Properties

Label 441.4.e.w.226.2
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Defining polynomial: \(x^{6} - x^{5} + 25 x^{4} + 12 x^{3} + 582 x^{2} - 144 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(0.124036 - 0.214837i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.w.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.124036 - 0.214837i) q^{2} +(3.96923 + 6.87491i) q^{4} +(6.21730 - 10.7687i) q^{5} +3.95388 q^{8} +O(q^{10})\) \(q+(0.124036 - 0.214837i) q^{2} +(3.96923 + 6.87491i) q^{4} +(6.21730 - 10.7687i) q^{5} +3.95388 q^{8} +(-1.54234 - 2.67141i) q^{10} +(30.1558 + 52.2313i) q^{11} -36.4269 q^{13} +(-31.2634 + 54.1498i) q^{16} +(24.3731 + 42.2154i) q^{17} +(-25.2750 + 43.7776i) q^{19} +98.7116 q^{20} +14.9616 q^{22} +(69.3962 - 120.198i) q^{23} +(-14.8097 - 25.6511i) q^{25} +(-4.51824 + 7.82583i) q^{26} +61.1345 q^{29} +(-0.584676 - 1.01269i) q^{31} +(23.5711 + 40.8264i) q^{32} +12.0925 q^{34} +(-34.7634 + 60.2120i) q^{37} +(6.27001 + 10.8600i) q^{38} +(24.5825 - 42.5781i) q^{40} +308.115 q^{41} +174.443 q^{43} +(-239.390 + 414.636i) q^{44} +(-17.2153 - 29.8177i) q^{46} +(-194.681 + 337.197i) q^{47} -7.34774 q^{50} +(-144.587 - 250.432i) q^{52} +(157.467 + 272.742i) q^{53} +749.950 q^{55} +(7.58287 - 13.1339i) q^{58} +(-422.263 - 731.381i) q^{59} +(-169.269 + 293.182i) q^{61} -0.290084 q^{62} -488.520 q^{64} +(-226.477 + 392.270i) q^{65} +(485.775 + 841.387i) q^{67} +(-193.485 + 335.125i) q^{68} +98.4698 q^{71} +(355.117 + 615.082i) q^{73} +(8.62383 + 14.9369i) q^{74} -401.289 q^{76} +(243.442 - 421.654i) q^{79} +(388.748 + 673.332i) q^{80} +(38.2174 - 66.1944i) q^{82} +605.688 q^{83} +606.139 q^{85} +(21.6372 - 37.4767i) q^{86} +(119.232 + 206.517i) q^{88} +(-109.034 + 188.853i) q^{89} +1101.80 q^{92} +(48.2949 + 83.6491i) q^{94} +(314.284 + 544.357i) q^{95} +782.288 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 25q^{4} - 11q^{5} - 78q^{8} + O(q^{10}) \) \( 6q + q^{2} - 25q^{4} - 11q^{5} - 78q^{8} - 55q^{10} + 35q^{11} - 124q^{13} - 241q^{16} - 48q^{17} - 202q^{19} + 878q^{20} - 14q^{22} + 216q^{23} - 130q^{25} - 274q^{26} - 106q^{29} - 95q^{31} + 683q^{32} + 48q^{34} - 262q^{37} + 398q^{38} + 21q^{40} + 488q^{41} + 720q^{43} - 905q^{44} + 1056q^{46} + 210q^{47} + 2756q^{50} + 324q^{52} + 393q^{53} + 2062q^{55} + 1249q^{58} - 1143q^{59} - 70q^{61} + 2118q^{62} - 798q^{64} - 472q^{65} + 628q^{67} - 1944q^{68} - 636q^{71} + 988q^{73} + 1002q^{74} + 4680q^{76} - 861q^{79} - 175q^{80} + 124q^{82} + 1038q^{83} + 3600q^{85} - 3208q^{86} + 891q^{88} - 1766q^{89} + 1344q^{92} - 3294q^{94} - 736q^{95} - 38q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.124036 0.214837i 0.0438533 0.0759562i −0.843266 0.537497i \(-0.819370\pi\)
0.887119 + 0.461541i \(0.152703\pi\)
\(3\) 0 0
\(4\) 3.96923 + 6.87491i 0.496154 + 0.859364i
\(5\) 6.21730 10.7687i 0.556092 0.963180i −0.441725 0.897150i \(-0.645633\pi\)
0.997818 0.0660299i \(-0.0210333\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 3.95388 0.174739
\(9\) 0 0
\(10\) −1.54234 2.67141i −0.0487730 0.0844773i
\(11\) 30.1558 + 52.2313i 0.826573 + 1.43167i 0.900711 + 0.434419i \(0.143046\pi\)
−0.0741379 + 0.997248i \(0.523621\pi\)
\(12\) 0 0
\(13\) −36.4269 −0.777154 −0.388577 0.921416i \(-0.627033\pi\)
−0.388577 + 0.921416i \(0.627033\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −31.2634 + 54.1498i −0.488491 + 0.846091i
\(17\) 24.3731 + 42.2154i 0.347726 + 0.602279i 0.985845 0.167659i \(-0.0536207\pi\)
−0.638119 + 0.769937i \(0.720287\pi\)
\(18\) 0 0
\(19\) −25.2750 + 43.7776i −0.305183 + 0.528593i −0.977302 0.211851i \(-0.932051\pi\)
0.672119 + 0.740443i \(0.265384\pi\)
\(20\) 98.7116 1.10363
\(21\) 0 0
\(22\) 14.9616 0.144992
\(23\) 69.3962 120.198i 0.629135 1.08969i −0.358590 0.933495i \(-0.616743\pi\)
0.987726 0.156199i \(-0.0499241\pi\)
\(24\) 0 0
\(25\) −14.8097 25.6511i −0.118478 0.205209i
\(26\) −4.51824 + 7.82583i −0.0340808 + 0.0590297i
\(27\) 0 0
\(28\) 0 0
\(29\) 61.1345 0.391462 0.195731 0.980658i \(-0.437292\pi\)
0.195731 + 0.980658i \(0.437292\pi\)
\(30\) 0 0
\(31\) −0.584676 1.01269i −0.00338745 0.00586724i 0.864327 0.502931i \(-0.167745\pi\)
−0.867714 + 0.497064i \(0.834412\pi\)
\(32\) 23.5711 + 40.8264i 0.130213 + 0.225536i
\(33\) 0 0
\(34\) 12.0925 0.0609957
\(35\) 0 0
\(36\) 0 0
\(37\) −34.7634 + 60.2120i −0.154461 + 0.267535i −0.932863 0.360232i \(-0.882698\pi\)
0.778401 + 0.627767i \(0.216031\pi\)
\(38\) 6.27001 + 10.8600i 0.0267666 + 0.0463611i
