Properties

Label 804.2.c.a.671.1
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 4
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.1
Root \(-0.707107 - 0.707107i\)
Character \(\chi\) = 804.671
Dual form 804.2.c.a.671.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-1.41421 + 1.00000i) q^{3} -2.00000 q^{4} +1.41421i q^{5} +(1.41421 + 2.00000i) q^{6} -2.00000i q^{7} +2.82843i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-1.41421 + 1.00000i) q^{3} -2.00000 q^{4} +1.41421i q^{5} +(1.41421 + 2.00000i) q^{6} -2.00000i q^{7} +2.82843i q^{8} +(1.00000 - 2.82843i) q^{9} +2.00000 q^{10} -5.65685 q^{11} +(2.82843 - 2.00000i) q^{12} +2.00000 q^{13} -2.82843 q^{14} +(-1.41421 - 2.00000i) q^{15} +4.00000 q^{16} +5.65685i q^{17} +(-4.00000 - 1.41421i) q^{18} -4.00000i q^{19} -2.82843i q^{20} +(2.00000 + 2.82843i) q^{21} +8.00000i q^{22} +7.07107 q^{23} +(-2.82843 - 4.00000i) q^{24} +3.00000 q^{25} -2.82843i q^{26} +(1.41421 + 5.00000i) q^{27} +4.00000i q^{28} -5.65685i q^{29} +(-2.82843 + 2.00000i) q^{30} -5.65685i q^{32} +(8.00000 - 5.65685i) q^{33} +8.00000 q^{34} +2.82843 q^{35} +(-2.00000 + 5.65685i) q^{36} +8.00000 q^{37} -5.65685 q^{38} +(-2.82843 + 2.00000i) q^{39} -4.00000 q^{40} -1.41421i q^{41} +(4.00000 - 2.82843i) q^{42} +4.00000i q^{43} +11.3137 q^{44} +(4.00000 + 1.41421i) q^{45} -10.0000i q^{46} +7.07107 q^{47} +(-5.65685 + 4.00000i) q^{48} +3.00000 q^{49} -4.24264i q^{50} +(-5.65685 - 8.00000i) q^{51} -4.00000 q^{52} -12.7279i q^{53} +(7.07107 - 2.00000i) q^{54} -8.00000i q^{55} +5.65685 q^{56} +(4.00000 + 5.65685i) q^{57} -8.00000 q^{58} +1.41421 q^{59} +(2.82843 + 4.00000i) q^{60} -6.00000 q^{61} +(-5.65685 - 2.00000i) q^{63} -8.00000 q^{64} +2.82843i q^{65} +(-8.00000 - 11.3137i) q^{66} -1.00000i q^{67} -11.3137i q^{68} +(-10.0000 + 7.07107i) q^{69} -4.00000i q^{70} +15.5563 q^{71} +(8.00000 + 2.82843i) q^{72} +10.0000 q^{73} -11.3137i q^{74} +(-4.24264 + 3.00000i) q^{75} +8.00000i q^{76} +11.3137i q^{77} +(2.82843 + 4.00000i) q^{78} -8.00000i q^{79} +5.65685i q^{80} +(-7.00000 - 5.65685i) q^{81} -2.00000 q^{82} -15.5563 q^{83} +(-4.00000 - 5.65685i) q^{84} -8.00000 q^{85} +5.65685 q^{86} +(5.65685 + 8.00000i) q^{87} -16.0000i q^{88} +16.9706i q^{89} +(2.00000 - 5.65685i) q^{90} -4.00000i q^{91} -14.1421 q^{92} -10.0000i q^{94} +5.65685 q^{95} +(5.65685 + 8.00000i) q^{96} -6.00000 q^{97} -4.24264i q^{98} +(-5.65685 + 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 8q^{4} + 4q^{9} + O(q^{10}) \) \( 4q - 8q^{4} + 4q^{9} + 8q^{10} + 8q^{13} + 16q^{16} - 16q^{18} + 8q^{21} + 12q^{25} + 32q^{33} + 32q^{34} - 8q^{36} + 32q^{37} - 16q^{40} + 16q^{42} + 16q^{45} + 12q^{49} - 16q^{52} + 16q^{57} - 32q^{58} - 24q^{61} - 32q^{64} - 32q^{66} - 40q^{69} + 32q^{72} + 40q^{73} - 28q^{81} - 8q^{82} - 16q^{84} - 32q^{85} + 8q^{90} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) −1.41421 + 1.00000i −0.816497 + 0.577350i
\(4\) −2.00000 −1.00000
\(5\) 1.41421i 0.632456i 0.948683 + 0.316228i \(0.102416\pi\)
−0.948683 + 0.316228i \(0.897584\pi\)
\(6\) 1.41421 + 2.00000i 0.577350 + 0.816497i
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 1.00000 2.82843i 0.333333 0.942809i
\(10\) 2.00000 0.632456
\(11\) −5.65685 −1.70561 −0.852803 0.522233i \(-0.825099\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 2.82843 2.00000i 0.816497 0.577350i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −2.82843 −0.755929
\(15\) −1.41421 2.00000i −0.365148 0.516398i
\(16\) 4.00000 1.00000
\(17\) 5.65685i 1.37199i 0.727607 + 0.685994i \(0.240633\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −4.00000 1.41421i −0.942809 0.333333i
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 2.82843i 0.632456i
\(21\) 2.00000 + 2.82843i 0.436436 + 0.617213i
\(22\) 8.00000i 1.70561i
\(23\) 7.07107 1.47442 0.737210 0.675664i \(-0.236143\pi\)
0.737210 + 0.675664i \(0.236143\pi\)
\(24\) −2.82843 4.00000i −0.577350 0.816497i
\(25\) 3.00000 0.600000
\(26\) 2.82843i 0.554700i
\(27\) 1.41421 + 5.00000i 0.272166 + 0.962250i
\(28\) 4.00000i 0.755929i
\(29\) 5.65685i 1.05045i −0.850963 0.525226i \(-0.823981\pi\)
0.850963 0.525226i \(-0.176019\pi\)
\(30\) −2.82843 + 2.00000i −0.516398 + 0.365148i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 8.00000 5.65685i 1.39262 0.984732i
\(34\) 8.00000 1.37199
\(35\) 2.82843 0.478091
\(36\) −2.00000 + 5.65685i −0.333333 + 0.942809i
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −5.65685 −0.917663
\(39\) −2.82843 + 2.00000i −0.452911 + 0.320256i
\(40\) −4.00000 −0.632456
\(41\) 1.41421i 0.220863i −0.993884 0.110432i \(-0.964777\pi\)
