Properties

Label 336.4.bc.d.17.1
Level $336$
Weight $4$
Character 336.17
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 17.1
Root \(-2.59957 + 1.49740i\) of defining polynomial
Character \(\chi\) \(=\) 336.17
Dual form 336.4.bc.d.257.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +O(q^{10})\) \(q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +(30.8296 + 17.7995i) q^{11} -7.40831i q^{13} +(-41.9486 - 72.4897i) q^{15} +(14.4601 - 25.0457i) q^{17} +(-30.4580 + 17.5849i) q^{19} +(-29.6010 - 91.5685i) q^{21} +(48.0017 - 27.7138i) q^{23} +(-67.3971 + 116.735i) q^{25} +(-140.295 + 0.420792i) q^{27} +68.1510i q^{29} +(154.734 + 89.3356i) q^{31} +(-160.288 - 92.3286i) q^{33} +(-200.297 + 221.338i) q^{35} +(116.838 + 202.370i) q^{37} +(0.0384859 + 38.4947i) q^{39} -370.068 q^{41} +187.068 q^{43} +(218.348 + 376.449i) q^{45} +(-87.3726 - 151.334i) q^{47} +(-278.496 + 200.222i) q^{49} +(-75.0068 + 130.216i) q^{51} +(235.715 + 136.090i) q^{53} +573.789i q^{55} +(158.173 - 91.5321i) q^{57} +(-48.4354 + 83.8926i) q^{59} +(-333.882 + 192.767i) q^{61} +(154.287 + 475.650i) q^{63} +(103.411 - 59.7041i) q^{65} +(-509.009 + 881.630i) q^{67} +(-249.280 + 144.254i) q^{69} -125.333i q^{71} +(195.346 + 112.783i) q^{73} +(349.599 - 606.924i) q^{75} +(-138.686 + 644.550i) q^{77} +(-532.154 - 921.718i) q^{79} +(728.994 - 2.91533i) q^{81} -601.040 q^{83} +466.140 q^{85} +(-0.354042 - 354.123i) q^{87} +(-752.606 - 1303.55i) q^{89} +(130.594 - 42.0725i) q^{91} +(-804.484 - 463.397i) q^{93} +(-490.926 - 283.436i) q^{95} +327.463i q^{97} +(833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

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

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
\(3\) −5.19615 + 0.00519496i −1.00000 + 0.000999771i
\(4\) 0 0
\(5\) 8.05907 + 13.9587i 0.720825 + 1.24851i 0.960670 + 0.277694i \(0.0895701\pi\)
−0.239845 + 0.970811i \(0.577097\pi\)
\(6\) 0 0
\(7\) 5.67909 + 17.6280i 0.306642 + 0.951825i
\(8\) 0 0
\(9\) 26.9999 0.0539876i 0.999998 0.00199954i
\(10\) 0 0
\(11\) 30.8296 + 17.7995i 0.845043 + 0.487886i 0.858975 0.512017i \(-0.171102\pi\)
−0.0139322 + 0.999903i \(0.504435\pi\)
\(12\) 0 0
\(13\) 7.40831i 0.158054i −0.996872 0.0790268i \(-0.974819\pi\)
0.996872 0.0790268i \(-0.0251813\pi\)
\(14\) 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 \(-0.767191\pi\)
0.950546 + 0.310584i \(0.100524\pi\)
\(18\) 0 0
\(19\) −30.4580 + 17.5849i −0.367765 + 0.212329i −0.672482 0.740114i \(-0.734772\pi\)
0.304716 + 0.952443i \(0.401438\pi\)
\(20\) 0 0
\(21\) −29.6010 91.5685i −0.307593 0.951518i
\(22\) 0 0
\(23\) 48.0017 27.7138i 0.435175 0.251249i −0.266374 0.963870i \(-0.585825\pi\)
0.701549 + 0.712621i \(0.252492\pi\)
\(24\) 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 0.876058 0.482206i \(-0.160164\pi\)
0.0204262 + 0.999791i \(0.493498\pi\)
\(32\) 0 0
\(33\) −160.288 92.3286i −0.845530 0.487041i
\(34\) 0 0
\(35\) −200.297 + 221.338i −0.967323 + 1.06894i
\(36\) 0 0
\(37\) 116.838 + 202.370i 0.519137 + 0.899172i 0.999753 + 0.0222405i \(0.00707996\pi\)
−0.480615 + 0.876931i \(0.659587\pi\)
\(38\) 0 0
\(39\) 0.0384859 + 38.4947i 0.000158017 + 0.158053i
\(40\) 0 0
\(41\) −370.068 −1.40963 −0.704816 0.709390i \(-0.748970\pi\)
−0.704816 + 0.709390i \(0.748970\pi\)
\(42\) 0 0
