Properties

Label 4029.2.a.l.1.2
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 1.2
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65510 q^{2} -1.00000 q^{3} +5.04957 q^{4} -3.36488 q^{5} +2.65510 q^{6} +2.92058 q^{7} -8.09693 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.65510 q^{2} -1.00000 q^{3} +5.04957 q^{4} -3.36488 q^{5} +2.65510 q^{6} +2.92058 q^{7} -8.09693 q^{8} +1.00000 q^{9} +8.93412 q^{10} +6.58118 q^{11} -5.04957 q^{12} -4.29464 q^{13} -7.75443 q^{14} +3.36488 q^{15} +11.3990 q^{16} -1.00000 q^{17} -2.65510 q^{18} -1.04245 q^{19} -16.9912 q^{20} -2.92058 q^{21} -17.4737 q^{22} -8.38753 q^{23} +8.09693 q^{24} +6.32245 q^{25} +11.4027 q^{26} -1.00000 q^{27} +14.7477 q^{28} -7.36681 q^{29} -8.93412 q^{30} +8.31935 q^{31} -14.0718 q^{32} -6.58118 q^{33} +2.65510 q^{34} -9.82740 q^{35} +5.04957 q^{36} +7.07631 q^{37} +2.76782 q^{38} +4.29464 q^{39} +27.2452 q^{40} +8.23725 q^{41} +7.75443 q^{42} +6.39224 q^{43} +33.2321 q^{44} -3.36488 q^{45} +22.2698 q^{46} +5.28278 q^{47} -11.3990 q^{48} +1.52977 q^{49} -16.7867 q^{50} +1.00000 q^{51} -21.6861 q^{52} +0.314028 q^{53} +2.65510 q^{54} -22.1449 q^{55} -23.6477 q^{56} +1.04245 q^{57} +19.5596 q^{58} +12.4816 q^{59} +16.9912 q^{60} -9.42298 q^{61} -22.0887 q^{62} +2.92058 q^{63} +14.5639 q^{64} +14.4510 q^{65} +17.4737 q^{66} +1.16403 q^{67} -5.04957 q^{68} +8.38753 q^{69} +26.0928 q^{70} -9.32796 q^{71} -8.09693 q^{72} -3.35625 q^{73} -18.7883 q^{74} -6.32245 q^{75} -5.26394 q^{76} +19.2208 q^{77} -11.4027 q^{78} +1.00000 q^{79} -38.3565 q^{80} +1.00000 q^{81} -21.8708 q^{82} -6.00075 q^{83} -14.7477 q^{84} +3.36488 q^{85} -16.9721 q^{86} +7.36681 q^{87} -53.2874 q^{88} -0.846116 q^{89} +8.93412 q^{90} -12.5428 q^{91} -42.3535 q^{92} -8.31935 q^{93} -14.0263 q^{94} +3.50773 q^{95} +14.0718 q^{96} +1.99768 q^{97} -4.06169 q^{98} +6.58118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65510 −1.87744 −0.938721 0.344679i \(-0.887988\pi\)
−0.938721 + 0.344679i \(0.887988\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.04957 2.52479
\(5\) −3.36488 −1.50482 −0.752411 0.658694i \(-0.771109\pi\)
−0.752411 + 0.658694i \(0.771109\pi\)
\(6\) 2.65510 1.08394
\(7\) 2.92058 1.10387 0.551937 0.833886i \(-0.313889\pi\)
0.551937 + 0.833886i \(0.313889\pi\)
\(8\) −8.09693 −2.86270
\(9\) 1.00000 0.333333
\(10\) 8.93412 2.82522
\(11\) 6.58118 1.98430 0.992150 0.125053i \(-0.0399102\pi\)
0.992150 + 0.125053i \(0.0399102\pi\)
\(12\) −5.04957 −1.45769
\(13\) −4.29464 −1.19112 −0.595560 0.803311i \(-0.703070\pi\)
−0.595560 + 0.803311i \(0.703070\pi\)
\(14\) −7.75443 −2.07246
\(15\) 3.36488 0.868809
\(16\) 11.3990 2.84976
\(17\) −1.00000 −0.242536
\(18\) −2.65510 −0.625814
\(19\) −1.04245 −0.239155 −0.119578 0.992825i \(-0.538154\pi\)
−0.119578 + 0.992825i \(0.538154\pi\)
\(20\) −16.9912 −3.79935
\(21\) −2.92058 −0.637322
\(22\) −17.4737 −3.72541
\(23\) −8.38753 −1.74892 −0.874461 0.485096i \(-0.838785\pi\)
−0.874461 + 0.485096i \(0.838785\pi\)
\(24\) 8.09693 1.65278
\(25\) 6.32245 1.26449
\(26\) 11.4027 2.23626
\(27\) −1.00000 −0.192450
\(28\) 14.7477 2.78705
\(29\) −7.36681 −1.36798 −0.683991 0.729490i \(-0.739757\pi\)
−0.683991 + 0.729490i \(0.739757\pi\)
\(30\) −8.93412 −1.63114
\(31\) 8.31935 1.49420 0.747100 0.664712i \(-0.231446\pi\)
0.747100 + 0.664712i \(0.231446\pi\)
\(32\) −14.0718 −2.48756
\(33\) −6.58118 −1.14564
\(34\) 2.65510 0.455346
\(35\) −9.82740 −1.66113
\(36\) 5.04957 0.841596
\(37\) 7.07631 1.16334 0.581669 0.813426i \(-0.302400\pi\)
0.581669 + 0.813426i \(0.302400\pi\)
\(38\) 2.76782 0.449000
\(39\) 4.29464 0.687693
\(40\) 27.2452 4.30785
\(41\) 8.23725 1.28644 0.643221 0.765680i \(-0.277598\pi\)
0.643221 + 0.765680i \(0.277598\pi\)
\(42\) 7.75443 1.19653
\(43\) 6.39224 0.974808 0.487404 0.873177i \(-0.337944\pi\)
0.487404 + 0.873177i \(0.337944\pi\)
\(44\) 33.2321 5.00993
\(45\) −3.36488 −0.501607
\(46\) 22.2698 3.28350
\(47\) 5.28278 0.770572 0.385286 0.922797i \(-0.374103\pi\)
0.385286 + 0.922797i \(0.374103\pi\)
\(48\) −11.3990 −1.64531
\(49\) 1.52977 0.218538
\(50\) −16.7867 −2.37400
\(51\) 1.00000 0.140028
\(52\) −21.6861 −3.00732
\(53\) 0.314028 0.0431350 0.0215675 0.999767i \(-0.493134\pi\)
0.0215675 + 0.999767i \(0.493134\pi\)
\(54\) 2.65510 0.361314
\(55\) −22.1449 −2.98602
\(56\) −23.6477 −3.16006
\(57\) 1.04245 0.138076
\(58\) 19.5596 2.56831
\(59\) 12.4816 1.62496 0.812482 0.582987i \(-0.198116\pi\)
0.812482 + 0.582987i \(0.198116\pi\)
\(60\) 16.9912 2.19356
\(61\) −9.42298 −1.20649 −0.603245 0.797556i \(-0.706126\pi\)
−0.603245 + 0.797556i \(0.706126\pi\)
\(62\) −22.0887 −2.80527
\(63\) 2.92058 0.367958
\(64\) 14.5639 1.82049
\(65\) 14.4510 1.79242
\(66\) 17.4737 2.15086
\(67\) 1.16403 0.142208 0.0711041 0.997469i \(-0.477348\pi\)
0.0711041 + 0.997469i \(0.477348\pi\)
\(68\) −5.04957 −0.612351
\(69\) 8.38753 1.00974
\(70\) 26.0928 3.11868
\(71\) −9.32796 −1.10702 −0.553512 0.832841i \(-0.686713\pi\)
−0.553512 + 0.832841i \(0.686713\pi\)
\(72\) −8.09693 −0.954233
