Properties

Label 4027.2.a.c.1.7
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58182 q^{2} +1.87364 q^{3} +4.66582 q^{4} +2.74921 q^{5} -4.83740 q^{6} +4.58392 q^{7} -6.88267 q^{8} +0.510512 q^{9} +O(q^{10})\) \(q-2.58182 q^{2} +1.87364 q^{3} +4.66582 q^{4} +2.74921 q^{5} -4.83740 q^{6} +4.58392 q^{7} -6.88267 q^{8} +0.510512 q^{9} -7.09798 q^{10} +3.67809 q^{11} +8.74204 q^{12} +0.712583 q^{13} -11.8349 q^{14} +5.15102 q^{15} +8.43822 q^{16} -3.71085 q^{17} -1.31805 q^{18} +2.31918 q^{19} +12.8273 q^{20} +8.58860 q^{21} -9.49619 q^{22} +5.08992 q^{23} -12.8956 q^{24} +2.55817 q^{25} -1.83977 q^{26} -4.66439 q^{27} +21.3877 q^{28} +7.27085 q^{29} -13.2990 q^{30} -3.51421 q^{31} -8.02065 q^{32} +6.89141 q^{33} +9.58076 q^{34} +12.6022 q^{35} +2.38196 q^{36} -11.0544 q^{37} -5.98771 q^{38} +1.33512 q^{39} -18.9219 q^{40} -9.75528 q^{41} -22.1743 q^{42} -1.05940 q^{43} +17.1613 q^{44} +1.40351 q^{45} -13.1413 q^{46} +4.58609 q^{47} +15.8101 q^{48} +14.0123 q^{49} -6.60475 q^{50} -6.95278 q^{51} +3.32478 q^{52} +14.0244 q^{53} +12.0426 q^{54} +10.1119 q^{55} -31.5496 q^{56} +4.34529 q^{57} -18.7721 q^{58} -1.70745 q^{59} +24.0337 q^{60} -11.0038 q^{61} +9.07308 q^{62} +2.34015 q^{63} +3.83147 q^{64} +1.95904 q^{65} -17.7924 q^{66} -13.3228 q^{67} -17.3141 q^{68} +9.53666 q^{69} -32.5366 q^{70} +6.15065 q^{71} -3.51369 q^{72} +9.71356 q^{73} +28.5404 q^{74} +4.79308 q^{75} +10.8209 q^{76} +16.8601 q^{77} -3.44705 q^{78} +1.19637 q^{79} +23.1985 q^{80} -10.2709 q^{81} +25.1864 q^{82} +9.58215 q^{83} +40.0728 q^{84} -10.2019 q^{85} +2.73519 q^{86} +13.6229 q^{87} -25.3151 q^{88} +5.77873 q^{89} -3.62361 q^{90} +3.26643 q^{91} +23.7487 q^{92} -6.58436 q^{93} -11.8405 q^{94} +6.37591 q^{95} -15.0278 q^{96} -0.332297 q^{97} -36.1774 q^{98} +1.87771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58182 −1.82563 −0.912813 0.408378i \(-0.866094\pi\)
−0.912813 + 0.408378i \(0.866094\pi\)
\(3\) 1.87364 1.08174 0.540872 0.841105i \(-0.318094\pi\)
0.540872 + 0.841105i \(0.318094\pi\)
\(4\) 4.66582 2.33291
\(5\) 2.74921 1.22949 0.614743 0.788728i \(-0.289260\pi\)
0.614743 + 0.788728i \(0.289260\pi\)
\(6\) −4.83740 −1.97486
\(7\) 4.58392 1.73256 0.866280 0.499559i \(-0.166505\pi\)
0.866280 + 0.499559i \(0.166505\pi\)
\(8\) −6.88267 −2.43339
\(9\) 0.510512 0.170171
\(10\) −7.09798 −2.24458
\(11\) 3.67809 1.10899 0.554493 0.832188i \(-0.312912\pi\)
0.554493 + 0.832188i \(0.312912\pi\)
\(12\) 8.74204 2.52361
\(13\) 0.712583 0.197635 0.0988175 0.995106i \(-0.468494\pi\)
0.0988175 + 0.995106i \(0.468494\pi\)
\(14\) −11.8349 −3.16300
\(15\) 5.15102 1.32999
\(16\) 8.43822 2.10955
\(17\) −3.71085 −0.900013 −0.450006 0.893025i \(-0.648578\pi\)
−0.450006 + 0.893025i \(0.648578\pi\)
\(18\) −1.31805 −0.310668
\(19\) 2.31918 0.532056 0.266028 0.963965i \(-0.414289\pi\)
0.266028 + 0.963965i \(0.414289\pi\)
\(20\) 12.8273 2.86828
\(21\) 8.58860 1.87419
\(22\) −9.49619 −2.02459
\(23\) 5.08992 1.06132 0.530661 0.847584i \(-0.321944\pi\)
0.530661 + 0.847584i \(0.321944\pi\)
\(24\) −12.8956 −2.63231
\(25\) 2.55817 0.511634
\(26\) −1.83977 −0.360808
\(27\) −4.66439 −0.897663
\(28\) 21.3877 4.04190
\(29\) 7.27085 1.35016 0.675081 0.737743i \(-0.264108\pi\)
0.675081 + 0.737743i \(0.264108\pi\)
\(30\) −13.2990 −2.42806
\(31\) −3.51421 −0.631171 −0.315586 0.948897i \(-0.602201\pi\)
−0.315586 + 0.948897i \(0.602201\pi\)
\(32\) −8.02065 −1.41786
\(33\) 6.89141 1.19964
\(34\) 9.58076 1.64309
\(35\) 12.6022 2.13016
\(36\) 2.38196 0.396993
\(37\) −11.0544 −1.81733 −0.908663 0.417529i \(-0.862896\pi\)
−0.908663 + 0.417529i \(0.862896\pi\)
\(38\) −5.98771 −0.971335
\(39\) 1.33512 0.213791
\(40\) −18.9219 −2.99182
\(41\) −9.75528 −1.52352 −0.761760 0.647860i \(-0.775664\pi\)
−0.761760 + 0.647860i \(0.775664\pi\)
\(42\) −22.1743 −3.42156
\(43\) −1.05940 −0.161557 −0.0807786 0.996732i \(-0.525741\pi\)
−0.0807786 + 0.996732i \(0.525741\pi\)
\(44\) 17.1613 2.58717
\(45\) 1.40351 0.209223
\(46\) −13.1413 −1.93758
\(47\) 4.58609 0.668950 0.334475 0.942405i \(-0.391441\pi\)
0.334475 + 0.942405i \(0.391441\pi\)
\(48\) 15.8101 2.28200
\(49\) 14.0123 2.00176
\(50\) −6.60475 −0.934053
\(51\) −6.95278 −0.973584
\(52\) 3.32478 0.461065
\(53\) 14.0244 1.92640 0.963198 0.268794i \(-0.0866251\pi\)
0.963198 + 0.268794i \(0.0866251\pi\)
\(54\) 12.0426 1.63880
\(55\) 10.1119 1.36348
\(56\) −31.5496 −4.21600
\(57\) 4.34529 0.575548
\(58\) −18.7721 −2.46489
\(59\) −1.70745 −0.222291 −0.111146 0.993804i \(-0.535452\pi\)
−0.111146 + 0.993804i \(0.535452\pi\)
\(60\) 24.0337 3.10274
\(61\) −11.0038 −1.40890 −0.704448 0.709755i \(-0.748806\pi\)
−0.704448 + 0.709755i \(0.748806\pi\)
\(62\) 9.07308 1.15228
\(63\) 2.34015 0.294831
\(64\) 3.83147 0.478934
\(65\) 1.95904 0.242989
\(66\) −17.7924 −2.19009
\(67\) −13.3228 −1.62763 −0.813817 0.581122i \(-0.802614\pi\)
−0.813817 + 0.581122i \(0.802614\pi\)
\(68\) −17.3141 −2.09965
\(69\) 9.53666 1.14808
\(70\) −32.5366 −3.88887
\(71\) 6.15065 0.729948 0.364974 0.931018i \(-0.381078\pi\)
0.364974 + 0.931018i \(0.381078\pi\)
