Properties

Label 105.3.h.a.76.4
Level 105
Weight 3
Character 105.76
Analytic conductor 2.861
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} - 5472 x^{3} + 4950 x^{2} - 1638 x + 441\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.4
Root \(0.198184 + 0.343264i\) of defining polynomial
Character \(\chi\) \(=\) 105.76
Dual form 105.3.h.a.76.3

$q$-expansion

\(f(q)\) \(=\) \(q-2.79155 q^{2} +1.73205i q^{3} +3.79273 q^{4} -2.23607i q^{5} -4.83510i q^{6} +(4.15782 + 5.63139i) q^{7} +0.578591 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-2.79155 q^{2} +1.73205i q^{3} +3.79273 q^{4} -2.23607i q^{5} -4.83510i q^{6} +(4.15782 + 5.63139i) q^{7} +0.578591 q^{8} -3.00000 q^{9} +6.24209i q^{10} -18.9690 q^{11} +6.56921i q^{12} +10.9807i q^{13} +(-11.6068 - 15.7203i) q^{14} +3.87298 q^{15} -16.7861 q^{16} +22.3060i q^{17} +8.37464 q^{18} +19.6057i q^{19} -8.48081i q^{20} +(-9.75385 + 7.20156i) q^{21} +52.9528 q^{22} -31.9991 q^{23} +1.00215i q^{24} -5.00000 q^{25} -30.6530i q^{26} -5.19615i q^{27} +(15.7695 + 21.3583i) q^{28} +39.9967 q^{29} -10.8116 q^{30} -36.6641i q^{31} +44.5448 q^{32} -32.8553i q^{33} -62.2683i q^{34} +(12.5922 - 9.29718i) q^{35} -11.3782 q^{36} +8.94699 q^{37} -54.7302i q^{38} -19.0191 q^{39} -1.29377i q^{40} +37.6320i q^{41} +(27.2283 - 20.1035i) q^{42} -18.8702 q^{43} -71.9443 q^{44} +6.70820i q^{45} +89.3269 q^{46} +49.3786i q^{47} -29.0744i q^{48} +(-14.4250 + 46.8286i) q^{49} +13.9577 q^{50} -38.6352 q^{51} +41.6468i q^{52} +49.2398 q^{53} +14.5053i q^{54} +42.4160i q^{55} +(2.40568 + 3.25827i) q^{56} -33.9580 q^{57} -111.653 q^{58} -35.2173i q^{59} +14.6892 q^{60} -63.4723i q^{61} +102.349i q^{62} +(-12.4735 - 16.8942i) q^{63} -57.2046 q^{64} +24.5535 q^{65} +91.7170i q^{66} +21.3544 q^{67} +84.6008i q^{68} -55.4240i q^{69} +(-35.1516 + 25.9535i) q^{70} +36.2998 q^{71} -1.73577 q^{72} +6.66818i q^{73} -24.9759 q^{74} -8.66025i q^{75} +74.3591i q^{76} +(-78.8697 - 106.822i) q^{77} +53.0926 q^{78} -16.2015 q^{79} +37.5349i q^{80} +9.00000 q^{81} -105.052i q^{82} +36.7822i q^{83} +(-36.9937 + 27.3136i) q^{84} +49.8778 q^{85} +52.6770 q^{86} +69.2763i q^{87} -10.9753 q^{88} +88.0954i q^{89} -18.7263i q^{90} +(-61.8364 + 45.6557i) q^{91} -121.364 q^{92} +63.5040 q^{93} -137.843i q^{94} +43.8396 q^{95} +77.1539i q^{96} -133.810i q^{97} +(40.2681 - 130.724i) q^{98} +56.9070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} - 16q^{11} - 40q^{14} + 92q^{16} + 12q^{18} + 36q^{21} - 88q^{22} - 64q^{23} - 60q^{25} + 88q^{28} + 104q^{29} - 228q^{32} + 60q^{35} - 132q^{36} + 32q^{37} - 24q^{39} - 60q^{42} + 152q^{43} + 192q^{44} + 200q^{46} + 60q^{49} + 20q^{50} + 24q^{51} + 176q^{53} - 368q^{56} - 240q^{57} - 400q^{58} + 24q^{63} - 20q^{64} - 240q^{65} + 168q^{67} - 60q^{70} + 32q^{71} - 12q^{72} + 184q^{74} + 8q^{77} + 456q^{78} + 120q^{79} + 108q^{81} + 108q^{84} + 120q^{85} + 400q^{86} - 536q^{88} + 24q^{91} + 192q^{92} + 48q^{93} + 884q^{98} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79155 −1.39577 −0.697887 0.716208i \(-0.745876\pi\)
−0.697887 + 0.716208i \(0.745876\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 3.79273 0.948184
\(5\) 2.23607i 0.447214i
\(6\) 4.83510i 0.805850i
\(7\) 4.15782 + 5.63139i 0.593975 + 0.804484i
\(8\) 0.578591 0.0723239
\(9\) −3.00000 −0.333333
\(10\) 6.24209i 0.624209i
\(11\) −18.9690 −1.72445 −0.862227 0.506522i \(-0.830931\pi\)
−0.862227 + 0.506522i \(0.830931\pi\)
\(12\) 6.56921i 0.547434i
\(13\) 10.9807i 0.844667i 0.906441 + 0.422333i \(0.138789\pi\)
−0.906441 + 0.422333i \(0.861211\pi\)
\(14\) −11.6068 15.7203i −0.829054 1.12288i
\(15\) 3.87298 0.258199
\(16\) −16.7861 −1.04913
\(17\) 22.3060i 1.31212i 0.754709 + 0.656060i \(0.227778\pi\)
−0.754709 + 0.656060i \(0.772222\pi\)
\(18\) 8.37464 0.465258
\(19\) 19.6057i 1.03188i 0.856625 + 0.515939i \(0.172557\pi\)
−0.856625 + 0.515939i \(0.827443\pi\)
\(20\) 8.48081i 0.424041i
\(21\) −9.75385 + 7.20156i −0.464469 + 0.342932i
\(22\) 52.9528 2.40695
\(23\) −31.9991 −1.39126 −0.695632 0.718399i \(-0.744875\pi\)
−0.695632 + 0.718399i \(0.744875\pi\)
\(24\) 1.00215i 0.0417562i
\(25\) −5.00000 −0.200000
\(26\) 30.6530i 1.17896i
\(27\) 5.19615i 0.192450i
\(28\) 15.7695 + 21.3583i 0.563197 + 0.762798i
\(29\) 39.9967 1.37920 0.689598 0.724192i \(-0.257787\pi\)
0.689598 + 0.724192i \(0.257787\pi\)
\(30\) −10.8116 −0.360387
\(31\) 36.6641i 1.18271i −0.806411 0.591356i \(-0.798593\pi\)
0.806411 0.591356i \(-0.201407\pi\)
\(32\) 44.5448 1.39203
\(33\) 32.8553i 0.995614i
\(34\) 62.2683i 1.83142i
