Properties

Label 750.2.l.b.107.4
Level $750$
Weight $2$
Character 750.107
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 107.4
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.b.743.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(1.37558 - 1.05251i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.784450 - 2.89562i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(1.37558 - 1.05251i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.784450 - 2.89562i) q^{9} +(-2.73512 + 0.888693i) q^{11} +(1.66004 + 0.494220i) q^{12} +(-1.97121 - 3.86872i) q^{13} +(0.202010 + 0.621723i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.75574 + 0.911620i) q^{17} +(-2.01354 + 2.22389i) q^{18} +(4.28299 - 5.89503i) q^{19} +(-1.12238 - 0.149340i) q^{21} +(2.84047 + 0.449885i) q^{22} +(-0.316926 + 0.622003i) q^{23} +(-1.25474 - 1.19400i) q^{24} +4.34197i q^{26} +(-1.96860 - 4.80881i) q^{27} +(0.102264 - 0.645670i) q^{28} +(2.60237 - 1.89073i) q^{29} +(-4.82678 - 3.50686i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.82702 + 4.10120i) q^{33} +(5.54227 + 1.80079i) q^{34} +(2.80370 - 1.06737i) q^{36} +(1.93977 - 0.988365i) q^{37} +(-6.49246 + 3.30807i) q^{38} +(-6.78343 - 3.24703i) q^{39} +(6.34331 + 2.06107i) q^{41} +(0.932251 + 0.642614i) q^{42} +(5.08751 - 5.08751i) q^{43} +(-2.32663 - 1.69040i) q^{44} +(0.564767 - 0.410327i) q^{46} +(0.474965 - 2.99881i) q^{47} +(0.575917 + 1.63350i) q^{48} -6.57265i q^{49} +(-6.95800 + 7.31198i) q^{51} +(1.97121 - 3.86872i) q^{52} +(-2.23241 - 0.353579i) q^{53} +(-0.429121 + 5.17840i) q^{54} +(-0.384246 + 0.528869i) q^{56} +(-0.312969 - 12.6170i) q^{57} +(-3.17710 + 0.503203i) q^{58} +(-2.66341 + 8.19714i) q^{59} +(2.77903 + 8.55298i) q^{61} +(2.70861 + 5.31594i) q^{62} +(-1.70111 + 0.975888i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(4.38080 - 2.37076i) q^{66} +(2.22497 + 14.0479i) q^{67} +(-4.12066 - 4.12066i) q^{68} +(0.218706 + 1.18918i) q^{69} +(-7.15246 - 9.84451i) q^{71} +(-2.98269 - 0.321816i) q^{72} +(-0.498794 - 0.254148i) q^{73} -2.17706 q^{74} +7.28665 q^{76} +(1.67510 + 0.853507i) q^{77} +(4.56996 + 5.97273i) q^{78} +(6.00067 + 8.25922i) q^{79} +(-7.76928 - 4.54294i) q^{81} +(-4.71623 - 4.71623i) q^{82} +(0.742236 + 4.68629i) q^{83} +(-0.538901 - 0.995806i) q^{84} +(-6.84269 + 2.22332i) q^{86} +(1.58976 - 5.33987i) q^{87} +(1.30562 + 2.56242i) q^{88} +(-1.78693 - 5.49959i) q^{89} +(-0.877122 + 2.69950i) q^{91} +(-0.689496 + 0.109205i) q^{92} +(-10.3306 + 0.256256i) q^{93} +(-1.78463 + 2.45633i) q^{94} +(0.228447 - 1.71692i) q^{96} +(-5.26300 - 0.833578i) q^{97} +(-2.98392 + 5.85628i) q^{98} +(0.427760 + 8.61700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 80q - 4q^{3} - 4q^{7} + 4q^{12} + 20q^{16} + 8q^{18} - 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} - 40q^{34} + 24q^{37} - 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} + 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} + 80q^{79} - 40q^{81} - 96q^{82} + 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.891007 0.453990i −0.630037 0.321020i
\(3\) 1.37558 1.05251i 0.794192 0.607666i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) −1.70348 + 0.313291i −0.695443 + 0.127901i
\(7\) −0.462249 0.462249i −0.174714 0.174714i 0.614333 0.789047i \(-0.289425\pi\)
−0.789047 + 0.614333i \(0.789425\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) 0.784450 2.89562i 0.261483 0.965208i
\(10\) 0 0
\(11\) −2.73512 + 0.888693i −0.824669 + 0.267951i −0.690798 0.723048i \(-0.742741\pi\)
−0.133871 + 0.990999i \(0.542741\pi\)
\(12\) 1.66004 + 0.494220i 0.479213 + 0.142669i
\(13\) −1.97121 3.86872i −0.546716 1.07299i −0.984741 0.174028i \(-0.944322\pi\)
0.438025 0.898963i \(-0.355678\pi\)
\(14\) 0.202010 + 0.621723i 0.0539895 + 0.166163i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −5.75574 + 0.911620i −1.39597 + 0.221100i −0.808668 0.588266i \(-0.799811\pi\)
−0.587305 + 0.809366i \(0.699811\pi\)
\(18\) −2.01354 + 2.22389i −0.474595 + 0.524175i
\(19\) 4.28299 5.89503i 0.982585 1.35241i 0.0471595 0.998887i \(-0.484983\pi\)
0.935425 0.353525i \(-0.115017\pi\)
\(20\) 0 0
\(21\) −1.12238 0.149340i −0.244924 0.0325886i
\(22\) 2.84047 + 0.449885i 0.605589 + 0.0959159i
\(23\) −0.316926 + 0.622003i −0.0660837 + 0.129697i −0.921685 0.387938i \(-0.873187\pi\)
0.855602 + 0.517635i \(0.173187\pi\)
\(24\) −1.25474 1.19400i −0.256123 0.243724i
\(25\) 0 0
\(26\) 4.34197i 0.851530i
\(27\) −1.96860 4.80881i −0.378856 0.925455i
\(28\) 0.102264 0.645670i 0.0193261 0.122020i
\(29\) 2.60237 1.89073i 0.483247 0.351100i −0.319334 0.947642i \(-0.603459\pi\)
0.802582 + 0.596542i \(0.203459\pi\)
\(30\) 0 0
\(31\) −4.82678 3.50686i −0.866915 0.629850i 0.0628427 0.998023i \(-0.479983\pi\)
−0.929757 + 0.368173i \(0.879983\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −2.82702 + 4.10120i −0.492121 + 0.713928i
\(34\) 5.54227 + 1.80079i 0.950491 + 0.308833i
\(35\) 0 0
\(36\) 2.80370 1.06737i 0.467283 0.177895i
\(37\) 1.93977 0.988365i 0.318897 0.162486i −0.287213 0.957867i \(-0.592729\pi\)
0.606110 + 0.795380i \(0.292729\pi\)
\(38\) −6.49246 + 3.30807i −1.05322 + 0.536640i
\(39\) −6.78343 3.24703i −1.08622 0.519940i
\(40\) 0 0
\(41\) 6.34331 + 2.06107i 0.990659 + 0.321884i 0.759127 0.650943i \(-0.225626\pi\)
0.231532 + 0.972827i \(0.425626\pi\)
\(42\) 0.932251 + 0.642614i 0.143849 + 0.0991574i
\(43\) 5.08751 5.08751i 0.775838 0.775838i −0.203282 0.979120i \(-0.565161\pi\)
0.979120 + 0.203282i \(0.0651609\pi\)