0.993884 0.110432i \(-0.0352233\pi\)
\(42\) 4.00000 2.82843i 0.617213 0.436436i
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 11.3137 1.70561
\(45\) 4.00000 + 1.41421i 0.596285 + 0.210819i
\(46\) 10.0000i 1.47442i
\(47\) 7.07107 1.03142 0.515711 0.856763i \(-0.327528\pi\)
0.515711 + 0.856763i \(0.327528\pi\)
\(48\) −5.65685 + 4.00000i −0.816497 + 0.577350i
\(49\) 3.00000 0.428571
\(50\) 4.24264i 0.600000i
\(51\) −5.65685 8.00000i −0.792118 1.12022i
\(52\) −4.00000 −0.554700
\(53\) 12.7279i 1.74831i −0.485643 0.874157i \(-0.661414\pi\)
0.485643 0.874157i \(-0.338586\pi\)
\(54\) 7.07107 2.00000i 0.962250 0.272166i
\(55\) 8.00000i 1.07872i
\(56\) 5.65685 0.755929
\(57\) 4.00000 + 5.65685i 0.529813 + 0.749269i
\(58\) −8.00000 −1.05045
\(59\) 1.41421 0.184115 0.0920575 0.995754i \(-0.470656\pi\)
0.0920575 + 0.995754i \(0.470656\pi\)
\(60\) 2.82843 + 4.00000i 0.365148 + 0.516398i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) −5.65685 2.00000i −0.712697 0.251976i
\(64\) −8.00000 −1.00000
\(65\) 2.82843i 0.350823i
\(66\) −8.00000 11.3137i −0.984732 1.39262i
\(67\) 1.00000i 0.122169i
\(68\) 11.3137i 1.37199i
\(69\) −10.0000 + 7.07107i −1.20386 + 0.851257i
\(70\) 4.00000i 0.478091i
\(71\) 15.5563 1.84620 0.923099 0.384561i \(-0.125647\pi\)
0.923099 + 0.384561i \(0.125647\pi\)
\(72\) 8.00000 + 2.82843i 0.942809 + 0.333333i
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 11.3137i 1.31519i
\(75\) −4.24264 + 3.00000i −0.489898 + 0.346410i
\(76\) 8.00000i 0.917663i
\(77\) 11.3137i 1.28932i
\(78\) 2.82843 + 4.00000i 0.320256 + 0.452911i
\(79\) 8.00000i 0.900070i −0.893011 0.450035i \(-0.851411\pi\)
0.893011 0.450035i \(-0.148589\pi\)
\(80\) 5.65685i 0.632456i
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) −2.00000 −0.220863
\(83\) −15.5563 −1.70753 −0.853766 0.520658i \(-0.825687\pi\)
−0.853766 + 0.520658i \(0.825687\pi\)
\(84\) −4.00000 5.65685i −0.436436 0.617213i
\(85\) −8.00000 −0.867722
\(86\) 5.65685 0.609994
\(87\) 5.65685 + 8.00000i 0.606478 + 0.857690i
\(88\) 16.0000i 1.70561i
\(89\) 16.9706i 1.79888i 0.437048 + 0.899438i \(0.356024\pi\)
−0.437048 + 0.899438i \(0.643976\pi\)
\(90\) 2.00000 5.65685i 0.210819 0.596285i
\(91\) 4.00000i 0.419314i
\(92\) −14.1421 −1.47442
\(93\) 0 0
\(94\) 10.0000i 1.03142i
\(95\) 5.65685 0.580381
\(96\) 5.65685 + 8.00000i 0.577350 + 0.816497i
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 4.24264i 0.428571i
\(99\) −5.65685 + 16.0000i −0.568535 + 1.60806i
\(100\) −6.00000 −0.600000
\(101\) 7.07107i 0.703598i 0.936076 + 0.351799i \(0.114430\pi\)
−0.936076 + 0.351799i \(0.885570\pi\)
\(102\) −11.3137 + 8.00000i −1.12022 + 0.792118i
\(103\) 4.00000i 0.394132i −0.980390 0.197066i \(-0.936859\pi\)
0.980390 0.197066i \(-0.0631413\pi\)
\(104\) 5.65685i 0.554700i
\(105\) −4.00000 + 2.82843i −0.390360 + 0.276026i
\(106\) −18.0000 −1.74831
\(107\) 12.7279 1.23045 0.615227 0.788350i \(-0.289064\pi\)
0.615227 + 0.788350i \(0.289064\pi\)
\(108\) −2.82843 10.0000i −0.272166 0.962250i
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) −11.3137 −1.07872
\(111\) −11.3137 + 8.00000i −1.07385 + 0.759326i
\(112\) 8.00000i 0.755929i
\(113\) 12.7279i 1.19734i −0.800995 0.598671i \(-0.795696\pi\)
0.800995 0.598671i \(-0.204304\pi\)
\(114\) 8.00000 5.65685i 0.749269 0.529813i
\(115\) 10.0000i 0.932505i
\(116\) 11.3137i 1.05045i
\(117\) 2.00000 5.65685i 0.184900 0.522976i
\(118\) 2.00000i 0.184115i
\(119\) 11.3137 1.03713
\(120\) 5.65685 4.00000i 0.516398 0.365148i
\(121\) 21.0000 1.90909
\(122\) 8.48528i 0.768221i
\(123\) 1.41421 + 2.00000i 0.127515 + 0.180334i
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) −2.82843 + 8.00000i −0.251976 + 0.712697i
\(127\) 16.0000i 1.41977i 0.704317 + 0.709885i \(0.251253\pi\)
−0.704317 + 0.709885i \(0.748747\pi\)
\(128\) 11.3137i 1.00000i
\(129\) −4.00000 5.65685i −0.352180 0.498058i
\(130\) 4.00000 0.350823
\(131\) −7.07107 −0.617802 −0.308901 0.951094i \(-0.599961\pi\)
−0.308901 + 0.951094i \(0.599961\pi\)
\(132\) −16.0000 + 11.3137i −1.39262 + 0.984732i
\(133\) −8.00000 −0.693688
\(134\) −1.41421 −0.122169
\(135\) −7.07107 + 2.00000i −0.608581 + 0.172133i
\(136\) −16.0000 −1.37199
\(137\) 7.07107i 0.604122i 0.953289 + 0.302061i \(0.0976746\pi\)
−0.953289 + 0.302061i \(0.902325\pi\)
\(138\) 10.0000 + 14.1421i 0.851257 + 1.20386i
\(139\) 2.00000i 0.169638i 0.996396 + 0.0848189i \(0.0270312\pi\)
−0.996396 + 0.0848189i \(0.972969\pi\)
\(140\) −5.65685 −0.478091
\(141\) −10.0000 + 7.07107i −0.842152 + 0.595491i
\(142\) 22.0000i 1.84620i
\(143\) −11.3137 −0.946100
\(144\) 4.00000 11.3137i 0.333333 0.942809i
