Properties

Label 2646.2.h.f.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.f.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +3.00000 q^{11} +(2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(2.50000 - 4.33013i) q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +3.00000 q^{23} +4.00000 q^{25} +(-2.50000 + 4.33013i) q^{26} +(-1.50000 + 2.59808i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{34} +(3.50000 - 6.06218i) q^{37} +5.00000 q^{38} +3.00000 q^{40} +(4.50000 + 7.79423i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.50000 + 2.59808i) q^{46} +(2.00000 + 3.46410i) q^{50} -5.00000 q^{52} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} -3.00000 q^{58} +(-6.00000 + 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-7.50000 - 12.9904i) q^{65} +(2.00000 - 3.46410i) q^{67} +3.00000 q^{68} +(5.50000 + 9.52628i) q^{73} +7.00000 q^{74} +(2.50000 + 4.33013i) q^{76} +(-4.00000 - 6.92820i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} -11.0000 q^{86} -3.00000 q^{88} +(-7.50000 + 12.9904i) q^{89} +(-1.50000 + 2.59808i) q^{92} +(-7.50000 + 12.9904i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - 6 q^{5} - 2 q^{8} + O(q^{10}) \) \( 2 q + q^{2} - q^{4} - 6 q^{5} - 2 q^{8} - 3 q^{10} + 6 q^{11} + 5 q^{13} - q^{16} - 3 q^{17} + 5 q^{19} + 3 q^{20} + 3 q^{22} + 6 q^{23} + 8 q^{25} - 5 q^{26} - 3 q^{29} - 4 q^{31} + q^{32} + 3 q^{34} + 7 q^{37} + 10 q^{38} + 6 q^{40} + 9 q^{41} - 11 q^{43} - 3 q^{44} + 3 q^{46} + 4 q^{50} - 10 q^{52} - 3 q^{53} - 18 q^{55} - 6 q^{58} - 12 q^{59} + 2 q^{61} - 8 q^{62} + 2 q^{64} - 15 q^{65} + 4 q^{67} + 6 q^{68} + 11 q^{73} + 14 q^{74} + 5 q^{76} - 8 q^{79} + 3 q^{80} - 9 q^{82} - 3 q^{83} + 9 q^{85} - 22 q^{86} - 6 q^{88} - 15 q^{89} - 3 q^{92} - 15 q^{95} - q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −2.50000 + 4.33013i −0.490290 + 0.849208i
\(27\) 0 0
\(28\) 0 0
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.50000 2.59808i 0.257248 0.445566i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 5.00000 0.811107
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i \(0.483375\pi\)
−0.890947 + 0.454108i \(0.849958\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 0 0
\(52\) −5.00000 −0.693375
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) 0 0
\(58\) −3.00000 −0.393919
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −7.50000 12.9904i −0.930261 1.61126i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) 7.00000 0.813733
\(75\) 0 0
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) 0 0
\(82\) −4.50000 + 7.79423i −0.496942 + 0.860729i
\(83\) −1.50000 + 2.59808i −0.164646 + 0.285176i −0.936530 0.350588i \(-0.885982\pi\)
0.771883 + 0.635764i \(0.219315\pi\)
\(84\) 0 0
\(85\) 4.50000 + 7.79423i 0.488094 + 0.845403i
\(86\) −11.0000 −1.18616
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.50000 + 2.59808i −0.156386 + 0.270868i
\(93\) 0 0
\(94\) 0 0
\(95\) −7.50000 + 12.9904i −0.769484 + 1.33278i
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 0 0
\(103\) −5.00000 −0.492665 −0.246332 0.969185i \(-0.579225\pi\)
−0.246332 + 0.969185i \(0.579225\pi\)
