Properties

Label 1110.2.o.a.487.7
Level $1110$
Weight $2$
Character 1110.487
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 487.7
Character \(\chi\) \(=\) 1110.487
Dual form 1110.2.o.a.253.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.866398 - 2.06140i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.662100 - 0.662100i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.866398 - 2.06140i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.662100 - 0.662100i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(0.866398 + 2.06140i) q^{10} -3.51735i q^{11} +(-0.707107 - 0.707107i) q^{12} +6.87657 q^{13} +(0.662100 + 0.662100i) q^{14} +(-0.844991 + 2.07026i) q^{15} +1.00000 q^{16} -2.17458i q^{17} -1.00000i q^{18} +(-1.01389 + 1.01389i) q^{19} +(-0.866398 - 2.06140i) q^{20} +0.936350i q^{21} +3.51735i q^{22} +9.57399 q^{23} +(0.707107 + 0.707107i) q^{24} +(-3.49871 + 3.57198i) q^{25} -6.87657 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.662100 - 0.662100i) q^{28} +(-6.49970 - 6.49970i) q^{29} +(0.844991 - 2.07026i) q^{30} +(2.38699 - 2.38699i) q^{31} -1.00000 q^{32} +(-2.48714 + 2.48714i) q^{33} +2.17458i q^{34} +(-0.791208 + 1.93849i) q^{35} +1.00000i q^{36} +(-5.95481 - 1.24106i) q^{37} +(1.01389 - 1.01389i) q^{38} +(-4.86247 - 4.86247i) q^{39} +(0.866398 + 2.06140i) q^{40} -3.47992i q^{41} -0.936350i q^{42} +2.74581 q^{43} -3.51735i q^{44} +(2.06140 - 0.866398i) q^{45} -9.57399 q^{46} +(3.59071 + 3.59071i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.12325i q^{49} +(3.49871 - 3.57198i) q^{50} +(-1.53766 + 1.53766i) q^{51} +6.87657 q^{52} +(-2.93440 + 2.93440i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-7.25065 + 3.04742i) q^{55} +(0.662100 + 0.662100i) q^{56} +1.43385 q^{57} +(6.49970 + 6.49970i) q^{58} +(-3.45523 + 3.45523i) q^{59} +(-0.844991 + 2.07026i) q^{60} +(-9.99355 + 9.99355i) q^{61} +(-2.38699 + 2.38699i) q^{62} +(0.662100 - 0.662100i) q^{63} +1.00000 q^{64} +(-5.95785 - 14.1753i) q^{65} +(2.48714 - 2.48714i) q^{66} +(-1.14933 + 1.14933i) q^{67} -2.17458i q^{68} +(-6.76983 - 6.76983i) q^{69} +(0.791208 - 1.93849i) q^{70} -7.32848 q^{71} -1.00000i q^{72} +(-0.292649 - 0.292649i) q^{73} +(5.95481 + 1.24106i) q^{74} +(4.99973 - 0.0518094i) q^{75} +(-1.01389 + 1.01389i) q^{76} +(-2.32883 + 2.32883i) q^{77} +(4.86247 + 4.86247i) q^{78} +(7.95594 - 7.95594i) q^{79} +(-0.866398 - 2.06140i) q^{80} -1.00000 q^{81} +3.47992i q^{82} +(-1.46770 + 1.46770i) q^{83} +0.936350i q^{84} +(-4.48266 + 1.88405i) q^{85} -2.74581 q^{86} +9.19196i q^{87} +3.51735i q^{88} +(-6.43088 - 6.43088i) q^{89} +(-2.06140 + 0.866398i) q^{90} +(-4.55298 - 4.55298i) q^{91} +9.57399 q^{92} -3.37571 q^{93} +(-3.59071 - 3.59071i) q^{94} +(2.96845 + 1.21159i) q^{95} +(0.707107 + 0.707107i) q^{96} +0.301015i q^{97} +6.12325i q^{98} +3.51735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) −0.866398 2.06140i −0.387465 0.921884i
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) −0.662100 0.662100i −0.250250 0.250250i 0.570823 0.821073i \(-0.306624\pi\)
−0.821073 + 0.570823i \(0.806624\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) 0.866398 + 2.06140i 0.273979 + 0.651871i
\(11\) 3.51735i 1.06052i −0.847835 0.530260i \(-0.822094\pi\)
0.847835 0.530260i \(-0.177906\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 6.87657 1.90722 0.953609 0.301047i \(-0.0973362\pi\)
0.953609 + 0.301047i \(0.0973362\pi\)
\(14\) 0.662100 + 0.662100i 0.176954 + 0.176954i
\(15\) −0.844991 + 2.07026i −0.218176 + 0.534540i
\(16\) 1.00000 0.250000
\(17\) 2.17458i 0.527412i −0.964603 0.263706i \(-0.915055\pi\)
0.964603 0.263706i \(-0.0849449\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.01389 + 1.01389i −0.232601 + 0.232601i −0.813778 0.581176i \(-0.802593\pi\)
0.581176 + 0.813778i \(0.302593\pi\)
\(20\) −0.866398 2.06140i −0.193732 0.460942i
\(21\) 0.936350i 0.204328i
\(22\) 3.51735i 0.749901i
\(23\) 9.57399 1.99632 0.998158 0.0606732i \(-0.0193247\pi\)
0.998158 + 0.0606732i \(0.0193247\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) −3.49871 + 3.57198i −0.699742 + 0.714396i
\(26\) −6.87657 −1.34861
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.662100 0.662100i −0.125125 0.125125i
\(29\) −6.49970 6.49970i −1.20696 1.20696i −0.972006 0.234958i \(-0.924505\pi\)
−0.234958 0.972006i \(-0.575495\pi\)
\(30\) 0.844991 2.07026i 0.154274 0.377977i
\(31\) 2.38699 2.38699i 0.428716 0.428716i −0.459475 0.888191i \(-0.651962\pi\)
0.888191 + 0.459475i \(0.151962\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.48714 + 2.48714i −0.432956 + 0.432956i
\(34\) 2.17458i 0.372937i
\(35\) −0.791208 + 1.93849i −0.133739 + 0.327665i
\(36\) 1.00000i 0.166667i
\(37\) −5.95481 1.24106i −0.978965 0.204029i
\(38\) 1.01389 1.01389i 0.164474 0.164474i
\(39\) −4.86247 4.86247i −0.778619 0.778619i
\(40\) 0.866398 + 2.06140i 0.136990 + 0.325935i
\(41\) 3.47992i 0.543472i −0.962372 0.271736i \(-0.912402\pi\)
0.962372 0.271736i \(-0.0875977\pi\)
\(42\) 0.936350i 0.144482i
\(43\) 2.74581 0.418732 0.209366 0.977837i \(-0.432860\pi\)
0.209366 + 0.977837i \(0.432860\pi\)
\(44\) 3.51735i 0.530260i
\(45\) 2.06140 0.866398i 0.307295 0.129155i
\(46\) −9.57399 −1.41161
\(47\) 3.59071 + 3.59071i 0.523759 + 0.523759i 0.918704 0.394946i \(-0.129237\pi\)
−0.394946 + 0.918704i \(0.629237\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.12325i 0.874750i
\(50\) 3.49871 3.57198i 0.494792 0.505154i
