Properties

Label 4029.2.a.l.1.14
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.510062 q^{2} -1.00000 q^{3} -1.73984 q^{4} -1.60726 q^{5} +0.510062 q^{6} -0.772958 q^{7} +1.90755 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.510062 q^{2} -1.00000 q^{3} -1.73984 q^{4} -1.60726 q^{5} +0.510062 q^{6} -0.772958 q^{7} +1.90755 q^{8} +1.00000 q^{9} +0.819801 q^{10} +5.11481 q^{11} +1.73984 q^{12} -4.25469 q^{13} +0.394257 q^{14} +1.60726 q^{15} +2.50671 q^{16} -1.00000 q^{17} -0.510062 q^{18} +0.139644 q^{19} +2.79637 q^{20} +0.772958 q^{21} -2.60887 q^{22} +2.39815 q^{23} -1.90755 q^{24} -2.41672 q^{25} +2.17016 q^{26} -1.00000 q^{27} +1.34482 q^{28} +7.73479 q^{29} -0.819801 q^{30} -0.727102 q^{31} -5.09367 q^{32} -5.11481 q^{33} +0.510062 q^{34} +1.24234 q^{35} -1.73984 q^{36} +1.12804 q^{37} -0.0712273 q^{38} +4.25469 q^{39} -3.06592 q^{40} -4.55066 q^{41} -0.394257 q^{42} -10.1625 q^{43} -8.89893 q^{44} -1.60726 q^{45} -1.22320 q^{46} +5.80251 q^{47} -2.50671 q^{48} -6.40254 q^{49} +1.23268 q^{50} +1.00000 q^{51} +7.40247 q^{52} -8.80818 q^{53} +0.510062 q^{54} -8.22081 q^{55} -1.47445 q^{56} -0.139644 q^{57} -3.94522 q^{58} +2.77156 q^{59} -2.79637 q^{60} +6.83036 q^{61} +0.370867 q^{62} -0.772958 q^{63} -2.41532 q^{64} +6.83838 q^{65} +2.60887 q^{66} -9.93419 q^{67} +1.73984 q^{68} -2.39815 q^{69} -0.633672 q^{70} -9.38080 q^{71} +1.90755 q^{72} +14.8634 q^{73} -0.575372 q^{74} +2.41672 q^{75} -0.242959 q^{76} -3.95353 q^{77} -2.17016 q^{78} +1.00000 q^{79} -4.02892 q^{80} +1.00000 q^{81} +2.32112 q^{82} +0.155778 q^{83} -1.34482 q^{84} +1.60726 q^{85} +5.18352 q^{86} -7.73479 q^{87} +9.75674 q^{88} +1.13427 q^{89} +0.819801 q^{90} +3.28870 q^{91} -4.17238 q^{92} +0.727102 q^{93} -2.95964 q^{94} -0.224445 q^{95} +5.09367 q^{96} +10.1795 q^{97} +3.26569 q^{98} +5.11481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.510062 −0.360668 −0.180334 0.983605i \(-0.557718\pi\)
−0.180334 + 0.983605i \(0.557718\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.73984 −0.869918
\(5\) −1.60726 −0.718787 −0.359394 0.933186i \(-0.617016\pi\)
−0.359394 + 0.933186i \(0.617016\pi\)
\(6\) 0.510062 0.208232
\(7\) −0.772958 −0.292151 −0.146075 0.989273i \(-0.546664\pi\)
−0.146075 + 0.989273i \(0.546664\pi\)
\(8\) 1.90755 0.674420
\(9\) 1.00000 0.333333
\(10\) 0.819801 0.259244
\(11\) 5.11481 1.54217 0.771086 0.636731i \(-0.219714\pi\)
0.771086 + 0.636731i \(0.219714\pi\)
\(12\) 1.73984 0.502248
\(13\) −4.25469 −1.18004 −0.590019 0.807389i \(-0.700880\pi\)
−0.590019 + 0.807389i \(0.700880\pi\)
\(14\) 0.394257 0.105369
\(15\) 1.60726 0.414992
\(16\) 2.50671 0.626676
\(17\) −1.00000 −0.242536
\(18\) −0.510062 −0.120223
\(19\) 0.139644 0.0320366 0.0160183 0.999872i \(-0.494901\pi\)
0.0160183 + 0.999872i \(0.494901\pi\)
\(20\) 2.79637 0.625286
\(21\) 0.772958 0.168673
\(22\) −2.60887 −0.556213
\(23\) 2.39815 0.500048 0.250024 0.968240i \(-0.419561\pi\)
0.250024 + 0.968240i \(0.419561\pi\)
\(24\) −1.90755 −0.389377
\(25\) −2.41672 −0.483345
\(26\) 2.17016 0.425603
\(27\) −1.00000 −0.192450
\(28\) 1.34482 0.254147
\(29\) 7.73479 1.43631 0.718157 0.695881i \(-0.244986\pi\)
0.718157 + 0.695881i \(0.244986\pi\)
\(30\) −0.819801 −0.149674
\(31\) −0.727102 −0.130591 −0.0652957 0.997866i \(-0.520799\pi\)
−0.0652957 + 0.997866i \(0.520799\pi\)
\(32\) −5.09367 −0.900443
\(33\) −5.11481 −0.890374
\(34\) 0.510062 0.0874749
\(35\) 1.24234 0.209994
\(36\) −1.73984 −0.289973
\(37\) 1.12804 0.185449 0.0927246 0.995692i \(-0.470442\pi\)
0.0927246 + 0.995692i \(0.470442\pi\)
\(38\) −0.0712273 −0.0115546
\(39\) 4.25469 0.681296
\(40\) −3.06592 −0.484765
\(41\) −4.55066 −0.710693 −0.355347 0.934735i \(-0.615637\pi\)
−0.355347 + 0.934735i \(0.615637\pi\)
\(42\) −0.394257 −0.0608351
\(43\) −10.1625 −1.54977 −0.774886 0.632101i \(-0.782193\pi\)
−0.774886 + 0.632101i \(0.782193\pi\)
\(44\) −8.89893 −1.34156
\(45\) −1.60726 −0.239596
\(46\) −1.22320 −0.180352
\(47\) 5.80251 0.846383 0.423191 0.906040i \(-0.360910\pi\)
0.423191 + 0.906040i \(0.360910\pi\)
\(48\) −2.50671 −0.361812
\(49\) −6.40254 −0.914648
\(50\) 1.23268 0.174327
\(51\) 1.00000 0.140028
\(52\) 7.40247 1.02654
\(53\) −8.80818 −1.20990 −0.604948 0.796265i \(-0.706806\pi\)
−0.604948 + 0.796265i \(0.706806\pi\)
\(54\) 0.510062 0.0694107
\(55\) −8.22081 −1.10849
\(56\) −1.47445 −0.197032
\(57\) −0.139644 −0.0184964
\(58\) −3.94522 −0.518033
\(59\) 2.77156 0.360827 0.180413 0.983591i \(-0.442256\pi\)
0.180413 + 0.983591i \(0.442256\pi\)
\(60\) −2.79637 −0.361009
\(61\) 6.83036 0.874538 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(62\) 0.370867 0.0471001
\(63\) −0.772958 −0.0973836
\(64\) −2.41532 −0.301915
\(65\) 6.83838 0.848197
\(66\) 2.60887 0.321130
\(67\) −9.93419 −1.21365 −0.606827 0.794834i \(-0.707558\pi\)
−0.606827 + 0.794834i \(0.707558\pi\)
\(68\) 1.73984 0.210986
\(69\) −2.39815 −0.288703
\(70\) −0.633672 −0.0757383
\(71\) −9.38080 −1.11330 −0.556648 0.830748i \(-0.687913\pi\)
−0.556648 + 0.830748i \(0.687913\pi\)
\(72\) 1.90755 0.224807
\(73\) 14.8634 1.73963 0.869815 0.493379i \(-0.164238\pi\)
