Properties

Label 1110.2.u.e.401.18
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 401.18
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.18

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.952541 + 1.44660i) q^{6} +2.97676 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.75590 - 1.18533i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.952541 + 1.44660i) 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} +(-1.44660 + 0.952541i) q^{15} -1.00000 q^{16} +(2.64124 + 2.64124i) q^{17} +(-2.78687 + 1.11056i) 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} +(1.44660 - 0.952541i) 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} +(4.55285 + 6.91433i) q^{39} -1.00000i q^{40} -7.04761 q^{41} +(2.83549 + 4.30620i) q^{42} +(-3.83120 + 3.83120i) q^{43} +2.43854i q^{44} +(-1.11056 - 2.78687i) 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} +(-5.40347 + 3.55800i) q^{51} +(-3.37975 - 3.37975i) q^{52} +0.00856748i q^{53} +(-0.910402 - 5.11578i) q^{54} +(-1.72431 - 1.72431i) q^{55} +(-2.10489 - 2.10489i) q^{56} +(6.98623 + 10.6098i) q^{57} +3.07883i q^{58} +(3.57544 + 3.57544i) q^{59} +(0.952541 + 1.44660i) 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} +(-2.32281 - 3.52760i) q^{66} +3.64813i q^{67} +(2.64124 - 2.64124i) q^{68} +(-9.34779 + 6.15521i) q^{69} +2.97676 q^{70} -9.63129i q^{71} +(1.11056 + 2.78687i) 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} +(-2.93271 - 4.45385i) 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} +(2.45796 - 1.61849i) q^{93} +(4.64528 + 4.64528i) q^{94} +7.33431 q^{95} +(-0.952541 - 1.44660i) 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
\(6\) 0.952541 + 1.44660i 0.388873 + 0.590574i
\(7\) 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 \(-0.619829\pi\)
−0.367624 + 0.929975i \(0.619829\pi\)
\(12\) 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
\(15\) −1.44660 + 0.952541i −0.373512 + 0.245945i
\(16\) −1.00000 −0.250000
\(17\) 2.64124 + 2.64124i 0.640594 + 0.640594i 0.950702 0.310107i \(-0.100365\pi\)
−0.310107 + 0.950702i \(0.600365\pi\)
\(18\) −2.78687 + 1.11056i −0.656872 + 0.261762i
\(19\) 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 0.998933 0.0461806i \(-0.0147050\pi\)
−0.0461806 + 0.998933i \(0.514705\pi\)
\(24\) 1.44660 0.952541i 0.295287 0.194437i
\(25\) 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 −0.879735 0.475465i \(-0.842280\pi\)
0.475465 + 0.879735i \(0.342280\pi\)
\(30\) −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
\(39\) 4.55285 + 6.91433i 0.729040 + 1.10718i
\(40\) 1.00000i 0.158114i
\(41\) −7.04761 −1.10065 −0.550326 0.834950i \(-0.685496\pi\)
−0.550326 + 0.834950i \(0.685496\pi\)
\(42\) 2.83549 + 4.30620i 0.437525 + 0.664460i
\(43\) −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
\(45\) −1.11056 2.78687i −0.165553 0.415442i
\(46\) 6.46188 0.952753
\(47\) 6.56942i 0.958249i 0.877747 + 0.479124i \(0.159046\pi\)
−0.877747 + 0.479124i \(0.840954\pi\)
\(48\) 0.349356 1.69645i 0.0504252 0.244862i
\(49\) 1.86110 0.265871