\(44\) −2.32663 1.69040i −0.350753 0.254837i
\(45\) 0 0
\(46\) 0.564767 0.410327i 0.0832703 0.0604994i
\(47\) 0.474965 2.99881i 0.0692808 0.437422i −0.928528 0.371262i \(-0.878925\pi\)
0.997809 0.0661599i \(-0.0210747\pi\)
\(48\) 0.575917 + 1.63350i 0.0831265 + 0.235775i
\(49\) 6.57265i 0.938950i
\(50\) 0 0
\(51\) −6.95800 + 7.31198i −0.974315 + 1.02388i
\(52\) 1.97121 3.86872i 0.273358 0.536495i
\(53\) −2.23241 0.353579i −0.306645 0.0485679i 0.00121543 0.999999i \(-0.499613\pi\)
−0.307861 + 0.951431i \(0.599613\pi\)
\(54\) −0.429121 + 5.17840i −0.0583960 + 0.704691i
\(55\) 0 0
\(56\) −0.384246 + 0.528869i −0.0513470 + 0.0706731i
\(57\) −0.312969 12.6170i −0.0414538 1.67116i
\(58\) −3.17710 + 0.503203i −0.417174 + 0.0660738i
\(59\) −2.66341 + 8.19714i −0.346747 + 1.06718i 0.613895 + 0.789388i \(0.289602\pi\)
−0.960642 + 0.277790i \(0.910398\pi\)
\(60\) 0 0
\(61\) 2.77903 + 8.55298i 0.355818 + 1.09510i 0.955533 + 0.294883i \(0.0952806\pi\)
−0.599715 + 0.800214i \(0.704719\pi\)
\(62\) 2.70861 + 5.31594i 0.343994 + 0.675126i
\(63\) −1.70111 + 0.975888i −0.214320 + 0.122950i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) 4.38080 2.37076i 0.539239 0.291820i
\(67\) 2.22497 + 14.0479i 0.271823 + 1.71622i 0.624964 + 0.780654i \(0.285114\pi\)
−0.353141 + 0.935570i \(0.614886\pi\)
\(68\) −4.12066 4.12066i −0.499703 0.499703i
\(69\) 0.218706 + 1.18918i 0.0263291 + 0.143161i
\(70\) 0 0
\(71\) −7.15246 9.84451i −0.848840 1.16833i −0.984117 0.177521i \(-0.943192\pi\)
0.135277 0.990808i \(-0.456808\pi\)
\(72\) −2.98269 0.321816i −0.351513 0.0379264i
\(73\) −0.498794 0.254148i −0.0583794 0.0297458i 0.424557 0.905401i \(-0.360430\pi\)
−0.482937 + 0.875655i \(0.660430\pi\)
\(74\) −2.17706 −0.253078
\(75\) 0 0
\(76\) 7.28665 0.835837
\(77\) 1.67510 + 0.853507i 0.190896 + 0.0972661i
\(78\) 4.56996 + 5.97273i 0.517446 + 0.676279i
\(79\) 6.00067 + 8.25922i 0.675128 + 0.929234i 0.999863 0.0165708i \(-0.00527490\pi\)
−0.324734 + 0.945805i \(0.605275\pi\)
\(80\) 0 0
\(81\) −7.76928 4.54294i −0.863253 0.504771i
\(82\) −4.71623 4.71623i −0.520820 0.520820i
\(83\) 0.742236 + 4.68629i 0.0814709 + 0.514387i 0.994349 + 0.106156i \(0.0338543\pi\)
−0.912879 + 0.408231i \(0.866146\pi\)
\(84\) −0.538901 0.995806i −0.0587989 0.108651i
\(85\) 0 0
\(86\) −6.84269 + 2.22332i −0.737866 + 0.239747i
\(87\) 1.58976 5.33987i 0.170440 0.572494i
\(88\) 1.30562 + 2.56242i 0.139179 + 0.273155i
\(89\) −1.78693 5.49959i −0.189414 0.582956i 0.810583 0.585624i \(-0.199151\pi\)
−0.999996 + 0.00266864i \(0.999151\pi\)
\(90\) 0 0
\(91\) −0.877122 + 2.69950i −0.0919473 + 0.282985i
\(92\) −0.689496 + 0.109205i −0.0718849 + 0.0113854i
\(93\) −10.3306 + 0.256256i −1.07124 + 0.0265725i
\(94\) −1.78463 + 2.45633i −0.184070 + 0.253351i
\(95\) 0 0
\(96\) 0.228447 1.71692i 0.0233158 0.175232i
\(97\) −5.26300 0.833578i −0.534377 0.0846370i −0.116587 0.993181i \(-0.537195\pi\)
−0.417790 + 0.908544i \(0.637195\pi\)
\(98\) −2.98392 + 5.85628i −0.301422 + 0.591573i
\(99\) 0.427760 + 8.61700i 0.0429915 + 0.866042i
\(100\) 0 0
\(101\) 12.5590i 1.24967i −0.780758 0.624833i \(-0.785167\pi\)
0.780758 0.624833i \(-0.214833\pi\)
\(102\) 9.51920 3.35615i 0.942541 0.332309i
\(103\) 0.958193 6.04979i 0.0944135 0.596104i −0.894437 0.447194i \(-0.852424\pi\)
0.988851 0.148910i \(-0.0475765\pi\)
\(104\) −3.51273 + 2.55215i −0.344451 + 0.250258i
\(105\) 0 0
\(106\) 1.82857 + 1.32854i 0.177607 + 0.129039i
\(107\) −0.411529 + 0.411529i −0.0397840 + 0.0397840i −0.726719 0.686935i \(-0.758956\pi\)
0.686935 + 0.726719i \(0.258956\pi\)
\(108\) 2.73330 4.41917i 0.263011 0.425235i
\(109\) −11.0499 3.59033i −1.05839 0.343891i −0.272433 0.962175i \(-0.587828\pi\)
−0.785955 + 0.618284i \(0.787828\pi\)
\(110\) 0 0
\(111\) 1.62806 3.40121i 0.154528 0.322828i
\(112\) 0.582467 0.296782i 0.0550380 0.0280433i
\(113\) 12.6233 6.43189i 1.18750 0.605061i 0.255249 0.966875i \(-0.417842\pi\)
0.932250 + 0.361814i \(0.117842\pi\)
\(114\) −5.44913 + 11.3839i −0.510358 + 1.06620i
\(115\) 0 0
\(116\) 3.05927 + 0.994016i 0.284046 + 0.0922921i
\(117\) −12.7487 + 2.67307i −1.17862 + 0.247126i
\(118\) 6.09455 6.09455i 0.561048 0.561048i
\(119\) 3.08198 + 2.23919i 0.282525 + 0.205266i
\(120\) 0 0
\(121\) −2.20810 + 1.60428i −0.200736 + 0.145844i
\(122\) 1.40684 8.88241i 0.127369 0.804176i
\(123\) 10.8950 3.84123i 0.982372 0.346352i
\(124\) 5.96622i 0.535783i
\(125\) 0 0
\(126\) 1.95874 0.0972348i 0.174499 0.00866236i
\(127\) −6.58036 + 12.9147i −0.583912 + 1.14599i 0.390369 + 0.920658i \(0.372347\pi\)
−0.974282 + 0.225334i \(0.927653\pi\)
\(128\) 0.987688 + 0.156434i 0.0873001 + 0.0138270i
\(129\) 1.64364 12.3529i 0.144714 1.08762i
\(130\) 0 0
\(131\) 3.23088 4.44693i 0.282283 0.388530i −0.644205 0.764853i \(-0.722812\pi\)
0.926489 + 0.376323i \(0.122812\pi\)
\(132\) −4.97962 + 0.123522i −0.433421 + 0.0107512i
\(133\) −4.70477 + 0.745163i −0.407956 + 0.0646138i
\(134\) 4.39515 13.5269i 0.379683 1.16854i
\(135\) 0 0
\(136\) 1.80079 + 5.54227i 0.154417 + 0.475246i
\(137\) 9.55034 + 18.7436i 0.815941 + 1.60137i 0.798858 + 0.601520i \(0.205438\pi\)
0.0170834 + 0.999854i \(0.494562\pi\)
\(138\) 0.345010 1.15886i 0.0293692 0.0986488i
\(139\) 11.0917 3.60392i 0.940788 0.305681i 0.201821 0.979422i \(-0.435314\pi\)
0.738967 + 0.673742i \(0.235314\pi\)
\(140\) 0 0
\(141\) −2.50292 4.62502i −0.210784 0.389497i
\(142\) 1.90357 + 12.0187i 0.159744 + 1.00858i
\(143\) 8.82961 + 8.82961i 0.738369 + 0.738369i
\(144\) 2.51149 + 1.64085i 0.209291 + 0.136738i
\(145\) 0 0
