Properties

Label 570.2.k.a.77.8
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.8
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.52000 - 0.830420i) q^{3} -1.00000i q^{4} +(-2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 - 2.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.62081 - 2.52448i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.52000 - 0.830420i) q^{3} -1.00000i q^{4} +(-2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 - 2.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.62081 - 2.52448i) q^{9} +(1.48722 - 1.66978i) q^{10} -0.319493i q^{11} +(-0.830420 - 1.52000i) q^{12} +(-3.95820 + 3.95820i) q^{13} +3.49979 q^{14} +(-3.28596 + 2.04999i) q^{15} -1.00000 q^{16} +(-4.30711 + 4.30711i) q^{17} +(0.638992 + 2.93116i) q^{18} +1.00000i q^{19} +(0.129088 + 2.23234i) q^{20} +(-5.81664 - 1.70652i) q^{21} +(0.225915 + 0.225915i) q^{22} +(-2.89538 - 2.89538i) q^{23} +(1.66200 + 0.487608i) q^{24} +(4.96667 - 0.576336i) q^{25} -5.59774i q^{26} +(0.367253 - 5.18316i) q^{27} +(-2.47472 + 2.47472i) q^{28} -8.60087 q^{29} +(0.873962 - 3.77309i) q^{30} -2.73939 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.265313 - 0.485629i) q^{33} -6.09118i q^{34} +(5.84388 + 5.20497i) q^{35} +(-2.52448 - 1.62081i) q^{36} +(1.42898 + 1.42898i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-2.72950 + 9.30344i) q^{39} +(-1.66978 - 1.48722i) q^{40} -7.07028i q^{41} +(5.31968 - 2.90629i) q^{42} +(6.45694 - 6.45694i) q^{43} -0.319493 q^{44} +(-3.29231 + 5.84472i) q^{45} +4.09469 q^{46} +(-4.12471 + 4.12471i) q^{47} +(-1.52000 + 0.830420i) q^{48} +5.24852i q^{49} +(-3.10444 + 3.91950i) q^{50} +(-2.97011 + 10.1235i) q^{51} +(3.95820 + 3.95820i) q^{52} +(1.15569 + 1.15569i) q^{53} +(3.40536 + 3.92473i) q^{54} +(0.0412426 + 0.713216i) q^{55} -3.49979i q^{56} +(0.830420 + 1.52000i) q^{57} +(6.08174 - 6.08174i) q^{58} +7.51199 q^{59} +(2.04999 + 3.28596i) q^{60} +8.09546 q^{61} +(1.93704 - 1.93704i) q^{62} +(-10.2584 + 2.23634i) q^{63} +1.00000i q^{64} +(8.32509 - 9.34700i) q^{65} +(0.530996 + 0.155787i) q^{66} +(-11.1750 - 11.1750i) q^{67} +(4.30711 + 4.30711i) q^{68} +(-6.80536 - 1.99660i) q^{69} +(-7.81272 + 0.451781i) q^{70} -13.8007i q^{71} +(2.93116 - 0.638992i) q^{72} +(-9.22508 + 9.22508i) q^{73} -2.02088 q^{74} +(7.07075 - 5.00045i) q^{75} +1.00000 q^{76} +(-0.790656 + 0.790656i) q^{77} +(-4.64848 - 8.50858i) q^{78} -3.00427i q^{79} +(2.23234 - 0.129088i) q^{80} +(-3.74597 - 8.18338i) q^{81} +(4.99944 + 4.99944i) q^{82} +(2.31688 + 2.31688i) q^{83} +(-1.70652 + 5.81664i) q^{84} +(9.05894 - 10.1709i) q^{85} +9.13149i q^{86} +(-13.0733 + 7.14233i) q^{87} +(0.225915 - 0.225915i) q^{88} -4.95832 q^{89} +(-1.80482 - 6.46085i) q^{90} +19.5909 q^{91} +(-2.89538 + 2.89538i) q^{92} +(-4.16388 + 2.27484i) q^{93} -5.83322i q^{94} +(-0.129088 - 2.23234i) q^{95} +(0.487608 - 1.66200i) q^{96} +(-2.21723 - 2.21723i) q^{97} +(-3.71127 - 3.71127i) q^{98} +(-0.806552 - 0.517836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} - 32q^{21} - 4q^{22} + 32q^{25} + 28q^{27} - 12q^{28} - 8q^{30} + 8q^{31} + 36q^{33} + 4q^{36} - 32q^{37} - 8q^{40} + 12q^{42} - 24q^{43} - 28q^{45} - 16q^{46} - 4q^{48} - 40q^{51} - 8q^{52} - 4q^{55} + 4q^{57} - 4q^{58} - 24q^{60} + 200q^{61} + 28q^{63} + 12q^{70} - 68q^{73} - 36q^{75} + 36q^{76} + 24q^{78} - 92q^{81} + 24q^{82} + 24q^{85} + 28q^{87} - 4q^{88} - 68q^{90} + 64q^{91} + 16q^{93} - 4q^{96} - 148q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.52000 0.830420i 0.877573 0.479443i
\(4\) 1.00000i 0.500000i
\(5\) −2.23234 + 0.129088i −0.998332 + 0.0577299i
\(6\) −0.487608 + 1.66200i −0.199065 + 0.678508i
\(7\) −2.47472 2.47472i −0.935358 0.935358i 0.0626759 0.998034i \(-0.480037\pi\)
−0.998034 + 0.0626759i \(0.980037\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.62081 2.52448i 0.540269 0.841492i
\(10\) 1.48722 1.66978i 0.470301 0.528031i
\(11\) 0.319493i 0.0963306i −0.998839 0.0481653i \(-0.984663\pi\)
0.998839 0.0481653i \(-0.0153374\pi\)
\(12\) −0.830420 1.52000i −0.239721 0.438787i
\(13\) −3.95820 + 3.95820i −1.09781 + 1.09781i −0.103141 + 0.994667i \(0.532889\pi\)
−0.994667 + 0.103141i \(0.967111\pi\)
\(14\) 3.49979 0.935358
\(15\) −3.28596 + 2.04999i −0.848431 + 0.529306i
\(16\) −1.00000 −0.250000
\(17\) −4.30711 + 4.30711i −1.04463 + 1.04463i −0.0456719 + 0.998956i \(0.514543\pi\)
−0.998956 + 0.0456719i \(0.985457\pi\)
\(18\) 0.638992 + 2.93116i 0.150612 + 0.690881i
\(19\) 1.00000i 0.229416i
\(20\) 0.129088 + 2.23234i 0.0288649 + 0.499166i
\(21\) −5.81664 1.70652i −1.26930 0.372394i
\(22\) 0.225915 + 0.225915i 0.0481653 + 0.0481653i
\(23\) −2.89538 2.89538i −0.603729 0.603729i 0.337571 0.941300i \(-0.390395\pi\)
−0.941300 + 0.337571i \(0.890395\pi\)
\(24\) 1.66200 + 0.487608i 0.339254 + 0.0995325i
\(25\) 4.96667 0.576336i 0.993335 0.115267i
\(26\) 5.59774i 1.09781i
\(27\) 0.367253 5.18316i 0.0706778 0.997499i
\(28\) −2.47472 + 2.47472i −0.467679 + 0.467679i
\(29\) −8.60087 −1.59714 −0.798571 0.601900i \(-0.794410\pi\)
−0.798571 + 0.601900i \(0.794410\pi\)
\(30\) 0.873962 3.77309i 0.159563 0.688868i
\(31\) −2.73939 −0.492009 −0.246005 0.969269i \(-0.579118\pi\)
−0.246005 + 0.969269i \(0.579118\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −0.265313 0.485629i −0.0461850 0.0845372i
\(34\) 6.09118i 1.04463i
\(35\) 5.84388 + 5.20497i 0.987796 + 0.879800i
\(36\) −2.52448 1.62081i −0.420746 0.270134i
\(37\) 1.42898 + 1.42898i 0.234923 + 0.234923i 0.814744 0.579821i \(-0.196878\pi\)
−0.579821 + 0.814744i \(0.696878\pi\)
\(38\) −0.707107 0.707107i −0.114708 0.114708i
\(39\) −2.72950 + 9.30344i −0.437070 + 1.48974i
\(40\) −1.66978 1.48722i −0.264016 0.235151i
\(41\) 7.07028i 1.10419i −0.833780 0.552096i \(-0.813828\pi\)
0.833780 0.552096i \(-0.186172\pi\)