\(39\) 0 0
\(40\) 24.5825 42.5781i 0.0971708 0.168305i
\(41\) 308.115 1.17365 0.586823 0.809715i \(-0.300378\pi\)
0.586823 + 0.809715i \(0.300378\pi\)
\(42\) 0 0
\(43\) 174.443 0.618657 0.309329 0.950955i \(-0.399896\pi\)
0.309329 + 0.950955i \(0.399896\pi\)
\(44\) −239.390 + 414.636i −0.820215 + 1.42065i
\(45\) 0 0
\(46\) −17.2153 29.8177i −0.0551794 0.0955734i
\(47\) −194.681 + 337.197i −0.604194 + 1.04649i 0.387984 + 0.921666i \(0.373172\pi\)
−0.992178 + 0.124829i \(0.960162\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −7.34774 −0.0207825
\(51\) 0 0
\(52\) −144.587 250.432i −0.385588 0.667858i
\(53\) 157.467 + 272.742i 0.408110 + 0.706867i 0.994678 0.103033i \(-0.0328547\pi\)
−0.586568 + 0.809900i \(0.699521\pi\)
\(54\) 0 0
\(55\) 749.950 1.83860
\(56\) 0 0
\(57\) 0 0
\(58\) 7.58287 13.1339i 0.0171669 0.0297339i
\(59\) −422.263 731.381i −0.931762 1.61386i −0.780308 0.625396i \(-0.784938\pi\)
−0.151455 0.988464i \(-0.548396\pi\)
\(60\) 0 0
\(61\) −169.269 + 293.182i −0.355290 + 0.615380i −0.987167 0.159688i \(-0.948951\pi\)
0.631878 + 0.775068i \(0.282284\pi\)
\(62\) −0.290084 −0.000594204
\(63\) 0 0
\(64\) −488.520 −0.954141
\(65\) −226.477 + 392.270i −0.432169 + 0.748539i
\(66\) 0 0
\(67\) 485.775 + 841.387i 0.885774 + 1.53421i 0.844824 + 0.535044i \(0.179705\pi\)
0.0409498 + 0.999161i \(0.486962\pi\)
\(68\) −193.485 + 335.125i −0.345051 + 0.597646i
\(69\) 0 0
\(70\) 0 0
\(71\) 98.4698 0.164595 0.0822973 0.996608i \(-0.473774\pi\)
0.0822973 + 0.996608i \(0.473774\pi\)
\(72\) 0 0
\(73\) 355.117 + 615.082i 0.569361 + 0.986162i 0.996629 + 0.0820374i \(0.0261427\pi\)
−0.427268 + 0.904125i \(0.640524\pi\)
\(74\) 8.62383 + 14.9369i 0.0135473 + 0.0234646i
\(75\) 0 0
\(76\) −401.289 −0.605671
\(77\) 0 0
\(78\) 0 0
\(79\) 243.442 421.654i 0.346701 0.600504i −0.638960 0.769240i \(-0.720635\pi\)
0.985661 + 0.168736i \(0.0539686\pi\)
\(80\) 388.748 + 673.332i 0.543292 + 0.941010i
\(81\) 0 0
\(82\) 38.2174 66.1944i 0.0514683 0.0891458i
\(83\) 605.688 0.800999 0.400499 0.916297i \(-0.368837\pi\)
0.400499 + 0.916297i \(0.368837\pi\)
\(84\) 0 0
\(85\) 606.139 0.773470
\(86\) 21.6372 37.4767i 0.0271302 0.0469908i
\(87\) 0 0
\(88\) 119.232 + 206.517i 0.144434 + 0.250168i
\(89\) −109.034 + 188.853i −0.129861 + 0.224925i −0.923622 0.383303i \(-0.874786\pi\)
0.793762 + 0.608229i \(0.208120\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1101.80 1.24859
\(93\) 0 0
\(94\) 48.2949 + 83.6491i 0.0529919 + 0.0917846i
\(95\) 314.284 + 544.357i 0.339420 + 0.587893i
\(96\) 0 0
\(97\) 782.288 0.818859 0.409429 0.912342i \(-0.365728\pi\)
0.409429 + 0.912342i \(0.365728\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 117.566 203.631i 0.117566 0.203631i
\(101\) 155.823 + 269.893i 0.153514 + 0.265895i 0.932517 0.361126i \(-0.117608\pi\)
−0.779003 + 0.627021i \(0.784274\pi\)
\(102\) 0 0
\(103\) −74.6289 + 129.261i −0.0713922 + 0.123655i −0.899512 0.436897i \(-0.856078\pi\)
0.828119 + 0.560552i \(0.189411\pi\)
\(104\) −144.028 −0.135799
\(105\) 0 0
\(106\) 78.1265 0.0715879
\(107\) 425.760 737.437i 0.384670 0.666269i −0.607053 0.794661i \(-0.707648\pi\)
0.991723 + 0.128393i \(0.0409818\pi\)
\(108\) 0 0
\(109\) −680.939 1179.42i −0.598369 1.03640i −0.993062 0.117592i \(-0.962483\pi\)
0.394694 0.918813i \(-0.370851\pi\)
\(110\) 93.0208 161.117i 0.0806289 0.139653i
\(111\) 0 0
\(112\) 0 0
\(113\) −1048.55 −0.872917 −0.436459 0.899724i \(-0.643767\pi\)
−0.436459 + 0.899724i \(0.643767\pi\)
\(114\) 0 0
\(115\) −862.914 1494.61i −0.699715 1.21194i
\(116\) 242.657 + 420.294i 0.194225 + 0.336408i
\(117\) 0 0
\(118\) −209.503 −0.163444
\(119\) 0 0
\(120\) 0 0
\(121\) −1153.24 + 1997.47i −0.866446 + 1.50073i
\(122\) 41.9909 + 72.7303i 0.0311613 + 0.0539729i
\(123\) 0 0
\(124\) 4.64143 8.03919i 0.00336139 0.00582210i
\(125\) 1186.02 0.848647
\(126\) 0 0
\(127\) 488.408 0.341254 0.170627 0.985336i \(-0.445421\pi\)
0.170627 + 0.985336i \(0.445421\pi\)
\(128\) −249.163 + 431.563i −0.172056 + 0.298009i
\(129\) 0 0
\(130\) 56.1826 + 97.3111i 0.0379041 + 0.0656519i
\(131\) 927.114 1605.81i 0.618338 1.07099i −0.371451 0.928453i \(-0.621139\pi\)
0.989789 0.142541i \(-0.0455272\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 241.014 0.155377
\(135\) 0 0
\(136\) 96.3683 + 166.915i 0.0607611 + 0.105241i
\(137\) −255.558 442.639i −0.159370 0.276038i 0.775271 0.631628i \(-0.217613\pi\)
−0.934642 + 0.355591i \(0.884280\pi\)
\(138\) 0 0