\(51\) −1.53766 + 1.53766i −0.215315 + 0.215315i
\(52\) 6.87657 0.953609
\(53\) −2.93440 + 2.93440i −0.403071 + 0.403071i −0.879314 0.476243i \(-0.841998\pi\)
0.476243 + 0.879314i \(0.341998\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) −7.25065 + 3.04742i −0.977677 + 0.410914i
\(56\) 0.662100 + 0.662100i 0.0884768 + 0.0884768i
\(57\) 1.43385 0.189918
\(58\) 6.49970 + 6.49970i 0.853452 + 0.853452i
\(59\) −3.45523 + 3.45523i −0.449833 + 0.449833i −0.895299 0.445466i \(-0.853038\pi\)
0.445466 + 0.895299i \(0.353038\pi\)
\(60\) −0.844991 + 2.07026i −0.109088 + 0.267270i
\(61\) −9.99355 + 9.99355i −1.27954 + 1.27954i −0.338619 + 0.940924i \(0.609960\pi\)
−0.940924 + 0.338619i \(0.890040\pi\)
\(62\) −2.38699 + 2.38699i −0.303148 + 0.303148i
\(63\) 0.662100 0.662100i 0.0834167 0.0834167i
\(64\) 1.00000 0.125000
\(65\) −5.95785 14.1753i −0.738980 1.75824i
\(66\) 2.48714 2.48714i 0.306146 0.306146i
\(67\) −1.14933 + 1.14933i −0.140413 + 0.140413i −0.773819 0.633406i \(-0.781656\pi\)
0.633406 + 0.773819i \(0.281656\pi\)
\(68\) 2.17458i 0.263706i
\(69\) −6.76983 6.76983i −0.814992 0.814992i
\(70\) 0.791208 1.93849i 0.0945674 0.231694i
\(71\) −7.32848 −0.869730 −0.434865 0.900496i \(-0.643204\pi\)
−0.434865 + 0.900496i \(0.643204\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −0.292649 0.292649i −0.0342519 0.0342519i 0.689773 0.724025i \(-0.257710\pi\)
−0.724025 + 0.689773i \(0.757710\pi\)
\(74\) 5.95481 + 1.24106i 0.692233 + 0.144270i
\(75\) 4.99973 0.0518094i 0.577319 0.00598243i
\(76\) −1.01389 + 1.01389i −0.116301 + 0.116301i
\(77\) −2.32883 + 2.32883i −0.265395 + 0.265395i
\(78\) 4.86247 + 4.86247i 0.550567 + 0.550567i
\(79\) 7.95594 7.95594i 0.895113 0.895113i −0.0998861 0.994999i \(-0.531848\pi\)
0.994999 + 0.0998861i \(0.0318478\pi\)
\(80\) −0.866398 2.06140i −0.0968662 0.230471i
\(81\) −1.00000 −0.111111
\(82\) 3.47992i 0.384293i
\(83\) −1.46770 + 1.46770i −0.161102 + 0.161102i −0.783055 0.621953i \(-0.786339\pi\)
0.621953 + 0.783055i \(0.286339\pi\)
\(84\) 0.936350i 0.102164i
\(85\) −4.48266 + 1.88405i −0.486213 + 0.204354i
\(86\) −2.74581 −0.296088
\(87\) 9.19196i 0.985481i
\(88\) 3.51735i 0.374951i
\(89\) −6.43088 6.43088i −0.681672 0.681672i 0.278705 0.960377i \(-0.410095\pi\)
−0.960377 + 0.278705i \(0.910095\pi\)
\(90\) −2.06140 + 0.866398i −0.217290 + 0.0913264i
\(91\) −4.55298 4.55298i −0.477282 0.477282i
\(92\) 9.57399 0.998158
\(93\) −3.37571 −0.350045
\(94\) −3.59071 3.59071i −0.370353 0.370353i
\(95\) 2.96845 + 1.21159i 0.304556 + 0.124307i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 0.301015i 0.0305635i 0.999883 + 0.0152817i \(0.00486451\pi\)
−0.999883 + 0.0152817i \(0.995135\pi\)
\(98\) 6.12325i 0.618541i
\(99\) 3.51735 0.353507
\(100\) −3.49871 + 3.57198i −0.349871 + 0.357198i
\(101\) 7.88206i 0.784294i −0.919903 0.392147i \(-0.871732\pi\)
0.919903 0.392147i \(-0.128268\pi\)
\(102\) 1.53766 1.53766i 0.152251 0.152251i
\(103\) 3.81714i 0.376114i 0.982158 + 0.188057i \(0.0602190\pi\)
−0.982158 + 0.188057i \(0.939781\pi\)
\(104\) −6.87657 −0.674304
\(105\) 1.93019 0.811252i 0.188367 0.0791701i
\(106\) 2.93440 2.93440i 0.285014 0.285014i
\(107\) −3.39625 3.39625i −0.328328 0.328328i 0.523622 0.851950i \(-0.324580\pi\)
−0.851950 + 0.523622i \(0.824580\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −1.95485 + 1.95485i −0.187241 + 0.187241i −0.794502 0.607261i \(-0.792268\pi\)
0.607261 + 0.794502i \(0.292268\pi\)
\(110\) 7.25065 3.04742i 0.691322 0.290560i
\(111\) 3.33312 + 5.08825i 0.316366 + 0.482955i
\(112\) −0.662100 0.662100i −0.0625625 0.0625625i
\(113\) 18.3281i 1.72416i −0.506773 0.862079i \(-0.669162\pi\)
0.506773 0.862079i \(-0.330838\pi\)
\(114\) −1.43385 −0.134292
\(115\) −8.29489 19.7358i −0.773502 1.84037i
\(116\) −6.49970 6.49970i −0.603482 0.603482i
\(117\) 6.87657i 0.635739i
\(118\) 3.45523 3.45523i 0.318080 0.318080i
\(119\) −1.43979 + 1.43979i −0.131985 + 0.131985i
\(120\) 0.844991 2.07026i 0.0771368 0.188988i
\(121\) −1.37173 −0.124703
\(122\) 9.99355 9.99355i 0.904773 0.904773i
\(123\) −2.46067 + 2.46067i −0.221871 + 0.221871i
\(124\) 2.38699 2.38699i 0.214358 0.214358i
\(125\) 10.3945 + 4.11747i 0.929716 + 0.368278i
\(126\) −0.662100 + 0.662100i −0.0589845 + 0.0589845i
\(127\) −0.247513 0.247513i −0.0219632 0.0219632i 0.696040 0.718003i \(-0.254944\pi\)
−0.718003 + 0.696040i \(0.754944\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.94158 1.94158i −0.170947 0.170947i
\(130\) 5.95785 + 14.1753i 0.522538 + 1.24326i
\(131\) −1.31529 + 1.31529i −0.114917 + 0.114917i −0.762227 0.647310i \(-0.775894\pi\)
0.647310 + 0.762227i \(0.275894\pi\)
\(132\) −2.48714 + 2.48714i −0.216478 + 0.216478i
\(133\) 1.34259 0.116417
\(134\) 1.14933 1.14933i 0.0992872 0.0992872i
\(135\) −2.07026 0.844991i −0.178180 0.0727253i
\(136\) 2.17458i 0.186468i
\(137\) −13.6827 13.6827i −1.16899 1.16899i −0.982447 0.186544i \(-0.940271\pi\)
−0.186544 0.982447i \(-0.559729\pi\)
\(138\) 6.76983 + 6.76983i 0.576287 + 0.576287i
\(139\) −17.7419 −1.50484 −0.752422 0.658681i \(-0.771115\pi\)
−0.752422 + 0.658681i \(0.771115\pi\)
\(140\) −0.791208 + 1.93849i −0.0668693 + 0.163832i
\(141\) 5.07803i 0.427647i
\(142\) 7.32848 0.614992
\(143\) 24.1873i 2.02264i
\(144\) 1.00000i 0.0833333i
\(145\) −7.76713 + 19.0298i −0.645025 + 1.58034i
\(146\) 0.292649 + 0.292649i 0.0242198 + 0.0242198i
\(147\) −4.32979 + 4.32979i −0.357115 + 0.357115i
\(148\) −5.95481 1.24106i −0.489482 0.102015i
