Properties

Label 230.3.f.b.47.12
Level $230$
Weight $3$
Character 230.47
Analytic conductor $6.267$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.12
Character \(\chi\) \(=\) 230.47
Dual form 230.3.f.b.93.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(4.03568 - 4.03568i) q^{3} +2.00000i q^{4} +(-1.56820 - 4.74771i) q^{5} +8.07136 q^{6} +(6.17013 + 6.17013i) q^{7} +(-2.00000 + 2.00000i) q^{8} -23.5735i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(4.03568 - 4.03568i) q^{3} +2.00000i q^{4} +(-1.56820 - 4.74771i) q^{5} +8.07136 q^{6} +(6.17013 + 6.17013i) q^{7} +(-2.00000 + 2.00000i) q^{8} -23.5735i q^{9} +(3.17952 - 6.31591i) q^{10} -0.724813 q^{11} +(8.07136 + 8.07136i) q^{12} +(-8.24673 + 8.24673i) q^{13} +12.3403i q^{14} +(-25.4890 - 12.8315i) q^{15} -4.00000 q^{16} +(12.1461 + 12.1461i) q^{17} +(23.5735 - 23.5735i) q^{18} -25.7326i q^{19} +(9.49542 - 3.13639i) q^{20} +49.8013 q^{21} +(-0.724813 - 0.724813i) q^{22} +(3.39116 - 3.39116i) q^{23} +16.1427i q^{24} +(-20.0815 + 14.8907i) q^{25} -16.4935 q^{26} +(-58.8138 - 58.8138i) q^{27} +(-12.3403 + 12.3403i) q^{28} +44.6652i q^{29} +(-12.6575 - 38.3205i) q^{30} -21.4180 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.92511 + 2.92511i) q^{33} +24.2922i q^{34} +(19.6180 - 38.9699i) q^{35} +47.1469 q^{36} +(-6.02016 - 6.02016i) q^{37} +(25.7326 - 25.7326i) q^{38} +66.5623i q^{39} +(12.6318 + 6.35903i) q^{40} +62.9812 q^{41} +(49.8013 + 49.8013i) q^{42} +(-22.3539 + 22.3539i) q^{43} -1.44963i q^{44} +(-111.920 + 36.9678i) q^{45} +6.78233 q^{46} +(59.0982 + 59.0982i) q^{47} +(-16.1427 + 16.1427i) q^{48} +27.1409i q^{49} +(-34.9722 - 5.19084i) q^{50} +98.0355 q^{51} +(-16.4935 - 16.4935i) q^{52} +(-23.4423 + 23.4423i) q^{53} -117.628i q^{54} +(1.13665 + 3.44120i) q^{55} -24.6805 q^{56} +(-103.849 - 103.849i) q^{57} +(-44.6652 + 44.6652i) q^{58} +65.3535i q^{59} +(25.6630 - 50.9780i) q^{60} +4.47673 q^{61} +(-21.4180 - 21.4180i) q^{62} +(145.451 - 145.451i) q^{63} -8.00000i q^{64} +(52.0856 + 26.2206i) q^{65} -5.85023 q^{66} +(3.14266 + 3.14266i) q^{67} +(-24.2922 + 24.2922i) q^{68} -27.3713i q^{69} +(58.5879 - 19.3519i) q^{70} -116.389 q^{71} +(47.1469 + 47.1469i) q^{72} +(-23.6714 + 23.6714i) q^{73} -12.0403i q^{74} +(-20.9486 + 141.137i) q^{75} +51.4652 q^{76} +(-4.47218 - 4.47218i) q^{77} +(-66.5623 + 66.5623i) q^{78} -35.5924i q^{79} +(6.27278 + 18.9908i) q^{80} -262.547 q^{81} +(62.9812 + 62.9812i) q^{82} +(24.3664 - 24.3664i) q^{83} +99.6026i q^{84} +(38.6187 - 76.7136i) q^{85} -44.7078 q^{86} +(180.254 + 180.254i) q^{87} +(1.44963 - 1.44963i) q^{88} -95.7824i q^{89} +(-148.888 - 74.9522i) q^{90} -101.767 q^{91} +(6.78233 + 6.78233i) q^{92} +(-86.4361 + 86.4361i) q^{93} +118.196i q^{94} +(-122.171 + 40.3537i) q^{95} -32.2855 q^{96} +(-33.7217 - 33.7217i) q^{97} +(-27.1409 + 27.1409i) q^{98} +17.0863i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 4.03568 4.03568i 1.34523 1.34523i 0.454460 0.890767i \(-0.349832\pi\)
0.890767 0.454460i \(-0.150168\pi\)
\(4\) 2.00000i 0.500000i
\(5\) −1.56820 4.74771i −0.313639 0.949542i
\(6\) 8.07136 1.34523
\(7\) 6.17013 + 6.17013i 0.881447 + 0.881447i 0.993682 0.112235i \(-0.0358010\pi\)
−0.112235 + 0.993682i \(0.535801\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 23.5735i 2.61927i
\(10\) 3.17952 6.31591i 0.317952 0.631591i
\(11\) −0.724813 −0.0658920 −0.0329460 0.999457i \(-0.510489\pi\)
−0.0329460 + 0.999457i \(0.510489\pi\)
\(12\) 8.07136 + 8.07136i 0.672614 + 0.672614i
\(13\) −8.24673 + 8.24673i −0.634364 + 0.634364i −0.949159 0.314796i \(-0.898064\pi\)
0.314796 + 0.949159i \(0.398064\pi\)
\(14\) 12.3403i 0.881447i
\(15\) −25.4890 12.8315i −1.69927 0.855434i
\(16\) −4.00000 −0.250000
\(17\) 12.1461 + 12.1461i 0.714476 + 0.714476i 0.967468 0.252993i \(-0.0814148\pi\)
−0.252993 + 0.967468i \(0.581415\pi\)
\(18\) 23.5735 23.5735i 1.30964 1.30964i
\(19\) 25.7326i 1.35435i −0.735824 0.677173i \(-0.763205\pi\)
0.735824 0.677173i \(-0.236795\pi\)
\(20\) 9.49542 3.13639i 0.474771 0.156820i
\(21\) 49.8013 2.37149
\(22\) −0.724813 0.724813i −0.0329460 0.0329460i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 16.1427i 0.672614i
\(25\) −20.0815 + 14.8907i −0.803261 + 0.595627i
\(26\) −16.4935 −0.634364
\(27\) −58.8138 58.8138i −2.17829 2.17829i
\(28\) −12.3403 + 12.3403i −0.440723 + 0.440723i
\(29\) 44.6652i 1.54018i 0.637936 + 0.770089i \(0.279788\pi\)
−0.637936 + 0.770089i \(0.720212\pi\)
\(30\) −12.6575 38.3205i −0.421916 1.27735i
\(31\) −21.4180 −0.690902 −0.345451 0.938437i \(-0.612274\pi\)
−0.345451 + 0.938437i \(0.612274\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −2.92511 + 2.92511i −0.0886398 + 0.0886398i
\(34\) 24.2922i 0.714476i
\(35\) 19.6180 38.9699i 0.560515 1.11343i
\(36\) 47.1469 1.30964
\(37\) −6.02016 6.02016i −0.162707 0.162707i 0.621058 0.783765i \(-0.286703\pi\)
−0.783765 + 0.621058i \(0.786703\pi\)
\(38\) 25.7326 25.7326i 0.677173 0.677173i
\(39\) 66.5623i 1.70673i
\(40\) 12.6318 + 6.35903i 0.315795 + 0.158976i
\(41\) 62.9812 1.53613 0.768064 0.640374i \(-0.221220\pi\)
0.768064 + 0.640374i \(0.221220\pi\)
\(42\) 49.8013 + 49.8013i 1.18575 + 1.18575i
\(43\) −22.3539 + 22.3539i −0.519859 + 0.519859i −0.917529 0.397670i \(-0.869819\pi\)
0.397670 + 0.917529i \(0.369819\pi\)
\(44\) 1.44963i 0.0329460i
\(45\) −111.920 + 36.9678i −2.48711 + 0.821506i
\(46\) 6.78233 0.147442
