Properties

Label 570.2.m.b.37.3
Level $570$
Weight $2$
Character 570.37
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
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.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 108 x^{16} + 1318 x^{12} + 4652 x^{8} + 5057 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.3
Root \(-1.20277 + 1.20277i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.b.493.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.528178 + 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 + 0.904140i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.528178 + 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 + 0.904140i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.90987 - 1.16292i) q^{10} +2.66147 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.143663 - 0.143663i) q^{13} -1.27865 q^{14} +(-1.16292 + 1.90987i) q^{15} -1.00000 q^{16} +(3.29524 + 3.29524i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-4.05688 - 1.59427i) q^{19} +(2.17279 - 0.528178i) q^{20} +1.27865i q^{21} +(-1.88194 + 1.88194i) q^{22} +(1.75733 - 1.75733i) q^{23} +1.00000i q^{24} +(-4.44206 + 2.29524i) q^{25} +0.203169 q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.904140 - 0.904140i) q^{28} -2.17494 q^{29} +(-0.528178 - 2.17279i) q^{30} +2.62167i q^{31} +(0.707107 - 0.707107i) q^{32} +(1.88194 + 1.88194i) q^{33} -4.66018 q^{34} +(-1.48696 + 2.44206i) q^{35} +1.00000 q^{36} +(0.984090 - 0.984090i) q^{37} +(3.99597 - 1.74133i) q^{38} -0.203169i q^{39} +(-1.16292 + 1.90987i) q^{40} +3.74005i q^{41} +(-0.904140 - 0.904140i) q^{42} +(-2.01084 + 2.01084i) q^{43} -2.66147i q^{44} +(-2.17279 + 0.528178i) q^{45} +2.48524i q^{46} +(3.24973 + 3.24973i) q^{47} +(-0.707107 - 0.707107i) q^{48} -5.36506i q^{49} +(1.51803 - 4.76399i) q^{50} +4.66018i q^{51} +(-0.143663 + 0.143663i) q^{52} +(2.54197 + 2.54197i) q^{53} -1.00000i q^{54} +(1.40573 + 5.78282i) q^{55} +1.27865i q^{56} +(-1.74133 - 3.99597i) q^{57} +(1.53792 - 1.53792i) q^{58} -2.19877 q^{59} +(1.90987 + 1.16292i) q^{60} -8.90579 q^{61} +(-1.85380 - 1.85380i) q^{62} +(-0.904140 + 0.904140i) q^{63} +1.00000i q^{64} +(0.236270 - 0.388028i) q^{65} -2.66147 q^{66} +(4.50928 - 4.50928i) q^{67} +(3.29524 - 3.29524i) q^{68} +2.48524 q^{69} +(-0.675353 - 2.77824i) q^{70} -2.55729i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-5.25513 + 5.25513i) q^{73} +1.39171i q^{74} +(-4.76399 - 1.51803i) q^{75} +(-1.59427 + 4.05688i) q^{76} +(2.40634 + 2.40634i) q^{77} +(0.143663 + 0.143663i) q^{78} -4.22731 q^{79} +(-0.528178 - 2.17279i) q^{80} -1.00000 q^{81} +(-2.64461 - 2.64461i) q^{82} +(6.55477 - 6.55477i) q^{83} +1.27865 q^{84} +(-5.41940 + 8.90035i) q^{85} -2.84376i q^{86} +(-1.53792 - 1.53792i) q^{87} +(1.88194 + 1.88194i) q^{88} -4.94664 q^{89} +(1.16292 - 1.90987i) q^{90} -0.259782i q^{91} +(-1.75733 - 1.75733i) q^{92} +(-1.85380 + 1.85380i) q^{93} -4.59581 q^{94} +(1.32127 - 9.65682i) q^{95} +1.00000 q^{96} +(11.8481 - 11.8481i) q^{97} +(3.79367 + 3.79367i) q^{98} +2.66147i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100}) \)

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
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 0.528178 + 2.17279i 0.236208 + 0.971702i
\(6\) −1.00000 −0.408248
\(7\) 0.904140 + 0.904140i 0.341733 + 0.341733i 0.857018 0.515286i \(-0.172314\pi\)
−0.515286 + 0.857018i \(0.672314\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −1.90987 1.16292i −0.603955 0.367747i
\(11\) 2.66147 0.802462 0.401231 0.915977i \(-0.368582\pi\)
0.401231 + 0.915977i \(0.368582\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −0.143663 0.143663i −0.0398448 0.0398448i 0.686904 0.726748i \(-0.258969\pi\)
−0.726748 + 0.686904i \(0.758969\pi\)
\(14\) −1.27865 −0.341733
\(15\) −1.16292 + 1.90987i −0.300264 + 0.493128i
\(16\) −1.00000 −0.250000
\(17\) 3.29524 + 3.29524i 0.799214 + 0.799214i 0.982972 0.183758i \(-0.0588262\pi\)
−0.183758 + 0.982972i \(0.558826\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −4.05688 1.59427i −0.930713 0.365751i
\(20\) 2.17279 0.528178i 0.485851 0.118104i
\(21\) 1.27865i 0.279024i
\(22\) −1.88194 + 1.88194i −0.401231 + 0.401231i
\(23\) 1.75733 1.75733i 0.366428 0.366428i −0.499745 0.866173i \(-0.666573\pi\)
0.866173 + 0.499745i \(0.166573\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −4.44206 + 2.29524i −0.888411 + 0.459049i
\(26\) 0.203169 0.0398448
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0.904140 0.904140i 0.170866 0.170866i
\(29\) −2.17494 −0.403876 −0.201938 0.979398i \(-0.564724\pi\)
−0.201938 + 0.979398i \(0.564724\pi\)
\(30\) −0.528178 2.17279i −0.0964317 0.396696i
\(31\) 2.62167i 0.470865i 0.971891 + 0.235432i \(0.0756507\pi\)
−0.971891 + 0.235432i \(0.924349\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 1.88194 + 1.88194i 0.327604 + 0.327604i
\(34\) −4.66018 −0.799214
\(35\) −1.48696 + 2.44206i −0.251342 + 0.412783i
\(36\) 1.00000 0.166667
\(37\) 0.984090 0.984090i 0.161783 0.161783i −0.621573 0.783356i \(-0.713506\pi\)
0.783356 + 0.621573i \(0.213506\pi\)
\(38\) 3.99597 1.74133i 0.648232 0.282481i
\(39\) 0.203169i 0.0325332i
\(40\) −1.16292 + 1.90987i −0.183874 + 0.301978i
\(41\) 3.74005i 0.584098i 0.956403 + 0.292049i \(0.0943370\pi\)
−0.956403 + 0.292049i \(0.905663\pi\)
\(42\) −0.904140 0.904140i −0.139512 0.139512i
\(43\) −2.01084 + 2.01084i −0.306650 + 0.306650i −0.843609 0.536959i \(-0.819573\pi\)
0.536959 + 0.843609i \(0.319573\pi\)
\(44\) 2.66147i 0.401231i
