Properties

Label 74.2.b.a.73.1
Level $74$
Weight $2$
Character 74.73
Analytic conductor $0.591$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{21})\)
Defining polynomial: \( x^{4} + 11x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 73.1
Root \(2.79129i\) of defining polynomial
Character \(\chi\) \(=\) 74.73
Dual form 74.2.b.a.73.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -2.79129 q^{3} -1.00000 q^{4} -3.79129i q^{5} +2.79129i q^{6} -2.00000 q^{7} +1.00000i q^{8} +4.79129 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -2.79129 q^{3} -1.00000 q^{4} -3.79129i q^{5} +2.79129i q^{6} -2.00000 q^{7} +1.00000i q^{8} +4.79129 q^{9} -3.79129 q^{10} +3.79129 q^{11} +2.79129 q^{12} +0.791288i q^{13} +2.00000i q^{14} +10.5826i q^{15} +1.00000 q^{16} -1.58258i q^{17} -4.79129i q^{18} -7.58258i q^{19} +3.79129i q^{20} +5.58258 q^{21} -3.79129i q^{22} +0.791288i q^{23} -2.79129i q^{24} -9.37386 q^{25} +0.791288 q^{26} -5.00000 q^{27} +2.00000 q^{28} -0.791288i q^{29} +10.5826 q^{30} +5.37386i q^{31} -1.00000i q^{32} -10.5826 q^{33} -1.58258 q^{34} +7.58258i q^{35} -4.79129 q^{36} +(4.00000 + 4.58258i) q^{37} -7.58258 q^{38} -2.20871i q^{39} +3.79129 q^{40} +5.20871 q^{41} -5.58258i q^{42} -6.00000i q^{43} -3.79129 q^{44} -18.1652i q^{45} +0.791288 q^{46} +1.58258 q^{47} -2.79129 q^{48} -3.00000 q^{49} +9.37386i q^{50} +4.41742i q^{51} -0.791288i q^{52} +7.58258 q^{53} +5.00000i q^{54} -14.3739i q^{55} -2.00000i q^{56} +21.1652i q^{57} -0.791288 q^{58} -7.58258i q^{59} -10.5826i q^{60} +8.20871i q^{61} +5.37386 q^{62} -9.58258 q^{63} -1.00000 q^{64} +3.00000 q^{65} +10.5826i q^{66} -7.37386 q^{67} +1.58258i q^{68} -2.20871i q^{69} +7.58258 q^{70} +9.16515 q^{71} +4.79129i q^{72} +9.37386 q^{73} +(4.58258 - 4.00000i) q^{74} +26.1652 q^{75} +7.58258i q^{76} -7.58258 q^{77} -2.20871 q^{78} +12.7913i q^{79} -3.79129i q^{80} -0.417424 q^{81} -5.20871i q^{82} -3.16515 q^{83} -5.58258 q^{84} -6.00000 q^{85} -6.00000 q^{86} +2.20871i q^{87} +3.79129i q^{88} +6.00000i q^{89} -18.1652 q^{90} -1.58258i q^{91} -0.791288i q^{92} -15.0000i q^{93} -1.58258i q^{94} -28.7477 q^{95} +2.79129i q^{96} -4.41742i q^{97} +3.00000i q^{98} +18.1652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9} - 6 q^{10} + 6 q^{11} + 2 q^{12} + 4 q^{16} + 4 q^{21} - 10 q^{25} - 6 q^{26} - 20 q^{27} + 8 q^{28} + 24 q^{30} - 24 q^{33} + 12 q^{34} - 10 q^{36} + 16 q^{37} - 12 q^{38} + 6 q^{40} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 12 q^{47} - 2 q^{48} - 12 q^{49} + 12 q^{53} + 6 q^{58} - 6 q^{62} - 20 q^{63} - 4 q^{64} + 12 q^{65} - 2 q^{67} + 12 q^{70} + 10 q^{73} + 68 q^{75} - 12 q^{77} - 18 q^{78} - 20 q^{81} + 24 q^{83} - 4 q^{84} - 24 q^{85} - 24 q^{86} - 36 q^{90} - 60 q^{95} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −2.79129 −1.61155 −0.805775 0.592221i \(-0.798251\pi\)
−0.805775 + 0.592221i \(0.798251\pi\)
\(4\) −1.00000 −0.500000
\(5\) 3.79129i 1.69552i −0.530384 0.847758i \(-0.677952\pi\)
0.530384 0.847758i \(-0.322048\pi\)
\(6\) 2.79129i 1.13954i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 4.79129 1.59710
\(10\) −3.79129 −1.19891
\(11\) 3.79129 1.14312 0.571558 0.820562i \(-0.306339\pi\)
0.571558 + 0.820562i \(0.306339\pi\)
\(12\) 2.79129 0.805775
\(13\) 0.791288i 0.219464i 0.993961 + 0.109732i \(0.0349992\pi\)
−0.993961 + 0.109732i \(0.965001\pi\)
\(14\) 2.00000i 0.534522i
\(15\) 10.5826i 2.73241i
\(16\) 1.00000 0.250000
\(17\) 1.58258i 0.383831i −0.981411 0.191915i \(-0.938530\pi\)
0.981411 0.191915i \(-0.0614700\pi\)
\(18\) 4.79129i 1.12932i
\(19\) 7.58258i 1.73956i −0.493438 0.869781i \(-0.664260\pi\)
0.493438 0.869781i \(-0.335740\pi\)
\(20\) 3.79129i 0.847758i
\(21\) 5.58258 1.21822
\(22\) 3.79129i 0.808305i
\(23\) 0.791288i 0.164995i 0.996591 + 0.0824975i \(0.0262896\pi\)
−0.996591 + 0.0824975i \(0.973710\pi\)
\(24\) 2.79129i 0.569769i
\(25\) −9.37386 −1.87477
\(26\) 0.791288 0.155184
\(27\) −5.00000 −0.962250
\(28\) 2.00000 0.377964
\(29\) 0.791288i 0.146938i −0.997297 0.0734692i \(-0.976593\pi\)
0.997297 0.0734692i \(-0.0234071\pi\)
\(30\) 10.5826 1.93211
\(31\) 5.37386i 0.965174i 0.875848 + 0.482587i \(0.160303\pi\)