\(139\) −2266.10 −1.38279 −0.691397 0.722475i \(-0.743005\pi\)
−0.691397 + 0.722475i \(0.743005\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 12.2138 21.1549i 0.00721802 0.0125020i
\(143\) −1098.48 1902.62i −0.642375 1.11263i
\(144\) 0 0
\(145\) 380.091 658.338i 0.217689 0.377048i
\(146\) 176.189 0.0998735
\(147\) 0 0
\(148\) −551.936 −0.306546
\(149\) 753.950 1305.88i 0.414537 0.717999i −0.580843 0.814016i \(-0.697277\pi\)
0.995380 + 0.0960168i \(0.0306102\pi\)
\(150\) 0 0
\(151\) −795.913 1378.56i −0.428943 0.742952i 0.567836 0.823142i \(-0.307781\pi\)
−0.996780 + 0.0801897i \(0.974447\pi\)
\(152\) −99.9344 + 173.091i −0.0533273 + 0.0923656i
\(153\) 0 0
\(154\) 0 0
\(155\) −14.5404 −0.00753494
\(156\) 0 0
\(157\) 582.080 + 1008.19i 0.295892 + 0.512500i 0.975192 0.221361i \(-0.0710498\pi\)
−0.679300 + 0.733861i \(0.737717\pi\)
\(158\) −60.3911 104.601i −0.0304080 0.0526682i
\(159\) 0 0
\(160\) 586.195 0.289642
\(161\) 0 0
\(162\) 0 0
\(163\) 577.940 1001.02i 0.277716 0.481019i −0.693101 0.720841i \(-0.743756\pi\)
0.970817 + 0.239822i \(0.0770892\pi\)
\(164\) 1222.98 + 2118.26i 0.582309 + 1.00859i
\(165\) 0 0
\(166\) 75.1271 130.124i 0.0351265 0.0608408i
\(167\) −2890.61 −1.33941 −0.669707 0.742626i \(-0.733580\pi\)
−0.669707 + 0.742626i \(0.733580\pi\)
\(168\) 0 0
\(169\) −870.082 −0.396032
\(170\) 75.1830 130.221i 0.0339193 0.0587499i
\(171\) 0 0
\(172\) 692.403 + 1199.28i 0.306949 + 0.531651i
\(173\) −947.468 + 1641.06i −0.416385 + 0.721200i −0.995573 0.0939940i \(-0.970037\pi\)
0.579188 + 0.815194i \(0.303370\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3771.09 −1.61509
\(177\) 0 0
\(178\) 27.0483 + 46.8491i 0.0113897 + 0.0197275i
\(179\) −2144.25 3713.94i −0.895355 1.55080i −0.833365 0.552723i \(-0.813589\pi\)
−0.0619893 0.998077i \(-0.519744\pi\)
\(180\) 0 0
\(181\) −383.732 −0.157583 −0.0787917 0.996891i \(-0.525106\pi\)
−0.0787917 + 0.996891i \(0.525106\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 274.385 475.248i 0.109934 0.190412i
\(185\) 432.269 + 748.712i 0.171790 + 0.297548i
\(186\) 0 0
\(187\) −1469.98 + 2546.07i −0.574841 + 0.995655i
\(188\) −3090.93 −1.19909
\(189\) 0 0
\(190\) 155.930 0.0595388
\(191\) 192.655 333.689i 0.0729845 0.126413i −0.827224 0.561873i \(-0.810081\pi\)
0.900208 + 0.435460i \(0.143414\pi\)
\(192\) 0 0
\(193\) −315.112 545.790i −0.117525 0.203559i 0.801262 0.598314i \(-0.204163\pi\)
−0.918786 + 0.394756i \(0.870829\pi\)
\(194\) 97.0318 168.064i 0.0359097 0.0621974i
\(195\) 0 0
\(196\) 0 0
\(197\) 1250.23 0.452158 0.226079 0.974109i \(-0.427409\pi\)
0.226079 + 0.974109i \(0.427409\pi\)
\(198\) 0 0
\(199\) −546.122 945.912i −0.194541 0.336954i 0.752209 0.658924i \(-0.228988\pi\)
−0.946750 + 0.321970i \(0.895655\pi\)
\(200\) −58.5558 101.422i −0.0207026 0.0358580i
\(201\) 0 0
\(202\) 77.3105 0.0269285
\(203\) 0 0
\(204\) 0 0
\(205\) 1915.65 3318.00i 0.652656 1.13043i
\(206\) 18.5133 + 32.0660i 0.00626158 + 0.0108454i
\(207\) 0 0
\(208\) 1138.83 1972.51i 0.379633 0.657543i
\(209\) −3048.75 −1.00902
\(210\) 0 0
\(211\) −3620.05 −1.18111 −0.590556 0.806997i \(-0.701091\pi\)
−0.590556 + 0.806997i \(0.701091\pi\)
\(212\) −1250.05 + 2165.15i −0.404970 + 0.701429i
\(213\) 0 0
\(214\) −105.619 182.937i −0.0337382 0.0584362i
\(215\) 1084.56 1878.52i 0.344030 0.595878i
\(216\) 0 0
\(217\) 0 0
\(218\) −337.844 −0.104962
\(219\) 0 0
\(220\) 2976.72 + 5155.84i 0.912230 + 1.58003i
\(221\) −887.835 1537.78i −0.270236 0.468063i
\(222\) 0 0
\(223\) 183.844 0.0552069 0.0276034 0.999619i \(-0.491212\pi\)
0.0276034 + 0.999619i \(0.491212\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −130.058 + 225.268i −0.0382803 + 0.0663035i
\(227\) −1139.76 1974.12i −0.333253 0.577211i 0.649895 0.760024i \(-0.274813\pi\)
−0.983148 + 0.182813i \(0.941480\pi\)
\(228\) 0 0
\(229\) 2706.34 4687.51i 0.780960 1.35266i −0.150424 0.988622i \(-0.548064\pi\)
0.931383 0.364040i \(-0.118603\pi\)
\(230\) −428.130 −0.122739
\(231\) 0 0
\(232\) 241.719 0.0684035
\(233\) 569.184 985.856i 0.160036 0.277191i −0.774845 0.632151i \(-0.782172\pi\)
0.934882 + 0.354960i \(0.115506\pi\)
\(234\) 0 0
\(235\) 2420.78 + 4192.91i 0.671975 + 1.16390i
\(236\) 3352.12 5806.04i 0.924595 1.60145i
\(237\) 0 0
\(238\) 0 0
\(239\) 6226.36 1.68515 0.842573 0.538583i \(-0.181040\pi\)
0.842573 + 0.538583i \(0.181040\pi\)
\(240\) 0 0
\(241\) −1598.10 2767.99i −0.427147 0.739841i 0.569471 0.822012i \(-0.307148\pi\)
−0.996618 + 0.0821704i \(0.973815\pi\)
