Properties

Label 690.2.i.f.47.9
Level $690$
Weight $2$
Character 690.47
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 47.9
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.47573 - 0.906765i) q^{3} -1.00000i q^{4} +(1.96911 + 1.05954i) q^{5} +(-1.68468 + 0.402318i) q^{6} +(-0.621187 - 0.621187i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.35555 + 2.67628i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.47573 - 0.906765i) 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} +(-0.906765 + 1.47573i) q^{12} +(-0.734549 + 0.734549i) q^{13} -0.878491 q^{14} +(-1.94512 - 3.34911i) q^{15} -1.00000 q^{16} +(2.50190 - 2.50190i) q^{17} +(2.85094 + 0.933895i) 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} +(0.426330 - 5.17863i) q^{27} +(-0.621187 + 0.621187i) q^{28} +7.83802 q^{29} +(-3.74358 - 0.992773i) q^{30} -7.07325 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.74439 + 6.09386i) 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} +(1.29641 + 0.796585i) q^{42} +(-6.31426 + 6.31426i) q^{43} -4.12939 q^{44} +(-0.166392 + 6.70614i) q^{45} +1.00000 q^{46} +(0.0280085 - 0.0280085i) q^{47} +(1.47573 + 0.906765i) 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} +(-7.14645 + 11.6306i) q^{57} +(5.54232 - 5.54232i) q^{58} +10.9630 q^{59} +(-3.34911 + 1.94512i) q^{60} +11.0841 q^{61} +(-5.00154 + 5.00154i) q^{62} +(0.820418 - 2.50452i) 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} +(0.933895 - 2.85094i) q^{72} +(-8.48742 + 8.48742i) q^{73} -9.14409 q^{74} +(-0.281632 - 8.65567i) q^{75} -7.88126 q^{76} +(-2.56512 + 2.56512i) q^{77} +(0.941956 - 1.53300i) 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} +(-11.5668 - 7.10725i) q^{87} +(-2.91992 + 2.91992i) q^{88} +6.08809 q^{89} +(4.62430 + 4.85961i) q^{90} +0.912584 q^{91} +(0.707107 - 0.707107i) q^{92} +(10.4382 + 6.41378i) 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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.47573 0.906765i −0.852013 0.523521i
\(4\) 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 0.579901 0.814687i \(-0.303091\pi\)
−0.814687 + 0.579901i \(0.803091\pi\)
\(8\) −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 \(-0.213895\pi\)
\(12\) −0.906765 + 1.47573i −0.261761 + 0.426006i
\(13\) −0.734549 + 0.734549i −0.203727 + 0.203727i −0.801595 0.597868i \(-0.796015\pi\)
0.597868 + 0.801595i \(0.296015\pi\)
\(14\) −0.878491 −0.234787
\(15\) −1.94512 3.34911i −0.502227 0.864736i
\(16\) −1.00000 −0.250000
\(17\) 2.50190 2.50190i 0.606801 0.606801i −0.335308 0.942109i \(-0.608840\pi\)
0.942109 + 0.335308i \(0.108840\pi\)
\(18\) 2.85094 + 0.933895i 0.671972 + 0.220121i
\(19\) 7.88126i 1.80808i −0.427443 0.904042i \(-0.640586\pi\)
0.427443 0.904042i \(-0.359414\pi\)
\(20\) 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
\(27\) 0.426330 5.17863i 0.0820472 0.996628i
\(28\) −0.621187 + 0.621187i −0.117393 + 0.117393i
\(29\) 7.83802 1.45548 0.727742 0.685851i \(-0.240570\pi\)
0.727742 + 0.685851i \(0.240570\pi\)
\(30\) −3.74358 0.992773i −0.683481 0.181255i
\(31\) −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
\(33\) −3.74439 + 6.09386i −0.651814 + 1.06080i
\(34\) 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 −0.997879 0.0651000i \(-0.979263\pi\)
−0.0651000 0.997879i \(-0.520737\pi\)
\(38\) −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 \(0.955805\pi\)
\(42\) 1.29641 + 0.796585i 0.200041 + 0.122916i
\(43\) −6.31426 + 6.31426i −0.962915 + 0.962915i −0.999337 0.0364216i \(-0.988404\pi\)
0.0364216 + 0.999337i \(0.488404\pi\)
\(44\) −4.12939 −0.622529
\(45\) −0.166392 + 6.70614i −0.0248043 + 0.999692i
\(46\) 1.00000 0.147442
\(47\) 0.0280085 0.0280085i 0.00408546 0.00408546i −0.705061 0.709147i \(-0.749080\pi\)
0.709147 + 0.705061i \(0.249080\pi\)
\(48\) 1.47573 + 0.906765i 0.213003 + 0.130880i
