Properties

Label 690.3.b.a.599.12
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.12
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.13931 + 2.10317i) q^{3} +2.00000 q^{4} +(-2.73059 - 4.18854i) q^{5} +(3.02545 - 2.97433i) q^{6} -4.11953i q^{7} -2.82843 q^{8} +(0.153334 - 8.99869i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.13931 + 2.10317i) q^{3} +2.00000 q^{4} +(-2.73059 - 4.18854i) q^{5} +(3.02545 - 2.97433i) q^{6} -4.11953i q^{7} -2.82843 q^{8} +(0.153334 - 8.99869i) q^{9} +(3.86164 + 5.92349i) q^{10} -11.6004i q^{11} +(-4.27863 + 4.20634i) q^{12} -7.53864i q^{13} +5.82590i q^{14} +(14.6508 + 3.21770i) q^{15} +4.00000 q^{16} -4.05192 q^{17} +(-0.216847 + 12.7261i) q^{18} +6.12099 q^{19} +(-5.46118 - 8.37708i) q^{20} +(8.66409 + 8.81298i) q^{21} +16.4054i q^{22} -4.79583 q^{23} +(6.05090 - 5.94867i) q^{24} +(-10.0877 + 22.8744i) q^{25} +10.6612i q^{26} +(18.5978 + 19.5735i) q^{27} -8.23907i q^{28} -12.4980i q^{29} +(-20.7194 - 4.55052i) q^{30} -7.25915 q^{31} -5.65685 q^{32} +(24.3976 + 24.8169i) q^{33} +5.73028 q^{34} +(-17.2548 + 11.2488i) q^{35} +(0.306667 - 17.9974i) q^{36} +16.1443i q^{37} -8.65639 q^{38} +(15.8551 + 16.1275i) q^{39} +(7.72328 + 11.8470i) q^{40} +40.8958i q^{41} +(-12.2529 - 12.4634i) q^{42} -54.8610i q^{43} -23.2008i q^{44} +(-38.1101 + 23.9295i) q^{45} +6.78233 q^{46} -14.5420 q^{47} +(-8.55726 + 8.41269i) q^{48} +32.0294 q^{49} +(14.2662 - 32.3493i) q^{50} +(8.66833 - 8.52188i) q^{51} -15.0773i q^{52} -5.66394 q^{53} +(-26.3012 - 27.6811i) q^{54} +(-48.5887 + 31.6759i) q^{55} +11.6518i q^{56} +(-13.0947 + 12.8735i) q^{57} +17.6748i q^{58} -8.63522i q^{59} +(29.3016 + 6.43541i) q^{60} -63.6248 q^{61} +10.2660 q^{62} +(-37.0704 - 0.631663i) q^{63} +8.00000 q^{64} +(-31.5759 + 20.5849i) q^{65} +(-34.5034 - 35.0964i) q^{66} -13.1875i q^{67} -8.10384 q^{68} +(10.2598 - 10.0865i) q^{69} +(24.4020 - 15.9082i) q^{70} +24.4620i q^{71} +(-0.433693 + 25.4521i) q^{72} -18.3104i q^{73} -22.8315i q^{74} +(-26.5279 - 70.1518i) q^{75} +12.2420 q^{76} -47.7882 q^{77} +(-22.4224 - 22.8078i) q^{78} -139.245 q^{79} +(-10.9224 - 16.7542i) q^{80} +(-80.9530 - 2.75961i) q^{81} -57.8354i q^{82} -68.7603 q^{83} +(17.3282 + 17.6260i) q^{84} +(11.0641 + 16.9716i) q^{85} +77.5852i q^{86} +(26.2855 + 26.7372i) q^{87} +32.8109i q^{88} -35.6250i q^{89} +(53.8958 - 33.8414i) q^{90} -31.0557 q^{91} -9.59166 q^{92} +(15.5296 - 15.2672i) q^{93} +20.5655 q^{94} +(-16.7139 - 25.6380i) q^{95} +(12.1018 - 11.8973i) q^{96} -14.7253i q^{97} -45.2965 q^{98} +(-104.388 - 1.77873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.13931 + 2.10317i −0.713105 + 0.701057i
\(4\) 2.00000 0.500000
\(5\) −2.73059 4.18854i −0.546118 0.837708i
\(6\) 3.02545 2.97433i 0.504241 0.495722i
\(7\) 4.11953i 0.588505i −0.955728 0.294252i \(-0.904929\pi\)
0.955728 0.294252i \(-0.0950706\pi\)
\(8\) −2.82843 −0.353553
\(9\) 0.153334 8.99869i 0.0170371 0.999855i
\(10\) 3.86164 + 5.92349i 0.386164 + 0.592349i
\(11\) 11.6004i 1.05458i −0.849685 0.527291i \(-0.823208\pi\)
0.849685 0.527291i \(-0.176792\pi\)
\(12\) −4.27863 + 4.20634i −0.356552 + 0.350529i
\(13\) 7.53864i 0.579895i −0.957043 0.289948i \(-0.906362\pi\)
0.957043 0.289948i \(-0.0936379\pi\)
\(14\) 5.82590i 0.416136i
\(15\) 14.6508 + 3.21770i 0.976721 + 0.214514i
\(16\) 4.00000 0.250000
\(17\) −4.05192 −0.238348 −0.119174 0.992873i \(-0.538025\pi\)
−0.119174 + 0.992873i \(0.538025\pi\)
\(18\) −0.216847 + 12.7261i −0.0120470 + 0.707004i
\(19\) 6.12099 0.322158 0.161079 0.986942i \(-0.448503\pi\)
0.161079 + 0.986942i \(0.448503\pi\)
\(20\) −5.46118 8.37708i −0.273059 0.418854i
\(21\) 8.66409 + 8.81298i 0.412576 + 0.419666i
\(22\) 16.4054i 0.745701i
\(23\) −4.79583 −0.208514
\(24\) 6.05090 5.94867i 0.252121 0.247861i
\(25\) −10.0877 + 22.8744i −0.403510 + 0.914975i
\(26\) 10.6612i 0.410048i
\(27\) 18.5978 + 19.5735i 0.688806 + 0.724945i
\(28\) 8.23907i 0.294252i
\(29\) 12.4980i 0.430966i −0.976508 0.215483i \(-0.930867\pi\)
0.976508 0.215483i \(-0.0691325\pi\)
\(30\) −20.7194 4.55052i −0.690646 0.151684i
\(31\) −7.25915 −0.234166 −0.117083 0.993122i \(-0.537354\pi\)
−0.117083 + 0.993122i \(0.537354\pi\)
\(32\) −5.65685 −0.176777
\(33\) 24.3976 + 24.8169i 0.739322 + 0.752027i
\(34\) 5.73028 0.168538
\(35\) −17.2548 + 11.2488i −0.492995 + 0.321393i
\(36\) 0.306667 17.9974i 0.00851854 0.499927i
\(37\) 16.1443i 0.436333i 0.975912 + 0.218166i \(0.0700075\pi\)
−0.975912 + 0.218166i \(0.929992\pi\)
\(38\) −8.65639 −0.227800
\(39\) 15.8551 + 16.1275i 0.406540 + 0.413526i
\(40\) 7.72328 + 11.8470i 0.193082 + 0.296175i
\(41\) 40.8958i 0.997458i 0.866758 + 0.498729i \(0.166200\pi\)
−0.866758 + 0.498729i \(0.833800\pi\)
\(42\) −12.2529 12.4634i −0.291735 0.296748i
\(43\) 54.8610i 1.27584i −0.770104 0.637918i \(-0.779796\pi\)
0.770104 0.637918i \(-0.220204\pi\)
\(44\) 23.2008i 0.527291i
\(45\) −38.1101 + 23.9295i −0.846891 + 0.531767i
\(46\) 6.78233 0.147442
\(47\) −14.5420 −0.309405 −0.154702 0.987961i \(-0.549442\pi\)
−0.154702 + 0.987961i \(0.549442\pi\)
\(48\) −8.55726 + 8.41269i −0.178276 + 0.175264i
\(49\) 32.0294 0.653662
\(50\) 14.2662 32.3493i 0.285325 0.646985i