\(35\) 12.5922 9.29718i 0.359776 0.265634i
\(36\) −11.3782 −0.316061
\(37\) 8.94699 0.241810 0.120905 0.992664i \(-0.461420\pi\)
0.120905 + 0.992664i \(0.461420\pi\)
\(38\) 54.7302i 1.44027i
\(39\) −19.0191 −0.487669
\(40\) 1.29377i 0.0323442i
\(41\) 37.6320i 0.917854i 0.888474 + 0.458927i \(0.151766\pi\)
−0.888474 + 0.458927i \(0.848234\pi\)
\(42\) 27.2283 20.1035i 0.648293 0.478655i
\(43\) −18.8702 −0.438841 −0.219421 0.975630i \(-0.570417\pi\)
−0.219421 + 0.975630i \(0.570417\pi\)
\(44\) −71.9443 −1.63510
\(45\) 6.70820i 0.149071i
\(46\) 89.3269 1.94189
\(47\) 49.3786i 1.05061i 0.850914 + 0.525304i \(0.176048\pi\)
−0.850914 + 0.525304i \(0.823952\pi\)
\(48\) 29.0744i 0.605716i
\(49\) −14.4250 + 46.8286i −0.294388 + 0.955686i
\(50\) 13.9577 0.279155
\(51\) −38.6352 −0.757552
\(52\) 41.6468i 0.800899i
\(53\) 49.2398 0.929052 0.464526 0.885559i \(-0.346225\pi\)
0.464526 + 0.885559i \(0.346225\pi\)
\(54\) 14.5053i 0.268617i
\(55\) 42.4160i 0.771199i
\(56\) 2.40568 + 3.25827i 0.0429586 + 0.0581834i
\(57\) −33.9580 −0.595755
\(58\) −111.653 −1.92505
\(59\) 35.2173i 0.596903i −0.954425 0.298452i \(-0.903530\pi\)
0.954425 0.298452i \(-0.0964701\pi\)
\(60\) 14.6892 0.244820
\(61\) 63.4723i 1.04053i −0.854005 0.520265i \(-0.825833\pi\)
0.854005 0.520265i \(-0.174167\pi\)
\(62\) 102.349i 1.65080i
\(63\) −12.4735 16.8942i −0.197992 0.268161i
\(64\) −57.2046 −0.893821
\(65\) 24.5535 0.377746
\(66\) 91.7170i 1.38965i
\(67\) 21.3544 0.318723 0.159361 0.987220i \(-0.449057\pi\)
0.159361 + 0.987220i \(0.449057\pi\)
\(68\) 84.6008i 1.24413i
\(69\) 55.4240i 0.803246i
\(70\) −35.1516 + 25.9535i −0.502166 + 0.370764i
\(71\) 36.2998 0.511265 0.255632 0.966774i \(-0.417716\pi\)
0.255632 + 0.966774i \(0.417716\pi\)
\(72\) −1.73577 −0.0241080
\(73\) 6.66818i 0.0913449i 0.998956 + 0.0456725i \(0.0145431\pi\)
−0.998956 + 0.0456725i \(0.985457\pi\)
\(74\) −24.9759 −0.337513
\(75\) 8.66025i 0.115470i
\(76\) 74.3591i 0.978409i
\(77\) −78.8697 106.822i −1.02428 1.38729i
\(78\) 53.0926 0.680675
\(79\) −16.2015 −0.205082 −0.102541 0.994729i \(-0.532697\pi\)
−0.102541 + 0.994729i \(0.532697\pi\)
\(80\) 37.5349i 0.469186i
\(81\) 9.00000 0.111111
\(82\) 105.052i 1.28112i
\(83\) 36.7822i 0.443159i 0.975142 + 0.221579i \(0.0711212\pi\)
−0.975142 + 0.221579i \(0.928879\pi\)
\(84\) −36.9937 + 27.3136i −0.440402 + 0.325162i
\(85\) 49.8778 0.586798
\(86\) 52.6770 0.612523
\(87\) 69.2763i 0.796279i
\(88\) −10.9753 −0.124719
\(89\) 88.0954i 0.989836i 0.868940 + 0.494918i \(0.164802\pi\)
−0.868940 + 0.494918i \(0.835198\pi\)
\(90\) 18.7263i 0.208070i
\(91\) −61.8364 + 45.6557i −0.679520 + 0.501711i
\(92\) −121.364 −1.31917
\(93\) 63.5040 0.682839
\(94\) 137.843i 1.46641i
\(95\) 43.8396 0.461470
\(96\) 77.1539i 0.803687i
\(97\) 133.810i 1.37948i −0.724055 0.689742i \(-0.757724\pi\)
0.724055 0.689742i \(-0.242276\pi\)
\(98\) 40.2681 130.724i 0.410899 1.33392i
\(99\) 56.9070 0.574818
\(100\) −18.9637 −0.189637
\(101\) 194.903i 1.92973i −0.262743 0.964866i \(-0.584627\pi\)
0.262743 0.964866i \(-0.415373\pi\)
\(102\) 107.852 1.05737
\(103\) 41.2629i 0.400610i 0.979734 + 0.200305i \(0.0641933\pi\)
−0.979734 + 0.200305i \(0.935807\pi\)
\(104\) 6.35332i 0.0610896i
\(105\) 16.1032 + 21.8103i 0.153364 + 0.207717i
\(106\) −137.455 −1.29675
\(107\) 29.7031 0.277599 0.138799 0.990321i \(-0.455676\pi\)
0.138799 + 0.990321i \(0.455676\pi\)
\(108\) 19.7076i 0.182478i
\(109\) 91.7028 0.841310 0.420655 0.907221i \(-0.361800\pi\)
0.420655 + 0.907221i \(0.361800\pi\)
\(110\) 118.406i 1.07642i
\(111\) 15.4966i 0.139609i
\(112\) −69.7937 94.5290i −0.623158 0.844009i
\(113\) 2.98301 0.0263983 0.0131992 0.999913i \(-0.495798\pi\)
0.0131992 + 0.999913i \(0.495798\pi\)
\(114\) 94.7954 0.831539
\(115\) 71.5521i 0.622192i
\(116\) 151.697 1.30773
\(117\) 32.9420i 0.281556i
\(118\) 98.3107i 0.833142i
\(119\) −125.614 + 92.7445i −1.05558 + 0.779366i
\(120\) 2.24087 0.0186739
\(121\) 238.823 1.97374
\(122\) 177.186i 1.45234i
\(123\) −65.1806 −0.529923
\(124\) 139.057i 1.12143i
\(125\) 11.1803i 0.0894427i
\(126\) 34.8203 + 47.1608i 0.276351 + 0.374292i
\(127\) 104.651 0.824023 0.412012 0.911179i \(-0.364826\pi\)
0.412012 + 0.911179i \(0.364826\pi\)
\(128\) −18.4901 −0.144454
\(129\) 32.6841i 0.253365i
\(130\) −68.5423 −0.527248
\(131\) 70.8051i 0.540497i 0.962791 + 0.270249i \(0.0871059\pi\)
−0.962791 + 0.270249i \(0.912894\pi\)
\(132\) 124.611i 0.944025i
\(133\) −110.407 + 81.5169i −0.830129 + 0.612909i
\(134\) −59.6118 −0.444864
\(135\) −11.6190 −0.0860663
\(136\) 12.9061i 0.0948976i
