Properties

Label 690.2.i.f.323.10
Level $690$
Weight $2$
Character 690.323
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 323.10
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.f.47.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.01467 + 1.40373i) q^{3} +1.00000i q^{4} +(-2.22721 - 0.198845i) q^{5} +(-1.71006 + 0.275105i) q^{6} +(0.787190 - 0.787190i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.940895 - 2.84863i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.01467 + 1.40373i) q^{3} +1.00000i q^{4} +(-2.22721 - 0.198845i) q^{5} +(-1.71006 + 0.275105i) q^{6} +(0.787190 - 0.787190i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.940895 - 2.84863i) q^{9} +(-1.43427 - 1.71548i) q^{10} -0.307245i q^{11} +(-1.40373 - 1.01467i) q^{12} +(-4.92204 - 4.92204i) q^{13} +1.11326 q^{14} +(2.53900 - 2.92463i) q^{15} -1.00000 q^{16} +(-0.790416 - 0.790416i) q^{17} +(1.34897 - 2.67960i) q^{18} +0.691928i q^{19} +(0.198845 - 2.22721i) q^{20} +(0.306263 + 1.90374i) q^{21} +(0.217255 - 0.217255i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-0.275105 - 1.71006i) q^{24} +(4.92092 + 0.885741i) q^{25} -6.96081i q^{26} +(4.95340 + 1.56966i) q^{27} +(0.787190 + 0.787190i) q^{28} -6.67517 q^{29} +(3.86337 - 0.272679i) q^{30} +4.52557 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.431287 + 0.311752i) q^{33} -1.11782i q^{34} +(-1.90977 + 1.59671i) q^{35} +(2.84863 - 0.940895i) q^{36} +(1.77676 - 1.77676i) q^{37} +(-0.489267 + 0.489267i) q^{38} +(11.9034 - 1.91496i) q^{39} +(1.71548 - 1.43427i) q^{40} -0.596103i q^{41} +(-1.12959 + 1.56271i) q^{42} +(-6.70489 - 6.70489i) q^{43} +0.307245 q^{44} +(1.52913 + 6.53160i) q^{45} +1.00000 q^{46} +(-6.88967 - 6.88967i) q^{47} +(1.01467 - 1.40373i) q^{48} +5.76066i q^{49} +(2.85330 + 4.10593i) q^{50} +(1.91154 - 0.307518i) q^{51} +(4.92204 - 4.92204i) q^{52} +(5.94467 - 5.94467i) q^{53} +(2.39267 + 4.61250i) q^{54} +(-0.0610942 + 0.684298i) q^{55} +1.11326i q^{56} +(-0.971277 - 0.702077i) q^{57} +(-4.72006 - 4.72006i) q^{58} -6.38319 q^{59} +(2.92463 + 2.53900i) q^{60} -9.95861 q^{61} +(3.20006 + 3.20006i) q^{62} +(-2.98308 - 1.50175i) q^{63} -1.00000i q^{64} +(9.98368 + 11.9411i) q^{65} +(0.0845247 + 0.525408i) q^{66} +(2.19342 - 2.19342i) q^{67} +(0.790416 - 0.790416i) q^{68} +(0.275105 + 1.71006i) q^{69} +(-2.47945 - 0.221366i) q^{70} -4.55564i q^{71} +(2.67960 + 1.34897i) q^{72} +(-4.90914 - 4.90914i) q^{73} +2.51272 q^{74} +(-6.23644 + 6.00889i) q^{75} -0.691928 q^{76} +(-0.241860 - 0.241860i) q^{77} +(9.77108 + 7.06292i) q^{78} +15.7352i q^{79} +(2.22721 + 0.198845i) q^{80} +(-7.22943 + 5.36053i) q^{81} +(0.421508 - 0.421508i) q^{82} +(-6.65861 + 6.65861i) q^{83} +(-1.90374 + 0.306263i) q^{84} +(1.60325 + 1.91759i) q^{85} -9.48214i q^{86} +(6.77309 - 9.37012i) q^{87} +(0.217255 + 0.217255i) q^{88} +11.5425 q^{89} +(-3.53728 + 5.69980i) q^{90} -7.74916 q^{91} +(0.707107 + 0.707107i) q^{92} +(-4.59195 + 6.35266i) q^{93} -9.74347i q^{94} +(0.137587 - 1.54107i) q^{95} +(1.71006 - 0.275105i) q^{96} +(-12.8277 + 12.8277i) q^{97} +(-4.07340 + 4.07340i) q^{98} +(-0.875228 + 0.289085i) 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
\(3\) −1.01467 + 1.40373i −0.585819 + 0.810442i
\(4\) 1.00000i 0.500000i
\(5\) −2.22721 0.198845i −0.996038 0.0889264i
\(6\) −1.71006 + 0.275105i −0.698130 + 0.112311i
\(7\) 0.787190 0.787190i 0.297530 0.297530i −0.542516 0.840046i \(-0.682528\pi\)
0.840046 + 0.542516i \(0.182528\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.940895 2.84863i −0.313632 0.949545i
\(10\) −1.43427 1.71548i −0.453556 0.542482i
\(11\) 0.307245i 0.0926378i −0.998927 0.0463189i \(-0.985251\pi\)
0.998927 0.0463189i \(-0.0147490\pi\)
\(12\) −1.40373 1.01467i −0.405221 0.292910i
\(13\) −4.92204 4.92204i −1.36513 1.36513i −0.867243 0.497885i \(-0.834110\pi\)
−0.497885 0.867243i \(-0.665890\pi\)
\(14\) 1.11326 0.297530
\(15\) 2.53900 2.92463i 0.655568 0.755136i
\(16\) −1.00000 −0.250000
\(17\) −0.790416 0.790416i −0.191704 0.191704i 0.604728 0.796432i \(-0.293282\pi\)
−0.796432 + 0.604728i \(0.793282\pi\)
\(18\) 1.34897 2.67960i 0.317956 0.631588i
\(19\) 0.691928i 0.158739i 0.996845 + 0.0793696i \(0.0252907\pi\)
−0.996845 + 0.0793696i \(0.974709\pi\)
\(20\) 0.198845 2.22721i 0.0444632 0.498019i
\(21\) 0.306263 + 1.90374i 0.0668320 + 0.415430i
\(22\) 0.217255 0.217255i 0.0463189 0.0463189i
\(23\) 0.707107 0.707107i 0.147442 0.147442i
\(24\) −0.275105 1.71006i −0.0561557 0.349065i
\(25\) 4.92092 + 0.885741i 0.984184 + 0.177148i
\(26\) 6.96081i 1.36513i
\(27\) 4.95340 + 1.56966i 0.953282 + 0.302081i
\(28\) 0.787190 + 0.787190i 0.148765 + 0.148765i
\(29\) −6.67517 −1.23955 −0.619774 0.784780i \(-0.712776\pi\)
−0.619774 + 0.784780i \(0.712776\pi\)
\(30\) 3.86337 0.272679i 0.705352 0.0497841i
\(31\) 4.52557 0.812817 0.406408 0.913692i \(-0.366781\pi\)
0.406408 + 0.913692i \(0.366781\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0.431287 + 0.311752i 0.0750775 + 0.0542690i
\(34\) 1.11782i 0.191704i
\(35\) −1.90977 + 1.59671i −0.322810 + 0.269893i
\(36\) 2.84863 0.940895i 0.474772 0.156816i
\(37\) 1.77676 1.77676i 0.292098 0.292098i −0.545811 0.837909i \(-0.683778\pi\)
0.837909 + 0.545811i \(0.183778\pi\)
\(38\) −0.489267 + 0.489267i −0.0793696 + 0.0793696i
\(39\) 11.9034 1.91496i 1.90607 0.306639i
\(40\) 1.71548 1.43427i 0.271241 0.226778i
\(41\) 0.596103i 0.0930956i −0.998916 0.0465478i \(-0.985178\pi\)
0.998916 0.0465478i \(-0.0148220\pi\)
\(42\) −1.12959 + 1.56271i −0.174299 + 0.241131i
\(43\) −6.70489 6.70489i −1.02249 1.02249i −0.999741 0.0227444i \(-0.992760\pi\)
−0.0227444 0.999741i \(-0.507240\pi\)
\(44\) 0.307245 0.0463189
\(45\) 1.52913 + 6.53160i 0.227950 + 0.973673i
\(46\) 1.00000 0.147442
