Properties

Label 750.2.l.b.107.7
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 107.7
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.b.743.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.891007 + 0.453990i) q^{2} +(-0.983013 - 1.42607i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.228447 - 1.71692i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.06737 + 2.80370i) q^{9} +O(q^{10})\) \(q+(0.891007 + 0.453990i) q^{2} +(-0.983013 - 1.42607i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.228447 - 1.71692i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.06737 + 2.80370i) q^{9} +(2.73512 - 0.888693i) q^{11} +(0.575917 - 1.63350i) 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} +(-2.22389 + 2.01354i) q^{18} +(4.28299 - 5.89503i) q^{19} +(-0.204804 + 1.11360i) q^{21} +(2.84047 + 0.449885i) q^{22} +(0.316926 - 0.622003i) q^{23} +(1.25474 - 1.19400i) q^{24} -4.34197i q^{26} +(5.04752 - 1.23392i) 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} +(-3.95600 - 3.02688i) q^{33} +(5.54227 + 1.80079i) q^{34} +(-2.89562 + 0.784450i) q^{36} +(1.93977 - 0.988365i) q^{37} +(6.49246 - 3.30807i) q^{38} +(-3.57936 + 6.61410i) q^{39} +(-6.34331 - 2.06107i) q^{41} +(-0.688045 + 0.899243i) 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} +(1.66004 - 0.494220i) q^{48} -6.57265i q^{49} +(-6.95800 - 7.31198i) q^{51} +(1.97121 - 3.86872i) q^{52} +(2.23241 + 0.353579i) q^{53} +(5.05756 + 1.19210i) q^{54} +(0.384246 - 0.528869i) q^{56} +(-12.6170 - 0.312969i) 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} +(1.78940 - 0.802614i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-2.15064 - 4.49296i) q^{66} +(2.22497 + 14.0479i) q^{67} +(4.12066 + 4.12066i) q^{68} +(-1.19856 + 0.159477i) q^{69} +(7.15246 + 9.84451i) q^{71} +(-2.93615 - 0.615636i) q^{72} +(-0.498794 - 0.254148i) q^{73} +2.17706 q^{74} +7.28665 q^{76} +(-1.67510 - 0.853507i) q^{77} +(-6.19197 + 4.26821i) q^{78} +(6.00067 + 8.25922i) q^{79} +(-6.72143 - 5.98518i) q^{81} +(-4.71623 - 4.71623i) q^{82} +(-0.742236 - 4.68629i) q^{83} +(-1.02130 + 0.488866i) q^{84} +(6.84269 - 2.22332i) q^{86} +(5.25448 + 1.85256i) 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} +(-0.256256 + 10.3306i) q^{93} +(-1.78463 + 2.45633i) q^{94} +(1.70348 + 0.313291i) 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
\(3\) −0.983013 1.42607i −0.567543 0.823344i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) −0.228447 1.71692i −0.0932630 0.700929i
\(7\) −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
\(9\) −1.06737 + 2.80370i −0.355791 + 0.934566i
\(10\) 0 0
\(11\) 2.73512 0.888693i 0.824669 0.267951i 0.133871 0.990999i \(-0.457259\pi\)
0.690798 + 0.723048i \(0.257259\pi\)
\(12\) 0.575917 1.63350i 0.166253 0.471551i
\(13\) −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 0.587305 0.809366i \(-0.300189\pi\)
0.808668 + 0.588266i \(0.200189\pi\)
\(18\) −2.22389 + 2.01354i −0.524175 + 0.474595i
\(19\) 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
\(21\) −0.204804 + 1.11360i −0.0446920 + 0.243007i
\(22\) 2.84047 + 0.449885i 0.605589 + 0.0959159i
\(23\) 0.316926 0.622003i 0.0660837 0.129697i −0.855602 0.517635i \(-0.826813\pi\)
0.921685 + 0.387938i \(0.126813\pi\)
\(24\) 1.25474 1.19400i 0.256123 0.243724i
\(25\) 0 0
\(26\) 4.34197i 0.851530i
\(27\) 5.04752 1.23392i 0.971395 0.237468i
\(28\) 0.102264 0.645670i 0.0193261 0.122020i
\(29\) −2.60237 + 1.89073i −0.483247 + 0.351100i −0.802582 0.596542i \(-0.796541\pi\)
0.319334 + 0.947642i \(0.396541\pi\)
\(30\) 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
\(33\) −3.95600 3.02688i −0.688651 0.526912i
\(34\) 5.54227 + 1.80079i 0.950491 + 0.308833i
\(35\) 0 0
\(36\) −2.89562 + 0.784450i −0.482604 + 0.130742i
\(37\) 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
