Properties

Label 336.4.bc.d.257.2
Level $336$
Weight $4$
Character 336.257
Analytic conductor $19.825$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.2
Root \(0.00299931 - 3.00000i\) of defining polynomial
Character \(\chi\) \(=\) 336.257
Dual form 336.4.bc.d.17.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.59358 + 4.50260i) q^{3} +(-8.05907 + 13.9587i) q^{5} +(5.67909 - 17.6280i) q^{7} +(-13.5467 - 23.3556i) q^{9} +O(q^{10})\) \(q+(-2.59358 + 4.50260i) q^{3} +(-8.05907 + 13.9587i) q^{5} +(5.67909 - 17.6280i) q^{7} +(-13.5467 - 23.3556i) q^{9} +(-30.8296 + 17.7995i) q^{11} +7.40831i q^{13} +(-41.9486 - 72.4897i) q^{15} +(-14.4601 - 25.0457i) q^{17} +(-30.4580 - 17.5849i) q^{19} +(64.6428 + 71.2903i) q^{21} +(-48.0017 - 27.7138i) q^{23} +(-67.3971 - 116.735i) q^{25} +(140.295 - 0.420792i) q^{27} +68.1510i q^{29} +(154.734 - 89.3356i) q^{31} +(-0.184935 - 184.977i) q^{33} +(200.297 + 221.338i) q^{35} +(116.838 - 202.370i) q^{37} +(-33.3566 - 19.2140i) q^{39} +370.068 q^{41} +187.068 q^{43} +(435.189 - 0.870180i) q^{45} +(87.3726 - 151.334i) q^{47} +(-278.496 - 200.222i) q^{49} +(150.274 - 0.150240i) q^{51} +(-235.715 + 136.090i) q^{53} -573.789i q^{55} +(158.173 - 91.5321i) q^{57} +(48.4354 + 83.8926i) q^{59} +(-333.882 - 192.767i) q^{61} +(-488.647 + 106.164i) q^{63} +(-103.411 - 59.7041i) q^{65} +(-509.009 - 881.630i) q^{67} +(249.280 - 144.254i) q^{69} -125.333i q^{71} +(195.346 - 112.783i) q^{73} +(700.411 - 0.700251i) q^{75} +(138.686 + 644.550i) q^{77} +(-532.154 + 921.718i) q^{79} +(-361.972 + 632.785i) q^{81} +601.040 q^{83} +466.140 q^{85} +(-306.856 - 176.755i) q^{87} +(752.606 - 1303.55i) q^{89} +(130.594 + 42.0725i) q^{91} +(0.928190 + 928.402i) q^{93} +(490.926 - 283.436i) q^{95} -327.463i q^{97} +(833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(3\) −2.59358 + 4.50260i −0.499134 + 0.866525i
\(4\) 0 0
\(5\) −8.05907 + 13.9587i −0.720825 + 1.24851i 0.239845 + 0.970811i \(0.422903\pi\)
−0.960670 + 0.277694i \(0.910430\pi\)
\(6\) 0 0
\(7\) 5.67909 17.6280i 0.306642 0.951825i
\(8\) 0 0
\(9\) −13.5467 23.3556i −0.501731 0.865024i
\(10\) 0 0
\(11\) −30.8296 + 17.7995i −0.845043 + 0.487886i −0.858975 0.512017i \(-0.828898\pi\)
0.0139322 + 0.999903i \(0.495565\pi\)
\(12\) 0 0
\(13\) 7.40831i 0.158054i 0.996872 + 0.0790268i \(0.0251813\pi\)
−0.996872 + 0.0790268i \(0.974819\pi\)
\(14\) 0 0
\(15\) −41.9486 72.4897i −0.722073 1.24778i
\(16\) 0 0
\(17\) −14.4601 25.0457i −0.206300 0.357322i 0.744246 0.667905i \(-0.232809\pi\)
−0.950546 + 0.310584i \(0.899476\pi\)
\(18\) 0 0
\(19\) −30.4580 17.5849i −0.367765 0.212329i 0.304716 0.952443i \(-0.401438\pi\)
−0.672482 + 0.740114i \(0.734772\pi\)
\(20\) 0 0
\(21\) 64.6428 + 71.2903i 0.671725 + 0.740801i
\(22\) 0 0
\(23\) −48.0017 27.7138i −0.435175 0.251249i 0.266374 0.963870i \(-0.414175\pi\)
−0.701549 + 0.712621i \(0.747508\pi\)
\(24\) 0 0
\(25\) −67.3971 116.735i −0.539177 0.933881i
\(26\) 0 0
\(27\) 140.295 0.420792i 0.999996 0.00299931i
\(28\) 0 0
\(29\) 68.1510i 0.436390i 0.975905 + 0.218195i \(0.0700169\pi\)
−0.975905 + 0.218195i \(0.929983\pi\)
\(30\) 0 0
\(31\) 154.734 89.3356i 0.896484 0.517585i 0.0204262 0.999791i \(-0.493498\pi\)
0.876058 + 0.482206i \(0.160164\pi\)
\(32\) 0 0
\(33\) −0.184935 184.977i −0.000975549 0.975771i
\(34\) 0 0
\(35\) 200.297 + 221.338i 0.967323 + 1.06894i
\(36\) 0 0
\(37\) 116.838 202.370i 0.519137 0.899172i −0.480615 0.876931i \(-0.659587\pi\)
0.999753 0.0222405i \(-0.00707996\pi\)
\(38\) 0 0
\(39\) −33.3566 19.2140i −0.136957 0.0788899i
\(40\) 0 0
\(41\) 370.068 1.40963 0.704816 0.709390i \(-0.251030\pi\)
0.704816 + 0.709390i \(0.251030\pi\)
\(42\) 0 0
\(43\) 187.068 0.663432 0.331716 0.943379i \(-0.392372\pi\)
0.331716 + 0.943379i \(0.392372\pi\)
\(44\) 0 0
\(45\) 435.189 0.870180i 1.44165 0.00288264i
\(46\) 0 0
\(47\) 87.3726 151.334i 0.271162 0.469666i −0.697998 0.716100i \(-0.745925\pi\)
0.969160 + 0.246434i \(0.0792588\pi\)
\(48\) 0 0
\(49\) −278.496 200.222i −0.811942 0.583739i
\(50\) 0 0
\(51\) 150.274 0.150240i 0.412599 0.000412505i
\(52\) 0 0
\(53\) −235.715 + 136.090i −0.610905 + 0.352706i −0.773319 0.634017i \(-0.781405\pi\)
0.162415 + 0.986723i \(0.448072\pi\)
\(54\) 0 0
\(55\) 573.789i 1.40672i
