Properties

Label 945.2.a.j.1.1
Level 945
Weight 2
Character 945.1
Self dual Yes
Analytic conductor 7.546
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.54586299101\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.30278\)
Character \(\chi\) = 945.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.30278 q^{2}\) \(-0.302776 q^{4}\) \(+1.00000 q^{5}\) \(+1.00000 q^{7}\) \(+3.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.30278 q^{2}\) \(-0.302776 q^{4}\) \(+1.00000 q^{5}\) \(+1.00000 q^{7}\) \(+3.00000 q^{8}\) \(-1.30278 q^{10}\) \(+3.00000 q^{11}\) \(-2.30278 q^{13}\) \(-1.30278 q^{14}\) \(-3.30278 q^{16}\) \(+1.30278 q^{17}\) \(+0.302776 q^{19}\) \(-0.302776 q^{20}\) \(-3.90833 q^{22}\) \(+4.30278 q^{23}\) \(+1.00000 q^{25}\) \(+3.00000 q^{26}\) \(-0.302776 q^{28}\) \(+1.69722 q^{29}\) \(-9.60555 q^{31}\) \(-1.69722 q^{32}\) \(-1.69722 q^{34}\) \(+1.00000 q^{35}\) \(-3.60555 q^{37}\) \(-0.394449 q^{38}\) \(+3.00000 q^{40}\) \(+3.90833 q^{41}\) \(+10.2111 q^{43}\) \(-0.908327 q^{44}\) \(-5.60555 q^{46}\) \(+0.394449 q^{47}\) \(+1.00000 q^{49}\) \(-1.30278 q^{50}\) \(+0.697224 q^{52}\) \(+12.5139 q^{53}\) \(+3.00000 q^{55}\) \(+3.00000 q^{56}\) \(-2.21110 q^{58}\) \(-8.21110 q^{59}\) \(+14.1194 q^{61}\) \(+12.5139 q^{62}\) \(+8.81665 q^{64}\) \(-2.30278 q^{65}\) \(-4.51388 q^{67}\) \(-0.394449 q^{68}\) \(-1.30278 q^{70}\) \(+12.9083 q^{71}\) \(+4.21110 q^{73}\) \(+4.69722 q^{74}\) \(-0.0916731 q^{76}\) \(+3.00000 q^{77}\) \(-6.09167 q^{79}\) \(-3.30278 q^{80}\) \(-5.09167 q^{82}\) \(+2.21110 q^{83}\) \(+1.30278 q^{85}\) \(-13.3028 q^{86}\) \(+9.00000 q^{88}\) \(-10.8167 q^{89}\) \(-2.30278 q^{91}\) \(-1.30278 q^{92}\) \(-0.513878 q^{94}\) \(+0.302776 q^{95}\) \(+8.51388 q^{97}\) \(-1.30278 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut -\mathstrut 3q^{19} \) \(\mathstrut +\mathstrut 3q^{20} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 5q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 3q^{28} \) \(\mathstrut +\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 7q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 3q^{41} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut +\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 7q^{53} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut 3q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut q^{65} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 11q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 23q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 21q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut q^{85} \) \(\mathstrut -\mathstrut 23q^{86} \) \(\mathstrut +\mathstrut 18q^{88} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut +\mathstrut q^{92} \) \(\mathstrut +\mathstrut 17q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30278 −0.921201 −0.460601 0.887607i \(-0.652366\pi\)
−0.460601 + 0.887607i \(0.652366\pi\)
\(3\) 0 0
\(4\) −0.302776 −0.151388
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −1.30278 −0.411974
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) −2.30278 −0.638675 −0.319338 0.947641i \(-0.603460\pi\)
−0.319338 + 0.947641i \(0.603460\pi\)
\(14\) −1.30278 −0.348181
\(15\) 0 0
\(16\) −3.30278 −0.825694
\(17\) 1.30278 0.315970 0.157985 0.987442i \(-0.449500\pi\)
0.157985 + 0.987442i \(0.449500\pi\)
\(18\) 0 0
\(19\) 0.302776 0.0694615 0.0347307 0.999397i \(-0.488943\pi\)
0.0347307 + 0.999397i \(0.488943\pi\)
\(20\) −0.302776 −0.0677027
\(21\) 0 0
\(22\) −3.90833 −0.833258
\(23\) 4.30278 0.897191 0.448595 0.893735i \(-0.351924\pi\)
0.448595 + 0.893735i \(0.351924\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) −0.302776 −0.0572192
\(29\) 1.69722 0.315167 0.157583 0.987506i \(-0.449630\pi\)
0.157583 + 0.987506i \(0.449630\pi\)
\(30\) 0 0
\(31\) −9.60555 −1.72521 −0.862604 0.505880i \(-0.831168\pi\)
−0.862604 + 0.505880i \(0.831168\pi\)
\(32\) −1.69722 −0.300030
\(33\) 0 0
\(34\) −1.69722 −0.291072
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −3.60555 −0.592749 −0.296374 0.955072i \(-0.595778\pi\)
−0.296374 + 0.955072i \(0.595778\pi\)
\(38\) −0.394449 −0.0639880
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 3.90833 0.610378 0.305189 0.952292i \(-0.401280\pi\)
0.305189 + 0.952292i \(0.401280\pi\)
\(42\) 0 0
\(43\) 10.2111 1.55718 0.778589 0.627534i \(-0.215936\pi\)
0.778589 + 0.627534i \(0.215936\pi\)
\(44\) −0.908327 −0.136935
\(45\) 0 0
\(46\) −5.60555 −0.826493
\(47\) 0.394449 0.0575363 0.0287681 0.999586i \(-0.490842\pi\)
