Properties

Label 570.2.k.a.77.14
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 77.14
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.830420 - 1.52000i) q^{3} -1.00000i q^{4} +(2.23234 - 0.129088i) q^{5} +(-0.487608 - 1.66200i) q^{6} +(-2.47472 - 2.47472i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.62081 - 2.52448i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.830420 - 1.52000i) 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} +(-1.52000 - 0.830420i) q^{12} +(-3.95820 + 3.95820i) q^{13} -3.49979 q^{14} +(1.65756 - 3.50035i) q^{15} -1.00000 q^{16} +(4.30711 - 4.30711i) q^{17} +(-2.93116 - 0.638992i) 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} +(-5.18316 + 0.367253i) q^{27} +(-2.47472 + 2.47472i) q^{28} +8.60087 q^{29} +(-1.30305 - 3.64720i) q^{30} -2.73939 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.485629 + 0.265313i) 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} +(-2.90629 + 5.31968i) q^{42} +(6.45694 - 6.45694i) q^{43} +0.319493 q^{44} +(-3.94407 - 5.42626i) q^{45} +4.09469 q^{46} +(4.12471 - 4.12471i) q^{47} +(-0.830420 + 1.52000i) 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} +(1.52000 + 0.830420i) q^{57} +(6.08174 - 6.08174i) q^{58} -7.51199 q^{59} +(-3.50035 - 1.65756i) q^{60} +8.09546 q^{61} +(-1.93704 + 1.93704i) q^{62} +(-2.23634 + 10.2584i) 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} +(-0.638992 + 2.93116i) q^{72} +(-9.22508 + 9.22508i) q^{73} +2.02088 q^{74} +(3.24839 - 8.02795i) q^{75} +1.00000 q^{76} +(0.790656 - 0.790656i) q^{77} +(8.50858 + 4.64848i) 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} +(7.14233 - 13.0733i) q^{87} +(0.225915 - 0.225915i) q^{88} +4.95832 q^{89} +(-6.62582 - 1.04807i) q^{90} +19.5909 q^{91} +(2.89538 - 2.89538i) q^{92} +(-2.27484 + 4.16388i) 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
\(3\) 0.830420 1.52000i 0.479443 0.877573i
\(4\) 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 \(0.0153374\pi\)
−0.998839 + 0.0481653i \(0.984663\pi\)
\(12\) −1.52000 0.830420i −0.438787 0.239721i
\(13\) −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
\(15\) 1.65756 3.50035i 0.427981 0.903788i
\(16\) −1.00000 −0.250000
\(17\) 4.30711 4.30711i 1.04463 1.04463i 0.0456719 0.998956i \(-0.485457\pi\)
0.998956 0.0456719i \(-0.0145429\pi\)
\(18\) −2.93116 0.638992i −0.690881 0.150612i
\(19\) 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 0.941300 0.337571i \(-0.109605\pi\)
−0.337571 + 0.941300i \(0.609605\pi\)
\(24\) −1.66200 + 0.487608i −0.339254 + 0.0995325i
\(25\) 4.96667 0.576336i 0.993335 0.115267i
\(26\) 5.59774i 1.09781i
\(27\) −5.18316 + 0.367253i −0.997499 + 0.0706778i
\(28\) −2.47472 + 2.47472i −0.467679 + 0.467679i
\(29\) 8.60087 1.59714 0.798571 0.601900i \(-0.205590\pi\)
0.798571 + 0.601900i \(0.205590\pi\)
\(30\) −1.30305 3.64720i −0.237903 0.665884i
\(31\) −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
\(33\) 0.485629 + 0.265313i 0.0845372 + 0.0461850i
\(34\) 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 \(0.186172\pi\)
−0.833780 + 0.552096i \(0.813828\pi\)
\(42\) −2.90629 + 5.31968i −0.448451 + 0.820845i
\(43\) 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
\(45\) −3.94407 5.42626i −0.587947 0.808899i
\(46\) 4.09469 0.603729
