Properties

Label 1155.2.l.b.1121.2
Level 1155
Weight 2
Character 1155.1121
Analytic conductor 9.223
Analytic rank 0
Dimension 4
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 1121.2
Root \(-0.707107 - 0.707107i\) of \(x^{4} + 1\)
Character \(\chi\) \(=\) 1155.1121
Dual form 1155.2.l.b.1121.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000i q^{5} +(-1.41421 - 2.00000i) q^{6} -1.00000i q^{7} +2.82843 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000i q^{5} +(-1.41421 - 2.00000i) q^{6} -1.00000i q^{7} +2.82843 q^{8} +(-1.00000 + 2.82843i) q^{9} +1.41421i q^{10} +(-3.00000 + 1.41421i) q^{11} -6.24264i q^{13} +1.41421i q^{14} +(1.41421 - 1.00000i) q^{15} -4.00000 q^{16} -0.171573 q^{17} +(1.41421 - 4.00000i) q^{18} +5.24264i q^{19} +(1.41421 - 1.00000i) q^{21} +(4.24264 - 2.00000i) q^{22} +7.24264i q^{23} +(2.82843 + 4.00000i) q^{24} -1.00000 q^{25} +8.82843i q^{26} +(-5.00000 + 1.41421i) q^{27} +0.171573 q^{29} +(-2.00000 + 1.41421i) q^{30} -0.242641 q^{31} +(-5.00000 - 2.82843i) q^{33} +0.242641 q^{34} -1.00000 q^{35} -0.242641 q^{37} -7.41421i q^{38} +(8.82843 - 6.24264i) q^{39} -2.82843i q^{40} -7.41421 q^{41} +(-2.00000 + 1.41421i) q^{42} +5.24264i q^{43} +(2.82843 + 1.00000i) q^{45} -10.2426i q^{46} +13.0711i q^{47} +(-4.00000 - 5.65685i) q^{48} -1.00000 q^{49} +1.41421 q^{50} +(-0.171573 - 0.242641i) q^{51} -1.58579i q^{53} +(7.07107 - 2.00000i) q^{54} +(1.41421 + 3.00000i) q^{55} -2.82843i q^{56} +(-7.41421 + 5.24264i) q^{57} -0.242641 q^{58} +6.89949i q^{59} +0.757359i q^{61} +0.343146 q^{62} +(2.82843 + 1.00000i) q^{63} +8.00000 q^{64} -6.24264 q^{65} +(7.07107 + 4.00000i) q^{66} +4.48528 q^{67} +(-10.2426 + 7.24264i) q^{69} +1.41421 q^{70} -10.2426i q^{71} +(-2.82843 + 8.00000i) q^{72} +10.4853i q^{73} +0.343146 q^{74} +(-1.00000 - 1.41421i) q^{75} +(1.41421 + 3.00000i) q^{77} +(-12.4853 + 8.82843i) q^{78} +2.24264i q^{79} +4.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} +10.4853 q^{82} -11.1421 q^{83} +0.171573i q^{85} -7.41421i q^{86} +(0.171573 + 0.242641i) q^{87} +(-8.48528 + 4.00000i) q^{88} -13.5858i q^{89} +(-4.00000 - 1.41421i) q^{90} -6.24264 q^{91} +(-0.242641 - 0.343146i) q^{93} -18.4853i q^{94} +5.24264 q^{95} -7.00000 q^{97} +1.41421 q^{98} +(-1.00000 - 9.89949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} - 4q^{9} - 12q^{11} - 16q^{16} - 12q^{17} - 4q^{25} - 20q^{27} + 12q^{29} - 8q^{30} + 16q^{31} - 20q^{33} - 16q^{34} - 4q^{35} + 16q^{37} + 24q^{39} - 24q^{41} - 8q^{42} - 16q^{48} - 4q^{49} - 12q^{51} - 24q^{57} + 16q^{58} + 24q^{62} + 32q^{64} - 8q^{65} - 16q^{67} - 24q^{69} + 24q^{74} - 4q^{75} - 16q^{78} - 28q^{81} + 8q^{82} + 12q^{83} + 12q^{87} - 16q^{90} - 8q^{91} + 16q^{93} + 4q^{95} - 28q^{97} - 4q^{99} + O(q^{100}) \)

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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 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
\(13\) 6.24264i 1.73140i −0.500566 0.865699i \(-0.666875\pi\)
0.500566 0.865699i \(-0.333125\pi\)
\(14\) 1.41421i 0.377964i
\(15\) 1.41421 1.00000i 0.365148 0.258199i
\(16\) −4.00000 −1.00000
\(17\) −0.171573 −0.0416125 −0.0208063 0.999784i \(-0.506623\pi\)
−0.0208063 + 0.999784i \(0.506623\pi\)
\(18\) 1.41421 4.00000i 0.333333 0.942809i
\(19\) 5.24264i 1.20274i 0.798969 + 0.601372i \(0.205379\pi\)
−0.798969 + 0.601372i \(0.794621\pi\)
\(20\) 0 0
\(21\) 1.41421 1.00000i 0.308607 0.218218i
\(22\) 4.24264 2.00000i 0.904534 0.426401i
\(23\) 7.24264i 1.51019i 0.655613 + 0.755097i \(0.272410\pi\)
−0.655613 + 0.755097i \(0.727590\pi\)
\(24\) 2.82843 + 4.00000i 0.577350 + 0.816497i
\(25\) −1.00000 −0.200000
\(26\) 8.82843i 1.73140i
\(27\) −5.00000 + 1.41421i −0.962250 + 0.272166i
\(28\) 0 0
\(29\) 0.171573 0.0318603 0.0159301 0.999873i \(-0.494929\pi\)
0.0159301 + 0.999873i \(0.494929\pi\)
\(30\) −2.00000 + 1.41421i −0.365148 + 0.258199i
\(31\) −0.242641 −0.0435796 −0.0217898 0.999763i \(-0.506936\pi\)
−0.0217898 + 0.999763i \(0.506936\pi\)
\(32\) 0 0
\(33\) −5.00000 2.82843i −0.870388 0.492366i
\(34\) 0.242641 0.0416125
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −0.242641 −0.0398899 −0.0199449 0.999801i \(-0.506349\pi\)
−0.0199449 + 0.999801i \(0.506349\pi\)
\(38\) 7.41421i 1.20274i
\(39\) 8.82843 6.24264i 1.41368 0.999623i
\(40\) 2.82843i 0.447214i
\(41\) −7.41421 −1.15791 −0.578953 0.815361i \(-0.696538\pi\)
−0.578953 + 0.815361i \(0.696538\pi\)
\(42\) −2.00000 + 1.41421i −0.308607 + 0.218218i
\(43\) 5.24264i 0.799495i 0.916625 + 0.399748i \(0.130902\pi\)
−0.916625 + 0.399748i \(0.869098\pi\)
\(44\) 0 0
\(45\) 2.82843 + 1.00000i 0.421637 + 0.149071i
