Properties

Label 690.3.k.b.277.2
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.2
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.35673 + 2.45335i) q^{5} +2.44949 q^{6} +(-3.40648 - 3.40648i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.35673 + 2.45335i) q^{5} +2.44949 q^{6} +(-3.40648 - 3.40648i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.81008 + 1.90338i) q^{10} -17.0916 q^{11} +(-2.44949 - 2.44949i) q^{12} +(9.51988 - 9.51988i) q^{13} +6.81296i q^{14} +(2.33116 - 8.34061i) q^{15} -4.00000 q^{16} +(-1.23132 - 1.23132i) q^{17} +(-3.00000 + 3.00000i) q^{18} -10.6522i q^{19} +(-4.90669 - 8.71346i) q^{20} +8.34414 q^{21} +(17.0916 + 17.0916i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(12.9622 - 21.3771i) q^{25} -19.0398 q^{26} +(3.67423 + 3.67423i) q^{27} +(6.81296 - 6.81296i) q^{28} +16.4830i q^{29} +(-10.6718 + 6.00945i) q^{30} -21.1370 q^{31} +(4.00000 + 4.00000i) q^{32} +(20.9328 - 20.9328i) q^{33} +2.46265i q^{34} +(23.1984 + 6.48384i) q^{35} +6.00000 q^{36} +(0.589707 + 0.589707i) q^{37} +(-10.6522 + 10.6522i) q^{38} +23.3188i q^{39} +(-3.80677 + 13.6202i) q^{40} +44.7585 q^{41} +(-8.34414 - 8.34414i) q^{42} +(-49.7416 + 49.7416i) q^{43} -34.1832i q^{44} +(7.36004 + 13.0702i) q^{45} +6.78233 q^{46} +(59.0386 + 59.0386i) q^{47} +(4.89898 - 4.89898i) q^{48} -25.7918i q^{49} +(-34.3393 + 8.41495i) q^{50} +3.01611 q^{51} +(19.0398 + 19.0398i) q^{52} +(-38.1796 + 38.1796i) q^{53} -7.34847i q^{54} +(74.4634 - 41.9316i) q^{55} -13.6259 q^{56} +(13.0463 + 13.0463i) q^{57} +(16.4830 - 16.4830i) q^{58} +16.5016i q^{59} +(16.6812 + 4.66232i) q^{60} +85.3928 q^{61} +(21.1370 + 21.1370i) q^{62} +(-10.2194 + 10.2194i) q^{63} -8.00000i q^{64} +(-18.1200 + 64.8311i) q^{65} -41.8657 q^{66} +(87.1773 + 87.1773i) q^{67} +(2.46265 - 2.46265i) q^{68} -8.30662i q^{69} +(-16.7145 - 29.6822i) q^{70} -18.0891 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-17.4717 + 17.4717i) q^{73} -1.17941i q^{74} +(10.3062 + 42.0569i) q^{75} +21.3045 q^{76} +(58.2221 + 58.2221i) q^{77} +(23.3188 - 23.3188i) q^{78} -67.2838i q^{79} +(17.4269 - 9.81339i) q^{80} -9.00000 q^{81} +(-44.7585 - 44.7585i) q^{82} +(8.41202 - 8.41202i) q^{83} +16.6883i q^{84} +(8.38541 + 2.34368i) q^{85} +99.4833 q^{86} +(-20.1875 - 20.1875i) q^{87} +(-34.1832 + 34.1832i) q^{88} -44.8108i q^{89} +(5.71015 - 20.4302i) q^{90} -64.8586 q^{91} +(-6.78233 - 6.78233i) q^{92} +(25.8875 - 25.8875i) q^{93} -118.077i q^{94} +(26.1336 + 46.4089i) q^{95} -9.79796 q^{96} +(84.0085 + 84.0085i) q^{97} +(-25.7918 + 25.7918i) q^{98} +51.2748i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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
\(5\) −4.35673 + 2.45335i −0.871346 + 0.490669i
\(6\) 2.44949 0.408248
\(7\) −3.40648 3.40648i −0.486640 0.486640i 0.420604 0.907244i \(-0.361818\pi\)
−0.907244 + 0.420604i \(0.861818\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.81008 + 1.90338i 0.681008 + 0.190338i
\(11\) −17.0916 −1.55378 −0.776890 0.629636i \(-0.783204\pi\)
−0.776890 + 0.629636i \(0.783204\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 9.51988 9.51988i 0.732298 0.732298i −0.238776 0.971075i \(-0.576746\pi\)
0.971075 + 0.238776i \(0.0767462\pi\)
\(14\) 6.81296i 0.486640i
\(15\) 2.33116 8.34061i 0.155411 0.556040i
\(16\) −4.00000 −0.250000
\(17\) −1.23132 1.23132i −0.0724308 0.0724308i 0.669963 0.742394i \(-0.266310\pi\)
−0.742394 + 0.669963i \(0.766310\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 10.6522i 0.560644i −0.959906 0.280322i \(-0.909559\pi\)
0.959906 0.280322i \(-0.0904413\pi\)
\(20\) −4.90669 8.71346i −0.245335 0.435673i
\(21\) 8.34414 0.397340
\(22\) 17.0916 + 17.0916i 0.776890 + 0.776890i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 12.9622 21.3771i 0.518487 0.855085i
\(26\) −19.0398 −0.732298
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 6.81296 6.81296i 0.243320 0.243320i
\(29\) 16.4830i 0.568380i 0.958768 + 0.284190i \(0.0917247\pi\)
−0.958768 + 0.284190i \(0.908275\pi\)
\(30\) −10.6718 + 6.00945i −0.355725 + 0.200315i
\(31\) −21.1370 −0.681839 −0.340920 0.940092i \(-0.610738\pi\)
−0.340920 + 0.940092i \(0.610738\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 20.9328 20.9328i 0.634328 0.634328i
\(34\) 2.46265i 0.0724308i
\(35\) 23.1984 + 6.48384i 0.662811 + 0.185252i
\(36\) 6.00000 0.166667
\(37\) 0.589707 + 0.589707i 0.0159380 + 0.0159380i 0.715031 0.699093i \(-0.246413\pi\)
−0.699093 + 0.715031i \(0.746413\pi\)
\(38\) −10.6522 + 10.6522i −0.280322 + 0.280322i
\(39\) 23.3188i 0.597919i
\(40\) −3.80677 + 13.6202i −0.0951692 + 0.340504i
\(41\) 44.7585 1.09167 0.545835 0.837893i \(-0.316213\pi\)
0.545835 + 0.837893i \(0.316213\pi\)
\(42\) −8.34414 8.34414i −0.198670 0.198670i
\(43\) −49.7416 + 49.7416i −1.15678 + 1.15678i −0.171619 + 0.985163i \(0.554900\pi\)
−0.985163 + 0.171619i \(0.945100\pi\)
\(44\) 34.1832i 0.776890i
\(45\) 7.36004 + 13.0702i 0.163556 + 0.290449i
\(46\) 6.78233 0.147442
\(47\) 59.0386 + 59.0386i 1.25614 + 1.25614i 0.952920 + 0.303220i \(0.0980619\pi\)
0.303220 + 0.952920i \(0.401938\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 25.7918i 0.526363i
\(50\) −34.3393 + 8.41495i −0.686786 + 0.168299i
\(51\) 3.01611 0.0591395
\(52\) 19.0398 + 19.0398i 0.366149 + 0.366149i
\(53\) −38.1796 + 38.1796i −0.720369 + 0.720369i −0.968680 0.248311i \(-0.920124\pi\)
