Properties

Label 3549.2.a.bf.1.4
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 11 x^{7} + 8 x^{6} + 37 x^{5} - 18 x^{4} - 41 x^{3} + 12 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.374817\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.374817 q^{2} -1.00000 q^{3} -1.85951 q^{4} +1.32690 q^{5} +0.374817 q^{6} -1.00000 q^{7} +1.44661 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.374817 q^{2} -1.00000 q^{3} -1.85951 q^{4} +1.32690 q^{5} +0.374817 q^{6} -1.00000 q^{7} +1.44661 q^{8} +1.00000 q^{9} -0.497345 q^{10} +5.82806 q^{11} +1.85951 q^{12} +0.374817 q^{14} -1.32690 q^{15} +3.17681 q^{16} -0.442994 q^{17} -0.374817 q^{18} +1.34585 q^{19} -2.46739 q^{20} +1.00000 q^{21} -2.18446 q^{22} -2.67807 q^{23} -1.44661 q^{24} -3.23933 q^{25} -1.00000 q^{27} +1.85951 q^{28} +3.35417 q^{29} +0.497345 q^{30} +8.32825 q^{31} -4.08395 q^{32} -5.82806 q^{33} +0.166042 q^{34} -1.32690 q^{35} -1.85951 q^{36} +7.93555 q^{37} -0.504446 q^{38} +1.91951 q^{40} -0.816015 q^{41} -0.374817 q^{42} +3.16166 q^{43} -10.8373 q^{44} +1.32690 q^{45} +1.00379 q^{46} +4.29060 q^{47} -3.17681 q^{48} +1.00000 q^{49} +1.21416 q^{50} +0.442994 q^{51} -1.85465 q^{53} +0.374817 q^{54} +7.73326 q^{55} -1.44661 q^{56} -1.34585 q^{57} -1.25720 q^{58} -6.16798 q^{59} +2.46739 q^{60} -11.0420 q^{61} -3.12157 q^{62} -1.00000 q^{63} -4.82289 q^{64} +2.18446 q^{66} -1.64442 q^{67} +0.823753 q^{68} +2.67807 q^{69} +0.497345 q^{70} -12.9896 q^{71} +1.44661 q^{72} +7.20060 q^{73} -2.97438 q^{74} +3.23933 q^{75} -2.50262 q^{76} -5.82806 q^{77} -2.54704 q^{79} +4.21531 q^{80} +1.00000 q^{81} +0.305856 q^{82} -16.2210 q^{83} -1.85951 q^{84} -0.587809 q^{85} -1.18504 q^{86} -3.35417 q^{87} +8.43094 q^{88} -0.249528 q^{89} -0.497345 q^{90} +4.97991 q^{92} -8.32825 q^{93} -1.60819 q^{94} +1.78580 q^{95} +4.08395 q^{96} -3.75470 q^{97} -0.374817 q^{98} +5.82806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.374817 −0.265036 −0.132518 0.991181i \(-0.542306\pi\)
−0.132518 + 0.991181i \(0.542306\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.85951 −0.929756
\(5\) 1.32690 0.593408 0.296704 0.954969i \(-0.404112\pi\)
0.296704 + 0.954969i \(0.404112\pi\)
\(6\) 0.374817 0.153018
\(7\) −1.00000 −0.377964
\(8\) 1.44661 0.511454
\(9\) 1.00000 0.333333
\(10\) −0.497345 −0.157274
\(11\) 5.82806 1.75723 0.878613 0.477534i \(-0.158469\pi\)
0.878613 + 0.477534i \(0.158469\pi\)
\(12\) 1.85951 0.536795
\(13\) 0 0
\(14\) 0.374817 0.100174
\(15\) −1.32690 −0.342604
\(16\) 3.17681 0.794202
\(17\) −0.442994 −0.107442 −0.0537209 0.998556i \(-0.517108\pi\)
−0.0537209 + 0.998556i \(0.517108\pi\)
\(18\) −0.374817 −0.0883452
\(19\) 1.34585 0.308758 0.154379 0.988012i \(-0.450662\pi\)
0.154379 + 0.988012i \(0.450662\pi\)
\(20\) −2.46739 −0.551725
\(21\) 1.00000 0.218218
\(22\) −2.18446 −0.465728
\(23\) −2.67807 −0.558417 −0.279209 0.960230i \(-0.590072\pi\)
−0.279209 + 0.960230i \(0.590072\pi\)
\(24\) −1.44661 −0.295288
\(25\) −3.23933 −0.647867
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.85951 0.351415
\(29\) 3.35417 0.622853 0.311427 0.950270i \(-0.399193\pi\)
0.311427 + 0.950270i \(0.399193\pi\)
\(30\) 0.497345 0.0908024
\(31\) 8.32825 1.49580 0.747899 0.663813i \(-0.231063\pi\)
0.747899 + 0.663813i \(0.231063\pi\)
\(32\) −4.08395 −0.721946
\(33\) −5.82806 −1.01454
\(34\) 0.166042 0.0284759
\(35\) −1.32690 −0.224287
\(36\) −1.85951 −0.309919
\(37\) 7.93555 1.30460 0.652298 0.757962i \(-0.273805\pi\)
0.652298 + 0.757962i \(0.273805\pi\)
\(38\) −0.504446 −0.0818319
\(39\) 0 0
\(40\) 1.91951 0.303501
\(41\) −0.816015 −0.127440 −0.0637201 0.997968i \(-0.520296\pi\)
−0.0637201 + 0.997968i \(0.520296\pi\)
\(42\) −0.374817 −0.0578355
\(43\) 3.16166 0.482149 0.241074 0.970507i \(-0.422500\pi\)
0.241074 + 0.970507i \(0.422500\pi\)
\(44\) −10.8373 −1.63379
\(45\) 1.32690 0.197803
\(46\) 1.00379 0.148000
\(47\) 4.29060 0.625848 0.312924 0.949778i \(-0.398692\pi\)
0.312924 + 0.949778i \(0.398692\pi\)
\(48\) −3.17681 −0.458533
\(49\) 1.00000 0.142857
\(50\) 1.21416 0.171708
\(51\) 0.442994 0.0620316
\(52\) 0 0
\(53\) −1.85465 −0.254756 −0.127378 0.991854i \(-0.540656\pi\)
−0.127378 + 0.991854i \(0.540656\pi\)
\(54\) 0.374817 0.0510061
\(55\) 7.73326 1.04275
\(56\) −1.44661 −0.193312
\(57\) −1.34585 −0.178262
\(58\) −1.25720 −0.165078
\(59\) −6.16798 −0.803002 −0.401501 0.915858i \(-0.631511\pi\)
−0.401501 + 0.915858i \(0.631511\pi\)
\(60\) 2.46739 0.318539
\(61\) −11.0420 −1.41379 −0.706893 0.707320i \(-0.749904\pi\)
−0.706893 + 0.707320i \(0.749904\pi\)
\(62\) −3.12157 −0.396440
\(63\) −1.00000 −0.125988
\(64\) −4.82289 −0.602861
\(65\) 0 0
\(66\) 2.18446 0.268888
\(67\) −1.64442 −0.200898 −0.100449 0.994942i \(-0.532028\pi\)
−0.100449 + 0.994942i \(0.532028\pi\)
\(68\) 0.823753 0.0998947
\(69\) 2.67807 0.322402
\(70\) 0.497345 0.0594441
\(71\) −12.9896 −1.54158 −0.770792 0.637087i \(-0.780139\pi\)
−0.770792 + 0.637087i \(0.780139\pi\)
\(72\) 1.44661 0.170485
