Properties

Label 690.3.k.b.277.17
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 277.17
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.17

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.08074 - 4.54648i) q^{5} -2.44949 q^{6} +(-1.45838 - 1.45838i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.08074 - 4.54648i) q^{5} -2.44949 q^{6} +(-1.45838 - 1.45838i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.62723 + 2.46574i) q^{10} +6.56968 q^{11} +(2.44949 + 2.44949i) q^{12} +(16.0299 - 16.0299i) q^{13} +2.91676i q^{14} +(-3.01990 - 8.11666i) q^{15} -4.00000 q^{16} +(10.8651 + 10.8651i) q^{17} +(-3.00000 + 3.00000i) q^{18} +8.18603i q^{19} +(9.09297 + 4.16148i) q^{20} -3.57228 q^{21} +(-6.56968 - 6.56968i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-16.3410 - 18.9201i) q^{25} -32.0598 q^{26} +(-3.67423 - 3.67423i) q^{27} +(2.91676 - 2.91676i) q^{28} -6.33745i q^{29} +(-5.09676 + 11.1366i) q^{30} +27.7263 q^{31} +(4.00000 + 4.00000i) q^{32} +(8.04619 - 8.04619i) q^{33} -21.7301i q^{34} +(-9.66500 + 3.59598i) q^{35} +6.00000 q^{36} +(-14.1170 - 14.1170i) q^{37} +(8.18603 - 8.18603i) q^{38} -39.2651i q^{39} +(-4.93148 - 13.2545i) q^{40} -69.6643 q^{41} +(3.57228 + 3.57228i) q^{42} +(17.6100 - 17.6100i) q^{43} +13.1394i q^{44} +(-13.6395 - 6.24223i) q^{45} -6.78233 q^{46} +(22.1675 + 22.1675i) q^{47} +(-4.89898 + 4.89898i) q^{48} -44.7463i q^{49} +(-2.57909 + 35.2611i) q^{50} +26.6138 q^{51} +(32.0598 + 32.0598i) q^{52} +(-1.75313 + 1.75313i) q^{53} +7.34847i q^{54} +(13.6698 - 29.8690i) q^{55} -5.83351 q^{56} +(10.0258 + 10.0258i) q^{57} +(-6.33745 + 6.33745i) q^{58} +84.6547i q^{59} +(16.2333 - 6.03981i) q^{60} +30.9806 q^{61} +(-27.7263 - 27.7263i) q^{62} +(-4.37513 + 4.37513i) q^{63} -8.00000i q^{64} +(-39.5256 - 106.234i) q^{65} -16.0924 q^{66} +(-30.7488 - 30.7488i) q^{67} +(-21.7301 + 21.7301i) q^{68} -8.30662i q^{69} +(13.2610 + 6.06902i) q^{70} -41.0485 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-37.1267 + 37.1267i) q^{73} +28.2340i q^{74} +(-43.1859 - 3.15873i) q^{75} -16.3721 q^{76} +(-9.58108 - 9.58108i) q^{77} +(-39.2651 + 39.2651i) q^{78} -95.7052i q^{79} +(-8.32297 + 18.1859i) q^{80} -9.00000 q^{81} +(69.6643 + 69.6643i) q^{82} +(44.3961 - 44.3961i) q^{83} -7.14456i q^{84} +(72.0051 - 26.7904i) q^{85} -35.2200 q^{86} +(-7.76176 - 7.76176i) q^{87} +(13.1394 - 13.1394i) q^{88} -142.109i q^{89} +(7.39723 + 19.8817i) q^{90} -46.7554 q^{91} +(6.78233 + 6.78233i) q^{92} +(33.9576 - 33.9576i) q^{93} -44.3349i q^{94} +(37.2176 + 17.0330i) q^{95} +9.79796 q^{96} +(99.3088 + 99.3088i) q^{97} +(-44.7463 + 44.7463i) q^{98} -19.7090i 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
\(5\) 2.08074 4.54648i 0.416148 0.909297i
\(6\) −2.44949 −0.408248
\(7\) −1.45838 1.45838i −0.208340 0.208340i 0.595222 0.803561i \(-0.297064\pi\)
−0.803561 + 0.595222i \(0.797064\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −6.62723 + 2.46574i −0.662723 + 0.246574i
\(11\) 6.56968 0.597244 0.298622 0.954371i \(-0.403473\pi\)
0.298622 + 0.954371i \(0.403473\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 16.0299 16.0299i 1.23307 1.23307i 0.270292 0.962778i \(-0.412880\pi\)
0.962778 0.270292i \(-0.0871204\pi\)
\(14\) 2.91676i 0.208340i
\(15\) −3.01990 8.11666i −0.201327 0.541111i
\(16\) −4.00000 −0.250000
\(17\) 10.8651 + 10.8651i 0.639121 + 0.639121i 0.950339 0.311218i \(-0.100737\pi\)
−0.311218 + 0.950339i \(0.600737\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 8.18603i 0.430844i 0.976521 + 0.215422i \(0.0691126\pi\)
−0.976521 + 0.215422i \(0.930887\pi\)
\(20\) 9.09297 + 4.16148i 0.454648 + 0.208074i
\(21\) −3.57228 −0.170109
\(22\) −6.56968 6.56968i −0.298622 0.298622i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −16.3410 18.9201i −0.653641 0.756805i
\(26\) −32.0598 −1.23307
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 2.91676 2.91676i 0.104170 0.104170i
\(29\) 6.33745i 0.218533i −0.994012 0.109266i \(-0.965150\pi\)
0.994012 0.109266i \(-0.0348502\pi\)
\(30\) −5.09676 + 11.1366i −0.169892 + 0.371219i
\(31\) 27.7263 0.894397 0.447198 0.894435i \(-0.352422\pi\)
0.447198 + 0.894435i \(0.352422\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 8.04619 8.04619i 0.243824 0.243824i
\(34\) 21.7301i 0.639121i
\(35\) −9.66500 + 3.59598i −0.276143 + 0.102742i
\(36\) 6.00000 0.166667
\(37\) −14.1170 14.1170i −0.381541 0.381541i 0.490116 0.871657i \(-0.336954\pi\)
−0.871657 + 0.490116i \(0.836954\pi\)
\(38\) 8.18603 8.18603i 0.215422 0.215422i
\(39\) 39.2651i 1.00680i
\(40\) −4.93148 13.2545i −0.123287 0.331361i
\(41\) −69.6643 −1.69913 −0.849564 0.527485i \(-0.823135\pi\)
−0.849564 + 0.527485i \(0.823135\pi\)
\(42\) 3.57228 + 3.57228i 0.0850543 + 0.0850543i
\(43\) 17.6100 17.6100i 0.409535 0.409535i −0.472042 0.881576i \(-0.656483\pi\)
0.881576 + 0.472042i \(0.156483\pi\)
\(44\) 13.1394i 0.298622i
\(45\) −13.6395 6.24223i −0.303099 0.138716i
\(46\) −6.78233 −0.147442
\(47\) 22.1675 + 22.1675i 0.471648 + 0.471648i 0.902448 0.430800i \(-0.141768\pi\)
−0.430800 + 0.902448i \(0.641768\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 44.7463i 0.913189i
\(50\) −2.57909 + 35.2611i −0.0515818 + 0.705223i
\(51\) 26.6138 0.521840
\(52\) 32.0598 + 32.0598i 0.616535 + 0.616535i
\(53\) −1.75313 + 1.75313i −0.0330779 + 0.0330779i −0.723452 0.690374i \(-0.757446\pi\)
