Properties

Label 210.3.l.b.43.6
Level 210
Weight 3
Character 210.43
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.6
Root \(5.71348 - 5.71348i\) of \(x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + 86081152 x^{5} + 178889856 x^{4} + 70149120 x^{3} + 10035200 x^{2} - 7168000 x + 2560000\)
Character \(\chi\) \(=\) 210.43
Dual form 210.3.l.b.127.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-2.20256 - 4.48873i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-2.20256 - 4.48873i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.69129 + 2.28617i) q^{10} +15.1276 q^{11} +(2.44949 - 2.44949i) q^{12} +(14.6465 + 14.6465i) q^{13} -3.74166i q^{14} +(2.79998 - 8.19513i) q^{15} -4.00000 q^{16} +(15.9948 - 15.9948i) q^{17} +(-3.00000 - 3.00000i) q^{18} -2.05015i q^{19} +(-8.97747 + 4.40512i) q^{20} -4.58258 q^{21} +(-15.1276 + 15.1276i) q^{22} +(19.4933 + 19.4933i) q^{23} +4.89898i q^{24} +(-15.2975 + 19.7734i) q^{25} -29.2929 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} -33.1037i q^{29} +(5.39515 + 10.9951i) q^{30} +27.8179 q^{31} +(4.00000 - 4.00000i) q^{32} +(18.5275 + 18.5275i) q^{33} +31.9896i q^{34} +(12.5183 + 4.27704i) q^{35} +6.00000 q^{36} +(-30.4627 + 30.4627i) q^{37} +(2.05015 + 2.05015i) q^{38} +35.8763i q^{39} +(4.57235 - 13.3826i) q^{40} -26.6233 q^{41} +(4.58258 - 4.58258i) q^{42} +(7.89901 + 7.89901i) q^{43} -30.2553i q^{44} +(13.4662 - 6.60768i) q^{45} -38.9867 q^{46} +(33.8904 - 33.8904i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +(-4.47595 - 35.0709i) q^{50} +39.1791 q^{51} +(29.2929 - 29.2929i) q^{52} +(5.60358 + 5.60358i) q^{53} -7.34847i q^{54} +(-33.3195 - 67.9040i) q^{55} -7.48331 q^{56} +(2.51091 - 2.51091i) q^{57} +(33.1037 + 33.1037i) q^{58} -5.80696i q^{59} +(-16.3903 - 5.59996i) q^{60} -98.2160 q^{61} +(-27.8179 + 27.8179i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +(33.4843 - 98.0037i) q^{65} -37.0550 q^{66} +(51.6510 - 51.6510i) q^{67} +(-31.9896 - 31.9896i) q^{68} +47.7487i q^{69} +(-16.7953 + 8.24122i) q^{70} -120.447 q^{71} +(-6.00000 + 6.00000i) q^{72} +(81.9558 + 81.9558i) q^{73} -60.9253i q^{74} +(-42.9529 + 5.48190i) q^{75} -4.10030 q^{76} +(-28.3012 + 28.3012i) q^{77} +(-35.8763 - 35.8763i) q^{78} -33.0831i q^{79} +(8.81024 + 17.9549i) q^{80} -9.00000 q^{81} +(26.6233 - 26.6233i) q^{82} +(-97.0860 - 97.0860i) q^{83} +9.16515i q^{84} +(-107.026 - 36.5669i) q^{85} -15.7980 q^{86} +(40.5435 - 40.5435i) q^{87} +(30.2553 + 30.2553i) q^{88} +34.2132i q^{89} +(-6.85852 + 20.0739i) q^{90} -54.8020 q^{91} +(38.9867 - 38.9867i) q^{92} +(34.0699 + 34.0699i) q^{93} +67.7807i q^{94} +(-9.20257 + 4.51558i) q^{95} +9.79796 q^{96} +(104.393 - 104.393i) q^{97} +(7.00000 + 7.00000i) q^{98} +45.3829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + O(q^{10}) \) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + 24q^{10} + 8q^{11} - 32q^{13} - 12q^{15} - 64q^{16} + 56q^{17} - 48q^{18} - 16q^{20} - 8q^{22} + 24q^{23} + 40q^{25} + 64q^{26} - 112q^{31} + 64q^{32} + 24q^{33} + 28q^{35} + 96q^{36} - 152q^{37} - 16q^{40} + 24q^{45} - 48q^{46} + 80q^{47} - 72q^{50} - 72q^{51} - 64q^{52} + 48q^{53} - 24q^{55} + 24q^{57} + 96q^{58} + 24q^{60} + 96q^{61} + 112q^{62} + 16q^{65} - 48q^{66} - 80q^{67} - 112q^{68} + 536q^{71} - 96q^{72} - 288q^{75} - 168q^{77} - 48q^{78} + 64q^{80} - 144q^{81} - 256q^{83} + 40q^{85} - 144q^{87} + 16q^{88} + 24q^{90} + 48q^{92} + 192q^{93} + 360q^{95} + 688q^{97} + 112q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.500000 + 0.500000i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −2.20256 4.48873i −0.440512 0.897747i
\(6\) −2.44949 −0.408248
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.69129 + 2.28617i 0.669129 + 0.228617i
\(11\) 15.1276 1.37524 0.687620 0.726071i \(-0.258655\pi\)
0.687620 + 0.726071i \(0.258655\pi\)
\(12\) 2.44949 2.44949i 0.204124 0.204124i
\(13\) 14.6465 + 14.6465i 1.12665 + 1.12665i 0.990718 + 0.135932i \(0.0434028\pi\)
0.135932 + 0.990718i \(0.456597\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 2.79998 8.19513i 0.186665 0.546342i
\(16\) −4.00000 −0.250000
\(17\) 15.9948 15.9948i 0.940872 0.940872i −0.0574751 0.998347i \(-0.518305\pi\)
0.998347 + 0.0574751i \(0.0183050\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 2.05015i 0.107903i −0.998544 0.0539513i \(-0.982818\pi\)
0.998544 0.0539513i \(-0.0171816\pi\)
\(20\) −8.97747 + 4.40512i −0.448873 + 0.220256i
\(21\) −4.58258 −0.218218
\(22\) −15.1276 + 15.1276i −0.687620 + 0.687620i
\(23\) 19.4933 + 19.4933i 0.847536 + 0.847536i 0.989825 0.142289i \(-0.0454462\pi\)
−0.142289 + 0.989825i \(0.545446\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −15.2975 + 19.7734i −0.611898 + 0.790936i
\(26\) −29.2929 −1.12665
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 3.74166 + 3.74166i 0.133631 + 0.133631i
\(29\) 33.1037i 1.14151i −0.821122 0.570753i \(-0.806651\pi\)
0.821122 0.570753i \(-0.193349\pi\)
\(30\) 5.39515 + 10.9951i 0.179838 + 0.366504i
\(31\) 27.8179 0.897352 0.448676 0.893694i \(-0.351896\pi\)
0.448676 + 0.893694i \(0.351896\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) 18.5275 + 18.5275i 0.561440 + 0.561440i
\(34\) 31.9896i 0.940872i
\(35\) 12.5183 + 4.27704i 0.357665 + 0.122201i
\(36\) 6.00000 0.166667
\(37\) −30.4627 + 30.4627i −0.823315 + 0.823315i −0.986582 0.163267i \(-0.947797\pi\)
0.163267 + 0.986582i \(0.447797\pi\)
\(38\) 2.05015 + 2.05015i 0.0539513 + 0.0539513i
