Properties

Label 1110.2.l.a.697.12
Level $1110$
Weight $2$
Character 1110.697
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.l (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 697.12
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.a.43.12

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −2.06140 + 0.866398i −0.921884 + 0.387465i
\(6\) 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 \(0.806624\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 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
\(13\) 6.87657i 1.90722i −0.301047 0.953609i \(-0.597336\pi\)
0.301047 0.953609i \(-0.402664\pi\)
\(14\) −0.662100 + 0.662100i −0.176954 + 0.176954i
\(15\) −2.07026 0.844991i −0.534540 0.218176i
\(16\) 1.00000 0.250000
\(17\) −2.17458 −0.527412 −0.263706 0.964603i \(-0.584945\pi\)
−0.263706 + 0.964603i \(0.584945\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.01389 + 1.01389i 0.232601 + 0.232601i 0.813778 0.581176i \(-0.197407\pi\)
−0.581176 + 0.813778i \(0.697407\pi\)
\(20\) 2.06140 0.866398i 0.460942 0.193732i
\(21\) 0.936350i 0.204328i
\(22\) 3.51735 0.749901
\(23\) 9.57399i 1.99632i −0.0606732 0.998158i \(-0.519325\pi\)
0.0606732 0.998158i \(-0.480675\pi\)
\(24\) −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 \(-0.424505\pi\)
0.972006 0.234958i \(-0.0754952\pi\)
\(30\) −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 \(0.651962\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.48714 + 2.48714i −0.432956 + 0.432956i
\(34\) 2.17458i 0.372937i
\(35\) 1.93849 + 0.791208i 0.327665 + 0.133739i
\(36\) 1.00000i 0.166667i
\(37\) −1.24106 5.95481i −0.204029 0.978965i
\(38\) 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 \(0.912402\pi\)
\(42\) −0.936350 −0.144482
\(43\) 2.74581i 0.418732i −0.977837 0.209366i \(-0.932860\pi\)
0.977837 0.209366i \(-0.0671400\pi\)
\(44\) 3.51735i 0.530260i
\(45\) −0.866398 2.06140i −0.129155 0.307295i
\(46\) −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
\(50\) −3.57198 3.49871i −0.505154 0.494792i
\(51\) −1.53766 1.53766i −0.215315 0.215315i
\(52\) 6.87657i 0.953609i
\(53\) −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
\(55\) −3.04742 7.25065i −0.410914 0.977677i
\(56\) 0.662100 0.662100i 0.0884768 0.0884768i
\(57\) 1.43385i 0.189918i
\(58\) −6.49970 6.49970i −0.853452 0.853452i
\(59\) 3.45523 + 3.45523i 0.449833 + 0.449833i 0.895299 0.445466i \(-0.146962\pi\)
−0.445466 + 0.895299i \(0.646962\pi\)
\(60\) 2.07026 + 0.844991i 0.267270 + 0.109088i
\(61\) −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 \(-0.718344\pi\)
0.773819 + 0.633406i \(0.218344\pi\)
\(68\) 2.17458 0.263706
\(69\) 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 \(0.643204\pi\)
\(72\) −1.00000 −0.117851
\(73\) 0.292649 + 0.292649i 0.0342519 + 0.0342519i 0.724025 0.689773i \(-0.242290\pi\)
−0.689773 + 0.724025i \(0.742290\pi\)
\(74\) −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 \(-0.468152\pi\)
−0.994999 + 0.0998861i \(0.968152\pi\)
\(80\) −2.06140 + 0.866398i −0.230471 + 0.0968662i
\(81\) −1.00000 −0.111111
\(82\) 3.47992 0.384293
\(83\) −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
\(87\) 9.19196 0.985481
\(88\) −3.51735 −0.374951
\(89\) 6.43088 6.43088i 0.681672 0.681672i −0.278705 0.960377i \(-0.589905\pi\)
0.960377 + 0.278705i \(0.0899052\pi\)
\(90\) −2.06140 + 0.866398i −0.217290 + 0.0913264i
\(91\) −4.55298 + 4.55298i −0.477282 + 0.477282i
\(92\) 9.57399i 0.998158i
\(93\) 3.37571i 0.350045i