\(39\) −3.57936 + 6.61410i −0.573156 + 1.05910i
\(40\) 0 0
\(41\) −6.34331 2.06107i −0.990659 0.321884i −0.231532 0.972827i \(-0.574374\pi\)
−0.759127 + 0.650943i \(0.774374\pi\)
\(42\) −0.688045 + 0.899243i −0.106168 + 0.138756i
\(43\) 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 \(0.121075\pi\)
−0.997809 + 0.0661599i \(0.978925\pi\)
\(48\) 1.66004 0.494220i 0.239607 0.0713345i
\(49\) 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 0.307861 0.951431i \(-0.400387\pi\)
−0.00121543 + 0.999999i \(0.500387\pi\)
\(54\) 5.05756 + 1.19210i 0.688247 + 0.162224i
\(55\) 0 0
\(56\) 0.384246 0.528869i 0.0513470 0.0706731i
\(57\) −12.6170 0.312969i −1.67116 0.0414538i
\(58\) −3.17710 + 0.503203i −0.417174 + 0.0660738i
\(59\) 2.66341 8.19714i 0.346747 1.06718i −0.613895 0.789388i \(-0.710398\pi\)
0.960642 0.277790i \(-0.0896018\pi\)
\(60\) 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
\(63\) 1.78940 0.802614i 0.225443 0.101120i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −2.15064 4.49296i −0.264726 0.553045i
\(67\) 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
\(69\) −1.19856 + 0.159477i −0.144290 + 0.0191987i
\(70\) 0 0
\(71\) 7.15246 + 9.84451i 0.848840 + 1.16833i 0.984117 + 0.177521i \(0.0568077\pi\)
−0.135277 + 0.990808i \(0.543192\pi\)
\(72\) −2.93615 0.615636i −0.346029 0.0725534i
\(73\) −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
\(78\) −6.19197 + 4.26821i −0.701102 + 0.483280i
\(79\) 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
\(81\) −6.72143 5.98518i −0.746826 0.665019i
\(82\) −4.71623 4.71623i −0.520820 0.520820i
\(83\) −0.742236 4.68629i −0.0814709 0.514387i −0.994349 0.106156i \(-0.966146\pi\)
0.912879 0.408231i \(-0.133854\pi\)
\(84\) −1.02130 + 0.488866i −0.111433 + 0.0533396i
\(85\) 0 0
\(86\) 6.84269 2.22332i 0.737866 0.239747i
\(87\) 5.25448 + 1.85256i 0.563340 + 0.198615i
\(88\) 1.30562 + 2.56242i 0.139179 + 0.273155i
\(89\) 1.78693 + 5.49959i 0.189414 + 0.582956i 0.999996 0.00266864i \(-0.000849456\pi\)
−0.810583 + 0.585624i \(0.800849\pi\)
\(90\) 0 0
\(91\) −0.877122 + 2.69950i −0.0919473 + 0.282985i
\(92\) 0.689496 0.109205i 0.0718849 0.0113854i
\(93\) −0.256256 + 10.3306i −0.0265725 + 1.07124i
\(94\) −1.78463 + 2.45633i −0.184070 + 0.253351i
\(95\) 0 0
\(96\) 1.70348 + 0.313291i 0.173861 + 0.0319752i
\(97\) −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 \(0.214833\pi\)
−0.780758 + 0.624833i \(0.785167\pi\)
\(102\) −2.88006 9.67389i −0.285168 0.957858i
\(103\) 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 −0.686935 0.726719i \(-0.741044\pi\)
0.726719 + 0.686935i \(0.241044\pi\)
\(108\) 3.96512 + 3.35825i 0.381544 + 0.323148i
\(109\) −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
\(111\) −3.31630 1.79469i −0.314770 0.170344i
\(112\) 0.582467 0.296782i 0.0550380 0.0280433i
\(113\) −12.6233 + 6.43189i −1.18750 + 0.605061i −0.932250 0.361814i \(-0.882158\pi\)
−0.255249 + 0.966875i \(0.582158\pi\)
\(114\) −11.0997 6.00684i −1.03958 0.562592i
\(115\) 0 0
\(116\) −3.05927 0.994016i −0.284046 0.0922921i
\(117\) 12.9507 1.39732i 1.19730 0.129182i
\(118\) 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
\(123\) 3.29632 + 11.0721i 0.297219 + 0.998336i
\(124\) 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
\(129\) −12.2563 2.25408i −1.07910 0.198460i
\(130\) 0 0
\(131\) −3.23088 + 4.44693i −0.282283 + 0.388530i −0.926489 0.376323i \(-0.877188\pi\)
0.644205 + 0.764853i \(0.277188\pi\)
\(132\) 0.123522 4.97962i 0.0107512 0.433421i
\(133\) −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 \(-0.794562\pi\)
−0.0170834 0.999854i \(-0.505438\pi\)
\(138\) −1.14033 0.402042i −0.0970713 0.0342241i
\(139\) 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
\(141\) 4.74342 2.27053i 0.399468 0.191214i
\(142\) 1.90357 + 12.0187i 0.159744 + 1.00858i
