LMFDB - Embedded newform 1441.4.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-4.04460 q^{2} -8.35230 q^{3} +8.35876 q^{4} -11.0565 q^{5} +33.7817 q^{6} -15.6748 q^{7} -1.45103 q^{8} +42.7609 q^{9} +O(q^{10})$	\(q-4.04460 q^{2} -8.35230 q^{3} +8.35876 q^{4} -11.0565 q^{5} +33.7817 q^{6} -15.6748 q^{7} -1.45103 q^{8} +42.7609 q^{9} +44.7191 q^{10} +11.0000 q^{11} -69.8149 q^{12} +49.2039 q^{13} +63.3981 q^{14} +92.3472 q^{15} -61.0012 q^{16} -71.4928 q^{17} -172.951 q^{18} -78.1611 q^{19} -92.4186 q^{20} +130.920 q^{21} -44.4906 q^{22} -114.397 q^{23} +12.1195 q^{24} -2.75389 q^{25} -199.010 q^{26} -131.640 q^{27} -131.022 q^{28} -176.088 q^{29} -373.507 q^{30} +56.2999 q^{31} +258.334 q^{32} -91.8753 q^{33} +289.159 q^{34} +173.308 q^{35} +357.428 q^{36} -227.935 q^{37} +316.130 q^{38} -410.966 q^{39} +16.0434 q^{40} -97.3230 q^{41} -529.520 q^{42} +364.848 q^{43} +91.9463 q^{44} -472.786 q^{45} +462.690 q^{46} +184.830 q^{47} +509.501 q^{48} -97.3016 q^{49} +11.1384 q^{50} +597.129 q^{51} +411.284 q^{52} +386.905 q^{53} +532.430 q^{54} -121.621 q^{55} +22.7446 q^{56} +652.825 q^{57} +712.204 q^{58} +13.7191 q^{59} +771.908 q^{60} -485.943 q^{61} -227.710 q^{62} -670.268 q^{63} -556.845 q^{64} -544.023 q^{65} +371.599 q^{66} -100.144 q^{67} -597.591 q^{68} +955.479 q^{69} -700.961 q^{70} +290.604 q^{71} -62.0476 q^{72} +862.182 q^{73} +921.903 q^{74} +23.0013 q^{75} -653.330 q^{76} -172.422 q^{77} +1662.19 q^{78} +542.352 q^{79} +674.460 q^{80} -55.0484 q^{81} +393.632 q^{82} -791.059 q^{83} +1094.33 q^{84} +790.460 q^{85} -1475.66 q^{86} +1470.74 q^{87} -15.9614 q^{88} +465.659 q^{89} +1912.23 q^{90} -771.260 q^{91} -956.218 q^{92} -470.234 q^{93} -747.561 q^{94} +864.188 q^{95} -2157.68 q^{96} +1480.33 q^{97} +393.546 q^{98} +470.370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.04460	−1.42998	−0.714990	−	0.699134i	$-0.753569\pi$
$2$	−4.04460	−1.42998	−0.714990	+	0.699134i	$0.753569\pi$
$3$	−8.35230	−1.60740	−0.803700	−	0.595034i	$-0.797139\pi$
$3$	−8.35230	−1.60740	−0.803700	+	0.595034i	$0.797139\pi$
$4$	8.35876	1.04484
$5$	−11.0565	−0.988923	−0.494462	−	0.869200i	$-0.664635\pi$
$5$	−11.0565	−0.988923	−0.494462	+	0.869200i	$0.664635\pi$
$6$	33.7817	2.29855
$7$	−15.6748	−0.846358	−0.423179	−	0.906046i	$-0.639086\pi$
$7$	−15.6748	−0.846358	−0.423179	+	0.906046i	$0.639086\pi$
$8$	−1.45103	−0.0641272
$9$	42.7609	1.58374
$10$	44.7191	1.41414
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−69.8149	−1.67948
$13$	49.2039	1.04975	0.524874	−	0.851180i	$-0.324113\pi$
$13$	49.2039	1.04975	0.524874	+	0.851180i	$0.324113\pi$
$14$	63.3981	1.21028
$15$	92.3472	1.58960
$16$	−61.0012	−0.953144
$17$	−71.4928	−1.01997	−0.509987	−	0.860182i	$-0.670350\pi$
$17$	−71.4928	−1.01997	−0.509987	+	0.860182i	$0.670350\pi$
$18$	−172.951	−2.26471
$19$	−78.1611	−0.943757	−0.471879	−	0.881664i	$-0.656424\pi$
$19$	−78.1611	−0.943757	−0.471879	+	0.881664i	$0.656424\pi$
$20$	−92.4186	−1.03327
$21$	130.920	1.36044
$22$	−44.4906	−0.431155
$23$	−114.397	−1.03711	−0.518553	−	0.855045i	$-0.673529\pi$
$23$	−114.397	−1.03711	−0.518553	+	0.855045i	$0.673529\pi$
$24$	12.1195	0.103078
$25$	−2.75389	−0.0220311
$26$	−199.010	−1.50112
$27$	−131.640	−0.938301
$28$	−131.022	−0.884313
$29$	−176.088	−1.12754	−0.563771	−	0.825931i	$-0.690650\pi$
$29$	−176.088	−1.12754	−0.563771	+	0.825931i	$0.690650\pi$
$30$	−373.507	−2.27309
$31$	56.2999	0.326186	0.163093	−	0.986611i	$-0.447853\pi$
$31$	56.2999	0.326186	0.163093	+	0.986611i	$0.447853\pi$
$32$	258.334	1.42710
$33$	−91.8753	−0.484650
$34$	289.159	1.45854
$35$	173.308	0.836983
$36$	357.428	1.65476
$37$	−227.935	−1.01276	−0.506381	−	0.862310i	$-0.669017\pi$
$37$	−227.935	−1.01276	−0.506381	+	0.862310i	$0.669017\pi$
$38$	316.130	1.34955
$39$	−410.966	−1.68737
$40$	16.0434	0.0634169
$41$	−97.3230	−0.370715	−0.185357	−	0.982671i	$-0.559344\pi$
$41$	−97.3230	−0.370715	−0.185357	+	0.982671i	$0.559344\pi$
$42$	−529.520	−1.94540
$43$	364.848	1.29393	0.646963	−	0.762521i	$-0.276039\pi$
$43$	364.848	1.29393	0.646963	+	0.762521i	$0.276039\pi$
$44$	91.9463	0.315033
$45$	−472.786	−1.56619
$46$	462.690	1.48304
$47$	184.830	0.573621	0.286810	−	0.957987i	$-0.407405\pi$
$47$	184.830	0.573621	0.286810	+	0.957987i	$0.407405\pi$
$48$	509.501	1.53208
$49$	−97.3016	−0.283678
$50$	11.1384	0.0315040
$51$	597.129	1.63951
$52$	411.284	1.09682
$53$	386.905	1.00274	0.501372	−	0.865232i	$-0.332829\pi$
$53$	386.905	1.00274	0.501372	+	0.865232i	$0.332829\pi$
$54$	532.430	1.34175
$55$	−121.621	−0.298172
$56$	22.7446	0.0542746
$57$	652.825	1.51700
$58$	712.204	1.61236
$59$	13.7191	0.0302724	0.0151362	−	0.999885i	$-0.495182\pi$
$59$	13.7191	0.0302724	0.0151362	+	0.999885i	$0.495182\pi$
$60$	771.908	1.66088
$61$	−485.943	−1.01998	−0.509989	−	0.860181i	$-0.670350\pi$
$61$	−485.943	−1.01998	−0.509989	+	0.860181i	$0.670350\pi$
$62$	−227.710	−0.466439
$63$	−670.268	−1.34041
$64$	−556.845	−1.08759
$65$	−544.023	−1.03812
$66$	371.599	0.693040
$67$	−100.144	−0.182605	−0.0913025	−	0.995823i	$-0.529103\pi$
$67$	−100.144	−0.182605	−0.0913025	+	0.995823i	$0.529103\pi$
$68$	−597.591	−1.06571
$69$	955.479	1.66705
$70$	−700.961	−1.19687
$71$	290.604	0.485751	0.242876	−	0.970057i	$-0.421909\pi$
$71$	290.604	0.485751	0.242876	+	0.970057i	$0.421909\pi$
$72$	−62.0476	−0.101561
$73$	862.182	1.38234	0.691170	−	0.722692i	$-0.257096\pi$
$73$	862.182	1.38234	0.691170	+	0.722692i	$0.257096\pi$
$74$	921.903	1.44823
$75$	23.0013	0.0354128
$76$	−653.330	−0.986080
