Properties

Label 403.2.c.b.311.20
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.20
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.13

$q$-expansion

\(f(q)\) \(=\) \(q+0.937316i q^{2} +1.68575 q^{3} +1.12144 q^{4} -0.290760i q^{5} +1.58008i q^{6} -3.85549i q^{7} +2.92577i q^{8} -0.158249 q^{9} +O(q^{10})\) \(q+0.937316i q^{2} +1.68575 q^{3} +1.12144 q^{4} -0.290760i q^{5} +1.58008i q^{6} -3.85549i q^{7} +2.92577i q^{8} -0.158249 q^{9} +0.272534 q^{10} +2.09645i q^{11} +1.89046 q^{12} +(2.07708 + 2.94716i) q^{13} +3.61382 q^{14} -0.490148i q^{15} -0.499499 q^{16} +5.29143 q^{17} -0.148329i q^{18} -3.22555i q^{19} -0.326069i q^{20} -6.49940i q^{21} -1.96504 q^{22} -6.80143 q^{23} +4.93212i q^{24} +4.91546 q^{25} +(-2.76242 + 1.94688i) q^{26} -5.32402 q^{27} -4.32370i q^{28} -4.52320 q^{29} +0.459424 q^{30} +1.00000i q^{31} +5.38336i q^{32} +3.53409i q^{33} +4.95974i q^{34} -1.12102 q^{35} -0.177466 q^{36} -4.81693i q^{37} +3.02336 q^{38} +(3.50143 + 4.96818i) q^{39} +0.850698 q^{40} -6.15845i q^{41} +6.09199 q^{42} -7.12251 q^{43} +2.35104i q^{44} +0.0460124i q^{45} -6.37509i q^{46} +4.76874i q^{47} -0.842031 q^{48} -7.86484 q^{49} +4.60734i q^{50} +8.92003 q^{51} +(2.32931 + 3.30506i) q^{52} -5.08219 q^{53} -4.99029i q^{54} +0.609564 q^{55} +11.2803 q^{56} -5.43746i q^{57} -4.23967i q^{58} +9.83912i q^{59} -0.549671i q^{60} -9.60411 q^{61} -0.937316 q^{62} +0.610127i q^{63} -6.04491 q^{64} +(0.856916 - 0.603930i) q^{65} -3.31256 q^{66} -6.38630i q^{67} +5.93402 q^{68} -11.4655 q^{69} -1.05075i q^{70} +3.60967i q^{71} -0.463000i q^{72} +8.21949i q^{73} +4.51499 q^{74} +8.28623 q^{75} -3.61725i q^{76} +8.08285 q^{77} +(-4.65675 + 3.28195i) q^{78} -4.16666 q^{79} +0.145234i q^{80} -8.50021 q^{81} +5.77241 q^{82} -5.60314i q^{83} -7.28867i q^{84} -1.53854i q^{85} -6.67605i q^{86} -7.62499 q^{87} -6.13374 q^{88} -5.99295i q^{89} -0.0431282 q^{90} +(11.3628 - 8.00815i) q^{91} -7.62739 q^{92} +1.68575i q^{93} -4.46982 q^{94} -0.937859 q^{95} +9.07500i q^{96} -1.49758i q^{97} -7.37184i q^{98} -0.331761i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.937316i 0.662783i 0.943493 + 0.331391i \(0.107518\pi\)
−0.943493 + 0.331391i \(0.892482\pi\)
\(3\) 1.68575 0.973268 0.486634 0.873606i \(-0.338225\pi\)
0.486634 + 0.873606i \(0.338225\pi\)
\(4\) 1.12144 0.560719
\(5\) 0.290760i 0.130032i −0.997884 0.0650159i \(-0.979290\pi\)
0.997884 0.0650159i \(-0.0207098\pi\)
\(6\) 1.58008i 0.645065i
\(7\) 3.85549i 1.45724i −0.684918 0.728620i \(-0.740162\pi\)
0.684918 0.728620i \(-0.259838\pi\)
\(8\) 2.92577i 1.03442i
\(9\) −0.158249 −0.0527496
\(10\) 0.272534 0.0861828
\(11\) 2.09645i 0.632104i 0.948742 + 0.316052i \(0.102357\pi\)
−0.948742 + 0.316052i \(0.897643\pi\)
\(12\) 1.89046 0.545730
\(13\) 2.07708 + 2.94716i 0.576077 + 0.817395i
\(14\) 3.61382 0.965833
\(15\) 0.490148i 0.126556i
\(16\) −0.499499 −0.124875
\(17\) 5.29143 1.28336 0.641680 0.766972i \(-0.278238\pi\)
0.641680 + 0.766972i \(0.278238\pi\)
\(18\) 0.148329i 0.0349615i
\(19\) 3.22555i 0.739991i −0.929034 0.369996i \(-0.879359\pi\)
0.929034 0.369996i \(-0.120641\pi\)
\(20\) 0.326069i 0.0729113i
\(21\) 6.49940i 1.41828i
\(22\) −1.96504 −0.418947
\(23\) −6.80143 −1.41820 −0.709098 0.705110i \(-0.750898\pi\)
−0.709098 + 0.705110i \(0.750898\pi\)
\(24\) 4.93212i 1.00677i
\(25\) 4.91546 0.983092
\(26\) −2.76242 + 1.94688i −0.541755 + 0.381814i
\(27\) −5.32402 −1.02461
\(28\) 4.32370i 0.817102i
\(29\) −4.52320 −0.839938 −0.419969 0.907539i \(-0.637959\pi\)
−0.419969 + 0.907539i \(0.637959\pi\)
\(30\) 0.459424 0.0838789
\(31\) 1.00000i 0.179605i
\(32\) 5.38336i 0.951653i
\(33\) 3.53409i 0.615206i
\(34\) 4.95974i 0.850589i
\(35\) −1.12102 −0.189487
\(36\) −0.177466 −0.0295777
\(37\) 4.81693i 0.791899i −0.918272 0.395950i \(-0.870416\pi\)
0.918272 0.395950i \(-0.129584\pi\)
\(38\) 3.02336 0.490453
\(39\) 3.50143 + 4.96818i 0.560677 + 0.795545i
\(40\) 0.850698 0.134507
\(41\) 6.15845i 0.961788i −0.876779 0.480894i \(-0.840312\pi\)
0.876779 0.480894i \(-0.159688\pi\)
\(42\) 6.09199 0.940015
\(43\) −7.12251 −1.08617 −0.543087 0.839677i \(-0.682744\pi\)
−0.543087 + 0.839677i \(0.682744\pi\)
\(44\) 2.35104i 0.354433i
\(45\) 0.0460124i 0.00685912i
\(46\) 6.37509i 0.939956i
\(47\) 4.76874i 0.695592i 0.937570 + 0.347796i \(0.113070\pi\)
