Properties

Label 1155.2.l.b.1121.3
Level 1155
Weight 2
Character 1155.1121
Analytic conductor 9.223
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1121.3
Root \(0.707107 + 0.707107i\) of \(x^{4} + 1\)
Character \(\chi\) \(=\) 1155.1121
Dual form 1155.2.l.b.1121.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} +(1.00000 - 1.41421i) q^{3} -1.00000i q^{5} +(1.41421 - 2.00000i) q^{6} -1.00000i q^{7} -2.82843 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +(1.00000 - 1.41421i) q^{3} -1.00000i q^{5} +(1.41421 - 2.00000i) q^{6} -1.00000i q^{7} -2.82843 q^{8} +(-1.00000 - 2.82843i) q^{9} -1.41421i q^{10} +(-3.00000 - 1.41421i) q^{11} +2.24264i q^{13} -1.41421i q^{14} +(-1.41421 - 1.00000i) q^{15} -4.00000 q^{16} -5.82843 q^{17} +(-1.41421 - 4.00000i) q^{18} -3.24264i q^{19} +(-1.41421 - 1.00000i) q^{21} +(-4.24264 - 2.00000i) q^{22} -1.24264i q^{23} +(-2.82843 + 4.00000i) q^{24} -1.00000 q^{25} +3.17157i q^{26} +(-5.00000 - 1.41421i) q^{27} +5.82843 q^{29} +(-2.00000 - 1.41421i) q^{30} +8.24264 q^{31} +(-5.00000 + 2.82843i) q^{33} -8.24264 q^{34} -1.00000 q^{35} +8.24264 q^{37} -4.58579i q^{38} +(3.17157 + 2.24264i) q^{39} +2.82843i q^{40} -4.58579 q^{41} +(-2.00000 - 1.41421i) q^{42} -3.24264i q^{43} +(-2.82843 + 1.00000i) q^{45} -1.75736i q^{46} -1.07107i q^{47} +(-4.00000 + 5.65685i) q^{48} -1.00000 q^{49} -1.41421 q^{50} +(-5.82843 + 8.24264i) q^{51} -4.41421i q^{53} +(-7.07107 - 2.00000i) q^{54} +(-1.41421 + 3.00000i) q^{55} +2.82843i q^{56} +(-4.58579 - 3.24264i) q^{57} +8.24264 q^{58} -12.8995i q^{59} +9.24264i q^{61} +11.6569 q^{62} +(-2.82843 + 1.00000i) q^{63} +8.00000 q^{64} +2.24264 q^{65} +(-7.07107 + 4.00000i) q^{66} -12.4853 q^{67} +(-1.75736 - 1.24264i) q^{69} -1.41421 q^{70} -1.75736i q^{71} +(2.82843 + 8.00000i) q^{72} -6.48528i q^{73} +11.6569 q^{74} +(-1.00000 + 1.41421i) q^{75} +(-1.41421 + 3.00000i) q^{77} +(4.48528 + 3.17157i) q^{78} -6.24264i q^{79} +4.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} -6.48528 q^{82} +17.1421 q^{83} +5.82843i q^{85} -4.58579i q^{86} +(5.82843 - 8.24264i) q^{87} +(8.48528 + 4.00000i) q^{88} -16.4142i q^{89} +(-4.00000 + 1.41421i) q^{90} +2.24264 q^{91} +(8.24264 - 11.6569i) q^{93} -1.51472i q^{94} -3.24264 q^{95} -7.00000 q^{97} -1.41421 q^{98} +(-1.00000 + 9.89949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} - 4q^{9} - 12q^{11} - 16q^{16} - 12q^{17} - 4q^{25} - 20q^{27} + 12q^{29} - 8q^{30} + 16q^{31} - 20q^{33} - 16q^{34} - 4q^{35} + 16q^{37} + 24q^{39} - 24q^{41} - 8q^{42} - 16q^{48} - 4q^{49} - 12q^{51} - 24q^{57} + 16q^{58} + 24q^{62} + 32q^{64} - 8q^{65} - 16q^{67} - 24q^{69} + 24q^{74} - 4q^{75} - 16q^{78} - 28q^{81} + 8q^{82} + 12q^{83} + 12q^{87} - 16q^{90} - 8q^{91} + 16q^{93} + 4q^{95} - 28q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 1.41421 2.00000i 0.577350 0.816497i
\(7\) 1.00000i 0.377964i
\(8\) −2.82843 −1.00000
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.41421i 0.447214i
\(11\) −3.00000 1.41421i −0.904534 0.426401i
\(12\) 0 0
\(13\) 2.24264i 0.621997i 0.950410 + 0.310998i \(0.100663\pi\)
−0.950410 + 0.310998i \(0.899337\pi\)
\(14\) 1.41421i 0.377964i
\(15\) −1.41421 1.00000i −0.365148 0.258199i
\(16\) −4.00000 −1.00000
\(17\) −5.82843 −1.41360 −0.706801 0.707413i \(-0.749862\pi\)
−0.706801 + 0.707413i \(0.749862\pi\)
\(18\) −1.41421 4.00000i −0.333333 0.942809i
\(19\) 3.24264i 0.743913i −0.928250 0.371956i \(-0.878687\pi\)
0.928250 0.371956i \(-0.121313\pi\)
\(20\) 0 0
\(21\) −1.41421 1.00000i −0.308607 0.218218i
\(22\) −4.24264 2.00000i −0.904534 0.426401i
\(23\) 1.24264i 0.259108i −0.991572 0.129554i \(-0.958645\pi\)
0.991572 0.129554i \(-0.0413546\pi\)
\(24\) −2.82843 + 4.00000i −0.577350 + 0.816497i
\(25\) −1.00000 −0.200000
\(26\) 3.17157i 0.621997i
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0 0
\(29\) 5.82843 1.08231 0.541156 0.840922i \(-0.317987\pi\)
0.541156 + 0.840922i \(0.317987\pi\)
\(30\) −2.00000 1.41421i −0.365148 0.258199i
\(31\) 8.24264 1.48042 0.740211 0.672375i \(-0.234726\pi\)
0.740211 + 0.672375i \(0.234726\pi\)
\(32\) 0 0
\(33\) −5.00000 + 2.82843i −0.870388 + 0.492366i
\(34\) −8.24264 −1.41360
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 8.24264 1.35508 0.677541 0.735485i \(-0.263046\pi\)
0.677541 + 0.735485i \(0.263046\pi\)
\(38\) 4.58579i 0.743913i
\(39\) 3.17157 + 2.24264i 0.507858 + 0.359110i
\(40\) 2.82843i 0.447214i
\(41\) −4.58579 −0.716180 −0.358090 0.933687i \(-0.616572\pi\)
−0.358090 + 0.933687i \(0.616572\pi\)
\(42\) −2.00000 1.41421i −0.308607 0.218218i
\(43\) 3.24264i 0.494498i −0.968952 0.247249i \(-0.920473\pi\)
0.968952 0.247249i \(-0.0795266\pi\)
\(44\) 0 0