\(49\) 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 −0.893880 0.448307i \(-0.852027\pi\)
−0.448307 0.893880i \(-0.647973\pi\)
\(54\) −3.36039 3.96331i −0.457291 0.539338i
\(55\) 4.37524 8.13121i 0.589958 1.09641i
\(56\) 0.878491i 0.117393i
\(57\) −7.14645 + 11.6306i −0.946571 + 1.54051i
\(58\) 5.54232 5.54232i 0.727742 0.727742i
\(59\) 10.9630 1.42726 0.713629 0.700524i \(-0.247050\pi\)
0.713629 + 0.700524i \(0.247050\pi\)
\(60\) −3.34911 + 1.94512i −0.432368 + 0.251113i
\(61\) 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
\(63\) 0.820418 2.50452i 0.103363 0.315540i
\(64\) 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 0.911373 + 0.411581i \(0.135023\pi\)
0.411581 + 0.911373i \(0.364977\pi\)
\(68\) −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 \(0.957258\pi\)
\(72\) 0.933895 2.85094i 0.110061 0.335986i
\(73\) −8.48742 + 8.48742i −0.993378 + 0.993378i −0.999978 0.00660049i \(-0.997899\pi\)
0.00660049 + 0.999978i \(0.497899\pi\)
\(74\) −9.14409 −1.06298
\(75\) −0.281632 8.65567i −0.0325201 0.999471i
\(76\) −7.88126 −0.904042
\(77\) −2.56512 + 2.56512i −0.292323 + 0.292323i
\(78\) 0.941956 1.53300i 0.106655 0.173578i
\(79\) 1.98214i 0.223008i −0.993764 0.111504i \(-0.964433\pi\)
0.993764 0.111504i \(-0.0355668\pi\)
\(80\) −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 \(-0.195059\pi\)
−0.575156 + 0.818043i \(0.695059\pi\)
\(84\) 1.47997 0.353433i 0.161478 0.0385627i
\(85\) 7.57738 2.27565i 0.821882 0.246829i
\(86\) 8.92971i 0.962915i
\(87\) −11.5668 7.10725i −1.24009 0.761977i
\(88\) −2.91992 + 2.91992i −0.311264 + 0.311264i
\(89\) 6.08809 0.645336 0.322668 0.946512i \(-0.395420\pi\)
0.322668 + 0.946512i \(0.395420\pi\)
\(90\) 4.62430 + 4.85961i 0.487444 + 0.512248i
\(91\) 0.912584 0.0956648
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) 10.4382 + 6.41378i 1.08239 + 0.665078i
\(94\) 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 0.973982 + 0.226625i \(0.0727691\pi\)
0.226625 + 0.973982i \(0.427231\pi\)
\(98\) −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 \(0.978409\pi\)
\(102\) −3.20834 + 5.22147i −0.317673 + 0.517002i
\(103\) 3.37589 3.37589i 0.332636 0.332636i −0.520950 0.853587i \(-0.674422\pi\)
0.853587 + 0.520950i \(0.174422\pi\)
\(104\) 1.03881 0.101864
\(105\) −0.872142 + 3.28870i −0.0851123 + 0.320944i
\(106\) −13.8187 −1.34219
\(107\) 2.39803 2.39803i 0.231826 0.231826i −0.581628 0.813455i \(-0.697584\pi\)
0.813455 + 0.581628i \(0.197584\pi\)
\(108\) −5.17863 0.426330i −0.498314 0.0410236i
\(109\) 0.531902i 0.0509470i −0.999675 0.0254735i \(-0.991891\pi\)
0.999675 0.0254735i \(-0.00810934\pi\)
\(110\) −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 \(-0.338966\pi\)
−0.874737 + 0.484597i \(0.838966\pi\)
\(114\) 3.17077 + 13.2774i 0.296970 + 1.24354i
\(115\) 0.643162 + 2.14157i 0.0599752 + 0.199703i
\(116\) 7.83802i 0.727742i
\(117\) −2.96158 0.970139i −0.273798 0.0896893i
\(118\) 7.75200 7.75200i 0.713629 0.713629i
\(119\) −3.10830 −0.284937
\(120\) −0.992773 + 3.74358i −0.0906274 + 0.341741i
\(121\) −6.05185 −0.550168
\(122\) 7.83764 7.83764i 0.709587 0.709587i
\(123\) 1.60712 2.61553i 0.144909 0.235834i
\(124\) 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 0.972610 0.232443i \(-0.0746718\pi\)
−0.232443 + 0.972610i \(0.574672\pi\)
\(128\) 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 \(-0.0374554\pi\)
\(132\) 6.09386 + 3.74439i 0.530402 + 0.325907i
\(133\) −4.89573 + 4.89573i −0.424514 + 0.424514i
\(134\) 15.3143 1.32295
\(135\) 6.32645 9.74557i 0.544494 0.838765i
\(136\) −3.53823 −0.303401
\(137\) −3.75896 + 3.75896i −0.321150 + 0.321150i −0.849208 0.528058i \(-0.822920\pi\)
0.528058 + 0.849208i \(0.322920\pi\)
\(138\) −1.47573 0.906765i −0.125622 0.0771890i
\(139\) 20.7808i 1.76261i 0.472551 + 0.881303i \(0.343333\pi\)
−0.472551 + 0.881303i \(0.656667\pi\)
\(140\) −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
\(147\) −5.64757 + 9.19122i −0.465803 + 0.758079i
