Properties

Label 690.2.i.f.323.6
Level $690$
Weight $2$
Character 690.323
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 323.6
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.f.47.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.906765 - 1.47573i) q^{3} +1.00000i q^{4} +(-1.96911 + 1.05954i) q^{5} +(-1.68468 + 0.402318i) q^{6} +(-0.621187 + 0.621187i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.35555 - 2.67628i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.906765 - 1.47573i) q^{3} +1.00000i q^{4} +(-1.96911 + 1.05954i) q^{5} +(-1.68468 + 0.402318i) q^{6} +(-0.621187 + 0.621187i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.35555 - 2.67628i) q^{9} +(2.14157 + 0.643162i) q^{10} -4.12939i q^{11} +(1.47573 + 0.906765i) q^{12} +(-0.734549 - 0.734549i) q^{13} +0.878491 q^{14} +(-0.221927 + 3.86662i) q^{15} -1.00000 q^{16} +(-2.50190 - 2.50190i) q^{17} +(-0.933895 + 2.85094i) q^{18} +7.88126i q^{19} +(-1.05954 - 1.96911i) q^{20} +(0.353433 + 1.47997i) q^{21} +(-2.91992 + 2.91992i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-0.402318 - 1.68468i) q^{24} +(2.75476 - 4.17269i) q^{25} +1.03881i q^{26} +(-5.17863 - 0.426330i) q^{27} +(-0.621187 - 0.621187i) q^{28} -7.83802 q^{29} +(2.89104 - 2.57719i) q^{30} -7.07325 q^{31} +(0.707107 + 0.707107i) q^{32} +(-6.09386 - 3.74439i) q^{33} +3.53823i q^{34} +(0.565012 - 1.88135i) q^{35} +(2.67628 - 1.35555i) q^{36} +(-6.46585 + 6.46585i) q^{37} +(5.57289 - 5.57289i) q^{38} +(-1.75006 + 0.417931i) q^{39} +(-0.643162 + 2.14157i) q^{40} +1.77236i q^{41} +(0.796585 - 1.29641i) q^{42} +(-6.31426 - 6.31426i) q^{43} +4.12939 q^{44} +(5.50485 + 3.83362i) q^{45} +1.00000 q^{46} +(-0.0280085 - 0.0280085i) q^{47} +(-0.906765 + 1.47573i) q^{48} +6.22825i q^{49} +(-4.89844 + 1.00262i) q^{50} +(-5.96077 + 1.42349i) q^{51} +(0.734549 - 0.734549i) q^{52} +(9.77127 - 9.77127i) q^{53} +(3.36039 + 3.96331i) q^{54} +(4.37524 + 8.13121i) q^{55} +0.878491i q^{56} +(11.6306 + 7.14645i) q^{57} +(5.54232 + 5.54232i) q^{58} -10.9630 q^{59} +(-3.86662 - 0.221927i) q^{60} +11.0841 q^{61} +(5.00154 + 5.00154i) q^{62} +(2.50452 + 0.820418i) q^{63} -1.00000i q^{64} +(2.22469 + 0.668122i) q^{65} +(1.66133 + 6.95669i) q^{66} +(10.8288 - 10.8288i) q^{67} +(2.50190 - 2.50190i) q^{68} +(0.402318 + 1.68468i) q^{69} +(-1.72984 + 0.930794i) q^{70} +2.25608i q^{71} +(-2.85094 - 0.933895i) q^{72} +(-8.48742 - 8.48742i) q^{73} +9.14409 q^{74} +(-3.65983 - 7.84893i) q^{75} -7.88126 q^{76} +(2.56512 + 2.56512i) q^{77} +(1.53300 + 0.941956i) q^{78} +1.98214i q^{79} +(1.96911 - 1.05954i) q^{80} +(-5.32495 + 7.25568i) q^{81} +(1.25325 - 1.25325i) q^{82} +(-2.21281 + 2.21281i) q^{83} +(-1.47997 + 0.353433i) q^{84} +(7.57738 + 2.27565i) q^{85} +8.92971i q^{86} +(-7.10725 + 11.5668i) q^{87} +(-2.91992 - 2.91992i) q^{88} -6.08809 q^{89} +(-1.18174 - 6.60329i) q^{90} +0.912584 q^{91} +(-0.707107 - 0.707107i) q^{92} +(-6.41378 + 10.4382i) q^{93} +0.0396100i q^{94} +(-8.35049 - 15.5190i) q^{95} +(1.68468 - 0.402318i) q^{96} +(11.8246 - 11.8246i) q^{97} +(4.40404 - 4.40404i) q^{98} +(-11.0514 + 5.59760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0.906765 1.47573i 0.523521 0.852013i
\(4\) 1.00000i 0.500000i
\(5\) −1.96911 + 1.05954i −0.880611 + 0.473840i
\(6\) −1.68468 + 0.402318i −0.687767 + 0.164246i
\(7\) −0.621187 + 0.621187i −0.234787 + 0.234787i −0.814687 0.579901i \(-0.803091\pi\)
0.579901 + 0.814687i \(0.303091\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −1.35555 2.67628i −0.451851 0.892093i
\(10\) 2.14157 + 0.643162i 0.677225 + 0.203386i
\(11\) 4.12939i 1.24506i −0.782597 0.622529i \(-0.786105\pi\)
0.782597 0.622529i \(-0.213895\pi\)
\(12\) 1.47573 + 0.906765i 0.426006 + 0.261761i
\(13\) −0.734549 0.734549i −0.203727 0.203727i 0.597868 0.801595i \(-0.296015\pi\)
−0.801595 + 0.597868i \(0.796015\pi\)
\(14\) 0.878491 0.234787
\(15\) −0.221927 + 3.86662i −0.0573013 + 0.998357i
\(16\) −1.00000 −0.250000
\(17\) −2.50190 2.50190i −0.606801 0.606801i 0.335308 0.942109i \(-0.391160\pi\)
−0.942109 + 0.335308i \(0.891160\pi\)
\(18\) −0.933895 + 2.85094i −0.220121 + 0.671972i
\(19\) 7.88126i 1.80808i 0.427443 + 0.904042i \(0.359414\pi\)
−0.427443 + 0.904042i \(0.640586\pi\)
\(20\) −1.05954 1.96911i −0.236920 0.440306i
\(21\) 0.353433 + 1.47997i 0.0771253 + 0.322957i
\(22\) −2.91992 + 2.91992i −0.622529 + 0.622529i
\(23\) −0.707107 + 0.707107i −0.147442 + 0.147442i
\(24\) −0.402318 1.68468i −0.0821228 0.343883i
\(25\) 2.75476 4.17269i 0.550952 0.834537i
\(26\) 1.03881i 0.203727i
\(27\) −5.17863 0.426330i −0.996628 0.0820472i
\(28\) −0.621187 0.621187i −0.117393 0.117393i
\(29\) −7.83802 −1.45548 −0.727742 0.685851i \(-0.759430\pi\)
−0.727742 + 0.685851i \(0.759430\pi\)
\(30\) 2.89104 2.57719i 0.527829 0.470528i
\(31\) −7.07325 −1.27039 −0.635197 0.772350i \(-0.719081\pi\)
−0.635197 + 0.772350i \(0.719081\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −6.09386 3.74439i −1.06080 0.651814i
\(34\) 3.53823i 0.606801i
\(35\) 0.565012 1.88135i 0.0955044 0.318007i
\(36\) 2.67628 1.35555i 0.446047 0.225925i
\(37\) −6.46585 + 6.46585i −1.06298 + 1.06298i −0.0651000 + 0.997879i \(0.520737\pi\)
−0.997879 + 0.0651000i \(0.979263\pi\)
\(38\) 5.57289 5.57289i 0.904042 0.904042i
\(39\) −1.75006 + 0.417931i −0.280234 + 0.0669226i
\(40\) −0.643162 + 2.14157i −0.101693 + 0.338613i
\(41\) 1.77236i 0.276796i 0.990377 + 0.138398i \(0.0441954\pi\)
−0.990377 + 0.138398i \(0.955805\pi\)
\(42\) 0.796585 1.29641i 0.122916 0.200041i
\(43\) −6.31426 6.31426i −0.962915 0.962915i 0.0364216 0.999337i \(-0.488404\pi\)
−0.999337 + 0.0364216i \(0.988404\pi\)
\(44\) 4.12939 0.622529
\(45\) 5.50485 + 3.83362i 0.820614 + 0.571482i
\(46\) 1.00000 0.147442
