Properties

Label 48.5.l.a.19.13
Level $48$
Weight $5$
Character 48.19
Analytic conductor $4.962$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,5,Mod(19,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.19");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), minimal)

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: no
Analytic conductor: \(4.96175822802\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.13
Character \(\chi\) \(=\) 48.19
Dual form 48.5.l.a.43.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.43325 + 2.05251i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(7.57441 + 14.0936i) q^{4} +(-15.8310 + 15.8310i) q^{5} +(-20.1560 + 5.07316i) q^{6} -14.0988 q^{7} +(-2.92234 + 63.9332i) q^{8} -27.0000i q^{9} +O(q^{10})\) \(q+(3.43325 + 2.05251i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(7.57441 + 14.0936i) q^{4} +(-15.8310 + 15.8310i) q^{5} +(-20.1560 + 5.07316i) q^{6} -14.0988 q^{7} +(-2.92234 + 63.9332i) q^{8} -27.0000i q^{9} +(-86.8452 + 21.8585i) q^{10} +(37.6905 + 37.6905i) q^{11} +(-79.6132 - 23.9529i) q^{12} +(127.319 + 127.319i) q^{13} +(-48.4046 - 28.9379i) q^{14} -116.334i q^{15} +(-141.257 + 213.501i) q^{16} -81.0525 q^{17} +(55.4178 - 92.6977i) q^{18} +(470.496 - 470.496i) q^{19} +(-343.026 - 103.205i) q^{20} +(51.8022 - 51.8022i) q^{21} +(52.0408 + 206.761i) q^{22} +259.447 q^{23} +(-224.168 - 245.643i) q^{24} +123.757i q^{25} +(175.795 + 698.443i) q^{26} +(99.2043 + 99.2043i) q^{27} +(-106.790 - 198.702i) q^{28} +(708.291 + 708.291i) q^{29} +(238.776 - 399.403i) q^{30} -1479.51i q^{31} +(-923.182 + 443.070i) q^{32} -276.967 q^{33} +(-278.274 - 166.361i) q^{34} +(223.198 - 223.198i) q^{35} +(380.526 - 204.509i) q^{36} +(564.843 - 564.843i) q^{37} +(2581.03 - 649.632i) q^{38} -935.602 q^{39} +(-965.866 - 1058.39i) q^{40} +579.599i q^{41} +(284.174 - 71.5253i) q^{42} +(-1348.23 - 1348.23i) q^{43} +(-245.710 + 816.676i) q^{44} +(427.438 + 427.438i) q^{45} +(890.747 + 532.518i) q^{46} +2487.32i q^{47} +(-265.441 - 1303.46i) q^{48} -2202.22 q^{49} +(-254.012 + 424.888i) q^{50} +(297.806 - 297.806i) q^{51} +(-830.014 + 2758.75i) q^{52} +(-3062.67 + 3062.67i) q^{53} +(136.975 + 544.211i) q^{54} -1193.36 q^{55} +(41.2013 - 901.380i) q^{56} +3457.42i q^{57} +(977.966 + 3885.51i) q^{58} +(-851.783 - 851.783i) q^{59} +(1639.56 - 881.160i) q^{60} +(3221.31 + 3221.31i) q^{61} +(3036.71 - 5079.52i) q^{62} +380.667i q^{63} +(-4078.92 - 373.669i) q^{64} -4031.19 q^{65} +(-950.898 - 568.478i) q^{66} +(4382.72 - 4382.72i) q^{67} +(-613.925 - 1142.32i) q^{68} +(-953.270 + 953.270i) q^{69} +(1224.41 - 308.178i) q^{70} -1927.00 q^{71} +(1726.20 + 78.9031i) q^{72} -6153.24i q^{73} +(3098.59 - 779.902i) q^{74} +(-454.711 - 454.711i) q^{75} +(10194.7 + 3067.23i) q^{76} +(-531.389 - 531.389i) q^{77} +(-3212.16 - 1920.33i) q^{78} +3815.82i q^{79} +(-1143.70 - 5616.18i) q^{80} -729.000 q^{81} +(-1189.63 + 1989.91i) q^{82} +(6196.26 - 6196.26i) q^{83} +(1122.45 + 337.706i) q^{84} +(1283.15 - 1283.15i) q^{85} +(-1861.56 - 7396.09i) q^{86} -5204.85 q^{87} +(-2519.82 + 2299.53i) q^{88} -15002.2i q^{89} +(590.181 + 2344.82i) q^{90} +(-1795.05 - 1795.05i) q^{91} +(1965.16 + 3656.53i) q^{92} +(5436.06 + 5436.06i) q^{93} +(-5105.25 + 8539.59i) q^{94} +14896.9i q^{95} +(1764.04 - 5019.93i) q^{96} +6079.50 q^{97} +(-7560.79 - 4520.09i) q^{98} +(1017.64 - 1017.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.43325 + 2.05251i 0.858312 + 0.513127i
\(3\) −3.67423 + 3.67423i −0.408248 + 0.408248i
\(4\) 7.57441 + 14.0936i 0.473400 + 0.880847i
\(5\) −15.8310 + 15.8310i −0.633241 + 0.633241i −0.948880 0.315638i \(-0.897781\pi\)
0.315638 + 0.948880i \(0.397781\pi\)
\(6\) −20.1560 + 5.07316i −0.559888 + 0.140921i
\(7\) −14.0988 −0.287730 −0.143865 0.989597i \(-0.545953\pi\)
−0.143865 + 0.989597i \(0.545953\pi\)
\(8\) −2.92234 + 63.9332i −0.0456615 + 0.998957i
\(9\) 27.0000i 0.333333i
\(10\) −86.8452 + 21.8585i −0.868452 + 0.218585i
\(11\) 37.6905 + 37.6905i 0.311492 + 0.311492i 0.845487 0.533996i \(-0.179310\pi\)
−0.533996 + 0.845487i \(0.679310\pi\)
\(12\) −79.6132 23.9529i −0.552869 0.166340i
\(13\) 127.319 + 127.319i 0.753369 + 0.753369i 0.975106 0.221737i \(-0.0711728\pi\)
−0.221737 + 0.975106i \(0.571173\pi\)
\(14\) −48.4046 28.9379i −0.246962 0.147642i
\(15\) 116.334i 0.517039i
\(16\) −141.257 + 213.501i −0.551784 + 0.833987i
\(17\) −81.0525 −0.280459 −0.140229 0.990119i \(-0.544784\pi\)
−0.140229 + 0.990119i \(0.544784\pi\)
\(18\) 55.4178 92.6977i 0.171042 0.286104i
\(19\) 470.496 470.496i 1.30331 1.30331i 0.377167 0.926145i \(-0.376898\pi\)
0.926145 0.377167i \(-0.123102\pi\)
\(20\) −343.026 103.205i −0.857566 0.258012i
\(21\) 51.8022 51.8022i 0.117465 0.117465i
\(22\) 52.0408 + 206.761i 0.107522 + 0.427192i
\(23\) 259.447 0.490449 0.245224 0.969466i \(-0.421138\pi\)
0.245224 + 0.969466i \(0.421138\pi\)
\(24\) −224.168 245.643i −0.389181 0.426464i
\(25\) 123.757i 0.198011i
\(26\) 175.795 + 698.443i 0.260052 + 1.03320i
\(27\) 99.2043 + 99.2043i 0.136083 + 0.136083i
\(28\) −106.790 198.702i −0.136211 0.253446i
\(29\) 708.291 + 708.291i 0.842201 + 0.842201i 0.989145 0.146944i \(-0.0469437\pi\)
−0.146944 + 0.989145i \(0.546944\pi\)
\(30\) 238.776 399.403i 0.265307 0.443781i
\(31\) 1479.51i 1.53955i −0.638315 0.769775i \(-0.720368\pi\)
0.638315 0.769775i \(-0.279632\pi\)
\(32\) −923.182 + 443.070i −0.901545 + 0.432686i
\(33\) −276.967 −0.254332
\(34\) −278.274 166.361i −0.240721 0.143911i
\(35\) 223.198 223.198i 0.182202 0.182202i
\(36\) 380.526 204.509i 0.293616 0.157800i
\(37\) 564.843 564.843i 0.412596 0.412596i −0.470046 0.882642i \(-0.655763\pi\)
0.882642 + 0.470046i \(0.155763\pi\)
\(38\) 2581.03 649.632i 1.78741 0.449884i
\(39\) −935.602 −0.615123
\(40\) −965.866 1058.39i −0.603666 0.661496i
\(41\) 579.599i 0.344794i 0.985028 + 0.172397i \(0.0551512\pi\)
−0.985028 + 0.172397i \(0.944849\pi\)
\(42\) 284.174 71.5253i 0.161097 0.0405472i
\(43\) −1348.23 1348.23i −0.729170 0.729170i 0.241285 0.970454i \(-0.422431\pi\)
−0.970454 + 0.241285i \(0.922431\pi\)
\(44\) −245.710 + 816.676i −0.126916 + 0.421837i
\(45\) 427.438 + 427.438i 0.211080 + 0.211080i
\(46\) 890.747 + 532.518i 0.420958 + 0.251663i
\(47\) 2487.32i 1.12599i 0.826459 + 0.562997i \(0.190352\pi\)
−0.826459 + 0.562997i \(0.809648\pi\)
\(48\) −265.441 1303.46i −0.115209 0.565739i
\(49\) −2202.22 −0.917212
\(50\) −254.012 + 424.888i −0.101605 + 0.169955i
\(51\) 297.806 297.806i 0.114497 0.114497i
\(52\) −830.014 + 2758.75i −0.306958 + 1.02025i
\(53\) −3062.67 + 3062.67i −1.09031 + 1.09031i −0.0948119 + 0.995495i \(0.530225\pi\)
−0.995495 + 0.0948119i \(0.969775\pi\)
\(54\) 136.975 + 544.211i 0.0469737 + 0.186629i
\(55\) −1193.36 −0.394499
\(56\) 41.2013 901.380i 0.0131382 0.287430i
\(57\) 3457.42i 1.06415i
\(58\) 977.966 + 3885.51i 0.290715 + 1.15503i
\(59\) −851.783 851.783i −0.244695 0.244695i 0.574094 0.818789i \(-0.305354\pi\)
−0.818789 + 0.574094i \(0.805354\pi\)
\(60\) 1639.56 881.160i 0.455433 0.244767i
\(61\) 3221.31 + 3221.31i 0.865711 + 0.865711i 0.991994 0.126283i \(-0.0403047\pi\)
−0.126283 + 0.991994i \(0.540305\pi\)
\(62\) 3036.71 5079.52i 0.789986 1.32142i
\(63\) 380.667i 0.0959100i
\(64\) −4078.92 373.669i −0.995830 0.0912277i
\(65\) −4031.19 −0.954129
\(66\) −950.898 568.478i −0.218296 0.130505i
\(67\) 4382.72 4382.72i 0.976324 0.976324i −0.0234023 0.999726i \(-0.507450\pi\)
