Properties

Label 4029.2.a.l.1.6
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 1.6
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.16757 q^{2} -1.00000 q^{3} +2.69838 q^{4} +2.47527 q^{5} +2.16757 q^{6} +5.12027 q^{7} -1.51379 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.16757 q^{2} -1.00000 q^{3} +2.69838 q^{4} +2.47527 q^{5} +2.16757 q^{6} +5.12027 q^{7} -1.51379 q^{8} +1.00000 q^{9} -5.36532 q^{10} +2.42824 q^{11} -2.69838 q^{12} +7.04772 q^{13} -11.0986 q^{14} -2.47527 q^{15} -2.11551 q^{16} -1.00000 q^{17} -2.16757 q^{18} +2.52534 q^{19} +6.67921 q^{20} -5.12027 q^{21} -5.26339 q^{22} -3.87880 q^{23} +1.51379 q^{24} +1.12694 q^{25} -15.2765 q^{26} -1.00000 q^{27} +13.8164 q^{28} -0.167280 q^{29} +5.36532 q^{30} +5.21971 q^{31} +7.61310 q^{32} -2.42824 q^{33} +2.16757 q^{34} +12.6740 q^{35} +2.69838 q^{36} +2.43133 q^{37} -5.47385 q^{38} -7.04772 q^{39} -3.74703 q^{40} -1.78589 q^{41} +11.0986 q^{42} -0.311392 q^{43} +6.55231 q^{44} +2.47527 q^{45} +8.40759 q^{46} +3.61845 q^{47} +2.11551 q^{48} +19.2172 q^{49} -2.44273 q^{50} +1.00000 q^{51} +19.0174 q^{52} +5.51254 q^{53} +2.16757 q^{54} +6.01054 q^{55} -7.75101 q^{56} -2.52534 q^{57} +0.362592 q^{58} +3.98504 q^{59} -6.67921 q^{60} -4.00554 q^{61} -11.3141 q^{62} +5.12027 q^{63} -12.2709 q^{64} +17.4450 q^{65} +5.26339 q^{66} -14.4965 q^{67} -2.69838 q^{68} +3.87880 q^{69} -27.4719 q^{70} -6.09993 q^{71} -1.51379 q^{72} +7.55480 q^{73} -5.27009 q^{74} -1.12694 q^{75} +6.81431 q^{76} +12.4333 q^{77} +15.2765 q^{78} +1.00000 q^{79} -5.23645 q^{80} +1.00000 q^{81} +3.87105 q^{82} +2.53409 q^{83} -13.8164 q^{84} -2.47527 q^{85} +0.674966 q^{86} +0.167280 q^{87} -3.67584 q^{88} -14.5588 q^{89} -5.36532 q^{90} +36.0863 q^{91} -10.4665 q^{92} -5.21971 q^{93} -7.84325 q^{94} +6.25088 q^{95} -7.61310 q^{96} +7.77175 q^{97} -41.6547 q^{98} +2.42824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.16757 −1.53271 −0.766353 0.642419i \(-0.777931\pi\)
−0.766353 + 0.642419i \(0.777931\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.69838 1.34919
\(5\) 2.47527 1.10697 0.553486 0.832858i \(-0.313297\pi\)
0.553486 + 0.832858i \(0.313297\pi\)
\(6\) 2.16757 0.884909
\(7\) 5.12027 1.93528 0.967641 0.252332i \(-0.0811974\pi\)
0.967641 + 0.252332i \(0.0811974\pi\)
\(8\) −1.51379 −0.535205
\(9\) 1.00000 0.333333
\(10\) −5.36532 −1.69666
\(11\) 2.42824 0.732142 0.366071 0.930587i \(-0.380703\pi\)
0.366071 + 0.930587i \(0.380703\pi\)
\(12\) −2.69838 −0.778955
\(13\) 7.04772 1.95469 0.977343 0.211661i \(-0.0678873\pi\)
0.977343 + 0.211661i \(0.0678873\pi\)
\(14\) −11.0986 −2.96622
\(15\) −2.47527 −0.639111
\(16\) −2.11551 −0.528877
\(17\) −1.00000 −0.242536
\(18\) −2.16757 −0.510902
\(19\) 2.52534 0.579352 0.289676 0.957125i \(-0.406453\pi\)
0.289676 + 0.957125i \(0.406453\pi\)
\(20\) 6.67921 1.49352
\(21\) −5.12027 −1.11734
\(22\) −5.26339 −1.12216
\(23\) −3.87880 −0.808786 −0.404393 0.914585i \(-0.632517\pi\)
−0.404393 + 0.914585i \(0.632517\pi\)
\(24\) 1.51379 0.309001
\(25\) 1.12694 0.225388
\(26\) −15.2765 −2.99596
\(27\) −1.00000 −0.192450
\(28\) 13.8164 2.61106
\(29\) −0.167280 −0.0310631 −0.0155316 0.999879i \(-0.504944\pi\)
−0.0155316 + 0.999879i \(0.504944\pi\)
\(30\) 5.36532 0.979570
\(31\) 5.21971 0.937487 0.468743 0.883334i \(-0.344707\pi\)
0.468743 + 0.883334i \(0.344707\pi\)
\(32\) 7.61310 1.34582
\(33\) −2.42824 −0.422702
\(34\) 2.16757 0.371736
\(35\) 12.6740 2.14230
\(36\) 2.69838 0.449730
\(37\) 2.43133 0.399708 0.199854 0.979826i \(-0.435953\pi\)
0.199854 + 0.979826i \(0.435953\pi\)
\(38\) −5.47385 −0.887976
\(39\) −7.04772 −1.12854
\(40\) −3.74703 −0.592457
\(41\) −1.78589 −0.278909 −0.139455 0.990228i \(-0.544535\pi\)
−0.139455 + 0.990228i \(0.544535\pi\)
\(42\) 11.0986 1.71255
\(43\) −0.311392 −0.0474869 −0.0237434 0.999718i \(-0.507558\pi\)
−0.0237434 + 0.999718i \(0.507558\pi\)
\(44\) 6.55231 0.987798
\(45\) 2.47527 0.368991
\(46\) 8.40759 1.23963
\(47\) 3.61845 0.527805 0.263902 0.964549i \(-0.414990\pi\)
0.263902 + 0.964549i \(0.414990\pi\)
\(48\) 2.11551 0.305347
\(49\) 19.2172 2.74531
\(50\) −2.44273 −0.345454
\(51\) 1.00000 0.140028
\(52\) 19.0174 2.63724
\(53\) 5.51254 0.757206 0.378603 0.925559i \(-0.376405\pi\)
0.378603 + 0.925559i \(0.376405\pi\)
\(54\) 2.16757 0.294970
\(55\) 6.01054 0.810461
\(56\) −7.75101 −1.03577
\(57\) −2.52534 −0.334489
\(58\) 0.362592 0.0476106
\(59\) 3.98504 0.518808 0.259404 0.965769i \(-0.416474\pi\)
0.259404 + 0.965769i \(0.416474\pi\)
\(60\) −6.67921 −0.862282
\(61\) −4.00554 −0.512857 −0.256428 0.966563i \(-0.582546\pi\)
−0.256428 + 0.966563i \(0.582546\pi\)
\(62\) −11.3141 −1.43689
\(63\) 5.12027 0.645094
\(64\) −12.2709 −1.53387
\(65\) 17.4450 2.16378
\(66\) 5.26339 0.647879
\(67\) −14.4965 −1.77103 −0.885514 0.464613i \(-0.846194\pi\)
−0.885514 + 0.464613i \(0.846194\pi\)
\(68\) −2.69838 −0.327227
\(69\) 3.87880 0.466953
\(70\) −27.4719 −3.28352
\(71\) −6.09993 −0.723929 −0.361964 0.932192i \(-0.617894\pi\)
−0.361964 + 0.932192i \(0.617894\pi\)
\(72\) −1.51379 −0.178402
