Properties

Label 8048.2.a.l.1.2
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.23607 q^{3}\) \(-3.23607 q^{5}\) \(-0.236068 q^{7}\) \(+2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.23607 q^{3}\) \(-3.23607 q^{5}\) \(-0.236068 q^{7}\) \(+2.00000 q^{9}\) \(-0.236068 q^{11}\) \(+3.47214 q^{13}\) \(-7.23607 q^{15}\) \(+2.00000 q^{17}\) \(-5.70820 q^{19}\) \(-0.527864 q^{21}\) \(+2.23607 q^{23}\) \(+5.47214 q^{25}\) \(-2.23607 q^{27}\) \(-7.23607 q^{29}\) \(+5.70820 q^{31}\) \(-0.527864 q^{33}\) \(+0.763932 q^{35}\) \(+4.47214 q^{37}\) \(+7.76393 q^{39}\) \(-0.763932 q^{41}\) \(-5.76393 q^{43}\) \(-6.47214 q^{45}\) \(+0.236068 q^{47}\) \(-6.94427 q^{49}\) \(+4.47214 q^{51}\) \(+8.47214 q^{53}\) \(+0.763932 q^{55}\) \(-12.7639 q^{57}\) \(+8.94427 q^{59}\) \(-1.47214 q^{61}\) \(-0.472136 q^{63}\) \(-11.2361 q^{65}\) \(+8.70820 q^{67}\) \(+5.00000 q^{69}\) \(-5.23607 q^{71}\) \(-16.4721 q^{73}\) \(+12.2361 q^{75}\) \(+0.0557281 q^{77}\) \(+4.94427 q^{79}\) \(-11.0000 q^{81}\) \(-3.29180 q^{83}\) \(-6.47214 q^{85}\) \(-16.1803 q^{87}\) \(-5.52786 q^{89}\) \(-0.819660 q^{91}\) \(+12.7639 q^{93}\) \(+18.4721 q^{95}\) \(-10.0000 q^{97}\) \(-0.472136 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 30q^{57} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut -\mathstrut 18q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 10q^{69} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 20q^{75} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 30q^{93} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.23607 1.29099 0.645497 0.763763i \(-0.276650\pi\)
0.645497 + 0.763763i \(0.276650\pi\)
\(4\) 0 0
\(5\) −3.23607 −1.44721 −0.723607 0.690212i \(-0.757517\pi\)
−0.723607 + 0.690212i \(0.757517\pi\)
\(6\) 0 0
\(7\) −0.236068 −0.0892253 −0.0446127 0.999004i \(-0.514205\pi\)
−0.0446127 + 0.999004i \(0.514205\pi\)
\(8\) 0 0
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) −0.236068 −0.0711772 −0.0355886 0.999367i \(-0.511331\pi\)
−0.0355886 + 0.999367i \(0.511331\pi\)
\(12\) 0 0
\(13\) 3.47214 0.962997 0.481499 0.876447i \(-0.340093\pi\)
0.481499 + 0.876447i \(0.340093\pi\)
\(14\) 0 0
\(15\) −7.23607 −1.86834
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −5.70820 −1.30955 −0.654776 0.755823i \(-0.727237\pi\)
−0.654776 + 0.755823i \(0.727237\pi\)
\(20\) 0 0
\(21\) −0.527864 −0.115189
\(22\) 0 0
\(23\) 2.23607 0.466252 0.233126 0.972446i \(-0.425104\pi\)
0.233126 + 0.972446i \(0.425104\pi\)
\(24\) 0 0
\(25\) 5.47214 1.09443
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) 0 0
\(29\) −7.23607 −1.34370 −0.671852 0.740685i \(-0.734501\pi\)
−0.671852 + 0.740685i \(0.734501\pi\)
\(30\) 0 0
\(31\) 5.70820 1.02522 0.512612 0.858620i \(-0.328678\pi\)
0.512612 + 0.858620i \(0.328678\pi\)
\(32\) 0 0
\(33\) −0.527864 −0.0918893
\(34\) 0 0
\(35\) 0.763932 0.129128
\(36\) 0 0
\(37\) 4.47214 0.735215 0.367607 0.929981i \(-0.380177\pi\)
0.367607 + 0.929981i \(0.380177\pi\)
\(38\) 0 0
\(39\) 7.76393 1.24322
\(40\) 0 0
\(41\) −0.763932 −0.119306 −0.0596531 0.998219i \(-0.518999\pi\)
−0.0596531 + 0.998219i \(0.518999\pi\)
\(42\) 0 0
\(43\) −5.76393 −0.878991 −0.439496 0.898245i \(-0.644843\pi\)
−0.439496 + 0.898245i \(0.644843\pi\)
\(44\) 0 0
\(45\) −6.47214 −0.964809
\(46\) 0 0
\(47\) 0.236068 0.0344341 0.0172170 0.999852i \(-0.494519\pi\)
0.0172170 + 0.999852i \(0.494519\pi\)
\(48\) 0 0
\(49\) −6.94427 −0.992039
\(50\) 0 0
\(51\) 4.47214 0.626224
\(52\) 0 0
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) 0 0
\(55\) 0.763932 0.103009
\(56\) 0 0
\(57\) −12.7639 −1.69062
\(58\) 0 0
\(59\) 8.94427 1.16445 0.582223 0.813029i \(-0.302183\pi\)
0.582223 + 0.813029i \(0.302183\pi\)
\(60\) 0 0
\(61\) −1.47214 −0.188488 −0.0942438 0.995549i \(-0.530043\pi\)
−0.0942438 + 0.995549i \(0.530043\pi\)
\(62\) 0 0
\(63\) −0.472136 −0.0594835
\(64\) 0 0
\(65\) −11.2361 −1.39366
\(66\) 0 0
\(67\) 8.70820 1.06388 0.531938 0.846783i \(-0.321464\pi\)
0.531938 + 0.846783i \(0.321464\pi\)
\(68\) 0 0
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) −5.23607 −0.621407 −0.310703 0.950507i \(-0.600565\pi\)
