Properties

Label 21.4.c.b.20.2
Level 21
Weight 4
Character 21.20
Analytic conductor 1.239
Analytic rank 0
Dimension 4
CM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 21.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.23904011012\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-6}, \sqrt{-17})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.2
Root \(1.67362i\)
Character \(\chi\) = 21.20
Dual form 21.4.c.b.20.4

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-4.12311i q^{2}\) \(+(5.04975 + 1.22474i) q^{3}\) \(-9.00000 q^{4}\) \(-10.0995 q^{5}\) \(+(5.04975 - 20.8207i) q^{6}\) \(+(7.00000 + 17.1464i) q^{7}\) \(+4.12311i q^{8}\) \(+(24.0000 + 12.3693i) q^{9}\) \(+O(q^{10})\) \(q\)\(-4.12311i q^{2}\) \(+(5.04975 + 1.22474i) q^{3}\) \(-9.00000 q^{4}\) \(-10.0995 q^{5}\) \(+(5.04975 - 20.8207i) q^{6}\) \(+(7.00000 + 17.1464i) q^{7}\) \(+4.12311i q^{8}\) \(+(24.0000 + 12.3693i) q^{9}\) \(+41.6413i q^{10}\) \(+32.9848i q^{11}\) \(+(-45.4478 - 11.0227i) q^{12}\) \(-56.3383i q^{13}\) \(+(70.6965 - 28.8617i) q^{14}\) \(+(-51.0000 - 12.3693i) q^{15}\) \(-55.0000 q^{16}\) \(-60.5970 q^{17}\) \(+(51.0000 - 98.9545i) q^{18}\) \(+36.7423i q^{19}\) \(+90.8955 q^{20}\) \(+(14.3483 + 95.1584i) q^{21}\) \(+136.000 q^{22}\) \(-90.7083i q^{23}\) \(+(-5.04975 + 20.8207i) q^{24}\) \(-23.0000 q^{25}\) \(-232.289 q^{26}\) \(+(106.045 + 91.8559i) q^{27}\) \(+(-63.0000 - 154.318i) q^{28}\) \(+57.7235i q^{29}\) \(+(-51.0000 + 210.278i) q^{30}\) \(-254.747i q^{31}\) \(+259.756i q^{32}\) \(+(-40.3980 + 166.565i) q^{33}\) \(+249.848i q^{34}\) \(+(-70.6965 - 173.170i) q^{35}\) \(+(-216.000 - 111.324i) q^{36}\) \(+230.000 q^{37}\) \(+151.493 q^{38}\) \(+(69.0000 - 284.494i) q^{39}\) \(-41.6413i q^{40}\) \(+141.393 q^{41}\) \(+(392.348 - 59.1594i) q^{42}\) \(+44.0000 q^{43}\) \(-296.864i q^{44}\) \(+(-242.388 - 124.924i) q^{45}\) \(-374.000 q^{46}\) \(+343.383 q^{47}\) \(+(-277.736 - 67.3610i) q^{48}\) \(+(-245.000 + 240.050i) q^{49}\) \(+94.8314i q^{50}\) \(+(-306.000 - 74.2159i) q^{51}\) \(+507.044i q^{52}\) \(+206.155i q^{53}\) \(+(378.731 - 437.234i) q^{54}\) \(-333.131i q^{55}\) \(+(-70.6965 + 28.8617i) q^{56}\) \(+(-45.0000 + 185.540i) q^{57}\) \(+238.000 q^{58}\) \(-131.294 q^{59}\) \(+(459.000 + 111.324i) q^{60}\) \(+71.0352i q^{61}\) \(-1050.35 q^{62}\) \(+(-44.0896 + 498.099i) q^{63}\) \(+631.000 q^{64}\) \(+568.989i q^{65}\) \(+(686.766 + 166.565i) q^{66}\) \(-64.0000 q^{67}\) \(+545.373 q^{68}\) \(+(111.095 - 458.055i) q^{69}\) \(+(-714.000 + 291.489i) q^{70}\) \(-461.788i q^{71}\) \(+(-51.0000 + 98.9545i) q^{72}\) \(+88.1816i q^{73}\) \(-948.314i q^{74}\) \(+(-116.144 - 28.1691i) q^{75}\) \(-330.681i q^{76}\) \(+(-565.572 + 230.894i) q^{77}\) \(+(-1173.00 - 284.494i) q^{78}\) \(-442.000 q^{79}\) \(+555.473 q^{80}\) \(+(423.000 + 593.727i) q^{81}\) \(-582.979i q^{82}\) \(+494.876 q^{83}\) \(+(-129.134 - 856.426i) q^{84}\) \(+612.000 q^{85}\) \(-181.417i q^{86}\) \(+(-70.6965 + 291.489i) q^{87}\) \(-136.000 q^{88}\) \(+484.776 q^{89}\) \(+(-515.075 + 999.392i) q^{90}\) \(+(966.000 - 394.368i) q^{91}\) \(+816.375i q^{92}\) \(+(312.000 - 1286.41i) q^{93}\) \(-1415.81i q^{94}\) \(-371.080i q^{95}\) \(+(-318.134 + 1311.70i) q^{96}\) \(+1092.47i q^{97}\) \(+(989.751 + 1010.16i) q^{98}\) \(+(-408.000 + 791.636i) q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut -\mathstrut 36q^{4} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 96q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 36q^{4} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 96q^{9} \) \(\mathstrut -\mathstrut 204q^{15} \) \(\mathstrut -\mathstrut 220q^{16} \) \(\mathstrut +\mathstrut 204q^{18} \) \(\mathstrut -\mathstrut 84q^{21} \) \(\mathstrut +\mathstrut 544q^{22} \) \(\mathstrut -\mathstrut 92q^{25} \) \(\mathstrut -\mathstrut 252q^{28} \) \(\mathstrut -\mathstrut 204q^{30} \) \(\mathstrut -\mathstrut 864q^{36} \) \(\mathstrut +\mathstrut 920q^{37} \) \(\mathstrut +\mathstrut 276q^{39} \) \(\mathstrut +\mathstrut 1428q^{42} \) \(\mathstrut +\mathstrut 176q^{43} \) \(\mathstrut -\mathstrut 1496q^{46} \) \(\mathstrut -\mathstrut 980q^{49} \) \(\mathstrut -\mathstrut 1224q^{51} \) \(\mathstrut -\mathstrut 180q^{57} \) \(\mathstrut +\mathstrut 952q^{58} \) \(\mathstrut +\mathstrut 1836q^{60} \) \(\mathstrut +\mathstrut 672q^{63} \) \(\mathstrut +\mathstrut 2524q^{64} \) \(\mathstrut -\mathstrut 256q^{67} \) \(\mathstrut -\mathstrut 2856q^{70} \) \(\mathstrut -\mathstrut 204q^{72} \) \(\mathstrut -\mathstrut 4692q^{78} \) \(\mathstrut -\mathstrut 1768q^{79} \) \(\mathstrut +\mathstrut 1692q^{81} \) \(\mathstrut +\mathstrut 756q^{84} \) \(\mathstrut +\mathstrut 2448q^{85} \) \(\mathstrut -\mathstrut 544q^{88} \) \(\mathstrut +\mathstrut 3864q^{91} \) \(\mathstrut +\mathstrut 1248q^{93} \) \(\mathstrut -\mathstrut 1632q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.12311i 1.45774i −0.684653 0.728869i \(-0.740046\pi\)
0.684653 0.728869i \(-0.259954\pi\)
\(3\) 5.04975 + 1.22474i 0.971825 + 0.235702i
\(4\) −9.00000 −1.12500
\(5\) −10.0995 −0.903327 −0.451664 0.892188i \(-0.649169\pi\)
−0.451664 + 0.892188i \(0.649169\pi\)
\(6\) 5.04975 20.8207i 0.343592 1.41667i
\(7\) 7.00000 + 17.1464i 0.377964 + 0.925820i
\(8\) 4.12311i 0.182217i
\(9\) 24.0000 + 12.3693i 0.888889 + 0.458123i
\(10\) 41.6413i 1.31681i