\(47\) 59.0982 + 59.0982i 1.25741 + 1.25741i 0.952326 + 0.305084i \(0.0986844\pi\)
0.305084 + 0.952326i \(0.401316\pi\)
\(48\) −16.1427 + 16.1427i −0.336307 + 0.336307i
\(49\) 27.1409i 0.553896i
\(50\) −34.9722 5.19084i −0.699444 0.103817i
\(51\) 98.0355 1.92226
\(52\) −16.4935 16.4935i −0.317182 0.317182i
\(53\) −23.4423 + 23.4423i −0.442307 + 0.442307i −0.892787 0.450480i \(-0.851253\pi\)
0.450480 + 0.892787i \(0.351253\pi\)
\(54\) 117.628i 2.17829i
\(55\) 1.13665 + 3.44120i 0.0206663 + 0.0625673i
\(56\) −24.6805 −0.440723
\(57\) −103.849 103.849i −1.82190 1.82190i
\(58\) −44.6652 + 44.6652i −0.770089 + 0.770089i
\(59\) 65.3535i 1.10769i 0.832621 + 0.553843i \(0.186839\pi\)
−0.832621 + 0.553843i \(0.813161\pi\)
\(60\) 25.6630 50.9780i 0.427717 0.849633i
\(61\) 4.47673 0.0733890 0.0366945 0.999327i \(-0.488317\pi\)
0.0366945 + 0.999327i \(0.488317\pi\)
\(62\) −21.4180 21.4180i −0.345451 0.345451i
\(63\) 145.451 145.451i 2.30875 2.30875i
\(64\) 8.00000i 0.125000i
\(65\) 52.0856 + 26.2206i 0.801316 + 0.403394i
\(66\) −5.85023 −0.0886398
\(67\) 3.14266 + 3.14266i 0.0469053 + 0.0469053i 0.730170 0.683265i \(-0.239441\pi\)
−0.683265 + 0.730170i \(0.739441\pi\)
\(68\) −24.2922 + 24.2922i −0.357238 + 0.357238i
\(69\) 27.3713i 0.396686i
\(70\) 58.5879 19.3519i 0.836971 0.276456i
\(71\) −116.389 −1.63928 −0.819641 0.572878i \(-0.805827\pi\)
−0.819641 + 0.572878i \(0.805827\pi\)
\(72\) 47.1469 + 47.1469i 0.654818 + 0.654818i
\(73\) −23.6714 + 23.6714i −0.324266 + 0.324266i −0.850401 0.526135i \(-0.823641\pi\)
0.526135 + 0.850401i \(0.323641\pi\)
\(74\) 12.0403i 0.162707i
\(75\) −20.9486 + 141.137i −0.279315 + 1.88182i
\(76\) 51.4652 0.677173
\(77\) −4.47218 4.47218i −0.0580803 0.0580803i
\(78\) −66.5623 + 66.5623i −0.853363 + 0.853363i
\(79\) 35.5924i 0.450536i −0.974297 0.225268i \(-0.927674\pi\)
0.974297 0.225268i \(-0.0723258\pi\)
\(80\) 6.27278 + 18.9908i 0.0784098 + 0.237386i
\(81\) −262.547 −3.24132
\(82\) 62.9812 + 62.9812i 0.768064 + 0.768064i
\(83\) 24.3664 24.3664i 0.293572 0.293572i −0.544918 0.838489i \(-0.683439\pi\)
0.838489 + 0.544918i \(0.183439\pi\)
\(84\) 99.6026i 1.18575i
\(85\) 38.6187 76.7136i 0.454337 0.902512i
\(86\) −44.7078 −0.519859
\(87\) 180.254 + 180.254i 2.07189 + 2.07189i
\(88\) 1.44963 1.44963i 0.0164730 0.0164730i
\(89\) 95.7824i 1.07621i −0.842879 0.538103i \(-0.819141\pi\)
0.842879 0.538103i \(-0.180859\pi\)
\(90\) −148.888 74.9522i −1.65431 0.832802i
\(91\) −101.767 −1.11832
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −86.4361 + 86.4361i −0.929420 + 0.929420i
\(94\) 118.196i 1.25741i
\(95\) −122.171 + 40.3537i −1.28601 + 0.424776i
\(96\) −32.2855 −0.336307
\(97\) −33.7217 33.7217i −0.347647 0.347647i 0.511586 0.859232i \(-0.329058\pi\)
−0.859232 + 0.511586i \(0.829058\pi\)
\(98\) −27.1409 + 27.1409i −0.276948 + 0.276948i
\(99\) 17.0863i 0.172589i
\(100\) −29.7814 40.1630i −0.297814 0.401630i
\(101\) −42.9802 −0.425546 −0.212773 0.977102i \(-0.568250\pi\)
−0.212773 + 0.977102i \(0.568250\pi\)
\(102\) 98.0355 + 98.0355i 0.961132 + 0.961132i
\(103\) 98.6987 98.6987i 0.958240 0.958240i −0.0409228 0.999162i \(-0.513030\pi\)
0.999162 + 0.0409228i \(0.0130298\pi\)
\(104\) 32.9869i 0.317182i
\(105\) −78.0982 236.442i −0.743793 2.25183i
\(106\) −46.8845 −0.442307
\(107\) −120.750 120.750i −1.12851 1.12851i −0.990420 0.138086i \(-0.955905\pi\)
−0.138086 0.990420i \(-0.544095\pi\)
\(108\) 117.628 117.628i 1.08914 1.08914i
\(109\) 131.422i 1.20571i −0.797851 0.602854i \(-0.794030\pi\)
0.797851 0.602854i \(-0.205970\pi\)
\(110\) −2.30455 + 4.57785i −0.0209505 + 0.0416168i
\(111\) −48.5909 −0.437756
\(112\) −24.6805 24.6805i −0.220362 0.220362i
\(113\) −31.8364 + 31.8364i −0.281738 + 0.281738i −0.833802 0.552064i \(-0.813840\pi\)
0.552064 + 0.833802i \(0.313840\pi\)
\(114\) 207.697i 1.82190i
\(115\) −21.4183 10.7823i −0.186246 0.0937588i
\(116\) −89.3304 −0.770089
\(117\) 194.404 + 194.404i 1.66157 + 1.66157i
\(118\) −65.3535 + 65.3535i −0.553843 + 0.553843i
\(119\) 149.886i 1.25954i
\(120\) 76.6410 25.3150i 0.638675 0.210958i
\(121\) −120.475 −0.995658
\(122\) 4.47673 + 4.47673i 0.0366945 + 0.0366945i
\(123\) 254.172 254.172i 2.06644 2.06644i
\(124\) 42.8359i 0.345451i
\(125\) 102.188 + 71.9898i 0.817507 + 0.575918i
\(126\) 290.902 2.30875
\(127\) 105.932 + 105.932i 0.834113 + 0.834113i 0.988077 0.153964i \(-0.0492038\pi\)
−0.153964 + 0.988077i \(0.549204\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 180.427i 1.39866i
\(130\) 25.8650 + 78.3062i 0.198961 + 0.602355i
\(131\) −28.6777 −0.218913 −0.109457 0.993992i \(-0.534911\pi\)
−0.109457 + 0.993992i \(0.534911\pi\)
\(132\) −5.85023 5.85023i −0.0443199 0.0443199i
\(133\) 158.773 158.773i 1.19378 1.19378i
\(134\) 6.28531i 0.0469053i
\(135\) −186.999 + 371.463i −1.38518 + 2.75157i
\(136\) −48.5843 −0.357238
\(137\) 51.4865 + 51.4865i 0.375814 + 0.375814i 0.869589 0.493775i \(-0.164384\pi\)
−0.493775 + 0.869589i \(0.664384\pi\)
\(138\) 27.3713 27.3713i 0.198343 0.198343i
\(139\) 19.6365i 0.141270i −0.997502 0.0706348i \(-0.977498\pi\)
0.997502 0.0706348i \(-0.0225025\pi\)
\(140\) 77.9399 + 39.2360i 0.556713 + 0.280257i
\(141\) 477.003 3.38300
\(142\) −116.389 116.389i −0.819641 0.819641i
\(143\) 5.97733 5.97733i 0.0417995 0.0417995i
\(144\) 94.2938i 0.654818i
\(145\) 212.057 70.0437i 1.46246 0.483060i
\(146\) −47.3429 −0.324266
\(147\) 109.532 + 109.532i 0.745116 + 0.745116i