\(73\) 7.55480 0.884223 0.442111 0.896960i \(-0.354230\pi\)
0.442111 + 0.896960i \(0.354230\pi\)
\(74\) −5.27009 −0.612635
\(75\) −1.12694 −0.130128
\(76\) 6.81431 0.781655
\(77\) 12.4333 1.41690
\(78\) 15.2765 1.72972
\(79\) 1.00000 0.112509
\(80\) −5.23645 −0.585452
\(81\) 1.00000 0.111111
\(82\) 3.87105 0.427486
\(83\) 2.53409 0.278153 0.139076 0.990282i \(-0.455587\pi\)
0.139076 + 0.990282i \(0.455587\pi\)
\(84\) −13.8164 −1.50750
\(85\) −2.47527 −0.268480
\(86\) 0.674966 0.0727835
\(87\) 0.167280 0.0179343
\(88\) −3.67584 −0.391846
\(89\) −14.5588 −1.54323 −0.771613 0.636093i \(-0.780550\pi\)
−0.771613 + 0.636093i \(0.780550\pi\)
\(90\) −5.36532 −0.565555
\(91\) 36.0863 3.78287
\(92\) −10.4665 −1.09121
\(93\) −5.21971 −0.541258
\(94\) −7.84325 −0.808969
\(95\) 6.25088 0.641326
\(96\) −7.61310 −0.777009
\(97\) 7.77175 0.789101 0.394551 0.918874i \(-0.370900\pi\)
0.394551 + 0.918874i \(0.370900\pi\)
\(98\) −41.6547 −4.20776
\(99\) 2.42824 0.244047
\(100\) 3.04091 0.304091
\(101\) −0.229038 −0.0227901 −0.0113951 0.999935i \(-0.503627\pi\)
−0.0113951 + 0.999935i \(0.503627\pi\)
\(102\) −2.16757 −0.214622
\(103\) 10.1599 1.00108 0.500541 0.865713i \(-0.333135\pi\)
0.500541 + 0.865713i \(0.333135\pi\)
\(104\) −10.6688 −1.04616
\(105\) −12.6740 −1.23686
\(106\) −11.9489 −1.16058
\(107\) 11.6953 1.13062 0.565311 0.824878i \(-0.308756\pi\)
0.565311 + 0.824878i \(0.308756\pi\)
\(108\) −2.69838 −0.259652
\(109\) −16.3823 −1.56914 −0.784569 0.620042i \(-0.787116\pi\)
−0.784569 + 0.620042i \(0.787116\pi\)
\(110\) −13.0283 −1.24220
\(111\) −2.43133 −0.230772
\(112\) −10.8320 −1.02353
\(113\) −7.09186 −0.667146 −0.333573 0.942724i \(-0.608254\pi\)
−0.333573 + 0.942724i \(0.608254\pi\)
\(114\) 5.47385 0.512673
\(115\) −9.60106 −0.895304
\(116\) −0.451385 −0.0419100
\(117\) 7.04772 0.651562
\(118\) −8.63788 −0.795181
\(119\) −5.12027 −0.469375
\(120\) 3.74703 0.342055
\(121\) −5.10365 −0.463968
\(122\) 8.68231 0.786059
\(123\) 1.78589 0.161028
\(124\) 14.0847 1.26485
\(125\) −9.58685 −0.857474
\(126\) −11.0986 −0.988740
\(127\) 16.8219 1.49271 0.746353 0.665551i \(-0.231803\pi\)
0.746353 + 0.665551i \(0.231803\pi\)
\(128\) 11.3720 1.00515
\(129\) 0.311392 0.0274166
\(130\) −37.8133 −3.31645
\(131\) 7.84035 0.685015 0.342507 0.939515i \(-0.388724\pi\)
0.342507 + 0.939515i \(0.388724\pi\)
\(132\) −6.55231 −0.570305
\(133\) 12.9304 1.12121
\(134\) 31.4222 2.71447
\(135\) −2.47527 −0.213037
\(136\) 1.51379 0.129806
\(137\) −10.3154 −0.881307 −0.440654 0.897677i \(-0.645253\pi\)
−0.440654 + 0.897677i \(0.645253\pi\)
\(138\) −8.40759 −0.715701
\(139\) −15.8844 −1.34729 −0.673647 0.739053i \(-0.735273\pi\)
−0.673647 + 0.739053i \(0.735273\pi\)
\(140\) 34.1994 2.89037
\(141\) −3.61845 −0.304728
\(142\) 13.2221 1.10957
\(143\) 17.1136 1.43111
\(144\) −2.11551 −0.176292
\(145\) −0.414062 −0.0343860
\(146\) −16.3756 −1.35525
\(147\) −19.2172 −1.58501
\(148\) 6.56065 0.539282
\(149\) −6.51186 −0.533473 −0.266736 0.963770i \(-0.585945\pi\)
−0.266736 + 0.963770i \(0.585945\pi\)
\(150\) 2.44273 0.199448
\(151\) 4.73906 0.385660 0.192830 0.981232i \(-0.438233\pi\)
0.192830 + 0.981232i \(0.438233\pi\)
\(152\) −3.82282 −0.310072
\(153\) −1.00000 −0.0808452
\(154\) −26.9500 −2.17169
\(155\) 12.9202 1.03777
\(156\) −19.0174 −1.52261
\(157\) −2.23083 −0.178039 −0.0890196 0.996030i \(-0.528373\pi\)
−0.0890196 + 0.996030i \(0.528373\pi\)
\(158\) −2.16757 −0.172443
\(159\) −5.51254 −0.437173
\(160\) 18.8444 1.48978
\(161\) −19.8605 −1.56523
\(162\) −2.16757 −0.170301
\(163\) 2.89238 0.226548 0.113274 0.993564i \(-0.463866\pi\)
0.113274 + 0.993564i \(0.463866\pi\)
\(164\) −4.81901 −0.376301
\(165\) −6.01054 −0.467920
\(166\) −5.49283 −0.426327
\(167\) −21.7528 −1.68328 −0.841640 0.540039i \(-0.818409\pi\)
−0.841640 + 0.540039i \(0.818409\pi\)
\(168\) 7.75101 0.598004
\(169\) 36.6704 2.82080
\(170\) 5.36532 0.411501
\(171\) 2.52534 0.193117
\(172\) −0.840255 −0.0640688
\(173\) −18.8395 −1.43234 −0.716170 0.697926i \(-0.754107\pi\)
−0.716170 + 0.697926i \(0.754107\pi\)
\(174\) −0.362592 −0.0274880
\(175\) 5.77025 0.436190
\(176\) −5.13696 −0.387213
\(177\) −3.98504 −0.299534
\(178\) 31.5572 2.36531
\(179\) 4.98517 0.372609 0.186305 0.982492i \(-0.440349\pi\)
0.186305 + 0.982492i \(0.440349\pi\)
\(180\) 6.67921 0.497839
\(181\) −9.78562 −0.727359 −0.363680 0.931524i \(-0.618480\pi\)
−0.363680 + 0.931524i \(0.618480\pi\)
\(182\) −78.2197 −5.79803
\(183\) 4.00554 0.296098
\(184\) 5.87168 0.432866
\(185\) 6.01819 0.442466
\(186\) 11.3141 0.829590
\(187\) −2.42824 −0.177570
\(188\) 9.76394 0.712108
\(189\) −5.12027 −0.372445
\(190\) −13.5492 −0.982965
\(191\) −25.8552 −1.87081 −0.935407 0.353573i \(-0.884967\pi\)
−0.935407 + 0.353573i \(0.884967\pi\)
\(192\) 12.2709 0.885579
\(193\) −16.6091 −1.19555 −0.597775 0.801664i \(-0.703948\pi\)
−0.597775 + 0.801664i \(0.703948\pi\)
\(194\) −16.8458 −1.20946
\(195\) −17.4450 −1.24926
\(196\) 51.8553 3.70395
\(197\) −11.8671 −0.845496 −0.422748 0.906247i \(-0.638934\pi\)
−0.422748 + 0.906247i \(0.638934\pi\)