\(146\) 0.329048 + 0.452896i 0.0272322 + 0.0374819i
\(147\) −6.91778 9.04122i −0.570569 0.745707i
\(148\) 1.93977 + 0.988365i 0.159449 + 0.0812431i
\(149\) 10.0289 0.821602 0.410801 0.911725i \(-0.365249\pi\)
0.410801 + 0.911725i \(0.365249\pi\)
\(150\) 0 0
\(151\) 17.9175 1.45811 0.729054 0.684456i \(-0.239960\pi\)
0.729054 + 0.684456i \(0.239960\pi\)
\(152\) −6.49246 3.30807i −0.526608 0.268320i
\(153\) −1.87538 + 17.3816i −0.151616 + 1.40522i
\(154\) −1.10504 1.52096i −0.0890469 0.122562i
\(155\) 0 0
\(156\) −1.36030 7.39646i −0.108911 0.592191i
\(157\) 6.42991 + 6.42991i 0.513163 + 0.513163i 0.915494 0.402331i \(-0.131800\pi\)
−0.402331 + 0.915494i \(0.631800\pi\)
\(158\) −1.59703 10.0833i −0.127053 0.802181i
\(159\) −3.44301 + 1.86326i −0.273049 + 0.147766i
\(160\) 0 0
\(161\) 0.434019 0.141021i 0.0342055 0.0111140i
\(162\) 4.86002 + 7.57497i 0.381840 + 0.595146i
\(163\) 4.21139 + 8.26532i 0.329862 + 0.647390i 0.995060 0.0992767i \(-0.0316529\pi\)
−0.665198 + 0.746667i \(0.731653\pi\)
\(164\) 2.06107 + 6.34331i 0.160942 + 0.495329i
\(165\) 0 0
\(166\) 1.46619 4.51248i 0.113799 0.350237i
\(167\) −5.01819 + 0.794803i −0.388319 + 0.0615037i −0.347542 0.937665i \(-0.612983\pi\)
−0.0407774 + 0.999168i \(0.512983\pi\)
\(168\) 0.0280779 + 1.13193i 0.00216626 + 0.0873299i
\(169\) −3.44013 + 4.73493i −0.264625 + 0.364226i
\(170\) 0 0
\(171\) −13.7100 17.0263i −1.04843 1.30203i
\(172\) 7.10625 + 1.12552i 0.541846 + 0.0858200i
\(173\) 8.65954 16.9953i 0.658373 1.29213i −0.284404 0.958705i \(-0.591796\pi\)
0.942777 0.333425i \(-0.108204\pi\)
\(174\) −3.84073 + 4.03612i −0.291165 + 0.305978i
\(175\) 0 0
\(176\) 2.87587i 0.216777i
\(177\) 4.96383 + 14.0791i 0.373104 + 1.05825i
\(178\) −0.904600 + 5.71142i −0.0678026 + 0.428089i
\(179\) −3.24712 + 2.35917i −0.242701 + 0.176332i −0.702486 0.711698i \(-0.747927\pi\)
0.459785 + 0.888030i \(0.347927\pi\)
\(180\) 0 0
\(181\) 3.30770 + 2.40319i 0.245860 + 0.178628i 0.703890 0.710309i \(-0.251445\pi\)
−0.458030 + 0.888937i \(0.651445\pi\)
\(182\) 2.00707 2.00707i 0.148774 0.148774i
\(183\) 12.8249 + 8.84036i 0.948042 + 0.653498i
\(184\) 0.663923 + 0.215722i 0.0489451 + 0.0159032i
\(185\) 0 0
\(186\) 9.32099 + 4.46168i 0.683448 + 0.327146i
\(187\) 14.9325 7.60848i 1.09197 0.556387i
\(188\) 2.70527 1.37840i 0.197302 0.100530i
\(189\) −1.31288 + 3.13285i −0.0954983 + 0.227881i
\(190\) 0 0
\(191\) 11.5725 + 3.76012i 0.837354 + 0.272073i 0.696140 0.717906i \(-0.254899\pi\)
0.141214 + 0.989979i \(0.454899\pi\)
\(192\) −0.983013 + 1.42607i −0.0709428 + 0.102918i
\(193\) 9.01719 9.01719i 0.649071 0.649071i −0.303697 0.952769i \(-0.598221\pi\)
0.952769 + 0.303697i \(0.0982211\pi\)
\(194\) 4.31093 + 3.13208i 0.309507 + 0.224870i
\(195\) 0 0
\(196\) 5.31739 3.86331i 0.379813 0.275951i
\(197\) 0.0641446 0.404993i 0.00457012 0.0288546i −0.985298 0.170845i \(-0.945350\pi\)
0.989868 + 0.141990i \(0.0453502\pi\)
\(198\) 3.53090 7.87201i 0.250930 0.559439i
\(199\) 10.9949i 0.779406i 0.920941 + 0.389703i \(0.127422\pi\)
−0.920941 + 0.389703i \(0.872578\pi\)
\(200\) 0 0
\(201\) 17.8462 + 16.9822i 1.25877 + 1.19783i
\(202\) −5.70166 + 11.1901i −0.401168 + 0.787336i
\(203\) −2.07693 0.328953i −0.145772 0.0230880i
\(204\) −10.0053 1.33127i −0.700513 0.0932076i
\(205\) 0 0
\(206\) −3.60030 + 4.95539i −0.250845 + 0.345259i
\(207\) 1.55247 + 1.40563i 0.107904 + 0.0976980i
\(208\) 4.28851 0.679234i 0.297355 0.0470964i
\(209\) −6.47560 + 19.9298i −0.447927 + 1.37858i
\(210\) 0 0
\(211\) 6.64735 + 20.4585i 0.457623 + 1.40842i 0.868028 + 0.496515i \(0.165387\pi\)
−0.410406 + 0.911903i \(0.634613\pi\)
\(212\) −1.02613 2.01389i −0.0704747 0.138314i
\(213\) −20.2002 6.01391i −1.38410 0.412066i
\(214\) 0.553505 0.179845i 0.0378368 0.0122939i
\(215\) 0 0
\(216\) −4.44165 + 2.69662i −0.302216 + 0.183482i
\(217\) 0.610130 + 3.85221i 0.0414184 + 0.261505i
\(218\) 8.21555 + 8.21555i 0.556427 + 0.556427i
\(219\) −0.953626 + 0.175384i −0.0644400 + 0.0118513i
\(220\) 0 0
\(221\) 14.8726 + 20.4704i 1.00044 + 1.37699i
\(222\) −2.99472 + 2.29138i −0.200993 + 0.153787i
\(223\) −5.65554 2.88164i −0.378723 0.192969i 0.254258 0.967137i \(-0.418169\pi\)
−0.632981 + 0.774167i \(0.718169\pi\)
\(224\) −0.653718 −0.0436784
\(225\) 0 0
\(226\) −14.1675 −0.942405
\(227\) 12.5844 + 6.41208i 0.835257 + 0.425584i 0.818660 0.574278i \(-0.194717\pi\)
0.0165960 + 0.999862i \(0.494717\pi\)
\(228\) 10.0234 7.66927i 0.663815 0.507910i
\(229\) −8.94288 12.3088i −0.590962 0.813389i 0.403882 0.914811i \(-0.367661\pi\)
−0.994844 + 0.101422i \(0.967661\pi\)
\(230\) 0 0
\(231\) 3.20256 0.588991i 0.210713 0.0387528i
\(232\) −2.27455 2.27455i −0.149332 0.149332i
\(233\) −1.18798 7.50060i −0.0778271 0.491381i −0.995556 0.0941731i \(-0.969979\pi\)
0.917729 0.397208i \(-0.130021\pi\)
\(234\) 12.5727 + 3.40606i 0.821904 + 0.222661i
\(235\) 0 0
\(236\) −8.19714 + 2.66341i −0.533589 + 0.173373i
\(237\) 16.9473 + 5.04547i 1.10085 + 0.327738i
\(238\) −1.72949 3.39432i −0.112106 0.220021i
\(239\) 3.85885 + 11.8763i 0.249608 + 0.768215i 0.994844 + 0.101414i \(0.0323367\pi\)
−0.745236 + 0.666801i \(0.767663\pi\)
\(240\) 0 0
\(241\) 7.01360 21.5856i 0.451786 1.39045i −0.423082 0.906092i \(-0.639052\pi\)
0.874868 0.484362i \(-0.160948\pi\)
\(242\) 2.69576 0.426966i 0.173290 0.0274464i
\(243\) −15.4688 + 1.92805i −0.992322 + 0.123684i
\(244\) −5.28603 + 7.27560i −0.338403 + 0.465772i
\(245\) 0 0
\(246\) −11.4514 1.52368i −0.730116 0.0971465i
\(247\) −31.2489 4.94934i −1.98832 0.314919i
\(248\) −2.70861 + 5.31594i −0.171997 + 0.337563i
