Properties

Label 570.2.m.a.493.2
Level $570$
Weight $2$
Character 570.493
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 153 x^{16} + 6416 x^{12} + 78648 x^{8} + 19120 x^{4} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 493.2
Root \(-0.120370 - 0.120370i\) of defining polynomial
Character \(\chi\) \(=\) 570.493
Dual form 570.2.m.a.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.66396 - 1.49373i) q^{5} +1.00000 q^{6} +(-0.170229 + 0.170229i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.66396 - 1.49373i) q^{5} +1.00000 q^{6} +(-0.170229 + 0.170229i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(0.120370 + 2.23283i) q^{10} +3.43349 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-4.54030 + 4.54030i) q^{13} +0.240740 q^{14} +(2.23283 - 0.120370i) q^{15} -1.00000 q^{16} +(0.537531 - 0.537531i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-2.42784 - 3.62016i) q^{19} +(1.49373 - 1.66396i) q^{20} -0.240740i q^{21} +(-2.42784 - 2.42784i) q^{22} +(5.15769 + 5.15769i) q^{23} +1.00000i q^{24} +(0.537531 + 4.97102i) q^{25} +6.42095 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.170229 - 0.170229i) q^{28} +5.37513 q^{29} +(-1.66396 - 1.49373i) q^{30} +5.37513i q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.42784 + 2.42784i) q^{33} -0.760184 q^{34} +(0.537531 - 0.0289779i) q^{35} +1.00000 q^{36} +(5.54122 + 5.54122i) q^{37} +(-0.843095 + 4.27659i) q^{38} -6.42095i q^{39} +(-2.23283 + 0.120370i) q^{40} +3.68222i q^{41} +(-0.170229 + 0.170229i) q^{42} +(2.29224 + 2.29224i) q^{43} +3.43349i q^{44} +(-1.49373 + 1.66396i) q^{45} -7.29408i q^{46} +(-9.57865 + 9.57865i) q^{47} +(0.707107 - 0.707107i) q^{48} +6.94204i q^{49} +(3.13495 - 3.89514i) q^{50} +0.760184i q^{51} +(-4.54030 - 4.54030i) q^{52} +(1.93366 - 1.93366i) q^{53} -1.00000i q^{54} +(-5.71319 - 5.12871i) q^{55} +0.240740i q^{56} +(4.27659 + 0.843095i) q^{57} +(-3.80079 - 3.80079i) q^{58} +4.20166 q^{59} +(0.120370 + 2.23283i) q^{60} +1.65954 q^{61} +(3.80079 - 3.80079i) q^{62} +(0.170229 + 0.170229i) q^{63} -1.00000i q^{64} +(14.3369 - 0.772891i) q^{65} +3.43349 q^{66} +(-0.481480 - 0.481480i) q^{67} +(0.537531 + 0.537531i) q^{68} -7.29408 q^{69} +(-0.400582 - 0.359601i) q^{70} -8.93130i q^{71} +(-0.707107 - 0.707107i) q^{72} +(8.74888 + 8.74888i) q^{73} -7.83647i q^{74} +(-3.89514 - 3.13495i) q^{75} +(3.62016 - 2.42784i) q^{76} +(-0.584480 + 0.584480i) q^{77} +(-4.54030 + 4.54030i) q^{78} -1.15022 q^{79} +(1.66396 + 1.49373i) q^{80} -1.00000 q^{81} +(2.60372 - 2.60372i) q^{82} +(-9.97102 - 9.97102i) q^{83} +0.240740 q^{84} +(-1.69736 + 0.0915034i) q^{85} -3.24172i q^{86} +(-3.80079 + 3.80079i) q^{87} +(2.42784 - 2.42784i) q^{88} -2.10098 q^{89} +(2.23283 - 0.120370i) q^{90} -1.54578i q^{91} +(-5.15769 + 5.15769i) q^{92} +(-3.80079 - 3.80079i) q^{93} +13.5463 q^{94} +(-1.36771 + 9.65036i) q^{95} -1.00000 q^{96} +(-10.8544 - 10.8544i) q^{97} +(4.90877 - 4.90877i) q^{98} -3.43349i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} + 4q^{17} + 44q^{23} + 4q^{25} - 8q^{26} - 4q^{28} - 4q^{30} + 4q^{35} + 20q^{36} - 4q^{38} - 4q^{42} + 52q^{43} + 4q^{47} + 16q^{55} - 4q^{57} + 8q^{58} + 32q^{61} - 8q^{62} + 4q^{63} - 8q^{66} + 4q^{68} - 20q^{73} + 20q^{76} - 24q^{77} + 4q^{80} - 20q^{81} - 24q^{82} - 116q^{83} - 60q^{85} + 8q^{87} - 44q^{92} + 8q^{93} - 32q^{95} - 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −1.66396 1.49373i −0.744146 0.668017i
\(6\) 1.00000 0.408248
\(7\) −0.170229 + 0.170229i −0.0643405 + 0.0643405i −0.738545 0.674204i \(-0.764487\pi\)
0.674204 + 0.738545i \(0.264487\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 0.120370 + 2.23283i 0.0380644 + 0.706082i
\(11\) 3.43349 1.03524 0.517618 0.855612i \(-0.326819\pi\)
0.517618 + 0.855612i \(0.326819\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) −4.54030 + 4.54030i −1.25925 + 1.25925i −0.307803 + 0.951450i \(0.599594\pi\)
−0.951450 + 0.307803i \(0.900406\pi\)
\(14\) 0.240740 0.0643405
\(15\) 2.23283 0.120370i 0.576513 0.0310794i
\(16\) −1.00000 −0.250000
\(17\) 0.537531 0.537531i 0.130370 0.130370i −0.638911 0.769281i \(-0.720615\pi\)
0.769281 + 0.638911i \(0.220615\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −2.42784 3.62016i −0.556986 0.830522i
\(20\) 1.49373 1.66396i 0.334009 0.372073i
\(21\) 0.240740i 0.0525338i
\(22\) −2.42784 2.42784i −0.517618 0.517618i
\(23\) 5.15769 + 5.15769i 1.07545 + 1.07545i 0.996911 + 0.0785425i \(0.0250266\pi\)
0.0785425 + 0.996911i \(0.474973\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 0.537531 + 4.97102i 0.107506 + 0.994204i
\(26\) 6.42095 1.25925
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −0.170229 0.170229i −0.0321703 0.0321703i
\(29\) 5.37513 0.998137 0.499069 0.866562i \(-0.333676\pi\)
0.499069 + 0.866562i \(0.333676\pi\)
\(30\) −1.66396 1.49373i −0.303796 0.272717i
\(31\) 5.37513i 0.965402i 0.875785 + 0.482701i \(0.160344\pi\)
−0.875785 + 0.482701i \(0.839656\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −2.42784 + 2.42784i −0.422634 + 0.422634i
\(34\) −0.760184 −0.130370
\(35\) 0.537531 0.0289779i 0.0908593 0.00489816i
\(36\) 1.00000 0.166667
\(37\) 5.54122 + 5.54122i 0.910972 + 0.910972i 0.996349 0.0853770i \(-0.0272095\pi\)
−0.0853770 + 0.996349i \(0.527209\pi\)
\(38\) −0.843095 + 4.27659i −0.136768 + 0.693754i
\(39\) 6.42095i 1.02818i
\(40\) −2.23283 + 0.120370i −0.353041 + 0.0190322i
\(41\) 3.68222i 0.575066i 0.957771 + 0.287533i \(0.0928350\pi\)
−0.957771 + 0.287533i \(0.907165\pi\)
\(42\) −0.170229 + 0.170229i −0.0262669 + 0.0262669i
