Properties

Label 230.3.d.a.91.13
Level $230$
Weight $3$
Character 230.91
Analytic conductor $6.267$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.13
Root \(-2.26343i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.14

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} +1.43837 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.03417 q^{6} -10.1866i q^{7} +2.82843 q^{8} -6.93108 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +1.43837 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.03417 q^{6} -10.1866i q^{7} +2.82843 q^{8} -6.93108 q^{9} -3.16228i q^{10} -13.0237i q^{11} +2.87675 q^{12} +23.2154 q^{13} -14.4060i q^{14} -3.21630i q^{15} +4.00000 q^{16} +28.2228i q^{17} -9.80202 q^{18} +11.6665i q^{19} -4.47214i q^{20} -14.6521i q^{21} -18.4183i q^{22} +(-17.3999 + 15.0414i) q^{23} +4.06834 q^{24} -5.00000 q^{25} +32.8315 q^{26} -22.9149 q^{27} -20.3731i q^{28} +42.4794 q^{29} -4.54854i q^{30} +18.7683 q^{31} +5.65685 q^{32} -18.7330i q^{33} +39.9131i q^{34} -22.7778 q^{35} -13.8622 q^{36} +1.14094i q^{37} +16.4989i q^{38} +33.3924 q^{39} -6.32456i q^{40} -72.8198 q^{41} -20.7212i q^{42} +4.96573i q^{43} -26.0474i q^{44} +15.4984i q^{45} +(-24.6071 + 21.2718i) q^{46} -0.813360 q^{47} +5.75350 q^{48} -54.7661 q^{49} -7.07107 q^{50} +40.5950i q^{51} +46.4308 q^{52} -26.7286i q^{53} -32.4065 q^{54} -29.1219 q^{55} -28.8120i q^{56} +16.7808i q^{57} +60.0750 q^{58} +94.0845 q^{59} -6.43261i q^{60} +74.5293i q^{61} +26.5423 q^{62} +70.6039i q^{63} +8.00000 q^{64} -51.9112i q^{65} -26.4925i q^{66} -80.0906i q^{67} +56.4456i q^{68} +(-25.0275 + 21.6352i) q^{69} -32.2127 q^{70} -83.5303 q^{71} -19.6040 q^{72} -8.98897 q^{73} +1.61354i q^{74} -7.19187 q^{75} +23.3330i q^{76} -132.667 q^{77} +47.2241 q^{78} +80.2841i q^{79} -8.94427i q^{80} +29.4195 q^{81} -102.983 q^{82} +94.6451i q^{83} -29.3042i q^{84} +63.1081 q^{85} +7.02261i q^{86} +61.1014 q^{87} -36.8367i q^{88} +136.812i q^{89} +21.9180i q^{90} -236.485i q^{91} +(-34.7997 + 30.0829i) q^{92} +26.9958 q^{93} -1.15026 q^{94} +26.0871 q^{95} +8.13668 q^{96} +2.32666i q^{97} -77.4509 q^{98} +90.2684i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) 1.43837 0.479458 0.239729 0.970840i \(-0.422941\pi\)
0.239729 + 0.970840i \(0.422941\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) 2.03417 0.339028
\(7\) 10.1866i 1.45522i −0.685989 0.727612i \(-0.740630\pi\)
0.685989 0.727612i \(-0.259370\pi\)
\(8\) 2.82843 0.353553
\(9\) −6.93108 −0.770120
\(10\) 3.16228i 0.316228i
\(11\) 13.0237i 1.18397i −0.805947 0.591987i \(-0.798343\pi\)
0.805947 0.591987i \(-0.201657\pi\)
\(12\) 2.87675 0.239729
\(13\) 23.2154 1.78580 0.892900 0.450255i \(-0.148667\pi\)
0.892900 + 0.450255i \(0.148667\pi\)
\(14\) 14.4060i 1.02900i
\(15\) 3.21630i 0.214420i
\(16\) 4.00000 0.250000
\(17\) 28.2228i 1.66016i 0.557641 + 0.830082i \(0.311707\pi\)
−0.557641 + 0.830082i \(0.688293\pi\)
\(18\) −9.80202 −0.544557
\(19\) 11.6665i 0.614027i 0.951705 + 0.307013i \(0.0993297\pi\)
−0.951705 + 0.307013i \(0.900670\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 14.6521i 0.697719i
\(22\) 18.4183i 0.837197i
\(23\) −17.3999 + 15.0414i −0.756516 + 0.653976i
\(24\) 4.06834 0.169514
\(25\) −5.00000 −0.200000
\(26\) 32.8315 1.26275
\(27\) −22.9149 −0.848699
\(28\) 20.3731i 0.727612i
\(29\) 42.4794 1.46481 0.732404 0.680870i \(-0.238398\pi\)
0.732404 + 0.680870i \(0.238398\pi\)
\(30\) 4.54854i 0.151618i
\(31\) 18.7683 0.605428 0.302714 0.953082i \(-0.402107\pi\)
0.302714 + 0.953082i \(0.402107\pi\)
\(32\) 5.65685 0.176777
\(33\) 18.7330i 0.567667i
\(34\) 39.9131i 1.17391i
\(35\) −22.7778 −0.650796
\(36\) −13.8622 −0.385060
\(37\) 1.14094i 0.0308363i 0.999881 + 0.0154182i \(0.00490795\pi\)
−0.999881 + 0.0154182i \(0.995092\pi\)
\(38\) 16.4989i 0.434183i
\(39\) 33.3924 0.856217
\(40\) 6.32456i 0.158114i
\(41\) −72.8198 −1.77609 −0.888046 0.459755i \(-0.847937\pi\)
−0.888046 + 0.459755i \(0.847937\pi\)
\(42\) 20.7212i 0.493362i
\(43\) 4.96573i 0.115482i 0.998332 + 0.0577411i \(0.0183898\pi\)
−0.998332 + 0.0577411i \(0.981610\pi\)
\(44\) 26.0474i 0.591987i
\(45\) 15.4984i 0.344408i
\(46\) −24.6071 + 21.2718i −0.534937 + 0.462431i
\(47\) −0.813360 −0.0173055 −0.00865277 0.999963i \(-0.502754\pi\)
