Properties

Label 1170.2.i.o.991.2
Level $1170$
Weight $2$
Character 1170.991
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.2
Root \(-0.780776 + 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 1170.991
Dual form 1170.2.i.o.451.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.280776 - 0.486319i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.280776 - 0.486319i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(2.06155 + 3.57071i) q^{11} +(2.84233 - 2.21837i) q^{13} +0.561553 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.56155 + 2.70469i) q^{17} +(-0.280776 + 0.486319i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.06155 + 3.57071i) q^{22} +(2.34233 + 4.05703i) q^{23} +1.00000 q^{25} +(3.34233 + 1.35234i) q^{26} +(0.280776 + 0.486319i) q^{28} +(1.21922 + 2.11176i) q^{29} -6.68466 q^{31} +(0.500000 - 0.866025i) q^{32} -3.12311 q^{34} +(-0.280776 + 0.486319i) q^{35} +(2.06155 + 3.57071i) q^{37} -0.561553 q^{38} +1.00000 q^{40} +(6.12311 + 10.6055i) q^{41} +(-0.219224 + 0.379706i) q^{43} -4.12311 q^{44} +(-2.34233 + 4.05703i) q^{46} -7.00000 q^{47} +(3.34233 + 5.78908i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.500000 + 3.57071i) q^{52} -8.56155 q^{53} +(-2.06155 - 3.57071i) q^{55} +(-0.280776 + 0.486319i) q^{56} +(-1.21922 + 2.11176i) q^{58} +(3.21922 - 5.57586i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-3.34233 - 5.78908i) q^{62} +1.00000 q^{64} +(-2.84233 + 2.21837i) q^{65} +(1.12311 + 1.94528i) q^{67} +(-1.56155 - 2.70469i) q^{68} -0.561553 q^{70} +(-6.56155 + 11.3649i) q^{71} +9.36932 q^{73} +(-2.06155 + 3.57071i) q^{74} +(-0.280776 - 0.486319i) q^{76} +2.31534 q^{77} +11.5616 q^{79} +(0.500000 + 0.866025i) q^{80} +(-6.12311 + 10.6055i) q^{82} +7.12311 q^{83} +(1.56155 - 2.70469i) q^{85} -0.438447 q^{86} +(-2.06155 - 3.57071i) q^{88} +(-9.40388 - 16.2880i) q^{89} +(-0.280776 - 2.00514i) q^{91} -4.68466 q^{92} +(-3.50000 - 6.06218i) q^{94} +(0.280776 - 0.486319i) q^{95} +(3.56155 - 6.16879i) q^{97} +(-3.34233 + 5.78908i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 3q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 3q^{7} - 4q^{8} - 2q^{10} - q^{13} - 6q^{14} - 2q^{16} + 2q^{17} + 3q^{19} + 2q^{20} - 3q^{23} + 4q^{25} + q^{26} - 3q^{28} + 9q^{29} - 2q^{31} + 2q^{32} + 4q^{34} + 3q^{35} + 6q^{38} + 4q^{40} + 8q^{41} - 5q^{43} + 3q^{46} - 28q^{47} + q^{49} + 2q^{50} + 2q^{52} - 26q^{53} + 3q^{56} - 9q^{58} + 17q^{59} - 12q^{61} - q^{62} + 4q^{64} + q^{65} - 12q^{67} + 2q^{68} + 6q^{70} - 18q^{71} - 12q^{73} + 3q^{76} + 34q^{77} + 38q^{79} + 2q^{80} - 8q^{82} + 12q^{83} - 2q^{85} - 10q^{86} - 17q^{89} + 3q^{91} + 6q^{92} - 14q^{94} - 3q^{95} + 6q^{97} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.280776 0.486319i 0.106124 0.183811i −0.808073 0.589082i \(-0.799489\pi\)
0.914197 + 0.405271i \(0.132823\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 2.06155 + 3.57071i 0.621582 + 1.07661i 0.989191 + 0.146631i \(0.0468429\pi\)
−0.367610 + 0.929980i \(0.619824\pi\)
\(12\) 0 0
\(13\) 2.84233 2.21837i 0.788320 0.615265i
\(14\) 0.561553 0.150081
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.56155 + 2.70469i −0.378732 + 0.655983i −0.990878 0.134761i \(-0.956973\pi\)
0.612146 + 0.790745i \(0.290307\pi\)
\(18\) 0 0
\(19\) −0.280776 + 0.486319i −0.0644145 + 0.111569i −0.896434 0.443177i \(-0.853851\pi\)
0.832020 + 0.554746i \(0.187185\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 0 0
\(22\) −2.06155 + 3.57071i −0.439525 + 0.761279i
\(23\) 2.34233 + 4.05703i 0.488409 + 0.845950i 0.999911 0.0133324i \(-0.00424395\pi\)
−0.511502 + 0.859282i \(0.670911\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 3.34233 + 1.35234i 0.655485 + 0.265217i
\(27\) 0 0
\(28\) 0.280776 + 0.486319i 0.0530618 + 0.0919057i
\(29\) 1.21922 + 2.11176i 0.226404 + 0.392143i 0.956740 0.290945i \(-0.0939697\pi\)
−0.730336 + 0.683088i \(0.760636\pi\)
\(30\) 0 0
\(31\) −6.68466 −1.20060 −0.600300 0.799775i \(-0.704952\pi\)
−0.600300 + 0.799775i \(0.704952\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.12311 −0.535608
\(35\) −0.280776 + 0.486319i −0.0474599 + 0.0822029i
\(36\) 0 0
\(37\) 2.06155 + 3.57071i 0.338917 + 0.587022i 0.984229 0.176897i \(-0.0566060\pi\)
−0.645312 + 0.763919i \(0.723273\pi\)
\(38\) −0.561553 −0.0910959
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 6.12311 + 10.6055i 0.956268 + 1.65631i 0.731438 + 0.681908i \(0.238849\pi\)
0.224830 + 0.974398i \(0.427817\pi\)
\(42\) 0 0
\(43\) −0.219224 + 0.379706i −0.0334313 + 0.0579047i −0.882257 0.470768i \(-0.843977\pi\)
0.848826 + 0.528673i \(0.177310\pi\)
