Properties

Label 1110.2.o.a.253.7
Level $1110$
Weight $2$
Character 1110.253
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 253.7
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.7

$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

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 −0.821073 0.570823i \(-0.806624\pi\)
0.570823 + 0.821073i \(0.306624\pi\)
\(8\) −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 \(0.177906\pi\)
−0.847835 + 0.530260i \(0.822094\pi\)
\(12\) −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 \(0.0849449\pi\)
−0.964603 + 0.263706i \(0.915055\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.01389 1.01389i −0.232601 0.232601i 0.581176 0.813778i \(-0.302593\pi\)
−0.813778 + 0.581176i \(0.802593\pi\)
\(20\) −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 −0.234958 + 0.972006i \(0.575495\pi\)
−0.972006 + 0.234958i \(0.924505\pi\)
\(30\) 0.844991 + 2.07026i 0.154274 + 0.377977i
\(31\) 2.38699 + 2.38699i 0.428716 + 0.428716i 0.888191 0.459475i \(-0.151962\pi\)
−0.459475 + 0.888191i \(0.651962\pi\)
\(32\) −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 \(0.0875977\pi\)
−0.962372 + 0.271736i \(0.912402\pi\)
\(42\) 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 −0.394946 0.918704i \(-0.629237\pi\)
0.918704 + 0.394946i \(0.129237\pi\)
\(48\) −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 0.476243 0.879314i \(-0.341998\pi\)
−0.879314 + 0.476243i \(0.841998\pi\)
\(54\) −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 0.445466 0.895299i \(-0.353038\pi\)
−0.895299 + 0.445466i \(0.853038\pi\)
\(60\) −0.844991 2.07026i −0.109088 0.267270i
\(61\) −9.99355 9.99355i −1.27954 1.27954i −0.940924 0.338619i \(-0.890040\pi\)
−0.338619 0.940924i \(-0.609960\pi\)
\(62\) −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 0.633406 0.773819i \(-0.281656\pi\)
−0.773819 + 0.633406i \(0.781656\pi\)
\(68\) 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 −0.724025 0.689773i \(-0.757710\pi\)
0.689773 + 0.724025i \(0.257710\pi\)
\(74\) 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 0.994999 0.0998861i \(-0.0318478\pi\)
−0.0998861 + 0.994999i \(0.531848\pi\)
\(80\) −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 0.621953 0.783055i \(-0.286339\pi\)
−0.783055 + 0.621953i \(0.786339\pi\)
\(84\) 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 −0.960377 0.278705i \(-0.910095\pi\)
0.278705 + 0.960377i \(0.410095\pi\)
\(90\) −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 \(-0.995135\pi\)
0.999883 0.0152817i \(-0.00486451\pi\)
\(98\) 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 \(0.128268\pi\)
−0.919903 + 0.392147i \(0.871732\pi\)
\(102\) 1.53766 + 1.53766i 0.152251 + 0.152251i
\(103\) 3.81714i 0.376114i −0.982158 0.188057i \(-0.939781\pi\)
0.982158 0.188057i \(-0.0602190\pi\)
\(104\) −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 −0.851950 0.523622i \(-0.824580\pi\)
0.523622 + 0.851950i \(0.324580\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −1.95485 1.95485i −0.187241 0.187241i 0.607261 0.794502i \(-0.292268\pi\)
−0.794502 + 0.607261i \(0.792268\pi\)
\(110\) 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 \(0.330838\pi\)
−0.506773 + 0.862079i \(0.669162\pi\)
\(114\) −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 −0.718003 0.696040i \(-0.754944\pi\)
0.696040 + 0.718003i \(0.254944\pi\)
\(128\) −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 0.647310 0.762227i \(-0.275894\pi\)
−0.762227 + 0.647310i \(0.775894\pi\)
\(132\) −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 −0.186544 + 0.982447i \(0.559729\pi\)
−0.982447 + 0.186544i \(0.940271\pi\)
\(138\) 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 \(-0.856897\pi\)
0.900633 0.434579i \(-0.143103\pi\)
\(150\) −4.99973 0.0518094i −0.408226 0.00423022i
\(151\) 3.90183i 0.317526i −0.987317 0.158763i \(-0.949249\pi\)
0.987317 0.158763i \(-0.0507506\pi\)
\(152\) 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 −0.633530 0.773718i \(-0.718395\pi\)
0.773718 + 0.633530i \(0.218395\pi\)
\(158\) −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 \(-0.880034\pi\)
0.929816 0.368025i \(-0.119966\pi\)
\(164\) 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 \(0.251052\pi\)
−0.704765 + 0.709441i \(0.748948\pi\)
\(168\) 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 −0.487606 0.873064i \(-0.662130\pi\)
0.873064 + 0.487606i \(0.162130\pi\)
\(174\) 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 0.106786 0.994282i \(-0.465944\pi\)
0.994282 0.106786i \(-0.0340560\pi\)