\(73\) 7.20060 0.842767 0.421384 0.906883i \(-0.361545\pi\)
0.421384 + 0.906883i \(0.361545\pi\)
\(74\) −2.97438 −0.345765
\(75\) 3.23933 0.374046
\(76\) −2.50262 −0.287070
\(77\) −5.82806 −0.664169
\(78\) 0 0
\(79\) −2.54704 −0.286565 −0.143282 0.989682i \(-0.545766\pi\)
−0.143282 + 0.989682i \(0.545766\pi\)
\(80\) 4.21531 0.471286
\(81\) 1.00000 0.111111
\(82\) 0.305856 0.0337762
\(83\) −16.2210 −1.78049 −0.890243 0.455486i \(-0.849465\pi\)
−0.890243 + 0.455486i \(0.849465\pi\)
\(84\) −1.85951 −0.202889
\(85\) −0.587809 −0.0637569
\(86\) −1.18504 −0.127787
\(87\) −3.35417 −0.359604
\(88\) 8.43094 0.898741
\(89\) −0.249528 −0.0264499 −0.0132249 0.999913i \(-0.504210\pi\)
−0.0132249 + 0.999913i \(0.504210\pi\)
\(90\) −0.497345 −0.0524248
\(91\) 0 0
\(92\) 4.97991 0.519192
\(93\) −8.32825 −0.863599
\(94\) −1.60819 −0.165872
\(95\) 1.78580 0.183220
\(96\) 4.08395 0.416816
\(97\) −3.75470 −0.381232 −0.190616 0.981665i \(-0.561048\pi\)
−0.190616 + 0.981665i \(0.561048\pi\)
\(98\) −0.374817 −0.0378622
\(99\) 5.82806 0.585742
\(100\) 6.02358 0.602358
\(101\) 2.83930 0.282521 0.141261 0.989972i \(-0.454884\pi\)
0.141261 + 0.989972i \(0.454884\pi\)
\(102\) −0.166042 −0.0164406
\(103\) −13.0189 −1.28279 −0.641395 0.767211i \(-0.721644\pi\)
−0.641395 + 0.767211i \(0.721644\pi\)
\(104\) 0 0
\(105\) 1.32690 0.129492
\(106\) 0.695154 0.0675194
\(107\) 14.5111 1.40284 0.701421 0.712748i \(-0.252550\pi\)
0.701421 + 0.712748i \(0.252550\pi\)
\(108\) 1.85951 0.178932
\(109\) 13.5778 1.30051 0.650257 0.759714i \(-0.274661\pi\)
0.650257 + 0.759714i \(0.274661\pi\)
\(110\) −2.89856 −0.276367
\(111\) −7.93555 −0.753209
\(112\) −3.17681 −0.300180
\(113\) 15.8715 1.49306 0.746532 0.665349i \(-0.231717\pi\)
0.746532 + 0.665349i \(0.231717\pi\)
\(114\) 0.504446 0.0472457
\(115\) −3.55354 −0.331369
\(116\) −6.23711 −0.579101
\(117\) 0 0
\(118\) 2.31186 0.212824
\(119\) 0.442994 0.0406092
\(120\) −1.91951 −0.175227
\(121\) 22.9663 2.08784
\(122\) 4.13874 0.374704
\(123\) 0.816015 0.0735776
\(124\) −15.4865 −1.39073
\(125\) −10.9328 −0.977858
\(126\) 0.374817 0.0333914
\(127\) −6.24679 −0.554313 −0.277157 0.960825i \(-0.589392\pi\)
−0.277157 + 0.960825i \(0.589392\pi\)
\(128\) 9.97559 0.881726
\(129\) −3.16166 −0.278369
\(130\) 0 0
\(131\) 14.6868 1.28319 0.641596 0.767043i \(-0.278273\pi\)
0.641596 + 0.767043i \(0.278273\pi\)
\(132\) 10.8373 0.943270
\(133\) −1.34585 −0.116700
\(134\) 0.616356 0.0532451
\(135\) −1.32690 −0.114201
\(136\) −0.640840 −0.0549516
\(137\) −0.933243 −0.0797323 −0.0398662 0.999205i \(-0.512693\pi\)
−0.0398662 + 0.999205i \(0.512693\pi\)
\(138\) −1.00379 −0.0854481
\(139\) 20.0765 1.70287 0.851435 0.524461i \(-0.175733\pi\)
0.851435 + 0.524461i \(0.175733\pi\)
\(140\) 2.46739 0.208532
\(141\) −4.29060 −0.361333
\(142\) 4.86873 0.408575
\(143\) 0 0
\(144\) 3.17681 0.264734
\(145\) 4.45065 0.369606
\(146\) −2.69891 −0.223363
\(147\) −1.00000 −0.0824786
\(148\) −14.7563 −1.21296
\(149\) 12.2978 1.00748 0.503739 0.863856i \(-0.331957\pi\)
0.503739 + 0.863856i \(0.331957\pi\)
\(150\) −1.21416 −0.0991355
\(151\) 18.6796 1.52013 0.760064 0.649849i \(-0.225168\pi\)
0.760064 + 0.649849i \(0.225168\pi\)
\(152\) 1.94692 0.157916
\(153\) −0.442994 −0.0358139
\(154\) 2.18446 0.176029
\(155\) 11.0508 0.887619
\(156\) 0 0
\(157\) 24.3864 1.94624 0.973122 0.230288i \(-0.0739669\pi\)
0.973122 + 0.230288i \(0.0739669\pi\)
\(158\) 0.954675 0.0759499
\(159\) 1.85465 0.147083
\(160\) −5.41899 −0.428409
\(161\) 2.67807 0.211062
\(162\) −0.374817 −0.0294484
\(163\) −22.2649 −1.74392 −0.871962 0.489574i \(-0.837152\pi\)
−0.871962 + 0.489574i \(0.837152\pi\)
\(164\) 1.51739 0.118488
\(165\) −7.73326 −0.602034
\(166\) 6.07991 0.471892
\(167\) 18.3284 1.41829 0.709146 0.705062i \(-0.249081\pi\)
0.709146 + 0.705062i \(0.249081\pi\)
\(168\) 1.44661 0.111608
\(169\) 0 0
\(170\) 0.220321 0.0168979
\(171\) 1.34585 0.102919
\(172\) −5.87914 −0.448281
\(173\) −12.7444 −0.968940 −0.484470 0.874808i \(-0.660988\pi\)
−0.484470 + 0.874808i \(0.660988\pi\)
\(174\) 1.25720 0.0953080
\(175\) 3.23933 0.244871
\(176\) 18.5146 1.39559
\(177\) 6.16798 0.463614
\(178\) 0.0935273 0.00701016
\(179\) 3.10502 0.232080 0.116040 0.993245i \(-0.462980\pi\)
0.116040 + 0.993245i \(0.462980\pi\)
\(180\) −2.46739 −0.183908
\(181\) −0.670686 −0.0498517 −0.0249259 0.999689i \(-0.507935\pi\)
−0.0249259 + 0.999689i \(0.507935\pi\)
\(182\) 0 0
\(183\) 11.0420 0.816250
\(184\) −3.87413 −0.285605
\(185\) 10.5297 0.774158
\(186\) 3.12157 0.228885
\(187\) −2.58180 −0.188800
\(188\) −7.97841 −0.581886
\(189\) 1.00000 0.0727393
\(190\) −0.669350 −0.0485598
\(191\) 17.8728 1.29323 0.646614 0.762817i \(-0.276184\pi\)
0.646614 + 0.762817i \(0.276184\pi\)
\(192\) 4.82289 0.348062
\(193\) −5.62386 −0.404814 −0.202407 0.979301i \(-0.564876\pi\)
−0.202407 + 0.979301i \(0.564876\pi\)
\(194\) 1.40732 0.101040
\(195\) 0 0
\(196\) −1.85951 −0.132822
\(197\) 16.5783 1.18116 0.590579 0.806980i \(-0.298900\pi\)
