Properties

Label 690.3.k.a.277.10
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
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: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.10
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.92281 + 0.875159i) q^{5} -2.44949 q^{6} +(-4.77467 - 4.77467i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.92281 + 0.875159i) q^{5} -2.44949 q^{6} +(-4.77467 - 4.77467i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-5.79797 - 4.04766i) q^{10} +6.21921 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-0.0977897 + 0.0977897i) q^{13} -9.54934i q^{14} +(4.95735 - 7.10104i) q^{15} -4.00000 q^{16} +(-3.54869 - 3.54869i) q^{17} +(3.00000 - 3.00000i) q^{18} +5.38855i q^{19} +(-1.75032 - 9.84563i) q^{20} +11.6955 q^{21} +(6.21921 + 6.21921i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(23.4682 - 8.61649i) q^{25} -0.195579 q^{26} +(3.67423 + 3.67423i) q^{27} +(9.54934 - 9.54934i) q^{28} -55.0596i q^{29} +(12.0584 - 2.14369i) q^{30} +14.2966 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-7.61695 + 7.61695i) q^{33} -7.09737i q^{34} +(27.6834 + 19.3262i) q^{35} +6.00000 q^{36} +(41.5964 + 41.5964i) q^{37} +(-5.38855 + 5.38855i) q^{38} -0.239535i q^{39} +(8.09531 - 11.5959i) q^{40} +15.3764 q^{41} +(11.6955 + 11.6955i) q^{42} +(40.4973 - 40.4973i) q^{43} +12.4384i q^{44} +(2.62548 + 14.7684i) q^{45} +6.78233 q^{46} +(18.5795 + 18.5795i) q^{47} +(4.89898 - 4.89898i) q^{48} -3.40508i q^{49} +(32.0847 + 14.8517i) q^{50} +8.69247 q^{51} +(-0.195579 - 0.195579i) q^{52} +(-30.0791 + 30.0791i) q^{53} +7.34847i q^{54} +(-30.6160 + 5.44280i) q^{55} +19.0987 q^{56} +(-6.59960 - 6.59960i) q^{57} +(55.0596 - 55.0596i) q^{58} -17.7359i q^{59} +(14.2021 + 9.91469i) q^{60} +104.425 q^{61} +(14.2966 + 14.2966i) q^{62} +(-14.3240 + 14.3240i) q^{63} -8.00000i q^{64} +(0.395819 - 0.566982i) q^{65} -15.2339 q^{66} +(-50.0903 - 50.0903i) q^{67} +(7.09737 - 7.09737i) q^{68} +8.30662i q^{69} +(8.35718 + 47.0096i) q^{70} -39.0537 q^{71} +(6.00000 + 6.00000i) q^{72} +(-39.1111 + 39.1111i) q^{73} +83.1928i q^{74} +(-18.1896 + 39.2955i) q^{75} -10.7771 q^{76} +(-29.6947 - 29.6947i) q^{77} +(0.239535 - 0.239535i) q^{78} -71.7211i q^{79} +(19.6913 - 3.50063i) q^{80} -9.00000 q^{81} +(15.3764 + 15.3764i) q^{82} +(-38.3908 + 38.3908i) q^{83} +23.3910i q^{84} +(20.5752 + 14.3639i) q^{85} +80.9945 q^{86} +(67.4339 + 67.4339i) q^{87} +(-12.4384 + 12.4384i) q^{88} -20.0099i q^{89} +(-12.1430 + 17.3939i) q^{90} +0.933827 q^{91} +(6.78233 + 6.78233i) q^{92} +(-17.5097 + 17.5097i) q^{93} +37.1591i q^{94} +(-4.71583 - 26.5268i) q^{95} +9.79796 q^{96} +(-22.7167 - 22.7167i) q^{97} +(3.40508 - 3.40508i) q^{98} -18.6576i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

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
\(5\) −4.92281 + 0.875159i −0.984563 + 0.175032i
\(6\) −2.44949 −0.408248
\(7\) −4.77467 4.77467i −0.682095 0.682095i 0.278377 0.960472i \(-0.410204\pi\)
−0.960472 + 0.278377i \(0.910204\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −5.79797 4.04766i −0.579797 0.404766i
\(11\) 6.21921 0.565383 0.282692 0.959211i \(-0.408773\pi\)
0.282692 + 0.959211i \(0.408773\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −0.0977897 + 0.0977897i −0.00752229 + 0.00752229i −0.710858 0.703336i \(-0.751693\pi\)
0.703336 + 0.710858i \(0.251693\pi\)
\(14\) 9.54934i 0.682095i
\(15\) 4.95735 7.10104i 0.330490 0.473402i
\(16\) −4.00000 −0.250000
\(17\) −3.54869 3.54869i −0.208746 0.208746i 0.594988 0.803734i \(-0.297157\pi\)
−0.803734 + 0.594988i \(0.797157\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 5.38855i 0.283608i 0.989895 + 0.141804i \(0.0452902\pi\)
−0.989895 + 0.141804i \(0.954710\pi\)
\(20\) −1.75032 9.84563i −0.0875159 0.492281i
\(21\) 11.6955 0.556929
\(22\) 6.21921 + 6.21921i 0.282692 + 0.282692i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 23.4682 8.61649i 0.938728 0.344659i
\(26\) −0.195579 −0.00752229
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 9.54934 9.54934i 0.341048 0.341048i
\(29\) 55.0596i 1.89861i −0.314362 0.949303i \(-0.601791\pi\)
0.314362 0.949303i \(-0.398209\pi\)
\(30\) 12.0584 2.14369i 0.401946 0.0714564i
\(31\) 14.2966 0.461182 0.230591 0.973051i \(-0.425934\pi\)
0.230591 + 0.973051i \(0.425934\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −7.61695 + 7.61695i −0.230817 + 0.230817i
\(34\) 7.09737i 0.208746i
\(35\) 27.6834 + 19.3262i 0.790954 + 0.552177i
\(36\) 6.00000 0.166667
\(37\) 41.5964 + 41.5964i 1.12423 + 1.12423i 0.991099 + 0.133128i \(0.0425022\pi\)
0.133128 + 0.991099i \(0.457498\pi\)
\(38\) −5.38855 + 5.38855i −0.141804 + 0.141804i
\(39\) 0.239535i 0.00614192i
\(40\) 8.09531 11.5959i 0.202383 0.289899i
\(41\) 15.3764 0.375034 0.187517 0.982261i \(-0.439956\pi\)
0.187517 + 0.982261i \(0.439956\pi\)
\(42\) 11.6955 + 11.6955i 0.278464 + 0.278464i
\(43\) 40.4973 40.4973i 0.941797 0.941797i −0.0566003 0.998397i \(-0.518026\pi\)
0.998397 + 0.0566003i \(0.0180261\pi\)
\(44\) 12.4384i 0.282692i
\(45\) 2.62548 + 14.7684i 0.0583439 + 0.328188i
\(46\) 6.78233 0.147442
\(47\) 18.5795 + 18.5795i 0.395309 + 0.395309i 0.876575 0.481266i \(-0.159823\pi\)
−0.481266 + 0.876575i \(0.659823\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 3.40508i 0.0694915i
\(50\) 32.0847 + 14.8517i 0.641694 + 0.297034i
\(51\) 8.69247 0.170441
\(52\) −0.195579 0.195579i −0.00376114 0.00376114i