\(137\) −158.673 −1.15820 −0.579100 0.815256i \(-0.696596\pi\)
−0.579100 + 0.815256i \(0.696596\pi\)
\(138\) 154.719i 1.12115i
\(139\) 54.4253i 0.391549i −0.980649 0.195774i \(-0.937278\pi\)
0.980649 0.195774i \(-0.0627220\pi\)
\(140\) 47.7587 35.2617i 0.341134 0.251869i
\(141\) −85.5262 −0.606569
\(142\) −101.333 −0.713610
\(143\) 208.292i 1.45659i
\(144\) 50.3583 0.349710
\(145\) 89.4353i 0.616795i
\(146\) 18.6145i 0.127497i
\(147\) −81.1095 24.9848i −0.551766 0.169965i
\(148\) 33.9335 0.229281
\(149\) 229.102 1.53760 0.768799 0.639490i \(-0.220854\pi\)
0.768799 + 0.639490i \(0.220854\pi\)
\(150\) 24.1755i 0.161170i
\(151\) −197.735 −1.30950 −0.654750 0.755845i \(-0.727226\pi\)
−0.654750 + 0.755845i \(0.727226\pi\)
\(152\) 11.3437i 0.0746294i
\(153\) 66.9181i 0.437373i
\(154\) 220.169 + 298.198i 1.42967 + 1.93635i
\(155\) −81.9833 −0.528925
\(156\) −72.1343 −0.462399
\(157\) 211.036i 1.34418i 0.740470 + 0.672089i \(0.234603\pi\)
−0.740470 + 0.672089i \(0.765397\pi\)
\(158\) 45.2271 0.286248
\(159\) 85.2858i 0.536389i
\(160\) 99.6053i 0.622533i
\(161\) −133.046 180.199i −0.826375 1.11925i
\(162\) −25.1239 −0.155086
\(163\) 181.823 1.11548 0.557741 0.830015i \(-0.311668\pi\)
0.557741 + 0.830015i \(0.311668\pi\)
\(164\) 142.728i 0.870295i
\(165\) −73.4666 −0.445252
\(166\) 102.679i 0.618549i
\(167\) 101.160i 0.605751i 0.953030 + 0.302876i \(0.0979467\pi\)
−0.953030 + 0.302876i \(0.902053\pi\)
\(168\) −5.64349 + 4.16676i −0.0335922 + 0.0248021i
\(169\) 48.4250 0.286538
\(170\) −139.236 −0.819037
\(171\) 58.8170i 0.343959i
\(172\) −71.5696 −0.416102
\(173\) 109.976i 0.635702i 0.948141 + 0.317851i \(0.102961\pi\)
−0.948141 + 0.317851i \(0.897039\pi\)
\(174\) 193.388i 1.11143i
\(175\) −20.7891 28.1569i −0.118795 0.160897i
\(176\) 318.415 1.80918
\(177\) 60.9981 0.344622
\(178\) 245.922i 1.38159i
\(179\) 91.8832 0.513314 0.256657 0.966503i \(-0.417379\pi\)
0.256657 + 0.966503i \(0.417379\pi\)
\(180\) 25.4424i 0.141347i
\(181\) 62.8649i 0.347320i 0.984806 + 0.173660i \(0.0555594\pi\)
−0.984806 + 0.173660i \(0.944441\pi\)
\(182\) 172.619 127.450i 0.948457 0.700275i
\(183\) 109.937 0.600750
\(184\) −18.5144 −0.100622
\(185\) 20.0061i 0.108141i
\(186\) −177.274 −0.953088
\(187\) 423.123i 2.26269i
\(188\) 187.280i 0.996170i
\(189\) 29.2615 21.6047i 0.154823 0.114311i
\(190\) −122.380 −0.644107
\(191\) −75.9925 −0.397866 −0.198933 0.980013i \(-0.563748\pi\)
−0.198933 + 0.980013i \(0.563748\pi\)
\(192\) 99.0812i 0.516048i
\(193\) 22.7530 0.117891 0.0589456 0.998261i \(-0.481226\pi\)
0.0589456 + 0.998261i \(0.481226\pi\)
\(194\) 373.537i 1.92545i
\(195\) 42.5279i 0.218092i
\(196\) −54.7102 + 177.609i −0.279134 + 0.906166i
\(197\) −137.485 −0.697891 −0.348946 0.937143i \(-0.613460\pi\)
−0.348946 + 0.937143i \(0.613460\pi\)
\(198\) −158.858 −0.802316
\(199\) 267.299i 1.34321i 0.740909 + 0.671606i \(0.234395\pi\)
−0.740909 + 0.671606i \(0.765605\pi\)
\(200\) −2.89296 −0.0144648
\(201\) 36.9869i 0.184015i
\(202\) 544.081i 2.69347i
\(203\) 166.299 + 225.237i 0.819208 + 1.10954i
\(204\) −146.533 −0.718299
\(205\) 84.1478 0.410477
\(206\) 115.187i 0.559161i
\(207\) 95.9972 0.463754
\(208\) 184.323i 0.886166i
\(209\) 371.900i 1.77943i
\(210\) −44.9528 60.8844i −0.214061 0.289926i
\(211\) −366.610 −1.73749 −0.868744 0.495261i \(-0.835073\pi\)
−0.868744 + 0.495261i \(0.835073\pi\)
\(212\) 186.753 0.880912
\(213\) 62.8731i 0.295179i
\(214\) −82.9175 −0.387465
\(215\) 42.1950i 0.196256i
\(216\) 3.00645i 0.0139187i
\(217\) 206.469 152.443i 0.951472 0.702501i
\(218\) −255.993 −1.17428
\(219\) −11.5496 −0.0527380
\(220\) 160.872i 0.731238i
\(221\) −244.935 −1.10830
\(222\) 43.2596i 0.194863i
\(223\) 282.872i 1.26848i 0.773134 + 0.634242i \(0.218688\pi\)
−0.773134 + 0.634242i \(0.781312\pi\)
\(224\) 185.210 + 250.849i 0.826828 + 1.11986i
\(225\) 15.0000 0.0666667
\(226\) −8.32722 −0.0368461
\(227\) 210.777i 0.928534i 0.885695 + 0.464267i \(0.153682\pi\)
−0.885695 + 0.464267i \(0.846318\pi\)
\(228\) −128.794 −0.564885
\(229\) 137.506i 0.600464i 0.953866 + 0.300232i \(0.0970641\pi\)
−0.953866 + 0.300232i \(0.902936\pi\)
\(230\) 199.741i 0.868439i
\(231\) 185.021 136.606i 0.800955 0.591370i
\(232\) 23.1417 0.0997488
\(233\) −77.7682 −0.333769 −0.166884 0.985976i \(-0.553371\pi\)
−0.166884 + 0.985976i \(0.553371\pi\)
\(234\) 91.9591i 0.392988i
\(235\) 110.414 0.469846
\(236\) 133.570i 0.565974i
\(237\) 28.0618i 0.118404i
\(238\) 350.657 258.901i 1.47335 1.08782i
\(239\) −123.843 −0.518173 −0.259086 0.965854i \(-0.583421\pi\)
−0.259086 + 0.965854i \(0.583421\pi\)
