Properties

Label 570.2.k.a.77.5
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 77.5
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.274986 - 1.71008i) q^{3} -1.00000i q^{4} +(2.05001 + 0.893014i) q^{5} +(1.40366 + 1.01477i) q^{6} +(2.76585 + 2.76585i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.84877 + 0.940499i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.274986 - 1.71008i) q^{3} -1.00000i q^{4} +(2.05001 + 0.893014i) q^{5} +(1.40366 + 1.01477i) q^{6} +(2.76585 + 2.76585i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.84877 + 0.940499i) q^{9} +(-2.08103 + 0.818117i) q^{10} +4.37906i q^{11} +(-1.71008 + 0.274986i) q^{12} +(-0.0858524 + 0.0858524i) q^{13} -3.91150 q^{14} +(0.963404 - 3.75125i) q^{15} -1.00000 q^{16} +(-4.90493 + 4.90493i) q^{17} +(1.34935 - 2.67941i) q^{18} +1.00000i q^{19} +(0.893014 - 2.05001i) q^{20} +(3.96926 - 5.49040i) q^{21} +(-3.09646 - 3.09646i) q^{22} +(-4.04057 - 4.04057i) q^{23} +(1.01477 - 1.40366i) q^{24} +(3.40505 + 3.66137i) q^{25} -0.121414i q^{26} +(2.39170 + 4.61300i) q^{27} +(2.76585 - 2.76585i) q^{28} +7.73552 q^{29} +(1.97130 + 3.33376i) q^{30} -4.80009 q^{31} +(0.707107 - 0.707107i) q^{32} +(7.48856 - 1.20418i) q^{33} -6.93661i q^{34} +(3.20007 + 8.13995i) q^{35} +(0.940499 + 2.84877i) q^{36} +(-1.15860 - 1.15860i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(0.170423 + 0.123206i) q^{39} +(0.818117 + 2.08103i) q^{40} +3.99475i q^{41} +(1.07561 + 6.68899i) q^{42} +(-2.22743 + 2.22743i) q^{43} +4.37906 q^{44} +(-6.67986 - 0.615959i) q^{45} +5.71423 q^{46} +(9.37516 - 9.37516i) q^{47} +(0.274986 + 1.71008i) q^{48} +8.29985i q^{49} +(-4.99671 - 0.181243i) q^{50} +(9.73662 + 7.03904i) q^{51} +(0.0858524 + 0.0858524i) q^{52} +(-1.61864 - 1.61864i) q^{53} +(-4.95307 - 1.57069i) q^{54} +(-3.91056 + 8.97711i) q^{55} +3.91150i q^{56} +(1.71008 - 0.274986i) q^{57} +(-5.46984 + 5.46984i) q^{58} +13.6615 q^{59} +(-3.75125 - 0.963404i) q^{60} +13.0690 q^{61} +(3.39418 - 3.39418i) q^{62} +(-10.4805 - 5.27798i) q^{63} +1.00000i q^{64} +(-0.252665 + 0.0993306i) q^{65} +(-4.44373 + 6.14670i) q^{66} +(-9.57951 - 9.57951i) q^{67} +(4.90493 + 4.90493i) q^{68} +(-5.79861 + 8.02081i) q^{69} +(-8.01860 - 3.49303i) q^{70} -10.1120i q^{71} +(-2.67941 - 1.34935i) q^{72} +(-3.04806 + 3.04806i) q^{73} +1.63851 q^{74} +(5.32490 - 6.82975i) q^{75} +1.00000 q^{76} +(-12.1118 + 12.1118i) q^{77} +(-0.207627 + 0.0333871i) q^{78} +1.24732i q^{79} +(-2.05001 - 0.893014i) q^{80} +(7.23092 - 5.35852i) q^{81} +(-2.82471 - 2.82471i) q^{82} +(-9.27133 - 9.27133i) q^{83} +(-5.49040 - 3.96926i) q^{84} +(-14.4353 + 5.67496i) q^{85} -3.15007i q^{86} +(-2.12716 - 13.2284i) q^{87} +(-3.09646 + 3.09646i) q^{88} +4.47665 q^{89} +(5.15893 - 4.28783i) q^{90} -0.474910 q^{91} +(-4.04057 + 4.04057i) q^{92} +(1.31996 + 8.20856i) q^{93} +13.2585i q^{94} +(-0.893014 + 2.05001i) q^{95} +(-1.40366 - 1.01477i) q^{96} +(-1.05430 - 1.05430i) q^{97} +(-5.86888 - 5.86888i) q^{98} +(-4.11850 - 12.4749i) 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
\(3\) −0.274986 1.71008i −0.158763 0.987317i
\(4\) 1.00000i 0.500000i
\(5\) 2.05001 + 0.893014i 0.916791 + 0.399368i
\(6\) 1.40366 + 1.01477i 0.573040 + 0.414277i
\(7\) 2.76585 + 2.76585i 1.04539 + 1.04539i 0.998920 + 0.0464734i \(0.0147983\pi\)
0.0464734 + 0.998920i \(0.485202\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.84877 + 0.940499i −0.949588 + 0.313500i
\(10\) −2.08103 + 0.818117i −0.658079 + 0.258711i
\(11\) 4.37906i 1.32034i 0.751117 + 0.660169i \(0.229515\pi\)
−0.751117 + 0.660169i \(0.770485\pi\)
\(12\) −1.71008 + 0.274986i −0.493658 + 0.0793817i
\(13\) −0.0858524 + 0.0858524i −0.0238112 + 0.0238112i −0.718912 0.695101i \(-0.755360\pi\)
0.695101 + 0.718912i \(0.255360\pi\)
\(14\) −3.91150 −1.04539
\(15\) 0.963404 3.75125i 0.248750 0.968568i
\(16\) −1.00000 −0.250000
\(17\) −4.90493 + 4.90493i −1.18962 + 1.18962i −0.212447 + 0.977173i \(0.568143\pi\)
−0.977173 + 0.212447i \(0.931857\pi\)
\(18\) 1.34935 2.67941i 0.318044 0.631544i
\(19\) 1.00000i 0.229416i
\(20\) 0.893014 2.05001i 0.199684 0.458395i
\(21\) 3.96926 5.49040i 0.866164 1.19810i
\(22\) −3.09646 3.09646i −0.660169 0.660169i
\(23\) −4.04057 4.04057i −0.842517 0.842517i 0.146669 0.989186i \(-0.453145\pi\)
−0.989186 + 0.146669i \(0.953145\pi\)
\(24\) 1.01477 1.40366i 0.207138 0.286520i
\(25\) 3.40505 + 3.66137i 0.681010 + 0.732274i
\(26\) 0.121414i 0.0238112i
\(27\) 2.39170 + 4.61300i 0.460283 + 0.887772i
\(28\) 2.76585 2.76585i 0.522696 0.522696i
\(29\) 7.73552 1.43645 0.718225 0.695811i \(-0.244955\pi\)
0.718225 + 0.695811i \(0.244955\pi\)
\(30\) 1.97130 + 3.33376i 0.359909 + 0.608659i
\(31\) −4.80009 −0.862122 −0.431061 0.902323i \(-0.641861\pi\)
−0.431061 + 0.902323i \(0.641861\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 7.48856 1.20418i 1.30359 0.209621i
\(34\) 6.93661i 1.18962i
\(35\) 3.20007 + 8.13995i 0.540910 + 1.37590i
\(36\) 0.940499 + 2.84877i 0.156750 + 0.474794i
\(37\) −1.15860 1.15860i −0.190473 0.190473i 0.605427 0.795901i \(-0.293002\pi\)
−0.795901 + 0.605427i \(0.793002\pi\)
\(38\) −0.707107 0.707107i −0.114708 0.114708i
\(39\) 0.170423 + 0.123206i 0.0272895 + 0.0197288i
\(40\) 0.818117 + 2.08103i 0.129356 + 0.329040i
\(41\) 3.99475i 0.623874i 0.950103 + 0.311937i \(0.100978\pi\)
−0.950103 + 0.311937i \(0.899022\pi\)
\(42\) 1.07561 + 6.68899i 0.165970 + 1.03213i
\(43\) −2.22743 + 2.22743i −0.339680 + 0.339680i −0.856247 0.516567i \(-0.827210\pi\)
0.516567 + 0.856247i \(0.327210\pi\)
\(44\) 4.37906 0.660169
\(45\) −6.67986 0.615959i −0.995775 0.0918217i
\(46\) 5.71423 0.842517
\(47\) 9.37516 9.37516i 1.36751 1.36751i 0.503528 0.863979i \(-0.332035\pi\)
0.863979 0.503528i \(-0.167965\pi\)