\(44\) −4.12311 −0.621582
\(45\) 0 0
\(46\) −2.34233 + 4.05703i −0.345358 + 0.598177i
\(47\) −7.00000 −1.02105 −0.510527 0.859861i \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) 0 0
\(49\) 3.34233 + 5.78908i 0.477476 + 0.827012i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) 0.500000 + 3.57071i 0.0693375 + 0.495169i
\(53\) −8.56155 −1.17602 −0.588010 0.808854i \(-0.700088\pi\)
−0.588010 + 0.808854i \(0.700088\pi\)
\(54\) 0 0
\(55\) −2.06155 3.57071i −0.277980 0.481475i
\(56\) −0.280776 + 0.486319i −0.0375203 + 0.0649871i
\(57\) 0 0
\(58\) −1.21922 + 2.11176i −0.160092 + 0.277287i
\(59\) 3.21922 5.57586i 0.419107 0.725915i −0.576743 0.816926i \(-0.695676\pi\)
0.995850 + 0.0910109i \(0.0290098\pi\)
\(60\) 0 0
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) −3.34233 5.78908i −0.424476 0.735214i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.84233 + 2.21837i −0.352548 + 0.275155i
\(66\) 0 0
\(67\) 1.12311 + 1.94528i 0.137209 + 0.237653i 0.926439 0.376444i \(-0.122853\pi\)
−0.789230 + 0.614098i \(0.789520\pi\)
\(68\) −1.56155 2.70469i −0.189366 0.327992i
\(69\) 0 0
\(70\) −0.561553 −0.0671184
\(71\) −6.56155 + 11.3649i −0.778713 + 1.34877i 0.153971 + 0.988075i \(0.450794\pi\)
−0.932684 + 0.360695i \(0.882539\pi\)
\(72\) 0 0
\(73\) 9.36932 1.09660 0.548298 0.836283i \(-0.315276\pi\)
0.548298 + 0.836283i \(0.315276\pi\)
\(74\) −2.06155 + 3.57071i −0.239651 + 0.415087i
\(75\) 0 0
\(76\) −0.280776 0.486319i −0.0322073 0.0557846i
\(77\) 2.31534 0.263858
\(78\) 0 0
\(79\) 11.5616 1.30078 0.650388 0.759602i \(-0.274606\pi\)
0.650388 + 0.759602i \(0.274606\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) −6.12311 + 10.6055i −0.676184 + 1.17118i
\(83\) 7.12311 0.781862 0.390931 0.920420i \(-0.372153\pi\)
0.390931 + 0.920420i \(0.372153\pi\)
\(84\) 0 0
\(85\) 1.56155 2.70469i 0.169374 0.293365i
\(86\) −0.438447 −0.0472790
\(87\) 0 0
\(88\) −2.06155 3.57071i −0.219762 0.380639i
\(89\) −9.40388 16.2880i −0.996810 1.72652i −0.567529 0.823354i \(-0.692100\pi\)
−0.429281 0.903171i \(-0.641233\pi\)
\(90\) 0 0
\(91\) −0.280776 2.00514i −0.0294334 0.210196i
\(92\) −4.68466 −0.488409
\(93\) 0 0
\(94\) −3.50000 6.06218i −0.360997 0.625266i
\(95\) 0.280776 0.486319i 0.0288071 0.0498953i
\(96\) 0 0
\(97\) 3.56155 6.16879i 0.361621 0.626346i −0.626607 0.779335i \(-0.715557\pi\)
0.988228 + 0.152990i \(0.0488901\pi\)
\(98\) −3.34233 + 5.78908i −0.337626 + 0.584786i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −4.43845 7.68762i −0.441642 0.764946i 0.556170 0.831069i \(-0.312271\pi\)
−0.997812 + 0.0661225i \(0.978937\pi\)
\(102\) 0 0
\(103\) 4.56155 0.449463 0.224732 0.974421i \(-0.427849\pi\)
0.224732 + 0.974421i \(0.427849\pi\)
\(104\) −2.84233 + 2.21837i −0.278713 + 0.217529i
\(105\) 0 0
\(106\) −4.28078 7.41452i −0.415786 0.720162i
\(107\) 1.00000 + 1.73205i 0.0966736 + 0.167444i 0.910306 0.413936i \(-0.135846\pi\)
−0.813632 + 0.581380i \(0.802513\pi\)
\(108\) 0 0
\(109\) −3.75379 −0.359548 −0.179774 0.983708i \(-0.557537\pi\)
−0.179774 + 0.983708i \(0.557537\pi\)
\(110\) 2.06155 3.57071i 0.196561 0.340454i
\(111\) 0 0
\(112\) −0.561553 −0.0530618
\(113\) 4.34233 7.52113i 0.408492 0.707529i −0.586229 0.810145i \(-0.699388\pi\)
0.994721 + 0.102617i \(0.0327215\pi\)
\(114\) 0 0
\(115\) −2.34233 4.05703i −0.218423 0.378320i
\(116\) −2.43845 −0.226404
\(117\) 0 0
\(118\) 6.43845 0.592707
\(119\) 0.876894 + 1.51883i 0.0803848 + 0.139231i
\(120\) 0 0
\(121\) −3.00000 + 5.19615i −0.272727 + 0.472377i
\(122\) −6.00000 −0.543214
\(123\) 0 0
\(124\) 3.34233 5.78908i 0.300150 0.519875i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.28078 + 7.41452i 0.379857 + 0.657932i 0.991041 0.133556i \(-0.0426397\pi\)
−0.611184 + 0.791489i \(0.709306\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −3.34233 1.35234i −0.293142 0.118608i
\(131\) 2.12311 0.185497 0.0927483 0.995690i \(-0.470435\pi\)
0.0927483 + 0.995690i \(0.470435\pi\)
\(132\) 0 0
\(133\) 0.157671 + 0.273094i 0.0136718 + 0.0236802i
\(134\) −1.12311 + 1.94528i −0.0970215 + 0.168046i
\(135\) 0 0
\(136\) 1.56155 2.70469i 0.133902 0.231925i
\(137\) 5.90388 10.2258i 0.504403 0.873651i −0.495584 0.868560i \(-0.665046\pi\)
0.999987 0.00509126i \(-0.00162061\pi\)
\(138\) 0 0
\(139\) −6.28078 + 10.8786i −0.532729 + 0.922713i 0.466541 + 0.884500i \(0.345500\pi\)
−0.999270 + 0.0382133i \(0.987833\pi\)
\(140\) −0.280776 0.486319i −0.0237299 0.0411015i
\(141\) 0 0
\(142\) −13.1231 −1.10127
\(143\) 13.7808 + 5.57586i 1.15241 + 0.466277i
\(144\) 0 0
\(145\) −1.21922 2.11176i −0.101251 0.175372i
\(146\) 4.68466 + 8.11407i 0.387705 + 0.671525i