\(72\) −3.51369 −0.414092
\(73\) 9.71356 1.13689 0.568443 0.822723i \(-0.307546\pi\)
0.568443 + 0.822723i \(0.307546\pi\)
\(74\) 28.5404 3.31776
\(75\) 4.79308 0.553458
\(76\) 10.8209 1.24124
\(77\) 16.8601 1.92139
\(78\) −3.44705 −0.390302
\(79\) 1.19637 0.134603 0.0673013 0.997733i \(-0.478561\pi\)
0.0673013 + 0.997733i \(0.478561\pi\)
\(80\) 23.1985 2.59367
\(81\) −10.2709 −1.14121
\(82\) 25.1864 2.78138
\(83\) 9.58215 1.05178 0.525889 0.850553i \(-0.323733\pi\)
0.525889 + 0.850553i \(0.323733\pi\)
\(84\) 40.0728 4.37230
\(85\) −10.2019 −1.10655
\(86\) 2.73519 0.294943
\(87\) 13.6229 1.46053
\(88\) −25.3151 −2.69860
\(89\) 5.77873 0.612544 0.306272 0.951944i \(-0.400918\pi\)
0.306272 + 0.951944i \(0.400918\pi\)
\(90\) −3.62361 −0.381962
\(91\) 3.26643 0.342415
\(92\) 23.7487 2.47597
\(93\) −6.58436 −0.682766
\(94\) −11.8405 −1.22125
\(95\) 6.37591 0.654155
\(96\) −15.0278 −1.53377
\(97\) −0.332297 −0.0337396 −0.0168698 0.999858i \(-0.505370\pi\)
−0.0168698 + 0.999858i \(0.505370\pi\)
\(98\) −36.1774 −3.65447
\(99\) 1.87771 0.188717
\(100\) 11.9360 1.19360
\(101\) −3.70414 −0.368576 −0.184288 0.982872i \(-0.558998\pi\)
−0.184288 + 0.982872i \(0.558998\pi\)
\(102\) 17.9509 1.77740
\(103\) 18.2236 1.79562 0.897811 0.440382i \(-0.145157\pi\)
0.897811 + 0.440382i \(0.145157\pi\)
\(104\) −4.90448 −0.480924
\(105\) 23.6119 2.30428
\(106\) −36.2085 −3.51688
\(107\) 1.96123 0.189599 0.0947996 0.995496i \(-0.469779\pi\)
0.0947996 + 0.995496i \(0.469779\pi\)
\(108\) −21.7632 −2.09417
\(109\) 2.25868 0.216342 0.108171 0.994132i \(-0.465501\pi\)
0.108171 + 0.994132i \(0.465501\pi\)
\(110\) −26.1071 −2.48921
\(111\) −20.7119 −1.96588
\(112\) 38.6801 3.65493
\(113\) −18.1321 −1.70572 −0.852862 0.522136i \(-0.825135\pi\)
−0.852862 + 0.522136i \(0.825135\pi\)
\(114\) −11.2188 −1.05074
\(115\) 13.9933 1.30488
\(116\) 33.9245 3.14981
\(117\) 0.363783 0.0336317
\(118\) 4.40834 0.405820
\(119\) −17.0102 −1.55933
\(120\) −35.4528 −3.23638
\(121\) 2.52837 0.229852
\(122\) 28.4100 2.57212
\(123\) −18.2779 −1.64806
\(124\) −16.3967 −1.47246
\(125\) −6.71311 −0.600438
\(126\) −6.04185 −0.538251
\(127\) −9.95974 −0.883784 −0.441892 0.897068i \(-0.645693\pi\)
−0.441892 + 0.897068i \(0.645693\pi\)
\(128\) 6.14911 0.543509
\(129\) −1.98493 −0.174764
\(130\) −5.05791 −0.443608
\(131\) 20.9465 1.83010 0.915051 0.403339i \(-0.132150\pi\)
0.915051 + 0.403339i \(0.132150\pi\)
\(132\) 32.1541 2.79865
\(133\) 10.6309 0.921818
\(134\) 34.3970 2.97145
\(135\) −12.8234 −1.10366
\(136\) 25.5405 2.19008
\(137\) 16.3246 1.39470 0.697351 0.716730i \(-0.254362\pi\)
0.697351 + 0.716730i \(0.254362\pi\)
\(138\) −24.6220 −2.09596
\(139\) 2.61179 0.221529 0.110765 0.993847i \(-0.464670\pi\)
0.110765 + 0.993847i \(0.464670\pi\)
\(140\) 58.7994 4.96946
\(141\) 8.59266 0.723633
\(142\) −15.8799 −1.33261
\(143\) 2.62095 0.219175
\(144\) 4.30781 0.358985
\(145\) 19.9891 1.66001
\(146\) −25.0787 −2.07553
\(147\) 26.2540 2.16539
\(148\) −51.5777 −4.23966
\(149\) 2.53569 0.207732 0.103866 0.994591i \(-0.466879\pi\)
0.103866 + 0.994591i \(0.466879\pi\)
\(150\) −12.3749 −1.01041
\(151\) 11.1125 0.904320 0.452160 0.891937i \(-0.350654\pi\)
0.452160 + 0.891937i \(0.350654\pi\)
\(152\) −15.9621 −1.29470
\(153\) −1.89443 −0.153156
\(154\) −43.5298 −3.50773
\(155\) −9.66132 −0.776016
\(156\) 6.22944 0.498754
\(157\) −0.725607 −0.0579098 −0.0289549 0.999581i \(-0.509218\pi\)
−0.0289549 + 0.999581i \(0.509218\pi\)
\(158\) −3.08883 −0.245734
\(159\) 26.2766 2.08387
\(160\) −22.0505 −1.74324
\(161\) 23.3318 1.83880
\(162\) 26.5177 2.08343
\(163\) 24.5696 1.92444 0.962218 0.272281i \(-0.0877779\pi\)
0.962218 + 0.272281i \(0.0877779\pi\)
\(164\) −45.5164 −3.55423
\(165\) 18.9459 1.47494
\(166\) −24.7394 −1.92015
\(167\) −2.11436 −0.163614 −0.0818072 0.996648i \(-0.526069\pi\)
−0.0818072 + 0.996648i \(0.526069\pi\)
\(168\) −59.1125 −4.56063
\(169\) −12.4922 −0.960940
\(170\) 26.3395 2.02015
\(171\) 1.18397 0.0905404
\(172\) −4.94297 −0.376898
\(173\) −19.5009 −1.48262 −0.741312 0.671160i \(-0.765796\pi\)
−0.741312 + 0.671160i \(0.765796\pi\)
\(174\) −35.1720 −2.66638
\(175\) 11.7265 0.886437
\(176\) 31.0365 2.33947
\(177\) −3.19914 −0.240462
\(178\) −14.9197 −1.11828
\(179\) 13.6972 1.02377 0.511887 0.859053i \(-0.328947\pi\)
0.511887 + 0.859053i \(0.328947\pi\)
\(180\) 6.54851 0.488097
\(181\) −11.4379 −0.850172 −0.425086 0.905153i \(-0.639756\pi\)
−0.425086 + 0.905153i \(0.639756\pi\)
\(182\) −8.43334 −0.625121
\(183\) −20.6172 −1.52407
\(184\) −35.0323 −2.58261
\(185\) −30.3908 −2.23438
\(186\) 16.9997 1.24648
\(187\) −13.6488 −0.998102
\(188\) 21.3979 1.56060
\(189\) −21.3812 −1.55525
\(190\) −16.4615 −1.19424
\(191\) 2.87314 0.207893 0.103947 0.994583i \(-0.466853\pi\)
0.103947 + 0.994583i \(0.466853\pi\)
\(192\) 7.17879 0.518084
\(193\) −11.0309 −0.794022 −0.397011 0.917814i \(-0.629953\pi\)
−0.397011 + 0.917814i \(0.629953\pi\)
\(194\) 0.857932 0.0615959
\(195\) 3.67054 0.262852
\(196\) 65.3790 4.66993