\(104\) −2.50000 4.33013i −0.245145 0.424604i
\(105\) 0 0
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) −7.50000 + 12.9904i −0.725052 + 1.25583i 0.233900 + 0.972261i \(0.424851\pi\)
−0.958952 + 0.283567i \(0.908482\pi\)
\(108\) 0 0
\(109\) 3.50000 + 6.06218i 0.335239 + 0.580651i 0.983531 0.180741i \(-0.0578495\pi\)
−0.648292 + 0.761392i \(0.724516\pi\)
\(110\) −4.50000 7.79423i −0.429058 0.743151i
\(111\) 0 0
\(112\) 0 0
\(113\) 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) 0 0
\(115\) −9.00000 −0.839254
\(116\) −1.50000 2.59808i −0.139272 0.241225i
\(117\) 0 0
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −1.00000 + 1.73205i −0.0905357 + 0.156813i
\(123\) 0 0
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 7.50000 12.9904i 0.657794 1.13933i
\(131\) 3.00000 0.262111 0.131056 0.991375i \(-0.458163\pi\)
0.131056 + 0.991375i \(0.458163\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7.50000 + 12.9904i 0.627182 + 1.08631i
\(144\) 0 0
\(145\) 4.50000 7.79423i 0.373705 0.647275i
\(146\) −5.50000 + 9.52628i −0.455183 + 0.788400i
\(147\) 0 0
\(148\) 3.50000 + 6.06218i 0.287698 + 0.498308i
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0 0
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) 0 0
\(154\) 0 0
\(155\) 6.00000 10.3923i 0.481932 0.834730i
\(156\) 0 0
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) 4.00000 6.92820i 0.318223 0.551178i
\(159\) 0 0
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i \(0.398564\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) −9.00000 −0.702782
\(165\) 0 0
\(166\) −3.00000 −0.232845
\(167\) −1.50000 2.59808i −0.116073 0.201045i 0.802135 0.597143i \(-0.203697\pi\)
−0.918208 + 0.396098i \(0.870364\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) −4.50000 + 7.79423i −0.345134 + 0.597790i
\(171\) 0 0
\(172\) −5.50000 9.52628i −0.419371 0.726372i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) −15.0000 −1.12430
\(179\) 1.50000 + 2.59808i 0.112115 + 0.194189i 0.916623 0.399753i \(-0.130904\pi\)
−0.804508 + 0.593942i \(0.797571\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.00000 −0.221163
\(185\) −10.5000 + 18.1865i −0.771975 + 1.33710i
\(186\) 0 0
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 0 0
\(189\) 0 0
\(190\) −15.0000 −1.08821
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −3.50000 6.06218i −0.248108 0.429736i 0.714893 0.699234i \(-0.246476\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(200\) −4.00000 −0.282843
\(201\) 0 0
\(202\) −1.50000 2.59808i −0.105540 0.182800i
\(203\) 0 0
\(204\) 0 0
\(205\) −13.5000 23.3827i −0.942881 1.63312i
\(206\) −2.50000 4.33013i −0.174183 0.301694i
\(207\) 0 0
\(208\) 2.50000 4.33013i 0.173344 0.300240i
\(209\) 7.50000 12.9904i 0.518786 0.898563i
\(210\) 0 0
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) 3.00000 0.206041
\(213\) 0 0
\(214\) −15.0000 −1.02538
\(215\) 16.5000 28.5788i 1.12529 1.94906i
\(216\) 0 0
\(217\) 0 0
\(218\) −3.50000 + 6.06218i −0.237050 + 0.410582i
\(219\) 0 0
\(220\) 4.50000 7.79423i 0.303390 0.525487i
\(221\) 7.50000 12.9904i 0.504505 0.873828i
\(222\) 0 0