\(94\) 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
\(97\) 0.301015 0.0305635 0.0152817 0.999883i \(-0.495135\pi\)
0.0152817 + 0.999883i \(0.495135\pi\)
\(98\) −6.12325 −0.618541
\(99\) −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
\(103\) −3.81714 −0.376114 −0.188057 0.982158i \(-0.560219\pi\)
−0.188057 + 0.982158i \(0.560219\pi\)
\(104\) 6.87657 0.674304
\(105\) 0.811252 + 1.93019i 0.0791701 + 0.188367i
\(106\) 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 \(-0.207732\pi\)
−0.607261 + 0.794502i \(0.707732\pi\)
\(110\) −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
\(113\) 18.3281 1.72416 0.862079 0.506773i \(-0.169162\pi\)
0.862079 + 0.506773i \(0.169162\pi\)
\(114\) 1.43385 0.134292
\(115\) 8.29489 + 19.7358i 0.773502 + 1.84037i
\(116\) −6.49970 + 6.49970i −0.603482 + 0.603482i
\(117\) 6.87657 0.635739
\(118\) 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
\(125\) −4.11747 + 10.3945i −0.368278 + 0.929716i
\(126\) −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 \(0.754944\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.94158 1.94158i 0.170947 0.170947i
\(130\) 14.1753 5.95785i 1.24326 0.522538i
\(131\) −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
\(133\) 1.34259i 0.116417i
\(134\) −1.14933 1.14933i −0.0992872 0.0992872i
\(135\) 0.844991 2.07026i 0.0727253 0.178180i
\(136\) 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 \(-0.228885\pi\)
0.752422 + 0.658681i \(0.228885\pi\)
\(140\) −1.93849 0.791208i −0.163832 0.0668693i
\(141\) 5.07803i 0.427647i
\(142\) 7.32848i 0.614992i
\(143\) 24.1873 2.02264
\(144\) 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
\(148\) 1.24106 + 5.95481i 0.102015 + 0.489482i
\(149\) 10.6094i 0.869159i 0.900633 + 0.434579i \(0.143103\pi\)
−0.900633 + 0.434579i \(0.856897\pi\)
\(150\) −0.0518094 4.99973i −0.00423022 0.408226i
\(151\) 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
\(153\) 2.17458i 0.175804i
\(154\) −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
\(162\) 1.00000i 0.0785674i
\(163\) −9.39725 −0.736049 −0.368025 0.929816i \(-0.619966\pi\)
−0.368025 + 0.929816i \(0.619966\pi\)
\(164\) 3.47992i 0.271736i
\(165\) 2.97213 7.28184i 0.231380 0.566890i
\(166\) 1.46770 + 1.46770i 0.113916 + 0.113916i
\(167\) −18.3360 −1.41888 −0.709441 0.704765i \(-0.751052\pi\)
−0.709441 + 0.704765i \(0.751052\pi\)
\(168\) 0.936350 0.0722410
\(169\) −34.2873 −2.63748
\(170\) −1.88405 4.48266i −0.144500 0.343805i
\(171\) −1.01389 + 1.01389i −0.0775338 + 0.0775338i
\(172\) 2.74581i 0.209366i
\(173\) −5.06991 5.06991i −0.385458 0.385458i 0.487606 0.873064i \(-0.337870\pi\)
−0.873064 + 0.487606i \(0.837870\pi\)
\(174\) 9.19196i 0.696841i
\(175\) −4.68150 + 0.0485117i −0.353888 + 0.00366714i
\(176\) 3.51735i 0.265130i
\(177\) 4.88643i 0.367287i
\(178\) −6.43088 6.43088i −0.482015 0.482015i
\(179\) −14.7313 + 14.7313i −1.10107 + 1.10107i −0.106786 + 0.994282i \(0.534056\pi\)
−0.994282 + 0.106786i \(0.965944\pi\)
\(180\) 0.866398 + 2.06140i 0.0645775 + 0.153647i
\(181\) −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
\(183\) 14.1330i 1.04474i
\(184\) 9.57399 0.705804
\(185\) 7.71755 + 11.2000i 0.567406 + 0.823438i
\(186\) 3.37571 0.247519
\(187\) 7.64874i 0.559331i
\(188\) −3.59071 3.59071i −0.261879 0.261879i
\(189\) 0.936350 0.0681095
\(190\) −1.21159 + 2.96845i −0.0878981 + 0.215354i
\(191\) 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
\(193\) 2.71107i 0.195147i −0.995228 0.0975736i \(-0.968892\pi\)
