Properties

Label 735.2.v.a.313.8
Level 735
Weight 2
Character 735.313
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 313.8
Character \(\chi\) \(=\) 735.313
Dual form 735.2.v.a.472.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.544785 + 2.03317i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-2.10492 + 1.21528i) q^{4} +(0.936763 + 2.03039i) q^{5} +2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.544785 + 2.03317i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-2.10492 + 1.21528i) q^{4} +(0.936763 + 2.03039i) q^{5} +2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-3.61778 + 3.01072i) q^{10} +(1.33594 + 2.31391i) q^{11} +(-2.34773 + 0.629073i) q^{12} +(-1.22714 + 1.22714i) q^{13} +(0.379340 + 2.20366i) q^{15} +(-1.47676 + 2.55782i) q^{16} +(1.73725 - 6.48349i) q^{17} +(-0.544785 + 2.03317i) q^{18} +(3.00865 - 5.21113i) q^{19} +(-4.43929 - 3.13538i) q^{20} +(-3.97676 + 3.97676i) q^{22} +(0.239989 - 0.0643048i) q^{23} +(-0.453132 - 0.784847i) q^{24} +(-3.24495 + 3.80398i) q^{25} +(-3.16351 - 1.82645i) q^{26} +(0.707107 + 0.707107i) q^{27} +0.304889i q^{29} +(-4.27374 + 1.97178i) q^{30} +(-6.28197 + 3.62690i) q^{31} +(-7.75576 - 2.07815i) q^{32} +(0.691531 + 2.58083i) q^{33} +14.1284 q^{34} -2.43055 q^{36} +(-0.269190 - 1.00463i) q^{37} +(12.2341 + 3.27813i) q^{38} +(-1.50294 + 0.867721i) q^{39} +(0.700822 - 1.90142i) q^{40} -7.05736i q^{41} +(0.304889 + 0.304889i) q^{43} +(-5.62407 - 3.24706i) q^{44} +(-0.203934 + 2.22675i) q^{45} +(0.261485 + 0.452905i) q^{46} +(0.760694 - 0.203827i) q^{47} +(-2.08845 + 2.08845i) q^{48} +(-9.50193 - 4.52517i) q^{50} +(3.35610 - 5.81294i) q^{51} +(1.09172 - 4.07435i) q^{52} +(-1.82658 + 6.81689i) q^{53} +(-1.05244 + 1.82289i) q^{54} +(-3.44668 + 4.88005i) q^{55} +(4.25487 - 4.25487i) q^{57} +(-0.619890 + 0.166099i) q^{58} +(-3.99419 - 6.91813i) q^{59} +(-3.47653 - 4.17752i) q^{60} +(-4.79266 - 2.76704i) q^{61} +(-10.7964 - 10.7964i) q^{62} -10.9939i q^{64} +(-3.64112 - 1.34203i) q^{65} +(-4.87052 + 2.81199i) q^{66} +(4.68622 + 1.25567i) q^{67} +(4.22247 + 15.7585i) q^{68} +0.248455 q^{69} +15.3087 q^{71} +(-0.234558 - 0.875383i) q^{72} +(13.6887 + 3.66788i) q^{73} +(1.89593 - 1.09462i) q^{74} +(-4.11893 + 2.83451i) q^{75} +14.6253i q^{76} +(-2.58300 - 2.58300i) q^{78} +(-9.78372 - 5.64863i) q^{79} +(-6.57675 - 0.602322i) q^{80} +(0.500000 + 0.866025i) q^{81} +(14.3488 - 3.84475i) q^{82} +(4.88941 - 4.88941i) q^{83} +(14.7914 - 2.54621i) q^{85} +(-0.453791 + 0.785990i) q^{86} +(-0.0789112 + 0.294500i) q^{87} +(0.626709 - 2.33891i) q^{88} +(3.45626 - 5.98641i) q^{89} +(-4.63845 + 0.798469i) q^{90} +(-0.427009 + 0.427009i) q^{92} +(-7.00662 + 1.87742i) q^{93} +(0.828829 + 1.43557i) q^{94} +(13.3990 + 1.22713i) 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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.544785 + 2.03317i 0.385221 + 1.43766i 0.837818 + 0.545950i \(0.183831\pi\)
−0.452597 + 0.891715i \(0.649502\pi\)
\(3\) 0.965926 + 0.258819i 0.557678 + 0.149429i
\(4\) −2.10492 + 1.21528i −1.05246 + 0.607638i
\(5\) 0.936763 + 2.03039i 0.418933 + 0.908017i
\(6\) 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
\(10\) −3.61778 + 3.01072i −1.14404 + 0.952073i
\(11\) 1.33594 + 2.31391i 0.402800 + 0.697670i 0.994063 0.108809i \(-0.0347038\pi\)
−0.591263 + 0.806479i \(0.701370\pi\)
\(12\) −2.34773 + 0.629073i −0.677732 + 0.181598i
\(13\) −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
\(17\) 1.73725 6.48349i 0.421344 1.57248i −0.350436 0.936587i \(-0.613966\pi\)
0.771780 0.635890i \(-0.219367\pi\)
\(18\) −0.544785 + 2.03317i −0.128407 + 0.479222i
\(19\) 3.00865 5.21113i 0.690231 1.19551i −0.281531 0.959552i \(-0.590842\pi\)
0.971762 0.235963i \(-0.0758243\pi\)
\(20\) −4.43929 3.13538i −0.992656 0.701092i
\(21\) 0 0
\(22\) −3.97676 + 3.97676i −0.847848 + 0.847848i
\(23\) 0.239989 0.0643048i 0.0500411 0.0134085i −0.233712 0.972306i \(-0.575087\pi\)
0.283753 + 0.958897i \(0.408421\pi\)
\(24\) −0.453132 0.784847i −0.0924951 0.160206i
\(25\) −3.24495 + 3.80398i −0.648990 + 0.760797i
\(26\) −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 \(0.990988\pi\)
\(30\) −4.27374 + 1.97178i −0.780274 + 0.359996i
\(31\) −6.28197 + 3.62690i −1.12827 + 0.651410i −0.943500 0.331371i \(-0.892489\pi\)
−0.184774 + 0.982781i \(0.559155\pi\)
\(32\) −7.75576 2.07815i −1.37104 0.367369i