\(47\) −6.88967 6.88967i −1.00496 1.00496i −0.999988 0.00497448i \(-0.998417\pi\)
−0.00497448 0.999988i \(-0.501583\pi\)
\(48\) 1.01467 1.40373i 0.146455 0.202610i
\(49\) 5.76066i 0.822952i
\(50\) 2.85330 + 4.10593i 0.403518 + 0.580666i
\(51\) 1.91154 0.307518i 0.267669 0.0430611i
\(52\) 4.92204 4.92204i 0.682564 0.682564i
\(53\) 5.94467 5.94467i 0.816563 0.816563i −0.169045 0.985608i \(-0.554068\pi\)
0.985608 + 0.169045i \(0.0540683\pi\)
\(54\) 2.39267 + 4.61250i 0.325601 + 0.627682i
\(55\) −0.0610942 + 0.684298i −0.00823794 + 0.0922707i
\(56\) 1.11326i 0.148765i
\(57\) −0.971277 0.702077i −0.128649 0.0929924i
\(58\) −4.72006 4.72006i −0.619774 0.619774i
\(59\) −6.38319 −0.831021 −0.415510 0.909588i \(-0.636397\pi\)
−0.415510 + 0.909588i \(0.636397\pi\)
\(60\) 2.92463 + 2.53900i 0.377568 + 0.327784i
\(61\) −9.95861 −1.27507 −0.637535 0.770422i \(-0.720046\pi\)
−0.637535 + 0.770422i \(0.720046\pi\)
\(62\) 3.20006 + 3.20006i 0.406408 + 0.406408i
\(63\) −2.98308 1.50175i −0.375833 0.189203i
\(64\) 1.00000i 0.125000i
\(65\) 9.98368 + 11.9411i 1.23832 + 1.48112i
\(66\) 0.0845247 + 0.525408i 0.0104043 + 0.0646732i
\(67\) 2.19342 2.19342i 0.267969 0.267969i −0.560312 0.828281i \(-0.689319\pi\)
0.828281 + 0.560312i \(0.189319\pi\)
\(68\) 0.790416 0.790416i 0.0958521 0.0958521i
\(69\) 0.275105 + 1.71006i 0.0331188 + 0.205867i
\(70\) −2.47945 0.221366i −0.296351 0.0264583i
\(71\) 4.55564i 0.540655i −0.962768 0.270327i \(-0.912868\pi\)
0.962768 0.270327i \(-0.0871320\pi\)
\(72\) 2.67960 + 1.34897i 0.315794 + 0.158978i
\(73\) −4.90914 4.90914i −0.574571 0.574571i 0.358831 0.933403i \(-0.383175\pi\)
−0.933403 + 0.358831i \(0.883175\pi\)
\(74\) 2.51272 0.292098
\(75\) −6.23644 + 6.00889i −0.720122 + 0.693847i
\(76\) −0.691928 −0.0793696
\(77\) −0.241860 0.241860i −0.0275625 0.0275625i
\(78\) 9.77108 + 7.06292i 1.10636 + 0.799718i
\(79\) 15.7352i 1.77035i 0.465255 + 0.885177i \(0.345963\pi\)
−0.465255 + 0.885177i \(0.654037\pi\)
\(80\) 2.22721 + 0.198845i 0.249010 + 0.0222316i
\(81\) −7.22943 + 5.36053i −0.803270 + 0.595615i
\(82\) 0.421508 0.421508i 0.0465478 0.0465478i
\(83\) −6.65861 + 6.65861i −0.730878 + 0.730878i −0.970794 0.239916i \(-0.922880\pi\)
0.239916 + 0.970794i \(0.422880\pi\)
\(84\) −1.90374 + 0.306263i −0.207715 + 0.0334160i
\(85\) 1.60325 + 1.91759i 0.173897 + 0.207992i
\(86\) 9.48214i 1.02249i
\(87\) 6.77309 9.37012i 0.726151 1.00458i
\(88\) 0.217255 + 0.217255i 0.0231594 + 0.0231594i
\(89\) 11.5425 1.22351 0.611753 0.791049i \(-0.290465\pi\)
0.611753 + 0.791049i \(0.290465\pi\)
\(90\) −3.53728 + 5.69980i −0.372862 + 0.600811i
\(91\) −7.74916 −0.812333
\(92\) 0.707107 + 0.707107i 0.0737210 + 0.0737210i
\(93\) −4.59195 + 6.35266i −0.476163 + 0.658740i
\(94\) 9.74347i 1.00496i
\(95\) 0.137587 1.54107i 0.0141161 0.158110i
\(96\) 1.71006 0.275105i 0.174533 0.0280778i
\(97\) −12.8277 + 12.8277i −1.30246 + 1.30246i −0.375726 + 0.926731i \(0.622606\pi\)
−0.926731 + 0.375726i \(0.877394\pi\)
\(98\) −4.07340 + 4.07340i −0.411476 + 0.411476i
\(99\) −0.875228 + 0.289085i −0.0879637 + 0.0290541i
\(100\) −0.885741 + 4.92092i −0.0885741 + 0.492092i
\(101\) 0.435698i 0.0433536i 0.999765 + 0.0216768i \(0.00690048\pi\)
−0.999765 + 0.0216768i \(0.993100\pi\)
\(102\) 1.56911 + 1.13421i 0.155365 + 0.112304i
\(103\) −2.47087 2.47087i −0.243463 0.243463i 0.574818 0.818281i \(-0.305073\pi\)
−0.818281 + 0.574818i \(0.805073\pi\)
\(104\) 6.96081 0.682564
\(105\) −0.303561 4.30092i −0.0296245 0.419727i
\(106\) 8.40703 0.816563
\(107\) −9.00580 9.00580i −0.870623 0.870623i 0.121917 0.992540i \(-0.461096\pi\)
−0.992540 + 0.121917i \(0.961096\pi\)
\(108\) −1.56966 + 4.95340i −0.151041 + 0.476641i
\(109\) 4.71540i 0.451654i −0.974167 0.225827i \(-0.927492\pi\)
0.974167 0.225827i \(-0.0725084\pi\)
\(110\) −0.527072 + 0.440672i −0.0502543 + 0.0420164i
\(111\) 0.691264 + 4.29692i 0.0656118 + 0.407845i
\(112\) −0.787190 + 0.787190i −0.0743825 + 0.0743825i
\(113\) −9.74177 + 9.74177i −0.916428 + 0.916428i −0.996768 0.0803391i \(-0.974400\pi\)
0.0803391 + 0.996768i \(0.474400\pi\)
\(114\) −0.190353 1.18324i −0.0178282 0.110821i
\(115\) −1.71548 + 1.43427i −0.159969 + 0.133746i
\(116\) 6.67517i 0.619774i
\(117\) −9.38996 + 18.6522i −0.868102 + 1.72440i
\(118\) −4.51360 4.51360i −0.415510 0.415510i
\(119\) −1.24442 −0.114075
\(120\) 0.272679 + 3.86337i 0.0248921 + 0.352676i
\(121\) 10.9056 0.991418
\(122\) −7.04180 7.04180i −0.637535 0.637535i
\(123\) 0.836765 + 0.604847i 0.0754486 + 0.0545372i
\(124\) 4.52557i 0.406408i
\(125\) −10.7838 2.95123i −0.964532 0.263966i
\(126\) −1.04746 3.17126i −0.0933149 0.282518i
\(127\) 13.7618 13.7618i 1.22116 1.22116i 0.253945 0.967219i \(-0.418272\pi\)
0.967219 0.253945i \(-0.0817282\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 16.2151 2.60859i 1.42766 0.229673i
\(130\) −1.38413 + 15.5032i −0.121396 + 1.35972i
\(131\) 9.08484i 0.793746i −0.917874 0.396873i \(-0.870095\pi\)
0.917874 0.396873i \(-0.129905\pi\)
\(132\) −0.311752 + 0.431287i −0.0271345 + 0.0375388i
\(133\) 0.544679 + 0.544679i 0.0472297 + 0.0472297i
\(134\) 3.10197 0.267969
\(135\) −10.7201 4.48092i −0.922643 0.385656i
\(136\) 1.11782 0.0958521
\(137\) −6.12207 6.12207i −0.523044 0.523044i 0.395445 0.918489i \(-0.370590\pi\)
−0.918489 + 0.395445i \(0.870590\pi\)
\(138\) −1.01467 + 1.40373i −0.0863743 + 0.119493i
\(139\) 1.70991i 0.145033i 0.997367 + 0.0725164i \(0.0231030\pi\)
−0.997367 + 0.0725164i \(0.976897\pi\)
\(140\) −1.59671 1.90977i −0.134946 0.161405i
\(141\) 16.6620 2.68048i 1.40319 0.225737i
\(142\) 3.22132 3.22132i 0.270327 0.270327i
\(143\) −1.51227 + 1.51227i −0.126462 + 0.126462i
\(144\) 0.940895 + 2.84863i 0.0784080 + 0.237386i
\(145\) 14.8670 + 1.32733i 1.23464 + 0.110229i
\(146\) 6.94257i 0.574571i
\(147\) −8.08639 5.84516i −0.666955 0.482101i