\(145\) 8.00000 0.664364
\(146\) 14.1421i 1.17041i
\(147\) −4.24264 + 3.00000i −0.349927 + 0.247436i
\(148\) −16.0000 −1.31519
\(149\) 2.82843i 0.231714i −0.993266 0.115857i \(-0.963039\pi\)
0.993266 0.115857i \(-0.0369614\pi\)
\(150\) 4.24264 + 6.00000i 0.346410 + 0.489898i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 11.3137 0.917663
\(153\) 16.0000 + 5.65685i 1.29352 + 0.457330i
\(154\) 16.0000 1.28932
\(155\) 0 0
\(156\) 5.65685 4.00000i 0.452911 0.320256i
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) −11.3137 −0.900070
\(159\) 12.7279 + 18.0000i 1.00939 + 1.42749i
\(160\) 8.00000 0.632456
\(161\) 14.1421i 1.11456i
\(162\) −8.00000 + 9.89949i −0.628539 + 0.777778i
\(163\) 8.00000i 0.626608i −0.949653 0.313304i \(-0.898564\pi\)
0.949653 0.313304i \(-0.101436\pi\)
\(164\) 2.82843i 0.220863i
\(165\) 8.00000 + 11.3137i 0.622799 + 0.880771i
\(166\) 22.0000i 1.70753i
\(167\) 4.24264 0.328305 0.164153 0.986435i \(-0.447511\pi\)
0.164153 + 0.986435i \(0.447511\pi\)
\(168\) −8.00000 + 5.65685i −0.617213 + 0.436436i
\(169\) −9.00000 −0.692308
\(170\) 11.3137i 0.867722i
\(171\) −11.3137 4.00000i −0.865181 0.305888i
\(172\) 8.00000i 0.609994i
\(173\) 22.6274i 1.72033i −0.510015 0.860165i \(-0.670360\pi\)
0.510015 0.860165i \(-0.329640\pi\)
\(174\) 11.3137 8.00000i 0.857690 0.606478i
\(175\) 6.00000i 0.453557i
\(176\) −22.6274 −1.70561
\(177\) −2.00000 + 1.41421i −0.150329 + 0.106299i
\(178\) 24.0000 1.79888
\(179\) 25.4558 1.90266 0.951330 0.308175i \(-0.0997184\pi\)
0.951330 + 0.308175i \(0.0997184\pi\)
\(180\) −8.00000 2.82843i −0.596285 0.210819i
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −5.65685 −0.419314
\(183\) 8.48528 6.00000i 0.627250 0.443533i
\(184\) 20.0000i 1.47442i
\(185\) 11.3137i 0.831800i
\(186\) 0 0
\(187\) 32.0000i 2.34007i
\(188\) −14.1421 −1.03142
\(189\) 10.0000 2.82843i 0.727393 0.205738i
\(190\) 8.00000i 0.580381i
\(191\) −8.48528 −0.613973 −0.306987 0.951714i \(-0.599321\pi\)
−0.306987 + 0.951714i \(0.599321\pi\)
\(192\) 11.3137 8.00000i 0.816497 0.577350i
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 8.48528i 0.609208i
\(195\) −2.82843 4.00000i −0.202548 0.286446i
\(196\) −6.00000 −0.428571
\(197\) 7.07107i 0.503793i −0.967754 0.251896i \(-0.918946\pi\)
0.967754 0.251896i \(-0.0810542\pi\)
\(198\) 22.6274 + 8.00000i 1.60806 + 0.568535i
\(199\) 4.00000i 0.283552i 0.989899 + 0.141776i \(0.0452813\pi\)
−0.989899 + 0.141776i \(0.954719\pi\)
\(200\) 8.48528i 0.600000i
\(201\) 1.00000 + 1.41421i 0.0705346 + 0.0997509i
\(202\) 10.0000 0.703598
\(203\) −11.3137 −0.794067
\(204\) 11.3137 + 16.0000i 0.792118 + 1.12022i
\(205\) 2.00000 0.139686
\(206\) −5.65685 −0.394132
\(207\) 7.07107 20.0000i 0.491473 1.39010i
\(208\) 8.00000 0.554700
\(209\) 22.6274i 1.56517i
\(210\) 4.00000 + 5.65685i 0.276026 + 0.390360i
\(211\) 4.00000i 0.275371i 0.990476 + 0.137686i \(0.0439664\pi\)
−0.990476 + 0.137686i \(0.956034\pi\)
\(212\) 25.4558i 1.74831i
\(213\) −22.0000 + 15.5563i −1.50742 + 1.06590i
\(214\) 18.0000i 1.23045i
\(215\) −5.65685 −0.385794
\(216\) −14.1421 + 4.00000i −0.962250 + 0.272166i
\(217\) 0 0
\(218\) 8.48528i 0.574696i
\(219\) −14.1421 + 10.0000i −0.955637 + 0.675737i
\(220\) 16.0000i 1.07872i
\(221\) 11.3137i 0.761042i
\(222\) 11.3137 + 16.0000i 0.759326 + 1.07385i
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) −11.3137 −0.755929
\(225\) 3.00000 8.48528i 0.200000 0.565685i
\(226\) −18.0000 −1.19734
\(227\) 7.07107 0.469323 0.234662 0.972077i \(-0.424602\pi\)
0.234662 + 0.972077i \(0.424602\pi\)
\(228\) −8.00000 11.3137i −0.529813 0.749269i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 14.1421 0.932505
\(231\) −11.3137 16.0000i −0.744387 1.05272i
\(232\) 16.0000 1.05045
\(233\) 18.3848i 1.20443i −0.798335 0.602213i \(-0.794286\pi\)
0.798335 0.602213i \(-0.205714\pi\)
\(234\) −8.00000 2.82843i −0.522976 0.184900i
\(235\) 10.0000i 0.652328i
\(236\) −2.82843 −0.184115
\(237\) 8.00000 + 11.3137i 0.519656 + 0.734904i
\(238\) 16.0000i 1.03713i
\(239\) 8.48528 0.548867 0.274434 0.961606i \(-0.411510\pi\)
0.274434 + 0.961606i \(0.411510\pi\)
\(240\) −5.65685 8.00000i −0.365148 0.516398i
\(241\) −16.0000 −1.03065 −0.515325 0.856995i \(-0.672329\pi\)
−0.515325 + 0.856995i \(0.672329\pi\)
\(242\) 29.6985i 1.90909i
\(243\) 15.5563 + 1.00000i 0.997940 + 0.0641500i
\(244\) 12.0000 0.768221
\(245\) 4.24264i 0.271052i
\(246\) 2.82843 2.00000i 0.180334 0.127515i
\(247\) 8.00000i 0.509028i
\(248\) 0 0
\(249\) 22.0000 15.5563i 1.39419 0.985844i
\(250\) 16.0000 1.01193
\(251\) −2.82843 −0.178529 −0.0892644 0.996008i \(-0.528452\pi\)
