Properties

Label 4003.2.a.c.1.13
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45370 q^{2} -0.415301 q^{3} +4.02066 q^{4} -3.18084 q^{5} +1.01903 q^{6} -2.85630 q^{7} -4.95811 q^{8} -2.82752 q^{9} +O(q^{10})\) \(q-2.45370 q^{2} -0.415301 q^{3} +4.02066 q^{4} -3.18084 q^{5} +1.01903 q^{6} -2.85630 q^{7} -4.95811 q^{8} -2.82752 q^{9} +7.80484 q^{10} +1.47266 q^{11} -1.66979 q^{12} +3.83328 q^{13} +7.00851 q^{14} +1.32101 q^{15} +4.12441 q^{16} +3.98568 q^{17} +6.93791 q^{18} -4.57320 q^{19} -12.7891 q^{20} +1.18622 q^{21} -3.61347 q^{22} +0.0487036 q^{23} +2.05911 q^{24} +5.11776 q^{25} -9.40574 q^{26} +2.42018 q^{27} -11.4842 q^{28} +7.06083 q^{29} -3.24136 q^{30} -1.88706 q^{31} -0.203855 q^{32} -0.611598 q^{33} -9.77968 q^{34} +9.08543 q^{35} -11.3685 q^{36} -3.06475 q^{37} +11.2213 q^{38} -1.59197 q^{39} +15.7710 q^{40} +1.59606 q^{41} -2.91064 q^{42} -9.79157 q^{43} +5.92107 q^{44} +8.99391 q^{45} -0.119504 q^{46} -12.2176 q^{47} -1.71287 q^{48} +1.15844 q^{49} -12.5575 q^{50} -1.65526 q^{51} +15.4123 q^{52} +1.66410 q^{53} -5.93840 q^{54} -4.68430 q^{55} +14.1618 q^{56} +1.89926 q^{57} -17.3252 q^{58} -9.23933 q^{59} +5.31133 q^{60} -1.01299 q^{61} +4.63028 q^{62} +8.07625 q^{63} -7.74862 q^{64} -12.1931 q^{65} +1.50068 q^{66} -10.5900 q^{67} +16.0251 q^{68} -0.0202267 q^{69} -22.2930 q^{70} -11.1767 q^{71} +14.0192 q^{72} +3.38359 q^{73} +7.51998 q^{74} -2.12541 q^{75} -18.3873 q^{76} -4.20636 q^{77} +3.90621 q^{78} -5.99683 q^{79} -13.1191 q^{80} +7.47747 q^{81} -3.91626 q^{82} -17.3073 q^{83} +4.76941 q^{84} -12.6778 q^{85} +24.0256 q^{86} -2.93237 q^{87} -7.30161 q^{88} -6.21452 q^{89} -22.0684 q^{90} -10.9490 q^{91} +0.195821 q^{92} +0.783696 q^{93} +29.9783 q^{94} +14.5466 q^{95} +0.0846611 q^{96} -3.11759 q^{97} -2.84247 q^{98} -4.16398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45370 −1.73503 −0.867515 0.497410i \(-0.834284\pi\)
−0.867515 + 0.497410i \(0.834284\pi\)
\(3\) −0.415301 −0.239774 −0.119887 0.992788i \(-0.538253\pi\)
−0.119887 + 0.992788i \(0.538253\pi\)
\(4\) 4.02066 2.01033
\(5\) −3.18084 −1.42252 −0.711258 0.702931i \(-0.751874\pi\)
−0.711258 + 0.702931i \(0.751874\pi\)
\(6\) 1.01903 0.416016
\(7\) −2.85630 −1.07958 −0.539790 0.841800i \(-0.681496\pi\)
−0.539790 + 0.841800i \(0.681496\pi\)
\(8\) −4.95811 −1.75296
\(9\) −2.82752 −0.942508
\(10\) 7.80484 2.46811
\(11\) 1.47266 0.444024 0.222012 0.975044i \(-0.428738\pi\)
0.222012 + 0.975044i \(0.428738\pi\)
\(12\) −1.66979 −0.482026
\(13\) 3.83328 1.06316 0.531581 0.847008i \(-0.321598\pi\)
0.531581 + 0.847008i \(0.321598\pi\)
\(14\) 7.00851 1.87310
\(15\) 1.32101 0.341083
\(16\) 4.12441 1.03110
\(17\) 3.98568 0.966669 0.483335 0.875436i \(-0.339425\pi\)
0.483335 + 0.875436i \(0.339425\pi\)
\(18\) 6.93791 1.63528
\(19\) −4.57320 −1.04917 −0.524583 0.851360i \(-0.675779\pi\)
−0.524583 + 0.851360i \(0.675779\pi\)
\(20\) −12.7891 −2.85973
\(21\) 1.18622 0.258855
\(22\) −3.61347 −0.770395
\(23\) 0.0487036 0.0101554 0.00507770 0.999987i \(-0.498384\pi\)
0.00507770 + 0.999987i \(0.498384\pi\)
\(24\) 2.05911 0.420314
\(25\) 5.11776 1.02355
\(26\) −9.40574 −1.84462
\(27\) 2.42018 0.465763
\(28\) −11.4842 −2.17031
\(29\) 7.06083 1.31116 0.655582 0.755124i \(-0.272423\pi\)
0.655582 + 0.755124i \(0.272423\pi\)
\(30\) −3.24136 −0.591789
\(31\) −1.88706 −0.338925 −0.169463 0.985537i \(-0.554203\pi\)
−0.169463 + 0.985537i \(0.554203\pi\)
\(32\) −0.203855 −0.0360368
\(33\) −0.611598 −0.106465
\(34\) −9.77968 −1.67720
\(35\) 9.08543 1.53572
\(36\) −11.3685 −1.89475
\(37\) −3.06475 −0.503841 −0.251921 0.967748i \(-0.581062\pi\)
−0.251921 + 0.967748i \(0.581062\pi\)
\(38\) 11.2213 1.82033
\(39\) −1.59197 −0.254919
\(40\) 15.7710 2.49361
\(41\) 1.59606 0.249263 0.124631 0.992203i \(-0.460225\pi\)
0.124631 + 0.992203i \(0.460225\pi\)
\(42\) −2.91064 −0.449122
\(43\) −9.79157 −1.49320 −0.746601 0.665273i \(-0.768315\pi\)
−0.746601 + 0.665273i \(0.768315\pi\)
\(44\) 5.92107 0.892635
\(45\) 8.99391 1.34073
\(46\) −0.119504 −0.0176199
\(47\) −12.2176 −1.78212 −0.891059 0.453887i \(-0.850037\pi\)
−0.891059 + 0.453887i \(0.850037\pi\)
\(48\) −1.71287 −0.247232
\(49\) 1.15844 0.165491
\(50\) −12.5575 −1.77589
\(51\) −1.65526 −0.231782
\(52\) 15.4123 2.13731
\(53\) 1.66410 0.228581 0.114291 0.993447i \(-0.463541\pi\)
0.114291 + 0.993447i \(0.463541\pi\)
\(54\) −5.93840 −0.808114
\(55\) −4.68430 −0.631631
\(56\) 14.1618 1.89246
\(57\) 1.89926 0.251563
\(58\) −17.3252 −2.27491
\(59\) −9.23933 −1.20286 −0.601429 0.798926i \(-0.705402\pi\)
−0.601429 + 0.798926i \(0.705402\pi\)
\(60\) 5.31133 0.685689
\(61\) −1.01299 −0.129701 −0.0648503 0.997895i \(-0.520657\pi\)
−0.0648503 + 0.997895i \(0.520657\pi\)
\(62\) 4.63028 0.588046
\(63\) 8.07625 1.01751
\(64\) −7.74862 −0.968577
\(65\) −12.1931 −1.51236
\(66\) 1.50068 0.184721
\(67\) −10.5900 −1.29377 −0.646887 0.762586i \(-0.723929\pi\)
−0.646887 + 0.762586i \(0.723929\pi\)
\(68\) 16.0251 1.94333
\(69\) −0.0202267 −0.00243500
\(70\) −22.2930 −2.66452
\(71\) −11.1767 −1.32644 −0.663218 0.748427i \(-0.730810\pi\)