\(53\) −30.0791 + 30.0791i −0.567530 + 0.567530i −0.931436 0.363906i \(-0.881443\pi\)
0.363906 + 0.931436i \(0.381443\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −30.6160 + 5.44280i −0.556655 + 0.0989600i
\(56\) 19.0987 0.341048
\(57\) −6.59960 6.59960i −0.115782 0.115782i
\(58\) 55.0596 55.0596i 0.949303 0.949303i
\(59\) 17.7359i 0.300609i −0.988640 0.150304i \(-0.951975\pi\)
0.988640 0.150304i \(-0.0480254\pi\)
\(60\) 14.2021 + 9.91469i 0.236701 + 0.165245i
\(61\) 104.425 1.71189 0.855944 0.517068i \(-0.172977\pi\)
0.855944 + 0.517068i \(0.172977\pi\)
\(62\) 14.2966 + 14.2966i 0.230591 + 0.230591i
\(63\) −14.3240 + 14.3240i −0.227365 + 0.227365i
\(64\) 8.00000i 0.125000i
\(65\) 0.395819 0.566982i 0.00608953 0.00872280i
\(66\) −15.2339 −0.230817
\(67\) −50.0903 50.0903i −0.747616 0.747616i 0.226415 0.974031i \(-0.427299\pi\)
−0.974031 + 0.226415i \(0.927299\pi\)
\(68\) 7.09737 7.09737i 0.104373 0.104373i
\(69\) 8.30662i 0.120386i
\(70\) 8.35718 + 47.0096i 0.119388 + 0.671566i
\(71\) −39.0537 −0.550052 −0.275026 0.961437i \(-0.588687\pi\)
−0.275026 + 0.961437i \(0.588687\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −39.1111 + 39.1111i −0.535768 + 0.535768i −0.922283 0.386515i \(-0.873679\pi\)
0.386515 + 0.922283i \(0.373679\pi\)
\(74\) 83.1928i 1.12423i
\(75\) −18.1896 + 39.2955i −0.242527 + 0.523941i
\(76\) −10.7771 −0.141804
\(77\) −29.6947 29.6947i −0.385645 0.385645i
\(78\) 0.239535 0.239535i 0.00307096 0.00307096i
\(79\) 71.7211i 0.907862i −0.891037 0.453931i \(-0.850021\pi\)
0.891037 0.453931i \(-0.149979\pi\)
\(80\) 19.6913 3.50063i 0.246141 0.0437579i
\(81\) −9.00000 −0.111111
\(82\) 15.3764 + 15.3764i 0.187517 + 0.187517i
\(83\) −38.3908 + 38.3908i −0.462540 + 0.462540i −0.899487 0.436947i \(-0.856060\pi\)
0.436947 + 0.899487i \(0.356060\pi\)
\(84\) 23.3910i 0.278464i
\(85\) 20.5752 + 14.3639i 0.242061 + 0.168987i
\(86\) 80.9945 0.941797
\(87\) 67.4339 + 67.4339i 0.775103 + 0.775103i
\(88\) −12.4384 + 12.4384i −0.141346 + 0.141346i
\(89\) 20.0099i 0.224830i −0.993661 0.112415i \(-0.964141\pi\)
0.993661 0.112415i \(-0.0358586\pi\)
\(90\) −12.1430 + 17.3939i −0.134922 + 0.193266i
\(91\) 0.933827 0.0102618
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −17.5097 + 17.5097i −0.188277 + 0.188277i
\(94\) 37.1591i 0.395309i
\(95\) −4.71583 26.5268i −0.0496404 0.279230i
\(96\) 9.79796 0.102062
\(97\) −22.7167 22.7167i −0.234193 0.234193i 0.580247 0.814440i \(-0.302956\pi\)
−0.814440 + 0.580247i \(0.802956\pi\)
\(98\) 3.40508 3.40508i 0.0347458 0.0347458i
\(99\) 18.6576i 0.188461i
\(100\) 17.2330 + 46.9364i 0.172330 + 0.469364i
\(101\) 82.8175 0.819975 0.409988 0.912091i \(-0.365533\pi\)
0.409988 + 0.912091i \(0.365533\pi\)
\(102\) 8.69247 + 8.69247i 0.0852203 + 0.0852203i
\(103\) 104.995 104.995i 1.01937 1.01937i 0.0195589 0.999809i \(-0.493774\pi\)
0.999809 0.0195589i \(-0.00622620\pi\)
\(104\) 0.391159i 0.00376114i
\(105\) −57.5748 + 10.2354i −0.548331 + 0.0974802i
\(106\) −60.1581 −0.567530
\(107\) −121.033 121.033i −1.13115 1.13115i −0.989986 0.141168i \(-0.954914\pi\)
−0.141168 0.989986i \(-0.545086\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 178.570i 1.63826i −0.573610 0.819128i \(-0.694458\pi\)
0.573610 0.819128i \(-0.305542\pi\)
\(110\) −36.0588 25.1732i −0.327808 0.228848i
\(111\) −101.890 −0.917927
\(112\) 19.0987 + 19.0987i 0.170524 + 0.170524i
\(113\) 25.4462 25.4462i 0.225188 0.225188i −0.585491 0.810679i \(-0.699098\pi\)
0.810679 + 0.585491i \(0.199098\pi\)
\(114\) 13.1992i 0.115782i
\(115\) −13.7263 + 19.6619i −0.119359 + 0.170973i
\(116\) 110.119 0.949303
\(117\) 0.293369 + 0.293369i 0.00250743 + 0.00250743i
\(118\) 17.7359 17.7359i 0.150304 0.150304i
\(119\) 33.8876i 0.284770i
\(120\) 4.28738 + 24.1168i 0.0357282 + 0.200973i
\(121\) −82.3214 −0.680342
\(122\) 104.425 + 104.425i 0.855944 + 0.855944i
\(123\) −18.8322 + 18.8322i −0.153107 + 0.153107i
\(124\) 28.5933i 0.230591i
\(125\) −107.989 + 62.9557i −0.863910 + 0.503646i
\(126\) −28.6480 −0.227365
\(127\) 83.0337 + 83.0337i 0.653809 + 0.653809i 0.953908 0.300099i \(-0.0970198\pi\)
−0.300099 + 0.953908i \(0.597020\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 99.1976i 0.768974i
\(130\) 0.962801 0.171163i 0.00740616 0.00131664i
\(131\) 133.089 1.01595 0.507973 0.861373i \(-0.330395\pi\)
0.507973 + 0.861373i \(0.330395\pi\)
\(132\) −15.2339 15.2339i −0.115408 0.115408i
\(133\) 25.7285 25.7285i 0.193448 0.193448i
\(134\) 100.181i 0.747616i
\(135\) −21.3031 14.8720i −0.157801 0.110163i
\(136\) 14.1947 0.104373
\(137\) −185.185 185.185i −1.35172 1.35172i −0.883741 0.467977i \(-0.844983\pi\)
−0.467977 0.883741i \(-0.655017\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 31.5467i 0.226954i −0.993541 0.113477i \(-0.963801\pi\)
0.993541 0.113477i \(-0.0361989\pi\)
\(140\) −38.6524 + 55.3668i −0.276089 + 0.395477i
\(141\) −45.5104 −0.322769
\(142\) −39.0537 39.0537i −0.275026 0.275026i
\(143\) −0.608175 + 0.608175i −0.00425297 + 0.00425297i
\(144\) 12.0000i 0.0833333i
\(145\) 48.1859 + 271.048i 0.332316 + 1.86930i
\(146\) −78.2222 −0.535768
\(147\) 4.17036 + 4.17036i 0.0283698 + 0.0283698i
\(148\) −83.1928 + 83.1928i −0.562113 + 0.562113i
\(149\) 112.726i 0.756550i −0.925693 0.378275i \(-0.876517\pi\)
0.925693 0.378275i \(-0.123483\pi\)
\(150\) −57.4851 + 21.1060i −0.383234 + 0.140707i
\(151\) 185.114 1.22592 0.612961 0.790113i \(-0.289978\pi\)
