Properties

Label 490.2.g.c.293.7
Level $490$
Weight $2$
Character 490.293
Analytic conductor $3.913$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 61 x^{12} + 266 x^{10} + 852 x^{8} + 1438 x^{6} + 1933 x^{4} + 3038 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 293.7
Root \(1.01089 + 0.750919i\) of defining polynomial
Character \(\chi\) \(=\) 490.293
Dual form 490.2.g.c.97.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.204875 - 0.204875i) q^{3} -1.00000i q^{4} +(1.42962 - 1.71936i) q^{5} -0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +2.91605i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.204875 - 0.204875i) q^{3} -1.00000i q^{4} +(1.42962 - 1.71936i) q^{5} -0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +2.91605i q^{9} +(-0.204875 - 2.22666i) q^{10} +5.62576 q^{11} +(-0.204875 - 0.204875i) q^{12} +(1.42962 - 1.42962i) q^{13} +(-0.0593598 - 0.645146i) q^{15} -1.00000 q^{16} +(-3.75384 - 3.75384i) q^{17} +(2.06196 + 2.06196i) q^{18} -3.89180 q^{19} +(-1.71936 - 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(-0.794732 - 0.794732i) q^{23} -0.289737 q^{24} +(-0.912375 - 4.91605i) q^{25} -2.02179i q^{26} +(1.21205 + 1.21205i) q^{27} +3.15502i q^{29} +(-0.498161 - 0.414214i) q^{30} -3.84846i q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.15258 - 1.15258i) q^{33} -5.30873 q^{34} +2.91605 q^{36} +(-3.56380 + 3.56380i) q^{37} +(-2.75192 + 2.75192i) q^{38} -0.585786i q^{39} +(-2.22666 + 0.204875i) q^{40} +7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} -5.62576i q^{44} +(5.01373 + 4.16885i) q^{45} -1.12392 q^{46} +(4.16885 + 4.16885i) q^{47} +(-0.204875 + 0.204875i) q^{48} +(-4.12132 - 2.83103i) q^{50} -1.53813 q^{51} +(-1.42962 - 1.42962i) q^{52} +(-0.978013 - 0.978013i) q^{53} +1.71410 q^{54} +(8.04270 - 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(2.23093 + 2.23093i) q^{58} +5.47845 q^{59} +(-0.645146 + 0.0593598i) q^{60} +4.60924i q^{61} +(-2.72127 - 2.72127i) q^{62} +1.00000i q^{64} +(-0.414214 - 4.50184i) q^{65} -1.62999i q^{66} +(0.597494 - 0.597494i) q^{67} +(-3.75384 + 3.75384i) q^{68} -0.325641 q^{69} +4.77710 q^{71} +(2.06196 - 2.06196i) q^{72} +(-3.96848 + 3.96848i) q^{73} +5.03997i q^{74} +(-1.19410 - 0.820253i) q^{75} +3.89180i q^{76} +(-0.414214 - 0.414214i) q^{78} +6.24784i q^{79} +(-1.42962 + 1.71936i) q^{80} -8.25152 q^{81} +(5.09860 + 5.09860i) q^{82} +(-5.67281 + 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +2.62576 q^{86} +(0.646383 + 0.646383i) q^{87} +(-3.97801 - 3.97801i) q^{88} -11.9218 q^{89} +(6.49307 - 0.597426i) q^{90} +(-0.794732 + 0.794732i) q^{92} +(-0.788454 - 0.788454i) q^{93} +5.89564 q^{94} +(-5.56380 + 6.69140i) q^{95} +0.289737i q^{96} +(6.63103 + 6.63103i) q^{97} +16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0.204875 0.204875i 0.118285 0.118285i −0.645487 0.763771i \(-0.723345\pi\)
0.763771 + 0.645487i \(0.223345\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 1.42962 1.71936i 0.639345 0.768920i
\(6\) 0.289737i 0.118285i
\(7\) 0 0
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 2.91605i 0.972018i
\(10\) −0.204875 2.22666i −0.0647871 0.704133i
\(11\) 5.62576 1.69623 0.848115 0.529812i \(-0.177737\pi\)
0.848115 + 0.529812i \(0.177737\pi\)
\(12\) −0.204875 0.204875i −0.0591423 0.0591423i
\(13\) 1.42962 1.42962i 0.396505 0.396505i −0.480493 0.876998i \(-0.659542\pi\)
0.876998 + 0.480493i \(0.159542\pi\)
\(14\) 0 0
\(15\) −0.0593598 0.645146i −0.0153266 0.166576i
\(16\) −1.00000 −0.250000
\(17\) −3.75384 3.75384i −0.910440 0.910440i 0.0858670 0.996307i \(-0.472634\pi\)
−0.996307 + 0.0858670i \(0.972634\pi\)
\(18\) 2.06196 + 2.06196i 0.486009 + 0.486009i
\(19\) −3.89180 −0.892841 −0.446420 0.894823i \(-0.647301\pi\)
−0.446420 + 0.894823i \(0.647301\pi\)
\(20\) −1.71936 1.42962i −0.384460 0.319673i
\(21\) 0 0
\(22\) 3.97801 3.97801i 0.848115 0.848115i
\(23\) −0.794732 0.794732i −0.165713 0.165713i 0.619379 0.785092i \(-0.287384\pi\)
−0.785092 + 0.619379i \(0.787384\pi\)
\(24\) −0.289737 −0.0591423
\(25\) −0.912375 4.91605i −0.182475 0.983211i
\(26\) 2.02179i 0.396505i
\(27\) 1.21205 + 1.21205i 0.233259 + 0.233259i
\(28\) 0 0
\(29\) 3.15502i 0.585872i 0.956132 + 0.292936i \(0.0946322\pi\)
−0.956132 + 0.292936i \(0.905368\pi\)
\(30\) −0.498161 0.414214i −0.0909513 0.0756247i
\(31\) 3.84846i 0.691204i −0.938381 0.345602i \(-0.887675\pi\)
0.938381 0.345602i \(-0.112325\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 1.15258 1.15258i 0.200638 0.200638i
\(34\) −5.30873 −0.910440
\(35\) 0 0
\(36\) 2.91605 0.486009
\(37\) −3.56380 + 3.56380i −0.585885 + 0.585885i −0.936514 0.350629i \(-0.885968\pi\)
0.350629 + 0.936514i \(0.385968\pi\)
\(38\) −2.75192 + 2.75192i −0.446420 + 0.446420i
\(39\) 0.585786i 0.0938009i
\(40\) −2.22666 + 0.204875i −0.352066 + 0.0323936i
\(41\) 7.21050i 1.12609i 0.826426 + 0.563046i \(0.190371\pi\)
−0.826426 + 0.563046i \(0.809629\pi\)
\(42\) 0 0
\(43\) 1.85669 + 1.85669i 0.283143 + 0.283143i 0.834361 0.551218i \(-0.185837\pi\)
−0.551218 + 0.834361i \(0.685837\pi\)
\(44\) 5.62576i 0.848115i