−0.937570 + 0.347796i \(0.886930\pi\)
\(48\) −0.842031 −0.121537
\(49\) −7.86484 −1.12355
\(50\) 4.60734i 0.651576i
\(51\) 8.92003 1.24905
\(52\) 2.32931 + 3.30506i 0.323017 + 0.458329i
\(53\) −5.08219 −0.698093 −0.349046 0.937105i \(-0.613494\pi\)
−0.349046 + 0.937105i \(0.613494\pi\)
\(54\) 4.99029i 0.679092i
\(55\) 0.609564 0.0821936
\(56\) 11.2803 1.50739
\(57\) 5.43746i 0.720210i
\(58\) 4.23967i 0.556696i
\(59\) 9.83912i 1.28094i 0.767981 + 0.640472i \(0.221261\pi\)
−0.767981 + 0.640472i \(0.778739\pi\)
\(60\) 0.549671i 0.0709622i
\(61\) −9.60411 −1.22968 −0.614840 0.788652i \(-0.710780\pi\)
−0.614840 + 0.788652i \(0.710780\pi\)
\(62\) −0.937316 −0.119039
\(63\) 0.610127i 0.0768688i
\(64\) −6.04491 −0.755614
\(65\) 0.856916 0.603930i 0.106287 0.0749083i
\(66\) −3.31256 −0.407748
\(67\) 6.38630i 0.780210i −0.920770 0.390105i \(-0.872439\pi\)
0.920770 0.390105i \(-0.127561\pi\)
\(68\) 5.93402 0.719605
\(69\) −11.4655 −1.38029
\(70\) 1.05075i 0.125589i
\(71\) 3.60967i 0.428389i 0.976791 + 0.214194i \(0.0687126\pi\)
−0.976791 + 0.214194i \(0.931287\pi\)
\(72\) 0.463000i 0.0545651i
\(73\) 8.21949i 0.962018i 0.876716 + 0.481009i \(0.159730\pi\)
−0.876716 + 0.481009i \(0.840270\pi\)
\(74\) 4.51499 0.524857
\(75\) 8.28623 0.956812
\(76\) 3.61725i 0.414927i
\(77\) 8.08285 0.921127
\(78\) −4.65675 + 3.28195i −0.527273 + 0.371607i
\(79\) −4.16666 −0.468786 −0.234393 0.972142i \(-0.575310\pi\)
−0.234393 + 0.972142i \(0.575310\pi\)
\(80\) 0.145234i 0.0162377i
\(81\) −8.50021 −0.944468
\(82\) 5.77241 0.637456
\(83\) 5.60314i 0.615024i −0.951544 0.307512i \(-0.900504\pi\)
0.951544 0.307512i \(-0.0994964\pi\)
\(84\) 7.28867i 0.795260i
\(85\) 1.53854i 0.166878i
\(86\) 6.67605i 0.719897i
\(87\) −7.62499 −0.817484
\(88\) −6.13374 −0.653859
\(89\) 5.99295i 0.635251i −0.948216 0.317626i \(-0.897115\pi\)
0.948216 0.317626i \(-0.102885\pi\)
\(90\) −0.0431282 −0.00454611
\(91\) 11.3628 8.00815i 1.19114 0.839483i
\(92\) −7.62739 −0.795210
\(93\) 1.68575i 0.174804i
\(94\) −4.46982 −0.461026
\(95\) −0.937859 −0.0962224
\(96\) 9.07500i 0.926213i
\(97\) 1.49758i 0.152056i −0.997106 0.0760282i \(-0.975776\pi\)
0.997106 0.0760282i \(-0.0242239\pi\)
\(98\) 7.37184i 0.744668i
\(99\) 0.331761i 0.0333432i
\(100\) 5.51238 0.551238
\(101\) 6.72002 0.668667 0.334333 0.942455i \(-0.391489\pi\)
0.334333 + 0.942455i \(0.391489\pi\)
\(102\) 8.36089i 0.827851i
\(103\) −10.1453 −0.999647 −0.499824 0.866127i \(-0.666602\pi\)
−0.499824 + 0.866127i \(0.666602\pi\)
\(104\) −8.62273 + 6.07705i −0.845528 + 0.595904i
\(105\) −1.88976 −0.184422
\(106\) 4.76362i 0.462684i
\(107\) −13.0831 −1.26479 −0.632397 0.774644i \(-0.717929\pi\)
−0.632397 + 0.774644i \(0.717929\pi\)
\(108\) −5.97056 −0.574517
\(109\) 8.14852i 0.780486i −0.920712 0.390243i \(-0.872391\pi\)
0.920712 0.390243i \(-0.127609\pi\)
\(110\) 0.571354i 0.0544765i
\(111\) 8.12014i 0.770730i
\(112\) 1.92582i 0.181973i
\(113\) 20.6286 1.94057 0.970287 0.241958i \(-0.0777895\pi\)
0.970287 + 0.241958i \(0.0777895\pi\)
\(114\) 5.09662 0.477342
\(115\) 1.97758i 0.184411i
\(116\) −5.07249 −0.470969
\(117\) −0.328695 0.466385i −0.0303878 0.0431173i
\(118\) −9.22237 −0.848988
\(119\) 20.4011i 1.87016i
\(120\) 1.43406 0.130911
\(121\) 6.60489 0.600445
\(122\) 9.00209i 0.815011i
\(123\) 10.3816i 0.936077i
\(124\) 1.12144i 0.100708i
\(125\) 2.88302i 0.257865i
\(126\) −0.571882 −0.0509473
\(127\) 1.36933 0.121509 0.0607544 0.998153i \(-0.480649\pi\)
0.0607544 + 0.998153i \(0.480649\pi\)
\(128\) 5.10073i 0.450845i
\(129\) −12.0068 −1.05714
\(130\) 0.566074 + 0.803201i 0.0496479 + 0.0704454i
\(131\) 9.73999 0.850987 0.425494 0.904961i \(-0.360100\pi\)
0.425494 + 0.904961i \(0.360100\pi\)
\(132\) 3.96327i 0.344958i
\(133\) −12.4361 −1.07834
\(134\) 5.98598 0.517110
\(135\) 1.54801i 0.133232i
\(136\) 15.4815i 1.32753i
\(137\) 11.0632i 0.945191i −0.881280 0.472595i \(-0.843317\pi\)
0.881280 0.472595i \(-0.156683\pi\)
\(138\) 10.7468i 0.914829i
\(139\) 15.7894 1.33924 0.669620 0.742704i \(-0.266457\pi\)
0.669620 + 0.742704i \(0.266457\pi\)
\(140\) −1.25716 −0.106249
\(141\) 8.03890i 0.676998i
\(142\) −3.38340 −0.283929
\(143\) −6.17858 + 4.35449i −0.516679 + 0.364140i
\(144\) 0.0790451 0.00658709
\(145\) 1.31517i 0.109219i
\(146\) −7.70426 −0.637609
\(147\) −13.2581 −1.09351
\(148\) 5.40189i 0.444033i