0.869815 + 0.493379i \(0.164238\pi\)
\(74\) −0.575372 −0.0668857
\(75\) 2.41672 0.279059
\(76\) −0.242959 −0.0278693
\(77\) −3.95353 −0.450547
\(78\) −2.17016 −0.245722
\(79\) 1.00000 0.112509
\(80\) −4.02892 −0.450447
\(81\) 1.00000 0.111111
\(82\) 2.32112 0.256325
\(83\) 0.155778 0.0170989 0.00854944 0.999963i \(-0.497279\pi\)
0.00854944 + 0.999963i \(0.497279\pi\)
\(84\) −1.34482 −0.146732
\(85\) 1.60726 0.174332
\(86\) 5.18352 0.558954
\(87\) −7.73479 −0.829256
\(88\) 9.75674 1.04007
\(89\) 1.13427 0.120232 0.0601160 0.998191i \(-0.480853\pi\)
0.0601160 + 0.998191i \(0.480853\pi\)
\(90\) 0.819801 0.0864146
\(91\) 3.28870 0.344749
\(92\) −4.17238 −0.435001
\(93\) 0.727102 0.0753969
\(94\) −2.95964 −0.305263
\(95\) −0.224445 −0.0230275
\(96\) 5.09367 0.519871
\(97\) 10.1795 1.03357 0.516784 0.856116i \(-0.327129\pi\)
0.516784 + 0.856116i \(0.327129\pi\)
\(98\) 3.26569 0.329885
\(99\) 5.11481 0.514058
\(100\) 4.20470 0.420470
\(101\) 1.50689 0.149941 0.0749706 0.997186i \(-0.476114\pi\)
0.0749706 + 0.997186i \(0.476114\pi\)
\(102\) −0.510062 −0.0505037
\(103\) −16.7719 −1.65258 −0.826291 0.563243i \(-0.809553\pi\)
−0.826291 + 0.563243i \(0.809553\pi\)
\(104\) −8.11603 −0.795842
\(105\) −1.24234 −0.121240
\(106\) 4.49272 0.436371
\(107\) −9.35639 −0.904517 −0.452258 0.891887i \(-0.649381\pi\)
−0.452258 + 0.891887i \(0.649381\pi\)
\(108\) 1.73984 0.167416
\(109\) −1.19641 −0.114595 −0.0572975 0.998357i \(-0.518248\pi\)
−0.0572975 + 0.998357i \(0.518248\pi\)
\(110\) 4.19312 0.399799
\(111\) −1.12804 −0.107069
\(112\) −1.93758 −0.183084
\(113\) −9.37198 −0.881642 −0.440821 0.897595i \(-0.645313\pi\)
−0.440821 + 0.897595i \(0.645313\pi\)
\(114\) 0.0712273 0.00667105
\(115\) −3.85444 −0.359428
\(116\) −13.4573 −1.24948
\(117\) −4.25469 −0.393346
\(118\) −1.41367 −0.130139
\(119\) 0.772958 0.0708569
\(120\) 3.06592 0.279879
\(121\) 15.1613 1.37830
\(122\) −3.48391 −0.315418
\(123\) 4.55066 0.410319
\(124\) 1.26504 0.113604
\(125\) 11.9206 1.06621
\(126\) 0.394257 0.0351232
\(127\) −10.1118 −0.897281 −0.448641 0.893712i \(-0.648092\pi\)
−0.448641 + 0.893712i \(0.648092\pi\)
\(128\) 11.4193 1.00933
\(129\) 10.1625 0.894761
\(130\) −3.48800 −0.305918
\(131\) 14.9108 1.30276 0.651382 0.758750i \(-0.274190\pi\)
0.651382 + 0.758750i \(0.274190\pi\)
\(132\) 8.89893 0.774552
\(133\) −0.107939 −0.00935952
\(134\) 5.06705 0.437727
\(135\) 1.60726 0.138331
\(136\) −1.90755 −0.163571
\(137\) 12.8494 1.09780 0.548898 0.835889i \(-0.315047\pi\)
0.548898 + 0.835889i \(0.315047\pi\)
\(138\) 1.22320 0.104126
\(139\) −8.69363 −0.737384 −0.368692 0.929552i \(-0.620194\pi\)
−0.368692 + 0.929552i \(0.620194\pi\)
\(140\) −2.16147 −0.182678
\(141\) −5.80251 −0.488659
\(142\) 4.78479 0.401531
\(143\) −21.7619 −1.81982
\(144\) 2.50671 0.208892
\(145\) −12.4318 −1.03240
\(146\) −7.58126 −0.627429
\(147\) 6.40254 0.528072
\(148\) −1.96261 −0.161326
\(149\) 2.99949 0.245728 0.122864 0.992424i \(-0.460792\pi\)
0.122864 + 0.992424i \(0.460792\pi\)
\(150\) −1.23268 −0.100648
\(151\) 16.8985 1.37518 0.687591 0.726099i \(-0.258668\pi\)
0.687591 + 0.726099i \(0.258668\pi\)
\(152\) 0.266379 0.0216062
\(153\) −1.00000 −0.0808452
\(154\) 2.01655 0.162498
\(155\) 1.16864 0.0938674
\(156\) −7.40247 −0.592672
\(157\) −4.67973 −0.373483 −0.186741 0.982409i \(-0.559793\pi\)
−0.186741 + 0.982409i \(0.559793\pi\)
\(158\) −0.510062 −0.0405784
\(159\) 8.80818 0.698534
\(160\) 8.18684 0.647227
\(161\) −1.85367 −0.146089
\(162\) −0.510062 −0.0400743
\(163\) 16.9424 1.32703 0.663517 0.748161i \(-0.269063\pi\)
0.663517 + 0.748161i \(0.269063\pi\)
\(164\) 7.91740 0.618245
\(165\) 8.22081 0.639989
\(166\) −0.0794566 −0.00616703
\(167\) 5.73607 0.443870 0.221935 0.975061i \(-0.428763\pi\)
0.221935 + 0.975061i \(0.428763\pi\)
\(168\) 1.47445 0.113757
\(169\) 5.10239 0.392491
\(170\) −0.819801 −0.0628759
\(171\) 0.139644 0.0106789
\(172\) 17.6812 1.34818
\(173\) −10.7165 −0.814763 −0.407382 0.913258i \(-0.633558\pi\)
−0.407382 + 0.913258i \(0.633558\pi\)
\(174\) 3.94522 0.299086
\(175\) 1.86803 0.141209
\(176\) 12.8213 0.966443
\(177\) −2.77156 −0.208324
\(178\) −0.578546 −0.0433638
\(179\) 7.40907 0.553780 0.276890 0.960902i \(-0.410696\pi\)
0.276890 + 0.960902i \(0.410696\pi\)
\(180\) 2.79637 0.208429
\(181\) 19.6108 1.45766 0.728829 0.684696i \(-0.240065\pi\)
0.728829 + 0.684696i \(0.240065\pi\)
\(182\) −1.67744 −0.124340
\(183\) −6.83036 −0.504915
\(184\) 4.57458 0.337243
\(185\) −1.81306 −0.133299
\(186\) −0.370867 −0.0271933
\(187\) −5.11481 −0.374032
\(188\) −10.0954 −0.736284
\(189\) 0.772958 0.0562244
\(190\) 0.114481 0.00830530
\(191\) −4.69270 −0.339552 −0.169776 0.985483i \(-0.554304\pi\)
−0.169776 + 0.985483i \(0.554304\pi\)
\(192\) 2.41532 0.174311
\(193\) 26.9839 1.94235 0.971173 0.238376i \(-0.0766151\pi\)
0.971173 + 0.238376i \(0.0766151\pi\)
\(194\) −5.19216 −0.372775
\(195\) −6.83838 −0.489707
\(196\) 11.1394 0.795669
\(197\) −4.65075 −0.331352 −0.165676 0.986180i \(-0.552981\pi\)
−0.165676 + 0.986180i \(0.552981\pi\)
\(198\) −2.60887 −0.185404
\(199\) 4.56935 0.323913 0.161956 0.986798i \(-0.448220\pi\)