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) −5.40347 + 3.55800i −0.756637 + 0.498220i
\(52\) −3.37975 3.37975i −0.468688 0.468688i
\(53\) 0.00856748i 0.00117683i 1.00000 0.000588417i \(0.000187299\pi\)
−1.00000 0.000588417i \(0.999813\pi\)
\(54\) −0.910402 5.11578i −0.123890 0.696169i
\(55\) −1.72431 1.72431i −0.232506 0.232506i
\(56\) −2.10489 2.10489i −0.281277 0.281277i
\(57\) 6.98623 + 10.6098i 0.925348 + 1.40531i
\(58\) 3.07883i 0.404270i
\(59\) 3.57544 + 3.57544i 0.465483 + 0.465483i 0.900447 0.434965i \(-0.143239\pi\)
−0.434965 + 0.900447i \(0.643239\pi\)
\(60\) 0.952541 + 1.44660i 0.122973 + 0.186756i
\(61\) 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
\(66\) −2.32281 3.52760i −0.285918 0.434218i
\(67\) 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
\(69\) −9.34779 + 6.15521i −1.12534 + 0.741000i
\(70\) 2.97676 0.355791
\(71\) 9.63129i 1.14302i −0.820594 0.571512i \(-0.806357\pi\)
0.820594 0.571512i \(-0.193643\pi\)
\(72\) 1.11056 + 2.78687i 0.130881 + 0.328436i
\(73\) 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 \(-0.626710\pi\)
0.387640 0.921811i \(-0.373290\pi\)
\(84\) 5.04993 + 1.03995i 0.550993 + 0.113468i
\(85\) 3.73527i 0.405147i
\(86\) 5.41814i 0.584253i
\(87\) −2.93271 4.45385i −0.314420 0.477503i
\(88\) 1.72431 + 1.72431i 0.183812 + 0.183812i
\(89\) 1.72334 1.72334i 0.182674 0.182674i −0.609846 0.792520i \(-0.708769\pi\)
0.792520 + 0.609846i \(0.208769\pi\)
\(90\) −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
\(93\) 2.45796 1.61849i 0.254879 0.167829i
\(94\) 4.64528 + 4.64528i 0.479124 + 0.479124i
\(95\) 7.33431 0.752484
\(96\) −0.952541 1.44660i −0.0972183 0.147643i
\(97\) −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 \(-0.496453\pi\)
0.0111443 + 0.999938i \(0.496453\pi\)
\(102\) −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
\(105\) −4.30620 + 2.83549i −0.420242 + 0.276715i
\(106\) 0.00605812 + 0.00605812i 0.000588417 + 0.000588417i
\(107\) 13.3421i 1.28983i −0.764256 0.644914i \(-0.776893\pi\)
0.764256 0.644914i \(-0.223107\pi\)
\(108\) −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
\(111\) −7.23106 + 7.66236i −0.686341 + 0.727279i
\(112\) −2.97676 −0.281277
\(113\) 1.62412 1.62412i 0.152784 0.152784i −0.626576 0.779360i \(-0.715544\pi\)
0.779360 + 0.626576i \(0.215544\pi\)
\(114\) 12.4423 + 2.56228i 1.16533 + 0.239980i
\(115\) 6.46188i 0.602574i
\(116\) 2.17706 + 2.17706i 0.202135 + 0.202135i
\(117\) −13.3204 + 5.30814i −1.23147 + 0.490738i
\(118\) 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
\(126\) −8.29585 + 3.30587i −0.739053 + 0.294510i
\(127\) −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
\(129\) −5.16100 7.83791i −0.454401 0.690090i
\(130\) 3.37975 3.37975i 0.296424 0.296424i
\(131\) −5.37214 + 5.37214i −0.469366 + 0.469366i −0.901709 0.432343i \(-0.857687\pi\)
0.432343 + 0.901709i \(0.357687\pi\)
\(132\) −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
\(135\) 5.11578 0.910402i 0.440296 0.0783549i
\(136\) 3.73527i 0.320297i