\(73\) −3.35625 −0.392819 −0.196409 0.980522i \(-0.562928\pi\)
−0.196409 + 0.980522i \(0.562928\pi\)
\(74\) −18.7883 −2.18410
\(75\) −6.32245 −0.730053
\(76\) −5.26394 −0.603815
\(77\) 19.2208 2.19042
\(78\) −11.4027 −1.29110
\(79\) 1.00000 0.112509
\(80\) −38.3565 −4.28838
\(81\) 1.00000 0.111111
\(82\) −21.8708 −2.41522
\(83\) −6.00075 −0.658668 −0.329334 0.944213i \(-0.606824\pi\)
−0.329334 + 0.944213i \(0.606824\pi\)
\(84\) −14.7477 −1.60910
\(85\) 3.36488 0.364973
\(86\) −16.9721 −1.83014
\(87\) 7.36681 0.789805
\(88\) −53.2874 −5.68045
\(89\) −0.846116 −0.0896881 −0.0448440 0.998994i \(-0.514279\pi\)
−0.0448440 + 0.998994i \(0.514279\pi\)
\(90\) 8.93412 0.941738
\(91\) −12.5428 −1.31485
\(92\) −42.3535 −4.41565
\(93\) −8.31935 −0.862677
\(94\) −14.0263 −1.44670
\(95\) 3.50773 0.359886
\(96\) 14.0718 1.43619
\(97\) 1.99768 0.202833 0.101417 0.994844i \(-0.467662\pi\)
0.101417 + 0.994844i \(0.467662\pi\)
\(98\) −4.06169 −0.410293
\(99\) 6.58118 0.661433
\(100\) 31.9257 3.19257
\(101\) −1.00288 −0.0997907 −0.0498954 0.998754i \(-0.515889\pi\)
−0.0498954 + 0.998754i \(0.515889\pi\)
\(102\) −2.65510 −0.262894
\(103\) −5.50565 −0.542488 −0.271244 0.962511i \(-0.587435\pi\)
−0.271244 + 0.962511i \(0.587435\pi\)
\(104\) 34.7734 3.40981
\(105\) 9.82740 0.959056
\(106\) −0.833776 −0.0809835
\(107\) −2.49209 −0.240920 −0.120460 0.992718i \(-0.538437\pi\)
−0.120460 + 0.992718i \(0.538437\pi\)
\(108\) −5.04957 −0.485895
\(109\) 8.18412 0.783897 0.391948 0.919987i \(-0.371801\pi\)
0.391948 + 0.919987i \(0.371801\pi\)
\(110\) 58.7970 5.60607
\(111\) −7.07631 −0.671653
\(112\) 33.2918 3.14578
\(113\) −15.5682 −1.46453 −0.732266 0.681018i \(-0.761537\pi\)
−0.732266 + 0.681018i \(0.761537\pi\)
\(114\) −2.76782 −0.259230
\(115\) 28.2231 2.63182
\(116\) −37.1992 −3.45386
\(117\) −4.29464 −0.397040
\(118\) −33.1399 −3.05077
\(119\) −2.92058 −0.267729
\(120\) −27.2452 −2.48714
\(121\) 32.3119 2.93745
\(122\) 25.0190 2.26511
\(123\) −8.23725 −0.742728
\(124\) 42.0092 3.77254
\(125\) −4.44988 −0.398009
\(126\) −7.75443 −0.690820
\(127\) −13.3078 −1.18088 −0.590438 0.807083i \(-0.701045\pi\)
−0.590438 + 0.807083i \(0.701045\pi\)
\(128\) −10.5252 −0.930303
\(129\) −6.39224 −0.562806
\(130\) −38.3688 −3.36517
\(131\) 4.45114 0.388898 0.194449 0.980913i \(-0.437708\pi\)
0.194449 + 0.980913i \(0.437708\pi\)
\(132\) −33.2321 −2.89249
\(133\) −3.04456 −0.263997
\(134\) −3.09061 −0.266988
\(135\) 3.36488 0.289603
\(136\) 8.09693 0.694306
\(137\) −10.9602 −0.936394 −0.468197 0.883624i \(-0.655096\pi\)
−0.468197 + 0.883624i \(0.655096\pi\)
\(138\) −22.2698 −1.89573
\(139\) 4.74131 0.402153 0.201076 0.979576i \(-0.435556\pi\)
0.201076 + 0.979576i \(0.435556\pi\)
\(140\) −49.6242 −4.19401
\(141\) −5.28278 −0.444890
\(142\) 24.7667 2.07837
\(143\) −28.2638 −2.36354
\(144\) 11.3990 0.949920
\(145\) 24.7885 2.05857
\(146\) 8.91118 0.737494
\(147\) −1.52977 −0.126173
\(148\) 35.7323 2.93718
\(149\) 14.1244 1.15712 0.578558 0.815641i \(-0.303616\pi\)
0.578558 + 0.815641i \(0.303616\pi\)
\(150\) 16.7867 1.37063
\(151\) −19.7812 −1.60977 −0.804884 0.593432i \(-0.797772\pi\)
−0.804884 + 0.593432i \(0.797772\pi\)
\(152\) 8.44067 0.684629
\(153\) −1.00000 −0.0808452
\(154\) −51.0333 −4.11238
\(155\) −27.9937 −2.24851
\(156\) 21.6861 1.73628
\(157\) −15.2035 −1.21337 −0.606685 0.794942i \(-0.707501\pi\)
−0.606685 + 0.794942i \(0.707501\pi\)
\(158\) −2.65510 −0.211229
\(159\) −0.314028 −0.0249040
\(160\) 47.3499 3.74334
\(161\) −24.4964 −1.93059
\(162\) −2.65510 −0.208605
\(163\) −14.2436 −1.11564 −0.557821 0.829961i \(-0.688363\pi\)
−0.557821 + 0.829961i \(0.688363\pi\)
\(164\) 41.5946 3.24799
\(165\) 22.1449 1.72398
\(166\) 15.9326 1.23661
\(167\) 13.6600 1.05704 0.528522 0.848919i \(-0.322746\pi\)
0.528522 + 0.848919i \(0.322746\pi\)
\(168\) 23.6477 1.82446
\(169\) 5.44394 0.418765
\(170\) −8.93412 −0.685215
\(171\) −1.04245 −0.0797184
\(172\) 32.2781 2.46118
\(173\) 21.3641 1.62428 0.812142 0.583460i \(-0.198302\pi\)
0.812142 + 0.583460i \(0.198302\pi\)
\(174\) −19.5596 −1.48281
\(175\) 18.4652 1.39584
\(176\) 75.0191 5.65478
\(177\) −12.4816 −0.938173
\(178\) 2.24652 0.168384
\(179\) 14.5126 1.08472 0.542360 0.840146i \(-0.317531\pi\)
0.542360 + 0.840146i \(0.317531\pi\)
\(180\) −16.9912 −1.26645
\(181\) 3.80550 0.282861 0.141430 0.989948i \(-0.454830\pi\)
0.141430 + 0.989948i \(0.454830\pi\)
\(182\) 33.3025 2.46855
\(183\) 9.42298 0.696567
\(184\) 67.9133 5.00663
\(185\) −23.8110 −1.75062
\(186\) 22.0887 1.61963
\(187\) −6.58118 −0.481263
\(188\) 26.6758 1.94553
\(189\) −2.92058 −0.212441
\(190\) −9.31339 −0.675665
\(191\) −12.1174 −0.876785 −0.438392 0.898784i \(-0.644452\pi\)
−0.438392 + 0.898784i \(0.644452\pi\)
\(192\) −14.5639 −1.05106
\(193\) 19.5362 1.40625 0.703124 0.711067i \(-0.251788\pi\)
0.703124 + 0.711067i \(0.251788\pi\)
\(194\) −5.30404 −0.380808
\(195\) −14.4510 −1.03486
\(196\) 7.72467 0.551762
\(197\) 18.7785 1.33792 0.668958 0.743300i \(-0.266741\pi\)
0.668958 + 0.743300i \(0.266741\pi\)