0.248311 + 0.968680i \(0.420124\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 74.4634 41.9316i 1.35388 0.762392i
\(56\) −13.6259 −0.243320
\(57\) 13.0463 + 13.0463i 0.228882 + 0.228882i
\(58\) 16.4830 16.4830i 0.284190 0.284190i
\(59\) 16.5016i 0.279688i 0.990174 + 0.139844i \(0.0446601\pi\)
−0.990174 + 0.139844i \(0.955340\pi\)
\(60\) 16.6812 + 4.66232i 0.278020 + 0.0777053i
\(61\) 85.3928 1.39988 0.699941 0.714201i \(-0.253210\pi\)
0.699941 + 0.714201i \(0.253210\pi\)
\(62\) 21.1370 + 21.1370i 0.340920 + 0.340920i
\(63\) −10.2194 + 10.2194i −0.162213 + 0.162213i
\(64\) 8.00000i 0.125000i
\(65\) −18.1200 + 64.8311i −0.278769 + 0.997402i
\(66\) −41.8657 −0.634328
\(67\) 87.1773 + 87.1773i 1.30115 + 1.30115i 0.927614 + 0.373540i \(0.121856\pi\)
0.373540 + 0.927614i \(0.378144\pi\)
\(68\) 2.46265 2.46265i 0.0362154 0.0362154i
\(69\) 8.30662i 0.120386i
\(70\) −16.7145 29.6822i −0.238779 0.424032i
\(71\) −18.0891 −0.254776 −0.127388 0.991853i \(-0.540659\pi\)
−0.127388 + 0.991853i \(0.540659\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −17.4717 + 17.4717i −0.239338 + 0.239338i −0.816576 0.577238i \(-0.804130\pi\)
0.577238 + 0.816576i \(0.304130\pi\)
\(74\) 1.17941i 0.0159380i
\(75\) 10.3062 + 42.0569i 0.137416 + 0.560759i
\(76\) 21.3045 0.280322
\(77\) 58.2221 + 58.2221i 0.756132 + 0.756132i
\(78\) 23.3188 23.3188i 0.298960 0.298960i
\(79\) 67.2838i 0.851693i −0.904795 0.425847i \(-0.859976\pi\)
0.904795 0.425847i \(-0.140024\pi\)
\(80\) 17.4269 9.81339i 0.217836 0.122667i
\(81\) −9.00000 −0.111111
\(82\) −44.7585 44.7585i −0.545835 0.545835i
\(83\) 8.41202 8.41202i 0.101350 0.101350i −0.654614 0.755963i \(-0.727169\pi\)
0.755963 + 0.654614i \(0.227169\pi\)
\(84\) 16.6883i 0.198670i
\(85\) 8.38541 + 2.34368i 0.0986518 + 0.0275727i
\(86\) 99.4833 1.15678
\(87\) −20.1875 20.1875i −0.232040 0.232040i
\(88\) −34.1832 + 34.1832i −0.388445 + 0.388445i
\(89\) 44.8108i 0.503492i −0.967793 0.251746i \(-0.918995\pi\)
0.967793 0.251746i \(-0.0810047\pi\)
\(90\) 5.71015 20.4302i 0.0634461 0.227003i
\(91\) −64.8586 −0.712731
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 25.8875 25.8875i 0.278360 0.278360i
\(94\) 118.077i 1.25614i
\(95\) 26.1336 + 46.4089i 0.275091 + 0.488515i
\(96\) −9.79796 −0.102062
\(97\) 84.0085 + 84.0085i 0.866067 + 0.866067i 0.992034 0.125967i \(-0.0402034\pi\)
−0.125967 + 0.992034i \(0.540203\pi\)
\(98\) −25.7918 + 25.7918i −0.263182 + 0.263182i
\(99\) 51.2748i 0.517927i
\(100\) 42.7543 + 25.9244i 0.427543 + 0.259244i
\(101\) 110.266 1.09174 0.545871 0.837869i \(-0.316199\pi\)
0.545871 + 0.837869i \(0.316199\pi\)
\(102\) −3.01611 3.01611i −0.0295697 0.0295697i
\(103\) 103.363 103.363i 1.00352 1.00352i 0.00352878 0.999994i \(-0.498877\pi\)
0.999994 0.00352878i \(-0.00112325\pi\)
\(104\) 38.0795i 0.366149i
\(105\) −36.3531 + 20.4711i −0.346220 + 0.194962i
\(106\) 76.3591 0.720369
\(107\) −39.1624 39.1624i −0.366004 0.366004i 0.500014 0.866018i \(-0.333328\pi\)
−0.866018 + 0.500014i \(0.833328\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 167.451i 1.53625i −0.640299 0.768126i \(-0.721190\pi\)
0.640299 0.768126i \(-0.278810\pi\)
\(110\) −116.395 32.5318i −1.05814 0.295744i
\(111\) −1.44448 −0.0130133
\(112\) 13.6259 + 13.6259i 0.121660 + 0.121660i
\(113\) −58.3978 + 58.3978i −0.516794 + 0.516794i −0.916600 0.399806i \(-0.869078\pi\)
0.399806 + 0.916600i \(0.369078\pi\)
\(114\) 26.0925i 0.228882i
\(115\) 6.45469 23.0941i 0.0561277 0.200818i
\(116\) −32.9661 −0.284190
\(117\) −28.5596 28.5596i −0.244099 0.244099i
\(118\) 16.5016 16.5016i 0.139844 0.139844i
\(119\) 8.38896i 0.0704954i
\(120\) −12.0189 21.3435i −0.100157 0.177863i
\(121\) 171.122 1.41423
\(122\) −85.3928 85.3928i −0.699941 0.699941i
\(123\) −54.8177 + 54.8177i −0.445672 + 0.445672i
\(124\) 42.2740i 0.340920i
\(125\) −4.02721 + 124.935i −0.0322177 + 0.999481i
\(126\) 20.4389 0.162213
\(127\) 38.7338 + 38.7338i 0.304990 + 0.304990i 0.842963 0.537972i \(-0.180809\pi\)
−0.537972 + 0.842963i \(0.680809\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 121.842i 0.944509i
\(130\) 82.9511 46.7111i 0.638085 0.359316i
\(131\) 53.9132 0.411551 0.205776 0.978599i \(-0.434028\pi\)
0.205776 + 0.978599i \(0.434028\pi\)
\(132\) 41.8657 + 41.8657i 0.317164 + 0.317164i
\(133\) −36.2866 + 36.2866i −0.272832 + 0.272832i
\(134\) 174.355i 1.30115i
\(135\) −25.0218 6.99348i −0.185347 0.0518035i
\(136\) −4.92529 −0.0362154
\(137\) −77.4818 77.4818i −0.565561 0.565561i 0.365321 0.930882i \(-0.380959\pi\)
−0.930882 + 0.365321i \(0.880959\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 39.5073i 0.284225i −0.989850 0.142113i \(-0.954610\pi\)
0.989850 0.142113i \(-0.0453895\pi\)
\(140\) −12.9677 + 46.3968i −0.0926262 + 0.331405i
\(141\) −144.614 −1.02563
\(142\) 18.0891 + 18.0891i 0.127388 + 0.127388i
\(143\) −162.710 + 162.710i −1.13783 + 1.13783i
\(144\) 12.0000i 0.0833333i
\(145\) −40.4386 71.8121i −0.278887 0.495256i
\(146\) 34.9433 0.239338
\(147\) 31.5884 + 31.5884i 0.214887 + 0.214887i
\(148\) −1.17941 + 1.17941i −0.00796901 + 0.00796901i
\(149\) 124.537i 0.835817i 0.908489 + 0.417909i \(0.137237\pi\)
−0.908489 + 0.417909i \(0.862763\pi\)
\(150\) 31.7507 52.3631i 0.211672 0.349087i
\(151\) 100.260 0.663973 0.331986 0.943284i \(-0.392281\pi\)
0.331986 + 0.943284i \(0.392281\pi\)
\(152\) −21.3045 21.3045i −0.140161 0.140161i
\(153\) −3.69397 + 3.69397i −0.0241436 + 0.0241436i
