Properties

Label 570.2.d.c.229.4
Level $570$
Weight $2$
Character 570.229
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.4
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.c.229.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.48119 - 1.67513i) q^{10} -0.962389 q^{11} -1.00000i q^{12} -1.61213i q^{13} -3.35026 q^{14} +(-1.48119 - 1.67513i) q^{15} +1.00000 q^{16} +0.387873i q^{17} -1.00000i q^{18} -1.00000 q^{19} +(1.67513 - 1.48119i) q^{20} -3.35026 q^{21} -0.962389i q^{22} -0.962389i q^{23} +1.00000 q^{24} +(0.612127 - 4.96239i) q^{25} +1.61213 q^{26} -1.00000i q^{27} -3.35026i q^{28} -6.96239 q^{29} +(1.67513 - 1.48119i) q^{30} +3.35026 q^{31} +1.00000i q^{32} -0.962389i q^{33} -0.387873 q^{34} +(-4.96239 - 5.61213i) q^{35} +1.00000 q^{36} +1.61213i q^{37} -1.00000i q^{38} +1.61213 q^{39} +(1.48119 + 1.67513i) q^{40} -9.27504 q^{41} -3.35026i q^{42} +6.18664i q^{43} +0.962389 q^{44} +(1.67513 - 1.48119i) q^{45} +0.962389 q^{46} -0.962389i q^{47} +1.00000i q^{48} -4.22425 q^{49} +(4.96239 + 0.612127i) q^{50} -0.387873 q^{51} +1.61213i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(1.61213 - 1.42548i) q^{55} +3.35026 q^{56} -1.00000i q^{57} -6.96239i q^{58} -10.3127 q^{59} +(1.48119 + 1.67513i) q^{60} +11.9248 q^{61} +3.35026i q^{62} -3.35026i q^{63} -1.00000 q^{64} +(2.38787 + 2.70052i) q^{65} +0.962389 q^{66} +7.22425i q^{67} -0.387873i q^{68} +0.962389 q^{69} +(5.61213 - 4.96239i) q^{70} +7.22425 q^{71} +1.00000i q^{72} -3.22425i q^{73} -1.61213 q^{74} +(4.96239 + 0.612127i) q^{75} +1.00000 q^{76} -3.22425i q^{77} +1.61213i q^{78} +3.35026 q^{79} +(-1.67513 + 1.48119i) q^{80} +1.00000 q^{81} -9.27504i q^{82} +15.0132i q^{83} +3.35026 q^{84} +(-0.574515 - 0.649738i) q^{85} -6.18664 q^{86} -6.96239i q^{87} +0.962389i q^{88} -4.64974 q^{89} +(1.48119 + 1.67513i) q^{90} +5.40105 q^{91} +0.962389i q^{92} +3.35026i q^{93} +0.962389 q^{94} +(1.67513 - 1.48119i) q^{95} -1.00000 q^{96} +10.9624i q^{97} -4.22425i q^{98} +0.962389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + 2q^{10} + 16q^{11} + 2q^{15} + 6q^{16} - 6q^{19} + 6q^{24} + 2q^{25} + 8q^{26} - 20q^{29} - 4q^{34} - 8q^{35} + 6q^{36} + 8q^{39} - 2q^{40} + 8q^{41} - 16q^{44} - 16q^{46} - 22q^{49} + 8q^{50} - 4q^{51} + 6q^{54} + 8q^{55} - 20q^{59} - 2q^{60} + 28q^{61} - 6q^{64} + 16q^{65} - 16q^{66} - 16q^{69} + 32q^{70} + 40q^{71} - 8q^{74} + 8q^{75} + 6q^{76} + 6q^{81} + 20q^{85} - 12q^{86} - 48q^{89} - 2q^{90} - 48q^{91} - 16q^{94} - 6q^{96} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −1.67513 + 1.48119i −0.749141 + 0.662410i
\(6\) −1.00000 −0.408248
\(7\) 3.35026i 1.26628i 0.774037 + 0.633140i \(0.218234\pi\)
−0.774037 + 0.633140i \(0.781766\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.48119 1.67513i −0.468395 0.529723i
\(11\) −0.962389 −0.290171 −0.145086 0.989419i \(-0.546346\pi\)
−0.145086 + 0.989419i \(0.546346\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.61213i 0.447124i −0.974690 0.223562i \(-0.928232\pi\)
0.974690 0.223562i \(-0.0717684\pi\)
\(14\) −3.35026 −0.895395
\(15\) −1.48119 1.67513i −0.382443 0.432517i
\(16\) 1.00000 0.250000
\(17\) 0.387873i 0.0940731i 0.998893 + 0.0470365i \(0.0149777\pi\)
−0.998893 + 0.0470365i \(0.985022\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.00000 −0.229416
\(20\) 1.67513 1.48119i 0.374571 0.331205i
\(21\) −3.35026 −0.731087
\(22\) 0.962389i 0.205182i
\(23\) 0.962389i 0.200672i −0.994954 0.100336i \(-0.968008\pi\)
0.994954 0.100336i \(-0.0319918\pi\)
\(24\) 1.00000 0.204124
\(25\) 0.612127 4.96239i 0.122425 0.992478i
\(26\) 1.61213 0.316164
\(27\) 1.00000i 0.192450i
\(28\) 3.35026i 0.633140i
\(29\) −6.96239 −1.29288 −0.646442 0.762964i \(-0.723744\pi\)
−0.646442 + 0.762964i \(0.723744\pi\)
\(30\) 1.67513 1.48119i 0.305836 0.270428i
\(31\) 3.35026 0.601725 0.300862 0.953668i \(-0.402726\pi\)
0.300862 + 0.953668i \(0.402726\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.962389i 0.167530i
\(34\) −0.387873 −0.0665197
\(35\) −4.96239 5.61213i −0.838797 0.948623i
\(36\) 1.00000 0.166667
\(37\) 1.61213i 0.265032i 0.991181 + 0.132516i \(0.0423056\pi\)
−0.991181 + 0.132516i \(0.957694\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 1.61213 0.258147
\(40\) 1.48119 + 1.67513i 0.234197 + 0.264861i
\(41\) −9.27504 −1.44852 −0.724259 0.689528i \(-0.757818\pi\)
−0.724259 + 0.689528i \(0.757818\pi\)
\(42\) 3.35026i 0.516957i
\(43\) 6.18664i 0.943454i 0.881745 + 0.471727i \(0.156369\pi\)
−0.881745 + 0.471727i \(0.843631\pi\)
\(44\) 0.962389 0.145086
\(45\) 1.67513 1.48119i 0.249714 0.220803i
\(46\) 0.962389 0.141896
\(47\) 0.962389i 0.140379i −0.997534 0.0701894i \(-0.977640\pi\)