\(197\) −5.51546 −0.392960 −0.196480 0.980508i \(-0.562951\pi\)
−0.196480 + 0.980508i \(0.562951\pi\)
\(198\) −4.84792 −0.344527
\(199\) −24.8527 −1.76176 −0.880882 0.473337i \(-0.843049\pi\)
−0.880882 + 0.473337i \(0.843049\pi\)
\(200\) −17.6071 −1.24501
\(201\) −24.9620 −1.76068
\(202\) 9.56343 0.672881
\(203\) 33.3290 2.33924
\(204\) −32.4404 −2.27128
\(205\) −26.8193 −1.87314
\(206\) −47.0500 −3.27813
\(207\) 2.59847 0.180606
\(208\) 6.01293 0.416922
\(209\) 8.53015 0.590043
\(210\) −60.9618 −4.20676
\(211\) 7.12974 0.490831 0.245416 0.969418i \(-0.421076\pi\)
0.245416 + 0.969418i \(0.421076\pi\)
\(212\) 65.4351 4.49410
\(213\) 11.5241 0.789617
\(214\) −5.06355 −0.346137
\(215\) −2.91252 −0.198632
\(216\) 32.1035 2.18437
\(217\) −16.1089 −1.09354
\(218\) −5.83151 −0.394960
\(219\) 18.1997 1.22982
\(220\) 47.1801 3.18088
\(221\) −2.64429 −0.177874
\(222\) 53.4744 3.58897
\(223\) −23.0869 −1.54602 −0.773008 0.634396i \(-0.781249\pi\)
−0.773008 + 0.634396i \(0.781249\pi\)
\(224\) −36.7660 −2.45653
\(225\) 1.30598 0.0870652
\(226\) 46.8139 3.11401
\(227\) 0.626585 0.0415879 0.0207939 0.999784i \(-0.493381\pi\)
0.0207939 + 0.999784i \(0.493381\pi\)
\(228\) 20.2743 1.34270
\(229\) −23.6709 −1.56422 −0.782109 0.623142i \(-0.785856\pi\)
−0.782109 + 0.623142i \(0.785856\pi\)
\(230\) −36.1282 −2.38222
\(231\) 31.5897 2.07845
\(232\) −50.0429 −3.28548
\(233\) −10.4120 −0.682114 −0.341057 0.940043i \(-0.610785\pi\)
−0.341057 + 0.940043i \(0.610785\pi\)
\(234\) −0.939223 −0.0613989
\(235\) 12.6081 0.822464
\(236\) −7.96665 −0.518585
\(237\) 2.24157 0.145606
\(238\) 43.9174 2.84674
\(239\) 12.5188 0.809776 0.404888 0.914366i \(-0.367311\pi\)
0.404888 + 0.914366i \(0.367311\pi\)
\(240\) 43.4655 2.80568
\(241\) −22.4684 −1.44732 −0.723658 0.690159i \(-0.757541\pi\)
−0.723658 + 0.690159i \(0.757541\pi\)
\(242\) −6.52781 −0.419623
\(243\) −5.25077 −0.336837
\(244\) −51.3419 −3.28683
\(245\) 38.5229 2.46114
\(246\) 47.1902 3.00874
\(247\) 1.65261 0.105153
\(248\) 24.1872 1.53589
\(249\) 17.9535 1.13775
\(250\) 17.3321 1.09618
\(251\) −18.3778 −1.15999 −0.579997 0.814618i \(-0.696946\pi\)
−0.579997 + 0.814618i \(0.696946\pi\)
\(252\) 10.9187 0.687814
\(253\) 18.7212 1.17699
\(254\) 25.7143 1.61346
\(255\) −19.1147 −1.19701
\(256\) −23.5389 −1.47118
\(257\) −31.8146 −1.98454 −0.992270 0.124099i \(-0.960396\pi\)
−0.992270 + 0.124099i \(0.960396\pi\)
\(258\) 5.12475 0.319053
\(259\) −50.6723 −3.14863
\(260\) 9.14054 0.566872
\(261\) 3.71186 0.229758
\(262\) −54.0801 −3.34108
\(263\) −11.9127 −0.734566 −0.367283 0.930109i \(-0.619712\pi\)
−0.367283 + 0.930109i \(0.619712\pi\)
\(264\) −47.4313 −2.91920
\(265\) 38.5560 2.36847
\(266\) −27.4472 −1.68289
\(267\) 10.8272 0.662616
\(268\) −62.1615 −3.79712
\(269\) −3.85198 −0.234859 −0.117430 0.993081i \(-0.537465\pi\)
−0.117430 + 0.993081i \(0.537465\pi\)
\(270\) 33.1078 2.01488
\(271\) 30.9797 1.88188 0.940940 0.338573i \(-0.109944\pi\)
0.940940 + 0.338573i \(0.109944\pi\)
\(272\) −31.3129 −1.89863
\(273\) 6.12009 0.370405
\(274\) −42.1472 −2.54620
\(275\) 9.40919 0.567396
\(276\) 44.4963 2.67836
\(277\) 9.15195 0.549888 0.274944 0.961460i \(-0.411341\pi\)
0.274944 + 0.961460i \(0.411341\pi\)
\(278\) −6.74319 −0.404430
\(279\) −1.79405 −0.107407
\(280\) −86.7366 −5.18351
\(281\) 2.60464 0.155380 0.0776900 0.996978i \(-0.475246\pi\)
0.0776900 + 0.996978i \(0.475246\pi\)
\(282\) −22.1847 −1.32108
\(283\) 12.6780 0.753627 0.376814 0.926289i \(-0.377020\pi\)
0.376814 + 0.926289i \(0.377020\pi\)
\(284\) 28.6978 1.70290
\(285\) 11.9461 0.707628
\(286\) −6.76683 −0.400131
\(287\) −44.7174 −2.63959
\(288\) −4.09464 −0.241279
\(289\) −3.22961 −0.189977
\(290\) −51.6084 −3.03055
\(291\) −0.622603 −0.0364977
\(292\) 45.3217 2.65225
\(293\) 3.50485 0.204756 0.102378 0.994746i \(-0.467355\pi\)
0.102378 + 0.994746i \(0.467355\pi\)
\(294\) −67.7832 −3.95320
\(295\) −4.69414 −0.273304
\(296\) 76.0836 4.42227
\(297\) −17.1561 −0.995497
\(298\) −6.54670 −0.379240
\(299\) 3.62700 0.209755
\(300\) 22.3636 1.29117
\(301\) −4.85621 −0.279907
\(302\) −28.6905 −1.65095
\(303\) −6.94021 −0.398705
\(304\) 19.5697 1.12240
\(305\) −30.2519 −1.73222
\(306\) 4.89110 0.279605
\(307\) −6.11552 −0.349031 −0.174516 0.984654i \(-0.555836\pi\)
−0.174516 + 0.984654i \(0.555836\pi\)
\(308\) 78.6661 4.48242
\(309\) 34.1443 1.94240
\(310\) 24.9438 1.41671
\(311\) −29.9333 −1.69736 −0.848680 0.528906i \(-0.822602\pi\)
−0.848680 + 0.528906i \(0.822602\pi\)
\(312\) −9.18921 −0.520236
\(313\) 12.8066 0.723872 0.361936 0.932203i \(-0.382116\pi\)
0.361936 + 0.932203i \(0.382116\pi\)
\(314\) 1.87339 0.105722
\(315\) 6.43357 0.362490
\(316\) 5.58206 0.314015
\(317\) −10.4285 −0.585724 −0.292862 0.956155i \(-0.594608\pi\)
−0.292862 + 0.956155i \(0.594608\pi\)
\(318\) −67.8415 −3.80436
\(319\) 26.7429 1.49731
\(320\) 10.5335 0.588842
\(321\) 3.67463 0.205098
\(322\) −60.2386 −3.35697
\(323\) −8.60611 −0.478857
\(324\) −47.9222 −2.66234
\(325\) 1.82291 0.101117
\(326\) −63.4343 −3.51330
\(327\) 4.23194 0.234027
\(328\) 67.1424 3.70732