0.0287681 + 0.999586i \(0.490842\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.30278 −0.184240
\(51\) 0 0
\(52\) 0.697224 0.0966876
\(53\) 12.5139 1.71891 0.859457 0.511209i \(-0.170802\pi\)
0.859457 + 0.511209i \(0.170802\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) −2.21110 −0.290332
\(59\) −8.21110 −1.06899 −0.534497 0.845170i \(-0.679499\pi\)
−0.534497 + 0.845170i \(0.679499\pi\)
\(60\) 0 0
\(61\) 14.1194 1.80781 0.903904 0.427736i \(-0.140689\pi\)
0.903904 + 0.427736i \(0.140689\pi\)
\(62\) 12.5139 1.58926
\(63\) 0 0
\(64\) 8.81665 1.10208
\(65\) −2.30278 −0.285624
\(66\) 0 0
\(67\) −4.51388 −0.551458 −0.275729 0.961235i \(-0.588919\pi\)
−0.275729 + 0.961235i \(0.588919\pi\)
\(68\) −0.394449 −0.0478339
\(69\) 0 0
\(70\) −1.30278 −0.155711
\(71\) 12.9083 1.53194 0.765968 0.642878i \(-0.222260\pi\)
0.765968 + 0.642878i \(0.222260\pi\)
\(72\) 0 0
\(73\) 4.21110 0.492872 0.246436 0.969159i \(-0.420740\pi\)
0.246436 + 0.969159i \(0.420740\pi\)
\(74\) 4.69722 0.546041
\(75\) 0 0
\(76\) −0.0916731 −0.0105156
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) −6.09167 −0.685367 −0.342683 0.939451i \(-0.611336\pi\)
−0.342683 + 0.939451i \(0.611336\pi\)
\(80\) −3.30278 −0.369262
\(81\) 0 0
\(82\) −5.09167 −0.562281
\(83\) 2.21110 0.242700 0.121350 0.992610i \(-0.461278\pi\)
0.121350 + 0.992610i \(0.461278\pi\)
\(84\) 0 0
\(85\) 1.30278 0.141306
\(86\) −13.3028 −1.43448
\(87\) 0 0
\(88\) 9.00000 0.959403
\(89\) −10.8167 −1.14656 −0.573282 0.819358i \(-0.694330\pi\)
−0.573282 + 0.819358i \(0.694330\pi\)
\(90\) 0 0
\(91\) −2.30278 −0.241396
\(92\) −1.30278 −0.135824
\(93\) 0 0
\(94\) −0.513878 −0.0530025
\(95\) 0.302776 0.0310641
\(96\) 0 0
\(97\) 8.51388 0.864453 0.432227 0.901765i \(-0.357728\pi\)
0.432227 + 0.901765i \(0.357728\pi\)
\(98\) −1.30278 −0.131600
\(99\) 0 0
\(100\) −0.302776 −0.0302776
\(101\) 5.21110 0.518524 0.259262 0.965807i \(-0.416521\pi\)
0.259262 + 0.965807i \(0.416521\pi\)
\(102\) 0 0
\(103\) 16.7250 1.64796 0.823981 0.566618i \(-0.191748\pi\)
0.823981 + 0.566618i \(0.191748\pi\)
\(104\) −6.90833 −0.677417
\(105\) 0 0
\(106\) −16.3028 −1.58347
\(107\) 15.0000 1.45010 0.725052 0.688694i \(-0.241816\pi\)
0.725052 + 0.688694i \(0.241816\pi\)
\(108\) 0 0
\(109\) −5.30278 −0.507914 −0.253957 0.967216i \(-0.581732\pi\)
−0.253957 + 0.967216i \(0.581732\pi\)
\(110\) −3.90833 −0.372644
\(111\) 0 0
\(112\) −3.30278 −0.312083
\(113\) 5.09167 0.478984 0.239492 0.970898i \(-0.423019\pi\)
0.239492 + 0.970898i \(0.423019\pi\)
\(114\) 0 0
\(115\) 4.30278 0.401236
\(116\) −0.513878 −0.0477124
\(117\) 0 0
\(118\) 10.6972 0.984759
\(119\) 1.30278 0.119425
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −18.3944 −1.66536
\(123\) 0 0
\(124\) 2.90833 0.261175
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 13.7250 1.21790 0.608948 0.793210i \(-0.291592\pi\)
0.608948 + 0.793210i \(0.291592\pi\)
\(128\) −8.09167 −0.715210
\(129\) 0 0
\(130\) 3.00000 0.263117
\(131\) −4.69722 −0.410398 −0.205199 0.978720i \(-0.565784\pi\)
−0.205199 + 0.978720i \(0.565784\pi\)
\(132\) 0 0
\(133\) 0.302776 0.0262540
\(134\) 5.88057 0.508004
\(135\) 0 0
\(136\) 3.90833 0.335136
\(137\) −10.4222 −0.890429 −0.445215 0.895424i \(-0.646873\pi\)
−0.445215 + 0.895424i \(0.646873\pi\)
\(138\) 0 0
\(139\) 1.60555 0.136181 0.0680905 0.997679i \(-0.478309\pi\)
0.0680905 + 0.997679i \(0.478309\pi\)
\(140\) −0.302776 −0.0255892
\(141\) 0 0
\(142\) −16.8167 −1.41122
\(143\) −6.90833 −0.577703
\(144\) 0 0
\(145\) 1.69722 0.140947
\(146\) −5.48612 −0.454035
\(147\) 0 0
\(148\) 1.09167 0.0897350
\(149\) −12.5139 −1.02518 −0.512588 0.858634i \(-0.671313\pi\)
−0.512588 + 0.858634i \(0.671313\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) 0.908327 0.0736750
\(153\) 0 0
\(154\) −3.90833 −0.314942
\(155\) −9.60555 −0.771536
\(156\) 0 0
\(157\) −0.605551 −0.0483283 −0.0241641 0.999708i \(-0.507692\pi\)
−0.0241641 + 0.999708i \(0.507692\pi\)
\(158\) 7.93608 0.631361
\(159\) 0 0
\(160\) −1.69722 −0.134177
\(161\) 4.30278 0.339106
\(162\) 0 0
\(163\) 8.78890 0.688400 0.344200 0.938896i \(-0.388150\pi\)
0.344200 + 0.938896i \(0.388150\pi\)
\(164\) −1.18335 −0.0924038
\(165\) 0 0
\(166\) −2.88057 −0.223576
\(167\) 12.3944 0.959111 0.479556 0.877511i \(-0.340798\pi\)
0.479556 + 0.877511i \(0.340798\pi\)
\(168\) 0 0
\(169\) −7.69722 −0.592094
\(170\) −1.69722 −0.130171
\(171\) 0 0
\(172\) −3.09167 −0.235738
\(173\) 4.81665 0.366203 0.183102 0.983094i \(-0.441386\pi\)
0.183102 + 0.983094i \(0.441386\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) −9.90833 −0.746868