0.997534 0.0701894i \(-0.0223604\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −4.22425 −0.603465
\(50\) 4.96239 + 0.612127i 0.701788 + 0.0865678i
\(51\) −0.387873 −0.0543131
\(52\) 1.61213i 0.223562i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 1.00000 0.136083
\(55\) 1.61213 1.42548i 0.217379 0.192212i
\(56\) 3.35026 0.447698
\(57\) 1.00000i 0.132453i
\(58\) 6.96239i 0.914206i
\(59\) −10.3127 −1.34259 −0.671296 0.741189i \(-0.734262\pi\)
−0.671296 + 0.741189i \(0.734262\pi\)
\(60\) 1.48119 + 1.67513i 0.191221 + 0.216258i
\(61\) 11.9248 1.52681 0.763406 0.645919i \(-0.223526\pi\)
0.763406 + 0.645919i \(0.223526\pi\)
\(62\) 3.35026i 0.425484i
\(63\) 3.35026i 0.422093i
\(64\) −1.00000 −0.125000
\(65\) 2.38787 + 2.70052i 0.296179 + 0.334959i
\(66\) 0.962389 0.118462
\(67\) 7.22425i 0.882583i 0.897364 + 0.441292i \(0.145480\pi\)
−0.897364 + 0.441292i \(0.854520\pi\)
\(68\) 0.387873i 0.0470365i
\(69\) 0.962389 0.115858
\(70\) 5.61213 4.96239i 0.670777 0.593119i
\(71\) 7.22425 0.857361 0.428681 0.903456i \(-0.358979\pi\)
0.428681 + 0.903456i \(0.358979\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 3.22425i 0.377370i −0.982038 0.188685i \(-0.939577\pi\)
0.982038 0.188685i \(-0.0604226\pi\)
\(74\) −1.61213 −0.187406
\(75\) 4.96239 + 0.612127i 0.573007 + 0.0706823i
\(76\) 1.00000 0.114708
\(77\) 3.22425i 0.367438i
\(78\) 1.61213i 0.182537i
\(79\) 3.35026 0.376934 0.188467 0.982080i \(-0.439648\pi\)
0.188467 + 0.982080i \(0.439648\pi\)
\(80\) −1.67513 + 1.48119i −0.187285 + 0.165603i
\(81\) 1.00000 0.111111
\(82\) 9.27504i 1.02426i
\(83\) 15.0132i 1.64791i 0.566655 + 0.823955i \(0.308237\pi\)
−0.566655 + 0.823955i \(0.691763\pi\)
\(84\) 3.35026 0.365544
\(85\) −0.574515 0.649738i −0.0623150 0.0704740i
\(86\) −6.18664 −0.667123
\(87\) 6.96239i 0.746446i
\(88\) 0.962389i 0.102591i
\(89\) −4.64974 −0.492871 −0.246436 0.969159i \(-0.579259\pi\)
−0.246436 + 0.969159i \(0.579259\pi\)
\(90\) 1.48119 + 1.67513i 0.156132 + 0.176574i
\(91\) 5.40105 0.566184
\(92\) 0.962389i 0.100336i
\(93\) 3.35026i 0.347406i
\(94\) 0.962389 0.0992628
\(95\) 1.67513 1.48119i 0.171865 0.151967i
\(96\) −1.00000 −0.102062
\(97\) 10.9624i 1.11306i 0.830827 + 0.556531i \(0.187868\pi\)
−0.830827 + 0.556531i \(0.812132\pi\)
\(98\) 4.22425i 0.426714i
\(99\) 0.962389 0.0967237
\(100\) −0.612127 + 4.96239i −0.0612127 + 0.496239i
\(101\) 2.72496 0.271144 0.135572 0.990768i \(-0.456713\pi\)
0.135572 + 0.990768i \(0.456713\pi\)
\(102\) 0.387873i 0.0384052i
\(103\) 0.574515i 0.0566087i 0.999599 + 0.0283043i \(0.00901076\pi\)
−0.999599 + 0.0283043i \(0.990989\pi\)
\(104\) −1.61213 −0.158082
\(105\) 5.61213 4.96239i 0.547688 0.484280i
\(106\) −6.00000 −0.582772
\(107\) 10.7005i 1.03446i −0.855847 0.517229i \(-0.826963\pi\)
0.855847 0.517229i \(-0.173037\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −10.1260 −0.969896 −0.484948 0.874543i \(-0.661161\pi\)
−0.484948 + 0.874543i \(0.661161\pi\)
\(110\) 1.42548 + 1.61213i 0.135915 + 0.153710i
\(111\) −1.61213 −0.153016
\(112\) 3.35026i 0.316570i
\(113\) 20.5501i 1.93319i 0.256311 + 0.966594i \(0.417493\pi\)
−0.256311 + 0.966594i \(0.582507\pi\)
\(114\) 1.00000 0.0936586
\(115\) 1.42548 + 1.61213i 0.132927 + 0.150332i
\(116\) 6.96239 0.646442
\(117\) 1.61213i 0.149041i
\(118\) 10.3127i 0.949356i
\(119\) −1.29948 −0.119123
\(120\) −1.67513 + 1.48119i −0.152918 + 0.135214i
\(121\) −10.0738 −0.915801
\(122\) 11.9248i 1.07962i
\(123\) 9.27504i 0.836302i
\(124\) −3.35026 −0.300862
\(125\) 6.32487 + 9.21933i 0.565713 + 0.824602i
\(126\) 3.35026 0.298465
\(127\) 1.35026i 0.119816i −0.998204 0.0599082i \(-0.980919\pi\)
0.998204 0.0599082i \(-0.0190808\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −6.18664 −0.544703
\(130\) −2.70052 + 2.38787i −0.236852 + 0.209430i
\(131\) 12.4387 1.08677 0.543385 0.839483i \(-0.317142\pi\)
0.543385 + 0.839483i \(0.317142\pi\)
\(132\) 0.962389i 0.0837652i
\(133\) 3.35026i 0.290505i
\(134\) −7.22425 −0.624080
\(135\) 1.48119 + 1.67513i 0.127481 + 0.144172i
\(136\) 0.387873 0.0332598
\(137\) 18.1622i 1.55170i 0.630916 + 0.775851i \(0.282679\pi\)
−0.630916 + 0.775851i \(0.717321\pi\)
\(138\) 0.962389i 0.0819240i
\(139\) −8.77575 −0.744349 −0.372175 0.928163i \(-0.621388\pi\)
−0.372175 + 0.928163i \(0.621388\pi\)
\(140\) 4.96239 + 5.61213i 0.419398 + 0.474311i
\(141\) 0.962389 0.0810477
\(142\) 7.22425i 0.606246i
\(143\) 1.55149i 0.129742i
\(144\) −1.00000 −0.0833333
\(145\) 11.6629 10.3127i 0.968552 0.856419i
\(146\) 3.22425 0.266841
\(147\) 4.22425i 0.348411i
\(148\) 1.61213i 0.132516i
\(149\) −15.9756 −1.30877 −0.654385 0.756162i \(-0.727072\pi\)