\(149\) 10.6094i 0.869159i 0.900633 + 0.434579i \(0.143103\pi\)
−0.900633 + 0.434579i \(0.856897\pi\)
\(150\) −4.99973 + 0.0518094i −0.408226 + 0.00423022i
\(151\) 3.90183i 0.317526i 0.987317 + 0.158763i \(0.0507506\pi\)
−0.987317 + 0.158763i \(0.949249\pi\)
\(152\) 1.01389 1.01389i 0.0822370 0.0822370i
\(153\) 2.17458 0.175804
\(154\) 2.32883 2.32883i 0.187663 0.187663i
\(155\) −6.98861 2.85245i −0.561339 0.229114i
\(156\) −4.86247 4.86247i −0.389309 0.389309i
\(157\) 1.75656 + 1.75656i 0.140188 + 0.140188i 0.773718 0.633530i \(-0.218395\pi\)
−0.633530 + 0.773718i \(0.718395\pi\)
\(158\) −7.95594 + 7.95594i −0.632940 + 0.632940i
\(159\) 4.14987 0.329106
\(160\) 0.866398 + 2.06140i 0.0684948 + 0.162968i
\(161\) −6.33894 6.33894i −0.499578 0.499578i
\(162\) 1.00000 0.0785674
\(163\) 9.39725i 0.736049i 0.929816 + 0.368025i \(0.119966\pi\)
−0.929816 + 0.368025i \(0.880034\pi\)
\(164\) 3.47992i 0.271736i
\(165\) 7.28184 + 2.97213i 0.566890 + 0.231380i
\(166\) 1.46770 1.46770i 0.113916 0.113916i
\(167\) 18.3360i 1.41888i −0.704765 0.709441i \(-0.748948\pi\)
0.704765 0.709441i \(-0.251052\pi\)
\(168\) 0.936350i 0.0722410i
\(169\) 34.2873 2.63748
\(170\) 4.48266 1.88405i 0.343805 0.144500i
\(171\) −1.01389 1.01389i −0.0775338 0.0775338i
\(172\) 2.74581 0.209366
\(173\) 5.06991 + 5.06991i 0.385458 + 0.385458i 0.873064 0.487606i \(-0.162130\pi\)
−0.487606 + 0.873064i \(0.662130\pi\)
\(174\) 9.19196i 0.696841i
\(175\) 4.68150 0.0485117i 0.353888 0.00366714i
\(176\) 3.51735i 0.265130i
\(177\) 4.88643 0.367287
\(178\) 6.43088 + 6.43088i 0.482015 + 0.482015i
\(179\) 14.7313 + 14.7313i 1.10107 + 1.10107i 0.994282 + 0.106786i \(0.0340560\pi\)
0.106786 + 0.994282i \(0.465944\pi\)
\(180\) 2.06140 0.866398i 0.153647 0.0645775i
\(181\) −4.07298 −0.302742 −0.151371 0.988477i \(-0.548369\pi\)
−0.151371 + 0.988477i \(0.548369\pi\)
\(182\) 4.55298 + 4.55298i 0.337489 + 0.337489i
\(183\) 14.1330 1.04474
\(184\) −9.57399 −0.705804
\(185\) 2.60092 + 13.3505i 0.191223 + 0.981547i
\(186\) 3.37571 0.247519
\(187\) −7.64874 −0.559331
\(188\) 3.59071 + 3.59071i 0.261879 + 0.261879i
\(189\) −0.936350 −0.0681095
\(190\) −2.96845 1.21159i −0.215354 0.0878981i
\(191\) 0.841106 + 0.841106i 0.0608603 + 0.0608603i 0.736882 0.676022i \(-0.236297\pi\)
−0.676022 + 0.736882i \(0.736297\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 2.71107 0.195147 0.0975736 0.995228i \(-0.468892\pi\)
0.0975736 + 0.995228i \(0.468892\pi\)
\(194\) 0.301015i 0.0216116i
\(195\) −5.81065 + 14.2363i −0.416109 + 1.01948i
\(196\) 6.12325i 0.437375i
\(197\) 14.0103 + 14.0103i 0.998195 + 0.998195i 0.999998 0.00180312i \(-0.000573952\pi\)
−0.00180312 + 0.999998i \(0.500574\pi\)
\(198\) −3.51735 −0.249967
\(199\) 2.28257 + 2.28257i 0.161807 + 0.161807i 0.783367 0.621560i \(-0.213501\pi\)
−0.621560 + 0.783367i \(0.713501\pi\)
\(200\) 3.49871 3.57198i 0.247396 0.252577i
\(201\) 1.62540 0.114647
\(202\) 7.88206i 0.554580i
\(203\) 8.60689i 0.604085i
\(204\) −1.53766 + 1.53766i −0.107658 + 0.107658i
\(205\) −7.17349 + 3.01499i −0.501018 + 0.210576i
\(206\) 3.81714i 0.265953i
\(207\) 9.57399i 0.665438i
\(208\) 6.87657 0.476805
\(209\) 3.56619 + 3.56619i 0.246678 + 0.246678i
\(210\) −1.93019 + 0.811252i −0.133196 + 0.0559817i
\(211\) 16.7409 1.15249 0.576247 0.817276i \(-0.304517\pi\)
0.576247 + 0.817276i \(0.304517\pi\)
\(212\) −2.93440 + 2.93440i −0.201536 + 0.201536i
\(213\) 5.18202 + 5.18202i 0.355066 + 0.355066i
\(214\) 3.39625 + 3.39625i 0.232163 + 0.232163i
\(215\) −2.37896 5.66020i −0.162244 0.386022i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) −3.16085 −0.214572
\(218\) 1.95485 1.95485i 0.132399 0.132399i
\(219\) 0.413868i 0.0279666i
\(220\) −7.25065 + 3.04742i −0.488839 + 0.205457i
\(221\) 14.9536i 1.00589i
\(222\) −3.33312 5.08825i −0.223705 0.341501i
\(223\) 16.5296 16.5296i 1.10690 1.10690i 0.113349 0.993555i \(-0.463842\pi\)
0.993555 0.113349i \(-0.0361580\pi\)
\(224\) 0.662100 + 0.662100i 0.0442384 + 0.0442384i
\(225\) −3.57198 3.49871i −0.238132 0.233247i
\(226\) 18.3281i 1.21916i
\(227\) 28.0799i 1.86373i 0.362805 + 0.931865i \(0.381819\pi\)
−0.362805 + 0.931865i \(0.618181\pi\)
\(228\) 1.43385 0.0949591
\(229\) 0.286568i 0.0189369i 0.999955 + 0.00946847i \(0.00301395\pi\)
−0.999955 + 0.00946847i \(0.996986\pi\)
\(230\) 8.29489 + 19.7358i 0.546949 + 1.30134i
\(231\) 3.29347 0.216694
\(232\) 6.49970 + 6.49970i 0.426726 + 0.426726i
\(233\) 10.2080 + 10.2080i 0.668751 + 0.668751i 0.957427 0.288676i \(-0.0932150\pi\)
−0.288676 + 0.957427i \(0.593215\pi\)
\(234\) 6.87657i 0.449536i
\(235\) 4.29089 10.5129i 0.279907 0.685783i
\(236\) −3.45523 + 3.45523i −0.224916 + 0.224916i
\(237\) −11.2514 −0.730857
\(238\) 1.43979 1.43979i 0.0933275 0.0933275i
\(239\) −16.6011 + 16.6011i −1.07384 + 1.07384i −0.0767893 + 0.997047i \(0.524467\pi\)
−0.997047 + 0.0767893i \(0.975533\pi\)
\(240\) −0.844991 + 2.07026i −0.0545440 + 0.133635i
\(241\) −17.4511 17.4511i −1.12412 1.12412i −0.991115 0.133010i \(-0.957536\pi\)
−0.133010 0.991115i \(-0.542464\pi\)
\(242\) 1.37173 0.0881784
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −9.99355 + 9.99355i −0.639771 + 0.639771i
\(245\) −12.6224 + 5.30517i −0.806418 + 0.338935i
\(246\) 2.46067 2.46067i 0.156887 0.156887i
\(247\) −6.97206 + 6.97206i −0.443622 + 0.443622i
\(248\) −2.38699 + 2.38699i −0.151574 + 0.151574i
\(249\) 2.07565 0.131539
\(250\) −10.3945 4.11747i −0.657408 0.260412i
\(251\) −0.992524 + 0.992524i −0.0626476 + 0.0626476i −0.737736 0.675089i \(-0.764105\pi\)