\(177\) 0 0
\(178\) 14.0917 1.05622
\(179\) −4.81665 −0.360014 −0.180007 0.983665i \(-0.557612\pi\)
−0.180007 + 0.983665i \(0.557612\pi\)
\(180\) 0 0
\(181\) −11.4222 −0.849006 −0.424503 0.905427i \(-0.639551\pi\)
−0.424503 + 0.905427i \(0.639551\pi\)
\(182\) 3.00000 0.222375
\(183\) 0 0
\(184\) 12.9083 0.951614
\(185\) −3.60555 −0.265085
\(186\) 0 0
\(187\) 3.90833 0.285805
\(188\) −0.119429 −0.00871029
\(189\) 0 0
\(190\) −0.394449 −0.0286163
\(191\) −10.3028 −0.745483 −0.372741 0.927935i \(-0.621582\pi\)
−0.372741 + 0.927935i \(0.621582\pi\)
\(192\) 0 0
\(193\) −19.1194 −1.37625 −0.688123 0.725594i \(-0.741565\pi\)
−0.688123 + 0.725594i \(0.741565\pi\)
\(194\) −11.0917 −0.796336
\(195\) 0 0
\(196\) −0.302776 −0.0216268
\(197\) −1.18335 −0.0843099 −0.0421550 0.999111i \(-0.513422\pi\)
−0.0421550 + 0.999111i \(0.513422\pi\)
\(198\) 0 0
\(199\) −9.72498 −0.689386 −0.344693 0.938716i \(-0.612017\pi\)
−0.344693 + 0.938716i \(0.612017\pi\)
\(200\) 3.00000 0.212132
\(201\) 0 0
\(202\) −6.78890 −0.477665
\(203\) 1.69722 0.119122
\(204\) 0 0
\(205\) 3.90833 0.272969
\(206\) −21.7889 −1.51810
\(207\) 0 0
\(208\) 7.60555 0.527350
\(209\) 0.908327 0.0628303
\(210\) 0 0
\(211\) −18.6056 −1.28086 −0.640429 0.768017i \(-0.721244\pi\)
−0.640429 + 0.768017i \(0.721244\pi\)
\(212\) −3.78890 −0.260223
\(213\) 0 0
\(214\) −19.5416 −1.33584
\(215\) 10.2111 0.696391
\(216\) 0 0
\(217\) −9.60555 −0.652067
\(218\) 6.90833 0.467891
\(219\) 0 0
\(220\) −0.908327 −0.0612394
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 5.78890 0.387653 0.193827 0.981036i \(-0.437910\pi\)
0.193827 + 0.981036i \(0.437910\pi\)
\(224\) −1.69722 −0.113401
\(225\) 0 0
\(226\) −6.63331 −0.441241
\(227\) −24.5139 −1.62704 −0.813522 0.581535i \(-0.802452\pi\)
−0.813522 + 0.581535i \(0.802452\pi\)
\(228\) 0 0
\(229\) 16.2111 1.07126 0.535630 0.844453i \(-0.320074\pi\)
0.535630 + 0.844453i \(0.320074\pi\)
\(230\) −5.60555 −0.369619
\(231\) 0 0
\(232\) 5.09167 0.334285
\(233\) 0.908327 0.0595065 0.0297532 0.999557i \(-0.490528\pi\)
0.0297532 + 0.999557i \(0.490528\pi\)
\(234\) 0 0
\(235\) 0.394449 0.0257310
\(236\) 2.48612 0.161833
\(237\) 0 0
\(238\) −1.69722 −0.110015
\(239\) 20.2111 1.30735 0.653674 0.756776i \(-0.273227\pi\)
0.653674 + 0.756776i \(0.273227\pi\)
\(240\) 0 0
\(241\) −25.1194 −1.61808 −0.809042 0.587750i \(-0.800014\pi\)
−0.809042 + 0.587750i \(0.800014\pi\)
\(242\) 2.60555 0.167491
\(243\) 0 0
\(244\) −4.27502 −0.273680
\(245\) 1.00000 0.0638877
\(246\) 0 0
\(247\) −0.697224 −0.0443633
\(248\) −28.8167 −1.82986
\(249\) 0 0
\(250\) −1.30278 −0.0823948
\(251\) 25.8167 1.62953 0.814766 0.579789i \(-0.196865\pi\)
0.814766 + 0.579789i \(0.196865\pi\)
\(252\) 0 0
\(253\) 12.9083 0.811540
\(254\) −17.8806 −1.12193
\(255\) 0 0
\(256\) −7.09167 −0.443230
\(257\) −12.0000 −0.748539 −0.374270 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 0 0
\(259\) −3.60555 −0.224038
\(260\) 0.697224 0.0432400
\(261\) 0 0
\(262\) 6.11943 0.378060
\(263\) 30.5139 1.88157 0.940783 0.339009i \(-0.110092\pi\)
0.940783 + 0.339009i \(0.110092\pi\)
\(264\) 0 0
\(265\) 12.5139 0.768721
\(266\) −0.394449 −0.0241852
\(267\) 0 0
\(268\) 1.36669 0.0834840
\(269\) −19.4222 −1.18419 −0.592096 0.805867i \(-0.701700\pi\)
−0.592096 + 0.805867i \(0.701700\pi\)
\(270\) 0 0
\(271\) −13.1194 −0.796949 −0.398474 0.917180i \(-0.630460\pi\)
−0.398474 + 0.917180i \(0.630460\pi\)
\(272\) −4.30278 −0.260894
\(273\) 0 0
\(274\) 13.5778 0.820265
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) −13.9083 −0.835670 −0.417835 0.908523i \(-0.637211\pi\)
−0.417835 + 0.908523i \(0.637211\pi\)
\(278\) −2.09167 −0.125450
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) 11.7250 0.699454 0.349727 0.936852i \(-0.386274\pi\)
0.349727 + 0.936852i \(0.386274\pi\)
\(282\) 0 0
\(283\) −7.90833 −0.470101 −0.235051 0.971983i \(-0.575526\pi\)
−0.235051 + 0.971983i \(0.575526\pi\)
\(284\) −3.90833 −0.231917
\(285\) 0 0
\(286\) 9.00000 0.532181
\(287\) 3.90833 0.230701
\(288\) 0 0
\(289\) −15.3028 −0.900163
\(290\) −2.21110 −0.129840
\(291\) 0 0
\(292\) −1.27502 −0.0746149
\(293\) −30.2389 −1.76657 −0.883287 0.468834i \(-0.844674\pi\)
−0.883287 + 0.468834i \(0.844674\pi\)
\(294\) 0 0
\(295\) −8.21110 −0.478069
\(296\) −10.8167 −0.628705
\(297\) 0 0
\(298\) 16.3028 0.944394
\(299\) −9.90833 −0.573013
\(300\) 0 0
\(301\) 10.2111 0.588558
\(302\) 1.30278 0.0749663
\(303\) 0 0
\(304\) −1.00000 −0.0573539
\(305\) 14.1194 0.808476
\(306\) 0 0
