Properties

Label 570.2.d.d.229.5
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 229.5
Root \(1.45161 - 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.d.229.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.311108 + 2.21432i) q^{5} +1.00000 q^{6} -4.42864i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.311108 + 2.21432i) q^{5} +1.00000 q^{6} -4.42864i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.21432 + 0.311108i) q^{10} -5.80642 q^{11} +1.00000i q^{12} -6.42864i q^{13} +4.42864 q^{14} +(2.21432 - 0.311108i) q^{15} +1.00000 q^{16} +3.37778i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(-0.311108 - 2.21432i) q^{20} -4.42864 q^{21} -5.80642i q^{22} -6.42864i q^{23} -1.00000 q^{24} +(-4.80642 + 1.37778i) q^{25} +6.42864 q^{26} +1.00000i q^{27} +4.42864i q^{28} -7.80642 q^{29} +(0.311108 + 2.21432i) q^{30} +9.05086 q^{31} +1.00000i q^{32} +5.80642i q^{33} -3.37778 q^{34} +(9.80642 - 1.37778i) q^{35} +1.00000 q^{36} -3.67307i q^{37} +1.00000i q^{38} -6.42864 q^{39} +(2.21432 - 0.311108i) q^{40} +4.42864 q^{41} -4.42864i q^{42} -1.05086i q^{43} +5.80642 q^{44} +(-0.311108 - 2.21432i) q^{45} +6.42864 q^{46} -5.18421i q^{47} -1.00000i q^{48} -12.6128 q^{49} +(-1.37778 - 4.80642i) q^{50} +3.37778 q^{51} +6.42864i q^{52} -4.75557i q^{53} -1.00000 q^{54} +(-1.80642 - 12.8573i) q^{55} -4.42864 q^{56} -1.00000i q^{57} -7.80642i q^{58} -4.62222 q^{59} +(-2.21432 + 0.311108i) q^{60} +2.00000 q^{61} +9.05086i q^{62} +4.42864i q^{63} -1.00000 q^{64} +(14.2351 - 2.00000i) q^{65} -5.80642 q^{66} -2.75557i q^{67} -3.37778i q^{68} -6.42864 q^{69} +(1.37778 + 9.80642i) q^{70} +7.61285 q^{71} +1.00000i q^{72} +11.6128i q^{73} +3.67307 q^{74} +(1.37778 + 4.80642i) q^{75} -1.00000 q^{76} +25.7146i q^{77} -6.42864i q^{78} -2.94914 q^{79} +(0.311108 + 2.21432i) q^{80} +1.00000 q^{81} +4.42864i q^{82} -0.133353i q^{83} +4.42864 q^{84} +(-7.47949 + 1.05086i) q^{85} +1.05086 q^{86} +7.80642i q^{87} +5.80642i q^{88} +3.18421 q^{89} +(2.21432 - 0.311108i) q^{90} -28.4701 q^{91} +6.42864i q^{92} -9.05086i q^{93} +5.18421 q^{94} +(0.311108 + 2.21432i) q^{95} +1.00000 q^{96} +11.4193i q^{97} -12.6128i q^{98} +5.80642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} - 8q^{11} + 6q^{16} + 6q^{19} - 2q^{20} - 6q^{24} - 2q^{25} + 12q^{26} - 20q^{29} + 2q^{30} + 28q^{31} - 20q^{34} + 32q^{35} + 6q^{36} - 12q^{39} + 8q^{44} - 2q^{45} + 12q^{46} - 22q^{49} - 8q^{50} + 20q^{51} - 6q^{54} + 16q^{55} - 28q^{59} + 12q^{61} - 6q^{64} + 32q^{65} - 8q^{66} - 12q^{69} + 8q^{70} - 8q^{71} - 4q^{74} + 8q^{75} - 6q^{76} - 44q^{79} + 2q^{80} + 6q^{81} + 8q^{85} - 20q^{86} - 8q^{89} - 64q^{91} + 4q^{94} + 2q^{95} + 6q^{96} + 8q^{99} + O(q^{100}) \)

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
\(5\) 0.311108 + 2.21432i 0.139132 + 0.990274i
\(6\) 1.00000 0.408248
\(7\) 4.42864i 1.67387i −0.547304 0.836934i \(-0.684346\pi\)
0.547304 0.836934i \(-0.315654\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −2.21432 + 0.311108i −0.700229 + 0.0983809i
\(11\) −5.80642 −1.75070 −0.875351 0.483487i \(-0.839370\pi\)
−0.875351 + 0.483487i \(0.839370\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 6.42864i 1.78298i −0.453037 0.891492i \(-0.649659\pi\)
0.453037 0.891492i \(-0.350341\pi\)
\(14\) 4.42864 1.18360
\(15\) 2.21432 0.311108i 0.571735 0.0803277i
\(16\) 1.00000 0.250000
\(17\) 3.37778i 0.819233i 0.912258 + 0.409617i \(0.134337\pi\)
−0.912258 + 0.409617i \(0.865663\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 0.229416
\(20\) −0.311108 2.21432i −0.0695658 0.495137i
\(21\) −4.42864 −0.966408
\(22\) 5.80642i 1.23793i
\(23\) 6.42864i 1.34046i −0.742152 0.670232i \(-0.766195\pi\)
0.742152 0.670232i \(-0.233805\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.80642 + 1.37778i −0.961285 + 0.275557i
\(26\) 6.42864 1.26076
\(27\) 1.00000i 0.192450i
\(28\) 4.42864i 0.836934i
\(29\) −7.80642 −1.44962 −0.724808 0.688951i \(-0.758072\pi\)
−0.724808 + 0.688951i \(0.758072\pi\)
\(30\) 0.311108 + 2.21432i 0.0568003 + 0.404278i
\(31\) 9.05086 1.62558 0.812791 0.582556i \(-0.197947\pi\)
0.812791 + 0.582556i \(0.197947\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 5.80642i 1.01077i
\(34\) −3.37778 −0.579285
\(35\) 9.80642 1.37778i 1.65759 0.232888i
\(36\) 1.00000 0.166667
\(37\) 3.67307i 0.603849i −0.953332 0.301925i \(-0.902371\pi\)
0.953332 0.301925i \(-0.0976291\pi\)
\(38\) 1.00000i 0.162221i
\(39\) −6.42864 −1.02941
\(40\) 2.21432 0.311108i 0.350115 0.0491905i
\(41\) 4.42864 0.691637 0.345819 0.938301i \(-0.387601\pi\)
0.345819 + 0.938301i \(0.387601\pi\)
\(42\) 4.42864i 0.683354i