0.999726 + 0.0234023i \(0.00744986\pi\)
\(68\) −613.925 1142.32i −0.132769 0.247041i
\(69\) −953.270 + 953.270i −0.200225 + 0.200225i
\(70\) 1224.41 308.178i 0.249880 0.0628935i
\(71\) −1927.00 −0.382265 −0.191133 0.981564i \(-0.561216\pi\)
−0.191133 + 0.981564i \(0.561216\pi\)
\(72\) 1726.20 + 78.9031i 0.332986 + 0.0152205i
\(73\) 6153.24i 1.15467i −0.816507 0.577335i \(-0.804093\pi\)
0.816507 0.577335i \(-0.195907\pi\)
\(74\) 3098.59 779.902i 0.565850 0.142422i
\(75\) −454.711 454.711i −0.0808376 0.0808376i
\(76\) 10194.7 + 3067.23i 1.76501 + 0.531031i
\(77\) −531.389 531.389i −0.0896255 0.0896255i
\(78\) −3212.16 1920.33i −0.527968 0.315637i
\(79\) 3815.82i 0.611411i 0.952126 + 0.305706i \(0.0988924\pi\)
−0.952126 + 0.305706i \(0.901108\pi\)
\(80\) −1143.70 5616.18i −0.178703 0.877528i
\(81\) −729.000 −0.111111
\(82\) −1189.63 + 1989.91i −0.176923 + 0.295941i
\(83\) 6196.26 6196.26i 0.899443 0.899443i −0.0959439 0.995387i \(-0.530587\pi\)
0.995387 + 0.0959439i \(0.0305870\pi\)
\(84\) 1122.45 + 337.706i 0.159077 + 0.0478608i
\(85\) 1283.15 1283.15i 0.177598 0.177598i
\(86\) −1861.56 7396.09i −0.251698 1.00001i
\(87\) −5204.85 −0.687654
\(88\) −2519.82 + 2299.53i −0.325390 + 0.296944i
\(89\) 15002.2i 1.89398i −0.321263 0.946990i \(-0.604107\pi\)
0.321263 0.946990i \(-0.395893\pi\)
\(90\) 590.181 + 2344.82i 0.0728618 + 0.289484i
\(91\) −1795.05 1795.05i −0.216767 0.216767i
\(92\) 1965.16 + 3656.53i 0.232179 + 0.432010i
\(93\) 5436.06 + 5436.06i 0.628519 + 0.628519i
\(94\) −5105.25 + 8539.59i −0.577778 + 0.966455i
\(95\) 14896.9i 1.65062i
\(96\) 1764.04 5019.93i 0.191411 0.544697i
\(97\) 6079.50 0.646137 0.323068 0.946376i \(-0.395286\pi\)
0.323068 + 0.946376i \(0.395286\pi\)
\(98\) −7560.79 4520.09i −0.787254 0.470646i
\(99\) 1017.64 1017.64i 0.103831 0.103831i
\(100\) −1744.17 + 937.384i −0.174417 + 0.0937384i
\(101\) 12060.7 12060.7i 1.18230 1.18230i 0.203158 0.979146i \(-0.434880\pi\)
0.979146 0.203158i \(-0.0651204\pi\)
\(102\) 1633.69 411.193i 0.157025 0.0395226i
\(103\) −1018.38 −0.0959923 −0.0479962 0.998848i \(-0.515284\pi\)
−0.0479962 + 0.998848i \(0.515284\pi\)
\(104\) −8512.01 + 7767.87i −0.786983 + 0.718183i
\(105\) 1640.16i 0.148768i
\(106\) −16801.1 + 4228.75i −1.49529 + 0.376358i
\(107\) 13049.5 + 13049.5i 1.13979 + 1.13979i 0.988488 + 0.151302i \(0.0483466\pi\)
0.151302 + 0.988488i \(0.451653\pi\)
\(108\) −646.728 + 2149.56i −0.0554465 + 0.184290i
\(109\) 7747.67 + 7747.67i 0.652106 + 0.652106i 0.953500 0.301394i \(-0.0974520\pi\)
−0.301394 + 0.953500i \(0.597452\pi\)
\(110\) −4097.10 2449.38i −0.338603 0.202428i
\(111\) 4150.73i 0.336883i
\(112\) 1991.55 3010.10i 0.158765 0.239963i
\(113\) −14420.3 −1.12932 −0.564661 0.825323i \(-0.690993\pi\)
−0.564661 + 0.825323i \(0.690993\pi\)
\(114\) −7096.40 + 11870.2i −0.546045 + 0.913373i
\(115\) −4107.32 + 4107.32i −0.310572 + 0.310572i
\(116\) −4617.46 + 15347.2i −0.343152 + 1.14055i
\(117\) 3437.62 3437.62i 0.251123 0.251123i
\(118\) −1176.09 4672.68i −0.0844650 0.335584i
\(119\) 1142.74 0.0806963
\(120\) 7437.60 + 339.967i 0.516500 + 0.0236088i
\(121\) 11799.9i 0.805946i
\(122\) 4447.79 + 17671.3i 0.298831 + 1.18727i
\(123\) −2129.58 2129.58i −0.140762 0.140762i
\(124\) 20851.5 11206.4i 1.35611 0.728824i
\(125\) −11853.6 11853.6i −0.758630 0.758630i
\(126\) −781.322 + 1306.92i −0.0492140 + 0.0823207i
\(127\) 1641.73i 0.101787i −0.998704 0.0508937i \(-0.983793\pi\)
0.998704 0.0508937i \(-0.0162070\pi\)
\(128\) −13237.0 9654.92i −0.807922 0.589290i
\(129\) 9907.46 0.595365
\(130\) −13840.1 8274.07i −0.818941 0.489590i
\(131\) −6768.96 + 6768.96i −0.394438 + 0.394438i −0.876266 0.481828i \(-0.839973\pi\)
0.481828 + 0.876266i \(0.339973\pi\)
\(132\) −2097.86 3903.46i −0.120401 0.224028i
\(133\) −6633.41 + 6633.41i −0.375002 + 0.375002i
\(134\) 24042.5 6051.39i 1.33897 0.337012i
\(135\) −3141.01 −0.172346
\(136\) 236.863 5181.95i 0.0128062 0.280166i
\(137\) 8848.71i 0.471453i 0.971819 + 0.235727i \(0.0757470\pi\)
−0.971819 + 0.235727i \(0.924253\pi\)
\(138\) −5229.41 + 1316.22i −0.274596 + 0.0691146i
\(139\) −15171.3 15171.3i −0.785224 0.785224i 0.195483 0.980707i \(-0.437373\pi\)
−0.980707 + 0.195483i \(0.937373\pi\)
\(140\) 4836.25 + 1455.06i 0.246747 + 0.0742378i
\(141\) −9139.00 9139.00i −0.459685 0.459685i
\(142\) −6615.87 3955.18i −0.328103 0.196151i
\(143\) 9597.46i 0.469336i
\(144\) 5764.52 + 3813.93i 0.277996 + 0.183928i
\(145\) −22426.0 −1.06663
\(146\) 12629.6 21125.6i 0.592493 0.991068i
\(147\) 8091.49 8091.49i 0.374450 0.374450i
\(148\) 12239.0 + 3682.30i 0.558757 + 0.168111i
\(149\) 9365.50 9365.50i 0.421850 0.421850i −0.463990 0.885840i \(-0.653583\pi\)
0.885840 + 0.463990i \(0.153583\pi\)
\(150\) −627.838 2494.44i −0.0279039 0.110864i
\(151\) 17852.7 0.782981 0.391490 0.920182i \(-0.371960\pi\)
0.391490 + 0.920182i \(0.371960\pi\)
\(152\) 28705.4 + 31455.3i 1.24244 + 1.36146i
\(153\) 2188.42i 0.0934862i
\(154\) −733.711 2915.07i −0.0309374 0.122916i
\(155\) 23422.1 + 23422.1i 0.974907 + 0.974907i
\(156\) −7086.63 13186.0i −0.291200 0.541830i
\(157\) 25381.0 + 25381.0i 1.02970 + 1.02970i 0.999545 + 0.0301510i \(0.00959882\pi\)
0.0301510 + 0.999545i \(0.490401\pi\)
\(158\) −7832.00 + 13100.7i −0.313732 + 0.524782i
\(159\) 22506.0i 0.890232i
\(160\) 7600.66 21629.2i 0.296901 0.844890i
\(161\) −3657.89 −0.141117
\(162\) −2502.84 1496.28i −0.0953680 0.0570142i
\(163\) −29621.2 + 29621.2i −1.11488 + 1.11488i −0.122397 + 0.992481i \(0.539058\pi\)
−0.992481 + 0.122397i \(0.960942\pi\)
\(164\) −8168.61 + 4390.12i −0.303711 + 0.163226i
\(165\) 4384.68 4384.68i 0.161053 0.161053i
\(166\) 33991.2 8555.43i 1.23353 0.310474i
\(167\) −17898.0 −0.641758 −0.320879 0.947120i \(-0.603978\pi\)
−0.320879 + 0.947120i \(0.603978\pi\)
\(168\) 3160.50 + 3463.26i 0.111979 + 0.122706i
\(169\) 3859.44i 0.135130i
\(170\) 7039.03 1771.69i 0.243565 0.0613042i
\(171\) −12703.4 12703.4i −0.434437 0.434437i
\(172\) 8789.35 29213.5i 0.297098 0.987476i
\(173\) −21617.0 21617.0i −0.722276 0.722276i 0.246792 0.969068i \(-0.420623\pi\)
−0.969068 + 0.246792i \(0.920623\pi\)
\(174\) −17869.6 10683.0i −0.590222 0.352854i
\(175\) 1744.82i 0.0569736i
\(176\) −13371.0 + 2722.91i −0.431656 + 0.0879039i
\(177\) 6259.30 0.199793
\(178\) 30792.2 51506.4i 0.971853 1.62563i
\(179\) 19481.5 19481.5i 0.608017 0.608017i −0.334410 0.942428i \(-0.608537\pi\)
0.942428 + 0.334410i \(0.108537\pi\)
\(180\) −2786.53 + 9261.71i −0.0860041 + 0.285855i
\(181\) −36095.6 + 36095.6i −1.10178 + 1.10178i −0.107589 + 0.994195i \(0.534313\pi\)
−0.994195 + 0.107589i \(0.965687\pi\)
\(182\) −2478.49 9847.19i −0.0748246 0.297283i
\(183\) −23671.7 −0.706850
\(184\) −758.192 + 16587.3i −0.0223946 + 0.489937i
\(185\) 17884.1i 0.522545i
\(186\) 7505.79 + 29820.9i 0.216955 + 0.861976i
\(187\) −3054.91 3054.91i −0.0873605 0.0873605i
\(188\) −35055.2 + 18840.0i −0.991829 + 0.533046i
\(189\) −1398.66 1398.66i −0.0391551 0.0391551i
\(190\) −30576.0 + 51144.7i −0.846980 + 1.41675i
\(191\) 38346.7i 1.05114i −0.850750 0.525571i \(-0.823852\pi\)
0.850750 0.525571i \(-0.176148\pi\)
\(192\) 16359.9 13614.0i 0.443789 0.369302i
\(193\) 33888.6 0.909785 0.454893 0.890546i \(-0.349678\pi\)
0.454893 + 0.890546i \(0.349678\pi\)
\(194\) 20872.4 + 12478.2i 0.554587 + 0.331551i
\(195\) 14811.6 14811.6i 0.389521 0.389521i
\(196\) −16680.5 31037.2i −0.434208 0.807923i