\(45\) 5.01373 + 4.16885i 0.747403 + 0.621455i
\(46\) −1.12392 −0.165713
\(47\) 4.16885 + 4.16885i 0.608089 + 0.608089i 0.942446 0.334358i \(-0.108519\pi\)
−0.334358 + 0.942446i \(0.608519\pi\)
\(48\) −0.204875 + 0.204875i −0.0295711 + 0.0295711i
\(49\) 0 0
\(50\) −4.12132 2.83103i −0.582843 0.400368i
\(51\) −1.53813 −0.215382
\(52\) −1.42962 1.42962i −0.198253 0.198253i
\(53\) −0.978013 0.978013i −0.134340 0.134340i 0.636739 0.771079i \(-0.280283\pi\)
−0.771079 + 0.636739i \(0.780283\pi\)
\(54\) 1.71410 0.233259
\(55\) 8.04270 9.67269i 1.08448 1.30426i
\(56\) 0 0
\(57\) −0.797333 + 0.797333i −0.105609 + 0.105609i
\(58\) 2.23093 + 2.23093i 0.292936 + 0.292936i
\(59\) 5.47845 0.713234 0.356617 0.934251i \(-0.383930\pi\)
0.356617 + 0.934251i \(0.383930\pi\)
\(60\) −0.645146 + 0.0593598i −0.0832880 + 0.00766332i
\(61\) 4.60924i 0.590153i 0.955474 + 0.295077i \(0.0953451\pi\)
−0.955474 + 0.295077i \(0.904655\pi\)
\(62\) −2.72127 2.72127i −0.345602 0.345602i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −0.414214 4.50184i −0.0513769 0.558384i
\(66\) 1.62999i 0.200638i
\(67\) 0.597494 0.597494i 0.0729956 0.0729956i −0.669666 0.742662i \(-0.733563\pi\)
0.742662 + 0.669666i \(0.233563\pi\)
\(68\) −3.75384 + 3.75384i −0.455220 + 0.455220i
\(69\) −0.325641 −0.0392026
\(70\) 0 0
\(71\) 4.77710 0.566937 0.283469 0.958982i \(-0.408515\pi\)
0.283469 + 0.958982i \(0.408515\pi\)
\(72\) 2.06196 2.06196i 0.243004 0.243004i
\(73\) −3.96848 + 3.96848i −0.464475 + 0.464475i −0.900119 0.435644i \(-0.856521\pi\)
0.435644 + 0.900119i \(0.356521\pi\)
\(74\) 5.03997i 0.585885i
\(75\) −1.19410 0.820253i −0.137883 0.0947147i
\(76\) 3.89180i 0.446420i
\(77\) 0 0
\(78\) −0.414214 0.414214i −0.0469005 0.0469005i
\(79\) 6.24784i 0.702937i 0.936200 + 0.351469i \(0.114318\pi\)
−0.936200 + 0.351469i \(0.885682\pi\)
\(80\) −1.42962 + 1.71936i −0.159836 + 0.192230i
\(81\) −8.25152 −0.916836
\(82\) 5.09860 + 5.09860i 0.563046 + 0.563046i
\(83\) −5.67281 + 5.67281i −0.622672 + 0.622672i −0.946214 0.323542i \(-0.895126\pi\)
0.323542 + 0.946214i \(0.395126\pi\)
\(84\) 0 0
\(85\) −11.8207 + 1.08763i −1.28214 + 0.117970i
\(86\) 2.62576 0.283143
\(87\) 0.646383 + 0.646383i 0.0692996 + 0.0692996i
\(88\) −3.97801 3.97801i −0.424058 0.424058i
\(89\) −11.9218 −1.26371 −0.631855 0.775087i \(-0.717706\pi\)
−0.631855 + 0.775087i \(0.717706\pi\)
\(90\) 6.49307 0.597426i 0.684429 0.0629742i
\(91\) 0 0
\(92\) −0.794732 + 0.794732i −0.0828566 + 0.0828566i
\(93\) −0.788454 0.788454i −0.0817588 0.0817588i
\(94\) 5.89564 0.608089
\(95\) −5.56380 + 6.69140i −0.570834 + 0.686523i
\(96\) 0.289737i 0.0295711i
\(97\) 6.63103 + 6.63103i 0.673279 + 0.673279i 0.958471 0.285191i \(-0.0920572\pi\)
−0.285191 + 0.958471i \(0.592057\pi\)
\(98\) 0 0
\(99\) 16.4050i 1.64877i
\(100\) −4.91605 + 0.912375i −0.491605 + 0.0912375i
\(101\) 16.0992i 1.60193i 0.598711 + 0.800965i \(0.295680\pi\)
−0.598711 + 0.800965i \(0.704320\pi\)
\(102\) −1.08763 + 1.08763i −0.107691 + 0.107691i
\(103\) 13.9084 13.9084i 1.37044 1.37044i 0.510653 0.859787i \(-0.329404\pi\)
0.859787 0.510653i \(-0.170596\pi\)
\(104\) −2.02179 −0.198253
\(105\) 0 0
\(106\) −1.38312 −0.134340
\(107\) 1.98061 1.98061i 0.191473 0.191473i −0.604859 0.796332i \(-0.706771\pi\)
0.796332 + 0.604859i \(0.206771\pi\)
\(108\) 1.21205 1.21205i 0.116630 0.116630i
\(109\) 5.91085i 0.566157i 0.959097 + 0.283078i \(0.0913557\pi\)
−0.959097 + 0.283078i \(0.908644\pi\)
\(110\) −1.15258 12.5267i −0.109894 1.19437i
\(111\) 1.46027i 0.138602i
\(112\) 0 0
\(113\) −13.5818 13.5818i −1.27767 1.27767i −0.941970 0.335697i \(-0.891028\pi\)
−0.335697 0.941970i \(-0.608972\pi\)
\(114\) 1.12760i 0.105609i
\(115\) −2.50259 + 0.230263i −0.233368 + 0.0214722i
\(116\) 3.15502 0.292936
\(117\) 4.16885 + 4.16885i 0.385410 + 0.385410i
\(118\) 3.87385 3.87385i 0.356617 0.356617i
\(119\) 0 0
\(120\) −0.414214 + 0.498161i −0.0378124 + 0.0454757i
\(121\) 20.6492 1.87720
\(122\) 3.25923 + 3.25923i 0.295077 + 0.295077i
\(123\) 1.47725 + 1.47725i 0.133199 + 0.133199i
\(124\) −3.84846 −0.345602
\(125\) −9.75680 5.45939i −0.872674 0.488303i
\(126\) 0 0
\(127\) 4.63487 4.63487i 0.411278 0.411278i −0.470906 0.882184i \(-0.656073\pi\)
0.882184 + 0.470906i \(0.156073\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0.760780 0.0669829
\(130\) −3.47617 2.89039i −0.304881 0.253504i
\(131\) 7.69535i 0.672346i 0.941800 + 0.336173i \(0.109133\pi\)
−0.941800 + 0.336173i \(0.890867\pi\)
\(132\) −1.15258 1.15258i −0.100319 0.100319i
\(133\) 0 0
\(134\) 0.844985i 0.0729956i
\(135\) 3.81672 0.351176i 0.328491 0.0302244i
\(136\) 5.30873i 0.455220i
\(137\) −6.24784 + 6.24784i −0.533789 + 0.533789i −0.921698 0.387909i \(-0.873198\pi\)
0.387909 + 0.921698i \(0.373198\pi\)
\(138\) −0.230263 + 0.230263i −0.0196013 + 0.0196013i
\(139\) −11.0631 −0.938361 −0.469180 0.883102i \(-0.655451\pi\)
−0.469180 + 0.883102i \(0.655451\pi\)
\(140\) 0 0
\(141\) 1.70818 0.143855
\(142\) 3.37792 3.37792i 0.283469 0.283469i
\(143\) 8.04270 8.04270i 0.672564 0.672564i
\(144\) 2.91605i 0.243004i
\(145\) 5.42460 + 4.51047i 0.450488 + 0.374574i