\(154\) 116.444i 0.756132i
\(155\) 92.0883 51.8564i 0.594118 0.334558i
\(156\) −46.6377 −0.298960
\(157\) 169.452 + 169.452i 1.07931 + 1.07931i 0.996571 + 0.0827379i \(0.0263664\pi\)
0.0827379 + 0.996571i \(0.473634\pi\)
\(158\) −67.2838 + 67.2838i −0.425847 + 0.425847i
\(159\) 93.5205i 0.588179i
\(160\) −27.2403 7.61353i −0.170252 0.0475846i
\(161\) 23.1039 0.143502
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 125.349 125.349i 0.769014 0.769014i −0.208919 0.977933i \(-0.566994\pi\)
0.977933 + 0.208919i \(0.0669944\pi\)
\(164\) 89.5169i 0.545835i
\(165\) −39.8432 + 142.554i −0.241474 + 0.863965i
\(166\) −16.8240 −0.101350
\(167\) 148.841 + 148.841i 0.891262 + 0.891262i 0.994642 0.103380i \(-0.0329657\pi\)
−0.103380 + 0.994642i \(0.532966\pi\)
\(168\) 16.6883 16.6883i 0.0993350 0.0993350i
\(169\) 12.2562i 0.0725222i
\(170\) −6.04173 10.7291i −0.0355396 0.0631123i
\(171\) −31.9567 −0.186881
\(172\) −99.4833 99.4833i −0.578391 0.578391i
\(173\) 89.4157 89.4157i 0.516854 0.516854i −0.399764 0.916618i \(-0.630908\pi\)
0.916618 + 0.399764i \(0.130908\pi\)
\(174\) 40.3750i 0.232040i
\(175\) −116.976 + 28.6654i −0.668435 + 0.163802i
\(176\) 68.3663 0.388445
\(177\) −20.2103 20.2103i −0.114182 0.114182i
\(178\) −44.8108 + 44.8108i −0.251746 + 0.251746i
\(179\) 82.4024i 0.460349i 0.973149 + 0.230174i \(0.0739296\pi\)
−0.973149 + 0.230174i \(0.926070\pi\)
\(180\) −26.1404 + 14.7201i −0.145224 + 0.0817782i
\(181\) −345.572 −1.90924 −0.954620 0.297828i \(-0.903738\pi\)
−0.954620 + 0.297828i \(0.903738\pi\)
\(182\) 64.8586 + 64.8586i 0.356366 + 0.356366i
\(183\) −104.584 + 104.584i −0.571499 + 0.571499i
\(184\) 13.5647i 0.0737210i
\(185\) −4.01595 1.12244i −0.0217078 0.00606723i
\(186\) −51.7749 −0.278360
\(187\) 21.0453 + 21.0453i 0.112542 + 0.112542i
\(188\) −118.077 + 118.077i −0.628070 + 0.628070i
\(189\) 25.0324i 0.132447i
\(190\) 20.2753 72.5425i 0.106712 0.381803i
\(191\) −263.122 −1.37760 −0.688801 0.724950i \(-0.741863\pi\)
−0.688801 + 0.724950i \(0.741863\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 140.875 140.875i 0.729920 0.729920i −0.240684 0.970604i \(-0.577372\pi\)
0.970604 + 0.240684i \(0.0773717\pi\)
\(194\) 168.017i 0.866067i
\(195\) −57.2092 101.594i −0.293381 0.520994i
\(196\) 51.5836 0.263182
\(197\) −85.4790 85.4790i −0.433903 0.433903i 0.456051 0.889954i \(-0.349264\pi\)
−0.889954 + 0.456051i \(0.849264\pi\)
\(198\) 51.2748 51.2748i 0.258963 0.258963i
\(199\) 234.435i 1.17806i 0.808110 + 0.589032i \(0.200491\pi\)
−0.808110 + 0.589032i \(0.799509\pi\)
\(200\) −16.8299 68.6786i −0.0841495 0.343393i
\(201\) −213.540 −1.06239
\(202\) −110.266 110.266i −0.545871 0.545871i
\(203\) 56.1491 56.1491i 0.276597 0.276597i
\(204\) 6.03223i 0.0295697i
\(205\) −195.001 + 109.808i −0.951222 + 0.535649i
\(206\) −206.726 −1.00352
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −38.0795 + 38.0795i −0.183075 + 0.183075i
\(209\) 182.064i 0.871118i
\(210\) 56.8242 + 15.8821i 0.270591 + 0.0756290i
\(211\) −145.969 −0.691795 −0.345897 0.938272i \(-0.612426\pi\)
−0.345897 + 0.938272i \(0.612426\pi\)
\(212\) −76.3591 76.3591i −0.360185 0.360185i
\(213\) 22.1545 22.1545i 0.104012 0.104012i
\(214\) 78.3249i 0.366004i
\(215\) 94.6774 338.744i 0.440360 1.57556i
\(216\) 14.6969 0.0680414
\(217\) 72.0028 + 72.0028i 0.331810 + 0.331810i
\(218\) −167.451 + 167.451i −0.768126 + 0.768126i
\(219\) 42.7967i 0.195419i
\(220\) 83.8632 + 148.927i 0.381196 + 0.676940i
\(221\) −23.4441 −0.106082
\(222\) 1.44448 + 1.44448i 0.00650667 + 0.00650667i
\(223\) −227.734 + 227.734i −1.02123 + 1.02123i −0.0214593 + 0.999770i \(0.506831\pi\)
−0.999770 + 0.0214593i \(0.993169\pi\)
\(224\) 27.2518i 0.121660i
\(225\) −64.1314 38.8865i −0.285028 0.172829i
\(226\) 116.796 0.516794
\(227\) −63.6156 63.6156i −0.280245 0.280245i 0.552962 0.833207i \(-0.313498\pi\)
−0.833207 + 0.552962i \(0.813498\pi\)
\(228\) −26.0925 + 26.0925i −0.114441 + 0.114441i
\(229\) 173.353i 0.757000i −0.925601 0.378500i \(-0.876440\pi\)
0.925601 0.378500i \(-0.123560\pi\)
\(230\) −29.5488 + 16.6394i −0.128473 + 0.0723452i
\(231\) −142.615 −0.617379
\(232\) 32.9661 + 32.9661i 0.142095 + 0.142095i
\(233\) 128.901 128.901i 0.553225 0.553225i −0.374145 0.927370i \(-0.622064\pi\)
0.927370 + 0.374145i \(0.122064\pi\)
\(234\) 57.1193i 0.244099i
\(235\) −402.057 112.373i −1.71088 0.478183i
\(236\) −33.0032 −0.139844
\(237\) 82.4054 + 82.4054i 0.347702 + 0.347702i
\(238\) 8.38896 8.38896i 0.0352477 0.0352477i
\(239\) 198.218i 0.829366i −0.909966 0.414683i \(-0.863892\pi\)
0.909966 0.414683i \(-0.136108\pi\)
\(240\) −9.32463 + 33.3624i −0.0388526 + 0.139010i
\(241\) 134.329 0.557381 0.278690 0.960381i \(-0.410100\pi\)
0.278690 + 0.960381i \(0.410100\pi\)
\(242\) −171.122 171.122i −0.707117 0.707117i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 170.786i 0.699941i
\(245\) 63.2762 + 112.368i 0.258270 + 0.458644i
\(246\) 109.635 0.445672
\(247\) −101.408 101.408i −0.410559 0.410559i
\(248\) −42.2740 + 42.2740i −0.170460 + 0.170460i
\(249\) 20.6052i 0.0827517i
\(250\) 128.962 120.908i 0.515849 0.483632i
\(251\) −85.1879 −0.339394 −0.169697 0.985496i \(-0.554279\pi\)
−0.169697 + 0.985496i \(0.554279\pi\)
\(252\) −20.4389 20.4389i −0.0811067 0.0811067i
\(253\) 57.9604 57.9604i 0.229092 0.229092i
\(254\) 77.4676i 0.304990i
\(255\) −13.1404 + 7.39957i −0.0515310 + 0.0290179i