0.590579 + 0.806980i \(0.298900\pi\)
\(198\) −2.18446 −0.155243
\(199\) 24.4240 1.73137 0.865687 0.500585i \(-0.166882\pi\)
0.865687 + 0.500585i \(0.166882\pi\)
\(200\) −4.68605 −0.331354
\(201\) 1.64442 0.115988
\(202\) −1.06422 −0.0748782
\(203\) −3.35417 −0.235416
\(204\) −0.823753 −0.0576742
\(205\) −1.08277 −0.0756240
\(206\) 4.87970 0.339985
\(207\) −2.67807 −0.186139
\(208\) 0 0
\(209\) 7.84367 0.542558
\(210\) −0.497345 −0.0343201
\(211\) −10.9881 −0.756454 −0.378227 0.925713i \(-0.623466\pi\)
−0.378227 + 0.925713i \(0.623466\pi\)
\(212\) 3.44874 0.236861
\(213\) 12.9896 0.890033
\(214\) −5.43901 −0.371803
\(215\) 4.19521 0.286111
\(216\) −1.44661 −0.0984294
\(217\) −8.32825 −0.565358
\(218\) −5.08918 −0.344683
\(219\) −7.20060 −0.486572
\(220\) −14.3801 −0.969506
\(221\) 0 0
\(222\) 2.97438 0.199627
\(223\) −14.6782 −0.982922 −0.491461 0.870900i \(-0.663537\pi\)
−0.491461 + 0.870900i \(0.663537\pi\)
\(224\) 4.08395 0.272870
\(225\) −3.23933 −0.215956
\(226\) −5.94891 −0.395715
\(227\) −0.615870 −0.0408767 −0.0204384 0.999791i \(-0.506506\pi\)
−0.0204384 + 0.999791i \(0.506506\pi\)
\(228\) 2.50262 0.165740
\(229\) −9.47389 −0.626053 −0.313026 0.949744i \(-0.601343\pi\)
−0.313026 + 0.949744i \(0.601343\pi\)
\(230\) 1.33193 0.0878247
\(231\) 5.82806 0.383458
\(232\) 4.85218 0.318561
\(233\) −8.35195 −0.547154 −0.273577 0.961850i \(-0.588207\pi\)
−0.273577 + 0.961850i \(0.588207\pi\)
\(234\) 0 0
\(235\) 5.69320 0.371383
\(236\) 11.4694 0.746596
\(237\) 2.54704 0.165448
\(238\) −0.166042 −0.0107629
\(239\) −3.25440 −0.210510 −0.105255 0.994445i \(-0.533566\pi\)
−0.105255 + 0.994445i \(0.533566\pi\)
\(240\) −4.21531 −0.272097
\(241\) 16.1085 1.03764 0.518819 0.854884i \(-0.326372\pi\)
0.518819 + 0.854884i \(0.326372\pi\)
\(242\) −8.60816 −0.553353
\(243\) −1.00000 −0.0641500
\(244\) 20.5328 1.31448
\(245\) 1.32690 0.0847726
\(246\) −0.305856 −0.0195007
\(247\) 0 0
\(248\) 12.0477 0.765032
\(249\) 16.2210 1.02796
\(250\) 4.09779 0.259167
\(251\) 20.4332 1.28973 0.644866 0.764296i \(-0.276913\pi\)
0.644866 + 0.764296i \(0.276913\pi\)
\(252\) 1.85951 0.117138
\(253\) −15.6080 −0.981265
\(254\) 2.34141 0.146913
\(255\) 0.587809 0.0368101
\(256\) 5.90675 0.369172
\(257\) −15.8411 −0.988142 −0.494071 0.869422i \(-0.664492\pi\)
−0.494071 + 0.869422i \(0.664492\pi\)
\(258\) 1.18504 0.0737776
\(259\) −7.93555 −0.493091
\(260\) 0 0
\(261\) 3.35417 0.207618
\(262\) −5.50487 −0.340092
\(263\) 17.0251 1.04982 0.524908 0.851159i \(-0.324100\pi\)
0.524908 + 0.851159i \(0.324100\pi\)
\(264\) −8.43094 −0.518888
\(265\) −2.46094 −0.151174
\(266\) 0.504446 0.0309296
\(267\) 0.249528 0.0152708
\(268\) 3.05782 0.186786
\(269\) −16.0150 −0.976454 −0.488227 0.872717i \(-0.662356\pi\)
−0.488227 + 0.872717i \(0.662356\pi\)
\(270\) 0.497345 0.0302675
\(271\) −10.3553 −0.629040 −0.314520 0.949251i \(-0.601844\pi\)
−0.314520 + 0.949251i \(0.601844\pi\)
\(272\) −1.40731 −0.0853306
\(273\) 0 0
\(274\) 0.349795 0.0211319
\(275\) −18.8790 −1.13845
\(276\) −4.97991 −0.299755
\(277\) −8.83806 −0.531027 −0.265514 0.964107i \(-0.585542\pi\)
−0.265514 + 0.964107i \(0.585542\pi\)
\(278\) −7.52503 −0.451321
\(279\) 8.32825 0.498599
\(280\) −1.91951 −0.114713
\(281\) 14.3408 0.855503 0.427752 0.903896i \(-0.359306\pi\)
0.427752 + 0.903896i \(0.359306\pi\)
\(282\) 1.60819 0.0957662
\(283\) 13.9259 0.827808 0.413904 0.910321i \(-0.364165\pi\)
0.413904 + 0.910321i \(0.364165\pi\)
\(284\) 24.1543 1.43330
\(285\) −1.78580 −0.105782
\(286\) 0 0
\(287\) 0.816015 0.0481678
\(288\) −4.08395 −0.240649
\(289\) −16.8038 −0.988456
\(290\) −1.66818 −0.0979589
\(291\) 3.75470 0.220104
\(292\) −13.3896 −0.783568
\(293\) −24.0035 −1.40230 −0.701149 0.713015i \(-0.747329\pi\)
−0.701149 + 0.713015i \(0.747329\pi\)
\(294\) 0.374817 0.0218598
\(295\) −8.18430 −0.476508
\(296\) 11.4797 0.667241
\(297\) −5.82806 −0.338178
\(298\) −4.60944 −0.267018
\(299\) 0 0
\(300\) −6.02358 −0.347771
\(301\) −3.16166 −0.182235
\(302\) −7.00145 −0.402888
\(303\) −2.83930 −0.163114
\(304\) 4.27550 0.245216
\(305\) −14.6517 −0.838953
\(306\) 0.166042 0.00949197
\(307\) 20.6185 1.17676 0.588381 0.808584i \(-0.299765\pi\)
0.588381 + 0.808584i \(0.299765\pi\)
\(308\) 10.8373 0.617515
\(309\) 13.0189 0.740619
\(310\) −4.14202 −0.235251
\(311\) 33.6435 1.90775 0.953873 0.300210i \(-0.0970566\pi\)
0.953873 + 0.300210i \(0.0970566\pi\)
\(312\) 0 0
\(313\) 9.87809 0.558342 0.279171 0.960241i \(-0.409940\pi\)
0.279171 + 0.960241i \(0.409940\pi\)
\(314\) −9.14043 −0.515824
\(315\) −1.32690 −0.0747624
\(316\) 4.73626 0.266435
\(317\) −13.6053 −0.764151 −0.382075 0.924131i \(-0.624791\pi\)
−0.382075 + 0.924131i \(0.624791\pi\)
\(318\) −0.695154 −0.0389823
\(319\) 19.5483 1.09449
\(320\) −6.39950 −0.357743
\(321\) −14.5111 −0.809931
\(322\) −1.00379 −0.0559389
\(323\) −0.596202 −0.0331735
\(324\) −1.85951 −0.103306
\(325\) 0 0
\(326\) 8.34527 0.462202
\(327\) −13.5778 −0.750853
\(328\) −1.18046 −0.0651798
\(329\) −4.29060 −0.236548