\(48\) 0.274986 + 1.71008i 0.0396909 + 0.246829i
\(49\) 8.29985i 1.18569i
\(50\) −4.99671 0.181243i −0.706642 0.0256317i
\(51\) 9.73662 + 7.03904i 1.36340 + 0.985663i
\(52\) 0.0858524 + 0.0858524i 0.0119056 + 0.0119056i
\(53\) −1.61864 1.61864i −0.222337 0.222337i 0.587145 0.809482i \(-0.300252\pi\)
−0.809482 + 0.587145i \(0.800252\pi\)
\(54\) −4.95307 1.57069i −0.674028 0.213744i
\(55\) −3.91056 + 8.97711i −0.527300 + 1.21047i
\(56\) 3.91150i 0.522696i
\(57\) 1.71008 0.274986i 0.226506 0.0364228i
\(58\) −5.46984 + 5.46984i −0.718225 + 0.718225i
\(59\) 13.6615 1.77857 0.889286 0.457351i \(-0.151202\pi\)
0.889286 + 0.457351i \(0.151202\pi\)
\(60\) −3.75125 0.963404i −0.484284 0.124375i
\(61\) 13.0690 1.67331 0.836655 0.547730i \(-0.184508\pi\)
0.836655 + 0.547730i \(0.184508\pi\)
\(62\) 3.39418 3.39418i 0.431061 0.431061i
\(63\) −10.4805 5.27798i −1.32042 0.664963i
\(64\) 1.00000i 0.125000i
\(65\) −0.252665 + 0.0993306i −0.0313393 + 0.0123204i
\(66\) −4.44373 + 6.14670i −0.546985 + 0.756606i
\(67\) −9.57951 9.57951i −1.17032 1.17032i −0.982132 0.188191i \(-0.939738\pi\)
−0.188191 0.982132i \(-0.560262\pi\)
\(68\) 4.90493 + 4.90493i 0.594810 + 0.594810i
\(69\) −5.79861 + 8.02081i −0.698070 + 0.965592i
\(70\) −8.01860 3.49303i −0.958407 0.417496i
\(71\) 10.1120i 1.20007i −0.799973 0.600036i \(-0.795153\pi\)
0.799973 0.600036i \(-0.204847\pi\)
\(72\) −2.67941 1.34935i −0.315772 0.159022i
\(73\) −3.04806 + 3.04806i −0.356748 + 0.356748i −0.862613 0.505865i \(-0.831174\pi\)
0.505865 + 0.862613i \(0.331174\pi\)
\(74\) 1.63851 0.190473
\(75\) 5.32490 6.82975i 0.614867 0.788631i
\(76\) 1.00000 0.114708
\(77\) −12.1118 + 12.1118i −1.38027 + 1.38027i
\(78\) −0.207627 + 0.0333871i −0.0235092 + 0.00378034i
\(79\) 1.24732i 0.140334i 0.997535 + 0.0701671i \(0.0223532\pi\)
−0.997535 + 0.0701671i \(0.977647\pi\)
\(80\) −2.05001 0.893014i −0.229198 0.0998420i
\(81\) 7.23092 5.35852i 0.803436 0.595391i
\(82\) −2.82471 2.82471i −0.311937 0.311937i
\(83\) −9.27133 9.27133i −1.01766 1.01766i −0.999841 0.0178196i \(-0.994328\pi\)
−0.0178196 0.999841i \(-0.505672\pi\)
\(84\) −5.49040 3.96926i −0.599052 0.433082i
\(85\) −14.4353 + 5.67496i −1.56573 + 0.615536i
\(86\) 3.15007i 0.339680i
\(87\) −2.12716 13.2284i −0.228056 1.41823i
\(88\) −3.09646 + 3.09646i −0.330084 + 0.330084i
\(89\) 4.47665 0.474524 0.237262 0.971446i \(-0.423750\pi\)
0.237262 + 0.971446i \(0.423750\pi\)
\(90\) 5.15893 4.28783i 0.543799 0.451977i
\(91\) −0.474910 −0.0497841
\(92\) −4.04057 + 4.04057i −0.421258 + 0.421258i
\(93\) 1.31996 + 8.20856i 0.136874 + 0.851188i
\(94\) 13.2585i 1.36751i
\(95\) −0.893014 + 2.05001i −0.0916213 + 0.210326i
\(96\) −1.40366 1.01477i −0.143260 0.103569i
\(97\) −1.05430 1.05430i −0.107048 0.107048i 0.651554 0.758602i \(-0.274117\pi\)
−0.758602 + 0.651554i \(0.774117\pi\)
\(98\) −5.86888 5.86888i −0.592846 0.592846i
\(99\) −4.11850 12.4749i −0.413925 1.25378i
\(100\) 3.66137 3.40505i 0.366137 0.340505i
\(101\) 1.32352i 0.131695i 0.997830 + 0.0658476i \(0.0209751\pi\)
−0.997830 + 0.0658476i \(0.979025\pi\)
\(102\) −11.8622 + 1.90747i −1.17453 + 0.188868i
\(103\) 8.88033 8.88033i 0.875005 0.875005i −0.118008 0.993013i \(-0.537651\pi\)
0.993013 + 0.118008i \(0.0376508\pi\)
\(104\) −0.121414 −0.0119056
\(105\) 13.0400 7.71075i 1.27258 0.752493i
\(106\) 2.28910 0.222337
\(107\) 7.02479 7.02479i 0.679112 0.679112i −0.280687 0.959799i \(-0.590562\pi\)
0.959799 + 0.280687i \(0.0905623\pi\)
\(108\) 4.61300 2.39170i 0.443886 0.230142i
\(109\) 0.223709i 0.0214274i −0.999943 0.0107137i \(-0.996590\pi\)
0.999943 0.0107137i \(-0.00341035\pi\)
\(110\) −3.58259 9.11296i −0.341586 0.868887i
\(111\) −1.66271 + 2.29991i −0.157817 + 0.218298i
\(112\) −2.76585 2.76585i −0.261348 0.261348i
\(113\) 4.90305 + 4.90305i 0.461240 + 0.461240i 0.899062 0.437822i \(-0.144250\pi\)
−0.437822 + 0.899062i \(0.644250\pi\)
\(114\) −1.01477 + 1.40366i −0.0950416 + 0.131464i
\(115\) −4.67491 11.8915i −0.435937 1.10889i
\(116\) 7.73552i 0.718225i
\(117\) 0.163829 0.325317i 0.0151460 0.0300756i
\(118\) −9.66012 + 9.66012i −0.889286 + 0.889286i
\(119\) −27.1326 −2.48724
\(120\) 3.33376 1.97130i 0.304329 0.179954i
\(121\) −8.17619 −0.743290
\(122\) −9.24116 + 9.24116i −0.836655 + 0.836655i
\(123\) 6.83135 1.09850i 0.615962 0.0990484i
\(124\) 4.80009i 0.431061i
\(125\) 3.71073 + 10.5466i 0.331897 + 0.943316i
\(126\) 11.1430 3.67876i 0.992693 0.327730i
\(127\) 1.71446 + 1.71446i 0.152134 + 0.152134i 0.779070 0.626936i \(-0.215691\pi\)
−0.626936 + 0.779070i \(0.715691\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 4.42161 + 3.19658i 0.389301 + 0.281443i
\(130\) 0.108424 0.248899i 0.00950942 0.0218299i
\(131\) 1.03462i 0.0903948i −0.998978 0.0451974i \(-0.985608\pi\)
0.998978 0.0451974i \(-0.0143917\pi\)
\(132\) −1.20418 7.48856i −0.104811 0.651795i
\(133\) −2.76585 + 2.76585i −0.239830 + 0.239830i
\(134\) 13.5475 1.17032
\(135\) 0.783531 + 11.5925i 0.0674356 + 0.997724i
\(136\) −6.93661 −0.594810
\(137\) 3.90513 3.90513i 0.333638 0.333638i −0.520328 0.853966i \(-0.674190\pi\)
0.853966 + 0.520328i \(0.174190\pi\)
\(138\) −1.57133 9.77180i −0.133761 0.831831i
\(139\) 0.884659i 0.0750358i −0.999296 0.0375179i \(-0.988055\pi\)
0.999296 0.0375179i \(-0.0119451\pi\)
\(140\) 8.13995 3.20007i 0.687952 0.270455i
\(141\) −18.6103 13.4543i −1.56727 1.13305i
\(142\) 7.15026 + 7.15026i 0.600036 + 0.600036i
\(143\) −0.375953 0.375953i −0.0314388 0.0314388i
\(144\) 2.84877 0.940499i 0.237397 0.0783749i
\(145\) 15.8579 + 6.90793i 1.31692 + 0.573672i
\(146\) 4.31060i 0.356748i
\(147\) 14.1934 2.28234i 1.17065 0.188245i
\(148\) −1.15860 + 1.15860i −0.0952366 + 0.0952366i
\(149\) 14.4191 1.18126 0.590629 0.806943i \(-0.298880\pi\)