\(45\) −2.82843 + 1.00000i −0.421637 + 0.149071i
\(46\) 1.75736i 0.259108i
\(47\) 1.07107i 0.156231i −0.996944 0.0781156i \(-0.975110\pi\)
0.996944 0.0781156i \(-0.0248903\pi\)
\(48\) −4.00000 + 5.65685i −0.577350 + 0.816497i
\(49\) −1.00000 −0.142857
\(50\) −1.41421 −0.200000
\(51\) −5.82843 + 8.24264i −0.816143 + 1.15420i
\(52\) 0 0
\(53\) 4.41421i 0.606339i −0.952937 0.303169i \(-0.901955\pi\)
0.952937 0.303169i \(-0.0980448\pi\)
\(54\) −7.07107 2.00000i −0.962250 0.272166i
\(55\) −1.41421 + 3.00000i −0.190693 + 0.404520i
\(56\) 2.82843i 0.377964i
\(57\) −4.58579 3.24264i −0.607402 0.429498i
\(58\) 8.24264 1.08231
\(59\) 12.8995i 1.67937i −0.543073 0.839686i \(-0.682739\pi\)
0.543073 0.839686i \(-0.317261\pi\)
\(60\) 0 0
\(61\) 9.24264i 1.18340i 0.806159 + 0.591699i \(0.201543\pi\)
−0.806159 + 0.591699i \(0.798457\pi\)
\(62\) 11.6569 1.48042
\(63\) −2.82843 + 1.00000i −0.356348 + 0.125988i
\(64\) 8.00000 1.00000
\(65\) 2.24264 0.278165
\(66\) −7.07107 + 4.00000i −0.870388 + 0.492366i
\(67\) −12.4853 −1.52532 −0.762660 0.646800i \(-0.776107\pi\)
−0.762660 + 0.646800i \(0.776107\pi\)
\(68\) 0 0
\(69\) −1.75736 1.24264i −0.211561 0.149596i
\(70\) −1.41421 −0.169031
\(71\) 1.75736i 0.208560i −0.994548 0.104280i \(-0.966746\pi\)
0.994548 0.104280i \(-0.0332538\pi\)
\(72\) 2.82843 + 8.00000i 0.333333 + 0.942809i
\(73\) 6.48528i 0.759045i −0.925183 0.379522i \(-0.876088\pi\)
0.925183 0.379522i \(-0.123912\pi\)
\(74\) 11.6569 1.35508
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 0 0
\(77\) −1.41421 + 3.00000i −0.161165 + 0.341882i
\(78\) 4.48528 + 3.17157i 0.507858 + 0.359110i
\(79\) 6.24264i 0.702352i −0.936309 0.351176i \(-0.885782\pi\)
0.936309 0.351176i \(-0.114218\pi\)
\(80\) 4.00000i 0.447214i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) −6.48528 −0.716180
\(83\) 17.1421 1.88159 0.940797 0.338971i \(-0.110079\pi\)
0.940797 + 0.338971i \(0.110079\pi\)
\(84\) 0 0
\(85\) 5.82843i 0.632182i
\(86\) 4.58579i 0.494498i
\(87\) 5.82843 8.24264i 0.624873 0.883704i
\(88\) 8.48528 + 4.00000i 0.904534 + 0.426401i
\(89\) 16.4142i 1.73990i −0.493137 0.869952i \(-0.664150\pi\)
0.493137 0.869952i \(-0.335850\pi\)
\(90\) −4.00000 + 1.41421i −0.421637 + 0.149071i
\(91\) 2.24264 0.235093
\(92\) 0 0
\(93\) 8.24264 11.6569i 0.854722 1.20876i
\(94\) 1.51472i 0.156231i
\(95\) −3.24264 −0.332688
\(96\) 0 0
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) −1.41421 −0.142857
\(99\) −1.00000 + 9.89949i −0.100504 + 0.994937i
\(100\) 0 0
\(101\) 2.48528 0.247295 0.123647 0.992326i \(-0.460541\pi\)
0.123647 + 0.992326i \(0.460541\pi\)
\(102\) −8.24264 + 11.6569i −0.816143 + 1.15420i
\(103\) −0.514719 −0.0507167 −0.0253584 0.999678i \(-0.508073\pi\)
−0.0253584 + 0.999678i \(0.508073\pi\)
\(104\) 6.34315i 0.621997i
\(105\) −1.00000 + 1.41421i −0.0975900 + 0.138013i
\(106\) 6.24264i 0.606339i
\(107\) 7.41421 0.716759 0.358380 0.933576i \(-0.383329\pi\)
0.358380 + 0.933576i \(0.383329\pi\)
\(108\) 0 0
\(109\) 3.75736i 0.359890i 0.983677 + 0.179945i \(0.0575919\pi\)
−0.983677 + 0.179945i \(0.942408\pi\)
\(110\) −2.00000 + 4.24264i −0.190693 + 0.404520i
\(111\) 8.24264 11.6569i 0.782357 1.10642i
\(112\) 4.00000i 0.377964i
\(113\) 18.8995i 1.77791i 0.457990 + 0.888957i \(0.348570\pi\)
−0.457990 + 0.888957i \(0.651430\pi\)
\(114\) −6.48528 4.58579i −0.607402 0.429498i
\(115\) −1.24264 −0.115877
\(116\) 0 0
\(117\) 6.34315 2.24264i 0.586424 0.207332i
\(118\) 18.2426i 1.67937i
\(119\) 5.82843i 0.534291i
\(120\) 4.00000 + 2.82843i 0.365148 + 0.258199i
\(121\) 7.00000 + 8.48528i 0.636364 + 0.771389i
\(122\) 13.0711i 1.18340i
\(123\) −4.58579 + 6.48528i −0.413486 + 0.584758i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) −4.00000 + 1.41421i −0.356348 + 0.125988i
\(127\) 13.2426i 1.17509i 0.809190 + 0.587547i \(0.199906\pi\)
−0.809190 + 0.587547i \(0.800094\pi\)
\(128\) 11.3137 1.00000
\(129\) −4.58579 3.24264i −0.403756 0.285499i
\(130\) 3.17157 0.278165
\(131\) −19.4142 −1.69623 −0.848114 0.529814i \(-0.822262\pi\)
−0.848114 + 0.529814i \(0.822262\pi\)
\(132\) 0 0
\(133\) −3.24264 −0.281173
\(134\) −17.6569 −1.52532
\(135\) −1.41421 + 5.00000i −0.121716 + 0.430331i
\(136\) 16.4853 1.41360
\(137\) 14.4853i 1.23756i −0.785564 0.618781i \(-0.787627\pi\)
0.785564 0.618781i \(-0.212373\pi\)
\(138\) −2.48528 1.75736i −0.211561 0.149596i
\(139\) 12.4853i 1.05899i −0.848314 0.529494i \(-0.822382\pi\)
0.848314 0.529494i \(-0.177618\pi\)
\(140\) 0 0
\(141\) −1.51472 1.07107i −0.127562 0.0902002i
\(142\) 2.48528i 0.208560i
\(143\) 3.17157 6.72792i 0.265220 0.562617i
\(144\) 4.00000 + 11.3137i 0.333333 + 0.942809i
\(145\) 5.82843i 0.484025i
\(146\) 9.17157i 0.759045i