\(51\) 8.66833 8.52188i 0.169967 0.167096i
\(52\) 15.0773i 0.289948i
\(53\) −5.66394 −0.106867 −0.0534334 0.998571i \(-0.517016\pi\)
−0.0534334 + 0.998571i \(0.517016\pi\)
\(54\) −26.3012 27.6811i −0.487060 0.512614i
\(55\) −48.5887 + 31.6759i −0.883431 + 0.575926i
\(56\) 11.6518i 0.208068i
\(57\) −13.0947 + 12.8735i −0.229732 + 0.225851i
\(58\) 17.6748i 0.304739i
\(59\) 8.63522i 0.146360i −0.997319 0.0731798i \(-0.976685\pi\)
0.997319 0.0731798i \(-0.0233147\pi\)
\(60\) 29.3016 + 6.43541i 0.488361 + 0.107257i
\(61\) −63.6248 −1.04303 −0.521515 0.853242i \(-0.674633\pi\)
−0.521515 + 0.853242i \(0.674633\pi\)
\(62\) 10.2660 0.165580
\(63\) −37.0704 0.631663i −0.588419 0.0100264i
\(64\) 8.00000 0.125000
\(65\) −31.5759 + 20.5849i −0.485783 + 0.316691i
\(66\) −34.5034 35.0964i −0.522780 0.531763i
\(67\) 13.1875i 0.196828i −0.995146 0.0984141i \(-0.968623\pi\)
0.995146 0.0984141i \(-0.0313770\pi\)
\(68\) −8.10384 −0.119174
\(69\) 10.2598 10.0865i 0.148693 0.146181i
\(70\) 24.4020 15.9082i 0.348600 0.227259i
\(71\) 24.4620i 0.344536i 0.985050 + 0.172268i \(0.0551094\pi\)
−0.985050 + 0.172268i \(0.944891\pi\)
\(72\) −0.433693 + 25.4521i −0.00602352 + 0.353502i
\(73\) 18.3104i 0.250827i −0.992105 0.125414i \(-0.959974\pi\)
0.992105 0.125414i \(-0.0400258\pi\)
\(74\) 22.8315i 0.308534i
\(75\) −26.5279 70.1518i −0.353705 0.935357i
\(76\) 12.2420 0.161079
\(77\) −47.7882 −0.620626
\(78\) −22.4224 22.8078i −0.287467 0.292407i
\(79\) −139.245 −1.76260 −0.881298 0.472561i \(-0.843330\pi\)
−0.881298 + 0.472561i \(0.843330\pi\)
\(80\) −10.9224 16.7542i −0.136530 0.209427i
\(81\) −80.9530 2.75961i −0.999419 0.0340692i
\(82\) 57.8354i 0.705310i
\(83\) −68.7603 −0.828437 −0.414219 0.910177i \(-0.635945\pi\)
−0.414219 + 0.910177i \(0.635945\pi\)
\(84\) 17.3282 + 17.6260i 0.206288 + 0.209833i
\(85\) 11.0641 + 16.9716i 0.130166 + 0.199666i
\(86\) 77.5852i 0.902153i
\(87\) 26.2855 + 26.7372i 0.302132 + 0.307324i
\(88\) 32.8109i 0.372851i
\(89\) 35.6250i 0.400281i −0.979767 0.200141i \(-0.935860\pi\)
0.979767 0.200141i \(-0.0641399\pi\)
\(90\) 53.8958 33.8414i 0.598842 0.376016i
\(91\) −31.0557 −0.341271
\(92\) −9.59166 −0.104257
\(93\) 15.5296 15.2672i 0.166985 0.164164i
\(94\) 20.5655 0.218782
\(95\) −16.7139 25.6380i −0.175936 0.269874i
\(96\) 12.1018 11.8973i 0.126060 0.123931i
\(97\) 14.7253i 0.151807i −0.997115 0.0759037i \(-0.975816\pi\)
0.997115 0.0759037i \(-0.0241842\pi\)
\(98\) −45.2965 −0.462209
\(99\) −104.388 1.77873i −1.05443 0.0179670i
\(100\) −20.1755 + 45.7488i −0.201755 + 0.457488i
\(101\) 115.541i 1.14397i 0.820264 + 0.571986i \(0.193827\pi\)
−0.820264 + 0.571986i \(0.806173\pi\)
\(102\) −12.2589 + 12.0518i −0.120185 + 0.118155i
\(103\) 7.01220i 0.0680796i −0.999420 0.0340398i \(-0.989163\pi\)
0.999420 0.0340398i \(-0.0108373\pi\)
\(104\) 21.3225i 0.205024i
\(105\) 13.2554 60.3545i 0.126242 0.574805i
\(106\) 8.01002 0.0755662
\(107\) −123.341 −1.15272 −0.576362 0.817194i \(-0.695528\pi\)
−0.576362 + 0.817194i \(0.695528\pi\)
\(108\) 37.1955 + 39.1470i 0.344403 + 0.362473i
\(109\) 138.067 1.26667 0.633335 0.773877i \(-0.281685\pi\)
0.633335 + 0.773877i \(0.281685\pi\)
\(110\) 68.7148 44.7965i 0.624680 0.407241i
\(111\) −33.9543 34.5378i −0.305894 0.311151i
\(112\) 16.4781i 0.147126i
\(113\) −200.726 −1.77634 −0.888169 0.459517i \(-0.848022\pi\)
−0.888169 + 0.459517i \(0.848022\pi\)
\(114\) 18.5187 18.2059i 0.162445 0.159701i
\(115\) 13.0955 + 20.0875i 0.113874 + 0.174674i
\(116\) 24.9960i 0.215483i
\(117\) −67.8379 1.15593i −0.579811 0.00987972i
\(118\) 12.2120i 0.103492i
\(119\) 16.6920i 0.140269i
\(120\) −41.4388 9.10104i −0.345323 0.0758420i
\(121\) −13.5691 −0.112141
\(122\) 89.9791 0.737533
\(123\) −86.0109 87.4890i −0.699276 0.711292i
\(124\) −14.5183 −0.117083
\(125\) 123.356 20.2077i 0.986846 0.161661i
\(126\) 52.4255 + 0.893307i 0.416075 + 0.00708974i
\(127\) 39.7961i 0.313355i 0.987650 + 0.156678i \(0.0500783\pi\)
−0.987650 + 0.156678i \(0.949922\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 115.382 + 117.365i 0.894435 + 0.909805i
\(130\) 44.6551 29.1115i 0.343500 0.223935i
\(131\) 154.311i 1.17794i 0.808153 + 0.588972i \(0.200467\pi\)
−0.808153 + 0.588972i \(0.799533\pi\)
\(132\) 48.7952 + 49.6338i 0.369661 + 0.376013i
\(133\) 25.2156i 0.189591i
\(134\) 18.6499i 0.139179i
\(135\) 31.2016 131.345i 0.231123 0.972925i
\(136\) 11.4606 0.0842688
\(137\) −17.1465 −0.125157 −0.0625785 0.998040i \(-0.519932\pi\)
−0.0625785 + 0.998040i \(0.519932\pi\)
\(138\) −14.5095 + 14.2644i −0.105142 + 0.103365i
\(139\) −4.42669 −0.0318467 −0.0159233 0.999873i \(-0.505069\pi\)
−0.0159233 + 0.999873i \(0.505069\pi\)
\(140\) −34.5097 + 22.4975i −0.246498 + 0.160697i
\(141\) 31.1100 30.5844i 0.220638 0.216910i
\(142\) 34.5945i 0.243623i
\(143\) −87.4512 −0.611547
\(144\) 0.613335 35.9948i 0.00425927 0.249964i
\(145\) −52.3484 + 34.1269i −0.361023 + 0.235358i
\(146\) 25.8948i 0.177362i
\(147\) −68.5210 + 67.3634i −0.466130 + 0.458255i
\(148\) 32.2886i 0.218166i
\(149\) 201.492i 1.35230i 0.736766 + 0.676148i \(0.236352\pi\)
−0.736766 + 0.676148i \(0.763648\pi\)
\(150\) 37.5161 + 99.2096i 0.250107 + 0.661397i