0.675089 + 0.737736i \(0.264105\pi\)
\(252\) 0.662100 0.662100i 0.0417084 0.0417084i
\(253\) 33.6751i 2.11713i
\(254\) 0.247513 + 0.247513i 0.0155303 + 0.0155303i
\(255\) 4.50195 + 1.83750i 0.281923 + 0.115069i
\(256\) 1.00000 0.0625000
\(257\) 9.19465i 0.573546i 0.957998 + 0.286773i \(0.0925826\pi\)
−0.957998 + 0.286773i \(0.907417\pi\)
\(258\) 1.94158 + 1.94158i 0.120877 + 0.120877i
\(259\) 3.12097 + 4.76438i 0.193928 + 0.296044i
\(260\) −5.95785 14.1753i −0.369490 0.879118i
\(261\) 6.49970 6.49970i 0.402321 0.402321i
\(262\) 1.31529 1.31529i 0.0812588 0.0812588i
\(263\) 10.1321 + 10.1321i 0.624774 + 0.624774i 0.946748 0.321974i \(-0.104346\pi\)
−0.321974 + 0.946748i \(0.604346\pi\)
\(264\) 2.48714 2.48714i 0.153073 0.153073i
\(265\) 8.59132 + 3.50660i 0.527761 + 0.215409i
\(266\) −1.34259 −0.0823193
\(267\) 9.09463i 0.556582i
\(268\) −1.14933 + 1.14933i −0.0702067 + 0.0702067i
\(269\) 25.8428i 1.57566i −0.615890 0.787832i \(-0.711204\pi\)
0.615890 0.787832i \(-0.288796\pi\)
\(270\) 2.07026 + 0.844991i 0.125992 + 0.0514245i
\(271\) 19.0523 1.15734 0.578672 0.815561i \(-0.303571\pi\)
0.578672 + 0.815561i \(0.303571\pi\)
\(272\) 2.17458i 0.131853i
\(273\) 6.43888i 0.389699i
\(274\) 13.6827 + 13.6827i 0.826601 + 0.826601i
\(275\) 12.5639 + 12.3062i 0.757631 + 0.742090i
\(276\) −6.76983 6.76983i −0.407496 0.407496i
\(277\) 2.31001 0.138795 0.0693974 0.997589i \(-0.477892\pi\)
0.0693974 + 0.997589i \(0.477892\pi\)
\(278\) 17.7419 1.06409
\(279\) 2.38699 + 2.38699i 0.142905 + 0.142905i
\(280\) 0.791208 1.93849i 0.0472837 0.115847i
\(281\) −13.8796 13.8796i −0.827987 0.827987i 0.159251 0.987238i \(-0.449092\pi\)
−0.987238 + 0.159251i \(0.949092\pi\)
\(282\) 5.07803i 0.302392i
\(283\) 20.9115i 1.24306i −0.783389 0.621531i \(-0.786511\pi\)
0.783389 0.621531i \(-0.213489\pi\)
\(284\) −7.32848 −0.434865
\(285\) −1.24229 2.95573i −0.0735866 0.175083i
\(286\) 24.1873i 1.43023i
\(287\) −2.30405 + 2.30405i −0.136004 + 0.136004i
\(288\) 1.00000i 0.0589256i
\(289\) 12.2712 0.721836
\(290\) 7.76713 19.0298i 0.456101 1.11747i
\(291\) 0.212850 0.212850i 0.0124775 0.0124775i
\(292\) −0.292649 0.292649i −0.0171260 0.0171260i
\(293\) −6.11142 + 6.11142i −0.357033 + 0.357033i −0.862718 0.505685i \(-0.831240\pi\)
0.505685 + 0.862718i \(0.331240\pi\)
\(294\) 4.32979 4.32979i 0.252518 0.252518i
\(295\) 10.1162 + 4.12899i 0.588988 + 0.240399i
\(296\) 5.95481 + 1.24106i 0.346116 + 0.0721352i
\(297\) −2.48714 2.48714i −0.144319 0.144319i
\(298\) 10.6094i 0.614588i
\(299\) 65.8363 3.80741
\(300\) 4.99973 0.0518094i 0.288660 0.00299122i
\(301\) −1.81800 1.81800i −0.104788 0.104788i
\(302\) 3.90183i 0.224525i
\(303\) −5.57346 + 5.57346i −0.320187 + 0.320187i
\(304\) −1.01389 + 1.01389i −0.0581503 + 0.0581503i
\(305\) 29.2590 + 11.9423i 1.67537 + 0.683812i
\(306\) −2.17458 −0.124312
\(307\) 11.2957 11.2957i 0.644681 0.644681i −0.307022 0.951703i \(-0.599332\pi\)
0.951703 + 0.307022i \(0.0993324\pi\)
\(308\) −2.32883 + 2.32883i −0.132698 + 0.132698i
\(309\) 2.69912 2.69912i 0.153548 0.153548i
\(310\) 6.98861 + 2.85245i 0.396927 + 0.162008i
\(311\) 9.84746 9.84746i 0.558398 0.558398i −0.370453 0.928851i \(-0.620798\pi\)
0.928851 + 0.370453i \(0.120798\pi\)
\(312\) 4.86247 + 4.86247i 0.275283 + 0.275283i
\(313\) −12.1322 −0.685752 −0.342876 0.939381i \(-0.611401\pi\)
−0.342876 + 0.939381i \(0.611401\pi\)
\(314\) −1.75656 1.75656i −0.0991282 0.0991282i
\(315\) −1.93849 0.791208i −0.109222 0.0445795i
\(316\) 7.95594 7.95594i 0.447556 0.447556i
\(317\) −9.66544 + 9.66544i −0.542865 + 0.542865i −0.924368 0.381502i \(-0.875407\pi\)
0.381502 + 0.924368i \(0.375407\pi\)
\(318\) −4.14987 −0.232713
\(319\) −22.8617 + 22.8617i −1.28001 + 1.28001i
\(320\) −0.866398 2.06140i −0.0484331 0.115236i
\(321\) 4.80302i 0.268079i
\(322\) 6.33894 + 6.33894i 0.353255 + 0.353255i
\(323\) 2.20477 + 2.20477i 0.122677 + 0.122677i
\(324\) −1.00000 −0.0555556
\(325\) −24.0591 + 24.5630i −1.33456 + 1.36251i
\(326\) 9.39725i 0.520465i
\(327\) 2.76458 0.152882
\(328\) 3.47992i 0.192146i
\(329\) 4.75481i 0.262141i
\(330\) −7.28184 2.97213i −0.400852 0.163610i
\(331\) 23.0765 + 23.0765i 1.26840 + 1.26840i 0.946914 + 0.321487i \(0.104183\pi\)
0.321487 + 0.946914i \(0.395817\pi\)
\(332\) −1.46770 + 1.46770i −0.0805508 + 0.0805508i
\(333\) 1.24106 5.95481i 0.0680097 0.326322i
\(334\) 18.3360i 1.00330i
\(335\) 3.36501 + 1.37345i 0.183850 + 0.0750396i
\(336\) 0.936350i 0.0510821i
\(337\) 10.8978 10.8978i 0.593640 0.593640i −0.344973 0.938613i \(-0.612112\pi\)
0.938613 + 0.344973i \(0.112112\pi\)
\(338\) −34.2873 −1.86498
\(339\) −12.9599 + 12.9599i −0.703885 + 0.703885i
\(340\) −4.48266 + 1.88405i −0.243107 + 0.102177i
\(341\) −8.39587 8.39587i −0.454662 0.454662i
\(342\) 1.01389 + 1.01389i 0.0548247 + 0.0548247i
\(343\) −8.68890 + 8.68890i −0.469156 + 0.469156i
\(344\) −2.74581 −0.148044
\(345\) −8.08994 + 19.8207i −0.435548 + 1.06711i
\(346\) −5.06991 5.06991i −0.272560 0.272560i
\(347\) 0.330476 0.0177409 0.00887043 0.999961i \(-0.497176\pi\)
0.00887043 + 0.999961i \(0.497176\pi\)
\(348\) 9.19196i 0.492741i
\(349\) 35.7141i 1.91173i −0.293799 0.955867i \(-0.594920\pi\)
0.293799 0.955867i \(-0.405080\pi\)
\(350\) −4.68150 + 0.0485117i −0.250237 + 0.00259306i
\(351\) 4.86247 4.86247i 0.259540 0.259540i
\(352\) 3.51735i 0.187475i
\(353\) 19.1728i 1.02047i 0.860036 + 0.510233i \(0.170441\pi\)
−0.860036 + 0.510233i \(0.829559\pi\)