\(11\) 32.9848i 0.904119i 0.891988 + 0.452059i \(0.149310\pi\)
−0.891988 + 0.452059i \(0.850690\pi\)
\(12\) −45.4478 11.0227i −1.09330 0.265165i
\(13\) 56.3383i 1.20196i −0.799266 0.600978i \(-0.794778\pi\)
0.799266 0.600978i \(-0.205222\pi\)
\(14\) 70.6965 28.8617i 1.34960 0.550973i
\(15\) −51.0000 12.3693i −0.877876 0.212916i
\(16\) −55.0000 −0.859375
\(17\) −60.5970 −0.864526 −0.432263 0.901748i \(-0.642285\pi\)
−0.432263 + 0.901748i \(0.642285\pi\)
\(18\) 51.0000 98.9545i 0.667823 1.29577i
\(19\) 36.7423i 0.443646i 0.975087 + 0.221823i \(0.0712007\pi\)
−0.975087 + 0.221823i \(0.928799\pi\)
\(20\) 90.8955 1.01624
\(21\) 14.3483 + 95.1584i 0.149098 + 0.988822i
\(22\) 136.000 1.31797
\(23\) 90.7083i 0.822348i −0.911557 0.411174i \(-0.865119\pi\)
0.911557 0.411174i \(-0.134881\pi\)
\(24\) −5.04975 + 20.8207i −0.0429490 + 0.177083i
\(25\) −23.0000 −0.184000
\(26\) −232.289 −1.75214
\(27\) 106.045 + 91.8559i 0.755864 + 0.654729i
\(28\) −63.0000 154.318i −0.425210 1.04155i
\(29\) 57.7235i 0.369620i 0.982774 + 0.184810i \(0.0591670\pi\)
−0.982774 + 0.184810i \(0.940833\pi\)
\(30\) −51.0000 + 210.278i −0.310376 + 1.27971i
\(31\) 254.747i 1.47593i −0.674838 0.737966i \(-0.735786\pi\)
0.674838 0.737966i \(-0.264214\pi\)
\(32\) 259.756i 1.43496i
\(33\) −40.3980 + 166.565i −0.213103 + 0.878645i
\(34\) 249.848i 1.26025i
\(35\) −70.6965 173.170i −0.341426 0.836318i
\(36\) −216.000 111.324i −1.00000 0.515388i
\(37\) 230.000 1.02194 0.510970 0.859599i \(-0.329286\pi\)
0.510970 + 0.859599i \(0.329286\pi\)
\(38\) 151.493 0.646719
\(39\) 69.0000 284.494i 0.283304 1.16809i
\(40\) 41.6413i 0.164602i
\(41\) 141.393 0.538583 0.269291 0.963059i \(-0.413211\pi\)
0.269291 + 0.963059i \(0.413211\pi\)
\(42\) 392.348 59.1594i 1.44144 0.217345i
\(43\) 44.0000 0.156045 0.0780225 0.996952i \(-0.475139\pi\)
0.0780225 + 0.996952i \(0.475139\pi\)
\(44\) 296.864i 1.01713i
\(45\) −242.388 124.924i −0.802957 0.413835i
\(46\) −374.000 −1.19877
\(47\) 343.383 1.06569 0.532847 0.846212i \(-0.321122\pi\)
0.532847 + 0.846212i \(0.321122\pi\)
\(48\) −277.736 67.3610i −0.835162 0.202557i
\(49\) −245.000 + 240.050i −0.714286 + 0.699854i
\(50\) 94.8314i 0.268224i
\(51\) −306.000 74.2159i −0.840168 0.203771i
\(52\) 507.044i 1.35220i
\(53\) 206.155i 0.534294i 0.963656 + 0.267147i \(0.0860810\pi\)
−0.963656 + 0.267147i \(0.913919\pi\)
\(54\) 378.731 437.234i 0.954423 1.10185i
\(55\) 333.131i 0.816715i
\(56\) −70.6965 + 28.8617i −0.168700 + 0.0688716i
\(57\) −45.0000 + 185.540i −0.104568 + 0.431146i
\(58\) 238.000 0.538809
\(59\) −131.294 −0.289711 −0.144856 0.989453i \(-0.546272\pi\)
−0.144856 + 0.989453i \(0.546272\pi\)
\(60\) 459.000 + 111.324i 0.987611 + 0.239531i
\(61\) 71.0352i 0.149100i 0.997217 + 0.0745502i \(0.0237521\pi\)
−0.997217 + 0.0745502i \(0.976248\pi\)
\(62\) −1050.35 −2.15152
\(63\) −44.0896 + 498.099i −0.0881709 + 0.996105i
\(64\) 631.000 1.23242
\(65\) 568.989i 1.08576i
\(66\) 686.766 + 166.565i 1.28083 + 0.310648i
\(67\) −64.0000 −0.116699 −0.0583496 0.998296i \(-0.518584\pi\)
−0.0583496 + 0.998296i \(0.518584\pi\)
\(68\) 545.373 0.972592
\(69\) 111.095 458.055i 0.193829 0.799178i
\(70\) −714.000 + 291.489i −1.21913 + 0.497709i
\(71\) 461.788i 0.771889i −0.922522 0.385945i \(-0.873876\pi\)
0.922522 0.385945i \(-0.126124\pi\)
\(72\) −51.0000 + 98.9545i −0.0834779 + 0.161971i
\(73\) 88.1816i 0.141382i 0.997498 + 0.0706910i \(0.0225204\pi\)
−0.997498 + 0.0706910i \(0.977480\pi\)
\(74\) 948.314i 1.48972i
\(75\) −116.144 28.1691i −0.178816 0.0433692i
\(76\) 330.681i 0.499102i
\(77\) −565.572 + 230.894i −0.837051 + 0.341725i
\(78\) −1173.00 284.494i −1.70277 0.412982i
\(79\) −442.000 −0.629480 −0.314740 0.949178i \(-0.601917\pi\)
−0.314740 + 0.949178i \(0.601917\pi\)
\(80\) 555.473 0.776297
\(81\) 423.000 + 593.727i 0.580247 + 0.814441i
\(82\) 582.979i 0.785112i
\(83\) 494.876 0.654454 0.327227 0.944946i \(-0.393886\pi\)
0.327227 + 0.944946i \(0.393886\pi\)
\(84\) −129.134 856.426i −0.167735 1.11243i
\(85\) 612.000 0.780950
\(86\) 181.417i 0.227473i
\(87\) −70.6965 + 291.489i −0.0871203 + 0.359206i
\(88\) −136.000 −0.164746
\(89\) 484.776 0.577373 0.288686 0.957424i \(-0.406782\pi\)
0.288686 + 0.957424i \(0.406782\pi\)
\(90\) −515.075 + 999.392i −0.603263 + 1.17050i
\(91\) 966.000 394.368i 1.11279 0.454297i
\(92\) 816.375i 0.925141i
\(93\) 312.000 1286.41i 0.347881 1.43435i
\(94\) 1415.81i 1.55350i
\(95\) 371.080i 0.400757i
\(96\) −318.134 + 1311.70i −0.338224 + 1.39453i
\(97\) 1092.47i 1.14354i 0.820413 + 0.571772i \(0.193744\pi\)
−0.820413 + 0.571772i \(0.806256\pi\)
\(98\) 989.751 + 1010.16i 1.02020 + 1.04124i
\(99\) −408.000 + 791.636i −0.414197 + 0.803661i
\(100\) 207.000 0.207000
\(101\) −1262.44 −1.24374 −0.621868 0.783122i \(-0.713626\pi\)
−0.621868 + 0.783122i \(0.713626\pi\)
\(102\) −306.000 + 1261.67i −0.297044 + 1.22474i
\(103\) 48.9898i 0.0468651i −0.999725 0.0234326i \(-0.992541\pi\)
0.999725 0.0234326i \(-0.00745950\pi\)
\(104\) 232.289 0.219017
\(105\) −144.910 961.053i −0.134684 0.893230i
\(106\) 850.000 0.778861
\(107\) 1467.83i 1.32617i 0.748545 + 0.663084i \(0.230753\pi\)
−0.748545 + 0.663084i \(0.769247\pi\)
\(108\) −954.403 826.703i −0.850347 0.736570i
\(109\) −1870.00 −1.64324 −0.821622 0.570033i \(-0.806930\pi\)
−0.821622 + 0.570033i \(0.806930\pi\)
\(110\) −1373.53 −1.19056
\(111\) 1161.44 + 281.691i 0.993147 + 0.240873i