\(147\) 0 0
\(148\) −4.12311 −0.338917
\(149\) −1.09612 + 1.89853i −0.0897975 + 0.155534i −0.907425 0.420213i \(-0.861955\pi\)
0.817628 + 0.575747i \(0.195289\pi\)
\(150\) 0 0
\(151\) −15.3693 −1.25074 −0.625369 0.780329i \(-0.715051\pi\)
−0.625369 + 0.780329i \(0.715051\pi\)
\(152\) 0.280776 0.486319i 0.0227740 0.0394457i
\(153\) 0 0
\(154\) 1.15767 + 2.00514i 0.0932878 + 0.161579i
\(155\) 6.68466 0.536925
\(156\) 0 0
\(157\) 13.8769 1.10750 0.553748 0.832684i \(-0.313197\pi\)
0.553748 + 0.832684i \(0.313197\pi\)
\(158\) 5.78078 + 10.0126i 0.459894 + 0.796560i
\(159\) 0 0
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 2.63068 0.207327
\(162\) 0 0
\(163\) 7.21922 12.5041i 0.565453 0.979394i −0.431554 0.902087i \(-0.642035\pi\)
0.997007 0.0773067i \(-0.0246321\pi\)
\(164\) −12.2462 −0.956268
\(165\) 0 0
\(166\) 3.56155 + 6.16879i 0.276430 + 0.478791i
\(167\) 2.18466 + 3.78394i 0.169054 + 0.292810i 0.938087 0.346398i \(-0.112595\pi\)
−0.769034 + 0.639208i \(0.779262\pi\)
\(168\) 0 0
\(169\) 3.15767 12.6107i 0.242898 0.970052i
\(170\) 3.12311 0.239531
\(171\) 0 0
\(172\) −0.219224 0.379706i −0.0167156 0.0289523i
\(173\) 10.0885 17.4739i 0.767018 1.32851i −0.172156 0.985070i \(-0.555073\pi\)
0.939173 0.343444i \(-0.111593\pi\)
\(174\) 0 0
\(175\) 0.280776 0.486319i 0.0212247 0.0367623i
\(176\) 2.06155 3.57071i 0.155395 0.269153i
\(177\) 0 0
\(178\) 9.40388 16.2880i 0.704851 1.22084i
\(179\) −6.34233 10.9852i −0.474048 0.821075i 0.525511 0.850787i \(-0.323874\pi\)
−0.999559 + 0.0297120i \(0.990541\pi\)
\(180\) 0 0
\(181\) 2.87689 0.213838 0.106919 0.994268i \(-0.465901\pi\)
0.106919 + 0.994268i \(0.465901\pi\)
\(182\) 1.59612 1.24573i 0.118312 0.0923398i
\(183\) 0 0
\(184\) −2.34233 4.05703i −0.172679 0.299088i
\(185\) −2.06155 3.57071i −0.151568 0.262524i
\(186\) 0 0
\(187\) −12.8769 −0.941652
\(188\) 3.50000 6.06218i 0.255264 0.442130i
\(189\) 0 0
\(190\) 0.561553 0.0407393
\(191\) 5.43845 9.41967i 0.393512 0.681583i −0.599398 0.800451i \(-0.704593\pi\)
0.992910 + 0.118868i \(0.0379266\pi\)
\(192\) 0 0
\(193\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 7.12311 0.511409
\(195\) 0 0
\(196\) −6.68466 −0.477476
\(197\) 6.40388 + 11.0918i 0.456258 + 0.790262i 0.998760 0.0497931i \(-0.0158562\pi\)
−0.542502 + 0.840055i \(0.682523\pi\)
\(198\) 0 0
\(199\) −1.43845 + 2.49146i −0.101969 + 0.176615i −0.912496 0.409086i \(-0.865848\pi\)
0.810527 + 0.585701i \(0.199181\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) 4.43845 7.68762i 0.312288 0.540899i
\(203\) 1.36932 0.0961072
\(204\) 0 0
\(205\) −6.12311 10.6055i −0.427656 0.740722i
\(206\) 2.28078 + 3.95042i 0.158909 + 0.275239i
\(207\) 0 0
\(208\) −3.34233 1.35234i −0.231749 0.0937682i
\(209\) −2.31534 −0.160156
\(210\) 0 0
\(211\) 10.9654 + 18.9927i 0.754892 + 1.30751i 0.945428 + 0.325831i \(0.105644\pi\)
−0.190536 + 0.981680i \(0.561023\pi\)
\(212\) 4.28078 7.41452i 0.294005 0.509231i
\(213\) 0 0
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 0.219224 0.379706i 0.0149509 0.0258958i
\(216\) 0 0
\(217\) −1.87689 + 3.25088i −0.127412 + 0.220684i
\(218\) −1.87689 3.25088i −0.127119 0.220177i
\(219\) 0 0
\(220\) 4.12311 0.277980
\(221\) 1.56155 + 11.1517i 0.105041 + 0.750146i
\(222\) 0 0
\(223\) −13.6501 23.6427i −0.914078 1.58323i −0.808246 0.588845i \(-0.799583\pi\)
−0.105832 0.994384i \(-0.533751\pi\)
\(224\) −0.280776 0.486319i −0.0187602 0.0324936i
\(225\) 0 0
\(226\) 8.68466 0.577695
\(227\) −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 0 0
\(229\) −24.2462 −1.60223 −0.801117 0.598507i \(-0.795761\pi\)
−0.801117 + 0.598507i \(0.795761\pi\)
\(230\) 2.34233 4.05703i 0.154449 0.267513i
\(231\) 0 0
\(232\) −1.21922 2.11176i −0.0800460 0.138644i
\(233\) 5.31534 0.348220 0.174110 0.984726i \(-0.444295\pi\)
0.174110 + 0.984726i \(0.444295\pi\)
\(234\) 0 0
\(235\) 7.00000 0.456630
\(236\) 3.21922 + 5.57586i 0.209554 + 0.362957i
\(237\) 0 0
\(238\) −0.876894 + 1.51883i −0.0568406 + 0.0984508i
\(239\) 11.3693 0.735420 0.367710 0.929941i \(-0.380142\pi\)
0.367710 + 0.929941i \(0.380142\pi\)
\(240\) 0 0
\(241\) 14.0616 24.3553i 0.905784 1.56886i 0.0859232 0.996302i \(-0.472616\pi\)
0.819861 0.572563i \(-0.194051\pi\)
\(242\) −6.00000 −0.385695
\(243\) 0 0
\(244\) −3.00000 5.19615i −0.192055 0.332650i
\(245\) −3.34233 5.78908i −0.213534 0.369851i
\(246\) 0 0
\(247\) 0.280776 + 2.00514i 0.0178654 + 0.127584i
\(248\) 6.68466 0.424476
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −4.06155 + 7.03482i −0.256363 + 0.444034i −0.965265 0.261273i \(-0.915858\pi\)
0.708902 + 0.705307i \(0.249191\pi\)
\(252\) 0 0