\(43\) 187.068 0.663432 0.331716 0.943379i \(-0.392372\pi\)
0.331716 + 0.943379i \(0.392372\pi\)
\(44\) 0 0
\(45\) 218.348 + 376.449i 0.723320 + 1.24706i
\(46\) 0 0
\(47\) −87.3726 151.334i −0.271162 0.469666i 0.697998 0.716100i \(-0.254075\pi\)
−0.969160 + 0.246434i \(0.920741\pi\)
\(48\) 0 0
\(49\) −278.496 + 200.222i −0.811942 + 0.583739i
\(50\) 0 0
\(51\) −75.0068 + 130.216i −0.205942 + 0.357528i
\(52\) 0 0
\(53\) 235.715 + 136.090i 0.610905 + 0.352706i 0.773319 0.634017i \(-0.218595\pi\)
−0.162415 + 0.986723i \(0.551928\pi\)
\(54\) 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 \(-0.867419\pi\)
0.807626 + 0.589695i \(0.200752\pi\)
\(60\) 0 0
\(61\) −333.882 + 192.767i −0.700807 + 0.404611i −0.807648 0.589665i \(-0.799260\pi\)
0.106841 + 0.994276i \(0.465927\pi\)
\(62\) 0 0
\(63\) 154.287 + 475.650i 0.308544 + 0.951210i
\(64\) 0 0
\(65\) 103.411 59.7041i 0.197331 0.113929i
\(66\) 0 0
\(67\) −509.009 + 881.630i −0.928140 + 1.60759i −0.141708 + 0.989908i \(0.545259\pi\)
−0.786432 + 0.617677i \(0.788074\pi\)
\(68\) 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 0.648357 0.761337i \(-0.275456\pi\)
−0.335158 + 0.942162i \(0.608790\pi\)
\(74\) 0 0
\(75\) 349.599 606.924i 0.538243 0.934420i
\(76\) 0 0
\(77\) −138.686 + 644.550i −0.205256 + 0.953939i
\(78\) 0 0
\(79\) −532.154 921.718i −0.757874 1.31268i −0.943933 0.330138i \(-0.892905\pi\)
0.186059 0.982539i \(-0.440428\pi\)
\(80\) 0 0
\(81\) 728.994 2.91533i 0.999992 0.00399908i
\(82\) 0 0
\(83\) −601.040 −0.794852 −0.397426 0.917634i \(-0.630096\pi\)
−0.397426 + 0.917634i \(0.630096\pi\)
\(84\) 0 0
\(85\) 466.140 0.594824
\(86\) 0 0
\(87\) −0.354042 354.123i −0.000436290 0.436390i
\(88\) 0 0
\(89\) −752.606 1303.55i −0.896360 1.55254i −0.832112 0.554607i \(-0.812869\pi\)
−0.0642474 0.997934i \(-0.520465\pi\)
\(90\) 0 0
\(91\) 130.594 42.0725i 0.150439 0.0484658i
\(92\) 0 0
\(93\) −804.484 463.397i −0.897001 0.516689i
\(94\) 0 0
\(95\) −490.926 283.436i −0.530189 0.306105i
\(96\) 0 0
\(97\) 327.463i 0.342771i 0.985204 + 0.171386i \(0.0548244\pi\)
−0.985204 + 0.171386i \(0.945176\pi\)
\(98\) 0 0
\(99\) 833.358 + 478.920i 0.846017 + 0.486195i
\(100\) 0 0
\(101\) 547.845 948.895i 0.539729 0.934837i −0.459190 0.888338i \(-0.651860\pi\)
0.998918 0.0464990i \(-0.0148064\pi\)
\(102\) 0 0
\(103\) −179.848 + 103.835i −0.172048 + 0.0993318i −0.583551 0.812076i \(-0.698337\pi\)
0.411503 + 0.911408i \(0.365004\pi\)
\(104\) 0 0
\(105\) 1039.62 1151.15i 0.966254 1.06991i
\(106\) 0 0
\(107\) 1561.25 901.391i 1.41058 0.814399i 0.415138 0.909759i \(-0.363733\pi\)
0.995443 + 0.0953593i \(0.0304000\pi\)
\(108\) 0 0
\(109\) −141.825 + 245.647i −0.124627 + 0.215860i −0.921587 0.388172i \(-0.873107\pi\)
0.796960 + 0.604032i \(0.206440\pi\)
\(110\) 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
\(117\) −0.399957 200.024i −0.000316035 0.158053i
\(118\) 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
\(123\) 1922.93 1.92249i 1.40963 0.00140931i
\(124\) 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
\(129\) −972.033 + 0.971811i −0.663432 + 0.000663281i
\(130\) 0 0
\(131\) 314.185 + 544.184i 0.209545 + 0.362943i 0.951571 0.307428i \(-0.0994683\pi\)
−0.742026 + 0.670371i \(0.766135\pi\)
\(132\) 0 0
\(133\) −482.961 437.048i −0.314873 0.284939i
\(134\) 0 0
\(135\) −1136.52 1954.95i −0.724566 1.24634i