\(39\) 35.8763i 0.919906i
\(40\) 4.57235 13.3826i 0.114309 0.334565i
\(41\) −26.6233 −0.649348 −0.324674 0.945826i \(-0.605255\pi\)
−0.324674 + 0.945826i \(0.605255\pi\)
\(42\) 4.58258 4.58258i 0.109109 0.109109i
\(43\) 7.89901 + 7.89901i 0.183698 + 0.183698i 0.792965 0.609267i \(-0.208536\pi\)
−0.609267 + 0.792965i \(0.708536\pi\)
\(44\) 30.2553i 0.687620i
\(45\) 13.4662 6.60768i 0.299249 0.146837i
\(46\) −38.9867 −0.847536
\(47\) 33.8904 33.8904i 0.721072 0.721072i −0.247752 0.968824i \(-0.579692\pi\)
0.968824 + 0.247752i \(0.0796918\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −4.47595 35.0709i −0.0895190 0.701417i
\(51\) 39.1791 0.768219
\(52\) 29.2929 29.2929i 0.563325 0.563325i
\(53\) 5.60358 + 5.60358i 0.105728 + 0.105728i 0.757992 0.652264i \(-0.226181\pi\)
−0.652264 + 0.757992i \(0.726181\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −33.3195 67.9040i −0.605810 1.23462i
\(56\) −7.48331 −0.133631
\(57\) 2.51091 2.51091i 0.0440511 0.0440511i
\(58\) 33.1037 + 33.1037i 0.570753 + 0.570753i
\(59\) 5.80696i 0.0984231i −0.998788 0.0492115i \(-0.984329\pi\)
0.998788 0.0492115i \(-0.0156709\pi\)
\(60\) −16.3903 5.59996i −0.273171 0.0933326i
\(61\) −98.2160 −1.61010 −0.805049 0.593208i \(-0.797861\pi\)
−0.805049 + 0.593208i \(0.797861\pi\)
\(62\) −27.8179 + 27.8179i −0.448676 + 0.448676i
\(63\) −5.61249 5.61249i −0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) 33.4843 98.0037i 0.515144 1.50775i
\(66\) −37.0550 −0.561440
\(67\) 51.6510 51.6510i 0.770910 0.770910i −0.207356 0.978266i \(-0.566486\pi\)
0.978266 + 0.207356i \(0.0664858\pi\)
\(68\) −31.9896 31.9896i −0.470436 0.470436i
\(69\) 47.7487i 0.692010i
\(70\) −16.7953 + 8.24122i −0.239933 + 0.117732i
\(71\) −120.447 −1.69643 −0.848216 0.529651i \(-0.822323\pi\)
−0.848216 + 0.529651i \(0.822323\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) 81.9558 + 81.9558i 1.12268 + 1.12268i 0.991337 + 0.131346i \(0.0419299\pi\)
0.131346 + 0.991337i \(0.458070\pi\)
\(74\) 60.9253i 0.823315i
\(75\) −42.9529 + 5.48190i −0.572705 + 0.0730920i
\(76\) −4.10030 −0.0539513
\(77\) −28.3012 + 28.3012i −0.367548 + 0.367548i
\(78\) −35.8763 35.8763i −0.459953 0.459953i
\(79\) 33.0831i 0.418774i −0.977833 0.209387i \(-0.932853\pi\)
0.977833 0.209387i \(-0.0671468\pi\)
\(80\) 8.81024 + 17.9549i 0.110128 + 0.224437i
\(81\) −9.00000 −0.111111
\(82\) 26.6233 26.6233i 0.324674 0.324674i
\(83\) −97.0860 97.0860i −1.16971 1.16971i −0.982277 0.187433i \(-0.939983\pi\)
−0.187433 0.982277i \(-0.560017\pi\)
\(84\) 9.16515i 0.109109i
\(85\) −107.026 36.5669i −1.25913 0.430199i
\(86\) −15.7980 −0.183698
\(87\) 40.5435 40.5435i 0.466018 0.466018i
\(88\) 30.2553 + 30.2553i 0.343810 + 0.343810i
\(89\) 34.2132i 0.384418i 0.981354 + 0.192209i \(0.0615652\pi\)
−0.981354 + 0.192209i \(0.938435\pi\)
\(90\) −6.85852 + 20.0739i −0.0762058 + 0.223043i
\(91\) −54.8020 −0.602220
\(92\) 38.9867 38.9867i 0.423768 0.423768i
\(93\) 34.0699 + 34.0699i 0.366343 + 0.366343i
\(94\) 67.7807i 0.721072i
\(95\) −9.20257 + 4.51558i −0.0968692 + 0.0475324i
\(96\) 9.79796 0.102062
\(97\) 104.393 104.393i 1.07622 1.07622i 0.0793705 0.996845i \(-0.474709\pi\)
0.996845 0.0793705i \(-0.0252910\pi\)
\(98\) 7.00000 + 7.00000i 0.0714286 + 0.0714286i
\(99\) 45.3829i 0.458413i
\(100\) 39.5468 + 30.5949i 0.395468 + 0.305949i
\(101\) 50.2854 0.497876 0.248938 0.968519i \(-0.419919\pi\)
0.248938 + 0.968519i \(0.419919\pi\)
\(102\) −39.1791 + 39.1791i −0.384109 + 0.384109i
\(103\) 7.11461 + 7.11461i 0.0690739 + 0.0690739i 0.740800 0.671726i \(-0.234447\pi\)
−0.671726 + 0.740800i \(0.734447\pi\)
\(104\) 58.5858i 0.563325i
\(105\) 10.0934 + 20.5700i 0.0961276 + 0.195904i
\(106\) −11.2072 −0.105728
\(107\) −4.56425 + 4.56425i −0.0426566 + 0.0426566i −0.728113 0.685457i \(-0.759603\pi\)
0.685457 + 0.728113i \(0.259603\pi\)
\(108\) 7.34847 + 7.34847i 0.0680414 + 0.0680414i
\(109\) 58.0783i 0.532829i 0.963859 + 0.266414i \(0.0858389\pi\)
−0.963859 + 0.266414i \(0.914161\pi\)
\(110\) 101.224 + 34.5844i 0.920214 + 0.314404i
\(111\) −74.6180 −0.672234
\(112\) 7.48331 7.48331i 0.0668153 0.0668153i
\(113\) 9.58688 + 9.58688i 0.0848396 + 0.0848396i 0.748253 0.663413i \(-0.230893\pi\)
−0.663413 + 0.748253i \(0.730893\pi\)
\(114\) 5.02182i 0.0440511i
\(115\) 44.5651 130.436i 0.387523 1.13422i
\(116\) −66.2073 −0.570753
\(117\) −43.9394 + 43.9394i −0.375550 + 0.375550i
\(118\) 5.80696 + 5.80696i 0.0492115 + 0.0492115i
\(119\) 59.8471i 0.502917i
\(120\) 21.9902 10.7903i 0.183252 0.0899191i
\(121\) 107.846 0.891286
\(122\) 98.2160 98.2160i 0.805049 0.805049i
\(123\) −32.6067 32.6067i −0.265095 0.265095i
\(124\) 55.6358i 0.448676i
\(125\) 122.451 + 25.1141i 0.979609 + 0.200913i
\(126\) 11.2250 0.0890871
\(127\) −140.998 + 140.998i −1.11022 + 1.11022i −0.117097 + 0.993120i \(0.537359\pi\)
−0.993120 + 0.117097i \(0.962641\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 19.3485i 0.149989i
\(130\) 64.5194 + 131.488i 0.496303 + 1.01145i
\(131\) 184.764 1.41041 0.705205 0.709004i \(-0.250855\pi\)
0.705205 + 0.709004i \(0.250855\pi\)
\(132\) 37.0550 37.0550i 0.280720 0.280720i
\(133\) 3.83548 + 3.83548i 0.0288382 + 0.0288382i
\(134\) 103.302i 0.770910i
\(135\) 24.5854 + 8.39994i 0.182114 + 0.0622218i
\(136\) 63.9793 0.470436
\(137\) −170.364 + 170.364i −1.24353 + 1.24353i −0.285002 + 0.958527i \(0.591994\pi\)
−0.958527 + 0.285002i \(0.908006\pi\)
\(138\) −47.7487 47.7487i −0.346005 0.346005i