−0.654385 + 0.756162i \(0.727072\pi\)
\(150\) −0.612127 + 4.96239i −0.0499799 + 0.405177i
\(151\) 18.4241 1.49933 0.749665 0.661818i \(-0.230215\pi\)
0.749665 + 0.661818i \(0.230215\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 0.387873i 0.0313577i
\(154\) 3.22425 0.259818
\(155\) −5.61213 + 4.96239i −0.450777 + 0.398589i
\(156\) −1.61213 −0.129073
\(157\) 13.7889i 1.10048i 0.835008 + 0.550238i \(0.185463\pi\)
−0.835008 + 0.550238i \(0.814537\pi\)
\(158\) 3.35026i 0.266533i
\(159\) −6.00000 −0.475831
\(160\) −1.48119 1.67513i −0.117099 0.132431i
\(161\) 3.22425 0.254107
\(162\) 1.00000i 0.0785674i
\(163\) 3.73813i 0.292793i −0.989226 0.146397i \(-0.953232\pi\)
0.989226 0.146397i \(-0.0467676\pi\)
\(164\) 9.27504 0.724259
\(165\) 1.42548 + 1.61213i 0.110974 + 0.125504i
\(166\) −15.0132 −1.16525
\(167\) 15.4763i 1.19759i −0.800902 0.598795i \(-0.795646\pi\)
0.800902 0.598795i \(-0.204354\pi\)
\(168\) 3.35026i 0.258478i
\(169\) 10.4010 0.800081
\(170\) 0.649738 0.574515i 0.0498326 0.0440633i
\(171\) 1.00000 0.0764719
\(172\) 6.18664i 0.471727i
\(173\) 1.47627i 0.112239i −0.998424 0.0561194i \(-0.982127\pi\)
0.998424 0.0561194i \(-0.0178727\pi\)
\(174\) 6.96239 0.527817
\(175\) 16.6253 + 2.05079i 1.25675 + 0.155025i
\(176\) −0.962389 −0.0725428
\(177\) 10.3127i 0.775146i
\(178\) 4.64974i 0.348513i
\(179\) 14.3127 1.06978 0.534889 0.844922i \(-0.320353\pi\)
0.534889 + 0.844922i \(0.320353\pi\)
\(180\) −1.67513 + 1.48119i −0.124857 + 0.110402i
\(181\) −8.82653 −0.656071 −0.328035 0.944665i \(-0.606387\pi\)
−0.328035 + 0.944665i \(0.606387\pi\)
\(182\) 5.40105i 0.400352i
\(183\) 11.9248i 0.881505i
\(184\) −0.962389 −0.0709482
\(185\) −2.38787 2.70052i −0.175560 0.198546i
\(186\) −3.35026 −0.245653
\(187\) 0.373285i 0.0272973i
\(188\) 0.962389i 0.0701894i
\(189\) 3.35026 0.243696
\(190\) 1.48119 + 1.67513i 0.107457 + 0.121527i
\(191\) 2.31265 0.167338 0.0836688 0.996494i \(-0.473336\pi\)
0.0836688 + 0.996494i \(0.473336\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 7.58769i 0.546174i 0.961989 + 0.273087i \(0.0880447\pi\)
−0.961989 + 0.273087i \(0.911955\pi\)
\(194\) −10.9624 −0.787054
\(195\) −2.70052 + 2.38787i −0.193389 + 0.170999i
\(196\) 4.22425 0.301732
\(197\) 18.8119i 1.34030i 0.742228 + 0.670148i \(0.233769\pi\)
−0.742228 + 0.670148i \(0.766231\pi\)
\(198\) 0.962389i 0.0683940i
\(199\) 9.40105 0.666423 0.333211 0.942852i \(-0.391868\pi\)
0.333211 + 0.942852i \(0.391868\pi\)
\(200\) −4.96239 0.612127i −0.350894 0.0432839i
\(201\) −7.22425 −0.509560
\(202\) 2.72496i 0.191728i
\(203\) 23.3258i 1.63715i
\(204\) 0.387873 0.0271566
\(205\) 15.5369 13.7381i 1.08514 0.959513i
\(206\) −0.574515 −0.0400284
\(207\) 0.962389i 0.0668906i
\(208\) 1.61213i 0.111781i
\(209\) 0.962389 0.0665698
\(210\) 4.96239 + 5.61213i 0.342437 + 0.387274i
\(211\) 4.77575 0.328776 0.164388 0.986396i \(-0.447435\pi\)
0.164388 + 0.986396i \(0.447435\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 7.22425i 0.494998i
\(214\) 10.7005 0.731473
\(215\) −9.16362 10.3634i −0.624954 0.706780i
\(216\) −1.00000 −0.0680414
\(217\) 11.2243i 0.761952i
\(218\) 10.1260i 0.685820i
\(219\) 3.22425 0.217875
\(220\) −1.61213 + 1.42548i −0.108690 + 0.0961061i
\(221\) 0.625301 0.0420623
\(222\) 1.61213i 0.108199i
\(223\) 24.6761i 1.65243i −0.563353 0.826216i \(-0.690489\pi\)
0.563353 0.826216i \(-0.309511\pi\)
\(224\) −3.35026 −0.223849
\(225\) −0.612127 + 4.96239i −0.0408085 + 0.330826i
\(226\) −20.5501 −1.36697
\(227\) 15.4763i 1.02720i −0.858031 0.513598i \(-0.828312\pi\)
0.858031 0.513598i \(-0.171688\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) −21.3258 −1.40925 −0.704625 0.709580i \(-0.748885\pi\)
−0.704625 + 0.709580i \(0.748885\pi\)
\(230\) −1.61213 + 1.42548i −0.106300 + 0.0939937i
\(231\) 3.22425 0.212140
\(232\) 6.96239i 0.457103i
\(233\) 9.01317i 0.590473i −0.955424 0.295236i \(-0.904602\pi\)
0.955424 0.295236i \(-0.0953984\pi\)
\(234\) −1.61213 −0.105388
\(235\) 1.42548 + 1.61213i 0.0929884 + 0.105164i
\(236\) 10.3127 0.671296
\(237\) 3.35026i 0.217623i
\(238\) 1.29948i 0.0842326i
\(239\) 0.135857 0.00878787 0.00439393 0.999990i \(-0.498601\pi\)
0.00439393 + 0.999990i \(0.498601\pi\)
\(240\) −1.48119 1.67513i −0.0956107 0.108129i
\(241\) −25.8496 −1.66512 −0.832558 0.553938i \(-0.813125\pi\)
−0.832558 + 0.553938i \(0.813125\pi\)
\(242\) 10.0738i 0.647569i
\(243\) 1.00000i 0.0641500i
\(244\) −11.9248 −0.763406
\(245\) 7.07618 6.25694i 0.452080 0.399741i
\(246\) 9.27504 0.591355
\(247\) 1.61213i 0.102577i
\(248\) 3.35026i 0.212742i
\(249\) −15.0132 −0.951421
\(250\) −9.21933 + 6.32487i −0.583082 + 0.400020i