\(256\) 16.0000 0.0625000
\(257\) −89.1736 89.1736i −0.346979 0.346979i 0.512004 0.858983i \(-0.328903\pi\)
−0.858983 + 0.512004i \(0.828903\pi\)
\(258\) −121.842 + 121.842i −0.472254 + 0.472254i
\(259\) 4.01765i 0.0155121i
\(260\) −129.662 36.2400i −0.498701 0.139384i
\(261\) 49.4491 0.189460
\(262\) −53.9132 53.9132i −0.205776 0.205776i
\(263\) 123.208 123.208i 0.468473 0.468473i −0.432947 0.901420i \(-0.642526\pi\)
0.901420 + 0.432947i \(0.142526\pi\)
\(264\) 83.7313i 0.317164i
\(265\) 72.6703 260.006i 0.274228 0.981154i
\(266\) 72.5733 0.272832
\(267\) 54.8818 + 54.8818i 0.205550 + 0.205550i
\(268\) −174.355 + 174.355i −0.650577 + 0.650577i
\(269\) 159.070i 0.591340i −0.955290 0.295670i \(-0.904457\pi\)
0.955290 0.295670i \(-0.0955429\pi\)
\(270\) 18.0283 + 32.0153i 0.0667716 + 0.118575i
\(271\) 262.498 0.968627 0.484313 0.874895i \(-0.339069\pi\)
0.484313 + 0.874895i \(0.339069\pi\)
\(272\) 4.92529 + 4.92529i 0.0181077 + 0.0181077i
\(273\) 79.4352 79.4352i 0.290971 0.290971i
\(274\) 154.964i 0.565561i
\(275\) −221.544 + 365.369i −0.805615 + 1.32861i
\(276\) 16.6132 0.0601929
\(277\) 249.767 + 249.767i 0.901686 + 0.901686i 0.995582 0.0938960i \(-0.0299321\pi\)
−0.0938960 + 0.995582i \(0.529932\pi\)
\(278\) −39.5073 + 39.5073i −0.142113 + 0.142113i
\(279\) 63.4111i 0.227280i
\(280\) 59.3644 33.4291i 0.212016 0.119390i
\(281\) 312.983 1.11382 0.556910 0.830573i \(-0.311987\pi\)
0.556910 + 0.830573i \(0.311987\pi\)
\(282\) 144.614 + 144.614i 0.512817 + 0.512817i
\(283\) −304.788 + 304.788i −1.07699 + 1.07699i −0.0802130 + 0.996778i \(0.525560\pi\)
−0.996778 + 0.0802130i \(0.974440\pi\)
\(284\) 36.1782i 0.127388i
\(285\) −88.8461 24.8321i −0.311741 0.0871300i
\(286\) 325.420 1.13783
\(287\) −152.469 152.469i −0.531250 0.531250i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 285.968i 0.989508i
\(290\) −31.3735 + 112.251i −0.108185 + 0.387071i
\(291\) −205.778 −0.707141
\(292\) −34.9433 34.9433i −0.119669 0.119669i
\(293\) −342.482 + 342.482i −1.16888 + 1.16888i −0.186408 + 0.982472i \(0.559685\pi\)
−0.982472 + 0.186408i \(0.940315\pi\)
\(294\) 63.1767i 0.214887i
\(295\) −40.4841 71.8930i −0.137234 0.243705i
\(296\) 2.35883 0.00796901
\(297\) −62.7985 62.7985i −0.211443 0.211443i
\(298\) 124.537 124.537i 0.417909 0.417909i
\(299\) 64.5670i 0.215943i
\(300\) −84.1138 + 20.6123i −0.280379 + 0.0687078i
\(301\) 338.888 1.12587
\(302\) −100.260 100.260i −0.331986 0.331986i
\(303\) −135.048 + 135.048i −0.445702 + 0.445702i
\(304\) 42.6090i 0.140161i
\(305\) −372.033 + 209.498i −1.21978 + 0.686879i
\(306\) 7.38794 0.0241436
\(307\) 242.539 + 242.539i 0.790030 + 0.790030i 0.981499 0.191469i \(-0.0613250\pi\)
−0.191469 + 0.981499i \(0.561325\pi\)
\(308\) −116.444 + 116.444i −0.378066 + 0.378066i
\(309\) 253.186i 0.819373i
\(310\) −143.945 40.2319i −0.464338 0.129780i
\(311\) −486.480 −1.56424 −0.782122 0.623125i \(-0.785863\pi\)
−0.782122 + 0.623125i \(0.785863\pi\)
\(312\) 46.6377 + 46.6377i 0.149480 + 0.149480i
\(313\) 58.2031 58.2031i 0.185953 0.185953i −0.607991 0.793944i \(-0.708024\pi\)
0.793944 + 0.607991i \(0.208024\pi\)
\(314\) 338.903i 1.07931i
\(315\) 19.4515 69.5952i 0.0617508 0.220937i
\(316\) 134.568 0.425847
\(317\) 331.965 + 331.965i 1.04721 + 1.04721i 0.998829 + 0.0483793i \(0.0154056\pi\)
0.0483793 + 0.998829i \(0.484594\pi\)
\(318\) −93.5205 + 93.5205i −0.294089 + 0.294089i
\(319\) 281.721i 0.883138i
\(320\) 19.6268 + 34.8538i 0.0613337 + 0.108918i
\(321\) 95.9280 0.298841
\(322\) −23.1039 23.1039i −0.0717511 0.0717511i
\(323\) −13.1164 + 13.1164i −0.0406079 + 0.0406079i
\(324\) 18.0000i 0.0555556i
\(325\) −80.1093 326.906i −0.246490 1.00587i
\(326\) −250.699 −0.769014
\(327\) 205.085 + 205.085i 0.627172 + 0.627172i
\(328\) 89.5169 89.5169i 0.272917 0.272917i
\(329\) 402.228i 1.22258i
\(330\) 182.397 102.711i 0.552719 0.311245i
\(331\) 57.4084 0.173439 0.0867196 0.996233i \(-0.472362\pi\)
0.0867196 + 0.996233i \(0.472362\pi\)
\(332\) 16.8240 + 16.8240i 0.0506748 + 0.0506748i
\(333\) 1.76912 1.76912i 0.00531267 0.00531267i
\(334\) 297.682i 0.891262i
\(335\) −593.684 165.932i −1.77219 0.495319i
\(336\) −33.3765 −0.0993350
\(337\) 17.5680 + 17.5680i 0.0521307 + 0.0521307i 0.732692 0.680561i \(-0.238264\pi\)
−0.680561 + 0.732692i \(0.738264\pi\)
\(338\) −12.2562 + 12.2562i −0.0362611 + 0.0362611i
\(339\) 143.045i 0.421961i
\(340\) −4.68736 + 16.7708i −0.0137864 + 0.0493259i
\(341\) 361.265 1.05943
\(342\) 31.9567 + 31.9567i 0.0934407 + 0.0934407i
\(343\) −254.777 + 254.777i −0.742789 + 0.742789i
\(344\) 198.967i 0.578391i
\(345\) 20.3790 + 36.1897i 0.0590696 + 0.104898i
\(346\) −178.831 −0.516854
\(347\) 71.5458 + 71.5458i 0.206184 + 0.206184i 0.802643 0.596459i \(-0.203426\pi\)
−0.596459 + 0.802643i \(0.703426\pi\)
\(348\) 40.3750 40.3750i 0.116020 0.116020i
\(349\) 21.0922i 0.0604360i 0.999543 + 0.0302180i \(0.00962015\pi\)
−0.999543 + 0.0302180i \(0.990380\pi\)
\(350\) 145.642 + 88.3108i 0.416119 + 0.252317i
\(351\) 69.9565 0.199306
\(352\) −68.3663 68.3663i −0.194223 0.194223i
\(353\) 267.728 267.728i 0.758436 0.758436i −0.217601 0.976038i \(-0.569823\pi\)
0.976038 + 0.217601i \(0.0698232\pi\)
\(354\) 40.4205i 0.114182i
\(355\) 78.8093 44.3788i 0.221998 0.125011i
\(356\) 89.6216 0.251746
\(357\) −10.2743 10.2743i −0.0287796 0.0287796i
\(358\) 82.4024 82.4024i 0.230174 0.230174i
