Properties

Label 1050.3.e.e.701.15
Level $1050$
Weight $3$
Character 1050.701
Analytic conductor $28.610$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 701.15
Character \(\chi\) \(=\) 1050.701
Dual form 1050.3.e.e.701.13

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(-0.554262 - 2.94835i) q^{3} -2.00000 q^{4} +(4.16960 - 0.783844i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(-8.38559 + 3.26832i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(-0.554262 - 2.94835i) q^{3} -2.00000 q^{4} +(4.16960 - 0.783844i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(-8.38559 + 3.26832i) q^{9} +2.58444i q^{11} +(1.10852 + 5.89671i) q^{12} -0.180526 q^{13} +3.74166i q^{14} +4.00000 q^{16} +7.25119i q^{17} +(-4.62210 - 11.8590i) q^{18} +21.4338 q^{19} +(-1.46644 - 7.80061i) q^{21} -3.65495 q^{22} -11.8858i q^{23} +(-8.33921 + 1.56769i) q^{24} -0.255303i q^{26} +(14.2840 + 22.9122i) q^{27} -5.29150 q^{28} +29.5458i q^{29} -49.5193 q^{31} +5.65685i q^{32} +(7.61985 - 1.43246i) q^{33} -10.2547 q^{34} +(16.7712 - 6.53664i) q^{36} +43.2958 q^{37} +30.3120i q^{38} +(0.100059 + 0.532256i) q^{39} -20.7847i q^{41} +(11.0317 - 2.07386i) q^{42} +74.2183 q^{43} -5.16888i q^{44} +16.8091 q^{46} +7.05106i q^{47} +(-2.21705 - 11.7934i) q^{48} +7.00000 q^{49} +(21.3791 - 4.01906i) q^{51} +0.361053 q^{52} +55.0572i q^{53} +(-32.4027 + 20.2006i) q^{54} -7.48331i q^{56} +(-11.8799 - 63.1944i) q^{57} -41.7841 q^{58} -100.110i q^{59} +8.44678 q^{61} -70.0309i q^{62} +(-22.1862 + 8.64716i) q^{63} -8.00000 q^{64} +(2.02580 + 10.7761i) q^{66} +85.7646 q^{67} -14.5024i q^{68} +(-35.0435 + 6.58784i) q^{69} -97.8086i q^{71} +(9.24420 + 23.7180i) q^{72} +17.8312 q^{73} +61.2295i q^{74} -42.8676 q^{76} +6.83779i q^{77} +(-0.752723 + 0.141505i) q^{78} +110.652 q^{79} +(59.6362 - 54.8136i) q^{81} +29.3940 q^{82} +3.08611i q^{83} +(2.93288 + 15.6012i) q^{84} +104.961i q^{86} +(87.1115 - 16.3761i) q^{87} +7.30991 q^{88} -80.1881i q^{89} -0.477628 q^{91} +23.7716i q^{92} +(27.4467 + 146.001i) q^{93} -9.97171 q^{94} +(16.6784 - 3.13538i) q^{96} +105.794 q^{97} +9.89949i q^{98} +(-8.44678 - 21.6721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −0.554262 2.94835i −0.184754 0.982785i
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) 4.16960 0.783844i 0.694934 0.130641i
\(7\) 2.64575 0.377964
\(8\) 2.82843i 0.353553i
\(9\) −8.38559 + 3.26832i −0.931732 + 0.363147i
\(10\) 0 0
\(11\) 2.58444i 0.234949i 0.993076 + 0.117475i \(0.0374799\pi\)
−0.993076 + 0.117475i \(0.962520\pi\)
\(12\) 1.10852 + 5.89671i 0.0923769 + 0.491392i
\(13\) −0.180526 −0.0138866 −0.00694332 0.999976i \(-0.502210\pi\)
−0.00694332 + 0.999976i \(0.502210\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 7.25119i 0.426541i 0.976993 + 0.213270i \(0.0684115\pi\)
−0.976993 + 0.213270i \(0.931589\pi\)
\(18\) −4.62210 11.8590i −0.256783 0.658834i
\(19\) 21.4338 1.12809 0.564047 0.825743i \(-0.309244\pi\)
0.564047 + 0.825743i \(0.309244\pi\)
\(20\) 0 0
\(21\) −1.46644 7.80061i −0.0698304 0.371458i
\(22\) −3.65495 −0.166134
\(23\) 11.8858i 0.516774i −0.966042 0.258387i \(-0.916809\pi\)
0.966042 0.258387i \(-0.0831909\pi\)
\(24\) −8.33921 + 1.56769i −0.347467 + 0.0653203i
\(25\) 0 0
\(26\) 0.255303i 0.00981934i
\(27\) 14.2840 + 22.9122i 0.529036 + 0.848599i
\(28\) −5.29150 −0.188982
\(29\) 29.5458i 1.01882i 0.860524 + 0.509410i \(0.170136\pi\)
−0.860524 + 0.509410i \(0.829864\pi\)
\(30\) 0 0
\(31\) −49.5193 −1.59740 −0.798699 0.601731i \(-0.794478\pi\)
−0.798699 + 0.601731i \(0.794478\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 7.61985 1.43246i 0.230905 0.0434078i
\(34\) −10.2547 −0.301610
\(35\) 0 0
\(36\) 16.7712 6.53664i 0.465866 0.181573i
\(37\) 43.2958 1.17016 0.585078 0.810977i \(-0.301064\pi\)
0.585078 + 0.810977i \(0.301064\pi\)
\(38\) 30.3120i 0.797683i
\(39\) 0.100059 + 0.532256i 0.00256561 + 0.0136476i
\(40\) 0 0
\(41\) 20.7847i 0.506944i −0.967343 0.253472i \(-0.918427\pi\)
0.967343 0.253472i \(-0.0815726\pi\)
\(42\) 11.0317 2.07386i 0.262660 0.0493775i
\(43\) 74.2183 1.72601 0.863004 0.505197i \(-0.168580\pi\)
0.863004 + 0.505197i \(0.168580\pi\)
\(44\) 5.16888i 0.117475i
\(45\) 0 0
\(46\) 16.8091 0.365414
\(47\) 7.05106i 0.150023i 0.997183 + 0.0750113i \(0.0238993\pi\)
−0.997183 + 0.0750113i \(0.976101\pi\)
\(48\) −2.21705 11.7934i −0.0461885 0.245696i
\(49\) 7.00000 0.142857
\(50\) 0 0
\(51\) 21.3791 4.01906i 0.419198 0.0788050i