−0.663218 + 0.748427i \(0.730810\pi\)
\(72\) 14.0192 1.65218
\(73\) 3.38359 0.396020 0.198010 0.980200i \(-0.436552\pi\)
0.198010 + 0.980200i \(0.436552\pi\)
\(74\) 7.51998 0.874180
\(75\) −2.12541 −0.245421
\(76\) −18.3873 −2.10917
\(77\) −4.20636 −0.479359
\(78\) 3.90621 0.442292
\(79\) −5.99683 −0.674696 −0.337348 0.941380i \(-0.609530\pi\)
−0.337348 + 0.941380i \(0.609530\pi\)
\(80\) −13.1191 −1.46676
\(81\) 7.47747 0.830830
\(82\) −3.91626 −0.432478
\(83\) −17.3073 −1.89972 −0.949862 0.312669i \(-0.898777\pi\)
−0.949862 + 0.312669i \(0.898777\pi\)
\(84\) 4.76941 0.520385
\(85\) −12.6778 −1.37510
\(86\) 24.0256 2.59075
\(87\) −2.93237 −0.314383
\(88\) −7.30161 −0.778355
\(89\) −6.21452 −0.658737 −0.329369 0.944201i \(-0.606836\pi\)
−0.329369 + 0.944201i \(0.606836\pi\)
\(90\) −22.0684 −2.32621
\(91\) −10.9490 −1.14777
\(92\) 0.195821 0.0204157
\(93\) 0.783696 0.0812655
\(94\) 29.9783 3.09203
\(95\) 14.5466 1.49245
\(96\) 0.0846611 0.00864069
\(97\) −3.11759 −0.316543 −0.158271 0.987396i \(-0.550592\pi\)
−0.158271 + 0.987396i \(0.550592\pi\)
\(98\) −2.84247 −0.287133
\(99\) −4.16398 −0.418496
\(100\) 20.5768 2.05768
\(101\) 11.4905 1.14334 0.571672 0.820482i \(-0.306295\pi\)
0.571672 + 0.820482i \(0.306295\pi\)
\(102\) 4.06151 0.402149
\(103\) 1.42647 0.140554 0.0702772 0.997528i \(-0.477612\pi\)
0.0702772 + 0.997528i \(0.477612\pi\)
\(104\) −19.0058 −1.86368
\(105\) −3.77319 −0.368226
\(106\) −4.08320 −0.396595
\(107\) 9.89389 0.956479 0.478239 0.878230i \(-0.341275\pi\)
0.478239 + 0.878230i \(0.341275\pi\)
\(108\) 9.73072 0.936339
\(109\) 15.9376 1.52655 0.763273 0.646076i \(-0.223591\pi\)
0.763273 + 0.646076i \(0.223591\pi\)
\(110\) 11.4939 1.09590
\(111\) 1.27279 0.120808
\(112\) −11.7805 −1.11316
\(113\) 12.7238 1.19695 0.598477 0.801140i \(-0.295773\pi\)
0.598477 + 0.801140i \(0.295773\pi\)
\(114\) −4.66021 −0.436469
\(115\) −0.154918 −0.0144462
\(116\) 28.3892 2.63587
\(117\) −10.8387 −1.00204
\(118\) 22.6706 2.08700
\(119\) −11.3843 −1.04360
\(120\) −6.54970 −0.597903
\(121\) −8.83127 −0.802843
\(122\) 2.48559 0.225034
\(123\) −0.662846 −0.0597668
\(124\) −7.58722 −0.681352
\(125\) −0.374563 −0.0335019
\(126\) −19.8167 −1.76542
\(127\) 8.13664 0.722010 0.361005 0.932564i \(-0.382434\pi\)
0.361005 + 0.932564i \(0.382434\pi\)
\(128\) 19.4205 1.71655
\(129\) 4.06645 0.358031
\(130\) 29.9182 2.62400
\(131\) 9.25580 0.808683 0.404342 0.914608i \(-0.367501\pi\)
0.404342 + 0.914608i \(0.367501\pi\)
\(132\) −2.45903 −0.214031
\(133\) 13.0624 1.13266
\(134\) 25.9847 2.24474
\(135\) −7.69820 −0.662556
\(136\) −19.7614 −1.69453
\(137\) 12.3617 1.05613 0.528065 0.849204i \(-0.322918\pi\)
0.528065 + 0.849204i \(0.322918\pi\)
\(138\) 0.0496302 0.00422480
\(139\) −16.8653 −1.43050 −0.715250 0.698869i \(-0.753687\pi\)
−0.715250 + 0.698869i \(0.753687\pi\)
\(140\) 36.5295 3.08730
\(141\) 5.07398 0.427306
\(142\) 27.4244 2.30141
\(143\) 5.64512 0.472069
\(144\) −11.6619 −0.971822
\(145\) −22.4594 −1.86515
\(146\) −8.30234 −0.687106
\(147\) −0.481101 −0.0396806
\(148\) −12.3223 −1.01289
\(149\) −16.4659 −1.34894 −0.674469 0.738303i \(-0.735627\pi\)
−0.674469 + 0.738303i \(0.735627\pi\)
\(150\) 5.21513 0.425813
\(151\) −14.5433 −1.18352 −0.591758 0.806116i \(-0.701566\pi\)
−0.591758 + 0.806116i \(0.701566\pi\)
\(152\) 22.6745 1.83914
\(153\) −11.2696 −0.911094
\(154\) 10.3212 0.831703
\(155\) 6.00243 0.482126
\(156\) −6.40076 −0.512471
\(157\) −16.4117 −1.30980 −0.654900 0.755716i \(-0.727289\pi\)
−0.654900 + 0.755716i \(0.727289\pi\)
\(158\) 14.7144 1.17062
\(159\) −0.691101 −0.0548078
\(160\) 0.648430 0.0512629
\(161\) −0.139112 −0.0109636
\(162\) −18.3475 −1.44152
\(163\) 22.9306 1.79606 0.898032 0.439931i \(-0.144997\pi\)
0.898032 + 0.439931i \(0.144997\pi\)
\(164\) 6.41722 0.501101
\(165\) 1.94540 0.151449
\(166\) 42.4670 3.29608
\(167\) 9.95056 0.769997 0.384999 0.922917i \(-0.374202\pi\)
0.384999 + 0.922917i \(0.374202\pi\)
\(168\) −5.88143 −0.453762
\(169\) 1.69405 0.130312
\(170\) 31.1076 2.38584
\(171\) 12.9309 0.988847
\(172\) −39.3686 −3.00183
\(173\) −1.17203 −0.0891079 −0.0445540 0.999007i \(-0.514187\pi\)
−0.0445540 + 0.999007i \(0.514187\pi\)
\(174\) 7.19517 0.545464
\(175\) −14.6178 −1.10500
\(176\) 6.07385 0.457834
\(177\) 3.83710 0.288414
\(178\) 15.2486 1.14293
\(179\) −11.0931 −0.829137 −0.414569 0.910018i \(-0.636068\pi\)
−0.414569 + 0.910018i \(0.636068\pi\)
\(180\) 36.1615 2.69532
\(181\) −14.6027 −1.08541 −0.542706 0.839922i \(-0.682600\pi\)
−0.542706 + 0.839922i \(0.682600\pi\)
\(182\) 26.8656 1.99141
\(183\) 0.420697 0.0310989
\(184\) −0.241478 −0.0178020
\(185\) 9.74848 0.716722
\(186\) −1.92296 −0.140998
\(187\) 5.86955 0.429224
\(188\) −49.1228 −3.58265
\(189\) −6.91275 −0.502829
\(190\) −35.6932 −2.58945
\(191\) 26.1706 1.89364 0.946818 0.321769i \(-0.104277\pi\)
0.946818 + 0.321769i \(0.104277\pi\)
\(192\) 3.21801 0.232240
\(193\) 12.7562 0.918210 0.459105 0.888382i \(-0.348170\pi\)
0.459105 + 0.888382i \(0.348170\pi\)
\(194\) 7.64963 0.549212
\(195\) 5.06379 0.362626
\(196\) 4.65770 0.332693
