Properties

Label 1148.2.k.b.337.8
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.8
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.350714 - 0.350714i) q^{3} +3.08423i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.75400i q^{9} +O(q^{10})\) \(q+(-0.350714 - 0.350714i) q^{3} +3.08423i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.75400i q^{9} +(1.14202 + 1.14202i) q^{11} +(-2.88280 - 2.88280i) q^{13} +(1.08168 - 1.08168i) q^{15} +(3.58376 - 3.58376i) q^{17} +(2.29327 - 2.29327i) q^{19} +0.495985i q^{21} +3.46961 q^{23} -4.51245 q^{25} +(-2.01801 + 2.01801i) q^{27} +(4.60631 + 4.60631i) q^{29} +2.08732 q^{31} -0.801046i q^{33} +(2.18088 - 2.18088i) q^{35} +6.46508 q^{37} +2.02208i q^{39} +(6.11172 - 1.90968i) q^{41} +6.95000i q^{43} +8.49395 q^{45} +(-3.66137 + 3.66137i) q^{47} +1.00000i q^{49} -2.51375 q^{51} +(5.69357 + 5.69357i) q^{53} +(-3.52225 + 3.52225i) q^{55} -1.60857 q^{57} +2.42066 q^{59} -8.24899i q^{61} +(-1.94737 + 1.94737i) q^{63} +(8.89122 - 8.89122i) q^{65} +(-5.59189 + 5.59189i) q^{67} +(-1.21684 - 1.21684i) q^{69} +(-3.14338 - 3.14338i) q^{71} -8.57857i q^{73} +(1.58258 + 1.58258i) q^{75} -1.61506i q^{77} +(5.97983 + 5.97983i) q^{79} -6.84651 q^{81} +13.2534 q^{83} +(11.0531 + 11.0531i) q^{85} -3.23100i q^{87} +(-3.25227 - 3.25227i) q^{89} +4.07690i q^{91} +(-0.732052 - 0.732052i) q^{93} +(7.07296 + 7.07296i) q^{95} +(-3.75610 + 3.75610i) q^{97} +(3.14513 - 3.14513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −0.350714 0.350714i −0.202485 0.202485i 0.598579 0.801064i \(-0.295732\pi\)
−0.801064 + 0.598579i \(0.795732\pi\)
\(4\) 0 0
\(5\) 3.08423i 1.37931i 0.724139 + 0.689654i \(0.242237\pi\)
−0.724139 + 0.689654i \(0.757763\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 2.75400i 0.918000i
\(10\) 0 0
\(11\) 1.14202 + 1.14202i 0.344332 + 0.344332i 0.857993 0.513661i \(-0.171711\pi\)
−0.513661 + 0.857993i \(0.671711\pi\)
\(12\) 0 0
\(13\) −2.88280 2.88280i −0.799546 0.799546i 0.183478 0.983024i \(-0.441264\pi\)
−0.983024 + 0.183478i \(0.941264\pi\)
\(14\) 0 0
\(15\) 1.08168 1.08168i 0.279289 0.279289i
\(16\) 0 0
\(17\) 3.58376 3.58376i 0.869188 0.869188i −0.123194 0.992383i \(-0.539314\pi\)
0.992383 + 0.123194i \(0.0393138\pi\)
\(18\) 0 0
\(19\) 2.29327 2.29327i 0.526112 0.526112i −0.393298 0.919411i \(-0.628666\pi\)
0.919411 + 0.393298i \(0.128666\pi\)
\(20\) 0 0
\(21\) 0.495985i 0.108233i
\(22\) 0 0
\(23\) 3.46961 0.723464 0.361732 0.932282i \(-0.382186\pi\)
0.361732 + 0.932282i \(0.382186\pi\)
\(24\) 0 0
\(25\) −4.51245 −0.902489
\(26\) 0 0
\(27\) −2.01801 + 2.01801i −0.388366 + 0.388366i
\(28\) 0 0
\(29\) 4.60631 + 4.60631i 0.855371 + 0.855371i 0.990789 0.135418i \(-0.0432377\pi\)
−0.135418 + 0.990789i \(0.543238\pi\)
\(30\) 0 0
\(31\) 2.08732 0.374893 0.187447 0.982275i \(-0.439979\pi\)
0.187447 + 0.982275i \(0.439979\pi\)
\(32\) 0 0
\(33\) 0.801046i 0.139444i
\(34\) 0 0
\(35\) 2.18088 2.18088i 0.368635 0.368635i
\(36\) 0 0
\(37\) 6.46508 1.06285 0.531427 0.847104i \(-0.321656\pi\)
0.531427 + 0.847104i \(0.321656\pi\)
\(38\) 0 0
\(39\) 2.02208i 0.323792i
\(40\) 0 0
\(41\) 6.11172 1.90968i 0.954490 0.298242i
\(42\) 0 0
\(43\) 6.95000i 1.05987i 0.848040 + 0.529933i \(0.177783\pi\)
−0.848040 + 0.529933i \(0.822217\pi\)
\(44\) 0 0
\(45\) 8.49395 1.26620
\(46\) 0 0
\(47\) −3.66137 + 3.66137i −0.534066 + 0.534066i −0.921780 0.387714i \(-0.873265\pi\)
0.387714 + 0.921780i \(0.373265\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −2.51375 −0.351995
\(52\) 0 0
\(53\) 5.69357 + 5.69357i 0.782072 + 0.782072i 0.980180 0.198108i \(-0.0634797\pi\)
−0.198108 + 0.980180i \(0.563480\pi\)
\(54\) 0 0
\(55\) −3.52225 + 3.52225i −0.474940 + 0.474940i
\(56\) 0 0
\(57\) −1.60857 −0.213060
\(58\) 0 0
\(59\) 2.42066 0.315143 0.157572 0.987508i \(-0.449633\pi\)
0.157572 + 0.987508i \(0.449633\pi\)
\(60\) 0 0
\(61\) 8.24899i 1.05618i −0.849190 0.528088i \(-0.822909\pi\)