\(151\) −96.1771 −0.636935 −0.318467 0.947934i \(-0.603168\pi\)
−0.318467 + 0.947934i \(0.603168\pi\)
\(152\) −17.3128 −0.113900
\(153\) −0.621296 + 36.4620i −0.00406076 + 0.238314i
\(154\) 67.5827 0.438849
\(155\) 19.8218 + 30.4052i 0.127882 + 0.196163i
\(156\) 31.7101 + 32.2550i 0.203270 + 0.206763i
\(157\) 188.931i 1.20338i 0.798729 + 0.601690i \(0.205506\pi\)
−0.798729 + 0.601690i \(0.794494\pi\)
\(158\) 196.922 1.24634
\(159\) 12.1169 11.9122i 0.0762072 0.0749198i
\(160\) 15.4466 + 23.6940i 0.0965410 + 0.148087i
\(161\) 19.7566i 0.122712i
\(162\) 114.485 + 3.90267i 0.706696 + 0.0240906i
\(163\) 224.570i 1.37773i −0.724889 0.688866i \(-0.758109\pi\)
0.724889 0.688866i \(-0.241891\pi\)
\(164\) 81.7916i 0.498729i
\(165\) 37.3266 169.955i 0.226222 1.03003i
\(166\) 97.2417 0.585794
\(167\) 35.4667 0.212375 0.106188 0.994346i \(-0.466136\pi\)
0.106188 + 0.994346i \(0.466136\pi\)
\(168\) −24.5057 24.9269i −0.145868 0.148374i
\(169\) 112.169 0.663721
\(170\) −15.6470 24.0015i −0.0920415 0.141185i
\(171\) 0.938555 55.0810i 0.00548862 0.322111i
\(172\) 109.722i 0.637918i
\(173\) 155.123 0.896666 0.448333 0.893867i \(-0.352018\pi\)
0.448333 + 0.893867i \(0.352018\pi\)
\(174\) −37.1732 37.8121i −0.213639 0.217311i
\(175\) 94.2318 + 41.5568i 0.538467 + 0.237467i
\(176\) 46.4016i 0.263645i
\(177\) 18.1614 + 18.4735i 0.102607 + 0.104370i
\(178\) 50.3814i 0.283042i
\(179\) 244.910i 1.36821i 0.729382 + 0.684107i \(0.239808\pi\)
−0.729382 + 0.684107i \(0.760192\pi\)
\(180\) −76.2202 + 47.8590i −0.423445 + 0.265883i
\(181\) −176.585 −0.975608 −0.487804 0.872953i \(-0.662202\pi\)
−0.487804 + 0.872953i \(0.662202\pi\)
\(182\) 43.9194 0.241315
\(183\) 136.113 133.814i 0.743790 0.731224i
\(184\) 13.5647 0.0737210
\(185\) 67.6211 44.0835i 0.365519 0.238289i
\(186\) −21.9622 + 21.5911i −0.118076 + 0.116081i
\(187\) 47.0039i 0.251357i
\(188\) −29.0840 −0.154702
\(189\) 80.6338 76.6142i 0.426634 0.405366i
\(190\) 23.6371 + 36.2577i 0.124406 + 0.190830i
\(191\) 102.841i 0.538437i −0.963079 0.269218i \(-0.913235\pi\)
0.963079 0.269218i \(-0.0867653\pi\)
\(192\) −17.1145 + 16.8254i −0.0891381 + 0.0876322i
\(193\) 61.3672i 0.317965i −0.987281 0.158982i \(-0.949179\pi\)
0.987281 0.158982i \(-0.0508213\pi\)
\(194\) 20.8247i 0.107344i
\(195\) 24.2571 110.447i 0.124395 0.566396i
\(196\) 64.0589 0.326831
\(197\) 307.422 1.56052 0.780258 0.625457i \(-0.215088\pi\)
0.780258 + 0.625457i \(0.215088\pi\)
\(198\) 147.627 + 2.51551i 0.745593 + 0.0127046i
\(199\) −9.97633 −0.0501323 −0.0250662 0.999686i \(-0.507980\pi\)
−0.0250662 + 0.999686i \(0.507980\pi\)
\(200\) 28.5325 64.6985i 0.142662 0.323493i
\(201\) 27.7356 + 28.2122i 0.137988 + 0.140359i
\(202\) 163.400i 0.808910i
\(203\) −51.4860 −0.253625
\(204\) 17.3367 17.0438i 0.0849836 0.0835479i
\(205\) 171.294 111.670i 0.835579 0.544730i
\(206\) 9.91675i 0.0481396i
\(207\) −0.735363 + 43.1562i −0.00355248 + 0.208484i
\(208\) 30.1546i 0.144974i
\(209\) 71.0059i 0.339741i
\(210\) −18.7460 + 85.3542i −0.0892668 + 0.406449i
\(211\) 157.898 0.748332 0.374166 0.927362i \(-0.377929\pi\)
0.374166 + 0.927362i \(0.377929\pi\)
\(212\) −11.3279 −0.0534334
\(213\) −51.4479 52.3320i −0.241539 0.245690i
\(214\) 174.431 0.815099
\(215\) −229.787 + 149.803i −1.06878 + 0.696758i
\(216\) −52.6024 55.3623i −0.243530 0.256307i
\(217\) 29.9043i 0.137808i
\(218\) −195.256 −0.895671
\(219\) 38.5099 + 39.1717i 0.175844 + 0.178866i
\(220\) −97.1774 + 63.3519i −0.441716 + 0.287963i
\(221\) 30.5460i 0.138217i
\(222\) 48.0186 + 48.8438i 0.216300 + 0.220017i
\(223\) 304.079i 1.36358i −0.731547 0.681791i \(-0.761202\pi\)
0.731547 0.681791i \(-0.238798\pi\)
\(224\) 23.3036i 0.104034i
\(225\) 204.293 + 94.2839i 0.907968 + 0.419040i
\(226\) 283.870 1.25606
\(227\) −30.9145 −0.136187 −0.0680935 0.997679i \(-0.521692\pi\)
−0.0680935 + 0.997679i \(0.521692\pi\)
\(228\) −26.1895 + 25.7470i −0.114866 + 0.112925i
\(229\) −100.974 −0.440932 −0.220466 0.975395i \(-0.570758\pi\)
−0.220466 + 0.975395i \(0.570758\pi\)
\(230\) −18.5198 28.4081i −0.0805207 0.123513i
\(231\) 102.234 100.507i 0.442572 0.435095i
\(232\) 35.3497i 0.152369i
\(233\) −238.450 −1.02339 −0.511694 0.859168i \(-0.670982\pi\)
−0.511694 + 0.859168i \(0.670982\pi\)
\(234\) 95.9373 + 1.63473i 0.409988 + 0.00698602i
\(235\) 39.7083 + 60.9098i 0.168972 + 0.259191i
\(236\) 17.2704i 0.0731798i
\(237\) 297.889 292.856i 1.25692 1.23568i
\(238\) 23.6061i 0.0991852i
\(239\) 316.519i 1.32435i 0.749351 + 0.662173i \(0.230365\pi\)
−0.749351 + 0.662173i \(0.769635\pi\)
\(240\) 58.6033 + 12.8708i 0.244180 + 0.0536284i
\(241\) 85.5318 0.354904 0.177452 0.984129i \(-0.443215\pi\)
0.177452 + 0.984129i \(0.443215\pi\)
\(242\) 19.1896 0.0792960
\(243\) 178.988 164.354i 0.736575 0.676355i
\(244\) −127.250 −0.521515
\(245\) −87.4593 134.157i −0.356977 0.547578i
\(246\) 121.638 + 123.728i 0.494462 + 0.502960i
\(247\) 46.1440i 0.186818i
\(248\) 20.5320 0.0827902
\(249\) 147.100 144.615i 0.590763 0.580782i
\(250\) −174.451 + 28.5779i −0.697806 + 0.114312i
\(251\) 316.502i 1.26096i −0.776204 0.630482i \(-0.782857\pi\)
0.776204 0.630482i \(-0.217143\pi\)
\(252\) −74.1409 1.26333i −0.294210 0.00501320i