\(148\) 12.0403 12.0403i 0.0813536 0.0813536i
\(149\) 1.97762i 0.0132726i 0.999978 + 0.00663632i \(0.00211242\pi\)
−0.999978 + 0.00663632i \(0.997888\pi\)
\(150\) −162.085 + 120.188i −1.08057 + 0.801254i
\(151\) −2.68828 −0.0178032 −0.00890160 0.999960i \(-0.502834\pi\)
−0.00890160 + 0.999960i \(0.502834\pi\)
\(152\) 51.4652 + 51.4652i 0.338587 + 0.338587i
\(153\) 286.325 286.325i 1.87141 1.87141i
\(154\) 8.94437i 0.0580803i
\(155\) 33.5876 + 101.686i 0.216694 + 0.656041i
\(156\) −133.125 −0.853363
\(157\) −168.859 168.859i −1.07554 1.07554i −0.996904 0.0786313i \(-0.974945\pi\)
−0.0786313 0.996904i \(-0.525055\pi\)
\(158\) 35.5924 35.5924i 0.225268 0.225268i
\(159\) 189.211i 1.19001i
\(160\) −12.7181 + 25.2636i −0.0794879 + 0.157898i
\(161\) 41.8478 0.259924
\(162\) −262.547 262.547i −1.62066 1.62066i
\(163\) 162.141 162.141i 0.994728 0.994728i −0.00525769 0.999986i \(-0.501674\pi\)
0.999986 + 0.00525769i \(0.00167358\pi\)
\(164\) 125.962i 0.768064i
\(165\) 18.4747 + 9.30044i 0.111968 + 0.0563663i
\(166\) 48.7329 0.293572
\(167\) −32.6312 32.6312i −0.195397 0.195397i 0.602627 0.798023i \(-0.294121\pi\)
−0.798023 + 0.602627i \(0.794121\pi\)
\(168\) −99.6026 + 99.6026i −0.592873 + 0.592873i
\(169\) 32.9829i 0.195165i
\(170\) 115.332 38.0949i 0.678425 0.224088i
\(171\) −606.606 −3.54740
\(172\) −44.7078 44.7078i −0.259929 0.259929i
\(173\) 92.0321 92.0321i 0.531977 0.531977i −0.389183 0.921160i \(-0.627243\pi\)
0.921160 + 0.389183i \(0.127243\pi\)
\(174\) 360.509i 2.07189i
\(175\) −215.783 32.0282i −1.23305 0.183018i
\(176\) 2.89925 0.0164730
\(177\) 263.746 + 263.746i 1.49009 + 1.49009i
\(178\) 95.7824 95.7824i 0.538103 0.538103i
\(179\) 253.117i 1.41406i −0.707184 0.707030i \(-0.750035\pi\)
0.707184 0.707030i \(-0.249965\pi\)
\(180\) −73.9356 223.840i −0.410753 1.24355i
\(181\) 17.8508 0.0986230 0.0493115 0.998783i \(-0.484297\pi\)
0.0493115 + 0.998783i \(0.484297\pi\)
\(182\) −101.767 101.767i −0.559158 0.559158i
\(183\) 18.0667 18.0667i 0.0987249 0.0987249i
\(184\) 13.5647i 0.0737210i
\(185\) −19.1412 + 38.0228i −0.103466 + 0.205529i
\(186\) −172.872 −0.929420
\(187\) −8.80364 8.80364i −0.0470783 0.0470783i
\(188\) −118.196 + 118.196i −0.628705 + 0.628705i
\(189\) 725.777i 3.84009i
\(190\) −162.525 81.8172i −0.855393 0.430617i
\(191\) 284.021 1.48702 0.743510 0.668725i \(-0.233160\pi\)
0.743510 + 0.668725i \(0.233160\pi\)
\(192\) −32.2855 32.2855i −0.168153 0.168153i
\(193\) 86.3395 86.3395i 0.447355 0.447355i −0.447119 0.894474i \(-0.647550\pi\)
0.894474 + 0.447119i \(0.147550\pi\)
\(194\) 67.4435i 0.347647i
\(195\) 316.019 104.383i 1.62061 0.535296i
\(196\) −54.2818 −0.276948
\(197\) −26.9977 26.9977i −0.137044 0.137044i 0.635257 0.772301i \(-0.280894\pi\)
−0.772301 + 0.635257i \(0.780894\pi\)
\(198\) −17.0863 + 17.0863i −0.0862946 + 0.0862946i
\(199\) 294.774i 1.48127i 0.671905 + 0.740637i \(0.265476\pi\)
−0.671905 + 0.740637i \(0.734524\pi\)
\(200\) 10.3817 69.9444i 0.0519084 0.349722i
\(201\) 25.3655 0.126197
\(202\) −42.9802 42.9802i −0.212773 0.212773i
\(203\) −275.590 + 275.590i −1.35759 + 1.35759i
\(204\) 196.071i 0.961132i
\(205\) −98.7669 299.017i −0.481790 1.45862i
\(206\) 197.397 0.958240
\(207\) −79.9415 79.9415i −0.386191 0.386191i
\(208\) 32.9869 32.9869i 0.158591 0.158591i
\(209\) 18.6513i 0.0892407i
\(210\) 158.344 314.541i 0.754019 1.49781i
\(211\) 9.20580 0.0436294 0.0218147 0.999762i \(-0.493056\pi\)
0.0218147 + 0.999762i \(0.493056\pi\)
\(212\) −46.8845 46.8845i −0.221153 0.221153i
\(213\) −469.709 + 469.709i −2.20521 + 2.20521i
\(214\) 241.500i 1.12851i
\(215\) 141.185 + 71.0746i 0.656676 + 0.330580i
\(216\) 235.255 1.08914
\(217\) −132.152 132.152i −0.608993 0.608993i
\(218\) 131.422 131.422i 0.602854 0.602854i
\(219\) 191.061i 0.872424i
\(220\) −6.88240 + 2.27330i −0.0312836 + 0.0103332i
\(221\) −200.331 −0.906475
\(222\) −48.5909 48.5909i −0.218878 0.218878i
\(223\) −198.904 + 198.904i −0.891948 + 0.891948i −0.994706 0.102758i \(-0.967233\pi\)
0.102758 + 0.994706i \(0.467233\pi\)
\(224\) 49.3610i 0.220362i
\(225\) 351.025 + 473.391i 1.56011 + 2.10396i
\(226\) −63.6728 −0.281738
\(227\) 176.347 + 176.347i 0.776860 + 0.776860i 0.979296 0.202436i \(-0.0648858\pi\)
−0.202436 + 0.979296i \(0.564886\pi\)
\(228\) 207.697 207.697i 0.910952 0.910952i
\(229\) 139.620i 0.609695i −0.952401 0.304848i \(-0.901394\pi\)
0.952401 0.304848i \(-0.0986055\pi\)
\(230\) −10.6360 32.2005i −0.0462436 0.140002i
\(231\) −36.0966 −0.156262
\(232\) −89.3304 89.3304i −0.385045 0.385045i
\(233\) −46.2369 + 46.2369i −0.198441 + 0.198441i −0.799332 0.600890i \(-0.794813\pi\)
0.600890 + 0.799332i \(0.294813\pi\)
\(234\) 388.808i 1.66157i
\(235\) 187.904 373.259i 0.799590 1.58834i
\(236\) −130.707 −0.553843
\(237\) −143.639 143.639i −0.606074 0.606074i
\(238\) −149.886 + 149.886i −0.629772 + 0.629772i
\(239\) 298.604i 1.24939i 0.780870 + 0.624694i \(0.214776\pi\)
−0.780870 + 0.624694i \(0.785224\pi\)
\(240\) 101.956 + 51.3261i 0.424816 + 0.213859i
\(241\) −402.475 −1.67002 −0.835011 0.550233i \(-0.814539\pi\)
−0.835011 + 0.550233i \(0.814539\pi\)
\(242\) −120.475 120.475i −0.497829 0.497829i
\(243\) −530.230 + 530.230i −2.18202 + 2.18202i
\(244\) 8.95346i 0.0366945i
\(245\) 128.857 42.5622i 0.525948 0.173723i
\(246\) 508.344 2.06644
\(247\) 212.210 + 212.210i 0.859148 + 0.859148i
\(248\) 42.8359 42.8359i 0.172726 0.172726i
\(249\) 196.670i 0.789841i