\(147\) −1.00000 + 1.41421i −0.0824786 + 0.116642i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −1.41421 + 2.00000i −0.115470 + 0.163299i
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 9.17157i 0.743913i
\(153\) 5.82843 + 16.4853i 0.471200 + 1.33276i
\(154\) −2.00000 + 4.24264i −0.161165 + 0.341882i
\(155\) 8.24264i 0.662065i
\(156\) 0 0
\(157\) 11.0000 0.877896 0.438948 0.898513i \(-0.355351\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) 8.82843i 0.702352i
\(159\) −6.24264 4.41421i −0.495074 0.350070i
\(160\) 0 0
\(161\) −1.24264 −0.0979338
\(162\) −9.89949 + 8.00000i −0.777778 + 0.628539i
\(163\) 2.24264 0.175657 0.0878286 0.996136i \(-0.472007\pi\)
0.0878286 + 0.996136i \(0.472007\pi\)
\(164\) 0 0
\(165\) 2.82843 + 5.00000i 0.220193 + 0.389249i
\(166\) 24.2426 1.88159
\(167\) 20.1421 1.55865 0.779323 0.626623i \(-0.215563\pi\)
0.779323 + 0.626623i \(0.215563\pi\)
\(168\) 4.00000 + 2.82843i 0.308607 + 0.218218i
\(169\) 7.97056 0.613120
\(170\) 8.24264i 0.632182i
\(171\) −9.17157 + 3.24264i −0.701368 + 0.247971i
\(172\) 0 0
\(173\) −2.82843 −0.215041 −0.107521 0.994203i \(-0.534291\pi\)
−0.107521 + 0.994203i \(0.534291\pi\)
\(174\) 8.24264 11.6569i 0.624873 0.883704i
\(175\) 1.00000i 0.0755929i
\(176\) 12.0000 + 5.65685i 0.904534 + 0.426401i
\(177\) −18.2426 12.8995i −1.37120 0.969585i
\(178\) 23.2132i 1.73990i
\(179\) 13.4142i 1.00263i 0.865266 + 0.501313i \(0.167149\pi\)
−0.865266 + 0.501313i \(0.832851\pi\)
\(180\) 0 0
\(181\) −10.9706 −0.815436 −0.407718 0.913108i \(-0.633675\pi\)
−0.407718 + 0.913108i \(0.633675\pi\)
\(182\) 3.17157 0.235093
\(183\) 13.0711 + 9.24264i 0.966241 + 0.683236i
\(184\) 3.51472i 0.259108i
\(185\) 8.24264i 0.606011i
\(186\) 11.6569 16.4853i 0.854722 1.20876i
\(187\) 17.4853 + 8.24264i 1.27865 + 0.602762i
\(188\) 0 0
\(189\) −1.41421 + 5.00000i −0.102869 + 0.363696i
\(190\) −4.58579 −0.332688
\(191\) 9.17157i 0.663632i −0.943344 0.331816i \(-0.892339\pi\)
0.943344 0.331816i \(-0.107661\pi\)
\(192\) 8.00000 11.3137i 0.577350 0.816497i
\(193\) 10.0000i 0.719816i −0.932988 0.359908i \(-0.882808\pi\)
0.932988 0.359908i \(-0.117192\pi\)
\(194\) −9.89949 −0.710742
\(195\) 2.24264 3.17157i 0.160599 0.227121i
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −1.41421 + 14.0000i −0.100504 + 0.994937i
\(199\) 7.51472 0.532704 0.266352 0.963876i \(-0.414182\pi\)
0.266352 + 0.963876i \(0.414182\pi\)
\(200\) 2.82843 0.200000
\(201\) −12.4853 + 17.6569i −0.880644 + 1.24542i
\(202\) 3.51472 0.247295
\(203\) 5.82843i 0.409075i
\(204\) 0 0
\(205\) 4.58579i 0.320285i
\(206\) −0.727922 −0.0507167
\(207\) −3.51472 + 1.24264i −0.244290 + 0.0863695i
\(208\) 8.97056i 0.621997i
\(209\) −4.58579 + 9.72792i −0.317205 + 0.672894i
\(210\) −1.41421 + 2.00000i −0.0975900 + 0.138013i
\(211\) 8.00000i 0.550743i 0.961338 + 0.275371i \(0.0888008\pi\)
−0.961338 + 0.275371i \(0.911199\pi\)
\(212\) 0 0
\(213\) −2.48528 1.75736i −0.170289 0.120412i
\(214\) 10.4853 0.716759
\(215\) −3.24264 −0.221146
\(216\) 14.1421 + 4.00000i 0.962250 + 0.272166i
\(217\) 8.24264i 0.559547i
\(218\) 5.31371i 0.359890i
\(219\) −9.17157 6.48528i −0.619757 0.438235i
\(220\) 0 0
\(221\) 13.0711i 0.879255i
\(222\) 11.6569 16.4853i 0.782357 1.10642i
\(223\) 17.0000 1.13840 0.569202 0.822198i \(-0.307252\pi\)
0.569202 + 0.822198i \(0.307252\pi\)
\(224\) 0 0
\(225\) 1.00000 + 2.82843i 0.0666667 + 0.188562i
\(226\) 26.7279i 1.77791i
\(227\) −6.17157 −0.409622 −0.204811 0.978802i \(-0.565658\pi\)
−0.204811 + 0.978802i \(0.565658\pi\)
\(228\) 0 0
\(229\) 18.7279 1.23758 0.618788 0.785558i \(-0.287624\pi\)
0.618788 + 0.785558i \(0.287624\pi\)
\(230\) −1.75736 −0.115877
\(231\) 2.82843 + 5.00000i 0.186097 + 0.328976i
\(232\) −16.4853 −1.08231
\(233\) −9.55635 −0.626057 −0.313029 0.949744i \(-0.601344\pi\)
−0.313029 + 0.949744i \(0.601344\pi\)
\(234\) 8.97056 3.17157i 0.586424 0.207332i
\(235\) −1.07107 −0.0698688
\(236\) 0 0
\(237\) −8.82843 6.24264i −0.573468 0.405503i
\(238\) 8.24264i 0.534291i
\(239\) −8.65685 −0.559965 −0.279983 0.960005i \(-0.590329\pi\)
−0.279983 + 0.960005i \(0.590329\pi\)
\(240\) 5.65685 + 4.00000i 0.365148 + 0.258199i
\(241\) 9.51472i 0.612897i −0.951887 0.306448i \(-0.900859\pi\)
0.951887 0.306448i \(-0.0991407\pi\)
\(242\) 9.89949 + 12.0000i 0.636364 + 0.771389i
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 0 0
\(245\) 1.00000i 0.0638877i
\(246\) −6.48528 + 9.17157i −0.413486 + 0.584758i
\(247\) 7.27208 0.462711
\(248\) −23.3137 −1.48042
\(249\) 17.1421 24.2426i 1.08634 1.53631i
\(250\) 1.41421i 0.0894427i
\(251\) 28.9706i 1.82861i 0.405031 + 0.914303i \(0.367261\pi\)
−0.405031 + 0.914303i \(0.632739\pi\)