\(47\) 4.12471 4.12471i 0.601650 0.601650i −0.339100 0.940750i \(-0.610123\pi\)
0.940750 + 0.339100i \(0.110123\pi\)
\(48\) −0.830420 + 1.52000i −0.119861 + 0.219393i
\(49\) 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 0.623264 0.782011i \(-0.285806\pi\)
−0.782011 + 0.623264i \(0.785806\pi\)
\(54\) −3.40536 + 3.92473i −0.463411 + 0.534088i
\(55\) 0.0412426 + 0.713216i 0.00556116 + 0.0961700i
\(56\) 3.49979i 0.467679i
\(57\) 1.52000 + 0.830420i 0.201329 + 0.109992i
\(58\) 6.08174 6.08174i 0.798571 0.798571i
\(59\) −7.51199 −0.977978 −0.488989 0.872290i \(-0.662634\pi\)
−0.488989 + 0.872290i \(0.662634\pi\)
\(60\) −3.50035 1.65756i −0.451894 0.213991i
\(61\) 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
\(63\) −2.23634 + 10.2584i −0.281752 + 1.29244i
\(64\) 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 \(0.305426\pi\)
−0.573909 + 0.818919i \(0.694574\pi\)
\(72\) −0.638992 + 2.93116i −0.0753059 + 0.345440i
\(73\) −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
\(75\) 3.24839 8.02795i 0.375092 0.926988i
\(76\) 1.00000 0.114708
\(77\) 0.790656 0.790656i 0.0901036 0.0901036i
\(78\) 8.50858 + 4.64848i 0.963407 + 0.526336i
\(79\) 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 0.568425 0.822735i \(-0.307553\pi\)
−0.822735 + 0.568425i \(0.807553\pi\)
\(84\) 1.70652 + 5.81664i 0.186197 + 0.634648i
\(85\) 9.05894 10.1709i 0.982580 1.10319i
\(86\) 9.13149i 0.984674i
\(87\) 7.14233 13.0733i 0.765739 1.40161i
\(88\) 0.225915 0.225915i 0.0240827 0.0240827i
\(89\) 4.95832 0.525580 0.262790 0.964853i \(-0.415357\pi\)
0.262790 + 0.964853i \(0.415357\pi\)
\(90\) −6.62582 1.04807i −0.698423 0.110476i
\(91\) 19.5909 2.05369
\(92\) 2.89538 2.89538i 0.301864 0.301864i
\(93\) −2.27484 + 4.16388i −0.235890 + 0.431774i
\(94\) 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 \(0.109371\pi\)
−0.941548 + 0.336878i \(0.890629\pi\)
\(102\) −9.25860 5.05823i −0.916738 0.500840i
\(103\) 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
\(105\) −12.7644 + 4.56040i −1.24568 + 0.445049i
\(106\) −1.63440 −0.158747
\(107\) 4.96947 4.96947i 0.480416 0.480416i −0.424848 0.905265i \(-0.639673\pi\)
0.905265 + 0.424848i \(0.139673\pi\)
\(108\) 0.367253 + 5.18316i 0.0353389 + 0.498750i
\(109\) 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 0.904118 0.427283i \(-0.140529\pi\)
−0.427283 + 0.904118i \(0.640529\pi\)
\(114\) 1.66200 0.487608i 0.155660 0.0456687i
\(115\) 6.83723 + 6.08971i 0.637575 + 0.567869i
\(116\) 8.60087i 0.798571i
\(117\) 16.4079 + 3.57691i 1.51691 + 0.330686i
\(118\) −5.31178 + 5.31178i −0.488989 + 0.488989i
\(119\) −21.3178 −1.95420
\(120\) −3.64720 + 1.30305i −0.332942 + 0.118952i
\(121\) 10.8979 0.990720
\(122\) 5.72435 5.72435i 0.518259 0.518259i
\(123\) 10.7468 + 5.87130i 0.969010 + 0.529397i
\(124\) 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 \(0.0435744\pi\)
−0.990645 + 0.136466i \(0.956426\pi\)
\(132\) 0.265313 0.485629i 0.0230925 0.0422686i
\(133\) 2.47472 2.47472i 0.214586 0.214586i
\(134\) −15.8038 −1.36524
\(135\) −11.5232 + 1.48892i −0.991755 + 0.128145i
\(136\) −6.09118 −0.522314
\(137\) 4.42417 4.42417i 0.377982 0.377982i −0.492392 0.870374i \(-0.663877\pi\)
0.870374 + 0.492392i \(0.163877\pi\)
\(138\) 3.40031 6.22393i 0.289453 0.529816i
\(139\) 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