−0.00865277 + 0.999963i \(0.502754\pi\)
\(48\) 5.75350 0.119865
\(49\) −54.7661 −1.11768
\(50\) −7.07107 −0.141421
\(51\) 40.5950i 0.795980i
\(52\) 46.4308 0.892900
\(53\) 26.7286i 0.504313i −0.967686 0.252157i \(-0.918860\pi\)
0.967686 0.252157i \(-0.0811398\pi\)
\(54\) −32.4065 −0.600121
\(55\) −29.1219 −0.529490
\(56\) 28.8120i 0.514499i
\(57\) 16.7808i 0.294400i
\(58\) 60.0750 1.03578
\(59\) 94.0845 1.59465 0.797326 0.603549i \(-0.206247\pi\)
0.797326 + 0.603549i \(0.206247\pi\)
\(60\) 6.43261i 0.107210i
\(61\) 74.5293i 1.22179i 0.791711 + 0.610896i \(0.209191\pi\)
−0.791711 + 0.610896i \(0.790809\pi\)
\(62\) 26.5423 0.428102
\(63\) 70.6039i 1.12070i
\(64\) 8.00000 0.125000
\(65\) 51.9112i 0.798634i
\(66\) 26.4925i 0.401401i
\(67\) 80.0906i 1.19538i −0.801727 0.597691i \(-0.796085\pi\)
0.801727 0.597691i \(-0.203915\pi\)
\(68\) 56.4456i 0.830082i
\(69\) −25.0275 + 21.6352i −0.362718 + 0.313554i
\(70\) −32.2127 −0.460182
\(71\) −83.5303 −1.17648 −0.588241 0.808686i \(-0.700179\pi\)
−0.588241 + 0.808686i \(0.700179\pi\)
\(72\) −19.6040 −0.272278
\(73\) −8.98897 −0.123137 −0.0615683 0.998103i \(-0.519610\pi\)
−0.0615683 + 0.998103i \(0.519610\pi\)
\(74\) 1.61354i 0.0218046i
\(75\) −7.19187 −0.0958917
\(76\) 23.3330i 0.307013i
\(77\) −132.667 −1.72295
\(78\) 47.2241 0.605437
\(79\) 80.2841i 1.01626i 0.861282 + 0.508128i \(0.169662\pi\)
−0.861282 + 0.508128i \(0.830338\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 29.4195 0.363204
\(82\) −102.983 −1.25589
\(83\) 94.6451i 1.14030i 0.821540 + 0.570151i \(0.193115\pi\)
−0.821540 + 0.570151i \(0.806885\pi\)
\(84\) 29.3042i 0.348859i
\(85\) 63.1081 0.742448
\(86\) 7.02261i 0.0816582i
\(87\) 61.1014 0.702315
\(88\) 36.8367i 0.418598i
\(89\) 136.812i 1.53722i 0.639720 + 0.768608i \(0.279050\pi\)
−0.639720 + 0.768608i \(0.720950\pi\)
\(90\) 21.9180i 0.243533i
\(91\) 236.485i 2.59874i
\(92\) −34.7997 + 30.0829i −0.378258 + 0.326988i
\(93\) 26.9958 0.290277
\(94\) −1.15026 −0.0122369
\(95\) 26.0871 0.274601
\(96\) 8.13668 0.0847571
\(97\) 2.32666i 0.0239862i 0.999928 + 0.0119931i \(0.00381761\pi\)
−0.999928 + 0.0119931i \(0.996182\pi\)
\(98\) −77.4509 −0.790316
\(99\) 90.2684i 0.911802i
\(100\) −10.0000 −0.100000
\(101\) 12.9918 0.128632 0.0643161 0.997930i \(-0.479513\pi\)
0.0643161 + 0.997930i \(0.479513\pi\)
\(102\) 57.4100i 0.562843i
\(103\) 90.3165i 0.876859i −0.898766 0.438430i \(-0.855535\pi\)
0.898766 0.438430i \(-0.144465\pi\)
\(104\) 65.6631 0.631376
\(105\) −32.7631 −0.312029
\(106\) 37.7999i 0.356603i
\(107\) 185.173i 1.73059i −0.501264 0.865294i \(-0.667131\pi\)
0.501264 0.865294i \(-0.332869\pi\)
\(108\) −45.8297 −0.424349
\(109\) 13.8248i 0.126833i −0.997987 0.0634167i \(-0.979800\pi\)
0.997987 0.0634167i \(-0.0201997\pi\)
\(110\) −41.1846 −0.374406
\(111\) 1.64110i 0.0147847i
\(112\) 40.7463i 0.363806i
\(113\) 178.530i 1.57991i 0.613164 + 0.789956i \(0.289897\pi\)
−0.613164 + 0.789956i \(0.710103\pi\)
\(114\) 23.7317i 0.208172i
\(115\) 33.6337 + 38.9073i 0.292467 + 0.338324i
\(116\) 84.9589 0.732404
\(117\) −160.908 −1.37528
\(118\) 133.056 1.12759
\(119\) 287.493 2.41591
\(120\) 9.09708i 0.0758090i
\(121\) −48.6174 −0.401797
\(122\) 105.400i 0.863938i
\(123\) −104.742 −0.851562
\(124\) 37.5365 0.302714
\(125\) 11.1803i 0.0894427i
\(126\) 99.8489i 0.792452i
\(127\) −112.959 −0.889442 −0.444721 0.895669i \(-0.646697\pi\)
−0.444721 + 0.895669i \(0.646697\pi\)
\(128\) 11.3137 0.0883883
\(129\) 7.14258i 0.0553689i
\(130\) 73.4135i 0.564720i
\(131\) −12.1419 −0.0926860 −0.0463430 0.998926i \(-0.514757\pi\)
−0.0463430 + 0.998926i \(0.514757\pi\)
\(132\) 37.4660i 0.283833i
\(133\) 118.842 0.893546
\(134\) 113.265i 0.845263i
\(135\) 51.2392i 0.379550i
\(136\) 79.8261i 0.586957i
\(137\) 170.543i 1.24484i −0.782685 0.622418i \(-0.786150\pi\)
0.782685 0.622418i \(-0.213850\pi\)
\(138\) −35.3943 + 30.5968i −0.256480 + 0.221716i
\(139\) 38.5478 0.277322 0.138661 0.990340i \(-0.455720\pi\)
0.138661 + 0.990340i \(0.455720\pi\)
\(140\) −45.5557 −0.325398
\(141\) −1.16992 −0.00829728
\(142\) −118.130 −0.831899
\(143\) 302.351i 2.11434i
\(144\) −27.7243 −0.192530
\(145\) 94.9869i 0.655082i
\(146\) −12.7123 −0.0870707
\(147\) −78.7742 −0.535879
\(148\) 2.28189i 0.0154182i