\(198\) −5.26339 −0.374053
\(199\) −14.9683 −1.06108 −0.530539 0.847661i \(-0.678010\pi\)
−0.530539 + 0.847661i \(0.678010\pi\)
\(200\) −1.70595 −0.120629
\(201\) 14.4965 1.02250
\(202\) 0.496456 0.0349306
\(203\) −0.856519 −0.0601159
\(204\) 2.69838 0.188924
\(205\) −4.42055 −0.308745
\(206\) −22.0223 −1.53436
\(207\) −3.87880 −0.269595
\(208\) −14.9095 −1.03379
\(209\) 6.13212 0.424168
\(210\) 27.4719 1.89574
\(211\) −0.457690 −0.0315087 −0.0157543 0.999876i \(-0.505015\pi\)
−0.0157543 + 0.999876i \(0.505015\pi\)
\(212\) 14.8749 1.02161
\(213\) 6.09993 0.417960
\(214\) −25.3503 −1.73291
\(215\) −0.770779 −0.0525667
\(216\) 1.51379 0.103000
\(217\) 26.7263 1.81430
\(218\) 35.5098 2.40503
\(219\) −7.55480 −0.510506
\(220\) 16.2187 1.09347
\(221\) −7.04772 −0.474081
\(222\) 5.27009 0.353705
\(223\) −5.26003 −0.352238 −0.176119 0.984369i \(-0.556354\pi\)
−0.176119 + 0.984369i \(0.556354\pi\)
\(224\) 38.9812 2.60454
\(225\) 1.12694 0.0751294
\(226\) 15.3721 1.02254
\(227\) −18.9322 −1.25658 −0.628289 0.777980i \(-0.716244\pi\)
−0.628289 + 0.777980i \(0.716244\pi\)
\(228\) −6.81431 −0.451289
\(229\) 20.5447 1.35763 0.678817 0.734308i \(-0.262493\pi\)
0.678817 + 0.734308i \(0.262493\pi\)
\(230\) 20.8110 1.37224
\(231\) −12.4333 −0.818048
\(232\) 0.253227 0.0166251
\(233\) −8.43882 −0.552845 −0.276423 0.961036i \(-0.589149\pi\)
−0.276423 + 0.961036i \(0.589149\pi\)
\(234\) −15.2765 −0.998653
\(235\) 8.95661 0.584265
\(236\) 10.7532 0.699971
\(237\) −1.00000 −0.0649570
\(238\) 11.0986 0.719414
\(239\) 17.9252 1.15948 0.579742 0.814800i \(-0.303153\pi\)
0.579742 + 0.814800i \(0.303153\pi\)
\(240\) 5.23645 0.338011
\(241\) 11.7543 0.757161 0.378580 0.925568i \(-0.376412\pi\)
0.378580 + 0.925568i \(0.376412\pi\)
\(242\) 11.0625 0.711128
\(243\) −1.00000 −0.0641500
\(244\) −10.8085 −0.691941
\(245\) 47.5677 3.03899
\(246\) −3.87105 −0.246809
\(247\) 17.7979 1.13245
\(248\) −7.90153 −0.501748
\(249\) −2.53409 −0.160592
\(250\) 20.7802 1.31426
\(251\) −9.50606 −0.600017 −0.300009 0.953936i \(-0.596990\pi\)
−0.300009 + 0.953936i \(0.596990\pi\)
\(252\) 13.8164 0.870354
\(253\) −9.41866 −0.592146
\(254\) −36.4628 −2.28788
\(255\) 2.47527 0.155007
\(256\) −0.107735 −0.00673344
\(257\) −12.9516 −0.807900 −0.403950 0.914781i \(-0.632363\pi\)
−0.403950 + 0.914781i \(0.632363\pi\)
\(258\) −0.674966 −0.0420216
\(259\) 12.4491 0.773548
\(260\) 47.0732 2.91935
\(261\) −0.167280 −0.0103544
\(262\) −16.9945 −1.04993
\(263\) 3.46583 0.213712 0.106856 0.994275i \(-0.465922\pi\)
0.106856 + 0.994275i \(0.465922\pi\)
\(264\) 3.67584 0.226232
\(265\) 13.6450 0.838207
\(266\) −28.0276 −1.71848
\(267\) 14.5588 0.890982
\(268\) −39.1170 −2.38945
\(269\) 17.0451 1.03926 0.519631 0.854391i \(-0.326070\pi\)
0.519631 + 0.854391i \(0.326070\pi\)
\(270\) 5.36532 0.326523
\(271\) −12.5484 −0.762260 −0.381130 0.924522i \(-0.624465\pi\)
−0.381130 + 0.924522i \(0.624465\pi\)
\(272\) 2.11551 0.128272
\(273\) −36.0863 −2.18404
\(274\) 22.3595 1.35079
\(275\) 2.73648 0.165016
\(276\) 10.4665 0.630008
\(277\) −26.0702 −1.56641 −0.783203 0.621766i \(-0.786415\pi\)
−0.783203 + 0.621766i \(0.786415\pi\)
\(278\) 34.4305 2.06501
\(279\) 5.21971 0.312496
\(280\) −19.1858 −1.14657
\(281\) 26.3755 1.57343 0.786715 0.617316i \(-0.211780\pi\)
0.786715 + 0.617316i \(0.211780\pi\)
\(282\) 7.84325 0.467059
\(283\) −26.2567 −1.56080 −0.780400 0.625280i \(-0.784985\pi\)
−0.780400 + 0.625280i \(0.784985\pi\)
\(284\) −16.4599 −0.976717
\(285\) −6.25088 −0.370270
\(286\) −37.0949 −2.19347
\(287\) −9.14425 −0.539768
\(288\) 7.61310 0.448606
\(289\) 1.00000 0.0588235
\(290\) 0.897511 0.0527037
\(291\) −7.77175 −0.455588
\(292\) 20.3857 1.19298
\(293\) −21.0956 −1.23242 −0.616210 0.787582i \(-0.711333\pi\)
−0.616210 + 0.787582i \(0.711333\pi\)
\(294\) 41.6547 2.42935
\(295\) 9.86404 0.574307
\(296\) −3.68052 −0.213926
\(297\) −2.42824 −0.140901
\(298\) 14.1149 0.817657
\(299\) −27.3367 −1.58092
\(300\) −3.04091 −0.175567
\(301\) −1.59441 −0.0919005
\(302\) −10.2723 −0.591103
\(303\) 0.229038 0.0131579
\(304\) −5.34237 −0.306406
\(305\) −9.91478 −0.567718
\(306\) 2.16757 0.123912
\(307\) 8.16138 0.465795 0.232897 0.972501i \(-0.425179\pi\)
0.232897 + 0.972501i \(0.425179\pi\)
\(308\) 33.5496 1.91167
\(309\) −10.1599 −0.577975
\(310\) −28.0054 −1.59060
\(311\) −6.22138 −0.352782 −0.176391 0.984320i \(-0.556442\pi\)
−0.176391 + 0.984320i \(0.556442\pi\)
\(312\) 10.6688 0.604000
\(313\) −1.24037 −0.0701097 −0.0350549 0.999385i \(-0.511161\pi\)
−0.0350549 + 0.999385i \(0.511161\pi\)
\(314\) 4.83548 0.272882
\(315\) 12.6740 0.714101
\(316\) 2.69838 0.151796
\(317\) 35.2664 1.98076 0.990380 0.138372i \(-0.0441869\pi\)
0.990380 + 0.138372i \(0.0441869\pi\)
\(318\) 11.9489 0.670058
\(319\) −0.406196 −0.0227426
\(320\) −30.3738 −1.69795
\(321\) −11.6953 −0.652765
\(322\) 43.0492 2.39904
\(323\) −2.52534 −0.140513
\(324\) 2.69838 0.149910
\(325\) 7.94237 0.440563
\(326\) −6.26944 −0.347232
\(327\) 16.3823 0.905942
\(328\) 2.70346 0.149274
\(329\) 18.5274 1.02145
\(330\) 13.0283 0.717184