\(252\) 0 0
\(253\) −1.75736 + 3.72792i −0.110484 + 0.234372i
\(254\) 18.7279i 1.17509i
\(255\) 8.24264 + 5.82843i 0.516174 + 0.364990i
\(256\) 0 0
\(257\) 22.2426i 1.38746i 0.720236 + 0.693729i \(0.244033\pi\)
−0.720236 + 0.693729i \(0.755967\pi\)
\(258\) −6.48528 4.58579i −0.403756 0.285499i
\(259\) 8.24264i 0.512173i
\(260\) 0 0
\(261\) −5.82843 16.4853i −0.360771 1.02041i
\(262\) −27.4558 −1.69623
\(263\) −20.8284 −1.28434 −0.642168 0.766564i \(-0.721965\pi\)
−0.642168 + 0.766564i \(0.721965\pi\)
\(264\) 14.1421 8.00000i 0.870388 0.492366i
\(265\) −4.41421 −0.271163
\(266\) −4.58579 −0.281173
\(267\) −23.2132 16.4142i −1.42062 1.00453i
\(268\) 0 0
\(269\) 0.556349i 0.0339212i −0.999856 0.0169606i \(-0.994601\pi\)
0.999856 0.0169606i \(-0.00539899\pi\)
\(270\) −2.00000 + 7.07107i −0.121716 + 0.430331i
\(271\) 14.7574i 0.896446i −0.893922 0.448223i \(-0.852057\pi\)
0.893922 0.448223i \(-0.147943\pi\)
\(272\) 23.3137 1.41360
\(273\) 2.24264 3.17157i 0.135731 0.191952i
\(274\) 20.4853i 1.23756i
\(275\) 3.00000 + 1.41421i 0.180907 + 0.0852803i
\(276\) 0 0
\(277\) 8.48528i 0.509831i 0.966963 + 0.254916i \(0.0820477\pi\)
−0.966963 + 0.254916i \(0.917952\pi\)
\(278\) 17.6569i 1.05899i
\(279\) −8.24264 23.3137i −0.493474 1.39576i
\(280\) 2.82843 0.169031
\(281\) −5.31371 −0.316989 −0.158495 0.987360i \(-0.550664\pi\)
−0.158495 + 0.987360i \(0.550664\pi\)
\(282\) −2.14214 1.51472i −0.127562 0.0902002i
\(283\) 29.2132i 1.73654i −0.496088 0.868272i \(-0.665231\pi\)
0.496088 0.868272i \(-0.334769\pi\)
\(284\) 0 0
\(285\) −3.24264 + 4.58579i −0.192077 + 0.271639i
\(286\) 4.48528 9.51472i 0.265220 0.562617i
\(287\) 4.58579i 0.270690i
\(288\) 0 0
\(289\) 16.9706 0.998268
\(290\) 8.24264i 0.484025i
\(291\) −7.00000 + 9.89949i −0.410347 + 0.580319i
\(292\) 0 0
\(293\) 3.34315 0.195309 0.0976543 0.995220i \(-0.468866\pi\)
0.0976543 + 0.995220i \(0.468866\pi\)
\(294\) −1.41421 + 2.00000i −0.0824786 + 0.116642i
\(295\) −12.8995 −0.751038
\(296\) −23.3137 −1.35508
\(297\) 13.0000 + 11.3137i 0.754337 + 0.656488i
\(298\) 0 0
\(299\) 2.78680 0.161165
\(300\) 0 0
\(301\) −3.24264 −0.186903
\(302\) 14.1421i 0.813788i
\(303\) 2.48528 3.51472i 0.142776 0.201915i
\(304\) 12.9706i 0.743913i
\(305\) 9.24264 0.529232
\(306\) 8.24264 + 23.3137i 0.471200 + 1.33276i
\(307\) 20.4853i 1.16916i −0.811337 0.584578i \(-0.801260\pi\)
0.811337 0.584578i \(-0.198740\pi\)
\(308\) 0 0
\(309\) −0.514719 + 0.727922i −0.0292813 + 0.0414100i
\(310\) 11.6569i 0.662065i
\(311\) 14.8284i 0.840843i −0.907329 0.420421i \(-0.861882\pi\)
0.907329 0.420421i \(-0.138118\pi\)
\(312\) −8.97056 6.34315i −0.507858 0.359110i
\(313\) −26.4558 −1.49537 −0.747686 0.664052i \(-0.768835\pi\)
−0.747686 + 0.664052i \(0.768835\pi\)
\(314\) 15.5563 0.877896
\(315\) 1.00000 + 2.82843i 0.0563436 + 0.159364i
\(316\) 0 0
\(317\) 32.8284i 1.84383i 0.387394 + 0.921914i \(0.373375\pi\)
−0.387394 + 0.921914i \(0.626625\pi\)
\(318\) −8.82843 6.24264i −0.495074 0.350070i
\(319\) −17.4853 8.24264i −0.978988 0.461499i
\(320\) 8.00000i 0.447214i
\(321\) 7.41421 10.4853i 0.413821 0.585231i
\(322\) −1.75736 −0.0979338
\(323\) 18.8995i 1.05160i
\(324\) 0 0
\(325\) 2.24264i 0.124399i
\(326\) 3.17157 0.175657
\(327\) 5.31371 + 3.75736i 0.293849 + 0.207782i
\(328\) 12.9706 0.716180
\(329\) −1.07107 −0.0590499
\(330\) 4.00000 + 7.07107i 0.220193 + 0.389249i
\(331\) 2.51472 0.138221 0.0691107 0.997609i \(-0.477984\pi\)
0.0691107 + 0.997609i \(0.477984\pi\)
\(332\) 0 0
\(333\) −8.24264 23.3137i −0.451694 1.27758i
\(334\) 28.4853 1.55865
\(335\) 12.4853i 0.682144i
\(336\) 5.65685 + 4.00000i 0.308607 + 0.218218i
\(337\) 27.2426i 1.48400i 0.670399 + 0.742001i \(0.266123\pi\)
−0.670399 + 0.742001i \(0.733877\pi\)
\(338\) 11.2721 0.613120
\(339\) 26.7279 + 18.8995i 1.45166 + 1.02648i
\(340\) 0 0
\(341\) −24.7279 11.6569i −1.33909 0.631254i
\(342\) −12.9706 + 4.58579i −0.701368 + 0.247971i
\(343\) 1.00000i 0.0539949i
\(344\) 9.17157i 0.494498i
\(345\) −1.24264 + 1.75736i −0.0669015 + 0.0946130i
\(346\) −4.00000 −0.215041
\(347\) 26.8284 1.44023 0.720113 0.693857i \(-0.244090\pi\)
0.720113 + 0.693857i \(0.244090\pi\)
\(348\) 0 0
\(349\) 12.7574i 0.682886i −0.939903 0.341443i \(-0.889084\pi\)
0.939903 0.341443i \(-0.110916\pi\)
\(350\) 1.41421i 0.0755929i
\(351\) 3.17157 11.2132i 0.169286 0.598517i
\(352\) 0 0
\(353\) 18.0000i 0.958043i −0.877803 0.479022i \(-0.840992\pi\)
0.877803 0.479022i \(-0.159008\pi\)
\(354\) −25.7990 18.2426i −1.37120 0.969585i
\(355\) −1.75736 −0.0932709
\(356\) 0 0
\(357\) 8.24264 + 5.82843i 0.436247 + 0.308473i
\(358\) 18.9706i 1.00263i
\(359\) −13.6274 −0.719228 −0.359614 0.933101i \(-0.617092\pi\)
