Properties

Label 1110.2.u.e.401.9
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.9
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.44660 - 0.952541i) q^{6} +2.97676 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75590 + 1.18533i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.44660 - 0.952541i) q^{6} +2.97676 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75590 + 1.18533i) q^{9} +1.00000 q^{10} +2.43854 q^{11} +(1.69645 - 0.349356i) q^{12} +(3.37975 - 3.37975i) q^{13} +(-2.10489 + 2.10489i) q^{14} +(0.952541 - 1.44660i) q^{15} -1.00000 q^{16} +(-2.64124 - 2.64124i) q^{17} +(1.11056 - 2.78687i) q^{18} +(5.18614 - 5.18614i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(1.03995 + 5.04993i) q^{21} +(-1.72431 + 1.72431i) q^{22} +(-4.56924 - 4.56924i) q^{23} +(-0.952541 + 1.44660i) q^{24} +1.00000i q^{25} +4.77969i q^{26} +(-2.97365 - 4.26115i) q^{27} -2.97676i q^{28} +(2.17706 - 2.17706i) q^{29} +(0.349356 + 1.69645i) q^{30} +(-1.20146 - 1.20146i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.851919 + 4.13687i) q^{33} +3.73527 q^{34} +(-2.10489 - 2.10489i) q^{35} +(1.18533 + 2.75590i) q^{36} +(5.17502 + 3.19675i) q^{37} +7.33431i q^{38} +(6.91433 + 4.55285i) q^{39} -1.00000i q^{40} +7.04761 q^{41} +(-4.30620 - 2.83549i) q^{42} +(-3.83120 + 3.83120i) q^{43} -2.43854i q^{44} +(2.78687 + 1.11056i) q^{45} +6.46188 q^{46} -6.56942i q^{47} +(-0.349356 - 1.69645i) q^{48} +1.86110 q^{49} +(-0.707107 - 0.707107i) q^{50} +(3.55800 - 5.40347i) q^{51} +(-3.37975 - 3.37975i) q^{52} -0.00856748i q^{53} +(5.11578 + 0.910402i) q^{54} +(-1.72431 - 1.72431i) q^{55} +(2.10489 + 2.10489i) q^{56} +(10.6098 + 6.98623i) q^{57} +3.07883i q^{58} +(-3.57544 - 3.57544i) q^{59} +(-1.44660 - 0.952541i) q^{60} +(8.28937 + 8.28937i) q^{61} +1.69913 q^{62} +(-8.20365 + 3.52845i) q^{63} +1.00000i q^{64} -4.77969 q^{65} +(-3.52760 - 2.32281i) q^{66} +3.64813i q^{67} +(-2.64124 + 2.64124i) q^{68} +(6.15521 - 9.34779i) q^{69} +2.97676 q^{70} +9.63129i q^{71} +(-2.78687 - 1.11056i) q^{72} -5.75117i q^{73} +(-5.91973 + 1.39885i) q^{74} +(-1.69645 + 0.349356i) q^{75} +(-5.18614 - 5.18614i) q^{76} +7.25895 q^{77} +(-8.10852 + 1.66982i) q^{78} +(6.34989 - 6.34989i) q^{79} +(0.707107 + 0.707107i) q^{80} +(6.18998 - 6.53331i) q^{81} +(-4.98341 + 4.98341i) q^{82} +16.7962i q^{83} +(5.04993 - 1.03995i) q^{84} +3.73527i q^{85} -5.41814i q^{86} +(4.45385 + 2.93271i) q^{87} +(1.72431 + 1.72431i) q^{88} +(-1.72334 + 1.72334i) q^{89} +(-2.75590 + 1.18533i) q^{90} +(10.0607 - 10.0607i) q^{91} +(-4.56924 + 4.56924i) q^{92} +(1.61849 - 2.45796i) q^{93} +(4.64528 + 4.64528i) q^{94} -7.33431 q^{95} +(1.44660 + 0.952541i) q^{96} +(-4.30682 + 4.30682i) q^{97} +(-1.31599 + 1.31599i) q^{98} +(-6.72037 + 2.89048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q - 24q^{7} - 8q^{9} + 40q^{10} - 8q^{12} - 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 24q^{31} + 24q^{33} - 8q^{34} + 16q^{39} - 20q^{42} - 32q^{43} - 8q^{45} + 72q^{46} + 96q^{49} + 20q^{51} + 16q^{52} + 24q^{54} - 16q^{57} + 40q^{61} - 24q^{63} - 44q^{66} - 24q^{70} + 8q^{72} + 8q^{75} - 16q^{76} + 48q^{79} + 24q^{81} - 56q^{82} - 8q^{84} + 12q^{87} - 8q^{90} - 64q^{91} + 12q^{93} + 24q^{94} + 8q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.349356 + 1.69645i 0.201701 + 0.979447i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) −1.44660 0.952541i −0.590574 0.388873i
\(7\) 2.97676 1.12511 0.562555 0.826760i \(-0.309819\pi\)
0.562555 + 0.826760i \(0.309819\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.75590 + 1.18533i −0.918634 + 0.395111i
\(10\) 1.00000 0.316228
\(11\) 2.43854 0.735247 0.367624 0.929975i \(-0.380171\pi\)
0.367624 + 0.929975i \(0.380171\pi\)
\(12\) 1.69645 0.349356i 0.489724 0.100850i
\(13\) 3.37975 3.37975i 0.937375 0.937375i −0.0607761 0.998151i \(-0.519358\pi\)
0.998151 + 0.0607761i \(0.0193576\pi\)
\(14\) −2.10489 + 2.10489i −0.562555 + 0.562555i
\(15\) 0.952541 1.44660i 0.245945 0.373512i
\(16\) −1.00000 −0.250000
\(17\) −2.64124 2.64124i −0.640594 0.640594i 0.310107 0.950702i \(-0.399635\pi\)
−0.950702 + 0.310107i \(0.899635\pi\)
\(18\) 1.11056 2.78687i 0.261762 0.656872i
\(19\) 5.18614 5.18614i 1.18978 1.18978i 0.212654 0.977128i \(-0.431789\pi\)
0.977128 0.212654i \(-0.0682108\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) 1.03995 + 5.04993i 0.226935 + 1.10199i
\(22\) −1.72431 + 1.72431i −0.367624 + 0.367624i
\(23\) −4.56924 4.56924i −0.952753 0.952753i 0.0461806 0.998933i \(-0.485295\pi\)
−0.998933 + 0.0461806i \(0.985295\pi\)
\(24\) −0.952541 + 1.44660i −0.194437 + 0.295287i
\(25\) 1.00000i 0.200000i
\(26\) 4.77969i 0.937375i
\(27\) −2.97365 4.26115i −0.572279 0.820059i
\(28\) 2.97676i 0.562555i
\(29\) 2.17706 2.17706i 0.404270 0.404270i −0.475465 0.879735i \(-0.657720\pi\)
0.879735 + 0.475465i \(0.157720\pi\)
\(30\) 0.349356 + 1.69645i 0.0637834 + 0.309728i
\(31\) −1.20146 1.20146i −0.215789 0.215789i 0.590932 0.806721i \(-0.298760\pi\)
−0.806721 + 0.590932i \(0.798760\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.851919 + 4.13687i 0.148300 + 0.720136i
\(34\) 3.73527 0.640594
\(35\) −2.10489 2.10489i −0.355791 0.355791i
\(36\) 1.18533 + 2.75590i 0.197555 + 0.459317i
\(37\) 5.17502 + 3.19675i 0.850767 + 0.525542i
\(38\) 7.33431i 1.18978i
\(39\) 6.91433 + 4.55285i 1.10718 + 0.729040i
\(40\) 1.00000i 0.158114i
\(41\) 7.04761 1.10065 0.550326 0.834950i \(-0.314504\pi\)
0.550326 + 0.834950i \(0.314504\pi\)
\(42\) −4.30620 2.83549i −0.664460 0.437525i
\(43\) −3.83120 + 3.83120i −0.584253 + 0.584253i −0.936069 0.351816i \(-0.885564\pi\)
0.351816 + 0.936069i \(0.385564\pi\)