\(251\) −10.1114 −0.638227 −0.319114 0.947716i \(-0.603385\pi\)
−0.319114 + 0.947716i \(0.603385\pi\)
\(252\) 3.35026i 0.211047i
\(253\) 0.926192i 0.0582292i
\(254\) 1.35026 0.0847230
\(255\) 0.649738 0.574515i 0.0406882 0.0359776i
\(256\) 1.00000 0.0625000
\(257\) 26.9986i 1.68413i −0.539380 0.842063i \(-0.681341\pi\)
0.539380 0.842063i \(-0.318659\pi\)
\(258\) 6.18664i 0.385164i
\(259\) −5.40105 −0.335605
\(260\) −2.38787 2.70052i −0.148090 0.167479i
\(261\) 6.96239 0.430961
\(262\) 12.4387i 0.768463i
\(263\) 15.0376i 0.927259i 0.886029 + 0.463629i \(0.153453\pi\)
−0.886029 + 0.463629i \(0.846547\pi\)
\(264\) −0.962389 −0.0592309
\(265\) −8.88717 10.0508i −0.545934 0.617415i
\(266\) 3.35026 0.205418
\(267\) 4.64974i 0.284559i
\(268\) 7.22425i 0.441292i
\(269\) 4.51388 0.275216 0.137608 0.990487i \(-0.456059\pi\)
0.137608 + 0.990487i \(0.456059\pi\)
\(270\) −1.67513 + 1.48119i −0.101945 + 0.0901426i
\(271\) 15.8496 0.962792 0.481396 0.876503i \(-0.340130\pi\)
0.481396 + 0.876503i \(0.340130\pi\)
\(272\) 0.387873i 0.0235183i
\(273\) 5.40105i 0.326886i
\(274\) −18.1622 −1.09722
\(275\) −0.589104 + 4.77575i −0.0355243 + 0.287988i
\(276\) −0.962389 −0.0579290
\(277\) 10.3127i 0.619627i −0.950797 0.309814i \(-0.899733\pi\)
0.950797 0.309814i \(-0.100267\pi\)
\(278\) 8.77575i 0.526334i
\(279\) −3.35026 −0.200575
\(280\) −5.61213 + 4.96239i −0.335389 + 0.296559i
\(281\) 24.3488 1.45253 0.726265 0.687415i \(-0.241254\pi\)
0.726265 + 0.687415i \(0.241254\pi\)
\(282\) 0.962389i 0.0573094i
\(283\) 26.2882i 1.56267i 0.624111 + 0.781336i \(0.285461\pi\)
−0.624111 + 0.781336i \(0.714539\pi\)
\(284\) −7.22425 −0.428681
\(285\) 1.48119 + 1.67513i 0.0877384 + 0.0992262i
\(286\) −1.55149 −0.0917417
\(287\) 31.0738i 1.83423i
\(288\) 1.00000i 0.0589256i
\(289\) 16.8496 0.991150
\(290\) 10.3127 + 11.6629i 0.605580 + 0.684870i
\(291\) −10.9624 −0.642627
\(292\) 3.22425i 0.188685i
\(293\) 13.0738i 0.763780i −0.924208 0.381890i \(-0.875273\pi\)
0.924208 0.381890i \(-0.124727\pi\)
\(294\) 4.22425 0.246363
\(295\) 17.2750 15.2750i 1.00579 0.889347i
\(296\) 1.61213 0.0937030
\(297\) 0.962389i 0.0558435i
\(298\) 15.9756i 0.925439i
\(299\) −1.55149 −0.0897251
\(300\) −4.96239 0.612127i −0.286504 0.0353412i
\(301\) −20.7269 −1.19468
\(302\) 18.4241i 1.06019i
\(303\) 2.72496i 0.156545i
\(304\) −1.00000 −0.0573539
\(305\) −19.9756 + 17.6629i −1.14380 + 1.01138i
\(306\) 0.387873 0.0221732
\(307\) 7.07381i 0.403724i 0.979414 + 0.201862i \(0.0646992\pi\)
−0.979414 + 0.201862i \(0.935301\pi\)
\(308\) 3.22425i 0.183719i
\(309\) −0.574515 −0.0326830
\(310\) −4.96239 5.61213i −0.281845 0.318747i
\(311\) 26.3127 1.49205 0.746027 0.665916i \(-0.231959\pi\)
0.746027 + 0.665916i \(0.231959\pi\)
\(312\) 1.61213i 0.0912687i
\(313\) 18.7005i 1.05702i −0.848928 0.528508i \(-0.822752\pi\)
0.848928 0.528508i \(-0.177248\pi\)
\(314\) −13.7889 −0.778154
\(315\) 4.96239 + 5.61213i 0.279599 + 0.316208i
\(316\) −3.35026 −0.188467
\(317\) 26.4749i 1.48698i −0.668749 0.743488i \(-0.733170\pi\)
0.668749 0.743488i \(-0.266830\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 6.70052 0.375157
\(320\) 1.67513 1.48119i 0.0936427 0.0828013i
\(321\) 10.7005 0.597245
\(322\) 3.22425i 0.179681i
\(323\) 0.387873i 0.0215818i
\(324\) −1.00000 −0.0555556
\(325\) −8.00000 0.986826i −0.443760 0.0547393i
\(326\) 3.73813 0.207036
\(327\) 10.1260i 0.559970i
\(328\) 9.27504i 0.512128i
\(329\) 3.22425 0.177759
\(330\) −1.61213 + 1.42548i −0.0887447 + 0.0784703i
\(331\) −30.7005 −1.68745 −0.843727 0.536773i \(-0.819643\pi\)
−0.843727 + 0.536773i \(0.819643\pi\)
\(332\) 15.0132i 0.823955i
\(333\) 1.61213i 0.0883440i
\(334\) 15.4763 0.846824
\(335\) −10.7005 12.1016i −0.584632 0.661179i
\(336\) −3.35026 −0.182772
\(337\) 6.81194i 0.371070i −0.982638 0.185535i \(-0.940598\pi\)
0.982638 0.185535i \(-0.0594018\pi\)
\(338\) 10.4010i 0.565742i
\(339\) −20.5501 −1.11613
\(340\) 0.574515 + 0.649738i 0.0311575 + 0.0352370i
\(341\) −3.22425 −0.174603
\(342\) 1.00000i 0.0540738i
\(343\) 9.29948i 0.502125i
\(344\) 6.18664 0.333561
\(345\) −1.61213 + 1.42548i −0.0867940 + 0.0767455i
\(346\) 1.47627 0.0793648
\(347\) 18.3879i 0.987113i −0.869714 0.493556i \(-0.835697\pi\)
0.869714 0.493556i \(-0.164303\pi\)
\(348\) 6.96239i 0.373223i
\(349\) −31.1490 −1.66737 −0.833685 0.552241i \(-0.813773\pi\)
−0.833685 + 0.552241i \(0.813773\pi\)
\(350\) −2.05079 + 16.6253i −0.109619 + 0.888660i
\(351\) −1.61213 −0.0860490
\(352\) 0.962389i 0.0512955i
\(353\) 7.61213i 0.405153i 0.979266 + 0.202576i \(0.0649314\pi\)
−0.979266 + 0.202576i \(0.935069\pi\)
\(354\) 10.3127 0.548111
\(355\) −12.1016 + 10.7005i −0.642285 + 0.567925i