\(240\) −65.0123 −0.270885
\(241\) 155.802i 0.646481i 0.946317 + 0.323240i \(0.104772\pi\)
−0.946317 + 0.323240i \(0.895228\pi\)
\(242\) −666.684 −2.75489
\(243\) 15.5885i 0.0641500i
\(244\) 240.734i 0.986613i
\(245\) 104.712 + 32.2553i 0.427396 + 0.131654i
\(246\) 181.955 0.739653
\(247\) −215.283 −0.871593
\(248\) 21.2135i 0.0855383i
\(249\) −63.7086 −0.255858
\(250\) 31.2104i 0.124842i
\(251\) 278.340i 1.10892i −0.832210 0.554461i \(-0.812924\pi\)
0.832210 0.554461i \(-0.187076\pi\)
\(252\) −47.3086 64.0750i −0.187732 0.254266i
\(253\) 606.990 2.39917
\(254\) −292.138 −1.15015
\(255\) 86.3909i 0.338788i
\(256\) 280.434 1.09545
\(257\) 220.802i 0.859151i −0.903031 0.429575i \(-0.858663\pi\)
0.903031 0.429575i \(-0.141337\pi\)
\(258\) 91.2392i 0.353640i
\(259\) 37.2000 + 50.3839i 0.143629 + 0.194533i
\(260\) 93.1250 0.358173
\(261\) −119.990 −0.459732
\(262\) 197.656i 0.754412i
\(263\) −17.3477 −0.0659609 −0.0329804 0.999456i \(-0.510500\pi\)
−0.0329804 + 0.999456i \(0.510500\pi\)
\(264\) 19.0098i 0.0720067i
\(265\) 110.103i 0.415485i
\(266\) 308.207 227.558i 1.15867 0.855483i
\(267\) −152.586 −0.571482
\(268\) 80.9916 0.302207
\(269\) 499.213i 1.85581i −0.372816 0.927905i \(-0.621608\pi\)
0.372816 0.927905i \(-0.378392\pi\)
\(270\) 32.4348 0.120129
\(271\) 330.005i 1.21773i 0.793273 + 0.608866i \(0.208375\pi\)
−0.793273 + 0.608866i \(0.791625\pi\)
\(272\) 374.431i 1.37659i
\(273\) −79.0780 107.104i −0.289663 0.392321i
\(274\) 442.944 1.61659
\(275\) 94.8449 0.344891
\(276\) 210.209i 0.761625i
\(277\) 147.766 0.533452 0.266726 0.963772i \(-0.414058\pi\)
0.266726 + 0.963772i \(0.414058\pi\)
\(278\) 151.931i 0.546513i
\(279\) 109.992i 0.394237i
\(280\) 7.28571 5.37926i 0.0260204 0.0192117i
\(281\) 353.405 1.25767 0.628834 0.777540i \(-0.283533\pi\)
0.628834 + 0.777540i \(0.283533\pi\)
\(282\) 238.751 0.846633
\(283\) 428.203i 1.51308i −0.653945 0.756542i \(-0.726887\pi\)
0.653945 0.756542i \(-0.273113\pi\)
\(284\) 137.675 0.484773
\(285\) 75.9325i 0.266430i
\(286\) 581.457i 2.03307i
\(287\) −211.920 + 156.467i −0.738399 + 0.545182i
\(288\) −133.634 −0.464009
\(289\) −208.559 −0.721657
\(290\) 249.663i 0.860906i
\(291\) 231.766 0.796446
\(292\) 25.2906i 0.0866117i
\(293\) 402.632i 1.37417i 0.726577 + 0.687085i \(0.241110\pi\)
−0.726577 + 0.687085i \(0.758890\pi\)
\(294\) 226.421 + 69.7463i 0.770140 + 0.237232i
\(295\) −78.7483 −0.266943
\(296\) 5.17665 0.0174887
\(297\) 98.5658i 0.331871i
\(298\) −639.550 −2.14614
\(299\) 351.371i 1.17515i
\(300\) 32.8460i 0.109487i
\(301\) −78.4589 106.265i −0.260661 0.353041i
\(302\) 551.986 1.82777
\(303\) 337.582 1.11413
\(304\) 329.103i 1.08258i
\(305\) −141.928 −0.465339
\(306\) 186.805i 0.610474i
\(307\) 92.7330i 0.302062i 0.988529 + 0.151031i \(0.0482593\pi\)
−0.988529 + 0.151031i \(0.951741\pi\)
\(308\) −299.132 405.146i −0.971207 1.31541i
\(309\) −71.4694 −0.231292
\(310\) 228.860 0.738259
\(311\) 218.118i 0.701343i 0.936498 + 0.350672i \(0.114047\pi\)
−0.936498 + 0.350672i \(0.885953\pi\)
\(312\) −11.0043 −0.0352701
\(313\) 293.684i 0.938288i −0.883122 0.469144i \(-0.844562\pi\)
0.883122 0.469144i \(-0.155438\pi\)
\(314\) 589.117i 1.87617i
\(315\) −37.7765 + 27.8915i −0.119925 + 0.0885445i
\(316\) −61.4479 −0.194455
\(317\) 109.074 0.344081 0.172041 0.985090i \(-0.444964\pi\)
0.172041 + 0.985090i \(0.444964\pi\)
\(318\) 238.079i 0.748677i
\(319\) −758.697 −2.37836
\(320\) 127.913i 0.399729i
\(321\) 51.4472i 0.160272i
\(322\) 371.405 + 503.034i 1.15343 + 1.56222i
\(323\) −437.325 −1.35395
\(324\) 34.1346 0.105354
\(325\) 54.9033i 0.168933i
\(326\) −507.569 −1.55696
\(327\) 158.834i 0.485731i
\(328\) 21.7736i 0.0663828i
\(329\) −278.070 + 205.308i −0.845197 + 0.624035i
\(330\) 205.085 0.621471
\(331\) 408.913 1.23539 0.617694 0.786419i \(-0.288067\pi\)
0.617694 + 0.786419i \(0.288067\pi\)
\(332\) 139.505i 0.420196i
\(333\) −26.8410 −0.0806035
\(334\) 282.394i 0.845492i
\(335\) 47.7499i 0.142537i
\(336\) 163.729 120.886i 0.487289 0.359780i
\(337\) −299.269 −0.888040 −0.444020 0.896017i \(-0.646448\pi\)
−0.444020 + 0.896017i \(0.646448\pi\)
\(338\) −135.181 −0.399942
\(339\) 5.16673i 0.0152411i
\(340\) 189.173 0.556392
\(341\) 695.480i 2.03953i
\(342\) 164.190i 0.480089i
\(343\) −323.687 + 113.472i −0.943693 + 0.330823i
\(344\) −10.9181 −0.0317387
\(345\) −123.932 −0.359223
\(346\) 307.004i 0.887296i
\(347\) 567.731 1.63611 0.818056 0.575138i \(-0.195052\pi\)
0.818056 + 0.575138i \(0.195052\pi\)
\(348\) 262.747i 0.755019i
\(349\) 141.703i 0.406025i 0.979176 + 0.203012i \(0.0650732\pi\)