−0.0892644 + 0.996008i \(0.528452\pi\)
\(252\) 11.3137 + 4.00000i 0.712697 + 0.251976i
\(253\) −40.0000 −2.51478
\(254\) 22.6274 1.41977
\(255\) 11.3137 8.00000i 0.708492 0.500979i
\(256\) 16.0000 1.00000
\(257\) 16.9706i 1.05859i −0.848436 0.529297i \(-0.822456\pi\)
0.848436 0.529297i \(-0.177544\pi\)
\(258\) −8.00000 + 5.65685i −0.498058 + 0.352180i
\(259\) 16.0000i 0.994192i
\(260\) 5.65685i 0.350823i
\(261\) −16.0000 5.65685i −0.990375 0.350150i
\(262\) 10.0000i 0.617802i
\(263\) −1.41421 −0.0872041 −0.0436021 0.999049i \(-0.513883\pi\)
−0.0436021 + 0.999049i \(0.513883\pi\)
\(264\) 16.0000 + 22.6274i 0.984732 + 1.39262i
\(265\) 18.0000 1.10573
\(266\) 11.3137i 0.693688i
\(267\) −16.9706 24.0000i −1.03858 1.46878i
\(268\) 2.00000i 0.122169i
\(269\) 19.7990i 1.20717i 0.797300 + 0.603583i \(0.206261\pi\)
−0.797300 + 0.603583i \(0.793739\pi\)
\(270\) 2.82843 + 10.0000i 0.172133 + 0.608581i
\(271\) 2.00000i 0.121491i 0.998153 + 0.0607457i \(0.0193479\pi\)
−0.998153 + 0.0607457i \(0.980652\pi\)
\(272\) 22.6274i 1.37199i
\(273\) 4.00000 + 5.65685i 0.242091 + 0.342368i
\(274\) 10.0000 0.604122
\(275\) −16.9706 −1.02336
\(276\) 20.0000 14.1421i 1.20386 0.851257i
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 2.82843 0.169638
\(279\) 0 0
\(280\) 8.00000i 0.478091i
\(281\) 4.24264i 0.253095i 0.991961 + 0.126547i \(0.0403896\pi\)
−0.991961 + 0.126547i \(0.959610\pi\)
\(282\) 10.0000 + 14.1421i 0.595491 + 0.842152i
\(283\) 28.0000i 1.66443i 0.554455 + 0.832214i \(0.312927\pi\)
−0.554455 + 0.832214i \(0.687073\pi\)
\(284\) −31.1127 −1.84620
\(285\) −8.00000 + 5.65685i −0.473879 + 0.335083i
\(286\) 16.0000i 0.946100i
\(287\) −2.82843 −0.166957
\(288\) −16.0000 5.65685i −0.942809 0.333333i
\(289\) −15.0000 −0.882353
\(290\) 11.3137i 0.664364i
\(291\) 8.48528 6.00000i 0.497416 0.351726i
\(292\) −20.0000 −1.17041
\(293\) 5.65685i 0.330477i −0.986254 0.165238i \(-0.947161\pi\)
0.986254 0.165238i \(-0.0528394\pi\)
\(294\) 4.24264 + 6.00000i 0.247436 + 0.349927i
\(295\) 2.00000i 0.116445i
\(296\) 22.6274i 1.31519i
\(297\) −8.00000 28.2843i −0.464207 1.64122i
\(298\) −4.00000 −0.231714
\(299\) 14.1421 0.817861
\(300\) 8.48528 6.00000i 0.489898 0.346410i
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) −7.07107 10.0000i −0.406222 0.574485i
\(304\) 16.0000i 0.917663i
\(305\) 8.48528i 0.485866i
\(306\) 8.00000 22.6274i 0.457330 1.29352i
\(307\) 8.00000i 0.456584i −0.973593 0.228292i \(-0.926686\pi\)
0.973593 0.228292i \(-0.0733141\pi\)
\(308\) 22.6274i 1.28932i
\(309\) 4.00000 + 5.65685i 0.227552 + 0.321807i
\(310\) 0 0
\(311\) 19.7990 1.12270 0.561349 0.827579i \(-0.310283\pi\)
0.561349 + 0.827579i \(0.310283\pi\)
\(312\) −5.65685 8.00000i −0.320256 0.452911i
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 19.7990i 1.11732i
\(315\) 2.82843 8.00000i 0.159364 0.450749i
\(316\) 16.0000i 0.900070i
\(317\) 25.4558i 1.42974i 0.699256 + 0.714871i \(0.253515\pi\)
−0.699256 + 0.714871i \(0.746485\pi\)
\(318\) 25.4558 18.0000i 1.42749 1.00939i
\(319\) 32.0000i 1.79166i
\(320\) 11.3137i 0.632456i
\(321\) −18.0000 + 12.7279i −1.00466 + 0.710403i
\(322\) −20.0000 −1.11456
\(323\) 22.6274 1.25902
\(324\) 14.0000 + 11.3137i 0.777778 + 0.628539i
\(325\) 6.00000 0.332820
\(326\) −11.3137 −0.626608
\(327\) −8.48528 + 6.00000i −0.469237 + 0.331801i
\(328\) 4.00000 0.220863
\(329\) 14.1421i 0.779681i
\(330\) 16.0000 11.3137i 0.880771 0.622799i
\(331\) 4.00000i 0.219860i 0.993939 + 0.109930i \(0.0350627\pi\)
−0.993939 + 0.109930i \(0.964937\pi\)
\(332\) 31.1127 1.70753
\(333\) 8.00000 22.6274i 0.438397 1.23997i
\(334\) 6.00000i 0.328305i
\(335\) 1.41421 0.0772667
\(336\) 8.00000 + 11.3137i 0.436436 + 0.617213i
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 12.7279i 0.692308i
\(339\) 12.7279 + 18.0000i 0.691286 + 0.977626i
\(340\) 16.0000 0.867722
\(341\) 0 0
\(342\) −5.65685 + 16.0000i −0.305888 + 0.865181i
\(343\) 20.0000i 1.07990i
\(344\) −11.3137 −0.609994
\(345\) −10.0000 14.1421i −0.538382 0.761387i
\(346\) −32.0000 −1.72033
\(347\) 11.3137 0.607352 0.303676 0.952775i \(-0.401786\pi\)
0.303676 + 0.952775i \(0.401786\pi\)
\(348\) −11.3137 16.0000i −0.606478 0.857690i
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) −8.48528 −0.453557
\(351\) 2.82843 + 10.0000i 0.150970 + 0.533761i
\(352\) 32.0000i 1.70561i
\(353\) 21.2132i 1.12906i −0.825411 0.564532i \(-0.809057\pi\)
0.825411 0.564532i \(-0.190943\pi\)
\(354\) 2.00000 + 2.82843i 0.106299 + 0.150329i
\(355\) 22.0000i 1.16764i
\(356\) 33.9411i 1.79888i
\(357\) −16.0000 + 11.3137i −0.846810 + 0.598785i