0.161956 + 0.986798i \(0.448220\pi\)
\(200\) −4.61002 −0.325977
\(201\) 9.93419 0.700704
\(202\) −0.768608 −0.0540790
\(203\) −5.97866 −0.419620
\(204\) −1.73984 −0.121813
\(205\) 7.31408 0.510837
\(206\) 8.55470 0.596034
\(207\) 2.39815 0.166683
\(208\) −10.6653 −0.739502
\(209\) 0.714255 0.0494060
\(210\) 0.633672 0.0437275
\(211\) −0.130965 −0.00901598 −0.00450799 0.999990i \(-0.501435\pi\)
−0.00450799 + 0.999990i \(0.501435\pi\)
\(212\) 15.3248 1.05251
\(213\) 9.38080 0.642762
\(214\) 4.77234 0.326230
\(215\) 16.3338 1.11396
\(216\) −1.90755 −0.129792
\(217\) 0.562019 0.0381523
\(218\) 0.610242 0.0413308
\(219\) −14.8634 −1.00438
\(220\) 14.3029 0.964299
\(221\) 4.25469 0.286201
\(222\) 0.575372 0.0386165
\(223\) 20.5196 1.37409 0.687045 0.726614i \(-0.258907\pi\)
0.687045 + 0.726614i \(0.258907\pi\)
\(224\) 3.93719 0.263065
\(225\) −2.41672 −0.161115
\(226\) 4.78029 0.317980
\(227\) 6.91983 0.459285 0.229643 0.973275i \(-0.426244\pi\)
0.229643 + 0.973275i \(0.426244\pi\)
\(228\) 0.242959 0.0160903
\(229\) 23.6514 1.56293 0.781463 0.623951i \(-0.214474\pi\)
0.781463 + 0.623951i \(0.214474\pi\)
\(230\) 1.96600 0.129634
\(231\) 3.95353 0.260123
\(232\) 14.7545 0.968679
\(233\) −2.04570 −0.134018 −0.0670092 0.997752i \(-0.521346\pi\)
−0.0670092 + 0.997752i \(0.521346\pi\)
\(234\) 2.17016 0.141868
\(235\) −9.32612 −0.608369
\(236\) −4.82207 −0.313890
\(237\) −1.00000 −0.0649570
\(238\) −0.394257 −0.0255559
\(239\) −6.32016 −0.408817 −0.204409 0.978886i \(-0.565527\pi\)
−0.204409 + 0.978886i \(0.565527\pi\)
\(240\) 4.02892 0.260066
\(241\) 10.5071 0.676820 0.338410 0.940999i \(-0.390111\pi\)
0.338410 + 0.940999i \(0.390111\pi\)
\(242\) −7.73318 −0.497108
\(243\) −1.00000 −0.0641500
\(244\) −11.8837 −0.760777
\(245\) 10.2905 0.657437
\(246\) −2.32112 −0.147989
\(247\) −0.594144 −0.0378045
\(248\) −1.38698 −0.0880734
\(249\) −0.155778 −0.00987205
\(250\) −6.08024 −0.384548
\(251\) 19.6393 1.23962 0.619810 0.784752i \(-0.287210\pi\)
0.619810 + 0.784752i \(0.287210\pi\)
\(252\) 1.34482 0.0847157
\(253\) 12.2661 0.771161
\(254\) 5.15767 0.323621
\(255\) −1.60726 −0.100650
\(256\) −0.993913 −0.0621195
\(257\) 29.8255 1.86047 0.930233 0.366970i \(-0.119605\pi\)
0.930233 + 0.366970i \(0.119605\pi\)
\(258\) −5.18352 −0.322712
\(259\) −0.871930 −0.0541791
\(260\) −11.8977 −0.737862
\(261\) 7.73479 0.478771
\(262\) −7.60544 −0.469866
\(263\) −10.2391 −0.631369 −0.315685 0.948864i \(-0.602234\pi\)
−0.315685 + 0.948864i \(0.602234\pi\)
\(264\) −9.75674 −0.600486
\(265\) 14.1570 0.869658
\(266\) 0.0550557 0.00337568
\(267\) −1.13427 −0.0694159
\(268\) 17.2839 1.05578
\(269\) −18.5321 −1.12992 −0.564961 0.825118i \(-0.691109\pi\)
−0.564961 + 0.825118i \(0.691109\pi\)
\(270\) −0.819801 −0.0498915
\(271\) −5.63643 −0.342388 −0.171194 0.985237i \(-0.554763\pi\)
−0.171194 + 0.985237i \(0.554763\pi\)
\(272\) −2.50671 −0.151991
\(273\) −3.28870 −0.199041
\(274\) −6.55398 −0.395940
\(275\) −12.3611 −0.745401
\(276\) 4.17238 0.251148
\(277\) −22.8345 −1.37199 −0.685996 0.727606i \(-0.740633\pi\)
−0.685996 + 0.727606i \(0.740633\pi\)
\(278\) 4.43429 0.265951
\(279\) −0.727102 −0.0435304
\(280\) 2.36983 0.141624
\(281\) −0.819303 −0.0488755 −0.0244378 0.999701i \(-0.507780\pi\)
−0.0244378 + 0.999701i \(0.507780\pi\)
\(282\) 2.95964 0.176244
\(283\) −5.08478 −0.302259 −0.151129 0.988514i \(-0.548291\pi\)
−0.151129 + 0.988514i \(0.548291\pi\)
\(284\) 16.3211 0.968477
\(285\) 0.224445 0.0132950
\(286\) 11.0999 0.656353
\(287\) 3.51747 0.207630
\(288\) −5.09367 −0.300148
\(289\) 1.00000 0.0588235
\(290\) 6.34099 0.372355
\(291\) −10.1795 −0.596731
\(292\) −25.8599 −1.51334
\(293\) −8.50443 −0.496834 −0.248417 0.968653i \(-0.579910\pi\)
−0.248417 + 0.968653i \(0.579910\pi\)
\(294\) −3.26569 −0.190459
\(295\) −4.45462 −0.259358
\(296\) 2.15180 0.125071
\(297\) −5.11481 −0.296791
\(298\) −1.52992 −0.0886262
\(299\) −10.2034 −0.590076
\(300\) −4.20470 −0.242759
\(301\) 7.85521 0.452767
\(302\) −8.61929 −0.495984
\(303\) −1.50689 −0.0865686
\(304\) 0.350048 0.0200766
\(305\) −10.9781 −0.628607
\(306\) 0.510062 0.0291583
\(307\) 28.5827 1.63130 0.815651 0.578545i \(-0.196379\pi\)
0.815651 + 0.578545i \(0.196379\pi\)
\(308\) 6.87850 0.391939
\(309\) 16.7719 0.954119
\(310\) −0.596079 −0.0338550
\(311\) 7.63659 0.433031 0.216516 0.976279i \(-0.430531\pi\)
0.216516 + 0.976279i \(0.430531\pi\)
\(312\) 8.11603 0.459480
\(313\) −10.8842 −0.615210 −0.307605 0.951514i \(-0.599527\pi\)
−0.307605 + 0.951514i \(0.599527\pi\)
\(314\) 2.38695 0.134703
\(315\) 1.24234 0.0699981
\(316\) −1.73984 −0.0978735
\(317\) 17.6907 0.993606 0.496803 0.867863i \(-0.334507\pi\)
0.496803 + 0.867863i \(0.334507\pi\)
\(318\) −4.49272 −0.251939
\(319\) 39.5619 2.21504
\(320\) 3.88204 0.217013
\(321\) 9.35639 0.522223
\(322\) 0.945485 0.0526898
\(323\) −0.139644 −0.00777003
\(324\) −1.73984 −0.0966576
\(325\) 10.2824 0.570365
\(326\) −8.64169 −0.478619
\(327\) 1.19641 0.0661614
\(328\) −8.68060 −0.479306
\(329\) −4.48510 −0.247271
\(330\) −4.19312 −0.230824
\(331\) 3.98286 0.218918 0.109459 0.993991i \(-0.465088\pi\)