0.612961 + 0.790113i \(0.289978\pi\)
\(152\) −10.7771 10.7771i −0.0709020 0.0709020i
\(153\) −10.6461 + 10.6461i −0.0695821 + 0.0695821i
\(154\) 59.3894i 0.385645i
\(155\) −70.3796 + 12.5118i −0.454062 + 0.0807214i
\(156\) 0.479070 0.00307096
\(157\) −139.491 139.491i −0.888479 0.888479i 0.105898 0.994377i \(-0.466228\pi\)
−0.994377 + 0.105898i \(0.966228\pi\)
\(158\) 71.7211 71.7211i 0.453931 0.453931i
\(159\) 73.6784i 0.463386i
\(160\) 23.1919 + 16.1906i 0.144949 + 0.101191i
\(161\) −32.3834 −0.201139
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 211.002 211.002i 1.29449 1.29449i 0.362515 0.931978i \(-0.381918\pi\)
0.931978 0.362515i \(-0.118082\pi\)
\(164\) 30.7528i 0.187517i
\(165\) 30.8308 44.1629i 0.186853 0.267654i
\(166\) −76.7817 −0.462540
\(167\) 50.5748 + 50.5748i 0.302843 + 0.302843i 0.842125 0.539282i \(-0.181304\pi\)
−0.539282 + 0.842125i \(0.681304\pi\)
\(168\) −23.3910 + 23.3910i −0.139232 + 0.139232i
\(169\) 168.981i 0.999887i
\(170\) 6.21133 + 34.9390i 0.0365372 + 0.205524i
\(171\) 16.1656 0.0945359
\(172\) 80.9945 + 80.9945i 0.470898 + 0.470898i
\(173\) −194.213 + 194.213i −1.12262 + 1.12262i −0.131271 + 0.991347i \(0.541906\pi\)
−0.991347 + 0.131271i \(0.958094\pi\)
\(174\) 134.868i 0.775103i
\(175\) −153.194 70.9120i −0.875393 0.405211i
\(176\) −24.8769 −0.141346
\(177\) 21.7220 + 21.7220i 0.122723 + 0.122723i
\(178\) 20.0099 20.0099i 0.112415 0.112415i
\(179\) 111.660i 0.623800i −0.950115 0.311900i \(-0.899035\pi\)
0.950115 0.311900i \(-0.100965\pi\)
\(180\) −29.5369 + 5.25095i −0.164094 + 0.0291720i
\(181\) 192.806 1.06523 0.532614 0.846358i \(-0.321210\pi\)
0.532614 + 0.846358i \(0.321210\pi\)
\(182\) 0.933827 + 0.933827i 0.00513092 + 0.00513092i
\(183\) −127.894 + 127.894i −0.698875 + 0.698875i
\(184\) 13.5647i 0.0737210i
\(185\) −241.175 168.368i −1.30365 0.910097i
\(186\) −35.0194 −0.188277
\(187\) −22.0700 22.0700i −0.118022 0.118022i
\(188\) −37.1591 + 37.1591i −0.197655 + 0.197655i
\(189\) 35.0865i 0.185643i
\(190\) 21.8110 31.2427i 0.114795 0.164435i
\(191\) 99.0271 0.518467 0.259233 0.965815i \(-0.416530\pi\)
0.259233 + 0.965815i \(0.416530\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −179.344 + 179.344i −0.929242 + 0.929242i −0.997657 0.0684148i \(-0.978206\pi\)
0.0684148 + 0.997657i \(0.478206\pi\)
\(194\) 45.4334i 0.234193i
\(195\) 0.209631 + 1.17919i 0.00107503 + 0.00604711i
\(196\) 6.81017 0.0347458
\(197\) −62.4550 62.4550i −0.317030 0.317030i 0.530595 0.847625i \(-0.321968\pi\)
−0.847625 + 0.530595i \(0.821968\pi\)
\(198\) 18.6576 18.6576i 0.0942305 0.0942305i
\(199\) 204.645i 1.02837i −0.857680 0.514183i \(-0.828095\pi\)
0.857680 0.514183i \(-0.171905\pi\)
\(200\) −29.7034 + 64.1694i −0.148517 + 0.320847i
\(201\) 122.696 0.610426
\(202\) 82.8175 + 82.8175i 0.409988 + 0.409988i
\(203\) −262.891 + 262.891i −1.29503 + 1.29503i
\(204\) 17.3849i 0.0852203i
\(205\) −75.6951 + 13.4568i −0.369245 + 0.0656428i
\(206\) 209.990 1.01937
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 0.391159 0.391159i 0.00188057 0.00188057i
\(209\) 33.5125i 0.160347i
\(210\) −67.8102 47.3394i −0.322906 0.225426i
\(211\) 7.31007 0.0346449 0.0173224 0.999850i \(-0.494486\pi\)
0.0173224 + 0.999850i \(0.494486\pi\)
\(212\) −60.1581 60.1581i −0.283765 0.283765i
\(213\) 47.8308 47.8308i 0.224558 0.224558i
\(214\) 242.067i 1.13115i
\(215\) −163.919 + 234.802i −0.762414 + 1.09210i
\(216\) −14.6969 −0.0680414
\(217\) −68.2617 68.2617i −0.314570 0.314570i
\(218\) 178.570 178.570i 0.819128 0.819128i
\(219\) 95.8022i 0.437453i
\(220\) −10.8856 61.2321i −0.0494800 0.278328i
\(221\) 0.694050 0.00314050
\(222\) −101.890 101.890i −0.458964 0.458964i
\(223\) 26.6273 26.6273i 0.119405 0.119405i −0.644879 0.764284i \(-0.723092\pi\)
0.764284 + 0.644879i \(0.223092\pi\)
\(224\) 38.1973i 0.170524i
\(225\) −25.8495 70.4046i −0.114886 0.312909i
\(226\) 50.8924 0.225188
\(227\) −114.877 114.877i −0.506068 0.506068i 0.407249 0.913317i \(-0.366488\pi\)
−0.913317 + 0.407249i \(0.866488\pi\)
\(228\) 13.1992 13.1992i 0.0578912 0.0578912i
\(229\) 56.2198i 0.245501i −0.992438 0.122751i \(-0.960828\pi\)
0.992438 0.122751i \(-0.0391715\pi\)
\(230\) −33.3881 + 5.93561i −0.145166 + 0.0258070i
\(231\) 72.7368 0.314878
\(232\) 110.119 + 110.119i 0.474652 + 0.474652i
\(233\) −170.729 + 170.729i −0.732742 + 0.732742i −0.971162 0.238420i \(-0.923371\pi\)
0.238420 + 0.971162i \(0.423371\pi\)
\(234\) 0.586738i 0.00250743i
\(235\) −107.724 75.2036i −0.458399 0.320015i
\(236\) 35.4719 0.150304
\(237\) 87.8401 + 87.8401i 0.370633 + 0.370633i
\(238\) −33.8876 + 33.8876i −0.142385 + 0.142385i
\(239\) 143.495i 0.600397i 0.953877 + 0.300199i \(0.0970530\pi\)
−0.953877 + 0.300199i \(0.902947\pi\)
\(240\) −19.8294 + 28.4041i −0.0826224 + 0.118351i
\(241\) −97.6832 −0.405325 −0.202662 0.979249i \(-0.564959\pi\)
−0.202662 + 0.979249i \(0.564959\pi\)
\(242\) −82.3214 82.3214i −0.340171 0.340171i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 208.850i 0.855944i
\(245\) 2.97999 + 16.7626i 0.0121632 + 0.0684188i
\(246\) −37.6643 −0.153107
\(247\) −0.526945 0.526945i −0.00213338 0.00213338i
\(248\) −28.5933 + 28.5933i −0.115295 + 0.115295i
\(249\) 94.0380i 0.377663i
\(250\) −170.945 45.0330i −0.683778 0.180132i
\(251\) 16.2884 0.0648940 0.0324470 0.999473i \(-0.489670\pi\)
0.0324470 + 0.999473i \(0.489670\pi\)
\(252\) −28.6480 28.6480i −0.113683 0.113683i
\(253\) 21.0904 21.0904i 0.0833612 0.0833612i