−0.875848 + 0.482587i \(0.839697\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −10.5826 −1.84219
\(34\) −1.58258 −0.271409
\(35\) 7.58258i 1.28169i
\(36\) −4.79129 −0.798548
\(37\) 4.00000 + 4.58258i 0.657596 + 0.753371i
\(38\) −7.58258 −1.23006
\(39\) 2.20871i 0.353677i
\(40\) 3.79129 0.599455
\(41\) 5.20871 0.813464 0.406732 0.913547i \(-0.366668\pi\)
0.406732 + 0.913547i \(0.366668\pi\)
\(42\) 5.58258i 0.861410i
\(43\) 6.00000i 0.914991i −0.889212 0.457496i \(-0.848747\pi\)
0.889212 0.457496i \(-0.151253\pi\)
\(44\) −3.79129 −0.571558
\(45\) 18.1652i 2.70790i
\(46\) 0.791288 0.116669
\(47\) 1.58258 0.230842 0.115421 0.993317i \(-0.463178\pi\)
0.115421 + 0.993317i \(0.463178\pi\)
\(48\) −2.79129 −0.402888
\(49\) −3.00000 −0.428571
\(50\) 9.37386i 1.32566i
\(51\) 4.41742i 0.618563i
\(52\) 0.791288i 0.109732i
\(53\) 7.58258 1.04155 0.520773 0.853695i \(-0.325644\pi\)
0.520773 + 0.853695i \(0.325644\pi\)
\(54\) 5.00000i 0.680414i
\(55\) 14.3739i 1.93817i
\(56\) 2.00000i 0.267261i
\(57\) 21.1652i 2.80339i
\(58\) −0.791288 −0.103901
\(59\) 7.58258i 0.987167i −0.869698 0.493584i \(-0.835687\pi\)
0.869698 0.493584i \(-0.164313\pi\)
\(60\) 10.5826i 1.36620i
\(61\) 8.20871i 1.05102i 0.850788 + 0.525509i \(0.176125\pi\)
−0.850788 + 0.525509i \(0.823875\pi\)
\(62\) 5.37386 0.682481
\(63\) −9.58258 −1.20729
\(64\) −1.00000 −0.125000
\(65\) 3.00000 0.372104
\(66\) 10.5826i 1.30263i
\(67\) −7.37386 −0.900861 −0.450430 0.892812i \(-0.648729\pi\)
−0.450430 + 0.892812i \(0.648729\pi\)
\(68\) 1.58258i 0.191915i
\(69\) 2.20871i 0.265898i
\(70\) 7.58258 0.906291
\(71\) 9.16515 1.08770 0.543852 0.839181i \(-0.316965\pi\)
0.543852 + 0.839181i \(0.316965\pi\)
\(72\) 4.79129i 0.564659i
\(73\) 9.37386 1.09713 0.548564 0.836109i \(-0.315175\pi\)
0.548564 + 0.836109i \(0.315175\pi\)
\(74\) 4.58258 4.00000i 0.532714 0.464991i
\(75\) 26.1652 3.02129
\(76\) 7.58258i 0.869781i
\(77\) −7.58258 −0.864115
\(78\) −2.20871 −0.250087
\(79\) 12.7913i 1.43913i 0.694424 + 0.719566i \(0.255659\pi\)
−0.694424 + 0.719566i \(0.744341\pi\)
\(80\) 3.79129i 0.423879i
\(81\) −0.417424 −0.0463805
\(82\) 5.20871i 0.575206i
\(83\) −3.16515 −0.347421 −0.173710 0.984797i \(-0.555576\pi\)
−0.173710 + 0.984797i \(0.555576\pi\)
\(84\) −5.58258 −0.609109
\(85\) −6.00000 −0.650791
\(86\) −6.00000 −0.646997
\(87\) 2.20871i 0.236799i
\(88\) 3.79129i 0.404153i
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) −18.1652 −1.91478
\(91\) 1.58258i 0.165899i
\(92\) 0.791288i 0.0824975i
\(93\) 15.0000i 1.55543i
\(94\) 1.58258i 0.163230i
\(95\) −28.7477 −2.94945
\(96\) 2.79129i 0.284885i
\(97\) 4.41742i 0.448521i −0.974529 0.224261i \(-0.928003\pi\)
0.974529 0.224261i \(-0.0719967\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 18.1652 1.82567
\(100\) 9.37386 0.937386
\(101\) −1.58258 −0.157472 −0.0787361 0.996895i \(-0.525088\pi\)
−0.0787361 + 0.996895i \(0.525088\pi\)
\(102\) 4.41742 0.437390
\(103\) 2.20871i 0.217631i 0.994062 + 0.108815i \(0.0347058\pi\)
−0.994062 + 0.108815i \(0.965294\pi\)
\(104\) −0.791288 −0.0775922
\(105\) 21.1652i 2.06551i
\(106\) 7.58258i 0.736485i
\(107\) 8.37386 0.809532 0.404766 0.914420i \(-0.367353\pi\)
0.404766 + 0.914420i \(0.367353\pi\)
\(108\) 5.00000 0.481125
\(109\) 6.00000i 0.574696i 0.957826 + 0.287348i \(0.0927736\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) −14.3739 −1.37049
\(111\) −11.1652 12.7913i −1.05975 1.21410i
\(112\) −2.00000 −0.188982
\(113\) 19.5826i 1.84217i −0.389357 0.921087i \(-0.627303\pi\)
0.389357 0.921087i \(-0.372697\pi\)
\(114\) 21.1652 1.98230
\(115\) 3.00000 0.279751
\(116\) 0.791288i 0.0734692i
\(117\) 3.79129i 0.350505i
\(118\) −7.58258 −0.698033
\(119\) 3.16515i 0.290149i
\(120\) −10.5826 −0.966053
\(121\) 3.37386 0.306715
\(122\) 8.20871 0.743182
\(123\) −14.5390 −1.31094
\(124\) 5.37386i 0.482587i
\(125\) 16.5826i 1.48319i
\(126\) 9.58258i 0.853684i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 16.7477i 1.47456i
\(130\) 3.00000i 0.263117i
\(131\) 10.7477i 0.939033i −0.882924 0.469517i \(-0.844428\pi\)
0.882924 0.469517i \(-0.155572\pi\)
\(132\) 10.5826 0.921095
\(133\) 15.1652i 1.31499i
\(134\) 7.37386i 0.637005i
\(135\) 18.9564i 1.63151i
\(136\) 1.58258 0.135705
\(137\) −17.3739 −1.48435 −0.742175 0.670207i \(-0.766206\pi\)