0.995228 0.0975736i \(-0.0311081\pi\)
\(194\) 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 \(0.500574\pi\)
\(198\) 3.51735i 0.249967i
\(199\) −2.28257 + 2.28257i −0.161807 + 0.161807i −0.783367 0.621560i \(-0.786499\pi\)
0.621560 + 0.783367i \(0.286499\pi\)
\(200\) 3.57198 + 3.49871i 0.252577 + 0.247396i
\(201\) 1.62540 0.114647
\(202\) 7.88206 0.554580
\(203\) −8.60689 −0.604085
\(204\) 1.53766 + 1.53766i 0.107658 + 0.107658i
\(205\) −3.01499 7.17349i −0.210576 0.501018i
\(206\) 3.81714i 0.265953i
\(207\) 9.57399 0.665438
\(208\) 6.87657i 0.476805i
\(209\) −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
\(217\) 3.16085i 0.214572i
\(218\) 1.95485 1.95485i 0.132399 0.132399i
\(219\) 0.413868i 0.0279666i
\(220\) 3.04742 + 7.25065i 0.205457 + 0.488839i
\(221\) 14.9536i 1.00589i
\(222\) −5.08825 3.33312i −0.341501 0.223705i
\(223\) 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
\(227\) 28.0799 1.86373 0.931865 0.362805i \(-0.118181\pi\)
0.931865 + 0.362805i \(0.118181\pi\)
\(228\) 1.43385i 0.0949591i
\(229\) 0.286568i 0.0189369i 0.999955 + 0.00946847i \(0.00301395\pi\)
−0.999955 + 0.00946847i \(0.996986\pi\)
\(230\) 19.7358 8.29489i 1.30134 0.546949i
\(231\) 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 \(-0.406785\pi\)
−0.957427 + 0.288676i \(0.906785\pi\)
\(234\) 6.87657i 0.449536i
\(235\) −10.5129 4.29089i −0.685783 0.279907i
\(236\) −3.45523 3.45523i −0.224916 0.224916i
\(237\) 11.2514i 0.730857i
\(238\) 1.43979 1.43979i 0.0933275 0.0933275i
\(239\) 16.6011 + 16.6011i 1.07384 + 1.07384i 0.997047 + 0.0767893i \(0.0244669\pi\)
0.0767893 + 0.997047i \(0.475533\pi\)
\(240\) −2.07026 0.844991i −0.133635 0.0545440i
\(241\) −17.4511 + 17.4511i −1.12412 + 1.12412i −0.133010 + 0.991115i \(0.542464\pi\)
−0.991115 + 0.133010i \(0.957536\pi\)
\(242\) 1.37173i 0.0881784i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 9.99355 + 9.99355i 0.639771 + 0.639771i
\(245\) 5.30517 + 12.6224i 0.338935 + 0.806418i
\(246\) 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
\(253\) 33.6751 2.11713
\(254\) −0.247513 + 0.247513i −0.0155303 + 0.0155303i
\(255\) 4.50195 + 1.83750i 0.281923 + 0.115069i
\(256\) 1.00000 0.0625000
\(257\) 9.19465 0.573546 0.286773 0.957998i \(-0.407417\pi\)
0.286773 + 0.957998i \(0.407417\pi\)
\(258\) −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 \(-0.395654\pi\)
−0.946748 + 0.321974i \(0.895654\pi\)
\(264\) −2.48714 2.48714i −0.153073 0.153073i
\(265\) 3.50660 8.59132i 0.215409 0.527761i
\(266\) −1.34259 −0.0823193
\(267\) 9.09463 0.556582
\(268\) −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 \(0.303571\pi\)
\(272\) −2.17458 −0.131853
\(273\) −6.43888 −0.389699
\(274\) −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
\(277\) 2.31001i 0.138795i 0.997589 + 0.0693974i \(0.0221077\pi\)
−0.997589 + 0.0693974i \(0.977892\pi\)
\(278\) 17.7419i 1.06409i
\(279\) −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 \(0.449092\pi\)
\(282\) 5.07803 0.302392
\(283\) 20.9115 1.24306 0.621531 0.783389i \(-0.286511\pi\)
0.621531 + 0.783389i \(0.286511\pi\)
\(284\) 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
\(288\) 1.00000 0.0589256
\(289\) −12.2712 −0.721836
\(290\) 19.0298 + 7.76713i 1.11747 + 0.456101i
\(291\) 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
\(298\) 10.6094 0.614588
\(299\) −65.8363 −3.80741
\(300\) −4.99973 + 0.0518094i −0.288660 + 0.00299122i
\(301\) −1.81800 + 1.81800i −0.104788 + 0.104788i
\(302\) −3.90183 −0.224525