\(331\) 14.7850 0.812659 0.406330 0.913727i \(-0.366808\pi\)
0.406330 + 0.913727i \(0.366808\pi\)
\(332\) 6.83794 0.375281
\(333\) 2.43133 0.133236
\(334\) 47.1507 2.57997
\(335\) −35.8827 −1.96048
\(336\) 10.8320 0.590933
\(337\) 2.79095 0.152033 0.0760163 0.997107i \(-0.475780\pi\)
0.0760163 + 0.997107i \(0.475780\pi\)
\(338\) −79.4858 −4.32346
\(339\) 7.09186 0.385177
\(340\) −6.67921 −0.362231
\(341\) 12.6747 0.686373
\(342\) −5.47385 −0.295992
\(343\) 62.5554 3.37768
\(344\) 0.471382 0.0254152
\(345\) 9.60106 0.516904
\(346\) 40.8360 2.19536
\(347\) −13.7185 −0.736448 −0.368224 0.929737i \(-0.620034\pi\)
−0.368224 + 0.929737i \(0.620034\pi\)
\(348\) 0.451385 0.0241968
\(349\) 21.4013 1.14559 0.572794 0.819700i \(-0.305860\pi\)
0.572794 + 0.819700i \(0.305860\pi\)
\(350\) −12.5074 −0.668551
\(351\) −7.04772 −0.376180
\(352\) 18.4864 0.985330
\(353\) 18.8139 1.00137 0.500683 0.865631i \(-0.333082\pi\)
0.500683 + 0.865631i \(0.333082\pi\)
\(354\) 8.63788 0.459098
\(355\) −15.0989 −0.801369
\(356\) −39.2850 −2.08210
\(357\) 5.12027 0.270994
\(358\) −10.8057 −0.571101
\(359\) 9.97827 0.526633 0.263316 0.964710i \(-0.415184\pi\)
0.263316 + 0.964710i \(0.415184\pi\)
\(360\) −3.74703 −0.197486
\(361\) −12.6227 −0.664352
\(362\) 21.2111 1.11483
\(363\) 5.10365 0.267872
\(364\) 97.3744 5.10381
\(365\) 18.7001 0.978810
\(366\) −8.68231 −0.453831
\(367\) −17.1927 −0.897451 −0.448726 0.893670i \(-0.648122\pi\)
−0.448726 + 0.893670i \(0.648122\pi\)
\(368\) 8.20563 0.427748
\(369\) −1.78589 −0.0929697
\(370\) −13.0449 −0.678171
\(371\) 28.2257 1.46541
\(372\) −14.0847 −0.730260
\(373\) −9.83404 −0.509187 −0.254594 0.967048i \(-0.581942\pi\)
−0.254594 + 0.967048i \(0.581942\pi\)
\(374\) 5.26339 0.272163
\(375\) 9.58685 0.495063
\(376\) −5.47756 −0.282484
\(377\) −1.17894 −0.0607186
\(378\) 11.0986 0.570849
\(379\) −8.75990 −0.449966 −0.224983 0.974363i \(-0.572233\pi\)
−0.224983 + 0.974363i \(0.572233\pi\)
\(380\) 16.8672 0.865271
\(381\) −16.8219 −0.861814
\(382\) 56.0430 2.86741
\(383\) −30.0557 −1.53577 −0.767886 0.640586i \(-0.778691\pi\)
−0.767886 + 0.640586i \(0.778691\pi\)
\(384\) −11.3720 −0.580324
\(385\) 30.7756 1.56847
\(386\) 36.0015 1.83243
\(387\) −0.311392 −0.0158290
\(388\) 20.9711 1.06465
\(389\) −22.0219 −1.11655 −0.558277 0.829655i \(-0.688537\pi\)
−0.558277 + 0.829655i \(0.688537\pi\)
\(390\) 37.8133 1.91475
\(391\) 3.87880 0.196159
\(392\) −29.0908 −1.46931
\(393\) −7.84035 −0.395493
\(394\) 25.7228 1.29590
\(395\) 2.47527 0.124544
\(396\) 6.55231 0.329266
\(397\) 32.9750 1.65497 0.827483 0.561491i \(-0.189772\pi\)
0.827483 + 0.561491i \(0.189772\pi\)
\(398\) 32.4450 1.62632
\(399\) −12.9304 −0.647330
\(400\) −2.38405 −0.119203
\(401\) −11.5924 −0.578895 −0.289448 0.957194i \(-0.593472\pi\)
−0.289448 + 0.957194i \(0.593472\pi\)
\(402\) −31.4222 −1.56720
\(403\) 36.7870 1.83249
\(404\) −0.618031 −0.0307482
\(405\) 2.47527 0.122997
\(406\) 1.85657 0.0921400
\(407\) 5.90385 0.292643
\(408\) −1.51379 −0.0749437
\(409\) −9.12106 −0.451007 −0.225504 0.974242i \(-0.572403\pi\)
−0.225504 + 0.974242i \(0.572403\pi\)
\(410\) 9.58188 0.473215
\(411\) 10.3154 0.508823
\(412\) 27.4152 1.35065
\(413\) 20.4045 1.00404
\(414\) 8.40759 0.413210
\(415\) 6.27255 0.307907
\(416\) 53.6550 2.63065
\(417\) 15.8844 0.777861
\(418\) −13.2918 −0.650124
\(419\) 37.1938 1.81704 0.908519 0.417843i \(-0.137214\pi\)
0.908519 + 0.417843i \(0.137214\pi\)
\(420\) −34.1994 −1.66876
\(421\) 17.5319 0.854453 0.427226 0.904145i \(-0.359491\pi\)
0.427226 + 0.904145i \(0.359491\pi\)
\(422\) 0.992078 0.0482936
\(423\) 3.61845 0.175935
\(424\) −8.34483 −0.405261
\(425\) −1.12694 −0.0546647
\(426\) −13.2221 −0.640611
\(427\) −20.5095 −0.992522
\(428\) 31.5582 1.52542
\(429\) −17.1136 −0.826250
\(430\) 1.67072 0.0805693
\(431\) 7.03499 0.338864 0.169432 0.985542i \(-0.445807\pi\)
0.169432 + 0.985542i \(0.445807\pi\)
\(432\) 2.11551 0.101782
\(433\) 14.4485 0.694351 0.347176 0.937800i \(-0.387141\pi\)
0.347176 + 0.937800i \(0.387141\pi\)
\(434\) −57.9313 −2.78079
\(435\) 0.414062 0.0198528
\(436\) −44.2056 −2.11706
\(437\) −9.79527 −0.468571
\(438\) 16.3756 0.782456
\(439\) −9.18460 −0.438357 −0.219179 0.975685i \(-0.570338\pi\)
−0.219179 + 0.975685i \(0.570338\pi\)
\(440\) −9.09868 −0.433763
\(441\) 19.2172 0.915105
\(442\) 15.2765 0.726627
\(443\) 15.7669 0.749106 0.374553 0.927205i \(-0.377796\pi\)
0.374553 + 0.927205i \(0.377796\pi\)
\(444\) −6.56065 −0.311355
\(445\) −36.0368 −1.70831
\(446\) 11.4015 0.539877
\(447\) 6.51186 0.308001
\(448\) −62.8306 −2.96847
\(449\) 13.9609 0.658854 0.329427 0.944181i \(-0.393144\pi\)
0.329427 + 0.944181i \(0.393144\pi\)
\(450\) −2.44273 −0.115151
\(451\) −4.33657 −0.204201
\(452\) −19.1365 −0.900106
\(453\) −4.73906 −0.222661
\(454\) 41.0371 1.92596
\(455\) 89.3231 4.18753
\(456\) 3.82282 0.179020
\(457\) −18.3974 −0.860592 −0.430296 0.902688i \(-0.641591\pi\)
−0.430296 + 0.902688i \(0.641591\pi\)
\(458\) −44.5322 −2.08085
\(459\) 1.00000 0.0466760
\(460\) −25.9073 −1.20793