0.690374 + 0.723452i \(0.257446\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 13.6698 29.8690i 0.248542 0.543072i
\(56\) −5.83351 −0.104170
\(57\) 10.0258 + 10.0258i 0.175891 + 0.175891i
\(58\) −6.33745 + 6.33745i −0.109266 + 0.109266i
\(59\) 84.6547i 1.43483i 0.696649 + 0.717413i \(0.254674\pi\)
−0.696649 + 0.717413i \(0.745326\pi\)
\(60\) 16.2333 6.03981i 0.270555 0.100663i
\(61\) 30.9806 0.507879 0.253939 0.967220i \(-0.418274\pi\)
0.253939 + 0.967220i \(0.418274\pi\)
\(62\) −27.7263 27.7263i −0.447198 0.447198i
\(63\) −4.37513 + 4.37513i −0.0694466 + 0.0694466i
\(64\) 8.00000i 0.125000i
\(65\) −39.5256 106.234i −0.608087 1.63437i
\(66\) −16.0924 −0.243824
\(67\) −30.7488 30.7488i −0.458937 0.458937i 0.439369 0.898307i \(-0.355202\pi\)
−0.898307 + 0.439369i \(0.855202\pi\)
\(68\) −21.7301 + 21.7301i −0.319560 + 0.319560i
\(69\) 8.30662i 0.120386i
\(70\) 13.2610 + 6.06902i 0.189443 + 0.0867002i
\(71\) −41.0485 −0.578148 −0.289074 0.957307i \(-0.593347\pi\)
−0.289074 + 0.957307i \(0.593347\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −37.1267 + 37.1267i −0.508584 + 0.508584i −0.914092 0.405507i \(-0.867095\pi\)
0.405507 + 0.914092i \(0.367095\pi\)
\(74\) 28.2340i 0.381541i
\(75\) −43.1859 3.15873i −0.575812 0.0421164i
\(76\) −16.3721 −0.215422
\(77\) −9.58108 9.58108i −0.124430 0.124430i
\(78\) −39.2651 + 39.2651i −0.503399 + 0.503399i
\(79\) 95.7052i 1.21146i −0.795671 0.605729i \(-0.792881\pi\)
0.795671 0.605729i \(-0.207119\pi\)
\(80\) −8.32297 + 18.1859i −0.104037 + 0.227324i
\(81\) −9.00000 −0.111111
\(82\) 69.6643 + 69.6643i 0.849564 + 0.849564i
\(83\) 44.3961 44.3961i 0.534893 0.534893i −0.387132 0.922024i \(-0.626534\pi\)
0.922024 + 0.387132i \(0.126534\pi\)
\(84\) 7.14456i 0.0850543i
\(85\) 72.0051 26.7904i 0.847119 0.315181i
\(86\) −35.2200 −0.409535
\(87\) −7.76176 7.76176i −0.0892157 0.0892157i
\(88\) 13.1394 13.1394i 0.149311 0.149311i
\(89\) 142.109i 1.59673i −0.602173 0.798366i \(-0.705698\pi\)
0.602173 0.798366i \(-0.294302\pi\)
\(90\) 7.39723 + 19.8817i 0.0821914 + 0.220908i
\(91\) −46.7554 −0.513795
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 33.9576 33.9576i 0.365136 0.365136i
\(94\) 44.3349i 0.471648i
\(95\) 37.2176 + 17.0330i 0.391765 + 0.179295i
\(96\) 9.79796 0.102062
\(97\) 99.3088 + 99.3088i 1.02380 + 1.02380i 0.999710 + 0.0240920i \(0.00766948\pi\)
0.0240920 + 0.999710i \(0.492331\pi\)
\(98\) −44.7463 + 44.7463i −0.456595 + 0.456595i
\(99\) 19.7090i 0.199081i
\(100\) 37.8402 32.6821i 0.378402 0.326821i
\(101\) −120.819 −1.19623 −0.598114 0.801411i \(-0.704083\pi\)
−0.598114 + 0.801411i \(0.704083\pi\)
\(102\) −26.6138 26.6138i −0.260920 0.260920i
\(103\) −31.7941 + 31.7941i −0.308681 + 0.308681i −0.844398 0.535717i \(-0.820041\pi\)
0.535717 + 0.844398i \(0.320041\pi\)
\(104\) 64.1197i 0.616535i
\(105\) −7.43300 + 16.2413i −0.0707904 + 0.154679i
\(106\) 3.50625 0.0330779
\(107\) −118.422 118.422i −1.10675 1.10675i −0.993575 0.113174i \(-0.963898\pi\)
−0.113174 0.993575i \(-0.536102\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 21.5303i 0.197526i −0.995111 0.0987628i \(-0.968511\pi\)
0.995111 0.0987628i \(-0.0314885\pi\)
\(110\) −43.5388 + 16.1991i −0.395807 + 0.147265i
\(111\) −34.5795 −0.311527
\(112\) 5.83351 + 5.83351i 0.0520849 + 0.0520849i
\(113\) −72.3235 + 72.3235i −0.640031 + 0.640031i −0.950563 0.310532i \(-0.899493\pi\)
0.310532 + 0.950563i \(0.399493\pi\)
\(114\) 20.0516i 0.175891i
\(115\) −8.36174 22.4740i −0.0727108 0.195426i
\(116\) 12.6749 0.109266
\(117\) −48.0898 48.0898i −0.411024 0.411024i
\(118\) 84.6547 84.6547i 0.717413 0.717413i
\(119\) 31.6907i 0.266308i
\(120\) −22.2731 10.1935i −0.185609 0.0849459i
\(121\) −77.8393 −0.643300
\(122\) −30.9806 30.9806i −0.253939 0.253939i
\(123\) −85.3210 + 85.3210i −0.693667 + 0.693667i
\(124\) 55.4526i 0.447198i
\(125\) −120.021 + 34.9263i −0.960172 + 0.279411i
\(126\) 8.75027 0.0694466
\(127\) 74.6311 + 74.6311i 0.587646 + 0.587646i 0.936993 0.349347i \(-0.113597\pi\)
−0.349347 + 0.936993i \(0.613597\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 43.1355i 0.334384i
\(130\) −66.7082 + 145.760i −0.513140 + 1.12123i
\(131\) −159.638 −1.21861 −0.609304 0.792936i \(-0.708551\pi\)
−0.609304 + 0.792936i \(0.708551\pi\)
\(132\) 16.0924 + 16.0924i 0.121912 + 0.121912i
\(133\) 11.9383 11.9383i 0.0897618 0.0897618i
\(134\) 61.4976i 0.458937i
\(135\) −24.3500 + 9.05971i −0.180370 + 0.0671090i
\(136\) 43.4602 0.319560
\(137\) 46.5130 + 46.5130i 0.339511 + 0.339511i 0.856183 0.516672i \(-0.172829\pi\)
−0.516672 + 0.856183i \(0.672829\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 128.651i 0.925547i 0.886477 + 0.462774i \(0.153146\pi\)
−0.886477 + 0.462774i \(0.846854\pi\)
\(140\) −7.19197 19.3300i −0.0513712 0.138071i
\(141\) 54.2990 0.385099
\(142\) 41.0485 + 41.0485i 0.289074 + 0.289074i
\(143\) 105.311 105.311i 0.736444 0.736444i
\(144\) 12.0000i 0.0833333i
\(145\) −28.8131 13.1866i −0.198711 0.0909421i
\(146\) 74.2533 0.508584
\(147\) −54.8028 54.8028i −0.372808 0.372808i
\(148\) 28.2340 28.2340i 0.190770 0.190770i
\(149\) 93.9923i 0.630821i 0.948955 + 0.315410i \(0.102142\pi\)
−0.948955 + 0.315410i \(0.897858\pi\)
\(150\) 40.0272 + 46.3446i 0.266848 + 0.308964i
\(151\) 170.451 1.12881 0.564406 0.825497i \(-0.309105\pi\)
0.564406 + 0.825497i \(0.309105\pi\)
\(152\) 16.3721 + 16.3721i 0.107711 + 0.107711i