\(56\) 0 0
\(57\) 158.173 91.5321i 0.367553 0.212697i
\(58\) 0 0
\(59\) 48.4354 + 83.8926i 0.106877 + 0.185117i 0.914504 0.404578i \(-0.132581\pi\)
−0.807626 + 0.589695i \(0.799248\pi\)
\(60\) 0 0
\(61\) −333.882 192.767i −0.700807 0.404611i 0.106841 0.994276i \(-0.465927\pi\)
−0.807648 + 0.589665i \(0.799260\pi\)
\(62\) 0 0
\(63\) −488.647 + 106.164i −0.977203 + 0.212307i
\(64\) 0 0
\(65\) −103.411 59.7041i −0.197331 0.113929i
\(66\) 0 0
\(67\) −509.009 881.630i −0.928140 1.60759i −0.786432 0.617677i \(-0.788074\pi\)
−0.141708 0.989908i \(-0.545259\pi\)
\(68\) 0 0
\(69\) 249.280 144.254i 0.434924 0.251684i
\(70\) 0 0
\(71\) 125.333i 0.209497i −0.994499 0.104749i \(-0.966596\pi\)
0.994499 0.104749i \(-0.0334038\pi\)
\(72\) 0 0
\(73\) 195.346 112.783i 0.313199 0.180825i −0.335158 0.942162i \(-0.608790\pi\)
0.648357 + 0.761337i \(0.275456\pi\)
\(74\) 0 0
\(75\) 700.411 0.700251i 1.07835 0.00107811i
\(76\) 0 0
\(77\) 138.686 + 644.550i 0.205256 + 0.953939i
\(78\) 0 0
\(79\) −532.154 + 921.718i −0.757874 + 1.31268i 0.186059 + 0.982539i \(0.440428\pi\)
−0.943933 + 0.330138i \(0.892905\pi\)
\(80\) 0 0
\(81\) −361.972 + 632.785i −0.496533 + 0.868018i
\(82\) 0 0
\(83\) 601.040 0.794852 0.397426 0.917634i \(-0.369904\pi\)
0.397426 + 0.917634i \(0.369904\pi\)
\(84\) 0 0
\(85\) 466.140 0.594824
\(86\) 0 0
\(87\) −306.856 176.755i −0.378143 0.217817i
\(88\) 0 0
\(89\) 752.606 1303.55i 0.896360 1.55254i 0.0642474 0.997934i \(-0.479535\pi\)
0.832112 0.554607i \(-0.187131\pi\)
\(90\) 0 0
\(91\) 130.594 + 42.0725i 0.150439 + 0.0484658i
\(92\) 0 0
\(93\) 0.928190 + 928.402i 0.00103493 + 1.03517i
\(94\) 0 0
\(95\) 490.926 283.436i 0.530189 0.306105i
\(96\) 0 0
\(97\) 327.463i 0.342771i −0.985204 0.171386i \(-0.945176\pi\)
0.985204 0.171386i \(-0.0548244\pi\)
\(98\) 0 0
\(99\) 833.358 + 478.920i 0.846017 + 0.486195i
\(100\) 0 0
\(101\) −547.845 948.895i −0.539729 0.934837i −0.998918 0.0464990i \(-0.985194\pi\)
0.459190 0.888338i \(-0.348140\pi\)
\(102\) 0 0
\(103\) −179.848 103.835i −0.172048 0.0993318i 0.411503 0.911408i \(-0.365004\pi\)
−0.583551 + 0.812076i \(0.698337\pi\)
\(104\) 0 0
\(105\) −1516.08 + 327.797i −1.40909 + 0.304664i
\(106\) 0 0
\(107\) −1561.25 901.391i −1.41058 0.814399i −0.415138 0.909759i \(-0.636267\pi\)
−0.995443 + 0.0953593i \(0.969600\pi\)
\(108\) 0 0
\(109\) −141.825 245.647i −0.124627 0.215860i 0.796960 0.604032i \(-0.206440\pi\)
−0.921587 + 0.388172i \(0.873107\pi\)
\(110\) 0 0
\(111\) 608.160 + 1050.94i 0.520036 + 0.898652i
\(112\) 0 0
\(113\) 1037.39i 0.863627i 0.901963 + 0.431814i \(0.142126\pi\)
−0.901963 + 0.431814i \(0.857874\pi\)
\(114\) 0 0
\(115\) 773.697 446.694i 0.627371 0.362213i
\(116\) 0 0
\(117\) 173.026 100.358i 0.136720 0.0793003i
\(118\) 0 0
\(119\) −523.626 + 112.667i −0.403368 + 0.0867915i
\(120\) 0 0
\(121\) −31.8573 + 55.1785i −0.0239349 + 0.0414564i
\(122\) 0 0
\(123\) −959.799 + 1666.27i −0.703595 + 1.22148i
\(124\) 0 0
\(125\) 157.864 0.112958
\(126\) 0 0
\(127\) −1645.81 −1.14994 −0.574968 0.818176i \(-0.694985\pi\)
−0.574968 + 0.818176i \(0.694985\pi\)
\(128\) 0 0
\(129\) −485.175 + 842.291i −0.331142 + 0.574881i
\(130\) 0 0
\(131\) −314.185 + 544.184i −0.209545 + 0.362943i −0.951571 0.307428i \(-0.900532\pi\)
0.742026 + 0.670371i \(0.233865\pi\)
\(132\) 0 0
\(133\) −482.961 + 437.048i −0.314873 + 0.284939i
\(134\) 0 0
\(135\) −1124.78 + 1961.74i −0.717077 + 1.25066i
\(136\) 0 0
\(137\) 432.079 249.461i 0.269453 0.155569i −0.359186 0.933266i \(-0.616946\pi\)
0.628639 + 0.777697i \(0.283612\pi\)
\(138\) 0 0
\(139\) 1216.65i 0.742410i −0.928551 0.371205i \(-0.878945\pi\)
0.928551 0.371205i \(-0.121055\pi\)
\(140\) 0 0
\(141\) 454.788 + 785.900i 0.271631 + 0.469395i
\(142\) 0 0
\(143\) −131.864 228.395i −0.0771121 0.133562i
\(144\) 0 0
\(145\) −951.300 549.233i −0.544835 0.314561i
\(146\) 0 0
\(147\) 1623.82 734.663i 0.911092 0.412204i
\(148\) 0 0
\(149\) −2010.18 1160.58i −1.10524 0.638111i −0.167648 0.985847i \(-0.553617\pi\)
−0.937592 + 0.347736i \(0.886950\pi\)
\(150\) 0 0
\(151\) 488.726 + 846.497i 0.263390 + 0.456205i 0.967141 0.254242i \(-0.0818260\pi\)
−0.703750 + 0.710447i \(0.748493\pi\)
\(152\) 0 0
\(153\) −389.070 + 677.012i −0.205585 + 0.357733i
\(154\) 0 0