0.849190 0.528088i \(-0.177091\pi\)
\(62\) 0 0
\(63\) −1.94737 + 1.94737i −0.245346 + 0.245346i
\(64\) 0 0
\(65\) 8.89122 8.89122i 1.10282 1.10282i
\(66\) 0 0
\(67\) −5.59189 + 5.59189i −0.683157 + 0.683157i −0.960710 0.277553i \(-0.910477\pi\)
0.277553 + 0.960710i \(0.410477\pi\)
\(68\) 0 0
\(69\) −1.21684 1.21684i −0.146491 0.146491i
\(70\) 0 0
\(71\) −3.14338 3.14338i −0.373051 0.373051i 0.495536 0.868587i \(-0.334972\pi\)
−0.868587 + 0.495536i \(0.834972\pi\)
\(72\) 0 0
\(73\) 8.57857i 1.00405i −0.864855 0.502023i \(-0.832589\pi\)
0.864855 0.502023i \(-0.167411\pi\)
\(74\) 0 0
\(75\) 1.58258 + 1.58258i 0.182740 + 0.182740i
\(76\) 0 0
\(77\) 1.61506i 0.184053i
\(78\) 0 0
\(79\) 5.97983 + 5.97983i 0.672783 + 0.672783i 0.958357 0.285574i \(-0.0921841\pi\)
−0.285574 + 0.958357i \(0.592184\pi\)
\(80\) 0 0
\(81\) −6.84651 −0.760723
\(82\) 0 0
\(83\) 13.2534 1.45474 0.727372 0.686243i \(-0.240741\pi\)
0.727372 + 0.686243i \(0.240741\pi\)
\(84\) 0 0
\(85\) 11.0531 + 11.0531i 1.19888 + 1.19888i
\(86\) 0 0
\(87\) 3.23100i 0.346399i
\(88\) 0 0
\(89\) −3.25227 3.25227i −0.344740 0.344740i 0.513406 0.858146i \(-0.328384\pi\)
−0.858146 + 0.513406i \(0.828384\pi\)
\(90\) 0 0
\(91\) 4.07690i 0.427375i
\(92\) 0 0
\(93\) −0.732052 0.732052i −0.0759102 0.0759102i
\(94\) 0 0
\(95\) 7.07296 + 7.07296i 0.725671 + 0.725671i
\(96\) 0 0
\(97\) −3.75610 + 3.75610i −0.381375 + 0.381375i −0.871597 0.490223i \(-0.836915\pi\)
0.490223 + 0.871597i \(0.336915\pi\)
\(98\) 0 0
\(99\) 3.14513 3.14513i 0.316097 0.316097i
\(100\) 0 0
\(101\) 12.9714 12.9714i 1.29071 1.29071i 0.356356 0.934350i \(-0.384019\pi\)
0.934350 0.356356i \(-0.115981\pi\)
\(102\) 0 0
\(103\) 15.3568i 1.51316i −0.653904 0.756578i \(-0.726870\pi\)
0.653904 0.756578i \(-0.273130\pi\)
\(104\) 0 0
\(105\) −1.52973 −0.149286
\(106\) 0 0
\(107\) −17.0156 −1.64496 −0.822482 0.568791i \(-0.807411\pi\)
−0.822482 + 0.568791i \(0.807411\pi\)
\(108\) 0 0
\(109\) 7.54205 7.54205i 0.722398 0.722398i −0.246695 0.969093i \(-0.579345\pi\)
0.969093 + 0.246695i \(0.0793447\pi\)
\(110\) 0 0
\(111\) −2.26740 2.26740i −0.215212 0.215212i
\(112\) 0 0
\(113\) −1.18116 −0.111114 −0.0555569 0.998456i \(-0.517693\pi\)
−0.0555569 + 0.998456i \(0.517693\pi\)
\(114\) 0 0
\(115\) 10.7011i 0.997880i
\(116\) 0 0
\(117\) −7.93924 + 7.93924i −0.733983 + 0.733983i
\(118\) 0 0
\(119\) −5.06820 −0.464601
\(120\) 0 0
\(121\) 8.39157i 0.762870i
\(122\) 0 0
\(123\) −2.81322 1.47372i −0.253659 0.132880i
\(124\) 0 0
\(125\) 1.50373i 0.134497i
\(126\) 0 0
\(127\) −4.49326 −0.398713 −0.199356 0.979927i \(-0.563885\pi\)
−0.199356 + 0.979927i \(0.563885\pi\)
\(128\) 0 0
\(129\) 2.43746 2.43746i 0.214607 0.214607i
\(130\) 0 0
\(131\) 21.3610i 1.86632i −0.359457 0.933162i \(-0.617038\pi\)
0.359457 0.933162i \(-0.382962\pi\)
\(132\) 0 0
\(133\) −3.24317 −0.281219
\(134\) 0 0
\(135\) −6.22399 6.22399i −0.535676 0.535676i
\(136\) 0 0
\(137\) 9.76621 9.76621i 0.834384 0.834384i −0.153729 0.988113i \(-0.549128\pi\)
0.988113 + 0.153729i \(0.0491283\pi\)
\(138\) 0 0
\(139\) −14.2159 −1.20577 −0.602887 0.797826i \(-0.705983\pi\)
−0.602887 + 0.797826i \(0.705983\pi\)
\(140\) 0 0
\(141\) 2.56819 0.216281
\(142\) 0 0
\(143\) 6.58445i 0.550619i
\(144\) 0 0
\(145\) −14.2069 + 14.2069i −1.17982 + 1.17982i
\(146\) 0 0
\(147\) 0.350714 0.350714i 0.0289264 0.0289264i
\(148\) 0 0
\(149\) −1.36730 + 1.36730i −0.112013 + 0.112013i −0.760892 0.648879i \(-0.775238\pi\)
0.648879 + 0.760892i \(0.275238\pi\)
\(150\) 0 0
\(151\) 13.6530 + 13.6530i 1.11106 + 1.11106i 0.993007 + 0.118057i \(0.0376667\pi\)
0.118057 + 0.993007i \(0.462333\pi\)
\(152\) 0 0
\(153\) −9.86966 9.86966i −0.797915 0.797915i
\(154\) 0 0
\(155\) 6.43776i 0.517093i
\(156\) 0 0
\(157\) 16.6525 + 16.6525i 1.32901 + 1.32901i 0.906234 + 0.422777i \(0.138945\pi\)
0.422777 + 0.906234i \(0.361055\pi\)
\(158\) 0 0
\(159\) 3.99363i 0.316716i
\(160\) 0 0