\(146\) 5.61227i 0.464475i
\(147\) 0 0
\(148\) 3.56380 + 3.56380i 0.292943 + 0.292943i
\(149\) 5.04885i 0.413618i −0.978381 0.206809i \(-0.933692\pi\)
0.978381 0.206809i \(-0.0663079\pi\)
\(150\) −1.42436 + 0.264349i −0.116299 + 0.0215840i
\(151\) 13.4428 1.09396 0.546981 0.837145i \(-0.315777\pi\)
0.546981 + 0.837145i \(0.315777\pi\)
\(152\) 2.75192 + 2.75192i 0.223210 + 0.223210i
\(153\) 10.9464 10.9464i 0.884963 0.884963i
\(154\) 0 0
\(155\) −6.61688 5.50184i −0.531481 0.441918i
\(156\) −0.585786 −0.0469005
\(157\) −0.779844 0.779844i −0.0622383 0.0622383i 0.675303 0.737541i \(-0.264013\pi\)
−0.737541 + 0.675303i \(0.764013\pi\)
\(158\) 4.41789 + 4.41789i 0.351469 + 0.351469i
\(159\) −0.400741 −0.0317808
\(160\) 0.204875 + 2.22666i 0.0161968 + 0.176033i
\(161\) 0 0
\(162\) −5.83471 + 5.83471i −0.458418 + 0.458418i
\(163\) −9.36288 9.36288i −0.733358 0.733358i 0.237926 0.971283i \(-0.423533\pi\)
−0.971283 + 0.237926i \(0.923533\pi\)
\(164\) 7.21050 0.563046
\(165\) −0.333944 3.62944i −0.0259975 0.282551i
\(166\) 8.02257i 0.622672i
\(167\) 4.70680 + 4.70680i 0.364223 + 0.364223i 0.865365 0.501142i \(-0.167087\pi\)
−0.501142 + 0.865365i \(0.667087\pi\)
\(168\) 0 0
\(169\) 8.91237i 0.685567i
\(170\) −7.58946 + 9.12760i −0.582085 + 0.700055i
\(171\) 11.3487i 0.867857i
\(172\) 1.85669 1.85669i 0.141571 0.141571i
\(173\) −4.98835 + 4.98835i −0.379257 + 0.379257i −0.870834 0.491577i \(-0.836421\pi\)
0.491577 + 0.870834i \(0.336421\pi\)
\(174\) 0.914124 0.0692996
\(175\) 0 0
\(176\) −5.62576 −0.424058
\(177\) 1.12240 1.12240i 0.0843646 0.0843646i
\(178\) −8.42999 + 8.42999i −0.631855 + 0.631855i
\(179\) 2.20635i 0.164910i −0.996595 0.0824550i \(-0.973724\pi\)
0.996595 0.0824550i \(-0.0262761\pi\)
\(180\) 4.16885 5.01373i 0.310727 0.373702i
\(181\) 4.11867i 0.306139i −0.988215 0.153069i \(-0.951084\pi\)
0.988215 0.153069i \(-0.0489158\pi\)
\(182\) 0 0
\(183\) 0.944318 + 0.944318i 0.0698060 + 0.0698060i
\(184\) 1.12392i 0.0828566i
\(185\) 1.03256 + 11.2223i 0.0759156 + 0.825081i
\(186\) −1.11504 −0.0817588
\(187\) −21.1182 21.1182i −1.54432 1.54432i
\(188\) 4.16885 4.16885i 0.304044 0.304044i
\(189\) 0 0
\(190\) 0.797333 + 8.66573i 0.0578446 + 0.628678i
\(191\) −17.2023 −1.24472 −0.622359 0.782732i \(-0.713826\pi\)
−0.622359 + 0.782732i \(0.713826\pi\)
\(192\) 0.204875 + 0.204875i 0.0147856 + 0.0147856i
\(193\) −8.53293 8.53293i −0.614214 0.614214i 0.329827 0.944041i \(-0.393009\pi\)
−0.944041 + 0.329827i \(0.893009\pi\)
\(194\) 9.37769 0.673279
\(195\) −1.00718 0.837452i −0.0721254 0.0599712i
\(196\) 0 0
\(197\) 14.3135 14.3135i 1.01979 1.01979i 0.0199932 0.999800i \(-0.493636\pi\)
0.999800 0.0199932i \(-0.00636444\pi\)
\(198\) 11.6001 + 11.6001i 0.824383 + 0.824383i
\(199\) −7.53307 −0.534005 −0.267002 0.963696i \(-0.586033\pi\)
−0.267002 + 0.963696i \(0.586033\pi\)
\(200\) −2.83103 + 4.12132i −0.200184 + 0.291421i
\(201\) 0.244823i 0.0172685i
\(202\) 11.3839 + 11.3839i 0.800965 + 0.800965i
\(203\) 0 0
\(204\) 1.53813i 0.107691i
\(205\) 12.3974 + 10.3083i 0.865874 + 0.719961i
\(206\) 19.6695i 1.37044i
\(207\) 2.31748 2.31748i 0.161076 0.161076i
\(208\) −1.42962 + 1.42962i −0.0991263 + 0.0991263i
\(209\) −21.8944 −1.51446
\(210\) 0 0
\(211\) 19.5766 1.34771 0.673854 0.738865i \(-0.264638\pi\)
0.673854 + 0.738865i \(0.264638\pi\)
\(212\) −0.978013 + 0.978013i −0.0671702 + 0.0671702i
\(213\) 0.978707 0.978707i 0.0670599 0.0670599i
\(214\) 2.80101i 0.191473i
\(215\) 5.84668 0.537952i 0.398740 0.0366880i
\(216\) 1.71410i 0.116630i
\(217\) 0 0
\(218\) 4.17960 + 4.17960i 0.283078 + 0.283078i
\(219\) 1.62608i 0.109880i
\(220\) −9.67269 8.04270i −0.652132 0.542239i
\(221\) −10.7331 −0.721988
\(222\) 1.03256 + 1.03256i 0.0693012 + 0.0693012i
\(223\) −1.46027 + 1.46027i −0.0977867 + 0.0977867i −0.754308 0.656521i \(-0.772027\pi\)
0.656521 + 0.754308i \(0.272027\pi\)
\(224\) 0 0
\(225\) 14.3355 2.66053i 0.955698 0.177369i
\(226\) −19.2075 −1.27767
\(227\) −13.1828 13.1828i −0.874974 0.874974i 0.118035 0.993009i \(-0.462340\pi\)
−0.993009 + 0.118035i \(0.962340\pi\)
\(228\) 0.797333 + 0.797333i 0.0528047 + 0.0528047i
\(229\) −4.00767 −0.264834 −0.132417 0.991194i \(-0.542274\pi\)
−0.132417 + 0.991194i \(0.542274\pi\)
\(230\) −1.60678 + 1.93242i −0.105948 + 0.127420i
\(231\) 0 0
\(232\) 2.23093 2.23093i 0.146468 0.146468i
\(233\) −9.70971 9.70971i −0.636104 0.636104i 0.313488 0.949592i \(-0.398502\pi\)
−0.949592 + 0.313488i \(0.898502\pi\)
\(234\) 5.89564 0.385410
\(235\) 13.1276 1.20787i 0.856350 0.0787927i
\(236\) 5.47845i 0.356617i
\(237\) 1.28003 + 1.28003i 0.0831466 + 0.0831466i
\(238\) 0 0
\(239\) 19.6621i 1.27183i −0.771758 0.635916i \(-0.780622\pi\)
0.771758 0.635916i \(-0.219378\pi\)
\(240\) 0.0593598 + 0.645146i 0.00383166 + 0.0416440i
\(241\) 5.88512i 0.379094i −0.981872 0.189547i \(-0.939298\pi\)
0.981872 0.189547i \(-0.0607020\pi\)
\(242\) 14.6012 14.6012i 0.938599 0.938599i
\(243\) −5.32668 + 5.32668i −0.341707 + 0.341707i
\(244\) 4.60924 0.295077
\(245\) 0 0
\(246\) 2.08915 0.133199
\(247\) −5.56380 + 5.56380i −0.354016 + 0.354016i