\(461\) −20.5938 −0.959151 −0.479575 0.877501i \(-0.659209\pi\)
−0.479575 + 0.877501i \(0.659209\pi\)
\(462\) 26.9500 1.25383
\(463\) −9.84685 −0.457622 −0.228811 0.973471i \(-0.573484\pi\)
−0.228811 + 0.973471i \(0.573484\pi\)
\(464\) 0.353882 0.0164286
\(465\) −12.9202 −0.599158
\(466\) 18.2918 0.847350
\(467\) −28.1626 −1.30321 −0.651604 0.758559i \(-0.725904\pi\)
−0.651604 + 0.758559i \(0.725904\pi\)
\(468\) 19.0174 0.879081
\(469\) −74.2260 −3.42744
\(470\) −19.4141 −0.895507
\(471\) 2.23083 0.102791
\(472\) −6.03251 −0.277669
\(473\) −0.756135 −0.0347671
\(474\) 2.16757 0.0995600
\(475\) 2.84590 0.130579
\(476\) −13.8164 −0.633275
\(477\) 5.51254 0.252402
\(478\) −38.8542 −1.77715
\(479\) −3.28478 −0.150085 −0.0750427 0.997180i \(-0.523909\pi\)
−0.0750427 + 0.997180i \(0.523909\pi\)
\(480\) −18.8444 −0.860127
\(481\) 17.1353 0.781304
\(482\) −25.4783 −1.16051
\(483\) 19.8605 0.903685
\(484\) −13.7716 −0.625981
\(485\) 19.2371 0.873514
\(486\) 2.16757 0.0983232
\(487\) 23.1347 1.04833 0.524167 0.851615i \(-0.324377\pi\)
0.524167 + 0.851615i \(0.324377\pi\)
\(488\) 6.06354 0.274484
\(489\) −2.89238 −0.130798
\(490\) −103.107 −4.65788
\(491\) 34.0061 1.53467 0.767336 0.641245i \(-0.221582\pi\)
0.767336 + 0.641245i \(0.221582\pi\)
\(492\) 4.81901 0.217258
\(493\) 0.167280 0.00753391
\(494\) −38.5782 −1.73571
\(495\) 6.01054 0.270154
\(496\) −11.0423 −0.495815
\(497\) −31.2333 −1.40101
\(498\) 5.49283 0.246140
\(499\) −11.3575 −0.508431 −0.254216 0.967148i \(-0.581817\pi\)
−0.254216 + 0.967148i \(0.581817\pi\)
\(500\) −25.8690 −1.15689
\(501\) 21.7528 0.971842
\(502\) 20.6051 0.919650
\(503\) 27.9115 1.24451 0.622256 0.782814i \(-0.286216\pi\)
0.622256 + 0.782814i \(0.286216\pi\)
\(504\) −7.75101 −0.345258
\(505\) −0.566929 −0.0252280
\(506\) 20.4156 0.907586
\(507\) −36.6704 −1.62859
\(508\) 45.3920 2.01394
\(509\) −41.2250 −1.82727 −0.913634 0.406538i \(-0.866736\pi\)
−0.913634 + 0.406538i \(0.866736\pi\)
\(510\) −5.36532 −0.237581
\(511\) 38.6827 1.71122
\(512\) −22.5104 −0.994830
\(513\) −2.52534 −0.111496
\(514\) 28.0736 1.23827
\(515\) 25.1484 1.10817
\(516\) 0.840255 0.0369902
\(517\) 8.78645 0.386428
\(518\) −26.9843 −1.18562
\(519\) 18.8395 0.826962
\(520\) −26.4080 −1.15807
\(521\) 5.89619 0.258317 0.129158 0.991624i \(-0.458772\pi\)
0.129158 + 0.991624i \(0.458772\pi\)
\(522\) 0.362592 0.0158702
\(523\) −21.6793 −0.947971 −0.473986 0.880533i \(-0.657185\pi\)
−0.473986 + 0.880533i \(0.657185\pi\)
\(524\) 21.1562 0.924215
\(525\) −5.77025 −0.251834
\(526\) −7.51244 −0.327558
\(527\) −5.21971 −0.227374
\(528\) 5.13696 0.223558
\(529\) −7.95491 −0.345866
\(530\) −29.5766 −1.28472
\(531\) 3.98504 0.172936
\(532\) 34.8911 1.51272
\(533\) −12.5865 −0.545180
\(534\) −31.5572 −1.36561
\(535\) 28.9489 1.25157
\(536\) 21.9446 0.947863
\(537\) −4.98517 −0.215126
\(538\) −36.9466 −1.59288
\(539\) 46.6640 2.00996
\(540\) −6.67921 −0.287427
\(541\) −19.7845 −0.850603 −0.425301 0.905052i \(-0.639832\pi\)
−0.425301 + 0.905052i \(0.639832\pi\)
\(542\) 27.1995 1.16832
\(543\) 9.78562 0.419941
\(544\) −7.61310 −0.326409
\(545\) −40.5505 −1.73699
\(546\) 78.2197 3.34749
\(547\) 32.5031 1.38973 0.694865 0.719140i \(-0.255464\pi\)
0.694865 + 0.719140i \(0.255464\pi\)
\(548\) −27.8350 −1.18905
\(549\) −4.00554 −0.170952
\(550\) −5.93153 −0.252921
\(551\) −0.422438 −0.0179965
\(552\) −5.87168 −0.249915
\(553\) 5.12027 0.217736
\(554\) 56.5091 2.40084
\(555\) −6.01819 −0.255458
\(556\) −42.8620 −1.81775
\(557\) −14.9361 −0.632863 −0.316432 0.948615i \(-0.602485\pi\)
−0.316432 + 0.948615i \(0.602485\pi\)
\(558\) −11.3141 −0.478964
\(559\) −2.19461 −0.0928220
\(560\) −26.8120 −1.13302
\(561\) 2.42824 0.102520
\(562\) −57.1708 −2.41161
\(563\) −15.6638 −0.660151 −0.330075 0.943955i \(-0.607074\pi\)
−0.330075 + 0.943955i \(0.607074\pi\)
\(564\) −9.76394 −0.411136
\(565\) −17.5542 −0.738512
\(566\) 56.9134 2.39225
\(567\) 5.12027 0.215031
\(568\) 9.23401 0.387450
\(569\) −35.5884 −1.49194 −0.745972 0.665977i \(-0.768015\pi\)
−0.745972 + 0.665977i \(0.768015\pi\)
\(570\) 13.5492 0.567515
\(571\) −31.1674 −1.30431 −0.652157 0.758084i \(-0.726136\pi\)
−0.652157 + 0.758084i \(0.726136\pi\)
\(572\) 46.1789 1.93084
\(573\) 25.8552 1.08011
\(574\) 19.8208 0.827306
\(575\) −4.37118 −0.182291
\(576\) −12.2709 −0.511289
\(577\) 13.7522 0.572513 0.286256 0.958153i \(-0.407589\pi\)
0.286256 + 0.958153i \(0.407589\pi\)
\(578\) −2.16757 −0.0901592
\(579\) 16.6091 0.690251
\(580\) −1.11730 −0.0463932
\(581\) 12.9752 0.538304
\(582\) 16.8458 0.698283
\(583\) 13.3858 0.554382
\(584\) −11.4364 −0.473241
\(585\) 17.4450 0.721261
\(586\) 45.7263 1.88894
\(587\) 7.23914 0.298791 0.149396 0.988778i \(-0.452267\pi\)
0.149396 + 0.988778i \(0.452267\pi\)
\(588\) −51.8553 −2.13848
\(589\) 13.1815 0.543135
\(590\) −21.3810 −0.880244
\(591\) 11.8671 0.488147
\(592\) −5.14350 −0.211397
\(593\) −32.2811 −1.32563 −0.662813 0.748785i \(-0.730638\pi\)
−0.662813 + 0.748785i \(0.730638\pi\)
\(594\) 5.26339 0.215960
\(595\) −12.6740 −0.519585
\(596\) −17.5715 −0.719756