\(139\) 110.608i 0.795741i −0.917442 0.397870i \(-0.869749\pi\)
0.917442 0.397870i \(-0.130251\pi\)
\(140\) 8.55408 25.0365i 0.0611006 0.178832i
\(141\) 83.0141 0.588753
\(142\) 120.447 120.447i 0.848216 0.848216i
\(143\) 221.566 + 221.566i 1.54941 + 1.54941i
\(144\) 12.0000i 0.0833333i
\(145\) −148.594 + 72.9128i −1.02478 + 0.502847i
\(146\) −163.912 −1.12268
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) 60.9253 + 60.9253i 0.411658 + 0.411658i
\(149\) 150.705i 1.01144i 0.862697 + 0.505721i \(0.168773\pi\)
−0.862697 + 0.505721i \(0.831227\pi\)
\(150\) 37.4710 48.4348i 0.249806 0.322898i
\(151\) −190.444 −1.26122 −0.630610 0.776100i \(-0.717195\pi\)
−0.630610 + 0.776100i \(0.717195\pi\)
\(152\) 4.10030 4.10030i 0.0269756 0.0269756i
\(153\) 47.9845 + 47.9845i 0.313624 + 0.313624i
\(154\) 56.6025i 0.367548i
\(155\) −61.2706 124.867i −0.395294 0.805595i
\(156\) 71.7527 0.459953
\(157\) −28.5711 + 28.5711i −0.181981 + 0.181981i −0.792219 0.610237i \(-0.791074\pi\)
0.610237 + 0.792219i \(0.291074\pi\)
\(158\) 33.0831 + 33.0831i 0.209387 + 0.209387i
\(159\) 13.7259i 0.0863265i
\(160\) −26.7652 9.14469i −0.167282 0.0571543i
\(161\) −72.9374 −0.453027
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) −37.2908 37.2908i −0.228778 0.228778i 0.583404 0.812182i \(-0.301720\pi\)
−0.812182 + 0.583404i \(0.801720\pi\)
\(164\) 53.2466i 0.324674i
\(165\) 42.3571 123.973i 0.256710 0.751351i
\(166\) 194.172 1.16971
\(167\) −70.7467 + 70.7467i −0.423633 + 0.423633i −0.886453 0.462820i \(-0.846838\pi\)
0.462820 + 0.886453i \(0.346838\pi\)
\(168\) −9.16515 9.16515i −0.0545545 0.0545545i
\(169\) 260.037i 1.53868i
\(170\) 143.593 70.4591i 0.844665 0.414465i
\(171\) 6.15045 0.0359675
\(172\) 15.7980 15.7980i 0.0918489 0.0918489i
\(173\) 73.9048 + 73.9048i 0.427196 + 0.427196i 0.887672 0.460476i \(-0.152321\pi\)
−0.460476 + 0.887672i \(0.652321\pi\)
\(174\) 81.0871i 0.466018i
\(175\) −8.37374 65.6116i −0.0478499 0.374923i
\(176\) −60.5106 −0.343810
\(177\) 7.11205 7.11205i 0.0401811 0.0401811i
\(178\) −34.2132 34.2132i −0.192209 0.192209i
\(179\) 280.292i 1.56588i −0.622100 0.782938i \(-0.713720\pi\)
0.622100 0.782938i \(-0.286280\pi\)
\(180\) −13.2154 26.9324i −0.0734187 0.149624i
\(181\) −139.086 −0.768430 −0.384215 0.923244i \(-0.625528\pi\)
−0.384215 + 0.923244i \(0.625528\pi\)
\(182\) 54.8020 54.8020i 0.301110 0.301110i
\(183\) −120.290 120.290i −0.657320 0.657320i
\(184\) 77.9733i 0.423768i
\(185\) 203.835 + 69.6430i 1.10181 + 0.376448i
\(186\) −68.1397 −0.366343
\(187\) 241.964 241.964i 1.29392 1.29392i
\(188\) −67.7807 67.7807i −0.360536 0.360536i
\(189\) 13.7477i 0.0727393i
\(190\) 4.68700 13.7182i 0.0246684 0.0722008i
\(191\) −231.713 −1.21316 −0.606580 0.795023i \(-0.707459\pi\)
−0.606580 + 0.795023i \(0.707459\pi\)
\(192\) −9.79796 + 9.79796i −0.0510310 + 0.0510310i
\(193\) −148.989 148.989i −0.771962 0.771962i 0.206488 0.978449i \(-0.433797\pi\)
−0.978449 + 0.206488i \(0.933797\pi\)
\(194\) 208.786i 1.07622i
\(195\) 161.039 79.0198i 0.825842 0.405230i
\(196\) −14.0000 −0.0714286
\(197\) −255.090 + 255.090i −1.29487 + 1.29487i −0.363135 + 0.931736i \(0.618294\pi\)
−0.931736 + 0.363135i \(0.881706\pi\)
\(198\) −45.3829 45.3829i −0.229207 0.229207i
\(199\) 321.154i 1.61384i −0.590660 0.806920i \(-0.701133\pi\)
0.590660 0.806920i \(-0.298867\pi\)
\(200\) −70.1417 + 8.95190i −0.350709 + 0.0447595i
\(201\) 126.518 0.629445
\(202\) −50.2854 + 50.2854i −0.248938 + 0.248938i
\(203\) 61.9313 + 61.9313i 0.305080 + 0.305080i
\(204\) 78.3583i 0.384109i
\(205\) 58.6394 + 119.505i 0.286046 + 0.582950i
\(206\) −14.2292 −0.0690739
\(207\) −58.4800 + 58.4800i −0.282512 + 0.282512i
\(208\) −58.5858 58.5858i −0.281663 0.281663i
\(209\) 31.0139i 0.148392i
\(210\) −30.6634 10.4766i −0.146016 0.0498884i
\(211\) 22.7166 0.107662 0.0538308 0.998550i \(-0.482857\pi\)
0.0538308 + 0.998550i \(0.482857\pi\)
\(212\) 11.2072 11.2072i 0.0528640 0.0528640i
\(213\) −147.516 147.516i −0.692565 0.692565i
\(214\) 9.12850i 0.0426566i
\(215\) 18.0585 52.8546i 0.0839931 0.245835i
\(216\) −14.6969 −0.0680414
\(217\) −52.0426 + 52.0426i −0.239828 + 0.239828i
\(218\) −58.0783 58.0783i −0.266414 0.266414i
\(219\) 200.750i 0.916667i
\(220\) −135.808 + 66.6391i −0.617309 + 0.302905i
\(221\) 468.535 2.12007
\(222\) 74.6180 74.6180i 0.336117 0.336117i
\(223\) 158.968 + 158.968i 0.712863 + 0.712863i 0.967133 0.254270i \(-0.0818353\pi\)
−0.254270 + 0.967133i \(0.581835\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −59.3202 45.8924i −0.263645 0.203966i
\(226\) −19.1738 −0.0848396
\(227\) −52.1650 + 52.1650i −0.229802 + 0.229802i −0.812610 0.582808i \(-0.801954\pi\)
0.582808 + 0.812610i \(0.301954\pi\)
\(228\) −5.02182 5.02182i −0.0220255 0.0220255i
\(229\) 115.486i 0.504305i −0.967688 0.252152i \(-0.918862\pi\)
0.967688 0.252152i \(-0.0811384\pi\)
\(230\) 85.8705 + 175.001i 0.373350 + 0.760873i
\(231\) −69.3236 −0.300102
\(232\) 66.2073 66.2073i 0.285376 0.285376i
\(233\) −297.575 297.575i −1.27714 1.27714i −0.942259 0.334885i \(-0.891302\pi\)
−0.334885 0.942259i \(-0.608698\pi\)
\(234\) 87.8787i 0.375550i
\(235\) −226.770 77.4793i −0.964980 0.329699i
\(236\) −11.6139 −0.0492115
\(237\) 40.5184 40.5184i 0.170964 0.170964i
\(238\) −59.8471 59.8471i −0.251459 0.251459i
\(239\) 136.556i 0.571362i −0.958325 0.285681i \(-0.907780\pi\)
0.958325 0.285681i \(-0.0922198\pi\)
\(240\) −11.1999 + 32.7805i −0.0466663 + 0.136585i