\(147\) 7.97776 + 4.35848i 0.657995 + 0.359481i
\(148\) 1.42898 1.42898i 0.117461 0.117461i
\(149\) −15.4792 −1.26810 −0.634052 0.773291i \(-0.718609\pi\)
−0.634052 + 0.773291i \(0.718609\pi\)
\(150\) −3.37966 7.97358i −0.275948 0.651040i
\(151\) −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
\(153\) −17.8542 3.89221i −1.44343 0.314667i
\(154\) 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
\(162\) 3.13772 + 8.43532i 0.246523 + 0.662742i
\(163\) −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
\(165\) 1.11834 + 0.529579i 0.0870624 + 0.0412277i
\(166\) −3.27656 −0.254311
\(167\) 9.29416 9.29416i 0.719204 0.719204i −0.249239 0.968442i \(-0.580180\pi\)
0.968442 + 0.249239i \(0.0801803\pi\)
\(168\) 5.31968 + 2.90629i 0.410422 + 0.224225i
\(169\) 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 0.852290 0.523070i \(-0.175213\pi\)
−0.523070 + 0.852290i \(0.675213\pi\)
\(174\) −4.19385 14.2946i −0.317935 1.08367i
\(175\) −13.7174 10.8649i −1.03694 0.821307i
\(176\) 0.319493i 0.0240827i
\(177\) −6.23810 + 11.4182i −0.468885 + 0.858247i
\(178\) 3.50606 3.50606i 0.262790 0.262790i
\(179\) −8.41749 −0.629153 −0.314576 0.949232i \(-0.601862\pi\)
−0.314576 + 0.949232i \(0.601862\pi\)
\(180\) −5.42626 + 3.94407i −0.404450 + 0.293974i
\(181\) −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
\(183\) 6.72263 12.3051i 0.496951 0.909619i
\(184\) 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 \(0.152481\pi\)
−0.887441 + 0.460921i \(0.847519\pi\)
\(192\) 1.52000 + 0.830420i 0.109697 + 0.0599304i
\(193\) 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
\(195\) 7.29414 + 20.4161i 0.522344 + 1.46203i
\(196\) 5.24852 0.374895
\(197\) −13.8117 + 13.8117i −0.984041 + 0.984041i −0.999875 0.0158340i \(-0.994960\pi\)
0.0158340 + 0.999875i \(0.494960\pi\)
\(198\) 0.204153 0.936483i 0.0145085 0.0665530i
\(199\) 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
\(207\) 2.61647 12.0022i 0.181857 0.834209i
\(208\) 3.95820 3.95820i 0.274452 0.274452i
\(209\) −0.319493 −0.0220998
\(210\) −5.80112 + 12.2505i −0.400316 + 0.845365i
\(211\) 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
\(213\) 20.9770 + 11.4603i 1.43732 + 0.785250i
\(214\) 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
\(222\) 1.67818 3.07174i 0.112632 0.206162i
\(223\) −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
\(225\) −9.50496 11.6041i −0.633664 0.773608i
\(226\) 7.16840 0.476835
\(227\) −3.64293 + 3.64293i −0.241790 + 0.241790i −0.817590 0.575800i \(-0.804691\pi\)
0.575800 + 0.817590i \(0.304691\pi\)
\(228\) 0.830420 1.52000i 0.0549959 0.100665i
\(229\) 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 0.820032 0.572318i \(-0.193956\pi\)
−0.572318 + 0.820032i \(0.693956\pi\)
\(234\) 14.1314 9.07286i 0.923797 0.593111i
\(235\) 8.67529 9.74019i 0.565914 0.635380i
\(236\) 7.51199i 0.488989i
\(237\) −4.56650 2.49481i −0.296626 0.162055i
\(238\) −15.0740 + 15.0740i −0.977102 + 0.977102i
\(239\) −14.2573 −0.922230 −0.461115 0.887340i \(-0.652550\pi\)
−0.461115 + 0.887340i \(0.652550\pi\)
\(240\) −1.65756 + 3.50035i −0.106995 + 0.225947i
\(241\) −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
\(243\) 9.32802 + 12.4895i 0.598393 + 0.801203i
\(244\) 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 \(-0.691895\pi\)