\(143\) −8.82961 8.82961i −0.738369 0.738369i
\(144\) −2.33664 1.88152i −0.194720 0.156793i
\(145\) 0 0
\(146\) −0.329048 0.452896i −0.0272322 0.0374819i
\(147\) −9.37309 + 6.46100i −0.773079 + 0.532894i
\(148\) 1.93977 + 0.988365i 0.159449 + 0.0812431i
\(149\) −10.0289 −0.821602 −0.410801 0.911725i \(-0.634751\pi\)
−0.410801 + 0.911725i \(0.634751\pi\)
\(150\) 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
\(153\) −3.58761 + 17.1104i −0.290041 + 1.38329i
\(154\) −1.10504 1.52096i −0.0890469 0.122562i
\(155\) 0 0
\(156\) −7.45481 + 0.991909i −0.596863 + 0.0794163i
\(157\) 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
\(159\) −1.69026 3.53116i −0.134046 0.280039i
\(160\) 0 0
\(161\) −0.434019 + 0.141021i −0.0342055 + 0.0111140i
\(162\) −3.27163 8.38430i −0.257043 0.658733i
\(163\) 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 0.0407774 0.999168i \(-0.487017\pi\)
0.347542 + 0.937665i \(0.387017\pi\)
\(168\) −1.13193 0.0280779i −0.0873299 0.00216626i
\(169\) −3.44013 + 4.73493i −0.264625 + 0.364226i
\(170\) 0 0
\(171\) 11.9563 + 18.3004i 0.914323 + 1.39947i
\(172\) 7.10625 + 1.12552i 0.541846 + 0.0858200i
\(173\) −8.65954 + 16.9953i −0.658373 + 1.29213i 0.284404 + 0.958705i \(0.408204\pi\)
−0.942777 + 0.333425i \(0.891796\pi\)
\(174\) 3.84073 + 4.03612i 0.291165 + 0.305978i
\(175\) 0 0
\(176\) 2.87587i 0.216777i
\(177\) −14.3079 + 4.25967i −1.07545 + 0.320177i
\(178\) −0.904600 + 5.71142i −0.0678026 + 0.428089i
\(179\) 3.24712 2.35917i 0.242701 0.176332i −0.459785 0.888030i \(-0.652073\pi\)
0.702486 + 0.711698i \(0.252073\pi\)
\(180\) 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
\(183\) 9.46535 12.3708i 0.699699 0.914475i
\(184\) 0.663923 + 0.215722i 0.0489451 + 0.0159032i
\(185\) 0 0
\(186\) −4.91833 + 9.08832i −0.360629 + 0.666388i
\(187\) 14.9325 7.60848i 1.09197 0.556387i
\(188\) −2.70527 + 1.37840i −0.197302 + 0.100530i
\(189\) −2.90359 1.76283i −0.211205 0.128227i
\(190\) 0 0
\(191\) −11.5725 3.76012i −0.837354 0.272073i −0.141214 0.989979i \(-0.545101\pi\)
−0.696140 + 0.717906i \(0.745101\pi\)
\(192\) 1.37558 + 1.05251i 0.0992741 + 0.0759583i
\(193\) 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 −0.989868 0.141990i \(-0.954650\pi\)
0.985298 + 0.170845i \(0.0546498\pi\)
\(198\) −4.29318 + 7.48361i −0.305103 + 0.531837i
\(199\) 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
\(204\) 1.82570 9.92702i 0.127825 0.695030i
\(205\) 0 0
\(206\) 3.60030 4.95539i 0.250845 0.345259i
\(207\) 1.40563 + 1.55247i 0.0976980 + 0.107904i
\(208\) 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
\(213\) 7.00804 19.8772i 0.480183 1.36196i
\(214\) 0.553505 0.179845i 0.0378368 0.0122939i
\(215\) 0 0
\(216\) 2.00833 + 4.79235i 0.136650 + 0.326078i
\(217\) 0.610130 + 3.85221i 0.0414184 + 0.261505i
\(218\) −8.21555 8.21555i −0.556427 0.556427i
\(219\) 0.127887 + 0.961148i 0.00864179 + 0.0649484i
\(220\) 0 0
\(221\) −14.8726 20.4704i −1.00044 1.37699i
\(222\) −2.14008 3.10465i −0.143633 0.208370i
\(223\) −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 −0.0165960 0.999862i \(-0.505283\pi\)
−0.818660 + 0.574278i \(0.805283\pi\)
\(228\) −7.16287 10.3913i −0.474373 0.688181i
\(229\) −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
\(231\) 0.429482 + 3.22783i 0.0282579 + 0.212375i
\(232\) −2.27455 2.27455i −0.149332 0.149332i
\(233\) 1.18798 + 7.50060i 0.0778271 + 0.491381i 0.995556 + 0.0941731i \(0.0300207\pi\)
−0.917729 + 0.397208i \(0.869979\pi\)
\(234\) 12.1736 + 4.63450i 0.795811 + 0.302967i
\(235\) 0 0
\(236\) 8.19714 2.66341i 0.533589 0.173373i
\(237\) 5.87951 16.6763i 0.381915 1.08324i
\(238\) −1.72949 3.39432i −0.112106 0.220021i
\(239\) −3.85885 11.8763i −0.249608 0.768215i −0.994844 0.101414i \(-0.967663\pi\)
0.745236 0.666801i \(-0.232337\pi\)
\(240\) 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