−0.310703 + 0.950507i \(0.600565\pi\)
\(72\) 0 0
\(73\) −16.4721 −1.92792 −0.963959 0.266051i \(-0.914281\pi\)
−0.963959 + 0.266051i \(0.914281\pi\)
\(74\) 0 0
\(75\) 12.2361 1.41290
\(76\) 0 0
\(77\) 0.0557281 0.00635081
\(78\) 0 0
\(79\) 4.94427 0.556274 0.278137 0.960541i \(-0.410283\pi\)
0.278137 + 0.960541i \(0.410283\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) −3.29180 −0.361322 −0.180661 0.983545i \(-0.557824\pi\)
−0.180661 + 0.983545i \(0.557824\pi\)
\(84\) 0 0
\(85\) −6.47214 −0.702002
\(86\) 0 0
\(87\) −16.1803 −1.73471
\(88\) 0 0
\(89\) −5.52786 −0.585952 −0.292976 0.956120i \(-0.594646\pi\)
−0.292976 + 0.956120i \(0.594646\pi\)
\(90\) 0 0
\(91\) −0.819660 −0.0859237
\(92\) 0 0
\(93\) 12.7639 1.32356
\(94\) 0 0
\(95\) 18.4721 1.89520
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) −0.472136 −0.0474514
\(100\) 0 0
\(101\) 3.70820 0.368980 0.184490 0.982834i \(-0.440937\pi\)
0.184490 + 0.982834i \(0.440937\pi\)
\(102\) 0 0
\(103\) −16.9443 −1.66957 −0.834784 0.550577i \(-0.814408\pi\)
−0.834784 + 0.550577i \(0.814408\pi\)
\(104\) 0 0
\(105\) 1.70820 0.166704
\(106\) 0 0
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 0 0
\(109\) −0.472136 −0.0452224 −0.0226112 0.999744i \(-0.507198\pi\)
−0.0226112 + 0.999744i \(0.507198\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −17.4721 −1.64364 −0.821820 0.569747i \(-0.807041\pi\)
−0.821820 + 0.569747i \(0.807041\pi\)
\(114\) 0 0
\(115\) −7.23607 −0.674767
\(116\) 0 0
\(117\) 6.94427 0.641998
\(118\) 0 0
\(119\) −0.472136 −0.0432806
\(120\) 0 0
\(121\) −10.9443 −0.994934
\(122\) 0 0
\(123\) −1.70820 −0.154024
\(124\) 0 0
\(125\) −1.52786 −0.136656
\(126\) 0 0
\(127\) −15.7082 −1.39388 −0.696939 0.717131i \(-0.745455\pi\)
−0.696939 + 0.717131i \(0.745455\pi\)
\(128\) 0 0
\(129\) −12.8885 −1.13477
\(130\) 0 0
\(131\) −1.18034 −0.103127 −0.0515634 0.998670i \(-0.516420\pi\)
−0.0515634 + 0.998670i \(0.516420\pi\)
\(132\) 0 0
\(133\) 1.34752 0.116845
\(134\) 0 0
\(135\) 7.23607 0.622782
\(136\) 0 0
\(137\) −2.76393 −0.236139 −0.118069 0.993005i \(-0.537671\pi\)
−0.118069 + 0.993005i \(0.537671\pi\)
\(138\) 0 0
\(139\) −12.1803 −1.03312 −0.516561 0.856250i \(-0.672788\pi\)
−0.516561 + 0.856250i \(0.672788\pi\)
\(140\) 0 0
\(141\) 0.527864 0.0444542
\(142\) 0 0
\(143\) −0.819660 −0.0685434
\(144\) 0 0
\(145\) 23.4164 1.94463
\(146\) 0 0
\(147\) −15.5279 −1.28072
\(148\) 0 0
\(149\) −17.2361 −1.41203 −0.706017 0.708195i \(-0.749510\pi\)
−0.706017 + 0.708195i \(0.749510\pi\)
\(150\) 0 0
\(151\) 9.52786 0.775367 0.387683 0.921793i \(-0.373275\pi\)
0.387683 + 0.921793i \(0.373275\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) −18.4721 −1.48372
\(156\) 0 0
\(157\) 3.52786 0.281554 0.140777 0.990041i \(-0.455040\pi\)
0.140777 + 0.990041i \(0.455040\pi\)
\(158\) 0 0
\(159\) 18.9443 1.50238
\(160\) 0 0
\(161\) −0.527864 −0.0416015
\(162\) 0 0
\(163\) −1.70820 −0.133797 −0.0668984 0.997760i \(-0.521310\pi\)
−0.0668984 + 0.997760i \(0.521310\pi\)
\(164\) 0 0
\(165\) 1.70820 0.132983
\(166\) 0 0
\(167\) −5.70820 −0.441714 −0.220857 0.975306i \(-0.570885\pi\)
−0.220857 + 0.975306i \(0.570885\pi\)
\(168\) 0 0
\(169\) −0.944272 −0.0726363
\(170\) 0 0
\(171\) −11.4164 −0.873035
\(172\) 0 0
\(173\) 11.0000 0.836315 0.418157 0.908375i \(-0.362676\pi\)
0.418157 + 0.908375i \(0.362676\pi\)
\(174\) 0 0
\(175\) −1.29180 −0.0976506
\(176\) 0 0
\(177\) 20.0000 1.50329
\(178\) 0 0
\(179\) 7.70820 0.576138 0.288069 0.957610i \(-0.406987\pi\)
0.288069 + 0.957610i \(0.406987\pi\)
\(180\) 0 0
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 0 0
\(183\) −3.29180 −0.243337
\(184\) 0 0
\(185\) −14.4721 −1.06401
\(186\) 0 0
\(187\) −0.472136 −0.0345260
\(188\) 0 0
\(189\) 0.527864 0.0383965
\(190\) 0 0
\(191\) 9.52786 0.689412 0.344706 0.938711i \(-0.387979\pi\)
0.344706 + 0.938711i \(0.387979\pi\)
\(192\) 0 0
\(193\) −11.2361 −0.808790 −0.404395 0.914584i \(-0.632518\pi\)
−0.404395 + 0.914584i \(0.632518\pi\)
\(194\) 0 0
\(195\) −25.1246 −1.79921
\(196\) 0 0