\(112\) −385.000 943.054i −0.324813 0.795627i
\(113\) 1673.98i 1.39358i −0.717274 0.696791i \(-0.754610\pi\)
0.717274 0.696791i \(-0.245390\pi\)
\(114\) 765.000 + 185.540i 0.628498 + 0.152433i
\(115\) 916.109i 0.742849i
\(116\) 519.511i 0.415823i
\(117\) 696.866 1352.12i 0.550643 1.06840i
\(118\) 541.337i 0.422323i
\(119\) −424.179 1039.02i −0.326760 0.800395i
\(120\) 51.0000 210.278i 0.0387970 0.159964i
\(121\) 243.000 0.182569
\(122\) 292.886 0.217349
\(123\) 714.000 + 173.170i 0.523408 + 0.126945i
\(124\) 2292.72i 1.66042i
\(125\) 1494.73 1.06954
\(126\) 2053.72 + 181.786i 1.45206 + 0.128530i
\(127\) −1048.00 −0.732244 −0.366122 0.930567i \(-0.619315\pi\)
−0.366122 + 0.930567i \(0.619315\pi\)
\(128\) 523.634i 0.361587i
\(129\) 222.189 + 53.8888i 0.151649 + 0.0367802i
\(130\) 2346.00 1.58275
\(131\) −2555.17 −1.70417 −0.852086 0.523401i \(-0.824663\pi\)
−0.852086 + 0.523401i \(0.824663\pi\)
\(132\) 363.582 1499.09i 0.239741 0.988476i
\(133\) −630.000 + 257.196i −0.410736 + 0.167682i
\(134\) 263.879i 0.170117i
\(135\) −1071.00 927.699i −0.682793 0.591434i
\(136\) 249.848i 0.157532i
\(137\) 1006.04i 0.627384i −0.949525 0.313692i \(-0.898434\pi\)
0.949525 0.313692i \(-0.101566\pi\)
\(138\) −1888.61 458.055i −1.16499 0.282552i
\(139\) 1393.76i 0.850483i −0.905080 0.425242i \(-0.860189\pi\)
0.905080 0.425242i \(-0.139811\pi\)
\(140\) 636.269 + 1558.53i 0.384104 + 0.940858i
\(141\) 1734.00 + 420.557i 1.03567 + 0.251186i
\(142\) −1904.00 −1.12521
\(143\) 1858.31 1.08671
\(144\) −1320.00 680.312i −0.763889 0.393699i
\(145\) 582.979i 0.333888i
\(146\) 363.582 0.206098
\(147\) −1531.19 + 912.131i −0.859118 + 0.511777i
\(148\) −2070.00 −1.14968
\(149\) 255.633i 0.140552i 0.997528 + 0.0702760i \(0.0223880\pi\)
−0.997528 + 0.0702760i \(0.977612\pi\)
\(150\) −116.144 + 478.875i −0.0632210 + 0.260667i
\(151\) 1448.00 0.780375 0.390187 0.920735i \(-0.372410\pi\)
0.390187 + 0.920735i \(0.372410\pi\)
\(152\) −151.493 −0.0808399
\(153\) −1454.33 749.544i −0.768467 0.396059i
\(154\) 952.000 + 2331.91i 0.498145 + 1.22020i
\(155\) 2572.82i 1.33325i
\(156\) −621.000 + 2560.45i −0.318717 + 1.31410i
\(157\) 3397.44i 1.72704i 0.504314 + 0.863520i \(0.331745\pi\)
−0.504314 + 0.863520i \(0.668255\pi\)
\(158\) 1822.41i 0.917616i
\(159\) −252.488 + 1041.03i −0.125934 + 0.519241i
\(160\) 2623.40i 1.29624i
\(161\) 1555.32 634.958i 0.761346 0.310818i
\(162\) 2448.00 1744.07i 1.18724 0.845848i
\(163\) 3128.00 1.50309 0.751546 0.659681i \(-0.229309\pi\)
0.751546 + 0.659681i \(0.229309\pi\)
\(164\) −1272.54 −0.605905
\(165\) 408.000 1682.23i 0.192502 0.793704i
\(166\) 2040.42i 0.954022i
\(167\) −706.965 −0.327585 −0.163792 0.986495i \(-0.552373\pi\)
−0.163792 + 0.986495i \(0.552373\pi\)
\(168\) −392.348 + 59.1594i −0.180181 + 0.0271681i
\(169\) −977.000 −0.444697
\(170\) 2523.34i 1.13842i
\(171\) −454.478 + 881.816i −0.203244 + 0.394352i
\(172\) −396.000 −0.175551
\(173\) 2252.19 0.989773 0.494887 0.868957i \(-0.335210\pi\)
0.494887 + 0.868957i \(0.335210\pi\)
\(174\) 1201.84 + 291.489i 0.523628 + 0.126999i
\(175\) −161.000 394.368i −0.0695455 0.170351i
\(176\) 1814.17i 0.776977i
\(177\) −663.000 160.801i −0.281549 0.0682856i
\(178\) 1998.78i 0.841658i
\(179\) 3496.39i 1.45996i 0.683469 + 0.729980i \(0.260471\pi\)
−0.683469 + 0.729980i \(0.739529\pi\)
\(180\) 2181.49 + 1124.32i 0.903327 + 0.465564i
\(181\) 183.712i 0.0754430i 0.999288 + 0.0377215i \(0.0120100\pi\)
−0.999288 + 0.0377215i \(0.987990\pi\)
\(182\) −1626.02 3982.92i −0.662245 1.62216i
\(183\) −87.0000 + 358.710i −0.0351433 + 0.144900i
\(184\) 374.000 0.149846
\(185\) −2322.89 −0.923146
\(186\) −5304.00 1286.41i −2.09090 0.507119i
\(187\) 1998.78i 0.781634i
\(188\) −3090.45 −1.19890
\(189\) −832.686 + 2461.28i −0.320471 + 0.947258i
\(190\) −1530.00 −0.584199
\(191\) 263.879i 0.0999665i −0.998750 0.0499832i \(-0.984083\pi\)
0.998750 0.0499832i \(-0.0159168\pi\)
\(192\) 3186.39 + 772.814i 1.19770 + 0.290485i
\(193\) −652.000 −0.243171 −0.121585 0.992581i \(-0.538798\pi\)
−0.121585 + 0.992581i \(0.538798\pi\)
\(194\) 4504.38 1.66699
\(195\) −696.866 + 2873.25i −0.255916 + 1.05517i
\(196\) 2205.00 2160.45i 0.803571 0.787336i
\(197\) 2020.32i 0.730670i −0.930876 0.365335i \(-0.880954\pi\)
0.930876 0.365335i \(-0.119046\pi\)
\(198\) 3264.00 + 1682.23i 1.17153 + 0.603791i
\(199\) 4849.99i 1.72767i −0.503773 0.863836i \(-0.668055\pi\)
0.503773 0.863836i \(-0.331945\pi\)
\(200\) 94.8314i 0.0335280i
\(201\) −323.184 78.3837i −0.113411 0.0275063i
\(202\) 5205.17i 1.81304i
\(203\) −989.751 + 404.064i −0.342202 + 0.139703i
\(204\) 2754.00 + 667.943i 0.945189 + 0.229242i
\(205\) −1428.00 −0.486516
\(206\) −201.990 −0.0683171
\(207\) 1122.00 2177.00i 0.376736 0.730976i
\(208\) 3098.60i 1.03293i
\(209\) −1211.94 −0.401109
\(210\) −3962.52 + 597.481i −1.30210 + 0.196334i
\(211\) −2224.00 −0.725623 −0.362812 0.931863i \(-0.618183\pi\)
−0.362812 + 0.931863i \(0.618183\pi\)
\(212\) 1855.40i 0.601081i
\(213\) 565.572 2331.91i 0.181936 0.750141i
\(214\) 6052.00 1.93321
\(215\) −444.378 −0.140960
\(216\) −378.731 + 437.234i −0.119303 + 0.137731i
\(217\) 4368.00 1783.23i 1.36645 0.557850i
\(218\) 7710.21i 2.39542i
\(219\) −108.000 + 445.295i −0.0333240 + 0.137399i
\(220\) 2998.18i 0.918804i
\(221\) 3413.93i 1.03912i
\(222\) 1161.44 4788.75i 0.351130 1.44775i