\(597\) 14.9683 0.612613
\(598\) 59.2543 2.42309
\(599\) 14.3937 0.588112 0.294056 0.955788i \(-0.404995\pi\)
0.294056 + 0.955788i \(0.404995\pi\)
\(600\) 1.70595 0.0696451
\(601\) −4.39997 −0.179479 −0.0897393 0.995965i \(-0.528603\pi\)
−0.0897393 + 0.995965i \(0.528603\pi\)
\(602\) 3.45601 0.140857
\(603\) −14.4965 −0.590343
\(604\) 12.7878 0.520328
\(605\) −12.6329 −0.513600
\(606\) −0.496456 −0.0201672
\(607\) −46.3385 −1.88082 −0.940411 0.340040i \(-0.889559\pi\)
−0.940411 + 0.340040i \(0.889559\pi\)
\(608\) 19.2256 0.779702
\(609\) 0.856519 0.0347079
\(610\) 21.4910 0.870146
\(611\) 25.5018 1.03169
\(612\) −2.69838 −0.109076
\(613\) −20.9925 −0.847880 −0.423940 0.905690i \(-0.639353\pi\)
−0.423940 + 0.905690i \(0.639353\pi\)
\(614\) −17.6904 −0.713927
\(615\) 4.42055 0.178254
\(616\) −18.8213 −0.758332
\(617\) 21.3941 0.861296 0.430648 0.902520i \(-0.358285\pi\)
0.430648 + 0.902520i \(0.358285\pi\)
\(618\) 22.0223 0.885865
\(619\) 10.8163 0.434743 0.217371 0.976089i \(-0.430252\pi\)
0.217371 + 0.976089i \(0.430252\pi\)
\(620\) 34.8635 1.40015
\(621\) 3.87880 0.155651
\(622\) 13.4853 0.540712
\(623\) −74.5448 −2.98658
\(624\) 14.9095 0.596858
\(625\) −29.3647 −1.17459
\(626\) 2.68859 0.107458
\(627\) −6.13212 −0.244893
\(628\) −6.01961 −0.240209
\(629\) −2.43133 −0.0969435
\(630\) −27.4719 −1.09451
\(631\) 30.5181 1.21491 0.607453 0.794356i \(-0.292191\pi\)
0.607453 + 0.794356i \(0.292191\pi\)
\(632\) −1.51379 −0.0602153
\(633\) 0.457690 0.0181916
\(634\) −76.4426 −3.03592
\(635\) 41.6388 1.65238
\(636\) −14.8749 −0.589830
\(637\) 135.438 5.36623
\(638\) 0.880460 0.0348577
\(639\) −6.09993 −0.241310
\(640\) 28.1487 1.11267
\(641\) 8.01768 0.316679 0.158340 0.987385i \(-0.449386\pi\)
0.158340 + 0.987385i \(0.449386\pi\)
\(642\) 25.3503 1.00050
\(643\) 5.53766 0.218384 0.109192 0.994021i \(-0.465174\pi\)
0.109192 + 0.994021i \(0.465174\pi\)
\(644\) −53.5912 −2.11179
\(645\) 0.770779 0.0303494
\(646\) 5.47385 0.215366
\(647\) 37.5761 1.47727 0.738634 0.674107i \(-0.235471\pi\)
0.738634 + 0.674107i \(0.235471\pi\)
\(648\) −1.51379 −0.0594672
\(649\) 9.67664 0.379841
\(650\) −17.2157 −0.675254
\(651\) −26.7263 −1.04749
\(652\) 7.80473 0.305657
\(653\) −47.8755 −1.87351 −0.936757 0.349979i \(-0.886189\pi\)
−0.936757 + 0.349979i \(0.886189\pi\)
\(654\) −35.5098 −1.38854
\(655\) 19.4070 0.758293
\(656\) 3.77807 0.147509
\(657\) 7.55480 0.294741
\(658\) −40.1596 −1.56558
\(659\) 14.5584 0.567114 0.283557 0.958955i \(-0.408486\pi\)
0.283557 + 0.958955i \(0.408486\pi\)
\(660\) −16.2187 −0.631312
\(661\) 46.5140 1.80919 0.904593 0.426276i \(-0.140175\pi\)
0.904593 + 0.426276i \(0.140175\pi\)
\(662\) −32.0477 −1.24557
\(663\) 7.04772 0.273711
\(664\) −3.83608 −0.148869
\(665\) 32.0062 1.24115
\(666\) −5.27009 −0.204212
\(667\) 0.648846 0.0251234
\(668\) −58.6972 −2.27106
\(669\) 5.26003 0.203364
\(670\) 77.7784 3.00484
\(671\) −9.72641 −0.375484
\(672\) −38.9812 −1.50373
\(673\) −46.0261 −1.77418 −0.887088 0.461601i \(-0.847275\pi\)
−0.887088 + 0.461601i \(0.847275\pi\)
\(674\) −6.04959 −0.233022
\(675\) −1.12694 −0.0433760
\(676\) 98.9506 3.80579
\(677\) 10.7557 0.413374 0.206687 0.978407i \(-0.433732\pi\)
0.206687 + 0.978407i \(0.433732\pi\)
\(678\) −15.3721 −0.590363
\(679\) 39.7935 1.52713
\(680\) 3.74703 0.143692
\(681\) 18.9322 0.725485
\(682\) −27.4733 −1.05201
\(683\) 18.2625 0.698793 0.349397 0.936975i \(-0.386387\pi\)
0.349397 + 0.936975i \(0.386387\pi\)
\(684\) 6.81431 0.260552
\(685\) −25.5335 −0.975583
\(686\) −135.594 −5.17699
\(687\) −20.5447 −0.783830
\(688\) 0.658753 0.0251147
\(689\) 38.8509 1.48010
\(690\) −20.8110 −0.792262
\(691\) −41.2896 −1.57073 −0.785365 0.619034i \(-0.787524\pi\)
−0.785365 + 0.619034i \(0.787524\pi\)
\(692\) −50.8361 −1.93250
\(693\) 12.4333 0.472300
\(694\) 29.7359 1.12876
\(695\) −39.3180 −1.49142
\(696\) −0.253227 −0.00959853
\(697\) 1.78589 0.0676454
\(698\) −46.3890 −1.75585
\(699\) 8.43882 0.319185
\(700\) 15.5703 0.588503
\(701\) −14.1273 −0.533580 −0.266790 0.963755i \(-0.585963\pi\)
−0.266790 + 0.963755i \(0.585963\pi\)
\(702\) 15.2765 0.576573
\(703\) 6.13992 0.231572
\(704\) −29.7968 −1.12301
\(705\) −8.95661 −0.337326
\(706\) −40.7806 −1.53480
\(707\) −1.17274 −0.0441053
\(708\) −10.7532 −0.404128
\(709\) −15.2007 −0.570874 −0.285437 0.958398i \(-0.592139\pi\)
−0.285437 + 0.958398i \(0.592139\pi\)
\(710\) 32.7281 1.22826
\(711\) 1.00000 0.0375029
\(712\) 22.0389 0.825942
\(713\) −20.2462 −0.758226
\(714\) −11.0986 −0.415354
\(715\) 42.3606 1.58420
\(716\) 13.4519 0.502720
\(717\) −17.9252 −0.669429
\(718\) −21.6286 −0.807174
\(719\) 12.4689 0.465012 0.232506 0.972595i \(-0.425307\pi\)
0.232506 + 0.972595i \(0.425307\pi\)
\(720\) −5.23645 −0.195151
\(721\) 52.0213 1.93737
\(722\) 27.3606 1.01826
\(723\) −11.7543 −0.437147
\(724\) −26.4053 −0.981346
\(725\) −0.188515 −0.00700126
\(726\) −11.0625 −0.410570
\(727\) −27.4760 −1.01903 −0.509515 0.860462i \(-0.670175\pi\)
−0.509515 + 0.860462i \(0.670175\pi\)
\(728\) −54.6270 −2.02461
\(729\) 1.00000 0.0370370
\(730\) −40.5340 −1.50023