\(197\) 6.41641 0.457150 0.228575 0.973526i \(-0.426593\pi\)
0.228575 + 0.973526i \(0.426593\pi\)
\(198\) 0 0
\(199\) 6.47214 0.458798 0.229399 0.973333i \(-0.426324\pi\)
0.229399 + 0.973333i \(0.426324\pi\)
\(200\) 0 0
\(201\) 19.4721 1.37346
\(202\) 0 0
\(203\) 1.70820 0.119892
\(204\) 0 0
\(205\) 2.47214 0.172661
\(206\) 0 0
\(207\) 4.47214 0.310835
\(208\) 0 0
\(209\) 1.34752 0.0932102
\(210\) 0 0
\(211\) −9.70820 −0.668340 −0.334170 0.942513i \(-0.608456\pi\)
−0.334170 + 0.942513i \(0.608456\pi\)
\(212\) 0 0
\(213\) −11.7082 −0.802233
\(214\) 0 0
\(215\) 18.6525 1.27209
\(216\) 0 0
\(217\) −1.34752 −0.0914759
\(218\) 0 0
\(219\) −36.8328 −2.48893
\(220\) 0 0
\(221\) 6.94427 0.467122
\(222\) 0 0
\(223\) −8.23607 −0.551528 −0.275764 0.961225i \(-0.588931\pi\)
−0.275764 + 0.961225i \(0.588931\pi\)
\(224\) 0 0
\(225\) 10.9443 0.729618
\(226\) 0 0
\(227\) 1.70820 0.113377 0.0566887 0.998392i \(-0.481946\pi\)
0.0566887 + 0.998392i \(0.481946\pi\)
\(228\) 0 0
\(229\) −8.41641 −0.556172 −0.278086 0.960556i \(-0.589700\pi\)
−0.278086 + 0.960556i \(0.589700\pi\)
\(230\) 0 0
\(231\) 0.124612 0.00819885
\(232\) 0 0
\(233\) −4.41641 −0.289328 −0.144664 0.989481i \(-0.546210\pi\)
−0.144664 + 0.989481i \(0.546210\pi\)
\(234\) 0 0
\(235\) −0.763932 −0.0498334
\(236\) 0 0
\(237\) 11.0557 0.718147
\(238\) 0 0
\(239\) −1.41641 −0.0916198 −0.0458099 0.998950i \(-0.514587\pi\)
−0.0458099 + 0.998950i \(0.514587\pi\)
\(240\) 0 0
\(241\) 12.9443 0.833814 0.416907 0.908949i \(-0.363114\pi\)
0.416907 + 0.908949i \(0.363114\pi\)
\(242\) 0 0
\(243\) −17.8885 −1.14755
\(244\) 0 0
\(245\) 22.4721 1.43569
\(246\) 0 0
\(247\) −19.8197 −1.26109
\(248\) 0 0
\(249\) −7.36068 −0.466464
\(250\) 0 0
\(251\) −18.1803 −1.14753 −0.573766 0.819019i \(-0.694518\pi\)
−0.573766 + 0.819019i \(0.694518\pi\)
\(252\) 0 0
\(253\) −0.527864 −0.0331865
\(254\) 0 0
\(255\) −14.4721 −0.906280
\(256\) 0 0
\(257\) 27.9443 1.74312 0.871558 0.490293i \(-0.163110\pi\)
0.871558 + 0.490293i \(0.163110\pi\)
\(258\) 0 0
\(259\) −1.05573 −0.0655998
\(260\) 0 0
\(261\) −14.4721 −0.895803
\(262\) 0 0
\(263\) 24.1246 1.48759 0.743794 0.668409i \(-0.233025\pi\)
0.743794 + 0.668409i \(0.233025\pi\)
\(264\) 0 0
\(265\) −27.4164 −1.68418
\(266\) 0 0
\(267\) −12.3607 −0.756461
\(268\) 0 0
\(269\) −0.944272 −0.0575733 −0.0287866 0.999586i \(-0.509164\pi\)
−0.0287866 + 0.999586i \(0.509164\pi\)
\(270\) 0 0
\(271\) −13.2918 −0.807419 −0.403710 0.914887i \(-0.632279\pi\)
−0.403710 + 0.914887i \(0.632279\pi\)
\(272\) 0 0
\(273\) −1.83282 −0.110927
\(274\) 0 0
\(275\) −1.29180 −0.0778982
\(276\) 0 0
\(277\) 3.81966 0.229501 0.114751 0.993394i \(-0.463393\pi\)
0.114751 + 0.993394i \(0.463393\pi\)
\(278\) 0 0
\(279\) 11.4164 0.683482
\(280\) 0 0
\(281\) −1.58359 −0.0944692 −0.0472346 0.998884i \(-0.515041\pi\)
−0.0472346 + 0.998884i \(0.515041\pi\)
\(282\) 0 0
\(283\) 9.52786 0.566373 0.283186 0.959065i \(-0.408609\pi\)
0.283186 + 0.959065i \(0.408609\pi\)
\(284\) 0 0
\(285\) 41.3050 2.44669
\(286\) 0 0
\(287\) 0.180340 0.0106451
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −22.3607 −1.31081
\(292\) 0 0
\(293\) 5.00000 0.292103 0.146052 0.989277i \(-0.453343\pi\)
0.146052 + 0.989277i \(0.453343\pi\)
\(294\) 0 0
\(295\) −28.9443 −1.68520
\(296\) 0 0
\(297\) 0.527864 0.0306298
\(298\) 0 0
\(299\) 7.76393 0.449000
\(300\) 0 0
\(301\) 1.36068 0.0784283
\(302\) 0 0
\(303\) 8.29180 0.476351
\(304\) 0 0
\(305\) 4.76393 0.272782
\(306\) 0 0
\(307\) 17.4164 0.994007 0.497003 0.867749i \(-0.334434\pi\)
0.497003 + 0.867749i \(0.334434\pi\)
\(308\) 0 0
\(309\) −37.8885 −2.15540
\(310\) 0 0
\(311\) 28.1803 1.59796 0.798980 0.601357i \(-0.205373\pi\)
0.798980 + 0.601357i \(0.205373\pi\)
\(312\) 0 0
\(313\) −13.0557 −0.737953 −0.368977 0.929439i \(-0.620292\pi\)
−0.368977 + 0.929439i \(0.620292\pi\)
\(314\) 0 0
\(315\) 1.52786 0.0860854
\(316\) 0 0
\(317\) −25.9443 −1.45718 −0.728588 0.684952i \(-0.759823\pi\)
−0.728588 + 0.684952i \(0.759823\pi\)
\(318\) 0 0
\(319\) 1.70820 0.0956411
\(320\) 0 0
\(321\) 17.8885 0.998441
\(322\) 0 0