\(180\) 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 −0.676022 0.736882i \(-0.736297\pi\)
0.736882 + 0.676022i \(0.236297\pi\)
\(192\) −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 −0.00180312 0.999998i \(-0.500574\pi\)
0.999998 + 0.00180312i \(0.000573952\pi\)
\(198\) −3.51735 −0.249967
\(199\) 2.28257 2.28257i 0.161807 0.161807i −0.621560 0.783367i \(-0.713501\pi\)
0.783367 + 0.621560i \(0.213501\pi\)
\(200\) 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 0.993555 + 0.113349i \(0.0361580\pi\)
0.113349 + 0.993555i \(0.463842\pi\)
\(224\) 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 \(-0.618181\pi\)
0.362805 0.931865i \(-0.381819\pi\)
\(228\) 1.43385 0.0949591
\(229\) 0.286568i 0.0189369i −0.999955 0.00946847i \(-0.996986\pi\)
0.999955 0.00946847i \(-0.00301395\pi\)
\(230\) 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 −0.288676 0.957427i \(-0.593215\pi\)
0.957427 + 0.288676i \(0.0932150\pi\)
\(234\) 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 −0.997047 0.0767893i \(-0.975533\pi\)
−0.0767893 0.997047i \(-0.524467\pi\)
\(240\) −0.844991 2.07026i −0.0545440 0.133635i
\(241\) −17.4511 + 17.4511i −1.12412 + 1.12412i −0.133010 + 0.991115i \(0.542464\pi\)
−0.991115 + 0.133010i \(0.957536\pi\)
\(242\) 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 0.675089 0.737736i \(-0.264105\pi\)
−0.737736 + 0.675089i \(0.764105\pi\)
\(252\) 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 \(-0.907417\pi\)
0.957998 0.286773i \(-0.0925826\pi\)
\(258\) 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 −0.321974 0.946748i \(-0.604346\pi\)
0.946748 + 0.321974i \(0.104346\pi\)
\(264\) 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 \(0.288796\pi\)
−0.615890 + 0.787832i \(0.711204\pi\)
\(270\) 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 −0.987238 0.159251i \(-0.949092\pi\)
0.159251 + 0.987238i \(0.449092\pi\)
\(282\) 5.07803i 0.302392i
\(283\) 20.9115i 1.24306i 0.783389 + 0.621531i \(0.213489\pi\)
−0.783389 + 0.621531i \(0.786511\pi\)
\(284\) −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 0.505685 0.862718i \(-0.331240\pi\)
−0.862718 + 0.505685i \(0.831240\pi\)
\(294\) 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 0.951703 0.307022i \(-0.0993324\pi\)
−0.307022 + 0.951703i \(0.599332\pi\)
\(308\) −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 0.928851 0.370453i \(-0.120798\pi\)
−0.370453 + 0.928851i \(0.620798\pi\)
\(312\) 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 0.381502 0.924368i \(-0.375407\pi\)
−0.924368 + 0.381502i \(0.875407\pi\)
\(318\) −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 0.321487 0.946914i \(-0.395817\pi\)
0.946914 0.321487i \(-0.104183\pi\)
\(332\) −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 0.938613 0.344973i \(-0.112112\pi\)
−0.344973 + 0.938613i \(0.612112\pi\)
\(338\) −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 \(0.405080\pi\)
−0.293799 + 0.955867i \(0.594920\pi\)
\(350\) −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 \(-0.829559\pi\)
0.860036 0.510233i \(-0.170441\pi\)
\(354\) −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 \(0.0584264\pi\)
−0.983202 + 0.182523i \(0.941574\pi\)
\(360\) −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 −0.0967284 0.995311i \(-0.530838\pi\)
0.995311 + 0.0967284i \(0.0308378\pi\)
\(368\) 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 −0.967516 0.252811i \(-0.918645\pi\)
0.252811 + 0.967516i \(0.418645\pi\)
\(374\) 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 \(0.00596527\pi\)
−0.999824 + 0.0187393i \(0.994035\pi\)
\(380\) 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 0.202106 0.979364i \(-0.435222\pi\)
−0.979364 + 0.202106i \(0.935222\pi\)
\(390\) 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 0.897139 0.441748i \(-0.145642\pi\)
−0.441748 + 0.897139i \(0.645642\pi\)
\(398\) −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 −0.986263 0.165182i \(-0.947179\pi\)
−0.165182 0.986263i \(-0.552821\pi\)
\(402\) −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 −0.318678 0.947863i \(-0.603239\pi\)
0.947863 + 0.318678i \(0.103239\pi\)
\(410\) 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 \(-0.968244\pi\)
0.995028 0.0995998i \(-0.0317563\pi\)
\(420\) 1.93019 + 0.811252i 0.0941836 + 0.0395850i
\(421\) −5.38925 5.38925i −0.262656 0.262656i 0.563476 0.826132i \(-0.309464\pi\)
−0.826132 + 0.563476i \(0.809464\pi\)
\(422\) −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 0.896478 0.443089i \(-0.146117\pi\)
−0.443089 + 0.896478i \(0.646117\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 18.0950 + 18.0950i 0.869588 + 0.869588i 0.992427 0.122839i \(-0.0391998\pi\)
