Properties

Label 570.2.k.b.77.17
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 77.17
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.17

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.47884 - 0.901679i) q^{3} -1.00000i q^{4} +(-1.61979 + 1.54152i) q^{5} +(0.408116 - 1.68328i) q^{6} +(-1.95232 - 1.95232i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.37395 - 2.66688i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.47884 - 0.901679i) q^{3} -1.00000i q^{4} +(-1.61979 + 1.54152i) q^{5} +(0.408116 - 1.68328i) q^{6} +(-1.95232 - 1.95232i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.37395 - 2.66688i) q^{9} +(-0.0553424 + 2.23538i) q^{10} -3.67926i q^{11} +(-0.901679 - 1.47884i) q^{12} +(2.60584 - 2.60584i) q^{13} -2.76100 q^{14} +(-1.00545 + 3.74020i) q^{15} -1.00000 q^{16} +(-1.52607 + 1.52607i) q^{17} +(-0.914240 - 2.85730i) q^{18} -1.00000i q^{19} +(1.54152 + 1.61979i) q^{20} +(-4.64754 - 1.12681i) q^{21} +(-2.60163 - 2.60163i) q^{22} +(0.483241 + 0.483241i) q^{23} +(-1.68328 - 0.408116i) q^{24} +(0.247423 - 4.99387i) q^{25} -3.68522i q^{26} +(-0.372814 - 5.18276i) q^{27} +(-1.95232 + 1.95232i) q^{28} +8.02750 q^{29} +(1.93375 + 3.35568i) q^{30} -3.06305 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.31751 - 5.44104i) q^{33} +2.15819i q^{34} +(6.17189 + 0.152800i) q^{35} +(-2.66688 - 1.37395i) q^{36} +(7.32517 + 7.32517i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(1.50400 - 6.20326i) q^{39} +(2.23538 + 0.0553424i) q^{40} +5.46374i q^{41} +(-4.08308 + 2.48954i) q^{42} +(-3.11201 + 3.11201i) q^{43} -3.67926 q^{44} +(1.88555 + 6.43776i) q^{45} +0.683406 q^{46} +(-3.44995 + 3.44995i) q^{47} +(-1.47884 + 0.901679i) q^{48} +0.623122i q^{49} +(-3.35625 - 3.70616i) q^{50} +(-0.880794 + 3.63285i) q^{51} +(-2.60584 - 2.60584i) q^{52} +(7.51422 + 7.51422i) q^{53} +(-3.92838 - 3.40115i) q^{54} +(5.67165 + 5.95961i) q^{55} +2.76100i q^{56} +(-0.901679 - 1.47884i) q^{57} +(5.67630 - 5.67630i) q^{58} -11.1184 q^{59} +(3.74020 + 1.00545i) q^{60} +0.989652 q^{61} +(-2.16590 + 2.16590i) q^{62} +(-7.88901 + 2.52422i) q^{63} +1.00000i q^{64} +(-0.203949 + 8.23787i) q^{65} +(-6.19323 - 1.50156i) q^{66} +(8.05094 + 8.05094i) q^{67} +(1.52607 + 1.52607i) q^{68} +(1.15037 + 0.278909i) q^{69} +(4.47223 - 4.25614i) q^{70} -4.07805i q^{71} +(-2.85730 + 0.914240i) q^{72} +(11.1477 - 11.1477i) q^{73} +10.3593 q^{74} +(-4.13697 - 7.60825i) q^{75} -1.00000 q^{76} +(-7.18309 + 7.18309i) q^{77} +(-3.32288 - 5.44985i) q^{78} +7.15671i q^{79} +(1.61979 - 1.54152i) q^{80} +(-5.22452 - 7.32833i) q^{81} +(3.86345 + 3.86345i) q^{82} +(-2.66585 - 2.66585i) q^{83} +(-1.12681 + 4.64754i) q^{84} +(0.119439 - 4.82439i) q^{85} +4.40105i q^{86} +(11.8714 - 7.23823i) q^{87} +(-2.60163 + 2.60163i) q^{88} -1.05913 q^{89} +(5.88546 + 3.21890i) q^{90} -10.1749 q^{91} +(0.483241 - 0.483241i) q^{92} +(-4.52976 + 2.76188i) q^{93} +4.87897i q^{94} +(1.54152 + 1.61979i) q^{95} +(-0.408116 + 1.68328i) q^{96} +(5.51911 + 5.51911i) q^{97} +(0.440614 + 0.440614i) q^{98} +(-9.81214 - 5.05512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} + 16q^{21} - 4q^{22} + 16q^{25} - 44q^{27} + 20q^{28} + 32q^{30} - 24q^{31} - 4q^{33} + 4q^{36} - 8q^{40} + 12q^{42} - 8q^{43} + 28q^{45} - 16q^{46} - 4q^{48} + 40q^{51} - 8q^{52} - 36q^{55} - 4q^{57} + 44q^{58} + 16q^{60} - 120q^{61} - 12q^{63} + 80q^{67} - 36q^{70} + 44q^{73} + 4q^{75} - 36q^{76} - 64q^{78} + 36q^{81} + 8q^{82} - 24q^{85} - 28q^{87} - 4q^{88} + 44q^{90} - 72q^{93} - 4q^{96} + 92q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.47884 0.901679i 0.853810 0.520584i
\(4\) 1.00000i 0.500000i
\(5\) −1.61979 + 1.54152i −0.724391 + 0.689389i
\(6\) 0.408116 1.68328i 0.166613 0.687197i
\(7\) −1.95232 1.95232i −0.737908 0.737908i 0.234265 0.972173i \(-0.424732\pi\)
−0.972173 + 0.234265i \(0.924732\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.37395 2.66688i 0.457984 0.888961i
\(10\) −0.0553424 + 2.23538i −0.0175008 + 0.706890i
\(11\) 3.67926i 1.10934i −0.832071 0.554669i \(-0.812845\pi\)
0.832071 0.554669i \(-0.187155\pi\)
\(12\) −0.901679 1.47884i −0.260292 0.426905i
\(13\) 2.60584 2.60584i 0.722730 0.722730i −0.246430 0.969161i \(-0.579258\pi\)
0.969161 + 0.246430i \(0.0792576\pi\)
\(14\) −2.76100 −0.737908
\(15\) −1.00545 + 3.74020i −0.259607 + 0.965714i
\(16\) −1.00000 −0.250000
\(17\) −1.52607 + 1.52607i −0.370127 + 0.370127i −0.867523 0.497396i \(-0.834289\pi\)
0.497396 + 0.867523i \(0.334289\pi\)
\(18\) −0.914240 2.85730i −0.215489 0.673472i
\(19\) 1.00000i 0.229416i
\(20\) 1.54152 + 1.61979i 0.344695 + 0.362195i
\(21\) −4.64754 1.12681i −1.01418 0.245890i
\(22\) −2.60163 2.60163i −0.554669 0.554669i
\(23\) 0.483241 + 0.483241i 0.100763 + 0.100763i 0.755691 0.654928i \(-0.227301\pi\)
−0.654928 + 0.755691i \(0.727301\pi\)
\(24\) −1.68328 0.408116i −0.343599 0.0833064i
\(25\) 0.247423 4.99387i 0.0494845 0.998775i
\(26\) 3.68522i 0.722730i
\(27\) −0.372814 5.18276i −0.0717481 0.997423i
\(28\) −1.95232 + 1.95232i −0.368954 + 0.368954i
\(29\) 8.02750 1.49067 0.745335 0.666691i \(-0.232290\pi\)
0.745335 + 0.666691i \(0.232290\pi\)
\(30\) 1.93375 + 3.35568i 0.353054 + 0.612661i
\(31\) −3.06305 −0.550139 −0.275070 0.961424i \(-0.588701\pi\)
−0.275070 + 0.961424i \(0.588701\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −3.31751 5.44104i −0.577504 0.947163i
\(34\) 2.15819i 0.370127i
\(35\) 6.17189 + 0.152800i 1.04324 + 0.0258280i
\(36\) −2.66688 1.37395i −0.444480 0.228992i
\(37\) 7.32517 + 7.32517i 1.20425 + 1.20425i 0.972861 + 0.231389i \(0.0743269\pi\)
0.231389 + 0.972861i \(0.425673\pi\)
\(38\) −0.707107 0.707107i −0.114708 0.114708i
\(39\) 1.50400 6.20326i 0.240832 0.993317i
\(40\) 2.23538 + 0.0553424i 0.353445 + 0.00875039i
\(41\) 5.46374i 0.853293i 0.904419 + 0.426646i \(0.140305\pi\)