\(148\) −6.46585 + 6.46585i −0.531489 + 0.531489i
\(149\) 6.11984 0.501357 0.250678 0.968070i \(-0.419346\pi\)
0.250678 + 0.968070i \(0.419346\pi\)
\(150\) −6.31963 5.92134i −0.515996 0.483476i
\(151\) 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
\(153\) 10.0873 + 3.30433i 0.815507 + 0.267140i
\(154\) 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 0.213519 0.976939i \(-0.431508\pi\)
−0.976939 + 0.213519i \(0.931508\pi\)
\(158\) −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
\(162\) 1.36523 + 8.89585i 0.107263 + 0.698924i
\(163\) 1.30077 1.30077i 0.101884 0.101884i −0.654327 0.756211i \(-0.727048\pi\)
0.756211 + 0.654327i \(0.227048\pi\)
\(164\) 1.77236 0.138398
\(165\) −13.8298 + 8.03214i −1.07665 + 0.625301i
\(166\) 3.12938 0.242887
\(167\) 7.75358 7.75358i 0.599990 0.599990i −0.340320 0.940310i \(-0.610535\pi\)
0.940310 + 0.340320i \(0.110535\pi\)
\(168\) 0.796585 1.29641i 0.0614579 0.100021i
\(169\) 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 \(-0.0605459\pi\)
−0.189066 + 0.981964i \(0.560546\pi\)
\(174\) −13.2045 + 3.15338i −1.00103 + 0.239057i
\(175\) 0.880797 4.30324i 0.0665820 0.325294i
\(176\) 4.12939i 0.311264i
\(177\) −16.1784 9.94085i −1.21604 0.747200i
\(178\) 4.30493 4.30493i 0.322668 0.322668i
\(179\) −0.719378 −0.0537688 −0.0268844 0.999639i \(-0.508559\pi\)
−0.0268844 + 0.999639i \(0.508559\pi\)
\(180\) 6.70614 + 0.166392i 0.499846 + 0.0124022i
\(181\) 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
\(183\) −16.3571 10.0507i −1.20915 0.742967i
\(184\) 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 \(-0.125577\pi\)
\(192\) 0.906765 1.47573i 0.0654402 0.106502i
\(193\) −0.732855 + 0.732855i −0.0527520 + 0.0527520i −0.732991 0.680239i \(-0.761876\pi\)
0.680239 + 0.732991i \(0.261876\pi\)
\(194\) 16.7225 1.20061
\(195\) 3.88886 + 1.03130i 0.278487 + 0.0738530i
\(196\) −6.22825 −0.444875
\(197\) −10.4745 + 10.4745i −0.746279 + 0.746279i −0.973778 0.227499i \(-0.926945\pi\)
0.227499 + 0.973778i \(0.426945\pi\)
\(198\) 3.85642 11.7726i 0.274064 0.836644i
\(199\) 3.02413i 0.214375i −0.994239 0.107188i \(-0.965815\pi\)
0.994239 0.107188i \(-0.0341845\pi\)
\(200\) 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
\(207\) −0.933895 + 2.85094i −0.0649102 + 0.198154i
\(208\) 0.734549 0.734549i 0.0509318 0.0509318i
\(209\) −32.5448 −2.25117
\(210\) 1.70877 + 2.94216i 0.117916 + 0.203028i
\(211\) −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
\(213\) 2.04574 3.32936i 0.140171 0.228124i
\(214\) 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
\(222\) 13.4942 + 8.29154i 0.905671 + 0.556492i
\(223\) −7.87712 + 7.87712i −0.527491 + 0.527491i −0.919824 0.392332i \(-0.871668\pi\)
0.392332 + 0.919824i \(0.371668\pi\)
\(224\) 0.878491 0.0586966
\(225\) −7.43305 + 13.0288i −0.495537 + 0.868587i
\(226\) −5.86509 −0.390140
\(227\) −8.11980 + 8.11980i −0.538930 + 0.538930i −0.923215 0.384284i \(-0.874448\pi\)
0.384284 + 0.923215i \(0.374448\pi\)
\(228\) 11.6306 + 7.14645i 0.770255 + 0.473285i
\(229\) 8.83078i 0.583554i −0.956486 0.291777i \(-0.905753\pi\)
0.956486 0.291777i \(-0.0942465\pi\)
\(230\) 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 \(-0.462299\pi\)
−0.992994 + 0.118163i \(0.962299\pi\)
\(234\) −2.78014 + 1.40816i −0.181744 + 0.0920543i
\(235\) 0.0848278 0.0254757i 0.00553356 0.00166185i
\(236\) 10.9630i 0.713629i
\(237\) −1.79734 + 2.92510i −0.116750 + 0.190006i
\(238\) −2.19790 + 2.19790i −0.142469 + 0.142469i
\(239\) −5.29769 −0.342679 −0.171340 0.985212i \(-0.554810\pi\)
−0.171340 + 0.985212i \(0.554810\pi\)
\(240\) 1.94512 + 3.34911i 0.125557 + 0.216184i
\(241\) 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
\(243\) 14.4374 5.87893i 0.926159 0.377134i
\(244\) 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 \(0.811833\pi\)
\(252\) −2.50452 0.820418i −0.157770 0.0516815i