\(44\) 2.43854i 0.367624i
\(45\) 2.78687 + 1.11056i 0.415442 + 0.165553i
\(46\) 6.46188 0.952753
\(47\) 6.56942i 0.958249i −0.877747 0.479124i \(-0.840954\pi\)
0.877747 0.479124i \(-0.159046\pi\)
\(48\) −0.349356 1.69645i −0.0504252 0.244862i
\(49\) 1.86110 0.265871
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 3.55800 5.40347i 0.498220 0.756637i
\(52\) −3.37975 3.37975i −0.468688 0.468688i
\(53\) 0.00856748i 0.00117683i −1.00000 0.000588417i \(-0.999813\pi\)
1.00000 0.000588417i \(-0.000187299\pi\)
\(54\) 5.11578 + 0.910402i 0.696169 + 0.123890i
\(55\) −1.72431 1.72431i −0.232506 0.232506i
\(56\) 2.10489 + 2.10489i 0.281277 + 0.281277i
\(57\) 10.6098 + 6.98623i 1.40531 + 0.925348i
\(58\) 3.07883i 0.404270i
\(59\) −3.57544 3.57544i −0.465483 0.465483i 0.434965 0.900447i \(-0.356761\pi\)
−0.900447 + 0.434965i \(0.856761\pi\)
\(60\) −1.44660 0.952541i −0.186756 0.122973i
\(61\) 8.28937 + 8.28937i 1.06135 + 1.06135i 0.997991 + 0.0633543i \(0.0201798\pi\)
0.0633543 + 0.997991i \(0.479820\pi\)
\(62\) 1.69913 0.215789
\(63\) −8.20365 + 3.52845i −1.03356 + 0.444543i
\(64\) 1.00000i 0.125000i
\(65\) −4.77969 −0.592848
\(66\) −3.52760 2.32281i −0.434218 0.285918i
\(67\) 3.64813i 0.445689i 0.974854 + 0.222845i \(0.0715343\pi\)
−0.974854 + 0.222845i \(0.928466\pi\)
\(68\) −2.64124 + 2.64124i −0.320297 + 0.320297i
\(69\) 6.15521 9.34779i 0.741000 1.12534i
\(70\) 2.97676 0.355791
\(71\) 9.63129i 1.14302i 0.820594 + 0.571512i \(0.193643\pi\)
−0.820594 + 0.571512i \(0.806357\pi\)
\(72\) −2.78687 1.11056i −0.328436 0.130881i
\(73\) 5.75117i 0.673123i −0.941661 0.336561i \(-0.890736\pi\)
0.941661 0.336561i \(-0.109264\pi\)
\(74\) −5.91973 + 1.39885i −0.688155 + 0.162613i
\(75\) −1.69645 + 0.349356i −0.195889 + 0.0403402i
\(76\) −5.18614 5.18614i −0.594891 0.594891i
\(77\) 7.25895 0.827234
\(78\) −8.10852 + 1.66982i −0.918110 + 0.189069i
\(79\) 6.34989 6.34989i 0.714419 0.714419i −0.253038 0.967456i \(-0.581430\pi\)
0.967456 + 0.253038i \(0.0814296\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) 6.18998 6.53331i 0.687775 0.725924i
\(82\) −4.98341 + 4.98341i −0.550326 + 0.550326i
\(83\) 16.7962i 1.84362i 0.387640 + 0.921811i \(0.373290\pi\)
−0.387640 + 0.921811i \(0.626710\pi\)
\(84\) 5.04993 1.03995i 0.550993 0.113468i
\(85\) 3.73527i 0.405147i
\(86\) 5.41814i 0.584253i
\(87\) 4.45385 + 2.93271i 0.477503 + 0.314420i
\(88\) 1.72431 + 1.72431i 0.183812 + 0.183812i
\(89\) −1.72334 + 1.72334i −0.182674 + 0.182674i −0.792520 0.609846i \(-0.791231\pi\)
0.609846 + 0.792520i \(0.291231\pi\)
\(90\) −2.75590 + 1.18533i −0.290497 + 0.124945i
\(91\) 10.0607 10.0607i 1.05465 1.05465i
\(92\) −4.56924 + 4.56924i −0.476376 + 0.476376i
\(93\) 1.61849 2.45796i 0.167829 0.254879i
\(94\) 4.64528 + 4.64528i 0.479124 + 0.479124i
\(95\) −7.33431 −0.752484
\(96\) 1.44660 + 0.952541i 0.147643 + 0.0972183i
\(97\) −4.30682 + 4.30682i −0.437291 + 0.437291i −0.891099 0.453808i \(-0.850065\pi\)
0.453808 + 0.891099i \(0.350065\pi\)
\(98\) −1.31599 + 1.31599i −0.132936 + 0.132936i
\(99\) −6.72037 + 2.89048i −0.675423 + 0.290504i
\(100\) 1.00000 0.100000
\(101\) −0.223998 −0.0222886 −0.0111443 0.999938i \(-0.503547\pi\)
−0.0111443 + 0.999938i \(0.503547\pi\)
\(102\) 1.30494 + 6.33672i 0.129208 + 0.627428i
\(103\) −0.790994 0.790994i −0.0779389 0.0779389i 0.667063 0.745002i \(-0.267551\pi\)
−0.745002 + 0.667063i \(0.767551\pi\)
\(104\) 4.77969 0.468688
\(105\) 2.83549 4.30620i 0.276715 0.420242i
\(106\) 0.00605812 + 0.00605812i 0.000588417 + 0.000588417i
\(107\) 13.3421i 1.28983i 0.764256 + 0.644914i \(0.223107\pi\)
−0.764256 + 0.644914i \(0.776893\pi\)
\(108\) −4.26115 + 2.97365i −0.410029 + 0.286140i
\(109\) −8.23612 + 8.23612i −0.788877 + 0.788877i −0.981310 0.192433i \(-0.938362\pi\)
0.192433 + 0.981310i \(0.438362\pi\)
\(110\) 2.43854 0.232506
\(111\) −3.61521 + 9.89597i −0.343140 + 0.939284i
\(112\) −2.97676 −0.281277
\(113\) −1.62412 + 1.62412i −0.152784 + 0.152784i −0.779360 0.626576i \(-0.784456\pi\)
0.626576 + 0.779360i \(0.284456\pi\)
\(114\) −12.4423 + 2.56228i −1.16533 + 0.239980i
\(115\) 6.46188i 0.602574i
\(116\) −2.17706 2.17706i −0.202135 0.202135i
\(117\) −5.30814 + 13.3204i −0.490738 + 1.23147i
\(118\) 5.05644 0.465483
\(119\) −7.86233 7.86233i −0.720739 0.720739i
\(120\) 1.69645 0.349356i 0.154864 0.0318917i
\(121\) −5.05352 −0.459411
\(122\) −11.7229 −1.06135
\(123\) 2.46212 + 11.9559i 0.222002 + 1.07803i
\(124\) −1.20146 + 1.20146i −0.107895 + 0.107895i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) 3.30587 8.29585i 0.294510 0.739053i
\(127\) −0.265733 −0.0235800 −0.0117900 0.999930i \(-0.503753\pi\)
−0.0117900 + 0.999930i \(0.503753\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −7.83791 5.16100i −0.690090 0.454401i
\(130\) 3.37975 3.37975i 0.296424 0.296424i
\(131\) 5.37214 5.37214i 0.469366 0.469366i −0.432343 0.901709i \(-0.642313\pi\)
0.901709 + 0.432343i \(0.142313\pi\)
\(132\) 4.13687 0.851919i 0.360068 0.0741500i
\(133\) 15.4379 15.4379i 1.33863 1.33863i
\(134\) −2.57961 2.57961i −0.222845 0.222845i
\(135\) −0.910402 + 5.11578i −0.0783549 + 0.440296i
\(136\) 3.73527i 0.320297i
\(137\) 7.45566i 0.636980i 0.947926 + 0.318490i \(0.103176\pi\)
−0.947926 + 0.318490i \(0.896824\pi\)
\(138\) 2.25750 + 10.9623i 0.192171 + 0.933171i
\(139\) 18.3826i 1.55920i −0.626281 0.779598i \(-0.715424\pi\)
0.626281 0.779598i \(-0.284576\pi\)
\(140\) −2.10489 + 2.10489i −0.177895 + 0.177895i
\(141\) 11.1447 2.29507i 0.938554 0.193280i
\(142\) −6.81035 6.81035i −0.571512 0.571512i
\(143\) 8.24167 8.24167i 0.689203 0.689203i
\(144\) 2.75590 1.18533i 0.229658 0.0987776i