0.590629 + 0.806943i \(0.298880\pi\)
\(150\) 1.06409 + 8.59463i 0.0868823 + 0.701749i
\(151\) 12.5541 1.02164 0.510820 0.859687i \(-0.329342\pi\)
0.510820 + 0.859687i \(0.329342\pi\)
\(152\) −0.707107 + 0.707107i −0.0573539 + 0.0573539i
\(153\) 9.35991 18.5861i 0.756704 1.50259i
\(154\) 17.1287i 1.38027i
\(155\) −9.84022 4.28655i −0.790386 0.344304i
\(156\) 0.123206 0.170423i 0.00986441 0.0136448i
\(157\) −9.08703 9.08703i −0.725224 0.725224i 0.244440 0.969664i \(-0.421396\pi\)
−0.969664 + 0.244440i \(0.921396\pi\)
\(158\) −0.881987 0.881987i −0.0701671 0.0701671i
\(159\) −2.32290 + 3.21311i −0.184218 + 0.254816i
\(160\) 2.08103 0.818117i 0.164520 0.0646778i
\(161\) 22.3512i 1.76152i
\(162\) −1.32399 + 8.90208i −0.104023 + 0.699414i
\(163\) −2.97919 + 2.97919i −0.233348 + 0.233348i −0.814089 0.580740i \(-0.802763\pi\)
0.580740 + 0.814089i \(0.302763\pi\)
\(164\) 3.99475 0.311937
\(165\) 16.4269 + 4.21881i 1.27884 + 0.328434i
\(166\) 13.1116 1.01766
\(167\) −6.66427 + 6.66427i −0.515697 + 0.515697i −0.916266 0.400569i \(-0.868812\pi\)
0.400569 + 0.916266i \(0.368812\pi\)
\(168\) 6.68899 1.07561i 0.516067 0.0829851i
\(169\) 12.9853i 0.998866i
\(170\) 6.19449 14.2201i 0.475096 1.09063i
\(171\) −0.940499 2.84877i −0.0719217 0.217851i
\(172\) 2.22743 + 2.22743i 0.169840 + 0.169840i
\(173\) 3.33173 + 3.33173i 0.253307 + 0.253307i 0.822325 0.569018i \(-0.192677\pi\)
−0.569018 + 0.822325i \(0.692677\pi\)
\(174\) 10.8580 + 7.84975i 0.823144 + 0.595088i
\(175\) −0.708933 + 19.5447i −0.0535903 + 1.47744i
\(176\) 4.37906i 0.330084i
\(177\) −3.75672 23.3622i −0.282372 1.75601i
\(178\) −3.16547 + 3.16547i −0.237262 + 0.237262i
\(179\) −20.3926 −1.52421 −0.762105 0.647453i \(-0.775834\pi\)
−0.762105 + 0.647453i \(0.775834\pi\)
\(180\) −0.615959 + 6.67986i −0.0459109 + 0.497888i
\(181\) −19.7998 −1.47171 −0.735855 0.677139i \(-0.763220\pi\)
−0.735855 + 0.677139i \(0.763220\pi\)
\(182\) 0.335812 0.335812i 0.0248920 0.0248920i
\(183\) −3.59379 22.3490i −0.265661 1.65209i
\(184\) 5.71423i 0.421258i
\(185\) −1.34050 3.40979i −0.0985552 0.250693i
\(186\) −6.73768 4.87097i −0.494031 0.357157i
\(187\) −21.4790 21.4790i −1.57070 1.57070i
\(188\) −9.37516 9.37516i −0.683754 0.683754i
\(189\) −6.14378 + 19.3740i −0.446894 + 1.40925i
\(190\) −0.818117 2.08103i −0.0593525 0.150974i
\(191\) 16.0949i 1.16458i −0.812979 0.582292i \(-0.802156\pi\)
0.812979 0.582292i \(-0.197844\pi\)
\(192\) 1.71008 0.274986i 0.123415 0.0198454i
\(193\) −2.75631 + 2.75631i −0.198404 + 0.198404i −0.799315 0.600912i \(-0.794804\pi\)
0.600912 + 0.799315i \(0.294804\pi\)
\(194\) 1.49100 0.107048
\(195\) 0.239343 + 0.404764i 0.0171397 + 0.0289858i
\(196\) 8.29985 0.592846
\(197\) −9.52900 + 9.52900i −0.678913 + 0.678913i −0.959754 0.280841i \(-0.909387\pi\)
0.280841 + 0.959754i \(0.409387\pi\)
\(198\) 11.7333 + 5.90888i 0.833851 + 0.419926i
\(199\) 7.61755i 0.539994i −0.962861 0.269997i \(-0.912977\pi\)
0.962861 0.269997i \(-0.0870227\pi\)
\(200\) −0.181243 + 4.99671i −0.0128158 + 0.353321i
\(201\) −13.7475 + 19.0160i −0.969675 + 1.34128i
\(202\) −0.935870 0.935870i −0.0658476 0.0658476i
\(203\) 21.3953 + 21.3953i 1.50166 + 1.50166i
\(204\) 7.03904 9.73662i 0.492831 0.681700i
\(205\) −3.56736 + 8.18925i −0.249155 + 0.571962i
\(206\) 12.5587i 0.875005i
\(207\) 15.3108 + 7.71048i 1.06417 + 0.535916i
\(208\) 0.0858524 0.0858524i 0.00595279 0.00595279i
\(209\) −4.37906 −0.302906
\(210\) −3.76836 + 14.6730i −0.260041 + 1.01253i
\(211\) 5.54199 0.381526 0.190763 0.981636i \(-0.438904\pi\)
0.190763 + 0.981636i \(0.438904\pi\)
\(212\) −1.61864 + 1.61864i −0.111168 + 0.111168i
\(213\) −17.2923 + 2.78066i −1.18485 + 0.190528i
\(214\) 9.93455i 0.679112i
\(215\) −6.55538 + 2.57712i −0.447073 + 0.175758i
\(216\) −1.57069 + 4.95307i −0.106872 + 0.337014i
\(217\) −13.2763 13.2763i −0.901257 0.901257i
\(218\) 0.158186 + 0.158186i 0.0107137 + 0.0107137i
\(219\) 6.05060 + 4.37426i 0.408862 + 0.295585i
\(220\) 8.97711 + 3.91056i 0.605236 + 0.263650i
\(221\) 0.842199i 0.0566525i
\(222\) −0.450568 2.80199i −0.0302402 0.188057i
\(223\) 9.53065 9.53065i 0.638219 0.638219i −0.311897 0.950116i \(-0.600964\pi\)
0.950116 + 0.311897i \(0.100964\pi\)
\(224\) 3.91150 0.261348
\(225\) −13.1437 7.22793i −0.876247 0.481862i
\(226\) −6.93395 −0.461240
\(227\) −13.7533 + 13.7533i −0.912836 + 0.912836i −0.996495 0.0836582i \(-0.973340\pi\)
0.0836582 + 0.996495i \(0.473340\pi\)
\(228\) −0.274986 1.71008i −0.0182114 0.113253i
\(229\) 6.49460i 0.429175i 0.976705 + 0.214588i \(0.0688407\pi\)
−0.976705 + 0.214588i \(0.931159\pi\)
\(230\) 11.7142 + 5.10289i 0.772412 + 0.336474i
\(231\) 24.0428 + 17.3816i 1.58190 + 1.14363i
\(232\) 5.46984 + 5.46984i 0.359113 + 0.359113i
\(233\) 7.94673 + 7.94673i 0.520608 + 0.520608i 0.917755 0.397147i \(-0.130000\pi\)
−0.397147 + 0.917755i \(0.630000\pi\)
\(234\) 0.114189 + 0.345879i 0.00746479 + 0.0226108i
\(235\) 27.5913 10.8470i 1.79986 0.707579i
\(236\) 13.6615i 0.889286i
\(237\) 2.13302 0.342995i 0.138554 0.0222799i
\(238\) 19.1856 19.1856i 1.24362 1.24362i
\(239\) −7.51189 −0.485903 −0.242952 0.970038i \(-0.578116\pi\)
−0.242952 + 0.970038i \(0.578116\pi\)
\(240\) −0.963404 + 3.75125i −0.0621875 + 0.242142i
\(241\) 11.2111 0.722170 0.361085 0.932533i \(-0.382406\pi\)
0.361085 + 0.932533i \(0.382406\pi\)
\(242\) 5.78144 5.78144i 0.371645 0.371645i
\(243\) −11.1519 10.8920i −0.715396 0.698720i
\(244\) 13.0690i 0.836655i
\(245\) −7.41188 + 17.0147i −0.473528 + 1.08703i
\(246\) −4.05373 + 5.60725i −0.258457 + 0.357505i
\(247\) −0.0858524 0.0858524i −0.00546266 0.00546266i
\(248\) −3.39418 3.39418i −0.215531 0.215531i
\(249\) −13.3053 + 18.4042i −0.843186 + 1.16632i
\(250\) −10.0814 4.83369i −0.637606 0.305709i
