Properties

Label 1110.2.h.f.961.1
Level $1110$
Weight $2$
Character 1110.961
Analytic conductor $8.863$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.279290944.1
Defining polynomial: \(x^{6} + 26 x^{4} + 169 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{37}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 961.1
Root \(-3.44055i\) of defining polynomial
Character \(\chi\) \(=\) 1110.961
Dual form 1110.2.h.f.961.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -4.44055 q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -4.44055 q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.44055 q^{11} -1.00000 q^{12} -0.440552i q^{13} +4.44055i q^{14} -1.00000i q^{15} +1.00000 q^{16} +4.83740i q^{17} -1.00000i q^{18} +0.440552i q^{19} +1.00000i q^{20} -4.44055 q^{21} +2.44055i q^{22} +2.83740i q^{23} +1.00000i q^{24} -1.00000 q^{25} -0.440552 q^{26} +1.00000 q^{27} +4.44055 q^{28} +2.00000i q^{29} -1.00000 q^{30} +5.27795i q^{31} -1.00000i q^{32} -2.44055 q^{33} +4.83740 q^{34} +4.44055i q^{35} -1.00000 q^{36} +(-0.198422 + 6.07953i) q^{37} +0.440552 q^{38} -0.440552i q^{39} +1.00000 q^{40} -2.00000 q^{41} +4.44055i q^{42} -0.396844i q^{43} +2.44055 q^{44} -1.00000i q^{45} +2.83740 q^{46} -10.8811 q^{47} +1.00000 q^{48} +12.7185 q^{49} +1.00000i q^{50} +4.83740i q^{51} +0.440552i q^{52} -2.44055 q^{53} -1.00000i q^{54} +2.44055i q^{55} -4.44055i q^{56} +0.440552i q^{57} +2.00000 q^{58} -2.39684i q^{59} +1.00000i q^{60} +2.00000i q^{61} +5.27795 q^{62} -4.44055 q^{63} -1.00000 q^{64} -0.440552 q^{65} +2.44055i q^{66} -13.7622 q^{67} -4.83740i q^{68} +2.83740i q^{69} +4.44055 q^{70} -9.67479 q^{71} +1.00000i q^{72} +5.71850 q^{73} +(6.07953 + 0.198422i) q^{74} -1.00000 q^{75} -0.440552i q^{76} +10.8374 q^{77} -0.440552 q^{78} -13.2779i q^{79} -1.00000i q^{80} +1.00000 q^{81} +2.00000i q^{82} -7.71850 q^{83} +4.44055 q^{84} +4.83740 q^{85} -0.396844 q^{86} +2.00000i q^{87} -2.44055i q^{88} -15.3217i q^{89} -1.00000 q^{90} +1.95629i q^{91} -2.83740i q^{92} +5.27795i q^{93} +10.8811i q^{94} +0.440552 q^{95} -1.00000i q^{96} +2.88110i q^{97} -12.7185i q^{98} -2.44055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{3} - 6q^{4} - 6q^{7} + 6q^{9} + O(q^{10}) \) \( 6q + 6q^{3} - 6q^{4} - 6q^{7} + 6q^{9} - 6q^{10} + 6q^{11} - 6q^{12} + 6q^{16} - 6q^{21} - 6q^{25} + 18q^{26} + 6q^{27} + 6q^{28} - 6q^{30} + 6q^{33} + 10q^{34} - 6q^{36} - 2q^{37} - 18q^{38} + 6q^{40} - 12q^{41} - 6q^{44} - 2q^{46} - 24q^{47} + 6q^{48} + 16q^{49} + 6q^{53} + 12q^{58} - 8q^{62} - 6q^{63} - 6q^{64} + 18q^{65} + 6q^{70} - 20q^{71} - 26q^{73} - 4q^{74} - 6q^{75} + 46q^{77} + 18q^{78} + 6q^{81} + 14q^{83} + 6q^{84} + 10q^{85} - 4q^{86} - 6q^{90} - 18q^{95} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 1.00000 0.577350
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i
\(6\) 1.00000i 0.408248i
\(7\) −4.44055 −1.67837 −0.839185 0.543845i \(-0.816968\pi\)
−0.839185 + 0.543845i \(0.816968\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −2.44055 −0.735854 −0.367927 0.929855i \(-0.619932\pi\)
−0.367927 + 0.929855i \(0.619932\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0.440552i 0.122187i −0.998132 0.0610935i \(-0.980541\pi\)
0.998132 0.0610935i \(-0.0194588\pi\)
\(14\) 4.44055i 1.18679i
\(15\) 1.00000i 0.258199i
\(16\) 1.00000 0.250000
\(17\) 4.83740i 1.17324i 0.809862 + 0.586620i \(0.199542\pi\)
−0.809862 + 0.586620i \(0.800458\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.440552i 0.101069i 0.998722 + 0.0505347i \(0.0160926\pi\)
−0.998722 + 0.0505347i \(0.983907\pi\)
\(20\) 1.00000i 0.223607i
\(21\) −4.44055 −0.969008
\(22\) 2.44055i 0.520327i
\(23\) 2.83740i 0.591638i 0.955244 + 0.295819i \(0.0955925\pi\)
−0.955244 + 0.295819i \(0.904407\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −1.00000 −0.200000
\(26\) −0.440552 −0.0863993
\(27\) 1.00000 0.192450
\(28\) 4.44055 0.839185
\(29\) 2.00000i 0.371391i 0.982607 + 0.185695i \(0.0594537\pi\)
−0.982607 + 0.185695i \(0.940546\pi\)
\(30\) −1.00000 −0.182574
\(31\) 5.27795i 0.947947i 0.880539 + 0.473974i \(0.157181\pi\)
−0.880539 + 0.473974i \(0.842819\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.44055 −0.424846
\(34\) 4.83740 0.829607
\(35\) 4.44055i 0.750590i
\(36\) −1.00000 −0.166667
\(37\) −0.198422 + 6.07953i −0.0326204 + 0.999468i