\(43\) 2.29224 + 2.29224i 0.349563 + 0.349563i 0.859947 0.510384i \(-0.170497\pi\)
−0.510384 + 0.859947i \(0.670497\pi\)
\(44\) 3.43349i 0.517618i
\(45\) −1.49373 + 1.66396i −0.222672 + 0.248049i
\(46\) 7.29408i 1.07545i
\(47\) −9.57865 + 9.57865i −1.39719 + 1.39719i −0.589208 + 0.807982i \(0.700560\pi\)
−0.807982 + 0.589208i \(0.799440\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 6.94204i 0.991721i
\(50\) 3.13495 3.89514i 0.443349 0.550855i
\(51\) 0.760184i 0.106447i
\(52\) −4.54030 4.54030i −0.629626 0.629626i
\(53\) 1.93366 1.93366i 0.265608 0.265608i −0.561720 0.827328i \(-0.689860\pi\)
0.827328 + 0.561720i \(0.189860\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −5.71319 5.12871i −0.770367 0.691556i
\(56\) 0.240740i 0.0321703i
\(57\) 4.27659 + 0.843095i 0.566448 + 0.111671i
\(58\) −3.80079 3.80079i −0.499069 0.499069i
\(59\) 4.20166 0.547010 0.273505 0.961871i \(-0.411817\pi\)
0.273505 + 0.961871i \(0.411817\pi\)
\(60\) 0.120370 + 2.23283i 0.0155397 + 0.288257i
\(61\) 1.65954 0.212483 0.106241 0.994340i \(-0.466118\pi\)
0.106241 + 0.994340i \(0.466118\pi\)
\(62\) 3.80079 3.80079i 0.482701 0.482701i
\(63\) 0.170229 + 0.170229i 0.0214468 + 0.0214468i
\(64\) 1.00000i 0.125000i
\(65\) 14.3369 0.772891i 1.77827 0.0958653i
\(66\) 3.43349 0.422634
\(67\) −0.481480 0.481480i −0.0588222 0.0588222i 0.677084 0.735906i \(-0.263243\pi\)
−0.735906 + 0.677084i \(0.763243\pi\)
\(68\) 0.537531 + 0.537531i 0.0651852 + 0.0651852i
\(69\) −7.29408 −0.878104
\(70\) −0.400582 0.359601i −0.0478787 0.0429806i
\(71\) 8.93130i 1.05995i −0.848013 0.529975i \(-0.822201\pi\)
0.848013 0.529975i \(-0.177799\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) 8.74888 + 8.74888i 1.02398 + 1.02398i 0.999705 + 0.0242731i \(0.00772714\pi\)
0.0242731 + 0.999705i \(0.492273\pi\)
\(74\) 7.83647i 0.910972i
\(75\) −3.89514 3.13495i −0.449771 0.361993i
\(76\) 3.62016 2.42784i 0.415261 0.278493i
\(77\) −0.584480 + 0.584480i −0.0666077 + 0.0666077i
\(78\) −4.54030 + 4.54030i −0.514088 + 0.514088i
\(79\) −1.15022 −0.129410 −0.0647050 0.997904i \(-0.520611\pi\)
−0.0647050 + 0.997904i \(0.520611\pi\)
\(80\) 1.66396 + 1.49373i 0.186036 + 0.167004i
\(81\) −1.00000 −0.111111
\(82\) 2.60372 2.60372i 0.287533 0.287533i
\(83\) −9.97102 9.97102i −1.09446 1.09446i −0.995046 0.0994159i \(-0.968303\pi\)
−0.0994159 0.995046i \(-0.531697\pi\)
\(84\) 0.240740 0.0262669
\(85\) −1.69736 + 0.0915034i −0.184104 + 0.00992494i
\(86\) 3.24172i 0.349563i
\(87\) −3.80079 + 3.80079i −0.407488 + 0.407488i
\(88\) 2.42784 2.42784i 0.258809 0.258809i
\(89\) −2.10098 −0.222703 −0.111351 0.993781i \(-0.535518\pi\)
−0.111351 + 0.993781i \(0.535518\pi\)
\(90\) 2.23283 0.120370i 0.235361 0.0126881i
\(91\) 1.54578i 0.162042i
\(92\) −5.15769 + 5.15769i −0.537727 + 0.537727i
\(93\) −3.80079 3.80079i −0.394124 0.394124i
\(94\) 13.5463 1.39719
\(95\) −1.36771 + 9.65036i −0.140324 + 0.990106i
\(96\) −1.00000 −0.102062
\(97\) −10.8544 10.8544i −1.10210 1.10210i −0.994157 0.107942i \(-0.965574\pi\)
−0.107942 0.994157i \(-0.534426\pi\)
\(98\) 4.90877 4.90877i 0.495860 0.495860i
\(99\) 3.43349i 0.345079i
\(100\) −4.97102 + 0.537531i −0.497102 + 0.0537531i
\(101\) 8.90870 0.886449 0.443225 0.896411i \(-0.353834\pi\)
0.443225 + 0.896411i \(0.353834\pi\)
\(102\) 0.537531 0.537531i 0.0532235 0.0532235i
\(103\) −6.26365 + 6.26365i −0.617176 + 0.617176i −0.944806 0.327630i \(-0.893750\pi\)
0.327630 + 0.944806i \(0.393750\pi\)
\(104\) 6.42095i 0.629626i
\(105\) −0.359601 + 0.400582i −0.0350935 + 0.0390928i
\(106\) −2.73460 −0.265608
\(107\) −5.59814 5.59814i −0.541193 0.541193i 0.382686 0.923879i \(-0.374999\pi\)
−0.923879 + 0.382686i \(0.874999\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) 10.7123 1.02605 0.513026 0.858373i \(-0.328524\pi\)
0.513026 + 0.858373i \(0.328524\pi\)
\(110\) 0.413290 + 7.66639i 0.0394056 + 0.730961i
\(111\) −7.83647 −0.743805
\(112\) 0.170229 0.170229i 0.0160851 0.0160851i
\(113\) 6.81260 6.81260i 0.640875 0.640875i −0.309895 0.950771i \(-0.600294\pi\)
0.950771 + 0.309895i \(0.100294\pi\)
\(114\) −2.42784 3.62016i −0.227389 0.339059i
\(115\) −0.877989 16.2864i −0.0818729 1.51872i
\(116\) 5.37513i 0.499069i
\(117\) 4.54030 + 4.54030i 0.419751 + 0.419751i
\(118\) −2.97102 2.97102i −0.273505 0.273505i
\(119\) 0.183007i 0.0167762i
\(120\) 1.49373 1.66396i 0.136358 0.151898i
\(121\) 0.788861 0.0717146
\(122\) −1.17347 1.17347i −0.106241 0.106241i
\(123\) −2.60372 2.60372i −0.234770 0.234770i
\(124\) −5.37513 −0.482701
\(125\) 6.53094 9.07451i 0.584145 0.811649i
\(126\) 0.240740i 0.0214468i
\(127\) −5.19935 5.19935i −0.461368 0.461368i 0.437736 0.899104i \(-0.355781\pi\)
−0.899104 + 0.437736i \(0.855781\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −3.24172 −0.285417
\(130\) −10.6842 9.59118i −0.937068 0.841202i
\(131\) 2.14729 0.187610 0.0938048 0.995591i \(-0.470097\pi\)
0.0938048 + 0.995591i \(0.470097\pi\)
\(132\) −2.42784 2.42784i −0.211317 0.211317i
\(133\) 1.02955 + 0.202967i 0.0892730 + 0.0175995i
\(134\) 0.680916i 0.0588222i
\(135\) −0.120370 2.23283i −0.0103598 0.192171i
\(136\) 0.760184i 0.0651852i
\(137\) −13.5518 + 13.5518i −1.15781 + 1.15781i −0.172863 + 0.984946i \(0.555302\pi\)
−0.984946 + 0.172863i \(0.944698\pi\)
\(138\) 5.15769 + 5.15769i 0.439052 + 0.439052i
\(139\) 10.5015i 0.890721i −0.895351 0.445361i \(-0.853075\pi\)
0.895351 0.445361i \(-0.146925\pi\)
\(140\) 0.0289779 + 0.537531i 0.00244908 + 0.0454297i
\(141\) 13.5463i 1.14080i
\(142\) −6.31539 + 6.31539i −0.529975 + 0.529975i
\(143\) −15.5891 + 15.5891i −1.30362 + 1.30362i