\(358\) 36.0000i 1.90266i
\(359\) −21.2132 −1.11959 −0.559795 0.828631i \(-0.689120\pi\)
−0.559795 + 0.828631i \(0.689120\pi\)
\(360\) −4.00000 + 11.3137i −0.210819 + 0.596285i
\(361\) 3.00000 0.157895
\(362\) 11.3137i 0.594635i
\(363\) −29.6985 + 21.0000i −1.55877 + 1.10221i
\(364\) 8.00000i 0.419314i
\(365\) 14.1421i 0.740233i
\(366\) −8.48528 12.0000i −0.443533 0.627250i
\(367\) 8.00000i 0.417597i −0.977959 0.208798i \(-0.933045\pi\)
0.977959 0.208798i \(-0.0669552\pi\)
\(368\) 28.2843 1.47442
\(369\) −4.00000 1.41421i −0.208232 0.0736210i
\(370\) 16.0000 0.831800
\(371\) −25.4558 −1.32160
\(372\) 0 0
\(373\) 18.0000 0.932005 0.466002 0.884783i \(-0.345694\pi\)
0.466002 + 0.884783i \(0.345694\pi\)
\(374\) −45.2548 −2.34007
\(375\) −11.3137 16.0000i −0.584237 0.826236i
\(376\) 20.0000i 1.03142i
\(377\) 11.3137i 0.582686i
\(378\) −4.00000 14.1421i −0.205738 0.727393i
\(379\) 34.0000i 1.74646i −0.487306 0.873231i \(-0.662020\pi\)
0.487306 0.873231i \(-0.337980\pi\)
\(380\) −11.3137 −0.580381
\(381\) −16.0000 22.6274i −0.819705 1.15924i
\(382\) 12.0000i 0.613973i
\(383\) 5.65685 0.289052 0.144526 0.989501i \(-0.453834\pi\)
0.144526 + 0.989501i \(0.453834\pi\)
\(384\) −11.3137 16.0000i −0.577350 0.816497i
\(385\) −16.0000 −0.815436
\(386\) 2.82843i 0.143963i
\(387\) 11.3137 + 4.00000i 0.575108 + 0.203331i
\(388\) 12.0000 0.609208
\(389\) 25.4558i 1.29066i −0.763903 0.645331i \(-0.776719\pi\)
0.763903 0.645331i \(-0.223281\pi\)
\(390\) −5.65685 + 4.00000i −0.286446 + 0.202548i
\(391\) 40.0000i 2.02289i
\(392\) 8.48528i 0.428571i
\(393\) 10.0000 7.07107i 0.504433 0.356688i
\(394\) −10.0000 −0.503793
\(395\) 11.3137 0.569254
\(396\) 11.3137 32.0000i 0.568535 1.60806i
\(397\) 12.0000 0.602263 0.301131 0.953583i \(-0.402636\pi\)
0.301131 + 0.953583i \(0.402636\pi\)
\(398\) 5.65685 0.283552
\(399\) 11.3137 8.00000i 0.566394 0.400501i
\(400\) 12.0000 0.600000
\(401\) 26.8701i 1.34183i −0.741536 0.670913i \(-0.765902\pi\)
0.741536 0.670913i \(-0.234098\pi\)
\(402\) 2.00000 1.41421i 0.0997509 0.0705346i
\(403\) 0 0
\(404\) 14.1421i 0.703598i
\(405\) 8.00000 9.89949i 0.397523 0.491910i
\(406\) 16.0000i 0.794067i
\(407\) −45.2548 −2.24320
\(408\) 22.6274 16.0000i 1.12022 0.792118i
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 2.82843i 0.139686i
\(411\) −7.07107 10.0000i −0.348790 0.493264i
\(412\) 8.00000i 0.394132i
\(413\) 2.82843i 0.139178i
\(414\) −28.2843 10.0000i −1.39010 0.491473i
\(415\) 22.0000i 1.07994i
\(416\) 11.3137i 0.554700i
\(417\) −2.00000 2.82843i −0.0979404 0.138509i
\(418\) 32.0000 1.56517
\(419\) −26.8701 −1.31269 −0.656344 0.754462i \(-0.727898\pi\)
−0.656344 + 0.754462i \(0.727898\pi\)
\(420\) 8.00000 5.65685i 0.390360 0.276026i
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 5.65685 0.275371
\(423\) 7.07107 20.0000i 0.343807 0.972433i
\(424\) 36.0000 1.74831
\(425\) 16.9706i 0.823193i
\(426\) 22.0000 + 31.1127i 1.06590 + 1.50742i
\(427\) 12.0000i 0.580721i
\(428\) −25.4558 −1.23045
\(429\) 16.0000 11.3137i 0.772487 0.546231i
\(430\) 8.00000i 0.385794i
\(431\) −15.5563 −0.749323 −0.374661 0.927162i \(-0.622241\pi\)
−0.374661 + 0.927162i \(0.622241\pi\)
\(432\) 5.65685 + 20.0000i 0.272166 + 0.962250i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) −11.3137 + 8.00000i −0.542451 + 0.383571i
\(436\) −12.0000 −0.574696
\(437\) 28.2843i 1.35302i
\(438\) 14.1421 + 20.0000i 0.675737 + 0.955637i
\(439\) 8.00000i 0.381819i −0.981608 0.190910i \(-0.938856\pi\)
0.981608 0.190910i \(-0.0611437\pi\)
\(440\) 22.6274 1.07872
\(441\) 3.00000 8.48528i 0.142857 0.404061i
\(442\) 16.0000 0.761042
\(443\) 11.3137 0.537531 0.268765 0.963206i \(-0.413384\pi\)
0.268765 + 0.963206i \(0.413384\pi\)
\(444\) 22.6274 16.0000i 1.07385 0.759326i
\(445\) −24.0000 −1.13771
\(446\) 11.3137 0.535720
\(447\) 2.82843 + 4.00000i 0.133780 + 0.189194i
\(448\) 16.0000i 0.755929i
\(449\) 22.6274i 1.06785i −0.845531 0.533927i \(-0.820716\pi\)
0.845531 0.533927i \(-0.179284\pi\)
\(450\) −12.0000 4.24264i −0.565685 0.200000i
\(451\) 8.00000i 0.376705i
\(452\) 25.4558i 1.19734i
\(453\) 0 0
\(454\) 10.0000i 0.469323i
\(455\) 5.65685 0.265197
\(456\) −16.0000 + 11.3137i −0.749269 + 0.529813i
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 14.1421i 0.660819i
\(459\) −28.2843 + 8.00000i −1.32020 + 0.373408i
\(460\) 20.0000i 0.932505i
\(461\) 31.1127i 1.44906i 0.689242 + 0.724531i \(0.257944\pi\)
−0.689242 + 0.724531i \(0.742056\pi\)
\(462\) −22.6274 + 16.0000i −1.05272 + 0.744387i
\(463\) 2.00000i 0.0929479i 0.998920 + 0.0464739i \(0.0147984\pi\)
−0.998920 + 0.0464739i \(0.985202\pi\)