−0.904419 + 0.426646i \(0.859695\pi\)
\(42\) −4.08308 + 2.48954i −0.630034 + 0.384144i
\(43\) −3.11201 + 3.11201i −0.474577 + 0.474577i −0.903392 0.428815i \(-0.858931\pi\)
0.428815 + 0.903392i \(0.358931\pi\)
\(44\) −3.67926 −0.554669
\(45\) 1.88555 + 6.43776i 0.281081 + 0.959684i
\(46\) 0.683406 0.100763
\(47\) −3.44995 + 3.44995i −0.503227 + 0.503227i −0.912439 0.409212i \(-0.865804\pi\)
0.409212 + 0.912439i \(0.365804\pi\)
\(48\) −1.47884 + 0.901679i −0.213453 + 0.130146i
\(49\) 0.623122i 0.0890174i
\(50\) −3.35625 3.70616i −0.474645 0.524130i
\(51\) −0.880794 + 3.63285i −0.123336 + 0.508700i
\(52\) −2.60584 2.60584i −0.361365 0.361365i
\(53\) 7.51422 + 7.51422i 1.03216 + 1.03216i 0.999465 + 0.0326918i \(0.0104080\pi\)
0.0326918 + 0.999465i \(0.489592\pi\)
\(54\) −3.92838 3.40115i −0.534585 0.462837i
\(55\) 5.67165 + 5.95961i 0.764765 + 0.803594i
\(56\) 2.76100i 0.368954i
\(57\) −0.901679 1.47884i −0.119430 0.195877i
\(58\) 5.67630 5.67630i 0.745335 0.745335i
\(59\) −11.1184 −1.44749 −0.723744 0.690068i \(-0.757580\pi\)
−0.723744 + 0.690068i \(0.757580\pi\)
\(60\) 3.74020 + 1.00545i 0.482857 + 0.129803i
\(61\) 0.989652 0.126712 0.0633559 0.997991i \(-0.479820\pi\)
0.0633559 + 0.997991i \(0.479820\pi\)
\(62\) −2.16590 + 2.16590i −0.275070 + 0.275070i
\(63\) −7.88901 + 2.52422i −0.993921 + 0.318022i
\(64\) 1.00000i 0.125000i
\(65\) −0.203949 + 8.23787i −0.0252967 + 1.02178i
\(66\) −6.19323 1.50156i −0.762334 0.184830i
\(67\) 8.05094 + 8.05094i 0.983579 + 0.983579i 0.999867 0.0162886i \(-0.00518506\pi\)
−0.0162886 + 0.999867i \(0.505185\pi\)
\(68\) 1.52607 + 1.52607i 0.185063 + 0.185063i
\(69\) 1.15037 + 0.278909i 0.138488 + 0.0335767i
\(70\) 4.47223 4.25614i 0.534534 0.508706i
\(71\) 4.07805i 0.483975i −0.970279 0.241988i \(-0.922201\pi\)
0.970279 0.241988i \(-0.0777993\pi\)
\(72\) −2.85730 + 0.914240i −0.336736 + 0.107744i
\(73\) 11.1477 11.1477i 1.30474 1.30474i 0.379579 0.925159i \(-0.376069\pi\)
0.925159 0.379579i \(-0.123931\pi\)
\(74\) 10.3593 1.20425
\(75\) −4.13697 7.60825i −0.477696 0.878525i
\(76\) −1.00000 −0.114708
\(77\) −7.18309 + 7.18309i −0.818589 + 0.818589i
\(78\) −3.32288 5.44985i −0.376242 0.617074i
\(79\) 7.15671i 0.805193i 0.915378 + 0.402596i \(0.131892\pi\)
−0.915378 + 0.402596i \(0.868108\pi\)
\(80\) 1.61979 1.54152i 0.181098 0.172347i
\(81\) −5.22452 7.32833i −0.580502 0.814259i
\(82\) 3.86345 + 3.86345i 0.426646 + 0.426646i
\(83\) −2.66585 2.66585i −0.292615 0.292615i 0.545497 0.838113i \(-0.316341\pi\)
−0.838113 + 0.545497i \(0.816341\pi\)
\(84\) −1.12681 + 4.64754i −0.122945 + 0.507089i
\(85\) 0.119439 4.82439i 0.0129550 0.523278i
\(86\) 4.40105i 0.474577i
\(87\) 11.8714 7.23823i 1.27275 0.776019i
\(88\) −2.60163 + 2.60163i −0.277334 + 0.277334i
\(89\) −1.05913 −0.112267 −0.0561336 0.998423i \(-0.517877\pi\)
−0.0561336 + 0.998423i \(0.517877\pi\)
\(90\) 5.88546 + 3.21890i 0.620382 + 0.339302i
\(91\) −10.1749 −1.06662
\(92\) 0.483241 0.483241i 0.0503814 0.0503814i
\(93\) −4.52976 + 2.76188i −0.469714 + 0.286394i
\(94\) 4.87897i 0.503227i
\(95\) 1.54152 + 1.61979i 0.158157 + 0.166187i
\(96\) −0.408116 + 1.68328i −0.0416532 + 0.171799i
\(97\) 5.51911 + 5.51911i 0.560381 + 0.560381i 0.929416 0.369035i \(-0.120312\pi\)
−0.369035 + 0.929416i \(0.620312\pi\)
\(98\) 0.440614 + 0.440614i 0.0445087 + 0.0445087i
\(99\) −9.81214 5.05512i −0.986157 0.508058i
\(100\) −4.99387 0.247423i −0.499387 0.0247423i
\(101\) 7.18857i 0.715289i −0.933858 0.357645i \(-0.883580\pi\)
0.933858 0.357645i \(-0.116420\pi\)
\(102\) 1.94600 + 3.19163i 0.192682 + 0.316018i
\(103\) 5.24203 5.24203i 0.516512 0.516512i −0.400002 0.916514i \(-0.630991\pi\)
0.916514 + 0.400002i \(0.130991\pi\)
\(104\) −3.68522 −0.361365
\(105\) 9.26503 5.33910i 0.904175 0.521043i
\(106\) 10.6267 1.03216
\(107\) −3.71052 + 3.71052i −0.358709 + 0.358709i −0.863337 0.504628i \(-0.831630\pi\)
0.504628 + 0.863337i \(0.331630\pi\)
\(108\) −5.18276 + 0.372814i −0.498711 + 0.0358740i
\(109\) 1.39041i 0.133178i −0.997781 0.0665888i \(-0.978788\pi\)
0.997781 0.0665888i \(-0.0212116\pi\)
\(110\) 8.22455 + 0.203619i 0.784180 + 0.0194143i
\(111\) 17.4377 + 4.22782i 1.65511 + 0.401287i
\(112\) 1.95232 + 1.95232i 0.184477 + 0.184477i
\(113\) −10.6045 10.6045i −0.997589 0.997589i 0.00240835 0.999997i \(-0.499233\pi\)
−0.999997 + 0.00240835i \(0.999233\pi\)
\(114\) −1.68328 0.408116i −0.157654 0.0382236i
\(115\) −1.52767 0.0378213i −0.142456 0.00352685i
\(116\) 8.02750i 0.745335i
\(117\) −3.36917 10.5298i −0.311480 0.973477i
\(118\) −7.86188 + 7.86188i −0.723744 + 0.723744i
\(119\) 5.95877 0.546239
\(120\) 3.35568 1.93375i 0.306330 0.176527i
\(121\) −2.53692 −0.230629
\(122\) 0.699789 0.699789i 0.0633559 0.0633559i
\(123\) 4.92654 + 8.08001i 0.444211 + 0.728550i
\(124\) 3.06305i 0.275070i
\(125\) 7.29739 + 8.47042i 0.652699 + 0.757618i
\(126\) −3.79348 + 7.36326i −0.337950 + 0.655971i
\(127\) 13.6390 + 13.6390i 1.21027 + 1.21027i 0.970938 + 0.239330i \(0.0769276\pi\)
0.239330 + 0.970938i \(0.423072\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −1.79614 + 7.40821i −0.158141 + 0.652256i
\(130\) 5.68084 + 5.96927i 0.498243 + 0.523539i
\(131\) 15.8526i 1.38505i −0.721396 0.692523i \(-0.756499\pi\)
0.721396 0.692523i \(-0.243501\pi\)
\(132\) −5.44104 + 3.31751i −0.473582 + 0.288752i
\(133\) −1.95232 + 1.95232i −0.169288 + 0.169288i
\(134\) 11.3857 0.983579
\(135\) 8.59322 + 7.82027i 0.739586 + 0.673062i
\(136\) 2.15819 0.185063
\(137\) 0.0250882 0.0250882i 0.00214343 0.00214343i −0.706034 0.708178i \(-0.749518\pi\)
0.708178 + 0.706034i \(0.249518\pi\)
\(138\) 1.01065 0.616213i 0.0860322 0.0524555i
\(139\) 15.9440i 1.35235i −0.736739 0.676177i \(-0.763635\pi\)
0.736739 0.676177i \(-0.236365\pi\)
\(140\) 0.152800 6.17189i 0.0129140 0.521620i