\(145\) −3.07883 −0.255683
\(146\) 4.06669 + 4.06669i 0.336561 + 0.336561i
\(147\) 0.650186 + 3.15726i 0.0536264 + 0.260407i
\(148\) 3.19675 5.17502i 0.262771 0.425384i
\(149\) 10.3217i 0.845589i −0.906226 0.422795i \(-0.861049\pi\)
0.906226 0.422795i \(-0.138951\pi\)
\(150\) 0.952541 1.44660i 0.0777746 0.118115i
\(151\) 21.8379i 1.77714i 0.458741 + 0.888570i \(0.348301\pi\)
−0.458741 + 0.888570i \(0.651699\pi\)
\(152\) 7.33431 0.594891
\(153\) 10.4097 + 4.14825i 0.841577 + 0.335366i
\(154\) −5.13285 + 5.13285i −0.413617 + 0.413617i
\(155\) 1.69913i 0.136477i
\(156\) 4.55285 6.91433i 0.364520 0.553589i
\(157\) −6.37842 −0.509053 −0.254527 0.967066i \(-0.581920\pi\)
−0.254527 + 0.967066i \(0.581920\pi\)
\(158\) 8.98011i 0.714419i
\(159\) 0.0145343 0.00299310i 0.00115265 0.000237368i
\(160\) −1.00000 −0.0790569
\(161\) −13.6015 13.6015i −1.07195 1.07195i
\(162\) 0.242774 + 8.99672i 0.0190742 + 0.706849i
\(163\) −13.2027 13.2027i −1.03412 1.03412i −0.999397 0.0347202i \(-0.988946\pi\)
−0.0347202 0.999397i \(-0.511054\pi\)
\(164\) 7.04761i 0.550326i
\(165\) 2.32281 3.52760i 0.180830 0.274624i
\(166\) −11.8767 11.8767i −0.921811 0.921811i
\(167\) 11.4214 + 11.4214i 0.883817 + 0.883817i 0.993920 0.110103i \(-0.0351182\pi\)
−0.110103 + 0.993920i \(0.535118\pi\)
\(168\) −2.83549 + 4.30620i −0.218762 + 0.332230i
\(169\) 9.84548i 0.757345i
\(170\) −2.64124 2.64124i −0.202574 0.202574i
\(171\) −8.14519 + 20.4398i −0.622878 + 1.56307i
\(172\) 3.83120 + 3.83120i 0.292127 + 0.292127i
\(173\) 18.3766 1.39715 0.698573 0.715539i \(-0.253819\pi\)
0.698573 + 0.715539i \(0.253819\pi\)
\(174\) −5.22309 + 1.07561i −0.395961 + 0.0815417i
\(175\) 2.97676i 0.225022i
\(176\) −2.43854 −0.183812
\(177\) 4.81646 7.31466i 0.362027 0.549804i
\(178\) 2.43717i 0.182674i
\(179\) 14.5304 14.5304i 1.08606 1.08606i 0.0901264 0.995930i \(-0.471273\pi\)
0.995930 0.0901264i \(-0.0287271\pi\)
\(180\) 1.11056 2.78687i 0.0827763 0.207721i
\(181\) −2.29142 −0.170320 −0.0851599 0.996367i \(-0.527140\pi\)
−0.0851599 + 0.996367i \(0.527140\pi\)
\(182\) 14.2280i 1.05465i
\(183\) −11.1666 + 16.9585i −0.825458 + 1.25361i
\(184\) 6.46188i 0.476376i
\(185\) −1.39885 5.91973i −0.102845 0.435227i
\(186\) 0.593600 + 2.88249i 0.0435248 + 0.211354i
\(187\) −6.44076 6.44076i −0.470995 0.470995i
\(188\) −6.56942 −0.479124
\(189\) −8.85184 12.6844i −0.643876 0.922656i
\(190\) 5.18614 5.18614i 0.376242 0.376242i
\(191\) 5.55986 + 5.55986i 0.402297 + 0.402297i 0.879042 0.476745i \(-0.158183\pi\)
−0.476745 + 0.879042i \(0.658183\pi\)
\(192\) −1.69645 + 0.349356i −0.122431 + 0.0252126i
\(193\) −6.93955 + 6.93955i −0.499519 + 0.499519i −0.911288 0.411769i \(-0.864911\pi\)
0.411769 + 0.911288i \(0.364911\pi\)
\(194\) 6.09076i 0.437291i
\(195\) −1.66982 8.10852i −0.119578 0.580663i
\(196\) 1.86110i 0.132936i
\(197\) 1.08968i 0.0776363i −0.999246 0.0388182i \(-0.987641\pi\)
0.999246 0.0388182i \(-0.0123593\pi\)
\(198\) 2.70815 6.79590i 0.192459 0.482964i
\(199\) −6.21327 6.21327i −0.440447 0.440447i 0.451715 0.892162i \(-0.350812\pi\)
−0.892162 + 0.451715i \(0.850812\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) −6.18887 + 1.27449i −0.436529 + 0.0898959i
\(202\) 0.158390 0.158390i 0.0111443 0.0111443i
\(203\) 6.48059 6.48059i 0.454848 0.454848i
\(204\) −5.40347 3.55800i −0.378318 0.249110i
\(205\) −4.98341 4.98341i −0.348057 0.348057i
\(206\) 1.11863 0.0779389
\(207\) 18.0084 + 7.17631i 1.25167 + 0.498788i
\(208\) −3.37975 + 3.37975i −0.234344 + 0.234344i
\(209\) 12.6466 12.6466i 0.874784 0.874784i
\(210\) 1.03995 + 5.04993i 0.0717633 + 0.348478i
\(211\) 19.8475 1.36636 0.683180 0.730250i \(-0.260597\pi\)
0.683180 + 0.730250i \(0.260597\pi\)
\(212\) −0.00856748 −0.000588417
\(213\) −16.3390 + 3.36475i −1.11953 + 0.230549i
\(214\) −9.43427 9.43427i −0.644914 0.644914i
\(215\) 5.41814 0.369514
\(216\) 0.910402 5.11578i 0.0619450 0.348084i
\(217\) −3.57647 3.57647i −0.242786 0.242786i
\(218\) 11.6476i 0.788877i
\(219\) 9.75658 2.00920i 0.659288 0.135769i
\(220\) −1.72431 + 1.72431i −0.116253 + 0.116253i
\(221\) −17.8535 −1.20095
\(222\) −4.44117 9.55385i −0.298072 0.641212i
\(223\) −18.7033 −1.25246 −0.626232 0.779637i \(-0.715404\pi\)
−0.626232 + 0.779637i \(0.715404\pi\)
\(224\) 2.10489 2.10489i 0.140639 0.140639i
\(225\) −1.18533 2.75590i −0.0790221 0.183727i
\(226\) 2.29685i 0.152784i
\(227\) −14.6213 14.6213i −0.970449 0.970449i 0.0291269 0.999576i \(-0.490727\pi\)
−0.999576 + 0.0291269i \(0.990727\pi\)
\(228\) 6.98623 10.6098i 0.462674 0.702654i
\(229\) −6.40334 −0.423145 −0.211572 0.977362i \(-0.567858\pi\)
−0.211572 + 0.977362i \(0.567858\pi\)
\(230\) −4.56924 4.56924i −0.301287 0.301287i
\(231\) 2.53596 + 12.3145i 0.166854 + 0.810232i
\(232\) 3.07883 0.202135
\(233\) 9.92789 0.650398 0.325199 0.945646i \(-0.394569\pi\)
0.325199 + 0.945646i \(0.394569\pi\)
\(234\) −5.66552 13.1724i −0.370367 0.861104i
\(235\) −4.64528 + 4.64528i −0.303025 + 0.303025i
\(236\) −3.57544 + 3.57544i −0.232741 + 0.232741i
\(237\) 12.9907 + 8.55392i 0.843834 + 0.555637i
\(238\) 11.1190 0.720739
\(239\) 18.3998 + 18.3998i 1.19018 + 1.19018i 0.977016 + 0.213168i \(0.0683782\pi\)
0.213168 + 0.977016i \(0.431622\pi\)
\(240\) −0.952541 + 1.44660i −0.0614863 + 0.0933779i
\(241\) 18.2602 18.2602i 1.17624 1.17624i 0.195550 0.980694i \(-0.437351\pi\)
0.980694 0.195550i \(-0.0626492\pi\)
\(242\) 3.57338 3.57338i 0.229706 0.229706i
\(243\) 13.2460 + 8.21855i 0.849729 + 0.527220i
\(244\) 8.28937 8.28937i 0.530673 0.530673i
\(245\) −1.31599 1.31599i −0.0840758 0.0840758i
\(246\) −10.1951 6.71314i −0.650016 0.428014i
\(247\) 35.0557i 2.23054i