\(136\) 0 0
\(137\) −432.079 249.461i −0.269453 0.155569i 0.359186 0.933266i \(-0.383054\pi\)
−0.628639 + 0.777697i \(0.716388\pi\)
\(138\) 0 0
\(139\) 1216.65i 0.742410i 0.928551 + 0.371205i \(0.121055\pi\)
−0.928551 + 0.371205i \(0.878945\pi\)
\(140\) 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
\(147\) 1446.07 1041.83i 0.811358 0.584550i
\(148\) 0 0
\(149\) 2010.18 1160.58i 1.10524 0.638111i 0.167648 0.985847i \(-0.446383\pi\)
0.937592 + 0.347736i \(0.113050\pi\)
\(150\) 0 0
\(151\) 488.726 846.497i 0.263390 0.456205i −0.703750 0.710447i \(-0.748493\pi\)
0.967141 + 0.254242i \(0.0818260\pi\)
\(152\) 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 0.463018 0.886349i \(-0.346767\pi\)
−0.536092 + 0.844160i \(0.680100\pi\)
\(158\) 0 0
\(159\) −1225.52 705.920i −0.611257 0.352095i
\(160\) 0 0
\(161\) 761.145 + 688.786i 0.372588 + 0.337168i
\(162\) 0 0
\(163\) 488.511 + 846.127i 0.234743 + 0.406587i 0.959198 0.282735i \(-0.0912417\pi\)
−0.724455 + 0.689322i \(0.757908\pi\)
\(164\) 0 0
\(165\) −2.98081 2981.49i −0.00140640 1.40672i
\(166\) 0 0
\(167\) 1.00709 0.000466651 0.000233326 1.00000i \(-0.499926\pi\)
0.000233326 1.00000i \(0.499926\pi\)
\(168\) 0 0
\(169\) 2142.12 0.975019
\(170\) 0 0
\(171\) −821.414 + 476.436i −0.367340 + 0.213064i
\(172\) 0 0
\(173\) 1978.27 + 3426.47i 0.869395 + 1.50584i 0.862616 + 0.505860i \(0.168825\pi\)
0.00677983 + 0.999977i \(0.497842\pi\)
\(174\) 0 0
\(175\) −2440.57 525.130i −1.05423 0.226835i
\(176\) 0 0
\(177\) 251.242 436.170i 0.106692 0.185224i
\(178\) 0 0
\(179\) −2423.54 1399.23i −1.01198 0.584266i −0.100208 0.994967i \(-0.531951\pi\)
−0.911770 + 0.410701i \(0.865284\pi\)
\(180\) 0 0
\(181\) 1506.74i 0.618758i 0.950939 + 0.309379i \(0.100121\pi\)
−0.950939 + 0.309379i \(0.899879\pi\)
\(182\) 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
\(189\) −804.168 2470.75i −0.309495 0.950901i
\(190\) 0 0
\(191\) 3184.51 1838.58i 1.20640 0.696518i 0.244433 0.969666i \(-0.421398\pi\)
0.961972 + 0.273148i \(0.0880650\pi\)
\(192\) 0 0
\(193\) 64.7335 112.122i 0.0241431 0.0418171i −0.853701 0.520763i \(-0.825648\pi\)
0.877845 + 0.478946i \(0.158981\pi\)
\(194\) 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 −0.264488 0.964389i \(-0.585203\pi\)
−0.967429 + 0.253141i \(0.918536\pi\)
\(200\) 0 0
\(201\) 2640.31 4583.73i 0.926532 1.60851i
\(202\) 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
\(207\) 1294.55 750.862i 0.434672 0.252118i
\(208\) 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
\(213\) 0.651100 + 651.249i 0.000209449 + 0.209497i
\(214\) 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
\(219\) −1015.63 585.022i −0.313379 0.180512i
\(220\) 0 0
\(221\) −185.546 107.125i −0.0564759 0.0326064i
\(222\) 0 0
\(223\) 4851.53i 1.45687i 0.685114 + 0.728436i \(0.259753\pi\)
−0.685114 + 0.728436i \(0.740247\pi\)
\(224\) 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 \(-0.945863\pi\)
0.639368 + 0.768901i \(0.279196\pi\)
\(228\) 0 0
\(229\) −3737.27 + 2157.72i −1.07845 + 0.622646i −0.930479 0.366345i \(-0.880609\pi\)
−0.147975 + 0.988991i \(0.547276\pi\)
\(230\) 0 0
\(231\) 717.285 3349.90i 0.204303 0.954144i
\(232\) 0 0
\(233\) 4826.98 2786.86i 1.35719 0.783576i 0.367949 0.929846i \(-0.380060\pi\)
0.989245 + 0.146270i \(0.0467267\pi\)