\(198\) −17.4737 −1.24180
\(199\) −16.7373 −1.18647 −0.593237 0.805028i \(-0.702150\pi\)
−0.593237 + 0.805028i \(0.702150\pi\)
\(200\) −51.1924 −3.61985
\(201\) −1.16403 −0.0821040
\(202\) 2.66276 0.187351
\(203\) −21.5153 −1.51008
\(204\) 5.04957 0.353541
\(205\) −27.7174 −1.93587
\(206\) 14.6181 1.01849
\(207\) −8.38753 −0.582974
\(208\) −48.9548 −3.39440
\(209\) −6.86057 −0.474555
\(210\) −26.0928 −1.80057
\(211\) 8.19938 0.564468 0.282234 0.959346i \(-0.408924\pi\)
0.282234 + 0.959346i \(0.408924\pi\)
\(212\) 1.58571 0.108907
\(213\) 9.32796 0.639141
\(214\) 6.61676 0.452313
\(215\) −21.5092 −1.46691
\(216\) 8.09693 0.550926
\(217\) 24.2973 1.64941
\(218\) −21.7297 −1.47172
\(219\) 3.35625 0.226794
\(220\) −111.822 −7.53906
\(221\) 4.29464 0.288889
\(222\) 18.7883 1.26099
\(223\) 7.62776 0.510793 0.255396 0.966836i \(-0.417794\pi\)
0.255396 + 0.966836i \(0.417794\pi\)
\(224\) −41.0977 −2.74595
\(225\) 6.32245 0.421496
\(226\) 41.3352 2.74957
\(227\) 23.9586 1.59019 0.795094 0.606487i \(-0.207422\pi\)
0.795094 + 0.606487i \(0.207422\pi\)
\(228\) 5.26394 0.348613
\(229\) 0.919568 0.0607668 0.0303834 0.999538i \(-0.490327\pi\)
0.0303834 + 0.999538i \(0.490327\pi\)
\(230\) −74.9352 −4.94108
\(231\) −19.2208 −1.26464
\(232\) 59.6485 3.91612
\(233\) −28.1339 −1.84311 −0.921556 0.388246i \(-0.873081\pi\)
−0.921556 + 0.388246i \(0.873081\pi\)
\(234\) 11.4027 0.745419
\(235\) −17.7759 −1.15957
\(236\) 63.0267 4.10269
\(237\) −1.00000 −0.0649570
\(238\) 7.75443 0.502645
\(239\) −24.5036 −1.58501 −0.792504 0.609867i \(-0.791223\pi\)
−0.792504 + 0.609867i \(0.791223\pi\)
\(240\) 38.3565 2.47590
\(241\) −1.08480 −0.0698781 −0.0349391 0.999389i \(-0.511124\pi\)
−0.0349391 + 0.999389i \(0.511124\pi\)
\(242\) −85.7915 −5.51488
\(243\) −1.00000 −0.0641500
\(244\) −47.5820 −3.04613
\(245\) −5.14749 −0.328861
\(246\) 21.8708 1.39443
\(247\) 4.47696 0.284862
\(248\) −67.3612 −4.27744
\(249\) 6.00075 0.380282
\(250\) 11.8149 0.747239
\(251\) −5.96177 −0.376303 −0.188152 0.982140i \(-0.560250\pi\)
−0.188152 + 0.982140i \(0.560250\pi\)
\(252\) 14.7477 0.929016
\(253\) −55.1999 −3.47038
\(254\) 35.3336 2.21703
\(255\) −3.36488 −0.210717
\(256\) −1.18242 −0.0739016
\(257\) 16.0042 0.998311 0.499156 0.866512i \(-0.333644\pi\)
0.499156 + 0.866512i \(0.333644\pi\)
\(258\) 16.9721 1.05663
\(259\) 20.6669 1.28418
\(260\) 72.9712 4.52548
\(261\) −7.36681 −0.455994
\(262\) −11.8182 −0.730133
\(263\) −15.8490 −0.977294 −0.488647 0.872482i \(-0.662509\pi\)
−0.488647 + 0.872482i \(0.662509\pi\)
\(264\) 53.2874 3.27961
\(265\) −1.05667 −0.0649105
\(266\) 8.08363 0.495639
\(267\) 0.846116 0.0517814
\(268\) 5.87783 0.359046
\(269\) 17.2651 1.05267 0.526337 0.850276i \(-0.323565\pi\)
0.526337 + 0.850276i \(0.323565\pi\)
\(270\) −8.93412 −0.543713
\(271\) 1.79677 0.109146 0.0545731 0.998510i \(-0.482620\pi\)
0.0545731 + 0.998510i \(0.482620\pi\)
\(272\) −11.3990 −0.691168
\(273\) 12.5428 0.759127
\(274\) 29.1005 1.75802
\(275\) 41.6092 2.50913
\(276\) 42.3535 2.54938
\(277\) 20.6950 1.24344 0.621720 0.783240i \(-0.286434\pi\)
0.621720 + 0.783240i \(0.286434\pi\)
\(278\) −12.5887 −0.755018
\(279\) 8.31935 0.498067
\(280\) 79.5718 4.75532
\(281\) 17.7871 1.06109 0.530545 0.847657i \(-0.321987\pi\)
0.530545 + 0.847657i \(0.321987\pi\)
\(282\) 14.0263 0.835255
\(283\) 7.33028 0.435740 0.217870 0.975978i \(-0.430089\pi\)
0.217870 + 0.975978i \(0.430089\pi\)
\(284\) −47.1022 −2.79500
\(285\) −3.50773 −0.207780
\(286\) 75.0433 4.43740
\(287\) 24.0575 1.42007
\(288\) −14.0718 −0.829187
\(289\) 1.00000 0.0588235
\(290\) −65.8159 −3.86484
\(291\) −1.99768 −0.117106
\(292\) −16.9476 −0.991784
\(293\) 12.7741 0.746272 0.373136 0.927777i \(-0.378282\pi\)
0.373136 + 0.927777i \(0.378282\pi\)
\(294\) 4.06169 0.236883
\(295\) −41.9991 −2.44528
\(296\) −57.2964 −3.33028
\(297\) −6.58118 −0.381879
\(298\) −37.5017 −2.17242
\(299\) 36.0214 2.08317
\(300\) −31.9257 −1.84323
\(301\) 18.6690 1.07607
\(302\) 52.5210 3.02225
\(303\) 1.00288 0.0576142
\(304\) −11.8830 −0.681535
\(305\) 31.7072 1.81555
\(306\) 2.65510 0.151782
\(307\) 19.4378 1.10937 0.554687 0.832059i \(-0.312838\pi\)
0.554687 + 0.832059i \(0.312838\pi\)
\(308\) 97.0570 5.53034
\(309\) 5.50565 0.313205
\(310\) 74.3261 4.22144
\(311\) 2.49362 0.141400 0.0707001 0.997498i \(-0.477477\pi\)
0.0707001 + 0.997498i \(0.477477\pi\)
\(312\) −34.7734 −1.96866
\(313\) −5.46325 −0.308801 −0.154401 0.988008i \(-0.549345\pi\)
−0.154401 + 0.988008i \(0.549345\pi\)
\(314\) 40.3668 2.27803
\(315\) −9.82740 −0.553711
\(316\) 5.04957 0.284061
\(317\) 8.53332 0.479279 0.239639 0.970862i \(-0.422971\pi\)
0.239639 + 0.970862i \(0.422971\pi\)
\(318\) 0.833776 0.0467558
\(319\) −48.4823 −2.71449
\(320\) −49.0059 −2.73951
\(321\) 2.49209 0.139095
\(322\) 65.0406 3.62457
\(323\) 1.04245 0.0580036
\(324\) 5.04957 0.280532
\(325\) −27.1526 −1.50616
\(326\) 37.8182 2.09455
\(327\) −8.18412 −0.452583
\(328\) −66.6965 −3.68270
\(329\) 15.4288 0.850615
\(330\) −58.7970 −3.23667