\(197\) −26521.3 + 26521.3i −0.683380 + 0.683380i −0.960760 0.277380i \(-0.910534\pi\)
0.277380 + 0.960760i \(0.410534\pi\)
\(198\) 5582.55 1405.10i 0.142397 0.0358408i
\(199\) 19874.7 0.501873 0.250936 0.968004i \(-0.419262\pi\)
0.250936 + 0.968004i \(0.419262\pi\)
\(200\) −7912.17 361.659i −0.197804 0.00904147i
\(201\) 32206.3i 0.797165i
\(202\) 66162.0 16652.7i 1.62146 0.408113i
\(203\) −9986.03 9986.03i −0.242326 0.242326i
\(204\) 6452.85 + 1941.44i 0.155057 + 0.0466514i
\(205\) −9175.65 9175.65i −0.218338 0.218338i
\(206\) −3496.36 2090.24i −0.0823914 0.0492563i
\(207\) 7005.08i 0.163483i
\(208\) −45167.5 + 9198.05i −1.04400 + 0.212603i
\(209\) 35466.4 0.811942
\(210\) −3366.45 + 5631.09i −0.0763368 + 0.127689i
\(211\) −29334.4 + 29334.4i −0.658889 + 0.658889i −0.955117 0.296228i \(-0.904271\pi\)
0.296228 + 0.955117i \(0.404271\pi\)
\(212\) −66361.9 19966.0i −1.47655 0.444242i
\(213\) 7080.25 7080.25i 0.156059 0.156059i
\(214\) 18017.9 + 71586.2i 0.393438 + 1.56315i
\(215\) 42687.9 0.923481
\(216\) −6632.36 + 6052.55i −0.142155 + 0.129727i
\(217\) 20859.2i 0.442975i
\(218\) 10697.5 + 42501.8i 0.225097 + 0.894324i
\(219\) 22608.4 + 22608.4i 0.471392 + 0.471392i
\(220\) −9038.99 16818.7i −0.186756 0.347493i
\(221\) −10319.6 10319.6i −0.211289 0.211289i
\(222\) −8519.42 + 14250.5i −0.172864 + 0.289151i
\(223\) 28991.8i 0.582996i −0.956571 0.291498i \(-0.905846\pi\)
0.956571 0.291498i \(-0.0941536\pi\)
\(224\) 13015.7 6246.74i 0.259401 0.124497i
\(225\) 3341.43 0.0660036
\(226\) −49508.6 29597.8i −0.969311 0.579486i
\(227\) −5936.67 + 5936.67i −0.115210 + 0.115210i −0.762362 0.647151i \(-0.775960\pi\)
0.647151 + 0.762362i \(0.275960\pi\)
\(228\) −48727.4 + 26187.9i −0.937354 + 0.503769i
\(229\) −8913.92 + 8913.92i −0.169980 + 0.169980i −0.786971 0.616991i \(-0.788352\pi\)
0.616991 + 0.786971i \(0.288352\pi\)
\(230\) −22531.8 + 5671.14i −0.425931 + 0.107205i
\(231\) 3904.90 0.0731789
\(232\) −47353.2 + 43213.5i −0.879779 + 0.802866i
\(233\) 21770.0i 0.401002i 0.979694 + 0.200501i \(0.0642569\pi\)
−0.979694 + 0.200501i \(0.935743\pi\)
\(234\) 18858.0 4746.46i 0.344400 0.0866839i
\(235\) −39376.9 39376.9i −0.713026 0.713026i
\(236\) 5552.90 18456.4i 0.0997002 0.331378i
\(237\) −14020.2 14020.2i −0.249608 0.249608i
\(238\) 3923.31 + 2345.49i 0.0692627 + 0.0414075i
\(239\) 28051.7i 0.491093i −0.969385 0.245546i \(-0.921033\pi\)
0.969385 0.245546i \(-0.0789673\pi\)
\(240\) 24837.4 + 16432.9i 0.431204 + 0.285294i
\(241\) 34321.7 0.590928 0.295464 0.955354i \(-0.404526\pi\)
0.295464 + 0.955354i \(0.404526\pi\)
\(242\) 24219.3 40511.8i 0.413553 0.691753i
\(243\) 2678.52 2678.52i 0.0453609 0.0453609i
\(244\) −21000.2 + 69799.3i −0.352731 + 1.17239i
\(245\) 34863.5 34863.5i 0.580816 0.580816i
\(246\) −2940.40 11682.4i −0.0485888 0.193046i
\(247\) 119806. 1.96375
\(248\) 94589.8 + 4323.62i 1.53795 + 0.0702982i
\(249\) 45533.0i 0.734392i
\(250\) −16366.7 65026.0i −0.261868 1.04042i
\(251\) −49564.4 49564.4i −0.786724 0.786724i 0.194232 0.980956i \(-0.437779\pi\)
−0.980956 + 0.194232i \(0.937779\pi\)
\(252\) −5364.95 + 2883.32i −0.0844820 + 0.0454038i
\(253\) 9778.70 + 9778.70i 0.152771 + 0.152771i
\(254\) 3369.66 5636.46i 0.0522299 0.0873654i
\(255\) 9429.16i 0.145008i
\(256\) −25629.1 60316.8i −0.391069 0.920362i
\(257\) 94112.3 1.42489 0.712443 0.701730i \(-0.247589\pi\)
0.712443 + 0.701730i \(0.247589\pi\)
\(258\) 34014.8 + 20335.2i 0.511009 + 0.305498i
\(259\) −7963.59 + 7963.59i −0.118716 + 0.118716i
\(260\) −30533.9 56813.9i −0.451685 0.840442i
\(261\) 19123.9 19123.9i 0.280734 0.280734i
\(262\) −37132.9 + 9346.17i −0.540949 + 0.136154i
\(263\) −3529.57 −0.0510282 −0.0255141 0.999674i \(-0.508122\pi\)
−0.0255141 + 0.999674i \(0.508122\pi\)
\(264\) 809.392 17707.4i 0.0116132 0.254067i
\(265\) 96970.5i 1.38086i
\(266\) −36389.3 + 9159.01i −0.514293 + 0.129445i
\(267\) 55121.7 + 55121.7i 0.773214 + 0.773214i
\(268\) 94964.6 + 28571.6i 1.32218 + 0.397800i
\(269\) −61684.8 61684.8i −0.852459 0.852459i 0.137976 0.990436i \(-0.455940\pi\)
−0.990436 + 0.137976i \(0.955940\pi\)
\(270\) −10783.9 6446.96i −0.147927 0.0884357i
\(271\) 94137.0i 1.28180i −0.767623 0.640902i \(-0.778560\pi\)
0.767623 0.640902i \(-0.221440\pi\)
\(272\) 11449.2 17304.8i 0.154753 0.233899i
\(273\) 13190.8 0.176989
\(274\) −18162.1 + 30379.8i −0.241916 + 0.404654i
\(275\) −4664.45 + 4664.45i −0.0616787 + 0.0616787i
\(276\) −20655.4 6214.51i −0.271154 0.0815810i
\(277\) 325.906 325.906i 0.00424749 0.00424749i −0.704980 0.709227i \(-0.749044\pi\)
0.709227 + 0.704980i \(0.249044\pi\)
\(278\) −20947.6 83226.2i −0.271048 1.07689i
\(279\) −39946.7 −0.513184
\(280\) 13617.5 + 14922.0i 0.173693 + 0.190332i
\(281\) 100158.i 1.26845i 0.773150 + 0.634224i \(0.218680\pi\)
−0.773150 + 0.634224i \(0.781320\pi\)
\(282\) −12618.6 50134.4i −0.158676 0.630430i
\(283\) 54557.6 + 54557.6i 0.681212 + 0.681212i 0.960273 0.279061i \(-0.0900232\pi\)
−0.279061 + 0.960273i \(0.590023\pi\)
\(284\) −14595.9 27158.3i −0.180965 0.336717i
\(285\) −54734.6 54734.6i −0.673864 0.673864i
\(286\) −19698.9 + 32950.5i −0.240829 + 0.402837i
\(287\) 8171.63i 0.0992075i
\(288\) 11962.9 + 24925.9i 0.144229 + 0.300515i
\(289\) −76951.5 −0.921343
\(290\) −76993.9 46029.5i −0.915504 0.547319i
\(291\) −22337.5 + 22337.5i −0.263784 + 0.263784i
\(292\) 86721.0 46607.1i 1.01709 0.546621i
\(293\) −34394.8 + 34394.8i −0.400643 + 0.400643i −0.878460 0.477817i \(-0.841428\pi\)
0.477817 + 0.878460i \(0.341428\pi\)
\(294\) 44388.0 11172.2i 0.513536 0.129255i
\(295\) 26969.2 0.309902
\(296\) 34461.6 + 37762.9i 0.393325 + 0.431005i
\(297\) 7478.12i 0.0847773i
\(298\) 51376.9 12931.3i 0.578542 0.145616i
\(299\) 33032.7 + 33032.7i 0.369489 + 0.369489i
\(300\) 2964.33 9852.67i 0.0329370 0.109474i
\(301\) 19008.4 + 19008.4i 0.209804 + 0.209804i
\(302\) 61292.9 + 36642.9i 0.672042 + 0.401769i
\(303\) 88627.5i 0.965347i
\(304\) 33990.5 + 166912.i 0.367799 + 1.80609i
\(305\) −101993. −1.09641
\(306\) −4491.75 + 7513.39i −0.0479703 + 0.0802404i
\(307\) −99642.0 + 99642.0i −1.05722 + 1.05722i −0.0589602 + 0.998260i \(0.518778\pi\)
−0.998260 + 0.0589602i \(0.981222\pi\)
\(308\) 3464.21 11514.1i 0.0365176 0.121375i
\(309\) 3741.78 3741.78i 0.0391887 0.0391887i
\(310\) 32339.9 + 128488.i 0.336523 + 1.33703i
\(311\) −163414. −1.68954 −0.844772 0.535126i \(-0.820264\pi\)
−0.844772 + 0.535126i \(0.820264\pi\)
\(312\) 2734.14 59816.1i 0.0280874 0.614482i
\(313\) 91968.7i 0.938753i −0.882998 0.469376i \(-0.844479\pi\)
0.882998 0.469376i \(-0.155521\pi\)
\(314\) 35044.5 + 139234.i 0.355436 + 1.41217i
\(315\) −6026.35 6026.35i −0.0607342 0.0607342i
\(316\) −53778.5 + 28902.6i −0.538560 + 0.289442i
\(317\) 92936.2 + 92936.2i 0.924840 + 0.924840i 0.997366 0.0725266i \(-0.0231062\pi\)
−0.0725266 + 0.997366i \(0.523106\pi\)
\(318\) 46193.7 77268.6i 0.456802 0.764097i
\(319\) 53391.7i 0.524677i
\(320\) 70489.1 58658.0i 0.688370 0.572832i
\(321\) −95893.5 −0.930634
\(322\) −12558.4 7507.85i −0.121122 0.0724109i
\(323\) −38134.9 + 38134.9i −0.365525 + 0.365525i
\(324\) −5521.74 10274.2i −0.0526000 0.0978719i
\(325\) −15756.6 + 15756.6i −0.149175 + 0.149175i
\(326\) −162495. + 40899.2i −1.52899 + 0.384839i
\(327\) −56933.5 −0.532442
\(328\) −37055.6 1693.78i −0.344434 0.0157438i
\(329\) 35068.1i 0.323982i
\(330\) 24053.3 6054.10i 0.220875 0.0555932i
\(331\) −48028.3 48028.3i −0.438370 0.438370i 0.453093 0.891463i \(-0.350320\pi\)