\(155\) 2879.85i 1.49235i
\(156\) 0 0
\(157\) −143.752 + 82.9950i −0.0730740 + 0.0421893i −0.536092 0.844160i \(-0.680100\pi\)
0.463018 + 0.886349i \(0.346767\pi\)
\(158\) 0 0
\(159\) −1.41397 1414.29i −0.000705251 0.705412i
\(160\) 0 0
\(161\) −761.145 + 688.786i −0.372588 + 0.337168i
\(162\) 0 0
\(163\) 488.511 846.127i 0.234743 0.406587i −0.724455 0.689322i \(-0.757908\pi\)
0.959198 + 0.282735i \(0.0912417\pi\)
\(164\) 0 0
\(165\) 2583.54 + 1488.16i 1.21896 + 0.702142i
\(166\) 0 0
\(167\) −1.00709 −0.000466651 −0.000233326 1.00000i \(-0.500074\pi\)
−0.000233326 1.00000i \(0.500074\pi\)
\(168\) 0 0
\(169\) 2142.12 0.975019
\(170\) 0 0
\(171\) 1.89874 + 949.584i 0.000849123 + 0.424658i
\(172\) 0 0
\(173\) −1978.27 + 3426.47i −0.869395 + 1.50584i −0.00677983 + 0.999977i \(0.502158\pi\)
−0.862616 + 0.505860i \(0.831175\pi\)
\(174\) 0 0
\(175\) −2440.57 + 525.130i −1.05423 + 0.226835i
\(176\) 0 0
\(177\) −503.356 + 0.503241i −0.213754 + 0.000213706i
\(178\) 0 0
\(179\) 2423.54 1399.23i 1.01198 0.584266i 0.100208 0.994967i \(-0.468049\pi\)
0.911770 + 0.410701i \(0.134716\pi\)
\(180\) 0 0
\(181\) 1506.74i 0.618758i −0.950939 0.309379i \(-0.899879\pi\)
0.950939 0.309379i \(-0.100121\pi\)
\(182\) 0 0
\(183\) 1733.90 1003.38i 0.700403 0.405312i
\(184\) 0 0
\(185\) 1883.21 + 3261.82i 0.748414 + 1.29629i
\(186\) 0 0
\(187\) 891.599 + 514.765i 0.348664 + 0.201301i
\(188\) 0 0
\(189\) 789.332 2475.52i 0.303786 0.952740i
\(190\) 0 0
\(191\) −3184.51 1838.58i −1.20640 0.696518i −0.244433 0.969666i \(-0.578602\pi\)
−0.961972 + 0.273148i \(0.911935\pi\)
\(192\) 0 0
\(193\) 64.7335 + 112.122i 0.0241431 + 0.0418171i 0.877845 0.478946i \(-0.158981\pi\)
−0.853701 + 0.520763i \(0.825648\pi\)
\(194\) 0 0
\(195\) 537.026 310.769i 0.197217 0.114126i
\(196\) 0 0
\(197\) 3044.81i 1.10119i −0.834774 0.550593i \(-0.814402\pi\)
0.834774 0.550593i \(-0.185598\pi\)
\(198\) 0 0
\(199\) −3458.29 + 1996.64i −1.23192 + 0.711248i −0.967429 0.253141i \(-0.918536\pi\)
−0.264488 + 0.964389i \(0.585203\pi\)
\(200\) 0 0
\(201\) 5289.78 5.28857i 1.85628 0.00185586i
\(202\) 0 0
\(203\) 1201.37 + 387.035i 0.415367 + 0.133815i
\(204\) 0 0
\(205\) −2982.40 + 5165.67i −1.01610 + 1.75993i
\(206\) 0 0
\(207\) 2.99240 + 1496.54i 0.00100476 + 0.502496i
\(208\) 0 0
\(209\) 1252.01 0.414370
\(210\) 0 0
\(211\) 4383.67 1.43026 0.715129 0.698992i \(-0.246368\pi\)
0.715129 + 0.698992i \(0.246368\pi\)
\(212\) 0 0
\(213\) 564.324 + 325.061i 0.181534 + 0.104567i
\(214\) 0 0
\(215\) −1507.59 + 2611.23i −0.478219 + 0.828299i
\(216\) 0 0
\(217\) −696.065 3235.00i −0.217751 1.01201i
\(218\) 0 0
\(219\) 1.17181 + 1172.07i 0.000361568 + 0.361650i
\(220\) 0 0
\(221\) 185.546 107.125i 0.0564759 0.0326064i
\(222\) 0 0
\(223\) 4851.53i 1.45687i −0.685114 0.728436i \(-0.740247\pi\)
0.685114 0.728436i \(-0.259753\pi\)
\(224\) 0 0
\(225\) −1813.42 + 3155.48i −0.537308 + 0.934958i
\(226\) 0 0
\(227\) 1184.05 + 2050.83i 0.346203 + 0.599642i 0.985572 0.169259i \(-0.0541374\pi\)
−0.639368 + 0.768901i \(0.720804\pi\)
\(228\) 0 0
\(229\) −3737.27 2157.72i −1.07845 0.622646i −0.147975 0.988991i \(-0.547276\pi\)
−0.930479 + 0.366345i \(0.880609\pi\)
\(230\) 0 0
\(231\) −3261.84 1047.24i −0.929062 0.298284i
\(232\) 0 0
\(233\) −4826.98 2786.86i −1.35719 0.783576i −0.367949 0.929846i \(-0.619940\pi\)
−0.989245 + 0.146270i \(0.953273\pi\)
\(234\) 0 0
\(235\) 1408.28 + 2439.22i 0.390920 + 0.677094i
\(236\) 0 0
\(237\) −2769.94 4786.62i −0.759186 1.31192i
\(238\) 0 0
\(239\) 4683.70i 1.26763i −0.773485 0.633814i \(-0.781488\pi\)
0.773485 0.633814i \(-0.218512\pi\)
\(240\) 0 0
\(241\) −1896.77 + 1095.10i −0.506977 + 0.292703i −0.731590 0.681745i \(-0.761222\pi\)
0.224613 + 0.974448i \(0.427888\pi\)
\(242\) 0 0
\(243\) −1910.37 3270.99i −0.504323 0.863515i
\(244\) 0 0
\(245\) 5039.26 2273.84i 1.31407 0.592940i
\(246\) 0 0
\(247\) 130.275 225.642i 0.0335594 0.0581266i
\(248\) 0 0
\(249\) −1558.84 + 2706.24i −0.396738 + 0.688759i
\(250\) 0 0
\(251\) −2240.70 −0.563473 −0.281736 0.959492i \(-0.590910\pi\)
−0.281736 + 0.959492i \(0.590910\pi\)
\(252\) 0 0
\(253\) 1973.16 0.490323
\(254\) 0 0
\(255\) −1208.97 + 2098.84i −0.296897 + 0.515429i
\(256\) 0 0