\(248\) −2.72127 + 2.72127i −0.172801 + 0.172801i
\(249\) 2.32443i 0.147305i
\(250\) −10.7595 + 3.03873i −0.680488 + 0.192186i
\(251\) 7.09950i 0.448116i −0.974576 0.224058i \(-0.928069\pi\)
0.974576 0.224058i \(-0.0719306\pi\)
\(252\) 0 0
\(253\) −4.47097 4.47097i −0.281088 0.281088i
\(254\) 6.55469i 0.411278i
\(255\) −2.19895 + 2.64460i −0.137703 + 0.165611i
\(256\) 1.00000 0.0625000
\(257\) 6.99107 + 6.99107i 0.436091 + 0.436091i 0.890694 0.454603i \(-0.150219\pi\)
−0.454603 + 0.890694i \(0.650219\pi\)
\(258\) 0.537952 0.537952i 0.0334915 0.0334915i
\(259\) 0 0
\(260\) −4.50184 + 0.414214i −0.279192 + 0.0256884i
\(261\) −9.20019 −0.569477
\(262\) 5.44144 + 5.44144i 0.336173 + 0.336173i
\(263\) 9.72142 + 9.72142i 0.599448 + 0.599448i 0.940166 0.340718i \(-0.110670\pi\)
−0.340718 + 0.940166i \(0.610670\pi\)
\(264\) −1.62999 −0.100319
\(265\) −3.07974 + 0.283366i −0.189187 + 0.0174071i
\(266\) 0 0
\(267\) −2.44248 + 2.44248i −0.149477 + 0.149477i
\(268\) −0.597494 0.597494i −0.0364978 0.0364978i
\(269\) −26.5020 −1.61586 −0.807928 0.589281i \(-0.799411\pi\)
−0.807928 + 0.589281i \(0.799411\pi\)
\(270\) 2.45051 2.94715i 0.149133 0.179358i
\(271\) 12.7969i 0.777355i 0.921374 + 0.388678i \(0.127068\pi\)
−0.921374 + 0.388678i \(0.872932\pi\)
\(272\) 3.75384 + 3.75384i 0.227610 + 0.227610i
\(273\) 0 0
\(274\) 8.83578i 0.533789i
\(275\) −5.13280 27.6565i −0.309520 1.66775i
\(276\) 0.325641i 0.0196013i
\(277\) 14.2152 14.2152i 0.854110 0.854110i −0.136526 0.990636i \(-0.543594\pi\)
0.990636 + 0.136526i \(0.0435938\pi\)
\(278\) −7.82280 + 7.82280i −0.469180 + 0.469180i
\(279\) 11.2223 0.671863
\(280\) 0 0
\(281\) −14.1498 −0.844107 −0.422054 0.906571i \(-0.638691\pi\)
−0.422054 + 0.906571i \(0.638691\pi\)
\(282\) 1.20787 1.20787i 0.0719275 0.0719275i
\(283\) 19.1397 19.1397i 1.13774 1.13774i 0.148885 0.988854i \(-0.452431\pi\)
0.988854 0.148885i \(-0.0475686\pi\)
\(284\) 4.77710i 0.283469i
\(285\) 0.231017 + 2.51078i 0.0136843 + 0.148726i
\(286\) 11.3741i 0.672564i
\(287\) 0 0
\(288\) −2.06196 2.06196i −0.121502 0.121502i
\(289\) 11.1826i 0.657800i
\(290\) 7.02515 0.646383i 0.412531 0.0379569i
\(291\) 2.71706 0.159277
\(292\) 3.96848 + 3.96848i 0.232237 + 0.232237i
\(293\) −17.1191 + 17.1191i −1.00011 + 1.00011i −0.000106876 1.00000i \(0.500034\pi\)
−1.00000 0.000106876i \(0.999966\pi\)
\(294\) 0 0
\(295\) 7.83211 9.41941i 0.456003 0.548420i
\(296\) 5.03997 0.292943
\(297\) 6.81871 + 6.81871i 0.395661 + 0.395661i
\(298\) −3.57008 3.57008i −0.206809 0.206809i
\(299\) −2.27233 −0.131412
\(300\) −0.820253 + 1.19410i −0.0473573 + 0.0689413i
\(301\) 0 0
\(302\) 9.50552 9.50552i 0.546981 0.546981i
\(303\) 3.29832 + 3.29832i 0.189484 + 0.189484i
\(304\) 3.89180 0.223210
\(305\) 7.92493 + 6.58946i 0.453780 + 0.377312i
\(306\) 15.4805i 0.884963i
\(307\) −17.2974 17.2974i −0.987217 0.987217i 0.0127019 0.999919i \(-0.495957\pi\)
−0.999919 + 0.0127019i \(0.995957\pi\)
\(308\) 0 0
\(309\) 5.69898i 0.324204i
\(310\) −8.56923 + 0.788454i −0.486699 + 0.0447812i
\(311\) 10.9823i 0.622749i −0.950287 0.311374i \(-0.899211\pi\)
0.950287 0.311374i \(-0.100789\pi\)
\(312\) −0.414214 + 0.414214i −0.0234502 + 0.0234502i
\(313\) 20.7967 20.7967i 1.17550 1.17550i 0.194620 0.980879i \(-0.437653\pi\)
0.980879 0.194620i \(-0.0623475\pi\)
\(314\) −1.10287 −0.0622383
\(315\) 0 0
\(316\) 6.24784 0.351469
\(317\) 3.03630 3.03630i 0.170535 0.170535i −0.616679 0.787215i \(-0.711522\pi\)
0.787215 + 0.616679i \(0.211522\pi\)
\(318\) −0.283366 + 0.283366i −0.0158904 + 0.0158904i
\(319\) 17.7494i 0.993773i
\(320\) 1.71936 + 1.42962i 0.0961150 + 0.0799182i
\(321\) 0.811556i 0.0452966i
\(322\) 0 0
\(323\) 14.6092 + 14.6092i 0.812878 + 0.812878i
\(324\) 8.25152i 0.458418i
\(325\) −8.33243 5.72374i −0.462200 0.317496i
\(326\) −13.2411 −0.733358
\(327\) 1.21099 + 1.21099i 0.0669676 + 0.0669676i
\(328\) 5.09860 5.09860i 0.281523 0.281523i
\(329\) 0 0
\(330\) −2.80253 2.33027i −0.154274 0.128277i
\(331\) 35.4499 1.94850 0.974250 0.225469i \(-0.0723914\pi\)
0.974250 + 0.225469i \(0.0723914\pi\)
\(332\) 5.67281 + 5.67281i 0.311336 + 0.311336i
\(333\) −10.3922 10.3922i −0.569491 0.569491i
\(334\) 6.65642 0.364223
\(335\) −0.173116 1.88150i −0.00945835 0.102797i
\(336\) 0 0
\(337\) −12.1473 + 12.1473i −0.661708 + 0.661708i −0.955782 0.294075i \(-0.904989\pi\)
0.294075 + 0.955782i \(0.404989\pi\)
\(338\) 6.30200 + 6.30200i 0.342784 + 0.342784i
\(339\) −5.56513 −0.302257
\(340\) 1.08763 + 11.8207i 0.0589848 + 0.641070i
\(341\) 21.6505i 1.17244i
\(342\) −8.02475 8.02475i −0.433929 0.433929i
\(343\) 0 0
\(344\) 2.62576i 0.141571i
\(345\) −0.465543 + 0.559894i −0.0250640 + 0.0301437i
\(346\) 7.05459i 0.379257i
\(347\) 6.34718 6.34718i 0.340734 0.340734i −0.515909 0.856643i \(-0.672546\pi\)
0.856643 + 0.515909i \(0.172546\pi\)
\(348\) 0.646383 0.646383i 0.0346498 0.0346498i
\(349\) 26.0251 1.39309 0.696546 0.717512i \(-0.254719\pi\)
0.696546 + 0.717512i \(0.254719\pi\)
\(350\) 0 0
\(351\) 3.46554 0.184977
\(352\) −3.97801 + 3.97801i −0.212029 + 0.212029i
\(353\) −7.04715 + 7.04715i −0.375082 + 0.375082i −0.869324 0.494242i \(-0.835446\pi\)