\(251\) 10.7576i 0.679015i 0.940603 + 0.339508i \(0.110260\pi\)
−0.940603 + 0.339508i \(0.889740\pi\)
\(252\) −5.27798 + 10.4805i −0.332481 + 0.660212i
\(253\) 17.6939 17.6939i 1.11241 1.11241i
\(254\) −2.42462 −0.152134
\(255\) 13.6742 + 23.1250i 0.856309 + 1.44814i
\(256\) 1.00000 0.0625000
\(257\) −2.67697 + 2.67697i −0.166985 + 0.166985i −0.785653 0.618668i \(-0.787673\pi\)
0.618668 + 0.785653i \(0.287673\pi\)
\(258\) −5.38688 + 0.866225i −0.335372 + 0.0539288i
\(259\) 6.40905i 0.398239i
\(260\) 0.0993306 + 0.252665i 0.00616022 + 0.0156696i
\(261\) −22.0367 + 7.27525i −1.36404 + 0.450327i
\(262\) 0.731584 + 0.731584i 0.0451974 + 0.0451974i
\(263\) 16.7660 + 16.7660i 1.03384 + 1.03384i 0.999407 + 0.0344303i \(0.0109617\pi\)
0.0344303 + 0.999407i \(0.489038\pi\)
\(264\) 6.14670 + 4.44373i 0.378303 + 0.273492i
\(265\) −1.87275 4.76368i −0.115042 0.292631i
\(266\) 3.91150i 0.239830i
\(267\) −1.23102 7.65545i −0.0753371 0.468506i
\(268\) −9.57951 + 9.57951i −0.585162 + 0.585162i
\(269\) −12.5500 −0.765186 −0.382593 0.923917i \(-0.624969\pi\)
−0.382593 + 0.923917i \(0.624969\pi\)
\(270\) −8.75118 7.64310i −0.532580 0.465144i
\(271\) −12.9702 −0.787886 −0.393943 0.919135i \(-0.628889\pi\)
−0.393943 + 0.919135i \(0.628889\pi\)
\(272\) 4.90493 4.90493i 0.297405 0.297405i
\(273\) 0.130594 + 0.812135i 0.00790389 + 0.0491526i
\(274\) 5.52269i 0.333638i
\(275\) −16.0334 + 14.9109i −0.966848 + 0.899163i
\(276\) 8.02081 + 5.79861i 0.482796 + 0.349035i
\(277\) 10.2241 + 10.2241i 0.614306 + 0.614306i 0.944065 0.329759i \(-0.106967\pi\)
−0.329759 + 0.944065i \(0.606967\pi\)
\(278\) 0.625548 + 0.625548i 0.0375179 + 0.0375179i
\(279\) 13.6743 4.51448i 0.818661 0.270275i
\(280\) −3.49303 + 8.01860i −0.208748 + 0.479203i
\(281\) 3.48157i 0.207693i 0.994593 + 0.103846i \(0.0331150\pi\)
−0.994593 + 0.103846i \(0.966885\pi\)
\(282\) 22.6731 3.64590i 1.35016 0.217110i
\(283\) −3.43456 + 3.43456i −0.204164 + 0.204164i −0.801781 0.597618i \(-0.796114\pi\)
0.597618 + 0.801781i \(0.296114\pi\)
\(284\) −10.1120 −0.600036
\(285\) 3.75125 + 0.963404i 0.222205 + 0.0570671i
\(286\) 0.531678 0.0314388
\(287\) −11.0489 + 11.0489i −0.652194 + 0.652194i
\(288\) −1.34935 + 2.67941i −0.0795111 + 0.157886i
\(289\) 31.1166i 1.83039i
\(290\) −16.0979 + 6.32856i −0.945299 + 0.371626i
\(291\) −1.51302 + 2.09286i −0.0886949 + 0.122685i
\(292\) 3.04806 + 3.04806i 0.178374 + 0.178374i
\(293\) 4.27164 + 4.27164i 0.249552 + 0.249552i 0.820787 0.571235i \(-0.193535\pi\)
−0.571235 + 0.820787i \(0.693535\pi\)
\(294\) −8.42241 + 11.6501i −0.491205 + 0.679449i
\(295\) 28.0061 + 12.1999i 1.63058 + 0.710305i
\(296\) 1.63851i 0.0952366i
\(297\) −20.2006 + 10.4734i −1.17216 + 0.607729i
\(298\) −10.1958 + 10.1958i −0.590629 + 0.590629i
\(299\) 0.693785 0.0401226
\(300\) −6.82975 5.32490i −0.394316 0.307433i
\(301\) −12.3215 −0.710199
\(302\) −8.87711 + 8.87711i −0.510820 + 0.510820i
\(303\) 2.26333 0.363950i 0.130025 0.0209084i
\(304\) 1.00000i 0.0573539i
\(305\) 26.7915 + 11.6708i 1.53408 + 0.668267i
\(306\) 6.52387 + 19.7608i 0.372945 + 1.12965i
\(307\) −12.5877 12.5877i −0.718417 0.718417i 0.249864 0.968281i \(-0.419614\pi\)
−0.968281 + 0.249864i \(0.919614\pi\)
\(308\) 12.1118 + 12.1118i 0.690136 + 0.690136i
\(309\) −17.6281 12.7441i −1.00283 0.724988i
\(310\) 9.98914 3.92704i 0.567345 0.223041i
\(311\) 2.19199i 0.124296i 0.998067 + 0.0621481i \(0.0197951\pi\)
−0.998067 + 0.0621481i \(0.980205\pi\)
\(312\) 0.0333871 + 0.207627i 0.00189017 + 0.0117546i
\(313\) 12.2938 12.2938i 0.694888 0.694888i −0.268416 0.963303i \(-0.586500\pi\)
0.963303 + 0.268416i \(0.0865001\pi\)
\(314\) 12.8510 0.725224
\(315\) −16.7719 20.1792i −0.944987 1.13697i
\(316\) 1.24732 0.0701671
\(317\) 5.00014 5.00014i 0.280836 0.280836i −0.552606 0.833442i \(-0.686367\pi\)
0.833442 + 0.552606i \(0.186367\pi\)
\(318\) −0.629471 3.91455i −0.0352990 0.219517i
\(319\) 33.8743i 1.89660i
\(320\) −0.893014 + 2.05001i −0.0499210 + 0.114599i
\(321\) −13.9447 10.0813i −0.778317 0.562681i
\(322\) 15.8047 + 15.8047i 0.880761 + 0.880761i
\(323\) −4.90493 4.90493i −0.272917 0.272917i
\(324\) −5.35852 7.23092i −0.297695 0.401718i
\(325\) −0.606669 0.0220054i −0.0336520 0.00122064i
\(326\) 4.21322i 0.233348i
\(327\) −0.382561 + 0.0615169i −0.0211557 + 0.00340189i
\(328\) −2.82471 + 2.82471i −0.155969 + 0.155969i
\(329\) 51.8605 2.85916
\(330\) −14.5988 + 8.63246i −0.803635 + 0.475201i
\(331\) 15.5843 0.856592 0.428296 0.903639i \(-0.359114\pi\)
0.428296 + 0.903639i \(0.359114\pi\)
\(332\) −9.27133 + 9.27133i −0.508830 + 0.508830i
\(333\) 4.39025 + 2.21092i 0.240584 + 0.121158i
\(334\) 9.42471i 0.515697i
\(335\) −11.0834 28.1927i −0.605552 1.54033i
\(336\) −3.96926 + 5.49040i −0.216541 + 0.299526i
\(337\) −12.8769 12.8769i −0.701449 0.701449i 0.263272 0.964722i \(-0.415198\pi\)
−0.964722 + 0.263272i \(0.915198\pi\)
\(338\) −9.18196 9.18196i −0.499433 0.499433i
\(339\) 7.03634 9.73288i 0.382162 0.528618i
\(340\) 5.67496 + 14.4353i 0.307768 + 0.782864i
\(341\) 21.0199i 1.13829i
\(342\) 2.67941 + 1.34935i 0.144886 + 0.0729644i
\(343\) −3.59519 + 3.59519i −0.194122 + 0.194122i
\(344\) −3.15007 −0.169840
\(345\) −19.0499 + 11.2645i −1.02561 + 0.606459i
\(346\) −4.71178 −0.253307
\(347\) −5.40671 + 5.40671i −0.290247 + 0.290247i −0.837178 0.546931i \(-0.815796\pi\)
0.546931 + 0.837178i \(0.315796\pi\)
\(348\) −13.2284 + 2.12716i −0.709116 + 0.114028i
\(349\) 4.70970i 0.252104i 0.992024 + 0.126052i \(0.0402307\pi\)
−0.992024 + 0.126052i \(0.959769\pi\)
\(350\) −13.3189 14.3215i −0.711923 0.765514i
\(351\) −0.601370 0.190704i −0.0320988 0.0101790i
\(352\) 3.09646 + 3.09646i 0.165042 + 0.165042i
\(353\) −1.82994 1.82994i −0.0973976 0.0973976i 0.656729 0.754127i \(-0.271940\pi\)
−0.754127 + 0.656729i \(0.771940\pi\)