\(149\) 81.4125i 0.546393i 0.961958 + 0.273196i \(0.0880808\pi\)
−0.961958 + 0.273196i \(0.911919\pi\)
\(150\) −10.1708 −0.0678056
\(151\) 159.680 1.05748 0.528742 0.848782i \(-0.322664\pi\)
0.528742 + 0.848782i \(0.322664\pi\)
\(152\) 32.9979i 0.217091i
\(153\) 195.614i 1.27853i
\(154\) −187.619 −1.21831
\(155\) 41.9671i 0.270755i
\(156\) 66.7849 0.428108
\(157\) 38.5953i 0.245830i −0.992417 0.122915i \(-0.960776\pi\)
0.992417 0.122915i \(-0.0392242\pi\)
\(158\) 113.539i 0.718601i
\(159\) 38.4457i 0.241797i
\(160\) 12.6491i 0.0790569i
\(161\) 153.221 + 177.245i 0.951681 + 1.10090i
\(162\) 41.6055 0.256824
\(163\) 150.291 0.922028 0.461014 0.887393i \(-0.347486\pi\)
0.461014 + 0.887393i \(0.347486\pi\)
\(164\) −145.640 −0.888046
\(165\) −41.8883 −0.253868
\(166\) 133.848i 0.806316i
\(167\) 27.7604 0.166230 0.0831149 0.996540i \(-0.473513\pi\)
0.0831149 + 0.996540i \(0.473513\pi\)
\(168\) 41.4424i 0.246681i
\(169\) 369.955 2.18908
\(170\) 89.2483 0.524990
\(171\) 80.8615i 0.472874i
\(172\) 9.93146i 0.0577411i
\(173\) −24.0064 −0.138765 −0.0693826 0.997590i \(-0.522103\pi\)
−0.0693826 + 0.997590i \(0.522103\pi\)
\(174\) 86.4104 0.496611
\(175\) 50.9328i 0.291045i
\(176\) 52.0949i 0.295994i
\(177\) 135.329 0.764569
\(178\) 193.482i 1.08698i
\(179\) −201.178 −1.12390 −0.561949 0.827172i \(-0.689948\pi\)
−0.561949 + 0.827172i \(0.689948\pi\)
\(180\) 30.9967i 0.172204i
\(181\) 202.358i 1.11800i −0.829168 0.558999i \(-0.811186\pi\)
0.829168 0.558999i \(-0.188814\pi\)
\(182\) 334.441i 1.83759i
\(183\) 107.201i 0.585798i
\(184\) −49.2142 + 42.5436i −0.267469 + 0.231215i
\(185\) 2.55123 0.0137904
\(186\) 38.1778 0.205257
\(187\) 367.566 1.96559
\(188\) −1.62672 −0.00865277
\(189\) 233.424i 1.23505i
\(190\) 36.8927 0.194172
\(191\) 111.302i 0.582735i 0.956611 + 0.291368i \(0.0941103\pi\)
−0.956611 + 0.291368i \(0.905890\pi\)
\(192\) 11.5070 0.0599323
\(193\) −164.081 −0.850163 −0.425081 0.905155i \(-0.639754\pi\)
−0.425081 + 0.905155i \(0.639754\pi\)
\(194\) 3.29040i 0.0169608i
\(195\) 74.6678i 0.382912i
\(196\) −109.532 −0.558838
\(197\) −329.562 −1.67290 −0.836451 0.548042i \(-0.815373\pi\)
−0.836451 + 0.548042i \(0.815373\pi\)
\(198\) 127.659i 0.644742i
\(199\) 337.886i 1.69792i −0.528455 0.848961i \(-0.677229\pi\)
0.528455 0.848961i \(-0.322771\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 115.200i 0.573136i
\(202\) 18.3732 0.0909566
\(203\) 432.720i 2.13162i
\(204\) 81.1899i 0.397990i
\(205\) 162.830i 0.794292i
\(206\) 127.727i 0.620033i
\(207\) 120.600 104.253i 0.582608 0.503640i
\(208\) 92.8616 0.446450
\(209\) 151.941 0.726992
\(210\) −46.3340 −0.220638
\(211\) 111.656 0.529173 0.264587 0.964362i \(-0.414765\pi\)
0.264587 + 0.964362i \(0.414765\pi\)
\(212\) 53.4572i 0.252157i
\(213\) −120.148 −0.564074
\(214\) 261.874i 1.22371i
\(215\) 11.1037 0.0516452
\(216\) −64.8130 −0.300060
\(217\) 191.184i 0.881032i
\(218\) 19.5513i 0.0896847i
\(219\) −12.9295 −0.0590389
\(220\) −58.2439 −0.264745
\(221\) 655.204i 2.96472i
\(222\) 2.32087i 0.0104544i
\(223\) −363.545 −1.63025 −0.815123 0.579288i \(-0.803331\pi\)
−0.815123 + 0.579288i \(0.803331\pi\)
\(224\) 57.6239i 0.257250i
\(225\) 34.6554 0.154024
\(226\) 252.480i 1.11717i
\(227\) 11.3368i 0.0499418i 0.999688 + 0.0249709i \(0.00794931\pi\)
−0.999688 + 0.0249709i \(0.992051\pi\)
\(228\) 33.5616i 0.147200i
\(229\) 112.509i 0.491306i −0.969358 0.245653i \(-0.920998\pi\)
0.969358 0.245653i \(-0.0790024\pi\)
\(230\) 47.5652 + 55.0232i 0.206805 + 0.239231i
\(231\) −190.825 −0.826082
\(232\) 120.150 0.517888
\(233\) −381.634 −1.63791 −0.818957 0.573855i \(-0.805447\pi\)
−0.818957 + 0.573855i \(0.805447\pi\)
\(234\) −227.558 −0.972470
\(235\) 1.81873i 0.00773927i
\(236\) 188.169 0.797326
\(237\) 115.479i 0.487252i
\(238\) 406.577 1.70831
\(239\) 139.296 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(240\) 12.8652i 0.0536051i
\(241\) 82.3347i 0.341638i −0.985302 0.170819i \(-0.945359\pi\)
0.985302 0.170819i \(-0.0546413\pi\)
\(242\) −68.7554 −0.284113
\(243\) 248.550 1.02284
\(244\) 149.059i 0.610896i
\(245\) 122.461i 0.499840i
\(246\) −148.128 −0.602145
\(247\) 270.843i 1.09653i
\(248\) 53.0846 0.214051
\(249\) 136.135i 0.546728i
\(250\) 15.8114i 0.0632456i
\(251\) 323.924i 1.29054i −0.763957 0.645268i \(-0.776746\pi\)