\(149\) 2.97069i 0.243368i −0.992569 0.121684i \(-0.961171\pi\)
0.992569 0.121684i \(-0.0388295\pi\)
\(150\) 7.76682i 0.634158i
\(151\) 20.1243i 1.63770i 0.574011 + 0.818848i \(0.305387\pi\)
−0.574011 + 0.818848i \(0.694613\pi\)
\(152\) 9.43722 0.765460
\(153\) −0.837363 −0.0676967
\(154\) 7.57619i 0.610507i
\(155\) 0.290760 0.0233544
\(156\) 3.92664 + 5.57150i 0.314383 + 0.446077i
\(157\) 18.9740 1.51429 0.757147 0.653245i \(-0.226593\pi\)
0.757147 + 0.653245i \(0.226593\pi\)
\(158\) 3.90548i 0.310703i
\(159\) −8.56730 −0.679431
\(160\) 1.56527 0.123745
\(161\) 26.2229i 2.06665i
\(162\) 7.96739i 0.625977i
\(163\) 19.5049i 1.52774i −0.645369 0.763871i \(-0.723296\pi\)
0.645369 0.763871i \(-0.276704\pi\)
\(164\) 6.90632i 0.539293i
\(165\) 1.02757 0.0799964
\(166\) 5.25191 0.407627
\(167\) 23.5293i 1.82075i 0.413785 + 0.910375i \(0.364207\pi\)
−0.413785 + 0.910375i \(0.635793\pi\)
\(168\) 19.0158 1.46710
\(169\) −4.37152 + 12.2430i −0.336270 + 0.941765i
\(170\) 1.44209 0.110604
\(171\) 0.510439i 0.0390342i
\(172\) −7.98746 −0.609038
\(173\) 11.3779 0.865043 0.432522 0.901624i \(-0.357624\pi\)
0.432522 + 0.901624i \(0.357624\pi\)
\(174\) 7.14702i 0.541814i
\(175\) 18.9515i 1.43260i
\(176\) 1.04718i 0.0789338i
\(177\) 16.5863i 1.24670i
\(178\) 5.61729 0.421033
\(179\) 20.7125 1.54813 0.774063 0.633108i \(-0.218221\pi\)
0.774063 + 0.633108i \(0.218221\pi\)
\(180\) 0.0516001i 0.00384604i
\(181\) 2.21171 0.164395 0.0821975 0.996616i \(-0.473806\pi\)
0.0821975 + 0.996616i \(0.473806\pi\)
\(182\) 7.50617 + 10.6505i 0.556394 + 0.789468i
\(183\) −16.1901 −1.19681
\(184\) 19.8995i 1.46701i
\(185\) −1.40057 −0.102972
\(186\) −1.58008 −0.115857
\(187\) 11.0932i 0.811217i
\(188\) 5.34785i 0.390032i
\(189\) 20.5267i 1.49310i
\(190\) 0.879071i 0.0637745i
\(191\) −5.93737 −0.429613 −0.214806 0.976657i \(-0.568912\pi\)
−0.214806 + 0.976657i \(0.568912\pi\)
\(192\) −10.1902 −0.735415
\(193\) 7.67380i 0.552372i 0.961104 + 0.276186i \(0.0890706\pi\)
−0.961104 + 0.276186i \(0.910929\pi\)
\(194\) 1.40371 0.100780
\(195\) 1.44455 1.01807i 0.103446 0.0729059i
\(196\) −8.81993 −0.629995
\(197\) 10.6398i 0.758057i 0.925385 + 0.379029i \(0.123742\pi\)
−0.925385 + 0.379029i \(0.876258\pi\)
\(198\) 0.310965 0.0220993
\(199\) −21.8838 −1.55130 −0.775650 0.631163i \(-0.782578\pi\)
−0.775650 + 0.631163i \(0.782578\pi\)
\(200\) 14.3815i 1.01693i
\(201\) 10.7657i 0.759354i
\(202\) 6.29878i 0.443181i
\(203\) 17.4392i 1.22399i
\(204\) 10.0033 0.700368
\(205\) −1.79063 −0.125063
\(206\) 9.50936i 0.662549i
\(207\) 1.07632 0.0748093
\(208\) −1.03750 1.47210i −0.0719375 0.102072i
\(209\) 6.76220 0.467751
\(210\) 1.77131i 0.122232i
\(211\) 27.2902 1.87873 0.939366 0.342917i \(-0.111415\pi\)
0.939366 + 0.342917i \(0.111415\pi\)
\(212\) −5.69937 −0.391434
\(213\) 6.08500i 0.416937i
\(214\) 12.2630i 0.838284i
\(215\) 2.07094i 0.141237i
\(216\) 15.5769i 1.05987i
\(217\) 3.85549 0.261728
\(218\) 7.63774 0.517293
\(219\) 13.8560i 0.936302i
\(220\) 0.683588 0.0460875
\(221\) 10.9907 + 15.5947i 0.739315 + 1.04901i
\(222\) 7.61114 0.510826
\(223\) 23.9038i 1.60071i −0.599524 0.800357i \(-0.704643\pi\)
0.599524 0.800357i \(-0.295357\pi\)
\(224\) 20.7555 1.38679
\(225\) −0.777865 −0.0518577
\(226\) 19.3355i 1.28618i
\(227\) 14.9621i 0.993072i −0.868016 0.496536i \(-0.834605\pi\)
0.868016 0.496536i \(-0.165395\pi\)
\(228\) 6.09778i 0.403835i
\(229\) 13.2617i 0.876355i −0.898888 0.438178i \(-0.855624\pi\)
0.898888 0.438178i \(-0.144376\pi\)
\(230\) −1.85362 −0.122224
\(231\) 13.6257 0.896503
\(232\) 13.2339i 0.868846i
\(233\) −0.641941 −0.0420549 −0.0210275 0.999779i \(-0.506694\pi\)
−0.0210275 + 0.999779i \(0.506694\pi\)
\(234\) 0.437150 0.308091i 0.0285774 0.0201405i
\(235\) 1.38656 0.0904491
\(236\) 11.0340i 0.718250i
\(237\) −7.02395 −0.456254
\(238\) 19.1223 1.23951
\(239\) 4.79323i 0.310048i 0.987911 + 0.155024i \(0.0495455\pi\)
−0.987911 + 0.155024i \(0.950454\pi\)
\(240\) 0.244829i 0.0158036i
\(241\) 20.2887i 1.30691i 0.756966 + 0.653454i \(0.226681\pi\)
−0.756966 + 0.653454i \(0.773319\pi\)
\(242\) 6.19087i 0.397964i
\(243\) 1.64282 0.105387
\(244\) −10.7704 −0.689506
\(245\) 2.28678i 0.146097i
\(246\) 9.73084 0.620416
\(247\) 9.50620 6.69970i 0.604865 0.426292i
\(248\) −2.92577 −0.185787
\(249\) 9.44548i 0.598583i