0.566996 0.823720i \(-0.308105\pi\)
\(252\) 10.2584 + 2.23634i 0.646221 + 0.140876i
\(253\) −0.925053 + 0.925053i −0.0581576 + 0.0581576i
\(254\) 16.1541 1.01360
\(255\) −7.93711 22.2157i −0.497041 1.39120i
\(256\) 1.00000 0.0625000
\(257\) −10.7603 + 10.7603i −0.671212 + 0.671212i −0.957995 0.286783i \(-0.907414\pi\)
0.286783 + 0.957995i \(0.407414\pi\)
\(258\) −13.8799 7.58297i −0.864124 0.472095i
\(259\) 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 0.441253 0.897383i \(-0.354534\pi\)
−0.897383 + 0.441253i \(0.854534\pi\)
\(264\) −0.155787 0.530996i −0.00958803 0.0326806i
\(265\) −2.72909 2.43071i −0.167646 0.149318i
\(266\) 3.49979i 0.214586i
\(267\) 4.11748 7.53664i 0.251986 0.461235i
\(268\) −11.1750 + 11.1750i −0.682622 + 0.682622i
\(269\) −12.5829 −0.767193 −0.383596 0.923501i \(-0.625315\pi\)
−0.383596 + 0.923501i \(0.625315\pi\)
\(270\) −7.09528 + 9.20092i −0.431805 + 0.559950i
\(271\) 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
\(273\) 16.2687 29.7782i 0.984626 1.80226i
\(274\) 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 \(0.182409\pi\)
−0.840249 + 0.542200i \(0.817591\pi\)
\(282\) −8.86649 4.84402i −0.527992 0.288457i
\(283\) 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
\(285\) 3.50035 + 1.65756i 0.207343 + 0.0981856i
\(286\) −1.78844 −0.105753
\(287\) 17.4970 17.4970i 1.03282 1.03282i
\(288\) 2.93116 + 0.638992i 0.172720 + 0.0376529i
\(289\) 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 \(0.0435094\pi\)
0.136264 + 0.990673i \(0.456491\pi\)
\(294\) 8.72304 2.55922i 0.508738 0.149257i
\(295\) −16.7693 + 0.969707i −0.976347 + 0.0564585i
\(296\) 2.02088i 0.117461i
\(297\) −0.117334 1.65598i −0.00680844 0.0960897i
\(298\) −10.9454 + 10.9454i −0.634052 + 0.634052i
\(299\) −22.9210 −1.32556
\(300\) −8.02795 3.24839i −0.463494 0.187546i
\(301\) −31.9583 −1.84205
\(302\) −9.53138 + 9.53138i −0.548469 + 0.548469i
\(303\) 10.2922 + 5.62291i 0.591271 + 0.323028i
\(304\) 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 \(-0.921583\pi\)
0.969808 0.243871i \(-0.0784173\pi\)
\(312\) 4.64848 8.50858i 0.263168 0.481703i
\(313\) −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
\(315\) −3.66802 + 23.1890i −0.206669 + 1.30655i
\(316\) −3.00427 −0.169004
\(317\) 19.7083 19.7083i 1.10693 1.10693i 0.113376 0.993552i \(-0.463834\pi\)
0.993552 0.113376i \(-0.0361664\pi\)
\(318\) −1.35724 + 2.48429i −0.0761100 + 0.139312i
\(319\) 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
\(327\) 18.3709 + 10.0366i 1.01591 + 0.555023i
\(328\) 4.99944 4.99944i 0.276048 0.276048i
\(329\) −20.4150 −1.12552
\(330\) 1.16525 0.416315i 0.0641451 0.0229174i
\(331\) −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
\(333\) 1.29133 5.92352i 0.0707642 0.324607i
\(334\) 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
\(342\) 0.638992 2.93116i 0.0345527 0.158499i
\(343\) −4.33442 + 4.33442i −0.234037 + 0.234037i
\(344\) −9.13149 −0.492337
\(345\) 14.9341 5.33558i 0.804027 0.287258i
\(346\) 6.12384 0.329220
\(347\) 5.55389 5.55389i 0.298149 0.298149i −0.542140 0.840288i \(-0.682386\pi\)
0.840288 + 0.542140i \(0.182386\pi\)
\(348\) −13.0733 7.14233i −0.700805 0.382869i
\(349\) 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 0.558366 0.829594i \(-0.311428\pi\)