\(464\) 22.6274i 1.05045i
\(465\) 0 0
\(466\) −26.0000 −1.20443
\(467\) 41.0122 1.89782 0.948909 0.315550i \(-0.102189\pi\)
0.948909 + 0.315550i \(0.102189\pi\)
\(468\) −4.00000 + 11.3137i −0.184900 + 0.522976i
\(469\) −2.00000 −0.0923514
\(470\) 14.1421 0.652328
\(471\) 19.7990 14.0000i 0.912289 0.645086i
\(472\) 4.00000i 0.184115i
\(473\) 22.6274i 1.04041i
\(474\) 16.0000 11.3137i 0.734904 0.519656i
\(475\) 12.0000i 0.550598i
\(476\) −22.6274 −1.03713
\(477\) −36.0000 12.7279i −1.64833 0.582772i
\(478\) 12.0000i 0.548867i
\(479\) 9.89949 0.452319 0.226160 0.974090i \(-0.427383\pi\)
0.226160 + 0.974090i \(0.427383\pi\)
\(480\) −11.3137 + 8.00000i −0.516398 + 0.365148i
\(481\) 16.0000 0.729537
\(482\) 22.6274i 1.03065i
\(483\) 14.1421 + 20.0000i 0.643489 + 0.910032i
\(484\) −42.0000 −1.90909
\(485\) 8.48528i 0.385297i
\(486\) 1.41421 22.0000i 0.0641500 0.997940i
\(487\) 8.00000i 0.362515i 0.983436 + 0.181257i \(0.0580167\pi\)
−0.983436 + 0.181257i \(0.941983\pi\)
\(488\) 16.9706i 0.768221i
\(489\) 8.00000 + 11.3137i 0.361773 + 0.511624i
\(490\) 6.00000 0.271052
\(491\) 18.3848 0.829693 0.414847 0.909891i \(-0.363835\pi\)
0.414847 + 0.909891i \(0.363835\pi\)
\(492\) −2.82843 4.00000i −0.127515 0.180334i
\(493\) 32.0000 1.44121
\(494\) −11.3137 −0.509028
\(495\) −22.6274 8.00000i −1.01703 0.359573i
\(496\) 0 0
\(497\) 31.1127i 1.39560i
\(498\) −22.0000 31.1127i −0.985844 1.39419i
\(499\) 4.00000i 0.179065i −0.995984 0.0895323i \(-0.971463\pi\)
0.995984 0.0895323i \(-0.0285372\pi\)
\(500\) 22.6274i 1.01193i
\(501\) −6.00000 + 4.24264i −0.268060 + 0.189547i
\(502\) 4.00000i 0.178529i
\(503\) 22.6274 1.00891 0.504453 0.863439i \(-0.331694\pi\)
0.504453 + 0.863439i \(0.331694\pi\)
\(504\) 5.65685 16.0000i 0.251976 0.712697i
\(505\) −10.0000 −0.444994
\(506\) 56.5685i 2.51478i
\(507\) 12.7279 9.00000i 0.565267 0.399704i
\(508\) 32.0000i 1.41977i
\(509\) 2.82843i 0.125368i 0.998033 + 0.0626839i \(0.0199660\pi\)
−0.998033 + 0.0626839i \(0.980034\pi\)
\(510\) −11.3137 16.0000i −0.500979 0.708492i
\(511\) 20.0000i 0.884748i
\(512\) 22.6274i 1.00000i
\(513\) 20.0000 5.65685i 0.883022 0.249756i
\(514\) −24.0000 −1.05859
\(515\) 5.65685 0.249271
\(516\) 8.00000 + 11.3137i 0.352180 + 0.498058i
\(517\) −40.0000 −1.75920
\(518\) −22.6274 −0.994192
\(519\) 22.6274 + 32.0000i 0.993233 + 1.40464i
\(520\) −8.00000 −0.350823
\(521\) 4.24264i 0.185873i −0.995672 0.0929367i \(-0.970375\pi\)
0.995672 0.0929367i \(-0.0296254\pi\)
\(522\) −8.00000 + 22.6274i −0.350150 + 0.990375i
\(523\) 32.0000i 1.39926i 0.714504 + 0.699631i \(0.246652\pi\)
−0.714504 + 0.699631i \(0.753348\pi\)
\(524\) 14.1421 0.617802
\(525\) 6.00000 + 8.48528i 0.261861 + 0.370328i
\(526\) 2.00000i 0.0872041i
\(527\) 0 0
\(528\) 32.0000 22.6274i 1.39262 0.984732i
\(529\) 27.0000 1.17391
\(530\) 25.4558i 1.10573i
\(531\) 1.41421 4.00000i 0.0613716 0.173585i
\(532\) 16.0000 0.693688
\(533\) 2.82843i 0.122513i
\(534\) −33.9411 + 24.0000i −1.46878 + 1.03858i
\(535\) 18.0000i 0.778208i
\(536\) 2.82843 0.122169
\(537\) −36.0000 + 25.4558i −1.55351 + 1.09850i
\(538\) 28.0000 1.20717
\(539\) −16.9706 −0.730974
\(540\) 14.1421 4.00000i 0.608581 0.172133i
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 2.82843 0.121491
\(543\) −11.3137 + 8.00000i −0.485518 + 0.343313i
\(544\) 32.0000 1.37199
\(545\) 8.48528i 0.363470i
\(546\) 8.00000 5.65685i 0.342368 0.242091i
\(547\) 2.00000i 0.0855138i 0.999086 + 0.0427569i \(0.0136141\pi\)
−0.999086 + 0.0427569i \(0.986386\pi\)
\(548\) 14.1421i 0.604122i
\(549\) −6.00000 + 16.9706i −0.256074 + 0.724286i
\(550\) 24.0000i 1.02336i
\(551\) −22.6274 −0.963960
\(552\) −20.0000 28.2843i −0.851257 1.20386i
\(553\) −16.0000 −0.680389
\(554\) 31.1127i 1.32185i
\(555\) −11.3137 16.0000i −0.480240 0.679162i
\(556\) 4.00000i 0.169638i
\(557\) 2.82843i 0.119844i −0.998203 0.0599222i \(-0.980915\pi\)
0.998203 0.0599222i \(-0.0190852\pi\)
\(558\) 0 0
\(559\) 8.00000i 0.338364i
\(560\) 11.3137 0.478091
\(561\) 32.0000 + 45.2548i 1.35104 + 1.91066i
\(562\) 6.00000 0.253095
\(563\) 36.7696 1.54965 0.774826 0.632175i \(-0.217837\pi\)
0.774826 + 0.632175i \(0.217837\pi\)
\(564\) 20.0000 14.1421i 0.842152 0.595491i
\(565\) 18.0000 0.757266
\(566\) 39.5980 1.66443
\(567\) −11.3137 + 14.0000i −0.475131 + 0.587945i
\(568\) 44.0000i 1.84620i
\(569\) 14.1421i 0.592869i 0.955053 + 0.296435i \(0.0957977\pi\)
−0.955053 + 0.296435i \(0.904202\pi\)
\(570\) 8.00000 + 11.3137i 0.335083 + 0.473879i
\(571\) 12.0000i 0.502184i 0.967963 + 0.251092i \(0.0807897\pi\)
−0.967963 + 0.251092i \(0.919210\pi\)
\(572\) 22.6274 0.946100