\(254\) 166.067i 0.653809i
\(255\) −42.7914 + 7.60729i −0.167809 + 0.0298325i
\(256\) 16.0000 0.0625000
\(257\) 65.4723 + 65.4723i 0.254756 + 0.254756i 0.822917 0.568161i \(-0.192345\pi\)
−0.568161 + 0.822917i \(0.692345\pi\)
\(258\) −99.1976 + 99.1976i −0.384487 + 0.384487i
\(259\) 397.218i 1.53366i
\(260\) 1.13396 + 0.791638i 0.00436140 + 0.00304476i
\(261\) −165.179 −0.632869
\(262\) 133.089 + 133.089i 0.507973 + 0.507973i
\(263\) −116.481 + 116.481i −0.442895 + 0.442895i −0.892984 0.450089i \(-0.851392\pi\)
0.450089 + 0.892984i \(0.351392\pi\)
\(264\) 30.4678i 0.115408i
\(265\) 121.750 174.398i 0.459433 0.658104i
\(266\) 51.4571 0.193448
\(267\) 24.5070 + 24.5070i 0.0917866 + 0.0917866i
\(268\) 100.181 100.181i 0.373808 0.373808i
\(269\) 296.382i 1.10179i 0.834574 + 0.550897i \(0.185714\pi\)
−0.834574 + 0.550897i \(0.814286\pi\)
\(270\) −6.43108 36.1751i −0.0238188 0.133982i
\(271\) 227.220 0.838449 0.419224 0.907883i \(-0.362302\pi\)
0.419224 + 0.907883i \(0.362302\pi\)
\(272\) 14.1947 + 14.1947i 0.0521866 + 0.0521866i
\(273\) −1.14370 + 1.14370i −0.00418938 + 0.00418938i
\(274\) 370.371i 1.35172i
\(275\) 145.954 53.5878i 0.530741 0.194865i
\(276\) −16.6132 −0.0601929
\(277\) 280.325 + 280.325i 1.01200 + 1.01200i 0.999927 + 0.0120768i \(0.00384425\pi\)
0.0120768 + 0.999927i \(0.496156\pi\)
\(278\) 31.5467 31.5467i 0.113477 0.113477i
\(279\) 42.8899i 0.153727i
\(280\) −94.0192 + 16.7144i −0.335783 + 0.0596942i
\(281\) −135.612 −0.482607 −0.241303 0.970450i \(-0.577575\pi\)
−0.241303 + 0.970450i \(0.577575\pi\)
\(282\) −45.5104 45.5104i −0.161384 0.161384i
\(283\) 191.782 191.782i 0.677675 0.677675i −0.281799 0.959474i \(-0.590931\pi\)
0.959474 + 0.281799i \(0.0909310\pi\)
\(284\) 78.1074i 0.275026i
\(285\) 38.2643 + 26.7129i 0.134261 + 0.0937295i
\(286\) −1.21635 −0.00425297
\(287\) −73.4172 73.4172i −0.255809 0.255809i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 263.814i 0.912850i
\(290\) −222.862 + 319.234i −0.768490 + 1.10081i
\(291\) 55.6444 0.191218
\(292\) −78.2222 78.2222i −0.267884 0.267884i
\(293\) 28.7884 28.7884i 0.0982538 0.0982538i −0.656271 0.754525i \(-0.727867\pi\)
0.754525 + 0.656271i \(0.227867\pi\)
\(294\) 8.34072i 0.0283698i
\(295\) 15.5218 + 87.3107i 0.0526161 + 0.295968i
\(296\) −166.386 −0.562113
\(297\) 22.8509 + 22.8509i 0.0769389 + 0.0769389i
\(298\) 112.726 112.726i 0.378275 0.378275i
\(299\) 0.663242i 0.00221820i
\(300\) −78.5911 36.3791i −0.261970 0.121264i
\(301\) −386.722 −1.28479
\(302\) 185.114 + 185.114i 0.612961 + 0.612961i
\(303\) −101.430 + 101.430i −0.334753 + 0.334753i
\(304\) 21.5542i 0.0709020i
\(305\) −514.066 + 91.3886i −1.68546 + 0.299635i
\(306\) −21.2921 −0.0695821
\(307\) 6.39515 + 6.39515i 0.0208311 + 0.0208311i 0.717446 0.696615i \(-0.245311\pi\)
−0.696615 + 0.717446i \(0.745311\pi\)
\(308\) 59.3894 59.3894i 0.192823 0.192823i
\(309\) 257.184i 0.832310i
\(310\) −82.8915 57.8678i −0.267392 0.186670i
\(311\) 375.884 1.20863 0.604315 0.796745i \(-0.293447\pi\)
0.604315 + 0.796745i \(0.293447\pi\)
\(312\) 0.479070 + 0.479070i 0.00153548 + 0.00153548i
\(313\) 24.7214 24.7214i 0.0789820 0.0789820i −0.666512 0.745494i \(-0.732214\pi\)
0.745494 + 0.666512i \(0.232214\pi\)
\(314\) 278.983i 0.888479i
\(315\) 57.9786 83.0502i 0.184059 0.263651i
\(316\) 143.442 0.453931
\(317\) −113.695 113.695i −0.358661 0.358661i 0.504658 0.863319i \(-0.331618\pi\)
−0.863319 + 0.504658i \(0.831618\pi\)
\(318\) 73.6784 73.6784i 0.231693 0.231693i
\(319\) 342.427i 1.07344i
\(320\) 7.00127 + 39.3825i 0.0218790 + 0.123070i
\(321\) 296.470 0.923583
\(322\) −32.3834 32.3834i −0.100569 0.100569i
\(323\) 19.1223 19.1223i 0.0592021 0.0592021i
\(324\) 18.0000i 0.0555556i
\(325\) −1.45234 + 3.13755i −0.00446875 + 0.00965401i
\(326\) 422.005 1.29449
\(327\) 218.703 + 218.703i 0.668816 + 0.668816i
\(328\) −30.7528 + 30.7528i −0.0937585 + 0.0937585i
\(329\) 177.422i 0.539277i
\(330\) 74.9937 13.3321i 0.227254 0.0404002i
\(331\) −299.118 −0.903681 −0.451840 0.892099i \(-0.649232\pi\)
−0.451840 + 0.892099i \(0.649232\pi\)
\(332\) −76.7817 76.7817i −0.231270 0.231270i
\(333\) 124.789 124.789i 0.374742 0.374742i
\(334\) 101.150i 0.302843i
\(335\) 290.422 + 202.748i 0.866931 + 0.605218i
\(336\) −46.7820 −0.139232
\(337\) −43.0548 43.0548i −0.127759 0.127759i 0.640336 0.768095i \(-0.278795\pi\)
−0.768095 + 0.640336i \(0.778795\pi\)
\(338\) −168.981 + 168.981i −0.499943 + 0.499943i
\(339\) 62.3302i 0.183865i
\(340\) −28.7277 + 41.1504i −0.0844933 + 0.121031i
\(341\) 88.9138 0.260744
\(342\) 16.1656 + 16.1656i 0.0472680 + 0.0472680i
\(343\) −250.217 + 250.217i −0.729495 + 0.729495i
\(344\) 161.989i 0.470898i
\(345\) −7.26961 40.8920i −0.0210713 0.118527i
\(346\) −388.426 −1.12262
\(347\) 180.407 + 180.407i 0.519904 + 0.519904i 0.917542 0.397639i \(-0.130170\pi\)
−0.397639 + 0.917542i \(0.630170\pi\)
\(348\) −134.868 + 134.868i −0.387551 + 0.387551i
\(349\) 76.9282i 0.220425i 0.993908 + 0.110212i \(0.0351531\pi\)
−0.993908 + 0.110212i \(0.964847\pi\)
\(350\) −82.2817 224.106i −0.235091 0.640302i
\(351\) −0.718605 −0.00204731
\(352\) −24.8769 24.8769i −0.0706729 0.0706729i
\(353\) −411.334 + 411.334i −1.16525 + 1.16525i −0.181943 + 0.983309i \(0.558239\pi\)
−0.983309 + 0.181943i \(0.941761\pi\)
\(354\) 43.4440i 0.122723i
\(355\) 192.254 34.1782i 0.541561 0.0962766i
\(356\) 40.0198 0.112415
\(357\) −41.5037 41.5037i −0.116257 0.116257i