−0.891463 + 0.453093i \(0.850320\pi\)
\(332\) 134260. + 40394.4i 1.21807 + 0.366475i
\(333\) −15250.8 15250.8i −0.137532 0.137532i
\(334\) −61448.3 36735.8i −0.550829 0.329304i
\(335\) 138766.i 1.23650i
\(336\) 3742.39 + 18377.2i 0.0331490 + 0.162780i
\(337\) −17371.9 −0.152964 −0.0764819 0.997071i \(-0.524369\pi\)
−0.0764819 + 0.997071i \(0.524369\pi\)
\(338\) −7921.54 + 13250.4i −0.0693387 + 0.115983i
\(339\) 52983.6 52983.6i 0.461044 0.461044i
\(340\) 27803.2 + 8365.02i 0.240512 + 0.0723618i
\(341\) 55763.4 55763.4i 0.479557 0.479557i
\(342\) −17540.1 69687.7i −0.149961 0.595805i
\(343\) 64899.8 0.551639
\(344\) 90137.0 82257.0i 0.761704 0.695114i
\(345\) 30182.5i 0.253581i
\(346\) −29847.4 118586.i −0.249319 0.990558i
\(347\) 53077.0 + 53077.0i 0.440806 + 0.440806i 0.892283 0.451477i \(-0.149103\pi\)
−0.451477 + 0.892283i \(0.649103\pi\)
\(348\) −39423.7 73354.9i −0.325536 0.605718i
\(349\) −44311.9 44311.9i −0.363806 0.363806i 0.501406 0.865212i \(-0.332816\pi\)
−0.865212 + 0.501406i \(0.832816\pi\)
\(350\) 3581.25 5990.39i 0.0292347 0.0489012i
\(351\) 25261.3i 0.205041i
\(352\) −51494.7 18095.6i −0.415602 0.146046i
\(353\) 92437.0 0.741816 0.370908 0.928670i \(-0.379046\pi\)
0.370908 + 0.928670i \(0.379046\pi\)
\(354\) 21489.7 + 12847.3i 0.171484 + 0.102519i
\(355\) 30506.4 30506.4i 0.242066 0.242066i
\(356\) 211435. 113633.i 1.66831 0.896611i
\(357\) −4198.70 + 4198.70i −0.0329441 + 0.0329441i
\(358\) 106871. 26898.9i 0.833859 0.209878i
\(359\) −138244. −1.07265 −0.536324 0.844012i \(-0.680187\pi\)
−0.536324 + 0.844012i \(0.680187\pi\)
\(360\) −28576.6 + 26078.4i −0.220499 + 0.201222i
\(361\) 312412.i 2.39725i
\(362\) −198012. + 49838.6i −1.51103 + 0.380319i
\(363\) 43355.4 + 43355.4i 0.329026 + 0.329026i
\(364\) 11702.2 38895.0i 0.0883210 0.293556i
\(365\) 97412.1 + 97412.1i 0.731185 + 0.731185i
\(366\) −81270.9 48586.4i −0.606699 0.362704i
\(367\) 118276.i 0.878140i 0.898453 + 0.439070i \(0.144692\pi\)
−0.898453 + 0.439070i \(0.855308\pi\)
\(368\) −36648.7 + 55392.2i −0.270622 + 0.409028i
\(369\) 15649.2 0.114931
\(370\) −36707.3 + 61400.6i −0.268132 + 0.448507i
\(371\) 43179.9 43179.9i 0.313714 0.313714i
\(372\) −35438.5 + 117788.i −0.256088 + 0.851170i
\(373\) 145050. 145050.i 1.04255 1.04255i 0.0435007 0.999053i \(-0.486149\pi\)
0.999053 0.0435007i \(-0.0138511\pi\)
\(374\) −4218.04 16758.5i −0.0301555 0.119810i
\(375\) 87105.8 0.619419
\(376\) −159022. 7268.79i −1.12482 0.0514146i
\(377\) 180358.i 1.26898i
\(378\) −1931.18 7672.70i −0.0135157 0.0536988i
\(379\) −20605.5 20605.5i −0.143451 0.143451i 0.631734 0.775185i \(-0.282343\pi\)
−0.775185 + 0.631734i \(0.782343\pi\)
\(380\) −209950. + 112835.i −1.45395 + 0.781405i
\(381\) 6032.09 + 6032.09i 0.0415545 + 0.0415545i
\(382\) 78707.0 131654.i 0.539370 0.902208i
\(383\) 130541.i 0.889915i −0.895552 0.444958i \(-0.853219\pi\)
0.895552 0.444958i \(-0.146781\pi\)
\(384\) 84110.3 13161.4i 0.570409 0.0892562i
\(385\) 16824.9 0.113509
\(386\) 116348. + 69556.7i 0.780880 + 0.466836i
\(387\) −36402.3 + 36402.3i −0.243057 + 0.243057i
\(388\) 46048.6 + 85681.8i 0.305881 + 0.569148i
\(389\) −20853.7 + 20853.7i −0.137811 + 0.137811i −0.772647 0.634836i \(-0.781068\pi\)
0.634836 + 0.772647i \(0.281068\pi\)
\(390\) 81252.6 20450.9i 0.534205 0.134457i
\(391\) −21028.9 −0.137551
\(392\) 6435.64 140795.i 0.0418812 0.916255i
\(393\) 49741.5i 0.322058i
\(394\) −145489. + 36619.0i −0.937215 + 0.235893i
\(395\) −60408.4 60408.4i −0.387171 0.387171i
\(396\) 22050.3 + 6634.17i 0.140612 + 0.0423054i
\(397\) 33470.8 + 33470.8i 0.212366 + 0.212366i 0.805272 0.592906i \(-0.202019\pi\)
−0.592906 + 0.805272i \(0.702019\pi\)
\(398\) 68234.6 + 40792.9i 0.430763 + 0.257525i
\(399\) 48745.4i 0.306188i
\(400\) −26422.1 17481.5i −0.165138 0.109259i
\(401\) −71101.8 −0.442172 −0.221086 0.975254i \(-0.570960\pi\)
−0.221086 + 0.975254i \(0.570960\pi\)
\(402\) −66103.7 + 110572.i −0.409047 + 0.684217i
\(403\) 188370. 188370.i 1.15985 1.15985i
\(404\) 261330. + 78625.4i 1.60113 + 0.481726i
\(405\) 11540.8 11540.8i 0.0703601 0.0703601i
\(406\) −13788.1 54780.9i −0.0836474 0.332336i
\(407\) 42578.4 0.257040
\(408\) 18169.4 + 19910.0i 0.109149 + 0.119605i
\(409\) 12068.1i 0.0721429i 0.999349 + 0.0360715i \(0.0114844\pi\)
−0.999349 + 0.0360715i \(0.988516\pi\)
\(410\) −12669.2 50335.4i −0.0753669 0.299437i
\(411\) −32512.2 32512.2i −0.192470 0.192470i
\(412\) −7713.65 14352.6i −0.0454428 0.0845546i
\(413\) 12009.1 + 12009.1i 0.0704060 + 0.0704060i
\(414\) 14378.0 24050.2i 0.0838875 0.140319i
\(415\) 196186.i 1.13913i
\(416\) −173950. 61127.5i −1.00517 0.353224i
\(417\) 111486. 0.641133
\(418\) 121765. + 72795.2i 0.696900 + 0.416630i
\(419\) 204428. 204428.i 1.16443 1.16443i 0.180932 0.983496i \(-0.442088\pi\)
0.983496 0.180932i \(-0.0579115\pi\)
\(420\) −23115.7 + 12423.3i −0.131042 + 0.0704267i
\(421\) −204135. + 204135.i −1.15174 + 1.15174i −0.165531 + 0.986205i \(0.552934\pi\)
−0.986205 + 0.165531i \(0.947066\pi\)
\(422\) −160921. + 40503.2i −0.903627 + 0.227439i
\(423\) 67157.7 0.375331
\(424\) −186856. 204757.i −1.03938 1.13895i
\(425\) 10030.8i 0.0555338i
\(426\) 38840.5 9775.98i 0.214026 0.0538693i
\(427\) −45416.5 45416.5i −0.249091 0.249091i
\(428\) −85071.3 + 282755.i −0.464404 + 1.54356i
\(429\) −35263.3 35263.3i −0.191606 0.191606i
\(430\) 146558. + 87617.3i 0.792635 + 0.473863i
\(431\) 48651.4i 0.261903i −0.991389 0.130952i \(-0.958197\pi\)
0.991389 0.130952i \(-0.0418033\pi\)
\(432\) −35193.5 + 7166.91i −0.188580 + 0.0384030i
\(433\) −225719. −1.20391 −0.601953 0.798532i \(-0.705610\pi\)
−0.601953 + 0.798532i \(0.705610\pi\)
\(434\) −42813.8 + 71615.0i −0.227303 + 0.380211i
\(435\) 82398.2 82398.2i 0.435451 0.435451i
\(436\) −50508.2 + 167876.i −0.265698 + 0.883112i
\(437\) 122069. 122069.i 0.639208 0.639208i
\(438\) 31216.4 + 124024.i 0.162718 + 0.646486i
\(439\) 58516.9 0.303635 0.151818 0.988409i \(-0.451487\pi\)
0.151818 + 0.988409i \(0.451487\pi\)
\(440\) 3487.40 76295.3i 0.0180134 0.394087i
\(441\) 59460.1i 0.305737i
\(442\) −14248.6 56610.6i −0.0729337 0.289770i
\(443\) −104599. 104599.i −0.532990 0.532990i 0.388471 0.921461i \(-0.373003\pi\)
−0.921461 + 0.388471i \(0.873003\pi\)
\(444\) −58498.6 + 31439.3i −0.296742 + 0.159480i
\(445\) 237501. + 237501.i 1.19935 + 1.19935i
\(446\) 59506.0 99536.1i 0.299151 0.500393i
\(447\) 68822.1i 0.344439i
\(448\) 57507.7 + 5268.27i 0.286530 + 0.0262489i
\(449\) −58514.6 −0.290250 −0.145125 0.989413i \(-0.546358\pi\)
−0.145125 + 0.989413i \(0.546358\pi\)
\(450\) 11472.0 + 6858.32i 0.0566517 + 0.0338683i
\(451\) −21845.4 + 21845.4i −0.107400 + 0.107400i
\(452\) −109225. 203234.i −0.534622 0.994761i
\(453\) −65595.2 + 65595.2i −0.319651 + 0.319651i
\(454\) −32567.1 + 8196.99i −0.158004 + 0.0397688i
\(455\) 56834.9 0.274531
\(456\) −221044. 10103.8i −1.06304 0.0485907i
\(457\) 295348.i 1.41417i 0.707130 + 0.707084i \(0.249990\pi\)
−0.707130 + 0.707084i \(0.750010\pi\)
\(458\) −48899.6 + 12307.8i −0.233117 + 0.0586746i
\(459\) −8040.76 8040.76i −0.0381656 0.0381656i
\(460\) −88997.2 26776.2i −0.420592 0.126542i
\(461\) 72481.0 + 72481.0i 0.341053 + 0.341053i 0.856763 0.515710i \(-0.172472\pi\)
−0.515710 + 0.856763i \(0.672472\pi\)
\(462\) 13406.5 + 8014.84i 0.0628104 + 0.0375501i
\(463\) 120288.i 0.561127i −0.959835 0.280564i \(-0.909479\pi\)
0.959835 0.280564i \(-0.0905214\pi\)