\(329\) 21.0223 1.15900
\(330\) −48.9151 −2.69269
\(331\) 7.98352 0.438814 0.219407 0.975633i \(-0.429588\pi\)
0.219407 + 0.975633i \(0.429588\pi\)
\(332\) 44.7086 2.45370
\(333\) −5.64339 −0.309256
\(334\) 5.45891 0.298699
\(335\) −36.6271 −2.00115
\(336\) 72.4725 3.95370
\(337\) −11.2684 −0.613830 −0.306915 0.951737i \(-0.599297\pi\)
−0.306915 + 0.951737i \(0.599297\pi\)
\(338\) 32.2527 1.75432
\(339\) −33.9730 −1.84516
\(340\) −47.6002 −2.58149
\(341\) −12.9256 −0.699961
\(342\) −3.05680 −0.165293
\(343\) 32.1440 1.73561
\(344\) 7.29151 0.393132
\(345\) 26.2183 1.41155
\(346\) 50.3479 2.70672
\(347\) 6.57310 0.352862 0.176431 0.984313i \(-0.443545\pi\)
0.176431 + 0.984313i \(0.443545\pi\)
\(348\) 63.5621 3.40729
\(349\) 22.4225 1.20025 0.600125 0.799906i \(-0.295118\pi\)
0.600125 + 0.799906i \(0.295118\pi\)
\(350\) −30.2757 −1.61830
\(351\) −3.32377 −0.177410
\(352\) −29.5007 −1.57239
\(353\) −20.1950 −1.07487 −0.537436 0.843304i \(-0.680607\pi\)
−0.537436 + 0.843304i \(0.680607\pi\)
\(354\) 8.25962 0.438994
\(355\) 16.9095 0.897461
\(356\) 26.9625 1.42901
\(357\) −31.8710 −1.68679
\(358\) −35.3637 −1.86903
\(359\) −14.1975 −0.749317 −0.374658 0.927163i \(-0.622240\pi\)
−0.374658 + 0.927163i \(0.622240\pi\)
\(360\) −9.65988 −0.509120
\(361\) −13.6214 −0.716917
\(362\) 29.5307 1.55210
\(363\) 4.73725 0.248641
\(364\) 15.2405 0.798822
\(365\) 26.7046 1.39778
\(366\) 53.2299 2.78237
\(367\) 29.1992 1.52419 0.762094 0.647466i \(-0.224171\pi\)
0.762094 + 0.647466i \(0.224171\pi\)
\(368\) 42.9499 2.23892
\(369\) −4.98019 −0.259259
\(370\) 78.4637 4.07914
\(371\) 64.2866 3.33759
\(372\) −30.7214 −1.59283
\(373\) −13.3216 −0.689765 −0.344882 0.938646i \(-0.612081\pi\)
−0.344882 + 0.938646i \(0.612081\pi\)
\(374\) 35.2389 1.82216
\(375\) −12.5779 −0.649521
\(376\) −31.5645 −1.62782
\(377\) 5.18109 0.266840
\(378\) 55.2025 2.83931
\(379\) −11.8223 −0.607271 −0.303636 0.952788i \(-0.598201\pi\)
−0.303636 + 0.952788i \(0.598201\pi\)
\(380\) 29.7488 1.52608
\(381\) −18.6609 −0.956028
\(382\) −7.41796 −0.379536
\(383\) 13.8347 0.706920 0.353460 0.935450i \(-0.385005\pi\)
0.353460 + 0.935450i \(0.385005\pi\)
\(384\) 11.5212 0.587938
\(385\) 46.3520 2.36232
\(386\) 28.4799 1.44959
\(387\) −0.540838 −0.0274923
\(388\) −1.55044 −0.0787115
\(389\) −12.4510 −0.631290 −0.315645 0.948877i \(-0.602221\pi\)
−0.315645 + 0.948877i \(0.602221\pi\)
\(390\) −9.47668 −0.479870
\(391\) −18.8879 −0.955204
\(392\) −96.4423 −4.87107
\(393\) 39.2461 1.97970
\(394\) 14.2400 0.717399
\(395\) 3.28909 0.165492
\(396\) 8.76106 0.440260
\(397\) −11.0832 −0.556251 −0.278125 0.960545i \(-0.589713\pi\)
−0.278125 + 0.960545i \(0.589713\pi\)
\(398\) 64.1654 3.21632
\(399\) 19.9185 0.997171
\(400\) 21.5864 1.07932
\(401\) −17.3857 −0.868200 −0.434100 0.900865i \(-0.642934\pi\)
−0.434100 + 0.900865i \(0.642934\pi\)
\(402\) 64.4475 3.21435
\(403\) −2.50417 −0.124742
\(404\) −17.2828 −0.859853
\(405\) −28.2369 −1.40310
\(406\) −86.0496 −4.27057
\(407\) −40.6590 −2.01539
\(408\) 47.8537 2.36911
\(409\) 30.6973 1.51788 0.758941 0.651159i \(-0.225717\pi\)
0.758941 + 0.651159i \(0.225717\pi\)
\(410\) 69.2429 3.41966
\(411\) 30.5863 1.50871
\(412\) 85.0278 4.18902
\(413\) −7.82681 −0.385132
\(414\) −6.70879 −0.329719
\(415\) 26.3434 1.29314
\(416\) −5.71538 −0.280220
\(417\) 4.89355 0.239638
\(418\) −22.0234 −1.07720
\(419\) 29.0148 1.41747 0.708734 0.705476i \(-0.249267\pi\)
0.708734 + 0.705476i \(0.249267\pi\)
\(420\) 110.169 5.37568
\(421\) −13.9572 −0.680232 −0.340116 0.940383i \(-0.610466\pi\)
−0.340116 + 0.940383i \(0.610466\pi\)
\(422\) −18.4077 −0.896074
\(423\) 2.34126 0.113836
\(424\) −96.5251 −4.68768
\(425\) −9.49298 −0.460477
\(426\) −29.7532 −1.44155
\(427\) −50.4407 −2.44100
\(428\) 9.15074 0.442318
\(429\) 4.91070 0.237091
\(430\) 7.51962 0.362628
\(431\) 21.8494 1.05245 0.526225 0.850345i \(-0.323607\pi\)
0.526225 + 0.850345i \(0.323607\pi\)
\(432\) −39.3592 −1.89367
\(433\) −17.3546 −0.834010 −0.417005 0.908904i \(-0.636920\pi\)
−0.417005 + 0.908904i \(0.636920\pi\)
\(434\) 41.5903 1.99640
\(435\) 37.4523 1.79570
\(436\) 10.5386 0.504707
\(437\) 11.8044 0.564683
\(438\) −46.9884 −2.24519
\(439\) 8.49182 0.405292 0.202646 0.979252i \(-0.435046\pi\)
0.202646 + 0.979252i \(0.435046\pi\)
\(440\) −69.5966 −3.31789
\(441\) 7.15347 0.340641
\(442\) 6.82709 0.324731
\(443\) 4.30519 0.204546 0.102273 0.994756i \(-0.467389\pi\)
0.102273 + 0.994756i \(0.467389\pi\)
\(444\) −96.6378 −4.58623
\(445\) 15.8870 0.753114
\(446\) 59.6065 2.82245
\(447\) 4.75096 0.224713
\(448\) 17.5632 0.829782
\(449\) 14.8433 0.700499 0.350250 0.936656i \(-0.386097\pi\)
0.350250 + 0.936656i \(0.386097\pi\)
\(450\) −3.37181 −0.158949
\(451\) −35.8808 −1.68956
\(452\) −84.6011 −3.97930
\(453\) 20.8207 0.978243
\(454\) −1.61773 −0.0759239
\(455\) 8.98010 0.420994
\(456\) −29.9072 −1.40053
\(457\) 12.8672 0.601902 0.300951 0.953640i \(-0.402696\pi\)
0.300951 + 0.953640i \(0.402696\pi\)
\(458\) 61.1141 2.85568
\(459\) 17.3089 0.807908
\(460\) 65.2901 3.04417
