Properties

Label 570.2.k.b.77.7
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 77.7
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.901679 - 1.47884i) q^{3} -1.00000i q^{4} +(1.61979 - 1.54152i) q^{5} +(0.408116 + 1.68328i) q^{6} +(-1.95232 - 1.95232i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.37395 - 2.66688i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.901679 - 1.47884i) 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} +(-1.47884 - 0.901679i) q^{12} +(2.60584 - 2.60584i) q^{13} +2.76100 q^{14} +(-0.819140 - 3.78537i) q^{15} -1.00000 q^{16} +(1.52607 - 1.52607i) q^{17} +(2.85730 + 0.914240i) 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} +(-5.18276 - 0.372814i) q^{27} +(-1.95232 + 1.95232i) q^{28} -8.02750 q^{29} +(3.25588 + 2.09744i) q^{30} -3.06305 q^{31} +(0.707107 - 0.707107i) q^{32} +(5.44104 + 3.31751i) 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} +(2.48954 - 4.08308i) q^{42} +(-3.11201 + 3.11201i) q^{43} +3.67926 q^{44} +(-6.33656 - 2.20181i) q^{45} +0.683406 q^{46} +(3.44995 - 3.44995i) q^{47} +(-0.901679 + 1.47884i) 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} +(-1.47884 - 0.901679i) q^{57} +(5.67630 - 5.67630i) q^{58} +11.1184 q^{59} +(-3.78537 + 0.819140i) q^{60} +0.989652 q^{61} +(2.16590 - 2.16590i) q^{62} +(-2.52422 + 7.88901i) 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} +(0.914240 - 2.85730i) q^{72} +(11.1477 - 11.1477i) q^{73} -10.3593 q^{74} +(-7.16206 - 4.86877i) q^{75} -1.00000 q^{76} +(7.18309 - 7.18309i) q^{77} +(5.44985 + 3.32288i) 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} +(-7.23823 + 11.8714i) q^{87} +(-2.60163 + 2.60163i) q^{88} +1.05913 q^{89} +(6.03754 - 2.92371i) q^{90} -10.1749 q^{91} +(-0.483241 + 0.483241i) q^{92} +(-2.76188 + 4.52976i) 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
\(3\) 0.901679 1.47884i 0.520584 0.853810i
\(4\) 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 \(0.187155\pi\)
−0.832071 + 0.554669i \(0.812845\pi\)
\(12\) −1.47884 0.901679i −0.426905 0.260292i
\(13\) 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
\(15\) −0.819140 3.78537i −0.211501 0.977378i
\(16\) −1.00000 −0.250000
\(17\) 1.52607 1.52607i 0.370127 0.370127i −0.497396 0.867523i \(-0.665711\pi\)
0.867523 + 0.497396i \(0.165711\pi\)
\(18\) 2.85730 + 0.914240i 0.673472 + 0.215489i
\(19\) 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 0.654928 0.755691i \(-0.272699\pi\)
−0.755691 + 0.654928i \(0.772699\pi\)
\(24\) 1.68328 0.408116i 0.343599 0.0833064i
\(25\) 0.247423 4.99387i 0.0494845 0.998775i
\(26\) 3.68522i 0.722730i
\(27\) −5.18276 0.372814i −0.997423 0.0717481i
\(28\) −1.95232 + 1.95232i −0.368954 + 0.368954i
\(29\) −8.02750 −1.49067 −0.745335 0.666691i \(-0.767710\pi\)
−0.745335 + 0.666691i \(0.767710\pi\)
\(30\) 3.25588 + 2.09744i 0.594439 + 0.382938i
\(31\) −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
\(33\) 5.44104 + 3.31751i 0.947163 + 0.577504i
\(34\) 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 \(-0.859695\pi\)
0.904419 0.426646i \(-0.140305\pi\)
\(42\) 2.48954 4.08308i 0.384144 0.630034i
\(43\) −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
\(45\) −6.33656 2.20181i −0.944599 0.328226i
\(46\) 0.683406 0.100763
\(47\) 3.44995 3.44995i 0.503227 0.503227i −0.409212 0.912439i \(-0.634196\pi\)