0.763957 0.645268i \(-0.223254\pi\)
\(252\) 141.208i 0.560348i
\(253\) 195.896 + 226.611i 0.774291 + 0.895695i
\(254\) −159.748 −0.628931
\(255\) 90.7731 0.355973
\(256\) 16.0000 0.0625000
\(257\) −250.796 −0.975858 −0.487929 0.872883i \(-0.662248\pi\)
−0.487929 + 0.872883i \(0.662248\pi\)
\(258\) 10.1011i 0.0391517i
\(259\) 11.6223 0.0448737
\(260\) 103.822i 0.399317i
\(261\) −294.428 −1.12808
\(262\) −17.1712 −0.0655389
\(263\) 276.878i 1.05277i 0.850247 + 0.526384i \(0.176452\pi\)
−0.850247 + 0.526384i \(0.823548\pi\)
\(264\) 52.9849i 0.200700i
\(265\) −59.7670 −0.225536
\(266\) 168.067 0.631833
\(267\) 196.787i 0.737031i
\(268\) 160.181i 0.597691i
\(269\) −78.1002 −0.290335 −0.145168 0.989407i \(-0.546372\pi\)
−0.145168 + 0.989407i \(0.546372\pi\)
\(270\) 72.4632i 0.268382i
\(271\) 331.551 1.22343 0.611717 0.791076i \(-0.290479\pi\)
0.611717 + 0.791076i \(0.290479\pi\)
\(272\) 112.891i 0.415041i
\(273\) 340.154i 1.24599i
\(274\) 241.184i 0.880232i
\(275\) 65.1186i 0.236795i
\(276\) −50.0550 + 43.2705i −0.181359 + 0.156777i
\(277\) −355.974 −1.28511 −0.642553 0.766241i \(-0.722125\pi\)
−0.642553 + 0.766241i \(0.722125\pi\)
\(278\) 54.5148 0.196097
\(279\) −130.084 −0.466252
\(280\) −64.4255 −0.230091
\(281\) 391.437i 1.39301i 0.717550 + 0.696507i \(0.245264\pi\)
−0.717550 + 0.696507i \(0.754736\pi\)
\(282\) −1.65451 −0.00586706
\(283\) 133.616i 0.472143i 0.971736 + 0.236071i \(0.0758599\pi\)
−0.971736 + 0.236071i \(0.924140\pi\)
\(284\) −167.061 −0.588241
\(285\) 37.5230 0.131660
\(286\) 427.589i 1.49507i
\(287\) 741.783i 2.58461i
\(288\) −39.2081 −0.136139
\(289\) −507.527 −1.75615
\(290\) 134.332i 0.463213i
\(291\) 3.34661i 0.0115004i
\(292\) −17.9779 −0.0615683
\(293\) 533.454i 1.82066i 0.413880 + 0.910331i \(0.364173\pi\)
−0.413880 + 0.910331i \(0.635827\pi\)
\(294\) −111.403 −0.378923
\(295\) 210.379i 0.713150i
\(296\) 3.22708i 0.0109023i
\(297\) 298.437i 1.00484i
\(298\) 115.135i 0.386358i
\(299\) −403.945 + 349.193i −1.35099 + 1.16787i
\(300\) −14.3837 −0.0479458
\(301\) 50.5837 0.168052
\(302\) 225.822 0.747755
\(303\) 18.6871 0.0616737
\(304\) 46.6660i 0.153507i
\(305\) 166.653 0.546402
\(306\) 276.641i 0.904054i
\(307\) 282.656 0.920705 0.460352 0.887736i \(-0.347723\pi\)
0.460352 + 0.887736i \(0.347723\pi\)
\(308\) −265.334 −0.861474
\(309\) 129.909i 0.420417i
\(310\) 59.3504i 0.191453i
\(311\) −193.206 −0.621241 −0.310620 0.950534i \(-0.600537\pi\)
−0.310620 + 0.950534i \(0.600537\pi\)
\(312\) 94.4481 0.302718
\(313\) 399.279i 1.27565i −0.770181 0.637826i \(-0.779834\pi\)
0.770181 0.637826i \(-0.220166\pi\)
\(314\) 54.5820i 0.173828i
\(315\) 157.875 0.501191
\(316\) 160.568i 0.508128i
\(317\) −36.5297 −0.115236 −0.0576178 0.998339i \(-0.518350\pi\)
−0.0576178 + 0.998339i \(0.518350\pi\)
\(318\) 54.3705i 0.170976i
\(319\) 553.241i 1.73430i
\(320\) 17.8885i 0.0559017i
\(321\) 266.348i 0.829745i
\(322\) 216.687 + 250.662i 0.672940 + 0.778453i
\(323\) −329.262 −1.01939
\(324\) 58.8391 0.181602
\(325\) −116.077 −0.357160
\(326\) 212.543 0.651973
\(327\) 19.8853i 0.0608113i
\(328\) −205.965 −0.627943
\(329\) 8.28534i 0.0251834i
\(330\) −59.2389 −0.179512
\(331\) 85.9406 0.259639 0.129820 0.991538i \(-0.458560\pi\)
0.129820 + 0.991538i \(0.458560\pi\)
\(332\) 189.290i 0.570151i
\(333\) 7.90797i 0.0237476i
\(334\) 39.2591 0.117542
\(335\) −179.088 −0.534591
\(336\) 58.6084i 0.174430i
\(337\) 548.713i 1.62823i −0.580706 0.814114i \(-0.697223\pi\)
0.580706 0.814114i \(-0.302777\pi\)
\(338\) 523.195 1.54791
\(339\) 256.793i 0.757502i
\(340\) 126.216 0.371224
\(341\) 244.433i 0.716811i
\(342\) 114.355i 0.334373i
\(343\) 58.7366i 0.171244i
\(344\) 14.0452i 0.0408291i
\(345\) 48.3778 + 55.9632i 0.140226 + 0.162212i
\(346\) −33.9502 −0.0981219
\(347\) 62.0036 0.178685 0.0893424 0.996001i \(-0.471523\pi\)
0.0893424 + 0.996001i \(0.471523\pi\)
\(348\) 122.203 0.351157
\(349\) −131.393 −0.376485 −0.188242 0.982123i \(-0.560279\pi\)
−0.188242 + 0.982123i \(0.560279\pi\)
\(350\) 72.0299i 0.205800i
\(351\) −531.978 −1.51561
\(352\) 73.6733i 0.209299i
\(353\) −176.990 −0.501389 −0.250694 0.968066i \(-0.580659\pi\)
−0.250694 + 0.968066i \(0.580659\pi\)
\(354\) 191.384 0.540632
\(355\) 186.779i 0.526139i
\(356\) 273.624i 0.768608i