\(461\) −40.2633 −1.87525 −0.937624 0.347651i \(-0.886979\pi\)
−0.937624 + 0.347651i \(0.886979\pi\)
\(462\) −81.5590 −3.79447
\(463\) −6.62642 −0.307956 −0.153978 0.988074i \(-0.549208\pi\)
−0.153978 + 0.988074i \(0.549208\pi\)
\(464\) 61.3530 2.84824
\(465\) −18.1018 −0.839451
\(466\) 26.8820 1.24528
\(467\) 5.82392 0.269499 0.134749 0.990880i \(-0.456977\pi\)
0.134749 + 0.990880i \(0.456977\pi\)
\(468\) 1.69734 0.0784597
\(469\) −61.0704 −2.81997
\(470\) −32.5520 −1.50151
\(471\) −1.35952 −0.0626436
\(472\) 11.7518 0.540921
\(473\) −3.89658 −0.179165
\(474\) −5.78734 −0.265821
\(475\) 5.93285 0.272218
\(476\) −79.3666 −3.63776
\(477\) 7.15962 0.327816
\(478\) −32.3214 −1.47835
\(479\) −34.0824 −1.55726 −0.778632 0.627480i \(-0.784086\pi\)
−0.778632 + 0.627480i \(0.784086\pi\)
\(480\) −41.3146 −1.88574
\(481\) −7.87716 −0.359168
\(482\) 58.0094 2.64226
\(483\) 43.7153 1.98912
\(484\) 11.7969 0.536223
\(485\) −0.913555 −0.0414824
\(486\) 13.5566 0.614939
\(487\) 36.6195 1.65939 0.829695 0.558218i \(-0.188515\pi\)
0.829695 + 0.558218i \(0.188515\pi\)
\(488\) 75.7358 3.42840
\(489\) 46.0344 2.08175
\(490\) −99.4593 −4.49311
\(491\) 11.1836 0.504710 0.252355 0.967635i \(-0.418795\pi\)
0.252355 + 0.967635i \(0.418795\pi\)
\(492\) −85.2811 −3.84477
\(493\) −26.9810 −1.21516
\(494\) −4.26674 −0.191970
\(495\) 5.16223 0.232025
\(496\) −29.6537 −1.33149
\(497\) 28.1941 1.26468
\(498\) −46.3527 −2.07711
\(499\) 22.7648 1.01909 0.509547 0.860443i \(-0.329813\pi\)
0.509547 + 0.860443i \(0.329813\pi\)
\(500\) −31.3221 −1.40077
\(501\) −3.96155 −0.176989
\(502\) 47.4482 2.11772
\(503\) 29.4992 1.31530 0.657651 0.753323i \(-0.271550\pi\)
0.657651 + 0.753323i \(0.271550\pi\)
\(504\) −16.1065 −0.717439
\(505\) −10.1835 −0.453158
\(506\) −48.3349 −2.14875
\(507\) −23.4059 −1.03949
\(508\) −46.4703 −2.06179
\(509\) −0.0808782 −0.00358486 −0.00179243 0.999998i \(-0.500571\pi\)
−0.00179243 + 0.999998i \(0.500571\pi\)
\(510\) 49.3507 2.18529
\(511\) 44.5262 1.96972
\(512\) 48.4750 2.14231
\(513\) −10.8176 −0.477607
\(514\) 82.1397 3.62303
\(515\) 50.1005 2.20769
\(516\) −9.26134 −0.407708
\(517\) 16.8681 0.741857
\(518\) 130.827 5.74821
\(519\) −36.5376 −1.60382
\(520\) −13.4835 −0.591289
\(521\) 41.1915 1.80463 0.902317 0.431074i \(-0.141865\pi\)
0.902317 + 0.431074i \(0.141865\pi\)
\(522\) −9.58337 −0.419453
\(523\) 2.12049 0.0927227 0.0463614 0.998925i \(-0.485237\pi\)
0.0463614 + 0.998925i \(0.485237\pi\)
\(524\) 97.7324 4.26946
\(525\) 21.9711 0.958898
\(526\) 30.7564 1.34104
\(527\) 13.0407 0.568062
\(528\) 58.1512 2.53071
\(529\) 2.90732 0.126405
\(530\) −99.5448 −4.32395
\(531\) −0.871674 −0.0378274
\(532\) 49.6020 2.15052
\(533\) −6.95145 −0.301101
\(534\) −27.9540 −1.20969
\(535\) 5.39184 0.233110
\(536\) 91.6961 3.96067
\(537\) 25.6635 1.10746
\(538\) 9.94513 0.428765
\(539\) 51.5387 2.21993
\(540\) −59.8317 −2.57475
\(541\) −3.88414 −0.166992 −0.0834962 0.996508i \(-0.526609\pi\)
−0.0834962 + 0.996508i \(0.526609\pi\)
\(542\) −79.9840 −3.43561
\(543\) −21.4305 −0.919669
\(544\) 29.7634 1.27610
\(545\) 6.20959 0.265990
\(546\) −15.8010 −0.676221
\(547\) −5.24979 −0.224465 −0.112233 0.993682i \(-0.535800\pi\)
−0.112233 + 0.993682i \(0.535800\pi\)
\(548\) 76.1674 3.25371
\(549\) −5.61759 −0.239753
\(550\) −24.2929 −1.03585
\(551\) 16.8624 0.718362
\(552\) −65.6377 −2.79373
\(553\) 5.48408 0.233207
\(554\) −23.6287 −1.00389
\(555\) −56.9413 −2.41702
\(556\) 12.1862 0.516808
\(557\) 14.9906 0.635174 0.317587 0.948229i \(-0.397127\pi\)
0.317587 + 0.948229i \(0.397127\pi\)
\(558\) 4.63192 0.196085
\(559\) −0.754912 −0.0319294
\(560\) 106.340 4.49368
\(561\) −25.5730 −1.07969
\(562\) −6.72473 −0.283666
\(563\) 16.4771 0.694429 0.347214 0.937786i \(-0.387128\pi\)
0.347214 + 0.937786i \(0.387128\pi\)
\(564\) 40.0918 1.68817
\(565\) −49.8490 −2.09716
\(566\) −32.7323 −1.37584
\(567\) −47.0811 −1.97722
\(568\) −42.3329 −1.77625
\(569\) −21.0167 −0.881068 −0.440534 0.897736i \(-0.645211\pi\)
−0.440534 + 0.897736i \(0.645211\pi\)
\(570\) −30.8428 −1.29186
\(571\) −15.8066 −0.661488 −0.330744 0.943721i \(-0.607300\pi\)
−0.330744 + 0.943721i \(0.607300\pi\)
\(572\) 12.2289 0.511315
\(573\) 5.38323 0.224888
\(574\) 115.453 4.81890
\(575\) 13.0209 0.543009
\(576\) 1.95601 0.0815006
\(577\) −8.21551 −0.342016 −0.171008 0.985270i \(-0.554702\pi\)
−0.171008 + 0.985270i \(0.554702\pi\)
\(578\) 8.33829 0.346827
\(579\) −20.6679 −0.858929
\(580\) 93.2655 3.87264
\(581\) 43.9238 1.82227
\(582\) 1.60745 0.0666311
\(583\) 51.5829 2.13635
\(584\) −66.8552 −2.76649
\(585\) 1.00012 0.0413497
\(586\) −9.04892 −0.373807
\(587\) 27.2374 1.12421 0.562105 0.827066i \(-0.309992\pi\)
0.562105 + 0.827066i \(0.309992\pi\)
\(588\) 122.496 5.05167
\(589\) −8.15008 −0.335818
\(590\) 12.1195 0.498950
\(591\) −10.3340 −0.425083
\(592\) −93.2791 −3.83375
\(593\) 17.8641 0.733589 0.366794 0.930302i \(-0.380455\pi\)
0.366794 + 0.930302i \(0.380455\pi\)
\(594\) 44.2940 1.81740
\(595\) −46.7647 −1.91717
\(596\) 11.8311 0.484619