\(153\) 32.5952 32.5952i 0.213040 0.213040i
\(154\) 19.1622i 0.124430i
\(155\) 57.6913 126.057i 0.372202 0.813272i
\(156\) 78.5302 0.503399
\(157\) 58.3661 + 58.3661i 0.371758 + 0.371758i 0.868117 0.496359i \(-0.165330\pi\)
−0.496359 + 0.868117i \(0.665330\pi\)
\(158\) −95.7052 + 95.7052i −0.605729 + 0.605729i
\(159\) 4.29427i 0.0270080i
\(160\) 26.5089 9.86297i 0.165681 0.0616435i
\(161\) −9.89120 −0.0614360
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 24.0343 24.0343i 0.147450 0.147450i −0.629528 0.776978i \(-0.716752\pi\)
0.776978 + 0.629528i \(0.216752\pi\)
\(164\) 139.329i 0.849564i
\(165\) −19.8398 53.3239i −0.120241 0.323175i
\(166\) −88.7922 −0.534893
\(167\) 128.995 + 128.995i 0.772426 + 0.772426i 0.978530 0.206104i \(-0.0660785\pi\)
−0.206104 + 0.978530i \(0.566078\pi\)
\(168\) −7.14456 + 7.14456i −0.0425272 + 0.0425272i
\(169\) 344.917i 2.04093i
\(170\) −98.7956 45.2147i −0.581150 0.265969i
\(171\) 24.5581 0.143615
\(172\) 35.2200 + 35.2200i 0.204767 + 0.204767i
\(173\) −14.8434 + 14.8434i −0.0858000 + 0.0858000i −0.748704 0.662904i \(-0.769324\pi\)
0.662904 + 0.748704i \(0.269324\pi\)
\(174\) 15.5235i 0.0892157i
\(175\) −3.76129 + 51.4241i −0.0214931 + 0.293852i
\(176\) −26.2787 −0.149311
\(177\) 103.680 + 103.680i 0.585765 + 0.585765i
\(178\) −142.109 + 142.109i −0.798366 + 0.798366i
\(179\) 10.8323i 0.0605158i 0.999542 + 0.0302579i \(0.00963286\pi\)
−0.999542 + 0.0302579i \(0.990367\pi\)
\(180\) 12.4845 27.2789i 0.0693581 0.151549i
\(181\) −2.96458 −0.0163789 −0.00818944 0.999966i \(-0.502607\pi\)
−0.00818944 + 0.999966i \(0.502607\pi\)
\(182\) 46.7554 + 46.7554i 0.256898 + 0.256898i
\(183\) 37.9433 37.9433i 0.207341 0.207341i
\(184\) 13.5647i 0.0737210i
\(185\) −93.5566 + 34.8089i −0.505711 + 0.188156i
\(186\) −67.9153 −0.365136
\(187\) 71.3799 + 71.3799i 0.381711 + 0.381711i
\(188\) −44.3349 + 44.3349i −0.235824 + 0.235824i
\(189\) 10.7168i 0.0567029i
\(190\) −20.1846 54.2507i −0.106235 0.285530i
\(191\) 225.451 1.18037 0.590186 0.807267i \(-0.299054\pi\)
0.590186 + 0.807267i \(0.299054\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 231.799 231.799i 1.20103 1.20103i 0.227175 0.973854i \(-0.427051\pi\)
0.973854 0.227175i \(-0.0729490\pi\)
\(194\) 198.618i 1.02380i
\(195\) −178.518 81.7006i −0.915478 0.418977i
\(196\) 89.4925 0.456595
\(197\) 240.985 + 240.985i 1.22327 + 1.22327i 0.966462 + 0.256811i \(0.0826717\pi\)
0.256811 + 0.966462i \(0.417328\pi\)
\(198\) −19.7090 + 19.7090i −0.0995407 + 0.0995407i
\(199\) 87.8703i 0.441559i −0.975324 0.220780i \(-0.929140\pi\)
0.975324 0.220780i \(-0.0708602\pi\)
\(200\) −70.5223 5.15818i −0.352611 0.0257909i
\(201\) −75.3189 −0.374721
\(202\) 120.819 + 120.819i 0.598114 + 0.598114i
\(203\) −9.24240 + 9.24240i −0.0455291 + 0.0455291i
\(204\) 53.2277i 0.260920i
\(205\) −144.953 + 316.728i −0.707090 + 1.54501i
\(206\) 63.5882 0.308681
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −64.1197 + 64.1197i −0.308268 + 0.308268i
\(209\) 53.7796i 0.257319i
\(210\) 23.6743 8.80832i 0.112735 0.0419444i
\(211\) 275.082 1.30371 0.651854 0.758345i \(-0.273992\pi\)
0.651854 + 0.758345i \(0.273992\pi\)
\(212\) −3.50625 3.50625i −0.0165389 0.0165389i
\(213\) −50.2739 + 50.2739i −0.236028 + 0.236028i
\(214\) 236.844i 1.10675i
\(215\) −43.4217 116.705i −0.201961 0.542816i
\(216\) −14.6969 −0.0680414
\(217\) −40.4354 40.4354i −0.186338 0.186338i
\(218\) −21.5303 + 21.5303i −0.0987628 + 0.0987628i
\(219\) 90.9414i 0.415257i
\(220\) 59.7379 + 27.3396i 0.271536 + 0.124271i
\(221\) 348.332 1.57616
\(222\) 34.5795 + 34.5795i 0.155763 + 0.155763i
\(223\) 75.3025 75.3025i 0.337679 0.337679i −0.517814 0.855493i \(-0.673254\pi\)
0.855493 + 0.517814i \(0.173254\pi\)
\(224\) 11.6670i 0.0520849i
\(225\) −56.7604 + 49.0231i −0.252268 + 0.217880i
\(226\) 144.647 0.640031
\(227\) 314.742 + 314.742i 1.38653 + 1.38653i 0.832491 + 0.554038i \(0.186914\pi\)
0.554038 + 0.832491i \(0.313086\pi\)
\(228\) −20.0516 + 20.0516i −0.0879456 + 0.0879456i
\(229\) 101.559i 0.443490i 0.975105 + 0.221745i \(0.0711752\pi\)
−0.975105 + 0.221745i \(0.928825\pi\)
\(230\) −14.1123 + 30.8358i −0.0613577 + 0.134068i
\(231\) −23.4688 −0.101596
\(232\) −12.6749 12.6749i −0.0546332 0.0546332i
\(233\) −195.602 + 195.602i −0.839494 + 0.839494i −0.988792 0.149298i \(-0.952299\pi\)
0.149298 + 0.988792i \(0.452299\pi\)
\(234\) 96.1795i 0.411024i
\(235\) 146.909 54.6592i 0.625144 0.232592i
\(236\) −169.309 −0.717413
\(237\) −117.215 117.215i −0.494576 0.494576i
\(238\) −31.6907 + 31.6907i −0.133154 + 0.133154i
\(239\) 262.676i 1.09906i −0.835473 0.549531i \(-0.814806\pi\)
0.835473 0.549531i \(-0.185194\pi\)
\(240\) 12.0796 + 32.4666i 0.0503317 + 0.135278i
\(241\) 290.284 1.20450 0.602249 0.798308i \(-0.294271\pi\)
0.602249 + 0.798308i \(0.294271\pi\)
\(242\) 77.8393 + 77.8393i 0.321650 + 0.321650i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 61.9612i 0.253939i
\(245\) −203.438 93.1054i −0.830360 0.380022i
\(246\) 170.642 0.693667
\(247\) 131.221 + 131.221i 0.531261 + 0.531261i
\(248\) 55.4526 55.4526i 0.223599 0.223599i
\(249\) 108.748i 0.436738i
\(250\) 154.948 + 85.0951i 0.619791 + 0.340381i
\(251\) 77.4485 0.308560 0.154280 0.988027i \(-0.450694\pi\)
0.154280 + 0.988027i \(0.450694\pi\)
\(252\) −8.75027 8.75027i −0.0347233 0.0347233i
\(253\) 22.2789 22.2789i 0.0880588 0.0880588i
\(254\) 149.262i 0.587646i