\(253\) 55.6335i 0.219895i
\(254\) 56.2802i 0.221575i
\(255\) −59.3639 13.0379i −0.232800 0.0511289i
\(256\) 16.0000 0.0625000
\(257\) 325.010 1.26463 0.632314 0.774712i \(-0.282105\pi\)
0.632314 + 0.774712i \(0.282105\pi\)
\(258\) −163.175 165.979i −0.632461 0.643330i
\(259\) 66.5070 0.256784
\(260\) −63.1518 + 41.1699i −0.242891 + 0.158346i
\(261\) −112.466 1.91637i −0.430903 0.00734240i
\(262\) 218.228i 0.832933i
\(263\) −400.567 −1.52307 −0.761534 0.648125i \(-0.775553\pi\)
−0.761534 + 0.648125i \(0.775553\pi\)
\(264\) −69.0069 70.1928i −0.261390 0.265882i
\(265\) 15.4659 + 23.7236i 0.0583619 + 0.0895232i
\(266\) 35.6603i 0.134061i
\(267\) 74.9256 + 76.2131i 0.280620 + 0.285442i
\(268\) 26.3750i 0.0984141i
\(269\) 91.5363i 0.340284i 0.985420 + 0.170142i \(0.0544226\pi\)
−0.985420 + 0.170142i \(0.945577\pi\)
\(270\) −44.1257 + 185.750i −0.163429 + 0.687962i
\(271\) −105.181 −0.388121 −0.194061 0.980990i \(-0.562166\pi\)
−0.194061 + 0.980990i \(0.562166\pi\)
\(272\) −16.2077 −0.0595870
\(273\) 66.4379 65.3154i 0.243362 0.239251i
\(274\) 24.2488 0.0884993
\(275\) 265.352 + 117.022i 0.964916 + 0.425534i
\(276\) 20.5196 20.1729i 0.0743463 0.0730903i
\(277\) 139.929i 0.505159i 0.967576 + 0.252580i \(0.0812789\pi\)
−0.967576 + 0.252580i \(0.918721\pi\)
\(278\) 6.26028 0.0225190
\(279\) −1.11307 + 65.3228i −0.00398950 + 0.234132i
\(280\) 48.8040 31.8163i 0.174300 0.113630i
\(281\) 155.759i 0.554302i −0.960826 0.277151i \(-0.910610\pi\)
0.960826 0.277151i \(-0.0893902\pi\)
\(282\) −43.9961 + 43.2528i −0.156015 + 0.153379i
\(283\) 9.60708i 0.0339473i −0.999856 0.0169736i \(-0.994597\pi\)
0.999856 0.0169736i \(-0.00540314\pi\)
\(284\) 48.9241i 0.172268i
\(285\) 89.6776 + 19.6955i 0.314658 + 0.0691072i
\(286\) 123.675 0.432429
\(287\) 168.472 0.587009
\(288\) −0.867386 + 50.9043i −0.00301176 + 0.176751i
\(289\) −272.582 −0.943190
\(290\) 74.0318 48.2628i 0.255282 0.166423i
\(291\) 30.9699 + 31.5021i 0.106426 + 0.108255i
\(292\) 36.6208i 0.125414i
\(293\) 279.677 0.954530 0.477265 0.878759i \(-0.341628\pi\)
0.477265 + 0.878759i \(0.341628\pi\)
\(294\) 96.9034 95.2663i 0.329603 0.324035i
\(295\) −36.1690 + 23.5793i −0.122607 + 0.0799297i
\(296\) 45.6630i 0.154267i
\(297\) 227.061 215.741i 0.764514 0.726402i
\(298\) 284.953i 0.956218i
\(299\) 36.1540i 0.120917i
\(300\) −53.0558 140.304i −0.176853 0.467678i
\(301\) −226.002 −0.750836
\(302\) 136.015 0.450381
\(303\) −243.003 247.179i −0.801990 0.815772i
\(304\) 24.4840 0.0805394
\(305\) 173.733 + 266.495i 0.569618 + 0.873754i
\(306\) 0.878645 51.5650i 0.00287139 0.168513i
\(307\) 40.1533i 0.130793i 0.997859 + 0.0653963i \(0.0208311\pi\)
−0.997859 + 0.0653963i \(0.979169\pi\)
\(308\) −95.5764 −0.310313
\(309\) 14.7479 + 15.0013i 0.0477277 + 0.0485479i
\(310\) −28.0322 42.9995i −0.0904265 0.138708i
\(311\) 325.670i 1.04717i 0.851973 + 0.523586i \(0.175406\pi\)
−0.851973 + 0.523586i \(0.824594\pi\)
\(312\) −44.8449 45.6155i −0.143734 0.146204i
\(313\) 374.375i 1.19609i 0.801464 + 0.598044i \(0.204055\pi\)
−0.801464 + 0.598044i \(0.795945\pi\)
\(314\) 267.188i 0.850919i
\(315\) 98.5784 + 156.996i 0.312947 + 0.498399i
\(316\) −278.490 −0.881298
\(317\) 430.778 1.35892 0.679461 0.733712i \(-0.262214\pi\)
0.679461 + 0.733712i \(0.262214\pi\)
\(318\) −17.1360 + 16.8465i −0.0538866 + 0.0529763i
\(319\) −144.982 −0.454488
\(320\) −21.8447 33.5083i −0.0682648 0.104714i
\(321\) 263.866 259.408i 0.822013 0.808126i
\(322\) 27.9400i 0.0867703i
\(323\) −24.8018 −0.0767857
\(324\) −161.906 5.51921i −0.499710 0.0170346i
\(325\) 172.442 + 76.0479i 0.530590 + 0.233993i
\(326\) 317.590i 0.974204i
\(327\) −295.369 + 290.379i −0.903269 + 0.888009i
\(328\) 115.671i 0.352655i
\(329\) 59.9063i 0.182086i
\(330\) −52.7878 + 240.353i −0.159963 + 0.728342i
\(331\) −551.313 −1.66560 −0.832799 0.553576i \(-0.813263\pi\)
−0.832799 + 0.553576i \(0.813263\pi\)
\(332\) −137.521 −0.414219
\(333\) 145.278 + 2.47547i 0.436269 + 0.00743383i
\(334\) −50.1574 −0.150172
\(335\) −55.2363 + 36.0096i −0.164885 + 0.107491i
\(336\) 34.6564 + 35.2519i 0.103144 + 0.104916i
\(337\) 270.945i 0.803991i 0.915642 + 0.401996i \(0.131683\pi\)
−0.915642 + 0.401996i \(0.868317\pi\)
\(338\) −158.631 −0.469322
\(339\) 429.416 422.162i 1.26672 1.24531i
\(340\) 22.1283 + 33.9433i 0.0650831 + 0.0998331i
\(341\) 84.2090i 0.246947i
\(342\) −1.32732 + 77.8962i −0.00388104 + 0.227767i
\(343\) 333.804i 0.973188i
\(344\) 155.170i 0.451076i
\(345\) −70.2628 15.4316i −0.203660 0.0447292i
\(346\) −219.377 −0.634039
\(347\) −100.948 −0.290917 −0.145459 0.989364i \(-0.546466\pi\)
−0.145459 + 0.989364i \(0.546466\pi\)
\(348\) 52.5709 + 53.4743i 0.151066 + 0.153662i
\(349\) 291.754 0.835971 0.417986 0.908454i \(-0.362736\pi\)
0.417986 + 0.908454i \(0.362736\pi\)
\(350\) −133.264 58.7702i −0.380754 0.167915i
\(351\) 147.558 140.202i 0.420392 0.399436i
\(352\) 65.6217i 0.186425i
\(353\) −630.650 −1.78654 −0.893272 0.449516i \(-0.851597\pi\)
−0.893272 + 0.449516i \(0.851597\pi\)
\(354\) −25.6840 26.1254i −0.0725538 0.0738006i
\(355\) 102.460 66.7958i 0.288620 0.188157i
\(356\) 71.2500i 0.200141i
\(357\) −35.1062 35.7095i −0.0983367 0.100027i