\(242\) 286.086 + 495.516i 0.0759931 + 0.131624i
\(243\) 0 0
\(244\) −2687.47 −0.705113
\(245\) 0 0
\(246\) 0 0
\(247\) 920.689 1594.68i 0.237174 0.410798i
\(248\) −2.31174 4.00406i −0.000591919 0.00102523i
\(249\) 0 0
\(250\) 147.109 254.801i 0.0372160 0.0644600i
\(251\) 239.608 0.0602546 0.0301273 0.999546i \(-0.490409\pi\)
0.0301273 + 0.999546i \(0.490409\pi\)
\(252\) 0 0
\(253\) 8370.78 2.08010
\(254\) 60.5802 104.928i 0.0149651 0.0259203i
\(255\) 0 0
\(256\) −1892.27 3277.51i −0.461980 0.800173i
\(257\) −349.559 + 605.453i −0.0848439 + 0.146954i −0.905325 0.424720i \(-0.860372\pi\)
0.820481 + 0.571674i \(0.193706\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3595.76 −0.857690
\(261\) 0 0
\(262\) −229.991 398.356i −0.0542324 0.0939333i
\(263\) −459.520 795.912i −0.107738 0.186609i 0.807115 0.590394i \(-0.201028\pi\)
−0.914854 + 0.403785i \(0.867694\pi\)
\(264\) 0 0
\(265\) 3916.09 0.907787
\(266\) 0 0
\(267\) 0 0
\(268\) −3856.30 + 6679.32i −0.878960 + 1.52240i
\(269\) 1389.59 + 2406.84i 0.314961 + 0.545529i 0.979429 0.201788i \(-0.0646751\pi\)
−0.664468 + 0.747317i \(0.731342\pi\)
\(270\) 0 0
\(271\) 1113.49 1928.62i 0.249593 0.432308i −0.713820 0.700329i \(-0.753036\pi\)
0.963413 + 0.268021i \(0.0863698\pi\)
\(272\) −3047.94 −0.679443
\(273\) 0 0
\(274\) −126.793 −0.0279557
\(275\) 893.195 1547.06i 0.195861 0.339241i
\(276\) 0 0
\(277\) −3653.85 6328.65i −0.792557 1.37275i −0.924379 0.381476i \(-0.875416\pi\)
0.131821 0.991273i \(-0.457917\pi\)
\(278\) −281.078 + 486.842i −0.0606402 + 0.105032i
\(279\) 0 0
\(280\) 0 0
\(281\) −2730.61 −0.579696 −0.289848 0.957073i \(-0.593605\pi\)
−0.289848 + 0.957073i \(0.593605\pi\)
\(282\) 0 0
\(283\) −884.926 1532.74i −0.185878 0.321950i 0.757994 0.652261i \(-0.226179\pi\)
−0.943872 + 0.330312i \(0.892846\pi\)
\(284\) 390.849 + 676.971i 0.0816642 + 0.141447i
\(285\) 0 0
\(286\) −545.004 −0.112681
\(287\) 0 0
\(288\) 0 0
\(289\) 1268.41 2196.95i 0.258174 0.447170i
\(290\) −94.2900 163.315i −0.0190928 0.0330696i
\(291\) 0 0
\(292\) −2819.09 + 4882.80i −0.564981 + 0.978576i
\(293\) 8228.81 1.64072 0.820362 0.571844i \(-0.193772\pi\)
0.820362 + 0.571844i \(0.193772\pi\)
\(294\) 0 0
\(295\) −10501.4 −2.07258
\(296\) −137.451 + 238.071i −0.0269904 + 0.0467487i
\(297\) 0 0
\(298\) −187.034 323.952i −0.0363577 0.0629733i
\(299\) −2527.89 + 4378.43i −0.488935 + 0.846860i
\(300\) 0 0
\(301\) 0 0
\(302\) −394.887 −0.0752424
\(303\) 0 0
\(304\) −1580.36 2737.27i −0.298158 0.516425i
\(305\) 2104.79 + 3645.61i 0.395148 + 0.684416i
\(306\) 0 0
\(307\) −6019.62 −1.11908 −0.559541 0.828803i \(-0.689023\pi\)
−0.559541 + 0.828803i \(0.689023\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.80354 + 3.12382i −0.000330432 + 0.000572326i
\(311\) −596.857 1033.79i −0.108825 0.188491i 0.806469 0.591276i \(-0.201376\pi\)
−0.915295 + 0.402785i \(0.868042\pi\)
\(312\) 0 0
\(313\) −4423.02 + 7660.89i −0.798734 + 1.38345i 0.121707 + 0.992566i \(0.461163\pi\)
−0.920441 + 0.390882i \(0.872170\pi\)
\(314\) 288.795 0.0519034
\(315\) 0 0
\(316\) 3865.11 0.688068
\(317\) 3040.72 5266.68i 0.538750 0.933142i −0.460222 0.887804i \(-0.652230\pi\)
0.998972 0.0453380i \(-0.0144365\pi\)
\(318\) 0 0
\(319\) 1843.56 + 3193.13i 0.323572 + 0.560442i
\(320\) −3037.28 + 5260.72i −0.530590 + 0.919009i
\(321\) 0 0
\(322\) 0 0
\(323\) −2464.12 −0.424480
\(324\) 0 0
\(325\) 539.471 + 934.391i 0.0920753 + 0.159479i
\(326\) −143.371 248.325i −0.0243576 0.0421885i
\(327\) 0 0
\(328\) 1218.25 0.205082
\(329\) 0 0
\(330\) 0 0
\(331\) −1526.65 + 2644.23i −0.253511 + 0.439094i −0.964490 0.264119i \(-0.914919\pi\)
0.710979 + 0.703213i \(0.248252\pi\)
\(332\) 2404.12 + 4164.05i 0.397419 + 0.688349i
\(333\) 0 0
\(334\) −358.539 + 621.009i −0.0587377 + 0.101737i
\(335\) 12080.8 1.97029
\(336\) 0 0
\(337\) 3865.80 0.624877 0.312438 0.949938i \(-0.398854\pi\)
0.312438 + 0.949938i \(0.398854\pi\)
\(338\) −107.921 + 186.925i −0.0173673 + 0.0300811i
\(339\) 0 0
\(340\) 2405.90 + 4167.15i 0.383760 + 0.664692i
\(341\) 35.2627 61.0768i 0.00559995 0.00969940i
\(342\) 0 0
\(343\) 0 0
\(344\) 689.726 0.108103
\(345\) 0 0
\(346\) 235.040 + 407.101i 0.0365198 + 0.0632541i
\(347\) −49.7965 86.2501i −0.00770380 0.0133434i 0.862148 0.506657i \(-0.169119\pi\)
−0.869852 + 0.493313i \(0.835786\pi\)
\(348\) 0 0
\(349\) 3607.34 0.553285 0.276643 0.960973i \(-0.410778\pi\)
0.276643 + 0.960973i \(0.410778\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1421.61 + 2462.30i −0.215262 + 0.372844i