\(255\) 55.3765 120.999i 0.217163 0.474507i
\(256\) 16.0000 0.0625000
\(257\) 214.236 + 214.236i 0.833602 + 0.833602i 0.988008 0.154406i \(-0.0493463\pi\)
−0.154406 + 0.988008i \(0.549346\pi\)
\(258\) −43.1355 + 43.1355i −0.167192 + 0.167192i
\(259\) 41.1758i 0.158980i
\(260\) 212.468 79.0513i 0.817184 0.304043i
\(261\) −19.0124 −0.0728443
\(262\) 159.638 + 159.638i 0.609304 + 0.609304i
\(263\) −208.462 + 208.462i −0.792632 + 0.792632i −0.981921 0.189289i \(-0.939382\pi\)
0.189289 + 0.981921i \(0.439382\pi\)
\(264\) 32.1847i 0.121912i
\(265\) 4.32276 + 11.6184i 0.0163123 + 0.0438429i
\(266\) −23.8766 −0.0897618
\(267\) −174.047 174.047i −0.651863 0.651863i
\(268\) 61.4976 61.4976i 0.229469 0.229469i
\(269\) 177.937i 0.661474i 0.943723 + 0.330737i \(0.107297\pi\)
−0.943723 + 0.330737i \(0.892703\pi\)
\(270\) 33.4097 + 15.2903i 0.123740 + 0.0566306i
\(271\) 196.940 0.726717 0.363359 0.931649i \(-0.381630\pi\)
0.363359 + 0.931649i \(0.381630\pi\)
\(272\) −43.4602 43.4602i −0.159780 0.159780i
\(273\) −57.2634 + 57.2634i −0.209756 + 0.209756i
\(274\) 93.0261i 0.339511i
\(275\) −107.355 124.299i −0.390383 0.451997i
\(276\) 16.6132 0.0601929
\(277\) 35.9249 + 35.9249i 0.129693 + 0.129693i 0.768973 0.639281i \(-0.220768\pi\)
−0.639281 + 0.768973i \(0.720768\pi\)
\(278\) 128.651 128.651i 0.462774 0.462774i
\(279\) 83.1789i 0.298132i
\(280\) −12.1380 + 26.5220i −0.0433501 + 0.0947213i
\(281\) −308.880 −1.09922 −0.549609 0.835422i \(-0.685223\pi\)
−0.549609 + 0.835422i \(0.685223\pi\)
\(282\) −54.2990 54.2990i −0.192549 0.192549i
\(283\) −145.332 + 145.332i −0.513541 + 0.513541i −0.915610 0.402068i \(-0.868291\pi\)
0.402068 + 0.915610i \(0.368291\pi\)
\(284\) 82.0970i 0.289074i
\(285\) 66.4432 24.7210i 0.233134 0.0867404i
\(286\) −210.623 −0.736444
\(287\) 101.597 + 101.597i 0.353996 + 0.353996i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 52.9013i 0.183050i
\(290\) 15.6265 + 41.9997i 0.0538846 + 0.144827i
\(291\) 243.256 0.835931
\(292\) −74.2533 74.2533i −0.254292 0.254292i
\(293\) −241.012 + 241.012i −0.822568 + 0.822568i −0.986476 0.163908i \(-0.947590\pi\)
0.163908 + 0.986476i \(0.447590\pi\)
\(294\) 109.606i 0.372808i
\(295\) 384.881 + 176.145i 1.30468 + 0.597100i
\(296\) −56.4680 −0.190770
\(297\) −24.1386 24.1386i −0.0812746 0.0812746i
\(298\) 93.9923 93.9923i 0.315410 0.315410i
\(299\) 108.720i 0.363613i
\(300\) 6.31746 86.3718i 0.0210582 0.287906i
\(301\) −51.3640 −0.170645
\(302\) −170.451 170.451i −0.564406 0.564406i
\(303\) −147.973 + 147.973i −0.488358 + 0.488358i
\(304\) 32.7441i 0.107711i
\(305\) 64.4626 140.853i 0.211353 0.461812i
\(306\) −65.1903 −0.213040
\(307\) 68.9379 + 68.9379i 0.224553 + 0.224553i 0.810413 0.585859i \(-0.199243\pi\)
−0.585859 + 0.810413i \(0.699243\pi\)
\(308\) 19.1622 19.1622i 0.0622148 0.0622148i
\(309\) 77.8793i 0.252037i
\(310\) −183.748 + 68.3659i −0.592737 + 0.220535i
\(311\) 516.333 1.66024 0.830118 0.557588i \(-0.188273\pi\)
0.830118 + 0.557588i \(0.188273\pi\)
\(312\) −78.5302 78.5302i −0.251700 0.251700i
\(313\) −41.6424 + 41.6424i −0.133043 + 0.133043i −0.770492 0.637449i \(-0.779989\pi\)
0.637449 + 0.770492i \(0.279989\pi\)
\(314\) 116.732i 0.371758i
\(315\) 10.7879 + 28.9950i 0.0342475 + 0.0920476i
\(316\) 191.410 0.605729
\(317\) 132.540 + 132.540i 0.418106 + 0.418106i 0.884551 0.466444i \(-0.154465\pi\)
−0.466444 + 0.884551i \(0.654465\pi\)
\(318\) 4.29427 4.29427i 0.0135040 0.0135040i
\(319\) 41.6351i 0.130517i
\(320\) −36.3719 16.6459i −0.113662 0.0520185i
\(321\) −290.074 −0.903657
\(322\) 9.89120 + 9.89120i 0.0307180 + 0.0307180i
\(323\) −88.9416 + 88.9416i −0.275361 + 0.275361i
\(324\) 18.0000i 0.0555556i
\(325\) −565.233 41.3426i −1.73918 0.127208i
\(326\) −48.0687 −0.147450
\(327\) −26.3691 26.3691i −0.0806395 0.0806395i
\(328\) −139.329 + 139.329i −0.424782 + 0.424782i
\(329\) 64.6570i 0.196526i
\(330\) −33.4841 + 73.1637i −0.101467 + 0.221708i
\(331\) −345.899 −1.04501 −0.522506 0.852635i \(-0.675003\pi\)
−0.522506 + 0.852635i \(0.675003\pi\)
\(332\) 88.7922 + 88.7922i 0.267446 + 0.267446i
\(333\) −42.3510 + 42.3510i −0.127180 + 0.127180i
\(334\) 257.990i 0.772426i
\(335\) −203.779 + 75.8186i −0.608296 + 0.226324i
\(336\) 14.2891 0.0425272
\(337\) −257.263 257.263i −0.763393 0.763393i 0.213541 0.976934i \(-0.431500\pi\)
−0.976934 + 0.213541i \(0.931500\pi\)
\(338\) −344.917 + 344.917i −1.02046 + 1.02046i
\(339\) 177.156i 0.522583i
\(340\) 53.5808 + 144.010i 0.157591 + 0.423560i
\(341\) 182.153 0.534173
\(342\) −24.5581 24.5581i −0.0718073 0.0718073i
\(343\) −136.717 + 136.717i −0.398593 + 0.398593i
\(344\) 70.4399i 0.204767i
\(345\) −37.7659 17.2839i −0.109466 0.0500984i
\(346\) 29.6868 0.0858000
\(347\) 212.920 + 212.920i 0.613601 + 0.613601i 0.943883 0.330281i \(-0.107144\pi\)
−0.330281 + 0.943883i \(0.607144\pi\)
\(348\) 15.5235 15.5235i 0.0446078 0.0446078i
\(349\) 377.789i 1.08249i −0.840865 0.541244i \(-0.817953\pi\)
0.840865 0.541244i \(-0.182047\pi\)
\(350\) 55.1854 47.6628i 0.157672 0.136179i
\(351\) −117.795 −0.335599
\(352\) 26.2787 + 26.2787i 0.0746555 + 0.0746555i
\(353\) 96.2068 96.2068i 0.272541 0.272541i −0.557582 0.830122i \(-0.688271\pi\)
0.830122 + 0.557582i \(0.188271\pi\)
\(354\) 207.361i 0.585765i
\(355\) −85.4113 + 186.626i −0.240595 + 0.525708i
\(356\) 284.218 0.798366
\(357\) −38.8130 38.8130i −0.108720 0.108720i
\(358\) 10.8323 10.8323i 0.0302579 0.0302579i