\(323\) −11.4164 −0.635226
\(324\) 0 0
\(325\) 19.0000 1.05393
\(326\) 0 0
\(327\) −1.05573 −0.0583819
\(328\) 0 0
\(329\) −0.0557281 −0.00307239
\(330\) 0 0
\(331\) 6.94427 0.381692 0.190846 0.981620i \(-0.438877\pi\)
0.190846 + 0.981620i \(0.438877\pi\)
\(332\) 0 0
\(333\) 8.94427 0.490143
\(334\) 0 0
\(335\) −28.1803 −1.53966
\(336\) 0 0
\(337\) −13.0557 −0.711191 −0.355595 0.934640i \(-0.615722\pi\)
−0.355595 + 0.934640i \(0.615722\pi\)
\(338\) 0 0
\(339\) −39.0689 −2.12193
\(340\) 0 0
\(341\) −1.34752 −0.0729725
\(342\) 0 0
\(343\) 3.29180 0.177740
\(344\) 0 0
\(345\) −16.1803 −0.871120
\(346\) 0 0
\(347\) 8.00000 0.429463 0.214731 0.976673i \(-0.431112\pi\)
0.214731 + 0.976673i \(0.431112\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 0 0
\(351\) −7.76393 −0.414408
\(352\) 0 0
\(353\) −29.2361 −1.55608 −0.778039 0.628215i \(-0.783786\pi\)
−0.778039 + 0.628215i \(0.783786\pi\)
\(354\) 0 0
\(355\) 16.9443 0.899309
\(356\) 0 0
\(357\) −1.05573 −0.0558751
\(358\) 0 0
\(359\) −3.70820 −0.195712 −0.0978558 0.995201i \(-0.531198\pi\)
−0.0978558 + 0.995201i \(0.531198\pi\)
\(360\) 0 0
\(361\) 13.5836 0.714926
\(362\) 0 0
\(363\) −24.4721 −1.28445
\(364\) 0 0
\(365\) 53.3050 2.79011
\(366\) 0 0
\(367\) −2.23607 −0.116722 −0.0583609 0.998296i \(-0.518587\pi\)
−0.0583609 + 0.998296i \(0.518587\pi\)
\(368\) 0 0
\(369\) −1.52786 −0.0795374
\(370\) 0 0
\(371\) −2.00000 −0.103835
\(372\) 0 0
\(373\) −36.3050 −1.87980 −0.939900 0.341451i \(-0.889082\pi\)
−0.939900 + 0.341451i \(0.889082\pi\)
\(374\) 0 0
\(375\) −3.41641 −0.176423
\(376\) 0 0
\(377\) −25.1246 −1.29398
\(378\) 0 0
\(379\) −6.70820 −0.344577 −0.172289 0.985047i \(-0.555116\pi\)
−0.172289 + 0.985047i \(0.555116\pi\)
\(380\) 0 0
\(381\) −35.1246 −1.79949
\(382\) 0 0
\(383\) −4.94427 −0.252640 −0.126320 0.991990i \(-0.540317\pi\)
−0.126320 + 0.991990i \(0.540317\pi\)
\(384\) 0 0
\(385\) −0.180340 −0.00919097
\(386\) 0 0
\(387\) −11.5279 −0.585994
\(388\) 0 0
\(389\) −36.8328 −1.86750 −0.933749 0.357929i \(-0.883483\pi\)
−0.933749 + 0.357929i \(0.883483\pi\)
\(390\) 0 0
\(391\) 4.47214 0.226166
\(392\) 0 0
\(393\) −2.63932 −0.133136
\(394\) 0 0
\(395\) −16.0000 −0.805047
\(396\) 0 0
\(397\) −7.36068 −0.369422 −0.184711 0.982793i \(-0.559135\pi\)
−0.184711 + 0.982793i \(0.559135\pi\)
\(398\) 0 0
\(399\) 3.01316 0.150846
\(400\) 0 0
\(401\) −14.4164 −0.719921 −0.359961 0.932968i \(-0.617210\pi\)
−0.359961 + 0.932968i \(0.617210\pi\)
\(402\) 0 0
\(403\) 19.8197 0.987288
\(404\) 0 0
\(405\) 35.5967 1.76882
\(406\) 0 0
\(407\) −1.05573 −0.0523305
\(408\) 0 0
\(409\) −11.7082 −0.578933 −0.289467 0.957188i \(-0.593478\pi\)
−0.289467 + 0.957188i \(0.593478\pi\)
\(410\) 0 0
\(411\) −6.18034 −0.304854
\(412\) 0 0
\(413\) −2.11146 −0.103898
\(414\) 0 0
\(415\) 10.6525 0.522909
\(416\) 0 0
\(417\) −27.2361 −1.33376
\(418\) 0 0
\(419\) 21.7082 1.06052 0.530258 0.847837i \(-0.322095\pi\)
0.530258 + 0.847837i \(0.322095\pi\)
\(420\) 0 0
\(421\) −22.9443 −1.11824 −0.559118 0.829088i \(-0.688860\pi\)
−0.559118 + 0.829088i \(0.688860\pi\)
\(422\) 0 0
\(423\) 0.472136 0.0229560
\(424\) 0 0
\(425\) 10.9443 0.530875
\(426\) 0 0
\(427\) 0.347524 0.0168179
\(428\) 0 0
\(429\) −1.83282 −0.0884892
\(430\) 0 0
\(431\) −32.6525 −1.57281 −0.786407 0.617708i \(-0.788061\pi\)
−0.786407 + 0.617708i \(0.788061\pi\)
\(432\) 0 0
\(433\) 11.5279 0.553994 0.276997 0.960871i \(-0.410661\pi\)
0.276997 + 0.960871i \(0.410661\pi\)
\(434\) 0 0
\(435\) 52.3607 2.51050
\(436\) 0 0
\(437\) −12.7639 −0.610582
\(438\) 0 0
\(439\) −17.8885 −0.853774 −0.426887 0.904305i \(-0.640390\pi\)
−0.426887 + 0.904305i \(0.640390\pi\)
\(440\) 0 0
\(441\) −13.8885 −0.661359
\(442\) 0 0
\(443\) −0.819660 −0.0389432 −0.0194716 0.999810i \(-0.506198\pi\)
−0.0194716 + 0.999810i \(0.506198\pi\)
\(444\) 0 0
\(445\) 17.8885 0.847998
\(446\) 0 0
\(447\) −38.5410 −1.82293
\(448\) 0 0
\(449\) −29.5967 −1.39676 −0.698378 0.715729i \(-0.746095\pi\)
−0.698378 + 0.715729i \(0.746095\pi\)
\(450\) 0 0
\(451\) 0.180340 0.00849187
\(452\) 0 0
\(453\) 21.3050 1.00099
\(454\) 0 0