\(356\) 4.64974 0.246436
\(357\) 1.29948i 0.0687756i
\(358\) 14.3127i 0.756447i
\(359\) 35.3112 1.86366 0.931828 0.362901i \(-0.118214\pi\)
0.931828 + 0.362901i \(0.118214\pi\)
\(360\) −1.48119 1.67513i −0.0780658 0.0882871i
\(361\) 1.00000 0.0526316
\(362\) 8.82653i 0.463912i
\(363\) 10.0738i 0.528738i
\(364\) −5.40105 −0.283092
\(365\) 4.77575 + 5.40105i 0.249974 + 0.282704i
\(366\) −11.9248 −0.623318
\(367\) 31.9756i 1.66911i −0.550924 0.834555i \(-0.685725\pi\)
0.550924 0.834555i \(-0.314275\pi\)
\(368\) 0.962389i 0.0501680i
\(369\) 9.27504 0.482839
\(370\) 2.70052 2.38787i 0.140394 0.124140i
\(371\) −20.1016 −1.04362
\(372\) 3.35026i 0.173703i
\(373\) 26.4894i 1.37157i 0.727804 + 0.685786i \(0.240541\pi\)
−0.727804 + 0.685786i \(0.759459\pi\)
\(374\) 0.373285 0.0193021
\(375\) −9.21933 + 6.32487i −0.476084 + 0.326615i
\(376\) −0.962389 −0.0496314
\(377\) 11.2243i 0.578078i
\(378\) 3.35026i 0.172319i
\(379\) 19.3258 0.992701 0.496350 0.868122i \(-0.334673\pi\)
0.496350 + 0.868122i \(0.334673\pi\)
\(380\) −1.67513 + 1.48119i −0.0859324 + 0.0759837i
\(381\) 1.35026 0.0691760
\(382\) 2.31265i 0.118325i
\(383\) 3.37470i 0.172439i 0.996276 + 0.0862195i \(0.0274786\pi\)
−0.996276 + 0.0862195i \(0.972521\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.77575 + 5.40105i 0.243395 + 0.275263i
\(386\) −7.58769 −0.386203
\(387\) 6.18664i 0.314485i
\(388\) 10.9624i 0.556531i
\(389\) 11.3503 0.575481 0.287741 0.957708i \(-0.407096\pi\)
0.287741 + 0.957708i \(0.407096\pi\)
\(390\) −2.38787 2.70052i −0.120915 0.136746i
\(391\) 0.373285 0.0188778
\(392\) 4.22425i 0.213357i
\(393\) 12.4387i 0.627447i
\(394\) −18.8119 −0.947732
\(395\) −5.61213 + 4.96239i −0.282377 + 0.249685i
\(396\) −0.962389 −0.0483618
\(397\) 18.8364i 0.945371i 0.881231 + 0.472685i \(0.156715\pi\)
−0.881231 + 0.472685i \(0.843285\pi\)
\(398\) 9.40105i 0.471232i
\(399\) 3.35026 0.167723
\(400\) 0.612127 4.96239i 0.0306063 0.248119i
\(401\) −4.12601 −0.206043 −0.103022 0.994679i \(-0.532851\pi\)
−0.103022 + 0.994679i \(0.532851\pi\)
\(402\) 7.22425i 0.360313i
\(403\) 5.40105i 0.269045i
\(404\) −2.72496 −0.135572
\(405\) −1.67513 + 1.48119i −0.0832379 + 0.0736011i
\(406\) 23.3258 1.15764
\(407\) 1.55149i 0.0769046i
\(408\) 0.387873i 0.0192026i
\(409\) −2.52373 −0.124790 −0.0623952 0.998052i \(-0.519874\pi\)
−0.0623952 + 0.998052i \(0.519874\pi\)
\(410\) 13.7381 + 15.5369i 0.678478 + 0.767313i
\(411\) −18.1622 −0.895875
\(412\) 0.574515i 0.0283043i
\(413\) 34.5501i 1.70010i
\(414\) −0.962389 −0.0472988
\(415\) −22.2374 25.1490i −1.09159 1.23452i
\(416\) 1.61213 0.0790410
\(417\) 8.77575i 0.429750i
\(418\) 0.962389i 0.0470720i
\(419\) −7.51247 −0.367008 −0.183504 0.983019i \(-0.558744\pi\)
−0.183504 + 0.983019i \(0.558744\pi\)
\(420\) −5.61213 + 4.96239i −0.273844 + 0.242140i
\(421\) 3.67750 0.179230 0.0896152 0.995976i \(-0.471436\pi\)
0.0896152 + 0.995976i \(0.471436\pi\)
\(422\) 4.77575i 0.232480i
\(423\) 0.962389i 0.0467929i
\(424\) 6.00000 0.291386
\(425\) 1.92478 + 0.237428i 0.0933654 + 0.0115169i
\(426\) −7.22425 −0.350016
\(427\) 39.9511i 1.93337i
\(428\) 10.7005i 0.517229i
\(429\) −1.55149 −0.0749068
\(430\) 10.3634 9.16362i 0.499769 0.441909i
\(431\) −10.3272 −0.497446 −0.248723 0.968575i \(-0.580011\pi\)
−0.248723 + 0.968575i \(0.580011\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 31.5877i 1.51801i 0.651086 + 0.759004i \(0.274314\pi\)
−0.651086 + 0.759004i \(0.725686\pi\)
\(434\) −11.2243 −0.538781
\(435\) 10.3127 + 11.6629i 0.494454 + 0.559194i
\(436\) 10.1260 0.484948
\(437\) 0.962389i 0.0460373i
\(438\) 3.22425i 0.154061i
\(439\) 38.1524 1.82091 0.910456 0.413605i \(-0.135731\pi\)
0.910456 + 0.413605i \(0.135731\pi\)
\(440\) −1.42548 1.61213i −0.0679573 0.0768551i
\(441\) 4.22425 0.201155
\(442\) 0.625301i 0.0297425i
\(443\) 16.3127i 0.775037i 0.921862 + 0.387519i \(0.126668\pi\)
−0.921862 + 0.387519i \(0.873332\pi\)
\(444\) 1.61213 0.0765082
\(445\) 7.78892 6.88717i 0.369230 0.326483i
\(446\) 24.6761 1.16845
\(447\) 15.9756i 0.755618i
\(448\) 3.35026i 0.158285i
\(449\) 37.5271 1.77101 0.885506 0.464629i \(-0.153812\pi\)
0.885506 + 0.464629i \(0.153812\pi\)
\(450\) −4.96239 0.612127i −0.233929 0.0288559i
\(451\) 8.92619 0.420318
\(452\) 20.5501i 0.966594i
\(453\) 18.4241i 0.865638i
\(454\) 15.4763 0.726337
\(455\) −9.04746 + 8.00000i −0.424151 + 0.375046i
\(456\) −1.00000 −0.0468293
\(457\) 8.00000i 0.374224i 0.982339 + 0.187112i \(0.0599128\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) 21.3258i 0.996490i
\(459\) 0.387873 0.0181044
\(460\) −1.42548 1.61213i −0.0664636 0.0751658i
\(461\) 12.3780 0.576502 0.288251 0.957555i \(-0.406926\pi\)
