Properties

Label 735.2.v.a.178.2
Level 735
Weight 2
Character 735.178
Analytic conductor 5.869
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.v (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 178.2
Character \(\chi\) \(=\) 735.178
Dual form 735.2.v.a.607.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.03317 - 0.544785i) q^{2} +(0.258819 + 0.965926i) q^{3} +(2.10492 + 1.21528i) q^{4} +(2.22675 + 0.203934i) q^{5} -2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-2.03317 - 0.544785i) q^{2} +(0.258819 + 0.965926i) q^{3} +(2.10492 + 1.21528i) q^{4} +(2.22675 + 0.203934i) q^{5} -2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-4.41625 - 1.62773i) q^{10} +(1.33594 - 2.31391i) q^{11} +(-0.629073 + 2.34773i) q^{12} +(1.22714 - 1.22714i) q^{13} +(0.379340 + 2.20366i) q^{15} +(-1.47676 - 2.55782i) q^{16} +(6.48349 - 1.73725i) q^{17} +(2.03317 - 0.544785i) q^{18} +(-3.00865 - 5.21113i) q^{19} +(4.43929 + 3.13538i) q^{20} +(-3.97676 + 3.97676i) q^{22} +(-0.0643048 + 0.239989i) q^{23} +(0.453132 - 0.784847i) q^{24} +(4.91682 + 0.908218i) q^{25} +(-3.16351 + 1.82645i) q^{26} +(-0.707107 - 0.707107i) q^{27} +0.304889i q^{29} +(0.429257 - 4.68706i) q^{30} +(-6.28197 - 3.62690i) q^{31} +(2.07815 + 7.75576i) q^{32} +(2.58083 + 0.691531i) q^{33} -14.1284 q^{34} -2.43055 q^{36} +(1.00463 + 0.269190i) q^{37} +(3.27813 + 12.2341i) q^{38} +(1.50294 + 0.867721i) q^{39} +(-1.29627 - 1.55764i) q^{40} +7.05736i q^{41} +(0.304889 + 0.304889i) q^{43} +(5.62407 - 3.24706i) q^{44} +(-2.03039 + 0.936763i) q^{45} +(0.261485 - 0.452905i) q^{46} +(0.203827 - 0.760694i) q^{47} +(2.08845 - 2.08845i) q^{48} +(-9.50193 - 4.52517i) q^{50} +(3.35610 + 5.81294i) q^{51} +(4.07435 - 1.09172i) q^{52} +(6.81689 - 1.82658i) q^{53} +(1.05244 + 1.82289i) q^{54} +(3.44668 - 4.88005i) q^{55} +(4.25487 - 4.25487i) q^{57} +(0.166099 - 0.619890i) q^{58} +(3.99419 - 6.91813i) q^{59} +(-1.87957 + 5.09952i) q^{60} +(-4.79266 + 2.76704i) q^{61} +(10.7964 + 10.7964i) q^{62} -10.9939i q^{64} +(2.98279 - 2.48228i) q^{65} +(-4.87052 - 2.81199i) q^{66} +(-1.25567 - 4.68622i) q^{67} +(15.7585 + 4.22247i) q^{68} -0.248455 q^{69} +15.3087 q^{71} +(0.875383 + 0.234558i) q^{72} +(3.66788 + 13.6887i) q^{73} +(-1.89593 - 1.09462i) q^{74} +(0.395296 + 4.98435i) q^{75} -14.6253i q^{76} +(-2.58300 - 2.58300i) q^{78} +(9.78372 - 5.64863i) q^{79} +(-2.76675 - 5.99679i) q^{80} +(0.500000 - 0.866025i) q^{81} +(3.84475 - 14.3488i) q^{82} +(-4.88941 + 4.88941i) q^{83} +(14.7914 - 2.54621i) q^{85} +(-0.453791 - 0.785990i) q^{86} +(-0.294500 + 0.0789112i) q^{87} +(-2.33891 + 0.626709i) q^{88} +(-3.45626 - 5.98641i) q^{89} +(4.63845 - 0.798469i) q^{90} +(-0.427009 + 0.427009i) q^{92} +(1.87742 - 7.00662i) q^{93} +(-0.828829 + 1.43557i) q^{94} +(-5.63678 - 12.2174i) q^{95} +(-6.95363 + 4.01468i) q^{96} +(-8.84137 - 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 48q^{8} + O(q^{10}) \) \( 32q + 48q^{8} + 16q^{11} + 16q^{15} + 48q^{16} - 32q^{22} + 40q^{23} + 8q^{30} - 48q^{32} - 32q^{36} - 32q^{37} - 32q^{43} - 64q^{46} - 144q^{50} + 16q^{51} - 24q^{53} + 16q^{57} - 32q^{58} - 40q^{60} - 40q^{65} + 32q^{67} + 128q^{71} - 24q^{72} - 16q^{78} + 16q^{81} + 96q^{85} - 64q^{86} + 64q^{88} - 80q^{92} - 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.03317 0.544785i −1.43766 0.385221i −0.545950 0.837818i \(-0.683831\pi\)
−0.891715 + 0.452597i \(0.850498\pi\)
\(3\) 0.258819 + 0.965926i 0.149429 + 0.557678i
\(4\) 2.10492 + 1.21528i 1.05246 + 0.607638i
\(5\) 2.22675 + 0.203934i 0.995832 + 0.0912019i
\(6\) 2.10489i 0.859317i
\(7\) 0 0
\(8\) −0.640825 0.640825i −0.226566 0.226566i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) −4.41625 1.62773i −1.39654 0.514733i
\(11\) 1.33594 2.31391i 0.402800 0.697670i −0.591263 0.806479i \(-0.701370\pi\)
0.994063 + 0.108809i \(0.0347038\pi\)
\(12\) −0.629073 + 2.34773i −0.181598 + 0.677732i
\(13\) 1.22714 1.22714i 0.340348 0.340348i −0.516150 0.856498i \(-0.672635\pi\)
0.856498 + 0.516150i \(0.172635\pi\)
\(14\) 0 0
\(15\) 0.379340 + 2.20366i 0.0979452 + 0.568982i
\(16\) −1.47676 2.55782i −0.369190 0.639456i
\(17\) 6.48349 1.73725i 1.57248 0.421344i 0.635890 0.771780i \(-0.280633\pi\)
0.936587 + 0.350436i \(0.113966\pi\)
\(18\) 2.03317 0.544785i 0.479222 0.128407i
\(19\) −3.00865 5.21113i −0.690231 1.19551i −0.971762 0.235963i \(-0.924176\pi\)
0.281531 0.959552i \(-0.409158\pi\)
\(20\) 4.43929 + 3.13538i 0.992656 + 0.701092i
\(21\) 0 0
\(22\) −3.97676 + 3.97676i −0.847848 + 0.847848i
\(23\) −0.0643048 + 0.239989i −0.0134085 + 0.0500411i −0.972306 0.233712i \(-0.924913\pi\)
0.958897 + 0.283753i \(0.0915795\pi\)
\(24\) 0.453132 0.784847i 0.0924951 0.160206i
\(25\) 4.91682 + 0.908218i 0.983364 + 0.181644i
\(26\) −3.16351 + 1.82645i −0.620416 + 0.358197i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0 0
\(29\) 0.304889i 0.0566165i 0.999599 + 0.0283083i \(0.00901200\pi\)
−0.999599 + 0.0283083i \(0.990988\pi\)
\(30\) 0.429257 4.68706i 0.0783713 0.855736i
\(31\) −6.28197 3.62690i −1.12827 0.651410i −0.184774 0.982781i \(-0.559155\pi\)
−0.943500 + 0.331371i \(0.892489\pi\)
\(32\) 2.07815 + 7.75576i 0.367369 + 1.37104i
\(33\) 2.58083 + 0.691531i 0.449265 + 0.120380i
\(34\) −14.1284 −2.42301
\(35\) 0 0
\(36\) −2.43055 −0.405092
\(37\) 1.00463 + 0.269190i 0.165160 + 0.0442546i 0.340452 0.940262i \(-0.389420\pi\)
−0.175291 + 0.984517i \(0.556087\pi\)
\(38\) 3.27813 + 12.2341i 0.531783 + 1.98464i
\(39\) 1.50294 + 0.867721i 0.240662 + 0.138947i
\(40\) −1.29627 1.55764i −0.204958 0.246285i