0.912439 + 0.409212i \(0.134196\pi\)
\(48\) −0.901679 + 1.47884i −0.130146 + 0.213453i
\(49\) 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 \(-0.989592\pi\)
−0.0326918 0.999465i \(-0.510408\pi\)
\(54\) 3.92838 3.40115i 0.534585 0.462837i
\(55\) 5.67165 + 5.95961i 0.764765 + 0.803594i
\(56\) 2.76100i 0.368954i
\(57\) −1.47884 0.901679i −0.195877 0.119430i
\(58\) 5.67630 5.67630i 0.745335 0.745335i
\(59\) 11.1184 1.44749 0.723744 0.690068i \(-0.242420\pi\)
0.723744 + 0.690068i \(0.242420\pi\)
\(60\) −3.78537 + 0.819140i −0.488689 + 0.105750i
\(61\) 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
\(63\) −2.52422 + 7.88901i −0.318022 + 0.993921i
\(64\) 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 \(0.0777993\pi\)
−0.970279 + 0.241988i \(0.922201\pi\)
\(72\) 0.914240 2.85730i 0.107744 0.336736i
\(73\) 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
\(75\) −7.16206 4.86877i −0.827003 0.562197i
\(76\) −1.00000 −0.114708
\(77\) 7.18309 7.18309i 0.818589 0.818589i
\(78\) 5.44985 + 3.32288i 0.617074 + 0.376242i
\(79\) 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 0.838113 0.545497i \(-0.183659\pi\)
−0.545497 + 0.838113i \(0.683659\pi\)
\(84\) 1.12681 + 4.64754i 0.122945 + 0.507089i
\(85\) 0.119439 4.82439i 0.0129550 0.523278i
\(86\) 4.40105i 0.474577i
\(87\) −7.23823 + 11.8714i −0.776019 + 1.27275i
\(88\) −2.60163 + 2.60163i −0.277334 + 0.277334i
\(89\) 1.05913 0.112267 0.0561336 0.998423i \(-0.482123\pi\)
0.0561336 + 0.998423i \(0.482123\pi\)
\(90\) 6.03754 2.92371i 0.636413 0.308187i
\(91\) −10.1749 −1.06662
\(92\) −0.483241 + 0.483241i −0.0503814 + 0.0503814i
\(93\) −2.76188 + 4.52976i −0.286394 + 0.469714i
\(94\) 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 \(0.116420\pi\)
−0.933858 + 0.357645i \(0.883580\pi\)
\(102\) 3.19163 + 1.94600i 0.316018 + 0.192682i
\(103\) 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
\(105\) −5.79103 + 8.98948i −0.565147 + 0.877284i
\(106\) 10.6267 1.03216
\(107\) 3.71052 3.71052i 0.358709 0.358709i −0.504628 0.863337i \(-0.668370\pi\)
0.863337 + 0.504628i \(0.168370\pi\)
\(108\) −0.372814 + 5.18276i −0.0358740 + 0.498711i
\(109\) 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 0.999997 0.00240835i \(-0.000766603\pi\)
−0.00240835 + 0.999997i \(0.500767\pi\)
\(114\) 1.68328 0.408116i 0.157654 0.0382236i
\(115\) −1.52767 0.0378213i −0.142456 0.00352685i
\(116\) 8.02750i 0.745335i
\(117\) −10.5298 3.36917i −0.973477 0.311480i
\(118\) −7.86188 + 7.86188i −0.723744 + 0.723744i
\(119\) −5.95877 −0.546239
\(120\) 2.09744 3.25588i 0.191469 0.297220i
\(121\) −2.53692 −0.230629
\(122\) −0.699789 + 0.699789i −0.0633559 + 0.0633559i
\(123\) −8.08001 4.92654i −0.728550 0.444211i
\(124\) 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 \(0.243501\pi\)
−0.721396 + 0.692523i \(0.756499\pi\)
\(132\) 3.31751 5.44104i 0.288752 0.473582i
\(133\) −1.95232 + 1.95232i −0.169288 + 0.169288i
\(134\) −11.3857 −0.983579
\(135\) −8.96967 + 7.38546i −0.771986 + 0.635639i
\(136\) 2.15819 0.185063
\(137\) −0.0250882 + 0.0250882i −0.00214343 + 0.00214343i −0.708178 0.706034i \(-0.750482\pi\)
0.706034 + 0.708178i \(0.250482\pi\)
\(138\) 0.616213 1.01065i 0.0524555 0.0860322i
\(139\) 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