\(303\) −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 \(-0.900668\pi\)
0.307022 + 0.951703i \(0.400668\pi\)
\(308\) −2.32883 + 2.32883i −0.132698 + 0.132698i
\(309\) −2.69912 2.69912i −0.153548 0.153548i
\(310\) −2.85245 + 6.98861i −0.162008 + 0.396927i
\(311\) 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
\(313\) 12.1322i 0.685752i 0.939381 + 0.342876i \(0.111401\pi\)
−0.939381 + 0.342876i \(0.888599\pi\)
\(314\) 1.75656 1.75656i 0.0991282 0.0991282i
\(315\) −0.791208 + 1.93849i −0.0445795 + 0.109222i
\(316\) 7.95594 + 7.95594i 0.447556 + 0.447556i
\(317\) 9.66544 9.66544i 0.542865 0.542865i −0.381502 0.924368i \(-0.624593\pi\)
0.924368 + 0.381502i \(0.124593\pi\)
\(318\) 4.14987i 0.232713i
\(319\) 22.8617 + 22.8617i 1.28001 + 1.28001i
\(320\) 2.06140 0.866398i 0.115236 0.0484331i
\(321\) 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
\(325\) −24.5630 24.0591i −1.36251 1.33456i
\(326\) 9.39725i 0.520465i
\(327\) 2.76458i 0.152882i
\(328\) −3.47992 −0.192146
\(329\) 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
\(333\) 5.95481 1.24106i 0.326322 0.0680097i
\(334\) 18.3360i 1.00330i
\(335\) −1.37345 + 3.36501i −0.0750396 + 0.183850i
\(336\) 0.936350i 0.0510821i
\(337\) −10.8978 + 10.8978i −0.593640 + 0.593640i −0.938613 0.344973i \(-0.887888\pi\)
0.344973 + 0.938613i \(0.387888\pi\)
\(338\) 34.2873i 1.86498i
\(339\) 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
\(347\) 0.330476i 0.0177409i 0.999961 + 0.00887043i \(0.00282358\pi\)
−0.999961 + 0.00887043i \(0.997176\pi\)
\(348\) −9.19196 −0.492741
\(349\) 35.7141i 1.91173i −0.293799 0.955867i \(-0.594920\pi\)
0.293799 0.955867i \(-0.405080\pi\)
\(350\) 0.0485117 + 4.68150i 0.00259306 + 0.250237i
\(351\) 4.86247 + 4.86247i 0.259540 + 0.259540i
\(352\) 3.51735 0.187475
\(353\) −19.1728 −1.02047 −0.510233 0.860036i \(-0.670441\pi\)
−0.510233 + 0.860036i \(0.670441\pi\)
\(354\) 4.88643 0.259711
\(355\) 15.1069 6.34938i 0.801791 0.336990i
\(356\) −6.43088 + 6.43088i −0.340836 + 0.340836i
\(357\) 2.03617i 0.107765i
\(358\) 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
\(362\) 4.07298i 0.214071i
\(363\) −0.969963 0.969963i −0.0509098 0.0509098i
\(364\) 4.55298 4.55298i 0.238641 0.238641i
\(365\) −0.856815 0.349715i −0.0448477 0.0183049i
\(366\) −14.1330 −0.738744
\(367\) 17.2144 + 17.2144i 0.898582 + 0.898582i 0.995311 0.0967284i \(-0.0308378\pi\)
−0.0967284 + 0.995311i \(0.530838\pi\)
\(368\) 9.57399i 0.499079i
\(369\) −3.47992 −0.181157
\(370\) 11.2000 7.71755i 0.582259 0.401217i
\(371\) 3.88573 0.201737
\(372\) 3.37571i 0.175023i
\(373\) 13.8033 + 13.8033i 0.714705 + 0.714705i 0.967516 0.252811i \(-0.0813549\pi\)
−0.252811 + 0.967516i \(0.581355\pi\)
\(374\) −7.64874 −0.395507
\(375\) −10.2615 + 4.43856i −0.529904 + 0.229206i
\(376\) −3.59071 + 3.59071i −0.185177 + 0.185177i
\(377\) −44.6956 44.6956i −2.30194 2.30194i
\(378\) 0.936350i 0.0481607i
\(379\) 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
\(383\) 28.2223i 1.44209i −0.692887 0.721047i \(-0.743661\pi\)
0.692887 0.721047i \(-0.256339\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −2.78295 + 6.81835i −0.141832 + 0.347495i
\(386\) −2.71107 −0.137990
\(387\) 2.74581 0.139577
\(388\) −0.301015 −0.0152817
\(389\) 15.3299 + 15.3299i 0.777258 + 0.777258i 0.979364 0.202106i \(-0.0647784\pi\)
−0.202106 + 0.979364i \(0.564778\pi\)
\(390\) 14.2363 + 5.81065i 0.720884 + 0.294234i
\(391\) 20.8194i 1.05288i
\(392\) 6.12325 0.309271
\(393\) 1.86010i 0.0938295i