\(41\) 7.05736i 1.10217i 0.834447 + 0.551087i \(0.185787\pi\)
−0.834447 + 0.551087i \(0.814213\pi\)
\(42\) 0 0
\(43\) 0.304889 + 0.304889i 0.0464952 + 0.0464952i 0.729972 0.683477i \(-0.239533\pi\)
−0.683477 + 0.729972i \(0.739533\pi\)
\(44\) 5.62407 3.24706i 0.847861 0.489513i
\(45\) −2.03039 + 0.936763i −0.302672 + 0.139644i
\(46\) 0.261485 0.452905i 0.0385538 0.0667772i
\(47\) 0.203827 0.760694i 0.0297313 0.110959i −0.949466 0.313871i \(-0.898374\pi\)
0.979197 + 0.202912i \(0.0650407\pi\)
\(48\) 2.08845 2.08845i 0.301442 0.301442i
\(49\) 0 0
\(50\) −9.50193 4.52517i −1.34378 0.639955i
\(51\) 3.35610 + 5.81294i 0.469948 + 0.813974i
\(52\) 4.07435 1.09172i 0.565011 0.151394i
\(53\) 6.81689 1.82658i 0.936372 0.250900i 0.241802 0.970326i \(-0.422262\pi\)
0.694570 + 0.719426i \(0.255595\pi\)
\(54\) 1.05244 + 1.82289i 0.143219 + 0.248063i
\(55\) 3.44668 4.88005i 0.464750 0.658026i
\(56\) 0 0
\(57\) 4.25487 4.25487i 0.563571 0.563571i
\(58\) 0.166099 0.619890i 0.0218099 0.0813956i
\(59\) 3.99419 6.91813i 0.519999 0.900664i −0.479731 0.877416i \(-0.659266\pi\)
0.999730 0.0232486i \(-0.00740092\pi\)
\(60\) −1.87957 + 5.09952i −0.242651 + 0.658346i
\(61\) −4.79266 + 2.76704i −0.613637 + 0.354284i −0.774388 0.632711i \(-0.781942\pi\)
0.160750 + 0.986995i \(0.448609\pi\)
\(62\) 10.7964 + 10.7964i 1.37114 + 1.37114i
\(63\) 0 0
\(64\) 10.9939i 1.37423i
\(65\) 2.98279 2.48228i 0.369970 0.307889i
\(66\) −4.87052 2.81199i −0.599519 0.346133i
\(67\) −1.25567 4.68622i −0.153404 0.572513i −0.999237 0.0390641i \(-0.987562\pi\)
0.845832 0.533449i \(-0.179104\pi\)
\(68\) 15.7585 + 4.22247i 1.91099 + 0.512049i
\(69\) −0.248455 −0.0299104
\(70\) 0 0
\(71\) 15.3087 1.81681 0.908407 0.418087i \(-0.137299\pi\)
0.908407 + 0.418087i \(0.137299\pi\)
\(72\) 0.875383 + 0.234558i 0.103165 + 0.0276430i
\(73\) 3.66788 + 13.6887i 0.429293 + 1.60214i 0.754366 + 0.656454i \(0.227944\pi\)
−0.325073 + 0.945689i \(0.605389\pi\)
\(74\) −1.89593 1.09462i −0.220397 0.127247i
\(75\) 0.395296 + 4.98435i 0.0456449 + 0.575543i
\(76\) 14.6253i 1.67764i
\(77\) 0 0
\(78\) −2.58300 2.58300i −0.292467 0.292467i
\(79\) 9.78372 5.64863i 1.10075 0.635521i 0.164335 0.986405i \(-0.447452\pi\)
0.936419 + 0.350884i \(0.114119\pi\)
\(80\) −2.76675 5.99679i −0.309332 0.670462i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) 3.84475 14.3488i 0.424581 1.58456i
\(83\) −4.88941 + 4.88941i −0.536682 + 0.536682i −0.922553 0.385871i \(-0.873901\pi\)
0.385871 + 0.922553i \(0.373901\pi\)
\(84\) 0 0
\(85\) 14.7914 2.54621i 1.60435 0.276175i
\(86\) −0.453791 0.785990i −0.0489336 0.0847554i
\(87\) −0.294500 + 0.0789112i −0.0315738 + 0.00846017i
\(88\) −2.33891 + 0.626709i −0.249329 + 0.0668074i
\(89\) −3.45626 5.98641i −0.366363 0.634559i 0.622631 0.782515i \(-0.286064\pi\)
−0.988994 + 0.147957i \(0.952730\pi\)
\(90\) 4.63845 0.798469i 0.488935 0.0841660i
\(91\) 0 0
\(92\) −0.427009 + 0.427009i −0.0445188 + 0.0445188i
\(93\) 1.87742 7.00662i 0.194679 0.726553i
\(94\) −0.828829 + 1.43557i −0.0854872 + 0.148068i
\(95\) −5.63678 12.2174i −0.578321 1.25348i
\(96\) −6.95363 + 4.01468i −0.709702 + 0.409746i
\(97\) −8.84137 8.84137i −0.897705 0.897705i 0.0975276 0.995233i \(-0.468907\pi\)
−0.995233 + 0.0975276i \(0.968907\pi\)
\(98\) 0 0
\(99\) 2.67187i 0.268533i
\(100\) 9.24578 + 7.88702i 0.924578 + 0.788702i
\(101\) −6.26104 3.61481i −0.622996 0.359687i 0.155038 0.987908i \(-0.450450\pi\)
−0.778035 + 0.628221i \(0.783783\pi\)
\(102\) −3.65671 13.6470i −0.362068 1.35126i
\(103\) 9.48757 + 2.54219i 0.934838 + 0.250489i 0.693916 0.720056i \(-0.255884\pi\)
0.240921 + 0.970545i \(0.422550\pi\)
\(104\) −1.57277 −0.154222
\(105\) 0 0
\(106\) −14.8550 −1.44284
\(107\) 10.2082 + 2.73529i 0.986867 + 0.264430i 0.715934 0.698168i \(-0.246001\pi\)
0.270933 + 0.962598i \(0.412668\pi\)
\(108\) −0.629073 2.34773i −0.0605326 0.225911i
\(109\) −5.15590 2.97676i −0.493846 0.285122i 0.232323 0.972639i \(-0.425367\pi\)
−0.726168 + 0.687517i \(0.758701\pi\)
\(110\) −9.66624 + 8.04425i −0.921640 + 0.766989i
\(111\) 1.04007i 0.0987192i
\(112\) 0 0
\(113\) 6.99031 + 6.99031i 0.657593 + 0.657593i 0.954810 0.297217i \(-0.0960585\pi\)
−0.297217 + 0.954810i \(0.596058\pi\)
\(114\) −10.9688 + 6.33286i −1.02733 + 0.593127i
\(115\) −0.192132 + 0.521281i −0.0179164 + 0.0486097i
\(116\) −0.370525 + 0.641768i −0.0344024 + 0.0595866i
\(117\) −0.449165 + 1.67631i −0.0415253 + 0.154975i
\(118\) −11.8897 + 11.8897i −1.09454 + 1.09454i
\(119\) 0 0
\(120\) 1.16907 1.65525i 0.106721 0.151103i
\(121\) 1.93055 + 3.34381i 0.175505 + 0.303983i
\(122\) 11.2517 3.01489i 1.01868 0.272955i
\(123\) −6.81689 + 1.82658i −0.614658 + 0.164697i
\(124\) −8.81536 15.2686i −0.791643 1.37117i
\(125\) 10.7633 + 3.02508i 0.962700 + 0.270571i
\(126\) 0 0
\(127\) 2.86110 2.86110i 0.253882 0.253882i −0.568678 0.822560i \(-0.692545\pi\)
0.822560 + 0.568678i \(0.192545\pi\)
\(128\) −1.83298 + 6.84079i −0.162014 + 0.604646i
\(129\) −0.215589 + 0.373412i −0.0189816 + 0.0328771i
\(130\) −7.41682 + 3.42191i −0.650498 + 0.300121i
\(131\) −8.09529 + 4.67382i −0.707289 + 0.408353i −0.810056 0.586352i \(-0.800564\pi\)
0.102767 + 0.994705i \(0.467230\pi\)
\(132\) 4.59204 + 4.59204i 0.399686 + 0.399686i
\(133\) 0 0
\(134\) 10.2119i 0.882177i
\(135\) −1.43035 1.71875i −0.123105 0.147927i
\(136\) −5.26805 3.04151i −0.451732 0.260807i
\(137\) 2.75230 + 10.2717i 0.235145 + 0.877573i 0.978083 + 0.208213i \(0.0667648\pi\)
−0.742938 + 0.669360i \(0.766569\pi\)
\(138\) 0.505150 + 0.135354i 0.0430012 + 0.0115221i