\(148\) 1.77676 + 1.77676i 0.146049 + 0.146049i
\(149\) 4.44032 0.363765 0.181883 0.983320i \(-0.441781\pi\)
0.181883 + 0.983320i \(0.441781\pi\)
\(150\) −8.65876 0.160901i −0.706985 0.0131375i
\(151\) −18.8511 −1.53408 −0.767040 0.641599i \(-0.778271\pi\)
−0.767040 + 0.641599i \(0.778271\pi\)
\(152\) −0.489267 0.489267i −0.0396848 0.0396848i
\(153\) −1.50791 + 2.99531i −0.121907 + 0.242156i
\(154\) 0.342042i 0.0275625i
\(155\) −10.0794 0.899889i −0.809596 0.0722808i
\(156\) 1.91496 + 11.9034i 0.153319 + 0.953037i
\(157\) −9.78600 + 9.78600i −0.781007 + 0.781007i −0.980001 0.198993i \(-0.936233\pi\)
0.198993 + 0.980001i \(0.436233\pi\)
\(158\) −11.1265 + 11.1265i −0.885177 + 0.885177i
\(159\) 2.31282 + 14.3766i 0.183419 + 1.14014i
\(160\) 1.43427 + 1.71548i 0.113389 + 0.135621i
\(161\) 1.11326i 0.0877368i
\(162\) −8.90245 1.32151i −0.699443 0.103828i
\(163\) 9.24359 + 9.24359i 0.724014 + 0.724014i 0.969420 0.245406i \(-0.0789214\pi\)
−0.245406 + 0.969420i \(0.578921\pi\)
\(164\) 0.596103 0.0465478
\(165\) −0.898577 0.780095i −0.0699541 0.0607303i
\(166\) −9.41670 −0.730878
\(167\) −7.44173 7.44173i −0.575858 0.575858i 0.357901 0.933759i \(-0.383492\pi\)
−0.933759 + 0.357901i \(0.883492\pi\)
\(168\) −1.56271 1.12959i −0.120565 0.0871494i
\(169\) 35.4529i 2.72715i
\(170\) −0.222273 + 2.48961i −0.0170476 + 0.190945i
\(171\) 1.97105 0.651032i 0.150730 0.0497856i
\(172\) 6.70489 6.70489i 0.511243 0.511243i
\(173\) 9.04703 9.04703i 0.687833 0.687833i −0.273920 0.961753i \(-0.588320\pi\)
0.961753 + 0.273920i \(0.0883202\pi\)
\(174\) 11.4150 1.83638i 0.865367 0.139215i
\(175\) 4.57095 3.17646i 0.345531 0.240117i
\(176\) 0.307245i 0.0231594i
\(177\) 6.47682 8.96025i 0.486828 0.673494i
\(178\) 8.16181 + 8.16181i 0.611753 + 0.611753i
\(179\) 11.2260 0.839068 0.419534 0.907740i \(-0.362193\pi\)
0.419534 + 0.907740i \(0.362193\pi\)
\(180\) −6.53160 + 1.52913i −0.486836 + 0.113975i
\(181\) −8.65815 −0.643555 −0.321778 0.946815i \(-0.604280\pi\)
−0.321778 + 0.946815i \(0.604280\pi\)
\(182\) −5.47949 5.47949i −0.406167 0.406167i
\(183\) 10.1047 13.9792i 0.746960 1.03337i
\(184\) 1.00000i 0.0737210i
\(185\) −4.31053 + 3.60392i −0.316916 + 0.264966i
\(186\) −7.73901 + 1.24501i −0.567452 + 0.0912885i
\(187\) −0.242851 + 0.242851i −0.0177590 + 0.0177590i
\(188\) 6.88967 6.88967i 0.502481 0.502481i
\(189\) 5.13489 2.66365i 0.373508 0.193752i
\(190\) 1.18699 0.992411i 0.0861132 0.0719971i
\(191\) 18.1677i 1.31457i −0.753643 0.657284i \(-0.771705\pi\)
0.753643 0.657284i \(-0.228295\pi\)
\(192\) 1.40373 + 1.01467i 0.101305 + 0.0732274i
\(193\) 6.41622 + 6.41622i 0.461850 + 0.461850i 0.899261 0.437412i \(-0.144105\pi\)
−0.437412 + 0.899261i \(0.644105\pi\)
\(194\) −18.1411 −1.30246
\(195\) −26.8922 + 1.89807i −1.92579 + 0.135923i
\(196\) −5.76066 −0.411476
\(197\) 14.6739 + 14.6739i 1.04547 + 1.04547i 0.998916 + 0.0465587i \(0.0148255\pi\)
0.0465587 + 0.998916i \(0.485175\pi\)
\(198\) −0.823293 0.414465i −0.0585089 0.0294548i
\(199\) 2.60795i 0.184873i 0.995719 + 0.0924363i \(0.0294655\pi\)
−0.995719 + 0.0924363i \(0.970535\pi\)
\(200\) −4.10593 + 2.85330i −0.290333 + 0.201759i
\(201\) 0.853368 + 5.30456i 0.0601919 + 0.374155i
\(202\) −0.308085 + 0.308085i −0.0216768 + 0.0216768i
\(203\) −5.25463 + 5.25463i −0.368803 + 0.368803i
\(204\) 0.307518 + 1.91154i 0.0215305 + 0.133834i
\(205\) −0.118532 + 1.32765i −0.00827865 + 0.0927268i
\(206\) 3.49434i 0.243463i
\(207\) −2.67960 1.34897i −0.186245 0.0937602i
\(208\) 4.92204 + 4.92204i 0.341282 + 0.341282i
\(209\) 0.212591 0.0147052
\(210\) 2.82656 3.25586i 0.195051 0.224676i
\(211\) 24.9846 1.72001 0.860004 0.510287i \(-0.170461\pi\)
0.860004 + 0.510287i \(0.170461\pi\)
\(212\) 5.94467 + 5.94467i 0.408282 + 0.408282i
\(213\) 6.39487 + 4.62246i 0.438169 + 0.316726i
\(214\) 12.7361i 0.870623i
\(215\) 13.5999 + 16.2664i 0.927509 + 1.10936i
\(216\) −4.61250 + 2.39267i −0.313841 + 0.162800i
\(217\) 3.56249 3.56249i 0.241837 0.241837i
\(218\) 3.33429 3.33429i 0.225827 0.225827i
\(219\) 11.8722 1.90994i 0.802252 0.129062i
\(220\) −0.684298 0.0610942i −0.0461354 0.00411897i
\(221\) 7.78092i 0.523401i
\(222\) −2.54958 + 3.52718i −0.171117 + 0.236729i
\(223\) 2.06860 + 2.06860i 0.138524 + 0.138524i 0.772968 0.634444i \(-0.218771\pi\)
−0.634444 + 0.772968i \(0.718771\pi\)
\(224\) −1.11326 −0.0743825
\(225\) −2.10692 14.8513i −0.140461 0.990086i
\(226\) −13.7769 −0.916428
\(227\) −14.8927 14.8927i −0.988463 0.988463i 0.0114717 0.999934i \(-0.496348\pi\)
−0.999934 + 0.0114717i \(0.996348\pi\)
\(228\) 0.702077 0.971277i 0.0464962 0.0643244i
\(229\) 4.61161i 0.304743i −0.988323 0.152372i \(-0.951309\pi\)
0.988323 0.152372i \(-0.0486911\pi\)
\(230\) −2.22721 0.198845i −0.146858 0.0131115i
\(231\) 0.584913 0.0940976i 0.0384845 0.00619116i
\(232\) 4.72006 4.72006i 0.309887 0.309887i
\(233\) −3.47172 + 3.47172i −0.227440 + 0.227440i −0.811622 0.584182i \(-0.801415\pi\)
0.584182 + 0.811622i \(0.301415\pi\)
\(234\) −19.8288 + 6.54940i −1.29625 + 0.428148i
\(235\) 13.9748 + 16.7147i 0.911613 + 1.09035i
\(236\) 6.38319i 0.415510i
\(237\) −22.0880 15.9661i −1.43477 1.03711i
\(238\) −0.879935 0.879935i −0.0570377 0.0570377i
\(239\) 20.2807 1.31185 0.655924 0.754827i \(-0.272279\pi\)
0.655924 + 0.754827i \(0.272279\pi\)
\(240\) −2.53900 + 2.92463i −0.163892 + 0.188784i
\(241\) 6.16685 0.397242 0.198621 0.980076i \(-0.436354\pi\)
0.198621 + 0.980076i \(0.436354\pi\)
\(242\) 7.71142 + 7.71142i 0.495709 + 0.495709i
\(243\) −0.189246 15.5873i −0.0121401 0.999926i
\(244\) 9.95861i 0.637535i
\(245\) 1.14548 12.8302i 0.0731821 0.819691i
\(246\) 0.163991 + 1.01937i 0.0104557 + 0.0649929i
\(247\) 3.40570 3.40570i 0.216699 0.216699i
\(248\) −3.20006 + 3.20006i −0.203204 + 0.203204i
\(249\) −2.59059 16.1032i −0.164172 1.02050i