\(358\) 111.660 111.660i 0.311900 0.311900i
\(359\) 112.879i 0.314426i 0.987565 + 0.157213i \(0.0502509\pi\)
−0.987565 + 0.157213i \(0.949749\pi\)
\(360\) −34.7878 24.2859i −0.0966329 0.0674609i
\(361\) 331.964 0.919567
\(362\) 192.806 + 192.806i 0.532614 + 0.532614i
\(363\) 100.823 100.823i 0.277748 0.277748i
\(364\) 1.86765i 0.00513092i
\(365\) 158.308 226.765i 0.433721 0.621274i
\(366\) −255.788 −0.698875
\(367\) 405.857 + 405.857i 1.10588 + 1.10588i 0.993687 + 0.112192i \(0.0357871\pi\)
0.112192 + 0.993687i \(0.464213\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 46.1292i 0.125011i
\(370\) −72.8069 409.543i −0.196775 1.10687i
\(371\) 287.235 0.774219
\(372\) −35.0194 35.0194i −0.0941383 0.0941383i
\(373\) −96.2819 + 96.2819i −0.258128 + 0.258128i −0.824293 0.566164i \(-0.808427\pi\)
0.566164 + 0.824293i \(0.308427\pi\)
\(374\) 44.1401i 0.118022i
\(375\) 55.1540 209.363i 0.147077 0.558302i
\(376\) −74.3182 −0.197655
\(377\) 5.38426 + 5.38426i 0.0142819 + 0.0142819i
\(378\) 35.0865 35.0865i 0.0928214 0.0928214i
\(379\) 200.497i 0.529017i −0.964383 0.264509i \(-0.914790\pi\)
0.964383 0.264509i \(-0.0852097\pi\)
\(380\) 53.0536 9.43167i 0.139615 0.0248202i
\(381\) −203.390 −0.533833
\(382\) 99.0271 + 99.0271i 0.259233 + 0.259233i
\(383\) 63.0994 63.0994i 0.164750 0.164750i −0.619917 0.784667i \(-0.712834\pi\)
0.784667 + 0.619917i \(0.212834\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 172.169 + 120.194i 0.447192 + 0.312192i
\(386\) −358.687 −0.929242
\(387\) −121.492 121.492i −0.313932 0.313932i
\(388\) 45.4334 45.4334i 0.117096 0.117096i
\(389\) 346.298i 0.890227i 0.895474 + 0.445113i \(0.146837\pi\)
−0.895474 + 0.445113i \(0.853163\pi\)
\(390\) −0.969555 + 1.38882i −0.00248604 + 0.00356107i
\(391\) −24.0684 −0.0615559
\(392\) 6.81017 + 6.81017i 0.0173729 + 0.0173729i
\(393\) −163.000 + 163.000i −0.414759 + 0.414759i
\(394\) 124.910i 0.317030i
\(395\) 62.7673 + 353.070i 0.158905 + 0.893847i
\(396\) 37.3153 0.0942305
\(397\) 16.2056 + 16.2056i 0.0408202 + 0.0408202i 0.727222 0.686402i \(-0.240811\pi\)
−0.686402 + 0.727222i \(0.740811\pi\)
\(398\) 204.645 204.645i 0.514183 0.514183i
\(399\) 63.0218i 0.157949i
\(400\) −93.8728 + 34.4659i −0.234682 + 0.0861649i
\(401\) −252.470 −0.629602 −0.314801 0.949158i \(-0.601938\pi\)
−0.314801 + 0.949158i \(0.601938\pi\)
\(402\) 122.696 + 122.696i 0.305213 + 0.305213i
\(403\) −1.39806 + 1.39806i −0.00346914 + 0.00346914i
\(404\) 165.635i 0.409988i
\(405\) 44.3053 7.87643i 0.109396 0.0194480i
\(406\) −525.782 −1.29503
\(407\) 258.697 + 258.697i 0.635619 + 0.635619i
\(408\) −17.3849 + 17.3849i −0.0426102 + 0.0426102i
\(409\) 448.966i 1.09772i 0.835915 + 0.548858i \(0.184937\pi\)
−0.835915 + 0.548858i \(0.815063\pi\)
\(410\) −89.1519 62.2384i −0.217444 0.151801i
\(411\) 453.610 1.10367
\(412\) 209.990 + 209.990i 0.509684 + 0.509684i
\(413\) −84.6832 + 84.6832i −0.205044 + 0.205044i
\(414\) 20.3470i 0.0491473i
\(415\) 155.393 222.589i 0.374441 0.536359i
\(416\) 0.782318 0.00188057
\(417\) 38.6366 + 38.6366i 0.0926538 + 0.0926538i
\(418\) −33.5125 + 33.5125i −0.0801735 + 0.0801735i
\(419\) 56.1614i 0.134037i −0.997752 0.0670184i \(-0.978651\pi\)
0.997752 0.0670184i \(-0.0213486\pi\)
\(420\) −20.4708 115.150i −0.0487401 0.274166i
\(421\) 302.461 0.718436 0.359218 0.933254i \(-0.383044\pi\)
0.359218 + 0.933254i \(0.383044\pi\)
\(422\) 7.31007 + 7.31007i 0.0173224 + 0.0173224i
\(423\) 55.7386 55.7386i 0.131770 0.131770i
\(424\) 120.316i 0.283765i
\(425\) −113.858 52.7041i −0.267902 0.124010i
\(426\) 95.6617 0.224558
\(427\) −498.596 498.596i −1.16767 1.16767i
\(428\) 242.067 242.067i 0.565577 0.565577i
\(429\) 1.48972i 0.00347254i
\(430\) −398.721 + 70.8830i −0.927258 + 0.164844i
\(431\) −294.456 −0.683192 −0.341596 0.939847i \(-0.610967\pi\)
−0.341596 + 0.939847i \(0.610967\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −510.866 + 510.866i −1.17983 + 1.17983i −0.200042 + 0.979787i \(0.564108\pi\)
−0.979787 + 0.200042i \(0.935892\pi\)
\(434\) 136.523i 0.314570i
\(435\) −390.980 272.949i −0.898805 0.627470i
\(436\) 357.140 0.819128
\(437\) 18.2735 + 18.2735i 0.0418157 + 0.0418157i
\(438\) 95.8022 95.8022i 0.218726 0.218726i
\(439\) 71.7873i 0.163525i −0.996652 0.0817623i \(-0.973945\pi\)
0.996652 0.0817623i \(-0.0260548\pi\)
\(440\) 50.3465 72.1177i 0.114424 0.163904i
\(441\) −10.2153 −0.0231638
\(442\) 0.694050 + 0.694050i 0.00157025 + 0.00157025i
\(443\) 271.317 271.317i 0.612455 0.612455i −0.331130 0.943585i \(-0.607430\pi\)
0.943585 + 0.331130i \(0.107430\pi\)
\(444\) 203.780i 0.458964i
\(445\) 17.5118 + 98.5050i 0.0393524 + 0.221359i
\(446\) 53.2546 0.119405
\(447\) 138.060 + 138.060i 0.308860 + 0.308860i
\(448\) −38.1973 + 38.1973i −0.0852619 + 0.0852619i
\(449\) 27.0296i 0.0601996i 0.999547 + 0.0300998i \(0.00958251\pi\)
−0.999547 + 0.0300998i \(0.990417\pi\)
\(450\) 44.5551 96.2540i 0.0990114 0.213898i
\(451\) 95.6291 0.212038
\(452\) 50.8924 + 50.8924i 0.112594 + 0.112594i
\(453\) −226.718 + 226.718i −0.500481 + 0.500481i
\(454\) 229.755i 0.506068i
\(455\) −4.59706 + 0.817247i −0.0101034 + 0.00179615i
\(456\) 26.3984 0.0578912
\(457\) 325.157 + 325.157i 0.711504 + 0.711504i 0.966850 0.255346i \(-0.0821893\pi\)
−0.255346 + 0.966850i \(0.582189\pi\)
\(458\) 56.2198 56.2198i 0.122751 0.122751i
\(459\) 26.0774i 0.0568135i
\(460\) −39.3238 27.4525i −0.0854864 0.0596794i
\(461\) 362.643 0.786645 0.393323 0.919401i \(-0.371326\pi\)
