Properties

Label 4028.2.a.d.1.2
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.97522\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.97522 q^{3} +0.840694 q^{5} -4.22061 q^{7} +5.85193 q^{9} +O(q^{10})\) \(q-2.97522 q^{3} +0.840694 q^{5} -4.22061 q^{7} +5.85193 q^{9} +3.71552 q^{11} -1.07012 q^{13} -2.50125 q^{15} +1.37513 q^{17} -1.00000 q^{19} +12.5573 q^{21} -4.51456 q^{23} -4.29323 q^{25} -8.48511 q^{27} +0.356792 q^{29} -4.24901 q^{31} -11.0545 q^{33} -3.54825 q^{35} +4.55793 q^{37} +3.18386 q^{39} +10.9742 q^{41} +5.17832 q^{43} +4.91968 q^{45} -4.68548 q^{47} +10.8136 q^{49} -4.09133 q^{51} +1.00000 q^{53} +3.12361 q^{55} +2.97522 q^{57} +7.35327 q^{59} +6.24655 q^{61} -24.6987 q^{63} -0.899648 q^{65} +3.54664 q^{67} +13.4318 q^{69} -5.04982 q^{71} +5.95668 q^{73} +12.7733 q^{75} -15.6818 q^{77} +11.2077 q^{79} +7.68928 q^{81} -3.23503 q^{83} +1.15607 q^{85} -1.06153 q^{87} -0.365040 q^{89} +4.51658 q^{91} +12.6417 q^{93} -0.840694 q^{95} -4.23679 q^{97} +21.7429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.97522 −1.71774 −0.858872 0.512191i \(-0.828834\pi\)
−0.858872 + 0.512191i \(0.828834\pi\)
\(4\) 0 0
\(5\) 0.840694 0.375970 0.187985 0.982172i \(-0.439804\pi\)
0.187985 + 0.982172i \(0.439804\pi\)
\(6\) 0 0
\(7\) −4.22061 −1.59524 −0.797621 0.603159i \(-0.793908\pi\)
−0.797621 + 0.603159i \(0.793908\pi\)
\(8\) 0 0
\(9\) 5.85193 1.95064
\(10\) 0 0
\(11\) 3.71552 1.12027 0.560135 0.828401i \(-0.310749\pi\)
0.560135 + 0.828401i \(0.310749\pi\)
\(12\) 0 0
\(13\) −1.07012 −0.296799 −0.148400 0.988927i \(-0.547412\pi\)
−0.148400 + 0.988927i \(0.547412\pi\)
\(14\) 0 0
\(15\) −2.50125 −0.645820
\(16\) 0 0
\(17\) 1.37513 0.333519 0.166760 0.985998i \(-0.446670\pi\)
0.166760 + 0.985998i \(0.446670\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 12.5573 2.74022
\(22\) 0 0
\(23\) −4.51456 −0.941351 −0.470676 0.882306i \(-0.655990\pi\)
−0.470676 + 0.882306i \(0.655990\pi\)
\(24\) 0 0
\(25\) −4.29323 −0.858647
\(26\) 0 0
\(27\) −8.48511 −1.63296
\(28\) 0 0
\(29\) 0.356792 0.0662546 0.0331273 0.999451i \(-0.489453\pi\)
0.0331273 + 0.999451i \(0.489453\pi\)
\(30\) 0 0
\(31\) −4.24901 −0.763144 −0.381572 0.924339i \(-0.624617\pi\)
−0.381572 + 0.924339i \(0.624617\pi\)
\(32\) 0 0
\(33\) −11.0545 −1.92434
\(34\) 0 0
\(35\) −3.54825 −0.599763
\(36\) 0 0
\(37\) 4.55793 0.749319 0.374659 0.927163i \(-0.377760\pi\)
0.374659 + 0.927163i \(0.377760\pi\)
\(38\) 0 0
\(39\) 3.18386 0.509825
\(40\) 0 0
\(41\) 10.9742 1.71388 0.856942 0.515412i \(-0.172361\pi\)
0.856942 + 0.515412i \(0.172361\pi\)
\(42\) 0 0
\(43\) 5.17832 0.789686 0.394843 0.918749i \(-0.370799\pi\)
0.394843 + 0.918749i \(0.370799\pi\)
\(44\) 0 0
\(45\) 4.91968 0.733383
\(46\) 0 0
\(47\) −4.68548 −0.683448 −0.341724 0.939800i \(-0.611011\pi\)
−0.341724 + 0.939800i \(0.611011\pi\)
\(48\) 0 0
\(49\) 10.8136 1.54480
\(50\) 0 0
\(51\) −4.09133 −0.572900
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 3.12361 0.421188
\(56\) 0 0
\(57\) 2.97522 0.394077
\(58\) 0 0
\(59\) 7.35327 0.957315 0.478657 0.878002i \(-0.341124\pi\)
0.478657 + 0.878002i \(0.341124\pi\)
\(60\) 0 0
\(61\) 6.24655 0.799789 0.399895 0.916561i \(-0.369047\pi\)
0.399895 + 0.916561i \(0.369047\pi\)
\(62\) 0 0
\(63\) −24.6987 −3.11175
\(64\) 0 0
\(65\) −0.899648 −0.111588
\(66\) 0 0
\(67\) 3.54664 0.433291 0.216646 0.976250i \(-0.430488\pi\)
0.216646 + 0.976250i \(0.430488\pi\)
\(68\) 0 0
\(69\) 13.4318 1.61700
\(70\) 0 0
\(71\) −5.04982 −0.599303 −0.299652 0.954049i \(-0.596870\pi\)
−0.299652 + 0.954049i \(0.596870\pi\)
\(72\) 0 0
\(73\) 5.95668 0.697177 0.348589 0.937276i \(-0.386661\pi\)
0.348589 + 0.937276i \(0.386661\pi\)
\(74\) 0 0
\(75\) 12.7733 1.47493
\(76\) 0 0
\(77\) −15.6818 −1.78710
\(78\) 0 0
\(79\) 11.2077 1.26096 0.630482 0.776204i \(-0.282857\pi\)
0.630482 + 0.776204i \(0.282857\pi\)
\(80\) 0 0
\(81\) 7.68928 0.854364
\(82\) 0 0
\(83\) −3.23503 −0.355091 −0.177545 0.984113i \(-0.556816\pi\)
−0.177545 + 0.984113i \(0.556816\pi\)
\(84\) 0 0
\(85\) 1.15607 0.125393
\(86\) 0 0