−0.829594 + 0.558366i \(0.811428\pi\)
\(354\) 3.66290 + 12.4849i 0.194681 + 0.663566i
\(355\) 1.78150 + 30.8078i 0.0945522 + 1.63511i
\(356\) 4.95832i 0.262790i
\(357\) −17.7028 + 32.4031i −0.936929 + 1.71496i
\(358\) −5.95206 + 5.95206i −0.314576 + 0.314576i
\(359\) 35.4806 1.87259 0.936297 0.351208i \(-0.114229\pi\)
0.936297 + 0.351208i \(0.114229\pi\)
\(360\) −1.04807 + 6.62582i −0.0552381 + 0.349212i
\(361\) −1.00000 −0.0526316
\(362\) −2.85836 + 2.85836i −0.150232 + 0.150232i
\(363\) 9.04985 16.5649i 0.474994 0.869430i
\(364\) 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
\(372\) 4.16388 + 2.27484i 0.215887 + 0.117945i
\(373\) 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
\(375\) 6.21520 18.3404i 0.320951 0.947096i
\(376\) −5.83322 −0.300825
\(377\) −34.0440 + 34.0440i −1.75336 + 1.75336i
\(378\) 18.1400 1.28531i 0.933019 0.0661090i
\(379\) 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 0.292164 0.956368i \(-0.405625\pi\)
−0.956368 + 0.292164i \(0.905625\pi\)
\(384\) 1.66200 0.487608i 0.0848135 0.0248831i
\(385\) 1.66295 1.86708i 0.0847517 0.0951550i
\(386\) 0.0722945i 0.00367970i
\(387\) −26.7659 5.83495i −1.36058 0.296607i
\(388\) −2.21723 + 2.21723i −0.112563 + 0.112563i
\(389\) −10.3234 −0.523419 −0.261709 0.965147i \(-0.584286\pi\)
−0.261709 + 0.965147i \(0.584286\pi\)
\(390\) 19.5941 + 9.27862i 0.992185 + 0.469841i
\(391\) 24.9415 1.26134
\(392\) 3.71127 3.71127i 0.187447 0.187447i
\(393\) 4.74825 + 2.59410i 0.239517 + 0.130855i
\(394\) 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 \(-0.851750\pi\)
0.893489 0.449086i \(-0.148250\pi\)
\(402\) −13.1238 + 24.0219i −0.654557 + 1.19810i
\(403\) 10.8431 10.8431i 0.540131 0.540131i
\(404\) 6.77117 0.336878
\(405\) −7.30590 + 18.7516i −0.363033 + 0.931776i
\(406\) −30.1012 −1.49390
\(407\) −0.456548 + 0.456548i −0.0226302 + 0.0226302i
\(408\) −5.05823 + 9.25860i −0.250420 + 0.458369i
\(409\) 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
\(417\) 20.6789 + 11.2975i 1.01265 + 0.553239i
\(418\) −0.225915 + 0.225915i −0.0110499 + 0.0110499i
\(419\) 1.37511 0.0671786 0.0335893 0.999436i \(-0.489306\pi\)
0.0335893 + 0.999436i \(0.489306\pi\)
\(420\) 4.56040 + 12.7644i 0.222525 + 0.622840i
\(421\) −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
\(423\) −17.0981 3.72738i −0.831337 0.181231i
\(424\) 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 \(-0.982372\pi\)
0.998467 0.0553512i \(-0.0176278\pi\)
\(432\) 5.18316 0.367253i 0.249375 0.0176694i
\(433\) −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
\(435\) 14.2565 30.1061i 0.683547 1.44348i
\(436\) 12.0861 0.578820
\(437\) −2.89538 + 2.89538i −0.138505 + 0.138505i
\(438\) 19.8303 + 10.8338i 0.947527 + 0.517661i
\(439\) 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 0.726605 0.687055i \(-0.241097\pi\)
−0.687055 + 0.726605i \(0.741097\pi\)
\(444\) −0.985397 3.35870i −0.0467649 0.159397i
\(445\) 11.0686 0.640059i 0.524704 0.0303417i
\(446\) 11.6125i 0.549866i
\(447\) −12.8542 + 23.5284i −0.607983 + 1.11285i
\(448\) 2.47472 2.47472i 0.116920 0.116920i
\(449\) 30.6819 1.44797 0.723984 0.689817i \(-0.242309\pi\)
0.723984 + 0.689817i \(0.242309\pi\)
\(450\) −14.9264 1.48433i −0.703636 0.0699720i
\(451\) −2.25890 −0.106368
\(452\) 5.06883 5.06883i 0.238418 0.238418i