\(243\) −1.92805 + 15.4688i −0.123684 + 0.992322i
\(244\) −5.28603 + 7.27560i −0.338403 + 0.465772i
\(245\) 0 0
\(246\) −2.08958 + 11.3618i −0.133226 + 0.724402i
\(247\) −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 \(-0.914553\pi\)
0.964186 0.265228i \(-0.0854471\pi\)
\(252\) 1.70111 + 0.975888i 0.107160 + 0.0614751i
\(253\) 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 \(0.635848\pi\)
−0.910303 + 0.413942i \(0.864152\pi\)
\(258\) −9.89707 7.57262i −0.616165 0.471451i
\(259\) −1.35353 0.439788i −0.0841042 0.0273271i
\(260\) 0 0
\(261\) −2.52334 9.31436i −0.156191 0.576545i
\(262\) −4.89760 + 2.49545i −0.302575 + 0.154169i
\(263\) −3.75527 + 1.91341i −0.231560 + 0.117986i −0.565921 0.824459i \(-0.691479\pi\)
0.334361 + 0.942445i \(0.391479\pi\)
\(264\) 2.37076 4.38080i 0.145910 0.269620i
\(265\) 0 0
\(266\) −4.53028 1.47198i −0.277769 0.0902527i
\(267\) 6.08625 7.95446i 0.372473 0.486805i
\(268\) −10.0572 + 10.0572i −0.614340 + 0.614340i
\(269\) 16.4085 + 11.9215i 1.00044 + 0.726865i 0.962183 0.272402i \(-0.0878182\pi\)
0.0382610 + 0.999268i \(0.487818\pi\)
\(270\) 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
\(273\) 4.71191 1.40281i 0.285178 0.0849017i
\(274\) 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
\(279\) 14.9841 9.78970i 0.897077 0.586094i
\(280\) 0 0
\(281\) −11.8968 + 16.3745i −0.709702 + 0.976820i 0.290102 + 0.956996i \(0.406311\pi\)
−0.999803 + 0.0198246i \(0.993689\pi\)
\(282\) 5.25722 + 0.130408i 0.313063 + 0.00776566i
\(283\) 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
\(288\) −1.22777 2.73726i −0.0723469 0.161295i
\(289\) 16.1295 5.24081i 0.948797 0.308283i
\(290\) 0 0
\(291\) 3.98486 + 8.32485i 0.233596 + 0.488011i
\(292\) −0.0875735 0.552918i −0.00512485 0.0323571i
\(293\) 1.20804 + 1.20804i 0.0705747 + 0.0705747i 0.741513 0.670938i \(-0.234109\pi\)
−0.670938 + 0.741513i \(0.734109\pi\)
\(294\) −11.2847 + 1.50150i −0.658138 + 0.0875694i
\(295\) 0 0
\(296\) 1.27964 + 1.76128i 0.0743778 + 0.102372i
\(297\) 12.7090 7.86061i 0.737450 0.456119i
\(298\) −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
\(303\) 17.9100 12.3456i 1.02891 0.709239i
\(304\) 4.28299 + 5.89503i 0.245646 + 0.338103i
\(305\) 0 0
\(306\) −10.9645 + 13.6167i −0.626801 + 0.778417i
\(307\) −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
\(309\) −9.56936 + 4.58057i −0.544382 + 0.260579i
\(310\) 0 0
\(311\) 32.9364 10.7017i 1.86765 0.606838i 0.875274 0.483628i \(-0.160681\pi\)
0.992381 0.123210i \(-0.0393188\pi\)
\(312\) −7.09260 2.50062i −0.401540 0.141569i
\(313\) 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 0.234638 0.972083i \(-0.424610\pi\)
0.523544 + 0.851999i \(0.324610\pi\)
\(318\) 0.0970796 3.91365i 0.00544396 0.219466i
\(319\) −5.43750 + 7.48407i −0.304441 + 0.419028i
\(320\) 0 0
\(321\) −0.991408 0.182332i −0.0553350 0.0101768i
\(322\) −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
\(327\) 5.74211 + 19.2873i 0.317540 + 1.06659i
\(328\) 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
\(333\) 0.700614 + 6.49349i 0.0383934 + 0.355841i
\(334\) 4.83207 + 1.57004i 0.264399 + 0.0859085i
\(335\) 0 0
\(336\) −0.995806 0.538901i −0.0543257 0.0293995i
\(337\) 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
\(339\) 21.5812 + 11.6791i 1.17213 + 0.634323i
\(340\) 0 0
\(341\) −16.3183 5.30214i −0.883686 0.287127i
\(342\) 2.34496 + 21.7338i 0.126801 + 1.17523i
\(343\) −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 \(-0.835935\pi\)
0.979814 0.199911i \(-0.0640652\pi\)
\(348\) 1.58976 + 5.33987i 0.0852200 + 0.286247i
\(349\) 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 0.232547 0.972585i \(-0.425294\pi\)
−0.0793796 + 0.996844i \(0.525294\pi\)
\(354\) −14.6823 2.70025i −0.780355 0.143517i
\(355\) 0 0
\(356\) −3.39893 + 4.67823i −0.180143 + 0.247946i