\(250\) 30.1986 + 174.178i 0.120795 + 0.696713i
\(251\) −13.3235 −0.0530816 −0.0265408 0.999648i \(-0.508449\pi\)
−0.0265408 + 0.999648i \(0.508449\pi\)
\(252\) 290.902 + 290.902i 1.15437 + 1.15437i
\(253\) −2.45796 + 2.45796i −0.00971525 + 0.00971525i
\(254\) 211.865i 0.834113i
\(255\) −153.739 465.444i −0.602897 1.82527i
\(256\) 16.0000 0.0625000
\(257\) −228.386 228.386i −0.888661 0.888661i 0.105734 0.994394i \(-0.466281\pi\)
−0.994394 + 0.105734i \(0.966281\pi\)
\(258\) −180.427 + 180.427i −0.699328 + 0.699328i
\(259\) 74.2903i 0.286835i
\(260\) −52.4412 + 104.171i −0.201697 + 0.400658i
\(261\) 1052.91 4.03415
\(262\) −28.6777 28.6777i −0.109457 0.109457i
\(263\) 315.031 315.031i 1.19784 1.19784i 0.223022 0.974814i \(-0.428408\pi\)
0.974814 0.223022i \(-0.0715920\pi\)
\(264\) 11.7005i 0.0443199i
\(265\) 148.059 + 74.5350i 0.558714 + 0.281264i
\(266\) 317.547 1.19378
\(267\) −386.547 386.547i −1.44774 1.44774i
\(268\) −6.28531 + 6.28531i −0.0234527 + 0.0234527i
\(269\) 220.576i 0.819986i −0.912089 0.409993i \(-0.865531\pi\)
0.912089 0.409993i \(-0.134469\pi\)
\(270\) −558.462 + 184.463i −2.06838 + 0.683197i
\(271\) −345.263 −1.27403 −0.637017 0.770850i \(-0.719832\pi\)
−0.637017 + 0.770850i \(0.719832\pi\)
\(272\) −48.5843 48.5843i −0.178619 0.178619i
\(273\) −410.698 + 410.698i −1.50439 + 1.50439i
\(274\) 102.973i 0.375814i
\(275\) 14.5553 10.7930i 0.0529285 0.0392471i
\(276\) 54.7426 0.198343
\(277\) 16.6105 + 16.6105i 0.0599656 + 0.0599656i 0.736454 0.676488i \(-0.236499\pi\)
−0.676488 + 0.736454i \(0.736499\pi\)
\(278\) 19.6365 19.6365i 0.0706348 0.0706348i
\(279\) 504.895i 1.80966i
\(280\) 38.7039 + 117.176i 0.138228 + 0.418485i
\(281\) −40.9492 −0.145727 −0.0728633 0.997342i \(-0.523214\pi\)
−0.0728633 + 0.997342i \(0.523214\pi\)
\(282\) 477.003 + 477.003i 1.69150 + 1.69150i
\(283\) −42.6150 + 42.6150i −0.150583 + 0.150583i −0.778378 0.627795i \(-0.783957\pi\)
0.627795 + 0.778378i \(0.283957\pi\)
\(284\) 232.778i 0.819641i
\(285\) −330.188 + 655.898i −1.15855 + 2.30140i
\(286\) 11.9547 0.0417995
\(287\) 388.602 + 388.602i 1.35401 + 1.35401i
\(288\) −94.2938 + 94.2938i −0.327409 + 0.327409i
\(289\) 6.05488i 0.0209512i
\(290\) 282.101 + 142.014i 0.972762 + 0.489702i
\(291\) −272.180 −0.935328
\(292\) −47.3429 47.3429i −0.162133 0.162133i
\(293\) 337.952 337.952i 1.15342 1.15342i 0.167558 0.985862i \(-0.446412\pi\)
0.985862 0.167558i \(-0.0535880\pi\)
\(294\) 219.064i 0.745116i
\(295\) 310.280 102.487i 1.05180 0.347414i
\(296\) 24.0807 0.0813536
\(297\) 42.6290 + 42.6290i 0.143532 + 0.143532i
\(298\) −1.97762 + 1.97762i −0.00663632 + 0.00663632i
\(299\) 55.9320i 0.187064i
\(300\) −282.273 41.8972i −0.940911 0.139657i
\(301\) −275.853 −0.916455
\(302\) −2.68828 2.68828i −0.00890160 0.00890160i
\(303\) −173.454 + 173.454i −0.572457 + 0.572457i
\(304\) 102.930i 0.338587i
\(305\) −7.02039 21.2542i −0.0230177 0.0696860i
\(306\) 572.650 1.87141
\(307\) −177.271 177.271i −0.577430 0.577430i 0.356764 0.934194i \(-0.383880\pi\)
−0.934194 + 0.356764i \(0.883880\pi\)
\(308\) 8.94437 8.94437i 0.0290402 0.0290402i
\(309\) 796.633i 2.57810i
\(310\) −68.0988 + 135.274i −0.219673 + 0.436367i
\(311\) 327.598 1.05337 0.526686 0.850060i \(-0.323435\pi\)
0.526686 + 0.850060i \(0.323435\pi\)
\(312\) −133.125 133.125i −0.426682 0.426682i
\(313\) −52.4677 + 52.4677i −0.167628 + 0.167628i −0.785936 0.618308i \(-0.787819\pi\)
0.618308 + 0.785936i \(0.287819\pi\)
\(314\) 337.718i 1.07554i
\(315\) −918.656 462.464i −2.91637 1.46814i
\(316\) 71.1847 0.225268
\(317\) −188.054 188.054i −0.593230 0.593230i 0.345272 0.938503i \(-0.387787\pi\)
−0.938503 + 0.345272i \(0.887787\pi\)
\(318\) −189.211 + 189.211i −0.595003 + 0.595003i
\(319\) 32.3739i 0.101486i
\(320\) −37.9817 + 12.5456i −0.118693 + 0.0392049i
\(321\) −974.619 −3.03620
\(322\) 41.8478 + 41.8478i 0.129962 + 0.129962i
\(323\) 312.550 312.550i 0.967648 0.967648i
\(324\) 525.093i 1.62066i
\(325\) 42.8075 288.406i 0.131715 0.887404i
\(326\) 324.281 0.994728
\(327\) −530.378 530.378i −1.62195 1.62195i
\(328\) −125.962 + 125.962i −0.384032 + 0.384032i
\(329\) 729.287i 2.21668i
\(330\) 9.17430 + 27.7752i 0.0278009 + 0.0841672i
\(331\) −411.903 −1.24442 −0.622211 0.782850i \(-0.713765\pi\)
−0.622211 + 0.782850i \(0.713765\pi\)
\(332\) 48.7329 + 48.7329i 0.146786 + 0.146786i
\(333\) −141.916 + 141.916i −0.426174 + 0.426174i
\(334\) 65.2625i 0.195397i
\(335\) 9.99212 19.8487i 0.0298272 0.0592499i
\(336\) −199.205 −0.592873
\(337\) 227.170 + 227.170i 0.674096 + 0.674096i 0.958658 0.284562i \(-0.0918480\pi\)
−0.284562 + 0.958658i \(0.591848\pi\)
\(338\) −32.9829 + 32.9829i −0.0975826 + 0.0975826i
\(339\) 256.963i 0.758003i
\(340\) 153.427 + 77.2374i 0.451256 + 0.227169i
\(341\) 15.5240 0.0455250
\(342\) −606.606 606.606i −1.77370 1.77370i
\(343\) 134.873 134.873i 0.393217 0.393217i
\(344\) 89.4157i 0.259929i
\(345\) −129.951 + 42.9236i −0.376670 + 0.124416i
\(346\) 184.064 0.531977
\(347\) 30.5267 + 30.5267i 0.0879731 + 0.0879731i 0.749724 0.661751i \(-0.230186\pi\)
−0.661751 + 0.749724i \(0.730186\pi\)
\(348\) −360.509 + 360.509i −1.03595 + 1.03595i
\(349\) 54.8757i 0.157237i 0.996905 + 0.0786185i \(0.0250509\pi\)
−0.996905 + 0.0786185i \(0.974949\pi\)
\(350\) −183.755 247.811i −0.525014 0.708032i
\(351\) 970.043 2.76366
\(352\) 2.89925 + 2.89925i 0.00823651 + 0.00823651i
\(353\) −286.119 + 286.119i −0.810536 + 0.810536i −0.984714 0.174178i \(-0.944273\pi\)