\(353\) −3565.37 6175.40i −0.537579 0.931114i −0.999034 0.0439501i \(-0.986006\pi\)
0.461455 0.887164i \(-0.347328\pi\)
\(354\) 0 0
\(355\) 612.216 1060.39i 0.0915298 0.158534i
\(356\) −1731.13 −0.257724
\(357\) 0 0
\(358\) −1063.85 −0.157057
\(359\) −3250.14 + 5629.41i −0.477816 + 0.827602i −0.999677 0.0254289i \(-0.991905\pi\)
0.521860 + 0.853031i \(0.325238\pi\)
\(360\) 0 0
\(361\) 2151.85 + 3727.11i 0.313727 + 0.543390i
\(362\) −47.5966 + 82.4398i −0.00691056 + 0.0119694i
\(363\) 0 0
\(364\) 0 0
\(365\) 8831.49 1.26647
\(366\) 0 0
\(367\) 412.443 + 714.372i 0.0586631 + 0.101607i 0.893866 0.448335i \(-0.147983\pi\)
−0.835202 + 0.549943i \(0.814650\pi\)
\(368\) 4339.12 + 7515.58i 0.614654 + 1.06461i
\(369\) 0 0
\(370\) 214.468 0.0301342
\(371\) 0 0
\(372\) 0 0
\(373\) −666.925 + 1155.15i −0.0925793 + 0.160352i −0.908596 0.417677i \(-0.862845\pi\)
0.816016 + 0.578029i \(0.196178\pi\)
\(374\) 364.660 + 631.610i 0.0504174 + 0.0873255i
\(375\) 0 0
\(376\) −769.746 + 1333.24i −0.105576 + 0.182863i
\(377\) −2226.94 −0.304226
\(378\) 0 0
\(379\) −1338.29 −0.181380 −0.0906902 0.995879i \(-0.528907\pi\)
−0.0906902 + 0.995879i \(0.528907\pi\)
\(380\) −2494.93 + 4321.35i −0.336809 + 0.583370i
\(381\) 0 0
\(382\) −47.7924 82.7788i −0.00640123 0.0110873i
\(383\) −176.688 + 306.032i −0.0235727 + 0.0408290i −0.877571 0.479447i \(-0.840837\pi\)
0.853998 + 0.520276i \(0.174171\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −156.341 −0.0206154
\(387\) 0 0
\(388\) 3105.08 + 5378.16i 0.406280 + 0.703697i
\(389\) 5868.59 + 10164.7i 0.764908 + 1.32486i 0.940295 + 0.340360i \(0.110549\pi\)
−0.175387 + 0.984500i \(0.556118\pi\)
\(390\) 0 0
\(391\) 6765.59 0.875066
\(392\) 0 0
\(393\) 0 0
\(394\) 155.073 268.595i 0.0198286 0.0343442i
\(395\) −3027.11 5243.10i −0.385595 0.667871i
\(396\) 0 0
\(397\) 6640.71 11502.1i 0.839516 1.45408i −0.0507841 0.998710i \(-0.516172\pi\)
0.890300 0.455374i \(-0.150495\pi\)
\(398\) −270.955 −0.0341250
\(399\) 0 0
\(400\) 1852.01 0.231501
\(401\) −3741.18 + 6479.91i −0.465899 + 0.806961i −0.999242 0.0389385i \(-0.987602\pi\)
0.533343 + 0.845899i \(0.320936\pi\)
\(402\) 0 0
\(403\) 21.2979 + 36.8891i 0.00263257 + 0.00455975i
\(404\) −1236.99 + 2142.54i −0.152333 + 0.263849i
\(405\) 0 0
\(406\) 0 0
\(407\) −4193.27 −0.510694
\(408\) 0 0
\(409\) −6898.30 11948.2i −0.833983 1.44450i −0.894856 0.446355i \(-0.852722\pi\)
0.0608735 0.998145i \(-0.480611\pi\)
\(410\) −475.218 823.102i −0.0572423 0.0991466i
\(411\) 0 0
\(412\) −1184.88 −0.141686
\(413\) 0 0
\(414\) 0 0
\(415\) 3765.75 6522.46i 0.445429 0.771506i
\(416\) −858.622 1487.18i −0.101196 0.175276i
\(417\) 0 0
\(418\) −378.154 + 654.982i −0.0442491 + 0.0766417i
\(419\) 9497.56 1.10737 0.553683 0.832728i \(-0.313222\pi\)
0.553683 + 0.832728i \(0.313222\pi\)
\(420\) 0 0
\(421\) 624.367 0.0722797 0.0361399 0.999347i \(-0.488494\pi\)
0.0361399 + 0.999347i \(0.488494\pi\)
\(422\) −449.016 + 777.719i −0.0517957 + 0.0897127i
\(423\) 0 0
\(424\) 622.608 + 1078.39i 0.0713126 + 0.123517i
\(425\) 721.915 1250.39i 0.0823954 0.142713i
\(426\) 0 0
\(427\) 0 0
\(428\) 6759.75 0.763423
\(429\) 0 0
\(430\) −269.050 466.007i −0.0301738 0.0522625i
\(431\) −6698.64 11602.4i −0.748636 1.29668i −0.948476 0.316848i \(-0.897376\pi\)
0.199840 0.979829i \(-0.435958\pi\)
\(432\) 0 0
\(433\) 14057.3 1.56016 0.780079 0.625681i \(-0.215179\pi\)
0.780079 + 0.625681i \(0.215179\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5405.61 9362.79i 0.593766 1.02843i
\(437\) 3507.98 + 6075.99i 0.384003 + 0.665112i
\(438\) 0 0
\(439\) −8184.42 + 14175.8i −0.889798 + 1.54117i −0.0496832 + 0.998765i \(0.515821\pi\)
−0.840114 + 0.542409i \(0.817512\pi\)
\(440\) 2965.22 0.321275
\(441\) 0 0
\(442\) −440.494 −0.0474031
\(443\) −589.354 + 1020.79i −0.0632078 + 0.109479i −0.895898 0.444261i \(-0.853466\pi\)
0.832690 + 0.553740i \(0.186800\pi\)
\(444\) 0 0
\(445\) 1355.80 + 2348.31i 0.144429 + 0.250159i
\(446\) 22.8033 39.4965i 0.00242101 0.00419331i
\(447\) 0 0
\(448\) 0 0
\(449\) 12400.9 1.30342 0.651709 0.758469i \(-0.274052\pi\)
0.651709 + 0.758469i \(0.274052\pi\)
\(450\) 0 0
\(451\) 9291.45 + 16093.3i 0.970105 + 1.68027i
\(452\) −4161.95 7208.71i −0.433101 0.750153i
\(453\) 0 0
\(454\) −565.484 −0.0584570
\(455\) 0 0
\(456\) 0 0
\(457\) −4962.79 + 8595.81i −0.507986 + 0.879858i 0.491971 + 0.870611i \(0.336277\pi\)
−0.999957 + 0.00924618i \(0.997057\pi\)
\(458\) −671.366 1162.84i −0.0684954 0.118637i