\(43\) 1.05086i 0.160254i −0.996785 0.0801270i \(-0.974467\pi\)
0.996785 0.0801270i \(-0.0255326\pi\)
\(44\) 5.80642 0.875351
\(45\) −0.311108 2.21432i −0.0463772 0.330091i
\(46\) 6.42864 0.947851
\(47\) 5.18421i 0.756194i −0.925766 0.378097i \(-0.876578\pi\)
0.925766 0.378097i \(-0.123422\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −12.6128 −1.80184
\(50\) −1.37778 4.80642i −0.194848 0.679731i
\(51\) 3.37778 0.472984
\(52\) 6.42864i 0.891492i
\(53\) 4.75557i 0.653228i −0.945158 0.326614i \(-0.894092\pi\)
0.945158 0.326614i \(-0.105908\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.80642 12.8573i −0.243578 1.73368i
\(56\) −4.42864 −0.591802
\(57\) 1.00000i 0.132453i
\(58\) 7.80642i 1.02503i
\(59\) −4.62222 −0.601761 −0.300881 0.953662i \(-0.597281\pi\)
−0.300881 + 0.953662i \(0.597281\pi\)
\(60\) −2.21432 + 0.311108i −0.285867 + 0.0401638i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 9.05086i 1.14946i
\(63\) 4.42864i 0.557956i
\(64\) −1.00000 −0.125000
\(65\) 14.2351 2.00000i 1.76564 0.248069i
\(66\) −5.80642 −0.714721
\(67\) 2.75557i 0.336646i −0.985732 0.168323i \(-0.946165\pi\)
0.985732 0.168323i \(-0.0538352\pi\)
\(68\) 3.37778i 0.409617i
\(69\) −6.42864 −0.773917
\(70\) 1.37778 + 9.80642i 0.164677 + 1.17209i
\(71\) 7.61285 0.903479 0.451739 0.892150i \(-0.350804\pi\)
0.451739 + 0.892150i \(0.350804\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 11.6128i 1.35918i 0.733592 + 0.679591i \(0.237843\pi\)
−0.733592 + 0.679591i \(0.762157\pi\)
\(74\) 3.67307 0.426986
\(75\) 1.37778 + 4.80642i 0.159093 + 0.554998i
\(76\) −1.00000 −0.114708
\(77\) 25.7146i 2.93045i
\(78\) 6.42864i 0.727900i
\(79\) −2.94914 −0.331805 −0.165902 0.986142i \(-0.553054\pi\)
−0.165902 + 0.986142i \(0.553054\pi\)
\(80\) 0.311108 + 2.21432i 0.0347829 + 0.247568i
\(81\) 1.00000 0.111111
\(82\) 4.42864i 0.489061i
\(83\) 0.133353i 0.0146374i −0.999973 0.00731870i \(-0.997670\pi\)
0.999973 0.00731870i \(-0.00232964\pi\)
\(84\) 4.42864 0.483204
\(85\) −7.47949 + 1.05086i −0.811265 + 0.113981i
\(86\) 1.05086 0.113317
\(87\) 7.80642i 0.836936i
\(88\) 5.80642i 0.618967i
\(89\) 3.18421 0.337525 0.168763 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(90\) 2.21432 0.311108i 0.233410 0.0327936i
\(91\) −28.4701 −2.98448
\(92\) 6.42864i 0.670232i
\(93\) 9.05086i 0.938530i
\(94\) 5.18421 0.534710
\(95\) 0.311108 + 2.21432i 0.0319190 + 0.227184i
\(96\) 1.00000 0.102062
\(97\) 11.4193i 1.15945i 0.814812 + 0.579726i \(0.196840\pi\)
−0.814812 + 0.579726i \(0.803160\pi\)
\(98\) 12.6128i 1.27409i
\(99\) 5.80642 0.583568
\(100\) 4.80642 1.37778i 0.480642 0.137778i
\(101\) −1.86665 −0.185738 −0.0928692 0.995678i \(-0.529604\pi\)
−0.0928692 + 0.995678i \(0.529604\pi\)
\(102\) 3.37778i 0.334450i
\(103\) 10.6222i 1.04664i 0.852137 + 0.523319i \(0.175306\pi\)
−0.852137 + 0.523319i \(0.824694\pi\)
\(104\) −6.42864 −0.630380
\(105\) −1.37778 9.80642i −0.134458 0.957009i
\(106\) 4.75557 0.461902
\(107\) 7.61285i 0.735962i −0.929833 0.367981i \(-0.880049\pi\)
0.929833 0.367981i \(-0.119951\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −5.53972 −0.530609 −0.265304 0.964165i \(-0.585472\pi\)
−0.265304 + 0.964165i \(0.585472\pi\)
\(110\) 12.8573 1.80642i 1.22589 0.172236i
\(111\) −3.67307 −0.348632
\(112\) 4.42864i 0.418467i
\(113\) 12.3684i 1.16352i 0.813360 + 0.581761i \(0.197636\pi\)
−0.813360 + 0.581761i \(0.802364\pi\)
\(114\) 1.00000 0.0936586
\(115\) 14.2351 2.00000i 1.32743 0.186501i
\(116\) 7.80642 0.724808
\(117\) 6.42864i 0.594328i
\(118\) 4.62222i 0.425509i
\(119\) 14.9590 1.37129
\(120\) −0.311108 2.21432i −0.0284001 0.202139i
\(121\) 22.7146 2.06496
\(122\) 2.00000i 0.181071i
\(123\) 4.42864i 0.399317i
\(124\) −9.05086 −0.812791
\(125\) −4.54617 10.2143i −0.406622 0.913597i
\(126\) −4.42864 −0.394535
\(127\) 1.76494i 0.156613i −0.996929 0.0783064i \(-0.975049\pi\)
0.996929 0.0783064i \(-0.0249512\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.05086 −0.0925226
\(130\) 2.00000 + 14.2351i 0.175412 + 1.24850i
\(131\) 9.80642 0.856791 0.428396 0.903591i \(-0.359079\pi\)
0.428396 + 0.903591i \(0.359079\pi\)
\(132\) 5.80642i 0.505384i
\(133\) 4.42864i 0.384012i
\(134\) 2.75557 0.238045
\(135\) −2.21432 + 0.311108i −0.190578 + 0.0267759i
\(136\) 3.37778 0.289643
\(137\) 1.47949i 0.126402i −0.998001 0.0632009i \(-0.979869\pi\)
0.998001 0.0632009i \(-0.0201309\pi\)
\(138\) 6.42864i 0.547242i
\(139\) 4.85728 0.411989 0.205995 0.978553i \(-0.433957\pi\)
0.205995 + 0.978553i \(0.433957\pi\)
\(140\) −9.80642 + 1.37778i −0.828794 + 0.116444i
\(141\) −5.18421 −0.436589
\(142\) 7.61285i 0.638856i
\(143\) 37.3274i 3.12147i