\(354\) −4.88643 −0.259711
\(355\) 6.34938 + 15.1069i 0.336990 + 0.801791i
\(356\) −6.43088 6.43088i −0.340836 0.340836i
\(357\) 2.03617 0.107765
\(358\) −14.7313 14.7313i −0.778573 0.778573i
\(359\) 6.91664i 0.365046i −0.983202 0.182523i \(-0.941574\pi\)
0.983202 0.182523i \(-0.0584264\pi\)
\(360\) −2.06140 + 0.866398i −0.108645 + 0.0456632i
\(361\) 16.9441i 0.891793i
\(362\) 4.07298 0.214071
\(363\) 0.969963 + 0.969963i 0.0509098 + 0.0509098i
\(364\) −4.55298 4.55298i −0.238641 0.238641i
\(365\) −0.349715 + 0.856815i −0.0183049 + 0.0448477i
\(366\) −14.1330 −0.738744
\(367\) 17.2144 + 17.2144i 0.898582 + 0.898582i 0.995311 0.0967284i \(-0.0308378\pi\)
−0.0967284 + 0.995311i \(0.530838\pi\)
\(368\) 9.57399 0.499079
\(369\) 3.47992 0.181157
\(370\) −2.60092 13.3505i −0.135215 0.694058i
\(371\) 3.88573 0.201737
\(372\) −3.37571 −0.175023
\(373\) −13.8033 13.8033i −0.714705 0.714705i 0.252811 0.967516i \(-0.418645\pi\)
−0.967516 + 0.252811i \(0.918645\pi\)
\(374\) 7.64874 0.395507
\(375\) −4.43856 10.2615i −0.229206 0.529904i
\(376\) −3.59071 3.59071i −0.185177 0.185177i
\(377\) −44.6956 44.6956i −2.30194 2.30194i
\(378\) 0.936350 0.0481607
\(379\) 0.729632i 0.0374787i −0.999824 0.0187393i \(-0.994035\pi\)
0.999824 0.0187393i \(-0.00596527\pi\)
\(380\) 2.96845 + 1.21159i 0.152278 + 0.0621533i
\(381\) 0.350036i 0.0179329i
\(382\) −0.841106 0.841106i −0.0430347 0.0430347i
\(383\) 28.2223 1.44209 0.721047 0.692887i \(-0.243661\pi\)
0.721047 + 0.692887i \(0.243661\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) 6.81835 + 2.78295i 0.347495 + 0.141832i
\(386\) −2.71107 −0.137990
\(387\) 2.74581i 0.139577i
\(388\) 0.301015i 0.0152817i
\(389\) −15.3299 + 15.3299i −0.777258 + 0.777258i −0.979364 0.202106i \(-0.935222\pi\)
0.202106 + 0.979364i \(0.435222\pi\)
\(390\) 5.81065 14.2363i 0.294234 0.720884i
\(391\) 20.8194i 1.05288i
\(392\) 6.12325i 0.309271i
\(393\) 1.86010 0.0938295
\(394\) −14.0103 14.0103i −0.705831 0.705831i
\(395\) −23.2933 9.50733i −1.17202 0.478366i
\(396\) 3.51735 0.176753
\(397\) 9.07360 9.07360i 0.455391 0.455391i −0.441748 0.897139i \(-0.645642\pi\)
0.897139 + 0.441748i \(0.145642\pi\)
\(398\) −2.28257 2.28257i −0.114415 0.114415i
\(399\) −0.949352 0.949352i −0.0475271 0.0475271i
\(400\) −3.49871 + 3.57198i −0.174935 + 0.178599i
\(401\) −23.0577 + 23.0577i −1.15144 + 1.15144i −0.165182 + 0.986263i \(0.552821\pi\)
−0.986263 + 0.165182i \(0.947179\pi\)
\(402\) −1.62540 −0.0810677
\(403\) 16.4143 16.4143i 0.817655 0.817655i
\(404\) 7.88206i 0.392147i
\(405\) 0.866398 + 2.06140i 0.0430517 + 0.102432i
\(406\) 8.60689i 0.427153i
\(407\) −4.36524 + 20.9451i −0.216377 + 1.03821i
\(408\) 1.53766 1.53766i 0.0761254 0.0761254i
\(409\) 12.7245 + 12.7245i 0.629185 + 0.629185i 0.947863 0.318678i \(-0.103239\pi\)
−0.318678 + 0.947863i \(0.603239\pi\)
\(410\) 7.17349 3.01499i 0.354273 0.148900i
\(411\) 19.3502i 0.954477i
\(412\) 3.81714i 0.188057i
\(413\) 4.57541 0.225141
\(414\) 9.57399i 0.470536i
\(415\) 4.29714 + 1.75390i 0.210938 + 0.0860958i
\(416\) −6.87657 −0.337152
\(417\) 12.5454 + 12.5454i 0.614350 + 0.614350i
\(418\) −3.56619 3.56619i −0.174428 0.174428i
\(419\) 4.07751i 0.199200i 0.995028 + 0.0995998i \(0.0317563\pi\)
−0.995028 + 0.0995998i \(0.968244\pi\)
\(420\) 1.93019 0.811252i 0.0941836 0.0395850i
\(421\) −5.38925 + 5.38925i −0.262656 + 0.262656i −0.826132 0.563476i \(-0.809464\pi\)
0.563476 + 0.826132i \(0.309464\pi\)
\(422\) −16.7409 −0.814936
\(423\) −3.59071 + 3.59071i −0.174586 + 0.174586i
\(424\) 2.93440 2.93440i 0.142507 0.142507i
\(425\) 7.76754 + 7.60821i 0.376781 + 0.369052i
\(426\) −5.18202 5.18202i −0.251070 0.251070i
\(427\) 13.2334 0.640411
\(428\) −3.39625 3.39625i −0.164164 0.164164i
\(429\) −17.1030 + 17.1030i −0.825741 + 0.825741i
\(430\) 2.37896 + 5.66020i 0.114724 + 0.272959i
\(431\) 9.41260 9.41260i 0.453389 0.453389i −0.443089 0.896478i \(-0.646117\pi\)
0.896478 + 0.443089i \(0.146117\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 18.0950 18.0950i 0.869588 0.869588i −0.122839 0.992427i \(-0.539200\pi\)
0.992427 + 0.122839i \(0.0391998\pi\)
\(434\) 3.16085 0.151726
\(435\) 18.9483 7.96389i 0.908500 0.381840i
\(436\) −1.95485 + 1.95485i −0.0936205 + 0.0936205i
\(437\) −9.70693 + 9.70693i −0.464346 + 0.464346i
\(438\) 0.413868i 0.0197754i
\(439\) −3.41744 3.41744i −0.163106 0.163106i 0.620835 0.783941i \(-0.286794\pi\)
−0.783941 + 0.620835i \(0.786794\pi\)
\(440\) 7.25065 3.04742i 0.345661 0.145280i
\(441\) 6.12325 0.291583
\(442\) 14.9536i 0.711272i
\(443\) −10.8466 10.8466i −0.515340 0.515340i 0.400818 0.916158i \(-0.368726\pi\)
−0.916158 + 0.400818i \(0.868726\pi\)
\(444\) 3.33312 + 5.08825i 0.158183 + 0.241478i
\(445\) −7.68489 + 18.8283i −0.364299 + 0.892546i
\(446\) −16.5296 + 16.5296i −0.782700 + 0.782700i
\(447\) 7.50200 7.50200i 0.354833 0.354833i
\(448\) −0.662100 0.662100i −0.0312813 0.0312813i
\(449\) 10.3811 10.3811i 0.489913 0.489913i −0.418366 0.908279i \(-0.637397\pi\)
0.908279 + 0.418366i \(0.137397\pi\)
\(450\) 3.57198 + 3.49871i 0.168385 + 0.164931i
\(451\) −12.2401 −0.576363
\(452\) 18.3281i 0.862079i
\(453\) 2.75901 2.75901i 0.129630 0.129630i
\(454\) 28.0799i 1.31786i
\(455\) −5.44080 + 13.3302i −0.255069 + 0.624928i
\(456\) −1.43385 −0.0671462
\(457\) 13.7780i 0.644509i −0.946653 0.322254i \(-0.895559\pi\)
0.946653 0.322254i \(-0.104441\pi\)
\(458\) 0.286568i 0.0133904i
\(459\) −1.53766 1.53766i −0.0717717 0.0717717i