\(87\) −1.06153 −0.113808
\(88\) 0 0
\(89\) −0.365040 −0.0386942 −0.0193471 0.999813i \(-0.506159\pi\)
−0.0193471 + 0.999813i \(0.506159\pi\)
\(90\) 0 0
\(91\) 4.51658 0.473467
\(92\) 0 0
\(93\) 12.6417 1.31089
\(94\) 0 0
\(95\) −0.840694 −0.0862534
\(96\) 0 0
\(97\) −4.23679 −0.430181 −0.215090 0.976594i \(-0.569005\pi\)
−0.215090 + 0.976594i \(0.569005\pi\)
\(98\) 0 0
\(99\) 21.7429 2.18525
\(100\) 0 0
\(101\) −5.24757 −0.522153 −0.261076 0.965318i \(-0.584077\pi\)
−0.261076 + 0.965318i \(0.584077\pi\)
\(102\) 0 0
\(103\) 11.5467 1.13773 0.568867 0.822429i \(-0.307382\pi\)
0.568867 + 0.822429i \(0.307382\pi\)
\(104\) 0 0
\(105\) 10.5568 1.03024
\(106\) 0 0
\(107\) −11.9642 −1.15662 −0.578310 0.815817i \(-0.696288\pi\)
−0.578310 + 0.815817i \(0.696288\pi\)
\(108\) 0 0
\(109\) −9.53419 −0.913209 −0.456605 0.889670i \(-0.650935\pi\)
−0.456605 + 0.889670i \(0.650935\pi\)
\(110\) 0 0
\(111\) −13.5608 −1.28714
\(112\) 0 0
\(113\) −7.29833 −0.686569 −0.343285 0.939231i \(-0.611540\pi\)
−0.343285 + 0.939231i \(0.611540\pi\)
\(114\) 0 0
\(115\) −3.79537 −0.353920
\(116\) 0 0
\(117\) −6.26229 −0.578949
\(118\) 0 0
\(119\) −5.80391 −0.532044
\(120\) 0 0
\(121\) 2.80506 0.255006
\(122\) 0 0
\(123\) −32.6507 −2.94401
\(124\) 0 0
\(125\) −7.81277 −0.698795
\(126\) 0 0
\(127\) −17.5407 −1.55649 −0.778245 0.627961i \(-0.783890\pi\)
−0.778245 + 0.627961i \(0.783890\pi\)
\(128\) 0 0
\(129\) −15.4066 −1.35648
\(130\) 0 0
\(131\) −1.77183 −0.154806 −0.0774028 0.997000i \(-0.524663\pi\)
−0.0774028 + 0.997000i \(0.524663\pi\)
\(132\) 0 0
\(133\) 4.22061 0.365974
\(134\) 0 0
\(135\) −7.13338 −0.613944
\(136\) 0 0
\(137\) −8.58520 −0.733483 −0.366741 0.930323i \(-0.619527\pi\)
−0.366741 + 0.930323i \(0.619527\pi\)
\(138\) 0 0
\(139\) −3.52199 −0.298731 −0.149366 0.988782i \(-0.547723\pi\)
−0.149366 + 0.988782i \(0.547723\pi\)
\(140\) 0 0
\(141\) 13.9403 1.17399
\(142\) 0 0
\(143\) −3.97607 −0.332495
\(144\) 0 0
\(145\) 0.299953 0.0249097
\(146\) 0 0
\(147\) −32.1728 −2.65357
\(148\) 0 0
\(149\) 5.33047 0.436689 0.218345 0.975872i \(-0.429934\pi\)
0.218345 + 0.975872i \(0.429934\pi\)
\(150\) 0 0
\(151\) −0.0625813 −0.00509280 −0.00254640 0.999997i \(-0.500811\pi\)
−0.00254640 + 0.999997i \(0.500811\pi\)
\(152\) 0 0
\(153\) 8.04719 0.650577
\(154\) 0 0
\(155\) −3.57211 −0.286919
\(156\) 0 0
\(157\) 14.1905 1.13253 0.566263 0.824225i \(-0.308389\pi\)
0.566263 + 0.824225i \(0.308389\pi\)
\(158\) 0 0
\(159\) −2.97522 −0.235950
\(160\) 0 0
\(161\) 19.0542 1.50168
\(162\) 0 0
\(163\) 0.0663669 0.00519825 0.00259913 0.999997i \(-0.499173\pi\)
0.00259913 + 0.999997i \(0.499173\pi\)
\(164\) 0 0
\(165\) −9.29343 −0.723493
\(166\) 0 0
\(167\) 5.05248 0.390973 0.195486 0.980706i \(-0.437371\pi\)
0.195486 + 0.980706i \(0.437371\pi\)
\(168\) 0 0
\(169\) −11.8548 −0.911910
\(170\) 0 0
\(171\) −5.85193 −0.447508
\(172\) 0 0
\(173\) −13.7174 −1.04292 −0.521458 0.853277i \(-0.674611\pi\)
−0.521458 + 0.853277i \(0.674611\pi\)
\(174\) 0 0
\(175\) 18.1201 1.36975
\(176\) 0 0
\(177\) −21.8776 −1.64442
\(178\) 0 0
\(179\) 1.86867 0.139671 0.0698355 0.997559i \(-0.477753\pi\)
0.0698355 + 0.997559i \(0.477753\pi\)
\(180\) 0 0
\(181\) 12.3639 0.919001 0.459500 0.888178i \(-0.348028\pi\)
0.459500 + 0.888178i \(0.348028\pi\)
\(182\) 0 0
\(183\) −18.5849 −1.37383
\(184\) 0 0
\(185\) 3.83182 0.281721
\(186\) 0 0
\(187\) 5.10934 0.373632
\(188\) 0 0
\(189\) 35.8124 2.60497
\(190\) 0 0
\(191\) −14.8145 −1.07194 −0.535971 0.844236i \(-0.680054\pi\)
−0.535971 + 0.844236i \(0.680054\pi\)
\(192\) 0 0
\(193\) 7.96136 0.573071 0.286536 0.958070i \(-0.407496\pi\)
0.286536 + 0.958070i \(0.407496\pi\)
\(194\) 0 0
\(195\) 2.67665 0.191679
\(196\) 0 0
\(197\) −9.57542 −0.682220 −0.341110 0.940023i \(-0.610803\pi\)
−0.341110 + 0.940023i \(0.610803\pi\)
\(198\) 0 0
\(199\) −0.699774 −0.0496056 −0.0248028 0.999692i \(-0.507896\pi\)
−0.0248028 + 0.999692i \(0.507896\pi\)
\(200\) 0 0
\(201\) −10.5520 −0.744284
\(202\) 0 0
\(203\) −1.50588 −0.105692
\(204\) 0 0
\(205\) 9.22596 0.644369
\(206\) 0 0
\(207\) −26.4189 −1.83624