\(139\) 7.78902 0.660656 0.330328 0.943866i \(-0.392841\pi\)
0.330328 + 0.943866i \(0.392841\pi\)
\(140\) 0 0
\(141\) 0.787528 0.0663218
\(142\) −31.1252 8.33998i −2.61197 0.699875i
\(143\) −1.20011 4.47888i −0.100358 0.374543i
\(144\) 2.55782 + 1.47676i 0.213152 + 0.123063i
\(145\) −0.0621772 + 0.678912i −0.00516353 + 0.0563806i
\(146\) 29.8296i 2.46872i
\(147\) 0 0
\(148\) 1.78753 + 1.78753i 0.146934 + 0.146934i
\(149\) −12.3716 + 7.14275i −1.01352 + 0.585157i −0.912221 0.409699i \(-0.865634\pi\)
−0.101301 + 0.994856i \(0.532301\pi\)
\(150\) 1.91170 10.3494i 0.156089 0.845022i
\(151\) −4.88995 + 8.46964i −0.397939 + 0.689250i −0.993471 0.114081i \(-0.963608\pi\)
0.595533 + 0.803331i \(0.296941\pi\)
\(152\) −1.41141 + 5.26744i −0.114480 + 0.427245i
\(153\) −4.74624 + 4.74624i −0.383711 + 0.383711i
\(154\) 0 0
\(155\) −13.2487 9.35729i −1.06416 0.751596i
\(156\) 2.10904 + 3.65296i 0.168858 + 0.292471i
\(157\) −2.97426 + 0.796951i −0.237372 + 0.0636036i −0.375544 0.926805i \(-0.622544\pi\)
0.138172 + 0.990408i \(0.455877\pi\)
\(158\) −22.9692 + 6.15458i −1.82733 + 0.489632i
\(159\) 3.52868 + 6.11186i 0.279843 + 0.484702i
\(160\) 3.04586 + 17.6939i 0.240796 + 1.39883i
\(161\) 0 0
\(162\) −1.48838 + 1.48838i −0.116938 + 0.116938i
\(163\) −5.00566 + 18.6814i −0.392074 + 1.46324i 0.434633 + 0.900607i \(0.356878\pi\)
−0.826707 + 0.562632i \(0.809789\pi\)
\(164\) −8.57664 + 14.8552i −0.669723 + 1.15999i
\(165\) 5.60583 + 2.06618i 0.436414 + 0.160852i
\(166\) 12.6047 7.27730i 0.978311 0.564828i
\(167\) −6.23288 6.23288i −0.482315 0.482315i 0.423555 0.905870i \(-0.360782\pi\)
−0.905870 + 0.423555i \(0.860782\pi\)
\(168\) 0 0
\(169\) 9.98824i 0.768326i
\(170\) −31.4605 2.88126i −2.41291 0.220983i
\(171\) 5.21113 + 3.00865i 0.398505 + 0.230077i
\(172\) 0.271243 + 1.01229i 0.0206821 + 0.0771866i
\(173\) −9.24710 2.47775i −0.703044 0.188380i −0.110450 0.993882i \(-0.535229\pi\)
−0.592594 + 0.805501i \(0.701896\pi\)
\(174\) 0.641758 0.0486515
\(175\) 0 0
\(176\) −7.89143 −0.594839
\(177\) 7.71617 + 2.06754i 0.579983 + 0.155406i
\(178\) 3.76583 + 14.0543i 0.282261 + 1.05341i
\(179\) 1.12673 + 0.650516i 0.0842155 + 0.0486218i 0.541516 0.840690i \(-0.317850\pi\)
−0.457301 + 0.889312i \(0.651184\pi\)
\(180\) −5.41223 0.495671i −0.403404 0.0369452i
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 0 0
\(183\) −3.91319 3.91319i −0.289271 0.289271i
\(184\) 0.194999 0.112583i 0.0143755 0.00829971i
\(185\) 2.18217 + 0.804297i 0.160436 + 0.0591331i
\(186\) −7.63421 + 13.2228i −0.559767 + 0.969545i
\(187\) 4.64170 17.3230i 0.339434 1.26679i
\(188\) 1.35349 1.35349i 0.0987136 0.0987136i
\(189\) 0 0
\(190\) 4.80462 + 27.9109i 0.348564 + 2.02487i
\(191\) −0.968954 1.67828i −0.0701110 0.121436i 0.828839 0.559488i \(-0.189002\pi\)
−0.898950 + 0.438052i \(0.855669\pi\)
\(192\) 10.6192 2.84542i 0.766378 0.205350i
\(193\) 10.6931 2.86520i 0.769703 0.206241i 0.147463 0.989068i \(-0.452889\pi\)
0.622240 + 0.782826i \(0.286223\pi\)
\(194\) 13.1593 + 22.7926i 0.944784 + 1.63641i
\(195\) 3.16970 + 2.23870i 0.226987 + 0.160316i
\(196\) 0 0
\(197\) −8.50767 + 8.50767i −0.606146 + 0.606146i −0.941937 0.335790i \(-0.890997\pi\)
0.335790 + 0.941937i \(0.390997\pi\)
\(198\) 1.45560 5.43236i 0.103445 0.386061i
\(199\) 1.62730 2.81856i 0.115356 0.199803i −0.802566 0.596563i \(-0.796532\pi\)
0.917922 + 0.396761i \(0.129866\pi\)
\(200\) −2.56881 3.73283i −0.181643 0.263951i
\(201\) 4.20155 2.42577i 0.296355 0.171100i
\(202\) 10.7604 + 10.7604i 0.757101 + 0.757101i
\(203\) 0 0
\(204\) 16.3144i 1.14223i
\(205\) −1.43923 + 15.7150i −0.100520 + 1.09758i
\(206\) −17.9048 10.3374i −1.24749 0.720238i
\(207\) −0.0643048 0.239989i −0.00446949 0.0166804i
\(208\) −4.95101 1.32662i −0.343291 0.0919845i
\(209\) −16.0774 −1.11210
\(210\) 0 0
\(211\) −17.2508 −1.18759 −0.593797 0.804615i \(-0.702372\pi\)
−0.593797 + 0.804615i \(0.702372\pi\)
\(212\) 16.5688 + 4.43960i 1.13795 + 0.304913i
\(213\) 3.96220 + 14.7871i 0.271485 + 1.01320i
\(214\) −19.2649 11.1226i −1.31692 0.760324i
\(215\) 0.616735 + 0.741089i 0.0420610 + 0.0505419i
\(216\) 0.906263i 0.0616634i
\(217\) 0 0
\(218\) 8.86110 + 8.86110i 0.600150 + 0.600150i
\(219\) −12.2730 + 7.08580i −0.829330 + 0.478814i
\(220\) 13.1856 6.08345i 0.888972 0.410146i
\(221\) 5.82432 10.0880i 0.391786 0.678593i
\(222\) 0.566615 2.11464i 0.0380287 0.141925i
\(223\) −4.58392 + 4.58392i −0.306962 + 0.306962i −0.843730 0.536768i \(-0.819645\pi\)
0.536768 + 0.843730i \(0.319645\pi\)
\(224\) 0 0
\(225\) −4.71220 + 1.67187i −0.314147 + 0.111458i
\(226\) −10.4042 18.0207i −0.692080 1.19872i
\(227\) −19.3447 + 5.18339i −1.28395 + 0.344034i −0.835360 0.549703i \(-0.814741\pi\)
−0.448592 + 0.893737i \(0.648074\pi\)
\(228\) 14.1270 3.78532i 0.935583 0.250689i
\(229\) 14.4654 + 25.0547i 0.955898 + 1.65566i 0.732300 + 0.680982i \(0.238447\pi\)
0.223598 + 0.974681i \(0.428220\pi\)
\(230\) 0.674623 0.955180i 0.0444833 0.0629827i
\(231\) 0 0
\(232\) 0.195381 0.195381i 0.0128274 0.0128274i
\(233\) −1.75160 + 6.53706i −0.114751 + 0.428257i −0.999268 0.0382507i \(-0.987821\pi\)
0.884517 + 0.466508i \(0.154488\pi\)
\(234\) 1.82645 3.16351i 0.119399 0.206805i
\(235\) 0.609003 1.65231i 0.0397270 0.107785i
\(236\) 16.8149 9.70808i 1.09456 0.631942i
\(237\) 7.98837 + 7.98837i 0.518901 + 0.518901i
\(238\) 0 0
\(239\) 16.1769i 1.04640i −0.852210 0.523200i \(-0.824738\pi\)
0.852210 0.523200i \(-0.175262\pi\)
\(240\) 5.07637 4.22456i 0.327678 0.272694i
\(241\) −9.84735 5.68537i −0.634324 0.366227i 0.148101 0.988972i \(-0.452684\pi\)