\(394\) 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 \(-0.854358\pi\)
0.441748 + 0.897139i \(0.354358\pi\)
\(398\) 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 \(-0.552821\pi\)
\(402\) 1.62540i 0.0810677i
\(403\) 16.4143 16.4143i 0.817655 0.817655i
\(404\) 7.88206i 0.392147i
\(405\) 2.06140 0.866398i 0.102432 0.0430517i
\(406\) 8.60689i 0.427153i
\(407\) 20.9451 4.36524i 1.03821 0.216377i
\(408\) 1.53766 1.53766i 0.0761254 0.0761254i
\(409\) −12.7245 + 12.7245i −0.629185 + 0.629185i −0.947863 0.318678i \(-0.896761\pi\)
0.318678 + 0.947863i \(0.396761\pi\)
\(410\) −7.17349 + 3.01499i −0.354273 + 0.148900i
\(411\) 19.3502i 0.954477i
\(412\) 3.81714 0.188057
\(413\) 4.57541i 0.225141i
\(414\) 9.57399i 0.470536i
\(415\) 1.75390 4.29714i 0.0860958 0.210938i
\(416\) −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 \(0.968244\pi\)
\(420\) −0.811252 1.93019i −0.0395850 0.0941836i
\(421\) −5.38925 5.38925i −0.262656 0.262656i 0.563476 0.826132i \(-0.309464\pi\)
−0.826132 + 0.563476i \(0.809464\pi\)
\(422\) 16.7409i 0.814936i
\(423\) −3.59071 + 3.59071i −0.174586 + 0.174586i
\(424\) −2.93440 2.93440i −0.142507 0.142507i
\(425\) −7.60821 + 7.76754i −0.369052 + 0.376781i
\(426\) −5.18202 + 5.18202i −0.251070 + 0.251070i
\(427\) 13.2334i 0.640411i
\(428\) 3.39625 + 3.39625i 0.164164 + 0.164164i
\(429\) 17.1030 + 17.1030i 0.825741 + 0.825741i
\(430\) 5.66020 2.37896i 0.272959 0.114724i
\(431\) 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 −0.122839 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
\(438\) 0.413868 0.0197754
\(439\) 3.41744 3.41744i 0.163106 0.163106i −0.620835 0.783941i \(-0.713206\pi\)
0.783941 + 0.620835i \(0.213206\pi\)
\(440\) 7.25065 3.04742i 0.345661 0.145280i
\(441\) 6.12325 0.291583
\(442\) 14.9536 0.711272
\(443\) 10.8466 + 10.8466i 0.515340 + 0.515340i 0.916158 0.400818i \(-0.131274\pi\)
−0.400818 + 0.916158i \(0.631274\pi\)
\(444\) −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 \(-0.362603\pi\)
−0.908279 + 0.418366i \(0.862603\pi\)
\(450\) 3.49871 3.57198i 0.164931 0.168385i
\(451\) −12.2401 −0.576363
\(452\) −18.3281 −0.862079
\(453\) 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
\(457\) −13.7780 −0.644509 −0.322254 0.946653i \(-0.604441\pi\)
−0.322254 + 0.946653i \(0.604441\pi\)
\(458\) 0.286568 0.0133904
\(459\) 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 \(0.866438\pi\)
\(462\) 3.29347i 0.153226i
\(463\) 27.1414i 1.26137i 0.776040 + 0.630683i \(0.217225\pi\)
−0.776040 + 0.630683i \(0.782775\pi\)
\(464\) 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
\(467\) 15.3540 0.710500 0.355250 0.934771i \(-0.384396\pi\)
0.355250 + 0.934771i \(0.384396\pi\)
\(468\) −6.87657 −0.317870
\(469\) −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
\(473\) 9.65796 0.444074
\(474\) −11.2514 −0.516794
\(475\) 7.16887 0.0742869i 0.328930 0.00340852i
\(476\) −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 \(-0.368967\pi\)
−0.916461 + 0.400123i \(0.868967\pi\)
\(480\) −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
\(483\) −8.96461 −0.407904
\(484\) 1.37173 0.0623516
\(485\) −0.620511 + 0.260799i −0.0281760 + 0.0118423i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) −21.7950 −0.987628 −0.493814 0.869568i \(-0.664398\pi\)
−0.493814 + 0.869568i \(0.664398\pi\)
\(488\) 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
\(495\) 7.25065 3.04742i 0.325892 0.136971i
\(496\) 2.38699 + 2.38699i 0.107179 + 0.107179i