\(453\) −11.1936 + 20.4887i −0.525919 + 0.962643i
\(454\) 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 \(0.0513408\pi\)
−0.987021 + 0.160593i \(0.948659\pi\)
\(462\) −1.69960 0.928539i −0.0790725 0.0431996i
\(463\) 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
\(465\) −4.54072 + 9.58884i −0.210571 + 0.444672i
\(466\) 5.34741 0.247714
\(467\) −26.3961 + 26.3961i −1.22147 + 1.22147i −0.254355 + 0.967111i \(0.581863\pi\)
−0.967111 + 0.254355i \(0.918137\pi\)
\(468\) 3.57691 16.4079i 0.165343 0.758454i
\(469\) 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
\(477\) −1.04437 + 4.79068i −0.0478183 + 0.219350i
\(478\) −10.0815 + 10.0815i −0.461115 + 0.461115i
\(479\) 17.9400 0.819700 0.409850 0.912153i \(-0.365581\pi\)
0.409850 + 0.912153i \(0.365581\pi\)
\(480\) 1.30305 + 3.64720i 0.0594758 + 0.166471i
\(481\) −11.3124 −0.515800
\(482\) −21.4294 + 21.4294i −0.976084 + 0.976084i
\(483\) −21.7824 11.9004i −0.991135 0.541485i
\(484\) 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 \(0.0133506\pi\)
−0.999121 + 0.0419298i \(0.986649\pi\)
\(492\) 5.87130 10.7468i 0.264699 0.484505i
\(493\) 37.0449 37.0449i 1.66842 1.66842i
\(494\) −5.59774 −0.251854
\(495\) 1.73365 1.26010i 0.0779218 0.0566373i
\(496\) 2.73939 0.123002
\(497\) 34.1529 34.1529i 1.53197 1.53197i
\(498\) −2.72092 + 4.98038i −0.121927 + 0.223176i
\(499\) 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 \(0.0401579\pi\)
0.125825 + 0.992052i \(0.459842\pi\)
\(504\) 8.83514 5.67248i 0.393548 0.252672i
\(505\) 0.874077 + 15.1156i 0.0388959 + 0.672633i
\(506\) 1.30822i 0.0581576i
\(507\) −27.8688 15.2255i −1.23770 0.676189i
\(508\) 11.4227 11.4227i 0.506801 0.506801i
\(509\) 30.4865 1.35129 0.675644 0.737228i \(-0.263866\pi\)
0.675644 + 0.737228i \(0.263866\pi\)
\(510\) −21.3213 10.0965i −0.944122 0.447081i
\(511\) 45.6590 2.01984
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −0.367253 5.18316i −0.0162146 0.228842i
\(514\) 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 \(0.0743729\pi\)
−0.972828 + 0.231529i \(0.925627\pi\)
\(522\) −25.2105 5.49589i −1.10343 0.240548i
\(523\) −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
\(525\) −27.9058 + 11.8281i −1.21791 + 0.516220i
\(526\) −10.4612 −0.456129
\(527\) −11.7989 + 11.7989i −0.513967 + 0.513967i
\(528\) −0.485629 0.265313i −0.0211343 0.0115463i
\(529\) 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
\(537\) −6.99005 + 12.7946i −0.301643 + 0.552127i
\(538\) −8.89745 + 8.89745i −0.383596 + 0.383596i
\(539\) −1.67686 −0.0722277
\(540\) 1.48892 + 11.5232i 0.0640727 + 0.495878i
\(541\) 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
\(543\) −3.35683 + 6.14435i −0.144055 + 0.263679i
\(544\) 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
\(552\) −6.22393 3.40031i −0.264908 0.144727i
\(553\) −7.43475 + 7.43475i −0.316158 + 0.316158i
\(554\) −12.6813 −0.538777
\(555\) 7.37055 2.63331i 0.312863 0.111778i
\(556\) 13.6045 0.576960
\(557\) 10.8415 10.8415i 0.459369 0.459369i −0.439079 0.898448i \(-0.644695\pi\)
0.898448 + 0.439079i \(0.144695\pi\)
\(558\) 8.02959 + 1.75045i 0.339920 + 0.0741024i
\(559\) 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 0.206478 0.978451i \(-0.433800\pi\)
−0.978451 + 0.206478i \(0.933800\pi\)
\(564\) −9.69479 + 2.84432i −0.408225 + 0.119768i
