Properties

Label 690.2.j.a.643.3
Level $690$
Weight $2$
Character 690.643
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 643.3
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.a.367.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-0.299475 + 2.21592i) q^{5} -1.00000 q^{6} +(3.52616 + 3.52616i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-0.299475 + 2.21592i) q^{5} -1.00000 q^{6} +(3.52616 + 3.52616i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.35513 - 1.77865i) q^{10} -3.55731i q^{11} +(0.707107 - 0.707107i) q^{12} +(1.85009 + 1.85009i) q^{13} -4.98675 q^{14} +(-1.77865 + 1.35513i) q^{15} -1.00000 q^{16} +(2.03324 + 2.03324i) q^{17} +(-0.707107 - 0.707107i) q^{18} +4.34206 q^{19} +(2.21592 + 0.299475i) q^{20} +4.98675i q^{21} +(2.51540 + 2.51540i) q^{22} +(-4.50903 - 1.63360i) q^{23} +1.00000i q^{24} +(-4.82063 - 1.32723i) q^{25} -2.61642 q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.52616 - 3.52616i) q^{28} -9.31080i q^{29} +(0.299475 - 2.21592i) q^{30} -5.68459 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.51540 - 2.51540i) q^{33} -2.87543 q^{34} +(-8.86970 + 6.75771i) q^{35} +1.00000 q^{36} +(5.97807 + 5.97807i) q^{37} +(-3.07030 + 3.07030i) q^{38} +2.61642i q^{39} +(-1.77865 + 1.35513i) q^{40} -0.173976 q^{41} +(-3.52616 - 3.52616i) q^{42} +(-1.69950 + 1.69950i) q^{43} -3.55731 q^{44} +(-2.21592 - 0.299475i) q^{45} +(4.34350 - 2.03324i) q^{46} +(4.77937 - 4.77937i) q^{47} +(-0.707107 - 0.707107i) q^{48} +17.8676i q^{49} +(4.34719 - 2.47021i) q^{50} +2.87543i q^{51} +(1.85009 - 1.85009i) q^{52} +(-4.53693 + 4.53693i) q^{53} -1.00000i q^{54} +(7.88272 + 1.06532i) q^{55} +4.98675i q^{56} +(3.07030 + 3.07030i) q^{57} +(6.58373 + 6.58373i) q^{58} +8.64060i q^{59} +(1.35513 + 1.77865i) q^{60} -5.58570i q^{61} +(4.01961 - 4.01961i) q^{62} +(-3.52616 + 3.52616i) q^{63} +1.00000i q^{64} +(-4.65372 + 3.54560i) q^{65} +3.55731i q^{66} +(-6.08730 - 6.08730i) q^{67} +(2.03324 - 2.03324i) q^{68} +(-2.03324 - 4.34350i) q^{69} +(1.49340 - 11.0502i) q^{70} -10.0272 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-7.81740 - 7.81740i) q^{73} -8.45427 q^{74} +(-2.47021 - 4.34719i) q^{75} -4.34206i q^{76} +(12.5437 - 12.5437i) q^{77} +(-1.85009 - 1.85009i) q^{78} +14.2774 q^{79} +(0.299475 - 2.21592i) q^{80} -1.00000 q^{81} +(0.123020 - 0.123020i) q^{82} +(-4.22527 + 4.22527i) q^{83} +4.98675 q^{84} +(-5.11440 + 3.89659i) q^{85} -2.40346i q^{86} +(6.58373 - 6.58373i) q^{87} +(2.51540 - 2.51540i) q^{88} -6.69008 q^{89} +(1.77865 - 1.35513i) q^{90} +13.0474i q^{91} +(-1.63360 + 4.50903i) q^{92} +(-4.01961 - 4.01961i) q^{93} +6.75905i q^{94} +(-1.30034 + 9.62167i) q^{95} +1.00000 q^{96} +(-9.17535 - 9.17535i) q^{97} +(-12.6343 - 12.6343i) q^{98} +3.55731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{6} + O(q^{10}) \) \( 24q - 24q^{6} - 24q^{16} - 8q^{23} - 16q^{25} - 16q^{26} + 16q^{31} - 16q^{35} + 24q^{36} - 8q^{46} - 8q^{47} + 24q^{50} + 24q^{55} + 16q^{58} - 56q^{62} - 32q^{70} - 16q^{71} - 48q^{73} - 24q^{81} + 24q^{82} + 16q^{87} - 8q^{92} + 56q^{93} + 24q^{95} + 24q^{96} - 32q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −0.299475 + 2.21592i −0.133929 + 0.990991i
\(6\) −1.00000 −0.408248
\(7\) 3.52616 + 3.52616i 1.33276 + 1.33276i 0.902888 + 0.429877i \(0.141443\pi\)
0.429877 + 0.902888i \(0.358557\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −1.35513 1.77865i −0.428531 0.562460i
\(11\) 3.55731i 1.07257i −0.844037 0.536285i \(-0.819827\pi\)
0.844037 0.536285i \(-0.180173\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 1.85009 + 1.85009i 0.513123 + 0.513123i 0.915482 0.402359i \(-0.131810\pi\)
−0.402359 + 0.915482i \(0.631810\pi\)
\(14\) −4.98675 −1.33276
\(15\) −1.77865 + 1.35513i −0.459247 + 0.349894i
\(16\) −1.00000 −0.250000
\(17\) 2.03324 + 2.03324i 0.493132 + 0.493132i 0.909292 0.416160i \(-0.136624\pi\)
−0.416160 + 0.909292i \(0.636624\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 4.34206 0.996136 0.498068 0.867138i \(-0.334043\pi\)
0.498068 + 0.867138i \(0.334043\pi\)
\(20\) 2.21592 + 0.299475i 0.495495 + 0.0669646i
\(21\) 4.98675i 1.08820i
\(22\) 2.51540 + 2.51540i 0.536285 + 0.536285i
\(23\) −4.50903 1.63360i −0.940198 0.340629i
\(24\) 1.00000i 0.204124i
\(25\) −4.82063 1.32723i −0.964126 0.265445i
\(26\) −2.61642 −0.513123
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 3.52616 3.52616i 0.666382 0.666382i
\(29\) 9.31080i 1.72897i −0.502656 0.864486i \(-0.667644\pi\)
0.502656 0.864486i \(-0.332356\pi\)
\(30\) 0.299475 2.21592i 0.0546763 0.404570i
\(31\) −5.68459 −1.02098 −0.510491 0.859883i \(-0.670536\pi\)
−0.510491 + 0.859883i \(0.670536\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 2.51540 2.51540i 0.437875 0.437875i
\(34\) −2.87543 −0.493132
\(35\) −8.86970 + 6.75771i −1.49925 + 1.14226i
\(36\) 1.00000 0.166667
\(37\) 5.97807 + 5.97807i 0.982789 + 0.982789i 0.999854 0.0170656i \(-0.00543240\pi\)
−0.0170656 + 0.999854i \(0.505432\pi\)
\(38\) −3.07030 + 3.07030i −0.498068 + 0.498068i
\(39\) 2.61642i 0.418963i
\(40\) −1.77865 + 1.35513i −0.281230 + 0.214265i
\(41\) −0.173976 −0.0271705 −0.0135852 0.999908i \(-0.504324\pi\)
−0.0135852 + 0.999908i \(0.504324\pi\)
\(42\) −3.52616 3.52616i −0.544099 0.544099i
\(43\) −1.69950 + 1.69950i −0.259172 + 0.259172i −0.824717 0.565545i \(-0.808666\pi\)
0.565545 + 0.824717i \(0.308666\pi\)
\(44\) −3.55731 −0.536285
\(45\) −2.21592 0.299475i −0.330330 0.0446430i