−0.979176 + 0.203012i \(0.934927\pi\)
\(350\) 58.0338 + 78.6014i 0.165811 + 0.224575i
\(351\) 57.0572 0.162556
\(352\) −844.970 −2.40048
\(353\) 452.435i 1.28169i 0.767672 + 0.640843i \(0.221415\pi\)
−0.767672 + 0.640843i \(0.778585\pi\)
\(354\) −170.279 −0.481015
\(355\) 81.1688i 0.228644i
\(356\) 334.123i 0.938546i
\(357\) −160.638 217.570i −0.449967 0.609439i
\(358\) −256.496 −0.716470
\(359\) 174.670 0.486546 0.243273 0.969958i \(-0.421779\pi\)
0.243273 + 0.969958i \(0.421779\pi\)
\(360\) 3.88131i 0.0107814i
\(361\) −23.3825 −0.0647714
\(362\) 175.490i 0.484780i
\(363\) 413.653i 1.13954i
\(364\) −234.529 + 173.160i −0.644310 + 0.475714i
\(365\) 14.9105 0.0408507
\(366\) −306.895 −0.838511
\(367\) 121.147i 0.330101i −0.986285 0.165051i \(-0.947221\pi\)
0.986285 0.165051i \(-0.0527788\pi\)
\(368\) 537.139 1.45962
\(369\) 112.896i 0.305951i
\(370\) 55.8479i 0.150940i
\(371\) 204.730 + 277.288i 0.551834 + 0.747407i
\(372\) 240.854 0.647456
\(373\) −90.9075 −0.243720 −0.121860 0.992547i \(-0.538886\pi\)
−0.121860 + 0.992547i \(0.538886\pi\)
\(374\) 1181.17i 3.15820i
\(375\) −19.3649 −0.0516398
\(376\) 28.5700i 0.0759841i
\(377\) 439.190i 1.16496i
\(378\) −81.6850 + 60.3105i −0.216098 + 0.159552i
\(379\) −638.344 −1.68429 −0.842143 0.539254i \(-0.818706\pi\)
−0.842143 + 0.539254i \(0.818706\pi\)
\(380\) 166.272 0.437558
\(381\) 181.261i 0.475750i
\(382\) 212.137 0.555331
\(383\) 176.395i 0.460561i −0.973124 0.230281i \(-0.926036\pi\)
0.973124 0.230281i \(-0.0739644\pi\)
\(384\) 32.0257i 0.0834003i
\(385\) −238.861 + 176.358i −0.620417 + 0.458073i
\(386\) −63.5160 −0.164549
\(387\) 56.6105 0.146280
\(388\) 507.506i 1.30800i
\(389\) 249.521 0.641442 0.320721 0.947174i \(-0.396075\pi\)
0.320721 + 0.947174i \(0.396075\pi\)
\(390\) 118.719i 0.304407i
\(391\) 713.772i 1.82550i
\(392\) −8.34618 + 27.0946i −0.0212913 + 0.0691189i
\(393\) −122.638 −0.312056
\(394\) 383.795 0.974098
\(395\) 36.2276i 0.0917154i
\(396\) 215.833 0.545033
\(397\) 186.071i 0.468694i 0.972153 + 0.234347i \(0.0752951\pi\)
−0.972153 + 0.234347i \(0.924705\pi\)
\(398\) 746.178i 1.87482i
\(399\) −141.191 191.231i −0.353863 0.479275i
\(400\) 83.9305 0.209826
\(401\) −188.067 −0.468996 −0.234498 0.972117i \(-0.575345\pi\)
−0.234498 + 0.972117i \(0.575345\pi\)
\(402\) 103.251i 0.256843i
\(403\) 402.596 0.998997
\(404\) 739.215i 1.82974i
\(405\) 20.1246i 0.0496904i
\(406\) −464.232 628.759i −1.14343 1.54867i
\(407\) −169.715 −0.416991
\(408\) −22.3540 −0.0547891
\(409\) 512.173i 1.25226i 0.779720 + 0.626128i \(0.215361\pi\)
−0.779720 + 0.626128i \(0.784639\pi\)
\(410\) −234.902 −0.572933
\(411\) 274.831i 0.668687i
\(412\) 156.499i 0.379852i
\(413\) 198.322 146.427i 0.480199 0.354545i
\(414\) −267.981 −0.647296
\(415\) 82.2475 0.198187
\(416\) 489.132i 1.17580i
\(417\) 94.2673 0.226061
\(418\) 1038.18i 2.48367i
\(419\) 323.661i 0.772461i −0.922402 0.386231i \(-0.873777\pi\)
0.922402 0.386231i \(-0.126223\pi\)
\(420\) 61.0751 + 82.7205i 0.145417 + 0.196954i
\(421\) −503.872 −1.19685 −0.598423 0.801180i \(-0.704206\pi\)
−0.598423 + 0.801180i \(0.704206\pi\)
\(422\) 1023.41 2.42514
\(423\) 148.136i 0.350203i
\(424\) 28.4897 0.0671927
\(425\) 111.530i 0.262424i
\(426\) 175.513i 0.412003i
\(427\) 357.437 263.907i 0.837089 0.618049i
\(428\) 112.656 0.263215
\(429\) 360.773 0.840962
\(430\) 117.789i 0.273929i
\(431\) 317.731 0.737195 0.368597 0.929589i \(-0.379838\pi\)
0.368597 + 0.929589i \(0.379838\pi\)
\(432\) 87.2231i 0.201905i
\(433\) 261.387i 0.603665i 0.953361 + 0.301833i \(0.0975984\pi\)
−0.953361 + 0.301833i \(0.902402\pi\)
\(434\) −576.369 + 425.551i −1.32804 + 0.980532i
\(435\) 154.906 0.356107
\(436\) 347.805 0.797717
\(437\) 627.363i 1.43561i
\(438\) 32.2413 0.0736103
\(439\) 789.513i 1.79844i −0.437501 0.899218i \(-0.644137\pi\)
0.437501 0.899218i \(-0.355863\pi\)
\(440\) 24.5415i 0.0557761i
\(441\) 43.2750 140.486i 0.0981293 0.318562i
\(442\) 683.748 1.54694
\(443\) 585.242 1.32109 0.660544 0.750787i \(-0.270326\pi\)
0.660544 + 0.750787i \(0.270326\pi\)
\(444\) 58.7746i 0.132375i
\(445\) 196.987 0.442668
\(446\) 789.651i 1.77052i
\(447\) 396.817i 0.887733i
\(448\) −237.847 322.141i −0.530907 0.719065i
\(449\) 528.147 1.17627 0.588137 0.808761i \(-0.299862\pi\)
0.588137 + 0.808761i \(0.299862\pi\)
\(450\) −41.8732 −0.0930516
\(451\) 713.842i 1.58280i
\(452\) 11.3138 0.0250305
\(453\) 342.486i 0.756041i
\(454\) 588.395i 1.29602i
\(455\) 102.089 + 138.270i 0.224372 + 0.303891i
\(456\) −19.6478 −0.0430873