$77$	−172.422	−0.255187
$78$	1662.19	2.41290
$79$	542.352	0.772397	0.386199	−	0.922416i	$-0.373788\pi$
$79$	542.352	0.772397	0.386199	+	0.922416i	$0.373788\pi$
$80$	674.460	0.942586
$81$	−55.0484	−0.0755122
$82$	393.632	0.530115
$83$	−791.059	−1.04614	−0.523072	−	0.852288i	$-0.675214\pi$
$83$	−791.059	−1.04614	−0.523072	+	0.852288i	$0.675214\pi$
$84$	1094.33	1.42145
$85$	790.460	1.00868
$86$	−1475.66	−1.85029
$87$	1470.74	1.81241
$88$	−15.9614	−0.0193351
$89$	465.659	0.554604	0.277302	−	0.960783i	$-0.410560\pi$
$89$	465.659	0.554604	0.277302	+	0.960783i	$0.410560\pi$
$90$	1912.23	2.23963
$91$	−771.260	−0.888462
$92$	−956.218	−1.08362
$93$	−470.234	−0.524311
$94$	−747.561	−0.820266
$95$	864.188	0.933303
$96$	−2157.68	−2.29393
$97$	1480.33	1.54954	0.774768	−	0.632245i	$-0.217866\pi$
$97$	1480.33	1.54954	0.774768	+	0.632245i	$0.217866\pi$
$98$	393.546	0.405654
$99$	470.370	0.477515
$100$	−23.0191	−0.0230191
$101$	−519.055	−0.511365	−0.255683	−	0.966761i	$-0.582300\pi$
$101$	−519.055	−0.511365	−0.255683	+	0.966761i	$0.582300\pi$
$102$	−2415.15	−2.34446
$103$	−679.053	−0.649603	−0.324801	−	0.945782i	$-0.605297\pi$
$103$	−679.053	−0.649603	−0.324801	+	0.945782i	$0.605297\pi$
$104$	−71.3966	−0.0673174
$105$	−1447.52	−1.34537
$106$	−1564.87	−1.43390
$107$	−1126.03	−1.01736	−0.508682	−	0.860955i	$-0.669867\pi$
$107$	−1126.03	−1.01736	−0.508682	+	0.860955i	$0.669867\pi$
$108$	−1100.35	−0.980379
$109$	1159.17	1.01861	0.509304	−	0.860587i	$-0.329903\pi$
$109$	1159.17	1.01861	0.509304	+	0.860587i	$0.329903\pi$
$110$	491.910	0.426380
$111$	1903.78	1.62792
$112$	956.180	0.806701
$113$	−118.716	−0.0988309	−0.0494154	−	0.998778i	$-0.515736\pi$
$113$	−118.716	−0.0988309	−0.0494154	+	0.998778i	$0.515736\pi$
$114$	−2640.41	−2.16928
$115$	1264.83	1.02562
$116$	−1471.88	−1.17811
$117$	2104.01	1.66253
$118$	−55.4882	−0.0432890
$119$	1120.63	0.863262
$120$	−133.999	−0.101936
$121$	121.000	0.0909091
$122$	1965.44	1.45855
$123$	812.871	0.595887
$124$	470.597	0.340814
$125$	1412.51	1.01071
$126$	2710.96	1.91676
$127$	1337.67	0.934637	0.467318	−	0.884089i	$-0.345220\pi$
$127$	1337.67	0.934637	0.467318	+	0.884089i	$0.345220\pi$
$128$	185.546	0.128126
$129$	−3047.32	−2.07986
$130$	2200.35	1.48449
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	−767.964	−0.506384
$133$	1225.16	0.798756
$134$	405.042	0.261122
$135$	1455.48	0.927907
$136$	103.738	0.0654081
$137$	557.999	0.347978	0.173989	−	0.984748i	$-0.444334\pi$
$137$	557.999	0.347978	0.173989	+	0.984748i	$0.444334\pi$
$138$	−3864.53	−2.38384
$139$	−16.9265	−0.0103287	−0.00516434	−	0.999987i	$-0.501644\pi$
$139$	−16.9265	−0.0103287	−0.00516434	+	0.999987i	$0.501644\pi$
$140$	1448.64	0.874517
$141$	−1543.75	−0.922038
$142$	−1175.38	−0.694615
$143$	541.243	0.316511
$144$	−2608.47	−1.50953
$145$	1946.91	1.11505
$146$	−3487.18	−1.97672
$147$	812.692	0.455985
$148$	−1905.25	−1.05818
$149$	3234.50	1.77839	0.889197	−	0.457524i	$-0.151264\pi$
$149$	3234.50	1.77839	0.889197	+	0.457524i	$0.151264\pi$
$150$	−93.0309	−0.0506396
$151$	1106.47	0.596315	0.298157	−	0.954517i	$-0.403628\pi$
$151$	1106.47	0.596315	0.298157	+	0.954517i	$0.403628\pi$
$152$	113.414	0.0605206
$153$	−3057.10	−1.61537
$154$	697.379	0.364912
$155$	−622.480	−0.322573
$156$	−3435.17	−1.76303
$157$	802.557	0.407968	0.203984	−	0.978974i	$-0.434611\pi$
$157$	802.557	0.407968	0.203984	+	0.978974i	$0.434611\pi$
$158$	−2193.59	−1.10451
$159$	−3231.54	−1.61181
$160$	−2856.26	−1.41130
$161$	1793.15	0.877764
$162$	222.649	0.107981
$163$	1737.53	0.834932	0.417466	−	0.908692i	$-0.362918\pi$
$163$	1737.53	0.834932	0.417466	+	0.908692i	$0.362918\pi$
$164$	−813.499	−0.387339
$165$	1015.82	0.479281
$166$	3199.51	1.49597
$167$	1940.71	0.899262	0.449631	−	0.893214i	$-0.351555\pi$
$167$	1940.71	0.899262	0.449631	+	0.893214i	$0.351555\pi$
$168$	−189.970	−0.0872411
$169$	224.028	0.101970
$170$	−3197.09	−1.44239
$171$	−3342.24	−1.49466
$172$	3049.68	1.35195
$173$	520.518	0.228753	0.114376	−	0.993437i	$-0.463513\pi$
$173$	520.518	0.228753	0.114376	+	0.993437i	$0.463513\pi$
$174$	−5948.54	−2.59171
$175$	43.1665	0.0186462
$176$	−671.013	−0.287384
$177$	−114.586	−0.0486599
$178$	−1883.40	−0.793073
$179$	−1119.83	−0.467600	−0.233800	−	0.972285i	$-0.575116\pi$
$179$	−1119.83	−0.467600	−0.233800	+	0.972285i	$0.575116\pi$
$180$	−3951.90	−1.63643
$181$	−1.75767	−0.000721803 0	−0.000360901	−	1.00000i	$-0.500115\pi$
$181$	−1.75767	−0.000721803 0	−0.000360901		1.00000i	$0.500115\pi$
$182$	3119.44	1.27048
$183$	4058.74	1.63951
$184$	165.994	0.0665068
$185$	2520.16	1.00154
$186$	1901.91	0.749755
$187$	−786.420	−0.307533
$188$	1544.95	0.599344
$189$	2063.43	0.794138
$190$	−3495.29	−1.33461
$191$	−2816.18	−1.06687	−0.533433	−	0.845842i	$-0.679099\pi$
$191$	−2816.18	−1.06687	−0.533433	+	0.845842i	$0.679099\pi$
$192$	4650.94	1.74819
$193$	1569.73	0.585447	0.292724	−	0.956197i	$-0.405438\pi$
$193$	1569.73	0.585447	0.292724	+	0.956197i	$0.405438\pi$
$194$	−5987.35	−2.21581
$195$	4543.85	1.66867
$196$	−813.321	−0.296400
$197$	848.556	0.306889	0.153445	−	0.988157i	$-0.450963\pi$
$197$	848.556	0.306889	0.153445	+	0.988157i	$0.450963\pi$
$198$	−1902.46	−0.682837
$199$	18.0888	0.00644362	0.00322181	−	0.999995i	$-0.498974\pi$
$199$	18.0888	0.00644362	0.00322181	+	0.999995i	$0.498974\pi$
$200$	3.99598	0.00141279
$201$	836.432	0.293519
$202$	2099.37	0.731243
$203$	2760.14	0.954303
$204$	4991.26	1.71303
$205$	1076.05	0.366608
$206$	2746.50	0.928919
$207$	−4891.73	−1.64251