\(47\) −0.0280085 0.0280085i −0.00408546 0.00408546i 0.705061 0.709147i \(-0.250920\pi\)
−0.709147 + 0.705061i \(0.750920\pi\)
\(48\) −0.906765 + 1.47573i −0.130880 + 0.213003i
\(49\) 6.22825i 0.889751i
\(50\) −4.89844 + 1.00262i −0.692744 + 0.141793i
\(51\) −5.96077 + 1.42349i −0.834675 + 0.199329i
\(52\) 0.734549 0.734549i 0.101864 0.101864i
\(53\) 9.77127 9.77127i 1.34219 1.34219i 0.448307 0.893880i \(-0.352027\pi\)
0.893880 0.448307i \(-0.147973\pi\)
\(54\) 3.36039 + 3.96331i 0.457291 + 0.539338i
\(55\) 4.37524 + 8.13121i 0.589958 + 1.09641i
\(56\) 0.878491i 0.117393i
\(57\) 11.6306 + 7.14645i 1.54051 + 0.946571i
\(58\) 5.54232 + 5.54232i 0.727742 + 0.727742i
\(59\) −10.9630 −1.42726 −0.713629 0.700524i \(-0.752950\pi\)
−0.713629 + 0.700524i \(0.752950\pi\)
\(60\) −3.86662 0.221927i −0.499178 0.0286506i
\(61\) 11.0841 1.41917 0.709587 0.704618i \(-0.248882\pi\)
0.709587 + 0.704618i \(0.248882\pi\)
\(62\) 5.00154 + 5.00154i 0.635197 + 0.635197i
\(63\) 2.50452 + 0.820418i 0.315540 + 0.103363i
\(64\) 1.00000i 0.125000i
\(65\) 2.22469 + 0.668122i 0.275938 + 0.0828704i
\(66\) 1.66133 + 6.95669i 0.204495 + 0.856309i
\(67\) 10.8288 10.8288i 1.32295 1.32295i 0.411581 0.911373i \(-0.364977\pi\)
0.911373 0.411581i \(-0.135023\pi\)
\(68\) 2.50190 2.50190i 0.303401 0.303401i
\(69\) 0.402318 + 1.68468i 0.0484334 + 0.202811i
\(70\) −1.72984 + 0.930794i −0.206756 + 0.111251i
\(71\) 2.25608i 0.267747i 0.990998 + 0.133874i \(0.0427417\pi\)
−0.990998 + 0.133874i \(0.957258\pi\)
\(72\) −2.85094 0.933895i −0.335986 0.110061i
\(73\) −8.48742 8.48742i −0.993378 0.993378i 0.00660049 0.999978i \(-0.497899\pi\)
−0.999978 + 0.00660049i \(0.997899\pi\)
\(74\) 9.14409 1.06298
\(75\) −3.65983 7.84893i −0.422601 0.906316i
\(76\) −7.88126 −0.904042
\(77\) 2.56512 + 2.56512i 0.292323 + 0.292323i
\(78\) 1.53300 + 0.941956i 0.173578 + 0.106655i
\(79\) 1.98214i 0.223008i 0.993764 + 0.111504i \(0.0355668\pi\)
−0.993764 + 0.111504i \(0.964433\pi\)
\(80\) 1.96911 1.05954i 0.220153 0.118460i
\(81\) −5.32495 + 7.25568i −0.591661 + 0.806187i
\(82\) 1.25325 1.25325i 0.138398 0.138398i
\(83\) −2.21281 + 2.21281i −0.242887 + 0.242887i −0.818043 0.575156i \(-0.804941\pi\)
0.575156 + 0.818043i \(0.304941\pi\)
\(84\) −1.47997 + 0.353433i −0.161478 + 0.0385627i
\(85\) 7.57738 + 2.27565i 0.821882 + 0.246829i
\(86\) 8.92971i 0.962915i
\(87\) −7.10725 + 11.5668i −0.761977 + 1.24009i
\(88\) −2.91992 2.91992i −0.311264 0.311264i
\(89\) −6.08809 −0.645336 −0.322668 0.946512i \(-0.604580\pi\)
−0.322668 + 0.946512i \(0.604580\pi\)
\(90\) −1.18174 6.60329i −0.124566 0.696048i
\(91\) 0.912584 0.0956648
\(92\) −0.707107 0.707107i −0.0737210 0.0737210i
\(93\) −6.41378 + 10.4382i −0.665078 + 1.08239i
\(94\) 0.0396100i 0.00408546i
\(95\) −8.35049 15.5190i −0.856742 1.59222i
\(96\) 1.68468 0.402318i 0.171942 0.0410614i
\(97\) 11.8246 11.8246i 1.20061 1.20061i 0.226625 0.973982i \(-0.427231\pi\)
0.973982 0.226625i \(-0.0727691\pi\)
\(98\) 4.40404 4.40404i 0.444875 0.444875i
\(99\) −11.0514 + 5.59760i −1.11071 + 0.562580i
\(100\) 4.17269 + 2.75476i 0.417269 + 0.275476i
\(101\) 1.36233i 0.135557i 0.997700 + 0.0677786i \(0.0215911\pi\)
−0.997700 + 0.0677786i \(0.978409\pi\)
\(102\) 5.22147 + 3.20834i 0.517002 + 0.317673i
\(103\) 3.37589 + 3.37589i 0.332636 + 0.332636i 0.853587 0.520950i \(-0.174422\pi\)
−0.520950 + 0.853587i \(0.674422\pi\)
\(104\) −1.03881 −0.101864
\(105\) −2.26403 2.53975i −0.220947 0.247854i
\(106\) −13.8187 −1.34219
\(107\) −2.39803 2.39803i −0.231826 0.231826i 0.581628 0.813455i \(-0.302416\pi\)
−0.813455 + 0.581628i \(0.802416\pi\)
\(108\) 0.426330 5.17863i 0.0410236 0.498314i
\(109\) 0.531902i 0.0509470i 0.999675 + 0.0254735i \(0.00810934\pi\)
−0.999675 + 0.0254735i \(0.991891\pi\)
\(110\) 2.65587 8.84339i 0.253227 0.843185i
\(111\) 3.67883 + 15.4048i 0.349179 + 1.46216i
\(112\) 0.621187 0.621187i 0.0586966 0.0586966i
\(113\) 4.14725 4.14725i 0.390140 0.390140i −0.484597 0.874737i \(-0.661034\pi\)
0.874737 + 0.484597i \(0.161034\pi\)
\(114\) −3.17077 13.2774i −0.296970 1.24354i
\(115\) 0.643162 2.14157i 0.0599752 0.199703i
\(116\) 7.83802i 0.727742i
\(117\) −0.970139 + 2.96158i −0.0896893 + 0.273798i
\(118\) 7.75200 + 7.75200i 0.713629 + 0.713629i
\(119\) 3.10830 0.284937
\(120\) 2.57719 + 2.89104i 0.235264 + 0.263915i
\(121\) −6.05185 −0.550168
\(122\) −7.83764 7.83764i −0.709587 0.709587i
\(123\) 2.61553 + 1.60712i 0.235834 + 0.144909i
\(124\) 7.07325i 0.635197i
\(125\) −1.00330 + 11.1352i −0.0897376 + 0.995965i
\(126\) −1.19084 2.35109i −0.106089 0.209452i
\(127\) 8.34126 8.34126i 0.740167 0.740167i −0.232443 0.972610i \(-0.574672\pi\)
0.972610 + 0.232443i \(0.0746718\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −15.0437 + 3.59258i −1.32452 + 0.316309i
\(130\) −1.10066 2.04552i −0.0965340 0.179404i
\(131\) 2.68737i 0.234797i −0.993085 0.117398i \(-0.962545\pi\)
0.993085 0.117398i \(-0.0374554\pi\)
\(132\) 3.74439 6.09386i 0.325907 0.530402i
\(133\) −4.89573 4.89573i −0.424514 0.424514i
\(134\) −15.3143 −1.32295
\(135\) 10.6490 4.64747i 0.916519 0.399990i
\(136\) −3.53823 −0.303401
\(137\) 3.75896 + 3.75896i 0.321150 + 0.321150i 0.849208 0.528058i \(-0.177080\pi\)
−0.528058 + 0.849208i \(0.677080\pi\)
\(138\) 0.906765 1.47573i 0.0771890 0.125622i
\(139\) 20.7808i 1.76261i −0.472551 0.881303i \(-0.656667\pi\)
0.472551 0.881303i \(-0.343333\pi\)
\(140\) 1.88135 + 0.565012i 0.159003 + 0.0477522i
\(141\) −0.0667301 + 0.0159358i −0.00561969 + 0.00134204i
\(142\) 1.59529 1.59529i 0.133874 0.133874i
\(143\) −3.03324 + 3.03324i −0.253652 + 0.253652i
\(144\) 1.35555 + 2.67628i 0.112963 + 0.223023i
\(145\) 15.4339 8.30468i 1.28172 0.689666i
\(146\) 12.0030i 0.993378i
\(147\) 9.19122 + 5.64757i 0.758079 + 0.465803i