\(38\) 0.440552 0.0714669
\(39\) 0.440552i 0.0705447i
\(40\) 1.00000 0.158114
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 4.44055i 0.685192i
\(43\) 0.396844i 0.0605182i −0.999542 0.0302591i \(-0.990367\pi\)
0.999542 0.0302591i \(-0.00963323\pi\)
\(44\) 2.44055 0.367927
\(45\) 1.00000i 0.149071i
\(46\) 2.83740 0.418351
\(47\) −10.8811 −1.58717 −0.793586 0.608458i \(-0.791788\pi\)
−0.793586 + 0.608458i \(0.791788\pi\)
\(48\) 1.00000 0.144338
\(49\) 12.7185 1.81693
\(50\) 1.00000i 0.141421i
\(51\) 4.83740i 0.677371i
\(52\) 0.440552i 0.0610935i
\(53\) −2.44055 −0.335236 −0.167618 0.985852i \(-0.553607\pi\)
−0.167618 + 0.985852i \(0.553607\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 2.44055i 0.329084i
\(56\) 4.44055i 0.593394i
\(57\) 0.440552i 0.0583525i
\(58\) 2.00000 0.262613
\(59\) 2.39684i 0.312043i −0.987754 0.156021i \(-0.950133\pi\)
0.987754 0.156021i \(-0.0498668\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 2.00000i 0.256074i 0.991769 + 0.128037i \(0.0408676\pi\)
−0.991769 + 0.128037i \(0.959132\pi\)
\(62\) 5.27795 0.670300
\(63\) −4.44055 −0.559457
\(64\) −1.00000 −0.125000
\(65\) −0.440552 −0.0546437
\(66\) 2.44055i 0.300411i
\(67\) −13.7622 −1.68132 −0.840661 0.541562i \(-0.817833\pi\)
−0.840661 + 0.541562i \(0.817833\pi\)
\(68\) 4.83740i 0.586620i
\(69\) 2.83740i 0.341582i
\(70\) 4.44055 0.530747
\(71\) −9.67479 −1.14819 −0.574093 0.818790i \(-0.694645\pi\)
−0.574093 + 0.818790i \(0.694645\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 5.71850 0.669300 0.334650 0.942343i \(-0.391382\pi\)
0.334650 + 0.942343i \(0.391382\pi\)
\(74\) 6.07953 + 0.198422i 0.706730 + 0.0230661i
\(75\) −1.00000 −0.115470
\(76\) 0.440552i 0.0505347i
\(77\) 10.8374 1.23504
\(78\) −0.440552 −0.0498827
\(79\) 13.2779i 1.49389i −0.664888 0.746943i \(-0.731521\pi\)
0.664888 0.746943i \(-0.268479\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) −7.71850 −0.847215 −0.423608 0.905846i \(-0.639236\pi\)
−0.423608 + 0.905846i \(0.639236\pi\)
\(84\) 4.44055 0.484504
\(85\) 4.83740 0.524689
\(86\) −0.396844 −0.0427928
\(87\) 2.00000i 0.214423i
\(88\) 2.44055i 0.260164i
\(89\) 15.3217i 1.62409i −0.583593 0.812046i \(-0.698354\pi\)
0.583593 0.812046i \(-0.301646\pi\)
\(90\) −1.00000 −0.105409
\(91\) 1.95629i 0.205075i
\(92\) 2.83740i 0.295819i
\(93\) 5.27795i 0.547298i
\(94\) 10.8811i 1.12230i
\(95\) 0.440552 0.0451996
\(96\) 1.00000i 0.102062i
\(97\) 2.88110i 0.292532i 0.989245 + 0.146266i \(0.0467255\pi\)
−0.989245 + 0.146266i \(0.953275\pi\)
\(98\) 12.7185i 1.28476i
\(99\) −2.44055 −0.245285
\(100\) 1.00000 0.100000
\(101\) −12.1591 −1.20987 −0.604935 0.796275i \(-0.706801\pi\)
−0.604935 + 0.796275i \(0.706801\pi\)
\(102\) 4.83740 0.478974
\(103\) 10.5559i 1.04010i 0.854135 + 0.520052i \(0.174087\pi\)
−0.854135 + 0.520052i \(0.825913\pi\)
\(104\) 0.440552 0.0431996
\(105\) 4.44055i 0.433353i
\(106\) 2.44055i 0.237047i
\(107\) 18.9248 1.82953 0.914765 0.403986i \(-0.132375\pi\)
0.914765 + 0.403986i \(0.132375\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 12.0437i 1.15358i 0.816893 + 0.576789i \(0.195695\pi\)
−0.816893 + 0.576789i \(0.804305\pi\)
\(110\) 2.44055 0.232697
\(111\) −0.198422 + 6.07953i −0.0188334 + 0.577043i
\(112\) −4.44055 −0.419593
\(113\) 2.00000i 0.188144i −0.995565 0.0940721i \(-0.970012\pi\)
0.995565 0.0940721i \(-0.0299884\pi\)
\(114\) 0.440552 0.0412614
\(115\) 2.83740 0.264589
\(116\) 2.00000i 0.185695i
\(117\) 0.440552i 0.0407290i
\(118\) −2.39684 −0.220647
\(119\) 21.4807i 1.96913i
\(120\) 1.00000 0.0912871
\(121\) −5.04371 −0.458519
\(122\) 2.00000 0.181071
\(123\) −2.00000 −0.180334
\(124\) 5.27795i 0.473974i
\(125\) 1.00000i 0.0894427i
\(126\) 4.44055i 0.395596i
\(127\) −7.55945 −0.670793 −0.335396 0.942077i \(-0.608870\pi\)
−0.335396 + 0.942077i \(0.608870\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.396844i 0.0349402i
\(130\) 0.440552i 0.0386389i
\(131\) 12.1591i 1.06234i −0.847265 0.531171i \(-0.821752\pi\)
0.847265 0.531171i \(-0.178248\pi\)
\(132\) 2.44055 0.212423
\(133\) 1.95629i 0.169632i
\(134\) 13.7622i 1.18887i
\(135\) 1.00000i 0.0860663i
\(136\) −4.83740 −0.414803
\(137\) 3.27795 0.280054 0.140027 0.990148i \(-0.455281\pi\)
0.140027 + 0.990148i \(0.455281\pi\)
\(138\) 2.83740 0.241535
\(139\) 5.76221 0.488744 0.244372 0.969682i \(-0.421418\pi\)