\(307\) −24.8444 −1.41795 −0.708973 0.705236i \(-0.750841\pi\)
−0.708973 + 0.705236i \(0.750841\pi\)
\(308\) −0.908327 −0.0517567
\(309\) 0 0
\(310\) 12.5139 0.710741
\(311\) 24.9083 1.41242 0.706211 0.708002i \(-0.250403\pi\)
0.706211 + 0.708002i \(0.250403\pi\)
\(312\) 0 0
\(313\) 6.81665 0.385300 0.192650 0.981268i \(-0.438292\pi\)
0.192650 + 0.981268i \(0.438292\pi\)
\(314\) 0.788897 0.0445201
\(315\) 0 0
\(316\) 1.84441 0.103756
\(317\) −33.2389 −1.86688 −0.933440 0.358733i \(-0.883209\pi\)
−0.933440 + 0.358733i \(0.883209\pi\)
\(318\) 0 0
\(319\) 5.09167 0.285079
\(320\) 8.81665 0.492866
\(321\) 0 0
\(322\) −5.60555 −0.312385
\(323\) 0.394449 0.0219477
\(324\) 0 0
\(325\) −2.30278 −0.127735
\(326\) −11.4500 −0.634155
\(327\) 0 0
\(328\) 11.7250 0.647404
\(329\) 0.394449 0.0217467
\(330\) 0 0
\(331\) 9.69722 0.533008 0.266504 0.963834i \(-0.414132\pi\)
0.266504 + 0.963834i \(0.414132\pi\)
\(332\) −0.669468 −0.0367418
\(333\) 0 0
\(334\) −16.1472 −0.883535
\(335\) −4.51388 −0.246620
\(336\) 0 0
\(337\) 12.3028 0.670175 0.335087 0.942187i \(-0.391234\pi\)
0.335087 + 0.942187i \(0.391234\pi\)
\(338\) 10.0278 0.545438
\(339\) 0 0
\(340\) −0.394449 −0.0213920
\(341\) −28.8167 −1.56051
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 30.6333 1.65164
\(345\) 0 0
\(346\) −6.27502 −0.337347
\(347\) 26.6056 1.42826 0.714130 0.700013i \(-0.246822\pi\)
0.714130 + 0.700013i \(0.246822\pi\)
\(348\) 0 0
\(349\) −16.6333 −0.890361 −0.445180 0.895441i \(-0.646860\pi\)
−0.445180 + 0.895441i \(0.646860\pi\)
\(350\) −1.30278 −0.0696363
\(351\) 0 0
\(352\) −5.09167 −0.271387
\(353\) −8.72498 −0.464384 −0.232192 0.972670i \(-0.574590\pi\)
−0.232192 + 0.972670i \(0.574590\pi\)
\(354\) 0 0
\(355\) 12.9083 0.685103
\(356\) 3.27502 0.173576
\(357\) 0 0
\(358\) 6.27502 0.331645
\(359\) 22.8167 1.20422 0.602108 0.798414i \(-0.294327\pi\)
0.602108 + 0.798414i \(0.294327\pi\)
\(360\) 0 0
\(361\) −18.9083 −0.995175
\(362\) 14.8806 0.782105
\(363\) 0 0
\(364\) 0.697224 0.0365445
\(365\) 4.21110 0.220419
\(366\) 0 0
\(367\) −2.69722 −0.140794 −0.0703970 0.997519i \(-0.522427\pi\)
−0.0703970 + 0.997519i \(0.522427\pi\)
\(368\) −14.2111 −0.740805
\(369\) 0 0
\(370\) 4.69722 0.244197
\(371\) 12.5139 0.649688
\(372\) 0 0
\(373\) 8.90833 0.461256 0.230628 0.973042i \(-0.425922\pi\)
0.230628 + 0.973042i \(0.425922\pi\)
\(374\) −5.09167 −0.263284
\(375\) 0 0
\(376\) 1.18335 0.0610264
\(377\) −3.90833 −0.201289
\(378\) 0 0
\(379\) 17.6333 0.905762 0.452881 0.891571i \(-0.350396\pi\)
0.452881 + 0.891571i \(0.350396\pi\)
\(380\) −0.0916731 −0.00470273
\(381\) 0 0
\(382\) 13.4222 0.686740
\(383\) −14.2111 −0.726153 −0.363077 0.931759i \(-0.618274\pi\)
−0.363077 + 0.931759i \(0.618274\pi\)
\(384\) 0 0
\(385\) 3.00000 0.152894
\(386\) 24.9083 1.26780
\(387\) 0 0
\(388\) −2.57779 −0.130868
\(389\) 23.7250 1.20290 0.601452 0.798909i \(-0.294589\pi\)
0.601452 + 0.798909i \(0.294589\pi\)
\(390\) 0 0
\(391\) 5.60555 0.283485
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) 1.54163 0.0776664
\(395\) −6.09167 −0.306505
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 12.6695 0.635063
\(399\) 0 0
\(400\) −3.30278 −0.165139
\(401\) 26.7250 1.33458 0.667291 0.744797i \(-0.267454\pi\)
0.667291 + 0.744797i \(0.267454\pi\)
\(402\) 0 0
\(403\) 22.1194 1.10185
\(404\) −1.57779 −0.0784982
\(405\) 0 0
\(406\) −2.21110 −0.109735
\(407\) −10.8167 −0.536162
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −5.09167 −0.251460
\(411\) 0 0
\(412\) −5.06392 −0.249481
\(413\) −8.21110 −0.404042
\(414\) 0 0
\(415\) 2.21110 0.108539
\(416\) 3.90833 0.191621
\(417\) 0 0
\(418\) −1.18335 −0.0578794
\(419\) 34.8167 1.70090 0.850452 0.526052i \(-0.176328\pi\)
0.850452 + 0.526052i \(0.176328\pi\)
\(420\) 0 0
\(421\) 6.30278 0.307178 0.153589 0.988135i \(-0.450917\pi\)
0.153589 + 0.988135i \(0.450917\pi\)
\(422\) 24.2389 1.17993
\(423\) 0 0
\(424\) 37.5416 1.82318
\(425\) 1.30278 0.0631939
\(426\) 0 0
\(427\) 14.1194 0.683287
\(428\) −4.54163 −0.219528
\(429\) 0 0
\(430\) −13.3028 −0.641517
\(431\) −10.9361 −0.526773 −0.263386 0.964690i \(-0.584839\pi\)
−0.263386 + 0.964690i \(0.584839\pi\)
\(432\) 0 0
\(433\) −24.3305 −1.16925 −0.584625 0.811303i \(-0.698758\pi\)
−0.584625 + 0.811303i \(0.698758\pi\)
\(434\) 12.5139 0.600685
\(435\) 0 0
\(436\) 1.60555 0.0768920
\(437\) 1.30278 0.0623202
\(438\) 0 0
\(439\) −33.6056 −1.60391 −0.801953 0.597387i \(-0.796205\pi\)
−0.801953 + 0.597387i \(0.796205\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) 3.90833 0.185900