\(250\) −5.53846 9.71213i −0.350283 0.614249i
\(251\) 6.43760i 0.406338i 0.979144 + 0.203169i \(0.0651240\pi\)
−0.979144 + 0.203169i \(0.934876\pi\)
\(252\) 1.50175 2.98308i 0.0946016 0.187916i
\(253\) −0.217255 0.217255i −0.0136587 0.0136587i
\(254\) 19.4621 1.22116
\(255\) −4.31855 + 0.304805i −0.270438 + 0.0190876i
\(256\) 1.00000 0.0625000
\(257\) 8.53147 + 8.53147i 0.532178 + 0.532178i 0.921220 0.389042i \(-0.127194\pi\)
−0.389042 + 0.921220i \(0.627194\pi\)
\(258\) 13.3103 + 9.62123i 0.828665 + 0.598992i
\(259\) 2.79730i 0.173816i
\(260\) −11.9411 + 9.98368i −0.740558 + 0.619162i
\(261\) 6.28064 + 19.0151i 0.388762 + 1.17701i
\(262\) 6.42395 6.42395i 0.396873 0.396873i
\(263\) 4.18176 4.18176i 0.257858 0.257858i −0.566324 0.824183i \(-0.691635\pi\)
0.824183 + 0.566324i \(0.191635\pi\)
\(264\) −0.525408 + 0.0845247i −0.0323366 + 0.00520213i
\(265\) −14.4221 + 12.0580i −0.885942 + 0.740714i
\(266\) 0.770292i 0.0472297i
\(267\) −11.7118 + 16.2026i −0.716754 + 0.991581i
\(268\) 2.19342 + 2.19342i 0.133985 + 0.133985i
\(269\) −4.70169 −0.286667 −0.143334 0.989674i \(-0.545782\pi\)
−0.143334 + 0.989674i \(0.545782\pi\)
\(270\) −4.41179 10.7488i −0.268493 0.654149i
\(271\) 2.81014 0.170704 0.0853521 0.996351i \(-0.472799\pi\)
0.0853521 + 0.996351i \(0.472799\pi\)
\(272\) 0.790416 + 0.790416i 0.0479260 + 0.0479260i
\(273\) 7.86283 10.8777i 0.475880 0.658349i
\(274\) 8.65792i 0.523044i
\(275\) 0.272139 1.51193i 0.0164106 0.0911726i
\(276\) −1.71006 + 0.275105i −0.102934 + 0.0165594i
\(277\) −7.56846 + 7.56846i −0.454744 + 0.454744i −0.896926 0.442181i \(-0.854205\pi\)
0.442181 + 0.896926i \(0.354205\pi\)
\(278\) −1.20909 + 1.20909i −0.0725164 + 0.0725164i
\(279\) −4.25809 12.8917i −0.254925 0.771806i
\(280\) 0.221366 2.47945i 0.0132291 0.148176i
\(281\) 6.92797i 0.413288i 0.978416 + 0.206644i \(0.0662542\pi\)
−0.978416 + 0.206644i \(0.933746\pi\)
\(282\) 13.6772 + 9.88639i 0.814463 + 0.588726i
\(283\) −12.5993 12.5993i −0.748951 0.748951i 0.225331 0.974282i \(-0.427654\pi\)
−0.974282 + 0.225331i \(0.927654\pi\)
\(284\) 4.55564 0.270327
\(285\) 2.02363 + 1.75681i 0.119870 + 0.104064i
\(286\) −2.13867 −0.126462
\(287\) −0.469246 0.469246i −0.0276987 0.0276987i
\(288\) −1.34897 + 2.67960i −0.0794891 + 0.157897i
\(289\) 15.7505i 0.926499i
\(290\) 9.57400 + 11.4511i 0.562205 + 0.672433i
\(291\) −4.99072 31.0225i −0.292561 1.81857i
\(292\) 4.90914 4.90914i 0.287286 0.287286i
\(293\) 4.71078 4.71078i 0.275207 0.275207i −0.555985 0.831192i \(-0.687659\pi\)
0.831192 + 0.555985i \(0.187659\pi\)
\(294\) −1.58479 9.85110i −0.0924268 0.574528i
\(295\) 14.2167 + 1.26927i 0.827728 + 0.0738997i
\(296\) 2.51272i 0.146049i
\(297\) 0.482270 1.52191i 0.0279841 0.0883099i
\(298\) 3.13978 + 3.13978i 0.181883 + 0.181883i
\(299\) −6.96081 −0.402554
\(300\) −6.00889 6.23644i −0.346924 0.360061i
\(301\) −10.5560 −0.608440
\(302\) −13.3297 13.3297i −0.767040 0.767040i
\(303\) −0.611601 0.442089i −0.0351356 0.0253974i
\(304\) 0.691928i 0.0396848i
\(305\) 22.1799 + 1.98022i 1.27002 + 0.113387i
\(306\) −3.18425 + 1.05175i −0.182032 + 0.0601245i
\(307\) 6.16188 6.16188i 0.351677 0.351677i −0.509056 0.860733i \(-0.670006\pi\)
0.860733 + 0.509056i \(0.170006\pi\)
\(308\) 0.241860 0.241860i 0.0137813 0.0137813i
\(309\) 5.97555 0.961313i 0.339937 0.0546872i
\(310\) −6.49089 7.76352i −0.368658 0.440939i
\(311\) 6.56745i 0.372406i −0.982511 0.186203i \(-0.940382\pi\)
0.982511 0.186203i \(-0.0596182\pi\)
\(312\) −7.06292 + 9.77108i −0.399859 + 0.553178i
\(313\) 5.15434 + 5.15434i 0.291341 + 0.291341i 0.837610 0.546269i \(-0.183952\pi\)
−0.546269 + 0.837610i \(0.683952\pi\)
\(314\) −13.8395 −0.781007
\(315\) 6.34533 + 3.93789i 0.357519 + 0.221875i
\(316\) −15.7352 −0.885177
\(317\) 18.9615 + 18.9615i 1.06498 + 1.06498i 0.997736 + 0.0672456i \(0.0214211\pi\)
0.0672456 + 0.997736i \(0.478579\pi\)
\(318\) −8.53035 + 11.8012i −0.478358 + 0.661777i
\(319\) 2.05091i 0.114829i
\(320\) −0.198845 + 2.22721i −0.0111158 + 0.124505i
\(321\) 21.7796 3.50378i 1.21562 0.195562i
\(322\) 0.787190 0.787190i 0.0438684 0.0438684i
\(323\) 0.546911 0.546911i 0.0304309 0.0304309i
\(324\) −5.36053 7.22943i −0.297807 0.401635i
\(325\) −19.8613 28.5806i −1.10171 1.58537i
\(326\) 13.0724i 0.724014i
\(327\) 6.61914 + 4.78457i 0.366039 + 0.264587i
\(328\) 0.421508 + 0.421508i 0.0232739 + 0.0232739i
\(329\) −10.8470 −0.598013
\(330\) −0.0837792 1.18700i −0.00461189 0.0653422i
\(331\) −0.116417 −0.00639884 −0.00319942 0.999995i \(-0.501018\pi\)
−0.00319942 + 0.999995i \(0.501018\pi\)
\(332\) −6.65861 6.65861i −0.365439 0.365439i
\(333\) −6.73310 3.38960i −0.368971 0.185749i
\(334\) 10.5242i 0.575858i
\(335\) −5.32136 + 4.44906i −0.290737 + 0.243078i
\(336\) −0.306263 1.90374i −0.0167080 0.103857i
\(337\) 8.19544 8.19544i 0.446434 0.446434i −0.447733 0.894167i \(-0.647769\pi\)
0.894167 + 0.447733i \(0.147769\pi\)
\(338\) −25.0690 + 25.0690i −1.36357 + 1.36357i
\(339\) −3.79011 23.5594i −0.205851 1.27957i
\(340\) −1.91759 + 1.60325i −0.103996 + 0.0869485i
\(341\) 1.39046i 0.0752975i
\(342\) 1.85409 + 0.933393i 0.100258 + 0.0504721i
\(343\) 10.0451 + 10.0451i 0.542383 + 0.542383i
\(344\) 9.48214 0.511243
\(345\) −0.272679 3.86337i −0.0146805 0.207997i
\(346\) 12.7944 0.687833
\(347\) 4.19660 + 4.19660i 0.225285 + 0.225285i 0.810720 0.585435i \(-0.199076\pi\)
−0.585435 + 0.810720i \(0.699076\pi\)
\(348\) 9.37012 + 6.77309i 0.502291 + 0.363076i
\(349\) 5.51143i 0.295020i 0.989061 + 0.147510i \(0.0471259\pi\)
−0.989061 + 0.147510i \(0.952874\pi\)
\(350\) 5.47824 + 0.986056i 0.292824 + 0.0527069i
\(351\) −16.6549 32.1067i −0.888973 1.71373i
\(352\) −0.217255 + 0.217255i −0.0115797 + 0.0115797i
\(353\) −2.34200 + 2.34200i −0.124652 + 0.124652i −0.766681 0.642029i \(-0.778093\pi\)