\(330\) 2.89856 0.159560
\(331\) −1.35950 −0.0747251 −0.0373625 0.999302i \(-0.511896\pi\)
−0.0373625 + 0.999302i \(0.511896\pi\)
\(332\) 30.1631 1.65542
\(333\) 7.93555 0.434865
\(334\) −6.86979 −0.375898
\(335\) −2.18198 −0.119214
\(336\) 3.17681 0.173309
\(337\) 31.6542 1.72432 0.862158 0.506640i \(-0.169113\pi\)
0.862158 + 0.506640i \(0.169113\pi\)
\(338\) 0 0
\(339\) −15.8715 −0.862021
\(340\) 1.09304 0.0592783
\(341\) 48.5375 2.62846
\(342\) −0.504446 −0.0272773
\(343\) −1.00000 −0.0539949
\(344\) 4.57369 0.246597
\(345\) 3.55354 0.191316
\(346\) 4.77683 0.256804
\(347\) 18.5368 0.995108 0.497554 0.867433i \(-0.334232\pi\)
0.497554 + 0.867433i \(0.334232\pi\)
\(348\) 6.23711 0.334344
\(349\) −31.9333 −1.70935 −0.854674 0.519165i \(-0.826243\pi\)
−0.854674 + 0.519165i \(0.826243\pi\)
\(350\) −1.21416 −0.0648994
\(351\) 0 0
\(352\) −23.8015 −1.26862
\(353\) −1.62631 −0.0865598 −0.0432799 0.999063i \(-0.513781\pi\)
−0.0432799 + 0.999063i \(0.513781\pi\)
\(354\) −2.31186 −0.122874
\(355\) −17.2359 −0.914788
\(356\) 0.464000 0.0245919
\(357\) −0.442994 −0.0234457
\(358\) −1.16381 −0.0615095
\(359\) 24.7731 1.30747 0.653736 0.756722i \(-0.273201\pi\)
0.653736 + 0.756722i \(0.273201\pi\)
\(360\) 1.91951 0.101167
\(361\) −17.1887 −0.904668
\(362\) 0.251385 0.0132125
\(363\) −22.9663 −1.20542
\(364\) 0 0
\(365\) 9.55449 0.500105
\(366\) −4.13874 −0.216335
\(367\) 5.26649 0.274909 0.137454 0.990508i \(-0.456108\pi\)
0.137454 + 0.990508i \(0.456108\pi\)
\(368\) −8.50773 −0.443496
\(369\) −0.816015 −0.0424800
\(370\) −3.94671 −0.205180
\(371\) 1.85465 0.0962886
\(372\) 15.4865 0.802937
\(373\) −27.3669 −1.41701 −0.708503 0.705708i \(-0.750629\pi\)
−0.708503 + 0.705708i \(0.750629\pi\)
\(374\) 0.967701 0.0500386
\(375\) 10.9328 0.564566
\(376\) 6.20682 0.320092
\(377\) 0 0
\(378\) −0.374817 −0.0192785
\(379\) 25.4725 1.30844 0.654218 0.756306i \(-0.272998\pi\)
0.654218 + 0.756306i \(0.272998\pi\)
\(380\) −3.32073 −0.170350
\(381\) 6.24679 0.320033
\(382\) −6.69902 −0.342752
\(383\) 22.9476 1.17257 0.586283 0.810106i \(-0.300591\pi\)
0.586283 + 0.810106i \(0.300591\pi\)
\(384\) −9.97559 −0.509065
\(385\) −7.73326 −0.394123
\(386\) 2.10792 0.107290
\(387\) 3.16166 0.160716
\(388\) 6.98190 0.354452
\(389\) 15.0422 0.762671 0.381335 0.924437i \(-0.375464\pi\)
0.381335 + 0.924437i \(0.375464\pi\)
\(390\) 0 0
\(391\) 1.18637 0.0599974
\(392\) 1.44661 0.0730649
\(393\) −14.6868 −0.740851
\(394\) −6.21384 −0.313049
\(395\) −3.37967 −0.170050
\(396\) −10.8373 −0.544597
\(397\) −16.4236 −0.824278 −0.412139 0.911121i \(-0.635218\pi\)
−0.412139 + 0.911121i \(0.635218\pi\)
\(398\) −9.15455 −0.458876
\(399\) 1.34585 0.0673766
\(400\) −10.2907 −0.514537
\(401\) −17.7054 −0.884168 −0.442084 0.896974i \(-0.645761\pi\)
−0.442084 + 0.896974i \(0.645761\pi\)
\(402\) −0.616356 −0.0307411
\(403\) 0 0
\(404\) −5.27972 −0.262676
\(405\) 1.32690 0.0659343
\(406\) 1.25720 0.0623937
\(407\) 46.2489 2.29247
\(408\) 0.640840 0.0317263
\(409\) −4.05274 −0.200395 −0.100198 0.994968i \(-0.531947\pi\)
−0.100198 + 0.994968i \(0.531947\pi\)
\(410\) 0.405841 0.0200431
\(411\) 0.933243 0.0460335
\(412\) 24.2088 1.19268
\(413\) 6.16798 0.303506
\(414\) 1.00379 0.0493335
\(415\) −21.5237 −1.05655
\(416\) 0 0
\(417\) −20.0765 −0.983152
\(418\) −2.93994 −0.143797
\(419\) −7.13923 −0.348774 −0.174387 0.984677i \(-0.555794\pi\)
−0.174387 + 0.984677i \(0.555794\pi\)
\(420\) −2.46739 −0.120396
\(421\) 32.2979 1.57410 0.787052 0.616887i \(-0.211606\pi\)
0.787052 + 0.616887i \(0.211606\pi\)
\(422\) 4.11854 0.200487
\(423\) 4.29060 0.208616
\(424\) −2.68296 −0.130296
\(425\) 1.43501 0.0696080
\(426\) −4.86873 −0.235891
\(427\) 11.0420 0.534361
\(428\) −26.9836 −1.30430
\(429\) 0 0
\(430\) −1.57244 −0.0758296
\(431\) −13.3707 −0.644046 −0.322023 0.946732i \(-0.604363\pi\)
−0.322023 + 0.946732i \(0.604363\pi\)
\(432\) −3.17681 −0.152844
\(433\) −30.7437 −1.47745 −0.738723 0.674009i \(-0.764571\pi\)
−0.738723 + 0.674009i \(0.764571\pi\)
\(434\) 3.12157 0.149840
\(435\) −4.45065 −0.213392
\(436\) −25.2480 −1.20916
\(437\) −3.60427 −0.172416
\(438\) 2.69891 0.128959
\(439\) −22.4974 −1.07374 −0.536871 0.843664i \(-0.680394\pi\)
−0.536871 + 0.843664i \(0.680394\pi\)
\(440\) 11.1870 0.533320
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −26.6355 −1.26549 −0.632746 0.774359i \(-0.718072\pi\)
−0.632746 + 0.774359i \(0.718072\pi\)
\(444\) 14.7563 0.700301
\(445\) −0.331099 −0.0156956
\(446\) 5.50162 0.260509
\(447\) −12.2978 −0.581668
\(448\) 4.82289 0.227860
\(449\) 30.2908 1.42951 0.714757 0.699373i \(-0.246537\pi\)
0.714757 + 0.699373i \(0.246537\pi\)
\(450\) 1.21416 0.0572359
\(451\) −4.75578 −0.223941
\(452\) −29.5132 −1.38819
\(453\) −18.6796 −0.877646
\(454\) 0.230839 0.0108338
\(455\) 0 0
\(456\) −1.94692 −0.0911727
\(457\) −7.92047 −0.370504 −0.185252 0.982691i \(-0.559310\pi\)
−0.185252 + 0.982691i \(0.559310\pi\)
\(458\) 3.55098 0.165926
\(459\) 0.442994 0.0206772
\(460\) 6.60785 0.308093