\(46\) 4.34350 2.03324i 0.640413 0.299784i
\(47\) 4.77937 4.77937i 0.697143 0.697143i −0.266650 0.963793i \(-0.585917\pi\)
0.963793 + 0.266650i \(0.0859168\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 17.8676i 2.55252i
\(50\) 4.34719 2.47021i 0.614786 0.349340i
\(51\) 2.87543i 0.402641i
\(52\) 1.85009 1.85009i 0.256561 0.256561i
\(53\) −4.53693 + 4.53693i −0.623195 + 0.623195i −0.946347 0.323152i \(-0.895257\pi\)
0.323152 + 0.946347i \(0.395257\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 7.88272 + 1.06532i 1.06291 + 0.143648i
\(56\) 4.98675i 0.666382i
\(57\) 3.07030 + 3.07030i 0.406671 + 0.406671i
\(58\) 6.58373 + 6.58373i 0.864486 + 0.864486i
\(59\) 8.64060i 1.12491i 0.826828 + 0.562455i \(0.190143\pi\)
−0.826828 + 0.562455i \(0.809857\pi\)
\(60\) 1.35513 + 1.77865i 0.174947 + 0.229623i
\(61\) 5.58570i 0.715175i −0.933880 0.357588i \(-0.883599\pi\)
0.933880 0.357588i \(-0.116401\pi\)
\(62\) 4.01961 4.01961i 0.510491 0.510491i
\(63\) −3.52616 + 3.52616i −0.444255 + 0.444255i
\(64\) 1.00000i 0.125000i
\(65\) −4.65372 + 3.54560i −0.577222 + 0.439778i
\(66\) 3.55731i 0.437875i
\(67\) −6.08730 6.08730i −0.743682 0.743682i 0.229602 0.973285i \(-0.426257\pi\)
−0.973285 + 0.229602i \(0.926257\pi\)
\(68\) 2.03324 2.03324i 0.246566 0.246566i
\(69\) −2.03324 4.34350i −0.244773 0.522895i
\(70\) 1.49340 11.0502i 0.178496 1.32076i
\(71\) −10.0272 −1.19001 −0.595007 0.803720i \(-0.702851\pi\)
−0.595007 + 0.803720i \(0.702851\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −7.81740 7.81740i −0.914957 0.914957i 0.0816995 0.996657i \(-0.473965\pi\)
−0.996657 + 0.0816995i \(0.973965\pi\)
\(74\) −8.45427 −0.982789
\(75\) −2.47021 4.34719i −0.285235 0.501970i
\(76\) 4.34206i 0.498068i
\(77\) 12.5437 12.5437i 1.42948 1.42948i
\(78\) −1.85009 1.85009i −0.209482 0.209482i
\(79\) 14.2774 1.60633 0.803165 0.595757i \(-0.203148\pi\)
0.803165 + 0.595757i \(0.203148\pi\)
\(80\) 0.299475 2.21592i 0.0334823 0.247748i
\(81\) −1.00000 −0.111111
\(82\) 0.123020 0.123020i 0.0135852 0.0135852i
\(83\) −4.22527 + 4.22527i −0.463784 + 0.463784i −0.899893 0.436110i \(-0.856356\pi\)
0.436110 + 0.899893i \(0.356356\pi\)
\(84\) 4.98675 0.544099
\(85\) −5.11440 + 3.89659i −0.554734 + 0.422645i
\(86\) 2.40346i 0.259172i
\(87\) 6.58373 6.58373i 0.705850 0.705850i
\(88\) 2.51540 2.51540i 0.268142 0.268142i
\(89\) −6.69008 −0.709147 −0.354574 0.935028i \(-0.615374\pi\)
−0.354574 + 0.935028i \(0.615374\pi\)
\(90\) 1.77865 1.35513i 0.187487 0.142844i
\(91\) 13.0474i 1.36774i
\(92\) −1.63360 + 4.50903i −0.170315 + 0.470099i
\(93\) −4.01961 4.01961i −0.416814 0.416814i
\(94\) 6.75905i 0.697143i
\(95\) −1.30034 + 9.62167i −0.133412 + 0.987162i
\(96\) 1.00000 0.102062
\(97\) −9.17535 9.17535i −0.931616 0.931616i 0.0661914 0.997807i \(-0.478915\pi\)
−0.997807 + 0.0661914i \(0.978915\pi\)
\(98\) −12.6343 12.6343i −1.27626 1.27626i
\(99\) 3.55731 0.357523
\(100\) −1.32723 + 4.82063i −0.132723 + 0.482063i
\(101\) 17.0241 1.69396 0.846982 0.531622i \(-0.178417\pi\)
0.846982 + 0.531622i \(0.178417\pi\)
\(102\) −2.03324 2.03324i −0.201320 0.201320i
\(103\) 11.4713 11.4713i 1.13030 1.13030i 0.140170 0.990127i \(-0.455235\pi\)
0.990127 0.140170i \(-0.0447651\pi\)
\(104\) 2.61642i 0.256561i
\(105\) −11.0502 1.49340i −1.07839 0.145741i
\(106\) 6.41619i 0.623195i
\(107\) 2.64136 + 2.64136i 0.255350 + 0.255350i 0.823160 0.567810i \(-0.192209\pi\)
−0.567810 + 0.823160i \(0.692209\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −9.41859 −0.902138 −0.451069 0.892489i \(-0.648957\pi\)
−0.451069 + 0.892489i \(0.648957\pi\)
\(110\) −6.32723 + 4.82063i −0.603277 + 0.459629i
\(111\) 8.45427i 0.802444i
\(112\) −3.52616 3.52616i −0.333191 0.333191i
\(113\) −3.00726 + 3.00726i −0.282899 + 0.282899i −0.834264 0.551365i \(-0.814107\pi\)
0.551365 + 0.834264i \(0.314107\pi\)
\(114\) −4.34206 −0.406671
\(115\) 4.97027 9.50244i 0.463480 0.886107i
\(116\) −9.31080 −0.864486
\(117\) −1.85009 + 1.85009i −0.171041 + 0.171041i
\(118\) −6.10983 6.10983i −0.562455 0.562455i
\(119\) 14.3390i 1.31446i
\(120\) −2.21592 0.299475i −0.202285 0.0273382i
\(121\) −1.65445 −0.150405
\(122\) 3.94968 + 3.94968i 0.357588 + 0.357588i
\(123\) −0.123020 0.123020i −0.0110923 0.0110923i
\(124\) 5.68459i 0.510491i
\(125\) 4.38469 10.2847i 0.392178 0.919889i
\(126\) 4.98675i 0.444255i
\(127\) 10.4069 10.4069i 0.923466 0.923466i −0.0738064 0.997273i \(-0.523515\pi\)
0.997273 + 0.0738064i \(0.0235147\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −2.40346 −0.211613
\(130\) 0.783553 5.79779i 0.0687221 0.508500i
\(131\) 14.0149 1.22449 0.612243 0.790670i \(-0.290267\pi\)
0.612243 + 0.790670i \(0.290267\pi\)
\(132\) −2.51540 2.51540i −0.218937 0.218937i
\(133\) 15.3108 + 15.3108i 1.32762 + 1.32762i
\(134\) 8.60874 0.743682
\(135\) −1.35513 1.77865i −0.116631 0.153082i
\(136\) 2.87543i 0.246566i
\(137\) 5.40475 + 5.40475i 0.461759 + 0.461759i 0.899232 0.437473i \(-0.144126\pi\)
−0.437473 + 0.899232i \(0.644126\pi\)
\(138\) 4.50903 + 1.63360i 0.383834 + 0.139061i
\(139\) 16.9435i 1.43713i −0.695461 0.718564i \(-0.744800\pi\)
0.695461 0.718564i \(-0.255200\pi\)
\(140\) 6.75771 + 8.86970i 0.571131 + 0.749627i
\(141\) 6.75905 0.569215
\(142\) 7.09033 7.09033i 0.595007 0.595007i
\(143\) 6.58135 6.58135i 0.550360 0.550360i
\(144\) 1.00000i 0.0833333i
\(145\) 20.6320 + 2.78835i 1.71340 + 0.231560i
\(146\) 11.0555 0.914957
\(147\) −12.6343 + 12.6343i −1.04206 + 1.04206i
\(148\) 5.97807 5.97807i 0.491394 0.491394i