\(597\) −46.5650 −1.90578
\(598\) −9.36427 −0.382933
\(599\) −2.09953 −0.0857846 −0.0428923 0.999080i \(-0.513657\pi\)
−0.0428923 + 0.999080i \(0.513657\pi\)
\(600\) −32.9892 −1.34678
\(601\) −1.28774 −0.0525280 −0.0262640 0.999655i \(-0.508361\pi\)
−0.0262640 + 0.999655i \(0.508361\pi\)
\(602\) 12.5379 0.511006
\(603\) −6.80143 −0.276976
\(604\) 51.8488 2.10970
\(605\) 6.95103 0.282600
\(606\) 17.9184 0.727885
\(607\) −27.6412 −1.12192 −0.560960 0.827843i \(-0.689568\pi\)
−0.560960 + 0.827843i \(0.689568\pi\)
\(608\) −18.6013 −0.754382
\(609\) 62.4464 2.53046
\(610\) 78.1051 3.16238
\(611\) 3.26797 0.132208
\(612\) −8.83908 −0.357299
\(613\) −38.8082 −1.56745 −0.783725 0.621108i \(-0.786683\pi\)
−0.783725 + 0.621108i \(0.786683\pi\)
\(614\) 15.7892 0.637200
\(615\) −50.2497 −2.02626
\(616\) −116.042 −4.67548
\(617\) −13.8383 −0.557109 −0.278554 0.960420i \(-0.589855\pi\)
−0.278554 + 0.960420i \(0.589855\pi\)
\(618\) −88.1547 −3.54610
\(619\) −21.4773 −0.863247 −0.431623 0.902054i \(-0.642059\pi\)
−0.431623 + 0.902054i \(0.642059\pi\)
\(620\) −45.0780 −1.81037
\(621\) −23.7414 −0.952710
\(622\) 77.2825 3.09874
\(623\) 26.4892 1.06127
\(624\) 11.2660 0.451003
\(625\) −31.2466 −1.24986
\(626\) −33.0644 −1.32152
\(627\) 15.9824 0.638276
\(628\) −3.38555 −0.135098
\(629\) 41.0211 1.63562
\(630\) −16.6103 −0.661772
\(631\) 13.3799 0.532644 0.266322 0.963884i \(-0.414191\pi\)
0.266322 + 0.963884i \(0.414191\pi\)
\(632\) −8.23425 −0.327541
\(633\) 13.3585 0.530954
\(634\) 26.9246 1.06931
\(635\) −27.3814 −1.08660
\(636\) 122.602 4.86147
\(637\) 9.98495 0.395618
\(638\) −69.0454 −2.73353
\(639\) 3.13999 0.124216
\(640\) 16.9052 0.668237
\(641\) −13.1260 −0.518447 −0.259223 0.965817i \(-0.583467\pi\)
−0.259223 + 0.965817i \(0.583467\pi\)
\(642\) −9.48725 −0.374432
\(643\) 6.15698 0.242808 0.121404 0.992603i \(-0.461260\pi\)
0.121404 + 0.992603i \(0.461260\pi\)
\(644\) 108.862 4.28976
\(645\) −5.45700 −0.214869
\(646\) 22.2195 0.874213
\(647\) −14.6103 −0.574390 −0.287195 0.957872i \(-0.592723\pi\)
−0.287195 + 0.957872i \(0.592723\pi\)
\(648\) 70.6913 2.77702
\(649\) −6.28016 −0.246518
\(650\) −4.70644 −0.184602
\(651\) −30.1822 −1.18293
\(652\) 114.637 4.48953
\(653\) 22.1990 0.868715 0.434357 0.900741i \(-0.356975\pi\)
0.434357 + 0.900741i \(0.356975\pi\)
\(654\) −10.9261 −0.427246
\(655\) 57.5863 2.25008
\(656\) −82.3172 −3.21395
\(657\) 4.95889 0.193465
\(658\) −54.2758 −2.11589
\(659\) −25.2871 −0.985044 −0.492522 0.870300i \(-0.663925\pi\)
−0.492522 + 0.870300i \(0.663925\pi\)
\(660\) 88.3983 3.44090
\(661\) 8.09077 0.314695 0.157347 0.987543i \(-0.449706\pi\)
0.157347 + 0.987543i \(0.449706\pi\)
\(662\) −20.6120 −0.801110
\(663\) −4.95443 −0.192414
\(664\) −65.9508 −2.55939
\(665\) 29.2267 1.13336
\(666\) 14.5702 0.564586
\(667\) 37.0081 1.43296
\(668\) −9.86523 −0.381697
\(669\) −43.2565 −1.67239
\(670\) 94.5647 3.65335
\(671\) −40.4731 −1.56245
\(672\) −68.8861 −2.65734
\(673\) 23.2076 0.894587 0.447293 0.894387i \(-0.352388\pi\)
0.447293 + 0.894387i \(0.352388\pi\)
\(674\) 29.0931 1.12062
\(675\) −11.9323 −0.459275
\(676\) −58.2864 −2.24179
\(677\) 10.9028 0.419028 0.209514 0.977806i \(-0.432812\pi\)
0.209514 + 0.977806i \(0.432812\pi\)
\(678\) 87.7122 3.36857
\(679\) −1.52322 −0.0584559
\(680\) 70.2164 2.69268
\(681\) 1.17399 0.0449875
\(682\) 33.3716 1.27787
\(683\) −44.3659 −1.69761 −0.848806 0.528704i \(-0.822678\pi\)
−0.848806 + 0.528704i \(0.822678\pi\)
\(684\) 5.52418 0.211222
\(685\) 44.8797 1.71477
\(686\) −82.9901 −3.16858
\(687\) −44.3507 −1.69208
\(688\) −8.93946 −0.340814
\(689\) 9.99353 0.380723
\(690\) −67.6911 −2.57696
\(691\) −25.9198 −0.986035 −0.493017 0.870019i \(-0.664106\pi\)
−0.493017 + 0.870019i \(0.664106\pi\)
\(692\) −90.9876 −3.45883
\(693\) 8.60729 0.326964
\(694\) −16.9706 −0.644194
\(695\) 7.18038 0.272367
\(696\) −93.7621 −3.55404
\(697\) 36.2004 1.37119
\(698\) −57.8910 −2.19121
\(699\) −19.5083 −0.737873
\(700\) 54.7135 2.06798
\(701\) −10.5159 −0.397180 −0.198590 0.980083i \(-0.563636\pi\)
−0.198590 + 0.980083i \(0.563636\pi\)
\(702\) 8.58139 0.323884
\(703\) −25.6370 −0.966919
\(704\) 14.0925 0.531132
\(705\) 23.6231 0.889696
\(706\) 52.1400 1.96231
\(707\) −16.9795 −0.638579
\(708\) −14.9266 −0.560976
\(709\) −49.7491 −1.86837 −0.934183 0.356793i \(-0.883870\pi\)
−0.934183 + 0.356793i \(0.883870\pi\)
\(710\) −43.6572 −1.63843
\(711\) 0.610764 0.0229054
\(712\) −39.7731 −1.49056
\(713\) −17.8871 −0.669876
\(714\) 82.2853 3.07945
\(715\) 7.20555 0.269472
\(716\) 63.9084 2.38837
\(717\) 23.4557 0.875971
\(718\) 36.6555 1.36797
\(719\) 18.2259 0.679710 0.339855 0.940478i \(-0.389622\pi\)
0.339855 + 0.940478i \(0.389622\pi\)
\(720\) 11.8431 0.441366
\(721\) 83.5354 3.11102
\(722\) 35.1681 1.30882
\(723\) −42.0976 −1.56563
\(724\) −53.3672 −1.98337
\(725\) 18.6001 0.690790
\(726\) −12.2307 −0.453925
\(727\) −22.2465 −0.825077 −0.412539 0.910940i \(-0.635358\pi\)
−0.412539 + 0.910940i \(0.635358\pi\)
\(728\) −22.4817 −0.833229
\(729\) 20.9747 0.776841