\(250\) 2.70230 0.170908
\(251\) −21.8713 −1.38050 −0.690251 0.723570i \(-0.742500\pi\)
−0.690251 + 0.723570i \(0.742500\pi\)
\(252\) 0.684220i 0.0431018i
\(253\) 14.2589i 0.896447i
\(254\) 1.28350i 0.0805339i
\(255\) 2.59359i 0.162417i
\(256\) −16.8708 −1.05443
\(257\) −15.8299 −0.987444 −0.493722 0.869620i \(-0.664364\pi\)
−0.493722 + 0.869620i \(0.664364\pi\)
\(258\) 11.2541i 0.700652i
\(259\) −18.5717 −1.15399
\(260\) 0.960979 0.677270i 0.0595974 0.0420025i
\(261\) 0.715791 0.0443064
\(262\) 9.12945i 0.564020i
\(263\) 3.06797 0.189179 0.0945897 0.995516i \(-0.469846\pi\)
0.0945897 + 0.995516i \(0.469846\pi\)
\(264\) −10.3400 −0.636380
\(265\) 1.47770i 0.0907742i
\(266\) 11.6565i 0.714708i
\(267\) 10.1026i 0.618269i
\(268\) 7.16184i 0.437479i
\(269\) 6.90791 0.421183 0.210591 0.977574i \(-0.432461\pi\)
0.210591 + 0.977574i \(0.432461\pi\)
\(270\) −1.45098 −0.0883035
\(271\) 32.2346i 1.95811i 0.203597 + 0.979055i \(0.434737\pi\)
−0.203597 + 0.979055i \(0.565263\pi\)
\(272\) −2.64307 −0.160259
\(273\) 19.1548 13.4997i 1.15930 0.817041i
\(274\) 10.3697 0.626456
\(275\) 10.3050i 0.621416i
\(276\) −12.8579 −0.773952
\(277\) 16.2761 0.977938 0.488969 0.872301i \(-0.337373\pi\)
0.488969 + 0.872301i \(0.337373\pi\)
\(278\) 14.7997i 0.887625i
\(279\) 0.158249i 0.00947410i
\(280\) 3.27986i 0.196009i
\(281\) 22.5291i 1.34397i 0.740563 + 0.671987i \(0.234559\pi\)
−0.740563 + 0.671987i \(0.765441\pi\)
\(282\) −7.53499 −0.448702
\(283\) −11.1486 −0.662718 −0.331359 0.943505i \(-0.607507\pi\)
−0.331359 + 0.943505i \(0.607507\pi\)
\(284\) 4.04802i 0.240206i
\(285\) −1.58100 −0.0936501
\(286\) −4.08153 5.79128i −0.241346 0.342446i
\(287\) −23.7439 −1.40156
\(288\) 0.851910i 0.0501993i
\(289\) 10.9993 0.647015
\(290\) −1.23273 −0.0723882
\(291\) 2.52455i 0.147992i
\(292\) 9.21765i 0.539422i
\(293\) 29.1854i 1.70503i −0.522705 0.852514i \(-0.675077\pi\)
0.522705 0.852514i \(-0.324923\pi\)
\(294\) 12.4271i 0.724762i
\(295\) 2.86082 0.166564
\(296\) 14.0933 0.819154
\(297\) 11.1615i 0.647658i
\(298\) 2.78447 0.161300
\(299\) −14.1271 20.0449i −0.816991 1.15923i
\(300\) 9.29250 0.536503
\(301\) 27.4608i 1.58281i
\(302\) −18.8629 −1.08544
\(303\) 11.3283 0.650792
\(304\) 1.61116i 0.0924062i
\(305\) 2.79249i 0.159898i
\(306\) 0.784873i 0.0448682i
\(307\) 10.2881i 0.587175i −0.955932 0.293588i \(-0.905151\pi\)
0.955932 0.293588i \(-0.0948493\pi\)
\(308\) 9.06442 0.516493
\(309\) −17.1025 −0.972925
\(310\) 0.272534i 0.0154789i
\(311\) 6.14155 0.348256 0.174128 0.984723i \(-0.444289\pi\)
0.174128 + 0.984723i \(0.444289\pi\)
\(312\) −14.5358 + 10.2444i −0.822925 + 0.579974i
\(313\) 8.55769 0.483709 0.241855 0.970313i \(-0.422244\pi\)
0.241855 + 0.970313i \(0.422244\pi\)
\(314\) 17.7847i 1.00365i
\(315\) 0.177401 0.00999539
\(316\) −4.67265 −0.262857
\(317\) 14.4222i 0.810032i −0.914310 0.405016i \(-0.867266\pi\)
0.914310 0.405016i \(-0.132734\pi\)
\(318\) 8.03027i 0.450315i
\(319\) 9.48267i 0.530928i
\(320\) 1.75762i 0.0982538i
\(321\) −22.0549 −1.23098
\(322\) −24.5791 −1.36974
\(323\) 17.0678i 0.949676i
\(324\) −9.53246 −0.529581
\(325\) 10.2098 + 14.4866i 0.566337 + 0.803575i
\(326\) 18.2823 1.01256
\(327\) 13.7364i 0.759622i
\(328\) 18.0182 0.994890
\(329\) 18.3859 1.01364
\(330\) 0.963160i 0.0530202i
\(331\) 21.6554i 1.19029i −0.803620 0.595143i \(-0.797095\pi\)
0.803620 0.595143i \(-0.202905\pi\)
\(332\) 6.28357i 0.344856i
\(333\) 0.762274i 0.0417723i
\(334\) −22.0544 −1.20676
\(335\) −1.85688 −0.101452
\(336\) 3.24644i 0.177108i
\(337\) 14.4456 0.786904 0.393452 0.919345i \(-0.371281\pi\)
0.393452 + 0.919345i \(0.371281\pi\)
\(338\) −11.4755 4.09749i −0.624186 0.222874i
\(339\) 34.7746 1.88870
\(340\) 1.72537i 0.0935715i
\(341\) −2.09645 −0.113529
\(342\) −0.478442 −0.0258712
\(343\) 3.33438i 0.180039i
\(344\) 20.8389i 1.12356i
\(345\) 3.33371i 0.179481i
\(346\) 10.6647i 0.573335i
\(347\) −9.70087 −0.520770 −0.260385 0.965505i \(-0.583849\pi\)
−0.260385 + 0.965505i \(0.583849\pi\)
\(348\) −8.55095 −0.458379
\(349\) 2.05208i 0.109845i −0.998491 0.0549227i \(-0.982509\pi\)
0.998491 0.0549227i \(-0.0174912\pi\)
\(350\) 17.7636 0.949503
\(351\) −11.0584 15.6907i −0.590253 0.837509i
\(352\) −11.2860 −0.601543
\(353\) 11.7324i 0.624452i −0.950008 0.312226i \(-0.898925\pi\)
0.950008 0.312226i \(-0.101075\pi\)