\(137\) 7.45566i 0.636980i −0.947926 0.318490i \(-0.896824\pi\)
0.947926 0.318490i \(-0.103176\pi\)
\(138\) −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 \(0.138951\pi\)
−0.906226 + 0.422795i \(0.861049\pi\)
\(150\) −1.44660 + 0.952541i −0.118115 + 0.0777746i
\(151\) 21.8379i 1.77714i 0.458741 + 0.888570i \(0.348301\pi\)
−0.458741 + 0.888570i \(0.651699\pi\)
\(152\) −7.33431 −0.594891
\(153\) −4.14825 10.4097i −0.335366 0.841577i
\(154\) −5.13285 + 5.13285i −0.413617 + 0.413617i
\(155\) 1.69913i 0.136477i
\(156\) 6.91433 4.55285i 0.553589 0.364520i
\(157\) −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
\(162\) 8.99672 + 0.242774i 0.706849 + 0.0190742i
\(163\) −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
\(165\) 3.52760 2.32281i 0.274624 0.180830i
\(166\) −11.8767 11.8767i −0.921811 0.921811i
\(167\) −11.4214 11.4214i −0.883817 0.883817i 0.110103 0.993920i \(-0.464882\pi\)
−0.993920 + 0.110103i \(0.964882\pi\)
\(168\) 4.30620 2.83549i 0.332230 0.218762i
\(169\) 9.84548i 0.757345i
\(170\) 2.64124 + 2.64124i 0.202574 + 0.202574i
\(171\) −20.4398 + 8.14519i −1.56307 + 0.622878i
\(172\) 3.83120 + 3.83120i 0.292127 + 0.292127i
\(173\) −18.3766 −1.39715 −0.698573 0.715539i \(-0.746181\pi\)
−0.698573 + 0.715539i \(0.746181\pi\)
\(174\) −5.22309 1.07561i −0.395961 0.0815417i
\(175\) 2.97676i 0.225022i
\(176\) 2.43854 0.183812
\(177\) −7.31466 + 4.81646i −0.549804 + 0.362027i
\(178\) 2.43717i 0.182674i
\(179\) −14.5304 + 14.5304i −1.08606 + 1.08606i −0.0901264 + 0.995930i \(0.528727\pi\)
−0.995930 + 0.0901264i \(0.971273\pi\)
\(180\) −2.78687 + 1.11056i −0.207721 + 0.0827763i
\(181\) −2.29142 −0.170320 −0.0851599 0.996367i \(-0.527140\pi\)
−0.0851599 + 0.996367i \(0.527140\pi\)
\(182\) 14.2280i 1.05465i
\(183\) −16.9585 + 11.1666i −1.25361 + 0.825458i
\(184\) 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 0.476745 0.879042i \(-0.341817\pi\)
−0.879042 + 0.476745i \(0.841817\pi\)
\(192\) −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 \(0.0123593\pi\)
−0.999246 + 0.0388182i \(0.987641\pi\)
\(198\) 6.79590 2.70815i 0.482964 0.192459i
\(199\) −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
\(204\) 3.55800 + 5.40347i 0.249110 + 0.378318i
\(205\) −4.98341 4.98341i −0.348057 0.348057i
\(206\) −1.11863 −0.0779389
\(207\) −7.17631 18.0084i −0.498788 1.25167i
\(208\) −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
\(216\) −5.11578 + 0.910402i −0.348084 + 0.0619450i
\(217\) −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
\(222\) 0.304982 + 10.5312i 0.0204690 + 0.706810i
\(223\) −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 0.999576 0.0291269i \(-0.00927268\pi\)
−0.0291269 + 0.999576i \(0.509273\pi\)
\(228\) 10.6098 6.98623i 0.702654 0.462674i
\(229\) −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 \(-0.605431\pi\)
−0.325199 + 0.945646i \(0.605431\pi\)
\(234\) −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
\(237\) 8.55392 + 12.9907i 0.555637 + 0.843834i
\(238\) 11.1190 0.720739
\(239\) −18.3998 18.3998i −1.19018 1.19018i −0.977016 0.213168i \(-0.931622\pi\)