−0.782425 + 0.622745i \(0.786017\pi\)
\(242\) −2.10347 7.85026i −0.135216 0.504634i
\(243\) 0.965926 + 0.258819i 0.0619642 + 0.0166032i
\(244\) −13.4509 −0.861105
\(245\) 0 0
\(246\) 14.8550 0.947117
\(247\) −10.0868 2.70276i −0.641810 0.171972i
\(248\) 1.70144 + 6.34985i 0.108041 + 0.403216i
\(249\) −5.98828 3.45733i −0.379492 0.219100i
\(250\) −20.2356 12.0142i −1.27981 0.759843i
\(251\) 6.95039i 0.438705i −0.975646 0.219352i \(-0.929606\pi\)
0.975646 0.219352i \(-0.0703944\pi\)
\(252\) 0 0
\(253\) 0.469405 + 0.469405i 0.0295112 + 0.0295112i
\(254\) −7.37578 + 4.25841i −0.462798 + 0.267196i
\(255\) 6.28774 + 13.6284i 0.393754 + 0.853442i
\(256\) −3.54033 + 6.13203i −0.221271 + 0.383252i
\(257\) 3.69280 13.7817i 0.230350 0.859679i −0.749840 0.661620i \(-0.769869\pi\)
0.980190 0.198060i \(-0.0634640\pi\)
\(258\) 0.641758 0.641758i 0.0399541 0.0399541i
\(259\) 0 0
\(260\) 9.29520 1.60009i 0.576464 0.0992332i
\(261\) −0.152445 0.264042i −0.00943609 0.0163438i
\(262\) 19.0053 5.09245i 1.17415 0.314613i
\(263\) −24.8595 + 6.66107i −1.53290 + 0.410739i −0.923964 0.382480i \(-0.875070\pi\)
−0.608936 + 0.793219i \(0.708403\pi\)
\(264\) −1.21071 2.09701i −0.0745140 0.129062i
\(265\) 15.5520 2.67714i 0.955352 0.164456i
\(266\) 0 0
\(267\) 4.88789 4.88789i 0.299134 0.299134i
\(268\) 3.05197 11.3901i 0.186429 0.695761i
\(269\) 7.75593 13.4337i 0.472888 0.819065i −0.526631 0.850094i \(-0.676545\pi\)
0.999518 + 0.0310287i \(0.00987831\pi\)
\(270\) 1.97178 + 4.27374i 0.119999 + 0.260091i
\(271\) −11.5544 + 6.67091i −0.701877 + 0.405229i −0.808046 0.589119i \(-0.799475\pi\)
0.106169 + 0.994348i \(0.466142\pi\)
\(272\) −14.0181 14.0181i −0.849974 0.849974i
\(273\) 0 0
\(274\) 22.3835i 1.35224i
\(275\) 8.67009 10.1638i 0.522826 0.612898i
\(276\) −0.522977 0.301941i −0.0314795 0.0181747i
\(277\) −0.734104 2.73971i −0.0441080 0.164613i 0.940359 0.340184i \(-0.110489\pi\)
−0.984467 + 0.175571i \(0.943823\pi\)
\(278\) −15.8364 4.24334i −0.949802 0.254499i
\(279\) 7.25379 0.434273
\(280\) 0 0
\(281\) 13.5557 0.808664 0.404332 0.914612i \(-0.367504\pi\)
0.404332 + 0.914612i \(0.367504\pi\)
\(282\) −1.60117 0.429034i −0.0953486 0.0255486i
\(283\) −5.94585 22.1902i −0.353444 1.31907i −0.882431 0.470441i \(-0.844095\pi\)
0.528987 0.848630i \(-0.322572\pi\)
\(284\) 32.2237 + 18.6044i 1.91212 + 1.10397i
\(285\) 10.3422 8.60681i 0.612621 0.509824i
\(286\) 9.76010i 0.577127i
\(287\) 0 0
\(288\) −5.67761 5.67761i −0.334557 0.334557i
\(289\) 24.2952 14.0268i 1.42913 0.825107i
\(290\) 0.496278 1.34647i 0.0291424 0.0790673i
\(291\) 6.25179 10.8284i 0.366487 0.634773i
\(292\) −8.91497 + 33.2711i −0.521709 + 1.94705i
\(293\) −2.41765 + 2.41765i −0.141240 + 0.141240i −0.774192 0.632951i \(-0.781843\pi\)
0.632951 + 0.774192i \(0.281843\pi\)
\(294\) 0 0
\(295\) 10.3049 14.5904i 0.599974 0.849486i
\(296\) −0.471289 0.816297i −0.0273931 0.0474463i
\(297\) −2.58083 + 0.691531i −0.149755 + 0.0401267i
\(298\) 29.0448 7.78253i 1.68252 0.450830i
\(299\) 0.215589 + 0.373412i 0.0124679 + 0.0215950i
\(300\) −5.22529 + 10.9720i −0.301682 + 0.633472i
\(301\) 0 0
\(302\) 14.5562 14.5562i 0.837616 0.837616i
\(303\) 1.87116 6.98328i 0.107496 0.401179i
\(304\) −8.88610 + 15.3912i −0.509653 + 0.882744i
\(305\) −11.2363 + 5.18413i −0.643391 + 0.296842i
\(306\) 12.2356 7.06422i 0.699462 0.403834i
\(307\) 7.21300 + 7.21300i 0.411667 + 0.411667i 0.882319 0.470652i \(-0.155981\pi\)
−0.470652 + 0.882319i \(0.655981\pi\)
\(308\) 0 0
\(309\) 9.82225i 0.558768i
\(310\) 21.8391 + 26.2426i 1.24038 + 1.49048i
\(311\) 8.88036 + 5.12708i 0.503559 + 0.290730i 0.730182 0.683253i \(-0.239435\pi\)
−0.226623 + 0.973983i \(0.572769\pi\)
\(312\) −0.407062 1.51918i −0.0230453 0.0860064i
\(313\) −30.1760 8.08564i −1.70565 0.457027i −0.731298 0.682059i \(-0.761085\pi\)
−0.974352 + 0.225031i \(0.927752\pi\)
\(314\) 6.48134 0.365763
\(315\) 0 0
\(316\) 27.4586 1.54467
\(317\) 16.7425 + 4.48613i 0.940351 + 0.251966i 0.696263 0.717787i \(-0.254845\pi\)
0.244088 + 0.969753i \(0.421511\pi\)
\(318\) −3.84475 14.3488i −0.215603 0.804640i
\(319\) 0.705486 + 0.407313i 0.0394996 + 0.0228051i
\(320\) 2.24202 24.4805i 0.125332 1.36850i
\(321\) 10.5683i 0.589867i
\(322\) 0 0
\(323\) −28.5595 28.5595i −1.58909 1.58909i
\(324\) 2.10492 1.21528i 0.116940 0.0675153i
\(325\) 7.14815 4.91913i 0.396508 0.272864i
\(326\) 20.3547 35.2553i 1.12734 1.95261i
\(327\) 1.54088 5.75066i 0.0852111 0.318012i
\(328\) 4.52253 4.52253i 0.249715 0.249715i
\(329\) 0 0
\(330\) −10.2720 7.25487i −0.565453 0.399367i
\(331\) −0.631541 1.09386i −0.0347126 0.0601240i 0.848147 0.529761i \(-0.177718\pi\)
−0.882860 + 0.469637i \(0.844385\pi\)
\(332\) −16.2338 + 4.34983i −0.890945 + 0.238728i
\(333\) −1.00463 + 0.269190i −0.0550535 + 0.0147515i
\(334\) 9.27690 + 16.0681i 0.507609 + 0.879205i
\(335\) −1.84038 10.6911i −0.100551 0.584118i
\(336\) 0 0
\(337\) −9.55621 + 9.55621i −0.520560 + 0.520560i −0.917741 0.397180i \(-0.869989\pi\)
0.397180 + 0.917741i \(0.369989\pi\)
\(338\) 5.44145 20.3078i 0.295976 1.10460i
\(339\) −4.94289 + 8.56135i −0.268461 + 0.464988i
\(340\) 34.2290 + 12.6161i 1.85633 + 0.684201i
\(341\) −16.7846 + 9.69060i −0.908938 + 0.524775i
\(342\) −8.95602 8.95602i −0.484286 0.484286i
\(343\) 0 0
\(344\) 0.390761i 0.0210684i
\(345\) −0.553246 0.0506683i −0.0297858 0.00272789i
\(346\) 17.4510 + 10.0754i 0.938174 + 0.541655i
\(347\) 2.39738 + 8.94713i 0.128698 + 0.480307i 0.999944 0.0105386i \(-0.00335460\pi\)
−0.871247 + 0.490846i \(0.836688\pi\)
\(348\) −0.715799 0.191798i −0.0383708 0.0102814i