\(354\) −15.5466 −0.826293
\(355\) 1.04955 0.0557042
\(356\) 6.72072i 0.356197i
\(357\) 34.3911i 1.82017i
\(358\) 19.4142i 1.02607i
\(359\) 24.9325i 1.31588i 0.753068 + 0.657942i \(0.228573\pi\)
−0.753068 + 0.657942i \(0.771427\pi\)
\(360\) −0.134622 −0.00709520
\(361\) 8.59585 0.452413
\(362\) 2.07307i 0.108958i
\(363\) 11.1342 0.584394
\(364\) 12.7426 8.98065i 0.667896 0.470714i
\(365\) 2.38990 0.125093
\(366\) 15.1753i 0.793224i
\(367\) 13.7018 0.715230 0.357615 0.933869i \(-0.383590\pi\)
0.357615 + 0.933869i \(0.383590\pi\)
\(368\) 3.39731 0.177097
\(369\) 0.974566i 0.0507339i
\(370\) 1.31278i 0.0682481i
\(371\) 19.5944i 1.01729i
\(372\) 1.89046i 0.0980160i
\(373\) −9.22059 −0.477424 −0.238712 0.971090i \(-0.576725\pi\)
−0.238712 + 0.971090i \(0.576725\pi\)
\(374\) −10.3979 −0.537661
\(375\) 4.86005i 0.250972i
\(376\) −13.9523 −0.719533
\(377\) −9.39503 13.3306i −0.483869 0.686561i
\(378\) −19.2400 −0.989600
\(379\) 7.66126i 0.393532i 0.980450 + 0.196766i \(0.0630440\pi\)
−0.980450 + 0.196766i \(0.936956\pi\)
\(380\) −1.05175 −0.0539537
\(381\) 2.30835 0.118261
\(382\) 5.56519i 0.284740i
\(383\) 3.77098i 0.192688i −0.995348 0.0963440i \(-0.969285\pi\)
0.995348 0.0963440i \(-0.0307149\pi\)
\(384\) 8.59855i 0.438793i
\(385\) 2.35017i 0.119776i
\(386\) −7.19278 −0.366103
\(387\) 1.12713 0.0572952
\(388\) 1.67944i 0.0852609i
\(389\) −1.98742 −0.100766 −0.0503831 0.998730i \(-0.516044\pi\)
−0.0503831 + 0.998730i \(0.516044\pi\)
\(390\) 0.954258 + 1.35400i 0.0483207 + 0.0685623i
\(391\) −35.9893 −1.82006
\(392\) 23.0107i 1.16222i
\(393\) 16.4192 0.828239
\(394\) −9.97289 −0.502427
\(395\) 1.21150i 0.0609571i
\(396\) 0.372049i 0.0186962i
\(397\) 7.83722i 0.393339i −0.980470 0.196669i \(-0.936987\pi\)
0.980470 0.196669i \(-0.0630126\pi\)
\(398\) 20.5120i 1.02817i
\(399\) −20.9641 −1.04952
\(400\) −2.45527 −0.122763
\(401\) 23.9276i 1.19489i 0.801911 + 0.597444i \(0.203817\pi\)
−0.801911 + 0.597444i \(0.796183\pi\)
\(402\) 10.0909 0.503286
\(403\) −2.94716 + 2.07708i −0.146809 + 0.103466i
\(404\) 7.53609 0.374934
\(405\) 2.47152i 0.122811i
\(406\) −16.3460 −0.811240
\(407\) 10.0985 0.500562
\(408\) 26.0980i 1.29204i
\(409\) 26.7159i 1.32101i 0.750820 + 0.660507i \(0.229659\pi\)
−0.750820 + 0.660507i \(0.770341\pi\)
\(410\) 1.67839i 0.0828896i
\(411\) 18.6497i 0.919924i
\(412\) −11.3773 −0.560521
\(413\) 37.9347 1.86664
\(414\) 1.00885i 0.0495823i
\(415\) −1.62917 −0.0799727
\(416\) −15.8656 + 11.1816i −0.777877 + 0.548225i
\(417\) 26.6170 1.30344
\(418\) 6.33832i 0.310017i
\(419\) −17.5555 −0.857641 −0.428821 0.903390i \(-0.641071\pi\)
−0.428821 + 0.903390i \(0.641071\pi\)
\(420\) −2.11925 −0.103409
\(421\) 27.6416i 1.34717i 0.739110 + 0.673585i \(0.235246\pi\)
−0.739110 + 0.673585i \(0.764754\pi\)
\(422\) 25.5795i 1.24519i
\(423\) 0.754647i 0.0366922i
\(424\) 14.8693i 0.722119i
\(425\) 26.0098 1.26166
\(426\) −5.70357 −0.276339
\(427\) 37.0286i 1.79194i
\(428\) −14.6719 −0.709195
\(429\) −10.4155 + 7.34057i −0.502867 + 0.354406i
\(430\) −1.94113 −0.0936094
\(431\) 23.6042i 1.13697i −0.822692 0.568487i \(-0.807529\pi\)
0.822692 0.568487i \(-0.192471\pi\)
\(432\) 2.65934 0.127948
\(433\) −17.3815 −0.835303 −0.417651 0.908607i \(-0.637147\pi\)
−0.417651 + 0.908607i \(0.637147\pi\)
\(434\) 3.61382i 0.173469i
\(435\) 2.21704i 0.106299i
\(436\) 9.13806i 0.437634i
\(437\) 21.9383i 1.04945i
\(438\) −12.9875 −0.620565
\(439\) −20.9810 −1.00137 −0.500684 0.865630i \(-0.666918\pi\)
−0.500684 + 0.865630i \(0.666918\pi\)
\(440\) 1.78345i 0.0850225i
\(441\) 1.24460 0.0592667
\(442\) −14.6172 + 10.3018i −0.695268 + 0.490005i
\(443\) −32.4721 −1.54280 −0.771399 0.636352i \(-0.780443\pi\)
−0.771399 + 0.636352i \(0.780443\pi\)
\(444\) 9.10624i 0.432163i
\(445\) −1.74251 −0.0826028
\(446\) 22.4054 1.06093
\(447\) 5.00783i 0.236862i
\(448\) 23.3061i 1.10111i
\(449\) 22.2111i 1.04821i −0.851655 0.524103i \(-0.824401\pi\)
0.851655 0.524103i \(-0.175599\pi\)
\(450\) 0.729106i 0.0343704i
\(451\) 12.9109 0.607950
\(452\) 23.1337 1.08812
\(453\) 33.9246i 1.59392i
\(454\) 14.0243 0.658191
\(455\) −2.32845 3.30384i −0.109159 0.154886i
\(456\) 15.9088 0.744997
\(457\) 24.7016i 1.15549i 0.816216 + 0.577747i \(0.196068\pi\)
−0.816216 + 0.577747i \(0.803932\pi\)
\(458\) 12.4304 0.580833
\(459\) −28.1717 −1.31494