\(46\) 10.2426i 1.51019i
\(47\) 13.0711i 1.90661i 0.302007 + 0.953306i \(0.402343\pi\)
−0.302007 + 0.953306i \(0.597657\pi\)
\(48\) −4.00000 5.65685i −0.577350 0.816497i
\(49\) −1.00000 −0.142857
\(50\) 1.41421 0.200000
\(51\) −0.171573 0.242641i −0.0240250 0.0339765i
\(52\) 0 0
\(53\) 1.58579i 0.217825i −0.994051 0.108912i \(-0.965263\pi\)
0.994051 0.108912i \(-0.0347368\pi\)
\(54\) 7.07107 2.00000i 0.962250 0.272166i
\(55\) 1.41421 + 3.00000i 0.190693 + 0.404520i
\(56\) 2.82843i 0.377964i
\(57\) −7.41421 + 5.24264i −0.982037 + 0.694405i
\(58\) −0.242641 −0.0318603
\(59\) 6.89949i 0.898238i 0.893472 + 0.449119i \(0.148262\pi\)
−0.893472 + 0.449119i \(0.851738\pi\)
\(60\) 0 0
\(61\) 0.757359i 0.0969699i 0.998824 + 0.0484850i \(0.0154393\pi\)
−0.998824 + 0.0484850i \(0.984561\pi\)
\(62\) 0.343146 0.0435796
\(63\) 2.82843 + 1.00000i 0.356348 + 0.125988i
\(64\) 8.00000 1.00000
\(65\) −6.24264 −0.774304
\(66\) 7.07107 + 4.00000i 0.870388 + 0.492366i
\(67\) 4.48528 0.547964 0.273982 0.961735i \(-0.411659\pi\)
0.273982 + 0.961735i \(0.411659\pi\)
\(68\) 0 0
\(69\) −10.2426 + 7.24264i −1.23307 + 0.871911i
\(70\) 1.41421 0.169031
\(71\) 10.2426i 1.21558i −0.794099 0.607789i \(-0.792057\pi\)
0.794099 0.607789i \(-0.207943\pi\)
\(72\) −2.82843 + 8.00000i −0.333333 + 0.942809i
\(73\) 10.4853i 1.22721i 0.789613 + 0.613605i \(0.210281\pi\)
−0.789613 + 0.613605i \(0.789719\pi\)
\(74\) 0.343146 0.0398899
\(75\) −1.00000 1.41421i −0.115470 0.163299i
\(76\) 0 0
\(77\) 1.41421 + 3.00000i 0.161165 + 0.341882i
\(78\) −12.4853 + 8.82843i −1.41368 + 0.999623i
\(79\) 2.24264i 0.252317i 0.992010 + 0.126158i \(0.0402648\pi\)
−0.992010 + 0.126158i \(0.959735\pi\)
\(80\) 4.00000i 0.447214i
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 10.4853 1.15791
\(83\) −11.1421 −1.22301 −0.611504 0.791241i \(-0.709435\pi\)
−0.611504 + 0.791241i \(0.709435\pi\)
\(84\) 0 0
\(85\) 0.171573i 0.0186097i
\(86\) 7.41421i 0.799495i
\(87\) 0.171573 + 0.242641i 0.0183945 + 0.0260138i
\(88\) −8.48528 + 4.00000i −0.904534 + 0.426401i
\(89\) 13.5858i 1.44009i −0.693927 0.720045i \(-0.744121\pi\)
0.693927 0.720045i \(-0.255879\pi\)
\(90\) −4.00000 1.41421i −0.421637 0.149071i
\(91\) −6.24264 −0.654407
\(92\) 0 0
\(93\) −0.242641 0.343146i −0.0251607 0.0355826i
\(94\) 18.4853i 1.90661i
\(95\) 5.24264 0.537884
\(96\) 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
\(101\) −14.4853 −1.44134 −0.720670 0.693279i \(-0.756166\pi\)
−0.720670 + 0.693279i \(0.756166\pi\)
\(102\) 0.242641 + 0.343146i 0.0240250 + 0.0339765i
\(103\) −17.4853 −1.72288 −0.861438 0.507863i \(-0.830436\pi\)
−0.861438 + 0.507863i \(0.830436\pi\)
\(104\) 17.6569i 1.73140i
\(105\) −1.00000 1.41421i −0.0975900 0.138013i
\(106\) 2.24264i 0.217825i
\(107\) 4.58579 0.443325 0.221662 0.975123i \(-0.428852\pi\)
0.221662 + 0.975123i \(0.428852\pi\)
\(108\) 0 0
\(109\) 12.2426i 1.17263i 0.810082 + 0.586316i \(0.199422\pi\)
−0.810082 + 0.586316i \(0.800578\pi\)
\(110\) −2.00000 4.24264i −0.190693 0.404520i
\(111\) −0.242641 0.343146i −0.0230304 0.0325700i
\(112\) 4.00000i 0.377964i
\(113\) 0.899495i 0.0846174i −0.999105 0.0423087i \(-0.986529\pi\)
0.999105 0.0423087i \(-0.0134713\pi\)
\(114\) 10.4853 7.41421i 0.982037 0.694405i
\(115\) 7.24264 0.675380
\(116\) 0 0
\(117\) 17.6569 + 6.24264i 1.63238 + 0.577132i
\(118\) 9.75736i 0.898238i
\(119\) 0.171573i 0.0157281i
\(120\) 4.00000 2.82843i 0.365148 0.258199i
\(121\) 7.00000 8.48528i 0.636364 0.771389i
\(122\) 1.07107i 0.0969699i
\(123\) −7.41421 10.4853i −0.668517 0.945426i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) −4.00000 1.41421i −0.356348 0.125988i
\(127\) 4.75736i 0.422147i 0.977470 + 0.211074i \(0.0676960\pi\)
−0.977470 + 0.211074i \(0.932304\pi\)
\(128\) −11.3137 −1.00000
\(129\) −7.41421 + 5.24264i −0.652785 + 0.461589i
\(130\) 8.82843 0.774304
\(131\) −16.5858 −1.44911 −0.724553 0.689219i \(-0.757954\pi\)
−0.724553 + 0.689219i \(0.757954\pi\)
\(132\) 0 0
\(133\) 5.24264 0.454595
\(134\) −6.34315 −0.547964
\(135\) 1.41421 + 5.00000i 0.121716 + 0.430331i
\(136\) −0.485281 −0.0416125
\(137\) 2.48528i 0.212332i 0.994348 + 0.106166i \(0.0338575\pi\)
−0.994348 + 0.106166i \(0.966143\pi\)
\(138\) 14.4853 10.2426i 1.23307 0.871911i
\(139\) 4.48528i 0.380437i 0.981742 + 0.190218i \(0.0609196\pi\)
−0.981742 + 0.190218i \(0.939080\pi\)
\(140\) 0 0
\(141\) −18.4853 + 13.0711i −1.55674 + 1.10078i
\(142\) 14.4853i 1.21558i
\(143\) 8.82843 + 18.7279i 0.738270 + 1.56611i
\(144\) 4.00000 11.3137i 0.333333 0.942809i
\(145\) 0.171573i 0.0142484i
\(146\) 14.8284i 1.22721i