\(33\) 0.691531 + 2.58083i 0.120380 + 0.449265i
\(34\) 14.1284 2.42301
\(35\) 0 0
\(36\) −2.43055 −0.405092
\(37\) −0.269190 1.00463i −0.0442546 0.165160i 0.940262 0.340452i \(-0.110580\pi\)
−0.984517 + 0.175291i \(0.943913\pi\)
\(38\) 12.2341 + 3.27813i 1.98464 + 0.531783i
\(39\) −1.50294 + 0.867721i −0.240662 + 0.138947i
\(40\) 0.700822 1.90142i 0.110810 0.300642i
\(41\) 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
\(45\) −0.203934 + 2.22675i −0.0304006 + 0.331944i
\(46\) 0.261485 + 0.452905i 0.0385538 + 0.0667772i
\(47\) 0.760694 0.203827i 0.110959 0.0297313i −0.202912 0.979197i \(-0.565041\pi\)
0.313871 + 0.949466i \(0.398374\pi\)
\(48\) −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
\(52\) 1.09172 4.07435i 0.151394 0.565011i
\(53\) −1.82658 + 6.81689i −0.250900 + 0.936372i 0.719426 + 0.694570i \(0.244405\pi\)
−0.970326 + 0.241802i \(0.922262\pi\)
\(54\) −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
\(58\) −0.619890 + 0.166099i −0.0813956 + 0.0218099i
\(59\) −3.99419 6.91813i −0.519999 0.900664i −0.999730 0.0232486i \(-0.992599\pi\)
0.479731 0.877416i \(-0.340734\pi\)
\(60\) −3.47653 4.17752i −0.448818 0.539315i
\(61\) −4.79266 2.76704i −0.613637 0.354284i 0.160750 0.986995i \(-0.448609\pi\)
−0.774388 + 0.632711i \(0.781942\pi\)
\(62\) −10.7964 10.7964i −1.37114 1.37114i
\(63\) 0 0
\(64\) 10.9939i 1.37423i
\(65\) −3.64112 1.34203i −0.451625 0.166459i
\(66\) −4.87052 + 2.81199i −0.599519 + 0.346133i
\(67\) 4.68622 + 1.25567i 0.572513 + 0.153404i 0.533449 0.845832i \(-0.320896\pi\)
0.0390641 + 0.999237i \(0.487562\pi\)
\(68\) 4.22247 + 15.7585i 0.512049 + 1.91099i
\(69\) 0.248455 0.0299104
\(70\) 0 0
\(71\) 15.3087 1.81681 0.908407 0.418087i \(-0.137299\pi\)
0.908407 + 0.418087i \(0.137299\pi\)
\(72\) −0.234558 0.875383i −0.0276430 0.103165i
\(73\) 13.6887 + 3.66788i 1.60214 + 0.429293i 0.945689 0.325073i \(-0.105389\pi\)
0.656454 + 0.754366i \(0.272056\pi\)
\(74\) 1.89593 1.09462i 0.220397 0.127247i
\(75\) −4.11893 + 2.83451i −0.475613 + 0.327301i
\(76\) 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 \(-0.552548\pi\)
−0.936419 + 0.350884i \(0.885881\pi\)
\(80\) −6.57675 0.602322i −0.735303 0.0673417i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 14.3488 3.84475i 1.58456 0.424581i
\(83\) 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
\(87\) −0.0789112 + 0.294500i −0.00846017 + 0.0315738i
\(88\) 0.626709 2.33891i 0.0668074 0.249329i
\(89\) 3.45626 5.98641i 0.366363 0.634559i −0.622631 0.782515i \(-0.713936\pi\)
0.988994 + 0.147957i \(0.0472697\pi\)
\(90\) −4.63845 + 0.798469i −0.488935 + 0.0841660i
\(91\) 0 0
\(92\) −0.427009 + 0.427009i −0.0445188 + 0.0445188i
\(93\) −7.00662 + 1.87742i −0.726553 + 0.194679i
\(94\) 0.828829 + 1.43557i 0.0854872 + 0.148068i
\(95\) 13.3990 + 1.22713i 1.37471 + 0.125901i
\(96\) −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
\(100\) 2.20747 11.9506i 0.220747 1.19506i
\(101\) −6.26104 + 3.61481i −0.622996 + 0.359687i −0.778035 0.628221i \(-0.783783\pi\)
0.155038 + 0.987908i \(0.450450\pi\)
\(102\) 13.6470 + 3.65671i 1.35126 + 0.362068i
\(103\) 2.54219 + 9.48757i 0.250489 + 0.934838i 0.970545 + 0.240921i \(0.0774496\pi\)
−0.720056 + 0.693916i \(0.755884\pi\)
\(104\) 1.57277 0.154222
\(105\) 0 0
\(106\) −14.8550 −1.44284
\(107\) −2.73529 10.2082i −0.264430 0.986867i −0.962598 0.270933i \(-0.912668\pi\)
0.698168 0.715934i \(-0.253999\pi\)
\(108\) −2.34773 0.629073i −0.225911 0.0605326i
\(109\) 5.15590 2.97676i 0.493846 0.285122i −0.232323 0.972639i \(-0.574633\pi\)
0.726168 + 0.687517i \(0.241299\pi\)
\(110\) −11.7996 4.34909i −1.12505 0.414669i
\(111\) 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
\(115\) 0.355376 + 0.427032i 0.0331390 + 0.0398210i
\(116\) −0.370525 0.641768i −0.0344024 0.0595866i
\(117\) −1.67631 + 0.449165i −0.154975 + 0.0415253i
\(118\) 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
\(122\) 3.01489 11.2517i 0.272955 1.01868i
\(123\) 1.82658 6.81689i 0.164697 0.614658i
\(124\) 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 \(0.192545\pi\)
\(128\) 6.84079 1.83298i 0.604646 0.162014i
\(129\) 0.215589 + 0.373412i 0.0189816 + 0.0328771i
\(130\) 0.744951 8.13411i 0.0653365 0.713409i
\(131\) −8.09529 4.67382i −0.707289 0.408353i 0.102767 0.994705i \(-0.467230\pi\)
−0.810056 + 0.586352i \(0.800564\pi\)