\(144\) 1.00000i 0.0833333i
\(145\) −8.94401 8.02901i −0.742760 0.666773i
\(146\) 12.3728i 1.02398i
\(147\) −4.90877 4.90877i −0.404868 0.404868i
\(148\) −5.54122 + 5.54122i −0.455486 + 0.455486i
\(149\) 1.02035i 0.0835900i 0.999126 + 0.0417950i \(0.0133076\pi\)
−0.999126 + 0.0417950i \(0.986692\pi\)
\(150\) 0.537531 + 4.97102i 0.0438892 + 0.405882i
\(151\) 19.8394i 1.61451i 0.590204 + 0.807254i \(0.299047\pi\)
−0.590204 + 0.807254i \(0.700953\pi\)
\(152\) −4.27659 0.843095i −0.346877 0.0683841i
\(153\) −0.537531 0.537531i −0.0434568 0.0434568i
\(154\) 0.826579 0.0666077
\(155\) 8.02901 8.94401i 0.644905 0.718400i
\(156\) 6.42095 0.514088
\(157\) −13.1863 + 13.1863i −1.05238 + 1.05238i −0.0538289 + 0.998550i \(0.517143\pi\)
−0.998550 + 0.0538289i \(0.982857\pi\)
\(158\) 0.813330 + 0.813330i 0.0647050 + 0.0647050i
\(159\) 2.73460i 0.216868i
\(160\) −0.120370 2.23283i −0.00951609 0.176520i
\(161\) −1.75598 −0.138390
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 1.19921 + 1.19921i 0.0939291 + 0.0939291i 0.752510 0.658581i \(-0.228843\pi\)
−0.658581 + 0.752510i \(0.728843\pi\)
\(164\) −3.68222 −0.287533
\(165\) 7.66639 0.413290i 0.596827 0.0321746i
\(166\) 14.1012i 1.09446i
\(167\) 11.1290 + 11.1290i 0.861184 + 0.861184i 0.991476 0.130292i \(-0.0415913\pi\)
−0.130292 + 0.991476i \(0.541591\pi\)
\(168\) −0.170229 0.170229i −0.0131335 0.0131335i
\(169\) 28.2287i 2.17144i
\(170\) 1.26492 + 1.13551i 0.0970146 + 0.0870897i
\(171\) −3.62016 + 2.42784i −0.276841 + 0.185662i
\(172\) −2.29224 + 2.29224i −0.174782 + 0.174782i
\(173\) 15.2012 15.2012i 1.15573 1.15573i 0.170341 0.985385i \(-0.445513\pi\)
0.985385 0.170341i \(-0.0544870\pi\)
\(174\) 5.37513 0.407488
\(175\) −0.937716 0.754709i −0.0708846 0.0570506i
\(176\) −3.43349 −0.258809
\(177\) −2.97102 + 2.97102i −0.223316 + 0.223316i
\(178\) 1.48561 + 1.48561i 0.111351 + 0.111351i
\(179\) −24.9536 −1.86512 −0.932559 0.361019i \(-0.882429\pi\)
−0.932559 + 0.361019i \(0.882429\pi\)
\(180\) −1.66396 1.49373i −0.124024 0.111336i
\(181\) 15.9721i 1.18720i 0.804762 + 0.593598i \(0.202293\pi\)
−0.804762 + 0.593598i \(0.797707\pi\)
\(182\) −1.09303 + 1.09303i −0.0810210 + 0.0810210i
\(183\) −1.17347 + 1.17347i −0.0867456 + 0.0867456i
\(184\) 7.29408 0.537727
\(185\) −0.943277 17.4975i −0.0693511 1.28644i
\(186\) 5.37513i 0.394124i
\(187\) 1.84561 1.84561i 0.134964 0.134964i
\(188\) −9.57865 9.57865i −0.698595 0.698595i
\(189\) −0.240740 −0.0175113
\(190\) 7.79095 5.85671i 0.565215 0.424891i
\(191\) 2.91580 0.210980 0.105490 0.994420i \(-0.466359\pi\)
0.105490 + 0.994420i \(0.466359\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 6.67601 6.67601i 0.480550 0.480550i −0.424758 0.905307i \(-0.639641\pi\)
0.905307 + 0.424758i \(0.139641\pi\)
\(194\) 15.3505i 1.10210i
\(195\) −9.59118 + 10.6842i −0.686839 + 0.765113i
\(196\) −6.94204 −0.495860
\(197\) −4.08263 + 4.08263i −0.290875 + 0.290875i −0.837426 0.546551i \(-0.815941\pi\)
0.546551 + 0.837426i \(0.315941\pi\)
\(198\) −2.42784 + 2.42784i −0.172539 + 0.172539i
\(199\) 8.23662i 0.583879i 0.956437 + 0.291939i \(0.0943006\pi\)
−0.956437 + 0.291939i \(0.905699\pi\)
\(200\) 3.89514 + 3.13495i 0.275428 + 0.221675i
\(201\) 0.680916 0.0480281
\(202\) −6.29940 6.29940i −0.443225 0.443225i
\(203\) −0.915004 + 0.915004i −0.0642207 + 0.0642207i
\(204\) −0.760184 −0.0532235
\(205\) 5.50024 6.12706i 0.384154 0.427933i
\(206\) 8.85814 0.617176
\(207\) 5.15769 5.15769i 0.358484 0.358484i
\(208\) 4.54030 4.54030i 0.314813 0.314813i
\(209\) −8.33598 12.4298i −0.576612 0.859787i
\(210\) 0.537531 0.0289779i 0.0370932 0.00199967i
\(211\) 14.6136i 1.00604i 0.864275 + 0.503020i \(0.167778\pi\)
−0.864275 + 0.503020i \(0.832222\pi\)
\(212\) 1.93366 + 1.93366i 0.132804 + 0.132804i
\(213\) 6.31539 + 6.31539i 0.432723 + 0.432723i
\(214\) 7.91697i 0.541193i
\(215\) −0.390206 7.23819i −0.0266118 0.493640i
\(216\) 1.00000 0.0680414
\(217\) −0.915004 0.915004i −0.0621145 0.0621145i
\(218\) −7.57474 7.57474i −0.513026 0.513026i
\(219\) −12.3728 −0.836075
\(220\) 5.12871 5.71319i 0.345778 0.385183i
\(221\) 4.88110i 0.328339i
\(222\) 5.54122 + 5.54122i 0.371903 + 0.371903i
\(223\) 15.9582 15.9582i 1.06864 1.06864i 0.0711734 0.997464i \(-0.477326\pi\)
0.997464 0.0711734i \(-0.0226744\pi\)
\(224\) −0.240740 −0.0160851
\(225\) 4.97102 0.537531i 0.331401 0.0358354i
\(226\) −9.63447 −0.640875
\(227\) −5.87132 5.87132i −0.389694 0.389694i 0.484885 0.874578i \(-0.338862\pi\)
−0.874578 + 0.484885i \(0.838862\pi\)
\(228\) −0.843095 + 4.27659i −0.0558353 + 0.283224i
\(229\) 10.2825i 0.679487i 0.940518 + 0.339743i \(0.110340\pi\)
−0.940518 + 0.339743i \(0.889660\pi\)
\(230\) −10.8954 + 12.1371i −0.718421 + 0.800294i
\(231\) 0.826579i 0.0543849i
\(232\) 3.80079 3.80079i 0.249534 0.249534i
\(233\) 14.4725 + 14.4725i 0.948123 + 0.948123i 0.998719 0.0505960i \(-0.0161121\pi\)
−0.0505960 + 0.998719i \(0.516112\pi\)
\(234\) 6.42095i 0.419751i
\(235\) 30.2464 1.63056i 1.97306 0.106366i
\(236\) 4.20166i 0.273505i
\(237\) 0.813330 0.813330i 0.0528314 0.0528314i
\(238\) 0.129405 0.129405i 0.00838810 0.00838810i
\(239\) 21.4459i 1.38722i −0.720352 0.693609i \(-0.756020\pi\)
0.720352 0.693609i \(-0.243980\pi\)
\(240\) −2.23283 + 0.120370i −0.144128 + 0.00776986i
\(241\) 1.51636i 0.0976773i 0.998807 + 0.0488387i \(0.0155520\pi\)
−0.998807 + 0.0488387i \(0.984448\pi\)
\(242\) −0.557809 0.557809i −0.0358573 0.0358573i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 1.65954i 0.106241i
\(245\) 10.3696 11.5513i 0.662486 0.737985i