\(565\) 11.9697 + 10.6610i 0.503567 + 0.448512i
\(566\) 20.0164i 0.841353i
\(567\) 29.5219 10.9814i 1.23980 0.461174i
\(568\) 9.75855 9.75855i 0.409460 0.409460i
\(569\) 5.23426 0.219432 0.109716 0.993963i \(-0.465006\pi\)
0.109716 + 0.993963i \(0.465006\pi\)
\(570\) 3.64720 1.30305i 0.152764 0.0545787i
\(571\) −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
\(573\) 19.3650 + 10.5796i 0.808983 + 0.441970i
\(574\) 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
\(582\) −2.60389 + 4.76617i −0.107935 + 0.197564i
\(583\) 0.369236 0.369236i 0.0152922 0.0152922i
\(584\) 13.0462 0.539857
\(585\) 37.0897 + 5.86682i 1.53347 + 0.242563i
\(586\) 27.2802 1.12694
\(587\) −22.7297 + 22.7297i −0.938154 + 0.938154i −0.998196 0.0600421i \(-0.980877\pi\)
0.0600421 + 0.998196i \(0.480877\pi\)
\(588\) 4.35848 7.97776i 0.179741 0.328997i
\(589\) 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 \(-0.884880\pi\)
−0.353828 0.935311i \(-0.615120\pi\)
\(594\) −1.25392 1.08799i −0.0514491 0.0446407i
\(595\) −47.5886 + 2.75188i −1.95094 + 0.112816i
\(596\) 15.4792i 0.634052i
\(597\) 15.7111 + 8.58344i 0.643014 + 0.351297i
\(598\) −16.2076 + 16.2076i −0.662778 + 0.662778i
\(599\) 27.0824 1.10656 0.553278 0.832997i \(-0.313377\pi\)
0.553278 + 0.832997i \(0.313377\pi\)
\(600\) −7.97358 + 3.37966i −0.325520 + 0.137974i
\(601\) 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
\(603\) −10.0985 + 46.3236i −0.411244 + 1.88644i
\(604\) 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
\(612\) −3.89221 + 17.8542i −0.157333 + 0.721714i
\(613\) 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
\(615\) 24.7485 + 11.7194i 0.997956 + 0.472574i
\(616\) −1.11816 −0.0450518
\(617\) 1.14572 1.14572i 0.0461251 0.0461251i −0.683668 0.729793i \(-0.739616\pi\)
0.729793 + 0.683668i \(0.239616\pi\)
\(618\) −15.3497 8.38596i −0.617454 0.337333i
\(619\) 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
\(627\) −0.265313 + 0.485629i −0.0105956 + 0.0193942i
\(628\) −5.84460 + 5.84460i −0.233225 + 0.233225i
\(629\) 12.3095 0.490814
\(630\) 13.8034 + 18.9908i 0.549941 + 0.756611i
\(631\) 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
\(633\) 5.19886 9.51601i 0.206636 0.378227i
\(634\) 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 \(-0.664811\pi\)
0.494942 0.868926i \(-0.335189\pi\)
\(642\) −10.6824 5.83609i −0.421601 0.230332i
\(643\) −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
\(645\) −11.8988 33.3044i −0.468514 1.31136i
\(646\) 6.09118 0.239654
\(647\) −11.7619 + 11.7619i −0.462407 + 0.462407i −0.899444 0.437037i \(-0.856028\pi\)
0.437037 + 0.899444i \(0.356028\pi\)
\(648\) 8.43532 3.13772i 0.331371 0.123261i
\(649\) 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 0.612905 0.790157i \(-0.290001\pi\)
−0.790157 + 0.612905i \(0.790001\pi\)
\(654\) 20.0871 5.89329i 0.785468 0.230446i
\(655\) 0.403251 + 6.97348i 0.0157563 + 0.272476i
\(656\) 7.07028i 0.276048i
\(657\) 38.2406 + 8.33643i 1.49191 + 0.325235i
\(658\) −14.4356 + 14.4356i −0.562758 + 0.562758i
\(659\) 2.17251 0.0846292 0.0423146 0.999104i \(-0.486527\pi\)
0.0423146 + 0.999104i \(0.486527\pi\)
\(660\) 0.529579 1.11834i 0.0206139 0.0435312i
\(661\) −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
\(663\) 51.8273 + 28.3147i 2.01280 + 1.09965i