0.642029 + 0.766681i \(0.278093\pi\)
\(354\) 10.9157 1.75605i 0.580161 0.0933330i
\(355\) −0.905868 + 10.1464i −0.0480785 + 0.538513i
\(356\) 11.5425i 0.611753i
\(357\) 1.26267 1.74682i 0.0668276 0.0924515i
\(358\) 7.93796 + 7.93796i 0.419534 + 0.419534i
\(359\) −12.4668 −0.657974 −0.328987 0.944334i \(-0.606707\pi\)
−0.328987 + 0.944334i \(0.606707\pi\)
\(360\) −5.69980 3.53728i −0.300406 0.186431i
\(361\) 18.5212 0.974802
\(362\) −6.12224 6.12224i −0.321778 0.321778i
\(363\) −11.0656 + 15.3085i −0.580792 + 0.803487i
\(364\) 7.74916i 0.406167i
\(365\) 9.95752 + 11.9098i 0.521201 + 0.623390i
\(366\) 17.0299 2.73967i 0.890165 0.143205i
\(367\) 3.53418 3.53418i 0.184483 0.184483i −0.608823 0.793306i \(-0.708358\pi\)
0.793306 + 0.608823i \(0.208358\pi\)
\(368\) −0.707107 + 0.707107i −0.0368605 + 0.0368605i
\(369\) −1.69808 + 0.560870i −0.0883984 + 0.0291977i
\(370\) −5.59636 0.499644i −0.290941 0.0259752i
\(371\) 9.35918i 0.485904i
\(372\) −6.35266 4.59195i −0.329370 0.238082i
\(373\) −17.4340 17.4340i −0.902700 0.902700i 0.0929686 0.995669i \(-0.470364\pi\)
−0.995669 + 0.0929686i \(0.970364\pi\)
\(374\) −0.343444 −0.0177590
\(375\) 15.0847 12.1430i 0.778971 0.627060i
\(376\) 9.74347 0.502481
\(377\) 32.8555 + 32.8555i 1.69214 + 1.69214i
\(378\) 5.51440 + 1.74743i 0.283630 + 0.0898782i
\(379\) 27.9253i 1.43443i 0.696853 + 0.717214i \(0.254583\pi\)
−0.696853 + 0.717214i \(0.745417\pi\)
\(380\) 1.54107 + 0.137587i 0.0790551 + 0.00705805i
\(381\) 5.35414 + 33.2815i 0.274301 + 1.70506i
\(382\) 12.8465 12.8465i 0.657284 0.657284i
\(383\) −10.0383 + 10.0383i −0.512932 + 0.512932i −0.915424 0.402492i \(-0.868144\pi\)
0.402492 + 0.915424i \(0.368144\pi\)
\(384\) 0.275105 + 1.71006i 0.0140389 + 0.0872663i
\(385\) 0.490580 + 0.586766i 0.0250023 + 0.0299044i
\(386\) 9.07391i 0.461850i
\(387\) −12.7912 + 25.4084i −0.650212 + 1.29158i
\(388\) −12.8277 12.8277i −0.651228 0.651228i
\(389\) 20.3937 1.03400 0.517000 0.855985i \(-0.327049\pi\)
0.517000 + 0.855985i \(0.327049\pi\)
\(390\) −20.3578 17.6735i −1.03086 0.894934i
\(391\) −1.11782 −0.0565305
\(392\) −4.07340 4.07340i −0.205738 0.205738i
\(393\) 12.7526 + 9.21810i 0.643285 + 0.464992i
\(394\) 20.7521i 1.04547i
\(395\) 3.12888 35.0457i 0.157431 1.76334i
\(396\) −0.289085 0.875228i −0.0145271 0.0439818i
\(397\) 11.8044 11.8044i 0.592447 0.592447i −0.345845 0.938292i \(-0.612408\pi\)
0.938292 + 0.345845i \(0.112408\pi\)
\(398\) −1.84410 + 1.84410i −0.0924363 + 0.0924363i
\(399\) −1.31725 + 0.211912i −0.0659449 + 0.0106089i
\(400\) −4.92092 0.885741i −0.246046 0.0442870i
\(401\) 8.66485i 0.432702i 0.976316 + 0.216351i \(0.0694156\pi\)
−0.976316 + 0.216351i \(0.930584\pi\)
\(402\) −3.14747 + 4.35431i −0.156981 + 0.217173i
\(403\) −22.2750 22.2750i −1.10960 1.10960i
\(404\) −0.435698 −0.0216768
\(405\) 17.1674 10.5015i 0.853054 0.521823i
\(406\) −7.43117 −0.368803
\(407\) −0.545901 0.545901i −0.0270593 0.0270593i
\(408\) −1.13421 + 1.56911i −0.0561520 + 0.0776825i
\(409\) 22.5197i 1.11353i −0.830670 0.556765i \(-0.812043\pi\)
0.830670 0.556765i \(-0.187957\pi\)
\(410\) −1.02260 + 0.854972i −0.0505027 + 0.0422241i
\(411\) 14.8056 2.38184i 0.730306 0.117488i
\(412\) 2.47087 2.47087i 0.121731 0.121731i
\(413\) −5.02479 + 5.02479i −0.247254 + 0.247254i
\(414\) −0.940895 2.84863i −0.0462425 0.140003i
\(415\) 16.1542 13.5061i 0.792977 0.662988i
\(416\) 6.96081i 0.341282i
\(417\) −2.40025 1.73499i −0.117541 0.0849630i
\(418\) 0.150325 + 0.150325i 0.00735262 + 0.00735262i
\(419\) −19.7745 −0.966048 −0.483024 0.875607i \(-0.660462\pi\)
−0.483024 + 0.875607i \(0.660462\pi\)
\(420\) 4.30092 0.303561i 0.209863 0.0148123i
\(421\) −3.54002 −0.172530 −0.0862649 0.996272i \(-0.527493\pi\)
−0.0862649 + 0.996272i \(0.527493\pi\)
\(422\) 17.6667 + 17.6667i 0.860004 + 0.860004i
\(423\) −13.1437 + 26.1086i −0.639068 + 1.26944i
\(424\) 8.40703i 0.408282i
\(425\) −3.18947 4.58968i −0.154712 0.222632i
\(426\) 1.25328 + 7.79043i 0.0607217 + 0.377448i
\(427\) −7.83932 + 7.83932i −0.379371 + 0.379371i
\(428\) 9.00580 9.00580i 0.435312 0.435312i
\(429\) −0.588361 3.65727i −0.0284063 0.176574i
\(430\) −1.88548 + 21.1187i −0.0909260 + 1.01843i
\(431\) 6.98806i 0.336603i 0.985736 + 0.168302i \(0.0538282\pi\)
−0.985736 + 0.168302i \(0.946172\pi\)
\(432\) −4.95340 1.56966i −0.238321 0.0755203i
\(433\) −22.0257 22.0257i −1.05849 1.05849i −0.998180 0.0603055i \(-0.980793\pi\)
−0.0603055 0.998180i \(-0.519207\pi\)
\(434\) 5.03812 0.241837
\(435\) −16.9483 + 19.5224i −0.812608 + 0.936028i
\(436\) 4.71540 0.225827
\(437\) 0.489267 + 0.489267i 0.0234048 + 0.0234048i
\(438\) 9.74547 + 7.04441i 0.465657 + 0.336595i
\(439\) 12.4962i 0.596410i −0.954502 0.298205i \(-0.903612\pi\)
0.954502 0.298205i \(-0.0963879\pi\)
\(440\) −0.440672 0.527072i −0.0210082 0.0251272i
\(441\) 16.4100 5.42018i 0.781429 0.258104i
\(442\) −5.50194 + 5.50194i −0.261701 + 0.261701i
\(443\) −3.45517 + 3.45517i −0.164160 + 0.164160i −0.784407 0.620247i \(-0.787033\pi\)
0.620247 + 0.784407i \(0.287033\pi\)
\(444\) −4.29692 + 0.691264i −0.203923 + 0.0328059i
\(445\) −25.7076 2.29518i −1.21866 0.108802i
\(446\) 2.92545i 0.138524i
\(447\) −4.50546 + 6.23300i −0.213101 + 0.294811i
\(448\) −0.787190 0.787190i −0.0371913 0.0371913i
\(449\) −5.44836 −0.257124 −0.128562 0.991701i \(-0.541036\pi\)
−0.128562 + 0.991701i \(0.541036\pi\)
\(450\) 9.01163 11.9913i 0.424812 0.565274i
\(451\) −0.183149 −0.00862417
\(452\) −9.74177 9.74177i −0.458214 0.458214i
\(453\) 19.1276 26.4618i 0.898694 1.24328i
\(454\) 21.0614i 0.988463i
\(455\) 17.2590 + 1.54089i 0.809115 + 0.0722378i
\(456\) 1.18324 0.190353i 0.0554103 0.00891410i
\(457\) −9.46760 + 9.46760i −0.442876 + 0.442876i −0.892977 0.450102i \(-0.851388\pi\)
0.450102 + 0.892977i \(0.351388\pi\)