\(42\) 5.31968 2.90629i 0.820845 0.448451i
\(43\) 6.45694 6.45694i 0.984674 0.984674i −0.0152099 0.999884i \(-0.504842\pi\)
0.999884 + 0.0152099i \(0.00484166\pi\)
\(44\) −0.319493 −0.0481653
\(45\) −3.29231 + 5.84472i −0.490789 + 0.871279i
\(46\) 4.09469 0.603729
\(47\) −4.12471 + 4.12471i −0.601650 + 0.601650i −0.940750 0.339100i \(-0.889877\pi\)
0.339100 + 0.940750i \(0.389877\pi\)
\(48\) −1.52000 + 0.830420i −0.219393 + 0.119861i
\(49\) 5.24852i 0.749789i
\(50\) −3.10444 + 3.91950i −0.439034 + 0.554301i
\(51\) −2.97011 + 10.1235i −0.415898 + 1.41758i
\(52\) 3.95820 + 3.95820i 0.548904 + 0.548904i
\(53\) 1.15569 + 1.15569i 0.158747 + 0.158747i 0.782011 0.623264i \(-0.214194\pi\)
−0.623264 + 0.782011i \(0.714194\pi\)
\(54\) 3.40536 + 3.92473i 0.463411 + 0.534088i
\(55\) 0.0412426 + 0.713216i 0.00556116 + 0.0961700i
\(56\) 3.49979i 0.467679i
\(57\) 0.830420 + 1.52000i 0.109992 + 0.201329i
\(58\) 6.08174 6.08174i 0.798571 0.798571i
\(59\) 7.51199 0.977978 0.488989 0.872290i \(-0.337366\pi\)
0.488989 + 0.872290i \(0.337366\pi\)
\(60\) 2.04999 + 3.28596i 0.264653 + 0.424216i
\(61\) 8.09546 1.03652 0.518259 0.855224i \(-0.326581\pi\)
0.518259 + 0.855224i \(0.326581\pi\)
\(62\) 1.93704 1.93704i 0.246005 0.246005i
\(63\) −10.2584 + 2.23634i −1.29244 + 0.281752i
\(64\) 1.00000i 0.125000i
\(65\) 8.32509 9.34700i 1.03260 1.15935i
\(66\) 0.530996 + 0.155787i 0.0653611 + 0.0191761i
\(67\) −11.1750 11.1750i −1.36524 1.36524i −0.867086 0.498158i \(-0.834010\pi\)
−0.498158 0.867086i \(-0.665990\pi\)
\(68\) 4.30711 + 4.30711i 0.522314 + 0.522314i
\(69\) −6.80536 1.99660i −0.819270 0.240363i
\(70\) −7.81272 + 0.451781i −0.933798 + 0.0539981i
\(71\) 13.8007i 1.63784i −0.573909 0.818919i \(-0.694574\pi\)
0.573909 0.818919i \(-0.305426\pi\)
\(72\) 2.93116 0.638992i 0.345440 0.0753059i
\(73\) −9.22508 + 9.22508i −1.07971 + 1.07971i −0.0831788 + 0.996535i \(0.526507\pi\)
−0.996535 + 0.0831788i \(0.973493\pi\)
\(74\) −2.02088 −0.234923
\(75\) 7.07075 5.00045i 0.816460 0.577403i
\(76\) 1.00000 0.114708
\(77\) −0.790656 + 0.790656i −0.0901036 + 0.0901036i
\(78\) −4.64848 8.50858i −0.526336 0.963407i
\(79\) 3.00427i 0.338007i −0.985615 0.169004i \(-0.945945\pi\)
0.985615 0.169004i \(-0.0540549\pi\)
\(80\) 2.23234 0.129088i 0.249583 0.0144325i
\(81\) −3.74597 8.18338i −0.416219 0.909264i
\(82\) 4.99944 + 4.99944i 0.552096 + 0.552096i
\(83\) 2.31688 + 2.31688i 0.254311 + 0.254311i 0.822735 0.568425i \(-0.192447\pi\)
−0.568425 + 0.822735i \(0.692447\pi\)
\(84\) −1.70652 + 5.81664i −0.186197 + 0.634648i
\(85\) 9.05894 10.1709i 0.982580 1.10319i
\(86\) 9.13149i 0.984674i
\(87\) −13.0733 + 7.14233i −1.40161 + 0.765739i
\(88\) 0.225915 0.225915i 0.0240827 0.0240827i
\(89\) −4.95832 −0.525580 −0.262790 0.964853i \(-0.584643\pi\)
−0.262790 + 0.964853i \(0.584643\pi\)
\(90\) −1.80482 6.46085i −0.190245 0.681034i
\(91\) 19.5909 2.05369
\(92\) −2.89538 + 2.89538i −0.301864 + 0.301864i
\(93\) −4.16388 + 2.27484i −0.431774 + 0.235890i
\(94\) 5.83322i 0.601650i
\(95\) −0.129088 2.23234i −0.0132441 0.229033i
\(96\) 0.487608 1.66200i 0.0497663 0.169627i
\(97\) −2.21723 2.21723i −0.225126 0.225126i 0.585527 0.810653i \(-0.300888\pi\)
−0.810653 + 0.585527i \(0.800888\pi\)
\(98\) −3.71127 3.71127i −0.374895 0.374895i
\(99\) −0.806552 0.517836i −0.0810615 0.0520445i
\(100\) −0.576336 4.96667i −0.0576336 0.496667i
\(101\) 6.77117i 0.673757i −0.941548 0.336878i \(-0.890629\pi\)
0.941548 0.336878i \(-0.109371\pi\)
\(102\) −5.05823 9.25860i −0.500840 0.916738i
\(103\) 7.14069 7.14069i 0.703593 0.703593i −0.261587 0.965180i \(-0.584246\pi\)
0.965180 + 0.261587i \(0.0842458\pi\)
\(104\) −5.59774 −0.548904
\(105\) 13.2050 + 3.05868i 1.28868 + 0.298497i
\(106\) −1.63440 −0.158747
\(107\) −4.96947 + 4.96947i −0.480416 + 0.480416i −0.905265 0.424848i \(-0.860327\pi\)
0.424848 + 0.905265i \(0.360327\pi\)
\(108\) −5.18316 0.367253i −0.498750 0.0353389i
\(109\) 12.0861i 1.15764i 0.815455 + 0.578820i \(0.196487\pi\)
−0.815455 + 0.578820i \(0.803513\pi\)
\(110\) −0.533483 0.475157i −0.0508656 0.0453044i
\(111\) 3.35870 + 0.985397i 0.318794 + 0.0935298i
\(112\) 2.47472 + 2.47472i 0.233840 + 0.233840i
\(113\) −5.06883 5.06883i −0.476835 0.476835i 0.427283 0.904118i \(-0.359471\pi\)
−0.904118 + 0.427283i \(0.859471\pi\)
\(114\) −1.66200 0.487608i −0.155660 0.0456687i
\(115\) 6.83723 + 6.08971i 0.637575 + 0.567869i
\(116\) 8.60087i 0.798571i
\(117\) 3.57691 + 16.4079i 0.330686 + 1.51691i
\(118\) −5.31178 + 5.31178i −0.488989 + 0.488989i
\(119\) 21.3178 1.95420
\(120\) −3.77309 0.873962i −0.344434 0.0797814i
\(121\) 10.8979 0.990720
\(122\) −5.72435 + 5.72435i −0.518259 + 0.518259i
\(123\) −5.87130 10.7468i −0.529397 0.969010i
\(124\) 2.73939i 0.246005i
\(125\) −11.0129 + 1.92771i −0.985024 + 0.172420i
\(126\) 5.67248 8.83514i 0.505345 0.787097i
\(127\) 11.4227 + 11.4227i 1.01360 + 1.01360i 0.999906 + 0.0136950i \(0.00435939\pi\)
0.0136950 + 0.999906i \(0.495641\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 4.45259 15.1765i 0.392028 1.33622i
\(130\) 0.722601 + 12.4961i 0.0633763 + 1.09598i
\(131\) 3.12384i 0.272931i −0.990645 0.136466i \(-0.956426\pi\)
0.990645 0.136466i \(-0.0435744\pi\)
\(132\) −0.485629 + 0.265313i −0.0422686 + 0.0230925i
\(133\) 2.47472 2.47472i 0.214586 0.214586i
\(134\) 15.8038 1.36524
\(135\) −0.150749 + 11.6180i −0.0129744 + 0.999916i
\(136\) −6.09118 −0.522314
\(137\) −4.42417 + 4.42417i −0.377982 + 0.377982i −0.870374 0.492392i \(-0.836123\pi\)
0.492392 + 0.870374i \(0.336123\pi\)
\(138\) 6.22393 3.40031i 0.529816 0.289453i
\(139\) 13.6045i 1.15392i 0.816772 + 0.576960i \(0.195761\pi\)
−0.816772 + 0.576960i \(0.804239\pi\)
\(140\) 5.20497 5.84388i 0.439900 0.493898i
\(141\) −2.84432 + 9.69479i −0.239535 + 0.816449i