\(497\) 4.85218 + 4.85218i 0.217650 + 0.217650i
\(498\) 2.07565i 0.0930120i
\(499\) 31.1536 31.1536i 1.39463 1.39463i 0.580034 0.814592i \(-0.303039\pi\)
0.814592 0.580034i \(-0.196961\pi\)
\(500\) 4.11747 10.3945i 0.184139 0.464858i
\(501\) −12.9655 12.9655i −0.579256 0.579256i
\(502\) −0.992524 + 0.992524i −0.0442985 + 0.0442985i
\(503\) 0.724954i 0.0323241i 0.999869 + 0.0161621i \(0.00514477\pi\)
−0.999869 + 0.0161621i \(0.994855\pi\)
\(504\) 0.662100 + 0.662100i 0.0294923 + 0.0294923i
\(505\) −6.82900 16.2480i −0.303886 0.723029i
\(506\) 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 \(-0.323729\pi\)
0.525899 + 0.850547i \(0.323729\pi\)
\(510\) 1.83750 4.50195i 0.0813658 0.199350i
\(511\) 0.387525i 0.0171431i
\(512\) 1.00000i 0.0441942i
\(513\) −1.43385 −0.0633061
\(514\) 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
\(518\) 4.76438 + 3.12097i 0.209335 + 0.137128i
\(519\) 7.16994i 0.314725i
\(520\) −14.1753 + 5.95785i −0.621630 + 0.261269i
\(521\) 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
\(523\) 15.4427i 0.675261i −0.941279 0.337631i \(-0.890375\pi\)
0.941279 0.337631i \(-0.109625\pi\)
\(524\) 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
\(532\) 1.34259i 0.0582085i
\(533\) 23.9299 1.03652
\(534\) 9.09463i 0.393563i
\(535\) 9.94353 + 4.05851i 0.429896 + 0.175465i
\(536\) 1.14933 + 1.14933i 0.0496436 + 0.0496436i
\(537\) −20.8332 −0.899018
\(538\) −25.8428 −1.11416
\(539\) 21.5376 0.927690
\(540\) −0.844991 + 2.07026i −0.0363626 + 0.0890899i
\(541\) 3.85083 3.85083i 0.165560 0.165560i −0.619465 0.785025i \(-0.712650\pi\)
0.785025 + 0.619465i \(0.212650\pi\)
\(542\) 19.0523i 0.818365i
\(543\) −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
\(547\) 5.49141i 0.234796i 0.993085 + 0.117398i \(0.0374552\pi\)
−0.993085 + 0.117398i \(0.962545\pi\)
\(548\) 13.6827 + 13.6827i 0.584495 + 0.584495i
\(549\) 9.99355 9.99355i 0.426514 0.426514i
\(550\) 12.3062 12.5639i 0.524737 0.535726i
\(551\) 13.1799 0.561483
\(552\) 6.76983 + 6.76983i 0.288143 + 0.288143i
\(553\) 10.5352i 0.448004i
\(554\) 2.31001 0.0981428
\(555\) −2.46244 + 13.3767i −0.104525 + 0.567810i
\(556\) −17.7419 −0.752422
\(557\) 20.3979i 0.864285i −0.901805 0.432142i \(-0.857758\pi\)
0.901805 0.432142i \(-0.142242\pi\)
\(558\) 2.38699 + 2.38699i 0.101049 + 0.101049i
\(559\) −18.8818 −0.798613
\(560\) 1.93849 + 0.791208i 0.0819162 + 0.0334346i
\(561\) 5.40848 5.40848i 0.228346 0.228346i
\(562\) 13.8796 + 13.8796i 0.585475 + 0.585475i
\(563\) 41.6497i 1.75533i −0.479278 0.877663i \(-0.659101\pi\)
0.479278 0.877663i \(-0.340899\pi\)
\(564\) 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
\(568\) 7.32848i 0.307496i
\(569\) −29.9799 + 29.9799i −1.25682 + 1.25682i −0.304220 + 0.952602i \(0.598396\pi\)
−0.952602 + 0.304220i \(0.901604\pi\)
\(570\) −2.95573 + 1.24229i −0.123802 + 0.0520336i
\(571\) −33.5003 −1.40195 −0.700973 0.713188i \(-0.747250\pi\)
−0.700973 + 0.713188i \(0.747250\pi\)
\(572\) −24.1873 −1.01132
\(573\) 1.18950 0.0496922
\(574\) −2.30405 2.30405i −0.0961693 0.0961693i
\(575\) −34.1981 33.4966i −1.42616 1.39691i
\(576\) 1.00000i 0.0416667i
\(577\) 11.2900 0.470008 0.235004 0.971994i \(-0.424490\pi\)
0.235004 + 0.971994i \(0.424490\pi\)
\(578\) 12.2712i 0.510415i
\(579\) 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
\(587\) 0.261793i 0.0108053i −0.999985 0.00540267i \(-0.998280\pi\)
0.999985 0.00540267i \(-0.00171973\pi\)
\(588\) −4.32979 + 4.32979i −0.178558 + 0.178558i