−0.359614 + 0.933101i \(0.617092\pi\)
\(360\) 8.00000 2.82843i 0.421637 0.149071i
\(361\) 8.48528 0.446594
\(362\) −15.5147 −0.815436
\(363\) 19.0000 1.41421i 0.997241 0.0742270i
\(364\) 0 0
\(365\) −6.48528 −0.339455
\(366\) 18.4853 + 13.0711i 0.966241 + 0.683236i
\(367\) 3.00000 0.156599 0.0782994 0.996930i \(-0.475051\pi\)
0.0782994 + 0.996930i \(0.475051\pi\)
\(368\) 4.97056i 0.259108i
\(369\) 4.58579 + 12.9706i 0.238727 + 0.675221i
\(370\) 11.6569i 0.606011i
\(371\) −4.41421 −0.229175
\(372\) 0 0
\(373\) 6.21320i 0.321707i −0.986978 0.160854i \(-0.948575\pi\)
0.986978 0.160854i \(-0.0514247\pi\)
\(374\) 24.7279 + 11.6569i 1.27865 + 0.602762i
\(375\) 1.41421 + 1.00000i 0.0730297 + 0.0516398i
\(376\) 3.02944i 0.156231i
\(377\) 13.0711i 0.673194i
\(378\) −2.00000 + 7.07107i −0.102869 + 0.363696i
\(379\) 18.4558 0.948013 0.474007 0.880521i \(-0.342807\pi\)
0.474007 + 0.880521i \(0.342807\pi\)
\(380\) 0 0
\(381\) 18.7279 + 13.2426i 0.959461 + 0.678441i
\(382\) 12.9706i 0.663632i
\(383\) 37.4142i 1.91178i 0.293730 + 0.955889i \(0.405103\pi\)
−0.293730 + 0.955889i \(0.594897\pi\)
\(384\) 11.3137 16.0000i 0.577350 0.816497i
\(385\) 3.00000 + 1.41421i 0.152894 + 0.0720750i
\(386\) 14.1421i 0.719816i
\(387\) −9.17157 + 3.24264i −0.466217 + 0.164833i
\(388\) 0 0
\(389\) 1.75736i 0.0891017i −0.999007 0.0445508i \(-0.985814\pi\)
0.999007 0.0445508i \(-0.0141857\pi\)
\(390\) 3.17157 4.48528i 0.160599 0.227121i
\(391\) 7.24264i 0.366276i
\(392\) 2.82843 0.142857
\(393\) −19.4142 + 27.4558i −0.979318 + 1.38496i
\(394\) 8.48528 0.427482
\(395\) −6.24264 −0.314101
\(396\) 0 0
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) 10.6274 0.532704
\(399\) −3.24264 + 4.58579i −0.162335 + 0.229576i
\(400\) 4.00000 0.200000
\(401\) 5.27208i 0.263275i −0.991298 0.131638i \(-0.957977\pi\)
0.991298 0.131638i \(-0.0420235\pi\)
\(402\) −17.6569 + 24.9706i −0.880644 + 1.24542i
\(403\) 18.4853i 0.920817i
\(404\) 0 0
\(405\) 5.65685 + 7.00000i 0.281091 + 0.347833i
\(406\) 8.24264i 0.409075i
\(407\) −24.7279 11.6569i −1.22572 0.577809i
\(408\) 16.4853 23.3137i 0.816143 1.15420i
\(409\) 18.4853i 0.914038i −0.889457 0.457019i \(-0.848917\pi\)
0.889457 0.457019i \(-0.151083\pi\)
\(410\) 6.48528i 0.320285i
\(411\) −20.4853 14.4853i −1.01046 0.714506i
\(412\) 0 0
\(413\) −12.8995 −0.634743
\(414\) −4.97056 + 1.75736i −0.244290 + 0.0863695i
\(415\) 17.1421i 0.841474i
\(416\) 0 0
\(417\) −17.6569 12.4853i −0.864660 0.611407i
\(418\) −6.48528 + 13.7574i −0.317205 + 0.672894i
\(419\) 25.5858i 1.24995i −0.780646 0.624974i \(-0.785110\pi\)
0.780646 0.624974i \(-0.214890\pi\)
\(420\) 0 0
\(421\) −21.4853 −1.04713 −0.523564 0.851986i \(-0.675398\pi\)
−0.523564 + 0.851986i \(0.675398\pi\)
\(422\) 11.3137i 0.550743i
\(423\) −3.02944 + 1.07107i −0.147296 + 0.0520771i
\(424\) 12.4853i 0.606339i
\(425\) 5.82843 0.282720
\(426\) −3.51472 2.48528i −0.170289 0.120412i
\(427\) 9.24264 0.447283
\(428\) 0 0
\(429\) −6.34315 11.2132i −0.306250 0.541379i
\(430\) −4.58579 −0.221146
\(431\) −23.6569 −1.13951 −0.569755 0.821814i \(-0.692962\pi\)
−0.569755 + 0.821814i \(0.692962\pi\)
\(432\) 20.0000 + 5.65685i 0.962250 + 0.272166i
\(433\) −12.0000 −0.576683 −0.288342 0.957528i \(-0.593104\pi\)
−0.288342 + 0.957528i \(0.593104\pi\)
\(434\) 11.6569i 0.559547i
\(435\) −8.24264 5.82843i −0.395204 0.279452i
\(436\) 0 0
\(437\) −4.02944 −0.192754
\(438\) −12.9706 9.17157i −0.619757 0.438235i
\(439\) 5.24264i 0.250218i 0.992143 + 0.125109i \(0.0399280\pi\)
−0.992143 + 0.125109i \(0.960072\pi\)
\(440\) 4.00000 8.48528i 0.190693 0.404520i
\(441\) 1.00000 + 2.82843i 0.0476190 + 0.134687i
\(442\) 18.4853i 0.879255i
\(443\) 11.3137i 0.537531i 0.963206 + 0.268765i \(0.0866156\pi\)
−0.963206 + 0.268765i \(0.913384\pi\)
\(444\) 0 0
\(445\) −16.4142 −0.778108
\(446\) 24.0416 1.13840
\(447\) 0 0
\(448\) 8.00000i 0.377964i
\(449\) 11.2721i 0.531962i 0.963978 + 0.265981i \(0.0856959\pi\)
−0.963978 + 0.265981i \(0.914304\pi\)
\(450\) 1.41421 + 4.00000i 0.0666667 + 0.188562i
\(451\) 13.7574 + 6.48528i 0.647809 + 0.305380i
\(452\) 0 0
\(453\) 14.1421 + 10.0000i 0.664455 + 0.469841i
\(454\) −8.72792 −0.409622
\(455\) 2.24264i 0.105137i
\(456\) 12.9706 + 9.17157i 0.607402 + 0.429498i
\(457\) 32.2132i 1.50687i 0.657522 + 0.753435i \(0.271605\pi\)
−0.657522 + 0.753435i \(0.728395\pi\)
\(458\) 26.4853 1.23758
\(459\) 29.1421 + 8.24264i 1.36024 + 0.384734i
\(460\) 0 0
\(461\) 18.3431 0.854325 0.427163 0.904175i \(-0.359513\pi\)
0.427163 + 0.904175i \(0.359513\pi\)
\(462\) 4.00000 + 7.07107i 0.186097 + 0.328976i
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) −23.3137 −1.08231
\(465\) −11.6569 8.24264i −0.540574 0.382243i