\(142\) 9.75855 + 9.75855i 0.818919 + 0.818919i
\(143\) 1.26462 + 1.26462i 0.105753 + 0.105753i
\(144\) −1.62081 + 2.52448i −0.135067 + 0.210373i
\(145\) 19.2001 1.11027i 1.59448 0.0922028i
\(146\) 13.0462i 1.07971i
\(147\) 4.35848 + 7.97776i 0.359481 + 0.657995i
\(148\) 1.42898 1.42898i 0.117461 0.117461i
\(149\) 15.4792 1.26810 0.634052 0.773291i \(-0.281391\pi\)
0.634052 + 0.773291i \(0.281391\pi\)
\(150\) −1.46392 + 8.53563i −0.119528 + 0.696931i
\(151\) −13.4794 −1.09694 −0.548469 0.836171i \(-0.684789\pi\)
−0.548469 + 0.836171i \(0.684789\pi\)
\(152\) −0.707107 + 0.707107i −0.0573539 + 0.0573539i
\(153\) 3.89221 + 17.8542i 0.314667 + 1.44343i
\(154\) 1.11816i 0.0901036i
\(155\) 6.11525 0.353622i 0.491189 0.0284036i
\(156\) 9.30344 + 2.72950i 0.744871 + 0.218535i
\(157\) −5.84460 5.84460i −0.466450 0.466450i 0.434313 0.900762i \(-0.356991\pi\)
−0.900762 + 0.434313i \(0.856991\pi\)
\(158\) 2.12434 + 2.12434i 0.169004 + 0.169004i
\(159\) 2.71637 + 0.796945i 0.215422 + 0.0632019i
\(160\) −1.48722 + 1.66978i −0.117575 + 0.132008i
\(161\) 14.3305i 1.12940i
\(162\) 8.43532 + 3.13772i 0.662742 + 0.246523i
\(163\) −9.68901 + 9.68901i −0.758902 + 0.758902i −0.976123 0.217221i \(-0.930301\pi\)
0.217221 + 0.976123i \(0.430301\pi\)
\(164\) −7.07028 −0.552096
\(165\) 0.654957 + 1.04984i 0.0509883 + 0.0817299i
\(166\) −3.27656 −0.254311
\(167\) −9.29416 + 9.29416i −0.719204 + 0.719204i −0.968442 0.249239i \(-0.919820\pi\)
0.249239 + 0.968442i \(0.419820\pi\)
\(168\) −2.90629 5.31968i −0.224225 0.410422i
\(169\) 18.3347i 1.41036i
\(170\) 0.786298 + 13.5976i 0.0603063 + 1.04289i
\(171\) 2.52448 + 1.62081i 0.193052 + 0.123946i
\(172\) −6.45694 6.45694i −0.492337 0.492337i
\(173\) −4.33021 4.33021i −0.329220 0.329220i 0.523070 0.852290i \(-0.324787\pi\)
−0.852290 + 0.523070i \(0.824787\pi\)
\(174\) 4.19385 14.2946i 0.317935 1.08367i
\(175\) −13.7174 10.8649i −1.03694 0.821307i
\(176\) 0.319493i 0.0240827i
\(177\) 11.4182 6.23810i 0.858247 0.468885i
\(178\) 3.50606 3.50606i 0.262790 0.262790i
\(179\) 8.41749 0.629153 0.314576 0.949232i \(-0.398138\pi\)
0.314576 + 0.949232i \(0.398138\pi\)
\(180\) 5.84472 + 3.29231i 0.435639 + 0.245394i
\(181\) −4.04233 −0.300464 −0.150232 0.988651i \(-0.548002\pi\)
−0.150232 + 0.988651i \(0.548002\pi\)
\(182\) −13.8529 + 13.8529i −1.02684 + 1.02684i
\(183\) 12.3051 6.72263i 0.909619 0.496951i
\(184\) 4.09469i 0.301864i
\(185\) −3.37443 3.00550i −0.248093 0.220969i
\(186\) 1.33575 4.55286i 0.0979418 0.333832i
\(187\) 1.37609 + 1.37609i 0.100630 + 0.100630i
\(188\) 4.12471 + 4.12471i 0.300825 + 0.300825i
\(189\) −13.7357 + 11.9180i −0.999128 + 0.866910i
\(190\) 1.66978 + 1.48722i 0.121139 + 0.107894i
\(191\) 12.7401i 0.921841i −0.887441 0.460921i \(-0.847519\pi\)
0.887441 0.460921i \(-0.152481\pi\)
\(192\) 0.830420 + 1.52000i 0.0599304 + 0.109697i
\(193\) 0.0511200 0.0511200i 0.00367970 0.00367970i −0.705265 0.708944i \(-0.749172\pi\)
0.708944 + 0.705265i \(0.249172\pi\)
\(194\) 3.13564 0.225126
\(195\) 4.89221 21.1208i 0.350339 1.51249i
\(196\) 5.24852 0.374895
\(197\) 13.8117 13.8117i 0.984041 0.984041i −0.0158340 0.999875i \(-0.505040\pi\)
0.999875 + 0.0158340i \(0.00504032\pi\)
\(198\) 0.936483 0.204153i 0.0665530 0.0145085i
\(199\) 10.3363i 0.732719i 0.930473 + 0.366359i \(0.119396\pi\)
−0.930473 + 0.366359i \(0.880604\pi\)
\(200\) 3.91950 + 3.10444i 0.277150 + 0.219517i
\(201\) −26.2660 7.70608i −1.85266 0.543545i
\(202\) 4.78794 + 4.78794i 0.336878 + 0.336878i
\(203\) 21.2848 + 21.2848i 1.49390 + 1.49390i
\(204\) 10.1235 + 2.97011i 0.708789 + 0.207949i
\(205\) 0.912688 + 15.7833i 0.0637449 + 1.10235i
\(206\) 10.0985i 0.703593i
\(207\) −12.0022 + 2.61647i −0.834209 + 0.181857i
\(208\) 3.95820 3.95820i 0.274452 0.274452i
\(209\) 0.319493 0.0220998
\(210\) −11.5002 + 7.17454i −0.793587 + 0.495090i
\(211\) 6.26053 0.430992 0.215496 0.976505i \(-0.430863\pi\)
0.215496 + 0.976505i \(0.430863\pi\)
\(212\) 1.15569 1.15569i 0.0793734 0.0793734i
\(213\) −11.4603 20.9770i −0.785250 1.43732i
\(214\) 7.02789i 0.480416i
\(215\) −13.5806 + 15.2476i −0.926187 + 1.03988i
\(216\) 3.92473 3.40536i 0.267044 0.231705i
\(217\) 6.77924 + 6.77924i 0.460205 + 0.460205i
\(218\) −8.54618 8.54618i −0.578820 0.578820i
\(219\) −6.36144 + 21.6828i −0.429866 + 1.46519i
\(220\) 0.713216 0.0412426i 0.0480850 0.00278058i
\(221\) 34.0969i 2.29360i
\(222\) −3.07174 + 1.67818i −0.206162 + 0.112632i
\(223\) −8.21125 + 8.21125i −0.549866 + 0.549866i −0.926402 0.376536i \(-0.877115\pi\)
0.376536 + 0.926402i \(0.377115\pi\)
\(224\) −3.49979 −0.233840
\(225\) 6.59507 13.4724i 0.439671 0.898159i
\(226\) 7.16840 0.476835
\(227\) 3.64293 3.64293i 0.241790 0.241790i −0.575800 0.817590i \(-0.695309\pi\)
0.817590 + 0.575800i \(0.195309\pi\)
\(228\) 1.52000 0.830420i 0.100665 0.0549959i
\(229\) 21.7636i 1.43818i −0.694917 0.719090i \(-0.744559\pi\)
0.694917 0.719090i \(-0.255441\pi\)
\(230\) −9.14073 + 0.528575i −0.602722 + 0.0348532i
\(231\) −0.545222 + 1.85837i −0.0358730 + 0.122272i
\(232\) −6.08174 6.08174i −0.399286 0.399286i
\(233\) −3.78119 3.78119i −0.247714 0.247714i 0.572318 0.820032i \(-0.306044\pi\)
−0.820032 + 0.572318i \(0.806044\pi\)
\(234\) −14.1314 9.07286i −0.923797 0.593111i
\(235\) 8.67529 9.74019i 0.565914 0.635380i
\(236\) 7.51199i 0.488989i
\(237\) −2.49481 4.56650i −0.162055 0.296626i
\(238\) −15.0740 + 15.0740i −0.977102 + 0.977102i
\(239\) 14.2573 0.922230 0.461115 0.887340i \(-0.347450\pi\)
0.461115 + 0.887340i \(0.347450\pi\)
\(240\) 3.28596 2.04999i 0.212108 0.132326i
\(241\) −30.3058 −1.95217 −0.976084 0.217394i \(-0.930244\pi\)
−0.976084 + 0.217394i \(0.930244\pi\)
\(242\) −7.70600 + 7.70600i −0.495360 + 0.495360i
\(243\) −12.4895 9.32802i −0.801203 0.598393i
\(244\) 8.09546i 0.518259i