\(358\) 346.355i 0.967473i
\(359\) 429.259i 1.19571i 0.801605 + 0.597854i \(0.203980\pi\)
−0.801605 + 0.597854i \(0.796020\pi\)
\(360\) 107.792 67.6829i 0.299421 0.188008i
\(361\) −323.533 −0.896214
\(362\) 249.729 0.689859
\(363\) 29.0286 28.5382i 0.0799686 0.0786176i
\(364\) −62.1114 −0.170636
\(365\) −76.6938 + 49.9982i −0.210120 + 0.136981i
\(366\) −192.494 + 189.241i −0.525939 + 0.517053i
\(367\) 276.970i 0.754688i 0.926073 + 0.377344i \(0.123162\pi\)
−0.926073 + 0.377344i \(0.876838\pi\)
\(368\) −19.1833 −0.0521286
\(369\) 368.009 + 6.27070i 0.997314 + 0.0169938i
\(370\) −95.6307 + 62.3435i −0.258461 + 0.168496i
\(371\) 23.3328i 0.0628916i
\(372\) 31.0592 30.5345i 0.0834925 0.0820819i
\(373\) 64.3715i 0.172578i 0.996270 + 0.0862889i \(0.0275008\pi\)
−0.996270 + 0.0862889i \(0.972499\pi\)
\(374\) 66.4735i 0.177737i
\(375\) −221.397 + 302.669i −0.590391 + 0.807117i
\(376\) 41.1310 0.109391
\(377\) −94.2179 −0.249915
\(378\) −114.033 + 108.349i −0.301676 + 0.286637i
\(379\) −454.045 −1.19801 −0.599004 0.800746i \(-0.704437\pi\)
−0.599004 + 0.800746i \(0.704437\pi\)
\(380\) −33.4279 51.2761i −0.0879681 0.134937i
\(381\) −83.6980 85.1364i −0.219680 0.223455i
\(382\) 145.440i 0.380732i
\(383\) −675.828 −1.76456 −0.882282 0.470722i \(-0.843994\pi\)
−0.882282 + 0.470722i \(0.843994\pi\)
\(384\) 24.2036 23.7947i 0.0630302 0.0619653i
\(385\) 130.490 + 200.163i 0.338935 + 0.519904i
\(386\) 86.7863i 0.224835i
\(387\) −493.677 8.41204i −1.27565 0.0217365i
\(388\) 29.4506i 0.0759037i
\(389\) 383.826i 0.986698i −0.869831 0.493349i \(-0.835772\pi\)
0.869831 0.493349i \(-0.164228\pi\)
\(390\) −34.3047 + 156.196i −0.0879608 + 0.400502i
\(391\) 19.4323 0.0496990
\(392\) −90.5929 −0.231104
\(393\) −324.542 330.119i −0.825807 0.839998i
\(394\) −434.760 −1.10345
\(395\) 380.221 + 583.234i 0.962586 + 1.47654i
\(396\) −208.777 3.55746i −0.527214 0.00898349i
\(397\) 475.506i 1.19775i 0.800843 + 0.598874i \(0.204385\pi\)
−0.800843 + 0.598874i \(0.795615\pi\)
\(398\) 14.1087 0.0354489
\(399\) 53.0328 + 53.9442i 0.132914 + 0.135198i
\(400\) −40.3510 + 91.4975i −0.100877 + 0.228744i
\(401\) 693.445i 1.72929i −0.502385 0.864644i \(-0.667544\pi\)
0.502385 0.864644i \(-0.332456\pi\)
\(402\) −39.2240 39.8981i −0.0975722 0.0992489i
\(403\) 54.7241i 0.135792i
\(404\) 231.082i 0.571986i
\(405\) 209.491 + 346.610i 0.517261 + 0.855828i
\(406\) 72.8121 0.179340
\(407\) 187.280 0.460148
\(408\) −24.5177 + 24.1035i −0.0600925 + 0.0590773i
\(409\) 20.9281 0.0511689 0.0255845 0.999673i \(-0.491855\pi\)
0.0255845 + 0.999673i \(0.491855\pi\)
\(410\) −242.246 + 157.925i −0.590844 + 0.385182i
\(411\) 36.6818 36.0620i 0.0892500 0.0877422i
\(412\) 14.0244i 0.0340398i
\(413\) −35.5731 −0.0861334
\(414\) 1.03996 61.0321i 0.00251198 0.147421i
\(415\) 187.756 + 288.005i 0.452425 + 0.693989i
\(416\) 42.6450i 0.102512i
\(417\) 9.47008 9.31009i 0.0227100 0.0223264i
\(418\) 100.418i 0.240233i
\(419\) 283.881i 0.677519i 0.940873 + 0.338760i \(0.110007\pi\)
−0.940873 + 0.338760i \(0.889993\pi\)
\(420\) 26.5109 120.709i 0.0631211 0.287403i
\(421\) 787.293 1.87005 0.935027 0.354575i \(-0.115375\pi\)
0.935027 + 0.354575i \(0.115375\pi\)
\(422\) −223.302 −0.529151
\(423\) −2.22978 + 130.859i −0.00527135 + 0.309360i
\(424\) 16.0200 0.0377831
\(425\) 40.8747 92.6851i 0.0961758 0.218083i
\(426\) 72.7582 + 74.0086i 0.170794 + 0.173729i
\(427\) 262.105i 0.613828i
\(428\) −246.683 −0.576362
\(429\) 187.086 183.925i 0.436097 0.428729i
\(430\) 324.969 211.853i 0.755741 0.492682i
\(431\) 452.979i 1.05100i −0.850795 0.525498i \(-0.823879\pi\)
0.850795 0.525498i \(-0.176121\pi\)
\(432\) 74.3911 + 78.2941i 0.172202 + 0.181236i
\(433\) 232.550i 0.537067i −0.963270 0.268533i \(-0.913461\pi\)
0.963270 0.268533i \(-0.0865389\pi\)
\(434\) 42.2911i 0.0974449i
\(435\) 40.2149 183.106i 0.0924480 0.420933i
\(436\) 276.134 0.633335
\(437\) −29.3553 −0.0671745
\(438\) −54.4612 55.3971i −0.124341 0.126477i
\(439\) −226.602 −0.516178 −0.258089 0.966121i \(-0.583093\pi\)
−0.258089 + 0.966121i \(0.583093\pi\)
\(440\) 137.430 89.5931i 0.312340 0.203621i
\(441\) 4.91119 288.223i 0.0111365 0.653567i
\(442\) 43.1985i 0.0977342i
\(443\) 551.312 1.24450 0.622248 0.782820i \(-0.286220\pi\)
0.622248 + 0.782820i \(0.286220\pi\)
\(444\) −67.9085 69.0755i −0.152947 0.155575i
\(445\) −149.217 + 97.2774i −0.335319 + 0.218601i
\(446\) 430.032i 0.964198i
\(447\) −423.773 431.055i −0.948037 0.964329i
\(448\) 32.9563i 0.0735631i
\(449\) 612.626i 1.36442i −0.731154 0.682212i \(-0.761018\pi\)
0.731154 0.682212i \(-0.238982\pi\)
\(450\) −288.914 133.338i −0.642030 0.296306i
\(451\) 474.407 1.05190
\(452\) −401.452 −0.888169
\(453\) 205.753 202.277i 0.454201 0.446528i
\(454\) 43.7197 0.0962988
\(455\) 84.8004 + 130.078i 0.186374 + 0.285886i
\(456\) 37.0375 36.4118i 0.0812226 0.0798504i
\(457\) 141.828i 0.310345i 0.987887 + 0.155173i \(0.0495934\pi\)
−0.987887 + 0.155173i \(0.950407\pi\)
\(458\) 142.798 0.311786
\(459\) −75.3567 79.3103i −0.164176 0.172789i
\(460\) 26.1909 + 40.1751i 0.0569368 + 0.0873371i
\(461\) 463.030i 1.00440i −0.864751 0.502202i \(-0.832524\pi\)