\(52\) 0.361053 0.00694332
\(53\) 55.0572i 1.03882i 0.854526 + 0.519408i \(0.173847\pi\)
−0.854526 + 0.519408i \(0.826153\pi\)
\(54\) −32.4027 + 20.2006i −0.600050 + 0.374085i
\(55\) 0 0
\(56\) 7.48331i 0.133631i
\(57\) −11.8799 63.1944i −0.208420 1.10867i
\(58\) −41.7841 −0.720415
\(59\) 100.110i 1.69678i −0.529375 0.848388i \(-0.677573\pi\)
0.529375 0.848388i \(-0.322427\pi\)
\(60\) 0 0
\(61\) 8.44678 0.138472 0.0692359 0.997600i \(-0.477944\pi\)
0.0692359 + 0.997600i \(0.477944\pi\)
\(62\) 70.0309i 1.12953i
\(63\) −22.1862 + 8.64716i −0.352162 + 0.137256i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 2.02580 + 10.7761i 0.0306939 + 0.163274i
\(67\) 85.7646 1.28007 0.640034 0.768347i \(-0.278920\pi\)
0.640034 + 0.768347i \(0.278920\pi\)
\(68\) 14.5024i 0.213270i
\(69\) −35.0435 + 6.58784i −0.507877 + 0.0954759i
\(70\) 0 0
\(71\) 97.8086i 1.37759i −0.724958 0.688793i \(-0.758141\pi\)
0.724958 0.688793i \(-0.241859\pi\)
\(72\) 9.24420 + 23.7180i 0.128392 + 0.329417i
\(73\) 17.8312 0.244264 0.122132 0.992514i \(-0.461027\pi\)
0.122132 + 0.992514i \(0.461027\pi\)
\(74\) 61.2295i 0.827426i
\(75\) 0 0
\(76\) −42.8676 −0.564047
\(77\) 6.83779i 0.0888025i
\(78\) −0.752723 + 0.141505i −0.00965030 + 0.00181416i
\(79\) 110.652 1.40066 0.700328 0.713821i \(-0.253037\pi\)
0.700328 + 0.713821i \(0.253037\pi\)
\(80\) 0 0
\(81\) 59.6362 54.8136i 0.736249 0.676711i
\(82\) 29.3940 0.358464
\(83\) 3.08611i 0.0371820i 0.999827 + 0.0185910i \(0.00591804\pi\)
−0.999827 + 0.0185910i \(0.994082\pi\)
\(84\) 2.93288 + 15.6012i 0.0349152 + 0.185729i
\(85\) 0 0
\(86\) 104.961i 1.22047i
\(87\) 87.1115 16.3761i 1.00128 0.188231i
\(88\) 7.30991 0.0830671
\(89\) 80.1881i 0.900990i −0.892779 0.450495i \(-0.851248\pi\)
0.892779 0.450495i \(-0.148752\pi\)
\(90\) 0 0
\(91\) −0.477628 −0.00524866
\(92\) 23.7716i 0.258387i
\(93\) 27.4467 + 146.001i 0.295125 + 1.56990i
\(94\) −9.97171 −0.106082
\(95\) 0 0
\(96\) 16.6784 3.13538i 0.173733 0.0326602i
\(97\) 105.794 1.09066 0.545328 0.838223i \(-0.316405\pi\)
0.545328 + 0.838223i \(0.316405\pi\)
\(98\) 9.89949i 0.101015i
\(99\) −8.44678 21.6721i −0.0853210 0.218910i
\(100\) 0 0
\(101\) 120.653i 1.19459i 0.802022 + 0.597294i \(0.203757\pi\)
−0.802022 + 0.597294i \(0.796243\pi\)
\(102\) 5.68380 + 30.2346i 0.0557236 + 0.296417i
\(103\) 173.031 1.67992 0.839958 0.542652i \(-0.182580\pi\)
0.839958 + 0.542652i \(0.182580\pi\)
\(104\) 0.510606i 0.00490967i
\(105\) 0 0
\(106\) −77.8627 −0.734554
\(107\) 82.1335i 0.767603i 0.923416 + 0.383802i \(0.125385\pi\)
−0.923416 + 0.383802i \(0.874615\pi\)
\(108\) −28.5679 45.8244i −0.264518 0.424300i
\(109\) −63.4890 −0.582468 −0.291234 0.956652i \(-0.594066\pi\)
−0.291234 + 0.956652i \(0.594066\pi\)
\(110\) 0 0
\(111\) −23.9972 127.651i −0.216191 1.15001i
\(112\) 10.5830 0.0944911
\(113\) 145.494i 1.28755i −0.765213 0.643777i \(-0.777366\pi\)
0.765213 0.643777i \(-0.222634\pi\)
\(114\) 89.3704 16.8008i 0.783951 0.147375i
\(115\) 0 0
\(116\) 59.0916i 0.509410i
\(117\) 1.51382 0.590018i 0.0129386 0.00504289i
\(118\) 141.577 1.19980
\(119\) 19.1848i 0.161217i
\(120\) 0 0
\(121\) 114.321 0.944799
\(122\) 11.9456i 0.0979144i
\(123\) −61.2807 + 11.5202i −0.498217 + 0.0936599i
\(124\) 99.0387 0.798699
\(125\) 0 0
\(126\) −12.2289 31.3760i −0.0970550 0.249016i
\(127\) 153.065 1.20523 0.602616 0.798031i \(-0.294125\pi\)
0.602616 + 0.798031i \(0.294125\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −41.1364 218.822i −0.318887 1.69629i
\(130\) 0 0
\(131\) 176.646i 1.34844i 0.738529 + 0.674222i \(0.235521\pi\)
−0.738529 + 0.674222i \(0.764479\pi\)
\(132\) −15.2397 + 2.86491i −0.115452 + 0.0217039i
\(133\) 56.7085 0.426380
\(134\) 121.289i 0.905145i
\(135\) 0 0
\(136\) 20.5095 0.150805
\(137\) 229.315i 1.67383i 0.547333 + 0.836915i \(0.315643\pi\)
−0.547333 + 0.836915i \(0.684357\pi\)
\(138\) −9.31661 49.5591i −0.0675117 0.359124i
\(139\) −7.93236 −0.0570673 −0.0285337 0.999593i \(-0.509084\pi\)
−0.0285337 + 0.999593i \(0.509084\pi\)
\(140\) 0 0
\(141\) 20.7890 3.90813i 0.147440 0.0277173i
\(142\) 138.322 0.974101
\(143\) 0.466560i 0.00326266i
\(144\) −33.5424 + 13.0733i −0.232933 + 0.0907866i
\(145\) 0 0
\(146\) 25.2172i 0.172720i
\(147\) −3.87983 20.6385i −0.0263934 0.140398i
\(148\) −86.5916 −0.585078
\(149\) 111.886i 0.750910i −0.926841 0.375455i \(-0.877487\pi\)
0.926841 0.375455i \(-0.122513\pi\)
\(150\) 0 0
\(151\) −73.7503 −0.488412 −0.244206 0.969723i \(-0.578527\pi\)