\(197\) 7.48480 0.533270 0.266635 0.963798i \(-0.414088\pi\)
0.266635 + 0.963798i \(0.414088\pi\)
\(198\) 10.2172 0.726104
\(199\) −12.7764 −0.905692 −0.452846 0.891589i \(-0.649591\pi\)
−0.452846 + 0.891589i \(0.649591\pi\)
\(200\) −25.3744 −1.79424
\(201\) 4.39804 0.310214
\(202\) −28.1942 −1.98374
\(203\) −20.1678 −1.41550
\(204\) −6.65523 −0.465959
\(205\) −5.07682 −0.354580
\(206\) −3.50014 −0.243866
\(207\) −0.137711 −0.00957155
\(208\) 15.8100 1.09623
\(209\) −6.73478 −0.465854
\(210\) 9.25829 0.638883
\(211\) 8.56374 0.589552 0.294776 0.955566i \(-0.404755\pi\)
0.294776 + 0.955566i \(0.404755\pi\)
\(212\) 6.69077 0.459524
\(213\) 4.64171 0.318045
\(214\) −24.2767 −1.65952
\(215\) 31.1455 2.12410
\(216\) −11.9995 −0.816463
\(217\) 5.38999 0.365897
\(218\) −39.1062 −2.64861
\(219\) −1.40521 −0.0949553
\(220\) −18.8340 −1.26979
\(221\) 15.2782 1.02773
\(222\) −3.12306 −0.209606
\(223\) −17.4201 −1.16654 −0.583268 0.812279i \(-0.698226\pi\)
−0.583268 + 0.812279i \(0.698226\pi\)
\(224\) 0.582270 0.0389045
\(225\) −14.4706 −0.964706
\(226\) −31.2204 −2.07675
\(227\) 9.44268 0.626732 0.313366 0.949632i \(-0.398543\pi\)
0.313366 + 0.949632i \(0.398543\pi\)
\(228\) 7.63627 0.505725
\(229\) −26.6402 −1.76043 −0.880215 0.474574i \(-0.842602\pi\)
−0.880215 + 0.474574i \(0.842602\pi\)
\(230\) 0.380124 0.0250646
\(231\) 1.74691 0.114938
\(232\) −35.0084 −2.29841
\(233\) 20.0451 1.31320 0.656600 0.754239i \(-0.271994\pi\)
0.656600 + 0.754239i \(0.271994\pi\)
\(234\) 26.5950 1.73857
\(235\) 38.8622 2.53509
\(236\) −37.1482 −2.41814
\(237\) 2.49049 0.161775
\(238\) 27.9337 1.81067
\(239\) 5.83490 0.377429 0.188714 0.982032i \(-0.439568\pi\)
0.188714 + 0.982032i \(0.439568\pi\)
\(240\) 5.44837 0.351691
\(241\) −1.21367 −0.0781797 −0.0390898 0.999236i \(-0.512446\pi\)
−0.0390898 + 0.999236i \(0.512446\pi\)
\(242\) 21.6693 1.39296
\(243\) −10.3659 −0.664975
\(244\) −4.07291 −0.260741
\(245\) −3.68481 −0.235414
\(246\) 1.62643 0.103697
\(247\) −17.5304 −1.11543
\(248\) 9.35623 0.594121
\(249\) 7.18775 0.455505
\(250\) 0.919067 0.0581269
\(251\) 14.5934 0.921128 0.460564 0.887626i \(-0.347647\pi\)
0.460564 + 0.887626i \(0.347647\pi\)
\(252\) 32.4719 2.04554
\(253\) 0.0717238 0.00450924
\(254\) −19.9649 −1.25271
\(255\) 5.26511 0.329714
\(256\) −32.1550 −2.00969
\(257\) −3.11554 −0.194342 −0.0971709 0.995268i \(-0.530979\pi\)
−0.0971709 + 0.995268i \(0.530979\pi\)
\(258\) −9.97787 −0.621195
\(259\) 8.75383 0.543937
\(260\) −49.0242 −3.04035
\(261\) −19.9647 −1.23578
\(262\) −22.7110 −1.40309
\(263\) −21.5673 −1.32990 −0.664950 0.746888i \(-0.731547\pi\)
−0.664950 + 0.746888i \(0.731547\pi\)
\(264\) 3.03237 0.186629
\(265\) −5.29322 −0.325160
\(266\) −32.0514 −1.96519
\(267\) 2.58090 0.157948
\(268\) −42.5788 −2.60091
\(269\) −3.82904 −0.233461 −0.116730 0.993164i \(-0.537241\pi\)
−0.116730 + 0.993164i \(0.537241\pi\)
\(270\) 18.8891 1.14955
\(271\) −12.5093 −0.759888 −0.379944 0.925009i \(-0.624057\pi\)
−0.379944 + 0.925009i \(0.624057\pi\)
\(272\) 16.4386 0.996734
\(273\) 4.54713 0.275205
\(274\) −30.3319 −1.83242
\(275\) 7.53672 0.454481
\(276\) −0.0813246 −0.00489516
\(277\) −8.80554 −0.529073 −0.264537 0.964376i \(-0.585219\pi\)
−0.264537 + 0.964376i \(0.585219\pi\)
\(278\) 41.3826 2.48196
\(279\) 5.33570 0.319440
\(280\) −45.0466 −2.69205
\(281\) 20.5445 1.22558 0.612790 0.790246i \(-0.290047\pi\)
0.612790 + 0.790246i \(0.290047\pi\)
\(282\) −12.4500 −0.741389
\(283\) 11.8855 0.706522 0.353261 0.935525i \(-0.385073\pi\)
0.353261 + 0.935525i \(0.385073\pi\)
\(284\) −44.9379 −2.66658
\(285\) −6.04124 −0.357852
\(286\) −13.8515 −0.819054
\(287\) −4.55882 −0.269099
\(288\) 0.576404 0.0339650
\(289\) −1.11436 −0.0655507
\(290\) 55.1087 3.23609
\(291\) 1.29474 0.0758988
\(292\) 13.6043 0.796131
\(293\) 14.4312 0.843078 0.421539 0.906810i \(-0.361490\pi\)
0.421539 + 0.906810i \(0.361490\pi\)
\(294\) 1.18048 0.0688470
\(295\) 29.3888 1.71108
\(296\) 15.1954 0.883212
\(297\) 3.56410 0.206810
\(298\) 40.4024 2.34045
\(299\) 0.186695 0.0107968
\(300\) −8.54556 −0.493378
\(301\) 27.9677 1.61203
\(302\) 35.6849 2.05344
\(303\) −4.77200 −0.274144
\(304\) −18.8618 −1.08180
\(305\) 3.22217 0.184501
\(306\) 27.6523 1.58078
\(307\) 17.1739 0.980165 0.490082 0.871676i \(-0.336967\pi\)
0.490082 + 0.871676i \(0.336967\pi\)
\(308\) −16.9124 −0.963671
\(309\) −0.592415 −0.0337013
\(310\) −14.7282 −0.836504
\(311\) −23.7296 −1.34558 −0.672791 0.739832i \(-0.734905\pi\)
−0.672791 + 0.739832i \(0.734905\pi\)
\(312\) 7.89314 0.446861
\(313\) −25.7050 −1.45293 −0.726467 0.687202i \(-0.758839\pi\)
−0.726467 + 0.687202i \(0.758839\pi\)
\(314\) 40.2696 2.27254
\(315\) −25.6893 −1.44743
\(316\) −24.1112 −1.35636
\(317\) −8.02788 −0.450891 −0.225445 0.974256i \(-0.572384\pi\)
−0.225445 + 0.974256i \(0.572384\pi\)
\(318\) 1.69576 0.0950933
\(319\) 10.3982 0.582188
\(320\) 24.6471 1.37782
\(321\) −4.10895 −0.229339
\(322\) 0.341340 0.0190221
\(323\) −18.2273 −1.01420
\(324\) 30.0644 1.67024
\(325\) 19.6178 1.08820
\(326\) −56.2649 −3.11622
\(327\) −6.61891 −0.366027