\(223\) 1915.50i 0.575208i 0.957749 + 0.287604i \(0.0928587\pi\)
−0.957749 + 0.287604i \(0.907141\pi\)
\(224\) −4453.88 + 1818.29i −1.32852 + 0.542364i
\(225\) −552.000 284.494i −0.163556 0.0842946i
\(226\) −6902.00 −2.03148
\(227\) 5948.61 1.73931 0.869654 0.493661i \(-0.164342\pi\)
0.869654 + 0.493661i \(0.164342\pi\)
\(228\) 405.000 1669.86i 0.117639 0.485040i
\(229\) 3706.08i 1.06945i 0.845025 + 0.534726i \(0.179585\pi\)
−0.845025 + 0.534726i \(0.820415\pi\)
\(230\) 3777.21 1.08288
\(231\) −3138.79 + 473.275i −0.894013 + 0.134802i
\(232\) −238.000 −0.0673511
\(233\) 956.561i 0.268954i −0.990917 0.134477i \(-0.957065\pi\)
0.990917 0.134477i \(-0.0429355\pi\)
\(234\) −5574.93 2873.25i −1.55745 0.802694i
\(235\) −3468.00 −0.962670
\(236\) 1181.64 0.325925
\(237\) −2231.99 541.337i −0.611744 0.148370i
\(238\) −4284.00 + 1748.94i −1.16677 + 0.476331i
\(239\) 4791.05i 1.29668i −0.761350 0.648341i \(-0.775463\pi\)
0.761350 0.648341i \(-0.224537\pi\)
\(240\) 2805.00 + 680.312i 0.754425 + 0.182975i
\(241\) 3786.91i 1.01218i −0.862479 0.506092i \(-0.831090\pi\)
0.862479 0.506092i \(-0.168910\pi\)
\(242\) 1001.91i 0.266138i
\(243\) 1408.88 + 3516.24i 0.371933 + 0.928260i
\(244\) 639.317i 0.167738i
\(245\) 2474.38 2424.39i 0.645234 0.632197i
\(246\) 714.000 2943.90i 0.185053 0.762992i
\(247\) 2070.00 0.533243
\(248\) 1050.35 0.268940
\(249\) 2499.00 + 606.097i 0.636015 + 0.154256i
\(250\) 6162.92i 1.55911i
\(251\) −4029.70 −1.01336 −0.506678 0.862135i \(-0.669127\pi\)
−0.506678 + 0.862135i \(0.669127\pi\)
\(252\) 396.806 4482.90i 0.0991923 1.12062i
\(253\) 2992.00 0.743500
\(254\) 4321.01i 1.06742i
\(255\) 3090.45 + 749.544i 0.758947 + 0.184072i
\(256\) 2889.00 0.705322
\(257\) 201.990 0.0490264 0.0245132 0.999700i \(-0.492196\pi\)
0.0245132 + 0.999700i \(0.492196\pi\)
\(258\) 222.189 916.109i 0.0536159 0.221064i
\(259\) 1610.00 + 3943.68i 0.386257 + 0.946132i
\(260\) 5120.90i 1.22148i
\(261\) −714.000 + 1385.36i −0.169331 + 0.328551i
\(262\) 10535.3i 2.48424i
\(263\) 8279.20i 1.94113i −0.240840 0.970565i \(-0.577423\pi\)
0.240840 0.970565i \(-0.422577\pi\)
\(264\) −686.766 166.565i −0.160104 0.0388310i
\(265\) 2082.07i 0.482643i
\(266\) 1060.45 + 2597.56i 0.244437 + 0.598746i
\(267\) 2448.00 + 593.727i 0.561105 + 0.136088i
\(268\) 576.000 0.131287
\(269\) −5787.02 −1.31168 −0.655838 0.754902i \(-0.727684\pi\)
−0.655838 + 0.754902i \(0.727684\pi\)
\(270\) −3825.00 + 4415.85i −0.862156 + 0.995333i
\(271\) 1219.85i 0.273433i 0.990610 + 0.136717i \(0.0436549\pi\)
−0.990610 + 0.136717i \(0.956345\pi\)
\(272\) 3332.84 0.742952
\(273\) 5361.06 808.356i 1.18852 0.179209i
\(274\) −4148.00 −0.914561
\(275\) 758.651i 0.166358i
\(276\) −999.851 + 4122.49i −0.218058 + 0.899075i
\(277\) −3214.00 −0.697150 −0.348575 0.937281i \(-0.613334\pi\)
−0.348575 + 0.937281i \(0.613334\pi\)
\(278\) −5746.62 −1.23978
\(279\) 3151.05 6113.93i 0.676158 1.31194i
\(280\) 714.000 291.489i 0.152392 0.0622136i
\(281\) 9235.76i 1.96071i 0.197245 + 0.980354i \(0.436800\pi\)
−0.197245 + 0.980354i \(0.563200\pi\)
\(282\) 1734.00 7149.47i 0.366164 1.50973i
\(283\) 2981.03i 0.626162i −0.949726 0.313081i \(-0.898639\pi\)
0.949726 0.313081i \(-0.101361\pi\)
\(284\) 4156.09i 0.868375i
\(285\) 454.478 1873.86i 0.0944594 0.389466i
\(286\) 7662.00i 1.58414i
\(287\) 989.751 + 2424.39i 0.203565 + 0.498631i
\(288\) −3213.00 + 6234.14i −0.657388 + 1.27552i
\(289\) −1241.00 −0.252595
\(290\) −2403.68 −0.486721
\(291\) −1338.00 + 5516.72i −0.269536 + 1.11133i
\(292\) 793.635i 0.159055i
\(293\) −5160.85 −1.02901 −0.514505 0.857487i \(-0.672024\pi\)
−0.514505 + 0.857487i \(0.672024\pi\)
\(294\) 3760.81 + 6313.26i 0.746037 + 1.25237i
\(295\) 1326.00 0.261704
\(296\) 948.314i 0.186215i
\(297\) −3029.85 + 3497.87i −0.591952 + 0.683391i
\(298\) 1054.00 0.204888
\(299\) −5110.35 −0.988425
\(300\) 1045.30 + 253.522i 0.201168 + 0.0487904i
\(301\) 308.000 + 754.443i 0.0589795 + 0.144470i
\(302\) 5970.26i 1.13758i
\(303\) −6375.00 1546.16i −1.20869 0.293151i
\(304\) 2020.83i 0.381258i
\(305\) 717.420i 0.134686i
\(306\) −3090.45 + 5996.35i −0.577350 + 1.12022i
\(307\) 1873.86i 0.348361i −0.984714 0.174180i \(-0.944272\pi\)
0.984714 0.174180i \(-0.0557276\pi\)
\(308\) 5090.15 2078.05i 0.941683 0.384440i
\(309\) 60.0000 247.386i 0.0110462 0.0455447i
\(310\) 10608.0 1.94353
\(311\) 8564.38 1.56155 0.780774 0.624814i \(-0.214825\pi\)
0.780774 + 0.624814i \(0.214825\pi\)
\(312\) 1173.00 + 284.494i 0.212846 + 0.0516228i
\(313\) 533.989i 0.0964308i 0.998837 + 0.0482154i \(0.0153534\pi\)
−0.998837 + 0.0482154i \(0.984647\pi\)
\(314\) 14008.0 2.51757
\(315\) 445.283 5030.56i 0.0796472 0.899809i
\(316\) 3978.00 0.708165
\(317\) 5104.40i 0.904391i 0.891919 + 0.452195i \(0.149359\pi\)
−0.891919 + 0.452195i \(0.850641\pi\)
\(318\) 4292.29 + 1041.03i 0.756917 + 0.183579i
\(319\) −1904.00 −0.334180
\(320\) −6372.79 −1.11328
\(321\) −1797.71 + 7412.16i −0.312581 + 1.28880i
\(322\) −2618.00 6412.76i −0.453091 1.10984i
\(323\) 2226.48i 0.383543i
\(324\) −3807.00 5343.54i −0.652778 0.916246i
\(325\) 1295.78i 0.221160i
\(326\) 12897.1i 2.19111i
\(327\) −9443.04 2290.27i −1.59695 0.387316i
\(328\) 582.979i 0.0981390i
\(329\) 2403.68 + 5887.79i 0.402794 + 0.986640i
\(330\) −6936.00 1682.23i −1.15701 0.280617i
\(331\) 3632.00 0.603120 0.301560 0.953447i \(-0.402493\pi\)
0.301560 + 0.953447i \(0.402493\pi\)