\(149\) −8.10858 −0.664281 −0.332140 0.943230i \(-0.607771\pi\)
−0.332140 + 0.943230i \(0.607771\pi\)
\(150\) 4.82063 + 1.32723i 0.393603 + 0.108368i
\(151\) −3.25889 −0.265205 −0.132602 0.991169i \(-0.542333\pi\)
−0.132602 + 0.991169i \(0.542333\pi\)
\(152\) 3.07030 + 3.07030i 0.249034 + 0.249034i
\(153\) −2.03324 + 2.03324i −0.164377 + 0.164377i
\(154\) 17.7394i 1.42948i
\(155\) 1.70239 12.5966i 0.136739 1.01178i
\(156\) 2.61642 0.209482
\(157\) 8.12046 + 8.12046i 0.648083 + 0.648083i 0.952530 0.304446i \(-0.0984714\pi\)
−0.304446 + 0.952530i \(0.598471\pi\)
\(158\) −10.0956 + 10.0956i −0.803165 + 0.803165i
\(159\) −6.41619 −0.508837
\(160\) 1.35513 + 1.77865i 0.107133 + 0.140615i
\(161\) −10.1392 21.6599i −0.799083 1.70704i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 1.70018 + 1.70018i 0.133169 + 0.133169i 0.770549 0.637381i \(-0.219982\pi\)
−0.637381 + 0.770549i \(0.719982\pi\)
\(164\) 0.173976i 0.0135852i
\(165\) 4.82063 + 6.32723i 0.375286 + 0.492574i
\(166\) 5.97544i 0.463784i
\(167\) 14.8406 14.8406i 1.14840 1.14840i 0.161537 0.986867i \(-0.448355\pi\)
0.986867 0.161537i \(-0.0516452\pi\)
\(168\) −3.52616 + 3.52616i −0.272049 + 0.272049i
\(169\) 6.15433i 0.473410i
\(170\) 0.861118 6.37173i 0.0660447 0.488689i
\(171\) 4.34206i 0.332045i
\(172\) 1.69950 + 1.69950i 0.129586 + 0.129586i
\(173\) −3.36044 3.36044i −0.255489 0.255489i 0.567727 0.823217i \(-0.307823\pi\)
−0.823217 + 0.567727i \(0.807823\pi\)
\(174\) 9.31080i 0.705850i
\(175\) −12.3183 21.6783i −0.931177 1.63873i
\(176\) 3.55731i 0.268142i
\(177\) −6.10983 + 6.10983i −0.459243 + 0.459243i
\(178\) 4.73060 4.73060i 0.354574 0.354574i
\(179\) 18.3275i 1.36986i 0.728607 + 0.684932i \(0.240168\pi\)
−0.728607 + 0.684932i \(0.759832\pi\)
\(180\) −0.299475 + 2.21592i −0.0223215 + 0.165165i
\(181\) 2.96040i 0.220044i 0.993929 + 0.110022i \(0.0350922\pi\)
−0.993929 + 0.110022i \(0.964908\pi\)
\(182\) −9.22594 9.22594i −0.683872 0.683872i
\(183\) 3.94968 3.94968i 0.291969 0.291969i
\(184\) −2.03324 4.34350i −0.149892 0.320207i
\(185\) −15.0372 + 11.4567i −1.10556 + 0.842311i
\(186\) 5.68459 0.416814
\(187\) 7.23285 7.23285i 0.528918 0.528918i
\(188\) −4.77937 4.77937i −0.348572 0.348572i
\(189\) −4.98675 −0.362732
\(190\) −5.88407 7.72302i −0.426875 0.560287i
\(191\) 15.1230i 1.09426i −0.837048 0.547130i \(-0.815720\pi\)
0.837048 0.547130i \(-0.184280\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) 7.54365 + 7.54365i 0.543004 + 0.543004i 0.924408 0.381404i \(-0.124559\pi\)
−0.381404 + 0.924408i \(0.624559\pi\)
\(194\) 12.9759 0.931616
\(195\) −5.79779 0.783553i −0.415189 0.0561114i
\(196\) 17.8676 1.27626
\(197\) −4.44245 + 4.44245i −0.316511 + 0.316511i −0.847426 0.530914i \(-0.821849\pi\)
0.530914 + 0.847426i \(0.321849\pi\)
\(198\) −2.51540 + 2.51540i −0.178762 + 0.178762i
\(199\) 3.49129 0.247491 0.123745 0.992314i \(-0.460509\pi\)
0.123745 + 0.992314i \(0.460509\pi\)
\(200\) −2.47021 4.34719i −0.174670 0.307393i
\(201\) 8.60874i 0.607214i
\(202\) −12.0379 + 12.0379i −0.846982 + 0.846982i
\(203\) 32.8314 32.8314i 2.30431 2.30431i
\(204\) 2.87543 0.201320
\(205\) 0.0521014 0.385518i 0.00363892 0.0269257i
\(206\) 16.2228i 1.13030i
\(207\) 1.63360 4.50903i 0.113543 0.313399i
\(208\) −1.85009 1.85009i −0.128281 0.128281i
\(209\) 15.4460i 1.06843i
\(210\) 8.86970 6.75771i 0.612068 0.466326i
\(211\) 12.0572 0.830050 0.415025 0.909810i \(-0.363773\pi\)
0.415025 + 0.909810i \(0.363773\pi\)
\(212\) 4.53693 + 4.53693i 0.311597 + 0.311597i
\(213\) −7.09033 7.09033i −0.485821 0.485821i
\(214\) −3.73545 −0.255350
\(215\) −3.25701 4.27492i −0.222126 0.291547i
\(216\) −1.00000 −0.0680414
\(217\) −20.0448 20.0448i −1.36073 1.36073i
\(218\) 6.65995 6.65995i 0.451069 0.451069i
\(219\) 11.0555i 0.747060i
\(220\) 1.06532 7.88272i 0.0718241 0.531453i
\(221\) 7.52334i 0.506075i
\(222\) −5.97807 5.97807i −0.401222 0.401222i
\(223\) −3.58953 3.58953i −0.240373 0.240373i 0.576631 0.817004i \(-0.304367\pi\)
−0.817004 + 0.576631i \(0.804367\pi\)
\(224\) 4.98675 0.333191
\(225\) 1.32723 4.82063i 0.0884817 0.321375i
\(226\) 4.25290i 0.282899i
\(227\) 9.88624 + 9.88624i 0.656173 + 0.656173i 0.954472 0.298300i \(-0.0964195\pi\)
−0.298300 + 0.954472i \(0.596419\pi\)
\(228\) 3.07030 3.07030i 0.203336 0.203336i
\(229\) −8.77187 −0.579661 −0.289831 0.957078i \(-0.593599\pi\)
−0.289831 + 0.957078i \(0.593599\pi\)
\(230\) 3.20473 + 10.2338i 0.211313 + 0.674794i
\(231\) 17.7394 1.16717
\(232\) 6.58373 6.58373i 0.432243 0.432243i
\(233\) −6.20098 6.20098i −0.406239 0.406239i 0.474186 0.880425i \(-0.342743\pi\)
−0.880425 + 0.474186i \(0.842743\pi\)
\(234\) 2.61642i 0.171041i
\(235\) 9.15942 + 12.0220i 0.597495 + 0.784230i
\(236\) 8.64060 0.562455
\(237\) 10.0956 + 10.0956i 0.655781 + 0.655781i
\(238\) −10.1392 10.1392i −0.657229 0.657229i
\(239\) 1.95717i 0.126599i 0.997995 + 0.0632993i \(0.0201623\pi\)
−0.997995 + 0.0632993i \(0.979838\pi\)
\(240\) 1.77865 1.35513i 0.114812 0.0874735i
\(241\) 9.45390i 0.608979i 0.952516 + 0.304490i \(0.0984859\pi\)
−0.952516 + 0.304490i \(0.901514\pi\)
\(242\) 1.16987 1.16987i 0.0752023 0.0752023i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −5.58570 −0.357588
\(245\) −39.5933 5.35091i −2.52953 0.341857i
\(246\) 0.173976 0.0110923
\(247\) 8.03320 + 8.03320i 0.511141 + 0.511141i
\(248\) −4.01961 4.01961i −0.255246 0.255246i
\(249\) −5.97544 −0.378678
\(250\) 4.17192 + 10.3728i 0.263856 + 0.656034i
\(251\) 15.0794i 0.951804i 0.879498 + 0.475902i \(0.157878\pi\)