\(466\) −13.5147 −0.626057
\(467\) 11.6569i 0.539415i 0.962942 + 0.269707i \(0.0869270\pi\)
−0.962942 + 0.269707i \(0.913073\pi\)
\(468\) 0 0
\(469\) 12.4853i 0.576517i
\(470\) −1.51472 −0.0698688
\(471\) 11.0000 15.5563i 0.506853 0.716799i
\(472\) 36.4853i 1.67937i
\(473\) −4.58579 + 9.72792i −0.210855 + 0.447290i
\(474\) −12.4853 8.82843i −0.573468 0.405503i
\(475\) 3.24264i 0.148783i
\(476\) 0 0
\(477\) −12.4853 + 4.41421i −0.571662 + 0.202113i
\(478\) −12.2426 −0.559965
\(479\) 15.2132 0.695109 0.347555 0.937660i \(-0.387012\pi\)
0.347555 + 0.937660i \(0.387012\pi\)
\(480\) 0 0
\(481\) 18.4853i 0.842856i
\(482\) 13.4558i 0.612897i
\(483\) −1.24264 + 1.75736i −0.0565421 + 0.0799626i
\(484\) 0 0
\(485\) 7.00000i 0.317854i
\(486\) 1.41421 + 22.0000i 0.0641500 + 0.997940i
\(487\) 36.9706 1.67530 0.837648 0.546210i \(-0.183930\pi\)
0.837648 + 0.546210i \(0.183930\pi\)
\(488\) 26.1421i 1.18340i
\(489\) 2.24264 3.17157i 0.101416 0.143423i
\(490\) 1.41421i 0.0638877i
\(491\) 26.6569 1.20301 0.601503 0.798870i \(-0.294569\pi\)
0.601503 + 0.798870i \(0.294569\pi\)
\(492\) 0 0
\(493\) −33.9706 −1.52996
\(494\) 10.2843 0.462711
\(495\) 9.89949 + 1.00000i 0.444949 + 0.0449467i
\(496\) −32.9706 −1.48042
\(497\) −1.75736 −0.0788283
\(498\) 24.2426 34.2843i 1.08634 1.53631i
\(499\) 5.48528 0.245555 0.122777 0.992434i \(-0.460820\pi\)
0.122777 + 0.992434i \(0.460820\pi\)
\(500\) 0 0
\(501\) 20.1421 28.4853i 0.899884 1.27263i
\(502\) 40.9706i 1.82861i
\(503\) −40.4558 −1.80384 −0.901918 0.431906i \(-0.857841\pi\)
−0.901918 + 0.431906i \(0.857841\pi\)
\(504\) 8.00000 2.82843i 0.356348 0.125988i
\(505\) 2.48528i 0.110594i
\(506\) −2.48528 + 5.27208i −0.110484 + 0.234372i
\(507\) 7.97056 11.2721i 0.353985 0.500611i
\(508\) 0 0
\(509\) 37.2426i 1.65075i −0.564584 0.825376i \(-0.690963\pi\)
0.564584 0.825376i \(-0.309037\pi\)
\(510\) 11.6569 + 8.24264i 0.516174 + 0.364990i
\(511\) −6.48528 −0.286892
\(512\) −22.6274 −1.00000
\(513\) −4.58579 + 16.2132i −0.202467 + 0.715830i
\(514\) 31.4558i 1.38746i
\(515\) 0.514719i 0.0226812i
\(516\) 0 0
\(517\) −1.51472 + 3.21320i −0.0666172 + 0.141317i
\(518\) 11.6569i 0.512173i
\(519\) −2.82843 + 4.00000i −0.124154 + 0.175581i
\(520\) −6.34315 −0.278165
\(521\) 10.4142i 0.456255i −0.973631 0.228127i \(-0.926740\pi\)
0.973631 0.228127i \(-0.0732603\pi\)
\(522\) −8.24264 23.3137i −0.360771 1.02041i
\(523\) 6.97056i 0.304801i −0.988319 0.152401i \(-0.951300\pi\)
0.988319 0.152401i \(-0.0487004\pi\)
\(524\) 0 0
\(525\) 1.41421 + 1.00000i 0.0617213 + 0.0436436i
\(526\) −29.4558 −1.28434
\(527\) −48.0416 −2.09273
\(528\) 20.0000 11.3137i 0.870388 0.492366i
\(529\) 21.4558 0.932863
\(530\) −6.24264 −0.271163
\(531\) −36.4853 + 12.8995i −1.58333 + 0.559790i
\(532\) 0 0
\(533\) 10.2843i 0.445461i
\(534\) −32.8284 23.2132i −1.42062 1.00453i
\(535\) 7.41421i 0.320544i
\(536\) 35.3137 1.52532
\(537\) 18.9706 + 13.4142i 0.818640 + 0.578866i
\(538\) 0.786797i 0.0339212i
\(539\) 3.00000 + 1.41421i 0.129219 + 0.0609145i
\(540\) 0 0
\(541\) 10.7279i 0.461229i 0.973045 + 0.230615i \(0.0740737\pi\)
−0.973045 + 0.230615i \(0.925926\pi\)
\(542\) 20.8701i 0.896446i
\(543\) −10.9706 + 15.5147i −0.470792 + 0.665800i
\(544\) 0 0
\(545\) 3.75736 0.160948
\(546\) 3.17157 4.48528i 0.135731 0.191952i
\(547\) 23.2426i 0.993784i −0.867813 0.496892i \(-0.834475\pi\)
0.867813 0.496892i \(-0.165525\pi\)
\(548\) 0 0
\(549\) 26.1421 9.24264i 1.11572 0.394466i
\(550\) 4.24264 + 2.00000i 0.180907 + 0.0852803i
\(551\) 18.8995i 0.805146i
\(552\) 4.97056 + 3.51472i 0.211561 + 0.149596i
\(553\) −6.24264 −0.265464
\(554\) 12.0000i 0.509831i
\(555\) −11.6569 8.24264i −0.494806 0.349881i
\(556\) 0 0
\(557\) −27.1716 −1.15130 −0.575648 0.817697i \(-0.695250\pi\)
−0.575648 + 0.817697i \(0.695250\pi\)
\(558\) −11.6569 32.9706i −0.493474 1.39576i
\(559\) 7.27208 0.307576
\(560\) 4.00000 0.169031
\(561\) 29.1421 16.4853i 1.23038 0.696009i
\(562\) −7.51472 −0.316989
\(563\) 25.1127 1.05837 0.529187 0.848505i \(-0.322497\pi\)
0.529187 + 0.848505i \(0.322497\pi\)
\(564\) 0 0
\(565\) 18.8995 0.795108
\(566\) 41.3137i 1.73654i
\(567\) 5.65685 + 7.00000i 0.237566 + 0.293972i
\(568\) 4.97056i 0.208560i
\(569\) 17.1421 0.718636 0.359318 0.933215i \(-0.383009\pi\)
0.359318 + 0.933215i \(0.383009\pi\)
\(570\) −4.58579 + 6.48528i −0.192077 + 0.271639i
\(571\) 40.1838i 1.68164i −0.541316 0.840819i \(-0.682074\pi\)
0.541316 0.840819i \(-0.317926\pi\)
\(572\) 0 0
\(573\) −12.9706 9.17157i −0.541853 0.383148i
\(574\) 6.48528i 0.270690i
\(575\) 1.24264i 0.0518217i
\(576\) −8.00000 22.6274i −0.333333 0.942809i
\(577\) −21.4558 −0.893218 −0.446609 0.894729i \(-0.647369\pi\)