\(455\) 2.65248 0.124350
\(456\) 0 0
\(457\) 22.3607 1.04599 0.522994 0.852336i \(-0.324815\pi\)
0.522994 + 0.852336i \(0.324815\pi\)
\(458\) 0 0
\(459\) −4.47214 −0.208741
\(460\) 0 0
\(461\) 42.0689 1.95934 0.979672 0.200608i \(-0.0642917\pi\)
0.979672 + 0.200608i \(0.0642917\pi\)
\(462\) 0 0
\(463\) 32.5967 1.51490 0.757450 0.652894i \(-0.226445\pi\)
0.757450 + 0.652894i \(0.226445\pi\)
\(464\) 0 0
\(465\) −41.3050 −1.91547
\(466\) 0 0
\(467\) 21.7082 1.00454 0.502268 0.864712i \(-0.332499\pi\)
0.502268 + 0.864712i \(0.332499\pi\)
\(468\) 0 0
\(469\) −2.05573 −0.0949247
\(470\) 0 0
\(471\) 7.88854 0.363485
\(472\) 0 0
\(473\) 1.36068 0.0625641
\(474\) 0 0
\(475\) −31.2361 −1.43321
\(476\) 0 0
\(477\) 16.9443 0.775825
\(478\) 0 0
\(479\) −4.94427 −0.225910 −0.112955 0.993600i \(-0.536032\pi\)
−0.112955 + 0.993600i \(0.536032\pi\)
\(480\) 0 0
\(481\) 15.5279 0.708010
\(482\) 0 0
\(483\) −1.18034 −0.0537073
\(484\) 0 0
\(485\) 32.3607 1.46942
\(486\) 0 0
\(487\) 13.5967 0.616127 0.308064 0.951366i \(-0.400319\pi\)
0.308064 + 0.951366i \(0.400319\pi\)
\(488\) 0 0
\(489\) −3.81966 −0.172731
\(490\) 0 0
\(491\) −39.1246 −1.76567 −0.882835 0.469684i \(-0.844368\pi\)
−0.882835 + 0.469684i \(0.844368\pi\)
\(492\) 0 0
\(493\) −14.4721 −0.651792
\(494\) 0 0
\(495\) 1.52786 0.0686724
\(496\) 0 0
\(497\) 1.23607 0.0554452
\(498\) 0 0
\(499\) 0.111456 0.00498946 0.00249473 0.999997i \(-0.499206\pi\)
0.00249473 + 0.999997i \(0.499206\pi\)
\(500\) 0 0
\(501\) −12.7639 −0.570250
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) −2.11146 −0.0937731
\(508\) 0 0
\(509\) −20.8885 −0.925868 −0.462934 0.886393i \(-0.653203\pi\)
−0.462934 + 0.886393i \(0.653203\pi\)
\(510\) 0 0
\(511\) 3.88854 0.172019
\(512\) 0 0
\(513\) 12.7639 0.563541
\(514\) 0 0
\(515\) 54.8328 2.41622
\(516\) 0 0
\(517\) −0.0557281 −0.00245092
\(518\) 0 0
\(519\) 24.5967 1.07968
\(520\) 0 0
\(521\) −41.0000 −1.79624 −0.898121 0.439748i \(-0.855068\pi\)
−0.898121 + 0.439748i \(0.855068\pi\)
\(522\) 0 0
\(523\) 32.3607 1.41503 0.707517 0.706696i \(-0.249815\pi\)
0.707517 + 0.706696i \(0.249815\pi\)
\(524\) 0 0
\(525\) −2.88854 −0.126066
\(526\) 0 0
\(527\) 11.4164 0.497307
\(528\) 0 0
\(529\) −18.0000 −0.782609
\(530\) 0 0
\(531\) 17.8885 0.776297
\(532\) 0 0
\(533\) −2.65248 −0.114891
\(534\) 0 0
\(535\) −25.8885 −1.11926
\(536\) 0 0
\(537\) 17.2361 0.743791
\(538\) 0 0
\(539\) 1.63932 0.0706105
\(540\) 0 0
\(541\) −24.6525 −1.05989 −0.529946 0.848031i \(-0.677788\pi\)
−0.529946 + 0.848031i \(0.677788\pi\)
\(542\) 0 0
\(543\) −44.7214 −1.91918
\(544\) 0 0
\(545\) 1.52786 0.0654465
\(546\) 0 0
\(547\) 8.36068 0.357477 0.178738 0.983897i \(-0.442798\pi\)
0.178738 + 0.983897i \(0.442798\pi\)
\(548\) 0 0
\(549\) −2.94427 −0.125658
\(550\) 0 0
\(551\) 41.3050 1.75965
\(552\) 0 0
\(553\) −1.16718 −0.0496337
\(554\) 0 0
\(555\) −32.3607 −1.37363
\(556\) 0 0
\(557\) 43.2492 1.83253 0.916264 0.400574i \(-0.131189\pi\)
0.916264 + 0.400574i \(0.131189\pi\)
\(558\) 0 0
\(559\) −20.0132 −0.846466
\(560\) 0 0
\(561\) −1.05573 −0.0445729
\(562\) 0 0
\(563\) −22.2918 −0.939487 −0.469744 0.882803i \(-0.655654\pi\)
−0.469744 + 0.882803i \(0.655654\pi\)
\(564\) 0 0
\(565\) 56.5410 2.37870
\(566\) 0 0
\(567\) 2.59675 0.109053
\(568\) 0 0
\(569\) −23.3050 −0.976994 −0.488497 0.872565i \(-0.662455\pi\)
−0.488497 + 0.872565i \(0.662455\pi\)
\(570\) 0 0
\(571\) 19.8885 0.832310 0.416155 0.909294i \(-0.363377\pi\)
0.416155 + 0.909294i \(0.363377\pi\)
\(572\) 0 0
\(573\) 21.3050 0.890027
\(574\) 0 0
\(575\) 12.2361 0.510279
\(576\) 0 0
\(577\) 22.3607 0.930887 0.465444 0.885078i \(-0.345895\pi\)
0.465444 + 0.885078i \(0.345895\pi\)
\(578\) 0 0
\(579\) −25.1246 −1.04414
\(580\) 0 0
\(581\) 0.777088 0.0322390
\(582\) 0 0
\(583\) −2.00000 −0.0828315
\(584\) 0 0
\(585\) −22.4721 −0.929108
\(586\) 0 0
\(587\) −38.8328 −1.60280 −0.801401 0.598128i \(-0.795912\pi\)
−0.801401 + 0.598128i \(0.795912\pi\)
\(588\) 0 0
\(589\) −32.5836 −1.34258
\(590\) 0 0
\(591\) 14.3475 0.590178
\(592\) 0 0
\(593\) 7.52786 0.309132 0.154566 0.987982i \(-0.450602\pi\)