\(730\) −68.9467 −2.55183
\(731\) 3.93128 0.145404
\(732\) −96.1960 −3.55551
\(733\) 26.5229 0.979647 0.489824 0.871822i \(-0.337061\pi\)
0.489824 + 0.871822i \(0.337061\pi\)
\(734\) −75.3873 −2.78260
\(735\) 72.1779 2.66232
\(736\) −40.8245 −1.50481
\(737\) −49.0023 −1.80502
\(738\) 12.8580 0.473309
\(739\) −18.5361 −0.681863 −0.340932 0.940088i \(-0.610742\pi\)
−0.340932 + 0.940088i \(0.610742\pi\)
\(740\) −141.798 −5.21260
\(741\) 3.09638 0.113749
\(742\) −165.977 −6.09320
\(743\) 0.313050 0.0114847 0.00574235 0.999984i \(-0.498172\pi\)
0.00574235 + 0.999984i \(0.498172\pi\)
\(744\) 45.3180 1.66144
\(745\) 6.97115 0.255403
\(746\) 34.3940 1.25925
\(747\) 4.89181 0.178982
\(748\) −63.6830 −2.32848
\(749\) 8.99012 0.328492
\(750\) 32.4740 1.18578
\(751\) −30.2827 −1.10503 −0.552515 0.833503i \(-0.686332\pi\)
−0.552515 + 0.833503i \(0.686332\pi\)
\(752\) 38.6984 1.41119
\(753\) −34.4333 −1.25482
\(754\) −13.3767 −0.487149
\(755\) 30.5506 1.11185
\(756\) −99.7608 −3.62827
\(757\) 2.88608 0.104896 0.0524482 0.998624i \(-0.483298\pi\)
0.0524482 + 0.998624i \(0.483298\pi\)
\(758\) 30.5231 1.10865
\(759\) 35.0767 1.27321
\(760\) −43.8833 −1.59181
\(761\) 25.6050 0.928181 0.464090 0.885788i \(-0.346381\pi\)
0.464090 + 0.885788i \(0.346381\pi\)
\(762\) 48.1792 1.74535
\(763\) 10.3536 0.374826
\(764\) 13.4056 0.484996
\(765\) −5.20820 −0.188303
\(766\) −35.7188 −1.29057
\(767\) −1.21670 −0.0439325
\(768\) −44.1033 −1.59144
\(769\) 12.9019 0.465254 0.232627 0.972566i \(-0.425268\pi\)
0.232627 + 0.972566i \(0.425268\pi\)
\(770\) −119.673 −4.31270
\(771\) −59.6090 −2.14676
\(772\) −51.4682 −1.85238
\(773\) −26.8433 −0.965486 −0.482743 0.875762i \(-0.660359\pi\)
−0.482743 + 0.875762i \(0.660359\pi\)
\(774\) 1.39635 0.0501907
\(775\) −8.98996 −0.322929
\(776\) 2.28709 0.0821018
\(777\) −94.9415 −3.40601
\(778\) 32.1463 1.15250
\(779\) −22.6242 −0.810597
\(780\) 17.1260 0.613211
\(781\) 22.6227 0.809503
\(782\) 48.7653 1.74384
\(783\) −33.9141 −1.21199
\(784\) 118.239 4.22282
\(785\) −1.99485 −0.0711992
\(786\) −101.326 −3.61419
\(787\) −10.6432 −0.379388 −0.189694 0.981843i \(-0.560750\pi\)
−0.189694 + 0.981843i \(0.560750\pi\)
\(788\) −25.7341 −0.916741
\(789\) −22.3200 −0.794613
\(790\) −8.49184 −0.302126
\(791\) −83.1161 −2.95527
\(792\) −12.9237 −0.459223
\(793\) −7.84115 −0.278447
\(794\) 28.6149 1.01551
\(795\) 72.2399 2.56208
\(796\) −115.958 −4.11003
\(797\) 24.9106 0.882379 0.441189 0.897414i \(-0.354557\pi\)
0.441189 + 0.897414i \(0.354557\pi\)
\(798\) −51.4260 −1.82046
\(799\) −17.0183 −0.602063
\(800\) −20.5182 −0.725428
\(801\) 2.95011 0.104237
\(802\) 44.8868 1.58501
\(803\) 35.7274 1.26079
\(804\) −116.468 −4.10751
\(805\) 64.1441 2.26078
\(806\) 6.46533 0.227731
\(807\) −7.21721 −0.254058
\(808\) 25.4944 0.896889
\(809\) 9.70851 0.341333 0.170666 0.985329i \(-0.445408\pi\)
0.170666 + 0.985329i \(0.445408\pi\)
\(810\) 72.9028 2.56154
\(811\) 48.9866 1.72015 0.860076 0.510166i \(-0.170416\pi\)
0.860076 + 0.510166i \(0.170416\pi\)
\(812\) 155.507 5.45723
\(813\) 58.0446 2.03571
\(814\) 104.974 3.67935
\(815\) 67.5469 2.36607
\(816\) −58.6690 −2.05383
\(817\) −2.45694 −0.0859575
\(818\) −79.2550 −2.77109
\(819\) 1.66755 0.0582690
\(820\) −125.134 −4.36988
\(821\) 52.7951 1.84256 0.921281 0.388897i \(-0.127144\pi\)
0.921281 + 0.388897i \(0.127144\pi\)
\(822\) −78.9684 −2.75434
\(823\) 18.4765 0.644049 0.322024 0.946731i \(-0.395637\pi\)
0.322024 + 0.946731i \(0.395637\pi\)
\(824\) −125.427 −4.36945
\(825\) 17.6294 0.613777
\(826\) 20.2075 0.703107
\(827\) 14.8922 0.517851 0.258926 0.965897i \(-0.416632\pi\)
0.258926 + 0.965897i \(0.416632\pi\)
\(828\) 12.1240 0.421338
\(829\) −38.9566 −1.35302 −0.676510 0.736434i \(-0.736508\pi\)
−0.676510 + 0.736434i \(0.736508\pi\)
\(830\) −68.0139 −2.36080
\(831\) 17.1474 0.594838
\(832\) 2.73024 0.0946542
\(833\) −51.9976 −1.80161
\(834\) −12.6343 −0.437490
\(835\) −5.81284 −0.201161
\(836\) 39.8001 1.37652
\(837\) 16.3917 0.566579
\(838\) −74.9112 −2.58777
\(839\) 34.0858 1.17677 0.588387 0.808579i \(-0.299763\pi\)
0.588387 + 0.808579i \(0.299763\pi\)
\(840\) −162.513 −5.60723
\(841\) 23.8652 0.822940
\(842\) 36.0350 1.24185
\(843\) 4.88015 0.168081
\(844\) 33.2661 1.14506
\(845\) −34.3438 −1.18146
\(846\) −6.04471 −0.207821
\(847\) 11.5899 0.398232
\(848\) 118.341 4.06383
\(849\) 23.7539 0.815232
\(850\) 24.5092 0.840659
\(851\) −56.2659 −1.92877
\(852\) 53.7693 1.84211
\(853\) 15.4810 0.530060 0.265030 0.964240i \(-0.414618\pi\)
0.265030 + 0.964240i \(0.414618\pi\)
\(854\) 130.229 4.45635
\(855\) 3.25498 0.111318
\(856\) −13.4985 −0.461369
\(857\) 55.6474 1.90088 0.950440 0.310907i \(-0.100633\pi\)
0.950440 + 0.310907i \(0.100633\pi\)
\(858\) −12.6786 −0.432839
\(859\) 1.48731 0.0507465 0.0253732 0.999678i \(-0.491923\pi\)
0.0253732 + 0.999678i \(0.491923\pi\)
\(860\) −13.5893 −0.463391
\(861\) −83.7842 −2.85536
\(862\) −56.4114 −1.92138
\(863\) −1.15526 −0.0393255 −0.0196628 0.999807i \(-0.506259\pi\)
−0.0196628 + 0.999807i \(0.506259\pi\)