−0.244206 + 0.969723i \(0.578527\pi\)
\(152\) 60.6239i 0.398842i
\(153\) −23.6992 60.8055i −0.154897 0.397421i
\(154\) −9.67010 −0.0627928
\(155\) 0 0
\(156\) −0.200118 1.06451i −0.00128281 0.00682379i
\(157\) 52.3958 0.333731 0.166866 0.985980i \(-0.446635\pi\)
0.166866 + 0.985980i \(0.446635\pi\)
\(158\) 156.485i 0.990414i
\(159\) 162.328 30.5161i 1.02093 0.191925i
\(160\) 0 0
\(161\) 31.4469i 0.195322i
\(162\) 77.5181 + 84.3383i 0.478507 + 0.520607i
\(163\) −16.9135 −0.103764 −0.0518819 0.998653i \(-0.516522\pi\)
−0.0518819 + 0.998653i \(0.516522\pi\)
\(164\) 41.5694i 0.253472i
\(165\) 0 0
\(166\) −4.36442 −0.0262917
\(167\) 2.03625i 0.0121931i 0.999981 + 0.00609657i \(0.00194061\pi\)
−0.999981 + 0.00609657i \(0.998059\pi\)
\(168\) −22.0635 + 4.14771i −0.131330 + 0.0246888i
\(169\) −168.967 −0.999807
\(170\) 0 0
\(171\) −179.735 + 70.0525i −1.05108 + 0.409664i
\(172\) −148.437 −0.863004
\(173\) 258.927i 1.49669i −0.663312 0.748343i \(-0.730850\pi\)
0.663312 0.748343i \(-0.269150\pi\)
\(174\) 23.1593 + 123.194i 0.133099 + 0.708013i
\(175\) 0 0
\(176\) 10.3378i 0.0587373i
\(177\) −295.159 + 55.4870i −1.66757 + 0.313486i
\(178\) 113.403 0.637096
\(179\) 38.3599i 0.214301i 0.994243 + 0.107150i \(0.0341727\pi\)
−0.994243 + 0.107150i \(0.965827\pi\)
\(180\) 0 0
\(181\) 213.719 1.18077 0.590384 0.807122i \(-0.298976\pi\)
0.590384 + 0.807122i \(0.298976\pi\)
\(182\) 0.675468i 0.00371136i
\(183\) −4.68173 24.9041i −0.0255832 0.136088i
\(184\) −33.6181 −0.182707
\(185\) 0 0
\(186\) −206.476 + 38.8154i −1.11009 + 0.208685i
\(187\) −18.7403 −0.100215
\(188\) 14.1021i 0.0750113i
\(189\) 37.7918 + 60.6199i 0.199957 + 0.320740i
\(190\) 0 0
\(191\) 245.546i 1.28558i 0.766043 + 0.642790i \(0.222223\pi\)
−0.766043 + 0.642790i \(0.777777\pi\)
\(192\) 4.43409 + 23.5868i 0.0230942 + 0.122848i
\(193\) −32.9007 −0.170470 −0.0852350 0.996361i \(-0.527164\pi\)
−0.0852350 + 0.996361i \(0.527164\pi\)
\(194\) 149.615i 0.771210i
\(195\) 0 0
\(196\) −14.0000 −0.0714286
\(197\) 219.340i 1.11340i −0.830714 0.556700i \(-0.812067\pi\)
0.830714 0.556700i \(-0.187933\pi\)
\(198\) 30.6489 11.9456i 0.154793 0.0603311i
\(199\) −100.635 −0.505703 −0.252852 0.967505i \(-0.581368\pi\)
−0.252852 + 0.967505i \(0.581368\pi\)
\(200\) 0 0
\(201\) −47.5360 252.864i −0.236498 1.25803i
\(202\) −170.630 −0.844701
\(203\) 78.1708i 0.385078i
\(204\) −42.7582 + 8.03811i −0.209599 + 0.0394025i
\(205\) 0 0
\(206\) 244.703i 1.18788i
\(207\) 38.8466 + 99.6694i 0.187665 + 0.481495i
\(208\) −0.722106 −0.00347166
\(209\) 55.3944i 0.265045i
\(210\) 0 0
\(211\) 119.865 0.568082 0.284041 0.958812i \(-0.408325\pi\)
0.284041 + 0.958812i \(0.408325\pi\)
\(212\) 110.114i 0.519408i
\(213\) −288.375 + 54.2116i −1.35387 + 0.254514i
\(214\) −116.154 −0.542777
\(215\) 0 0
\(216\) 64.8054 40.4012i 0.300025 0.187042i
\(217\) −131.016 −0.603760
\(218\) 89.7870i 0.411867i
\(219\) −9.88317 52.5728i −0.0451286 0.240059i
\(220\) 0 0
\(221\) 1.30903i 0.00592322i
\(222\) 180.526 33.9372i 0.813182 0.152870i
\(223\) −315.561 −1.41507 −0.707536 0.706677i \(-0.750193\pi\)
−0.707536 + 0.706677i \(0.750193\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) 205.759 0.910438
\(227\) 315.509i 1.38991i −0.719054 0.694954i \(-0.755425\pi\)
0.719054 0.694954i \(-0.244575\pi\)
\(228\) 23.7599 + 126.389i 0.104210 + 0.554337i
\(229\) −66.8556 −0.291946 −0.145973 0.989289i \(-0.546631\pi\)
−0.145973 + 0.989289i \(0.546631\pi\)
\(230\) 0 0
\(231\) 20.1602 3.78992i 0.0872737 0.0164066i
\(232\) 83.5681 0.360207
\(233\) 301.826i 1.29539i 0.761900 + 0.647695i \(0.224267\pi\)
−0.761900 + 0.647695i \(0.775733\pi\)
\(234\) 0.834411 + 2.14086i 0.00356586 + 0.00914899i
\(235\) 0 0
\(236\) 200.220i 0.848388i
\(237\) −61.3301 326.241i −0.258777 1.37654i
\(238\) −27.1315 −0.113998
\(239\) 241.028i 1.00849i 0.863562 + 0.504243i \(0.168229\pi\)
−0.863562 + 0.504243i \(0.831771\pi\)
\(240\) 0 0
\(241\) −196.843 −0.816775 −0.408388 0.912809i \(-0.633909\pi\)
−0.408388 + 0.912809i \(0.633909\pi\)
\(242\) 161.674i 0.668074i
\(243\) −194.664 145.448i −0.801086 0.598550i
\(244\) −16.8936 −0.0692359
\(245\) 0 0
\(246\) −16.2920 86.6640i −0.0662275 0.352293i
\(247\) −3.86937 −0.0156654
\(248\) 140.062i 0.564766i
\(249\) 9.09894 1.71051i 0.0365419 0.00686952i
\(250\) 0 0
\(251\) 349.301i 1.39164i 0.718217 + 0.695819i \(0.244959\pi\)
−0.718217 + 0.695819i \(0.755041\pi\)
\(252\) 44.3724 17.2943i 0.176081 0.0686282i