\(328\) −7.91344 −0.436947
\(329\) 34.8971 1.92394
\(330\) −4.77342 −0.262768
\(331\) 5.24402 0.288237 0.144119 0.989560i \(-0.453965\pi\)
0.144119 + 0.989560i \(0.453965\pi\)
\(332\) −69.5869 −3.81908
\(333\) 8.66565 0.474875
\(334\) −24.4157 −1.33597
\(335\) 33.6851 1.84041
\(336\) 4.89247 0.266906
\(337\) 17.6574 0.961861 0.480930 0.876759i \(-0.340299\pi\)
0.480930 + 0.876759i \(0.340299\pi\)
\(338\) −4.15670 −0.226095
\(339\) −5.28421 −0.286999
\(340\) −50.9732 −2.76441
\(341\) −2.77899 −0.150491
\(342\) −31.7285 −1.71568
\(343\) 16.6852 0.900918
\(344\) 48.5477 2.61752
\(345\) 0.0643378 0.00346383
\(346\) 2.87582 0.154605
\(347\) −12.9881 −0.697238 −0.348619 0.937265i \(-0.613349\pi\)
−0.348619 + 0.937265i \(0.613349\pi\)
\(348\) −11.7901 −0.632014
\(349\) 16.4846 0.882401 0.441201 0.897408i \(-0.354553\pi\)
0.441201 + 0.897408i \(0.354553\pi\)
\(350\) 35.8678 1.91722
\(351\) 9.27722 0.495182
\(352\) −0.300209 −0.0160012
\(353\) 13.8669 0.738063 0.369032 0.929417i \(-0.379689\pi\)
0.369032 + 0.929417i \(0.379689\pi\)
\(354\) −9.41512 −0.500408
\(355\) 35.5515 1.88688
\(356\) −24.9865 −1.32428
\(357\) 4.72791 0.250227
\(358\) 27.2192 1.43858
\(359\) −32.4774 −1.71409 −0.857047 0.515238i \(-0.827703\pi\)
−0.857047 + 0.515238i \(0.827703\pi\)
\(360\) −44.5928 −2.35025
\(361\) 1.91420 0.100747
\(362\) 35.8308 1.88322
\(363\) 3.66764 0.192501
\(364\) −44.0222 −2.30739
\(365\) −10.7627 −0.563344
\(366\) −1.03227 −0.0539575
\(367\) 8.16012 0.425955 0.212978 0.977057i \(-0.431684\pi\)
0.212978 + 0.977057i \(0.431684\pi\)
\(368\) 0.200873 0.0104712
\(369\) −4.51290 −0.234932
\(370\) −23.9199 −1.24354
\(371\) −4.75315 −0.246771
\(372\) 3.15098 0.163371
\(373\) 24.1101 1.24837 0.624187 0.781275i \(-0.285430\pi\)
0.624187 + 0.781275i \(0.285430\pi\)
\(374\) −14.4021 −0.744717
\(375\) 0.155556 0.00803290
\(376\) 60.5761 3.12398
\(377\) 27.0662 1.39398
\(378\) 16.9618 0.872423
\(379\) 11.5728 0.594454 0.297227 0.954807i \(-0.403938\pi\)
0.297227 + 0.954807i \(0.403938\pi\)
\(380\) 58.4871 3.00033
\(381\) −3.37916 −0.173119
\(382\) −64.2148 −3.28552
\(383\) 16.0663 0.820951 0.410476 0.911872i \(-0.365363\pi\)
0.410476 + 0.911872i \(0.365363\pi\)
\(384\) −8.06536 −0.411584
\(385\) 13.3798 0.681896
\(386\) −31.2999 −1.59312
\(387\) 27.6859 1.40735
\(388\) −12.5348 −0.636356
\(389\) 21.8451 1.10759 0.553796 0.832652i \(-0.313179\pi\)
0.553796 + 0.832652i \(0.313179\pi\)
\(390\) −12.4251 −0.629167
\(391\) 0.194117 0.00981691
\(392\) −5.74367 −0.290099
\(393\) −3.84394 −0.193901
\(394\) −18.3655 −0.925240
\(395\) 19.0750 0.959765
\(396\) −16.7420 −0.841316
\(397\) −9.07170 −0.455295 −0.227648 0.973744i \(-0.573103\pi\)
−0.227648 + 0.973744i \(0.573103\pi\)
\(398\) 31.3494 1.57140
\(399\) −5.42484 −0.271582
\(400\) 21.1077 1.05539
\(401\) −25.5092 −1.27387 −0.636934 0.770918i \(-0.719798\pi\)
−0.636934 + 0.770918i \(0.719798\pi\)
\(402\) −10.7915 −0.538230
\(403\) −7.23362 −0.360332
\(404\) 46.1993 2.29850
\(405\) −23.7847 −1.18187
\(406\) 49.4859 2.45594
\(407\) −4.51333 −0.223718
\(408\) 8.20695 0.406304
\(409\) −7.55183 −0.373414 −0.186707 0.982416i \(-0.559782\pi\)
−0.186707 + 0.982416i \(0.559782\pi\)
\(410\) 12.4570 0.615207
\(411\) −5.13382 −0.253233
\(412\) 5.73536 0.282561
\(413\) 26.3903 1.29858
\(414\) 0.337901 0.0166069
\(415\) 55.0518 2.70239
\(416\) −0.781433 −0.0383129
\(417\) 7.00420 0.342997
\(418\) 16.5252 0.808272
\(419\) 1.89237 0.0924485 0.0462243 0.998931i \(-0.485281\pi\)
0.0462243 + 0.998931i \(0.485281\pi\)
\(420\) −15.1707 −0.740256
\(421\) −9.42961 −0.459571 −0.229786 0.973241i \(-0.573803\pi\)
−0.229786 + 0.973241i \(0.573803\pi\)
\(422\) −21.0129 −1.02289
\(423\) 34.5455 1.67966
\(424\) −8.25077 −0.400693
\(425\) 20.3977 0.989435
\(426\) −11.3894 −0.551818
\(427\) 2.89341 0.140022
\(428\) 39.7800 1.92284
\(429\) −2.34443 −0.113190
\(430\) −76.4217 −3.68538
\(431\) 3.05460 0.147135 0.0735674 0.997290i \(-0.476562\pi\)
0.0735674 + 0.997290i \(0.476562\pi\)
\(432\) 9.98180 0.480249
\(433\) 14.5869 0.701001 0.350501 0.936563i \(-0.386011\pi\)
0.350501 + 0.936563i \(0.386011\pi\)
\(434\) −13.2255 −0.634842
\(435\) 9.32741 0.447215
\(436\) 64.0798 3.06887
\(437\) −0.222731 −0.0106547
\(438\) 3.44797 0.164750
\(439\) 37.0215 1.76694 0.883471 0.468486i \(-0.155200\pi\)
0.883471 + 0.468486i \(0.155200\pi\)
\(440\) 23.2253 1.10722
\(441\) −3.27552 −0.155977
\(442\) −37.4883 −1.78313
\(443\) −28.9365 −1.37481 −0.687407 0.726272i \(-0.741251\pi\)
−0.687407 + 0.726272i \(0.741251\pi\)
\(444\) 5.11747 0.242865
\(445\) 19.7674 0.937064
\(446\) 42.7438 2.02398
\(447\) 6.83830 0.323441
\(448\) 22.1324 1.04566
\(449\) −29.4580 −1.39021 −0.695104 0.718909i \(-0.744642\pi\)
−0.695104 + 0.718909i \(0.744642\pi\)
\(450\) 35.5065 1.67379
\(451\) 2.35046 0.110679
\(452\) 51.1581 2.40628
\(453\) 6.03984 0.283776
\(454\) −23.1695 −1.08740
\(455\) 34.8270 1.63272
\(456\) −9.41672 −0.440979
\(457\) 22.4801 1.05157 0.525787 0.850616i \(-0.323771\pi\)
0.525787 + 0.850616i \(0.323771\pi\)
\(458\) 65.3671 3.05440
\(459\) 9.64605 0.450239