\(245\) −0.677521 11.7165i −0.0432852 0.748539i
\(246\) 11.7508 + 3.44752i 0.749204 + 0.219806i
\(247\) −3.95820 3.95820i −0.251854 0.251854i
\(248\) −1.93704 1.93704i −0.123002 0.123002i
\(249\) 5.44564 + 1.59768i 0.345103 + 0.101249i
\(250\) 6.42419 9.15039i 0.406302 0.578722i
\(251\) 26.1004i 1.64744i 0.566996 + 0.823720i \(0.308105\pi\)
−0.566996 + 0.823720i \(0.691895\pi\)
\(252\) 2.23634 + 10.2584i 0.140876 + 0.646221i
\(253\) −0.925053 + 0.925053i −0.0581576 + 0.0581576i
\(254\) −16.1541 −1.01360
\(255\) 5.32346 22.9825i 0.333368 1.43922i
\(256\) 1.00000 0.0625000
\(257\) 10.7603 10.7603i 0.671212 0.671212i −0.286783 0.957995i \(-0.592586\pi\)
0.957995 + 0.286783i \(0.0925860\pi\)
\(258\) 7.58297 + 13.8799i 0.472095 + 0.864124i
\(259\) 7.07266i 0.439474i
\(260\) −9.34700 8.32509i −0.579677 0.516300i
\(261\) −13.9404 + 21.7127i −0.862886 + 1.34398i
\(262\) 2.20889 + 2.20889i 0.136466 + 0.136466i
\(263\) 7.39717 + 7.39717i 0.456129 + 0.456129i 0.897383 0.441253i \(-0.145466\pi\)
−0.441253 + 0.897383i \(0.645466\pi\)
\(264\) 0.155787 0.530996i 0.00958803 0.0326806i
\(265\) −2.72909 2.43071i −0.167646 0.149318i
\(266\) 3.49979i 0.214586i
\(267\) −7.53664 + 4.11748i −0.461235 + 0.251986i
\(268\) −11.1750 + 11.1750i −0.682622 + 0.682622i
\(269\) 12.5829 0.767193 0.383596 0.923501i \(-0.374685\pi\)
0.383596 + 0.923501i \(0.374685\pi\)
\(270\) −8.10855 8.32174i −0.493471 0.506445i
\(271\) 1.82465 0.110840 0.0554198 0.998463i \(-0.482350\pi\)
0.0554198 + 0.998463i \(0.482350\pi\)
\(272\) 4.30711 4.30711i 0.261157 0.261157i
\(273\) 29.7782 16.2687i 1.80226 0.984626i
\(274\) 6.25672i 0.377982i
\(275\) −0.184135 1.58682i −0.0111038 0.0956886i
\(276\) −1.99660 + 6.80536i −0.120181 + 0.409635i
\(277\) −8.96703 8.96703i −0.538777 0.538777i 0.384393 0.923170i \(-0.374411\pi\)
−0.923170 + 0.384393i \(0.874411\pi\)
\(278\) −9.61985 9.61985i −0.576960 0.576960i
\(279\) −4.44002 + 6.91553i −0.265817 + 0.414022i
\(280\) 0.451781 + 7.81272i 0.0269991 + 0.466899i
\(281\) 18.1779i 1.08440i −0.840249 0.542200i \(-0.817591\pi\)
0.840249 0.542200i \(-0.182409\pi\)
\(282\) −4.84402 8.86649i −0.288457 0.527992i
\(283\) 14.1537 14.1537i 0.841353 0.841353i −0.147682 0.989035i \(-0.547181\pi\)
0.989035 + 0.147682i \(0.0471812\pi\)
\(284\) −13.8007 −0.818919
\(285\) −2.04999 3.28596i −0.121431 0.194643i
\(286\) −1.78844 −0.105753
\(287\) −17.4970 + 17.4970i −1.03282 + 1.03282i
\(288\) −0.638992 2.93116i −0.0376529 0.172720i
\(289\) 20.1024i 1.18250i
\(290\) −12.7914 + 14.3616i −0.751138 + 0.843341i
\(291\) −5.21142 1.52896i −0.305499 0.0896293i
\(292\) 9.22508 + 9.22508i 0.539857 + 0.539857i
\(293\) −19.2900 19.2900i −1.12694 1.12694i −0.990673 0.136264i \(-0.956491\pi\)
−0.136264 0.990673i \(-0.543509\pi\)
\(294\) −8.72304 2.55922i −0.508738 0.149257i
\(295\) −16.7693 + 0.969707i −0.976347 + 0.0564585i
\(296\) 2.02088i 0.117461i
\(297\) −1.65598 0.117334i −0.0960897 0.00680844i
\(298\) −10.9454 + 10.9454i −0.634052 + 0.634052i
\(299\) 22.9210 1.32556
\(300\) −5.00045 7.07075i −0.288701 0.408230i
\(301\) −31.9583 −1.84205
\(302\) 9.53138 9.53138i 0.548469 0.548469i
\(303\) −5.62291 10.2922i −0.323028 0.591271i
\(304\) 1.00000i 0.0573539i
\(305\) −18.0718 + 1.04503i −1.03479 + 0.0598380i
\(306\) −15.3770 9.87262i −0.879047 0.564380i
\(307\) −2.74294 2.74294i −0.156548 0.156548i 0.624487 0.781035i \(-0.285308\pi\)
−0.781035 + 0.624487i \(0.785308\pi\)
\(308\) 0.790656 + 0.790656i 0.0450518 + 0.0450518i
\(309\) 4.92409 16.7836i 0.280121 0.954787i
\(310\) −4.07409 + 4.57418i −0.231392 + 0.259796i
\(311\) 8.60142i 0.487742i 0.969808 + 0.243871i \(0.0784173\pi\)
−0.969808 + 0.243871i \(0.921583\pi\)
\(312\) −8.50858 + 4.64848i −0.481703 + 0.263168i
\(313\) −6.25964 + 6.25964i −0.353816 + 0.353816i −0.861527 0.507711i \(-0.830492\pi\)
0.507711 + 0.861527i \(0.330492\pi\)
\(314\) 8.26551 0.466450
\(315\) 22.6116 6.31650i 1.27402 0.355894i
\(316\) −3.00427 −0.169004
\(317\) −19.7083 + 19.7083i −1.10693 + 1.10693i −0.113376 + 0.993552i \(0.536166\pi\)
−0.993552 + 0.113376i \(0.963834\pi\)
\(318\) −2.48429 + 1.35724i −0.139312 + 0.0761100i
\(319\) 2.74792i 0.153854i
\(320\) −0.129088 2.23234i −0.00721624 0.124792i
\(321\) −3.42685 + 11.6803i −0.191268 + 0.651933i
\(322\) −10.1332 10.1332i −0.564702 0.564702i
\(323\) −4.30711 4.30711i −0.239654 0.239654i
\(324\) −8.18338 + 3.74597i −0.454632 + 0.208110i
\(325\) −17.3778 + 21.9403i −0.963949 + 1.21703i
\(326\) 13.7023i 0.758902i
\(327\) 10.0366 + 18.3709i 0.555023 + 1.01591i
\(328\) 4.99944 4.99944i 0.276048 0.276048i
\(329\) 20.4150 1.12552
\(330\) −1.20547 0.279224i −0.0663591 0.0153708i
\(331\) −17.7975 −0.978237 −0.489119 0.872217i \(-0.662682\pi\)
−0.489119 + 0.872217i \(0.662682\pi\)
\(332\) 2.31688 2.31688i 0.127155 0.127155i
\(333\) 5.92352 1.29133i 0.324607 0.0707642i
\(334\) 13.1439i 0.719204i
\(335\) 26.3890 + 23.5038i 1.44178 + 1.28415i
\(336\) 5.81664 + 1.70652i 0.317324 + 0.0930985i
\(337\) −10.3711 10.3711i −0.564952 0.564952i 0.365758 0.930710i \(-0.380810\pi\)
−0.930710 + 0.365758i \(0.880810\pi\)
\(338\) 12.9646 + 12.9646i 0.705182 + 0.705182i
\(339\) −11.9139 3.49537i −0.647073 0.189842i
\(340\) −10.1709 9.05894i −0.551596 0.491290i
\(341\) 0.875215i 0.0473956i
\(342\) −2.93116 + 0.638992i −0.158499 + 0.0345527i
\(343\) −4.33442 + 4.33442i −0.234037 + 0.234037i
\(344\) 9.13149 0.492337
\(345\) 15.4496 + 3.57860i 0.831779 + 0.192665i
\(346\) 6.12384 0.329220
\(347\) −5.55389 + 5.55389i −0.298149 + 0.298149i −0.840288 0.542140i \(-0.817614\pi\)
0.542140 + 0.840288i \(0.317614\pi\)
\(348\) 7.14233 + 13.0733i 0.382869 + 0.700805i
\(349\) 10.2761i 0.550066i 0.961435 + 0.275033i \(0.0886889\pi\)
−0.961435 + 0.275033i \(0.911311\pi\)
\(350\) 17.3823 2.01705i 0.929123 0.107816i