\(460\) 2.21774i 0.103403i
\(461\) 1.87166i 0.0871720i −0.999050 0.0435860i \(-0.986122\pi\)
0.999050 0.0435860i \(-0.0138783\pi\)
\(462\) 12.7716i 0.594187i
\(463\) 33.6330i 1.56306i −0.623869 0.781529i \(-0.714440\pi\)
0.623869 0.781529i \(-0.285560\pi\)
\(464\) 2.25934 0.104887
\(465\) 0.490148 0.0227301
\(466\) 0.601701i 0.0278733i
\(467\) −11.9042 −0.550861 −0.275430 0.961321i \(-0.588820\pi\)
−0.275430 + 0.961321i \(0.588820\pi\)
\(468\) −0.368611 0.523022i −0.0170390 0.0241767i
\(469\) −24.6223 −1.13695
\(470\) 1.29964i 0.0599481i
\(471\) 31.9855 1.47381
\(472\) −28.7871 −1.32503
\(473\) 14.9320i 0.686574i
\(474\) 6.58366i 0.302397i
\(475\) 15.8550i 0.727479i
\(476\) 22.8786i 1.04864i
\(477\) 0.804251 0.0368241
\(478\) −4.49277 −0.205495
\(479\) 9.00430i 0.411417i −0.978613 0.205708i \(-0.934050\pi\)
0.978613 0.205708i \(-0.0659499\pi\)
\(480\) 2.63865 0.120437
\(481\) 14.1963 10.0051i 0.647295 0.456195i
\(482\) −19.0169 −0.866196
\(483\) 44.2052i 2.01141i
\(484\) 7.40698 0.336681
\(485\) −0.435436 −0.0197722
\(486\) 1.53984i 0.0698487i
\(487\) 36.5025i 1.65409i −0.562139 0.827043i \(-0.690021\pi\)
0.562139 0.827043i \(-0.309979\pi\)
\(488\) 28.0995i 1.27200i
\(489\) 32.8804i 1.48690i
\(490\) −2.14344 −0.0968305
\(491\) 9.04853 0.408355 0.204177 0.978934i \(-0.434548\pi\)
0.204177 + 0.978934i \(0.434548\pi\)
\(492\) 11.6423i 0.524876i
\(493\) −23.9342 −1.07794
\(494\) 6.27974 + 8.91032i 0.282539 + 0.400894i
\(495\) −0.0964627 −0.00433568
\(496\) 0.499499i 0.0224282i
\(497\) 13.9171 0.624265
\(498\) 8.85340 0.396731
\(499\) 26.1949i 1.17264i 0.810078 + 0.586322i \(0.199425\pi\)
−0.810078 + 0.586322i \(0.800575\pi\)
\(500\) 3.23313i 0.144590i
\(501\) 39.6645i 1.77208i
\(502\) 20.5003i 0.914972i
\(503\) −19.4070 −0.865315 −0.432657 0.901558i \(-0.642424\pi\)
−0.432657 + 0.901558i \(0.642424\pi\)
\(504\) −1.78509 −0.0795144
\(505\) 1.95391i 0.0869479i
\(506\) 13.3651 0.594150
\(507\) −7.36928 + 20.6385i −0.327281 + 0.916590i
\(508\) 1.53562 0.0681323
\(509\) 2.27885i 0.101008i −0.998724 0.0505041i \(-0.983917\pi\)
0.998724 0.0505041i \(-0.0160828\pi\)
\(510\) 2.43101 0.107647
\(511\) 31.6902 1.40189
\(512\) 5.61183i 0.248010i
\(513\) 17.1729i 0.758200i
\(514\) 14.8376i 0.654460i
\(515\) 2.94985i 0.129986i
\(516\) −13.4649 −0.592757
\(517\) −9.99743 −0.439686
\(518\) 17.4075i 0.764842i
\(519\) 19.1802 0.841919
\(520\) 1.76696 + 2.50714i 0.0774865 + 0.109946i
\(521\) 29.5904 1.29638 0.648189 0.761479i \(-0.275527\pi\)
0.648189 + 0.761479i \(0.275527\pi\)
\(522\) 0.670923i 0.0293655i
\(523\) 31.9338 1.39637 0.698183 0.715919i \(-0.253992\pi\)
0.698183 + 0.715919i \(0.253992\pi\)
\(524\) 10.9228 0.477165
\(525\) 31.9475i 1.39430i
\(526\) 2.87566i 0.125385i
\(527\) 5.29143i 0.230498i
\(528\) 1.76528i 0.0768238i
\(529\) 23.2595 1.01128
\(530\) −1.38507 −0.0601636
\(531\) 1.55703i 0.0675693i
\(532\) −13.9463 −0.604649
\(533\) 18.1499 12.7916i 0.786161 0.554064i
\(534\) 9.46934 0.409778
\(535\) 3.80405i 0.164464i
\(536\) 18.6849 0.807063
\(537\) 34.9161 1.50674
\(538\) 6.47490i 0.279153i
\(539\) 16.4882i 0.710199i
\(540\) 1.73600i 0.0747055i
\(541\) 14.7693i 0.634983i −0.948261 0.317491i \(-0.897160\pi\)
0.948261 0.317491i \(-0.102840\pi\)
\(542\) −30.2140 −1.29780
\(543\) 3.72839 0.160000
\(544\) 28.4857i 1.22131i
\(545\) −2.36926 −0.101488
\(546\) 12.6535 + 17.9541i 0.541521 + 0.768364i
\(547\) 11.1112 0.475082 0.237541 0.971377i \(-0.423659\pi\)
0.237541 + 0.971377i \(0.423659\pi\)
\(548\) 12.4067i 0.529987i
\(549\) 1.51984 0.0648651
\(550\) −9.65906 −0.411864
\(551\) 14.5898i 0.621546i
\(552\) 33.5455i 1.42779i
\(553\) 16.0645i 0.683134i
\(554\) 15.2559i 0.648160i
\(555\) −2.36101 −0.100219
\(556\) 17.7069 0.750938
\(557\) 22.7023i 0.961925i −0.876741 0.480963i \(-0.840287\pi\)
0.876741 0.480963i \(-0.159713\pi\)
\(558\) 0.148329 0.00627927
\(559\) −14.7940 20.9912i −0.625719 0.887833i
\(560\) 0.559950 0.0236622
\(561\) 18.7004i 0.789532i
\(562\) −21.1169 −0.890762
\(563\) −1.26121 −0.0531536 −0.0265768 0.999647i \(-0.508461\pi\)
−0.0265768 + 0.999647i \(0.508461\pi\)
\(564\) 9.01513i 0.379606i
\(565\) 5.99796i 0.252336i
\(566\) 10.4498i 0.439238i
\(567\) 32.7725i 1.37632i
\(568\) −10.5611 −0.443133
\(569\) −5.71226 −0.239470 −0.119735 0.992806i \(-0.538205\pi\)
−0.119735 + 0.992806i \(0.538205\pi\)