\(257\) −555.785 + 962.648i −0.134898 + 0.233651i −0.925559 0.378604i \(-0.876404\pi\)
0.790660 + 0.612255i \(0.209737\pi\)
\(258\) 0 0
\(259\) −2903.85 3208.90i −0.696665 0.769851i
\(260\) 0 0
\(261\) 1591.71 923.223i 0.377488 0.218950i
\(262\) 0 0
\(263\) −1782.86 + 1029.34i −0.418007 + 0.241337i −0.694224 0.719759i \(-0.744252\pi\)
0.276217 + 0.961095i \(0.410919\pi\)
\(264\) 0 0
\(265\) 4387.04i 1.01696i
\(266\) 0 0
\(267\) 3917.42 + 6769.54i 0.897912 + 1.55164i
\(268\) 0 0
\(269\) −2414.62 4182.24i −0.547294 0.947940i −0.998459 0.0554999i \(-0.982325\pi\)
0.451165 0.892441i \(-0.351009\pi\)
\(270\) 0 0
\(271\) 191.772 + 110.720i 0.0429865 + 0.0248183i 0.521339 0.853350i \(-0.325433\pi\)
−0.478353 + 0.878168i \(0.658766\pi\)
\(272\) 0 0
\(273\) −528.141 + 478.894i −0.117086 + 0.106168i
\(274\) 0 0
\(275\) 4155.65 + 2399.27i 0.911255 + 0.526113i
\(276\) 0 0
\(277\) −1233.58 2136.62i −0.267576 0.463455i 0.700660 0.713496i \(-0.252889\pi\)
−0.968235 + 0.250041i \(0.919556\pi\)
\(278\) 0 0
\(279\) −4182.63 2403.70i −0.897517 0.515792i
\(280\) 0 0
\(281\) 4174.76i 0.886282i 0.896452 + 0.443141i \(0.146136\pi\)
−0.896452 + 0.443141i \(0.853864\pi\)
\(282\) 0 0
\(283\) 5628.39 3249.55i 1.18224 0.682565i 0.225706 0.974195i \(-0.427531\pi\)
0.956531 + 0.291630i \(0.0941977\pi\)
\(284\) 0 0
\(285\) 2.94488 + 2945.55i 0.000612069 + 0.612209i
\(286\) 0 0
\(287\) 2101.65 6523.57i 0.432252 1.34172i
\(288\) 0 0
\(289\) 2038.31 3530.46i 0.414881 0.718595i
\(290\) 0 0
\(291\) 1474.43 + 849.300i 0.297020 + 0.171089i
\(292\) 0 0
\(293\) 5637.32 1.12401 0.562007 0.827133i \(-0.310030\pi\)
0.562007 + 0.827133i \(0.310030\pi\)
\(294\) 0 0
\(295\) −1561.38 −0.308159
\(296\) 0 0
\(297\) −4317.76 + 2510.16i −0.843576 + 0.490418i
\(298\) 0 0
\(299\) 205.312 355.611i 0.0397108 0.0687810i
\(300\) 0 0
\(301\) 1062.38 3297.64i 0.203436 0.631472i
\(302\) 0 0
\(303\) 5693.37 5.69207i 1.07946 0.00107921i
\(304\) 0 0
\(305\) 5381.56 3107.05i 1.01032 0.583308i
\(306\) 0 0
\(307\) 3442.95i 0.640064i −0.947407 0.320032i \(-0.896306\pi\)
0.947407 0.320032i \(-0.103694\pi\)
\(308\) 0 0
\(309\) 933.976 540.477i 0.171948 0.0995037i
\(310\) 0 0
\(311\) 75.7324 + 131.172i 0.0138083 + 0.0239167i 0.872847 0.487994i \(-0.162271\pi\)
−0.859039 + 0.511911i \(0.828938\pi\)
\(312\) 0 0
\(313\) 8335.31 + 4812.40i 1.50524 + 0.869050i 0.999982 + 0.00608123i \(0.00193573\pi\)
0.505257 + 0.862969i \(0.331398\pi\)
\(314\) 0 0
\(315\) 2456.13 7676.47i 0.439325 1.37308i
\(316\) 0 0
\(317\) 7866.93 + 4541.98i 1.39385 + 0.804741i 0.993739 0.111726i \(-0.0356377\pi\)
0.400112 + 0.916466i \(0.368971\pi\)
\(318\) 0 0
\(319\) −1213.05 2101.07i −0.212909 0.368768i
\(320\) 0 0
\(321\) 8107.83 4691.87i 1.40977 0.815809i
\(322\) 0 0
\(323\) 1017.12i 0.175214i
\(324\) 0 0
\(325\) 864.811 499.299i 0.147603 0.0852188i
\(326\) 0 0
\(327\) 1473.88 1.47355i 0.249254 0.000249197i
\(328\) 0 0
\(329\) −2171.52 2399.65i −0.363890 0.402118i
\(330\) 0 0
\(331\) −702.788 + 1217.26i −0.116703 + 0.202136i −0.918459 0.395516i \(-0.870566\pi\)
0.801756 + 0.597651i \(0.203899\pi\)
\(332\) 0 0
\(333\) −6309.25 + 12.6156i −1.03827 + 0.00207607i
\(334\) 0 0
\(335\) 16408.6 2.67611
\(336\) 0 0
\(337\) 7983.35 1.29045 0.645223 0.763994i \(-0.276764\pi\)
0.645223 + 0.763994i \(0.276764\pi\)
\(338\) 0 0
\(339\) −4670.97 2690.56i −0.748354 0.431066i
\(340\) 0 0
\(341\) −3180.25 + 5508.36i −0.505045 + 0.874764i
\(342\) 0 0
\(343\) −5111.13 + 3772.26i −0.804592 + 0.593828i
\(344\) 0 0
\(345\) 4.64112 + 4642.18i 0.000724260 + 0.724425i
\(346\) 0 0
\(347\) −2268.41 + 1309.67i −0.350935 + 0.202612i −0.665097 0.746757i \(-0.731610\pi\)
0.314162 + 0.949369i \(0.398276\pi\)
\(348\) 0 0
\(349\) 6032.33i 0.925224i 0.886561 + 0.462612i \(0.153088\pi\)
−0.886561 + 0.462612i \(0.846912\pi\)
\(350\) 0 0
\(351\) 3.11736 + 1039.35i 0.000474052 + 0.158053i
\(352\) 0 0
\(353\) −2658.15 4604.06i −0.400791 0.694190i 0.593031 0.805180i \(-0.297931\pi\)
−0.993822 + 0.110990i \(0.964598\pi\)
\(354\) 0 0
\(355\) 1749.49 + 1010.07i 0.261558 + 0.151011i
\(356\) 0 0
\(357\) 850.770 2649.89i 0.126128 0.392849i
\(358\) 0 0
\(359\) −1612.51 930.982i −0.237061 0.136867i 0.376764 0.926309i \(-0.377037\pi\)
−0.613825 + 0.789442i \(0.710370\pi\)
\(360\) 0 0