\(357\) −0.163624 + 6.59628i −0.00865988 + 0.349112i
\(358\) 3.96424 0.627874i 0.209517 0.0331842i
\(359\) −2.44510 + 7.52523i −0.129047 + 0.397167i −0.994617 0.103622i \(-0.966957\pi\)
0.865569 + 0.500789i \(0.166957\pi\)
\(360\) 0 0
\(361\) −10.5360 32.4266i −0.554528 1.70666i
\(362\) 1.85616 + 3.64292i 0.0975577 + 0.191468i
\(363\) 4.45841 + 1.57189i 0.234006 + 0.0825027i
\(364\) −2.69950 + 0.877122i −0.141492 + 0.0459737i
\(365\) 0 0
\(366\) 14.0499 6.72527i 0.734401 0.351536i
\(367\) −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
\(369\) 12.5493 15.5848i 0.653289 0.811312i
\(370\) 0 0
\(371\) −0.868488 1.19537i −0.0450897 0.0620606i
\(372\) −8.50827 + 5.86487i −0.441133 + 0.304080i
\(373\) −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
\(378\) −1.78681 2.88890i −0.0919034 0.148589i
\(379\) −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
\(381\) 24.8859 3.31122i 1.27494 0.169639i
\(382\) −8.60408 8.60408i −0.440223 0.440223i
\(383\) 1.97847 + 12.4916i 0.101095 + 0.638289i 0.985253 + 0.171102i \(0.0547326\pi\)
−0.884158 + 0.467187i \(0.845267\pi\)
\(384\) 0.747823 + 1.56229i 0.0381622 + 0.0797254i
\(385\) 0 0
\(386\) 12.1281 3.94066i 0.617304 0.200574i
\(387\) 8.83357 + 19.6941i 0.449036 + 1.00111i
\(388\) −2.41914 4.74782i −0.122813 0.241034i
\(389\) 8.45598 + 26.0248i 0.428735 + 1.31951i 0.899372 + 0.437185i \(0.144024\pi\)
−0.470636 + 0.882327i \(0.655976\pi\)
\(390\) 0 0
\(391\) 1.25712 3.86900i 0.0635751 0.195664i
\(392\) 6.49173 1.02819i 0.327882 0.0519314i
\(393\) 9.51764 + 0.236089i 0.480102 + 0.0119091i
\(394\) −0.241016 + 0.331731i −0.0121422 + 0.0167123i
\(395\) 0 0
\(396\) −7.22273 + 4.71888i −0.362956 + 0.237133i
\(397\) −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 \(0.136473\pi\)
−0.909489 + 0.415729i \(0.863527\pi\)
\(402\) 23.6108 7.02929i 1.17760 0.350589i
\(403\) −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
\(408\) 6.13348 8.01618i 0.303653 0.396860i
\(409\) −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
\(411\) −17.3417 + 32.0447i −0.855401 + 1.58065i
\(412\) 5.45760 2.78078i 0.268876 0.136999i
\(413\) −5.02028 + 2.55796i −0.247032 + 0.125869i
\(414\) 0.547617 + 2.02141i 0.0269139 + 0.0993467i
\(415\) 0 0
\(416\) 4.12946 + 1.34174i 0.202463 + 0.0657843i
\(417\) −16.0428 12.2749i −0.785618 0.601105i
\(418\) 14.8178 14.8178i 0.724761 0.724761i
\(419\) 5.84455 + 4.24631i 0.285525 + 0.207446i 0.721324 0.692598i \(-0.243534\pi\)
−0.435799 + 0.900044i \(0.643534\pi\)
\(420\) 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
\(423\) −7.90079 4.53251i −0.384150 0.220378i
\(424\) 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
\(429\) −3.91205 + 21.2713i −0.188876 + 1.02699i
\(430\) 0 0
\(431\) 2.43967 3.35792i 0.117515 0.161745i −0.746207 0.665714i \(-0.768127\pi\)
0.863722 + 0.503968i \(0.168127\pi\)
\(432\) −0.386242 + 5.18178i −0.0185831 + 0.249308i
\(433\) −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
\(438\) −0.322404 + 0.914449i −0.0154051 + 0.0436941i
\(439\) 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
\(441\) 18.4277 + 7.01546i 0.877511 + 0.334070i
\(442\) −3.95823 24.9913i −0.188274 1.18871i
\(443\) −12.3286 12.3286i −0.585749 0.585749i 0.350728 0.936477i \(-0.385934\pi\)
−0.936477 + 0.350728i \(0.885934\pi\)
\(444\) −0.497343 3.73784i −0.0236028 0.177390i
\(445\) 0 0
\(446\) −3.73089 5.13513i −0.176663 0.243155i
\(447\) 9.85857 + 14.3020i 0.466294 + 0.676461i
\(448\) 0.582467 + 0.296782i 0.0275190 + 0.0140216i
\(449\) 11.4060 0.538284 0.269142 0.963101i \(-0.413260\pi\)
0.269142 + 0.963101i \(0.413260\pi\)
\(450\) 0 0
\(451\) −19.1813 −0.903214
\(452\) −12.6233 6.43189i −0.593750 0.302531i
\(453\) −17.6132 25.5517i −0.827538 1.20052i
\(454\) −8.30177 11.4264i −0.389621 0.536268i
\(455\) 0 0
\(456\) −1.66461 12.5106i −0.0779527 0.585862i