\(161\) −2.45339 2.45339i −0.193354 0.193354i
\(162\) 0 0
\(163\) −12.6265 −0.988984 −0.494492 0.869182i \(-0.664646\pi\)
−0.494492 + 0.869182i \(0.664646\pi\)
\(164\) 0 0
\(165\) 2.47061 0.192336
\(166\) 0 0
\(167\) −8.16594 8.16594i −0.631900 0.631900i 0.316645 0.948544i \(-0.397444\pi\)
−0.948544 + 0.316645i \(0.897444\pi\)
\(168\) 0 0
\(169\) 3.62112i 0.278547i
\(170\) 0 0
\(171\) −6.31567 6.31567i −0.482971 0.482971i
\(172\) 0 0
\(173\) 7.35324i 0.559056i 0.960138 + 0.279528i \(0.0901780\pi\)
−0.960138 + 0.279528i \(0.909822\pi\)
\(174\) 0 0
\(175\) 3.19078 + 3.19078i 0.241200 + 0.241200i
\(176\) 0 0
\(177\) −0.848961 0.848961i −0.0638118 0.0638118i
\(178\) 0 0
\(179\) 3.78388 3.78388i 0.282820 0.282820i −0.551413 0.834233i \(-0.685911\pi\)
0.834233 + 0.551413i \(0.185911\pi\)
\(180\) 0 0
\(181\) 1.72775 1.72775i 0.128423 0.128423i −0.639974 0.768397i \(-0.721055\pi\)
0.768397 + 0.639974i \(0.221055\pi\)
\(182\) 0 0
\(183\) −2.89304 + 2.89304i −0.213860 + 0.213860i
\(184\) 0 0
\(185\) 19.9398i 1.46600i
\(186\) 0 0
\(187\) 8.18545 0.598579
\(188\) 0 0
\(189\) 2.85390 0.207590
\(190\) 0 0
\(191\) −2.38197 + 2.38197i −0.172353 + 0.172353i −0.788012 0.615659i \(-0.788890\pi\)
0.615659 + 0.788012i \(0.288890\pi\)
\(192\) 0 0
\(193\) 4.79415 + 4.79415i 0.345091 + 0.345091i 0.858277 0.513187i \(-0.171535\pi\)
−0.513187 + 0.858277i \(0.671535\pi\)
\(194\) 0 0
\(195\) −6.23655 −0.446609
\(196\) 0 0
\(197\) 13.5041i 0.962126i 0.876686 + 0.481063i \(0.159749\pi\)
−0.876686 + 0.481063i \(0.840251\pi\)
\(198\) 0 0
\(199\) −6.97853 + 6.97853i −0.494695 + 0.494695i −0.909782 0.415087i \(-0.863751\pi\)
0.415087 + 0.909782i \(0.363751\pi\)
\(200\) 0 0
\(201\) 3.92231 0.276658
\(202\) 0 0
\(203\) 6.51431i 0.457215i
\(204\) 0 0
\(205\) 5.88988 + 18.8499i 0.411367 + 1.31654i
\(206\) 0 0
\(207\) 9.55531i 0.664140i
\(208\) 0 0
\(209\) 5.23793 0.362315
\(210\) 0 0
\(211\) 3.62001 3.62001i 0.249212 0.249212i −0.571435 0.820647i \(-0.693613\pi\)
0.820647 + 0.571435i \(0.193613\pi\)
\(212\) 0 0
\(213\) 2.20486i 0.151074i
\(214\) 0 0
\(215\) −21.4354 −1.46188
\(216\) 0 0
\(217\) −1.47596 1.47596i −0.100194 0.100194i
\(218\) 0 0
\(219\) −3.00862 + 3.00862i −0.203304 + 0.203304i
\(220\) 0 0
\(221\) −20.6625 −1.38991
\(222\) 0 0
\(223\) −7.04165 −0.471544 −0.235772 0.971808i \(-0.575762\pi\)
−0.235772 + 0.971808i \(0.575762\pi\)
\(224\) 0 0
\(225\) 12.4273i 0.828485i
\(226\) 0 0
\(227\) −14.6416 + 14.6416i −0.971798 + 0.971798i −0.999613 0.0278151i \(-0.991145\pi\)
0.0278151 + 0.999613i \(0.491145\pi\)
\(228\) 0 0
\(229\) −8.53015 + 8.53015i −0.563688 + 0.563688i −0.930353 0.366665i \(-0.880500\pi\)
0.366665 + 0.930353i \(0.380500\pi\)
\(230\) 0 0
\(231\) −0.566425 + 0.566425i −0.0372680 + 0.0372680i
\(232\) 0 0
\(233\) −6.94405 6.94405i −0.454920 0.454920i 0.442064 0.896984i \(-0.354246\pi\)
−0.896984 + 0.442064i \(0.854246\pi\)
\(234\) 0 0
\(235\) −11.2925 11.2925i −0.736641 0.736641i
\(236\) 0 0
\(237\) 4.19442i 0.272457i
\(238\) 0 0
\(239\) 17.5762 + 17.5762i 1.13691 + 1.13691i 0.989001 + 0.147910i \(0.0472545\pi\)
0.147910 + 0.989001i \(0.452745\pi\)
\(240\) 0 0
\(241\) 16.6390i 1.07181i 0.844277 + 0.535906i \(0.180030\pi\)
−0.844277 + 0.535906i \(0.819970\pi\)
\(242\) 0 0
\(243\) 8.45519 + 8.45519i 0.542401 + 0.542401i
\(244\) 0 0
\(245\) −3.08423 −0.197044
\(246\) 0 0
\(247\) −13.2221 −0.841302
\(248\) 0 0
\(249\) −4.64814 4.64814i −0.294564 0.294564i
\(250\) 0 0
\(251\) 15.1077i 0.953591i 0.879014 + 0.476796i \(0.158202\pi\)
−0.879014 + 0.476796i \(0.841798\pi\)
\(252\) 0 0
\(253\) 3.96237 + 3.96237i 0.249112 + 0.249112i
\(254\) 0 0
\(255\) 7.75296i 0.485509i
\(256\) 0 0
\(257\) −9.96474 9.96474i −0.621583 0.621583i 0.324353 0.945936i \(-0.394854\pi\)
−0.945936 + 0.324353i \(0.894854\pi\)
\(258\) 0 0
\(259\) −4.57150 4.57150i −0.284059 0.284059i
\(260\) 0 0
\(261\) 12.6858 12.6858i 0.785230 0.785230i
\(262\) 0 0