\(141\) −1.99119 + 8.21268i −0.167688 + 0.691633i
\(142\) −2.88361 2.88361i −0.241988 0.241988i
\(143\) −9.58756 9.58756i −0.801752 0.801752i
\(144\) −1.37395 + 2.66688i −0.114496 + 0.222240i
\(145\) −13.0028 + 12.3746i −1.07983 + 1.02765i
\(146\) 15.7652i 1.30474i
\(147\) 0.561856 + 0.921499i 0.0463411 + 0.0760039i
\(148\) 7.32517 7.32517i 0.602125 0.602125i
\(149\) 17.7034 1.45032 0.725160 0.688580i \(-0.241766\pi\)
0.725160 + 0.688580i \(0.241766\pi\)
\(150\) −8.30513 2.45456i −0.678111 0.200414i
\(151\) −13.6930 −1.11432 −0.557160 0.830405i \(-0.688109\pi\)
−0.557160 + 0.830405i \(0.688109\pi\)
\(152\) −0.707107 + 0.707107i −0.0573539 + 0.0573539i
\(153\) 1.97311 + 6.16660i 0.159516 + 0.498540i
\(154\) 10.1584i 0.818589i
\(155\) 4.96148 4.72175i 0.398516 0.379260i
\(156\) −6.20326 1.50400i −0.496658 0.120416i
\(157\) −1.10214 1.10214i −0.0879600 0.0879600i 0.661758 0.749718i \(-0.269811\pi\)
−0.749718 + 0.661758i \(0.769811\pi\)
\(158\) 5.06056 + 5.06056i 0.402596 + 0.402596i
\(159\) 17.8878 + 4.33693i 1.41859 + 0.343941i
\(160\) 0.0553424 2.23538i 0.00437520 0.176723i
\(161\) 1.88688i 0.148707i
\(162\) −8.87620 1.48762i −0.697380 0.116878i
\(163\) −11.0666 + 11.0666i −0.866806 + 0.866806i −0.992117 0.125311i \(-0.960007\pi\)
0.125311 + 0.992117i \(0.460007\pi\)
\(164\) 5.46374 0.426646
\(165\) 13.7611 + 3.69932i 1.07130 + 0.287992i
\(166\) −3.77008 −0.292615
\(167\) −6.38610 + 6.38610i −0.494171 + 0.494171i −0.909618 0.415446i \(-0.863625\pi\)
0.415446 + 0.909618i \(0.363625\pi\)
\(168\) 2.48954 + 4.08308i 0.192072 + 0.315017i
\(169\) 0.580815i 0.0446781i
\(170\) −3.32690 3.49581i −0.255162 0.268117i
\(171\) −2.66688 1.37395i −0.203942 0.105069i
\(172\) 3.11201 + 3.11201i 0.237289 + 0.237289i
\(173\) −0.393098 0.393098i −0.0298867 0.0298867i 0.692006 0.721892i \(-0.256727\pi\)
−0.721892 + 0.692006i \(0.756727\pi\)
\(174\) 3.27615 13.5126i 0.248365 1.02438i
\(175\) −10.2327 + 9.26660i −0.773519 + 0.700489i
\(176\) 3.67926i 0.277334i
\(177\) −16.4423 + 10.0252i −1.23588 + 0.753540i
\(178\) −0.748916 + 0.748916i −0.0561336 + 0.0561336i
\(179\) 7.26370 0.542915 0.271457 0.962450i \(-0.412494\pi\)
0.271457 + 0.962450i \(0.412494\pi\)
\(180\) 6.43776 1.88555i 0.479842 0.140540i
\(181\) 11.4499 0.851061 0.425531 0.904944i \(-0.360087\pi\)
0.425531 + 0.904944i \(0.360087\pi\)
\(182\) −7.19473 + 7.19473i −0.533309 + 0.533309i
\(183\) 1.46354 0.892348i 0.108188 0.0659642i
\(184\) 0.683406i 0.0503814i
\(185\) −23.1571 0.573311i −1.70254 0.0421506i
\(186\) −1.25008 + 5.15597i −0.0916603 + 0.378054i
\(187\) 5.61481 + 5.61481i 0.410596 + 0.410596i
\(188\) 3.44995 + 3.44995i 0.251614 + 0.251614i
\(189\) −9.39056 + 10.8463i −0.683063 + 0.788950i
\(190\) 2.23538 + 0.0553424i 0.162172 + 0.00401496i
\(191\) 14.1961i 1.02720i −0.858031 0.513598i \(-0.828312\pi\)
0.858031 0.513598i \(-0.171688\pi\)
\(192\) 0.901679 + 1.47884i 0.0650731 + 0.106726i
\(193\) −11.5541 + 11.5541i −0.831685 + 0.831685i −0.987747 0.156063i \(-0.950120\pi\)
0.156063 + 0.987747i \(0.450120\pi\)
\(194\) 7.80520 0.560381
\(195\) 7.12630 + 12.3664i 0.510325 + 0.885577i
\(196\) 0.623122 0.0445087
\(197\) −18.1909 + 18.1909i −1.29605 + 1.29605i −0.365065 + 0.930982i \(0.618953\pi\)
−0.930982 + 0.365065i \(0.881047\pi\)
\(198\) −10.5127 + 3.36372i −0.747108 + 0.239049i
\(199\) 0.0497425i 0.00352616i −0.999998 0.00176308i \(-0.999439\pi\)
0.999998 0.00176308i \(-0.000561205\pi\)
\(200\) −3.70616 + 3.35625i −0.262065 + 0.237323i
\(201\) 19.1654 + 4.64671i 1.35183 + 0.327754i
\(202\) −5.08309 5.08309i −0.357645 0.357645i
\(203\) −15.6723 15.6723i −1.09998 1.09998i
\(204\) 3.63285 + 0.880794i 0.254350 + 0.0616679i
\(205\) −8.42247 8.85010i −0.588251 0.618117i
\(206\) 7.41335i 0.516512i
\(207\) 1.95270 0.624797i 0.135722 0.0434264i
\(208\) −2.60584 + 2.60584i −0.180683 + 0.180683i
\(209\) −3.67926 −0.254499
\(210\) 2.77606 10.3267i 0.191566 0.712609i
\(211\) 27.0957 1.86535 0.932674 0.360721i \(-0.117469\pi\)
0.932674 + 0.360721i \(0.117469\pi\)
\(212\) 7.51422 7.51422i 0.516079 0.516079i
\(213\) −3.67709 6.03079i −0.251950 0.413223i
\(214\) 5.24746i 0.358709i
\(215\) 0.243564 9.83803i 0.0166109 0.670948i
\(216\) −3.40115 + 3.92838i −0.231419 + 0.267293i
\(217\) 5.98005 + 5.98005i 0.405952 + 0.405952i
\(218\) −0.983171 0.983171i −0.0665888 0.0665888i
\(219\) 6.43404 26.5373i 0.434772 1.79323i
\(220\) 5.95961 5.67165i 0.401797 0.382383i
\(221\) 7.95340i 0.535004i
\(222\) 15.3198 9.34081i 1.02820 0.626914i
\(223\) 19.2124 19.2124i 1.28656 1.28656i 0.349689 0.936866i \(-0.386287\pi\)
0.936866 0.349689i \(-0.113713\pi\)
\(224\) 2.76100 0.184477
\(225\) −12.9781 7.52118i −0.865208 0.501412i
\(226\) −14.9970 −0.997589
\(227\) 3.11027 3.11027i 0.206436 0.206436i −0.596315 0.802751i \(-0.703369\pi\)
0.802751 + 0.596315i \(0.203369\pi\)
\(228\) −1.47884 + 0.901679i −0.0979387 + 0.0597151i
\(229\) 6.10439i 0.403389i 0.979448 + 0.201695i \(0.0646448\pi\)
−0.979448 + 0.201695i \(0.935355\pi\)
\(230\) −1.10697 + 1.05348i −0.0729916 + 0.0694647i
\(231\) −4.14582 + 17.0995i −0.272775 + 1.12506i
\(232\) −5.67630 5.67630i −0.372667 0.372667i
\(233\) 10.7007 + 10.7007i 0.701026 + 0.701026i 0.964631 0.263605i \(-0.0849116\pi\)
−0.263605 + 0.964631i \(0.584912\pi\)
\(234\) −9.82804 5.06330i −0.642479 0.330999i
\(235\) 0.270014 10.9064i 0.0176137 0.711452i
\(236\) 11.1184i 0.723744i
\(237\) 6.45305 + 10.5836i 0.419171 + 0.687482i
\(238\) 4.21349 4.21349i 0.273120 0.273120i
\(239\) 7.74663 0.501088 0.250544 0.968105i \(-0.419391\pi\)
0.250544 + 0.968105i \(0.419391\pi\)
\(240\) 1.00545 3.74020i 0.0649017 0.241429i
\(241\) 11.5977 0.747071 0.373535 0.927616i \(-0.378145\pi\)
0.373535 + 0.927616i \(0.378145\pi\)
\(242\) −1.79388 + 1.79388i −0.115315 + 0.115315i
\(243\) −14.3340 6.12661i −0.919529 0.393022i