\(147\) 0.921499 + 0.561856i 0.0760039 + 0.0463411i
\(148\) 7.32517 7.32517i 0.602125 0.602125i
\(149\) −17.7034 −1.45032 −0.725160 0.688580i \(-0.758234\pi\)
−0.725160 + 0.688580i \(0.758234\pi\)
\(150\) 8.50708 1.62160i 0.694600 0.132403i
\(151\) −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
\(153\) −6.16660 1.97311i −0.498540 0.159516i
\(154\) 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
\(162\) −1.48762 8.87620i −0.116878 0.697380i
\(163\) −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
\(165\) 13.9273 3.01382i 1.08424 0.234626i
\(166\) −3.77008 −0.292615
\(167\) 6.38610 6.38610i 0.494171 0.494171i −0.415446 0.909618i \(-0.636375\pi\)
0.909618 + 0.415446i \(0.136375\pi\)
\(168\) −4.08308 2.48954i −0.315017 0.192072i
\(169\) 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 0.721892 0.692006i \(-0.243273\pi\)
−0.692006 + 0.721892i \(0.743273\pi\)
\(174\) −3.27615 13.5126i −0.248365 1.02438i
\(175\) −10.2327 + 9.26660i −0.773519 + 0.700489i
\(176\) 3.67926i 0.277334i
\(177\) 10.0252 16.4423i 0.753540 1.23588i
\(178\) −0.748916 + 0.748916i −0.0561336 + 0.0561336i
\(179\) −7.26370 −0.542915 −0.271457 0.962450i \(-0.587506\pi\)
−0.271457 + 0.962450i \(0.587506\pi\)
\(180\) −2.20181 + 6.33656i −0.164113 + 0.472300i
\(181\) 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
\(183\) 0.892348 1.46354i 0.0659642 0.108188i
\(184\) 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 \(0.171688\pi\)
−0.858031 + 0.513598i \(0.828312\pi\)
\(192\) 1.47884 + 0.901679i 0.106726 + 0.0650731i
\(193\) −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
\(195\) −11.9986 7.72952i −0.859239 0.553522i
\(196\) 0.623122 0.0445087
\(197\) 18.1909 18.1909i 1.29605 1.29605i 0.365065 0.930982i \(-0.381047\pi\)
0.930982 0.365065i \(-0.118953\pi\)
\(198\) −3.36372 + 10.5127i −0.239049 + 0.747108i
\(199\) 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
\(207\) −0.624797 + 1.95270i −0.0434264 + 0.135722i
\(208\) −2.60584 + 2.60584i −0.180683 + 0.180683i
\(209\) 3.67926 0.254499
\(210\) −2.26164 10.4514i −0.156068 0.721215i
\(211\) 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
\(213\) 6.03079 + 3.67709i 0.413223 + 0.251950i
\(214\) 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
\(222\) −9.34081 + 15.3198i −0.626914 + 1.02820i
\(223\) 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
\(225\) −13.6580 + 6.20149i −0.910535 + 0.413433i
\(226\) −14.9970 −0.997589
\(227\) −3.11027 + 3.11027i −0.206436 + 0.206436i −0.802751 0.596315i \(-0.796631\pi\)
0.596315 + 0.802751i \(0.296631\pi\)
\(228\) −0.901679 + 1.47884i −0.0597151 + 0.0979387i
\(229\) 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 0.263605 0.964631i \(-0.415088\pi\)
−0.964631 + 0.263605i \(0.915088\pi\)
\(234\) 9.82804 5.06330i 0.642479 0.330999i
\(235\) 0.270014 10.9064i 0.0176137 0.711452i
\(236\) 11.1184i 0.723744i
\(237\) 10.5836 + 6.45305i 0.687482 + 0.419171i
\(238\) 4.21349 4.21349i 0.273120 0.273120i
\(239\) −7.74663 −0.501088 −0.250544 0.968105i \(-0.580609\pi\)
−0.250544 + 0.968105i \(0.580609\pi\)
\(240\) 0.819140 + 3.78537i 0.0528752 + 0.244344i
\(241\) 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
\(243\) 6.12661 + 14.3340i 0.393022 + 0.919529i
\(244\) 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 \(0.178184\pi\)