−0.213168 0.977016i \(-0.568378\pi\)
\(240\) 1.44660 0.952541i 0.0933779 0.0614863i
\(241\) 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
\(246\) −6.71314 10.1951i −0.428014 0.650016i
\(247\) 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 \(-0.468394\pi\)
0.995075 0.0991297i \(-0.0316059\pi\)
\(252\) −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 \(0.145563\pi\)
0.441526 + 0.897248i \(0.354437\pi\)
\(258\) −9.19162 1.89286i −0.572245 0.117844i
\(259\) 15.4048 + 9.51595i 0.957206 + 0.591293i
\(260\) 4.77969i 0.296424i
\(261\) 8.58031 3.41923i 0.531108 0.211645i
\(262\) 7.59736i 0.469366i
\(263\) 7.76918 0.479068 0.239534 0.970888i \(-0.423005\pi\)
0.239534 + 0.970888i \(0.423005\pi\)
\(264\) −3.52760 + 2.32281i −0.217109 + 0.142959i
\(265\) −0.00605812 + 0.00605812i −0.000372147 + 0.000372147i
\(266\) 21.8325i 1.33863i
\(267\) 2.32150 + 3.52562i 0.142074 + 0.215764i
\(268\) 3.64813 0.222845
\(269\) 25.5891i 1.56019i 0.625659 + 0.780097i \(0.284830\pi\)
−0.625659 + 0.780097i \(0.715170\pi\)
\(270\) 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
\(273\) 13.5528 + 20.5823i 0.820250 + 1.24570i
\(274\) −5.27195 5.27195i −0.318490 0.318490i
\(275\) 2.43854i 0.147049i
\(276\) 6.15521 + 9.34779i 0.370500 + 0.562671i
\(277\) 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
\(279\) 1.88698 + 4.73525i 0.112971 + 0.283492i
\(280\) 2.97676i 0.177895i
\(281\) −16.5786 16.5786i −0.988999 0.988999i 0.0109410 0.999940i \(-0.496517\pi\)
−0.999940 + 0.0109410i \(0.996517\pi\)
\(282\) −9.50336 + 6.25765i −0.565917 + 0.372637i
\(283\) −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
\(288\) 2.78687 1.11056i 0.164218 0.0654404i
\(289\) 3.04772i 0.179278i
\(290\) −2.17706 + 2.17706i −0.127842 + 0.127842i
\(291\) −5.80170 8.81093i −0.340102 0.516506i
\(292\) −5.75117 −0.336561
\(293\) 16.8721i 0.985681i −0.870120 0.492840i \(-0.835959\pi\)
0.870120 0.492840i \(-0.164041\pi\)
\(294\) 1.77277 + 2.69227i 0.103390 + 0.157017i
\(295\) 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
\(309\) 1.61822 1.06554i 0.0920574 0.0606167i
\(310\) −1.20146 1.20146i −0.0682385 0.0682385i
\(311\) 2.69292 2.69292i 0.152702 0.152702i −0.626622 0.779323i \(-0.715563\pi\)
0.779323 + 0.626622i \(0.215563\pi\)
\(312\) 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
\(315\) −3.30587 8.29585i −0.186265 0.467418i
\(316\) −6.34989 6.34989i −0.357209 0.357209i
\(317\) 12.5140 0.702854 0.351427 0.936215i \(-0.385697\pi\)
0.351427 + 0.936215i \(0.385697\pi\)
\(318\) −0.0123938 + 0.00816087i −0.000695007 + 0.000457639i
\(319\) 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
\(327\) −11.0948 16.8495i −0.613546 0.931780i
\(328\) 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
\(333\) −10.4726 14.9440i −0.573896 0.818928i
\(334\) −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
\(339\) 2.18784 + 3.32263i 0.118827 + 0.180461i
\(340\) 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 \(-0.384933\pi\)
0.935370 0.353671i \(-0.115067\pi\)