\(354\) 19.1760 + 13.8632i 1.01919 + 0.736821i
\(355\) 9.03015 20.7296i 0.479271 1.10022i
\(356\) 4.47665i 0.237262i
\(357\) 7.46109 + 46.3990i 0.394883 + 2.45569i
\(358\) 14.4197 14.4197i 0.762105 0.762105i
\(359\) 9.20818 0.485989 0.242995 0.970028i \(-0.421870\pi\)
0.242995 + 0.970028i \(0.421870\pi\)
\(360\) −4.28783 5.15893i −0.225988 0.271899i
\(361\) −1.00000 −0.0526316
\(362\) 14.0006 14.0006i 0.735855 0.735855i
\(363\) 2.24834 + 13.9820i 0.118007 + 0.733863i
\(364\) 0.474910i 0.0248920i
\(365\) −8.97050 + 3.52658i −0.469537 + 0.184590i
\(366\) 18.3443 + 13.2620i 0.958874 + 0.693214i
\(367\) 14.0925 + 14.0925i 0.735621 + 0.735621i 0.971727 0.236107i \(-0.0758715\pi\)
−0.236107 + 0.971727i \(0.575871\pi\)
\(368\) 4.04057 + 4.04057i 0.210629 + 0.210629i
\(369\) −3.75705 11.3801i −0.195584 0.592424i
\(370\) 3.35896 + 1.46321i 0.174624 + 0.0760689i
\(371\) 8.95381i 0.464859i
\(372\) 8.20856 1.31996i 0.425594 0.0684368i
\(373\) −6.94081 + 6.94081i −0.359382 + 0.359382i −0.863585 0.504203i \(-0.831786\pi\)
0.504203 + 0.863585i \(0.331786\pi\)
\(374\) 30.3759 1.57070
\(375\) 17.0151 9.24581i 0.878658 0.477452i
\(376\) 13.2585 0.683754
\(377\) −0.664113 + 0.664113i −0.0342036 + 0.0342036i
\(378\) −9.35515 18.0438i −0.481177 0.928071i
\(379\) 34.8937i 1.79237i 0.443683 + 0.896184i \(0.353671\pi\)
−0.443683 + 0.896184i \(0.646329\pi\)
\(380\) 2.05001 + 0.893014i 0.105163 + 0.0458107i
\(381\) 2.46042 3.40333i 0.126051 0.174358i
\(382\) 11.3808 + 11.3808i 0.582292 + 0.582292i
\(383\) −3.00238 3.00238i −0.153415 0.153415i 0.626227 0.779641i \(-0.284599\pi\)
−0.779641 + 0.626227i \(0.784599\pi\)
\(384\) −1.01477 + 1.40366i −0.0517846 + 0.0716300i
\(385\) −35.6454 + 14.0133i −1.81666 + 0.714184i
\(386\) 3.89801i 0.198404i
\(387\) 4.25054 8.44033i 0.216067 0.429046i
\(388\) −1.05430 + 1.05430i −0.0535239 + 0.0535239i
\(389\) 4.18737 0.212308 0.106154 0.994350i \(-0.466146\pi\)
0.106154 + 0.994350i \(0.466146\pi\)
\(390\) −0.455453 0.116970i −0.0230627 0.00592303i
\(391\) 39.6374 2.00455
\(392\) −5.86888 + 5.86888i −0.296423 + 0.296423i
\(393\) −1.76928 + 0.284505i −0.0892483 + 0.0143514i
\(394\) 13.4760i 0.678913i
\(395\) −1.11387 + 2.55701i −0.0560450 + 0.128657i
\(396\) −12.4749 + 4.11850i −0.626888 + 0.206963i
\(397\) −6.47953 6.47953i −0.325198 0.325198i 0.525559 0.850757i \(-0.323856\pi\)
−0.850757 + 0.525559i \(0.823856\pi\)
\(398\) 5.38642 + 5.38642i 0.269997 + 0.269997i
\(399\) 5.49040 + 3.96926i 0.274864 + 0.198712i
\(400\) −3.40505 3.66137i −0.170253 0.183068i
\(401\) 12.0856i 0.603528i −0.953383 0.301764i \(-0.902425\pi\)
0.953383 0.301764i \(-0.0975754\pi\)
\(402\) −3.72537 23.1673i −0.185805 1.15548i
\(403\) 0.412100 0.412100i 0.0205281 0.0205281i
\(404\) 1.32352 0.0658476
\(405\) 19.6087 4.52768i 0.974363 0.224982i
\(406\) −30.2575 −1.50166
\(407\) 5.07360 5.07360i 0.251489 0.251489i
\(408\) 1.90747 + 11.8622i 0.0944340 + 0.587266i
\(409\) 14.2278i 0.703521i −0.936090 0.351760i \(-0.885583\pi\)
0.936090 0.351760i \(-0.114417\pi\)
\(410\) −3.26817 8.31318i −0.161403 0.410559i
\(411\) −7.75196 5.60424i −0.382376 0.276437i
\(412\) −8.88033 8.88033i −0.437502 0.437502i
\(413\) 37.7856 + 37.7856i 1.85931 + 1.85931i
\(414\) −16.2785 + 5.37422i −0.800044 + 0.264129i
\(415\) −10.7269 27.2857i −0.526561 1.33940i
\(416\) 0.121414i 0.00595279i
\(417\) −1.51284 + 0.243269i −0.0740841 + 0.0119129i
\(418\) 3.09646 3.09646i 0.151453 0.151453i
\(419\) −27.8666 −1.36137 −0.680686 0.732576i \(-0.738318\pi\)
−0.680686 + 0.732576i \(0.738318\pi\)
\(420\) −7.71075 13.0400i −0.376246 0.636288i
\(421\) 30.3012 1.47679 0.738396 0.674368i \(-0.235584\pi\)
0.738396 + 0.674368i \(0.235584\pi\)
\(422\) −3.91878 + 3.91878i −0.190763 + 0.190763i
\(423\) −17.8903 + 35.5249i −0.869856 + 1.72728i
\(424\) 2.28910i 0.111168i
\(425\) −34.6603 1.25721i −1.68127 0.0609838i
\(426\) 10.2613 14.1938i 0.497162 0.687690i
\(427\) 36.1468 + 36.1468i 1.74927 + 1.74927i
\(428\) −7.02479 7.02479i −0.339556 0.339556i
\(429\) −0.539529 + 0.746293i −0.0260487 + 0.0360314i
\(430\) 2.81305 6.45766i 0.135658 0.311416i
\(431\) 23.2155i 1.11825i −0.829082 0.559126i \(-0.811137\pi\)
0.829082 0.559126i \(-0.188863\pi\)
\(432\) −2.39170 4.61300i −0.115071 0.221943i
\(433\) 20.5816 20.5816i 0.989090 0.989090i −0.0108515 0.999941i \(-0.503454\pi\)
0.999941 + 0.0108515i \(0.00345420\pi\)
\(434\) 18.7756 0.901257
\(435\) 7.45243 29.0179i 0.357317 1.39130i
\(436\) −0.223709 −0.0107137
\(437\) 4.04057 4.04057i 0.193287 0.193287i
\(438\) −7.37149 + 1.18536i −0.352223 + 0.0566386i
\(439\) 29.7544i 1.42010i −0.704151 0.710050i \(-0.748672\pi\)
0.704151 0.710050i \(-0.251328\pi\)
\(440\) −9.11296 + 3.58259i −0.434443 + 0.170793i
\(441\) −7.80600 23.6443i −0.371714 1.12592i
\(442\) 0.595525 + 0.595525i 0.0283262 + 0.0283262i
\(443\) 12.8988 + 12.8988i 0.612842 + 0.612842i 0.943686 0.330844i \(-0.107333\pi\)
−0.330844 + 0.943686i \(0.607333\pi\)
\(444\) 2.29991 + 1.66271i 0.109149 + 0.0789086i
\(445\) 9.17717 + 3.99771i 0.435040 + 0.189510i
\(446\) 13.4784i 0.638219i
\(447\) −3.96505 24.6578i −0.187541 1.16628i
\(448\) −2.76585 + 2.76585i −0.130674 + 0.130674i
\(449\) −6.08743 −0.287284 −0.143642 0.989630i \(-0.545881\pi\)
−0.143642 + 0.989630i \(0.545881\pi\)
\(450\) 14.4049 4.18308i 0.679055 0.197192i
\(451\) −17.4932 −0.823725
\(452\) 4.90305 4.90305i 0.230620 0.230620i
\(453\) −3.45221 21.4686i −0.162199 1.00868i
\(454\) 19.4501i 0.912836i
\(455\) −0.973568 0.424101i −0.0456416 0.0198822i
\(456\) 1.40366 + 1.01477i 0.0657322 + 0.0475208i
\(457\) 13.6315 + 13.6315i 0.637656 + 0.637656i 0.949977 0.312321i \(-0.101106\pi\)
−0.312321 + 0.949977i \(0.601106\pi\)
\(458\) −4.59237 4.59237i −0.214588 0.214588i