\(45\) −2.17279 + 0.528178i −0.323901 + 0.0787361i
\(46\) 2.48524i 0.366428i
\(47\) 3.24973 + 3.24973i 0.474021 + 0.474021i 0.903213 0.429192i \(-0.141202\pi\)
−0.429192 + 0.903213i \(0.641202\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 5.36506i 0.766437i
\(50\) 1.51803 4.76399i 0.214681 0.673730i
\(51\) 4.66018i 0.652555i
\(52\) −0.143663 + 0.143663i −0.0199224 + 0.0199224i
\(53\) 2.54197 + 2.54197i 0.349166 + 0.349166i 0.859799 0.510633i \(-0.170589\pi\)
−0.510633 + 0.859799i \(0.670589\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 1.40573 + 5.78282i 0.189548 + 0.779755i
\(56\) 1.27865i 0.170866i
\(57\) −1.74133 3.99597i −0.230645 0.529279i
\(58\) 1.53792 1.53792i 0.201938 0.201938i
\(59\) −2.19877 −0.286256 −0.143128 0.989704i \(-0.545716\pi\)
−0.143128 + 0.989704i \(0.545716\pi\)
\(60\) 1.90987 + 1.16292i 0.246564 + 0.150132i
\(61\) −8.90579 −1.14027 −0.570135 0.821551i \(-0.693109\pi\)
−0.570135 + 0.821551i \(0.693109\pi\)
\(62\) −1.85380 1.85380i −0.235432 0.235432i
\(63\) −0.904140 + 0.904140i −0.113911 + 0.113911i
\(64\) 1.00000i 0.125000i
\(65\) 0.236270 0.388028i 0.0293056 0.0481290i
\(66\) −2.66147 −0.327604
\(67\) 4.50928 4.50928i 0.550896 0.550896i −0.375803 0.926700i \(-0.622633\pi\)
0.926700 + 0.375803i \(0.122633\pi\)
\(68\) 3.29524 3.29524i 0.399607 0.399607i
\(69\) 2.48524 0.299187
\(70\) −0.675353 2.77824i −0.0807202 0.332063i
\(71\) 2.55729i 0.303495i −0.988419 0.151748i \(-0.951510\pi\)
0.988419 0.151748i \(-0.0484901\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −5.25513 + 5.25513i −0.615066 + 0.615066i −0.944262 0.329196i \(-0.893222\pi\)
0.329196 + 0.944262i \(0.393222\pi\)
\(74\) 1.39171i 0.161783i
\(75\) −4.76399 1.51803i −0.550098 0.175287i
\(76\) −1.59427 + 4.05688i −0.182876 + 0.465356i
\(77\) 2.40634 + 2.40634i 0.274228 + 0.274228i
\(78\) 0.143663 + 0.143663i 0.0162666 + 0.0162666i
\(79\) −4.22731 −0.475610 −0.237805 0.971313i \(-0.576428\pi\)
−0.237805 + 0.971313i \(0.576428\pi\)
\(80\) −0.528178 2.17279i −0.0590521 0.242926i
\(81\) −1.00000 −0.111111
\(82\) −2.64461 2.64461i −0.292049 0.292049i
\(83\) 6.55477 6.55477i 0.719479 0.719479i −0.249019 0.968499i \(-0.580108\pi\)
0.968499 + 0.249019i \(0.0801083\pi\)
\(84\) 1.27865 0.139512
\(85\) −5.41940 + 8.90035i −0.587817 + 0.965379i
\(86\) 2.84376i 0.306650i
\(87\) −1.53792 1.53792i −0.164882 0.164882i
\(88\) 1.88194 + 1.88194i 0.200616 + 0.200616i
\(89\) −4.94664 −0.524343 −0.262171 0.965021i \(-0.584439\pi\)
−0.262171 + 0.965021i \(0.584439\pi\)
\(90\) 1.16292 1.90987i 0.122582 0.201318i
\(91\) 0.259782i 0.0272326i
\(92\) −1.75733 1.75733i −0.183214 0.183214i
\(93\) −1.85380 + 1.85380i −0.192230 + 0.192230i
\(94\) −4.59581 −0.474021
\(95\) 1.32127 9.65682i 0.135559 0.990769i
\(96\) 1.00000 0.102062
\(97\) 11.8481 11.8481i 1.20300 1.20300i 0.229746 0.973251i \(-0.426211\pi\)
0.973251 0.229746i \(-0.0737894\pi\)
\(98\) 3.79367 + 3.79367i 0.383219 + 0.383219i
\(99\) 2.66147i 0.267487i
\(100\) 2.29524 + 4.44206i 0.229524 + 0.444206i
\(101\) 3.64684 0.362874 0.181437 0.983403i \(-0.441925\pi\)
0.181437 + 0.983403i \(0.441925\pi\)
\(102\) −3.29524 3.29524i −0.326278 0.326278i
\(103\) 4.27174 + 4.27174i 0.420907 + 0.420907i 0.885516 0.464609i \(-0.153805\pi\)
−0.464609 + 0.885516i \(0.653805\pi\)
\(104\) 0.203169i 0.0199224i
\(105\) −2.77824 + 0.675353i −0.271128 + 0.0659077i
\(106\) −3.59488 −0.349166
\(107\) 9.39155 9.39155i 0.907915 0.907915i −0.0881885 0.996104i \(-0.528108\pi\)
0.996104 + 0.0881885i \(0.0281078\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 12.0254 1.15182 0.575912 0.817512i \(-0.304647\pi\)
0.575912 + 0.817512i \(0.304647\pi\)
\(110\) −5.08307 3.09507i −0.484652 0.295103i
\(111\) 1.39171 0.132096
\(112\) −0.904140 0.904140i −0.0854332 0.0854332i
\(113\) −1.99650 1.99650i −0.187815 0.187815i 0.606936 0.794751i \(-0.292399\pi\)
−0.794751 + 0.606936i \(0.792399\pi\)
\(114\) 4.05688 + 1.59427i 0.379962 + 0.149317i
\(115\) 4.74649 + 2.89013i 0.442612 + 0.269506i
\(116\) 2.17494i 0.201938i
\(117\) 0.143663 0.143663i 0.0132816 0.0132816i
\(118\) 1.55477 1.55477i 0.143128 0.143128i
\(119\) 5.95872i 0.546235i
\(120\) −2.17279 + 0.528178i −0.198348 + 0.0482158i
\(121\) −3.91659 −0.356054
\(122\) 6.29734 6.29734i 0.570135 0.570135i
\(123\) −2.64461 + 2.64461i −0.238457 + 0.238457i
\(124\) 2.62167 0.235432
\(125\) −7.33328 8.43937i −0.655909 0.754840i
\(126\) 1.27865i 0.113911i
\(127\) 12.5449 12.5449i 1.11318 1.11318i 0.120462 0.992718i \(-0.461562\pi\)
0.992718 0.120462i \(-0.0384377\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −2.84376 −0.250379
\(130\) 0.107310 + 0.441445i 0.00941168 + 0.0387173i
\(131\) 20.6202 1.80159 0.900797 0.434240i \(-0.142983\pi\)
0.900797 + 0.434240i \(0.142983\pi\)
\(132\) 1.88194 1.88194i 0.163802 0.163802i
\(133\) −2.22655 5.10944i −0.193066 0.443044i
\(134\) 6.37709i 0.550896i
\(135\) −1.90987 1.16292i −0.164376 0.100088i
\(136\) 4.66018i 0.399607i
\(137\) −2.44206 2.44206i −0.208639 0.208639i 0.595050 0.803689i \(-0.297132\pi\)
−0.803689 + 0.595050i \(0.797132\pi\)
\(138\) −1.75733 + 1.75733i −0.149594 + 0.149594i
\(139\) 16.1995i 1.37402i −0.726647 0.687011i \(-0.758923\pi\)
0.726647 0.687011i \(-0.241077\pi\)
\(140\) 2.44206 + 1.48696i 0.206391 + 0.125671i
\(141\) 4.59581i 0.387037i
\(142\) 1.80828 + 1.80828i 0.151748 + 0.151748i
\(143\) −0.382353 0.382353i −0.0319740 0.0319740i
\(144\) 1.00000i 0.0833333i
\(145\) −1.14876 4.72570i −0.0953990 0.392448i
\(146\) 7.43187i 0.615066i
\(147\) 3.79367 3.79367i 0.312897 0.312897i