\(244\) 0.989652i 0.0633559i
\(245\) −0.960555 1.00932i −0.0613676 0.0644834i
\(246\) 9.19702 + 2.22984i 0.586380 + 0.142169i
\(247\) −2.60584 2.60584i −0.165806 0.165806i
\(248\) 2.16590 + 2.16590i 0.137535 + 0.137535i
\(249\) −6.34612 1.53863i −0.402169 0.0975069i
\(250\) 11.1495 + 0.829457i 0.705158 + 0.0524595i
\(251\) 16.8253i 1.06200i −0.847371 0.531001i \(-0.821816\pi\)
0.847371 0.531001i \(-0.178184\pi\)
\(252\) 2.52422 + 7.88901i 0.159011 + 0.496961i
\(253\) 1.77797 1.77797i 0.111780 0.111780i
\(254\) 19.2885 1.21027
\(255\) −4.17341 7.24220i −0.261349 0.453524i
\(256\) 1.00000 0.0625000
\(257\) −14.5714 + 14.5714i −0.908942 + 0.908942i −0.996187 0.0872448i \(-0.972194\pi\)
0.0872448 + 0.996187i \(0.472194\pi\)
\(258\) 3.96833 + 6.50846i 0.247058 + 0.405199i
\(259\) 28.6022i 1.77725i
\(260\) 8.23787 + 0.203949i 0.510891 + 0.0126484i
\(261\) 11.0294 21.4084i 0.682702 1.32515i
\(262\) −11.2095 11.2095i −0.692523 0.692523i
\(263\) 17.7679 + 17.7679i 1.09562 + 1.09562i 0.994917 + 0.100700i \(0.0321082\pi\)
0.100700 + 0.994917i \(0.467892\pi\)
\(264\) −1.50156 + 6.19323i −0.0924149 + 0.381167i
\(265\) −23.7548 0.588107i −1.45924 0.0361271i
\(266\) 2.76100i 0.169288i
\(267\) −1.56628 + 0.954992i −0.0958549 + 0.0584446i
\(268\) 8.05094 8.05094i 0.491789 0.491789i
\(269\) −27.3733 −1.66898 −0.834488 0.551026i \(-0.814237\pi\)
−0.834488 + 0.551026i \(0.814237\pi\)
\(270\) 11.6061 0.546556i 0.706324 0.0332623i
\(271\) −25.6490 −1.55807 −0.779034 0.626981i \(-0.784290\pi\)
−0.779034 + 0.626981i \(0.784290\pi\)
\(272\) 1.52607 1.52607i 0.0925317 0.0925317i
\(273\) −15.0470 + 9.17447i −0.910689 + 0.555264i
\(274\) 0.0354800i 0.00214343i
\(275\) −18.3737 0.910331i −1.10798 0.0548951i
\(276\) 0.278909 1.15037i 0.0167884 0.0692439i
\(277\) −10.7585 10.7585i −0.646419 0.646419i 0.305707 0.952126i \(-0.401107\pi\)
−0.952126 + 0.305707i \(0.901107\pi\)
\(278\) −11.2741 11.2741i −0.676177 0.676177i
\(279\) −4.20847 + 8.16878i −0.251955 + 0.489052i
\(280\) −4.25614 4.47223i −0.254353 0.267267i
\(281\) 14.9620i 0.892559i −0.894894 0.446279i \(-0.852749\pi\)
0.894894 0.446279i \(-0.147251\pi\)
\(282\) 4.39926 + 7.21522i 0.261972 + 0.429660i
\(283\) −14.6425 + 14.6425i −0.870404 + 0.870404i −0.992516 0.122112i \(-0.961033\pi\)
0.122112 + 0.992516i \(0.461033\pi\)
\(284\) −4.07805 −0.241988
\(285\) 3.74020 + 1.00545i 0.221550 + 0.0595579i
\(286\) −13.5589 −0.801752
\(287\) 10.6670 10.6670i 0.629652 0.629652i
\(288\) 0.914240 + 2.85730i 0.0538721 + 0.168368i
\(289\) 12.3422i 0.726012i
\(290\) −0.444261 + 17.9445i −0.0260879 + 1.05374i
\(291\) 13.1384 + 3.18543i 0.770184 + 0.186733i
\(292\) −11.1477 11.1477i −0.652369 0.652369i
\(293\) −2.83956 2.83956i −0.165889 0.165889i 0.619281 0.785170i \(-0.287424\pi\)
−0.785170 + 0.619281i \(0.787424\pi\)
\(294\) 1.04889 + 0.254306i 0.0611725 + 0.0148314i
\(295\) 18.0094 17.1392i 1.04855 0.997883i
\(296\) 10.3593i 0.602125i
\(297\) −19.0687 + 1.37168i −1.10648 + 0.0795928i
\(298\) 12.5182 12.5182i 0.725160 0.725160i
\(299\) 2.51850 0.145649
\(300\) −7.60825 + 4.13697i −0.439263 + 0.238848i
\(301\) 12.1513 0.700389
\(302\) −9.68240 + 9.68240i −0.557160 + 0.557160i
\(303\) −6.48178 10.6308i −0.372369 0.610721i
\(304\) 1.00000i 0.0573539i
\(305\) −1.60303 + 1.52557i −0.0917890 + 0.0873538i
\(306\) 5.75564 + 2.96525i 0.329028 + 0.169512i
\(307\) −13.1684 13.1684i −0.751562 0.751562i 0.223209 0.974771i \(-0.428347\pi\)
−0.974771 + 0.223209i \(0.928347\pi\)
\(308\) 7.18309 + 7.18309i 0.409295 + 0.409295i
\(309\) 3.02551 12.4788i 0.172115 0.709892i
\(310\) 0.169516 6.84708i 0.00962787 0.388888i
\(311\) 22.0732i 1.25166i 0.779961 + 0.625828i \(0.215239\pi\)
−0.779961 + 0.625828i \(0.784761\pi\)
\(312\) −5.44985 + 3.32288i −0.308537 + 0.188121i
\(313\) 10.3013 10.3013i 0.582265 0.582265i −0.353260 0.935525i \(-0.614927\pi\)
0.935525 + 0.353260i \(0.114927\pi\)
\(314\) −1.55866 −0.0879600
\(315\) 8.88738 16.2498i 0.500747 0.915571i
\(316\) 7.15671 0.402596
\(317\) −13.0482 + 13.0482i −0.732860 + 0.732860i −0.971185 0.238325i \(-0.923402\pi\)
0.238325 + 0.971185i \(0.423402\pi\)
\(318\) 15.7152 9.58188i 0.881266 0.537325i
\(319\) 29.5352i 1.65365i
\(320\) −1.54152 1.61979i −0.0861737 0.0905489i
\(321\) −2.14158 + 8.83297i −0.119531 + 0.493008i
\(322\) −1.33423 1.33423i −0.0743536 0.0743536i
\(323\) 1.52607 + 1.52607i 0.0849129 + 0.0849129i
\(324\) −7.32833 + 5.22452i −0.407129 + 0.290251i
\(325\) −12.3685 13.6580i −0.686081 0.757609i
\(326\) 15.6506i 0.866806i
\(327\) −1.25371 2.05620i −0.0693301 0.113708i
\(328\) 3.86345 3.86345i 0.213323 0.213323i
\(329\) 13.4708 0.742671
\(330\) 12.3464 7.11478i 0.679647 0.391656i
\(331\) −24.9937 −1.37378 −0.686888 0.726763i \(-0.741024\pi\)
−0.686888 + 0.726763i \(0.741024\pi\)
\(332\) −2.66585 + 2.66585i −0.146308 + 0.146308i
\(333\) 29.5998 9.47094i 1.62206 0.519004i
\(334\) 9.03131i 0.494171i
\(335\) −25.4515 0.630114i −1.39056 0.0344268i
\(336\) 4.64754 + 1.12681i 0.253544 + 0.0614725i
\(337\) −1.90830 1.90830i −0.103952 0.103952i 0.653218 0.757170i \(-0.273419\pi\)
−0.757170 + 0.653218i \(0.773419\pi\)
\(338\) −0.410698 0.410698i −0.0223390 0.0223390i
\(339\) −25.2443 6.12054i −1.37108 0.332422i
\(340\) −4.82439 0.119439i −0.261639 0.00647751i
\(341\) 11.2697i 0.610290i
\(342\) −2.85730 + 0.914240i −0.154505 + 0.0494365i
\(343\) −12.4497 + 12.4497i −0.672222 + 0.672222i
\(344\) 4.40105 0.237289
\(345\) −2.29329 + 1.32154i −0.123467 + 0.0711493i
\(346\) −0.555924 −0.0298867
\(347\) 13.4880 13.4880i 0.724074 0.724074i −0.245358 0.969432i \(-0.578906\pi\)
0.969432 + 0.245358i \(0.0789056\pi\)
\(348\) −7.23823 11.8714i −0.388010 0.636374i
\(349\) 3.83364i 0.205210i 0.994722 + 0.102605i \(0.0327178\pi\)
−0.994722 + 0.102605i \(0.967282\pi\)
\(350\) −0.683134 + 13.7881i −0.0365151 + 0.737004i