\(241\) 61.0110 0.253157 0.126579 0.991957i \(-0.459600\pi\)
0.126579 + 0.991957i \(0.459600\pi\)
\(242\) −107.846 + 107.846i −0.445643 + 0.445643i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 196.432i 0.805049i
\(245\) −31.4211 + 15.4179i −0.128250 + 0.0629303i
\(246\) 65.2134 0.265095
\(247\) 30.0274 30.0274i 0.121568 0.121568i
\(248\) 55.6358 + 55.6358i 0.224338 + 0.224338i
\(249\) 237.811i 0.955064i
\(250\) −147.565 + 97.3370i −0.590261 + 0.389348i
\(251\) 215.934 0.860295 0.430147 0.902759i \(-0.358462\pi\)
0.430147 + 0.902759i \(0.358462\pi\)
\(252\) −11.2250 + 11.2250i −0.0445435 + 0.0445435i
\(253\) 294.888 + 294.888i 1.16557 + 1.16557i
\(254\) 281.995i 1.11022i
\(255\) −86.2944 175.865i −0.338410 0.689666i
\(256\) 16.0000 0.0625000
\(257\) −144.579 + 144.579i −0.562564 + 0.562564i −0.930035 0.367471i \(-0.880224\pi\)
0.367471 + 0.930035i \(0.380224\pi\)
\(258\) −19.3485 19.3485i −0.0749944 0.0749944i
\(259\) 113.981i 0.440081i
\(260\) −196.007 66.9687i −0.753875 0.257572i
\(261\) 99.3110 0.380502
\(262\) −184.764 + 184.764i −0.705205 + 0.705205i
\(263\) −0.389678 0.389678i −0.00148167 0.00148167i 0.706366 0.707847i \(-0.250333\pi\)
−0.707847 + 0.706366i \(0.750333\pi\)
\(264\) 74.1100i 0.280720i
\(265\) 12.8108 37.4952i 0.0483425 0.141491i
\(266\) −7.67096 −0.0288382
\(267\) −41.9025 + 41.9025i −0.156938 + 0.156938i
\(268\) −103.302 103.302i −0.385455 0.385455i
\(269\) 272.956i 1.01471i −0.861738 0.507353i \(-0.830624\pi\)
0.861738 0.507353i \(-0.169376\pi\)
\(270\) −32.9853 + 16.1854i −0.122168 + 0.0599461i
\(271\) −176.708 −0.652058 −0.326029 0.945360i \(-0.605711\pi\)
−0.326029 + 0.945360i \(0.605711\pi\)
\(272\) −63.9793 + 63.9793i −0.235218 + 0.235218i
\(273\) −67.1185 67.1185i −0.245855 0.245855i
\(274\) 340.727i 1.24353i
\(275\) −231.415 + 299.125i −0.841507 + 1.08773i
\(276\) 95.4974 0.346005
\(277\) −203.152 + 203.152i −0.733402 + 0.733402i −0.971292 0.237890i \(-0.923544\pi\)
0.237890 + 0.971292i \(0.423544\pi\)
\(278\) 110.608 + 110.608i 0.397870 + 0.397870i
\(279\) 83.4538i 0.299117i
\(280\) 16.4824 + 33.5906i 0.0588659 + 0.119966i
\(281\) 368.543 1.31154 0.655770 0.754961i \(-0.272344\pi\)
0.655770 + 0.754961i \(0.272344\pi\)
\(282\) −83.0141 + 83.0141i −0.294376 + 0.294376i
\(283\) 385.601 + 385.601i 1.36255 + 1.36255i 0.870659 + 0.491888i \(0.163693\pi\)
0.491888 + 0.870659i \(0.336307\pi\)
\(284\) 240.893i 0.848216i
\(285\) −16.8012 5.74038i −0.0589517 0.0201417i
\(286\) −443.133 −1.54941
\(287\) 49.8076 49.8076i 0.173546 0.173546i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 222.669i 0.770480i
\(290\) 75.6807 221.506i 0.260968 0.763815i
\(291\) 255.709 0.878726
\(292\) 163.912 163.912i 0.561341 0.561341i
\(293\) −241.653 241.653i −0.824754 0.824754i 0.162032 0.986786i \(-0.448195\pi\)
−0.986786 + 0.162032i \(0.948195\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) −26.0659 + 12.7902i −0.0883590 + 0.0433566i
\(296\) −121.851 −0.411658
\(297\) −55.5825 + 55.5825i −0.187147 + 0.187147i
\(298\) −150.705 150.705i −0.505721 0.505721i
\(299\) 571.016i 1.90975i
\(300\) 10.9638 + 85.9057i 0.0365460 + 0.286352i
\(301\) −29.5554 −0.0981907
\(302\) 190.444 190.444i 0.630610 0.630610i
\(303\) 61.5868 + 61.5868i 0.203257 + 0.203257i
\(304\) 8.20060i 0.0269756i
\(305\) 216.327 + 440.865i 0.709268 + 1.44546i
\(306\) −95.9689 −0.313624
\(307\) 315.513 315.513i 1.02773 1.02773i 0.0281252 0.999604i \(-0.491046\pi\)
0.999604 0.0281252i \(-0.00895372\pi\)
\(308\) 56.6025 + 56.6025i 0.183774 + 0.183774i
\(309\) 17.4272i 0.0563986i
\(310\) 186.138 + 63.5966i 0.600445 + 0.205150i
\(311\) 84.6545 0.272201 0.136101 0.990695i \(-0.456543\pi\)
0.136101 + 0.990695i \(0.456543\pi\)
\(312\) −71.7527 + 71.7527i −0.229976 + 0.229976i
\(313\) −189.513 189.513i −0.605474 0.605474i 0.336286 0.941760i \(-0.390829\pi\)
−0.941760 + 0.336286i \(0.890829\pi\)
\(314\) 57.1422i 0.181981i
\(315\) −12.8311 + 37.5548i −0.0407337 + 0.119222i
\(316\) −66.1663 −0.209387
\(317\) −21.9357 + 21.9357i −0.0691977 + 0.0691977i −0.740859 0.671661i \(-0.765581\pi\)
0.671661 + 0.740859i \(0.265581\pi\)
\(318\) −13.7259 13.7259i −0.0431633 0.0431633i
\(319\) 500.780i 1.56984i
\(320\) 35.9099 17.6205i 0.112218 0.0550640i
\(321\) −11.1801 −0.0348289
\(322\) 72.9374 72.9374i 0.226514 0.226514i
\(323\) −32.7918 32.7918i −0.101523 0.101523i
\(324\) 18.0000i 0.0555556i
\(325\) −513.664 + 65.5568i −1.58050 + 0.201713i
\(326\) 74.5817 0.228778
\(327\) −71.1311 + 71.1311i −0.217526 + 0.217526i
\(328\) −53.2466 53.2466i −0.162337 0.162337i
\(329\) 126.806i 0.385429i
\(330\) 81.6159 + 166.330i 0.247321 + 0.504030i
\(331\) 165.937 0.501320 0.250660 0.968075i \(-0.419352\pi\)
0.250660 + 0.968075i \(0.419352\pi\)
\(332\) −194.172 + 194.172i −0.584855 + 0.584855i
\(333\) −91.3880 91.3880i −0.274438 0.274438i
\(334\) 141.493i 0.423633i
\(335\) −345.612 118.083i −1.03168 0.352487i
\(336\) 18.3303 0.0545545
\(337\) 73.8705 73.8705i 0.219200 0.219200i −0.588961 0.808161i \(-0.700463\pi\)
0.808161 + 0.588961i \(0.200463\pi\)
\(338\) −260.037 260.037i −0.769340 0.769340i
\(339\) 23.4830i 0.0692713i
\(340\) −73.1339 + 214.052i −0.215100 + 0.629565i
\(341\) 420.820 1.23408
\(342\) −6.15045 + 6.15045i −0.0179838 + 0.0179838i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 31.5960i 0.0918489i
\(345\) 214.331 105.169i 0.621250 0.304839i
\(346\) −147.810 −0.427196
\(347\) 31.2699 31.2699i 0.0901149 0.0901149i −0.660612 0.750727i \(-0.729703\pi\)