\(357\) 413.523 1.15833
\(358\) −284.508 −0.794716
\(359\) 187.851i 0.523260i 0.965168 + 0.261630i \(0.0842601\pi\)
−0.965168 + 0.261630i \(0.915740\pi\)
\(360\) 43.8360i 0.121767i
\(361\) 224.893 0.622971
\(362\) 286.177i 0.790544i
\(363\) −69.9300 −0.192645
\(364\) 472.970i 1.29937i
\(365\) 20.0999i 0.0550684i
\(366\) 151.605i 0.414222i
\(367\) 128.510i 0.350162i 0.984554 + 0.175081i \(0.0560188\pi\)
−0.984554 + 0.175081i \(0.943981\pi\)
\(368\) −69.5994 + 60.1658i −0.189129 + 0.163494i
\(369\) 504.719 1.36780
\(370\) 3.60798 0.00975130
\(371\) −272.273 −0.733888
\(372\) 53.9916 0.145139
\(373\) 79.2928i 0.212581i 0.994335 + 0.106291i \(0.0338974\pi\)
−0.994335 + 0.106291i \(0.966103\pi\)
\(374\) 519.817 1.38988
\(375\) 16.0815i 0.0428841i
\(376\) −2.30053 −0.00611843
\(377\) 986.177 2.61585
\(378\) 330.111i 0.873309i
\(379\) 402.569i 1.06219i 0.847313 + 0.531094i \(0.178219\pi\)
−0.847313 + 0.531094i \(0.821781\pi\)
\(380\) 52.1742 0.137301
\(381\) −162.478 −0.426450
\(382\) 157.405i 0.412056i
\(383\) 370.198i 0.966575i −0.875462 0.483288i \(-0.839443\pi\)
0.875462 0.483288i \(-0.160557\pi\)
\(384\) 16.2734 0.0423785
\(385\) 296.652i 0.770526i
\(386\) −232.046 −0.601156
\(387\) 34.4179i 0.0889351i
\(388\) 4.65332i 0.0119931i
\(389\) 12.0598i 0.0310021i 0.999880 + 0.0155011i \(0.00493434\pi\)
−0.999880 + 0.0155011i \(0.995066\pi\)
\(390\) 105.596i 0.270759i
\(391\) −424.512 491.073i −1.08571 1.25594i
\(392\) −154.902 −0.395158
\(393\) −17.4645 −0.0444391
\(394\) −466.071 −1.18292
\(395\) 179.521 0.454483
\(396\) 180.537i 0.455901i
\(397\) 233.543 0.588270 0.294135 0.955764i \(-0.404968\pi\)
0.294135 + 0.955764i \(0.404968\pi\)
\(398\) 477.844i 1.20061i
\(399\) 170.939 0.428418
\(400\) −20.0000 −0.0500000
\(401\) 114.072i 0.284469i 0.989833 + 0.142235i \(0.0454287\pi\)
−0.989833 + 0.142235i \(0.954571\pi\)
\(402\) 162.918i 0.405268i
\(403\) 435.713 1.08117
\(404\) 25.9837 0.0643161
\(405\) 65.7841i 0.162430i
\(406\) 611.958i 1.50729i
\(407\) 14.8593 0.0365094
\(408\) 114.820i 0.281421i
\(409\) 125.952 0.307950 0.153975 0.988075i \(-0.450792\pi\)
0.153975 + 0.988075i \(0.450792\pi\)
\(410\) 230.276i 0.561650i
\(411\) 245.304i 0.596847i
\(412\) 180.633i 0.438430i
\(413\) 958.397i 2.32057i
\(414\) 170.554 147.437i 0.411966 0.356127i
\(415\) 211.633 0.509959
\(416\) 131.326 0.315688
\(417\) 55.4462 0.132965
\(418\) 214.878 0.514061
\(419\) 135.868i 0.324268i −0.986769 0.162134i \(-0.948162\pi\)
0.986769 0.162134i \(-0.0518377\pi\)
\(420\) −65.5262 −0.156015
\(421\) 194.111i 0.461070i −0.973064 0.230535i \(-0.925952\pi\)
0.973064 0.230535i \(-0.0740477\pi\)
\(422\) 157.905 0.374182
\(423\) 5.63746 0.0133273
\(424\) 75.5999i 0.178302i
\(425\) 141.114i 0.332033i
\(426\) −169.915 −0.398861
\(427\) 759.198 1.77798
\(428\) 370.346i 0.865294i
\(429\) 434.894i 1.01374i
\(430\) 15.7030 0.0365187
\(431\) 421.699i 0.978420i −0.872166 0.489210i \(-0.837285\pi\)
0.872166 0.489210i \(-0.162715\pi\)
\(432\) −91.6595 −0.212175
\(433\) 3.78505i 0.00874144i −0.999990 0.00437072i \(-0.998609\pi\)
0.999990 0.00437072i \(-0.00139125\pi\)
\(434\) 270.375i 0.622984i
\(435\) 136.627i 0.314085i
\(436\) 27.6497i 0.0634167i
\(437\) −175.481 202.996i −0.401559 0.464521i
\(438\) −18.2851 −0.0417468
\(439\) −6.17744 −0.0140716 −0.00703581 0.999975i \(-0.502240\pi\)
−0.00703581 + 0.999975i \(0.502240\pi\)
\(440\) −82.3693 −0.187203
\(441\) 379.588 0.860744
\(442\) 926.598i 2.09638i
\(443\) −406.821 −0.918331 −0.459166 0.888351i \(-0.651852\pi\)
−0.459166 + 0.888351i \(0.651852\pi\)
\(444\) 3.28221i 0.00739236i
\(445\) 305.921 0.687464
\(446\) −514.130 −1.15276
\(447\) 117.102i 0.261972i
\(448\) 81.4925i 0.181903i
\(449\) −289.981 −0.645837 −0.322918 0.946427i \(-0.604664\pi\)
−0.322918 + 0.946427i \(0.604664\pi\)
\(450\) 49.0101 0.108911
\(451\) 948.385i 2.10285i
\(452\) 357.060i 0.789956i
\(453\) 229.680 0.507020
\(454\) 16.0326i 0.0353142i
\(455\) −528.797 −1.16219
\(456\) 47.4633i 0.104086i
\(457\) 224.430i 0.491094i −0.969385 0.245547i \(-0.921032\pi\)
0.969385 0.245547i \(-0.0789676\pi\)
\(458\) 159.112i 0.347406i
\(459\) 646.722i 1.40898i
\(460\) 67.2674 + 77.8145i 0.146233 + 0.169162i
\(461\) 534.660 1.15978 0.579891 0.814694i \(-0.303095\pi\)
0.579891 + 0.814694i \(0.303095\pi\)