\(351\) 19.0623 + 21.9696i 1.01747 + 1.17265i
\(352\) −0.225915 0.225915i −0.0120413 0.0120413i
\(353\) 5.09591 + 5.09591i 0.271228 + 0.271228i 0.829594 0.558366i \(-0.188572\pi\)
−0.558366 + 0.829594i \(0.688572\pi\)
\(354\) −3.66290 + 12.4849i −0.194681 + 0.663566i
\(355\) 1.78150 + 30.8078i 0.0945522 + 1.63511i
\(356\) 4.95832i 0.262790i
\(357\) 32.4031 17.7028i 1.71496 0.936929i
\(358\) −5.95206 + 5.95206i −0.314576 + 0.314576i
\(359\) −35.4806 −1.87259 −0.936297 0.351208i \(-0.885771\pi\)
−0.936297 + 0.351208i \(0.885771\pi\)
\(360\) −6.46085 + 1.80482i −0.340517 + 0.0951225i
\(361\) −1.00000 −0.0526316
\(362\) 2.85836 2.85836i 0.150232 0.150232i
\(363\) 16.5649 9.04985i 0.869430 0.474994i
\(364\) 19.5909i 1.02684i
\(365\) 19.4026 21.7843i 1.01558 1.14024i
\(366\) −3.94741 + 13.4546i −0.206334 + 0.703285i
\(367\) −3.42185 3.42185i −0.178619 0.178619i 0.612134 0.790754i \(-0.290311\pi\)
−0.790754 + 0.612134i \(0.790311\pi\)
\(368\) 2.89538 + 2.89538i 0.150932 + 0.150932i
\(369\) −17.8488 11.4596i −0.929170 0.596561i
\(370\) 4.51129 0.260871i 0.234531 0.0135621i
\(371\) 5.72005i 0.296970i
\(372\) 2.27484 + 4.16388i 0.117945 + 0.215887i
\(373\) 3.03363 3.03363i 0.157075 0.157075i −0.624194 0.781269i \(-0.714573\pi\)
0.781269 + 0.624194i \(0.214573\pi\)
\(374\) −1.94609 −0.100630
\(375\) −15.1388 + 12.0755i −0.781764 + 0.623574i
\(376\) −5.83322 −0.300825
\(377\) 34.0440 34.0440i 1.75336 1.75336i
\(378\) 1.28531 18.1400i 0.0661090 0.933019i
\(379\) 19.3076i 0.991764i −0.868390 0.495882i \(-0.834845\pi\)
0.868390 0.495882i \(-0.165155\pi\)
\(380\) −2.23234 + 0.129088i −0.114517 + 0.00662207i
\(381\) 26.8482 + 7.87689i 1.37547 + 0.403545i
\(382\) 9.00861 + 9.00861i 0.460921 + 0.460921i
\(383\) 12.9987 + 12.9987i 0.664204 + 0.664204i 0.956368 0.292164i \(-0.0943752\pi\)
−0.292164 + 0.956368i \(0.594375\pi\)
\(384\) −1.66200 0.487608i −0.0848135 0.0248831i
\(385\) 1.66295 1.86708i 0.0847517 0.0951550i
\(386\) 0.0722945i 0.00367970i
\(387\) −5.83495 26.7659i −0.296607 1.36058i
\(388\) −2.21723 + 2.21723i −0.112563 + 0.112563i
\(389\) 10.3234 0.523419 0.261709 0.965147i \(-0.415714\pi\)
0.261709 + 0.965147i \(0.415714\pi\)
\(390\) 11.4753 + 18.3940i 0.581076 + 0.931414i
\(391\) 24.9415 1.26134
\(392\) −3.71127 + 3.71127i −0.187447 + 0.187447i
\(393\) −2.59410 4.74825i −0.130855 0.239517i
\(394\) 19.5326i 0.984041i
\(395\) 0.387815 + 6.70655i 0.0195131 + 0.337443i
\(396\) −0.517836 + 0.806552i −0.0260222 + 0.0405308i
\(397\) −13.5127 13.5127i −0.678181 0.678181i 0.281407 0.959588i \(-0.409199\pi\)
−0.959588 + 0.281407i \(0.909199\pi\)
\(398\) −7.30885 7.30885i −0.366359 0.366359i
\(399\) 1.70652 5.81664i 0.0854331 0.291196i
\(400\) −4.96667 + 0.576336i −0.248334 + 0.0288168i
\(401\) 17.9859i 0.898171i 0.893489 + 0.449086i \(0.148250\pi\)
−0.893489 + 0.449086i \(0.851750\pi\)
\(402\) 24.0219 13.1238i 1.19810 0.654557i
\(403\) 10.8431 10.8431i 0.540131 0.540131i
\(404\) −6.77117 −0.336878
\(405\) 9.41865 + 17.7845i 0.468017 + 0.883720i
\(406\) −30.1012 −1.49390
\(407\) 0.456548 0.456548i 0.0226302 0.0226302i
\(408\) −9.25860 + 5.05823i −0.458369 + 0.250420i
\(409\) 38.6156i 1.90942i 0.297542 + 0.954709i \(0.403833\pi\)
−0.297542 + 0.954709i \(0.596167\pi\)
\(410\) −11.8058 10.5151i −0.583048 0.519303i
\(411\) −3.05082 + 10.3987i −0.150486 + 0.512928i
\(412\) −7.14069 7.14069i −0.351796 0.351796i
\(413\) −18.5901 18.5901i −0.914759 0.914759i
\(414\) 6.63670 10.3369i 0.326176 0.508033i
\(415\) −5.47114 4.87298i −0.268568 0.239205i
\(416\) 5.59774i 0.274452i
\(417\) 11.2975 + 20.6789i 0.553239 + 1.01265i
\(418\) −0.225915 + 0.225915i −0.0110499 + 0.0110499i
\(419\) −1.37511 −0.0671786 −0.0335893 0.999436i \(-0.510694\pi\)
−0.0335893 + 0.999436i \(0.510694\pi\)
\(420\) 3.05868 13.2050i 0.149248 0.644339i
\(421\) −3.07765 −0.149996 −0.0749978 0.997184i \(-0.523895\pi\)
−0.0749978 + 0.997184i \(0.523895\pi\)
\(422\) −4.42686 + 4.42686i −0.215496 + 0.215496i
\(423\) 3.72738 + 17.0981i 0.181231 + 0.831337i
\(424\) 1.63440i 0.0793734i
\(425\) −18.9097 + 23.8744i −0.917254 + 1.15808i
\(426\) 22.9367 + 6.72932i 1.11129 + 0.326036i
\(427\) −20.0340 20.0340i −0.969515 0.969515i
\(428\) 4.96947 + 4.96947i 0.240208 + 0.240208i
\(429\) 2.97238 + 0.872056i 0.143508 + 0.0421033i
\(430\) −1.17877 20.3846i −0.0568451 0.983032i
\(431\) 2.29824i 0.110702i 0.998467 + 0.0553512i \(0.0176278\pi\)
−0.998467 + 0.0553512i \(0.982372\pi\)
\(432\) −0.367253 + 5.18316i −0.0176694 + 0.249375i
\(433\) −0.650645 + 0.650645i −0.0312680 + 0.0312680i −0.722568 0.691300i \(-0.757038\pi\)
0.691300 + 0.722568i \(0.257038\pi\)
\(434\) −9.58729 −0.460205
\(435\) 28.2621 17.6317i 1.35507 0.845376i
\(436\) 12.0861 0.578820
\(437\) 2.89538 2.89538i 0.138505 0.138505i
\(438\) −10.8338 19.8303i −0.517661 0.947527i
\(439\) 18.3241i 0.874563i 0.899325 + 0.437281i \(0.144059\pi\)
−0.899325 + 0.437281i \(0.855941\pi\)
\(440\) −0.475157 + 0.533483i −0.0226522 + 0.0254328i
\(441\) 13.2498 + 8.50684i 0.630942 + 0.405088i
\(442\) 24.1101 + 24.1101i 1.14680 + 1.14680i
\(443\) −0.832433 0.832433i −0.0395501 0.0395501i 0.687055 0.726605i \(-0.258903\pi\)
−0.726605 + 0.687055i \(0.758903\pi\)
\(444\) 0.985397 3.35870i 0.0467649 0.159397i
\(445\) 11.0686 0.640059i 0.524704 0.0303417i
\(446\) 11.6125i 0.549866i
\(447\) 23.5284 12.8542i 1.11285 0.607983i
\(448\) 2.47472 2.47472i 0.116920 0.116920i
\(449\) −30.6819 −1.44797 −0.723984 0.689817i \(-0.757691\pi\)
−0.723984 + 0.689817i \(0.757691\pi\)
\(450\) 4.86299 + 14.1898i 0.229244 + 0.668915i
\(451\) −2.25890 −0.106368
\(452\) −5.06883 + 5.06883i −0.238418 + 0.238418i
\(453\) −20.4887 + 11.1936i −0.962643 + 0.525919i
\(454\) 5.15188i 0.241790i
\(455\) −43.7336 + 2.52895i −2.05026 + 0.118559i
\(456\) −0.487608 + 1.66200i −0.0228343 + 0.0778302i