\(144\) −1.00000 −0.0833333
\(145\) −2.42864 17.2859i −0.201688 1.43552i
\(146\) −11.6128 −0.961086
\(147\) 12.6128i 1.04029i
\(148\) 3.67307i 0.301925i
\(149\) −4.62222 −0.378667 −0.189333 0.981913i \(-0.560633\pi\)
−0.189333 + 0.981913i \(0.560633\pi\)
\(150\) −4.80642 + 1.37778i −0.392443 + 0.112496i
\(151\) −11.4193 −0.929287 −0.464644 0.885498i \(-0.653818\pi\)
−0.464644 + 0.885498i \(0.653818\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 3.37778i 0.273078i
\(154\) −25.7146 −2.07214
\(155\) 2.81579 + 20.0415i 0.226170 + 1.60977i
\(156\) 6.42864 0.514703
\(157\) 7.37778i 0.588811i −0.955681 0.294406i \(-0.904878\pi\)
0.955681 0.294406i \(-0.0951217\pi\)
\(158\) 2.94914i 0.234621i
\(159\) −4.75557 −0.377141
\(160\) −2.21432 + 0.311108i −0.175057 + 0.0245952i
\(161\) −28.4701 −2.24376
\(162\) 1.00000i 0.0785674i
\(163\) 5.90813i 0.462761i −0.972863 0.231380i \(-0.925676\pi\)
0.972863 0.231380i \(-0.0743242\pi\)
\(164\) −4.42864 −0.345819
\(165\) −12.8573 + 1.80642i −1.00094 + 0.140630i
\(166\) 0.133353 0.0103502
\(167\) 2.75557i 0.213232i −0.994300 0.106616i \(-0.965998\pi\)
0.994300 0.106616i \(-0.0340016\pi\)
\(168\) 4.42864i 0.341677i
\(169\) −28.3274 −2.17903
\(170\) −1.05086 7.47949i −0.0805969 0.573651i
\(171\) −1.00000 −0.0764719
\(172\) 1.05086i 0.0801270i
\(173\) 8.10171i 0.615962i −0.951393 0.307981i \(-0.900347\pi\)
0.951393 0.307981i \(-0.0996533\pi\)
\(174\) −7.80642 −0.591803
\(175\) 6.10171 + 21.2859i 0.461246 + 1.60906i
\(176\) −5.80642 −0.437676
\(177\) 4.62222i 0.347427i
\(178\) 3.18421i 0.238666i
\(179\) 0.235063 0.0175695 0.00878473 0.999961i \(-0.497204\pi\)
0.00878473 + 0.999961i \(0.497204\pi\)
\(180\) 0.311108 + 2.21432i 0.0231886 + 0.165046i
\(181\) 11.3176 0.841228 0.420614 0.907240i \(-0.361815\pi\)
0.420614 + 0.907240i \(0.361815\pi\)
\(182\) 28.4701i 2.11035i
\(183\) 2.00000i 0.147844i
\(184\) −6.42864 −0.473926
\(185\) 8.13335 1.14272i 0.597976 0.0840145i
\(186\) 9.05086 0.663641
\(187\) 19.6128i 1.43423i
\(188\) 5.18421i 0.378097i
\(189\) 4.42864 0.322136
\(190\) −2.21432 + 0.311108i −0.160644 + 0.0225701i
\(191\) −6.32693 −0.457801 −0.228900 0.973450i \(-0.573513\pi\)
−0.228900 + 0.973450i \(0.573513\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 11.5397i 0.830647i 0.909674 + 0.415324i \(0.136332\pi\)
−0.909674 + 0.415324i \(0.863668\pi\)
\(194\) −11.4193 −0.819856
\(195\) −2.00000 14.2351i −0.143223 1.01939i
\(196\) 12.6128 0.900918
\(197\) 20.0415i 1.42790i −0.700198 0.713948i \(-0.746905\pi\)
0.700198 0.713948i \(-0.253095\pi\)
\(198\) 5.80642i 0.412645i
\(199\) 20.4701 1.45109 0.725544 0.688175i \(-0.241588\pi\)
0.725544 + 0.688175i \(0.241588\pi\)
\(200\) 1.37778 + 4.80642i 0.0974241 + 0.339865i
\(201\) −2.75557 −0.194363
\(202\) 1.86665i 0.131337i
\(203\) 34.5718i 2.42647i
\(204\) −3.37778 −0.236492
\(205\) 1.37778 + 9.80642i 0.0962286 + 0.684910i
\(206\) −10.6222 −0.740085
\(207\) 6.42864i 0.446821i
\(208\) 6.42864i 0.445746i
\(209\) −5.80642 −0.401639
\(210\) 9.80642 1.37778i 0.676708 0.0950762i
\(211\) 2.75557 0.189701 0.0948506 0.995492i \(-0.469763\pi\)
0.0948506 + 0.995492i \(0.469763\pi\)
\(212\) 4.75557i 0.326614i
\(213\) 7.61285i 0.521624i
\(214\) 7.61285 0.520404
\(215\) 2.32693 0.326929i 0.158695 0.0222964i
\(216\) 1.00000 0.0680414
\(217\) 40.0830i 2.72101i
\(218\) 5.53972i 0.375197i
\(219\) 11.6128 0.784724
\(220\) 1.80642 + 12.8573i 0.121789 + 0.866838i
\(221\) 21.7146 1.46068
\(222\) 3.67307i 0.246520i
\(223\) 10.6222i 0.711316i 0.934616 + 0.355658i \(0.115743\pi\)
−0.934616 + 0.355658i \(0.884257\pi\)
\(224\) 4.42864 0.295901
\(225\) 4.80642 1.37778i 0.320428 0.0918523i
\(226\) −12.3684 −0.822735
\(227\) 15.3461i 1.01856i −0.860601 0.509280i \(-0.829912\pi\)
0.860601 0.509280i \(-0.170088\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) 19.7146 1.30277 0.651387 0.758745i \(-0.274187\pi\)
0.651387 + 0.758745i \(0.274187\pi\)
\(230\) 2.00000 + 14.2351i 0.131876 + 0.938632i
\(231\) 25.7146 1.69189
\(232\) 7.80642i 0.512517i
\(233\) 29.5625i 1.93670i −0.249593 0.968351i \(-0.580297\pi\)
0.249593 0.968351i \(-0.419703\pi\)
\(234\) −6.42864 −0.420253
\(235\) 11.4795 1.61285i 0.748840 0.105211i
\(236\) 4.62222 0.300881
\(237\) 2.94914i 0.191568i
\(238\) 14.9590i 0.969647i
\(239\) −1.67307 −0.108222 −0.0541110 0.998535i \(-0.517232\pi\)
−0.0541110 + 0.998535i \(0.517232\pi\)
\(240\) 2.21432 0.311108i 0.142934 0.0200819i
\(241\) −16.9590 −1.09242 −0.546212 0.837647i \(-0.683931\pi\)
−0.546212 + 0.837647i \(0.683931\pi\)
\(242\) 22.7146i 1.46015i
\(243\) 1.00000i 0.0641500i
\(244\) −2.00000 −0.128037
\(245\) −3.92396 27.9289i −0.250692 1.78431i