0.864751 0.502202i \(-0.167476\pi\)
\(462\) −144.581 + 142.138i −0.312945 + 0.307658i
\(463\) 601.446i 1.29902i 0.760354 + 0.649509i \(0.225026\pi\)
−0.760354 + 0.649509i \(0.774974\pi\)
\(464\) 49.9920i 0.107741i
\(465\) −106.352 23.3578i −0.228715 0.0502318i
\(466\) 337.219 0.723645
\(467\) 560.940 1.20116 0.600578 0.799566i \(-0.294937\pi\)
0.600578 + 0.799566i \(0.294937\pi\)
\(468\) −135.676 2.31185i −0.289906 0.00493986i
\(469\) −54.3263 −0.115834
\(470\) −56.1560 86.1395i −0.119481 0.183276i
\(471\) −397.354 404.182i −0.843639 0.858137i
\(472\) 24.4241i 0.0517460i
\(473\) −636.409 −1.34547
\(474\) −421.279 + 414.162i −0.888774 + 0.873759i
\(475\) −61.7470 + 140.014i −0.129994 + 0.294766i
\(476\) 33.3840i 0.0701345i
\(477\) −0.868473 + 50.9681i −0.00182070 + 0.106851i
\(478\) 447.625i 0.936454i
\(479\) 165.257i 0.345004i −0.985009 0.172502i \(-0.944815\pi\)
0.985009 0.172502i \(-0.0551852\pi\)
\(480\) −82.8775 18.2021i −0.172662 0.0379210i
\(481\) 121.706 0.253027
\(482\) −120.960 −0.250955
\(483\) −41.5515 42.2656i −0.0860280 0.0875063i
\(484\) −27.1382 −0.0560707
\(485\) −61.6776 + 40.2088i −0.127170 + 0.0829048i
\(486\) −253.127 + 232.432i −0.520837 + 0.478256i
\(487\) 670.868i 1.37755i 0.724974 + 0.688776i \(0.241852\pi\)
−0.724974 + 0.688776i \(0.758148\pi\)
\(488\) 179.958 0.368767
\(489\) 472.310 + 480.427i 0.965869 + 0.982467i
\(490\) 123.686 + 189.726i 0.252421 + 0.387196i
\(491\) 454.572i 0.925808i −0.886408 0.462904i \(-0.846807\pi\)
0.886408 0.462904i \(-0.153193\pi\)
\(492\) −172.022 174.978i −0.349638 0.355646i
\(493\) 50.6409i 0.102720i
\(494\) 65.2574i 0.132100i
\(495\) 277.592 + 442.092i 0.560791 + 0.893115i
\(496\) −29.0366 −0.0585415
\(497\) 100.772 0.202761
\(498\) −208.031 + 204.516i −0.417732 + 0.410675i
\(499\) −803.276 −1.60977 −0.804886 0.593430i \(-0.797774\pi\)
−0.804886 + 0.593430i \(0.797774\pi\)
\(500\) 246.712 40.4153i 0.493423 0.0808306i
\(501\) −75.8743 + 74.5925i −0.151446 + 0.148887i
\(502\) 447.601i 0.891636i
\(503\) −560.373 −1.11406 −0.557031 0.830492i \(-0.688059\pi\)
−0.557031 + 0.830492i \(0.688059\pi\)
\(504\) 104.851 + 1.78661i 0.208038 + 0.00354487i
\(505\) 483.949 315.496i 0.958314 0.624744i
\(506\) 78.6777i 0.155490i
\(507\) −239.965 + 235.911i −0.473303 + 0.465307i
\(508\) 79.5922i 0.156678i
\(509\) 443.933i 0.872166i −0.899906 0.436083i \(-0.856365\pi\)
0.899906 0.436083i \(-0.143635\pi\)
\(510\) 83.9533 + 18.4383i 0.164614 + 0.0361536i
\(511\) −75.4303 −0.147613
\(512\) −22.6274 −0.0441942
\(513\) 113.837 + 119.809i 0.221904 + 0.233547i
\(514\) −459.633 −0.894227
\(515\) −29.3709 + 19.1475i −0.0570309 + 0.0371795i
\(516\) 230.764 + 234.730i 0.447217 + 0.454903i
\(517\) 168.693i 0.326292i
\(518\) −94.0552 −0.181574
\(519\) −331.857 + 326.251i −0.639417 + 0.628614i
\(520\) 89.3101 58.2230i 0.171750 0.111967i
\(521\) 522.885i 1.00362i −0.864979 0.501809i \(-0.832668\pi\)
0.864979 0.501809i \(-0.167332\pi\)
\(522\) 159.051 + 2.71015i 0.304695 + 0.00519186i
\(523\) 978.533i 1.87100i −0.353325 0.935500i \(-0.614949\pi\)
0.353325 0.935500i \(-0.385051\pi\)
\(524\) 308.621i 0.588972i
\(525\) −288.993 + 109.283i −0.550462 + 0.208157i
\(526\) 566.487 1.07697
\(527\) 29.4135 0.0558130
\(528\) 97.5905 + 99.2676i 0.184830 + 0.188007i
\(529\) 23.0000 0.0434783
\(530\) −21.8721 33.5503i −0.0412681 0.0633024i
\(531\) −77.7057 1.32407i −0.146338 0.00249354i
\(532\) 50.4313i 0.0947957i
\(533\) 308.299 0.578421
\(534\) −105.961 107.782i −0.198428 0.201838i
\(535\) 336.795 + 516.621i 0.629524 + 0.965646i
\(536\) 37.2999i 0.0695893i
\(537\) −515.088 523.940i −0.959196 0.975679i
\(538\) 129.452i 0.240617i
\(539\) 371.554i 0.689340i
\(540\) 62.4032 262.690i 0.115561 0.486462i
\(541\) −925.219 −1.71020 −0.855100 0.518462i \(-0.826505\pi\)
−0.855100 + 0.518462i \(0.826505\pi\)
\(542\) 148.748 0.274443
\(543\) 377.771 371.389i 0.695711 0.683957i
\(544\) 22.9211 0.0421344
\(545\) −377.005 578.300i −0.691752 1.06110i
\(546\) −93.9573 + 92.3700i −0.172083 + 0.169176i
\(547\) 540.020i 0.987240i −0.869678 0.493620i \(-0.835673\pi\)
0.869678 0.493620i \(-0.164327\pi\)
\(548\) −34.2930 −0.0625785
\(549\) −9.75583 + 572.540i −0.0177702 + 1.04288i
\(550\) −375.264 165.494i −0.682298 0.300898i
\(551\) 76.5002i 0.138839i
\(552\) −29.0191 + 28.5288i −0.0525708 + 0.0516826i
\(553\) 573.625i 1.03730i
\(554\) 197.890i 0.357201i
\(555\) −51.9476 + 236.527i −0.0935993 + 0.426175i
\(556\) −8.85338 −0.0159233
\(557\) −344.569 −0.618616 −0.309308 0.950962i \(-0.600097\pi\)
−0.309308 + 0.950962i \(0.600097\pi\)
\(558\) 1.57412 92.3804i 0.00282101 0.165556i
\(559\) −413.577 −0.739852
\(560\) −69.0193 + 44.9951i −0.123249 + 0.0803483i
\(561\) −98.8572 100.556i −0.176216 0.179244i
\(562\) 220.276i 0.391950i
\(563\) −144.496 −0.256653 −0.128326 0.991732i \(-0.540961\pi\)
−0.128326 + 0.991732i \(0.540961\pi\)
\(564\) 62.2199 61.1687i 0.110319 0.108455i
\(565\) 548.101 + 840.750i 0.970090 + 1.48805i
\(566\) 13.5865i 0.0240043i
\(567\) −11.3683 + 333.489i −0.0200499 + 0.588163i
\(568\) 69.1891i 0.121812i
\(569\) 1086.99i 1.91035i −0.296041 0.955175i \(-0.595666\pi\)
0.296041 0.955175i \(-0.404334\pi\)