−0.742175 + 0.670207i \(0.766206\pi\)
\(138\) −2.20871 −0.188018
\(139\) 0.373864 0.0317107 0.0158553 0.999874i \(-0.494953\pi\)
0.0158553 + 0.999874i \(0.494953\pi\)
\(140\) 7.58258i 0.640845i
\(141\) −4.41742 −0.372014
\(142\) 9.16515i 0.769122i
\(143\) 3.00000i 0.250873i
\(144\) 4.79129 0.399274
\(145\) −3.00000 −0.249136
\(146\) 9.37386i 0.775786i
\(147\) 8.37386 0.690665
\(148\) −4.00000 4.58258i −0.328798 0.376685i
\(149\) −13.5826 −1.11273 −0.556364 0.830939i \(-0.687804\pi\)
−0.556364 + 0.830939i \(0.687804\pi\)
\(150\) 26.1652i 2.13638i
\(151\) 12.7477 1.03740 0.518698 0.854958i \(-0.326417\pi\)
0.518698 + 0.854958i \(0.326417\pi\)
\(152\) 7.58258 0.615028
\(153\) 7.58258i 0.613015i
\(154\) 7.58258i 0.611021i
\(155\) 20.3739 1.63647
\(156\) 2.20871i 0.176838i
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 12.7913 1.01762
\(159\) −21.1652 −1.67851
\(160\) −3.79129 −0.299728
\(161\) 1.58258i 0.124724i
\(162\) 0.417424i 0.0327960i
\(163\) 10.4174i 0.815956i 0.912992 + 0.407978i \(0.133766\pi\)
−0.912992 + 0.407978i \(0.866234\pi\)
\(164\) −5.20871 −0.406732
\(165\) 40.1216i 3.12346i
\(166\) 3.16515i 0.245663i
\(167\) 0.956439i 0.0740115i 0.999315 + 0.0370057i \(0.0117820\pi\)
−0.999315 + 0.0370057i \(0.988218\pi\)
\(168\) 5.58258i 0.430705i
\(169\) 12.3739 0.951836
\(170\) 6.00000i 0.460179i
\(171\) 36.3303i 2.77825i
\(172\) 6.00000i 0.457496i
\(173\) −3.16515 −0.240642 −0.120321 0.992735i \(-0.538392\pi\)
−0.120321 + 0.992735i \(0.538392\pi\)
\(174\) 2.20871 0.167442
\(175\) 18.7477 1.41719
\(176\) 3.79129 0.285779
\(177\) 21.1652i 1.59087i
\(178\) 6.00000 0.449719
\(179\) 7.58258i 0.566748i −0.959009 0.283374i \(-0.908546\pi\)
0.959009 0.283374i \(-0.0914538\pi\)
\(180\) 18.1652i 1.35395i
\(181\) −18.7477 −1.39351 −0.696754 0.717310i \(-0.745373\pi\)
−0.696754 + 0.717310i \(0.745373\pi\)
\(182\) −1.58258 −0.117308
\(183\) 22.9129i 1.69377i
\(184\) −0.791288 −0.0583345
\(185\) 17.3739 15.1652i 1.27735 1.11496i
\(186\) −15.0000 −1.09985
\(187\) 6.00000i 0.438763i
\(188\) −1.58258 −0.115421
\(189\) 10.0000 0.727393
\(190\) 28.7477i 2.08558i
\(191\) 5.37386i 0.388839i −0.980918 0.194420i \(-0.937718\pi\)
0.980918 0.194420i \(-0.0622823\pi\)
\(192\) 2.79129 0.201444
\(193\) 18.3303i 1.31944i 0.751510 + 0.659722i \(0.229326\pi\)
−0.751510 + 0.659722i \(0.770674\pi\)
\(194\) −4.41742 −0.317153
\(195\) −8.37386 −0.599665
\(196\) 3.00000 0.214286
\(197\) 25.9129 1.84622 0.923108 0.384541i \(-0.125640\pi\)
0.923108 + 0.384541i \(0.125640\pi\)
\(198\) 18.1652i 1.29094i
\(199\) 3.16515i 0.224372i 0.993687 + 0.112186i \(0.0357852\pi\)
−0.993687 + 0.112186i \(0.964215\pi\)
\(200\) 9.37386i 0.662832i
\(201\) 20.5826 1.45178
\(202\) 1.58258i 0.111350i
\(203\) 1.58258i 0.111075i
\(204\) 4.41742i 0.309282i
\(205\) 19.7477i 1.37924i
\(206\) 2.20871 0.153888
\(207\) 3.79129i 0.263513i
\(208\) 0.791288i 0.0548659i
\(209\) 28.7477i 1.98852i
\(210\) −21.1652 −1.46053
\(211\) −3.37386 −0.232266 −0.116133 0.993234i \(-0.537050\pi\)
−0.116133 + 0.993234i \(0.537050\pi\)
\(212\) −7.58258 −0.520773
\(213\) −25.5826 −1.75289
\(214\) 8.37386i 0.572426i
\(215\) −22.7477 −1.55138
\(216\) 5.00000i 0.340207i
\(217\) 10.7477i 0.729603i
\(218\) 6.00000 0.406371
\(219\) −26.1652 −1.76808
\(220\) 14.3739i 0.969086i
\(221\) 1.25227 0.0842370
\(222\) −12.7913 + 11.1652i −0.858495 + 0.749356i
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 2.00000i 0.133631i
\(225\) −44.9129 −2.99419
\(226\) −19.5826 −1.30261
\(227\) 19.9129i 1.32166i 0.750534 + 0.660832i \(0.229796\pi\)
−0.750534 + 0.660832i \(0.770204\pi\)
\(228\) 21.1652i 1.40170i
\(229\) −20.7477 −1.37105 −0.685524 0.728050i \(-0.740427\pi\)
−0.685524 + 0.728050i \(0.740427\pi\)
\(230\) 3.00000i 0.197814i
\(231\) 21.1652 1.39256
\(232\) 0.791288 0.0519506
\(233\) 25.1216 1.64577 0.822885 0.568208i \(-0.192363\pi\)
0.822885 + 0.568208i \(0.192363\pi\)
\(234\) 3.79129 0.247844
\(235\) 6.00000i 0.391397i
\(236\) 7.58258i 0.493584i
\(237\) 35.7042i 2.31923i
\(238\) 3.16515 0.205166
\(239\) 24.9564i 1.61430i 0.590348 + 0.807149i \(0.298991\pi\)
−0.590348 + 0.807149i \(0.701009\pi\)
\(240\) 10.5826i 0.683102i