\(443\) −32.7250 −1.55481 −0.777405 0.629000i \(-0.783465\pi\)
−0.777405 + 0.629000i \(0.783465\pi\)
\(444\) 0 0
\(445\) −10.8167 −0.512759
\(446\) −7.54163 −0.357107
\(447\) 0 0
\(448\) 8.81665 0.416548
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) 11.7250 0.552108
\(452\) −1.54163 −0.0725124
\(453\) 0 0
\(454\) 31.9361 1.49883
\(455\) −2.30278 −0.107956
\(456\) 0 0
\(457\) 18.6972 0.874619 0.437310 0.899311i \(-0.355931\pi\)
0.437310 + 0.899311i \(0.355931\pi\)
\(458\) −21.1194 −0.986846
\(459\) 0 0
\(460\) −1.30278 −0.0607422
\(461\) −8.48612 −0.395238 −0.197619 0.980279i \(-0.563321\pi\)
−0.197619 + 0.980279i \(0.563321\pi\)
\(462\) 0 0
\(463\) −35.9361 −1.67009 −0.835046 0.550181i \(-0.814559\pi\)
−0.835046 + 0.550181i \(0.814559\pi\)
\(464\) −5.60555 −0.260231
\(465\) 0 0
\(466\) −1.18335 −0.0548175
\(467\) −5.21110 −0.241141 −0.120571 0.992705i \(-0.538472\pi\)
−0.120571 + 0.992705i \(0.538472\pi\)
\(468\) 0 0
\(469\) −4.51388 −0.208432
\(470\) −0.513878 −0.0237034
\(471\) 0 0
\(472\) −24.6333 −1.13384
\(473\) 30.6333 1.40852
\(474\) 0 0
\(475\) 0.302776 0.0138923
\(476\) −0.394449 −0.0180795
\(477\) 0 0
\(478\) −26.3305 −1.20433
\(479\) 34.9361 1.59627 0.798135 0.602478i \(-0.205820\pi\)
0.798135 + 0.602478i \(0.205820\pi\)
\(480\) 0 0
\(481\) 8.30278 0.378574
\(482\) 32.7250 1.49058
\(483\) 0 0
\(484\) 0.605551 0.0275251
\(485\) 8.51388 0.386595
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 42.3583 1.91747
\(489\) 0 0
\(490\) −1.30278 −0.0588534
\(491\) 11.7250 0.529141 0.264570 0.964366i \(-0.414770\pi\)
0.264570 + 0.964366i \(0.414770\pi\)
\(492\) 0 0
\(493\) 2.21110 0.0995831
\(494\) 0.908327 0.0408676
\(495\) 0 0
\(496\) 31.7250 1.42449
\(497\) 12.9083 0.579018
\(498\) 0 0
\(499\) 2.63331 0.117883 0.0589415 0.998261i \(-0.481227\pi\)
0.0589415 + 0.998261i \(0.481227\pi\)
\(500\) −0.302776 −0.0135405
\(501\) 0 0
\(502\) −33.6333 −1.50113
\(503\) −6.11943 −0.272852 −0.136426 0.990650i \(-0.543562\pi\)
−0.136426 + 0.990650i \(0.543562\pi\)
\(504\) 0 0
\(505\) 5.21110 0.231891
\(506\) −16.8167 −0.747591
\(507\) 0 0
\(508\) −4.15559 −0.184374
\(509\) 27.2389 1.20734 0.603671 0.797234i \(-0.293704\pi\)
0.603671 + 0.797234i \(0.293704\pi\)
\(510\) 0 0
\(511\) 4.21110 0.186288
\(512\) 25.4222 1.12351
\(513\) 0 0
\(514\) 15.6333 0.689556
\(515\) 16.7250 0.736991
\(516\) 0 0
\(517\) 1.18335 0.0520435
\(518\) 4.69722 0.206384
\(519\) 0 0
\(520\) −6.90833 −0.302950
\(521\) −36.3944 −1.59447 −0.797235 0.603669i \(-0.793705\pi\)
−0.797235 + 0.603669i \(0.793705\pi\)
\(522\) 0 0
\(523\) −18.7250 −0.818786 −0.409393 0.912358i \(-0.634260\pi\)
−0.409393 + 0.912358i \(0.634260\pi\)
\(524\) 1.42221 0.0621293
\(525\) 0 0
\(526\) −39.7527 −1.73330
\(527\) −12.5139 −0.545113
\(528\) 0 0
\(529\) −4.48612 −0.195049
\(530\) −16.3028 −0.708147
\(531\) 0 0
\(532\) −0.0916731 −0.00397453
\(533\) −9.00000 −0.389833
\(534\) 0 0
\(535\) 15.0000 0.648507
\(536\) −13.5416 −0.584910
\(537\) 0 0
\(538\) 25.3028 1.09088
\(539\) 3.00000 0.129219
\(540\) 0 0
\(541\) 2.51388 0.108080 0.0540400 0.998539i \(-0.482790\pi\)
0.0540400 + 0.998539i \(0.482790\pi\)
\(542\) 17.0917 0.734150
\(543\) 0 0
\(544\) −2.21110 −0.0948002
\(545\) −5.30278 −0.227146
\(546\) 0 0
\(547\) 23.7889 1.01714 0.508570 0.861021i \(-0.330174\pi\)
0.508570 + 0.861021i \(0.330174\pi\)
\(548\) 3.15559 0.134800
\(549\) 0 0
\(550\) −3.90833 −0.166652
\(551\) 0.513878 0.0218919
\(552\) 0 0
\(553\) −6.09167 −0.259044
\(554\) 18.1194 0.769821
\(555\) 0 0
\(556\) −0.486122 −0.0206162
\(557\) −33.5139 −1.42003 −0.710014 0.704187i \(-0.751312\pi\)
−0.710014 + 0.704187i \(0.751312\pi\)
\(558\) 0 0
\(559\) −23.5139 −0.994531
\(560\) −3.30278 −0.139568
\(561\) 0 0
\(562\) −15.2750 −0.644338
\(563\) −10.9361 −0.460901 −0.230450 0.973084i \(-0.574020\pi\)
−0.230450 + 0.973084i \(0.574020\pi\)
\(564\) 0 0
\(565\) 5.09167 0.214208
\(566\) 10.3028 0.433058
\(567\) 0 0
\(568\) 38.7250 1.62486
\(569\) 12.6333 0.529616 0.264808 0.964301i \(-0.414691\pi\)
0.264808 + 0.964301i \(0.414691\pi\)
\(570\) 0 0
\(571\) −26.9361 −1.12724 −0.563620 0.826034i \(-0.690592\pi\)
−0.563620 + 0.826034i \(0.690592\pi\)
\(572\) 2.09167 0.0874572
\(573\) 0 0
\(574\) −5.09167 −0.212522
\(575\) 4.30278 0.179438
\(576\) 0 0
\(577\) 32.3944 1.34860 0.674299 0.738458i \(-0.264446\pi\)
0.674299 + 0.738458i \(0.264446\pi\)
\(578\) 19.9361 0.829232
\(579\) 0 0
\(580\) −0.513878 −0.0213376
\(581\) 2.21110 0.0917320
\(582\) 0 0
\(583\) 37.5416 1.55482
\(584\) 12.6333 0.522770
\(585\) 0 0
\(586\) 39.3944 1.62737