−0.847371 + 0.531001i \(0.821816\pi\)
\(252\) 7.88901 + 2.52422i 0.496961 + 0.159011i
\(253\) 1.77797 1.77797i 0.111780 0.111780i
\(254\) −19.2885 −1.21027
\(255\) −7.02681 4.52668i −0.440036 0.283472i
\(256\) 1.00000 0.0625000
\(257\) 14.5714 14.5714i 0.908942 0.908942i −0.0872448 0.996187i \(-0.527806\pi\)
0.996187 + 0.0872448i \(0.0278062\pi\)
\(258\) −6.50846 3.96833i −0.405199 0.247058i
\(259\) 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 \(-0.967892\pi\)
−0.100700 0.994917i \(-0.532108\pi\)
\(264\) 1.50156 + 6.19323i 0.0924149 + 0.381167i
\(265\) −23.7548 0.588107i −1.45924 0.0361271i
\(266\) 2.76100i 0.169288i
\(267\) 0.954992 1.56628i 0.0584446 0.0958549i
\(268\) 8.05094 8.05094i 0.491789 0.491789i
\(269\) 27.3733 1.66898 0.834488 0.551026i \(-0.185763\pi\)
0.834488 + 0.551026i \(0.185763\pi\)
\(270\) 1.12021 11.5648i 0.0681737 0.703813i
\(271\) −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
\(273\) −9.17447 + 15.0470i −0.555264 + 0.910689i
\(274\) 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 \(0.147251\pi\)
−0.894894 + 0.446279i \(0.852749\pi\)
\(282\) 7.21522 + 4.39926i 0.429660 + 0.261972i
\(283\) −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
\(285\) −3.78537 + 0.819140i −0.224226 + 0.0485216i
\(286\) −13.5589 −0.801752
\(287\) −10.6670 + 10.6670i −0.629652 + 0.629652i
\(288\) −2.85730 0.914240i −0.168368 0.0538721i
\(289\) 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 0.785170 0.619281i \(-0.212576\pi\)
−0.619281 + 0.785170i \(0.712576\pi\)
\(294\) −1.04889 + 0.254306i −0.0611725 + 0.0148314i
\(295\) 18.0094 17.1392i 1.04855 0.997883i
\(296\) 10.3593i 0.602125i
\(297\) 1.37168 19.0687i 0.0795928 1.10648i
\(298\) 12.5182 12.5182i 0.725160 0.725160i
\(299\) −2.51850 −0.145649
\(300\) −4.86877 + 7.16206i −0.281099 + 0.413502i
\(301\) 12.1513 0.700389
\(302\) 9.68240 9.68240i 0.557160 0.557160i
\(303\) 10.6308 + 6.48178i 0.610721 + 0.372369i
\(304\) 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 \(-0.784761\pi\)
0.779961 0.625828i \(-0.215239\pi\)
\(312\) 3.32288 5.44985i 0.188121 0.308537i
\(313\) 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
\(315\) 8.07238 + 16.6696i 0.454827 + 0.939228i
\(316\) 7.15671 0.402596
\(317\) 13.0482 13.0482i 0.732860 0.732860i −0.238325 0.971185i \(-0.576598\pi\)
0.971185 + 0.238325i \(0.0765985\pi\)
\(318\) 9.58188 15.7152i 0.537325 0.881266i
\(319\) 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
\(327\) −2.05620 1.25371i −0.113708 0.0693301i
\(328\) 3.86345 3.86345i 0.213323 0.213323i
\(329\) −13.4708 −0.742671
\(330\) −7.71702 + 11.9792i −0.424808 + 0.659434i
\(331\) −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
\(333\) 9.47094 29.5998i 0.519004 1.62206i
\(334\) 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
\(342\) 0.914240 2.85730i 0.0494365 0.154505i
\(343\) −12.4497 + 12.4497i −0.672222 + 0.672222i
\(344\) −4.40105 −0.237289
\(345\) −1.43340 + 2.22509i −0.0771718 + 0.119795i
\(346\) −0.555924 −0.0298867
\(347\) −13.4880 + 13.4880i −0.724074 + 0.724074i −0.969432 0.245358i \(-0.921094\pi\)
0.245358 + 0.969432i \(0.421094\pi\)
\(348\) 11.8714 + 7.23823i 0.636374 + 0.388010i
\(349\) 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 \(0.0607527\pi\)
0.189704 + 0.981841i \(0.439247\pi\)
\(354\) 4.53759 + 18.7154i 0.241170 + 0.994710i