\(573\) 12.0000 8.48528i 0.501307 0.354478i
\(574\) 4.00000i 0.166957i
\(575\) 21.2132 0.884652
\(576\) −8.00000 + 22.6274i −0.333333 + 0.942809i
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 21.2132i 0.882353i
\(579\) 2.82843 2.00000i 0.117545 0.0831172i
\(580\) −16.0000 −0.664364
\(581\) 31.1127i 1.29077i
\(582\) −8.48528 12.0000i −0.351726 0.497416i
\(583\) 72.0000i 2.98194i
\(584\) 28.2843i 1.17041i
\(585\) 8.00000 + 2.82843i 0.330759 + 0.116941i
\(586\) −8.00000 −0.330477
\(587\) 33.9411 1.40090 0.700450 0.713701i \(-0.252983\pi\)
0.700450 + 0.713701i \(0.252983\pi\)
\(588\) 8.48528 6.00000i 0.349927 0.247436i
\(589\) 0 0
\(590\) 2.82843 0.116445
\(591\) 7.07107 + 10.0000i 0.290865 + 0.411345i
\(592\) 32.0000 1.31519
\(593\) 9.89949i 0.406524i 0.979124 + 0.203262i \(0.0651542\pi\)
−0.979124 + 0.203262i \(0.934846\pi\)
\(594\) −40.0000 + 11.3137i −1.64122 + 0.464207i
\(595\) 16.0000i 0.655936i
\(596\) 5.65685i 0.231714i
\(597\) −4.00000 5.65685i −0.163709 0.231520i
\(598\) 20.0000i 0.817861i
\(599\) 16.9706 0.693398 0.346699 0.937976i \(-0.387302\pi\)
0.346699 + 0.937976i \(0.387302\pi\)
\(600\) −8.48528 12.0000i −0.346410 0.489898i
\(601\) 28.0000 1.14214 0.571072 0.820900i \(-0.306528\pi\)
0.571072 + 0.820900i \(0.306528\pi\)
\(602\) 11.3137i 0.461112i
\(603\) −2.82843 1.00000i −0.115182 0.0407231i
\(604\) 0 0
\(605\) 29.6985i 1.20742i
\(606\) −14.1421 + 10.0000i −0.574485 + 0.406222i
\(607\) 36.0000i 1.46119i −0.682808 0.730597i \(-0.739242\pi\)
0.682808 0.730597i \(-0.260758\pi\)
\(608\) −22.6274 −0.917663
\(609\) 16.0000 11.3137i 0.648353 0.458455i
\(610\) −12.0000 −0.485866
\(611\) 14.1421 0.572130
\(612\) −32.0000 11.3137i −1.29352 0.457330i
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) −11.3137 −0.456584
\(615\) −2.82843 + 2.00000i −0.114053 + 0.0806478i
\(616\) −32.0000 −1.28932
\(617\) 5.65685i 0.227736i −0.993496 0.113868i \(-0.963676\pi\)
0.993496 0.113868i \(-0.0363242\pi\)
\(618\) 8.00000 5.65685i 0.321807 0.227552i
\(619\) 48.0000i 1.92928i −0.263566 0.964641i \(-0.584899\pi\)
0.263566 0.964641i \(-0.415101\pi\)
\(620\) 0 0
\(621\) 10.0000 + 35.3553i 0.401286 + 1.41876i
\(622\) 28.0000i 1.12270i
\(623\) 33.9411 1.35982
\(624\) −11.3137 + 8.00000i −0.452911 + 0.320256i
\(625\) −1.00000 −0.0400000
\(626\) 36.7696i 1.46961i
\(627\) −22.6274 32.0000i −0.903652 1.27796i
\(628\) 28.0000 1.11732
\(629\) 45.2548i 1.80443i
\(630\) −11.3137 4.00000i −0.450749 0.159364i
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 22.6274 0.900070
\(633\) −4.00000 5.65685i −0.158986 0.224840i
\(634\) 36.0000 1.42974
\(635\) −22.6274 −0.897942
\(636\) −25.4558 36.0000i −1.00939 1.42749i
\(637\) 6.00000 0.237729
\(638\) 45.2548 1.79166
\(639\) 15.5563 44.0000i 0.615400 1.74061i
\(640\) −16.0000 −0.632456
\(641\) 1.41421i 0.0558581i 0.999610 + 0.0279290i \(0.00889125\pi\)
−0.999610 + 0.0279290i \(0.991109\pi\)
\(642\) 18.0000 + 25.4558i 0.710403 + 1.00466i
\(643\) 16.0000i 0.630978i 0.948929 + 0.315489i \(0.102169\pi\)
−0.948929 + 0.315489i \(0.897831\pi\)
\(644\) 28.2843i 1.11456i
\(645\) 8.00000 5.65685i 0.315000 0.222738i
\(646\) 32.0000i 1.25902i
\(647\) −48.0833 −1.89035 −0.945174 0.326567i \(-0.894108\pi\)
−0.945174 + 0.326567i \(0.894108\pi\)
\(648\) 16.0000 19.7990i 0.628539 0.777778i
\(649\) −8.00000 −0.314027
\(650\) 8.48528i 0.332820i
\(651\) 0 0
\(652\) 16.0000i 0.626608i
\(653\) 43.8406i 1.71562i 0.513970 + 0.857808i \(0.328174\pi\)
−0.513970 + 0.857808i \(0.671826\pi\)
\(654\) 8.48528 + 12.0000i 0.331801 + 0.469237i
\(655\) 10.0000i 0.390732i
\(656\) 5.65685i 0.220863i
\(657\) 10.0000 28.2843i 0.390137 1.10347i
\(658\) −20.0000 −0.779681
\(659\) −32.5269 −1.26707 −0.633534 0.773715i \(-0.718396\pi\)
−0.633534 + 0.773715i \(0.718396\pi\)
\(660\) −16.0000 22.6274i −0.622799 0.880771i
\(661\) 26.0000 1.01128 0.505641 0.862744i \(-0.331256\pi\)
0.505641 + 0.862744i \(0.331256\pi\)
\(662\) 5.65685 0.219860
\(663\) −11.3137 16.0000i −0.439388 0.621389i
\(664\) 44.0000i 1.70753i
\(665\) 11.3137i 0.438727i
\(666\) −32.0000 11.3137i −1.23997 0.438397i
\(667\) 40.0000i 1.54881i
\(668\) −8.48528 −0.328305
\(669\) −8.00000 11.3137i −0.309298 0.437413i
\(670\) 2.00000i 0.0772667i
\(671\) 33.9411 1.31028
\(672\) 16.0000 11.3137i 0.617213 0.436436i
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 14.1421i 0.544735i
\(675\) 4.24264 + 15.0000i 0.163299 + 0.577350i
\(676\) 18.0000 0.692308
\(677\) 24.0416i 0.923995i 0.886881 + 0.461997i \(0.152867\pi\)
−0.886881 + 0.461997i \(0.847133\pi\)
\(678\) 25.4558 18.0000i 0.977626 0.691286i
\(679\) 12.0000i 0.460518i