\(148\) −0.984090 0.984090i −0.0808917 0.0808917i
\(149\) 2.85261i 0.233695i 0.993150 + 0.116847i \(0.0372789\pi\)
−0.993150 + 0.116847i \(0.962721\pi\)
\(150\) 4.44206 2.29524i 0.362692 0.187406i
\(151\) 18.6146i 1.51483i 0.652932 + 0.757417i \(0.273539\pi\)
−0.652932 + 0.757417i \(0.726461\pi\)
\(152\) −1.74133 3.99597i −0.141240 0.324116i
\(153\) −3.29524 + 3.29524i −0.266405 + 0.266405i
\(154\) −3.40308 −0.274228
\(155\) −5.69634 + 1.38471i −0.457541 + 0.111222i
\(156\) −0.203169 −0.0162666
\(157\) −10.0694 10.0694i −0.803627 0.803627i 0.180033 0.983661i \(-0.442379\pi\)
−0.983661 + 0.180033i \(0.942379\pi\)
\(158\) 2.98916 2.98916i 0.237805 0.237805i
\(159\) 3.59488i 0.285093i
\(160\) 1.90987 + 1.16292i 0.150989 + 0.0919368i
\(161\) 3.17774 0.250441
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 16.5520 16.5520i 1.29645 1.29645i 0.365735 0.930719i \(-0.380818\pi\)
0.930719 0.365735i \(-0.119182\pi\)
\(164\) 3.74005 0.292049
\(165\) −3.09507 + 5.08307i −0.240951 + 0.395716i
\(166\) 9.26984i 0.719479i
\(167\) 7.05038 7.05038i 0.545575 0.545575i −0.379583 0.925158i \(-0.623932\pi\)
0.925158 + 0.379583i \(0.123932\pi\)
\(168\) −0.904140 + 0.904140i −0.0697559 + 0.0697559i
\(169\) 12.9587i 0.996825i
\(170\) −2.46140 10.1256i −0.188781 0.776598i
\(171\) 1.59427 4.05688i 0.121917 0.310238i
\(172\) 2.01084 + 2.01084i 0.153325 + 0.153325i
\(173\) 14.7696 + 14.7696i 1.12291 + 1.12291i 0.991302 + 0.131609i \(0.0420143\pi\)
0.131609 + 0.991302i \(0.457986\pi\)
\(174\) 2.17494 0.164882
\(175\) −6.09146 1.94102i −0.460471 0.146727i
\(176\) −2.66147 −0.200616
\(177\) −1.55477 1.55477i −0.116864 0.116864i
\(178\) 3.49780 3.49780i 0.262171 0.262171i
\(179\) 6.48791 0.484929 0.242465 0.970160i \(-0.422044\pi\)
0.242465 + 0.970160i \(0.422044\pi\)
\(180\) 0.528178 + 2.17279i 0.0393681 + 0.161950i
\(181\) 0.122571i 0.00911063i 0.999990 + 0.00455531i \(0.00145001\pi\)
−0.999990 + 0.00455531i \(0.998550\pi\)
\(182\) 0.183694 + 0.183694i 0.0136163 + 0.0136163i
\(183\) −6.29734 6.29734i −0.465513 0.465513i
\(184\) 2.48524 0.183214
\(185\) 2.65800 + 1.61845i 0.195420 + 0.118991i
\(186\) 2.62167i 0.192230i
\(187\) 8.77018 + 8.77018i 0.641339 + 0.641339i
\(188\) 3.24973 3.24973i 0.237011 0.237011i
\(189\) −1.27865 −0.0930079
\(190\) 5.89413 + 7.76268i 0.427605 + 0.563164i
\(191\) −0.473897 −0.0342900 −0.0171450 0.999853i \(-0.505458\pi\)
−0.0171450 + 0.999853i \(0.505458\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −8.37158 8.37158i −0.602600 0.602600i 0.338402 0.941002i \(-0.390114\pi\)
−0.941002 + 0.338402i \(0.890114\pi\)
\(194\) 16.7558i 1.20300i
\(195\) 0.441445 0.107310i 0.0316125 0.00768460i
\(196\) −5.36506 −0.383219
\(197\) −9.45290 9.45290i −0.673491 0.673491i 0.285028 0.958519i \(-0.407997\pi\)
−0.958519 + 0.285028i \(0.907997\pi\)
\(198\) −1.88194 1.88194i −0.133744 0.133744i
\(199\) 3.17530i 0.225091i 0.993647 + 0.112545i \(0.0359004\pi\)
−0.993647 + 0.112545i \(0.964100\pi\)
\(200\) −4.76399 1.51803i −0.336865 0.107341i
\(201\) 6.37709 0.449805
\(202\) −2.57871 + 2.57871i −0.181437 + 0.181437i
\(203\) −1.96645 1.96645i −0.138018 0.138018i
\(204\) 4.66018 0.326278
\(205\) −8.12635 + 1.97541i −0.567569 + 0.137969i
\(206\) −6.04115 −0.420907
\(207\) 1.75733 + 1.75733i 0.122143 + 0.122143i
\(208\) 0.143663 + 0.143663i 0.00996120 + 0.00996120i
\(209\) −10.7973 4.24310i −0.746862 0.293501i
\(210\) 1.48696 2.44206i 0.102610 0.168518i
\(211\) 14.4553i 0.995142i −0.867423 0.497571i \(-0.834225\pi\)
0.867423 0.497571i \(-0.165775\pi\)
\(212\) 2.54197 2.54197i 0.174583 0.174583i
\(213\) 1.80828 1.80828i 0.123901 0.123901i
\(214\) 13.2817i 0.907915i
\(215\) −5.43122 3.30706i −0.370406 0.225539i
\(216\) −1.00000 −0.0680414
\(217\) −2.37035 + 2.37035i −0.160910 + 0.160910i
\(218\) −8.50324 + 8.50324i −0.575912 + 0.575912i
\(219\) −7.43187 −0.502199
\(220\) 5.78282 1.40573i 0.389877 0.0947742i
\(221\) 0.946806i 0.0636890i
\(222\) −0.984090 + 0.984090i −0.0660478 + 0.0660478i
\(223\) 13.3101 + 13.3101i 0.891312 + 0.891312i 0.994647 0.103335i \(-0.0329513\pi\)
−0.103335 + 0.994647i \(0.532951\pi\)
\(224\) 1.27865 0.0854332
\(225\) −2.29524 4.44206i −0.153016 0.296137i
\(226\) 2.82348 0.187815
\(227\) −21.0661 + 21.0661i −1.39820 + 1.39820i −0.593005 + 0.805199i \(0.702058\pi\)
−0.805199 + 0.593005i \(0.797942\pi\)
\(228\) −3.99597 + 1.74133i −0.264640 + 0.115322i
\(229\) 18.2167i 1.20379i −0.798574 0.601897i \(-0.794412\pi\)
0.798574 0.601897i \(-0.205588\pi\)
\(230\) −5.39990 + 1.31265i −0.356059 + 0.0865533i
\(231\) 3.40308i 0.223906i
\(232\) −1.53792 1.53792i −0.100969 0.100969i
\(233\) −20.6479 + 20.6479i −1.35269 + 1.35269i −0.470045 + 0.882642i \(0.655762\pi\)
−0.882642 + 0.470045i \(0.844238\pi\)
\(234\) 0.203169i 0.0132816i
\(235\) −5.34455 + 8.77741i −0.348640 + 0.572575i
\(236\) 2.19877i 0.143128i
\(237\) −2.98916 2.98916i −0.194167 0.194167i
\(238\) −4.21345 4.21345i −0.273118 0.273118i
\(239\) 1.78480i 0.115449i −0.998333 0.0577247i \(-0.981615\pi\)
0.998333 0.0577247i \(-0.0183846\pi\)
\(240\) 1.16292 1.90987i 0.0750660 0.123282i
\(241\) 6.17706i 0.397899i 0.980010 + 0.198950i \(0.0637530\pi\)
−0.980010 + 0.198950i \(0.936247\pi\)
\(242\) 2.76945 2.76945i 0.178027 0.178027i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 8.90579i 0.570135i
\(245\) 11.6572 2.83371i 0.744749 0.181039i
\(246\) 3.74005i 0.238457i
\(247\) 0.353785 + 0.811859i 0.0225108 + 0.0516574i
\(248\) −1.85380 + 1.85380i −0.117716 + 0.117716i
\(249\) 9.26984 0.587452