\(246\) 3.68222i 0.234770i
\(247\) 27.4598 + 5.41348i 1.74722 + 0.344451i
\(248\) 3.80079 + 3.80079i 0.241351 + 0.241351i
\(249\) 14.1012 0.893624
\(250\) −11.0347 + 1.79858i −0.697897 + 0.113752i
\(251\) 11.6524 0.735495 0.367748 0.929926i \(-0.380129\pi\)
0.367748 + 0.929926i \(0.380129\pi\)
\(252\) −0.170229 + 0.170229i −0.0107234 + 0.0107234i
\(253\) 17.7089 + 17.7089i 1.11335 + 1.11335i
\(254\) 7.35299i 0.461368i
\(255\) 1.13551 1.26492i 0.0711084 0.0792121i
\(256\) 1.00000 0.0625000
\(257\) 1.00645 + 1.00645i 0.0627804 + 0.0627804i 0.737800 0.675020i \(-0.235865\pi\)
−0.675020 + 0.737800i \(0.735865\pi\)
\(258\) 2.29224 + 2.29224i 0.142709 + 0.142709i
\(259\) −1.88655 −0.117225
\(260\) 0.772891 + 14.3369i 0.0479327 + 0.889135i
\(261\) 5.37513i 0.332712i
\(262\) −1.51836 1.51836i −0.0938048 0.0938048i
\(263\) 0.396280 + 0.396280i 0.0244357 + 0.0244357i 0.719219 0.694783i \(-0.244500\pi\)
−0.694783 + 0.719219i \(0.744500\pi\)
\(264\) 3.43349i 0.211317i
\(265\) −6.10589 + 0.329165i −0.375082 + 0.0202204i
\(266\) −0.584480 0.871519i −0.0358368 0.0534362i
\(267\) 1.48561 1.48561i 0.0909181 0.0909181i
\(268\) 0.481480 0.481480i 0.0294111 0.0294111i
\(269\) 20.9263 1.27590 0.637948 0.770079i \(-0.279783\pi\)
0.637948 + 0.770079i \(0.279783\pi\)
\(270\) −1.49373 + 1.66396i −0.0909056 + 0.101265i
\(271\) −16.9175 −1.02767 −0.513834 0.857890i \(-0.671775\pi\)
−0.513834 + 0.857890i \(0.671775\pi\)
\(272\) −0.537531 + 0.537531i −0.0325926 + 0.0325926i
\(273\) 1.09303 + 1.09303i 0.0661534 + 0.0661534i
\(274\) 19.1651 1.15781
\(275\) 1.84561 + 17.0680i 0.111294 + 1.02924i
\(276\) 7.29408i 0.439052i
\(277\) 15.6769 15.6769i 0.941931 0.941931i −0.0564732 0.998404i \(-0.517986\pi\)
0.998404 + 0.0564732i \(0.0179856\pi\)
\(278\) −7.42565 + 7.42565i −0.445361 + 0.445361i
\(279\) 5.37513 0.321801
\(280\) 0.359601 0.400582i 0.0214903 0.0239394i
\(281\) 10.3485i 0.617342i 0.951169 + 0.308671i \(0.0998842\pi\)
−0.951169 + 0.308671i \(0.900116\pi\)
\(282\) −9.57865 + 9.57865i −0.570400 + 0.570400i
\(283\) 6.03331 + 6.03331i 0.358643 + 0.358643i 0.863313 0.504670i \(-0.168386\pi\)
−0.504670 + 0.863313i \(0.668386\pi\)
\(284\) 8.93130 0.529975
\(285\) −5.85671 7.79095i −0.346922 0.461496i
\(286\) 22.0463 1.30362
\(287\) −0.626820 0.626820i −0.0370000 0.0370000i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 16.4221i 0.966007i
\(290\) 0.647005 + 12.0017i 0.0379935 + 0.704766i
\(291\) 15.3505 0.899860
\(292\) −8.74888 + 8.74888i −0.511989 + 0.511989i
\(293\) −6.64005 + 6.64005i −0.387916 + 0.387916i −0.873943 0.486028i \(-0.838445\pi\)
0.486028 + 0.873943i \(0.338445\pi\)
\(294\) 6.94204i 0.404868i
\(295\) −6.99140 6.27615i −0.407055 0.365412i
\(296\) 7.83647 0.455486
\(297\) 2.42784 + 2.42784i 0.140878 + 0.140878i
\(298\) 0.721494 0.721494i 0.0417950 0.0417950i
\(299\) −46.8349 −2.70853
\(300\) 3.13495 3.89514i 0.180997 0.224886i
\(301\) −0.780412 −0.0449822
\(302\) 14.0286 14.0286i 0.807254 0.807254i
\(303\) −6.29940 + 6.29940i −0.361891 + 0.361891i
\(304\) 2.42784 + 3.62016i 0.139246 + 0.207631i
\(305\) −2.76141 2.47891i −0.158118 0.141942i
\(306\) 0.760184i 0.0434568i
\(307\) −6.21426 6.21426i −0.354667 0.354667i 0.507176 0.861843i \(-0.330689\pi\)
−0.861843 + 0.507176i \(0.830689\pi\)
\(308\) −0.584480 0.584480i −0.0333038 0.0333038i
\(309\) 8.85814i 0.503922i
\(310\) −12.0017 + 0.647005i −0.681653 + 0.0367474i
\(311\) −4.55027 −0.258022 −0.129011 0.991643i \(-0.541180\pi\)
−0.129011 + 0.991643i \(0.541180\pi\)
\(312\) −4.54030 4.54030i −0.257044 0.257044i
\(313\) 20.0429 + 20.0429i 1.13289 + 1.13289i 0.989694 + 0.143197i \(0.0457382\pi\)
0.143197 + 0.989694i \(0.454262\pi\)
\(314\) 18.6482 1.05238
\(315\) −0.0289779 0.537531i −0.00163272 0.0302864i
\(316\) 1.15022i 0.0647050i
\(317\) −21.4280 21.4280i −1.20351 1.20351i −0.973090 0.230424i \(-0.925989\pi\)
−0.230424 0.973090i \(-0.574011\pi\)
\(318\) 1.93366 1.93366i 0.108434 0.108434i
\(319\) 18.4555 1.03331
\(320\) −1.49373 + 1.66396i −0.0835021 + 0.0930182i
\(321\) 7.91697 0.441882
\(322\) 1.24166 + 1.24166i 0.0691952 + 0.0691952i
\(323\) −3.25099 0.640907i −0.180890 0.0356610i
\(324\) 1.00000i 0.0555556i
\(325\) −25.0105 20.1294i −1.38733 1.11658i
\(326\) 1.69593i 0.0939291i
\(327\) −7.57474 + 7.57474i −0.418884 + 0.418884i
\(328\) 2.60372 + 2.60372i 0.143766 + 0.143766i
\(329\) 3.26113i 0.179792i
\(330\) −5.71319 5.12871i −0.314501 0.282326i
\(331\) 31.9582i 1.75658i −0.478125 0.878292i \(-0.658683\pi\)
0.478125 0.878292i \(-0.341317\pi\)
\(332\) 9.97102 9.97102i 0.547231 0.547231i
\(333\) 5.54122 5.54122i 0.303657 0.303657i
\(334\) 15.7387i 0.861184i
\(335\) 0.0819620 + 1.52037i 0.00447806 + 0.0830665i
\(336\) 0.240740i 0.0131335i
\(337\) 6.27191 + 6.27191i 0.341653 + 0.341653i 0.856988 0.515336i \(-0.172333\pi\)
−0.515336 + 0.856988i \(0.672333\pi\)
\(338\) −19.9607 + 19.9607i −1.08572 + 1.08572i
\(339\) 9.63447i 0.523273i
\(340\) −0.0915034 1.69736i −0.00496247 0.0920521i
\(341\) 18.4555i 0.999420i
\(342\) 4.27659 + 0.843095i 0.231251 + 0.0455894i
\(343\) −2.37334 2.37334i −0.128148 0.128148i
\(344\) 3.24172 0.174782
\(345\) 12.1371 + 10.8954i 0.653437 + 0.586588i
\(346\) −21.4978 −1.15573
\(347\) −9.84922 + 9.84922i −0.528734 + 0.528734i −0.920195 0.391461i \(-0.871970\pi\)
0.391461 + 0.920195i \(0.371970\pi\)
\(348\) −3.80079 3.80079i −0.203744 0.203744i
\(349\) 23.7919i 1.27355i 0.771049 + 0.636776i \(0.219732\pi\)
−0.771049 + 0.636776i \(0.780268\pi\)
\(350\) 0.129405 + 1.19672i 0.00691701 + 0.0639676i
\(351\) −6.42095 −0.342725
\(352\) 2.42784 + 2.42784i 0.129405 + 0.129405i