\(570\) 1.48189i 0.0620697i
\(571\) 10.4480 0.437234 0.218617 0.975811i \(-0.429846\pi\)
0.218617 + 0.975811i \(0.429846\pi\)
\(572\) −6.92889 + 4.88329i −0.289712 + 0.204181i
\(573\) −10.0089 −0.418128
\(574\) 22.2555i 0.928927i
\(575\) −33.4322 −1.39422
\(576\) 0.956599 0.0398583
\(577\) 15.5655i 0.647999i −0.946057 0.324000i \(-0.894972\pi\)
0.946057 0.324000i \(-0.105028\pi\)
\(578\) 10.3098i 0.428830i
\(579\) 12.9361i 0.537606i
\(580\) 1.47488i 0.0612410i
\(581\) −21.6029 −0.896238
\(582\) 2.36630 0.0980862
\(583\) 10.6546i 0.441267i
\(584\) −24.0484 −0.995129
\(585\) −0.135606 + 0.0955712i −0.00560661 + 0.00395138i
\(586\) 27.3559 1.13006
\(587\) 10.6110i 0.437962i −0.975729 0.218981i \(-0.929727\pi\)
0.975729 0.218981i \(-0.0702733\pi\)
\(588\) −14.8682 −0.613154
\(589\) 3.22555 0.132906
\(590\) 2.68149i 0.110395i
\(591\) 17.9361i 0.737793i
\(592\) 2.40605i 0.0988882i
\(593\) 46.0558i 1.89129i 0.325206 + 0.945643i \(0.394566\pi\)
−0.325206 + 0.945643i \(0.605434\pi\)
\(594\) 10.4619 0.429257
\(595\) −5.93182 −0.243181
\(596\) 3.33144i 0.136461i
\(597\) −36.8906 −1.50983
\(598\) 18.7884 13.2415i 0.768316 0.541487i
\(599\) −8.40314 −0.343343 −0.171672 0.985154i \(-0.554917\pi\)
−0.171672 + 0.985154i \(0.554917\pi\)
\(600\) 24.2436i 0.989743i
\(601\) 44.1276 1.80000 0.900001 0.435888i \(-0.143566\pi\)
0.900001 + 0.435888i \(0.143566\pi\)
\(602\) −25.7395 −1.04906
\(603\) 1.01062i 0.0411558i
\(604\) 22.5682i 0.918287i
\(605\) 1.92044i 0.0780769i
\(606\) 10.6182i 0.431334i
\(607\) 10.1399 0.411564 0.205782 0.978598i \(-0.434026\pi\)
0.205782 + 0.978598i \(0.434026\pi\)
\(608\) 17.3643 0.704215
\(609\) 29.3981i 1.19127i
\(610\) −2.61745 −0.105977
\(611\) −14.0542 + 9.90503i −0.568574 + 0.400715i
\(612\) −0.939050 −0.0379589
\(613\) 0.969289i 0.0391492i −0.999808 0.0195746i \(-0.993769\pi\)
0.999808 0.0195746i \(-0.00623119\pi\)
\(614\) 9.64325 0.389170
\(615\) −3.01855 −0.121720
\(616\) 23.6486i 0.952830i
\(617\) 8.86561i 0.356916i 0.983948 + 0.178458i \(0.0571108\pi\)
−0.983948 + 0.178458i \(0.942889\pi\)
\(618\) 16.0304i 0.644838i
\(619\) 23.1571i 0.930763i 0.885110 + 0.465381i \(0.154083\pi\)
−0.885110 + 0.465381i \(0.845917\pi\)
\(620\) 0.326069 0.0130953
\(621\) 36.2109 1.45309
\(622\) 5.75658i 0.230818i
\(623\) −23.1058 −0.925713
\(624\) −1.74896 2.48160i −0.0700145 0.0993435i
\(625\) 23.7390 0.949561
\(626\) 8.02126i 0.320594i
\(627\) 11.3994 0.455247
\(628\) 21.2782 0.849094
\(629\) 25.4885i 1.01629i
\(630\) 0.166280i 0.00662477i
\(631\) 0.538705i 0.0214455i 0.999943 + 0.0107228i \(0.00341323\pi\)
−0.999943 + 0.0107228i \(0.996587\pi\)
\(632\) 12.1907i 0.484921i
\(633\) 46.0044 1.82851
\(634\) 13.5182 0.536875
\(635\) 0.398147i 0.0158000i
\(636\) −9.60770 −0.380970
\(637\) −16.3359 23.1789i −0.647250 0.918383i
\(638\) 8.88826 0.351890
\(639\) 0.571226i 0.0225973i
\(640\) 1.48309 0.0586242
\(641\) −10.1422 −0.400593 −0.200296 0.979735i \(-0.564191\pi\)
−0.200296 + 0.979735i \(0.564191\pi\)
\(642\) 20.6724i 0.815875i
\(643\) 40.0663i 1.58006i 0.613068 + 0.790030i \(0.289935\pi\)
−0.613068 + 0.790030i \(0.710065\pi\)
\(644\) 29.4074i 1.15881i
\(645\) 3.49109i 0.137461i
\(646\) 15.9979 0.629428
\(647\) −9.30740 −0.365912 −0.182956 0.983121i \(-0.558567\pi\)
−0.182956 + 0.983121i \(0.558567\pi\)
\(648\) 24.8697i 0.976974i
\(649\) −20.6272 −0.809690
\(650\) −13.5786 + 9.56979i −0.532595 + 0.375358i
\(651\) 6.49940 0.254731
\(652\) 21.8735i 0.856634i
\(653\) −18.5912 −0.727530 −0.363765 0.931491i \(-0.618509\pi\)
−0.363765 + 0.931491i \(0.618509\pi\)
\(654\) 12.8753 0.503464
\(655\) 2.83200i 0.110655i
\(656\) 3.07614i 0.120103i
\(657\) 1.30072i 0.0507461i
\(658\) 17.2334i 0.671826i
\(659\) 46.6156 1.81589 0.907944 0.419092i \(-0.137651\pi\)
0.907944 + 0.419092i \(0.137651\pi\)
\(660\) 1.15236 0.0448555
\(661\) 11.4634i 0.445874i −0.974833 0.222937i \(-0.928436\pi\)
0.974833 0.222937i \(-0.0715645\pi\)
\(662\) 20.2979 0.788901
\(663\) 18.5276 + 26.2888i 0.719551 + 1.02097i
\(664\) 16.3935 0.636192
\(665\) 3.61591i 0.140219i
\(666\) −0.714491 −0.0276860
\(667\) 30.7643 1.19120
\(668\) 26.3866i 1.02093i
\(669\) 40.2957i 1.55792i
\(670\) 1.74048i 0.0672407i
\(671\) 20.1346i 0.777286i
\(672\) 34.9886 1.34971
\(673\) 21.9979 0.847957 0.423978 0.905672i \(-0.360633\pi\)