0.109459 + 0.993991i \(0.465088\pi\)
\(332\) −0.271029 −0.0148746
\(333\) 1.12804 0.0618164
\(334\) −2.92575 −0.160090
\(335\) 15.9668 0.872360
\(336\) 1.93758 0.105704
\(337\) 3.26509 0.177861 0.0889305 0.996038i \(-0.471655\pi\)
0.0889305 + 0.996038i \(0.471655\pi\)
\(338\) −2.60253 −0.141559
\(339\) 9.37198 0.509016
\(340\) −2.79637 −0.151654
\(341\) −3.71898 −0.201394
\(342\) −0.0712273 −0.00385153
\(343\) 10.3596 0.559366
\(344\) −19.3855 −1.04520
\(345\) 3.85444 0.207516
\(346\) 5.46610 0.293859
\(347\) 14.7628 0.792507 0.396253 0.918141i \(-0.370310\pi\)
0.396253 + 0.918141i \(0.370310\pi\)
\(348\) 13.4573 0.721385
\(349\) 20.3942 1.09167 0.545837 0.837891i \(-0.316212\pi\)
0.545837 + 0.837891i \(0.316212\pi\)
\(350\) −0.952809 −0.0509298
\(351\) 4.25469 0.227099
\(352\) −26.0532 −1.38864
\(353\) −22.1391 −1.17834 −0.589172 0.808008i \(-0.700546\pi\)
−0.589172 + 0.808008i \(0.700546\pi\)
\(354\) 1.41367 0.0751357
\(355\) 15.0774 0.800223
\(356\) −1.97344 −0.104592
\(357\) −0.772958 −0.0409093
\(358\) −3.77908 −0.199731
\(359\) −3.75177 −0.198011 −0.0990054 0.995087i \(-0.531566\pi\)
−0.0990054 + 0.995087i \(0.531566\pi\)
\(360\) −3.06592 −0.161588
\(361\) −18.9805 −0.998974
\(362\) −10.0027 −0.525731
\(363\) −15.1613 −0.795760
\(364\) −5.72179 −0.299904
\(365\) −23.8893 −1.25042
\(366\) 3.48391 0.182107
\(367\) 7.71466 0.402702 0.201351 0.979519i \(-0.435467\pi\)
0.201351 + 0.979519i \(0.435467\pi\)
\(368\) 6.01145 0.313368
\(369\) −4.55066 −0.236898
\(370\) 0.924771 0.0480766
\(371\) 6.80835 0.353472
\(372\) −1.26504 −0.0655892
\(373\) −26.9773 −1.39683 −0.698417 0.715691i \(-0.746112\pi\)
−0.698417 + 0.715691i \(0.746112\pi\)
\(374\) 2.60887 0.134901
\(375\) −11.9206 −0.615576
\(376\) 11.0686 0.570818
\(377\) −32.9091 −1.69491
\(378\) −0.394257 −0.0202784
\(379\) 25.9799 1.33450 0.667249 0.744835i \(-0.267472\pi\)
0.667249 + 0.744835i \(0.267472\pi\)
\(380\) 0.390497 0.0200321
\(381\) 10.1118 0.518046
\(382\) 2.39357 0.122465
\(383\) −12.2388 −0.625374 −0.312687 0.949856i \(-0.601229\pi\)
−0.312687 + 0.949856i \(0.601229\pi\)
\(384\) −11.4193 −0.582739
\(385\) 6.35434 0.323847
\(386\) −13.7635 −0.700543
\(387\) −10.1625 −0.516591
\(388\) −17.7106 −0.899120
\(389\) 9.76147 0.494926 0.247463 0.968897i \(-0.420403\pi\)
0.247463 + 0.968897i \(0.420403\pi\)
\(390\) 3.48800 0.176622
\(391\) −2.39815 −0.121280
\(392\) −12.2131 −0.616857
\(393\) −14.9108 −0.752151
\(394\) 2.37217 0.119508
\(395\) −1.60726 −0.0808699
\(396\) −8.89893 −0.447188
\(397\) −17.6259 −0.884617 −0.442309 0.896863i \(-0.645840\pi\)
−0.442309 + 0.896863i \(0.645840\pi\)
\(398\) −2.33065 −0.116825
\(399\) 0.107939 0.00540372
\(400\) −6.05801 −0.302901
\(401\) −0.0129089 −0.000644641 0 −0.000322321 1.00000i \(-0.500103\pi\)
−0.000322321 1.00000i \(0.500103\pi\)
\(402\) −5.06705 −0.252722
\(403\) 3.09359 0.154103
\(404\) −2.62174 −0.130437
\(405\) −1.60726 −0.0798653
\(406\) 3.04949 0.151344
\(407\) 5.76973 0.285995
\(408\) 1.90755 0.0944377
\(409\) 6.07683 0.300480 0.150240 0.988650i \(-0.451995\pi\)
0.150240 + 0.988650i \(0.451995\pi\)
\(410\) −3.73063 −0.184243
\(411\) −12.8494 −0.633813
\(412\) 29.1803 1.43761
\(413\) −2.14230 −0.105416
\(414\) −1.22320 −0.0601172
\(415\) −0.250376 −0.0122905
\(416\) 21.6720 1.06256
\(417\) 8.69363 0.425729
\(418\) −0.364314 −0.0178192
\(419\) 6.81338 0.332856 0.166428 0.986054i \(-0.446777\pi\)
0.166428 + 0.986054i \(0.446777\pi\)
\(420\) 2.16147 0.105469
\(421\) 11.4340 0.557257 0.278628 0.960399i \(-0.410120\pi\)
0.278628 + 0.960399i \(0.410120\pi\)
\(422\) 0.0668001 0.00325178
\(423\) 5.80251 0.282128
\(424\) −16.8020 −0.815979
\(425\) 2.41672 0.117228
\(426\) −4.78479 −0.231824
\(427\) −5.27958 −0.255497
\(428\) 16.2786 0.786856
\(429\) 21.7619 1.05068
\(430\) −8.33126 −0.401769
\(431\) 24.9948 1.20396 0.601980 0.798511i \(-0.294379\pi\)
0.601980 + 0.798511i \(0.294379\pi\)
\(432\) −2.50671 −0.120604
\(433\) 9.79759 0.470842 0.235421 0.971893i \(-0.424353\pi\)
0.235421 + 0.971893i \(0.424353\pi\)
\(434\) −0.286665 −0.0137603
\(435\) 12.4318 0.596059
\(436\) 2.08155 0.0996883
\(437\) 0.334888 0.0160199
\(438\) 7.58126 0.362246
\(439\) 17.0727 0.814837 0.407418 0.913242i \(-0.366429\pi\)
0.407418 + 0.913242i \(0.366429\pi\)
\(440\) −15.6816 −0.747591
\(441\) −6.40254 −0.304883
\(442\) −2.17016 −0.103224
\(443\) −32.3480 −1.53690 −0.768449 0.639911i \(-0.778971\pi\)
−0.768449 + 0.639911i \(0.778971\pi\)
\(444\) 1.96261 0.0931414
\(445\) −1.82306 −0.0864212
\(446\) −10.4662 −0.495591
\(447\) −2.99949 −0.141871
\(448\) 1.86694 0.0882047
\(449\) −17.3359 −0.818134 −0.409067 0.912504i \(-0.634146\pi\)
−0.409067 + 0.912504i \(0.634146\pi\)
\(450\) 1.23268 0.0581090
\(451\) −23.2757 −1.09601
\(452\) 16.3057 0.766957
\(453\) −16.8985 −0.793961
\(454\) −3.52954 −0.165650
\(455\) −5.28578 −0.247801
\(456\) −0.266379 −0.0124743
\(457\) 3.37493 0.157873 0.0789363 0.996880i \(-0.474848\pi\)
0.0789363 + 0.996880i \(0.474848\pi\)
\(458\) −12.0637 −0.563698
\(459\) 1.00000 0.0466760
\(460\) 6.70610 0.312673
\(461\) −2.57908 −0.120120 −0.0600599 0.998195i \(-0.519129\pi\)