\(462\) −269.867 −0.584128
\(463\) 166.226 0.359019 0.179509 0.983756i \(-0.442549\pi\)
0.179509 + 0.983756i \(0.442549\pi\)
\(464\) 169.918 0.366202
\(465\) 60.3644i 0.129816i
\(466\) −539.712 −1.15818
\(467\) 113.755i 0.243587i 0.992555 + 0.121794i \(0.0388646\pi\)
−0.992555 + 0.121794i \(0.961135\pi\)
\(468\) −321.815 −0.687640
\(469\) −815.848 −1.73955
\(470\) 2.57207i 0.00547249i
\(471\) 55.5145i 0.117865i
\(472\) 266.111 0.563795
\(473\) 64.6723 0.136728
\(474\) 163.312i 0.344539i
\(475\) 58.3326i 0.122805i
\(476\) 574.987 1.20796
\(477\) 185.258i 0.388382i
\(478\) 196.994 0.412121
\(479\) 156.314i 0.326334i −0.986598 0.163167i \(-0.947829\pi\)
0.986598 0.163167i \(-0.0521710\pi\)
\(480\) 18.1942i 0.0379045i
\(481\) 26.4875i 0.0550675i
\(482\) 116.439i 0.241574i
\(483\) 220.389 + 254.944i 0.456291 + 0.527835i
\(484\) −97.2348 −0.200898
\(485\) 5.20257 0.0107270
\(486\) 351.503 0.723257
\(487\) −207.919 −0.426938 −0.213469 0.976950i \(-0.568476\pi\)
−0.213469 + 0.976950i \(0.568476\pi\)
\(488\) 210.801i 0.431969i
\(489\) 216.174 0.442074
\(490\) 173.186i 0.353440i
\(491\) −463.345 −0.943676 −0.471838 0.881685i \(-0.656409\pi\)
−0.471838 + 0.881685i \(0.656409\pi\)
\(492\) −209.484 −0.425781
\(493\) 1198.89i 2.43182i
\(494\) 383.029i 0.775363i
\(495\) 201.846 0.407770
\(496\) 75.0730 0.151357
\(497\) 850.886i 1.71204i
\(498\) 192.524i 0.386595i
\(499\) −50.7777 −0.101759 −0.0508794 0.998705i \(-0.516202\pi\)
−0.0508794 + 0.998705i \(0.516202\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 39.9298 0.0797003
\(502\) 458.098i 0.912546i
\(503\) 91.1857i 0.181284i −0.995884 0.0906419i \(-0.971108\pi\)
0.995884 0.0906419i \(-0.0288919\pi\)
\(504\) 199.698i 0.396226i
\(505\) 29.0506i 0.0575260i
\(506\) 277.038 + 320.476i 0.547506 + 0.633352i
\(507\) 532.134 1.04957
\(508\) −225.918 −0.444721
\(509\) 317.681 0.624128 0.312064 0.950061i \(-0.398980\pi\)
0.312064 + 0.950061i \(0.398980\pi\)
\(510\) 128.373 0.251711
\(511\) 91.5667i 0.179191i
\(512\) 22.6274 0.0441942
\(513\) 267.337i 0.521124i
\(514\) −354.678 −0.690036
\(515\) −201.954 −0.392143
\(516\) 14.2852i 0.0276844i
\(517\) 10.5930i 0.0204893i
\(518\) 16.4364 0.0317305
\(519\) −34.5302 −0.0665322
\(520\) 146.827i 0.282360i
\(521\) 522.346i 1.00258i −0.865279 0.501291i \(-0.832858\pi\)
0.865279 0.501291i \(-0.167142\pi\)
\(522\) −416.385 −0.797671
\(523\) 245.926i 0.470221i 0.971969 + 0.235111i \(0.0755452\pi\)
−0.971969 + 0.235111i \(0.924455\pi\)
\(524\) −24.2837 −0.0463430
\(525\) 73.2605i 0.139544i
\(526\) 391.564i 0.744419i
\(527\) 529.693i 1.00511i
\(528\) 74.9320i 0.141917i
\(529\) 76.5101 523.438i 0.144632 0.989486i
\(530\) −84.5232 −0.159478
\(531\) −652.107 −1.22807
\(532\) 237.683 0.446773
\(533\) −1690.54 −3.17174
\(534\) 278.299i 0.521160i
\(535\) −414.059 −0.773943
\(536\) 226.530i 0.422631i
\(537\) −289.369 −0.538862
\(538\) −110.450 −0.205298
\(539\) 713.258i 1.32330i
\(540\) 102.478i 0.189775i
\(541\) −307.138 −0.567723 −0.283861 0.958865i \(-0.591616\pi\)
−0.283861 + 0.958865i \(0.591616\pi\)
\(542\) 468.884 0.865099
\(543\) 291.066i 0.536033i
\(544\) 159.652i 0.293478i
\(545\) −30.9133 −0.0567216
\(546\) 481.051i 0.881046i
\(547\) −712.547 −1.30265 −0.651323 0.758801i \(-0.725786\pi\)
−0.651323 + 0.758801i \(0.725786\pi\)
\(548\) 341.085i 0.622418i
\(549\) 516.569i 0.940926i
\(550\) 92.0916i 0.167439i
\(551\) 495.587i 0.899432i
\(552\) −70.7885 + 61.1937i −0.128240 + 0.110858i
\(553\) 817.820 1.47888
\(554\) −503.424 −0.908707
\(555\) 3.66962 0.00661193
\(556\) 77.0956 0.138661
\(557\) 1.17109i 0.00210250i −0.999999 0.00105125i \(-0.999665\pi\)
0.999999 0.00105125i \(-0.000334623\pi\)
\(558\) −183.967 −0.329690
\(559\) 115.281i 0.206228i
\(560\) −91.1114 −0.162699
\(561\) 528.698 0.942420
\(562\) 553.575i 0.985010i
\(563\) 900.058i 1.59868i −0.600878 0.799341i \(-0.705182\pi\)
0.600878 0.799341i \(-0.294818\pi\)
\(564\) −2.33983 −0.00414864
\(565\) 399.205 0.706558
\(566\) 188.962i 0.333855i
\(567\) 299.684i 0.528543i
\(568\) −236.259 −0.415949
\(569\) 589.836i 1.03662i 0.855193 + 0.518309i \(0.173438\pi\)
−0.855193 + 0.518309i \(0.826562\pi\)
\(570\) 53.0656 0.0930976
\(571\) 117.755i 0.206225i −0.994670 0.103113i \(-0.967120\pi\)