−0.879498 + 0.475902i \(0.842122\pi\)
\(252\) 3.52616 + 3.52616i 0.222127 + 0.222127i
\(253\) −5.81122 + 16.0400i −0.365348 + 1.00843i
\(254\) 14.7176i 0.923466i
\(255\) −6.37173 0.861118i −0.399013 0.0539253i
\(256\) 1.00000 0.0625000
\(257\) 1.78800 1.78800i 0.111532 0.111532i −0.649138 0.760670i \(-0.724870\pi\)
0.760670 + 0.649138i \(0.224870\pi\)
\(258\) 1.69950 1.69950i 0.105806 0.105806i
\(259\) 42.1593i 2.61965i
\(260\) 3.54560 + 4.65372i 0.219889 + 0.288611i
\(261\) 9.31080 0.576324
\(262\) −9.91002 + 9.91002i −0.612243 + 0.612243i
\(263\) 10.1360 10.1360i 0.625011 0.625011i −0.321798 0.946808i \(-0.604287\pi\)
0.946808 + 0.321798i \(0.104287\pi\)
\(264\) 3.55731 0.218937
\(265\) −8.69479 11.4122i −0.534117 0.701045i
\(266\) −21.6527 −1.32762
\(267\) −4.73060 4.73060i −0.289508 0.289508i
\(268\) −6.08730 + 6.08730i −0.371841 + 0.371841i
\(269\) 4.31486i 0.263082i −0.991311 0.131541i \(-0.958008\pi\)
0.991311 0.131541i \(-0.0419925\pi\)
\(270\) 2.21592 + 0.299475i 0.134857 + 0.0182254i
\(271\) 12.2392 0.743481 0.371741 0.928337i \(-0.378761\pi\)
0.371741 + 0.928337i \(0.378761\pi\)
\(272\) −2.03324 2.03324i −0.123283 0.123283i
\(273\) −9.22594 + 9.22594i −0.558379 + 0.558379i
\(274\) −7.64346 −0.461759
\(275\) −4.72135 + 17.1485i −0.284708 + 1.03409i
\(276\) −4.34350 + 2.03324i −0.261448 + 0.122386i
\(277\) −4.35452 + 4.35452i −0.261638 + 0.261638i −0.825719 0.564081i \(-0.809230\pi\)
0.564081 + 0.825719i \(0.309230\pi\)
\(278\) 11.9809 + 11.9809i 0.718564 + 0.718564i
\(279\) 5.68459i 0.340327i
\(280\) −11.0502 1.49340i −0.660379 0.0892480i
\(281\) 6.75477i 0.402956i −0.979493 0.201478i \(-0.935426\pi\)
0.979493 0.201478i \(-0.0645744\pi\)
\(282\) −4.77937 + 4.77937i −0.284608 + 0.284608i
\(283\) 4.40365 4.40365i 0.261770 0.261770i −0.564003 0.825773i \(-0.690739\pi\)
0.825773 + 0.564003i \(0.190739\pi\)
\(284\) 10.0272i 0.595007i
\(285\) −7.72302 + 5.88407i −0.457472 + 0.348542i
\(286\) 9.30743i 0.550360i
\(287\) −0.613468 0.613468i −0.0362119 0.0362119i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 8.73191i 0.513642i
\(290\) −16.5607 + 12.6174i −0.972478 + 0.740918i
\(291\) 12.9759i 0.760661i
\(292\) −7.81740 + 7.81740i −0.457479 + 0.457479i
\(293\) 3.25957 3.25957i 0.190426 0.190426i −0.605454 0.795880i \(-0.707008\pi\)
0.795880 + 0.605454i \(0.207008\pi\)
\(294\) 17.8676i 1.04206i
\(295\) −19.1469 2.58764i −1.11478 0.150658i
\(296\) 8.45427i 0.491394i
\(297\) 2.51540 + 2.51540i 0.145958 + 0.145958i
\(298\) 5.73363 5.73363i 0.332140 0.332140i
\(299\) −5.31981 11.3644i −0.307652 0.657222i
\(300\) −4.34719 + 2.47021i −0.250985 + 0.142618i
\(301\) −11.9854 −0.690829
\(302\) 2.30439 2.30439i 0.132602 0.132602i
\(303\) 12.0379 + 12.0379i 0.691558 + 0.691558i
\(304\) −4.34206 −0.249034
\(305\) 12.3775 + 1.67277i 0.708732 + 0.0957828i
\(306\) 2.87543i 0.164377i
\(307\) −19.9198 + 19.9198i −1.13689 + 1.13689i −0.147880 + 0.989005i \(0.547245\pi\)
−0.989005 + 0.147880i \(0.952755\pi\)
\(308\) −12.5437 12.5437i −0.714741 0.714741i
\(309\) 16.2228 0.922884
\(310\) 7.70338 + 10.1109i 0.437522 + 0.574262i
\(311\) 6.46953 0.366853 0.183427 0.983033i \(-0.441281\pi\)
0.183427 + 0.983033i \(0.441281\pi\)
\(312\) −1.85009 + 1.85009i −0.104741 + 0.104741i
\(313\) −24.2861 + 24.2861i −1.37273 + 1.37273i −0.516358 + 0.856373i \(0.672712\pi\)
−0.856373 + 0.516358i \(0.827288\pi\)
\(314\) −11.4841 −0.648083
\(315\) −6.75771 8.86970i −0.380754 0.499751i
\(316\) 14.2774i 0.803165i
\(317\) −5.81863 + 5.81863i −0.326807 + 0.326807i −0.851371 0.524564i \(-0.824228\pi\)
0.524564 + 0.851371i \(0.324228\pi\)
\(318\) 4.53693 4.53693i 0.254418 0.254418i
\(319\) −33.1214 −1.85444
\(320\) −2.21592 0.299475i −0.123874 0.0167411i
\(321\) 3.73545i 0.208492i
\(322\) 22.4854 + 8.14635i 1.25306 + 0.453979i
\(323\) 8.82843 + 8.82843i 0.491227 + 0.491227i
\(324\) 1.00000i 0.0555556i
\(325\) −6.46312 11.3741i −0.358509 0.630921i
\(326\) −2.40442 −0.133169
\(327\) −6.65995 6.65995i −0.368296 0.368296i
\(328\) −0.123020 0.123020i −0.00679262 0.00679262i
\(329\) 33.7057 1.85826
\(330\) −7.88272 1.06532i −0.433930 0.0586442i
\(331\) −20.2812 −1.11475 −0.557377 0.830260i \(-0.688192\pi\)
−0.557377 + 0.830260i \(0.688192\pi\)
\(332\) 4.22527 + 4.22527i 0.231892 + 0.231892i
\(333\) −5.97807 + 5.97807i −0.327596 + 0.327596i
\(334\) 20.9878i 1.14840i
\(335\) 15.3120 11.6660i 0.836583 0.637381i
\(336\) 4.98675i 0.272049i
\(337\) 8.75011 + 8.75011i 0.476649 + 0.476649i 0.904058 0.427409i \(-0.140574\pi\)
−0.427409 + 0.904058i \(0.640574\pi\)
\(338\) 4.35177 + 4.35177i 0.236705 + 0.236705i
\(339\) −4.25290 −0.230986
\(340\) 3.89659 + 5.11440i 0.211322 + 0.277367i
\(341\) 20.2218i 1.09507i
\(342\) −3.07030 3.07030i −0.166023 0.166023i
\(343\) −38.3211 + 38.3211i −2.06914 + 2.06914i
\(344\) −2.40346 −0.129586
\(345\) 10.2338 3.20473i 0.550967 0.172537i
\(346\) 4.75237 0.255489
\(347\) 1.58819 1.58819i 0.0852585 0.0852585i −0.663191 0.748450i \(-0.730798\pi\)
0.748450 + 0.663191i \(0.230798\pi\)
\(348\) −6.58373 6.58373i −0.352925 0.352925i
\(349\) 28.4591i 1.52338i −0.647941 0.761691i \(-0.724369\pi\)
0.647941 0.761691i \(-0.275631\pi\)
\(350\) 24.0393 + 6.61854i 1.28495 + 0.353776i
\(351\) −2.61642 −0.139654
\(352\) −2.51540 2.51540i −0.134071 0.134071i
\(353\) −11.0665 11.0665i −0.589010 0.589010i 0.348353 0.937363i \(-0.386741\pi\)
−0.937363 + 0.348353i \(0.886741\pi\)
\(354\) 8.64060i 0.459243i
\(355\) 3.00290 22.2196i 0.159378 1.17929i