\(587\) −12.9083 −0.532784 −0.266392 0.963865i \(-0.585832\pi\)
−0.266392 + 0.963865i \(0.585832\pi\)
\(588\) 0 0
\(589\) −2.90833 −0.119836
\(590\) 10.6972 0.440398
\(591\) 0 0
\(592\) 11.9083 0.489429
\(593\) −13.1833 −0.541375 −0.270688 0.962667i \(-0.587251\pi\)
−0.270688 + 0.962667i \(0.587251\pi\)
\(594\) 0 0
\(595\) 1.30278 0.0534086
\(596\) 3.78890 0.155199
\(597\) 0 0
\(598\) 12.9083 0.527861
\(599\) 7.57779 0.309620 0.154810 0.987944i \(-0.450523\pi\)
0.154810 + 0.987944i \(0.450523\pi\)
\(600\) 0 0
\(601\) 19.8806 0.810945 0.405473 0.914107i \(-0.367107\pi\)
0.405473 + 0.914107i \(0.367107\pi\)
\(602\) −13.3028 −0.542181
\(603\) 0 0
\(604\) 0.302776 0.0123198
\(605\) −2.00000 −0.0813116
\(606\) 0 0
\(607\) −28.6333 −1.16219 −0.581095 0.813836i \(-0.697376\pi\)
−0.581095 + 0.813836i \(0.697376\pi\)
\(608\) −0.513878 −0.0208405
\(609\) 0 0
\(610\) −18.3944 −0.744769
\(611\) −0.908327 −0.0367470
\(612\) 0 0
\(613\) 23.2389 0.938609 0.469304 0.883036i \(-0.344505\pi\)
0.469304 + 0.883036i \(0.344505\pi\)
\(614\) 32.3667 1.30621
\(615\) 0 0
\(616\) 9.00000 0.362620
\(617\) 32.0917 1.29196 0.645981 0.763353i \(-0.276448\pi\)
0.645981 + 0.763353i \(0.276448\pi\)
\(618\) 0 0
\(619\) −20.0278 −0.804983 −0.402492 0.915424i \(-0.631856\pi\)
−0.402492 + 0.915424i \(0.631856\pi\)
\(620\) 2.90833 0.116801
\(621\) 0 0
\(622\) −32.4500 −1.30112
\(623\) −10.8167 −0.433360
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −8.88057 −0.354939
\(627\) 0 0
\(628\) 0.183346 0.00731631
\(629\) −4.69722 −0.187291
\(630\) 0 0
\(631\) −45.2111 −1.79983 −0.899913 0.436070i \(-0.856370\pi\)
−0.899913 + 0.436070i \(0.856370\pi\)
\(632\) −18.2750 −0.726941
\(633\) 0 0
\(634\) 43.3028 1.71977
\(635\) 13.7250 0.544659
\(636\) 0 0
\(637\) −2.30278 −0.0912393
\(638\) −6.63331 −0.262615
\(639\) 0 0
\(640\) −8.09167 −0.319851
\(641\) −26.7250 −1.05557 −0.527787 0.849377i \(-0.676978\pi\)
−0.527787 + 0.849377i \(0.676978\pi\)
\(642\) 0 0
\(643\) −31.5139 −1.24279 −0.621393 0.783499i \(-0.713433\pi\)
−0.621393 + 0.783499i \(0.713433\pi\)
\(644\) −1.30278 −0.0513366
\(645\) 0 0
\(646\) −0.513878 −0.0202183
\(647\) 30.0000 1.17942 0.589711 0.807614i \(-0.299242\pi\)
0.589711 + 0.807614i \(0.299242\pi\)
\(648\) 0 0
\(649\) −24.6333 −0.966942
\(650\) 3.00000 0.117670
\(651\) 0 0
\(652\) −2.66106 −0.104215
\(653\) 30.1194 1.17866 0.589332 0.807891i \(-0.299391\pi\)
0.589332 + 0.807891i \(0.299391\pi\)
\(654\) 0 0
\(655\) −4.69722 −0.183536
\(656\) −12.9083 −0.503985
\(657\) 0 0
\(658\) −0.513878 −0.0200331
\(659\) −43.8167 −1.70685 −0.853427 0.521212i \(-0.825480\pi\)
−0.853427 + 0.521212i \(0.825480\pi\)
\(660\) 0 0
\(661\) −24.7250 −0.961690 −0.480845 0.876806i \(-0.659670\pi\)
−0.480845 + 0.876806i \(0.659670\pi\)
\(662\) −12.6333 −0.491007
\(663\) 0 0
\(664\) 6.63331 0.257422
\(665\) 0.302776 0.0117411
\(666\) 0 0
\(667\) 7.30278 0.282765
\(668\) −3.75274 −0.145198
\(669\) 0 0
\(670\) 5.88057 0.227186
\(671\) 42.3583 1.63522
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) −16.0278 −0.617366
\(675\) 0 0
\(676\) 2.33053 0.0896358
\(677\) −32.2111 −1.23797 −0.618987 0.785402i \(-0.712456\pi\)
−0.618987 + 0.785402i \(0.712456\pi\)
\(678\) 0 0
\(679\) 8.51388 0.326733
\(680\) 3.90833 0.149877
\(681\) 0 0
\(682\) 37.5416 1.43754
\(683\) 30.3583 1.16163 0.580814 0.814036i \(-0.302734\pi\)
0.580814 + 0.814036i \(0.302734\pi\)
\(684\) 0 0
\(685\) −10.4222 −0.398212
\(686\) −1.30278 −0.0497402
\(687\) 0 0
\(688\) −33.7250 −1.28575
\(689\) −28.8167 −1.09783
\(690\) 0 0
\(691\) 21.4222 0.814939 0.407470 0.913219i \(-0.366411\pi\)
0.407470 + 0.913219i \(0.366411\pi\)
\(692\) −1.45837 −0.0554387
\(693\) 0 0
\(694\) −34.6611 −1.31572
\(695\) 1.60555 0.0609020
\(696\) 0 0
\(697\) 5.09167 0.192861
\(698\) 21.6695 0.820201
\(699\) 0 0
\(700\) −0.302776 −0.0114438
\(701\) −10.0278 −0.378743 −0.189372 0.981905i \(-0.560645\pi\)
−0.189372 + 0.981905i \(0.560645\pi\)
\(702\) 0 0
\(703\) −1.09167 −0.0411732
\(704\) 26.4500 0.996870
\(705\) 0 0
\(706\) 11.3667 0.427791
\(707\) 5.21110 0.195984
\(708\) 0 0
\(709\) −8.97224 −0.336960 −0.168480 0.985705i \(-0.553886\pi\)
−0.168480 + 0.985705i \(0.553886\pi\)
\(710\) −16.8167 −0.631118
\(711\) 0 0
\(712\) −32.4500 −1.21611
\(713\) −41.3305 −1.54784
\(714\) 0 0
\(715\) −6.90833 −0.258357
\(716\) 1.45837 0.0545017
\(717\) 0 0
\(718\) −29.7250 −1.10933
\(719\) −20.3305 −0.758201 −0.379100 0.925356i \(-0.623767\pi\)
−0.379100 + 0.925356i \(0.623767\pi\)
\(720\) 0 0
\(721\) 16.7250 0.622871
\(722\) 24.6333 0.916757