\(132\) −4.59204 4.59204i −0.399686 0.399686i
\(133\) 0 0
\(134\) 10.2119i 0.882177i
\(135\) −0.773310 + 2.09809i −0.0665559 + 0.180575i
\(136\) −5.26805 + 3.04151i −0.451732 + 0.260807i
\(137\) −10.2717 2.75230i −0.877573 0.235145i −0.208213 0.978083i \(-0.566765\pi\)
−0.669360 + 0.742938i \(0.733431\pi\)
\(138\) 0.135354 + 0.505150i 0.0115221 + 0.0430012i
\(139\) −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
\(142\) 8.33998 + 31.1252i 0.699875 + 2.61197i
\(143\) −4.47888 1.20011i −0.374543 0.100358i
\(144\) −2.55782 + 1.47676i −0.213152 + 0.123063i
\(145\) −0.619044 + 0.285609i −0.0514088 + 0.0237185i
\(146\) 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 \(-0.134366\pi\)
0.101301 + 0.994856i \(0.467699\pi\)
\(150\) −8.00696 6.83026i −0.653765 0.557688i
\(151\) −4.88995 8.46964i −0.397939 0.689250i 0.595533 0.803331i \(-0.296941\pi\)
−0.993471 + 0.114081i \(0.963608\pi\)
\(152\) −5.26744 + 1.41141i −0.427245 + 0.114480i
\(153\) 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
\(157\) −0.796951 + 2.97426i −0.0636036 + 0.237372i −0.990408 0.138172i \(-0.955877\pi\)
0.926805 + 0.375544i \(0.122544\pi\)
\(158\) 6.15458 22.9692i 0.489632 1.82733i
\(159\) −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
\(163\) 18.6814 5.00566i 1.46324 0.392074i 0.562632 0.826707i \(-0.309789\pi\)
0.900607 + 0.434633i \(0.143122\pi\)
\(164\) 8.57664 + 14.8552i 0.669723 + 1.15999i
\(165\) −4.59228 + 3.82170i −0.357509 + 0.297519i
\(166\) 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
\(170\) 13.2350 + 28.6862i 1.01508 + 2.20013i
\(171\) 5.21113 3.00865i 0.398505 0.230077i
\(172\) −1.01229 0.271243i −0.0771866 0.0206821i
\(173\) −2.47775 9.24710i −0.188380 0.703044i −0.993882 0.110450i \(-0.964771\pi\)
0.805501 0.592594i \(-0.201896\pi\)
\(174\) −0.641758 −0.0486515
\(175\) 0 0
\(176\) −7.89143 −0.594839
\(177\) −2.06754 7.71617i −0.155406 0.579983i
\(178\) 14.0543 + 3.76583i 1.05341 + 0.282261i
\(179\) −1.12673 + 0.650516i −0.0842155 + 0.0486218i −0.541516 0.840690i \(-0.682150\pi\)
0.457301 + 0.889312i \(0.348816\pi\)
\(180\) −2.27685 4.93496i −0.169706 0.367830i
\(181\) 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
\(185\) 1.78762 1.48766i 0.131429 0.109375i
\(186\) −7.63421 13.2228i −0.559767 0.969545i
\(187\) 17.3230 4.64170i 1.26679 0.339434i
\(188\) −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 −0.898950 0.438052i \(-0.855669\pi\)
0.828839 + 0.559488i \(0.189002\pi\)
\(192\) 2.84542 10.6192i 0.205350 0.766378i
\(193\) −2.86520 + 10.6931i −0.206241 + 0.769703i 0.782826 + 0.622240i \(0.213777\pi\)
−0.989068 + 0.147463i \(0.952889\pi\)
\(194\) −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 \(0.390997\pi\)
\(198\) −5.43236 + 1.45560i −0.386061 + 0.103445i
\(199\) −1.62730 2.81856i −0.115356 0.199803i 0.802566 0.596563i \(-0.203468\pi\)
−0.917922 + 0.396761i \(0.870134\pi\)
\(200\) 4.51713 0.358242i 0.319410 0.0253316i
\(201\) 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
\(205\) 14.3292 6.61108i 1.00079 0.461738i
\(206\) −17.9048 + 10.3374i −1.24749 + 0.720238i
\(207\) 0.239989 + 0.0643048i 0.0166804 + 0.00446949i
\(208\) −1.32662 4.95101i −0.0919845 0.343291i
\(209\) 16.0774 1.11210
\(210\) 0 0
\(211\) −17.2508 −1.18759 −0.593797 0.804615i \(-0.702372\pi\)
−0.593797 + 0.804615i \(0.702372\pi\)
\(212\) −4.43960 16.5688i −0.304913 1.13795i
\(213\) 14.7871 + 3.96220i 1.01320 + 0.271485i
\(214\) 19.2649 11.1226i 1.31692 0.760324i
\(215\) −0.333435 + 0.904653i −0.0227401 + 0.0616968i
\(216\) 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
\(220\) 1.32437 14.4608i 0.0892890 0.974946i
\(221\) 5.82432 + 10.0880i 0.391786 + 0.678593i
\(222\) 2.11464 0.566615i 0.141925 0.0380287i
\(223\) 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
\(227\) −5.18339 + 19.3447i −0.344034 + 1.28395i 0.549703 + 0.835360i \(0.314741\pi\)
−0.893737 + 0.448592i \(0.851926\pi\)
\(228\) −3.78532 + 14.1270i −0.250689 + 0.935583i
\(229\) −14.4654 + 25.0547i −0.955898 + 1.65566i −0.223598 + 0.974681i \(0.571780\pi\)
−0.732300 + 0.680982i \(0.761553\pi\)
\(230\) −0.674623 + 0.955180i −0.0444833 + 0.0629827i
\(231\) 0 0
\(232\) 0.195381 0.195381i 0.0128274 0.0128274i
\(233\) 6.53706 1.75160i 0.428257 0.114751i −0.0382507 0.999268i \(-0.512179\pi\)
0.466508 + 0.884517i \(0.345512\pi\)
\(234\) −1.82645 3.16351i −0.119399 0.206805i