\(349\) −2.77139 −0.148349 −0.0741746 0.997245i \(-0.523632\pi\)
−0.0741746 + 0.997245i \(0.523632\pi\)
\(350\) 0 0
\(351\) −1.73544 −0.0926310
\(352\) 20.7224 + 5.55255i 1.10451 + 0.295952i
\(353\) −0.355252 1.32582i −0.0189082 0.0705663i 0.955827 0.293929i \(-0.0949631\pi\)
−0.974735 + 0.223363i \(0.928296\pi\)
\(354\) −14.5619 8.40731i −0.773956 0.446844i
\(355\) 34.0887 + 3.12197i 1.80924 + 0.165697i
\(356\) 16.8012i 0.890463i
\(357\) 0 0
\(358\) −1.93643 1.93643i −0.102344 0.102344i
\(359\) 8.07840 4.66406i 0.426361 0.246160i −0.271434 0.962457i \(-0.587498\pi\)
0.697795 + 0.716297i \(0.254164\pi\)
\(360\) 1.90142 + 0.700822i 0.100214 + 0.0369366i
\(361\) −8.60390 + 14.9024i −0.452837 + 0.784336i
\(362\) −4.62265 + 17.2520i −0.242961 + 0.906744i
\(363\) −2.73021 + 2.73021i −0.143299 + 0.143299i
\(364\) 0 0
\(365\) 5.37586 + 31.2293i 0.281385 + 1.63462i
\(366\) 5.82432 + 10.0880i 0.304442 + 0.527309i
\(367\) −17.7631 + 4.75960i −0.927225 + 0.248449i −0.690671 0.723169i \(-0.742685\pi\)
−0.236554 + 0.971618i \(0.576018\pi\)
\(368\) 0.708812 0.189926i 0.0369494 0.00990056i
\(369\) −3.52868 6.11186i −0.183696 0.318170i
\(370\) −3.99853 2.82408i −0.207874 0.146817i
\(371\) 0 0
\(372\) 12.4668 12.4668i 0.646373 0.646373i
\(373\) 7.56784 28.2436i 0.391848 1.46240i −0.435235 0.900317i \(-0.643335\pi\)
0.827083 0.562080i \(-0.189999\pi\)
\(374\) −18.8747 + 32.6919i −0.975986 + 1.69046i
\(375\) −0.136251 + 11.1795i −0.00703599 + 0.577307i
\(376\) −0.618089 + 0.356854i −0.0318755 + 0.0184033i
\(377\) 0.374143 + 0.374143i 0.0192693 + 0.0192693i
\(378\) 0 0
\(379\) 22.0077i 1.13046i −0.824933 0.565230i \(-0.808787\pi\)
0.824933 0.565230i \(-0.191213\pi\)
\(380\) 2.98260 32.5670i 0.153004 1.67065i
\(381\) 3.50412 + 2.02311i 0.179522 + 0.103647i
\(382\) 1.05574 + 3.94009i 0.0540165 + 0.201592i
\(383\) 0.533272 + 0.142890i 0.0272489 + 0.00730133i 0.272418 0.962179i \(-0.412177\pi\)
−0.245169 + 0.969480i \(0.578843\pi\)
\(384\) −7.08211 −0.361407
\(385\) 0 0
\(386\) −23.3017 −1.18602
\(387\) −0.416487 0.111597i −0.0211712 0.00567281i
\(388\) −7.86567 29.3551i −0.399319 1.49028i
\(389\) 22.4560 + 12.9650i 1.13857 + 0.657352i 0.946075 0.323947i \(-0.105010\pi\)
0.192491 + 0.981299i \(0.438343\pi\)
\(390\) −5.22493 6.27844i −0.264574 0.317921i
\(391\) 1.66768i 0.0843381i
\(392\) 0 0
\(393\) −6.60978 6.60978i −0.333419 0.333419i
\(394\) 21.9324 12.6626i 1.10494 0.637935i
\(395\) 22.9378 10.5829i 1.15413 0.532481i
\(396\) −3.24706 + 5.62407i −0.163171 + 0.282620i
\(397\) −6.28213 + 23.4452i −0.315291 + 1.17668i 0.608427 + 0.793609i \(0.291801\pi\)
−0.923718 + 0.383072i \(0.874866\pi\)
\(398\) −4.84408 + 4.84408i −0.242812 + 0.242812i
\(399\) 0 0
\(400\) −4.93791 13.9176i −0.246895 0.695879i
\(401\) 6.47088 + 11.2079i 0.323140 + 0.559696i 0.981134 0.193328i \(-0.0619280\pi\)
−0.657994 + 0.753023i \(0.728595\pi\)
\(402\) −9.86397 + 2.64304i −0.491970 + 0.131823i
\(403\) −12.1596 + 3.25815i −0.605712 + 0.162300i
\(404\) −8.78598 15.2178i −0.437119 0.757112i
\(405\) 1.28999 1.82645i 0.0640999 0.0907572i
\(406\) 0 0
\(407\) 1.96500 1.96500i 0.0974016 0.0974016i
\(408\) 1.57440 5.87575i 0.0779445 0.290893i
\(409\) 1.32139 2.28872i 0.0653386 0.113170i −0.831506 0.555516i \(-0.812521\pi\)
0.896844 + 0.442347i \(0.145854\pi\)
\(410\) 11.4875 31.1671i 0.567326 1.53923i
\(411\) −9.20938 + 5.31704i −0.454265 + 0.262270i
\(412\) 16.8811 + 16.8811i 0.831672 + 0.831672i
\(413\) 0 0
\(414\) 0.522969i 0.0257025i
\(415\) −11.8846 + 9.89037i −0.583392 + 0.485499i
\(416\) 12.0676 + 6.96724i 0.591663 + 0.341597i
\(417\) 2.01595 + 7.52362i 0.0987214 + 0.368433i
\(418\) 32.6881 + 8.75874i 1.59883 + 0.428404i
\(419\) 10.0302 0.490007 0.245003 0.969522i \(-0.421211\pi\)
0.245003 + 0.969522i \(0.421211\pi\)
\(420\) 0 0
\(421\) −26.6440 −1.29855 −0.649274 0.760555i \(-0.724927\pi\)
−0.649274 + 0.760555i \(0.724927\pi\)
\(422\) 35.0737 + 9.39797i 1.70736 + 0.457486i
\(423\) 0.203827 + 0.760694i 0.00991042 + 0.0369862i
\(424\) −5.53895 3.19791i −0.268995 0.155304i
\(425\) 33.4560 2.65331i 1.62285 0.128704i
\(426\) 32.2232i 1.56122i
\(427\) 0 0
\(428\) 18.1634 + 18.1634i 0.877960 + 0.877960i
\(429\) 4.01565 2.31844i 0.193878 0.111935i
\(430\) −0.850190 1.84274i −0.0409998 0.0888650i
\(431\) −11.1873 + 19.3771i −0.538876 + 0.933360i 0.460089 + 0.887873i \(0.347817\pi\)
−0.998965 + 0.0454873i \(0.985516\pi\)
\(432\) −0.764428 + 2.85288i −0.0367785 + 0.137259i
\(433\) 13.4723 13.4723i 0.647438 0.647438i −0.304935 0.952373i \(-0.598635\pi\)
0.952373 + 0.304935i \(0.0986349\pi\)
\(434\) 0 0
\(435\) −0.671871 + 0.115657i −0.0322138 + 0.00554532i
\(436\) −7.23517 12.5317i −0.346502 0.600159i
\(437\) 1.44408 0.386941i 0.0690799 0.0185099i
\(438\) 28.8132 7.72048i 1.37675 0.368899i
\(439\) −12.8395 22.2386i −0.612795 1.06139i −0.990767 0.135576i \(-0.956712\pi\)
0.377972 0.925817i \(-0.376622\pi\)
\(440\) −5.33598 + 0.918542i −0.254383 + 0.0437898i
\(441\) 0 0
\(442\) −17.3376 + 17.3376i −0.824665 + 0.824665i
\(443\) −5.72284 + 21.3579i −0.271900 + 1.01475i 0.685990 + 0.727611i \(0.259369\pi\)
−0.957890 + 0.287135i \(0.907297\pi\)
\(444\) −1.26397 + 2.18927i −0.0599855 + 0.103898i
\(445\) −6.47539 14.0351i −0.306963 0.665327i
\(446\) 11.8171 6.82261i 0.559556 0.323060i
\(447\) −10.1014 10.1014i −0.477779 0.477779i
\(448\) 0 0
\(449\) 7.01947i 0.331269i 0.986187 + 0.165635i \(0.0529673\pi\)
−0.986187 + 0.165635i \(0.947033\pi\)
\(450\) 10.4915 0.832054i 0.494574 0.0392234i
\(451\) 16.3301 + 9.42818i 0.768954 + 0.443956i