\(331\) −9.15171 −0.503023 −0.251512 0.967854i \(-0.580928\pi\)
−0.251512 + 0.967854i \(0.580928\pi\)
\(332\) −30.3012 −1.66300
\(333\) 7.07631 0.387779
\(334\) −36.2688 −1.98454
\(335\) −3.91681 −0.213998
\(336\) −33.2918 −1.81622
\(337\) −22.5816 −1.23010 −0.615050 0.788488i \(-0.710864\pi\)
−0.615050 + 0.788488i \(0.710864\pi\)
\(338\) −14.4542 −0.786207
\(339\) 15.5682 0.845548
\(340\) 16.9912 0.921479
\(341\) 54.7512 2.96494
\(342\) 2.76782 0.149667
\(343\) −15.9762 −0.862635
\(344\) −51.7576 −2.79058
\(345\) −28.2231 −1.51948
\(346\) −56.7239 −3.04950
\(347\) −19.8752 −1.06696 −0.533478 0.845814i \(-0.679115\pi\)
−0.533478 + 0.845814i \(0.679115\pi\)
\(348\) 37.1992 1.99409
\(349\) −6.31241 −0.337895 −0.168948 0.985625i \(-0.554037\pi\)
−0.168948 + 0.985625i \(0.554037\pi\)
\(350\) −49.0270 −2.62060
\(351\) 4.29464 0.229231
\(352\) −92.6088 −4.93607
\(353\) 8.21038 0.436995 0.218497 0.975838i \(-0.429885\pi\)
0.218497 + 0.975838i \(0.429885\pi\)
\(354\) 33.1399 1.76137
\(355\) 31.3875 1.66588
\(356\) −4.27252 −0.226443
\(357\) 2.92058 0.154573
\(358\) −38.5323 −2.03650
\(359\) 10.2711 0.542087 0.271043 0.962567i \(-0.412631\pi\)
0.271043 + 0.962567i \(0.412631\pi\)
\(360\) 27.2452 1.43595
\(361\) −17.9133 −0.942805
\(362\) −10.1040 −0.531054
\(363\) −32.3119 −1.69594
\(364\) −63.3359 −3.31970
\(365\) 11.2934 0.591122
\(366\) −25.0190 −1.30776
\(367\) 23.1479 1.20831 0.604156 0.796866i \(-0.293510\pi\)
0.604156 + 0.796866i \(0.293510\pi\)
\(368\) −95.6098 −4.98401
\(369\) 8.23725 0.428814
\(370\) 63.2205 3.28668
\(371\) 0.917142 0.0476156
\(372\) −42.0092 −2.17807
\(373\) 13.2727 0.687237 0.343618 0.939109i \(-0.388347\pi\)
0.343618 + 0.939109i \(0.388347\pi\)
\(374\) 17.4737 0.903544
\(375\) 4.44988 0.229791
\(376\) −42.7743 −2.20592
\(377\) 31.6378 1.62943
\(378\) 7.75443 0.398845
\(379\) −21.5358 −1.10622 −0.553109 0.833109i \(-0.686559\pi\)
−0.553109 + 0.833109i \(0.686559\pi\)
\(380\) 17.7126 0.908635
\(381\) 13.3078 0.681779
\(382\) 32.1730 1.64611
\(383\) 2.53977 0.129776 0.0648881 0.997893i \(-0.479331\pi\)
0.0648881 + 0.997893i \(0.479331\pi\)
\(384\) 10.5252 0.537110
\(385\) −64.6759 −3.29619
\(386\) −51.8707 −2.64015
\(387\) 6.39224 0.324936
\(388\) 10.0874 0.512111
\(389\) 2.85208 0.144606 0.0723030 0.997383i \(-0.476965\pi\)
0.0723030 + 0.997383i \(0.476965\pi\)
\(390\) 38.3688 1.94288
\(391\) 8.38753 0.424176
\(392\) −12.3864 −0.625609
\(393\) −4.45114 −0.224530
\(394\) −49.8590 −2.51186
\(395\) −3.36488 −0.169306
\(396\) 33.2321 1.66998
\(397\) 29.2386 1.46744 0.733722 0.679450i \(-0.237782\pi\)
0.733722 + 0.679450i \(0.237782\pi\)
\(398\) 44.4392 2.22754
\(399\) 3.04456 0.152419
\(400\) 72.0698 3.60349
\(401\) 9.36875 0.467853 0.233926 0.972254i \(-0.424843\pi\)
0.233926 + 0.972254i \(0.424843\pi\)
\(402\) 3.09061 0.154145
\(403\) −35.7286 −1.77977
\(404\) −5.06414 −0.251950
\(405\) −3.36488 −0.167202
\(406\) 57.1254 2.83509
\(407\) 46.5704 2.30841
\(408\) −8.09693 −0.400858
\(409\) 31.7885 1.57184 0.785920 0.618329i \(-0.212190\pi\)
0.785920 + 0.618329i \(0.212190\pi\)
\(410\) 73.5926 3.63448
\(411\) 10.9602 0.540627
\(412\) −27.8012 −1.36967
\(413\) 36.4534 1.79376
\(414\) 22.2698 1.09450
\(415\) 20.1918 0.991178
\(416\) 60.4332 2.96298
\(417\) −4.74131 −0.232183
\(418\) 18.2155 0.890950
\(419\) 24.8895 1.21593 0.607966 0.793963i \(-0.291986\pi\)
0.607966 + 0.793963i \(0.291986\pi\)
\(420\) 49.6242 2.42141
\(421\) −31.0362 −1.51261 −0.756306 0.654218i \(-0.772998\pi\)
−0.756306 + 0.654218i \(0.772998\pi\)
\(422\) −21.7702 −1.05976
\(423\) 5.28278 0.256857
\(424\) −2.54266 −0.123483
\(425\) −6.32245 −0.306684
\(426\) −24.7667 −1.19995
\(427\) −27.5205 −1.33181
\(428\) −12.5840 −0.608271
\(429\) 28.2638 1.36459
\(430\) 57.1090 2.75404
\(431\) −31.8529 −1.53430 −0.767151 0.641467i \(-0.778326\pi\)
−0.767151 + 0.641467i \(0.778326\pi\)
\(432\) −11.3990 −0.548437
\(433\) 14.8952 0.715820 0.357910 0.933756i \(-0.383490\pi\)
0.357910 + 0.933756i \(0.383490\pi\)
\(434\) −64.5119 −3.09667
\(435\) −24.7885 −1.18852
\(436\) 41.3263 1.97917
\(437\) 8.74361 0.418263
\(438\) −8.91118 −0.425793
\(439\) −0.624805 −0.0298203 −0.0149102 0.999889i \(-0.504746\pi\)
−0.0149102 + 0.999889i \(0.504746\pi\)
\(440\) 179.306 8.54807
\(441\) 1.52977 0.0728461
\(442\) −11.4027 −0.542372
\(443\) 2.41810 0.114888 0.0574438 0.998349i \(-0.481705\pi\)
0.0574438 + 0.998349i \(0.481705\pi\)
\(444\) −35.7323 −1.69578
\(445\) 2.84708 0.134965
\(446\) −20.2525 −0.958983
\(447\) −14.1244 −0.668061
\(448\) 42.5350 2.00959
\(449\) 11.1299 0.525254 0.262627 0.964897i \(-0.415411\pi\)
0.262627 + 0.964897i \(0.415411\pi\)
\(450\) −16.7867 −0.791335
\(451\) 54.2108 2.55269
\(452\) −78.6128 −3.69763
\(453\) 19.7812 0.929400
\(454\) −63.6125 −2.98548
\(455\) 42.2052 1.97861
\(456\) −8.44067 −0.395271
\(457\) 10.4726 0.489886 0.244943 0.969537i \(-0.421231\pi\)
0.244943 + 0.969537i \(0.421231\pi\)
\(458\) −2.44155 −0.114086
\(459\) 1.00000 0.0466760
\(460\) 142.514 6.64477
\(461\) −39.2782 −1.82937 −0.914684 0.404170i \(-0.867560\pi\)
