Properties

Label 570.2.m.b.37.8
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 37.8
Root \(1.20277 - 1.20277i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.b.493.8

$q$-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} +(1.74133 - 3.99597i) 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} +(-3.99597 - 1.74133i) 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} +(5.60678 + 7.97271i) 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 0.726748 0.686904i \(-0.241031\pi\)
−0.686904 + 0.726748i \(0.741031\pi\)
\(14\) 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 \(-0.435276\pi\)
0.201938 + 0.979398i \(0.435276\pi\)
\(30\) −0.528178 2.17279i −0.0964317 0.396696i
\(31\) 2.62167i 0.470865i −0.971891 0.235432i \(-0.924349\pi\)
0.971891 0.235432i \(-0.0756507\pi\)
\(32\) −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 −0.783356 0.621573i \(-0.786494\pi\)
0.621573 + 0.783356i \(0.286494\pi\)
\(38\) 1.74133 3.99597i 0.282481 0.648232i
\(39\) 0.203169i 0.0325332i
\(40\) 1.16292 1.90987i 0.183874 0.301978i
\(41\) 3.74005i 0.584098i −0.956403 0.292049i \(-0.905663\pi\)
0.956403 0.292049i \(-0.0943370\pi\)
\(42\) −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 0.510633 0.859799i \(-0.329411\pi\)
−0.859799 + 0.510633i \(0.829411\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 1.40573 + 5.78282i 0.189548 + 0.779755i
\(56\) 1.27865i 0.170866i
\(57\) −3.99597 1.74133i −0.529279 0.230645i
\(58\) 1.53792 1.53792i 0.201938 0.201938i
\(59\) 2.19877 0.286256 0.143128 0.989704i \(-0.454284\pi\)
0.143128 + 0.989704i \(0.454284\pi\)
\(60\) −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 −0.926700 0.375803i \(-0.877367\pi\)
0.375803 + 0.926700i \(0.377367\pi\)
\(68\) 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 \(0.0484901\pi\)
−0.988419 + 0.151748i \(0.951510\pi\)
\(72\) 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 \(-0.423572\pi\)
0.237805 + 0.971313i \(0.423572\pi\)
\(80\) −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 \(-0.415561\pi\)
0.262171 + 0.965021i \(0.415561\pi\)
\(90\) −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
\(95\) 5.60678 + 7.97271i 0.575243 + 0.817982i
\(96\) 1.00000 0.102062
\(97\) −11.8481 + 11.8481i −1.20300 + 1.20300i −0.229746 + 0.973251i \(0.573789\pi\)
−0.973251 + 0.229746i \(0.926211\pi\)
\(98\) −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 0.464609 0.885516i \(-0.346195\pi\)
−0.885516 + 0.464609i \(0.846195\pi\)
\(104\) 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 −0.996104 0.0881885i \(-0.971892\pi\)
0.0881885 + 0.996104i \(0.471892\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −12.0254 −1.15182 −0.575912 0.817512i \(-0.695353\pi\)
−0.575912 + 0.817512i \(0.695353\pi\)
\(110\) 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 0.794751 0.606936i \(-0.207601\pi\)
−0.606936 + 0.794751i \(0.707601\pi\)
\(114\) −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 \(0.538438\pi\)
−0.992718 + 0.120462i \(0.961562\pi\)
\(128\) 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
\(133\) 5.10944 + 2.22655i 0.443044 + 0.193066i
\(134\) 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 \(-0.726461\pi\)
0.652932 0.757417i \(-0.273539\pi\)
\(152\) −3.99597 1.74133i −0.324116 0.141240i
\(153\) −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 −0.925158 0.379583i \(-0.876068\pi\)
0.379583 + 0.925158i \(0.376068\pi\)
\(168\) −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 \(-0.957986\pi\)
−0.131609 0.991302i \(-0.542014\pi\)
\(174\) −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 \(-0.577956\pi\)
−0.242465 + 0.970160i \(0.577956\pi\)
\(180\) 0.528178 + 2.17279i 0.0393681 + 0.161950i
\(181\) 0.122571i 0.00911063i −0.999990 0.00455531i \(-0.998550\pi\)