\(253\) 30.7182 0.121416
\(254\) 216.466i 0.852228i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 4.18732i 0.0162931i 0.999967 + 0.00814653i \(0.00259315\pi\)
−0.999967 + 0.00814653i \(0.997407\pi\)
\(258\) 309.461 58.1756i 1.19946 0.225487i
\(259\) 114.550 0.442278
\(260\) 0 0
\(261\) −96.5651 247.759i −0.369981 0.949267i
\(262\) −249.815 −0.953493
\(263\) 268.485i 1.02086i 0.859921 + 0.510428i \(0.170513\pi\)
−0.859921 + 0.510428i \(0.829487\pi\)
\(264\) −4.05160 21.5522i −0.0153470 0.0816371i
\(265\) 0 0
\(266\) 80.1979i 0.301496i
\(267\) −236.423 + 44.4452i −0.885479 + 0.166461i
\(268\) −171.529 −0.640034
\(269\) 59.1206i 0.219779i 0.993944 + 0.109890i \(0.0350497\pi\)
−0.993944 + 0.109890i \(0.964950\pi\)
\(270\) 0 0
\(271\) −206.348 −0.761433 −0.380717 0.924692i \(-0.624323\pi\)
−0.380717 + 0.924692i \(0.624323\pi\)
\(272\) 29.0048i 0.106635i
\(273\) 0.264731 + 1.40822i 0.000969710 + 0.00515830i
\(274\) −324.300 −1.18358
\(275\) 0 0
\(276\) 70.0871 13.1757i 0.253939 0.0477380i
\(277\) −370.482 −1.33748 −0.668740 0.743496i \(-0.733166\pi\)
−0.668740 + 0.743496i \(0.733166\pi\)
\(278\) 11.2180i 0.0403527i
\(279\) 415.249 161.845i 1.48835 0.580090i
\(280\) 0 0
\(281\) 71.0258i 0.252761i 0.991982 + 0.126380i \(0.0403360\pi\)
−0.991982 + 0.126380i \(0.959664\pi\)
\(282\) 5.52693 + 29.4001i 0.0195991 + 0.104256i
\(283\) 255.816 0.903944 0.451972 0.892032i \(-0.350721\pi\)
0.451972 + 0.892032i \(0.350721\pi\)
\(284\) 195.617i 0.688793i
\(285\) 0 0
\(286\) 0.659816 0.00230705
\(287\) 54.9912i 0.191607i
\(288\) −18.4884 47.4361i −0.0641958 0.164709i
\(289\) 236.420 0.818063
\(290\) 0 0
\(291\) −58.6373 311.917i −0.201503 1.07188i
\(292\) −35.6625 −0.122132
\(293\) 162.409i 0.554297i −0.960827 0.277148i \(-0.910611\pi\)
0.960827 0.277148i \(-0.0893894\pi\)
\(294\) 29.1872 5.48691i 0.0992763 0.0186630i
\(295\) 0 0
\(296\) 122.459i 0.413713i
\(297\) −59.2152 + 36.9161i −0.199378 + 0.124297i
\(298\) 158.230 0.530973
\(299\) 2.14570i 0.00717625i
\(300\) 0 0
\(301\) 196.363 0.652370
\(302\) 104.299i 0.345360i
\(303\) 355.729 66.8735i 1.17402 0.220705i
\(304\) 85.7352 0.282024
\(305\) 0 0
\(306\) 85.9919 33.5157i 0.281019 0.109529i
\(307\) 532.774 1.73542 0.867709 0.497072i \(-0.165592\pi\)
0.867709 + 0.497072i \(0.165592\pi\)
\(308\) 13.6756i 0.0444012i
\(309\) −95.9046 510.158i −0.310371 1.65100i
\(310\) 0 0
\(311\) 353.139i 1.13549i −0.823203 0.567747i \(-0.807815\pi\)
0.823203 0.567747i \(-0.192185\pi\)
\(312\) 1.50545 0.283009i 0.00482515 0.000907081i
\(313\) 113.835 0.363689 0.181845 0.983327i \(-0.441793\pi\)
0.181845 + 0.983327i \(0.441793\pi\)
\(314\) 74.0989i 0.235984i
\(315\) 0 0
\(316\) −221.304 −0.700328
\(317\) 73.1423i 0.230733i 0.993323 + 0.115366i \(0.0368042\pi\)
−0.993323 + 0.115366i \(0.963196\pi\)
\(318\) 43.1563 + 229.567i 0.135712 + 0.721908i
\(319\) −76.3594 −0.239371
\(320\) 0 0
\(321\) 242.159 45.5235i 0.754389 0.141818i
\(322\) 44.4726 0.138114
\(323\) 155.420i 0.481178i
\(324\) −119.272 + 109.627i −0.368125 + 0.338355i
\(325\) 0 0
\(326\) 23.9193i 0.0733720i
\(327\) 35.1895 + 187.188i 0.107613 + 0.572441i
\(328\) −58.7880 −0.179232
\(329\) 18.6554i 0.0567032i
\(330\) 0 0
\(331\) −244.549 −0.738818 −0.369409 0.929267i \(-0.620440\pi\)
−0.369409 + 0.929267i \(0.620440\pi\)
\(332\) 6.17222i 0.0185910i
\(333\) −363.061 + 141.505i −1.09027 + 0.424938i
\(334\) −2.87970 −0.00862185
\(335\) 0 0
\(336\) −5.86575 31.2025i −0.0174576 0.0928644i
\(337\) −360.620 −1.07009 −0.535045 0.844824i \(-0.679705\pi\)
−0.535045 + 0.844824i \(0.679705\pi\)
\(338\) 238.956i 0.706970i
\(339\) −428.967 + 80.6415i −1.26539 + 0.237881i
\(340\) 0 0
\(341\) 127.980i 0.375308i
\(342\) −99.0692 254.184i −0.289676 0.743227i
\(343\) 18.5203 0.0539949
\(344\) 209.921i 0.610236i
\(345\) 0 0
\(346\) 366.178 1.05832
\(347\) 320.079i 0.922417i 0.887292 + 0.461209i \(0.152584\pi\)
−0.887292 + 0.461209i \(0.847416\pi\)
\(348\) −174.223 + 32.7522i −0.500641 + 0.0941155i
\(349\) 656.250 1.88037 0.940187 0.340660i \(-0.110650\pi\)
0.940187 + 0.340660i \(0.110650\pi\)
\(350\) 0 0
\(351\) −2.57863 4.13625i −0.00734654 0.0117842i
\(352\) −14.6198 −0.0415336
\(353\) 307.348i 0.870673i −0.900268 0.435337i \(-0.856629\pi\)
0.900268 0.435337i \(-0.143371\pi\)
\(354\) −78.4705 417.418i −0.221668 1.17915i
\(355\) 0 0
\(356\) 160.376i 0.450495i
\(357\) 56.5637 10.6334i 0.158442 0.0297855i
\(358\) −54.2490 −0.151534
\(359\) 149.072i 0.415244i −0.978209 0.207622i \(-0.933428\pi\)