\(458\) 3.26090 3.26090i 0.152372 0.152372i
\(459\) −2.67456 5.15593i −0.124838 0.240658i
\(460\) −1.43427 1.71548i −0.0668732 0.0799847i
\(461\) 29.8517i 1.39033i −0.718849 0.695166i \(-0.755331\pi\)
0.718849 0.695166i \(-0.244669\pi\)
\(462\) 0.480133 + 0.347059i 0.0223378 + 0.0161466i
\(463\) −17.9865 17.9865i −0.835905 0.835905i 0.152412 0.988317i \(-0.451296\pi\)
−0.988317 + 0.152412i \(0.951296\pi\)
\(464\) 6.67517 0.309887
\(465\) 11.4904 13.2356i 0.532856 0.613787i
\(466\) −4.90975 −0.227440
\(467\) 3.58351 + 3.58351i 0.165825 + 0.165825i 0.785141 0.619317i \(-0.212590\pi\)
−0.619317 + 0.785141i \(0.712590\pi\)
\(468\) −18.6522 9.38996i −0.862199 0.434051i
\(469\) 3.45328i 0.159458i
\(470\) −1.93744 + 21.7007i −0.0893677 + 1.00098i
\(471\) −3.80732 23.6664i −0.175432 1.09049i
\(472\) 4.51360 4.51360i 0.207755 0.207755i
\(473\) −2.06004 + 2.06004i −0.0947208 + 0.0947208i
\(474\) −4.32885 26.9083i −0.198831 1.23594i
\(475\) −0.612869 + 3.40492i −0.0281203 + 0.156229i
\(476\) 1.24442i 0.0570377i
\(477\) −22.5275 11.3409i −1.03146 0.519263i
\(478\) 14.3406 + 14.3406i 0.655924 + 0.655924i
\(479\) 39.2172 1.79188 0.895939 0.444177i \(-0.146504\pi\)
0.895939 + 0.444177i \(0.146504\pi\)
\(480\) −3.86337 + 0.272679i −0.176338 + 0.0124460i
\(481\) −17.4906 −0.797503
\(482\) 4.36062 + 4.36062i 0.198621 + 0.198621i
\(483\) 1.56271 + 1.12959i 0.0711056 + 0.0513979i
\(484\) 10.9056i 0.495709i
\(485\) 31.1207 26.0193i 1.41312 1.18147i
\(486\) 10.8881 11.1557i 0.493893 0.506033i
\(487\) 18.9608 18.9608i 0.859194 0.859194i −0.132049 0.991243i \(-0.542156\pi\)
0.991243 + 0.132049i \(0.0421556\pi\)
\(488\) 7.04180 7.04180i 0.318767 0.318767i
\(489\) −22.3547 + 3.59629i −1.01091 + 0.162630i
\(490\) 9.88230 8.26234i 0.446437 0.373255i
\(491\) 14.7080i 0.663761i 0.943321 + 0.331880i \(0.107683\pi\)
−0.943321 + 0.331880i \(0.892317\pi\)
\(492\) −0.604847 + 0.836765i −0.0272686 + 0.0377243i
\(493\) 5.27617 + 5.27617i 0.237627 + 0.237627i
\(494\) 4.81638 0.216699
\(495\) 2.00680 0.469818i 0.0901989 0.0211167i
\(496\) −4.52557 −0.203204
\(497\) −3.58616 3.58616i −0.160861 0.160861i
\(498\) 9.55483 13.2185i 0.428162 0.592334i
\(499\) 12.6459i 0.566109i −0.959104 0.283055i \(-0.908652\pi\)
0.959104 0.283055i \(-0.0913477\pi\)
\(500\) 2.95123 10.7838i 0.131983 0.482266i
\(501\) 17.9970 2.89526i 0.804048 0.129351i
\(502\) −4.55207 + 4.55207i −0.203169 + 0.203169i
\(503\) 29.2502 29.2502i 1.30420 1.30420i 0.378668 0.925532i \(-0.376382\pi\)
0.925532 0.378668i \(-0.123618\pi\)
\(504\) 3.17126 1.04746i 0.141259 0.0466574i
\(505\) 0.0866366 0.970391i 0.00385528 0.0431818i
\(506\) 0.307245i 0.0136587i
\(507\) −49.7662 35.9730i −2.21019 1.59762i
\(508\) 13.7618 + 13.7618i 0.610582 + 0.610582i
\(509\) −17.2813 −0.765978 −0.382989 0.923753i \(-0.625105\pi\)
−0.382989 + 0.923753i \(0.625105\pi\)
\(510\) −3.26920 2.83814i −0.144763 0.125675i
\(511\) −7.72886 −0.341904
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −1.08609 + 3.42740i −0.0479521 + 0.151323i
\(514\) 12.0653i 0.532178i
\(515\) 5.01183 + 5.99448i 0.220848 + 0.264148i
\(516\) 2.60859 + 16.2151i 0.114837 + 0.713828i
\(517\) −2.11682 + 2.11682i −0.0930974 + 0.0930974i
\(518\) 1.97799 1.97799i 0.0869080 0.0869080i
\(519\) 3.51982 + 21.8793i 0.154503 + 0.960394i
\(520\) −15.5032 1.38413i −0.679860 0.0606980i
\(521\) 34.5203i 1.51236i −0.654363 0.756181i \(-0.727063\pi\)
0.654363 0.756181i \(-0.272937\pi\)
\(522\) −9.00464 + 17.8868i −0.394123 + 0.782884i
\(523\) 29.4556 + 29.4556i 1.28800 + 1.28800i 0.935998 + 0.352005i \(0.114500\pi\)
0.352005 + 0.935998i \(0.385500\pi\)
\(524\) 9.08484 0.396873
\(525\) −0.179124 + 9.63941i −0.00781761 + 0.420698i
\(526\) 5.91390 0.257858
\(527\) −3.57709 3.57709i −0.155820 0.155820i
\(528\) −0.431287 0.311752i −0.0187694 0.0135672i
\(529\) 1.00000i 0.0434783i
\(530\) −18.7242 1.67170i −0.813328 0.0726140i
\(531\) 6.00591 + 18.1834i 0.260634 + 0.789091i
\(532\) −0.544679 + 0.544679i −0.0236148 + 0.0236148i
\(533\) −2.93404 + 2.93404i −0.127087 + 0.127087i
\(534\) −19.7385 + 3.17541i −0.854167 + 0.137414i
\(535\) 18.2670 + 21.8486i 0.789753 + 0.944595i
\(536\) 3.10197i 0.133985i
\(537\) −11.3906 + 15.7582i −0.491542 + 0.680016i
\(538\) −3.32460 3.32460i −0.143334 0.143334i
\(539\) 1.76993 0.0762364
\(540\) 4.48092 10.7201i 0.192828 0.461321i
\(541\) −22.6506 −0.973824 −0.486912 0.873451i \(-0.661877\pi\)
−0.486912 + 0.873451i \(0.661877\pi\)
\(542\) 1.98707 + 1.98707i 0.0853521 + 0.0853521i
\(543\) 8.78515 12.1537i 0.377007 0.521564i
\(544\) 1.11782i 0.0479260i
\(545\) −0.937637 + 10.5022i −0.0401639 + 0.449864i
\(546\) 13.2516 2.13184i 0.567114 0.0912342i
\(547\) 0.166563 0.166563i 0.00712170 0.00712170i −0.703537 0.710659i \(-0.748397\pi\)
0.710659 + 0.703537i \(0.248397\pi\)
\(548\) 6.12207 6.12207i 0.261522 0.261522i
\(549\) 9.37001 + 28.3684i 0.399902 + 1.21074i
\(550\) 1.26153 0.876662i 0.0537916 0.0373810i
\(551\) 4.61874i 0.196765i
\(552\) −1.40373 1.01467i −0.0597466 0.0431872i
\(553\) 12.3866 + 12.3866i 0.526733 + 0.526733i
\(554\) −10.7034 −0.454744
\(555\) −0.685167 9.70758i −0.0290837 0.412064i
\(556\) −1.70991 −0.0725164
\(557\) −22.4801 22.4801i −0.952511 0.952511i 0.0464113 0.998922i \(-0.485222\pi\)
−0.998922 + 0.0464113i \(0.985222\pi\)
\(558\) 6.10488 12.1267i 0.258440 0.513365i
\(559\) 66.0034i 2.79165i
\(560\) 1.90977 1.59671i 0.0807024 0.0674732i
\(561\) −0.0944832 0.587310i −0.00398908 0.0247963i
\(562\) −4.89882 + 4.89882i −0.206644 + 0.206644i
\(563\) −24.7485 + 24.7485i −1.04302 + 1.04302i −0.0439915 + 0.999032i \(0.514007\pi\)
−0.999032 + 0.0439915i \(0.985993\pi\)
\(564\) 2.68048 + 16.6620i 0.112869 + 0.701595i
\(565\) 23.6341 19.7598i 0.994292 0.831303i
\(566\) 17.8181i 0.748951i
\(567\) −1.47118 + 9.91070i −0.0617837 + 0.416210i