\(147\) −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 \(0.866612\pi\)
\(152\) 14.8284i 1.20274i
\(153\) 0.171573 0.485281i 0.0138708 0.0392327i
\(154\) −2.00000 4.24264i −0.161165 0.341882i
\(155\) 0.242641i 0.0194894i
\(156\) 0 0
\(157\) 11.0000 0.877896 0.438948 0.898513i \(-0.355351\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) 3.17157i 0.252317i
\(159\) 2.24264 1.58579i 0.177853 0.125761i
\(160\) 0 0
\(161\) 7.24264 0.570800
\(162\) 9.89949 + 8.00000i 0.777778 + 0.628539i
\(163\) −6.24264 −0.488961 −0.244481 0.969654i \(-0.578617\pi\)
−0.244481 + 0.969654i \(0.578617\pi\)
\(164\) 0 0
\(165\) −2.82843 + 5.00000i −0.220193 + 0.389249i
\(166\) 15.7574 1.22301
\(167\) −8.14214 −0.630057 −0.315029 0.949082i \(-0.602014\pi\)
−0.315029 + 0.949082i \(0.602014\pi\)
\(168\) 4.00000 2.82843i 0.308607 0.218218i
\(169\) −25.9706 −1.99774
\(170\) 0.242641i 0.0186097i
\(171\) −14.8284 5.24264i −1.13396 0.400915i
\(172\) 0 0
\(173\) 2.82843 0.215041 0.107521 0.994203i \(-0.465709\pi\)
0.107521 + 0.994203i \(0.465709\pi\)
\(174\) −0.242641 0.343146i −0.0183945 0.0260138i
\(175\) 1.00000i 0.0755929i
\(176\) 12.0000 5.65685i 0.904534 0.426401i
\(177\) −9.75736 + 6.89949i −0.733408 + 0.518598i
\(178\) 19.2132i 1.44009i
\(179\) 10.5858i 0.791219i 0.918419 + 0.395609i \(0.129467\pi\)
−0.918419 + 0.395609i \(0.870533\pi\)
\(180\) 0 0
\(181\) 22.9706 1.70739 0.853694 0.520775i \(-0.174357\pi\)
0.853694 + 0.520775i \(0.174357\pi\)
\(182\) 8.82843 0.654407
\(183\) −1.07107 + 0.757359i −0.0791756 + 0.0559856i
\(184\) 20.4853i 1.51019i
\(185\) 0.242641i 0.0178393i
\(186\) 0.343146 + 0.485281i 0.0251607 + 0.0355826i
\(187\) 0.514719 0.242641i 0.0376400 0.0177436i
\(188\) 0 0
\(189\) 1.41421 + 5.00000i 0.102869 + 0.363696i
\(190\) −7.41421 −0.537884
\(191\) 14.8284i 1.07295i −0.843917 0.536474i \(-0.819756\pi\)
0.843917 0.536474i \(-0.180244\pi\)
\(192\) 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
\(195\) −6.24264 8.82843i −0.447045 0.632217i
\(196\) 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
\(199\) 24.4853 1.73572 0.867858 0.496813i \(-0.165496\pi\)
0.867858 + 0.496813i \(0.165496\pi\)
\(200\) −2.82843 −0.200000
\(201\) 4.48528 + 6.34315i 0.316367 + 0.447411i
\(202\) 20.4853 1.44134
\(203\) 0.171573i 0.0120421i
\(204\) 0 0
\(205\) 7.41421i 0.517831i
\(206\) 24.7279 1.72288
\(207\) −20.4853 7.24264i −1.42383 0.503398i
\(208\) 24.9706i 1.73140i
\(209\) −7.41421 15.7279i −0.512852 1.08792i
\(210\) 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
\(213\) 14.4853 10.2426i 0.992515 0.701814i
\(214\) −6.48528 −0.443325
\(215\) 5.24264 0.357545
\(216\) −14.1421 + 4.00000i −0.962250 + 0.272166i
\(217\) 0.242641i 0.0164715i
\(218\) 17.3137i 1.17263i
\(219\) −14.8284 + 10.4853i −1.00201 + 0.708530i
\(220\) 0 0
\(221\) 1.07107i 0.0720478i
\(222\) 0.343146 + 0.485281i 0.0230304 + 0.0325700i
\(223\) 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
\(226\) 1.27208i 0.0846174i
\(227\) −11.8284 −0.785080 −0.392540 0.919735i \(-0.628404\pi\)
−0.392540 + 0.919735i \(0.628404\pi\)
\(228\) 0 0
\(229\) −6.72792 −0.444594 −0.222297 0.974979i \(-0.571355\pi\)
−0.222297 + 0.974979i \(0.571355\pi\)
\(230\) −10.2426 −0.675380
\(231\) −2.82843 + 5.00000i −0.186097 + 0.328976i
\(232\) 0.485281 0.0318603
\(233\) 21.5563 1.41220 0.706102 0.708110i \(-0.250452\pi\)
0.706102 + 0.708110i \(0.250452\pi\)
\(234\) −24.9706 8.82843i −1.63238 0.577132i
\(235\) 13.0711 0.852662
\(236\) 0 0
\(237\) −3.17157 + 2.24264i −0.206016 + 0.145675i
\(238\) 0.242641i 0.0157281i
\(239\) 2.65685 0.171858 0.0859288 0.996301i \(-0.472614\pi\)
0.0859288 + 0.996301i \(0.472614\pi\)
\(240\) −5.65685 + 4.00000i −0.365148 + 0.258199i
\(241\) 26.4853i 1.70607i −0.521856 0.853033i \(-0.674760\pi\)
0.521856 0.853033i \(-0.325240\pi\)
\(242\) −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
\(246\) 10.4853 + 14.8284i 0.668517 + 0.945426i
\(247\) 32.7279 2.08243
\(248\) −0.686292 −0.0435796
\(249\) −11.1421 15.7574i −0.706104 0.998582i
\(250\) 1.41421i 0.0894427i
\(251\) 4.97056i 0.313739i −0.987619 0.156870i \(-0.949860\pi\)
0.987619 0.156870i \(-0.0501402\pi\)
\(252\) 0 0
\(253\) −10.2426 21.7279i −0.643949 1.36602i
\(254\) 6.72792i 0.422147i
\(255\) −0.242641 + 0.171573i −0.0151947 + 0.0107443i
\(256\) 0 0
\(257\) 13.7574i 0.858160i 0.903266 + 0.429080i \(0.141162\pi\)
−0.903266 + 0.429080i \(0.858838\pi\)
\(258\) 10.4853 7.41421i 0.652785 0.461589i
\(259\) 0.242641i 0.0150770i
\(260\) 0 0
\(261\) −0.171573 + 0.485281i −0.0106201 + 0.0300382i
\(262\) 23.4558 1.44911
\(263\) −15.1716 −0.935519 −0.467760 0.883856i \(-0.654939\pi\)