0.288251 + 0.957555i \(0.406926\pi\)
\(462\) 3.22425i 0.150006i
\(463\) 32.4504i 1.50810i 0.656818 + 0.754049i \(0.271902\pi\)
−0.656818 + 0.754049i \(0.728098\pi\)
\(464\) −6.96239 −0.323221
\(465\) −4.96239 5.61213i −0.230125 0.260256i
\(466\) 9.01317 0.417527
\(467\) 7.53690i 0.348766i −0.984678 0.174383i \(-0.944207\pi\)
0.984678 0.174383i \(-0.0557931\pi\)
\(468\) 1.61213i 0.0745206i
\(469\) −24.2031 −1.11760
\(470\) −1.61213 + 1.42548i −0.0743619 + 0.0657527i
\(471\) −13.7889 −0.635360
\(472\) 10.3127i 0.474678i
\(473\) 5.95395i 0.273763i
\(474\) −3.35026 −0.153883
\(475\) −0.612127 + 4.96239i −0.0280863 + 0.227690i
\(476\) 1.29948 0.0595614
\(477\) 6.00000i 0.274721i
\(478\) 0.135857i 0.00621396i
\(479\) −15.2097 −0.694947 −0.347474 0.937690i \(-0.612960\pi\)
−0.347474 + 0.937690i \(0.612960\pi\)
\(480\) 1.67513 1.48119i 0.0764589 0.0676070i
\(481\) 2.59895 0.118502
\(482\) 25.8496i 1.17741i
\(483\) 3.22425i 0.146709i
\(484\) 10.0738 0.457900
\(485\) −16.2374 18.3634i −0.737304 0.833841i
\(486\) −1.00000 −0.0453609
\(487\) 1.19982i 0.0543689i 0.999630 + 0.0271844i \(0.00865414\pi\)
−0.999630 + 0.0271844i \(0.991346\pi\)
\(488\) 11.9248i 0.539809i
\(489\) 3.73813 0.169044
\(490\) 6.25694 + 7.07618i 0.282660 + 0.319669i
\(491\) −5.11283 −0.230739 −0.115369 0.993323i \(-0.536805\pi\)
−0.115369 + 0.993323i \(0.536805\pi\)
\(492\) 9.27504i 0.418151i
\(493\) 2.70052i 0.121625i
\(494\) −1.61213 −0.0725330
\(495\) −1.61213 + 1.42548i −0.0724597 + 0.0640708i
\(496\) 3.35026 0.150431
\(497\) 24.2031i 1.08566i
\(498\) 15.0132i 0.672756i
\(499\) −14.2981 −0.640069 −0.320035 0.947406i \(-0.603695\pi\)
−0.320035 + 0.947406i \(0.603695\pi\)
\(500\) −6.32487 9.21933i −0.282857 0.412301i
\(501\) 15.4763 0.691429
\(502\) 10.1114i 0.451295i
\(503\) 11.5125i 0.513316i 0.966502 + 0.256658i \(0.0826213\pi\)
−0.966502 + 0.256658i \(0.917379\pi\)
\(504\) −3.35026 −0.149233
\(505\) −4.56467 + 4.03620i −0.203125 + 0.179608i
\(506\) −0.926192 −0.0411742
\(507\) 10.4010i 0.461927i
\(508\) 1.35026i 0.0599082i
\(509\) 31.9610 1.41665 0.708323 0.705889i \(-0.249452\pi\)
0.708323 + 0.705889i \(0.249452\pi\)
\(510\) 0.574515 + 0.649738i 0.0254400 + 0.0287709i
\(511\) 10.8021 0.477857
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) 26.9986 1.19086
\(515\) −0.850969 0.962389i −0.0374982 0.0424079i
\(516\) 6.18664 0.272352
\(517\) 0.926192i 0.0407339i
\(518\) 5.40105i 0.237308i
\(519\) 1.47627 0.0648010
\(520\) 2.70052 2.38787i 0.118426 0.104715i
\(521\) −33.2750 −1.45781 −0.728903 0.684617i \(-0.759969\pi\)
−0.728903 + 0.684617i \(0.759969\pi\)
\(522\) 6.96239i 0.304735i
\(523\) 9.29948i 0.406638i −0.979113 0.203319i \(-0.934827\pi\)
0.979113 0.203319i \(-0.0651728\pi\)
\(524\) −12.4387 −0.543385
\(525\) −2.05079 + 16.6253i −0.0895036 + 0.725588i
\(526\) −15.0376 −0.655671
\(527\) 1.29948i 0.0566061i
\(528\) 0.962389i 0.0418826i
\(529\) 22.0738 0.959731
\(530\) 10.0508 8.88717i 0.436578 0.386034i
\(531\) 10.3127 0.447531
\(532\) 3.35026i 0.145252i
\(533\) 14.9525i 0.647666i
\(534\) 4.64974 0.201214
\(535\) 15.8496 + 17.9248i 0.685236 + 0.774956i
\(536\) 7.22425 0.312040
\(537\) 14.3127i 0.617636i
\(538\) 4.51388i 0.194607i
\(539\) 4.06537 0.175108
\(540\) −1.48119 1.67513i −0.0637405 0.0720862i
\(541\) 28.5501 1.22746 0.613732 0.789515i \(-0.289668\pi\)
0.613732 + 0.789515i \(0.289668\pi\)
\(542\) 15.8496i 0.680797i
\(543\) 8.82653i 0.378783i
\(544\) −0.387873 −0.0166299
\(545\) 16.9624 14.9986i 0.726589 0.642469i
\(546\) −5.40105 −0.231143
\(547\) 28.4749i 1.21750i 0.793363 + 0.608748i \(0.208328\pi\)
−0.793363 + 0.608748i \(0.791672\pi\)
\(548\) 18.1622i 0.775851i
\(549\) −11.9248 −0.508937
\(550\) −4.77575 0.589104i −0.203639 0.0251195i
\(551\) 6.96239 0.296608
\(552\) 0.962389i 0.0409620i
\(553\) 11.2243i 0.477304i
\(554\) 10.3127 0.438143
\(555\) 2.70052 2.38787i 0.114631 0.101360i
\(556\) 8.77575 0.372175
\(557\) 4.88717i 0.207076i 0.994626 + 0.103538i \(0.0330163\pi\)
−0.994626 + 0.103538i \(0.966984\pi\)
\(558\) 3.35026i 0.141828i
\(559\) 9.97365 0.421841
\(560\) −4.96239 5.61213i −0.209699 0.237156i
\(561\) 0.373285 0.0157601
\(562\) 24.3488i 1.02709i
\(563\) 30.8021i 1.29815i 0.760723 + 0.649077i \(0.224845\pi\)
−0.760723 + 0.649077i \(0.775155\pi\)
\(564\) −0.962389 −0.0405239
\(565\) −30.4387 34.4241i −1.28056 1.44823i
\(566\) −26.2882 −1.10498
\(567\) 3.35026i 0.140698i
\(568\) 7.22425i 0.303123i
\(569\) 24.1260 1.01141 0.505707 0.862705i \(-0.331232\pi\)
0.505707 + 0.862705i \(0.331232\pi\)
\(570\) −1.67513 + 1.48119i −0.0701635 + 0.0620404i
\(571\) −5.67276 −0.237398 −0.118699 0.992930i \(-0.537872\pi\)