0.244372 + 0.969682i \(0.421418\pi\)
\(140\) 4.44055i 0.375295i
\(141\) −10.8811 −0.916354
\(142\) 9.67479i 0.811890i
\(143\) 1.07519i 0.0899118i
\(144\) 1.00000 0.0833333
\(145\) 2.00000 0.166091
\(146\) 5.71850i 0.473266i
\(147\) 12.7185 1.04900
\(148\) 0.198422 6.07953i 0.0163102 0.499734i
\(149\) 1.60316 0.131336 0.0656678 0.997842i \(-0.479082\pi\)
0.0656678 + 0.997842i \(0.479082\pi\)
\(150\) 1.00000i 0.0816497i
\(151\) 4.28150 0.348424 0.174212 0.984708i \(-0.444262\pi\)
0.174212 + 0.984708i \(0.444262\pi\)
\(152\) −0.440552 −0.0357335
\(153\) 4.83740i 0.391080i
\(154\) 10.8374i 0.873302i
\(155\) 5.27795 0.423935
\(156\) 0.440552i 0.0352724i
\(157\) 3.60316 0.287563 0.143782 0.989609i \(-0.454074\pi\)
0.143782 + 0.989609i \(0.454074\pi\)
\(158\) −13.2779 −1.05634
\(159\) −2.44055 −0.193548
\(160\) −1.00000 −0.0790569
\(161\) 12.5996i 0.992988i
\(162\) 1.00000i 0.0785674i
\(163\) 3.32165i 0.260172i 0.991503 + 0.130086i \(0.0415254\pi\)
−0.991503 + 0.130086i \(0.958475\pi\)
\(164\) 2.00000 0.156174
\(165\) 2.44055i 0.189997i
\(166\) 7.71850i 0.599072i
\(167\) 2.83740i 0.219564i −0.993956 0.109782i \(-0.964985\pi\)
0.993956 0.109782i \(-0.0350153\pi\)
\(168\) 4.44055i 0.342596i
\(169\) 12.8059 0.985070
\(170\) 4.83740i 0.371011i
\(171\) 0.440552i 0.0336898i
\(172\) 0.396844i 0.0302591i
\(173\) −12.9964 −0.988102 −0.494051 0.869433i \(-0.664484\pi\)
−0.494051 + 0.869433i \(0.664484\pi\)
\(174\) 2.00000 0.151620
\(175\) 4.44055 0.335674
\(176\) −2.44055 −0.183964
\(177\) 2.39684i 0.180158i
\(178\) −15.3217 −1.14841
\(179\) 4.72205i 0.352943i 0.984306 + 0.176471i \(0.0564683\pi\)
−0.984306 + 0.176471i \(0.943532\pi\)
\(180\) 1.00000i 0.0745356i
\(181\) 20.5559 1.52791 0.763954 0.645271i \(-0.223256\pi\)
0.763954 + 0.645271i \(0.223256\pi\)
\(182\) 1.95629 0.145010
\(183\) 2.00000i 0.147844i
\(184\) −2.83740 −0.209176
\(185\) 6.07953 + 0.198422i 0.446976 + 0.0145883i
\(186\) 5.27795 0.386998
\(187\) 11.8059i 0.863334i
\(188\) 10.8811 0.793586
\(189\) −4.44055 −0.323003
\(190\) 0.440552i 0.0319610i
\(191\) 9.16260i 0.662983i −0.943458 0.331491i \(-0.892448\pi\)
0.943458 0.331491i \(-0.107552\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 14.8811i 1.07117i 0.844483 + 0.535583i \(0.179908\pi\)
−0.844483 + 0.535583i \(0.820092\pi\)
\(194\) 2.88110 0.206851
\(195\) −0.440552 −0.0315486
\(196\) −12.7185 −0.908464
\(197\) −9.55945 −0.681082 −0.340541 0.940230i \(-0.610610\pi\)
−0.340541 + 0.940230i \(0.610610\pi\)
\(198\) 2.44055i 0.173442i
\(199\) 20.4843i 1.45209i 0.687647 + 0.726045i \(0.258644\pi\)
−0.687647 + 0.726045i \(0.741356\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −13.7622 −0.970711
\(202\) 12.1591i 0.855508i
\(203\) 8.88110i 0.623331i
\(204\) 4.83740i 0.338685i
\(205\) 2.00000i 0.139686i
\(206\) 10.5559 0.735464
\(207\) 2.83740i 0.197213i
\(208\) 0.440552i 0.0305468i
\(209\) 1.07519i 0.0743724i
\(210\) 4.44055 0.306427
\(211\) 0.881103 0.0606577 0.0303288 0.999540i \(-0.490345\pi\)
0.0303288 + 0.999540i \(0.490345\pi\)
\(212\) 2.44055 0.167618
\(213\) −9.67479 −0.662906
\(214\) 18.9248i 1.29367i
\(215\) −0.396844 −0.0270645
\(216\) 1.00000i 0.0680414i
\(217\) 23.4370i 1.59101i
\(218\) 12.0437 0.815703
\(219\) 5.71850 0.386420
\(220\) 2.44055i 0.164542i
\(221\) 2.13112 0.143355
\(222\) 6.07953 + 0.198422i 0.408031 + 0.0133172i
\(223\) 1.51574 0.101502 0.0507508 0.998711i \(-0.483839\pi\)
0.0507508 + 0.998711i \(0.483839\pi\)
\(224\) 4.44055i 0.296697i
\(225\) −1.00000 −0.0666667
\(226\) −2.00000 −0.133038
\(227\) 14.5559i 0.966109i 0.875590 + 0.483054i \(0.160473\pi\)
−0.875590 + 0.483054i \(0.839527\pi\)
\(228\) 0.440552i 0.0291762i
\(229\) 15.6748 1.03582 0.517910 0.855435i \(-0.326710\pi\)
0.517910 + 0.855435i \(0.326710\pi\)
\(230\) 2.83740i 0.187092i
\(231\) 10.8374 0.713048
\(232\) −2.00000 −0.131306
\(233\) −11.2779 −0.738843 −0.369421 0.929262i \(-0.620444\pi\)
−0.369421 + 0.929262i \(0.620444\pi\)
\(234\) −0.440552 −0.0287998
\(235\) 10.8811i 0.709805i
\(236\) 2.39684i 0.156021i
\(237\) 13.2779i 0.862495i
\(238\) −21.4807 −1.39239
\(239\) 22.5559i 1.45902i −0.683970 0.729510i \(-0.739748\pi\)
0.683970 0.729510i \(-0.260252\pi\)
\(240\) 1.00000i 0.0645497i
\(241\) 26.5559i 1.71062i −0.518120 0.855308i \(-0.673368\pi\)
0.518120 0.855308i \(-0.326632\pi\)
\(242\) 5.04371i 0.324222i