\(253\) 2.91992 2.91992i 0.183574 0.183574i
\(254\) 11.7963 0.740167
\(255\) −13.2456 3.51266i −0.829474 0.219971i
\(256\) 1.00000 0.0625000
\(257\) 3.83128 3.83128i 0.238989 0.238989i −0.577442 0.816431i \(-0.695949\pi\)
0.816431 + 0.577442i \(0.195949\pi\)
\(258\) 8.09715 13.1778i 0.504106 0.820416i
\(259\) 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 \(-0.392843\pi\)
−0.943869 + 0.330321i \(0.892843\pi\)
\(264\) 6.95669 1.66133i 0.428155 0.102248i
\(265\) −8.88764 29.5937i −0.545963 1.81793i
\(266\) 6.92361i 0.424514i
\(267\) −8.98437 5.52047i −0.549835 0.337847i
\(268\) 10.8288 10.8288i 0.661477 0.661477i
\(269\) 10.4792 0.638928 0.319464 0.947598i \(-0.396497\pi\)
0.319464 + 0.947598i \(0.396497\pi\)
\(270\) −2.41768 11.3646i −0.147136 0.691629i
\(271\) −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
\(273\) −1.34673 0.827499i −0.0815076 0.0500825i
\(274\) 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 0.417592 0.908634i \(-0.362874\pi\)
−0.908634 + 0.417592i \(0.862874\pi\)
\(278\) 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 \(0.744963\pi\)
\(282\) −0.0359170 + 0.0584537i −0.00213883 + 0.00348087i
\(283\) −19.2731 + 19.2731i −1.14567 + 1.14567i −0.158271 + 0.987396i \(0.550592\pi\)
−0.987396 + 0.158271i \(0.949408\pi\)
\(284\) 2.25608 0.133874
\(285\) −26.3952 + 15.3300i −1.56352 + 0.908068i
\(286\) 4.28964 0.253652
\(287\) 1.10097 1.10097i 0.0649880 0.0649880i
\(288\) −2.85094 0.933895i −0.167993 0.0550303i
\(289\) 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 0.999632 + 0.0271332i \(0.00863783\pi\)
0.0271332 + 0.999632i \(0.491362\pi\)
\(294\) 2.50574 + 10.4926i 0.146138 + 0.611941i
\(295\) 21.5873 + 11.6157i 1.25686 + 0.676292i
\(296\) 9.14409i 0.531489i
\(297\) −21.3846 1.76048i −1.24086 0.102153i
\(298\) 4.32738 4.32738i 0.250678 0.250678i
\(299\) −1.03881 −0.0600759
\(300\) −8.65567 + 0.281632i −0.499736 + 0.0162600i
\(301\) 7.84466 0.452159
\(302\) 5.66375 5.66375i 0.325912 0.325912i
\(303\) 1.23532 2.01043i 0.0709670 0.115496i
\(304\) 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 0.864552 0.502544i \(-0.167602\pi\)
−0.502544 + 0.864552i \(0.667602\pi\)
\(308\) 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 \(-0.0139862\pi\)
\(312\) −1.53300 0.941956i −0.0867890 0.0533277i
\(313\) 0.449127 0.449127i 0.0253861 0.0253861i −0.694300 0.719686i \(-0.744286\pi\)
0.719686 + 0.694300i \(0.244286\pi\)
\(314\) −13.5278 −0.763420
\(315\) 4.26913 4.06240i 0.240538 0.228891i
\(316\) −1.98214 −0.111504
\(317\) 17.7857 17.7857i 0.998943 0.998943i −0.00105667 0.999999i \(-0.500336\pi\)
0.999999 + 0.00105667i \(0.000336349\pi\)
\(318\) 20.3926 + 12.5303i 1.14356 + 0.702663i
\(319\) 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
\(327\) −0.482310 + 0.784943i −0.0266718 + 0.0434075i
\(328\) 1.25325 1.25325i 0.0691991 0.0691991i
\(329\) −0.0347970 −0.00191842
\(330\) −4.09955 + 15.4587i −0.225673 + 0.850974i
\(331\) −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
\(333\) 8.53962 26.0692i 0.467968 1.42858i
\(334\) 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 0.829821 0.558029i \(-0.188442\pi\)
−0.558029 + 0.829821i \(0.688442\pi\)
\(338\) 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
\(342\) 7.36027 22.4690i 0.397998 1.21498i
\(343\) −8.21722 + 8.21722i −0.443688 + 0.443688i
\(344\) 8.92971 0.481457
\(345\) 0.992773 3.74358i 0.0534491 0.201548i
\(346\) 14.7488 0.792899
\(347\) 11.2296 11.2296i 0.602837 0.602837i −0.338228 0.941064i \(-0.609827\pi\)
0.941064 + 0.338228i \(0.109827\pi\)
\(348\) −7.10725 + 11.5668i −0.380988 + 0.620045i
\(349\) 23.8817i 1.27836i −0.769059 0.639178i \(-0.779275\pi\)
0.769059 0.639178i \(-0.220725\pi\)
\(350\) −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 \(-0.0982865\pi\)
−0.303893 + 0.952706i \(0.598287\pi\)
\(354\) −18.4691 + 4.41060i −0.981621 + 0.234421i
\(355\) −2.39040 + 4.44246i −0.126869 + 0.235781i