\(356\) 6.69008i 0.354574i
\(357\) −10.1392 + 10.1392i −0.536625 + 0.536625i
\(358\) −12.9595 12.9595i −0.684932 0.684932i
\(359\) 14.1671 0.747711 0.373855 0.927487i \(-0.378036\pi\)
0.373855 + 0.927487i \(0.378036\pi\)
\(360\) −1.35513 1.77865i −0.0714218 0.0937433i
\(361\) −0.146530 −0.00771209
\(362\) −2.09332 2.09332i −0.110022 0.110022i
\(363\) −1.16987 1.16987i −0.0614024 0.0614024i
\(364\) 13.0474 0.683872
\(365\) 19.6639 14.9816i 1.02925 0.784175i
\(366\) 5.58570i 0.291969i
\(367\) 4.28331 + 4.28331i 0.223587 + 0.223587i 0.810007 0.586420i \(-0.199463\pi\)
−0.586420 + 0.810007i \(0.699463\pi\)
\(368\) 4.50903 + 1.63360i 0.235049 + 0.0851573i
\(369\) 0.173976i 0.00905683i
\(370\) 2.53184 18.7340i 0.131624 0.973935i
\(371\) −31.9959 −1.66114
\(372\) −4.01961 + 4.01961i −0.208407 + 0.208407i
\(373\) −15.9027 + 15.9027i −0.823410 + 0.823410i −0.986595 0.163185i \(-0.947823\pi\)
0.163185 + 0.986595i \(0.447823\pi\)
\(374\) 10.2288i 0.528918i
\(375\) 10.3728 4.17192i 0.535649 0.215437i
\(376\) 6.75905 0.348572
\(377\) 17.2258 17.2258i 0.887176 0.887176i
\(378\) 3.52616 3.52616i 0.181366 0.181366i
\(379\) 26.3876 1.35544 0.677721 0.735319i \(-0.262968\pi\)
0.677721 + 0.735319i \(0.262968\pi\)
\(380\) 9.62167 + 1.30034i 0.493581 + 0.0667058i
\(381\) 14.7176 0.754007
\(382\) 10.6936 + 10.6936i 0.547130 + 0.547130i
\(383\) 15.7267 15.7267i 0.803599 0.803599i −0.180057 0.983656i \(-0.557628\pi\)
0.983656 + 0.180057i \(0.0576282\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 24.0393 + 31.5523i 1.22515 + 1.60805i
\(386\) −10.6683 −0.543004
\(387\) −1.69950 1.69950i −0.0863906 0.0863906i
\(388\) −9.17535 + 9.17535i −0.465808 + 0.465808i
\(389\) −30.2903 −1.53578 −0.767889 0.640583i \(-0.778693\pi\)
−0.767889 + 0.640583i \(0.778693\pi\)
\(390\) 4.65372 3.54560i 0.235650 0.179539i
\(391\) −5.84642 12.4894i −0.295666 0.631617i
\(392\) −12.6343 + 12.6343i −0.638130 + 0.638130i
\(393\) 9.91002 + 9.91002i 0.499894 + 0.499894i
\(394\) 6.28257i 0.316511i
\(395\) −4.27571 + 31.6376i −0.215134 + 1.59186i
\(396\) 3.55731i 0.178762i
\(397\) −22.4983 + 22.4983i −1.12916 + 1.12916i −0.138846 + 0.990314i \(0.544339\pi\)
−0.990314 + 0.138846i \(0.955661\pi\)
\(398\) −2.46871 + 2.46871i −0.123745 + 0.123745i
\(399\) 21.6527i 1.08399i
\(400\) 4.82063 + 1.32723i 0.241031 + 0.0663613i
\(401\) 16.3195i 0.814959i 0.913214 + 0.407479i \(0.133592\pi\)
−0.913214 + 0.407479i \(0.866408\pi\)
\(402\) 6.08730 + 6.08730i 0.303607 + 0.303607i
\(403\) −10.5170 10.5170i −0.523889 0.523889i
\(404\) 17.0241i 0.846982i
\(405\) 0.299475 2.21592i 0.0148810 0.110110i
\(406\) 46.4306i 2.30431i
\(407\) 21.2658 21.2658i 1.05411 1.05411i
\(408\) −2.03324 + 2.03324i −0.100660 + 0.100660i
\(409\) 37.8176i 1.86996i −0.354699 0.934981i \(-0.615417\pi\)
0.354699 0.934981i \(-0.384583\pi\)
\(410\) 0.235761 + 0.309443i 0.0116434 + 0.0152823i
\(411\) 7.64346i 0.377024i
\(412\) −11.4713 11.4713i −0.565149 0.565149i
\(413\) −30.4682 + 30.4682i −1.49924 + 1.49924i
\(414\) 2.03324 + 4.34350i 0.0999281 + 0.213471i
\(415\) −8.09751 10.6282i −0.397491 0.521720i
\(416\) 2.61642 0.128281
\(417\) 11.9809 11.9809i 0.586705 0.586705i
\(418\) 10.9220 + 10.9220i 0.534213 + 0.534213i
\(419\) −39.5086 −1.93012 −0.965060 0.262030i \(-0.915608\pi\)
−0.965060 + 0.262030i \(0.915608\pi\)
\(420\) −1.49340 + 11.0502i −0.0728707 + 0.539197i
\(421\) 19.9633i 0.972951i −0.873694 0.486476i \(-0.838282\pi\)
0.873694 0.486476i \(-0.161718\pi\)
\(422\) −8.52571 + 8.52571i −0.415025 + 0.415025i
\(423\) 4.77937 + 4.77937i 0.232381 + 0.232381i
\(424\) −6.41619 −0.311597
\(425\) −7.10291 12.5000i −0.344542 0.606341i
\(426\) 10.0272 0.485821
\(427\) 19.6961 19.6961i 0.953160 0.953160i
\(428\) 2.64136 2.64136i 0.127675 0.127675i
\(429\) 9.30743 0.449367
\(430\) 5.32588 + 0.719775i 0.256837 + 0.0347106i
\(431\) 4.31840i 0.208010i −0.994577 0.104005i \(-0.966834\pi\)
0.994577 0.104005i \(-0.0331658\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 11.0514 11.0514i 0.531096 0.531096i −0.389802 0.920899i \(-0.627457\pi\)
0.920899 + 0.389802i \(0.127457\pi\)
\(434\) 28.3476 1.36073
\(435\) 12.6174 + 16.5607i 0.604957 + 0.794025i
\(436\) 9.41859i 0.451069i
\(437\) −19.5785 7.09319i −0.936565 0.339313i
\(438\) 7.81740 + 7.81740i 0.373530 + 0.373530i
\(439\) 6.07173i 0.289788i 0.989447 + 0.144894i \(0.0462841\pi\)
−0.989447 + 0.144894i \(0.953716\pi\)
\(440\) 4.82063 + 6.32723i 0.229815 + 0.301639i
\(441\) −17.8676 −0.850840
\(442\) −5.31981 5.31981i −0.253037 0.253037i
\(443\) 20.9363 + 20.9363i 0.994714 + 0.994714i 0.999986 0.00527186i \(-0.00167809\pi\)
−0.00527186 + 0.999986i \(0.501678\pi\)
\(444\) 8.45427 0.401222
\(445\) 2.00351 14.8247i 0.0949755 0.702758i
\(446\) 5.07637 0.240373
\(447\) −5.73363 5.73363i −0.271191 0.271191i
\(448\) −3.52616 + 3.52616i −0.166596 + 0.166596i
\(449\) 40.0456i 1.88987i 0.327260 + 0.944934i \(0.393875\pi\)
−0.327260 + 0.944934i \(0.606125\pi\)
\(450\) 2.47021 + 4.34719i 0.116447 + 0.204929i
\(451\) 0.618887i 0.0291422i
\(452\) 3.00726 + 3.00726i 0.141449 + 0.141449i
\(453\) −2.30439 2.30439i −0.108269 0.108269i
\(454\) −13.9813 −0.656173
\(455\) −28.9121 3.90738i −1.35542 0.183181i
\(456\) 4.34206i 0.203336i
\(457\) −1.02292 1.02292i −0.0478501 0.0478501i 0.682777 0.730627i \(-0.260772\pi\)
−0.730627 + 0.682777i \(0.760772\pi\)
\(458\) 6.20265 6.20265i 0.289831 0.289831i
\(459\) −2.87543 −0.134214
\(460\) −9.50244 4.97027i −0.443054 0.231740i