0.494242 + 0.869324i \(0.335446\pi\)
\(354\) 1.58731i 0.0843646i
\(355\) 6.82943 8.21353i 0.362469 0.435929i
\(356\) 11.9218i 0.631855i
\(357\) 0 0
\(358\) −1.56012 1.56012i −0.0824550 0.0824550i
\(359\) 11.5741i 0.610858i 0.952215 + 0.305429i \(0.0987999\pi\)
−0.952215 + 0.305429i \(0.901200\pi\)
\(360\) −0.597426 6.49307i −0.0314871 0.342215i
\(361\) −3.85386 −0.202835
\(362\) −2.91234 2.91234i −0.153069 0.153069i
\(363\) 4.23050 4.23050i 0.222044 0.222044i
\(364\) 0 0
\(365\) 1.14981 + 12.4966i 0.0601840 + 0.654104i
\(366\) 1.33547 0.0698060
\(367\) 11.8047 + 11.8047i 0.616202 + 0.616202i 0.944555 0.328353i \(-0.106494\pi\)
−0.328353 + 0.944555i \(0.606494\pi\)
\(368\) 0.794732 + 0.794732i 0.0414283 + 0.0414283i
\(369\) −21.0262 −1.09458
\(370\) 8.66551 + 7.20525i 0.450499 + 0.374583i
\(371\) 0 0
\(372\) −0.788454 + 0.788454i −0.0408794 + 0.0408794i
\(373\) 2.24784 + 2.24784i 0.116389 + 0.116389i 0.762902 0.646514i \(-0.223774\pi\)
−0.646514 + 0.762902i \(0.723774\pi\)
\(374\) −29.8656 −1.54432
\(375\) −3.11741 + 0.880431i −0.160983 + 0.0454653i
\(376\) 5.89564i 0.304044i
\(377\) 4.51047 + 4.51047i 0.232301 + 0.232301i
\(378\) 0 0
\(379\) 7.15349i 0.367450i −0.982978 0.183725i \(-0.941184\pi\)
0.982978 0.183725i \(-0.0588156\pi\)
\(380\) 6.69140 + 5.56380i 0.343262 + 0.285417i
\(381\) 1.89914i 0.0972957i
\(382\) −12.1639 + 12.1639i −0.622359 + 0.622359i
\(383\) −10.3191 + 10.3191i −0.527280 + 0.527280i −0.919760 0.392480i \(-0.871617\pi\)
0.392480 + 0.919760i \(0.371617\pi\)
\(384\) 0.289737 0.0147856
\(385\) 0 0
\(386\) −12.0674 −0.614214
\(387\) −5.41421 + 5.41421i −0.275220 + 0.275220i
\(388\) 6.63103 6.63103i 0.336640 0.336640i
\(389\) 6.19651i 0.314176i −0.987585 0.157088i \(-0.949789\pi\)
0.987585 0.157088i \(-0.0502106\pi\)
\(390\) −1.30435 + 0.120013i −0.0660483 + 0.00607709i
\(391\) 5.96659i 0.301744i
\(392\) 0 0
\(393\) 1.57658 + 1.57658i 0.0795282 + 0.0795282i
\(394\) 20.2423i 1.01979i
\(395\) 10.7423 + 8.93204i 0.540502 + 0.449420i
\(396\) 16.4050 0.824383
\(397\) −2.06184 2.06184i −0.103481 0.103481i 0.653471 0.756952i \(-0.273312\pi\)
−0.756952 + 0.653471i \(0.773312\pi\)
\(398\) −5.32668 + 5.32668i −0.267002 + 0.267002i
\(399\) 0 0
\(400\) 0.912375 + 4.91605i 0.0456187 + 0.245803i
\(401\) −19.9706 −0.997282 −0.498641 0.866809i \(-0.666167\pi\)
−0.498641 + 0.866809i \(0.666167\pi\)
\(402\) −0.173116 0.173116i −0.00863425 0.00863425i
\(403\) −5.50184 5.50184i −0.274066 0.274066i
\(404\) 16.0992 0.800965
\(405\) −11.7965 + 14.1873i −0.586175 + 0.704973i
\(406\) 0 0
\(407\) −20.0491 + 20.0491i −0.993796 + 0.993796i
\(408\) 1.08763 + 1.08763i 0.0538455 + 0.0538455i
\(409\) 34.3582 1.69890 0.849451 0.527668i \(-0.176933\pi\)
0.849451 + 0.527668i \(0.176933\pi\)
\(410\) 16.0554 1.47725i 0.792918 0.0729562i
\(411\) 2.56005i 0.126278i
\(412\) −13.9084 13.9084i −0.685220 0.685220i
\(413\) 0 0
\(414\) 3.27741i 0.161076i
\(415\) 1.64362 + 17.8636i 0.0806823 + 0.876887i
\(416\) 2.02179i 0.0991263i
\(417\) −2.26655 + 2.26655i −0.110994 + 0.110994i
\(418\) −15.4816 + 15.4816i −0.757232 + 0.757232i
\(419\) 31.1360 1.52109 0.760547 0.649283i \(-0.224931\pi\)
0.760547 + 0.649283i \(0.224931\pi\)
\(420\) 0 0
\(421\) −33.6728 −1.64111 −0.820555 0.571567i \(-0.806336\pi\)
−0.820555 + 0.571567i \(0.806336\pi\)
\(422\) 13.8427 13.8427i 0.673854 0.673854i
\(423\) −12.1566 + 12.1566i −0.591073 + 0.591073i
\(424\) 1.38312i 0.0671702i
\(425\) −15.0292 + 21.8790i −0.729021 + 1.06129i
\(426\) 1.38410i 0.0670599i
\(427\) 0 0
\(428\) −1.98061 1.98061i −0.0957366 0.0957366i
\(429\) 3.29549i 0.159108i
\(430\) 3.75384 4.51462i 0.181026 0.217714i
\(431\) −14.7457 −0.710274 −0.355137 0.934814i \(-0.615566\pi\)
−0.355137 + 0.934814i \(0.615566\pi\)
\(432\) −1.21205 1.21205i −0.0583148 0.0583148i
\(433\) 9.98256 9.98256i 0.479731 0.479731i −0.425315 0.905046i \(-0.639837\pi\)
0.905046 + 0.425315i \(0.139837\pi\)
\(434\) 0 0
\(435\) 2.03545 0.187281i 0.0975922 0.00897944i
\(436\) 5.91085 0.283078
\(437\) 3.09294 + 3.09294i 0.147955 + 0.147955i
\(438\) 1.14981 + 1.14981i 0.0549402 + 0.0549402i
\(439\) 38.4285 1.83409 0.917046 0.398782i \(-0.130567\pi\)
0.917046 + 0.398782i \(0.130567\pi\)
\(440\) −12.5267 + 1.15258i −0.597186 + 0.0549470i
\(441\) 0 0
\(442\) −7.58946 + 7.58946i −0.360994 + 0.360994i
\(443\) 4.05568 + 4.05568i 0.192691 + 0.192691i 0.796858 0.604167i \(-0.206494\pi\)
−0.604167 + 0.796858i \(0.706494\pi\)
\(444\) 1.46027 0.0693012
\(445\) −17.0437 + 20.4978i −0.807947 + 0.971691i
\(446\) 2.06513i 0.0977867i
\(447\) −1.03438 1.03438i −0.0489247 0.0489247i
\(448\) 0 0
\(449\) 7.30267i 0.344635i −0.985042 0.172317i \(-0.944875\pi\)
0.985042 0.172317i \(-0.0551254\pi\)
\(450\) 8.25543 12.0180i 0.389165 0.566533i
\(451\) 40.5646i 1.91011i
\(452\) −13.5818 + 13.5818i −0.638833 + 0.638833i
\(453\) 2.75410 2.75410i 0.129399 0.129399i
\(454\) −18.6433 −0.874974
\(455\) 0 0
\(456\) 1.12760 0.0528047
\(457\) 3.63864 3.63864i 0.170208 0.170208i −0.616863 0.787071i \(-0.711597\pi\)
0.787071 + 0.616863i \(0.211597\pi\)
\(458\) −2.83385 + 2.83385i −0.132417 + 0.132417i