0.174178 + 0.984714i \(0.444273\pi\)
\(354\) 527.492i 1.49009i
\(355\) 182.521 + 552.581i 0.514143 + 1.55657i
\(356\) 191.565 0.538103
\(357\) 604.891 + 604.891i 1.69437 + 1.69437i
\(358\) 253.117 253.117i 0.707030 0.707030i
\(359\) 545.919i 1.52067i 0.649533 + 0.760333i \(0.274964\pi\)
−0.649533 + 0.760333i \(0.725036\pi\)
\(360\) 149.904 297.775i 0.416401 0.827154i
\(361\) −301.166 −0.834255
\(362\) 17.8508 + 17.8508i 0.0493115 + 0.0493115i
\(363\) −486.197 + 486.197i −1.33939 + 1.33939i
\(364\) 203.533i 0.559158i
\(365\) 149.507 + 75.2637i 0.409607 + 0.206202i
\(366\) 36.1333 0.0987249
\(367\) −99.6848 99.6848i −0.271621 0.271621i 0.558132 0.829752i \(-0.311518\pi\)
−0.829752 + 0.558132i \(0.811518\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 1484.68i 4.02354i
\(370\) −57.1640 + 18.8816i −0.154497 + 0.0510313i
\(371\) −289.283 −0.779740
\(372\) −172.872 172.872i −0.464710 0.464710i
\(373\) 184.070 184.070i 0.493485 0.493485i −0.415917 0.909402i \(-0.636539\pi\)
0.909402 + 0.415917i \(0.136539\pi\)
\(374\) 17.6073i 0.0470783i
\(375\) 702.928 121.872i 1.87447 0.324992i
\(376\) −236.393 −0.628705
\(377\) −368.342 368.342i −0.977034 0.977034i
\(378\) 725.777 725.777i 1.92005 1.92005i
\(379\) 425.333i 1.12225i −0.827731 0.561125i \(-0.810369\pi\)
0.827731 0.561125i \(-0.189631\pi\)
\(380\) −80.7075 244.342i −0.212388 0.643005i
\(381\) 855.018 2.24414
\(382\) 284.021 + 284.021i 0.743510 + 0.743510i
\(383\) −322.962 + 322.962i −0.843244 + 0.843244i −0.989279 0.146035i \(-0.953349\pi\)
0.146035 + 0.989279i \(0.453349\pi\)
\(384\) 64.5709i 0.168153i
\(385\) −14.2194 + 28.2459i −0.0369335 + 0.0733660i
\(386\) 172.679 0.447355
\(387\) 526.959 + 526.959i 1.36165 + 1.36165i
\(388\) 67.4435 67.4435i 0.173823 0.173823i
\(389\) 38.7279i 0.0995577i 0.998760 + 0.0497788i \(0.0158516\pi\)
−0.998760 + 0.0497788i \(0.984148\pi\)
\(390\) 420.402 + 211.636i 1.07795 + 0.542656i
\(391\) 82.3788 0.210687
\(392\) −54.2818 54.2818i −0.138474 0.138474i
\(393\) −115.734 + 115.734i −0.294488 + 0.294488i
\(394\) 53.9953i 0.137044i
\(395\) −168.982 + 55.8158i −0.427803 + 0.141306i
\(396\) −34.1727 −0.0862946
\(397\) 310.122 + 310.122i 0.781165 + 0.781165i 0.980027 0.198863i \(-0.0637248\pi\)
−0.198863 + 0.980027i \(0.563725\pi\)
\(398\) −294.774 + 294.774i −0.740637 + 0.740637i
\(399\) 1281.52i 3.21182i
\(400\) 80.3261 59.5627i 0.200815 0.148907i
\(401\) 154.599 0.385534 0.192767 0.981245i \(-0.438254\pi\)
0.192767 + 0.981245i \(0.438254\pi\)
\(402\) 25.3655 + 25.3655i 0.0630983 + 0.0630983i
\(403\) 176.628 176.628i 0.438283 0.438283i
\(404\) 85.9604i 0.212773i
\(405\) 411.724 + 1246.50i 1.01660 + 3.07777i
\(406\) −551.180 −1.35759
\(407\) 4.36349 + 4.36349i 0.0107211 + 0.0107211i
\(408\) −196.071 + 196.071i −0.480566 + 0.480566i
\(409\) 199.354i 0.487419i 0.969848 + 0.243709i \(0.0783643\pi\)
−0.969848 + 0.243709i \(0.921636\pi\)
\(410\) 200.250 397.784i 0.488414 0.970204i
\(411\) 415.566 1.01111
\(412\) 197.397 + 197.397i 0.479120 + 0.479120i
\(413\) −403.239 + 403.239i −0.976366 + 0.976366i
\(414\) 159.883i 0.386191i
\(415\) −153.896 77.4735i −0.370834 0.186683i
\(416\) 65.9738 0.158591
\(417\) −79.2465 79.2465i −0.190040 0.190040i
\(418\) −18.6513 + 18.6513i −0.0446203 + 0.0446203i
\(419\) 508.909i 1.21458i 0.794480 + 0.607290i \(0.207743\pi\)
−0.794480 + 0.607290i \(0.792257\pi\)
\(420\) 472.885 156.196i 1.12592 0.371896i
\(421\) −402.703 −0.956538 −0.478269 0.878213i \(-0.658736\pi\)
−0.478269 + 0.878213i \(0.658736\pi\)
\(422\) 9.20580 + 9.20580i 0.0218147 + 0.0218147i
\(423\) 1393.15 1393.15i 3.29350 3.29350i
\(424\) 93.7690i 0.221153i
\(425\) −424.775 63.0485i −0.999472 0.148349i
\(426\) −939.418 −2.20521
\(427\) 27.6220 + 27.6220i 0.0646885 + 0.0646885i
\(428\) 241.500 241.500i 0.564253 0.564253i
\(429\) 48.2452i 0.112460i
\(430\) 70.1106 + 212.260i 0.163048 + 0.493628i
\(431\) 168.573 0.391120 0.195560 0.980692i \(-0.437348\pi\)
0.195560 + 0.980692i \(0.437348\pi\)
\(432\) 235.255 + 235.255i 0.544572 + 0.544572i
\(433\) 491.359 491.359i 1.13478 1.13478i 0.145405 0.989372i \(-0.453551\pi\)
0.989372 0.145405i \(-0.0464485\pi\)
\(434\) 264.303i 0.608993i
\(435\) 573.122 1138.47i 1.31752 2.61717i
\(436\) 262.845 0.602854
\(437\) −87.2634 87.2634i −0.199688 0.199688i
\(438\) −191.061 + 191.061i −0.436212 + 0.436212i
\(439\) 112.222i 0.255631i −0.991798 0.127816i \(-0.959203\pi\)
0.991798 0.127816i \(-0.0407966\pi\)
\(440\) −9.15570 4.60911i −0.0208084 0.0104752i
\(441\) 639.805 1.45080
\(442\) −200.331 200.331i −0.453238 0.453238i
\(443\) 463.871 463.871i 1.04711 1.04711i 0.0482799 0.998834i \(-0.484626\pi\)
0.998834 0.0482799i \(-0.0153739\pi\)
\(444\) 97.1818i 0.218878i
\(445\) −454.747 + 150.206i −1.02190 + 0.337541i
\(446\) −397.809 −0.891948
\(447\) 7.98105 + 7.98105i 0.0178547 + 0.0178547i
\(448\) 49.3610 49.3610i 0.110181 0.110181i
\(449\) 342.770i 0.763408i 0.924285 + 0.381704i \(0.124663\pi\)
−0.924285 + 0.381704i \(0.875337\pi\)
\(450\) −122.366 + 824.416i −0.271925 + 1.83203i
\(451\) −45.6496 −0.101219
\(452\) −63.6728 63.6728i −0.140869 0.140869i
\(453\) −10.8491 + 10.8491i −0.0239494 + 0.0239494i
\(454\) 352.694i 0.776860i
\(455\) 159.590 + 483.159i 0.350747 + 1.06189i
\(456\) 415.394 0.910952
\(457\) −249.571 249.571i −0.546107 0.546107i 0.379206 0.925312i \(-0.376197\pi\)
−0.925312 + 0.379206i \(0.876197\pi\)