−0.914684 + 0.404170i \(0.867560\pi\)
\(462\) 51.0333 2.37428
\(463\) −12.6819 −0.589376 −0.294688 0.955594i \(-0.595216\pi\)
−0.294688 + 0.955594i \(0.595216\pi\)
\(464\) −83.9746 −3.89842
\(465\) 27.9937 1.29818
\(466\) 74.6983 3.46033
\(467\) 10.0949 0.467137 0.233568 0.972340i \(-0.424960\pi\)
0.233568 + 0.972340i \(0.424960\pi\)
\(468\) −21.6861 −1.00244
\(469\) 3.39962 0.156980
\(470\) 47.1969 2.17703
\(471\) 15.2035 0.700539
\(472\) −101.063 −4.65178
\(473\) 42.0685 1.93431
\(474\) 2.65510 0.121953
\(475\) −6.59085 −0.302409
\(476\) −14.7477 −0.675958
\(477\) 0.314028 0.0143783
\(478\) 65.0597 2.97576
\(479\) 42.1168 1.92436 0.962182 0.272408i \(-0.0878202\pi\)
0.962182 + 0.272408i \(0.0878202\pi\)
\(480\) −47.3499 −2.16122
\(481\) −30.3902 −1.38567
\(482\) 2.88026 0.131192
\(483\) 24.4964 1.11463
\(484\) 163.161 7.41643
\(485\) −6.72195 −0.305228
\(486\) 2.65510 0.120438
\(487\) 5.85373 0.265258 0.132629 0.991166i \(-0.457658\pi\)
0.132629 + 0.991166i \(0.457658\pi\)
\(488\) 76.2972 3.45381
\(489\) 14.2436 0.644117
\(490\) 13.6671 0.617417
\(491\) 25.9625 1.17167 0.585835 0.810430i \(-0.300767\pi\)
0.585835 + 0.810430i \(0.300767\pi\)
\(492\) −41.5946 −1.87523
\(493\) 7.36681 0.331784
\(494\) −11.8868 −0.534812
\(495\) −22.1449 −0.995339
\(496\) 94.8327 4.25811
\(497\) −27.2430 −1.22202
\(498\) −15.9326 −0.713958
\(499\) 8.40078 0.376070 0.188035 0.982162i \(-0.439788\pi\)
0.188035 + 0.982162i \(0.439788\pi\)
\(500\) −22.4700 −1.00489
\(501\) −13.6600 −0.610285
\(502\) 15.8291 0.706487
\(503\) 23.7472 1.05883 0.529417 0.848362i \(-0.322411\pi\)
0.529417 + 0.848362i \(0.322411\pi\)
\(504\) −23.6477 −1.05335
\(505\) 3.37459 0.150167
\(506\) 146.561 6.51544
\(507\) −5.44394 −0.241774
\(508\) −67.1987 −2.98146
\(509\) 10.6551 0.472280 0.236140 0.971719i \(-0.424118\pi\)
0.236140 + 0.971719i \(0.424118\pi\)
\(510\) 8.93412 0.395609
\(511\) −9.80217 −0.433622
\(512\) 24.1898 1.06905
\(513\) 1.04245 0.0460254
\(514\) −42.4927 −1.87427
\(515\) 18.5259 0.816348
\(516\) −32.2781 −1.42096
\(517\) 34.7669 1.52905
\(518\) −54.8727 −2.41097
\(519\) −21.3641 −0.937780
\(520\) −117.009 −5.13116
\(521\) 23.2009 1.01645 0.508226 0.861224i \(-0.330302\pi\)
0.508226 + 0.861224i \(0.330302\pi\)
\(522\) 19.5596 0.856102
\(523\) 22.3541 0.977478 0.488739 0.872430i \(-0.337457\pi\)
0.488739 + 0.872430i \(0.337457\pi\)
\(524\) 22.4764 0.981885
\(525\) −18.4652 −0.805887
\(526\) 42.0809 1.83481
\(527\) −8.31935 −0.362397
\(528\) −75.0191 −3.26479
\(529\) 47.3507 2.05873
\(530\) 2.80556 0.121866
\(531\) 12.4816 0.541655
\(532\) −15.3737 −0.666536
\(533\) −35.3760 −1.53231
\(534\) −2.24652 −0.0972166
\(535\) 8.38561 0.362541
\(536\) −9.42503 −0.407099
\(537\) −14.5126 −0.626263
\(538\) −45.8407 −1.97633
\(539\) 10.0677 0.433645
\(540\) 16.9912 0.731186
\(541\) −19.7725 −0.850085 −0.425042 0.905173i \(-0.639741\pi\)
−0.425042 + 0.905173i \(0.639741\pi\)
\(542\) −4.77062 −0.204916
\(543\) −3.80550 −0.163310
\(544\) 14.0718 0.603322
\(545\) −27.5386 −1.17963
\(546\) −33.3025 −1.42522
\(547\) −33.4523 −1.43032 −0.715159 0.698962i \(-0.753646\pi\)
−0.715159 + 0.698962i \(0.753646\pi\)
\(548\) −55.3444 −2.36419
\(549\) −9.42298 −0.402163
\(550\) −110.477 −4.71074
\(551\) 7.67955 0.327160
\(552\) −67.9133 −2.89058
\(553\) 2.92058 0.124196
\(554\) −54.9473 −2.33449
\(555\) 23.8110 1.01072
\(556\) 23.9416 1.01535
\(557\) 2.10604 0.0892359 0.0446180 0.999004i \(-0.485793\pi\)
0.0446180 + 0.999004i \(0.485793\pi\)
\(558\) −22.0887 −0.935091
\(559\) −27.4524 −1.16111
\(560\) −112.023 −4.73383
\(561\) 6.58118 0.277858
\(562\) −47.2266 −1.99214
\(563\) 39.4165 1.66121 0.830605 0.556863i \(-0.187995\pi\)
0.830605 + 0.556863i \(0.187995\pi\)
\(564\) −26.6758 −1.12325
\(565\) 52.3852 2.20386
\(566\) −19.4627 −0.818077
\(567\) 2.92058 0.122653
\(568\) 75.5278 3.16908
\(569\) −21.1168 −0.885264 −0.442632 0.896703i \(-0.645955\pi\)
−0.442632 + 0.896703i \(0.645955\pi\)
\(570\) 9.31339 0.390095
\(571\) 45.7963 1.91652 0.958258 0.285906i \(-0.0922944\pi\)
0.958258 + 0.285906i \(0.0922944\pi\)
\(572\) −142.720 −5.96743
\(573\) 12.1174 0.506212
\(574\) −63.8752 −2.66610
\(575\) −53.0297 −2.21149
\(576\) 14.5639 0.606830
\(577\) 13.3376 0.555251 0.277626 0.960689i \(-0.410452\pi\)
0.277626 + 0.960689i \(0.410452\pi\)
\(578\) −2.65510 −0.110438
\(579\) −19.5362 −0.811898
\(580\) 125.171 5.19745
\(581\) −17.5257 −0.727087
\(582\) 5.30404 0.219859
\(583\) 2.06667 0.0855928
\(584\) 27.1753 1.12452
\(585\) 14.4510 0.597474
\(586\) −33.9166 −1.40108
\(587\) 42.7337 1.76381 0.881905 0.471427i \(-0.156261\pi\)
0.881905 + 0.471427i \(0.156261\pi\)
\(588\) −7.72467 −0.318560
\(589\) −8.67253 −0.357345
\(590\) 111.512 4.59087
\(591\) −18.7785 −0.772446
\(592\) 80.6631 3.31523
\(593\) −29.5411 −1.21311 −0.606554 0.795042i \(-0.707449\pi\)
−0.606554 + 0.795042i \(0.707449\pi\)
\(594\) 17.4737 0.716955
\(595\) 9.82740 0.402884
\(596\) 71.3222 2.92147
\(597\) 16.7373 0.685012
\(598\) −95.6407 −3.91104