\(263\) 7.19183 7.19183i 0.443467 0.443467i −0.449708 0.893175i \(-0.648472\pi\)
0.893175 + 0.449708i \(0.148472\pi\)
\(264\) 0 0
\(265\) −17.5603 + 17.5603i −1.07872 + 1.07872i
\(266\) 0 0
\(267\) 2.28124i 0.139609i
\(268\) 0 0
\(269\) −24.3989 −1.48763 −0.743815 0.668386i \(-0.766986\pi\)
−0.743815 + 0.668386i \(0.766986\pi\)
\(270\) 0 0
\(271\) −14.4777 −0.879455 −0.439727 0.898131i \(-0.644925\pi\)
−0.439727 + 0.898131i \(0.644925\pi\)
\(272\) 0 0
\(273\) 1.42983 1.42983i 0.0865370 0.0865370i
\(274\) 0 0
\(275\) −5.15331 5.15331i −0.310756 0.310756i
\(276\) 0 0
\(277\) −0.579517 −0.0348198 −0.0174099 0.999848i \(-0.505542\pi\)
−0.0174099 + 0.999848i \(0.505542\pi\)
\(278\) 0 0
\(279\) 5.74847i 0.344152i
\(280\) 0 0
\(281\) 21.1972 21.1972i 1.26452 1.26452i 0.315639 0.948879i \(-0.397781\pi\)
0.948879 0.315639i \(-0.102219\pi\)
\(282\) 0 0
\(283\) 6.92684 0.411758 0.205879 0.978577i \(-0.433995\pi\)
0.205879 + 0.978577i \(0.433995\pi\)
\(284\) 0 0
\(285\) 4.96118i 0.293875i
\(286\) 0 0
\(287\) −5.67199 2.97129i −0.334807 0.175390i
\(288\) 0 0
\(289\) 8.68660i 0.510977i
\(290\) 0 0
\(291\) 2.63464 0.154445
\(292\) 0 0
\(293\) −8.37536 + 8.37536i −0.489294 + 0.489294i −0.908083 0.418790i \(-0.862455\pi\)
0.418790 + 0.908083i \(0.362455\pi\)
\(294\) 0 0
\(295\) 7.46587i 0.434680i
\(296\) 0 0
\(297\) −4.60922 −0.267454
\(298\) 0 0
\(299\) −10.0022 10.0022i −0.578443 0.578443i
\(300\) 0 0
\(301\) 4.91439 4.91439i 0.283261 0.283261i
\(302\) 0 0
\(303\) −9.09853 −0.522697
\(304\) 0 0
\(305\) 25.4418 1.45679
\(306\) 0 0
\(307\) 33.0329i 1.88529i −0.333803 0.942643i \(-0.608332\pi\)
0.333803 0.942643i \(-0.391668\pi\)
\(308\) 0 0
\(309\) −5.38586 + 5.38586i −0.306391 + 0.306391i
\(310\) 0 0
\(311\) −1.21706 + 1.21706i −0.0690130 + 0.0690130i −0.740771 0.671758i \(-0.765540\pi\)
0.671758 + 0.740771i \(0.265540\pi\)
\(312\) 0 0
\(313\) 4.53381 4.53381i 0.256266 0.256266i −0.567267 0.823534i \(-0.691999\pi\)
0.823534 + 0.567267i \(0.191999\pi\)
\(314\) 0 0
\(315\) −6.00613 6.00613i −0.338407 0.338407i
\(316\) 0 0
\(317\) −11.9738 11.9738i −0.672515 0.672515i 0.285780 0.958295i \(-0.407747\pi\)
−0.958295 + 0.285780i \(0.907747\pi\)
\(318\) 0 0
\(319\) 10.5210i 0.589064i
\(320\) 0 0
\(321\) 5.96763 + 5.96763i 0.333080 + 0.333080i
\(322\) 0 0
\(323\) 16.4370i 0.914582i
\(324\) 0 0
\(325\) 13.0085 + 13.0085i 0.721582 + 0.721582i
\(326\) 0 0
\(327\) −5.29021 −0.292549
\(328\) 0 0
\(329\) 5.17796 0.285470
\(330\) 0 0
\(331\) 18.8893 + 18.8893i 1.03825 + 1.03825i 0.999239 + 0.0390120i \(0.0124211\pi\)
0.0390120 + 0.999239i \(0.487579\pi\)
\(332\) 0 0
\(333\) 17.8048i 0.975699i
\(334\) 0 0
\(335\) −17.2466 17.2466i −0.942284 0.942284i
\(336\) 0 0
\(337\) 10.4913i 0.571495i −0.958305 0.285748i \(-0.907758\pi\)
0.958305 0.285748i \(-0.0922419\pi\)
\(338\) 0 0
\(339\) 0.414248 + 0.414248i 0.0224989 + 0.0224989i
\(340\) 0 0
\(341\) 2.38376 + 2.38376i 0.129088 + 0.129088i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) 3.75302 3.75302i 0.202056 0.202056i
\(346\) 0 0
\(347\) −24.3424 + 24.3424i −1.30677 + 1.30677i −0.383035 + 0.923734i \(0.625121\pi\)
−0.923734 + 0.383035i \(0.874879\pi\)
\(348\) 0 0
\(349\) 9.46542i 0.506672i 0.967378 + 0.253336i \(0.0815279\pi\)
−0.967378 + 0.253336i \(0.918472\pi\)
\(350\) 0 0
\(351\) 11.6350 0.621033
\(352\) 0 0
\(353\) −7.45234 −0.396648 −0.198324 0.980137i \(-0.563550\pi\)
−0.198324 + 0.980137i \(0.563550\pi\)
\(354\) 0 0
\(355\) 9.69490 9.69490i 0.514552 0.514552i
\(356\) 0 0
\(357\) 1.77749 + 1.77749i 0.0940746 + 0.0940746i
\(358\) 0 0
\(359\) −22.9714 −1.21238 −0.606192 0.795319i \(-0.707304\pi\)
−0.606192 + 0.795319i \(0.707304\pi\)
\(360\) 0 0
\(361\) 8.48182i 0.446411i
\(362\) 0 0
\(363\) −2.94304 + 2.94304i −0.154470 + 0.154470i
\(364\) 0 0
\(365\) 26.4582 1.38489
\(366\) 0 0
\(367\) 3.19066i 0.166551i 0.996527 + 0.0832756i \(0.0265382\pi\)
−0.996527 + 0.0832756i \(0.973462\pi\)
\(368\) 0 0