\(356\) 6.08809i 0.322668i
\(357\) 4.58701 + 2.81850i 0.242770 + 0.149171i
\(358\) −0.508677 + 0.508677i −0.0268844 + 0.0268844i
\(359\) −7.16299 −0.378048 −0.189024 0.981972i \(-0.560532\pi\)
−0.189024 + 0.981972i \(0.560532\pi\)
\(360\) 4.85961 4.62430i 0.256124 0.243722i
\(361\) −43.1142 −2.26917
\(362\) 11.8197 11.8197i 0.621229 0.621229i
\(363\) 8.93089 + 5.48761i 0.468750 + 0.288025i
\(364\) 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 0.963756 0.266785i \(-0.0859613\pi\)
−0.266785 + 0.963756i \(0.585961\pi\)
\(368\) −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
\(372\) 6.41378 10.4382i 0.332539 0.541196i
\(373\) −2.87275 + 2.87275i −0.148745 + 0.148745i −0.777557 0.628812i \(-0.783541\pi\)
0.628812 + 0.777557i \(0.283541\pi\)
\(374\) −14.6107 −0.755502
\(375\) 8.61645 17.3423i 0.444952 0.895555i
\(376\) −0.0396100 −0.00204273
\(377\) −5.75741 + 5.75741i −0.296522 + 0.296522i
\(378\) −0.374527 + 4.54938i −0.0192636 + 0.233995i
\(379\) 24.7455i 1.27109i 0.772063 + 0.635546i \(0.219225\pi\)
−0.772063 + 0.635546i \(0.780775\pi\)
\(380\) −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 \(-0.443414\pi\)
−0.984240 + 0.176836i \(0.943414\pi\)
\(384\) −0.402318 1.68468i −0.0205307 0.0859709i
\(385\) −7.76884 + 2.33315i −0.395937 + 0.118909i
\(386\) 1.03641i 0.0527520i
\(387\) −25.4580 8.33941i −1.29410 0.423916i
\(388\) 11.8246 11.8246i 0.600303 0.600303i
\(389\) −1.35053 −0.0684745 −0.0342372 0.999414i \(-0.510900\pi\)
−0.0342372 + 0.999414i \(0.510900\pi\)
\(390\) 3.47908 2.02060i 0.176170 0.102317i
\(391\) 3.53823 0.178936
\(392\) −4.40404 + 4.40404i −0.222438 + 0.222438i
\(393\) −2.43682 + 3.96583i −0.122921 + 0.200050i
\(394\) 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 0.570124 0.821559i \(-0.306895\pi\)
−0.821559 + 0.570124i \(0.806895\pi\)
\(398\) −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 \(0.894169\pi\)
\(402\) −22.5998 13.8865i −1.12717 0.692595i
\(403\) 5.19565 5.19565i 0.258814 0.258814i
\(404\) 1.36233 0.0677786
\(405\) −18.1731 + 8.64521i −0.903027 + 0.429584i
\(406\) −6.88563 −0.341728
\(407\) −26.7000 + 26.7000i −1.32347 + 1.32347i
\(408\) 5.22147 + 3.20834i 0.258501 + 0.158837i
\(409\) 15.7658i 0.779567i −0.920907 0.389784i \(-0.872550\pi\)
0.920907 0.389784i \(-0.127450\pi\)
\(410\) 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
\(417\) 18.8433 30.6669i 0.922762 1.50176i
\(418\) −23.0126 + 23.0126i −1.12558 + 1.12558i
\(419\) 28.4327 1.38903 0.694514 0.719480i \(-0.255620\pi\)
0.694514 + 0.719480i \(0.255620\pi\)
\(420\) 3.28870 + 0.872142i 0.160472 + 0.0425562i
\(421\) 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
\(423\) 0.112926 + 0.0369916i 0.00549063 + 0.00179859i
\(424\) 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 \(-0.224798\pi\)
\(432\) −0.426330 + 5.17863i −0.0205118 + 0.249157i
\(433\) 10.1590 10.1590i 0.488212 0.488212i −0.419530 0.907742i \(-0.637805\pi\)
0.907742 + 0.419530i \(0.137805\pi\)
\(434\) 6.21379 0.298271
\(435\) −15.2459 26.2504i −0.730983 1.25861i
\(436\) −0.531902 −0.0254735
\(437\) 5.57289 5.57289i 0.266588 0.266588i
\(438\) 10.8839 17.7132i 0.520054 0.846370i
\(439\) 2.41233i 0.115134i −0.998342 0.0575670i \(-0.981666\pi\)
0.998342 0.0575670i \(-0.0183343\pi\)
\(440\) −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 \(-0.331913\pi\)
−0.863786 + 0.503859i \(0.831913\pi\)
\(444\) 15.4048 3.67883i 0.731082 0.174590i
\(445\) 11.9881 + 6.45056i 0.568290 + 0.305786i
\(446\) 11.1399i 0.527491i
\(447\) −9.03122 5.54926i −0.427162 0.262471i
\(448\) 0.621187 0.621187i 0.0293483 0.0293483i
\(449\) −31.6647 −1.49435 −0.747174 0.664628i \(-0.768590\pi\)
−0.747174 + 0.664628i \(0.768590\pi\)
\(450\) 3.95679 + 14.4687i 0.186525 + 0.682062i
\(451\) 7.31877 0.344627
\(452\) −4.14725 + 4.14725i −0.195070 + 0.195070i
\(453\) −11.8202 7.26297i −0.555363 0.341244i