\(599\) 9.83650 0.401909 0.200954 0.979601i \(-0.435596\pi\)
0.200954 + 0.979601i \(0.435596\pi\)
\(600\) 51.1924 2.08992
\(601\) 20.0058 0.816052 0.408026 0.912970i \(-0.366217\pi\)
0.408026 + 0.912970i \(0.366217\pi\)
\(602\) −49.5682 −2.02025
\(603\) 1.16403 0.0474028
\(604\) −99.8864 −4.06432
\(605\) −108.726 −4.42033
\(606\) −2.66276 −0.108167
\(607\) 9.58695 0.389122 0.194561 0.980890i \(-0.437672\pi\)
0.194561 + 0.980890i \(0.437672\pi\)
\(608\) 14.6692 0.594913
\(609\) 21.5153 0.871845
\(610\) −84.1860 −3.40859
\(611\) −22.6876 −0.917844
\(612\) −5.04957 −0.204117
\(613\) 28.6052 1.15535 0.577677 0.816265i \(-0.303959\pi\)
0.577677 + 0.816265i \(0.303959\pi\)
\(614\) −51.6093 −2.08278
\(615\) 27.7174 1.11767
\(616\) −155.630 −6.27050
\(617\) 19.0249 0.765916 0.382958 0.923766i \(-0.374905\pi\)
0.382958 + 0.923766i \(0.374905\pi\)
\(618\) −14.6181 −0.588025
\(619\) 12.2797 0.493564 0.246782 0.969071i \(-0.420627\pi\)
0.246782 + 0.969071i \(0.420627\pi\)
\(620\) −141.356 −5.67700
\(621\) 8.38753 0.336580
\(622\) −6.62082 −0.265471
\(623\) −2.47115 −0.0990044
\(624\) 48.9548 1.95976
\(625\) −16.6389 −0.665556
\(626\) 14.5055 0.579756
\(627\) 6.86057 0.273985
\(628\) −76.7711 −3.06350
\(629\) −7.07631 −0.282151
\(630\) 26.0928 1.03956
\(631\) 31.0476 1.23598 0.617992 0.786184i \(-0.287946\pi\)
0.617992 + 0.786184i \(0.287946\pi\)
\(632\) −8.09693 −0.322079
\(633\) −8.19938 −0.325896
\(634\) −22.6568 −0.899818
\(635\) 44.7792 1.77701
\(636\) −1.58571 −0.0628773
\(637\) −6.56980 −0.260305
\(638\) 128.725 5.09629
\(639\) −9.32796 −0.369008
\(640\) 35.4160 1.39994
\(641\) 39.1331 1.54567 0.772833 0.634610i \(-0.218839\pi\)
0.772833 + 0.634610i \(0.218839\pi\)
\(642\) −6.61676 −0.261143
\(643\) −33.2323 −1.31056 −0.655278 0.755388i \(-0.727448\pi\)
−0.655278 + 0.755388i \(0.727448\pi\)
\(644\) −123.697 −4.87433
\(645\) 21.5092 0.846922
\(646\) −2.76782 −0.108898
\(647\) −22.4668 −0.883261 −0.441630 0.897197i \(-0.645600\pi\)
−0.441630 + 0.897197i \(0.645600\pi\)
\(648\) −8.09693 −0.318078
\(649\) 82.1435 3.22442
\(650\) 72.0931 2.82772
\(651\) −24.2973 −0.952287
\(652\) −71.9240 −2.81676
\(653\) 34.0925 1.33414 0.667072 0.744994i \(-0.267548\pi\)
0.667072 + 0.744994i \(0.267548\pi\)
\(654\) 21.7297 0.849698
\(655\) −14.9776 −0.585222
\(656\) 93.8968 3.66605
\(657\) −3.35625 −0.130940
\(658\) −40.9649 −1.59698
\(659\) 17.4291 0.678940 0.339470 0.940617i \(-0.389752\pi\)
0.339470 + 0.940617i \(0.389752\pi\)
\(660\) 111.822 4.35268
\(661\) 9.05940 0.352370 0.176185 0.984357i \(-0.443624\pi\)
0.176185 + 0.984357i \(0.443624\pi\)
\(662\) 24.2987 0.944397
\(663\) −4.29464 −0.166790
\(664\) 48.5877 1.88557
\(665\) 10.2446 0.397269
\(666\) −18.7883 −0.728033
\(667\) 61.7893 2.39249
\(668\) 68.9773 2.66881
\(669\) −7.62776 −0.294906
\(670\) 10.3995 0.401769
\(671\) −62.0143 −2.39404
\(672\) 41.0977 1.58538
\(673\) −6.32183 −0.243689 −0.121844 0.992549i \(-0.538881\pi\)
−0.121844 + 0.992549i \(0.538881\pi\)
\(674\) 59.9566 2.30944
\(675\) −6.32245 −0.243351
\(676\) 27.4896 1.05729
\(677\) −14.0424 −0.539694 −0.269847 0.962903i \(-0.586973\pi\)
−0.269847 + 0.962903i \(0.586973\pi\)
\(678\) −41.3352 −1.58747
\(679\) 5.83437 0.223902
\(680\) −27.2452 −1.04481
\(681\) −23.9586 −0.918095
\(682\) −145.370 −5.56650
\(683\) −38.0059 −1.45426 −0.727128 0.686502i \(-0.759145\pi\)
−0.727128 + 0.686502i \(0.759145\pi\)
\(684\) −5.26394 −0.201272
\(685\) 36.8798 1.40911
\(686\) 42.4185 1.61955
\(687\) −0.919568 −0.0350837
\(688\) 72.8654 2.77797
\(689\) −1.34864 −0.0513790
\(690\) 74.9352 2.85273
\(691\) −5.32630 −0.202622 −0.101311 0.994855i \(-0.532304\pi\)
−0.101311 + 0.994855i \(0.532304\pi\)
\(692\) 107.880 4.10097
\(693\) 19.2208 0.730139
\(694\) 52.7707 2.00315
\(695\) −15.9540 −0.605168
\(696\) −59.6485 −2.26097
\(697\) −8.23725 −0.312008
\(698\) 16.7601 0.634379
\(699\) 28.1339 1.06412
\(700\) 93.2413 3.52419
\(701\) 16.9542 0.640352 0.320176 0.947358i \(-0.396258\pi\)
0.320176 + 0.947358i \(0.396258\pi\)
\(702\) −11.4027 −0.430368
\(703\) −7.37672 −0.278218
\(704\) 95.8478 3.61240
\(705\) 17.7759 0.669481
\(706\) −21.7994 −0.820432
\(707\) −2.92900 −0.110156
\(708\) −63.0267 −2.36869
\(709\) −3.77497 −0.141772 −0.0708860 0.997484i \(-0.522583\pi\)
−0.0708860 + 0.997484i \(0.522583\pi\)
\(710\) −83.3371 −3.12758
\(711\) 1.00000 0.0375029
\(712\) 6.85094 0.256750
\(713\) −69.7788 −2.61324
\(714\) −7.75443 −0.290202
\(715\) 95.1044 3.55670
\(716\) 73.2822 2.73869
\(717\) 24.5036 0.915105
\(718\) −27.2708 −1.01774
\(719\) −29.4620 −1.09875 −0.549373 0.835577i \(-0.685134\pi\)
−0.549373 + 0.835577i \(0.685134\pi\)
\(720\) −38.3565 −1.42946
\(721\) −16.0797 −0.598838
\(722\) 47.5616 1.77006
\(723\) 1.08480 0.0403441
\(724\) 19.2162 0.714163
\(725\) −46.5763 −1.72980
\(726\) 85.7915 3.18402
\(727\) −3.28683 −0.121902 −0.0609509 0.998141i \(-0.519413\pi\)
−0.0609509 + 0.998141i \(0.519413\pi\)
\(728\) 101.558 3.76401
\(729\) 1.00000 0.0370370
\(730\) −29.9851 −1.10980
\(731\) −6.39224 −0.236426