\(148\) −6.46585 6.46585i −0.531489 0.531489i
\(149\) −6.11984 −0.501357 −0.250678 0.968070i \(-0.580654\pi\)
−0.250678 + 0.968070i \(0.580654\pi\)
\(150\) −2.96214 + 8.13792i −0.241857 + 0.664458i
\(151\) 8.00975 0.651825 0.325912 0.945400i \(-0.394329\pi\)
0.325912 + 0.945400i \(0.394329\pi\)
\(152\) 5.57289 + 5.57289i 0.452021 + 0.452021i
\(153\) −3.30433 + 10.0873i −0.267140 + 0.815507i
\(154\) 3.62763i 0.292323i
\(155\) 13.9280 7.49438i 1.11872 0.601963i
\(156\) −0.417931 1.75006i −0.0334613 0.140117i
\(157\) −9.56563 + 9.56563i −0.763420 + 0.763420i −0.976939 0.213519i \(-0.931508\pi\)
0.213519 + 0.976939i \(0.431508\pi\)
\(158\) 1.40159 1.40159i 0.111504 0.111504i
\(159\) −5.55950 23.2800i −0.440897 1.84622i
\(160\) −2.14157 0.643162i −0.169306 0.0508464i
\(161\) 0.878491i 0.0692348i
\(162\) 8.89585 1.36523i 0.698924 0.107263i
\(163\) 1.30077 + 1.30077i 0.101884 + 0.101884i 0.756211 0.654327i \(-0.227048\pi\)
−0.654327 + 0.756211i \(0.727048\pi\)
\(164\) −1.77236 −0.138398
\(165\) 15.9668 + 0.916422i 1.24301 + 0.0713434i
\(166\) 3.12938 0.242887
\(167\) −7.75358 7.75358i −0.599990 0.599990i 0.340320 0.940310i \(-0.389465\pi\)
−0.940310 + 0.340320i \(0.889465\pi\)
\(168\) 1.29641 + 0.796585i 0.100021 + 0.0614579i
\(169\) 11.9209i 0.916991i
\(170\) −3.74889 6.96715i −0.287526 0.534356i
\(171\) 21.0925 10.6835i 1.61298 0.816985i
\(172\) 6.31426 6.31426i 0.481457 0.481457i
\(173\) −10.4290 + 10.4290i −0.792899 + 0.792899i −0.981964 0.189066i \(-0.939454\pi\)
0.189066 + 0.981964i \(0.439454\pi\)
\(174\) 13.2045 3.15338i 1.00103 0.239057i
\(175\) 0.880797 + 4.30324i 0.0665820 + 0.325294i
\(176\) 4.12939i 0.311264i
\(177\) −9.94085 + 16.1784i −0.747200 + 1.21604i
\(178\) 4.30493 + 4.30493i 0.322668 + 0.322668i
\(179\) 0.719378 0.0537688 0.0268844 0.999639i \(-0.491441\pi\)
0.0268844 + 0.999639i \(0.491441\pi\)
\(180\) −3.83362 + 5.50485i −0.285741 + 0.410307i
\(181\) 16.7156 1.24246 0.621229 0.783629i \(-0.286634\pi\)
0.621229 + 0.783629i \(0.286634\pi\)
\(182\) −0.645294 0.645294i −0.0478324 0.0478324i
\(183\) 10.0507 16.3571i 0.742967 1.20915i
\(184\) 1.00000i 0.0737210i
\(185\) 5.88113 19.5828i 0.432389 1.43975i
\(186\) 11.9162 2.84570i 0.873735 0.208657i
\(187\) −10.3313 + 10.3313i −0.755502 + 0.755502i
\(188\) 0.0280085 0.0280085i 0.00204273 0.00204273i
\(189\) 3.48173 2.95207i 0.253258 0.214731i
\(190\) −5.06893 + 16.8783i −0.367739 + 1.22448i
\(191\) 10.6239i 0.768718i −0.923184 0.384359i \(-0.874423\pi\)
0.923184 0.384359i \(-0.125577\pi\)
\(192\) −1.47573 0.906765i −0.106502 0.0654402i
\(193\) −0.732855 0.732855i −0.0527520 0.0527520i 0.680239 0.732991i \(-0.261876\pi\)
−0.732991 + 0.680239i \(0.761876\pi\)
\(194\) −16.7225 −1.20061
\(195\) 3.00324 2.67720i 0.215066 0.191719i
\(196\) −6.22825 −0.444875
\(197\) 10.4745 + 10.4745i 0.746279 + 0.746279i 0.973778 0.227499i \(-0.0730548\pi\)
−0.227499 + 0.973778i \(0.573055\pi\)
\(198\) 11.7726 + 3.85642i 0.836644 + 0.274064i
\(199\) 3.02413i 0.214375i 0.994239 + 0.107188i \(0.0341845\pi\)
−0.994239 + 0.107188i \(0.965815\pi\)
\(200\) −1.00262 4.89844i −0.0708963 0.346372i
\(201\) −6.16122 25.7997i −0.434579 1.81977i
\(202\) 0.963314 0.963314i 0.0677786 0.0677786i
\(203\) 4.86887 4.86887i 0.341728 0.341728i
\(204\) −1.42349 5.96077i −0.0996644 0.417338i
\(205\) −1.87788 3.48997i −0.131157 0.243750i
\(206\) 4.77423i 0.332636i
\(207\) 2.85094 + 0.933895i 0.198154 + 0.0649102i
\(208\) 0.734549 + 0.734549i 0.0509318 + 0.0509318i
\(209\) 32.5448 2.25117
\(210\) −0.194961 + 3.39679i −0.0134536 + 0.234401i
\(211\) −19.3102 −1.32937 −0.664684 0.747125i \(-0.731434\pi\)
−0.664684 + 0.747125i \(0.731434\pi\)
\(212\) 9.77127 + 9.77127i 0.671093 + 0.671093i
\(213\) 3.32936 + 2.04574i 0.228124 + 0.140171i
\(214\) 3.39132i 0.231826i
\(215\) 19.1236 + 5.74325i 1.30422 + 0.391686i
\(216\) −3.96331 + 3.36039i −0.269669 + 0.228645i
\(217\) 4.39381 4.39381i 0.298271 0.298271i
\(218\) 0.376112 0.376112i 0.0254735 0.0254735i
\(219\) −20.2212 + 4.82904i −1.36642 + 0.326316i
\(220\) −8.13121 + 4.37524i −0.548206 + 0.294979i
\(221\) 3.67554i 0.247244i
\(222\) 8.29154 13.4942i 0.556492 0.905671i
\(223\) −7.87712 7.87712i −0.527491 0.527491i 0.392332 0.919824i \(-0.371668\pi\)
−0.919824 + 0.392332i \(0.871668\pi\)
\(224\) −0.878491 −0.0586966
\(225\) −14.9015 1.71621i −0.993433 0.114414i
\(226\) −5.86509 −0.390140
\(227\) 8.11980 + 8.11980i 0.538930 + 0.538930i 0.923215 0.384284i \(-0.125552\pi\)
−0.384284 + 0.923215i \(0.625552\pi\)
\(228\) −7.14645 + 11.6306i −0.473285 + 0.770255i
\(229\) 8.83078i 0.583554i 0.956486 + 0.291777i \(0.0942465\pi\)
−0.956486 + 0.291777i \(0.905753\pi\)
\(230\) −1.96911 + 1.05954i −0.129839 + 0.0698639i
\(231\) 6.11139 1.45946i 0.402100 0.0960255i
\(232\) −5.54232 + 5.54232i −0.363871 + 0.363871i
\(233\) 13.3537 13.3537i 0.874831 0.874831i −0.118163 0.992994i \(-0.537701\pi\)
0.992994 + 0.118163i \(0.0377005\pi\)
\(234\) 2.78014 1.40816i 0.181744 0.0920543i
\(235\) 0.0848278 + 0.0254757i 0.00553356 + 0.00166185i
\(236\) 10.9630i 0.713629i
\(237\) 2.92510 + 1.79734i 0.190006 + 0.116750i
\(238\) −2.19790 2.19790i −0.142469 0.142469i
\(239\) 5.29769 0.342679 0.171340 0.985212i \(-0.445190\pi\)
0.171340 + 0.985212i \(0.445190\pi\)
\(240\) 0.221927 3.86662i 0.0143253 0.249589i
\(241\) 3.24318 0.208912 0.104456 0.994530i \(-0.466690\pi\)
0.104456 + 0.994530i \(0.466690\pi\)
\(242\) 4.27930 + 4.27930i 0.275084 + 0.275084i
\(243\) 5.87893 + 14.4374i 0.377134 + 0.926159i
\(244\) 11.0841i 0.709587i
\(245\) −6.59907 12.2641i −0.421599 0.783524i
\(246\) −0.713053 2.98586i −0.0454626 0.190371i
\(247\) 5.78917 5.78917i 0.368356 0.368356i
\(248\) −5.00154 + 5.00154i −0.317598 + 0.317598i