\(241\) 13.5826i 0.874931i 0.899235 + 0.437465i \(0.144124\pi\)
−0.899235 + 0.437465i \(0.855876\pi\)
\(242\) 3.37386i 0.216880i
\(243\) 16.1652 1.03699
\(244\) 8.20871i 0.525509i
\(245\) 11.3739i 0.726649i
\(246\) 14.5390i 0.926974i
\(247\) 6.00000 0.381771
\(248\) −5.37386 −0.341241
\(249\) 8.83485 0.559886
\(250\) 16.5826 1.04877
\(251\) 13.5826i 0.857325i 0.903465 + 0.428662i \(0.141015\pi\)
−0.903465 + 0.428662i \(0.858985\pi\)
\(252\) 9.58258 0.603646
\(253\) 3.00000i 0.188608i
\(254\) 8.00000i 0.501965i
\(255\) 16.7477 1.04878
\(256\) 1.00000 0.0625000
\(257\) 22.7477i 1.41896i 0.704723 + 0.709482i \(0.251071\pi\)
−0.704723 + 0.709482i \(0.748929\pi\)
\(258\) 16.7477 1.04267
\(259\) −8.00000 9.16515i −0.497096 0.569495i
\(260\) −3.00000 −0.186052
\(261\) 3.79129i 0.234675i
\(262\) −10.7477 −0.663997
\(263\) −8.83485 −0.544780 −0.272390 0.962187i \(-0.587814\pi\)
−0.272390 + 0.962187i \(0.587814\pi\)
\(264\) 10.5826i 0.651313i
\(265\) 28.7477i 1.76596i
\(266\) 15.1652 0.929835
\(267\) 16.7477i 1.02494i
\(268\) 7.37386 0.450430
\(269\) −10.7477 −0.655300 −0.327650 0.944799i \(-0.606257\pi\)
−0.327650 + 0.944799i \(0.606257\pi\)
\(270\) 18.9564 1.15365
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 1.58258i 0.0959577i
\(273\) 4.41742i 0.267355i
\(274\) 17.3739i 1.04959i
\(275\) −35.5390 −2.14308
\(276\) 2.20871i 0.132949i
\(277\) 23.3739i 1.40440i −0.711980 0.702200i \(-0.752201\pi\)
0.711980 0.702200i \(-0.247799\pi\)
\(278\) 0.373864i 0.0224228i
\(279\) 25.7477i 1.54148i
\(280\) −7.58258 −0.453146
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 4.41742i 0.263054i
\(283\) 24.0000i 1.42665i 0.700832 + 0.713326i \(0.252812\pi\)
−0.700832 + 0.713326i \(0.747188\pi\)
\(284\) −9.16515 −0.543852
\(285\) 80.2432 4.75320
\(286\) 3.00000 0.177394
\(287\) −10.4174 −0.614921
\(288\) 4.79129i 0.282329i
\(289\) 14.4955 0.852674
\(290\) 3.00000i 0.176166i
\(291\) 12.3303i 0.722815i
\(292\) −9.37386 −0.548564
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 8.37386i 0.488374i
\(295\) −28.7477 −1.67376
\(296\) −4.58258 + 4.00000i −0.266357 + 0.232495i
\(297\) −18.9564 −1.09996
\(298\) 13.5826i 0.786817i
\(299\) −0.626136 −0.0362104
\(300\) −26.1652 −1.51065
\(301\) 12.0000i 0.691669i
\(302\) 12.7477i 0.733549i
\(303\) 4.41742 0.253774
\(304\) 7.58258i 0.434891i
\(305\) 31.1216 1.78202
\(306\) −7.58258 −0.433467
\(307\) −12.3739 −0.706214 −0.353107 0.935583i \(-0.614875\pi\)
−0.353107 + 0.935583i \(0.614875\pi\)
\(308\) 7.58258 0.432057
\(309\) 6.16515i 0.350723i
\(310\) 20.3739i 1.15716i
\(311\) 9.62614i 0.545848i −0.962036 0.272924i \(-0.912009\pi\)
0.962036 0.272924i \(-0.0879908\pi\)
\(312\) 2.20871 0.125044
\(313\) 33.1652i 1.87461i −0.348517 0.937303i \(-0.613315\pi\)
0.348517 0.937303i \(-0.386685\pi\)
\(314\) 2.00000i 0.112867i
\(315\) 36.3303i 2.04698i
\(316\) 12.7913i 0.719566i
\(317\) −1.25227 −0.0703347 −0.0351673 0.999381i \(-0.511196\pi\)
−0.0351673 + 0.999381i \(0.511196\pi\)
\(318\) 21.1652i 1.18688i
\(319\) 3.00000i 0.167968i
\(320\) 3.79129i 0.211939i
\(321\) −23.3739 −1.30460
\(322\) −1.58258 −0.0881935
\(323\) −12.0000 −0.667698
\(324\) 0.417424 0.0231902
\(325\) 7.41742i 0.411445i
\(326\) 10.4174 0.576968
\(327\) 16.7477i 0.926151i
\(328\) 5.20871i 0.287603i
\(329\) −3.16515 −0.174500
\(330\) 40.1216 2.20862
\(331\) 16.4174i 0.902383i −0.892427 0.451192i \(-0.850999\pi\)
0.892427 0.451192i \(-0.149001\pi\)
\(332\) 3.16515 0.173710
\(333\) 19.1652 + 21.9564i 1.05024 + 1.20321i
\(334\) 0.956439 0.0523340
\(335\) 27.9564i 1.52742i
\(336\) 5.58258 0.304554
\(337\) −8.12159 −0.442411 −0.221206 0.975227i \(-0.570999\pi\)
−0.221206 + 0.975227i \(0.570999\pi\)
\(338\) 12.3739i 0.673049i
\(339\) 54.6606i 2.96876i
\(340\) 6.00000 0.325396
\(341\) 20.3739i 1.10331i
\(342\) −36.3303 −1.96452
\(343\) 20.0000 1.07990
\(344\) 6.00000 0.323498
\(345\) −8.37386 −0.450834
\(346\) 3.16515i 0.170160i
\(347\) 1.58258i 0.0849571i −0.999097 0.0424786i \(-0.986475\pi\)
0.999097 0.0424786i \(-0.0135254\pi\)
\(348\) 2.20871i 0.118399i
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 18.7477i 1.00211i
\(351\) 3.95644i 0.211179i
\(352\) 3.79129i 0.202076i
\(353\) 7.58258i 0.403580i 0.979429 + 0.201790i \(0.0646758\pi\)