$208$	−3001.50	−1.00056
$209$	−859.772	−0.284553
$210$	5854.64	1.92385
$211$	−1163.11	−0.379487	−0.189744	−	0.981834i	$-0.560766\pi$
$211$	−1163.11	−0.379487	−0.189744	+	0.981834i	$0.560766\pi$
$212$	3234.04	1.04771
$213$	−2427.21	−0.780797
$214$	4554.35	1.45481
$215$	−4033.94	−1.27959
$216$	191.014	0.0601707
$217$	−882.488	−0.276070
$218$	−4688.37	−1.45659
$219$	−7201.21	−2.22197
$220$	−1016.60	−0.311543
$221$	−3517.73	−1.07071
$222$	−7700.01	−2.32789
$223$	−3428.17	−1.02945	−0.514725	−	0.857355i	$-0.672106\pi$
$223$	−3428.17	−1.02945	−0.514725	+	0.857355i	$0.672106\pi$
$224$	−4049.32	−1.20784
$225$	−117.759	−0.0348915
$226$	480.159	0.141326
$227$	5993.25	1.75236	0.876181	−	0.481983i	$-0.160083\pi$
$227$	5993.25	1.75236	0.876181	+	0.481983i	$0.160083\pi$
$228$	5456.81	1.58503
$229$	−173.320	−0.0500144	−0.0250072	−	0.999687i	$-0.507961\pi$
$229$	−173.320	−0.0500144	−0.0250072	+	0.999687i	$0.507961\pi$
$230$	−5115.73	−1.46662
$231$	1440.12	0.410187
$232$	255.509	0.0723061
$233$	−3507.01	−0.986060	−0.493030	−	0.870012i	$-0.664111\pi$
$233$	−3507.01	−0.986060	−0.493030	+	0.870012i	$0.664111\pi$
$234$	−8509.86	−2.37738
$235$	−2043.57	−0.567267
$236$	114.675	0.0316300
$237$	−4529.89	−1.24155
$238$	−4532.51	−1.23445
$239$	−5346.15	−1.44692	−0.723459	−	0.690367i	$-0.757449\pi$
$239$	−5346.15	−1.44692	−0.723459	+	0.690367i	$0.757449\pi$
$240$	−5633.29	−1.51511
$241$	2228.66	0.595687	0.297844	−	0.954615i	$-0.403733\pi$
$241$	2228.66	0.595687	0.297844	+	0.954615i	$0.403733\pi$
$242$	−489.396	−0.129998
$243$	4014.06	1.05968
$244$	−4061.88	−1.06572
$245$	1075.82	0.280536
$246$	−3287.73	−0.852107
$247$	−3845.83	−0.990707
$248$	−81.6931	−0.0209174
$249$	6607.16	1.68157
$250$	−5713.03	−1.44530
$251$	−6269.89	−1.57670	−0.788351	−	0.615226i	$-0.789065\pi$
$251$	−6269.89	−1.57670	−0.788351	+	0.615226i	$0.789065\pi$
$252$	−5602.60	−1.40052
$253$	−1258.37	−0.312699
$254$	−5410.33	−1.33651
$255$	−6602.16	−1.62135
$256$	3704.31	0.904371
$257$	4034.80	0.979315	0.489658	−	0.871915i	$-0.337122\pi$
$257$	4034.80	0.979315	0.489658	+	0.871915i	$0.337122\pi$
$258$	12325.2	2.97416
$259$	3572.82	0.857159
$260$	−4547.36	−1.08467
$261$	−7529.68	−1.78573
$262$	529.842	0.124938
$263$	−4017.75	−0.941998	−0.470999	−	0.882134i	$-0.656106\pi$
$263$	−4017.75	−0.941998	−0.470999	+	0.882134i	$0.656106\pi$
$264$	133.314	0.0310792
$265$	−4277.81	−0.991637
$266$	−4955.27	−1.14221
$267$	−3889.32	−0.891471
$268$	−837.079	−0.190794
$269$	4453.39	1.00940	0.504699	−	0.863296i	$-0.331604\pi$
$269$	4453.39	1.00940	0.504699	+	0.863296i	$0.331604\pi$
$270$	−5886.82	−1.32689
$271$	337.163	0.0755764	0.0377882	−	0.999286i	$-0.487969\pi$
$271$	337.163	0.0755764	0.0377882	+	0.999286i	$0.487969\pi$
$272$	4361.15	0.972181
$273$	6441.80	1.42812
$274$	−2256.88	−0.497602
$275$	−30.2927	−0.00664262
$276$	7986.62	1.74180
$277$	8766.83	1.90162	0.950808	−	0.309779i	$-0.100255\pi$
$277$	8766.83	1.90162	0.950808	+	0.309779i	$0.100255\pi$
$278$	68.4608	0.0147698
$279$	2407.44	0.516593
$280$	−251.476	−0.0536734
$281$	1181.81	0.250893	0.125446	−	0.992100i	$-0.459964\pi$
$281$	1181.81	0.250893	0.125446	+	0.992100i	$0.459964\pi$
$282$	6243.85	1.31850
$283$	−1655.41	−0.347717	−0.173859	−	0.984771i	$-0.555624\pi$
$283$	−1655.41	−0.347717	−0.173859	+	0.984771i	$0.555624\pi$
$284$	2429.09	0.507535
$285$	−7217.96	−1.50019
$286$	−2189.11	−0.452604
$287$	1525.52	0.313757
$288$	11046.6	2.26016
$289$	198.217	0.0403453
$290$	−7874.48	−1.59450
$291$	−12364.2	−2.49073
$292$	7206.77	1.44433
$293$	6919.13	1.37959	0.689795	−	0.724004i	$-0.257700\pi$
$293$	6919.13	1.37959	0.689795	+	0.724004i	$0.257700\pi$
$294$	−3287.01	−0.652049
$295$	−151.685	−0.0299371
$296$	330.741	0.0649457
$297$	−1448.04	−0.282908
$298$	−13082.3	−2.54307
$299$	−5628.79	−1.08870
$300$	192.262	0.0370009
$301$	−5718.91	−1.09512
$302$	−4475.24	−0.852718
$303$	4335.30	0.821969
$304$	4767.92	0.899537
$305$	5372.83	1.00868
$306$	12364.7	2.30995
$307$	3946.11	0.733605	0.366802	−	0.930299i	$-0.380453\pi$
$307$	3946.11	0.733605	0.366802	+	0.930299i	$0.380453\pi$
$308$	−1441.24	−0.266630
$309$	5671.66	1.04417
$310$	2517.68	0.461273
$311$	−10788.8	−1.96712	−0.983562	−	0.180571i	$-0.942205\pi$
$311$	−10788.8	−1.96712	−0.983562	+	0.180571i	$0.942205\pi$
$312$	596.326	0.108206
$313$	7503.97	1.35511	0.677555	−	0.735472i	$-0.263039\pi$
$313$	7503.97	1.35511	0.677555	+	0.735472i	$0.263039\pi$
$314$	−3246.02	−0.583387
$315$	7410.81	1.32556
$316$	4533.39	0.807035
$317$	−5366.63	−0.950852	−0.475426	−	0.879756i	$-0.657706\pi$
$317$	−5366.63	−0.950852	−0.475426	+	0.879756i	$0.657706\pi$
$318$	13070.3	2.30486
$319$	−1936.97	−0.339966
$320$	6156.76	1.07554
$321$	9404.98	1.63531
$322$	−7252.56	−1.25518
$323$	5587.95	0.962607
$324$	−460.136	−0.0788985
$325$	−135.502	−0.0231271
$326$	−7027.61	−1.19394
$327$	−9681.73	−1.63731
$328$	141.219	0.0237729
$329$	−2897.16	−0.485488
$330$	−4108.58	−0.685363
$331$	−5645.80	−0.937526	−0.468763	−	0.883324i	$-0.655300\pi$
$331$	−5645.80	−0.937526	−0.468763	+	0.883324i	$0.655300\pi$
$332$	−6612.27	−1.09306
$333$	−9746.69	−1.60395
$334$	−7849.40	−1.28593
$335$	1107.24	0.180582
$336$	−7986.30	−1.29669
$337$	1167.25	0.188677	0.0943383	−	0.995540i	$-0.469926\pi$
$337$	1167.25	0.188677	0.0943383	+	0.995540i	$0.469926\pi$
$338$	−906.104	−0.145815
$339$	991.554	0.158861
$340$	6607.26	1.05391
$341$	619.299	0.0983487
$342$	13518.0	2.13734
$343$	6901.63	1.08645
$344$	−529.407	−0.0829759
$345$	−10564.3	−1.64858