\(568\) 3.22132 + 3.22132i 0.135164 + 0.135164i
\(569\) −41.8001 −1.75235 −0.876176 0.481991i \(-0.839914\pi\)
−0.876176 + 0.481991i \(0.839914\pi\)
\(570\) 0.188674 + 2.67317i 0.00790269 + 0.111967i
\(571\) −6.16454 −0.257978 −0.128989 0.991646i \(-0.541173\pi\)
−0.128989 + 0.991646i \(0.541173\pi\)
\(572\) −1.51227 1.51227i −0.0632312 0.0632312i
\(573\) 25.5025 + 18.4342i 1.06538 + 0.770099i
\(574\) 0.663614i 0.0276987i
\(575\) 4.10593 2.85330i 0.171229 0.118991i
\(576\) −2.84863 + 0.940895i −0.118693 + 0.0392040i
\(577\) −32.6610 + 32.6610i −1.35970 + 1.35970i −0.485410 + 0.874287i \(0.661330\pi\)
−0.874287 + 0.485410i \(0.838670\pi\)
\(578\) 11.1373 11.1373i 0.463250 0.463250i
\(579\) −15.5170 + 2.49628i −0.644863 + 0.103742i
\(580\) −1.32733 + 14.8670i −0.0551143 + 0.617319i
\(581\) 10.4832i 0.434916i
\(582\) 18.4072 25.4652i 0.763004 1.05557i
\(583\) −1.82647 1.82647i −0.0756446 0.0756446i
\(584\) 6.94257 0.287286
\(585\) 24.6223 39.6752i 1.01801 1.64037i
\(586\) 6.66204 0.275207
\(587\) 22.6013 + 22.6013i 0.932856 + 0.932856i 0.997883 0.0650272i \(-0.0207134\pi\)
−0.0650272 + 0.997883i \(0.520713\pi\)
\(588\) 5.84516 8.08639i 0.241050 0.333477i
\(589\) 3.13137i 0.129026i
\(590\) 9.15522 + 10.9502i 0.376914 + 0.450814i
\(591\) −35.4874 + 5.70901i −1.45975 + 0.234837i
\(592\) −1.77676 + 1.77676i −0.0730245 + 0.0730245i
\(593\) 16.9395 16.9395i 0.695621 0.695621i −0.267842 0.963463i \(-0.586311\pi\)
0.963463 + 0.267842i \(0.0863106\pi\)
\(594\) 1.41717 0.735134i 0.0581470 0.0301629i
\(595\) 2.77158 + 0.247447i 0.113624 + 0.0101443i
\(596\) 4.44032i 0.181883i
\(597\) −3.66085 2.64620i −0.149828 0.108302i
\(598\) −4.92204 4.92204i −0.201277 0.201277i
\(599\) −35.0050 −1.43027 −0.715133 0.698988i \(-0.753634\pi\)
−0.715133 + 0.698988i \(0.753634\pi\)
\(600\) 0.160901 8.65876i 0.00656876 0.353492i
\(601\) −2.10282 −0.0857759 −0.0428880 0.999080i \(-0.513656\pi\)
−0.0428880 + 0.999080i \(0.513656\pi\)
\(602\) −7.46425 7.46425i −0.304220 0.304220i
\(603\) −8.31203 4.18447i −0.338492 0.170405i
\(604\) 18.8511i 0.767040i
\(605\) −24.2891 2.16853i −0.987490 0.0881633i
\(606\) −0.119863 0.745072i −0.00486910 0.0302665i
\(607\) 3.54626 3.54626i 0.143938 0.143938i −0.631466 0.775404i \(-0.717546\pi\)
0.775404 + 0.631466i \(0.217546\pi\)
\(608\) 0.489267 0.489267i 0.0198424 0.0198424i
\(609\) −2.04436 12.7078i −0.0828415 0.514945i
\(610\) 14.2833 + 17.0838i 0.578315 + 0.691703i
\(611\) 67.8225i 2.74380i
\(612\) −2.99531 1.50791i −0.121078 0.0609536i
\(613\) −29.6529 29.6529i −1.19767 1.19767i −0.974862 0.222808i \(-0.928478\pi\)
−0.222808 0.974862i \(-0.571522\pi\)
\(614\) 8.71421 0.351677
\(615\) −1.74338 1.51351i −0.0702998 0.0610305i
\(616\) 0.342042 0.0137813
\(617\) 32.2270 + 32.2270i 1.29741 + 1.29741i 0.930098 + 0.367311i \(0.119721\pi\)
0.367311 + 0.930098i \(0.380279\pi\)
\(618\) 4.90510 + 3.54560i 0.197312 + 0.142625i
\(619\) 17.9166i 0.720130i 0.932927 + 0.360065i \(0.117245\pi\)
−0.932927 + 0.360065i \(0.882755\pi\)
\(620\) 0.899889 10.0794i 0.0361404 0.404798i
\(621\) 4.61250 2.39267i 0.185093 0.0960144i
\(622\) 4.64389 4.64389i 0.186203 0.186203i
\(623\) 9.08617 9.08617i 0.364030 0.364030i
\(624\) −11.9034 + 1.91496i −0.476519 + 0.0766597i
\(625\) 23.4309 + 8.71732i 0.937237 + 0.348693i
\(626\) 7.28934i 0.291341i
\(627\) −0.215710 + 0.298420i −0.00861461 + 0.0119177i
\(628\) −9.78600 9.78600i −0.390504 0.390504i
\(629\) −2.80877 −0.111993
\(630\) 1.70232 + 7.27133i 0.0678219 + 0.289697i
\(631\) −7.91640 −0.315147 −0.157573 0.987507i \(-0.550367\pi\)
−0.157573 + 0.987507i \(0.550367\pi\)
\(632\) −11.1265 11.1265i −0.442588 0.442588i
\(633\) −25.3510 + 35.0715i −1.00761 + 1.39397i
\(634\) 26.8156i 1.06498i
\(635\) −33.3869 + 27.9140i −1.32492 + 1.10773i
\(636\) −14.3766 + 2.31282i −0.570068 + 0.0917093i
\(637\) 28.3542 28.3542i 1.12343 1.12343i
\(638\) −1.45021 + 1.45021i −0.0574145 + 0.0574145i
\(639\) −12.9773 + 4.28638i −0.513376 + 0.169567i
\(640\) −1.71548 + 1.43427i −0.0678103 + 0.0566945i
\(641\) 27.3529i 1.08037i 0.841545 + 0.540187i \(0.181646\pi\)
−0.841545 + 0.540187i \(0.818354\pi\)
\(642\) 17.8780 + 12.9229i 0.705589 + 0.510028i
\(643\) −9.00024 9.00024i −0.354935 0.354935i 0.507007 0.861942i \(-0.330752\pi\)
−0.861942 + 0.507007i \(0.830752\pi\)
\(644\) 1.11326 0.0438684
\(645\) −36.6330 + 2.58558i −1.44242 + 0.101807i
\(646\) 0.773449 0.0304309
\(647\) −15.7372 15.7372i −0.618691 0.618691i 0.326504 0.945196i \(-0.394129\pi\)
−0.945196 + 0.326504i \(0.894129\pi\)
\(648\) 1.32151 8.90245i 0.0519138 0.349721i
\(649\) 1.96120i 0.0769839i
\(650\) 6.16548 34.2536i 0.241830 1.34354i
\(651\) 1.38601 + 8.61550i 0.0543221 + 0.337668i
\(652\) −9.24359 + 9.24359i −0.362007 + 0.362007i
\(653\) −9.00813 + 9.00813i −0.352515 + 0.352515i −0.861045 0.508529i \(-0.830189\pi\)
0.508529 + 0.861045i \(0.330189\pi\)
\(654\) 1.29723 + 8.06364i 0.0507258 + 0.315313i
\(655\) −1.80648 + 20.2338i −0.0705850 + 0.790601i
\(656\) 0.596103i 0.0232739i
\(657\) −9.36536 + 18.6033i −0.365377 + 0.725785i
\(658\) −7.66997 7.66997i −0.299006 0.299006i
\(659\) −0.859802 −0.0334931 −0.0167466 0.999860i \(-0.505331\pi\)
−0.0167466 + 0.999860i \(0.505331\pi\)
\(660\) 0.780095 0.898577i 0.0303652 0.0349771i
\(661\) −2.50289 −0.0973513 −0.0486757 0.998815i \(-0.515500\pi\)
−0.0486757 + 0.998815i \(0.515500\pi\)
\(662\) −0.0823190 0.0823190i −0.00319942 0.00319942i
\(663\) −10.9223 7.89505i −0.424186 0.306619i
\(664\) 9.41670i 0.365439i
\(665\) −1.10481 1.32142i −0.0428426 0.0512425i
\(666\) −2.36421 7.15783i −0.0916113 0.277360i
\(667\) −4.72006 + 4.72006i −0.182762 + 0.182762i
\(668\) 7.44173 7.44173i 0.287929 0.287929i
\(669\) −5.00270 + 0.804807i −0.193416 + 0.0311156i
\(670\) −6.90873 0.616812i −0.266907 0.0238295i