\(459\) 0 0
\(460\) 6850.21 11864.9i 0.694332 1.20262i
\(461\) −16010.3 −1.61751 −0.808755 0.588146i \(-0.799858\pi\)
−0.808755 + 0.588146i \(0.799858\pi\)
\(462\) 0 0
\(463\) 17372.4 1.74377 0.871883 0.489714i \(-0.162899\pi\)
0.871883 + 0.489714i \(0.162899\pi\)
\(464\) −1911.27 + 3310.42i −0.191225 + 0.331212i
\(465\) 0 0
\(466\) −141.199 244.563i −0.0140363 0.0243115i
\(467\) −1054.03 + 1825.64i −0.104443 + 0.180900i −0.913510 0.406815i \(-0.866639\pi\)
0.809068 + 0.587716i \(0.199973\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1201.05 0.117873
\(471\) 0 0
\(472\) −1669.58 2891.80i −0.162815 0.282004i
\(473\) 5260.45 + 9111.37i 0.511365 + 0.885711i
\(474\) 0 0
\(475\) 1497.26 0.144629
\(476\) 0 0
\(477\) 0 0
\(478\) 772.293 1337.65i 0.0738992 0.127997i
\(479\) 1225.02 + 2121.80i 0.116853 + 0.202395i 0.918519 0.395377i \(-0.129386\pi\)
−0.801666 + 0.597772i \(0.796053\pi\)
\(480\) 0 0
\(481\) 1266.32 2193.34i 0.120040 0.207916i
\(482\) −792.887 −0.0749274
\(483\) 0 0
\(484\) −18309.9 −1.71956
\(485\) 4863.72 8424.21i 0.455361 0.788709i
\(486\) 0 0
\(487\) −322.618 558.791i −0.0300189 0.0519943i 0.850626 0.525772i \(-0.176223\pi\)
−0.880645 + 0.473778i \(0.842890\pi\)
\(488\) −669.270 + 1159.21i −0.0620828 + 0.107531i
\(489\) 0 0
\(490\) 0 0
\(491\) −11766.1 −1.08146 −0.540731 0.841196i \(-0.681852\pi\)
−0.540731 + 0.841196i \(0.681852\pi\)
\(492\) 0 0
\(493\) 1490.03 + 2580.81i 0.136121 + 0.235769i
\(494\) −228.397 395.595i −0.0208018 0.0360297i
\(495\) 0 0
\(496\) 73.1159 0.00661896
\(497\) 0 0
\(498\) 0 0
\(499\) 22.0104 38.1232i 0.00197459 0.00342010i −0.865036 0.501709i \(-0.832705\pi\)
0.867011 + 0.498289i \(0.166038\pi\)
\(500\) 4707.59 + 8153.78i 0.421059 + 0.729296i
\(501\) 0 0
\(502\) 29.7200 51.4765i 0.00264236 0.00457671i
\(503\) 8290.27 0.734880 0.367440 0.930047i \(-0.380234\pi\)
0.367440 + 0.930047i \(0.380234\pi\)
\(504\) 0 0
\(505\) 3875.19 0.341473
\(506\) 1038.28 1798.35i 0.0912195 0.157997i
\(507\) 0 0
\(508\) 1938.60 + 3357.76i 0.169314 + 0.293261i
\(509\) −3457.52 + 5988.60i −0.301084 + 0.521493i −0.976382 0.216052i \(-0.930682\pi\)
0.675298 + 0.737545i \(0.264015\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −4925.45 −0.425148
\(513\) 0 0
\(514\) 86.7157 + 150.196i 0.00744137 + 0.0128888i
\(515\) 927.980 + 1607.31i 0.0794014 + 0.137527i
\(516\) 0 0
\(517\) −23483.0 −1.99764
\(518\) 0 0
\(519\) 0 0
\(520\) −895.464 + 1550.99i −0.0755167 + 0.130799i
\(521\) −6699.64 11604.1i −0.563371 0.975788i −0.997199 0.0747919i \(-0.976171\pi\)
0.433828 0.900996i \(-0.357163\pi\)
\(522\) 0 0
\(523\) −4968.50 + 8605.69i −0.415406 + 0.719504i −0.995471 0.0950662i \(-0.969694\pi\)
0.580065 + 0.814570i \(0.303027\pi\)
\(524\) 14719.7 1.22716
\(525\) 0 0
\(526\) −227.988 −0.0188988
\(527\) 28.5007 49.3647i 0.00235581 0.00408038i
\(528\) 0 0
\(529\) −3548.17 6145.60i −0.291622 0.505104i
\(530\) 485.736 841.320i 0.0398095 0.0689521i
\(531\) 0 0
\(532\) 0 0
\(533\) −11223.7 −0.912104
\(534\) 0 0
\(535\) −5294.15 9169.74i −0.427825 0.741014i
\(536\) 1920.70 + 3326.75i 0.154779 + 0.268085i
\(537\) 0 0
\(538\) 689.435 0.0552484
\(539\) 0 0
\(540\) 0 0
\(541\) −4643.08 + 8042.06i −0.368987 + 0.639103i −0.989407 0.145166i \(-0.953628\pi\)
0.620421 + 0.784269i \(0.286962\pi\)
\(542\) −276.226 478.437i −0.0218910 0.0379163i
\(543\) 0 0
\(544\) −1149.00 + 1990.13i −0.0905570 + 0.156849i
\(545\) −16934.4 −1.33099
\(546\) 0 0
\(547\) −16821.6 −1.31488 −0.657438 0.753508i \(-0.728360\pi\)
−0.657438 + 0.753508i \(0.728360\pi\)
\(548\) 2028.73 3513.87i 0.158144 0.273914i
\(549\) 0 0
\(550\) −221.577 383.782i −0.0171783 0.0297537i
\(551\) −1545.17 + 2676.32i −0.119467 + 0.206924i
\(552\) 0 0
\(553\) 0 0
\(554\) −1812.83 −0.139025
\(555\) 0 0
\(556\) −8994.69 15579.3i −0.686079 1.18832i
\(557\) 902.972 + 1563.99i 0.0686897 + 0.118974i 0.898325 0.439332i \(-0.144785\pi\)
−0.829635 + 0.558306i \(0.811451\pi\)
\(558\) 0 0
\(559\) −6354.40 −0.480792
\(560\) 0 0
\(561\) 0 0
\(562\) −338.694 + 586.635i −0.0254216 + 0.0440315i
\(563\) −6107.45 10578.4i −0.457190 0.791877i 0.541621 0.840623i \(-0.317811\pi\)
−0.998811 + 0.0487460i \(0.984478\pi\)
\(564\) 0 0
\(565\) −6519.17 + 11291.5i −0.485423 + 0.840776i
\(566\) −439.050 −0.0326054
\(567\) 0 0
\(568\) 389.338 0.0287610
\(569\) 2141.89 3709.86i 0.157808 0.273331i −0.776270 0.630400i \(-0.782891\pi\)
0.934078 + 0.357070i \(0.116224\pi\)
\(570\) 0 0