\(460\) −0.622875 −0.0290417
\(461\) 6.96743 0.324505 0.162253 0.986749i \(-0.448124\pi\)
0.162253 + 0.986749i \(0.448124\pi\)
\(462\) −4.28639 −0.199421
\(463\) −10.2555 −0.476615 −0.238308 0.971190i \(-0.576593\pi\)
−0.238308 + 0.971190i \(0.576593\pi\)
\(464\) 29.1217 1.35194
\(465\) −2.49281 −0.115601
\(466\) −49.1848 −2.27844
\(467\) 4.05232 0.187519 0.0937595 0.995595i \(-0.470112\pi\)
0.0937595 + 0.995595i \(0.470112\pi\)
\(468\) −43.5788 −2.01443
\(469\) 30.2482 1.39673
\(470\) −95.3564 −4.39846
\(471\) 6.81581 0.314056
\(472\) 45.8096 2.10856
\(473\) −14.4197 −0.663017
\(474\) −6.11092 −0.280684
\(475\) −23.4045 −1.07387
\(476\) −45.7724 −2.09797
\(477\) −4.70527 −0.215440
\(478\) −14.3171 −0.654850
\(479\) 36.2095 1.65446 0.827228 0.561867i \(-0.189917\pi\)
0.827228 + 0.561867i \(0.189917\pi\)
\(480\) −0.269294 −0.0122915
\(481\) −11.7480 −0.535665
\(482\) 2.97800 0.135644
\(483\) 0.0577733 0.00262878
\(484\) −35.5076 −1.61398
\(485\) 9.91655 0.450287
\(486\) 25.4349 1.15375
\(487\) 7.21245 0.326827 0.163414 0.986558i \(-0.447749\pi\)
0.163414 + 0.986558i \(0.447749\pi\)
\(488\) 5.02253 0.227359
\(489\) −9.52310 −0.430650
\(490\) 9.04144 0.408451
\(491\) −30.7216 −1.38645 −0.693223 0.720723i \(-0.743810\pi\)
−0.693223 + 0.720723i \(0.743810\pi\)
\(492\) −2.66508 −0.120151
\(493\) 28.1422 1.26746
\(494\) 43.0144 1.93531
\(495\) 13.2450 0.595318
\(496\) −7.78299 −0.349466
\(497\) 31.9241 1.43199
\(498\) −17.6366 −0.790315
\(499\) −2.36094 −0.105690 −0.0528451 0.998603i \(-0.516829\pi\)
−0.0528451 + 0.998603i \(0.516829\pi\)
\(500\) −1.50599 −0.0673500
\(501\) −4.13248 −0.184626
\(502\) −35.8079 −1.59819
\(503\) 15.9751 0.712296 0.356148 0.934430i \(-0.384090\pi\)
0.356148 + 0.934430i \(0.384090\pi\)
\(504\) −40.0430 −1.78366
\(505\) −36.5493 −1.62642
\(506\) −0.175989 −0.00782367
\(507\) −0.703542 −0.0312454
\(508\) 32.7147 1.45148
\(509\) 18.4502 0.817792 0.408896 0.912581i \(-0.365914\pi\)
0.408896 + 0.912581i \(0.365914\pi\)
\(510\) −12.9190 −0.572064
\(511\) −9.66455 −0.427535
\(512\) 40.0577 1.77032
\(513\) −11.0680 −0.488663
\(514\) 7.64460 0.337189
\(515\) −4.53738 −0.199941
\(516\) 16.3498 0.719761
\(517\) −17.9924 −0.791303
\(518\) −21.4793 −0.943747
\(519\) 0.486746 0.0213658
\(520\) 60.4546 2.65111
\(521\) 40.0816 1.75601 0.878004 0.478653i \(-0.158875\pi\)
0.878004 + 0.478653i \(0.158875\pi\)
\(522\) 48.9874 2.14412
\(523\) 25.7630 1.12654 0.563269 0.826273i \(-0.309543\pi\)
0.563269 + 0.826273i \(0.309543\pi\)
\(524\) 37.2145 1.62572
\(525\) 6.07080 0.264952
\(526\) 52.9199 2.30742
\(527\) −7.52120 −0.327629
\(528\) −2.52248 −0.109777
\(529\) −22.9976 −0.999897
\(530\) 12.9880 0.564163
\(531\) 26.1244 1.13370
\(532\) 52.5197 2.27702
\(533\) 6.11815 0.265006
\(534\) −6.33275 −0.274045
\(535\) −31.4709 −1.36061
\(536\) 52.5064 2.26793
\(537\) 4.60698 0.198806
\(538\) 9.39534 0.405062
\(539\) 1.70599 0.0734821
\(540\) −30.9519 −1.33196
\(541\) 8.30184 0.356924 0.178462 0.983947i \(-0.442888\pi\)
0.178462 + 0.983947i \(0.442888\pi\)
\(542\) 30.6942 1.31843
\(543\) 6.06453 0.260254
\(544\) −0.812500 −0.0348356
\(545\) −50.6950 −2.17154
\(546\) −11.1573 −0.477489
\(547\) 14.2221 0.608094 0.304047 0.952657i \(-0.401662\pi\)
0.304047 + 0.952657i \(0.401662\pi\)
\(548\) 49.7021 2.12317
\(549\) 2.86427 0.122244
\(550\) −18.4929 −0.788539
\(551\) −32.2906 −1.37563
\(552\) 0.100286 0.00426845
\(553\) 17.1287 0.728387
\(554\) 21.6062 0.917959
\(555\) −4.04855 −0.171852
\(556\) −67.8099 −2.87578
\(557\) −40.0926 −1.69878 −0.849388 0.527768i \(-0.823029\pi\)
−0.849388 + 0.527768i \(0.823029\pi\)
\(558\) −13.0922 −0.554238
\(559\) −37.5339 −1.58751
\(560\) 37.4720 1.58348
\(561\) −2.43763 −0.102917
\(562\) −50.4101 −2.12642
\(563\) 3.96606 0.167149 0.0835747 0.996502i \(-0.473366\pi\)
0.0835747 + 0.996502i \(0.473366\pi\)
\(564\) 20.4008 0.859027
\(565\) −40.4724 −1.70269
\(566\) −29.1636 −1.22584
\(567\) −21.3579 −0.896947
\(568\) 55.4155 2.32518
\(569\) −0.313860 −0.0131577 −0.00657884 0.999978i \(-0.502094\pi\)
−0.00657884 + 0.999978i \(0.502094\pi\)
\(570\) 14.8234 0.620884
\(571\) −27.3508 −1.14459 −0.572297 0.820046i \(-0.693948\pi\)
−0.572297 + 0.820046i \(0.693948\pi\)
\(572\) 22.6971 0.949015
\(573\) −10.8687 −0.454045
\(574\) 11.1860 0.466895
\(575\) 0.249253 0.0103946
\(576\) 21.9094 0.912892
\(577\) 32.3912 1.34846 0.674232 0.738520i \(-0.264475\pi\)
0.674232 + 0.738520i \(0.264475\pi\)
\(578\) 2.73432 0.113733
\(579\) −5.29766 −0.220163
\(580\) −90.3016 −3.74957
\(581\) 49.4348 2.05090
\(582\) −3.17690 −0.131687
\(583\) 2.45065 0.101495
\(584\) −16.7762 −0.694205
\(585\) 34.4762 1.42542
\(586\) −35.4098 −1.46277
\(587\) −43.1957 −1.78288 −0.891439 0.453141i \(-0.850303\pi\)
−0.891439 + 0.453141i \(0.850303\pi\)
\(588\) −1.93435 −0.0797711
\(589\) 8.62989 0.355589
\(590\) −72.1115 −2.96878
\(591\) −3.10845 −0.127864
\(592\) −12.6403 −0.519512
\(593\) 17.4547 0.716780 0.358390 0.933572i \(-0.383326\pi\)
0.358390 + 0.933572i \(0.383326\pi\)
\(594\) −8.74525 −0.358822
\(595\) 36.2116 1.48453
\(596\) −66.2038 −2.71181