\(359\) 181.790i 0.506380i 0.967417 + 0.253190i \(0.0814798\pi\)
−0.967417 + 0.253190i \(0.918520\pi\)
\(360\) −39.7634 + 14.7945i −0.110454 + 0.0410957i
\(361\) 293.989 0.814374
\(362\) 2.96458 + 2.96458i 0.00818944 + 0.00818944i
\(363\) −95.3332 + 95.3332i −0.262626 + 0.262626i
\(364\) 93.5107i 0.256898i
\(365\) 91.5447 + 246.047i 0.250808 + 0.674101i
\(366\) −75.8867 −0.207341
\(367\) 28.4702 + 28.4702i 0.0775756 + 0.0775756i 0.744830 0.667254i \(-0.232531\pi\)
−0.667254 + 0.744830i \(0.732531\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 208.993i 0.566376i
\(370\) 128.365 + 58.7477i 0.346934 + 0.158778i
\(371\) 5.11344 0.0137829
\(372\) 67.9153 + 67.9153i 0.182568 + 0.182568i
\(373\) −94.2294 + 94.2294i −0.252626 + 0.252626i −0.822046 0.569421i \(-0.807168\pi\)
0.569421 + 0.822046i \(0.307168\pi\)
\(374\) 142.760i 0.381711i
\(375\) −104.220 + 189.772i −0.277920 + 0.506057i
\(376\) 88.6698 0.235824
\(377\) −101.589 101.589i −0.269466 0.269466i
\(378\) 10.7168 10.7168i 0.0283514 0.0283514i
\(379\) 139.587i 0.368302i −0.982898 0.184151i \(-0.941046\pi\)
0.982898 0.184151i \(-0.0589536\pi\)
\(380\) −34.0660 + 74.4353i −0.0896474 + 0.195882i
\(381\) 182.808 0.479811
\(382\) −225.451 225.451i −0.590186 0.590186i
\(383\) 115.635 115.635i 0.301920 0.301920i −0.539845 0.841764i \(-0.681517\pi\)
0.841764 + 0.539845i \(0.181517\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −63.4960 + 23.6245i −0.164925 + 0.0613623i
\(386\) −463.597 −1.20103
\(387\) −52.8300 52.8300i −0.136512 0.136512i
\(388\) −198.618 + 198.618i −0.511901 + 0.511901i
\(389\) 443.439i 1.13995i 0.821663 + 0.569974i \(0.193047\pi\)
−0.821663 + 0.569974i \(0.806953\pi\)
\(390\) 96.8177 + 260.219i 0.248250 + 0.667228i
\(391\) 73.6904 0.188466
\(392\) −89.4925 89.4925i −0.228297 0.228297i
\(393\) −195.515 + 195.515i −0.497495 + 0.497495i
\(394\) 481.969i 1.22327i
\(395\) −435.122 199.138i −1.10158 0.504147i
\(396\) 39.4181 0.0995407
\(397\) −471.063 471.063i −1.18656 1.18656i −0.978013 0.208544i \(-0.933128\pi\)
−0.208544 0.978013i \(-0.566872\pi\)
\(398\) −87.8703 + 87.8703i −0.220780 + 0.220780i
\(399\) 29.2428i 0.0732902i
\(400\) 65.3641 + 75.6805i 0.163410 + 0.189201i
\(401\) 736.854 1.83754 0.918771 0.394791i \(-0.129183\pi\)
0.918771 + 0.394791i \(0.129183\pi\)
\(402\) 75.3189 + 75.3189i 0.187360 + 0.187360i
\(403\) 444.450 444.450i 1.10285 1.10285i
\(404\) 241.638i 0.598114i
\(405\) −18.7267 + 40.9184i −0.0462387 + 0.101033i
\(406\) 18.4848 0.0455291
\(407\) −92.7442 92.7442i −0.227873 0.227873i
\(408\) 53.2277 53.2277i 0.130460 0.130460i
\(409\) 593.667i 1.45151i 0.687954 + 0.725754i \(0.258509\pi\)
−0.687954 + 0.725754i \(0.741491\pi\)
\(410\) 461.681 171.774i 1.12605 0.418961i
\(411\) 113.933 0.277210
\(412\) −63.5882 63.5882i −0.154340 0.154340i
\(413\) 123.459 123.459i 0.298931 0.298931i
\(414\) 20.3470i 0.0491473i
\(415\) −109.469 294.223i −0.263781 0.708971i
\(416\) 128.239 0.308268
\(417\) 157.565 + 157.565i 0.377853 + 0.377853i
\(418\) 53.7796 53.7796i 0.128659 0.128659i
\(419\) 450.030i 1.07406i −0.843564 0.537028i \(-0.819547\pi\)
0.843564 0.537028i \(-0.180453\pi\)
\(420\) −32.4826 14.8660i −0.0773396 0.0353952i
\(421\) −715.043 −1.69844 −0.849220 0.528039i \(-0.822928\pi\)
−0.849220 + 0.528039i \(0.822928\pi\)
\(422\) −275.082 275.082i −0.651854 0.651854i
\(423\) 66.5024 66.5024i 0.157216 0.157216i
\(424\) 7.01251i 0.0165389i
\(425\) 28.0220 383.114i 0.0659340 0.901445i
\(426\) 100.548 0.236028
\(427\) −45.1814 45.1814i −0.105811 0.105811i
\(428\) 236.844 236.844i 0.553374 0.553374i
\(429\) 257.959i 0.601304i
\(430\) −73.2837 + 160.127i −0.170427 + 0.372388i
\(431\) −643.338 −1.49266 −0.746332 0.665574i \(-0.768187\pi\)
−0.746332 + 0.665574i \(0.768187\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 198.297 198.297i 0.457961 0.457961i −0.440025 0.897986i \(-0.645030\pi\)
0.897986 + 0.440025i \(0.145030\pi\)
\(434\) 80.8708i 0.186338i
\(435\) −51.4390 + 19.1385i −0.118250 + 0.0439966i
\(436\) 43.0606 0.0987628
\(437\) 27.7602 + 27.7602i 0.0635244 + 0.0635244i
\(438\) 90.9414 90.9414i 0.207629 0.207629i
\(439\) 337.344i 0.768438i −0.923242 0.384219i \(-0.874471\pi\)
0.923242 0.384219i \(-0.125529\pi\)
\(440\) −32.3983 87.0775i −0.0736325 0.197904i
\(441\) −134.239 −0.304396
\(442\) −348.332 348.332i −0.788081 0.788081i
\(443\) 109.373 109.373i 0.246892 0.246892i −0.572802 0.819694i \(-0.694143\pi\)
0.819694 + 0.572802i \(0.194143\pi\)
\(444\) 69.1589i 0.155763i
\(445\) −646.097 295.692i −1.45190 0.664477i
\(446\) −150.605 −0.337679
\(447\) 115.117 + 115.117i 0.257531 + 0.257531i
\(448\) −11.6670 + 11.6670i −0.0260425 + 0.0260425i
\(449\) 372.277i 0.829124i −0.910021 0.414562i \(-0.863935\pi\)
0.910021 0.414562i \(-0.136065\pi\)
\(450\) 105.783 + 7.73727i 0.235074 + 0.0171939i
\(451\) −457.672 −1.01479
\(452\) −144.647 144.647i −0.320016 0.320016i
\(453\) 208.758 208.758i 0.460835 0.460835i
\(454\) 629.484i 1.38653i
\(455\) −97.2858 + 212.572i −0.213815 + 0.467192i
\(456\) 40.1032 0.0879456
\(457\) 10.4967 + 10.4967i 0.0229688 + 0.0229688i 0.718498 0.695529i \(-0.244830\pi\)
−0.695529 + 0.718498i \(0.744830\pi\)
\(458\) 101.559 101.559i 0.221745 0.221745i
\(459\) 79.8415i 0.173947i
\(460\) 44.9480 16.7235i 0.0977131 0.0363554i
\(461\) −833.333 −1.80766 −0.903832 0.427887i \(-0.859258\pi\)
−0.903832 + 0.427887i \(0.859258\pi\)