\(464\) −251271. + 51169.7i −1.16710 + 0.237672i
\(465\) −172117. −0.796008
\(466\) −44683.1 + 74741.8i −0.205765 + 0.344185i
\(467\) 85420.9 85420.9i 0.391679 0.391679i −0.483606 0.875286i \(-0.660673\pi\)
0.875286 + 0.483606i \(0.160673\pi\)
\(468\) 74486.3 + 22410.4i 0.340083 + 0.102319i
\(469\) −61790.9 + 61790.9i −0.280918 + 0.280918i
\(470\) −54369.2 216012.i −0.246126 0.977872i
\(471\) −186511. −0.840744
\(472\) 56946.4 51968.1i 0.255613 0.233267i
\(473\) 101631.i 0.454261i
\(474\) −19358.3 76911.5i −0.0861608 0.342322i
\(475\) 58227.0 + 58227.0i 0.258070 + 0.258070i
\(476\) 8655.58 + 16105.3i 0.0382017 + 0.0710811i
\(477\) 82692.2 + 82692.2i 0.363436 + 0.363436i
\(478\) 57576.4 96308.5i 0.251993 0.421511i
\(479\) 39356.8i 0.171533i −0.996315 0.0857666i \(-0.972666\pi\)
0.996315 0.0857666i \(-0.0273339\pi\)
\(480\) 51544.1 + 107397.i 0.223716 + 0.466134i
\(481\) 143831. 0.621673
\(482\) 117835. + 70445.5i 0.507200 + 0.303221i
\(483\) 13439.9 13439.9i 0.0576106 0.0576106i
\(484\) 166302. 89376.9i 0.709915 0.381535i
\(485\) −96244.8 + 96244.8i −0.409161 + 0.409161i
\(486\) 14693.7 3698.34i 0.0622098 0.0156579i
\(487\) −158483. −0.668230 −0.334115 0.942532i \(-0.608437\pi\)
−0.334115 + 0.942532i \(0.608437\pi\)
\(488\) −215363. + 196535.i −0.904338 + 0.825279i
\(489\) 217671.i 0.910295i
\(490\) 191253. 48137.4i 0.796555 0.200489i
\(491\) −50847.6 50847.6i −0.210915 0.210915i 0.593741 0.804656i \(-0.297650\pi\)
−0.804656 + 0.593741i \(0.797650\pi\)
\(492\) 13883.1 46143.7i 0.0573529 0.190626i
\(493\) −57408.8 57408.8i −0.236203 0.236203i
\(494\) 411325. + 245904.i 1.68551 + 1.00765i
\(495\) 32220.7i 0.131500i
\(496\) 315876. + 208991.i 1.28397 + 0.849500i
\(497\) 27168.3 0.109989
\(498\) −93457.0 + 156326.i −0.376837 + 0.630338i
\(499\) −193612. + 193612.i −0.777555 + 0.777555i −0.979414 0.201860i \(-0.935301\pi\)
0.201860 + 0.979414i \(0.435301\pi\)
\(500\) 77275.4 256843.i 0.309101 1.02737i
\(501\) 65761.4 65761.4i 0.261997 0.261997i
\(502\) −68435.5 271898.i −0.271565 1.07894i
\(503\) −353152. −1.39581 −0.697904 0.716192i \(-0.745884\pi\)
−0.697904 + 0.716192i \(0.745884\pi\)
\(504\) −24337.3 1112.44i −0.0958099 0.00437939i
\(505\) 381866.i 1.49737i
\(506\) 13501.8 + 53643.6i 0.0527341 + 0.209516i
\(507\) −14180.5 14180.5i −0.0551665 0.0551665i
\(508\) 23137.8 12435.1i 0.0896591 0.0481862i
\(509\) −37267.3 37267.3i −0.143844 0.143844i 0.631518 0.775362i \(-0.282432\pi\)
−0.775362 + 0.631518i \(0.782432\pi\)
\(510\) −19353.4 + 32372.6i −0.0744077 + 0.124462i
\(511\) 86753.1i 0.332233i
\(512\) 35809.8 259687.i 0.136604 0.990626i
\(513\) 93350.4 0.354717
\(514\) 323111. + 193166.i 1.22300 + 0.731148i
\(515\) 16122.1 16122.1i 0.0607863 0.0607863i
\(516\) 75043.1 + 139631.i 0.281846 + 0.524425i
\(517\) −93748.3 + 93748.3i −0.350738 + 0.350738i
\(518\) −43686.4 + 10995.6i −0.162812 + 0.0409790i
\(519\) 158852. 0.589736
\(520\) 11780.5 257727.i 0.0435669 0.953134i
\(521\) 454022.i 1.67264i −0.548245 0.836318i \(-0.684704\pi\)
0.548245 0.836318i \(-0.315296\pi\)
\(522\) 104909. 26405.1i 0.385009 0.0969050i
\(523\) 119641. + 119641.i 0.437399 + 0.437399i 0.891136 0.453737i \(-0.149909\pi\)
−0.453737 + 0.891136i \(0.649909\pi\)
\(524\) −146670. 44127.9i −0.534167 0.160713i
\(525\) 6410.87 + 6410.87i 0.0232594 + 0.0232594i
\(526\) −12117.9 7244.47i −0.0437981 0.0261840i
\(527\) 119918.i 0.431780i
\(528\) 39123.5 59132.7i 0.140336 0.212110i
\(529\) −212528. −0.759460
\(530\) 199033. 332924.i 0.708555 1.18521i
\(531\) −22998.1 + 22998.1i −0.0815650 + 0.0815650i
\(532\) −143732. 43244.2i −0.507846 0.152793i
\(533\) −73794.1 + 73794.1i −0.259757 + 0.259757i
\(534\) 76108.7 + 302384.i 0.266902 + 1.06042i
\(535\) −413173. −1.44352
\(536\) 267394. + 293009.i 0.930725 + 1.01989i
\(537\) 143159.i 0.496444i
\(538\) −85170.7 338388.i −0.294256 1.16910i
\(539\) −83002.9 83002.9i −0.285704 0.285704i
\(540\) −23791.3 44268.1i −0.0815889 0.151811i
\(541\) 190892. + 190892.i 0.652218 + 0.652218i 0.953527 0.301309i \(-0.0974235\pi\)
−0.301309 + 0.953527i \(0.597423\pi\)
\(542\) 193217. 323196.i 0.657729 1.10019i
\(543\) 265247.i 0.899603i
\(544\) 74826.2 35912.0i 0.252846 0.121350i
\(545\) −245307. −0.825880
\(546\) 45287.4 + 27074.3i 0.151912 + 0.0908181i
\(547\) 278955. 278955.i 0.932308 0.932308i −0.0655419 0.997850i \(-0.520878\pi\)
0.997850 + 0.0655419i \(0.0208776\pi\)
\(548\) −124710. + 67023.7i −0.415279 + 0.223186i
\(549\) 86975.4 86975.4i 0.288570 0.288570i
\(550\) −25588.1 + 6440.40i −0.0845887 + 0.0212906i
\(551\) 666496. 2.19530
\(552\) −58159.9 63731.4i −0.190873 0.209158i
\(553\) 53798.3i 0.175921i
\(554\) 1787.84 449.991i 0.00582518 0.00146617i
\(555\) −65710.4 65710.4i −0.213328 0.213328i
\(556\) 98904.1 328732.i 0.319937 1.06339i
\(557\) −230862. 230862.i −0.744118 0.744118i 0.229250 0.973368i \(-0.426373\pi\)
−0.973368 + 0.229250i \(0.926373\pi\)
\(558\) −137147. 81991.0i −0.440472 0.263329i
\(559\) 343313.i 1.09867i
\(560\) 16124.7 + 79181.1i 0.0514181 + 0.252491i
\(561\) 22448.9 0.0713296
\(562\) −205575. + 343867.i −0.650875 + 1.08872i
\(563\) −393297. + 393297.i −1.24081 + 1.24081i −0.281138 + 0.959667i \(0.590712\pi\)
−0.959667 + 0.281138i \(0.909288\pi\)
\(564\) 59578.5 198024.i 0.187297 0.622528i
\(565\) 228289. 228289.i 0.715134 0.715134i
\(566\) 75329.9 + 299290.i 0.235144 + 0.934242i
\(567\) 10278.0 0.0319700
\(568\) 5631.34 123199.i 0.0174548 0.381866i
\(569\) 36240.2i 0.111935i −0.998433 0.0559675i \(-0.982176\pi\)
0.998433 0.0559675i \(-0.0178243\pi\)
\(570\) −75574.2 300261.i −0.232608 0.924164i
\(571\) −10226.1 10226.1i −0.0313644 0.0313644i 0.691251 0.722615i \(-0.257060\pi\)
−0.722615 + 0.691251i \(0.757060\pi\)
\(572\) −135262. + 72695.1i −0.413414 + 0.222184i
\(573\) 140895. + 140895.i 0.429127 + 0.429127i
\(574\) 16772.3 28055.2i 0.0509061 0.0851511i
\(575\) 32108.3i 0.0971141i
\(576\) −10089.1 + 110131.i −0.0304092 + 0.331943i
\(577\) 225041. 0.675942 0.337971 0.941157i \(-0.390259\pi\)
0.337971 + 0.941157i \(0.390259\pi\)
\(578\) −264194. 157944.i −0.790800 0.472766i
\(579\) −124515. + 124515.i −0.371418 + 0.371418i
\(580\) −169863. 316062.i −0.504944 0.939541i
\(581\) −87359.6 + 87359.6i −0.258797 + 0.258797i
\(582\) −122538. + 30842.3i −0.361764 + 0.0910543i
\(583\) −230867. −0.679243
\(584\) 393397. + 17981.8i 1.15347 + 0.0527240i
\(585\) 108842.i 0.318043i
\(586\) −188682. + 47490.3i −0.549458 + 0.138296i
\(587\) 456085. + 456085.i 1.32364 + 1.32364i 0.910807 + 0.412832i \(0.135460\pi\)
0.412832 + 0.910807i \(0.364540\pi\)
\(588\) 175326. + 52749.6i 0.507098 + 0.152569i
\(589\) −696102. 696102.i −2.00652 2.00652i
\(590\) 92592.0 + 55354.6i 0.265993 + 0.159019i
\(591\) 194891.i 0.557978i
\(592\) 40806.5 + 200382.i 0.116436 + 0.571763i
\(593\) 33923.9 0.0964709 0.0482355 0.998836i \(-0.484640\pi\)
0.0482355 + 0.998836i \(0.484640\pi\)
\(594\) −15348.9 + 25674.3i −0.0435016 + 0.0727654i
\(595\) −18090.8 + 18090.8i −0.0511003 + 0.0511003i
\(596\) 202931. + 61055.1i 0.571290 + 0.171882i
\(597\) −73024.1 + 73024.1i −0.204889 + 0.204889i
\(598\) 45609.5 + 181209.i 0.127542 + 0.506732i
\(599\) 612011. 1.70571 0.852856 0.522146i \(-0.174868\pi\)
0.852856 + 0.522146i \(0.174868\pi\)
\(600\) 30400.0 27742.4i 0.0844444 0.0770621i
\(601\) 470989.i 1.30395i 0.758240 + 0.651976i \(0.226060\pi\)
−0.758240 + 0.651976i \(0.773940\pi\)
\(602\) 26245.7 + 104276.i 0.0724212 + 0.287733i