\(250\) 11.1529 + 0.782122i 0.705374 + 0.0494658i
\(251\) −3.89007 −0.245539 −0.122769 0.992435i \(-0.539178\pi\)
−0.122769 + 0.992435i \(0.539178\pi\)
\(252\) 0.904140 + 0.904140i 0.0569555 + 0.0569555i
\(253\) 4.67707 4.67707i 0.294045 0.294045i
\(254\) 17.7412i 1.11318i
\(255\) −10.1256 + 2.46140i −0.634090 + 0.154139i
\(256\) 1.00000 0.0625000
\(257\) −13.9017 + 13.9017i −0.867164 + 0.867164i −0.992158 0.124994i \(-0.960109\pi\)
0.124994 + 0.992158i \(0.460109\pi\)
\(258\) 2.01084 2.01084i 0.125189 0.125189i
\(259\) 1.77951 0.110573
\(260\) −0.388028 0.236270i −0.0240645 0.0146528i
\(261\) 2.17494i 0.134625i
\(262\) −14.5807 + 14.5807i −0.900797 + 0.900797i
\(263\) −12.6517 + 12.6517i −0.780135 + 0.780135i −0.979853 0.199718i \(-0.935997\pi\)
0.199718 + 0.979853i \(0.435997\pi\)
\(264\) 2.66147i 0.163802i
\(265\) −4.18055 + 6.86578i −0.256809 + 0.421761i
\(266\) 5.18732 + 2.03851i 0.318055 + 0.124989i
\(267\) −3.49780 3.49780i −0.214062 0.214062i
\(268\) −4.50928 4.50928i −0.275448 0.275448i
\(269\) −23.7972 −1.45094 −0.725470 0.688254i \(-0.758377\pi\)
−0.725470 + 0.688254i \(0.758377\pi\)
\(270\) 2.17279 0.528178i 0.132232 0.0321439i
\(271\) −13.5524 −0.823249 −0.411624 0.911354i \(-0.635038\pi\)
−0.411624 + 0.911354i \(0.635038\pi\)
\(272\) −3.29524 3.29524i −0.199803 0.199803i
\(273\) 0.183694 0.183694i 0.0111176 0.0111176i
\(274\) 3.45359 0.208639
\(275\) −11.8224 + 6.10871i −0.712917 + 0.368369i
\(276\) 2.48524i 0.149594i
\(277\) 11.8777 + 11.8777i 0.713662 + 0.713662i 0.967299 0.253637i \(-0.0816270\pi\)
−0.253637 + 0.967299i \(0.581627\pi\)
\(278\) 11.4548 + 11.4548i 0.687011 + 0.687011i
\(279\) −2.62167 −0.156955
\(280\) −2.77824 + 0.675353i −0.166031 + 0.0403601i
\(281\) 16.4158i 0.979285i −0.871923 0.489643i \(-0.837127\pi\)
0.871923 0.489643i \(-0.162873\pi\)
\(282\) −3.24973 3.24973i −0.193518 0.193518i
\(283\) 15.5488 15.5488i 0.924283 0.924283i −0.0730457 0.997329i \(-0.523272\pi\)
0.997329 + 0.0730457i \(0.0232719\pi\)
\(284\) −2.55729 −0.151748
\(285\) 7.76268 5.89413i 0.459822 0.349138i
\(286\) 0.540729 0.0319740
\(287\) −3.38153 + 3.38153i −0.199605 + 0.199605i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 4.71725i 0.277485i
\(290\) 4.15387 + 2.52928i 0.243923 + 0.148524i
\(291\) 16.7558 0.982242
\(292\) 5.25513 + 5.25513i 0.307533 + 0.307533i
\(293\) 19.2031 + 19.2031i 1.12186 + 1.12186i 0.991462 + 0.130398i \(0.0416254\pi\)
0.130398 + 0.991462i \(0.458375\pi\)
\(294\) 5.36506i 0.312897i
\(295\) −1.16134 4.77748i −0.0676161 0.278156i
\(296\) 1.39171 0.0808917
\(297\) −1.88194 + 1.88194i −0.109201 + 0.109201i
\(298\) −2.01710 2.01710i −0.116847 0.116847i
\(299\) −0.504924 −0.0292005
\(300\) −1.51803 + 4.76399i −0.0876433 + 0.275049i
\(301\) −3.63616 −0.209585
\(302\) −13.1625 13.1625i −0.757417 0.757417i
\(303\) 2.57871 + 2.57871i 0.148143 + 0.148143i
\(304\) 4.05688 + 1.59427i 0.232678 + 0.0914378i
\(305\) −4.70384 19.3504i −0.269341 1.10800i
\(306\) 4.66018i 0.266405i
\(307\) 15.2483 15.2483i 0.870269 0.870269i −0.122233 0.992501i \(-0.539005\pi\)
0.992501 + 0.122233i \(0.0390054\pi\)
\(308\) 2.40634 2.40634i 0.137114 0.137114i
\(309\) 6.04115i 0.343669i
\(310\) 3.04878 5.00705i 0.173159 0.284381i
\(311\) 0.213974 0.0121334 0.00606668 0.999982i \(-0.498069\pi\)
0.00606668 + 0.999982i \(0.498069\pi\)
\(312\) 0.143663 0.143663i 0.00813329 0.00813329i
\(313\) −18.2399 + 18.2399i −1.03098 + 1.03098i −0.0314771 + 0.999504i \(0.510021\pi\)
−0.999504 + 0.0314771i \(0.989979\pi\)
\(314\) 14.2403 0.803627
\(315\) −2.44206 1.48696i −0.137594 0.0837808i
\(316\) 4.22731i 0.237805i
\(317\) −12.5740 + 12.5740i −0.706226 + 0.706226i −0.965740 0.259513i \(-0.916438\pi\)
0.259513 + 0.965740i \(0.416438\pi\)
\(318\) −2.54197 2.54197i −0.142546 0.142546i
\(319\) −5.78853 −0.324096
\(320\) −2.17279 + 0.528178i −0.121463 + 0.0295260i
\(321\) 13.2817 0.741310
\(322\) −2.24700 + 2.24700i −0.125220 + 0.125220i
\(323\) −8.11490 18.6219i −0.451525 1.03615i
\(324\) 1.00000i 0.0555556i
\(325\) 0.967897 + 0.308417i 0.0536893 + 0.0171079i
\(326\) 23.4081i 1.29645i
\(327\) 8.50324 + 8.50324i 0.470230 + 0.470230i
\(328\) −2.64461 + 2.64461i −0.146024 + 0.146024i
\(329\) 5.87641i 0.323977i
\(330\) −1.40573 5.78282i −0.0773828 0.318334i
\(331\) 12.5316i 0.688802i 0.938823 + 0.344401i \(0.111918\pi\)
−0.938823 + 0.344401i \(0.888082\pi\)
\(332\) −6.55477 6.55477i −0.359740 0.359740i
\(333\) 0.984090 + 0.984090i 0.0539278 + 0.0539278i
\(334\) 9.97075i 0.545575i
\(335\) 12.1794 + 7.41603i 0.665434 + 0.405181i
\(336\) 1.27865i 0.0697559i
\(337\) −10.1843 + 10.1843i −0.554774 + 0.554774i −0.927815 0.373041i \(-0.878315\pi\)
0.373041 + 0.927815i \(0.378315\pi\)
\(338\) 9.16320 + 9.16320i 0.498412 + 0.498412i
\(339\) 2.82348i 0.153351i
\(340\) 8.90035 + 5.41940i 0.482689 + 0.293908i
\(341\) 6.97748i 0.377851i
\(342\) 1.74133 + 3.99597i 0.0941603 + 0.216077i
\(343\) 11.1797 11.1797i 0.603650 0.603650i
\(344\) −2.84376 −0.153325
\(345\) 1.31265 + 5.39990i 0.0706705 + 0.290721i
\(346\) −20.8873 −1.12291
\(347\) 3.39715 + 3.39715i 0.182369 + 0.182369i 0.792387 0.610019i \(-0.208838\pi\)
−0.610019 + 0.792387i \(0.708838\pi\)
\(348\) −1.53792 + 1.53792i −0.0824409 + 0.0824409i
\(349\) 18.4982i 0.990188i 0.868840 + 0.495094i \(0.164866\pi\)
−0.868840 + 0.495094i \(0.835134\pi\)
\(350\) 5.67982 2.93481i 0.303599 0.156872i
\(351\) 0.203169 0.0108444
\(352\) 1.88194 1.88194i 0.100308 0.100308i
\(353\) −2.03694 + 2.03694i −0.108415 + 0.108415i −0.759234 0.650818i \(-0.774426\pi\)