\(452\) 6.21888 + 23.2092i 0.292512 + 1.09167i
\(453\) −9.44666 2.53123i −0.443843 0.118927i
\(454\) 42.1548 1.97842
\(455\) 0 0
\(456\) −5.45325 −0.255372
\(457\) −15.3158 4.10385i −0.716442 0.191970i −0.117858 0.993030i \(-0.537603\pi\)
−0.598584 + 0.801060i \(0.704270\pi\)
\(458\) −15.7610 58.8209i −0.736464 2.74852i
\(459\) −5.81294 3.35610i −0.271325 0.156649i
\(460\) −1.03792 + 0.863761i −0.0483934 + 0.0402731i
\(461\) 29.9845i 1.39652i 0.715846 + 0.698259i \(0.246041\pi\)
−0.715846 + 0.698259i \(0.753959\pi\)
\(462\) 0 0
\(463\) 7.70220 + 7.70220i 0.357951 + 0.357951i 0.863057 0.505106i \(-0.168547\pi\)
−0.505106 + 0.863057i \(0.668547\pi\)
\(464\) 0.779853 0.450249i 0.0362038 0.0209023i
\(465\) 5.60943 15.2191i 0.260131 0.705770i
\(466\) 7.12259 12.3367i 0.329948 0.571486i
\(467\) 0.662362 2.47197i 0.0306504 0.114389i −0.948906 0.315559i \(-0.897808\pi\)
0.979556 + 0.201170i \(0.0644745\pi\)
\(468\) −2.98263 + 2.98263i −0.137872 + 0.137872i
\(469\) 0 0
\(470\) −2.13836 + 3.02764i −0.0986350 + 0.139654i
\(471\) −1.53959 2.66665i −0.0709407 0.122873i
\(472\) −6.99289 + 1.87374i −0.321874 + 0.0862458i
\(473\) 1.11280 0.298173i 0.0511665 0.0137100i
\(474\) −11.8897 20.5936i −0.546114 0.945897i
\(475\) −10.0601 28.3547i −0.461591 1.30100i
\(476\) 0 0
\(477\) −4.99031 + 4.99031i −0.228491 + 0.228491i
\(478\) −8.81295 + 32.8904i −0.403095 + 1.50437i
\(479\) −2.04728 + 3.54599i −0.0935425 + 0.162020i −0.908999 0.416798i \(-0.863152\pi\)
0.815457 + 0.578818i \(0.196486\pi\)
\(480\) −16.3027 + 7.52160i −0.744114 + 0.343313i
\(481\) 1.56316 0.902491i 0.0712740 0.0411500i
\(482\) 16.9240 + 16.9240i 0.770867 + 0.770867i
\(483\) 0 0
\(484\) 9.38461i 0.426573i
\(485\) −17.8845 21.4906i −0.812092 0.975836i
\(486\) −1.82289 1.05244i −0.0826878 0.0477398i
\(487\) −3.77185 14.0767i −0.170919 0.637878i −0.997211 0.0746360i \(-0.976221\pi\)
0.826292 0.563242i \(-0.190446\pi\)
\(488\) 4.84445 + 1.29807i 0.219298 + 0.0587607i
\(489\) −19.3404 −0.874603
\(490\) 0 0
\(491\) −8.55953 −0.386286 −0.193143 0.981171i \(-0.561868\pi\)
−0.193143 + 0.981171i \(0.561868\pi\)
\(492\) −16.5688 4.43960i −0.746979 0.200153i
\(493\) 0.529668 + 1.97675i 0.0238550 + 0.0890282i
\(494\) 19.0358 + 10.9903i 0.856460 + 0.494477i
\(495\) −0.544884 + 5.94959i −0.0244907 + 0.267414i
\(496\) 21.4242i 0.961976i
\(497\) 0 0
\(498\) 10.2917 + 10.2917i 0.461180 + 0.461180i
\(499\) −20.5736 + 11.8782i −0.921002 + 0.531741i −0.883955 0.467572i \(-0.845129\pi\)
−0.0370477 + 0.999313i \(0.511795\pi\)
\(500\) 18.9796 + 19.4479i 0.848794 + 0.869738i
\(501\) 4.40731 7.63369i 0.196904 0.341048i
\(502\) −3.78647 + 14.1313i −0.168998 + 0.630710i
\(503\) −17.9504 + 17.9504i −0.800367 + 0.800367i −0.983153 0.182786i \(-0.941489\pi\)
0.182786 + 0.983153i \(0.441489\pi\)
\(504\) 0 0
\(505\) −13.2046 9.32611i −0.587596 0.415007i
\(506\) −0.698653 1.21010i −0.0310589 0.0537956i
\(507\) −9.64790 + 2.58515i −0.428478 + 0.114810i
\(508\) 9.49942 2.54536i 0.421469 0.112932i
\(509\) −8.44887 14.6339i −0.374489 0.648635i 0.615761 0.787933i \(-0.288849\pi\)
−0.990250 + 0.139298i \(0.955515\pi\)
\(510\) −5.35948 31.1342i −0.237322 1.37865i
\(511\) 0 0
\(512\) 20.5543 20.5543i 0.908382 0.908382i
\(513\) −1.55739 + 5.81226i −0.0687604 + 0.256617i
\(514\) −15.0161 + 26.0087i −0.662333 + 1.14720i
\(515\) 20.6080 + 7.59564i 0.908097 + 0.334704i
\(516\) −0.907596 + 0.524001i −0.0399547 + 0.0230679i
\(517\) −1.48788 1.48788i −0.0654367 0.0654367i
\(518\) 0 0
\(519\) 9.57331i 0.420221i
\(520\) −3.50216 0.320740i −0.153580 0.0140654i
\(521\) −6.82841 3.94238i −0.299158 0.172719i 0.342907 0.939370i \(-0.388589\pi\)
−0.642065 + 0.766651i \(0.721922\pi\)
\(522\) 0.166099 + 0.619890i 0.00726996 + 0.0271319i
\(523\) 1.68225 + 0.450757i 0.0735595 + 0.0197102i 0.295411 0.955370i \(-0.404543\pi\)
−0.221852 + 0.975080i \(0.571210\pi\)
\(524\) −22.7199 −0.992524
\(525\) 0 0
\(526\) 54.1722 2.36202
\(527\) −47.0299 12.6016i −2.04865 0.548935i
\(528\) −2.04245 7.62253i −0.0888863 0.331728i
\(529\) 19.8651 + 11.4691i 0.863701 + 0.498658i
\(530\) −33.0783 3.02942i −1.43683 0.131590i
\(531\) 7.98837i 0.346666i
\(532\) 0 0
\(533\) 8.66039 + 8.66039i 0.375123 + 0.375123i
\(534\) −12.6007 + 7.27503i −0.545287 + 0.314821i
\(535\) 22.1734 + 8.17260i 0.958638 + 0.353332i
\(536\) −2.19838 + 3.80771i −0.0949557 + 0.164468i
\(537\) −0.336732 + 1.25670i −0.0145310 + 0.0542306i
\(538\) −23.0876 + 23.0876i −0.995375 + 0.995375i
\(539\) 0 0
\(540\) −0.922006 5.35610i −0.0396768 0.230490i
\(541\) −17.4747 30.2671i −0.751298 1.30129i −0.947194 0.320661i \(-0.896095\pi\)
0.195896 0.980625i \(-0.437238\pi\)
\(542\) 27.1261 7.26843i 1.16517 0.312206i
\(543\) 8.19615 2.19615i 0.351731 0.0942459i
\(544\) 26.9473 + 46.6741i 1.15536 + 2.00114i
\(545\) −10.8738 7.67996i −0.465784 0.328973i
\(546\) 0 0
\(547\) 3.83548 3.83548i 0.163993 0.163993i −0.620340 0.784333i \(-0.713005\pi\)
0.784333 + 0.620340i \(0.213005\pi\)
\(548\) −6.68961 + 24.9660i −0.285766 + 1.06649i
\(549\) 2.76704 4.79266i 0.118095 0.204546i
\(550\) −23.1648 + 15.9413i −0.987750 + 0.679738i
\(551\) 1.58882 0.917304i 0.0676859 0.0390785i
\(552\) 0.159216 + 0.159216i 0.00677668 + 0.00677668i
\(553\) 0 0
\(554\) 5.97022i 0.253650i
\(555\) −0.212105 + 2.31598i −0.00900337 + 0.0983077i
\(556\) 16.3953 + 9.46581i 0.695314 + 0.401440i
\(557\) −5.97158 22.2863i −0.253024 0.944299i −0.969179 0.246358i \(-0.920766\pi\)
0.716155 0.697941i \(-0.245900\pi\)
\(558\) −14.7482 3.95176i −0.624339 0.167291i
\(559\) 0.748285 0.0316491