\(348\) −4.45385 + 2.93271i −0.238752 + 0.157210i
\(349\) 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
\(351\) −4.35144 24.4519i −0.232263 1.30514i
\(352\) 1.72431 1.72431i 0.0919059 0.0919059i
\(353\) −22.0357 + 22.0357i −1.17284 + 1.17284i −0.191310 + 0.981530i \(0.561273\pi\)
−0.981530 + 0.191310i \(0.938727\pi\)
\(354\) −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
\(357\) −16.0848 + 10.5913i −0.851299 + 0.560552i
\(358\) 20.5492i 1.08606i
\(359\) 2.38803i 0.126035i −0.998012 0.0630177i \(-0.979928\pi\)
0.998012 0.0630177i \(-0.0200725\pi\)
\(360\) −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
\(372\) −1.61849 2.45796i −0.0839146 0.127439i
\(373\) 6.01294i 0.311338i 0.987809 + 0.155669i \(0.0497533\pi\)
−0.987809 + 0.155669i \(0.950247\pi\)
\(374\) −9.10862 −0.470995
\(375\) −0.952541 1.44660i −0.0491890 0.0747024i
\(376\) 4.64528 4.64528i 0.239562 0.239562i
\(377\) 14.7159i 0.757906i
\(378\) −2.71005 15.2284i −0.139390 0.783266i
\(379\) −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 0.331717 0.943379i \(-0.392372\pi\)
−0.943379 + 0.331717i \(0.892372\pi\)
\(384\) −1.44660 + 0.952541i −0.0738217 + 0.0486091i
\(385\) −5.13285 5.13285i −0.261594 0.261594i
\(386\) 9.81400i 0.499519i
\(387\) 15.0997 6.01717i 0.767559 0.305870i
\(388\) 4.30682 + 4.30682i 0.218646 + 0.218646i
\(389\) 19.1226 + 19.1226i 0.969555 + 0.969555i 0.999550 0.0299951i \(-0.00954917\pi\)
−0.0299951 + 0.999550i \(0.509549\pi\)
\(390\) 4.55285 + 6.91433i 0.230543 + 0.350121i
\(391\) 24.1369i 1.22066i
\(392\) −1.31599 1.31599i −0.0664678 0.0664678i
\(393\) −7.23680 10.9904i −0.365048 0.554391i
\(394\) 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
\(399\) 20.7963 + 31.5830i 1.04112 + 1.58113i
\(400\) 1.00000i 0.0500000i
\(401\) −14.1223 + 14.1223i −0.705233 + 0.705233i −0.965529 0.260296i \(-0.916180\pi\)
0.260296 + 0.965529i \(0.416180\pi\)
\(402\) −5.27740 + 3.47499i −0.263213 + 0.173317i
\(403\) −8.12130 −0.404551
\(404\) 0.223998i 0.0111443i
\(405\) −0.242774 + 8.99672i −0.0120636 + 0.447051i
\(406\) 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 \(-0.977674\pi\)
0.997541 0.0700825i \(-0.0223262\pi\)
\(420\) 2.83549 + 4.30620i 0.138358 + 0.210121i
\(421\) 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
\(426\) 13.9327 9.17419i 0.675040 0.444491i
\(427\) 24.6755 + 24.6755i 1.19413 + 1.19413i
\(428\) −13.3421 −0.644914
\(429\) −11.1023 16.8609i −0.536025 0.814050i
\(430\) −3.83120 + 3.83120i −0.184757 + 0.184757i
\(431\) −9.00474 + 9.00474i −0.433743 + 0.433743i −0.889900 0.456157i \(-0.849226\pi\)
0.456157 + 0.889900i \(0.349226\pi\)
\(432\) −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
\(438\) 8.31966 5.47822i 0.397529 0.261759i
\(439\) 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 \(-0.721002\pi\)
−0.639847 + 0.768502i \(0.721002\pi\)
\(444\) 7.66236 + 7.23106i 0.363640 + 0.343171i
\(445\) 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 0.495034 0.868874i \(-0.335156\pi\)
−0.868874 + 0.495034i \(0.835156\pi\)
\(450\) −1.11056 2.78687i −0.0523523 0.131374i