−0.979429 + 0.201790i \(0.935324\pi\)
\(354\) 21.1652 1.12492
\(355\) 34.7477i 1.84422i
\(356\) 6.00000i 0.317999i
\(357\) 8.83485i 0.467590i
\(358\) −7.58258 −0.400752
\(359\) −27.1652 −1.43372 −0.716861 0.697216i \(-0.754422\pi\)
−0.716861 + 0.697216i \(0.754422\pi\)
\(360\) 18.1652 0.957388
\(361\) −38.4955 −2.02608
\(362\) 18.7477i 0.985359i
\(363\) −9.41742 −0.494287
\(364\) 1.58258i 0.0829495i
\(365\) 35.5390i 1.86020i
\(366\) −22.9129 −1.19768
\(367\) −32.7477 −1.70942 −0.854709 0.519108i \(-0.826264\pi\)
−0.854709 + 0.519108i \(0.826264\pi\)
\(368\) 0.791288i 0.0412487i
\(369\) 24.9564 1.29918
\(370\) −15.1652 17.3739i −0.788399 0.903224i
\(371\) −15.1652 −0.787335
\(372\) 15.0000i 0.777714i
\(373\) 14.7477 0.763608 0.381804 0.924243i \(-0.375303\pi\)
0.381804 + 0.924243i \(0.375303\pi\)
\(374\) −6.00000 −0.310253
\(375\) 46.2867i 2.39024i
\(376\) 1.58258i 0.0816151i
\(377\) 0.626136 0.0322477
\(378\) 10.0000i 0.514344i
\(379\) −21.1216 −1.08494 −0.542472 0.840074i \(-0.682511\pi\)
−0.542472 + 0.840074i \(0.682511\pi\)
\(380\) 28.7477 1.47473
\(381\) −22.3303 −1.14402
\(382\) −5.37386 −0.274951
\(383\) 18.3303i 0.936635i 0.883560 + 0.468317i \(0.155140\pi\)
−0.883560 + 0.468317i \(0.844860\pi\)
\(384\) 2.79129i 0.142442i
\(385\) 28.7477i 1.46512i
\(386\) 18.3303 0.932988
\(387\) 28.7477i 1.46133i
\(388\) 4.41742i 0.224261i
\(389\) 35.8693i 1.81865i −0.416090 0.909323i \(-0.636600\pi\)
0.416090 0.909323i \(-0.363400\pi\)
\(390\) 8.37386i 0.424027i
\(391\) 1.25227 0.0633302
\(392\) 3.00000i 0.151523i
\(393\) 30.0000i 1.51330i
\(394\) 25.9129i 1.30547i
\(395\) 48.4955 2.44007
\(396\) −18.1652 −0.912833
\(397\) −12.7477 −0.639790 −0.319895 0.947453i \(-0.603648\pi\)
−0.319895 + 0.947453i \(0.603648\pi\)
\(398\) 3.16515 0.158655
\(399\) 42.3303i 2.11917i
\(400\) −9.37386 −0.468693
\(401\) 10.7477i 0.536716i 0.963319 + 0.268358i \(0.0864810\pi\)
−0.963319 + 0.268358i \(0.913519\pi\)
\(402\) 20.5826i 1.02657i
\(403\) −4.25227 −0.211821
\(404\) 1.58258 0.0787361
\(405\) 1.58258i 0.0786388i
\(406\) 1.58258 0.0785419
\(407\) 15.1652 + 17.3739i 0.751709 + 0.861190i
\(408\) −4.41742 −0.218695
\(409\) 8.83485i 0.436855i 0.975853 + 0.218428i \(0.0700927\pi\)
−0.975853 + 0.218428i \(0.929907\pi\)
\(410\) −19.7477 −0.975271
\(411\) 48.4955 2.39210
\(412\) 2.20871i 0.108815i
\(413\) 15.1652i 0.746228i
\(414\) 3.79129 0.186332
\(415\) 12.0000i 0.589057i
\(416\) 0.791288 0.0387961
\(417\) −1.04356 −0.0511034
\(418\) −28.7477 −1.40610
\(419\) 6.79129 0.331776 0.165888 0.986145i \(-0.446951\pi\)
0.165888 + 0.986145i \(0.446951\pi\)
\(420\) 21.1652i 1.03275i
\(421\) 3.95644i 0.192825i 0.995341 + 0.0964125i \(0.0307368\pi\)
−0.995341 + 0.0964125i \(0.969263\pi\)
\(422\) 3.37386i 0.164237i
\(423\) 7.58258 0.368677
\(424\) 7.58258i 0.368242i
\(425\) 14.8348i 0.719596i
\(426\) 25.5826i 1.23948i
\(427\) 16.4174i 0.794495i
\(428\) −8.37386 −0.404766
\(429\) 8.37386i 0.404294i
\(430\) 22.7477i 1.09699i
\(431\) 27.1652i 1.30850i −0.756279 0.654250i \(-0.772985\pi\)
0.756279 0.654250i \(-0.227015\pi\)
\(432\) −5.00000 −0.240563
\(433\) 24.3739 1.17133 0.585667 0.810552i \(-0.300833\pi\)
0.585667 + 0.810552i \(0.300833\pi\)
\(434\) −10.7477 −0.515907
\(435\) 8.37386 0.401496
\(436\) 6.00000i 0.287348i
\(437\) 6.00000 0.287019
\(438\) 26.1652i 1.25022i
\(439\) 26.3739i 1.25876i 0.777099 + 0.629378i \(0.216690\pi\)
−0.777099 + 0.629378i \(0.783310\pi\)
\(440\) 14.3739 0.685247
\(441\) −14.3739 −0.684470
\(442\) 1.25227i 0.0595645i
\(443\) 5.04356 0.239627 0.119813 0.992796i \(-0.461770\pi\)
0.119813 + 0.992796i \(0.461770\pi\)
\(444\) 11.1652 + 12.7913i 0.529875 + 0.607048i
\(445\) 22.7477 1.07835
\(446\) 14.0000i 0.662919i
\(447\) 37.9129 1.79322
\(448\) 2.00000 0.0944911
\(449\) 21.1652i 0.998845i −0.866358 0.499423i \(-0.833546\pi\)
0.866358 0.499423i \(-0.166454\pi\)
\(450\) 44.9129i 2.11721i
\(451\) 19.7477 0.929884
\(452\) 19.5826i 0.921087i
\(453\) −35.5826 −1.67182
\(454\) 19.9129 0.934558
\(455\) −6.00000 −0.281284
\(456\) −21.1652 −0.991149
\(457\) 33.4955i 1.56685i 0.621486 + 0.783426i \(0.286529\pi\)
−0.621486 + 0.783426i \(0.713471\pi\)
\(458\) 20.7477i 0.969478i
\(459\) 7.91288i 0.369342i