\(208\) 0 0
\(209\) −3.71552 −0.257008
\(210\) 0 0
\(211\) −15.8027 −1.08790 −0.543950 0.839118i \(-0.683072\pi\)
−0.543950 + 0.839118i \(0.683072\pi\)
\(212\) 0 0
\(213\) 15.0243 1.02945
\(214\) 0 0
\(215\) 4.35338 0.296898
\(216\) 0 0
\(217\) 17.9334 1.21740
\(218\) 0 0
\(219\) −17.7224 −1.19757
\(220\) 0 0
\(221\) −1.47157 −0.0989882
\(222\) 0 0
\(223\) −2.10067 −0.140671 −0.0703356 0.997523i \(-0.522407\pi\)
−0.0703356 + 0.997523i \(0.522407\pi\)
\(224\) 0 0
\(225\) −25.1237 −1.67491
\(226\) 0 0
\(227\) −2.78860 −0.185086 −0.0925431 0.995709i \(-0.529500\pi\)
−0.0925431 + 0.995709i \(0.529500\pi\)
\(228\) 0 0
\(229\) −21.3824 −1.41299 −0.706495 0.707718i \(-0.749725\pi\)
−0.706495 + 0.707718i \(0.749725\pi\)
\(230\) 0 0
\(231\) 46.6567 3.06978
\(232\) 0 0
\(233\) −15.8652 −1.03936 −0.519681 0.854361i \(-0.673949\pi\)
−0.519681 + 0.854361i \(0.673949\pi\)
\(234\) 0 0
\(235\) −3.93906 −0.256956
\(236\) 0 0
\(237\) −33.3453 −2.16601
\(238\) 0 0
\(239\) 3.04028 0.196659 0.0983295 0.995154i \(-0.468650\pi\)
0.0983295 + 0.995154i \(0.468650\pi\)
\(240\) 0 0
\(241\) 1.15242 0.0742338 0.0371169 0.999311i \(-0.488183\pi\)
0.0371169 + 0.999311i \(0.488183\pi\)
\(242\) 0 0
\(243\) 2.57804 0.165382
\(244\) 0 0
\(245\) 9.09092 0.580797
\(246\) 0 0
\(247\) 1.07012 0.0680904
\(248\) 0 0
\(249\) 9.62493 0.609955
\(250\) 0 0
\(251\) 8.88283 0.560679 0.280340 0.959901i \(-0.409553\pi\)
0.280340 + 0.959901i \(0.409553\pi\)
\(252\) 0 0
\(253\) −16.7739 −1.05457
\(254\) 0 0
\(255\) −3.43955 −0.215393
\(256\) 0 0
\(257\) 2.86797 0.178899 0.0894496 0.995991i \(-0.471489\pi\)
0.0894496 + 0.995991i \(0.471489\pi\)
\(258\) 0 0
\(259\) −19.2373 −1.19535
\(260\) 0 0
\(261\) 2.08792 0.129239
\(262\) 0 0
\(263\) −11.0299 −0.680131 −0.340065 0.940402i \(-0.610449\pi\)
−0.340065 + 0.940402i \(0.610449\pi\)
\(264\) 0 0
\(265\) 0.840694 0.0516434
\(266\) 0 0
\(267\) 1.08607 0.0664666
\(268\) 0 0
\(269\) 11.3740 0.693488 0.346744 0.937960i \(-0.387287\pi\)
0.346744 + 0.937960i \(0.387287\pi\)
\(270\) 0 0
\(271\) −29.6727 −1.80249 −0.901244 0.433311i \(-0.857345\pi\)
−0.901244 + 0.433311i \(0.857345\pi\)
\(272\) 0 0
\(273\) −13.4378 −0.813294
\(274\) 0 0
\(275\) −15.9516 −0.961916
\(276\) 0 0
\(277\) −30.2485 −1.81745 −0.908727 0.417390i \(-0.862945\pi\)
−0.908727 + 0.417390i \(0.862945\pi\)
\(278\) 0 0
\(279\) −24.8649 −1.48862
\(280\) 0 0
\(281\) 28.5911 1.70560 0.852802 0.522234i \(-0.174901\pi\)
0.852802 + 0.522234i \(0.174901\pi\)
\(282\) 0 0
\(283\) −15.2731 −0.907894 −0.453947 0.891029i \(-0.649984\pi\)
−0.453947 + 0.891029i \(0.649984\pi\)
\(284\) 0 0
\(285\) 2.50125 0.148161
\(286\) 0 0
\(287\) −46.3179 −2.73406
\(288\) 0 0
\(289\) −15.1090 −0.888765
\(290\) 0 0
\(291\) 12.6054 0.738940
\(292\) 0 0
\(293\) −25.0308 −1.46232 −0.731158 0.682208i \(-0.761020\pi\)
−0.731158 + 0.682208i \(0.761020\pi\)
\(294\) 0 0
\(295\) 6.18185 0.359921
\(296\) 0 0
\(297\) −31.5266 −1.82936
\(298\) 0 0
\(299\) 4.83114 0.279392
\(300\) 0 0
\(301\) −21.8557 −1.25974
\(302\) 0 0
\(303\) 15.6127 0.896925
\(304\) 0 0
\(305\) 5.25144 0.300697
\(306\) 0 0
\(307\) 22.0251 1.25704 0.628521 0.777793i \(-0.283661\pi\)
0.628521 + 0.777793i \(0.283661\pi\)
\(308\) 0 0
\(309\) −34.3541 −1.95434
\(310\) 0 0
\(311\) 4.76915 0.270434 0.135217 0.990816i \(-0.456827\pi\)
0.135217 + 0.990816i \(0.456827\pi\)
\(312\) 0 0
\(313\) 24.7241 1.39749 0.698745 0.715371i \(-0.253742\pi\)
0.698745 + 0.715371i \(0.253742\pi\)
\(314\) 0 0
\(315\) −20.7641 −1.16992
\(316\) 0 0
\(317\) −7.67668 −0.431165 −0.215583 0.976486i \(-0.569165\pi\)
−0.215583 + 0.976486i \(0.569165\pi\)
\(318\) 0 0
\(319\) 1.32567 0.0742230
\(320\) 0 0
\(321\) 35.5960 1.98678
\(322\) 0 0
\(323\) −1.37513 −0.0765145
\(324\) 0 0
\(325\) 4.59429 0.254846
\(326\) 0 0
\(327\) 28.3663 1.56866
\(328\) 0 0
\(329\) 19.7756 1.09027
\(330\) 0 0
\(331\) −30.0635 −1.65244 −0.826219 0.563349i \(-0.809513\pi\)
−0.826219 + 0.563349i \(0.809513\pi\)
\(332\) 0 0
\(333\) 26.6727 1.46165
\(334\) 0 0
\(335\) 2.98164 0.162905
\(336\) 0 0
