 q^{27} -140.095 q^{28} -90.0435 q^{29} -397.415 q^{30} -112.526 q^{31} +243.905 q^{32} +86.6126 q^{33} -211.217 q^{34} -151.408 q^{35} +377.184 q^{36} +164.998 q^{37} +435.598 q^{38} -87.0789 q^{39} -140.179 q^{40} -433.295 q^{41} +443.522 q^{42} -91.4821 q^{43} +118.551 q^{44} +407.644 q^{45} +446.451 q^{46} +338.083 q^{47} -268.245 q^{48} -174.026 q^{49} -46.2272 q^{50} +383.795 q^{51} -119.189 q^{52} -98.6017 q^{53} -272.888 q^{54} +128.124 q^{55} +156.443 q^{56} -791.512 q^{57} +390.184 q^{58} +590.523 q^{59} +988.413 q^{60} -759.385 q^{61} +487.607 q^{62} -454.938 q^{63} -784.367 q^{64} -128.814 q^{65} -375.317 q^{66} -823.260 q^{67} +525.318 q^{68} -811.232 q^{69} +656.093 q^{70} +901.699 q^{71} -421.199 q^{72} -1138.15 q^{73} -714.981 q^{74} +83.9981 q^{75} -1083.38 q^{76} -142.989 q^{77} +377.337 q^{78} -209.539 q^{79} -396.809 q^{80} -449.089 q^{81} +1877.59 q^{82} -1321.30 q^{83} -1103.09 q^{84} +567.740 q^{85} +396.418 q^{86} -708.992 q^{87} -132.385 q^{88} +1323.65 q^{89} -1766.44 q^{90} +143.759 q^{91} -1110.37 q^{92} -886.017 q^{93} -1465.01 q^{94} -1170.87 q^{95} +1920.48 q^{96} -1512.75 q^{97} +754.104 q^{98} +384.977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.33328	−1.53205	−0.766023	−	0.642813i	$-0.777767\pi$
$2$	−4.33328	−1.53205	−0.766023	+	0.642813i	$0.777767\pi$
$3$	7.87388	1.51533	0.757664	−	0.652645i	$-0.226341\pi$
$3$	7.87388	1.51533	0.757664	+	0.652645i	$0.226341\pi$
$4$	10.7773	1.34717
$5$	11.6477	1.04180	0.520899	−	0.853618i	$-0.325597\pi$
$5$	11.6477	1.04180	0.520899	+	0.853618i	$0.325597\pi$
$6$	−34.1197	−2.32155
$7$	−12.9990	−0.701880	−0.350940	−	0.936398i	$-0.614138\pi$
$7$	−12.9990	−0.701880	−0.350940	+	0.936398i	$0.614138\pi$
$8$	−12.0350	−0.531876
$9$	34.9979	1.29622
$10$	−50.4726	−1.59608
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	84.8594	2.04140
$13$	−11.0592	−0.235944	−0.117972	−	0.993017i	$-0.537639\pi$
$13$	−11.0592	−0.235944	−0.117972	+	0.993017i	$0.537639\pi$
$14$	56.3283	1.07531
$15$	91.7122	1.57867
$16$	−34.0677	−0.532308
$17$	48.7429	0.695405	0.347702	−	0.937605i	$-0.386962\pi$
$17$	48.7429	0.695405	0.347702	+	0.937605i	$0.386962\pi$
$18$	−151.656	−1.98587
$19$	−100.524	−1.21378	−0.606888	−	0.794787i	$-0.707582\pi$
$19$	−100.524	−1.21378	−0.606888	+	0.794787i	$0.707582\pi$
$20$	125.531	1.40348
$21$	−102.353	−1.06358
$22$	−47.6661	−0.461929
$23$	−103.028	−0.934039	−0.467019	−	0.884247i	$-0.654672\pi$
$23$	−103.028	−0.934039	−0.467019	+	0.884247i	$0.654672\pi$
$24$	−94.7619	−0.805966
$25$	10.6679	0.0853436
$26$	47.9227	0.361477
$27$	62.9748	0.448870
$28$	−140.095	−0.945549
$29$	−90.0435	−0.576575	−0.288287	−	0.957544i	$-0.593086\pi$
$29$	−90.0435	−0.576575	−0.288287	+	0.957544i	$0.593086\pi$
$30$	−397.415	−2.41859
$31$	−112.526	−0.651945	−0.325972	−	0.945379i	$-0.605692\pi$
$31$	−112.526	−0.651945	−0.325972	+	0.945379i	$0.605692\pi$
$32$	243.905	1.34740
$33$	86.6126	0.456889
$34$	−211.217	−1.06539
$35$	−151.408	−0.731217
$36$	377.184	1.74622
$37$	164.998	0.733120	0.366560	−	0.930394i	$-0.380535\pi$
$37$	164.998	0.733120	0.366560	+	0.930394i	$0.380535\pi$
$38$	435.598	1.85956
$39$	−87.0789	−0.357533
$40$	−140.179	−0.554107
$41$	−433.295	−1.65047	−0.825235	−	0.564790i	$-0.808957\pi$
$41$	−433.295	−1.65047	−0.825235	+	0.564790i	$0.808957\pi$
$42$	443.522	1.62945
$43$	−91.4821	−0.324439	−0.162220	−	0.986755i	$-0.551865\pi$
$43$	−91.4821	−0.324439	−0.162220	+	0.986755i	$0.551865\pi$
$44$	118.551	0.406186
$45$	407.644	1.35040
$46$	446.451	1.43099
$47$	338.083	1.04924	0.524622	−	0.851336i	$-0.324207\pi$
$47$	338.083	1.04924	0.524622	+	0.851336i	$0.324207\pi$
$48$	−268.245	−0.806622
$49$	−174.026	−0.507364
$50$	−46.2272	−0.130750
$51$	383.795	1.05377
$52$	−119.189	−0.317856
$53$	−98.6017	−0.255547	−0.127773	−	0.991803i	$-0.540783\pi$
$53$	−98.6017	−0.255547	−0.127773	+	0.991803i	$0.540783\pi$
$54$	−272.888	−0.687691
$55$	128.124	0.314114
$56$	156.443	0.373313
$57$	−791.512	−1.83927
$58$	390.184	0.883339
$59$	590.523	1.30304	0.651522	−	0.758630i	$-0.274131\pi$
$59$	590.523	1.30304	0.651522	+	0.758630i	$0.274131\pi$
$60$	988.413	2.12673
$61$	−759.385	−1.59392	−0.796962	−	0.604030i	$-0.793561\pi$
$61$	−759.385	−1.59392	−0.796962	+	0.604030i	$0.793561\pi$
$62$	487.607	0.998810
$63$	−454.938	−0.909791
$64$	−784.367	−1.53197
$65$	−128.814	−0.245806
$66$	−375.317	−0.699975
$67$	−823.260	−1.50115	−0.750576	−	0.660784i	$-0.770224\pi$
$67$	−823.260	−1.50115	−0.750576	+	0.660784i	$0.770224\pi$
$68$	525.318	0.936826
$69$	−811.232	−1.41538
$70$	656.093	1.12026
$71$	901.699	1.50721	0.753605	−	0.657327i	$-0.228313\pi$
$71$	901.699	1.50721	0.753605	+	0.657327i	$0.228313\pi$
$72$	−421.199	−0.689428
$73$	−1138.15	−1.82480	−0.912399	−	0.409302i	$-0.865772\pi$
$73$	−1138.15	−1.82480	−0.912399	+	0.409302i	$0.865772\pi$
$74$	−714.981	−1.12317
$75$	83.9981	0.129324
$76$	−1083.38	−1.63516
$77$	−142.989	−0.211625
$78$	377.337	0.547757
$79$	−209.539	−0.298417	−0.149208	−	0.988806i	$-0.547673\pi$
$79$	−209.539	−0.298417	−0.149208	+	0.988806i	$0.547673\pi$
$80$	−396.809	−0.554558
$81$	−449.089	−0.616034
$82$	1877.59	2.52860
$83$	−1321.30	−1.74736	−0.873682	−	0.486498i	$-0.838274\pi$
$83$	−1321.30	−1.74736	−0.873682	+	0.486498i	$0.838274\pi$
$84$	−1103.09	−1.43282
$85$	567.740	0.724472
$86$	396.418	0.497056
$87$	−708.992	−0.873700
$88$	−132.385	−0.160367
$89$	1323.65	1.57647	0.788237	−	0.615372i	$-0.210994\pi$