\(235\) 1.12644 + 1.35357i 0.0734807 + 0.0882969i
\(236\) 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 \(-0.175262\pi\)
\(240\) −6.19676 2.28399i −0.399999 0.147431i
\(241\) −9.84735 + 5.68537i −0.634324 + 0.366227i −0.782425 0.622745i \(-0.786017\pi\)
0.148101 + 0.988972i \(0.452684\pi\)
\(242\) 7.85026 + 2.10347i 0.504634 + 0.135216i
\(243\) 0.258819 + 0.965926i 0.0166032 + 0.0619642i
\(244\) 13.4509 0.861105
\(245\) 0 0
\(246\) 14.8550 0.947117
\(247\) 2.70276 + 10.0868i 0.171972 + 0.641810i
\(248\) 6.34985 + 1.70144i 0.403216 + 0.108041i
\(249\) 5.98828 3.45733i 0.379492 0.219100i
\(250\) 0.286794 23.5316i 0.0181384 1.48827i
\(251\) 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
\(255\) 14.9464 + 1.36884i 0.935979 + 0.0857203i
\(256\) −3.54033 6.13203i −0.221271 0.383252i
\(257\) 13.7817 3.69280i 0.859679 0.230350i 0.198060 0.980190i \(-0.436536\pi\)
0.661620 + 0.749840i \(0.269869\pi\)
\(258\) −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
\(262\) 5.09245 19.0053i 0.314613 1.17415i
\(263\) 6.66107 24.8595i 0.410739 1.53290i −0.382480 0.923964i \(-0.624930\pi\)
0.793219 0.608936i \(-0.208403\pi\)
\(264\) 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
\(268\) −11.3901 + 3.05197i −0.695761 + 0.186429i
\(269\) −7.75593 13.4337i −0.472888 0.819065i 0.526631 0.850094i \(-0.323455\pi\)
−0.999518 + 0.0310287i \(0.990122\pi\)
\(270\) −4.68706 0.429257i −0.285245 0.0261238i
\(271\) −11.5544 6.67091i −0.701877 0.405229i 0.106169 0.994348i \(-0.466142\pi\)
−0.808046 + 0.589119i \(0.799475\pi\)
\(272\) 14.0181 + 14.0181i 0.849974 + 0.849974i
\(273\) 0 0
\(274\) 22.3835i 1.35224i
\(275\) −13.1371 2.42664i −0.792198 0.146332i
\(276\) −0.522977 + 0.301941i −0.0314795 + 0.0181747i
\(277\) 2.73971 + 0.734104i 0.164613 + 0.0441080i 0.340184 0.940359i \(-0.389511\pi\)
−0.175571 + 0.984467i \(0.556177\pi\)
\(278\) −4.24334 15.8364i −0.254499 0.949802i
\(279\) −7.25379 −0.434273
\(280\) 0 0
\(281\) 13.5557 0.808664 0.404332 0.914612i \(-0.367504\pi\)
0.404332 + 0.914612i \(0.367504\pi\)
\(282\) 0.429034 + 1.60117i 0.0255486 + 0.0953486i
\(283\) −22.1902 5.94585i −1.31907 0.353444i −0.470441 0.882431i \(-0.655905\pi\)
−0.848630 + 0.528987i \(0.822572\pi\)
\(284\) −32.2237 + 18.6044i −1.91212 + 1.10397i
\(285\) 12.6248 + 4.65323i 0.747831 + 0.275634i
\(286\) 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
\(290\) −0.917936 1.10302i −0.0539031 0.0647717i
\(291\) 6.25179 + 10.8284i 0.366487 + 0.634773i
\(292\) −33.2711 + 8.91497i −1.94705 + 0.521709i
\(293\) 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
\(297\) −0.691531 + 2.58083i −0.0401267 + 0.149755i
\(298\) −7.78253 + 29.0448i −0.450830 + 1.68252i
\(299\) −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
\(303\) −6.98328 + 1.87116i −0.401179 + 0.107496i
\(304\) 8.88610 + 15.3912i 0.509653 + 0.882744i
\(305\) 1.12859 12.3230i 0.0646227 0.705614i
\(306\) 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
\(310\) 11.8072 32.0345i 0.670605 1.81944i
\(311\) 8.88036 5.12708i 0.503559 0.290730i −0.226623 0.973983i \(-0.572769\pi\)
0.730182 + 0.683253i \(0.239435\pi\)
\(312\) 1.51918 + 0.407062i 0.0860064 + 0.0230453i
\(313\) −8.08564 30.1760i −0.457027 1.70565i −0.682059 0.731298i \(-0.738915\pi\)
0.225031 0.974352i \(-0.427752\pi\)
\(314\) −6.48134 −0.365763
\(315\) 0 0
\(316\) 27.4586 1.54467
\(317\) −4.48613 16.7425i −0.251966 0.940351i −0.969753 0.244088i \(-0.921511\pi\)
0.717787 0.696263i \(-0.245155\pi\)
\(318\) −14.3488 3.84475i −0.804640 0.215603i
\(319\) −0.705486 + 0.407313i −0.0394996 + 0.0228051i
\(320\) 22.3218 10.2986i 1.24783 0.575711i
\(321\) 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
\(325\) −0.686013 8.65005i −0.0380532 0.479818i
\(326\) 20.3547 + 35.2553i 1.12734 + 1.95261i
\(327\) 5.75066 1.54088i 0.318012 0.0852111i
\(328\) −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 −0.882860 0.469637i \(-0.844385\pi\)
0.848147 + 0.529761i \(0.177718\pi\)
\(332\) −4.34983 + 16.2338i −0.238728 + 0.890945i
\(333\) 0.269190 1.00463i 0.0147515 0.0550535i
\(334\) −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 \(0.369989\pi\)
\(338\) −20.3078 + 5.44145i −1.10460 + 0.295976i
\(339\) 4.94289 + 8.56135i 0.268461 + 0.464988i
\(340\) −28.0403 + 23.3352i −1.52070 + 1.26553i
\(341\) −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