\(459\) −34.3575 10.8953i −1.60367 0.508549i
\(460\) −11.8915 + 4.67491i −0.554443 + 0.217969i
\(461\) 20.6355i 0.961091i −0.876970 0.480546i \(-0.840439\pi\)
0.876970 0.480546i \(-0.159561\pi\)
\(462\) −29.2915 + 4.71016i −1.36276 + 0.219137i
\(463\) 1.47081 1.47081i 0.0683543 0.0683543i −0.672103 0.740458i \(-0.734609\pi\)
0.740458 + 0.672103i \(0.234609\pi\)
\(464\) −7.73552 −0.359113
\(465\) −4.62443 + 18.0063i −0.214453 + 0.835024i
\(466\) −11.2384 −0.520608
\(467\) 24.9074 24.9074i 1.15258 1.15258i 0.166541 0.986035i \(-0.446740\pi\)
0.986035 0.166541i \(-0.0532597\pi\)
\(468\) −0.325317 0.163829i −0.0150378 0.00757301i
\(469\) 52.9910i 2.44690i
\(470\) −11.8400 + 27.1800i −0.546139 + 1.25372i
\(471\) −13.0408 + 18.0384i −0.600887 + 0.831165i
\(472\) 9.66012 + 9.66012i 0.444643 + 0.444643i
\(473\) −9.75407 9.75407i −0.448493 0.448493i
\(474\) −1.26574 + 1.75080i −0.0581372 + 0.0804171i
\(475\) −3.66137 + 3.40505i −0.167995 + 0.156235i
\(476\) 27.1326i 1.24362i
\(477\) 6.13344 + 3.08879i 0.280831 + 0.141426i
\(478\) 5.31171 5.31171i 0.242952 0.242952i
\(479\) −11.4278 −0.522150 −0.261075 0.965318i \(-0.584077\pi\)
−0.261075 + 0.965318i \(0.584077\pi\)
\(480\) −1.97130 3.33376i −0.0899772 0.152165i
\(481\) 0.198938 0.00907078
\(482\) −7.92744 + 7.92744i −0.361085 + 0.361085i
\(483\) −38.2224 + 6.14628i −1.73918 + 0.279665i
\(484\) 8.17619i 0.371645i
\(485\) −1.21982 3.10282i −0.0553890 0.140892i
\(486\) 15.5874 0.183816i 0.707058 0.00833808i
\(487\) −6.40458 6.40458i −0.290219 0.290219i 0.546948 0.837167i \(-0.315790\pi\)
−0.837167 + 0.546948i \(0.815790\pi\)
\(488\) 9.24116 + 9.24116i 0.418328 + 0.418328i
\(489\) 5.91390 + 4.27543i 0.267436 + 0.193342i
\(490\) −6.79025 17.2722i −0.306752 0.780280i
\(491\) 8.15301i 0.367940i 0.982932 + 0.183970i \(0.0588950\pi\)
−0.982932 + 0.183970i \(0.941105\pi\)
\(492\) −1.09850 6.83135i −0.0495242 0.307981i
\(493\) −37.9422 + 37.9422i −1.70883 + 1.70883i
\(494\) 0.121414 0.00546266
\(495\) 2.69732 29.2515i 0.121236 1.31476i
\(496\) 4.80009 0.215531
\(497\) 27.9683 27.9683i 1.25455 1.25455i
\(498\) −3.60552 22.4220i −0.161567 1.00475i
\(499\) 1.46257i 0.0654738i 0.999464 + 0.0327369i \(0.0104223\pi\)
−0.999464 + 0.0327369i \(0.989578\pi\)
\(500\) 10.5466 3.71073i 0.471658 0.165949i
\(501\) 13.2290 + 9.56387i 0.591030 + 0.427282i
\(502\) −7.60679 7.60679i −0.339508 0.339508i
\(503\) −27.1555 27.1555i −1.21081 1.21081i −0.970762 0.240043i \(-0.922839\pi\)
−0.240043 0.970762i \(-0.577161\pi\)
\(504\) −3.67876 11.1430i −0.163865 0.496346i
\(505\) −1.18192 + 2.71323i −0.0525949 + 0.120737i
\(506\) 25.0230i 1.11241i
\(507\) 22.2059 3.57077i 0.986197 0.158583i
\(508\) 1.71446 1.71446i 0.0760670 0.0760670i
\(509\) 3.41038 0.151162 0.0755812 0.997140i \(-0.475919\pi\)
0.0755812 + 0.997140i \(0.475919\pi\)
\(510\) −26.0209 6.68276i −1.15223 0.295918i
\(511\) −16.8609 −0.745884
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.61300 + 2.39170i −0.203669 + 0.105596i
\(514\) 3.78581i 0.166985i
\(515\) 26.1350 10.2745i 1.15165 0.452747i
\(516\) 3.19658 4.42161i 0.140722 0.194651i
\(517\) 41.0544 + 41.0544i 1.80557 + 1.80557i
\(518\) 4.53188 + 4.53188i 0.199119 + 0.199119i
\(519\) 4.78135 6.61371i 0.209878 0.290310i
\(520\) −0.248899 0.108424i −0.0109149 0.00475471i
\(521\) 26.3131i 1.15280i 0.817169 + 0.576399i \(0.195543\pi\)
−0.817169 + 0.576399i \(0.804457\pi\)
\(522\) 10.4379 20.7267i 0.456855 0.907182i
\(523\) 1.67071 1.67071i 0.0730549 0.0730549i −0.669635 0.742690i \(-0.733550\pi\)
0.742690 + 0.669635i \(0.233550\pi\)
\(524\) −1.03462 −0.0451974
\(525\) 33.6179 4.16218i 1.46721 0.181652i
\(526\) −23.7107 −1.03384
\(527\) 23.5441 23.5441i 1.02560 1.02560i
\(528\) −7.48856 + 1.20418i −0.325898 + 0.0524053i
\(529\) 9.65240i 0.419669i
\(530\) 4.69267 + 2.04420i 0.203836 + 0.0887942i
\(531\) −38.9183 + 12.8486i −1.68891 + 0.557582i
\(532\) 2.76585 + 2.76585i 0.119915 + 0.119915i
\(533\) −0.342959 0.342959i −0.0148552 0.0148552i
\(534\) 6.28368 + 4.54276i 0.271921 + 0.196584i
\(535\) 20.6741 8.12763i 0.893819 0.351388i
\(536\) 13.5475i 0.585162i
\(537\) 5.60767 + 34.8729i 0.241989 + 1.50488i
\(538\) 8.87418 8.87418i 0.382593 0.382593i
\(539\) −36.3456 −1.56551
\(540\) 11.5925 0.783531i 0.498862 0.0337178i
\(541\) −23.9511 −1.02974 −0.514870 0.857269i \(-0.672160\pi\)
−0.514870 + 0.857269i \(0.672160\pi\)
\(542\) 9.17134 9.17134i 0.393943 0.393943i
\(543\) 5.44469 + 33.8594i 0.233654 + 1.45304i
\(544\) 6.93661i 0.297405i
\(545\) 0.199775 0.458605i 0.00855743 0.0196445i
\(546\) −0.666610 0.481922i −0.0285283 0.0206244i
\(547\) −18.6458 18.6458i −0.797236 0.797236i 0.185423 0.982659i \(-0.440634\pi\)
−0.982659 + 0.185423i \(0.940634\pi\)
\(548\) −3.90513 3.90513i −0.166819 0.166819i
\(549\) −37.2304 + 12.2914i −1.58896 + 0.524582i
\(550\) 0.793675 21.8809i 0.0338424 0.933006i
\(551\) 7.73552i 0.329544i
\(552\) −9.77180 + 1.57133i −0.415915 + 0.0668804i
\(553\) −3.44989 + 3.44989i −0.146704 + 0.146704i
\(554\) −14.4590 −0.614306
\(555\) −5.46241 + 3.23000i −0.231866 + 0.137106i
\(556\) −0.884659 −0.0375179
\(557\) −4.22121 + 4.22121i −0.178859 + 0.178859i −0.790858 0.612000i \(-0.790365\pi\)
0.612000 + 0.790858i \(0.290365\pi\)
\(558\) −6.47700 + 12.8614i −0.274193 + 0.544468i
\(559\) 0.382461i 0.0161764i
\(560\) −3.20007 8.13995i −0.135228 0.343976i
\(561\) −30.8244 + 42.6373i −1.30141 + 1.80015i
\(562\) −2.46184 2.46184i −0.103846 0.103846i
\(563\) 11.0358 + 11.0358i 0.465105 + 0.465105i 0.900325 0.435219i \(-0.143329\pi\)
−0.435219 + 0.900325i \(0.643329\pi\)
\(564\) −13.4543 + 18.6103i −0.566526 + 0.783636i
\(565\) 5.67279 + 14.4298i 0.238656 + 0.607065i
\(566\) 4.85720i 0.204164i
\(567\) 34.8205 + 5.17879i 1.46232 + 0.217489i