$346$	−2105.28	−0.327112
$347$	1205.99	0.186573	0.0932864	−	0.995639i	$-0.470263\pi$
$347$	1205.99	0.186573	0.0932864	+	0.995639i	$0.470263\pi$
$348$	12293.5	1.89369
$349$	7972.64	1.22282	0.611412	−	0.791312i	$-0.290602\pi$
$349$	7972.64	1.22282	0.611412	+	0.791312i	$0.290602\pi$
$350$	−174.591	−0.0266637
$351$	−6477.21	−0.984979
$352$	2841.67	0.430288
$353$	2815.40	0.424501	0.212251	−	0.977215i	$-0.431921\pi$
$353$	2815.40	0.424501	0.212251	+	0.977215i	$0.431921\pi$
$354$	463.454	0.0695828
$355$	−3213.06	−0.480371
$356$	3892.33	0.579475
$357$	−9359.86	−1.38761
$358$	4529.28	0.668659
$359$	−12808.0	−1.88296	−0.941480	−	0.337068i	$-0.890565\pi$
$359$	−12808.0	−1.88296	−0.941480	+	0.337068i	$0.890565\pi$
$360$	686.029	0.100436
$361$	−749.843	−0.109322
$362$	7.10905	0.00103216
$363$	−1010.63	−0.146127
$364$	−6446.78	−0.928305
$365$	−9532.72	−1.36703
$366$	−16416.0	−2.34447
$367$	−3736.38	−0.531437	−0.265719	−	0.964051i	$-0.585609\pi$
$367$	−3736.38	−0.531437	−0.265719	+	0.964051i	$0.585609\pi$
$368$	6978.37	0.988512
$369$	−4161.62	−0.587115
$370$	−10193.0	−1.43219
$371$	−6064.64	−0.848680
$372$	−3930.57	−0.547824
$373$	−12452.4	−1.72858	−0.864292	−	0.502990i	$-0.832233\pi$
$373$	−12452.4	−1.72858	−0.864292	+	0.502990i	$0.832233\pi$
$374$	3180.75	0.439767
$375$	−11797.7	−1.62462
$376$	−268.194	−0.0367847
$377$	−8664.22	−1.18363
$378$	−8345.72	−1.13560
$379$	5709.19	0.773776	0.386888	−	0.922127i	$-0.373550\pi$
$379$	5709.19	0.773776	0.386888	+	0.922127i	$0.373550\pi$
$380$	7223.54	0.975157
$381$	−11172.6	−1.50234
$382$	11390.3	1.52560
$383$	5706.61	0.761342	0.380671	−	0.924710i	$-0.375693\pi$
$383$	5706.61	0.761342	0.380671	+	0.924710i	$0.375693\pi$
$384$	−1549.73	−0.205949
$385$	1906.39	0.252360
$386$	−6348.91	−0.837178
$387$	15601.2	2.04924
$388$	12373.7	1.61903
$389$	7530.97	0.981582	0.490791	−	0.871277i	$-0.336708\pi$
$389$	7530.97	0.981582	0.490791	+	0.871277i	$0.336708\pi$
$390$	−18378.0	−2.38617
$391$	8178.57	1.05782
$392$	141.188	0.0181915
$393$	1094.15	0.140439
$394$	−3432.07	−0.438845
$395$	−5996.51	−0.763841
$396$	3931.71	0.498929
$397$	−1777.58	−0.224721	−0.112361	−	0.993667i	$-0.535841\pi$
$397$	−1777.58	−0.224721	−0.112361	+	0.993667i	$0.535841\pi$
$398$	−73.1618	−0.00921425
$399$	−10232.9	−1.28392
$400$	167.990	0.0209988
$401$	1582.46	0.197068	0.0985340	−	0.995134i	$-0.468585\pi$
$401$	1582.46	0.197068	0.0985340	+	0.995134i	$0.468585\pi$
$402$	−3383.03	−0.419727
$403$	2770.18	0.342413
$404$	−4338.65	−0.534297
$405$	608.642	0.0746758
$406$	−11163.6	−1.36464
$407$	−2507.28	−0.305359
$408$	−866.455	−0.105137
$409$	−1562.36	−0.188885	−0.0944423	−	0.995530i	$-0.530107\pi$
$409$	−1562.36	−0.188885	−0.0944423	+	0.995530i	$0.530107\pi$
$410$	−4352.19	−0.524243
$411$	−4660.57	−0.559341
$412$	−5676.04	−0.678734
$413$	−215.044	−0.0256213
$414$	19785.1	2.34875
$415$	8746.34	1.03456
$416$	12711.0	1.49810
$417$	141.375	0.0166023
$418$	3477.43	0.406906
$419$	5773.76	0.673190	0.336595	−	0.941650i	$-0.390725\pi$
$419$	5773.76	0.673190	0.336595	+	0.941650i	$0.390725\pi$
$420$	−12099.5	−1.40570
$421$	208.939	0.0241878	0.0120939	−	0.999927i	$-0.496150\pi$
$421$	208.939	0.0241878	0.0120939	+	0.999927i	$0.496150\pi$
$422$	4704.31	0.542659
$423$	7903.48	0.908465
$424$	−561.412	−0.0643032
$425$	196.883	0.0224711
$426$	9817.09	1.11652
$427$	7617.04	0.863266
$428$	−9412.25	−1.06299
$429$	−4520.63	−0.508760
$430$	16315.7	1.82979
$431$	6136.75	0.685840	0.342920	−	0.939365i	$-0.388584\pi$
$431$	6136.75	0.685840	0.342920	+	0.939365i	$0.388584\pi$
$432$	8030.20	0.894336
$433$	9264.16	1.02819	0.514096	−	0.857733i	$-0.328127\pi$
$433$	9264.16	1.02819	0.514096	+	0.857733i	$0.328127\pi$
$434$	3569.31	0.394775
$435$	−16261.2	−1.79233
$436$	9689.22	1.06429
$437$	8941.41	0.978777
$438$	29126.0	3.17738
$439$	15932.4	1.73215	0.866074	−	0.499915i	$-0.166635\pi$
$439$	15932.4	1.73215	0.866074	+	0.499915i	$0.166635\pi$
$440$	176.477	0.0191209
$441$	−4160.71	−0.449272
$442$	14227.8	1.53110
$443$	2431.20	0.260744	0.130372	−	0.991465i	$-0.458383\pi$
$443$	2431.20	0.260744	0.130372	+	0.991465i	$0.458383\pi$
$444$	15913.2	1.70092
$445$	−5148.55	−0.548460
$446$	13865.6	1.47209
$447$	−27015.5	−2.85859
$448$	8728.42	0.920489
$449$	−131.231	−0.0137932	−0.00689662	−	0.999976i	$-0.502195\pi$
$449$	−131.231	−0.0137932	−0.00689662	+	0.999976i	$0.502195\pi$
$450$	476.286	0.0498941
$451$	−1070.55	−0.111775
$452$	−992.321	−0.103263
$453$	−9241.60	−0.958517
$454$	−24240.3	−2.50584
$455$	8527.44	0.878621
$456$	−947.271	−0.0972808
$457$	10240.6	1.04821	0.524107	−	0.851652i	$-0.324399\pi$
$457$	10240.6	1.04821	0.524107	+	0.851652i	$0.324399\pi$
$458$	701.008	0.0715196
$459$	9411.31	0.957042
$460$	10572.4	1.07161
$461$	−14337.3	−1.44849	−0.724244	−	0.689544i	$-0.757811\pi$
$461$	−14337.3	−1.44849	−0.724244	+	0.689544i	$0.757811\pi$
$462$	−5824.72	−0.586560
$463$	14095.7	1.41487	0.707434	−	0.706779i	$-0.249852\pi$
$463$	14095.7	1.41487	0.707434	+	0.706779i	$0.249852\pi$
$464$	10741.6	1.07471
$465$	5199.14	0.518504
$466$	14184.4	1.41005
$467$	−10147.7	−1.00552	−0.502761	−	0.864425i	$-0.667682\pi$
$467$	−10147.7	−1.00552	−0.502761	+	0.864425i	$0.667682\pi$
$468$	17586.9	1.73708
$469$	1569.73	0.154549
$470$	8265.41	0.811180
$471$	−6703.20	−0.655769
$472$	−19.9069	−0.00194129
$473$	4013.33	0.390133
$474$	18321.6	1.77540
$475$	215.247	0.0207920
$476$	9367.10	0.901975
$477$	16544.4	1.58808
$478$	21623.0	2.06906
$479$	−3377.52	−0.322177	−0.161089	−	0.986940i	$-0.551500\pi$