\(460\) −8.29489 19.7358i −0.386751 0.920186i
\(461\) −28.3555 28.3555i −1.32065 1.32065i −0.913253 0.407393i \(-0.866438\pi\)
−0.407393 0.913253i \(-0.633562\pi\)
\(462\) −3.29347 −0.153226
\(463\) −27.1414 −1.26137 −0.630683 0.776040i \(-0.717225\pi\)
−0.630683 + 0.776040i \(0.717225\pi\)
\(464\) −6.49970 6.49970i −0.301741 0.301741i
\(465\) 2.92471 + 6.95868i 0.135630 + 0.322701i
\(466\) −10.2080 10.2080i −0.472878 0.472878i
\(467\) 15.3540i 0.710500i 0.934771 + 0.355250i \(0.115604\pi\)
−0.934771 + 0.355250i \(0.884396\pi\)
\(468\) 6.87657i 0.317870i
\(469\) 1.52195 0.0702769
\(470\) −4.29089 + 10.5129i −0.197924 + 0.484922i
\(471\) 2.48415i 0.114463i
\(472\) 3.45523 3.45523i 0.159040 0.159040i
\(473\) 9.65796i 0.444074i
\(474\) 11.2514 0.516794
\(475\) −0.0742869 7.16887i −0.00340852 0.328930i
\(476\) −1.43979 + 1.43979i −0.0659925 + 0.0659925i
\(477\) −2.93440 2.93440i −0.134357 0.134357i
\(478\) 16.6011 16.6011i 0.759317 0.759317i
\(479\) 11.3006 11.3006i 0.516338 0.516338i −0.400123 0.916461i \(-0.631033\pi\)
0.916461 + 0.400123i \(0.131033\pi\)
\(480\) 0.844991 2.07026i 0.0385684 0.0944942i
\(481\) −40.9487 8.53425i −1.86710 0.389128i
\(482\) 17.4511 + 17.4511i 0.794876 + 0.794876i
\(483\) 8.96461i 0.407904i
\(484\) −1.37173 −0.0623516
\(485\) 0.620511 0.260799i 0.0281760 0.0118423i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) 21.7950i 0.987628i −0.869568 0.493814i \(-0.835602\pi\)
0.869568 0.493814i \(-0.164398\pi\)
\(488\) 9.99355 9.99355i 0.452387 0.452387i
\(489\) 6.64486 6.64486i 0.300491 0.300491i
\(490\) 12.6224 5.30517i 0.570224 0.239663i
\(491\) −6.69716 −0.302239 −0.151119 0.988516i \(-0.548288\pi\)
−0.151119 + 0.988516i \(0.548288\pi\)
\(492\) −2.46067 + 2.46067i −0.110936 + 0.110936i
\(493\) −14.1341 + 14.1341i −0.636567 + 0.636567i
\(494\) 6.97206 6.97206i 0.313688 0.313688i
\(495\) −3.04742 7.25065i −0.136971 0.325892i
\(496\) 2.38699 2.38699i 0.107179 0.107179i
\(497\) 4.85218 + 4.85218i 0.217650 + 0.217650i
\(498\) −2.07565 −0.0930120
\(499\) −31.1536 31.1536i −1.39463 1.39463i −0.814592 0.580034i \(-0.803039\pi\)
−0.580034 0.814592i \(-0.696961\pi\)
\(500\) 10.3945 + 4.11747i 0.464858 + 0.184139i
\(501\) −12.9655 + 12.9655i −0.579256 + 0.579256i
\(502\) 0.992524 0.992524i 0.0442985 0.0442985i
\(503\) −0.724954 −0.0323241 −0.0161621 0.999869i \(-0.505145\pi\)
−0.0161621 + 0.999869i \(0.505145\pi\)
\(504\) −0.662100 + 0.662100i −0.0294923 + 0.0294923i
\(505\) −16.2480 + 6.82900i −0.723029 + 0.303886i
\(506\) 33.6751i 1.49704i
\(507\) −24.2448 24.2448i −1.07675 1.07675i
\(508\) −0.247513 0.247513i −0.0109816 0.0109816i
\(509\) −23.7296 −1.05180 −0.525899 0.850547i \(-0.676271\pi\)
−0.525899 + 0.850547i \(0.676271\pi\)
\(510\) −4.50195 1.83750i −0.199350 0.0813658i
\(511\) 0.387525i 0.0171431i
\(512\) −1.00000 −0.0441942
\(513\) 1.43385i 0.0633061i
\(514\) 9.19465i 0.405559i
\(515\) 7.86864 3.30716i 0.346734 0.145731i
\(516\) −1.94158 1.94158i −0.0854733 0.0854733i
\(517\) 12.6298 12.6298i 0.555456 0.555456i
\(518\) −3.12097 4.76438i −0.137128 0.209335i
\(519\) 7.16994i 0.314725i
\(520\) 5.95785 + 14.1753i 0.261269 + 0.621630i
\(521\) 23.1177i 1.01281i 0.862297 + 0.506403i \(0.169025\pi\)
−0.862297 + 0.506403i \(0.830975\pi\)
\(522\) −6.49970 + 6.49970i −0.284484 + 0.284484i
\(523\) 15.4427 0.675261 0.337631 0.941279i \(-0.390375\pi\)
0.337631 + 0.941279i \(0.390375\pi\)
\(524\) −1.31529 + 1.31529i −0.0574586 + 0.0574586i
\(525\) −3.34462 3.27602i −0.145971 0.142977i
\(526\) −10.1321 10.1321i −0.441782 0.441782i
\(527\) −5.19069 5.19069i −0.226110 0.226110i
\(528\) −2.48714 + 2.48714i −0.108239 + 0.108239i
\(529\) 68.6613 2.98528
\(530\) −8.59132 3.50660i −0.373183 0.152317i
\(531\) −3.45523 3.45523i −0.149944 0.149944i
\(532\) 1.34259 0.0582085
\(533\) 23.9299i 1.03652i
\(534\) 9.09463i 0.393563i
\(535\) −4.05851 + 9.94353i −0.175465 + 0.429896i
\(536\) 1.14933 1.14933i 0.0496436 0.0496436i
\(537\) 20.8332i 0.899018i
\(538\) 25.8428i 1.11416i
\(539\) −21.5376 −0.927690
\(540\) −2.07026 0.844991i −0.0890899 0.0363626i
\(541\) 3.85083 + 3.85083i 0.165560 + 0.165560i 0.785025 0.619465i \(-0.212650\pi\)
−0.619465 + 0.785025i \(0.712650\pi\)
\(542\) −19.0523 −0.818365
\(543\) 2.88003 + 2.88003i 0.123594 + 0.123594i
\(544\) 2.17458i 0.0932342i
\(545\) 5.72341 + 2.33605i 0.245164 + 0.100065i
\(546\) 6.43888i 0.275559i
\(547\) 5.49141 0.234796 0.117398 0.993085i \(-0.462545\pi\)
0.117398 + 0.993085i \(0.462545\pi\)
\(548\) −13.6827 13.6827i −0.584495 0.584495i
\(549\) −9.99355 9.99355i −0.426514 0.426514i
\(550\) −12.5639 12.3062i −0.535726 0.524737i
\(551\) 13.1799 0.561483
\(552\) 6.76983 + 6.76983i 0.288143 + 0.288143i
\(553\) −10.5352 −0.448004
\(554\) −2.31001 −0.0981428
\(555\) 7.60109 11.2793i 0.322648 0.478781i
\(556\) −17.7419 −0.752422
\(557\) −20.3979 −0.864285 −0.432142 0.901805i \(-0.642242\pi\)
−0.432142 + 0.901805i \(0.642242\pi\)
\(558\) −2.38699 2.38699i −0.101049 0.101049i
\(559\) 18.8818 0.798613
\(560\) −0.791208 + 1.93849i −0.0334346 + 0.0819162i
\(561\) 5.40848 + 5.40848i 0.228346 + 0.228346i
\(562\) 13.8796 + 13.8796i 0.585475 + 0.585475i
\(563\) 41.6497 1.75533 0.877663 0.479278i \(-0.159101\pi\)
0.877663 + 0.479278i \(0.159101\pi\)
\(564\) 5.07803i 0.213824i
\(565\) −37.7814 + 15.8794i −1.58948 + 0.668051i
\(566\) 20.9115i 0.878978i
\(567\) 0.662100 + 0.662100i 0.0278056 + 0.0278056i
\(568\) 7.32848 0.307496
\(569\) 29.9799 + 29.9799i 1.25682 + 1.25682i 0.952602 + 0.304220i \(0.0983957\pi\)