\(345\) 0.232743 + 0.504460i 0.0125305 + 0.0271592i
\(346\) 17.4510 10.0754i 0.938174 0.541655i
\(347\) −8.94713 2.39738i −0.480307 0.128698i 0.0105386 0.999944i \(-0.496645\pi\)
−0.490846 + 0.871247i \(0.663312\pi\)
\(348\) −0.191798 0.715799i −0.0102814 0.0383708i
\(349\) 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
\(352\) −5.55255 20.7224i −0.295952 1.10451i
\(353\) −1.32582 0.355252i −0.0705663 0.0189082i 0.223363 0.974735i \(-0.428296\pi\)
−0.293929 + 0.955827i \(0.594963\pi\)
\(354\) 14.5619 8.40731i 0.773956 0.446844i
\(355\) 14.3407 + 31.0827i 0.761123 + 1.64970i
\(356\) 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 \(-0.412502\pi\)
−0.697795 + 0.716297i \(0.745836\pi\)
\(360\) 1.55764 1.29627i 0.0820949 0.0683195i
\(361\) −8.60390 14.9024i −0.452837 0.784336i
\(362\) −17.2520 + 4.62265i −0.906744 + 0.242961i
\(363\) 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
\(367\) −4.75960 + 17.7631i −0.248449 + 0.927225i 0.723169 + 0.690671i \(0.242685\pi\)
−0.971618 + 0.236554i \(0.923982\pi\)
\(368\) −0.189926 + 0.708812i −0.00990056 + 0.0369494i
\(369\) 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
\(373\) −28.2436 + 7.56784i −1.46240 + 0.391848i −0.900317 0.435235i \(-0.856665\pi\)
−0.562080 + 0.827083i \(0.689999\pi\)
\(374\) 18.8747 + 32.6919i 0.975986 + 1.69046i
\(375\) −9.61361 5.70775i −0.496445 0.294747i
\(376\) −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 \(-0.191213\pi\)
\(380\) −29.6951 + 13.7005i −1.52333 + 0.702820i
\(381\) 3.50412 2.02311i 0.179522 0.103647i
\(382\) −3.94009 1.05574i −0.201592 0.0540165i
\(383\) 0.142890 + 0.533272i 0.00730133 + 0.0272489i 0.969480 0.245169i \(-0.0788434\pi\)
−0.962179 + 0.272418i \(0.912177\pi\)
\(384\) 7.08211 0.361407
\(385\) 0 0
\(386\) −23.3017 −1.18602
\(387\) 0.111597 + 0.416487i 0.00567281 + 0.0211712i
\(388\) −29.3551 7.86567i −1.49028 0.399319i
\(389\) −22.4560 + 12.9650i −1.13857 + 0.657352i −0.946075 0.323947i \(-0.894990\pi\)
−0.192491 + 0.981299i \(0.561657\pi\)
\(390\) 2.82483 7.66414i 0.143041 0.388089i
\(391\) 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
\(395\) 2.30389 25.1562i 0.115921 1.26574i
\(396\) −3.24706 5.62407i −0.163171 0.282620i
\(397\) −23.4452 + 6.28213i −1.17668 + 0.315291i −0.793609 0.608427i \(-0.791801\pi\)
−0.383072 + 0.923718i \(0.625134\pi\)
\(398\) 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 −0.657994 0.753023i \(-0.728595\pi\)
0.981134 + 0.193328i \(0.0619280\pi\)
\(402\) −2.64304 + 9.86397i −0.131823 + 0.491970i
\(403\) 3.25815 12.1596i 0.162300 0.605712i
\(404\) 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
\(408\) −5.87575 + 1.57440i −0.290893 + 0.0779445i
\(409\) −1.32139 2.28872i −0.0653386 0.113170i 0.831506 0.555516i \(-0.187479\pi\)
−0.896844 + 0.442347i \(0.854146\pi\)
\(410\) 21.2477 + 25.5320i 1.04935 + 1.26093i
\(411\) −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
\(415\) 14.5076 + 5.34718i 0.712151 + 0.262483i
\(416\) 12.0676 6.96724i 0.591663 0.341597i
\(417\) −7.52362 2.01595i −0.368433 0.0987214i
\(418\) 8.75874 + 32.6881i 0.428404 + 1.59883i
\(419\) −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 \(0.724927\pi\)
\(422\) −9.39797 35.0737i −0.457486 1.70736i
\(423\) 0.760694 + 0.203827i 0.0369862 + 0.00991042i
\(424\) 5.53895 3.19791i 0.268995 0.155304i
\(425\) 19.0258 + 27.6471i 0.922887 + 1.34108i
\(426\) 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
\(430\) −2.02096 0.185087i −0.0974593 0.00892567i
\(431\) −11.1873 19.3771i −0.538876 0.933360i −0.998965 0.0454873i \(-0.985516\pi\)
0.460089 0.887873i \(-0.347817\pi\)
\(432\) −2.85288 + 0.764428i −0.137259 + 0.0367785i
\(433\) −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
\(437\) 0.386941 1.44408i 0.0185099 0.0690799i
\(438\) −7.72048 + 28.8132i −0.368899 + 1.37675i
\(439\) 12.8395 22.2386i 0.612795 1.06139i −0.377972 0.925817i \(-0.623378\pi\)
0.990767 0.135576i \(-0.0432883\pi\)
\(440\) 5.33598 0.918542i 0.254383 0.0437898i
\(441\) 0 0
\(442\) −17.3376 + 17.3376i −0.824665 + 0.824665i
\(443\) 21.3579 5.72284i 1.01475 0.271900i 0.287135 0.957890i \(-0.407297\pi\)
0.727611 + 0.685990i \(0.240631\pi\)
\(444\) 1.26397 + 2.18927i 0.0599855 + 0.103898i
\(445\) 15.3924 + 1.40969i 0.729671 + 0.0668259i
\(446\) 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 \(0.947033\pi\)