−0.0600599 + 0.998195i \(0.519129\pi\)
\(462\) −2.01655 −0.0938182
\(463\) 2.05356 0.0954372 0.0477186 0.998861i \(-0.484805\pi\)
0.0477186 + 0.998861i \(0.484805\pi\)
\(464\) 19.3888 0.900104
\(465\) −1.16864 −0.0541944
\(466\) 1.04344 0.0483362
\(467\) −4.60299 −0.213001 −0.106500 0.994313i \(-0.533965\pi\)
−0.106500 + 0.994313i \(0.533965\pi\)
\(468\) 7.40247 0.342179
\(469\) 7.67871 0.354570
\(470\) 4.75690 0.219420
\(471\) 4.67973 0.215630
\(472\) 5.28689 0.243349
\(473\) −51.9794 −2.39002
\(474\) 0.510062 0.0234279
\(475\) −0.337482 −0.0154847
\(476\) −1.34482 −0.0616398
\(477\) −8.80818 −0.403299
\(478\) 3.22367 0.147447
\(479\) −5.94766 −0.271755 −0.135878 0.990726i \(-0.543385\pi\)
−0.135878 + 0.990726i \(0.543385\pi\)
\(480\) −8.18684 −0.373677
\(481\) −4.79948 −0.218837
\(482\) −5.35926 −0.244108
\(483\) 1.85367 0.0843448
\(484\) −26.3781 −1.19901
\(485\) −16.3610 −0.742916
\(486\) 0.510062 0.0231369
\(487\) 20.3347 0.921454 0.460727 0.887542i \(-0.347589\pi\)
0.460727 + 0.887542i \(0.347589\pi\)
\(488\) 13.0292 0.589806
\(489\) −16.9424 −0.766163
\(490\) −5.24881 −0.237117
\(491\) 20.9077 0.943550 0.471775 0.881719i \(-0.343614\pi\)
0.471775 + 0.881719i \(0.343614\pi\)
\(492\) −7.91740 −0.356944
\(493\) −7.73479 −0.348357
\(494\) 0.303050 0.0136349
\(495\) −8.22081 −0.369498
\(496\) −1.82263 −0.0818385
\(497\) 7.25097 0.325250
\(498\) 0.0794566 0.00356054
\(499\) −17.1176 −0.766289 −0.383145 0.923688i \(-0.625159\pi\)
−0.383145 + 0.923688i \(0.625159\pi\)
\(500\) −20.7399 −0.927515
\(501\) −5.73607 −0.256269
\(502\) −10.0172 −0.447092
\(503\) −14.9037 −0.664523 −0.332261 0.943187i \(-0.607812\pi\)
−0.332261 + 0.943187i \(0.607812\pi\)
\(504\) −1.47445 −0.0656774
\(505\) −2.42196 −0.107776
\(506\) −6.25645 −0.278133
\(507\) −5.10239 −0.226605
\(508\) 17.5930 0.780561
\(509\) 19.4362 0.861493 0.430747 0.902473i \(-0.358250\pi\)
0.430747 + 0.902473i \(0.358250\pi\)
\(510\) 0.819801 0.0363014
\(511\) −11.4888 −0.508234
\(512\) −22.3317 −0.986929
\(513\) −0.139644 −0.00616545
\(514\) −15.2129 −0.671011
\(515\) 26.9567 1.18786
\(516\) −17.6812 −0.778369
\(517\) 29.6787 1.30527
\(518\) 0.444739 0.0195407
\(519\) 10.7165 0.470404
\(520\) 13.0445 0.572041
\(521\) 33.2196 1.45538 0.727688 0.685908i \(-0.240595\pi\)
0.727688 + 0.685908i \(0.240595\pi\)
\(522\) −3.94522 −0.172678
\(523\) 8.57448 0.374936 0.187468 0.982271i \(-0.439972\pi\)
0.187468 + 0.982271i \(0.439972\pi\)
\(524\) −25.9424 −1.13330
\(525\) −1.86803 −0.0815273
\(526\) 5.22257 0.227715
\(527\) 0.727102 0.0316730
\(528\) −12.8213 −0.557976
\(529\) −17.2489 −0.749952
\(530\) −7.22095 −0.313658
\(531\) 2.77156 0.120276
\(532\) 0.187797 0.00814202
\(533\) 19.3616 0.838646
\(534\) 0.578546 0.0250361
\(535\) 15.0381 0.650155
\(536\) −18.9500 −0.818513
\(537\) −7.40907 −0.319725
\(538\) 9.45252 0.407527
\(539\) −32.7477 −1.41055
\(540\) −2.79637 −0.120336
\(541\) −24.7280 −1.06314 −0.531570 0.847014i \(-0.678398\pi\)
−0.531570 + 0.847014i \(0.678398\pi\)
\(542\) 2.87493 0.123489
\(543\) −19.6108 −0.841579
\(544\) 5.09367 0.218389
\(545\) 1.92293 0.0823694
\(546\) 1.67744 0.0717878
\(547\) 16.7662 0.716872 0.358436 0.933554i \(-0.383310\pi\)
0.358436 + 0.933554i \(0.383310\pi\)
\(548\) −22.3558 −0.954993
\(549\) 6.83036 0.291513
\(550\) 6.30492 0.268842
\(551\) 1.08012 0.0460147
\(552\) −4.57458 −0.194707
\(553\) −0.772958 −0.0328695
\(554\) 11.6470 0.494834
\(555\) 1.81306 0.0769600
\(556\) 15.1255 0.641464
\(557\) 15.3333 0.649691 0.324845 0.945767i \(-0.394688\pi\)
0.324845 + 0.945767i \(0.394688\pi\)
\(558\) 0.370867 0.0157000
\(559\) 43.2384 1.82879
\(560\) 3.11419 0.131598
\(561\) 5.11481 0.215947
\(562\) 0.417896 0.0176279
\(563\) −20.4118 −0.860254 −0.430127 0.902768i \(-0.641531\pi\)
−0.430127 + 0.902768i \(0.641531\pi\)
\(564\) 10.0954 0.425094
\(565\) 15.0632 0.633713
\(566\) 2.59355 0.109015
\(567\) −0.772958 −0.0324612
\(568\) −17.8943 −0.750830
\(569\) −0.929251 −0.0389562 −0.0194781 0.999810i \(-0.506200\pi\)
−0.0194781 + 0.999810i \(0.506200\pi\)
\(570\) −0.114481 −0.00479507
\(571\) −31.4706 −1.31700 −0.658502 0.752579i \(-0.728810\pi\)
−0.658502 + 0.752579i \(0.728810\pi\)
\(572\) 37.8622 1.58310
\(573\) 4.69270 0.196040
\(574\) −1.79413 −0.0748854
\(575\) −5.79566 −0.241696
\(576\) −2.41532 −0.100638
\(577\) 13.3141 0.554275 0.277137 0.960830i \(-0.410614\pi\)
0.277137 + 0.960830i \(0.410614\pi\)
\(578\) −0.510062 −0.0212158
\(579\) −26.9839 −1.12141
\(580\) 21.6293 0.898107
\(581\) −0.120410 −0.00499545
\(582\) 5.19216 0.215222
\(583\) −45.0521 −1.86587
\(584\) 28.3527 1.17324
\(585\) 6.83838 0.282732
\(586\) 4.33779 0.179192
\(587\) 40.0412 1.65268 0.826339 0.563173i \(-0.190420\pi\)
0.826339 + 0.563173i \(0.190420\pi\)
\(588\) −11.1394 −0.459380
\(589\) −0.101536 −0.00418371
\(590\) 2.27213 0.0935422
\(591\) 4.65075 0.191306
\(592\) 2.82767 0.116217
\(593\) 30.6403 1.25825 0.629123 0.777306i \(-0.283414\pi\)
0.629123 + 0.777306i \(0.283414\pi\)
\(594\) 2.60887 0.107043
\(595\) −1.24234 −0.0509311
\(596\) −5.21862 −0.213763
\(597\) −4.56935 −0.187011
\(598\) 5.20435 0.212822