−0.118699 + 0.992930i \(0.537872\pi\)
\(572\) 1.55149i 0.0648712i
\(573\) 2.31265i 0.0966124i
\(574\) 31.0738 1.29700
\(575\) −4.77575 0.589104i −0.199162 0.0245673i
\(576\) 1.00000 0.0416667
\(577\) 32.0000i 1.33218i 0.745873 + 0.666089i \(0.232033\pi\)
−0.745873 + 0.666089i \(0.767967\pi\)
\(578\) 16.8496i 0.700849i
\(579\) −7.58769 −0.315334
\(580\) −11.6629 + 10.3127i −0.484276 + 0.428209i
\(581\) −50.2981 −2.08672
\(582\) 10.9624i 0.454406i
\(583\) 5.77433i 0.239148i
\(584\) −3.22425 −0.133421
\(585\) −2.38787 2.70052i −0.0987264 0.111653i
\(586\) 13.0738 0.540074
\(587\) 13.6121i 0.561833i 0.959732 + 0.280916i \(0.0906383\pi\)
−0.959732 + 0.280916i \(0.909362\pi\)
\(588\) 4.22425i 0.174205i
\(589\) −3.35026 −0.138045
\(590\) 15.2750 + 17.2750i 0.628863 + 0.711202i
\(591\) −18.8119 −0.773820
\(592\) 1.61213i 0.0662580i
\(593\) 23.4617i 0.963456i 0.876321 + 0.481728i \(0.159991\pi\)
−0.876321 + 0.481728i \(0.840009\pi\)
\(594\) −0.962389 −0.0394873
\(595\) 2.17679 1.92478i 0.0892398 0.0789082i
\(596\) 15.9756 0.654385
\(597\) 9.40105i 0.384759i
\(598\) 1.55149i 0.0634452i
\(599\) −10.0263 −0.409665 −0.204833 0.978797i \(-0.565665\pi\)
−0.204833 + 0.978797i \(0.565665\pi\)
\(600\) 0.612127 4.96239i 0.0249900 0.202589i
\(601\) 11.7743 0.480285 0.240143 0.970738i \(-0.422806\pi\)
0.240143 + 0.970738i \(0.422806\pi\)
\(602\) 20.7269i 0.844764i
\(603\) 7.22425i 0.294194i
\(604\) −18.4241 −0.749665
\(605\) 16.8749 14.9213i 0.686064 0.606636i
\(606\) −2.72496 −0.110694
\(607\) 38.4993i 1.56264i −0.624132 0.781319i \(-0.714547\pi\)
0.624132 0.781319i \(-0.285453\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 23.3258 0.945210
\(610\) −17.6629 19.9756i −0.715150 0.808787i
\(611\) −1.55149 −0.0627667
\(612\) 0.387873i 0.0156788i
\(613\) 7.61213i 0.307451i −0.988114 0.153725i \(-0.950873\pi\)
0.988114 0.153725i \(-0.0491271\pi\)
\(614\) −7.07381 −0.285476
\(615\) 13.7381 + 15.5369i 0.553975 + 0.626508i
\(616\) −3.22425 −0.129909
\(617\) 29.5369i 1.18911i 0.804055 + 0.594555i \(0.202672\pi\)
−0.804055 + 0.594555i \(0.797328\pi\)
\(618\) 0.574515i 0.0231104i
\(619\) 22.5501 0.906364 0.453182 0.891418i \(-0.350289\pi\)
0.453182 + 0.891418i \(0.350289\pi\)
\(620\) 5.61213 4.96239i 0.225388 0.199294i
\(621\) −0.962389 −0.0386193
\(622\) 26.3127i 1.05504i
\(623\) 15.5778i 0.624113i
\(624\) 1.61213 0.0645367
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) 18.7005 0.747423
\(627\) 0.962389i 0.0384341i
\(628\) 13.7889i 0.550238i
\(629\) −0.625301 −0.0249324
\(630\) −5.61213 + 4.96239i −0.223592 + 0.197706i
\(631\) −37.9248 −1.50976 −0.754881 0.655862i \(-0.772305\pi\)
−0.754881 + 0.655862i \(0.772305\pi\)
\(632\) 3.35026i 0.133266i
\(633\) 4.77575i 0.189819i
\(634\) 26.4749 1.05145
\(635\) 2.00000 + 2.26187i 0.0793676 + 0.0897594i
\(636\) 6.00000 0.237915
\(637\) 6.81003i 0.269823i
\(638\) 6.70052i 0.265276i
\(639\) −7.22425 −0.285787
\(640\) 1.48119 + 1.67513i 0.0585493 + 0.0662154i
\(641\) 6.67609 0.263690 0.131845 0.991270i \(-0.457910\pi\)
0.131845 + 0.991270i \(0.457910\pi\)
\(642\) 10.7005i 0.422316i
\(643\) 25.2605i 0.996175i −0.867127 0.498087i \(-0.834036\pi\)
0.867127 0.498087i \(-0.165964\pi\)
\(644\) −3.22425 −0.127053
\(645\) 10.3634 9.16362i 0.408060 0.360817i
\(646\) 0.387873 0.0152607
\(647\) 16.9135i 0.664939i 0.943114 + 0.332469i \(0.107882\pi\)
−0.943114 + 0.332469i \(0.892118\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 9.92478 0.389582
\(650\) 0.986826 8.00000i 0.0387065 0.313786i
\(651\) −11.2243 −0.439913
\(652\) 3.73813i 0.146397i
\(653\) 24.1114i 0.943553i −0.881718 0.471776i \(-0.843613\pi\)
0.881718 0.471776i \(-0.156387\pi\)
\(654\) 10.1260 0.395958
\(655\) −20.8364 + 18.4241i −0.814145 + 0.719888i
\(656\) −9.27504 −0.362129
\(657\) 3.22425i 0.125790i
\(658\) 3.22425i 0.125694i
\(659\) 20.3879 0.794199 0.397099 0.917776i \(-0.370017\pi\)
0.397099 + 0.917776i \(0.370017\pi\)
\(660\) −1.42548 1.61213i −0.0554869 0.0627520i
\(661\) 17.6023 0.684649 0.342325 0.939582i \(-0.388786\pi\)
0.342325 + 0.939582i \(0.388786\pi\)
\(662\) 30.7005i 1.19321i
\(663\) 0.625301i 0.0242847i
\(664\) 15.0132 0.582624
\(665\) 4.96239 + 5.61213i 0.192433 + 0.217629i
\(666\) 1.61213 0.0624686
\(667\) 6.70052i 0.259445i
\(668\) 15.4763i 0.598795i
\(669\) 24.6761 0.954033
\(670\) 12.1016 10.7005i 0.467524 0.413397i
\(671\) −11.4763 −0.443036
\(672\) 3.35026i 0.129239i
\(673\) 44.3634i 1.71008i −0.518558 0.855042i \(-0.673531\pi\)
0.518558 0.855042i \(-0.326469\pi\)
\(674\) 6.81194 0.262386
\(675\) −4.96239 0.612127i −0.191002 0.0235608i
\(676\) −10.4010 −0.400040
\(677\) 8.70052i 0.334388i 0.985924 + 0.167194i \(0.0534707\pi\)