\(359\) 184.468i 0.513837i −0.966433 0.256919i \(-0.917293\pi\)
0.966433 0.256919i \(-0.0827073\pi\)
\(360\) 40.8605 + 11.4203i 0.113501 + 0.0317231i
\(361\) 247.530 0.685678
\(362\) 345.572 + 345.572i 0.954620 + 0.954620i
\(363\) −209.581 + 209.581i −0.577358 + 0.577358i
\(364\) 129.717i 0.356366i
\(365\) 33.2553 118.983i 0.0911103 0.325982i
\(366\) 209.169 0.571499
\(367\) −370.206 370.206i −1.00874 1.00874i −0.999962 0.00877369i \(-0.997207\pi\)
−0.00877369 0.999962i \(-0.502793\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 134.275i 0.363890i
\(370\) 2.89351 + 5.13838i 0.00782029 + 0.0138875i
\(371\) 260.116 0.701121
\(372\) 51.7749 + 51.7749i 0.139180 + 0.139180i
\(373\) 479.170 479.170i 1.28464 1.28464i 0.346638 0.937999i \(-0.387323\pi\)
0.937999 0.346638i \(-0.112677\pi\)
\(374\) 42.0905i 0.112542i
\(375\) −148.081 157.946i −0.394884 0.421189i
\(376\) 236.154 0.628070
\(377\) 156.916 + 156.916i 0.416224 + 0.416224i
\(378\) −25.0324 + 25.0324i −0.0662233 + 0.0662233i
\(379\) 415.235i 1.09561i 0.836607 + 0.547804i \(0.184536\pi\)
−0.836607 + 0.547804i \(0.815464\pi\)
\(380\) −92.8178 + 52.2673i −0.244257 + 0.137545i
\(381\) −94.8780 −0.249024
\(382\) 263.122 + 263.122i 0.688801 + 0.688801i
\(383\) 445.768 445.768i 1.16389 1.16389i 0.180268 0.983617i \(-0.442303\pi\)
0.983617 0.180268i \(-0.0576966\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −396.497 110.819i −1.02986 0.287842i
\(386\) −281.749 −0.729920
\(387\) 149.225 + 149.225i 0.385594 + 0.385594i
\(388\) −168.017 + 168.017i −0.433034 + 0.433034i
\(389\) 274.994i 0.706925i 0.935449 + 0.353462i \(0.114996\pi\)
−0.935449 + 0.353462i \(0.885004\pi\)
\(390\) −44.3847 + 158.803i −0.113807 + 0.407188i
\(391\) 8.35124 0.0213587
\(392\) −51.5836 51.5836i −0.131591 0.131591i
\(393\) −66.0299 + 66.0299i −0.168015 + 0.168015i
\(394\) 170.958i 0.433903i
\(395\) 165.070 + 293.137i 0.417900 + 0.742119i
\(396\) −102.550 −0.258963
\(397\) 23.6184 + 23.6184i 0.0594921 + 0.0594921i 0.736227 0.676735i \(-0.236606\pi\)
−0.676735 + 0.736227i \(0.736606\pi\)
\(398\) 234.435 234.435i 0.589032 0.589032i
\(399\) 88.8837i 0.222766i
\(400\) −51.8487 + 85.5085i −0.129622 + 0.213771i
\(401\) 673.867 1.68047 0.840233 0.542225i \(-0.182418\pi\)
0.840233 + 0.542225i \(0.182418\pi\)
\(402\) 213.540 + 213.540i 0.531194 + 0.531194i
\(403\) −201.222 + 201.222i −0.499310 + 0.499310i
\(404\) 220.532i 0.545871i
\(405\) 39.2106 22.0801i 0.0968162 0.0545188i
\(406\) −112.298 −0.276597
\(407\) −10.0790 10.0790i −0.0247642 0.0247642i
\(408\) 6.03223 6.03223i 0.0147849 0.0147849i
\(409\) 37.4601i 0.0915894i 0.998951 + 0.0457947i \(0.0145820\pi\)
−0.998951 + 0.0457947i \(0.985418\pi\)
\(410\) 304.809 + 85.1925i 0.743435 + 0.207787i
\(411\) 189.791 0.461778
\(412\) 206.726 + 206.726i 0.501761 + 0.501761i
\(413\) 56.2124 56.2124i 0.136107 0.136107i
\(414\) 20.3470i 0.0491473i
\(415\) −16.0113 + 57.2865i −0.0385815 + 0.138040i
\(416\) 76.1590 0.183075
\(417\) 48.3864 + 48.3864i 0.116035 + 0.116035i
\(418\) 182.064 182.064i 0.435559 0.435559i
\(419\) 251.336i 0.599846i −0.953963 0.299923i \(-0.903039\pi\)
0.953963 0.299923i \(-0.0969610\pi\)
\(420\) −40.9421 72.7063i −0.0974812 0.173110i
\(421\) 555.687 1.31992 0.659961 0.751300i \(-0.270573\pi\)
0.659961 + 0.751300i \(0.270573\pi\)
\(422\) 145.969 + 145.969i 0.345897 + 0.345897i
\(423\) 177.116 177.116i 0.418714 0.418714i
\(424\) 152.718i 0.360185i
\(425\) −42.2828 + 10.3615i −0.0994890 + 0.0243801i
\(426\) −44.3090 −0.104012
\(427\) −290.889 290.889i −0.681238 0.681238i
\(428\) 78.3249 78.3249i 0.183002 0.183002i
\(429\) 398.556i 0.929035i
\(430\) −433.422 + 244.067i −1.00796 + 0.567598i
\(431\) −61.4001 −0.142460 −0.0712298 0.997460i \(-0.522692\pi\)
−0.0712298 + 0.997460i \(0.522692\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 449.062 449.062i 1.03709 1.03709i 0.0378095 0.999285i \(-0.487962\pi\)
0.999285 0.0378095i \(-0.0120380\pi\)
\(434\) 144.006i 0.331810i
\(435\) 137.478 + 38.4246i 0.316042 + 0.0883323i
\(436\) 334.903 0.768126
\(437\) 36.1235 + 36.1235i 0.0826625 + 0.0826625i
\(438\) −42.7967 + 42.7967i −0.0977093 + 0.0977093i
\(439\) 522.143i 1.18939i −0.803951 0.594695i \(-0.797273\pi\)
0.803951 0.594695i \(-0.202727\pi\)
\(440\) 65.0637 232.790i 0.147872 0.529068i
\(441\) −77.3754 −0.175454
\(442\) 23.4441 + 23.4441i 0.0530410 + 0.0530410i
\(443\) −170.957 + 170.957i −0.385907 + 0.385907i −0.873225 0.487318i \(-0.837975\pi\)
0.487318 + 0.873225i \(0.337975\pi\)
\(444\) 2.88896i 0.00650667i
\(445\) 109.936 + 195.228i 0.247048 + 0.438716i
\(446\) 455.468 1.02123
\(447\) −152.526 152.526i −0.341221 0.341221i
\(448\) −27.2518 + 27.2518i −0.0608300 + 0.0608300i
\(449\) 129.721i 0.288912i −0.989511 0.144456i \(-0.953857\pi\)
0.989511 0.144456i \(-0.0461432\pi\)
\(450\) 25.2448 + 103.018i 0.0560997 + 0.228929i
\(451\) −764.993 −1.69622
\(452\) −116.796 116.796i −0.258397 0.258397i
\(453\) −122.793 + 122.793i −0.271066 + 0.271066i
\(454\) 127.231i 0.280245i
\(455\) 282.571 159.121i 0.621036 0.349715i
\(456\) 52.1851 0.114441
\(457\) 487.821 + 487.821i 1.06744 + 1.06744i 0.997555 + 0.0698870i \(0.0222639\pi\)
0.0698870 + 0.997555i \(0.477736\pi\)
\(458\) −173.353 + 173.353i −0.378500 + 0.378500i
\(459\) 9.04834i 0.0197132i
\(460\) 46.1882 + 12.9094i 0.100409 + 0.0280639i
\(461\) 10.8881 0.0236185 0.0118093 0.999930i \(-0.496241\pi\)
0.0118093 + 0.999930i \(0.496241\pi\)