\(457\) 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
\(459\) 27.9273 11.7035i 1.30354 0.546274i
\(460\) 0 0
\(461\) 18.3653 5.96726i 0.855359 0.277923i 0.151670 0.988431i \(-0.451535\pi\)
0.703689 + 0.710508i \(0.251535\pi\)
\(462\) −1.08273 + 3.07100i −0.0503732 + 0.142876i
\(463\) −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 −0.196613 0.980481i \(-0.562994\pi\)
0.115996 + 0.993250i \(0.462994\pi\)
\(468\) 8.74271 + 9.65605i 0.404132 + 0.446351i
\(469\) 5.46513 7.52211i 0.252356 0.347339i
\(470\) 0 0
\(471\) 2.84884 15.4902i 0.131268 0.713752i
\(472\) 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
\(477\) −3.37414 + 5.88161i −0.154491 + 0.269300i
\(478\) 1.95347 12.3338i 0.0893498 0.564133i
\(479\) 13.7743 10.0076i 0.629363 0.457259i −0.226817 0.973937i \(-0.572832\pi\)
0.856179 + 0.516679i \(0.172832\pi\)
\(480\) 0 0
\(481\) −7.64742 5.55617i −0.348692 0.253340i
\(482\) 16.0488 16.0488i 0.731005 0.731005i
\(483\) 0.627753 + 0.480317i 0.0285637 + 0.0218552i
\(484\) −2.59578 0.843419i −0.117990 0.0383372i
\(485\) 0 0
\(486\) −8.74057 + 12.9075i −0.396480 + 0.585494i
\(487\) −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
\(489\) 7.64711 14.1307i 0.345814 0.639011i
\(490\) 0 0
\(491\) 8.69557 + 2.82536i 0.392426 + 0.127507i 0.498582 0.866843i \(-0.333854\pi\)
−0.106156 + 0.994349i \(0.533854\pi\)
\(492\) −7.01997 + 9.17479i −0.316485 + 0.413631i
\(493\) −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
\(498\) −7.87642 + 2.34493i −0.352951 + 0.105079i
\(499\) 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 0.631450 0.775416i \(-0.282460\pi\)
0.360928 + 0.932594i \(0.382460\pi\)
\(504\) 1.07266 + 1.64181i 0.0477799 + 0.0731320i
\(505\) 0 0
\(506\) 1.18005 1.62420i 0.0524595 0.0722044i
\(507\) 10.1341 + 0.251380i 0.450069 + 0.0111642i
\(508\) −14.3160 + 2.26744i −0.635171 + 0.100601i
\(509\) −1.15005 + 3.53949i −0.0509750 + 0.156885i −0.973304 0.229522i \(-0.926284\pi\)
0.922329 + 0.386407i \(0.126284\pi\)
\(510\) 0 0
\(511\) 0.113087 + 0.348047i 0.00500268 + 0.0153967i
\(512\) −0.453990 0.891007i −0.0200637 0.0393773i
\(513\) 14.3445 35.0401i 0.633324 1.54706i
\(514\) −28.5533 + 9.27753i −1.25943 + 0.409214i
\(515\) 0 0
\(516\) −5.38046 11.2404i −0.236861 0.494832i
\(517\) 1.36594 + 8.62420i 0.0600739 + 0.379292i
\(518\) −1.00634 1.00634i −0.0442162 0.0442162i
\(519\) 32.7490 4.35746i 1.43752 0.191271i
\(520\) 0 0
\(521\) −25.0327 34.4546i −1.09670 1.50948i −0.839683 0.543077i \(-0.817259\pi\)
−0.257021 0.966406i \(-0.582741\pi\)
\(522\) 1.98032 9.44473i 0.0866762 0.413385i
\(523\) 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
\(528\) 4.10120 2.82702i 0.178482 0.123030i
\(529\) 13.2326 + 18.2131i 0.575331 + 0.791875i
\(530\) 0 0
\(531\) 20.1395 + 16.2168i 0.873978 + 0.703750i
\(532\) −3.36825 3.36825i −0.146032 0.146032i
\(533\) 4.53032 + 28.6033i 0.196230 + 1.23895i
\(534\) 9.03414 4.32437i 0.390945 0.187134i
\(535\) 0 0
\(536\) −13.5269 + 4.39515i −0.584272 + 0.189842i
\(537\) −6.55630 2.31153i −0.282925 0.0997501i
\(538\) 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
\(543\) 0.175607 7.07940i 0.00753604 0.303806i
\(544\) −3.42531 + 4.71454i −0.146859 + 0.202134i
\(545\) 0 0
\(546\) 4.83520 + 0.889254i 0.206928 + 0.0380566i
\(547\) 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
\(552\) −0.345010 1.15886i −0.0146846 0.0493244i
\(553\) 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 −0.204281 0.978912i \(-0.565485\pi\)
0.978912 + 0.204281i \(0.0654855\pi\)
\(558\) 17.7954 1.92003i 0.753339 0.0812813i
\(559\) −29.7107 9.65360i −1.25663 0.408304i
\(560\) 0 0
\(561\) −25.5291 13.8156i −1.07784 0.583294i
\(562\) −18.0340 + 9.18876i −0.760717 + 0.387604i
\(563\) −0.869364 + 0.442963i −0.0366393 + 0.0186687i −0.472214 0.881484i \(-0.656545\pi\)