\(223\) 8.50000 14.7224i 0.569202 0.985887i −0.427443 0.904042i \(-0.640586\pi\)
0.996645 0.0818447i \(-0.0260811\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.50000 + 12.9904i −0.498893 + 0.864107i
\(227\) 9.00000 0.597351 0.298675 0.954355i \(-0.403455\pi\)
0.298675 + 0.954355i \(0.403455\pi\)
\(228\) 0 0
\(229\) −17.0000 −1.12339 −0.561696 0.827344i \(-0.689851\pi\)
−0.561696 + 0.827344i \(0.689851\pi\)
\(230\) −4.50000 7.79423i −0.296721 0.513936i
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) 13.5000 23.3827i 0.884414 1.53185i 0.0380310 0.999277i \(-0.487891\pi\)
0.846383 0.532574i \(-0.178775\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 0 0
\(238\) 0 0
\(239\) 13.5000 + 23.3827i 0.873242 + 1.51250i 0.858623 + 0.512607i \(0.171320\pi\)
0.0146191 + 0.999893i \(0.495346\pi\)
\(240\) 0 0
\(241\) −23.0000 −1.48156 −0.740780 0.671748i \(-0.765544\pi\)
−0.740780 + 0.671748i \(0.765544\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0 0
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 0 0
\(247\) 25.0000 1.59071
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) 0 0
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) −8.00000 13.8564i −0.501965 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.0000 0.935674 0.467837 0.883815i \(-0.345033\pi\)
0.467837 + 0.883815i \(0.345033\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 15.0000 0.930261
\(261\) 0 0
\(262\) 1.50000 + 2.59808i 0.0926703 + 0.160510i
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) 0 0
\(265\) 4.50000 + 7.79423i 0.276433 + 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −10.5000 18.1865i −0.640196 1.10885i −0.985389 0.170321i \(-0.945520\pi\)
0.345192 0.938532i \(-0.387814\pi\)
\(270\) 0 0
\(271\) −6.50000 + 11.2583i −0.394847 + 0.683895i −0.993082 0.117426i \(-0.962536\pi\)
0.598235 + 0.801321i \(0.295869\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) −1.50000 2.59808i −0.0906183 0.156956i
\(275\) 12.0000 0.723627
\(276\) 0 0
\(277\) −7.00000 −0.420589 −0.210295 0.977638i \(-0.567442\pi\)
−0.210295 + 0.977638i \(0.567442\pi\)
\(278\) −2.50000 + 4.33013i −0.149940 + 0.259704i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.50000 2.59808i 0.0894825 0.154988i −0.817810 0.575488i \(-0.804812\pi\)
0.907293 + 0.420500i \(0.138145\pi\)
\(282\) 0 0
\(283\) 4.00000 6.92820i 0.237775 0.411839i −0.722300 0.691580i \(-0.756915\pi\)
0.960076 + 0.279741i \(0.0902485\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −7.50000 + 12.9904i −0.443484 + 0.768137i
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 9.00000 0.528498
\(291\) 0 0
\(292\) −11.0000 −0.643726
\(293\) 13.5000 + 23.3827i 0.788678 + 1.36603i 0.926777 + 0.375613i \(0.122568\pi\)
−0.138098 + 0.990419i \(0.544099\pi\)
\(294\) 0 0
\(295\) 18.0000 31.1769i 1.04800 1.81519i
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) 0 0
\(298\) 1.50000 + 2.59808i 0.0868927 + 0.150503i
\(299\) 7.50000 + 12.9904i 0.433736 + 0.751253i
\(300\) 0 0
\(301\) 0 0
\(302\) 5.50000 + 9.52628i 0.316489 + 0.548176i
\(303\) 0 0
\(304\) −5.00000 −0.286770
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 12.0000 0.681554