\(246\) 4.42864 0.282360
\(247\) 6.42864i 0.409045i
\(248\) 9.05086i 0.574730i
\(249\) −0.133353 −0.00845091
\(250\) 10.2143 4.54617i 0.646010 0.287525i
\(251\) 4.94914 0.312387 0.156194 0.987726i \(-0.450078\pi\)
0.156194 + 0.987726i \(0.450078\pi\)
\(252\) 4.42864i 0.278978i
\(253\) 37.3274i 2.34675i
\(254\) 1.76494 0.110742
\(255\) 1.05086 + 7.47949i 0.0658071 + 0.468384i
\(256\) 1.00000 0.0625000
\(257\) 5.34614i 0.333483i −0.986001 0.166742i \(-0.946675\pi\)
0.986001 0.166742i \(-0.0533246\pi\)
\(258\) 1.05086i 0.0654234i
\(259\) −16.2667 −1.01076
\(260\) −14.2351 + 2.00000i −0.882821 + 0.124035i
\(261\) 7.80642 0.483206
\(262\) 9.80642i 0.605843i
\(263\) 9.45091i 0.582768i −0.956606 0.291384i \(-0.905884\pi\)
0.956606 0.291384i \(-0.0941158\pi\)
\(264\) 5.80642 0.357361
\(265\) 10.5303 1.47949i 0.646874 0.0908846i
\(266\) 4.42864 0.271537
\(267\) 3.18421i 0.194870i
\(268\) 2.75557i 0.168323i
\(269\) −2.94914 −0.179813 −0.0899063 0.995950i \(-0.528657\pi\)
−0.0899063 + 0.995950i \(0.528657\pi\)
\(270\) −0.311108 2.21432i −0.0189334 0.134759i
\(271\) 30.9590 1.88062 0.940312 0.340313i \(-0.110533\pi\)
0.940312 + 0.340313i \(0.110533\pi\)
\(272\) 3.37778i 0.204808i
\(273\) 28.4701i 1.72309i
\(274\) 1.47949 0.0893795
\(275\) 27.9081 8.00000i 1.68292 0.482418i
\(276\) 6.42864 0.386959
\(277\) 13.0923i 0.786643i 0.919401 + 0.393321i \(0.128674\pi\)
−0.919401 + 0.393321i \(0.871326\pi\)
\(278\) 4.85728i 0.291320i
\(279\) −9.05086 −0.541861
\(280\) −1.37778 9.80642i −0.0823384 0.586046i
\(281\) 18.5303 1.10543 0.552714 0.833371i \(-0.313592\pi\)
0.552714 + 0.833371i \(0.313592\pi\)
\(282\) 5.18421i 0.308715i
\(283\) 26.3783i 1.56802i −0.620745 0.784012i \(-0.713170\pi\)
0.620745 0.784012i \(-0.286830\pi\)
\(284\) −7.61285 −0.451739
\(285\) 2.21432 0.311108i 0.131165 0.0184284i
\(286\) −37.3274 −2.20722
\(287\) 19.6128i 1.15771i
\(288\) 1.00000i 0.0589256i
\(289\) 5.59057 0.328857
\(290\) 17.2859 2.42864i 1.01506 0.142615i
\(291\) 11.4193 0.669410
\(292\) 11.6128i 0.679591i
\(293\) 28.5718i 1.66918i −0.550868 0.834592i \(-0.685703\pi\)
0.550868 0.834592i \(-0.314297\pi\)
\(294\) −12.6128 −0.735596
\(295\) −1.43801 10.2351i −0.0837240 0.595908i
\(296\) −3.67307 −0.213493
\(297\) 5.80642i 0.336923i
\(298\) 4.62222i 0.267758i
\(299\) −41.3274 −2.39003
\(300\) −1.37778 4.80642i −0.0795464 0.277499i
\(301\) −4.65386 −0.268244
\(302\) 11.4193i 0.657105i
\(303\) 1.86665i 0.107236i
\(304\) 1.00000 0.0573539
\(305\) 0.622216 + 4.42864i 0.0356280 + 0.253583i
\(306\) 3.37778 0.193095
\(307\) 22.7556i 1.29873i −0.760477 0.649364i \(-0.775035\pi\)
0.760477 0.649364i \(-0.224965\pi\)
\(308\) 25.7146i 1.46522i
\(309\) 10.6222 0.604277
\(310\) −20.0415 + 2.81579i −1.13828 + 0.159926i
\(311\) −6.32693 −0.358767 −0.179384 0.983779i \(-0.557410\pi\)
−0.179384 + 0.983779i \(0.557410\pi\)
\(312\) 6.42864i 0.363950i
\(313\) 13.7146i 0.775193i −0.921829 0.387596i \(-0.873305\pi\)
0.921829 0.387596i \(-0.126695\pi\)
\(314\) 7.37778 0.416352
\(315\) −9.80642 + 1.37778i −0.552529 + 0.0776294i
\(316\) 2.94914 0.165902
\(317\) 32.5718i 1.82942i 0.404115 + 0.914708i \(0.367580\pi\)
−0.404115 + 0.914708i \(0.632420\pi\)
\(318\) 4.75557i 0.266679i
\(319\) 45.3274 2.53785
\(320\) −0.311108 2.21432i −0.0173915 0.123784i
\(321\) −7.61285 −0.424908
\(322\) 28.4701i 1.58658i
\(323\) 3.37778i 0.187945i
\(324\) −1.00000 −0.0555556
\(325\) 8.85728 + 30.8988i 0.491313 + 1.71396i
\(326\) 5.90813 0.327221
\(327\) 5.53972i 0.306347i
\(328\) 4.42864i 0.244531i
\(329\) −22.9590 −1.26577
\(330\) −1.80642 12.8573i −0.0994404 0.707770i
\(331\) 5.63158 0.309540 0.154770 0.987951i \(-0.450536\pi\)
0.154770 + 0.987951i \(0.450536\pi\)
\(332\) 0.133353i 0.00731870i
\(333\) 3.67307i 0.201283i
\(334\) 2.75557 0.150778
\(335\) 6.10171 0.857279i 0.333372 0.0468382i
\(336\) −4.42864 −0.241602
\(337\) 5.70471i 0.310756i −0.987855 0.155378i \(-0.950341\pi\)
0.987855 0.155378i \(-0.0496595\pi\)
\(338\) 28.3274i 1.54081i
\(339\) 12.3684 0.671760
\(340\) 7.47949 1.05086i 0.405633 0.0569906i
\(341\) −52.5531 −2.84591
\(342\) 1.00000i 0.0540738i
\(343\) 24.8573i 1.34217i
\(344\) −1.05086 −0.0566583
\(345\) −2.00000 14.2351i −0.107676 0.766390i
\(346\) 8.10171 0.435551
\(347\) 2.62222i 0.140768i 0.997520 + 0.0703840i \(0.0224224\pi\)
−0.997520 + 0.0703840i \(0.977578\pi\)
\(348\) 7.80642i 0.418468i
\(349\) 24.1017 1.29013 0.645067 0.764126i \(-0.276829\pi\)
0.645067 + 0.764126i \(0.276829\pi\)
\(350\) −21.2859 + 6.10171i −1.13778 + 0.326150i
\(351\) 6.42864 0.343135
\(352\) 5.80642i 0.309483i
\(353\) 3.64449i 0.193977i 0.995286 + 0.0969883i \(0.0309210\pi\)