\(460\) −3.00000 −0.139876
\(461\) 24.3303i 1.13318i −0.824002 0.566588i \(-0.808263\pi\)
0.824002 0.566588i \(-0.191737\pi\)
\(462\) 21.1652i 0.984692i
\(463\) 20.7042i 0.962204i −0.876665 0.481102i \(-0.840237\pi\)
0.876665 0.481102i \(-0.159763\pi\)
\(464\) 0.791288i 0.0367346i
\(465\) −56.8693 −2.63725
\(466\) 25.1216i 1.16374i
\(467\) 25.5826i 1.18382i 0.806004 + 0.591910i \(0.201626\pi\)
−0.806004 + 0.591910i \(0.798374\pi\)
\(468\) 3.79129i 0.175252i
\(469\) 14.7477 0.680987
\(470\) −6.00000 −0.276759
\(471\) 5.58258 0.257232
\(472\) 7.58258 0.349016
\(473\) 22.7477i 1.04594i
\(474\) −35.7042 −1.63995
\(475\) 71.0780i 3.26128i
\(476\) 3.16515i 0.145074i
\(477\) 36.3303 1.66345
\(478\) 24.9564 1.14148
\(479\) 0.791288i 0.0361549i −0.999837 0.0180774i \(-0.994245\pi\)
0.999837 0.0180774i \(-0.00575454\pi\)
\(480\) 10.5826 0.483026
\(481\) −3.62614 + 3.16515i −0.165338 + 0.144318i
\(482\) 13.5826 0.618669
\(483\) 4.41742i 0.201000i
\(484\) −3.37386 −0.153357
\(485\) −16.7477 −0.760475
\(486\) 16.1652i 0.733266i
\(487\) 36.6606i 1.66125i −0.556832 0.830625i \(-0.687983\pi\)
0.556832 0.830625i \(-0.312017\pi\)
\(488\) −8.20871 −0.371591
\(489\) 29.0780i 1.31495i
\(490\) 11.3739 0.513819
\(491\) −8.37386 −0.377907 −0.188954 0.981986i \(-0.560510\pi\)
−0.188954 + 0.981986i \(0.560510\pi\)
\(492\) 14.5390 0.655469
\(493\) −1.25227 −0.0563995
\(494\) 6.00000i 0.269953i
\(495\) 68.8693i 3.09545i
\(496\) 5.37386i 0.241294i
\(497\) −18.3303 −0.822226
\(498\) 8.83485i 0.395899i
\(499\) 16.7477i 0.749731i 0.927079 + 0.374866i \(0.122311\pi\)
−0.927079 + 0.374866i \(0.877689\pi\)
\(500\) 16.5826i 0.741595i
\(501\) 2.66970i 0.119273i
\(502\) 13.5826 0.606220
\(503\) 29.3739i 1.30972i 0.755752 + 0.654858i \(0.227272\pi\)
−0.755752 + 0.654858i \(0.772728\pi\)
\(504\) 9.58258i 0.426842i
\(505\) 6.00000i 0.266996i
\(506\) 3.00000 0.133366
\(507\) −34.5390 −1.53393
\(508\) −8.00000 −0.354943
\(509\) 13.5826 0.602037 0.301019 0.953618i \(-0.402673\pi\)
0.301019 + 0.953618i \(0.402673\pi\)
\(510\) 16.7477i 0.741602i
\(511\) −18.7477 −0.829351
\(512\) 1.00000i 0.0441942i
\(513\) 37.9129i 1.67389i
\(514\) 22.7477 1.00336
\(515\) 8.37386 0.368997
\(516\) 16.7477i 0.737278i
\(517\) 6.00000 0.263880
\(518\) −9.16515 + 8.00000i −0.402694 + 0.351500i
\(519\) 8.83485 0.387807
\(520\) 3.00000i 0.131559i
\(521\) 9.16515 0.401533 0.200766 0.979639i \(-0.435657\pi\)
0.200766 + 0.979639i \(0.435657\pi\)
\(522\) −3.79129 −0.165940
\(523\) 3.16515i 0.138402i −0.997603 0.0692012i \(-0.977955\pi\)
0.997603 0.0692012i \(-0.0220450\pi\)
\(524\) 10.7477i 0.469517i
\(525\) −52.3303 −2.28388
\(526\) 8.83485i 0.385218i
\(527\) 8.50455 0.370464
\(528\) −10.5826 −0.460547
\(529\) 22.3739 0.972777
\(530\) −28.7477 −1.24872
\(531\) 36.3303i 1.57660i
\(532\) 15.1652i 0.657493i
\(533\) 4.12159i 0.178526i
\(534\) −16.7477 −0.724745
\(535\) 31.7477i 1.37257i
\(536\) 7.37386i 0.318502i
\(537\) 21.1652i 0.913344i
\(538\) 10.7477i 0.463367i
\(539\) −11.3739 −0.489907
\(540\) 18.9564i 0.815755i
\(541\) 8.20871i 0.352920i −0.984308 0.176460i \(-0.943535\pi\)
0.984308 0.176460i \(-0.0564646\pi\)
\(542\) 22.0000i 0.944981i
\(543\) 52.3303 2.24571
\(544\) −1.58258 −0.0678524
\(545\) 22.7477 0.974406
\(546\) 4.41742 0.189048
\(547\) 19.9129i 0.851413i 0.904861 + 0.425707i \(0.139974\pi\)
−0.904861 + 0.425707i \(0.860026\pi\)
\(548\) 17.3739 0.742175
\(549\) 39.3303i 1.67858i
\(550\) 35.5390i 1.51539i
\(551\) −6.00000 −0.255609
\(552\) 2.20871 0.0940090
\(553\) 25.5826i 1.08788i
\(554\) −23.3739 −0.993060
\(555\) −48.4955 + 42.3303i −2.05852 + 1.79682i
\(556\) −0.373864 −0.0158553
\(557\) 41.7042i 1.76706i 0.468372 + 0.883531i \(0.344841\pi\)
−0.468372 + 0.883531i \(0.655159\pi\)
\(558\) 25.7477 1.08999
\(559\) 4.74773 0.200807
\(560\) 7.58258i 0.320422i
\(561\) 16.7477i 0.707090i
\(562\) 0 0
\(563\) 16.7477i 0.705833i −0.935655 0.352916i \(-0.885190\pi\)
0.935655 0.352916i \(-0.114810\pi\)
\(564\) 4.41742 0.186007
\(565\) −74.2432 −3.12343
\(566\) 24.0000 1.00880
\(567\) 0.834849 0.0350603
\(568\) 9.16515i 0.384561i
\(569\) 26.8348i 1.12498i −0.826806 0.562488i \(-0.809844\pi\)
0.826806 0.562488i \(-0.190156\pi\)
\(570\) 80.2432i 3.36102i