\(461\) 10.9884 0.511783 0.255891 0.966706i \(-0.417631\pi\)
0.255891 + 0.966706i \(0.417631\pi\)
\(462\) −2.18446 −0.101630
\(463\) 8.71786 0.405153 0.202577 0.979266i \(-0.435068\pi\)
0.202577 + 0.979266i \(0.435068\pi\)
\(464\) 10.6555 0.494671
\(465\) −11.0508 −0.512467
\(466\) 3.13045 0.145015
\(467\) 33.7907 1.56365 0.781824 0.623499i \(-0.214289\pi\)
0.781824 + 0.623499i \(0.214289\pi\)
\(468\) 0 0
\(469\) 1.64442 0.0759322
\(470\) −2.13391 −0.0984298
\(471\) −24.3864 −1.12367
\(472\) −8.92267 −0.410699
\(473\) 18.4263 0.847244
\(474\) −0.954675 −0.0438497
\(475\) −4.35964 −0.200034
\(476\) −0.823753 −0.0377566
\(477\) −1.85465 −0.0849186
\(478\) 1.21981 0.0557926
\(479\) 39.0440 1.78396 0.891982 0.452071i \(-0.149315\pi\)
0.891982 + 0.452071i \(0.149315\pi\)
\(480\) 5.41899 0.247342
\(481\) 0 0
\(482\) −6.03773 −0.275011
\(483\) −2.67807 −0.121857
\(484\) −42.7061 −1.94119
\(485\) −4.98211 −0.226226
\(486\) 0.374817 0.0170020
\(487\) 12.0804 0.547416 0.273708 0.961813i \(-0.411750\pi\)
0.273708 + 0.961813i \(0.411750\pi\)
\(488\) −15.9735 −0.723087
\(489\) 22.2649 1.00685
\(490\) −0.497345 −0.0224678
\(491\) −42.4080 −1.91385 −0.956923 0.290343i \(-0.906231\pi\)
−0.956923 + 0.290343i \(0.906231\pi\)
\(492\) −1.51739 −0.0684092
\(493\) −1.48588 −0.0669205
\(494\) 0 0
\(495\) 7.73326 0.347584
\(496\) 26.4573 1.18797
\(497\) 12.9896 0.582664
\(498\) −6.07991 −0.272447
\(499\) 23.7535 1.06335 0.531677 0.846947i \(-0.321562\pi\)
0.531677 + 0.846947i \(0.321562\pi\)
\(500\) 20.3296 0.909169
\(501\) −18.3284 −0.818851
\(502\) −7.65871 −0.341825
\(503\) −18.4558 −0.822905 −0.411453 0.911431i \(-0.634978\pi\)
−0.411453 + 0.911431i \(0.634978\pi\)
\(504\) −1.44661 −0.0644372
\(505\) 3.76747 0.167650
\(506\) 5.85014 0.260070
\(507\) 0 0
\(508\) 11.6160 0.515376
\(509\) −12.5610 −0.556755 −0.278378 0.960472i \(-0.589797\pi\)
−0.278378 + 0.960472i \(0.589797\pi\)
\(510\) −0.220321 −0.00975598
\(511\) −7.20060 −0.318536
\(512\) −22.1651 −0.979570
\(513\) −1.34585 −0.0594205
\(514\) 5.93752 0.261893
\(515\) −17.2748 −0.761218
\(516\) 5.87914 0.258815
\(517\) 25.0058 1.09976
\(518\) 2.97438 0.130687
\(519\) 12.7444 0.559418
\(520\) 0 0
\(521\) −23.8796 −1.04618 −0.523092 0.852276i \(-0.675221\pi\)
−0.523092 + 0.852276i \(0.675221\pi\)
\(522\) −1.25720 −0.0550261
\(523\) 27.5520 1.20476 0.602382 0.798208i \(-0.294218\pi\)
0.602382 + 0.798208i \(0.294218\pi\)
\(524\) −27.3103 −1.19306
\(525\) −3.23933 −0.141376
\(526\) −6.38132 −0.278239
\(527\) −3.68937 −0.160711
\(528\) −18.5146 −0.805746
\(529\) −15.8279 −0.688170
\(530\) 0.922401 0.0400666
\(531\) −6.16798 −0.267667
\(532\) 2.50262 0.108502
\(533\) 0 0
\(534\) −0.0935273 −0.00404732
\(535\) 19.2548 0.832458
\(536\) −2.37884 −0.102750
\(537\) −3.10502 −0.133992
\(538\) 6.00271 0.258795
\(539\) 5.82806 0.251032
\(540\) 2.46739 0.106180
\(541\) −8.30651 −0.357125 −0.178562 0.983929i \(-0.557145\pi\)
−0.178562 + 0.983929i \(0.557145\pi\)
\(542\) 3.88134 0.166718
\(543\) 0.670686 0.0287819
\(544\) 1.80916 0.0775672
\(545\) 18.0164 0.771736
\(546\) 0 0
\(547\) −19.1011 −0.816705 −0.408353 0.912824i \(-0.633897\pi\)
−0.408353 + 0.912824i \(0.633897\pi\)
\(548\) 1.73538 0.0741316
\(549\) −11.0420 −0.471262
\(550\) 7.07618 0.301729
\(551\) 4.51419 0.192311
\(552\) 3.87413 0.164894
\(553\) 2.54704 0.108311
\(554\) 3.31266 0.140741
\(555\) −10.5297 −0.446961
\(556\) −37.3326 −1.58325
\(557\) 0.238603 0.0101099 0.00505496 0.999987i \(-0.498391\pi\)
0.00505496 + 0.999987i \(0.498391\pi\)
\(558\) −3.12157 −0.132147
\(559\) 0 0
\(560\) −4.21531 −0.178129
\(561\) 2.58180 0.109004
\(562\) −5.37519 −0.226739
\(563\) 20.7512 0.874559 0.437279 0.899326i \(-0.355942\pi\)
0.437279 + 0.899326i \(0.355942\pi\)
\(564\) 7.97841 0.335952
\(565\) 21.0599 0.885997
\(566\) −5.21966 −0.219399
\(567\) −1.00000 −0.0419961
\(568\) −18.7909 −0.788449
\(569\) 6.55284 0.274709 0.137355 0.990522i \(-0.456140\pi\)
0.137355 + 0.990522i \(0.456140\pi\)
\(570\) 0.669350 0.0280360
\(571\) 1.75392 0.0733995 0.0366997 0.999326i \(-0.488315\pi\)
0.0366997 + 0.999326i \(0.488315\pi\)
\(572\) 0 0
\(573\) −17.8728 −0.746646
\(574\) −0.305856 −0.0127662
\(575\) 8.67517 0.361780
\(576\) −4.82289 −0.200954
\(577\) 3.46646 0.144311 0.0721553 0.997393i \(-0.477012\pi\)
0.0721553 + 0.997393i \(0.477012\pi\)
\(578\) 6.29834 0.261976
\(579\) 5.62386 0.233720
\(580\) −8.27603 −0.343644
\(581\) 16.2210 0.672960
\(582\) −1.40732 −0.0583355
\(583\) −10.8090 −0.447663
\(584\) 10.4165 0.431037
\(585\) 0 0
\(586\) 8.99692 0.371659
\(587\) −38.9101 −1.60599 −0.802997 0.595984i \(-0.796762\pi\)
−0.802997 + 0.595984i \(0.796762\pi\)
\(588\) 1.85951 0.0766850
\(589\) 11.2085 0.461840
\(590\) 3.06762 0.126292
\(591\) −16.5783 −0.681941
\(592\) 25.2097 1.03611
\(593\) −25.4135 −1.04361 −0.521803 0.853066i \(-0.674740\pi\)
−0.521803 + 0.853066i \(0.674740\pi\)
\(594\) 2.18446 0.0896293
\(595\) 0.587809 0.0240978
\(596\) −22.8680 −0.936709
\(597\) −24.4240 −0.999610