0.750727 + 0.660612i \(0.229703\pi\)
\(348\) −81.0871 81.0871i −0.233009 0.233009i
\(349\) 546.387i 1.56558i 0.622287 + 0.782789i \(0.286204\pi\)
−0.622287 + 0.782789i \(0.713796\pi\)
\(350\) 73.9853 + 57.2379i 0.211387 + 0.163537i
\(351\) −107.629 −0.306635
\(352\) 60.5106 60.5106i 0.171905 0.171905i
\(353\) −184.331 184.331i −0.522184 0.522184i 0.396046 0.918231i \(-0.370382\pi\)
−0.918231 + 0.396046i \(0.870382\pi\)
\(354\) 14.2241i 0.0401811i
\(355\) 265.291 + 540.653i 0.747298 + 1.52297i
\(356\) 68.4265 0.192209
\(357\) −73.2975 + 73.2975i −0.205315 + 0.205315i
\(358\) 280.292 + 280.292i 0.782938 + 0.782938i
\(359\) 319.232i 0.889226i −0.895723 0.444613i \(-0.853341\pi\)
0.895723 0.444613i \(-0.146659\pi\)
\(360\) 40.1478 + 13.7170i 0.111522 + 0.0381029i
\(361\) 356.797 0.988357
\(362\) 139.086 139.086i 0.384215 0.384215i
\(363\) 132.083 + 132.083i 0.363866 + 0.363866i
\(364\) 109.604i 0.301110i
\(365\) 187.365 548.391i 0.513330 1.50244i
\(366\) 240.579 0.657320
\(367\) 116.440 116.440i 0.317276 0.317276i −0.530444 0.847720i \(-0.677975\pi\)
0.847720 + 0.530444i \(0.177975\pi\)
\(368\) −77.9733 77.9733i −0.211884 0.211884i
\(369\) 79.8698i 0.216449i
\(370\) −273.478 + 134.192i −0.739129 + 0.362680i
\(371\) −20.9667 −0.0565140
\(372\) 68.1397 68.1397i 0.183171 0.183171i
\(373\) 380.962 + 380.962i 1.02135 + 1.02135i 0.999767 + 0.0215784i \(0.00686914\pi\)
0.0215784 + 0.999767i \(0.493131\pi\)
\(374\) 483.928i 1.29392i
\(375\) 119.213 + 180.730i 0.317901 + 0.481946i
\(376\) 135.561 0.360536
\(377\) 484.851 484.851i 1.28608 1.28608i
\(378\) 13.7477 + 13.7477i 0.0363696 + 0.0363696i
\(379\) 189.542i 0.500111i −0.968231 0.250056i \(-0.919551\pi\)
0.968231 0.250056i \(-0.0804489\pi\)
\(380\) 9.03115 + 18.4051i 0.0237662 + 0.0484346i
\(381\) −345.372 −0.906489
\(382\) 231.713 231.713i 0.606580 0.606580i
\(383\) −306.102 306.102i −0.799222 0.799222i 0.183751 0.982973i \(-0.441176\pi\)
−0.982973 + 0.183751i \(0.941176\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 189.372 + 64.7015i 0.491875 + 0.168056i
\(386\) 297.977 0.771962
\(387\) −23.6970 + 23.6970i −0.0612326 + 0.0612326i
\(388\) −208.786 208.786i −0.538108 0.538108i
\(389\) 316.187i 0.812819i −0.913691 0.406410i \(-0.866781\pi\)
0.913691 0.406410i \(-0.133219\pi\)
\(390\) −82.0195 + 240.059i −0.210306 + 0.615536i
\(391\) 623.585 1.59485
\(392\) 14.0000 14.0000i 0.0357143 0.0357143i
\(393\) 226.288 + 226.288i 0.575797 + 0.575797i
\(394\) 510.179i 1.29487i
\(395\) −148.501 + 72.8676i −0.375953 + 0.184475i
\(396\) 90.7659 0.229207
\(397\) −134.126 + 134.126i −0.337849 + 0.337849i −0.855557 0.517709i \(-0.826785\pi\)
0.517709 + 0.855557i \(0.326785\pi\)
\(398\) 321.154 + 321.154i 0.806920 + 0.806920i
\(399\) 9.39496i 0.0235463i
\(400\) 61.1898 79.0936i 0.152975 0.197734i
\(401\) −504.024 −1.25692 −0.628459 0.777842i \(-0.716314\pi\)
−0.628459 + 0.777842i \(0.716314\pi\)
\(402\) −126.518 + 126.518i −0.314723 + 0.314723i
\(403\) 407.434 + 407.434i 1.01100 + 1.01100i
\(404\) 100.571i 0.248938i
\(405\) 19.8230 + 40.3986i 0.0489458 + 0.0997496i
\(406\) −123.863 −0.305080
\(407\) −460.828 + 460.828i −1.13226 + 1.13226i
\(408\) 78.3583 + 78.3583i 0.192055 + 0.192055i
\(409\) 112.495i 0.275048i −0.990498 0.137524i \(-0.956086\pi\)
0.990498 0.137524i \(-0.0439145\pi\)
\(410\) −178.144 60.8654i −0.434498 0.148452i
\(411\) −417.304 −1.01534
\(412\) 14.2292 14.2292i 0.0345370 0.0345370i
\(413\) 10.8638 + 10.8638i 0.0263047 + 0.0263047i
\(414\) 116.960i 0.282512i
\(415\) −221.955 + 649.631i −0.534832 + 1.56538i
\(416\) 117.172 0.281663
\(417\) 135.466 135.466i 0.324860 0.324860i
\(418\) 31.0139 + 31.0139i 0.0741960 + 0.0741960i
\(419\) 224.563i 0.535950i −0.963426 0.267975i \(-0.913645\pi\)
0.963426 0.267975i \(-0.0863545\pi\)
\(420\) 41.1399 20.1868i 0.0979522 0.0480638i
\(421\) 474.635 1.12740 0.563699 0.825980i \(-0.309378\pi\)
0.563699 + 0.825980i \(0.309378\pi\)
\(422\) −22.7166 + 22.7166i −0.0538308 + 0.0538308i
\(423\) 101.671 + 101.671i 0.240357 + 0.240357i
\(424\) 22.4143i 0.0528640i
\(425\) 71.5920 + 560.952i 0.168452 + 1.31989i
\(426\) 295.033 0.692565
\(427\) 183.745 183.745i 0.430317 0.430317i
\(428\) 9.12850 + 9.12850i 0.0213283 + 0.0213283i
\(429\) 542.724i 1.26509i
\(430\) 34.7961 + 70.9131i 0.0809211 + 0.164914i
\(431\) 142.798 0.331317 0.165659 0.986183i \(-0.447025\pi\)
0.165659 + 0.986183i \(0.447025\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) −226.490 226.490i −0.523072 0.523072i 0.395426 0.918498i \(-0.370597\pi\)
−0.918498 + 0.395426i \(0.870597\pi\)
\(434\) 104.085i 0.239828i
\(435\) −271.289 92.6896i −0.623652 0.213079i
\(436\) 116.157 0.266414
\(437\) 39.9642 39.9642i 0.0914514 0.0914514i
\(438\) −200.750 200.750i −0.458333 0.458333i
\(439\) 231.354i 0.527003i −0.964659 0.263502i \(-0.915123\pi\)
0.964659 0.263502i \(-0.0848774\pi\)
\(440\) 69.1688 202.447i 0.157202 0.460107i
\(441\) 21.0000 0.0476190
\(442\) −468.535 + 468.535i −1.06003 + 1.06003i
\(443\) −291.498 291.498i −0.658008 0.658008i 0.296900 0.954909i \(-0.404047\pi\)
−0.954909 + 0.296900i \(0.904047\pi\)
\(444\) 149.236i 0.336117i
\(445\) 153.574 75.3567i 0.345110 0.169341i
\(446\) −317.937 −0.712863
\(447\) −184.575 + 184.575i −0.412919 + 0.412919i
\(448\) −14.9666 14.9666i −0.0334077 0.0334077i
\(449\) 186.920i 0.416303i −0.978097 0.208152i \(-0.933255\pi\)
0.978097 0.208152i \(-0.0667448\pi\)
\(450\) 105.213 13.4279i 0.233806 0.0298397i