\(234\) 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 0.224613 0.974448i \(-0.427888\pi\)
−0.731590 + 0.681745i \(0.761222\pi\)
\(242\) 0 0
\(243\) −3787.95 + 18.9356i −0.999988 + 0.00499884i
\(244\) 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
\(249\) 3123.09 3.12238i 0.794851 0.000794670i
\(250\) 0 0
\(251\) 2240.70 0.563473 0.281736 0.959492i \(-0.409090\pi\)
0.281736 + 0.959492i \(0.409090\pi\)
\(252\) 0 0
\(253\) 1973.16 0.490323
\(254\) 0 0
\(255\) −2422.13 + 2.42158i −0.594823 + 0.000594688i
\(256\) 0 0
\(257\) 555.785 + 962.648i 0.134898 + 0.233651i 0.925559 0.378604i \(-0.123596\pi\)
−0.790660 + 0.612255i \(0.790263\pi\)
\(258\) 0 0
\(259\) −2903.85 + 3208.90i −0.696665 + 0.769851i
\(260\) 0 0
\(261\) 3.67931 + 1840.07i 0.000872580 + 0.436389i
\(262\) 0 0
\(263\) 1782.86 + 1029.34i 0.418007 + 0.241337i 0.694224 0.719759i \(-0.255748\pi\)
−0.276217 + 0.961095i \(0.589081\pi\)
\(264\) 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 −0.451165 0.892441i \(-0.648991\pi\)
0.998459 0.0554999i \(-0.0176752\pi\)
\(270\) 0 0
\(271\) 191.772 110.720i 0.0429865 0.0248183i −0.478353 0.878168i \(-0.658766\pi\)
0.521339 + 0.853350i \(0.325433\pi\)
\(272\) 0 0
\(273\) −678.368 + 219.293i −0.150391 + 0.0486162i
\(274\) 0 0
\(275\) −4155.65 + 2399.27i −0.911255 + 0.526113i
\(276\) 0 0
\(277\) −1233.58 + 2136.62i −0.267576 + 0.463455i −0.968235 0.250041i \(-0.919556\pi\)
0.700660 + 0.713496i \(0.252889\pi\)
\(278\) 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 0.956531 0.291630i \(-0.0941977\pi\)
0.225706 + 0.974195i \(0.427531\pi\)
\(284\) 0 0
\(285\) 2552.40 + 1470.23i 0.530494 + 0.305574i
\(286\) 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
\(291\) −1.70116 1701.55i −0.000342693 0.342771i
\(292\) 0 0
\(293\) −5637.32 −1.12401 −0.562007 0.827133i \(-0.689970\pi\)
−0.562007 + 0.827133i \(0.689970\pi\)
\(294\) 0 0
\(295\) −1561.38 −0.308159
\(296\) 0 0
\(297\) −4332.74 2484.21i −0.846503 0.485349i
\(298\) 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
\(303\) −2841.75 + 4933.45i −0.538794 + 0.935376i
\(304\) 0 0
\(305\) −5381.56 3107.05i −1.01032 0.583308i
\(306\) 0 0
\(307\) 3442.95i 0.640064i 0.947407 + 0.320032i \(0.103694\pi\)
−0.947407 + 0.320032i \(0.896306\pi\)
\(308\) 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 \(-0.837729\pi\)
0.859039 + 0.511911i \(0.171062\pi\)
\(312\) 0 0
\(313\) 8335.31 4812.40i 1.50524 0.869050i 0.505257 0.862969i \(-0.331398\pi\)
0.999982 0.00608123i \(-0.00193573\pi\)
\(314\) 0 0
\(315\) −5396.05 + 5986.94i −0.965184 + 1.07087i
\(316\) 0 0
\(317\) −7866.93 + 4541.98i −1.39385 + 0.804741i −0.993739 0.111726i \(-0.964362\pi\)
−0.400112 + 0.916466i \(0.631029\pi\)
\(318\) 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
\(327\) 735.666 1277.16i 0.124411 0.215985i
\(328\) 0 0
\(329\) 2171.52 2399.65i 0.363890 0.402118i
\(330\) 0 0
\(331\) −702.788 1217.26i −0.116703 0.202136i 0.801756 0.597651i \(-0.203899\pi\)
−0.918459 + 0.395516i \(0.870566\pi\)
\(332\) 0 0
\(333\) 3165.55 + 5457.66i 0.520934 + 0.898132i
\(334\) 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
\(339\) −5.38923 5390.46i −0.000863430 0.863627i
\(340\) 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
\(345\) −4022.57 2317.07i −0.627732 0.361585i
\(346\) 0 0