\(248\) 1.69913i 0.107895i
\(249\) −28.4939 + 5.86785i −1.80573 + 0.371860i
\(250\) 1.00000i 0.0632456i
\(251\) −17.3355 + 17.3355i −1.09420 + 1.09420i −0.0991297 + 0.995075i \(0.531606\pi\)
−0.995075 + 0.0991297i \(0.968394\pi\)
\(252\) 3.52845 + 8.20365i 0.222271 + 0.516782i
\(253\) −11.1423 11.1423i −0.700509 0.700509i
\(254\) 0.187902 0.187902i 0.0117900 0.0117900i
\(255\) −6.33672 + 1.30494i −0.396821 + 0.0817186i
\(256\) 1.00000 0.0625000
\(257\) −21.4622 21.4622i −1.33877 1.33877i −0.897248 0.441526i \(-0.854437\pi\)
−0.441526 0.897248i \(-0.645563\pi\)
\(258\) 9.19162 1.89286i 0.572245 0.117844i
\(259\) 15.4048 + 9.51595i 0.957206 + 0.591293i
\(260\) 4.77969i 0.296424i
\(261\) −3.41923 + 8.58031i −0.211645 + 0.531108i
\(262\) 7.59736i 0.469366i
\(263\) −7.76918 −0.479068 −0.239534 0.970888i \(-0.576995\pi\)
−0.239534 + 0.970888i \(0.576995\pi\)
\(264\) −2.32281 + 3.52760i −0.142959 + 0.217109i
\(265\) −0.00605812 + 0.00605812i −0.000372147 + 0.000372147i
\(266\) 21.8325i 1.33863i
\(267\) −3.52562 2.32150i −0.215764 0.142074i
\(268\) 3.64813 0.222845
\(269\) 25.5891i 1.56019i −0.625659 0.780097i \(-0.715170\pi\)
0.625659 0.780097i \(-0.284830\pi\)
\(270\) −2.97365 4.26115i −0.180971 0.259325i
\(271\) −7.34693 −0.446294 −0.223147 0.974785i \(-0.571633\pi\)
−0.223147 + 0.974785i \(0.571633\pi\)
\(272\) 2.64124 + 2.64124i 0.160149 + 0.160149i
\(273\) 20.5823 + 13.5528i 1.24570 + 0.820250i
\(274\) −5.27195 5.27195i −0.318490 0.318490i
\(275\) 2.43854i 0.147049i
\(276\) −9.34779 6.15521i −0.562671 0.370500i
\(277\) 3.64147 + 3.64147i 0.218795 + 0.218795i 0.807990 0.589196i \(-0.200555\pi\)
−0.589196 + 0.807990i \(0.700555\pi\)
\(278\) 12.9985 + 12.9985i 0.779598 + 0.779598i
\(279\) 4.73525 + 1.88698i 0.283492 + 0.112971i
\(280\) 2.97676i 0.177895i
\(281\) 16.5786 + 16.5786i 0.988999 + 0.988999i 0.999940 0.0109410i \(-0.00348270\pi\)
−0.0109410 + 0.999940i \(0.503483\pi\)
\(282\) −6.25765 + 9.50336i −0.372637 + 0.565917i
\(283\) −4.84935 4.84935i −0.288264 0.288264i 0.548130 0.836393i \(-0.315340\pi\)
−0.836393 + 0.548130i \(0.815340\pi\)
\(284\) 9.63129 0.571512
\(285\) −2.56228 12.4423i −0.151777 0.737018i
\(286\) 11.6555i 0.689203i
\(287\) 20.9790 1.23835
\(288\) −1.11056 + 2.78687i −0.0654404 + 0.164218i
\(289\) 3.04772i 0.179278i
\(290\) 2.17706 2.17706i 0.127842 0.127842i
\(291\) −8.81093 5.80170i −0.516506 0.340102i
\(292\) −5.75117 −0.336561
\(293\) 16.8721i 0.985681i 0.870120 + 0.492840i \(0.164041\pi\)
−0.870120 + 0.492840i \(0.835959\pi\)
\(294\) −2.69227 1.77277i −0.157017 0.103390i
\(295\) 5.05644i 0.294397i
\(296\) 1.39885 + 5.91973i 0.0813063 + 0.344077i
\(297\) −7.25136 10.3910i −0.420767 0.602946i
\(298\) 7.29857 + 7.29857i 0.422795 + 0.422795i
\(299\) −30.8858 −1.78617
\(300\) 0.349356 + 1.69645i 0.0201701 + 0.0979447i
\(301\) −11.4046 + 11.4046i −0.657349 + 0.657349i
\(302\) −15.4417 15.4417i −0.888570 0.888570i
\(303\) −0.0782550 0.380001i −0.00449563 0.0218305i
\(304\) −5.18614 + 5.18614i −0.297445 + 0.297445i
\(305\) 11.7229i 0.671254i
\(306\) −10.2940 + 4.42754i −0.588471 + 0.253106i
\(307\) 2.59584i 0.148153i 0.997253 + 0.0740763i \(0.0236008\pi\)
−0.997253 + 0.0740763i \(0.976399\pi\)
\(308\) 7.25895i 0.413617i
\(309\) 1.06554 1.61822i 0.0606167 0.0920574i
\(310\) −1.20146 1.20146i −0.0682385 0.0682385i
\(311\) −2.69292 + 2.69292i −0.152702 + 0.152702i −0.779323 0.626622i \(-0.784437\pi\)
0.626622 + 0.779323i \(0.284437\pi\)
\(312\) 1.66982 + 8.10852i 0.0945347 + 0.459055i
\(313\) −7.66085 + 7.66085i −0.433017 + 0.433017i −0.889653 0.456636i \(-0.849054\pi\)
0.456636 + 0.889653i \(0.349054\pi\)
\(314\) 4.51022 4.51022i 0.254527 0.254527i
\(315\) 8.29585 + 3.30587i 0.467418 + 0.186265i
\(316\) −6.34989 6.34989i −0.357209 0.357209i
\(317\) −12.5140 −0.702854 −0.351427 0.936215i \(-0.614303\pi\)
−0.351427 + 0.936215i \(0.614303\pi\)
\(318\) −0.00816087 + 0.0123938i −0.000457639 + 0.000695007i
\(319\) 5.30885 5.30885i 0.297239 0.297239i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) −22.6342 + 4.66113i −1.26332 + 0.260159i
\(322\) 19.2355 1.07195
\(323\) −27.3957 −1.52433
\(324\) −6.53331 6.18998i −0.362962 0.343888i
\(325\) 3.37975 + 3.37975i 0.187475 + 0.187475i
\(326\) 18.6715 1.03412
\(327\) −16.8495 11.0948i −0.931780 0.613546i
\(328\) 4.98341 + 4.98341i 0.275163 + 0.275163i
\(329\) 19.5556i 1.07813i
\(330\) 0.851919 + 4.13687i 0.0468966 + 0.227727i
\(331\) −5.65251 + 5.65251i −0.310690 + 0.310690i −0.845177 0.534487i \(-0.820505\pi\)
0.534487 + 0.845177i \(0.320505\pi\)
\(332\) 16.7962 0.921811
\(333\) −18.0510 2.67581i −0.989191 0.146634i
\(334\) −16.1523 −0.883817
\(335\) 2.57961 2.57961i 0.140939 0.140939i
\(336\) −1.03995 5.04993i −0.0567339 0.275496i
\(337\) 6.95275i 0.378740i −0.981906 0.189370i \(-0.939355\pi\)
0.981906 0.189370i \(-0.0606446\pi\)
\(338\) 6.96181 + 6.96181i 0.378672 + 0.378672i
\(339\) −3.32263 2.18784i −0.180461 0.118827i
\(340\) 3.73527 0.202574
\(341\) −2.92982 2.92982i −0.158658 0.158658i
\(342\) −8.69359 20.2126i −0.470095 1.09297i
\(343\) −15.2973 −0.825975
\(344\) −5.41814 −0.292127
\(345\) −10.9623 + 2.25750i −0.590189 + 0.121540i
\(346\) −12.9942 + 12.9942i −0.698573 + 0.698573i
\(347\) −24.0122 + 24.0122i −1.28904 + 1.28904i −0.353671 + 0.935370i \(0.615067\pi\)
−0.935370 + 0.353671i \(0.884933\pi\)
\(348\) 2.93271 4.45385i 0.157210 0.238752i
\(349\) 18.2431 0.976531 0.488266 0.872695i \(-0.337630\pi\)
0.488266 + 0.872695i \(0.337630\pi\)
\(350\) −2.10489 2.10489i −0.112511 0.112511i
\(351\) −24.4519 4.35144i −1.30514 0.232263i
\(352\) 1.72431 1.72431i 0.0919059 0.0919059i