\(597\) 5.30604 0.217162
\(598\) −0.458093 −0.0187328
\(599\) −3.40234 −0.139016 −0.0695079 0.997581i \(-0.522143\pi\)
−0.0695079 + 0.997581i \(0.522143\pi\)
\(600\) 10.5380 0.430213
\(601\) 7.96270 0.324805 0.162403 0.986725i \(-0.448076\pi\)
0.162403 + 0.986725i \(0.448076\pi\)
\(602\) −68.6244 −2.79692
\(603\) 29.9435 1.21939
\(604\) −58.4736 −2.37926
\(605\) 28.0909 1.14206
\(606\) 11.7091 0.475649
\(607\) 47.8410 1.94181 0.970904 0.239469i \(-0.0769732\pi\)
0.970904 + 0.239469i \(0.0769732\pi\)
\(608\) 0.932269 0.0378085
\(609\) 8.37573 0.339402
\(610\) −7.90626 −0.320115
\(611\) −46.8335 −1.89468
\(612\) −45.3113 −1.83160
\(613\) 17.1970 0.694582 0.347291 0.937757i \(-0.387102\pi\)
0.347291 + 0.937757i \(0.387102\pi\)
\(614\) −42.1396 −1.70062
\(615\) 2.10841 0.0850192
\(616\) 20.8556 0.840295
\(617\) −25.6380 −1.03215 −0.516073 0.856545i \(-0.672607\pi\)
−0.516073 + 0.856545i \(0.672607\pi\)
\(618\) 1.45361 0.0584728
\(619\) −27.3832 −1.10063 −0.550313 0.834959i \(-0.685492\pi\)
−0.550313 + 0.834959i \(0.685492\pi\)
\(620\) 24.1337 0.969234
\(621\) 0.117871 0.00473001
\(622\) 58.2254 2.33463
\(623\) 17.7505 0.711159
\(624\) −6.56592 −0.262847
\(625\) −24.3974 −0.975894
\(626\) 63.0725 2.52088
\(627\) 2.79696 0.111700
\(628\) −65.9861 −2.63313
\(629\) −12.2151 −0.487048
\(630\) 63.0339 2.51133
\(631\) 3.42616 0.136393 0.0681967 0.997672i \(-0.478275\pi\)
0.0681967 + 0.997672i \(0.478275\pi\)
\(632\) 29.7329 1.18271
\(633\) −3.55653 −0.141359
\(634\) 19.6980 0.782309
\(635\) −25.8814 −1.02707
\(636\) −2.77868 −0.110182
\(637\) 4.44063 0.175944
\(638\) −25.5141 −1.01011
\(639\) 31.6025 1.25018
\(640\) −61.7736 −2.44182
\(641\) 0.940539 0.0371491 0.0185745 0.999827i \(-0.494087\pi\)
0.0185745 + 0.999827i \(0.494087\pi\)
\(642\) 10.0821 0.397910
\(643\) −21.0572 −0.830415 −0.415207 0.909727i \(-0.636291\pi\)
−0.415207 + 0.909727i \(0.636291\pi\)
\(644\) −0.559322 −0.0220404
\(645\) −12.9347 −0.509305
\(646\) 44.7245 1.75966
\(647\) 39.4010 1.54902 0.774508 0.632565i \(-0.217998\pi\)
0.774508 + 0.632565i \(0.217998\pi\)
\(648\) −37.0741 −1.45641
\(649\) −13.6064 −0.534098
\(650\) −48.1363 −1.88806
\(651\) −2.23847 −0.0877326
\(652\) 92.1962 3.61068
\(653\) 15.6535 0.612571 0.306285 0.951940i \(-0.400914\pi\)
0.306285 + 0.951940i \(0.400914\pi\)
\(654\) 16.2408 0.635067
\(655\) −29.4412 −1.15036
\(656\) 6.58280 0.257015
\(657\) −9.56720 −0.373252
\(658\) −85.6271 −3.33809
\(659\) −30.4412 −1.18582 −0.592911 0.805268i \(-0.702021\pi\)
−0.592911 + 0.805268i \(0.702021\pi\)
\(660\) 7.82178 0.304462
\(661\) −11.9942 −0.466522 −0.233261 0.972414i \(-0.574940\pi\)
−0.233261 + 0.972414i \(0.574940\pi\)
\(662\) −12.8673 −0.500100
\(663\) −6.34507 −0.246422
\(664\) 85.8116 3.33013
\(665\) −41.5495 −1.61122
\(666\) −21.2629 −0.823922
\(667\) 0.343888 0.0133154
\(668\) 40.0079 1.54795
\(669\) 7.23459 0.279705
\(670\) −82.6533 −3.19317
\(671\) −1.49180 −0.0575902
\(672\) −0.241817 −0.00932831
\(673\) 15.7547 0.607297 0.303649 0.952784i \(-0.401795\pi\)
0.303649 + 0.952784i \(0.401795\pi\)
\(674\) −43.3261 −1.66886
\(675\) 12.3859 0.476733
\(676\) 6.81121 0.261970
\(677\) −6.69488 −0.257305 −0.128653 0.991690i \(-0.541065\pi\)
−0.128653 + 0.991690i \(0.541065\pi\)
\(678\) 12.9659 0.497952
\(679\) 8.90476 0.341733
\(680\) 62.8580 2.41049
\(681\) −3.92155 −0.150274
\(682\) 6.81883 0.261106
\(683\) 30.9121 1.18282 0.591410 0.806371i \(-0.298571\pi\)
0.591410 + 0.806371i \(0.298571\pi\)
\(684\) 51.9906 1.98791
\(685\) −39.3205 −1.50236
\(686\) −40.9406 −1.56312
\(687\) 11.0637 0.422106
\(688\) −40.3844 −1.53964
\(689\) 6.37895 0.243018
\(690\) −0.157866 −0.00600985
\(691\) 19.9693 0.759670 0.379835 0.925054i \(-0.375981\pi\)
0.379835 + 0.925054i \(0.375981\pi\)
\(692\) −4.71235 −0.179137
\(693\) 11.8936 0.451800
\(694\) 31.8689 1.20973
\(695\) 53.6460 2.03491
\(696\) 14.5390 0.551100
\(697\) 6.36138 0.240955
\(698\) −40.4484 −1.53099
\(699\) −8.32476 −0.314871
\(700\) −58.7734 −2.22143
\(701\) −28.7748 −1.08681 −0.543405 0.839471i \(-0.682865\pi\)
−0.543405 + 0.839471i \(0.682865\pi\)
\(702\) −22.7636 −0.859155
\(703\) 14.0157 0.528613
\(704\) −11.4111 −0.430071
\(705\) −16.1395 −0.607849
\(706\) −34.0254 −1.28056
\(707\) −32.8202 −1.23433
\(708\) 15.4277 0.579809
\(709\) 10.0280 0.376609 0.188305 0.982111i \(-0.439701\pi\)
0.188305 + 0.982111i \(0.439701\pi\)
\(710\) −87.2327 −3.27379
\(711\) 16.9562 0.635906
\(712\) 30.8122 1.15474
\(713\) −0.0919064 −0.00344192
\(714\) −11.6009 −0.434152
\(715\) −17.9562 −0.671526
\(716\) −44.6016 −1.66684
\(717\) −2.42324 −0.0904976
\(718\) 79.6900 2.97401
\(719\) −16.6360 −0.620419 −0.310210 0.950668i \(-0.600399\pi\)
−0.310210 + 0.950668i \(0.600399\pi\)
\(720\) 37.0945 1.38243
\(721\) −4.07443 −0.151740
\(722\) −4.69688 −0.174800
\(723\) 0.504040 0.0187455
\(724\) −58.7127 −2.18204
\(725\) 36.1356 1.34204
\(726\) −8.99929 −0.333995
\(727\) 29.3994 1.09036 0.545182 0.838318i \(-0.316461\pi\)
0.545182 + 0.838318i \(0.316461\pi\)
\(728\) 54.2863 2.01199
\(729\) −18.1274 −0.671386