\(571\) −3179.97 5507.87i −0.233060 0.403673i 0.725647 0.688067i \(-0.241541\pi\)
−0.958707 + 0.284395i \(0.908207\pi\)
\(572\) 8720.25 15103.9i 0.637433 1.10407i
\(573\) 0 0
\(574\) 0 0
\(575\) −4110.95 −0.298153
\(576\) 0 0
\(577\) 7234.36 + 12530.3i 0.521959 + 0.904059i 0.999674 + 0.0255444i \(0.00813192\pi\)
−0.477715 + 0.878515i \(0.658535\pi\)
\(578\) −314.656 545.001i −0.0226436 0.0392198i
\(579\) 0 0
\(580\) 6034.68 0.432028
\(581\) 0 0
\(582\) 0 0
\(583\) −9497.10 + 16449.5i −0.674665 + 1.16855i
\(584\) 1404.09 + 2431.96i 0.0994894 + 0.172321i
\(585\) 0 0
\(586\) 1020.67 1767.85i 0.0719513 0.124623i
\(587\) −11132.6 −0.782777 −0.391388 0.920226i \(-0.628005\pi\)
−0.391388 + 0.920226i \(0.628005\pi\)
\(588\) 0 0
\(589\) 59.1108 0.00413517
\(590\) −1302.55 + 2256.07i −0.0908897 + 0.157426i
\(591\) 0 0
\(592\) −2173.65 3764.87i −0.150906 0.261377i
\(593\) 9887.81 17126.2i 0.684728 1.18598i −0.288794 0.957391i \(-0.593254\pi\)
0.973522 0.228592i \(-0.0734123\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11970.4 0.822696
\(597\) 0 0
\(598\) 627.098 + 1086.17i 0.0428829 + 0.0742753i
\(599\) −11945.5 20690.2i −0.814825 1.41132i −0.909453 0.415806i \(-0.863500\pi\)
0.0946282 0.995513i \(-0.469834\pi\)
\(600\) 0 0
\(601\) −19395.5 −1.31641 −0.658204 0.752840i \(-0.728683\pi\)
−0.658204 + 0.752840i \(0.728683\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 6318.32 10943.7i 0.425644 0.737237i
\(605\) 14340.1 + 24837.8i 0.963648 + 1.66909i
\(606\) 0 0
\(607\) 7298.36 12641.1i 0.488025 0.845285i −0.511880 0.859057i \(-0.671051\pi\)
0.999905 + 0.0137724i \(0.00438402\pi\)
\(608\) −2383.04 −0.158956
\(609\) 0 0
\(610\) 1044.28 0.0693142
\(611\) 7091.62 12283.0i 0.469552 0.813288i
\(612\) 0 0
\(613\) −989.898 1714.55i −0.0652229 0.112969i 0.831570 0.555420i \(-0.187442\pi\)
−0.896793 + 0.442451i \(0.854109\pi\)
\(614\) −746.650 + 1293.24i −0.0490755 + 0.0850012i
\(615\) 0 0
\(616\) 0 0
\(617\) −16262.4 −1.06110 −0.530551 0.847653i \(-0.678015\pi\)
−0.530551 + 0.847653i \(0.678015\pi\)
\(618\) 0 0
\(619\) −6010.49 10410.5i −0.390278 0.675981i 0.602208 0.798339i \(-0.294288\pi\)
−0.992486 + 0.122358i \(0.960954\pi\)
\(620\) −57.7143 99.9642i −0.00373849 0.00647526i
\(621\) 0 0
\(622\) −296.127 −0.0190894
\(623\) 0 0
\(624\) 0 0
\(625\) 9225.06 15978.3i 0.590404 1.02261i
\(626\) 1097.23 + 1900.45i 0.0700543 + 0.121338i
\(627\) 0 0
\(628\) −4620.82 + 8003.49i −0.293616 + 0.508557i
\(629\) −3389.16 −0.214841
\(630\) 0 0
\(631\) 25347.6 1.59916 0.799582 0.600557i \(-0.205055\pi\)
0.799582 + 0.600557i \(0.205055\pi\)
\(632\) 962.542 1667.17i 0.0605821 0.104931i
\(633\) 0 0
\(634\) −754.317 1306.51i −0.0472519 0.0818428i
\(635\) 3036.58 5259.51i 0.189769 0.328689i
\(636\) 0 0
\(637\) 0 0
\(638\) 914.669 0.0567588
\(639\) 0 0
\(640\) 3098.24 + 5366.31i 0.191358 + 0.331441i
\(641\) −2555.80 4426.78i −0.157485 0.272772i 0.776476 0.630147i \(-0.217005\pi\)
−0.933961 + 0.357374i \(0.883672\pi\)
\(642\) 0 0
\(643\) 10931.3 0.670435 0.335217 0.942141i \(-0.391190\pi\)
0.335217 + 0.942141i \(0.391190\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −305.639 + 529.382i −0.0186149 + 0.0322419i
\(647\) 9203.06 + 15940.2i 0.559211 + 0.968582i 0.997563 + 0.0697783i \(0.0222292\pi\)
−0.438352 + 0.898804i \(0.644437\pi\)
\(648\) 0 0
\(649\) 25467.3 44110.7i 1.54034 2.66795i
\(650\) 267.655 0.0161512
\(651\) 0 0
\(652\) 9175.91 0.551160
\(653\) 9960.71 17252.5i 0.596926 1.03391i −0.396346 0.918101i \(-0.629722\pi\)
0.993272 0.115805i \(-0.0369447\pi\)
\(654\) 0 0
\(655\) −11528.3 19967.6i −0.687707 1.19114i
\(656\) −9632.74 + 16684.4i −0.573316 + 0.993012i
\(657\) 0 0
\(658\) 0 0
\(659\) 18858.8 1.11477 0.557385 0.830254i \(-0.311805\pi\)
0.557385 + 0.830254i \(0.311805\pi\)
\(660\) 0 0
\(661\) 12916.0 + 22371.2i 0.760023 + 1.31640i 0.942838 + 0.333251i \(0.108146\pi\)
−0.182815 + 0.983147i \(0.558521\pi\)
\(662\) 378.718 + 655.960i 0.0222346 + 0.0385115i
\(663\) 0 0
\(664\) 2394.82 0.139965
\(665\) 0 0
\(666\) 0 0
\(667\) 4242.50 7348.22i 0.246282 0.426573i
\(668\) −11473.5 19872.7i −0.664555 1.15104i
\(669\) 0 0
\(670\) 1498.46 2595.41i 0.0864037 0.149656i
\(671\) −20417.7 −1.17469
\(672\) 0 0
\(673\) −16275.0 −0.932178 −0.466089 0.884738i \(-0.654337\pi\)
−0.466089 + 0.884738i \(0.654337\pi\)
\(674\) 479.498 830.515i 0.0274029 0.0474633i
\(675\) 0 0
\(676\) −3453.55 5981.73i −0.196493 0.340335i
\(677\) 13135.9 22752.0i 0.745720 1.29163i −0.204137 0.978942i \(-0.565439\pi\)