$479$	−3377.52	−0.322177	−0.161089	+	0.986940i	$0.551500\pi$
$480$	23856.4	2.26852
$481$	−11215.3	−1.06314
$482$	−9014.03	−0.851821
$483$	−14976.9	−1.41092
$484$	1011.41	0.0949859
$485$	−16367.3	−1.53237
$486$	−16235.3	−1.51532
$487$	2248.20	0.209191	0.104595	−	0.994515i	$-0.466645\pi$
$487$	2248.20	0.209191	0.104595	+	0.994515i	$0.466645\pi$
$488$	705.120	0.0654083
$489$	−14512.4	−1.34207
$490$	−4351.24	−0.401161
$491$	−17542.7	−1.61240	−0.806201	−	0.591642i	$-0.798480\pi$
$491$	−17542.7	−1.61240	−0.806201	+	0.591642i	$0.798480\pi$
$492$	6794.59	0.622609
$493$	12589.0	1.15006
$494$	15554.8	1.41669
$495$	−5200.65	−0.472226
$496$	−3434.36	−0.310902
$497$	−4555.15	−0.411119
$498$	−26723.3	−2.40462
$499$	6992.02	0.627266	0.313633	−	0.949544i	$-0.398454\pi$
$499$	6992.02	0.627266	0.313633	+	0.949544i	$0.398454\pi$
$500$	11806.8	1.05604
$501$	−16209.4	−1.44547
$502$	25359.2	2.25465
$503$	7312.00	0.648163	0.324081	−	0.946029i	$-0.394945\pi$
$503$	7312.00	0.648163	0.324081	+	0.946029i	$0.394945\pi$
$504$	972.581	0.0859568
$505$	5738.93	0.505701
$506$	5089.59	0.447154
$507$	−1871.15	−0.163907
$508$	11181.2	0.976551
$509$	−10542.0	−0.918012	−0.459006	−	0.888433i	$-0.651794\pi$
$509$	−10542.0	−0.918012	−0.459006	+	0.888433i	$0.651794\pi$
$510$	26703.1	2.31849
$511$	−13514.5	−1.16995
$512$	−16466.8	−1.42136
$513$	10289.1	0.885528
$514$	−16319.1	−1.40040
$515$	7507.95	0.642407
$516$	−25471.8	−2.17313
$517$	2033.13	0.172953
$518$	−14450.6	−1.22572
$519$	−4347.52	−0.367697
$520$	789.396	0.0665718
$521$	−606.149	−0.0509710	−0.0254855	−	0.999675i	$-0.508113\pi$
$521$	−606.149	−0.0509710	−0.0254855	+	0.999675i	$0.508113\pi$
$522$	30454.5	2.55356
$523$	−1881.79	−0.157333	−0.0786663	−	0.996901i	$-0.525066\pi$
$523$	−1881.79	−0.157333	−0.0786663	+	0.996901i	$0.525066\pi$
$524$	−1095.00	−0.0912885
$525$	−360.540	−0.0299719
$526$	16250.2	1.34704
$527$	−4025.04	−0.332701
$528$	5604.51	0.461941
$529$	919.709	0.0755904
$530$	17302.0	1.41802
$531$	586.641	0.0479436
$532$	10240.8	0.834576
$533$	−4788.67	−0.389157
$534$	15730.7	1.27479
$535$	12450.0	1.00609
$536$	145.312	0.0117100
$537$	9353.19	0.751620
$538$	−18012.2	−1.44342
$539$	−1070.32	−0.0855322
$540$	12166.0	0.969519
$541$	24401.2	1.93917	0.969585	−	0.244755i	$-0.0787075\pi$
$541$	24401.2	1.93917	0.969585	+	0.244755i	$0.0787075\pi$
$542$	−1363.69	−0.108073
$543$	14.6806	0.00116023
$544$	−18469.0	−1.45561
$545$	−12816.4	−1.00733
$546$	−26054.5	−2.04218
$547$	1785.57	0.139571	0.0697857	−	0.997562i	$-0.477768\pi$
$547$	1785.57	0.139571	0.0697857	+	0.997562i	$0.477768\pi$
$548$	4664.18	0.363583
$549$	−20779.4	−1.61538
$550$	122.522	0.00949882
$551$	13763.2	1.06412
$552$	−1386.43	−0.106903
$553$	−8501.24	−0.653724
$554$	−35458.3	−2.71928
$555$	−21049.1	−1.60988
$556$	−141.484	−0.0107919
$557$	1643.67	0.125035	0.0625175	−	0.998044i	$-0.480087\pi$
$557$	1643.67	0.125035	0.0625175	+	0.998044i	$0.480087\pi$
$558$	−9737.10	−0.738718
$559$	17952.0	1.35830
$560$	−10572.0	−0.797765
$561$	6568.42	0.494330
$562$	−4779.94	−0.358772
$563$	−1558.84	−0.116691	−0.0583457	−	0.998296i	$-0.518583\pi$
$563$	−1558.84	−0.116691	−0.0583457	+	0.998296i	$0.518583\pi$
$564$	−12903.9	−0.963387
$565$	1312.59	0.0977361
$566$	6695.47	0.497229
$567$	862.871	0.0639104
$568$	−421.676	−0.0311499
$569$	14662.8	1.08031	0.540156	−	0.841565i	$-0.318365\pi$
$569$	14662.8	1.08031	0.540156	+	0.841565i	$0.318365\pi$
$570$	29193.7	2.14525
$571$	−177.430	−0.0130039	−0.00650193	−	0.999979i	$-0.502070\pi$
$571$	−177.430	−0.0130039	−0.00650193	+	0.999979i	$0.502070\pi$
$572$	4524.12	0.330705
$573$	23521.6	1.71488
$574$	−6170.09	−0.448667
$575$	315.037	0.0228486
$576$	−23811.2	−1.72245
$577$	6693.35	0.482925	0.241463	−	0.970410i	$-0.422373\pi$
$577$	6693.35	0.482925	0.241463	+	0.970410i	$0.422373\pi$
$578$	−801.706	−0.0576930
$579$	−13110.8	−0.941048
$580$	16273.8	1.16506
$581$	12399.7	0.885413
$582$	50008.1	3.56169
$583$	4255.95	0.302339
$584$	−1251.06	−0.0886456
$585$	−23262.9	−1.64411
$586$	−27985.1	−1.97279
$587$	−15987.8	−1.12417	−0.562084	−	0.827080i	$-0.690000\pi$
$587$	−15987.8	−1.12417	−0.562084	+	0.827080i	$0.690000\pi$
$588$	6793.10	0.476433
$589$	−4400.46	−0.307840
$590$	613.505	0.0428095
$591$	−7087.40	−0.493294
$592$	13904.3	0.965308
$593$	−24553.3	−1.70031	−0.850156	−	0.526531i	$-0.823492\pi$
$593$	−24553.3	−1.70031	−0.850156	+	0.526531i	$0.823492\pi$
$594$	5856.74	0.404553
$595$	−12390.3	−0.853700
$596$	27036.4	1.85815
$597$	−151.083	−0.0103575
$598$	22766.2	1.55682
$599$	−1158.80	−0.0790438	−0.0395219	−	0.999219i	$-0.512583\pi$
$599$	−1158.80	−0.0790438	−0.0395219	+	0.999219i	$0.512583\pi$
$600$	−33.3756	−0.00227092
$601$	11320.8	0.768362	0.384181	−	0.923258i	$-0.374484\pi$
$601$	11320.8	0.768362	0.384181	+	0.923258i	$0.374484\pi$
$602$	23130.7	1.56601
$603$	−4282.25	−0.289198
$604$	9248.74	0.623056
$605$	−1337.84	−0.0899021
$606$	−17534.5	−1.17540
$607$	7697.49	0.514714	0.257357	−	0.966316i	$-0.417148\pi$
$607$	7697.49	0.514714	0.257357	+	0.966316i	$0.417148\pi$
$608$	−20191.6	−1.34684
$609$	−23053.5	−1.53395
$610$	−21730.9	−1.44239
$611$	9094.34	0.602157
$612$	−25553.5	−1.68781
$613$	−26432.8	−1.74161	−0.870807	−	0.491625i	$-0.836403\pi$
$613$	−26432.8	−1.74161	−0.870807	+	0.491625i	$0.836403\pi$
$614$	−15960.4	−1.04904
$615$	−8987.50	−0.589286
$616$	250.191	0.0163644
$617$	−24114.6	−1.57345	−0.786723	−	0.617307i	$-0.788224\pi$
$617$	−24114.6	−1.57345	−0.786723	+	0.617307i	$0.788224\pi$
$618$	−22939.6	−1.49315