\(347\) 2268.41 + 1309.67i 0.350935 + 0.202612i 0.665097 0.746757i \(-0.268390\pi\)
−0.314162 + 0.949369i \(0.601724\pi\)
\(348\) 0 0
\(349\) 6032.33i 0.925224i −0.886561 0.462612i \(-0.846912\pi\)
0.886561 0.462612i \(-0.153088\pi\)
\(350\) 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 \(-0.702069\pi\)
0.993822 + 0.110990i \(0.0354020\pi\)
\(354\) 0 0
\(355\) 1749.49 1010.07i 0.261558 0.151011i
\(356\) 0 0
\(357\) −2721.43 582.715i −0.403454 0.0863881i
\(358\) 0 0
\(359\) 1612.51 930.982i 0.237061 0.136867i −0.376764 0.926309i \(-0.622963\pi\)
0.613825 + 0.789442i \(0.289630\pi\)
\(360\) 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 0.614426 0.788975i \(-0.289388\pi\)
−0.376059 + 0.926596i \(0.622721\pi\)
\(368\) 0 0
\(369\) −9991.81 + 19.9791i −1.40963 + 0.00281862i
\(370\) 0 0
\(371\) −1060.36 + 4928.06i −0.148385 + 0.689629i
\(372\) 0 0
\(373\) −3871.04 6704.83i −0.537359 0.930732i −0.999045 0.0436892i \(-0.986089\pi\)
0.461687 0.887043i \(-0.347244\pi\)
\(374\) 0 0
\(375\) 820.284 0.820097i 0.112958 0.000112932i
\(376\) 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
\(381\) 8551.86 8.54991i 1.14994 0.00114967i
\(382\) 0 0
\(383\) 3546.73 + 6143.12i 0.473184 + 0.819578i 0.999529 0.0306926i \(-0.00977131\pi\)
−0.526345 + 0.850271i \(0.676438\pi\)
\(384\) 0 0
\(385\) −10114.8 + 3258.60i −1.33895 + 0.431359i
\(386\) 0 0
\(387\) 5050.82 10.0994i 0.663431 0.00132656i
\(388\) 0 0
\(389\) 6173.12 + 3564.05i 0.804601 + 0.464537i 0.845077 0.534644i \(-0.179554\pi\)
−0.0404765 + 0.999180i \(0.512888\pi\)
\(390\) 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 0.0765855 0.997063i \(-0.475598\pi\)
0.901775 + 0.432206i \(0.142265\pi\)
\(398\) 0 0
\(399\) 2511.81 + 2268.46i 0.315157 + 0.284624i
\(400\) 0 0
\(401\) 7719.60 4456.91i 0.961343 0.555032i 0.0647568 0.997901i \(-0.479373\pi\)
0.896586 + 0.442869i \(0.146039\pi\)
\(402\) 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 0.329163 0.944273i \(-0.393233\pi\)
−0.653183 + 0.757200i \(0.726567\pi\)
\(410\) 0 0
\(411\) 2246.44 + 1293.99i 0.269608 + 0.155299i
\(412\) 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
\(417\) −6.32046 6321.90i −0.000742240 0.742409i
\(418\) 0 0
\(419\) 7234.25 0.843476 0.421738 0.906718i \(-0.361420\pi\)
0.421738 + 0.906718i \(0.361420\pi\)
\(420\) 0 0
\(421\) 406.124 0.0470148 0.0235074 0.999724i \(-0.492517\pi\)
0.0235074 + 0.999724i \(0.492517\pi\)
\(422\) 0 0
\(423\) −2367.23 4081.29i −0.272101 0.469123i
\(424\) 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
\(429\) −683.999 + 1187.46i −0.0769785 + 0.133639i
\(430\) 0 0
\(431\) 10590.4 + 6114.37i 1.18358 + 0.683338i 0.956839 0.290618i \(-0.0938609\pi\)
0.226737 + 0.973956i \(0.427194\pi\)
\(432\) 0 0
\(433\) 3252.79i 0.361014i −0.983574 0.180507i \(-0.942226\pi\)
0.983574 0.180507i \(-0.0577738\pi\)
\(434\) 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 0.421278 0.906932i \(-0.361582\pi\)
0.996065 + 0.0886287i \(0.0282485\pi\)
\(440\) 0 0
\(441\) −7508.57 + 5421.03i −0.810773 + 0.585361i
\(442\) 0 0
\(443\) 204.373 117.995i 0.0219189 0.0126549i −0.489001 0.872283i \(-0.662638\pi\)
0.510919 + 0.859629i \(0.329305\pi\)
\(444\) 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
\(453\) −2535.09 + 4401.07i −0.262934 + 0.456468i
\(454\) 0 0
\(455\) 1639.74 + 1483.86i 0.168950 + 0.152889i
\(456\) 0 0