\(457\) −164.041 −0.358953 −0.179476 0.983762i \(-0.557440\pi\)
−0.179476 + 0.983762i \(0.557440\pi\)
\(458\) 383.855i 0.838112i
\(459\) 115.906 0.252517
\(460\) 271.378i 0.589952i
\(461\) 399.626i 0.866867i −0.901186 0.433434i \(-0.857302\pi\)
0.901186 0.433434i \(-0.142698\pi\)
\(462\) −516.494 + 381.343i −1.11795 + 0.825418i
\(463\) −680.267 −1.46926 −0.734630 0.678468i \(-0.762644\pi\)
−0.734630 + 0.678468i \(0.762644\pi\)
\(464\) −671.388 −1.44696
\(465\) 141.999i 0.305375i
\(466\) 217.093 0.465866
\(467\) 725.217i 1.55293i 0.630162 + 0.776464i \(0.282989\pi\)
−0.630162 + 0.776464i \(0.717011\pi\)
\(468\) 124.940i 0.266966i
\(469\) 88.7879 + 120.255i 0.189313 + 0.256407i
\(470\) −308.226 −0.655799
\(471\) −365.525 −0.776062
\(472\) 20.3764i 0.0431704i
\(473\) 357.948 0.756762
\(474\) 78.3357i 0.165265i
\(475\) 98.0284i 0.206376i
\(476\) −476.420 + 351.755i −1.00088 + 0.738982i
\(477\) −147.719 −0.309684
\(478\) 345.714 0.723252
\(479\) 317.103i 0.662010i 0.943629 + 0.331005i \(0.107388\pi\)
−0.943629 + 0.331005i \(0.892612\pi\)
\(480\) 172.521 0.359420
\(481\) 98.2439i 0.204249i
\(482\) 434.928i 0.902341i
\(483\) 312.114 230.443i 0.646198 0.477108i
\(484\) 905.791 1.87147
\(485\) −299.208 −0.616924
\(486\) 43.5159i 0.0895389i
\(487\) 353.125 0.725103 0.362551 0.931964i \(-0.381906\pi\)
0.362551 + 0.931964i \(0.381906\pi\)
\(488\) 36.7245i 0.0752552i
\(489\) 314.927i 0.644023i
\(490\) −292.308 90.0421i −0.596548 0.183759i
\(491\) −343.280 −0.699145 −0.349572 0.936909i \(-0.613673\pi\)
−0.349572 + 0.936909i \(0.613673\pi\)
\(492\) −247.213 −0.502465
\(493\) 892.167i 1.80967i
\(494\) 600.974 1.21655
\(495\) 127.248i 0.257066i
\(496\) 615.447i 1.24082i
\(497\) 150.928 + 204.418i 0.303678 + 0.411304i
\(498\) 177.846 0.357120
\(499\) −420.584 −0.842853 −0.421427 0.906863i \(-0.638470\pi\)
−0.421427 + 0.906863i \(0.638470\pi\)
\(500\) 42.4041i 0.0848081i
\(501\) −175.215 −0.349731
\(502\) 776.998i 1.54780i
\(503\) 183.030i 0.363876i 0.983310 + 0.181938i \(0.0582370\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(504\) −7.21704 9.77481i −0.0143195 0.0193945i
\(505\) −435.816 −0.863002
\(506\) −1694.44 −3.34870
\(507\) 83.8745i 0.165433i
\(508\) 396.913 0.781326
\(509\) 261.854i 0.514448i 0.966352 + 0.257224i \(0.0828079\pi\)
−0.966352 + 0.257224i \(0.917192\pi\)
\(510\) 241.164i 0.472871i
\(511\) −37.5511 + 27.7251i −0.0734855 + 0.0542566i
\(512\) −708.885 −1.38454
\(513\) 101.874 0.198585
\(514\) 616.378i 1.19918i
\(515\) 92.2665 0.179158
\(516\) 123.962i 0.240237i
\(517\) 936.662i 1.81173i
\(518\) −103.846 140.649i −0.200474 0.271523i
\(519\) −190.485 −0.367023
\(520\) 14.2064 0.0273201
\(521\) 477.677i 0.916846i −0.888734 0.458423i \(-0.848414\pi\)
0.888734 0.458423i \(-0.151586\pi\)
\(522\) 334.958 0.641682
\(523\) 770.784i 1.47377i −0.676016 0.736887i \(-0.736295\pi\)
0.676016 0.736887i \(-0.263705\pi\)
\(524\) 268.545i 0.512491i
\(525\) 48.7692 36.0078i 0.0928938 0.0685863i
\(526\) 48.4269 0.0920664
\(527\) 817.829 1.55186
\(528\) 551.512i 1.04453i
\(529\) 494.940 0.935614
\(530\) 307.359i 0.579923i
\(531\) 105.652i 0.198968i
\(532\) −418.745 + 309.172i −0.787114 + 0.581151i
\(533\) −413.225 −0.775281
\(534\) 425.950 0.797660
\(535\) 66.4181i 0.124146i
\(536\) 12.3555 0.0230513
\(537\) 159.146i 0.296362i
\(538\) 1393.58i 2.59029i
\(539\) 273.628 888.292i 0.507658 1.64804i
\(540\) −44.0676 −0.0816067
\(541\) 1054.53 1.94922 0.974609 0.223912i \(-0.0718828\pi\)
0.974609 + 0.223912i \(0.0718828\pi\)
\(542\) 921.225i 1.69968i
\(543\) −108.885 −0.200525
\(544\) 993.618i 1.82650i
\(545\) 205.054i 0.376245i
\(546\) 220.750 + 298.985i 0.404304 + 0.547592i
\(547\) 697.821 1.27572 0.637862 0.770151i \(-0.279819\pi\)
0.637862 + 0.770151i \(0.279819\pi\)
\(548\) −601.806 −1.09819
\(549\) 190.417i 0.346843i
\(550\) −264.764 −0.481389
\(551\) 784.162i 1.42316i
\(552\) 32.0678i 0.0580939i
\(553\) −67.3628 91.2367i −0.121813 0.164985i
\(554\) −412.496 −0.744578
\(555\) 34.6515 0.0624352
\(556\) 206.421i 0.371260i
\(557\) −941.244 −1.68985 −0.844923 0.534888i \(-0.820354\pi\)
−0.844923 + 0.534888i \(0.820354\pi\)
\(558\) 307.048i 0.550266i
\(559\) 207.207i 0.370675i
\(560\) −211.373 + 156.063i −0.377452 + 0.278685i
\(561\) 732.870 1.30636
\(562\) −986.545 −1.75542
\(563\) 768.996i 1.36589i −0.730470 0.682945i \(-0.760699\pi\)
0.730470 0.682945i \(-0.239301\pi\)
\(564\) −324.378 −0.575139
\(565\) 6.67022i 0.0118057i
\(566\) 1195.35i 2.11192i
\(567\) 37.4204 + 50.6825i 0.0659972 + 0.0893871i
\(568\) 21.0027 0.0369766