\(253\) −9.65767 + 16.7276i −0.607173 + 1.05165i
\(254\) −4.28078 + 7.41452i −0.268600 + 0.465229i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.78078 4.81645i −0.173460 0.300442i 0.766167 0.642641i \(-0.222161\pi\)
−0.939627 + 0.342200i \(0.888828\pi\)
\(258\) 0 0
\(259\) 2.31534 0.143868
\(260\) −0.500000 3.57071i −0.0310087 0.221446i
\(261\) 0 0
\(262\) 1.06155 + 1.83866i 0.0655830 + 0.113593i
\(263\) −6.50000 11.2583i −0.400807 0.694218i 0.593016 0.805190i \(-0.297937\pi\)
−0.993824 + 0.110972i \(0.964604\pi\)
\(264\) 0 0
\(265\) 8.56155 0.525932
\(266\) −0.157671 + 0.273094i −0.00966742 + 0.0167445i
\(267\) 0 0
\(268\) −2.24621 −0.137209
\(269\) 10.6847 18.5064i 0.651455 1.12835i −0.331315 0.943520i \(-0.607492\pi\)
0.982770 0.184833i \(-0.0591745\pi\)
\(270\) 0 0
\(271\) 6.58854 + 11.4117i 0.400225 + 0.693211i 0.993753 0.111603i \(-0.0355985\pi\)
−0.593528 + 0.804814i \(0.702265\pi\)
\(272\) 3.12311 0.189366
\(273\) 0 0
\(274\) 11.8078 0.713333
\(275\) 2.06155 + 3.57071i 0.124316 + 0.215322i
\(276\) 0 0
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) −12.5616 −0.753392
\(279\) 0 0
\(280\) 0.280776 0.486319i 0.0167796 0.0290631i
\(281\) −16.2462 −0.969168 −0.484584 0.874745i \(-0.661029\pi\)
−0.484584 + 0.874745i \(0.661029\pi\)
\(282\) 0 0
\(283\) −7.78078 13.4767i −0.462519 0.801107i 0.536567 0.843858i \(-0.319721\pi\)
−0.999086 + 0.0427513i \(0.986388\pi\)
\(284\) −6.56155 11.3649i −0.389357 0.674385i
\(285\) 0 0
\(286\) 2.06155 + 14.7224i 0.121902 + 0.870556i
\(287\) 6.87689 0.405930
\(288\) 0 0
\(289\) 3.62311 + 6.27540i 0.213124 + 0.369141i
\(290\) 1.21922 2.11176i 0.0715953 0.124007i
\(291\) 0 0
\(292\) −4.68466 + 8.11407i −0.274149 + 0.474840i
\(293\) 1.96543 3.40423i 0.114822 0.198877i −0.802887 0.596132i \(-0.796704\pi\)
0.917709 + 0.397254i \(0.130037\pi\)
\(294\) 0 0
\(295\) −3.21922 + 5.57586i −0.187430 + 0.324639i
\(296\) −2.06155 3.57071i −0.119825 0.207544i
\(297\) 0 0
\(298\) −2.19224 −0.126993
\(299\) 15.6577 + 6.33527i 0.905506 + 0.366378i
\(300\) 0 0
\(301\) 0.123106 + 0.213225i 0.00709569 + 0.0122901i
\(302\) −7.68466 13.3102i −0.442202 0.765917i
\(303\) 0 0
\(304\) 0.561553 0.0322073
\(305\) 3.00000 5.19615i 0.171780 0.297531i
\(306\) 0 0
\(307\) 25.6155 1.46196 0.730978 0.682401i \(-0.239064\pi\)
0.730978 + 0.682401i \(0.239064\pi\)
\(308\) −1.15767 + 2.00514i −0.0659644 + 0.114254i
\(309\) 0 0
\(310\) 3.34233 + 5.78908i 0.189832 + 0.328798i
\(311\) −30.7386 −1.74303 −0.871514 0.490371i \(-0.836861\pi\)
−0.871514 + 0.490371i \(0.836861\pi\)
\(312\) 0 0
\(313\) 31.3693 1.77310 0.886549 0.462634i \(-0.153096\pi\)
0.886549 + 0.462634i \(0.153096\pi\)
\(314\) 6.93845 + 12.0177i 0.391559 + 0.678200i
\(315\) 0 0
\(316\) −5.78078 + 10.0126i −0.325194 + 0.563253i
\(317\) 24.8078 1.39334 0.696671 0.717390i \(-0.254664\pi\)
0.696671 + 0.717390i \(0.254664\pi\)
\(318\) 0 0
\(319\) −5.02699 + 8.70700i −0.281457 + 0.487498i
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 1.31534 + 2.27824i 0.0733011 + 0.126961i
\(323\) −0.876894 1.51883i −0.0487917 0.0845097i
\(324\) 0 0
\(325\) 2.84233 2.21837i 0.157664 0.123053i
\(326\) 14.4384 0.799672
\(327\) 0 0
\(328\) −6.12311 10.6055i −0.338092 0.585592i
\(329\) −1.96543 + 3.40423i −0.108358 + 0.187681i
\(330\) 0 0
\(331\) −15.3693 + 26.6204i −0.844774 + 1.46319i 0.0410432 + 0.999157i \(0.486932\pi\)
−0.885817 + 0.464034i \(0.846401\pi\)
\(332\) −3.56155 + 6.16879i −0.195466 + 0.338556i
\(333\) 0 0
\(334\) −2.18466 + 3.78394i −0.119539 + 0.207048i
\(335\) −1.12311 1.94528i −0.0613618 0.106282i
\(336\) 0 0
\(337\) −6.00000 −0.326841 −0.163420 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 12.5000 3.57071i 0.679910 0.194221i
\(339\) 0 0
\(340\) 1.56155 + 2.70469i 0.0846871 + 0.146682i
\(341\) −13.7808 23.8690i −0.746271 1.29258i
\(342\) 0 0
\(343\) 7.68466 0.414933
\(344\) 0.219224 0.379706i 0.0118197 0.0204724i
\(345\) 0 0
\(346\) 20.1771 1.08473
\(347\) 0.438447 0.759413i 0.0235371 0.0407674i −0.854017 0.520245i \(-0.825841\pi\)
0.877554 + 0.479478i \(0.159174\pi\)
\(348\) 0 0
\(349\) −4.24621 7.35465i −0.227294 0.393686i 0.729711 0.683756i \(-0.239655\pi\)
−0.957005 + 0.290070i \(0.906321\pi\)
\(350\) 0.561553 0.0300163
\(351\) 0 0
\(352\) 4.12311 0.219762
\(353\) −12.9309 22.3969i −0.688241 1.19207i −0.972407 0.233293i \(-0.925050\pi\)
0.284166 0.958775i \(-0.408283\pi\)
\(354\) 0 0
\(355\) 6.56155 11.3649i 0.348251 0.603189i
\(356\) 18.8078 0.996810
\(357\) 0 0
\(358\) 6.34233 10.9852i 0.335203 0.580588i
\(359\) −13.1231 −0.692611 −0.346306 0.938122i \(-0.612564\pi\)
−0.346306 + 0.938122i \(0.612564\pi\)