\(361\) −2811.04 4868.87i −0.409832 0.709851i
\(362\) 0 0
\(363\) −165.822 286.550i −0.0239763 0.0414325i
\(364\) 0 0
\(365\) 3635.70i 0.521373i
\(366\) 0 0
\(367\) 1675.89 967.574i 0.238367 0.137621i −0.376059 0.926596i \(-0.622721\pi\)
0.614426 + 0.788975i \(0.289388\pi\)
\(368\) 0 0
\(369\) −5013.21 8643.18i −0.707255 1.21937i
\(370\) 0 0
\(371\) 1060.36 + 4928.06i 0.148385 + 0.689629i
\(372\) 0 0
\(373\) −3871.04 + 6704.83i −0.537359 + 0.930732i 0.461687 + 0.887043i \(0.347244\pi\)
−0.999045 + 0.0436892i \(0.986089\pi\)
\(374\) 0 0
\(375\) −409.432 + 710.797i −0.0563812 + 0.0978810i
\(376\) 0 0
\(377\) −504.884 −0.0689730
\(378\) 0 0
\(379\) 3722.15 0.504470 0.252235 0.967666i \(-0.418834\pi\)
0.252235 + 0.967666i \(0.418834\pi\)
\(380\) 0 0
\(381\) 4268.53 7410.41i 0.573972 0.996448i
\(382\) 0 0
\(383\) −3546.73 + 6143.12i −0.473184 + 0.819578i −0.999529 0.0306926i \(-0.990229\pi\)
0.526345 + 0.850271i \(0.323562\pi\)
\(384\) 0 0
\(385\) −10114.8 3258.60i −1.33895 0.431359i
\(386\) 0 0
\(387\) −2534.16 4369.09i −0.332864 0.573885i
\(388\) 0 0
\(389\) −6173.12 + 3564.05i −0.804601 + 0.464537i −0.845077 0.534644i \(-0.820446\pi\)
0.0404765 + 0.999180i \(0.487112\pi\)
\(390\) 0 0
\(391\) 1602.98i 0.207330i
\(392\) 0 0
\(393\) −1635.38 2826.03i −0.209908 0.362733i
\(394\) 0 0
\(395\) −8577.33 14856.4i −1.09259 1.89242i
\(396\) 0 0
\(397\) 7738.99 + 4468.11i 0.978360 + 0.564857i 0.901775 0.432206i \(-0.142265\pi\)
0.0765855 + 0.997063i \(0.475598\pi\)
\(398\) 0 0
\(399\) −715.255 3308.10i −0.0897432 0.415068i
\(400\) 0 0
\(401\) −7719.60 4456.91i −0.961343 0.555032i −0.0647568 0.997901i \(-0.520627\pi\)
−0.896586 + 0.442869i \(0.853961\pi\)
\(402\) 0 0
\(403\) 661.826 + 1146.32i 0.0818062 + 0.141692i
\(404\) 0 0
\(405\) −5915.71 10152.3i −0.725812 1.24561i
\(406\) 0 0
\(407\) 8318.63i 1.01312i
\(408\) 0 0
\(409\) −2680.13 + 1547.37i −0.324019 + 0.187073i −0.653183 0.757200i \(-0.726567\pi\)
0.329163 + 0.944273i \(0.393233\pi\)
\(410\) 0 0
\(411\) 2.59188 + 2592.47i 0.000311066 + 0.311137i
\(412\) 0 0
\(413\) 1753.93 377.389i 0.208972 0.0449639i
\(414\) 0 0
\(415\) −4843.82 + 8389.74i −0.572949 + 0.992377i
\(416\) 0 0
\(417\) 5478.09 + 3155.48i 0.643317 + 0.370562i
\(418\) 0 0
\(419\) −7234.25 −0.843476 −0.421738 0.906718i \(-0.638580\pi\)
−0.421738 + 0.906718i \(0.638580\pi\)
\(420\) 0 0
\(421\) 406.124 0.0470148 0.0235074 0.999724i \(-0.492517\pi\)
0.0235074 + 0.999724i \(0.492517\pi\)
\(422\) 0 0
\(423\) −4718.11 + 9.43408i −0.542323 + 0.00108440i
\(424\) 0 0
\(425\) −1949.14 + 3376.01i −0.222464 + 0.385319i
\(426\) 0 0
\(427\) −5294.25 + 4790.95i −0.600016 + 0.542975i
\(428\) 0 0
\(429\) 1370.37 1.37006i 0.154224 0.000154189i
\(430\) 0 0
\(431\) −10590.4 + 6114.37i −1.18358 + 0.683338i −0.956839 0.290618i \(-0.906139\pi\)
−0.226737 + 0.973956i \(0.572806\pi\)
\(432\) 0 0
\(433\) 3252.79i 0.361014i 0.983574 + 0.180507i \(0.0577738\pi\)
−0.983574 + 0.180507i \(0.942226\pi\)
\(434\) 0 0
\(435\) 4940.24 2858.84i 0.544521 0.315105i
\(436\) 0 0
\(437\) 974.689 + 1688.21i 0.106695 + 0.184801i
\(438\) 0 0
\(439\) 13036.8 + 7526.81i 1.41734 + 0.818303i 0.996065 0.0886287i \(-0.0282485\pi\)
0.421278 + 0.906932i \(0.361582\pi\)
\(440\) 0 0
\(441\) −903.614 + 9216.81i −0.0975720 + 0.995228i
\(442\) 0 0
\(443\) −204.373 117.995i −0.0219189 0.0126549i 0.489001 0.872283i \(-0.337362\pi\)
−0.510919 + 0.859629i \(0.670695\pi\)
\(444\) 0 0
\(445\) 12130.6 + 21010.8i 1.29224 + 2.23822i
\(446\) 0 0
\(447\) 10439.2 6040.99i 1.10460 0.639215i
\(448\) 0 0
\(449\) 5874.66i 0.617466i −0.951149 0.308733i \(-0.900095\pi\)
0.951149 0.308733i \(-0.0999049\pi\)
\(450\) 0 0
\(451\) −11409.0 + 6587.02i −1.19120 + 0.687739i
\(452\) 0 0
\(453\) −5078.98 + 5.07782i −0.526780 + 0.000526660i
\(454\) 0 0
\(455\) −1639.74 + 1483.86i −0.168950 + 0.152889i
\(456\) 0 0
\(457\) −153.883 + 266.533i −0.0157513 + 0.0272821i −0.873794 0.486297i \(-0.838347\pi\)
0.858042 + 0.513579i \(0.171681\pi\)
\(458\) 0 0
\(459\) −2039.23 3507.71i −0.207370 0.356701i
\(460\) 0 0
\(461\) −4752.26 −0.480119 −0.240060 0.970758i \(-0.577167\pi\)
−0.240060 + 0.970758i \(0.577167\pi\)
\(462\) 0 0
\(463\) 9529.43 0.956523 0.478261 0.878218i \(-0.341267\pi\)
0.478261 + 0.878218i \(0.341267\pi\)