\(671\) 3.05973i 0.118120i
\(672\) 1.12959 1.56271i 0.0435747 0.0602827i
\(673\) −22.4457 22.4457i −0.865220 0.865220i 0.126719 0.991939i \(-0.459555\pi\)
−0.991939 + 0.126719i \(0.959555\pi\)
\(674\) 11.5901 0.446434
\(675\) 22.9850 + 12.1116i 0.884692 + 0.466176i
\(676\) −35.4529 −1.36357
\(677\) 28.5893 + 28.5893i 1.09878 + 1.09878i 0.994554 + 0.104222i \(0.0332354\pi\)
0.104222 + 0.994554i \(0.466765\pi\)
\(678\) 13.9790 19.3391i 0.536861 0.742712i
\(679\) 20.1957i 0.775040i
\(680\) −2.48961 0.222273i −0.0954723 0.00852378i
\(681\) 36.0164 5.79412i 1.38015 0.222031i
\(682\) 0.983202 0.983202i 0.0376488 0.0376488i
\(683\) 14.6754 14.6754i 0.561537 0.561537i −0.368207 0.929744i \(-0.620028\pi\)
0.929744 + 0.368207i \(0.120028\pi\)
\(684\) 0.651032 + 1.97105i 0.0248928 + 0.0753650i
\(685\) 12.4178 + 14.8525i 0.474459 + 0.567484i
\(686\) 14.2059i 0.542383i
\(687\) 6.47343 + 4.67925i 0.246977 + 0.178525i
\(688\) 6.70489 + 6.70489i 0.255621 + 0.255621i
\(689\) −58.5198 −2.22943
\(690\) 2.53900 2.92463i 0.0966582 0.111339i
\(691\) 41.2032 1.56744 0.783721 0.621113i \(-0.213319\pi\)
0.783721 + 0.621113i \(0.213319\pi\)
\(692\) 9.04703 + 9.04703i 0.343916 + 0.343916i
\(693\) −0.461406 + 0.916536i −0.0175274 + 0.0348163i
\(694\) 5.93489i 0.225285i
\(695\) 0.340008 3.80833i 0.0128972 0.144458i
\(696\) 1.83638 + 11.4150i 0.0696077 + 0.432683i
\(697\) −0.471169 + 0.471169i −0.0178468 + 0.0178468i
\(698\) −3.89717 + 3.89717i −0.147510 + 0.147510i
\(699\) −1.35070 8.39599i −0.0510882 0.317566i
\(700\) 3.17646 + 4.57095i 0.120059 + 0.172766i
\(701\) 15.0725i 0.569281i 0.958634 + 0.284641i \(0.0918743\pi\)
−0.958634 + 0.284641i \(0.908126\pi\)
\(702\) 10.9261 34.4797i 0.412379 1.30135i
\(703\) 1.22939 + 1.22939i 0.0463674 + 0.0463674i
\(704\) −0.307245 −0.0115797
\(705\) −37.6426 + 2.65684i −1.41770 + 0.100062i
\(706\) −3.31208 −0.124652
\(707\) 0.342978 + 0.342978i 0.0128990 + 0.0128990i
\(708\) 8.96025 + 6.47682i 0.336747 + 0.243414i
\(709\) 18.9496i 0.711666i 0.934550 + 0.355833i \(0.115803\pi\)
−0.934550 + 0.355833i \(0.884197\pi\)
\(710\) −7.81511 + 6.53402i −0.293296 + 0.245217i
\(711\) 44.8240 14.8052i 1.68103 0.555239i
\(712\) −8.16181 + 8.16181i −0.305877 + 0.305877i
\(713\) 3.20006 3.20006i 0.119843 0.119843i
\(714\) 2.12803 0.342346i 0.0796396 0.0128120i
\(715\) 3.66885 3.06743i 0.137207 0.114716i
\(716\) 11.2260i 0.419534i
\(717\) −20.5782 + 28.4685i −0.768506 + 1.06318i
\(718\) −8.81537 8.81537i −0.328987 0.328987i
\(719\) −32.0644 −1.19580 −0.597900 0.801571i \(-0.703998\pi\)
−0.597900 + 0.801571i \(0.703998\pi\)
\(720\) −1.52913 6.53160i −0.0569874 0.243418i
\(721\) −3.89010 −0.144875
\(722\) 13.0965 + 13.0965i 0.487401 + 0.487401i
\(723\) −6.25731 + 8.65657i −0.232712 + 0.321941i
\(724\) 8.65815i 0.321778i
\(725\) −32.8480 5.91248i −1.21994 0.219584i
\(726\) −18.6493 + 3.00019i −0.692139 + 0.111347i
\(727\) −24.2721 + 24.2721i −0.900201 + 0.900201i −0.995453 0.0952521i \(-0.969634\pi\)
0.0952521 + 0.995453i \(0.469634\pi\)
\(728\) 5.47949 5.47949i 0.203083 0.203083i
\(729\) 22.0723 + 15.5503i 0.817494 + 0.575937i
\(730\) −1.38050 + 15.4626i −0.0510946 + 0.572295i
\(731\) 10.5993i 0.392029i
\(732\) 13.9792 + 10.1047i 0.516685 + 0.373480i
\(733\) 26.6081 + 26.6081i 0.982793 + 0.982793i 0.999854 0.0170616i \(-0.00543113\pi\)
−0.0170616 + 0.999854i \(0.505431\pi\)
\(734\) 4.99809 0.184483
\(735\) 16.8478 + 14.6263i 0.621441 + 0.539501i
\(736\) −1.00000 −0.0368605
\(737\) −0.673917 0.673917i −0.0248240 0.0248240i
\(738\) −1.59732 0.804127i −0.0587981 0.0296003i
\(739\) 38.0885i 1.40111i −0.713599 0.700554i \(-0.752936\pi\)
0.713599 0.700554i \(-0.247064\pi\)
\(740\) −3.60392 4.31053i −0.132483 0.158458i
\(741\) 1.32501 + 8.23632i 0.0486756 + 0.302569i
\(742\) 6.61794 6.61794i 0.242952 0.242952i
\(743\) 27.8032 27.8032i 1.02000 1.02000i 0.0202029 0.999796i \(-0.493569\pi\)
0.999796 0.0202029i \(-0.00643121\pi\)
\(744\) −1.24501 7.73901i −0.0456442 0.283726i
\(745\) −9.88953 0.882938i −0.362324 0.0323484i
\(746\) 24.6555i 0.902700i
\(747\) 25.2330 + 12.7029i 0.923228 + 0.464775i
\(748\) −0.242851 0.242851i −0.00887952 0.00887952i
\(749\) −14.1786 −0.518073
\(750\) 19.2529 + 2.08012i 0.703016 + 0.0759551i
\(751\) 11.8305 0.431701 0.215850 0.976426i \(-0.430748\pi\)
0.215850 + 0.976426i \(0.430748\pi\)
\(752\) 6.88967 + 6.88967i 0.251241 + 0.251241i
\(753\) −9.03663 6.53203i −0.329313 0.238040i
\(754\) 46.4646i 1.69214i
\(755\) 41.9853 + 3.74846i 1.52800 + 0.136420i
\(756\) 2.66365 + 5.13489i 0.0968759 + 0.186754i
\(757\) −9.09388 + 9.09388i −0.330523 + 0.330523i −0.852785 0.522262i \(-0.825088\pi\)
0.522262 + 0.852785i \(0.325088\pi\)
\(758\) −19.7462 + 19.7462i −0.717214 + 0.717214i
\(759\) 0.525408 0.0845247i 0.0190711 0.00306805i
\(760\) 0.992411 + 1.18699i 0.0359985 + 0.0430566i
\(761\) 41.4873i 1.50391i 0.659213 + 0.751956i \(0.270889\pi\)
−0.659213 + 0.751956i \(0.729111\pi\)
\(762\) −19.7476 + 27.3195i −0.715381 + 0.989682i
\(763\) −3.71192 3.71192i −0.134381 0.134381i
\(764\) 18.1677 0.657284
\(765\) 3.95403 6.37133i 0.142958 0.230356i
\(766\) −14.1963 −0.512932
\(767\) 31.4183 + 31.4183i 1.13445 + 1.13445i
\(768\) −1.01467 + 1.40373i −0.0366137 + 0.0506526i
\(769\) 45.6787i 1.64722i −0.567159 0.823608i \(-0.691958\pi\)
0.567159 0.823608i \(-0.308042\pi\)
\(770\) −0.0680135 + 0.761799i −0.00245104 + 0.0274533i
\(771\) −20.6325 + 3.31923i −0.743060 + 0.119539i
\(772\) −6.41622 + 6.41622i −0.230925 + 0.230925i
\(773\) −29.1634 + 29.1634i −1.04894 + 1.04894i −0.0501962 + 0.998739i \(0.515985\pi\)
−0.998739 + 0.0501962i \(0.984015\pi\)
\(774\) −27.0112 + 8.92170i −0.970896 + 0.320684i
\(775\) 22.2700 + 4.00848i 0.799961 + 0.143989i
\(776\) 18.1411i 0.651228i
\(777\) 3.92665 + 2.83833i 0.140868