0.393323 + 0.919401i \(0.371326\pi\)
\(462\) 72.7368 + 72.7368i 0.157439 + 0.157439i
\(463\) 489.243 489.243i 1.05668 1.05668i 0.0583859 0.998294i \(-0.481405\pi\)
0.998294 0.0583859i \(-0.0185954\pi\)
\(464\) 220.238i 0.474652i
\(465\) 70.8733 101.521i 0.152416 0.218324i
\(466\) −341.458 −0.732742
\(467\) −102.330 102.330i −0.219122 0.219122i 0.589006 0.808128i \(-0.299519\pi\)
−0.808128 + 0.589006i \(0.799519\pi\)
\(468\) −0.586738 + 0.586738i −0.00125371 + 0.00125371i
\(469\) 478.329i 1.01989i
\(470\) −32.5201 182.927i −0.0691917 0.389207i
\(471\) 341.682 0.725440
\(472\) 35.4719 + 35.4719i 0.0751522 + 0.0751522i
\(473\) 251.861 251.861i 0.532476 0.532476i
\(474\) 175.680i 0.370633i
\(475\) 46.4304 + 126.460i 0.0977481 + 0.266231i
\(476\) −67.7752 −0.142385
\(477\) 90.2372 + 90.2372i 0.189177 + 0.189177i
\(478\) −143.495 + 143.495i −0.300199 + 0.300199i
\(479\) 543.454i 1.13456i −0.823525 0.567280i \(-0.807996\pi\)
0.823525 0.567280i \(-0.192004\pi\)
\(480\) −48.2335 + 8.57477i −0.100487 + 0.0178641i
\(481\) −8.13540 −0.0169135
\(482\) −97.6832 97.6832i −0.202662 0.202662i
\(483\) 39.6614 39.6614i 0.0821146 0.0821146i
\(484\) 164.643i 0.340171i
\(485\) 131.711 + 91.9494i 0.271569 + 0.189586i
\(486\) 22.0454 0.0453609
\(487\) 423.656 + 423.656i 0.869931 + 0.869931i 0.992464 0.122533i \(-0.0391018\pi\)
−0.122533 + 0.992464i \(0.539102\pi\)
\(488\) −208.850 + 208.850i −0.427972 + 0.427972i
\(489\) 516.848i 1.05695i
\(490\) −13.7826 + 19.7426i −0.0281278 + 0.0402910i
\(491\) −366.712 −0.746868 −0.373434 0.927657i \(-0.621820\pi\)
−0.373434 + 0.927657i \(0.621820\pi\)
\(492\) −37.6643 37.6643i −0.0765535 0.0765535i
\(493\) −195.389 + 195.389i −0.396327 + 0.396327i
\(494\) 1.05389i 0.00213338i
\(495\) 16.3284 + 91.8481i 0.0329867 + 0.185552i
\(496\) −57.1865 −0.115295
\(497\) 186.469 + 186.469i 0.375188 + 0.375188i
\(498\) 94.0380 94.0380i 0.188831 0.188831i
\(499\) 500.886i 1.00378i −0.864932 0.501890i \(-0.832638\pi\)
0.864932 0.501890i \(-0.167362\pi\)
\(500\) −125.911 215.978i −0.251823 0.431955i
\(501\) −123.882 −0.247270
\(502\) 16.2884 + 16.2884i 0.0324470 + 0.0324470i
\(503\) 449.857 449.857i 0.894348 0.894348i −0.100581 0.994929i \(-0.532070\pi\)
0.994929 + 0.100581i \(0.0320701\pi\)
\(504\) 57.2960i 0.113683i
\(505\) −407.695 + 72.4784i −0.807317 + 0.143522i
\(506\) 42.1808 0.0833612
\(507\) −206.958 206.958i −0.408202 0.408202i
\(508\) −166.067 + 166.067i −0.326904 + 0.326904i
\(509\) 851.790i 1.67346i −0.547618 0.836728i \(-0.684465\pi\)
0.547618 0.836728i \(-0.315535\pi\)
\(510\) −50.3987 35.1841i −0.0988210 0.0689885i
\(511\) 373.485 0.730890
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −19.7988 + 19.7988i −0.0385941 + 0.0385941i
\(514\) 130.945i 0.254756i
\(515\) −424.983 + 608.757i −0.825210 + 1.18205i
\(516\) −198.395 −0.384487
\(517\) 115.550 + 115.550i 0.223501 + 0.223501i
\(518\) 397.218 397.218i 0.766830 0.766830i
\(519\) 475.722i 0.916613i
\(520\) 0.342326 + 1.92560i 0.000658319 + 0.00370308i
\(521\) 701.483 1.34642 0.673208 0.739453i \(-0.264916\pi\)
0.673208 + 0.739453i \(0.264916\pi\)
\(522\) −165.179 165.179i −0.316434 0.316434i
\(523\) 402.773 402.773i 0.770121 0.770121i −0.208007 0.978127i \(-0.566698\pi\)
0.978127 + 0.208007i \(0.0666975\pi\)
\(524\) 266.178i 0.507973i
\(525\) 274.472 100.774i 0.522804 0.191951i
\(526\) −232.963 −0.442895
\(527\) −50.7343 50.7343i −0.0962699 0.0962699i
\(528\) 30.4678 30.4678i 0.0577042 0.0577042i
\(529\) 23.0000i 0.0434783i
\(530\) 296.147 52.6479i 0.558769 0.0993357i
\(531\) −53.2078 −0.100203
\(532\) 51.4571 + 51.4571i 0.0967238 + 0.0967238i
\(533\) −1.50365 + 1.50365i −0.00282111 + 0.00282111i
\(534\) 49.0140i 0.0917866i
\(535\) 701.749 + 489.902i 1.31168 + 0.915704i
\(536\) 200.361 0.373808
\(537\) 136.755 + 136.755i 0.254665 + 0.254665i
\(538\) −296.382 + 296.382i −0.550897 + 0.550897i
\(539\) 21.1769i 0.0392893i
\(540\) 29.7441 42.6062i 0.0550816 0.0789004i
\(541\) 37.5641 0.0694345 0.0347172 0.999397i \(-0.488947\pi\)
0.0347172 + 0.999397i \(0.488947\pi\)
\(542\) 227.220 + 227.220i 0.419224 + 0.419224i
\(543\) −236.138 + 236.138i −0.434877 + 0.434877i
\(544\) 28.3895i 0.0521866i
\(545\) 156.277 + 879.067i 0.286747 + 1.61297i
\(546\) −2.28740 −0.00418938
\(547\) 592.447 + 592.447i 1.08308 + 1.08308i 0.996220 + 0.0868632i \(0.0276843\pi\)
0.0868632 + 0.996220i \(0.472316\pi\)
\(548\) 370.371 370.371i 0.675859 0.675859i
\(549\) 313.276i 0.570629i
\(550\) 199.542 + 92.3660i 0.362803 + 0.167938i
\(551\) 296.691 0.538460
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −342.445 + 342.445i −0.619249 + 0.619249i
\(554\) 560.650i 1.01200i
\(555\) 501.585 89.1699i 0.903757 0.160666i
\(556\) 63.0933 0.113477
\(557\) −260.273 260.273i −0.467277 0.467277i 0.433754 0.901031i \(-0.357189\pi\)
−0.901031 + 0.433754i \(0.857189\pi\)
\(558\) 42.8899 42.8899i 0.0768636 0.0768636i
\(559\) 7.92043i 0.0141689i
\(560\) −110.734 77.3048i −0.197739 0.138044i
\(561\) 54.0603 0.0963642
\(562\) −135.612 135.612i −0.241303 0.241303i
\(563\) −188.827 + 188.827i −0.335394 + 0.335394i −0.854631 0.519236i \(-0.826216\pi\)
0.519236 + 0.854631i \(0.326216\pi\)
\(564\) 91.0208i 0.161384i
\(565\) −102.997 + 147.536i −0.182296 + 0.261126i
\(566\) 383.564 0.677675
\(567\) 42.9720 + 42.9720i 0.0757884 + 0.0757884i
\(568\) 78.1074 78.1074i 0.137513 0.137513i
\(569\) 181.407i 0.318817i −0.987213 0.159409i \(-0.949041\pi\)