$89$	1323.65	1.57647	0.788237	+	0.615372i	$0.210994\pi$
$90$	−1766.44	−2.06888
$91$	143.759	0.165604
$92$	−1110.37	−1.25831
$93$	−886.017	−0.987910
$94$	−1465.01	−1.60749
$95$	−1170.87	−1.26451
$96$	1920.48	2.04175
$97$	−1512.75	−1.58347	−0.791737	−	0.610862i	$-0.790823\pi$
$97$	−1512.75	−1.58347	−0.791737	+	0.610862i	$0.790823\pi$
$98$	754.104	0.777306
$99$	384.977	0.390825
$100$	114.972	0.114972
$101$	1407.90	1.38704	0.693521	−	0.720437i	$-0.256059\pi$
$101$	1407.90	1.38704	0.693521	+	0.720437i	$0.256059\pi$
$102$	−1663.09	−1.61442
$103$	−59.5672	−0.0569838	−0.0284919	−	0.999594i	$-0.509070\pi$
$103$	−59.5672	−0.0569838	−0.0284919	+	0.999594i	$0.509070\pi$
$104$	133.097	0.125493
$105$	−1192.17	−1.10803
$106$	427.269	0.391510
$107$	−991.556	−0.895863	−0.447932	−	0.894068i	$-0.647839\pi$
$107$	−991.556	−0.895863	−0.447932	+	0.894068i	$0.647839\pi$
$108$	678.700	0.604703
$109$	791.023	0.695103	0.347552	−	0.937661i	$-0.387013\pi$
$109$	791.023	0.695103	0.347552	+	0.937661i	$0.387013\pi$
$110$	−555.198	−0.481237
$111$	1299.17	1.11092
$112$	442.847	0.373617
$113$	178.956	0.148980	0.0744902	−	0.997222i	$-0.476267\pi$
$113$	178.956	0.148980	0.0744902	+	0.997222i	$0.476267\pi$
$114$	3429.85	2.81785
$115$	−1200.04	−0.973080
$116$	−970.429	−0.776742
$117$	−387.050	−0.305835
$118$	−2558.90	−1.99632
$119$	−633.609	−0.488091
$120$	−1103.75	−0.839654
$121$	121.000	0.0909091
$122$	3290.63	2.44197
$123$	−3411.71	−2.50100
$124$	−1212.73	−0.878278
$125$	−1331.70	−0.952887
$126$	1971.38	1.39384
$127$	438.775	0.306575	0.153287	−	0.988182i	$-0.451014\pi$
$127$	438.775	0.306575	0.153287	+	0.988182i	$0.451014\pi$
$128$	1447.64	0.999647
$129$	−720.319	−0.491632
$130$	558.187	0.376587
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	933.453	0.615505
$133$	1306.71	0.851925
$134$	3567.42	2.29983
$135$	733.509	0.467632
$136$	−586.619	−0.369869
$137$	−6.03893	−0.00376599	−0.00188299	−	0.999998i	$-0.500599\pi$
$137$	−6.03893	−0.00376599	−0.00188299	+	0.999998i	$0.500599\pi$
$138$	3515.30	2.16842
$139$	242.200	0.147792	0.0738960	−	0.997266i	$-0.476457\pi$
$139$	242.200	0.147792	0.0738960	+	0.997266i	$0.476457\pi$
$140$	−1631.77	−0.985072
$141$	2662.02	1.58995
$142$	−3907.32	−2.30912
$143$	−121.651	−0.0711398
$144$	−1192.30	−0.689989
$145$	−1048.80	−0.600674
$146$	4931.92	2.79568
$147$	−1370.26	−0.768824
$148$	1778.23	0.987635
$149$	−1415.16	−0.778085	−0.389042	−	0.921220i	$-0.627194\pi$
$149$	−1415.16	−0.778085	−0.389042	+	0.921220i	$0.627194\pi$
$150$	−363.987	−0.198130
$151$	466.738	0.251541	0.125770	−	0.992059i	$-0.459860\pi$
$151$	466.738	0.251541	0.125770	+	0.992059i	$0.459860\pi$
$152$	1209.80	0.645578
$153$	1705.90	0.901398
$154$	619.612	0.324219
$155$	−1310.67	−0.679195
$156$	−938.478	−0.481656
$157$	796.389	0.404833	0.202417	−	0.979300i	$-0.435121\pi$
$157$	796.389	0.404833	0.202417	+	0.979300i	$0.435121\pi$
$158$	907.990	0.457189
$159$	−776.377	−0.387237
$160$	2840.92	1.40372
$161$	1339.27	0.655583
$162$	1946.03	0.943792
$163$	2427.78	1.16662	0.583308	−	0.812251i	$-0.301758\pi$
$163$	2427.78	1.16662	0.583308	+	0.812251i	$0.301758\pi$
$164$	−4669.76	−2.22346
$165$	1008.83	0.475986
$166$	5725.55	2.67704
$167$	3061.67	1.41868	0.709340	−	0.704867i	$-0.248993\pi$
$167$	3061.67	1.41868	0.709340	+	0.704867i	$0.248993\pi$
$168$	1231.81	0.565692
$169$	−2074.69	−0.944330
$170$	−2460.18	−1.10992
$171$	−3518.13	−1.57332
$172$	−985.934	−0.437074
$173$	1879.86	0.826146	0.413073	−	0.910698i	$-0.364455\pi$
$173$	1879.86	0.826146	0.413073	+	0.910698i	$0.364455\pi$
$174$	3072.26	1.33855
$175$	−138.673	−0.0599009
$176$	−374.745	−0.160497
$177$	4649.71	1.97454
$178$	−5735.73	−2.41523
$179$	3605.46	1.50550	0.752750	−	0.658307i	$-0.228727\pi$
$179$	3605.46	1.50550	0.752750	+	0.658307i	$0.228727\pi$
$180$	4393.32	1.81921
$181$	532.785	0.218793	0.109397	−	0.993998i	$-0.465108\pi$
$181$	532.785	0.218793	0.109397	+	0.993998i	$0.465108\pi$
$182$	−622.947	−0.253714
$183$	−5979.31	−2.41532
$184$	1239.94	0.496792
$185$	1921.84	0.763763
$186$	3839.36	1.51352
$187$	536.172	0.209672
$188$	3643.63	1.41351
$189$	−818.609	−0.315053
$190$	5073.70	1.93729
$191$	4581.81	1.73575	0.867876	−	0.496782i	$-0.165485\pi$
$191$	4581.81	1.73575	0.867876	+	0.496782i	$0.165485\pi$
$192$	−6176.01	−2.32143
$193$	3733.36	1.39240	0.696199	−	0.717849i	$-0.254873\pi$
$193$	3733.36	1.39240	0.696199	+	0.717849i	$0.254873\pi$
$194$	6555.19	2.42596
$195$	−1014.27	−0.372477
$196$	−1875.54	−0.683505
$197$	−1830.02	−0.661845	−0.330923	−	0.943658i	$-0.607360\pi$
$197$	−1830.02	−0.661845	−0.330923	+	0.943658i	$0.607360\pi$
$198$	−1668.22	−0.598762
$199$	−1193.02	−0.424981	−0.212491	−	0.977163i	$-0.568157\pi$
$199$	−1193.02	−0.424981	−0.212491	+	0.977163i	$0.568157\pi$
$200$	−128.388	−0.0453922
$201$	−6482.25	−2.27474
$202$	−6100.82	−2.12501
$203$	1170.48	0.404686
$204$	4136.29	1.41960
$205$	−5046.87	−1.71946
$206$	258.121	0.0873018
$207$	−3605.78	−1.21072
$208$	376.762	0.125595
$209$	−1105.76	−0.365967
$210$	5166.00	1.69756
$211$	−4452.37	−1.45267	−0.726337	−	0.687339i	$-0.758779\pi$
$211$	−4452.37	−1.45267	−0.726337	+	0.687339i	$0.758779\pi$
$212$	−1062.66	−0.344264
$213$	7099.87	2.28392
$214$	4296.69	1.37250
$215$	−1065.55	−0.338000
$216$	−757.900	−0.238743
$217$	1462.73	0.457587
$218$	−3427.73	−1.06493
$219$	−8961.65	−2.76517
$220$	1380.84	0.423164
$221$	−539.058	−0.164077
$222$	−5629.67	−1.70198