\(680\) 22.6274i 0.867722i
\(681\) −10.0000 + 7.07107i −0.383201 + 0.270964i
\(682\) 0 0
\(683\) −36.7696 −1.40695 −0.703474 0.710721i \(-0.748369\pi\)
−0.703474 + 0.710721i \(0.748369\pi\)
\(684\) 22.6274 + 8.00000i 0.865181 + 0.305888i
\(685\) −10.0000 −0.382080
\(686\) −28.2843 −1.07990
\(687\) −14.1421 + 10.0000i −0.539556 + 0.381524i
\(688\) 16.0000i 0.609994i
\(689\) 25.4558i 0.969790i
\(690\) −20.0000 + 14.1421i −0.761387 + 0.538382i
\(691\) 8.00000i 0.304334i −0.988355 0.152167i \(-0.951375\pi\)
0.988355 0.152167i \(-0.0486252\pi\)
\(692\) 45.2548i 1.72033i
\(693\) 32.0000 + 11.3137i 1.21558 + 0.429772i
\(694\) 16.0000i 0.607352i
\(695\) −2.82843 −0.107288
\(696\) −22.6274 + 16.0000i −0.857690 + 0.606478i
\(697\) 8.00000 0.303022
\(698\) 28.2843i 1.07058i
\(699\) 18.3848 + 26.0000i 0.695376 + 0.983410i
\(700\) 12.0000i 0.453557i
\(701\) 15.5563i 0.587555i 0.955874 + 0.293778i \(0.0949125\pi\)
−0.955874 + 0.293778i \(0.905087\pi\)
\(702\) 14.1421 4.00000i 0.533761 0.150970i
\(703\) 32.0000i 1.20690i
\(704\) 45.2548 1.70561
\(705\) −10.0000 14.1421i −0.376622 0.532624i
\(706\) −30.0000 −1.12906
\(707\) 14.1421 0.531870
\(708\) 4.00000 2.82843i 0.150329 0.106299i
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 31.1127 1.16764
\(711\) −22.6274 8.00000i −0.848594 0.300023i
\(712\) −48.0000 −1.79888
\(713\) 0 0
\(714\) 16.0000 + 22.6274i 0.598785 + 0.846810i
\(715\) 16.0000i 0.598366i
\(716\) −50.9117 −1.90266
\(717\) −12.0000 + 8.48528i −0.448148 + 0.316889i
\(718\) 30.0000i 1.11959i
\(719\) −35.3553 −1.31853 −0.659266 0.751910i \(-0.729133\pi\)
−0.659266 + 0.751910i \(0.729133\pi\)
\(720\) 16.0000 + 5.65685i 0.596285 + 0.210819i
\(721\) −8.00000 −0.297936
\(722\) 4.24264i 0.157895i
\(723\) 22.6274 16.0000i 0.841523 0.595046i
\(724\) −16.0000 −0.594635
\(725\) 16.9706i 0.630271i
\(726\) 29.6985 + 42.0000i 1.10221 + 1.55877i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 11.3137 0.419314
\(729\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(730\) 20.0000 0.740233
\(731\) −22.6274 −0.836905
\(732\) −16.9706 + 12.0000i −0.627250 + 0.443533i
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −11.3137 −0.417597
\(735\) −4.24264 6.00000i −0.156492 0.221313i
\(736\) 40.0000i 1.47442i
\(737\) 5.65685i 0.208373i
\(738\) −2.00000 + 5.65685i −0.0736210 + 0.208232i
\(739\) 44.0000i 1.61857i 0.587419 + 0.809283i \(0.300144\pi\)
−0.587419 + 0.809283i \(0.699856\pi\)
\(740\) 22.6274i 0.831800i
\(741\) 8.00000 + 11.3137i 0.293887 + 0.415619i
\(742\) 36.0000i 1.32160i
\(743\) −35.3553 −1.29706 −0.648531 0.761188i \(-0.724616\pi\)
−0.648531 + 0.761188i \(0.724616\pi\)
\(744\) 0 0
\(745\) 4.00000 0.146549
\(746\) 25.4558i 0.932005i
\(747\) −15.5563 + 44.0000i −0.569177 + 1.60988i
\(748\) 64.0000i 2.34007i
\(749\) 25.4558i 0.930136i
\(750\) −22.6274 + 16.0000i −0.826236 + 0.584237i
\(751\) 16.0000i 0.583848i 0.956441 + 0.291924i \(0.0942955\pi\)
−0.956441 + 0.291924i \(0.905705\pi\)
\(752\) 28.2843 1.03142
\(753\) 4.00000 2.82843i 0.145768 0.103074i
\(754\) −16.0000 −0.582686
\(755\) 0 0
\(756\) −20.0000 + 5.65685i −0.727393 + 0.205738i
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) −48.0833 −1.74646
\(759\) 56.5685 40.0000i 2.05331 1.45191i
\(760\) 16.0000i 0.580381i
\(761\) 5.65685i 0.205061i 0.994730 + 0.102530i \(0.0326939\pi\)
−0.994730 + 0.102530i \(0.967306\pi\)
\(762\) −32.0000 + 22.6274i −1.15924 + 0.819705i
\(763\) 12.0000i 0.434429i
\(764\) 16.9706 0.613973
\(765\) −8.00000 + 22.6274i −0.289241 + 0.818096i
\(766\) 8.00000i 0.289052i
\(767\) 2.82843 0.102129
\(768\) −22.6274 + 16.0000i −0.816497 + 0.577350i
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 22.6274i 0.815436i
\(771\) 16.9706 + 24.0000i 0.611180 + 0.864339i
\(772\) 4.00000 0.143963
\(773\) 36.7696i 1.32251i −0.750162 0.661254i \(-0.770024\pi\)
0.750162 0.661254i \(-0.229976\pi\)
\(774\) 5.65685 16.0000i 0.203331 0.575108i
\(775\) 0 0
\(776\) 16.9706i 0.609208i
\(777\) 16.0000 + 22.6274i 0.573997 + 0.811754i
\(778\) −36.0000 −1.29066
\(779\) −5.65685 −0.202678
\(780\) 5.65685 + 8.00000i 0.202548 + 0.286446i
\(781\) −88.0000 −3.14889
\(782\) 56.5685 2.02289
\(783\) 28.2843 8.00000i 1.01080 0.285897i
\(784\) 12.0000 0.428571
\(785\) 19.7990i 0.706656i
\(786\) −10.0000 14.1421i −0.356688 0.504433i
\(787\) 44.0000i 1.56843i −0.620489 0.784215i \(-0.713066\pi\)
0.620489 0.784215i \(-0.286934\pi\)
\(788\) 14.1421i 0.503793i
\(789\) 2.00000 1.41421i 0.0712019 0.0503473i
\(790\) 16.0000i 0.569254i
\(791\) −25.4558 −0.905106
\(792\) −45.2548 16.0000i −1.60806 0.568535i
\(793\) −12.0000 −0.426132