\(360\) 0 0
\(361\) 9.34233 + 16.1814i 0.491702 + 0.851652i
\(362\) 1.43845 + 2.49146i 0.0756031 + 0.130948i
\(363\) 0 0
\(364\) 1.87689 + 0.759413i 0.0983760 + 0.0398040i
\(365\) −9.36932 −0.490412
\(366\) 0 0
\(367\) −6.24621 10.8188i −0.326050 0.564734i 0.655675 0.755044i \(-0.272384\pi\)
−0.981724 + 0.190309i \(0.939051\pi\)
\(368\) 2.34233 4.05703i 0.122102 0.211487i
\(369\) 0 0
\(370\) 2.06155 3.57071i 0.107175 0.185633i
\(371\) −2.40388 + 4.16365i −0.124803 + 0.216166i
\(372\) 0 0
\(373\) 12.9039 22.3502i 0.668138 1.15725i −0.310287 0.950643i \(-0.600425\pi\)
0.978424 0.206605i \(-0.0662416\pi\)
\(374\) −6.43845 11.1517i −0.332924 0.576642i
\(375\) 0 0
\(376\) 7.00000 0.360997
\(377\) 8.15009 + 3.29762i 0.419751 + 0.169836i
\(378\) 0 0
\(379\) 8.84233 + 15.3154i 0.454200 + 0.786697i 0.998642 0.0521012i \(-0.0165918\pi\)
−0.544442 + 0.838799i \(0.683259\pi\)
\(380\) 0.280776 + 0.486319i 0.0144035 + 0.0249476i
\(381\) 0 0
\(382\) 10.8769 0.556510
\(383\) 0.0961180 0.166481i 0.00491140 0.00850679i −0.863559 0.504247i \(-0.831770\pi\)
0.868471 + 0.495741i \(0.165103\pi\)
\(384\) 0 0
\(385\) −2.31534 −0.118001
\(386\) 0 0
\(387\) 0 0
\(388\) 3.56155 + 6.16879i 0.180810 + 0.313173i
\(389\) 18.0540 0.915373 0.457686 0.889114i \(-0.348678\pi\)
0.457686 + 0.889114i \(0.348678\pi\)
\(390\) 0 0
\(391\) −14.6307 −0.739905
\(392\) −3.34233 5.78908i −0.168813 0.292393i
\(393\) 0 0
\(394\) −6.40388 + 11.0918i −0.322623 + 0.558799i
\(395\) −11.5616 −0.581725
\(396\) 0 0
\(397\) 10.0616 17.4271i 0.504975 0.874642i −0.495009 0.868888i \(-0.664835\pi\)
0.999983 0.00575403i \(-0.00183158\pi\)
\(398\) −2.87689 −0.144206
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 0.157671 + 0.273094i 0.00787370 + 0.0136377i 0.869935 0.493166i \(-0.164160\pi\)
−0.862062 + 0.506803i \(0.830827\pi\)
\(402\) 0 0
\(403\) −19.0000 + 14.8290i −0.946457 + 0.738687i
\(404\) 8.87689 0.441642
\(405\) 0 0
\(406\) 0.684658 + 1.18586i 0.0339790 + 0.0588534i
\(407\) −8.50000 + 14.7224i −0.421329 + 0.729764i
\(408\) 0 0
\(409\) 9.40388 16.2880i 0.464992 0.805390i −0.534209 0.845352i \(-0.679391\pi\)
0.999201 + 0.0399625i \(0.0127239\pi\)
\(410\) 6.12311 10.6055i 0.302399 0.523770i
\(411\) 0 0
\(412\) −2.28078 + 3.95042i −0.112366 + 0.194623i
\(413\) −1.80776 3.13114i −0.0889543 0.154073i
\(414\) 0 0
\(415\) −7.12311 −0.349660
\(416\) −0.500000 3.57071i −0.0245145 0.175069i
\(417\) 0 0
\(418\) −1.15767 2.00514i −0.0566235 0.0980748i
\(419\) 16.2462 + 28.1393i 0.793679 + 1.37469i 0.923674 + 0.383178i \(0.125171\pi\)
−0.129995 + 0.991515i \(0.541496\pi\)
\(420\) 0 0
\(421\) −32.4924 −1.58358 −0.791792 0.610791i \(-0.790852\pi\)
−0.791792 + 0.610791i \(0.790852\pi\)
\(422\) −10.9654 + 18.9927i −0.533789 + 0.924550i
\(423\) 0 0
\(424\) 8.56155 0.415786
\(425\) −1.56155 + 2.70469i −0.0757464 + 0.131197i
\(426\) 0 0
\(427\) 1.68466 + 2.91791i 0.0815263 + 0.141208i
\(428\) −2.00000 −0.0966736
\(429\) 0 0
\(430\) 0.438447 0.0211438
\(431\) −11.3693 19.6922i −0.547641 0.948542i −0.998436 0.0559140i \(-0.982193\pi\)
0.450795 0.892628i \(-0.351141\pi\)
\(432\) 0 0
\(433\) 9.36932 16.2281i 0.450261 0.779874i −0.548141 0.836386i \(-0.684664\pi\)
0.998402 + 0.0565114i \(0.0179977\pi\)
\(434\) −3.75379 −0.180188
\(435\) 0 0
\(436\) 1.87689 3.25088i 0.0898869 0.155689i
\(437\) −2.63068 −0.125843
\(438\) 0 0
\(439\) −12.5616 21.7572i −0.599530 1.03842i −0.992890 0.119032i \(-0.962021\pi\)
0.393360 0.919384i \(-0.371313\pi\)
\(440\) 2.06155 + 3.57071i 0.0982807 + 0.170227i
\(441\) 0 0
\(442\) −8.87689 + 6.92820i −0.422231 + 0.329541i
\(443\) 13.1231 0.623498 0.311749 0.950165i \(-0.399085\pi\)
0.311749 + 0.950165i \(0.399085\pi\)
\(444\) 0 0
\(445\) 9.40388 + 16.2880i 0.445787 + 0.772125i
\(446\) 13.6501 23.6427i 0.646351 1.11951i
\(447\) 0 0
\(448\) 0.280776 0.486319i 0.0132654 0.0229764i
\(449\) −10.0885 + 17.4739i −0.476108 + 0.824643i −0.999625 0.0273722i \(-0.991286\pi\)
0.523518 + 0.852015i \(0.324619\pi\)
\(450\) 0 0
\(451\) −25.2462 + 43.7277i −1.18880 + 2.05906i
\(452\) 4.34233 + 7.52113i 0.204246 + 0.353764i
\(453\) 0 0
\(454\) −20.0000 −0.938647
\(455\) 0.280776 + 2.00514i 0.0131630 + 0.0940026i
\(456\) 0 0
\(457\) −10.1231 17.5337i −0.473539 0.820193i 0.526002 0.850483i \(-0.323690\pi\)
−0.999541 + 0.0302897i \(0.990357\pi\)
\(458\) −12.1231 20.9978i −0.566476 0.981164i
\(459\) 0 0
\(460\) 4.68466 0.218423
\(461\) −15.0270 + 26.0275i −0.699877 + 1.21222i 0.268632 + 0.963243i \(0.413428\pi\)
−0.968509 + 0.248979i \(0.919905\pi\)
\(462\) 0 0
\(463\) −7.61553 −0.353924 −0.176962 0.984218i \(-0.556627\pi\)
−0.176962 + 0.984218i \(0.556627\pi\)