\(353\) −16.4474 16.4474i −0.875407 0.875407i 0.117649 0.993055i \(-0.462464\pi\)
−0.993055 + 0.117649i \(0.962464\pi\)
\(354\) 4.20166 0.223316
\(355\) −13.3410 + 14.8613i −0.708065 + 0.788758i
\(356\) 2.10098i 0.111351i
\(357\) −0.129405 0.129405i −0.00684886 0.00684886i
\(358\) 17.6448 + 17.6448i 0.932559 + 0.932559i
\(359\) 9.08979i 0.479741i 0.970805 + 0.239870i \(0.0771050\pi\)
−0.970805 + 0.239870i \(0.922895\pi\)
\(360\) 0.120370 + 2.23283i 0.00634406 + 0.117680i
\(361\) −7.21114 + 17.5784i −0.379534 + 0.925178i
\(362\) 11.2940 11.2940i 0.593598 0.593598i
\(363\) −0.557809 + 0.557809i −0.0292774 + 0.0292774i
\(364\) 1.54578 0.0810210
\(365\) −1.48931 27.6263i −0.0779542 1.44602i
\(366\) 1.65954 0.0867456
\(367\) 17.6931 17.6931i 0.923570 0.923570i −0.0737098 0.997280i \(-0.523484\pi\)
0.997280 + 0.0737098i \(0.0234839\pi\)
\(368\) −5.15769 5.15769i −0.268863 0.268863i
\(369\) 3.68222 0.191689
\(370\) −11.7056 + 13.0396i −0.608545 + 0.677896i
\(371\) 0.658329i 0.0341787i
\(372\) 3.80079 3.80079i 0.197062 0.197062i
\(373\) 4.93586 4.93586i 0.255569 0.255569i −0.567680 0.823249i \(-0.692159\pi\)
0.823249 + 0.567680i \(0.192159\pi\)
\(374\) −2.61008 −0.134964
\(375\) 1.79858 + 11.0347i 0.0928780 + 0.569831i
\(376\) 13.5463i 0.698595i
\(377\) −24.4047 + 24.4047i −1.25691 + 1.25691i
\(378\) 0.170229 + 0.170229i 0.00875564 + 0.00875564i
\(379\) −9.44824 −0.485324 −0.242662 0.970111i \(-0.578021\pi\)
−0.242662 + 0.970111i \(0.578021\pi\)
\(380\) −9.65036 1.36771i −0.495053 0.0701621i
\(381\) 7.35299 0.376705
\(382\) −2.06179 2.06179i −0.105490 0.105490i
\(383\) −17.3196 + 17.3196i −0.884991 + 0.884991i −0.994037 0.109046i \(-0.965221\pi\)
0.109046 + 0.994037i \(0.465221\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 1.84561 0.0994955i 0.0940609 0.00507076i
\(386\) −9.44130 −0.480550
\(387\) 2.29224 2.29224i 0.116521 0.116521i
\(388\) 10.8544 10.8544i 0.551049 0.551049i
\(389\) 20.3705i 1.03283i 0.856340 + 0.516413i \(0.172733\pi\)
−0.856340 + 0.516413i \(0.827267\pi\)
\(390\) 14.3369 0.772891i 0.725976 0.0391369i
\(391\) 5.54484 0.280415
\(392\) 4.90877 + 4.90877i 0.247930 + 0.247930i
\(393\) −1.51836 + 1.51836i −0.0765913 + 0.0765913i
\(394\) 5.77371 0.290875
\(395\) 1.91392 + 1.71812i 0.0963000 + 0.0864481i
\(396\) 3.43349 0.172539
\(397\) 13.9251 13.9251i 0.698883 0.698883i −0.265287 0.964170i \(-0.585467\pi\)
0.964170 + 0.265287i \(0.0854666\pi\)
\(398\) 5.82417 5.82417i 0.291939 0.291939i
\(399\) −0.871519 + 0.584480i −0.0436305 + 0.0292606i
\(400\) −0.537531 4.97102i −0.0268765 0.248551i
\(401\) 0.407767i 0.0203629i 0.999948 + 0.0101815i \(0.00324092\pi\)
−0.999948 + 0.0101815i \(0.996759\pi\)
\(402\) −0.481480 0.481480i −0.0240141 0.0240141i
\(403\) −24.4047 24.4047i −1.21569 1.21569i
\(404\) 8.90870i 0.443225i
\(405\) 1.66396 + 1.49373i 0.0826829 + 0.0742241i
\(406\) 1.29401 0.0642207
\(407\) 19.0257 + 19.0257i 0.943071 + 0.943071i
\(408\) 0.537531 + 0.537531i 0.0266117 + 0.0266117i
\(409\) −6.82208 −0.337330 −0.168665 0.985673i \(-0.553946\pi\)
−0.168665 + 0.985673i \(0.553946\pi\)
\(410\) −8.22175 + 0.443229i −0.406043 + 0.0218895i
\(411\) 19.1651i 0.945347i
\(412\) −6.26365 6.26365i −0.308588 0.308588i
\(413\) −0.715245 + 0.715245i −0.0351949 + 0.0351949i
\(414\) −7.29408 −0.358484
\(415\) 1.69736 + 31.4854i 0.0833200 + 1.54556i
\(416\) −6.42095 −0.314813
\(417\) 7.42565 + 7.42565i 0.363636 + 0.363636i
\(418\) −2.89476 + 14.6836i −0.141587 + 0.718199i
\(419\) 30.8811i 1.50864i −0.656507 0.754320i \(-0.727967\pi\)
0.656507 0.754320i \(-0.272033\pi\)
\(420\) −0.400582 0.359601i −0.0195464 0.0175467i
\(421\) 5.62994i 0.274386i 0.990544 + 0.137193i \(0.0438081\pi\)
−0.990544 + 0.137193i \(0.956192\pi\)
\(422\) 10.3334 10.3334i 0.503020 0.503020i
\(423\) 9.57865 + 9.57865i 0.465730 + 0.465730i
\(424\) 2.73460i 0.132804i
\(425\) 2.96102 + 2.38314i 0.143630 + 0.115599i
\(426\) 8.93130i 0.432723i
\(427\) −0.282502 + 0.282502i −0.0136712 + 0.0136712i
\(428\) 5.59814 5.59814i 0.270597 0.270597i
\(429\) 22.0463i 1.06440i
\(430\) −4.84226 + 5.39409i −0.233514 + 0.260126i
\(431\) 8.03322i 0.386947i 0.981106 + 0.193473i \(0.0619753\pi\)
−0.981106 + 0.193473i \(0.938025\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 27.5643 27.5643i 1.32466 1.32466i 0.414695 0.909960i \(-0.363888\pi\)
0.909960 0.414695i \(-0.136112\pi\)
\(434\) 1.29401i 0.0621145i
\(435\) 12.0017 0.647005i 0.575439 0.0310215i
\(436\) 10.7123i 0.513026i
\(437\) 6.14960 31.1938i 0.294175 1.49220i
\(438\) 8.74888 + 8.74888i 0.418037 + 0.418037i
\(439\) 2.72959 0.130276 0.0651381 0.997876i \(-0.479251\pi\)
0.0651381 + 0.997876i \(0.479251\pi\)
\(440\) −7.66639 + 0.413290i −0.365481 + 0.0197028i
\(441\) 6.94204 0.330574
\(442\) 3.45146 3.45146i 0.164169 0.164169i
\(443\) −21.7450 21.7450i −1.03313 1.03313i −0.999432 0.0337029i \(-0.989270\pi\)
−0.0337029 0.999432i \(-0.510730\pi\)
\(444\) 7.83647i 0.371903i
\(445\) 3.49594 + 3.13829i 0.165723 + 0.148769i
\(446\) −22.5682 −1.06864
\(447\) −0.721494 0.721494i −0.0341255 0.0341255i
\(448\) 0.170229 + 0.170229i 0.00804257 + 0.00804257i
\(449\) −6.33780 −0.299099 −0.149550 0.988754i \(-0.547782\pi\)
−0.149550 + 0.988754i \(0.547782\pi\)
\(450\) −3.89514 3.13495i −0.183618 0.147783i
\(451\) 12.6429i 0.595329i
\(452\) 6.81260 + 6.81260i 0.320438 + 0.320438i
\(453\) −14.0286 14.0286i −0.659120 0.659120i
\(454\) 8.30331i 0.389694i
\(455\) −2.30898 + 2.57212i −0.108247 + 0.120583i
\(456\) 3.62016 2.42784i 0.169530 0.113694i