\(589\) 4.84027i 0.199440i
\(590\) −4.12899 + 10.1162i −0.169988 + 0.416477i
\(591\) 19.8136i 0.815023i
\(592\) −1.24106 5.95481i −0.0510073 0.244741i
\(593\) −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
\(597\) −3.22805 −0.132115
\(598\) 65.8363i 2.69225i
\(599\) 40.4441i 1.65250i −0.563303 0.826251i \(-0.690470\pi\)
0.563303 0.826251i \(-0.309530\pi\)
\(600\) 0.0518094 + 4.99973i 0.00211511 + 0.204113i
\(601\) 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
\(605\) 2.82769 1.18847i 0.114962 0.0483181i
\(606\) 5.57346 + 5.57346i 0.226406 + 0.226406i
\(607\) 14.3687i 0.583208i −0.956539 0.291604i \(-0.905811\pi\)
0.956539 0.291604i \(-0.0941890\pi\)
\(608\) 1.01389 1.01389i 0.0411185 0.0411185i
\(609\) −6.08599 6.08599i −0.246617 0.246617i
\(610\) 11.9423 29.2590i 0.483528 1.18466i
\(611\) 24.6918 24.6918i 0.998922 0.998922i
\(612\) 2.17458i 0.0879020i
\(613\) 10.7011 + 10.7011i 0.432213 + 0.432213i 0.889381 0.457167i \(-0.151136\pi\)
−0.457167 + 0.889381i \(0.651136\pi\)
\(614\) 11.2957 + 11.2957i 0.455858 + 0.455858i
\(615\) 2.94050 7.20434i 0.118572 0.290507i
\(616\) 2.32883 + 2.32883i 0.0938314 + 0.0938314i
\(617\) −14.0957 + 14.0957i −0.567470 + 0.567470i −0.931419 0.363949i \(-0.881428\pi\)
0.363949 + 0.931419i \(0.381428\pi\)
\(618\) −2.69912 + 2.69912i −0.108575 + 0.108575i
\(619\) 4.28502 0.172230 0.0861148 0.996285i \(-0.472555\pi\)
0.0861148 + 0.996285i \(0.472555\pi\)
\(620\) 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
\(623\) −8.51576 −0.341177
\(624\) 4.86247 4.86247i 0.194655 0.194655i
\(625\) −0.518066 24.9946i −0.0207226 0.999785i
\(626\) 12.1322 0.484900
\(627\) −5.04335 −0.201412
\(628\) −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
\(635\) 0.724667 + 0.295777i 0.0287575 + 0.0117376i
\(636\) 4.14987 0.164553
\(637\) −42.1070 −1.66834
\(638\) 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 \(0.192251\pi\)
\(642\) −4.80302 −0.189560
\(643\) 25.1480 0.991742 0.495871 0.868396i \(-0.334849\pi\)
0.495871 + 0.868396i \(0.334849\pi\)
\(644\) 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
\(647\) 29.9330i 1.17679i −0.808575 0.588394i \(-0.799761\pi\)
0.808575 0.588394i \(-0.200239\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −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
\(652\) 9.39725 0.368025
\(653\) −16.5783 −0.648759 −0.324380 0.945927i \(-0.605156\pi\)
−0.324380 + 0.945927i \(0.605156\pi\)
\(654\) 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
\(658\) −4.75481 −0.185362
\(659\) −19.3767 −0.754807 −0.377404 0.926049i \(-0.623183\pi\)
−0.377404 + 0.926049i \(0.623183\pi\)
\(660\) −2.97213 + 7.28184i −0.115690 + 0.283445i
\(661\) −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
\(668\) 18.3360 0.709441
\(669\) 23.3764 0.903784
\(670\) 3.36501 + 1.37345i 0.130002 + 0.0530610i
\(671\) 35.1508 35.1508i 1.35698 1.35698i
\(672\) −0.936350 −0.0361205
\(673\) 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 −0.971599 0.236635i \(-0.923955\pi\)
0.236635 + 0.971599i \(0.423955\pi\)
\(678\) 12.9599 12.9599i 0.497722 0.497722i
\(679\) −0.199302 0.199302i −0.00764851 0.00764851i
\(680\) 1.88405 + 4.48266i 0.0722500 + 0.171902i
\(681\) 19.8555 + 19.8555i 0.760865 + 0.760865i
\(682\) 8.39587 + 8.39587i 0.321494 + 0.321494i
\(683\) 5.31945i 0.203543i 0.994808 + 0.101772i \(0.0324511\pi\)
−0.994808 + 0.101772i \(0.967549\pi\)
\(684\) 1.01389 1.01389i 0.0387669 0.0387669i
\(685\) 40.0601 + 16.3508i 1.53062 + 0.624732i