\(462\) 23.4688 + 23.4688i 0.0507982 + 0.0507982i
\(463\) 52.1194 52.1194i 0.112569 0.112569i −0.648579 0.761148i \(-0.724636\pi\)
0.761148 + 0.648579i \(0.224636\pi\)
\(464\) 25.3498i 0.0546332i
\(465\) −83.7308 225.045i −0.180066 0.483968i
\(466\) 391.204 0.839494
\(467\) −185.727 185.727i −0.397703 0.397703i 0.479719 0.877422i \(-0.340738\pi\)
−0.877422 + 0.479719i \(0.840738\pi\)
\(468\) 96.1795 96.1795i 0.205512 0.205512i
\(469\) 89.6867i 0.191230i
\(470\) −201.568 92.2495i −0.428868 0.196276i
\(471\) 142.967 0.303539
\(472\) 169.309 + 169.309i 0.358706 + 0.358706i
\(473\) 115.692 115.692i 0.244592 0.244592i
\(474\) 234.429i 0.494576i
\(475\) 154.881 133.768i 0.326064 0.281617i
\(476\) 63.3814 0.133154
\(477\) 5.25938 + 5.25938i 0.0110260 + 0.0110260i
\(478\) −262.676 + 262.676i −0.549531 + 0.549531i
\(479\) 384.415i 0.802536i 0.915961 + 0.401268i \(0.131430\pi\)
−0.915961 + 0.401268i \(0.868570\pi\)
\(480\) 20.3870 44.5463i 0.0424730 0.0928047i
\(481\) −452.589 −0.940933
\(482\) −290.284 290.284i −0.602249 0.602249i
\(483\) −12.1142 + 12.1142i −0.0250811 + 0.0250811i
\(484\) 155.679i 0.321650i
\(485\) 658.142 244.870i 1.35699 0.504886i
\(486\) 22.0454 0.0453609
\(487\) 176.011 + 176.011i 0.361420 + 0.361420i 0.864335 0.502916i \(-0.167739\pi\)
−0.502916 + 0.864335i \(0.667739\pi\)
\(488\) 61.9612 61.9612i 0.126970 0.126970i
\(489\) 58.8719i 0.120392i
\(490\) 110.333 + 296.544i 0.225169 + 0.605191i
\(491\) 565.321 1.15137 0.575683 0.817673i \(-0.304736\pi\)
0.575683 + 0.817673i \(0.304736\pi\)
\(492\) −170.642 170.642i −0.346833 0.346833i
\(493\) 68.8568 68.8568i 0.139669 0.139669i
\(494\) 262.443i 0.531261i
\(495\) −89.6069 41.0094i −0.181024 0.0828474i
\(496\) −110.905 −0.223599
\(497\) 59.8642 + 59.8642i 0.120451 + 0.120451i
\(498\) −108.748 + 108.748i −0.218369 + 0.218369i
\(499\) 876.225i 1.75596i 0.478696 + 0.877981i \(0.341110\pi\)
−0.478696 + 0.877981i \(0.658890\pi\)
\(500\) −69.8527 240.043i −0.139705 0.480086i
\(501\) 315.972 0.630683
\(502\) −77.4485 77.4485i −0.154280 0.154280i
\(503\) 617.070 617.070i 1.22678 1.22678i 0.261605 0.965175i \(-0.415748\pi\)
0.965175 0.261605i \(-0.0842516\pi\)
\(504\) 17.5005i 0.0347233i
\(505\) −251.393 + 549.302i −0.497809 + 1.08773i
\(506\) −44.5578 −0.0880588
\(507\) −422.435 422.435i −0.833205 0.833205i
\(508\) −149.262 + 149.262i −0.293823 + 0.293823i
\(509\) 466.623i 0.916744i −0.888760 0.458372i \(-0.848433\pi\)
0.888760 0.458372i \(-0.151567\pi\)
\(510\) −176.376 + 65.6228i −0.345835 + 0.128672i
\(511\) 108.289 0.211917
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 30.0774 30.0774i 0.0586304 0.0586304i
\(514\) 428.471i 0.833602i
\(515\) 78.3961 + 210.707i 0.152225 + 0.409139i
\(516\) 86.2710 0.167192
\(517\) 145.633 + 145.633i 0.281689 + 0.281689i
\(518\) 41.1758 41.1758i 0.0794900 0.0794900i
\(519\) 36.3587i 0.0700554i
\(520\) −291.519 133.416i −0.560614 0.256570i
\(521\) −562.863 −1.08035 −0.540176 0.841552i \(-0.681642\pi\)
−0.540176 + 0.841552i \(0.681642\pi\)
\(522\) 19.0124 + 19.0124i 0.0364221 + 0.0364221i
\(523\) 205.814 205.814i 0.393526 0.393526i −0.482416 0.875942i \(-0.660241\pi\)
0.875942 + 0.482416i \(0.160241\pi\)
\(524\) 319.275i 0.609304i
\(525\) 58.3747 + 67.5880i 0.111190 + 0.128739i
\(526\) 416.924 0.792632
\(527\) 301.248 + 301.248i 0.571627 + 0.571627i
\(528\) −32.1847 + 32.1847i −0.0609560 + 0.0609560i
\(529\) 23.0000i 0.0434783i
\(530\) 7.29561 15.9411i 0.0137653 0.0300776i
\(531\) 253.964 0.478275
\(532\) 23.8766 + 23.8766i 0.0448809 + 0.0448809i
\(533\) −1116.71 + 1116.71i −2.09515 + 2.09515i
\(534\) 348.095i 0.651863i
\(535\) −784.810 + 291.998i −1.46693 + 0.545791i
\(536\) −122.995 −0.229469
\(537\) 13.2668 + 13.2668i 0.0247055 + 0.0247055i
\(538\) 177.937 177.937i 0.330737 0.330737i
\(539\) 293.969i 0.545397i
\(540\) −18.1194 48.7000i −0.0335545 0.0901851i
\(541\) −152.262 −0.281445 −0.140723 0.990049i \(-0.544943\pi\)
−0.140723 + 0.990049i \(0.544943\pi\)
\(542\) −196.940 196.940i −0.363359 0.363359i
\(543\) −3.63085 + 3.63085i −0.00668665 + 0.00668665i
\(544\) 86.9204i 0.159780i
\(545\) −97.8871 44.7990i −0.179609 0.0822000i
\(546\) 114.527 0.209756
\(547\) 486.325 + 486.325i 0.889076 + 0.889076i 0.994434 0.105358i \(-0.0335989\pi\)
−0.105358 + 0.994434i \(0.533599\pi\)
\(548\) −93.0261 + 93.0261i −0.169756 + 0.169756i
\(549\) 92.9418i 0.169293i
\(550\) −16.9438 + 231.655i −0.0308069 + 0.421190i
\(551\) 51.8786 0.0941535
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −139.574 + 139.574i −0.252395 + 0.252395i
\(554\) 71.8498i 0.129693i
\(555\) −71.9509 + 157.215i −0.129641 + 0.283270i
\(556\) −257.302 −0.462774
\(557\) −93.7887 93.7887i −0.168382 0.168382i 0.617886 0.786268i \(-0.287989\pi\)
−0.786268 + 0.617886i \(0.787989\pi\)
\(558\) −83.1789 + 83.1789i −0.149066 + 0.149066i
\(559\) 564.573i 1.00997i
\(560\) 38.6600 14.3839i 0.0690357 0.0256856i
\(561\) 174.844 0.311666
\(562\) 308.880 + 308.880i 0.549609 + 0.549609i
\(563\) −4.76825 + 4.76825i −0.00846936 + 0.00846936i −0.711329 0.702859i \(-0.751906\pi\)
0.702859 + 0.711329i \(0.251906\pi\)
\(564\) 108.598i 0.192549i
\(565\) 178.331 + 479.304i 0.315630 + 0.848326i
\(566\) 290.664 0.513541
\(567\) 13.1254 + 13.1254i 0.0231489 + 0.0231489i
\(568\) −82.0970 + 82.0970i −0.144537 + 0.144537i
\(569\) 993.556i 1.74614i 0.487591 + 0.873072i \(0.337876\pi\)
−0.487591 + 0.873072i \(0.662124\pi\)