\(458\) 139.620 139.620i 0.304848 0.304848i
\(459\) 1428.72i 3.11267i
\(460\) 21.5645 42.8366i 0.0468794 0.0931230i
\(461\) 73.6640 0.159792 0.0798959 0.996803i \(-0.474541\pi\)
0.0798959 + 0.996803i \(0.474541\pi\)
\(462\) −36.0966 36.0966i −0.0781312 0.0781312i
\(463\) −179.579 + 179.579i −0.387859 + 0.387859i −0.873923 0.486064i \(-0.838432\pi\)
0.486064 + 0.873923i \(0.338432\pi\)
\(464\) 178.661i 0.385045i
\(465\) 545.922 + 274.825i 1.17403 + 0.591021i
\(466\) −92.4737 −0.198441
\(467\) 13.8984 + 13.8984i 0.0297609 + 0.0297609i 0.721831 0.692070i \(-0.243301\pi\)
−0.692070 + 0.721831i \(0.743301\pi\)
\(468\) −388.808 + 388.808i −0.830786 + 0.830786i
\(469\) 38.7812i 0.0826891i
\(470\) 561.163 185.355i 1.19396 0.394373i
\(471\) −1362.92 −2.89368
\(472\) −130.707 130.707i −0.276922 0.276922i
\(473\) 16.2024 16.2024i 0.0342546 0.0342546i
\(474\) 287.279i 0.606074i
\(475\) 383.176 + 516.750i 0.806686 + 1.08789i
\(476\) −299.772 −0.629772
\(477\) 552.615 + 552.615i 1.15852 + 1.15852i
\(478\) −298.604 + 298.604i −0.624694 + 0.624694i
\(479\) 707.716i 1.47749i 0.673987 + 0.738743i \(0.264580\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(480\) 50.6299 + 153.282i 0.105479 + 0.319338i
\(481\) 99.2933 0.206431
\(482\) −402.475 402.475i −0.835011 0.835011i
\(483\) 168.885 168.885i 0.349657 0.349657i
\(484\) 240.949i 0.497829i
\(485\) −107.219 + 212.983i −0.221070 + 0.439141i
\(486\) −1060.46 −2.18202
\(487\) 128.922 + 128.922i 0.264727 + 0.264727i 0.826971 0.562244i \(-0.190062\pi\)
−0.562244 + 0.826971i \(0.690062\pi\)
\(488\) −8.95346 + 8.95346i −0.0183473 + 0.0183473i
\(489\) 1308.70i 2.67627i
\(490\) 171.419 + 86.2949i 0.349835 + 0.176112i
\(491\) −195.979 −0.399142 −0.199571 0.979883i \(-0.563955\pi\)
−0.199571 + 0.979883i \(0.563955\pi\)
\(492\) 508.344 + 508.344i 1.03322 + 1.03322i
\(493\) −542.507 + 542.507i −1.10042 + 1.10042i
\(494\) 424.419i 0.859148i
\(495\) 81.1210 26.7947i 0.163881 0.0541307i
\(496\) 85.6719 0.172726
\(497\) −718.135 718.135i −1.44494 1.44494i
\(498\) 196.670 196.670i 0.394921 0.394921i
\(499\) 842.473i 1.68832i 0.536089 + 0.844161i \(0.319901\pi\)
−0.536089 + 0.844161i \(0.680099\pi\)
\(500\) −143.980 + 204.377i −0.287959 + 0.408754i
\(501\) −263.379 −0.525706
\(502\) −13.3235 13.3235i −0.0265408 0.0265408i
\(503\) 72.0448 72.0448i 0.143230 0.143230i −0.631856 0.775086i \(-0.717707\pi\)
0.775086 + 0.631856i \(0.217707\pi\)
\(504\) 581.805i 1.15437i
\(505\) 67.4013 + 204.057i 0.133468 + 0.404074i
\(506\) −4.91592 −0.00971525
\(507\) 133.109 + 133.109i 0.262542 + 0.262542i
\(508\) −211.865 + 211.865i −0.417056 + 0.417056i
\(509\) 737.964i 1.44983i 0.688837 + 0.724916i \(0.258121\pi\)
−0.688837 + 0.724916i \(0.741879\pi\)
\(510\) 311.705 619.183i 0.611187 1.21408i
\(511\) −292.112 −0.571647
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −1513.43 + 1513.43i −2.95016 + 2.95016i
\(514\) 456.772i 0.888661i
\(515\) −623.372 313.814i −1.21043 0.609348i
\(516\) −360.853 −0.699328
\(517\) −42.8351 42.8351i −0.0828533 0.0828533i
\(518\) 74.2903 74.2903i 0.143418 0.143418i
\(519\) 742.825i 1.43126i
\(520\) −156.612 + 51.7299i −0.301178 + 0.0994806i
\(521\) 892.279 1.71263 0.856314 0.516456i \(-0.172749\pi\)
0.856314 + 0.516456i \(0.172749\pi\)
\(522\) 1052.91 + 1052.91i 2.01707 + 2.01707i
\(523\) −332.739 + 332.739i −0.636213 + 0.636213i −0.949619 0.313406i \(-0.898530\pi\)
0.313406 + 0.949619i \(0.398530\pi\)
\(524\) 57.3553i 0.109457i
\(525\) −1000.09 + 741.576i −1.90493 + 1.41252i
\(526\) 630.061 1.19784
\(527\) −260.144 260.144i −0.493633 0.493633i
\(528\) 11.7005 11.7005i 0.0221599 0.0221599i
\(529\) 23.0000i 0.0434783i
\(530\) 73.5241 + 222.594i 0.138725 + 0.419989i
\(531\) 1540.61 2.90133
\(532\) 317.547 + 317.547i 0.596892 + 0.596892i
\(533\) −519.389 + 519.389i −0.974463 + 0.974463i
\(534\) 773.094i 1.44774i
\(535\) −383.927 + 762.647i −0.717621 + 1.42551i
\(536\) −12.5706 −0.0234527
\(537\) −1021.50 1021.50i −1.90223 1.90223i
\(538\) 220.576 220.576i 0.409993 0.409993i
\(539\) 19.6721i 0.0364973i
\(540\) −742.925 373.999i −1.37579 0.692590i
\(541\) −167.411 −0.309447 −0.154724 0.987958i \(-0.549449\pi\)
−0.154724 + 0.987958i \(0.549449\pi\)
\(542\) −345.263 345.263i −0.637017 0.637017i
\(543\) 72.0400 72.0400i 0.132670 0.132670i
\(544\) 97.1687i 0.178619i
\(545\) −623.955 + 206.096i −1.14487 + 0.378158i
\(546\) −821.396 −1.50439
\(547\) −30.6410 30.6410i −0.0560165 0.0560165i 0.678544 0.734560i \(-0.262611\pi\)
−0.734560 + 0.678544i \(0.762611\pi\)
\(548\) −102.973 + 102.973i −0.187907 + 0.187907i
\(549\) 105.532i 0.192226i
\(550\) 25.3483 + 3.76239i 0.0460878 + 0.00684071i
\(551\) 1149.35 2.08594
\(552\) 54.7426 + 54.7426i 0.0991715 + 0.0991715i
\(553\) 219.609 219.609i 0.397124 0.397124i
\(554\) 33.2209i 0.0599656i
\(555\) 76.2001 + 230.696i 0.137297 + 0.415668i
\(556\) 39.2729 0.0706348
\(557\) −74.7071 74.7071i −0.134124 0.134124i 0.636857 0.770982i \(-0.280234\pi\)
−0.770982 + 0.636857i \(0.780234\pi\)
\(558\) −504.895 + 504.895i −0.904830 + 0.904830i
\(559\) 368.693i 0.659559i
\(560\) −78.4720 + 155.880i −0.140129 + 0.278357i
\(561\) −71.0573 −0.126662
\(562\) −40.9492 40.9492i −0.0728633 0.0728633i
\(563\) 475.349 475.349i 0.844315 0.844315i −0.145102 0.989417i \(-0.546351\pi\)
0.989417 + 0.145102i \(0.0463510\pi\)
\(564\) 954.007i 1.69150i
\(565\) 201.076 + 101.224i 0.355886 + 0.179158i
\(566\) −85.2299 −0.150583