$223$	441.953	0.132715	0.0663573	−	0.997796i	$-0.478862\pi$
$223$	441.953	0.132715	0.0663573	+	0.997796i	$0.478862\pi$
$224$	−3170.52	−0.945711
$225$	373.356	0.110624
$226$	−775.468	−0.228245
$227$	−2842.47	−0.831109	−0.415554	−	0.909568i	$-0.636412\pi$
$227$	−2842.47	−0.831109	−0.415554	+	0.909568i	$0.636412\pi$
$228$	−8530.39	−2.47780
$229$	365.694	0.105527	0.0527637	−	0.998607i	$-0.483197\pi$
$229$	365.694	0.105527	0.0527637	+	0.998607i	$0.483197\pi$
$230$	5200.11	1.49080
$231$	−1125.88	−0.320681
$232$	1083.67	0.306666
$233$	468.477	0.131721	0.0658605	−	0.997829i	$-0.479021\pi$
$233$	468.477	0.131721	0.0658605	+	0.997829i	$0.479021\pi$
$234$	1677.20	0.468554
$235$	3937.87	1.09310
$236$	6364.27	1.75542
$237$	−1649.88	−0.452200
$238$	2745.60	0.747778
$239$	−5632.57	−1.52444	−0.762219	−	0.647320i	$-0.775890\pi$
$239$	−5632.57	−1.52444	−0.762219	+	0.647320i	$0.775890\pi$
$240$	−3124.43	−0.840337
$241$	6811.40	1.82059	0.910293	−	0.413965i	$-0.135857\pi$
$241$	6811.40	1.82059	0.910293	+	0.413965i	$0.135857\pi$
$242$	−524.327	−0.139277
$243$	−5236.39	−1.38236
$244$	−8184.15	−2.14728
$245$	−2027.00	−0.528571
$246$	14783.9	3.83165
$247$	1111.71	0.286383
$248$	1354.25	0.346754
$249$	−10403.7	−2.64783
$250$	5770.63	1.45987
$251$	2032.00	0.510991	0.255495	−	0.966810i	$-0.417761\pi$
$251$	2032.00	0.510991	0.255495	+	0.966810i	$0.417761\pi$
$252$	−4903.02	−1.22564
$253$	−1133.31	−0.281623
$254$	−1901.34	−0.469687
$255$	4470.32	1.09781
$256$	1.88659	0.000460594 0
$257$	−7692.50	−1.86710	−0.933550	−	0.358446i	$-0.883307\pi$
$257$	−7692.50	−1.86710	−0.933550	+	0.358446i	$0.883307\pi$
$258$	3121.35	0.753204
$259$	−2144.80	−0.514562
$260$	−1388.27	−0.331142
$261$	−3151.34	−0.747368
$262$	567.660	0.133856
$263$	−5282.51	−1.23853	−0.619266	−	0.785182i	$-0.712570\pi$
$263$	−5282.51	−1.23853	−0.619266	+	0.785182i	$0.712570\pi$
$264$	−1042.38	−0.243008
$265$	−1148.48	−0.266228
$266$	−5662.34	−1.30519
$267$	10422.2	2.38888
$268$	−8872.54	−2.02230
$269$	−486.681	−0.110310	−0.0551552	−	0.998478i	$-0.517565\pi$
$269$	−486.681	−0.110310	−0.0551552	+	0.998478i	$0.517565\pi$
$270$	−3178.50	−0.716435
$271$	−6060.32	−1.35844	−0.679222	−	0.733933i	$-0.737683\pi$
$271$	−6060.32	−1.35844	−0.679222	+	0.733933i	$0.737683\pi$
$272$	−1660.56	−0.370170
$273$	1131.94	0.250945
$274$	26.1684	0.00576967
$275$	117.347	0.0257321
$276$	−8742.92	−1.90675
$277$	6839.26	1.48351	0.741753	−	0.670673i	$-0.233995\pi$
$277$	6839.26	1.48351	0.741753	+	0.670673i	$0.233995\pi$
$278$	−1049.52	−0.226424
$279$	−3938.18	−0.845064
$280$	1822.19	0.388917
$281$	6248.64	1.32656	0.663279	−	0.748373i	$-0.269164\pi$
$281$	6248.64	1.32656	0.663279	+	0.748373i	$0.269164\pi$
$282$	−11535.3	−2.43587
$283$	1511.43	0.317473	0.158737	−	0.987321i	$-0.449258\pi$
$283$	1511.43	0.317473	0.158737	+	0.987321i	$0.449258\pi$
$284$	9717.91	2.03046
$285$	−9219.26	−1.91615
$286$	527.150	0.108990
$287$	5632.40	1.15843
$288$	8536.17	1.74652
$289$	−2537.13	−0.516412
$290$	4544.73	0.920261
$291$	−11911.2	−2.39948
$292$	−12266.2	−2.45831
$293$	−5937.37	−1.18384	−0.591919	−	0.805997i	$-0.701630\pi$
$293$	−5937.37	−1.18384	−0.591919	+	0.805997i	$0.701630\pi$
$294$	5937.72	1.17787
$295$	6878.21	1.35751
$296$	−1985.74	−0.389929
$297$	692.723	0.135340
$298$	6132.30	1.19206
$299$	1139.41	0.220381
$300$	905.276	0.174220
$301$	1189.18	0.227718
$302$	−2022.51	−0.385372
$303$	11085.6	2.10182
$304$	3424.62	0.646103
$305$	−8845.06	−1.66055
$306$	−7392.15	−1.38098
$307$	7264.20	1.35046	0.675228	−	0.737610i	$-0.264045\pi$
$307$	7264.20	1.35046	0.675228	+	0.737610i	$0.264045\pi$
$308$	−1541.04	−0.285094
$309$	−469.025	−0.0863491
$310$	5679.48	1.04056
$311$	−5429.81	−0.990020	−0.495010	−	0.868887i	$-0.664836\pi$
$311$	−5429.81	−0.990020	−0.495010	+	0.868887i	$0.664836\pi$
$312$	1047.99	0.190163
$313$	7012.82	1.26641	0.633207	−	0.773982i	$-0.281738\pi$
$313$	7012.82	1.26641	0.633207	+	0.773982i	$0.281738\pi$
$314$	−3450.98	−0.620223
$315$	−5298.96	−0.947819
$316$	−2258.27	−0.402017
$317$	−6615.99	−1.17221	−0.586106	−	0.810234i	$-0.699340\pi$
$317$	−6615.99	−1.17221	−0.586106	+	0.810234i	$0.699340\pi$
$318$	3364.26	0.593266
$319$	−990.479	−0.173844
$320$	−9136.04	−1.59600
$321$	−7807.39	−1.35753
$322$	−5803.41	−1.00438
$323$	−4899.82	−0.844066
$324$	−4839.98	−0.829900
$325$	−117.979	−0.0201363
$326$	−10520.3	−1.78731
$327$	6228.42	1.05331
$328$	5214.69	0.877845
$329$	−4394.74	−0.736443
$330$	−4371.56	−0.729232
$331$	2188.63	0.363438	0.181719	−	0.983351i	$-0.441834\pi$
$331$	2188.63	0.363438	0.181719	+	0.983351i	$0.441834\pi$
$332$	−14240.1	−2.35399
$333$	5774.58	0.950285
$334$	−13267.1	−2.17348
$335$	−9589.05	−1.56390
$336$	3486.92	0.566152
$337$	3561.75	0.575730	0.287865	−	0.957671i	$-0.407055\pi$
$337$	3561.75	0.575730	0.287865	+	0.957671i	$0.407055\pi$
$338$	8990.23	1.44676
$339$	1409.08	0.225754
$340$	6118.73	0.975984
$341$	−1237.79	−0.196569
$342$	15245.0	2.41040
$343$	6720.82	1.05799
$344$	1100.99	0.172561
$345$	−9448.96	−1.47454
$346$	−8145.97	−1.26569
$347$	−12152.6	−1.88007	−0.940035	−	0.341078i	$-0.889208\pi$
$347$	−12152.6	−1.88007	−0.940035	+	0.341078i	$0.889208\pi$
$348$	−7641.04	−1.17702
$349$	−10191.0	−1.56308	−0.781539	−	0.623857i	$-0.785565\pi$
$349$	−10191.0	−1.56308	−0.781539	+	0.623857i	$0.785565\pi$
$350$	600.908	0.0917710
$351$	−696.452	−0.105908
$352$	2682.95	0.406255
$353$	10954.8	1.65175	0.825875	−	0.563854i	$-0.190682\pi$