−0.995286 + 0.0969883i \(0.969079\pi\)
\(354\) −4.62222 −0.245668
\(355\) 2.36842 + 16.8573i 0.125702 + 0.894691i
\(356\) −3.18421 −0.168763
\(357\) 14.9590i 0.791714i
\(358\) 0.235063i 0.0124235i
\(359\) −9.08250 −0.479356 −0.239678 0.970852i \(-0.577042\pi\)
−0.239678 + 0.970852i \(0.577042\pi\)
\(360\) −2.21432 + 0.311108i −0.116705 + 0.0163968i
\(361\) 1.00000 0.0526316
\(362\) 11.3176i 0.594838i
\(363\) 22.7146i 1.19221i
\(364\) 28.4701 1.49224
\(365\) −25.7146 + 3.61285i −1.34596 + 0.189105i
\(366\) 2.00000 0.104542
\(367\) 3.95851i 0.206633i −0.994649 0.103316i \(-0.967055\pi\)
0.994649 0.103316i \(-0.0329454\pi\)
\(368\) 6.42864i 0.335116i
\(369\) −4.42864 −0.230546
\(370\) 1.14272 + 8.13335i 0.0594072 + 0.422833i
\(371\) −21.0607 −1.09342
\(372\) 9.05086i 0.469265i
\(373\) 12.5303i 0.648797i 0.945921 + 0.324398i \(0.105162\pi\)
−0.945921 + 0.324398i \(0.894838\pi\)
\(374\) 19.6128 1.01416
\(375\) −10.2143 + 4.54617i −0.527465 + 0.234763i
\(376\) −5.18421 −0.267355
\(377\) 50.1847i 2.58464i
\(378\) 4.42864i 0.227785i
\(379\) −26.8385 −1.37860 −0.689302 0.724474i \(-0.742083\pi\)
−0.689302 + 0.724474i \(0.742083\pi\)
\(380\) −0.311108 2.21432i −0.0159595 0.113592i
\(381\) −1.76494 −0.0904204
\(382\) 6.32693i 0.323714i
\(383\) 17.5111i 0.894777i 0.894340 + 0.447389i \(0.147646\pi\)
−0.894340 + 0.447389i \(0.852354\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −56.9403 + 8.00000i −2.90194 + 0.407718i
\(386\) −11.5397 −0.587356
\(387\) 1.05086i 0.0534180i
\(388\) 11.4193i 0.579726i
\(389\) 29.4795 1.49467 0.747335 0.664448i \(-0.231333\pi\)
0.747335 + 0.664448i \(0.231333\pi\)
\(390\) 14.2351 2.00000i 0.720820 0.101274i
\(391\) 21.7146 1.09815
\(392\) 12.6128i 0.637045i
\(393\) 9.80642i 0.494669i
\(394\) 20.0415 1.00968
\(395\) −0.917502 6.53035i −0.0461645 0.328578i
\(396\) −5.80642 −0.291784
\(397\) 9.21279i 0.462377i −0.972909 0.231188i \(-0.925739\pi\)
0.972909 0.231188i \(-0.0742613\pi\)
\(398\) 20.4701i 1.02607i
\(399\) −4.42864 −0.221709
\(400\) −4.80642 + 1.37778i −0.240321 + 0.0688892i
\(401\) 29.2859 1.46247 0.731234 0.682126i \(-0.238945\pi\)
0.731234 + 0.682126i \(0.238945\pi\)
\(402\) 2.75557i 0.137435i
\(403\) 58.1847i 2.89839i
\(404\) 1.86665 0.0928692
\(405\) 0.311108 + 2.21432i 0.0154591 + 0.110030i
\(406\) −34.5718 −1.71577
\(407\) 21.3274i 1.05716i
\(408\) 3.37778i 0.167225i
\(409\) 17.8796 0.884087 0.442044 0.896994i \(-0.354254\pi\)
0.442044 + 0.896994i \(0.354254\pi\)
\(410\) −9.80642 + 1.37778i −0.484305 + 0.0680439i
\(411\) −1.47949 −0.0729781
\(412\) 10.6222i 0.523319i
\(413\) 20.4701i 1.00727i
\(414\) −6.42864 −0.315950
\(415\) 0.295286 0.0414872i 0.0144950 0.00203653i
\(416\) 6.42864 0.315190
\(417\) 4.85728i 0.237862i
\(418\) 5.80642i 0.284001i
\(419\) −30.8671 −1.50796 −0.753979 0.656899i \(-0.771868\pi\)
−0.753979 + 0.656899i \(0.771868\pi\)
\(420\) 1.37778 + 9.80642i 0.0672290 + 0.478504i
\(421\) −18.3970 −0.896615 −0.448307 0.893879i \(-0.647973\pi\)
−0.448307 + 0.893879i \(0.647973\pi\)
\(422\) 2.75557i 0.134139i
\(423\) 5.18421i 0.252065i
\(424\) −4.75557 −0.230951
\(425\) −4.65386 16.2351i −0.225745 0.787516i
\(426\) 7.61285 0.368844
\(427\) 8.85728i 0.428634i
\(428\) 7.61285i 0.367981i
\(429\) 37.3274 1.80218
\(430\) 0.326929 + 2.32693i 0.0157659 + 0.112214i
\(431\) 29.5941 1.42550 0.712749 0.701419i \(-0.247450\pi\)
0.712749 + 0.701419i \(0.247450\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 27.2988i 1.31190i 0.754805 + 0.655949i \(0.227731\pi\)
−0.754805 + 0.655949i \(0.772269\pi\)
\(434\) 40.0830 1.92404
\(435\) −17.2859 + 2.42864i −0.828796 + 0.116444i
\(436\) 5.53972 0.265304
\(437\) 6.42864i 0.307524i
\(438\) 11.6128i 0.554883i
\(439\) −9.64143 −0.460160 −0.230080 0.973172i \(-0.573899\pi\)
−0.230080 + 0.973172i \(0.573899\pi\)
\(440\) −12.8573 + 1.80642i −0.612947 + 0.0861179i
\(441\) 12.6128 0.600612
\(442\) 21.7146i 1.03286i
\(443\) 6.70519i 0.318573i 0.987232 + 0.159287i \(0.0509194\pi\)
−0.987232 + 0.159287i \(0.949081\pi\)
\(444\) 3.67307 0.174316
\(445\) 0.990632 + 7.05086i 0.0469605 + 0.334243i
\(446\) −10.6222 −0.502976
\(447\) 4.62222i 0.218623i
\(448\) 4.42864i 0.209234i
\(449\) 13.9398 0.657859 0.328929 0.944355i \(-0.393312\pi\)
0.328929 + 0.944355i \(0.393312\pi\)
\(450\) 1.37778 + 4.80642i 0.0649494 + 0.226577i
\(451\) −25.7146 −1.21085
\(452\) 12.3684i 0.581761i
\(453\) 11.4193i 0.536524i
\(454\) 15.3461 0.720230
\(455\) −8.85728 63.0420i −0.415236 2.95545i
\(456\) −1.00000 −0.0468293
\(457\) 23.2257i 1.08645i −0.839586 0.543226i \(-0.817203\pi\)
0.839586 0.543226i \(-0.182797\pi\)
\(458\) 19.7146i 0.921201i
\(459\) −3.37778 −0.157661