\(369\) −5.25925 16.8317i −0.273786 0.876222i
\(370\) 0 0
\(371\) 8.05192i 0.418035i
\(372\) 0 0
\(373\) 3.74084 0.193693 0.0968467 0.995299i \(-0.469124\pi\)
0.0968467 + 0.995299i \(0.469124\pi\)
\(374\) 0 0
\(375\) 0.527378 0.527378i 0.0272337 0.0272337i
\(376\) 0 0
\(377\) 26.5582i 1.36782i
\(378\) 0 0
\(379\) 32.2983 1.65905 0.829525 0.558470i \(-0.188611\pi\)
0.829525 + 0.558470i \(0.188611\pi\)
\(380\) 0 0
\(381\) 1.57585 + 1.57585i 0.0807333 + 0.0807333i
\(382\) 0 0
\(383\) −11.6140 + 11.6140i −0.593449 + 0.593449i −0.938561 0.345112i \(-0.887841\pi\)
0.345112 + 0.938561i \(0.387841\pi\)
\(384\) 0 0
\(385\) 4.98122 0.253866
\(386\) 0 0
\(387\) 19.1403 0.972956
\(388\) 0 0
\(389\) 16.1631i 0.819504i −0.912197 0.409752i \(-0.865615\pi\)
0.912197 0.409752i \(-0.134385\pi\)
\(390\) 0 0
\(391\) 12.4342 12.4342i 0.628827 0.628827i
\(392\) 0 0
\(393\) −7.49162 + 7.49162i −0.377902 + 0.377902i
\(394\) 0 0
\(395\) −18.4431 + 18.4431i −0.927975 + 0.927975i
\(396\) 0 0
\(397\) −5.34629 5.34629i −0.268323 0.268323i 0.560101 0.828424i \(-0.310762\pi\)
−0.828424 + 0.560101i \(0.810762\pi\)
\(398\) 0 0
\(399\) 1.13743 + 1.13743i 0.0569426 + 0.0569426i
\(400\) 0 0
\(401\) 15.7388i 0.785960i −0.919547 0.392980i \(-0.871444\pi\)
0.919547 0.392980i \(-0.128556\pi\)
\(402\) 0 0
\(403\) −6.01733 6.01733i −0.299744 0.299744i
\(404\) 0 0
\(405\) 21.1162i 1.04927i
\(406\) 0 0
\(407\) 7.38326 + 7.38326i 0.365975 + 0.365975i
\(408\) 0 0
\(409\) −16.5501 −0.818351 −0.409175 0.912456i \(-0.634184\pi\)
−0.409175 + 0.912456i \(0.634184\pi\)
\(410\) 0 0
\(411\) −6.85030 −0.337900
\(412\) 0 0
\(413\) −1.71167 1.71167i −0.0842256 0.0842256i
\(414\) 0 0
\(415\) 40.8763i 2.00654i
\(416\) 0 0
\(417\) 4.98571 + 4.98571i 0.244151 + 0.244151i
\(418\) 0 0
\(419\) 10.1682i 0.496747i −0.968664 0.248374i \(-0.920104\pi\)
0.968664 0.248374i \(-0.0798960\pi\)
\(420\) 0 0
\(421\) 23.6838 + 23.6838i 1.15428 + 1.15428i 0.985686 + 0.168594i \(0.0539228\pi\)
0.168594 + 0.985686i \(0.446077\pi\)
\(422\) 0 0
\(423\) 10.0834 + 10.0834i 0.490272 + 0.490272i
\(424\) 0 0
\(425\) −16.1715 + 16.1715i −0.784433 + 0.784433i
\(426\) 0 0
\(427\) −5.83292 + 5.83292i −0.282275 + 0.282275i
\(428\) 0 0
\(429\) −2.30926 + 2.30926i −0.111492 + 0.111492i
\(430\) 0 0
\(431\) 13.0393i 0.628080i 0.949410 + 0.314040i \(0.101683\pi\)
−0.949410 + 0.314040i \(0.898317\pi\)
\(432\) 0 0
\(433\) −24.1559 −1.16086 −0.580430 0.814310i \(-0.697115\pi\)
−0.580430 + 0.814310i \(0.697115\pi\)
\(434\) 0 0
\(435\) 9.96513 0.477791
\(436\) 0 0
\(437\) 7.95676 7.95676i 0.380623 0.380623i
\(438\) 0 0
\(439\) −3.76046 3.76046i −0.179477 0.179477i 0.611651 0.791128i \(-0.290506\pi\)
−0.791128 + 0.611651i \(0.790506\pi\)
\(440\) 0 0
\(441\) 2.75400 0.131143
\(442\) 0 0
\(443\) 2.59993i 0.123526i 0.998091 + 0.0617632i \(0.0196723\pi\)
−0.998091 + 0.0617632i \(0.980328\pi\)
\(444\) 0 0
\(445\) 10.0307 10.0307i 0.475503 0.475503i
\(446\) 0 0
\(447\) 0.959060 0.0453620
\(448\) 0 0
\(449\) 19.5739i 0.923751i −0.886945 0.461876i \(-0.847177\pi\)
0.886945 0.461876i \(-0.152823\pi\)
\(450\) 0 0
\(451\) 9.16061 + 4.79882i 0.431356 + 0.225968i
\(452\) 0 0
\(453\) 9.57659i 0.449947i
\(454\) 0 0
\(455\) −12.5741 −0.589482
\(456\) 0 0
\(457\) −28.8002 + 28.8002i −1.34721 + 1.34721i −0.458542 + 0.888672i \(0.651628\pi\)
−0.888672 + 0.458542i \(0.848372\pi\)
\(458\) 0 0
\(459\) 14.4641i 0.675126i
\(460\) 0 0
\(461\) 36.7491 1.71157 0.855787 0.517328i \(-0.173073\pi\)
0.855787 + 0.517328i \(0.173073\pi\)
\(462\) 0 0
\(463\) 1.01334 + 1.01334i 0.0470941 + 0.0470941i 0.730262 0.683168i \(-0.239398\pi\)
−0.683168 + 0.730262i \(0.739398\pi\)
\(464\) 0 0
\(465\) 2.25781 2.25781i 0.104704 0.104704i
\(466\) 0 0
\(467\) 2.72582 0.126136 0.0630679 0.998009i \(-0.479912\pi\)
0.0630679 + 0.998009i \(0.479912\pi\)
\(468\) 0 0
\(469\) 7.90812 0.365163
\(470\) 0 0
\(471\) 11.6805i 0.538209i
\(472\) 0 0