\(355\) 6.28640 + 6.60557i 0.333647 + 0.350587i
\(356\) 1.05913i 0.0561336i
\(357\) −5.37290 + 8.81208i −0.284364 + 0.466385i
\(358\) 5.13621 5.13621i 0.271457 0.271457i
\(359\) −2.29765 −0.121265 −0.0606327 0.998160i \(-0.519312\pi\)
−0.0606327 + 0.998160i \(0.519312\pi\)
\(360\) −2.92371 6.03754i −0.154093 0.318206i
\(361\) −1.00000 −0.0526316
\(362\) −8.09627 + 8.09627i −0.425531 + 0.425531i
\(363\) −2.28749 + 3.75171i −0.120062 + 0.196914i
\(364\) 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
\(372\) 4.52976 + 2.76188i 0.234857 + 0.143197i
\(373\) −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
\(375\) −19.1063 + 3.15409i −0.986646 + 0.162877i
\(376\) 4.87897 0.251614
\(377\) −20.9184 + 20.9184i −1.07735 + 1.07735i
\(378\) −14.3096 1.02934i −0.736007 0.0529435i
\(379\) 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 \(-0.927420\pi\)
−0.226045 0.974117i \(-0.572580\pi\)
\(384\) −1.68328 + 0.408116i −0.0858997 + 0.0208266i
\(385\) 0.562191 22.7080i 0.0286519 1.15731i
\(386\) 16.3400i 0.831685i
\(387\) 12.5751 + 4.02362i 0.639229 + 0.204532i
\(388\) 5.51911 5.51911i 0.280190 0.280190i
\(389\) 26.9154 1.36466 0.682332 0.731043i \(-0.260966\pi\)
0.682332 + 0.731043i \(0.260966\pi\)
\(390\) 13.9499 3.01871i 0.706381 0.152858i
\(391\) −1.47492 −0.0745900
\(392\) −0.440614 + 0.440614i −0.0222543 + 0.0222543i
\(393\) 23.4435 + 14.2939i 1.18257 + 0.721033i
\(394\) 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 \(-0.957862\pi\)
0.991251 0.131994i \(-0.0421378\pi\)
\(402\) −10.2663 + 16.8377i −0.512036 + 0.839789i
\(403\) −7.98181 + 7.98181i −0.397602 + 0.397602i
\(404\) 7.18857 0.357645
\(405\) 2.83417 + 19.9240i 0.140831 + 0.990034i
\(406\) −22.1639 −1.09998
\(407\) −26.9512 + 26.9512i −1.33592 + 1.33592i
\(408\) 1.94600 3.19163i 0.0963412 0.158009i
\(409\) 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
\(417\) −23.5787 14.3764i −1.15465 0.704015i
\(418\) −2.60163 + 2.60163i −0.127250 + 0.127250i
\(419\) 13.9765 0.682795 0.341397 0.939919i \(-0.389100\pi\)
0.341397 + 0.939919i \(0.389100\pi\)
\(420\) 8.98948 + 5.79103i 0.438642 + 0.282573i
\(421\) 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
\(423\) −13.9407 4.46055i −0.677819 0.216879i
\(424\) 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 \(-0.877530\pi\)
0.926892 0.375327i \(-0.122470\pi\)
\(432\) 5.18276 + 0.372814i 0.249356 + 0.0179370i
\(433\) −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
\(435\) 6.57564 + 30.3870i 0.315278 + 1.45695i
\(436\) −1.39041 −0.0665888
\(437\) −0.483241 + 0.483241i −0.0231165 + 0.0231165i
\(438\) 23.3143 + 14.2152i 1.11400 + 0.679227i
\(439\) 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 0.815011 0.579446i \(-0.196731\pi\)
−0.579446 + 0.815011i \(0.696731\pi\)
\(444\) −4.22782 17.4377i −0.200643 0.827557i
\(445\) 1.71556 1.63267i 0.0813254 0.0773959i
\(446\) 27.1704i 1.28656i
\(447\) −15.9628 + 26.1806i −0.755014 + 1.23830i
\(448\) 1.95232 1.95232i 0.0922385 0.0922385i
\(449\) −32.0557 −1.51280 −0.756401 0.654109i \(-0.773044\pi\)
−0.756401 + 0.654109i \(0.773044\pi\)
\(450\) 5.27256 14.0428i 0.248551 0.661984i
\(451\) 20.1025 0.946589
\(452\) 10.6045 10.6045i 0.498794 0.498794i
\(453\) −12.3467 + 20.2498i −0.580097 + 0.951417i
\(454\) 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 \(-0.937747\pi\)