\(451\) 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
\(459\) 19.1088 3.40060i 0.891924 0.158726i
\(460\) 6.46188 0.301287
\(461\) 6.14385 + 6.14385i 0.286148 + 0.286148i 0.835555 0.549407i \(-0.185146\pi\)
−0.549407 + 0.835555i \(0.685146\pi\)
\(462\) −6.91444 10.5008i −0.321689 0.488543i
\(463\) −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 0.701111 0.713052i \(-0.252688\pi\)
−0.713052 + 0.701111i \(0.752688\pi\)
\(468\) 5.30814 + 13.3204i 0.245369 + 0.615736i
\(469\) 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 \(-0.909067\pi\)
−0.281804 0.959472i \(-0.590933\pi\)
\(480\) 0.349356 1.69645i 0.0159458 0.0774321i
\(481\) 28.2945 6.68606i 1.29012 0.304858i
\(482\) 25.8238i 1.17624i
\(483\) −27.8261 + 18.3226i −1.26613 + 0.833706i
\(484\) 5.05352i 0.229706i
\(485\) −6.09076 −0.276567
\(486\) −3.55492 + 15.1777i −0.161254 + 0.688474i
\(487\) 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
\(489\) 27.0102 17.7853i 1.22145 0.804281i
\(490\) 1.86110 0.0840758
\(491\) 0.227143i 0.0102508i −0.999987 0.00512541i \(-0.998369\pi\)
0.999987 0.00512541i \(-0.00163148\pi\)
\(492\) −11.9559 2.46212i −0.539015 0.111001i
\(493\) −11.5003 −0.517947
\(494\) −24.7882 24.7882i −1.11527 1.11527i
\(495\) 2.70815 + 6.79590i 0.121722 + 0.305453i
\(496\) 1.20146 + 1.20146i 0.0539473 + 0.0539473i
\(497\) 28.6700i 1.28603i
\(498\) 24.2975 15.9991i 1.08880 0.716935i
\(499\) −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
\(501\) 23.3661 15.3858i 1.04392 0.687385i
\(502\) 24.5160i 1.09420i
\(503\) −9.08858 9.08858i −0.405240 0.405240i 0.474835 0.880075i \(-0.342508\pi\)
−0.880075 + 0.474835i \(0.842508\pi\)
\(504\) 3.30587 + 8.29585i 0.147255 + 0.369526i
\(505\) 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 \(-0.404320\pi\)
0.296082 + 0.955163i \(0.404320\pi\)
\(510\) −5.40347 + 3.55800i −0.239270 + 0.157551i
\(511\) 17.1198i 0.757337i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −6.67716 37.5207i −0.294804 1.65658i
\(514\) 30.3521 1.33877
\(515\) 1.11863i 0.0492929i
\(516\) −7.83791 + 5.16100i −0.345045 + 0.227200i
\(517\) 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 \(-0.629533\pi\)
−0.395801 + 0.918337i \(0.629533\pi\)
\(522\) 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
\(531\) −5.61548 14.0916i −0.243691 0.611525i
\(532\) −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
\(537\) −19.5739 29.7265i −0.844677 1.28279i
\(538\) 18.0942 + 18.0942i 0.780097 + 0.780097i
\(539\) −4.53836 −0.195481
\(540\) −0.910402 5.11578i −0.0391774 0.220148i
\(541\) 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
\(549\) −13.0190 32.6703i −0.555639 1.39434i
\(550\) −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
\(555\) −10.5312 + 0.304982i −0.447026 + 0.0129458i
\(556\) −18.3826 −0.779598
\(557\) 15.3019 15.3019i 0.648361 0.648361i −0.304236 0.952597i \(-0.598401\pi\)
0.952597 + 0.304236i \(0.0984011\pi\)
\(558\) 4.68262 + 2.01403i 0.198231 + 0.0852606i
\(559\) 25.8971i 1.09533i
\(560\) −2.10489 2.10489i −0.0889477 0.0889477i