0.987213 0.159409i \(-0.0509587\pi\)
\(570\) 11.5514 + 64.9772i 0.0202656 + 0.113995i
\(571\) −700.274 −1.22640 −0.613200 0.789928i \(-0.710118\pi\)
−0.613200 + 0.789928i \(0.710118\pi\)
\(572\) −1.21635 1.21635i −0.00212649 0.00212649i
\(573\) −121.283 + 121.283i −0.211663 + 0.211663i
\(574\) 146.834i 0.255809i
\(575\) 50.3646 108.804i 0.0875906 0.189225i
\(576\) −24.0000 −0.0416667
\(577\) 435.694 + 435.694i 0.755102 + 0.755102i 0.975427 0.220325i \(-0.0707117\pi\)
−0.220325 + 0.975427i \(0.570712\pi\)
\(578\) 263.814 263.814i 0.456425 0.456425i
\(579\) 439.301i 0.758723i
\(580\) −542.096 + 96.3717i −0.934649 + 0.166158i
\(581\) 366.607 0.630993
\(582\) 55.6444 + 55.6444i 0.0956089 + 0.0956089i
\(583\) −187.068 + 187.068i −0.320872 + 0.320872i
\(584\) 156.444i 0.267884i
\(585\) −1.70095 1.18746i −0.00290760 0.00202984i
\(586\) 57.5767 0.0982538
\(587\) −123.516 123.516i −0.210419 0.210419i 0.594027 0.804445i \(-0.297537\pi\)
−0.804445 + 0.594027i \(0.797537\pi\)
\(588\) −8.34072 + 8.34072i −0.0141849 + 0.0141849i
\(589\) 77.0381i 0.130795i
\(590\) −71.7889 + 102.832i −0.121676 + 0.174292i
\(591\) 152.983 0.258854
\(592\) −166.386 166.386i −0.281057 0.281057i
\(593\) 131.838 131.838i 0.222323 0.222323i −0.587153 0.809476i \(-0.699751\pi\)
0.809476 + 0.587153i \(0.199751\pi\)
\(594\) 45.7017i 0.0769389i
\(595\) −29.6570 166.822i −0.0498437 0.280374i
\(596\) 225.452 0.378275
\(597\) 250.638 + 250.638i 0.419829 + 0.419829i
\(598\) −0.663242 + 0.663242i −0.00110910 + 0.00110910i
\(599\) 933.159i 1.55786i −0.627110 0.778931i \(-0.715762\pi\)
0.627110 0.778931i \(-0.284238\pi\)
\(600\) −42.2120 114.970i −0.0703533 0.191617i
\(601\) −355.783 −0.591986 −0.295993 0.955190i \(-0.595650\pi\)
−0.295993 + 0.955190i \(0.595650\pi\)
\(602\) −386.722 386.722i −0.642395 0.642395i
\(603\) −150.271 + 150.271i −0.249205 + 0.249205i
\(604\) 370.228i 0.612961i
\(605\) 405.253 72.0443i 0.669839 0.119081i
\(606\) −202.861 −0.334753
\(607\) 238.085 + 238.085i 0.392232 + 0.392232i 0.875482 0.483250i \(-0.160544\pi\)
−0.483250 + 0.875482i \(0.660544\pi\)
\(608\) 21.5542 21.5542i 0.0354510 0.0354510i
\(609\) 643.949i 1.05739i
\(610\) −605.454 422.677i −0.992548 0.692913i
\(611\) −3.63378 −0.00594726
\(612\) −21.2921 21.2921i −0.0347910 0.0347910i
\(613\) 411.262 411.262i 0.670900 0.670900i −0.287023 0.957924i \(-0.592666\pi\)
0.957924 + 0.287023i \(0.0926658\pi\)
\(614\) 12.7903i 0.0208311i
\(615\) 76.2261 109.188i 0.123945 0.177542i
\(616\) 118.779 0.192823
\(617\) 9.19782 + 9.19782i 0.0149073 + 0.0149073i 0.714521 0.699614i \(-0.246645\pi\)
−0.699614 + 0.714521i \(0.746645\pi\)
\(618\) −257.184 + 257.184i −0.416155 + 0.416155i
\(619\) 821.926i 1.32783i 0.747809 + 0.663914i \(0.231106\pi\)
−0.747809 + 0.663914i \(0.768894\pi\)
\(620\) −25.0236 140.759i −0.0403607 0.227031i
\(621\) 24.9199 0.0401286
\(622\) 375.884 + 375.884i 0.604315 + 0.604315i
\(623\) −95.5406 + 95.5406i −0.153356 + 0.153356i
\(624\) 0.958140i 0.00153548i
\(625\) 476.512 404.427i 0.762420 0.647083i
\(626\) 49.4427 0.0789820
\(627\) −41.0443 41.0443i −0.0654614 0.0654614i
\(628\) 278.983 278.983i 0.444240 0.444240i
\(629\) 295.225i 0.469356i
\(630\) 141.029 25.0716i 0.223855 0.0397961i
\(631\) 17.9920 0.0285135 0.0142568 0.999898i \(-0.495462\pi\)
0.0142568 + 0.999898i \(0.495462\pi\)
\(632\) 143.442 + 143.442i 0.226966 + 0.226966i
\(633\) −8.95297 + 8.95297i −0.0141437 + 0.0141437i
\(634\) 227.391i 0.358661i
\(635\) −481.427 336.092i −0.758153 0.529278i
\(636\) 147.357 0.231693
\(637\) 0.332982 + 0.332982i 0.000522735 + 0.000522735i
\(638\) 342.427 342.427i 0.536720 0.536720i
\(639\) 117.161i 0.183351i
\(640\) −32.3812 + 46.3838i −0.0505957 + 0.0724747i
\(641\) 411.466 0.641912 0.320956 0.947094i \(-0.395996\pi\)
0.320956 + 0.947094i \(0.395996\pi\)
\(642\) 296.470 + 296.470i 0.461792 + 0.461792i
\(643\) 118.655 118.655i 0.184534 0.184534i −0.608794 0.793328i \(-0.708347\pi\)
0.793328 + 0.608794i \(0.208347\pi\)
\(644\) 64.7668i 0.100569i
\(645\) −86.8136 488.331i −0.134595 0.757103i
\(646\) 38.2445 0.0592021
\(647\) 183.932 + 183.932i 0.284285 + 0.284285i 0.834815 0.550531i \(-0.185575\pi\)
−0.550531 + 0.834815i \(0.685575\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 110.304i 0.169959i
\(650\) −4.58990 + 1.68521i −0.00706138 + 0.00259263i
\(651\) 167.206 0.256845
\(652\) 422.005 + 422.005i 0.647247 + 0.647247i
\(653\) 116.529 116.529i 0.178452 0.178452i −0.612229 0.790681i \(-0.709727\pi\)
0.790681 + 0.612229i \(0.209727\pi\)
\(654\) 437.405i 0.668816i
\(655\) −655.173 + 116.474i −1.00026 + 0.177823i
\(656\) −61.5056 −0.0937585
\(657\) 117.333 + 117.333i 0.178589 + 0.178589i
\(658\) 177.422 177.422i 0.269639 0.269639i
\(659\) 612.241i 0.929045i −0.885561 0.464523i \(-0.846226\pi\)
0.885561 0.464523i \(-0.153774\pi\)
\(660\) 88.3257 + 61.6616i 0.133827 + 0.0934266i
\(661\) −455.394 −0.688947 −0.344473 0.938796i \(-0.611943\pi\)
−0.344473 + 0.938796i \(0.611943\pi\)
\(662\) −299.118 299.118i −0.451840 0.451840i
\(663\) −0.850034 + 0.850034i −0.00128210 + 0.00128210i
\(664\) 153.563i 0.231270i
\(665\) −104.140 + 149.173i −0.156602 + 0.224321i
\(666\) 249.578 0.374742
\(667\) −186.716 186.716i −0.279934 0.279934i
\(668\) −101.150 + 101.150i −0.151422 + 0.151422i
\(669\) 65.2233i 0.0974937i
\(670\) 87.6738 + 493.170i 0.130856 + 0.736075i
\(671\) 649.443 0.967873
\(672\) −46.7820 46.7820i −0.0696161 0.0696161i