\(457\) −153.883 266.533i −0.0157513 0.0272821i 0.858042 0.513579i \(-0.171681\pi\)
−0.873794 + 0.486297i \(0.838347\pi\)
\(458\) 0 0
\(459\) −2018.15 + 3519.88i −0.205227 + 0.357939i
\(460\) 0 0
\(461\) 4752.26 0.480119 0.240060 0.970758i \(-0.422833\pi\)
0.240060 + 0.970758i \(0.422833\pi\)
\(462\) 0 0
\(463\) 9529.43 0.956523 0.478261 0.878218i \(-0.341267\pi\)
0.478261 + 0.878218i \(0.341267\pi\)
\(464\) 0 0
\(465\) −14.9607 14964.1i −0.00149201 1.49235i
\(466\) 0 0
\(467\) −3269.28 5662.56i −0.323949 0.561097i 0.657350 0.753586i \(-0.271677\pi\)
−0.981299 + 0.192489i \(0.938344\pi\)
\(468\) 0 0
\(469\) −18432.1 3965.99i −1.81475 0.390474i
\(470\) 0 0
\(471\) 747.386 + 430.508i 0.0731162 + 0.0421162i
\(472\) 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 \(-0.719447\pi\)
0.986284 + 0.165057i \(0.0527807\pi\)
\(480\) 0 0
\(481\) 1499.22 865.574i 0.142117 0.0820515i
\(482\) 0 0
\(483\) −3958.60 3575.08i −0.372925 0.336795i
\(484\) 0 0
\(485\) −4570.96 + 2639.05i −0.427952 + 0.247078i
\(486\) 0 0
\(487\) 3508.78 6077.39i 0.326485 0.565489i −0.655327 0.755345i \(-0.727469\pi\)
0.981812 + 0.189857i \(0.0608024\pi\)
\(488\) 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
\(495\) 30.9775 + 15492.3i 0.00281280 + 1.40672i
\(496\) 0 0
\(497\) 2209.38 711.777i 0.199405 0.0642406i
\(498\) 0 0
\(499\) −10396.1 18006.6i −0.932651 1.61540i −0.778770 0.627309i \(-0.784156\pi\)
−0.153881 0.988089i \(-0.549177\pi\)
\(500\) 0 0
\(501\) −5.23298 + 0.00523178i −0.000466651 + 4.66545e-7i
\(502\) 0 0
\(503\) −7341.52 −0.650780 −0.325390 0.945580i \(-0.605496\pi\)
−0.325390 + 0.945580i \(0.605496\pi\)
\(504\) 0 0
\(505\) 17660.5 1.55620
\(506\) 0 0
\(507\) −11130.8 + 11.1282i −0.975019 + 0.000974796i
\(508\) 0 0
\(509\) −9956.11 17244.5i −0.866988 1.50167i −0.865060 0.501669i \(-0.832720\pi\)
−0.00192778 0.999998i \(-0.500614\pi\)
\(510\) 0 0
\(511\) −878.757 + 4084.07i −0.0760742 + 0.353559i
\(512\) 0 0
\(513\) 4265.72 2479.90i 0.367127 0.213431i
\(514\) 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 \(-0.935335\pi\)
0.664444 + 0.747338i \(0.268668\pi\)
\(522\) 0 0
\(523\) −249.515 + 144.058i −0.0208614 + 0.0120444i −0.510394 0.859940i \(-0.670501\pi\)
0.489533 + 0.871985i \(0.337167\pi\)
\(524\) 0 0
\(525\) 12684.3 + 2715.97i 1.05445 + 0.225781i
\(526\) 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
\(537\) 12600.4 + 7258.03i 1.01256 + 0.583254i
\(538\) 0 0
\(539\) −12149.8 + 1215.69i −0.970923 + 0.0971496i
\(540\) 0 0
\(541\) −7400.87 12818.7i −0.588149 1.01870i −0.994475 0.104975i \(-0.966524\pi\)
0.406326 0.913728i \(-0.366810\pi\)
\(542\) 0 0
\(543\) −7.82747 7829.25i −0.000618616 0.618758i
\(544\) 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
\(549\) −9004.40 + 5222.73i −0.699997 + 0.406012i
\(550\) 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
\(555\) 9768.51 16958.7i 0.747117 1.29704i
\(556\) 0 0
\(557\) 14891.1 + 8597.36i 1.13277 + 0.654007i 0.944631 0.328135i \(-0.106420\pi\)
0.188142 + 0.982142i \(0.439754\pi\)
\(558\) 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 0.258038 + 0.966135i \(0.416924\pi\)
−0.965716 + 0.259600i \(0.916409\pi\)
\(564\) 0 0
\(565\) −14480.7 + 8360.43i −1.07824 + 0.622524i
\(566\) 0 0
\(567\) 4191.41 + 12834.2i 0.310446 + 0.950591i
\(568\) 0 0