\(451\) −402.747 −0.893010
\(452\) 19.1738 19.1738i 0.0424198 0.0424198i
\(453\) −233.245 233.245i −0.514891 0.514891i
\(454\) 104.330i 0.229802i
\(455\) 120.705 + 245.992i 0.265285 + 0.540641i
\(456\) 10.0436 0.0220255
\(457\) −358.683 + 358.683i −0.784865 + 0.784865i −0.980647 0.195782i \(-0.937275\pi\)
0.195782 + 0.980647i \(0.437275\pi\)
\(458\) 115.486 + 115.486i 0.252152 + 0.252152i
\(459\) 117.537i 0.256073i
\(460\) −260.871 89.1303i −0.567111 0.193761i
\(461\) −178.973 −0.388227 −0.194113 0.980979i \(-0.562183\pi\)
−0.194113 + 0.980979i \(0.562183\pi\)
\(462\) 69.3236 69.3236i 0.150051 0.150051i
\(463\) 244.313 + 244.313i 0.527675 + 0.527675i 0.919878 0.392204i \(-0.128287\pi\)
−0.392204 + 0.919878i \(0.628287\pi\)
\(464\) 132.415i 0.285376i
\(465\) 77.8896 227.971i 0.167505 0.490261i
\(466\) 595.149 1.27714
\(467\) 165.494 165.494i 0.354377 0.354377i −0.507358 0.861735i \(-0.669378\pi\)
0.861735 + 0.507358i \(0.169378\pi\)
\(468\) 87.8787 + 87.8787i 0.187775 + 0.187775i
\(469\) 193.260i 0.412069i
\(470\) 304.250 149.291i 0.647340 0.317641i
\(471\) −69.9846 −0.148587
\(472\) 11.6139 11.6139i 0.0246058 0.0246058i
\(473\) 119.493 + 119.493i 0.252629 + 0.252629i
\(474\) 81.0368i 0.170964i
\(475\) 40.5384 + 31.3621i 0.0853441 + 0.0660254i
\(476\) 119.694 0.251459
\(477\) −16.8107 + 16.8107i −0.0352427 + 0.0352427i
\(478\) 136.556 + 136.556i 0.285681 + 0.285681i
\(479\) 326.343i 0.681300i 0.940190 + 0.340650i \(0.110647\pi\)
−0.940190 + 0.340650i \(0.889353\pi\)
\(480\) −21.5806 43.9804i −0.0449596 0.0916259i
\(481\) −892.340 −1.85518
\(482\) −61.0110 + 61.0110i −0.126579 + 0.126579i
\(483\) −89.3297 89.3297i −0.184948 0.184948i
\(484\) 215.691i 0.445643i
\(485\) −698.524 238.660i −1.44026 0.492083i
\(486\) 22.0454 0.0453609
\(487\) −373.708 + 373.708i −0.767367 + 0.767367i −0.977642 0.210275i \(-0.932564\pi\)
0.210275 + 0.977642i \(0.432564\pi\)
\(488\) −196.432 196.432i −0.402525 0.402525i
\(489\) 91.3435i 0.186797i
\(490\) 16.0032 46.8391i 0.0326596 0.0955899i
\(491\) 418.263 0.851859 0.425930 0.904756i \(-0.359947\pi\)
0.425930 + 0.904756i \(0.359947\pi\)
\(492\) −65.2134 + 65.2134i −0.132548 + 0.132548i
\(493\) −529.487 529.487i −1.07401 1.07401i
\(494\) 60.0548i 0.121568i
\(495\) 203.712 99.9586i 0.411539 0.201937i
\(496\) −111.272 −0.224338
\(497\) 225.335 225.335i 0.453390 0.453390i
\(498\) 237.811 + 237.811i 0.477532 + 0.477532i
\(499\) 541.732i 1.08563i 0.839851 + 0.542817i \(0.182642\pi\)
−0.839851 + 0.542817i \(0.817358\pi\)
\(500\) 50.2282 244.902i 0.100456 0.489805i
\(501\) −173.293 −0.345895
\(502\) −215.934 + 215.934i −0.430147 + 0.430147i
\(503\) −419.289 419.289i −0.833578 0.833578i 0.154427 0.988004i \(-0.450647\pi\)
−0.988004 + 0.154427i \(0.950647\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −110.757 225.718i −0.219320 0.446966i
\(506\) −589.776 −1.16557
\(507\) −318.479 + 318.479i −0.628164 + 0.628164i
\(508\) 281.995 + 281.995i 0.555109 + 0.555109i
\(509\) 340.522i 0.669002i −0.942395 0.334501i \(-0.891432\pi\)
0.942395 0.334501i \(-0.108568\pi\)
\(510\) 262.159 + 89.5703i 0.514038 + 0.175628i
\(511\) −306.651 −0.600099
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) 7.53273 + 7.53273i 0.0146837 + 0.0146837i
\(514\) 289.158i 0.562564i
\(515\) 16.2652 47.6060i 0.0315830 0.0924388i
\(516\) 38.6971 0.0749944
\(517\) 512.681 512.681i 0.991647 0.991647i
\(518\) 113.981 + 113.981i 0.220040 + 0.220040i
\(519\) 181.029i 0.348804i
\(520\) 262.976 129.039i 0.505723 0.248151i
\(521\) −507.014 −0.973155 −0.486578 0.873637i \(-0.661755\pi\)
−0.486578 + 0.873637i \(0.661755\pi\)
\(522\) −99.3110 + 99.3110i −0.190251 + 0.190251i
\(523\) −286.897 286.897i −0.548561 0.548561i 0.377464 0.926024i \(-0.376796\pi\)
−0.926024 + 0.377464i \(0.876796\pi\)
\(524\) 369.527i 0.705205i
\(525\) 70.1018 90.6131i 0.133527 0.172596i
\(526\) 0.779357 0.00148167
\(527\) 444.943 444.943i 0.844294 0.844294i
\(528\) −74.1100 74.1100i −0.140360 0.140360i
\(529\) 230.980i 0.436635i
\(530\) 24.6845 + 50.3060i 0.0465744 + 0.0949169i
\(531\) 17.4209 0.0328077
\(532\) 7.67096 7.67096i 0.0144191 0.0144191i
\(533\) −389.937 389.937i −0.731588 0.731588i
\(534\) 83.8050i 0.156938i
\(535\) 30.5407 + 10.4347i 0.0570855 + 0.0195041i
\(536\) 206.604 0.385455
\(537\) 343.286 343.286i 0.639266 0.639266i
\(538\) 272.956 + 272.956i 0.507353 + 0.507353i
\(539\) 105.894i 0.196463i
\(540\) 16.7999 49.1708i 0.0311109 0.0910570i
\(541\) −604.754 −1.11784 −0.558922 0.829220i \(-0.688785\pi\)
−0.558922 + 0.829220i \(0.688785\pi\)
\(542\) 176.708 176.708i 0.326029 0.326029i
\(543\) −170.345 170.345i −0.313710 0.313710i
\(544\) 127.959i 0.235218i
\(545\) 260.698 127.921i 0.478345 0.234717i
\(546\) 134.237 0.245855
\(547\) 298.464 298.464i 0.545637 0.545637i −0.379539 0.925176i \(-0.623917\pi\)
0.925176 + 0.379539i \(0.123917\pi\)
\(548\) 340.727 + 340.727i 0.621765 + 0.621765i
\(549\) 294.648i 0.536699i
\(550\) −67.7106 530.540i −0.123110 0.964617i
\(551\) −67.8675 −0.123171
\(552\) −95.4974 + 95.4974i −0.173003 + 0.173003i
\(553\) 61.8929 + 61.8929i 0.111922 + 0.111922i
\(554\) 406.304i 0.733402i
\(555\) 164.351 + 334.940i 0.296127 + 0.603496i
\(556\) −221.216 −0.397870
\(557\) 392.034 392.034i 0.703831 0.703831i −0.261400 0.965231i \(-0.584184\pi\)
0.965231 + 0.261400i \(0.0841841\pi\)
\(558\) −83.4538 83.4538i −0.149559 0.149559i
\(559\) 231.385i 0.413926i
\(560\) −50.0731 17.1082i −0.0894162 0.0305503i