\(457\) −3.78531 3.78531i −0.177069 0.177069i 0.613008 0.790077i \(-0.289959\pi\)
−0.790077 + 0.613008i \(0.789959\pi\)
\(458\) 15.3892 + 15.3892i 0.719090 + 0.719090i
\(459\) 20.7426 + 23.9062i 0.968184 + 1.11585i
\(460\) 6.08971 6.83723i 0.283934 0.318788i
\(461\) 6.89618i 0.321187i −0.987021 0.160593i \(-0.948659\pi\)
0.987021 0.160593i \(-0.0513408\pi\)
\(462\) −0.928539 1.69960i −0.0431996 0.0790725i
\(463\) 12.6005 12.6005i 0.585597 0.585597i −0.350839 0.936436i \(-0.614104\pi\)
0.936436 + 0.350839i \(0.114104\pi\)
\(464\) 8.60087 0.399286
\(465\) 9.00153 5.61573i 0.417436 0.260423i
\(466\) 5.34741 0.247714
\(467\) 26.3961 26.3961i 1.22147 1.22147i 0.254355 0.967111i \(-0.418137\pi\)
0.967111 0.254355i \(-0.0818630\pi\)
\(468\) 16.4079 3.57691i 0.758454 0.165343i
\(469\) 55.3101i 2.55398i
\(470\) 0.752998 + 13.0217i 0.0347332 + 0.600647i
\(471\) −13.7373 4.03033i −0.632980 0.185708i
\(472\) 5.31178 + 5.31178i 0.244494 + 0.244494i
\(473\) −2.06295 2.06295i −0.0948543 0.0948543i
\(474\) 4.99310 + 1.46491i 0.229340 + 0.0672854i
\(475\) 0.576336 + 4.96667i 0.0264441 + 0.227887i
\(476\) 21.3178i 0.977102i
\(477\) 4.79068 1.04437i 0.219350 0.0478183i
\(478\) −10.0815 + 10.0815i −0.461115 + 0.461115i
\(479\) −17.9400 −0.819700 −0.409850 0.912153i \(-0.634419\pi\)
−0.409850 + 0.912153i \(0.634419\pi\)
\(480\) −0.873962 + 3.77309i −0.0398907 + 0.172217i
\(481\) −11.3124 −0.515800
\(482\) 21.4294 21.4294i 0.976084 0.976084i
\(483\) 11.9004 + 21.7824i 0.541485 + 0.991135i
\(484\) 10.8979i 0.495360i
\(485\) 5.23583 + 4.66339i 0.237747 + 0.211754i
\(486\) 15.4273 2.23552i 0.699798 0.101405i
\(487\) 8.76993 + 8.76993i 0.397403 + 0.397403i 0.877316 0.479913i \(-0.159332\pi\)
−0.479913 + 0.877316i \(0.659332\pi\)
\(488\) 5.72435 + 5.72435i 0.259129 + 0.259129i
\(489\) −6.68136 + 22.7732i −0.302142 + 1.02984i
\(490\) 8.76389 + 7.80573i 0.395912 + 0.352627i
\(491\) 1.85820i 0.0838595i −0.999121 0.0419298i \(-0.986649\pi\)
0.999121 0.0419298i \(-0.0133506\pi\)
\(492\) −10.7468 + 5.87130i −0.484505 + 0.264699i
\(493\) 37.0449 37.0449i 1.66842 1.66842i
\(494\) 5.59774 0.251854
\(495\) 1.86734 + 1.05187i 0.0839308 + 0.0472780i
\(496\) 2.73939 0.123002
\(497\) −34.1529 + 34.1529i −1.53197 + 1.53197i
\(498\) −4.98038 + 2.72092i −0.223176 + 0.121927i
\(499\) 6.79733i 0.304290i −0.988358 0.152145i \(-0.951382\pi\)
0.988358 0.152145i \(-0.0486181\pi\)
\(500\) 1.92771 + 11.0129i 0.0862100 + 0.492512i
\(501\) −6.40908 + 21.8452i −0.286337 + 0.975971i
\(502\) −18.4557 18.4557i −0.823720 0.823720i
\(503\) −25.0714 25.0714i −1.11788 1.11788i −0.992052 0.125825i \(-0.959842\pi\)
−0.125825 0.992052i \(-0.540158\pi\)
\(504\) −8.83514 5.67248i −0.393548 0.252672i
\(505\) 0.874077 + 15.1156i 0.0388959 + 0.672633i
\(506\) 1.30822i 0.0581576i
\(507\) −15.2255 27.8688i −0.676189 1.23770i
\(508\) 11.4227 11.4227i 0.506801 0.506801i
\(509\) −30.4865 −1.35129 −0.675644 0.737228i \(-0.736134\pi\)
−0.675644 + 0.737228i \(0.736134\pi\)
\(510\) 12.4869 + 20.0154i 0.552928 + 0.886295i
\(511\) 45.6590 2.01984
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 5.18316 + 0.367253i 0.228842 + 0.0162146i
\(514\) 15.2174i 0.671212i
\(515\) −15.0187 + 16.8622i −0.661801 + 0.743038i
\(516\) −15.1765 4.45259i −0.668109 0.196014i
\(517\) 1.31781 + 1.31781i 0.0579574 + 0.0579574i
\(518\) 5.00112 + 5.00112i 0.219737 + 0.219737i
\(519\) −10.1778 2.98603i −0.446756 0.131072i
\(520\) 12.4961 0.722601i 0.547988 0.0316882i
\(521\) 10.5695i 0.463058i −0.972828 0.231529i \(-0.925627\pi\)
0.972828 0.231529i \(-0.0743729\pi\)
\(522\) −5.49589 25.2105i −0.240548 1.10343i
\(523\) −13.0333 + 13.0333i −0.569906 + 0.569906i −0.932102 0.362196i \(-0.882027\pi\)
0.362196 + 0.932102i \(0.382027\pi\)
\(524\) −3.12384 −0.136466
\(525\) −29.8729 5.12341i −1.30376 0.223604i
\(526\) −10.4612 −0.456129
\(527\) 11.7989 11.7989i 0.513967 0.513967i
\(528\) 0.265313 + 0.485629i 0.0115463 + 0.0211343i
\(529\) 6.23354i 0.271023i
\(530\) 3.64853 0.210981i 0.158482 0.00916443i
\(531\) 12.1755 18.9638i 0.528371 0.822961i
\(532\) −2.47472 2.47472i −0.107293 0.107293i
\(533\) 27.9856 + 27.9856i 1.21219 + 1.21219i
\(534\) 2.41771 8.24071i 0.104625 0.356610i
\(535\) 10.4520 11.7350i 0.451881 0.507350i
\(536\) 15.8038i 0.682622i
\(537\) 12.7946 6.99005i 0.552127 0.301643i
\(538\) −8.89745 + 8.89745i −0.383596 + 0.383596i
\(539\) 1.67686 0.0722277
\(540\) 11.6180 + 0.150749i 0.499958 + 0.00648720i
\(541\) 4.01245 0.172509 0.0862544 0.996273i \(-0.472510\pi\)
0.0862544 + 0.996273i \(0.472510\pi\)
\(542\) −1.29022 + 1.29022i −0.0554198 + 0.0554198i
\(543\) −6.14435 + 3.35683i −0.263679 + 0.144055i
\(544\) 6.09118i 0.261157i
\(545\) −1.56017 26.9803i −0.0668305 1.15571i
\(546\) −9.55269 + 32.5601i −0.408817 + 1.39344i
\(547\) −8.37945 8.37945i −0.358279 0.358279i 0.504899 0.863178i \(-0.331530\pi\)
−0.863178 + 0.504899i \(0.831530\pi\)
\(548\) 4.42417 + 4.42417i 0.188991 + 0.188991i
\(549\) 13.1212 20.4368i 0.559998 0.872221i
\(550\) 1.25225 + 0.991845i 0.0533962 + 0.0422924i
\(551\) 8.60087i 0.366410i
\(552\) −3.40031 6.22393i −0.144727 0.264908i
\(553\) −7.43475 + 7.43475i −0.316158 + 0.316158i
\(554\) 12.6813 0.538777
\(555\) −7.62496 1.76617i −0.323662 0.0749699i
\(556\) 13.6045 0.576960
\(557\) −10.8415 + 10.8415i −0.459369 + 0.459369i −0.898448 0.439079i \(-0.855305\pi\)
0.439079 + 0.898448i \(0.355305\pi\)
\(558\) −1.75045 8.02959i −0.0741024 0.339920i
\(559\) 51.1158i 2.16197i
\(560\) −5.84388 5.20497i −0.246949 0.219950i
\(561\) 3.23439 + 0.948927i 0.136556 + 0.0400637i
\(562\) 12.8537 + 12.8537i 0.542200 + 0.542200i
\(563\) 18.3171 + 18.3171i 0.771973 + 0.771973i 0.978451 0.206478i \(-0.0662002\pi\)
−0.206478 + 0.978451i \(0.566200\pi\)
\(564\) 9.69479 + 2.84432i 0.408225 + 0.119768i