\(461\) −12.4686 −0.580721 −0.290360 0.956917i \(-0.593775\pi\)
−0.290360 + 0.956917i \(0.593775\pi\)
\(462\) −12.5437 + 12.5437i −0.583584 + 0.583584i
\(463\) 10.3193 + 10.3193i 0.479577 + 0.479577i 0.904996 0.425419i \(-0.139873\pi\)
−0.425419 + 0.904996i \(0.639873\pi\)
\(464\) 9.31080i 0.432243i
\(465\) 10.1109 7.70338i 0.468883 0.357236i
\(466\) 8.76950 0.406239
\(467\) 17.3361 + 17.3361i 0.802218 + 0.802218i 0.983442 0.181224i \(-0.0580060\pi\)
−0.181224 + 0.983442i \(0.558006\pi\)
\(468\) 1.85009 + 1.85009i 0.0855205 + 0.0855205i
\(469\) 42.9296i 1.98231i
\(470\) −14.9775 2.02417i −0.690863 0.0933678i
\(471\) 11.4841i 0.529158i
\(472\) −6.10983 + 6.10983i −0.281228 + 0.281228i
\(473\) 6.04566 + 6.04566i 0.277980 + 0.277980i
\(474\) −14.2774 −0.655781
\(475\) −20.9315 5.76289i −0.960401 0.264420i
\(476\) 14.3390 0.657229
\(477\) −4.53693 4.53693i −0.207732 0.207732i
\(478\) −1.38393 1.38393i −0.0632993 0.0632993i
\(479\) 26.2470 1.19926 0.599629 0.800278i \(-0.295315\pi\)
0.599629 + 0.800278i \(0.295315\pi\)
\(480\) −0.299475 + 2.21592i −0.0136691 + 0.101143i
\(481\) 22.1200i 1.00858i
\(482\) −6.68492 6.68492i −0.304490 0.304490i
\(483\) 8.14635 22.4854i 0.370672 1.02312i
\(484\) 1.65445i 0.0752023i
\(485\) 23.0797 17.5841i 1.04799 0.798452i
\(486\) 1.00000 0.0453609
\(487\) 1.23197 1.23197i 0.0558260 0.0558260i −0.678643 0.734469i \(-0.737431\pi\)
0.734469 + 0.678643i \(0.237431\pi\)
\(488\) 3.94968 3.94968i 0.178794 0.178794i
\(489\) 2.40442i 0.108732i
\(490\) 31.7804 24.2131i 1.43569 1.09383i
\(491\) 0.214208 0.00966705 0.00483353 0.999988i \(-0.498461\pi\)
0.00483353 + 0.999988i \(0.498461\pi\)
\(492\) −0.123020 + 0.123020i −0.00554615 + 0.00554615i
\(493\) 18.9311 18.9311i 0.852612 0.852612i
\(494\) −11.3607 −0.511141
\(495\) −1.06532 + 7.88272i −0.0478828 + 0.354302i
\(496\) 5.68459 0.255246
\(497\) −35.3577 35.3577i −1.58601 1.58601i
\(498\) 4.22527 4.22527i 0.189339 0.189339i
\(499\) 2.91098i 0.130313i −0.997875 0.0651566i \(-0.979245\pi\)
0.997875 0.0651566i \(-0.0207547\pi\)
\(500\) −10.2847 4.38469i −0.459945 0.196089i
\(501\) 20.9878 0.937668
\(502\) −10.6628 10.6628i −0.475902 0.475902i
\(503\) −11.2871 + 11.2871i −0.503266 + 0.503266i −0.912451 0.409185i \(-0.865813\pi\)
0.409185 + 0.912451i \(0.365813\pi\)
\(504\) −4.98675 −0.222127
\(505\) −5.09829 + 37.7242i −0.226871 + 1.67870i
\(506\) −7.23285 15.4512i −0.321539 0.686888i
\(507\) 4.35177 4.35177i 0.193269 0.193269i
\(508\) −10.4069 10.4069i −0.461733 0.461733i
\(509\) 0.259394i 0.0114974i 0.999983 + 0.00574871i \(0.00182988\pi\)
−0.999983 + 0.00574871i \(0.998170\pi\)
\(510\) 5.11440 3.89659i 0.226469 0.172544i
\(511\) 55.1309i 2.43885i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −3.07030 + 3.07030i −0.135557 + 0.135557i
\(514\) 2.52861i 0.111532i
\(515\) 21.9841 + 28.8548i 0.968735 + 1.27149i
\(516\) 2.40346i 0.105806i
\(517\) −17.0017 17.0017i −0.747734 0.747734i
\(518\) −29.8111 29.8111i −1.30983 1.30983i
\(519\) 4.75237i 0.208606i
\(520\) −5.79779 0.783553i −0.254250 0.0343611i
\(521\) 19.5054i 0.854545i 0.904123 + 0.427273i \(0.140526\pi\)
−0.904123 + 0.427273i \(0.859474\pi\)
\(522\) −6.58373 + 6.58373i −0.288162 + 0.288162i
\(523\) −7.38191 + 7.38191i −0.322788 + 0.322788i −0.849836 0.527047i \(-0.823299\pi\)
0.527047 + 0.849836i \(0.323299\pi\)
\(524\) 14.0149i 0.612243i
\(525\) 6.61854 24.0393i 0.288857 1.04916i
\(526\) 14.3344i 0.625011i
\(527\) −11.5581 11.5581i −0.503479 0.503479i
\(528\) −2.51540 + 2.51540i −0.109469 + 0.109469i
\(529\) 17.6627 + 14.7319i 0.767943 + 0.640518i
\(530\) 14.2178 + 1.92148i 0.617581 + 0.0834640i
\(531\) −8.64060 −0.374970
\(532\) 15.3108 15.3108i 0.663808 0.663808i
\(533\) −0.321872 0.321872i −0.0139418 0.0139418i
\(534\) 6.69008 0.289508
\(535\) −6.64407 + 5.06203i −0.287248 + 0.218851i
\(536\) 8.60874i 0.371841i
\(537\) −12.9595 + 12.9595i −0.559245 + 0.559245i
\(538\) 3.05107 + 3.05107i 0.131541 + 0.131541i
\(539\) 63.5608 2.73776
\(540\) −1.77865 + 1.35513i −0.0765411 + 0.0583157i
\(541\) −30.9021 −1.32858 −0.664292 0.747473i \(-0.731267\pi\)
−0.664292 + 0.747473i \(0.731267\pi\)
\(542\) −8.65445 + 8.65445i −0.371741 + 0.371741i
\(543\) −2.09332 + 2.09332i −0.0898328 + 0.0898328i
\(544\) 2.87543 0.123283
\(545\) 2.82063 20.8709i 0.120823 0.894010i
\(546\) 13.0474i 0.558379i
\(547\) 10.8020 10.8020i 0.461862 0.461862i −0.437403 0.899265i \(-0.644102\pi\)
0.899265 + 0.437403i \(0.144102\pi\)
\(548\) 5.40475 5.40475i 0.230879 0.230879i
\(549\) 5.58570 0.238392
\(550\) −8.78730 15.4643i −0.374692 0.659400i
\(551\) 40.4281i 1.72229i
\(552\) 1.63360 4.50903i 0.0695307 0.191917i
\(553\) 50.3443 + 50.3443i 2.14086 + 2.14086i
\(554\) 6.15822i 0.261638i
\(555\) −18.7340 2.53184i −0.795214 0.107471i
\(556\) −16.9435 −0.718564
\(557\) 15.6411 + 15.6411i 0.662733 + 0.662733i 0.956023 0.293291i \(-0.0947503\pi\)
−0.293291 + 0.956023i \(0.594750\pi\)
\(558\) 4.01961 + 4.01961i 0.170164 + 0.170164i
\(559\) −6.28847 −0.265974
\(560\) 8.86970 6.75771i 0.374813 0.285565i
\(561\) 10.2288 0.431860
\(562\) 4.77634 + 4.77634i 0.201478 + 0.201478i
\(563\) −7.40726 + 7.40726i −0.312179 + 0.312179i −0.845753 0.533574i \(-0.820848\pi\)
0.533574 + 0.845753i \(0.320848\pi\)
\(564\) 6.75905i 0.284608i
\(565\) −5.76325 7.56445i −0.242462 0.318239i
\(566\) 6.22770i 0.261770i
\(567\) −3.52616 3.52616i −0.148085 0.148085i
\(568\) −7.09033 7.09033i −0.297504 0.297504i
\(569\) −11.9076 −0.499194 −0.249597 0.968350i \(-0.580298\pi\)