\(353\) 22.0357 22.0357i 1.17284 1.17284i 0.191310 0.981530i \(-0.438727\pi\)
0.981530 0.191310i \(-0.0612735\pi\)
\(354\) 1.76650 + 8.57800i 0.0938882 + 0.455916i
\(355\) 6.81035 6.81035i 0.361456 0.361456i
\(356\) 1.72334 + 1.72334i 0.0913368 + 0.0913368i
\(357\) 10.5913 16.0848i 0.560552 0.851299i
\(358\) 20.5492i 1.08606i
\(359\) 2.38803i 0.126035i 0.998012 + 0.0630177i \(0.0200725\pi\)
−0.998012 + 0.0630177i \(0.979928\pi\)
\(360\) 1.18533 + 2.75590i 0.0624725 + 0.145249i
\(361\) 34.7921i 1.83116i
\(362\) 1.62028 1.62028i 0.0851599 0.0851599i
\(363\) −1.76548 8.57306i −0.0926636 0.449969i
\(364\) −10.0607 10.0607i −0.527325 0.527325i
\(365\) −4.06669 + 4.06669i −0.212860 + 0.212860i
\(366\) −4.09548 19.8874i −0.214074 1.03953i
\(367\) −21.6442 −1.12982 −0.564909 0.825153i \(-0.691089\pi\)
−0.564909 + 0.825153i \(0.691089\pi\)
\(368\) 4.56924 + 4.56924i 0.238188 + 0.238188i
\(369\) −19.4225 + 8.35375i −1.01110 + 0.434879i
\(370\) 5.17502 + 3.19675i 0.269036 + 0.166191i
\(371\) 0.0255033i 0.00132407i
\(372\) −2.45796 1.61849i −0.127439 0.0839146i
\(373\) 6.01294i 0.311338i 0.987809 + 0.155669i \(0.0497533\pi\)
−0.987809 + 0.155669i \(0.950247\pi\)
\(374\) 9.10862 0.470995
\(375\) 1.44660 + 0.952541i 0.0747024 + 0.0491890i
\(376\) 4.64528 4.64528i 0.239562 0.239562i
\(377\) 14.7159i 0.757906i
\(378\) 15.2284 + 2.71005i 0.783266 + 0.139390i
\(379\) −38.0594 −1.95498 −0.977491 0.210977i \(-0.932336\pi\)
−0.977491 + 0.210977i \(0.932336\pi\)
\(380\) 7.33431i 0.376242i
\(381\) −0.0928354 0.450803i −0.00475610 0.0230953i
\(382\) −7.86283 −0.402297
\(383\) 11.9705 + 11.9705i 0.611662 + 0.611662i 0.943379 0.331717i \(-0.107628\pi\)
−0.331717 + 0.943379i \(0.607628\pi\)
\(384\) 0.952541 1.44660i 0.0486091 0.0738217i
\(385\) −5.13285 5.13285i −0.261594 0.261594i
\(386\) 9.81400i 0.499519i
\(387\) 6.01717 15.0997i 0.305870 0.767559i
\(388\) 4.30682 + 4.30682i 0.218646 + 0.218646i
\(389\) −19.1226 19.1226i −0.969555 0.969555i 0.0299951 0.999550i \(-0.490451\pi\)
−0.999550 + 0.0299951i \(0.990451\pi\)
\(390\) 6.91433 + 4.55285i 0.350121 + 0.230543i
\(391\) 24.1369i 1.22066i
\(392\) 1.31599 + 1.31599i 0.0664678 + 0.0664678i
\(393\) 10.9904 + 7.23680i 0.554391 + 0.365048i
\(394\) 0.770518 + 0.770518i 0.0388182 + 0.0388182i
\(395\) −8.98011 −0.451838
\(396\) 2.89048 + 6.72037i 0.145252 + 0.337711i
\(397\) 22.1145i 1.10990i 0.831885 + 0.554948i \(0.187262\pi\)
−0.831885 + 0.554948i \(0.812738\pi\)
\(398\) 8.78688 0.440447
\(399\) 31.5830 + 20.7963i 1.58113 + 1.04112i
\(400\) 1.00000i 0.0500000i
\(401\) 14.1223 14.1223i 0.705233 0.705233i −0.260296 0.965529i \(-0.583820\pi\)
0.965529 + 0.260296i \(0.0838202\pi\)
\(402\) 3.47499 5.27740i 0.173317 0.263213i
\(403\) −8.12130 −0.404551
\(404\) 0.223998i 0.0111443i
\(405\) −8.99672 + 0.242774i −0.447051 + 0.0120636i
\(406\) 9.16494i 0.454848i
\(407\) 12.6195 + 7.79540i 0.625525 + 0.386404i
\(408\) 6.33672 1.30494i 0.313714 0.0646042i
\(409\) 5.85980 + 5.85980i 0.289749 + 0.289749i 0.836981 0.547232i \(-0.184319\pi\)
−0.547232 + 0.836981i \(0.684319\pi\)
\(410\) 7.04761 0.348057
\(411\) −12.6482 + 2.60468i −0.623889 + 0.128479i
\(412\) −0.790994 + 0.790994i −0.0389695 + 0.0389695i
\(413\) −10.6432 10.6432i −0.523719 0.523719i
\(414\) −17.8083 + 7.65947i −0.875230 + 0.376443i
\(415\) 11.8767 11.8767i 0.583004 0.583004i
\(416\) 4.77969i 0.234344i
\(417\) 31.1853 6.42209i 1.52715 0.314491i
\(418\) 17.8850i 0.874784i
\(419\) 2.86911i 0.140165i 0.997541 + 0.0700825i \(0.0223262\pi\)
−0.997541 + 0.0700825i \(0.977674\pi\)
\(420\) −4.30620 2.83549i −0.210121 0.138358i
\(421\) 16.1956 + 16.1956i 0.789327 + 0.789327i 0.981384 0.192057i \(-0.0615157\pi\)
−0.192057 + 0.981384i \(0.561516\pi\)
\(422\) −14.0343 + 14.0343i −0.683180 + 0.683180i
\(423\) 7.78695 + 18.1047i 0.378614 + 0.880280i
\(424\) 0.00605812 0.00605812i 0.000294208 0.000294208i
\(425\) 2.64124 2.64124i 0.128119 0.128119i
\(426\) 9.17419 13.9327i 0.444491 0.675040i
\(427\) 24.6755 + 24.6755i 1.19413 + 1.19413i
\(428\) 13.3421 0.644914
\(429\) 16.8609 + 11.1023i 0.814050 + 0.536025i
\(430\) −3.83120 + 3.83120i −0.184757 + 0.184757i
\(431\) 9.00474 9.00474i 0.433743 0.433743i −0.456157 0.889900i \(-0.650774\pi\)
0.889900 + 0.456157i \(0.150774\pi\)
\(432\) 2.97365 + 4.26115i 0.143070 + 0.205015i
\(433\) 22.2256 1.06809 0.534046 0.845455i \(-0.320671\pi\)
0.534046 + 0.845455i \(0.320671\pi\)
\(434\) 5.05789 0.242786
\(435\) −1.07561 5.22309i −0.0515715 0.250428i
\(436\) 8.23612 + 8.23612i 0.394438 + 0.394438i
\(437\) −47.3934 −2.26714
\(438\) −5.47822 + 8.31966i −0.261759 + 0.397529i
\(439\) 25.2304 + 25.2304i 1.20418 + 1.20418i 0.972883 + 0.231298i \(0.0742971\pi\)
0.231298 + 0.972883i \(0.425703\pi\)
\(440\) 2.43854i 0.116253i
\(441\) −5.12900 + 2.20602i −0.244238 + 0.105048i
\(442\) 12.6243 12.6243i 0.600477 0.600477i
\(443\) 26.9345 1.27969 0.639847 0.768502i \(-0.278998\pi\)
0.639847 + 0.768502i \(0.278998\pi\)
\(444\) 9.89597 + 3.61521i 0.469642 + 0.171570i
\(445\) 2.43717 0.115533
\(446\) 13.2252 13.2252i 0.626232 0.626232i
\(447\) 17.5103 3.60596i 0.828210 0.170556i
\(448\) 2.97676i 0.140639i
\(449\) 7.92152 + 7.92152i 0.373840 + 0.373840i 0.868874 0.495034i \(-0.164844\pi\)
−0.495034 + 0.868874i \(0.664844\pi\)
\(450\) 2.78687 + 1.11056i 0.131374 + 0.0523523i
\(451\) 17.1859 0.809251
\(452\) 1.62412 + 1.62412i 0.0763921 + 0.0763921i
\(453\) −37.0469 + 7.62919i −1.74062 + 0.358451i
\(454\) 20.6776 0.970449
\(455\) −14.2280 −0.667019
\(456\) 2.56228 + 12.4423i 0.119990 + 0.582664i
\(457\) −20.7696 + 20.7696i −0.971561 + 0.971561i −0.999607 0.0280458i \(-0.991072\pi\)
0.0280458 + 0.999607i \(0.491072\pi\)