0.994670 0.103113i \(-0.0328802\pi\)
\(572\) 604.702i 1.05717i
\(573\) 160.095i 0.279397i
\(574\) 1049.04i 1.82760i
\(575\) 86.9993 75.2072i 0.151303 0.130795i
\(576\) −55.4486 −0.0962650
\(577\) −403.533 −0.699365 −0.349682 0.936868i \(-0.613710\pi\)
−0.349682 + 0.936868i \(0.613710\pi\)
\(578\) −717.751 −1.24178
\(579\) −236.011 −0.407618
\(580\) 189.974i 0.327541i
\(581\) 964.109 1.65940
\(582\) 4.73282i 0.00813200i
\(583\) −348.106 −0.597094
\(584\) −25.4246 −0.0435354
\(585\) 359.801i 0.615044i
\(586\) 754.418i 1.28740i
\(587\) 607.731 1.03532 0.517659 0.855587i \(-0.326804\pi\)
0.517659 + 0.855587i \(0.326804\pi\)
\(588\) −157.548 −0.267939
\(589\) 218.960i 0.371749i
\(590\) 297.521i 0.504273i
\(591\) −474.033 −0.802087
\(592\) 4.56377i 0.00770908i
\(593\) 428.555 0.722690 0.361345 0.932432i \(-0.382318\pi\)
0.361345 + 0.932432i \(0.382318\pi\)
\(594\) 422.053i 0.710528i
\(595\) 642.855i 1.08043i
\(596\) 162.825i 0.273196i
\(597\) 486.007i 0.814083i
\(598\) −571.264 + 493.834i −0.955291 + 0.825809i
\(599\) −162.171 −0.270736 −0.135368 0.990795i \(-0.543222\pi\)
−0.135368 + 0.990795i \(0.543222\pi\)
\(600\) −20.3417 −0.0339028
\(601\) 957.407 1.59302 0.796512 0.604623i \(-0.206676\pi\)
0.796512 + 0.604623i \(0.206676\pi\)
\(602\) 71.5362 0.118831
\(603\) 555.114i 0.920587i
\(604\) 319.360 0.528742
\(605\) 108.712i 0.179689i
\(606\) 26.4276 0.0436099
\(607\) −989.893 −1.63080 −0.815398 0.578901i \(-0.803482\pi\)
−0.815398 + 0.578901i \(0.803482\pi\)
\(608\) 65.9958i 0.108546i
\(609\) 622.413i 1.02202i
\(610\) 235.682 0.386365
\(611\) −18.8825 −0.0309042
\(612\) 391.229i 0.639263i
\(613\) 134.181i 0.218892i 0.993993 + 0.109446i \(0.0349076\pi\)
−0.993993 + 0.109446i \(0.965092\pi\)
\(614\) 399.736 0.651037
\(615\) 234.211i 0.380830i
\(616\) −375.239 −0.609154
\(617\) 151.269i 0.245168i −0.992458 0.122584i \(-0.960882\pi\)
0.992458 0.122584i \(-0.0391181\pi\)
\(618\) 183.719i 0.297280i
\(619\) 115.852i 0.187159i 0.995612 + 0.0935797i \(0.0298310\pi\)
−0.995612 + 0.0935797i \(0.970169\pi\)
\(620\) 83.9342i 0.135378i
\(621\) 398.715 344.673i 0.642054 0.555028i
\(622\) −273.234 −0.439284
\(623\) 1393.65 2.23699
\(624\) 133.570 0.214054
\(625\) 25.0000 0.0400000
\(626\) 564.665i 0.902022i
\(627\) 218.549 0.348563
\(628\) 77.1906i 0.122915i
\(629\) −32.2006 −0.0511934
\(630\) 223.269 0.354395
\(631\) 730.187i 1.15719i 0.815615 + 0.578595i \(0.196399\pi\)
−0.815615 + 0.578595i \(0.803601\pi\)
\(632\) 227.078i 0.359300i
\(633\) 160.602 0.253716
\(634\) −51.6608 −0.0814839
\(635\) 252.584i 0.397771i
\(636\) 76.8915i 0.120899i
\(637\) −1271.42 −1.99594
\(638\) 782.400i 1.22633i
\(639\) 578.955 0.906032
\(640\) 25.2982i 0.0395285i
\(641\) 725.551i 1.13190i −0.824438 0.565952i \(-0.808509\pi\)
0.824438 0.565952i \(-0.191491\pi\)
\(642\) 376.673i 0.586718i
\(643\) 505.908i 0.786792i 0.919369 + 0.393396i \(0.128700\pi\)
−0.919369 + 0.393396i \(0.871300\pi\)
\(644\) 306.441 + 354.490i 0.475840 + 0.550450i
\(645\) 15.9713 0.0247617
\(646\) −465.646 −0.720815
\(647\) −324.943 −0.502230 −0.251115 0.967957i \(-0.580797\pi\)
−0.251115 + 0.967957i \(0.580797\pi\)
\(648\) 83.2110 0.128412
\(649\) 1225.33i 1.88803i
\(650\) −164.158 −0.252550
\(651\) 274.994i 0.422418i
\(652\) 300.581 0.461014
\(653\) −146.801 −0.224810 −0.112405 0.993662i \(-0.535855\pi\)
−0.112405 + 0.993662i \(0.535855\pi\)
\(654\) 28.1220i 0.0430001i
\(655\) 27.1500i 0.0414504i
\(656\) −291.279 −0.444023
\(657\) 62.3033 0.0948299
\(658\) 11.7172i 0.0178074i
\(659\) 366.667i 0.556399i 0.960523 + 0.278200i \(0.0897377\pi\)
−0.960523 + 0.278200i \(0.910262\pi\)
\(660\) −83.7765 −0.126934
\(661\) 1241.87i 1.87878i 0.342852 + 0.939389i \(0.388607\pi\)
−0.342852 + 0.939389i \(0.611393\pi\)
\(662\) 121.538 0.183593
\(663\) 942.428i 1.42146i
\(664\) 267.697i 0.403158i
\(665\) 265.738i 0.399606i
\(666\) 11.1836i 0.0167921i
\(667\) −739.136 + 638.952i −1.10815 + 0.957949i
\(668\) 55.5208 0.0831149
\(669\) −522.914 −0.781635
\(670\) −253.269 −0.378013
\(671\) 970.649 1.44657
\(672\) 82.8848i 0.123340i
\(673\) 812.966 1.20797 0.603987 0.796994i \(-0.293578\pi\)
0.603987 + 0.796994i \(0.293578\pi\)
\(674\) 775.997i 1.15133i
\(675\) 114.574 0.169740
\(676\) 739.910 1.09454
\(677\) 1053.03i 1.55544i −0.628610 0.777721i \(-0.716376\pi\)