\(731\) 0.311392 0.0115173
\(732\) 10.8085 0.399492
\(733\) −29.6131 −1.09378 −0.546892 0.837203i \(-0.684189\pi\)
−0.546892 + 0.837203i \(0.684189\pi\)
\(734\) 37.2664 1.37553
\(735\) −47.5677 −1.75456
\(736\) −29.5297 −1.08848
\(737\) −35.2009 −1.29664
\(738\) 3.87105 0.142495
\(739\) 7.13099 0.262318 0.131159 0.991361i \(-0.458130\pi\)
0.131159 + 0.991361i \(0.458130\pi\)
\(740\) 16.2394 0.596971
\(741\) −17.7979 −0.653821
\(742\) −61.1814 −2.24604
\(743\) 14.1961 0.520805 0.260402 0.965500i \(-0.416145\pi\)
0.260402 + 0.965500i \(0.416145\pi\)
\(744\) 7.90153 0.289684
\(745\) −16.1186 −0.590539
\(746\) 21.3160 0.780435
\(747\) 2.53409 0.0927176
\(748\) −6.55231 −0.239576
\(749\) 59.8829 2.18807
\(750\) −20.7802 −0.758786
\(751\) 48.4564 1.76820 0.884100 0.467298i \(-0.154772\pi\)
0.884100 + 0.467298i \(0.154772\pi\)
\(752\) −7.65485 −0.279144
\(753\) 9.50606 0.346420
\(754\) 2.55545 0.0930639
\(755\) 11.7304 0.426915
\(756\) −13.8164 −0.502499
\(757\) −32.3755 −1.17671 −0.588354 0.808603i \(-0.700224\pi\)
−0.588354 + 0.808603i \(0.700224\pi\)
\(758\) 18.9877 0.689665
\(759\) 9.41866 0.341876
\(760\) −9.46251 −0.343241
\(761\) 41.4460 1.50242 0.751209 0.660064i \(-0.229471\pi\)
0.751209 + 0.660064i \(0.229471\pi\)
\(762\) 36.4628 1.32091
\(763\) −83.8817 −3.03672
\(764\) −69.7670 −2.52408
\(765\) −2.47527 −0.0894934
\(766\) 65.1479 2.35389
\(767\) 28.0855 1.01411
\(768\) 0.107735 0.00388755
\(769\) −42.1921 −1.52149 −0.760743 0.649054i \(-0.775165\pi\)
−0.760743 + 0.649054i \(0.775165\pi\)
\(770\) −66.7084 −2.40400
\(771\) 12.9516 0.466441
\(772\) −44.8177 −1.61302
\(773\) −40.0966 −1.44218 −0.721088 0.692844i \(-0.756358\pi\)
−0.721088 + 0.692844i \(0.756358\pi\)
\(774\) 0.674966 0.0242612
\(775\) 5.88230 0.211299
\(776\) −11.7648 −0.422331
\(777\) −12.4491 −0.446608
\(778\) 47.7341 1.71135
\(779\) −4.50997 −0.161586
\(780\) −47.0732 −1.68549
\(781\) −14.8121 −0.530018
\(782\) −8.40759 −0.300655
\(783\) 0.167280 0.00597810
\(784\) −40.6542 −1.45193
\(785\) −5.52189 −0.197085
\(786\) 16.9945 0.606175
\(787\) 19.5618 0.697303 0.348652 0.937252i \(-0.386640\pi\)
0.348652 + 0.937252i \(0.386640\pi\)
\(788\) −32.0219 −1.14073
\(789\) −3.46583 −0.123387
\(790\) −5.36532 −0.190890
\(791\) −36.3123 −1.29112
\(792\) −3.67584 −0.130615
\(793\) −28.2299 −1.00247
\(794\) −71.4757 −2.53658
\(795\) −13.6450 −0.483939
\(796\) −40.3903 −1.43159
\(797\) 8.01909 0.284051 0.142025 0.989863i \(-0.454639\pi\)
0.142025 + 0.989863i \(0.454639\pi\)
\(798\) 28.0276 0.992167
\(799\) −3.61845 −0.128011
\(800\) 8.57952 0.303332
\(801\) −14.5588 −0.514408
\(802\) 25.1273 0.887277
\(803\) 18.3449 0.647376
\(804\) 39.1170 1.37955
\(805\) −49.1601 −1.73266
\(806\) −79.7386 −2.80867
\(807\) −17.0451 −0.600018
\(808\) 0.346715 0.0121974
\(809\) 52.4358 1.84354 0.921772 0.387732i \(-0.126742\pi\)
0.921772 + 0.387732i \(0.126742\pi\)
\(810\) −5.36532 −0.188518
\(811\) 38.9257 1.36687 0.683433 0.730013i \(-0.260486\pi\)
0.683433 + 0.730013i \(0.260486\pi\)
\(812\) −2.31121 −0.0811077
\(813\) 12.5484 0.440091
\(814\) −12.7970 −0.448536
\(815\) 7.15940 0.250783
\(816\) −2.11551 −0.0740576
\(817\) −0.786370 −0.0275116
\(818\) 19.7706 0.691262
\(819\) 36.0863 1.26096
\(820\) −11.9283 −0.416555
\(821\) 29.4619 1.02823 0.514113 0.857722i \(-0.328121\pi\)
0.514113 + 0.857722i \(0.328121\pi\)
\(822\) −22.3595 −0.779876
\(823\) −16.6954 −0.581965 −0.290983 0.956728i \(-0.593982\pi\)
−0.290983 + 0.956728i \(0.593982\pi\)
\(824\) −15.3799 −0.535784
\(825\) −2.73648 −0.0952721
\(826\) −44.2283 −1.53890
\(827\) 41.0647 1.42796 0.713980 0.700167i \(-0.246891\pi\)
0.713980 + 0.700167i \(0.246891\pi\)
\(828\) −10.4665 −0.363735
\(829\) 18.6798 0.648776 0.324388 0.945924i \(-0.394842\pi\)
0.324388 + 0.945924i \(0.394842\pi\)
\(830\) −13.5962 −0.471932
\(831\) 26.0702 0.904365
\(832\) −86.4822 −2.99823
\(833\) −19.2172 −0.665837
\(834\) −34.4305 −1.19223
\(835\) −53.8439 −1.86334
\(836\) 16.5468 0.572282
\(837\) −5.21971 −0.180419
\(838\) −80.6204 −2.78499
\(839\) 11.2582 0.388675 0.194338 0.980935i \(-0.437744\pi\)
0.194338 + 0.980935i \(0.437744\pi\)
\(840\) 19.1858 0.661974
\(841\) −28.9720 −0.999035
\(842\) −38.0017 −1.30963
\(843\) −26.3755 −0.908420
\(844\) −1.23502 −0.0425112
\(845\) 90.7689 3.12255
\(846\) −7.84325 −0.269656
\(847\) −26.1321 −0.897910
\(848\) −11.6618 −0.400469
\(849\) 26.2567 0.901129
\(850\) 2.44273 0.0837849
\(851\) −9.43064 −0.323278
\(852\) 16.4599 0.563908
\(853\) −2.47791 −0.0848421 −0.0424211 0.999100i \(-0.513507\pi\)
−0.0424211 + 0.999100i \(0.513507\pi\)
\(854\) 44.4558 1.52125
\(855\) 6.25088 0.213775
\(856\) −17.7041 −0.605115
\(857\) 10.1054 0.345195 0.172598 0.984992i \(-0.444784\pi\)
0.172598 + 0.984992i \(0.444784\pi\)
\(858\) 37.0949 1.26640
\(859\) 43.5451 1.48574 0.742871 0.669435i \(-0.233464\pi\)
0.742871 + 0.669435i \(0.233464\pi\)
\(860\) −2.07985 −0.0709224
\(861\) 9.14425 0.311635
\(862\) −15.2489 −0.519379
\(863\) 44.8796 1.52772 0.763859 0.645383i \(-0.223302\pi\)
0.763859 + 0.645383i \(0.223302\pi\)