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i \(-0.0371814\pi\)
−0.597522 + 0.801852i \(0.703848\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 15.0000 + 25.9808i 0.842484 + 1.45922i 0.887788 + 0.460252i \(0.152241\pi\)
−0.0453045 + 0.998973i \(0.514426\pi\)
\(318\) 0 0
\(319\) −4.50000 + 7.79423i −0.251952 + 0.436393i
\(320\) −3.00000 −0.167705
\(321\) 0 0
\(322\) 0 0
\(323\) −15.0000 −0.834622
\(324\) 0 0
\(325\) 10.0000 + 17.3205i 0.554700 + 0.960769i
\(326\) −17.0000 −0.941543
\(327\) 0 0
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) −1.50000 2.59808i −0.0823232 0.142588i
\(333\) 0 0
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) −6.00000 + 10.3923i −0.327815 + 0.567792i
\(336\) 0 0
\(337\) 12.5000 + 21.6506i 0.680918 + 1.17939i 0.974701 + 0.223513i \(0.0717525\pi\)
−0.293783 + 0.955872i \(0.594914\pi\)
\(338\) −12.0000 −0.652714
\(339\) 0 0
\(340\) −9.00000 −0.488094
\(341\) −6.00000 + 10.3923i −0.324918 + 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) 5.50000 9.52628i 0.296540 0.513623i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −9.00000 −0.479022 −0.239511 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.50000 12.9904i −0.397499 0.688489i
\(357\) 0 0
\(358\) −1.50000 + 2.59808i −0.0792775 + 0.137313i
\(359\) 7.50000 12.9904i 0.395835 0.685606i −0.597372 0.801964i \(-0.703789\pi\)
0.993207 + 0.116358i \(0.0371219\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 0 0
\(364\) 0 0
\(365\) −16.5000 28.5788i −0.863649 1.49588i
\(366\) 0 0
\(367\) 1.00000 0.0521996 0.0260998 0.999659i \(-0.491691\pi\)
0.0260998 + 0.999659i \(0.491691\pi\)
\(368\) −1.50000 2.59808i −0.0781929 0.135434i
\(369\) 0 0
\(370\) −21.0000 −1.09174
\(371\) 0 0
\(372\) 0 0
\(373\) 17.0000 0.880227 0.440113 0.897942i \(-0.354938\pi\)
0.440113 + 0.897942i \(0.354938\pi\)
\(374\) 4.50000 7.79423i 0.232689 0.403030i
\(375\) 0 0
\(376\) 0 0
\(377\) −15.0000 −0.772539
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −7.50000 12.9904i −0.384742 0.666392i
\(381\) 0 0
\(382\) −6.00000 + 10.3923i −0.306987 + 0.531717i
\(383\) −15.0000 −0.766464 −0.383232 0.923652i \(-0.625189\pi\)
−0.383232 + 0.923652i \(0.625189\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) −0.500000 0.866025i −0.0253837 0.0439658i
\(389\) −9.00000 −0.456318 −0.228159 0.973624i \(-0.573271\pi\)
−0.228159 + 0.973624i \(0.573271\pi\)
\(390\) 0 0
\(391\) −4.50000 7.79423i −0.227575 0.394171i
\(392\) 0 0
\(393\) 0 0
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) 12.0000 + 20.7846i 0.603786 + 1.04579i
\(396\) 0 0
\(397\) 14.5000 25.1147i 0.727734 1.26047i −0.230105 0.973166i \(-0.573907\pi\)
0.957839 0.287307i \(-0.0927599\pi\)
\(398\) 3.50000 6.06218i 0.175439 0.303870i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −27.0000 −1.34832 −0.674158 0.738587i \(-0.735493\pi\)
−0.674158 + 0.738587i \(0.735493\pi\)
\(402\) 0 0
\(403\) −20.0000 −0.996271
\(404\) 1.50000 2.59808i 0.0746278 0.129259i
\(405\) 0 0
\(406\) 0 0
\(407\) 10.5000 18.1865i 0.520466 0.901473i
\(408\) 0 0
\(409\) −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) 13.5000 23.3827i 0.666717 1.15479i