\(454\) 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 −0.944451 0.328653i \(-0.893405\pi\)
−0.328653 0.944451i \(-0.606595\pi\)
\(458\) −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 \(-0.146765\pi\)
\(462\) 3.28941 5.35340i 0.153037 0.249063i
\(463\) 17.9935 17.9935i 0.836230 0.836230i −0.152131 0.988360i \(-0.548613\pi\)
0.988360 + 0.152131i \(0.0486135\pi\)
\(464\) −7.83802 −0.363871
\(465\) 13.7583 + 23.6891i 0.638025 + 1.09856i
\(466\) −18.8850 −0.874831
\(467\) 13.5425 13.5425i 0.626673 0.626673i −0.320557 0.947229i \(-0.603870\pi\)
0.947229 + 0.320557i \(0.103870\pi\)
\(468\) −0.970139 + 2.96158i −0.0448447 + 0.136899i
\(469\) 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
\(477\) 12.9052 39.3961i 0.590888 1.80382i
\(478\) −3.74603 + 3.74603i −0.171340 + 0.171340i
\(479\) −10.1525 −0.463880 −0.231940 0.972730i \(-0.574507\pi\)
−0.231940 + 0.972730i \(0.574507\pi\)
\(480\) 3.74358 + 0.992773i 0.170870 + 0.0453137i
\(481\) 9.49896 0.433115
\(482\) 2.29328 2.29328i 0.104456 0.104456i
\(483\) −0.796585 + 1.29641i −0.0362459 + 0.0589889i
\(484\) 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 0.839128 0.543933i \(-0.183066\pi\)
−0.543933 + 0.839128i \(0.683066\pi\)
\(488\) −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 \(0.640143\pi\)
\(492\) −2.61553 1.60712i −0.117917 0.0724544i
\(493\) 19.6100 19.6100i 0.883189 0.883189i
\(494\) 8.18712 0.368356
\(495\) 27.6923 + 0.687099i 1.24467 + 0.0308828i
\(496\) 7.07325 0.317598
\(497\) 1.40145 1.40145i 0.0628635 0.0628635i
\(498\) −4.61812 2.83761i −0.206943 0.127157i
\(499\) 3.33567i 0.149325i −0.997209 0.0746625i \(-0.976212\pi\)
0.997209 0.0746625i \(-0.0237880\pi\)
\(500\) 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 \(-0.196223\pi\)
−0.578144 + 0.815935i \(0.696223\pi\)
\(504\) −2.35109 + 1.19084i −0.104726 + 0.0530443i
\(505\) −1.44344 + 2.68258i −0.0642323 + 0.119373i
\(506\) 4.12939i 0.183574i
\(507\) 10.8094 17.5920i 0.480064 0.781287i
\(508\) 8.34126 8.34126i 0.370084 0.370084i
\(509\) −0.551066 −0.0244256 −0.0122128 0.999925i \(-0.503888\pi\)
−0.0122128 + 0.999925i \(0.503888\pi\)
\(510\) −11.8499 + 6.88226i −0.524723 + 0.304752i
\(511\) 10.5445 0.466463
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −40.8141 3.36002i −1.80199 0.148348i
\(514\) 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 \(0.945261\pi\)
\(522\) 22.3457 + 7.31989i 0.978045 + 0.320383i
\(523\) 3.95100 3.95100i 0.172765 0.172765i −0.615428 0.788193i \(-0.711017\pi\)
0.788193 + 0.615428i \(0.211017\pi\)
\(524\) −2.68737 −0.117398
\(525\) −5.20184 + 5.55174i −0.227027 + 0.242298i
\(526\) −14.0715 −0.613548
\(527\) −17.6966 + 17.6966i −0.770876 + 0.770876i
\(528\) 3.74439 6.09386i 0.162954 0.265201i
\(529\) 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
\(537\) 1.06161 + 0.652307i 0.0458117 + 0.0281491i
\(538\) 7.40991 7.40991i 0.319464 0.319464i
\(539\) −25.7189 −1.10779
\(540\) −9.74557 6.32645i −0.419382 0.272247i
\(541\) −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
\(543\) −24.6676 15.1571i −1.05859 0.650453i
\(544\) 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 0.795495 0.605960i \(-0.207211\pi\)
−0.605960 + 0.795495i \(0.707211\pi\)
\(548\) 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
\(552\) −0.906765 + 1.47573i −0.0385945 + 0.0628112i
\(553\) −1.23128 + 1.23128i −0.0523593 + 0.0523593i
\(554\) −11.5578 −0.491042
\(555\) −9.07800 + 34.2316i −0.385340 + 1.45305i
\(556\) 20.7808 0.881303
\(557\) 19.7470 19.7470i 0.836707 0.836707i −0.151717 0.988424i \(-0.548480\pi\)
0.988424 + 0.151717i \(0.0484803\pi\)
\(558\) −20.1654 6.60568i −0.853669 0.279641i
\(559\) 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 \(-0.106457\pi\)
−0.328244 + 0.944593i \(0.606457\pi\)
\(564\) 0.0159358 + 0.0667301i 0.000671019 + 0.00280985i
\(565\) −3.77221 12.5605i −0.158698 0.528426i
\(566\) 27.2563i 1.14567i