0.650818 + 0.759234i \(0.274426\pi\)
\(354\) 2.19877 0.116864
\(355\) 5.55647 1.35071i 0.294907 0.0716881i
\(356\) 4.94664i 0.262171i
\(357\) −4.21345 + 4.21345i −0.223000 + 0.223000i
\(358\) −4.58765 + 4.58765i −0.242465 + 0.242465i
\(359\) 20.9321i 1.10475i −0.833595 0.552376i \(-0.813721\pi\)
0.833595 0.552376i \(-0.186279\pi\)
\(360\) −1.90987 1.16292i −0.100659 0.0612912i
\(361\) 13.9166 + 12.9355i 0.732452 + 0.680818i
\(362\) −0.0866707 0.0866707i −0.00455531 0.00455531i
\(363\) −2.76945 2.76945i −0.145358 0.145358i
\(364\) −0.259782 −0.0136163
\(365\) −14.1939 8.64266i −0.742945 0.452378i
\(366\) 8.90579 0.465513
\(367\) 20.7061 + 20.7061i 1.08085 + 1.08085i 0.996430 + 0.0844175i \(0.0269029\pi\)
0.0844175 + 0.996430i \(0.473097\pi\)
\(368\) −1.75733 + 1.75733i −0.0916070 + 0.0916070i
\(369\) −3.74005 −0.194699
\(370\) −3.02390 + 0.735072i −0.157205 + 0.0382146i
\(371\) 4.59659i 0.238643i
\(372\) 1.85380 + 1.85380i 0.0961149 + 0.0961149i
\(373\) −7.00175 7.00175i −0.362537 0.362537i 0.502209 0.864746i \(-0.332521\pi\)
−0.864746 + 0.502209i \(0.832521\pi\)
\(374\) −12.4029 −0.641339
\(375\) 0.782122 11.1529i 0.0403886 0.575936i
\(376\) 4.59581i 0.237011i
\(377\) 0.312458 + 0.312458i 0.0160924 + 0.0160924i
\(378\) 0.904140 0.904140i 0.0465040 0.0465040i
\(379\) −8.60331 −0.441922 −0.220961 0.975283i \(-0.570919\pi\)
−0.220961 + 0.975283i \(0.570919\pi\)
\(380\) −9.65682 1.32127i −0.495385 0.0677795i
\(381\) 17.7412 0.908908
\(382\) 0.335096 0.335096i 0.0171450 0.0171450i
\(383\) −1.41335 1.41335i −0.0722188 0.0722188i 0.670075 0.742294i \(-0.266262\pi\)
−0.742294 + 0.670075i \(0.766262\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −3.95750 + 6.49945i −0.201693 + 0.331243i
\(386\) 11.8392 0.602600
\(387\) −2.01084 2.01084i −0.102217 0.102217i
\(388\) −11.8481 11.8481i −0.601498 0.601498i
\(389\) 14.9165i 0.756295i 0.925745 + 0.378148i \(0.123439\pi\)
−0.925745 + 0.378148i \(0.876561\pi\)
\(390\) −0.236270 + 0.388028i −0.0119640 + 0.0196486i
\(391\) 11.5816 0.585708
\(392\) 3.79367 3.79367i 0.191609 0.191609i
\(393\) 14.5807 + 14.5807i 0.735498 + 0.735498i
\(394\) 13.3684 0.673491
\(395\) −2.23277 9.18507i −0.112343 0.462151i
\(396\) 2.66147 0.133744
\(397\) −20.0161 20.0161i −1.00458 1.00458i −0.999989 0.00459066i \(-0.998539\pi\)
−0.00459066 0.999989i \(-0.501461\pi\)
\(398\) −2.24527 2.24527i −0.112545 0.112545i
\(399\) 2.03851 5.18732i 0.102053 0.259691i
\(400\) 4.44206 2.29524i 0.222103 0.114762i
\(401\) 9.55630i 0.477219i −0.971116 0.238609i \(-0.923308\pi\)
0.971116 0.238609i \(-0.0766916\pi\)
\(402\) −4.50928 + 4.50928i −0.224903 + 0.224903i
\(403\) 0.376635 0.376635i 0.0187615 0.0187615i
\(404\) 3.64684i 0.181437i
\(405\) −0.528178 2.17279i −0.0262454 0.107967i
\(406\) 2.78098 0.138018
\(407\) 2.61912 2.61912i 0.129825 0.129825i
\(408\) −3.29524 + 3.29524i −0.163139 + 0.163139i
\(409\) −37.3114 −1.84493 −0.922466 0.386079i \(-0.873829\pi\)
−0.922466 + 0.386079i \(0.873829\pi\)
\(410\) 4.34937 7.14303i 0.214800 0.352769i
\(411\) 3.45359i 0.170353i
\(412\) 4.27174 4.27174i 0.210454 0.210454i
\(413\) −1.98800 1.98800i −0.0978231 0.0978231i
\(414\) −2.48524 −0.122143
\(415\) 17.7042 + 10.7801i 0.869067 + 0.529173i
\(416\) −0.203169 −0.00996120
\(417\) 11.4548 11.4548i 0.560942 0.560942i
\(418\) 10.6351 4.63449i 0.520182 0.226680i
\(419\) 33.2272i 1.62326i −0.584175 0.811628i \(-0.698582\pi\)
0.584175 0.811628i \(-0.301418\pi\)
\(420\) 0.675353 + 2.77824i 0.0329539 + 0.135564i
\(421\) 38.3380i 1.86848i −0.356646 0.934240i \(-0.616080\pi\)
0.356646 0.934240i \(-0.383920\pi\)
\(422\) 10.2214 + 10.2214i 0.497571 + 0.497571i
\(423\) −3.24973 + 3.24973i −0.158007 + 0.158007i
\(424\) 3.59488i 0.174583i
\(425\) −22.2010 7.07427i −1.07691 0.343153i
\(426\) 2.55729i 0.123901i
\(427\) −8.05208 8.05208i −0.389668 0.389668i
\(428\) −9.39155 9.39155i −0.453958 0.453958i
\(429\) 0.540729i 0.0261066i
\(430\) 6.17889 1.50201i 0.297973 0.0724333i
\(431\) 21.2257i 1.02241i −0.859460 0.511203i \(-0.829200\pi\)
0.859460 0.511203i \(-0.170800\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −10.9862 10.9862i −0.527961 0.527961i 0.392003 0.919964i \(-0.371782\pi\)
−0.919964 + 0.392003i \(0.871782\pi\)
\(434\) 3.35219i 0.160910i
\(435\) 2.52928 4.15387i 0.121270 0.199163i
\(436\) 12.0254i 0.575912i
\(437\) −9.93092 + 4.32761i −0.475061 + 0.207018i
\(438\) 5.25513 5.25513i 0.251100 0.251100i
\(439\) −1.43541 −0.0685084 −0.0342542 0.999413i \(-0.510906\pi\)
−0.0342542 + 0.999413i \(0.510906\pi\)
\(440\) −3.09507 + 5.08307i −0.147552 + 0.242326i
\(441\) 5.36506 0.255479
\(442\) 0.669493 + 0.669493i 0.0318445 + 0.0318445i
\(443\) 9.49661 9.49661i 0.451198 0.451198i −0.444554 0.895752i \(-0.646638\pi\)
0.895752 + 0.444554i \(0.146638\pi\)
\(444\) 1.39171i 0.0660478i
\(445\) −2.61271 10.7480i −0.123854 0.509505i
\(446\) −18.8234 −0.891312
\(447\) −2.01710 + 2.01710i −0.0954056 + 0.0954056i
\(448\) −0.904140 + 0.904140i −0.0427166 + 0.0427166i
\(449\) 17.7665 0.838454 0.419227 0.907881i \(-0.362301\pi\)
0.419227 + 0.907881i \(0.362301\pi\)
\(450\) 4.76399 + 1.51803i 0.224577 + 0.0715605i
\(451\) 9.95402i 0.468716i
\(452\) −1.99650 + 1.99650i −0.0939076 + 0.0939076i
\(453\) −13.1625 + 13.1625i −0.618428 + 0.618428i
\(454\) 29.7919i 1.39820i
\(455\) 0.564453 0.137211i 0.0264620 0.00643256i
\(456\) 1.59427 4.05688i 0.0746586 0.189981i
\(457\) 6.74008 + 6.74008i 0.315288 + 0.315288i 0.846954 0.531666i \(-0.178434\pi\)
−0.531666 + 0.846954i \(0.678434\pi\)