0.154566 + 0.987982i \(0.450602\pi\)
\(594\) 0 0
\(595\) 1.52786 0.0626363
\(596\) 0 0
\(597\) 14.4721 0.592305
\(598\) 0 0
\(599\) −34.4721 −1.40849 −0.704247 0.709955i \(-0.748715\pi\)
−0.704247 + 0.709955i \(0.748715\pi\)
\(600\) 0 0
\(601\) −0.527864 −0.0215320 −0.0107660 0.999942i \(-0.503427\pi\)
−0.0107660 + 0.999942i \(0.503427\pi\)
\(602\) 0 0
\(603\) 17.4164 0.709251
\(604\) 0 0
\(605\) 35.4164 1.43988
\(606\) 0 0
\(607\) −5.76393 −0.233951 −0.116975 0.993135i \(-0.537320\pi\)
−0.116975 + 0.993135i \(0.537320\pi\)
\(608\) 0 0
\(609\) 3.81966 0.154780
\(610\) 0 0
\(611\) 0.819660 0.0331599
\(612\) 0 0
\(613\) 30.1803 1.21897 0.609486 0.792797i \(-0.291376\pi\)
0.609486 + 0.792797i \(0.291376\pi\)
\(614\) 0 0
\(615\) 5.52786 0.222905
\(616\) 0 0
\(617\) 11.8885 0.478615 0.239307 0.970944i \(-0.423080\pi\)
0.239307 + 0.970944i \(0.423080\pi\)
\(618\) 0 0
\(619\) −18.2918 −0.735209 −0.367605 0.929982i \(-0.619822\pi\)
−0.367605 + 0.929982i \(0.619822\pi\)
\(620\) 0 0
\(621\) −5.00000 −0.200643
\(622\) 0 0
\(623\) 1.30495 0.0522818
\(624\) 0 0
\(625\) −22.4164 −0.896656
\(626\) 0 0
\(627\) 3.01316 0.120334
\(628\) 0 0
\(629\) 8.94427 0.356631
\(630\) 0 0
\(631\) −7.76393 −0.309077 −0.154539 0.987987i \(-0.549389\pi\)
−0.154539 + 0.987987i \(0.549389\pi\)
\(632\) 0 0
\(633\) −21.7082 −0.862824
\(634\) 0 0
\(635\) 50.8328 2.01724
\(636\) 0 0
\(637\) −24.1115 −0.955331
\(638\) 0 0
\(639\) −10.4721 −0.414271
\(640\) 0 0
\(641\) 16.4164 0.648409 0.324205 0.945987i \(-0.394903\pi\)
0.324205 + 0.945987i \(0.394903\pi\)
\(642\) 0 0
\(643\) −38.9443 −1.53581 −0.767906 0.640562i \(-0.778701\pi\)
−0.767906 + 0.640562i \(0.778701\pi\)
\(644\) 0 0
\(645\) 41.7082 1.64226
\(646\) 0 0
\(647\) 27.0557 1.06367 0.531835 0.846848i \(-0.321503\pi\)
0.531835 + 0.846848i \(0.321503\pi\)
\(648\) 0 0
\(649\) −2.11146 −0.0828819
\(650\) 0 0
\(651\) −3.01316 −0.118095
\(652\) 0 0
\(653\) 9.00000 0.352197 0.176099 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(654\) 0 0
\(655\) 3.81966 0.149246
\(656\) 0 0
\(657\) −32.9443 −1.28528
\(658\) 0 0
\(659\) 46.0132 1.79242 0.896209 0.443632i \(-0.146310\pi\)
0.896209 + 0.443632i \(0.146310\pi\)
\(660\) 0 0
\(661\) −2.63932 −0.102658 −0.0513288 0.998682i \(-0.516346\pi\)
−0.0513288 + 0.998682i \(0.516346\pi\)
\(662\) 0 0
\(663\) 15.5279 0.603052
\(664\) 0 0
\(665\) −4.36068 −0.169100
\(666\) 0 0
\(667\) −16.1803 −0.626505
\(668\) 0 0
\(669\) −18.4164 −0.712019
\(670\) 0 0
\(671\) 0.347524 0.0134160
\(672\) 0 0
\(673\) 5.05573 0.194884 0.0974420 0.995241i \(-0.468934\pi\)
0.0974420 + 0.995241i \(0.468934\pi\)
\(674\) 0 0
\(675\) −12.2361 −0.470966
\(676\) 0 0
\(677\) 36.4721 1.40174 0.700869 0.713290i \(-0.252796\pi\)
0.700869 + 0.713290i \(0.252796\pi\)
\(678\) 0 0
\(679\) 2.36068 0.0905946
\(680\) 0 0
\(681\) 3.81966 0.146370
\(682\) 0 0
\(683\) 46.1803 1.76704 0.883521 0.468392i \(-0.155166\pi\)
0.883521 + 0.468392i \(0.155166\pi\)
\(684\) 0 0
\(685\) 8.94427 0.341743
\(686\) 0 0
\(687\) −18.8197 −0.718015
\(688\) 0 0
\(689\) 29.4164 1.12068
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 0 0
\(693\) 0.111456 0.00423387
\(694\) 0 0
\(695\) 39.4164 1.49515
\(696\) 0 0
\(697\) −1.52786 −0.0578720
\(698\) 0 0
\(699\) −9.87539 −0.373521
\(700\) 0 0
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 0 0
\(703\) −25.5279 −0.962802
\(704\) 0 0
\(705\) −1.70820 −0.0643347
\(706\) 0 0
\(707\) −0.875388 −0.0329224
\(708\) 0 0
\(709\) 30.0000 1.12667 0.563337 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) 0 0
\(711\) 9.88854 0.370849
\(712\) 0 0
\(713\) 12.7639 0.478013
\(714\) 0 0
\(715\) 2.65248 0.0991970
\(716\) 0 0
\(717\) −3.16718 −0.118281
\(718\) 0 0
\(719\) −25.8885 −0.965480 −0.482740 0.875764i \(-0.660358\pi\)
−0.482740 + 0.875764i \(0.660358\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 0 0
\(723\) 28.9443 1.07645
\(724\) 0 0
\(725\) −39.5967 −1.47059
\(726\) 0 0
\(727\) 37.0689 1.37481 0.687404 0.726275i \(-0.258750\pi\)
0.687404 + 0.726275i \(0.258750\pi\)
\(728\) 0 0