\(457\) −14.1287 + 14.1287i −0.660915 + 0.660915i −0.955596 0.294681i \(-0.904787\pi\)
0.294681 + 0.955596i \(0.404787\pi\)
\(458\) 7.27083 7.27083i 0.339743 0.339743i
\(459\) 0.760184 0.0354823
\(460\) 16.2864 0.877989i 0.759358 0.0409365i
\(461\) −10.3701 −0.482984 −0.241492 0.970403i \(-0.577637\pi\)
−0.241492 + 0.970403i \(0.577637\pi\)
\(462\) −0.584480 + 0.584480i −0.0271925 + 0.0271925i
\(463\) −21.5966 21.5966i −1.00368 1.00368i −0.999993 0.00368676i \(-0.998826\pi\)
−0.00368676 0.999993i \(-0.501174\pi\)
\(464\) −5.37513 −0.249534
\(465\) 0.647005 + 12.0017i 0.0300042 + 0.556567i
\(466\) 20.4672i 0.948123i
\(467\) 5.68112 5.68112i 0.262891 0.262891i −0.563337 0.826228i \(-0.690483\pi\)
0.826228 + 0.563337i \(0.190483\pi\)
\(468\) −4.54030 + 4.54030i −0.209875 + 0.209875i
\(469\) 0.163924 0.00756930
\(470\) −22.5404 20.2345i −1.03971 0.933346i
\(471\) 18.6482i 0.859264i
\(472\) 2.97102 2.97102i 0.136752 0.136752i
\(473\) 7.87039 + 7.87039i 0.361881 + 0.361881i
\(474\) −1.15022 −0.0528314
\(475\) 16.6909 14.0148i 0.765829 0.643044i
\(476\) −0.183007 −0.00838810
\(477\) −1.93366 1.93366i −0.0885361 0.0885361i
\(478\) −15.1645 + 15.1645i −0.693609 + 0.693609i
\(479\) 18.3301i 0.837524i −0.908096 0.418762i \(-0.862464\pi\)
0.908096 0.418762i \(-0.137536\pi\)
\(480\) 1.66396 + 1.49373i 0.0759491 + 0.0681792i
\(481\) −50.3176 −2.29429
\(482\) 1.07223 1.07223i 0.0488387 0.0488387i
\(483\) 1.24166 1.24166i 0.0564977 0.0564977i
\(484\) 0.788861i 0.0358573i
\(485\) 1.84774 + 34.2749i 0.0839014 + 1.55634i
\(486\) −1.00000 −0.0453609
\(487\) 8.21504 + 8.21504i 0.372259 + 0.372259i 0.868299 0.496040i \(-0.165213\pi\)
−0.496040 + 0.868299i \(0.665213\pi\)
\(488\) 1.17347 1.17347i 0.0531206 0.0531206i
\(489\) −1.69593 −0.0766928
\(490\) −15.5004 + 0.835615i −0.700236 + 0.0377492i
\(491\) 5.85271 0.264129 0.132065 0.991241i \(-0.457839\pi\)
0.132065 + 0.991241i \(0.457839\pi\)
\(492\) 2.60372 2.60372i 0.117385 0.117385i
\(493\) 2.88930 2.88930i 0.130128 0.130128i
\(494\) −15.5891 23.2449i −0.701386 1.04584i
\(495\) −5.12871 + 5.71319i −0.230519 + 0.256789i
\(496\) 5.37513i 0.241351i
\(497\) 1.52037 + 1.52037i 0.0681978 + 0.0681978i
\(498\) −9.97102 9.97102i −0.446812 0.446812i
\(499\) 24.4054i 1.09254i 0.837610 + 0.546268i \(0.183952\pi\)
−0.837610 + 0.546268i \(0.816048\pi\)
\(500\) 9.07451 + 6.53094i 0.405825 + 0.292073i
\(501\) −15.7387 −0.703154
\(502\) −8.23952 8.23952i −0.367748 0.367748i
\(503\) 19.8672 + 19.8672i 0.885836 + 0.885836i 0.994120 0.108284i \(-0.0345357\pi\)
−0.108284 + 0.994120i \(0.534536\pi\)
\(504\) 0.240740 0.0107234
\(505\) −14.8237 13.3072i −0.659647 0.592163i
\(506\) 25.0442i 1.11335i
\(507\) 19.9607 + 19.9607i 0.886485 + 0.886485i
\(508\) 5.19935 5.19935i 0.230684 0.230684i
\(509\) 19.2340 0.852534 0.426267 0.904597i \(-0.359828\pi\)
0.426267 + 0.904597i \(0.359828\pi\)
\(510\) −1.69736 + 0.0915034i −0.0751603 + 0.00405184i
\(511\) −2.97863 −0.131767
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0.843095 4.27659i 0.0372236 0.188816i
\(514\) 1.42333i 0.0627804i
\(515\) 19.7787 1.06626i 0.871553 0.0469848i
\(516\) 3.24172i 0.142709i
\(517\) −32.8882 + 32.8882i −1.44642 + 1.44642i
\(518\) 1.33400 + 1.33400i 0.0586124 + 0.0586124i
\(519\) 21.4978i 0.943647i
\(520\) 9.59118 10.6842i 0.420601 0.468534i
\(521\) 19.1370i 0.838407i 0.907892 + 0.419204i \(0.137691\pi\)
−0.907892 + 0.419204i \(0.862309\pi\)
\(522\) −3.80079 + 3.80079i −0.166356 + 0.166356i
\(523\) 13.3664 13.3664i 0.584471 0.584471i −0.351657 0.936129i \(-0.614382\pi\)
0.936129 + 0.351657i \(0.114382\pi\)
\(524\) 2.14729i 0.0938048i
\(525\) 1.19672 0.129405i 0.0522294 0.00564771i
\(526\) 0.560424i 0.0244357i
\(527\) 2.88930 + 2.88930i 0.125860 + 0.125860i
\(528\) 2.42784 2.42784i 0.105658 0.105658i
\(529\) 30.2036i 1.31320i
\(530\) 4.55027 + 4.08476i 0.197651 + 0.177431i
\(531\) 4.20166i 0.182337i
\(532\) −0.202967 + 1.02955i −0.00879973 + 0.0446365i
\(533\) −16.7184 16.7184i −0.724153 0.724153i
\(534\) −2.10098 −0.0909181
\(535\) 0.952967 + 17.6772i 0.0412003 + 0.764253i
\(536\) −0.680916 −0.0294111
\(537\) 17.6448 17.6448i 0.761431 0.761431i
\(538\) −14.7971 14.7971i −0.637948 0.637948i
\(539\) 23.8354i 1.02667i
\(540\) 2.23283 0.120370i 0.0960855 0.00517990i
\(541\) −36.4227 −1.56593 −0.782967 0.622063i \(-0.786295\pi\)
−0.782967 + 0.622063i \(0.786295\pi\)
\(542\) 11.9625 + 11.9625i 0.513834 + 0.513834i
\(543\) −11.2940 11.2940i −0.484671 0.484671i
\(544\) 0.760184 0.0325926
\(545\) −17.8249 16.0013i −0.763533 0.685421i
\(546\) 1.54578i 0.0661534i
\(547\) −7.49691 7.49691i −0.320545 0.320545i 0.528431 0.848976i \(-0.322780\pi\)
−0.848976 + 0.528431i \(0.822780\pi\)
\(548\) −13.5518 13.5518i −0.578904 0.578904i
\(549\) 1.65954i 0.0708275i
\(550\) 10.7638 13.3739i 0.458971 0.570266i
\(551\) −13.0500 19.4588i −0.555948 0.828975i
\(552\) −5.15769 + 5.15769i −0.219526 + 0.219526i
\(553\) 0.195801 0.195801i 0.00832631 0.00832631i
\(554\) −22.1704 −0.941931
\(555\) 13.0396 + 11.7056i 0.553500 + 0.496875i
\(556\) 10.5015 0.445361
\(557\) 6.66081 6.66081i 0.282228 0.282228i −0.551769 0.833997i \(-0.686047\pi\)
0.833997 + 0.551769i \(0.186047\pi\)
\(558\) −3.80079 3.80079i −0.160900 0.160900i
\(559\) −20.8149 −0.880377
\(560\) −0.537531 + 0.0289779i −0.0227148 + 0.00122454i
\(561\) 2.61008i 0.110198i
\(562\) 7.31752 7.31752i 0.308671 0.308671i
\(563\) 18.2264 18.2264i 0.768150 0.768150i −0.209631 0.977781i \(-0.567226\pi\)
0.977781 + 0.209631i \(0.0672261\pi\)
\(564\) 13.5463 0.570400
\(565\) −21.5121 + 1.15970i −0.905020 + 0.0487890i
\(566\) 8.53238i 0.358643i