\(458\) 4.52784 4.52784i 0.211572 0.211572i
\(459\) −3.40060 + 19.1088i −0.158726 + 0.891924i
\(460\) 6.46188 0.301287
\(461\) −6.14385 6.14385i −0.286148 0.286148i 0.549407 0.835555i \(-0.314854\pi\)
−0.835555 + 0.549407i \(0.814854\pi\)
\(462\) −10.5008 6.91444i −0.488543 0.321689i
\(463\) −22.3895 + 22.3895i −1.04053 + 1.04053i −0.0413850 + 0.999143i \(0.513177\pi\)
−0.999143 + 0.0413850i \(0.986823\pi\)
\(464\) −2.17706 + 2.17706i −0.101068 + 0.101068i
\(465\) −2.88249 + 0.593600i −0.133672 + 0.0275275i
\(466\) −7.02008 + 7.02008i −0.325199 + 0.325199i
\(467\) 0.258047 + 0.258047i 0.0119410 + 0.0119410i 0.713052 0.701111i \(-0.247312\pi\)
−0.701111 + 0.713052i \(0.747312\pi\)
\(468\) 13.3204 + 5.30814i 0.615736 + 0.245369i
\(469\) 10.8596i 0.501449i
\(470\) 6.56942i 0.303025i
\(471\) −2.22834 10.8207i −0.102676 0.498591i
\(472\) 5.05644i 0.232741i
\(473\) −9.34255 + 9.34255i −0.429571 + 0.429571i
\(474\) −15.2343 + 3.13725i −0.699735 + 0.144099i
\(475\) 5.18614 + 5.18614i 0.237956 + 0.237956i
\(476\) −7.86233 + 7.86233i −0.360369 + 0.360369i
\(477\) 0.0101553 + 0.0236111i 0.000464979 + 0.00108108i
\(478\) −26.0212 −1.19018
\(479\) 27.1667 + 27.1667i 1.24128 + 1.24128i 0.959472 + 0.281804i \(0.0909329\pi\)
0.281804 + 0.959472i \(0.409067\pi\)
\(480\) −0.349356 1.69645i −0.0159458 0.0774321i
\(481\) 28.2945 6.68606i 1.29012 0.304858i
\(482\) 25.8238i 1.17624i
\(483\) 18.3226 27.8261i 0.833706 1.26613i
\(484\) 5.05352i 0.229706i
\(485\) 6.09076 0.276567
\(486\) −15.1777 + 3.55492i −0.688474 + 0.161254i
\(487\) 23.3376 23.3376i 1.05753 1.05753i 0.0592882 0.998241i \(-0.481117\pi\)
0.998241 0.0592882i \(-0.0188831\pi\)
\(488\) 11.7229i 0.530673i
\(489\) 17.7853 27.0102i 0.804281 1.22145i
\(490\) 1.86110 0.0840758
\(491\) 0.227143i 0.0102508i 0.999987 + 0.00512541i \(0.00163148\pi\)
−0.999987 + 0.00512541i \(0.998369\pi\)
\(492\) 11.9559 2.46212i 0.539015 0.111001i
\(493\) −11.5003 −0.517947
\(494\) 24.7882 + 24.7882i 1.11527 + 1.11527i
\(495\) 6.79590 + 2.70815i 0.305453 + 0.121722i
\(496\) 1.20146 + 1.20146i 0.0539473 + 0.0539473i
\(497\) 28.6700i 1.28603i
\(498\) 15.9991 24.2975i 0.716935 1.08880i
\(499\) −10.1088 10.1088i −0.452530 0.452530i 0.443663 0.896194i \(-0.353679\pi\)
−0.896194 + 0.443663i \(0.853679\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) −15.3858 + 23.3661i −0.687385 + 1.04392i
\(502\) 24.5160i 1.09420i
\(503\) 9.08858 + 9.08858i 0.405240 + 0.405240i 0.880075 0.474835i \(-0.157492\pi\)
−0.474835 + 0.880075i \(0.657492\pi\)
\(504\) −8.29585 3.30587i −0.369526 0.147255i
\(505\) 0.158390 + 0.158390i 0.00704828 + 0.00704828i
\(506\) 15.7576 0.700509
\(507\) 16.7024 3.43958i 0.741779 0.152757i
\(508\) 0.265733i 0.0117900i
\(509\) −13.3598 −0.592163 −0.296082 0.955163i \(-0.595680\pi\)
−0.296082 + 0.955163i \(0.595680\pi\)
\(510\) 3.55800 5.40347i 0.157551 0.239270i
\(511\) 17.1198i 0.757337i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −37.5207 6.67716i −1.65658 0.294804i
\(514\) 30.3521 1.33877
\(515\) 1.11863i 0.0492929i
\(516\) −5.16100 + 7.83791i −0.227200 + 0.345045i
\(517\) 16.0198i 0.704550i
\(518\) −17.6216 + 4.16403i −0.774250 + 0.182957i
\(519\) 6.41997 + 31.1750i 0.281805 + 1.36843i
\(520\) −3.37975 3.37975i −0.148212 0.148212i
\(521\) 18.0686 0.791601 0.395801 0.918337i \(-0.370467\pi\)
0.395801 + 0.918337i \(0.370467\pi\)
\(522\) −3.64944 8.48495i −0.159731 0.371376i
\(523\) 19.5508 19.5508i 0.854895 0.854895i −0.135836 0.990731i \(-0.543372\pi\)
0.990731 + 0.135836i \(0.0433721\pi\)
\(524\) −5.37214 5.37214i −0.234683 0.234683i
\(525\) −5.04993 + 1.03995i −0.220397 + 0.0453871i
\(526\) 5.49364 5.49364i 0.239534 0.239534i
\(527\) 6.34670i 0.276467i
\(528\) −0.851919 4.13687i −0.0370750 0.180034i
\(529\) 18.7559i 0.815475i
\(530\) 0.00856748i 0.000372147i
\(531\) 14.0916 + 5.61548i 0.611525 + 0.243691i
\(532\) −15.4379 15.4379i −0.669317 0.669317i
\(533\) 23.8192 23.8192i 1.03172 1.03172i
\(534\) 4.13454 0.851439i 0.178919 0.0368454i
\(535\) 9.43427 9.43427i 0.407879 0.407879i
\(536\) −2.57961 + 2.57961i −0.111422 + 0.111422i
\(537\) 29.7265 + 19.5739i 1.28279 + 0.844677i
\(538\) 18.0942 + 18.0942i 0.780097 + 0.780097i
\(539\) 4.53836 0.195481
\(540\) 5.11578 + 0.910402i 0.220148 + 0.0391774i
\(541\) 11.4750 11.4750i 0.493349 0.493349i −0.416011 0.909360i \(-0.636572\pi\)
0.909360 + 0.416011i \(0.136572\pi\)
\(542\) 5.19506 5.19506i 0.223147 0.223147i
\(543\) −0.800521 3.88728i −0.0343536 0.166819i
\(544\) −3.73527 −0.160149
\(545\) 11.6476 0.498930
\(546\) −24.1371 + 4.97064i −1.03297 + 0.212724i
\(547\) 16.5717 + 16.5717i 0.708555 + 0.708555i 0.966231 0.257676i \(-0.0829567\pi\)
−0.257676 + 0.966231i \(0.582957\pi\)
\(548\) 7.45566 0.318490
\(549\) −32.6703 13.0190i −1.39434 0.555639i
\(550\) −1.72431 1.72431i −0.0735247 0.0735247i
\(551\) 22.5811i 0.961987i
\(552\) 10.9623 2.25750i 0.466585 0.0960855i
\(553\) 18.9021 18.9021i 0.803799 0.803799i
\(554\) −5.14981 −0.218795
\(555\) 9.55385 4.44117i 0.405538 0.188517i
\(556\) −18.3826 −0.779598
\(557\) −15.3019 + 15.3019i −0.648361 + 0.648361i −0.952597 0.304236i \(-0.901599\pi\)
0.304236 + 0.952597i \(0.401599\pi\)
\(558\) −4.68262 + 2.01403i −0.198231 + 0.0852606i
\(559\) 25.8971i 1.09533i
\(560\) 2.10489 + 2.10489i 0.0889477 + 0.0889477i
\(561\) 8.67633 13.1766i 0.366315 0.556315i
\(562\) −23.4457 −0.988999
\(563\) −19.7443 19.7443i −0.832124 0.832124i 0.155683 0.987807i \(-0.450242\pi\)
−0.987807 + 0.155683i \(0.950242\pi\)
\(564\) −2.29507 11.1447i −0.0966398 0.469277i
\(565\) 2.29685 0.0966292
\(566\) 6.85802 0.288264
\(567\) 18.4261 19.4481i 0.773822 0.816743i