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) −11.5279 −0.426373
\(732\) 0 0
\(733\) −24.7639 −0.914677 −0.457338 0.889293i \(-0.651197\pi\)
−0.457338 + 0.889293i \(0.651197\pi\)
\(734\) 0 0
\(735\) 50.2492 1.85347
\(736\) 0 0
\(737\) −2.05573 −0.0757237
\(738\) 0 0
\(739\) 25.7639 0.947742 0.473871 0.880594i \(-0.342856\pi\)
0.473871 + 0.880594i \(0.342856\pi\)
\(740\) 0 0
\(741\) −44.3181 −1.62807
\(742\) 0 0
\(743\) 49.7082 1.82362 0.911809 0.410616i \(-0.134686\pi\)
0.911809 + 0.410616i \(0.134686\pi\)
\(744\) 0 0
\(745\) 55.7771 2.04351
\(746\) 0 0
\(747\) −6.58359 −0.240881
\(748\) 0 0
\(749\) −1.88854 −0.0690059
\(750\) 0 0
\(751\) −4.36068 −0.159123 −0.0795617 0.996830i \(-0.525352\pi\)
−0.0795617 + 0.996830i \(0.525352\pi\)
\(752\) 0 0
\(753\) −40.6525 −1.48146
\(754\) 0 0
\(755\) −30.8328 −1.12212
\(756\) 0 0
\(757\) −2.36068 −0.0858004 −0.0429002 0.999079i \(-0.513660\pi\)
−0.0429002 + 0.999079i \(0.513660\pi\)
\(758\) 0 0
\(759\) −1.18034 −0.0428436
\(760\) 0 0
\(761\) 7.00000 0.253750 0.126875 0.991919i \(-0.459505\pi\)
0.126875 + 0.991919i \(0.459505\pi\)
\(762\) 0 0
\(763\) 0.111456 0.00403498
\(764\) 0 0
\(765\) −12.9443 −0.468001
\(766\) 0 0
\(767\) 31.0557 1.12136
\(768\) 0 0
\(769\) −25.7771 −0.929546 −0.464773 0.885430i \(-0.653864\pi\)
−0.464773 + 0.885430i \(0.653864\pi\)
\(770\) 0 0
\(771\) 62.4853 2.25035
\(772\) 0 0
\(773\) −15.5967 −0.560976 −0.280488 0.959858i \(-0.590496\pi\)
−0.280488 + 0.959858i \(0.590496\pi\)
\(774\) 0 0
\(775\) 31.2361 1.12203
\(776\) 0 0
\(777\) −2.36068 −0.0846889
\(778\) 0 0
\(779\) 4.36068 0.156238
\(780\) 0 0
\(781\) 1.23607 0.0442300
\(782\) 0 0
\(783\) 16.1803 0.578238
\(784\) 0 0
\(785\) −11.4164 −0.407469
\(786\) 0 0
\(787\) 6.06888 0.216332 0.108166 0.994133i \(-0.465502\pi\)
0.108166 + 0.994133i \(0.465502\pi\)
\(788\) 0 0
\(789\) 53.9443 1.92047
\(790\) 0 0
\(791\) 4.12461 0.146654
\(792\) 0 0
\(793\) −5.11146 −0.181513
\(794\) 0 0
\(795\) −61.3050 −2.17426
\(796\) 0 0
\(797\) 48.8328 1.72975 0.864874 0.501990i \(-0.167399\pi\)
0.864874 + 0.501990i \(0.167399\pi\)
\(798\) 0 0
\(799\) 0.472136 0.0167030
\(800\) 0 0
\(801\) −11.0557 −0.390635
\(802\) 0 0
\(803\) 3.88854 0.137224
\(804\) 0 0
\(805\) 1.70820 0.0602063
\(806\) 0 0
\(807\) −2.11146 −0.0743268
\(808\) 0 0
\(809\) 16.1803 0.568870 0.284435 0.958695i \(-0.408194\pi\)
0.284435 + 0.958695i \(0.408194\pi\)
\(810\) 0 0
\(811\) 3.76393 0.132170 0.0660848 0.997814i \(-0.478949\pi\)
0.0660848 + 0.997814i \(0.478949\pi\)
\(812\) 0 0
\(813\) −29.7214 −1.04237
\(814\) 0 0
\(815\) 5.52786 0.193633
\(816\) 0 0
\(817\) 32.9017 1.15108
\(818\) 0 0
\(819\) −1.63932 −0.0572825
\(820\) 0 0
\(821\) 23.0557 0.804650 0.402325 0.915497i \(-0.368202\pi\)
0.402325 + 0.915497i \(0.368202\pi\)
\(822\) 0 0
\(823\) 1.81966 0.0634294 0.0317147 0.999497i \(-0.489903\pi\)
0.0317147 + 0.999497i \(0.489903\pi\)
\(824\) 0 0
\(825\) −2.88854 −0.100566
\(826\) 0 0
\(827\) −8.00000 −0.278187 −0.139094 0.990279i \(-0.544419\pi\)
−0.139094 + 0.990279i \(0.544419\pi\)
\(828\) 0 0
\(829\) 3.59675 0.124920 0.0624601 0.998047i \(-0.480105\pi\)
0.0624601 + 0.998047i \(0.480105\pi\)
\(830\) 0 0
\(831\) 8.54102 0.296285
\(832\) 0 0
\(833\) −13.8885 −0.481210
\(834\) 0 0
\(835\) 18.4721 0.639255
\(836\) 0 0
\(837\) −12.7639 −0.441186
\(838\) 0 0
\(839\) 14.5967 0.503936 0.251968 0.967736i \(-0.418922\pi\)
0.251968 + 0.967736i \(0.418922\pi\)
\(840\) 0 0
\(841\) 23.3607 0.805541
\(842\) 0 0
\(843\) −3.54102 −0.121959
\(844\) 0 0
\(845\) 3.05573 0.105120
\(846\) 0 0
\(847\) 2.58359 0.0887733
\(848\) 0 0
\(849\) 21.3050 0.731184
\(850\) 0 0
\(851\) 10.0000 0.342796
\(852\) 0 0
\(853\) −37.8328 −1.29537 −0.647685 0.761908i \(-0.724263\pi\)
−0.647685 + 0.761908i \(0.724263\pi\)
\(854\) 0 0
\(855\) 36.9443 1.26347
\(856\) 0 0
\(857\) 33.9443 1.15951 0.579757 0.814789i \(-0.303147\pi\)
0.579757 + 0.814789i \(0.303147\pi\)
\(858\) 0 0
\(859\) 27.7082 0.945392 0.472696 0.881226i \(-0.343281\pi\)
0.472696 + 0.881226i \(0.343281\pi\)
\(860\) 0 0
\(861\) 0.403252 0.0137428
\(862\) 0 0