\(730\) 26.4084 0.977420
\(731\) −39.0261 −1.44343
\(732\) 1.69148 0.0625190
\(733\) 22.8461 0.843840 0.421920 0.906633i \(-0.361356\pi\)
0.421920 + 0.906633i \(0.361356\pi\)
\(734\) −20.0225 −0.739045
\(735\) 1.53031 0.0564462
\(736\) −0.00992846 −0.000365968 0
\(737\) −15.5955 −0.574467
\(738\) 11.0733 0.407615
\(739\) 38.3670 1.41135 0.705677 0.708533i \(-0.250643\pi\)
0.705677 + 0.708533i \(0.250643\pi\)
\(740\) 39.1954 1.44085
\(741\) 7.28039 0.267452
\(742\) 11.6628 0.428156
\(743\) 40.3801 1.48140 0.740701 0.671834i \(-0.234493\pi\)
0.740701 + 0.671834i \(0.234493\pi\)
\(744\) −3.88565 −0.142455
\(745\) 52.3754 1.91889
\(746\) −59.1590 −2.16597
\(747\) 48.9369 1.79051
\(748\) 23.5995 0.862883
\(749\) −28.2599 −1.03259
\(750\) −0.381689 −0.0139373
\(751\) 29.2280 1.06655 0.533273 0.845943i \(-0.320962\pi\)
0.533273 + 0.845943i \(0.320962\pi\)
\(752\) −50.3903 −1.83755
\(753\) −6.06066 −0.220863
\(754\) −66.4123 −2.41859
\(755\) 46.2599 1.68357
\(756\) −27.7938 −1.01085
\(757\) 31.2717 1.13659 0.568294 0.822826i \(-0.307604\pi\)
0.568294 + 0.822826i \(0.307604\pi\)
\(758\) −28.3962 −1.03140
\(759\) −0.0297870 −0.00108120
\(760\) −72.1238 −2.61621
\(761\) −11.5473 −0.418588 −0.209294 0.977853i \(-0.567117\pi\)
−0.209294 + 0.977853i \(0.567117\pi\)
\(762\) 8.29145 0.300368
\(763\) −45.5226 −1.64803
\(764\) 105.223 3.80684
\(765\) 35.8468 1.29605
\(766\) −39.4220 −1.42438
\(767\) −35.4170 −1.27883
\(768\) 13.3540 0.481871
\(769\) −25.3576 −0.914418 −0.457209 0.889359i \(-0.651151\pi\)
−0.457209 + 0.889359i \(0.651151\pi\)
\(770\) −32.8300 −1.18311
\(771\) 1.29389 0.0465982
\(772\) 51.2883 1.84591
\(773\) −4.45434 −0.160211 −0.0801057 0.996786i \(-0.525526\pi\)
−0.0801057 + 0.996786i \(0.525526\pi\)
\(774\) −67.9331 −2.44180
\(775\) −9.65749 −0.346907
\(776\) 15.4573 0.554886
\(777\) −3.63548 −0.130422
\(778\) −53.6015 −1.92171
\(779\) −7.29911 −0.261518
\(780\) 20.3598 0.728998
\(781\) −16.4596 −0.588969
\(782\) −0.476305 −0.0170326
\(783\) 17.0885 0.610692
\(784\) 4.77788 0.170638
\(785\) 52.2032 1.86321
\(786\) 9.43190 0.336425
\(787\) 29.7128 1.05915 0.529573 0.848264i \(-0.322352\pi\)
0.529573 + 0.848264i \(0.322352\pi\)
\(788\) 30.0939 1.07205
\(789\) 8.95694 0.318876
\(790\) −46.8043 −1.66522
\(791\) −36.3430 −1.29221
\(792\) 20.6455 0.733606
\(793\) −3.88309 −0.137893
\(794\) 22.2593 0.789952
\(795\) 2.19828 0.0779650
\(796\) −51.3694 −1.82074
\(797\) 36.7236 1.30082 0.650408 0.759585i \(-0.274598\pi\)
0.650408 + 0.759585i \(0.274598\pi\)
\(798\) 13.3110 0.471203
\(799\) −48.6954 −1.72272
\(800\) −1.04328 −0.0368855
\(801\) 17.5717 0.620865
\(802\) 62.5920 2.21020
\(803\) 4.98289 0.175842
\(804\) 17.6830 0.623632
\(805\) 0.442493 0.0155958
\(806\) 17.7492 0.625187
\(807\) 1.59021 0.0559779
\(808\) −56.9710 −2.00423
\(809\) 2.17184 0.0763578 0.0381789 0.999271i \(-0.487844\pi\)
0.0381789 + 0.999271i \(0.487844\pi\)
\(810\) 58.3605 2.05058
\(811\) 11.9110 0.418254 0.209127 0.977889i \(-0.432938\pi\)
0.209127 + 0.977889i \(0.432938\pi\)
\(812\) −81.0881 −2.84563
\(813\) 5.19514 0.182202
\(814\) 11.0744 0.388157
\(815\) −72.9386 −2.55493
\(816\) −6.82695 −0.238991
\(817\) 44.7789 1.56661
\(818\) 18.5300 0.647885
\(819\) 30.9586 1.08178
\(820\) −20.4122 −0.712824
\(821\) −13.6014 −0.474693 −0.237347 0.971425i \(-0.576278\pi\)
−0.237347 + 0.971425i \(0.576278\pi\)
\(822\) 12.5969 0.439366
\(823\) 27.5095 0.958922 0.479461 0.877563i \(-0.340832\pi\)
0.479461 + 0.877563i \(0.340832\pi\)
\(824\) −7.07260 −0.246386
\(825\) −3.13001 −0.108973
\(826\) −64.7539 −2.25308
\(827\) 35.5469 1.23609 0.618043 0.786144i \(-0.287926\pi\)
0.618043 + 0.786144i \(0.287926\pi\)
\(828\) −0.553688 −0.0192420
\(829\) −29.5771 −1.02726 −0.513628 0.858013i \(-0.671699\pi\)
−0.513628 + 0.858013i \(0.671699\pi\)
\(830\) −135.081 −4.68873
\(831\) 3.65695 0.126858
\(832\) −29.7026 −1.02975
\(833\) 4.61717 0.159975
\(834\) −17.1862 −0.595110
\(835\) −31.6512 −1.09533
\(836\) −27.0783 −0.936522
\(837\) −4.56701 −0.157859
\(838\) −4.64333 −0.160401
\(839\) 4.37288 0.150969 0.0754844 0.997147i \(-0.475950\pi\)
0.0754844 + 0.997147i \(0.475950\pi\)
\(840\) 18.7079 0.645484
\(841\) 20.8553 0.719150
\(842\) 23.1375 0.797370
\(843\) −8.53214 −0.293863
\(844\) 34.4319 1.18520
\(845\) −5.38851 −0.185370
\(846\) −84.7645 −2.91426
\(847\) 25.2247 0.866732
\(848\) 6.86341 0.235690
\(849\) −4.93608 −0.169406
\(850\) −50.0500 −1.71670
\(851\) −0.149264 −0.00511671
\(852\) 18.6628 0.639376
\(853\) −4.06987 −0.139350 −0.0696749 0.997570i \(-0.522196\pi\)
−0.0696749 + 0.997570i \(0.522196\pi\)
\(854\) −7.09958 −0.242943
\(855\) −41.1310 −1.40665
\(856\) −49.0550 −1.67667
\(857\) −52.4420 −1.79139 −0.895693 0.444673i \(-0.853320\pi\)
−0.895693 + 0.444673i \(0.853320\pi\)
\(858\) 5.75253 0.196388
\(859\) 18.9272 0.645788 0.322894 0.946435i \(-0.395344\pi\)
0.322894 + 0.946435i \(0.395344\pi\)
\(860\) 125.225 4.27015
\(861\) 1.89328 0.0645230
\(862\) −7.49508 −0.255283
\(863\) 16.3931 0.558027 0.279014 0.960287i \(-0.409993\pi\)
0.279014 + 0.960287i \(0.409993\pi\)