\(565\) 11.9697 + 10.6610i 0.503567 + 0.448512i
\(566\) 20.0164i 0.841353i
\(567\) −10.9814 + 29.5219i −0.461174 + 1.23980i
\(568\) 9.75855 9.75855i 0.409460 0.409460i
\(569\) −5.23426 −0.219432 −0.109716 0.993963i \(-0.534994\pi\)
−0.109716 + 0.993963i \(0.534994\pi\)
\(570\) 3.77309 + 0.873962i 0.158037 + 0.0366062i
\(571\) −36.1118 −1.51123 −0.755616 0.655015i \(-0.772662\pi\)
−0.755616 + 0.655015i \(0.772662\pi\)
\(572\) 1.26462 1.26462i 0.0528763 0.0528763i
\(573\) −10.5796 19.3650i −0.441970 0.808983i
\(574\) 24.7445i 1.03282i
\(575\) −16.0491 12.7117i −0.669295 0.530114i
\(576\) 2.52448 + 1.62081i 0.105187 + 0.0675336i
\(577\) −0.690796 0.690796i −0.0287582 0.0287582i 0.692581 0.721340i \(-0.256473\pi\)
−0.721340 + 0.692581i \(0.756473\pi\)
\(578\) 14.2146 + 14.2146i 0.591248 + 0.591248i
\(579\) 0.0352514 0.120153i 0.00146500 0.00499341i
\(580\) −1.11027 19.2001i −0.0461014 0.797239i
\(581\) 11.4673i 0.475743i
\(582\) 4.76617 2.60389i 0.197564 0.107935i
\(583\) 0.369236 0.369236i 0.0152922 0.0152922i
\(584\) −13.0462 −0.539857
\(585\) −10.1029 36.1662i −0.417705 1.49529i
\(586\) 27.2802 1.12694
\(587\) 22.7297 22.7297i 0.938154 0.938154i −0.0600421 0.998196i \(-0.519123\pi\)
0.998196 + 0.0600421i \(0.0191235\pi\)
\(588\) 7.97776 4.35848i 0.328997 0.179741i
\(589\) 2.73939i 0.112875i
\(590\) 11.1720 12.5434i 0.459944 0.516403i
\(591\) 9.52427 32.4632i 0.391776 1.33536i
\(592\) −1.42898 1.42898i −0.0587307 0.0587307i
\(593\) 31.3926 + 31.3926i 1.28914 + 1.28914i 0.935311 + 0.353828i \(0.115120\pi\)
0.353828 + 0.935311i \(0.384880\pi\)
\(594\) 1.25392 1.08799i 0.0514491 0.0446407i
\(595\) −47.5886 + 2.75188i −1.95094 + 0.112816i
\(596\) 15.4792i 0.634052i
\(597\) 8.58344 + 15.7111i 0.351297 + 0.643014i
\(598\) −16.2076 + 16.2076i −0.662778 + 0.662778i
\(599\) −27.0824 −1.10656 −0.553278 0.832997i \(-0.686623\pi\)
−0.553278 + 0.832997i \(0.686623\pi\)
\(600\) 8.53563 + 1.46392i 0.348466 + 0.0597642i
\(601\) 10.0478 0.409860 0.204930 0.978777i \(-0.434303\pi\)
0.204930 + 0.978777i \(0.434303\pi\)
\(602\) 22.5979 22.5979i 0.921023 0.921023i
\(603\) −46.3236 + 10.0985i −1.88644 + 0.411244i
\(604\) 13.4794i 0.548469i
\(605\) −24.3279 + 1.40679i −0.989068 + 0.0571942i
\(606\) 11.2537 + 3.30168i 0.457149 + 0.134121i
\(607\) 7.08962 + 7.08962i 0.287759 + 0.287759i 0.836193 0.548435i \(-0.184776\pi\)
−0.548435 + 0.836193i \(0.684776\pi\)
\(608\) 0.707107 + 0.707107i 0.0286770 + 0.0286770i
\(609\) 50.0282 + 14.6776i 2.02725 + 0.594766i
\(610\) 12.0397 13.5176i 0.487475 0.547313i
\(611\) 32.6528i 1.32099i
\(612\) 17.8542 3.89221i 0.721714 0.157333i
\(613\) 24.9931 24.9931i 1.00946 1.00946i 0.00950519 0.999955i \(-0.496974\pi\)
0.999955 0.00950519i \(-0.00302564\pi\)
\(614\) 3.87911 0.156548
\(615\) 14.4940 + 23.2327i 0.584455 + 0.936832i
\(616\) −1.11816 −0.0450518
\(617\) −1.14572 + 1.14572i −0.0461251 + 0.0461251i −0.729793 0.683668i \(-0.760384\pi\)
0.683668 + 0.729793i \(0.260384\pi\)
\(618\) 8.38596 + 15.3497i 0.337333 + 0.617454i
\(619\) 38.1788i 1.53454i −0.641327 0.767268i \(-0.721616\pi\)
0.641327 0.767268i \(-0.278384\pi\)
\(620\) −0.353622 6.11525i −0.0142018 0.245594i
\(621\) −16.0706 + 13.9439i −0.644889 + 0.559549i
\(622\) −6.08212 6.08212i −0.243871 0.243871i
\(623\) 12.2705 + 12.2705i 0.491606 + 0.491606i
\(624\) 2.72950 9.30344i 0.109268 0.372436i
\(625\) 24.3357 5.72495i 0.973427 0.228998i
\(626\) 8.85247i 0.353816i
\(627\) 0.485629 0.265313i 0.0193942 0.0105956i
\(628\) −5.84460 + 5.84460i −0.233225 + 0.233225i
\(629\) −12.3095 −0.490814
\(630\) −11.5224 + 20.4553i −0.459063 + 0.814958i
\(631\) 37.8573 1.50707 0.753537 0.657405i \(-0.228346\pi\)
0.753537 + 0.657405i \(0.228346\pi\)
\(632\) 2.12434 2.12434i 0.0845018 0.0845018i
\(633\) 9.51601 5.19886i 0.378227 0.206636i
\(634\) 27.8717i 1.10693i
\(635\) −26.9739 24.0248i −1.07043 0.953396i
\(636\) 0.796945 2.71637i 0.0316009 0.107711i
\(637\) −20.7747 20.7747i −0.823124 0.823124i
\(638\) −1.94307 1.94307i −0.0769269 0.0769269i
\(639\) −34.8395 22.3682i −1.37823 0.884873i
\(640\) 1.66978 + 1.48722i 0.0660039 + 0.0587876i
\(641\) 43.9989i 1.73785i 0.494942 + 0.868926i \(0.335189\pi\)
−0.494942 + 0.868926i \(0.664811\pi\)
\(642\) −5.83609 10.6824i −0.230332 0.421601i
\(643\) −17.5175 + 17.5175i −0.690823 + 0.690823i −0.962413 0.271590i \(-0.912450\pi\)
0.271590 + 0.962413i \(0.412450\pi\)
\(644\) 14.3305 0.564702
\(645\) −7.98058 + 34.4539i −0.314235 + 1.35662i
\(646\) 6.09118 0.239654
\(647\) 11.7619 11.7619i 0.462407 0.462407i −0.437037 0.899444i \(-0.643972\pi\)
0.899444 + 0.437037i \(0.143972\pi\)
\(648\) 3.13772 8.43532i 0.123261 0.331371i
\(649\) 2.40003i 0.0942092i
\(650\) −3.22618 27.8022i −0.126541 1.09049i
\(651\) 15.9341 + 4.67484i 0.624505 + 0.183221i
\(652\) 9.68901 + 9.68901i 0.379451 + 0.379451i
\(653\) 4.52948 + 4.52948i 0.177252 + 0.177252i 0.790157 0.612905i \(-0.209999\pi\)
−0.612905 + 0.790157i \(0.709999\pi\)
\(654\) −20.0871 5.89329i −0.785468 0.230446i
\(655\) 0.403251 + 6.97348i 0.0157563 + 0.272476i
\(656\) 7.07028i 0.276048i
\(657\) 8.33643 + 38.2406i 0.325235 + 1.49191i
\(658\) −14.4356 + 14.4356i −0.562758 + 0.562758i
\(659\) −2.17251 −0.0846292 −0.0423146 0.999104i \(-0.513473\pi\)
−0.0423146 + 0.999104i \(0.513473\pi\)
\(660\) 1.04984 0.654957i 0.0408650 0.0254942i
\(661\) −13.3844 −0.520595 −0.260297 0.965529i \(-0.583821\pi\)
−0.260297 + 0.965529i \(0.583821\pi\)
\(662\) 12.5847 12.5847i 0.489119 0.489119i
\(663\) −28.3147 51.8273i −1.09965 2.01280i
\(664\) 3.27656i 0.127155i
\(665\) −5.20497 + 5.84388i −0.201840 + 0.226616i
\(666\) −3.27546 + 5.10167i −0.126921 + 0.197686i
\(667\) 24.9028 + 24.9028i 0.964241 + 0.964241i
\(668\) 9.29416 + 9.29416i 0.359602 + 0.359602i