−0.249597 + 0.968350i \(0.580298\pi\)
\(570\) 1.30034 9.62167i 0.0544651 0.403007i
\(571\) 22.4163i 0.938092i 0.883174 + 0.469046i \(0.155402\pi\)
−0.883174 + 0.469046i \(0.844598\pi\)
\(572\) −6.58135 6.58135i −0.275180 0.275180i
\(573\) 10.6936 10.6936i 0.446730 0.446730i
\(574\) 0.867575 0.0362119
\(575\) 19.5682 + 13.8595i 0.816051 + 0.577980i
\(576\) −1.00000 −0.0416667
\(577\) 4.75499 4.75499i 0.197953 0.197953i −0.601169 0.799122i \(-0.705298\pi\)
0.799122 + 0.601169i \(0.205298\pi\)
\(578\) 6.17439 + 6.17439i 0.256821 + 0.256821i
\(579\) 10.6683i 0.443361i
\(580\) 2.78835 20.6320i 0.115780 0.856698i
\(581\) −29.7980 −1.23623
\(582\) 9.17535 + 9.17535i 0.380330 + 0.380330i
\(583\) 16.1393 + 16.1393i 0.668420 + 0.668420i
\(584\) 11.0555i 0.457479i
\(585\) −3.54560 4.65372i −0.146593 0.192407i
\(586\) 4.60973i 0.190426i
\(587\) 13.8586 13.8586i 0.572004 0.572004i −0.360684 0.932688i \(-0.617457\pi\)
0.932688 + 0.360684i \(0.117457\pi\)
\(588\) 12.6343 + 12.6343i 0.521031 + 0.521031i
\(589\) −24.6828 −1.01704
\(590\) 15.3686 11.7092i 0.632717 0.482059i
\(591\) −6.28257 −0.258430
\(592\) −5.97807 5.97807i −0.245697 0.245697i
\(593\) 2.48988 + 2.48988i 0.102247 + 0.102247i 0.756380 0.654133i \(-0.226966\pi\)
−0.654133 + 0.756380i \(0.726966\pi\)
\(594\) −3.55731 −0.145958
\(595\) −31.7742 4.29418i −1.30262 0.176044i
\(596\) 8.10858i 0.332140i
\(597\) 2.46871 + 2.46871i 0.101038 + 0.101038i
\(598\) 11.7975 + 4.27419i 0.482437 + 0.174785i
\(599\) 18.3558i 0.749997i −0.927025 0.374999i \(-0.877643\pi\)
0.927025 0.374999i \(-0.122357\pi\)
\(600\) 1.32723 4.82063i 0.0541838 0.196801i
\(601\) −11.3916 −0.464672 −0.232336 0.972636i \(-0.574637\pi\)
−0.232336 + 0.972636i \(0.574637\pi\)
\(602\) 8.47499 8.47499i 0.345415 0.345415i
\(603\) 6.08730 6.08730i 0.247894 0.247894i
\(604\) 3.25889i 0.132602i
\(605\) 0.495466 3.66614i 0.0201436 0.149050i
\(606\) −17.0241 −0.691558
\(607\) −22.8486 + 22.8486i −0.927398 + 0.927398i −0.997537 0.0701391i \(-0.977656\pi\)
0.0701391 + 0.997537i \(0.477656\pi\)
\(608\) 3.07030 3.07030i 0.124517 0.124517i
\(609\) 46.4306 1.88146
\(610\) −9.93503 + 7.56937i −0.402257 + 0.306475i
\(611\) 17.6846 0.715440
\(612\) 2.03324 + 2.03324i 0.0821887 + 0.0821887i
\(613\) 16.6871 16.6871i 0.673985 0.673985i −0.284647 0.958632i \(-0.591876\pi\)
0.958632 + 0.284647i \(0.0918765\pi\)
\(614\) 28.1709i 1.13689i
\(615\) 0.309443 0.235761i 0.0124780 0.00950679i
\(616\) 17.7394 0.714741
\(617\) −3.52666 3.52666i −0.141978 0.141978i 0.632545 0.774523i \(-0.282010\pi\)
−0.774523 + 0.632545i \(0.782010\pi\)
\(618\) −11.4713 + 11.4713i −0.461442 + 0.461442i
\(619\) 13.6535 0.548781 0.274390 0.961618i \(-0.411524\pi\)
0.274390 + 0.961618i \(0.411524\pi\)
\(620\) −12.5966 1.70239i −0.505892 0.0683696i
\(621\) 4.34350 2.03324i 0.174298 0.0815909i
\(622\) −4.57465 + 4.57465i −0.183427 + 0.183427i
\(623\) −23.5903 23.5903i −0.945126 0.945126i
\(624\) 2.61642i 0.104741i
\(625\) 21.4769 + 12.7961i 0.859078 + 0.511845i
\(626\) 34.3457i 1.37273i
\(627\) 10.9220 10.9220i 0.436183 0.436183i
\(628\) 8.12046 8.12046i 0.324042 0.324042i
\(629\) 24.3097i 0.969289i
\(630\) 11.0502 + 1.49340i 0.440252 + 0.0594987i
\(631\) 3.15280i 0.125511i −0.998029 0.0627555i \(-0.980011\pi\)
0.998029 0.0627555i \(-0.0199888\pi\)
\(632\) 10.0956 + 10.0956i 0.401582 + 0.401582i
\(633\) 8.52571 + 8.52571i 0.338866 + 0.338866i
\(634\) 8.22879i 0.326807i
\(635\) 19.9444 + 26.1776i 0.791468 + 1.03883i
\(636\) 6.41619i 0.254418i
\(637\) −33.0568 + 33.0568i −1.30976 + 1.30976i
\(638\) 23.4204 23.4204i 0.927222 0.927222i
\(639\) 10.0272i 0.396671i
\(640\) 1.77865 1.35513i 0.0703075 0.0535664i
\(641\) 47.5668i 1.87878i −0.342857 0.939388i \(-0.611395\pi\)
0.342857 0.939388i \(-0.388605\pi\)
\(642\) −2.64136 2.64136i −0.104246 0.104246i
\(643\) −0.429808 + 0.429808i −0.0169500 + 0.0169500i −0.715531 0.698581i \(-0.753815\pi\)
0.698581 + 0.715531i \(0.253815\pi\)
\(644\) −21.6599 + 10.1392i −0.853520 + 0.399542i
\(645\) 0.719775 5.32588i 0.0283411 0.209706i
\(646\) −12.4853 −0.491227
\(647\) 27.5034 27.5034i 1.08127 1.08127i 0.0848805 0.996391i \(-0.472949\pi\)
0.996391 0.0848805i \(-0.0270509\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) 30.7373 1.20654
\(650\) 12.6128 + 3.47258i 0.494715 + 0.136206i
\(651\) 28.3476i 1.11103i
\(652\) 1.70018 1.70018i 0.0665843 0.0665843i
\(653\) −24.3356 24.3356i −0.952327 0.952327i 0.0465870 0.998914i \(-0.485166\pi\)
−0.998914 + 0.0465870i \(0.985166\pi\)
\(654\) 9.41859 0.368296
\(655\) −4.19710 + 31.0559i −0.163994 + 1.21345i
\(656\) 0.173976 0.00679262
\(657\) 7.81740 7.81740i 0.304986 0.304986i
\(658\) −23.8335 + 23.8335i −0.929128 + 0.929128i
\(659\) −24.4880 −0.953918 −0.476959 0.878926i \(-0.658261\pi\)
−0.476959 + 0.878926i \(0.658261\pi\)
\(660\) 6.32723 4.82063i 0.246287 0.187643i
\(661\) 5.54696i 0.215752i −0.994164 0.107876i \(-0.965595\pi\)
0.994164 0.107876i \(-0.0344049\pi\)
\(662\) 14.3409 14.3409i 0.557377 0.557377i
\(663\) −5.31981 + 5.31981i −0.206604 + 0.206604i
\(664\) −5.97544 −0.231892
\(665\) −38.5128 + 29.3424i −1.49346 + 1.13785i
\(666\) 8.45427i 0.327596i
\(667\) −15.2101 + 41.9827i −0.588939 + 1.62558i
\(668\) −14.8406 14.8406i −0.574202 0.574202i
\(669\) 5.07637i 0.196264i
\(670\) −2.57810 + 19.0763i −0.0996007 + 0.736982i
\(671\) −19.8701 −0.767075
\(672\) 3.52616 + 3.52616i 0.136025 + 0.136025i
\(673\) 16.5963 + 16.5963i 0.639741 + 0.639741i 0.950491 0.310751i \(-0.100580\pi\)