\(464\) 0 0
\(465\) −12966.8 7469.10i −1.29316 0.744884i
\(466\) 0 0
\(467\) 3269.28 5662.56i 0.323949 0.561097i −0.657350 0.753586i \(-0.728323\pi\)
0.981299 + 0.192489i \(0.0616559\pi\)
\(468\) 0 0
\(469\) −18432.1 + 3965.99i −1.81475 + 0.390474i
\(470\) 0 0
\(471\) −0.862312 862.509i −8.43593e−5 0.0843786i
\(472\) 0 0
\(473\) −5767.23 + 3329.71i −0.560629 + 0.323679i
\(474\) 0 0
\(475\) 4740.69i 0.457932i
\(476\) 0 0
\(477\) 6371.64 + 3661.70i 0.611609 + 0.351484i
\(478\) 0 0
\(479\) −3671.28 6358.85i −0.350199 0.606562i 0.636085 0.771619i \(-0.280553\pi\)
−0.986284 + 0.165057i \(0.947219\pi\)
\(480\) 0 0
\(481\) 1499.22 + 865.574i 0.142117 + 0.0820515i
\(482\) 0 0
\(483\) −1127.24 5213.55i −0.106193 0.491148i
\(484\) 0 0
\(485\) 4570.96 + 2639.05i 0.427952 + 0.247078i
\(486\) 0 0
\(487\) 3508.78 + 6077.39i 0.326485 + 0.565489i 0.981812 0.189857i \(-0.0608024\pi\)
−0.655327 + 0.755345i \(0.727469\pi\)
\(488\) 0 0
\(489\) 2542.77 + 4394.06i 0.235150 + 0.406352i
\(490\) 0 0
\(491\) 224.222i 0.0206089i 0.999947 + 0.0103045i \(0.00328007\pi\)
−0.999947 + 0.0103045i \(0.996720\pi\)
\(492\) 0 0
\(493\) 1706.89 985.471i 0.155932 0.0900272i
\(494\) 0 0
\(495\) −13401.2 + 7772.96i −1.21685 + 0.705795i
\(496\) 0 0
\(497\) −2209.38 711.777i −0.199405 0.0642406i
\(498\) 0 0
\(499\) −10396.1 + 18006.6i −0.932651 + 1.61540i −0.153881 + 0.988089i \(0.549177\pi\)
−0.778770 + 0.627309i \(0.784156\pi\)
\(500\) 0 0
\(501\) 2.61196 4.53451i 0.000232922 0.000404365i
\(502\) 0 0
\(503\) 7341.52 0.650780 0.325390 0.945580i \(-0.394504\pi\)
0.325390 + 0.945580i \(0.394504\pi\)
\(504\) 0 0
\(505\) 17660.5 1.55620
\(506\) 0 0
\(507\) −5555.74 + 9645.09i −0.486665 + 0.844878i
\(508\) 0 0
\(509\) 9956.11 17244.5i 0.866988 1.50167i 0.00192778 0.999998i \(-0.499386\pi\)
0.865060 0.501669i \(-0.167280\pi\)
\(510\) 0 0
\(511\) −878.757 4084.07i −0.0760742 0.353559i
\(512\) 0 0
\(513\) −4280.52 2454.27i −0.368400 0.211225i
\(514\) 0 0
\(515\) 2898.81 1673.63i 0.248032 0.143202i
\(516\) 0 0
\(517\) 6220.75i 0.529184i
\(518\) 0 0
\(519\) −10297.2 17794.2i −0.870900 1.50497i
\(520\) 0 0
\(521\) 3745.90 + 6488.08i 0.314992 + 0.545582i 0.979436 0.201756i \(-0.0646649\pi\)
−0.664444 + 0.747338i \(0.731332\pi\)
\(522\) 0 0
\(523\) −249.515 144.058i −0.0208614 0.0120444i 0.489533 0.871985i \(-0.337167\pi\)
−0.510394 + 0.859940i \(0.670501\pi\)
\(524\) 0 0
\(525\) 3965.35 12350.8i 0.329642 1.02673i
\(526\) 0 0
\(527\) −4474.94 2583.61i −0.369889 0.213555i
\(528\) 0 0
\(529\) −4547.39 7876.32i −0.373748 0.647351i
\(530\) 0 0
\(531\) 1303.23 2267.71i 0.106507 0.185330i
\(532\) 0 0
\(533\) 2741.58i 0.222797i
\(534\) 0 0
\(535\) 25164.5 14528.7i 2.03356 1.17408i
\(536\) 0 0
\(537\) 14.5379 + 14541.2i 0.00116826 + 1.16853i
\(538\) 0 0
\(539\) 12149.8 + 1215.69i 0.970923 + 0.0971496i
\(540\) 0 0
\(541\) −7400.87 + 12818.7i −0.588149 + 1.01870i 0.406326 + 0.913728i \(0.366810\pi\)
−0.994475 + 0.104975i \(0.966524\pi\)
\(542\) 0 0
\(543\) 6784.24 + 3907.85i 0.536169 + 0.308843i
\(544\) 0 0
\(545\) 4571.90 0.359337
\(546\) 0 0
\(547\) 4036.80 0.315541 0.157771 0.987476i \(-0.449569\pi\)
0.157771 + 0.987476i \(0.449569\pi\)
\(548\) 0 0
\(549\) 20.8141 + 10409.4i 0.00161807 + 0.809221i
\(550\) 0 0
\(551\) 1198.43 2075.74i 0.0926585 0.160489i
\(552\) 0 0
\(553\) 13225.9 + 14615.4i 1.01704 + 1.12388i
\(554\) 0 0
\(555\) −19570.9 + 19.5664i −1.49683 + 0.00149649i
\(556\) 0 0
\(557\) −14891.1 + 8597.36i −1.13277 + 0.654007i −0.944631 0.328135i \(-0.893580\pi\)
−0.188142 + 0.982142i \(0.560246\pi\)
\(558\) 0 0
\(559\) 1385.86i 0.104858i
\(560\) 0 0
\(561\) −4630.21 + 2679.43i −0.348463 + 0.201650i
\(562\) 0 0
\(563\) 9453.63 + 16374.2i 0.707678 + 1.22573i 0.965716 + 0.259600i \(0.0835907\pi\)
−0.258038 + 0.966135i \(0.583076\pi\)
\(564\) 0 0
\(565\) −14480.7 8360.43i −1.07824 0.622524i
\(566\) 0 0
\(567\) 9099.09 + 9974.51i 0.673944 + 0.738783i
\(568\) 0 0
\(569\) 6255.57 + 3611.66i 0.460891 + 0.266096i 0.712419 0.701754i \(-0.247600\pi\)
−0.251528 + 0.967850i \(0.580933\pi\)
\(570\) 0 0
\(571\) −4965.17 8599.93i −0.363898 0.630290i 0.624700 0.780865i \(-0.285221\pi\)
−0.988599 + 0.150574i \(0.951888\pi\)
\(572\) 0 0
\(573\) 16537.7 9570.08i 1.20571 0.697724i