$619$	−7533.38	−0.489163	−0.244582	−	0.969629i	$-0.578651\pi$
$619$	−7533.38	−0.489163	−0.244582	+	0.969629i	$0.578651\pi$
$620$	−5203.16	−0.337038
$621$	15059.2	0.973118
$622$	43636.3	2.81295
$623$	−7299.09	−0.469393
$624$	25069.4	1.60830
$625$	−15273.2	−0.977484
$626$	−30350.5	−1.93778
$627$	7181.07	0.457392
$628$	6708.38	0.426264
$629$	16295.7	1.03299
$630$	−29973.7	−1.89553
$631$	−15925.5	−1.00473	−0.502363	−	0.864657i	$-0.667536\pi$
$631$	−15925.5	−1.00473	−0.502363	+	0.864657i	$0.667536\pi$
$632$	−786.971	−0.0495317
$633$	9714.65	0.609988
$634$	21705.9	1.35970
$635$	−14789.9	−0.924284
$636$	−27011.7	−1.68409
$637$	−4787.62	−0.297791
$638$	7834.25	0.486145
$639$	12426.5	0.769303
$640$	−2051.48	−0.126706
$641$	13680.3	0.842961	0.421481	−	0.906837i	$-0.361511\pi$
$641$	13680.3	0.842961	0.421481	+	0.906837i	$0.361511\pi$
$642$	−38039.3	−2.33846
$643$	−8045.04	−0.493415	−0.246707	−	0.969090i	$-0.579349\pi$
$643$	−8045.04	−0.493415	−0.246707	+	0.969090i	$0.579349\pi$
$644$	14988.5	0.917127
$645$	33692.7	2.05682
$646$	−22601.0	−1.37651
$647$	−13643.6	−0.829033	−0.414516	−	0.910042i	$-0.636049\pi$
$647$	−13643.6	−0.829033	−0.414516	+	0.910042i	$0.636049\pi$
$648$	79.8771	0.00484239
$649$	150.910	0.00912748
$650$	548.051	0.0330713
$651$	7370.80	0.443755
$652$	14523.6	0.872375
$653$	−10888.3	−0.652517	−0.326259	−	0.945281i	$-0.605788\pi$
$653$	−10888.3	−0.652517	−0.326259	+	0.945281i	$0.605788\pi$
$654$	39158.7	2.34133
$655$	1448.40	0.0864026
$656$	5936.82	0.353344
$657$	36867.7	2.18926
$658$	11717.8	0.694239
$659$	−20781.4	−1.22842	−0.614211	−	0.789142i	$-0.710526\pi$
$659$	−20781.4	−1.22842	−0.614211	+	0.789142i	$0.710526\pi$
$660$	8490.99	0.500775
$661$	16146.8	0.950134	0.475067	−	0.879950i	$-0.342424\pi$
$661$	16146.8	0.950134	0.475067	+	0.879950i	$0.342424\pi$
$662$	22835.0	1.34064
$663$	29381.1	1.72107
$664$	1147.85	0.0670864
$665$	−13545.9	−0.789909
$666$	39421.4	2.29362
$667$	20143.9	1.16938
$668$	16221.9	0.939589
$669$	28633.1	1.65474
$670$	−4478.34	−0.258229
$671$	−5345.37	−0.307535
$672$	33821.1	1.94149
$673$	20231.3	1.15878	0.579391	−	0.815049i	$-0.303290\pi$
$673$	20231.3	1.15878	0.579391	+	0.815049i	$0.303290\pi$
$674$	−4721.05	−0.269804
$675$	362.521	0.0206718
$676$	1872.60	0.106543
$677$	8635.65	0.490244	0.245122	−	0.969492i	$-0.421172\pi$
$677$	8635.65	0.490244	0.245122	+	0.969492i	$0.421172\pi$
$678$	−4010.44	−0.227168
$679$	−23203.9	−1.31146
$680$	−1146.98	−0.0646836
$681$	−50057.4	−2.81675
$682$	−2504.81	−0.140637
$683$	26038.9	1.45878	0.729392	−	0.684096i	$-0.239803\pi$
$683$	26038.9	1.45878	0.729392	+	0.684096i	$0.239803\pi$
$684$	−27937.0	−1.56169
$685$	−6169.51	−0.344124
$686$	−27914.3	−1.55360
$687$	1447.62	0.0803931
$688$	−22256.2	−1.23330
$689$	19037.2	1.05263
$690$	42728.1	2.35744
$691$	−9494.41	−0.522698	−0.261349	−	0.965244i	$-0.584167\pi$
$691$	−9494.41	−0.522698	−0.261349	+	0.965244i	$0.584167\pi$
$692$	4350.88	0.239011
$693$	−7372.94	−0.404149
$694$	−4877.73	−0.266795
$695$	187.148	0.0102143
$696$	−2134.09	−0.116225
$697$	6957.89	0.378119
$698$	−32246.1	−1.74862
$699$	29291.6	1.58499
$700$	360.819	0.0194824
$701$	−7218.86	−0.388948	−0.194474	−	0.980908i	$-0.562300\pi$
$701$	−7218.86	−0.388948	−0.194474	+	0.980908i	$0.562300\pi$
$702$	26197.7	1.40850
$703$	17815.6	0.955802
$704$	−6125.30	−0.327920
$705$	17068.5	0.911825
$706$	−11387.2	−0.607028
$707$	8136.07	0.432798
$708$	−957.797	−0.0508421
$709$	−13822.1	−0.732156	−0.366078	−	0.930584i	$-0.619300\pi$
$709$	−13822.1	−0.732156	−0.366078	+	0.930584i	$0.619300\pi$
$710$	12995.5	0.686921
$711$	23191.5	1.22327
$712$	−675.687	−0.0355652
$713$	−6440.55	−0.338289
$714$	37856.9	1.98425
$715$	−5984.26	−0.313005
$716$	−9360.43	−0.488569
$717$	44652.6	2.32578
$718$	51803.4	2.69260
$719$	19641.1	1.01876	0.509381	−	0.860541i	$-0.329875\pi$
$719$	19641.1	1.01876	0.509381	+	0.860541i	$0.329875\pi$
$720$	28840.5	1.49281
$721$	10644.0	0.549796
$722$	3032.81	0.156329
$723$	−18614.4	−0.957508
$724$	−14.6919	−0.000754172 0
$725$	484.926	0.0248410
$726$	4087.58	0.208959
$727$	−31301.8	−1.59686	−0.798431	−	0.602086i	$-0.794336\pi$
$727$	−31301.8	−1.59686	−0.798431	+	0.602086i	$0.794336\pi$
$728$	1119.13	0.0569746
$729$	−32040.3	−1.62782
$730$	38556.0	1.95482
$731$	−26084.0	−1.31977
$732$	33926.0	1.71304
$733$	−13866.3	−0.698720	−0.349360	−	0.936989i	$-0.613601\pi$
$733$	−13866.3	−0.698720	−0.349360	+	0.936989i	$0.613601\pi$
$734$	15112.2	0.759945
$735$	−8985.53	−0.450934
$736$	−29552.6	−1.48006
$737$	−1101.58	−0.0550575
$738$	16832.1	0.839563
$739$	−18906.3	−0.941106	−0.470553	−	0.882372i	$-0.655946\pi$
$739$	−18906.3	−0.941106	−0.470553	+	0.882372i	$0.655946\pi$
$740$	21065.4	1.04646
$741$	32121.6	1.59246
$742$	24529.0	1.21360
$743$	−38945.6	−1.92298	−0.961491	−	0.274837i	$-0.911376\pi$
$743$	−38945.6	−1.92298	−0.961491	+	0.274837i	$0.911376\pi$
$744$	682.325	0.0336226
$745$	−35762.3	−1.75870
$746$	50365.0	2.47184
$747$	−33826.4	−1.65682
$748$	−6573.50	−0.321325
$749$	17650.3	0.861053
$750$	47717.0	2.32317
$751$	26802.6	1.30232	0.651158	−	0.758942i	$-0.274284\pi$
$751$	26802.6	1.30232	0.651158	+	0.758942i	$0.274284\pi$
$752$	−11274.8	−0.546743
$753$	52368.0	2.53439
$754$	35043.3	1.69257
$755$	−12233.7	−0.589709
$756$	17247.7	0.829751
$757$	21402.8	1.02761	0.513803	−	0.857908i	$-0.328236\pi$
$757$	21402.8	1.02761	0.513803	+	0.857908i	$0.328236\pi$
$758$	−23091.4	−1.10649
$759$	10510.3	0.502633
$760$	−1253.97	−0.0598502
$761$	10309.6	0.491094	0.245547	−	0.969385i	$-0.421032\pi$