−0.310751 + 0.950491i \(0.600580\pi\)
\(674\) −12.3745 −0.476649
\(675\) 4.34719 2.47021i 0.167323 0.0950784i
\(676\) −6.15433 −0.236705
\(677\) 9.91246 + 9.91246i 0.380967 + 0.380967i 0.871450 0.490484i \(-0.163180\pi\)
−0.490484 + 0.871450i \(0.663180\pi\)
\(678\) 3.00726 3.00726i 0.115493 0.115493i
\(679\) 64.7075i 2.48325i
\(680\) −6.37173 0.861118i −0.244345 0.0330224i
\(681\) 13.9813i 0.535763i
\(682\) −14.2990 14.2990i −0.547537 0.547537i
\(683\) −21.1411 21.1411i −0.808941 0.808941i 0.175533 0.984474i \(-0.443835\pi\)
−0.984474 + 0.175533i \(0.943835\pi\)
\(684\) 4.34206 0.166023
\(685\) −13.5951 + 10.3579i −0.519441 + 0.395756i
\(686\) 54.1942i 2.06914i
\(687\) −6.20265 6.20265i −0.236646 0.236646i
\(688\) 1.69950 1.69950i 0.0647929 0.0647929i
\(689\) −16.7875 −0.639551
\(690\) −4.97027 + 9.50244i −0.189215 + 0.361752i
\(691\) −5.79799 −0.220566 −0.110283 0.993900i \(-0.535176\pi\)
−0.110283 + 0.993900i \(0.535176\pi\)
\(692\) −3.36044 + 3.36044i −0.127745 + 0.127745i
\(693\) 12.5437 + 12.5437i 0.476494 + 0.476494i
\(694\) 2.24604i 0.0852585i
\(695\) 37.5454 + 5.07414i 1.42418 + 0.192473i
\(696\) 9.31080 0.352925
\(697\) −0.353734 0.353734i −0.0133986 0.0133986i
\(698\) 20.1236 + 20.1236i 0.761691 + 0.761691i
\(699\) 8.76950i 0.331693i
\(700\) −21.6783 + 12.3183i −0.819364 + 0.465588i
\(701\) 8.81493i 0.332935i 0.986047 + 0.166468i \(0.0532361\pi\)
−0.986047 + 0.166468i \(0.946764\pi\)
\(702\) 1.85009 1.85009i 0.0698272 0.0698272i
\(703\) 25.9571 + 25.9571i 0.978992 + 0.978992i
\(704\) 3.55731 0.134071
\(705\) −2.02417 + 14.9775i −0.0762345 + 0.564087i
\(706\) 15.6504 0.589010
\(707\) 60.0298 + 60.0298i 2.25765 + 2.25765i
\(708\) 6.10983 + 6.10983i 0.229621 + 0.229621i
\(709\) 20.7494 0.779260 0.389630 0.920972i \(-0.372603\pi\)
0.389630 + 0.920972i \(0.372603\pi\)
\(710\) 13.5882 + 17.8350i 0.509958 + 0.669335i
\(711\) 14.2774i 0.535443i
\(712\) −4.73060 4.73060i −0.177287 0.177287i
\(713\) 25.6320 + 9.28635i 0.959925 + 0.347776i
\(714\) 14.3390i 0.536625i
\(715\) 12.6128 + 16.5547i 0.471692 + 0.619111i
\(716\) 18.3275 0.684932
\(717\) −1.38393 + 1.38393i −0.0516837 + 0.0516837i
\(718\) −10.0176 + 10.0176i −0.373855 + 0.373855i
\(719\) 10.7490i 0.400869i −0.979707 0.200435i \(-0.935765\pi\)
0.979707 0.200435i \(-0.0642354\pi\)
\(720\) 2.21592 + 0.299475i 0.0825826 + 0.0111608i
\(721\) 80.8991 3.01284
\(722\) 0.103612 0.103612i 0.00385604 0.00385604i
\(723\) −6.68492 + 6.68492i −0.248615 + 0.248615i
\(724\) 2.96040 0.110022
\(725\) −12.3575 + 44.8839i −0.458947 + 1.66695i
\(726\) 1.65445 0.0614024
\(727\) −4.60271 4.60271i −0.170705 0.170705i 0.616584 0.787289i \(-0.288516\pi\)
−0.787289 + 0.616584i \(0.788516\pi\)
\(728\) −9.22594 + 9.22594i −0.341936 + 0.341936i
\(729\) 1.00000i 0.0370370i
\(730\) −3.31083 + 24.4981i −0.122539 + 0.906715i
\(731\) −6.91098 −0.255612
\(732\) −3.94968 3.94968i −0.145985 0.145985i
\(733\) 13.8564 13.8564i 0.511796 0.511796i −0.403280 0.915076i \(-0.632130\pi\)
0.915076 + 0.403280i \(0.132130\pi\)
\(734\) −6.05752 −0.223587
\(735\) −24.2131 31.7804i −0.893112 1.17224i
\(736\) −4.34350 + 2.03324i −0.160103 + 0.0749461i
\(737\) −21.6544 + 21.6544i −0.797650 + 0.797650i
\(738\) 0.123020 + 0.123020i 0.00452842 + 0.00452842i
\(739\) 8.74615i 0.321732i −0.986976 0.160866i \(-0.948571\pi\)
0.986976 0.160866i \(-0.0514288\pi\)
\(740\) 11.4567 + 15.0372i 0.421155 + 0.552779i
\(741\) 11.3607i 0.417344i
\(742\) 22.6245 22.6245i 0.830572 0.830572i
\(743\) 17.1923 17.1923i 0.630725 0.630725i −0.317525 0.948250i \(-0.602852\pi\)
0.948250 + 0.317525i \(0.102852\pi\)
\(744\) 5.68459i 0.208407i
\(745\) 2.42831 17.9680i 0.0889665 0.658296i
\(746\) 22.4898i 0.823410i
\(747\) −4.22527 4.22527i −0.154595 0.154595i
\(748\) −7.23285 7.23285i −0.264459 0.264459i
\(749\) 18.6277i 0.680642i
\(750\) −4.38469 + 10.2847i −0.160106 + 0.375543i
\(751\) 34.8556i 1.27190i −0.771731 0.635950i \(-0.780609\pi\)
0.771731 0.635950i \(-0.219391\pi\)
\(752\) −4.77937 + 4.77937i −0.174286 + 0.174286i
\(753\) −10.6628 + 10.6628i −0.388572 + 0.388572i
\(754\) 24.3610i 0.887176i
\(755\) 0.975956 7.22146i 0.0355187 0.262816i
\(756\) 4.98675i 0.181366i
\(757\) −7.34710 7.34710i −0.267035 0.267035i 0.560869 0.827904i \(-0.310467\pi\)
−0.827904 + 0.560869i \(0.810467\pi\)
\(758\) −18.6589 + 18.6589i −0.677721 + 0.677721i
\(759\) −15.4512 + 7.23285i −0.560842 + 0.262536i
\(760\) −7.72302 + 5.88407i −0.280143 + 0.213438i
\(761\) 29.4084 1.06605 0.533027 0.846098i \(-0.321054\pi\)
0.533027 + 0.846098i \(0.321054\pi\)
\(762\) −10.4069 + 10.4069i −0.377003 + 0.377003i
\(763\) −33.2115 33.2115i −1.20234 1.20234i
\(764\) −15.1230 −0.547130
\(765\) −3.89659 5.11440i −0.140882 0.184911i
\(766\) 22.2410i 0.803599i
\(767\) −15.9859 + 15.9859i −0.577217 + 0.577217i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) −20.2771 −0.731211 −0.365606 0.930770i \(-0.619138\pi\)
−0.365606 + 0.930770i \(0.619138\pi\)
\(770\) −39.3092 5.31250i −1.41660 0.191449i
\(771\) 2.52861 0.0910656
\(772\) 7.54365 7.54365i 0.271502 0.271502i
\(773\) −5.35673 + 5.35673i −0.192668 + 0.192668i −0.796848 0.604180i \(-0.793501\pi\)
0.604180 + 0.796848i \(0.293501\pi\)
\(774\) 2.40346 0.0863906
\(775\) 27.4033 + 7.54473i 0.984355 + 0.271015i
\(776\) 12.9759i 0.465808i
\(777\) −29.8111 + 29.8111i −1.06947 + 1.06947i
\(778\) 21.4185 21.4185i 0.767889 0.767889i
\(779\) −0.755414 −0.0270655
\(780\) −0.783553 + 5.79779i −0.0280557 + 0.207594i