\(249\) 5.95337 + 5.66517i 0.377279 + 0.359015i
\(250\) 0 0
\(251\) 8.40399i 0.530455i 0.964186 + 0.265228i \(0.0854471\pi\)
−0.964186 + 0.265228i \(0.914553\pi\)
\(252\) −1.78940 0.802614i −0.112721 0.0505599i
\(253\) 0.314061 1.98290i 0.0197448 0.124664i
\(254\) 11.7263 8.51964i 0.735773 0.534570i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 21.2293 21.2293i 1.32425 1.32425i 0.413942 0.910303i \(-0.364152\pi\)
0.910303 0.413942i \(-0.135848\pi\)
\(258\) −7.07261 + 10.2604i −0.440321 + 0.638782i
\(259\) −1.35353 0.439788i −0.0841042 0.0273271i
\(260\) 0 0
\(261\) −3.43342 9.01866i −0.212523 0.558241i
\(262\) −4.89760 + 2.49545i −0.302575 + 0.154169i
\(263\) 3.75527 1.91341i 0.231560 0.117986i −0.334361 0.942445i \(-0.608521\pi\)
0.565921 + 0.824459i \(0.308521\pi\)
\(264\) 4.49296 + 2.15064i 0.276522 + 0.132363i
\(265\) 0 0
\(266\) 4.53028 + 1.47198i 0.277769 + 0.0902527i
\(267\) −8.24643 5.68438i −0.504673 0.347879i
\(268\) −10.0572 + 10.0572i −0.614340 + 0.614340i
\(269\) −16.4085 11.9215i −1.00044 0.726865i −0.0382610 0.999268i \(-0.512182\pi\)
−0.962183 + 0.272402i \(0.912182\pi\)
\(270\) 0 0
\(271\) −5.48031 + 3.98168i −0.332905 + 0.241870i −0.741662 0.670773i \(-0.765962\pi\)
0.408757 + 0.912643i \(0.365962\pi\)
\(272\) 0.911620 5.75574i 0.0552751 0.348993i
\(273\) 1.63470 + 4.63657i 0.0989365 + 0.280618i
\(274\) 21.0364i 1.27086i
\(275\) 0 0
\(276\) −0.833518 + 0.875921i −0.0501719 + 0.0527243i
\(277\) 11.1150 21.8145i 0.667837 1.31070i −0.269742 0.962933i \(-0.586938\pi\)
0.937579 0.347772i \(-0.113062\pi\)
\(278\) −11.5189 1.82442i −0.690861 0.109422i
\(279\) −13.9409 + 11.2256i −0.834620 + 0.672058i
\(280\) 0 0
\(281\) 11.8968 16.3745i 0.709702 0.976820i −0.290102 0.956996i \(-0.593689\pi\)
0.999803 0.0198246i \(-0.00631077\pi\)
\(282\) 0.130408 + 5.25722i 0.00776566 + 0.313063i
\(283\) 8.20158 1.29900i 0.487533 0.0772177i 0.0921715 0.995743i \(-0.470619\pi\)
0.395362 + 0.918525i \(0.370619\pi\)
\(284\) 3.76027 11.5729i 0.223131 0.686726i
\(285\) 0 0
\(286\) −3.85868 11.8758i −0.228168 0.702230i
\(287\) −1.97946 3.88491i −0.116844 0.229319i
\(288\) −1.49283 2.60221i −0.0879656 0.153336i
\(289\) 16.1295 5.24081i 0.948797 0.308283i
\(290\) 0 0
\(291\) −8.11704 + 4.39270i −0.475829 + 0.257505i
\(292\) −0.0875735 0.552918i −0.00512485 0.0323571i
\(293\) −1.20804 1.20804i −0.0705747 0.0705747i 0.670938 0.741513i \(-0.265891\pi\)
−0.741513 + 0.670938i \(0.765891\pi\)
\(294\) 2.05916 + 11.1964i 0.120092 + 0.652987i
\(295\) 0 0
\(296\) −1.27964 1.76128i −0.0743778 0.102372i
\(297\) 9.65789 + 11.4032i 0.560408 + 0.661679i
\(298\) −8.93584 4.55304i −0.517639 0.263750i
\(299\) 3.03109 0.175292
\(300\) 0 0
\(301\) −4.70339 −0.271099
\(302\) −15.9646 8.13439i −0.918661 0.468081i
\(303\) −13.2185 17.2759i −0.759380 0.992475i
\(304\) 4.28299 + 5.89503i 0.245646 + 0.338103i
\(305\) 0 0
\(306\) 9.56205 14.6357i 0.546626 0.836667i
\(307\) −4.52656 4.52656i −0.258344 0.258344i 0.566036 0.824380i \(-0.308476\pi\)
−0.824380 + 0.566036i \(0.808476\pi\)
\(308\) 0.294098 + 1.85686i 0.0167578 + 0.105805i
\(309\) −5.04939 9.33049i −0.287250 0.530793i
\(310\) 0 0
\(311\) −32.9364 + 10.7017i −1.86765 + 0.606838i −0.875274 + 0.483628i \(0.839319\pi\)
−0.992381 + 0.123210i \(0.960681\pi\)
\(312\) −2.14589 + 7.20786i −0.121487 + 0.408065i
\(313\) 11.8701 + 23.2965i 0.670940 + 1.31679i 0.935808 + 0.352509i \(0.114671\pi\)
−0.264869 + 0.964285i \(0.585329\pi\)
\(314\) −2.80998 8.64821i −0.158576 0.488047i
\(315\) 0 0
\(316\) −3.15474 + 9.70929i −0.177468 + 0.546190i
\(317\) −13.4990 + 2.13804i −0.758181 + 0.120084i −0.523544 0.851999i \(-0.675390\pi\)
−0.234638 + 0.972083i \(0.575390\pi\)
\(318\) 3.91365 0.0970796i 0.219466 0.00544396i
\(319\) −5.43750 + 7.48407i −0.304441 + 0.419028i
\(320\) 0 0
\(321\) −0.132954 + 0.999229i −0.00742075 + 0.0557715i
\(322\) −0.450736 0.0713896i −0.0251185 0.00397838i
\(323\) −19.2777 + 37.8347i −1.07264 + 2.10518i
\(324\) −0.891349 8.95575i −0.0495194 0.497542i
\(325\) 0 0
\(326\) 9.27639i 0.513772i
\(327\) −18.9789 + 6.69132i −1.04953 + 0.370031i
\(328\) 1.04338 6.58764i 0.0576110 0.363741i
\(329\) −1.60575 + 1.16664i −0.0885278 + 0.0643192i
\(330\) 0 0
\(331\) −8.55071 6.21245i −0.469989 0.341467i 0.327448 0.944869i \(-0.393811\pi\)
−0.797437 + 0.603402i \(0.793811\pi\)
\(332\) −3.35501 + 3.35501i −0.184130 + 0.184130i
\(333\) −1.34028 6.39218i −0.0734467 0.350289i
\(334\) 4.83207 + 1.57004i 0.264399 + 0.0859085i
\(335\) 0 0
\(336\) 0.488866 1.02130i 0.0266698 0.0557165i
\(337\) 28.0951 14.3152i 1.53044 0.779796i 0.532652 0.846334i \(-0.321195\pi\)
0.997784 + 0.0665380i \(0.0211954\pi\)
\(338\) 5.21479 2.65707i 0.283647 0.144526i
\(339\) 10.5947 22.1337i 0.575428 1.20214i
\(340\) 0 0
\(341\) 16.3183 + 5.30214i 0.883686 + 0.287127i
\(342\) 4.48593 + 21.3947i 0.242571 + 1.15689i
\(343\) −6.27394 + 6.27394i −0.338761 + 0.338761i
\(344\) −5.82074 4.22901i −0.313833 0.228013i
\(345\) 0 0
\(346\) −15.4314 + 11.2116i −0.829598 + 0.602738i
\(347\) −2.04407 + 12.9057i −0.109731 + 0.692816i 0.870083 + 0.492905i \(0.164065\pi\)
−0.979814 + 0.199911i \(0.935935\pi\)
\(348\) 5.25448 1.85256i 0.281670 0.0993074i
\(349\) 30.4326i 1.62902i 0.580151 + 0.814509i \(0.302993\pi\)
−0.580151 + 0.814509i \(0.697007\pi\)
\(350\) 0 0
\(351\) −14.7234 + 17.0951i −0.785878 + 0.912471i
\(352\) −1.30562 + 2.56242i −0.0695897 + 0.136577i
\(353\) −2.87776 0.455793i −0.153168 0.0242594i 0.0793796 0.996844i \(-0.474706\pi\)