\(603\) −118333. 118333.i −0.325441 0.325441i
\(604\) 135224. + 251609.i 0.370663 + 0.689687i
\(605\) 186804. + 186804.i 0.510358 + 0.510358i
\(606\) −181909. + 304280.i −0.495346 + 0.828569i
\(607\) 211710.i 0.574598i 0.957841 + 0.287299i \(0.0927573\pi\)
−0.957841 + 0.287299i \(0.907243\pi\)
\(608\) −225890. + 642816.i −0.611070 + 1.73892i
\(609\) 73382.0 0.197859
\(610\) −350169. 209342.i −0.941061 0.562597i
\(611\) −316684. + 316684.i −0.848289 + 0.848289i
\(612\) −30842.6 + 16576.0i −0.0823471 + 0.0442564i
\(613\) 310327. 310327.i 0.825846 0.825846i −0.161094 0.986939i \(-0.551502\pi\)
0.986939 + 0.161094i \(0.0515021\pi\)
\(614\) −546612. + 137580.i −1.44991 + 0.364937i
\(615\) 67427.0 0.178272
\(616\) 35526.3 32420.6i 0.0936244 0.0854396i
\(617\) 61142.3i 0.160610i 0.996770 + 0.0803048i \(0.0255894\pi\)
−0.996770 + 0.0803048i \(0.974411\pi\)
\(618\) 20526.5 5166.42i 0.0537450 0.0135274i
\(619\) 95031.3 + 95031.3i 0.248019 + 0.248019i 0.820157 0.572138i \(-0.193886\pi\)
−0.572138 + 0.820157i \(0.693886\pi\)
\(620\) −152693. + 507510.i −0.397223 + 1.32027i
\(621\) 25738.3 + 25738.3i 0.0667416 + 0.0667416i
\(622\) −561042. 335410.i −1.45016 0.866952i
\(623\) 211513.i 0.544955i
\(624\) 132160. 199752.i 0.339415 0.513005i
\(625\) 297961. 0.762781
\(626\) 188767. 315751.i 0.481700 0.805743i
\(627\) −130312. + 130312.i −0.331474 + 0.331474i
\(628\) −165462. + 549954.i −0.419547 + 1.39446i
\(629\) −45782.0 + 45782.0i −0.115716 + 0.115716i
\(630\) −8320.82 33059.1i −0.0209645 0.0832932i
\(631\) 268083. 0.673303 0.336651 0.941629i \(-0.390706\pi\)
0.336651 + 0.941629i \(0.390706\pi\)
\(632\) −243958. 11151.1i −0.610774 0.0279180i
\(633\) 215563.i 0.537981i
\(634\) 128321. + 509826.i 0.319241 + 1.26836i
\(635\) 25990.3 + 25990.3i 0.0644560 + 0.0644560i
\(636\) 317189. 170469.i 0.784159 0.421436i
\(637\) −280386. 280386.i −0.690999 0.690999i
\(638\) −109587. + 183307.i −0.269226 + 0.450337i
\(639\) 52029.0i 0.127422i
\(640\) 362403. 56707.9i 0.884772 0.138447i
\(641\) 791424. 1.92616 0.963081 0.269211i \(-0.0867629\pi\)
0.963081 + 0.269211i \(0.0867629\pi\)
\(642\) −329226. 196822.i −0.798775 0.477534i
\(643\) −228349. + 228349.i −0.552303 + 0.552303i −0.927105 0.374802i \(-0.877711\pi\)
0.374802 + 0.927105i \(0.377711\pi\)
\(644\) −27706.3 51552.6i −0.0668047 0.124302i
\(645\) −156845. + 156845.i −0.377009 + 0.377009i
\(646\) −209199. + 52654.3i −0.501296 + 0.126174i
\(647\) −88355.9 −0.211070 −0.105535 0.994416i \(-0.533656\pi\)
−0.105535 + 0.994416i \(0.533656\pi\)
\(648\) 2130.38 46607.3i 0.00507350 0.110995i
\(649\) 64208.2i 0.152441i
\(650\) −86437.1 + 21755.8i −0.204585 + 0.0514930i
\(651\) −76641.7 76641.7i −0.180844 0.180844i
\(652\) −641831. 193105.i −1.50982 0.454254i
\(653\) −539514. 539514.i −1.26525 1.26525i −0.948514 0.316735i \(-0.897413\pi\)
−0.316735 0.948514i \(-0.602587\pi\)
\(654\) −195467. 116857.i −0.457002 0.273211i
\(655\) 214319.i 0.499549i
\(656\) −123745. 81872.2i −0.287554 0.190252i
\(657\) −166137. −0.384890
\(658\) 71977.7 120398.i 0.166244 0.278078i
\(659\) −27362.6 + 27362.6i −0.0630066 + 0.0630066i −0.737908 0.674901i \(-0.764186\pi\)
0.674901 + 0.737908i \(0.264186\pi\)
\(660\) 95007.1 + 28584.4i 0.218106 + 0.0656207i
\(661\) 466632. 466632.i 1.06800 1.06800i 0.0704871 0.997513i \(-0.477545\pi\)
0.997513 0.0704871i \(-0.0224554\pi\)
\(662\) −66314.5 263471.i −0.151319 0.601198i
\(663\) 75833.0 0.172517
\(664\) 378040. + 414255.i 0.857435 + 0.939575i
\(665\) 210027.i 0.474933i
\(666\) −21057.3 83662.0i −0.0474739 0.188617i
\(667\) 183764. + 183764.i 0.413056 + 0.413056i
\(668\) −135567. 252246.i −0.303809 0.565291i
\(669\) 106523. + 106523.i 0.238007 + 0.238007i
\(670\) −284818. + 476418.i −0.634481 + 1.06130i
\(671\) 242826.i 0.539324i
\(672\) −24870.8 + 70774.8i −0.0550746 + 0.156726i
\(673\) 723002. 1.59628 0.798141 0.602471i \(-0.205817\pi\)
0.798141 + 0.602471i \(0.205817\pi\)
\(674\) −59642.2 35656.1i −0.131291 0.0784899i
\(675\) −12277.2 + 12277.2i −0.0269459 + 0.0269459i
\(676\) −54393.2 + 29233.0i −0.119029 + 0.0639704i
\(677\) 157815. 157815.i 0.344326 0.344326i −0.513665 0.857991i \(-0.671712\pi\)
0.857991 + 0.513665i \(0.171712\pi\)
\(678\) 290655. 73156.6i 0.632294 0.159145i
\(679\) −85713.4 −0.185913
\(680\) 78285.9 + 85785.4i 0.169303 + 0.185522i
\(681\) 43625.4i 0.0940687i
\(682\) 305905. 76994.8i 0.657684 0.165536i
\(683\) −53616.3 53616.3i −0.114936 0.114936i 0.647300 0.762236i \(-0.275898\pi\)
−0.762236 + 0.647300i \(0.775898\pi\)
\(684\) 82815.3 275257.i 0.177010 0.588336i
\(685\) −140084. 140084.i −0.298544 0.298544i
\(686\) 222817. + 133207.i 0.473479 + 0.283061i
\(687\) 65503.7i 0.138788i
\(688\) 478296. 97401.8i 1.01046 0.205774i
\(689\) −779875. −1.64281
\(690\) 61949.9 103624.i 0.130119 0.217652i
\(691\) 222699. 222699.i 0.466404 0.466404i −0.434344 0.900747i \(-0.643020\pi\)
0.900747 + 0.434344i \(0.143020\pi\)
\(692\) 140924. 468396.i 0.294289 0.978140i
\(693\) −14347.5 + 14347.5i −0.0298752 + 0.0298752i
\(694\) 73285.5 + 291167.i 0.152159 + 0.604538i
\(695\) 480355. 0.994473
\(696\) 15210.3 332763.i 0.0313993 0.686937i
\(697\) 46977.9i 0.0967005i
\(698\) −61183.2 243085.i −0.125580 0.498938i
\(699\) −79988.0 79988.0i −0.163708 0.163708i
\(700\) 24590.7 13216.0i 0.0501851 0.0269713i
\(701\) −7694.62 7694.62i −0.0156585 0.0156585i 0.699234 0.714893i \(-0.253524\pi\)
−0.714893 + 0.699234i \(0.753524\pi\)
\(702\) −51849.0 + 86728.2i −0.105212 + 0.175989i
\(703\) 531513.i 1.07548i
\(704\) −139653. 167820.i −0.281776 0.338609i
\(705\) 289360. 0.582183
\(706\) 317359. + 189728.i 0.636710 + 0.380646i
\(707\) −170041. + 170041.i −0.340184 + 0.340184i
\(708\) 47410.5 + 88215.8i 0.0945819 + 0.175987i
\(709\) −352000. + 352000.i −0.700245 + 0.700245i −0.964463 0.264218i \(-0.914886\pi\)
0.264218 + 0.964463i \(0.414886\pi\)
\(710\) 167351. 42121.4i 0.331979 0.0835576i
\(711\) 103027. 0.203804
\(712\) 959140. + 43841.5i 1.89200 + 0.0864820i
\(713\) 383854.i 0.755070i
\(714\) −23033.0 + 5797.31i −0.0451809 + 0.0113718i
\(715\) −151938. 151938.i −0.297203 0.297203i
\(716\) 422124. + 127003.i 0.823406 + 0.247735i
\(717\) 103069. + 103069.i 0.200488 + 0.200488i
\(718\) −474626. 283747.i −0.920667 0.550405i
\(719\) 42870.7i 0.0829284i −0.999140 0.0414642i \(-0.986798\pi\)
0.999140 0.0414642i \(-0.0132022\pi\)
\(720\) −151637. + 30879.8i −0.292509 + 0.0595675i
\(721\) 14357.9 0.0276199
\(722\) 641228. 1.07259e6i 1.23009 2.05759i
\(723\) −126106. + 126106.i −0.241245 + 0.241245i
\(724\) −782117. 235312.i −1.49209 0.448919i
\(725\) −87655.8 + 87655.8i −0.166765 + 0.166765i
\(726\) 59862.6 + 237837.i 0.113575 + 0.451239i
\(727\) −457506. −0.865622 −0.432811 0.901485i \(-0.642478\pi\)
−0.432811 + 0.901485i \(0.642478\pi\)
\(728\) 120009. 109517.i 0.226439 0.206643i
\(729\) 19683.0i 0.0370370i
\(730\) 134501. + 534379.i 0.252394 + 1.00278i
\(731\) 109278. + 109278.i 0.204502 + 0.204502i
\(732\) −179299. 333619.i −0.334623 0.622627i
\(733\) 152573. + 152573.i 0.283969 + 0.283969i 0.834690 0.550721i \(-0.185647\pi\)
−0.550721 + 0.834690i \(0.685647\pi\)
\(734\) −242762. + 406070.i −0.450598 + 0.753719i
\(735\) 256193.i 0.474234i
\(736\) −239517. + 114953.i −0.442161 + 0.212210i
\(737\) 330374. 0.608234
\(738\) 53727.5 + 32120.1i 0.0986470 + 0.0589744i
\(739\) 567943. 567943.i 1.03996 1.03996i 0.0407903 0.999168i \(-0.487012\pi\)