\(411\) 0 0
\(412\) 2.50000 4.33013i 0.123166 0.213330i
\(413\) 0 0
\(414\) 0 0
\(415\) 4.50000 7.79423i 0.220896 0.382604i
\(416\) 5.00000 0.245145
\(417\) 0 0
\(418\) 15.0000 0.733674
\(419\) 1.50000 + 2.59808i 0.0732798 + 0.126924i 0.900337 0.435194i \(-0.143320\pi\)
−0.827057 + 0.562118i \(0.809987\pi\)
\(420\) 0 0
\(421\) 15.5000 26.8468i 0.755424 1.30843i −0.189740 0.981834i \(-0.560764\pi\)
0.945163 0.326598i \(-0.105902\pi\)
\(422\) 2.50000 4.33013i 0.121698 0.210787i
\(423\) 0 0
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 0 0
\(427\) 0 0
\(428\) −7.50000 12.9904i −0.362526 0.627914i
\(429\) 0 0
\(430\) 33.0000 1.59140
\(431\) −1.50000 2.59808i −0.0722525 0.125145i 0.827636 0.561266i \(-0.189685\pi\)
−0.899888 + 0.436121i \(0.856352\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7.00000 −0.335239
\(437\) 7.50000 12.9904i 0.358774 0.621414i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) 15.0000 0.713477
\(443\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(444\) 0 0
\(445\) 22.5000 38.9711i 1.06660 1.84741i
\(446\) 17.0000 0.804973
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 13.5000 + 23.3827i 0.635690 + 1.10105i
\(452\) −15.0000 −0.705541
\(453\) 0 0
\(454\) 4.50000 + 7.79423i 0.211195 + 0.365801i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 + 29.4449i 0.795226 + 1.37737i 0.922695 + 0.385530i \(0.125981\pi\)
−0.127469 + 0.991843i \(0.540685\pi\)
\(458\) −8.50000 14.7224i −0.397179 0.687934i
\(459\) 0 0
\(460\) 4.50000 7.79423i 0.209814 0.363408i
\(461\) −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i \(-0.900545\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(462\) 0 0
\(463\) −17.5000 30.3109i −0.813294 1.40867i −0.910546 0.413407i \(-0.864339\pi\)
0.0972525 0.995260i \(-0.468995\pi\)
\(464\) 3.00000 0.139272
\(465\) 0 0
\(466\) 27.0000 1.25075
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 6.00000 10.3923i 0.276172 0.478345i
\(473\) −16.5000 + 28.5788i −0.758671 + 1.31406i
\(474\) 0 0
\(475\) 10.0000 17.3205i 0.458831 0.794719i
\(476\) 0 0
\(477\) 0 0
\(478\) −13.5000 + 23.3827i −0.617476 + 1.06950i
\(479\) −9.00000 −0.411220 −0.205610 0.978634i \(-0.565918\pi\)
−0.205610 + 0.978634i \(0.565918\pi\)
\(480\) 0 0
\(481\) 35.0000 1.59586
\(482\) −11.5000 19.9186i −0.523811 0.907267i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 1.50000 2.59808i 0.0681115 0.117973i
\(486\) 0 0
\(487\) 15.5000 + 26.8468i 0.702372 + 1.21654i 0.967632 + 0.252367i \(0.0812090\pi\)
−0.265260 + 0.964177i \(0.585458\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) 0 0
\(490\) 0 0
\(491\) −19.5000 33.7750i −0.880023 1.52424i −0.851314 0.524656i \(-0.824194\pi\)
−0.0287085 0.999588i \(-0.509139\pi\)
\(492\) 0 0
\(493\) 9.00000 0.405340
\(494\) 12.5000 + 21.6506i 0.562402 + 0.974108i
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 11.0000 0.492428 0.246214 0.969216i \(-0.420813\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 0 0
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 4.50000 + 7.79423i 0.200049 + 0.346496i
\(507\) 0 0
\(508\) 8.00000 13.8564i 0.354943 0.614779i