\(561\) 13.1766 8.67633i 0.556315 0.366315i
\(562\) −23.4457 −0.988999
\(563\) 19.7443 + 19.7443i 0.832124 + 0.832124i 0.987807 0.155683i \(-0.0497579\pi\)
−0.155683 + 0.987807i \(0.549758\pi\)
\(564\) −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 −0.873361 0.487074i \(-0.838064\pi\)
0.487074 + 0.873361i \(0.338064\pi\)
\(570\) 6.98623 + 10.6098i 0.292621 + 0.444397i
\(571\) −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
\(573\) 11.3744 7.48967i 0.475173 0.312885i
\(574\) −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
\(579\) −9.34824 14.1970i −0.388499 0.590006i
\(580\) 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 −0.621757 0.783210i \(-0.713581\pi\)
0.783210 + 0.621757i \(0.213581\pi\)
\(588\) 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 \(0.146793\pi\)
−0.895535 + 0.444991i \(0.853207\pi\)
\(594\) 2.22005 + 12.4750i 0.0910898 + 0.511856i
\(595\) 11.1190i 0.455835i
\(596\) 10.3217 0.422795
\(597\) 12.7112 8.36987i 0.520233 0.342556i
\(598\) 21.8396 21.8396i 0.893087 0.893087i
\(599\) 14.8293i 0.605907i 0.953005 + 0.302954i \(0.0979727\pi\)
−0.953005 + 0.302954i \(0.902027\pi\)
\(600\) 0.952541 + 1.44660i 0.0388873 + 0.0590574i
\(601\) −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
\(606\) 0.213367 + 0.324036i 0.00866744 + 0.0131631i
\(607\) 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
\(609\) −8.72998 13.2580i −0.353757 0.537243i
\(610\) 8.28937 + 8.28937i 0.335627 + 0.335627i
\(611\) 22.2030 + 22.2030i 0.898239 + 0.898239i
\(612\) −10.4097 + 4.14825i −0.420789 + 0.167683i
\(613\) 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
\(615\) 10.1951 6.71314i 0.411106 0.270700i
\(616\) 5.13285 + 5.13285i 0.206808 + 0.206808i
\(617\) −4.87072 −0.196088 −0.0980438 0.995182i \(-0.531259\pi\)
−0.0980438 + 0.995182i \(0.531259\pi\)
\(618\) 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
\(621\) 33.0575 5.88291i 1.32655 0.236073i
\(622\) 3.80837i 0.152702i
\(623\) 5.12996 5.12996i 0.205528 0.205528i
\(624\) −4.55285 6.91433i −0.182260 0.276795i
\(625\) −1.00000 −0.0400000
\(626\) 10.8341i 0.433017i
\(627\) −17.0362 25.8725i −0.680360 1.03325i
\(628\) 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 \(-0.616423\pi\)
0.357653 0.933854i \(-0.383577\pi\)
\(642\) 19.3007 12.7089i 0.761738 0.501579i
\(643\) 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 −0.341213 0.939986i \(-0.610838\pi\)
0.939986 + 0.341213i \(0.110838\pi\)
\(648\) 0.242774 8.99672i 0.00953708 0.353425i
\(649\) −8.71885 8.71885i −0.342245 0.342245i
\(650\) 4.77969 0.187475
\(651\) 7.31677 4.81785i 0.286767 0.188826i
\(652\) −13.2027 + 13.2027i −0.517059 + 0.517059i
\(653\) 23.9793 23.9793i 0.938382 0.938382i −0.0598267 0.998209i \(-0.519055\pi\)
0.998209 + 0.0598267i \(0.0190548\pi\)
\(654\) −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 \(-0.210816\pi\)
0.788581 + 0.614931i \(0.210816\pi\)
\(660\) −2.32281 3.52760i −0.0904152 0.137312i
\(661\) −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