$353$	10954.8	1.65175	0.825875	+	0.563854i	$0.190682\pi$
$354$	−20148.5	−3.02509
$355$	10502.7	1.57021
$356$	14265.4	2.12377
$357$	−4988.96	−0.739618
$358$	−15623.5	−2.30650
$359$	−4189.04	−0.615846	−0.307923	−	0.951411i	$-0.599634\pi$
$359$	−4189.04	−0.615846	−0.307923	+	0.951411i	$0.599634\pi$
$360$	−4905.98	−0.718245
$361$	3246.04	0.473252
$362$	−2308.71	−0.335202
$363$	952.739	0.137757
$364$	1549.34	0.223097
$365$	−13256.8	−1.90107
$366$	25910.0	3.70038
$367$	−6124.10	−0.871050	−0.435525	−	0.900177i	$-0.643437\pi$
$367$	−6124.10	−0.871050	−0.435525	+	0.900177i	$0.643437\pi$
$368$	3509.94	0.497197
$369$	−15164.4	−2.13937
$370$	−8327.86	−1.17012
$371$	1281.72	0.179363
$372$	−9548.90	−1.33088
$373$	9435.93	1.30985	0.654925	−	0.755694i	$-0.272700\pi$
$373$	9435.93	1.30985	0.654925	+	0.755694i	$0.272700\pi$
$374$	−2323.38	−0.321228
$375$	−10485.6	−1.44394
$376$	−4068.82	−0.558067
$377$	995.811	0.136039
$378$	3547.26	0.482676
$379$	−1270.76	−0.172229	−0.0861145	−	0.996285i	$-0.527445\pi$
$379$	−1270.76	−0.172229	−0.0861145	+	0.996285i	$0.527445\pi$
$380$	−12618.8	−1.70351
$381$	3454.86	0.464561
$382$	−19854.3	−2.65925
$383$	−5675.76	−0.757226	−0.378613	−	0.925555i	$-0.623599\pi$
$383$	−5675.76	−0.757226	−0.378613	+	0.925555i	$0.623599\pi$
$384$	11398.6	1.51479
$385$	−1665.49	−0.220470
$386$	−16177.7	−2.13322
$387$	−3201.69	−0.420545
$388$	−16303.5	−2.13320
$389$	−3925.33	−0.511625	−0.255813	−	0.966726i	$-0.582343\pi$
$389$	−3925.33	−0.511625	−0.255813	+	0.966726i	$0.582343\pi$
$390$	4395.10	0.570652
$391$	−5021.90	−0.649535
$392$	2094.40	0.269855
$393$	−1031.48	−0.132395
$394$	7929.99	1.01398
$395$	−2440.63	−0.310890
$396$	4149.03	0.526506
$397$	−14255.2	−1.80214	−0.901068	−	0.433678i	$-0.857216\pi$
$397$	−14255.2	−1.80214	−0.901068	+	0.433678i	$0.857216\pi$
$398$	5169.71	0.651091
$399$	10288.9	1.29095
$400$	−363.433	−0.0454291
$401$	3497.48	0.435550	0.217775	−	0.975999i	$-0.430120\pi$
$401$	3497.48	0.435550	0.217775	+	0.975999i	$0.430120\pi$
$402$	28089.4	3.48500
$403$	1244.45	0.153823
$404$	15173.4	1.86858
$405$	−5230.83	−0.641783
$406$	−5072.00	−0.619998
$407$	1814.97	0.221044
$408$	−4618.97	−0.560473
$409$	7477.87	0.904052	0.452026	−	0.892005i	$-0.350702\pi$
$409$	7477.87	0.904052	0.452026	+	0.892005i	$0.350702\pi$
$410$	21869.5	2.63429
$411$	−47.5498	−0.00570671
$412$	−641.976	−0.0767667
$413$	−7676.21	−0.914580
$414$	15624.9	1.85488
$415$	−15390.0	−1.82040
$416$	−2697.40	−0.317910
$417$	1907.05	0.223954
$418$	4791.58	0.560679
$419$	−723.982	−0.0844125	−0.0422062	−	0.999109i	$-0.513439\pi$
$419$	−723.982	−0.0844125	−0.0422062	+	0.999109i	$0.513439\pi$
$420$	−12848.4	−1.49271
$421$	−145.070	−0.0167940	−0.00839699	−	0.999965i	$-0.502673\pi$
$421$	−145.070	−0.0167940	−0.00839699	+	0.999965i	$0.502673\pi$
$422$	19293.4	2.22556
$423$	11832.2	1.36005
$424$	1186.67	0.135919
$425$	519.986	0.0593483
$426$	−30765.7	−3.49907
$427$	9871.25	1.11874
$428$	−10686.3	−1.20688
$429$	−957.868	−0.107800
$430$	4617.34	0.517832
$431$	−13853.2	−1.54822	−0.774112	−	0.633048i	$-0.781803\pi$
$431$	−13853.2	−1.54822	−0.774112	+	0.633048i	$0.781803\pi$
$432$	−2145.41	−0.238938
$433$	−9573.88	−1.06257	−0.531283	−	0.847194i	$-0.678290\pi$
$433$	−9573.88	−1.06257	−0.531283	+	0.847194i	$0.678290\pi$
$434$	−6338.41	−0.701045
$435$	−8258.09	−0.910219
$436$	8525.12	0.936420
$437$	10356.8	1.13371
$438$	38833.3	4.23637
$439$	−920.736	−0.100101	−0.0500505	−	0.998747i	$-0.515938\pi$
$439$	−920.736	−0.100101	−0.0500505	+	0.998747i	$0.515938\pi$
$440$	−1541.97	−0.167070
$441$	−6090.55	−0.657656
$442$	2335.89	0.251373
$443$	8306.30	0.890845	0.445423	−	0.895320i	$-0.353053\pi$
$443$	8306.30	0.890845	0.445423	+	0.895320i	$0.353053\pi$
$444$	14001.6	1.49659
$445$	15417.4	1.64237
$446$	−1915.11	−0.203325
$447$	−11142.8	−1.17905
$448$	10196.0	1.07526
$449$	5017.54	0.527377	0.263688	−	0.964608i	$-0.415061\pi$
$449$	5017.54	0.527377	0.263688	+	0.964608i	$0.415061\pi$
$450$	−1617.86	−0.169481
$451$	−4766.24	−0.497635
$452$	1928.67	0.200702
$453$	3675.04	0.381166
$454$	12317.2	1.27330
$455$	1674.45	0.172526
$456$	9525.83	0.978263
$457$	10797.5	1.10522	0.552609	−	0.833441i	$-0.313632\pi$
$457$	10797.5	1.10522	0.552609	+	0.833441i	$0.313632\pi$
$458$	−1584.66	−0.161673
$459$	3069.57	0.312147
$460$	−12933.2	−1.31090
$461$	6803.00	0.687305	0.343652	−	0.939097i	$-0.388336\pi$
$461$	6803.00	0.687305	0.343652	+	0.939097i	$0.388336\pi$
$462$	4878.75	0.491298
$463$	−16650.5	−1.67130	−0.835652	−	0.549259i	$-0.814910\pi$
$463$	−16650.5	−1.67130	−0.835652	+	0.549259i	$0.814910\pi$
$464$	3067.58	0.306916
$465$	−10320.0	−1.02920
$466$	−2030.04	−0.201803
$467$	−6459.28	−0.640042	−0.320021	−	0.947410i	$-0.603690\pi$
$467$	−6459.28	−0.640042	−0.320021	+	0.947410i	$0.603690\pi$
$468$	−4171.36	−0.412011
$469$	10701.6	1.05363
$470$	−17063.9	−1.67468
$471$	6270.67	0.613455
$472$	−7106.93	−0.693057
$473$	−1006.30	−0.0978222
$474$	7149.40	0.692791
$475$	−1072.38	−0.103588
$476$	−6828.61	−0.657540
$477$	−3450.85	−0.331245
$478$	24407.5	2.33551
$479$	11074.7	1.05640	0.528199	−	0.849121i	$-0.322868\pi$
$479$	11074.7	1.05640	0.528199	+	0.849121i	$0.322868\pi$
$480$	22369.1	2.12709
$481$	−1824.74	−0.172975
$482$	−29515.7	−2.78922
$483$	10545.2	0.993424
$484$	1304.06	0.122470
$485$	−17620.1	−1.64966
$486$	22690.7	2.11785
$487$	−4524.90	−0.421033	−0.210516	−	0.977590i	$-0.567515\pi$