\(450\) −5.96633 8.66987i −0.281255 0.408702i
\(451\) 16.3301 9.42818i 0.768954 0.443956i
\(452\) −23.2092 6.21888i −1.09167 0.292512i
\(453\) −2.53123 9.44666i −0.118927 0.443843i
\(454\) −42.1548 −1.97842
\(455\) 0 0
\(456\) −5.45325 −0.255372
\(457\) 4.10385 + 15.3158i 0.191970 + 0.716442i 0.993030 + 0.117858i \(0.0376029\pi\)
−0.801060 + 0.598584i \(0.795730\pi\)
\(458\) −58.8209 15.7610i −2.74852 0.736464i
\(459\) 5.81294 3.35610i 0.271325 0.156649i
\(460\) −1.26700 0.466988i −0.0590742 0.0217734i
\(461\) 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
\(465\) −10.3754 12.4675i −0.481149 0.578165i
\(466\) 7.12259 + 12.3367i 0.329948 + 0.571486i
\(467\) 2.47197 0.662362i 0.114389 0.0306504i −0.201170 0.979556i \(-0.564475\pi\)
0.315559 + 0.948906i \(0.397808\pi\)
\(468\) 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
\(472\) −1.87374 + 6.99289i −0.0862458 + 0.321874i
\(473\) −0.298173 + 1.11280i −0.0137100 + 0.0511665i
\(474\) 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
\(478\) 32.8904 8.81295i 1.50437 0.403095i
\(479\) 2.04728 + 3.54599i 0.0935425 + 0.162020i 0.908999 0.416798i \(-0.136848\pi\)
−0.815457 + 0.578818i \(0.803514\pi\)
\(480\) 1.63746 17.8794i 0.0747393 0.816078i
\(481\) 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
\(485\) −9.66915 + 26.2337i −0.439053 + 1.19121i
\(486\) −1.82289 + 1.05244i −0.0826878 + 0.0477398i
\(487\) 14.0767 + 3.77185i 0.637878 + 0.170919i 0.563242 0.826292i \(-0.309554\pi\)
0.0746360 + 0.997211i \(0.476221\pi\)
\(488\) 1.29807 + 4.84445i 0.0587607 + 0.219298i
\(489\) 19.3404 0.874603
\(490\) 0 0
\(491\) −8.55953 −0.386286 −0.193143 0.981171i \(-0.561868\pi\)
−0.193143 + 0.981171i \(0.561868\pi\)
\(492\) 4.43960 + 16.5688i 0.200153 + 0.746979i
\(493\) 1.97675 + 0.529668i 0.0890282 + 0.0238550i
\(494\) −19.0358 + 10.9903i −0.856460 + 0.494477i
\(495\) −5.42494 + 2.50291i −0.243833 + 0.112497i
\(496\) 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 \(-0.154871\pi\)
0.0370477 + 0.999313i \(0.488205\pi\)
\(500\) 26.3322 6.71285i 1.17761 0.300208i
\(501\) 4.40731 + 7.63369i 0.196904 + 0.341048i
\(502\) −14.1313 + 3.78647i −0.630710 + 0.168998i
\(503\) 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
\(507\) −2.58515 + 9.64790i −0.114810 + 0.428478i
\(508\) −2.54536 + 9.49942i −0.112932 + 0.421469i
\(509\) 8.44887 14.6339i 0.374489 0.648635i −0.615761 0.787933i \(-0.711151\pi\)
0.990250 + 0.139298i \(0.0444847\pi\)
\(510\) 5.35948 + 31.1342i 0.237322 + 1.37865i
\(511\) 0 0
\(512\) 20.5543 20.5543i 0.908382 0.908382i
\(513\) 5.81226 1.55739i 0.256617 0.0687604i
\(514\) 15.0161 + 26.0087i 0.662333 + 1.14720i
\(515\) −16.8820 + 14.0492i −0.743910 + 0.619083i
\(516\) −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
\(520\) 1.47331 + 3.19333i 0.0646089 + 0.140037i
\(521\) −6.82841 + 3.94238i −0.299158 + 0.172719i −0.642065 0.766651i \(-0.721922\pi\)
0.342907 + 0.939370i \(0.388589\pi\)
\(522\) −0.619890 0.166099i −0.0271319 0.00726996i
\(523\) 0.450757 + 1.68225i 0.0197102 + 0.0735595i 0.975080 0.221852i \(-0.0712101\pi\)
−0.955370 + 0.295411i \(0.904543\pi\)
\(524\) 22.7199 0.992524
\(525\) 0 0
\(526\) 54.1722 2.36202
\(527\) 12.6016 + 47.0299i 0.548935 + 2.04865i
\(528\) −7.62253 2.04245i −0.331728 0.0888863i
\(529\) −19.8651 + 11.4691i −0.863701 + 0.498658i
\(530\) −13.9156 30.1613i −0.604454 1.31012i
\(531\) 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
\(535\) 18.1644 15.1164i 0.785314 0.653539i
\(536\) −2.19838 3.80771i −0.0949557 0.164468i
\(537\) −1.25670 + 0.336732i −0.0542306 + 0.0145310i
\(538\) 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 0.195896 + 0.980625i \(0.437238\pi\)
−0.947194 + 0.320661i \(0.896095\pi\)
\(542\) 7.26843 27.1261i 0.312206 1.16517i
\(543\) −2.19615 + 8.19615i −0.0942459 + 0.351731i
\(544\) −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 \(0.213005\pi\)
\(548\) 24.9660 6.68961i 1.06649 0.285766i
\(549\) −2.76704 4.79266i −0.118095 0.204546i
\(550\) −2.22314 28.0319i −0.0947950 1.19529i
\(551\) 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
\(555\) 2.11175 0.974300i 0.0896387 0.0413567i
\(556\) 16.3953 9.46581i 0.695314 0.401440i
\(557\) 22.2863 + 5.97158i 0.944299 + 0.253024i 0.697941 0.716155i \(-0.254100\pi\)
0.246358 + 0.969179i \(0.420766\pi\)
\(558\) −3.95176 14.7482i −0.167291 0.624339i