\(599\) −0.634987 −0.0259449 −0.0129724 0.999916i \(-0.504129\pi\)
−0.0129724 + 0.999916i \(0.504129\pi\)
\(600\) 4.61002 0.188203
\(601\) −8.64444 −0.352614 −0.176307 0.984335i \(-0.556415\pi\)
−0.176307 + 0.984335i \(0.556415\pi\)
\(602\) −4.00665 −0.163299
\(603\) −9.93419 −0.404552
\(604\) −29.4006 −1.19630
\(605\) −24.3680 −0.990702
\(606\) 0.768608 0.0312226
\(607\) 17.2389 0.699704 0.349852 0.936805i \(-0.386232\pi\)
0.349852 + 0.936805i \(0.386232\pi\)
\(608\) −0.711303 −0.0288472
\(609\) 5.97866 0.242268
\(610\) 5.59953 0.226719
\(611\) −24.6879 −0.998764
\(612\) 1.73984 0.0703287
\(613\) −20.7633 −0.838624 −0.419312 0.907842i \(-0.637729\pi\)
−0.419312 + 0.907842i \(0.637729\pi\)
\(614\) −14.5790 −0.588359
\(615\) −7.31408 −0.294932
\(616\) −7.54155 −0.303858
\(617\) −12.7284 −0.512426 −0.256213 0.966620i \(-0.582475\pi\)
−0.256213 + 0.966620i \(0.582475\pi\)
\(618\) −8.55470 −0.344120
\(619\) 25.1062 1.00910 0.504552 0.863381i \(-0.331658\pi\)
0.504552 + 0.863381i \(0.331658\pi\)
\(620\) −2.03324 −0.0816570
\(621\) −2.39815 −0.0962343
\(622\) −3.89513 −0.156181
\(623\) −0.876740 −0.0351258
\(624\) 10.6653 0.426952
\(625\) −7.07583 −0.283033
\(626\) 5.55160 0.221887
\(627\) −0.714255 −0.0285246
\(628\) 8.14196 0.324900
\(629\) −1.12804 −0.0449781
\(630\) −0.633672 −0.0252461
\(631\) −19.8552 −0.790422 −0.395211 0.918590i \(-0.629328\pi\)
−0.395211 + 0.918590i \(0.629328\pi\)
\(632\) 1.90755 0.0758782
\(633\) 0.130965 0.00520538
\(634\) −9.02333 −0.358362
\(635\) 16.2523 0.644954
\(636\) −15.3248 −0.607667
\(637\) 27.2408 1.07932
\(638\) −20.1790 −0.798896
\(639\) −9.38080 −0.371099
\(640\) −18.3538 −0.725496
\(641\) 0.862217 0.0340555 0.0170278 0.999855i \(-0.494580\pi\)
0.0170278 + 0.999855i \(0.494580\pi\)
\(642\) −4.77234 −0.188349
\(643\) 9.91531 0.391022 0.195511 0.980702i \(-0.437364\pi\)
0.195511 + 0.980702i \(0.437364\pi\)
\(644\) 3.22508 0.127086
\(645\) −16.3338 −0.643143
\(646\) 0.0712273 0.00280240
\(647\) 29.4141 1.15639 0.578193 0.815900i \(-0.303758\pi\)
0.578193 + 0.815900i \(0.303758\pi\)
\(648\) 1.90755 0.0749356
\(649\) 14.1760 0.556457
\(650\) −5.24467 −0.205713
\(651\) −0.562019 −0.0220273
\(652\) −29.4771 −1.15441
\(653\) −9.23466 −0.361380 −0.180690 0.983540i \(-0.557833\pi\)
−0.180690 + 0.983540i \(0.557833\pi\)
\(654\) −0.610242 −0.0238623
\(655\) −23.9655 −0.936410
\(656\) −11.4072 −0.445375
\(657\) 14.8634 0.579876
\(658\) 2.28768 0.0891829
\(659\) 9.05610 0.352775 0.176388 0.984321i \(-0.443559\pi\)
0.176388 + 0.984321i \(0.443559\pi\)
\(660\) −14.3029 −0.556739
\(661\) 38.1014 1.48197 0.740985 0.671521i \(-0.234359\pi\)
0.740985 + 0.671521i \(0.234359\pi\)
\(662\) −2.03150 −0.0789567
\(663\) −4.25469 −0.165238
\(664\) 0.297155 0.0115318
\(665\) 0.173486 0.00672751
\(666\) −0.575372 −0.0222952
\(667\) 18.5492 0.718226
\(668\) −9.97983 −0.386131
\(669\) −20.5196 −0.793332
\(670\) −8.14406 −0.314632
\(671\) 34.9360 1.34869
\(672\) −3.93719 −0.151881
\(673\) −19.4204 −0.748601 −0.374300 0.927308i \(-0.622117\pi\)
−0.374300 + 0.927308i \(0.622117\pi\)
\(674\) −1.66540 −0.0641488
\(675\) 2.41672 0.0930197
\(676\) −8.87732 −0.341435
\(677\) 42.4802 1.63265 0.816323 0.577596i \(-0.196009\pi\)
0.816323 + 0.577596i \(0.196009\pi\)
\(678\) −4.78029 −0.183586
\(679\) −7.86830 −0.301958
\(680\) 3.06592 0.117573
\(681\) −6.91983 −0.265168
\(682\) 1.89691 0.0726366
\(683\) 4.77934 0.182876 0.0914382 0.995811i \(-0.470854\pi\)
0.0914382 + 0.995811i \(0.470854\pi\)
\(684\) −0.242959 −0.00928975
\(685\) −20.6523 −0.789082
\(686\) −5.28404 −0.201745
\(687\) −23.6514 −0.902356
\(688\) −25.4745 −0.971206
\(689\) 37.4761 1.42772
\(690\) −1.96600 −0.0748445
\(691\) 19.9362 0.758408 0.379204 0.925313i \(-0.376198\pi\)
0.379204 + 0.925313i \(0.376198\pi\)
\(692\) 18.6450 0.708777
\(693\) −3.95353 −0.150182
\(694\) −7.52993 −0.285832
\(695\) 13.9729 0.530022
\(696\) −14.7545 −0.559267
\(697\) 4.55066 0.172368
\(698\) −10.4023 −0.393733
\(699\) 2.04570 0.0773756
\(700\) −3.25006 −0.122841
\(701\) 17.0991 0.645823 0.322912 0.946429i \(-0.395338\pi\)
0.322912 + 0.946429i \(0.395338\pi\)
\(702\) −2.17016 −0.0819072
\(703\) 0.157525 0.00594117
\(704\) −12.3539 −0.465605
\(705\) 9.32612 0.351242
\(706\) 11.2923 0.424991
\(707\) −1.16476 −0.0438054
\(708\) 4.82207 0.181224
\(709\) −1.41763 −0.0532403 −0.0266201 0.999646i \(-0.508474\pi\)
−0.0266201 + 0.999646i \(0.508474\pi\)
\(710\) −7.69039 −0.288615
\(711\) 1.00000 0.0375029
\(712\) 2.16367 0.0810868
\(713\) −1.74370 −0.0653020
\(714\) 0.394257 0.0147547
\(715\) 34.9770 1.30807
\(716\) −12.8906 −0.481743
\(717\) 6.32016 0.236031
\(718\) 1.91364 0.0714162
\(719\) −34.4537 −1.28491 −0.642453 0.766325i \(-0.722083\pi\)
−0.642453 + 0.766325i \(0.722083\pi\)
\(720\) −4.02892 −0.150149
\(721\) 12.9640 0.482803
\(722\) 9.68123 0.360298
\(723\) −10.5071 −0.390762
\(724\) −34.1195 −1.26804
\(725\) −18.6928 −0.694235
\(726\) 7.73318 0.287005
\(727\) 31.6046 1.17215 0.586076 0.810256i \(-0.300672\pi\)
0.586076 + 0.810256i \(0.300672\pi\)
\(728\) 6.27335 0.232506
\(729\) 1.00000 0.0370370
\(730\) 12.1850 0.450988