−0.467760 + 0.883856i \(0.654939\pi\)
\(264\) −14.1421 8.00000i −0.870388 0.492366i
\(265\) −1.58579 −0.0974141
\(266\) −7.41421 −0.454595
\(267\) 19.2132 13.5858i 1.17583 0.831437i
\(268\) 0 0
\(269\) 30.5563i 1.86305i 0.363673 + 0.931527i \(0.381523\pi\)
−0.363673 + 0.931527i \(0.618477\pi\)
\(270\) −2.00000 7.07107i −0.121716 0.430331i
\(271\) 23.2426i 1.41189i −0.708267 0.705945i \(-0.750523\pi\)
0.708267 0.705945i \(-0.249477\pi\)
\(272\) 0.686292 0.0416125
\(273\) −6.24264 8.82843i −0.377822 0.534321i
\(274\) 3.51472i 0.212332i
\(275\) 3.00000 1.41421i 0.180907 0.0852803i
\(276\) 0 0
\(277\) 8.48528i 0.509831i −0.966963 0.254916i \(-0.917952\pi\)
0.966963 0.254916i \(-0.0820477\pi\)
\(278\) 6.34315i 0.380437i
\(279\) 0.242641 0.686292i 0.0145265 0.0410872i
\(280\) −2.82843 −0.169031
\(281\) 17.3137 1.03285 0.516425 0.856333i \(-0.327263\pi\)
0.516425 + 0.856333i \(0.327263\pi\)
\(282\) 26.1421 18.4853i 1.55674 1.10078i
\(283\) 13.2132i 0.785443i 0.919657 + 0.392722i \(0.128466\pi\)
−0.919657 + 0.392722i \(0.871534\pi\)
\(284\) 0 0
\(285\) 5.24264 + 7.41421i 0.310547 + 0.439180i
\(286\) −12.4853 26.4853i −0.738270 1.56611i
\(287\) 7.41421i 0.437647i
\(288\) 0 0
\(289\) −16.9706 −0.998268
\(290\) 0.242641i 0.0142484i
\(291\) −7.00000 9.89949i −0.410347 0.580319i
\(292\) 0 0
\(293\) 14.6569 0.856263 0.428131 0.903717i \(-0.359172\pi\)
0.428131 + 0.903717i \(0.359172\pi\)
\(294\) 1.41421 + 2.00000i 0.0824786 + 0.116642i
\(295\) 6.89949 0.401704
\(296\) −0.686292 −0.0398899
\(297\) 13.0000 11.3137i 0.754337 0.656488i
\(298\) 0 0
\(299\) 45.2132 2.61475
\(300\) 0 0
\(301\) 5.24264 0.302181
\(302\) 14.1421i 0.813788i
\(303\) −14.4853 20.4853i −0.832158 1.17685i
\(304\) 20.9706i 1.20274i
\(305\) 0.757359 0.0433663
\(306\) −0.242641 + 0.686292i −0.0138708 + 0.0392327i
\(307\) 3.51472i 0.200596i −0.994957 0.100298i \(-0.968020\pi\)
0.994957 0.100298i \(-0.0319796\pi\)
\(308\) 0 0
\(309\) −17.4853 24.7279i −0.994703 1.40672i
\(310\) 0.343146i 0.0194894i
\(311\) 9.17157i 0.520072i −0.965599 0.260036i \(-0.916266\pi\)
0.965599 0.260036i \(-0.0837345\pi\)
\(312\) 24.9706 17.6569i 1.41368 0.999623i
\(313\) 24.4558 1.38233 0.691163 0.722699i \(-0.257099\pi\)
0.691163 + 0.722699i \(0.257099\pi\)
\(314\) −15.5563 −0.877896
\(315\) 1.00000 2.82843i 0.0563436 0.159364i
\(316\) 0 0
\(317\) 27.1716i 1.52611i 0.646335 + 0.763054i \(0.276301\pi\)
−0.646335 + 0.763054i \(0.723699\pi\)
\(318\) −3.17157 + 2.24264i −0.177853 + 0.125761i
\(319\) −0.514719 + 0.242641i −0.0288187 + 0.0135853i
\(320\) 8.00000i 0.447214i
\(321\) 4.58579 + 6.48528i 0.255954 + 0.361973i
\(322\) −10.2426 −0.570800
\(323\) 0.899495i 0.0500492i
\(324\) 0 0
\(325\) 6.24264i 0.346279i
\(326\) 8.82843 0.488961
\(327\) −17.3137 + 12.2426i −0.957450 + 0.677020i
\(328\) −20.9706 −1.15791
\(329\) 13.0711 0.720631
\(330\) 4.00000 7.07107i 0.220193 0.389249i
\(331\) 19.4853 1.07101 0.535504 0.844533i \(-0.320122\pi\)
0.535504 + 0.844533i \(0.320122\pi\)
\(332\) 0 0
\(333\) 0.242641 0.686292i 0.0132966 0.0376085i
\(334\) 11.5147 0.630057
\(335\) 4.48528i 0.245057i
\(336\) −5.65685 + 4.00000i −0.308607 + 0.218218i
\(337\) 18.7574i 1.02178i 0.859647 + 0.510889i \(0.170684\pi\)
−0.859647 + 0.510889i \(0.829316\pi\)
\(338\) 36.7279 1.99774
\(339\) 1.27208 0.899495i 0.0690898 0.0488539i
\(340\) 0 0
\(341\) 0.727922 0.343146i 0.0394192 0.0185824i
\(342\) 20.9706 + 7.41421i 1.13396 + 0.400915i
\(343\) 1.00000i 0.0539949i
\(344\) 14.8284i 0.799495i
\(345\) 7.24264 + 10.2426i 0.389931 + 0.551445i
\(346\) −4.00000 −0.215041
\(347\) 21.1716 1.13655 0.568275 0.822839i \(-0.307611\pi\)
0.568275 + 0.822839i \(0.307611\pi\)
\(348\) 0 0
\(349\) 21.2426i 1.13709i −0.822651 0.568546i \(-0.807506\pi\)
0.822651 0.568546i \(-0.192494\pi\)
\(350\) 1.41421i 0.0755929i
\(351\) 8.82843 + 31.2132i 0.471227 + 1.66604i
\(352\) 0 0
\(353\) 18.0000i 0.958043i −0.877803 0.479022i \(-0.840992\pi\)
0.877803 0.479022i \(-0.159008\pi\)
\(354\) 13.7990 9.75736i 0.733408 0.518598i
\(355\) −10.2426 −0.543623
\(356\) 0 0
\(357\) −0.242641 + 0.171573i −0.0128419 + 0.00908060i
\(358\) 14.9706i 0.791219i
\(359\) 31.6274 1.66923 0.834616 0.550833i \(-0.185690\pi\)
0.834616 + 0.550833i \(0.185690\pi\)
\(360\) 8.00000 + 2.82843i 0.421637 + 0.149071i
\(361\) −8.48528 −0.446594
\(362\) −32.4853 −1.70739
\(363\) 19.0000 + 1.41421i 0.997241 + 0.0742270i
\(364\) 0 0
\(365\) 10.4853 0.548825
\(366\) 1.51472 1.07107i 0.0791756 0.0559856i
\(367\) 3.00000 0.156599 0.0782994 0.996930i \(-0.475051\pi\)
0.0782994 + 0.996930i \(0.475051\pi\)
\(368\) 28.9706i 1.51019i