\(460\) −14.2351 + 2.00000i −0.663713 + 0.0932505i
\(461\) 19.9684 0.930019 0.465010 0.885306i \(-0.346051\pi\)
0.465010 + 0.885306i \(0.346051\pi\)
\(462\) 25.7146i 1.19635i
\(463\) 2.79706i 0.129990i −0.997886 0.0649951i \(-0.979297\pi\)
0.997886 0.0649951i \(-0.0207032\pi\)
\(464\) −7.80642 −0.362404
\(465\) 20.0415 2.81579i 0.929402 0.130579i
\(466\) 29.5625 1.36945
\(467\) 30.9719i 1.43321i 0.697480 + 0.716604i \(0.254305\pi\)
−0.697480 + 0.716604i \(0.745695\pi\)
\(468\) 6.42864i 0.297164i
\(469\) −12.2034 −0.563502
\(470\) 1.61285 + 11.4795i 0.0743951 + 0.529510i
\(471\) −7.37778 −0.339950
\(472\) 4.62222i 0.212755i
\(473\) 6.10171i 0.280557i
\(474\) −2.94914 −0.135459
\(475\) −4.80642 + 1.37778i −0.220534 + 0.0632171i
\(476\) −14.9590 −0.685644
\(477\) 4.75557i 0.217743i
\(478\) 1.67307i 0.0765245i
\(479\) −29.8765 −1.36509 −0.682546 0.730843i \(-0.739127\pi\)
−0.682546 + 0.730843i \(0.739127\pi\)
\(480\) 0.311108 + 2.21432i 0.0142001 + 0.101069i
\(481\) −23.6128 −1.07665
\(482\) 16.9590i 0.772461i
\(483\) 28.4701i 1.29544i
\(484\) −22.7146 −1.03248
\(485\) −25.2859 + 3.55262i −1.14817 + 0.161316i
\(486\) 1.00000 0.0453609
\(487\) 17.8479i 0.808766i −0.914590 0.404383i \(-0.867486\pi\)
0.914590 0.404383i \(-0.132514\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) −5.90813 −0.267175
\(490\) 27.9289 3.92396i 1.26170 0.177266i
\(491\) −8.68244 −0.391833 −0.195916 0.980621i \(-0.562768\pi\)
−0.195916 + 0.980621i \(0.562768\pi\)
\(492\) 4.42864i 0.199658i
\(493\) 26.3684i 1.18757i
\(494\) 6.42864 0.289238
\(495\) 1.80642 + 12.8573i 0.0811927 + 0.577892i
\(496\) 9.05086 0.406395
\(497\) 33.7146i 1.51230i
\(498\) 0.133353i 0.00597570i
\(499\) −11.2257 −0.502531 −0.251266 0.967918i \(-0.580847\pi\)
−0.251266 + 0.967918i \(0.580847\pi\)
\(500\) 4.54617 + 10.2143i 0.203311 + 0.456798i
\(501\) −2.75557 −0.123110
\(502\) 4.94914i 0.220891i
\(503\) 17.6543i 0.787168i −0.919289 0.393584i \(-0.871235\pi\)
0.919289 0.393584i \(-0.128765\pi\)
\(504\) 4.42864 0.197267
\(505\) −0.580728 4.13335i −0.0258421 0.183932i
\(506\) −37.3274 −1.65941
\(507\) 28.3274i 1.25806i
\(508\) 1.76494i 0.0783064i
\(509\) −14.1748 −0.628289 −0.314144 0.949375i \(-0.601718\pi\)
−0.314144 + 0.949375i \(0.601718\pi\)
\(510\) −7.47949 + 1.05086i −0.331198 + 0.0465326i
\(511\) 51.4291 2.27509
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) 5.34614 0.235808
\(515\) −23.5210 + 3.30465i −1.03646 + 0.145620i
\(516\) 1.05086 0.0462613
\(517\) 30.1017i 1.32387i
\(518\) 16.2667i 0.714718i
\(519\) −8.10171 −0.355626
\(520\) −2.00000 14.2351i −0.0877058 0.624249i
\(521\) −15.0005 −0.657183 −0.328591 0.944472i \(-0.606574\pi\)
−0.328591 + 0.944472i \(0.606574\pi\)
\(522\) 7.80642i 0.341678i
\(523\) 40.2864i 1.76160i 0.473488 + 0.880801i \(0.342995\pi\)
−0.473488 + 0.880801i \(0.657005\pi\)
\(524\) −9.80642 −0.428396
\(525\) 21.2859 6.10171i 0.928994 0.266300i
\(526\) 9.45091 0.412079
\(527\) 30.5718i 1.33173i
\(528\) 5.80642i 0.252692i
\(529\) −18.3274 −0.796844
\(530\) 1.47949 + 10.5303i 0.0642651 + 0.457409i
\(531\) 4.62222 0.200587
\(532\) 4.42864i 0.192006i
\(533\) 28.4701i 1.23318i
\(534\) 3.18421 0.137794
\(535\) 16.8573 2.36842i 0.728804 0.102396i
\(536\) −2.75557 −0.119022
\(537\) 0.235063i 0.0101437i
\(538\) 2.94914i 0.127147i
\(539\) 73.2355 3.15448
\(540\) 2.21432 0.311108i 0.0952891 0.0133879i
\(541\) −22.3872 −0.962499 −0.481249 0.876584i \(-0.659817\pi\)
−0.481249 + 0.876584i \(0.659817\pi\)
\(542\) 30.9590i 1.32980i
\(543\) 11.3176i 0.485683i
\(544\) −3.37778 −0.144821
\(545\) −1.72345 12.2667i −0.0738245 0.525448i
\(546\) −28.4701 −1.21841
\(547\) 19.7333i 0.843735i −0.906658 0.421867i \(-0.861375\pi\)
0.906658 0.421867i \(-0.138625\pi\)
\(548\) 1.47949i 0.0632009i
\(549\) −2.00000 −0.0853579
\(550\) 8.00000 + 27.9081i 0.341121 + 1.19001i
\(551\) −7.80642 −0.332565
\(552\) 6.42864i 0.273621i
\(553\) 13.0607i 0.555397i
\(554\) −13.0923 −0.556240
\(555\) −1.14272 8.13335i −0.0485058 0.345242i
\(556\) −4.85728 −0.205995
\(557\) 15.6543i 0.663295i −0.943403 0.331648i \(-0.892395\pi\)
0.943403 0.331648i \(-0.107605\pi\)
\(558\) 9.05086i 0.383153i
\(559\) −6.75557 −0.285730
\(560\) 9.80642 1.37778i 0.414397 0.0582220i
\(561\) −19.6128 −0.828055
\(562\) 18.5303i 0.781656i
\(563\) 36.9403i 1.55685i 0.627740 + 0.778423i \(0.283980\pi\)
−0.627740 + 0.778423i \(0.716020\pi\)
\(564\) 5.18421 0.218295
\(565\) −27.3876 + 3.84791i −1.15221 + 0.161883i
\(566\) 26.3783 1.10876
\(567\) 4.42864i 0.185985i
\(568\) 7.61285i 0.319428i
\(569\) 1.20294 0.0504300 0.0252150 0.999682i \(-0.491973\pi\)
0.0252150 + 0.999682i \(0.491973\pi\)