\(598\) 0 0
\(599\) −7.40004 −0.302357 −0.151179 0.988506i \(-0.548307\pi\)
−0.151179 + 0.988506i \(0.548307\pi\)
\(600\) 4.68605 0.191307
\(601\) −14.4392 −0.588988 −0.294494 0.955653i \(-0.595151\pi\)
−0.294494 + 0.955653i \(0.595151\pi\)
\(602\) 1.18504 0.0482988
\(603\) −1.64442 −0.0669659
\(604\) −34.7350 −1.41335
\(605\) 30.4740 1.23894
\(606\) 1.06422 0.0432309
\(607\) 6.40534 0.259985 0.129992 0.991515i \(-0.458505\pi\)
0.129992 + 0.991515i \(0.458505\pi\)
\(608\) −5.49636 −0.222907
\(609\) 3.35417 0.135918
\(610\) 5.49170 0.222352
\(611\) 0 0
\(612\) 0.823753 0.0332982
\(613\) −9.33764 −0.377144 −0.188572 0.982059i \(-0.560386\pi\)
−0.188572 + 0.982059i \(0.560386\pi\)
\(614\) −7.72818 −0.311884
\(615\) 1.08277 0.0436616
\(616\) −8.43094 −0.339692
\(617\) −4.02033 −0.161852 −0.0809262 0.996720i \(-0.525788\pi\)
−0.0809262 + 0.996720i \(0.525788\pi\)
\(618\) −4.87970 −0.196290
\(619\) −22.6258 −0.909408 −0.454704 0.890643i \(-0.650255\pi\)
−0.454704 + 0.890643i \(0.650255\pi\)
\(620\) −20.5490 −0.825269
\(621\) 2.67807 0.107467
\(622\) −12.6102 −0.505621
\(623\) 0.249528 0.00999712
\(624\) 0 0
\(625\) 1.68994 0.0675975
\(626\) −3.70248 −0.147981
\(627\) −7.84367 −0.313246
\(628\) −45.3468 −1.80953
\(629\) −3.51540 −0.140168
\(630\) 0.497345 0.0198147
\(631\) 24.6591 0.981665 0.490832 0.871254i \(-0.336693\pi\)
0.490832 + 0.871254i \(0.336693\pi\)
\(632\) −3.68458 −0.146565
\(633\) 10.9881 0.436739
\(634\) 5.09951 0.202527
\(635\) −8.28888 −0.328934
\(636\) −3.44874 −0.136752
\(637\) 0 0
\(638\) −7.32703 −0.290080
\(639\) −12.9896 −0.513861
\(640\) 13.2366 0.523224
\(641\) 39.3652 1.55483 0.777416 0.628987i \(-0.216530\pi\)
0.777416 + 0.628987i \(0.216530\pi\)
\(642\) 5.43901 0.214661
\(643\) 40.6170 1.60178 0.800889 0.598812i \(-0.204361\pi\)
0.800889 + 0.598812i \(0.204361\pi\)
\(644\) −4.97991 −0.196236
\(645\) −4.19521 −0.165186
\(646\) 0.223467 0.00879217
\(647\) 4.38181 0.172267 0.0861333 0.996284i \(-0.472549\pi\)
0.0861333 + 0.996284i \(0.472549\pi\)
\(648\) 1.44661 0.0568283
\(649\) −35.9473 −1.41106
\(650\) 0 0
\(651\) 8.32825 0.326410
\(652\) 41.4019 1.62142
\(653\) 18.0074 0.704683 0.352342 0.935871i \(-0.385386\pi\)
0.352342 + 0.935871i \(0.385386\pi\)
\(654\) 5.08918 0.199003
\(655\) 19.4879 0.761457
\(656\) −2.59232 −0.101213
\(657\) 7.20060 0.280922
\(658\) 1.60819 0.0626937
\(659\) −9.85306 −0.383821 −0.191910 0.981412i \(-0.561468\pi\)
−0.191910 + 0.981412i \(0.561468\pi\)
\(660\) 14.3801 0.559744
\(661\) −27.3954 −1.06556 −0.532779 0.846254i \(-0.678852\pi\)
−0.532779 + 0.846254i \(0.678852\pi\)
\(662\) 0.509565 0.0198048
\(663\) 0 0
\(664\) −23.4655 −0.910637
\(665\) −1.78580 −0.0692505
\(666\) −2.97438 −0.115255
\(667\) −8.98271 −0.347812
\(668\) −34.0818 −1.31867
\(669\) 14.6782 0.567490
\(670\) 0.817844 0.0315961
\(671\) −64.3536 −2.48434
\(672\) −4.08395 −0.157542
\(673\) −17.8948 −0.689796 −0.344898 0.938640i \(-0.612086\pi\)
−0.344898 + 0.938640i \(0.612086\pi\)
\(674\) −11.8645 −0.457005
\(675\) 3.23933 0.124682
\(676\) 0 0
\(677\) −37.6226 −1.44595 −0.722977 0.690872i \(-0.757227\pi\)
−0.722977 + 0.690872i \(0.757227\pi\)
\(678\) 5.94891 0.228466
\(679\) 3.75470 0.144092
\(680\) −0.850332 −0.0326087
\(681\) 0.615870 0.0236002
\(682\) −18.1927 −0.696635
\(683\) 37.2441 1.42511 0.712553 0.701618i \(-0.247539\pi\)
0.712553 + 0.701618i \(0.247539\pi\)
\(684\) −2.50262 −0.0956899
\(685\) −1.23832 −0.0473138
\(686\) 0.374817 0.0143106
\(687\) 9.47389 0.361452
\(688\) 10.0440 0.382924
\(689\) 0 0
\(690\) −1.33193 −0.0507056
\(691\) −13.3126 −0.506437 −0.253218 0.967409i \(-0.581489\pi\)
−0.253218 + 0.967409i \(0.581489\pi\)
\(692\) 23.6984 0.900878
\(693\) −5.82806 −0.221390
\(694\) −6.94791 −0.263739
\(695\) 26.6396 1.01050
\(696\) −4.85218 −0.183921
\(697\) 0.361490 0.0136924
\(698\) 11.9691 0.453038
\(699\) 8.35195 0.315900
\(700\) −6.02358 −0.227670
\(701\) 40.6477 1.53524 0.767622 0.640903i \(-0.221440\pi\)
0.767622 + 0.640903i \(0.221440\pi\)
\(702\) 0 0
\(703\) 10.6800 0.402805
\(704\) −28.1081 −1.05936
\(705\) −5.69320 −0.214418
\(706\) 0.609570 0.0229415
\(707\) −2.83930 −0.106783
\(708\) −11.4694 −0.431048
\(709\) −22.3533 −0.839497 −0.419748 0.907641i \(-0.637882\pi\)
−0.419748 + 0.907641i \(0.637882\pi\)
\(710\) 6.46032 0.242452
\(711\) −2.54704 −0.0955215
\(712\) −0.360970 −0.0135279
\(713\) −22.3037 −0.835279
\(714\) 0.166042 0.00621396
\(715\) 0 0
\(716\) −5.77382 −0.215778
\(717\) 3.25440 0.121538
\(718\) −9.28537 −0.346527
\(719\) −13.6829 −0.510288 −0.255144 0.966903i \(-0.582123\pi\)
−0.255144 + 0.966903i \(0.582123\pi\)
\(720\) 4.21531 0.157095
\(721\) 13.0189 0.484849
\(722\) 6.44262 0.239769
\(723\) −16.1085 −0.599080
\(724\) 1.24715 0.0463499
\(725\) −10.8653 −0.403526
\(726\) 8.60816 0.319479
\(727\) −9.65059 −0.357920 −0.178960 0.983856i \(-0.557273\pi\)
−0.178960 + 0.983856i \(0.557273\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −3.58119 −0.132546