\(666\) −17.9723 3.16176i −0.696412 0.122516i
\(667\) −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
\(672\) −2.83549 4.30620i −0.109381 0.166115i
\(673\) −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 \(-0.454292\pi\)
0.143104 + 0.989708i \(0.454292\pi\)
\(678\) 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
\(681\) −29.9123 + 19.6963i −1.14624 + 0.754763i
\(682\) 4.14339 0.158658
\(683\) −16.2355 16.2355i −0.621235 0.621235i 0.324612 0.945847i \(-0.394766\pi\)
−0.945847 + 0.324612i \(0.894766\pi\)
\(684\) 8.14519 + 20.4398i 0.311439 + 0.781534i
\(685\) 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
\(690\) −9.34779 + 6.15521i −0.355864 + 0.234325i
\(691\) 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 \(0.114058\pi\)
0.350705 + 0.936486i \(0.385942\pi\)
\(702\) −20.3670 14.2131i −0.768703 0.536440i
\(703\) 43.4171 10.2596i 1.63751 0.386947i
\(704\) 2.43854i 0.0919059i
\(705\) −6.25765 9.50336i −0.235677 0.357917i
\(706\) 31.1631i 1.17284i
\(707\) 0.666787 0.0250771
\(708\) 4.81646 + 7.31466i 0.181014 + 0.274902i
\(709\) 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
\(711\) −25.0264 + 9.97295i −0.938564 + 0.374015i
\(712\) −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
\(717\) 37.6424 24.7863i 1.40578 0.925661i
\(718\) −1.68859 1.68859i −0.0630177 0.0630177i
\(719\) 12.6157i 0.470487i −0.971936 0.235243i \(-0.924411\pi\)
0.971936 0.235243i \(-0.0755887\pi\)
\(720\) 1.11056 + 2.78687i 0.0413881 + 0.103861i
\(721\) −2.35460 2.35460i −0.0876898 0.0876898i
\(722\) −24.6017 24.6017i −0.915580 0.915580i
\(723\) 24.5983 + 37.3569i 0.914819 + 1.38932i
\(724\) 2.29142i 0.0851599i
\(725\) −2.17706 2.17706i −0.0808541 0.0808541i
\(726\) −4.81369 7.31045i −0.178653 0.271316i
\(727\) −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
\(732\) 11.1666 + 16.9585i 0.412729 + 0.626803i
\(733\) 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
\(735\) −2.69227 + 1.77277i −0.0993060 + 0.0653897i
\(736\) −6.46188 −0.238188
\(737\) 8.89610i 0.327692i
\(738\) 19.6408 7.82679i 0.722987 0.288108i
\(739\) 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 \(-0.426248\pi\)
0.229630 + 0.973278i \(0.426248\pi\)
\(744\) −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
\(753\) 23.3525 + 35.4650i 0.851013 + 1.29242i
\(754\) 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
\(759\) 22.7950 15.0097i 0.827405 0.544818i
\(760\) −5.18614 5.18614i −0.188121 0.188121i
\(761\) −22.0349 −0.798766 −0.399383 0.916784i \(-0.630776\pi\)
−0.399383 + 0.916784i \(0.630776\pi\)
\(762\) −0.253121 0.384411i −0.00916962 0.0139257i
\(763\) −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
\(771\) −43.9075 + 28.9116i −1.58129 + 1.04123i
\(772\) 6.93955 + 6.93955i 0.249760 + 0.249760i
\(773\) 11.9686i 0.430481i 0.976561 + 0.215240i \(0.0690535\pi\)
−0.976561 + 0.215240i \(0.930947\pi\)
\(774\) 6.42229 14.9319i 0.230845 0.536715i
\(775\) 1.20146 1.20146i 0.0431578 0.0431578i
\(776\) 6.09076 0.218646
\(777\) −21.5251 + 22.8090i −0.772209 + 0.818269i
\(778\) 27.0435 0.969555