\(332\) −4453.88 −0.736261
\(333\) 5520.00 + 2844.94i 0.908391 + 0.468174i
\(334\) 2914.89i 0.477532i
\(335\) 646.368 0.105418
\(336\) −789.155 5233.71i −0.128131 0.849769i
\(337\) −6256.00 −1.01123 −0.505617 0.862758i \(-0.668735\pi\)
−0.505617 + 0.862758i \(0.668735\pi\)
\(338\) 4028.27i 0.648252i
\(339\) 2050.20 8453.19i 0.328471 1.35432i
\(340\) −5508.00 −0.878568
\(341\) 8402.79 1.33442
\(342\) 3635.82 + 1873.86i 0.574862 + 0.296277i
\(343\) −5831.00 2520.52i −0.917914 0.396780i
\(344\) 181.417i 0.0284341i
\(345\) −1122.00 + 4626.12i −0.175091 + 0.721919i
\(346\) 9286.02i 1.44283i
\(347\) 1072.01i 0.165845i 0.996556 + 0.0829227i \(0.0264255\pi\)
−0.996556 + 0.0829227i \(0.973575\pi\)
\(348\) 636.269 2623.40i 0.0980103 0.404107i
\(349\) 6287.84i 0.964414i 0.876057 + 0.482207i \(0.160165\pi\)
−0.876057 + 0.482207i \(0.839835\pi\)
\(350\) −1626.02 + 663.820i −0.248327 + 0.101379i
\(351\) 5175.00 5974.38i 0.786955 0.908515i
\(352\) −8568.00 −1.29737
\(353\) −5292.14 −0.797938 −0.398969 0.916964i \(-0.630632\pi\)
−0.398969 + 0.916964i \(0.630632\pi\)
\(354\) −663.000 + 2733.62i −0.0995425 + 0.410424i
\(355\) 4663.83i 0.697268i
\(356\) −4362.99 −0.649544
\(357\) −869.462 5766.32i −0.128899 0.854863i
\(358\) 14416.0 2.12824
\(359\) 3207.78i 0.471588i −0.971803 0.235794i \(-0.924231\pi\)
0.971803 0.235794i \(-0.0757690\pi\)
\(360\) 515.075 999.392i 0.0754078 0.146313i
\(361\) 5509.00 0.803178
\(362\) 757.463 0.109976
\(363\) 1227.09 + 297.613i 0.177426 + 0.0430320i
\(364\) −8694.00 + 3549.31i −1.25189 + 0.511084i
\(365\) 890.591i 0.127714i
\(366\) 1479.00 + 358.710i 0.211226 + 0.0512297i
\(367\) 9381.55i 1.33437i 0.744893 + 0.667184i \(0.232500\pi\)
−0.744893 + 0.667184i \(0.767500\pi\)
\(368\) 4988.96i 0.706705i
\(369\) 3393.43 + 1748.94i 0.478740 + 0.246737i
\(370\) 9577.50i 1.34570i
\(371\) −3534.83 + 1443.09i −0.494661 + 0.201944i
\(372\) −2808.00 + 11577.7i −0.391366 + 1.61364i
\(373\) 4598.00 0.638272 0.319136 0.947709i \(-0.396607\pi\)
0.319136 + 0.947709i \(0.396607\pi\)
\(374\) −8241.20 −1.13942
\(375\) 7548.00 + 1830.66i 1.03941 + 0.252093i
\(376\) 1415.81i 0.194188i
\(377\) 3252.04 0.444267
\(378\) 10148.1 + 3433.25i 1.38085 + 0.467163i
\(379\) 5252.00 0.711813 0.355906 0.934522i \(-0.384172\pi\)
0.355906 + 0.934522i \(0.384172\pi\)
\(380\) 3339.72i 0.450852i
\(381\) −5292.14 1283.53i −0.711613 0.172592i
\(382\) −1088.00 −0.145725
\(383\) −1918.91 −0.256009 −0.128005 0.991774i \(-0.540857\pi\)
−0.128005 + 0.991774i \(0.540857\pi\)
\(384\) 641.319 2644.22i 0.0852270 0.351400i
\(385\) 5712.00 2331.91i 0.756131 0.308689i
\(386\) 2688.26i 0.354479i
\(387\) 1056.00 + 544.250i 0.138707 + 0.0714878i
\(388\) 9832.25i 1.28649i
\(389\) 7067.00i 0.921109i −0.887632 0.460554i \(-0.847651\pi\)
0.887632 0.460554i \(-0.152349\pi\)
\(390\) 11846.7 + 2873.25i 1.53816 + 0.373058i
\(391\) 5496.65i 0.710941i
\(392\) −989.751 1010.16i −0.127526 0.130155i
\(393\) −12903.0 3129.44i −1.65616 0.401677i
\(394\) −8330.00 −1.06513
\(395\) 4463.98 0.568626
\(396\) 3672.00 7124.73i 0.465972 0.904119i
\(397\) 13337.5i 1.68612i −0.537822 0.843059i \(-0.680753\pi\)
0.537822 0.843059i \(-0.319247\pi\)
\(398\) −19997.0 −2.51849
\(399\) −3496.34 + 527.189i −0.438687 + 0.0661465i
\(400\) 1265.00 0.158125
\(401\) 13251.7i 1.65027i −0.564939 0.825133i \(-0.691100\pi\)
0.564939 0.825133i \(-0.308900\pi\)
\(402\) −323.184 + 1332.52i −0.0400969 + 0.165324i
\(403\) −14352.0 −1.77401
\(404\) 11361.9 1.39920
\(405\) −4272.09 5996.35i −0.524153 0.735706i
\(406\) 1666.00 + 4080.85i 0.203651 + 0.498840i
\(407\) 7586.51i 0.923955i
\(408\) 306.000 1261.67i 0.0371305 0.153093i
\(409\) 7461.15i 0.902029i 0.892517 + 0.451015i \(0.148938\pi\)
−0.892517 + 0.451015i \(0.851062\pi\)
\(410\) 5887.79i 0.709213i
\(411\) 1232.14 5080.24i 0.147876 0.609708i
\(412\) 440.908i 0.0527233i
\(413\) −919.055 2251.22i −0.109501 0.268221i
\(414\) −8976.00 4626.12i −1.06557 0.549183i
\(415\) −4998.00 −0.591186
\(416\) 14634.2 1.72476
\(417\) 1707.00 7038.14i 0.200461 0.826521i
\(418\) 4996.96i 0.584711i
\(419\) 9261.25 1.07981 0.539906 0.841725i \(-0.318460\pi\)
0.539906 + 0.841725i \(0.318460\pi\)
\(420\) 1304.19 + 8649.48i 0.151519 + 1.00488i
\(421\) −2854.00 −0.330393 −0.165196 0.986261i \(-0.552826\pi\)
−0.165196 + 0.986261i \(0.552826\pi\)
\(422\) 9169.79i 1.05777i
\(423\) 8241.20 + 4247.42i 0.947283 + 0.488218i
\(424\) −850.000 −0.0973577
\(425\) 1393.73 0.159073
\(426\) −9614.73 2331.91i −1.09351 0.265215i
\(427\) −1218.00 + 497.246i −0.138040 + 0.0563547i
\(428\) 13210.4i 1.49194i
\(429\) 9384.00 + 2275.95i 1.05609 + 0.256140i
\(430\) 1832.22i 0.205482i
\(431\) 11289.1i 1.26166i 0.775921 + 0.630830i \(0.217285\pi\)
−0.775921 + 0.630830i \(0.782715\pi\)
\(432\) −5832.46 5052.07i −0.649571 0.562657i
\(433\) 13036.2i 1.44683i −0.690411 0.723417i \(-0.742570\pi\)
0.690411 0.723417i \(-0.257430\pi\)
\(434\) −7352.44 18009.7i −0.813199 1.99192i
\(435\) 714.000 2943.90i 0.0786981 0.324481i
\(436\) 16830.0 1.84865
\(437\) 3332.84 0.364831
\(438\) 1836.00 + 445.295i 0.200291 + 0.0485777i
\(439\) 3003.07i 0.326490i 0.986586 + 0.163245i \(0.0521960\pi\)
−0.986586 + 0.163245i \(0.947804\pi\)
\(440\) 1373.53 0.148820
\(441\) −8849.25 + 2730.72i −0.955540 + 0.294862i
\(442\) 14076.0 1.51477
\(443\) 6844.36i 0.734052i −0.930211 0.367026i \(-0.880376\pi\)