\(560\) 0 0
\(561\) 17.9341 0.757180
\(562\) −27.5609 7.38493i −1.16259 0.311514i
\(563\) 8.69386 + 32.4459i 0.366402 + 1.36743i 0.865510 + 0.500892i \(0.166995\pi\)
−0.499107 + 0.866540i \(0.666339\pi\)
\(564\) 1.65768 + 0.957064i 0.0698011 + 0.0402997i
\(565\) 14.1401 + 16.9912i 0.594879 + 0.714826i
\(566\) 48.3556i 2.03254i
\(567\) 0 0
\(568\) −9.81023 9.81023i −0.411628 0.411628i
\(569\) 0.240575 0.138896i 0.0100854 0.00582283i −0.494949 0.868922i \(-0.664813\pi\)
0.505034 + 0.863099i \(0.331480\pi\)
\(570\) −25.7163 + 11.8648i −1.07714 + 0.496961i
\(571\) 1.55769 2.69800i 0.0651874 0.112908i −0.831590 0.555390i \(-0.812569\pi\)
0.896777 + 0.442483i \(0.145902\pi\)
\(572\) 2.91693 10.8861i 0.121963 0.455173i
\(573\) 1.37031 1.37031i 0.0572454 0.0572454i
\(574\) 0 0
\(575\) −0.534138 + 1.12158i −0.0222751 + 0.0467731i
\(576\) 5.49693 + 9.52095i 0.229039 + 0.396706i
\(577\) −40.4214 + 10.8309i −1.68277 + 0.450896i −0.968507 0.248986i \(-0.919903\pi\)
−0.714259 + 0.699882i \(0.753236\pi\)
\(578\) −57.0377 + 15.2832i −2.37246 + 0.635698i
\(579\) 5.53513 + 9.58713i 0.230032 + 0.398428i
\(580\) −0.955943 + 1.35349i −0.0396934 + 0.0562007i
\(581\) 0 0
\(582\) −18.6101 + 18.6101i −0.771413 + 0.771413i
\(583\) 4.88039 18.2139i 0.202125 0.754341i
\(584\) 6.42160 11.1225i 0.265728 0.460254i
\(585\) −1.34203 + 3.64112i −0.0554863 + 0.150542i
\(586\) 6.23257 3.59838i 0.257465 0.148648i
\(587\) 26.6462 + 26.6462i 1.09981 + 1.09981i 0.994433 + 0.105375i \(0.0336041\pi\)
0.105375 + 0.994433i \(0.466396\pi\)
\(588\) 0 0
\(589\) 43.6482i 1.79849i
\(590\) −28.9002 + 24.0507i −1.18980 + 0.990153i
\(591\) −10.4197 6.01583i −0.428610 0.247458i
\(592\) −0.795059 2.96720i −0.0326767 0.121951i
\(593\) −20.7484 5.55952i −0.852036 0.228302i −0.193732 0.981055i \(-0.562059\pi\)
−0.658304 + 0.752752i \(0.728726\pi\)
\(594\) 5.62399 0.230755
\(595\) 0 0
\(596\) −34.7217 −1.42225
\(597\) 3.14370 + 0.842351i 0.128663 + 0.0344751i
\(598\) −0.234900 0.876657i −0.00960576 0.0358492i
\(599\) −19.2930 11.1388i −0.788290 0.455119i 0.0510705 0.998695i \(-0.483737\pi\)
−0.839360 + 0.543576i \(0.817070\pi\)
\(600\) 2.94078 3.44741i 0.120057 0.140740i
\(601\) 22.3458i 0.911503i −0.890107 0.455752i \(-0.849371\pi\)
0.890107 0.455752i \(-0.150629\pi\)
\(602\) 0 0
\(603\) 3.43055 + 3.43055i 0.139703 + 0.139703i
\(604\) −20.5859 + 11.8853i −0.837629 + 0.483605i
\(605\) 3.61694 + 7.83954i 0.147049 + 0.318723i
\(606\) −7.60877 + 13.1788i −0.309085 + 0.535351i
\(607\) −0.210840 + 0.786867i −0.00855775 + 0.0319380i −0.970073 0.242815i \(-0.921929\pi\)
0.961515 + 0.274753i \(0.0885960\pi\)
\(608\) 34.1639 34.1639i 1.38553 1.38553i
\(609\) 0 0
\(610\) 25.6696 4.41880i 1.03933 0.178912i
\(611\) −0.683354 1.18360i −0.0276456 0.0478835i
\(612\) −15.7585 + 4.22247i −0.636998 + 0.170683i
\(613\) 22.4996 6.02876i 0.908752 0.243499i 0.225981 0.974132i \(-0.427441\pi\)
0.682771 + 0.730632i \(0.260775\pi\)
\(614\) −10.7357 18.5947i −0.433257 0.750423i
\(615\) −15.5520 + 2.67714i −0.627117 + 0.107953i
\(616\) 0 0
\(617\) −3.70013 + 3.70013i −0.148962 + 0.148962i −0.777654 0.628692i \(-0.783590\pi\)
0.628692 + 0.777654i \(0.283590\pi\)
\(618\) 5.35101 19.9703i 0.215249 0.803322i
\(619\) 19.9420 34.5405i 0.801536 1.38830i −0.117068 0.993124i \(-0.537350\pi\)
0.918605 0.395178i \(-0.129317\pi\)
\(620\) −16.5158 35.7972i −0.663290 1.43765i
\(621\) 0.215168 0.124227i 0.00863440 0.00498507i
\(622\) −15.2621 15.2621i −0.611954 0.611954i
\(623\) 0 0
\(624\) 5.12566i 0.205191i
\(625\) 23.3503 + 8.93109i 0.934011 + 0.357244i
\(626\) 56.9479 + 32.8789i 2.27610 + 1.31410i
\(627\) −4.16114 15.5296i −0.166180 0.620193i
\(628\) −7.22910 1.93703i −0.288473 0.0772960i
\(629\) 6.98117 0.278357
\(630\) 0 0
\(631\) −33.9725 −1.35242 −0.676211 0.736708i \(-0.736379\pi\)
−0.676211 + 0.736708i \(0.736379\pi\)
\(632\) −9.88943 2.64987i −0.393381 0.105406i
\(633\) −4.46483 16.6630i −0.177461 0.662294i
\(634\) −31.5962 18.2421i −1.25485 0.724486i
\(635\) 6.95444 5.78748i 0.275978 0.229669i
\(636\) 17.1533i 0.680172i
\(637\) 0 0
\(638\) −1.21247 1.21247i −0.0480022 0.0480022i
\(639\) −13.2578 + 7.65437i −0.524469 + 0.302802i
\(640\) −5.47666 + 14.8589i −0.216484 + 0.587350i
\(641\) 9.05563 15.6848i 0.357676 0.619513i −0.629896 0.776679i \(-0.716903\pi\)
0.987572 + 0.157167i \(0.0502359\pi\)
\(642\) 5.75748 21.4872i 0.227229 0.848032i
\(643\) 32.1062 32.1062i 1.26614 1.26614i 0.318082 0.948063i \(-0.396961\pi\)
0.948063 0.318082i \(-0.103039\pi\)
\(644\) 0 0
\(645\) −0.556214 + 0.787528i −0.0219009 + 0.0310089i
\(646\) 42.5074 + 73.6251i 1.67243 + 2.89674i
\(647\) −17.6596 + 4.73187i −0.694270 + 0.186029i −0.588663 0.808379i \(-0.700345\pi\)
−0.105607 + 0.994408i \(0.533679\pi\)
\(648\) −0.875383 + 0.234558i −0.0343883 + 0.00921432i
\(649\) −10.6720 18.4844i −0.418911 0.725575i
\(650\) −17.2132 + 6.10719i −0.675159 + 0.239544i
\(651\) 0 0
\(652\) −33.2396 + 33.2396i −1.30176 + 1.30176i
\(653\) −3.44041 + 12.8398i −0.134634 + 0.502459i 0.865366 + 0.501141i \(0.167086\pi\)
−0.999999 + 0.00131826i \(0.999580\pi\)
\(654\) −6.26575 + 10.8526i −0.245010 + 0.424370i
\(655\) −18.9793 + 8.75652i −0.741584 + 0.342146i
\(656\) 18.0515 10.4220i 0.704792 0.406912i
\(657\) −10.0208 10.0208i −0.390950 0.390950i
\(658\) 0 0
\(659\) 9.13808i 0.355969i 0.984033 + 0.177985i \(0.0569577\pi\)
−0.984033 + 0.177985i \(0.943042\pi\)
\(660\) 9.28884 + 11.1618i 0.361568 + 0.434472i
\(661\) −24.6676 14.2418i −0.959458 0.553943i −0.0634519 0.997985i \(-0.520211\pi\)