\(337\) 2.64397 0.144026 0.0720130 0.997404i \(-0.477058\pi\)
0.0720130 + 0.997404i \(0.477058\pi\)
\(338\) 0 0
\(339\) 21.7141 1.17935
\(340\) 0 0
\(341\) −15.7872 −0.854928
\(342\) 0 0
\(343\) −16.0957 −0.869084
\(344\) 0 0
\(345\) 11.2920 0.607943
\(346\) 0 0
\(347\) −23.9516 −1.28579 −0.642896 0.765954i \(-0.722267\pi\)
−0.642896 + 0.765954i \(0.722267\pi\)
\(348\) 0 0
\(349\) −3.59212 −0.192282 −0.0961409 0.995368i \(-0.530650\pi\)
−0.0961409 + 0.995368i \(0.530650\pi\)
\(350\) 0 0
\(351\) 9.08013 0.484661
\(352\) 0 0
\(353\) 10.7761 0.573554 0.286777 0.957997i \(-0.407416\pi\)
0.286777 + 0.957997i \(0.407416\pi\)
\(354\) 0 0
\(355\) −4.24535 −0.225320
\(356\) 0 0
\(357\) 17.2679 0.913915
\(358\) 0 0
\(359\) −23.7132 −1.25153 −0.625767 0.780010i \(-0.715214\pi\)
−0.625767 + 0.780010i \(0.715214\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −8.34567 −0.438034
\(364\) 0 0
\(365\) 5.00775 0.262118
\(366\) 0 0
\(367\) −24.5017 −1.27898 −0.639489 0.768800i \(-0.720854\pi\)
−0.639489 + 0.768800i \(0.720854\pi\)
\(368\) 0 0
\(369\) 64.2203 3.34318
\(370\) 0 0
\(371\) −4.22061 −0.219123
\(372\) 0 0
\(373\) 17.0247 0.881505 0.440752 0.897629i \(-0.354712\pi\)
0.440752 + 0.897629i \(0.354712\pi\)
\(374\) 0 0
\(375\) 23.2447 1.20035
\(376\) 0 0
\(377\) −0.381812 −0.0196643
\(378\) 0 0
\(379\) 22.2487 1.14284 0.571418 0.820659i \(-0.306393\pi\)
0.571418 + 0.820659i \(0.306393\pi\)
\(380\) 0 0
\(381\) 52.1876 2.67365
\(382\) 0 0
\(383\) −15.2777 −0.780654 −0.390327 0.920676i \(-0.627638\pi\)
−0.390327 + 0.920676i \(0.627638\pi\)
\(384\) 0 0
\(385\) −13.1836 −0.671897
\(386\) 0 0
\(387\) 30.3032 1.54040
\(388\) 0 0
\(389\) −27.2173 −1.37997 −0.689987 0.723822i \(-0.742384\pi\)
−0.689987 + 0.723822i \(0.742384\pi\)
\(390\) 0 0
\(391\) −6.20813 −0.313959
\(392\) 0 0
\(393\) 5.27159 0.265916
\(394\) 0 0
\(395\) 9.42224 0.474084
\(396\) 0 0
\(397\) −14.1764 −0.711492 −0.355746 0.934583i \(-0.615773\pi\)
−0.355746 + 0.934583i \(0.615773\pi\)
\(398\) 0 0
\(399\) −12.5573 −0.628649
\(400\) 0 0
\(401\) −4.72260 −0.235835 −0.117918 0.993023i \(-0.537622\pi\)
−0.117918 + 0.993023i \(0.537622\pi\)
\(402\) 0 0
\(403\) 4.54697 0.226500
\(404\) 0 0
\(405\) 6.46433 0.321215
\(406\) 0 0
\(407\) 16.9351 0.839440
\(408\) 0 0
\(409\) 11.3145 0.559465 0.279733 0.960078i \(-0.409754\pi\)
0.279733 + 0.960078i \(0.409754\pi\)
\(410\) 0 0
\(411\) 25.5428 1.25994
\(412\) 0 0
\(413\) −31.0353 −1.52715
\(414\) 0 0
\(415\) −2.71967 −0.133503
\(416\) 0 0
\(417\) 10.4787 0.513144
\(418\) 0 0
\(419\) −5.08754 −0.248543 −0.124271 0.992248i \(-0.539659\pi\)
−0.124271 + 0.992248i \(0.539659\pi\)
\(420\) 0 0
\(421\) 16.1078 0.785048 0.392524 0.919742i \(-0.371602\pi\)
0.392524 + 0.919742i \(0.371602\pi\)
\(422\) 0 0
\(423\) −27.4191 −1.33316
\(424\) 0 0
\(425\) −5.90377 −0.286375
\(426\) 0 0
\(427\) −26.3643 −1.27586
\(428\) 0 0
\(429\) 11.8297 0.571142
\(430\) 0 0
\(431\) 7.87058 0.379113 0.189556 0.981870i \(-0.439295\pi\)
0.189556 + 0.981870i \(0.439295\pi\)
\(432\) 0 0
\(433\) 7.98769 0.383864 0.191932 0.981408i \(-0.438525\pi\)
0.191932 + 0.981408i \(0.438525\pi\)
\(434\) 0 0
\(435\) −0.892425 −0.0427885
\(436\) 0 0
\(437\) 4.51456 0.215961
\(438\) 0 0
\(439\) −0.796487 −0.0380143 −0.0190071 0.999819i \(-0.506051\pi\)
−0.0190071 + 0.999819i \(0.506051\pi\)
\(440\) 0 0
\(441\) 63.2803 3.01335
\(442\) 0 0
\(443\) 27.3640 1.30010 0.650050 0.759891i \(-0.274748\pi\)
0.650050 + 0.759891i \(0.274748\pi\)
\(444\) 0 0
\(445\) −0.306887 −0.0145478
\(446\) 0 0
\(447\) −15.8593 −0.750120
\(448\) 0 0
\(449\) −30.3688 −1.43319 −0.716597 0.697488i \(-0.754301\pi\)
−0.716597 + 0.697488i \(0.754301\pi\)
\(450\) 0 0
\(451\) 40.7749 1.92001
\(452\) 0 0
\(453\) 0.186193 0.00874812
\(454\) 0 0
\(455\) 3.79706 0.178009
\(456\) 0 0
\(457\) 17.1263 0.801137 0.400568 0.916267i \(-0.368813\pi\)
0.400568 + 0.916267i \(0.368813\pi\)
\(458\) 0 0
\(459\) −11.6682 −0.544624
\(460\) 0 0
\(461\) −18.1700 −0.846260 −0.423130 0.906069i \(-0.639069\pi\)
−0.423130 + 0.906069i \(0.639069\pi\)
\(462\) 0 0
\(463\) −24.8465 −1.15471 −0.577357 0.816492i \(-0.695916\pi\)