0.978209 0.207622i \(-0.0665723\pi\)
\(360\) 0 0
\(361\) 98.4076 0.272597
\(362\) 302.245i 0.834930i
\(363\) −63.3635 337.058i −0.174555 0.928534i
\(364\) 0.955256 0.00262433
\(365\) 0 0
\(366\) 35.2197 6.62096i 0.0962287 0.0180901i
\(367\) −394.930 −1.07610 −0.538052 0.842912i \(-0.680840\pi\)
−0.538052 + 0.842912i \(0.680840\pi\)
\(368\) 47.5432i 0.129193i
\(369\) 67.9311 + 174.292i 0.184095 + 0.472336i
\(370\) 0 0
\(371\) 145.668i 0.392635i
\(372\) −54.8933 292.001i −0.147563 0.784949i
\(373\) −567.874 −1.52245 −0.761225 0.648488i \(-0.775402\pi\)
−0.761225 + 0.648488i \(0.775402\pi\)
\(374\) 26.5028i 0.0708630i
\(375\) 0 0
\(376\) 19.9434 0.0530410
\(377\) 5.33379i 0.0141480i
\(378\) −85.7295 + 53.4457i −0.226798 + 0.141391i
\(379\) −641.443 −1.69246 −0.846230 0.532817i \(-0.821133\pi\)
−0.846230 + 0.532817i \(0.821133\pi\)
\(380\) 0 0
\(381\) −84.8378 451.289i −0.222671 1.18448i
\(382\) −347.254 −0.909042
\(383\) 340.090i 0.887963i −0.896036 0.443982i \(-0.853566\pi\)
0.896036 0.443982i \(-0.146434\pi\)
\(384\) −33.3568 + 6.27075i −0.0868667 + 0.0163301i
\(385\) 0 0
\(386\) 46.5286i 0.120541i
\(387\) −622.365 + 242.569i −1.60818 + 0.626794i
\(388\) −211.587 −0.545328
\(389\) 432.582i 1.11204i −0.831170 0.556018i \(-0.812328\pi\)
0.831170 0.556018i \(-0.187672\pi\)
\(390\) 0 0
\(391\) 86.1862 0.220425
\(392\) 19.7990i 0.0505076i
\(393\) 520.815 97.9081i 1.32523 0.249130i
\(394\) 310.193 0.787292
\(395\) 0 0
\(396\) 16.8936 + 43.3441i 0.0426605 + 0.109455i
\(397\) −471.352 −1.18728 −0.593642 0.804729i \(-0.702310\pi\)
−0.593642 + 0.804729i \(0.702310\pi\)
\(398\) 142.319i 0.357586i
\(399\) −31.4313 167.197i −0.0787753 0.419039i
\(400\) 0 0
\(401\) 180.124i 0.449186i −0.974453 0.224593i \(-0.927895\pi\)
0.974453 0.224593i \(-0.0721053\pi\)
\(402\) 357.604 67.2261i 0.889563 0.167229i
\(403\) 8.93955 0.0221825
\(404\) 241.307i 0.597294i
\(405\) 0 0
\(406\) −110.550 −0.272291
\(407\) 111.896i 0.274928i
\(408\) −11.3676 60.4692i −0.0278618 0.148209i
\(409\) −259.241 −0.633842 −0.316921 0.948452i \(-0.602649\pi\)
−0.316921 + 0.948452i \(0.602649\pi\)
\(410\) 0 0
\(411\) 676.101 127.100i 1.64501 0.309246i
\(412\) −346.063 −0.839958
\(413\) 264.866i 0.641321i
\(414\) −140.954 + 54.9374i −0.340468 + 0.132699i
\(415\) 0 0
\(416\) 1.02121i 0.00245484i
\(417\) 4.39660 + 23.3874i 0.0105434 + 0.0560849i
\(418\) −78.3395 −0.187415
\(419\) 146.134i 0.348769i 0.984678 + 0.174384i \(0.0557935\pi\)
−0.984678 + 0.174384i \(0.944207\pi\)
\(420\) 0 0
\(421\) −599.808 −1.42472 −0.712361 0.701813i \(-0.752374\pi\)
−0.712361 + 0.701813i \(0.752374\pi\)
\(422\) 169.515i 0.401695i
\(423\) −23.0451 59.1273i −0.0544802 0.139781i
\(424\) 155.725 0.367277
\(425\) 0 0
\(426\) −76.6667 407.823i −0.179969 0.957331i
\(427\) 22.3481 0.0523374
\(428\) 164.267i 0.383802i
\(429\) −1.37558 + 0.258596i −0.00320649 + 0.000602789i
\(430\) 0 0
\(431\) 825.631i 1.91562i 0.287409 + 0.957808i \(0.407206\pi\)
−0.287409 + 0.957808i \(0.592794\pi\)
\(432\) 57.1359 + 91.6487i 0.132259 + 0.212150i
\(433\) −185.307 −0.427962 −0.213981 0.976838i \(-0.568643\pi\)
−0.213981 + 0.976838i \(0.568643\pi\)
\(434\) 185.284i 0.426923i
\(435\) 0 0
\(436\) 126.978 0.291234
\(437\) 254.758i 0.582970i
\(438\) 74.3492 13.9769i 0.169747 0.0319108i
\(439\) 809.103 1.84306 0.921529 0.388309i \(-0.126941\pi\)
0.921529 + 0.388309i \(0.126941\pi\)
\(440\) 0 0
\(441\) −58.6991 + 22.8782i −0.133105 + 0.0518781i
\(442\) 1.85125 0.00418835
\(443\) 449.922i 1.01563i 0.861467 + 0.507813i \(0.169546\pi\)
−0.861467 + 0.507813i \(0.830454\pi\)
\(444\) 47.9944 + 255.303i 0.108095 + 0.575006i
\(445\) 0 0
\(446\) 446.271i 1.00061i
\(447\) −329.878 + 62.0138i −0.737983 + 0.138733i
\(448\) −21.1660 −0.0472456
\(449\) 676.008i 1.50559i −0.658257 0.752793i \(-0.728706\pi\)
0.658257 0.752793i \(-0.271294\pi\)
\(450\) 0 0
\(451\) 53.7169 0.119106
\(452\) 290.987i 0.643777i
\(453\) 40.8769 + 217.442i 0.0902361 + 0.480004i
\(454\) 446.198 0.982814
\(455\) 0 0
\(456\) −178.741 + 33.6015i −0.391975 + 0.0736875i
\(457\) 588.327 1.28737 0.643683 0.765292i \(-0.277405\pi\)
0.643683 + 0.765292i \(0.277405\pi\)
\(458\) 94.5481i 0.206437i
\(459\) −166.141 + 103.576i −0.361962 + 0.225655i
\(460\) 0 0
\(461\) 344.268i 0.746785i −0.927673 0.373393i \(-0.878194\pi\)
0.927673 0.373393i \(-0.121806\pi\)
\(462\) 5.35976 + 28.5109i 0.0116012 + 0.0617119i
\(463\) −220.223 −0.475643 −0.237821 0.971309i \(-0.576433\pi\)