\(459\) 9.09969i 0.424737i
\(460\) 0.230263 + 2.50259i 0.0107361 + 0.116684i
\(461\) 29.4110i 1.36981i −0.728634 0.684903i \(-0.759845\pi\)
0.728634 0.684903i \(-0.240155\pi\)
\(462\) 0 0
\(463\) −4.04625 4.04625i −0.188045 0.188045i 0.606805 0.794851i \(-0.292451\pi\)
−0.794851 + 0.606805i \(0.792451\pi\)
\(464\) 3.15502i 0.146468i
\(465\) −2.48282 + 0.228444i −0.115138 + 0.0105938i
\(466\) −13.7316 −0.636104
\(467\) −11.7682 11.7682i −0.544568 0.544568i 0.380297 0.924865i \(-0.375822\pi\)
−0.924865 + 0.380297i \(0.875822\pi\)
\(468\) 4.16885 4.16885i 0.192705 0.192705i
\(469\) 0 0
\(470\) 8.42852 10.1367i 0.388779 0.467571i
\(471\) −0.319541 −0.0147237
\(472\) −3.87385 3.87385i −0.178308 0.178308i
\(473\) 10.4453 + 10.4453i 0.480276 + 0.480276i
\(474\) 1.81023 0.0831466
\(475\) 3.55078 + 19.1323i 0.162921 + 0.877851i
\(476\) 0 0
\(477\) 2.85194 2.85194i 0.130581 0.130581i
\(478\) −13.9032 13.9032i −0.635916 0.635916i
\(479\) 15.3892 0.703150 0.351575 0.936160i \(-0.385646\pi\)
0.351575 + 0.936160i \(0.385646\pi\)
\(480\) 0.498161 + 0.414214i 0.0227378 + 0.0189062i
\(481\) 10.1898i 0.464613i
\(482\) −4.16141 4.16141i −0.189547 0.189547i
\(483\) 0 0
\(484\) 20.6492i 0.938599i
\(485\) 20.8810 1.92125i 0.948155 0.0872396i
\(486\) 7.53307i 0.341707i
\(487\) −25.4502 + 25.4502i −1.15326 + 1.15326i −0.167363 + 0.985895i \(0.553525\pi\)
−0.985895 + 0.167363i \(0.946475\pi\)
\(488\) 3.25923 3.25923i 0.147538 0.147538i
\(489\) −3.83644 −0.173490
\(490\) 0 0
\(491\) −15.2823 −0.689680 −0.344840 0.938661i \(-0.612067\pi\)
−0.344840 + 0.938661i \(0.612067\pi\)
\(492\) 1.47725 1.47725i 0.0665996 0.0665996i
\(493\) 11.8434 11.8434i 0.533401 0.533401i
\(494\) 7.86840i 0.354016i
\(495\) 28.2061 + 23.4529i 1.26777 + 1.05413i
\(496\) 3.84846i 0.172801i
\(497\) 0 0
\(498\) 1.64362 + 1.64362i 0.0736525 + 0.0736525i
\(499\) 31.5850i 1.41394i −0.707245 0.706969i \(-0.750062\pi\)
0.707245 0.706969i \(-0.249938\pi\)
\(500\) −5.45939 + 9.75680i −0.244151 + 0.436337i
\(501\) 1.92861 0.0861639
\(502\) −5.02010 5.02010i −0.224058 0.224058i
\(503\) −16.9777 + 16.9777i −0.756997 + 0.756997i −0.975775 0.218778i \(-0.929793\pi\)
0.218778 + 0.975775i \(0.429793\pi\)
\(504\) 0 0
\(505\) 27.6803 + 23.0157i 1.23176 + 1.02419i
\(506\) −6.32291 −0.281088
\(507\) 1.82592 + 1.82592i 0.0810920 + 0.0810920i
\(508\) −4.63487 4.63487i −0.205639 0.205639i
\(509\) 21.5141 0.953597 0.476799 0.879013i \(-0.341797\pi\)
0.476799 + 0.879013i \(0.341797\pi\)
\(510\) 0.315125 + 3.42491i 0.0139540 + 0.151657i
\(511\) 0 0
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −4.71706 4.71706i −0.208263 0.208263i
\(514\) 9.88686 0.436091
\(515\) −4.02979 43.7974i −0.177574 1.92994i
\(516\) 0.760780i 0.0334915i
\(517\) 23.4529 + 23.4529i 1.03146 + 1.03146i
\(518\) 0 0
\(519\) 2.04397i 0.0897205i
\(520\) −2.89039 + 3.47617i −0.126752 + 0.152440i
\(521\) 13.2395i 0.580031i 0.957022 + 0.290016i \(0.0936605\pi\)
−0.957022 + 0.290016i \(0.906340\pi\)
\(522\) −6.50552 + 6.50552i −0.284739 + 0.284739i
\(523\) −19.0426 + 19.0426i −0.832673 + 0.832673i −0.987882 0.155209i \(-0.950395\pi\)
0.155209 + 0.987882i \(0.450395\pi\)
\(524\) 7.69535 0.336173
\(525\) 0 0
\(526\) 13.7482 0.599448
\(527\) −14.4465 + 14.4465i −0.629300 + 0.629300i
\(528\) −1.15258 + 1.15258i −0.0501595 + 0.0501595i
\(529\) 21.7368i 0.945078i
\(530\) −1.97733 + 2.37808i −0.0858899 + 0.103297i
\(531\) 15.9755i 0.693276i
\(532\) 0 0
\(533\) 10.3083 + 10.3083i 0.446501 + 0.446501i
\(534\) 3.45419i 0.149477i
\(535\) −0.573857 6.23691i −0.0248100 0.269645i
\(536\) −0.844985 −0.0364978
\(537\) −0.452025 0.452025i −0.0195063 0.0195063i
\(538\) −18.7398 + 18.7398i −0.807928 + 0.807928i
\(539\) 0 0
\(540\) −0.351176 3.81672i −0.0151122 0.164245i
\(541\) −11.3298 −0.487107 −0.243553 0.969888i \(-0.578313\pi\)
−0.243553 + 0.969888i \(0.578313\pi\)
\(542\) 9.04876 + 9.04876i 0.388678 + 0.388678i
\(543\) −0.843813 0.843813i −0.0362115 0.0362115i
\(544\) 5.30873 0.227610
\(545\) 10.1629 + 8.45027i 0.435329 + 0.361970i
\(546\) 0 0
\(547\) −30.9149 + 30.9149i −1.32182 + 1.32182i −0.409527 + 0.912298i \(0.634306\pi\)
−0.912298 + 0.409527i \(0.865694\pi\)
\(548\) 6.24784 + 6.24784i 0.266895 + 0.266895i
\(549\) −13.4408 −0.573639
\(550\) −23.1856 15.9267i −0.988636 0.679116i
\(551\) 12.2787i 0.523090i
\(552\) 0.230263 + 0.230263i 0.00980065 + 0.00980065i
\(553\) 0 0
\(554\) 20.1034i 0.854110i
\(555\) 2.51072 + 2.08763i 0.106574 + 0.0886148i
\(556\) 11.0631i 0.469180i
\(557\) −18.6675 + 18.6675i −0.790967 + 0.790967i −0.981651 0.190685i \(-0.938929\pi\)
0.190685 + 0.981651i \(0.438929\pi\)
\(558\) 7.93538 7.93538i 0.335931 0.335931i
\(559\) 5.30873 0.224535
\(560\) 0 0
\(561\) −8.65318 −0.365337
\(562\) −10.0054 + 10.0054i −0.422054 + 0.422054i
\(563\) −14.2790 + 14.2790i −0.601788 + 0.601788i −0.940787 0.338999i \(-0.889912\pi\)
0.338999 + 0.940787i \(0.389912\pi\)
\(564\) 1.70818i 0.0719275i
\(565\) −42.7687 + 3.93514i −1.79929 + 0.165553i
\(566\) 27.0677i 1.13774i
\(567\) 0 0
\(568\) −3.37792 3.37792i −0.141734 0.141734i