\(731\) −1.40060 −0.0518029
\(732\) −20.5328 −0.758914
\(733\) −42.0579 −1.55344 −0.776722 0.629844i \(-0.783119\pi\)
−0.776722 + 0.629844i \(0.783119\pi\)
\(734\) −1.97397 −0.0728606
\(735\) −1.32690 −0.0489435
\(736\) 10.9371 0.403147
\(737\) −9.58377 −0.353023
\(738\) 0.305856 0.0112587
\(739\) −19.4048 −0.713818 −0.356909 0.934139i \(-0.616169\pi\)
−0.356909 + 0.934139i \(0.616169\pi\)
\(740\) −19.5801 −0.719778
\(741\) 0 0
\(742\) −0.695154 −0.0255199
\(743\) 35.6920 1.30941 0.654706 0.755884i \(-0.272793\pi\)
0.654706 + 0.755884i \(0.272793\pi\)
\(744\) −12.0477 −0.441692
\(745\) 16.3180 0.597846
\(746\) 10.2576 0.375557
\(747\) −16.2210 −0.593495
\(748\) 4.80088 0.175538
\(749\) −14.5111 −0.530224
\(750\) −4.09779 −0.149630
\(751\) 51.8856 1.89333 0.946666 0.322217i \(-0.104428\pi\)
0.946666 + 0.322217i \(0.104428\pi\)
\(752\) 13.6304 0.497050
\(753\) −20.4332 −0.744627
\(754\) 0 0
\(755\) 24.7860 0.902056
\(756\) −1.85951 −0.0676298
\(757\) −29.7035 −1.07959 −0.539796 0.841796i \(-0.681499\pi\)
−0.539796 + 0.841796i \(0.681499\pi\)
\(758\) −9.54754 −0.346782
\(759\) 15.6080 0.566534
\(760\) 2.58336 0.0937085
\(761\) −11.5829 −0.419879 −0.209940 0.977714i \(-0.567327\pi\)
−0.209940 + 0.977714i \(0.567327\pi\)
\(762\) −2.34141 −0.0848202
\(763\) −13.5778 −0.491548
\(764\) −33.2346 −1.20239
\(765\) −0.587809 −0.0212523
\(766\) −8.60114 −0.310772
\(767\) 0 0
\(768\) −5.90675 −0.213142
\(769\) −7.72447 −0.278551 −0.139276 0.990254i \(-0.544477\pi\)
−0.139276 + 0.990254i \(0.544477\pi\)
\(770\) 2.89856 0.104457
\(771\) 15.8411 0.570504
\(772\) 10.4576 0.376378
\(773\) 5.56390 0.200120 0.100060 0.994981i \(-0.468097\pi\)
0.100060 + 0.994981i \(0.468097\pi\)
\(774\) −1.18504 −0.0425955
\(775\) −26.9780 −0.969077
\(776\) −5.43158 −0.194983
\(777\) 7.93555 0.284686
\(778\) −5.63808 −0.202135
\(779\) −1.09823 −0.0393482
\(780\) 0 0
\(781\) −75.7042 −2.70891
\(782\) −0.444672 −0.0159014
\(783\) −3.35417 −0.119868
\(784\) 3.17681 0.113457
\(785\) 32.3583 1.15492
\(786\) 5.50487 0.196352
\(787\) 1.31894 0.0470150 0.0235075 0.999724i \(-0.492517\pi\)
0.0235075 + 0.999724i \(0.492517\pi\)
\(788\) −30.8276 −1.09819
\(789\) −17.0251 −0.606111
\(790\) 1.26676 0.0450693
\(791\) −15.8715 −0.564325
\(792\) 8.43094 0.299580
\(793\) 0 0
\(794\) 6.15586 0.218463
\(795\) 2.46094 0.0872805
\(796\) −45.4168 −1.60976
\(797\) −15.5957 −0.552429 −0.276215 0.961096i \(-0.589080\pi\)
−0.276215 + 0.961096i \(0.589080\pi\)
\(798\) −0.504446 −0.0178572
\(799\) −1.90071 −0.0672422
\(800\) 13.2293 0.467725
\(801\) −0.249528 −0.00881663
\(802\) 6.63631 0.234336
\(803\) 41.9656 1.48093
\(804\) −3.05782 −0.107841
\(805\) 3.55354 0.125246
\(806\) 0 0
\(807\) 16.0150 0.563756
\(808\) 4.10737 0.144497
\(809\) −37.9340 −1.33369 −0.666844 0.745197i \(-0.732355\pi\)
−0.666844 + 0.745197i \(0.732355\pi\)
\(810\) −0.497345 −0.0174749
\(811\) −23.0022 −0.807718 −0.403859 0.914821i \(-0.632331\pi\)
−0.403859 + 0.914821i \(0.632331\pi\)
\(812\) 6.23711 0.218880
\(813\) 10.3553 0.363176
\(814\) −17.3349 −0.607587
\(815\) −29.5434 −1.03486
\(816\) 1.40731 0.0492656
\(817\) 4.25511 0.148867
\(818\) 1.51904 0.0531118
\(819\) 0 0
\(820\) 2.01343 0.0703119
\(821\) 16.9276 0.590778 0.295389 0.955377i \(-0.404551\pi\)
0.295389 + 0.955377i \(0.404551\pi\)
\(822\) −0.349795 −0.0122005
\(823\) 7.69045 0.268072 0.134036 0.990976i \(-0.457206\pi\)
0.134036 + 0.990976i \(0.457206\pi\)
\(824\) −18.8333 −0.656088
\(825\) 18.8790 0.657283
\(826\) −2.31186 −0.0804400
\(827\) −42.2818 −1.47028 −0.735140 0.677915i \(-0.762884\pi\)
−0.735140 + 0.677915i \(0.762884\pi\)
\(828\) 4.97991 0.173064
\(829\) 9.67366 0.335980 0.167990 0.985789i \(-0.446272\pi\)
0.167990 + 0.985789i \(0.446272\pi\)
\(830\) 8.06744 0.280025
\(831\) 8.83806 0.306589
\(832\) 0 0
\(833\) −0.442994 −0.0153488
\(834\) 7.52503 0.260570
\(835\) 24.3199 0.841626
\(836\) −14.5854 −0.504447
\(837\) −8.32825 −0.287866
\(838\) 2.67591 0.0924377
\(839\) −12.2804 −0.423967 −0.211983 0.977273i \(-0.567992\pi\)
−0.211983 + 0.977273i \(0.567992\pi\)
\(840\) 1.91951 0.0662294
\(841\) −17.7496 −0.612054
\(842\) −12.1058 −0.417194
\(843\) −14.3408 −0.493925
\(844\) 20.4326 0.703318
\(845\) 0 0
\(846\) −1.60819 −0.0552907
\(847\) −22.9663 −0.789131
\(848\) −5.89187 −0.202328
\(849\) −13.9259 −0.477935
\(850\) −0.537864 −0.0184486
\(851\) −21.2520 −0.728509
\(852\) −24.1543 −0.827514
\(853\) 0.0616267 0.00211006 0.00105503 0.999999i \(-0.499664\pi\)
0.00105503 + 0.999999i \(0.499664\pi\)
\(854\) −4.13874 −0.141625
\(855\) 1.78580 0.0610732
\(856\) 20.9919 0.717489
\(857\) 56.0433 1.91440 0.957202 0.289421i \(-0.0934629\pi\)
0.957202 + 0.289421i \(0.0934629\pi\)
\(858\) 0 0
\(859\) −16.0721 −0.548372 −0.274186 0.961677i \(-0.588408\pi\)
−0.274186 + 0.961677i \(0.588408\pi\)
\(860\) −7.80104 −0.266013
\(861\) −0.816015 −0.0278097
\(862\) 5.01158 0.170695
\(863\) 5.29127 0.180117 0.0900585 0.995936i \(-0.471295\pi\)
0.0900585 + 0.995936i \(0.471295\pi\)