−0.985924 + 0.167194i \(0.946529\pi\)
\(678\) 20.5501i 0.789221i
\(679\) −36.7269 −1.40945
\(680\) −0.649738 + 0.574515i −0.0249163 + 0.0220317i
\(681\) 15.4763 0.593052
\(682\) 3.22425i 0.123463i
\(683\) 37.8759i 1.44928i 0.689127 + 0.724641i \(0.257994\pi\)
−0.689127 + 0.724641i \(0.742006\pi\)
\(684\) −1.00000 −0.0382360
\(685\) −26.9018 30.4241i −1.02786 1.16244i
\(686\) −9.29948 −0.355056
\(687\) 21.3258i 0.813631i
\(688\) 6.18664i 0.235864i
\(689\) 9.67276 0.368503
\(690\) −1.42548 1.61213i −0.0542673 0.0613726i
\(691\) −0.775746 −0.0295108 −0.0147554 0.999891i \(-0.504697\pi\)
−0.0147554 + 0.999891i \(0.504697\pi\)
\(692\) 1.47627i 0.0561194i
\(693\) 3.22425i 0.122479i
\(694\) 18.3879 0.697994
\(695\) 14.7005 12.9986i 0.557623 0.493064i
\(696\) −6.96239 −0.263909
\(697\) 3.59754i 0.136266i
\(698\) 31.1490i 1.17901i
\(699\) 9.01317 0.340910
\(700\) −16.6253 2.05079i −0.628377 0.0775124i
\(701\) 42.3752 1.60049 0.800245 0.599674i \(-0.204703\pi\)
0.800245 + 0.599674i \(0.204703\pi\)
\(702\) 1.61213i 0.0608458i
\(703\) 1.61213i 0.0608025i
\(704\) 0.962389 0.0362714
\(705\) −1.61213 + 1.42548i −0.0607162 + 0.0536869i
\(706\) −7.61213 −0.286486
\(707\) 9.12933i 0.343344i
\(708\) 10.3127i 0.387573i
\(709\) −36.2784 −1.36246 −0.681231 0.732068i \(-0.738555\pi\)
−0.681231 + 0.732068i \(0.738555\pi\)
\(710\) −10.7005 12.1016i −0.401583 0.454164i
\(711\) −3.35026 −0.125645
\(712\) 4.64974i 0.174256i
\(713\) 3.22425i 0.120749i
\(714\) 1.29948 0.0486317
\(715\) −2.29806 2.59895i −0.0859426 0.0971953i
\(716\) −14.3127 −0.534889
\(717\) 0.135857i 0.00507368i
\(718\) 35.3112i 1.31780i
\(719\) 42.5355 1.58631 0.793153 0.609022i \(-0.208438\pi\)
0.793153 + 0.609022i \(0.208438\pi\)
\(720\) 1.67513 1.48119i 0.0624284 0.0552009i
\(721\) −1.92478 −0.0716824
\(722\) 1.00000i 0.0372161i
\(723\) 25.8496i 0.961355i
\(724\) 8.82653 0.328035
\(725\) −4.26187 + 34.5501i −0.158282 + 1.28316i
\(726\) 10.0738 0.373874
\(727\) 0.378024i 0.0140201i −0.999975 0.00701007i \(-0.997769\pi\)
0.999975 0.00701007i \(-0.00223139\pi\)
\(728\) 5.40105i 0.200176i
\(729\) −1.00000 −0.0370370
\(730\) −5.40105 + 4.77575i −0.199902 + 0.176758i
\(731\) −2.39963 −0.0887536
\(732\) 11.9248i 0.440752i
\(733\) 26.0118i 0.960766i −0.877059 0.480383i \(-0.840498\pi\)
0.877059 0.480383i \(-0.159502\pi\)
\(734\) 31.9756 1.18024
\(735\) 6.25694 + 7.07618i 0.230791 + 0.261009i
\(736\) 0.962389 0.0354741
\(737\) 6.95254i 0.256100i
\(738\) 9.27504i 0.341419i
\(739\) 44.8773 1.65084 0.825419 0.564520i \(-0.190939\pi\)
0.825419 + 0.564520i \(0.190939\pi\)
\(740\) 2.38787 + 2.70052i 0.0877800 + 0.0992732i
\(741\) −1.61213 −0.0592230
\(742\) 20.1016i 0.737952i
\(743\) 4.67418i 0.171479i 0.996318 + 0.0857394i \(0.0273253\pi\)
−0.996318 + 0.0857394i \(0.972675\pi\)
\(744\) 3.35026 0.122827
\(745\) 26.7612 23.6629i 0.980453 0.866942i
\(746\) −26.4894 −0.969847
\(747\) 15.0132i 0.549303i
\(748\) 0.373285i 0.0136486i
\(749\) 35.8496 1.30991
\(750\) −6.32487 9.21933i −0.230952 0.336642i
\(751\) −6.57452 −0.239907 −0.119954 0.992779i \(-0.538275\pi\)
−0.119954 + 0.992779i \(0.538275\pi\)
\(752\) 0.962389i 0.0350947i
\(753\) 10.1114i 0.368481i
\(754\) −11.2243 −0.408763
\(755\) −30.8627 + 27.2896i −1.12321 + 0.993171i
\(756\) −3.35026 −0.121848
\(757\) 15.5633i 0.565656i −0.959171 0.282828i \(-0.908727\pi\)
0.959171 0.282828i \(-0.0912726\pi\)
\(758\) 19.3258i 0.701946i
\(759\) −0.926192 −0.0336186
\(760\) −1.48119 1.67513i −0.0537286 0.0607634i
\(761\) −23.8759 −0.865501 −0.432750 0.901514i \(-0.642457\pi\)
−0.432750 + 0.901514i \(0.642457\pi\)
\(762\) 1.35026i 0.0489148i
\(763\) 33.9248i 1.22816i
\(764\) −2.31265 −0.0836688
\(765\) 0.574515 + 0.649738i 0.0207717 + 0.0234913i
\(766\) −3.37470 −0.121933
\(767\) 16.6253i 0.600305i
\(768\) 1.00000i 0.0360844i
\(769\) −30.4749 −1.09895 −0.549476 0.835510i \(-0.685173\pi\)
−0.549476 + 0.835510i \(0.685173\pi\)
\(770\) −5.40105 + 4.77575i −0.194640 + 0.172106i
\(771\) 26.9986 0.972330
\(772\) 7.58769i 0.273087i
\(773\) 16.3272i 0.587250i −0.955921 0.293625i \(-0.905138\pi\)
0.955921 0.293625i \(-0.0948617\pi\)
\(774\) 6.18664 0.222374
\(775\) 2.05079 16.6253i 0.0736664 0.597198i
\(776\) 10.9624 0.393527
\(777\) 5.40105i 0.193761i
\(778\) 11.3503i 0.406927i
\(779\) 9.27504 0.332313
\(780\) 2.70052 2.38787i 0.0966943 0.0854996i
\(781\) −6.95254 −0.248781
\(782\) 0.373285i 0.0133486i
\(783\) 6.96239i 0.248815i
\(784\) −4.22425 −0.150866
\(785\) −20.4241 23.0982i −0.728966 0.824412i
\(786\) −12.4387 −0.443672
\(787\) 30.9525i 1.10334i 0.834063 + 0.551669i \(0.186009\pi\)
−0.834063 + 0.551669i \(0.813991\pi\)
\(788\)