\(561\) 592.688 1.05649
\(562\) −368.543 + 368.543i −0.655770 + 0.655770i
\(563\) 575.129 + 575.129i 1.02154 + 1.02154i 0.999763 + 0.0217803i \(0.00693342\pi\)
0.0217803 + 0.999763i \(0.493067\pi\)
\(564\) 166.028i 0.294376i
\(565\) 21.9173 64.1486i 0.0387916 0.113537i
\(566\) −771.201 −1.36255
\(567\) 16.8375 16.8375i 0.0296957 0.0296957i
\(568\) −240.893 240.893i −0.424108 0.424108i
\(569\) 193.452i 0.339986i −0.985445 0.169993i \(-0.945625\pi\)
0.985445 0.169993i \(-0.0543745\pi\)
\(570\) 22.5416 11.0609i 0.0395467 0.0194050i
\(571\) 117.456 0.205703 0.102851 0.994697i \(-0.467203\pi\)
0.102851 + 0.994697i \(0.467203\pi\)
\(572\) 443.133 443.133i 0.774707 0.774707i
\(573\) −283.790 283.790i −0.495270 0.495270i
\(574\) 99.6152i 0.173546i
\(575\) −683.648 + 87.2512i −1.18895 + 0.151741i
\(576\) −24.0000 −0.0416667
\(577\) −703.423 + 703.423i −1.21910 + 1.21910i −0.251157 + 0.967946i \(0.580811\pi\)
−0.967946 + 0.251157i \(0.919189\pi\)
\(578\) 222.669 + 222.669i 0.385240 + 0.385240i
\(579\) 364.946i 0.630304i
\(580\) 145.826 + 297.187i 0.251423 + 0.512391i
\(581\) 363.262 0.625236
\(582\) −255.709 + 255.709i −0.439363 + 0.439363i
\(583\) 84.7690 + 84.7690i 0.145401 + 0.145401i
\(584\) 327.823i 0.561341i
\(585\) 294.011 + 100.453i 0.502583 + 0.171715i
\(586\) 483.306 0.824754
\(587\) −180.492 + 180.492i −0.307483 + 0.307483i −0.843932 0.536450i \(-0.819765\pi\)
0.536450 + 0.843932i \(0.319765\pi\)
\(588\) −17.1464 17.1464i −0.0291606 0.0291606i
\(589\) 57.0309i 0.0968267i
\(590\) 13.2757 38.8561i 0.0225012 0.0658578i
\(591\) −624.840 −1.05726
\(592\) 121.851 121.851i 0.205829 0.205829i
\(593\) −701.554 701.554i −1.18306 1.18306i −0.978948 0.204111i \(-0.934570\pi\)
−0.204111 0.978948i \(-0.565430\pi\)
\(594\) 111.165i 0.187147i
\(595\) 268.638 131.817i 0.451492 0.221541i
\(596\) 301.410 0.505721
\(597\) 393.332 393.332i 0.658848 0.658848i
\(598\) −571.016 571.016i −0.954877 0.954877i
\(599\) 349.739i 0.583871i 0.956438 + 0.291935i \(0.0942992\pi\)
−0.956438 + 0.291935i \(0.905701\pi\)
\(600\) −96.8695 74.9419i −0.161449 0.124903i
\(601\) −227.029 −0.377752 −0.188876 0.982001i \(-0.560484\pi\)
−0.188876 + 0.982001i \(0.560484\pi\)
\(602\) 29.5554 29.5554i 0.0490953 0.0490953i
\(603\) 154.953 + 154.953i 0.256970 + 0.256970i
\(604\) 380.888i 0.630610i
\(605\) −237.536 484.090i −0.392622 0.800149i
\(606\) −123.174 −0.203257
\(607\) 13.0530 13.0530i 0.0215042 0.0215042i −0.696273 0.717777i \(-0.745160\pi\)
0.717777 + 0.696273i \(0.245160\pi\)
\(608\) −8.20060 8.20060i −0.0134878 0.0134878i
\(609\) 151.700i 0.249097i
\(610\) −657.192 224.539i −1.07736 0.368096i
\(611\) 992.747 1.62479
\(612\) 95.9689 95.9689i 0.156812 0.156812i
\(613\) −301.420 301.420i −0.491713 0.491713i 0.417133 0.908846i \(-0.363035\pi\)
−0.908846 + 0.417133i \(0.863035\pi\)
\(614\) 631.026i 1.02773i
\(615\) −74.5446 + 218.181i −0.121211 + 0.354766i
\(616\) −113.205 −0.183774
\(617\) −676.069 + 676.069i −1.09574 + 1.09574i −0.100832 + 0.994904i \(0.532150\pi\)
−0.994904 + 0.100832i \(0.967850\pi\)
\(618\) −17.4272 17.4272i −0.0281993 0.0281993i
\(619\) 180.575i 0.291721i 0.989305 + 0.145860i \(0.0465950\pi\)
−0.989305 + 0.145860i \(0.953405\pi\)
\(620\) −249.735 + 122.541i −0.402798 + 0.197647i
\(621\) −143.246 −0.230670
\(622\) −84.6545 + 84.6545i −0.136101 + 0.136101i
\(623\) −64.0071 64.0071i −0.102740 0.102740i
\(624\) 143.505i 0.229976i
\(625\) −156.975 604.966i −0.251161 0.967945i
\(626\) 379.027 0.605474
\(627\) 37.9842 37.9842i 0.0605808 0.0605808i
\(628\) 57.1422 + 57.1422i 0.0909907 + 0.0909907i
\(629\) 974.490i 1.54927i
\(630\) −24.7237 50.3859i −0.0392439 0.0799776i
\(631\) −778.962 −1.23449 −0.617244 0.786771i \(-0.711751\pi\)
−0.617244 + 0.786771i \(0.711751\pi\)
\(632\) 66.1663 66.1663i 0.104693 0.104693i
\(633\) 27.8220 + 27.8220i 0.0439527 + 0.0439527i
\(634\) 43.8713i 0.0691977i
\(635\) 943.457 + 322.345i 1.48576 + 0.507630i
\(636\) 27.4518 0.0431633
\(637\) 102.525 102.525i 0.160950 0.160950i
\(638\) 500.780 + 500.780i 0.784922 + 0.784922i
\(639\) 361.340i 0.565477i
\(640\) −18.2894 + 53.5303i −0.0285772 + 0.0836412i
\(641\) 773.498 1.20671 0.603353 0.797475i \(-0.293831\pi\)
0.603353 + 0.797475i \(0.293831\pi\)
\(642\) 11.1801 11.1801i 0.0174145 0.0174145i
\(643\) 544.963 + 544.963i 0.847532 + 0.847532i 0.989825 0.142292i \(-0.0454473\pi\)
−0.142292 + 0.989825i \(0.545447\pi\)
\(644\) 145.875i 0.226514i
\(645\) 86.8505 42.6163i 0.134652 0.0660718i
\(646\) 65.5835 0.101523
\(647\) −654.936 + 654.936i −1.01227 + 1.01227i −0.0123424 + 0.999924i \(0.503929\pi\)
−0.999924 + 0.0123424i \(0.996071\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 87.8457i 0.135355i
\(650\) 448.107 579.221i 0.689395 0.891109i
\(651\) −127.478 −0.195818
\(652\) −74.5817 + 74.5817i −0.114389 + 0.114389i
\(653\) −504.090 504.090i −0.771960 0.771960i 0.206489 0.978449i \(-0.433796\pi\)
−0.978449 + 0.206489i \(0.933796\pi\)
\(654\) 142.262i 0.217526i
\(655\) −406.953 829.355i −0.621302 1.26619i
\(656\) 106.493 0.162337
\(657\) −245.868 + 245.868i −0.374228 + 0.374228i
\(658\) −126.806 126.806i −0.192715 0.192715i
\(659\) 726.533i 1.10248i 0.834347 + 0.551239i \(0.185845\pi\)
−0.834347 + 0.551239i \(0.814155\pi\)
\(660\) −247.946 84.7142i −0.375676 0.128355i
\(661\) 1149.24 1.73865 0.869323 0.494245i \(-0.164555\pi\)
0.869323 + 0.494245i \(0.164555\pi\)
\(662\) −165.937 + 165.937i −0.250660 + 0.250660i
\(663\) 573.835 + 573.835i 0.865514 + 0.865514i