\(686\) 8.68890 + 8.68890i 0.331744 + 0.331744i
\(687\) −0.202634 + 0.202634i −0.00773097 + 0.00773097i
\(688\) 2.74581i 0.104683i
\(689\) 20.1786 + 20.1786i 0.768745 + 0.768745i
\(690\) 19.8207 + 8.08994i 0.754561 + 0.307979i
\(691\) 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
\(695\) −36.5730 + 15.3715i −1.38729 + 0.583074i
\(696\) 9.19196i 0.348420i
\(697\) 7.56735i 0.286634i
\(698\) −35.7141 −1.35180
\(699\) 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
\(703\) 4.77920 7.29579i 0.180251 0.275166i
\(704\) 3.51735i 0.132565i
\(705\) −4.39959 10.4678i −0.165698 0.394241i
\(706\) 19.1728i 0.721579i
\(707\) 5.21871 5.21871i 0.196270 0.196270i
\(708\) 4.88643i 0.183643i
\(709\) 7.74624 + 7.74624i 0.290916 + 0.290916i 0.837442 0.546526i \(-0.184050\pi\)
−0.546526 + 0.837442i \(0.684050\pi\)
\(710\) −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
\(717\) 23.4775i 0.876784i
\(718\) −6.91664 −0.258127
\(719\) 28.4115i 1.05957i 0.848132 + 0.529785i \(0.177727\pi\)
−0.848132 + 0.529785i \(0.822273\pi\)
\(720\) −0.866398 2.06140i −0.0322887 0.0768237i
\(721\) 2.52733 + 2.52733i 0.0941226 + 0.0941226i
\(722\) −16.9441 −0.630593
\(723\) −24.6796 −0.917844
\(724\) 4.07298 0.151371
\(725\) −0.476230 45.9573i −0.0176867 1.70681i
\(726\) −0.969963 + 0.969963i −0.0359987 + 0.0359987i
\(727\) 10.2341i 0.379561i 0.981827 + 0.189780i \(0.0607776\pi\)
−0.981827 + 0.189780i \(0.939222\pi\)
\(728\) −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
\(732\) 14.1330i 0.522371i
\(733\) 27.1770 + 27.1770i 1.00380 + 1.00380i 0.999993 + 0.00381081i \(0.00121302\pi\)
0.00381081 + 0.999993i \(0.498787\pi\)
\(734\) 17.2144 17.2144i 0.635394 0.635394i
\(735\) −5.17409 + 12.6767i −0.190849 + 0.467588i
\(736\) −9.57399 −0.352902
\(737\) 4.04260 + 4.04260i 0.148911 + 0.148911i
\(738\) 3.47992i 0.128098i
\(739\) −17.3037 −0.636527 −0.318264 0.948002i \(-0.603100\pi\)
−0.318264 + 0.948002i \(0.603100\pi\)
\(740\) −7.71755 11.2000i −0.283703 0.411719i
\(741\) 9.85998 0.362215
\(742\) 3.88573i 0.142650i
\(743\) −24.1248 24.1248i −0.885055 0.885055i 0.108988 0.994043i \(-0.465239\pi\)
−0.994043 + 0.108988i \(0.965239\pi\)
\(744\) −3.37571 −0.123760
\(745\) −9.19199 21.8703i −0.336769 0.801264i
\(746\) 13.8033 13.8033i 0.505373 0.505373i
\(747\) −1.46770 1.46770i −0.0537005 0.0537005i
\(748\) 7.64874i 0.279666i
\(749\) 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
\(753\) 1.40364i 0.0511515i
\(754\) −44.6956 + 44.6956i −1.62772 + 1.62772i
\(755\) 3.38053 + 8.04321i 0.123030 + 0.292722i
\(756\) −0.936350 −0.0340547
\(757\) −20.9126 −0.760081 −0.380040 0.924970i \(-0.624090\pi\)
−0.380040 + 0.924970i \(0.624090\pi\)
\(758\) −0.729632 −0.0265014
\(759\) 23.8119 + 23.8119i 0.864316 + 0.864316i
\(760\) 1.21159 2.96845i 0.0439491 0.107677i
\(761\) 22.5447i 0.817245i 0.912704 + 0.408622i \(0.133991\pi\)
−0.912704 + 0.408622i \(0.866009\pi\)
\(762\) −0.350036 −0.0126805
\(763\) 2.58862i 0.0937142i
\(764\) −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 \(-0.764561\pi\)
0.674033 + 0.738701i \(0.264561\pi\)
\(770\) 6.81835 + 2.78295i 0.245716 + 0.100291i
\(771\) 6.50160 + 6.50160i 0.234149 + 0.234149i
\(772\) 2.71107i 0.0975736i
\(773\) −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
\(775\) 16.8777 0.174894i 0.606263 0.00628236i
\(776\) 0.301015i 0.0108058i
\(777\) −5.57579 + 1.16207i −0.200030 + 0.0416890i
\(778\) 15.3299 15.3299i 0.549604 0.549604i
\(779\) −3.52824 + 3.52824i −0.126412 + 0.126412i
\(780\) 5.81065