−0.237821 + 0.971309i \(0.576433\pi\)
\(464\) 118.183i 0.254705i
\(465\) 0 0
\(466\) −426.846 −0.915978
\(467\) 595.502i 1.27516i −0.770382 0.637582i \(-0.779935\pi\)
0.770382 0.637582i \(-0.220065\pi\)
\(468\) −3.02764 + 1.18004i −0.00646932 + 0.00252144i
\(469\) 226.912 0.483820
\(470\) 0 0
\(471\) −29.0410 154.481i −0.0616581 0.327986i
\(472\) −283.153 −0.599901
\(473\) 191.813i 0.405524i
\(474\) 461.374 86.7338i 0.973364 0.182983i
\(475\) 0 0
\(476\) 38.3697i 0.0806086i
\(477\) −179.945 461.687i −0.377242 0.967898i
\(478\) −340.865 −0.713108
\(479\) 710.354i 1.48299i 0.670956 + 0.741497i \(0.265884\pi\)
−0.670956 + 0.741497i \(0.734116\pi\)
\(480\) 0 0
\(481\) −7.81604 −0.0162496
\(482\) 278.378i 0.577547i
\(483\) −92.7165 + 17.4298i −0.191960 + 0.0360865i
\(484\) −228.641 −0.472399
\(485\) 0 0
\(486\) 205.694 275.296i 0.423239 0.566453i
\(487\) 325.987 0.669378 0.334689 0.942329i \(-0.391369\pi\)
0.334689 + 0.942329i \(0.391369\pi\)
\(488\) 23.8911i 0.0489572i
\(489\) 9.37450 + 49.8670i 0.0191708 + 0.101977i
\(490\) 0 0
\(491\) 573.407i 1.16784i 0.811813 + 0.583918i \(0.198481\pi\)
−0.811813 + 0.583918i \(0.801519\pi\)
\(492\) 122.561 23.0403i 0.249108 0.0468299i
\(493\) −214.242 −0.434568
\(494\) 5.47211i 0.0110771i
\(495\) 0 0
\(496\) −198.077 −0.399350
\(497\) 258.777i 0.520679i
\(498\) 2.41903 + 12.8678i 0.00485749 + 0.0258390i
\(499\) −410.671 −0.822989 −0.411494 0.911412i \(-0.634993\pi\)
−0.411494 + 0.911412i \(0.634993\pi\)
\(500\) 0 0
\(501\) 6.00360 1.12862i 0.0119832 0.00225273i
\(502\) −493.987 −0.984037
\(503\) 903.370i 1.79596i 0.440032 + 0.897982i \(0.354967\pi\)
−0.440032 + 0.897982i \(0.645033\pi\)
\(504\) 24.4579 + 62.7520i 0.0485275 + 0.124508i
\(505\) 0 0
\(506\) 43.4420i 0.0858538i
\(507\) 93.6521 + 498.176i 0.184718 + 0.982595i
\(508\) −306.129 −0.602616
\(509\) 323.535i 0.635628i 0.948153 + 0.317814i \(0.102949\pi\)
−0.948153 + 0.317814i \(0.897051\pi\)
\(510\) 0 0
\(511\) 47.1770 0.0923230
\(512\) 22.6274i 0.0441942i
\(513\) 306.160 + 491.095i 0.596803 + 0.957300i
\(514\) −5.92176 −0.0115209
\(515\) 0 0
\(516\) 82.2728 + 437.644i 0.159443 + 0.848147i
\(517\) −18.2231 −0.0352477
\(518\) 161.998i 0.312738i
\(519\) −763.408 + 143.513i −1.47092 + 0.276519i
\(520\) 0 0
\(521\) 687.287i 1.31917i −0.751631 0.659584i \(-0.770732\pi\)
0.751631 0.659584i \(-0.229268\pi\)
\(522\) 350.384 136.564i 0.671233 0.261616i
\(523\) 760.416 1.45395 0.726975 0.686664i \(-0.240926\pi\)
0.726975 + 0.686664i \(0.240926\pi\)
\(524\) 353.292i 0.674222i
\(525\) 0 0
\(526\) −379.695 −0.721854
\(527\) 359.074i 0.681355i
\(528\) 30.4794 5.72983i 0.0577262 0.0108519i
\(529\) 387.728 0.732945
\(530\) 0 0
\(531\) 327.191 + 839.480i 0.616179 + 1.58094i
\(532\) −113.417 −0.213190
\(533\) 3.75219i 0.00703975i
\(534\) −62.8550 334.353i −0.117706 0.626128i
\(535\) 0 0
\(536\) 242.579i 0.452572i
\(537\) 113.098 21.2614i 0.210612 0.0395929i
\(538\) −83.6091 −0.155407
\(539\) 18.0911i 0.0335642i
\(540\) 0 0
\(541\) 472.370 0.873142 0.436571 0.899670i \(-0.356193\pi\)
0.436571 + 0.899670i \(0.356193\pi\)
\(542\) 291.821i 0.538415i
\(543\) −118.456 630.120i −0.218152 1.16044i
\(544\) −41.0189 −0.0754024
\(545\) 0 0
\(546\) −1.99152 + 0.374386i −0.00364747 + 0.000685688i
\(547\) 536.508 0.980818 0.490409 0.871492i \(-0.336847\pi\)
0.490409 + 0.871492i \(0.336847\pi\)
\(548\) 458.629i 0.836915i
\(549\) −70.8312 + 27.6068i −0.129019 + 0.0502856i
\(550\) 0 0
\(551\) 633.278i 1.14933i
\(552\) 18.6332 + 99.1181i 0.0337558 + 0.179562i
\(553\) 292.757 0.529398
\(554\) 523.941i 0.945741i
\(555\) 0 0
\(556\) 15.8647 0.0285337
\(557\) 288.061i 0.517165i 0.965989 + 0.258583i \(0.0832554\pi\)
−0.965989 + 0.258583i \(0.916745\pi\)
\(558\) 228.883 + 587.250i 0.410185 + 1.05242i
\(559\) −13.3984 −0.0239685
\(560\) 0 0
\(561\) 10.3870 + 55.2530i 0.0185152 + 0.0984902i
\(562\) −100.446 −0.178729
\(563\) 16.4938i 0.0292963i −0.999893 0.0146482i \(-0.995337\pi\)
0.999893 0.0146482i \(-0.00466282\pi\)
\(564\) −41.5781 + 7.81627i −0.0737200 + 0.0138586i
\(565\) 0 0
\(566\) 361.779i 0.639185i
\(567\) 157.783 145.023i 0.278276 0.255773i
\(568\) −276.645 −0.487050
\(569\) 1076.66i 1.89219i 0.323889 + 0.946095i \(0.395009\pi\)
−0.323889 + 0.946095i \(0.604991\pi\)
\(570\) 0 0
\(571\) 1009.39 1.76775 0.883876 0.467721i \(-0.154925\pi\)
0.883876 + 0.467721i \(0.154925\pi\)
\(572\) 0.933120i 0.00163133i
\(573\) 723.956 136.097i 1.26345 0.237516i