\(509\) −27.0000 −1.19675 −0.598377 0.801215i \(-0.704187\pi\)
−0.598377 + 0.801215i \(0.704187\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 7.50000 + 12.9904i 0.330811 + 0.572981i
\(515\) 15.0000 0.660979
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 7.50000 + 12.9904i 0.328897 + 0.569666i
\(521\) −1.50000 2.59808i −0.0657162 0.113824i 0.831295 0.555831i \(-0.187600\pi\)
−0.897011 + 0.442007i \(0.854267\pi\)
\(522\) 0 0
\(523\) −3.50000 + 6.06218i −0.153044 + 0.265081i −0.932345 0.361569i \(-0.882241\pi\)
0.779301 + 0.626650i \(0.215574\pi\)
\(524\) −1.50000 + 2.59808i −0.0655278 + 0.113497i
\(525\) 0 0
\(526\) 4.50000 + 7.79423i 0.196209 + 0.339845i
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) 0 0
\(532\) 0 0
\(533\) −22.5000 + 38.9711i −0.974583 + 1.68803i
\(534\) 0 0
\(535\) 22.5000 38.9711i 0.972760 1.68487i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 0 0
\(538\) 10.5000 18.1865i 0.452687 0.784077i
\(539\) 0 0
\(540\) 0 0
\(541\) −8.50000 + 14.7224i −0.365444 + 0.632967i −0.988847 0.148933i \(-0.952416\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) −13.0000 −0.558398
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) −10.5000 18.1865i −0.449771 0.779026i
\(546\) 0 0
\(547\) −5.50000 + 9.52628i −0.235163 + 0.407314i −0.959320 0.282321i \(-0.908896\pi\)
0.724157 + 0.689635i \(0.242229\pi\)
\(548\) 1.50000 2.59808i 0.0640768 0.110984i
\(549\) 0 0
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) 7.50000 + 12.9904i 0.319511 + 0.553409i
\(552\) 0 0
\(553\) 0 0
\(554\) −3.50000 6.06218i −0.148701 0.257557i
\(555\) 0 0
\(556\) −5.00000 −0.212047
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) 0 0
\(559\) −55.0000 −2.32625
\(560\) 0 0
\(561\) 0 0
\(562\) 3.00000 0.126547
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 0 0
\(565\) −22.5000 38.9711i −0.946582 1.63953i
\(566\) 8.00000 0.336265
\(567\) 0 0
\(568\) 0 0
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) −15.0000 −0.627182
\(573\) 0 0
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) 5.50000 + 9.52628i 0.228968 + 0.396584i 0.957503 0.288425i \(-0.0931316\pi\)
−0.728535 + 0.685009i \(0.759798\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) 4.50000 + 7.79423i 0.186852 + 0.323638i
\(581\) 0 0
\(582\) 0 0
\(583\) −4.50000 7.79423i −0.186371 0.322804i
\(584\) −5.50000 9.52628i −0.227592 0.394200i
\(585\) 0 0
\(586\) −13.5000 + 23.3827i −0.557680 + 0.965930i
\(587\) 16.5000 28.5788i 0.681028 1.17957i −0.293640 0.955916i \(-0.594867\pi\)
0.974668 0.223659i \(-0.0718001\pi\)
\(588\) 0 0
\(589\) 10.0000 + 17.3205i 0.412043 + 0.713679i
\(590\) 36.0000 1.48210
\(591\) 0 0
\(592\) −7.00000 −0.287698
\(593\) 10.5000 18.1865i 0.431183 0.746831i −0.565792 0.824548i \(-0.691430\pi\)
0.996976 + 0.0777165i \(0.0247629\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.50000 + 2.59808i −0.0614424 + 0.106421i
\(597\) 0 0
\(598\) −7.50000 + 12.9904i −0.306698 + 0.531216i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −0.500000 + 0.866025i −0.0203954 + 0.0353259i −0.876043 0.482233i \(-0.839826\pi\)
