Properties

Label 735.2.v.a.178.1
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 178.1
Character \(\chi\) \(=\) 735.178
Dual form 735.2.v.a.607.1

$q$-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 −0.856498 0.516150i \(-0.827365\pi\)
0.516150 + 0.856498i \(0.327365\pi\)
\(14\) 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 −0.936587 0.350436i \(-0.886034\pi\)
−0.635890 + 0.771780i \(0.719367\pi\)
\(18\) 2.03317 0.544785i 0.479222 0.128407i
\(19\) 3.00865 + 5.21113i 0.690231 + 1.19551i 0.971762 + 0.235963i \(0.0758243\pi\)
−0.281531 + 0.959552i \(0.590842\pi\)
\(20\) −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 0.943500 0.331371i \(-0.107511\pi\)
0.184774 + 0.982781i \(0.440845\pi\)
\(32\) 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 \(-0.814213\pi\)
0.834447 0.551087i \(-0.185787\pi\)
\(42\) 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 −0.979197 0.202912i \(-0.934959\pi\)
0.949466 + 0.313871i \(0.101626\pi\)
\(48\) −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 \(0.340734\pi\)
−0.999730 + 0.0232486i \(0.992599\pi\)
\(60\) −1.87957 + 5.09952i −0.242651 + 0.658346i
\(61\) 4.79266 2.76704i 0.613637 0.354284i −0.160750 0.986995i \(-0.551391\pi\)
0.774388 + 0.632711i \(0.218058\pi\)
\(62\) −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 \(-0.772056\pi\)
0.325073 0.945689i \(-0.394611\pi\)
\(74\) −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 −0.385871 0.922553i \(-0.626099\pi\)
0.922553 + 0.385871i \(0.126099\pi\)
\(84\) 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 0.988994 0.147957i \(-0.0472697\pi\)
−0.622631 + 0.782515i \(0.713936\pi\)
\(90\) −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 0.995233 0.0975276i \(-0.0310934\pi\)
−0.0975276 + 0.995233i \(0.531093\pi\)
\(98\) 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 0.778035 0.628221i \(-0.216217\pi\)
−0.155038 + 0.987908i \(0.549550\pi\)
\(102\) −3.65671 13.6470i −0.362068 1.35126i
\(103\) −9.48757 2.54219i −0.934838 0.250489i −0.240921 0.970545i \(-0.577450\pi\)
−0.693916 + 0.720056i \(0.744116\pi\)
\(104\) 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 −0.102767 0.994705i \(-0.532770\pi\)
0.810056 + 0.586352i \(0.199436\pi\)
\(132\) −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 \(-0.607159\pi\)
−0.330328 + 0.943866i \(0.607159\pi\)
\(140\) 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 −0.138172 0.990408i \(-0.544123\pi\)
0.375544 + 0.926805i \(0.377456\pi\)
\(158\) −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 0.905870 0.423555i \(-0.139218\pi\)
−0.423555 + 0.905870i \(0.639218\pi\)
\(168\) 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 0.592594 0.805501i \(-0.298104\pi\)
0.110450 + 0.993882i \(0.464771\pi\)
\(174\) −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 \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 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 −0.917922 0.396761i \(-0.870134\pi\)
0.802566 + 0.596563i \(0.203468\pi\)
\(200\) −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 −0.536768 0.843730i \(-0.680355\pi\)
0.843730 + 0.536768i \(0.180355\pi\)
\(224\) 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 0.448592 0.893737i \(-0.351926\pi\)
0.835360 + 0.549703i \(0.185259\pi\)
\(228\) 14.1270 3.78532i 0.935583 0.250689i
\(229\) −14.4654 25.0547i −0.955898 1.65566i −0.732300 0.680982i \(-0.761553\pi\)
−0.223598 0.974681i \(-0.571780\pi\)
\(230\) −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 0.782425 0.622745i \(-0.213983\pi\)
−0.148101 + 0.988972i \(0.547316\pi\)
\(242\) −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 \(0.0703944\pi\)
−0.975646 + 0.219352i \(0.929606\pi\)
\(252\) 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 \(0.230131\pi\)
−0.980190 + 0.198060i \(0.936536\pi\)
\(258\) −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 −0.999518 0.0310287i \(-0.990122\pi\)
0.526631 + 0.850094i \(0.323455\pi\)
\(270\) 1.97178 + 4.27374i 0.119999 + 0.260091i
\(271\) 11.5544 6.67091i 0.701877 0.405229i −0.106169 0.994348i \(-0.533858\pi\)
0.808046 + 0.589119i \(0.200525\pi\)
\(272\) 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 \(0.155905\pi\)
−0.528987 + 0.848630i \(0.677428\pi\)
\(284\) 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 −0.632951 0.774192i \(-0.718157\pi\)
0.774192 + 0.632951i \(0.218157\pi\)
\(294\) 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 0.470652 0.882319i \(-0.344019\pi\)
−0.882319 + 0.470652i \(0.844019\pi\)
\(308\) 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 0.226623 0.973983i \(-0.427231\pi\)