\(569\) 24.8134i 1.04023i 0.854096 + 0.520116i \(0.174111\pi\)
−0.854096 + 0.520116i \(0.825889\pi\)
\(570\) 1.93874 + 1.61204i 0.0812051 + 0.0675208i
\(571\) 4.58059 0.191692 0.0958458 0.995396i \(-0.469444\pi\)
0.0958458 + 0.995396i \(0.469444\pi\)
\(572\) −8.04270 8.04270i −0.336282 0.336282i
\(573\) −3.52433 + 3.52433i −0.147231 + 0.147231i
\(574\) 0 0
\(575\) −3.18185 + 4.63204i −0.132692 + 0.193169i
\(576\) −2.91605 −0.121502
\(577\) −13.9869 13.9869i −0.582284 0.582284i 0.353247 0.935530i \(-0.385078\pi\)
−0.935530 + 0.353247i \(0.885078\pi\)
\(578\) 7.90730 + 7.90730i 0.328900 + 0.328900i
\(579\) −3.49637 −0.145304
\(580\) 4.51047 5.42460i 0.187287 0.225244i
\(581\) 0 0
\(582\) 1.92125 1.92125i 0.0796385 0.0796385i
\(583\) −5.50207 5.50207i −0.227872 0.227872i
\(584\) 5.61227 0.232237
\(585\) 13.1276 1.20787i 0.542759 0.0499392i
\(586\) 24.2100i 1.00011i
\(587\) −19.3782 19.3782i −0.799824 0.799824i 0.183244 0.983068i \(-0.441340\pi\)
−0.983068 + 0.183244i \(0.941340\pi\)
\(588\) 0 0
\(589\) 14.9775i 0.617136i
\(590\) −1.12240 12.1987i −0.0462084 0.502211i
\(591\) 5.86495i 0.241252i
\(592\) 3.56380 3.56380i 0.146471 0.146471i
\(593\) 2.28943 2.28943i 0.0940155 0.0940155i −0.658535 0.752550i \(-0.728823\pi\)
0.752550 + 0.658535i \(0.228823\pi\)
\(594\) 9.64311 0.395661
\(595\) 0 0
\(596\) −5.04885 −0.206809
\(597\) −1.54334 + 1.54334i −0.0631645 + 0.0631645i
\(598\) −1.60678 + 1.60678i −0.0657061 + 0.0657061i
\(599\) 7.80349i 0.318842i −0.987211 0.159421i \(-0.949037\pi\)
0.987211 0.159421i \(-0.0509627\pi\)
\(600\) 0.264349 + 1.42436i 0.0107920 + 0.0581493i
\(601\) 31.7170i 1.29377i −0.762590 0.646883i \(-0.776072\pi\)
0.762590 0.646883i \(-0.223928\pi\)
\(602\) 0 0
\(603\) 1.74233 + 1.74233i 0.0709530 + 0.0709530i
\(604\) 13.4428i 0.546981i
\(605\) 29.5205 35.5033i 1.20018 1.44341i
\(606\) 4.66453 0.189484
\(607\) −0.544276 0.544276i −0.0220915 0.0220915i 0.695975 0.718066i \(-0.254973\pi\)
−0.718066 + 0.695975i \(0.754973\pi\)
\(608\) 2.75192 2.75192i 0.111605 0.111605i
\(609\) 0 0
\(610\) 10.2632 0.944318i 0.415546 0.0382343i
\(611\) 11.9197 0.482221
\(612\) −10.9464 10.9464i −0.442482 0.442482i
\(613\) 24.7496 + 24.7496i 0.999626 + 0.999626i 1.00000 0.000373538i \(-0.000118901\pi\)
−0.000373538 1.00000i \(0.500119\pi\)
\(614\) −24.4623 −0.987217
\(615\) 4.65183 0.428014i 0.187580 0.0172592i
\(616\) 0 0
\(617\) 21.5403 21.5403i 0.867179 0.867179i −0.124980 0.992159i \(-0.539887\pi\)
0.992159 + 0.124980i \(0.0398866\pi\)
\(618\) −4.02979 4.02979i −0.162102 0.162102i
\(619\) −43.3415 −1.74204 −0.871021 0.491247i \(-0.836541\pi\)
−0.871021 + 0.491247i \(0.836541\pi\)
\(620\) −5.50184 + 6.61688i −0.220959 + 0.265740i
\(621\) 1.92651i 0.0773082i
\(622\) −7.76566 7.76566i −0.311374 0.311374i
\(623\) 0 0
\(624\) 0.585786i 0.0234502i
\(625\) −23.3351 + 8.97056i −0.933406 + 0.358823i
\(626\) 29.4110i 1.17550i
\(627\) −4.48560 + 4.48560i −0.179138 + 0.179138i
\(628\) −0.779844 + 0.779844i −0.0311192 + 0.0311192i
\(629\) 26.7559 1.06683
\(630\) 0 0
\(631\) 7.53463 0.299949 0.149974 0.988690i \(-0.452081\pi\)
0.149974 + 0.988690i \(0.452081\pi\)
\(632\) 4.41789 4.41789i 0.175734 0.175734i
\(633\) 4.01075 4.01075i 0.159413 0.159413i
\(634\) 4.29397i 0.170535i
\(635\) −1.34289 14.5951i −0.0532910 0.579188i
\(636\) 0.400741i 0.0158904i
\(637\) 0 0
\(638\) 12.5507 + 12.5507i 0.496887 + 0.496887i
\(639\) 13.9303i 0.551073i
\(640\) 2.22666 0.204875i 0.0880166 0.00809839i
\(641\) 24.3315 0.961035 0.480518 0.876985i \(-0.340449\pi\)
0.480518 + 0.876985i \(0.340449\pi\)
\(642\) −0.573857 0.573857i −0.0226483 0.0226483i
\(643\) 6.21713 6.21713i 0.245180 0.245180i −0.573809 0.818989i \(-0.694535\pi\)
0.818989 + 0.573809i \(0.194535\pi\)
\(644\) 0 0
\(645\) 1.08763 1.30805i 0.0428252 0.0515045i
\(646\) 20.6605 0.812878
\(647\) 14.5856 + 14.5856i 0.573418 + 0.573418i 0.933082 0.359664i \(-0.117109\pi\)
−0.359664 + 0.933082i \(0.617109\pi\)
\(648\) 5.83471 + 5.83471i 0.229209 + 0.229209i
\(649\) 30.8205 1.20981
\(650\) −9.93921 + 1.84463i −0.389848 + 0.0723523i
\(651\) 0 0
\(652\) −9.36288 + 9.36288i −0.366679 + 0.366679i
\(653\) 18.4835 + 18.4835i 0.723316 + 0.723316i 0.969279 0.245963i \(-0.0791041\pi\)
−0.245963 + 0.969279i \(0.579104\pi\)
\(654\) 1.71259 0.0669676
\(655\) 13.2311 + 11.0014i 0.516980 + 0.429861i
\(656\) 7.21050i 0.281523i
\(657\) −11.5723 11.5723i −0.451478 0.451478i
\(658\) 0 0
\(659\) 24.2448i 0.944443i −0.881480 0.472222i \(-0.843452\pi\)
0.881480 0.472222i \(-0.156548\pi\)
\(660\) −3.62944 + 0.333944i −0.141276 + 0.0129988i
\(661\) 17.9326i 0.697497i 0.937216 + 0.348749i \(0.113393\pi\)
−0.937216 + 0.348749i \(0.886607\pi\)
\(662\) 25.0668 25.0668i 0.974250 0.974250i
\(663\) −2.19895 + 2.19895i −0.0854001 + 0.0854001i
\(664\) 8.02257 0.311336
\(665\) 0 0
\(666\) −14.6968 −0.569491
\(667\) 2.50739 2.50739i 0.0970866 0.0970866i
\(668\) 4.70680 4.70680i 0.182112 0.182112i
\(669\) 0.598344i 0.0231333i
\(670\) −1.45283 1.20801i −0.0561277 0.0466694i
\(671\) 25.9305i 1.00104i
\(672\) 0 0
\(673\) −4.85386 4.85386i −0.187103 0.187103i 0.607340 0.794442i \(-0.292237\pi\)