0.855648 + 0.517559i \(0.173159\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.50000 + 9.52628i −0.223792 + 0.387619i
\(605\) 6.00000 0.243935
\(606\) 0 0
\(607\) 43.0000 1.74532 0.872658 0.488332i \(-0.162394\pi\)
0.872658 + 0.488332i \(0.162394\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 0 0
\(610\) 3.00000 5.19615i 0.121466 0.210386i
\(611\) 0 0
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 + 2.59808i 0.0603877 + 0.104595i 0.894639 0.446790i \(-0.147433\pi\)
−0.834251 + 0.551385i \(0.814100\pi\)
\(618\) 0 0
\(619\) 19.0000 0.763674 0.381837 0.924230i \(-0.375291\pi\)
0.381837 + 0.924230i \(0.375291\pi\)
\(620\) 6.00000 + 10.3923i 0.240966 + 0.417365i
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −7.00000 + 12.1244i −0.279776 + 0.484587i
\(627\) 0 0
\(628\) 7.00000 + 12.1244i 0.279330 + 0.483814i
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 4.00000 + 6.92820i 0.159111 + 0.275589i
\(633\) 0 0
\(634\) −15.0000 + 25.9808i −0.595726 + 1.03183i
\(635\) 48.0000 1.90482
\(636\) 0 0
\(637\) 0 0
\(638\) −9.00000 −0.356313
\(639\) 0 0
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) 45.0000 1.77739 0.888697 0.458496i \(-0.151612\pi\)
0.888697 + 0.458496i \(0.151612\pi\)
\(642\) 0 0
\(643\) 14.5000 + 25.1147i 0.571824 + 0.990429i 0.996379 + 0.0850262i \(0.0270974\pi\)
−0.424555 + 0.905402i \(0.639569\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7.50000 12.9904i −0.295084 0.511100i
\(647\) 1.50000 + 2.59808i 0.0589711 + 0.102141i 0.894004 0.448059i \(-0.147885\pi\)
−0.835033 + 0.550200i \(0.814551\pi\)
\(648\) 0 0
\(649\) −18.0000 + 31.1769i −0.706562 + 1.22380i
\(650\) −10.0000 + 17.3205i −0.392232 + 0.679366i
\(651\) 0 0
\(652\) −8.50000 14.7224i −0.332886 0.576575i
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) 0 0
\(655\) −9.00000 −0.351659
\(656\) 4.50000 7.79423i 0.175695 0.304314i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.5000 33.7750i 0.759612 1.31569i −0.183436 0.983032i \(-0.558722\pi\)
0.943049 0.332655i \(-0.107945\pi\)
\(660\) 0 0
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) 10.0000 17.3205i 0.388661 0.673181i
\(663\) 0 0
\(664\) 1.50000 2.59808i 0.0582113 0.100825i
\(665\) 0 0
\(666\) 0 0
\(667\) −4.50000 + 7.79423i −0.174241 + 0.301794i
\(668\) 3.00000 0.116073
\(669\) 0 0
\(670\) −12.0000 −0.463600
\(671\) 3.00000 + 5.19615i 0.115814 + 0.200595i
\(672\) 0 0
\(673\) −5.50000 + 9.52628i −0.212009 + 0.367211i −0.952343 0.305028i \(-0.901334\pi\)
0.740334 + 0.672239i \(0.234667\pi\)
\(674\) −12.5000 + 21.6506i −0.481482 + 0.833951i
\(675\) 0 0
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) 0 0
\(682\) −12.0000 −0.459504
\(683\) −16.5000 28.5788i −0.631355 1.09354i −0.987275 0.159022i \(-0.949166\pi\)
0.355920 0.934516i \(-0.384168\pi\)
\(684\) 0 0
\(685\) 9.00000 0.343872
\(686\) 0 0
\(687\) 0 0
\(688\) 11.0000 0.419371
\(689\) 7.50000 12.9904i 0.285727 0.494894i
\(690\) 0 0
\(691\) 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −7.50000 12.9904i −0.284491 0.492753i
\(696\) 0 0
\(697\) 13.5000 23.3827i 0.511349 0.885682i
\(698\) 5.00000 0.189253
\(699\) 0 0