\(571\) −28.3739 −1.18741 −0.593705 0.804683i \(-0.702335\pi\)
−0.593705 + 0.804683i \(0.702335\pi\)
\(572\) 3.00000i 0.125436i
\(573\) 15.0000i 0.626634i
\(574\) 10.4174i 0.434815i
\(575\) 7.41742i 0.309328i
\(576\) −4.79129 −0.199637
\(577\) 4.41742i 0.183900i −0.995764 0.0919499i \(-0.970690\pi\)
0.995764 0.0919499i \(-0.0293100\pi\)
\(578\) 14.4955i 0.602931i
\(579\) 51.1652i 2.12635i
\(580\) 3.00000 0.124568
\(581\) 6.33030 0.262625
\(582\) 12.3303 0.511107
\(583\) 28.7477 1.19061
\(584\) 9.37386i 0.387893i
\(585\) 14.3739 0.594286
\(586\) 6.00000i 0.247858i
\(587\) 25.9129i 1.06954i −0.844998 0.534769i \(-0.820398\pi\)
0.844998 0.534769i \(-0.179602\pi\)
\(588\) −8.37386 −0.345332
\(589\) 40.7477 1.67898
\(590\) 28.7477i 1.18353i
\(591\) −72.3303 −2.97527
\(592\) 4.00000 + 4.58258i 0.164399 + 0.188343i
\(593\) −14.2087 −0.583482 −0.291741 0.956497i \(-0.594235\pi\)
−0.291741 + 0.956497i \(0.594235\pi\)
\(594\) 18.9564i 0.777792i
\(595\) 12.0000 0.491952
\(596\) 13.5826 0.556364
\(597\) 8.83485i 0.361586i
\(598\) 0.626136i 0.0256046i
\(599\) 27.1652 1.10994 0.554969 0.831871i \(-0.312730\pi\)
0.554969 + 0.831871i \(0.312730\pi\)
\(600\) 26.1652i 1.06819i
\(601\) 8.12159 0.331287 0.165643 0.986186i \(-0.447030\pi\)
0.165643 + 0.986186i \(0.447030\pi\)
\(602\) 12.0000 0.489083
\(603\) −35.3303 −1.43876
\(604\) −12.7477 −0.518698
\(605\) 12.7913i 0.520040i
\(606\) 4.41742i 0.179446i
\(607\) 5.53901i 0.224822i −0.993662 0.112411i \(-0.964143\pi\)
0.993662 0.112411i \(-0.0358573\pi\)
\(608\) −7.58258 −0.307514
\(609\) 4.41742i 0.179003i
\(610\) 31.1216i 1.26008i
\(611\) 1.25227i 0.0506615i
\(612\) 7.58258i 0.306507i
\(613\) 5.49545 0.221959 0.110980 0.993823i \(-0.464601\pi\)
0.110980 + 0.993823i \(0.464601\pi\)
\(614\) 12.3739i 0.499368i
\(615\) 55.1216i 2.22272i
\(616\) 7.58258i 0.305511i
\(617\) −45.9564 −1.85014 −0.925068 0.379801i \(-0.875993\pi\)
−0.925068 + 0.379801i \(0.875993\pi\)
\(618\) −6.16515 −0.247999
\(619\) 6.12159 0.246048 0.123024 0.992404i \(-0.460741\pi\)
0.123024 + 0.992404i \(0.460741\pi\)
\(620\) −20.3739 −0.818234
\(621\) 3.95644i 0.158766i
\(622\) −9.62614 −0.385973
\(623\) 12.0000i 0.480770i
\(624\) 2.20871i 0.0884192i
\(625\) 16.0000 0.640000
\(626\) −33.1652 −1.32555
\(627\) 80.2432i 3.20460i
\(628\) 2.00000 0.0798087
\(629\) 7.25227 6.33030i 0.289167 0.252406i
\(630\) 36.3303 1.44743
\(631\) 3.95644i 0.157503i −0.996894 0.0787517i \(-0.974907\pi\)
0.996894 0.0787517i \(-0.0250934\pi\)
\(632\) −12.7913 −0.508810
\(633\) 9.41742 0.374309
\(634\) 1.25227i 0.0497341i
\(635\) 30.3303i 1.20362i
\(636\) 21.1652 0.839253
\(637\) 2.37386i 0.0940559i
\(638\) −3.00000 −0.118771
\(639\) 43.9129 1.73717
\(640\) 3.79129 0.149864
\(641\) −35.5390 −1.40371 −0.701853 0.712321i \(-0.747644\pi\)
−0.701853 + 0.712321i \(0.747644\pi\)
\(642\) 23.3739i 0.922493i
\(643\) 15.4955i 0.611081i 0.952179 + 0.305541i \(0.0988371\pi\)
−0.952179 + 0.305541i \(0.901163\pi\)
\(644\) 1.58258i 0.0623622i
\(645\) 63.4955 2.50013
\(646\) 12.0000i 0.472134i
\(647\) 32.7042i 1.28573i −0.765978 0.642867i \(-0.777745\pi\)
0.765978 0.642867i \(-0.222255\pi\)
\(648\) 0.417424i 0.0163980i
\(649\) 28.7477i 1.12845i
\(650\) −7.41742 −0.290935
\(651\) 30.0000i 1.17579i
\(652\) 10.4174i 0.407978i
\(653\) 14.3739i 0.562493i 0.959636 + 0.281246i \(0.0907478\pi\)
−0.959636 + 0.281246i \(0.909252\pi\)
\(654\) −16.7477 −0.654888
\(655\) −40.7477 −1.59215
\(656\) 5.20871 0.203366
\(657\) 44.9129 1.75222
\(658\) 3.16515i 0.123390i
\(659\) 33.9564 1.32276 0.661378 0.750053i \(-0.269972\pi\)
0.661378 + 0.750053i \(0.269972\pi\)
\(660\) 40.1216i 1.56173i
\(661\) 36.7913i 1.43102i 0.698605 + 0.715508i \(0.253805\pi\)
−0.698605 + 0.715508i \(0.746195\pi\)
\(662\) −16.4174 −0.638081
\(663\) −3.49545 −0.135752
\(664\) 3.16515i 0.122832i
\(665\) 57.4955 2.22958
\(666\) 21.9564 19.1652i 0.850795 0.742635i
\(667\) 0.626136 0.0242441
\(668\) 0.956439i 0.0370057i
\(669\) −39.0780 −1.51084
\(670\) 27.9564 1.08005
\(671\) 31.1216i 1.20144i
\(672\) 5.58258i 0.215353i
\(673\) 5.12159 0.197423 0.0987114 0.995116i \(-0.468528\pi\)
0.0987114 + 0.995116i \(0.468528\pi\)
\(674\) 8.12159i 0.312832i
\(675\) 46.8693 1.80400
\(676\) −12.3739 −0.475918