0.999990 0.00455531i \(-0.00145001\pi\)
\(182\) 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
\(190\) 9.60215 + 1.67296i 0.696613 + 0.121370i
\(191\) −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 0.941002 0.338402i \(-0.109886\pi\)
−0.338402 + 0.941002i \(0.609886\pi\)
\(194\) 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 \(0.165775\pi\)
−0.867423 + 0.497571i \(0.834225\pi\)
\(212\) −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 0.103335 0.994647i \(-0.467049\pi\)
−0.994647 + 0.103335i \(0.967049\pi\)
\(224\) −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 \(-0.297942\pi\)
0.805199 0.593005i \(-0.202058\pi\)
\(228\) −1.74133 + 3.99597i −0.115322 + 0.264640i
\(229\) 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 \(-0.936247\pi\)
0.980010 0.198950i \(-0.0637530\pi\)
\(242\) −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
\(247\) 0.811859 + 0.353785i 0.0516574 + 0.0225108i
\(248\) −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 −0.124994 0.992158i \(-0.539891\pi\)
0.992158 + 0.124994i \(0.0398911\pi\)
\(258\) 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 \(-0.241623\pi\)
0.725470 + 0.688254i \(0.241623\pi\)
\(270\) 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 \(0.162873\pi\)
−0.871923 + 0.489643i \(0.837127\pi\)
\(282\) −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
\(285\) 1.67296 9.60215i 0.0990978 0.568782i
\(286\) 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 \(-0.958375\pi\)
−0.130398 0.991462i \(-0.541625\pi\)
\(294\) 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 −0.992501 0.122233i \(-0.960995\pi\)
0.122233 + 0.992501i \(0.460995\pi\)
\(308\) 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 −0.259513 0.965740i \(-0.583562\pi\)
0.965740 + 0.259513i \(0.0835621\pi\)
\(318\) 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
\(323\) 18.6219 + 8.11490i 1.03615 + 0.451525i
\(324\) 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 \(-0.888082\pi\)
0.938823 0.344401i \(-0.111918\pi\)
\(332\) −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 −0.373041 0.927815i \(-0.621685\pi\)
0.927815 + 0.373041i \(0.121685\pi\)
\(338\) −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
\(342\) 3.99597 + 1.74133i 0.216077 + 0.0941603i
\(343\) 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 0.864746 0.502209i \(-0.167479\pi\)
−0.502209 + 0.864746i \(0.667479\pi\)
\(374\) 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 \(-0.429081\pi\)
0.220961 + 0.975283i \(0.429081\pi\)
\(380\) 7.97271 5.60678i 0.408991 0.287622i
\(381\) 17.7412 0.908908
\(382\) −0.335096 + 0.335096i −0.0171450 + 0.0171450i
\(383\) 1.41335 + 1.41335i 0.0722188 + 0.0722188i 0.742294 0.670075i \(-0.233738\pi\)
−0.670075 + 0.742294i \(0.733738\pi\)
\(384\) 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 \(0.0766916\pi\)
−0.971116 + 0.238609i \(0.923308\pi\)
\(402\) 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 \(-0.126171\pi\)
0.922466 + 0.386079i \(0.126171\pi\)
\(410\) 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
\(418\) 4.63449 10.6351i 0.226680 0.520182i
\(419\) 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 \(0.383920\pi\)
−0.356646 + 0.934240i \(0.616080\pi\)
\(422\) 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 \(0.170800\pi\)
−0.859460 + 0.511203i \(0.829200\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 10.9862 + 10.9862i 0.527961 + 0.527961i 0.919964 0.392003i \(-0.128218\pi\)
−0.392003 + 0.919964i \(0.628218\pi\)
\(434\) 3.35219i 0.160910i
\(435\) 2.52928 4.15387i 0.121270 0.199163i
\(436\) 12.0254i 0.575912i
\(437\) 4.32761 9.93092i 0.207018 0.475061i
\(438\) 5.25513 5.25513i 0.251100 0.251100i
\(439\) 1.43541 0.0685084 0.0342542 0.999413i \(-0.489094\pi\)
0.0342542 + 0.999413i \(0.489094\pi\)