−0.730182 + 0.683253i \(0.760565\pi\)
\(312\) −0.407062 1.51918i −0.0230453 0.0860064i
\(313\) 30.1760 + 8.08564i 1.70565 + 0.457027i 0.974352 0.225031i \(-0.0722485\pi\)
0.731298 + 0.682059i \(0.238915\pi\)
\(314\) −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 \(-0.476368\pi\)
0.0741746 + 0.997245i \(0.476368\pi\)
\(350\) 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 0.974735 0.223363i \(-0.0717036\pi\)
−0.955827 + 0.293929i \(0.905037\pi\)
\(354\) −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 0.236554 0.971618i \(-0.423982\pi\)
0.690671 + 0.723169i \(0.257315\pi\)
\(368\) 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 0.245169 0.969480i \(-0.421157\pi\)
−0.272418 + 0.962179i \(0.587823\pi\)
\(384\) 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 \(-0.708199\pi\)
0.923718 0.383072i \(-0.125134\pi\)
\(398\) 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 −0.896844 0.442347i \(-0.854146\pi\)
0.831506 + 0.555516i \(0.187479\pi\)
\(410\) 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 \(-0.578789\pi\)
−0.245003 + 0.969522i \(0.578789\pi\)
\(420\) 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 −0.952373 0.304935i \(-0.901365\pi\)
0.304935 + 0.952373i \(0.401365\pi\)
\(434\) 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 \(0.0432883\pi\)
−0.377972 + 0.925817i \(0.623378\pi\)
\(440\) 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 \(-0.753959\pi\)
0.715846 0.698259i \(-0.246041\pi\)
\(462\) 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 −0.979556 0.201170i \(-0.935525\pi\)
0.948906 + 0.315559i \(0.102192\pi\)
\(468\) 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 −0.815457 0.578818i \(-0.803514\pi\)
0.908999 + 0.416798i \(0.136848\pi\)
\(480\) −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 −0.182786 0.983153i \(-0.558511\pi\)
0.983153 + 0.182786i \(0.0585115\pi\)
\(504\) 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 0.990250 0.139298i \(-0.0444847\pi\)
−0.615761 + 0.787933i \(0.711151\pi\)
\(510\) 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 0.642065 0.766651i \(-0.278078\pi\)
−0.342907 + 0.939370i \(0.611411\pi\)
\(522\) 0.166099 + 0.619890i 0.00726996 + 0.0271319i
\(523\) −1.68225 0.450757i −0.0735595 0.0197102i 0.221852 0.975080i \(-0.428790\pi\)
−0.295411 + 0.955370i \(0.595457\pi\)
\(524\) 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 \(-0.833005\pi\)
0.499107 0.866540i \(-0.333661\pi\)
\(564\) 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 0.714259 0.699882i \(-0.246764\pi\)
0.968507 + 0.248986i \(0.0800974\pi\)
\(578\) −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 \(-0.966396\pi\)
−0.105375 0.994433i \(-0.533604\pi\)
\(588\) 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 0.658304 0.752752i \(-0.271274\pi\)
0.193732 + 0.981055i \(0.437941\pi\)
\(594\) −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 \(0.150629\pi\)
−0.890107 + 0.455752i \(0.849371\pi\)
\(602\) 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 −0.961515 0.274753i \(-0.911404\pi\)
0.970073 + 0.242815i \(0.0780707\pi\)
\(608\) −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 \(0.462650\pi\)
−0.918605 + 0.395178i \(0.870683\pi\)
\(620\) −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 \(0.603039\pi\)
−0.948063 + 0.318082i \(0.896961\pi\)
\(644\) 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 0.105607 0.994408i \(-0.466321\pi\)
0.588663 + 0.808379i \(0.299655\pi\)
\(648\) −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 0.896006 0.444042i \(-0.146456\pi\)
0.0634519 + 0.997985i \(0.479789\pi\)
\(662\) 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 −0.956996 0.290102i \(-0.906311\pi\)
0.973834 + 0.227262i \(0.0729774\pi\)
\(678\) −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 0.381549 0.924348i \(-0.375391\pi\)
0.991284 + 0.131743i \(0.0420573\pi\)
\(692\) 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 \(-0.978328\pi\)
0.439925 0.898035i \(-0.355005\pi\)
\(720\) −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 \(0.0362034\pi\)
0.113491 + 0.993539i \(0.463797\pi\)
\(728\) 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 0.159938 0.987127i \(-0.448870\pi\)
−0.355053 + 0.934846i \(0.615537\pi\)
\(734\) −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 −0.912364 0.409381i \(-0.865745\pi\)
−0.101648 + 0.994820i \(0.532411\pi\)
\(762\) 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 \(-0.607831\pi\)
−0.332320 + 0.943167i \(0.607831\pi\)