\(243\) 1.00000 0.0641500
\(244\) 2.00000i 0.128037i
\(245\) 12.7185i 0.812555i
\(246\) 2.00000i 0.127515i
\(247\) 0.194086 0.0123494
\(248\) −5.27795 −0.335150
\(249\) −7.71850 −0.489140
\(250\) 1.00000 0.0632456
\(251\) 3.27795i 0.206902i −0.994635 0.103451i \(-0.967011\pi\)
0.994635 0.103451i \(-0.0329885\pi\)
\(252\) 4.44055 0.279728
\(253\) 6.92481i 0.435359i
\(254\) 7.55945i 0.474322i
\(255\) 4.83740 0.302929
\(256\) 1.00000 0.0625000
\(257\) 20.0437i 1.25029i 0.780508 + 0.625146i \(0.214961\pi\)
−0.780508 + 0.625146i \(0.785039\pi\)
\(258\) −0.396844 −0.0247064
\(259\) 0.881103 26.9964i 0.0547491 1.67748i
\(260\) 0.440552 0.0273219
\(261\) 2.00000i 0.123797i
\(262\) −12.1591 −0.751189
\(263\) −17.4370 −1.07521 −0.537606 0.843196i \(-0.680671\pi\)
−0.537606 + 0.843196i \(0.680671\pi\)
\(264\) 2.44055i 0.150206i
\(265\) 2.44055i 0.149922i
\(266\) −1.95629 −0.119948
\(267\) 15.3217i 0.937670i
\(268\) 13.7622 0.840661
\(269\) −16.4406 −1.00240 −0.501199 0.865332i \(-0.667108\pi\)
−0.501199 + 0.865332i \(0.667108\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −24.3181 −1.47722 −0.738610 0.674133i \(-0.764517\pi\)
−0.738610 + 0.674133i \(0.764517\pi\)
\(272\) 4.83740i 0.293310i
\(273\) 1.95629i 0.118400i
\(274\) 3.27795i 0.198028i
\(275\) 2.44055 0.147171
\(276\) 2.83740i 0.170791i
\(277\) 0.353137i 0.0212179i 0.999944 + 0.0106090i \(0.00337700\pi\)
−0.999944 + 0.0106090i \(0.996623\pi\)
\(278\) 5.76221i 0.345594i
\(279\) 5.27795i 0.315982i
\(280\) −4.44055 −0.265374
\(281\) 20.2028i 1.20520i −0.798045 0.602598i \(-0.794132\pi\)
0.798045 0.602598i \(-0.205868\pi\)
\(282\) 10.8811i 0.647960i
\(283\) 13.6469i 0.811222i −0.914046 0.405611i \(-0.867059\pi\)
0.914046 0.405611i \(-0.132941\pi\)
\(284\) 9.67479 0.574093
\(285\) 0.440552 0.0260960
\(286\) 1.07519 0.0635773
\(287\) 8.88110 0.524235
\(288\) 1.00000i 0.0589256i
\(289\) −6.40040 −0.376494
\(290\) 2.00000i 0.117444i
\(291\) 2.88110i 0.168893i
\(292\) −5.71850 −0.334650
\(293\) −6.44055 −0.376261 −0.188131 0.982144i \(-0.560243\pi\)
−0.188131 + 0.982144i \(0.560243\pi\)
\(294\) 12.7185i 0.741758i
\(295\) −2.39684 −0.139550
\(296\) −6.07953 0.198422i −0.353365 0.0115330i
\(297\) −2.44055 −0.141615
\(298\) 1.60316i 0.0928683i
\(299\) 1.25002 0.0722905
\(300\) 1.00000 0.0577350
\(301\) 1.76221i 0.101572i
\(302\) 4.28150i 0.246373i
\(303\) −12.1591 −0.698519
\(304\) 0.440552i 0.0252674i
\(305\) 2.00000 0.114520
\(306\) 4.83740 0.276536
\(307\) −20.3181 −1.15962 −0.579808 0.814753i \(-0.696872\pi\)
−0.579808 + 0.814753i \(0.696872\pi\)
\(308\) −10.8374 −0.617518
\(309\) 10.5559i 0.600504i
\(310\) 5.27795i 0.299767i
\(311\) 6.23779i 0.353713i 0.984237 + 0.176856i \(0.0565928\pi\)
−0.984237 + 0.176856i \(0.943407\pi\)
\(312\) 0.440552 0.0249413
\(313\) 8.55589i 0.483608i −0.970325 0.241804i \(-0.922261\pi\)
0.970325 0.241804i \(-0.0777391\pi\)
\(314\) 3.60316i 0.203338i
\(315\) 4.44055i 0.250197i
\(316\) 13.2779i 0.746943i
\(317\) −33.5960 −1.88694 −0.943471 0.331455i \(-0.892461\pi\)
−0.943471 + 0.331455i \(0.892461\pi\)
\(318\) 2.44055i 0.136859i
\(319\) 4.88110i 0.273289i
\(320\) 1.00000i 0.0559017i
\(321\) 18.9248 1.05628
\(322\) −12.5996 −0.702148
\(323\) −2.13112 −0.118579
\(324\) −1.00000 −0.0555556
\(325\) 0.440552i 0.0244374i
\(326\) 3.32165 0.183969
\(327\) 12.0437i 0.666019i
\(328\) 2.00000i 0.110432i
\(329\) 48.3181 2.66386
\(330\) 2.44055 0.134348
\(331\) 31.2779i 1.71919i 0.510975 + 0.859596i \(0.329285\pi\)
−0.510975 + 0.859596i \(0.670715\pi\)
\(332\) 7.71850 0.423608
\(333\) −0.198422 + 6.07953i −0.0108735 + 0.333156i
\(334\) −2.83740 −0.155255
\(335\) 13.7622i 0.751910i
\(336\) −4.44055 −0.242252
\(337\) −5.63108 −0.306745 −0.153372 0.988168i \(-0.549013\pi\)
−0.153372 + 0.988168i \(0.549013\pi\)
\(338\) 12.8059i 0.696550i
\(339\) 2.00000i 0.108625i
\(340\) −4.83740 −0.262345
\(341\) 12.8811i 0.697551i
\(342\) 0.440552 0.0238223
\(343\) −25.3933 −1.37111
\(344\) 0.396844 0.0213964
\(345\) 2.83740 0.152760
\(346\) 12.9964i 0.698693i
\(347\) 0.881103i 0.0473001i 0.999720 + 0.0236501i \(0.00752875\pi\)
−0.999720 + 0.0236501i \(0.992471\pi\)
\(348\) 2.00000i 0.107211i
\(349\) 0.555895 0.0297564 0.0148782 0.999889i \(-0.495264\pi\)
0.0148782 + 0.999889i \(0.495264\pi\)
\(350\) 4.44055i 0.237357i
\(351\) 0.440552i 0.0235149i
\(352\) 2.44055i 0.130082i