\(574\) 77.7693 0.135487
\(575\) 0 0
\(576\) 67.0847 26.1466i 0.116467 0.0453933i
\(577\) 901.098 1.56169 0.780847 0.624722i \(-0.214788\pi\)
0.780847 + 0.624722i \(0.214788\pi\)
\(578\) 334.349i 0.578458i
\(579\) 18.2356 + 97.0030i 0.0314950 + 0.167535i
\(580\) 0 0
\(581\) 8.16507i 0.0140535i
\(582\) 441.117 82.9257i 0.757933 0.142484i
\(583\) −142.292 −0.244069
\(584\) 50.4344i 0.0863602i
\(585\) 0 0
\(586\) 229.681 0.391947
\(587\) 265.739i 0.452707i −0.974045 0.226354i \(-0.927319\pi\)
0.974045 0.226354i \(-0.0726805\pi\)
\(588\) 7.75966 + 41.2770i 0.0131967 + 0.0701989i
\(589\) −1061.39 −1.80202
\(590\) 0 0
\(591\) −646.691 + 121.572i −1.09423 + 0.205705i
\(592\) 173.183 0.292539
\(593\) 548.447i 0.924869i 0.886653 + 0.462435i \(0.153024\pi\)
−0.886653 + 0.462435i \(0.846976\pi\)
\(594\) −52.2073 83.7430i −0.0878910 0.140981i
\(595\) 0 0
\(596\) 223.771i 0.375455i
\(597\) 55.7781 + 296.708i 0.0934306 + 0.496998i
\(598\) −3.03448 −0.00507438
\(599\) 237.976i 0.397289i −0.980072 0.198644i \(-0.936346\pi\)
0.980072 0.198644i \(-0.0636538\pi\)
\(600\) 0 0
\(601\) −566.317 −0.942291 −0.471146 0.882055i \(-0.656159\pi\)
−0.471146 + 0.882055i \(0.656159\pi\)
\(602\) 277.700i 0.461295i
\(603\) −719.186 + 280.306i −1.19268 + 0.464852i
\(604\) 147.501 0.244206
\(605\) 0 0
\(606\) 94.5734 + 503.077i 0.156062 + 0.830159i
\(607\) 60.4291 0.0995537 0.0497769 0.998760i \(-0.484149\pi\)
0.0497769 + 0.998760i \(0.484149\pi\)
\(608\) 121.248i 0.199421i
\(609\) 230.475 43.3271i 0.378449 0.0711446i
\(610\) 0 0
\(611\) 1.27290i 0.00208331i
\(612\) 47.3984 + 121.611i 0.0774484 + 0.198711i
\(613\) 307.983 0.502419 0.251210 0.967933i \(-0.419172\pi\)
0.251210 + 0.967933i \(0.419172\pi\)
\(614\) 753.456i 1.22713i
\(615\) 0 0
\(616\) 19.3402 0.0313964
\(617\) 780.226i 1.26455i 0.774745 + 0.632274i \(0.217878\pi\)
−0.774745 + 0.632274i \(0.782122\pi\)
\(618\) 721.472 135.630i 1.16743 0.219465i
\(619\) −838.604 −1.35477 −0.677386 0.735627i \(-0.736887\pi\)
−0.677386 + 0.735627i \(0.736887\pi\)
\(620\) 0 0
\(621\) 272.330 169.776i 0.438534 0.273392i
\(622\) 499.413 0.802916
\(623\) 212.158i 0.340542i
\(624\) 0.400235 + 2.12902i 0.000641403 + 0.00341190i
\(625\) 0 0
\(626\) 160.987i 0.257167i
\(627\) 163.322 30.7030i 0.260482 0.0489681i
\(628\) −104.792 −0.166866
\(629\) 313.946i 0.499119i
\(630\) 0 0
\(631\) −433.178 −0.686494 −0.343247 0.939245i \(-0.611527\pi\)
−0.343247 + 0.939245i \(0.611527\pi\)
\(632\) 312.971i 0.495207i
\(633\) −66.4368 353.406i −0.104955 0.558303i
\(634\) −103.439 −0.163153
\(635\) 0 0
\(636\) −324.656 + 61.0322i −0.510466 + 0.0959626i
\(637\) −1.26368 −0.00198381
\(638\) 107.988i 0.169261i
\(639\) 319.670 + 820.183i 0.500266 + 1.28354i
\(640\) 0 0
\(641\) 571.035i 0.890850i 0.895319 + 0.445425i \(0.146947\pi\)
−0.895319 + 0.445425i \(0.853053\pi\)
\(642\) 64.3799 + 342.464i 0.100280 + 0.533433i
\(643\) 194.578 0.302609 0.151304 0.988487i \(-0.451653\pi\)
0.151304 + 0.988487i \(0.451653\pi\)
\(644\) 62.8937i 0.0976611i
\(645\) 0 0
\(646\) −219.798 −0.340244
\(647\) 432.986i 0.669220i −0.942357 0.334610i \(-0.891395\pi\)
0.942357 0.334610i \(-0.108605\pi\)
\(648\) −155.036 168.677i −0.239253 0.260303i
\(649\) 258.728 0.398656
\(650\) 0 0
\(651\) 72.6171 + 386.281i 0.111547 + 0.593366i
\(652\) 33.8270 0.0518819
\(653\) 870.907i 1.33370i −0.745192 0.666850i \(-0.767642\pi\)
0.745192 0.666850i \(-0.232358\pi\)
\(654\) −264.724 + 49.7655i −0.404777 + 0.0760940i
\(655\) 0 0
\(656\) 83.1388i 0.126736i
\(657\) −149.525 + 58.2782i −0.227588 + 0.0887035i
\(658\) −26.3827 −0.0400952
\(659\) 95.3946i 0.144757i 0.997377 + 0.0723783i \(0.0230589\pi\)
−0.997377 + 0.0723783i \(0.976941\pi\)
\(660\) 0 0
\(661\) −532.252 −0.805222 −0.402611 0.915371i \(-0.631897\pi\)
−0.402611 + 0.915371i \(0.631897\pi\)
\(662\) 345.844i 0.522423i
\(663\) −3.85949 + 0.725546i −0.00582125 + 0.00109434i
\(664\) 8.72883 0.0131458
\(665\) 0 0
\(666\) −200.118 513.446i −0.300477 0.770939i
\(667\) 351.175 0.526500
\(668\) 4.07251i 0.00609657i
\(669\) 174.903 + 930.386i 0.261440 + 1.39071i
\(670\) 0 0
\(671\) 21.8302i 0.0325339i
\(672\) 44.1269 8.29543i 0.0656651 0.0123444i
\(673\) 256.746 0.381494 0.190747 0.981639i \(-0.438909\pi\)
0.190747 + 0.981639i \(0.438909\pi\)
\(674\) 509.994i 0.756667i
\(675\) 0 0
\(676\) 337.935 0.499904
\(677\) 962.182i 1.42124i 0.703574 + 0.710622i \(0.251586\pi\)
−0.703574 + 0.710622i \(0.748414\pi\)