\(458\) 12.8812 + 12.8812i 0.601897 + 0.601897i
\(459\) −4.66018 −0.217518
\(460\) 2.89013 4.74649i 0.134753 0.221306i
\(461\) −4.22763 −0.196900 −0.0984501 0.995142i \(-0.531388\pi\)
−0.0984501 + 0.995142i \(0.531388\pi\)
\(462\) −2.40634 2.40634i −0.111953 0.111953i
\(463\) 12.2736 12.2736i 0.570403 0.570403i −0.361838 0.932241i \(-0.617851\pi\)
0.932241 + 0.361838i \(0.117851\pi\)
\(464\) 2.17494 0.100969
\(465\) −5.00705 3.04878i −0.232196 0.141384i
\(466\) 29.2005i 1.35269i
\(467\) 9.12358 + 9.12358i 0.422189 + 0.422189i 0.885957 0.463768i \(-0.153503\pi\)
−0.463768 + 0.885957i \(0.653503\pi\)
\(468\) −0.143663 0.143663i −0.00664080 0.00664080i
\(469\) 8.15405 0.376519
\(470\) −2.42740 9.98573i −0.111968 0.460608i
\(471\) 14.2403i 0.656159i
\(472\) −1.55477 1.55477i −0.0715640 0.0715640i
\(473\) −5.35178 + 5.35178i −0.246075 + 0.246075i
\(474\) 4.22731 0.194167
\(475\) 21.6801 2.22968i 0.994753 0.102305i
\(476\) 5.95872 0.273118
\(477\) −2.54197 + 2.54197i −0.116389 + 0.116389i
\(478\) 1.26205 + 1.26205i 0.0577247 + 0.0577247i
\(479\) 36.9313i 1.68744i 0.536787 + 0.843718i \(0.319638\pi\)
−0.536787 + 0.843718i \(0.680362\pi\)
\(480\) 0.528178 + 2.17279i 0.0241079 + 0.0991740i
\(481\) −0.282754 −0.0128925
\(482\) −4.36784 4.36784i −0.198950 0.198950i
\(483\) 2.24700 + 2.24700i 0.102242 + 0.102242i
\(484\) 3.91659i 0.178027i
\(485\) 32.0015 + 19.4856i 1.45311 + 0.884797i
\(486\) 1.00000 0.0453609
\(487\) 10.3862 10.3862i 0.470642 0.470642i −0.431481 0.902122i \(-0.642009\pi\)
0.902122 + 0.431481i \(0.142009\pi\)
\(488\) −6.29734 6.29734i −0.285067 0.285067i
\(489\) 23.4081 1.05855
\(490\) −6.23913 + 10.2466i −0.281855 + 0.462894i
\(491\) −31.2661 −1.41102 −0.705509 0.708701i \(-0.749281\pi\)
−0.705509 + 0.708701i \(0.749281\pi\)
\(492\) 2.64461 + 2.64461i 0.119228 + 0.119228i
\(493\) −7.16696 7.16696i −0.322784 0.322784i
\(494\) −0.824235 0.323907i −0.0370841 0.0145733i
\(495\) −5.78282 + 1.40573i −0.259918 + 0.0631828i
\(496\) 2.62167i 0.117716i
\(497\) 2.31215 2.31215i 0.103714 0.103714i
\(498\) −6.55477 + 6.55477i −0.293726 + 0.293726i
\(499\) 31.8064i 1.42385i −0.702256 0.711925i \(-0.747824\pi\)
0.702256 0.711925i \(-0.252176\pi\)
\(500\) −8.43937 + 7.33328i −0.377420 + 0.327954i
\(501\) 9.97075 0.445460
\(502\) 2.75069 2.75069i 0.122769 0.122769i
\(503\) −30.1365 + 30.1365i −1.34372 + 1.34372i −0.451396 + 0.892324i \(0.649074\pi\)
−0.892324 + 0.451396i \(0.850926\pi\)
\(504\) −1.27865 −0.0569555
\(505\) 1.92618 + 7.92383i 0.0857139 + 0.352606i
\(506\) 6.61437i 0.294045i
\(507\) 9.16320 9.16320i 0.406952 0.406952i
\(508\) −12.5449 12.5449i −0.556590 0.556590i
\(509\) 39.4733 1.74962 0.874811 0.484463i \(-0.160985\pi\)
0.874811 + 0.484463i \(0.160985\pi\)
\(510\) 5.41940 8.90035i 0.239975 0.394114i
\(511\) −9.50274 −0.420377
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 3.99597 1.74133i 0.176426 0.0768815i
\(514\) 19.6600i 0.867164i
\(515\) −7.02537 + 11.5378i −0.309575 + 0.508418i
\(516\) 2.84376i 0.125189i
\(517\) 8.64904 + 8.64904i 0.380384 + 0.380384i
\(518\) −1.25830 + 1.25830i −0.0552867 + 0.0552867i
\(519\) 20.8873i 0.916853i
\(520\) 0.441445 0.107310i 0.0193587 0.00470584i
\(521\) 43.0892i 1.88777i −0.330271 0.943886i \(-0.607140\pi\)
0.330271 0.943886i \(-0.392860\pi\)
\(522\) 1.53792 + 1.53792i 0.0673127 + 0.0673127i
\(523\) 12.0200 + 12.0200i 0.525600 + 0.525600i 0.919257 0.393658i \(-0.128790\pi\)
−0.393658 + 0.919257i \(0.628790\pi\)
\(524\) 20.6202i 0.900797i
\(525\) −2.93481 5.67982i −0.128085 0.247888i
\(526\) 17.8922i 0.780135i
\(527\) −8.63902 + 8.63902i −0.376322 + 0.376322i
\(528\) −1.88194 1.88194i −0.0819010 0.0819010i
\(529\) 16.8236i 0.731461i
\(530\) −1.89874 7.81093i −0.0824759 0.339285i
\(531\) 2.19877i 0.0954187i
\(532\) −5.10944 + 2.22655i −0.221522 + 0.0965330i
\(533\) 0.537305 0.537305i 0.0232733 0.0232733i
\(534\) 4.94664 0.214062
\(535\) 25.3663 + 15.4455i 1.09668 + 0.667766i
\(536\) 6.37709 0.275448
\(537\) 4.58765 + 4.58765i 0.197972 + 0.197972i
\(538\) 16.8271 16.8271i 0.725470 0.725470i
\(539\) 14.2789i 0.615037i
\(540\) −1.16292 + 1.90987i −0.0500440 + 0.0821879i
\(541\) −8.87532 −0.381580 −0.190790 0.981631i \(-0.561105\pi\)
−0.190790 + 0.981631i \(0.561105\pi\)
\(542\) 9.58298 9.58298i 0.411624 0.411624i
\(543\) −0.0866707 + 0.0866707i −0.00371940 + 0.00371940i
\(544\) 4.66018 0.199803
\(545\) 6.35155 + 26.1287i 0.272070 + 1.11923i
\(546\) 0.259782i 0.0111176i
\(547\) −13.9130 + 13.9130i −0.594877 + 0.594877i −0.938945 0.344068i \(-0.888195\pi\)
0.344068 + 0.938945i \(0.388195\pi\)
\(548\) −2.44206 + 2.44206i −0.104319 + 0.104319i
\(549\) 8.90579i 0.380090i
\(550\) 4.04018 12.6792i 0.172274 0.540643i
\(551\) 8.82348 + 3.46745i 0.375893 + 0.147718i
\(552\) 1.75733 + 1.75733i 0.0747968 + 0.0747968i
\(553\) −3.82208 3.82208i −0.162531 0.162531i
\(554\) −16.7976 −0.713662
\(555\) 0.735072 + 3.02390i 0.0312021 + 0.128358i
\(556\) −16.1995 −0.687011
\(557\) 14.7010 + 14.7010i 0.622900 + 0.622900i 0.946272 0.323372i \(-0.104816\pi\)
−0.323372 + 0.946272i \(0.604816\pi\)
\(558\) 1.85380 1.85380i 0.0784775 0.0784775i
\(559\) 0.577764 0.0244368
\(560\) 1.48696 2.44206i 0.0628356 0.103196i
\(561\) 12.4029i 0.523651i
\(562\) 11.6077 + 11.6077i 0.489643 + 0.489643i
\(563\) −9.68060 9.68060i −0.407989 0.407989i 0.473048 0.881037i \(-0.343154\pi\)
−0.881037 + 0.473048i \(0.843154\pi\)
\(564\) 4.59581 0.193518
\(565\) 3.28348 5.39250i 0.138137 0.226864i
\(566\) 21.9894i 0.924283i
\(567\) −0.904140 0.904140i −0.0379703 0.0379703i