\(732\) 47.5820 1.75868
\(733\) −13.2649 −0.489952 −0.244976 0.969529i \(-0.578780\pi\)
−0.244976 + 0.969529i \(0.578780\pi\)
\(734\) −61.4602 −2.26854
\(735\) 5.14749 0.189868
\(736\) 118.027 4.35055
\(737\) 7.66066 0.282184
\(738\) −21.8708 −0.805074
\(739\) −22.4138 −0.824504 −0.412252 0.911070i \(-0.635258\pi\)
−0.412252 + 0.911070i \(0.635258\pi\)
\(740\) −120.235 −4.41993
\(741\) −4.47696 −0.164465
\(742\) −2.43511 −0.0893956
\(743\) 41.7486 1.53161 0.765803 0.643075i \(-0.222342\pi\)
0.765803 + 0.643075i \(0.222342\pi\)
\(744\) 67.3612 2.46958
\(745\) −47.5270 −1.74125
\(746\) −35.2405 −1.29025
\(747\) −6.00075 −0.219556
\(748\) −33.2321 −1.21509
\(749\) −7.27835 −0.265945
\(750\) −11.8149 −0.431419
\(751\) −36.8217 −1.34364 −0.671821 0.740713i \(-0.734488\pi\)
−0.671821 + 0.740713i \(0.734488\pi\)
\(752\) 60.2186 2.19595
\(753\) 5.96177 0.217259
\(754\) −84.0016 −3.05916
\(755\) 66.5613 2.42241
\(756\) −14.7477 −0.536367
\(757\) 2.25723 0.0820405 0.0410203 0.999158i \(-0.486939\pi\)
0.0410203 + 0.999158i \(0.486939\pi\)
\(758\) 57.1797 2.07686
\(759\) 55.1999 2.00363
\(760\) −28.4019 −1.03024
\(761\) 14.5837 0.528657 0.264329 0.964433i \(-0.414850\pi\)
0.264329 + 0.964433i \(0.414850\pi\)
\(762\) −35.3336 −1.28000
\(763\) 23.9024 0.865324
\(764\) −61.1877 −2.21369
\(765\) 3.36488 0.121658
\(766\) −6.74335 −0.243647
\(767\) −53.6039 −1.93553
\(768\) 1.18242 0.0426671
\(769\) 0.273702 0.00986995 0.00493498 0.999988i \(-0.498429\pi\)
0.00493498 + 0.999988i \(0.498429\pi\)
\(770\) 171.721 6.18840
\(771\) −16.0042 −0.576375
\(772\) 98.6496 3.55048
\(773\) 44.7455 1.60938 0.804692 0.593692i \(-0.202330\pi\)
0.804692 + 0.593692i \(0.202330\pi\)
\(774\) −16.9721 −0.610048
\(775\) 52.5987 1.88940
\(776\) −16.1750 −0.580650
\(777\) −20.6669 −0.741421
\(778\) −7.57256 −0.271489
\(779\) −8.58695 −0.307659
\(780\) −72.9712 −2.61279
\(781\) −61.3890 −2.19667
\(782\) −22.2698 −0.796365
\(783\) 7.36681 0.263268
\(784\) 17.4379 0.622782
\(785\) 51.1579 1.82591
\(786\) 11.8182 0.421543
\(787\) −38.6654 −1.37827 −0.689137 0.724631i \(-0.742010\pi\)
−0.689137 + 0.724631i \(0.742010\pi\)
\(788\) 94.8236 3.37795
\(789\) 15.8490 0.564241
\(790\) 8.93412 0.317862
\(791\) −45.4681 −1.61666
\(792\) −53.2874 −1.89348
\(793\) 40.4683 1.43707
\(794\) −77.6315 −2.75504
\(795\) 1.05667 0.0374761
\(796\) −84.5161 −2.99560
\(797\) −54.2141 −1.92036 −0.960181 0.279377i \(-0.909872\pi\)
−0.960181 + 0.279377i \(0.909872\pi\)
\(798\) −8.08363 −0.286157
\(799\) −5.28278 −0.186891
\(800\) −88.9680 −3.14549
\(801\) −0.846116 −0.0298960
\(802\) −24.8750 −0.878366
\(803\) −22.0880 −0.779470
\(804\) −5.87783 −0.207295
\(805\) 82.4277 2.90519
\(806\) 94.8632 3.34141
\(807\) −17.2651 −0.607762
\(808\) 8.12029 0.285671
\(809\) −21.1087 −0.742143 −0.371071 0.928604i \(-0.621009\pi\)
−0.371071 + 0.928604i \(0.621009\pi\)
\(810\) 8.93412 0.313913
\(811\) 24.5967 0.863706 0.431853 0.901944i \(-0.357860\pi\)
0.431853 + 0.901944i \(0.357860\pi\)
\(812\) −108.643 −3.81263
\(813\) −1.79677 −0.0630156
\(814\) −123.649 −4.33391
\(815\) 47.9280 1.67884
\(816\) 11.3990 0.399046
\(817\) −6.66361 −0.233130
\(818\) −84.4017 −2.95104
\(819\) −12.5428 −0.438282
\(820\) −139.961 −4.88765
\(821\) −1.02183 −0.0356622 −0.0178311 0.999841i \(-0.505676\pi\)
−0.0178311 + 0.999841i \(0.505676\pi\)
\(822\) −29.1005 −1.01500
\(823\) −27.0699 −0.943597 −0.471799 0.881706i \(-0.656395\pi\)
−0.471799 + 0.881706i \(0.656395\pi\)
\(824\) 44.5789 1.55298
\(825\) −41.6092 −1.44864
\(826\) −96.7876 −3.36767
\(827\) 0.444434 0.0154545 0.00772724 0.999970i \(-0.497540\pi\)
0.00772724 + 0.999970i \(0.497540\pi\)
\(828\) −42.3535 −1.47188
\(829\) 38.8429 1.34907 0.674534 0.738244i \(-0.264344\pi\)
0.674534 + 0.738244i \(0.264344\pi\)
\(830\) −53.6114 −1.86088
\(831\) −20.6950 −0.717900
\(832\) −62.5468 −2.16842
\(833\) −1.52977 −0.0530033
\(834\) 12.5887 0.435910
\(835\) −45.9644 −1.59066
\(836\) −34.6429 −1.19815
\(837\) −8.31935 −0.287559
\(838\) −66.0842 −2.28284
\(839\) −13.4504 −0.464360 −0.232180 0.972673i \(-0.574586\pi\)
−0.232180 + 0.972673i \(0.574586\pi\)
\(840\) −79.5718 −2.74549
\(841\) 25.2699 0.871375
\(842\) 82.4044 2.83984
\(843\) −17.7871 −0.612621
\(844\) 41.4034 1.42516
\(845\) −18.3182 −0.630167
\(846\) −14.0263 −0.482235
\(847\) 94.3694 3.24257
\(848\) 3.57962 0.122924
\(849\) −7.33028 −0.251575
\(850\) 16.7867 0.575781
\(851\) −59.3528 −2.03459
\(852\) 47.1022 1.61369
\(853\) 22.8360 0.781889 0.390944 0.920414i \(-0.372148\pi\)
0.390944 + 0.920414i \(0.372148\pi\)
\(854\) 73.0699 2.50040
\(855\) 3.50773 0.119962
\(856\) 20.1783 0.689680
\(857\) −41.2584 −1.40936 −0.704680 0.709525i \(-0.748909\pi\)
−0.704680 + 0.709525i \(0.748909\pi\)
\(858\) −75.0433 −2.56194
\(859\) −3.27100 −0.111605 −0.0558026 0.998442i \(-0.517772\pi\)
−0.0558026 + 0.998442i \(0.517772\pi\)
\(860\) −108.612 −3.70364
\(861\) −24.0575 −0.819878
\(862\) 84.5728 2.88056
\(863\) 36.8793 1.25538 0.627692 0.778462i \(-0.284000\pi\)
0.627692 + 0.778462i \(0.284000\pi\)