0.999168 0.0407903i \(-0.0129876\pi\)
\(740\) −252051. + 135461.i −0.460282 + 0.247373i
\(741\) −440197. + 440197.i −0.801698 + 0.801698i
\(742\) 236875. 59620.2i 0.430240 0.108289i
\(743\) −566258. −1.02574 −0.512869 0.858467i \(-0.671417\pi\)
−0.512869 + 0.858467i \(0.671417\pi\)
\(744\) −363431. + 331659.i −0.656563 + 0.599164i
\(745\) 296531.i 0.534266i
\(746\) 795707. 200276.i 1.42980 0.359874i
\(747\) −167299. 167299.i −0.299814 0.299814i
\(748\) 19915.4 66193.7i 0.0355948 0.118308i
\(749\) −183981. 183981.i −0.327952 0.327952i
\(750\) 299056. + 178785.i 0.531655 + 0.317841i
\(751\) 303992.i 0.538991i 0.963002 + 0.269496i \(0.0868570\pi\)
−0.963002 + 0.269496i \(0.913143\pi\)
\(752\) −531045. 351351.i −0.939064 0.621306i
\(753\) 364222. 0.642357
\(754\) −370187. + 619215.i −0.651146 + 1.08918i
\(755\) −282627. + 282627.i −0.495816 + 0.495816i
\(756\) 9118.07 30306.1i 0.0159536 0.0530257i
\(757\) −19158.8 + 19158.8i −0.0334331 + 0.0334331i −0.723626 0.690193i \(-0.757526\pi\)
0.690193 + 0.723626i \(0.257526\pi\)
\(758\) −28450.8 113037.i −0.0495172 0.196735i
\(759\) −71858.4 −0.124737
\(760\) −952405. 43533.7i −1.64890 0.0753699i
\(761\) 506267.i 0.874199i 0.899413 + 0.437100i \(0.143994\pi\)
−0.899413 + 0.437100i \(0.856006\pi\)
\(762\) 8328.75 + 33090.6i 0.0143440 + 0.0569895i
\(763\) −109233. 109233.i −0.187630 0.187630i
\(764\) 540442. 290454.i 0.925896 0.497611i
\(765\) −34644.9 34644.9i −0.0591993 0.0591993i
\(766\) 267936. 448179.i 0.456640 0.763825i
\(767\) 216897.i 0.368691i
\(768\) 315785. + 127451.i 0.535389 + 0.216083i
\(769\) −79751.5 −0.134861 −0.0674305 0.997724i \(-0.521480\pi\)
−0.0674305 + 0.997724i \(0.521480\pi\)
\(770\) 57764.0 + 34533.2i 0.0974263 + 0.0582446i
\(771\) −345791. + 345791.i −0.581707 + 0.581707i
\(772\) 256686. + 477611.i 0.430693 + 0.801382i
\(773\) −618926. + 618926.i −1.03581 + 1.03581i −0.0364753 + 0.999335i \(0.511613\pi\)
−0.999335 + 0.0364753i \(0.988387\pi\)
\(774\) −199694. + 50262.2i −0.333337 + 0.0838995i
\(775\) 183099. 0.304848
\(776\) −17766.3 + 388682.i −0.0295036 + 0.645463i
\(777\) 58520.2i 0.0969313i
\(778\) −114398. + 28793.5i −0.188999 + 0.0475703i
\(779\) 272699. + 272699.i 0.449374 + 0.449374i
\(780\) 320936. + 96558.7i 0.527509 + 0.158709i
\(781\) −72629.5 72629.5i −0.119072 0.119072i
\(782\) −72197.3 43161.9i −0.118061 0.0705810i
\(783\) 140531.i 0.229218i
\(784\) 311079. 470176.i 0.506103 0.764942i
\(785\) −803614. −1.30409
\(786\) 102095. 170775.i 0.165257 0.276426i
\(787\) −78356.7 + 78356.7i −0.126511 + 0.126511i −0.767527 0.641017i \(-0.778513\pi\)
0.641017 + 0.767527i \(0.278513\pi\)
\(788\) −574663. 172896.i −0.925466 0.278441i
\(789\) 12968.5 12968.5i 0.0208322 0.0208322i
\(790\) −83408.2 331386.i −0.133646 0.530982i
\(791\) 203309. 0.324940
\(792\) 62087.4 + 68035.1i 0.0989812 + 0.108463i
\(793\) 820271.i 1.30440i
\(794\) 46214.4 + 183613.i 0.0733055 + 0.291247i
\(795\) 356293. + 356293.i 0.563732 + 0.563732i
\(796\) 150539. + 280105.i 0.237587 + 0.442073i
\(797\) 585144. + 585144.i 0.921184 + 0.921184i 0.997113 0.0759296i \(-0.0241924\pi\)
−0.0759296 + 0.997113i \(0.524192\pi\)
\(798\) 100050. 167355.i 0.157113 0.262805i
\(799\) 201604.i 0.315795i
\(800\) −54832.9 114250.i −0.0856765 0.178516i
\(801\) −405060. −0.631327
\(802\) −244110. 145937.i −0.379522 0.226891i
\(803\) 231919. 231919.i 0.359670 0.359670i
\(804\) −453901. + 243943.i −0.702181 + 0.377378i
\(805\) 57908.1 57908.1i 0.0893609 0.0893609i
\(806\) 1.03335e6 260090.i 1.59066 0.400363i
\(807\) 453289. 0.696030
\(808\) 735833. + 806324.i 1.12708 + 1.23506i
\(809\) 113161.i 0.172901i −0.996256 0.0864506i \(-0.972448\pi\)
0.996256 0.0864506i \(-0.0275525\pi\)
\(810\) 63310.2 15934.9i 0.0964947 0.0242873i
\(811\) −156533. 156533.i −0.237993 0.237993i 0.578025 0.816019i \(-0.303823\pi\)
−0.816019 + 0.578025i \(0.803823\pi\)
\(812\) 65100.4 216377.i 0.0987351 0.328170i
\(813\) 345881. + 345881.i 0.523294 + 0.523294i
\(814\) 146182. + 87392.7i 0.220621 + 0.131894i
\(815\) 937869.i 1.41197i
\(816\) 21514.7 + 105649.i 0.0323113 + 0.158666i
\(817\) −1.26868e6 −1.90067
\(818\) −24770.0 + 41433.0i −0.0370185 + 0.0619212i
\(819\) −48466.2 + 48466.2i −0.0722556 + 0.0722556i
\(820\) 59817.4 198818.i 0.0889611 0.295683i
\(821\) 727942. 727942.i 1.07997 1.07997i 0.0834551 0.996512i \(-0.473404\pi\)
0.996512 0.0834551i \(-0.0265955\pi\)
\(822\) −44890.9 178354.i −0.0664378 0.263961i
\(823\) −1.29556e6 −1.91275 −0.956375 0.292142i \(-0.905632\pi\)
−0.956375 + 0.292142i \(0.905632\pi\)
\(824\) 2976.06 65108.5i 0.00438315 0.0958922i
\(825\) 34276.6i 0.0503605i
\(826\) 16581.4 + 65879.0i 0.0243031 + 0.0965576i
\(827\) −885753. 885753.i −1.29509 1.29509i −0.931594 0.363500i \(-0.881582\pi\)
−0.363500 0.931594i \(-0.618418\pi\)
\(828\) 98726.4 53059.3i 0.144003 0.0773928i
\(829\) −113239. 113239.i −0.164773 0.164773i 0.619904 0.784677i \(-0.287171\pi\)
−0.784677 + 0.619904i \(0.787171\pi\)
\(830\) −402675. + 673557.i −0.584518 + 0.977728i
\(831\) 2394.91i 0.00346806i
\(832\) −471750. 566901.i −0.681499 0.818956i
\(833\) 178496. 0.257240
\(834\) 382759. + 228826.i 0.550292 + 0.328983i
\(835\) 283344. 283344.i 0.406388 0.406388i
\(836\) 268637. + 499848.i 0.384374 + 0.715197i
\(837\) 146774. 146774.i 0.209506 0.209506i
\(838\) 1.12144e6 282262.i 1.59694 0.401943i
\(839\) −524009. −0.744414 −0.372207 0.928150i \(-0.621399\pi\)
−0.372207 + 0.928150i \(0.621399\pi\)
\(840\) −104861. 4793.11i −0.148613 0.00679295i
\(841\) 296071.i 0.418605i
\(842\) −1.11983e6 + 281857.i −1.57954 + 0.397562i
\(843\) −368004. 368004.i −0.517842 0.517842i
\(844\) −635617. 191235.i −0.892299 0.268462i
\(845\) −61098.9 61098.9i −0.0855697 0.0855697i
\(846\) 230569. + 137842.i 0.322152 + 0.192593i
\(847\) 166363.i 0.231895i
\(848\) −221260. 1.08651e6i −0.307688 1.51092i
\(849\) −400915. −0.556208
\(850\) 20588.3 34438.2i 0.0284959 0.0476654i
\(851\) 146547. 146547.i 0.202357 0.202357i
\(852\) 153415. + 46157.2i 0.211343 + 0.0635858i
\(853\) −331577. + 331577.i −0.455708 + 0.455708i −0.897244 0.441536i \(-0.854434\pi\)
0.441536 + 0.897244i \(0.354434\pi\)
\(854\) −62708.4 249144.i −0.0859825 0.341613i
\(855\) 402215. 0.550208
\(856\) −872429. + 796159.i −1.19065 + 1.08656i
\(857\) 731561.i 0.996068i 0.867157 + 0.498034i \(0.165945\pi\)
−0.867157 + 0.498034i \(0.834055\pi\)
\(858\) −48689.5 193446.i −0.0661394 0.262776i
\(859\) 308744. + 308744.i 0.418420 + 0.418420i 0.884659 0.466239i \(-0.154391\pi\)
−0.466239 + 0.884659i \(0.654391\pi\)
\(860\) 323336. + 601624.i 0.437176 + 0.813446i
\(861\) 30024.5 + 30024.5i 0.0405013 + 0.0405013i
\(862\) 99857.5 167033.i 0.134390 0.224795i
\(863\) 38525.4i 0.0517280i −0.999665 0.0258640i \(-0.991766\pi\)
0.999665 0.0258640i \(-0.00823369\pi\)
\(864\) −135538. 47629.1i −0.181566 0.0638036i
\(865\) 684439. 0.914750
\(866\) −774950. 463291.i −1.03333 0.617757i
\(867\) 282738. 282738.i 0.376137 0.376137i
\(868\) −293981. + 157996.i −0.390193 + 0.209704i
\(869\) −143820. + 143820.i −0.190450 + 0.190450i
\(870\) 452017. 113771.i 0.597195 0.150311i
\(871\) 1.11601e6 1.47106
\(872\) −517975. + 472692.i −0.681202 + 0.621649i
\(873\) 164147.i 0.215379i
\(874\) 669640. 168545.i 0.876635 0.220645i
\(875\) 167121. + 167121.i 0.218281 + 0.218281i
\(876\) −147388. + 489879.i −0.192067 + 0.638382i
\(877\) 220189. + 220189.i 0.286283 + 0.286283i 0.835609 0.549325i \(-0.185115\pi\)