$487$	−4524.90	−0.421033	−0.210516	+	0.977590i	$0.567515\pi$
$488$	9139.18	0.847769
$489$	19116.0	1.76781
$490$	8783.54	0.809796
$491$	−189.160	−0.0173863	−0.00869313	−	0.999962i	$-0.502767\pi$
$491$	−189.160	−0.0173863	−0.00869313	+	0.999962i	$0.502767\pi$
$492$	−36769.1	−3.36927
$493$	−4388.98	−0.400953
$494$	−4817.37	−0.438753
$495$	4484.08	0.407161
$496$	3833.51	0.347036
$497$	−11721.2	−1.05788
$498$	45082.3	4.05660
$499$	−15599.2	−1.39943	−0.699714	−	0.714423i	$-0.746689\pi$
$499$	−15599.2	−1.39943	−0.699714	+	0.714423i	$0.746689\pi$
$500$	−14352.2	−1.28370
$501$	24107.3	2.14977
$502$	−8805.23	−0.782862
$503$	−18144.0	−1.60835	−0.804176	−	0.594391i	$-0.797393\pi$
$503$	−18144.0	−1.60835	−0.804176	+	0.594391i	$0.797393\pi$
$504$	5475.17	0.483896
$505$	16398.7	1.44502
$506$	4910.96	0.431460
$507$	−16335.9	−1.43097
$508$	4728.82	0.413007
$509$	−1630.45	−0.141981	−0.0709905	−	0.997477i	$-0.522616\pi$
$509$	−1630.45	−0.141981	−0.0709905	+	0.997477i	$0.522616\pi$
$510$	−19371.1	−1.68190
$511$	14794.8	1.28079
$512$	−11589.3	−1.00035
$513$	−6330.47	−0.544828
$514$	33333.8	2.86049
$515$	−693.818	−0.0593656
$516$	−7763.12	−0.662311
$517$	3718.91	0.316359
$518$	9294.04	0.788333
$519$	14801.8	1.25188
$520$	1550.27	0.130738
$521$	−5697.25	−0.479080	−0.239540	−	0.970886i	$-0.576997\pi$
$521$	−5697.25	−0.479080	−0.239540	+	0.970886i	$0.576997\pi$
$522$	13655.6	1.14500
$523$	10231.3	0.855419	0.427710	−	0.903916i	$-0.359321\pi$
$523$	10231.3	0.855419	0.427710	+	0.903916i	$0.359321\pi$
$524$	−1411.83	−0.117703
$525$	−1091.89	−0.0907696
$526$	22890.6	1.89749
$527$	−5484.85	−0.453366
$528$	−2950.70	−0.243206
$529$	−1552.16	−0.127572
$530$	4976.68	0.407874
$531$	20667.1	1.68903
$532$	14082.8	1.14769
$533$	4791.90	0.389419
$534$	−45162.4	−3.65987
$535$	−11549.3	−0.933309
$536$	9907.91	0.798426
$537$	28388.9	2.28133
$538$	2108.93	0.169001
$539$	−1914.29	−0.152976
$540$	7905.27	0.629979
$541$	276.148	0.0219455	0.0109728	−	0.999940i	$-0.496507\pi$
$541$	276.148	0.0219455	0.0109728	+	0.999940i	$0.496507\pi$
$542$	26261.1	2.08120
$543$	4195.08	0.331544
$544$	11888.6	0.936986
$545$	9213.57	0.724158
$546$	−4905.01	−0.384460
$547$	10093.8	0.788992	0.394496	−	0.918898i	$-0.370919\pi$
$547$	10093.8	0.788992	0.394496	+	0.918898i	$0.370919\pi$
$548$	−65.0835	−0.00507341
$549$	−26576.9	−2.06608
$550$	−508.499	−0.0394227
$551$	9051.52	0.699833
$552$	9763.16	0.752804
$553$	2723.79	0.209453
$554$	−29636.4	−2.27280
$555$	15132.3	1.15735
$556$	2610.27	0.199101
$557$	21746.1	1.65424	0.827121	−	0.562024i	$-0.189977\pi$
$557$	21746.1	1.65424	0.827121	+	0.562024i	$0.189977\pi$
$558$	17065.3	1.29468
$559$	1011.72	0.0765496
$560$	5158.13	0.389233
$561$	4221.75	0.317723
$562$	−27077.1	−2.03235
$563$	2227.94	0.166779	0.0833894	−	0.996517i	$-0.473425\pi$
$563$	2227.94	0.166779	0.0833894	+	0.996517i	$0.473425\pi$
$564$	28689.5	2.14193
$565$	2084.42	0.155208
$566$	−6549.44	−0.486384
$567$	5837.70	0.432382
$568$	−10851.9	−0.801649
$569$	25333.9	1.86653	0.933264	−	0.359192i	$-0.116948\pi$
$569$	25333.9	1.86653	0.933264	+	0.359192i	$0.116948\pi$
$570$	39949.7	2.93563
$571$	−396.120	−0.0290317	−0.0145158	−	0.999895i	$-0.504621\pi$
$571$	−396.120	−0.0290317	−0.0145158	+	0.999895i	$0.504621\pi$
$572$	−1311.08	−0.0958372
$573$	36076.6	2.63023
$574$	−24406.8	−1.77477
$575$	−1099.10	−0.0797142
$576$	−27451.2	−1.98577
$577$	14351.0	1.03542	0.517712	−	0.855555i	$-0.326784\pi$
$577$	14351.0	1.03542	0.517712	+	0.855555i	$0.326784\pi$
$578$	10994.1	0.791167
$579$	29396.0	2.10994
$580$	−11303.2	−0.809209
$581$	17175.5	1.22644
$582$	51614.8	3.67612
$583$	−1084.62	−0.0770502
$584$	13697.6	0.970566
$585$	−4508.22	−0.318619
$586$	25728.3	1.81370
$587$	−6661.36	−0.468388	−0.234194	−	0.972190i	$-0.575245\pi$
$587$	−6661.36	−0.468388	−0.234194	+	0.972190i	$0.575245\pi$
$588$	−14767.7	−1.03573
$589$	11311.6	0.791315
$590$	−29805.2	−2.07977
$591$	−14409.4	−1.00291
$592$	−5621.10	−0.390246
$593$	11202.1	0.775740	0.387870	−	0.921714i	$-0.373211\pi$
$593$	11202.1	0.775740	0.387870	+	0.921714i	$0.373211\pi$
$594$	−3001.76	−0.207346
$595$	−7380.06	−0.508492
$596$	−15251.7	−1.04821
$597$	−9393.73	−0.643986
$598$	−4937.39	−0.337634
$599$	−3915.76	−0.267101	−0.133551	−	0.991042i	$-0.542638\pi$
$599$	−3915.76	−0.267101	−0.133551	+	0.991042i	$0.542638\pi$
$600$	−1010.91	−0.0687840
$601$	−8400.64	−0.570165	−0.285083	−	0.958503i	$-0.592021\pi$
$601$	−8400.64	−0.570165	−0.285083	+	0.958503i	$0.592021\pi$
$602$	−5153.04	−0.348874
$603$	−28812.4	−1.94582
$604$	5030.19	0.338867
$605$	1409.37	0.0947089
$606$	−48037.1	−3.22009
$607$	−10566.6	−0.706564	−0.353282	−	0.935517i	$-0.614934\pi$
$607$	−10566.6	−0.706564	−0.353282	+	0.935517i	$0.614934\pi$
$608$	−24518.3	−1.63544
$609$	9216.18	0.613233
$610$	38328.2	2.54404
$611$	−3738.93	−0.247563
$612$	18385.1	1.21433
$613$	19827.6	1.30641	0.653204	−	0.757182i	$-0.273424\pi$
$613$	19827.6	1.30641	0.653204	+	0.757182i	$0.273424\pi$
$614$	−31477.8	−2.06896
$615$	−39738.4	−2.60554
$616$	1720.87	0.112558
$617$	−21490.8	−1.40225	−0.701123	−	0.713040i	$-0.747318\pi$
$617$	−21490.8	−1.40225	−0.701123	+	0.713040i	$0.747318\pi$
$618$	2032.42	0.132291
$619$	−14729.9	−0.956452	−0.478226	−	0.878237i	$-0.658720\pi$
$619$	−14729.9	−0.956452	−0.478226	+	0.878237i	$0.658720\pi$
$620$	−14125.5	−0.914989
$621$	−6488.19	−0.419262
$622$	23528.9	1.51676
$623$	−17206.1	−1.10650
$624$	2966.58	0.190318