\(464\) 1.21922 2.11176i 0.0566010 0.0980359i
\(465\) 0 0
\(466\) 2.65767 + 4.60322i 0.123114 + 0.213240i
\(467\) 17.8617 0.826543 0.413271 0.910608i \(-0.364386\pi\)
0.413271 + 0.910608i \(0.364386\pi\)
\(468\) 0 0
\(469\) 1.26137 0.0582445
\(470\) 3.50000 + 6.06218i 0.161443 + 0.279627i
\(471\) 0 0
\(472\) −3.21922 + 5.57586i −0.148177 + 0.256650i
\(473\) −1.80776 −0.0831211
\(474\) 0 0
\(475\) −0.280776 + 0.486319i −0.0128829 + 0.0223138i
\(476\) −1.75379 −0.0803848
\(477\) 0 0
\(478\) 5.68466 + 9.84612i 0.260010 + 0.450351i
\(479\) −19.1231 33.1222i −0.873757 1.51339i −0.858081 0.513514i \(-0.828343\pi\)
−0.0156760 0.999877i \(-0.504990\pi\)
\(480\) 0 0
\(481\) 13.7808 + 5.57586i 0.628349 + 0.254237i
\(482\) 28.1231 1.28097
\(483\) 0 0
\(484\) −3.00000 5.19615i −0.136364 0.236189i
\(485\) −3.56155 + 6.16879i −0.161722 + 0.280110i
\(486\) 0 0
\(487\) −6.52699 + 11.3051i −0.295766 + 0.512282i −0.975163 0.221489i \(-0.928908\pi\)
0.679397 + 0.733771i \(0.262242\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) 0 0
\(490\) 3.34233 5.78908i 0.150991 0.261524i
\(491\) −8.71922 15.1021i −0.393493 0.681550i 0.599415 0.800439i \(-0.295400\pi\)
−0.992908 + 0.118889i \(0.962067\pi\)
\(492\) 0 0
\(493\) −7.61553 −0.342986
\(494\) −1.59612 + 1.24573i −0.0718127 + 0.0560481i
\(495\) 0 0
\(496\) 3.34233 + 5.78908i 0.150075 + 0.259938i
\(497\) 3.68466 + 6.38202i 0.165280 + 0.286273i
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) −8.12311 −0.362552
\(503\) −21.5270 + 37.2858i −0.959841 + 1.66249i −0.236962 + 0.971519i \(0.576152\pi\)
−0.722879 + 0.690974i \(0.757182\pi\)
\(504\) 0 0
\(505\) 4.43845 + 7.68762i 0.197508 + 0.342094i
\(506\) −19.3153 −0.858672
\(507\) 0 0
\(508\) −8.56155 −0.379857
\(509\) 20.2732 + 35.1142i 0.898594 + 1.55641i 0.829293 + 0.558814i \(0.188744\pi\)
0.0693009 + 0.997596i \(0.477923\pi\)
\(510\) 0 0
\(511\) 2.63068 4.55648i 0.116375 0.201567i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 2.78078 4.81645i 0.122655 0.212444i
\(515\) −4.56155 −0.201006
\(516\) 0 0
\(517\) −14.4309 24.9950i −0.634669 1.09928i
\(518\) 1.15767 + 2.00514i 0.0508651 + 0.0881010i
\(519\) 0 0
\(520\) 2.84233 2.21837i 0.124644 0.0972820i
\(521\) 6.31534 0.276680 0.138340 0.990385i \(-0.455823\pi\)
0.138340 + 0.990385i \(0.455823\pi\)
\(522\) 0 0
\(523\) 14.9039 + 25.8143i 0.651701 + 1.12878i 0.982710 + 0.185152i \(0.0592777\pi\)
−0.331009 + 0.943628i \(0.607389\pi\)
\(524\) −1.06155 + 1.83866i −0.0463741 + 0.0803224i
\(525\) 0 0
\(526\) 6.50000 11.2583i 0.283413 0.490887i
\(527\) 10.4384 18.0799i 0.454706 0.787574i
\(528\) 0 0
\(529\) 0.526988 0.912769i 0.0229125 0.0396856i
\(530\) 4.28078 + 7.41452i 0.185945 + 0.322066i
\(531\) 0 0
\(532\) −0.315342 −0.0136718
\(533\) 40.9309 + 16.5611i 1.77291 + 0.717341i
\(534\) 0 0
\(535\) −1.00000 1.73205i −0.0432338 0.0748831i
\(536\) −1.12311 1.94528i −0.0485108 0.0840231i
\(537\) 0 0
\(538\) 21.3693 0.921297
\(539\) −13.7808 + 23.8690i −0.593580 + 1.02811i
\(540\) 0 0
\(541\) −27.3693 −1.17670 −0.588349 0.808607i \(-0.700222\pi\)
−0.588349 + 0.808607i \(0.700222\pi\)
\(542\) −6.58854 + 11.4117i −0.283002 + 0.490174i
\(543\) 0 0
\(544\) 1.56155 + 2.70469i 0.0669510 + 0.115963i
\(545\) 3.75379 0.160795
\(546\) 0 0
\(547\) −5.61553 −0.240103 −0.120051 0.992768i \(-0.538306\pi\)
−0.120051 + 0.992768i \(0.538306\pi\)
\(548\) 5.90388 + 10.2258i 0.252201 + 0.436826i
\(549\) 0 0
\(550\) −2.06155 + 3.57071i −0.0879049 + 0.152256i
\(551\) −1.36932 −0.0583349
\(552\) 0 0
\(553\) 3.24621 5.62260i 0.138043 0.239097i
\(554\) 1.00000 0.0424859
\(555\) 0 0
\(556\) −6.28078 10.8786i −0.266364 0.461356i
\(557\) −4.28078 7.41452i −0.181382 0.314163i 0.760969 0.648788i \(-0.224724\pi\)
−0.942352 + 0.334625i \(0.891390\pi\)
\(558\) 0 0
\(559\) 0.219224 + 1.56557i 0.00927217 + 0.0662165i
\(560\) 0.561553 0.0237299
\(561\) 0 0
\(562\) −8.12311 14.0696i −0.342653 0.593492i
\(563\) −16.4924 + 28.5657i −0.695073 + 1.20390i 0.275083 + 0.961420i \(0.411295\pi\)
−0.970156 + 0.242481i \(0.922039\pi\)
\(564\) 0 0
\(565\) −4.34233 + 7.52113i −0.182683 + 0.316417i
\(566\) 7.78078 13.4767i 0.327050 0.566468i
\(567\) 0 0
\(568\) 6.56155 11.3649i 0.275317 0.476862i
\(569\) 13.0885 + 22.6700i 0.548700 + 0.950377i 0.998364 + 0.0571787i \(0.0182105\pi\)
−0.449664 + 0.893198i \(0.648456\pi\)
\(570\) 0 0
\(571\) 23.6847 0.991172 0.495586 0.868559i \(-0.334953\pi\)
0.495586 + 0.868559i \(0.334953\pi\)
\(572\) −11.7192 + 9.14657i −0.490005 + 0.382437i
\(573\) 0 0
\(574\) 3.43845 + 5.95557i 0.143518 + 0.248580i
\(575\) 2.34233 + 4.05703i 0.0976819 + 0.169190i