\(353\) 5.20631i 0.277104i −0.990355 0.138552i \(-0.955755\pi\)
0.990355 0.138552i \(-0.0442448\pi\)
\(354\) −2.39684 −0.127391
\(355\) 9.67479i 0.513485i
\(356\) 15.3217i 0.812046i
\(357\) 21.4807i 1.13688i
\(358\) 4.72205 0.249568
\(359\) −15.4370 −0.814734 −0.407367 0.913265i \(-0.633553\pi\)
−0.407367 + 0.913265i \(0.633553\pi\)
\(360\) 1.00000 0.0527046
\(361\) 18.8059 0.989785
\(362\) 20.5559i 1.08039i
\(363\) −5.04371 −0.264726
\(364\) 1.95629i 0.102538i
\(365\) 5.71850i 0.299320i
\(366\) 2.00000 0.104542
\(367\) −14.9964 −0.782808 −0.391404 0.920219i \(-0.628011\pi\)
−0.391404 + 0.920219i \(0.628011\pi\)
\(368\) 2.83740i 0.147909i
\(369\) −2.00000 −0.104116
\(370\) 0.198422 6.07953i 0.0103155 0.316059i
\(371\) 10.8374 0.562650
\(372\) 5.27795i 0.273649i
\(373\) 33.5086 1.73501 0.867506 0.497427i \(-0.165722\pi\)
0.867506 + 0.497427i \(0.165722\pi\)
\(374\) −11.8059 −0.610469
\(375\) 1.00000i 0.0516398i
\(376\) 10.8811i 0.561150i
\(377\) 0.881103 0.0453791
\(378\) 4.44055i 0.228397i
\(379\) 34.6433 1.77951 0.889754 0.456441i \(-0.150876\pi\)
0.889754 + 0.456441i \(0.150876\pi\)
\(380\) −0.440552 −0.0225998
\(381\) −7.55945 −0.387282
\(382\) −9.16260 −0.468800
\(383\) 8.51219i 0.434952i 0.976066 + 0.217476i \(0.0697825\pi\)
−0.976066 + 0.217476i \(0.930218\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 10.8374i 0.552325i
\(386\) 14.8811 0.757428
\(387\) 0.396844i 0.0201727i
\(388\) 2.88110i 0.146266i
\(389\) 27.6748i 1.40317i 0.712587 + 0.701584i \(0.247523\pi\)
−0.712587 + 0.701584i \(0.752477\pi\)
\(390\) 0.440552i 0.0223082i
\(391\) −13.7256 −0.694134
\(392\) 12.7185i 0.642381i
\(393\) 12.1591i 0.613343i
\(394\) 9.55945i 0.481598i
\(395\) −13.2779 −0.668086
\(396\) 2.44055 0.122642
\(397\) 9.36536 0.470034 0.235017 0.971991i \(-0.424485\pi\)
0.235017 + 0.971991i \(0.424485\pi\)
\(398\) 20.4843 1.02678
\(399\) 1.95629i 0.0979371i
\(400\) −1.00000 −0.0500000
\(401\) 7.88466i 0.393741i 0.980430 + 0.196870i \(0.0630778\pi\)
−0.980430 + 0.196870i \(0.936922\pi\)
\(402\) 13.7622i 0.686396i
\(403\) 2.32521 0.115827
\(404\) 12.1591 0.604935
\(405\) 1.00000i 0.0496904i
\(406\) −8.88110 −0.440762
\(407\) 0.484259 14.8374i 0.0240038 0.735462i
\(408\) −4.83740 −0.239487
\(409\) 38.7307i 1.91511i 0.288249 + 0.957556i \(0.406927\pi\)
−0.288249 + 0.957556i \(0.593073\pi\)
\(410\) 2.00000 0.0987730
\(411\) 3.27795 0.161689
\(412\) 10.5559i 0.520052i
\(413\) 10.6433i 0.523723i
\(414\) 2.83740 0.139450
\(415\) 7.71850i 0.378886i
\(416\) −0.440552 −0.0215998
\(417\) 5.76221 0.282176
\(418\) −1.07519 −0.0525892
\(419\) 34.6712 1.69380 0.846900 0.531752i \(-0.178466\pi\)
0.846900 + 0.531752i \(0.178466\pi\)
\(420\) 4.44055i 0.216677i
\(421\) 23.1118i 1.12640i −0.826321 0.563200i \(-0.809570\pi\)
0.826321 0.563200i \(-0.190430\pi\)
\(422\) 0.881103i 0.0428914i
\(423\) −10.8811 −0.529057
\(424\) 2.44055i 0.118524i
\(425\) 4.83740i 0.234648i
\(426\) 9.67479i 0.468745i
\(427\) 8.88110i 0.429787i
\(428\) −18.9248 −0.914765
\(429\) 1.07519i 0.0519106i
\(430\) 0.396844i 0.0191375i
\(431\) 9.95629i 0.479578i −0.970825 0.239789i \(-0.922922\pi\)
0.970825 0.239789i \(-0.0770782\pi\)
\(432\) 1.00000 0.0481125
\(433\) −8.04371 −0.386556 −0.193278 0.981144i \(-0.561912\pi\)
−0.193278 + 0.981144i \(0.561912\pi\)
\(434\) −23.4370 −1.12501
\(435\) 2.00000 0.0958927
\(436\) 12.0437i 0.576789i
\(437\) −1.25002 −0.0597965
\(438\) 5.71850i 0.273240i
\(439\) 13.2779i 0.633722i −0.948472 0.316861i \(-0.897371\pi\)
0.948472 0.316861i \(-0.102629\pi\)
\(440\) −2.44055 −0.116349
\(441\) 12.7185 0.605643
\(442\) 2.13112i 0.101367i
\(443\) −2.41262 −0.114627 −0.0573136 0.998356i \(-0.518253\pi\)
−0.0573136 + 0.998356i \(0.518253\pi\)
\(444\) 0.198422 6.07953i 0.00941669 0.288522i
\(445\) −15.3217 −0.726316
\(446\) 1.51574i 0.0717724i
\(447\) 1.60316 0.0758267
\(448\) 4.44055 0.209796
\(449\) 22.2465i 1.04988i 0.851141 + 0.524938i \(0.175911\pi\)
−0.851141 + 0.524938i \(0.824089\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 4.88110 0.229842
\(452\) 2.00000i 0.0940721i
\(453\) 4.28150 0.201162
\(454\) 14.5559 0.683142
\(455\) 1.95629 0.0917124
\(456\) −0.440552 −0.0206307
\(457\) 20.5559i 0.961564i −0.876840 0.480782i \(-0.840353\pi\)
0.876840 0.480782i \(-0.159647\pi\)
\(458\) 15.6748i 0.732435i
\(459\) 4.83740i 0.225790i
\(460\) −2.83740 −0.132294