\(249\) 1.25901 + 5.27200i 0.0797863 + 0.334099i
\(250\) 8.58324 7.16436i 0.542852 0.453114i
\(251\) 17.6589i 1.11462i 0.830304 + 0.557310i \(0.188167\pi\)
−0.830304 + 0.557310i \(0.811833\pi\)
\(252\) −0.820418 + 2.50452i −0.0516815 + 0.157770i
\(253\) 2.91992 + 2.91992i 0.183574 + 0.183574i
\(254\) −11.7963 −0.740167
\(255\) 10.2292 9.11868i 0.640575 0.571034i
\(256\) 1.00000 0.0625000
\(257\) −3.83128 3.83128i −0.238989 0.238989i 0.577442 0.816431i \(-0.304051\pi\)
−0.816431 + 0.577442i \(0.804051\pi\)
\(258\) 13.1778 + 8.09715i 0.820416 + 0.504106i
\(259\) 8.03300i 0.499146i
\(260\) −0.668122 + 2.22469i −0.0414352 + 0.137969i
\(261\) 10.6249 + 20.9767i 0.657662 + 1.29843i
\(262\) −1.90026 + 1.90026i −0.117398 + 0.117398i
\(263\) 9.95007 9.95007i 0.613548 0.613548i −0.330321 0.943869i \(-0.607157\pi\)
0.943869 + 0.330321i \(0.107157\pi\)
\(264\) −6.95669 + 1.66133i −0.428155 + 0.102248i
\(265\) −8.88764 + 29.5937i −0.545963 + 1.81793i
\(266\) 6.92361i 0.424514i
\(267\) −5.52047 + 8.98437i −0.337847 + 0.549835i
\(268\) 10.8288 + 10.8288i 0.661477 + 0.661477i
\(269\) −10.4792 −0.638928 −0.319464 0.947598i \(-0.603503\pi\)
−0.319464 + 0.947598i \(0.603503\pi\)
\(270\) −10.8162 4.24372i −0.658255 0.258264i
\(271\) −15.4253 −0.937021 −0.468511 0.883458i \(-0.655209\pi\)
−0.468511 + 0.883458i \(0.655209\pi\)
\(272\) 2.50190 + 2.50190i 0.151700 + 0.151700i
\(273\) 0.827499 1.34673i 0.0500825 0.0815076i
\(274\) 5.31597i 0.321150i
\(275\) −17.2306 11.3755i −1.03905 0.685967i
\(276\) −1.68468 + 0.402318i −0.101406 + 0.0242167i
\(277\) −8.17257 + 8.17257i −0.491042 + 0.491042i −0.908634 0.417592i \(-0.862874\pi\)
0.417592 + 0.908634i \(0.362874\pi\)
\(278\) −14.6943 + 14.6943i −0.881303 + 0.881303i
\(279\) 9.58817 + 18.9300i 0.574028 + 1.13331i
\(280\) −0.930794 1.72984i −0.0556256 0.103378i
\(281\) 24.0787i 1.43641i 0.695830 + 0.718206i \(0.255037\pi\)
−0.695830 + 0.718206i \(0.744963\pi\)
\(282\) 0.0584537 + 0.0359170i 0.00348087 + 0.00213883i
\(283\) −19.2731 19.2731i −1.14567 1.14567i −0.987396 0.158271i \(-0.949408\pi\)
−0.158271 0.987396i \(-0.550592\pi\)
\(284\) −2.25608 −0.133874
\(285\) −30.4738 1.74906i −1.80511 0.103606i
\(286\) 4.28964 0.253652
\(287\) −1.10097 1.10097i −0.0649880 0.0649880i
\(288\) 0.933895 2.85094i 0.0550303 0.167993i
\(289\) 4.48094i 0.263585i
\(290\) −16.7857 5.04112i −0.985691 0.296025i
\(291\) −6.72777 28.1721i −0.394389 1.65148i
\(292\) 8.48742 8.48742i 0.496689 0.496689i
\(293\) −17.5754 + 17.5754i −1.02677 + 1.02677i −0.0271332 + 0.999632i \(0.508638\pi\)
−0.999632 + 0.0271332i \(0.991362\pi\)
\(294\) −2.50574 10.4926i −0.146138 0.611941i
\(295\) 21.5873 11.6157i 1.25686 0.676292i
\(296\) 9.14409i 0.531489i
\(297\) −1.76048 + 21.3846i −0.102153 + 1.24086i
\(298\) 4.32738 + 4.32738i 0.250678 + 0.250678i
\(299\) 1.03881 0.0600759
\(300\) 7.84893 3.65983i 0.453158 0.211301i
\(301\) 7.84466 0.452159
\(302\) −5.66375 5.66375i −0.325912 0.325912i
\(303\) 2.01043 + 1.23532i 0.115496 + 0.0709670i
\(304\) 7.88126i 0.452021i
\(305\) −21.8258 + 11.7440i −1.24974 + 0.672461i
\(306\) 9.46929 4.79625i 0.541323 0.274184i
\(307\) 6.34290 6.34290i 0.362008 0.362008i −0.502544 0.864552i \(-0.667602\pi\)
0.864552 + 0.502544i \(0.167602\pi\)
\(308\) −2.56512 + 2.56512i −0.146161 + 0.146161i
\(309\) 8.04304 1.92076i 0.457553 0.109268i
\(310\) −15.1479 4.54925i −0.860343 0.258380i
\(311\) 1.54924i 0.0878496i −0.999035 0.0439248i \(-0.986014\pi\)
0.999035 0.0439248i \(-0.0139862\pi\)
\(312\) −0.941956 + 1.53300i −0.0533277 + 0.0867890i
\(313\) 0.449127 + 0.449127i 0.0253861 + 0.0253861i 0.719686 0.694300i \(-0.244286\pi\)
−0.694300 + 0.719686i \(0.744286\pi\)
\(314\) 13.5278 0.763420
\(315\) −5.80093 + 1.03814i −0.326846 + 0.0584928i
\(316\) −1.98214 −0.111504
\(317\) −17.7857 17.7857i −0.998943 0.998943i 0.00105667 0.999999i \(-0.499664\pi\)
−0.999999 + 0.00105667i \(0.999664\pi\)
\(318\) −12.5303 + 20.3926i −0.702663 + 1.14356i
\(319\) 32.3662i 1.81216i
\(320\) 1.05954 + 1.96911i 0.0592300 + 0.110076i
\(321\) −5.71329 + 1.36439i −0.318885 + 0.0761529i
\(322\) −0.621187 + 0.621187i −0.0346174 + 0.0346174i
\(323\) 19.7182 19.7182i 1.09715 1.09715i
\(324\) −7.25568 5.32495i −0.403093 0.295831i
\(325\) −5.08854 + 1.04154i −0.282262 + 0.0577740i
\(326\) 1.83956i 0.101884i
\(327\) 0.784943 + 0.482310i 0.0434075 + 0.0266718i
\(328\) 1.25325 + 1.25325i 0.0691991 + 0.0691991i
\(329\) 0.0347970 0.00191842
\(330\) −10.6422 11.9382i −0.585834 0.657178i
\(331\) −9.69040 −0.532633 −0.266316 0.963886i \(-0.585807\pi\)
−0.266316 + 0.963886i \(0.585807\pi\)
\(332\) −2.21281 2.21281i −0.121443 0.121443i
\(333\) 26.0692 + 8.53962i 1.42858 + 0.467968i
\(334\) 10.9652i 0.599990i
\(335\) −9.84958 + 32.7967i −0.538140 + 1.79188i
\(336\) −0.353433 1.47997i −0.0192813 0.0807392i
\(337\) 4.98944 4.98944i 0.271792 0.271792i −0.558029 0.829821i \(-0.688442\pi\)
0.829821 + 0.558029i \(0.188442\pi\)
\(338\) −8.42933 + 8.42933i −0.458495 + 0.458495i
\(339\) −2.35963 9.88080i −0.128158 0.536651i
\(340\) −2.27565 + 7.57738i −0.123415 + 0.410941i
\(341\) 29.2082i 1.58171i
\(342\) −22.4690 7.36027i −1.21498 0.397998i
\(343\) −8.21722 8.21722i −0.443688 0.443688i
\(344\) −8.92971 −0.481457
\(345\) −2.57719 2.89104i −0.138751 0.155648i
\(346\) 14.7488 0.792899
\(347\) −11.2296 11.2296i −0.602837 0.602837i 0.338228 0.941064i \(-0.390173\pi\)
−0.941064 + 0.338228i \(0.890173\pi\)
\(348\) −11.5668 7.10725i −0.620045 0.380988i
\(349\) 23.8817i 1.27836i 0.769059 + 0.639178i \(0.220725\pi\)
−0.769059 + 0.639178i \(0.779275\pi\)
\(350\) 2.42003 3.66566i 0.129356 0.195938i
\(351\) 3.49080 + 4.11712i 0.186325 + 0.219756i
\(352\) 2.91992 2.91992i 0.155632 0.155632i
\(353\) −12.1901 + 12.1901i −0.648813 + 0.648813i −0.952706 0.303893i \(-0.901713\pi\)