0.949857 0.312683i \(-0.101228\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2396.60 0.135155
\(681\) 0 0
\(682\) −8.74769 15.1514i −0.000491153 0.000850702i
\(683\) −4036.14 6990.81i −0.226118 0.391648i 0.730536 0.682874i \(-0.239270\pi\)
−0.956654 + 0.291226i \(0.905937\pi\)
\(684\) 0 0
\(685\) −6355.51 −0.354499
\(686\) 0 0
\(687\) 0 0
\(688\) −5453.67 + 9446.04i −0.302208 + 0.523440i
\(689\) −5736.05 9935.13i −0.317164 0.549344i
\(690\) 0 0
\(691\) −12242.6 + 21204.9i −0.673997 + 1.16740i 0.302763 + 0.953066i \(0.402091\pi\)
−0.976761 + 0.214332i \(0.931243\pi\)
\(692\) −15042.9 −0.826364
\(693\) 0 0
\(694\) −24.7062 −0.00135135
\(695\) −14089.1 + 24403.0i −0.768962 + 1.33188i
\(696\) 0 0
\(697\) 7509.71 + 13007.2i 0.408107 + 0.706862i
\(698\) 447.440 774.989i 0.0242634 0.0420254i
\(699\) 0 0
\(700\) 0 0
\(701\) −778.448 −0.0419423 −0.0209712 0.999780i \(-0.506676\pi\)
−0.0209712 + 0.999780i \(0.506676\pi\)
\(702\) 0 0
\(703\) −1757.29 3043.72i −0.0942780 0.163294i
\(704\) −14731.7 25516.0i −0.788667 1.36601i
\(705\) 0 0
\(706\) −1768.93 −0.0942985
\(707\) 0 0
\(708\) 0 0
\(709\) 12086.0 20933.6i 0.640197 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170322i \(-0.0544806\pi\)
\(710\) −151.874 263.053i −0.00802777 0.0139045i
\(711\) 0 0
\(712\) −431.109 + 746.703i −0.0226917 + 0.0393032i
\(713\) −162.297 −0.00852466
\(714\) 0 0
\(715\) −27318.3 −1.42888
\(716\) 17022.0 29483.0i 0.888467 1.53887i
\(717\) 0 0
\(718\) 806.269 + 1396.50i 0.0419077 + 0.0725862i
\(719\) 40.9418 70.9132i 0.00212360 0.00367819i −0.864962 0.501838i \(-0.832657\pi\)
0.867085 + 0.498160i \(0.165991\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1067.63 0.0550318
\(723\) 0 0
\(724\) −1523.12 2638.13i −0.0781856 0.135421i
\(725\) −905.382 1568.17i −0.0463794 0.0803315i
\(726\) 0 0
\(727\) 32542.9 1.66018 0.830088 0.557632i \(-0.188290\pi\)
0.830088 + 0.557632i \(0.188290\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1095.42 1897.33i 0.0555389 0.0961962i
\(731\) 4251.70 + 7364.16i 0.215123 + 0.372604i
\(732\) 0 0
\(733\) −2534.47 + 4389.83i −0.127712 + 0.221203i −0.922790 0.385304i \(-0.874097\pi\)
0.795078 + 0.606507i \(0.207430\pi\)
\(734\) 204.631 0.0102903
\(735\) 0 0
\(736\) 6542.98 0.327687
\(737\) −29297.8 + 50745.3i −1.46431 + 2.53627i
\(738\) 0 0
\(739\) 19214.2 + 33280.0i 0.956437 + 1.65660i 0.731045 + 0.682329i \(0.239033\pi\)
0.225392 + 0.974268i \(0.427634\pi\)
\(740\) −3431.55 + 5943.62i −0.170468 + 0.295259i
\(741\) 0 0
\(742\) 0 0
\(743\) −21592.9 −1.06617 −0.533086 0.846061i \(-0.678968\pi\)
−0.533086 + 0.846061i \(0.678968\pi\)
\(744\) 0 0
\(745\) −9375.07 16238.1i −0.461042 0.798548i
\(746\) 165.445 + 286.560i 0.00811982 + 0.0140639i
\(747\) 0 0
\(748\) −23338.7 −1.14084
\(749\) 0 0
\(750\) 0 0
\(751\) −4056.30 + 7025.72i −0.197093 + 0.341374i −0.947585 0.319505i \(-0.896483\pi\)
0.750492 + 0.660880i \(0.229817\pi\)
\(752\) −12172.8 21083.9i −0.590287 1.02241i
\(753\) 0 0
\(754\) −276.220 + 478.428i −0.0133413 + 0.0231078i
\(755\) −19793.7 −0.954129
\(756\) 0 0
\(757\) 3108.01 0.149224 0.0746120 0.997213i \(-0.476228\pi\)
0.0746120 + 0.997213i \(0.476228\pi\)
\(758\) −165.996 + 287.513i −0.00795414 + 0.0137770i
\(759\) 0 0
\(760\) 1242.64 + 2152.32i 0.0593098 + 0.102728i
\(761\) 3605.96 6245.71i 0.171769 0.297512i −0.767269 0.641325i \(-0.778385\pi\)
0.939038 + 0.343812i \(0.111718\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 3058.77 0.144846
\(765\) 0 0
\(766\) 43.8313 + 75.9181i 0.00206748 + 0.00358098i
\(767\) 15381.7 + 26641.9i 0.724123 + 1.25422i
\(768\) 0 0
\(769\) 7533.07 0.353250 0.176625 0.984278i \(-0.443482\pi\)
0.176625 + 0.984278i \(0.443482\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2501.50 4332.73i 0.116621 0.201993i
\(773\) 12416.3 + 21505.7i 0.577728 + 1.00065i 0.995739 + 0.0922122i \(0.0293938\pi\)
−0.418012 + 0.908442i \(0.637273\pi\)
\(774\) 0 0
\(775\) −17.3178 + 29.9952i −0.000802674 + 0.00139027i
\(776\) 3093.08 0.143086
\(777\) 0 0
\(778\) 2911.66 0.134175
\(779\) −7787.61 + 13488.5i −0.358177 + 0.620381i
\(780\) 0 0
\(781\) 2969.43 + 5143.20i 0.136049 + 0.235644i
\(782\) 839.177 1453.50i 0.0383746 0.0664667i
\(783\) 0 0
\(784\) 0 0
\(785\) 14475.9 0.658173
\(786\) 0 0
\(787\) 18156.6 + 31448.1i 0.822378 + 1.42440i 0.903907 + 0.427730i \(0.140686\pi\)
−0.0815287 + 0.996671i \(0.525980\pi\)
\(788\) 4962.45 + 8595.21i 0.224340 + 0.388568i
\(789\) 0 0
\(790\) −1501.88