\(678\) −114.044 606.651i −0.168207 0.894765i
\(679\) 279.903 0.412229
\(680\) 0 0
\(681\) −930.233 + 174.875i −1.36598 + 0.256791i
\(682\) 180.991 0.265383
\(683\) 981.986i 1.43775i −0.695137 0.718877i \(-0.744656\pi\)
0.695137 0.718877i \(-0.255344\pi\)
\(684\) 359.470 140.105i 0.525541 0.204832i
\(685\) 0 0
\(686\) 26.1916i 0.0381802i
\(687\) 37.0555 + 197.114i 0.0539381 + 0.286920i
\(688\) 296.873 0.431502
\(689\) 9.93928i 0.0144257i
\(690\) 0 0
\(691\) −38.5649 −0.0558103 −0.0279052 0.999611i \(-0.508884\pi\)
−0.0279052 + 0.999611i \(0.508884\pi\)
\(692\) 517.853i 0.748343i
\(693\) −22.3481 57.3389i −0.0322483 0.0827401i
\(694\) −452.660 −0.652247
\(695\) 0 0
\(696\) −46.3186 246.388i −0.0665497 0.354006i
\(697\) 150.714 0.216232
\(698\) 928.078i 1.32962i
\(699\) 889.889 167.290i 1.27309 0.239328i
\(700\) 0 0
\(701\) 301.635i 0.430293i −0.976582 0.215146i \(-0.930977\pi\)
0.976582 0.215146i \(-0.0690228\pi\)
\(702\) 5.84955 3.64674i 0.00833269 0.00519478i
\(703\) 927.993 1.32005
\(704\) 20.6755i 0.0293687i
\(705\) 0 0
\(706\) 434.655 0.615659
\(707\) 319.219i 0.451512i
\(708\) 590.318 110.974i 0.833783 0.156743i
\(709\) 910.699 1.28448 0.642242 0.766502i \(-0.278005\pi\)
0.642242 + 0.766502i \(0.278005\pi\)
\(710\) 0 0
\(711\) −927.881 + 361.646i −1.30504 + 0.508644i
\(712\) −226.806 −0.318548
\(713\) 588.577i 0.825493i
\(714\) 15.0379 + 79.9932i 0.0210615 + 0.112035i
\(715\) 0 0
\(716\) 76.7197i 0.107150i
\(717\) 710.637 133.593i 0.991125 0.186322i
\(718\) 210.820 0.293622
\(719\) 526.394i 0.732119i 0.930591 + 0.366060i \(0.119293\pi\)
−0.930591 + 0.366060i \(0.880707\pi\)
\(720\) 0 0
\(721\) 457.798 0.634948
\(722\) 139.169i 0.192755i
\(723\) 109.102 + 580.362i 0.150902 + 0.802714i
\(724\) −427.438 −0.590384
\(725\) 0 0
\(726\) 476.672 89.6096i 0.656573 0.123429i
\(727\) 348.251 0.479025 0.239513 0.970893i \(-0.423012\pi\)
0.239513 + 0.970893i \(0.423012\pi\)
\(728\) 1.35094i 0.00185568i
\(729\) −320.936 + 654.554i −0.440242 + 0.897879i
\(730\) 0 0
\(731\) 538.171i 0.736212i
\(732\) 9.36345 + 49.8082i 0.0127916 + 0.0680440i
\(733\) −1270.52 −1.73332 −0.866658 0.498903i \(-0.833736\pi\)
−0.866658 + 0.498903i \(0.833736\pi\)
\(734\) 558.515i 0.760920i
\(735\) 0 0
\(736\) 67.2362 0.0913536
\(737\) 221.654i 0.300751i
\(738\) −246.486 + 96.0690i −0.333992 + 0.130175i
\(739\) −1072.31 −1.45103 −0.725514 0.688207i \(-0.758398\pi\)
−0.725514 + 0.688207i \(0.758398\pi\)
\(740\) 0 0
\(741\) 2.14464 + 11.4083i 0.00289425 + 0.0153958i
\(742\) −206.005 −0.277635
\(743\) 205.210i 0.276191i 0.990419 + 0.138095i \(0.0440981\pi\)
−0.990419 + 0.138095i \(0.955902\pi\)
\(744\) 412.952 77.6309i 0.555043 0.104343i
\(745\) 0 0
\(746\) 803.094i 1.07653i
\(747\) −10.0864 25.8788i −0.0135025 0.0346437i
\(748\) 37.4806 0.0501077
\(749\) 217.305i 0.290127i
\(750\) 0 0
\(751\) −167.702 −0.223306 −0.111653 0.993747i \(-0.535614\pi\)
−0.111653 + 0.993747i \(0.535614\pi\)
\(752\) 28.2043i 0.0375057i
\(753\) 1029.86 193.604i 1.36768 0.257111i
\(754\) 7.54312 0.0100041
\(755\) 0 0
\(756\) −75.5837 121.240i −0.0999784 0.160370i
\(757\) 468.004 0.618236 0.309118 0.951024i \(-0.399966\pi\)
0.309118 + 0.951024i \(0.399966\pi\)
\(758\) 907.137i 1.19675i
\(759\) −17.0259 90.5680i −0.0224320 0.119325i
\(760\) 0 0
\(761\) 252.487i 0.331784i −0.986144 0.165892i \(-0.946950\pi\)
0.986144 0.165892i \(-0.0530503\pi\)
\(762\) 638.218 119.979i 0.837557 0.157452i
\(763\) −167.976 −0.220152
\(764\) 491.091i 0.642790i
\(765\) 0 0
\(766\) 480.960 0.627885
\(767\) 18.0725i 0.0235625i
\(768\) −8.86818 47.1737i −0.0115471 0.0614241i
\(769\) −146.391 −0.190366 −0.0951828 0.995460i \(-0.530344\pi\)
−0.0951828 + 0.995460i \(0.530344\pi\)
\(770\) 0 0
\(771\) 12.3457 2.32087i 0.0160126 0.00301021i
\(772\) 65.8014 0.0852350
\(773\) 1105.53i 1.43018i −0.699032 0.715091i \(-0.746385\pi\)
0.699032 0.715091i \(-0.253615\pi\)
\(774\) −343.045 880.156i −0.443210 1.13715i
\(775\) 0 0
\(776\) 299.229i 0.385605i
\(777\) −63.4906 337.734i −0.0817125 0.434664i
\(778\) 611.764 0.786328
\(779\) 445.495i 0.571881i
\(780\) 0 0
\(781\) 252.781 0.323663
\(782\) 121.886i 0.155864i
\(783\) −676.958 + 422.031i −0.864570 + 0.538993i
\(784\) 28.0000 0.0357143
\(785\) 0 0
\(786\) 138.463 + 736.544i 0.176162 + 0.937079i
\(787\) −1176.01 −1.49430 −0.747150 0.664655i \(-0.768578\pi\)
−0.747150 + 0.664655i \(0.768578\pi\)
\(788\) 438.679i 0.556700i
\(789\) 791.589 148.811i 1.00328 0.188607i