$625$	−16844.7	−1.07806
$626$	−30388.5	−1.94021
$627$	−8706.63	−0.554561
$628$	8582.95	0.545378
$629$	8042.46	0.509815
$630$	22961.9	1.45210
$631$	−22037.4	−1.39032	−0.695162	−	0.718853i	$-0.744667\pi$
$631$	−22037.4	−1.39032	−0.695162	+	0.718853i	$0.744667\pi$
$632$	2521.79	0.158721
$633$	−35057.4	−2.20128
$634$	28669.0	1.79588
$635$	5110.70	0.319389
$636$	−8367.28	−0.521673
$637$	1924.59	0.119710
$638$	4292.02	0.266337
$639$	31557.6	1.95368
$640$	16861.7	1.04143
$641$	2041.35	0.125785	0.0628927	−	0.998020i	$-0.479967\pi$
$641$	2041.35	0.125785	0.0628927	+	0.998020i	$0.479967\pi$
$642$	33831.6	2.07979
$643$	−20386.3	−1.25033	−0.625163	−	0.780495i	$-0.714967\pi$
$643$	−20386.3	−1.25033	−0.625163	+	0.780495i	$0.714967\pi$
$644$	14433.7	0.883180
$645$	−8390.03	−0.512182
$646$	21232.3	1.29315
$647$	−7732.19	−0.469836	−0.234918	−	0.972015i	$-0.575482\pi$
$647$	−7732.19	−0.469836	−0.234918	+	0.972015i	$0.575482\pi$
$648$	5404.77	0.327653
$649$	6495.76	0.392883
$650$	511.237	0.0308498
$651$	11517.3	0.693395
$652$	26165.0	1.57163
$653$	27587.8	1.65328	0.826642	−	0.562729i	$-0.190248\pi$
$653$	27587.8	1.65328	0.826642	+	0.562729i	$0.190248\pi$
$654$	−26989.5	−1.61372
$655$	−1525.84	−0.0910223
$656$	14761.4	0.878559
$657$	−39832.9	−2.36534
$658$	19043.6	1.12826
$659$	−2025.08	−0.119706	−0.0598528	−	0.998207i	$-0.519063\pi$
$659$	−2025.08	−0.119706	−0.0598528	+	0.998207i	$0.519063\pi$
$660$	10872.5	0.641232
$661$	−31394.8	−1.84738	−0.923688	−	0.383146i	$-0.874841\pi$
$661$	−31394.8	−1.84738	−0.923688	+	0.383146i	$0.874841\pi$
$662$	−9483.94	−0.556803
$663$	−4244.47	−0.248630
$664$	15901.8	0.929380
$665$	15220.1	0.887534
$666$	−25022.9	−1.45588
$667$	9277.03	0.538543
$668$	32996.7	1.91120
$669$	3479.88	0.201106
$670$	41552.0	2.39596
$671$	−8353.24	−0.480586
$672$	−24964.3	−1.43306
$673$	12629.0	0.723348	0.361674	−	0.932305i	$-0.382205\pi$
$673$	12629.0	0.723348	0.361674	+	0.932305i	$0.382205\pi$
$674$	−15434.1	−0.882045
$675$	671.812	0.0383082
$676$	−22359.7	−1.27217
$677$	3338.37	0.189518	0.0947592	−	0.995500i	$-0.469792\pi$
$677$	3338.37	0.189518	0.0947592	+	0.995500i	$0.469792\pi$
$678$	−6105.94	−0.345866
$679$	19664.3	1.11141
$680$	−6832.74	−0.385329
$681$	−22381.3	−1.25940
$682$	5363.68	0.301152
$683$	−15439.5	−0.864971	−0.432486	−	0.901641i	$-0.642363\pi$
$683$	−15439.5	−0.864971	−0.432486	+	0.901641i	$0.642363\pi$
$684$	−37916.0	−2.11953
$685$	−70.3394	−0.00392340
$686$	−29123.2	−1.62089
$687$	2879.43	0.159909
$688$	3116.59	0.172702
$689$	1090.46	0.0602948
$690$	40945.0	2.25906
$691$	25139.4	1.38401	0.692004	−	0.721894i	$-0.256728\pi$
$691$	25139.4	1.38401	0.692004	+	0.721894i	$0.256728\pi$
$692$	20259.9	1.11296
$693$	−5004.32	−0.274312
$694$	52660.5	2.88035
$695$	2821.06	0.153970
$696$	8532.70	0.464700
$697$	−21120.0	−1.14774
$698$	44160.7	2.39471
$699$	3688.73	0.199600
$700$	−1494.52	−0.0806966
$701$	3998.08	0.215414	0.107707	−	0.994183i	$-0.465649\pi$
$701$	3998.08	0.215414	0.107707	+	0.994183i	$0.465649\pi$
$702$	3017.92	0.162257
$703$	−16586.2	−0.889843
$704$	−8628.04	−0.461905
$705$	31006.3	1.65641
$706$	−47470.4	−2.53056
$707$	−18301.3	−0.973536
$708$	50111.5	2.66003
$709$	−24514.1	−1.29852	−0.649258	−	0.760568i	$-0.724920\pi$
$709$	−24514.1	−1.29852	−0.649258	+	0.760568i	$0.724920\pi$
$710$	−45511.1	−2.40563
$711$	−7333.42	−0.386814
$712$	−15930.0	−0.838488
$713$	11593.4	0.608942
$714$	21618.6	1.13313
$715$	−1416.95	−0.0741134
$716$	38857.2	2.02816
$717$	−44350.1	−2.31002
$718$	18152.3	0.943505
$719$	17740.4	0.920176	0.460088	−	0.887873i	$-0.347818\pi$
$719$	17740.4	0.920176	0.460088	+	0.887873i	$0.347818\pi$
$720$	−13887.5	−0.718829
$721$	774.314	0.0399958
$722$	−14066.0	−0.725045
$723$	53632.2	2.75878
$724$	5742.00	0.294751
$725$	−960.580	−0.0492069
$726$	−4128.49	−0.211050
$727$	−25659.5	−1.30902	−0.654510	−	0.756054i	$-0.727125\pi$
$727$	−25659.5	−1.30902	−0.654510	+	0.756054i	$0.727125\pi$
$728$	−1730.13	−0.0880810
$729$	−29105.3	−1.47870
$730$	57445.3	2.91253
$731$	−4459.10	−0.225617
$732$	−64441.0	−3.25384
$733$	−2476.68	−0.124800	−0.0623998	−	0.998051i	$-0.519875\pi$
$733$	−2476.68	−0.124800	−0.0623998	+	0.998051i	$0.519875\pi$
$734$	26537.4	1.33449
$735$	−15960.3	−0.800959
$736$	−25129.1	−1.25852
$737$	−9055.86	−0.452614
$738$	65711.7	3.27762
$739$	7192.88	0.358044	0.179022	−	0.983845i	$-0.442707\pi$
$739$	7192.88	0.358044	0.179022	+	0.983845i	$0.442707\pi$
$740$	20712.3	1.02892
$741$	8753.50	0.433965
$742$	−5554.07	−0.274793
$743$	4376.25	0.216082	0.108041	−	0.994146i	$-0.465542\pi$
$743$	4376.25	0.216082	0.108041	+	0.994146i	$0.465542\pi$
$744$	10663.2	0.525445
$745$	−16483.3	−0.810607
$746$	−40888.6	−2.00675
$747$	−46242.7	−2.26497
$748$	5778.50	0.282464
$749$	12889.2	0.628788
$750$	45437.3	2.21218
$751$	18296.1	0.888995	0.444497	−	0.895780i	$-0.353382\pi$
$751$	18296.1	0.888995	0.444497	+	0.895780i	$0.353382\pi$
$752$	−11517.7	−0.558521
$753$	15999.7	0.774319
$754$	−4315.13	−0.208419
$755$	5436.41	0.262054
$756$	−8822.43	−0.424429
$757$	16207.5	0.778166	0.389083	−	0.921203i	$-0.372792\pi$
$757$	16207.5	0.778166	0.389083	+	0.921203i	$0.372792\pi$
$758$	5506.58	0.263863
$759$	−8923.56	−0.426752
$760$	14091.4	0.672562
$761$	−23638.8	−1.12603	−0.563013	−	0.826448i	$-0.690358\pi$
$761$	−23638.8	−1.12603	−0.563013	+	0.826448i	$0.690358\pi$
$762$	−14970.9	−0.711730
$763$	−10282.5	−0.487879
$764$	49379.7	2.33835
$765$	19869.7	0.939074