\(576\) 0 0
\(577\) −40.7386 −1.69597 −0.847986 0.530019i \(-0.822185\pi\)
−0.847986 + 0.530019i \(0.822185\pi\)
\(578\) −3.62311 + 6.27540i −0.150701 + 0.261022i
\(579\) 0 0
\(580\) 2.43845 0.101251
\(581\) 2.00000 3.46410i 0.0829740 0.143715i
\(582\) 0 0
\(583\) −17.6501 30.5709i −0.730992 1.26612i
\(584\) −9.36932 −0.387705
\(585\) 0 0
\(586\) 3.93087 0.162383
\(587\) −20.1231 34.8542i −0.830569 1.43859i −0.897587 0.440837i \(-0.854682\pi\)
0.0670179 0.997752i \(-0.478652\pi\)
\(588\) 0 0
\(589\) 1.87689 3.25088i 0.0773361 0.133950i
\(590\) −6.43845 −0.265067
\(591\) 0 0
\(592\) 2.06155 3.57071i 0.0847293 0.146755i
\(593\) −33.1771 −1.36242 −0.681210 0.732088i \(-0.738546\pi\)
−0.681210 + 0.732088i \(0.738546\pi\)
\(594\) 0 0
\(595\) −0.876894 1.51883i −0.0359492 0.0622658i
\(596\) −1.09612 1.89853i −0.0448987 0.0777669i
\(597\) 0 0
\(598\) 2.34233 + 16.7276i 0.0957850 + 0.684041i
\(599\) 14.0000 0.572024 0.286012 0.958226i \(-0.407670\pi\)
0.286012 + 0.958226i \(0.407670\pi\)
\(600\) 0 0
\(601\) −14.9924 25.9676i −0.611554 1.05924i −0.990979 0.134020i \(-0.957212\pi\)
0.379425 0.925222i \(-0.376122\pi\)
\(602\) −0.123106 + 0.213225i −0.00501741 + 0.00869041i
\(603\) 0 0
\(604\) 7.68466 13.3102i 0.312684 0.541585i
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 0 0
\(607\) −16.2116 + 28.0794i −0.658010 + 1.13971i 0.323120 + 0.946358i \(0.395268\pi\)
−0.981130 + 0.193349i \(0.938065\pi\)
\(608\) 0.280776 + 0.486319i 0.0113870 + 0.0197228i
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) −19.8963 + 15.5286i −0.804918 + 0.628219i
\(612\) 0 0
\(613\) −9.93845 17.2139i −0.401410 0.695263i 0.592486 0.805581i \(-0.298146\pi\)
−0.993896 + 0.110318i \(0.964813\pi\)
\(614\) 12.8078 + 22.1837i 0.516879 + 0.895261i
\(615\) 0 0
\(616\) −2.31534 −0.0932878
\(617\) −14.6577 + 25.3878i −0.590096 + 1.02208i 0.404123 + 0.914704i \(0.367577\pi\)
−0.994219 + 0.107371i \(0.965757\pi\)
\(618\) 0 0
\(619\) −20.5616 −0.826439 −0.413219 0.910632i \(-0.635596\pi\)
−0.413219 + 0.910632i \(0.635596\pi\)
\(620\) −3.34233 + 5.78908i −0.134231 + 0.232495i
\(621\) 0 0
\(622\) −15.3693 26.6204i −0.616253 1.06738i
\(623\) −10.5616 −0.423140
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 15.6847 + 27.1666i 0.626885 + 1.08580i
\(627\) 0 0
\(628\) −6.93845 + 12.0177i −0.276874 + 0.479560i
\(629\) −12.8769 −0.513435
\(630\) 0 0
\(631\) 6.87689 11.9111i 0.273765 0.474175i −0.696058 0.717986i \(-0.745064\pi\)
0.969823 + 0.243811i \(0.0783977\pi\)
\(632\) −11.5616 −0.459894
\(633\) 0 0
\(634\) 12.4039 + 21.4842i 0.492621 + 0.853245i
\(635\) −4.28078 7.41452i −0.169877 0.294236i
\(636\) 0 0
\(637\) 22.3423 + 9.03996i 0.885235 + 0.358176i
\(638\) −10.0540 −0.398041
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −5.71922 + 9.90599i −0.225896 + 0.391263i −0.956588 0.291444i \(-0.905864\pi\)
0.730692 + 0.682707i \(0.239198\pi\)
\(642\) 0 0
\(643\) −10.8769 + 18.8393i −0.428943 + 0.742951i −0.996780 0.0801904i \(-0.974447\pi\)
0.567837 + 0.823141i \(0.307780\pi\)
\(644\) −1.31534 + 2.27824i −0.0518317 + 0.0897752i
\(645\) 0 0
\(646\) 0.876894 1.51883i 0.0345009 0.0597574i
\(647\) 17.5270 + 30.3576i 0.689057 + 1.19348i 0.972143 + 0.234387i \(0.0753084\pi\)
−0.283086 + 0.959094i \(0.591358\pi\)
\(648\) 0 0
\(649\) 26.5464 1.04204
\(650\) 3.34233 + 1.35234i 0.131097 + 0.0530433i
\(651\) 0 0
\(652\) 7.21922 + 12.5041i 0.282727 + 0.489697i
\(653\) −22.2808 38.5914i −0.871914 1.51020i −0.860014 0.510270i \(-0.829545\pi\)
−0.0119002 0.999929i \(-0.503788\pi\)
\(654\) 0 0
\(655\) −2.12311 −0.0829566
\(656\) 6.12311 10.6055i 0.239067 0.414076i
\(657\) 0 0
\(658\) −3.93087 −0.153241
\(659\) −3.02699 + 5.24290i −0.117915 + 0.204234i −0.918941 0.394395i \(-0.870954\pi\)
0.801026 + 0.598629i \(0.204288\pi\)
\(660\) 0 0
\(661\) −14.8078 25.6478i −0.575955 0.997584i −0.995937 0.0900513i \(-0.971297\pi\)
0.419982 0.907532i \(-0.362036\pi\)
\(662\) −30.7386 −1.19469
\(663\) 0 0
\(664\) −7.12311 −0.276430
\(665\) −0.157671 0.273094i −0.00611421 0.0105901i
\(666\) 0 0
\(667\) −5.71165 + 9.89286i −0.221156 + 0.383053i
\(668\) −4.36932 −0.169054
\(669\) 0 0
\(670\) 1.12311 1.94528i 0.0433894 0.0751526i
\(671\) −24.7386 −0.955024
\(672\) 0 0
\(673\) −12.8769 22.3034i −0.496368 0.859734i 0.503623 0.863923i \(-0.332000\pi\)
−0.999991 + 0.00418904i \(0.998667\pi\)
\(674\) −3.00000 5.19615i −0.115556 0.200148i
\(675\) 0 0
\(676\) 9.34233 + 9.03996i 0.359320 + 0.347691i
\(677\) 37.1231 1.42676 0.713378 0.700779i \(-0.247164\pi\)
0.713378 + 0.700779i \(0.247164\pi\)
\(678\) 0 0
\(679\) −2.00000 3.46410i −0.0767530 0.132940i