\(864\) 4.08395 0.138939
\(865\) −16.9106 −0.574977
\(866\) 11.5233 0.391576
\(867\) 16.8038 0.570685
\(868\) 15.4865 0.525645
\(869\) −14.8443 −0.503559
\(870\) 1.66818 0.0565566
\(871\) 0 0
\(872\) 19.6418 0.665154
\(873\) −3.75470 −0.127077
\(874\) 1.35094 0.0456964
\(875\) 10.9328 0.369595
\(876\) 13.3896 0.452393
\(877\) 33.2558 1.12297 0.561484 0.827487i \(-0.310230\pi\)
0.561484 + 0.827487i \(0.310230\pi\)
\(878\) 8.43241 0.284580
\(879\) 24.0035 0.809617
\(880\) 24.5671 0.828157
\(881\) 35.0421 1.18060 0.590299 0.807185i \(-0.299010\pi\)
0.590299 + 0.807185i \(0.299010\pi\)
\(882\) −0.374817 −0.0126207
\(883\) 31.8305 1.07118 0.535590 0.844478i \(-0.320089\pi\)
0.535590 + 0.844478i \(0.320089\pi\)
\(884\) 0 0
\(885\) 8.18430 0.275112
\(886\) 9.98346 0.335401
\(887\) 49.6809 1.66812 0.834060 0.551673i \(-0.186010\pi\)
0.834060 + 0.551673i \(0.186010\pi\)
\(888\) −11.4797 −0.385232
\(889\) 6.24679 0.209511
\(890\) 0.124101 0.00415989
\(891\) 5.82806 0.195247
\(892\) 27.2942 0.913878
\(893\) 5.77448 0.193236
\(894\) 4.60944 0.154163
\(895\) 4.12006 0.137718
\(896\) −9.97559 −0.333261
\(897\) 0 0
\(898\) −11.3535 −0.378872
\(899\) 27.9343 0.931662
\(900\) 6.02358 0.200786
\(901\) 0.821599 0.0273714
\(902\) 1.78255 0.0593524
\(903\) 3.16166 0.105213
\(904\) 22.9599 0.763634
\(905\) −0.889935 −0.0295824
\(906\) 7.00145 0.232607
\(907\) −8.42301 −0.279681 −0.139841 0.990174i \(-0.544659\pi\)
−0.139841 + 0.990174i \(0.544659\pi\)
\(908\) 1.14522 0.0380054
\(909\) 2.83930 0.0941737
\(910\) 0 0
\(911\) 1.84825 0.0612351 0.0306176 0.999531i \(-0.490253\pi\)
0.0306176 + 0.999531i \(0.490253\pi\)
\(912\) −4.27550 −0.141576
\(913\) −94.5369 −3.12872
\(914\) 2.96873 0.0981968
\(915\) 14.6517 0.484370
\(916\) 17.6168 0.582076
\(917\) −14.6868 −0.485001
\(918\) −0.166042 −0.00548019
\(919\) 55.6552 1.83590 0.917948 0.396700i \(-0.129845\pi\)
0.917948 + 0.396700i \(0.129845\pi\)
\(920\) −5.14059 −0.169480
\(921\) −20.6185 −0.679404
\(922\) −4.11866 −0.135641
\(923\) 0 0
\(924\) −10.8373 −0.356523
\(925\) −25.7059 −0.845204
\(926\) −3.26760 −0.107380
\(927\) −13.0189 −0.427596
\(928\) −13.6982 −0.449667
\(929\) 39.2038 1.28624 0.643118 0.765767i \(-0.277641\pi\)
0.643118 + 0.765767i \(0.277641\pi\)
\(930\) 4.14202 0.135822
\(931\) 1.34585 0.0441083
\(932\) 15.5306 0.508720
\(933\) −33.6435 −1.10144
\(934\) −12.6653 −0.414423
\(935\) −3.42579 −0.112035
\(936\) 0 0
\(937\) −12.6724 −0.413989 −0.206995 0.978342i \(-0.566368\pi\)
−0.206995 + 0.978342i \(0.566368\pi\)
\(938\) −0.616356 −0.0201248
\(939\) −9.87809 −0.322359
\(940\) −10.5866 −0.345296
\(941\) 7.81644 0.254809 0.127404 0.991851i \(-0.459335\pi\)
0.127404 + 0.991851i \(0.459335\pi\)
\(942\) 9.14043 0.297811
\(943\) 2.18535 0.0711648
\(944\) −19.5945 −0.637746
\(945\) 1.32690 0.0431641
\(946\) −6.90651 −0.224550
\(947\) 48.1824 1.56572 0.782859 0.622199i \(-0.213760\pi\)
0.782859 + 0.622199i \(0.213760\pi\)
\(948\) −4.73626 −0.153826
\(949\) 0 0
\(950\) 1.63407 0.0530162
\(951\) 13.6053 0.441183
\(952\) 0.640840 0.0207697
\(953\) 51.8052 1.67813 0.839067 0.544028i \(-0.183101\pi\)
0.839067 + 0.544028i \(0.183101\pi\)
\(954\) 0.695154 0.0225065
\(955\) 23.7154 0.767412
\(956\) 6.05160 0.195723
\(957\) −19.5483 −0.631906
\(958\) −14.6343 −0.472814
\(959\) 0.933243 0.0301360
\(960\) 6.39950 0.206543
\(961\) 38.3598 1.23741
\(962\) 0 0
\(963\) 14.5111 0.467614
\(964\) −29.9539 −0.964750
\(965\) −7.46231 −0.240220
\(966\) 1.00379 0.0322964
\(967\) −5.87478 −0.188920 −0.0944602 0.995529i \(-0.530113\pi\)
−0.0944602 + 0.995529i \(0.530113\pi\)
\(968\) 33.2233 1.06784
\(969\) 0.596202 0.0191528
\(970\) 1.86738 0.0599580
\(971\) 53.1421 1.70541 0.852705 0.522392i \(-0.174960\pi\)
0.852705 + 0.522392i \(0.174960\pi\)
\(972\) 1.85951 0.0596439
\(973\) −20.0765 −0.643624
\(974\) −4.52795 −0.145085
\(975\) 0 0
\(976\) −35.0784 −1.12283
\(977\) 16.9292 0.541612 0.270806 0.962634i \(-0.412710\pi\)
0.270806 + 0.962634i \(0.412710\pi\)
\(978\) −8.34527 −0.266852
\(979\) −1.45426 −0.0464784
\(980\) −2.46739 −0.0788179
\(981\) 13.5778 0.433505
\(982\) 15.8952 0.507237
\(983\) 34.7612 1.10871 0.554355 0.832281i \(-0.312965\pi\)
0.554355 + 0.832281i \(0.312965\pi\)
\(984\) 1.18046 0.0376316
\(985\) 21.9978 0.700908
\(986\) 0.556932 0.0177363
\(987\) 4.29060 0.136571
\(988\) 0 0
\(989\) −8.46716 −0.269240
\(990\) −2.89856 −0.0921222
\(991\) 33.6843 1.07002 0.535009 0.844846i \(-0.320308\pi\)
0.535009 + 0.844846i \(0.320308\pi\)
\(992\) −34.0121 −1.07989
\(993\) 1.35950 0.0431426
\(994\) −4.86873 −0.154427
\(995\) 32.4083 1.02741
\(996\) −30.1631 −0.955756
\(997\) 9.21153 0.291732 0.145866 0.989304i \(-0.453403\pi\)
0.145866 + 0.989304i \(0.453403\pi\)
\(998\) −8.90322 −0.281827
\(999\) −7.93555 −0.251070
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 3549.2.a.bf.1.4 yes 9
13.12 even 2 3549.2.a.be.1.6 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.6 9 13.12 even 2
3549.2.a.bf.1.4 yes 9 1.1 even 1 trivial