\(568\) −6.81035 + 6.81035i −0.285756 + 0.285756i
\(569\) 9.21438 9.21438i 0.386287 0.386287i −0.487074 0.873361i \(-0.661936\pi\)
0.873361 + 0.487074i \(0.161936\pi\)
\(570\) 10.6098 + 6.98623i 0.444397 + 0.292621i
\(571\) −20.1810 −0.844548 −0.422274 0.906468i \(-0.638768\pi\)
−0.422274 + 0.906468i \(0.638768\pi\)
\(572\) −8.24167 8.24167i −0.344601 0.344601i
\(573\) −7.48967 + 11.3744i −0.312885 + 0.475173i
\(574\) −14.8344 + 14.8344i −0.619177 + 0.619177i
\(575\) 4.56924 4.56924i 0.190551 0.190551i
\(576\) −1.18533 2.75590i −0.0493888 0.114829i
\(577\) −10.8935 + 10.8935i −0.453502 + 0.453502i −0.896515 0.443013i \(-0.853909\pi\)
0.443013 + 0.896515i \(0.353909\pi\)
\(578\) 2.15506 + 2.15506i 0.0896389 + 0.0896389i
\(579\) −14.1970 9.34824i −0.590006 0.388499i
\(580\) 3.07883i 0.127842i
\(581\) 49.9982i 2.07428i
\(582\) 10.3327 2.12784i 0.428304 0.0882020i
\(583\) 0.0208921i 0.000865264i
\(584\) 4.06669 4.06669i 0.168281 0.168281i
\(585\) 13.1724 5.66552i 0.544610 0.234241i
\(586\) −11.9304 11.9304i −0.492840 0.492840i
\(587\) −3.91169 + 3.91169i −0.161453 + 0.161453i −0.783210 0.621757i \(-0.786419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(588\) 3.15726 0.650186i 0.130203 0.0268132i
\(589\) −12.4619 −0.513484
\(590\) −3.57544 3.57544i −0.147199 0.147199i
\(591\) 1.84859 0.380685i 0.0760407 0.0156593i
\(592\) −5.17502 3.19675i −0.212692 0.131386i
\(593\) 21.6725i 0.889983i −0.895535 0.444991i \(-0.853207\pi\)
0.895535 0.444991i \(-0.146793\pi\)
\(594\) 12.4750 + 2.22005i 0.511856 + 0.0910898i
\(595\) 11.1190i 0.455835i
\(596\) −10.3217 −0.422795
\(597\) 8.36987 12.7112i 0.342556 0.520233i
\(598\) 21.8396 21.8396i 0.893087 0.893087i
\(599\) 14.8293i 0.605907i −0.953005 0.302954i \(-0.902027\pi\)
0.953005 0.302954i \(-0.0979727\pi\)
\(600\) −1.44660 0.952541i −0.0590574 0.0388873i
\(601\) −19.8353 −0.809097 −0.404549 0.914517i \(-0.632571\pi\)
−0.404549 + 0.914517i \(0.632571\pi\)
\(602\) 16.1285i 0.657349i
\(603\) −4.32424 10.0539i −0.176097 0.409425i
\(604\) 21.8379 0.888570
\(605\) 3.57338 + 3.57338i 0.145279 + 0.145279i
\(606\) 0.324036 + 0.213367i 0.0131631 + 0.00866744i
\(607\) 12.9523 + 12.9523i 0.525718 + 0.525718i 0.919293 0.393575i \(-0.128762\pi\)
−0.393575 + 0.919293i \(0.628762\pi\)
\(608\) 7.33431i 0.297445i
\(609\) 13.2580 + 8.72998i 0.537243 + 0.353757i
\(610\) 8.28937 + 8.28937i 0.335627 + 0.335627i
\(611\) −22.2030 22.2030i −0.898239 0.898239i
\(612\) 4.14825 10.4097i 0.167683 0.420789i
\(613\) 1.24321i 0.0502128i 0.999685 + 0.0251064i \(0.00799245\pi\)
−0.999685 + 0.0251064i \(0.992008\pi\)
\(614\) −1.83554 1.83554i −0.0740763 0.0740763i
\(615\) 6.71314 10.1951i 0.270700 0.411106i
\(616\) 5.13285 + 5.13285i 0.206808 + 0.206808i
\(617\) 4.87072 0.196088 0.0980438 0.995182i \(-0.468741\pi\)
0.0980438 + 0.995182i \(0.468741\pi\)
\(618\) 0.390801 + 1.89771i 0.0157203 + 0.0763371i
\(619\) 29.3840i 1.18104i 0.807023 + 0.590521i \(0.201078\pi\)
−0.807023 + 0.590521i \(0.798922\pi\)
\(620\) 1.69913 0.0682385
\(621\) −5.88291 + 33.0575i −0.236073 + 1.32655i
\(622\) 3.80837i 0.152702i
\(623\) −5.12996 + 5.12996i −0.205528 + 0.205528i
\(624\) −6.91433 4.55285i −0.276795 0.182260i
\(625\) −1.00000 −0.0400000
\(626\) 10.8341i 0.433017i
\(627\) 25.8725 + 17.0362i 1.03325 + 0.680360i
\(628\) 6.37842i 0.254527i
\(629\) −5.22507 22.1118i −0.208337 0.881656i
\(630\) −8.20365 + 3.52845i −0.326841 + 0.140577i
\(631\) 23.3422 + 23.3422i 0.929237 + 0.929237i 0.997657 0.0684200i \(-0.0217958\pi\)
−0.0684200 + 0.997657i \(0.521796\pi\)
\(632\) 8.98011 0.357209
\(633\) 6.93385 + 33.6704i 0.275596 + 1.33828i
\(634\) 8.84871 8.84871i 0.351427 0.351427i
\(635\) 0.187902 + 0.187902i 0.00745664 + 0.00745664i
\(636\) −0.00299310 0.0145343i −0.000118684 0.000576323i
\(637\) 6.29005 6.29005i 0.249221 0.249221i
\(638\) 7.50785i 0.297239i
\(639\) −11.4163 26.5429i −0.451621 1.05002i
\(640\) 1.00000i 0.0395285i
\(641\) 47.2866i 1.86771i 0.357653 + 0.933854i \(0.383577\pi\)
−0.357653 + 0.933854i \(0.616423\pi\)
\(642\) 12.7089 19.3007i 0.501579 0.761738i
\(643\) 7.59274 + 7.59274i 0.299428 + 0.299428i 0.840790 0.541362i \(-0.182091\pi\)
−0.541362 + 0.840790i \(0.682091\pi\)
\(644\) −13.6015 + 13.6015i −0.535975 + 0.535975i
\(645\) 1.89286 + 9.19162i 0.0745313 + 0.361920i
\(646\) 19.3717 19.3717i 0.762167 0.762167i
\(647\) −15.2305 + 15.2305i −0.598773 + 0.598773i −0.939986 0.341213i \(-0.889162\pi\)
0.341213 + 0.939986i \(0.389162\pi\)
\(648\) 8.99672 0.242774i 0.353425 0.00953708i
\(649\) −8.71885 8.71885i −0.342245 0.342245i
\(650\) −4.77969 −0.187475
\(651\) 4.81785 7.31677i 0.188826 0.286767i
\(652\) −13.2027 + 13.2027i −0.517059 + 0.517059i
\(653\) −23.9793 + 23.9793i −0.938382 + 0.938382i −0.998209 0.0598267i \(-0.980945\pi\)
0.0598267 + 0.998209i \(0.480945\pi\)
\(654\) 19.7596 4.06917i 0.772663 0.159117i
\(655\) −7.59736 −0.296853
\(656\) −7.04761 −0.275163
\(657\) 6.81704 + 15.8496i 0.265958 + 0.618353i
\(658\) 13.8279 + 13.8279i 0.539067 + 0.539067i
\(659\) −40.4873 −1.57716 −0.788581 0.614931i \(-0.789184\pi\)
−0.788581 + 0.614931i \(0.789184\pi\)
\(660\) −3.52760 2.32281i −0.137312 0.0904152i
\(661\) −0.591033 0.591033i −0.0229885 0.0229885i 0.695519 0.718508i \(-0.255174\pi\)
−0.718508 + 0.695519i \(0.755174\pi\)
\(662\) 7.99386i 0.310690i
\(663\) −6.23722 30.2876i −0.242233 1.17627i
\(664\) −11.8767 + 11.8767i −0.460905 + 0.460905i
\(665\) −21.8325 −0.846627
\(666\) 14.6561 10.8719i 0.567912 0.421279i
\(667\) −19.8950 −0.770339
\(668\) 11.4214 11.4214i 0.441908 0.441908i
\(669\) −6.53410 31.7292i −0.252623 1.22672i
\(670\) 3.64813i 0.140939i