0.303893 + 0.952706i \(0.401713\pi\)
\(354\) 18.4691 4.41060i 0.981621 0.234421i
\(355\) −2.39040 4.44246i −0.126869 0.235781i
\(356\) 6.08809i 0.322668i
\(357\) 2.81850 4.58701i 0.149171 0.242770i
\(358\) −0.508677 0.508677i −0.0268844 0.0268844i
\(359\) 7.16299 0.378048 0.189024 0.981972i \(-0.439468\pi\)
0.189024 + 0.981972i \(0.439468\pi\)
\(360\) 6.60329 1.18174i 0.348024 0.0622829i
\(361\) −43.1142 −2.26917
\(362\) −11.8197 11.8197i −0.621229 0.621229i
\(363\) −5.48761 + 8.93089i −0.288025 + 0.468750i
\(364\) 0.912584i 0.0478324i
\(365\) 25.7054 + 7.71989i 1.34548 + 0.404078i
\(366\) −18.6731 + 4.45933i −0.976060 + 0.233093i
\(367\) 13.3521 13.3521i 0.696971 0.696971i −0.266785 0.963756i \(-0.585961\pi\)
0.963756 + 0.266785i \(0.0859613\pi\)
\(368\) 0.707107 0.707107i 0.0368605 0.0368605i
\(369\) 4.74334 2.40253i 0.246928 0.125071i
\(370\) −18.0057 + 9.68851i −0.936071 + 0.503682i
\(371\) 12.1396i 0.630255i
\(372\) −10.4382 6.41378i −0.541196 0.332539i
\(373\) −2.87275 2.87275i −0.148745 0.148745i 0.628812 0.777557i \(-0.283541\pi\)
−0.777557 + 0.628812i \(0.783541\pi\)
\(374\) 14.6107 0.755502
\(375\) 15.5228 + 11.5776i 0.801596 + 0.597867i
\(376\) −0.0396100 −0.00204273
\(377\) 5.75741 + 5.75741i 0.296522 + 0.296522i
\(378\) −4.54938 0.374527i −0.233995 0.0192636i
\(379\) 24.7455i 1.27109i −0.772063 0.635546i \(-0.780775\pi\)
0.772063 0.635546i \(-0.219225\pi\)
\(380\) 15.5190 8.35049i 0.796110 0.428371i
\(381\) −4.74587 19.8730i −0.243139 1.01813i
\(382\) −7.51222 + 7.51222i −0.384359 + 0.384359i
\(383\) 15.8012 15.8012i 0.807405 0.807405i −0.176836 0.984240i \(-0.556586\pi\)
0.984240 + 0.176836i \(0.0565861\pi\)
\(384\) 0.402318 + 1.68468i 0.0205307 + 0.0859709i
\(385\) −7.76884 2.33315i −0.395937 0.118909i
\(386\) 1.03641i 0.0527520i
\(387\) −8.33941 + 25.4580i −0.423916 + 1.29410i
\(388\) 11.8246 + 11.8246i 0.600303 + 0.600303i
\(389\) 1.35053 0.0684745 0.0342372 0.999414i \(-0.489100\pi\)
0.0342372 + 0.999414i \(0.489100\pi\)
\(390\) −4.01668 0.230540i −0.203392 0.0116738i
\(391\) 3.53823 0.178936
\(392\) 4.40404 + 4.40404i 0.222438 + 0.222438i
\(393\) −3.96583 2.43682i −0.200050 0.122921i
\(394\) 14.8132i 0.746279i
\(395\) −2.10015 3.90305i −0.105670 0.196384i
\(396\) −5.59760 11.0514i −0.281290 0.555354i
\(397\) −5.00981 + 5.00981i −0.251435 + 0.251435i −0.821559 0.570124i \(-0.806895\pi\)
0.570124 + 0.821559i \(0.306895\pi\)
\(398\) 2.13839 2.13839i 0.107188 0.107188i
\(399\) −11.6641 + 2.78549i −0.583933 + 0.139449i
\(400\) −2.75476 + 4.17269i −0.137738 + 0.208634i
\(401\) 13.0718i 0.652775i 0.945236 + 0.326387i \(0.105831\pi\)
−0.945236 + 0.326387i \(0.894169\pi\)
\(402\) −13.8865 + 22.5998i −0.692595 + 1.12717i
\(403\) 5.19565 + 5.19565i 0.258814 + 0.258814i
\(404\) −1.36233 −0.0677786
\(405\) 2.79773 19.9292i 0.139020 0.990290i
\(406\) −6.88563 −0.341728
\(407\) 26.7000 + 26.7000i 1.32347 + 1.32347i
\(408\) −3.20834 + 5.22147i −0.158837 + 0.258501i
\(409\) 15.7658i 0.779567i 0.920907 + 0.389784i \(0.127450\pi\)
−0.920907 + 0.389784i \(0.872550\pi\)
\(410\) −1.13992 + 3.79564i −0.0562964 + 0.187454i
\(411\) 8.95570 2.13871i 0.441752 0.105495i
\(412\) −3.37589 + 3.37589i −0.166318 + 0.166318i
\(413\) 6.81006 6.81006i 0.335101 0.335101i
\(414\) −1.35555 2.67628i −0.0666218 0.131532i
\(415\) 2.01270 6.70180i 0.0987995 0.328978i
\(416\) 1.03881i 0.0509318i
\(417\) −30.6669 18.8433i −1.50176 0.922762i
\(418\) −23.0126 23.0126i −1.12558 1.12558i
\(419\) −28.4327 −1.38903 −0.694514 0.719480i \(-0.744380\pi\)
−0.694514 + 0.719480i \(0.744380\pi\)
\(420\) 2.53975 2.26403i 0.123927 0.110474i
\(421\) 24.0167 1.17050 0.585252 0.810851i \(-0.300995\pi\)
0.585252 + 0.810851i \(0.300995\pi\)
\(422\) 13.6544 + 13.6544i 0.664684 + 0.664684i
\(423\) −0.0369916 + 0.112926i −0.00179859 + 0.00549063i
\(424\) 13.8187i 0.671093i
\(425\) −17.3318 + 3.54752i −0.840716 + 0.172080i
\(426\) −0.907662 3.80077i −0.0439764 0.184148i
\(427\) −6.88529 + 6.88529i −0.333203 + 0.333203i
\(428\) 2.39803 2.39803i 0.115913 0.115913i
\(429\) 1.72580 + 7.22667i 0.0833225 + 0.348907i
\(430\) −9.46136 17.5835i −0.456267 0.847954i
\(431\) 26.9458i 1.29793i −0.760817 0.648967i \(-0.775202\pi\)
0.760817 0.648967i \(-0.224798\pi\)
\(432\) 5.17863 + 0.426330i 0.249157 + 0.0205118i
\(433\) 10.1590 + 10.1590i 0.488212 + 0.488212i 0.907742 0.419530i \(-0.137805\pi\)
−0.419530 + 0.907742i \(0.637805\pi\)
\(434\) −6.21379 −0.298271
\(435\) 1.73947 30.3067i 0.0834011 1.45309i
\(436\) −0.531902 −0.0254735
\(437\) −5.57289 5.57289i −0.266588 0.266588i
\(438\) 17.7132 + 10.8839i 0.846370 + 0.520054i
\(439\) 2.41233i 0.115134i 0.998342 + 0.0575670i \(0.0183343\pi\)
−0.998342 + 0.0575670i \(0.981666\pi\)
\(440\) 8.84339 + 2.65587i 0.421592 + 0.126613i
\(441\) 16.6686 8.44273i 0.793741 0.402035i
\(442\) 2.59900 2.59900i 0.123622 0.123622i
\(443\) 7.57559 7.57559i 0.359927 0.359927i −0.503859 0.863786i \(-0.668087\pi\)
0.863786 + 0.503859i \(0.168087\pi\)
\(444\) −15.4048 + 3.67883i −0.731082 + 0.174590i
\(445\) 11.9881 6.45056i 0.568290 0.305786i
\(446\) 11.1399i 0.527491i
\(447\) −5.54926 + 9.03122i −0.262471 + 0.427162i
\(448\) 0.621187 + 0.621187i 0.0293483 + 0.0293483i
\(449\) 31.6647 1.49435 0.747174 0.664628i \(-0.231410\pi\)
0.747174 + 0.664628i \(0.231410\pi\)
\(450\) 9.32340 + 11.7505i 0.439509 + 0.553924i
\(451\) 7.31877 0.344627
\(452\) 4.14725 + 4.14725i 0.195070 + 0.195070i
\(453\) 7.26297 11.8202i 0.341244 0.555363i
\(454\) 11.4831i 0.538930i
\(455\) −1.79697 + 0.966917i −0.0842435 + 0.0453298i
\(456\) 13.2774 3.17077i 0.621770 0.148485i
\(457\) −27.2159 + 27.2159i −1.27310 + 1.27310i −0.328653 + 0.944451i \(0.606595\pi\)
−0.944451 + 0.328653i \(0.893405\pi\)