\(570\) −126.823 27.8537i −0.222497 0.0488661i
\(571\) −927.563 −1.62445 −0.812227 0.583341i \(-0.801745\pi\)
−0.812227 + 0.583341i \(0.801745\pi\)
\(572\) −174.902 −0.305773
\(573\) 216.293 + 220.010i 0.377475 + 0.383962i
\(574\) −238.255 −0.415078
\(575\) 48.3791 109.702i 0.0841376 0.190786i
\(576\) 1.22667 71.9895i 0.00212963 0.124982i
\(577\) 24.5326i 0.0425175i 0.999774 + 0.0212587i \(0.00676738\pi\)
−0.999774 + 0.0212587i \(0.993233\pi\)
\(578\) 385.489 0.666936
\(579\) 129.066 + 131.284i 0.222912 + 0.226742i
\(580\) −104.697 + 68.2539i −0.180512 + 0.117679i
\(581\) 283.260i 0.487539i
\(582\) −43.7980 44.5507i −0.0752543 0.0765475i
\(583\) 65.7039i 0.112700i
\(584\) 51.7896i 0.0886808i
\(585\) 180.396 + 287.298i 0.308369 + 0.491108i
\(586\) −395.523 −0.674955
\(587\) 106.531 0.181484 0.0907419 0.995874i \(-0.471076\pi\)
0.0907419 + 0.995874i \(0.471076\pi\)
\(588\) −137.042 + 134.727i −0.233065 + 0.229127i
\(589\) −44.4332 −0.0754384
\(590\) 51.1507 33.3461i 0.0866960 0.0565188i
\(591\) −657.672 + 646.561i −1.11281 + 1.09401i
\(592\) 64.5772i 0.109083i
\(593\) 653.922 1.10274 0.551368 0.834262i \(-0.314106\pi\)
0.551368 + 0.834262i \(0.314106\pi\)
\(594\) −321.112 + 305.105i −0.540593 + 0.513644i
\(595\) 69.9152 45.5791i 0.117505 0.0766035i
\(596\) 402.984i 0.676148i
\(597\) 21.3425 20.9819i 0.0357496 0.0351456i
\(598\) 51.1295i 0.0855009i
\(599\) 240.809i 0.402018i −0.979589 0.201009i \(-0.935578\pi\)
0.979589 0.201009i \(-0.0644221\pi\)
\(600\) 75.0322 + 198.419i 0.125054 + 0.330699i
\(601\) 541.585 0.901140 0.450570 0.892741i \(-0.351221\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(602\) 319.615 0.530921
\(603\) −118.670 2.02209i −0.196800 0.00335338i
\(604\) −192.354 −0.318467
\(605\) 37.0517 + 56.8348i 0.0612425 + 0.0939418i
\(606\) 343.658 + 349.564i 0.567092 + 0.576838i
\(607\) 1061.86i 1.74936i −0.484704 0.874678i \(-0.661073\pi\)
0.484704 0.874678i \(-0.338927\pi\)
\(608\) −34.6256 −0.0569500
\(609\) 110.145 108.284i 0.180861 0.177806i
\(610\) −245.696 376.881i −0.402780 0.617838i
\(611\) 109.627i 0.179422i
\(612\) −1.24259 + 72.9240i −0.00203038 + 0.119157i
\(613\) 862.389i 1.40683i 0.710778 + 0.703417i \(0.248343\pi\)
−0.710778 + 0.703417i \(0.751657\pi\)
\(614\) 56.7854i 0.0924843i
\(615\) −131.591 + 599.157i −0.213968 + 0.974238i
\(616\) 135.165 0.219424
\(617\) −531.839 −0.861976 −0.430988 0.902358i \(-0.641835\pi\)
−0.430988 + 0.902358i \(0.641835\pi\)
\(618\) −20.8566 21.2151i −0.0337486 0.0343286i
\(619\) 52.5720 0.0849306 0.0424653 0.999098i \(-0.486479\pi\)
0.0424653 + 0.999098i \(0.486479\pi\)
\(620\) 39.6435 + 60.8105i 0.0639412 + 0.0980814i
\(621\) −89.1918 93.8713i −0.143626 0.151162i
\(622\) 460.567i 0.740462i
\(623\) −146.758 −0.235567
\(624\) 63.4202 + 64.5101i 0.101635 + 0.103382i
\(625\) −421.475 461.502i −0.674360 0.738403i
\(626\) 529.447i 0.845761i
\(627\) 149.338 + 151.904i 0.238178 + 0.242271i
\(628\) 377.862i 0.601690i
\(629\) 65.4154i 0.103999i
\(630\) −139.411 222.026i −0.221287 0.352422i
\(631\) 260.306 0.412529 0.206265 0.978496i \(-0.433869\pi\)
0.206265 + 0.978496i \(0.433869\pi\)
\(632\) 393.845 0.623172
\(633\) −337.794 + 332.087i −0.533639 + 0.524624i
\(634\) −609.212 −0.960903
\(635\) 166.688 108.667i 0.262500 0.171129i
\(636\) 24.2339 23.8245i 0.0381036 0.0374599i
\(637\) 241.458i 0.379056i
\(638\) 205.035 0.321372
\(639\) 220.126 + 3.75085i 0.344486 + 0.00586988i
\(640\) 30.8931 + 47.3879i 0.0482705 + 0.0740436i
\(641\) 487.122i 0.759941i −0.924999 0.379970i \(-0.875934\pi\)
0.924999 0.379970i \(-0.124066\pi\)
\(642\) −373.163 + 366.859i −0.581251 + 0.571431i
\(643\) 249.806i 0.388501i −0.980952 0.194250i \(-0.937773\pi\)
0.980952 0.194250i \(-0.0622274\pi\)
\(644\) 39.5132i 0.0613559i
\(645\) 176.526 803.758i 0.273684 1.24614i
\(646\) 35.0750 0.0542957
\(647\) 422.416 0.652885 0.326442 0.945217i \(-0.394150\pi\)
0.326442 + 0.945217i \(0.394150\pi\)
\(648\) 228.970 + 7.80534i 0.353348 + 0.0120453i
\(649\) −100.172 −0.154348
\(650\) −243.869 107.548i −0.375184 0.165458i
\(651\) −62.8939 63.9747i −0.0966112 0.0982714i
\(652\) 449.141i 0.688866i
\(653\) −350.697 −0.537056 −0.268528 0.963272i \(-0.586537\pi\)
−0.268528 + 0.963272i \(0.586537\pi\)
\(654\) 417.715 410.658i 0.638708 0.627917i
\(655\) 646.337 421.360i 0.986774 0.643297i
\(656\) 163.583i 0.249365i
\(657\) −164.770 2.80760i −0.250791 0.00427336i
\(658\) 84.7204i 0.128754i
\(659\) 921.124i 1.39776i −0.715239 0.698880i \(-0.753682\pi\)
0.715239 0.698880i \(-0.246318\pi\)
\(660\) 74.6532 339.910i 0.113111 0.515016i
\(661\) 170.099 0.257337 0.128668 0.991688i \(-0.458930\pi\)
0.128668 + 0.991688i \(0.458930\pi\)
\(662\) 779.674 1.17776
\(663\) −64.2434 65.3474i −0.0968980 0.0985632i
\(664\) 194.483 0.292897
\(665\) −105.617 + 68.8536i −0.158822 + 0.103539i
\(666\) −205.454 3.50084i −0.308489 0.00525651i
\(667\) 59.9383i 0.0898625i
\(668\) 70.9333 0.106188
\(669\) 639.530 + 650.520i 0.955949 + 0.972376i
\(670\) 78.1160 50.9253i 0.116591 0.0760079i
\(671\) 738.073i 1.09996i
\(672\) −49.0115 49.8537i −0.0729338 0.0741871i
\(673\) 66.6181i 0.0989868i −0.998774 0.0494934i \(-0.984239\pi\)