\(461\) 12.6433i 0.588858i 0.955673 + 0.294429i \(0.0951294\pi\)
−0.955673 + 0.294429i \(0.904871\pi\)
\(462\) 10.8374i 0.504201i
\(463\) 32.4055i 1.50601i 0.658014 + 0.753006i \(0.271397\pi\)
−0.658014 + 0.753006i \(0.728603\pi\)
\(464\) 2.00000i 0.0928477i
\(465\) 5.27795 0.244759
\(466\) 11.2779i 0.522441i
\(467\) 26.5559i 1.22886i −0.788971 0.614430i \(-0.789386\pi\)
0.788971 0.614430i \(-0.210614\pi\)
\(468\) 0.440552i 0.0203645i
\(469\) 61.1118 2.82188
\(470\) 10.8811 0.501908
\(471\) 3.60316 0.166025
\(472\) 2.39684 0.110324
\(473\) 0.968518i 0.0445325i
\(474\) −13.2779 −0.609876
\(475\) 0.440552i 0.0202139i
\(476\) 21.4807i 0.984567i
\(477\) −2.44055 −0.111745
\(478\) −22.5559 −1.03168
\(479\) 31.0122i 1.41698i −0.705718 0.708492i \(-0.749376\pi\)
0.705718 0.708492i \(-0.250624\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 2.67835 + 0.0874152i 0.122122 + 0.00398579i
\(482\) −26.5559 −1.20959
\(483\) 12.5996i 0.573302i
\(484\) 5.04371 0.229259
\(485\) 2.88110 0.130824
\(486\) 1.00000i 0.0453609i
\(487\) 7.20631i 0.326549i −0.986581 0.163275i \(-0.947794\pi\)
0.986581 0.163275i \(-0.0522056\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 3.32165i 0.150210i
\(490\) −12.7185 −0.574563
\(491\) 2.44055 0.110141 0.0550703 0.998482i \(-0.482462\pi\)
0.0550703 + 0.998482i \(0.482462\pi\)
\(492\) 2.00000 0.0901670
\(493\) −9.67479 −0.435731
\(494\) 0.194086i 0.00873233i
\(495\) 2.44055i 0.109695i
\(496\) 5.27795i 0.236987i
\(497\) 42.9614 1.92708
\(498\) 7.71850i 0.345874i
\(499\) 36.7587i 1.64554i 0.568372 + 0.822772i \(0.307573\pi\)
−0.568372 + 0.822772i \(0.692427\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 2.83740i 0.126765i
\(502\) −3.27795 −0.146302
\(503\) 29.1118i 1.29803i 0.760775 + 0.649015i \(0.224819\pi\)
−0.760775 + 0.649015i \(0.775181\pi\)
\(504\) 4.44055i 0.197798i
\(505\) 12.1591i 0.541071i
\(506\) −6.92481 −0.307845
\(507\) 12.8059 0.568731
\(508\) 7.55945 0.335396
\(509\) 6.90903 0.306237 0.153119 0.988208i \(-0.451068\pi\)
0.153119 + 0.988208i \(0.451068\pi\)
\(510\) 4.83740i 0.214203i
\(511\) −25.3933 −1.12333
\(512\) 1.00000i 0.0441942i
\(513\) 0.440552i 0.0194508i
\(514\) 20.0437 0.884090
\(515\) 10.5559 0.465148
\(516\) 0.396844i 0.0174701i
\(517\) 26.5559 1.16793
\(518\) −26.9964 0.881103i −1.18616 0.0387135i
\(519\) −12.9964 −0.570481
\(520\) 0.440552i 0.0193195i
\(521\) 40.5559 1.77679 0.888393 0.459084i \(-0.151822\pi\)
0.888393 + 0.459084i \(0.151822\pi\)
\(522\) 2.00000 0.0875376
\(523\) 42.4772i 1.85740i −0.370837 0.928698i \(-0.620929\pi\)
0.370837 0.928698i \(-0.379071\pi\)
\(524\) 12.1591i 0.531171i
\(525\) 4.44055 0.193802
\(526\) 17.4370i 0.760289i
\(527\) −25.5315 −1.11217
\(528\) −2.44055 −0.106211
\(529\) 14.9492 0.649965
\(530\) 2.44055 0.106011
\(531\) 2.39684i 0.104014i
\(532\) 1.95629i 0.0848160i
\(533\) 0.881103i 0.0381648i
\(534\) −15.3217 −0.663033
\(535\) 18.9248i 0.818191i
\(536\) 13.7622i 0.594437i
\(537\) 4.72205i 0.203772i
\(538\) 16.4406i 0.708803i
\(539\) −31.0402 −1.33699
\(540\) 1.00000i 0.0430331i
\(541\) 20.0437i 0.861746i −0.902413 0.430873i \(-0.858206\pi\)
0.902413 0.430873i \(-0.141794\pi\)
\(542\) 24.3181i 1.04455i
\(543\) 20.5559 0.882138
\(544\) 4.83740 0.207402
\(545\) 12.0437 0.515896
\(546\) 1.95629 0.0837216
\(547\) 20.1153i 0.860070i 0.902812 + 0.430035i \(0.141499\pi\)
−0.902812 + 0.430035i \(0.858501\pi\)
\(548\) −3.27795 −0.140027
\(549\) 2.00000i 0.0853579i
\(550\) 2.44055i 0.104065i
\(551\) −0.881103 −0.0375363
\(552\) −2.83740 −0.120768
\(553\) 58.9614i 2.50729i
\(554\) 0.353137 0.0150033
\(555\) 6.07953 + 0.198422i 0.258061 + 0.00842255i
\(556\) −5.76221 −0.244372
\(557\) 11.7622i 0.498381i 0.968455 + 0.249190i \(0.0801645\pi\)
−0.968455 + 0.249190i \(0.919836\pi\)
\(558\) 5.27795 0.223433
\(559\) −0.174830 −0.00739453
\(560\) 4.44055i 0.187648i
\(561\) 11.8059i 0.498446i
\(562\) −20.2028 −0.852202
\(563\) 42.9614i 1.81061i 0.424765 + 0.905304i \(0.360357\pi\)
−0.424765 + 0.905304i \(0.639643\pi\)
\(564\) 10.8811 0.458177
\(565\) −2.00000 −0.0841406
\(566\) −13.6469 −0.573620
\(567\) −4.44055 −0.186486
\(568\) 9.67479i 0.405945i
\(569\) 41.8775i 1.75560i 0.479029 + 0.877799i \(0.340989\pi\)
−0.479029 + 0.877799i \(0.659011\pi\)
\(570\) 0.440552i 0.0184527i
\(571\) −37.7622 −1.58030 −0.790150 0.612914i \(-0.789997\pi\)