−0.122839 + 0.992427i \(0.539200\pi\)
\(434\) 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 −0.783941 0.620835i \(-0.786794\pi\)
0.620835 + 0.783941i \(0.286794\pi\)
\(440\) 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 −0.916158 0.400818i \(-0.868726\pi\)
0.400818 + 0.916158i \(0.368726\pi\)
\(444\) 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 0.908279 0.418366i \(-0.137397\pi\)
−0.418366 + 0.908279i \(0.637397\pi\)
\(450\) 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 \(0.104441\pi\)
−0.946653 + 0.322254i \(0.895559\pi\)
\(458\) 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 −0.407393 + 0.913253i \(0.633562\pi\)
−0.913253 + 0.407393i \(0.866438\pi\)
\(462\) −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 \(-0.884396\pi\)
0.934771 0.355250i \(-0.115604\pi\)
\(468\) 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 0.916461 0.400123i \(-0.131033\pi\)
−0.400123 + 0.916461i \(0.631033\pi\)
\(480\) 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 \(0.164398\pi\)
−0.869568 + 0.493814i \(0.835602\pi\)
\(488\) 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 −0.580034 + 0.814592i \(0.696961\pi\)
−0.814592 + 0.580034i \(0.803039\pi\)
\(500\) 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 \(-0.830975\pi\)
0.862297 0.506403i \(-0.169025\pi\)
\(522\) −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 −0.619465 0.785025i \(-0.712650\pi\)
0.785025 + 0.619465i \(0.212650\pi\)
\(542\) −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 0.304220 0.952602i \(-0.401604\pi\)
0.952602 0.304220i \(-0.0983957\pi\)
\(570\) 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 \(-0.924490\pi\)
0.971994 0.235004i \(-0.0755104\pi\)
\(578\) −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 0.0182800 0.999833i \(-0.494181\pi\)
−0.999833 + 0.0182800i \(0.994181\pi\)
\(594\) 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 \(0.309530\pi\)
−0.563303 + 0.826251i \(0.690470\pi\)
\(600\) −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 −0.889381 0.457167i \(-0.848864\pi\)
0.457167 + 0.889381i \(0.348864\pi\)
\(614\) −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 0.931419 0.363949i \(-0.118572\pi\)
−0.363949 + 0.931419i \(0.618572\pi\)
\(618\) −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 0.466416 0.884565i \(-0.345545\pi\)
−0.884565 + 0.466416i \(0.845545\pi\)
\(632\) −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 \(0.165151\pi\)
−0.868396 + 0.495871i \(0.834849\pi\)
\(644\) −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 \(-0.894844\pi\)
0.945927 0.324380i \(-0.105156\pi\)
\(654\) −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 0.447674 0.894197i \(-0.352252\pi\)
−0.894197 + 0.447674i \(0.852252\pi\)
\(662\) −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 0.998084 0.0618787i \(-0.0197092\pi\)
−0.0618787 + 0.998084i \(0.519709\pi\)
\(674\) −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 0.971599 0.236635i \(-0.0760446\pi\)
−0.236635 + 0.971599i \(0.576045\pi\)
\(678\) 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 \(0.237966\pi\)
−0.733328 + 0.679875i \(0.762034\pi\)
\(692\) 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 −0.979669 0.200618i \(-0.935705\pi\)
0.200618 + 0.979669i \(0.435705\pi\)
\(702\) −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 0.546526 0.837442i \(-0.315950\pi\)
−0.837442 + 0.546526i \(0.815950\pi\)
\(710\) −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 \(-0.822273\pi\)
0.848132 0.529785i \(-0.177727\pi\)
\(720\) 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 −0.00381081 + 0.999993i \(0.501213\pi\)
−0.999993 + 0.00381081i \(0.998787\pi\)
\(734\) −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 −0.108988 0.994043i \(-0.534761\pi\)
0.994043 + 0.108988i \(0.0347611\pi\)
\(744\) 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 \(0.353730\pi\)
−0.443517 + 0.896266i \(0.646270\pi\)
\(752\) 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 \(0.124090\pi\)
−0.924970 + 0.380040i \(0.875910\pi\)
\(758\) 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 \(0.133991\pi\)
−0.912704 + 0.408622i \(0.866009\pi\)
\(762\) 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 −0.674033 0.738701i \(-0.735439\pi\)
0.738701 + 0.674033i \(0.235439\pi\)
\(770\) −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 0.496974 0.867765i \(-0.334444\pi\)
−0.867765 + 0.496974i \(0.834444\pi\)
\(774\) 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 0.126412i
\(780\) −5.81065