\(570\) 0.311108 + 2.21432i 0.0130309 + 0.0927476i
\(571\) 37.7975 1.58178 0.790889 0.611960i \(-0.209619\pi\)
0.790889 + 0.611960i \(0.209619\pi\)
\(572\) 37.3274i 1.56074i
\(573\) 6.32693i 0.264311i
\(574\) 19.6128 0.818624
\(575\) 8.85728 + 30.8988i 0.369374 + 1.28857i
\(576\) 1.00000 0.0416667
\(577\) 23.2257i 0.966898i −0.875372 0.483449i \(-0.839384\pi\)
0.875372 0.483449i \(-0.160616\pi\)
\(578\) 5.59057i 0.232537i
\(579\) 11.5397 0.479574
\(580\) 2.42864 + 17.2859i 0.100844 + 0.717759i
\(581\) −0.590573 −0.0245011
\(582\) 11.4193i 0.473344i
\(583\) 27.6128i 1.14361i
\(584\) 11.6128 0.480543
\(585\) −14.2351 + 2.00000i −0.588547 + 0.0826898i
\(586\) 28.5718 1.18029
\(587\) 16.8069i 0.693695i −0.937922 0.346848i \(-0.887252\pi\)
0.937922 0.346848i \(-0.112748\pi\)
\(588\) 12.6128i 0.520145i
\(589\) 9.05086 0.372934
\(590\) 10.2351 1.43801i 0.421371 0.0592018i
\(591\) −20.0415 −0.824397
\(592\) 3.67307i 0.150962i
\(593\) 16.3555i 0.671640i −0.941926 0.335820i \(-0.890987\pi\)
0.941926 0.335820i \(-0.109013\pi\)
\(594\) 5.80642 0.238240
\(595\) 4.65386 + 33.1240i 0.190790 + 1.35795i
\(596\) 4.62222 0.189333
\(597\) 20.4701i 0.837787i
\(598\) 41.3274i 1.69000i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 4.80642 1.37778i 0.196221 0.0562478i
\(601\) 7.89829 0.322178 0.161089 0.986940i \(-0.448499\pi\)
0.161089 + 0.986940i \(0.448499\pi\)
\(602\) 4.65386i 0.189677i
\(603\) 2.75557i 0.112215i
\(604\) 11.4193 0.464644
\(605\) 7.06668 + 50.2973i 0.287301 + 2.04488i
\(606\) −1.86665 −0.0758273
\(607\) 17.8479i 0.724424i −0.932096 0.362212i \(-0.882022\pi\)
0.932096 0.362212i \(-0.117978\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 34.5718 1.40092
\(610\) −4.42864 + 0.622216i −0.179310 + 0.0251928i
\(611\) −33.3274 −1.34828
\(612\) 3.37778i 0.136539i
\(613\) 0.622216i 0.0251311i 0.999921 + 0.0125655i \(0.00399984\pi\)
−0.999921 + 0.0125655i \(0.996000\pi\)
\(614\) 22.7556 0.918340
\(615\) 9.80642 1.37778i 0.395433 0.0555576i
\(616\) 25.7146 1.03607
\(617\) 37.4795i 1.50887i 0.656376 + 0.754434i \(0.272088\pi\)
−0.656376 + 0.754434i \(0.727912\pi\)
\(618\) 10.6222i 0.427288i
\(619\) −28.6735 −1.15249 −0.576244 0.817278i \(-0.695482\pi\)
−0.576244 + 0.817278i \(0.695482\pi\)
\(620\) −2.81579 20.0415i −0.113085 0.804885i
\(621\) 6.42864 0.257972
\(622\) 6.32693i 0.253687i
\(623\) 14.1017i 0.564973i
\(624\) −6.42864 −0.257352
\(625\) 21.2034 13.2444i 0.848137 0.529777i
\(626\) 13.7146 0.548144
\(627\) 5.80642i 0.231886i
\(628\) 7.37778i 0.294406i
\(629\) 12.4068 0.494693
\(630\) −1.37778 9.80642i −0.0548922 0.390697i
\(631\) 1.24443 0.0495400 0.0247700 0.999693i \(-0.492115\pi\)
0.0247700 + 0.999693i \(0.492115\pi\)
\(632\) 2.94914i 0.117311i
\(633\) 2.75557i 0.109524i
\(634\) −32.5718 −1.29359
\(635\) 3.90813 0.549086i 0.155090 0.0217898i
\(636\) 4.75557 0.188571
\(637\) 81.0835i 3.21264i
\(638\) 45.3274i 1.79453i
\(639\) −7.61285 −0.301160
\(640\) 2.21432 0.311108i 0.0875287 0.0122976i
\(641\) −17.4064 −0.687510 −0.343755 0.939059i \(-0.611699\pi\)
−0.343755 + 0.939059i \(0.611699\pi\)
\(642\) 7.61285i 0.300455i
\(643\) 35.1526i 1.38628i −0.720802 0.693141i \(-0.756226\pi\)
0.720802 0.693141i \(-0.243774\pi\)
\(644\) 28.4701 1.12188
\(645\) −0.326929 2.32693i −0.0128728 0.0916227i
\(646\) −3.37778 −0.132897
\(647\) 34.4286i 1.35353i −0.736199 0.676765i \(-0.763381\pi\)
0.736199 0.676765i \(-0.236619\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 26.8385 1.05350
\(650\) −30.8988 + 8.85728i −1.21195 + 0.347411i
\(651\) −40.0830 −1.57098
\(652\) 5.90813i 0.231380i
\(653\) 4.30819i 0.168593i −0.996441 0.0842963i \(-0.973136\pi\)
0.996441 0.0842963i \(-0.0268642\pi\)
\(654\) −5.53972 −0.216620
\(655\) 3.05086 + 21.7146i 0.119207 + 0.848458i
\(656\) 4.42864 0.172909
\(657\) 11.6128i 0.453060i
\(658\) 22.9590i 0.895035i
\(659\) 27.0736 1.05464 0.527319 0.849667i \(-0.323197\pi\)
0.527319 + 0.849667i \(0.323197\pi\)
\(660\) 12.8573 1.80642i 0.500469 0.0703150i
\(661\) −43.2543 −1.68240 −0.841198 0.540727i \(-0.818149\pi\)
−0.841198 + 0.540727i \(0.818149\pi\)
\(662\) 5.63158i 0.218878i
\(663\) 21.7146i 0.843324i
\(664\) −0.133353 −0.00517510
\(665\) 9.80642 1.37778i 0.380277 0.0534282i
\(666\) −3.67307 −0.142329
\(667\) 50.1847i 1.94316i
\(668\) 2.75557i 0.106616i
\(669\) 10.6222 0.410679
\(670\) 0.857279 + 6.10171i 0.0331196 + 0.235730i
\(671\) −11.6128 −0.448309
\(672\) 4.42864i 0.170838i
\(673\) 15.0321i 0.579446i 0.957111 + 0.289723i \(0.0935631\pi\)
−0.957111 + 0.289723i \(0.906437\pi\)
\(674\) 5.70471 0.219737
\(675\) −1.37778 4.80642i −0.0530309 0.184999i
\(676\) 28.3274 1.08952