0.930211 0.367026i \(-0.119624\pi\)
\(444\) −10453.0 2535.22i −1.11729 0.270983i
\(445\) −4896.00 −0.521557
\(446\) 7897.81 0.838503
\(447\) −313.085 + 1290.88i −0.0331284 + 0.136592i
\(448\) 4417.00 + 10819.4i 0.465812 + 1.14100i
\(449\) 2655.28i 0.279088i 0.990216 + 0.139544i \(0.0445636\pi\)
−0.990216 + 0.139544i \(0.955436\pi\)
\(450\) −1173.00 + 2275.95i −0.122879 + 0.238421i
\(451\) 4663.83i 0.486943i
\(452\) 15065.8i 1.56778i
\(453\) 7312.04 + 1773.43i 0.758388 + 0.183936i
\(454\) 24526.7i 2.53546i
\(455\) −9756.12 + 3982.92i −1.00522 + 0.410378i
\(456\) −765.000 185.540i −0.0785623 0.0190542i
\(457\) 1196.00 0.122421 0.0612106 0.998125i \(-0.480504\pi\)
0.0612106 + 0.998125i \(0.480504\pi\)
\(458\) 15280.6 1.55898
\(459\) −6426.00 5566.19i −0.653464 0.566030i
\(460\) 8244.98i 0.835705i
\(461\) −5443.63 −0.549968 −0.274984 0.961449i \(-0.588673\pi\)
−0.274984 + 0.961449i \(0.588673\pi\)
\(462\) 1951.36 + 12941.5i 0.196506 + 1.30324i
\(463\) 926.000 0.0929479 0.0464739 0.998920i \(-0.485202\pi\)
0.0464739 + 0.998920i \(0.485202\pi\)
\(464\) 3174.79i 0.317642i
\(465\) −3151.05 + 12992.1i −0.314250 + 1.29569i
\(466\) −3944.00 −0.392065
\(467\) −7786.72 −0.771577 −0.385788 0.922587i \(-0.626071\pi\)
−0.385788 + 0.922587i \(0.626071\pi\)
\(468\) −6271.79 + 12169.1i −0.619474 + 1.20196i
\(469\) −448.000 1097.37i −0.0441081 0.108042i
\(470\) 14298.9i 1.40332i
\(471\) −4161.00 + 17156.2i −0.407067 + 1.67838i
\(472\) 541.337i 0.0527904i
\(473\) 1451.33i 0.141083i
\(474\) −2231.99 + 9202.73i −0.216284 + 0.891763i
\(475\) 845.074i 0.0816308i
\(476\) 3817.61 + 9351.20i 0.367605 + 0.900445i
\(477\) −2550.00 + 4947.73i −0.244772 + 0.474928i
\(478\) −19754.0 −1.89022
\(479\) −12503.2 −1.19266 −0.596331 0.802739i \(-0.703375\pi\)
−0.596331 + 0.802739i \(0.703375\pi\)
\(480\) 3213.00 13247.5i 0.305526 1.25972i
\(481\) 12957.8i 1.22833i
\(482\) −15613.8 −1.47550
\(483\) 8631.66 1301.51i 0.813156 0.122610i
\(484\) −2187.00 −0.205391
\(485\) 11033.4i 1.03299i
\(486\) 14497.8 5808.96i 1.35316 0.542181i
\(487\) 13712.0 1.27587 0.637936 0.770089i \(-0.279788\pi\)
0.637936 + 0.770089i \(0.279788\pi\)
\(488\) −292.886 −0.0271687
\(489\) 15795.6 + 3831.00i 1.46074 + 0.354282i
\(490\) −9996.00 10202.1i −0.921578 0.940582i
\(491\) 5772.35i 0.530555i 0.964172 + 0.265277i \(0.0854635\pi\)
−0.964172 + 0.265277i \(0.914536\pi\)
\(492\) −6426.00 1558.53i −0.588834 0.142813i
\(493\) 3497.87i 0.319546i
\(494\) 8534.83i 0.777328i
\(495\) 4120.60 7995.13i 0.374156 0.725969i
\(496\) 14011.1i 1.26838i
\(497\) 7918.01 3232.51i 0.714631 0.291747i
\(498\) 2499.00 10303.6i 0.224865 0.927143i
\(499\) 15476.0 1.38838 0.694189 0.719792i \(-0.255763\pi\)
0.694189 + 0.719792i \(0.255763\pi\)
\(500\) −13452.5 −1.20323
\(501\) −3570.00 865.852i −0.318355 0.0772124i
\(502\) 16614.9i 1.47721i
\(503\) 1696.72 0.150403 0.0752017 0.997168i \(-0.476040\pi\)
0.0752017 + 0.997168i \(0.476040\pi\)
\(504\) −2053.72 181.786i −0.181508 0.0160663i
\(505\) 12750.0 1.12350
\(506\) 12336.3i 1.08383i
\(507\) −4933.61 1196.58i −0.432168 0.104816i
\(508\) 9432.00 0.823774
\(509\) 4231.69 0.368500 0.184250 0.982879i \(-0.441014\pi\)
0.184250 + 0.982879i \(0.441014\pi\)
\(510\) 3090.45 12742.2i 0.268328 1.10635i
\(511\) −1512.00 + 617.271i −0.130894 + 0.0534373i
\(512\) 16100.7i 1.38976i
\(513\) −3375.00 + 3896.33i −0.290468 + 0.335336i
\(514\) 832.827i 0.0714677i
\(515\) 494.773i 0.0423345i
\(516\) −1999.70 484.999i −0.170605 0.0413777i
\(517\) 11326.4i 0.963513i
\(518\) 16260.2 6638.20i 1.37921 0.563061i
\(519\) 11373.0 + 2758.36i 0.961887 + 0.233292i
\(520\) −2346.00 −0.197844
\(521\) −19572.8 −1.64588 −0.822938 0.568131i \(-0.807667\pi\)
−0.822938 + 0.568131i \(0.807667\pi\)
\(522\) 5712.00 + 2943.90i 0.478941 + 0.246841i
\(523\) 8369.91i 0.699791i 0.936789 + 0.349895i \(0.113783\pi\)
−0.936789 + 0.349895i \(0.886217\pi\)
\(524\) 22996.6 1.91719
\(525\) −330.010 2188.64i −0.0274339 0.181943i
\(526\) −34136.0 −2.82966
\(527\) 15436.9i 1.27598i
\(528\) 2221.89 9161.09i 0.183135 0.755086i
\(529\) 3939.00 0.323745
\(530\) −8584.58 −0.703567
\(531\) −3151.05 1624.01i −0.257521 0.132723i
\(532\) 5670.00 2314.77i 0.462078 0.188643i
\(533\) 7965.84i 0.647352i
\(534\) 2448.00 10093.4i 0.198381 0.817945i
\(535\) 14824.3i 1.19796i
\(536\) 263.879i 0.0212646i
\(537\) −4282.19 + 17655.9i −0.344116 + 1.41883i
\(538\) 23860.5i 1.91208i
\(539\) −7918.01 8081.29i −0.632751 0.645799i
\(540\) 9639.00 + 8349.29i 0.768142 + 0.665363i
\(541\) −16150.0 −1.28344 −0.641722 0.766938i \(-0.721780\pi\)
−0.641722 + 0.766938i \(0.721780\pi\)
\(542\) 5029.55 0.398594
\(543\) −225.000 + 927.699i −0.0177821 + 0.0733174i
\(544\) 15740.4i 1.24056i
\(545\) 18886.1 1.48439
\(546\) −3332.94 22104.2i −0.261239 1.73255i
\(547\) −18352.0 −1.43451 −0.717253 0.696813i \(-0.754601\pi\)
−0.717253 + 0.696813i \(0.754601\pi\)
\(548\) 9054.34i 0.705807i
\(549\) −878.657 + 1704.84i −0.0683063 + 0.132534i
\(550\) −3128.00 −0.242506
\(551\) −2120.90 −0.163980
\(552\) 1888.61 + 458.055i 0.145624 + 0.0353190i
\(553\) −3094.00 7578.72i −0.237921 0.582785i
\(554\) 13251.7i 1.01626i
\(555\) −11730.0 2844.94i −0.897137 0.217588i
\(556\) 12543.8i 0.956793i
\(557\) 3323.22i 0.252800i 0.991979 + 0.126400i \(0.0403423\pi\)
−0.991979 + 0.126400i \(0.959658\pi\)
\(558\) −25208.4 12992.1i −1.91246 0.985662i