\(458\) 6.24430 6.24430i 0.291777 0.291777i
\(459\) 11.8898 + 14.0231i 0.554969 + 0.654542i
\(460\) 2.14157 + 0.643162i 0.0998514 + 0.0299876i
\(461\) 19.1053i 0.889824i −0.895574 0.444912i \(-0.853235\pi\)
0.895574 0.444912i \(-0.146765\pi\)
\(462\) −5.35340 3.28941i −0.249063 0.153037i
\(463\) 17.9935 + 17.9935i 0.836230 + 0.836230i 0.988360 0.152131i \(-0.0486135\pi\)
−0.152131 + 0.988360i \(0.548613\pi\)
\(464\) 7.83802 0.363871
\(465\) 1.56974 27.3496i 0.0727952 1.26831i
\(466\) −18.8850 −0.874831
\(467\) −13.5425 13.5425i −0.626673 0.626673i 0.320557 0.947229i \(-0.396130\pi\)
−0.947229 + 0.320557i \(0.896130\pi\)
\(468\) −2.96158 0.970139i −0.136899 0.0448447i
\(469\) 13.4535i 0.621224i
\(470\) −0.0419683 0.0779963i −0.00193585 0.00359770i
\(471\) 5.44250 + 22.7901i 0.250777 + 1.05011i
\(472\) −7.75200 + 7.75200i −0.356815 + 0.356815i
\(473\) −26.0740 + 26.0740i −1.19888 + 1.19888i
\(474\) −0.797451 3.33927i −0.0366281 0.153378i
\(475\) 32.8860 + 21.7110i 1.50891 + 0.996168i
\(476\) 3.10830i 0.142469i
\(477\) −39.3961 12.9052i −1.80382 0.590888i
\(478\) −3.74603 3.74603i −0.171340 0.171340i
\(479\) 10.1525 0.463880 0.231940 0.972730i \(-0.425493\pi\)
0.231940 + 0.972730i \(0.425493\pi\)
\(480\) −2.89104 + 2.57719i −0.131957 + 0.117632i
\(481\) 9.49896 0.433115
\(482\) −2.29328 2.29328i −0.104456 0.104456i
\(483\) −1.29641 0.796585i −0.0589889 0.0362459i
\(484\) 6.05185i 0.275084i
\(485\) −10.7553 + 35.8125i −0.488373 + 1.62616i
\(486\) 6.05174 14.3658i 0.274513 0.651646i
\(487\) 6.51439 6.51439i 0.295195 0.295195i −0.543933 0.839128i \(-0.683066\pi\)
0.839128 + 0.543933i \(0.183066\pi\)
\(488\) 7.83764 7.83764i 0.354793 0.354793i
\(489\) 3.09907 0.740089i 0.140145 0.0334680i
\(490\) −4.00578 + 13.3383i −0.180963 + 0.602562i
\(491\) 40.0908i 1.80927i 0.426186 + 0.904636i \(0.359857\pi\)
−0.426186 + 0.904636i \(0.640143\pi\)
\(492\) −1.60712 + 2.61553i −0.0724544 + 0.117917i
\(493\) 19.6100 + 19.6100i 0.883189 + 0.883189i
\(494\) −8.18712 −0.368356
\(495\) 15.8305 22.7317i 0.711529 1.02171i
\(496\) 7.07325 0.317598
\(497\) −1.40145 1.40145i −0.0628635 0.0628635i
\(498\) 2.83761 4.61812i 0.127157 0.206943i
\(499\) 3.33567i 0.149325i 0.997209 + 0.0746625i \(0.0237880\pi\)
−0.997209 + 0.0746625i \(0.976212\pi\)
\(500\) −11.1352 1.00330i −0.497983 0.0448688i
\(501\) −18.4729 + 4.41151i −0.825307 + 0.197092i
\(502\) 12.4867 12.4867i 0.557310 0.557310i
\(503\) −5.33310 + 5.33310i −0.237791 + 0.237791i −0.815935 0.578144i \(-0.803777\pi\)
0.578144 + 0.815935i \(0.303777\pi\)
\(504\) 2.35109 1.19084i 0.104726 0.0530443i
\(505\) −1.44344 2.68258i −0.0642323 0.119373i
\(506\) 4.12939i 0.183574i
\(507\) −17.5920 10.8094i −0.781287 0.480064i
\(508\) 8.34126 + 8.34126i 0.370084 + 0.370084i
\(509\) 0.551066 0.0244256 0.0122128 0.999925i \(-0.496112\pi\)
0.0122128 + 0.999925i \(0.496112\pi\)
\(510\) −13.6810 0.785228i −0.605804 0.0347705i
\(511\) 10.5445 0.466463
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 3.36002 40.8141i 0.148348 1.80199i
\(514\) 5.41825i 0.238989i
\(515\) −10.2244 3.07060i −0.450540 0.135307i
\(516\) −3.59258 15.0437i −0.158155 0.662261i
\(517\) −0.115658 + 0.115658i −0.00508664 + 0.00508664i
\(518\) −5.68019 + 5.68019i −0.249573 + 0.249573i
\(519\) 5.93370 + 24.8469i 0.260460 + 1.09066i
\(520\) 2.04552 1.10066i 0.0897022 0.0482670i
\(521\) 7.81178i 0.342240i 0.985250 + 0.171120i \(0.0547387\pi\)
−0.985250 + 0.171120i \(0.945261\pi\)
\(522\) 7.31989 22.3457i 0.320383 0.978045i
\(523\) 3.95100 + 3.95100i 0.172765 + 0.172765i 0.788193 0.615428i \(-0.211017\pi\)
−0.615428 + 0.788193i \(0.711017\pi\)
\(524\) 2.68737 0.117398
\(525\) 7.14909 + 2.60221i 0.312012 + 0.113570i
\(526\) −14.0715 −0.613548
\(527\) 17.6966 + 17.6966i 0.770876 + 0.770876i
\(528\) 6.09386 + 3.74439i 0.265201 + 0.162954i
\(529\) 1.00000i 0.0434783i
\(530\) 27.2104 14.6414i 1.18194 0.635981i
\(531\) 14.8609 + 29.3400i 0.644908 + 1.27325i
\(532\) 4.89573 4.89573i 0.212257 0.212257i
\(533\) 1.30189 1.30189i 0.0563909 0.0563909i
\(534\) 10.2565 2.44935i 0.443841 0.105994i
\(535\) 7.26278 + 2.18117i 0.313997 + 0.0943003i
\(536\) 15.3143i 0.661477i
\(537\) 0.652307 1.06161i 0.0281491 0.0458117i
\(538\) 7.40991 + 7.40991i 0.319464 + 0.319464i
\(539\) 25.7189 1.10779
\(540\) 4.64747 + 10.6490i 0.199995 + 0.458260i
\(541\) −12.6873 −0.545469 −0.272735 0.962089i \(-0.587928\pi\)
−0.272735 + 0.962089i \(0.587928\pi\)
\(542\) 10.9073 + 10.9073i 0.468511 + 0.468511i
\(543\) 15.1571 24.6676i 0.650453 1.05859i
\(544\) 3.53823i 0.151700i
\(545\) −0.563570 1.04737i −0.0241407 0.0448645i
\(546\) −1.53741 + 0.367149i −0.0657951 + 0.0157125i
\(547\) 4.43286 4.43286i 0.189535 0.189535i −0.605960 0.795495i \(-0.707211\pi\)
0.795495 + 0.605960i \(0.207211\pi\)
\(548\) −3.75896 + 3.75896i −0.160575 + 0.160575i
\(549\) −15.0251 29.6641i −0.641255 1.26603i
\(550\) 4.14023 + 20.2276i 0.176540 + 0.862507i
\(551\) 61.7735i 2.63164i
\(552\) 1.47573 + 0.906765i 0.0628112 + 0.0385945i
\(553\) −1.23128 1.23128i −0.0523593 0.0523593i
\(554\) 11.5578 0.491042
\(555\) −23.5660 26.4359i −1.00032 1.12214i
\(556\) 20.7808 0.881303
\(557\) −19.7470 19.7470i −0.836707 0.836707i 0.151717 0.988424i \(-0.451520\pi\)
−0.988424 + 0.151717i \(0.951520\pi\)
\(558\) 6.60568 20.1654i 0.279641 0.853669i
\(559\) 9.27626i 0.392344i
\(560\) −0.565012 + 1.88135i −0.0238761 + 0.0795017i
\(561\) 5.87816 + 24.6144i 0.248176 + 1.03922i
\(562\) 17.0262 17.0262i 0.718206 0.718206i
\(563\) −14.6245 + 14.6245i −0.616349 + 0.616349i −0.944593 0.328244i \(-0.893543\pi\)
0.328244 + 0.944593i \(0.393543\pi\)
\(564\) −0.0159358 0.0667301i −0.000671019 0.00280985i
\(565\) −3.77221 + 12.5605i −0.158698 + 0.528426i
\(566\) 27.2563i 1.14567i