−0.896006 + 0.444042i \(0.853544\pi\)
\(662\) 0.688108 + 2.56805i 0.0267441 + 0.0998102i
\(663\) 11.2517 + 3.01489i 0.436980 + 0.117089i
\(664\) 6.26651 0.243188
\(665\) 0 0
\(666\) 2.18923 0.0848310
\(667\) −0.0731700 0.0196059i −0.00283316 0.000759142i
\(668\) −5.54504 20.6944i −0.214544 0.800690i
\(669\) −5.61413 3.24132i −0.217055 0.125317i
\(670\) −2.08256 + 22.7394i −0.0804562 + 0.878500i
\(671\) 14.7864i 0.570821i
\(672\) 0 0
\(673\) 26.8815 + 26.8815i 1.03621 + 1.03621i 0.999319 + 0.0368867i \(0.0117441\pi\)
0.0368867 + 0.999319i \(0.488256\pi\)
\(674\) 24.6354 14.2233i 0.948922 0.547860i
\(675\) −2.83451 4.11893i −0.109100 0.158538i
\(676\) −12.1385 + 21.0245i −0.466864 + 0.808633i
\(677\) −0.438111 + 1.63505i −0.0168380 + 0.0628402i −0.973834 0.227262i \(-0.927023\pi\)
0.956996 + 0.290102i \(0.0936893\pi\)
\(678\) 14.7138 14.7138i 0.565081 0.565081i
\(679\) 0 0
\(680\) −11.1104 7.84702i −0.426063 0.300919i
\(681\) −10.0135 17.3440i −0.383720 0.664623i
\(682\) 39.4052 10.5586i 1.50890 0.404309i
\(683\) −3.29967 + 0.884144i −0.126258 + 0.0338308i −0.321395 0.946945i \(-0.604152\pi\)
0.195137 + 0.980776i \(0.437485\pi\)
\(684\) 7.31267 + 12.6659i 0.279607 + 0.484293i
\(685\) 4.03393 + 23.4338i 0.154129 + 0.895361i
\(686\) 0 0
\(687\) −20.4571 + 20.4571i −0.780487 + 0.780487i
\(688\) 0.329605 1.23010i 0.0125661 0.0468972i
\(689\) 6.12382 10.6068i 0.233299 0.404086i
\(690\) 1.09724 + 0.404417i 0.0417711 + 0.0153959i
\(691\) −36.0875 + 20.8351i −1.37283 + 0.792606i −0.991284 0.131743i \(-0.957943\pi\)
−0.381549 + 0.924348i \(0.624609\pi\)
\(692\) −16.4533 16.4533i −0.625459 0.625459i
\(693\) 0 0
\(694\) 19.4970i 0.740098i
\(695\) 17.3442 + 1.58844i 0.657903 + 0.0602531i
\(696\) 0.239292 + 0.138155i 0.00907032 + 0.00523675i
\(697\) 12.2604 + 45.7563i 0.464395 + 1.73314i
\(698\) 5.63470 + 1.50981i 0.213276 + 0.0571472i
\(699\) −6.76767 −0.255977
\(700\) 0 0
\(701\) 13.7870 0.520727 0.260364 0.965511i \(-0.416158\pi\)
0.260364 + 0.965511i \(0.416158\pi\)
\(702\) 3.52844 + 0.945442i 0.133172 + 0.0356834i
\(703\) −1.61980 6.04516i −0.0610918 0.227998i
\(704\) −25.4388 14.6871i −0.958760 0.553540i
\(705\) 1.75363 + 0.160603i 0.0660454 + 0.00604868i
\(706\) 2.88915i 0.108735i
\(707\) 0 0
\(708\) 13.7293 + 13.7293i 0.515978 + 0.515978i
\(709\) −21.3668 + 12.3361i −0.802446 + 0.463293i −0.844326 0.535830i \(-0.819999\pi\)
0.0418795 + 0.999123i \(0.486665\pi\)
\(710\) −67.6072 24.9185i −2.53725 0.935175i
\(711\) −5.64863 + 9.78372i −0.211840 + 0.366918i
\(712\) −1.62139 + 6.05110i −0.0607641 + 0.226775i
\(713\) 1.27438 1.27438i 0.0477257 0.0477257i
\(714\) 0 0
\(715\) −1.75895 10.2181i −0.0657811 0.382135i
\(716\) 1.58111 + 2.73857i 0.0590890 + 0.102345i
\(717\) 15.6257 4.18690i 0.583553 0.156363i
\(718\) −18.9656 + 5.08182i −0.707791 + 0.189652i
\(719\) 14.9558 + 25.9043i 0.557758 + 0.966066i 0.997683 + 0.0680313i \(0.0216718\pi\)
−0.439925 + 0.898035i \(0.644995\pi\)
\(720\) 5.39447 + 3.81000i 0.201040 + 0.141990i
\(721\) 0 0
\(722\) 25.6118 25.6118i 0.953171 0.953171i
\(723\) 2.94297 10.9833i 0.109450 0.408473i
\(724\) 10.3120 17.8608i 0.383241 0.663793i
\(725\) −0.276906 + 1.49909i −0.0102840 + 0.0556747i
\(726\) 7.03835 4.06359i 0.261218 0.150814i
\(727\) −29.8488 29.8488i −1.10703 1.10703i −0.993539 0.113491i \(-0.963797\pi\)
−0.113491 0.993539i \(-0.536203\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 6.08326 66.4231i 0.225152 2.45843i
\(731\) 2.50641 + 1.44708i 0.0927031 + 0.0535222i
\(732\) −3.48135 12.9926i −0.128674 0.480219i
\(733\) 5.28252 + 1.41545i 0.195114 + 0.0522807i 0.355053 0.934846i \(-0.384463\pi\)
−0.159938 + 0.987127i \(0.551130\pi\)
\(734\) 38.7082 1.42875
\(735\) 0 0
\(736\) −1.99493 −0.0735342
\(737\) −12.5210 3.35499i −0.461216 0.123583i
\(738\) 3.84475 + 14.3488i 0.141527 + 0.528186i
\(739\) −10.3694 5.98677i −0.381444 0.220227i 0.297002 0.954877i \(-0.404013\pi\)
−0.678446 + 0.734650i \(0.737346\pi\)
\(740\) 3.61584 + 4.34491i 0.132921 + 0.159722i
\(741\) 10.4427i 0.383621i
\(742\) 0 0
\(743\) −12.0406 12.0406i −0.441728 0.441728i 0.450864 0.892593i \(-0.351116\pi\)
−0.892593 + 0.450864i \(0.851116\pi\)
\(744\) −5.69312 + 3.28692i −0.208720 + 0.120504i
\(745\) −29.0051 + 13.3821i −1.06267 + 0.490283i
\(746\) −30.7733 + 53.3010i −1.12669 + 1.95149i
\(747\) 1.78965 6.67906i 0.0654798 0.244374i
\(748\) 30.8227 30.8227i 1.12699 1.12699i
\(749\) 0 0
\(750\) 6.36745 22.6556i 0.232506 0.827264i
\(751\) 12.0559 + 20.8815i 0.439928 + 0.761977i 0.997683 0.0680281i \(-0.0216707\pi\)
−0.557756 + 0.830005i \(0.688337\pi\)
\(752\) −2.24673 + 0.602008i −0.0819296 + 0.0219530i
\(753\) 6.71356 1.79889i 0.244656 0.0655553i
\(754\) −0.556866 0.964521i −0.0202799 0.0351258i
\(755\) −12.6159 + 17.8625i −0.459141 + 0.650085i
\(756\) 0 0
\(757\) 29.2896 29.2896i 1.06455 1.06455i 0.0667825 0.997768i \(-0.478727\pi\)
0.997768 0.0667825i \(-0.0212733\pi\)
\(758\) −11.9895 + 44.7453i −0.435477 + 1.62522i
\(759\) −0.331920 + 0.574902i −0.0120479 + 0.0208676i
\(760\) −4.21705 + 11.4414i −0.152969 + 0.415024i
\(761\) 27.9728 16.1501i 1.01401 0.585440i 0.101648 0.994820i \(-0.467589\pi\)
0.912364 + 0.409381i \(0.134255\pi\)
\(762\) −6.02230 6.02230i −0.218165 0.218165i
\(763\) 0 0
\(764\) 4.71018i 0.170408i
\(765\) −11.5366 + 9.60077i −0.417107 + 0.347117i
\(766\) −1.00639 0.581037i −0.0363622 0.0209937i
\(767\) −3.58810 13.3910i −0.129559 0.483520i
\(768\) −6.83939 1.83261i −0.246795 0.0661286i
\(769\) 18.4310 0.664640 0.332320 0.943167i \(-0.392169\pi\)
0.332320 + 0.943167i \(0.392169\pi\)