\(567\) 7.81492 1.19934i 0.328196 0.0503676i
\(568\) 1.59529 1.59529i 0.0669369 0.0669369i
\(569\) −45.5814 −1.91087 −0.955436 0.295197i \(-0.904615\pi\)
−0.955436 + 0.295197i \(0.904615\pi\)
\(570\) −7.82430 + 29.5041i −0.327724 + 1.23579i
\(571\) −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
\(573\) −9.63337 + 15.6780i −0.402440 + 0.654957i
\(574\) 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 0.995293 + 0.0969147i \(0.0308974\pi\)
0.0969147 + 0.995293i \(0.469103\pi\)
\(578\) 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
\(582\) −24.6779 15.1634i −1.02293 0.628543i
\(583\) −40.3494 + 40.3494i −1.67110 + 1.67110i
\(584\) 12.0030 0.496689
\(585\) −4.80376 5.04821i −0.198611 0.208718i
\(586\) 24.8553 1.02677
\(587\) −1.72536 + 1.72536i −0.0712134 + 0.0712134i −0.741816 0.670603i \(-0.766035\pi\)
0.670603 + 0.741816i \(0.266035\pi\)
\(588\) 9.19122 + 5.64757i 0.379039 + 0.232902i
\(589\) 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 \(-0.275713\pi\)
−0.761858 + 0.647744i \(0.775713\pi\)
\(594\) −16.3660 + 13.8763i −0.671507 + 0.569353i
\(595\) −6.12057 3.29336i −0.250919 0.135015i
\(596\) 6.11984i 0.250678i
\(597\) −2.74218 + 4.46280i −0.112230 + 0.182650i
\(598\) −0.734549 + 0.734549i −0.0300379 + 0.0300379i
\(599\) 37.0107 1.51222 0.756108 0.654447i \(-0.227098\pi\)
0.756108 + 0.654447i \(0.227098\pi\)
\(600\) −5.92134 + 6.31963i −0.241738 + 0.257998i
\(601\) 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
\(603\) −14.3020 + 43.6601i −0.582421 + 1.77798i
\(604\) 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 0.626343 0.779548i \(-0.284551\pi\)
−0.779548 + 0.626343i \(0.784551\pi\)
\(608\) 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
\(612\) 3.30433 10.0873i 0.133570 0.407753i
\(613\) −12.5789 + 12.5789i −0.508056 + 0.508056i −0.913929 0.405873i \(-0.866967\pi\)
0.405873 + 0.913929i \(0.366967\pi\)
\(614\) 8.97021 0.362008
\(615\) 5.93583 3.44745i 0.239356 0.139014i
\(616\) 3.62763 0.146161
\(617\) −3.87788 + 3.87788i −0.156118 + 0.156118i −0.780844 0.624726i \(-0.785211\pi\)
0.624726 + 0.780844i \(0.285211\pi\)
\(618\) −4.32911 + 7.04547i −0.174142 + 0.283410i
\(619\) 8.64542i 0.347489i −0.984791 0.173744i \(-0.944413\pi\)
0.984791 0.173744i \(-0.0555867\pi\)
\(620\) −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
\(627\) 48.0273 + 29.5105i 1.91802 + 1.17854i
\(628\) −9.56563 + 9.56563i −0.381710 + 0.381710i
\(629\) −32.3539 −1.29003
\(630\) 0.146174 5.89128i 0.00582372 0.234714i
\(631\) −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
\(633\) 28.4966 + 17.5098i 1.13264 + 0.695952i
\(634\) 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 \(0.982831\pi\)
\(642\) −3.07514 + 5.00468i −0.121366 + 0.197519i
\(643\) 17.4028 17.4028i 0.686298 0.686298i −0.275114 0.961412i \(-0.588715\pi\)
0.961412 + 0.275114i \(0.0887155\pi\)
\(644\) −0.878491 −0.0346174
\(645\) 33.4291 + 8.86517i 1.31627 + 0.349066i
\(646\) −27.8857 −1.09715
\(647\) 9.72994 9.72994i 0.382523 0.382523i −0.489487 0.872011i \(-0.662816\pi\)
0.872011 + 0.489487i \(0.162816\pi\)
\(648\) 8.89585 1.36523i 0.349462 0.0536313i
\(649\) 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 \(-0.0466169\pi\)
−0.145928 + 0.989295i \(0.546617\pi\)
\(654\) 0.213994 + 0.896084i 0.00836782 + 0.0350396i
\(655\) 2.84737 5.29172i 0.111256 0.206765i
\(656\) 1.77236i 0.0691991i
\(657\) −34.2199 11.2096i −1.33504 0.437327i
\(658\) −0.0246052 + 0.0246052i −0.000959211 + 0.000959211i
\(659\) 44.3615 1.72808 0.864039 0.503425i \(-0.167927\pi\)
0.864039 + 0.503425i \(0.167927\pi\)
\(660\) 8.03214 + 13.8298i 0.312651 + 0.538323i
\(661\) 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
\(663\) 3.33285 5.42410i 0.129437 0.210655i
\(664\) 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
\(672\) −1.29641 0.796585i −0.0500103 0.0307289i