0.980936 0.194330i \(-0.0622532\pi\)
\(462\) 15.0227 + 9.15964i 0.698920 + 0.426145i
\(463\) −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
\(465\) 2.50906 + 11.5948i 0.116355 + 0.537694i
\(466\) 15.1331 0.701026
\(467\) −2.44668 + 2.44668i −0.113219 + 0.113219i −0.761447 0.648228i \(-0.775511\pi\)
0.648228 + 0.761447i \(0.275511\pi\)
\(468\) −3.36917 + 10.5298i −0.155740 + 0.486739i
\(469\) 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
\(477\) −9.71537 + 30.3637i −0.444836 + 1.39026i
\(478\) 5.47769 5.47769i 0.250544 0.250544i
\(479\) 1.05345 0.0481333 0.0240667 0.999710i \(-0.492339\pi\)
0.0240667 + 0.999710i \(0.492339\pi\)
\(480\) −3.25588 2.09744i −0.148610 0.0957346i
\(481\) 38.1764 1.74070
\(482\) −8.20078 + 8.20078i −0.373535 + 0.373535i
\(483\) 2.79040 + 1.70136i 0.126968 + 0.0774147i
\(484\) 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 \(0.134784\pi\)
−0.911682 + 0.410897i \(0.865216\pi\)
\(492\) −4.92654 + 8.08001i −0.222105 + 0.364275i
\(493\) −12.2505 + 12.2505i −0.551737 + 0.551737i
\(494\) 3.68522 0.165806
\(495\) 8.10101 23.3138i 0.364113 1.04788i
\(496\) 3.06305 0.137535
\(497\) 7.96166 7.96166i 0.357129 0.357129i
\(498\) −3.39940 + 5.57536i −0.152331 + 0.249838i
\(499\) 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 \(-0.999334\pi\)
−0.00209079 0.999998i \(-0.500666\pi\)
\(504\) −7.36326 + 3.79348i −0.327986 + 0.168975i
\(505\) 11.0813 + 11.6440i 0.493113 + 0.518149i
\(506\) 2.51443i 0.111780i
\(507\) −0.858934 0.523709i −0.0381466 0.0232587i
\(508\) 13.6390 13.6390i 0.605134 0.605134i
\(509\) 22.2471 0.986087 0.493043 0.870005i \(-0.335884\pi\)
0.493043 + 0.870005i \(0.335884\pi\)
\(510\) 8.16955 1.76786i 0.361754 0.0782822i
\(511\) −43.5278 −1.92555
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −0.372814 + 5.18276i −0.0164601 + 0.228824i
\(514\) 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 \(0.0801653\pi\)
−0.968454 + 0.249193i \(0.919835\pi\)
\(522\) −22.9370 7.33906i −1.00392 0.321222i
\(523\) −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
\(525\) 4.47724 + 23.4880i 0.195403 + 1.02510i
\(526\) 25.1276 1.09562
\(527\) −4.67443 + 4.67443i −0.203621 + 0.203621i
\(528\) −5.44104 3.31751i −0.236791 0.144376i
\(529\) 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
\(537\) −6.54953 + 10.7419i −0.282633 + 0.463546i
\(538\) −19.3558 + 19.3558i −0.834488 + 0.834488i
\(539\) −2.29262 −0.0987503
\(540\) 7.38546 + 8.96967i 0.317820 + 0.385993i
\(541\) −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
\(543\) 10.3241 16.9325i 0.443049 0.726645i
\(544\) 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
\(552\) −1.01065 0.616213i −0.0430161 0.0262278i
\(553\) 13.9722 13.9722i 0.594158 0.594158i
\(554\) 15.2149 0.646419
\(555\) 21.7281 33.7288i 0.922307 1.43171i
\(556\) −15.9440 −0.676177
\(557\) −18.6904 + 18.6904i −0.791939 + 0.791939i −0.981809 0.189871i \(-0.939193\pi\)
0.189871 + 0.981809i \(0.439193\pi\)
\(558\) −8.75204 2.80036i −0.370503 0.118549i
\(559\) 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 0.401967 0.915654i \(-0.368327\pi\)
−0.915654 + 0.401967i \(0.868327\pi\)
\(564\) −8.21268 + 1.99119i −0.345816 + 0.0838441i
\(565\) 33.5241 + 0.829972i 1.41037 + 0.0349172i
\(566\) 20.7076i 0.870404i