\(569\) −46.4935 −0.0817108 −0.0408554 0.999165i \(-0.513008\pi\)
−0.0408554 + 0.999165i \(0.513008\pi\)
\(570\) 211.969i 0.371875i
\(571\) 774.153 1.35578 0.677892 0.735161i \(-0.262894\pi\)
0.677892 + 0.735161i \(0.262894\pi\)
\(572\) 789.997i 1.38111i
\(573\) 131.623i 0.229708i
\(574\) 591.586 436.786i 1.03064 0.760951i
\(575\) 159.995 0.278253
\(576\) 171.614 0.297940
\(577\) 66.7246i 0.115641i 0.998327 + 0.0578203i \(0.0184150\pi\)
−0.998327 + 0.0578203i \(0.981585\pi\)
\(578\) 582.202 1.00727
\(579\) 39.4093i 0.0680645i
\(580\) 339.204i 0.584835i
\(581\) −207.135 + 152.934i −0.356514 + 0.263225i
\(582\) −646.985 −1.11166
\(583\) −934.029 −1.60211
\(584\) 3.85815i 0.00660642i
\(585\) −73.6606 −0.125915
\(586\) 1123.97i 1.91803i
\(587\) 678.789i 1.15637i −0.815906 0.578185i \(-0.803761\pi\)
0.815906 0.578185i \(-0.196239\pi\)
\(588\) −307.627 94.7608i −0.523175 0.161158i
\(589\) 718.823 1.22041
\(590\) 219.829 0.372592
\(591\) 238.130i 0.402928i
\(592\) −150.185 −0.253691
\(593\) 289.610i 0.488381i −0.969727 0.244190i \(-0.921478\pi\)
0.969727 0.244190i \(-0.0785222\pi\)
\(594\) 275.151i 0.463217i
\(595\) 207.383 + 280.881i 0.348543 + 0.472069i
\(596\) 868.924 1.45793
\(597\) −462.976 −0.775503
\(598\) 980.869i 1.64025i
\(599\) 384.076 0.641195 0.320598 0.947216i \(-0.396116\pi\)
0.320598 + 0.947216i \(0.396116\pi\)
\(600\) 5.01075i 0.00835124i
\(601\) 37.4083i 0.0622434i 0.999516 + 0.0311217i \(0.00990794\pi\)
−0.999516 + 0.0311217i \(0.990092\pi\)
\(602\) 219.022 + 296.644i 0.363823 + 0.492765i
\(603\) −64.0632 −0.106241
\(604\) −749.955 −1.24165
\(605\) 534.023i 0.882683i
\(606\) −942.375 −1.55507
\(607\) 876.691i 1.44430i 0.691736 + 0.722150i \(0.256846\pi\)
−0.691736 + 0.722150i \(0.743154\pi\)
\(608\) 873.331i 1.43640i
\(609\) −390.121 + 288.039i −0.640594 + 0.472970i
\(610\) 396.200 0.649508
\(611\) −542.210 −0.887414
\(612\) 253.803i 0.414710i
\(613\) −591.071 −0.964226 −0.482113 0.876109i \(-0.660131\pi\)
−0.482113 + 0.876109i \(0.660131\pi\)
\(614\) 258.868i 0.421610i
\(615\) 145.748i 0.236989i
\(616\) −45.6333 61.8061i −0.0740801 0.100335i
\(617\) −744.668 −1.20692 −0.603459 0.797394i \(-0.706211\pi\)
−0.603459 + 0.797394i \(0.706211\pi\)
\(618\) 199.510 0.322832
\(619\) 851.811i 1.37611i 0.725659 + 0.688054i \(0.241535\pi\)
−0.725659 + 0.688054i \(0.758465\pi\)
\(620\) −310.941 −0.501518
\(621\) 166.272i 0.267749i
\(622\) 608.886i 0.978917i
\(623\) −496.099 + 366.285i −0.796307 + 0.587938i
\(624\) 319.256 0.511628
\(625\) 25.0000 0.0400000
\(626\) 819.833i 1.30964i
\(627\) 644.149 1.02735
\(628\) 800.404i 1.27453i
\(629\) 199.572i 0.317284i
\(630\) 105.455 77.8605i 0.167389 0.123588i
\(631\) 316.625 0.501783 0.250891 0.968015i \(-0.419276\pi\)
0.250891 + 0.968015i \(0.419276\pi\)
\(632\) −9.37402 −0.0148323
\(633\) 634.987i 1.00314i
\(634\) −304.485 −0.480260
\(635\) 234.007i 0.368514i
\(636\) 323.466i 0.508595i
\(637\) −514.209 158.396i −0.807236 0.248660i
\(638\) 2117.94 3.31965
\(639\) −108.899 −0.170422
\(640\) 41.3450i 0.0646016i
\(641\) 173.979 0.271418 0.135709 0.990749i \(-0.456669\pi\)
0.135709 + 0.990749i \(0.456669\pi\)
\(642\) 143.617i 0.223703i
\(643\) 926.785i 1.44135i −0.693275 0.720673i \(-0.743833\pi\)
0.693275 0.720673i \(-0.256167\pi\)
\(644\) −504.610 683.447i −0.783556 1.06125i
\(645\) −73.0839 −0.113308
\(646\) 1220.81 1.88980
\(647\) 429.625i 0.664027i −0.943275 0.332013i \(-0.892272\pi\)
0.943275 0.332013i \(-0.107728\pi\)
\(648\) 5.20732 0.00803599
\(649\) 668.036i 1.02933i
\(650\) 153.265i 0.235793i
\(651\) 264.038 + 357.615i 0.405589 + 0.549333i
\(652\) 689.608 1.05768
\(653\) −927.100 −1.41976 −0.709878 0.704325i \(-0.751250\pi\)
−0.709878 + 0.704325i \(0.751250\pi\)
\(654\) 443.392i 0.677970i
\(655\) 158.325 0.241718
\(656\) 631.695i 0.962950i
\(657\) 20.0045i 0.0304483i
\(658\) 776.245 573.126i 1.17970 0.871012i
\(659\) 692.153 1.05031 0.525154 0.851007i \(-0.324008\pi\)
0.525154 + 0.851007i \(0.324008\pi\)
\(660\) −278.639 −0.422181
\(661\) 1101.42i 1.66629i 0.553053 + 0.833146i \(0.313463\pi\)
−0.553053 + 0.833146i \(0.686537\pi\)
\(662\) −1141.50 −1.72432
\(663\) 424.240i 0.639879i
\(664\) 21.2818i 0.0320510i
\(665\) 182.277 + 246.878i 0.274101 + 0.371245i
\(666\) 74.9278 0.112504
\(667\) −1279.86 −1.91882
\(668\) 383.675i 0.574364i
\(669\) −489.949 −0.732360
\(670\) 133.296i 0.198949i
\(671\) 1204.01i 1.79435i
\(672\) −434.483 + 320.792i −0.646553 + 0.477370i
\(673\) 701.861 1.04288 0.521442 0.853287i \(-0.325394\pi\)
0.521442 + 0.853287i \(0.325394\pi\)
\(674\) 835.424 1.23950