\(677\) 22.9403i 0.881666i −0.897589 0.440833i \(-0.854683\pi\)
0.897589 0.440833i \(-0.145317\pi\)
\(678\) 12.3684i 0.475006i
\(679\) 50.5718 1.94077
\(680\) 1.05086 + 7.47949i 0.0402985 + 0.286826i
\(681\) −15.3461 −0.588065
\(682\) 52.5531i 2.01236i
\(683\) 9.77784i 0.374139i 0.982347 + 0.187069i \(0.0598989\pi\)
−0.982347 + 0.187069i \(0.940101\pi\)
\(684\) 1.00000 0.0382360
\(685\) 3.27607 0.460282i 0.125172 0.0175865i
\(686\) −24.8573 −0.949055
\(687\) 19.7146i 0.752157i
\(688\) 1.05086i 0.0400635i
\(689\) −30.5718 −1.16469
\(690\) 14.2351 2.00000i 0.541920 0.0761387i
\(691\) −44.0830 −1.67700 −0.838498 0.544905i \(-0.816566\pi\)
−0.838498 + 0.544905i \(0.816566\pi\)
\(692\) 8.10171i 0.307981i
\(693\) 25.7146i 0.976815i
\(694\) −2.62222 −0.0995379
\(695\) 1.51114 + 10.7556i 0.0573207 + 0.407982i
\(696\) 7.80642 0.295902
\(697\) 14.9590i 0.566612i
\(698\) 24.1017i 0.912263i
\(699\) −29.5625 −1.11816
\(700\) −6.10171 21.2859i −0.230623 0.804532i
\(701\) −12.7685 −0.482259 −0.241129 0.970493i \(-0.577518\pi\)
−0.241129 + 0.970493i \(0.577518\pi\)
\(702\) 6.42864i 0.242633i
\(703\) 3.67307i 0.138532i
\(704\) 5.80642 0.218838
\(705\) −1.61285 11.4795i −0.0607434 0.432343i
\(706\) −3.64449 −0.137162
\(707\) 8.26671i 0.310901i
\(708\) 4.62222i 0.173714i
\(709\) 47.5941 1.78743 0.893717 0.448631i \(-0.148088\pi\)
0.893717 + 0.448631i \(0.148088\pi\)
\(710\) −16.8573 + 2.36842i −0.632642 + 0.0888851i
\(711\) 2.94914 0.110602
\(712\) 3.18421i 0.119333i
\(713\) 58.1847i 2.17903i
\(714\) 14.9590 0.559826
\(715\) −82.6548 + 11.6128i −3.09111 + 0.434296i
\(716\) −0.235063 −0.00878473
\(717\) 1.67307i 0.0624820i
\(718\) 9.08250i 0.338956i
\(719\) 47.0005 1.75282 0.876411 0.481564i \(-0.159931\pi\)
0.876411 + 0.481564i \(0.159931\pi\)
\(720\) −0.311108 2.21432i −0.0115943 0.0825228i
\(721\) 47.0420 1.75193
\(722\) 1.00000i 0.0372161i
\(723\) 16.9590i 0.630712i
\(724\) −11.3176 −0.420614
\(725\) 37.5210 10.7556i 1.39349 0.399452i
\(726\) 22.7146 0.843016
\(727\) 52.6321i 1.95202i −0.217737 0.976008i \(-0.569867\pi\)
0.217737 0.976008i \(-0.430133\pi\)
\(728\) 28.4701i 1.05517i
\(729\) −1.00000 −0.0370370
\(730\) −3.61285 25.7146i −0.133717 0.951738i
\(731\) 3.54956 0.131285
\(732\) 2.00000i 0.0739221i
\(733\) 27.3145i 1.00888i 0.863446 + 0.504442i \(0.168302\pi\)
−0.863446 + 0.504442i \(0.831698\pi\)
\(734\) 3.95851 0.146111
\(735\) −27.9289 + 3.92396i −1.03017 + 0.144737i
\(736\) 6.42864 0.236963
\(737\) 16.0000i 0.589368i
\(738\) 4.42864i 0.163020i
\(739\) −25.3274 −0.931684 −0.465842 0.884868i \(-0.654248\pi\)
−0.465842 + 0.884868i \(0.654248\pi\)
\(740\) −8.13335 + 1.14272i −0.298988 + 0.0420073i
\(741\) −6.42864 −0.236162
\(742\) 21.0607i 0.773163i
\(743\) 11.8796i 0.435819i −0.975969 0.217909i \(-0.930076\pi\)
0.975969 0.217909i \(-0.0699237\pi\)
\(744\) −9.05086 −0.331820
\(745\) −1.43801 10.2351i −0.0526845 0.374984i
\(746\) −12.5303 −0.458769
\(747\) 0.133353i 0.00487913i
\(748\) 19.6128i 0.717117i
\(749\) −33.7146 −1.23190
\(750\) −4.54617 10.2143i −0.166003 0.372974i
\(751\) −45.5210 −1.66108 −0.830542 0.556956i \(-0.811969\pi\)
−0.830542 + 0.556956i \(0.811969\pi\)
\(752\) 5.18421i 0.189049i
\(753\) 4.94914i 0.180357i
\(754\) −50.1847 −1.82762
\(755\) −3.55262 25.2859i −0.129293 0.920249i
\(756\) −4.42864 −0.161068
\(757\) 51.7275i 1.88007i 0.341083 + 0.940033i \(0.389206\pi\)
−0.341083 + 0.940033i \(0.610794\pi\)
\(758\) 26.8385i 0.974820i
\(759\) 37.3274 1.35490
\(760\) 2.21432 0.311108i 0.0803218 0.0112851i
\(761\) 28.3684 1.02835 0.514177 0.857684i \(-0.328097\pi\)
0.514177 + 0.857684i \(0.328097\pi\)
\(762\) 1.76494i 0.0639369i
\(763\) 24.5334i 0.888169i
\(764\) 6.32693 0.228900
\(765\) 7.47949 1.05086i 0.270422 0.0379937i
\(766\) −17.5111 −0.632703
\(767\) 29.7146i 1.07293i
\(768\) 1.00000i 0.0360844i
\(769\) 0.285442 0.0102933 0.00514665 0.999987i \(-0.498362\pi\)
0.00514665 + 0.999987i \(0.498362\pi\)
\(770\) −8.00000 56.9403i −0.288300 2.05198i
\(771\) −5.34614 −0.192537
\(772\) 11.5397i 0.415324i
\(773\) 49.8163i 1.79177i 0.444289 + 0.895883i \(0.353456\pi\)
−0.444289 + 0.895883i \(0.646544\pi\)
\(774\) −1.05086 −0.0377722
\(775\) −43.5022 + 12.4701i −1.56265 + 0.447940i
\(776\) 11.4193 0.409928
\(777\) 16.2667i 0.583565i
\(778\) 29.4795i 1.05689i
\(779\) 4.42864 0.158672
\(780\) 2.00000 + 14.2351i 0.0716115 + 0.509697i
\(781\) −44.2034 −1.58172
\(782\) 21.7146i 0.776511i
\(783\) 7.80642i 0.278979i
\(784\) −12.6128 −0.450459
\(785\) 16.3368 2.29529i 0.583084 0.0819223i
\(786\) 9.80642 0.349784
\(787\) 20.7368i 0.739188i 0.929193 + 0.369594i \(0.120503\pi\)
−0.929193 + 0.369594i \(0.879497\pi\)
\(788\) 20.0415i