\(473\) −7.93705 + 7.93705i −0.364946 + 0.364946i
\(474\) 0 0
\(475\) −10.3483 + 10.3483i −0.474811 + 0.474811i
\(476\) 0 0
\(477\) 15.6801 15.6801i 0.717942 0.717942i
\(478\) 0 0
\(479\) 12.2164 + 12.2164i 0.558183 + 0.558183i 0.928790 0.370607i \(-0.120850\pi\)
−0.370607 + 0.928790i \(0.620850\pi\)
\(480\) 0 0
\(481\) −18.6376 18.6376i −0.849800 0.849800i
\(482\) 0 0
\(483\) 1.72087i 0.0783025i
\(484\) 0 0
\(485\) −11.5847 11.5847i −0.526033 0.526033i
\(486\) 0 0
\(487\) 18.8554i 0.854420i 0.904152 + 0.427210i \(0.140504\pi\)
−0.904152 + 0.427210i \(0.859496\pi\)
\(488\) 0 0
\(489\) 4.42829 + 4.42829i 0.200254 + 0.200254i
\(490\) 0 0
\(491\) −23.8689 −1.07719 −0.538594 0.842565i \(-0.681044\pi\)
−0.538594 + 0.842565i \(0.681044\pi\)
\(492\) 0 0
\(493\) 33.0158 1.48696
\(494\) 0 0
\(495\) 9.70028 + 9.70028i 0.435995 + 0.435995i
\(496\) 0 0
\(497\) 4.44542i 0.199404i
\(498\) 0 0
\(499\) −11.8815 11.8815i −0.531887 0.531887i 0.389246 0.921134i \(-0.372735\pi\)
−0.921134 + 0.389246i \(0.872735\pi\)
\(500\) 0 0
\(501\) 5.72782i 0.255900i
\(502\) 0 0
\(503\) 4.58613 + 4.58613i 0.204485 + 0.204485i 0.801919 0.597433i \(-0.203813\pi\)
−0.597433 + 0.801919i \(0.703813\pi\)
\(504\) 0 0
\(505\) 40.0068 + 40.0068i 1.78028 + 1.78028i
\(506\) 0 0
\(507\) 1.26998 1.26998i 0.0564016 0.0564016i
\(508\) 0 0
\(509\) 2.65834 2.65834i 0.117829 0.117829i −0.645734 0.763563i \(-0.723448\pi\)
0.763563 + 0.645734i \(0.223448\pi\)
\(510\) 0 0
\(511\) −6.06596 + 6.06596i −0.268342 + 0.268342i
\(512\) 0 0
\(513\) 9.25568i 0.408648i
\(514\) 0 0
\(515\) 47.3640 2.08711
\(516\) 0 0
\(517\) −8.36273 −0.367792
\(518\) 0 0
\(519\) 2.57888 2.57888i 0.113200 0.113200i
\(520\) 0 0
\(521\) 16.0084 + 16.0084i 0.701341 + 0.701341i 0.964698 0.263358i \(-0.0848299\pi\)
−0.263358 + 0.964698i \(0.584830\pi\)
\(522\) 0 0
\(523\) 35.7387 1.56274 0.781371 0.624067i \(-0.214521\pi\)
0.781371 + 0.624067i \(0.214521\pi\)
\(524\) 0 0
\(525\) 2.23810i 0.0976789i
\(526\) 0 0
\(527\) 7.48044 7.48044i 0.325853 0.325853i
\(528\) 0 0
\(529\) −10.9618 −0.476600
\(530\) 0 0
\(531\) 6.66650i 0.289302i
\(532\) 0 0
\(533\) −23.1241 12.1137i −1.00162 0.524701i
\(534\) 0 0
\(535\) 52.4801i 2.26891i
\(536\) 0 0
\(537\) −2.65412 −0.114534
\(538\) 0 0
\(539\) −1.14202 + 1.14202i −0.0491903 + 0.0491903i
\(540\) 0 0
\(541\) 16.3733i 0.703945i −0.936010 0.351973i \(-0.885511\pi\)
0.936010 0.351973i \(-0.114489\pi\)
\(542\) 0 0
\(543\) −1.21189 −0.0520074
\(544\) 0 0
\(545\) 23.2614 + 23.2614i 0.996409 + 0.996409i
\(546\) 0 0
\(547\) 6.15079 6.15079i 0.262989 0.262989i −0.563278 0.826267i \(-0.690460\pi\)
0.826267 + 0.563278i \(0.190460\pi\)
\(548\) 0 0
\(549\) −22.7177 −0.969569
\(550\) 0 0
\(551\) 21.1270 0.900042
\(552\) 0 0
\(553\) 8.45675i 0.359618i
\(554\) 0 0
\(555\) 6.99316 6.99316i 0.296843 0.296843i
\(556\) 0 0
\(557\) 0.278382 0.278382i 0.0117954 0.0117954i −0.701184 0.712980i \(-0.747345\pi\)
0.712980 + 0.701184i \(0.247345\pi\)
\(558\) 0 0
\(559\) 20.0355 20.0355i 0.847411 0.847411i
\(560\) 0 0
\(561\) −2.87075 2.87075i −0.121203 0.121203i
\(562\) 0 0
\(563\) 9.87314 + 9.87314i 0.416103 + 0.416103i 0.883858 0.467755i \(-0.154937\pi\)
−0.467755 + 0.883858i \(0.654937\pi\)
\(564\) 0 0
\(565\) 3.64295i 0.153260i
\(566\) 0 0
\(567\) 4.84121 + 4.84121i 0.203312 + 0.203312i
\(568\) 0 0
\(569\) 0.289569i 0.0121394i 0.999982 + 0.00606968i \(0.00193205\pi\)
−0.999982 + 0.00606968i \(0.998068\pi\)
\(570\) 0 0
\(571\) 13.2936 + 13.2936i 0.556320 + 0.556320i 0.928258 0.371938i \(-0.121307\pi\)
−0.371938 + 0.928258i \(0.621307\pi\)
\(572\) 0 0
\(573\) 1.67078 0.0697978
\(574\) 0 0
\(575\) −15.6564 −0.652919
\(576\) 0 0
\(577\) 10.2346 + 10.2346i 0.426073 + 0.426073i 0.887288 0.461215i \(-0.152586\pi\)
−0.461215 + 0.887288i \(0.652586\pi\)
\(578\) 0 0
\(579\) 3.36275i 0.139751i
\(580\) 0 0
\(581\) −9.37154 9.37154i −0.388797 0.388797i
\(582\) 0 0
\(583\) 13.0044i 0.538585i