\(567\) 24.5072 4.10731i 1.02921 0.172491i
\(568\) −2.88361 + 2.88361i −0.120994 + 0.120994i
\(569\) −15.7219 −0.659095 −0.329548 0.944139i \(-0.606896\pi\)
−0.329548 + 0.944139i \(0.606896\pi\)
\(570\) 2.09744 3.25588i 0.0878521 0.136374i
\(571\) −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
\(573\) 20.9938 + 12.8004i 0.877031 + 0.534742i
\(574\) 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
\(582\) −7.03778 + 11.5427i −0.291725 + 0.478459i
\(583\) 27.6467 27.6467i 1.14501 1.14501i
\(584\) 15.7652 0.652369
\(585\) −22.2496 + 10.7745i −0.919909 + 0.445472i
\(586\) −4.01575 −0.165889
\(587\) 9.84222 9.84222i 0.406232 0.406232i −0.474190 0.880422i \(-0.657259\pi\)
0.880422 + 0.474190i \(0.157259\pi\)
\(588\) 0.561856 0.921499i 0.0231705 0.0380020i
\(589\) 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 \(-0.969030\pi\)
−0.0971411 0.995271i \(-0.530970\pi\)
\(594\) 12.5137 + 14.4535i 0.513443 + 0.593036i
\(595\) −9.65194 + 9.18557i −0.395691 + 0.376572i
\(596\) 17.7034i 0.725160i
\(597\) −0.0735614 0.0448518i −0.00301067 0.00183566i
\(598\) 1.78085 1.78085i 0.0728243 0.0728243i
\(599\) −1.72077 −0.0703088 −0.0351544 0.999382i \(-0.511192\pi\)
−0.0351544 + 0.999382i \(0.511192\pi\)
\(600\) −1.62160 8.50708i −0.0662015 0.347300i
\(601\) 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
\(603\) 10.4093 32.5325i 0.423900 1.32483i
\(604\) 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
\(612\) −1.97311 + 6.16660i −0.0797581 + 0.249270i
\(613\) −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
\(615\) −20.6823 + 4.47557i −0.833989 + 0.180472i
\(616\) 10.1584 0.409295
\(617\) 12.2561 12.2561i 0.493413 0.493413i −0.415967 0.909380i \(-0.636557\pi\)
0.909380 + 0.415967i \(0.136557\pi\)
\(618\) 10.9632 + 6.68446i 0.441003 + 0.268888i
\(619\) 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
\(627\) 3.31751 5.44104i 0.132488 0.217294i
\(628\) −1.10214 + 1.10214i −0.0439800 + 0.0439800i
\(629\) 22.3575 0.891451
\(630\) −17.4953 6.07919i −0.697028 0.242201i
\(631\) −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
\(633\) 24.4317 40.0703i 0.971071 1.59265i
\(634\) 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 \(0.253189\pi\)
−0.699988 + 0.714155i \(0.746811\pi\)
\(642\) 7.76017 + 4.73153i 0.306270 + 0.186739i
\(643\) 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
\(645\) 14.3293 + 9.23093i 0.564215 + 0.363468i
\(646\) 2.15819 0.0849129
\(647\) −4.82277 + 4.82277i −0.189603 + 0.189603i −0.795524 0.605922i \(-0.792804\pi\)
0.605922 + 0.795524i \(0.292804\pi\)
\(648\) −8.87620 + 1.48762i −0.348690 + 0.0584392i
\(649\) 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 0.0628489 0.998023i \(-0.479981\pi\)
−0.998023 + 0.0628489i \(0.979981\pi\)
\(654\) 2.34046 0.567451i 0.0915192 0.0221891i
\(655\) 24.4371 + 25.6778i 0.954836 + 1.00331i
\(656\) 5.46374i 0.213323i
\(657\) −45.0460 14.4132i −1.75741 0.562312i
\(658\) 9.52531 9.52531i 0.371335 0.371335i
\(659\) 5.45910 0.212656 0.106328 0.994331i \(-0.466091\pi\)
0.106328 + 0.994331i \(0.466091\pi\)
\(660\) −3.01382 13.9273i −0.117313 0.542121i
\(661\) 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
\(663\) −11.7618 7.17142i −0.456792 0.278515i
\(664\) 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
\(672\) −2.48954 + 4.08308i −0.0960359 + 0.157508i