\(664\) 388.344i 0.584855i
\(665\) 8.76857 25.6643i 0.0131858 0.0385929i
\(666\) 182.776 0.274438
\(667\) 645.301 645.301i 0.967467 0.967467i
\(668\) 141.493 + 141.493i 0.211816 + 0.211816i
\(669\) 389.391i 0.582050i
\(670\) 463.695 227.529i 0.692082 0.339595i
\(671\) −1485.78 −2.21427
\(672\) −18.3303 + 18.3303i −0.0272772 + 0.0272772i
\(673\) 743.671 + 743.671i 1.10501 + 1.10501i 0.993797 + 0.111212i \(0.0354732\pi\)
0.111212 + 0.993797i \(0.464527\pi\)
\(674\) 147.741i 0.219200i
\(675\) −16.4457 128.859i −0.0243640 0.190902i
\(676\) 520.074 0.769340
\(677\) −182.111 + 182.111i −0.268997 + 0.268997i −0.828696 0.559699i \(-0.810917\pi\)
0.559699 + 0.828696i \(0.310917\pi\)
\(678\) −23.4830 23.4830i −0.0346356 0.0346356i
\(679\) 390.603i 0.575261i
\(680\) −140.918 287.186i −0.207233 0.422332i
\(681\) −127.778 −0.187632
\(682\) −420.820 + 420.820i −0.617038 + 0.617038i
\(683\) 309.149 + 309.149i 0.452634 + 0.452634i 0.896228 0.443594i \(-0.146297\pi\)
−0.443594 + 0.896228i \(0.646297\pi\)
\(684\) 12.3009i 0.0179838i
\(685\) 1139.95 + 389.481i 1.66416 + 0.568585i
\(686\) −26.1916 −0.0381802
\(687\) 141.441 141.441i 0.205882 0.205882i
\(688\) −31.5960 31.5960i −0.0459245 0.0459245i
\(689\) 164.145i 0.238237i
\(690\) −109.162 + 319.501i −0.158206 + 0.463044i
\(691\) −634.866 −0.918764 −0.459382 0.888239i \(-0.651929\pi\)
−0.459382 + 0.888239i \(0.651929\pi\)
\(692\) 147.810 147.810i 0.213598 0.213598i
\(693\) −84.9037 84.9037i −0.122516 0.122516i
\(694\) 62.5397i 0.0901149i
\(695\) −496.490 + 243.621i −0.714373 + 0.350533i
\(696\) 162.174 0.233009
\(697\) −425.835 + 425.835i −0.610953 + 0.610953i
\(698\) −546.387 546.387i −0.782789 0.782789i
\(699\) 728.906i 1.04278i
\(700\) −131.223 + 16.7475i −0.187462 + 0.0239250i
\(701\) 863.013 1.23112 0.615559 0.788091i \(-0.288930\pi\)
0.615559 + 0.788091i \(0.288930\pi\)
\(702\) 107.629 107.629i 0.153318 0.153318i
\(703\) 62.4530 + 62.4530i 0.0888379 + 0.0888379i
\(704\) 121.021i 0.171905i
\(705\) −182.844 372.628i −0.259353 0.528551i
\(706\) 368.662 0.522184
\(707\) −94.0754 + 94.0754i −0.133063 + 0.133063i
\(708\) −14.2241 14.2241i −0.0200905 0.0200905i
\(709\) 653.419i 0.921607i 0.887502 + 0.460803i \(0.152439\pi\)
−0.887502 + 0.460803i \(0.847561\pi\)
\(710\) −805.944 275.362i −1.13513 0.387834i
\(711\) 99.2494 0.139591
\(712\) −68.4265 + 68.4265i −0.0961046 + 0.0961046i
\(713\) 542.264 + 542.264i 0.760539 + 0.760539i
\(714\) 146.595i 0.205315i
\(715\) 506.539 1482.56i 0.708446 2.07352i
\(716\) −560.583 −0.782938
\(717\) 167.246 167.246i 0.233258 0.233258i
\(718\) 319.232 + 319.232i 0.444613 + 0.444613i
\(719\) 961.796i 1.33769i 0.743404 + 0.668843i \(0.233210\pi\)
−0.743404 + 0.668843i \(0.766790\pi\)
\(720\) −53.8648 + 26.4307i −0.0748122 + 0.0367093i
\(721\) −26.6204 −0.0369216
\(722\) −356.797 + 356.797i −0.494179 + 0.494179i
\(723\) 74.7229 + 74.7229i 0.103351 + 0.103351i
\(724\) 278.172i 0.384215i
\(725\) 654.572 + 506.402i 0.902858 + 0.698485i
\(726\) −264.167 −0.363866
\(727\) 948.990 948.990i 1.30535 1.30535i 0.380618 0.924733i \(-0.375711\pi\)
0.924733 0.380618i \(-0.124289\pi\)
\(728\) −109.604 109.604i −0.150555 0.150555i
\(729\) 27.0000i 0.0370370i
\(730\) 361.025 + 735.756i 0.494555 + 1.00788i
\(731\) 252.686 0.345672
\(732\) −240.579 + 240.579i −0.328660 + 0.328660i
\(733\) 731.489 + 731.489i 0.997938 + 0.997938i 0.999998 0.00205981i \(-0.000655659\pi\)
−0.00205981 + 0.999998i \(0.500656\pi\)
\(734\) 232.880i 0.317276i
\(735\) −57.3659 19.5999i −0.0780488 0.0266665i
\(736\) 155.947 0.211884
\(737\) 781.357 781.357i 1.06019 1.06019i
\(738\) 79.8698 + 79.8698i 0.108225 + 0.108225i
\(739\) 33.8430i 0.0457956i −0.999738 0.0228978i \(-0.992711\pi\)
0.999738 0.0228978i \(-0.00728924\pi\)
\(740\) 139.286 407.669i 0.188224 0.550905i
\(741\) 73.5518 0.0992602
\(742\) 20.9667 20.9667i 0.0282570 0.0282570i
\(743\) 39.7475 + 39.7475i 0.0534959 + 0.0534959i 0.733349 0.679853i \(-0.237956\pi\)
−0.679853 + 0.733349i \(0.737956\pi\)
\(744\) 136.279i 0.183171i
\(745\) 676.474 331.936i 0.908018 0.445552i
\(746\) −761.924 −1.02135
\(747\) 291.258 291.258i 0.389903 0.389903i
\(748\) −483.928 483.928i −0.646962 0.646962i
\(749\) 17.0779i 0.0228009i
\(750\) −299.943 61.5167i −0.399924 0.0820223i
\(751\) 578.927 0.770874 0.385437 0.922734i \(-0.374051\pi\)
0.385437 + 0.922734i \(0.374051\pi\)
\(752\) −135.561 + 135.561i −0.180268 + 0.180268i
\(753\) 264.464 + 264.464i 0.351214 + 0.351214i
\(754\) 969.702i 1.28608i
\(755\) 419.465 + 854.853i 0.555582 + 1.13226i
\(756\) −27.4955 −0.0363696
\(757\) 114.632 114.632i 0.151429 0.151429i −0.627327 0.778756i \(-0.715851\pi\)
0.778756 + 0.627327i \(0.215851\pi\)
\(758\) 189.542 + 189.542i 0.250056 + 0.250056i
\(759\) 722.326i 0.951681i
\(760\) −27.4363 9.37400i −0.0361004 0.0123342i
\(761\) −87.5262 −0.115015 −0.0575073 0.998345i \(-0.518315\pi\)
−0.0575073 + 0.998345i \(0.518315\pi\)
\(762\) 345.372 345.372i 0.453245 0.453245i
\(763\) −108.655 108.655i −0.142404 0.142404i
\(764\) 463.427i 0.606580i
\(765\) 109.701 321.078i 0.143400 0.419710i
\(766\) 612.204 0.799222
\(767\) 85.0514 85.0514i 0.110888 0.110888i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) 780.679i 1.01519i 0.861596 + 0.507594i \(0.169465\pi\)
−0.861596 + 0.507594i \(0.830535\pi\)
\(770\) −254.073 + 124.670i −0.329965 + 0.161909i
\(771\) −354.144 −0.459331
\(772\) −297.977 + 297.977i −0.385981 + 0.385981i
\(773\) 692.751 + 692.751i