\(568\) 1.80828 1.80828i 0.0758738 0.0758738i
\(569\) 36.5026 1.53027 0.765133 0.643872i \(-0.222673\pi\)
0.765133 + 0.643872i \(0.222673\pi\)
\(570\) −1.32127 + 9.65682i −0.0553417 + 0.404480i
\(571\) −18.0651 −0.756000 −0.378000 0.925806i \(-0.623388\pi\)
−0.378000 + 0.925806i \(0.623388\pi\)
\(572\) −0.382353 + 0.382353i −0.0159870 + 0.0159870i
\(573\) −0.335096 0.335096i −0.0139988 0.0139988i
\(574\) 4.78220i 0.199605i
\(575\) −3.77265 + 11.8396i −0.157330 + 0.493747i
\(576\) −1.00000 −0.0416667
\(577\) 13.7843 + 13.7843i 0.573847 + 0.573847i 0.933201 0.359354i \(-0.117003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(578\) −3.33560 3.33560i −0.138743 0.138743i
\(579\) 11.8392i 0.492021i
\(580\) −4.72570 + 1.14876i −0.196224 + 0.0476995i
\(581\) 11.8529 0.491739
\(582\) −11.8481 + 11.8481i −0.491121 + 0.491121i
\(583\) 6.76536 + 6.76536i 0.280192 + 0.280192i
\(584\) −7.43187 −0.307533
\(585\) 0.388028 + 0.236270i 0.0160430 + 0.00976854i
\(586\) −27.1573 −1.12186
\(587\) −12.9491 12.9491i −0.534466 0.534466i 0.387432 0.921898i \(-0.373362\pi\)
−0.921898 + 0.387432i \(0.873362\pi\)
\(588\) −3.79367 3.79367i −0.156448 0.156448i
\(589\) 4.17965 10.6358i 0.172219 0.438240i
\(590\) 4.19938 + 2.55699i 0.172886 + 0.105270i
\(591\) 13.3684i 0.549903i
\(592\) −0.984090 + 0.984090i −0.0404458 + 0.0404458i
\(593\) 1.56552 1.56552i 0.0642881 0.0642881i −0.674232 0.738520i \(-0.735525\pi\)
0.738520 + 0.674232i \(0.235525\pi\)
\(594\) 2.66147i 0.109201i
\(595\) −12.9471 + 3.14727i −0.530778 + 0.129025i
\(596\) 2.85261 0.116847
\(597\) −2.24527 + 2.24527i −0.0918929 + 0.0918929i
\(598\) 0.357035 0.357035i 0.0146003 0.0146003i
\(599\) 31.2077 1.27511 0.637556 0.770404i \(-0.279946\pi\)
0.637556 + 0.770404i \(0.279946\pi\)
\(600\) −2.29524 4.44206i −0.0937029 0.181346i
\(601\) 27.0296i 1.10256i 0.834320 + 0.551281i \(0.185861\pi\)
−0.834320 + 0.551281i \(0.814139\pi\)
\(602\) 2.57115 2.57115i 0.104792 0.104792i
\(603\) 4.50928 + 4.50928i 0.183632 + 0.183632i
\(604\) 18.6146 0.757417
\(605\) −2.06866 8.50995i −0.0841029 0.345979i
\(606\) −3.64684 −0.148143
\(607\) −10.1961 + 10.1961i −0.413847 + 0.413847i −0.883076 0.469229i \(-0.844532\pi\)
0.469229 + 0.883076i \(0.344532\pi\)
\(608\) −3.99597 + 1.74133i −0.162058 + 0.0706202i
\(609\) 2.78098i 0.112691i
\(610\) 17.0089 + 10.3567i 0.688672 + 0.419331i
\(611\) 0.933728i 0.0377746i
\(612\) 3.29524 + 3.29524i 0.133202 + 0.133202i
\(613\) −22.4225 + 22.4225i −0.905634 + 0.905634i −0.995916 0.0902818i \(-0.971223\pi\)
0.0902818 + 0.995916i \(0.471223\pi\)
\(614\) 21.5644i 0.870269i
\(615\) −7.14303 4.34937i −0.288035 0.175384i
\(616\) 3.40308i 0.137114i
\(617\) −1.22259 1.22259i −0.0492195 0.0492195i 0.682069 0.731288i \(-0.261081\pi\)
−0.731288 + 0.682069i \(0.761081\pi\)
\(618\) −4.27174 4.27174i −0.171835 0.171835i
\(619\) 26.1462i 1.05090i −0.850823 0.525452i \(-0.823896\pi\)
0.850823 0.525452i \(-0.176104\pi\)
\(620\) 1.38471 + 5.69634i 0.0556111 + 0.228770i
\(621\) 2.48524i 0.0997291i
\(622\) −0.151302 + 0.151302i −0.00606668 + 0.00606668i
\(623\) −4.47245 4.47245i −0.179185 0.179185i
\(624\) 0.203169i 0.00813329i
\(625\) 14.4637 20.3912i 0.578549 0.815648i
\(626\) 25.7952i 1.03098i
\(627\) −4.63449 10.6351i −0.185084 0.424727i
\(628\) −10.0694 + 10.0694i −0.401814 + 0.401814i
\(629\) 6.48563 0.258599
\(630\) 2.77824 0.675353i 0.110688 0.0269067i
\(631\) −33.3652 −1.32825 −0.664124 0.747623i \(-0.731195\pi\)
−0.664124 + 0.747623i \(0.731195\pi\)
\(632\) −2.98916 2.98916i −0.118902 0.118902i
\(633\) 10.2214 10.2214i 0.406265 0.406265i
\(634\) 17.7823i 0.706226i
\(635\) 33.8834 + 20.6315i 1.34462 + 0.818737i
\(636\) 3.59488 0.142546
\(637\) −0.770758 + 0.770758i −0.0305386 + 0.0305386i
\(638\) 4.09311 4.09311i 0.162048 0.162048i
\(639\) 2.55729 0.101165
\(640\) 1.16292 1.90987i 0.0459684 0.0754944i
\(641\) 31.2439i 1.23406i −0.786940 0.617029i \(-0.788336\pi\)
0.786940 0.617029i \(-0.211664\pi\)
\(642\) −9.39155 + 9.39155i −0.370655 + 0.370655i
\(643\) −3.28874 + 3.28874i −0.129695 + 0.129695i −0.768975 0.639279i \(-0.779233\pi\)
0.639279 + 0.768975i \(0.279233\pi\)
\(644\) 3.17774i 0.125220i
\(645\) −1.50201 6.17889i −0.0591416 0.243294i
\(646\) 18.9058 + 7.42959i 0.743838 + 0.292313i
\(647\) 24.2688 + 24.2688i 0.954105 + 0.954105i 0.998992 0.0448869i \(-0.0142928\pi\)
−0.0448869 + 0.998992i \(0.514293\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −5.85196 −0.229710
\(650\) −0.902490 + 0.466323i −0.0353986 + 0.0182907i
\(651\) −3.35219 −0.131382
\(652\) −16.5520 16.5520i −0.648227 0.648227i
\(653\) 0.820035 0.820035i 0.0320904 0.0320904i −0.690879 0.722970i \(-0.742776\pi\)
0.722970 + 0.690879i \(0.242776\pi\)
\(654\) −12.0254 −0.470230
\(655\) 10.8911 + 44.8034i 0.425552 + 1.75061i
\(656\) 3.74005i 0.146024i
\(657\) −5.25513 5.25513i −0.205022 0.205022i
\(658\) −4.15525 4.15525i −0.161989 0.161989i
\(659\) −42.2189 −1.64461 −0.822307 0.569044i \(-0.807313\pi\)
−0.822307 + 0.569044i \(0.807313\pi\)
\(660\) 5.08307 + 3.09507i 0.197858 + 0.120475i
\(661\) 26.8163i 1.04303i −0.853241 0.521517i \(-0.825366\pi\)
0.853241 0.521517i \(-0.174634\pi\)
\(662\) −8.86121 8.86121i −0.344401 0.344401i
\(663\) 0.669493 0.669493i 0.0260009 0.0260009i
\(664\) 9.26984 0.359740
\(665\) 9.92573 7.53651i 0.384903 0.292253i
\(666\) −1.39171 −0.0539278
\(667\) −3.82208 + 3.82208i −0.147992 + 0.147992i
\(668\) −7.05038 7.05038i −0.272788 0.272788i
\(669\) 18.8234i 0.727753i
\(670\) −13.8561 + 3.36824i −0.535307 + 0.130126i
\(671\) −23.7025 −0.915023