\(584\) 0 0
\(585\) −24.4864 24.4864i −1.01239 1.01239i
\(586\) 0 0
\(587\) −1.81926 1.81926i −0.0750888 0.0750888i 0.668565 0.743654i \(-0.266909\pi\)
−0.743654 + 0.668565i \(0.766909\pi\)
\(588\) 0 0
\(589\) 4.78678 4.78678i 0.197236 0.197236i
\(590\) 0 0
\(591\) 4.73607 4.73607i 0.194816 0.194816i
\(592\) 0 0
\(593\) −6.36714 + 6.36714i −0.261467 + 0.261467i −0.825650 0.564183i \(-0.809191\pi\)
0.564183 + 0.825650i \(0.309191\pi\)
\(594\) 0 0
\(595\) 15.6315i 0.640827i
\(596\) 0 0
\(597\) 4.89494 0.200337
\(598\) 0 0
\(599\) 15.0843 0.616329 0.308165 0.951333i \(-0.400285\pi\)
0.308165 + 0.951333i \(0.400285\pi\)
\(600\) 0 0
\(601\) −14.4682 + 14.4682i −0.590172 + 0.590172i −0.937678 0.347506i \(-0.887029\pi\)
0.347506 + 0.937678i \(0.387029\pi\)
\(602\) 0 0
\(603\) 15.4000 + 15.4000i 0.627138 + 0.627138i
\(604\) 0 0
\(605\) 25.8815 1.05223
\(606\) 0 0
\(607\) 41.4685i 1.68315i 0.540137 + 0.841577i \(0.318372\pi\)
−0.540137 + 0.841577i \(0.681628\pi\)
\(608\) 0 0
\(609\) −2.28466 + 2.28466i −0.0925791 + 0.0925791i
\(610\) 0 0
\(611\) 21.1100 0.854020
\(612\) 0 0
\(613\) 3.69825i 0.149371i 0.997207 + 0.0746854i \(0.0237953\pi\)
−0.997207 + 0.0746854i \(0.976205\pi\)
\(614\) 0 0
\(615\) 4.54527 8.67660i 0.183283 0.349874i
\(616\) 0 0
\(617\) 3.24686i 0.130714i −0.997862 0.0653569i \(-0.979181\pi\)
0.997862 0.0653569i \(-0.0208186\pi\)
\(618\) 0 0
\(619\) −25.9486 −1.04296 −0.521481 0.853263i \(-0.674620\pi\)
−0.521481 + 0.853263i \(0.674620\pi\)
\(620\) 0 0
\(621\) −7.00171 + 7.00171i −0.280969 + 0.280969i
\(622\) 0 0
\(623\) 4.59941i 0.184271i
\(624\) 0 0
\(625\) −27.2001 −1.08800
\(626\) 0 0
\(627\) −1.83702 1.83702i −0.0733633 0.0733633i
\(628\) 0 0
\(629\) 23.1693 23.1693i 0.923820 0.923820i
\(630\) 0 0
\(631\) −18.0145 −0.717145 −0.358572 0.933502i \(-0.616736\pi\)
−0.358572 + 0.933502i \(0.616736\pi\)
\(632\) 0 0
\(633\) −2.53918 −0.100923
\(634\) 0 0
\(635\) 13.8582i 0.549947i
\(636\) 0 0
\(637\) 2.88280 2.88280i 0.114221 0.114221i
\(638\) 0 0
\(639\) −8.65688 + 8.65688i −0.342461 + 0.342461i
\(640\) 0 0
\(641\) −28.6846 + 28.6846i −1.13297 + 1.13297i −0.143294 + 0.989680i \(0.545770\pi\)
−0.989680 + 0.143294i \(0.954230\pi\)
\(642\) 0 0
\(643\) −8.96702 8.96702i −0.353625 0.353625i 0.507832 0.861456i \(-0.330447\pi\)
−0.861456 + 0.507832i \(0.830447\pi\)
\(644\) 0 0
\(645\) 7.51769 + 7.51769i 0.296009 + 0.296009i
\(646\) 0 0
\(647\) 21.6818i 0.852399i 0.904629 + 0.426199i \(0.140148\pi\)
−0.904629 + 0.426199i \(0.859852\pi\)
\(648\) 0 0
\(649\) 2.76445 + 2.76445i 0.108514 + 0.108514i
\(650\) 0 0
\(651\) 1.03528i 0.0405757i
\(652\) 0 0
\(653\) −20.3145 20.3145i −0.794969 0.794969i 0.187328 0.982297i \(-0.440017\pi\)
−0.982297 + 0.187328i \(0.940017\pi\)
\(654\) 0 0
\(655\) 65.8823 2.57423
\(656\) 0 0
\(657\) −23.6254 −0.921713
\(658\) 0 0
\(659\) −23.9096 23.9096i −0.931385 0.931385i 0.0664074 0.997793i \(-0.478846\pi\)
−0.997793 + 0.0664074i \(0.978846\pi\)
\(660\) 0 0
\(661\) 12.1735i 0.473494i 0.971571 + 0.236747i \(0.0760813\pi\)
−0.971571 + 0.236747i \(0.923919\pi\)
\(662\) 0 0
\(663\) 7.24664 + 7.24664i 0.281436 + 0.281436i
\(664\) 0 0
\(665\) 10.0027i 0.387887i
\(666\) 0 0
\(667\) 15.9821 + 15.9821i 0.618830 + 0.618830i
\(668\) 0 0
\(669\) 2.46961 + 2.46961i 0.0954805 + 0.0954805i
\(670\) 0 0
\(671\) 9.42053 9.42053i 0.363675 0.363675i
\(672\) 0 0
\(673\) −22.0905 + 22.0905i −0.851525 + 0.851525i −0.990321 0.138796i \(-0.955677\pi\)
0.138796 + 0.990321i \(0.455677\pi\)
\(674\) 0 0
\(675\) 9.10616 9.10616i 0.350496 0.350496i
\(676\) 0 0
\(677\) 28.0742i 1.07898i −0.841992 0.539490i \(-0.818617\pi\)
0.841992 0.539490i \(-0.181383\pi\)
\(678\) 0 0
\(679\) 5.31193 0.203853
\(680\) 0 0
\(681\) 10.2700 0.393549
\(682\) 0 0
\(683\) −7.78438 + 7.78438i −0.297861 + 0.297861i −0.840176 0.542315i \(-0.817548\pi\)
0.542315 + 0.840176i \(0.317548\pi\)
\(684\) 0 0
\(685\) 30.1212 + 30.1212i 1.15087 + 1.15087i