−0.232547 + 0.972585i \(0.574706\pi\)
\(354\) 1.96898 14.7981i 0.104650 0.786511i
\(355\) 0 0
\(356\) 3.39893 4.67823i 0.180143 0.247946i
\(357\) 6.59628 0.163624i 0.349112 0.00865988i
\(358\) 3.96424 0.627874i 0.209517 0.0331842i
\(359\) 2.44510 7.52523i 0.129047 0.397167i −0.865569 0.500789i \(-0.833043\pi\)
0.994617 + 0.103622i \(0.0330433\pi\)
\(360\) 0 0
\(361\) −10.5360 32.4266i −0.554528 1.70666i
\(362\) −1.85616 3.64292i −0.0975577 0.191468i
\(363\) −1.34890 + 4.53086i −0.0707991 + 0.237809i
\(364\) −2.69950 + 0.877122i −0.141492 + 0.0459737i
\(365\) 0 0
\(366\) −7.41360 13.6992i −0.387515 0.716068i
\(367\) −3.44380 21.7433i −0.179765 1.13499i −0.898262 0.439460i \(-0.855170\pi\)
0.718497 0.695530i \(-0.244830\pi\)
\(368\) −0.493624 0.493624i −0.0257319 0.0257319i
\(369\) 10.9441 16.7510i 0.569726 0.872024i
\(370\) 0 0
\(371\) 0.868488 + 1.19537i 0.0450897 + 0.0620606i
\(372\) −6.27950 8.20703i −0.325577 0.425515i
\(373\) −19.0344 9.69853i −0.985566 0.502171i −0.114545 0.993418i \(-0.536541\pi\)
−0.871020 + 0.491247i \(0.836541\pi\)
\(374\) −16.7591 −0.866593
\(375\) 0 0
\(376\) −3.03619 −0.156580
\(377\) −12.4445 6.34081i −0.640926 0.326568i
\(378\) 2.59207 2.19535i 0.133322 0.112917i
\(379\) −0.581554 0.800441i −0.0298724 0.0411159i 0.793820 0.608153i \(-0.208089\pi\)
−0.823692 + 0.567038i \(0.808089\pi\)
\(380\) 0 0
\(381\) 4.54100 + 24.6911i 0.232642 + 1.26496i
\(382\) −8.60408 8.60408i −0.440223 0.440223i
\(383\) −1.97847 12.4916i −0.101095 0.638289i −0.985253 0.171102i \(-0.945267\pi\)
0.884158 0.467187i \(-0.154733\pi\)
\(384\) 1.52329 0.824362i 0.0777353 0.0420681i
\(385\) 0 0
\(386\) −12.1281 + 3.94066i −0.617304 + 0.200574i
\(387\) −10.7406 18.7224i −0.545976 0.951714i
\(388\) −2.41914 4.74782i −0.122813 0.241034i
\(389\) −8.45598 26.0248i −0.428735 1.31951i −0.899372 0.437185i \(-0.855976\pi\)
0.470636 0.882327i \(-0.344024\pi\)
\(390\) 0 0
\(391\) 1.25712 3.86900i 0.0635751 0.195664i
\(392\) −6.49173 + 1.02819i −0.327882 + 0.0519314i
\(393\) −0.236089 9.51764i −0.0119091 0.480102i
\(394\) −0.241016 + 0.331731i −0.0121422 + 0.0167123i
\(395\) 0 0
\(396\) −6.71987 + 5.41101i −0.337686 + 0.271914i
\(397\) −3.51235 0.556301i −0.176280 0.0279199i 0.0676706 0.997708i \(-0.478443\pi\)
−0.243950 + 0.969788i \(0.578443\pi\)
\(398\) 4.99157 9.79650i 0.250205 0.491054i
\(399\) −5.68751 + 5.97685i −0.284732 + 0.299217i
\(400\) 0 0
\(401\) 16.6499i 0.831458i −0.909489 0.415729i \(-0.863527\pi\)
0.909489 0.415729i \(-0.136473\pi\)
\(402\) −8.19128 23.2333i −0.408544 1.15877i
\(403\) −4.05246 + 25.5862i −0.201867 + 1.27454i
\(404\) 10.1604 7.38199i 0.505501 0.367268i
\(405\) 0 0
\(406\) 1.70122 + 1.23601i 0.0844299 + 0.0613419i
\(407\) −4.42716 + 4.42716i −0.219446 + 0.219446i
\(408\) 8.31043 + 5.72849i 0.411427 + 0.283603i
\(409\) −4.09420 1.33029i −0.202445 0.0657784i 0.206039 0.978544i \(-0.433943\pi\)
−0.408484 + 0.912765i \(0.633943\pi\)
\(410\) 0 0
\(411\) 32.8651 + 15.7315i 1.62112 + 0.775979i
\(412\) 5.45760 2.78078i 0.268876 0.136999i
\(413\) 5.02028 2.55796i 0.247032 0.125869i
\(414\) −0.745122 1.95723i −0.0366207 0.0961928i
\(415\) 0 0
\(416\) −4.12946 1.34174i −0.202463 0.0657843i
\(417\) 11.4644 16.6316i 0.561415 0.814454i
\(418\) 14.8178 14.8178i 0.724761 0.724761i
\(419\) −5.84455 4.24631i −0.285525 0.207446i 0.435799 0.900044i \(-0.356466\pi\)
−0.721324 + 0.692598i \(0.756466\pi\)
\(420\) 0 0
\(421\) −11.7630 + 8.54631i −0.573293 + 0.416521i −0.836300 0.548272i \(-0.815286\pi\)
0.263007 + 0.964794i \(0.415286\pi\)
\(422\) 3.36511 21.2464i 0.163811 1.03426i
\(423\) −8.31084 3.72774i −0.404087 0.181249i
\(424\) 2.26024i 0.109767i
\(425\) 0 0
\(426\) 15.2683 + 14.5291i 0.739750 + 0.703939i
\(427\) 2.66900 5.23821i 0.129162 0.253495i
\(428\) −0.574824 0.0910432i −0.0277852 0.00440074i
\(429\) 21.4391 + 2.85260i 1.03509 + 0.137725i
\(430\) 0 0
\(431\) −2.43967 + 3.35792i −0.117515 + 0.161745i −0.863722 0.503968i \(-0.831873\pi\)
0.746207 + 0.665714i \(0.231873\pi\)
\(432\) 5.18178 0.386242i 0.249308 0.0185831i
\(433\) −28.8682 + 4.57227i −1.38732 + 0.219729i −0.805020 0.593248i \(-0.797846\pi\)
−0.582296 + 0.812977i \(0.697846\pi\)
\(434\) 1.20524 3.70934i 0.0578532 0.178054i
\(435\) 0 0
\(436\) −3.59033 11.0499i −0.171945 0.529194i
\(437\) 2.30933 + 4.53232i 0.110470 + 0.216810i
\(438\) 0.929309 + 0.276669i 0.0444041 + 0.0132198i
\(439\) 10.7432 3.49067i 0.512744 0.166601i −0.0412056 0.999151i \(-0.513120\pi\)
0.553950 + 0.832550i \(0.313120\pi\)
\(440\) 0 0
\(441\) −19.0319 5.15592i −0.906282 0.245520i
\(442\) −3.95823 24.9913i −0.188274 1.18871i
\(443\) 12.3286 + 12.3286i 0.585749 + 0.585749i 0.936477 0.350728i \(-0.114066\pi\)
−0.350728 + 0.936477i \(0.614066\pi\)
\(444\) 3.70858 0.682054i 0.176001 0.0323689i
\(445\) 0 0
\(446\) 3.73089 + 5.13513i 0.176663 + 0.243155i
\(447\) 13.7956 10.5555i 0.652510 0.499260i
\(448\) 0.582467 + 0.296782i 0.0275190 + 0.0140216i
\(449\) −11.4060 −0.538284 −0.269142 0.963101i \(-0.586740\pi\)
−0.269142 + 0.963101i \(0.586740\pi\)
\(450\) 0 0
\(451\) −19.1813 −0.903214
\(452\) 12.6233 + 6.43189i 0.593750 + 0.302531i
\(453\) 24.6470 18.8584i 1.15802 0.886043i
\(454\) −8.30177 11.4264i −0.389621 0.536268i
\(455\) 0 0
\(456\) −12.4127 + 2.28285i −0.581277 + 0.106904i
\(457\) 4.54539 + 4.54539i 0.212624 + 0.212624i 0.805381 0.592757i \(-0.201961\pi\)
−0.592757 + 0.805381i \(0.701961\pi\)
\(458\) 2.38008 + 15.0272i 0.111214 + 0.702176i
\(459\) 15.7145 + 25.8836i 0.733492 + 1.20814i
\(460\) 0 0