\(723\) 0 0
\(724\) 3.45837 0.128529
\(725\) 1.69722 0.0630333
\(726\) 0 0
\(727\) −37.5139 −1.39131 −0.695656 0.718375i \(-0.744886\pi\)
−0.695656 + 0.718375i \(0.744886\pi\)
\(728\) −6.90833 −0.256040
\(729\) 0 0
\(730\) −5.48612 −0.203050
\(731\) 13.3028 0.492021
\(732\) 0 0
\(733\) −41.5416 −1.53438 −0.767188 0.641423i \(-0.778344\pi\)
−0.767188 + 0.641423i \(0.778344\pi\)
\(734\) 3.51388 0.129700
\(735\) 0 0
\(736\) −7.30278 −0.269184
\(737\) −13.5416 −0.498813
\(738\) 0 0
\(739\) −41.8167 −1.53825 −0.769125 0.639098i \(-0.779308\pi\)
−0.769125 + 0.639098i \(0.779308\pi\)
\(740\) 1.09167 0.0401307
\(741\) 0 0
\(742\) −16.3028 −0.598494
\(743\) −19.5416 −0.716913 −0.358457 0.933546i \(-0.616697\pi\)
−0.358457 + 0.933546i \(0.616697\pi\)
\(744\) 0 0
\(745\) −12.5139 −0.458473
\(746\) −11.6056 −0.424909
\(747\) 0 0
\(748\) −1.18335 −0.0432674
\(749\) 15.0000 0.548088
\(750\) 0 0
\(751\) 14.0000 0.510867 0.255434 0.966827i \(-0.417782\pi\)
0.255434 + 0.966827i \(0.417782\pi\)
\(752\) −1.30278 −0.0475073
\(753\) 0 0
\(754\) 5.09167 0.185428
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) 39.5416 1.43717 0.718583 0.695442i \(-0.244791\pi\)
0.718583 + 0.695442i \(0.244791\pi\)
\(758\) −22.9722 −0.834389
\(759\) 0 0
\(760\) 0.908327 0.0329485
\(761\) −40.5416 −1.46963 −0.734817 0.678266i \(-0.762732\pi\)
−0.734817 + 0.678266i \(0.762732\pi\)
\(762\) 0 0
\(763\) −5.30278 −0.191973
\(764\) 3.11943 0.112857
\(765\) 0 0
\(766\) 18.5139 0.668934
\(767\) 18.9083 0.682740
\(768\) 0 0
\(769\) −5.18335 −0.186916 −0.0934581 0.995623i \(-0.529792\pi\)
−0.0934581 + 0.995623i \(0.529792\pi\)
\(770\) −3.90833 −0.140846
\(771\) 0 0
\(772\) 5.78890 0.208347
\(773\) −52.5416 −1.88979 −0.944896 0.327372i \(-0.893837\pi\)
−0.944896 + 0.327372i \(0.893837\pi\)
\(774\) 0 0
\(775\) −9.60555 −0.345042
\(776\) 25.5416 0.916891
\(777\) 0 0
\(778\) −30.9083 −1.10812
\(779\) 1.18335 0.0423978
\(780\) 0 0
\(781\) 38.7250 1.38569
\(782\) −7.30278 −0.261147
\(783\) 0 0
\(784\) −3.30278 −0.117956
\(785\) −0.605551 −0.0216131
\(786\) 0 0
\(787\) 33.0278 1.17731 0.588656 0.808384i \(-0.299657\pi\)
0.588656 + 0.808384i \(0.299657\pi\)
\(788\) 0.358288 0.0127635
\(789\) 0 0
\(790\) 7.93608 0.282353
\(791\) 5.09167 0.181039
\(792\) 0 0
\(793\) −32.5139 −1.15460
\(794\) −2.60555 −0.0924676
\(795\) 0 0
\(796\) 2.94449 0.104365
\(797\) −32.0917 −1.13675 −0.568373 0.822771i \(-0.692427\pi\)
−0.568373 + 0.822771i \(0.692427\pi\)
\(798\) 0 0
\(799\) 0.513878 0.0181797
\(800\) −1.69722 −0.0600059
\(801\) 0 0
\(802\) −34.8167 −1.22942
\(803\) 12.6333 0.445820
\(804\) 0 0
\(805\) 4.30278 0.151653
\(806\) −28.8167 −1.01502
\(807\) 0 0
\(808\) 15.6333 0.549978
\(809\) −40.8167 −1.43504 −0.717519 0.696539i \(-0.754722\pi\)
−0.717519 + 0.696539i \(0.754722\pi\)
\(810\) 0 0
\(811\) −6.48612 −0.227759 −0.113879 0.993495i \(-0.536328\pi\)
−0.113879 + 0.993495i \(0.536328\pi\)
\(812\) −0.513878 −0.0180336
\(813\) 0 0
\(814\) 14.0917 0.493913
\(815\) 8.78890 0.307862
\(816\) 0 0
\(817\) 3.09167 0.108164
\(818\) −18.2389 −0.637707
\(819\) 0 0
\(820\) −1.18335 −0.0413242
\(821\) −10.8167 −0.377504 −0.188752 0.982025i \(-0.560444\pi\)
−0.188752 + 0.982025i \(0.560444\pi\)
\(822\) 0 0
\(823\) −10.6333 −0.370654 −0.185327 0.982677i \(-0.559334\pi\)
−0.185327 + 0.982677i \(0.559334\pi\)
\(824\) 50.1749 1.74793
\(825\) 0 0
\(826\) 10.6972 0.372204
\(827\) −42.6333 −1.48251 −0.741253 0.671226i \(-0.765768\pi\)
−0.741253 + 0.671226i \(0.765768\pi\)
\(828\) 0 0
\(829\) 49.0555 1.70377 0.851884 0.523730i \(-0.175460\pi\)
0.851884 + 0.523730i \(0.175460\pi\)
\(830\) −2.88057 −0.0999861
\(831\) 0 0
\(832\) −20.3028 −0.703872
\(833\) 1.30278 0.0451385
\(834\) 0 0
\(835\) 12.3944 0.428928
\(836\) −0.275019 −0.00951174
\(837\) 0 0
\(838\) −45.3583 −1.56688
\(839\) −21.9083 −0.756359 −0.378180 0.925732i \(-0.623450\pi\)
−0.378180 + 0.925732i \(0.623450\pi\)
\(840\) 0 0
\(841\) −26.1194 −0.900670
\(842\) −8.21110 −0.282973
\(843\) 0 0
\(844\) 5.63331 0.193906
\(845\) −7.69722 −0.264793
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) −41.3305 −1.41930
\(849\) 0 0
\(850\) −1.69722 −0.0582143
\(851\) −15.5139 −0.531809
\(852\) 0 0
\(853\) −27.8444 −0.953374 −0.476687 0.879073i \(-0.658163\pi\)
−0.476687 + 0.879073i \(0.658163\pi\)
\(854\) −18.3944 −0.629445
\(855\) 0 0
\(856\) 45.0000 1.53807
\(857\) 52.2666 1.78539 0.892697 0.450658i \(-0.148811\pi\)
0.892697 + 0.450658i \(0.148811\pi\)
\(858\) 0 0
\(859\) 6.18335 0.210973 0.105487 0.994421i \(-0.466360\pi\)