\(559\) 2478.88i 0.187559i
\(560\) 3888.31 + 9524.37i 0.293413 + 0.718711i
\(561\) 2448.00 10093.4i 0.184233 0.759612i
\(562\) 38080.0 2.85820
\(563\) 14290.8 1.06978 0.534889 0.844922i \(-0.320353\pi\)
0.534889 + 0.844922i \(0.320353\pi\)
\(564\) −15606.0 3785.01i −1.16513 0.282585i
\(565\) 16906.4i 1.25886i
\(566\) −12291.1 −0.912780
\(567\) −7219.30 + 11409.0i −0.534713 + 0.845034i
\(568\) 1904.00 0.140652
\(569\) 14801.9i 1.09056i 0.838253 + 0.545281i \(0.183577\pi\)
−0.838253 + 0.545281i \(0.816423\pi\)
\(570\) −7726.12 1873.86i −0.567740 0.137697i
\(571\) 4136.00 0.303128 0.151564 0.988447i \(-0.451569\pi\)
0.151564 + 0.988447i \(0.451569\pi\)
\(572\) −16724.8 −1.22255
\(573\) 323.184 1332.52i 0.0235623 0.0971500i
\(574\) 9996.00 4080.85i 0.726873 0.296745i
\(575\) 2086.29i 0.151312i
\(576\) 15144.0 + 7805.04i 1.09549 + 0.564601i
\(577\) 19458.7i 1.40395i −0.712202 0.701974i \(-0.752302\pi\)
0.712202 0.701974i \(-0.247698\pi\)
\(578\) 5116.77i 0.368218i
\(579\) −3292.44 798.534i −0.236320 0.0573159i
\(580\) 5246.81i 0.375624i
\(581\) 3464.13 + 8485.35i 0.247360 + 0.605907i
\(582\) 22746.0 + 5516.72i 1.62002 + 0.392913i
\(583\) −6800.00 −0.483066
\(584\) −363.582 −0.0257622
\(585\) −7038.00 + 13655.7i −0.497411 + 0.965119i
\(586\) 21278.7i 1.50003i
\(587\) 18310.4 1.28748 0.643740 0.765244i \(-0.277382\pi\)
0.643740 + 0.765244i \(0.277382\pi\)
\(588\) 13780.7 8209.18i 0.966508 0.575749i
\(589\) 9360.00 0.654791
\(590\) 5467.24i 0.381496i
\(591\) 2474.38 10202.1i 0.172221 0.710083i
\(592\) −12650.0 −0.878229
\(593\) −7998.81 −0.553915 −0.276958 0.960882i \(-0.589326\pi\)
−0.276958 + 0.960882i \(0.589326\pi\)
\(594\) 14422.1 + 12492.4i 0.996205 + 0.862911i
\(595\) 4284.00 + 10493.6i 0.295171 + 0.723019i
\(596\) 2300.69i 0.158121i
\(597\) 5940.00 24491.2i 0.407216 1.67900i
\(598\) 21070.5i 1.44086i
\(599\) 12435.3i 0.848234i −0.905607 0.424117i \(-0.860585\pi\)
0.905607 0.424117i \(-0.139415\pi\)
\(600\) 116.144 478.875i 0.00790262 0.0325833i
\(601\) 18557.3i 1.25952i −0.776791 0.629758i \(-0.783154\pi\)
0.776791 0.629758i \(-0.216846\pi\)
\(602\) 3110.65 1269.92i 0.210599 0.0859766i
\(603\) −1536.00 791.636i −0.103733 0.0534626i
\(604\) −13032.0 −0.877921
\(605\) −2454.18 −0.164920
\(606\) −6375.00 + 26284.8i −0.427338 + 1.76196i
\(607\) 1592.17i 0.106465i −0.998582 0.0532324i \(-0.983048\pi\)
0.998582 0.0532324i \(-0.0169524\pi\)
\(608\) −9544.03 −0.636614
\(609\) −5492.88 + 828.232i −0.365489 + 0.0551094i
\(610\) −2958.00 −0.196338
\(611\) 19345.6i 1.28092i
\(612\) 13089.0 + 6745.89i 0.864526 + 0.445566i
\(613\) −1786.00 −0.117677 −0.0588384 0.998268i \(-0.518740\pi\)
−0.0588384 + 0.998268i \(0.518740\pi\)
\(614\) −7726.12 −0.507819
\(615\) −7211.05 1748.94i −0.472809 0.114673i
\(616\) −952.000 2331.91i −0.0622681 0.152525i
\(617\) 8254.46i 0.538593i −0.963057 0.269297i \(-0.913209\pi\)
0.963057 0.269297i \(-0.0867912\pi\)
\(618\) −1020.00 247.386i −0.0663923 0.0161025i
\(619\) 8301.32i 0.539028i 0.962996 + 0.269514i \(0.0868630\pi\)
−0.962996 + 0.269514i \(0.913137\pi\)
\(620\) 23155.4i 1.49991i
\(621\) 8332.09 9619.15i 0.538414 0.621583i
\(622\) 35311.8i 2.27633i
\(623\) 3393.43 + 8312.18i 0.218226 + 0.534543i
\(624\) −3795.00 + 15647.2i −0.243464 + 1.00383i
\(625\) −12221.0 −0.782144
\(626\) 2201.69 0.140571
\(627\) −6120.00 1484.32i −0.389807 0.0945422i
\(628\) 30577.0i 1.94292i
\(629\) −13937.3 −0.883493
\(630\) −20741.5 1835.95i −1.31169 0.116105i
\(631\) −13102.0 −0.826596 −0.413298 0.910596i \(-0.635623\pi\)
−0.413298 + 0.910596i \(0.635623\pi\)
\(632\) 1822.41i 0.114702i
\(633\) −11230.6 2723.83i −0.705179 0.171031i
\(634\) 21046.0 1.31837
\(635\) 10584.3 0.661456
\(636\) 2272.39 9369.30i 0.141676 0.584146i
\(637\) 13524.0 + 13802.9i 0.841194 + 0.858540i
\(638\) 7850.39i 0.487147i
\(639\) 5712.00 11082.9i 0.353620 0.686124i
\(640\) 5288.45i 0.326632i
\(641\) 9837.73i 0.606189i −0.952961 0.303094i \(-0.901980\pi\)
0.952961 0.303094i \(-0.0980197\pi\)
\(642\) 30561.1 + 7412.16i 1.87874 + 0.455661i
\(643\) 9624.05i 0.590257i −0.955458 0.295129i \(-0.904638\pi\)
0.955458 0.295129i \(-0.0953625\pi\)
\(644\) −13997.9 + 5714.62i −0.856514 + 0.349670i
\(645\) −2244.00 544.250i −0.136988 0.0332245i
\(646\) −9180.00 −0.559106
\(647\) −7695.82 −0.467626 −0.233813 0.972282i \(-0.575120\pi\)
−0.233813 + 0.972282i \(0.575120\pi\)
\(648\) −2448.00 + 1744.07i −0.148405 + 0.105731i
\(649\) 4330.70i 0.261933i
\(650\) 5342.64 0.322393
\(651\) 24241.3 3655.18i 1.45944 0.220058i
\(652\) −28152.0 −1.69098
\(653\) 28309.2i 1.69652i 0.529582 + 0.848259i \(0.322349\pi\)
−0.529582 + 0.848259i \(0.677651\pi\)
\(654\) −9443.04 + 38934.6i −0.564605 + 2.32793i
\(655\) 25806.0 1.53943
\(656\) −7776.62 −0.462844
\(657\) −1090.75 + 2116.36i −0.0647703 + 0.125673i
\(658\) 24276.0 9910.64i 1.43826 0.587168i
\(659\) 22973.9i 1.35802i −0.734127 0.679012i \(-0.762408\pi\)
0.734127 0.679012i \(-0.237592\pi\)
\(660\) −3672.00 + 15140.0i −0.216564 + 0.892917i
\(661\) 10804.7i 0.635785i 0.948127 + 0.317893i \(0.102975\pi\)
−0.948127 + 0.317893i \(0.897025\pi\)
\(662\) 14975.1i 0.879191i
\(663\) −4181.20 + 17239.5i −0.244923 + 1.00984i
\(664\) 2040.42i 0.119253i
\(665\) 6362.69 2597.56i 0.371029 0.151472i
\(666\) 11730.0 22759.5i 0.682475 1.32420i
\(667\) 5236.00 0.303956
\(668\) 6362.69 0.368533