\(440\) 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 \(-0.637699\pi\)
−0.419227 + 0.907881i \(0.637699\pi\)
\(450\) −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
\(475\) −14.3617 + 16.3934i −0.658958 + 0.752180i
\(476\) 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 −0.902122 0.431481i \(-0.857991\pi\)
0.431481 + 0.902122i \(0.357991\pi\)
\(488\) 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 \(-0.839015\pi\)
−0.874811 + 0.484463i \(0.839015\pi\)
\(510\) 5.41940 8.90035i 0.239975 0.394114i
\(511\) −9.50274 −0.420377
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 1.74133 3.99597i 0.0768815 0.176426i
\(514\) 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 \(0.392860\pi\)
−0.330271 + 0.943886i \(0.607140\pi\)
\(522\) 1.53792 + 1.53792i 0.0673127 + 0.0673127i
\(523\) −12.0200 12.0200i −0.525600 0.525600i 0.393658 0.919257i \(-0.371210\pi\)
−0.919257 + 0.393658i \(0.871210\pi\)
\(524\) 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
\(532\) 2.22655 5.10944i 0.0965330 0.221522i
\(533\) 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 −0.344068 0.938945i \(-0.611805\pi\)
0.938945 + 0.344068i \(0.111805\pi\)
\(548\) −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 0.881037 0.473048i \(-0.156846\pi\)
−0.473048 + 0.881037i \(0.656846\pi\)
\(564\) −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 \(-0.777327\pi\)
−0.765133 + 0.643872i \(0.777327\pi\)
\(570\) −5.60678 7.97271i −0.234842 0.333940i
\(571\) −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 \(-0.720054\pi\)
−0.637556 + 0.770404i \(0.720054\pi\)
\(600\) −2.29524 4.44206i −0.0937029 0.181346i
\(601\) 27.0296i 1.10256i −0.834320 0.551281i \(-0.814139\pi\)
0.834320 0.551281i \(-0.185861\pi\)
\(602\) −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 −0.469229 0.883076i \(-0.655468\pi\)
0.883076 + 0.469229i \(0.155468\pi\)
\(608\) −1.74133 + 3.99597i −0.0706202 + 0.162058i
\(609\) 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
\(627\) −10.6351 4.63449i −0.424727 0.185084i
\(628\) −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 \(0.211664\pi\)
−0.786940 + 0.617029i \(0.788336\pi\)
\(642\) 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 \(-0.192687\pi\)
0.822307 + 0.569044i \(0.192687\pi\)
\(660\) −5.08307 3.09507i −0.197858 0.120475i
\(661\) 26.8163i 1.04303i 0.853241 + 0.521517i \(0.174634\pi\)
−0.853241 + 0.521517i \(0.825366\pi\)
\(662\) −8.86121 8.86121i −0.344401 0.344401i
\(663\) 0.669493 0.669493i 0.0260009 0.0260009i
\(664\) −9.26984 −0.359740
\(665\) −2.13913 + 12.2778i −0.0829519 + 0.476111i
\(666\) −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 0.994788 0.101964i \(-0.0325128\pi\)
−0.101964 + 0.994788i \(0.532513\pi\)
\(674\) 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 −0.269606 0.962971i \(-0.586894\pi\)
0.962971 + 0.269606i \(0.0868935\pi\)
\(678\) −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 0.978668 0.205448i \(-0.0658651\pi\)
−0.205448 + 0.978668i \(0.565865\pi\)
\(684\) 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
\(703\) −2.42343 + 5.56124i −0.0914014 + 0.209746i
\(704\) 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
\(722\) 0.693705 18.9873i 0.0258170 0.706635i
\(723\) −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 0.958074 0.286521i \(-0.0924989\pi\)
−0.286521 + 0.958074i \(0.592499\pi\)
\(744\) 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 \(-0.796232\pi\)
0.802002 0.597321i \(-0.203768\pi\)
\(752\) −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
\(760\) 1.67296 9.60215i 0.0606848 0.348306i
\(761\) 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 0.736665 0.676258i \(-0.236400\pi\)
−0.676258 + 0.736665i \(0.736400\pi\)
\(774\) −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