\(672\) 0.904140 + 0.904140i 0.0348780 + 0.0348780i
\(673\) −23.1618 23.1618i −0.892824 0.892824i 0.101964 0.994788i \(-0.467487\pi\)
−0.994788 + 0.101964i \(0.967487\pi\)
\(674\) 14.4028i 0.554774i
\(675\) 1.51803 4.76399i 0.0584289 0.183366i
\(676\) −12.9587 −0.498412
\(677\) −18.0408 + 18.0408i −0.693364 + 0.693364i −0.962971 0.269606i \(-0.913106\pi\)
0.269606 + 0.962971i \(0.413106\pi\)
\(678\) 1.99650 + 1.99650i 0.0766753 + 0.0766753i
\(679\) 21.4248 0.822207
\(680\) −10.1256 + 2.46140i −0.388299 + 0.0943905i
\(681\) −29.7919 −1.14163
\(682\) −4.93382 4.93382i −0.188926 0.188926i
\(683\) −20.2075 20.2075i −0.773220 0.773220i 0.205448 0.978668i \(-0.434135\pi\)
−0.978668 + 0.205448i \(0.934135\pi\)
\(684\) −4.05688 1.59427i −0.155119 0.0609585i
\(685\) 4.01624 6.59592i 0.153453 0.252017i
\(686\) 15.8106i 0.603650i
\(687\) 12.8812 12.8812i 0.491447 0.491447i
\(688\) 2.01084 2.01084i 0.0766625 0.0766625i
\(689\) 0.730371i 0.0278249i
\(690\) −4.74649 2.89013i −0.180696 0.110025i
\(691\) −5.06618 −0.192727 −0.0963633 0.995346i \(-0.530721\pi\)
−0.0963633 + 0.995346i \(0.530721\pi\)
\(692\) 14.7696 14.7696i 0.561455 0.561455i
\(693\) −2.40634 + 2.40634i −0.0914093 + 0.0914093i
\(694\) −4.80430 −0.182369
\(695\) 35.1981 8.55620i 1.33514 0.324555i
\(696\) 2.17494i 0.0824409i
\(697\) −12.3244 + 12.3244i −0.466819 + 0.466819i
\(698\) −13.0802 13.0802i −0.495094 0.495094i
\(699\) −29.2005 −1.10446
\(700\) −1.94102 + 6.09146i −0.0733637 + 0.230236i
\(701\) 31.7812 1.20036 0.600180 0.799865i \(-0.295096\pi\)
0.600180 + 0.799865i \(0.295096\pi\)
\(702\) −0.143663 + 0.143663i −0.00542219 + 0.00542219i
\(703\) −5.56124 + 2.42343i −0.209746 + 0.0914014i
\(704\) 2.66147i 0.100308i
\(705\) −9.98573 + 2.42740i −0.376084 + 0.0914213i
\(706\) 2.88067i 0.108415i
\(707\) 3.29726 + 3.29726i 0.124006 + 0.124006i
\(708\) −1.55477 + 1.55477i −0.0584318 + 0.0584318i
\(709\) 40.1995i 1.50972i 0.655884 + 0.754861i \(0.272296\pi\)
−0.655884 + 0.754861i \(0.727704\pi\)
\(710\) −2.97392 + 4.88411i −0.111609 + 0.183297i
\(711\) 4.22731i 0.158537i
\(712\) −3.49780 3.49780i −0.131086 0.131086i
\(713\) 4.60712 + 4.60712i 0.172538 + 0.172538i
\(714\) 5.95872i 0.223000i
\(715\) 0.628823 1.03272i 0.0235167 0.0386217i
\(716\) 6.48791i 0.242465i
\(717\) 1.26205 1.26205i 0.0471320 0.0471320i
\(718\) 14.8012 + 14.8012i 0.552376 + 0.552376i
\(719\) 9.60719i 0.358288i 0.983823 + 0.179144i \(0.0573328\pi\)
−0.983823 + 0.179144i \(0.942667\pi\)
\(720\) 2.17279 0.528178i 0.0809752 0.0196840i
\(721\) 7.72450i 0.287676i
\(722\) −18.9873 + 0.693705i −0.706635 + 0.0258170i
\(723\) −4.36784 + 4.36784i −0.162442 + 0.162442i
\(724\) 0.122571 0.00455531
\(725\) 9.66121 4.99202i 0.358808 0.185399i
\(726\) 3.91659 0.145358
\(727\) 7.58566 + 7.58566i 0.281337 + 0.281337i 0.833642 0.552305i \(-0.186252\pi\)
−0.552305 + 0.833642i \(0.686252\pi\)
\(728\) 0.183694 0.183694i 0.00680814 0.00680814i
\(729\) 1.00000i 0.0370370i
\(730\) 16.1479 3.92535i 0.597661 0.145284i
\(731\) −13.2524 −0.490158
\(732\) −6.29734 + 6.29734i −0.232757 + 0.232757i
\(733\) 16.6371 16.6371i 0.614504 0.614504i −0.329612 0.944116i \(-0.606918\pi\)
0.944116 + 0.329612i \(0.106918\pi\)
\(734\) −29.2828 −1.08085
\(735\) 10.2466 + 6.23913i 0.377951 + 0.230134i
\(736\) 2.48524i 0.0916070i
\(737\) 12.0013 12.0013i 0.442074 0.442074i
\(738\) 2.64461 2.64461i 0.0973496 0.0973496i
\(739\) 18.7582i 0.690030i −0.938597 0.345015i \(-0.887874\pi\)
0.938597 0.345015i \(-0.112126\pi\)
\(740\) 1.61845 2.65800i 0.0594954 0.0977099i
\(741\) −0.323907 + 0.824235i −0.0118990 + 0.0302790i
\(742\) −3.25028 3.25028i −0.119321 0.119321i
\(743\) −18.3052 18.3052i −0.671553 0.671553i 0.286521 0.958074i \(-0.407501\pi\)
−0.958074 + 0.286521i \(0.907501\pi\)
\(744\) −2.62167 −0.0961149
\(745\) −6.19813 + 1.50669i −0.227082 + 0.0552007i
\(746\) 9.90197 0.362537
\(747\) 6.55477 + 6.55477i 0.239826 + 0.239826i
\(748\) 8.77018 8.77018i 0.320669 0.320669i
\(749\) 16.9826 0.620529
\(750\) 7.33328 + 8.43937i 0.267774 + 0.308162i
\(751\) 32.7384i 1.19464i 0.802002 + 0.597321i \(0.203768\pi\)
−0.802002 + 0.597321i \(0.796232\pi\)
\(752\) −3.24973 3.24973i −0.118505 0.118505i
\(753\) −2.75069 2.75069i −0.100241 0.100241i
\(754\) −0.441882 −0.0160924
\(755\) −40.4456 + 9.83182i −1.47197 + 0.357816i
\(756\) 1.27865i 0.0465040i
\(757\) 18.8701 + 18.8701i 0.685844 + 0.685844i 0.961311 0.275466i \(-0.0888322\pi\)
−0.275466 + 0.961311i \(0.588832\pi\)
\(758\) 6.08346 6.08346i 0.220961 0.220961i
\(759\) 6.61437 0.240086
\(760\) 7.76268 5.89413i 0.281582 0.213803i
\(761\) 6.60459 0.239416 0.119708 0.992809i \(-0.461804\pi\)
0.119708 + 0.992809i \(0.461804\pi\)
\(762\) −12.5449 + 12.5449i −0.454454 + 0.454454i
\(763\) 10.8726 + 10.8726i 0.393616 + 0.393616i
\(764\) 0.473897i 0.0171450i
\(765\) −8.90035 5.41940i −0.321793 0.195939i
\(766\) 1.99878 0.0722188
\(767\) 0.315881 + 0.315881i 0.0114058 + 0.0114058i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 5.37624i 0.193872i −0.995291 0.0969360i \(-0.969096\pi\)
0.995291 0.0969360i \(-0.0309042\pi\)
\(770\) −1.79743 7.39418i −0.0647749 0.266468i
\(771\) −19.6600 −0.708036
\(772\) −8.37158 + 8.37158i −0.301300 + 0.301300i
\(773\) −1.67948 1.67948i −0.0604066 0.0604066i 0.676258 0.736665i \(-0.263600\pi\)
−0.736665 + 0.676258i \(0.763600\pi\)
\(774\) 2.84376 0.102217
\(775\) −6.01736 11.6456i −0.216150 0.418322i
\(776\) 16.7558 0.601498
\(777\) 1.25830 + 1.25830i 0.0451414 + 0.0451414i
\(778\) −10.5475 10.5475i −0.378148 0.378148i