\(680\) −1.56155 + 2.70469i −0.0598828 + 0.103720i
\(681\) 0 0
\(682\) 13.7808 23.8690i 0.527693 0.913991i
\(683\) 8.56155 14.8290i 0.327599 0.567418i −0.654436 0.756117i \(-0.727094\pi\)
0.982035 + 0.188700i \(0.0604273\pi\)
\(684\) 0 0
\(685\) −5.90388 + 10.2258i −0.225576 + 0.390709i
\(686\) 3.84233 + 6.65511i 0.146701 + 0.254093i
\(687\) 0 0
\(688\) 0.438447 0.0167156
\(689\) −24.3348 + 18.9927i −0.927080 + 0.723564i
\(690\) 0 0
\(691\) 10.2808 + 17.8068i 0.391099 + 0.677404i 0.992595 0.121472i \(-0.0387616\pi\)
−0.601496 + 0.798876i \(0.705428\pi\)
\(692\) 10.0885 + 17.4739i 0.383509 + 0.664257i
\(693\) 0 0
\(694\) 0.876894 0.0332865
\(695\) 6.28078 10.8786i 0.238243 0.412650i
\(696\) 0 0
\(697\) −38.2462 −1.44868
\(698\) 4.24621 7.35465i 0.160721 0.278378i
\(699\) 0 0
\(700\) 0.280776 + 0.486319i 0.0106124 + 0.0183811i
\(701\) 36.3002 1.37104 0.685520 0.728054i \(-0.259575\pi\)
0.685520 + 0.728054i \(0.259575\pi\)
\(702\) 0 0
\(703\) −2.31534 −0.0873248
\(704\) 2.06155 + 3.57071i 0.0776977 + 0.134576i
\(705\) 0 0
\(706\) 12.9309 22.3969i 0.486660 0.842919i
\(707\) −4.98485 −0.187474
\(708\) 0 0
\(709\) −17.1231 + 29.6581i −0.643072 + 1.11383i 0.341672 + 0.939819i \(0.389007\pi\)
−0.984743 + 0.174013i \(0.944326\pi\)
\(710\) 13.1231 0.492501
\(711\) 0 0
\(712\) 9.40388 + 16.2880i 0.352425 + 0.610419i
\(713\) −15.6577 27.1199i −0.586384 1.01565i
\(714\) 0 0
\(715\) −13.7808 5.57586i −0.515372 0.208525i
\(716\) 12.6847 0.474048
\(717\) 0 0
\(718\) −6.56155 11.3649i −0.244875 0.424136i
\(719\) 22.4924 38.9580i 0.838826 1.45289i −0.0520512 0.998644i \(-0.516576\pi\)
0.890877 0.454245i \(-0.150091\pi\)
\(720\) 0 0
\(721\) 1.28078 2.21837i 0.0476986 0.0826164i
\(722\) −9.34233 + 16.1814i −0.347685 + 0.602209i
\(723\) 0 0
\(724\) −1.43845 + 2.49146i −0.0534595 + 0.0925945i
\(725\) 1.21922 + 2.11176i 0.0452808 + 0.0784287i
\(726\) 0 0
\(727\) 38.4233 1.42504 0.712521 0.701651i \(-0.247554\pi\)
0.712521 + 0.701651i \(0.247554\pi\)
\(728\) 0.280776 + 2.00514i 0.0104063 + 0.0743156i
\(729\) 0 0
\(730\) −4.68466 8.11407i −0.173387 0.300315i
\(731\) −0.684658 1.18586i −0.0253230 0.0438607i
\(732\) 0 0
\(733\) 20.0691 0.741270 0.370635 0.928779i \(-0.379140\pi\)
0.370635 + 0.928779i \(0.379140\pi\)
\(734\) 6.24621 10.8188i 0.230552 0.399328i
\(735\) 0 0
\(736\) 4.68466 0.172679
\(737\) −4.63068 + 8.02058i −0.170573 + 0.295442i
\(738\) 0 0
\(739\) 13.7732 + 23.8559i 0.506655 + 0.877553i 0.999970 + 0.00770202i \(0.00245165\pi\)
−0.493315 + 0.869851i \(0.664215\pi\)
\(740\) 4.12311 0.151568
\(741\) 0 0
\(742\) −4.80776 −0.176499
\(743\) 6.58854 + 11.4117i 0.241710 + 0.418654i 0.961202 0.275847i \(-0.0889584\pi\)
−0.719491 + 0.694501i \(0.755625\pi\)
\(744\) 0 0
\(745\) 1.09612 1.89853i 0.0401587 0.0695568i
\(746\) 25.8078 0.944889
\(747\) 0 0
\(748\) 6.43845 11.1517i 0.235413 0.407747i
\(749\) 1.12311 0.0410374
\(750\) 0 0
\(751\) 11.9039 + 20.6181i 0.434379 + 0.752366i 0.997245 0.0741820i \(-0.0236346\pi\)
−0.562866 + 0.826548i \(0.690301\pi\)
\(752\) 3.50000 + 6.06218i 0.127632 + 0.221065i
\(753\) 0 0
\(754\) 1.21922 + 8.70700i 0.0444015 + 0.317090i
\(755\) 15.3693 0.559347
\(756\) 0 0
\(757\) 14.2116 + 24.6153i 0.516531 + 0.894658i 0.999816 + 0.0191948i \(0.00611027\pi\)
−0.483285 + 0.875463i \(0.660556\pi\)
\(758\) −8.84233 + 15.3154i −0.321168 + 0.556279i
\(759\) 0 0
\(760\) −0.280776 + 0.486319i −0.0101848 + 0.0176406i
\(761\) −8.96543 + 15.5286i −0.324997 + 0.562911i −0.981512 0.191402i \(-0.938697\pi\)
0.656515 + 0.754313i \(0.272030\pi\)
\(762\) 0 0
\(763\) −1.05398 + 1.82554i −0.0381565 + 0.0660889i
\(764\) 5.43845 + 9.41967i 0.196756 + 0.340792i
\(765\) 0 0
\(766\) 0.192236 0.00694577
\(767\) −3.21922 22.9899i −0.116239 0.830116i
\(768\) 0 0
\(769\) 16.6577 + 28.8519i 0.600691 + 1.04043i 0.992717 + 0.120473i \(0.0384411\pi\)
−0.392026 + 0.919954i \(0.628226\pi\)
\(770\) −1.15767 2.00514i −0.0417196 0.0722604i
\(771\) 0 0
\(772\) 0 0
\(773\) 12.0885 20.9380i 0.434795 0.753086i −0.562484 0.826808i \(-0.690154\pi\)
0.997279 + 0.0737217i \(0.0234876\pi\)
\(774\) 0 0
\(775\) −6.68466 −0.240120
\(776\) −3.56155 + 6.16879i −0.127852 + 0.221447i
\(777\) 0 0
\(778\) 9.02699 + 15.6352i 0.323633 + 0.560549i
\(779\) −6.87689 −0.246390
\(780\) 0 0
\(781\) −54.1080 −1.93613
\(782\) −7.31534 12.6705i −0.261596 0.453098i
\(783\) 0 0
\(784\) 3.34233 5.78908i 0.119369 0.206753i
\(785\) −13.8769 −0.495288
\(786\) 0 0
\(787\) −15.6577 + 27.1199i −0.558136 + 0.966719i 0.439516 + 0.898235i \(0.355150\pi\)
−0.997652 + 0.0684848i \(0.978184\pi\)
\(788\) −12.8078 −0.456258
\(789\) 0 0
\(790\) −5.78078 10.0126i −0.205671