\(569\) −6255.57 + 3611.66i −0.460891 + 0.266096i −0.712419 0.701754i \(-0.752400\pi\)
0.251528 + 0.967850i \(0.419067\pi\)
\(570\) 0 0
\(571\) −4965.17 + 8599.93i −0.363898 + 0.630290i −0.988599 0.150574i \(-0.951888\pi\)
0.624700 + 0.780865i \(0.285221\pi\)
\(572\) 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 0.738320 0.674451i \(-0.235620\pi\)
−0.214932 + 0.976629i \(0.568953\pi\)
\(578\) 0 0
\(579\) −335.782 + 582.937i −0.0241013 + 0.0418412i
\(580\) 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
\(585\) 2788.85 1617.59i 0.197102 0.114323i
\(586\) 0 0
\(587\) 21277.2 1.49609 0.748043 0.663650i \(-0.230994\pi\)
0.748043 + 0.663650i \(0.230994\pi\)
\(588\) 0 0
\(589\) −6283.84 −0.439594
\(590\) 0 0
\(591\) 15.8177 + 15821.3i 0.00110093 + 1.10118i
\(592\) 0 0
\(593\) −1424.49 2467.29i −0.0986454 0.170859i 0.812479 0.582991i \(-0.198118\pi\)
−0.911124 + 0.412132i \(0.864784\pi\)
\(594\) 0 0
\(595\) 2647.25 + 8217.14i 0.182398 + 0.566168i
\(596\) 0 0
\(597\) 17980.2 + 10356.9i 1.23263 + 0.710016i
\(598\) 0 0
\(599\) −3844.40 2219.57i −0.262234 0.151401i 0.363119 0.931743i \(-0.381712\pi\)
−0.625353 + 0.780342i \(0.715045\pi\)
\(600\) 0 0
\(601\) 7868.29i 0.534033i 0.963692 + 0.267017i \(0.0860379\pi\)
−0.963692 + 0.267017i \(0.913962\pi\)
\(602\) 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 0.100724 0.994914i \(-0.467884\pi\)
0.911983 + 0.410228i \(0.134551\pi\)
\(608\) 0 0
\(609\) 6240.48 2017.33i 0.415233 0.134231i
\(610\) 0 0
\(611\) −1121.13 + 647.284i −0.0742324 + 0.0428581i
\(612\) 0 0
\(613\) −6422.07 + 11123.3i −0.423140 + 0.732900i −0.996245 0.0865820i \(-0.972406\pi\)
0.573105 + 0.819482i \(0.305739\pi\)
\(614\) 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 −0.144202 0.989548i \(-0.546062\pi\)
−0.929075 + 0.369891i \(0.879395\pi\)
\(620\) 0 0
\(621\) −6722.75 + 3908.32i −0.434420 + 0.252553i
\(622\) 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
\(627\) 6505.63 6.50415i 0.414370 0.000414275i
\(628\) 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
\(633\) −22778.2 + 22.7730i −1.43026 + 0.00142993i
\(634\) 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
\(639\) −6.76643 3383.98i −0.000418898 0.209497i
\(640\) 0 0
\(641\) −18742.7 10821.1i −1.15490 0.666784i −0.204827 0.978798i \(-0.565663\pi\)
−0.950078 + 0.312014i \(0.898996\pi\)
\(642\) 0 0
\(643\) 19867.3i 1.21849i −0.792982 0.609246i \(-0.791472\pi\)
0.792982 0.609246i \(-0.208528\pi\)
\(644\) 0 0
\(645\) −7847.24 13560.5i −0.479046 0.827820i
\(646\) 0 0
\(647\) −11212.2 + 19420.1i −0.681294 + 1.18004i 0.293293 + 0.956023i \(0.405249\pi\)
−0.974586 + 0.224012i \(0.928084\pi\)
\(648\) 0 0
\(649\) −2986.49 + 1724.25i −0.180632 + 0.104288i
\(650\) 0 0
\(651\) 3600.05 16813.2i 0.216739 1.01223i
\(652\) 0 0
\(653\) 17358.5 10021.9i 1.04026 0.600594i 0.120353 0.992731i \(-0.461597\pi\)
0.919907 + 0.392137i \(0.128264\pi\)
\(654\) 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 0.728076 0.685496i \(-0.240415\pi\)
−0.229619 + 0.973281i \(0.573748\pi\)
\(662\) 0 0
\(663\) 964.682 + 555.674i 0.0565085 + 0.0325499i
\(664\) 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
\(669\) −25.2035 25209.3i −0.00145654 1.45687i
\(670\) 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
\(675\) 9406.39 16405.8i 0.536373 0.935494i
\(676\) 0 0