\(559\) −0.748285 −0.0316491
\(560\) 0 0
\(561\) 17.9341 0.757180
\(562\) 7.38493 + 27.5609i 0.311514 + 1.16259i
\(563\) 32.4459 + 8.69386i 1.36743 + 0.366402i 0.866540 0.499107i \(-0.166339\pi\)
0.500892 + 0.865510i \(0.333005\pi\)
\(564\) −1.65768 + 0.957064i −0.0698011 + 0.0402997i
\(565\) −7.64478 + 20.7413i −0.321618 + 0.872593i
\(566\) 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 \(-0.335187\pi\)
−0.505034 + 0.863099i \(0.668520\pi\)
\(570\) −2.58297 + 28.2034i −0.108189 + 1.18131i
\(571\) 1.55769 + 2.69800i 0.0651874 + 0.112908i 0.896777 0.442483i \(-0.145902\pi\)
−0.831590 + 0.555390i \(0.812569\pi\)
\(572\) 10.8861 2.91693i 0.455173 0.121963i
\(573\) −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
\(577\) −10.8309 + 40.4214i −0.450896 + 1.68277i 0.248986 + 0.968507i \(0.419903\pi\)
−0.699882 + 0.714259i \(0.746764\pi\)
\(578\) 15.2832 57.0377i 0.635698 2.37246i
\(579\) −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
\(583\) −18.2139 + 4.88039i −0.754341 + 0.202125i
\(584\) −6.42160 11.1225i −0.265728 0.460254i
\(585\) −2.48228 2.98279i −0.102630 0.123323i
\(586\) 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
\(590\) 35.2786 + 13.0029i 1.45240 + 0.535322i
\(591\) −10.4197 + 6.01583i −0.428610 + 0.247458i
\(592\) 2.96720 + 0.795059i 0.121951 + 0.0326767i
\(593\) −5.55952 20.7484i −0.228302 0.852036i −0.981055 0.193732i \(-0.937941\pi\)
0.752752 0.658304i \(-0.228726\pi\)
\(594\) −5.62399 −0.230755
\(595\) 0 0
\(596\) −34.7217 −1.42225
\(597\) −0.842351 3.14370i −0.0344751 0.128663i
\(598\) −0.876657 0.234900i −0.0358492 0.00960576i
\(599\) 19.2930 11.1388i 0.788290 0.455119i −0.0510705 0.998695i \(-0.516263\pi\)
0.839360 + 0.543576i \(0.182930\pi\)
\(600\) 4.45594 + 0.823085i 0.181913 + 0.0336023i
\(601\) 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
\(605\) 8.59771 + 0.787409i 0.349547 + 0.0320127i
\(606\) −7.60877 13.1788i −0.309085 0.535351i
\(607\) −0.786867 + 0.210840i −0.0319380 + 0.00855775i −0.274753 0.961515i \(-0.588596\pi\)
0.242815 + 0.970073i \(0.421929\pi\)
\(608\) −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
\(612\) −4.22247 + 15.7585i −0.170683 + 0.636998i
\(613\) −6.02876 + 22.4996i −0.243499 + 0.908752i 0.730632 + 0.682771i \(0.239225\pi\)
−0.974132 + 0.225981i \(0.927441\pi\)
\(614\) 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 \(0.283590\pi\)
\(618\) −19.9703 + 5.35101i −0.803322 + 0.215249i
\(619\) −19.9420 34.5405i −0.801536 1.38830i −0.918605 0.395178i \(-0.870683\pi\)
0.117068 0.993124i \(-0.462650\pi\)
\(620\) 39.2592 + 3.59550i 1.57669 + 0.144399i
\(621\) 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
\(625\) −3.94059 24.6875i −0.157624 0.987499i
\(626\) 56.9479 32.8789i 2.27610 1.31410i
\(627\) 15.5296 + 4.16114i 0.620193 + 0.166180i
\(628\) −1.93703 7.22910i −0.0772960 0.288473i
\(629\) −6.98117 −0.278357
\(630\) 0 0
\(631\) −33.9725 −1.35242 −0.676211 0.736708i \(-0.736379\pi\)
−0.676211 + 0.736708i \(0.736379\pi\)
\(632\) 2.64987 + 9.88943i 0.105406 + 0.393381i
\(633\) −16.6630 4.46483i −0.662294 0.177461i
\(634\) 31.5962 18.2421i 1.25485 0.724486i
\(635\) 8.48933 + 3.12898i 0.336889 + 0.124170i
\(636\) 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
\(640\) 10.1299 + 12.1724i 0.400418 + 0.481156i
\(641\) 9.05563 + 15.6848i 0.357676 + 0.619513i 0.987572 0.157167i \(-0.0502359\pi\)
−0.629896 + 0.776679i \(0.716903\pi\)
\(642\) 21.4872 5.75748i 0.848032 0.227229i
\(643\) −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
\(647\) −4.73187 + 17.6596i −0.186029 + 0.694270i 0.808379 + 0.588663i \(0.200345\pi\)
−0.994408 + 0.105607i \(0.966321\pi\)
\(648\) 0.234558 0.875383i 0.00921432 0.0343883i
\(649\) 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
\(653\) 12.8398 3.44041i 0.502459 0.134634i 0.00131826 0.999999i \(-0.499580\pi\)
0.501141 + 0.865366i \(0.332914\pi\)
\(654\) 6.26575 + 10.8526i 0.245010 + 0.424370i
\(655\) 1.90630 20.8148i 0.0744852 0.813303i
\(656\) 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 \(0.943042\pi\)
\(660\) 5.02197 13.6253i 0.195480 0.530363i
\(661\) −24.6676 + 14.2418i −0.959458 + 0.553943i −0.896006 0.444042i \(-0.853544\pi\)
−0.0634519 + 0.997985i \(0.520211\pi\)
\(662\) −2.56805 0.688108i −0.0998102 0.0267441i
\(663\) 3.01489 + 11.2517i 0.117089 + 0.436980i
\(664\) −6.26651 −0.243188