\(369\) 7.41421 20.9706i 0.385969 1.09168i
\(370\) 0.343146i 0.0178393i
\(371\) −1.58579 −0.0823299
\(372\) 0 0
\(373\) 36.2132i 1.87505i 0.347920 + 0.937524i \(0.386888\pi\)
−0.347920 + 0.937524i \(0.613112\pi\)
\(374\) −0.727922 + 0.343146i −0.0376400 + 0.0177436i
\(375\) −1.41421 + 1.00000i −0.0730297 + 0.0516398i
\(376\) 36.9706i 1.90661i
\(377\) 1.07107i 0.0551628i
\(378\) −2.00000 7.07107i −0.102869 0.363696i
\(379\) −32.4558 −1.66714 −0.833572 0.552410i \(-0.813708\pi\)
−0.833572 + 0.552410i \(0.813708\pi\)
\(380\) 0 0
\(381\) −6.72792 + 4.75736i −0.344682 + 0.243727i
\(382\) 20.9706i 1.07295i
\(383\) 34.5858i 1.76725i 0.468194 + 0.883626i \(0.344905\pi\)
−0.468194 + 0.883626i \(0.655095\pi\)
\(384\) −11.3137 16.0000i −0.577350 0.816497i
\(385\) 3.00000 1.41421i 0.152894 0.0720750i
\(386\) 14.1421i 0.719816i
\(387\) −14.8284 5.24264i −0.753771 0.266498i
\(388\) 0 0
\(389\) 10.2426i 0.519322i −0.965700 0.259661i \(-0.916389\pi\)
0.965700 0.259661i \(-0.0836109\pi\)
\(390\) 8.82843 + 12.4853i 0.447045 + 0.632217i
\(391\) 1.24264i 0.0628430i
\(392\) −2.82843 −0.142857
\(393\) −16.5858 23.4558i −0.836642 1.18319i
\(394\) −8.48528 −0.427482
\(395\) 2.24264 0.112839
\(396\) 0 0
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −34.6274 −1.73572
\(399\) 5.24264 + 7.41421i 0.262460 + 0.371175i
\(400\) 4.00000 0.200000
\(401\) 30.7279i 1.53448i −0.641361 0.767240i \(-0.721630\pi\)
0.641361 0.767240i \(-0.278370\pi\)
\(402\) −6.34315 8.97056i −0.316367 0.447411i
\(403\) 1.51472i 0.0754535i
\(404\) 0 0
\(405\) −5.65685 + 7.00000i −0.281091 + 0.347833i
\(406\) 0.242641i 0.0120421i
\(407\) 0.727922 0.343146i 0.0360818 0.0170091i
\(408\) −0.485281 0.686292i −0.0240250 0.0339765i
\(409\) 1.51472i 0.0748980i −0.999299 0.0374490i \(-0.988077\pi\)
0.999299 0.0374490i \(-0.0119232\pi\)
\(410\) 10.4853i 0.517831i
\(411\) −3.51472 + 2.48528i −0.173368 + 0.122590i
\(412\) 0 0
\(413\) 6.89949 0.339502
\(414\) 28.9706 + 10.2426i 1.42383 + 0.503398i
\(415\) 11.1421i 0.546946i
\(416\) 0 0
\(417\) −6.34315 + 4.48528i −0.310625 + 0.219645i
\(418\) 10.4853 + 22.2426i 0.512852 + 1.08792i
\(419\) 28.4142i 1.38813i −0.719915 0.694063i \(-0.755819\pi\)
0.719915 0.694063i \(-0.244181\pi\)
\(420\) 0 0
\(421\) −4.51472 −0.220034 −0.110017 0.993930i \(-0.535091\pi\)
−0.110017 + 0.993930i \(0.535091\pi\)
\(422\) 11.3137i 0.550743i
\(423\) −36.9706 13.0711i −1.79757 0.635537i
\(424\) 4.48528i 0.217825i
\(425\) 0.171573 0.00832251
\(426\) −20.4853 + 14.4853i −0.992515 + 0.701814i
\(427\) 0.757359 0.0366512
\(428\) 0 0
\(429\) −17.6569 + 31.2132i −0.852481 + 1.50699i
\(430\) −7.41421 −0.357545
\(431\) −12.3431 −0.594548 −0.297274 0.954792i \(-0.596078\pi\)
−0.297274 + 0.954792i \(0.596078\pi\)
\(432\) 20.0000 5.65685i 0.962250 0.272166i
\(433\) −12.0000 −0.576683 −0.288342 0.957528i \(-0.593104\pi\)
−0.288342 + 0.957528i \(0.593104\pi\)
\(434\) 0.343146i 0.0164715i
\(435\) 0.242641 0.171573i 0.0116337 0.00822629i
\(436\) 0 0
\(437\) −37.9706 −1.81638
\(438\) 20.9706 14.8284i 1.00201 0.708530i
\(439\) 3.24264i 0.154763i −0.997002 0.0773814i \(-0.975344\pi\)
0.997002 0.0773814i \(-0.0246559\pi\)
\(440\) 4.00000 + 8.48528i 0.190693 + 0.404520i
\(441\) 1.00000 2.82843i 0.0476190 0.134687i
\(442\) 1.51472i 0.0720478i
\(443\) 11.3137i 0.537531i −0.963206 0.268765i \(-0.913384\pi\)
0.963206 0.268765i \(-0.0866156\pi\)
\(444\) 0 0
\(445\) −13.5858 −0.644028
\(446\) −24.0416 −1.13840
\(447\) 0 0
\(448\) 8.00000i 0.377964i
\(449\) 36.7279i 1.73330i 0.498919 + 0.866649i \(0.333731\pi\)
−0.498919 + 0.866649i \(0.666269\pi\)
\(450\) −1.41421 + 4.00000i −0.0666667 + 0.188562i
\(451\) 22.2426 10.4853i 1.04737 0.493733i
\(452\) 0 0
\(453\) −14.1421 + 10.0000i −0.664455 + 0.469841i
\(454\) 16.7279 0.785080
\(455\) 6.24264i 0.292660i
\(456\) −20.9706 + 14.8284i −0.982037 + 0.694405i
\(457\) 10.2132i 0.477754i −0.971050 0.238877i \(-0.923221\pi\)
0.971050 0.238877i \(-0.0767792\pi\)
\(458\) 9.51472 0.444594
\(459\) 0.857864 0.242641i 0.0400417 0.0113255i
\(460\) 0 0
\(461\) 29.6569 1.38126 0.690629 0.723210i \(-0.257334\pi\)
0.690629 + 0.723210i \(0.257334\pi\)
\(462\) 4.00000 7.07107i 0.186097 0.328976i
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) −0.686292 −0.0318603
\(465\) −0.343146 + 0.242641i −0.0159130 + 0.0112522i
\(466\) −30.4853 −1.41220
\(467\) 0.343146i 0.0158789i 0.999968 + 0.00793945i \(0.00252723\pi\)
−0.999968 + 0.00793945i \(0.997473\pi\)
\(468\) 0 0
\(469\) 4.48528i 0.207111i
\(470\) −18.4853 −0.852662
\(471\) 11.0000 + 15.5563i 0.506853 + 0.716799i
\(472\) 19.5147i 0.898238i
\(473\) −7.41421 15.7279i −0.340906 0.723171i