\(568\) 7.15026 7.15026i 0.300018 0.300018i
\(569\) 16.3299 0.684585 0.342293 0.939593i \(-0.388797\pi\)
0.342293 + 0.939593i \(0.388797\pi\)
\(570\) −3.33376 + 1.97130i −0.139636 + 0.0825688i
\(571\) 28.8841 1.20876 0.604381 0.796695i \(-0.293421\pi\)
0.604381 + 0.796695i \(0.293421\pi\)
\(572\) −0.375953 + 0.375953i −0.0157194 + 0.0157194i
\(573\) −27.5236 + 4.42587i −1.14981 + 0.184893i
\(574\) 15.6255i 0.652194i
\(575\) 1.03566 28.5524i 0.0431902 1.19072i
\(576\) −0.940499 2.84877i −0.0391874 0.118699i
\(577\) −10.6942 10.6942i −0.445205 0.445205i 0.448552 0.893757i \(-0.351940\pi\)
−0.893757 + 0.448552i \(0.851940\pi\)
\(578\) 22.0028 + 22.0028i 0.915194 + 0.915194i
\(579\) 5.47147 + 3.95557i 0.227386 + 0.164388i
\(580\) 6.90793 15.8579i 0.286836 0.658462i
\(581\) 51.2862i 2.12771i
\(582\) −0.410006 2.54974i −0.0169953 0.105690i
\(583\) 7.08811 7.08811i 0.293560 0.293560i
\(584\) −4.31060 −0.178374
\(585\) 0.626364 0.520601i 0.0258970 0.0215242i
\(586\) −6.04102 −0.249552
\(587\) −26.1994 + 26.1994i −1.08136 + 1.08136i −0.0849807 + 0.996383i \(0.527083\pi\)
−0.996383 + 0.0849807i \(0.972917\pi\)
\(588\) −2.28234 14.1934i −0.0941223 0.585327i
\(589\) 4.80009i 0.197784i
\(590\) −28.4299 + 11.1767i −1.17044 + 0.460137i
\(591\) 18.9157 + 13.6750i 0.778089 + 0.562516i
\(592\) 1.15860 + 1.15860i 0.0476183 + 0.0476183i
\(593\) 13.6587 + 13.6587i 0.560897 + 0.560897i 0.929562 0.368665i \(-0.120185\pi\)
−0.368665 + 0.929562i \(0.620185\pi\)
\(594\) 6.87817 21.6898i 0.282215 0.889944i
\(595\) −55.6220 24.2298i −2.28028 0.993324i
\(596\) 14.4191i 0.590629i
\(597\) −13.0266 + 2.09472i −0.533145 + 0.0857313i
\(598\) −0.490580 + 0.490580i −0.0200613 + 0.0200613i
\(599\) 29.0472 1.18684 0.593418 0.804894i \(-0.297778\pi\)
0.593418 + 0.804894i \(0.297778\pi\)
\(600\) 8.59463 1.06409i 0.350874 0.0434412i
\(601\) −14.9410 −0.609458 −0.304729 0.952439i \(-0.598566\pi\)
−0.304729 + 0.952439i \(0.598566\pi\)
\(602\) 8.71261 8.71261i 0.355100 0.355100i
\(603\) 36.2993 + 18.2803i 1.47822 + 0.744430i
\(604\) 12.5541i 0.510820i
\(605\) −16.7612 7.30145i −0.681441 0.296846i
\(606\) −1.34306 + 1.85777i −0.0545583 + 0.0754666i
\(607\) 8.68114 + 8.68114i 0.352357 + 0.352357i 0.860986 0.508629i \(-0.169848\pi\)
−0.508629 + 0.860986i \(0.669848\pi\)
\(608\) 0.707107 + 0.707107i 0.0286770 + 0.0286770i
\(609\) 30.7043 42.4711i 1.24420 1.72102i
\(610\) −27.1969 + 10.6920i −1.10117 + 0.432905i
\(611\) 1.60976i 0.0651239i
\(612\) −18.5861 9.35991i −0.751297 0.378352i
\(613\) −5.07536 + 5.07536i −0.204992 + 0.204992i −0.802135 0.597143i \(-0.796303\pi\)
0.597143 + 0.802135i \(0.296303\pi\)
\(614\) 17.8017 0.718417
\(615\) 14.9853 + 3.84855i 0.604265 + 0.155189i
\(616\) −17.1287 −0.690136
\(617\) −4.31435 + 4.31435i −0.173689 + 0.173689i −0.788598 0.614909i \(-0.789193\pi\)
0.614909 + 0.788598i \(0.289193\pi\)
\(618\) 21.4764 3.45346i 0.863907 0.138919i
\(619\) 6.95816i 0.279672i −0.990175 0.139836i \(-0.955342\pi\)
0.990175 0.139836i \(-0.0446575\pi\)
\(620\) −4.28655 + 9.84022i −0.172152 + 0.395193i
\(621\) 8.97531 28.3030i 0.360167 1.13576i
\(622\) −1.54997 1.54997i −0.0621481 0.0621481i
\(623\) 12.3818 + 12.3818i 0.496064 + 0.496064i
\(624\) −0.170423 0.123206i −0.00682238 0.00493221i
\(625\) −1.81124 + 24.9343i −0.0724496 + 0.997372i
\(626\) 17.3861i 0.694888i
\(627\) 1.20418 + 7.48856i 0.0480904 + 0.299064i
\(628\) −9.08703 + 9.08703i −0.362612 + 0.362612i
\(629\) 11.3657 0.453181
\(630\) 26.1283 + 2.40932i 1.04098 + 0.0959898i
\(631\) −16.5313 −0.658102 −0.329051 0.944312i \(-0.606729\pi\)
−0.329051 + 0.944312i \(0.606729\pi\)
\(632\) −0.881987 + 0.881987i −0.0350835 + 0.0350835i
\(633\) −1.52397 9.47726i −0.0605724 0.376687i
\(634\) 7.07127i 0.280836i
\(635\) 1.98362 + 5.04570i 0.0787176 + 0.200233i
\(636\) 3.21311 + 2.32290i 0.127408 + 0.0921090i
\(637\) −0.712562 0.712562i −0.0282327 0.0282327i
\(638\) −23.9528 23.9528i −0.948300 0.948300i
\(639\) 9.51031 + 28.8067i 0.376222 + 1.13958i
\(640\) −0.818117 2.08103i −0.0323389 0.0822599i
\(641\) 16.7295i 0.660775i 0.943845 + 0.330388i \(0.107180\pi\)
−0.943845 + 0.330388i \(0.892820\pi\)
\(642\) 16.9889 2.73187i 0.670499 0.107818i
\(643\) 21.5217 21.5217i 0.848733 0.848733i −0.141242 0.989975i \(-0.545110\pi\)
0.989975 + 0.141242i \(0.0451095\pi\)
\(644\) −22.3512 −0.880761
\(645\) 6.20974 + 10.5016i 0.244508 + 0.413499i
\(646\) 6.93661 0.272917
\(647\) 7.41491 7.41491i 0.291510 0.291510i −0.546166 0.837677i \(-0.683913\pi\)
0.837677 + 0.546166i \(0.183913\pi\)
\(648\) 8.90208 + 1.32399i 0.349707 + 0.0520113i
\(649\) 59.8244i 2.34831i
\(650\) 0.444540 0.413420i 0.0174363 0.0162157i
\(651\) −19.0528 + 26.3545i −0.746739 + 1.03291i
\(652\) 2.97919 + 2.97919i 0.116674 + 0.116674i
\(653\) −19.0621 19.0621i −0.745959 0.745959i 0.227758 0.973718i \(-0.426860\pi\)
−0.973718 + 0.227758i \(0.926860\pi\)
\(654\) 0.227012 0.314010i 0.00887688 0.0122788i
\(655\) 0.923926 2.12097i 0.0361008 0.0828731i
\(656\) 3.99475i 0.155969i
\(657\) 5.81651 11.5499i 0.226924 0.450604i
\(658\) −36.6709 + 36.6709i −1.42958 + 1.42958i
\(659\) −43.8126 −1.70670 −0.853349 0.521341i \(-0.825432\pi\)
−0.853349 + 0.521341i \(0.825432\pi\)
\(660\) 4.21881 16.4269i 0.164217 0.639418i
\(661\) −16.9162 −0.657963 −0.328982 0.944336i \(-0.606705\pi\)
−0.328982 + 0.944336i \(0.606705\pi\)
\(662\) −11.0198 + 11.0198i −0.428296 + 0.428296i
\(663\) −1.44023 + 0.231593i −0.0559339 + 0.00899434i
\(664\) 13.1116i 0.508830i
\(665\) −8.13995 + 3.20007i −0.315654 + 0.124093i
\(666\) −4.66774 + 1.54102i −0.180871 + 0.0597133i
\(667\) −31.2559 31.2559i −1.21023 1.21023i
\(668\) 6.66427 + 6.66427i 0.257848 + 0.257848i
\(669\) −18.9190 13.6774i −0.731451 0.528799i
\(670\) 27.7724 + 12.0981i 1.07294 + 0.467390i