\(665\) 0 0
\(666\) 2.18923 0.0848310
\(667\) 0.0196059 + 0.0731700i 0.000759142 + 0.00283316i
\(668\) −20.6944 5.54504i −0.800690 0.214544i
\(669\) 5.61413 3.24132i 0.217055 0.125317i
\(670\) −20.7342 + 9.56616i −0.801031 + 0.369573i
\(671\) 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
\(675\) −4.98435 + 0.395296i −0.191848 + 0.0152150i
\(676\) −12.1385 21.0245i −0.466864 0.808633i
\(677\) −1.63505 + 0.438111i −0.0628402 + 0.0168380i −0.290102 0.956996i \(-0.593689\pi\)
0.227262 + 0.973834i \(0.427023\pi\)
\(678\) −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
\(682\) 10.5586 39.4052i 0.404309 1.50890i
\(683\) 0.884144 3.29967i 0.0338308 0.126258i −0.946945 0.321395i \(-0.895848\pi\)
0.980776 + 0.195137i \(0.0625150\pi\)
\(684\) −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
\(688\) −1.23010 + 0.329605i −0.0468972 + 0.0125661i
\(689\) −6.12382 10.6068i −0.233299 0.404086i
\(690\) −0.898855 + 0.748027i −0.0342188 + 0.0284769i
\(691\) −36.0875 20.8351i −1.37283 0.792606i −0.381549 0.924348i \(-0.624609\pi\)
−0.991284 + 0.131743i \(0.957943\pi\)
\(692\) 16.4533 + 16.4533i 0.625459 + 0.625459i
\(693\) 0 0
\(694\) 19.4970i 0.740098i
\(695\) −7.29647 15.8147i −0.276771 0.599887i
\(696\) 0.239292 0.138155i 0.00907032 0.00523675i
\(697\) −45.7563 12.2604i −1.73314 0.464395i
\(698\) 1.50981 + 5.63470i 0.0571472 + 0.213276i
\(699\) 6.76767 0.255977
\(700\) 0 0
\(701\) 13.7870 0.520727 0.260364 0.965511i \(-0.416158\pi\)
0.260364 + 0.965511i \(0.416158\pi\)
\(702\) −0.945442 3.52844i −0.0356834 0.133172i
\(703\) −6.04516 1.61980i −0.227998 0.0610918i
\(704\) 25.4388 14.6871i 0.958760 0.553540i
\(705\) 0.737727 + 1.59899i 0.0277844 + 0.0602214i
\(706\) 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 \(-0.180001\pi\)
−0.0418795 + 0.999123i \(0.513335\pi\)
\(710\) −55.3837 + 46.0903i −2.07851 + 1.72974i
\(711\) −5.64863 9.78372i −0.211840 0.366918i
\(712\) −6.05110 + 1.62139i −0.226775 + 0.0607641i
\(713\) −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
\(717\) 4.18690 15.6257i 0.156363 0.583553i
\(718\) 5.08182 18.9656i 0.189652 0.707791i
\(719\) −14.9558 + 25.9043i −0.557758 + 0.966066i 0.439925 + 0.898035i \(0.355005\pi\)
−0.997683 + 0.0680313i \(0.978328\pi\)
\(720\) −5.39447 3.81000i −0.201040 0.141990i
\(721\) 0 0
\(722\) 25.6118 25.6118i 0.953171 0.953171i
\(723\) −10.9833 + 2.94297i −0.408473 + 0.109450i
\(724\) −10.3120 17.8608i −0.383241 0.663793i
\(725\) −1.15979 0.989351i −0.0430737 0.0367436i
\(726\) 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
\(730\) −60.5657 + 27.9433i −2.24164 + 1.03423i
\(731\) 2.50641 1.44708i 0.0927031 0.0535222i
\(732\) 12.9926 + 3.48135i 0.480219 + 0.128674i
\(733\) 1.41545 + 5.28252i 0.0522807 + 0.195114i 0.987127 0.159938i \(-0.0511296\pi\)
−0.934846 + 0.355053i \(0.884463\pi\)
\(734\) −38.7082 −1.42875
\(735\) 0 0
\(736\) −1.99493 −0.0735342
\(737\) 3.35499 + 12.5210i 0.123583 + 0.461216i
\(738\) 14.3488 + 3.84475i 0.528186 + 0.141527i
\(739\) 10.3694 5.98677i 0.381444 0.220227i −0.297002 0.954877i \(-0.595987\pi\)
0.678446 + 0.734650i \(0.262654\pi\)
\(740\) −1.95489 + 5.30387i −0.0718630 + 0.194974i
\(741\) 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
\(745\) −2.91330 + 31.8102i −0.106735 + 1.16544i
\(746\) −30.7733 53.3010i −1.12669 1.95149i
\(747\) 6.67906 1.78965i 0.244374 0.0654798i
\(748\) −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 −0.557756 0.830005i \(-0.688337\pi\)
0.997683 + 0.0680281i \(0.0216707\pi\)
\(752\) −0.602008 + 2.24673i −0.0219530 + 0.0819296i
\(753\) −1.79889 + 6.71356i −0.0655553 + 0.244656i
\(754\) 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 \(-0.0212733\pi\)
\(758\) 44.7453 11.9895i 1.62522 0.435477i
\(759\) 0.331920 + 0.574902i 0.0120479 + 0.0208676i
\(760\) −7.80004 9.37279i −0.282937 0.339987i
\(761\) 27.9728 + 16.1501i 1.01401 + 0.585440i 0.912364 0.409381i \(-0.134255\pi\)
0.101648 + 0.994820i \(0.467589\pi\)
\(762\) 6.02230 + 6.02230i 0.218165 + 0.218165i
\(763\) 0 0
\(764\) 4.71018i 0.170408i
\(765\) 14.0828 + 5.19061i 0.509165 + 0.187667i
\(766\) −1.00639 + 0.581037i −0.0363622 + 0.0209937i
\(767\) 13.3910 + 3.58810i 0.483520 + 0.129559i
\(768\) −1.83261 6.83939i −0.0661286 0.246795i
\(769\) −18.4310 −0.664640 −0.332320 0.943167i \(-0.607831\pi\)
−0.332320 + 0.943167i \(0.607831\pi\)
\(770\)