\(567\) −1.19934 7.81492i −0.0503676 0.328196i
\(568\) 1.59529 + 1.59529i 0.0669369 + 0.0669369i
\(569\) 45.5814 1.91087 0.955436 0.295197i \(-0.0953854\pi\)
0.955436 + 0.295197i \(0.0953854\pi\)
\(570\) 20.3115 + 22.7850i 0.850754 + 0.954360i
\(571\) −13.8634 −0.580166 −0.290083 0.957001i \(-0.593683\pi\)
−0.290083 + 0.957001i \(0.593683\pi\)
\(572\) −3.03324 3.03324i −0.126826 0.126826i
\(573\) −15.6780 9.63337i −0.654957 0.402440i
\(574\) 1.55700i 0.0649880i
\(575\) 1.00262 + 4.89844i 0.0418123 + 0.204279i
\(576\) −2.67628 + 1.35555i −0.111512 + 0.0564814i
\(577\) 26.2357 26.2357i 1.09221 1.09221i 0.0969147 0.995293i \(-0.469103\pi\)
0.995293 0.0969147i \(-0.0308974\pi\)
\(578\) −3.16851 + 3.16851i −0.131792 + 0.131792i
\(579\) −1.74602 + 0.416968i −0.0725622 + 0.0173286i
\(580\) 8.30468 + 15.4339i 0.344833 + 0.640858i
\(581\) 2.74913i 0.114053i
\(582\) −15.1634 + 24.6779i −0.628543 + 1.02293i
\(583\) −40.3494 40.3494i −1.67110 1.67110i
\(584\) −12.0030 −0.496689
\(585\) −1.22760 6.85956i −0.0507549 0.283608i
\(586\) 24.8553 1.02677
\(587\) 1.72536 + 1.72536i 0.0712134 + 0.0712134i 0.741816 0.670603i \(-0.233965\pi\)
−0.670603 + 0.741816i \(0.733965\pi\)
\(588\) −5.64757 + 9.19122i −0.232902 + 0.379039i
\(589\) 55.7461i 2.29698i
\(590\) −23.4780 7.05097i −0.966576 0.290284i
\(591\) 24.9555 5.95963i 1.02653 0.245146i
\(592\) 6.46585 6.46585i 0.265745 0.265745i
\(593\) 2.77888 2.77888i 0.114115 0.114115i −0.647744 0.761858i \(-0.724287\pi\)
0.761858 + 0.647744i \(0.224287\pi\)
\(594\) 16.3660 13.8763i 0.671507 0.569353i
\(595\) −6.12057 + 3.29336i −0.250919 + 0.135015i
\(596\) 6.11984i 0.250678i
\(597\) 4.46280 + 2.74218i 0.182650 + 0.112230i
\(598\) −0.734549 0.734549i −0.0300379 0.0300379i
\(599\) −37.0107 −1.51222 −0.756108 0.654447i \(-0.772902\pi\)
−0.756108 + 0.654447i \(0.772902\pi\)
\(600\) −8.13792 2.96214i −0.332229 0.120929i
\(601\) 34.9685 1.42639 0.713196 0.700964i \(-0.247247\pi\)
0.713196 + 0.700964i \(0.247247\pi\)
\(602\) −5.54701 5.54701i −0.226079 0.226079i
\(603\) −43.6601 14.3020i −1.77798 0.582421i
\(604\) 8.00975i 0.325912i
\(605\) 11.9167 6.41216i 0.484484 0.260692i
\(606\) −0.548091 2.29509i −0.0222647 0.0932317i
\(607\) −3.77458 + 3.77458i −0.153205 + 0.153205i −0.779548 0.626343i \(-0.784551\pi\)
0.626343 + 0.779548i \(0.284551\pi\)
\(608\) −5.57289 + 5.57289i −0.226011 + 0.226011i
\(609\) −2.77021 11.6001i −0.112255 0.470058i
\(610\) 23.7374 + 7.12887i 0.961100 + 0.288640i
\(611\) 0.0411472i 0.00166464i
\(612\) −10.0873 3.30433i −0.407753 0.133570i
\(613\) −12.5789 12.5789i −0.508056 0.508056i 0.405873 0.913929i \(-0.366967\pi\)
−0.913929 + 0.405873i \(0.866967\pi\)
\(614\) −8.97021 −0.362008
\(615\) −6.85305 0.393335i −0.276342 0.0158608i
\(616\) 3.62763 0.146161
\(617\) 3.87788 + 3.87788i 0.156118 + 0.156118i 0.780844 0.624726i \(-0.214789\pi\)
−0.624726 + 0.780844i \(0.714789\pi\)
\(618\) −7.04547 4.32911i −0.283410 0.174142i
\(619\) 8.64542i 0.347489i 0.984791 + 0.173744i \(0.0555867\pi\)
−0.984791 + 0.173744i \(0.944413\pi\)
\(620\) 7.49438 + 13.9280i 0.300981 + 0.559361i
\(621\) 3.96331 3.36039i 0.159042 0.134848i
\(622\) −1.09548 + 1.09548i −0.0439248 + 0.0439248i
\(623\) 3.78184 3.78184i 0.151516 0.151516i
\(624\) 1.75006 0.417931i 0.0700584 0.0167306i
\(625\) −9.82260 22.9895i −0.392904 0.919579i
\(626\) 0.635161i 0.0253861i
\(627\) 29.5105 48.0273i 1.17854 1.91802i
\(628\) −9.56563 9.56563i −0.381710 0.381710i
\(629\) 32.3539 1.29003
\(630\) 4.83596 + 3.36780i 0.192669 + 0.134176i
\(631\) −41.6995 −1.66003 −0.830015 0.557742i \(-0.811668\pi\)
−0.830015 + 0.557742i \(0.811668\pi\)
\(632\) 1.40159 + 1.40159i 0.0557521 + 0.0557521i
\(633\) −17.5098 + 28.4966i −0.695952 + 1.13264i
\(634\) 25.1527i 0.998943i
\(635\) −7.58695 + 25.2627i −0.301079 + 1.00252i
\(636\) 23.2800 5.55950i 0.923112 0.220448i
\(637\) 4.57496 4.57496i 0.181266 0.181266i
\(638\) 22.8864 22.8864i 0.906081 0.906081i
\(639\) 6.03790 3.05824i 0.238856 0.120982i
\(640\) 0.643162 2.14157i 0.0254232 0.0846532i
\(641\) 2.72989i 0.107824i 0.998546 + 0.0539121i \(0.0171691\pi\)
−0.998546 + 0.0539121i \(0.982831\pi\)
\(642\) 5.00468 + 3.07514i 0.197519 + 0.121366i
\(643\) 17.4028 + 17.4028i 0.686298 + 0.686298i 0.961412 0.275114i \(-0.0887155\pi\)
−0.275114 + 0.961412i \(0.588715\pi\)
\(644\) 0.878491 0.0346174
\(645\) 25.8161 23.0135i 1.01651 0.906157i
\(646\) −27.8857 −1.09715
\(647\) −9.72994 9.72994i −0.382523 0.382523i 0.489487 0.872011i \(-0.337184\pi\)
−0.872011 + 0.489487i \(0.837184\pi\)
\(648\) 1.36523 + 8.89585i 0.0536313 + 0.349462i
\(649\) 45.2704i 1.77702i
\(650\) 4.33462 + 2.86167i 0.170018 + 0.112244i
\(651\) −2.49992 10.4682i −0.0979795 0.410282i
\(652\) −1.30077 + 1.30077i −0.0509420 + 0.0509420i
\(653\) −21.5513 + 21.5513i −0.843367 + 0.843367i −0.989295 0.145928i \(-0.953383\pi\)
0.145928 + 0.989295i \(0.453383\pi\)
\(654\) −0.213994 0.896084i −0.00836782 0.0350396i
\(655\) 2.84737 + 5.29172i 0.111256 + 0.206765i
\(656\) 1.77236i 0.0691991i
\(657\) −11.2096 + 34.2199i −0.437327 + 1.33504i
\(658\) −0.0246052 0.0246052i −0.000959211 0.000959211i
\(659\) −44.3615 −1.72808 −0.864039 0.503425i \(-0.832073\pi\)
−0.864039 + 0.503425i \(0.832073\pi\)
\(660\) −0.916422 + 15.9668i −0.0356717 + 0.621506i
\(661\) 43.3242 1.68512 0.842559 0.538605i \(-0.181048\pi\)
0.842559 + 0.538605i \(0.181048\pi\)
\(662\) 6.85215 + 6.85215i 0.266316 + 0.266316i
\(663\) 5.42410 + 3.33285i 0.210655 + 0.129437i
\(664\) 3.12938i 0.121443i
\(665\) 14.8274 + 4.45300i 0.574983 + 0.172680i
\(666\) −12.3953 24.4721i −0.480308 0.948276i
\(667\) 5.54232 5.54232i 0.214599 0.214599i
\(668\) 7.75358 7.75358i 0.299995 0.299995i
\(669\) −18.7672 + 4.48180i −0.725582 + 0.173276i