−0.577357 + 0.816492i \(0.695916\pi\)
\(464\) 0 0
\(465\) 10.6278 0.492853
\(466\) 0 0
\(467\) 17.0875 0.790714 0.395357 0.918528i \(-0.370621\pi\)
0.395357 + 0.918528i \(0.370621\pi\)
\(468\) 0 0
\(469\) −14.9690 −0.691205
\(470\) 0 0
\(471\) −42.2199 −1.94539
\(472\) 0 0
\(473\) 19.2401 0.884662
\(474\) 0 0
\(475\) 4.29323 0.196987
\(476\) 0 0
\(477\) 5.85193 0.267941
\(478\) 0 0
\(479\) 35.4945 1.62179 0.810893 0.585194i \(-0.198982\pi\)
0.810893 + 0.585194i \(0.198982\pi\)
\(480\) 0 0
\(481\) −4.87755 −0.222397
\(482\) 0 0
\(483\) −56.6905 −2.57951
\(484\) 0 0
\(485\) −3.56184 −0.161735
\(486\) 0 0
\(487\) 15.5860 0.706269 0.353134 0.935573i \(-0.385116\pi\)
0.353134 + 0.935573i \(0.385116\pi\)
\(488\) 0 0
\(489\) −0.197456 −0.00892927
\(490\) 0 0
\(491\) −4.33672 −0.195713 −0.0978567 0.995201i \(-0.531199\pi\)
−0.0978567 + 0.995201i \(0.531199\pi\)
\(492\) 0 0
\(493\) 0.490637 0.0220972
\(494\) 0 0
\(495\) 18.2792 0.821587
\(496\) 0 0
\(497\) 21.3133 0.956034
\(498\) 0 0
\(499\) −25.6908 −1.15008 −0.575038 0.818127i \(-0.695013\pi\)
−0.575038 + 0.818127i \(0.695013\pi\)
\(500\) 0 0
\(501\) −15.0322 −0.671591
\(502\) 0 0
\(503\) 12.0218 0.536024 0.268012 0.963416i \(-0.413633\pi\)
0.268012 + 0.963416i \(0.413633\pi\)
\(504\) 0 0
\(505\) −4.41160 −0.196314
\(506\) 0 0
\(507\) 35.2707 1.56643
\(508\) 0 0
\(509\) −30.8346 −1.36672 −0.683361 0.730081i \(-0.739482\pi\)
−0.683361 + 0.730081i \(0.739482\pi\)
\(510\) 0 0
\(511\) −25.1409 −1.11217
\(512\) 0 0
\(513\) 8.48511 0.374627
\(514\) 0 0
\(515\) 9.70728 0.427754
\(516\) 0 0
\(517\) −17.4090 −0.765647
\(518\) 0 0
\(519\) 40.8123 1.79146
\(520\) 0 0
\(521\) −32.0129 −1.40251 −0.701255 0.712910i \(-0.747377\pi\)
−0.701255 + 0.712910i \(0.747377\pi\)
\(522\) 0 0
\(523\) 13.8228 0.604431 0.302215 0.953240i \(-0.402274\pi\)
0.302215 + 0.953240i \(0.402274\pi\)
\(524\) 0 0
\(525\) −53.9112 −2.35288
\(526\) 0 0
\(527\) −5.84296 −0.254523
\(528\) 0 0
\(529\) −2.61874 −0.113858
\(530\) 0 0
\(531\) 43.0308 1.86738
\(532\) 0 0
\(533\) −11.7438 −0.508680
\(534\) 0 0
\(535\) −10.0582 −0.434854
\(536\) 0 0
\(537\) −5.55971 −0.239919
\(538\) 0 0
\(539\) 40.1780 1.73059
\(540\) 0 0
\(541\) 8.13116 0.349586 0.174793 0.984605i \(-0.444074\pi\)
0.174793 + 0.984605i \(0.444074\pi\)
\(542\) 0 0
\(543\) −36.7853 −1.57861
\(544\) 0 0
\(545\) −8.01534 −0.343339
\(546\) 0 0
\(547\) −35.8326 −1.53209 −0.766046 0.642786i \(-0.777779\pi\)
−0.766046 + 0.642786i \(0.777779\pi\)
\(548\) 0 0
\(549\) 36.5544 1.56010
\(550\) 0 0
\(551\) −0.356792 −0.0151998
\(552\) 0 0
\(553\) −47.3033 −2.01154
\(554\) 0 0
\(555\) −11.4005 −0.483925
\(556\) 0 0
\(557\) −20.1896 −0.855461 −0.427730 0.903906i \(-0.640687\pi\)
−0.427730 + 0.903906i \(0.640687\pi\)
\(558\) 0 0
\(559\) −5.54145 −0.234378
\(560\) 0 0
\(561\) −15.2014 −0.641803
\(562\) 0 0
\(563\) −35.0089 −1.47545 −0.737725 0.675102i \(-0.764100\pi\)
−0.737725 + 0.675102i \(0.764100\pi\)
\(564\) 0 0
\(565\) −6.13566 −0.258129
\(566\) 0 0
\(567\) −32.4535 −1.36292
\(568\) 0 0
\(569\) 19.6655 0.824422 0.412211 0.911088i \(-0.364757\pi\)
0.412211 + 0.911088i \(0.364757\pi\)
\(570\) 0 0
\(571\) 0.832125 0.0348234 0.0174117 0.999848i \(-0.494457\pi\)
0.0174117 + 0.999848i \(0.494457\pi\)
\(572\) 0 0
\(573\) 44.0765 1.84132
\(574\) 0 0
\(575\) 19.3821 0.808288
\(576\) 0 0
\(577\) −14.0792 −0.586127 −0.293063 0.956093i \(-0.594675\pi\)
−0.293063 + 0.956093i \(0.594675\pi\)
\(578\) 0 0
\(579\) −23.6868 −0.984389
\(580\) 0 0
\(581\) 13.6538 0.566456
\(582\) 0 0
\(583\) 3.71552 0.153881
\(584\) 0 0
\(585\) −5.26467 −0.217667
\(586\) 0 0
\(587\) −13.5544 −0.559451 −0.279725 0.960080i \(-0.590243\pi\)
−0.279725 + 0.960080i \(0.590243\pi\)
\(588\) 0 0
\(589\) 4.24901 0.175077
\(590\) 0 0
\(591\) 28.4890 1.17188
\(592\) 0 0
\(593\) −9.31694 −0.382601 −0.191301 0.981532i \(-0.561271\pi\)
−0.191301 + 0.981532i \(0.561271\pi\)
\(594\) 0 0
\(595\) −4.87932 −0.200032
\(596\) 0 0
\(597\) 2.08198 0.0852098
\(598\) 0 0
\(599\) 26.2330 1.07185 0.535926 0.844265i \(-0.319963\pi\)