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) −17.5000 30.3109i −0.660025 1.14320i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) −4.50000 7.79423i −0.169360 0.293340i
\(707\) 0 0
\(708\) 0 0
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 7.50000 12.9904i 0.281074 0.486835i
\(713\) −6.00000 + 10.3923i −0.224702 + 0.389195i
\(714\) 0 0
\(715\) −22.5000 38.9711i −0.841452 1.45744i
\(716\) −3.00000 −0.112115
\(717\) 0 0
\(718\) 15.0000 0.559795
\(719\) −19.5000 + 33.7750i −0.727227 + 1.25959i 0.230823 + 0.972996i \(0.425858\pi\)
−0.958051 + 0.286599i \(0.907475\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) 0 0
\(724\) −5.00000 + 8.66025i −0.185824 + 0.321856i
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) 0 0
\(727\) 2.50000 4.33013i 0.0927199 0.160596i −0.815935 0.578144i \(-0.803777\pi\)
0.908655 + 0.417548i \(0.137111\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 16.5000 28.5788i 0.610692 1.05775i
\(731\) 33.0000 1.22055
\(732\) 0 0
\(733\) −41.0000 −1.51437 −0.757185 0.653201i \(-0.773426\pi\)
−0.757185 + 0.653201i \(0.773426\pi\)
\(734\) 0.500000 + 0.866025i 0.0184553 + 0.0319656i
\(735\) 0 0
\(736\) 1.50000 2.59808i 0.0552907 0.0957664i
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) −23.5000 40.7032i −0.864461 1.49729i −0.867581 0.497296i \(-0.834326\pi\)
0.00311943 0.999995i \(-0.499007\pi\)
\(740\) −10.5000 18.1865i −0.385988 0.668550i
\(741\) 0 0
\(742\) 0 0
\(743\) 1.50000 + 2.59808i 0.0550297 + 0.0953142i 0.892228 0.451585i \(-0.149141\pi\)
−0.837198 + 0.546899i \(0.815808\pi\)
\(744\) 0 0
\(745\) −9.00000 −0.329734
\(746\) 8.50000 + 14.7224i 0.311207 + 0.539027i
\(747\) 0 0
\(748\) 9.00000 0.329073
\(749\) 0 0
\(750\) 0 0
\(751\) 29.0000 1.05823 0.529113 0.848552i \(-0.322525\pi\)
0.529113 + 0.848552i \(0.322525\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −7.50000 12.9904i −0.273134 0.473082i
\(755\) −33.0000 −1.20099
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) −8.00000 13.8564i −0.290573 0.503287i
\(759\) 0 0
\(760\) 7.50000 12.9904i 0.272054 0.471211i
\(761\) 3.00000 0.108750 0.0543750 0.998521i \(-0.482683\pi\)
0.0543750 + 0.998521i \(0.482683\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −7.50000 12.9904i −0.270986 0.469362i
\(767\) −60.0000 −2.16647
\(768\) 0 0
\(769\) −0.500000 0.866025i −0.0180305 0.0312297i 0.856869 0.515534i \(-0.172406\pi\)
−0.874900 + 0.484304i \(0.839073\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i \(-0.289937\pi\)
−0.990721 + 0.135910i \(0.956604\pi\)
\(774\) 0 0
\(775\) −8.00000 + 13.8564i −0.287368 + 0.497737i
\(776\) 0.500000 0.866025i 0.0179490 0.0310885i
\(777\) 0 0
\(778\) −4.50000 7.79423i −0.161333 0.279437i
\(779\) 45.0000 1.61229
\(780\) 0 0
\(781\) 0 0
\(782\) 4.50000 7.79423i 0.160920 0.278721i
\(783\) 0 0
\(784\) 0 0
\(785\) −21.0000 + 36.3731i −0.749522 + 1.29821i
\(786\) 0 0
\(787\) 22.0000 38.1051i 0.784215 1.35830i −0.145251 0.989395i \(-0.546399\pi\)
0.929467 0.368906i \(-0.120268\pi\)
\(788\) −3.00000 + 5.19615i −0.106871 + 0.185105i
\(789\) 0 0
\(790\) −12.0000 + 20.7846i −0.426941 + 0.739483i
\(791\) 0 0
\(792\) 0 0
\(793\) −5.00000 + 8.66025i −0.177555 + 0.307535i