\(474\) 4.48528 3.17157i 0.206016 0.145675i
\(475\) 5.24264i 0.240549i
\(476\) 0 0
\(477\) 4.48528 + 1.58579i 0.205367 + 0.0726082i
\(478\) −3.75736 −0.171858
\(479\) −27.2132 −1.24340 −0.621702 0.783254i \(-0.713558\pi\)
−0.621702 + 0.783254i \(0.713558\pi\)
\(480\) 0 0
\(481\) 1.51472i 0.0690652i
\(482\) 37.4558i 1.70607i
\(483\) 7.24264 + 10.2426i 0.329552 + 0.466056i
\(484\) 0 0
\(485\) 7.00000i 0.317854i
\(486\) −1.41421 + 22.0000i −0.0641500 + 0.997940i
\(487\) 3.02944 0.137277 0.0686385 0.997642i \(-0.478135\pi\)
0.0686385 + 0.997642i \(0.478135\pi\)
\(488\) 2.14214i 0.0969699i
\(489\) −6.24264 8.82843i −0.282302 0.399235i
\(490\) 1.41421i 0.0638877i
\(491\) 15.3431 0.692426 0.346213 0.938156i \(-0.387467\pi\)
0.346213 + 0.938156i \(0.387467\pi\)
\(492\) 0 0
\(493\) −0.0294373 −0.00132579
\(494\) −46.2843 −2.08243
\(495\) −9.89949 + 1.00000i −0.444949 + 0.0449467i
\(496\) 0.970563 0.0435796
\(497\) −10.2426 −0.459445
\(498\) 15.7574 + 22.2843i 0.706104 + 0.998582i
\(499\) −11.4853 −0.514152 −0.257076 0.966391i \(-0.582759\pi\)
−0.257076 + 0.966391i \(0.582759\pi\)
\(500\) 0 0
\(501\) −8.14214 11.5147i −0.363764 0.514440i
\(502\) 7.02944i 0.313739i
\(503\) 10.4558 0.466203 0.233102 0.972452i \(-0.425113\pi\)
0.233102 + 0.972452i \(0.425113\pi\)
\(504\) 8.00000 + 2.82843i 0.356348 + 0.125988i
\(505\) 14.4853i 0.644587i
\(506\) 14.4853 + 30.7279i 0.643949 + 1.36602i
\(507\) −25.9706 36.7279i −1.15339 1.63114i
\(508\) 0 0
\(509\) 28.7574i 1.27465i −0.770596 0.637324i \(-0.780041\pi\)
0.770596 0.637324i \(-0.219959\pi\)
\(510\) 0.343146 0.242641i 0.0151947 0.0107443i
\(511\) 10.4853 0.463842
\(512\) 22.6274 1.00000
\(513\) −7.41421 26.2132i −0.327346 1.15734i
\(514\) 19.4558i 0.858160i
\(515\) 17.4853i 0.770494i
\(516\) 0 0
\(517\) −18.4853 39.2132i −0.812982 1.72459i
\(518\) 0.343146i 0.0150770i
\(519\) 2.82843 + 4.00000i 0.124154 + 0.175581i
\(520\) −17.6569 −0.774304
\(521\) 7.58579i 0.332339i −0.986097 0.166170i \(-0.946860\pi\)
0.986097 0.166170i \(-0.0531399\pi\)
\(522\) 0.242641 0.686292i 0.0106201 0.0300382i
\(523\) 26.9706i 1.17934i 0.807644 + 0.589670i \(0.200742\pi\)
−0.807644 + 0.589670i \(0.799258\pi\)
\(524\) 0 0
\(525\) −1.41421 + 1.00000i −0.0617213 + 0.0436436i
\(526\) 21.4558 0.935519
\(527\) 0.0416306 0.00181346
\(528\) 20.0000 + 11.3137i 0.870388 + 0.492366i
\(529\) −29.4558 −1.28069
\(530\) 2.24264 0.0974141
\(531\) −19.5147 6.89949i −0.846867 0.299413i
\(532\) 0 0
\(533\) 46.2843i 2.00479i
\(534\) −27.1716 + 19.2132i −1.17583 + 0.831437i
\(535\) 4.58579i 0.198261i
\(536\) 12.6863 0.547964
\(537\) −14.9706 + 10.5858i −0.646027 + 0.456810i
\(538\) 43.2132i 1.86305i
\(539\) 3.00000 1.41421i 0.129219 0.0609145i
\(540\) 0 0
\(541\) 14.7279i 0.633203i −0.948559 0.316601i \(-0.897458\pi\)
0.948559 0.316601i \(-0.102542\pi\)
\(542\) 32.8701i 1.41189i
\(543\) 22.9706 + 32.4853i 0.985761 + 1.39408i
\(544\) 0 0
\(545\) 12.2426 0.524417
\(546\) 8.82843 + 12.4853i 0.377822 + 0.534321i
\(547\) 14.7574i 0.630979i −0.948929 0.315490i \(-0.897831\pi\)
0.948929 0.315490i \(-0.102169\pi\)
\(548\) 0 0
\(549\) −2.14214 0.757359i −0.0914241 0.0323233i
\(550\) −4.24264 + 2.00000i −0.180907 + 0.0852803i
\(551\) 0.899495i 0.0383198i
\(552\) −28.9706 + 20.4853i −1.23307 + 0.871911i
\(553\) 2.24264 0.0953668
\(554\) 12.0000i 0.509831i
\(555\) −0.343146 + 0.242641i −0.0145657 + 0.0102995i
\(556\) 0 0
\(557\) −32.8284 −1.39099 −0.695493 0.718533i \(-0.744814\pi\)
−0.695493 + 0.718533i \(0.744814\pi\)
\(558\) −0.343146 + 0.970563i −0.0145265 + 0.0410872i
\(559\) 32.7279 1.38424
\(560\) 4.00000 0.169031
\(561\) 0.857864 + 0.485281i 0.0362191 + 0.0204886i
\(562\) −24.4853 −1.03285
\(563\) −37.1127 −1.56411 −0.782057 0.623207i \(-0.785829\pi\)
−0.782057 + 0.623207i \(0.785829\pi\)
\(564\) 0 0
\(565\) −0.899495 −0.0378420
\(566\) 18.6863i 0.785443i
\(567\) −5.65685 + 7.00000i −0.237566 + 0.293972i
\(568\) 28.9706i 1.21558i
\(569\) −11.1421 −0.467103 −0.233551 0.972344i \(-0.575035\pi\)
−0.233551 + 0.972344i \(0.575035\pi\)
\(570\) −7.41421 10.4853i −0.310547 0.439180i
\(571\) 36.1838i 1.51424i 0.653274 + 0.757122i \(0.273395\pi\)
−0.653274 + 0.757122i \(0.726605\pi\)
\(572\) 0 0
\(573\) 20.9706 14.8284i 0.876058 0.619466i
\(574\) 10.4853i 0.437647i
\(575\) 7.24264i 0.302039i
\(576\) −8.00000 + 22.6274i −0.333333 + 0.942809i
\(577\) 29.4558 1.22626 0.613131 0.789981i \(-0.289910\pi\)
0.613131 + 0.789981i \(0.289910\pi\)
\(578\) 24.0000 0.998268
\(579\) 14.1421 10.0000i 0.587727 0.415586i
\(580\) 0 0
\(581\) 11.1421i 0.462254i
\(582\) 9.89949 + 14.0000i 0.410347 + 0.580319i