\(686\) 0 0
\(687\) 5.98329 0.228277
\(688\) 0 0
\(689\) 32.8269i 1.25061i
\(690\) 0 0
\(691\) 16.1447 16.1447i 0.614173 0.614173i −0.329857 0.944031i \(-0.607001\pi\)
0.944031 + 0.329857i \(0.107001\pi\)
\(692\) 0 0
\(693\) −4.44788 −0.168961
\(694\) 0 0
\(695\) 43.8449i 1.66313i
\(696\) 0 0
\(697\) 15.0591 28.7467i 0.570404 1.08886i
\(698\) 0 0
\(699\) 4.87075i 0.184229i
\(700\) 0 0
\(701\) 43.5009 1.64300 0.821502 0.570205i \(-0.193136\pi\)
0.821502 + 0.570205i \(0.193136\pi\)
\(702\) 0 0
\(703\) 14.8262 14.8262i 0.559180 0.559180i
\(704\) 0 0
\(705\) 7.92088i 0.298317i
\(706\) 0 0
\(707\) −18.3444 −0.689912
\(708\) 0 0
\(709\) 28.7431 + 28.7431i 1.07947 + 1.07947i 0.996557 + 0.0829115i \(0.0264219\pi\)
0.0829115 + 0.996557i \(0.473578\pi\)
\(710\) 0 0
\(711\) 16.4684 16.4684i 0.617615 0.617615i
\(712\) 0 0
\(713\) 7.24218 0.271222
\(714\) 0 0
\(715\) 20.3079 0.759473
\(716\) 0 0
\(717\) 12.3285i 0.460415i
\(718\) 0 0
\(719\) 5.06655 5.06655i 0.188951 0.188951i −0.606292 0.795242i \(-0.707344\pi\)
0.795242 + 0.606292i \(0.207344\pi\)
\(720\) 0 0
\(721\) −10.8589 + 10.8589i −0.404408 + 0.404408i
\(722\) 0 0
\(723\) 5.83554 5.83554i 0.217026 0.217026i
\(724\) 0 0
\(725\) −20.7857 20.7857i −0.771963 0.771963i
\(726\) 0 0
\(727\) −20.0991 20.0991i −0.745435 0.745435i 0.228183 0.973618i \(-0.426722\pi\)
−0.973618 + 0.228183i \(0.926722\pi\)
\(728\) 0 0
\(729\) 14.6088i 0.541067i
\(730\) 0 0
\(731\) 24.9071 + 24.9071i 0.921223 + 0.921223i
\(732\) 0 0
\(733\) 21.8279i 0.806231i −0.915149 0.403116i \(-0.867927\pi\)
0.915149 0.403116i \(-0.132073\pi\)
\(734\) 0 0
\(735\) 1.08168 + 1.08168i 0.0398984 + 0.0398984i
\(736\) 0 0
\(737\) −12.7721 −0.470466
\(738\) 0 0
\(739\) −52.4937 −1.93101 −0.965507 0.260378i \(-0.916153\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(740\) 0 0
\(741\) 4.63718 + 4.63718i 0.170351 + 0.170351i
\(742\) 0 0
\(743\) 8.77031i 0.321751i 0.986975 + 0.160876i \(0.0514318\pi\)
−0.986975 + 0.160876i \(0.948568\pi\)
\(744\) 0 0
\(745\) −4.21705 4.21705i −0.154501 0.154501i
\(746\) 0 0
\(747\) 36.4997i 1.33546i
\(748\) 0 0
\(749\) 12.0319 + 12.0319i 0.439635 + 0.439635i
\(750\) 0 0
\(751\) −18.3382 18.3382i −0.669170 0.669170i 0.288354 0.957524i \(-0.406892\pi\)
−0.957524 + 0.288354i \(0.906892\pi\)
\(752\) 0 0
\(753\) 5.29849 5.29849i 0.193088 0.193088i
\(754\) 0 0
\(755\) −42.1089 + 42.1089i −1.53250 + 1.53250i
\(756\) 0 0
\(757\) 7.70846 7.70846i 0.280169 0.280169i −0.553007 0.833176i \(-0.686520\pi\)
0.833176 + 0.553007i \(0.186520\pi\)
\(758\) 0 0
\(759\) 2.77932i 0.100883i
\(760\) 0 0
\(761\) 2.73457 0.0991282 0.0495641 0.998771i \(-0.484217\pi\)
0.0495641 + 0.998771i \(0.484217\pi\)
\(762\) 0 0
\(763\) −10.6661 −0.386138
\(764\) 0 0
\(765\) 30.4403 30.4403i 1.10057 1.10057i
\(766\) 0 0
\(767\) −6.97829 6.97829i −0.251972 0.251972i
\(768\) 0 0
\(769\) 27.1439 0.978834 0.489417 0.872050i \(-0.337210\pi\)
0.489417 + 0.872050i \(0.337210\pi\)
\(770\) 0 0
\(771\) 6.98955i 0.251723i
\(772\) 0 0
\(773\) 29.7365 29.7365i 1.06955 1.06955i 0.0721522 0.997394i \(-0.477013\pi\)
0.997394 0.0721522i \(-0.0229867\pi\)
\(774\) 0 0
\(775\) −9.41891 −0.338337
\(776\) 0 0
\(777\) 3.20658i 0.115036i
\(778\) 0 0
\(779\) 9.63642 18.3952i 0.345261 0.659078i
\(780\) 0 0
\(781\) 7.17962i 0.256907i
\(782\) 0 0
\(783\) −18.5912 −0.664394
\(784\) 0 0
\(785\) −51.3599 + 51.3599i −1.83311 + 1.83311i
\(786\) 0 0
\(787\) 24.9010i 0.887626i −0.896119 0.443813i \(-0.853625\pi\)
0.896119 0.443813i \(-0.146375\pi\)
\(788\) 0 0
\(789\) −5.04455 −0.179591
\(790\) 0 0
\(791\) 0.835203 + 0.835203i 0.0296964 + 0.0296964i
\(792\) 0 0
\(793\) −23.7802 + 23.7802i −0.844461 + 0.844461i
\(794\) 0 0
\(795\) 12.3173 0.436848
\(796\) 0 0
\(797\) −23.9782 −0.849352 −0.424676 0.905345i \(-0.639612\pi\)
−0.424676 + 0.905345i \(0.639612\pi\)
\(798\) 0 0
\(799\) 26.2429i 0.928408i
\(800\) 0 0
\(801\) −8.95675 + 8.95675i