−0.790150 + 0.612914i \(0.789997\pi\)
\(572\) 1.07519i 0.0449559i
\(573\) 9.16260i 0.382773i
\(574\) 8.88110i 0.370690i
\(575\) 2.83740i 0.118328i
\(576\) −1.00000 −0.0416667
\(577\) 2.56300i 0.106699i 0.998576 + 0.0533496i \(0.0169898\pi\)
−0.998576 + 0.0533496i \(0.983010\pi\)
\(578\) 6.40040i 0.266221i
\(579\) 14.8811i 0.618438i
\(580\) −2.00000 −0.0830455
\(581\) 34.2744 1.42194
\(582\) 2.88110 0.119426
\(583\) 5.95629 0.246684
\(584\) 5.71850i 0.236633i
\(585\) −0.440552 −0.0182146
\(586\) 6.44055i 0.266057i
\(587\) 45.1992i 1.86557i 0.360432 + 0.932785i \(0.382629\pi\)
−0.360432 + 0.932785i \(0.617371\pi\)
\(588\) −12.7185 −0.524502
\(589\) −2.32521 −0.0958085
\(590\) 2.39684i 0.0986765i
\(591\) −9.55945 −0.393223
\(592\) −0.198422 + 6.07953i −0.00815510 + 0.249867i
\(593\) 43.5086 1.78669 0.893343 0.449376i \(-0.148354\pi\)
0.893343 + 0.449376i \(0.148354\pi\)
\(594\) 2.44055i 0.100137i
\(595\) −21.4807 −0.880623
\(596\) −1.60316 −0.0656678
\(597\) 20.4843i 0.838365i
\(598\) 1.25002i 0.0511171i
\(599\) 26.6433 1.08862 0.544308 0.838885i \(-0.316792\pi\)
0.544308 + 0.838885i \(0.316792\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 0.924811 0.0377238 0.0188619 0.999822i \(-0.493996\pi\)
0.0188619 + 0.999822i \(0.493996\pi\)
\(602\) 1.76221 0.0718222
\(603\) −13.7622 −0.560440
\(604\) −4.28150 −0.174212
\(605\) 5.04371i 0.205056i
\(606\) 12.1591i 0.493928i
\(607\) 2.55589i 0.103741i 0.998654 + 0.0518703i \(0.0165182\pi\)
−0.998654 + 0.0518703i \(0.983482\pi\)
\(608\) 0.440552 0.0178667
\(609\) 8.88110i 0.359880i
\(610\) 2.00000i 0.0809776i
\(611\) 4.79369i 0.193932i
\(612\) 4.83740i 0.195540i
\(613\) 10.1591 0.410320 0.205160 0.978728i \(-0.434228\pi\)
0.205160 + 0.978728i \(0.434228\pi\)
\(614\) 20.3181i 0.819972i
\(615\) 2.00000i 0.0806478i
\(616\) 10.8374i 0.436651i
\(617\) −12.1591 −0.489505 −0.244752 0.969586i \(-0.578707\pi\)
−0.244752 + 0.969586i \(0.578707\pi\)
\(618\) 10.5559 0.424620
\(619\) 23.5244 0.945526 0.472763 0.881190i \(-0.343257\pi\)
0.472763 + 0.881190i \(0.343257\pi\)
\(620\) −5.27795 −0.211967
\(621\) 2.83740i 0.113861i
\(622\) 6.23779 0.250113
\(623\) 68.0366i 2.72583i
\(624\) 0.440552i 0.0176362i
\(625\) 1.00000 0.0400000
\(626\) −8.55589 −0.341962
\(627\) 1.07519i 0.0429389i
\(628\) −3.60316 −0.143782
\(629\) −29.4091 0.959846i −1.17262 0.0382716i
\(630\) 4.44055 0.176916
\(631\) 3.60316i 0.143439i −0.997425 0.0717197i \(-0.977151\pi\)
0.997425 0.0717197i \(-0.0228487\pi\)
\(632\) 13.2779 0.528168
\(633\) 0.881103 0.0350207
\(634\) 33.5960i 1.33427i
\(635\) 7.55945i 0.299988i
\(636\) 2.44055 0.0967742
\(637\) 5.60316i 0.222005i
\(638\) −4.88110 −0.193245
\(639\) −9.67479 −0.382729
\(640\) 1.00000 0.0395285
\(641\) −37.4370 −1.47867 −0.739336 0.673336i \(-0.764861\pi\)
−0.739336 + 0.673336i \(0.764861\pi\)
\(642\) 18.9248i 0.746903i
\(643\) 0.678345i 0.0267513i 0.999911 + 0.0133757i \(0.00425773\pi\)
−0.999911 + 0.0133757i \(0.995742\pi\)
\(644\) 12.5996i 0.496494i
\(645\) −0.396844 −0.0156257
\(646\) 2.13112i 0.0838479i
\(647\) 6.92481i 0.272242i 0.990692 + 0.136121i \(0.0434637\pi\)
−0.990692 + 0.136121i \(0.956536\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 5.84962i 0.229618i
\(650\) 0.440552 0.0172799
\(651\) 23.4370i 0.918568i
\(652\) 3.32165i 0.130086i
\(653\) 15.4441i 0.604375i −0.953249 0.302187i \(-0.902283\pi\)
0.953249 0.302187i \(-0.0977168\pi\)
\(654\) 12.0437 0.470946
\(655\) −12.1591 −0.475093
\(656\) −2.00000 −0.0780869
\(657\) 5.71850 0.223100
\(658\) 48.3181i 1.88364i
\(659\) −18.9527 −0.738294 −0.369147 0.929371i \(-0.620350\pi\)
−0.369147 + 0.929371i \(0.620350\pi\)
\(660\) 2.44055i 0.0949983i
\(661\) 36.3618i 1.41431i 0.707058 + 0.707155i \(0.250022\pi\)
−0.707058 + 0.707155i \(0.749978\pi\)
\(662\) 31.2779 1.21565
\(663\) 2.13112 0.0827659
\(664\) 7.71850i 0.299536i
\(665\) −1.95629 −0.0758618
\(666\) 6.07953 + 0.198422i 0.235577 + 0.00768870i
\(667\) −5.67479 −0.219729
\(668\) 2.83740i 0.109782i
\(669\) 1.51574 0.0586019
\(670\) 13.7622 0.531680
\(671\) 4.88110i 0.188433i
\(672\) 4.44055i 0.171298i
\(673\) 9.80591 0.377990 0.188995 0.981978i \(-0.439477\pi\)
0.188995 + 0.981978i \(0.439477\pi\)
\(674\) 5.63108i 0.216901i
\(675\) −1.00000 −0.0384900
\(676\) −12.8059 −0.492535
\(677\) 28.2902 1.08728 0.543640 0.839319i \(-0.317046\pi\)