0.998774 0.0494934i \(-0.0157607\pi\)
\(674\) 383.174i 0.568508i
\(675\) −635.342 + 227.960i −0.941247 + 0.337718i
\(676\) 224.338 0.331861
\(677\) 141.243 0.208631 0.104315 0.994544i \(-0.466735\pi\)
0.104315 + 0.994544i \(0.466735\pi\)
\(678\) −607.286 + 597.027i −0.895703 + 0.880570i
\(679\) −60.6614 −0.0893394
\(680\) −31.2941 48.0030i −0.0460207 0.0705927i
\(681\) 66.1358 65.0184i 0.0971157 0.0954749i
\(682\) 119.089i 0.174618i
\(683\) 631.227 0.924197 0.462099 0.886829i \(-0.347097\pi\)
0.462099 + 0.886829i \(0.347097\pi\)
\(684\) 1.87711 110.162i 0.00274431 0.161055i
\(685\) 46.8201 + 71.8188i 0.0683505 + 0.104845i
\(686\) 472.069i 0.688148i
\(687\) 216.014 212.365i 0.314431 0.309119i
\(688\) 219.444i 0.318959i
\(689\) 42.6984i 0.0619715i
\(690\) 99.3667 + 21.8235i 0.144010 + 0.0316283i
\(691\) 1179.97 1.70762 0.853811 0.520582i \(-0.174285\pi\)
0.853811 + 0.520582i \(0.174285\pi\)
\(692\) 310.246 0.448333
\(693\) −7.32754 + 430.031i −0.0105737 + 0.620536i
\(694\) 142.762 0.205710
\(695\) 12.0875 + 18.5414i 0.0173921 + 0.0266782i
\(696\) −74.3465 75.6241i −0.106820 0.108655i
\(697\) 165.706i 0.237742i
\(698\) −412.602 −0.591121
\(699\) 510.119 501.500i 0.729783 0.717454i
\(700\) 188.464 + 83.1136i 0.269234 + 0.118734i
\(701\) 36.1293i 0.0515397i −0.999668 0.0257698i \(-0.991796\pi\)
0.999668 0.0257698i \(-0.00820370\pi\)
\(702\) −208.678 + 198.275i −0.297262 + 0.282444i
\(703\) 98.8192i 0.140568i
\(704\) 92.8031i 0.131823i
\(705\) −213.052 46.7919i −0.302202 0.0663715i
\(706\) 891.874 1.26328
\(707\) 475.976 0.673233
\(708\) 36.3227 + 36.9469i 0.0513033 + 0.0521849i
\(709\) −932.937 −1.31585 −0.657924 0.753084i \(-0.728565\pi\)
−0.657924 + 0.753084i \(0.728565\pi\)
\(710\) −144.901 + 94.4635i −0.204085 + 0.133047i
\(711\) −21.3510 + 1253.02i −0.0300295 + 1.76234i
\(712\) 100.763i 0.141521i
\(713\) 34.8136 0.0488270
\(714\) 49.6476 + 50.5008i 0.0695345 + 0.0707295i
\(715\) 238.793 + 366.293i 0.333977 + 0.512298i
\(716\) 489.820i 0.684107i
\(717\) −665.693 677.133i −0.928442 0.944397i
\(718\) 607.064i 0.845494i
\(719\) 155.602i 0.216415i −0.994128 0.108207i \(-0.965489\pi\)
0.994128 0.108207i \(-0.0345111\pi\)
\(720\) −152.440 + 95.7180i −0.211723 + 0.132942i
\(721\) −28.8870 −0.0400652
\(722\) 457.545 0.633719
\(723\) −182.979 + 179.888i −0.253084 + 0.248808i
\(724\) −353.170 −0.487804
\(725\) 285.884 + 126.077i 0.394323 + 0.173899i
\(726\) −41.0526 + 40.3591i −0.0565463 + 0.0555910i
\(727\) 1270.93i 1.74818i −0.485764 0.874090i \(-0.661459\pi\)
0.485764 0.874090i \(-0.338541\pi\)
\(728\) 87.8387 0.120658
\(729\) −37.2457 + 728.048i −0.0510915 + 0.998694i
\(730\) 108.461 70.7081i 0.148577 0.0968604i
\(731\) 222.292i 0.304093i
\(732\) 272.227 267.628i 0.371895 0.365612i
\(733\) 753.726i 1.02828i 0.857708 + 0.514138i \(0.171888\pi\)
−0.857708 + 0.514138i \(0.828112\pi\)
\(734\) 391.695i 0.533645i
\(735\) 469.257 + 103.061i 0.638445 + 0.140219i
\(736\) 27.1293 0.0368605
\(737\) −152.980 −0.207571
\(738\) −520.443 8.86811i −0.705207 0.0120164i
\(739\) 1093.13 1.47920 0.739600 0.673047i \(-0.235015\pi\)
0.739600 + 0.673047i \(0.235015\pi\)
\(740\) 135.242 88.1670i 0.182760 0.119145i
\(741\) 97.0487 + 98.7165i 0.130970 + 0.133221i
\(742\) 32.9976i 0.0444711i
\(743\) 1038.88 1.39823 0.699114 0.715011i \(-0.253578\pi\)
0.699114 + 0.715011i \(0.253578\pi\)
\(744\) −43.9243 + 43.1823i −0.0590381 + 0.0580407i
\(745\) 843.958 550.193i 1.13283 0.738514i
\(746\) 91.0351i 0.122031i
\(747\) −10.5433 + 618.753i −0.0141141 + 0.828317i
\(748\) 94.0077i 0.125679i
\(749\) 508.109i 0.678384i
\(750\) 313.102 428.039i 0.417470 0.570718i
\(751\) −449.017 −0.597892 −0.298946 0.954270i \(-0.596635\pi\)
−0.298946 + 0.954270i \(0.596635\pi\)
\(752\) −58.1681 −0.0773512
\(753\) 665.658 + 677.097i 0.884008 + 0.899200i
\(754\) 133.244 0.176717
\(755\) 262.620 + 402.842i 0.347842 + 0.533565i
\(756\) 161.268 153.228i 0.213317 0.202683i
\(757\) 318.876i 0.421237i −0.977568 0.210618i \(-0.932452\pi\)
0.977568 0.210618i \(-0.0675477\pi\)
\(758\) 642.117 0.847120
\(759\) −117.007 119.018i −0.154159 0.156808i
\(760\) 47.2741 + 72.5153i 0.0622028 + 0.0954149i
\(761\) 230.754i 0.303225i 0.988440 + 0.151612i \(0.0484466\pi\)
−0.988440 + 0.151612i \(0.951553\pi\)
\(762\) 118.367 + 120.401i 0.155337 + 0.158007i
\(763\) 568.772i 0.745442i
\(764\) 205.683i 0.269218i
\(765\) 154.419 96.9604i 0.201855 0.126746i
\(766\) 955.765 1.24773
\(767\) −65.0978 −0.0848733
\(768\) −34.2290 + 33.6508i −0.0445691 + 0.0438161i
\(769\) −828.980 −1.07800 −0.538998 0.842307i \(-0.681197\pi\)
−0.538998 + 0.842307i \(0.681197\pi\)
\(770\) −184.541 283.073i −0.239663 0.367627i
\(771\) −695.298 + 683.551i −0.901813 + 0.886577i
\(772\) 122.734i 0.158982i
\(773\) 765.288 0.990024 0.495012 0.868886i \(-0.335164\pi\)
0.495012 + 0.868886i \(0.335164\pi\)
\(774\) 698.165 + 11.8964i 0.902022 + 0.0153700i
\(775\) 73.2284 166.049i 0.0944883 0.214256i
\(776\) 41.6495i 0.0536720i
\(777\) −142.279 + 139.876i −0.183114 + 0.180020i
\(778\) 542.812i 0.697701i
\(779\) 250.323i 0.321339i
\(780\) 48.5142 220.894i 0.0621977 0.283198i
\(781\) 283.769 0.363341
\(782\) −27.4815 −0.0351425