\(669\) −5.66232 + 19.2999i −0.218918 + 0.746177i
\(670\) −35.2795 + 2.04009i −1.36297 + 0.0788154i
\(671\) 2.58644i 0.0998484i
\(672\) −5.31968 + 2.90629i −0.205211 + 0.112113i
\(673\) 5.79495 5.79495i 0.223379 0.223379i −0.586541 0.809920i \(-0.699511\pi\)
0.809920 + 0.586541i \(0.199511\pi\)
\(674\) 14.6670 0.564952
\(675\) −1.16322 25.9547i −0.0447723 0.998997i
\(676\) −18.3347 −0.705182
\(677\) 3.09214 3.09214i 0.118841 0.118841i −0.645185 0.764026i \(-0.723220\pi\)
0.764026 + 0.645185i \(0.223220\pi\)
\(678\) 10.8960 5.95278i 0.418458 0.228615i
\(679\) 10.9741i 0.421146i
\(680\) 13.5976 0.786298i 0.521443 0.0301531i
\(681\) 2.51210 8.56242i 0.0962638 0.328113i
\(682\) −0.618871 0.618871i −0.0236978 0.0236978i
\(683\) 28.9452 + 28.9452i 1.10756 + 1.10756i 0.993471 + 0.114089i \(0.0363947\pi\)
0.114089 + 0.993471i \(0.463605\pi\)
\(684\) 1.62081 2.52448i 0.0619731 0.0965258i
\(685\) 9.30513 10.4473i 0.355531 0.399173i
\(686\) 6.12979i 0.234037i
\(687\) −18.0729 33.0807i −0.689525 1.26211i
\(688\) −6.45694 + 6.45694i −0.246169 + 0.246169i
\(689\) −9.14894 −0.348547
\(690\) −13.4550 + 8.39407i −0.512222 + 0.319557i
\(691\) 14.2335 0.541468 0.270734 0.962654i \(-0.412734\pi\)
0.270734 + 0.962654i \(0.412734\pi\)
\(692\) −4.33021 + 4.33021i −0.164610 + 0.164610i
\(693\) 0.714493 + 3.27749i 0.0271413 + 0.124502i
\(694\) 7.85439i 0.298149i
\(695\) −1.75618 30.3699i −0.0666157 1.15200i
\(696\) −14.2946 4.19385i −0.541837 0.158968i
\(697\) 30.4525 + 30.4525i 1.15347 + 1.15347i
\(698\) −7.26629 7.26629i −0.275033 0.275033i
\(699\) −8.88739 2.60744i −0.336152 0.0986224i
\(700\) −10.8649 + 13.7174i −0.410654 + 0.518470i
\(701\) 32.5972i 1.23118i −0.788067 0.615589i \(-0.788918\pi\)
0.788067 0.615589i \(-0.211082\pi\)
\(702\) −29.0140 2.05579i −1.09506 0.0775906i
\(703\) −1.42898 + 1.42898i −0.0538949 + 0.0538949i
\(704\) 0.319493 0.0120413
\(705\) 5.09801 22.0092i 0.192002 0.828916i
\(706\) −7.20671 −0.271228
\(707\) −16.7568 + 16.7568i −0.630204 + 0.630204i
\(708\) −6.23810 11.4182i −0.234442 0.429123i
\(709\) 15.6457i 0.587587i 0.955869 + 0.293794i \(0.0949178\pi\)
−0.955869 + 0.293794i \(0.905082\pi\)
\(710\) −23.0441 20.5247i −0.864830 0.770277i
\(711\) −7.58422 4.86934i −0.284430 0.182615i
\(712\) −3.50606 3.50606i −0.131395 0.131395i
\(713\) 7.93158 + 7.93158i 0.297040 + 0.297040i
\(714\) −10.3947 + 35.4302i −0.389014 + 1.32594i
\(715\) −2.98630 2.65981i −0.111681 0.0994711i
\(716\) 8.41749i 0.314576i
\(717\) 21.6712 11.8396i 0.809324 0.442157i
\(718\) 25.0886 25.0886i 0.936297 0.936297i
\(719\) 11.4282 0.426200 0.213100 0.977030i \(-0.431644\pi\)
0.213100 + 0.977030i \(0.431644\pi\)
\(720\) 3.29231 5.84472i 0.122697 0.217820i
\(721\) −35.3425 −1.31622
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −46.0648 + 25.1665i −1.71317 + 0.935953i
\(724\) 4.04233i 0.150232i
\(725\) −42.7177 + 4.95699i −1.58650 + 0.184098i
\(726\) −5.31391 + 18.1123i −0.197218 + 0.672212i
\(727\) −22.6001 22.6001i −0.838192 0.838192i 0.150429 0.988621i \(-0.451935\pi\)
−0.988621 + 0.150429i \(0.951935\pi\)
\(728\) 13.8529 + 13.8529i 0.513422 + 0.513422i
\(729\) −26.7303 3.80706i −0.990009 0.141002i
\(730\) 1.68411 + 29.1236i 0.0623317 + 1.07791i
\(731\) 55.6216i 2.05724i
\(732\) −6.72263 12.3051i −0.248475 0.454810i
\(733\) 31.3451 31.3451i 1.15776 1.15776i 0.172801 0.984957i \(-0.444718\pi\)
0.984957 0.172801i \(-0.0552819\pi\)
\(734\) 4.83923 0.178619
\(735\) −10.7594 17.2464i −0.396868 0.636145i
\(736\) −4.09469 −0.150932
\(737\) −3.57033 + 3.57033i −0.131515 + 0.131515i
\(738\) 20.7241 4.51785i 0.762865 0.166304i
\(739\) 43.9564i 1.61696i 0.588523 + 0.808481i \(0.299710\pi\)
−0.588523 + 0.808481i \(0.700290\pi\)
\(740\) −3.00550 + 3.37443i −0.110484 + 0.124046i
\(741\) −9.30344 2.72950i −0.341770 0.100271i
\(742\) 4.04469 + 4.04469i 0.148485 + 0.148485i
\(743\) −17.5022 17.5022i −0.642094 0.642094i 0.308976 0.951070i \(-0.400014\pi\)
−0.951070 + 0.308976i \(0.900014\pi\)
\(744\) −4.55286 1.33575i −0.166916 0.0489709i
\(745\) −34.5548 + 1.99817i −1.26599 + 0.0732075i
\(746\) 4.29019i 0.157075i
\(747\) 9.60412 2.09370i 0.351396 0.0766043i
\(748\) 1.37609 1.37609i 0.0503149 0.0503149i
\(749\) 24.5961 0.898723
\(750\) 2.16612 19.2434i 0.0790954 0.702669i
\(751\) −1.27690 −0.0465948 −0.0232974 0.999729i \(-0.507416\pi\)
−0.0232974 + 0.999729i \(0.507416\pi\)
\(752\) 4.12471 4.12471i 0.150413 0.150413i
\(753\) 21.6743 + 39.6726i 0.789854 + 1.44575i
\(754\) 48.1455i 1.75336i
\(755\) 30.0906 1.74003i 1.09511 0.0633261i
\(756\) 11.9180 + 13.7357i 0.433455 + 0.499564i
\(757\) 31.4744 + 31.4744i 1.14396 + 1.14396i 0.987720 + 0.156236i \(0.0499360\pi\)
0.156236 + 0.987720i \(0.450064\pi\)
\(758\) 13.6525 + 13.6525i 0.495882 + 0.495882i
\(759\) −0.637899 + 2.17426i −0.0231543 + 0.0789208i
\(760\) 1.48722 1.66978i 0.0539472 0.0605693i
\(761\) 35.4794i 1.28613i 0.765813 + 0.643063i \(0.222337\pi\)
−0.765813 + 0.643063i \(0.777663\pi\)
\(762\) −24.5543 + 13.4147i −0.889509 + 0.485964i
\(763\) 29.9098 29.9098i 1.08281 1.08281i
\(764\) −12.7401 −0.460921
\(765\) −10.9935 39.3542i −0.397471 1.42285i
\(766\) −18.3830 −0.664204
\(767\) −29.7340 + 29.7340i −1.07363 + 1.07363i
\(768\) 1.52000 0.830420i 0.0548483 0.0299652i
\(769\) 32.3859i 1.16786i −0.811803 0.583932i \(-0.801513\pi\)
0.811803 0.583932i \(-0.198487\pi\)
\(770\) 0.144341 + 2.49610i 0.00520167 + 0.0899534i
\(771\) 7.42014 25.2913i 0.267230 0.910845i
\(772\) −0.0511200 0.0511200i −0.00183985 0.00183985i
\(773\) 34.7488 + 34.7488i 1.24983 + 1.24983i 0.955796 + 0.294032i \(0.0949971\pi\)
0.294032 + 0.955796i \(0.405003\pi\)
\(774\) 23.0523 + 14.8004i 0.828596 + 0.531989i
\(775\) −13.6057 + 1.57881i −0.488730 + 0.0567125i
\(776\) 3.13564i 0.112563i
\(777\) −5.87327 10.7504i −0.210702 0.385670i
\(778\)