\(677\) −9.16515 −0.352245 −0.176123 0.984368i \(-0.556356\pi\)
−0.176123 + 0.984368i \(0.556356\pi\)
\(678\) 54.6606 2.09923
\(679\) 8.83485i 0.339050i
\(680\) 6.00000i 0.230089i
\(681\) 55.5826i 2.12993i
\(682\) 20.3739 0.780156
\(683\) 22.4174i 0.857779i −0.903357 0.428889i \(-0.858905\pi\)
0.903357 0.428889i \(-0.141095\pi\)
\(684\) 36.3303i 1.38912i
\(685\) 65.8693i 2.51674i
\(686\) 20.0000i 0.763604i
\(687\) 57.9129 2.20951
\(688\) 6.00000i 0.228748i
\(689\) 6.00000i 0.228582i
\(690\) 8.37386i 0.318788i
\(691\) −29.4955 −1.12206 −0.561030 0.827795i \(-0.689595\pi\)
−0.561030 + 0.827795i \(0.689595\pi\)
\(692\) 3.16515 0.120321
\(693\) −36.3303 −1.38007
\(694\) −1.58258 −0.0600738
\(695\) 1.41742i 0.0537660i
\(696\) −2.20871 −0.0837210
\(697\) 8.24318i 0.312233i
\(698\) 10.0000i 0.378506i
\(699\) −70.1216 −2.65224
\(700\) −18.7477 −0.708597
\(701\) 18.9564i 0.715975i −0.933726 0.357987i \(-0.883463\pi\)
0.933726 0.357987i \(-0.116537\pi\)
\(702\) −3.95644 −0.149326
\(703\) 34.7477 30.3303i 1.31054 1.14393i
\(704\) −3.79129 −0.142890
\(705\) 16.7477i 0.630756i
\(706\) 7.58258 0.285374
\(707\) 3.16515 0.119038
\(708\) 21.1652i 0.795435i
\(709\) 27.7913i 1.04372i 0.853030 + 0.521862i \(0.174762\pi\)
−0.853030 + 0.521862i \(0.825238\pi\)
\(710\) −34.7477 −1.30406
\(711\) 61.2867i 2.29843i
\(712\) −6.00000 −0.224860
\(713\) −4.25227 −0.159249
\(714\) −8.83485 −0.330636
\(715\) 11.3739 0.425358
\(716\) 7.58258i 0.283374i
\(717\) 69.6606i 2.60152i
\(718\) 27.1652i 1.01379i
\(719\) −2.83485 −0.105722 −0.0528610 0.998602i \(-0.516834\pi\)
−0.0528610 + 0.998602i \(0.516834\pi\)
\(720\) 18.1652i 0.676975i
\(721\) 4.41742i 0.164513i
\(722\) 38.4955i 1.43265i
\(723\) 37.9129i 1.41000i
\(724\) 18.7477 0.696754
\(725\) 7.41742i 0.275476i
\(726\) 9.41742i 0.349513i
\(727\) 28.1216i 1.04297i 0.853260 + 0.521486i \(0.174622\pi\)
−0.853260 + 0.521486i \(0.825378\pi\)
\(728\) 1.58258 0.0586542
\(729\) −43.8693 −1.62479
\(730\) −35.5390 −1.31536
\(731\) −9.49545 −0.351202
\(732\) 22.9129i 0.846884i
\(733\) −7.49545 −0.276851 −0.138425 0.990373i \(-0.544204\pi\)
−0.138425 + 0.990373i \(0.544204\pi\)
\(734\) 32.7477i 1.20874i
\(735\) 31.7477i 1.17103i
\(736\) 0.791288 0.0291673
\(737\) −27.9564 −1.02979
\(738\) 24.9564i 0.918659i
\(739\) 6.12159 0.225186 0.112593 0.993641i \(-0.464084\pi\)
0.112593 + 0.993641i \(0.464084\pi\)
\(740\) −17.3739 + 15.1652i −0.638676 + 0.557482i
\(741\) −16.7477 −0.615243
\(742\) 15.1652i 0.556730i
\(743\) −3.16515 −0.116118 −0.0580591 0.998313i \(-0.518491\pi\)
−0.0580591 + 0.998313i \(0.518491\pi\)
\(744\) 15.0000 0.549927
\(745\) 51.4955i 1.88665i
\(746\) 14.7477i 0.539953i
\(747\) −15.1652 −0.554864
\(748\) 6.00000i 0.219382i
\(749\) −16.7477 −0.611949
\(750\) −46.2867 −1.69015
\(751\) 13.4955 0.492456 0.246228 0.969212i \(-0.420809\pi\)
0.246228 + 0.969212i \(0.420809\pi\)
\(752\) 1.58258 0.0577106
\(753\) 37.9129i 1.38162i
\(754\) 0.626136i 0.0228025i
\(755\) 48.3303i 1.75892i
\(756\) −10.0000 −0.363696
\(757\) 39.7913i 1.44624i −0.690723 0.723119i \(-0.742708\pi\)
0.690723 0.723119i \(-0.257292\pi\)
\(758\) 21.1216i 0.767171i
\(759\) 8.37386i 0.303952i
\(760\) 28.7477i 1.04279i
\(761\) 18.7913 0.681184 0.340592 0.940211i \(-0.389373\pi\)
0.340592 + 0.940211i \(0.389373\pi\)
\(762\) 22.3303i 0.808942i
\(763\) 12.0000i 0.434429i
\(764\) 5.37386i 0.194420i
\(765\) −28.7477 −1.03938
\(766\) 18.3303 0.662301
\(767\) 6.00000 0.216647
\(768\) −2.79129 −0.100722
\(769\) 48.3303i 1.74284i −0.490542 0.871418i \(-0.663201\pi\)
0.490542 0.871418i \(-0.336799\pi\)
\(770\) 28.7477 1.03600
\(771\) 63.4955i 2.28673i
\(772\) 18.3303i 0.659722i
\(773\) −13.9129 −0.500411 −0.250206 0.968193i \(-0.580498\pi\)
−0.250206 + 0.968193i \(0.580498\pi\)
\(774\) −28.7477 −1.03332
\(775\) 50.3739i 1.80948i
\(776\) 4.41742 0.158576
\(777\) 22.3303 + 25.5826i 0.801095 + 0.917770i
\(778\) −35.8693 −1.28598
\(779\) 39.4955i 1.41507i
\(780\) 8.37386 0.299832
\(781\) 34.7477 1.24337
\(782\) 1.25227i 0.0447812i
\(783\) 3.95644i 0.141392i
\(784\) −3.00000 −0.107143
\(785\) 7.58258i 0.270634i
\(786\) 30.0000 1.07006
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) −25.9129 −0.923108
\(789\) 24.6606 0.877941
\(790\)