0.304220 + 0.952602i \(0.401604\pi\)
\(570\) 1.24229 + 2.95573i 0.0520336 + 0.123802i
\(571\) −33.5003 −1.40195 −0.700973 0.713188i \(-0.747250\pi\)
−0.700973 + 0.713188i \(0.747250\pi\)
\(572\) 24.1873i 1.01132i
\(573\) 1.18950i 0.0496922i
\(574\) 2.30405 2.30405i 0.0961693 0.0961693i
\(575\) −33.4966 + 34.1981i −1.39691 + 1.42616i
\(576\) 1.00000i 0.0416667i
\(577\) 11.2900i 0.470008i 0.971994 + 0.235004i \(0.0755104\pi\)
−0.971994 + 0.235004i \(0.924490\pi\)
\(578\) −12.2712 −0.510415
\(579\) −1.91702 1.91702i −0.0796685 0.0796685i
\(580\) −7.76713 + 19.0298i −0.322512 + 0.790168i
\(581\) 1.94353 0.0806313
\(582\) −0.212850 + 0.212850i −0.00882291 + 0.00882291i
\(583\) 10.3213 + 10.3213i 0.427465 + 0.427465i
\(584\) 0.292649 + 0.292649i 0.0121099 + 0.0121099i
\(585\) 14.1753 5.95785i 0.586078 0.246327i
\(586\) 6.11142 6.11142i 0.252461 0.252461i
\(587\) −0.261793 −0.0108053 −0.00540267 0.999985i \(-0.501720\pi\)
−0.00540267 + 0.999985i \(0.501720\pi\)
\(588\) −4.32979 + 4.32979i −0.178558 + 0.178558i
\(589\) 4.84027i 0.199440i
\(590\) −10.1162 4.12899i −0.416477 0.169988i
\(591\) 19.8136i 0.815023i
\(592\) −5.95481 1.24106i −0.244741 0.0510073i
\(593\) −23.9024 + 23.9024i −0.981553 + 0.981553i −0.999833 0.0182800i \(-0.994181\pi\)
0.0182800 + 0.999833i \(0.494181\pi\)
\(594\) 2.48714 + 2.48714i 0.102049 + 0.102049i
\(595\) 4.21540 + 1.72054i 0.172814 + 0.0705354i
\(596\) 10.6094i 0.434579i
\(597\) 3.22805i 0.132115i
\(598\) −65.8363 −2.69225
\(599\) 40.4441i 1.65250i −0.563303 0.826251i \(-0.690470\pi\)
0.563303 0.826251i \(-0.309530\pi\)
\(600\) −4.99973 + 0.0518094i −0.204113 + 0.00211511i
\(601\) 38.4258 1.56742 0.783710 0.621127i \(-0.213325\pi\)
0.783710 + 0.621127i \(0.213325\pi\)
\(602\) 1.81800 + 1.81800i 0.0740961 + 0.0740961i
\(603\) −1.14933 1.14933i −0.0468044 0.0468044i
\(604\) 3.90183i 0.158763i
\(605\) 1.18847 + 2.82769i 0.0483181 + 0.114962i
\(606\) 5.57346 5.57346i 0.226406 0.226406i
\(607\) −14.3687 −0.583208 −0.291604 0.956539i \(-0.594189\pi\)
−0.291604 + 0.956539i \(0.594189\pi\)
\(608\) 1.01389 1.01389i 0.0411185 0.0411185i
\(609\) 6.08599 6.08599i 0.246617 0.246617i
\(610\) −29.2590 11.9423i −1.18466 0.483528i
\(611\) 24.6918 + 24.6918i 0.998922 + 0.998922i
\(612\) 2.17458 0.0879020
\(613\) −10.7011 10.7011i −0.432213 0.432213i 0.457167 0.889381i \(-0.348864\pi\)
−0.889381 + 0.457167i \(0.848864\pi\)
\(614\) −11.2957 + 11.2957i −0.455858 + 0.455858i
\(615\) 7.20434 + 2.94050i 0.290507 + 0.118572i
\(616\) 2.32883 2.32883i 0.0938314 0.0938314i
\(617\) 14.0957 14.0957i 0.567470 0.567470i −0.363949 0.931419i \(-0.618572\pi\)
0.931419 + 0.363949i \(0.118572\pi\)
\(618\) −2.69912 + 2.69912i −0.108575 + 0.108575i
\(619\) −4.28502 −0.172230 −0.0861148 0.996285i \(-0.527445\pi\)
−0.0861148 + 0.996285i \(0.527445\pi\)
\(620\) −6.98861 2.85245i −0.280669 0.114557i
\(621\) 6.76983 6.76983i 0.271664 0.271664i
\(622\) −9.84746 + 9.84746i −0.394847 + 0.394847i
\(623\) 8.51576i 0.341177i
\(624\) −4.86247 4.86247i −0.194655 0.194655i
\(625\) −0.518066 24.9946i −0.0207226 0.999785i
\(626\) 12.1322 0.484900
\(627\) 5.04335i 0.201412i
\(628\) 1.75656 + 1.75656i 0.0700942 + 0.0700942i
\(629\) −2.69878 + 12.9492i −0.107607 + 0.516318i
\(630\) 1.93849 + 0.791208i 0.0772313 + 0.0315225i
\(631\) −10.5038 + 10.5038i −0.418149 + 0.418149i −0.884565 0.466416i \(-0.845545\pi\)
0.466416 + 0.884565i \(0.345545\pi\)
\(632\) −7.95594 + 7.95594i −0.316470 + 0.316470i
\(633\) −11.8376 11.8376i −0.470504 0.470504i
\(634\) 9.66544 9.66544i 0.383864 0.383864i
\(635\) −0.295777 + 0.724667i −0.0117376 + 0.0287575i
\(636\) 4.14987 0.164553
\(637\) 42.1070i 1.66834i
\(638\) 22.8617 22.8617i 0.905103 0.905103i
\(639\) 7.32848i 0.289910i
\(640\) 0.866398 + 2.06140i 0.0342474 + 0.0814838i
\(641\) 41.6777 1.64617 0.823085 0.567919i \(-0.192251\pi\)
0.823085 + 0.567919i \(0.192251\pi\)
\(642\) 4.80302i 0.189560i
\(643\) 25.1480i 0.991742i −0.868396 0.495871i \(-0.834849\pi\)
0.868396 0.495871i \(-0.165151\pi\)
\(644\) −6.33894 6.33894i −0.249789 0.249789i
\(645\) −2.32018 + 5.68455i −0.0913572 + 0.223829i
\(646\) −2.20477 2.20477i −0.0867456 0.0867456i
\(647\) −29.9330 −1.17679 −0.588394 0.808575i \(-0.700239\pi\)
−0.588394 + 0.808575i \(0.700239\pi\)
\(648\) 1.00000 0.0392837
\(649\) 12.1532 + 12.1532i 0.477057 + 0.477057i
\(650\) 24.0591 24.5630i 0.943677 0.963439i
\(651\) 2.23506 + 2.23506i 0.0875988 + 0.0875988i
\(652\) 9.39725i 0.368025i
\(653\) 16.5783i 0.648759i 0.945927 + 0.324380i \(0.105156\pi\)
−0.945927 + 0.324380i \(0.894844\pi\)
\(654\) −2.76458 −0.108104
\(655\) 3.85089 + 1.57177i 0.150467 + 0.0614140i
\(656\) 3.47992i 0.135868i
\(657\) 0.292649 0.292649i 0.0114173 0.0114173i
\(658\) 4.75481i 0.185362i
\(659\) 19.3767 0.754807 0.377404 0.926049i \(-0.376817\pi\)
0.377404 + 0.926049i \(0.376817\pi\)
\(660\) 7.28184 + 2.97213i 0.283445 + 0.115690i
\(661\) −11.4801 + 11.4801i −0.446523 + 0.446523i −0.894197 0.447674i \(-0.852252\pi\)
0.447674 + 0.894197i \(0.352252\pi\)
\(662\) −23.0765 23.0765i −0.896895 0.896895i
\(663\) −10.5738 + 10.5738i −0.410653 + 0.410653i
\(664\) 1.46770 1.46770i 0.0569580 0.0569580i
\(665\) −1.16321 2.76760i −0.0451075 0.107323i
\(666\) −1.24106 + 5.95481i −0.0480901 + 0.230744i
\(667\) −62.2280 62.2280i −2.40948 2.40948i
\(668\) 18.3360i 0.709441i
\(669\) −23.3764 −0.903784
\(670\) −3.36501 1.37345i −0.130002 0.0530610i
\(671\) 35.1508 + 35.1508i 1.35698 + 1.35698i