\(864\) −0.493365 −0.0167846
\(865\) 3.72805 0.126757
\(866\) −35.7919 −1.21626
\(867\) 0.462796 0.0157174
\(868\) 21.6714 0.735574
\(869\) −8.83129 −0.299581
\(870\) −22.8867 −0.775932
\(871\) −40.5944 −1.37549
\(872\) −79.0205 −2.67597
\(873\) 8.81505 0.298344
\(874\) 0.546517 0.0184862
\(875\) 1.06986 0.0361680
\(876\) −5.64988 −0.190892
\(877\) −31.1690 −1.05250 −0.526251 0.850329i \(-0.676403\pi\)
−0.526251 + 0.850329i \(0.676403\pi\)
\(878\) −90.8399 −3.06570
\(879\) −5.99328 −0.202148
\(880\) −19.3200 −0.651276
\(881\) 18.4490 0.621563 0.310781 0.950481i \(-0.399409\pi\)
0.310781 + 0.950481i \(0.399409\pi\)
\(882\) 8.03715 0.270625
\(883\) −29.0624 −0.978029 −0.489015 0.872276i \(-0.662644\pi\)
−0.489015 + 0.872276i \(0.662644\pi\)
\(884\) 61.4286 2.06607
\(885\) −12.2052 −0.410274
\(886\) 71.0016 2.38535
\(887\) −21.9044 −0.735476 −0.367738 0.929929i \(-0.619868\pi\)
−0.367738 + 0.929929i \(0.619868\pi\)
\(888\) −6.31065 −0.211772
\(889\) −23.2407 −0.779467
\(890\) −48.5033 −1.62584
\(891\) 11.0118 0.368909
\(892\) −70.0404 −2.34513
\(893\) 55.8735 1.86974
\(894\) −16.7792 −0.561179
\(895\) 35.2854 1.17946
\(896\) −55.4708 −1.85315
\(897\) −0.0775345 −0.00258880
\(898\) 72.2812 2.41205
\(899\) −13.3242 −0.444386
\(900\) −58.1813 −1.93938
\(901\) 6.63255 0.220962
\(902\) −5.76732 −0.192031
\(903\) −11.6150 −0.386523
\(904\) −63.0860 −2.09821
\(905\) 46.4490 1.54402
\(906\) −14.8200 −0.492361
\(907\) −13.1867 −0.437857 −0.218928 0.975741i \(-0.570256\pi\)
−0.218928 + 0.975741i \(0.570256\pi\)
\(908\) 37.9658 1.25994
\(909\) −32.4896 −1.07761
\(910\) −85.4552 −2.83281
\(911\) 18.2306 0.604008 0.302004 0.953307i \(-0.402344\pi\)
0.302004 + 0.953307i \(0.402344\pi\)
\(912\) 7.83331 0.259387
\(913\) −25.4878 −0.843523
\(914\) −55.1595 −1.82451
\(915\) −1.33817 −0.0442386
\(916\) −107.111 −3.53905
\(917\) −26.4373 −0.873038
\(918\) −23.6686 −0.781179
\(919\) −3.48482 −0.114954 −0.0574768 0.998347i \(-0.518306\pi\)
−0.0574768 + 0.998347i \(0.518306\pi\)
\(920\) 0.768102 0.0253236
\(921\) −7.13233 −0.235018
\(922\) −17.0960 −0.563027
\(923\) −42.8436 −1.41021
\(924\) 7.02372 0.231063
\(925\) −15.6846 −0.515708
\(926\) 25.1641 0.826942
\(927\) −4.03338 −0.132474
\(928\) −1.43938 −0.0472501
\(929\) −36.1583 −1.18631 −0.593157 0.805087i \(-0.702119\pi\)
−0.593157 + 0.805087i \(0.702119\pi\)
\(930\) 6.11663 0.200572
\(931\) −5.29778 −0.173628
\(932\) 80.5947 2.63997
\(933\) 9.85493 0.322636
\(934\) −9.94319 −0.325351
\(935\) −18.6701 −0.610578
\(936\) 53.7395 1.75653
\(937\) −55.7418 −1.82100 −0.910502 0.413504i \(-0.864305\pi\)
−0.910502 + 0.413504i \(0.864305\pi\)
\(938\) −74.2201 −2.42337
\(939\) 10.6753 0.348376
\(940\) 156.252 5.09637
\(941\) 36.3584 1.18525 0.592625 0.805478i \(-0.298091\pi\)
0.592625 + 0.805478i \(0.298091\pi\)
\(942\) −16.7240 −0.544897
\(943\) 0.0777338 0.00253136
\(944\) −38.1068 −1.24027
\(945\) 21.9884 0.715281
\(946\) 35.3816 1.15035
\(947\) 5.51942 0.179357 0.0896785 0.995971i \(-0.471416\pi\)
0.0896785 + 0.995971i \(0.471416\pi\)
\(948\) 10.0134 0.325221
\(949\) 12.9703 0.421033
\(950\) 57.4278 1.86320
\(951\) 3.33399 0.108112
\(952\) 56.4445 1.82938
\(953\) 0.837997 0.0271454 0.0135727 0.999908i \(-0.495680\pi\)
0.0135727 + 0.999908i \(0.495680\pi\)
\(954\) 11.5453 0.373794
\(955\) −83.2445 −2.69373
\(956\) 23.4602 0.758757
\(957\) −4.31839 −0.139594
\(958\) −88.8475 −2.87053
\(959\) −35.3086 −1.14018
\(960\) −10.2360 −0.330365
\(961\) −27.4390 −0.885130
\(962\) 28.8262 0.929395
\(963\) −27.9752 −0.901489
\(964\) −4.87978 −0.157167
\(965\) −40.5754 −1.30617
\(966\) −0.141759 −0.00456101
\(967\) −16.0683 −0.516720 −0.258360 0.966049i \(-0.583182\pi\)
−0.258360 + 0.966049i \(0.583182\pi\)
\(968\) 43.7864 1.40735
\(969\) 7.56983 0.243178
\(970\) −24.3323 −0.781262
\(971\) 52.6248 1.68881 0.844406 0.535704i \(-0.179954\pi\)
0.844406 + 0.535704i \(0.179954\pi\)
\(972\) −41.6779 −1.33682
\(973\) 48.1724 1.54434
\(974\) −17.6972 −0.567056
\(975\) −8.14730 −0.260922
\(976\) −4.17800 −0.133734
\(977\) 45.7366 1.46324 0.731622 0.681710i \(-0.238763\pi\)
0.731622 + 0.681710i \(0.238763\pi\)
\(978\) 23.3669 0.747190
\(979\) −9.15187 −0.292495
\(980\) −14.8154 −0.473260
\(981\) −45.0640 −1.43878
\(982\) 75.3817 2.40553
\(983\) 11.6657 0.372079 0.186040 0.982542i \(-0.440435\pi\)
0.186040 + 0.982542i \(0.440435\pi\)
\(984\) 3.28646 0.104769
\(985\) −23.8080 −0.758585
\(986\) −69.0526 −2.19908
\(987\) −14.4928 −0.461311
\(988\) −70.4838 −2.24239
\(989\) −0.476885 −0.0151641
\(990\) −32.4993 −1.03289
\(991\) 29.2300 0.928521 0.464261 0.885699i \(-0.346320\pi\)
0.464261 + 0.885699i \(0.346320\pi\)
\(992\) 0.384685 0.0122138
\(993\) −2.17785 −0.0691119
\(994\) −78.3323 −2.48455
\(995\) 40.6396 1.28836
\(996\) 28.8995 0.915716
\(997\) 17.1860 0.544286 0.272143 0.962257i \(-0.412268\pi\)
0.272143 + 0.962257i \(0.412268\pi\)
\(998\) 5.79305 0.183376
\(999\) −7.41723 −0.234671
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 4003.2.a.c.1.13 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.13 179 1.1 even 1 trivial