0.543640 + 0.839319i \(0.317046\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 12.7937i 0.490977i
\(680\) 4.83740i 0.185506i
\(681\) 14.5559i 0.557783i
\(682\) −12.8811 −0.493243
\(683\) 24.3181i 0.930506i 0.885178 + 0.465253i \(0.154037\pi\)
−0.885178 + 0.465253i \(0.845963\pi\)
\(684\) 0.440552i 0.0168449i
\(685\) 3.27795i 0.125244i
\(686\) 25.3933i 0.969520i
\(687\) 15.6748 0.598031
\(688\) 0.396844i 0.0151295i
\(689\) 1.07519i 0.0409614i
\(690\) 2.83740i 0.108018i
\(691\) 5.53152 0.210429 0.105214 0.994450i \(-0.466447\pi\)
0.105214 + 0.994450i \(0.466447\pi\)
\(692\) 12.9964 0.494051
\(693\) 10.8374 0.411679
\(694\) 0.881103 0.0334462
\(695\) 5.76221i 0.218573i
\(696\) −2.00000 −0.0758098
\(697\) 9.67479i 0.366459i
\(698\) 0.555895i 0.0210409i
\(699\) −11.2779 −0.426571
\(700\) −4.44055 −0.167837
\(701\) 23.6748i 0.894185i 0.894488 + 0.447092i \(0.147540\pi\)
−0.894488 + 0.447092i \(0.852460\pi\)
\(702\) −0.440552 −0.0166276
\(703\) −2.67835 0.0874152i −0.101016 0.00329693i
\(704\) 2.44055 0.0919818
\(705\) 10.8811i 0.409806i
\(706\) −5.20631 −0.195942
\(707\) 53.9929 2.03061
\(708\) 2.39684i 0.0900789i
\(709\) 3.07519i 0.115491i −0.998331 0.0577456i \(-0.981609\pi\)
0.998331 0.0577456i \(-0.0183912\pi\)
\(710\) 9.67479 0.363088
\(711\) 13.2779i 0.497962i
\(712\) 15.3217 0.574203
\(713\) −14.9756 −0.560842
\(714\) −21.4807 −0.803895
\(715\) 1.07519 0.0402098
\(716\) 4.72205i 0.176471i
\(717\) 22.5559i 0.842365i
\(718\) 15.4370i 0.576104i
\(719\) −31.3496 −1.16914 −0.584571 0.811342i \(-0.698737\pi\)
−0.584571 + 0.811342i \(0.698737\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 46.8740i 1.74568i
\(722\) 18.8059i 0.699884i
\(723\) 26.5559i 0.987624i
\(724\) −20.5559 −0.763954
\(725\) 2.00000i 0.0742781i
\(726\) 5.04371i 0.187190i
\(727\) 20.0874i 0.745001i 0.928032 + 0.372500i \(0.121500\pi\)
−0.928032 + 0.372500i \(0.878500\pi\)
\(728\) −1.95629 −0.0725050
\(729\) 1.00000 0.0370370
\(730\) −5.71850 −0.211651
\(731\) 1.91969 0.0710024
\(732\) 2.00000i 0.0739221i
\(733\) 7.83384 0.289350 0.144675 0.989479i \(-0.453786\pi\)
0.144675 + 0.989479i \(0.453786\pi\)
\(734\) 14.9964i 0.553529i
\(735\) 12.7185i 0.469129i
\(736\) 2.83740 0.104588
\(737\) 33.5874 1.23721
\(738\) 2.00000i 0.0736210i
\(739\) −52.6362 −1.93625 −0.968127 0.250460i \(-0.919418\pi\)
−0.968127 + 0.250460i \(0.919418\pi\)
\(740\) −6.07953 0.198422i −0.223488 0.00729414i
\(741\) 0.194086 0.00712992
\(742\) 10.8374i 0.397853i
\(743\) −8.55589 −0.313885 −0.156943 0.987608i \(-0.550164\pi\)
−0.156943 + 0.987608i \(0.550164\pi\)
\(744\) −5.27795 −0.193499
\(745\) 1.60316i 0.0587351i
\(746\) 33.5086i 1.22684i
\(747\) −7.71850 −0.282405
\(748\) 11.8059i 0.431667i
\(749\) −84.0366 −3.07063
\(750\) 1.00000 0.0365148
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) −10.8811 −0.396793
\(753\) 3.27795i 0.119455i
\(754\) 0.881103i 0.0320879i
\(755\) 4.28150i 0.155820i
\(756\) 4.44055 0.161501
\(757\) 39.4020i 1.43209i −0.698055 0.716044i \(-0.745951\pi\)
0.698055 0.716044i \(-0.254049\pi\)
\(758\) 34.6433i 1.25830i
\(759\) 6.92481i 0.251355i
\(760\) 0.440552i 0.0159805i
\(761\) −40.5559 −1.47015 −0.735075 0.677986i \(-0.762853\pi\)
−0.735075 + 0.677986i \(0.762853\pi\)
\(762\) 7.55945i 0.273850i
\(763\) 53.4807i 1.93613i
\(764\) 9.16260i 0.331491i
\(765\) 4.83740 0.174896
\(766\) 8.51219 0.307558
\(767\) −1.05593 −0.0381276
\(768\) 1.00000 0.0360844
\(769\) 4.08742i 0.147396i 0.997281 + 0.0736980i \(0.0234801\pi\)
−0.997281 + 0.0736980i \(0.976520\pi\)
\(770\) −10.8374 −0.390553
\(771\) 20.0437i 0.721856i
\(772\) 14.8811i 0.535583i
\(773\) 24.6783 0.887618 0.443809 0.896121i \(-0.353627\pi\)
0.443809 + 0.896121i \(0.353627\pi\)
\(774\) −0.396844 −0.0142643
\(775\) 5.27795i 0.189589i
\(776\) −2.88110 −0.103426
\(777\) 0.881103 26.9964i 0.0316094 0.968492i
\(778\) 27.6748 0.992189
\(779\) 0.881103i 0.0315688i
\(780\) 0.440552 0.0157743
\(781\) 23.6118 0.844898
\(782\) 13.7256i 0.490827i
\(783\) 2.00000i 0.0714742i
\(784\) 12.7185 0.454232
\(785\) 3.60316i 0.128602i
\(786\) −12.1591 −0.433699
\(787\) −37.1992 −1.32601 −0.663004 0.748616i \(-0.730719\pi\)
−0.663004 + 0.748616i \(0.730719\pi\)
\(788\) 9.55945 0.340541
\(789\) −17.4370 −0.620774
\(790\) 13.2779i 0.472408i
\(791\) 8.88110i 0.315776i
\(792\) 2.44055i 0.0867212i
\(793\) 0.881103 0.0312889