\(351\) −14.4769 12.5340i −0.772722 0.669013i
\(352\) 2.60163 + 2.60163i 0.138667 + 0.138667i
\(353\) −22.0113 22.0113i −1.17155 1.17155i −0.981841 0.189704i \(-0.939247\pi\)
−0.189704 0.981841i \(-0.560753\pi\)
\(354\) −4.53759 + 18.7154i −0.241170 + 0.994710i
\(355\) 6.28640 + 6.60557i 0.333647 + 0.350587i
\(356\) 1.05913i 0.0561336i
\(357\) 8.81208 5.37290i 0.466385 0.284364i
\(358\) 5.13621 5.13621i 0.271457 0.271457i
\(359\) 2.29765 0.121265 0.0606327 0.998160i \(-0.480688\pi\)
0.0606327 + 0.998160i \(0.480688\pi\)
\(360\) 3.21890 5.88546i 0.169651 0.310191i
\(361\) −1.00000 −0.0526316
\(362\) 8.09627 8.09627i 0.425531 0.425531i
\(363\) −3.75171 + 2.28749i −0.196914 + 0.120062i
\(364\) 10.1749i 0.533309i
\(365\) −0.872484 + 35.2413i −0.0456679 + 1.84461i
\(366\) 0.403893 1.66586i 0.0211118 0.0870761i
\(367\) 8.45018 + 8.45018i 0.441096 + 0.441096i 0.892380 0.451284i \(-0.149034\pi\)
−0.451284 + 0.892380i \(0.649034\pi\)
\(368\) −0.483241 0.483241i −0.0251907 0.0251907i
\(369\) 14.5711 + 7.50691i 0.758544 + 0.390794i
\(370\) −16.7799 + 15.9692i −0.872348 + 0.830197i
\(371\) 29.3403i 1.52327i
\(372\) 2.76188 + 4.52976i 0.143197 + 0.234857i
\(373\) −16.3447 + 16.3447i −0.846298 + 0.846298i −0.989669 0.143371i \(-0.954206\pi\)
0.143371 + 0.989669i \(0.454206\pi\)
\(374\) 7.94054 0.410596
\(375\) 18.4293 + 5.94652i 0.951685 + 0.307077i
\(376\) 4.87897 0.251614
\(377\) 20.9184 20.9184i 1.07735 1.07735i
\(378\) 1.02934 + 14.3096i 0.0529435 + 0.736007i
\(379\) 19.6159i 1.00760i 0.863821 + 0.503800i \(0.168065\pi\)
−0.863821 + 0.503800i \(0.831935\pi\)
\(380\) 1.61979 1.54152i 0.0830933 0.0790784i
\(381\) 32.4680 + 7.87195i 1.66339 + 0.403292i
\(382\) −10.0382 10.0382i −0.513598 0.513598i
\(383\) 23.4876 + 23.4876i 1.20016 + 1.20016i 0.974117 + 0.226045i \(0.0725797\pi\)
0.226045 + 0.974117i \(0.427420\pi\)
\(384\) 1.68328 + 0.408116i 0.0858997 + 0.0208266i
\(385\) 0.562191 22.7080i 0.0286519 1.15731i
\(386\) 16.3400i 0.831685i
\(387\) 4.02362 + 12.5751i 0.204532 + 0.639229i
\(388\) 5.51911 5.51911i 0.280190 0.280190i
\(389\) −26.9154 −1.36466 −0.682332 0.731043i \(-0.739034\pi\)
−0.682332 + 0.731043i \(0.739034\pi\)
\(390\) 13.7834 + 3.70531i 0.697951 + 0.187626i
\(391\) −1.47492 −0.0745900
\(392\) 0.440614 0.440614i 0.0222543 0.0222543i
\(393\) −14.2939 23.4435i −0.721033 1.18257i
\(394\) 25.7258i 1.29605i
\(395\) −11.0322 11.5923i −0.555091 0.583274i
\(396\) −5.05512 + 9.81214i −0.254029 + 0.493079i
\(397\) −17.6233 17.6233i −0.884487 0.884487i 0.109500 0.993987i \(-0.465075\pi\)
−0.993987 + 0.109500i \(0.965075\pi\)
\(398\) −0.0351733 0.0351733i −0.00176308 0.00176308i
\(399\) −1.12681 + 4.64754i −0.0564110 + 0.232668i
\(400\) −0.247423 + 4.99387i −0.0123711 + 0.249694i
\(401\) 5.28634i 0.263987i 0.991251 + 0.131994i \(0.0421378\pi\)
−0.991251 + 0.131994i \(0.957862\pi\)
\(402\) 16.8377 10.2663i 0.839789 0.512036i
\(403\) −7.98181 + 7.98181i −0.397602 + 0.397602i
\(404\) −7.18857 −0.357645
\(405\) 19.7594 + 3.81663i 0.981852 + 0.189650i
\(406\) −22.1639 −1.09998
\(407\) 26.9512 26.9512i 1.33592 1.33592i
\(408\) 3.19163 1.94600i 0.158009 0.0963412i
\(409\) 15.6120i 0.771963i 0.922507 + 0.385981i \(0.126137\pi\)
−0.922507 + 0.385981i \(0.873863\pi\)
\(410\) −12.2135 0.302376i −0.603184 0.0149333i
\(411\) 0.0144800 0.0597229i 0.000714245 0.00294591i
\(412\) −5.24203 5.24203i −0.258256 0.258256i
\(413\) 21.7066 + 21.7066i 1.06811 + 1.06811i
\(414\) 0.938966 1.82256i 0.0461477 0.0895741i
\(415\) 8.42758 + 0.208645i 0.413694 + 0.0102420i
\(416\) 3.68522i 0.180683i
\(417\) −14.3764 23.5787i −0.704015 1.15465i
\(418\) −2.60163 + 2.60163i −0.127250 + 0.127250i
\(419\) −13.9765 −0.682795 −0.341397 0.939919i \(-0.610900\pi\)
−0.341397 + 0.939919i \(0.610900\pi\)
\(420\) −5.33910 9.26503i −0.260521 0.452087i
\(421\) 20.4247 0.995439 0.497719 0.867338i \(-0.334171\pi\)
0.497719 + 0.867338i \(0.334171\pi\)
\(422\) 19.1596 19.1596i 0.932674 0.932674i
\(423\) 4.46055 + 13.9407i 0.216879 + 0.677819i
\(424\) 10.6267i 0.516079i
\(425\) 7.24343 + 7.99860i 0.351358 + 0.387989i
\(426\) −6.86450 1.66432i −0.332586 0.0806364i
\(427\) −1.93212 1.93212i −0.0935018 0.0935018i
\(428\) 3.71052 + 3.71052i 0.179355 + 0.179355i
\(429\) −22.8234 5.53359i −1.10192 0.267164i
\(430\) −6.78431 7.12876i −0.327168 0.343779i
\(431\) 15.5840i 0.750654i 0.926892 + 0.375327i \(0.122470\pi\)
−0.926892 + 0.375327i \(0.877530\pi\)
\(432\) 0.372814 + 5.18276i 0.0179370 + 0.249356i
\(433\) −23.3156 + 23.3156i −1.12048 + 1.12048i −0.128806 + 0.991670i \(0.541114\pi\)
−0.991670 + 0.128806i \(0.958886\pi\)
\(434\) 8.45707 0.405952
\(435\) −8.07128 + 30.0244i −0.386988 + 1.43956i
\(436\) −1.39041 −0.0665888
\(437\) 0.483241 0.483241i 0.0231165 0.0231165i
\(438\) −14.2152 23.3143i −0.679227 1.11400i
\(439\) 18.2344i 0.870279i −0.900363 0.435139i \(-0.856699\pi\)
0.900363 0.435139i \(-0.143301\pi\)
\(440\) 0.203619 8.22455i 0.00970714 0.392090i
\(441\) 1.66179 + 0.856138i 0.0791329 + 0.0407685i
\(442\) 5.62391 + 5.62391i 0.267502 + 0.267502i
\(443\) −4.95807 4.95807i −0.235565 0.235565i 0.579446 0.815011i \(-0.303269\pi\)
−0.815011 + 0.579446i \(0.803269\pi\)
\(444\) 4.22782 17.4377i 0.200643 0.827557i
\(445\) 1.71556 1.63267i 0.0813254 0.0773959i
\(446\) 27.1704i 1.28656i
\(447\) 26.1806 15.9628i 1.23830 0.755014i
\(448\) 1.95232 1.95232i 0.0922385 0.0922385i
\(449\) 32.0557 1.51280 0.756401 0.654109i \(-0.226956\pi\)
0.756401 + 0.654109i \(0.226956\pi\)
\(450\) −14.4952 + 3.85864i −0.683310 + 0.181898i
\(451\) 20.1025 0.946589
\(452\) −10.6045 + 10.6045i −0.498794 + 0.498794i
\(453\) −20.2498 + 12.3467i −0.951417 + 0.580097i
\(454\) 4.39859i 0.206436i
\(455\) 16.4811 15.6848i 0.772648 0.735315i
\(456\) −0.408116 + 1.68328i −0.0191118 + 0.0788269i