−0.794442 + 0.607340i \(0.792237\pi\)
\(674\) 17.1789i 0.661708i
\(675\) 4.85266 7.06435i 0.186779 0.271907i
\(676\) 8.91237 0.342784
\(677\) 13.0676 + 13.0676i 0.502227 + 0.502227i 0.912129 0.409902i \(-0.134437\pi\)
−0.409902 + 0.912129i \(0.634437\pi\)
\(678\) −3.93514 + 3.93514i −0.151128 + 0.151128i
\(679\) 0 0
\(680\) 9.12760 + 7.58946i 0.350027 + 0.291043i
\(681\) −5.40166 −0.206992
\(682\) −15.3092 15.3092i −0.586221 0.586221i
\(683\) −18.9512 18.9512i −0.725147 0.725147i 0.244502 0.969649i \(-0.421375\pi\)
−0.969649 + 0.244502i \(0.921375\pi\)
\(684\) −11.3487 −0.433929
\(685\) 1.81023 + 19.6743i 0.0691653 + 0.751717i
\(686\) 0 0
\(687\) −0.821071 + 0.821071i −0.0313258 + 0.0313258i
\(688\) −1.85669 1.85669i −0.0707857 0.0707857i
\(689\) −2.79637 −0.106533
\(690\) 0.0667157 + 0.725093i 0.00253983 + 0.0276038i
\(691\) 29.0722i 1.10596i −0.833194 0.552980i \(-0.813491\pi\)
0.833194 0.552980i \(-0.186509\pi\)
\(692\) 4.98835 + 4.98835i 0.189628 + 0.189628i
\(693\) 0 0
\(694\) 8.97626i 0.340734i
\(695\) −15.8160 + 19.0214i −0.599937 + 0.721524i
\(696\) 0.914124i 0.0346498i
\(697\) 27.0671 27.0671i 1.02524 1.02524i
\(698\) 18.4025 18.4025i 0.696546 0.696546i
\(699\) −3.97855 −0.150483
\(700\) 0 0
\(701\) 25.4462 0.961089 0.480545 0.876970i \(-0.340439\pi\)
0.480545 + 0.876970i \(0.340439\pi\)
\(702\) 2.45051 2.45051i 0.0924885 0.0924885i
\(703\) 13.8696 13.8696i 0.523102 0.523102i
\(704\) 5.62576i 0.212029i
\(705\) 2.44205 2.93698i 0.0919731 0.110613i
\(706\) 9.96618i 0.375082i
\(707\) 0 0
\(708\) −1.12240 1.12240i −0.0421823 0.0421823i
\(709\) 31.4072i 1.17952i −0.807578 0.589760i \(-0.799222\pi\)
0.807578 0.589760i \(-0.200778\pi\)
\(710\) −0.978707 10.6370i −0.0367302 0.399199i
\(711\) −18.2190 −0.683267
\(712\) 8.42999 + 8.42999i 0.315927 + 0.315927i
\(713\) −3.05850 + 3.05850i −0.114542 + 0.114542i
\(714\) 0 0
\(715\) −2.33027 25.3263i −0.0871470 0.947149i
\(716\) −2.20635 −0.0824550
\(717\) −4.02826 4.02826i −0.150438 0.150438i
\(718\) 8.18413 + 8.18413i 0.305429 + 0.305429i
\(719\) −10.8043 −0.402932 −0.201466 0.979496i \(-0.564570\pi\)
−0.201466 + 0.979496i \(0.564570\pi\)
\(720\) −5.01373 4.16885i −0.186851 0.155364i
\(721\) 0 0
\(722\) −2.72509 + 2.72509i −0.101417 + 0.101417i
\(723\) −1.20571 1.20571i −0.0448410 0.0448410i
\(724\) −4.11867 −0.153069
\(725\) 15.5102 2.87856i 0.576035 0.106907i
\(726\) 5.98283i 0.222044i
\(727\) −33.6108 33.6108i −1.24656 1.24656i −0.957231 0.289326i \(-0.906569\pi\)
−0.289326 0.957231i \(-0.593431\pi\)
\(728\) 0 0
\(729\) 22.5720i 0.835998i
\(730\) 9.64950 + 8.02342i 0.357144 + 0.296960i
\(731\) 13.9394i 0.515569i
\(732\) 0.944318 0.944318i 0.0349030 0.0349030i
\(733\) 18.2134 18.2134i 0.672729 0.672729i −0.285616 0.958344i \(-0.592198\pi\)
0.958344 + 0.285616i \(0.0921981\pi\)
\(734\) 16.6944 0.616202
\(735\) 0 0
\(736\) 1.12392 0.0414283
\(737\) 3.36136 3.36136i 0.123817 0.123817i
\(738\) −14.8678 + 14.8678i −0.547290 + 0.547290i
\(739\) 12.1184i 0.445782i −0.974843 0.222891i \(-0.928451\pi\)
0.974843 0.222891i \(-0.0715495\pi\)
\(740\) 11.2223 1.03256i 0.412541 0.0379578i
\(741\) 2.27977i 0.0837493i
\(742\) 0 0
\(743\) 23.2618 + 23.2618i 0.853393 + 0.853393i 0.990549 0.137157i \(-0.0437964\pi\)
−0.137157 + 0.990549i \(0.543796\pi\)
\(744\) 1.11504i 0.0408794i
\(745\) −8.68078 7.21794i −0.318039 0.264445i
\(746\) 3.17893 0.116389
\(747\) −16.5422 16.5422i −0.605248 0.605248i
\(748\) −21.1182 + 21.1182i −0.772158 + 0.772158i
\(749\) 0 0
\(750\) −1.58179 + 2.82690i −0.0577587 + 0.103224i
\(751\) 13.9777 0.510055 0.255028 0.966934i \(-0.417915\pi\)
0.255028 + 0.966934i \(0.417915\pi\)
\(752\) −4.16885 4.16885i −0.152022 0.152022i
\(753\) −1.45451 1.45451i −0.0530053 0.0530053i
\(754\) 6.37877 0.232301
\(755\) 19.2181 23.1130i 0.699420 0.841169i
\(756\) 0 0
\(757\) 17.5547 17.5547i 0.638036 0.638036i −0.312035 0.950071i \(-0.601010\pi\)
0.950071 + 0.312035i \(0.101010\pi\)
\(758\) −5.05828 5.05828i −0.183725 0.183725i
\(759\) −1.83198 −0.0664967
\(760\) 8.66573 0.797333i 0.314339 0.0289223i
\(761\) 21.8667i 0.792669i −0.918106 0.396334i \(-0.870282\pi\)
0.918106 0.396334i \(-0.129718\pi\)
\(762\) −1.34289 1.34289i −0.0486478 0.0486478i
\(763\) 0 0
\(764\) 17.2023i 0.622359i
\(765\) −3.17157 34.4699i −0.114668 1.24626i
\(766\) 14.5934i 0.527280i
\(767\) 7.83211 7.83211i 0.282801 0.282801i
\(768\) 0.204875 0.204875i 0.00739279 0.00739279i
\(769\) −31.0506 −1.11971 −0.559857 0.828589i \(-0.689144\pi\)
−0.559857 + 0.828589i \(0.689144\pi\)
\(770\) 0 0
\(771\) 2.86459 0.103166
\(772\) −8.53293 + 8.53293i −0.307107 + 0.307107i
\(773\) 4.29108 4.29108i 0.154340 0.154340i −0.625713 0.780053i \(-0.715192\pi\)
0.780053 + 0.625713i \(0.215192\pi\)
\(774\) 7.65685i 0.275220i
\(775\) −18.9192 + 3.51124i −0.679599 + 0.126127i
\(776\) 9.37769i 0.336640i
\(777\) 0 0
\(778\) −4.38160 4.38160i −0.157088 0.157088i
\(779\) 28.0619i 1.00542i
\(780\) −0.837452 + 1.00718i −0.0299856 + 0.0360627i
\(781\) 26.8748 0.961656
\(782\) 4.21902 + 4.21902i 0.150872 + 0.150872i
\(783\) −3.82404 + 3.82404i −0.136660 + 0.136660i
\(784\) 0