\(671\) 57.2299i 2.20933i
\(672\) −1.07561 6.68899i −0.0414925 0.258033i
\(673\) −29.1932 + 29.1932i −1.12532 + 1.12532i −0.134386 + 0.990929i \(0.542906\pi\)
−0.990929 + 0.134386i \(0.957094\pi\)
\(674\) 18.2107 0.701449
\(675\) −8.74602 + 24.4644i −0.336635 + 0.941635i
\(676\) 12.9853 0.499433
\(677\) 10.7238 10.7238i 0.412148 0.412148i −0.470338 0.882486i \(-0.655868\pi\)
0.882486 + 0.470338i \(0.155868\pi\)
\(678\) 1.90674 + 11.8576i 0.0732280 + 0.455390i
\(679\) 5.83207i 0.223814i
\(680\) −14.2201 6.19449i −0.545316 0.237548i
\(681\) 27.3012 + 19.7373i 1.04618 + 0.756333i
\(682\) 14.8633 + 14.8633i 0.569146 + 0.569146i
\(683\) −35.6719 35.6719i −1.36495 1.36495i −0.867488 0.497459i \(-0.834267\pi\)
−0.497459 0.867488i \(-0.665733\pi\)
\(684\) −2.84877 + 0.940499i −0.108925 + 0.0359609i
\(685\) 11.4929 4.51821i 0.439121 0.172632i
\(686\) 5.08436i 0.194122i
\(687\) 11.1063 1.78593i 0.423732 0.0681373i
\(688\) 2.22743 2.22743i 0.0849201 0.0849201i
\(689\) 0.277928 0.0105882
\(690\) 5.50511 21.4355i 0.209576 0.816035i
\(691\) −26.9995 −1.02711 −0.513554 0.858057i \(-0.671671\pi\)
−0.513554 + 0.858057i \(0.671671\pi\)
\(692\) 3.33173 3.33173i 0.126653 0.126653i
\(693\) 23.1126 45.8949i 0.877975 1.74340i
\(694\) 7.64624i 0.290247i
\(695\) 0.790013 1.81356i 0.0299669 0.0687921i
\(696\) 7.84975 10.8580i 0.297544 0.411572i
\(697\) −19.5939 19.5939i −0.742173 0.742173i
\(698\) −3.33026 3.33026i −0.126052 0.126052i
\(699\) 11.4043 15.7748i 0.431351 0.596658i
\(700\) 19.5447 + 0.708933i 0.738719 + 0.0267951i
\(701\) 43.3103i 1.63581i −0.575354 0.817905i \(-0.695136\pi\)
0.575354 0.817905i \(-0.304864\pi\)
\(702\) 0.560081 0.290385i 0.0211389 0.0109599i
\(703\) 1.15860 1.15860i 0.0436975 0.0436975i
\(704\) −4.37906 −0.165042
\(705\) −26.1365 44.2006i −0.984356 1.66469i
\(706\) 2.58792 0.0973976
\(707\) −3.66066 + 3.66066i −0.137673 + 0.137673i
\(708\) −23.3622 + 3.75672i −0.878007 + 0.141186i
\(709\) 5.62201i 0.211139i −0.994412 0.105569i \(-0.966333\pi\)
0.994412 0.105569i \(-0.0336665\pi\)
\(710\) 8.27279 + 21.0434i 0.310472 + 0.789743i
\(711\) −1.17310 3.55331i −0.0439947 0.133260i
\(712\) 3.16547 + 3.16547i 0.118631 + 0.118631i
\(713\) 19.3951 + 19.3951i 0.726353 + 0.726353i
\(714\) −38.0848 27.5332i −1.42529 1.03041i
\(715\) −0.434975 1.10644i −0.0162671 0.0413784i
\(716\) 20.3926i 0.762105i
\(717\) 2.06567 + 12.8459i 0.0771437 + 0.479741i
\(718\) −6.51117 + 6.51117i −0.242995 + 0.242995i
\(719\) 36.9146 1.37668 0.688340 0.725388i \(-0.258340\pi\)
0.688340 + 0.725388i \(0.258340\pi\)
\(720\) 6.67986 + 0.615959i 0.248944 + 0.0229554i
\(721\) 49.1233 1.82945
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −3.08290 19.1719i −0.114654 0.713010i
\(724\) 19.7998i 0.735855i
\(725\) 26.3399 + 28.3226i 0.978238 + 1.05188i
\(726\) −11.4766 8.29692i −0.425935 0.307928i
\(727\) 23.0361 + 23.0361i 0.854362 + 0.854362i 0.990667 0.136305i \(-0.0435227\pi\)
−0.136305 + 0.990667i \(0.543523\pi\)
\(728\) −0.335812 0.335812i −0.0124460 0.0124460i
\(729\) −15.5595 + 22.0658i −0.576279 + 0.817253i
\(730\) 3.84943 8.83677i 0.142474 0.327063i
\(731\) 21.8508i 0.808181i
\(732\) −22.3490 + 3.59379i −0.826044 + 0.132830i
\(733\) −32.4240 + 32.4240i −1.19761 + 1.19761i −0.222726 + 0.974881i \(0.571495\pi\)
−0.974881 + 0.222726i \(0.928505\pi\)
\(734\) −19.9298 −0.735621
\(735\) 31.1348 + 7.99611i 1.14842 + 0.294941i
\(736\) −5.71423 −0.210629
\(737\) 41.9493 41.9493i 1.54522 1.54522i
\(738\) 10.7036 + 5.39030i 0.394004 + 0.198420i
\(739\) 36.8773i 1.35655i 0.734806 + 0.678277i \(0.237273\pi\)
−0.734806 + 0.678277i \(0.762727\pi\)
\(740\) −3.40979 + 1.34050i −0.125346 + 0.0492776i
\(741\) −0.123206 + 0.170423i −0.00452610 + 0.00626064i
\(742\) 6.33130 + 6.33130i 0.232429 + 0.232429i
\(743\) −25.4177 25.4177i −0.932483 0.932483i 0.0653772 0.997861i \(-0.479175\pi\)
−0.997861 + 0.0653772i \(0.979175\pi\)
\(744\) −4.87097 + 6.73768i −0.178579 + 0.247015i
\(745\) 29.5592 + 12.8765i 1.08297 + 0.471757i
\(746\) 9.81579i 0.359382i
\(747\) 35.1315 + 17.6922i 1.28540 + 0.647323i
\(748\) −21.4790 + 21.4790i −0.785349 + 0.785349i
\(749\) 38.8590 1.41988
\(750\) −5.49374 + 18.5693i −0.200603 + 0.678055i
\(751\) 4.92408 0.179682 0.0898412 0.995956i \(-0.471364\pi\)
0.0898412 + 0.995956i \(0.471364\pi\)
\(752\) −9.37516 + 9.37516i −0.341877 + 0.341877i
\(753\) 18.3964 2.95820i 0.670403 0.107803i
\(754\) 0.939198i 0.0342036i
\(755\) 25.7361 + 11.2110i 0.936631 + 0.408011i
\(756\) 19.3740 + 6.14378i 0.704624 + 0.223447i
\(757\) 13.6895 + 13.6895i 0.497555 + 0.497555i 0.910676 0.413121i \(-0.135561\pi\)
−0.413121 + 0.910676i \(0.635561\pi\)
\(758\) −24.6735 24.6735i −0.896184 0.896184i
\(759\) −35.1236 25.3925i −1.27491 0.921688i
\(760\) −2.08103 + 0.818117i −0.0754869 + 0.0296762i
\(761\) 20.7833i 0.753394i 0.926337 + 0.376697i \(0.122940\pi\)
−0.926337 + 0.376697i \(0.877060\pi\)
\(762\) 0.666737 + 4.14630i 0.0241533 + 0.150204i
\(763\) 0.618745 0.618745i 0.0224001 0.0224001i
\(764\) −16.0949 −0.582292
\(765\) 35.7855 29.7430i 1.29383 1.07536i
\(766\) 4.24601 0.153415
\(767\) −1.17287 + 1.17287i −0.0423499 + 0.0423499i
\(768\) −0.274986 1.71008i −0.00992271 0.0617073i
\(769\) 41.2077i 1.48599i −0.669297 0.742995i \(-0.733405\pi\)
0.669297 0.742995i \(-0.266595\pi\)
\(770\) 15.2962 35.1140i 0.551236 1.26542i
\(771\) 5.31397 + 3.84171i 0.191378 + 0.138356i
\(772\) 2.75631 + 2.75631i 0.0992018 + 0.0992018i
\(773\) 12.8806 + 12.8806i 0.463282 + 0.463282i 0.899729 0.436448i \(-0.143764\pi\)
−0.436448 + 0.899729i \(0.643764\pi\)
\(774\) 2.96263 + 8.97380i 0.106490 + 0.322557i
\(775\) −16.3446 17.5749i −0.587114 0.631310i
\(776\) 1.49100i 0.0535239i
\(777\) −10.9600 + 1.76240i −0.393188 + 0.0632257i