\(673\) 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
\(675\) −3.14412 + 25.7898i −0.121017 + 0.992650i
\(676\) −0.580815 −0.0223390
\(677\) −31.7382 + 31.7382i −1.21980 + 1.21980i −0.252097 + 0.967702i \(0.581120\pi\)
−0.967702 + 0.252097i \(0.918880\pi\)
\(678\) −13.5225 + 22.1783i −0.519329 + 0.851751i
\(679\) 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 0.207208 0.978297i \(-0.433562\pi\)
−0.978297 + 0.207208i \(0.933562\pi\)
\(684\) 1.37395 + 2.66688i 0.0525343 + 0.101971i
\(685\) −0.00196355 + 0.0793114i −7.50233e−5 + 0.00303033i
\(686\) 17.6066i 0.672222i
\(687\) 9.02743 + 5.50420i 0.344418 + 0.209998i
\(688\) 3.11201 3.11201i 0.118644 0.118644i
\(689\) −39.1617 −1.49194
\(690\) −0.559805 2.58694i −0.0213114 0.0984832i
\(691\) −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
\(693\) −29.0257 9.28724i −1.10259 0.352793i
\(694\) 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 \(0.0607699\pi\)
−0.981831 + 0.189757i \(0.939230\pi\)
\(702\) 1.37390 19.0996i 0.0518545 0.720868i
\(703\) 7.32517 7.32517i 0.276274 0.276274i
\(704\) −3.67926 −0.138667
\(705\) −15.8853 10.2333i −0.598276 0.385410i
\(706\) −31.1287 −1.17155
\(707\) 14.0344 14.0344i 0.527818 0.527818i
\(708\) −16.4423 10.0252i −0.617940 0.376770i
\(709\) 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
\(717\) −6.98497 + 11.4560i −0.260858 + 0.427834i
\(718\) 1.62469 1.62469i 0.0606327 0.0606327i
\(719\) 4.57697 0.170692 0.0853460 0.996351i \(-0.472800\pi\)
0.0853460 + 0.996351i \(0.472800\pi\)
\(720\) 6.33656 + 2.20181i 0.236150 + 0.0820565i
\(721\) −20.4682 −0.762277
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) 10.4574 17.1511i 0.388914 0.637857i
\(724\) 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
\(732\) −1.46354 0.892348i −0.0540940 0.0329821i
\(733\) −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
\(735\) 2.35874 0.510424i 0.0870036 0.0188273i
\(736\) −0.683406 −0.0251907
\(737\) −29.6215 + 29.6215i −1.09112 + 1.09112i
\(738\) 4.99517 15.6115i 0.183875 0.574669i
\(739\) 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 0.993003 0.118091i \(-0.0376775\pi\)
−0.118091 + 0.993003i \(0.537678\pi\)
\(744\) −5.15597 + 1.25008i −0.189027 + 0.0458301i
\(745\) −28.6758 + 27.2902i −1.05060 + 0.999836i
\(746\) 23.1149i 0.846298i
\(747\) 3.44676 10.7723i 0.126110 0.394136i
\(748\) 5.61481 5.61481i 0.205298 0.205298i
\(749\) −14.4883 −0.529389
\(750\) 11.2799 15.7405i 0.411885 0.574762i
\(751\) −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
\(753\) 24.8819 + 15.1710i 0.906748 + 0.552862i
\(754\) 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 \(-0.672113\pi\)
0.514744 0.857344i \(-0.327887\pi\)
\(762\) −17.3920 + 28.5247i −0.630047 + 1.03334i
\(763\) −2.71454 + 2.71454i −0.0982728 + 0.0982728i
\(764\) 14.1961 0.513598
\(765\) −13.0302 + 6.30994i −0.471107 + 0.228136i
\(766\) 33.2165 1.20016
\(767\) 28.9727 28.9727i 1.04614 1.04614i
\(768\) 0.901679 1.47884i 0.0325365 0.0533631i
\(769\) 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 0.881325 0.472511i \(-0.156652\pi\)
−0.472511 + 0.881325i \(0.656652\pi\)
\(774\) −11.7371 + 6.04682i −0.421880 + 0.217349i
\(775\) −0.757867 + 15.2965i −0.0272234 + 0.549465i
\(776\) 7.80520i 0.280190i
\(777\) −42.2981 25.7900i −1.51744 0.925210i