0.105487 + 0.994421i \(0.466360\pi\)
\(860\) −3.09167 −0.105425
\(861\) 0 0
\(862\) 14.2473 0.485264
\(863\) 55.2666 1.88130 0.940649 0.339382i \(-0.110218\pi\)
0.940649 + 0.339382i \(0.110218\pi\)
\(864\) 0 0
\(865\) 4.81665 0.163771
\(866\) 31.6972 1.07712
\(867\) 0 0
\(868\) 2.90833 0.0987150
\(869\) −18.2750 −0.619938
\(870\) 0 0
\(871\) 10.3944 0.352202
\(872\) −15.9083 −0.538724
\(873\) 0 0
\(874\) −1.69722 −0.0574095
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) 20.6333 0.696737 0.348369 0.937358i \(-0.386736\pi\)
0.348369 + 0.937358i \(0.386736\pi\)
\(878\) 43.7805 1.47752
\(879\) 0 0
\(880\) −9.90833 −0.334010
\(881\) −2.36669 −0.0797359 −0.0398679 0.999205i \(-0.512694\pi\)
−0.0398679 + 0.999205i \(0.512694\pi\)
\(882\) 0 0
\(883\) 30.0278 1.01051 0.505257 0.862969i \(-0.331398\pi\)
0.505257 + 0.862969i \(0.331398\pi\)
\(884\) 0.908327 0.0305503
\(885\) 0 0
\(886\) 42.6333 1.43229
\(887\) −15.3944 −0.516895 −0.258448 0.966025i \(-0.583211\pi\)
−0.258448 + 0.966025i \(0.583211\pi\)
\(888\) 0 0
\(889\) 13.7250 0.460321
\(890\) 14.0917 0.472354
\(891\) 0 0
\(892\) −1.75274 −0.0586860
\(893\) 0.119429 0.00399655
\(894\) 0 0
\(895\) −4.81665 −0.161003
\(896\) −8.09167 −0.270324
\(897\) 0 0
\(898\) 23.4500 0.782535
\(899\) −16.3028 −0.543728
\(900\) 0 0
\(901\) 16.3028 0.543124
\(902\) −15.2750 −0.508603
\(903\) 0 0
\(904\) 15.2750 0.508040
\(905\) −11.4222 −0.379687
\(906\) 0 0
\(907\) 37.5694 1.24747 0.623736 0.781635i \(-0.285614\pi\)
0.623736 + 0.781635i \(0.285614\pi\)
\(908\) 7.42221 0.246315
\(909\) 0 0
\(910\) 3.00000 0.0994490
\(911\) 15.6333 0.517955 0.258977 0.965883i \(-0.416615\pi\)
0.258977 + 0.965883i \(0.416615\pi\)
\(912\) 0 0
\(913\) 6.63331 0.219530
\(914\) −24.3583 −0.805701
\(915\) 0 0
\(916\) −4.90833 −0.162176
\(917\) −4.69722 −0.155116
\(918\) 0 0
\(919\) 20.5139 0.676690 0.338345 0.941022i \(-0.390133\pi\)
0.338345 + 0.941022i \(0.390133\pi\)
\(920\) 12.9083 0.425575
\(921\) 0 0
\(922\) 11.0555 0.364094
\(923\) −29.7250 −0.978410
\(924\) 0 0
\(925\) −3.60555 −0.118550
\(926\) 46.8167 1.53849
\(927\) 0 0
\(928\) −2.88057 −0.0945594
\(929\) −50.5694 −1.65913 −0.829564 0.558412i \(-0.811411\pi\)
−0.829564 + 0.558412i \(0.811411\pi\)
\(930\) 0 0
\(931\) 0.302776 0.00992307
\(932\) −0.275019 −0.00900856
\(933\) 0 0
\(934\) 6.78890 0.222140
\(935\) 3.90833 0.127816
\(936\) 0 0
\(937\) 15.5778 0.508904 0.254452 0.967085i \(-0.418105\pi\)
0.254452 + 0.967085i \(0.418105\pi\)
\(938\) 5.88057 0.192007
\(939\) 0 0
\(940\) −0.119429 −0.00389536
\(941\) 52.2666 1.70384 0.851921 0.523670i \(-0.175437\pi\)
0.851921 + 0.523670i \(0.175437\pi\)
\(942\) 0 0
\(943\) 16.8167 0.547626
\(944\) 27.1194 0.882662
\(945\) 0 0
\(946\) −39.9083 −1.29753
\(947\) −38.3305 −1.24557 −0.622787 0.782391i \(-0.714000\pi\)
−0.622787 + 0.782391i \(0.714000\pi\)
\(948\) 0 0
\(949\) −9.69722 −0.314785
\(950\) −0.394449 −0.0127976
\(951\) 0 0
\(952\) 3.90833 0.126670
\(953\) −22.5778 −0.731367 −0.365683 0.930739i \(-0.619165\pi\)
−0.365683 + 0.930739i \(0.619165\pi\)
\(954\) 0 0
\(955\) −10.3028 −0.333390
\(956\) −6.11943 −0.197916
\(957\) 0 0
\(958\) −45.5139 −1.47049
\(959\) −10.4222 −0.336551
\(960\) 0 0
\(961\) 61.2666 1.97634
\(962\) −10.8167 −0.348743
\(963\) 0 0
\(964\) 7.60555 0.244958
\(965\) −19.1194 −0.615476
\(966\) 0 0
\(967\) 31.8444 1.02405 0.512024 0.858971i \(-0.328896\pi\)
0.512024 + 0.858971i \(0.328896\pi\)
\(968\) −6.00000 −0.192847
\(969\) 0 0
\(970\) −11.0917 −0.356132
\(971\) −34.4222 −1.10466 −0.552331 0.833625i \(-0.686261\pi\)
−0.552331 + 0.833625i \(0.686261\pi\)
\(972\) 0 0
\(973\) 1.60555 0.0514716
\(974\) −49.5055 −1.58626
\(975\) 0 0
\(976\) −46.6333 −1.49270
\(977\) −28.4222 −0.909307 −0.454653 0.890668i \(-0.650237\pi\)
−0.454653 + 0.890668i \(0.650237\pi\)
\(978\) 0 0
\(979\) −32.4500 −1.03711
\(980\) −0.302776 −0.00967181
\(981\) 0 0
\(982\) −15.2750 −0.487445
\(983\) 2.48612 0.0792950 0.0396475 0.999214i \(-0.487377\pi\)
0.0396475 + 0.999214i \(0.487377\pi\)
\(984\) 0 0
\(985\) −1.18335 −0.0377045
\(986\) −2.88057 −0.0917361
\(987\) 0 0
\(988\) 0.211103 0.00671607
\(989\) 43.9361 1.39709
\(990\) 0 0
\(991\) 13.0555 0.414722 0.207361 0.978264i \(-0.433513\pi\)
0.207361 + 0.978264i \(0.433513\pi\)
\(992\) 16.3028 0.517614
\(993\) 0 0
\(994\) −16.8167 −0.533392
\(995\) −9.72498 −0.308303
\(996\) 0 0
\(997\) 6.81665 0.215886 0.107943 0.994157i \(-0.465574\pi\)
0.107943 + 0.994157i \(0.465574\pi\)
\(998\) −3.43061 −0.108594
\(999\) 0 0
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 \(a_p\))