\(567\) −1619.95 1619.95i −2.85705 2.85705i
\(568\) 232.778 232.778i 0.409820 0.409820i
\(569\) 470.572i 0.827016i 0.910501 + 0.413508i \(0.135697\pi\)
−0.910501 + 0.413508i \(0.864303\pi\)
\(570\) −986.086 + 325.710i −1.72997 + 0.571420i
\(571\) 695.175 1.21747 0.608735 0.793374i \(-0.291677\pi\)
0.608735 + 0.793374i \(0.291677\pi\)
\(572\) 11.9547 + 11.9547i 0.0208998 + 0.0208998i
\(573\) 1146.22 1146.22i 2.00038 2.00038i
\(574\) 777.204i 1.35401i
\(575\) −17.6030 + 118.597i −0.0306139 + 0.206255i
\(576\) −188.588 −0.327409
\(577\) 136.810 + 136.810i 0.237106 + 0.237106i 0.815651 0.578545i \(-0.196379\pi\)
−0.578545 + 0.815651i \(0.696379\pi\)
\(578\) −6.05488 + 6.05488i −0.0104756 + 0.0104756i
\(579\) 696.878i 1.20359i
\(580\) 140.087 + 424.115i 0.241530 + 0.731232i
\(581\) 300.688 0.517535
\(582\) −272.180 272.180i −0.467664 0.467664i
\(583\) 16.9912 16.9912i 0.0291445 0.0291445i
\(584\) 94.6858i 0.162133i
\(585\) 618.110 1227.84i 1.05660 2.09887i
\(586\) 675.904 1.15342
\(587\) 636.514 + 636.514i 1.08435 + 1.08435i 0.996098 + 0.0882531i \(0.0281284\pi\)
0.0882531 + 0.996098i \(0.471872\pi\)
\(588\) −219.064 + 219.064i −0.372558 + 0.372558i
\(589\) 551.140i 0.935721i
\(590\) 412.767 + 207.792i 0.699604 + 0.352191i
\(591\) −217.908 −0.368710
\(592\) 24.0807 + 24.0807i 0.0406768 + 0.0406768i
\(593\) −541.335 + 541.335i −0.912876 + 0.912876i −0.996498 0.0836220i \(-0.973351\pi\)
0.0836220 + 0.996498i \(0.473351\pi\)
\(594\) 85.2580i 0.143532i
\(595\) 711.614 235.050i 1.19599 0.395042i
\(596\) −3.95524 −0.00663632
\(597\) 1189.61 + 1189.61i 1.99265 + 1.99265i
\(598\) −55.9320 + 55.9320i −0.0935318 + 0.0935318i
\(599\) 75.3917i 0.125863i 0.998018 + 0.0629313i \(0.0200449\pi\)
−0.998018 + 0.0629313i \(0.979955\pi\)
\(600\) −240.376 324.171i −0.400627 0.540284i
\(601\) 579.293 0.963881 0.481941 0.876204i \(-0.339932\pi\)
0.481941 + 0.876204i \(0.339932\pi\)
\(602\) −275.853 275.853i −0.458228 0.458228i
\(603\) 74.0833 74.0833i 0.122858 0.122858i
\(604\) 5.37657i 0.00890160i
\(605\) 188.928 + 571.979i 0.312277 + 0.945420i
\(606\) −346.909 −0.572457
\(607\) 277.236 + 277.236i 0.456731 + 0.456731i 0.897581 0.440850i \(-0.145323\pi\)
−0.440850 + 0.897581i \(0.645323\pi\)
\(608\) −102.930 + 102.930i −0.169293 + 0.169293i
\(609\) 2224.39i 3.65252i
\(610\) 14.2338 28.2746i 0.0233342 0.0463518i
\(611\) −974.734 −1.59531
\(612\) 572.650 + 572.650i 0.935703 + 0.935703i
\(613\) 686.889 686.889i 1.12054 1.12054i 0.128876 0.991661i \(-0.458863\pi\)
0.991661 0.128876i \(-0.0411368\pi\)
\(614\) 354.542i 0.577430i
\(615\) −1605.33 808.144i −2.61029 1.31406i
\(616\) 17.8887 0.0290402
\(617\) −588.091 588.091i −0.953145 0.953145i 0.0458050 0.998950i \(-0.485415\pi\)
−0.998950 + 0.0458050i \(0.985415\pi\)
\(618\) 796.633 796.633i 1.28905 1.28905i
\(619\) 510.860i 0.825298i 0.910890 + 0.412649i \(0.135396\pi\)
−0.910890 + 0.412649i \(0.864604\pi\)
\(620\) −203.373 + 67.1751i −0.328020 + 0.108347i
\(621\) −398.895 −0.642342
\(622\) 327.598 + 327.598i 0.526686 + 0.526686i
\(623\) 590.989 590.989i 0.948619 0.948619i
\(624\) 266.249i 0.426682i
\(625\) 181.535 598.055i 0.290456 0.956888i
\(626\) −104.935 −0.167628
\(627\) 75.2707 + 75.2707i 0.120049 + 0.120049i
\(628\) 337.718 337.718i 0.537768 0.537768i
\(629\) 146.243i 0.232501i
\(630\) −456.192 1381.12i −0.724114 2.19225i
\(631\) −1013.58 −1.60631 −0.803157 0.595768i \(-0.796848\pi\)
−0.803157 + 0.595768i \(0.796848\pi\)
\(632\) 71.1847 + 71.1847i 0.112634 + 0.112634i
\(633\) 37.1517 37.1517i 0.0586915 0.0586915i
\(634\) 376.108i 0.593230i
\(635\) 336.814 669.059i 0.530415 1.05364i
\(636\) −378.422 −0.595003
\(637\) −223.824 223.824i −0.351371 0.351371i
\(638\) 32.3739 32.3739i 0.0507428 0.0507428i
\(639\) 2743.69i 4.29373i
\(640\) −50.5273 25.4361i −0.0789488 0.0397439i
\(641\) 741.895 1.15740 0.578701 0.815540i \(-0.303560\pi\)
0.578701 + 0.815540i \(0.303560\pi\)
\(642\) −974.619 974.619i −1.51810 1.51810i
\(643\) −649.933 + 649.933i −1.01078 + 1.01078i −0.0108409 + 0.999941i \(0.503451\pi\)
−0.999941 + 0.0108409i \(0.996549\pi\)
\(644\) 83.6957i 0.129962i
\(645\) 856.614 282.944i 1.32808 0.438673i
\(646\) 625.101 0.967648
\(647\) −186.236 186.236i −0.287846 0.287846i 0.548382 0.836228i \(-0.315244\pi\)
−0.836228 + 0.548382i \(0.815244\pi\)
\(648\) 525.093 525.093i 0.810329 0.810329i
\(649\) 47.3690i 0.0729877i
\(650\) 331.214 245.599i 0.509560 0.377844i
\(651\) −1066.64 −1.63847
\(652\) 324.281 + 324.281i 0.497364 + 0.497364i
\(653\) 572.840 572.840i 0.877243 0.877243i −0.116005 0.993249i \(-0.537009\pi\)
0.993249 + 0.116005i \(0.0370090\pi\)
\(654\) 1060.76i 1.62195i
\(655\) 44.9722 + 136.153i 0.0686598 + 0.207867i
\(656\) −251.925 −0.384032
\(657\) 558.018 + 558.018i 0.849342 + 0.849342i
\(658\) −729.287 + 729.287i −1.10834 + 1.10834i
\(659\) 186.044i 0.282312i 0.989987 + 0.141156i \(0.0450820\pi\)
−0.989987 + 0.141156i \(0.954918\pi\)
\(660\) −18.6009 + 36.9495i −0.0281832 + 0.0559841i
\(661\) −269.862 −0.408263 −0.204131 0.978944i \(-0.565437\pi\)
−0.204131 + 0.978944i \(0.565437\pi\)
\(662\) −411.903 411.903i −0.622211 0.622211i
\(663\) −808.472 + 808.472i −1.21941 + 1.21941i
\(664\) 97.4658i 0.146786i
\(665\) −1002.80 504.822i −1.50797 0.759131i
\(666\) −283.832 −0.426174
\(667\) 151.467 + 151.467i 0.227087 + 0.227087i
\(668\) 65.2625 65.2625i 0.0976983 0.0976983i
\(669\) 1605.43i 2.39975i