\(457\) 4.40540 + 4.40540i 0.206076 + 0.206076i 0.802597 0.596521i \(-0.203451\pi\)
−0.596521 + 0.802597i \(0.703451\pi\)
\(458\) 4.31645 + 4.31645i 0.201695 + 0.201695i
\(459\) 8.47821 + 7.34033i 0.395729 + 0.342617i
\(460\) −0.0378213 + 1.52767i −0.00176343 + 0.0712282i
\(461\) 8.34487i 0.388659i 0.980936 + 0.194330i \(0.0622532\pi\)
−0.980936 + 0.194330i \(0.937747\pi\)
\(462\) 9.15964 + 15.0227i 0.426145 + 0.698920i
\(463\) −0.884571 + 0.884571i −0.0411095 + 0.0411095i −0.727363 0.686253i \(-0.759254\pi\)
0.686253 + 0.727363i \(0.259254\pi\)
\(464\) −8.02750 −0.372667
\(465\) 3.07975 11.4564i 0.142820 0.531277i
\(466\) 15.1331 0.701026
\(467\) 2.44668 2.44668i 0.113219 0.113219i −0.648228 0.761447i \(-0.724489\pi\)
0.761447 + 0.648228i \(0.224489\pi\)
\(468\) −10.5298 + 3.36917i −0.486739 + 0.155740i
\(469\) 31.4360i 1.45158i
\(470\) −7.52103 7.90289i −0.346919 0.364533i
\(471\) −2.62366 0.636113i −0.120892 0.0293105i
\(472\) 7.86188 + 7.86188i 0.361872 + 0.361872i
\(473\) 11.4499 + 11.4499i 0.526466 + 0.526466i
\(474\) 12.0468 + 2.92077i 0.553326 + 0.134155i
\(475\) −4.99387 0.247423i −0.229135 0.0113525i
\(476\) 5.95877i 0.273120i
\(477\) 30.3637 9.71537i 1.39026 0.444836i
\(478\) 5.47769 5.47769i 0.250544 0.250544i
\(479\) −1.05345 −0.0481333 −0.0240667 0.999710i \(-0.507661\pi\)
−0.0240667 + 0.999710i \(0.507661\pi\)
\(480\) −1.93375 3.35568i −0.0882634 0.153165i
\(481\) 38.1764 1.74070
\(482\) 8.20078 8.20078i 0.373535 0.373535i
\(483\) −1.70136 2.79040i −0.0774147 0.126968i
\(484\) 2.53692i 0.115315i
\(485\) −17.4476 0.431958i −0.792255 0.0196142i
\(486\) −14.4679 + 5.80353i −0.656276 + 0.263254i
\(487\) −6.07963 6.07963i −0.275494 0.275494i 0.555813 0.831307i \(-0.312407\pi\)
−0.831307 + 0.555813i \(0.812407\pi\)
\(488\) −0.699789 0.699789i −0.0316780 0.0316780i
\(489\) −6.38727 + 26.3444i −0.288842 + 1.19133i
\(490\) −1.39292 0.0344850i −0.0629255 0.00155787i
\(491\) 18.2097i 0.821794i −0.911682 0.410897i \(-0.865216\pi\)
0.911682 0.410897i \(-0.134784\pi\)
\(492\) 8.08001 4.92654i 0.364275 0.222105i
\(493\) −12.2505 + 12.2505i −0.551737 + 0.551737i
\(494\) −3.68522 −0.165806
\(495\) 23.6862 6.93741i 1.06461 0.311814i
\(496\) 3.06305 0.137535
\(497\) −7.96166 + 7.96166i −0.357129 + 0.357129i
\(498\) −5.57536 + 3.39940i −0.249838 + 0.152331i
\(499\) 8.59031i 0.384555i 0.981341 + 0.192278i \(0.0615874\pi\)
−0.981341 + 0.192278i \(0.938413\pi\)
\(500\) 8.47042 7.29739i 0.378809 0.326349i
\(501\) −3.68583 + 15.2022i −0.164671 + 0.679186i
\(502\) −11.8973 11.8973i −0.531001 0.531001i
\(503\) 22.4745 + 22.4745i 1.00209 + 1.00209i 0.999998 + 0.00209079i \(0.000665520\pi\)
0.00209079 + 0.999998i \(0.499334\pi\)
\(504\) 7.36326 + 3.79348i 0.327986 + 0.168975i
\(505\) 11.0813 + 11.6440i 0.493113 + 0.518149i
\(506\) 2.51443i 0.111780i
\(507\) −0.523709 0.858934i −0.0232587 0.0381466i
\(508\) 13.6390 13.6390i 0.605134 0.605134i
\(509\) −22.2471 −0.986087 −0.493043 0.870005i \(-0.664116\pi\)
−0.493043 + 0.870005i \(0.664116\pi\)
\(510\) −8.07206 2.16996i −0.357437 0.0960875i
\(511\) −43.5278 −1.92555
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −5.18276 + 0.372814i −0.228824 + 0.0164601i
\(514\) 20.6071i 0.908942i
\(515\) −0.410272 + 16.5717i −0.0180787 + 0.730235i
\(516\) 7.40821 + 1.79614i 0.326128 + 0.0790706i
\(517\) 12.6933 + 12.6933i 0.558249 + 0.558249i
\(518\) −20.2248 20.2248i −0.888626 0.888626i
\(519\) −0.935778 0.226882i −0.0410761 0.00995900i
\(520\) 5.96927 5.68084i 0.261770 0.249121i
\(521\) 11.3759i 0.498385i −0.968454 0.249193i \(-0.919835\pi\)
0.968454 0.249193i \(-0.0801653\pi\)
\(522\) −7.33906 22.9370i −0.321222 1.00392i
\(523\) −9.78826 + 9.78826i −0.428011 + 0.428011i −0.887950 0.459940i \(-0.847871\pi\)
0.459940 + 0.887950i \(0.347871\pi\)
\(524\) −15.8526 −0.692523
\(525\) −6.77705 + 22.9305i −0.295775 + 1.00077i
\(526\) 25.1276 1.09562
\(527\) 4.67443 4.67443i 0.203621 0.203621i
\(528\) 3.31751 + 5.44104i 0.144376 + 0.236791i
\(529\) 22.5330i 0.979694i
\(530\) −17.2130 + 16.3813i −0.747685 + 0.711558i
\(531\) −15.2761 + 29.6514i −0.662926 + 1.28676i
\(532\) 1.95232 + 1.95232i 0.0846439 + 0.0846439i
\(533\) 14.2376 + 14.2376i 0.616700 + 0.616700i
\(534\) −0.432247 + 1.78281i −0.0187052 + 0.0771498i
\(535\) 0.290407 11.7301i 0.0125554 0.507136i
\(536\) 11.3857i 0.491789i
\(537\) 10.7419 6.54953i 0.463546 0.282633i
\(538\) −19.3558 + 19.3558i −0.834488 + 0.834488i
\(539\) 2.29262 0.0987503
\(540\) 7.82027 8.59322i 0.336531 0.369793i
\(541\) −29.7432 −1.27876 −0.639380 0.768891i \(-0.720809\pi\)
−0.639380 + 0.768891i \(0.720809\pi\)
\(542\) −18.1366 + 18.1366i −0.779034 + 0.779034i
\(543\) 16.9325 10.3241i 0.726645 0.443049i
\(544\) 2.15819i 0.0925317i
\(545\) 2.14335 + 2.25218i 0.0918112 + 0.0964726i
\(546\) −4.15254 + 17.1272i −0.177712 + 0.732977i
\(547\) 27.7770 + 27.7770i 1.18766 + 1.18766i 0.977713 + 0.209945i \(0.0673286\pi\)
0.209945 + 0.977713i \(0.432671\pi\)
\(548\) −0.0250882 0.0250882i −0.00107171 0.00107171i
\(549\) 1.35973 2.63928i 0.0580320 0.112642i
\(550\) −13.6359 + 12.3485i −0.581437 + 0.526542i
\(551\) 8.02750i 0.341983i
\(552\) −0.616213 1.01065i −0.0262278 0.0430161i
\(553\) 13.9722 13.9722i 0.594158 0.594158i
\(554\) −15.2149 −0.646419
\(555\) −34.7627 + 20.0324i −1.47559 + 0.850330i
\(556\) −15.9440 −0.676177
\(557\) 18.6904 18.6904i 0.791939 0.791939i −0.189871 0.981809i \(-0.560807\pi\)
0.981809 + 0.189871i \(0.0608069\pi\)
\(558\) 2.80036 + 8.75204i 0.118549 + 0.370503i
\(559\) 16.2188i 0.685983i
\(560\) −6.17189 0.152800i −0.260810 0.00645699i
\(561\) 13.3662 + 3.24067i 0.564320 + 0.136821i
\(562\) −10.5797 10.5797i −0.446279 0.446279i
\(563\) 12.1886 + 12.1886i 0.513687 + 0.513687i 0.915654 0.401967i \(-0.131673\pi\)
−0.401967 + 0.915654i \(0.631673\pi\)
\(564\) 8.21268 + 1.99119i 0.345816 + 0.0838441i