\(570\) −91.1642 41.7222i −0.159937 0.0731968i
\(571\) 524.502 0.918567 0.459284 0.888290i \(-0.348106\pi\)
0.459284 + 0.888290i \(0.348106\pi\)
\(572\) 210.623 + 210.623i 0.368222 + 0.368222i
\(573\) 276.120 276.120i 0.481885 0.481885i
\(574\) 203.194i 0.353996i
\(575\) −119.576 8.74612i −0.207959 0.0152107i
\(576\) −24.0000 −0.0416667
\(577\) −441.957 441.957i −0.765956 0.765956i 0.211435 0.977392i \(-0.432186\pi\)
−0.977392 + 0.211435i \(0.932186\pi\)
\(578\) −52.9013 + 52.9013i −0.0915248 + 0.0915248i
\(579\) 567.788i 0.980636i
\(580\) 26.3732 57.6263i 0.0454710 0.0993556i
\(581\) −129.493 −0.222879
\(582\) −243.256 243.256i −0.417965 0.417965i
\(583\) −11.5175 + 11.5175i −0.0197556 + 0.0197556i
\(584\) 148.507i 0.254292i
\(585\) −318.702 + 118.577i −0.544789 + 0.202696i
\(586\) 482.025 0.822568
\(587\) 659.069 + 659.069i 1.12278 + 1.12278i 0.991322 + 0.131453i \(0.0419644\pi\)
0.131453 + 0.991322i \(0.458036\pi\)
\(588\) 109.606 109.606i 0.186404 0.186404i
\(589\) 226.968i 0.385345i
\(590\) −208.737 561.026i −0.353791 0.950891i
\(591\) 590.290 0.998798
\(592\) 56.4680 + 56.4680i 0.0953852 + 0.0953852i
\(593\) −224.731 + 224.731i −0.378973 + 0.378973i −0.870732 0.491758i \(-0.836354\pi\)
0.491758 + 0.870732i \(0.336354\pi\)
\(594\) 48.2771i 0.0812746i
\(595\) −144.081 65.9402i −0.242153 0.110824i
\(596\) −187.985 −0.315410
\(597\) −107.619 107.619i −0.180266 0.180266i
\(598\) −108.720 + 108.720i −0.181806 + 0.181806i
\(599\) 104.512i 0.174477i 0.996187 + 0.0872386i \(0.0278043\pi\)
−0.996187 + 0.0872386i \(0.972196\pi\)
\(600\) −92.6893 + 80.0544i −0.154482 + 0.133424i
\(601\) −368.220 −0.612679 −0.306340 0.951922i \(-0.599104\pi\)
−0.306340 + 0.951922i \(0.599104\pi\)
\(602\) 51.3640 + 51.3640i 0.0853223 + 0.0853223i
\(603\) −92.2464 + 92.2464i −0.152979 + 0.152979i
\(604\) 340.901i 0.564406i
\(605\) −161.963 + 353.895i −0.267708 + 0.584950i
\(606\) 295.945 0.488358
\(607\) 697.004 + 697.004i 1.14828 + 1.14828i 0.986891 + 0.161385i \(0.0515962\pi\)
0.161385 + 0.986891i \(0.448404\pi\)
\(608\) −32.7441 + 32.7441i −0.0538554 + 0.0538554i
\(609\) 22.6392i 0.0371743i
\(610\) −205.315 + 76.3902i −0.336583 + 0.125230i
\(611\) 710.685 1.16315
\(612\) 65.1903 + 65.1903i 0.106520 + 0.106520i
\(613\) 314.788 314.788i 0.513520 0.513520i −0.402083 0.915603i \(-0.631714\pi\)
0.915603 + 0.402083i \(0.131714\pi\)
\(614\) 137.876i 0.224553i
\(615\) 210.379 + 565.441i 0.342080 + 0.919417i
\(616\) −38.3243 −0.0622148
\(617\) −371.648 371.648i −0.602346 0.602346i 0.338588 0.940935i \(-0.390051\pi\)
−0.940935 + 0.338588i \(0.890051\pi\)
\(618\) 77.8793 77.8793i 0.126018 0.126018i
\(619\) 522.132i 0.843509i −0.906710 0.421755i \(-0.861414\pi\)
0.906710 0.421755i \(-0.138586\pi\)
\(620\) 252.114 + 115.383i 0.406636 + 0.186101i
\(621\) −24.9199 −0.0401286
\(622\) −516.333 516.333i −0.830118 0.830118i
\(623\) −207.249 + 207.249i −0.332663 + 0.332663i
\(624\) 157.060i 0.251700i
\(625\) −90.9417 + 618.348i −0.145507 + 0.989357i
\(626\) 83.2848 0.133043
\(627\) 65.8663 + 65.8663i 0.105050 + 0.105050i
\(628\) −116.732 + 116.732i −0.185879 + 0.185879i
\(629\) 306.764i 0.487701i
\(630\) 18.2070 39.7829i 0.0289001 0.0631475i
\(631\) −1205.43 −1.91034 −0.955171 0.296056i \(-0.904329\pi\)
−0.955171 + 0.296056i \(0.904329\pi\)
\(632\) −191.410 191.410i −0.302865 0.302865i
\(633\) 336.905 336.905i 0.532236 0.532236i
\(634\) 265.079i 0.418106i
\(635\) 494.597 184.021i 0.778893 0.289797i
\(636\) −8.58853 −0.0135040
\(637\) −717.279 717.279i −1.12603 1.12603i
\(638\) −41.6351 + 41.6351i −0.0652587 + 0.0652587i
\(639\) 123.145i 0.192716i
\(640\) 19.7259 + 53.0178i 0.0308218 + 0.0828403i
\(641\) 274.948 0.428936 0.214468 0.976731i \(-0.431198\pi\)
0.214468 + 0.976731i \(0.431198\pi\)
\(642\) 290.074 + 290.074i 0.451828 + 0.451828i
\(643\) −253.931 + 253.931i −0.394916 + 0.394916i −0.876435 0.481520i \(-0.840085\pi\)
0.481520 + 0.876435i \(0.340085\pi\)
\(644\) 19.7824i 0.0307180i
\(645\) −196.115 89.7538i −0.304054 0.139153i
\(646\) 177.883 0.275361
\(647\) 486.345 + 486.345i 0.751693 + 0.751693i 0.974795 0.223102i \(-0.0716184\pi\)
−0.223102 + 0.974795i \(0.571618\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 556.154i 0.856941i
\(650\) 523.891 + 606.576i 0.805986 + 0.933194i
\(651\) −99.0461 −0.152145
\(652\) 48.0687 + 48.0687i 0.0737250 + 0.0737250i
\(653\) 85.6860 85.6860i 0.131219 0.131219i −0.638447 0.769666i \(-0.720423\pi\)
0.769666 + 0.638447i \(0.220423\pi\)
\(654\) 52.7382i 0.0806395i
\(655\) −332.165 + 725.790i −0.507122 + 1.10808i
\(656\) 278.657 0.424782
\(657\) 111.380 + 111.380i 0.169528 + 0.169528i
\(658\) −64.6570 + 64.6570i −0.0982630 + 0.0982630i
\(659\) 329.137i 0.499450i 0.968317 + 0.249725i \(0.0803402\pi\)
−0.968317 + 0.249725i \(0.919660\pi\)
\(660\) 106.648 39.6796i 0.161588 0.0601207i
\(661\) −845.705 −1.27943 −0.639717 0.768611i \(-0.720948\pi\)
−0.639717 + 0.768611i \(0.720948\pi\)
\(662\) 345.899 + 345.899i 0.522506 + 0.522506i
\(663\) 426.618 426.618i 0.643465 0.643465i
\(664\) 177.584i 0.267446i
\(665\) −29.4368 79.1179i −0.0442659 0.118974i
\(666\) 84.7020 0.127180
\(667\) −21.4913 21.4913i −0.0322209 0.0322209i
\(668\) −257.990 + 257.990i −0.386213 + 0.386213i
\(669\) 184.453i 0.275714i
\(670\) 279.598 + 127.961i 0.417310 + 0.190986i
\(671\) 203.533 0.303328
\(672\) −14.2891 14.2891i −0.0212636 0.0212636i