$761$	10309.6	0.491094	0.245547	+	0.969385i	$0.421032\pi$
$762$	45188.7	2.14831
$763$	−18169.7	−0.862107
$764$	−23539.8	−1.11471
$765$	33800.8	1.59748
$766$	−23080.9	−1.08870
$767$	675.034	0.0317784
$768$	−30939.5	−1.45369
$769$	−38540.7	−1.80730	−0.903649	−	0.428275i	$-0.859122\pi$
$769$	−38540.7	−1.80730	−0.903649	+	0.428275i	$0.859122\pi$
$770$	−7710.57	−0.360870
$771$	−33699.9	−1.57415
$772$	13121.0	0.611701
$773$	20527.4	0.955137	0.477569	−	0.878594i	$-0.341518\pi$
$773$	20527.4	0.955137	0.477569	+	0.878594i	$0.341518\pi$
$774$	−63100.7	−2.93037
$775$	−155.043	−0.00718623
$776$	−2148.01	−0.0993675
$777$	−29841.3	−1.37780
$778$	−30459.7	−1.40364
$779$	7606.87	0.349865
$780$	37980.9	1.74351
$781$	3196.64	0.146459
$782$	−33079.0	−1.51266
$783$	23180.2	1.05797
$784$	5935.52	0.270386
$785$	−8873.47	−0.403449
$786$	−4425.40	−0.200825
$787$	−5357.55	−0.242663	−0.121332	−	0.992612i	$-0.538716\pi$
$787$	−5357.55	−0.242663	−0.121332	+	0.992612i	$0.538716\pi$
$788$	7092.88	0.320651
$789$	33557.5	1.51417
$790$	24253.5	1.09228
$791$	1860.85	0.0836463
$792$	−682.523	−0.0306217
$793$	−23910.3	−1.07072
$794$	7189.61	0.321347
$795$	35729.6	1.59396
$796$	151.200	0.00673258
$797$	2672.63	0.118782	0.0593911	−	0.998235i	$-0.481084\pi$
$797$	2672.63	0.118782	0.0593911	+	0.998235i	$0.481084\pi$
$798$	41387.9	1.83598
$799$	−13214.0	−0.585078
$800$	−711.421	−0.0314407
$801$	19912.0	0.878347
$802$	−6400.41	−0.281804
$803$	9484.00	0.416791
$804$	6991.54	0.306682
$805$	−19825.9	−0.868041
$806$	−11204.2	−0.489644
$807$	−37196.0	−1.62251
$808$	753.166	0.0327925
$809$	8514.24	0.370018	0.185009	−	0.982737i	$-0.440769\pi$
$809$	8514.24	0.370018	0.185009	+	0.982737i	$0.440769\pi$
$810$	−2461.71	−0.106785
$811$	37760.9	1.63498	0.817488	−	0.575946i	$-0.195366\pi$
$811$	37760.9	1.63498	0.817488	+	0.575946i	$0.195366\pi$
$812$	23071.3	0.997099
$813$	−2816.09	−0.121482
$814$	10140.9	0.436658
$815$	−19211.0	−0.825684
$816$	−36425.6	−1.56269
$817$	−28516.9	−1.22115
$818$	6319.12	0.270101
$819$	−32979.8	−1.40709
$820$	8994.45	0.383049
$821$	−20120.9	−0.855330	−0.427665	−	0.903937i	$-0.640664\pi$
$821$	−20120.9	−0.855330	−0.427665	+	0.903937i	$0.640664\pi$
$822$	18850.1	0.799846
$823$	−10809.8	−0.457845	−0.228923	−	0.973445i	$-0.573520\pi$
$823$	−10809.8	−0.457845	−0.228923	+	0.973445i	$0.573520\pi$
$824$	985.329	0.0416572
$825$	253.014	0.0106774
$826$	869.765	0.0366380
$827$	−15773.3	−0.663229	−0.331615	−	0.943415i	$-0.607593\pi$
$827$	−15773.3	−0.663229	−0.331615	+	0.943415i	$0.607593\pi$
$828$	−40888.8	−1.71616
$829$	19735.6	0.826834	0.413417	−	0.910542i	$-0.364335\pi$
$829$	19735.6	0.826834	0.413417	+	0.910542i	$0.364335\pi$
$830$	−35375.4	−1.47940
$831$	−73223.2	−3.05666
$832$	−27399.0	−1.14169
$833$	6956.36	0.289344
$834$	−571.805	−0.0237410
$835$	−21457.5	−0.889301
$836$	−7186.63	−0.297314
$837$	−7411.32	−0.306060
$838$	−23352.5	−0.962649
$839$	38651.8	1.59048	0.795238	−	0.606297i	$-0.207346\pi$
$839$	38651.8	1.59048	0.795238	+	0.606297i	$0.207346\pi$
$840$	2100.40	0.0862747
$841$	6617.93	0.271349
$842$	−845.073	−0.0345880
$843$	−9870.83	−0.403285
$844$	−9722.16	−0.396505
$845$	−2476.97	−0.100841
$846$	−31966.4	−1.29909
$847$	−1896.65	−0.0769416
$848$	−23601.7	−0.955760
$849$	13826.5	0.558921
$850$	−796.312	−0.0321333
$851$	26075.1	1.05034
$852$	−20288.5	−0.815812
$853$	24975.9	1.00253	0.501266	−	0.865293i	$-0.332868\pi$
$853$	24975.9	1.00253	0.501266	+	0.865293i	$0.332868\pi$
$854$	−30807.9	−1.23445
$855$	36953.5	1.47811
$856$	1633.91	0.0652407
$857$	−39482.4	−1.57374	−0.786869	−	0.617119i	$-0.788300\pi$
$857$	−39482.4	−1.57374	−0.786869	+	0.617119i	$0.788300\pi$
$858$	18284.1	0.727517
$859$	7254.02	0.288130	0.144065	−	0.989568i	$-0.453983\pi$
$859$	7254.02	0.288130	0.144065	+	0.989568i	$0.453983\pi$
$860$	−33718.7	−1.33698
$861$	−12741.6	−0.504334
$862$	−24820.7	−0.980738
$863$	−8703.84	−0.343317	−0.171658	−	0.985157i	$-0.554913\pi$
$863$	−8703.84	−0.343317	−0.171658	+	0.985157i	$0.554913\pi$
$864$	−34007.0	−1.33905
$865$	−5755.10	−0.226219
$866$	−37469.8	−1.47030
$867$	−1655.56	−0.0648511
$868$	−7376.50	−0.288450
$869$	5965.87	0.232886
$870$	65770.1	2.56300
$871$	−4927.48	−0.191689
$872$	−1681.99	−0.0653206
$873$	63300.4	2.45406
$874$	−36164.4	−1.39963
$875$	−22140.8	−0.855423
$876$	−60193.1	−2.32162
$877$	−3584.65	−0.138022	−0.0690109	−	0.997616i	$-0.521984\pi$
$877$	−3584.65	−0.138022	−0.0690109	+	0.997616i	$0.521984\pi$
$878$	−64440.2	−2.47694
$879$	−57790.7	−2.21756
$880$	7419.06	0.284200
$881$	−9773.25	−0.373745	−0.186872	−	0.982384i	$-0.559835\pi$
$881$	−9773.25	−0.373745	−0.186872	+	0.982384i	$0.559835\pi$
$882$	16828.4	0.642450
$883$	−10627.2	−0.405021	−0.202511	−	0.979280i	$-0.564910\pi$
$883$	−10627.2	−0.405021	−0.202511	+	0.979280i	$0.564910\pi$
$884$	−29403.8	−1.11873
$885$	1266.92	0.0481209
$886$	−9833.21	−0.372859
$887$	−35916.1	−1.35958	−0.679788	−	0.733409i	$-0.737928\pi$
$887$	−35916.1	−1.35958	−0.679788	+	0.733409i	$0.737928\pi$
$888$	−2762.45	−0.104394
$889$	−20967.6	−0.791037
$890$	20823.8	0.784288
$891$	−605.532	−0.0227678
$892$	−28655.2	−1.07562
$893$	−14446.5	−0.541359
$894$	109267.	4.08773
$895$	12381.4	0.462420
$896$	−2908.38	−0.108440
$897$	47013.4	1.74998
$898$	530.776	0.0197241
$899$	−9913.73	−0.367788
$900$	−984.316	−0.0364562
$901$	−27660.9	−1.02277
$902$	4329.95	0.159836
$903$	47766.0	1.76030
$904$	172.261	0.00633775
$905$	19.4336	0.000713807 0
$906$	37378.5	1.37066