\(574\) 0 0
\(575\) 7471.31i 0.541870i
\(576\) 0 0
\(577\) 7254.16 4188.19i 0.523388 0.302178i −0.214932 0.976629i \(-0.568953\pi\)
0.738320 + 0.674451i \(0.235620\pi\)
\(578\) 0 0
\(579\) −672.730 + 0.672576i −0.0482862 + 4.82752e-5i
\(580\) 0 0
\(581\) 3413.36 10595.2i 0.243735 0.756560i
\(582\) 0 0
\(583\) 4844.67 8391.21i 0.344161 0.596104i
\(584\) 0 0
\(585\) 6.44656 + 3224.01i 0.000455611 + 0.227857i
\(586\) 0 0
\(587\) −21277.2 −1.49609 −0.748043 0.663650i \(-0.769006\pi\)
−0.748043 + 0.663650i \(0.769006\pi\)
\(588\) 0 0
\(589\) −6283.84 −0.439594
\(590\) 0 0
\(591\) 13709.5 + 7896.94i 0.954204 + 0.549639i
\(592\) 0 0
\(593\) 1424.49 2467.29i 0.0986454 0.170859i −0.812479 0.582991i \(-0.801882\pi\)
0.911124 + 0.412132i \(0.135216\pi\)
\(594\) 0 0
\(595\) 2647.25 8217.14i 0.182398 0.566168i
\(596\) 0 0
\(597\) −20.7450 20749.7i −0.00142217 1.42249i
\(598\) 0 0
\(599\) 3844.40 2219.57i 0.262234 0.151401i −0.363119 0.931743i \(-0.618288\pi\)
0.625353 + 0.780342i \(0.284955\pi\)
\(600\) 0 0
\(601\) 7868.29i 0.534033i −0.963692 0.267017i \(-0.913962\pi\)
0.963692 0.267017i \(-0.0860379\pi\)
\(602\) 0 0
\(603\) −13695.6 + 23831.4i −0.924924 + 1.60944i
\(604\) 0 0
\(605\) −513.480 889.374i −0.0345057 0.0597656i
\(606\) 0 0
\(607\) 15144.9 + 8743.92i 1.01271 + 0.584686i 0.911983 0.410228i \(-0.134551\pi\)
0.100724 + 0.994914i \(0.467884\pi\)
\(608\) 0 0
\(609\) −4858.50 + 4405.47i −0.323278 + 0.293134i
\(610\) 0 0
\(611\) 1121.13 + 647.284i 0.0742324 + 0.0428581i
\(612\) 0 0
\(613\) −6422.07 11123.3i −0.423140 0.732900i 0.573105 0.819482i \(-0.305739\pi\)
−0.996245 + 0.0865820i \(0.972406\pi\)
\(614\) 0 0
\(615\) −15523.8 26826.1i −1.01786 1.75892i
\(616\) 0 0
\(617\) 23625.5i 1.54153i 0.637117 + 0.770767i \(0.280127\pi\)
−0.637117 + 0.770767i \(0.719873\pi\)
\(618\) 0 0
\(619\) −16529.1 + 9543.05i −1.07328 + 0.619657i −0.929075 0.369891i \(-0.879395\pi\)
−0.144202 + 0.989548i \(0.546062\pi\)
\(620\) 0 0
\(621\) −6746.08 3867.92i −0.435927 0.249942i
\(622\) 0 0
\(623\) −18704.9 20669.9i −1.20289 1.32925i
\(624\) 0 0
\(625\) 7152.40 12388.3i 0.457754 0.792853i
\(626\) 0 0
\(627\) −3247.18 + 5637.29i −0.206826 + 0.359062i
\(628\) 0 0
\(629\) −6757.98 −0.428391
\(630\) 0 0
\(631\) −32.3893 −0.00204342 −0.00102171 0.999999i \(-0.500325\pi\)
−0.00102171 + 0.999999i \(0.500325\pi\)
\(632\) 0 0
\(633\) −11369.4 + 19737.9i −0.713891 + 1.23935i
\(634\) 0 0
\(635\) 13263.7 22973.4i 0.828902 1.43570i
\(636\) 0 0
\(637\) 1483.31 2063.19i 0.0922620 0.128330i
\(638\) 0 0
\(639\) −2927.23 + 1697.85i −0.181220 + 0.105111i
\(640\) 0 0
\(641\) 18742.7 10821.1i 1.15490 0.666784i 0.204827 0.978798i \(-0.434337\pi\)
0.950078 + 0.312014i \(0.101004\pi\)
\(642\) 0 0
\(643\) 19867.3i 1.21849i 0.792982 + 0.609246i \(0.208528\pi\)
−0.792982 + 0.609246i \(0.791472\pi\)
\(644\) 0 0
\(645\) −7847.24 13560.5i −0.479046 0.827820i
\(646\) 0 0
\(647\) 11212.2 + 19420.1i 0.681294 + 1.18004i 0.974586 + 0.224012i \(0.0719156\pi\)
−0.293293 + 0.956023i \(0.594751\pi\)
\(648\) 0 0
\(649\) −2986.49 1724.25i −0.180632 0.104288i
\(650\) 0 0
\(651\) 16371.2 + 5256.11i 0.985618 + 0.316441i
\(652\) 0 0
\(653\) −17358.5 10021.9i −1.04026 0.600594i −0.120353 0.992731i \(-0.538403\pi\)
−0.919907 + 0.392137i \(0.871736\pi\)
\(654\) 0 0
\(655\) −5064.07 8771.22i −0.302091 0.523237i
\(656\) 0 0
\(657\) −5280.41 3034.59i −0.313559 0.180199i
\(658\) 0 0
\(659\) 13217.9i 0.781327i −0.920533 0.390664i \(-0.872246\pi\)
0.920533 0.390664i \(-0.127754\pi\)
\(660\) 0 0
\(661\) 8470.90 4890.68i 0.498457 0.287784i −0.229619 0.973281i \(-0.573748\pi\)
0.728076 + 0.685496i \(0.240415\pi\)
\(662\) 0 0
\(663\) 1.11302 + 1113.28i 6.51979e−5 + 0.0652128i
\(664\) 0 0
\(665\) −2208.41 10263.7i −0.128780 0.598511i
\(666\) 0 0
\(667\) 1888.72 3271.36i 0.109642 0.189906i
\(668\) 0 0
\(669\) 21844.5 + 12582.8i 1.26242 + 0.727174i
\(670\) 0 0
\(671\) 13724.6 0.789617
\(672\) 0 0
\(673\) −4670.73 −0.267524 −0.133762 0.991014i \(-0.542706\pi\)
−0.133762 + 0.991014i \(0.542706\pi\)
\(674\) 0 0
\(675\) −9504.63 16349.1i −0.541975 0.932260i
\(676\) 0 0
\(677\) 13521.0 23419.1i 0.767584 1.32949i −0.171286 0.985221i \(-0.554792\pi\)
0.938870 0.344273i \(-0.111875\pi\)
\(678\) 0 0