0.423978 + 0.905672i \(0.360633\pi\)
\(674\) 13.5401i 0.521546i
\(675\) −26.1700 −1.00728
\(676\) −4.90239 + 13.7297i −0.188553 + 0.528066i
\(677\) −21.3442 −0.820325 −0.410162 0.912013i \(-0.634528\pi\)
−0.410162 + 0.912013i \(0.634528\pi\)
\(678\) 32.5948i 1.25180i
\(679\) −5.77392 −0.221583
\(680\) 4.50141 0.172621
\(681\) 25.2224i 0.966525i
\(682\) 1.96504i 0.0752452i
\(683\) 51.2441i 1.96080i −0.197019 0.980400i \(-0.563126\pi\)
0.197019 0.980400i \(-0.436874\pi\)
\(684\) 0.572426i 0.0218872i
\(685\) −3.21673 −0.122905
\(686\) −3.12537 −0.119327
\(687\) 22.3558i 0.852928i
\(688\) 3.55769 0.135636
\(689\) −10.5561 14.9780i −0.402155 0.570618i
\(690\) −3.12474 −0.118957
\(691\) 1.09848i 0.0417883i −0.999782 0.0208942i \(-0.993349\pi\)
0.999782 0.0208942i \(-0.00665130\pi\)
\(692\) 12.7596 0.485046
\(693\) −1.27910 −0.0485891
\(694\) 9.09278i 0.345157i
\(695\) 4.59093i 0.174144i
\(696\) 22.3090i 0.845620i
\(697\) 32.5870i 1.23432i
\(698\) 1.92345 0.0728036
\(699\) −1.08215 −0.0409307
\(700\) 21.2530i 0.803287i
\(701\) −15.7633 −0.595372 −0.297686 0.954664i \(-0.596215\pi\)
−0.297686 + 0.954664i \(0.596215\pi\)
\(702\) 14.7072 10.3652i 0.555087 0.391209i
\(703\) −15.5372 −0.585998
\(704\) 12.6729i 0.477626i
\(705\) 2.33739 0.0880312
\(706\) 10.9970 0.413876
\(707\) 25.9090i 0.974408i
\(708\) 18.6005i 0.699050i
\(709\) 16.6481i 0.625233i −0.949879 0.312617i \(-0.898794\pi\)
0.949879 0.312617i \(-0.101206\pi\)
\(710\) 0.983757i 0.0369198i
\(711\) 0.659369 0.0247283
\(712\) 17.5340 0.657115
\(713\) 6.80143i 0.254716i
\(714\) 32.2354 1.20638
\(715\) 1.26611 + 1.79648i 0.0473498 + 0.0671846i
\(716\) 23.2278 0.868064
\(717\) 8.08018i 0.301760i
\(718\) −23.3696 −0.872145
\(719\) −20.8992 −0.779408 −0.389704 0.920940i \(-0.627423\pi\)
−0.389704 + 0.920940i \(0.627423\pi\)
\(720\) 0.0229831i 0.000856531i
\(721\) 39.1152i 1.45673i
\(722\) 8.05703i 0.299852i
\(723\) 34.2016i 1.27197i
\(724\) 2.48029 0.0921794
\(725\) −22.2336 −0.825736
\(726\) 10.4363i 0.387326i
\(727\) −12.5078 −0.463889 −0.231945 0.972729i \(-0.574509\pi\)
−0.231945 + 0.972729i \(0.574509\pi\)
\(728\) 23.4301 + 33.2449i 0.868375 + 1.23214i
\(729\) 28.2700 1.04704
\(730\) 2.24009i 0.0829094i
\(731\) −37.6883 −1.39395
\(732\) −18.1562 −0.671074
\(733\) 21.1736i 0.782064i 0.920377 + 0.391032i \(0.127882\pi\)
−0.920377 + 0.391032i \(0.872118\pi\)
\(734\) 12.8429i 0.474042i
\(735\) 3.85494i 0.142191i
\(736\) 36.6146i 1.34963i
\(737\) 13.3886 0.493174
\(738\) −0.913477 −0.0336255
\(739\) 23.8513i 0.877385i 0.898637 + 0.438693i \(0.144558\pi\)
−0.898637 + 0.438693i \(0.855442\pi\)
\(740\) −1.57065 −0.0577384
\(741\) 16.0251 11.2940i 0.588696 0.414896i
\(742\) −18.3661 −0.674241
\(743\) 10.3245i 0.378771i −0.981903 0.189385i \(-0.939350\pi\)
0.981903 0.189385i \(-0.0606496\pi\)
\(744\) −4.93212 −0.180820
\(745\) −0.863756 −0.0316456
\(746\) 8.64260i 0.316428i
\(747\) 0.886689i 0.0324423i
\(748\) 12.4404i 0.454865i
\(749\) 50.4420i 1.84311i
\(750\) 4.55540 0.166340
\(751\) 43.3903 1.58333 0.791667 0.610953i \(-0.209213\pi\)
0.791667 + 0.610953i \(0.209213\pi\)
\(752\) 2.38198i 0.0868619i
\(753\) −36.8695 −1.34360
\(754\) 12.4950 8.80612i 0.455041 0.320700i
\(755\) 5.85135 0.212952
\(756\) 23.0194i 0.837209i
\(757\) 14.4887 0.526600 0.263300 0.964714i \(-0.415189\pi\)
0.263300 + 0.964714i \(0.415189\pi\)
\(758\) −7.18102 −0.260826
\(759\) 24.0369i 0.872483i
\(760\) 2.74397i 0.0995341i
\(761\) 45.1186i 1.63555i 0.575541 + 0.817773i \(0.304792\pi\)
−0.575541 + 0.817773i \(0.695208\pi\)
\(762\) 2.16366i 0.0783811i
\(763\) −31.4166 −1.13736
\(764\) −6.65839 −0.240892
\(765\) 0.243471i 0.00880273i
\(766\) 3.53460 0.127710
\(767\) −28.9975 + 20.4366i −1.04704 + 0.737923i
\(768\) −28.4400 −1.02624
\(769\) 13.9625i 0.503502i 0.967792 + 0.251751i \(0.0810064\pi\)
−0.967792 + 0.251751i \(0.918994\pi\)
\(770\) 2.20285 0.0793853
\(771\) −26.6853 −0.961047
\(772\) 8.60569i 0.309726i
\(773\) 20.2617i 0.728762i 0.931250 + 0.364381i \(0.118719\pi\)
−0.931250 + 0.364381i \(0.881281\pi\)
\(774\) 1.05648i 0.0379743i
\(775\) 4.91546i 0.176568i
\(776\) 4.38158 0.157290
\(777\) −31.3072 −1.12314
\(778\) 1.86284i 0.0667860i
\(779\) −19.8644 −0.711714
\(780\) 1.61997 1.14171i 0.0580042 0.0408797i
\(781\) −7.56749 −0.270786
\(782\) 33.7334i 1.20630i
\(783\) 24.0816