\(731\) 10.1625 0.375875
\(732\) 11.8837 0.439235
\(733\) 18.3870 0.679138 0.339569 0.940581i \(-0.389719\pi\)
0.339569 + 0.940581i \(0.389719\pi\)
\(734\) −3.93495 −0.145242
\(735\) −10.2905 −0.379572
\(736\) −12.2154 −0.450265
\(737\) −50.8115 −1.87166
\(738\) 2.32112 0.0854415
\(739\) 7.42605 0.273172 0.136586 0.990628i \(-0.456387\pi\)
0.136586 + 0.990628i \(0.456387\pi\)
\(740\) 3.15442 0.115959
\(741\) 0.594144 0.0218264
\(742\) −3.47268 −0.127486
\(743\) 10.9476 0.401628 0.200814 0.979629i \(-0.435641\pi\)
0.200814 + 0.979629i \(0.435641\pi\)
\(744\) 1.38698 0.0508492
\(745\) −4.82095 −0.176626
\(746\) 13.7601 0.503794
\(747\) 0.155778 0.00569963
\(748\) 8.89893 0.325377
\(749\) 7.23210 0.264255
\(750\) 6.08024 0.222019
\(751\) 26.8378 0.979324 0.489662 0.871912i \(-0.337120\pi\)
0.489662 + 0.871912i \(0.337120\pi\)
\(752\) 14.5452 0.530408
\(753\) −19.6393 −0.715695
\(754\) 16.7857 0.611299
\(755\) −27.1603 −0.988463
\(756\) −1.34482 −0.0489107
\(757\) 8.31975 0.302386 0.151193 0.988504i \(-0.451688\pi\)
0.151193 + 0.988504i \(0.451688\pi\)
\(758\) −13.2514 −0.481311
\(759\) −12.2661 −0.445230
\(760\) −0.428139 −0.0155302
\(761\) −51.2196 −1.85671 −0.928355 0.371695i \(-0.878777\pi\)
−0.928355 + 0.371695i \(0.878777\pi\)
\(762\) −5.15767 −0.186843
\(763\) 0.924772 0.0334790
\(764\) 8.16452 0.295382
\(765\) 1.60726 0.0581105
\(766\) 6.24256 0.225553
\(767\) −11.7921 −0.425790
\(768\) 0.993913 0.0358647
\(769\) −25.2340 −0.909961 −0.454981 0.890501i \(-0.650354\pi\)
−0.454981 + 0.890501i \(0.650354\pi\)
\(770\) −3.24111 −0.116801
\(771\) −29.8255 −1.07414
\(772\) −46.9476 −1.68968
\(773\) −9.41633 −0.338682 −0.169341 0.985558i \(-0.554164\pi\)
−0.169341 + 0.985558i \(0.554164\pi\)
\(774\) 5.18352 0.186318
\(775\) 1.75720 0.0631206
\(776\) 19.4178 0.697060
\(777\) 0.871930 0.0312803
\(778\) −4.97895 −0.178504
\(779\) −0.635474 −0.0227682
\(780\) 11.8977 0.426005
\(781\) −47.9810 −1.71690
\(782\) 1.22320 0.0437417
\(783\) −7.73479 −0.276419
\(784\) −16.0493 −0.573188
\(785\) 7.52153 0.268455
\(786\) 7.60544 0.271277
\(787\) 5.75429 0.205118 0.102559 0.994727i \(-0.467297\pi\)
0.102559 + 0.994727i \(0.467297\pi\)
\(788\) 8.09154 0.288249
\(789\) 10.2391 0.364521
\(790\) 0.819801 0.0291672
\(791\) 7.24415 0.257572
\(792\) 9.75674 0.346691
\(793\) −29.0611 −1.03199
\(794\) 8.99029 0.319053
\(795\) −14.1570 −0.502097
\(796\) −7.94993 −0.281778
\(797\) −14.0063 −0.496127 −0.248064 0.968744i \(-0.579794\pi\)
−0.248064 + 0.968744i \(0.579794\pi\)
\(798\) −0.0550557 −0.00194895
\(799\) −5.80251 −0.205278
\(800\) 12.3100 0.435224
\(801\) 1.13427 0.0400773
\(802\) 0.00658435 0.000232502 0
\(803\) 76.0234 2.68281
\(804\) −17.2839 −0.609555
\(805\) 2.97932 0.105007
\(806\) −1.57792 −0.0555800
\(807\) 18.5321 0.652361
\(808\) 2.87447 0.101123
\(809\) −7.04469 −0.247678 −0.123839 0.992302i \(-0.539521\pi\)
−0.123839 + 0.992302i \(0.539521\pi\)
\(810\) 0.819801 0.0288049
\(811\) 33.5005 1.17636 0.588181 0.808730i \(-0.299844\pi\)
0.588181 + 0.808730i \(0.299844\pi\)
\(812\) 10.4019 0.365035
\(813\) 5.63643 0.197678
\(814\) −2.94292 −0.103149
\(815\) −27.2309 −0.953855
\(816\) 2.50671 0.0877522
\(817\) −1.41914 −0.0496495
\(818\) −3.09956 −0.108374
\(819\) 3.28870 0.114916
\(820\) −12.7253 −0.444387
\(821\) −18.0776 −0.630914 −0.315457 0.948940i \(-0.602158\pi\)
−0.315457 + 0.948940i \(0.602158\pi\)
\(822\) 6.55398 0.228596
\(823\) 35.3510 1.23226 0.616129 0.787645i \(-0.288700\pi\)
0.616129 + 0.787645i \(0.288700\pi\)
\(824\) −31.9932 −1.11453
\(825\) 12.3611 0.430357
\(826\) 1.09271 0.0380202
\(827\) −50.3601 −1.75119 −0.875597 0.483043i \(-0.839532\pi\)
−0.875597 + 0.483043i \(0.839532\pi\)
\(828\) −4.17238 −0.145000
\(829\) 22.8922 0.795080 0.397540 0.917585i \(-0.369864\pi\)
0.397540 + 0.917585i \(0.369864\pi\)
\(830\) 0.127707 0.00443278
\(831\) 22.8345 0.792120
\(832\) 10.2764 0.356272
\(833\) 6.40254 0.221835
\(834\) −4.43429 −0.153547
\(835\) −9.21934 −0.319048
\(836\) −1.24269 −0.0429792
\(837\) 0.727102 0.0251323
\(838\) −3.47525 −0.120050
\(839\) −30.6388 −1.05777 −0.528885 0.848694i \(-0.677390\pi\)
−0.528885 + 0.848694i \(0.677390\pi\)
\(840\) −2.36983 −0.0817669
\(841\) 30.8269 1.06300
\(842\) −5.83203 −0.200985
\(843\) 0.819303 0.0282183
\(844\) 0.227857 0.00784317
\(845\) −8.20085 −0.282118
\(846\) −2.95964 −0.101754
\(847\) −11.7190 −0.402670
\(848\) −22.0795 −0.758213
\(849\) 5.08478 0.174509
\(850\) −1.23268 −0.0422805
\(851\) 2.70522 0.0927336
\(852\) −16.3211 −0.559150
\(853\) −28.1815 −0.964917 −0.482459 0.875919i \(-0.660256\pi\)
−0.482459 + 0.875919i \(0.660256\pi\)
\(854\) 2.69291 0.0921496
\(855\) −0.224445 −0.00767584
\(856\) −17.8478 −0.610024
\(857\) −6.97770 −0.238354 −0.119177 0.992873i \(-0.538026\pi\)
−0.119177 + 0.992873i \(0.538026\pi\)
\(858\) −11.0999 −0.378945
\(859\) 24.4451 0.834055 0.417027 0.908894i \(-0.363072\pi\)
0.417027 + 0.908894i \(0.363072\pi\)
\(860\) −28.4182 −0.969051
\(861\) −3.51747 −0.119875
\(862\) −12.7489 −0.434230
\(863\) 11.4944 0.391275 0.195637 0.980676i \(-0.437322\pi\)
0.195637 + 0.980676i \(0.437322\pi\)