\(670\) 29.8408 9.85660i 0.0445386 0.0147113i
\(671\) −3.24479 −0.00483575
\(672\) −199.205 199.205i −0.296436 0.296436i
\(673\) 801.955 801.955i 1.19161 1.19161i 0.214997 0.976615i \(-0.431026\pi\)
0.976615 0.214997i \(-0.0689741\pi\)
\(674\) 454.341i 0.674096i
\(675\) 2056.85 + 305.293i 3.04718 + 0.452286i
\(676\) −65.9659 −0.0975826
\(677\) −563.323 563.323i −0.832088 0.832088i 0.155714 0.987802i \(-0.450232\pi\)
−0.987802 + 0.155714i \(0.950232\pi\)
\(678\) −256.963 + 256.963i −0.379002 + 0.379002i
\(679\) 416.135i 0.612864i
\(680\) 76.1898 + 230.664i 0.112044 + 0.339212i
\(681\) 1423.36 2.09011
\(682\) 15.5240 + 15.5240i 0.0227625 + 0.0227625i
\(683\) −22.0385 + 22.0385i −0.0322672 + 0.0322672i −0.723056 0.690789i \(-0.757263\pi\)
0.690789 + 0.723056i \(0.257263\pi\)
\(684\) 1213.21i 1.77370i
\(685\) 163.702 325.184i 0.238981 0.474721i
\(686\) 269.747 0.393217
\(687\) −563.463 563.463i −0.820178 0.820178i
\(688\) 89.4157 89.4157i 0.129965 0.129965i
\(689\) 386.644i 0.561167i
\(690\) −172.875 87.0276i −0.250543 0.126127i
\(691\) −66.4937 −0.0962283 −0.0481141 0.998842i \(-0.515321\pi\)
−0.0481141 + 0.998842i \(0.515321\pi\)
\(692\) 184.064 + 184.064i 0.265989 + 0.265989i
\(693\) −105.425 + 105.425i −0.152128 + 0.152128i
\(694\) 61.0534i 0.0879731i
\(695\) −93.2283 + 30.7938i −0.134141 + 0.0443077i
\(696\) −721.018 −1.03595
\(697\) 764.975 + 764.975i 1.09753 + 1.09753i
\(698\) −54.8757 + 54.8757i −0.0786185 + 0.0786185i
\(699\) 373.195i 0.533898i
\(700\) 64.0563 431.566i 0.0915090 0.616523i
\(701\) 112.563 0.160576 0.0802878 0.996772i \(-0.474416\pi\)
0.0802878 + 0.996772i \(0.474416\pi\)
\(702\) 970.043 + 970.043i 1.38183 + 1.38183i
\(703\) −154.914 + 154.914i −0.220362 + 0.220362i
\(704\) 5.79850i 0.00823651i
\(705\) −748.034 2264.67i −1.06104 3.21230i
\(706\) −572.238 −0.810536
\(707\) −265.193 265.193i −0.375096 0.375096i
\(708\) −527.492 + 527.492i −0.745045 + 0.745045i
\(709\) 566.340i 0.798787i −0.916780 0.399394i \(-0.869221\pi\)
0.916780 0.399394i \(-0.130779\pi\)
\(710\) −370.061 + 735.102i −0.521212 + 1.03536i
\(711\) −839.035 −1.18008
\(712\) 191.565 + 191.565i 0.269052 + 0.269052i
\(713\) −72.6319 + 72.6319i −0.101868 + 0.101868i
\(714\) 1209.78i 1.69437i
\(715\) −37.7523 19.0050i −0.0528004 0.0265804i
\(716\) 506.233 0.707030
\(717\) 1205.07 + 1205.07i 1.68071 + 1.68071i
\(718\) −545.919 + 545.919i −0.760333 + 0.760333i
\(719\) 828.194i 1.15187i 0.817496 + 0.575934i \(0.195362\pi\)
−0.817496 + 0.575934i \(0.804638\pi\)
\(720\) 447.680 147.871i 0.621777 0.205377i
\(721\) 1217.97 1.68927
\(722\) −301.166 301.166i −0.417127 0.417127i
\(723\) −1624.26 + 1624.26i −2.24656 + 2.24656i
\(724\) 35.7015i 0.0493115i
\(725\) −665.095 896.945i −0.917372 1.23717i
\(726\) −972.395 −1.33939
\(727\) −137.468 137.468i −0.189090 0.189090i 0.606213 0.795303i \(-0.292688\pi\)
−0.795303 + 0.606213i \(0.792688\pi\)
\(728\) 203.533 203.533i 0.279579 0.279579i
\(729\) 1916.76i 2.62930i
\(730\) 74.2429 + 224.770i 0.101703 + 0.307905i
\(731\) −543.025 −0.742853
\(732\) 36.1333 + 36.1333i 0.0493625 + 0.0493625i
\(733\) −690.713 + 690.713i −0.942310 + 0.942310i −0.998424 0.0561147i \(-0.982129\pi\)
0.0561147 + 0.998424i \(0.482129\pi\)
\(734\) 199.370i 0.271621i
\(735\) 348.259 691.794i 0.473821 0.941216i
\(736\) −27.1293 −0.0368605
\(737\) −2.27784 2.27784i −0.00309069 0.00309069i
\(738\) 1484.68 1484.68i 2.01177 2.01177i
\(739\) 77.5070i 0.104881i 0.998624 + 0.0524405i \(0.0167000\pi\)
−0.998624 + 0.0524405i \(0.983300\pi\)
\(740\) −76.0456 38.2824i −0.102764 0.0517330i
\(741\) 1712.82 2.31150
\(742\) −289.283 289.283i −0.389870 0.389870i
\(743\) −154.641 + 154.641i −0.208131 + 0.208131i −0.803473 0.595342i \(-0.797017\pi\)
0.595342 + 0.803473i \(0.297017\pi\)
\(744\) 345.744i 0.464710i
\(745\) 9.38918 3.10130i 0.0126029 0.00416282i
\(746\) 368.140 0.493485
\(747\) −574.401 574.401i −0.768944 0.768944i
\(748\) 17.6073 17.6073i 0.0235391 0.0235391i
\(749\) 1490.09i 1.98944i
\(750\) 824.800 + 581.056i 1.09973 + 0.774741i
\(751\) 691.108 0.920250 0.460125 0.887854i \(-0.347805\pi\)
0.460125 + 0.887854i \(0.347805\pi\)
\(752\) −236.393 236.393i −0.314352 0.314352i
\(753\) −53.7693 + 53.7693i −0.0714068 + 0.0714068i
\(754\) 736.683i 0.977034i
\(755\) 4.21576 + 12.7632i 0.00558378 + 0.0169049i
\(756\) 1451.55 1.92005
\(757\) 198.386 + 198.386i 0.262068 + 0.262068i 0.825894 0.563826i \(-0.190671\pi\)
−0.563826 + 0.825894i \(0.690671\pi\)
\(758\) 425.333 425.333i 0.561125 0.561125i
\(759\) 19.8391i 0.0261384i
\(760\) 163.634 325.049i 0.215308 0.427696i
\(761\) −506.006 −0.664923 −0.332461 0.943117i \(-0.607879\pi\)
−0.332461 + 0.943117i \(0.607879\pi\)
\(762\) 855.018 + 855.018i 1.12207 + 1.12207i
\(763\) 810.892 810.892i 1.06277 1.06277i
\(764\) 568.042i 0.743510i
\(765\) −1808.40 910.375i −2.36393 1.19003i
\(766\) −645.925 −0.843244
\(767\) −538.953 538.953i −0.702676 0.702676i
\(768\) 64.5709 64.5709i 0.0840767 0.0840767i
\(769\) 293.494i 0.381657i −0.981623 0.190828i \(-0.938883\pi\)
0.981623 0.190828i \(-0.0611174\pi\)
\(770\) −42.4653 + 14.0265i −0.0551497 + 0.0182163i
\(771\) −1843.39 −2.39090
\(772\) 172.679 + 172.679i 0.223678 + 0.223678i
\(773\) −101.751 + 101.751i −0.131631 + 0.131631i −0.769853 0.638222i \(-0.779670\pi\)
0.638222 + 0.769853i \(0.279670\pi\)
\(774\) 1053.92i 1.36165i
\(775\) 430.105 318.928i 0.554975 0.411520i
\(776\) 134.887 0.173823
\(777\) −299.812 &minu