\(673\) 462.307 462.307i 0.686935 0.686935i −0.274619 0.961553i \(-0.588552\pi\)
0.961553 + 0.274619i \(0.0885516\pi\)
\(674\) 514.527i 0.763393i
\(675\) −9.47619 + 129.558i −0.0140388 + 0.191937i
\(676\) 689.833 1.02046
\(677\) −324.228 324.228i −0.478919 0.478919i 0.425867 0.904786i \(-0.359969\pi\)
−0.904786 + 0.425867i \(0.859969\pi\)
\(678\) 177.156 177.156i 0.261292 0.261292i
\(679\) 289.659i 0.426597i
\(680\) 90.4295 197.591i 0.132985 0.290575i
\(681\) 770.958 1.13210
\(682\) −182.153 182.153i −0.267086 0.267086i
\(683\) 448.652 448.652i 0.656884 0.656884i −0.297757 0.954642i \(-0.596239\pi\)
0.954642 + 0.297757i \(0.0962386\pi\)
\(684\) 49.1162i 0.0718073i
\(685\) 308.252 114.689i 0.450004 0.167429i
\(686\) 273.435 0.398593
\(687\) 124.384 + 124.384i 0.181054 + 0.181054i
\(688\) −70.4399 + 70.4399i −0.102384 + 0.102384i
\(689\) 56.2050i 0.0815747i
\(690\) 20.4820 + 55.0499i 0.0296840 + 0.0797824i
\(691\) −570.580 −0.825731 −0.412866 0.910792i \(-0.635472\pi\)
−0.412866 + 0.910792i \(0.635472\pi\)
\(692\) −29.6868 29.6868i −0.0429000 0.0429000i
\(693\) −28.7432 + 28.7432i −0.0414765 + 0.0414765i
\(694\) 425.839i 0.613601i
\(695\) 584.910 + 267.690i 0.841597 + 0.385165i
\(696\) −31.0471 −0.0446078
\(697\) −756.906 756.906i −1.08595 1.08595i
\(698\) −377.789 + 377.789i −0.541244 + 0.541244i
\(699\) 479.125i 0.685444i
\(700\) −102.848 7.52258i −0.146926 0.0107465i
\(701\) −250.724 −0.357666 −0.178833 0.983879i \(-0.557232\pi\)
−0.178833 + 0.983879i \(0.557232\pi\)
\(702\) 117.795 + 117.795i 0.167800 + 0.167800i
\(703\) 115.562 115.562i 0.164384 0.164384i
\(704\) 52.5575i 0.0746555i
\(705\) 112.982 246.869i 0.160258 0.350169i
\(706\) −192.414 −0.272541
\(707\) 176.200 + 176.200i 0.249222 + 0.249222i
\(708\) −207.361 + 207.361i −0.292882 + 0.292882i
\(709\) 1105.31i 1.55898i 0.626417 + 0.779488i \(0.284521\pi\)
−0.626417 + 0.779488i \(0.715479\pi\)
\(710\) 272.038 101.215i 0.383152 0.142556i
\(711\) −287.116 −0.403820
\(712\) −284.218 284.218i −0.399183 0.399183i
\(713\) 94.0244 94.0244i 0.131872 0.131872i
\(714\) 77.6260i 0.108720i
\(715\) −259.671 697.923i −0.363176 0.976116i
\(716\) −21.6647 −0.0302579
\(717\) −321.711 321.711i −0.448690 0.448690i
\(718\) 181.790 181.790i 0.253190 0.253190i
\(719\) 693.532i 0.964579i 0.876012 + 0.482289i \(0.160195\pi\)
−0.876012 + 0.482289i \(0.839805\pi\)
\(720\) 54.5578 + 24.9689i 0.0757747 + 0.0346790i
\(721\) 92.7356 0.128621
\(722\) −293.989 293.989i −0.407187 0.407187i
\(723\) 355.524 355.524i 0.491735 0.491735i
\(724\) 5.92916i 0.00818944i
\(725\) −119.905 + 103.560i −0.165387 + 0.142842i
\(726\) 190.666 0.262626
\(727\) 508.634 + 508.634i 0.699634 + 0.699634i 0.964332 0.264697i \(-0.0852721\pi\)
−0.264697 + 0.964332i \(0.585272\pi\)
\(728\) −93.5107 + 93.5107i −0.128449 + 0.128449i
\(729\) 27.0000i 0.0370370i
\(730\) 154.502 337.591i 0.211647 0.462454i
\(731\) 382.667 0.523484
\(732\) 75.8867 + 75.8867i 0.103670 + 0.103670i
\(733\) 685.681 685.681i 0.935445 0.935445i −0.0625940 0.998039i \(-0.519937\pi\)
0.998039 + 0.0625940i \(0.0199373\pi\)
\(734\) 56.9405i 0.0775756i
\(735\) −363.190 + 135.129i −0.494136 + 0.183850i
\(736\) 27.1293 0.0368605
\(737\) −202.010 202.010i −0.274098 0.274098i
\(738\) 208.993 208.993i 0.283188 0.283188i
\(739\) 60.5009i 0.0818686i 0.999162 + 0.0409343i \(0.0130334\pi\)
−0.999162 + 0.0409343i \(0.986967\pi\)
\(740\) −69.6178 187.113i −0.0940781 0.252856i
\(741\) 321.425 0.433772
\(742\) −5.11344 5.11344i −0.00689143 0.00689143i
\(743\) −323.462 + 323.462i −0.435346 + 0.435346i −0.890442 0.455096i \(-0.849605\pi\)
0.455096 + 0.890442i \(0.349605\pi\)
\(744\) 135.831i 0.182568i
\(745\) 427.334 + 195.574i 0.573603 + 0.262515i
\(746\) 188.459 0.252626
\(747\) −133.188 133.188i −0.178298 0.178298i
\(748\) −142.760 + 142.760i −0.190855 + 0.190855i
\(749\) 345.408i 0.461159i
\(750\) 293.991 85.5517i 0.391988 0.114069i
\(751\) −20.9996 −0.0279622 −0.0139811 0.999902i \(-0.504450\pi\)
−0.0139811 + 0.999902i \(0.504450\pi\)
\(752\) −88.6698 88.6698i −0.117912 0.117912i
\(753\) 94.8546 94.8546i 0.125969 0.125969i
\(754\) 203.178i 0.269466i
\(755\) 354.664 774.951i 0.469753 1.02642i
\(756\) −21.4337 −0.0283514
\(757\) −315.246 315.246i −0.416441 0.416441i 0.467534 0.883975i \(-0.345143\pi\)
−0.883975 + 0.467534i \(0.845143\pi\)
\(758\) −139.587 + 139.587i −0.184151 + 0.184151i
\(759\) 54.5719i 0.0718997i
\(760\) 108.501 40.3693i 0.142765 0.0531174i
\(761\) −828.712 −1.08898 −0.544489 0.838768i \(-0.683276\pi\)
−0.544489 + 0.838768i \(0.683276\pi\)
\(762\) −182.808 182.808i −0.239906 0.239906i
\(763\) −31.3993 + 31.3993i −0.0411524 + 0.0411524i
\(764\) 450.902i 0.590186i
\(765\) −80.3712 216.015i −0.105060 0.282373i
\(766\) −231.270 −0.301920
\(767\) 1357.01 + 1357.01i 1.76924 + 1.76924i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 968.106i 1.25892i −0.777035 0.629458i \(-0.783277\pi\)
0.777035 0.629458i \(-0.216723\pi\)
\(770\) 87.1204 + 39.8715i 0.113143 + 0.0517812i
\(771\) 524.768 0.680633
\(772\) 463.597 + 463.597i 0.600515 + 0.600515i
\(773\) −74.5415 + 74.5415i −0.0964314 + 0.0964314i −0.753677 0.657245i \(-0.771722\pi\)
0.657245 + 0.753677i \(0.271722\pi\)
\(774\) 105.660i 0.136512i
\(775\) −453.076 524.585i −0.584614 0.676884i
\(776\) 397.235 0.511901
\(777\) 50.4299 + 50.4299i 0.0649033 + 0.0649033i
\(778\) 443.439 443.439i 0.569974 0.569974i
\(779\)