\(864\) 5.09367 0.173290
\(865\) 17.2242 0.585642
\(866\) −4.99738 −0.169818
\(867\) −1.00000 −0.0339618
\(868\) −0.977821 −0.0331894
\(869\) 5.11481 0.173508
\(870\) −6.34099 −0.214980
\(871\) 42.2669 1.43216
\(872\) −2.28220 −0.0772852
\(873\) 10.1795 0.344523
\(874\) −0.170814 −0.00577786
\(875\) −9.21411 −0.311494
\(876\) 25.8599 0.873725
\(877\) −9.31690 −0.314609 −0.157305 0.987550i \(-0.550280\pi\)
−0.157305 + 0.987550i \(0.550280\pi\)
\(878\) −8.70815 −0.293886
\(879\) 8.50443 0.286847
\(880\) −20.6072 −0.694667
\(881\) −3.16807 −0.106735 −0.0533674 0.998575i \(-0.516995\pi\)
−0.0533674 + 0.998575i \(0.516995\pi\)
\(882\) 3.26569 0.109962
\(883\) −17.8681 −0.601308 −0.300654 0.953733i \(-0.597205\pi\)
−0.300654 + 0.953733i \(0.597205\pi\)
\(884\) −7.40247 −0.248972
\(885\) 4.45462 0.149740
\(886\) 16.4995 0.554311
\(887\) −6.52473 −0.219079 −0.109540 0.993982i \(-0.534938\pi\)
−0.109540 + 0.993982i \(0.534938\pi\)
\(888\) −2.15180 −0.0722096
\(889\) 7.81603 0.262141
\(890\) 0.929872 0.0311694
\(891\) 5.11481 0.171353
\(892\) −35.7007 −1.19535
\(893\) 0.810288 0.0271153
\(894\) 1.52992 0.0511683
\(895\) −11.9083 −0.398050
\(896\) −8.82665 −0.294878
\(897\) 10.2034 0.340681
\(898\) 8.84241 0.295075
\(899\) −5.62398 −0.187570
\(900\) 4.20470 0.140157
\(901\) 8.80818 0.293443
\(902\) 11.8721 0.395297
\(903\) −7.85521 −0.261405
\(904\) −17.8775 −0.594597
\(905\) −31.5196 −1.04775
\(906\) 8.61929 0.286357
\(907\) 5.15987 0.171331 0.0856653 0.996324i \(-0.472698\pi\)
0.0856653 + 0.996324i \(0.472698\pi\)
\(908\) −12.0394 −0.399540
\(909\) 1.50689 0.0499804
\(910\) 2.69608 0.0893741
\(911\) 4.85421 0.160827 0.0804136 0.996762i \(-0.474376\pi\)
0.0804136 + 0.996762i \(0.474376\pi\)
\(912\) −0.350048 −0.0115912
\(913\) 0.796776 0.0263694
\(914\) −1.72142 −0.0569396
\(915\) 10.9781 0.362926
\(916\) −41.1495 −1.35962
\(917\) −11.5254 −0.380603
\(918\) −0.510062 −0.0168346
\(919\) −12.5063 −0.412545 −0.206273 0.978495i \(-0.566133\pi\)
−0.206273 + 0.978495i \(0.566133\pi\)
\(920\) −7.35253 −0.242406
\(921\) −28.5827 −0.941832
\(922\) 1.31549 0.0433234
\(923\) 39.9124 1.31373
\(924\) −6.87850 −0.226286
\(925\) −2.72617 −0.0896359
\(926\) −1.04745 −0.0344212
\(927\) −16.7719 −0.550861
\(928\) −39.3985 −1.29332
\(929\) −27.2787 −0.894987 −0.447493 0.894287i \(-0.647683\pi\)
−0.447493 + 0.894287i \(0.647683\pi\)
\(930\) 0.596079 0.0195462
\(931\) −0.894079 −0.0293022
\(932\) 3.55919 0.116585
\(933\) −7.63659 −0.250011
\(934\) 2.34781 0.0768226
\(935\) 8.22081 0.268849
\(936\) −8.11603 −0.265281
\(937\) 11.8756 0.387958 0.193979 0.981006i \(-0.437861\pi\)
0.193979 + 0.981006i \(0.437861\pi\)
\(938\) −3.91662 −0.127882
\(939\) 10.8842 0.355191
\(940\) 16.2259 0.529232
\(941\) 48.3497 1.57615 0.788077 0.615576i \(-0.211077\pi\)
0.788077 + 0.615576i \(0.211077\pi\)
\(942\) −2.38695 −0.0777711
\(943\) −10.9131 −0.355381
\(944\) 6.94750 0.226122
\(945\) −1.24234 −0.0404134
\(946\) 26.5127 0.862003
\(947\) 17.4820 0.568090 0.284045 0.958811i \(-0.408324\pi\)
0.284045 + 0.958811i \(0.408324\pi\)
\(948\) 1.73984 0.0565073
\(949\) −63.2391 −2.05283
\(950\) 0.172137 0.00558485
\(951\) −17.6907 −0.573659
\(952\) 1.47445 0.0477874
\(953\) −13.9910 −0.453213 −0.226606 0.973986i \(-0.572763\pi\)
−0.226606 + 0.973986i \(0.572763\pi\)
\(954\) 4.49272 0.145457
\(955\) 7.54237 0.244065
\(956\) 10.9960 0.355637
\(957\) −39.5619 −1.27886
\(958\) 3.03368 0.0980136
\(959\) −9.93203 −0.320722
\(960\) −3.88204 −0.125292
\(961\) −30.4713 −0.982946
\(962\) 2.44803 0.0789277
\(963\) −9.35639 −0.301506
\(964\) −18.2806 −0.588778
\(965\) −43.3701 −1.39613
\(966\) −0.945485 −0.0304205
\(967\) 20.8099 0.669202 0.334601 0.942360i \(-0.391398\pi\)
0.334601 + 0.942360i \(0.391398\pi\)
\(968\) 28.9208 0.929551
\(969\) 0.139644 0.00448603
\(970\) 8.34514 0.267946
\(971\) −49.2271 −1.57977 −0.789886 0.613254i \(-0.789860\pi\)
−0.789886 + 0.613254i \(0.789860\pi\)
\(972\) 1.73984 0.0558053
\(973\) 6.71981 0.215427
\(974\) −10.3720 −0.332339
\(975\) −10.2824 −0.329301
\(976\) 17.1217 0.548052
\(977\) 50.1669 1.60498 0.802490 0.596665i \(-0.203508\pi\)
0.802490 + 0.596665i \(0.203508\pi\)
\(978\) 8.64169 0.276331
\(979\) 5.80155 0.185418
\(980\) −17.9038 −0.571917
\(981\) −1.19641 −0.0381983
\(982\) −10.6642 −0.340308
\(983\) 42.1134 1.34321 0.671605 0.740909i \(-0.265605\pi\)
0.671605 + 0.740909i \(0.265605\pi\)
\(984\) 8.68060 0.276727
\(985\) 7.47495 0.238172
\(986\) 3.94522 0.125641
\(987\) 4.48510 0.142762
\(988\) 1.03371 0.0328868
\(989\) −24.3713 −0.774961
\(990\) 4.19312 0.133266
\(991\) 1.69004 0.0536860 0.0268430 0.999640i \(-0.491455\pi\)
0.0268430 + 0.999640i \(0.491455\pi\)
\(992\) 3.70362 0.117590
\(993\) −3.98286 −0.126392
\(994\) −3.69844 −0.117307
\(995\) −7.34413 −0.232824
\(996\) 0.271029 0.00858788
\(997\) 11.6609 0.369305 0.184653 0.982804i \(-0.440884\pi\)
0.184653 + 0.982804i \(0.440884\pi\)
\(998\) 8.73104 0.276376
\(999\) −1.12804 −0.0356897
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 4029.2.a.l.1.14 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.14 32 1.1 even 1 trivial