\(664\) 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
\(672\) 2.90629 5.31968i 0.112113 0.205211i
\(673\) 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
\(675\) −25.5314 + 4.81126i −0.982704 + 0.185186i
\(676\) −18.3347 −0.705182
\(677\) −3.09214 + 3.09214i −0.118841 + 0.118841i −0.764026 0.645185i \(-0.776780\pi\)
0.645185 + 0.764026i \(0.276780\pi\)
\(678\) 5.95278 10.8960i 0.228615 0.418458i
\(679\) 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 \(-0.963605\pi\)
−0.114089 0.993471i \(-0.536395\pi\)
\(684\) −1.62081 2.52448i −0.0619731 0.0965258i
\(685\) 9.30513 10.4473i 0.355531 0.399173i
\(686\) 6.12979i 0.234037i
\(687\) −33.0807 18.0729i −1.26211 0.689525i
\(688\) −6.45694 + 6.45694i −0.246169 + 0.246169i
\(689\) 9.14894 0.348547
\(690\) 6.78721 14.3329i 0.258385 0.545643i
\(691\) 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
\(693\) −3.27749 0.714493i −0.124502 0.0271413i
\(694\) 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 \(0.211082\pi\)
−0.788067 + 0.615589i \(0.788918\pi\)
\(702\) −2.05579 29.0140i −0.0775906 1.09506i
\(703\) −1.42898 + 1.42898i −0.0538949 + 0.0538949i
\(704\) −0.319493 −0.0120413
\(705\) −7.60097 21.2749i −0.286269 0.801259i
\(706\) −7.20671 −0.271228
\(707\) 16.7568 16.7568i 0.630204 0.630204i
\(708\) 11.4182 + 6.23810i 0.429123 + 0.234442i
\(709\) 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
\(717\) −11.8396 + 21.6712i −0.442157 + 0.809324i
\(718\) 25.0886 25.0886i 0.936297 0.936297i
\(719\) −11.4282 −0.426200 −0.213100 0.977030i \(-0.568356\pi\)
−0.213100 + 0.977030i \(0.568356\pi\)
\(720\) 3.94407 + 5.42626i 0.146987 + 0.202225i
\(721\) −35.3425 −1.31622
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) −25.1665 + 46.0648i −0.935953 + 1.71317i
\(724\) 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
\(732\) −12.3051 6.72263i −0.454810 0.248475i
\(733\) 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
\(735\) 18.3717 + 8.69977i 0.677650 + 0.320896i
\(736\) −4.09469 −0.150932
\(737\) 3.57033 3.57033i 0.131515 0.131515i
\(738\) 4.51785 20.7241i 0.166304 0.762865i
\(739\) 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 0.951070 0.308976i \(-0.0999863\pi\)
−0.308976 + 0.951070i \(0.599986\pi\)
\(744\) 4.55286 1.33575i 0.166916 0.0489709i
\(745\) −34.5548 + 1.99817i −1.26599 + 0.0732075i
\(746\) 4.29019i 0.157075i
\(747\) −2.09370 + 9.60412i −0.0766043 + 0.351396i
\(748\) 1.37609 1.37609i 0.0503149 0.0503149i
\(749\) −24.5961 −0.898723
\(750\) −8.57383 17.3634i −0.313072 0.634024i
\(751\) −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
\(753\) −39.6726 21.6743i −1.44575 0.789854i
\(754\) 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 \(-0.777663\pi\)
0.765813 0.643063i \(-0.222337\pi\)
\(762\) 13.4147 24.5543i 0.485964 0.889509i
\(763\) 29.9098 29.9098i 1.08281 1.08281i
\(764\) 12.7401 0.460921
\(765\) −40.3591 6.38397i −1.45919 0.230813i
\(766\) −18.3830 −0.664204
\(767\) 29.7340 29.7340i 1.07363 1.07363i
\(768\) 0.830420 1.52000i 0.0299652 0.0548483i
\(769\) 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 \(-0.905003\pi\)
−0.294032 0.955796i \(-0.594997\pi\)
\(774\) −23.0523 + 14.8004i −0.828596 + 0.531989i
\(775\) −13.6057 + 1.57881i −0.488730 + 0.0567125i
\(776\) 3.13564i 0.112563i
\(777\) −10.7504 5.87327i −0.385670 0.210702i