\(565\) 33.5241 + 0.829972i 1.41037 + 0.0349172i
\(566\) 20.7076i 0.870404i
\(567\) −4.10731 + 24.5072i −0.172491 + 1.02921i
\(568\) −2.88361 + 2.88361i −0.120994 + 0.120994i
\(569\) 15.7219 0.659095 0.329548 0.944139i \(-0.393104\pi\)
0.329548 + 0.944139i \(0.393104\pi\)
\(570\) 3.35568 1.93375i 0.140554 0.0809961i
\(571\) −9.79901 −0.410076 −0.205038 0.978754i \(-0.565732\pi\)
−0.205038 + 0.978754i \(0.565732\pi\)
\(572\) −9.58756 + 9.58756i −0.400876 + 0.400876i
\(573\) −12.8004 20.9938i −0.534742 0.877031i
\(574\) 15.0854i 0.629652i
\(575\) 2.53281 2.29368i 0.105625 0.0956531i
\(576\) 2.66688 + 1.37395i 0.111120 + 0.0572479i
\(577\) 3.10041 + 3.10041i 0.129072 + 0.129072i 0.768691 0.639620i \(-0.220908\pi\)
−0.639620 + 0.768691i \(0.720908\pi\)
\(578\) 8.72726 + 8.72726i 0.363006 + 0.363006i
\(579\) −6.66863 + 27.5049i −0.277139 + 1.14306i
\(580\) 12.3746 + 13.0028i 0.513826 + 0.539914i
\(581\) 10.4092i 0.431846i
\(582\) 11.5427 7.03778i 0.478459 0.291725i
\(583\) 27.6467 27.6467i 1.14501 1.14501i
\(584\) −15.7652 −0.652369
\(585\) 21.6892 + 11.8623i 0.896738 + 0.490447i
\(586\) −4.01575 −0.165889
\(587\) −9.84222 + 9.84222i −0.406232 + 0.406232i −0.880422 0.474190i \(-0.842741\pi\)
0.474190 + 0.880422i \(0.342741\pi\)
\(588\) 0.921499 0.561856i 0.0380020 0.0231705i
\(589\) 3.06305i 0.126211i
\(590\) 0.615317 24.8538i 0.0253322 1.02322i
\(591\) −10.4991 + 43.3038i −0.431876 + 1.78128i
\(592\) −7.32517 7.32517i −0.301062 0.301062i
\(593\) 26.6020 + 26.6020i 1.09241 + 1.09241i 0.995271 + 0.0971411i \(0.0309698\pi\)
0.0971411 + 0.995271i \(0.469030\pi\)
\(594\) −12.5137 + 14.4535i −0.513443 + 0.593036i
\(595\) −9.65194 + 9.18557i −0.395691 + 0.376572i
\(596\) 17.7034i 0.725160i
\(597\) −0.0448518 0.0735614i −0.00183566 0.00301067i
\(598\) 1.78085 1.78085i 0.0728243 0.0728243i
\(599\) 1.72077 0.0703088 0.0351544 0.999382i \(-0.488808\pi\)
0.0351544 + 0.999382i \(0.488808\pi\)
\(600\) −2.45456 + 8.30513i −0.100207 + 0.339055i
\(601\) 22.1111 0.901930 0.450965 0.892542i \(-0.351080\pi\)
0.450965 + 0.892542i \(0.351080\pi\)
\(602\) 8.59226 8.59226i 0.350194 0.350194i
\(603\) 32.5325 10.4093i 1.32483 0.423900i
\(604\) 13.6930i 0.557160i
\(605\) 4.10928 3.91072i 0.167066 0.158993i
\(606\) −12.1004 2.93377i −0.491545 0.119176i
\(607\) 19.6650 + 19.6650i 0.798178 + 0.798178i 0.982808 0.184630i \(-0.0591088\pi\)
−0.184630 + 0.982808i \(0.559109\pi\)
\(608\) 0.707107 + 0.707107i 0.0286770 + 0.0286770i
\(609\) −37.3082 9.04546i −1.51180 0.366541i
\(610\) −0.0547696 + 2.21225i −0.00221756 + 0.0895714i
\(611\) 17.9800i 0.727395i
\(612\) 6.16660 1.97311i 0.249270 0.0797581i
\(613\) −14.6901 + 14.6901i −0.593327 + 0.593327i −0.938529 0.345201i \(-0.887811\pi\)
0.345201 + 0.938529i \(0.387811\pi\)
\(614\) −18.6230 −0.751562
\(615\) −20.4355 5.49353i −0.824037 0.221521i
\(616\) 10.1584 0.409295
\(617\) −12.2561 + 12.2561i −0.493413 + 0.493413i −0.909380 0.415967i \(-0.863443\pi\)
0.415967 + 0.909380i \(0.363443\pi\)
\(618\) −6.68446 10.9632i −0.268888 0.441003i
\(619\) 1.71268i 0.0688385i −0.999407 0.0344193i \(-0.989042\pi\)
0.999407 0.0344193i \(-0.0109582\pi\)
\(620\) −4.72175 4.96148i −0.189630 0.199258i
\(621\) 2.32436 2.68468i 0.0932735 0.107733i
\(622\) 15.6081 + 15.6081i 0.625828 + 0.625828i
\(623\) 2.06776 + 2.06776i 0.0828429 + 0.0828429i
\(624\) −1.50400 + 6.20326i −0.0602081 + 0.248329i
\(625\) −24.8776 2.47120i −0.995103 0.0988478i
\(626\) 14.5683i 0.582265i
\(627\) −5.44104 + 3.31751i −0.217294 + 0.132488i
\(628\) −1.10214 + 1.10214i −0.0439800 + 0.0439800i
\(629\) −22.3575 −0.891451
\(630\) −5.20600 17.7746i −0.207412 0.708159i
\(631\) −16.1064 −0.641187 −0.320594 0.947217i \(-0.603882\pi\)
−0.320594 + 0.947217i \(0.603882\pi\)
\(632\) 5.06056 5.06056i 0.201298 0.201298i
\(633\) 40.0703 24.4317i 1.59265 0.971071i
\(634\) 18.4529i 0.732860i
\(635\) −43.1172 1.06747i −1.71105 0.0423613i
\(636\) 4.33693 17.8878i 0.171971 0.709296i
\(637\) 1.62376 + 1.62376i 0.0643356 + 0.0643356i
\(638\) −20.8846 20.8846i −0.826827 0.826827i
\(639\) −10.8757 5.60303i −0.430235 0.221653i
\(640\) −2.23538 0.0553424i −0.0883613 0.00218760i
\(641\) 36.1619i 1.42831i −0.699988 0.714155i \(-0.746811\pi\)
0.699988 0.714155i \(-0.253189\pi\)
\(642\) 4.73153 + 7.76017i 0.186739 + 0.306270i
\(643\) 12.4536 12.4536i 0.491122 0.491122i −0.417537 0.908660i \(-0.637107\pi\)
0.908660 + 0.417537i \(0.137107\pi\)
\(644\) −1.88688 −0.0743536
\(645\) −8.51055 14.7685i −0.335102 0.581510i
\(646\) 2.15819 0.0849129
\(647\) 4.82277 4.82277i 0.189603 0.189603i −0.605922 0.795524i \(-0.707196\pi\)
0.795524 + 0.605922i \(0.207196\pi\)
\(648\) −1.48762 + 8.87620i −0.0584392 + 0.348690i
\(649\) 40.9073i 1.60575i
\(650\) −18.4035 0.911806i −0.721845 0.0357640i
\(651\) 14.2356 + 3.45147i 0.557939 + 0.135274i
\(652\) 11.0666 + 11.0666i 0.433403 + 0.433403i
\(653\) 23.8973 + 23.8973i 0.935174 + 0.935174i 0.998023 0.0628489i \(-0.0200186\pi\)
−0.0628489 + 0.998023i \(0.520019\pi\)
\(654\) −2.34046 0.567451i −0.0915192 0.0221891i
\(655\) 24.4371 + 25.6778i 0.954836 + 1.00331i
\(656\) 5.46374i 0.213323i
\(657\) −14.4132 45.0460i −0.562312 1.75741i
\(658\) 9.52531 9.52531i 0.371335 0.371335i
\(659\) −5.45910 −0.212656 −0.106328 0.994331i \(-0.533909\pi\)
−0.106328 + 0.994331i \(0.533909\pi\)
\(660\) 3.69932 13.7611i 0.143996 0.535652i
\(661\) 13.7047 0.533053 0.266526 0.963828i \(-0.414124\pi\)
0.266526 + 0.963828i \(0.414124\pi\)
\(662\) −17.6732 + 17.6732i −0.686888 + 0.686888i
\(663\) 7.17142 + 11.7618i 0.278515 + 0.456792i
\(664\) 3.77008i 0.146308i
\(665\) 0.152800 6.17189i 0.00592534 0.239336i
\(666\) 14.2332 27.6272i 0.551527 1.07053i
\(667\) 3.87922 + 3.87922i 0.150204 + 0.150204i
\(668\) 6.38610 + 6.38610i 0.247086 + 0.247086i
\(669\) 11.0887 45.7354i 0.428713 1.76823i