\(671\) 20.2140 + 20.2140i 0.780351 + 0.780351i
\(672\) 4.30620 + 2.83549i 0.166115 + 0.109381i
\(673\) −27.2271 −1.04953 −0.524765 0.851247i \(-0.675847\pi\)
−0.524765 + 0.851247i \(0.675847\pi\)
\(674\) 4.91634 + 4.91634i 0.189370 + 0.189370i
\(675\) 4.26115 2.97365i 0.164012 0.114456i
\(676\) −9.84548 −0.378672
\(677\) −7.44693 −0.286209 −0.143104 0.989708i \(-0.545708\pi\)
−0.143104 + 0.989708i \(0.545708\pi\)
\(678\) 3.89650 0.802418i 0.149644 0.0308167i
\(679\) −12.8204 + 12.8204i −0.492001 + 0.492001i
\(680\) −2.64124 + 2.64124i −0.101287 + 0.101287i
\(681\) 19.6963 29.9123i 0.754763 1.14624i
\(682\) 4.14339 0.158658
\(683\) 16.2355 + 16.2355i 0.621235 + 0.621235i 0.945847 0.324612i \(-0.105234\pi\)
−0.324612 + 0.945847i \(0.605234\pi\)
\(684\) 20.4398 + 8.14519i 0.781534 + 0.311439i
\(685\) 5.27195 5.27195i 0.201431 0.201431i
\(686\) 10.8168 10.8168i 0.412988 0.412988i
\(687\) −2.23704 10.8630i −0.0853486 0.414448i
\(688\) 3.83120 3.83120i 0.146063 0.146063i
\(689\) −0.0289560 0.0289560i −0.00110313 0.00110313i
\(690\) 6.15521 9.34779i 0.234325 0.355864i
\(691\) 6.50183i 0.247341i −0.992323 0.123671i \(-0.960533\pi\)
0.992323 0.123671i \(-0.0394666\pi\)
\(692\) 18.3766i 0.698573i
\(693\) −20.0049 + 8.60426i −0.759925 + 0.326849i
\(694\) 33.9583i 1.28904i
\(695\) −12.9985 + 12.9985i −0.493061 + 0.493061i
\(696\) 1.07561 + 5.22309i 0.0407708 + 0.197981i
\(697\) −18.6144 18.6144i −0.705071 0.705071i
\(698\) −12.8998 + 12.8998i −0.488266 + 0.488266i
\(699\) 3.46837 + 16.8422i 0.131186 + 0.637030i
\(700\) 2.97676 0.112511
\(701\) −34.0802 34.0802i −1.28719 1.28719i −0.936486 0.350705i \(-0.885942\pi\)
−0.350705 0.936486i \(-0.614058\pi\)
\(702\) 20.3670 14.2131i 0.768703 0.536440i
\(703\) 43.4171 10.2596i 1.63751 0.386947i
\(704\) 2.43854i 0.0919059i
\(705\) −9.50336 6.25765i −0.357917 0.235677i
\(706\) 31.1631i 1.17284i
\(707\) −0.666787 −0.0250771
\(708\) −7.31466 4.81646i −0.274902 0.181014i
\(709\) 1.56111 1.56111i 0.0586286 0.0586286i −0.677185 0.735813i \(-0.736800\pi\)
0.735813 + 0.677185i \(0.236800\pi\)
\(710\) 9.63129i 0.361456i
\(711\) −9.97295 + 25.0264i −0.374015 + 0.938564i
\(712\) −2.43717 −0.0913368
\(713\) 10.9795i 0.411187i
\(714\) 3.88449 + 18.8629i 0.145374 + 0.705925i
\(715\) −11.6555 −0.435890
\(716\) −14.5304 14.5304i −0.543028 0.543028i
\(717\) −24.7863 + 37.6424i −0.925661 + 1.40578i
\(718\) −1.68859 1.68859i −0.0630177 0.0630177i
\(719\) 12.6157i 0.470487i 0.971936 + 0.235243i \(0.0755887\pi\)
−0.971936 + 0.235243i \(0.924411\pi\)
\(720\) −2.78687 1.11056i −0.103861 0.0413881i
\(721\) −2.35460 2.35460i −0.0876898 0.0876898i
\(722\) 24.6017 + 24.6017i 0.915580 + 0.915580i
\(723\) 37.3569 + 24.5983i 1.38932 + 0.914819i
\(724\) 2.29142i 0.0851599i
\(725\) 2.17706 + 2.17706i 0.0808541 + 0.0808541i
\(726\) 7.31045 + 4.81369i 0.271316 + 0.178653i
\(727\) −29.4763 29.4763i −1.09322 1.09322i −0.995183 0.0980326i \(-0.968745\pi\)
−0.0980326 0.995183i \(-0.531255\pi\)
\(728\) 14.2280 0.527325
\(729\) −9.31482 + 25.3423i −0.344993 + 0.938605i
\(730\) 5.75117i 0.212860i
\(731\) 20.2382 0.748539
\(732\) 16.9585 + 11.1666i 0.626803 + 0.412729i
\(733\) 33.6287i 1.24210i 0.783769 + 0.621052i \(0.213294\pi\)
−0.783769 + 0.621052i \(0.786706\pi\)
\(734\) 15.3048 15.3048i 0.564909 0.564909i
\(735\) 1.77277 2.69227i 0.0653897 0.0993060i
\(736\) −6.46188 −0.238188
\(737\) 8.89610i 0.327692i
\(738\) 7.82679 19.6408i 0.288108 0.722987i
\(739\) 7.04612i 0.259196i −0.991567 0.129598i \(-0.958631\pi\)
0.991567 0.129598i \(-0.0413687\pi\)
\(740\) −5.91973 + 1.39885i −0.217614 + 0.0514226i
\(741\) 59.4704 12.2469i 2.18470 0.449902i
\(742\) 0.0180336 + 0.0180336i 0.000662033 + 0.000662033i
\(743\) −12.5185 −0.459260 −0.229630 0.973278i \(-0.573752\pi\)
−0.229630 + 0.973278i \(0.573752\pi\)
\(744\) 2.88249 0.593600i 0.105677 0.0217624i
\(745\) −7.29857 + 7.29857i −0.267399 + 0.267399i
\(746\) −4.25179 4.25179i −0.155669 0.155669i
\(747\) −19.9091 46.2886i −0.728434 1.69361i
\(748\) −6.44076 + 6.44076i −0.235498 + 0.235498i
\(749\) 39.7162i 1.45120i
\(750\) −1.69645 + 0.349356i −0.0619457 + 0.0127567i
\(751\) 13.2399i 0.483131i 0.970385 + 0.241566i \(0.0776609\pi\)
−0.970385 + 0.241566i \(0.922339\pi\)
\(752\) 6.56942i 0.239562i
\(753\) −35.4650 23.3525i −1.29242 0.851013i
\(754\) 10.4057 + 10.4057i 0.378953 + 0.378953i
\(755\) 15.4417 15.4417i 0.561981 0.561981i
\(756\) −12.6844 + 8.85184i −0.461328 + 0.321938i
\(757\) 30.6772 30.6772i 1.11498 1.11498i 0.122516 0.992466i \(-0.460904\pi\)
0.992466 0.122516i \(-0.0390964\pi\)
\(758\) 26.9121 26.9121i 0.977491 0.977491i
\(759\) 15.0097 22.7950i 0.544818 0.827405i
\(760\) −5.18614 5.18614i −0.188121 0.188121i
\(761\) 22.0349 0.798766 0.399383 0.916784i \(-0.369224\pi\)
0.399383 + 0.916784i \(0.369224\pi\)
\(762\) 0.384411 + 0.253121i 0.0139257 + 0.00916962i
\(763\) −24.5169 + 24.5169i −0.887573 + 0.887573i
\(764\) 5.55986 5.55986i 0.201149 0.201149i
\(765\) −4.42754 10.2940i −0.160078 0.372182i
\(766\) −16.9288 −0.611662
\(767\) −24.1682 −0.872664
\(768\) 0.349356 + 1.69645i 0.0126063 + 0.0612154i
\(769\) 21.8399 + 21.8399i 0.787567 + 0.787567i 0.981095 0.193528i \(-0.0619929\pi\)
−0.193528 + 0.981095i \(0.561993\pi\)
\(770\) 7.25895 0.261594
\(771\) 28.9116 43.9075i 1.04123 1.58129i
\(772\) 6.93955 + 6.93955i 0.249760 + 0.249760i
\(773\) 11.9686i 0.430481i −0.976561 0.215240i \(-0.930947\pi\)
0.976561 0.215240i \(-0.0690535\pi\)
\(774\) 6.42229 + 14.9319i 0.230845 + 0.536715i
\(775\) 1.20146 1.20146i 0.0431578 0.0431578i
\(776\) −6.09076 −0.218646
\(777\) −10.7616 + 29.4579i −0.386071 + 1.05680i
\(778\) 27.0435 0.969555
\(779\) 36.5499 <