0.435575 + 0.900153i \(0.356545\pi\)
\(564\) 4.62502 + 2.50292i 0.194748 + 0.105392i
\(565\) 0 0
\(566\) 7.89740 + 2.56602i 0.331952 + 0.107858i
\(567\) 0.340335 + 5.87361i 0.0142927 + 0.246669i
\(568\) −8.60442 + 8.60442i −0.361033 + 0.361033i
\(569\) −22.6112 16.4280i −0.947909 0.688696i 0.00240243 0.999997i \(-0.499235\pi\)
−0.950311 + 0.311301i \(0.899235\pi\)
\(570\) 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
\(573\) 6.01367 + 20.1994i 0.251224 + 0.843843i
\(574\) 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
\(579\) −21.7232 3.99516i −0.902785 0.166033i
\(580\) 0 0
\(581\) −1.82313 + 2.50933i −0.0756364 + 0.104105i
\(582\) −0.228869 + 9.22658i −0.00948694 + 0.382454i
\(583\) 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 \(0.109023\pi\)
−0.281939 + 0.959432i \(0.590977\pi\)
\(588\) −10.7364 3.78530i −0.442763 0.156103i
\(589\) −41.3460 + 13.4341i −1.70363 + 0.553544i
\(590\) 0 0
\(591\) 0.640605 0.306639i 0.0263510 0.0126134i
\(592\) 0.340567 + 2.15026i 0.0139972 + 0.0883750i
\(593\) 2.52481 + 2.52481i 0.103681 + 0.103681i 0.757045 0.653363i \(-0.226643\pi\)
−0.653363 + 0.757045i \(0.726643\pi\)
\(594\) 14.8924 1.23410i 0.611043 0.0506357i
\(595\) 0 0
\(596\) −5.89486 8.11358i −0.241463 0.332345i
\(597\) 15.6795 10.8081i 0.641719 0.442346i
\(598\) −2.70072 1.37608i −0.110441 0.0562723i
\(599\) −39.4333 −1.61120 −0.805600 0.592460i \(-0.798157\pi\)
−0.805600 + 0.592460i \(0.798157\pi\)
\(600\) 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
\(603\) −41.7609 8.75620i −1.70064 0.356580i
\(604\) 10.5317 + 14.4956i 0.428527 + 0.589817i
\(605\) 0 0
\(606\) 21.5628 2.86906i 0.875928 0.116548i
\(607\) 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
\(609\) −1.57254 3.28522i −0.0637224 0.133124i
\(610\) 0 0
\(611\) 12.5378 4.07379i 0.507226 0.164808i
\(612\) −15.9513 + 7.15480i −0.644795 + 0.289216i
\(613\) −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 −0.297829 0.954619i \(-0.596262\pi\)
0.0117417 + 0.999931i \(0.496262\pi\)
\(618\) −10.6059 0.263084i −0.426632 0.0105828i
\(619\) −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
\(621\) 0.832190 3.53063i 0.0333946 0.141679i
\(622\) 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
\(627\) −34.7870 + 10.3566i −1.38926 + 0.413603i
\(628\) −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
\(633\) 22.6408 29.5905i 0.899892 1.17612i
\(634\) 12.9984 + 4.22343i 0.516231 + 0.167734i
\(635\) 0 0
\(636\) 1.86326 3.44301i 0.0738829 0.136524i
\(637\) −25.4278 + 12.9561i −1.00748 + 0.513339i
\(638\) −8.24255 + 4.19979i −0.326326 + 0.166271i
\(639\) −35.2354 + 9.54557i −1.39389 + 0.377617i
\(640\) 0 0
\(641\) −3.49095 1.13428i −0.137884 0.0448012i 0.239262 0.970955i \(-0.423095\pi\)
−0.377146 + 0.926154i \(0.623095\pi\)
\(642\) −0.800574 0.612549i −0.0315961 0.0241754i
\(643\) −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 −0.972570 0.232612i \(-0.925273\pi\)
0.996850 + 0.0793138i \(0.0252729\pi\)
\(648\) 4.86002 7.57497i 0.190920 0.297573i
\(649\) 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 −0.131534 0.991312i \(-0.541990\pi\)
−0.431428 + 0.902147i \(0.641990\pi\)
\(654\) −3.63999 + 19.7920i −0.142335 + 0.773927i
\(655\) 0 0
\(656\) 3.92038 5.39594i 0.153065 0.210676i
\(657\) 1.24495 1.12720i 0.0485703 0.0439761i
\(658\) 1.96038 0.310493i 0.0764235 0.0121043i
\(659\) 4.21526 12.9732i 0.164203 0.505365i −0.834774 0.550593i \(-0.814402\pi\)
0.998977 + 0.0452283i \(0.0144015\pi\)
\(660\) 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
\(663\) −14.5723 + 41.3321i −0.565942 + 1.60520i
\(664\) 4.51248 1.46619i 0.175118 0.0568994i
\(665\) 0 0
\(666\) −2.32373 + 6.10382i −0.0900428 + 0.236518i
\(667\) 0.351281 + 2.21790i 0.0136017 + 0.0858775i
\(668\) 3.59263 + 3.59263i 0.139003 + 0.139003i
\(669\) 1.45004 + 10.8979i 0.0560616 + 0.421338i