\(864\) 37.4115 1.27276
\(865\) −53.6121 −1.82287
\(866\) 44.8066 1.52259
\(867\) −6.05112 −0.205507
\(868\) −75.1611 −2.55113
\(869\) 4.40037 0.149272
\(870\) −96.6953 −3.27828
\(871\) −9.49357 −0.321677
\(872\) −15.5457 −0.526445
\(873\) −0.169642 −0.00574150
\(874\) −30.4770 −1.03090
\(875\) −30.7723 −1.04030
\(876\) 84.9163 2.86906
\(877\) −49.1255 −1.65885 −0.829424 0.558619i \(-0.811331\pi\)
−0.829424 + 0.558619i \(0.811331\pi\)
\(878\) −21.9244 −0.739912
\(879\) 6.56682 0.221493
\(880\) 85.3261 2.87634
\(881\) −19.5061 −0.657179 −0.328589 0.944473i \(-0.606573\pi\)
−0.328589 + 0.944473i \(0.606573\pi\)
\(882\) −18.4690 −0.621884
\(883\) −6.33877 −0.213317 −0.106658 0.994296i \(-0.534015\pi\)
−0.106658 + 0.994296i \(0.534015\pi\)
\(884\) −12.3378 −0.414964
\(885\) −8.79512 −0.295645
\(886\) −11.1152 −0.373424
\(887\) 49.0081 1.64553 0.822765 0.568382i \(-0.192430\pi\)
0.822765 + 0.568382i \(0.192430\pi\)
\(888\) 142.553 4.78376
\(889\) −45.6547 −1.53121
\(890\) −41.0173 −1.37490
\(891\) −37.7774 −1.26559
\(892\) −107.719 −3.60672
\(893\) 10.6360 0.355919
\(894\) −12.2661 −0.410241
\(895\) 37.6564 1.25871
\(896\) 28.1870 0.941662
\(897\) 6.79567 0.226901
\(898\) −38.3228 −1.27885
\(899\) −25.5513 −0.852184
\(900\) 6.09346 0.203115
\(901\) −52.0423 −1.73378
\(902\) 92.6380 3.08451
\(903\) −9.09878 −0.302788
\(904\) 124.797 4.15070
\(905\) −31.4452 −1.04527
\(906\) −53.7555 −1.78591
\(907\) 23.4597 0.778967 0.389483 0.921034i \(-0.372654\pi\)
0.389483 + 0.921034i \(0.372654\pi\)
\(908\) 2.92353 0.0970208
\(909\) −1.89101 −0.0627208
\(910\) −23.1850 −0.768577
\(911\) −8.73940 −0.289549 −0.144775 0.989465i \(-0.546246\pi\)
−0.144775 + 0.989465i \(0.546246\pi\)
\(912\) 36.6665 1.21415
\(913\) 35.2440 1.16641
\(914\) −33.2208 −1.09885
\(915\) −56.6810 −1.87382
\(916\) −110.444 −3.64918
\(917\) 96.0169 3.17076
\(918\) −44.6884 −1.47494
\(919\) −18.8856 −0.622980 −0.311490 0.950249i \(-0.600828\pi\)
−0.311490 + 0.950249i \(0.600828\pi\)
\(920\) −96.3112 −3.17529
\(921\) −11.4583 −0.377562
\(922\) 103.953 3.42350
\(923\) 4.38285 0.144263
\(924\) 147.392 4.84883
\(925\) −28.2790 −0.929807
\(926\) 17.1082 0.562212
\(927\) 9.30336 0.305562
\(928\) −58.3169 −1.91435
\(929\) −23.5243 −0.771808 −0.385904 0.922539i \(-0.626110\pi\)
−0.385904 + 0.922539i \(0.626110\pi\)
\(930\) 46.7357 1.53252
\(931\) 32.4971 1.06505
\(932\) −48.5806 −1.59131
\(933\) −56.0841 −1.83611
\(934\) −15.0363 −0.492004
\(935\) −37.5236 −1.22715
\(936\) −2.50380 −0.0818392
\(937\) 40.4819 1.32249 0.661244 0.750171i \(-0.270029\pi\)
0.661244 + 0.750171i \(0.270029\pi\)
\(938\) 157.673 5.14821
\(939\) 23.9949 0.783044
\(940\) 58.8273 1.91873
\(941\) −49.7853 −1.62295 −0.811477 0.584385i \(-0.801336\pi\)
−0.811477 + 0.584385i \(0.801336\pi\)
\(942\) 3.51005 0.114364
\(943\) −49.6536 −1.61695
\(944\) −14.4078 −0.468935
\(945\) −58.7815 −1.91216
\(946\) 10.0603 0.327088
\(947\) −35.6643 −1.15893 −0.579467 0.814996i \(-0.696739\pi\)
−0.579467 + 0.814996i \(0.696739\pi\)
\(948\) 10.4588 0.339684
\(949\) 6.92172 0.224689
\(950\) −15.3176 −0.496968
\(951\) −19.5392 −0.633603
\(952\) 117.076 3.79445
\(953\) 3.90283 0.126425 0.0632125 0.998000i \(-0.479865\pi\)
0.0632125 + 0.998000i \(0.479865\pi\)
\(954\) −18.4849 −0.598470
\(955\) 7.89889 0.255602
\(956\) 58.4106 1.88913
\(957\) 50.1064 1.61971
\(958\) 87.9948 2.84298
\(959\) 74.8305 2.41640
\(960\) 19.7360 0.636977
\(961\) −18.6503 −0.601623
\(962\) 20.3374 0.655705
\(963\) 1.00123 0.0322643
\(964\) −104.833 −3.37646
\(965\) −30.3263 −0.976238
\(966\) −112.865 −3.63138
\(967\) −14.9555 −0.480935 −0.240468 0.970657i \(-0.577301\pi\)
−0.240468 + 0.970657i \(0.577301\pi\)
\(968\) −17.4019 −0.559320
\(969\) −16.1247 −0.518001
\(970\) 2.35864 0.0757313
\(971\) −35.0620 −1.12519 −0.562597 0.826732i \(-0.690198\pi\)
−0.562597 + 0.826732i \(0.690198\pi\)
\(972\) −24.4992 −0.785811
\(973\) 11.9723 0.383813
\(974\) −94.5452 −3.02942
\(975\) 3.41547 0.109383
\(976\) −92.8527 −2.97214
\(977\) 38.5713 1.23400 0.617002 0.786961i \(-0.288347\pi\)
0.617002 + 0.786961i \(0.288347\pi\)
\(978\) −118.853 −3.80049
\(979\) 21.2547 0.679303
\(980\) 179.741 5.74161
\(981\) 1.15308 0.0368151
\(982\) −28.8742 −0.921412
\(983\) 0.342307 0.0109179 0.00545894 0.999985i \(-0.498262\pi\)
0.00545894 + 0.999985i \(0.498262\pi\)
\(984\) 125.800 4.01037
\(985\) −15.1632 −0.483139
\(986\) 69.6602 2.21843
\(987\) 39.3881 1.25374
\(988\) 7.71076 0.245312
\(989\) −5.39227 −0.171464
\(990\) −13.3280 −0.423591
\(991\) −31.6194 −1.00442 −0.502211 0.864745i \(-0.667480\pi\)
−0.502211 + 0.864745i \(0.667480\pi\)
\(992\) 28.1863 0.894915
\(993\) 14.9582 0.474684
\(994\) −72.7922 −2.30883
\(995\) −68.3254 −2.16606
\(996\) 83.7676 2.65428
\(997\) −55.8895 −1.77004 −0.885018 0.465556i \(-0.845854\pi\)
−0.885018 + 0.465556i \(0.845854\pi\)
\(998\) −58.7748 −1.86048
\(999\) 51.5619 1.63135
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 4027.2.a.c.1.7 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.7 174 1.1 even 1 trivial