$766$	24594.7	1.16011
$767$	−6530.72	−0.307446
$768$	14.8548	0.000697952 0
$769$	−32893.1	−1.54247	−0.771233	−	0.636554i	$-0.780359\pi$
$769$	−32893.1	−1.54247	−0.771233	+	0.636554i	$0.780359\pi$
$770$	7217.03	0.337771
$771$	−60569.8	−2.82927
$772$	40235.6	1.87579
$773$	24662.9	1.14756	0.573779	−	0.819010i	$-0.305477\pi$
$773$	24662.9	1.14756	0.573779	+	0.819010i	$0.305477\pi$
$774$	13873.8	0.644294
$775$	−1200.42	−0.0556393
$776$	18206.0	0.842211
$777$	−16887.9	−0.779731
$778$	17009.6	0.783833
$779$	43556.4	2.00330
$780$	−10931.1	−0.501789
$781$	9918.69	0.454441
$782$	21761.3	0.995118
$783$	−5670.47	−0.258807
$784$	5928.67	0.270074
$785$	9276.07	0.421754
$786$	4469.68	0.202835
$787$	28884.0	1.30826	0.654131	−	0.756382i	$-0.273035\pi$
$787$	28884.0	1.30826	0.654131	+	0.756382i	$0.273035\pi$
$788$	−19722.7	−0.891616
$789$	−41593.9	−1.87678
$790$	10576.0	0.476298
$791$	−2326.25	−0.104566
$792$	−4633.19	−0.207870
$793$	8398.21	0.376077
$794$	61771.8	2.76096
$795$	−9042.98	−0.403423
$796$	−12857.6	−0.572521
$797$	11474.0	0.509951	0.254975	−	0.966948i	$-0.417933\pi$
$797$	11474.0	0.509951	0.254975	+	0.966948i	$0.417933\pi$
$798$	−44584.6	−1.97779
$799$	16479.1	0.729649
$800$	2601.96	0.114992
$801$	46324.9	2.04346
$802$	−15155.6	−0.667283
$803$	−12519.6	−0.550197
$804$	−69861.3	−3.06445
$805$	15599.3	0.682985
$806$	−5392.55	−0.235663
$807$	−3832.07	−0.167156
$808$	−16944.0	−0.737733
$809$	−12202.0	−0.530282	−0.265141	−	0.964210i	$-0.585419\pi$
$809$	−12202.0	−0.530282	−0.265141	+	0.964210i	$0.585419\pi$
$810$	22666.7	0.983241
$811$	10278.0	0.445017	0.222509	−	0.974931i	$-0.428575\pi$
$811$	10278.0	0.445017	0.222509	+	0.974931i	$0.428575\pi$
$812$	12614.6	0.545180
$813$	−47718.2	−2.05849
$814$	−7864.79	−0.338650
$815$	28277.9	1.21538
$816$	−13075.0	−0.560929
$817$	9196.13	0.393797
$818$	−32403.7	−1.38505
$819$	5031.26	0.214660
$820$	−54391.8	−2.31639
$821$	−4882.90	−0.207569	−0.103785	−	0.994600i	$-0.533095\pi$
$821$	−4882.90	−0.207569	−0.103785	+	0.994600i	$0.533095\pi$
$822$	206.047	0.00874294
$823$	−24280.5	−1.02839	−0.514194	−	0.857674i	$-0.671909\pi$
$823$	−24280.5	−1.02839	−0.514194	+	0.857674i	$0.671909\pi$
$824$	716.890	0.0303083
$825$	923.979	0.0389925
$826$	33263.2	1.40118
$827$	2257.89	0.0949388	0.0474694	−	0.998873i	$-0.484884\pi$
$827$	2257.89	0.0949388	0.0474694	+	0.998873i	$0.484884\pi$
$828$	−38860.7	−1.63104
$829$	−25204.6	−1.05596	−0.527980	−	0.849257i	$-0.677050\pi$
$829$	−25204.6	−1.05596	−0.527980	+	0.849257i	$0.677050\pi$
$830$	66689.3	2.78894
$831$	53851.5	2.24800
$832$	8674.48	0.361459
$833$	−8482.53	−0.352824
$834$	−8263.78	−0.343107
$835$	35661.3	1.47798
$836$	−11917.2	−0.493019
$837$	−7086.31	−0.292639
$838$	3137.22	0.129324
$839$	17247.8	0.709727	0.354864	−	0.934918i	$-0.384527\pi$
$839$	17247.8	0.709727	0.354864	+	0.934918i	$0.384527\pi$
$840$	14347.7	0.589337
$841$	−16281.2	−0.667562
$842$	628.628	0.0257292
$843$	49201.0	2.01017
$844$	−47984.7	−1.95699
$845$	−24165.3	−0.983802
$846$	−51272.3	−2.08366
$847$	−1572.88	−0.0638073
$848$	3359.14	0.136030
$849$	11900.8	0.481077
$850$	−2253.25	−0.0909244
$851$	−16999.4	−0.684762
$852$	76517.6	3.07682
$853$	−29320.9	−1.17694	−0.588470	−	0.808519i	$-0.700270\pi$
$853$	−29320.9	−1.17694	−0.588470	+	0.808519i	$0.700270\pi$
$854$	−42774.9	−1.71397
$855$	−40977.9	−1.63908
$856$	11933.4	0.476488
$857$	21708.7	0.865293	0.432647	−	0.901564i	$-0.357580\pi$
$857$	21708.7	0.865293	0.432647	+	0.901564i	$0.357580\pi$
$858$	4150.71	0.165155
$859$	33017.1	1.31144	0.655721	−	0.755003i	$-0.272365\pi$
$859$	33017.1	1.31144	0.655721	+	0.755003i	$0.272365\pi$
$860$	−11483.8	−0.455343
$861$	44348.8	1.75540
$862$	60029.8	2.37195
$863$	−32955.5	−1.29990	−0.649952	−	0.759975i	$-0.725211\pi$
$863$	−32955.5	−1.29990	−0.649952	+	0.759975i	$0.725211\pi$
$864$	15359.9	0.604807
$865$	21896.0	0.860678
$866$	41486.3	1.62790
$867$	−19977.1	−0.782534
$868$	15764.3	0.616446
$869$	−2304.92	−0.0899761
$870$	35784.6	1.39450
$871$	9104.60	0.354188
$872$	−9519.94	−0.369709
$873$	−52943.3	−2.05253
$874$	−44878.9	−1.73690
$875$	17310.8	0.668813
$876$	−96582.6	−3.72514
$877$	12147.5	0.467723	0.233862	−	0.972270i	$-0.424864\pi$
$877$	12147.5	0.467723	0.233862	+	0.972270i	$0.424864\pi$
$878$	3989.81	0.153359
$879$	−46750.1	−1.79390
$880$	−4364.90	−0.167206
$881$	10893.6	0.416590	0.208295	−	0.978066i	$-0.433209\pi$
$881$	10893.6	0.416590	0.208295	+	0.978066i	$0.433209\pi$
$882$	26392.1	1.00756
$883$	51448.3	1.96078	0.980392	−	0.197059i	$-0.0631391\pi$
$883$	51448.3	1.96078	0.980392	+	0.197059i	$0.0631391\pi$
$884$	−5809.61	−0.221039
$885$	54158.2	2.05707
$886$	−35993.6	−1.36482
$887$	−19022.2	−0.720070	−0.360035	−	0.932939i	$-0.617235\pi$
$887$	−19022.2	−0.720070	−0.360035	+	0.932939i	$0.617235\pi$
$888$	−15635.5	−0.590870
$889$	−5703.64	−0.215179
$890$	−66807.8	−2.51618
$891$	−4939.97	−0.185741
$892$	4763.07	0.178789
$893$	−33985.4	−1.27355
$894$	48285.0	1.80637
$895$	41995.1	1.56843
$896$	−18817.9	−0.701632
$897$	8971.59	0.333950
$898$	−21742.4	−0.807966
$899$	10132.2	0.375895
$900$	4023.78	0.149029
$901$	−4806.13	−0.177708
$902$	20653.5	0.762400
$903$	9363.43	0.345067
$904$	−2153.73	−0.0792391
$905$	6205.70	0.227939
$906$	−15925.0	−0.583965
$907$	14198.3	0.519785	0.259893	−	0.965638i	$-0.416313\pi$
$907$	14198.3	0.519785	0.259893	+	0.965638i	$0.416313\pi$
$908$	−30634.3	−1.11964
$909$	49273.5	1.79791