\(583\) 2.24264 + 4.75736i 0.0928807 + 0.197030i
\(584\) 29.6569i 1.22721i
\(585\) 6.24264 17.6569i 0.258101 0.730021i
\(586\) −20.7279 −0.856263
\(587\) 12.0416i 0.497011i −0.968630 0.248506i \(-0.920061\pi\)
0.968630 0.248506i \(-0.0799395\pi\)
\(588\) 0 0
\(589\) 1.27208i 0.0524151i
\(590\) −9.75736 −0.401704
\(591\) 6.00000 + 8.48528i 0.246807 + 0.349038i
\(592\) 0.970563 0.0398899
\(593\) −21.1716 −0.869412 −0.434706 0.900572i \(-0.643148\pi\)
−0.434706 + 0.900572i \(0.643148\pi\)
\(594\) −18.3848 + 16.0000i −0.754337 + 0.656488i
\(595\) 0.171573 0.00703380
\(596\) 0 0
\(597\) 24.4853 + 34.6274i 1.00212 + 1.41721i
\(598\) −63.9411 −2.61475
\(599\) 37.1127i 1.51638i 0.652032 + 0.758192i \(0.273917\pi\)
−0.652032 + 0.758192i \(0.726083\pi\)
\(600\) −2.82843 4.00000i −0.115470 0.163299i
\(601\) 29.7279i 1.21263i −0.795226 0.606314i \(-0.792648\pi\)
0.795226 0.606314i \(-0.207352\pi\)
\(602\) −7.41421 −0.302181
\(603\) −4.48528 + 12.6863i −0.182655 + 0.516626i
\(604\) 0 0
\(605\) −8.48528 7.00000i −0.344976 0.284590i
\(606\) 20.4853 + 28.9706i 0.832158 + 1.17685i
\(607\) 9.51472i 0.386191i −0.981180 0.193095i \(-0.938147\pi\)
0.981180 0.193095i \(-0.0618526\pi\)
\(608\) 0 0
\(609\) 0.242641 0.171573i 0.00983230 0.00695248i
\(610\) −1.07107 −0.0433663
\(611\) 81.5980 3.30110
\(612\) 0 0
\(613\) 1.51472i 0.0611789i 0.999532 + 0.0305895i \(0.00973844\pi\)
−0.999532 + 0.0305895i \(0.990262\pi\)
\(614\) 4.97056i 0.200596i
\(615\) −10.4853 + 7.41421i −0.422807 + 0.298970i
\(616\) 4.00000 + 8.48528i 0.161165 + 0.341882i
\(617\) 17.3137i 0.697024i −0.937304 0.348512i \(-0.886687\pi\)
0.937304 0.348512i \(-0.113313\pi\)
\(618\) 24.7279 + 34.9706i 0.994703 + 1.40672i
\(619\) −14.4853 −0.582213 −0.291106 0.956691i \(-0.594023\pi\)
−0.291106 + 0.956691i \(0.594023\pi\)
\(620\) 0 0
\(621\) −10.2426 36.2132i −0.411023 1.45319i
\(622\) 12.9706i 0.520072i
\(623\) −13.5858 −0.544303
\(624\) −35.3137 + 24.9706i −1.41368 + 0.999623i
\(625\) 1.00000 0.0400000
\(626\) −34.5858 −1.38233
\(627\) 14.8284 26.2132i 0.592190 1.04685i
\(628\) 0 0
\(629\) 0.0416306 0.00165992
\(630\) −1.41421 + 4.00000i −0.0563436 + 0.159364i
\(631\) 15.0000 0.597141 0.298570 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(632\) 6.34315i 0.252317i
\(633\) −11.3137 + 8.00000i −0.449680 + 0.317971i
\(634\) 38.4264i 1.52611i
\(635\) 4.75736 0.188790
\(636\) 0 0
\(637\) 6.24264i 0.247342i
\(638\) 0.727922 0.343146i 0.0288187 0.0135853i
\(639\) 28.9706 + 10.2426i 1.14606 + 0.405193i
\(640\) 11.3137i 0.447214i
\(641\) 19.4558i 0.768460i 0.923237 + 0.384230i \(0.125533\pi\)
−0.923237 + 0.384230i \(0.874467\pi\)
\(642\) −6.48528 9.17157i −0.255954 0.361973i
\(643\) 17.9706 0.708690 0.354345 0.935115i \(-0.384704\pi\)
0.354345 + 0.935115i \(0.384704\pi\)
\(644\) 0 0
\(645\) 5.24264 + 7.41421i 0.206429 + 0.291934i
\(646\) 1.27208i 0.0500492i
\(647\) 4.20101i 0.165159i −0.996584 0.0825794i \(-0.973684\pi\)
0.996584 0.0825794i \(-0.0263158\pi\)
\(648\) −19.7990 16.0000i −0.777778 0.628539i
\(649\) −9.75736 20.6985i −0.383010 0.812487i
\(650\) 8.82843i 0.346279i
\(651\) −0.343146 + 0.242641i −0.0134489 + 0.00950984i
\(652\) 0 0
\(653\) 24.2132i 0.947536i 0.880650 + 0.473768i \(0.157106\pi\)
−0.880650 + 0.473768i \(0.842894\pi\)
\(654\) 24.4853 17.3137i 0.957450 0.677020i
\(655\) 16.5858i 0.648060i
\(656\) 29.6569 1.15791
\(657\) −29.6569 10.4853i −1.15702 0.409070i
\(658\) −18.4853 −0.720631
\(659\) −43.2843 −1.68612 −0.843058 0.537823i \(-0.819247\pi\)
−0.843058 + 0.537823i \(0.819247\pi\)
\(660\) 0 0
\(661\) −25.2132 −0.980680 −0.490340 0.871531i \(-0.663127\pi\)
−0.490340 + 0.871531i \(0.663127\pi\)
\(662\) −27.5563 −1.07101
\(663\) −1.51472 + 1.07107i −0.0588268 + 0.0415968i
\(664\) −31.5147 −1.22301
\(665\) 5.24264i 0.203301i
\(666\) −0.343146 + 0.970563i −0.0132966 + 0.0376085i
\(667\) 1.24264i 0.0481152i
\(668\) 0 0
\(669\) 17.0000 + 24.0416i 0.657258 + 0.929503i
\(670\) 6.34315i 0.245057i
\(671\) −1.07107 2.27208i −0.0413481 0.0877126i
\(672\) 0 0
\(673\) 35.7279i 1.37721i 0.725137 + 0.688605i \(0.241777\pi\)
−0.725137 + 0.688605i \(0.758223\pi\)
\(674\) 26.5269i 1.02178i
\(675\) 5.00000 1.41421i 0.192450 0.0544331i
\(676\) 0 0
\(677\) 11.8284 0.454603 0.227302 0.973824i \(-0.427010\pi\)
0.227302 + 0.973824i \(0.427010\pi\)
\(678\) −1.79899 + 1.27208i −0.0690898 + 0.0488539i
\(679\) 7.00000i 0.268635i
\(680\) 0.485281i 0.0186097i
\(681\) −11.8284 16.7279i −0.453266 0.641015i
\(682\) −1.02944 + 0.485281i −0.0394192 + 0.0185824i
\(683\) 0.343146i 0.0131301i 0.999978 + 0.00656505i \(0.00208974\pi\)
−0.999978 + 0.00656505i \(0.997910\pi\)