0.535926 + 0.844265i \(0.319963\pi\)
\(600\) 0 0
\(601\) −21.0201 −0.857427 −0.428713 0.903441i \(-0.641033\pi\)
−0.428713 + 0.903441i \(0.641033\pi\)
\(602\) 0 0
\(603\) 20.7547 0.845197
\(604\) 0 0
\(605\) 2.35820 0.0958744
\(606\) 0 0
\(607\) 5.61623 0.227956 0.113978 0.993483i \(-0.463641\pi\)
0.113978 + 0.993483i \(0.463641\pi\)
\(608\) 0 0
\(609\) 4.48032 0.181552
\(610\) 0 0
\(611\) 5.01405 0.202847
\(612\) 0 0
\(613\) −48.9131 −1.97558 −0.987790 0.155790i \(-0.950208\pi\)
−0.987790 + 0.155790i \(0.950208\pi\)
\(614\) 0 0
\(615\) −27.4493 −1.10686
\(616\) 0 0
\(617\) 30.2094 1.21618 0.608092 0.793867i \(-0.291935\pi\)
0.608092 + 0.793867i \(0.291935\pi\)
\(618\) 0 0
\(619\) −9.72482 −0.390874 −0.195437 0.980716i \(-0.562612\pi\)
−0.195437 + 0.980716i \(0.562612\pi\)
\(620\) 0 0
\(621\) 38.3066 1.53719
\(622\) 0 0
\(623\) 1.54069 0.0617266
\(624\) 0 0
\(625\) 14.8980 0.595921
\(626\) 0 0
\(627\) 11.0545 0.441473
\(628\) 0 0
\(629\) 6.26777 0.249912
\(630\) 0 0
\(631\) 41.1987 1.64009 0.820047 0.572296i \(-0.193947\pi\)
0.820047 + 0.572296i \(0.193947\pi\)
\(632\) 0 0
\(633\) 47.0164 1.86873
\(634\) 0 0
\(635\) −14.7464 −0.585193
\(636\) 0 0
\(637\) −11.5719 −0.458495
\(638\) 0 0
\(639\) −29.5512 −1.16903
\(640\) 0 0
\(641\) 15.0491 0.594403 0.297201 0.954815i \(-0.403947\pi\)
0.297201 + 0.954815i \(0.403947\pi\)
\(642\) 0 0
\(643\) 20.7314 0.817567 0.408783 0.912631i \(-0.365953\pi\)
0.408783 + 0.912631i \(0.365953\pi\)
\(644\) 0 0
\(645\) −12.9523 −0.509995
\(646\) 0 0
\(647\) −4.60478 −0.181033 −0.0905163 0.995895i \(-0.528852\pi\)
−0.0905163 + 0.995895i \(0.528852\pi\)
\(648\) 0 0
\(649\) 27.3212 1.07245
\(650\) 0 0
\(651\) −53.3558 −2.09118
\(652\) 0 0
\(653\) 21.4907 0.840994 0.420497 0.907294i \(-0.361856\pi\)
0.420497 + 0.907294i \(0.361856\pi\)
\(654\) 0 0
\(655\) −1.48957 −0.0582023
\(656\) 0 0
\(657\) 34.8581 1.35994
\(658\) 0 0
\(659\) 42.4486 1.65356 0.826782 0.562523i \(-0.190169\pi\)
0.826782 + 0.562523i \(0.190169\pi\)
\(660\) 0 0
\(661\) −23.9112 −0.930039 −0.465020 0.885300i \(-0.653953\pi\)
−0.465020 + 0.885300i \(0.653953\pi\)
\(662\) 0 0
\(663\) 4.37823 0.170036
\(664\) 0 0
\(665\) 3.54825 0.137595
\(666\) 0 0
\(667\) −1.61076 −0.0623688
\(668\) 0 0
\(669\) 6.24995 0.241637
\(670\) 0 0
\(671\) 23.2092 0.895980
\(672\) 0 0
\(673\) 6.60761 0.254705 0.127352 0.991858i \(-0.459352\pi\)
0.127352 + 0.991858i \(0.459352\pi\)
\(674\) 0 0
\(675\) 36.4286 1.40214
\(676\) 0 0
\(677\) −47.8559 −1.83925 −0.919626 0.392796i \(-0.871508\pi\)
−0.919626 + 0.392796i \(0.871508\pi\)
\(678\) 0 0
\(679\) 17.8818 0.686242
\(680\) 0 0
\(681\) 8.29671 0.317930
\(682\) 0 0
\(683\) −1.39775 −0.0534835 −0.0267418 0.999642i \(-0.508513\pi\)
−0.0267418 + 0.999642i \(0.508513\pi\)
\(684\) 0 0
\(685\) −7.21752 −0.275767
\(686\) 0 0
\(687\) 63.6174 2.42716
\(688\) 0 0
\(689\) −1.07012 −0.0407685
\(690\) 0 0
\(691\) 5.22951 0.198940 0.0994699 0.995041i \(-0.468285\pi\)
0.0994699 + 0.995041i \(0.468285\pi\)
\(692\) 0 0
\(693\) −91.7685 −3.48600
\(694\) 0 0
\(695\) −2.96092 −0.112314
\(696\) 0 0
\(697\) 15.0910 0.571613
\(698\) 0 0
\(699\) 47.2023 1.78536
\(700\) 0 0
\(701\) −51.4662 −1.94385 −0.971925 0.235291i \(-0.924396\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(702\) 0 0
\(703\) −4.55793 −0.171906
\(704\) 0 0
\(705\) 11.7196 0.441384
\(706\) 0 0
\(707\) 22.1480 0.832960
\(708\) 0 0
\(709\) −17.9661 −0.674732 −0.337366 0.941374i \(-0.609536\pi\)
−0.337366 + 0.941374i \(0.609536\pi\)
\(710\) 0 0
\(711\) 65.5866 2.45969
\(712\) 0 0
\(713\) 19.1824 0.718386
\(714\) 0 0
\(715\) −3.34265 −0.125008
\(716\) 0 0
\(717\) −9.04548 −0.337810
\(718\) 0 0
\(719\) −3.13026 −0.116739 −0.0583695 0.998295i \(-0.518590\pi\)
−0.0583695 + 0.998295i \(0.518590\pi\)
\(720\) 0 0
\(721\) −48.7343 −1.81496
\(722\) 0 0
\(723\) −3.42870 −0.127515
\(724\) 0 0
\(725\) −1.53179 −0.0568893
\(726\) 0 0
\(727\) 6.94895 0.257722 0.128861 0.991663i \(-0.458868\pi\)
0.128861 + 0.991663i \(0.458868\pi\)
\(728\) 0 0
\(729\) −30.7381 −1.13845
\(730\) 0 0
\(731\) 7.12089 0.263375