\(673\) −30.3342 + 30.3342i −1.16930 + 1.16930i −0.186921 + 0.982375i \(0.559851\pi\)
−0.982375 + 0.186921i \(0.940149\pi\)
\(674\) 7.05614 0.271792
\(675\) 22.7832 12.4869i 0.876927 0.480623i
\(676\) 11.9209 0.458495
\(677\) −8.39686 + 8.39686i −0.322718 + 0.322718i −0.849809 0.527091i \(-0.823283\pi\)
0.527091 + 0.849809i \(0.323283\pi\)
\(678\) 8.65529 + 5.31826i 0.332404 + 0.204247i
\(679\) 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 \(-0.106648\pi\)
−0.328811 + 0.944396i \(0.606648\pi\)
\(684\) −10.6835 21.0925i −0.408492 0.806490i
\(685\) −11.3845 + 3.41903i −0.434981 + 0.130634i
\(686\) 11.6209i 0.443688i
\(687\) −8.00744 + 13.0318i −0.305503 + 0.497196i
\(688\) 6.31426 6.31426i 0.240729 0.240729i
\(689\) 14.3549 0.546880
\(690\) −1.94512 3.34911i −0.0740493 0.127498i
\(691\) −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
\(693\) −10.3421 3.38783i −0.392865 0.128693i
\(694\) 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 \(-0.169070\pi\)
\(702\) 5.37961 + 0.442875i 0.203040 + 0.0167152i
\(703\) −50.9590 + 50.9590i −1.92196 + 1.92196i
\(704\) 4.12939 0.155632
\(705\) −0.148283 0.0393238i −0.00558467 0.00148102i
\(706\) 17.2394 0.648813
\(707\) 0.846263 0.846263i 0.0318270 0.0318270i
\(708\) −9.94085 + 16.1784i −0.373600 + 0.608021i
\(709\) 4.26519i 0.160183i −0.996788 0.0800914i \(-0.974479\pi\)
0.996788 0.0800914i \(-0.0255212\pi\)
\(710\) 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
\(717\) 7.81796 + 4.80376i 0.291967 + 0.179400i
\(718\) −5.06500 + 5.06500i −0.189024 + 0.189024i
\(719\) −34.9727 −1.30426 −0.652130 0.758107i \(-0.726125\pi\)
−0.652130 + 0.758107i \(0.726125\pi\)
\(720\) 0.166392 6.70614i 0.00620108 0.249923i
\(721\) −4.19412 −0.156197
\(722\) −30.4864 + 30.4864i −1.13459 + 1.13459i
\(723\) −4.78606 2.94081i −0.177996 0.109370i
\(724\) 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 0.911452 0.411407i \(-0.134963\pi\)
−0.411407 + 0.911452i \(0.634963\pi\)
\(728\) −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
\(732\) −10.0507 + 16.3571i −0.371484 + 0.604577i
\(733\) 32.6105 32.6105i 1.20450 1.20450i 0.231710 0.972785i \(-0.425568\pi\)
0.972785 0.231710i \(-0.0744321\pi\)
\(734\) 18.8827 0.696971
\(735\) −20.8591 + 12.1147i −0.769399 + 0.446856i
\(736\) −1.00000 −0.0368605
\(737\) 44.7165 44.7165i 1.64715 1.64715i
\(738\) −1.65520 + 5.05289i −0.0609288 + 0.185999i
\(739\) 7.71809i 0.283915i 0.989873 + 0.141957i \(0.0453396\pi\)
−0.989873 + 0.141957i \(0.954660\pi\)
\(740\) −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 \(-0.210489\pi\)
−0.614121 + 0.789212i \(0.710489\pi\)
\(744\) −2.84570 11.9162i −0.104328 0.436867i
\(745\) 12.0506 + 6.48420i 0.441500 + 0.237563i
\(746\) 4.06268i 0.148745i
\(747\) −2.92251 + 8.92166i −0.106929 + 0.326427i
\(748\) −10.3313 + 10.3313i −0.377751 + 0.377751i
\(749\) −2.97925 −0.108859
\(750\) −6.17014 18.3556i −0.225302 0.670253i
\(751\) −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
\(753\) 16.0125 26.0598i 0.583528 0.949671i
\(754\) 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 0.625542 0.780190i \(-0.284878\pi\)
−0.780190 + 0.625542i \(0.784878\pi\)
\(758\) 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 \(-0.0610650\pi\)
\(762\) −17.4082 10.6965i −0.630632 0.387493i
\(763\) −0.330410 + 0.330410i −0.0119617 + 0.0119617i
\(764\) −10.6239 −0.384359
\(765\) 16.3618 + 17.1944i 0.591563 + 0.621666i
\(766\) −22.3463 −0.807405
\(767\) −8.05284 + 8.05284i −0.290771 + 0.290771i
\(768\) −1.47573 0.906765i −0.0532508 0.0327201i
\(769\) 20.7974i 0.749972i −0.927030 0.374986i \(-0.877647\pi\)
0.927030 0.374986i \(-0.122353\pi\)
\(770\) −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 \(-0.192041\pi\)
−0.567375 + 0.823459i \(0.692041\pi\)
\(774\) −23.8984 + 12.1047i −0.859010 + 0.435094i
\(775\) −19.4851 29.5145i −0.699926 1.06019i
\(776\) 16.7225i 0.600303i
\(777\) 7.28404 11.8545i 0.261314 0.425279i