\(863\) −2.76393 −0.0940853 −0.0470427 0.998893i \(-0.514980\pi\)
−0.0470427 + 0.998893i \(0.514980\pi\)
\(864\) 0 0
\(865\) −35.5967 −1.21033
\(866\) 0 0
\(867\) −29.0689 −0.987231
\(868\) 0 0
\(869\) −1.16718 −0.0395940
\(870\) 0 0
\(871\) 30.2361 1.02451
\(872\) 0 0
\(873\) −20.0000 −0.676897
\(874\) 0 0
\(875\) 0.360680 0.0121932
\(876\) 0 0
\(877\) 53.7771 1.81592 0.907962 0.419053i \(-0.137638\pi\)
0.907962 + 0.419053i \(0.137638\pi\)
\(878\) 0 0
\(879\) 11.1803 0.377104
\(880\) 0 0
\(881\) 23.8885 0.804825 0.402413 0.915458i \(-0.368172\pi\)
0.402413 + 0.915458i \(0.368172\pi\)
\(882\) 0 0
\(883\) −50.4721 −1.69852 −0.849261 0.527973i \(-0.822952\pi\)
−0.849261 + 0.527973i \(0.822952\pi\)
\(884\) 0 0
\(885\) −64.7214 −2.17558
\(886\) 0 0
\(887\) −48.7214 −1.63590 −0.817952 0.575287i \(-0.804890\pi\)
−0.817952 + 0.575287i \(0.804890\pi\)
\(888\) 0 0
\(889\) 3.70820 0.124369
\(890\) 0 0
\(891\) 2.59675 0.0869943
\(892\) 0 0
\(893\) −1.34752 −0.0450932
\(894\) 0 0
\(895\) −24.9443 −0.833795
\(896\) 0 0
\(897\) 17.3607 0.579656
\(898\) 0 0
\(899\) −41.3050 −1.37760
\(900\) 0 0
\(901\) 16.9443 0.564496
\(902\) 0 0
\(903\) 3.04257 0.101250
\(904\) 0 0
\(905\) 64.7214 2.15141
\(906\) 0 0
\(907\) −14.9443 −0.496216 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(908\) 0 0
\(909\) 7.41641 0.245987
\(910\) 0 0
\(911\) −11.2361 −0.372268 −0.186134 0.982524i \(-0.559596\pi\)
−0.186134 + 0.982524i \(0.559596\pi\)
\(912\) 0 0
\(913\) 0.777088 0.0257178
\(914\) 0 0
\(915\) 10.6525 0.352160
\(916\) 0 0
\(917\) 0.278640 0.00920152
\(918\) 0 0
\(919\) 12.9443 0.426992 0.213496 0.976944i \(-0.431515\pi\)
0.213496 + 0.976944i \(0.431515\pi\)
\(920\) 0 0
\(921\) 38.9443 1.28326
\(922\) 0 0
\(923\) −18.1803 −0.598413
\(924\) 0 0
\(925\) 24.4721 0.804639
\(926\) 0 0
\(927\) −33.8885 −1.11305
\(928\) 0 0
\(929\) −4.65248 −0.152643 −0.0763214 0.997083i \(-0.524318\pi\)
−0.0763214 + 0.997083i \(0.524318\pi\)
\(930\) 0 0
\(931\) 39.6393 1.29913
\(932\) 0 0
\(933\) 63.0132 2.06296
\(934\) 0 0
\(935\) 1.52786 0.0499665
\(936\) 0 0
\(937\) 42.0689 1.37433 0.687165 0.726501i \(-0.258855\pi\)
0.687165 + 0.726501i \(0.258855\pi\)
\(938\) 0 0
\(939\) −29.1935 −0.952694
\(940\) 0 0
\(941\) 9.58359 0.312416 0.156208 0.987724i \(-0.450073\pi\)
0.156208 + 0.987724i \(0.450073\pi\)
\(942\) 0 0
\(943\) −1.70820 −0.0556268
\(944\) 0 0
\(945\) −1.70820 −0.0555679
\(946\) 0 0
\(947\) 24.7639 0.804720 0.402360 0.915482i \(-0.368190\pi\)
0.402360 + 0.915482i \(0.368190\pi\)
\(948\) 0 0
\(949\) −57.1935 −1.85658
\(950\) 0 0
\(951\) −58.0132 −1.88121
\(952\) 0 0
\(953\) 37.9443 1.22914 0.614568 0.788864i \(-0.289330\pi\)
0.614568 + 0.788864i \(0.289330\pi\)
\(954\) 0 0
\(955\) −30.8328 −0.997726
\(956\) 0 0
\(957\) 3.81966 0.123472
\(958\) 0 0
\(959\) 0.652476 0.0210695
\(960\) 0 0
\(961\) 1.58359 0.0510836
\(962\) 0 0
\(963\) 16.0000 0.515593
\(964\) 0 0
\(965\) 36.3607 1.17049
\(966\) 0 0
\(967\) 1.30495 0.0419644 0.0209822 0.999780i \(-0.493321\pi\)
0.0209822 + 0.999780i \(0.493321\pi\)
\(968\) 0 0
\(969\) −25.5279 −0.820073
\(970\) 0 0
\(971\) −1.06888 −0.0343021 −0.0171511 0.999853i \(-0.505460\pi\)
−0.0171511 + 0.999853i \(0.505460\pi\)
\(972\) 0 0
\(973\) 2.87539 0.0921807
\(974\) 0 0
\(975\) 42.4853 1.36062
\(976\) 0 0
\(977\) 4.11146 0.131537 0.0657686 0.997835i \(-0.479050\pi\)
0.0657686 + 0.997835i \(0.479050\pi\)
\(978\) 0 0
\(979\) 1.30495 0.0417064
\(980\) 0 0
\(981\) −0.944272 −0.0301483
\(982\) 0 0
\(983\) 34.7639 1.10880 0.554399 0.832251i \(-0.312948\pi\)
0.554399 + 0.832251i \(0.312948\pi\)
\(984\) 0 0
\(985\) −20.7639 −0.661594
\(986\) 0 0
\(987\) −0.124612 −0.00396644
\(988\) 0 0
\(989\) −12.8885 −0.409832
\(990\) 0 0
\(991\) −56.9574 −1.80931 −0.904656 0.426142i \(-0.859872\pi\)
−0.904656 + 0.426142i \(0.859872\pi\)
\(992\) 0 0
\(993\) 15.5279 0.492762
\(994\) 0 0
\(995\) −20.9443 −0.663978
\(996\) 0 0
\(997\) 56.0689 1.77572 0.887860 0.460114i \(-0.152192\pi\)
0.887860 + 0.460114i \(0.152192\pi\)
\(998\) 0 0
\(999\) −10.0000 −0.316386
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 \(a_p\))