\(567\) 0.170229 0.170229i 0.00714895 0.00714895i
\(568\) −6.31539 6.31539i −0.264988 0.264988i
\(569\) −12.9797 −0.544138 −0.272069 0.962278i \(-0.587708\pi\)
−0.272069 + 0.962278i \(0.587708\pi\)
\(570\) −1.36771 + 9.65036i −0.0572871 + 0.404209i
\(571\) −4.34400 −0.181791 −0.0908954 0.995860i \(-0.528973\pi\)
−0.0908954 + 0.995860i \(0.528973\pi\)
\(572\) −15.5891 15.5891i −0.651812 0.651812i
\(573\) −2.06179 + 2.06179i −0.0861323 + 0.0861323i
\(574\) 0.886458i 0.0370000i
\(575\) −22.8666 + 28.4114i −0.953602 + 1.18484i
\(576\) −1.00000 −0.0416667
\(577\) 22.6630 22.6630i 0.943474 0.943474i −0.0550121 0.998486i \(-0.517520\pi\)
0.998486 + 0.0550121i \(0.0175197\pi\)
\(578\) 11.6122 11.6122i 0.483004 0.483004i
\(579\) 9.44130i 0.392367i
\(580\) 8.02901 8.94401i 0.333386 0.371380i
\(581\) 3.39472 0.140837
\(582\) −10.8544 10.8544i −0.449930 0.449930i
\(583\) 6.63919 6.63919i 0.274967 0.274967i
\(584\) 12.3728 0.511989
\(585\) −0.772891 14.3369i −0.0319551 0.592757i
\(586\) 9.39045 0.387916
\(587\) −1.52632 + 1.52632i −0.0629979 + 0.0629979i −0.737904 0.674906i \(-0.764184\pi\)
0.674906 + 0.737904i \(0.264184\pi\)
\(588\) 4.90877 4.90877i 0.202434 0.202434i
\(589\) 19.4588 13.0500i 0.801788 0.537715i
\(590\) 0.505754 + 9.38157i 0.0208216 + 0.386233i
\(591\) 5.77371i 0.237499i
\(592\) −5.54122 5.54122i −0.227743 0.227743i
\(593\) 2.34436 + 2.34436i 0.0962714 + 0.0962714i 0.753602 0.657331i \(-0.228315\pi\)
−0.657331 + 0.753602i \(0.728315\pi\)
\(594\) 3.43349i 0.140878i
\(595\) 0.273363 0.304516i 0.0112068 0.0124839i
\(596\) −1.02035 −0.0417950
\(597\) −5.82417 5.82417i −0.238368 0.238368i
\(598\) 33.1173 + 33.1173i 1.35427 + 1.35427i
\(599\) 20.2744 0.828391 0.414195 0.910188i \(-0.364063\pi\)
0.414195 + 0.910188i \(0.364063\pi\)
\(600\) −4.97102 + 0.537531i −0.202941 + 0.0219446i
\(601\) 18.2726i 0.745354i −0.927961 0.372677i \(-0.878440\pi\)
0.927961 0.372677i \(-0.121560\pi\)
\(602\) 0.551834 + 0.551834i 0.0224911 + 0.0224911i
\(603\) −0.481480 + 0.481480i −0.0196074 + 0.0196074i
\(604\) −19.8394 −0.807254
\(605\) −1.31263 1.17835i −0.0533662 0.0479066i
\(606\) 8.90870 0.361891
\(607\) 21.4067 + 21.4067i 0.868872 + 0.868872i 0.992348 0.123476i \(-0.0394042\pi\)
−0.123476 + 0.992348i \(0.539404\pi\)
\(608\) 0.843095 4.27659i 0.0341920 0.173438i
\(609\) 1.29401i 0.0524360i
\(610\) 0.199759 + 3.70547i 0.00808802 + 0.150030i
\(611\) 86.9799i 3.51883i
\(612\) 0.537531 0.537531i 0.0217284 0.0217284i
\(613\) −21.6012 21.6012i −0.872462 0.872462i 0.120278 0.992740i \(-0.461621\pi\)
−0.992740 + 0.120278i \(0.961621\pi\)
\(614\) 8.78829i 0.354667i
\(615\) 0.443229 + 8.22175i 0.0178727 + 0.331533i
\(616\) 0.826579i 0.0333038i
\(617\) 13.3582 13.3582i 0.537782 0.537782i −0.385095 0.922877i \(-0.625831\pi\)
0.922877 + 0.385095i \(0.125831\pi\)
\(618\) −6.26365 + 6.26365i −0.251961 + 0.251961i
\(619\) 35.7297i 1.43610i −0.695993 0.718049i \(-0.745035\pi\)
0.695993 0.718049i \(-0.254965\pi\)
\(620\) 8.94401 + 8.02901i 0.359200 + 0.322453i
\(621\) 7.29408i 0.292701i
\(622\) 3.21753 + 3.21753i 0.129011 + 0.129011i
\(623\) 0.357647 0.357647i 0.0143288 0.0143288i
\(624\) 6.42095i 0.257044i
\(625\) −24.4221 + 5.34416i −0.976885 + 0.213766i
\(626\) 28.3449i 1.13289i
\(627\) 14.6836 + 2.89476i 0.586407 + 0.115606i
\(628\) −13.1863 13.1863i −0.526190 0.526190i
\(629\) 5.95716 0.237528
\(630\) −0.359601 + 0.400582i −0.0143269 + 0.0159596i
\(631\) −5.92905 −0.236032 −0.118016 0.993012i \(-0.537653\pi\)
−0.118016 + 0.993012i \(0.537653\pi\)
\(632\) −0.813330 + 0.813330i −0.0323525 + 0.0323525i
\(633\) −10.3334 10.3334i −0.410714 0.410714i
\(634\) 30.3037i 1.20351i
\(635\) 0.885081 + 16.4180i 0.0351234 + 0.651527i
\(636\) −2.73460 −0.108434
\(637\) −31.5190 31.5190i −1.24883 1.24883i
\(638\) −13.0500 13.0500i −0.516654 0.516654i
\(639\) −8.93130 −0.353317
\(640\) 2.23283 0.120370i 0.0882602 0.00475805i
\(641\) 6.60094i 0.260721i 0.991467 + 0.130361i \(0.0416135\pi\)
−0.991467 + 0.130361i \(0.958386\pi\)
\(642\) −5.59814 5.59814i −0.220941 0.220941i
\(643\) 13.4065 + 13.4065i 0.528700 + 0.528700i 0.920185 0.391484i \(-0.128038\pi\)
−0.391484 + 0.920185i \(0.628038\pi\)
\(644\) 1.75598i 0.0691952i
\(645\) 5.39409 + 4.84226i 0.212392 + 0.190664i
\(646\) 1.84561 + 2.75199i 0.0726145 + 0.108275i
\(647\) 10.3980 10.3980i 0.408788 0.408788i −0.472528 0.881316i \(-0.656658\pi\)
0.881316 + 0.472528i \(0.156658\pi\)
\(648\) −0.707107 + 0.707107i −0.0277778 + 0.0277778i
\(649\) 14.4264 0.566284
\(650\) 3.45146 + 31.9187i 0.135377 + 1.25195i
\(651\) 1.29401 0.0507163
\(652\) −1.19921 + 1.19921i −0.0469646 + 0.0469646i
\(653\) −9.88773 9.88773i −0.386937 0.386937i 0.486657 0.873593i \(-0.338216\pi\)
−0.873593 + 0.486657i \(0.838216\pi\)
\(654\) 10.7123 0.418884
\(655\) −3.57301 3.20748i −0.139609 0.125326i
\(656\) 3.68222i 0.143766i
\(657\) 8.74888 8.74888i 0.341326 0.341326i
\(658\) −2.30597 + 2.30597i −0.0898959 + 0.0898959i
\(659\) 13.1768 0.513294 0.256647 0.966505i \(-0.417382\pi\)
0.256647 + 0.966505i \(0.417382\pi\)
\(660\) 0.413290 + 7.66639i 0.0160873 + 0.298414i
\(661\) 27.6493i 1.07543i 0.843126 + 0.537716i \(0.180713\pi\)
−0.843126 + 0.537716i \(0.819287\pi\)
\(662\) −22.5979 + 22.5979i −0.878292 + 0.878292i
\(663\) −3.45146 3.45146i −0.134044 0.134044i
\(664\) −14.1012 −0.547231
\(665\) −1.40995 1.87560i −0.0546754 0.0727325i
\(666\) −7.83647 −0.303657
\(667\) 27.7233 + 27.7233i 1.07345 + 1.07345i
\(668\) −11.1290 + 11.1290i −0.430592 + 0.430592i
\(669\) 22.5682i 0.872539i
\(670\) 1.01711 1.13302i 0.0392942 0.0437723i