\(670\) 30.1555 16.2261i 1.16501 0.626868i
\(671\) 45.7705i 1.76695i
\(672\) −0.796585 + 1.29641i −0.0307289 + 0.0500103i
\(673\) −30.3342 30.3342i −1.16930 1.16930i −0.982375 0.186921i \(-0.940149\pi\)
−0.186921 0.982375i \(-0.559851\pi\)
\(674\) −7.05614 −0.271792
\(675\) −16.0448 + 20.4344i −0.617566 + 0.786519i
\(676\) 11.9209 0.458495
\(677\) 8.39686 + 8.39686i 0.322718 + 0.322718i 0.849809 0.527091i \(-0.176717\pi\)
−0.527091 + 0.849809i \(0.676717\pi\)
\(678\) −5.31826 + 8.65529i −0.204247 + 0.332404i
\(679\) 14.6906i 0.563773i
\(680\) 6.96715 3.74889i 0.267178 0.143763i
\(681\) 19.3454 4.61987i 0.741317 0.177034i
\(682\) 20.6533 20.6533i 0.790856 0.790856i
\(683\) −16.0879 + 16.0879i −0.615584 + 0.615584i −0.944396 0.328811i \(-0.893352\pi\)
0.328811 + 0.944396i \(0.393352\pi\)
\(684\) 10.6835 + 21.0925i 0.408492 + 0.806490i
\(685\) −11.3845 3.41903i −0.434981 0.130634i
\(686\) 11.6209i 0.443688i
\(687\) 13.0318 + 8.00744i 0.497196 + 0.305503i
\(688\) 6.31426 + 6.31426i 0.240729 + 0.240729i
\(689\) −14.3549 −0.546880
\(690\) −0.221927 + 3.86662i −0.00844861 + 0.147200i
\(691\) −13.0690 −0.497169 −0.248585 0.968610i \(-0.579965\pi\)
−0.248585 + 0.968610i \(0.579965\pi\)
\(692\) −10.4290 10.4290i −0.396449 0.396449i
\(693\) 3.38783 10.3421i 0.128693 0.392865i
\(694\) 15.8811i 0.602837i
\(695\) 22.0181 + 40.9197i 0.835193 + 1.55217i
\(696\) 3.15338 + 13.2045i 0.119528 + 0.500517i
\(697\) 4.43428 4.43428i 0.167960 0.167960i
\(698\) 16.8869 16.8869i 0.639178 0.639178i
\(699\) −7.59778 31.8152i −0.287374 1.20336i
\(700\) −4.30324 + 0.880797i −0.162647 + 0.0332910i
\(701\) 26.8220i 1.01305i −0.862225 0.506526i \(-0.830930\pi\)
0.862225 0.506526i \(-0.169070\pi\)
\(702\) 0.442875 5.37961i 0.0167152 0.203040i
\(703\) −50.9590 50.9590i −1.92196 1.92196i
\(704\) −4.12939 −0.155632
\(705\) 0.114514 0.102082i 0.00431285 0.00384465i
\(706\) 17.2394 0.648813
\(707\) −0.846263 0.846263i −0.0318270 0.0318270i
\(708\) −16.1784 9.94085i −0.608021 0.373600i
\(709\) 4.26519i 0.160183i 0.996788 + 0.0800914i \(0.0255212\pi\)
−0.996788 + 0.0800914i \(0.974479\pi\)
\(710\) −1.45103 + 4.83156i −0.0544560 + 0.181325i
\(711\) 5.30476 2.68690i 0.198944 0.100766i
\(712\) −4.30493 + 4.30493i −0.161334 + 0.161334i
\(713\) 5.00154 5.00154i 0.187309 0.187309i
\(714\) −5.23649 + 1.25053i −0.195971 + 0.0467997i
\(715\) 2.75894 9.18659i 0.103178 0.343559i
\(716\) 0.719378i 0.0268844i
\(717\) 4.80376 7.81796i 0.179400 0.291967i
\(718\) −5.06500 5.06500i −0.189024 0.189024i
\(719\) 34.9727 1.30426 0.652130 0.758107i \(-0.273875\pi\)
0.652130 + 0.758107i \(0.273875\pi\)
\(720\) −5.50485 3.83362i −0.205154 0.142871i
\(721\) −4.19412 −0.156197
\(722\) 30.4864 + 30.4864i 1.13459 + 1.13459i
\(723\) 2.94081 4.78606i 0.109370 0.177996i
\(724\) 16.7156i 0.621229i
\(725\) −21.5919 + 32.7056i −0.801902 + 1.21466i
\(726\) 10.1954 2.43477i 0.378388 0.0903627i
\(727\) 13.4827 13.4827i 0.500044 0.500044i −0.411407 0.911452i \(-0.634963\pi\)
0.911452 + 0.411407i \(0.134963\pi\)
\(728\) 0.645294 0.645294i 0.0239162 0.0239162i
\(729\) 26.6365 + 4.41561i 0.986537 + 0.163541i
\(730\) −12.7177 23.6352i −0.470702 0.874779i
\(731\) 31.5953i 1.16860i
\(732\) 16.3571 + 10.0507i 0.604577 + 0.371484i
\(733\) 32.6105 + 32.6105i 1.20450 + 1.20450i 0.972785 + 0.231710i \(0.0744321\pi\)
0.231710 + 0.972785i \(0.425568\pi\)
\(734\) −18.8827 −0.696971
\(735\) −24.0823 1.38222i −0.888289 0.0509838i
\(736\) −1.00000 −0.0368605
\(737\) −44.7165 44.7165i −1.64715 1.64715i
\(738\) −5.05289 1.65520i −0.185999 0.0609288i
\(739\) 7.71809i 0.283915i −0.989873 0.141957i \(-0.954660\pi\)
0.989873 0.141957i \(-0.0453396\pi\)
\(740\) 19.5828 + 5.88113i 0.719876 + 0.216195i
\(741\) −3.29383 13.7927i −0.121002 0.506686i
\(742\) 8.58397 8.58397i 0.315127 0.315127i
\(743\) −4.77261 + 4.77261i −0.175090 + 0.175090i −0.789212 0.614121i \(-0.789511\pi\)
0.614121 + 0.789212i \(0.289511\pi\)
\(744\) 2.84570 + 11.9162i 0.104328 + 0.436867i
\(745\) 12.0506 6.48420i 0.441500 0.237563i
\(746\) 4.06268i 0.148745i
\(747\) 8.92166 + 2.92251i 0.326427 + 0.106929i
\(748\) −10.3313 10.3313i −0.377751 0.377751i
\(749\) 2.97925 0.108859
\(750\) −2.78967 19.1629i −0.101864 0.699731i
\(751\) −52.9204 −1.93109 −0.965547 0.260229i \(-0.916202\pi\)
−0.965547 + 0.260229i \(0.916202\pi\)
\(752\) 0.0280085 + 0.0280085i 0.00102137 + 0.00102137i
\(753\) 26.0598 + 16.0125i 0.949671 + 0.583528i
\(754\) 8.14220i 0.296522i
\(755\) −15.7721 + 8.48664i −0.574004 + 0.308860i
\(756\) 2.95207 + 3.48173i 0.107366 + 0.126629i
\(757\) −4.25493 + 4.25493i −0.154648 + 0.154648i −0.780190 0.625542i \(-0.784878\pi\)
0.625542 + 0.780190i \(0.284878\pi\)
\(758\) −17.4977 + 17.4977i −0.635546 + 0.635546i
\(759\) 6.95669 1.66133i 0.252512 0.0603024i
\(760\) −16.8783 5.06893i −0.612240 0.183869i
\(761\) 10.5196i 0.381334i −0.981655 0.190667i \(-0.938935\pi\)
0.981655 0.190667i \(-0.0610650\pi\)
\(762\) −10.6965 + 17.4082i −0.387493 + 0.630632i
\(763\) −0.330410 0.330410i −0.0119617 0.0119617i
\(764\) 10.6239 0.384359
\(765\) −4.18125 23.3640i −0.151173 0.844726i
\(766\) −22.3463 −0.807405
\(767\) 8.05284 + 8.05284i 0.290771 + 0.290771i
\(768\) 0.906765 1.47573i 0.0327201 0.0532508i
\(769\) 20.7974i 0.749972i 0.927030 + 0.374986i \(0.122353\pi\)
−0.927030 + 0.374986i \(0.877647\pi\)
\(770\) 3.84361 + 7.14319i 0.138514 + 0.257423i
\(771\) −9.12801 + 2.17986i −0.328737 + 0.0785058i
\(772\) 0.732855 0.732855i 0.0263760 0.0263760i
\(773\) −7.11987 + 7.11987i −0.256084 + 0.256084i −0.823459 0.567375i \(-0.807959\pi\)
0.567375 + 0.823459i \(0.307959\pi\)
\(774\) 23.8984 12.1047i 0.859010 0.435094i
\(775\) −19.4851 + 29.5145i −0.699926 + 1.06019i
\(776\) 16.7225i 0.600303i
\(777\) −11.8545 7.28404i −0.425279 0.261314i