\(679\) −5772.53 1859.69i −0.326258 0.105108i
\(680\) 0 0
\(681\) −12305.0 + 12.3022i −0.692406 + 0.000692248i
\(682\) 0 0
\(683\) 11596.9 6695.45i 0.649694 0.375101i −0.138645 0.990342i \(-0.544275\pi\)
0.788339 + 0.615241i \(0.210941\pi\)
\(684\) 0 0
\(685\) 8041.69i 0.448551i
\(686\) 0 0
\(687\) 19408.2 11231.2i 1.07783 0.623724i
\(688\) 0 0
\(689\) −1008.20 1746.25i −0.0557464 0.0965557i
\(690\) 0 0
\(691\) −26837.3 15494.6i −1.47748 0.853025i −0.477807 0.878465i \(-0.658568\pi\)
−0.999676 + 0.0254396i \(0.991901\pi\)
\(692\) 0 0
\(693\) 13175.1 11970.6i 0.722197 0.656172i
\(694\) 0 0
\(695\) 16982.9 + 9805.07i 0.926903 + 0.535147i
\(696\) 0 0
\(697\) −5351.23 9268.60i −0.290807 0.503692i
\(698\) 0 0
\(699\) 25067.3 14506.0i 1.35641 0.784933i
\(700\) 0 0
\(701\) 2892.67i 0.155855i 0.996959 + 0.0779277i \(0.0248303\pi\)
−0.996959 + 0.0779277i \(0.975170\pi\)
\(702\) 0 0
\(703\) −7117.31 + 4109.18i −0.381841 + 0.220456i
\(704\) 0 0
\(705\) −14635.3 + 14.6320i −0.781841 + 0.000781662i
\(706\) 0 0
\(707\) −19838.4 + 4268.57i −1.05530 + 0.227067i
\(708\) 0 0
\(709\) −7965.19 + 13796.1i −0.421917 + 0.730781i −0.996127 0.0879267i \(-0.971976\pi\)
0.574210 + 0.818708i \(0.305309\pi\)
\(710\) 0 0
\(711\) 28736.3 57.4595i 1.51574 0.00303080i
\(712\) 0 0
\(713\) −9903.30 −0.520171
\(714\) 0 0
\(715\) 4250.81 0.222337
\(716\) 0 0
\(717\) 21088.8 + 12147.5i 1.09843 + 0.632716i
\(718\) 0 0
\(719\) −5938.87 + 10286.4i −0.308042 + 0.533545i −0.977934 0.208914i \(-0.933007\pi\)
0.669892 + 0.742459i \(0.266341\pi\)
\(720\) 0 0
\(721\) −2851.78 + 2580.67i −0.147303 + 0.133300i
\(722\) 0 0
\(723\) −11.3780 11380.6i −0.000585273 0.585407i
\(724\) 0 0
\(725\) 7955.61 4593.18i 0.407537 0.235291i
\(726\) 0 0
\(727\) 16795.8i 0.856839i −0.903580 0.428419i \(-0.859071\pi\)
0.903580 0.428419i \(-0.140929\pi\)
\(728\) 0 0
\(729\) 19682.6 118.070i 0.999982 0.00599859i
\(730\) 0 0
\(731\) −2705.03 4685.24i −0.136866 0.237059i
\(732\) 0 0
\(733\) 22048.4 + 12729.7i 1.11102 + 0.641447i 0.939093 0.343663i \(-0.111668\pi\)
0.171926 + 0.985110i \(0.445001\pi\)
\(734\) 0 0
\(735\) −2831.54 + 28587.1i −0.142099 + 1.43463i
\(736\) 0 0
\(737\) 31385.1 + 18120.2i 1.56864 + 0.905653i
\(738\) 0 0
\(739\) −9319.48 16141.8i −0.463901 0.803499i 0.535251 0.844693i \(-0.320217\pi\)
−0.999151 + 0.0411940i \(0.986884\pi\)
\(740\) 0 0
\(741\) 678.099 + 1171.79i 0.0336175 + 0.0580930i
\(742\) 0 0
\(743\) 14043.3i 0.693401i 0.937976 + 0.346700i \(0.112698\pi\)
−0.937976 + 0.346700i \(0.887302\pi\)
\(744\) 0 0
\(745\) 32400.4 18706.4i 1.59337 0.919932i
\(746\) 0 0
\(747\) −8142.12 14037.7i −0.398802 0.687566i
\(748\) 0 0
\(749\) −24756.3 + 22402.8i −1.20771 + 1.09290i
\(750\) 0 0
\(751\) 8115.13 14055.8i 0.394308 0.682961i −0.598705 0.800970i \(-0.704318\pi\)
0.993013 + 0.118009i \(0.0376510\pi\)
\(752\) 0 0
\(753\) 5811.43 10089.0i 0.281248 0.488263i
\(754\) 0 0
\(755\) −15754.7 −0.759433
\(756\) 0 0
\(757\) −33345.7 −1.60102 −0.800508 0.599322i \(-0.795437\pi\)
−0.800508 + 0.599322i \(0.795437\pi\)
\(758\) 0 0
\(759\) −5117.55 + 8884.35i −0.244737 + 0.424877i
\(760\) 0 0
\(761\) −5394.02 + 9342.71i −0.256942 + 0.445037i −0.965421 0.260695i \(-0.916048\pi\)
0.708479 + 0.705732i \(0.249382\pi\)
\(762\) 0 0
\(763\) −5135.72 + 1105.04i −0.243677 + 0.0524313i
\(764\) 0 0
\(765\) −6314.68 10887.0i −0.298441 0.514537i
\(766\) 0 0
\(767\) −621.503 + 358.825i −0.0292584 + 0.0168923i
\(768\) 0 0
\(769\) 35799.6i 1.67876i −0.543543 0.839381i \(-0.682918\pi\)
0.543543 0.839381i \(-0.317082\pi\)
\(770\) 0 0
\(771\) −2892.94 4999.17i −0.135132 0.233516i
\(772\) 0 0
\(773\) 18306.3 + 31707.5i 0.851788 + 1.47534i 0.879593 + 0.475727i \(0.157815\pi\)
−0.0278053 + 0.999613i \(0.508852\pi\)
\(774\) 0 0
\(775\) −20857.2 12041.9i −0.966727 0.558140i
\(776\) 0 0
\(777\) 21979.7 4752.31i 1.01482 0.219419i
\(778\) 0 0
\(779\) −11271.5 6507.62i −0.518414 0.299306i
\(780\) 0 0
\(781\) 2230.86 + 3863.97i 0.102211 + 0.177034i
\(782\) 0 0
\(783\) 28.6773 + 9561.27i 0.00130887 + 0.436388i
\(784\) 0 0
\(785\) 2675.45i 0.121644i
\(786\) 0 0
\(787\) 34874.9 20135.0i 1.57961 0.911990i 0.584701 0.811249i \(-0.301212\pi\)
0.994913 0.100742i \(-0.0321216\pi\)
\(788\) 0 0
\(789\) −10.6947