−0.549325 + 0.835609i \(0.685115\pi\)
\(878\) 200903. + 120107.i 0.260614 + 0.155804i
\(879\) 252749.i 0.327124i
\(880\) 168570. 254783.i 0.217678 0.329007i
\(881\) 141526. 0.182341 0.0911703 0.995835i \(-0.470939\pi\)
0.0911703 + 0.995835i \(0.470939\pi\)
\(882\) −122042. + 204141.i −0.156882 + 0.262418i
\(883\) 529860. 529860.i 0.679578 0.679578i −0.280327 0.959905i \(-0.590443\pi\)
0.959905 + 0.280327i \(0.0904428\pi\)
\(884\) 67274.8 223604.i 0.0860890 0.286137i
\(885\) −99091.2 + 99091.2i −0.126517 + 0.126517i
\(886\) −144424. 573803.i −0.183980 0.730964i
\(887\) 415500. 0.528109 0.264054 0.964508i \(-0.414940\pi\)
0.264054 + 0.964508i \(0.414940\pi\)
\(888\) −265370. 12129.8i −0.336531 0.0153826i
\(889\) 23146.3i 0.0292873i
\(890\) 327927. + 1.30287e6i 0.413996 + 1.64483i
\(891\) −27476.4 27476.4i −0.0346102 0.0346102i
\(892\) 408598. 219596.i 0.513530 0.275990i
\(893\) 1.17027e6 + 1.17027e6i 1.46752 + 1.46752i
\(894\) −141258. + 236283.i −0.176741 + 0.295637i
\(895\) 616824.i 0.770043i
\(896\) 186625. + 136122.i 0.232463 + 0.169556i
\(897\) −242739. −0.301686
\(898\) −200895. 120102.i −0.249125 0.148935i
\(899\) 1.04792e6 1.04792e6i 1.29661 1.29661i
\(900\) 25309.4 + 47092.7i 0.0312461 + 0.0581391i
\(901\) 248237. 248237.i 0.305786 0.305786i
\(902\) −119838. + 30162.8i −0.147293 + 0.0370730i
\(903\) −139683. −0.171304
\(904\) 42141.0 921938.i 0.0515665 1.12814i
\(905\) 1.14286e6i 1.39539i
\(906\) −359839. + 90569.9i −0.438382 + 0.110339i
\(907\) 377257. + 377257.i 0.458588 + 0.458588i 0.898192 0.439604i \(-0.144881\pi\)
−0.439604 + 0.898192i \(0.644881\pi\)
\(908\) −128635. 38702.0i −0.156023 0.0469420i
\(909\) −325638. 325638.i −0.394101 0.394101i
\(910\) 195128. + 116654.i 0.235634 + 0.140870i
\(911\) 30235.1i 0.0364313i 0.999834 + 0.0182157i \(0.00579855\pi\)
−0.999834 + 0.0182157i \(0.994201\pi\)
\(912\) −738162. 488384.i −0.887487 0.587181i
\(913\) 467080. 0.560338
\(914\) −606204. + 1.01400e6i −0.725648 + 1.21380i
\(915\) 374748. 374748.i 0.447607 0.447607i
\(916\) −193147. 58111.2i −0.230195 0.0692579i
\(917\) 95433.9 95433.9i 0.113492 0.113492i
\(918\) −11102.2 44109.7i −0.0131742 0.0523418i
\(919\) 156253. 0.185011 0.0925053 0.995712i \(-0.470512\pi\)
0.0925053 + 0.995712i \(0.470512\pi\)
\(920\) −250591. 274597.i −0.296067 0.324430i
\(921\) 732216.i 0.863217i
\(922\) 100077. + 397613.i 0.117726 + 0.467734i
\(923\) −245344. 245344.i −0.287987 0.287987i
\(924\) 29577.3 + 55033.9i 0.0346429 + 0.0644594i
\(925\) 69903.2 + 69903.2i 0.0816984 + 0.0816984i
\(926\) 246893. 412980.i 0.287930 0.481623i
\(927\) 27496.3i 0.0319974i
\(928\) −967704. 340059.i −1.12369 0.394873i
\(929\) −171947. −0.199234 −0.0996168 0.995026i \(-0.531762\pi\)
−0.0996168 + 0.995026i \(0.531762\pi\)
\(930\) −590920. 353272.i −0.683224 0.408454i
\(931\) −1.03614e6 + 1.03614e6i −1.19541 + 1.19541i
\(932\) −306817. + 164895.i −0.353221 + 0.189834i
\(933\) 600423. 600423.i 0.689754 0.689754i
\(934\) 468599. 117944.i 0.537165 0.135202i
\(935\) 96724.8 0.110641
\(936\) 209732. + 229824.i 0.239394 + 0.262328i
\(937\) 1.23829e6i 1.41040i −0.709006 0.705202i \(-0.750856\pi\)
0.709006 0.705202i \(-0.249144\pi\)
\(938\) −338970. + 85317.2i −0.385262 + 0.0969685i
\(939\) 337914. + 337914.i 0.383244 + 0.383244i
\(940\) 256704. 853216.i 0.290520 0.965614i
\(941\) 795144. + 795144.i 0.897980 + 0.897980i 0.995257 0.0972772i \(-0.0310133\pi\)
−0.0972772 + 0.995257i \(0.531013\pi\)
\(942\) −640340. 382816.i −0.721621 0.431409i
\(943\) 150375.i 0.169104i
\(944\) 302176. 61536.2i 0.339091 0.0690536i
\(945\) 44284.4 0.0495892
\(946\) 208599. 348926.i 0.233094 0.389898i
\(947\) 126444. 126444.i 0.140993 0.140993i −0.633087 0.774081i \(-0.718213\pi\)
0.774081 + 0.633087i \(0.218213\pi\)
\(948\) 91399.9 303789.i 0.101702 0.338031i
\(949\) 783426. 783426.i 0.869893 0.869893i
\(950\) 80396.4 + 319419.i 0.0890819 + 0.353927i
\(951\) −682939. −0.755129
\(952\) −3339.47 + 73059.1i −0.00368471 + 0.0806122i
\(953\) 359882.i 0.396254i 0.980176 + 0.198127i \(0.0634859\pi\)
−0.980176 + 0.198127i \(0.936514\pi\)
\(954\) 114176. + 453629.i 0.125453 + 0.498430i
\(955\) 607068. + 607068.i 0.665627 + 0.665627i
\(956\) 395348. 212475.i 0.432578 0.232483i
\(957\) −196174. 196174.i −0.214199 0.214199i
\(958\) 80780.1 135122.i 0.0880184 0.147229i
\(959\) 124756.i 0.135651i
\(960\) −43470.3 + 474517.i −0.0471683 + 0.514883i
\(961\) −1.26542e6 −1.37022
\(962\) 493808. + 295214.i 0.533590 + 0.318998i
\(963\) 352335. 352335.i 0.379930 0.379930i
\(964\) 259966. + 483714.i 0.279745 + 0.520517i
\(965\) −536491. + 536491.i −0.576114 + 0.576114i
\(966\) 73728.2 18557.0i 0.0790095 0.0198863i
\(967\) −1.22648e6 −1.31162 −0.655810 0.754926i \(-0.727673\pi\)
−0.655810 + 0.754926i \(0.727673\pi\)
\(968\) 754403. + 34483.1i 0.805105 + 0.0368007i
\(969\) 280233.i 0.298450i
\(970\) −527976. + 132889.i −0.561139 + 0.141236i
\(971\) −1.03007e6 1.03007e6i −1.09251 1.09251i −0.995260 0.0972546i \(-0.968994\pi\)
−0.0972546 0.995260i \(-0.531006\pi\)
\(972\) 58038.0 + 17461.7i 0.0614299 + 0.0184822i
\(973\) 213897. + 213897.i 0.225932 + 0.225932i
\(974\) −544113. 325289.i −0.573550 0.342887i
\(975\) 115787.i 0.121801i
\(976\) −1.14278e6 + 232720.i −1.19968 + 0.244306i
\(977\) 949908. 0.995159 0.497580 0.867418i \(-0.334222\pi\)
0.497580 + 0.867418i \(0.334222\pi\)
\(978\) 446771. 747317.i 0.467097 0.781317i
\(979\) 565441. 565441.i 0.589959 0.589959i
\(980\) 755421. + 227280.i 0.786569 + 0.236652i
\(981\) 209187. 209187.i 0.217369 0.217369i
\(982\) −70207.3 278938.i −0.0728047 0.289257i
\(983\) −1.15419e6 −1.19446 −0.597229 0.802071i \(-0.703732\pi\)
−0.597229 + 0.802071i \(0.703732\pi\)
\(984\) 142374. 129928.i 0.147042 0.134187i
\(985\) 839719.i 0.865489i
\(986\) −79266.6 314931.i −0.0815336 0.323938i
\(987\) 128849. + 128849.i 0.132265 + 0.132265i
\(988\) 907463. + 1.68850e6i 0.929640 + 1.72976i
\(989\) −349796. 349796.i −0.357620 0.357620i
\(990\) −66133.3 + 110622.i −0.0674761 + 0.112868i
\(991\) 1.60156e6i 1.63078i 0.578911 + 0.815391i \(0.303478\pi\)
−0.578911 + 0.815391i \(0.696522\pi\)
\(992\) 655526. + 1.36586e6i 0.666142 + 1.38797i
\(993\) 352934. 0.357928
\(994\) 93275.6 + 55763.2i 0.0944050 + 0.0564384i
\(995\) −314636. + 314636.i −0.317806 + 0.317806i
\(996\) −641722. + 344886.i −0.646887 + 0.347661i
\(997\) −699293. + 699293.i −0.703508 + 0.703508i −0.965162 0.261654i \(-0.915732\pi\)
0.261654 + 0.965162i \(0.415732\pi\)
\(998\) −1.06211e6 + 267328.i −1.06637 + 0.268400i
\(999\) 112070. 0.112294
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 48.5.l.a.19.13 32
3.2 odd 2 144.5.m.c.19.4 32
4.3 odd 2 192.5.l.a.175.13 32
8.3 odd 2 384.5.l.a.223.4 32
8.5 even 2 384.5.l.b.223.13 32
12.11 even 2 576.5.m.b.559.12 32
16.3 odd 4 384.5.l.b.31.13 32
16.5 even 4 192.5.l.a.79.13 32
16.11 odd 4 inner 48.5.l.a.43.13 yes 32
16.13 even 4 384.5.l.a.31.4 32
48.5 odd 4 576.5.m.b.271.12 32
48.11 even 4 144.5.m.c.91.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.5.l.a.19.13 32 1.1 even 1 trivial
48.5.l.a.43.13 yes 32 16.11 odd 4 inner
144.5.m.c.19.4 32 3.2 odd 2
144.5.m.c.91.4 32 48.11 even 4
192.5.l.a.79.13 32 16.5 even 4
192.5.l.a.175.13 32 4.3 odd 2
384.5.l.a.31.4 32 16.13 even 4
384.5.l.a.223.4 32 8.3 odd 2
384.5.l.b.31.13 32 16.3 odd 4
384.5.l.b.223.13 32 8.5 even 2
576.5.m.b.271.12 32 48.5 odd 4
576.5.m.b.559.12 32 12.11 even 2