\(462\) 142.615 + 142.615i 0.308689 + 0.308689i
\(463\) −400.834 + 400.834i −0.865732 + 0.865732i −0.991997 0.126265i \(-0.959701\pi\)
0.126265 + 0.991997i \(0.459701\pi\)
\(464\) 65.9321i 0.142095i
\(465\) −49.2738 + 176.296i −0.105965 + 0.379130i
\(466\) −257.803 −0.553225
\(467\) 108.014 + 108.014i 0.231293 + 0.231293i 0.813232 0.581939i \(-0.197706\pi\)
−0.581939 + 0.813232i \(0.697706\pi\)
\(468\) 57.1193 57.1193i 0.122050 0.122050i
\(469\) 593.935i 1.26639i
\(470\) 289.684 + 514.431i 0.616350 + 1.09453i
\(471\) −415.070 −0.881252
\(472\) 33.0032 + 33.0032i 0.0699220 + 0.0699220i
\(473\) 850.163 850.163i 1.79739 1.79739i
\(474\) 164.811i 0.347702i
\(475\) −227.714 138.076i −0.479399 0.290687i
\(476\) −16.7779 −0.0352477
\(477\) 114.539 + 114.539i 0.240123 + 0.240123i
\(478\) −198.218 + 198.218i −0.414683 + 0.414683i
\(479\) 517.840i 1.08109i −0.841316 0.540543i \(-0.818219\pi\)
0.841316 0.540543i \(-0.181781\pi\)
\(480\) 42.6871 24.0378i 0.0889314 0.0500787i
\(481\) 11.2279 0.0233428
\(482\) −134.329 134.329i −0.278690 0.278690i
\(483\) −28.2963 + 28.2963i −0.0585846 + 0.0585846i
\(484\) 342.244i 0.707117i
\(485\) −572.105 159.900i −1.17960 0.329692i
\(486\) −22.0454 −0.0453609
\(487\) 389.872 + 389.872i 0.800559 + 0.800559i 0.983183 0.182623i \(-0.0584589\pi\)
−0.182623 + 0.983183i \(0.558459\pi\)
\(488\) 170.786 170.786i 0.349970 0.349970i
\(489\) 307.042i 0.627897i
\(490\) 49.0917 175.644i 0.100187 0.358457i
\(491\) 559.841 1.14021 0.570103 0.821573i \(-0.306903\pi\)
0.570103 + 0.821573i \(0.306903\pi\)
\(492\) −109.635 109.635i −0.222836 0.222836i
\(493\) 20.2959 20.2959i 0.0411682 0.0411682i
\(494\) 202.816i 0.410559i
\(495\) −125.795 223.390i −0.254131 0.451293i
\(496\) 84.5481 0.170460
\(497\) 61.6201 + 61.6201i 0.123984 + 0.123984i
\(498\) 20.6052 20.6052i 0.0413758 0.0413758i
\(499\) 528.700i 1.05952i 0.848148 + 0.529760i \(0.177718\pi\)
−0.848148 + 0.529760i \(0.822282\pi\)
\(500\) −249.870 8.05443i −0.499740 0.0161089i
\(501\) −364.584 −0.727713
\(502\) 85.1879 + 85.1879i 0.169697 + 0.169697i
\(503\) 424.981 424.981i 0.844892 0.844892i −0.144599 0.989490i \(-0.546189\pi\)
0.989490 + 0.144599i \(0.0461891\pi\)
\(504\) 40.8778i 0.0811067i
\(505\) −480.399 + 270.521i −0.951285 + 0.535684i
\(506\) −115.921 −0.229092
\(507\) 15.0108 + 15.0108i 0.0296071 + 0.0296071i
\(508\) −77.4676 + 77.4676i −0.152495 + 0.152495i
\(509\) 273.415i 0.537161i −0.963257 0.268580i \(-0.913445\pi\)
0.963257 0.268580i \(-0.0865545\pi\)
\(510\) 20.5400 + 5.74082i 0.0402744 + 0.0112565i
\(511\) 119.034 0.232943
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 39.1388 39.1388i 0.0762940 0.0762940i
\(514\) 178.347i 0.346979i
\(515\) −196.739 + 703.909i −0.382018 + 1.36681i
\(516\) 243.683 0.472254
\(517\) −1009.06 1009.06i −1.95177 1.95177i
\(518\) −4.01765 + 4.01765i −0.00775607 + 0.00775607i
\(519\) 219.023i 0.422009i
\(520\) 93.4223 + 165.902i 0.179658 + 0.319043i
\(521\) −17.9068 −0.0343701 −0.0171850 0.999852i \(-0.505470\pi\)
−0.0171850 + 0.999852i \(0.505470\pi\)
\(522\) −49.4491 49.4491i −0.0947300 0.0947300i
\(523\) −709.418 + 709.418i −1.35644 + 1.35644i −0.478176 + 0.878264i \(0.658702\pi\)
−0.878264 + 0.478176i \(0.841298\pi\)
\(524\) 107.826i 0.205776i
\(525\) 108.158 178.374i 0.206016 0.339759i
\(526\) −246.417 −0.468473
\(527\) 26.0265 + 26.0265i 0.0493862 + 0.0493862i
\(528\) −83.7313 + 83.7313i −0.158582 + 0.158582i
\(529\) 23.0000i 0.0434783i
\(530\) −332.676 + 187.335i −0.627691 + 0.353463i
\(531\) 49.5048 0.0932294
\(532\) −72.5733 72.5733i −0.136416 0.136416i
\(533\) 426.095 426.095i 0.799428 0.799428i
\(534\) 109.764i 0.205550i
\(535\) 266.699 + 74.5411i 0.498503 + 0.139329i
\(536\) 348.709 0.650577
\(537\) −100.922 100.922i −0.187937 0.187937i
\(538\) −159.070 + 159.070i −0.295670 + 0.295670i
\(539\) 440.823i 0.817853i
\(540\) 13.9870 50.0436i 0.0259018 0.0926734i
\(541\) −755.019 −1.39560 −0.697799 0.716293i \(-0.745837\pi\)
−0.697799 + 0.716293i \(0.745837\pi\)
\(542\) −262.498 262.498i −0.484313 0.484313i
\(543\) 423.238 423.238i 0.779444 0.779444i
\(544\) 9.85059i 0.0181077i
\(545\) 410.816 + 729.540i 0.753791 + 1.33861i
\(546\) −158.870 −0.290971
\(547\) −90.7385 90.7385i −0.165884 0.165884i 0.619283 0.785167i \(-0.287423\pi\)
−0.785167 + 0.619283i \(0.787423\pi\)
\(548\) 154.964 154.964i 0.282780 0.282780i
\(549\) 256.178i 0.466627i
\(550\) 586.913 143.825i 1.06712 0.261500i
\(551\) 175.581 0.318659
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −229.201 + 229.201i −0.414468 + 0.414468i
\(554\) 499.534i 0.901686i
\(555\) 6.29321 3.54381i 0.0113391 0.00638524i
\(556\) 79.0147 0.142113
\(557\) 305.442 + 305.442i 0.548370 + 0.548370i 0.925969 0.377599i \(-0.123250\pi\)
−0.377599 + 0.925969i \(0.623250\pi\)
\(558\) 63.4111 63.4111i 0.113640 0.113640i
\(559\) 947.069i 1.69422i
\(560\) −92.7935 25.9353i −0.165703 0.0463131i
\(561\) −51.5502 −0.0918898
\(562\) −312.983 312.983i −0.556910 0.556910i
\(563\) 357.189 357.189i 0.634438 0.634438i −0.314740 0.949178i \(-0.601917\pi\)
0.949178 + 0.314740i \(0.101917\pi\)
\(564\) 289.229i 0.512817i
\(565\) 111.153 397.693i 0.196732 0.703882i
\(566\) 609.577 1.07699
\(567\) 30.6583 + 30.6583i 0.0540711 + 0.0540711i
\(568\) −36.1782 + 36.1782i −0.0636940 + 0.0636940i
\(569\) 661.718i 1.16295i 0.813565 + 0.581474i \(0.197524\pi\)
−0.813565 + 0.581474i \(0.802476\pi\)