\(677\) −13521.0 23419.1i −0.767584 1.32949i −0.938870 0.344273i \(-0.888125\pi\)
0.171286 0.985221i \(-0.445208\pi\)
\(678\) 0 0
\(679\) −5772.53 + 1859.69i −0.326258 + 0.105108i
\(680\) 0 0
\(681\) 6141.85 10662.6i 0.345604 0.599988i
\(682\) 0 0
\(683\) −11596.9 6695.45i −0.649694 0.375101i 0.138645 0.990342i \(-0.455725\pi\)
−0.788339 + 0.615241i \(0.789059\pi\)
\(684\) 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 −0.999676 0.0254396i \(-0.991901\pi\)
−0.477807 + 0.878465i \(0.658568\pi\)
\(692\) 0 0
\(693\) −3709.72 + 17410.3i −0.203348 + 0.954348i
\(694\) 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
\(705\) −7304.98 + 12681.9i −0.390243 + 0.677485i
\(706\) 0 0
\(707\) 19838.4 + 4268.57i 1.05530 + 0.227067i
\(708\) 0 0
\(709\) −7965.19 13796.1i −0.421917 0.730781i 0.574210 0.818708i \(-0.305309\pi\)
−0.996127 + 0.0879267i \(0.971976\pi\)
\(710\) 0 0
\(711\) −14417.9 24857.6i −0.760497 1.31116i
\(712\) 0 0
\(713\) 9903.30 0.520171
\(714\) 0 0
\(715\) 4250.81 0.222337
\(716\) 0 0
\(717\) 24.3316 + 24337.2i 0.00126734 + 1.26763i
\(718\) 0 0
\(719\) 5938.87 + 10286.4i 0.308042 + 0.533545i 0.977934 0.208914i \(-0.0669928\pi\)
−0.669892 + 0.742459i \(0.733659\pi\)
\(720\) 0 0
\(721\) −2851.78 2580.67i −0.147303 0.133300i
\(722\) 0 0
\(723\) 9861.57 + 5680.44i 0.507270 + 0.292196i
\(724\) 0 0
\(725\) −7955.61 4593.18i −0.407537 0.235291i
\(726\) 0 0
\(727\) 16795.8i 0.856839i 0.903580 + 0.428419i \(0.140929\pi\)
−0.903580 + 0.428419i \(0.859071\pi\)
\(728\) 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 0.171926 0.985110i \(-0.445001\pi\)
0.939093 + 0.343663i \(0.111668\pi\)
\(734\) 0 0
\(735\) 26196.6 + 11789.0i 1.31466 + 0.591626i
\(736\) 0 0
\(737\) −31385.1 + 18120.2i −1.56864 + 0.905653i
\(738\) 0 0
\(739\) −9319.48 + 16141.8i −0.463901 + 0.803499i −0.999151 0.0411940i \(-0.986884\pi\)
0.535251 + 0.844693i \(0.320217\pi\)
\(740\) 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
\(747\) −16228.0 + 32.4487i −0.794850 + 0.00158934i
\(748\) 0 0
\(749\) 24756.3 + 22402.8i 1.20771 + 1.09290i
\(750\) 0 0
\(751\) 8115.13 + 14055.8i 0.394308 + 0.682961i 0.993013 0.118009i \(-0.0376510\pi\)
−0.598705 + 0.800970i \(0.704318\pi\)
\(752\) 0 0
\(753\) −11643.0 + 11.6404i −0.563473 + 0.000563344i
\(754\) 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
\(759\) −10252.8 + 10.2505i −0.490322 + 0.000490211i
\(760\) 0 0
\(761\) 5394.02 + 9342.71i 0.256942 + 0.445037i 0.965421 0.260695i \(-0.0839517\pi\)
−0.708479 + 0.705732i \(0.750618\pi\)
\(762\) 0 0
\(763\) −5135.72 1105.04i −0.243677 0.0524313i
\(764\) 0 0
\(765\) 12585.8 25.1658i 0.594822 0.00118937i
\(766\) 0 0
\(767\) 621.503 + 358.825i 0.0292584 + 0.0168923i
\(768\) 0 0
\(769\) 35799.6i 1.67876i 0.543543 + 0.839381i \(0.317082\pi\)
−0.543543 + 0.839381i \(0.682918\pi\)
\(770\) 0 0
\(771\) −2892.94 4999.17i −0.135132 0.233516i
\(772\) 0 0
\(773\) −18306.3 + 31707.5i −0.851788 + 1.47534i 0.0278053 + 0.999613i \(0.491148\pi\)
−0.879593 + 0.475727i \(0.842185\pi\)
\(774\) 0 0
\(775\) −20857.2 + 12041.9i −0.966727 + 0.558140i
\(776\) 0 0
\(777\) 15072.2 16689.0i 0.695895 0.770548i
\(778\) 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 0.994913 + 0.100742i \(0.0321216\pi\)
0.584701 + 0.811249i \(0.301212\pi\)
\(788\) 0 0
\(789\) −9269.36 5339.32i −0.418248