\(672\) 0.936350i 0.0361205i
\(673\) 24.2873 24.2873i 0.936205 0.936205i −0.0618787 0.998084i \(-0.519709\pi\)
0.998084 + 0.0618787i \(0.0197092\pi\)
\(674\) −10.8978 + 10.8978i −0.419767 + 0.419767i
\(675\) 0.0518094 + 4.99973i 0.00199414 + 0.192440i
\(676\) 34.2873 1.31874
\(677\) 19.1232 19.1232i 0.734963 0.734963i −0.236635 0.971599i \(-0.576045\pi\)
0.971599 + 0.236635i \(0.0760446\pi\)
\(678\) 12.9599 12.9599i 0.497722 0.497722i
\(679\) 0.199302 0.199302i 0.00764851 0.00764851i
\(680\) 4.48266 1.88405i 0.171902 0.0722500i
\(681\) 19.8555 19.8555i 0.760865 0.760865i
\(682\) 8.39587 + 8.39587i 0.321494 + 0.321494i
\(683\) −5.31945 −0.203543 −0.101772 0.994808i \(-0.532451\pi\)
−0.101772 + 0.994808i \(0.532451\pi\)
\(684\) −1.01389 1.01389i −0.0387669 0.0387669i
\(685\) −16.3508 + 40.0601i −0.624732 + 1.53062i
\(686\) 8.68890 8.68890i 0.331744 0.331744i
\(687\) 0.202634 0.202634i 0.00773097 0.00773097i
\(688\) 2.74581 0.104683
\(689\) −20.1786 + 20.1786i −0.768745 + 0.768745i
\(690\) 8.08994 19.8207i 0.307979 0.754561i
\(691\) 35.7436i 1.35975i −0.733328 0.679875i \(-0.762034\pi\)
0.733328 0.679875i \(-0.237966\pi\)
\(692\) 5.06991 + 5.06991i 0.192729 + 0.192729i
\(693\) −2.32883 2.32883i −0.0884651 0.0884651i
\(694\) −0.330476 −0.0125447
\(695\) 15.3715 + 36.5730i 0.583074 + 1.38729i
\(696\) 9.19196i 0.348420i
\(697\) −7.56735 −0.286634
\(698\) 35.7141i 1.35180i
\(699\) 14.4363i 0.546033i
\(700\) 4.68150 0.0485117i 0.176944 0.00183357i
\(701\) −20.6265 20.6265i −0.779051 0.779051i 0.200618 0.979669i \(-0.435705\pi\)
−0.979669 + 0.200618i \(0.935705\pi\)
\(702\) −4.86247 + 4.86247i −0.183522 + 0.183522i
\(703\) 7.29579 4.77920i 0.275166 0.180251i
\(704\) 3.51735i 0.132565i
\(705\) −10.4678 + 4.39959i −0.394241 + 0.165698i
\(706\) 19.1728i 0.721579i
\(707\) −5.21871 + 5.21871i −0.196270 + 0.196270i
\(708\) 4.88643 0.183643
\(709\) −7.74624 + 7.74624i −0.290916 + 0.290916i −0.837442 0.546526i \(-0.815950\pi\)
0.546526 + 0.837442i \(0.315950\pi\)
\(710\) −6.34938 15.1069i −0.238288 0.566952i
\(711\) 7.95594 + 7.95594i 0.298371 + 0.298371i
\(712\) 6.43088 + 6.43088i 0.241007 + 0.241007i
\(713\) 22.8530 22.8530i 0.855852 0.855852i
\(714\) −2.03617 −0.0762016
\(715\) −49.8596 + 20.9558i −1.86464 + 0.783704i
\(716\) 14.7313 + 14.7313i 0.550534 + 0.550534i
\(717\) 23.4775 0.876784
\(718\) 6.91664i 0.258127i
\(719\) 28.4115i 1.05957i 0.848132 + 0.529785i \(0.177727\pi\)
−0.848132 + 0.529785i \(0.822273\pi\)
\(720\) 2.06140 0.866398i 0.0768237 0.0322887i
\(721\) 2.52733 2.52733i 0.0941226 0.0941226i
\(722\) 16.9441i 0.630593i
\(723\) 24.6796i 0.917844i
\(724\) −4.07298 −0.151371
\(725\) 45.9573 0.476230i 1.70681 0.0176867i
\(726\) −0.969963 0.969963i −0.0359987 0.0359987i
\(727\) 10.2341 0.379561 0.189780 0.981827i \(-0.439222\pi\)
0.189780 + 0.981827i \(0.439222\pi\)
\(728\) 4.55298 + 4.55298i 0.168745 + 0.168745i
\(729\) 1.00000i 0.0370370i
\(730\) 0.349715 0.856815i 0.0129435 0.0317121i
\(731\) 5.97097i 0.220844i
\(732\) 14.1330 0.522371
\(733\) −27.1770 27.1770i −1.00380 1.00380i −0.999993 0.00381081i \(-0.998787\pi\)
−0.00381081 0.999993i \(-0.501213\pi\)
\(734\) −17.2144 17.2144i −0.635394 0.635394i
\(735\) 12.6767 + 5.17409i 0.467588 + 0.190849i
\(736\) −9.57399 −0.352902
\(737\) 4.04260 + 4.04260i 0.148911 + 0.148911i
\(738\) −3.47992 −0.128098
\(739\) 17.3037 0.636527 0.318264 0.948002i \(-0.396900\pi\)
0.318264 + 0.948002i \(0.396900\pi\)
\(740\) 2.60092 + 13.3505i 0.0956116 + 0.490773i
\(741\) 9.85998 0.362215
\(742\) −3.88573 −0.142650
\(743\) 24.1248 + 24.1248i 0.885055 + 0.885055i 0.994043 0.108988i \(-0.0347611\pi\)
−0.108988 + 0.994043i \(0.534761\pi\)
\(744\) 3.37571 0.123760
\(745\) 21.8703 9.19199i 0.801264 0.336769i
\(746\) 13.8033 + 13.8033i 0.505373 + 0.505373i
\(747\) −1.46770 1.46770i −0.0537005 0.0537005i
\(748\) −7.64874 −0.279666
\(749\) 4.49731i 0.164328i
\(750\) 4.43856 + 10.2615i 0.162073 + 0.374698i
\(751\) 49.1232i 1.79253i −0.443517 0.896266i \(-0.646270\pi\)
0.443517 0.896266i \(-0.353730\pi\)
\(752\) 3.59071 + 3.59071i 0.130940 + 0.130940i
\(753\) 1.40364 0.0511515
\(754\) 44.6956 + 44.6956i 1.62772 + 1.62772i
\(755\) 8.04321 3.38053i 0.292722 0.123030i
\(756\) −0.936350 −0.0340547
\(757\) 20.9126i 0.760081i −0.924970 0.380040i \(-0.875910\pi\)
0.924970 0.380040i \(-0.124090\pi\)
\(758\) 0.729632i 0.0265014i
\(759\) −23.8119 + 23.8119i −0.864316 + 0.864316i
\(760\) −2.96845 1.21159i −0.107677 0.0439491i
\(761\) 22.5447i 0.817245i −0.912704 0.408622i \(-0.866009\pi\)
0.912704 0.408622i \(-0.133991\pi\)
\(762\) 0.350036i 0.0126805i
\(763\) 2.58862 0.0937142
\(764\) 0.841106 + 0.841106i 0.0304301 + 0.0304301i
\(765\) −1.88405 4.48266i −0.0681179 0.162071i
\(766\) −28.2223 −1.01971
\(767\) −23.7601 + 23.7601i −0.857929 + 0.857929i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 1.79332 + 1.79332i 0.0646688 + 0.0646688i 0.738701 0.674033i \(-0.235439\pi\)
−0.674033 + 0.738701i \(0.735439\pi\)
\(770\) −6.81835 2.78295i −0.245716 0.100291i
\(771\) 6.50160 6.50160i 0.234149 0.234149i
\(772\) 2.71107 0.0975736
\(773\) −10.3091 + 10.3091i −0.370791 + 0.370791i −0.867765 0.496974i \(-0.834444\pi\)
0.496974 + 0.867765i \(0.334444\pi\)
\(774\) 2.74581i 0.0986961i
\(775\) 0.174894 + 16.8777i 0.00628236 + 0.606263i
\(776\) 0.301015i 0.0108058i
\(777\) 1.16207 5.57579i 0.0416890 0.200030i
\(778\) 15.3299 15.3299i 0.549604 0.549604i
\(779\) 3.52824 + 3.52824i 0.126412 +