\(570\) 64.0141 + 113.678i 0.112305 + 0.199435i
\(571\) 806.448 1.41234 0.706172 0.708041i \(-0.250421\pi\)
0.706172 + 0.708041i \(0.250421\pi\)
\(572\) −325.420 325.420i −0.568916 0.568916i
\(573\) 322.257 322.257i 0.562404 0.562404i
\(574\) 304.938i 0.531250i
\(575\) 28.5365 + 116.450i 0.0496287 + 0.202522i
\(576\) −24.0000 −0.0416667
\(577\) 308.495 + 308.495i 0.534654 + 0.534654i 0.921954 0.387300i \(-0.126592\pi\)
−0.387300 + 0.921954i \(0.626592\pi\)
\(578\) −285.968 + 285.968i −0.494754 + 0.494754i
\(579\) 345.071i 0.595977i
\(580\) 143.624 80.8772i 0.247628 0.139443i
\(581\) −57.3108 −0.0986416
\(582\) 205.778 + 205.778i 0.353571 + 0.353571i
\(583\) 652.549 652.549i 1.11930 1.11930i
\(584\) 69.8867i 0.119669i
\(585\) 194.493 + 54.3599i 0.332467 + 0.0929230i
\(586\) 684.964 1.16888
\(587\) 266.598 + 266.598i 0.454170 + 0.454170i 0.896736 0.442566i \(-0.145932\pi\)
−0.442566 + 0.896736i \(0.645932\pi\)
\(588\) −63.1767 + 63.1767i −0.107443 + 0.107443i
\(589\) 225.157i 0.382269i
\(590\) −31.4089 + 112.377i −0.0532354 + 0.190470i
\(591\) 209.380 0.354281
\(592\) −2.35883 2.35883i −0.00398450 0.00398450i
\(593\) −167.862 + 167.862i −0.283073 + 0.283073i −0.834333 0.551260i \(-0.814147\pi\)
0.551260 + 0.834333i \(0.314147\pi\)
\(594\) 125.597i 0.211443i
\(595\) −20.5810 36.5484i −0.0345899 0.0614259i
\(596\) −249.074 −0.417909
\(597\) −287.123 287.123i −0.480942 0.480942i
\(598\) 64.5670 64.5670i 0.107972 0.107972i
\(599\) 356.744i 0.595566i 0.954634 + 0.297783i \(0.0962472\pi\)
−0.954634 + 0.297783i \(0.903753\pi\)
\(600\) 104.726 + 63.5015i 0.174544 + 0.105836i
\(601\) −18.7334 −0.0311704 −0.0155852 0.999879i \(-0.504961\pi\)
−0.0155852 + 0.999879i \(0.504961\pi\)
\(602\) −338.888 338.888i −0.562936 0.562936i
\(603\) 261.532 261.532i 0.433718 0.433718i
\(604\) 200.520i 0.331986i
\(605\) −745.533 + 419.822i −1.23229 + 0.693921i
\(606\) 270.095 0.445702
\(607\) 325.300 + 325.300i 0.535914 + 0.535914i 0.922326 0.386412i \(-0.126286\pi\)
−0.386412 + 0.922326i \(0.626286\pi\)
\(608\) 42.6090 42.6090i 0.0700805 0.0700805i
\(609\) 137.537i 0.225840i
\(610\) 581.531 + 162.535i 0.953330 + 0.266451i
\(611\) 1124.08 1.83974
\(612\) −7.38794 7.38794i −0.0120718 0.0120718i
\(613\) −572.991 + 572.991i −0.934733 + 0.934733i −0.997997 0.0632636i \(-0.979849\pi\)
0.0632636 + 0.997997i \(0.479849\pi\)
\(614\) 485.079i 0.790030i
\(615\) 104.339 373.313i 0.169657 0.607013i
\(616\) 232.889 0.378066
\(617\) −136.873 136.873i −0.221836 0.221836i 0.587435 0.809271i \(-0.300138\pi\)
−0.809271 + 0.587435i \(0.800138\pi\)
\(618\) 253.186 253.186i 0.409686 0.409686i
\(619\) 1159.59i 1.87333i 0.350221 + 0.936667i \(0.386106\pi\)
−0.350221 + 0.936667i \(0.613894\pi\)
\(620\) 103.713 + 184.177i 0.167279 + 0.297059i
\(621\) −24.9199 −0.0401286
\(622\) 486.480 + 486.480i 0.782122 + 0.782122i
\(623\) −152.647 + 152.647i −0.245019 + 0.245019i
\(624\) 93.2754i 0.149480i
\(625\) −288.964 554.189i −0.462342 0.886702i
\(626\) −116.406 −0.185953
\(627\) −222.981 222.981i −0.355632 0.355632i
\(628\) −338.903 + 338.903i −0.539655 + 0.539655i
\(629\) 1.45224i 0.00230881i
\(630\) −89.0467 + 50.1436i −0.141344 + 0.0795931i
\(631\) −625.005 −0.990500 −0.495250 0.868751i \(-0.664924\pi\)
−0.495250 + 0.868751i \(0.664924\pi\)
\(632\) −134.568 134.568i −0.212923 0.212923i
\(633\) 178.774 178.774i 0.282424 0.282424i
\(634\) 663.930i 1.04721i
\(635\) −263.780 73.7252i −0.415402 0.116103i
\(636\) 187.041 0.294089
\(637\) −245.535 245.535i −0.385455 0.385455i
\(638\) −281.721 + 281.721i −0.441569 + 0.441569i
\(639\) 54.2673i 0.0849253i
\(640\) 15.2271 54.4806i 0.0237923 0.0851259i
\(641\) −73.3454 −0.114423 −0.0572117 0.998362i \(-0.518221\pi\)
−0.0572117 + 0.998362i \(0.518221\pi\)
\(642\) −95.9280 95.9280i −0.149421 0.149421i
\(643\) −268.941 + 268.941i −0.418260 + 0.418260i −0.884604 0.466343i \(-0.845571\pi\)
0.466343 + 0.884604i \(0.345571\pi\)
\(644\) 46.2077i 0.0717511i
\(645\) 298.920 + 530.831i 0.463441 + 0.822994i
\(646\) 26.2327 0.0406079
\(647\) −529.742 529.742i −0.818767 0.818767i 0.167162 0.985929i \(-0.446540\pi\)
−0.985929 + 0.167162i \(0.946540\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 282.039i 0.434574i
\(650\) −246.797 + 407.015i −0.379687 + 0.626178i
\(651\) −176.370 −0.270922
\(652\) 250.699 + 250.699i 0.384507 + 0.384507i
\(653\) −541.919 + 541.919i −0.829891 + 0.829891i −0.987501 0.157610i \(-0.949621\pi\)
0.157610 + 0.987501i \(0.449621\pi\)
\(654\) 410.170i 0.627172i
\(655\) −234.885 + 132.268i −0.358604 + 0.201936i
\(656\) −179.034 −0.272917
\(657\) 52.4150 + 52.4150i 0.0797793 + 0.0797793i
\(658\) −402.228 + 402.228i −0.611288 + 0.611288i
\(659\) 631.568i 0.958374i 0.877713 + 0.479187i \(0.159068\pi\)
−0.877713 + 0.479187i \(0.840932\pi\)
\(660\) −285.108 79.6864i −0.431982 0.120737i
\(661\) −556.971 −0.842618 −0.421309 0.906917i \(-0.638429\pi\)
−0.421309 + 0.906917i \(0.638429\pi\)
\(662\) −57.4084 57.4084i −0.0867196 0.0867196i
\(663\) 28.7130 28.7130i 0.0433078 0.0433078i
\(664\) 33.6481i 0.0506748i
\(665\) 69.0674 247.115i 0.103861 0.371601i
\(666\) −3.53824 −0.00531267
\(667\) −55.8967 55.8967i −0.0838031 0.0838031i
\(668\) −297.682 + 297.682i −0.445631 + 0.445631i
\(669\) 557.832i 0.833830i
\(670\) 427.752 + 759.616i 0.638436 + 1.13376i
\(671\) −1459.50 −2.17511
\(672\) 33.3765 + 33.3765i 0.0496675 + 0.0496675i