\(732\) 0 0
\(733\) 36.2491 1.33889 0.669446 0.742861i \(-0.266532\pi\)
0.669446 + 0.742861i \(0.266532\pi\)
\(734\) 0 0
\(735\) −27.0475 −0.997661
\(736\) 0 0
\(737\) 13.1776 0.485404
\(738\) 0 0
\(739\) 0.968430 0.0356243 0.0178121 0.999841i \(-0.494330\pi\)
0.0178121 + 0.999841i \(0.494330\pi\)
\(740\) 0 0
\(741\) −3.18386 −0.116962
\(742\) 0 0
\(743\) 41.6326 1.52735 0.763677 0.645599i \(-0.223392\pi\)
0.763677 + 0.645599i \(0.223392\pi\)
\(744\) 0 0
\(745\) 4.48129 0.164182
\(746\) 0 0
\(747\) −18.9312 −0.692655
\(748\) 0 0
\(749\) 50.4962 1.84509
\(750\) 0 0
\(751\) 27.9606 1.02030 0.510149 0.860086i \(-0.329590\pi\)
0.510149 + 0.860086i \(0.329590\pi\)
\(752\) 0 0
\(753\) −26.4284 −0.963103
\(754\) 0 0
\(755\) −0.0526118 −0.00191474
\(756\) 0 0
\(757\) −8.32862 −0.302709 −0.151354 0.988480i \(-0.548363\pi\)
−0.151354 + 0.988480i \(0.548363\pi\)
\(758\) 0 0
\(759\) 49.9061 1.81148
\(760\) 0 0
\(761\) 1.42069 0.0514998 0.0257499 0.999668i \(-0.491803\pi\)
0.0257499 + 0.999668i \(0.491803\pi\)
\(762\) 0 0
\(763\) 40.2401 1.45679
\(764\) 0 0
\(765\) 6.76523 0.244597
\(766\) 0 0
\(767\) −7.86892 −0.284130
\(768\) 0 0
\(769\) 53.3760 1.92479 0.962394 0.271657i \(-0.0875715\pi\)
0.962394 + 0.271657i \(0.0875715\pi\)
\(770\) 0 0
\(771\) −8.53285 −0.307303
\(772\) 0 0
\(773\) 24.5422 0.882722 0.441361 0.897330i \(-0.354496\pi\)
0.441361 + 0.897330i \(0.354496\pi\)
\(774\) 0 0
\(775\) 18.2420 0.655271
\(776\) 0 0
\(777\) 57.2351 2.05330
\(778\) 0 0
\(779\) −10.9742 −0.393192
\(780\) 0 0
\(781\) −18.7627 −0.671381
\(782\) 0 0
\(783\) −3.02742 −0.108191
\(784\) 0 0
\(785\) 11.9299 0.425795
\(786\) 0 0
\(787\) −53.6965 −1.91407 −0.957036 0.289969i \(-0.906355\pi\)
−0.957036 + 0.289969i \(0.906355\pi\)
\(788\) 0 0
\(789\) 32.8163 1.16829
\(790\) 0 0
\(791\) 30.8034 1.09524
\(792\) 0 0
\(793\) −6.68459 −0.237377
\(794\) 0 0
\(795\) −2.50125 −0.0887102
\(796\) 0 0
\(797\) 40.3147 1.42802 0.714010 0.700135i \(-0.246877\pi\)
0.714010 + 0.700135i \(0.246877\pi\)
\(798\) 0 0
\(799\) −6.44317 −0.227943
\(800\) 0 0
\(801\) −2.13619 −0.0754785
\(802\) 0 0
\(803\) 22.1322 0.781027
\(804\) 0 0
\(805\) 16.0188 0.564588
\(806\) 0 0
\(807\) −33.8403 −1.19123
\(808\) 0 0
\(809\) −11.8672 −0.417227 −0.208614 0.977998i \(-0.566895\pi\)
−0.208614 + 0.977998i \(0.566895\pi\)
\(810\) 0 0
\(811\) −25.8087 −0.906266 −0.453133 0.891443i \(-0.649694\pi\)
−0.453133 + 0.891443i \(0.649694\pi\)
\(812\) 0 0
\(813\) 88.2828 3.09621
\(814\) 0 0
\(815\) 0.0557942 0.00195439
\(816\) 0 0
\(817\) −5.17832 −0.181166
\(818\) 0 0
\(819\) 26.4307 0.923564
\(820\) 0 0
\(821\) −36.8624 −1.28651 −0.643253 0.765654i \(-0.722416\pi\)
−0.643253 + 0.765654i \(0.722416\pi\)
\(822\) 0 0
\(823\) −25.7764 −0.898509 −0.449255 0.893404i \(-0.648310\pi\)
−0.449255 + 0.893404i \(0.648310\pi\)
\(824\) 0 0
\(825\) 47.4594 1.65233
\(826\) 0 0
\(827\) 16.9229 0.588466 0.294233 0.955734i \(-0.404936\pi\)
0.294233 + 0.955734i \(0.404936\pi\)
\(828\) 0 0
\(829\) 27.5392 0.956475 0.478237 0.878231i \(-0.341276\pi\)
0.478237 + 0.878231i \(0.341276\pi\)
\(830\) 0 0
\(831\) 89.9958 3.12192
\(832\) 0 0
\(833\) 14.8701 0.515220
\(834\) 0 0
\(835\) 4.24759 0.146994
\(836\) 0 0
\(837\) 36.0533 1.24618
\(838\) 0 0
\(839\) 34.5599 1.19314 0.596570 0.802561i \(-0.296530\pi\)
0.596570 + 0.802561i \(0.296530\pi\)
\(840\) 0 0
\(841\) −28.8727 −0.995610
\(842\) 0 0
\(843\) −85.0649 −2.92979
\(844\) 0 0
\(845\) −9.96629 −0.342851
\(846\) 0 0
\(847\) −11.8391 −0.406796
\(848\) 0 0
\(849\) 45.4409 1.55953
\(850\) 0 0
\(851\) −20.5770 −0.705372
\(852\) 0 0
\(853\) 29.3711 1.00565 0.502824 0.864389i \(-0.332294\pi\)
0.502824 + 0.864389i \(0.332294\pi\)
\(854\) 0 0
\(855\) −4.91968 −0.168250
\(856\) 0 0
\(857\) −37.4480 −1.27920 −0.639600 0.768708i \(-0.720900\pi\)
−0.639600 + 0.768708i \(0.720900\pi\)
\(858\) 0 0
\(859\) 10.4648 0.357054 0.178527 0.983935i \(-0.442867\pi\)
0.178527 + 0.983935i \(0.442867\pi\)
\(860\) 0 0
\(861\) 137.806 4.69642
\(862\) 0 0
\(863\) −52.7941 −1.79713 −0.898567 0.438837i \(-0.855391\pi\)