\(669\) −2346.00 + 9672.81i −0.135578 + 0.559002i
\(670\) 2665.04i 0.153671i
\(671\) −2343.09 −0.134804
\(672\) −24717.9 + 3727.04i −1.41892 + 0.213949i
\(673\) 26882.0 1.53971 0.769855 0.638219i \(-0.220328\pi\)
0.769855 + 0.638219i \(0.220328\pi\)
\(674\) 25794.1i 1.47411i
\(675\) −2439.03 2112.68i −0.139079 0.120470i
\(676\) 8793.00 0.500284
\(677\) 20491.9 1.16332 0.581660 0.813432i \(-0.302403\pi\)
0.581660 + 0.813432i \(0.302403\pi\)
\(678\) −34853.4 8453.19i −1.97424 0.478824i
\(679\) −18732.0 + 7647.31i −1.05872 + 0.432219i
\(680\) 2523.34i 0.142302i
\(681\) 30039.0 + 7285.53i 1.69030 + 0.409959i
\(682\) 34645.6i 1.94523i
\(683\) 725.667i 0.0406543i 0.999793 + 0.0203271i \(0.00647077\pi\)
−0.999793 + 0.0203271i \(0.993529\pi\)
\(684\) 4090.30 7936.35i 0.228650 0.443646i
\(685\) 10160.5i 0.566733i
\(686\) −10392.4 + 24041.8i −0.578401 + 1.33808i
\(687\) −4539.00 + 18714.8i −0.252072 + 1.03932i
\(688\) −2420.00 −0.134101
\(689\) 11614.4 0.642198
\(690\) 19074.0 + 4626.12i 1.05237 + 0.255237i
\(691\) 11760.0i 0.647426i −0.946155 0.323713i \(-0.895069\pi\)
0.946155 0.323713i \(-0.104931\pi\)
\(692\) −20269.7 −1.11350
\(693\) −16429.7 1454.29i −0.900597 0.0797170i
\(694\) 4420.00 0.241759
\(695\) 14076.3i 0.768265i
\(696\) −1201.84 291.489i −0.0654535 0.0158748i
\(697\) −8568.00 −0.465619
\(698\) 25925.4 1.40586
\(699\) 1171.54 4830.39i 0.0633931 0.261377i
\(700\) 1449.00 + 3549.31i 0.0782386 + 0.191645i
\(701\) 21877.2i 1.17873i 0.807867 + 0.589365i \(0.200622\pi\)
−0.807867 + 0.589365i \(0.799378\pi\)
\(702\) −24633.0 21337.1i −1.32438 1.14717i
\(703\) 8450.74i 0.453379i
\(704\) 20813.4i 1.11426i
\(705\) −17512.5 4247.42i −0.935547 0.226903i
\(706\) 21820.1i 1.16318i
\(707\) −8837.07 21646.3i −0.470088 1.15148i
\(708\) 5967.00 + 1447.21i 0.316742 + 0.0768213i
\(709\) −24382.0 −1.29152 −0.645758 0.763542i \(-0.723459\pi\)
−0.645758 + 0.763542i \(0.723459\pi\)
\(710\) 19229.5 1.01643
\(711\) −10608.0 5467.24i −0.559537 0.288379i
\(712\) 1998.78i 0.105207i
\(713\) −23107.7 −1.21373
\(714\) −23775.1 + 3584.89i −1.24617 + 0.187901i
\(715\) −18768.0 −0.981655
\(716\) 31467.5i 1.64245i
\(717\) 5867.81 24193.6i 0.305631 1.26015i
\(718\) −13226.0 −0.687451
\(719\) 11089.3 0.575187 0.287594 0.957753i \(-0.407145\pi\)
0.287594 + 0.957753i \(0.407145\pi\)
\(720\) 13331.3 + 6870.82i 0.690042 + 0.355639i
\(721\) 840.000 342.929i 0.0433887 0.0177134i
\(722\) 22714.2i 1.17082i
\(723\) 4638.00 19123.0i 0.238574 0.983666i
\(724\) 1653.41i 0.0848734i
\(725\) 1327.64i 0.0680101i
\(726\) 1227.09 5059.42i 0.0627294 0.258640i
\(727\) 5927.77i 0.302405i 0.988503 + 0.151203i \(0.0483146\pi\)
−0.988503 + 0.151203i \(0.951685\pi\)
\(728\) 1626.02 + 3982.92i 0.0827807 + 0.202770i
\(729\) 2808.00 + 19481.7i 0.142661 + 0.989772i
\(730\) −3672.00 −0.186174
\(731\) −2666.27 −0.134905
\(732\) 783.000 3228.39i 0.0395362 0.163012i
\(733\) 22532.9i 1.13543i 0.823225 + 0.567715i \(0.192172\pi\)
−0.823225 + 0.567715i \(0.807828\pi\)
\(734\) 38681.1 1.94516
\(735\) 15464.3 9212.07i 0.776065 0.462302i
\(736\) 23562.0 1.18004
\(737\) 2111.03i 0.105510i
\(738\) 7211.05 13991.5i 0.359678 0.697878i
\(739\) −9220.00 −0.458949 −0.229474 0.973315i \(-0.573701\pi\)
−0.229474 + 0.973315i \(0.573701\pi\)
\(740\) 20906.0 1.03854
\(741\) 10453.0 + 2535.22i 0.518219 + 0.125687i
\(742\) 5950.00 + 14574.5i 0.294382 + 0.721085i
\(743\) 14950.4i 0.738191i 0.929391 + 0.369096i \(0.120333\pi\)
−0.929391 + 0.369096i \(0.879667\pi\)
\(744\) 5304.00 + 1286.41i 0.261363 + 0.0633898i
\(745\) 2581.76i 0.126964i
\(746\) 18958.0i 0.930433i
\(747\) 11877.0 + 6121.27i 0.581737 + 0.299820i
\(748\) 17989.1i 0.879338i
\(749\) −25168.0 + 10274.8i −1.22779 + 0.501245i
\(750\) 7548.00 31121.2i 0.367485 1.51518i
\(751\) 26648.0 1.29481 0.647403 0.762148i \(-0.275855\pi\)
0.647403 + 0.762148i \(0.275855\pi\)
\(752\) −18886.1 −0.915830
\(753\) −20349.0 4935.36i −0.984806 0.238850i
\(754\) 13408.5i 0.647625i
\(755\) −14624.1 −0.704934
\(756\) 7494.18 22151.5i 0.360530 1.06567i
\(757\) −3274.00 −0.157194 −0.0785968 0.996906i \(-0.525044\pi\)
−0.0785968 + 0.996906i \(0.525044\pi\)
\(758\) 21654.6i 1.03764i
\(759\) 15108.9 + 3664.44i 0.722552 + 0.175245i
\(760\) 1530.00 0.0730249
\(761\) −36701.6 −1.74827 −0.874134 0.485685i \(-0.838570\pi\)
−0.874134 + 0.485685i \(0.838570\pi\)
\(762\) −5292.14 + 21820.1i −0.251593 + 1.03735i
\(763\) −13090.0 32063.8i −0.621088 1.52135i
\(764\) 2374.91i 0.112462i
\(765\) 14688.0 + 7570.02i 0.694177 + 0.357771i
\(766\) 7911.85i 0.373194i
\(767\) 7396.85i 0.348220i
\(768\) 14588.7 + 3538.29i 0.685450 + 0.166246i
\(769\) 20570.8i 0.964633i 0.875997 + 0.482316i \(0.160204\pi\)
−0.875997 + 0.482316i \(0.839796\pi\)
\(770\) −9614.73 23551.2i −0.449988 1.10224i
\(771\) 1020.00 + 247.386i 0.0476451 + 0.0115556i
\(772\) 5868.00 0.273567
\(773\) 26450.6 1.23074 0.615370 0.788238i \(-0.289007\pi\)
0.615370 + 0.788238i \(0.289007\pi\)
\(774\) 2244.00 4354.00i 0.104210 0.202198i
\(775\) 5859.18i 0.271572i
\(776\) −4504.38 −0.208373
\(777\) 3300.10 + 21886.4i 0.152369 + 1.01052i
\(778\) −29138.0 −1.34274
\(779\) 5195.11i 0.238940i
\(780\) 6271.79 25859.3i 0.287905 1.18706i
\(781\) 15232.0 0.697879
\(782\) 22663.3 1.03637
\(783\) −5302.24 + 6121.27i −0.242001 + 0.279383i
\(784\) 13475.0 13202.7i 0.613839 0.601437i
\(785\) 34312.5i 1.56008i
\(786\) −12903.0 + 53200.4i