\(461\) −18.3653 + 5.96726i −0.855359 + 0.277923i −0.703689 0.710508i \(-0.748465\pi\)
−0.151670 + 0.988431i \(0.548465\pi\)
\(462\) −3.12090 0.929138i −0.145197 0.0432274i
\(463\) −2.03171 3.98746i −0.0944216 0.185313i 0.838965 0.544186i \(-0.183161\pi\)
−0.933387 + 0.358873i \(0.883161\pi\)
\(464\) 0.994016 + 3.05927i 0.0461460 + 0.142023i
\(465\) 0 0
\(466\) −2.34671 + 7.22242i −0.108709 + 0.334572i
\(467\) 1.74215 0.275929i 0.0806170 0.0127685i −0.115996 0.993250i \(-0.537006\pi\)
0.196613 + 0.980481i \(0.437006\pi\)
\(468\) −9.65605 8.74271i −0.446351 0.404132i
\(469\) 5.46513 7.52211i 0.252356 0.347339i
\(470\) 0 0
\(471\) 15.6124 + 2.07733i 0.719382 + 0.0957183i
\(472\) 8.51287 + 1.34831i 0.391837 + 0.0620609i
\(473\) −9.39370 + 18.4362i −0.431923 + 0.847696i
\(474\) −12.8096 12.1895i −0.588363 0.559881i
\(475\) 0 0
\(476\) 3.80954i 0.174610i
\(477\) −2.77505 + 6.18686i −0.127061 + 0.283277i
\(478\) 1.95347 12.3338i 0.0893498 0.564133i
\(479\) −13.7743 + 10.0076i −0.629363 + 0.457259i −0.856179 0.516679i \(-0.827168\pi\)
0.226817 + 0.973937i \(0.427168\pi\)
\(480\) 0 0
\(481\) −7.64742 5.55617i −0.348692 0.253340i
\(482\) −16.0488 + 16.0488i −0.731005 + 0.731005i
\(483\) 0.448602 0.650795i 0.0204121 0.0296122i
\(484\) −2.59578 0.843419i −0.117990 0.0383372i
\(485\) 0 0
\(486\) 14.6581 + 5.30477i 0.664904 + 0.240629i
\(487\) −25.0891 + 12.7835i −1.13690 + 0.579277i −0.918043 0.396481i \(-0.870231\pi\)
−0.218852 + 0.975758i \(0.570231\pi\)
\(488\) 8.01294 4.08280i 0.362729 0.184820i
\(489\) 14.4924 + 6.93710i 0.655371 + 0.313706i
\(490\) 0 0
\(491\) −8.69557 2.82536i −0.392426 0.127507i 0.106156 0.994349i \(-0.466146\pi\)
−0.498582 + 0.866843i \(0.666146\pi\)
\(492\) 9.51156 + 6.55645i 0.428814 + 0.295588i
\(493\) −13.2549 + 13.2549i −0.596972 + 0.596972i
\(494\) 25.5960 + 18.5966i 1.15162 + 0.836701i
\(495\) 0 0
\(496\) 4.82678 3.50686i 0.216729 0.157463i
\(497\) −1.24440 + 7.85683i −0.0558189 + 0.352427i
\(498\) −2.73256 7.75047i −0.122449 0.347307i
\(499\) 12.9235i 0.578536i −0.957248 0.289268i \(-0.906588\pi\)
0.957248 0.289268i \(-0.0934119\pi\)
\(500\) 0 0
\(501\) −6.06639 + 6.37500i −0.271026 + 0.284814i
\(502\) 3.81533 7.48801i 0.170287 0.334206i
\(503\) −22.2567 3.52512i −0.992379 0.157177i −0.360928 0.932594i \(-0.617540\pi\)
−0.631450 + 0.775416i \(0.717540\pi\)
\(504\) 1.22999 + 1.52750i 0.0547879 + 0.0680404i
\(505\) 0 0
\(506\) −1.18005 + 1.62420i −0.0524595 + 0.0722044i
\(507\) 0.251380 + 10.1341i 0.0111642 + 0.450069i
\(508\) −14.3160 + 2.26744i −0.635171 + 0.100601i
\(509\) 1.15005 3.53949i 0.0509750 0.156885i −0.922329 0.386407i \(-0.873716\pi\)
0.973304 + 0.229522i \(0.0737162\pi\)
\(510\) 0 0
\(511\) 0.113087 + 0.348047i 0.00500268 + 0.0153967i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) −36.7795 8.99114i −1.62386 0.396969i
\(514\) −28.5533 + 9.27753i −1.25943 + 0.409214i
\(515\) 0 0
\(516\) 10.9598 5.93114i 0.482480 0.261104i
\(517\) 1.36594 + 8.62420i 0.0600739 + 0.379292i
\(518\) 1.00634 + 1.00634i 0.0442162 + 0.0442162i
\(519\) −5.97581 32.4927i −0.262309 1.42627i
\(520\) 0 0
\(521\) 25.0327 + 34.4546i 1.09670 + 1.50948i 0.839683 + 0.543077i \(0.182741\pi\)
0.257021 + 0.966406i \(0.417259\pi\)
\(522\) −1.03519 + 9.59442i −0.0453089 + 0.419937i
\(523\) 19.8847 + 10.1317i 0.869495 + 0.443030i 0.831028 0.556230i \(-0.187753\pi\)
0.0384667 + 0.999260i \(0.487753\pi\)
\(524\) 5.49670 0.240125
\(525\) 0 0
\(526\) −4.21464 −0.183767
\(527\) 30.9786 + 15.7844i 1.34945 + 0.687579i
\(528\) −3.02688 3.95600i −0.131728 0.172163i
\(529\) 13.2326 + 18.2131i 0.575331 + 0.791875i
\(530\) 0 0
\(531\) 21.6465 + 14.1425i 0.939380 + 0.613732i
\(532\) −3.36825 3.36825i −0.146032 0.146032i
\(533\) −4.53032 28.6033i −0.196230 1.23895i
\(534\) 4.76697 + 8.80862i 0.206287 + 0.381186i
\(535\) 0 0
\(536\) 13.5269 4.39515i 0.584272 0.189842i
\(537\) −1.98363 + 6.66285i −0.0855999 + 0.287523i
\(538\) 9.20785 + 18.0714i 0.396979 + 0.779114i
\(539\) 5.84107 + 17.9770i 0.251593 + 0.774323i
\(540\) 0 0
\(541\) 0.576378 1.77391i 0.0247804 0.0762663i −0.937902 0.346902i \(-0.887234\pi\)
0.962682 + 0.270635i \(0.0872338\pi\)
\(542\) 6.69064 1.05969i 0.287387 0.0455177i
\(543\) 7.07940 0.175607i 0.303806 0.00753604i
\(544\) −3.42531 + 4.71454i −0.146859 + 0.202134i
\(545\) 0 0
\(546\) 0.648429 4.87335i 0.0277502 0.208560i
\(547\) 24.0199 + 3.80438i 1.02702 + 0.162663i 0.647138 0.762373i \(-0.275966\pi\)
0.379878 + 0.925036i \(0.375966\pi\)
\(548\) −9.55034 + 18.7436i −0.407970 + 0.800687i
\(549\) 26.9462 1.33765i 1.15004 0.0570894i
\(550\) 0 0
\(551\) 23.4390i 0.998535i
\(552\) 1.14033 0.402042i 0.0485357 0.0171121i
\(553\) 1.04401 6.59162i 0.0443958 0.280304i
\(554\) −19.8071 + 14.3907i −0.841524 + 0.611403i
\(555\) 0 0
\(556\) 9.43519 + 6.85506i 0.400141 + 0.290720i
\(557\) −18.2820 + 18.2820i −0.774632 + 0.774632i −0.978912 0.204281i \(-0.934515\pi\)
0.204281 + 0.978912i \(0.434515\pi\)
\(558\) 17.5177 3.67302i 0.741585 0.155491i
\(559\) −29.7107 9.65360i −1.25663 0.408304i
\(560\) 0 0
\(561\) 12.5328 26.1826i 0.529137 1.10543i
\(562\) −18.0340 + 9.18876i −0.760717 + 0.387604i
\(563\) 0.869364 0.442963i 0.0366393 0.0186687i −0.435575 0.900153i \(-0.643455\pi\)
0.472214 + 0.881484i \(0.343455\pi\)
\(564\) 2.27053 4.74342i 0.0956068 0.199734i
\(565\) 0 0
\(566\) −7.89740 2.56602i −0.331952 0.107858i
\(567\) 1.49137 + 5.69131i 0.0626316 + 0.239012i
\(568\) −8.60442 + 8.60442i −0.361033 + 0.361033i
\(569\) 22.6112 + 16.4280i 0.947909 + 0.688696i 0.950311 0.311301i \(-0.100765\pi\)