−0.898567 + 0.438837i \(0.855391\pi\)
\(864\) 0 0
\(865\) −11.5321 −0.392105
\(866\) 0 0
\(867\) 44.9526 1.52667
\(868\) 0 0
\(869\) 41.6424 1.41262
\(870\) 0 0
\(871\) −3.79535 −0.128601
\(872\) 0 0
\(873\) −24.7934 −0.839129
\(874\) 0 0
\(875\) 32.9747 1.11475
\(876\) 0 0
\(877\) −50.6830 −1.71144 −0.855722 0.517437i \(-0.826886\pi\)
−0.855722 + 0.517437i \(0.826886\pi\)
\(878\) 0 0
\(879\) 74.4722 2.51189
\(880\) 0 0
\(881\) 34.8273 1.17336 0.586681 0.809818i \(-0.300434\pi\)
0.586681 + 0.809818i \(0.300434\pi\)
\(882\) 0 0
\(883\) −6.49713 −0.218646 −0.109323 0.994006i \(-0.534868\pi\)
−0.109323 + 0.994006i \(0.534868\pi\)
\(884\) 0 0
\(885\) −18.3924 −0.618253
\(886\) 0 0
\(887\) 59.3534 1.99289 0.996447 0.0842241i \(-0.0268412\pi\)
0.996447 + 0.0842241i \(0.0268412\pi\)
\(888\) 0 0
\(889\) 74.0327 2.48298
\(890\) 0 0
\(891\) 28.5696 0.957119
\(892\) 0 0
\(893\) 4.68548 0.156794
\(894\) 0 0
\(895\) 1.57098 0.0525121
\(896\) 0 0
\(897\) −14.3737 −0.479924
\(898\) 0 0
\(899\) −1.51601 −0.0505618
\(900\) 0 0
\(901\) 1.37513 0.0458124
\(902\) 0 0
\(903\) 65.0254 2.16391
\(904\) 0 0
\(905\) 10.3943 0.345517
\(906\) 0 0
\(907\) 7.55945 0.251007 0.125504 0.992093i \(-0.459945\pi\)
0.125504 + 0.992093i \(0.459945\pi\)
\(908\) 0 0
\(909\) −30.7084 −1.01853
\(910\) 0 0
\(911\) 27.4756 0.910308 0.455154 0.890413i \(-0.349584\pi\)
0.455154 + 0.890413i \(0.349584\pi\)
\(912\) 0 0
\(913\) −12.0198 −0.397798
\(914\) 0 0
\(915\) −15.6242 −0.516520
\(916\) 0 0
\(917\) 7.47822 0.246952
\(918\) 0 0
\(919\) −7.51453 −0.247882 −0.123941 0.992290i \(-0.539553\pi\)
−0.123941 + 0.992290i \(0.539553\pi\)
\(920\) 0 0
\(921\) −65.5296 −2.15927
\(922\) 0 0
\(923\) 5.40393 0.177873
\(924\) 0 0
\(925\) −19.5683 −0.643400
\(926\) 0 0
\(927\) 67.5707 2.21931
\(928\) 0 0
\(929\) 19.0716 0.625718 0.312859 0.949800i \(-0.398713\pi\)
0.312859 + 0.949800i \(0.398713\pi\)
\(930\) 0 0
\(931\) −10.8136 −0.354401
\(932\) 0 0
\(933\) −14.1893 −0.464536
\(934\) 0 0
\(935\) 4.29539 0.140474
\(936\) 0 0
\(937\) −0.0609918 −0.00199252 −0.000996258 1.00000i \(-0.500317\pi\)
−0.000996258 1.00000i \(0.500317\pi\)
\(938\) 0 0
\(939\) −73.5597 −2.40053
\(940\) 0 0
\(941\) −53.9013 −1.75713 −0.878566 0.477621i \(-0.841499\pi\)
−0.878566 + 0.477621i \(0.841499\pi\)
\(942\) 0 0
\(943\) −49.5438 −1.61337
\(944\) 0 0
\(945\) 30.1073 0.979389
\(946\) 0 0
\(947\) 35.1185 1.14120 0.570600 0.821228i \(-0.306711\pi\)
0.570600 + 0.821228i \(0.306711\pi\)
\(948\) 0 0
\(949\) −6.37439 −0.206922
\(950\) 0 0
\(951\) 22.8398 0.740631
\(952\) 0 0
\(953\) 6.25933 0.202760 0.101380 0.994848i \(-0.467674\pi\)
0.101380 + 0.994848i \(0.467674\pi\)
\(954\) 0 0
\(955\) −12.4545 −0.403018
\(956\) 0 0
\(957\) −3.94415 −0.127496
\(958\) 0 0
\(959\) 36.2348 1.17008
\(960\) 0 0
\(961\) −12.9460 −0.417611
\(962\) 0 0
\(963\) −70.0135 −2.25615
\(964\) 0 0
\(965\) 6.69307 0.215457
\(966\) 0 0
\(967\) −25.1928 −0.810147 −0.405073 0.914284i \(-0.632754\pi\)
−0.405073 + 0.914284i \(0.632754\pi\)
\(968\) 0 0
\(969\) 4.09133 0.131432
\(970\) 0 0
\(971\) −12.4247 −0.398728 −0.199364 0.979926i \(-0.563888\pi\)
−0.199364 + 0.979926i \(0.563888\pi\)
\(972\) 0 0
\(973\) 14.8650 0.476549
\(974\) 0 0
\(975\) −13.6690 −0.437759
\(976\) 0 0
\(977\) −23.2577 −0.744079 −0.372040 0.928217i \(-0.621341\pi\)
−0.372040 + 0.928217i \(0.621341\pi\)
\(978\) 0 0
\(979\) −1.35631 −0.0433479
\(980\) 0 0
\(981\) −55.7934 −1.78135
\(982\) 0 0
\(983\) 40.5385 1.29298 0.646489 0.762923i \(-0.276236\pi\)
0.646489 + 0.762923i \(0.276236\pi\)
\(984\) 0 0
\(985\) −8.05000 −0.256494
\(986\) 0 0
\(987\) −58.8368 −1.87280
\(988\) 0 0
\(989\) −23.3778 −0.743372
\(990\) 0 0
\(991\) −31.8507 −1.01177 −0.505886 0.862600i \(-0.668834\pi\)
−0.505886 + 0.862600i \(0.668834\pi\)
\(992\) 0 0
\(993\) 89.4454 2.83846
\(994\) 0 0
\(995\) −0.588296 −0.0186502
\(996\) 0 0
\(997\) 8.18740 0.259297 0.129649 0.991560i \(-0.458615\pi\)
0.129649 + 0.991560i \(0.458615\pi\)
\(998\) 0 0
\(999\) −38.6745 −1.22361
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 \(a_p\))