$907$	31632.3	1.15803	0.579015	−	0.815317i	$-0.303437\pi$
$907$	31632.3	1.15803	0.579015	+	0.815317i	$0.303437\pi$
$908$	50096.1	1.83095
$909$	−22195.3	−0.809869
$910$	−34490.0	−1.25641
$911$	−25180.3	−0.915765	−0.457882	−	0.889013i	$-0.651392\pi$
$911$	−25180.3	−0.915765	−0.457882	+	0.889013i	$0.651392\pi$
$912$	−39823.1	−1.44592
$913$	−8701.65	−0.315425
$914$	−41419.0	−1.49893
$915$	−44875.5	−1.62135
$916$	−1448.74	−0.0522572
$917$	2053.39	0.0739466
$918$	−38064.9	−1.36855
$919$	−18254.7	−0.655242	−0.327621	−	0.944809i	$-0.606247\pi$
$919$	−18254.7	−0.655242	−0.327621	+	0.944809i	$0.606247\pi$
$920$	−1835.31	−0.0657701
$921$	−32959.1	−1.17920
$922$	57988.4	2.07131
$923$	14298.9	0.509916
$924$	12037.7	0.428582
$925$	627.706	0.0223123
$926$	−57011.6	−2.02324
$927$	−29036.9	−1.02880
$928$	−45489.4	−1.60912
$929$	26577.6	0.938625	0.469312	−	0.883032i	$-0.344502\pi$
$929$	26577.6	0.938625	0.469312	+	0.883032i	$0.344502\pi$
$930$	−21028.4	−0.741450
$931$	7605.20	0.267723
$932$	−29314.3	−1.03028
$933$	90111.1	3.16196
$934$	41043.3	1.43788
$935$	8695.06	0.304127
$936$	−3052.98	−0.106613
$937$	12123.1	0.422672	0.211336	−	0.977413i	$-0.432218\pi$
$937$	12123.1	0.422672	0.211336	+	0.977413i	$0.432218\pi$
$938$	−6348.94	−0.221002
$939$	−62675.4	−2.17821
$940$	−17081.7	−0.592706
$941$	−38618.8	−1.33787	−0.668935	−	0.743321i	$-0.733249\pi$
$941$	−38618.8	−1.33787	−0.668935	+	0.743321i	$0.733249\pi$
$942$	27111.7	0.937737
$943$	11133.5	0.384471
$944$	−836.882	−0.0288540
$945$	−22814.3	−0.785342
$946$	−16232.3	−0.557883
$947$	−6493.41	−0.222817	−0.111408	−	0.993775i	$-0.535536\pi$
$947$	−6493.41	−0.222817	−0.111408	+	0.993775i	$0.535536\pi$
$948$	−37864.2	−1.29723
$949$	42422.8	1.45111
$950$	−870.586	−0.0297322
$951$	44823.7	1.52840
$952$	−1626.08	−0.0553586
$953$	2482.07	0.0843675	0.0421838	−	0.999110i	$-0.486569\pi$
$953$	2482.07	0.0843675	0.0421838	+	0.999110i	$0.486569\pi$
$954$	−66915.4	−2.27093
$955$	31137.1	1.05505
$956$	−44687.1	−1.51180
$957$	16178.1	0.546462
$958$	13660.7	0.460707
$959$	−8746.50	−0.294514
$960$	−51423.1	−1.72883
$961$	−26621.3	−0.893603
$962$	45361.3	1.52028
$963$	−48150.3	−1.61124
$964$	18628.8	0.622401
$965$	−17355.7	−0.578962
$966$	60575.6	2.01759
$967$	−1244.08	−0.0413723	−0.0206861	−	0.999786i	$-0.506585\pi$
$967$	−1244.08	−0.0413723	−0.0206861	+	0.999786i	$0.506585\pi$
$968$	−175.575	−0.00582975
$969$	−46672.3	−1.54730
$970$	66199.1	2.19126
$971$	33007.5	1.09090	0.545449	−	0.838144i	$-0.316359\pi$
$971$	33007.5	1.09090	0.545449	+	0.838144i	$0.316359\pi$
$972$	33552.6	1.10720
$973$	265.319	0.00874175
$974$	−9093.08	−0.299139
$975$	1131.75	0.0371745
$976$	29643.1	0.972185
$977$	−4970.38	−0.162760	−0.0813799	−	0.996683i	$-0.525933\pi$
$977$	−4970.38	−0.162760	−0.0813799	+	0.996683i	$0.525933\pi$
$978$	58696.7	1.91914
$979$	5122.25	0.167219
$980$	8992.48	0.293117
$981$	49567.2	1.61321
$982$	70953.0	2.30570
$983$	37269.0	1.20925	0.604627	−	0.796508i	$-0.293322\pi$
$983$	37269.0	1.20925	0.604627	+	0.796508i	$0.293322\pi$
$984$	−1179.50	−0.0382126
$985$	−9382.06	−0.303490
$986$	−50917.5	−1.64457
$987$	24198.0	0.780374
$988$	−32146.4	−1.03513
$989$	−41737.6	−1.34194
$990$	21034.5	0.675273
$991$	−14003.2	−0.448866	−0.224433	−	0.974490i	$-0.572053\pi$
$991$	−14003.2	−0.448866	−0.224433	+	0.974490i	$0.572053\pi$
$992$	14544.2	0.465501
$993$	47155.4	1.50698
$994$	18423.7	0.587893
$995$	−199.999	−0.00637224
$996$	55227.7	1.75698
$997$	−328.798	−0.0104445	−0.00522224	−	0.999986i	$-0.501662\pi$
$997$	−328.798	−0.0104445	−0.00522224	+	0.999986i	$0.501662\pi$
$998$	−28279.9	−0.896978
$999$	30005.3	0.950276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.16	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-4.04460 q^{2} -8.35230 q^{3} +8.35876 q^{4} -11.0565 q^{5} +33.7817 q^{6} -15.6748 q^{7} -1.45103 q^{8} +42.7609 q^{9} +O(q^{10})\)	\(q-4.04460 q^{2} -8.35230 q^{3} +8.35876 q^{4} -11.0565 q^{5} +33.7817 q^{6} -15.6748 q^{7} -1.45103 q^{8} +42.7609 q^{9} +44.7191 q^{10} +11.0000 q^{11} -69.8149 q^{12} +49.2039 q^{13} +63.3981 q^{14} +92.3472 q^{15} -61.0012 q^{16} -71.4928 q^{17} -172.951 q^{18} -78.1611 q^{19} -92.4186 q^{20} +130.920 q^{21} -44.4906 q^{22} -114.397 q^{23} +12.1195 q^{24} -2.75389 q^{25} -199.010 q^{26} -131.640 q^{27} -131.022 q^{28} -176.088 q^{29} -373.507 q^{30} +56.2999 q^{31} +258.334 q^{32} -91.8753 q^{33} +289.159 q^{34} +173.308 q^{35} +357.428 q^{36} -227.935 q^{37} +316.130 q^{38} -410.966 q^{39} +16.0434 q^{40} -97.3230 q^{41} -529.520 q^{42} +364.848 q^{43} +91.9463 q^{44} -472.786 q^{45} +462.690 q^{46} +184.830 q^{47} +509.501 q^{48} -97.3016 q^{49} +11.1384 q^{50} +597.129 q^{51} +411.284 q^{52} +386.905 q^{53} +532.430 q^{54} -121.621 q^{55} +22.7446 q^{56} +652.825 q^{57} +712.204 q^{58} +13.7191 q^{59} +771.908 q^{60} -485.943 q^{61} -227.710 q^{62} -670.268 q^{63} -556.845 q^{64} -544.023 q^{65} +371.599 q^{66} -100.144 q^{67} -597.591 q^{68} +955.479 q^{69} -700.961 q^{70} +290.604 q^{71} -62.0476 q^{72} +862.182 q^{73} +921.903 q^{74} +23.0013 q^{75} -653.330 q^{76} -172.422 q^{77} +1662.19 q^{78} +542.352 q^{79} +674.460 q^{80} -55.0484 q^{81} +393.632 q^{82} -791.059 q^{83} +1094.33 q^{84} +790.460 q^{85} -1475.66 q^{86} +1470.74 q^{87} -15.9614 q^{88} +465.659 q^{89} +1912.23 q^{90} -771.260 q^{91} -956.218 q^{92} -470.234 q^{93} -747.561 q^{94} +864.188 q^{95} -2157.68 q^{96} +1480.33 q^{97} +393.546 q^{98} +470.370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more