−0.00240243 + 0.999997i \(0.500765\pi\)
\(570\) 0 0
\(571\) −4.29121 + 3.11775i −0.179582 + 0.130474i −0.673945 0.738782i \(-0.735401\pi\)
0.494363 + 0.869256i \(0.335401\pi\)
\(572\) −1.95339 + 12.3332i −0.0816753 + 0.515678i
\(573\) 19.8764 7.00776i 0.830349 0.292754i
\(574\) 4.36014i 0.181989i
\(575\) 0 0
\(576\) 0.148741 + 2.99631i 0.00619754 + 0.124846i
\(577\) 3.71857 7.29810i 0.154806 0.303824i −0.800558 0.599255i \(-0.795463\pi\)
0.955364 + 0.295432i \(0.0954634\pi\)
\(578\) −16.7508 2.65307i −0.696742 0.110353i
\(579\) 2.91321 21.8946i 0.121069 0.909907i
\(580\) 0 0
\(581\) 1.82313 2.50933i 0.0756364 0.104105i
\(582\) 9.22658 0.228869i 0.382454 0.00948694i
\(583\) 6.42013 1.01685i 0.265895 0.0421136i
\(584\) −0.172991 + 0.532411i −0.00715841 + 0.0220313i
\(585\) 0 0
\(586\) 0.527935 + 1.62482i 0.0218088 + 0.0671205i
\(587\) −15.9900 31.3821i −0.659978 1.29528i −0.941917 0.335847i \(-0.890977\pi\)
0.281939 0.959432i \(-0.409023\pi\)
\(588\) 3.24833 10.9109i 0.133959 0.449958i
\(589\) −41.3460 + 13.4341i −1.70363 + 0.553544i
\(590\) 0 0
\(591\) −0.338023 0.624614i −0.0139044 0.0256932i
\(592\) 0.340567 + 2.15026i 0.0139972 + 0.0883750i
\(593\) −2.52481 2.52481i −0.103681 0.103681i 0.653363 0.757045i \(-0.273357\pi\)
−0.757045 + 0.653363i \(0.773357\pi\)
\(594\) −3.42831 14.5449i −0.140665 0.596784i
\(595\) 0 0
\(596\) 5.89486 + 8.11358i 0.241463 + 0.332345i
\(597\) 11.5722 + 15.1243i 0.473619 + 0.618998i
\(598\) −2.70072 1.37608i −0.110441 0.0562723i
\(599\) 39.4333 1.61120 0.805600 0.592460i \(-0.201843\pi\)
0.805600 + 0.592460i \(0.201843\pi\)
\(600\) 0 0
\(601\) 28.0191 1.14292 0.571462 0.820629i \(-0.306376\pi\)
0.571462 + 0.820629i \(0.306376\pi\)
\(602\) 4.19075 + 2.13529i 0.170802 + 0.0870281i
\(603\) 42.4228 + 4.57720i 1.72759 + 0.186398i
\(604\) 10.5317 + 14.4956i 0.428527 + 0.589817i
\(605\) 0 0
\(606\) 3.93462 + 21.3940i 0.159833 + 0.869072i
\(607\) 3.59236 + 3.59236i 0.145809 + 0.145809i 0.776243 0.630434i \(-0.217123\pi\)
−0.630434 + 0.776243i \(0.717123\pi\)
\(608\) −1.13988 7.19694i −0.0462284 0.291875i
\(609\) −3.20321 + 1.73348i −0.129801 + 0.0702443i
\(610\) 0 0
\(611\) −12.5378 + 4.07379i −0.507226 + 0.164808i
\(612\) −15.1643 + 8.69942i −0.612981 + 0.351653i
\(613\) −6.96688 13.6733i −0.281390 0.552258i 0.706445 0.707768i \(-0.250298\pi\)
−0.987834 + 0.155510i \(0.950298\pi\)
\(614\) 1.97818 + 6.08821i 0.0798328 + 0.245700i
\(615\) 0 0
\(616\) 0.580955 1.78800i 0.0234074 0.0720404i
\(617\) 7.10625 1.12552i 0.286087 0.0453117i −0.0117417 0.999931i \(-0.503738\pi\)
0.297829 + 0.954619i \(0.403738\pi\)
\(618\) 0.263084 + 10.6059i 0.0105828 + 0.426632i
\(619\) −7.42133 + 10.2146i −0.298288 + 0.410559i −0.931684 0.363269i \(-0.881661\pi\)
0.633396 + 0.773828i \(0.281661\pi\)
\(620\) 0 0
\(621\) 3.61499 + 0.299565i 0.145065 + 0.0120211i
\(622\) 34.2051 + 5.41755i 1.37150 + 0.217224i
\(623\) −1.71618 + 3.36818i −0.0687571 + 0.134943i
\(624\) 5.18430 5.44804i 0.207538 0.218096i
\(625\) 0 0
\(626\) 26.1462i 1.04501i
\(627\) 12.0686 + 34.2308i 0.481975 + 1.36704i
\(628\) −1.42250 + 8.98132i −0.0567640 + 0.358394i
\(629\) −10.2638 + 7.45711i −0.409246 + 0.297334i
\(630\) 0 0
\(631\) −2.09574 1.52265i −0.0834301 0.0606155i 0.545288 0.838249i \(-0.316420\pi\)
−0.628718 + 0.777633i \(0.716420\pi\)
\(632\) 7.21882 7.21882i 0.287149 0.287149i
\(633\) 30.6767 + 21.1459i 1.21929 + 0.840473i
\(634\) 12.9984 + 4.22343i 0.516231 + 0.167734i
\(635\) 0 0
\(636\) −3.53116 1.69026i −0.140019 0.0670231i
\(637\) −25.4278 + 12.9561i −1.00748 + 0.513339i
\(638\) 8.24255 4.19979i 0.326326 0.166271i
\(639\) −34.1167 + 12.9883i −1.34964 + 0.513809i
\(640\) 0 0
\(641\) 3.49095 + 1.13428i 0.137884 + 0.0448012i 0.377146 0.926154i \(-0.376905\pi\)
−0.239262 + 0.970955i \(0.576905\pi\)
\(642\) 0.572103 0.829960i 0.0225791 0.0327559i
\(643\) −9.94703 + 9.94703i −0.392273 + 0.392273i −0.875497 0.483224i \(-0.839466\pi\)
0.483224 + 0.875497i \(0.339466\pi\)
\(644\) 0.369198 + 0.268238i 0.0145485 + 0.0105701i
\(645\) 0 0
\(646\) 34.3532 24.9591i 1.35161 0.982001i
\(647\) −0.617590 + 3.89931i −0.0242800 + 0.153298i −0.996850 0.0793138i \(-0.974727\pi\)
0.972570 + 0.232612i \(0.0747271\pi\)
\(648\) −3.27163 + 8.38430i −0.128522 + 0.329366i
\(649\) 24.7871i 0.972979i
\(650\) 0 0
\(651\) 4.89377 + 4.65686i 0.191802 + 0.182517i
\(652\) −4.21139 + 8.26532i −0.164931 + 0.323695i
\(653\) 14.3859 + 2.27850i 0.562962 + 0.0891644i 0.431428 0.902147i \(-0.358010\pi\)
0.131534 + 0.991312i \(0.458010\pi\)
\(654\) 19.9481 + 2.65422i 0.780033 + 0.103788i
\(655\) 0 0
\(656\) −3.92038 + 5.39594i −0.153065 + 0.210676i
\(657\) −1.12720 + 1.24495i −0.0439761 + 0.0485703i
\(658\) 1.96038 0.310493i 0.0764235 0.0121043i
\(659\) −4.21526 + 12.9732i −0.164203 + 0.505365i −0.998977 0.0452283i \(-0.985598\pi\)
0.834774 + 0.550593i \(0.185598\pi\)
\(660\) 0 0
\(661\) −2.48143 7.63705i −0.0965164 0.297047i 0.891130 0.453749i \(-0.149914\pi\)
−0.987646 + 0.156702i \(0.949914\pi\)
\(662\) 4.79834 + 9.41728i 0.186493 + 0.366013i
\(663\) 42.0037 + 12.5051i 1.63129 + 0.485659i
\(664\) 4.51248 1.46619i 0.175118 0.0568994i
\(665\) 0 0
\(666\) −1.70779 + 6.30395i −0.0661757 + 0.244273i
\(667\) 0.351281 + 2.21790i 0.0136017 + 0.0858775i
\(668\) −3.59263 3.59263i −0.139003 0.139003i
\(669\) −10.8126 + 1.98857i −0.418040 + 0.0768828i
\(670\) 0 0
\(671\) −15.2019 20.9237i −0.586865 0.807750i
\(672\) −0.899243 + 0.688045i −0.0346891 + 0.0265419i
\(673\) 24.0809 + 12.2698i 0.928251 + 0.472967i 0.851660 0.524095i \(-0.175596\pi\)