\(864\) 14.0718 0.478731
\(865\) −71.8878 −2.44426
\(866\) −39.5484 −1.34391
\(867\) −1.00000 −0.0339618
\(868\) 122.691 4.16441
\(869\) 6.58118 0.223251
\(870\) 65.8159 2.23137
\(871\) −4.99907 −0.169387
\(872\) −66.2663 −2.24406
\(873\) 1.99768 0.0676111
\(874\) −23.2152 −0.785265
\(875\) −12.9962 −0.439352
\(876\) 16.9476 0.572607
\(877\) 32.4616 1.09615 0.548076 0.836429i \(-0.315361\pi\)
0.548076 + 0.836429i \(0.315361\pi\)
\(878\) 1.65892 0.0559859
\(879\) −12.7741 −0.430861
\(880\) −252.431 −8.50944
\(881\) 6.32308 0.213030 0.106515 0.994311i \(-0.466031\pi\)
0.106515 + 0.994311i \(0.466031\pi\)
\(882\) −4.06169 −0.136764
\(883\) 19.1139 0.643235 0.321618 0.946870i \(-0.395773\pi\)
0.321618 + 0.946870i \(0.395773\pi\)
\(884\) 21.6861 0.729383
\(885\) 41.9991 1.41178
\(886\) −6.42032 −0.215695
\(887\) 22.7111 0.762564 0.381282 0.924459i \(-0.375483\pi\)
0.381282 + 0.924459i \(0.375483\pi\)
\(888\) 57.2964 1.92274
\(889\) −38.8665 −1.30354
\(890\) −7.55930 −0.253388
\(891\) 6.58118 0.220478
\(892\) 38.5169 1.28964
\(893\) −5.50705 −0.184286
\(894\) 37.5017 1.25425
\(895\) −48.8331 −1.63231
\(896\) −30.7396 −1.02694
\(897\) −36.0214 −1.20272
\(898\) −29.5511 −0.986134
\(899\) −61.2871 −2.04404
\(900\) 31.9257 1.06419
\(901\) −0.314028 −0.0104618
\(902\) −143.935 −4.79252
\(903\) −18.6690 −0.621267
\(904\) 126.055 4.19251
\(905\) −12.8051 −0.425655
\(906\) −52.5210 −1.74489
\(907\) −40.1184 −1.33211 −0.666054 0.745903i \(-0.732018\pi\)
−0.666054 + 0.745903i \(0.732018\pi\)
\(908\) 120.981 4.01488
\(909\) −1.00288 −0.0332636
\(910\) −112.059 −3.71472
\(911\) −16.5464 −0.548208 −0.274104 0.961700i \(-0.588381\pi\)
−0.274104 + 0.961700i \(0.588381\pi\)
\(912\) 11.8830 0.393484
\(913\) −39.4920 −1.30700
\(914\) −27.8057 −0.919732
\(915\) −31.7072 −1.04821
\(916\) 4.64343 0.153423
\(917\) 12.9999 0.429295
\(918\) −2.65510 −0.0876315
\(919\) 58.0336 1.91435 0.957176 0.289507i \(-0.0934915\pi\)
0.957176 + 0.289507i \(0.0934915\pi\)
\(920\) −228.520 −7.53409
\(921\) −19.4378 −0.640497
\(922\) 104.288 3.43453
\(923\) 40.0602 1.31860
\(924\) −97.0570 −3.19294
\(925\) 44.7396 1.47103
\(926\) 33.6716 1.10652
\(927\) −5.50565 −0.180829
\(928\) 103.664 3.40294
\(929\) −18.6503 −0.611897 −0.305948 0.952048i \(-0.598973\pi\)
−0.305948 + 0.952048i \(0.598973\pi\)
\(930\) −74.3261 −2.43725
\(931\) −1.59471 −0.0522645
\(932\) −142.064 −4.65346
\(933\) −2.49362 −0.0816374
\(934\) −26.8030 −0.877022
\(935\) 22.1449 0.724216
\(936\) 34.7734 1.13660
\(937\) −10.0582 −0.328586 −0.164293 0.986412i \(-0.552534\pi\)
−0.164293 + 0.986412i \(0.552534\pi\)
\(938\) −9.02635 −0.294721
\(939\) 5.46325 0.178286
\(940\) −89.7609 −2.92768
\(941\) −2.36206 −0.0770010 −0.0385005 0.999259i \(-0.512258\pi\)
−0.0385005 + 0.999259i \(0.512258\pi\)
\(942\) −40.3668 −1.31522
\(943\) −69.0902 −2.24989
\(944\) 142.278 4.63076
\(945\) 9.82740 0.319685
\(946\) −111.696 −3.63156
\(947\) 16.7739 0.545080 0.272540 0.962144i \(-0.412136\pi\)
0.272540 + 0.962144i \(0.412136\pi\)
\(948\) −5.04957 −0.164003
\(949\) 14.4139 0.467894
\(950\) 17.4994 0.567755
\(951\) −8.53332 −0.276712
\(952\) 23.6477 0.766427
\(953\) 12.7004 0.411406 0.205703 0.978614i \(-0.434052\pi\)
0.205703 + 0.978614i \(0.434052\pi\)
\(954\) −0.833776 −0.0269945
\(955\) 40.7737 1.31940
\(956\) −123.733 −4.00181
\(957\) 48.4823 1.56721
\(958\) −111.824 −3.61288
\(959\) −32.0101 −1.03366
\(960\) 49.0059 1.58166
\(961\) 38.2116 1.23263
\(962\) 80.6891 2.60152
\(963\) −2.49209 −0.0803066
\(964\) −5.47778 −0.176427
\(965\) −65.7372 −2.11615
\(966\) −65.0406 −2.09265
\(967\) 46.6241 1.49933 0.749666 0.661817i \(-0.230214\pi\)
0.749666 + 0.661817i \(0.230214\pi\)
\(968\) −261.627 −8.40902
\(969\) −1.04245 −0.0334884
\(970\) 17.8475 0.573048
\(971\) 15.7122 0.504228 0.252114 0.967698i \(-0.418874\pi\)
0.252114 + 0.967698i \(0.418874\pi\)
\(972\) −5.04957 −0.161965
\(973\) 13.8474 0.443926
\(974\) −15.5423 −0.498006
\(975\) 27.1526 0.869580
\(976\) −107.413 −3.43821
\(977\) 15.9999 0.511882 0.255941 0.966692i \(-0.417615\pi\)
0.255941 + 0.966692i \(0.417615\pi\)
\(978\) −37.8182 −1.20929
\(979\) −5.56844 −0.177968
\(980\) −25.9926 −0.830304
\(981\) 8.18412 0.261299
\(982\) −68.9330 −2.19974
\(983\) 26.0124 0.829666 0.414833 0.909898i \(-0.363840\pi\)
0.414833 + 0.909898i \(0.363840\pi\)
\(984\) 66.6965 2.12621
\(985\) −63.1876 −2.01333
\(986\) −19.5596 −0.622906
\(987\) −15.4288 −0.491103
\(988\) 22.6067 0.719216
\(989\) −53.6151 −1.70486
\(990\) 58.7970 1.86869
\(991\) 16.8593 0.535554 0.267777 0.963481i \(-0.413711\pi\)
0.267777 + 0.963481i \(0.413711\pi\)
\(992\) −117.068 −3.71691
\(993\) 9.15171 0.290421
\(994\) 72.3330 2.29426
\(995\) 56.3190 1.78543
\(996\) 30.3012 0.960131
\(997\) 21.7364 0.688399 0.344199 0.938897i \(-0.388150\pi\)
0.344199 + 0.938897i \(0.388150\pi\)
\(998\) −22.3049 −0.706050
\(999\) −7.07631 −0.223884
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.1.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.2 32 1.1 even 1 trivial