\(670\) 0 0
\(671\) 15.2019 + 20.9237i 0.586865 + 0.807750i
\(672\) −0.642614 0.932251i −0.0247894 0.0359623i
\(673\) 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 0.740746 0.671785i \(-0.234472\pi\)
−0.108086 + 0.994142i \(0.534472\pi\)
\(678\) 13.9268 + 20.2038i 0.534855 + 0.775924i
\(679\) 2.04750 + 2.81814i 0.0785757 + 0.108150i
\(680\) 0 0
\(681\) 3.22654 + 24.2494i 0.123641 + 0.929241i
\(682\) −12.1326 12.1326i −0.464581 0.464581i
\(683\) 5.94046 + 37.5066i 0.227305 + 1.43515i 0.792338 + 0.610082i \(0.208863\pi\)
−0.565033 + 0.825068i \(0.691137\pi\)
\(684\) −7.77757 + 20.4296i −0.297383 + 0.781144i
\(685\) 0 0
\(686\) −8.43843 + 2.74181i −0.322181 + 0.104683i
\(687\) −8.76231 + 24.8529i −0.334303 + 0.948198i
\(688\) 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
\(693\) 4.18093 3.78547i 0.158820 0.143798i
\(694\) 7.68036 10.5711i 0.291542 0.401274i
\(695\) 0 0
\(696\) −1.00777 + 5.47959i −0.0381992 + 0.207703i
\(697\) −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 \(0.456131\pi\)
−0.137384 + 0.990518i \(0.543869\pi\)
\(702\) −5.35764 21.9162i −0.202211 0.827173i
\(703\) 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
\(708\) −11.8561 9.07156i −0.445580 0.340930i
\(709\) 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
\(711\) −29.5613 + 8.00841i −1.10863 + 0.300339i
\(712\) −5.15235 + 2.62525i −0.193092 + 0.0983855i
\(713\) −3.71101 + 1.89085i −0.138978 + 0.0708130i
\(714\) −3.14044 + 5.80305i −0.117528 + 0.217174i
\(715\) 0 0
\(716\) 3.81721 + 1.24029i 0.142656 + 0.0463517i
\(717\) −13.1432 + 17.1776i −0.490842 + 0.641508i
\(718\) −5.59498 + 5.59498i −0.208803 + 0.208803i
\(719\) −3.26095 2.36922i −0.121613 0.0883570i 0.525316 0.850907i \(-0.323947\pi\)
−0.646929 + 0.762550i \(0.723947\pi\)
\(720\) 0 0
\(721\) −3.23943 + 2.35359i −0.120643 + 0.0876521i
\(722\) 5.33368 33.6756i 0.198499 1.25327i
\(723\) −37.6772 + 11.2171i −1.40123 + 0.417167i
\(724\) 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
\(729\) 23.9549 12.4565i 0.887218 0.461350i
\(730\) 0 0
\(731\) 24.6445 33.9203i 0.911510 1.25459i
\(732\) 15.5718 + 0.386264i 0.575549 + 0.0142767i
\(733\) 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
\(738\) 18.2568 8.18890i 0.672043 0.301438i
\(739\) −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
\(741\) 23.6599 + 49.4285i 0.869170 + 1.81580i
\(742\) −0.231141 1.45937i −0.00848547 0.0535751i
\(743\) −19.0708 19.0708i −0.699641 0.699641i 0.264692 0.964333i \(-0.414730\pi\)
−0.964333 + 0.264692i \(0.914730\pi\)
\(744\) −10.2435 + 1.36297i −0.375546 + 0.0499687i
\(745\) 0 0
\(746\) −12.5568 17.2829i −0.459736 0.632772i
\(747\) 13.9312 + 2.92101i 0.509715 + 0.106874i
\(748\) 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
\(753\) −11.9847 + 8.26123i −0.436747 + 0.301056i
\(754\) 8.20949 + 11.2994i 0.298972 + 0.411500i
\(755\) 0 0
\(756\) −0.280525 3.38522i −0.0102026 0.123119i
\(757\) 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
\(759\) −3.13649 + 1.50134i −0.113847 + 0.0544953i
\(760\) 0 0
\(761\) −20.4602 + 6.64792i −0.741681 + 0.240987i −0.655398 0.755284i \(-0.727499\pi\)
−0.0862835 + 0.996271i \(0.527499\pi\)
\(762\) 23.6767 + 8.34763i 0.857717 + 0.302403i
\(763\) 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
\(768\) −0.0429510 + 1.73152i −0.00154986 + 0.0624808i
\(769\) 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
\(771\) 51.1431 + 9.40586i 1.84188 + 0.338744i
\(772\) 12.5952 + 1.99489i 0.453312 + 0.0717976i
\(773\) −20.4388 + 40.1134i −0.735132 + 1.44278i 0.155397 + 0.987852i \(0.450334\pi\)
−0.890529 + 0.454926i \(0.849666\pi\)
\(774\) −1.07017 + 21.5579i −0.0384663 + 0.774884i
\(775\) 0 0
\(776\) 5.32861i 0.191286i
\(777\) 0.703366 + 2.36255i 0.0252331 + 0.0847560i
\(778\) −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