0.0765912 + 0.997063i \(0.475596\pi\)
\(674\) −31.5318 −1.21456
\(675\) 0 0
\(676\) −5.85270 −0.225104
\(677\) −16.4613 8.38747i −0.632660 0.322357i 0.108086 0.994142i \(-0.465528\pi\)
−0.740746 + 0.671785i \(0.765528\pi\)
\(678\) −19.4885 + 14.9114i −0.748451 + 0.572668i
\(679\) 2.04750 + 2.81814i 0.0785757 + 0.108150i
\(680\) 0 0
\(681\) 24.0596 4.42487i 0.921968 0.169561i
\(682\) −12.1326 12.1326i −0.464581 0.464581i
\(683\) −5.94046 37.5066i −0.227305 1.43515i −0.792338 0.610082i \(-0.791137\pi\)
0.565033 0.825068i \(-0.308863\pi\)
\(684\) 5.71601 21.0994i 0.218557 0.806756i
\(685\) 0 0
\(686\) 8.43843 2.74181i 0.322181 0.104683i
\(687\) −25.2568 7.51932i −0.963607 0.286880i
\(688\) 3.26638 + 6.41064i 0.124530 + 0.244403i
\(689\) 3.03266 + 9.33356i 0.115535 + 0.355580i
\(690\) 0 0
\(691\) −2.65184 + 8.16151i −0.100881 + 0.310479i −0.988742 0.149633i \(-0.952191\pi\)
0.887861 + 0.460112i \(0.152191\pi\)
\(692\) 18.8394 2.98388i 0.716168 0.113430i
\(693\) 3.78547 4.18093i 0.143798 0.158820i
\(694\) 7.68036 10.5711i 0.291542 0.401274i
\(695\) 0 0
\(696\) −5.52282 0.734846i −0.209342 0.0278543i
\(697\) −38.3894 6.08028i −1.45410 0.230307i
\(698\) 13.8161 27.1156i 0.522947 1.02634i
\(699\) −9.52861 9.06733i −0.360405 0.342958i
\(700\) 0 0
\(701\) 52.4507i 1.98104i −0.137384 0.990518i \(-0.543869\pi\)
0.137384 0.990518i \(-0.456131\pi\)
\(702\) 20.8797 8.54758i 0.788053 0.322608i
\(703\) 2.48160 15.6682i 0.0935951 0.590937i
\(704\) 2.32663 1.69040i 0.0876881 0.0637092i
\(705\) 0 0
\(706\) 2.35718 + 1.71259i 0.0887136 + 0.0644542i
\(707\) −5.80538 + 5.80538i −0.218334 + 0.218334i
\(708\) −8.47258 + 12.2913i −0.318419 + 0.461936i
\(709\) 5.89184 + 1.91438i 0.221273 + 0.0718959i 0.417555 0.908652i \(-0.362887\pi\)
−0.196283 + 0.980547i \(0.562887\pi\)
\(710\) 0 0
\(711\) 28.6228 10.8967i 1.07344 0.408660i
\(712\) −5.15235 + 2.62525i −0.193092 + 0.0983855i
\(713\) 3.71101 1.89085i 0.138978 0.0708130i
\(714\) −5.95161 2.84886i −0.222734 0.106616i
\(715\) 0 0
\(716\) −3.81721 1.24029i −0.142656 0.0463517i
\(717\) 17.8081 + 12.2754i 0.665055 + 0.458432i
\(718\) −5.59498 + 5.59498i −0.208803 + 0.208803i
\(719\) 3.26095 + 2.36922i 0.121613 + 0.0883570i 0.646929 0.762550i \(-0.276053\pi\)
−0.525316 + 0.850907i \(0.676053\pi\)
\(720\) 0 0
\(721\) −3.23943 + 2.35359i −0.120643 + 0.0876521i
\(722\) −5.33368 + 33.6756i −0.198499 + 1.25327i
\(723\) −13.0713 37.0747i −0.486127 1.37882i
\(724\) 4.08855i 0.151950i
\(725\) 0 0
\(726\) 3.25885 3.42464i 0.120947 0.127100i
\(727\) 13.8279 27.1388i 0.512850 1.00652i −0.478844 0.877900i \(-0.658944\pi\)
0.991693 0.128624i \(-0.0410560\pi\)
\(728\) 2.80348 + 0.444028i 0.103904 + 0.0164568i
\(729\) −19.2493 + 18.9332i −0.712936 + 0.701229i
\(730\) 0 0
\(731\) −24.6445 + 33.9203i −0.911510 + 1.25459i
\(732\) 0.386264 + 15.5718i 0.0142767 + 0.575549i
\(733\) 13.6402 2.16039i 0.503812 0.0797960i 0.100645 0.994922i \(-0.467909\pi\)
0.403167 + 0.915126i \(0.367909\pi\)
\(734\) −6.80279 + 20.9368i −0.251096 + 0.772793i
\(735\) 0 0
\(736\) 0.215722 + 0.663923i 0.00795161 + 0.0244725i
\(737\) −18.5698 36.4453i −0.684028 1.34248i
\(738\) −17.3561 + 9.95678i −0.638885 + 0.366514i
\(739\) −25.2888 + 8.21683i −0.930264 + 0.302261i −0.734671 0.678424i \(-0.762663\pi\)
−0.195593 + 0.980685i \(0.562663\pi\)
\(740\) 0 0
\(741\) −48.1946 + 26.0815i −1.77047 + 0.958129i
\(742\) −0.231141 1.45937i −0.00848547 0.0535751i
\(743\) 19.0708 + 19.0708i 0.699641 + 0.699641i 0.964333 0.264692i \(-0.0852703\pi\)
−0.264692 + 0.964333i \(0.585270\pi\)
\(744\) 1.86917 + 10.1633i 0.0685270 + 0.372606i
\(745\) 0 0
\(746\) 12.5568 + 17.2829i 0.459736 + 0.632772i
\(747\) 14.1520 + 1.52692i 0.517794 + 0.0558672i
\(748\) 14.9325 + 7.60848i 0.545985 + 0.278193i
\(749\) 0.380457 0.0139016
\(750\) 0 0
\(751\) −27.8529 −1.01637 −0.508183 0.861249i \(-0.669683\pi\)
−0.508183 + 0.861249i \(0.669683\pi\)
\(752\) 2.70527 + 1.37840i 0.0986509 + 0.0502652i
\(753\) 8.84528 + 11.5604i 0.322340 + 0.421283i
\(754\) 8.20949 + 11.2994i 0.298972 + 0.411500i
\(755\) 0 0
\(756\) −3.30622 + 0.779295i −0.120246 + 0.0283427i
\(757\) 14.2550 + 14.2550i 0.518108 + 0.518108i 0.916998 0.398891i \(-0.130605\pi\)
−0.398891 + 0.916998i \(0.630605\pi\)
\(758\) 0.154776 + 0.977218i 0.00562172 + 0.0354942i
\(759\) −1.65500 3.05819i −0.0600729 0.111005i
\(760\) 0 0
\(761\) 20.4602 6.64792i 0.741681 0.240987i 0.0862835 0.996271i \(-0.472501\pi\)
0.655398 + 0.755284i \(0.272501\pi\)
\(762\) 7.16346 24.0615i 0.259505 0.871656i
\(763\) 3.44817 + 6.76742i 0.124832 + 0.244997i
\(764\) 3.76012 + 11.5725i 0.136036 + 0.418677i
\(765\) 0 0
\(766\) −3.90822 + 12.0283i −0.141210 + 0.434599i
\(767\) 36.9626 5.85431i 1.33464 0.211387i
\(768\) −1.73152 + 0.0429510i −0.0624808 + 0.00154986i
\(769\) 5.35630 7.37231i 0.193153 0.265852i −0.701446 0.712723i \(-0.747462\pi\)
0.894599 + 0.446871i \(0.147462\pi\)
\(770\) 0 0
\(771\) 6.85860 51.5466i 0.247006 1.85641i
\(772\) 12.5952 + 1.99489i 0.453312 + 0.0717976i
\(773\) 20.4388 40.1134i 0.735132 1.44278i −0.155397 0.987852i \(-0.549666\pi\)
0.890529 0.454926i \(-0.150334\pi\)
\(774\) 1.07017 + 21.5579i 0.0384663 + 0.774884i
\(775\) 0 0
\(776\) 5.32861i 0.191286i
\(777\) −2.32477 + 0.819637i −0.0834007 + 0.0294043i
\(778\) −4.28069 + 27.0272i −0.153470 + 0.968973i
\(779\) 39.3184 28.5665i 1.40873 1.02350i
\(780\) 0 0
\(781\) 28.3116 + 20.5695i 1.01307 + 0.736036i
\(782\) −2.87659 + 2.87659i −0.102867 + 0.102867i
\(783\) −14.2152 &minu