\(673\) 101.805 101.805i 0.151271 0.151271i −0.627415 0.778685i \(-0.715887\pi\)
0.778685 + 0.627415i \(0.215887\pi\)
\(674\) 86.1096i 0.127759i
\(675\) 117.887 + 54.5687i 0.174647 + 0.0808425i
\(676\) −337.962 −0.499943
\(677\) −590.792 590.792i −0.872662 0.872662i 0.120099 0.992762i \(-0.461679\pi\)
−0.992762 + 0.120099i \(0.961679\pi\)
\(678\) −62.3302 + 62.3302i −0.0919324 + 0.0919324i
\(679\) 216.930i 0.319484i
\(680\) −69.8781 + 12.4227i −0.102762 + 0.0182686i
\(681\) 281.391 0.413203
\(682\) 88.9138 + 88.9138i 0.130372 + 0.130372i
\(683\) −50.6235 + 50.6235i −0.0741194 + 0.0741194i −0.743195 0.669075i \(-0.766690\pi\)
0.669075 + 0.743195i \(0.266690\pi\)
\(684\) 32.3313i 0.0472680i
\(685\) 1073.70 + 749.566i 1.56744 + 1.09426i
\(686\) −500.434 −0.729495
\(687\) 68.8549 + 68.8549i 0.100225 + 0.100225i
\(688\) −161.989 + 161.989i −0.235449 + 0.235449i
\(689\) 5.88285i 0.00853824i
\(690\) 33.6224 48.1616i 0.0487280 0.0697994i
\(691\) 293.780 0.425152 0.212576 0.977145i \(-0.431815\pi\)
0.212576 + 0.977145i \(0.431815\pi\)
\(692\) −388.426 388.426i −0.561309 0.561309i
\(693\) −89.0841 + 89.0841i −0.128548 + 0.128548i
\(694\) 360.813i 0.519904i
\(695\) 27.6083 + 155.298i 0.0397242 + 0.223451i
\(696\) −269.736 −0.387551
\(697\) −54.5660 54.5660i −0.0782870 0.0782870i
\(698\) −76.9282 + 76.9282i −0.110212 + 0.110212i
\(699\) 418.199i 0.598282i
\(700\) 141.824 306.387i 0.202606 0.437696i
\(701\) −880.820 −1.25652 −0.628259 0.778004i \(-0.716232\pi\)
−0.628259 + 0.778004i \(0.716232\pi\)
\(702\) −0.718605 0.718605i −0.00102365 0.00102365i
\(703\) −224.144 + 224.144i −0.318840 + 0.318840i
\(704\) 49.7537i 0.0706729i
\(705\) 224.039 39.8288i 0.317786 0.0564948i
\(706\) −822.668 −1.16525
\(707\) −395.426 395.426i −0.559301 0.559301i
\(708\) −43.4440 + 43.4440i −0.0613616 + 0.0613616i
\(709\) 347.660i 0.490353i 0.969478 + 0.245176i \(0.0788459\pi\)
−0.969478 + 0.245176i \(0.921154\pi\)
\(710\) 226.432 + 158.076i 0.318919 + 0.222642i
\(711\) −215.163 −0.302621
\(712\) 40.0198 + 40.0198i 0.0562076 + 0.0562076i
\(713\) 48.4822 48.4822i 0.0679975 0.0679975i
\(714\) 83.0073i 0.116257i
\(715\) 2.46168 3.52618i 0.00344291 0.00493173i
\(716\) 223.320 0.311900
\(717\) −175.745 175.745i −0.245111 0.245111i
\(718\) −112.879 + 112.879i −0.157213 + 0.157213i
\(719\) 99.3256i 0.138144i −0.997612 0.0690721i \(-0.977996\pi\)
0.997612 0.0690721i \(-0.0220038\pi\)
\(720\) −10.5019 59.0738i −0.0145860 0.0820469i
\(721\) −1002.63 −1.39061
\(722\) 331.964 + 331.964i 0.459783 + 0.459783i
\(723\) 119.637 119.637i 0.165473 0.165473i
\(724\) 385.613i 0.532614i
\(725\) −474.420 1292.15i −0.654372 1.78227i
\(726\) 201.645 0.277748
\(727\) −786.876 786.876i −1.08236 1.08236i −0.996289 0.0860721i \(-0.972568\pi\)
−0.0860721 0.996289i \(-0.527432\pi\)
\(728\) −1.86765 + 1.86765i −0.00256546 + 0.00256546i
\(729\) 27.0000i 0.0370370i
\(730\) 385.073 68.4568i 0.527497 0.0937764i
\(731\) −287.424 −0.393193
\(732\) −255.788 255.788i −0.349438 0.349438i
\(733\) −969.091 + 969.091i −1.32209 + 1.32209i −0.410006 + 0.912083i \(0.634473\pi\)
−0.912083 + 0.410006i \(0.865527\pi\)
\(734\) 811.715i 1.10588i
\(735\) −24.1796 16.8802i −0.0328975 0.0229662i
\(736\) −27.1293 −0.0368605
\(737\) −311.522 311.522i −0.422689 0.422689i
\(738\) 46.1292 46.1292i 0.0625057 0.0625057i
\(739\) 1051.09i 1.42232i −0.703030 0.711160i \(-0.748170\pi\)
0.703030 0.711160i \(-0.251830\pi\)
\(740\) 336.736 482.350i 0.455048 0.651824i
\(741\) 1.29075 0.00174190
\(742\) 287.235 + 287.235i 0.387109 + 0.387109i
\(743\) 205.793 205.793i 0.276976 0.276976i −0.554925 0.831901i \(-0.687253\pi\)
0.831901 + 0.554925i \(0.187253\pi\)
\(744\) 70.0389i 0.0941383i
\(745\) 98.6530 + 554.929i 0.132420 + 0.744871i
\(746\) −192.564 −0.258128
\(747\) 115.173 + 115.173i 0.154180 + 0.154180i
\(748\) 44.1401 44.1401i 0.0590108 0.0590108i
\(749\) 1155.79i 1.54311i
\(750\) 264.517 154.209i 0.352690 0.205613i
\(751\) 33.6100 0.0447537 0.0223768 0.999750i \(-0.492877\pi\)
0.0223768 + 0.999750i \(0.492877\pi\)
\(752\) −74.3182 74.3182i −0.0988273 0.0988273i
\(753\) −19.9491 + 19.9491i −0.0264929 + 0.0264929i
\(754\) 10.7685i 0.0142819i
\(755\) −911.283 + 162.004i −1.20700 + 0.214575i
\(756\) 70.1730 0.0928214
\(757\) −614.446 614.446i −0.811685 0.811685i 0.173201 0.984886i \(-0.444589\pi\)
−0.984886 + 0.173201i \(0.944589\pi\)
\(758\) 200.497 200.497i 0.264509 0.264509i
\(759\) 51.6607i 0.0680641i
\(760\) 62.4853 + 43.6220i 0.0822175 + 0.0573973i
\(761\) −417.553 −0.548690 −0.274345 0.961631i \(-0.588461\pi\)
−0.274345 + 0.961631i \(0.588461\pi\)
\(762\) −203.390 203.390i −0.266916 0.266916i
\(763\) −852.612 + 852.612i −1.11745 + 1.11745i
\(764\) 198.054i 0.259233i
\(765\) 43.0916 61.7256i 0.0563289 0.0806870i
\(766\) 126.199 0.164750
\(767\) 1.73439 + 1.73439i 0.00226127 + 0.00226127i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 613.533i 0.797833i −0.916987 0.398916i \(-0.869386\pi\)
0.916987 0.398916i \(-0.130614\pi\)
\(770\) 51.9751 + 292.363i 0.0675001 + 0.379692i
\(771\) −160.374 −0.208007
\(772\) −358.687 358.687i −0.464621 0.464621i
\(773\) −804.283 + 804.283i −1.04047 + 1.04047i −0.0413235 + 0.999146i \(0.513157\pi\)
−0.999146 + 0.0413235i \(0.986843\pi\)
\(774\) 242.984i 0.313932i
\(775\) 335.516 123.187i 0.432924 0.158951i
\(776\) 90.8669 0.117096
\(777\) 486.491 + 486.491i 0.626114 + 0.626114i
\(778\) −346.298 + 346.298i −0.445113 + 0.445113i
\(779\) 82.8565i