\(864\) −7.61310 −0.259003
\(865\) −46.6328 −1.58556
\(866\) −31.3182 −1.06424
\(867\) −1.00000 −0.0339618
\(868\) 72.1178 2.44784
\(869\) 2.42824 0.0823724
\(870\) −0.897511 −0.0304285
\(871\) −102.167 −3.46180
\(872\) 24.7993 0.839810
\(873\) 7.77175 0.263034
\(874\) 21.2320 0.718182
\(875\) −49.0873 −1.65945
\(876\) −20.3857 −0.688770
\(877\) 26.1083 0.881614 0.440807 0.897602i \(-0.354692\pi\)
0.440807 + 0.897602i \(0.354692\pi\)
\(878\) 19.9083 0.671873
\(879\) 21.0956 0.711538
\(880\) −12.7153 −0.428634
\(881\) −16.8874 −0.568950 −0.284475 0.958683i \(-0.591819\pi\)
−0.284475 + 0.958683i \(0.591819\pi\)
\(882\) −41.6547 −1.40259
\(883\) −0.726610 −0.0244524 −0.0122262 0.999925i \(-0.503892\pi\)
−0.0122262 + 0.999925i \(0.503892\pi\)
\(884\) −19.0174 −0.639625
\(885\) −9.86404 −0.331576
\(886\) −34.1759 −1.14816
\(887\) −11.5875 −0.389072 −0.194536 0.980895i \(-0.562320\pi\)
−0.194536 + 0.980895i \(0.562320\pi\)
\(888\) 3.68052 0.123510
\(889\) 86.1329 2.88881
\(890\) 78.1124 2.61834
\(891\) 2.42824 0.0813491
\(892\) −14.1936 −0.475235
\(893\) 9.13779 0.305784
\(894\) −14.1149 −0.472074
\(895\) 12.3396 0.412468
\(896\) 58.2277 1.94525
\(897\) 27.3367 0.912746
\(898\) −30.2612 −1.00983
\(899\) −0.873152 −0.0291213
\(900\) 3.04091 0.101364
\(901\) −5.51254 −0.183649
\(902\) 9.39984 0.312980
\(903\) 1.59441 0.0530588
\(904\) 10.7356 0.357060
\(905\) −24.2220 −0.805167
\(906\) 10.2723 0.341273
\(907\) −18.7024 −0.621003 −0.310502 0.950573i \(-0.600497\pi\)
−0.310502 + 0.950573i \(0.600497\pi\)
\(908\) −51.0864 −1.69536
\(909\) −0.229038 −0.00759670
\(910\) −193.614 −6.41826
\(911\) 18.4736 0.612057 0.306028 0.952022i \(-0.401000\pi\)
0.306028 + 0.952022i \(0.401000\pi\)
\(912\) 5.34237 0.176904
\(913\) 6.15338 0.203647
\(914\) 39.8777 1.31904
\(915\) 9.91478 0.327772
\(916\) 55.4375 1.83171
\(917\) 40.1448 1.32570
\(918\) −2.16757 −0.0715406
\(919\) 41.5190 1.36959 0.684793 0.728738i \(-0.259893\pi\)
0.684793 + 0.728738i \(0.259893\pi\)
\(920\) 14.5340 0.479171
\(921\) −8.16138 −0.268927
\(922\) 44.6387 1.47010
\(923\) −42.9906 −1.41505
\(924\) −33.5496 −1.10370
\(925\) 2.73997 0.0900895
\(926\) 21.3438 0.701400
\(927\) 10.1599 0.333694
\(928\) −1.27352 −0.0418053
\(929\) 14.8350 0.486721 0.243361 0.969936i \(-0.421750\pi\)
0.243361 + 0.969936i \(0.421750\pi\)
\(930\) 28.0054 0.918334
\(931\) 48.5299 1.59050
\(932\) −22.7711 −0.745893
\(933\) 6.22138 0.203679
\(934\) 61.0444 1.99744
\(935\) −6.01054 −0.196566
\(936\) −10.6688 −0.348719
\(937\) −29.3327 −0.958258 −0.479129 0.877744i \(-0.659047\pi\)
−0.479129 + 0.877744i \(0.659047\pi\)
\(938\) 160.890 5.25326
\(939\) 1.24037 0.0404779
\(940\) 24.1683 0.788284
\(941\) 52.4865 1.71101 0.855505 0.517794i \(-0.173247\pi\)
0.855505 + 0.517794i \(0.173247\pi\)
\(942\) −4.83548 −0.157548
\(943\) 6.92711 0.225578
\(944\) −8.43039 −0.274386
\(945\) −12.6740 −0.412287
\(946\) 1.63898 0.0532878
\(947\) −12.9005 −0.419208 −0.209604 0.977786i \(-0.567218\pi\)
−0.209604 + 0.977786i \(0.567218\pi\)
\(948\) −2.69838 −0.0876393
\(949\) 53.2442 1.72838
\(950\) −6.16871 −0.200139
\(951\) −35.2664 −1.14359
\(952\) 7.75101 0.251212
\(953\) −35.3562 −1.14530 −0.572649 0.819801i \(-0.694084\pi\)
−0.572649 + 0.819801i \(0.694084\pi\)
\(954\) −11.9489 −0.386858
\(955\) −63.9984 −2.07094
\(956\) 48.3690 1.56436
\(957\) 0.406196 0.0131304
\(958\) 7.12000 0.230037
\(959\) −52.8179 −1.70558
\(960\) 30.3738 0.980312
\(961\) −3.75467 −0.121118
\(962\) −37.1421 −1.19751
\(963\) 11.6953 0.376874
\(964\) 31.7175 1.02155
\(965\) −41.1119 −1.32344
\(966\) −43.0492 −1.38508
\(967\) 36.8112 1.18377 0.591884 0.806023i \(-0.298384\pi\)
0.591884 + 0.806023i \(0.298384\pi\)
\(968\) 7.72585 0.248318
\(969\) 2.52534 0.0811255
\(970\) −41.6979 −1.33884
\(971\) 21.6642 0.695239 0.347619 0.937636i \(-0.386990\pi\)
0.347619 + 0.937636i \(0.386990\pi\)
\(972\) −2.69838 −0.0865505
\(973\) −81.3323 −2.60739
\(974\) −50.1463 −1.60679
\(975\) −7.94237 −0.254359
\(976\) 8.47375 0.271238
\(977\) 11.2438 0.359722 0.179861 0.983692i \(-0.442435\pi\)
0.179861 + 0.983692i \(0.442435\pi\)
\(978\) 6.26944 0.200475
\(979\) −35.3522 −1.12986
\(980\) 128.356 4.10017
\(981\) −16.3823 −0.523046
\(982\) −73.7107 −2.35220
\(983\) −17.6194 −0.561970 −0.280985 0.959712i \(-0.590661\pi\)
−0.280985 + 0.959712i \(0.590661\pi\)
\(984\) −2.70346 −0.0861832
\(985\) −29.3742 −0.935941
\(986\) −0.362592 −0.0115473
\(987\) −18.5274 −0.589735
\(988\) 48.0254 1.52789
\(989\) 1.20783 0.0384067
\(990\) −13.0283 −0.414066
\(991\) 62.4034 1.98231 0.991154 0.132718i \(-0.0423704\pi\)
0.991154 + 0.132718i \(0.0423704\pi\)
\(992\) 39.7381 1.26169
\(993\) −14.7850 −0.469189
\(994\) 67.7005 2.14733
\(995\) −37.0506 −1.17458
\(996\) −6.83794 −0.216668
\(997\) −49.3450 −1.56277 −0.781386 0.624048i \(-0.785487\pi\)
−0.781386 + 0.624048i \(0.785487\pi\)
\(998\) 24.6182 0.779276
\(999\) −2.43133 −0.0769239
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.1.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.6 32 1.1 even 1 trivial