\(670\) −18.4425 + 17.5514i −0.712496 + 0.678069i
\(671\) 3.64118i 0.140566i
\(672\) 4.08308 2.48954i 0.157508 0.0960359i
\(673\) 21.2329 21.2329i 0.818469 0.818469i −0.167417 0.985886i \(-0.553543\pi\)
0.985886 + 0.167417i \(0.0535427\pi\)
\(674\) −2.69875 −0.103952
\(675\) −25.9743 + 0.579454i −0.999751 + 0.0223032i
\(676\) −0.580815 −0.0223390
\(677\) 31.7382 31.7382i 1.21980 1.21980i 0.252097 0.967702i \(-0.418880\pi\)
0.967702 0.252097i \(-0.0811202\pi\)
\(678\) −22.1783 + 13.5225i −0.851751 + 0.519329i
\(679\) 21.5502i 0.827019i
\(680\) −3.49581 + 3.32690i −0.134058 + 0.127581i
\(681\) 1.79514 7.40407i 0.0687898 0.283725i
\(682\) 7.96890 + 7.96890i 0.305145 + 0.305145i
\(683\) 20.1518 + 20.1518i 0.771089 + 0.771089i 0.978297 0.207208i \(-0.0664377\pi\)
−0.207208 + 0.978297i \(0.566438\pi\)
\(684\) −1.37395 + 2.66688i −0.0525343 + 0.101971i
\(685\) −0.00196355 + 0.0793114i −7.50233e−5 + 0.00303033i
\(686\) 17.6066i 0.672222i
\(687\) 5.50420 + 9.02743i 0.209998 + 0.344418i
\(688\) 3.11201 3.11201i 0.118644 0.118644i
\(689\) 39.1617 1.49194
\(690\) −0.687133 + 2.55607i −0.0261587 + 0.0973080i
\(691\) −31.1608 −1.18541 −0.592707 0.805418i \(-0.701941\pi\)
−0.592707 + 0.805418i \(0.701941\pi\)
\(692\) −0.393098 + 0.393098i −0.0149433 + 0.0149433i
\(693\) 9.28724 + 29.0257i 0.352793 + 1.10259i
\(694\) 19.0749i 0.724074i
\(695\) 24.5781 + 25.8259i 0.932299 + 0.979633i
\(696\) −13.5126 3.27615i −0.512192 0.124182i
\(697\) −8.33806 8.33806i −0.315827 0.315827i
\(698\) 2.71079 + 2.71079i 0.102605 + 0.102605i
\(699\) 25.4732 + 6.17605i 0.963486 + 0.233600i
\(700\) 9.26660 + 10.2327i 0.350245 + 0.386760i
\(701\) 10.0481i 0.379513i −0.981831 0.189757i \(-0.939230\pi\)
0.981831 0.189757i \(-0.0607699\pi\)
\(702\) −19.0996 + 1.37390i −0.720868 + 0.0518545i
\(703\) 7.32517 7.32517i 0.276274 0.276274i
\(704\) 3.67926 0.138667
\(705\) −9.43473 16.3723i −0.355332 0.616615i
\(706\) −31.1287 −1.17155
\(707\) −14.0344 + 14.0344i −0.527818 + 0.527818i
\(708\) 10.0252 + 16.4423i 0.376770 + 0.617940i
\(709\) 28.4137i 1.06710i 0.845768 + 0.533550i \(0.179142\pi\)
−0.845768 + 0.533550i \(0.820858\pi\)
\(710\) 9.11599 + 0.225689i 0.342117 + 0.00846994i
\(711\) 19.0861 + 9.83296i 0.715784 + 0.368765i
\(712\) 0.748916 + 0.748916i 0.0280668 + 0.0280668i
\(713\) −1.48019 1.48019i −0.0554335 0.0554335i
\(714\) 2.43187 10.0303i 0.0910105 0.375374i
\(715\) 30.3092 + 0.750379i 1.13350 + 0.0280626i
\(716\) 7.26370i 0.271457i
\(717\) 11.4560 6.98497i 0.427834 0.260858i
\(718\) 1.62469 1.62469i 0.0606327 0.0606327i
\(719\) −4.57697 −0.170692 −0.0853460 0.996351i \(-0.527200\pi\)
−0.0853460 + 0.996351i \(0.527200\pi\)
\(720\) −1.88555 6.43776i −0.0702702 0.239921i
\(721\) −20.4682 −0.762277
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) 17.1511 10.4574i 0.637857 0.388914i
\(724\) 11.4499i 0.425531i
\(725\) 1.98619 40.0883i 0.0737651 1.48884i
\(726\) −1.03536 + 4.27036i −0.0384258 + 0.158488i
\(727\) −35.7671 35.7671i −1.32653 1.32653i −0.908378 0.418149i \(-0.862679\pi\)
−0.418149 0.908378i \(-0.637321\pi\)
\(728\) 7.19473 + 7.19473i 0.266654 + 0.266654i
\(729\) −26.7220 + 3.86441i −0.989704 + 0.143126i
\(730\) 24.3024 + 25.5363i 0.899473 + 0.945141i
\(731\) 9.49831i 0.351308i
\(732\) −0.892348 1.46354i −0.0329821 0.0540940i
\(733\) −20.7681 + 20.7681i −0.767088 + 0.767088i −0.977593 0.210505i \(-0.932489\pi\)
0.210505 + 0.977593i \(0.432489\pi\)
\(734\) 11.9504 0.441096
\(735\) −2.33060 0.626520i −0.0859654 0.0231095i
\(736\) −0.683406 −0.0251907
\(737\) 29.6215 29.6215i 1.09112 1.09112i
\(738\) 15.6115 4.99517i 0.574669 0.183875i
\(739\) 6.83000i 0.251246i −0.992078 0.125623i \(-0.959907\pi\)
0.992078 0.125623i \(-0.0400929\pi\)
\(740\) −0.573311 + 23.1571i −0.0210753 + 0.851272i
\(741\) −6.20326 1.50400i −0.227882 0.0552507i
\(742\) −20.7468 20.7468i −0.761637 0.761637i
\(743\) −23.8484 23.8484i −0.874912 0.874912i 0.118091 0.993003i \(-0.462322\pi\)
−0.993003 + 0.118091i \(0.962322\pi\)
\(744\) 5.15597 + 1.25008i 0.189027 + 0.0458301i
\(745\) −28.6758 + 27.2902i −1.05060 + 0.999836i
\(746\) 23.1149i 0.846298i
\(747\) −10.7723 + 3.44676i −0.394136 + 0.126110i
\(748\) 5.61481 5.61481i 0.205298 0.205298i
\(749\) 14.4883 0.529389
\(750\) 17.2363 8.82666i 0.629381 0.322304i
\(751\) −26.8233 −0.978797 −0.489399 0.872060i \(-0.662784\pi\)
−0.489399 + 0.872060i \(0.662784\pi\)
\(752\) 3.44995 3.44995i 0.125807 0.125807i
\(753\) −15.1710 24.8819i −0.552862 0.906748i
\(754\) 29.5831i 1.07735i
\(755\) 22.1797 21.1080i 0.807203 0.768200i
\(756\) 10.8463 + 9.39056i 0.394475 + 0.341532i
\(757\) −17.2746 17.2746i −0.627856 0.627856i 0.319672 0.947528i \(-0.396427\pi\)
−0.947528 + 0.319672i \(0.896427\pi\)
\(758\) 13.8705 + 13.8705i 0.503800 + 0.503800i
\(759\) 1.02618 4.23249i 0.0372479 0.153630i
\(760\) 0.0553424 2.23538i 0.00200748 0.0810859i
\(761\) 47.3018i 1.71469i 0.514744 + 0.857344i \(0.327887\pi\)
−0.514744 + 0.857344i \(0.672113\pi\)
\(762\) 28.5247 17.3920i 1.03334 0.630047i
\(763\) −2.71454 + 2.71454i −0.0982728 + 0.0982728i
\(764\) −14.1961 −0.513598
\(765\) −12.7020 6.94700i −0.459240 0.251169i
\(766\) 33.2165 1.20016
\(767\) −28.9727 + 28.9727i −1.04614 + 1.04614i
\(768\) 1.47884 0.901679i 0.0533631 0.0325365i
\(769\) 14.3683i 0.518135i −0.965859 0.259068i \(-0.916585\pi\)
0.965859 0.259068i \(-0.0834153\pi\)
\(770\) −15.6594 16.4545i −0.564327 0.592979i
\(771\) −8.41011 + 34.6876i −0.302883 + 1.24925i
\(772\) 11.5541 + 11.5541i 0.415842 + 0.415842i
\(773\) −11.3662 11.3662i −0.408814 0.408814i 0.472511 0.881325i \(-0.343348\pi\)
−0.881325 + 0.472511i \(0.843348\pi\)
\(774\) 11.7371 + 6.04682i 0.421880 + 0.217349i
\(775\) −0.757867 + 15.2965i −0.0272234 + 0.549465i
\(776\) 7.80520i 0.280190i
\(777\) −25.7900 42.2981i −0.925210 1.51744i