−0.446609 + 0.894729i \(0.647369\pi\)
\(578\) 24.0000 0.998268
\(579\) −14.1421 10.0000i −0.587727 0.415586i
\(580\) 0 0
\(581\) 17.1421i 0.711176i
\(582\) −9.89949 + 14.0000i −0.410347 + 0.580319i
\(583\) −6.24264 + 13.2426i −0.258544 + 0.548454i
\(584\) 18.3431i 0.759045i
\(585\) −2.24264 6.34315i −0.0927218 0.262257i
\(586\) 4.72792 0.195309
\(587\) 36.0416i 1.48760i 0.668404 + 0.743799i \(0.266978\pi\)
−0.668404 + 0.743799i \(0.733022\pi\)
\(588\) 0 0
\(589\) 26.7279i 1.10130i
\(590\) −18.2426 −0.751038
\(591\) 6.00000 8.48528i 0.246807 0.349038i
\(592\) −32.9706 −1.35508
\(593\) −26.8284 −1.10171 −0.550856 0.834600i \(-0.685699\pi\)
−0.550856 + 0.834600i \(0.685699\pi\)
\(594\) 18.3848 + 16.0000i 0.754337 + 0.656488i
\(595\) 5.82843 0.238942
\(596\) 0 0
\(597\) 7.51472 10.6274i 0.307557 0.434951i
\(598\) 3.94113 0.161165
\(599\) 25.1127i 1.02608i −0.858366 0.513039i \(-0.828520\pi\)
0.858366 0.513039i \(-0.171480\pi\)
\(600\) 2.82843 4.00000i 0.115470 0.163299i
\(601\) 4.27208i 0.174262i −0.996197 0.0871308i \(-0.972230\pi\)
0.996197 0.0871308i \(-0.0277698\pi\)
\(602\) −4.58579 −0.186903
\(603\) 12.4853 + 35.3137i 0.508440 + 1.43809i
\(604\) 0 0
\(605\) 8.48528 7.00000i 0.344976 0.284590i
\(606\) 3.51472 4.97056i 0.142776 0.201915i
\(607\) 26.4853i 1.07500i −0.843262 0.537502i \(-0.819368\pi\)
0.843262 0.537502i \(-0.180632\pi\)
\(608\) 0 0
\(609\) −8.24264 5.82843i −0.334009 0.236180i
\(610\) 13.0711 0.529232
\(611\) 2.40202 0.0971753
\(612\) 0 0
\(613\) 18.4853i 0.746613i 0.927708 + 0.373307i \(0.121776\pi\)
−0.927708 + 0.373307i \(0.878224\pi\)
\(614\) 28.9706i 1.16916i
\(615\) 6.48528 + 4.58579i 0.261512 + 0.184917i
\(616\) 4.00000 8.48528i 0.161165 0.341882i
\(617\) 5.31371i 0.213922i 0.994263 + 0.106961i \(0.0341120\pi\)
−0.994263 + 0.106961i \(0.965888\pi\)
\(618\) −0.727922 + 1.02944i −0.0292813 + 0.0414100i
\(619\) 2.48528 0.0998919 0.0499459 0.998752i \(-0.484095\pi\)
0.0499459 + 0.998752i \(0.484095\pi\)
\(620\) 0 0
\(621\) −1.75736 + 6.21320i −0.0705204 + 0.249327i
\(622\) 20.9706i 0.840843i
\(623\) −16.4142 −0.657622
\(624\) −12.6863 8.97056i −0.507858 0.359110i
\(625\) 1.00000 0.0400000
\(626\) −37.4142 −1.49537
\(627\) 9.17157 + 16.2132i 0.366277 + 0.647493i
\(628\) 0 0
\(629\) −48.0416 −1.91555
\(630\) 1.41421 + 4.00000i 0.0563436 + 0.159364i
\(631\) 15.0000 0.597141 0.298570 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(632\) 17.6569i 0.702352i
\(633\) 11.3137 + 8.00000i 0.449680 + 0.317971i
\(634\) 46.4264i 1.84383i
\(635\) 13.2426 0.525518
\(636\) 0 0
\(637\) 2.24264i 0.0888567i
\(638\) −24.7279 11.6569i −0.978988 0.461499i
\(639\) −4.97056 + 1.75736i −0.196632 + 0.0695201i
\(640\) 11.3137i 0.447214i
\(641\) 31.4558i 1.24243i −0.783640 0.621216i \(-0.786639\pi\)
0.783640 0.621216i \(-0.213361\pi\)
\(642\) 10.4853 14.8284i 0.413821 0.585231i
\(643\) −15.9706 −0.629818 −0.314909 0.949122i \(-0.601974\pi\)
−0.314909 + 0.949122i \(0.601974\pi\)
\(644\) 0 0
\(645\) −3.24264 + 4.58579i −0.127679 + 0.180565i
\(646\) 26.7279i 1.05160i
\(647\) 43.7990i 1.72192i −0.508676 0.860958i \(-0.669865\pi\)
0.508676 0.860958i \(-0.330135\pi\)
\(648\) 19.7990 16.0000i 0.777778 0.628539i
\(649\) −18.2426 + 38.6985i −0.716086 + 1.51905i
\(650\) 3.17157i 0.124399i
\(651\) −11.6569 8.24264i −0.456868 0.323055i
\(652\) 0 0
\(653\) 18.2132i 0.712738i −0.934345 0.356369i \(-0.884015\pi\)
0.934345 0.356369i \(-0.115985\pi\)
\(654\) 7.51472 + 5.31371i 0.293849 + 0.207782i
\(655\) 19.4142i 0.758576i
\(656\) 18.3431 0.716180
\(657\) −18.3431 + 6.48528i −0.715634 + 0.253015i
\(658\) −1.51472 −0.0590499
\(659\) 13.2843 0.517482 0.258741 0.965947i \(-0.416692\pi\)
0.258741 + 0.965947i \(0.416692\pi\)
\(660\) 0 0
\(661\) 17.2132 0.669516 0.334758 0.942304i \(-0.391345\pi\)
0.334758 + 0.942304i \(0.391345\pi\)
\(662\) 3.55635 0.138221
\(663\) −18.4853 13.0711i −0.717909 0.507638i
\(664\) −48.4853 −1.88159
\(665\) 3.24264i 0.125744i
\(666\) −11.6569 32.9706i −0.451694 1.27758i
\(667\) 7.24264i 0.280436i
\(668\) 0 0
\(669\) 17.0000 24.0416i 0.657258 0.929503i
\(670\) 17.6569i 0.682144i
\(671\) 13.0711 27.7279i 0.504603 1.07042i
\(672\) 0 0
\(673\) 10.2721i 0.395960i 0.980206 + 0.197980i \(0.0634380\pi\)
−0.980206 + 0.197980i \(0.936562\pi\)
\(674\) 38.5269i 1.48400i
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) 0 0
\(677\) 6.17157 0.237193 0.118596 0.992943i \(-0.462161\pi\)
0.118596 + 0.992943i \(0.462161\pi\)
\(678\) 37.7990 + 26.7279i 1.45166 + 1.02648i
\(679\) 7.00000i 0.268635i
\(680\) 16.4853i 0.632182i
\(681\) −6.17157 + 8.72792i −0.236495 + 0.334455i
\(682\) −34.9706 16.4853i −1.33909 0.631254i