\(671\) 5.69802 0.219970
\(672\) 0.170229 0.170229i 0.00656673 0.00656673i
\(673\) −15.0414 + 15.0414i −0.579804 + 0.579804i −0.934849 0.355045i \(-0.884465\pi\)
0.355045 + 0.934849i \(0.384465\pi\)
\(674\) 8.86982i 0.341653i
\(675\) −3.13495 + 3.89514i −0.120664 + 0.149924i
\(676\) 28.2287 1.08572
\(677\) 32.6303 + 32.6303i 1.25408 + 1.25408i 0.953873 + 0.300211i \(0.0970571\pi\)
0.300211 + 0.953873i \(0.402943\pi\)
\(678\) 6.81260 6.81260i 0.261636 0.261636i
\(679\) 3.69547 0.141819
\(680\) −1.13551 + 1.26492i −0.0435448 + 0.0485073i
\(681\) 8.30331 0.318183
\(682\) 13.0500 13.0500i 0.499710 0.499710i
\(683\) −19.7427 + 19.7427i −0.755435 + 0.755435i −0.975488 0.220053i \(-0.929377\pi\)
0.220053 + 0.975488i \(0.429377\pi\)
\(684\) −2.42784 3.62016i −0.0928310 0.138420i
\(685\) 42.7924 2.30691i 1.63501 0.0881425i
\(686\) 3.35641i 0.128148i
\(687\) −7.27083 7.27083i −0.277399 0.277399i
\(688\) −2.29224 2.29224i −0.0873908 0.0873908i
\(689\) 17.5588i 0.668936i
\(690\) −0.877989 16.2864i −0.0334245 0.620013i
\(691\) −1.07506 −0.0408973 −0.0204486 0.999791i \(-0.506509\pi\)
−0.0204486 + 0.999791i \(0.506509\pi\)
\(692\) 15.2012 + 15.2012i 0.577863 + 0.577863i
\(693\) 0.584480 + 0.584480i 0.0222026 + 0.0222026i
\(694\) 13.9289 0.528734
\(695\) −15.6864 + 17.4740i −0.595017 + 0.662827i
\(696\) 5.37513i 0.203744i
\(697\) 1.97931 + 1.97931i 0.0749715 + 0.0749715i
\(698\) 16.8234 16.8234i 0.636776 0.636776i
\(699\) −20.4672 −0.774139
\(700\) 0.754709 0.937716i 0.0285253 0.0354423i
\(701\) 49.0251 1.85165 0.925827 0.377947i \(-0.123370\pi\)
0.925827 + 0.377947i \(0.123370\pi\)
\(702\) 4.54030 + 4.54030i 0.171363 + 0.171363i
\(703\) 6.60689 33.5134i 0.249184 1.26398i
\(704\) 3.43349i 0.129405i
\(705\) −20.2345 + 22.5404i −0.762074 + 0.848922i
\(706\) 23.2601i 0.875407i
\(707\) −1.51652 + 1.51652i −0.0570346 + 0.0570346i
\(708\) −2.97102 2.97102i −0.111658 0.111658i
\(709\) 1.20397i 0.0452160i 0.999744 + 0.0226080i \(0.00719696\pi\)
−0.999744 + 0.0226080i \(0.992803\pi\)
\(710\) 19.9420 1.07506i 0.748412 0.0403464i
\(711\) 1.15022i 0.0431367i
\(712\) −1.48561 + 1.48561i −0.0556757 + 0.0556757i
\(713\) −27.7233 + 27.7233i −1.03825 + 1.03825i
\(714\) 0.183007i 0.00684886i
\(715\) 49.2255 2.65371i 1.84093 0.0992433i
\(716\) 24.9536i 0.932559i
\(717\) 15.1645 + 15.1645i 0.566329 + 0.566329i
\(718\) 6.42745 6.42745i 0.239870 0.239870i
\(719\) 13.0396i 0.486297i 0.969989 + 0.243148i \(0.0781802\pi\)
−0.969989 + 0.243148i \(0.921820\pi\)
\(720\) 1.49373 1.66396i 0.0556681 0.0620122i
\(721\) 2.13251i 0.0794189i
\(722\) 17.5288 7.33075i 0.652356 0.272822i
\(723\) −1.07223 1.07223i −0.0398766 0.0398766i
\(724\) −15.9721 −0.593598
\(725\) 2.88930 + 26.7199i 0.107306 + 0.992352i
\(726\) 0.788861 0.0292774
\(727\) −11.3275 + 11.3275i −0.420115 + 0.420115i −0.885243 0.465129i \(-0.846008\pi\)
0.465129 + 0.885243i \(0.346008\pi\)
\(728\) −1.09303 1.09303i −0.0405105 0.0405105i
\(729\) 1.00000i 0.0370370i
\(730\) −18.4816 + 20.5878i −0.684035 + 0.761989i
\(731\) 2.46430 0.0911454
\(732\) −1.17347 1.17347i −0.0433728 0.0433728i
\(733\) 30.7800 + 30.7800i 1.13689 + 1.13689i 0.989005 + 0.147882i \(0.0472456\pi\)
0.147882 + 0.989005i \(0.452754\pi\)
\(734\) −25.0218 −0.923570
\(735\) 0.835615 + 15.5004i 0.0308221 + 0.571740i
\(736\) 7.29408i 0.268863i
\(737\) −1.65316 1.65316i −0.0608949 0.0608949i
\(738\) −2.60372 2.60372i −0.0958443 0.0958443i
\(739\) 44.9834i 1.65474i −0.561656 0.827371i \(-0.689835\pi\)
0.561656 0.827371i \(-0.310165\pi\)
\(740\) 17.4975 0.943277i 0.643220 0.0346756i
\(741\) −23.2449 + 15.5891i −0.853922 + 0.572679i
\(742\) 0.465509 0.465509i 0.0170894 0.0170894i
\(743\) −16.4071 + 16.4071i −0.601917 + 0.601917i −0.940821 0.338904i \(-0.889944\pi\)
0.338904 + 0.940821i \(0.389944\pi\)
\(744\) −5.37513 −0.197062
\(745\) 1.52412 1.69782i 0.0558396 0.0622032i
\(746\) −6.98036 −0.255569
\(747\) −9.97102 + 9.97102i −0.364821 + 0.364821i
\(748\) 1.84561 + 1.84561i 0.0674821 + 0.0674821i
\(749\) 1.90593 0.0696413
\(750\) 6.53094 9.07451i 0.238476 0.331354i
\(751\) 10.0580i 0.367021i 0.983018 + 0.183510i \(0.0587461\pi\)
−0.983018 + 0.183510i \(0.941254\pi\)
\(752\) 9.57865 9.57865i 0.349297 0.349297i
\(753\) −8.23952 + 8.23952i −0.300265 + 0.300265i
\(754\) 34.5135 1.25691
\(755\) 29.6348 33.0120i 1.07852 1.20143i
\(756\) 0.240740i 0.00875564i
\(757\) −0.0674583 + 0.0674583i −0.00245182 + 0.00245182i −0.708332 0.705880i \(-0.750552\pi\)
0.705880 + 0.708332i \(0.250552\pi\)
\(758\) 6.68092 + 6.68092i 0.242662 + 0.242662i
\(759\) −25.0442 −0.909045
\(760\) 5.85671 + 7.79095i 0.212445 + 0.282607i
\(761\) 15.9170 0.576990 0.288495 0.957481i \(-0.406845\pi\)
0.288495 + 0.957481i \(0.406845\pi\)
\(762\) −5.19935 5.19935i −0.188353 0.188353i
\(763\) −1.82355 + 1.82355i −0.0660168 + 0.0660168i
\(764\) 2.91580i 0.105490i
\(765\) 0.0915034 + 1.69736i 0.00330831 + 0.0613681i
\(766\) 24.4936 0.884991
\(767\) −19.0768 + 19.0768i −0.688823 + 0.688823i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 4.99203i 0.180017i 0.995941 + 0.0900087i \(0.0286895\pi\)
−0.995941 + 0.0900087i \(0.971311\pi\)
\(770\) −1.37540 1.23469i −0.0495658 0.0444951i
\(771\) −1.42333 −0.0512600
\(772\) 6.67601 + 6.67601i 0.240275 + 0.240275i
\(773\) 0.387825 0.387825i 0.0139491 0.0139491i −0.700098 0.714047i \(-0.746860\pi\)
0.714047 + 0.700098i \(0.246860\pi\)
\(774\) −3.24172 −0.116521
\(775\) −26.7199 + 2.88930i −0.959807 + 0.103787i
\(776\) −15.3505 −0.551049
\(777\) 1.33400 1.33400i 0.0478568 0.0478568i
\(778\) 14.4041 14.4041i 0.516413 0.516413i