\(684\) 0 0
\(685\) 2.48528 0.0949577
\(686\) 1.41421i 0.0539949i
\(687\) −6.72792 9.51472i −0.256686 0.363009i
\(688\) 20.9706i 0.799495i
\(689\) −9.89949 −0.377141
\(690\) −10.2426 14.4853i −0.389931 0.551445i
\(691\) −42.9706 −1.63468 −0.817339 0.576158i \(-0.804551\pi\)
−0.817339 + 0.576158i \(0.804551\pi\)
\(692\) 0 0
\(693\) −9.89949 + 1.00000i −0.376051 + 0.0379869i
\(694\) −29.9411 −1.13655
\(695\) 4.48528 0.170136
\(696\) 0.485281 + 0.686292i 0.0183945 + 0.0260138i
\(697\) 1.27208 0.0481834
\(698\) 30.0416i 1.13709i
\(699\) 21.5563 + 30.4853i 0.815336 + 1.15306i
\(700\) 0 0
\(701\) −4.02944 −0.152190 −0.0760949 0.997101i \(-0.524245\pi\)
−0.0760949 + 0.997101i \(0.524245\pi\)
\(702\) −12.4853 44.1421i −0.471227 1.66604i
\(703\) 1.27208i 0.0479773i
\(704\) −24.0000 + 11.3137i −0.904534 + 0.426401i
\(705\) 13.0711 + 18.4853i 0.492285 + 0.696196i
\(706\) 25.4558i 0.958043i
\(707\) 14.4853i 0.544775i
\(708\) 0 0
\(709\) 16.9411 0.636237 0.318119 0.948051i \(-0.396949\pi\)
0.318119 + 0.948051i \(0.396949\pi\)
\(710\) 14.4853 0.543623
\(711\) −6.34315 2.24264i −0.237887 0.0841056i
\(712\) 38.4264i 1.44009i
\(713\) 1.75736i 0.0658136i
\(714\) 0.343146 0.242641i 0.0128419 0.00908060i
\(715\) 18.7279 8.82843i 0.700385 0.330164i
\(716\) 0 0
\(717\) 2.65685 + 3.75736i 0.0992220 + 0.140321i
\(718\) −44.7279 −1.66923
\(719\) 17.5269i 0.653644i −0.945086 0.326822i \(-0.894022\pi\)
0.945086 0.326822i \(-0.105978\pi\)
\(720\) −11.3137 4.00000i −0.421637 0.149071i
\(721\) 17.4853i 0.651186i
\(722\) 12.0000 0.446594
\(723\) 37.4558 26.4853i 1.39300 0.984998i
\(724\) 0 0
\(725\) −0.171573 −0.00637206
\(726\) −26.8701 2.00000i −0.997241 0.0742270i
\(727\) −30.4558 −1.12954 −0.564772 0.825247i \(-0.691036\pi\)
−0.564772 + 0.825247i \(0.691036\pi\)
\(728\) −17.6569 −0.654407
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) −14.8284 −0.548825
\(731\) 0.899495i 0.0332690i
\(732\) 0 0
\(733\) 29.4558i 1.08798i 0.839093 + 0.543988i \(0.183086\pi\)
−0.839093 + 0.543988i \(0.816914\pi\)
\(734\) −4.24264 −0.156599
\(735\) −1.41421 + 1.00000i −0.0521641 + 0.0368856i
\(736\) 0 0
\(737\) −13.4558 + 6.34315i −0.495652 + 0.233653i
\(738\) −10.4853 + 29.6569i −0.385969 + 1.09168i
\(739\) 13.5147i 0.497147i 0.968613 + 0.248573i \(0.0799617\pi\)
−0.968613 + 0.248573i \(0.920038\pi\)
\(740\) 0 0
\(741\) 32.7279 + 46.2843i 1.20229 + 1.70030i
\(742\) 2.24264 0.0823299
\(743\) 1.37258 0.0503552 0.0251776 0.999683i \(-0.491985\pi\)
0.0251776 + 0.999683i \(0.491985\pi\)
\(744\) −0.686292 0.970563i −0.0251607 0.0355826i
\(745\) 0 0
\(746\) 51.2132i 1.87505i
\(747\) 11.1421 31.5147i 0.407669 1.15306i
\(748\) 0 0
\(749\) 4.58579i 0.167561i
\(750\) 2.00000 1.41421i 0.0730297 0.0516398i
\(751\) −25.9706 −0.947679 −0.473840 0.880611i \(-0.657132\pi\)
−0.473840 + 0.880611i \(0.657132\pi\)
\(752\) 52.2843i 1.90661i
\(753\) 7.02944 4.97056i 0.256167 0.181137i
\(754\) 1.51472i 0.0551628i
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) 41.4558 1.50674 0.753369 0.657598i \(-0.228427\pi\)
0.753369 + 0.657598i \(0.228427\pi\)
\(758\) 45.8995 1.66714
\(759\) 20.4853 36.2132i 0.743569 1.31446i
\(760\) 14.8284 0.537884
\(761\) 40.9706 1.48518 0.742591 0.669745i \(-0.233597\pi\)
0.742591 + 0.669745i \(0.233597\pi\)
\(762\) 9.51472 6.72792i 0.344682 0.243727i
\(763\) 12.2426 0.443213
\(764\) 0 0
\(765\) −0.485281 0.171573i −0.0175454 0.00620323i
\(766\) 48.9117i 1.76725i
\(767\) 43.0711 1.55521
\(768\) 0 0
\(769\) 41.6690i 1.50262i 0.659947 + 0.751312i \(0.270579\pi\)
−0.659947 + 0.751312i \(0.729421\pi\)
\(770\) −4.24264 + 2.00000i −0.152894 + 0.0720750i
\(771\) −19.4558 + 13.7574i −0.700685 + 0.495459i
\(772\) 0 0
\(773\) 9.17157i 0.329879i 0.986304 + 0.164939i \(0.0527428\pi\)
−0.986304 + 0.164939i \(0.947257\pi\)
\(774\) 20.9706 + 7.41421i 0.753771 + 0.266498i
\(775\) 0.242641 0.00871591
\(776\) −19.7990 −0.710742
\(777\) −0.343146 + 0.242641i −0.0123103 + 0.00870469i
\(778\) 14.4853i 0.519322i
\(779\) 38.8701i 1.39266i
\(780\) 0 0
\(781\) 14.4853 + 30.7279i 0.518324 + 1.09953i
\(782\) 1.75736i 0.0628430i
\(783\) −0.857864 + 0.242641i −0.0306576 + 0.00867127i
\(784\) 4.00000 0.142857
\(785\) 11.0000i 0.392607i
\(786\) 23.4558 + 33.1716i 0.836642 + 1.18319i
\(787\) 35.4558i 1.26386i −0.775024 0.631932i \(-0.782262\pi\)
0.775024 0.631932i \(-0.217738\pi\)
\(788\) 0 0
\(789\) −15.1716 21.4558i −0.540122 0.763848i
\(790\) −3.17157 −0.112839
\(791\) −0.899495 −0.0319824
\(792\) −2.82843 28.0000i −0.100504 0.994937i
\(793\) 4.72792 0.167893
\(794\) 48.0833 1.70641
\(795\) −1.58579 2.24264i −0.0562420 0.0795383i