\(683\) 11.6569i 0.446037i 0.974814 + 0.223019i \(0.0715911\pi\)
−0.974814 + 0.223019i \(0.928409\pi\)
\(684\) 0 0
\(685\) −14.4853 −0.553454
\(686\) 1.41421i 0.0539949i
\(687\) 18.7279 26.4853i 0.714515 1.01048i
\(688\) 12.9706i 0.494498i
\(689\) 9.89949 0.377141
\(690\) −1.75736 + 2.48528i −0.0669015 + 0.0946130i
\(691\) −9.02944 −0.343496 −0.171748 0.985141i \(-0.554941\pi\)
−0.171748 + 0.985141i \(0.554941\pi\)
\(692\) 0 0
\(693\) 9.89949 + 1.00000i 0.376051 + 0.0379869i
\(694\) 37.9411 1.44023
\(695\) −12.4853 −0.473594
\(696\) −16.4853 + 23.3137i −0.624873 + 0.883704i
\(697\) 26.7279 1.01239
\(698\) 18.0416i 0.682886i
\(699\) −9.55635 + 13.5147i −0.361454 + 0.511174i
\(700\) 0 0
\(701\) −37.9706 −1.43413 −0.717064 0.697007i \(-0.754515\pi\)
−0.717064 + 0.697007i \(0.754515\pi\)
\(702\) 4.48528 15.8579i 0.169286 0.598517i
\(703\) 26.7279i 1.00806i
\(704\) −24.0000 11.3137i −0.904534 0.426401i
\(705\) −1.07107 + 1.51472i −0.0403387 + 0.0570476i
\(706\) 25.4558i 0.958043i
\(707\) 2.48528i 0.0934686i
\(708\) 0 0
\(709\) −50.9411 −1.91313 −0.956567 0.291512i \(-0.905842\pi\)
−0.956567 + 0.291512i \(0.905842\pi\)
\(710\) −2.48528 −0.0932709
\(711\) −17.6569 + 6.24264i −0.662184 + 0.234117i
\(712\) 46.4264i 1.73990i
\(713\) 10.2426i 0.383590i
\(714\) 11.6569 + 8.24264i 0.436247 + 0.308473i
\(715\) −6.72792 3.17157i −0.251610 0.118610i
\(716\) 0 0
\(717\) −8.65685 + 12.2426i −0.323296 + 0.457210i
\(718\) −19.2721 −0.719228
\(719\) 47.5269i 1.77245i 0.463251 + 0.886227i \(0.346683\pi\)
−0.463251 + 0.886227i \(0.653317\pi\)
\(720\) 11.3137 4.00000i 0.421637 0.149071i
\(721\) 0.514719i 0.0191691i
\(722\) 12.0000 0.446594
\(723\) −13.4558 9.51472i −0.500428 0.353856i
\(724\) 0 0
\(725\) −5.82843 −0.216462
\(726\) 26.8701 2.00000i 0.997241 0.0742270i
\(727\) 20.4558 0.758665 0.379333 0.925260i \(-0.376154\pi\)
0.379333 + 0.925260i \(0.376154\pi\)
\(728\) −6.34315 −0.235093
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) −9.17157 −0.339455
\(731\) 18.8995i 0.699023i
\(732\) 0 0
\(733\) 21.4558i 0.792490i −0.918145 0.396245i \(-0.870313\pi\)
0.918145 0.396245i \(-0.129687\pi\)
\(734\) 4.24264 0.156599
\(735\) 1.41421 + 1.00000i 0.0521641 + 0.0368856i
\(736\) 0 0
\(737\) 37.4558 + 17.6569i 1.37970 + 0.650399i
\(738\) 6.48528 + 18.3431i 0.238727 + 0.675221i
\(739\) 30.4853i 1.12142i 0.828013 + 0.560710i \(0.189472\pi\)
−0.828013 + 0.560710i \(0.810528\pi\)
\(740\) 0 0
\(741\) 7.27208 10.2843i 0.267146 0.377802i
\(742\) −6.24264 −0.229175
\(743\) 46.6274 1.71059 0.855297 0.518138i \(-0.173375\pi\)
0.855297 + 0.518138i \(0.173375\pi\)
\(744\) −23.3137 + 32.9706i −0.854722 + 1.20876i
\(745\) 0 0
\(746\) 8.78680i 0.321707i
\(747\) −17.1421 48.4853i −0.627198 1.77398i
\(748\) 0 0
\(749\) 7.41421i 0.270909i
\(750\) 2.00000 + 1.41421i 0.0730297 + 0.0516398i
\(751\) 7.97056 0.290850 0.145425 0.989369i \(-0.453545\pi\)
0.145425 + 0.989369i \(0.453545\pi\)
\(752\) 4.28427i 0.156231i
\(753\) 40.9706 + 28.9706i 1.49305 + 1.05575i
\(754\) 18.4853i 0.673194i
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) −9.45584 −0.343679 −0.171839 0.985125i \(-0.554971\pi\)
−0.171839 + 0.985125i \(0.554971\pi\)
\(758\) 26.1005 0.948013
\(759\) 3.51472 + 6.21320i 0.127576 + 0.225525i
\(760\) 9.17157 0.332688
\(761\) 7.02944 0.254817 0.127408 0.991850i \(-0.459334\pi\)
0.127408 + 0.991850i \(0.459334\pi\)
\(762\) 26.4853 + 18.7279i 0.959461 + 0.678441i
\(763\) 3.75736 0.136026
\(764\) 0 0
\(765\) 16.4853 5.82843i 0.596027 0.210727i
\(766\) 52.9117i 1.91178i
\(767\) 28.9289 1.04456
\(768\) 0 0
\(769\) 51.6690i 1.86323i −0.363442 0.931617i \(-0.618399\pi\)
0.363442 0.931617i \(-0.381601\pi\)
\(770\) 4.24264 + 2.00000i 0.152894 + 0.0720750i
\(771\) 31.4558 + 22.2426i 1.13285 + 0.801049i
\(772\) 0 0
\(773\) 14.8284i 0.533341i 0.963788 + 0.266671i \(0.0859236\pi\)
−0.963788 + 0.266671i \(0.914076\pi\)
\(774\) −12.9706 + 4.58579i −0.466217 + 0.164833i
\(775\) −8.24264 −0.296084
\(776\) 19.7990 0.710742
\(777\) −11.6569 8.24264i −0.418187 0.295703i
\(778\) 2.48528i 0.0891017i
\(779\) 14.8701i 0.532775i
\(780\) 0 0
\(781\) −2.48528 + 5.27208i −0.0889304 + 0.188650i
\(782\) 10.2426i 0.366276i
\(783\) −29.1421 8.24264i −1.04145 0.294568i
\(784\) 4.00000 0.142857
\(785\) 11.0000i 0.392607i
\(786\) −27.4558 + 38.8284i −0.979318 + 1.38496i
\(787\) 15.4558i 0.550941i 0.961309 + 0.275471i \(0.0888337\pi\)
−0.961309 + 0.275471i \(0.911166\pi\)
\(788\) 0 0
\(789\) −20.8284 + 29.4558i −0.741512 + 1.04866i
\(790\) −8.82843 −0.314101
\(791\) 18.8995 0.671989
\(792\) 2.82843 28.0000i 0.100504 0.994937i
\(793\) −20.7279 −0.736070
\(794\) −48.0833 −1.70641
\(795\) −4.41421 + 6.24264i −0.156556 + 0.221404i
\(796\) 0