$910$	−7255.87	−0.264319
$911$	17159.2	0.624052	0.312026	−	0.950074i	$-0.398992\pi$
$911$	17159.2	0.624052	0.312026	+	0.950074i	$0.398992\pi$
$912$	26965.0	0.979059
$913$	−14534.3	−0.526850
$914$	−46788.5	−1.69324
$915$	−69644.9	−2.51627
$916$	3941.21	0.142163
$917$	1702.87	0.0613235
$918$	−13301.3	−0.478223
$919$	337.759	0.0121237	0.00606184	−	0.999982i	$-0.498070\pi$
$919$	337.759	0.0121237	0.00606184	+	0.999982i	$0.498070\pi$
$920$	14442.4	0.517558
$921$	57197.4	2.04638
$922$	−29479.3	−1.05298
$923$	−9972.08	−0.355618
$924$	−12134.0	−0.432011
$925$	1760.19	0.0625671
$926$	72151.3	2.56052
$927$	−2084.73	−0.0738635
$928$	−21962.1	−0.776875
$929$	19610.0	0.692555	0.346277	−	0.938132i	$-0.387446\pi$
$929$	19610.0	0.692555	0.346277	+	0.938132i	$0.387446\pi$
$930$	44719.6	1.57679
$931$	17493.8	0.615827
$932$	5048.94	0.177450
$933$	−42753.6	−1.50021
$934$	27989.9	0.980574
$935$	6245.14	0.218436
$936$	4658.13	0.162666
$937$	36562.2	1.27475	0.637373	−	0.770556i	$-0.280021\pi$
$937$	36562.2	1.27475	0.637373	+	0.770556i	$0.280021\pi$
$938$	−46372.8	−1.61421
$939$	55218.1	1.91903
$940$	42439.8	1.47259
$941$	−35224.7	−1.22029	−0.610145	−	0.792289i	$-0.708889\pi$
$941$	−35224.7	−1.22029	−0.610145	+	0.792289i	$0.708889\pi$
$942$	−27172.6	−0.939842
$943$	44641.6	1.54160
$944$	−20117.8	−0.693621
$945$	−9534.88	−0.328222
$946$	4360.60	0.149868
$947$	−53096.0	−1.82195	−0.910976	−	0.412459i	$-0.864670\pi$
$947$	−53096.0	−1.82195	−0.910976	+	0.412459i	$0.864670\pi$
$948$	−17781.3	−0.609188
$949$	12587.0	0.430550
$950$	4646.94	0.158702
$951$	−52093.5	−1.77629
$952$	7625.46	0.259604
$953$	38407.2	1.30549	0.652745	−	0.757578i	$-0.273617\pi$
$953$	38407.2	1.30549	0.652745	+	0.757578i	$0.273617\pi$
$954$	14953.5	0.507482
$955$	53367.4	1.80830
$956$	−60704.1	−2.05367
$957$	−7798.91	−0.263430
$958$	−47989.6	−1.61845
$959$	78.5000	0.00264327
$960$	−71936.0	−2.41846
$961$	−17128.9	−0.574968
$962$	7907.13	0.265006
$963$	−34702.4	−1.16124
$964$	73408.8	2.45263
$965$	43484.9	1.45060
$966$	−45695.4	−1.52197
$967$	16663.4	0.554146	0.277073	−	0.960849i	$-0.410636\pi$
$967$	16663.4	0.554146	0.277073	+	0.960849i	$0.410636\pi$
$968$	−1456.23	−0.0483523
$969$	−38580.6	−1.27904
$970$	76352.7	2.52736
$971$	48134.4	1.59084	0.795421	−	0.606057i	$-0.207250\pi$
$971$	48134.4	1.59084	0.795421	+	0.606057i	$0.207250\pi$
$972$	−56434.3	−1.86227
$973$	−3148.35	−0.103732
$974$	19607.7	0.645042
$975$	−928.953	−0.0305131
$976$	25870.5	0.848459
$977$	−7738.78	−0.253414	−0.126707	−	0.991940i	$-0.540441\pi$
$977$	−7738.78	−0.253414	−0.126707	+	0.991940i	$0.540441\pi$
$978$	−82835.2	−2.70836
$979$	14560.1	0.475325
$980$	−21845.6	−0.712074
$981$	27684.2	0.901007
$982$	819.682	0.0266366
$983$	−27432.8	−0.890104	−0.445052	−	0.895505i	$-0.646815\pi$
$983$	−27432.8	−0.890104	−0.445052	+	0.895505i	$0.646815\pi$
$984$	41059.8	1.33022
$985$	−21315.5	−0.689509
$986$	19018.7	0.614278
$987$	−34603.6	−1.11595
$988$	11981.3	0.385806
$989$	9425.25	0.303039
$990$	−19430.8	−0.623789
$991$	−46132.4	−1.47875	−0.739376	−	0.673293i	$-0.764879\pi$
$991$	−46132.4	−1.47875	−0.739376	+	0.673293i	$0.764879\pi$
$992$	−27445.7	−0.878428
$993$	17233.0	0.550727
$994$	50791.2	1.62072
$995$	−13895.9	−0.442745
$996$	−112124.	−3.56707
$997$	12447.4	0.395401	0.197700	−	0.980263i	$-0.436653\pi$
$997$	12447.4	0.395401	0.197700	+	0.980263i	$0.436653\pi$
$998$	67595.6	2.14399
$999$	10390.7	0.329076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.13	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-4.33328 q^{2} +7.87388 q^{3} +10.7773 q^{4} +11.6477 q^{5} -34.1197 q^{6} -12.9990 q^{7} -12.0350 q^{8} +34.9979 q^{9} +O(q^{10})\)	\(q-4.33328 q^{2} +7.87388 q^{3} +10.7773 q^{4} +11.6477 q^{5} -34.1197 q^{6} -12.9990 q^{7} -12.0350 q^{8} +34.9979 q^{9} -50.4726 q^{10} +11.0000 q^{11} +84.8594 q^{12} -11.0592 q^{13} +56.3283 q^{14} +91.7122 q^{15} -34.0677 q^{16} +48.7429 q^{17} -151.656 q^{18} -100.524 q^{19} +125.531 q^{20} -102.353 q^{21} -47.6661 q^{22} -103.028 q^{23} -94.7619 q^{24} +10.6679 q^{25} +47.9227 q^{26} +62.9748 q^{27} -140.095 q^{28} -90.0435 q^{29} -397.415 q^{30} -112.526 q^{31} +243.905 q^{32} +86.6126 q^{33} -211.217 q^{34} -151.408 q^{35} +377.184 q^{36} +164.998 q^{37} +435.598 q^{38} -87.0789 q^{39} -140.179 q^{40} -433.295 q^{41} +443.522 q^{42} -91.4821 q^{43} +118.551 q^{44} +407.644 q^{45} +446.451 q^{46} +338.083 q^{47} -268.245 q^{48} -174.026 q^{49} -46.2272 q^{50} +383.795 q^{51} -119.189 q^{52} -98.6017 q^{53} -272.888 q^{54} +128.124 q^{55} +156.443 q^{56} -791.512 q^{57} +390.184 q^{58} +590.523 q^{59} +988.413 q^{60} -759.385 q^{61} +487.607 q^{62} -454.938 q^{63} -784.367 q^{64} -128.814 q^{65} -375.317 q^{66} -823.260 q^{67} +525.318 q^{68} -811.232 q^{69} +656.093 q^{70} +901.699 q^{71} -421.199 q^{72} -1138.15 q^{73} -714.981 q^{74} +83.9981 q^{75} -1083.38 q^{76} -142.989 q^{77} +377.337 q^{78} -209.539 q^{79} -396.809 q^{80} -449.089 q^{81} +1877.59 q^{82} -1321.30 q^{83} -1103.09 q^{84} +567.740 q^{85} +396.418 q^{86} -708.992 q^{87} -132.385 q^{88} +1323.65 q^{89} -1766.44 q^{90} +143.759 q^{91} -1110.37 q^{92} -886.017 q^{93} -1465.01 q^{94} -1170.87 q^{95} +1920.48 q^{96} -1512.75 q^{97} +754.104 q^{98} +384.977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 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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