\(673\) −52.4456 + 52.4456i −0.0779280 + 0.0779280i −0.744996 0.667068i \(-0.767549\pi\)
0.667068 + 0.744996i \(0.267549\pi\)
\(674\) 35.1361i 0.0521307i
\(675\) 126.171 30.9185i 0.186920 0.0458052i
\(676\) 24.5125 0.0362611
\(677\) −82.3557 82.3557i −0.121648 0.121648i 0.643662 0.765310i \(-0.277414\pi\)
−0.765310 + 0.643662i \(0.777414\pi\)
\(678\) −143.045 + 143.045i −0.210980 + 0.210980i
\(679\) 572.347i 0.842926i
\(680\) 21.4582 12.0835i 0.0315561 0.0177698i
\(681\) 155.826 0.228819
\(682\) −361.265 361.265i −0.529714 0.529714i
\(683\) 532.493 532.493i 0.779639 0.779639i −0.200131 0.979769i \(-0.564137\pi\)
0.979769 + 0.200131i \(0.0641367\pi\)
\(684\) 63.9134i 0.0934407i
\(685\) 527.657 + 147.478i 0.770302 + 0.215296i
\(686\) 509.553 0.742789
\(687\) 212.313 + 212.313i 0.309044 + 0.309044i
\(688\) 198.967 198.967i 0.289196 0.289196i
\(689\) 726.930i 1.05505i
\(690\) 15.8107 56.5687i 0.0229140 0.0819837i
\(691\) −1042.26 −1.50834 −0.754171 0.656678i \(-0.771961\pi\)
−0.754171 + 0.656678i \(0.771961\pi\)
\(692\) 178.831 + 178.831i 0.258427 + 0.258427i
\(693\) 174.666 174.666i 0.252044 0.252044i
\(694\) 143.092i 0.206184i
\(695\) 96.9252 + 172.123i 0.139461 + 0.247659i
\(696\) −80.7500 −0.116020
\(697\) −55.1121 55.1121i −0.0790705 0.0790705i
\(698\) 21.0922 21.0922i 0.0302180 0.0302180i
\(699\) 315.743i 0.451707i
\(700\) −57.3307 233.952i −0.0819010 0.334218i
\(701\) 910.607 1.29901 0.649506 0.760357i \(-0.274976\pi\)
0.649506 + 0.760357i \(0.274976\pi\)
\(702\) −69.9565 69.9565i −0.0996532 0.0996532i
\(703\) 6.28169 6.28169i 0.00893555 0.00893555i
\(704\) 136.733i 0.194223i
\(705\) 630.046 354.789i 0.893683 0.503247i
\(706\) −535.456 −0.758436
\(707\) −375.619 375.619i −0.531285 0.531285i
\(708\) 40.4205 40.4205i 0.0570911 0.0570911i
\(709\) 1061.58i 1.49729i −0.662970 0.748646i \(-0.730704\pi\)
0.662970 0.748646i \(-0.269296\pi\)
\(710\) −123.188 34.4305i −0.173504 0.0484936i
\(711\) −201.851 −0.283898
\(712\) −89.6216 89.6216i −0.125873 0.125873i
\(713\) 71.6791 71.6791i 0.100532 0.100532i
\(714\) 20.5487i 0.0287796i
\(715\) 309.699 1108.07i 0.433146 1.54974i
\(716\) −164.805 −0.230174
\(717\) 242.767 + 242.767i 0.338587 + 0.338587i
\(718\) −184.468 + 184.468i −0.256919 + 0.256919i
\(719\) 126.651i 0.176149i −0.996114 0.0880745i \(-0.971929\pi\)
0.996114 0.0880745i \(-0.0280714\pi\)
\(720\) −29.4402 52.2808i −0.0408891 0.0726122i
\(721\) −704.207 −0.976708
\(722\) −247.530 247.530i −0.342839 0.342839i
\(723\) −164.518 + 164.518i −0.227550 + 0.227550i
\(724\) 691.145i 0.954620i
\(725\) 352.360 + 213.656i 0.486014 + 0.294698i
\(726\) 419.162 0.577358
\(727\) −629.310 629.310i −0.865626 0.865626i 0.126358 0.991985i \(-0.459671\pi\)
−0.991985 + 0.126358i \(0.959671\pi\)
\(728\) −129.717 + 129.717i −0.178183 + 0.178183i
\(729\) 27.0000i 0.0370370i
\(730\) −152.239 + 85.7281i −0.208546 + 0.117436i
\(731\) 122.496 0.167573
\(732\) −209.169 209.169i −0.285750 0.285750i
\(733\) −618.111 + 618.111i −0.843262 + 0.843262i −0.989282 0.146020i \(-0.953354\pi\)
0.146020 + 0.989282i \(0.453354\pi\)
\(734\) 740.412i 1.00874i
\(735\) −215.119 60.1248i −0.292679 0.0818024i
\(736\) −27.1293 −0.0368605
\(737\) −1490.00 1490.00i −2.02171 2.02171i
\(738\) −134.275 + 134.275i −0.181945 + 0.181945i
\(739\) 736.343i 0.996405i −0.867061 0.498202i \(-0.833994\pi\)
0.867061 0.498202i \(-0.166006\pi\)
\(740\) 2.24487 8.03189i 0.00303361 0.0108539i
\(741\) 248.398 0.335220
\(742\) −260.116 260.116i −0.350560 0.350560i
\(743\) −276.121 + 276.121i −0.371630 + 0.371630i −0.868071 0.496441i \(-0.834640\pi\)
0.496441 + 0.868071i \(0.334640\pi\)
\(744\) 103.550i 0.139180i
\(745\) −305.532 542.573i −0.410110 0.728286i
\(746\) −958.339 −1.28464
\(747\) −25.2361 25.2361i −0.0337832 0.0337832i
\(748\) −42.0905 + 42.0905i −0.0562708 + 0.0562708i
\(749\) 266.812i 0.356224i
\(750\) −9.86462 + 306.027i −0.0131528 + 0.408036i
\(751\) 189.510 0.252343 0.126172 0.992008i \(-0.459731\pi\)
0.126172 + 0.992008i \(0.459731\pi\)
\(752\) −236.154 236.154i −0.314035 0.314035i
\(753\) 104.333 104.333i 0.138557 0.138557i
\(754\) 313.833i 0.416224i
\(755\) −436.805 + 245.972i −0.578550 + 0.325791i
\(756\) 50.0648 0.0662233
\(757\) 12.7982 + 12.7982i 0.0169065 + 0.0169065i 0.715509 0.698603i \(-0.246195\pi\)
−0.698603 + 0.715509i \(0.746195\pi\)
\(758\) 415.235 415.235i 0.547804 0.547804i
\(759\) 141.973i 0.187053i
\(760\) 145.085 + 40.5506i 0.190901 + 0.0533560i
\(761\) −565.864 −0.743579 −0.371790 0.928317i \(-0.621256\pi\)
−0.371790 + 0.928317i \(0.621256\pi\)
\(762\) 94.8780 + 94.8780i 0.124512 + 0.124512i
\(763\) −570.420 + 570.420i −0.747601 + 0.747601i
\(764\) 526.244i 0.688801i
\(765\) 7.03104 25.1562i 0.00919090 0.0328839i
\(766\) −891.537 −1.16389
\(767\) 157.093 + 157.093i 0.204815 + 0.204815i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 973.731i 1.26623i 0.774058 + 0.633115i \(0.218224\pi\)
−0.774058 + 0.633115i \(0.781776\pi\)
\(770\) 285.678 + 507.316i 0.371011 + 0.658852i
\(771\) 218.430 0.283307
\(772\) 281.749 + 281.749i 0.364960 + 0.364960i
\(773\) 554.230 554.230i 0.716986 0.716986i −0.251001 0.967987i \(-0.580760\pi\)
0.967987 + 0.251001i \(0.0807596\pi\)
\(774\) 298.450i 0.385594i
\(775\) −273.982 + 451.849i −0.353525 + 0.583031i
\(776\) 336.034 0.433034
\(777\) 4.92059 + 4.92059i 0.00633281 + 0.00633281i
\(778\) 274.994 274.994i 0.353462 0.353462i
\(779\)