\(675\) 25.9808i 0.0384900i
\(676\) 183.663 0.271691
\(677\) 404.920i 0.598110i 0.954236 + 0.299055i \(0.0966714\pi\)
−0.954236 + 0.299055i \(0.903329\pi\)
\(678\) 14.4232i 0.0212731i
\(679\) 753.535 556.358i 1.10977 0.819379i
\(680\) 28.8589 0.0424395
\(681\) −365.077 −0.536090
\(682\) 1941.47i 2.84672i
\(683\) −766.177 −1.12178 −0.560891 0.827890i \(-0.689541\pi\)
−0.560891 + 0.827890i \(0.689541\pi\)
\(684\) 223.077i 0.326136i
\(685\) 354.805i 0.517963i
\(686\) 903.586 316.764i 1.31718 0.461754i
\(687\) −238.168 −0.346678
\(688\) 316.757 0.460402
\(689\) 540.686i 0.784740i
\(690\) 345.962 0.501393
\(691\) 162.333i 0.234925i −0.993077 0.117462i \(-0.962524\pi\)
0.993077 0.117462i \(-0.0374760\pi\)
\(692\) 417.111i 0.602762i
\(693\) 236.609 + 320.465i 0.341427 + 0.462432i
\(694\) −1584.85 −2.28364
\(695\) −121.699 −0.175106
\(696\) 40.0826i 0.0575900i
\(697\) −839.421 −1.20433
\(698\) 395.570i 0.566719i
\(699\) 134.698i 0.192702i
\(700\) −78.8476 106.792i −0.112639 0.152560i
\(701\) −69.5098 −0.0991581 −0.0495790 0.998770i \(-0.515788\pi\)
−0.0495790 + 0.998770i \(0.515788\pi\)
\(702\) −159.278 −0.226892
\(703\) 175.412i 0.249519i
\(704\) 1085.11 1.54135
\(705\) 191.242i 0.271266i
\(706\) 1262.99i 1.78894i
\(707\) 1097.57 810.372i 1.55244 1.14621i
\(708\) 231.350 0.326765
\(709\) 134.839 0.190182 0.0950912 0.995469i \(-0.469686\pi\)
0.0950912 + 0.995469i \(0.469686\pi\)
\(710\) 226.586i 0.319136i
\(711\) 48.6044 0.0683606
\(712\) 50.9712i 0.0715888i
\(713\) 1173.22i 1.64546i
\(714\) 448.429 + 607.356i 0.628052 + 0.850638i
\(715\) −465.755 −0.651406
\(716\) 348.489 0.486716
\(717\) 214.503i 0.299167i
\(718\) −487.600 −0.679109
\(719\) 638.863i 0.888544i −0.895892 0.444272i \(-0.853462\pi\)
0.895892 0.444272i \(-0.146538\pi\)
\(720\) 112.605i 0.156395i
\(721\) −232.367 + 171.564i −0.322284 + 0.237952i
\(722\) 65.2732 0.0904062
\(723\) −269.857 −0.373246
\(724\) 238.430i 0.329323i
\(725\) −199.983 −0.275839
\(726\) 1154.73i 1.59054i
\(727\) 704.430i 0.968955i 0.874804 + 0.484477i \(0.160990\pi\)
−0.874804 + 0.484477i \(0.839010\pi\)
\(728\) −35.7780 + 26.4160i −0.0491456 + 0.0362857i
\(729\) −27.0000 −0.0370370
\(730\) −41.6234 −0.0570183
\(731\) 420.919i 0.575812i
\(732\) 416.963 0.569622
\(733\) 275.472i 0.375815i −0.982187 0.187907i \(-0.939830\pi\)
0.982187 0.187907i \(-0.0601705\pi\)
\(734\) 338.188i 0.460747i
\(735\) −55.8678 + 181.366i −0.0760106 + 0.246757i
\(736\) −1425.39 −1.93667
\(737\) −405.072 −0.549622
\(738\) 315.155i 0.427039i
\(739\) 238.655 0.322943 0.161471 0.986877i \(-0.448376\pi\)
0.161471 + 0.986877i \(0.448376\pi\)
\(740\) 75.8777i 0.102537i
\(741\) 372.882i 0.503214i
\(742\) −571.514 774.063i −0.770235 1.04321i
\(743\) 221.162 0.297661 0.148831 0.988863i \(-0.452449\pi\)
0.148831 + 0.988863i \(0.452449\pi\)
\(744\) 36.7429 0.0493856
\(745\) 512.288i 0.687635i
\(746\) 253.773 0.340178
\(747\) 110.347i 0.147720i
\(748\) 1604.79i 2.14544i
\(749\) 123.500 + 167.269i 0.164887 + 0.223324i
\(750\) 54.0581 0.0720774
\(751\) −496.682 −0.661361 −0.330680 0.943743i \(-0.607278\pi\)
−0.330680 + 0.943743i \(0.607278\pi\)
\(752\) 828.874i 1.10223i
\(753\) 482.098 0.640237
\(754\) 1226.02i 1.62602i
\(755\) 442.148i 0.585627i
\(756\) 110.981 81.9408i 0.146801 0.108387i
\(757\) 866.706 1.14492 0.572461 0.819932i \(-0.305989\pi\)
0.572461 + 0.819932i \(0.305989\pi\)
\(758\) 1781.97 2.35088
\(759\) 1051.34i 1.38516i
\(760\) 25.3652 0.0333753
\(761\) 621.621i 0.816847i 0.912793 + 0.408424i \(0.133921\pi\)
−0.912793 + 0.408424i \(0.866079\pi\)
\(762\) 505.998i 0.664039i
\(763\) 381.284 + 516.414i 0.499717 + 0.676820i
\(764\) −288.219 −0.377250
\(765\) −149.633 −0.195599
\(766\) 492.415i 0.642839i
\(767\) 386.709 0.504184
\(768\) 485.726i 0.632456i
\(769\) 316.574i 0.411669i −0.978587 0.205835i \(-0.934009\pi\)
0.978587 0.205835i \(-0.0659909\pi\)
\(770\) 666.790 492.312i 0.865962 0.639366i
\(771\) 382.440 0.496031
\(772\) 86.2961 0.111782
\(773\) 710.993i 0.919784i −0.887975 0.459892i \(-0.847888\pi\)
0.887975 0.459892i \(-0.152112\pi\)
\(774\) −158.031 −0.204174
\(775\) 183.320i 0.236542i
\(776\) 77.4213i 0.0997697i
\(777\) −87.2675 + 64.4323i −0.112313 + 0.0829244i
\(778\) −696.550 −0.895308
\(779\) −737.801 −0.947113
\(780\) 161.297i 0.206791i
\(781\) −688.570 −0.881652
\(782\) 1992.53i 2.54799i
\(783\) 207.829i 0.265426i
\(784\) 242.140 786.070i 0.308851 1.00264i
\(785\) 471.891 0.601135
\(786\) 342.350 0.435560
\(787\) 845.181i 1.07393i 0.843605 + 0.536964i \(0.180429\pi\)
−0.843605 + 0.536964i \(0.819571\pi\)