0.628610 0.777721i \(-0.283624\pi\)
\(678\) 363.160i 0.535635i
\(679\) 23.7007 0.0349053
\(680\) 178.497 0.262495
\(681\) 16.3066i 0.0239450i
\(682\) 345.680i 0.506862i
\(683\) 947.718 1.38758 0.693791 0.720177i \(-0.255939\pi\)
0.693791 + 0.720177i \(0.255939\pi\)
\(684\) 161.723i 0.236437i
\(685\) −381.345 −0.556708
\(686\) 83.0661i 0.121088i
\(687\) 161.830i 0.235561i
\(688\) 19.8629i 0.0288705i
\(689\) 620.515i 0.900602i
\(690\) 68.4166 + 79.1440i 0.0991545 + 0.114701i
\(691\) −600.541 −0.869090 −0.434545 0.900650i \(-0.643091\pi\)
−0.434545 + 0.900650i \(0.643091\pi\)
\(692\) −48.0128 −0.0693826
\(693\) 919.525 1.32688
\(694\) 87.6863 0.126349
\(695\) 86.1955i 0.124022i
\(696\) 172.821 0.248306
\(697\) 2055.18i 2.94861i
\(698\) −185.818 −0.266215
\(699\) −548.932 −0.785311
\(700\) 101.866i 0.145522i
\(701\) 907.376i 1.29440i 0.762319 + 0.647201i \(0.224061\pi\)
−0.762319 + 0.647201i \(0.775939\pi\)
\(702\) −752.330 −1.07170
\(703\) −13.3108 −0.0189343
\(704\) 104.190i 0.147997i
\(705\) 2.61601i 0.00371066i
\(706\) −250.302 −0.354536
\(707\) 132.342i 0.187188i
\(708\) 270.657 0.382285
\(709\) 657.300i 0.927081i 0.886076 + 0.463540i \(0.153421\pi\)
−0.886076 + 0.463540i \(0.846579\pi\)
\(710\) 264.146i 0.372036i
\(711\) 556.456i 0.782638i
\(712\) 386.963i 0.543488i
\(713\) −326.565 + 282.302i −0.458015 + 0.395935i
\(714\) 584.810 0.819062
\(715\) −676.077 −0.945563
\(716\) −402.356 −0.561949
\(717\) 200.360 0.279442
\(718\) 265.661i 0.370001i
\(719\) 1095.72 1.52395 0.761975 0.647606i \(-0.224230\pi\)
0.761975 + 0.647606i \(0.224230\pi\)
\(720\) 61.9934i 0.0861020i
\(721\) −920.015 −1.27603
\(722\) 318.046 0.440507
\(723\) 118.428i 0.163801i
\(724\) 404.715i 0.558999i
\(725\) −212.397 −0.292962
\(726\) −98.8960 −0.136220
\(727\) 814.942i 1.12097i 0.828166 + 0.560483i \(0.189384\pi\)
−0.828166 + 0.560483i \(0.810616\pi\)
\(728\) 668.881i 0.918793i
\(729\) 92.7324 0.127205
\(730\) 28.4256i 0.0389392i
\(731\) −140.147 −0.191719
\(732\) 214.402i 0.292899i
\(733\) 742.293i 1.01268i −0.862335 0.506339i \(-0.830999\pi\)
0.862335 0.506339i \(-0.169001\pi\)
\(734\) 181.740i 0.247602i
\(735\) 176.144i 0.239652i
\(736\) −98.4285 + 85.0872i −0.133734 + 0.115608i
\(737\) −1043.08 −1.41530
\(738\) 713.781 0.967183
\(739\) −288.013 −0.389733 −0.194866 0.980830i \(-0.562427\pi\)
−0.194866 + 0.980830i \(0.562427\pi\)
\(740\) 5.10245 0.00689521
\(741\) 389.573i 0.525740i
\(742\) −385.052 −0.518937
\(743\) 199.651i 0.268709i 0.990933 + 0.134354i \(0.0428961\pi\)
−0.990933 + 0.134354i \(0.957104\pi\)
\(744\) 76.3556 0.102629
\(745\) 182.044 0.244354
\(746\) 112.137i 0.150318i
\(747\) 655.993i 0.878170i
\(748\) 735.132 0.982797
\(749\) −1886.28 −2.51839
\(750\) 22.7427i 0.0303236i
\(751\) 610.667i 0.813138i 0.913620 + 0.406569i \(0.133275\pi\)
−0.913620 + 0.406569i \(0.866725\pi\)
\(752\) −3.25344 −0.00432638
\(753\) 465.925i 0.618758i
\(754\) 1394.67 1.84969
\(755\) 357.056i 0.472922i
\(756\) 466.847i 0.617523i
\(757\) 241.235i 0.318672i 0.987224 + 0.159336i \(0.0509354\pi\)
−0.987224 + 0.159336i \(0.949065\pi\)
\(758\) 569.319i 0.751080i
\(759\) 281.771 + 325.952i 0.371240 + 0.429449i
\(760\) 73.7855 0.0970862
\(761\) 568.126 0.746552 0.373276 0.927720i \(-0.378235\pi\)
0.373276 + 0.927720i \(0.378235\pi\)
\(762\) −229.778 −0.301546
\(763\) −140.828 −0.184571
\(764\) 222.605i 0.291368i
\(765\) −437.407 −0.571774
\(766\) 523.539i 0.683472i
\(767\) 2184.21 2.84773
\(768\) 23.0140 0.0299661
\(769\) 425.966i 0.553922i −0.960881 0.276961i \(-0.910673\pi\)
0.960881 0.276961i \(-0.0893273\pi\)
\(770\) 419.530i 0.544844i
\(771\) −360.738 −0.467883
\(772\) −328.163 −0.425081
\(773\) 849.417i 1.09886i 0.835540 + 0.549429i \(0.185155\pi\)
−0.835540 + 0.549429i \(0.814845\pi\)
\(774\) 48.6742i 0.0628866i
\(775\) −93.8413 −0.121086
\(776\) 6.58079i 0.00848040i
\(777\) 16.7172 0.0215151
\(778\) 17.0552i 0.0219218i
\(779\) 849.553i 1.09057i
\(780\) 149.336i 0.191456i
\(781\) 1087.87i 1.39293i
\(782\) −600.350 694.482i −0.767711 0.888084i
\(783\) −973.411 −1.24318
\(784\) −219.064 −0.279419
\(785\) −86.3017 −0.109938
\(786\) −24.6986 −0.0314232
\(787\) 1448.81i 1.84093i −0.390828 0.920464i \(-0.627811\pi\)
0.390828 0.920464i \(-0.372189\pi\)