Properties

Label 2646.2.e.n.2125.2
Level $2646$
Weight $2$
Character 2646.2125
Analytic conductor $21.128$
Analytic rank $0$
Dimension $4$
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.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2125.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 2646.2125
Dual form 2646.2.e.n.1549.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(2.18614 - 3.78651i) q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(2.18614 - 3.78651i) q^{5} +1.00000 q^{8} +(2.18614 - 3.78651i) q^{10} +(-0.686141 - 1.18843i) q^{11} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(0.686141 - 1.18843i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(2.18614 - 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} +(-0.813859 + 1.40965i) q^{23} +(-7.05842 - 12.2255i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-4.37228 + 7.57301i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(0.686141 - 1.18843i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(-2.50000 - 4.33013i) q^{38} +(2.18614 - 3.78651i) q^{40} +(2.31386 + 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +(-0.686141 - 1.18843i) q^{44} +(-0.813859 + 1.40965i) q^{46} +(-7.05842 - 12.2255i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(-4.37228 + 7.57301i) q^{53} -6.00000 q^{55} +(-4.37228 + 7.57301i) q^{58} +10.1168 q^{59} +3.11684 q^{61} +2.00000 q^{62} +1.00000 q^{64} -8.74456 q^{65} -2.11684 q^{67} +(0.686141 - 1.18843i) q^{68} +7.11684 q^{71} +(-6.05842 + 10.4935i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.50000 - 4.33013i) q^{76} -5.11684 q^{79} +(2.18614 - 3.78651i) q^{80} +(2.31386 + 4.00772i) q^{82} +(8.74456 - 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(4.05842 - 7.02939i) q^{86} +(-0.686141 - 1.18843i) q^{88} +(7.37228 + 12.7692i) q^{89} +(-0.813859 + 1.40965i) q^{92} -21.8614 q^{95} +(4.05842 - 7.02939i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + O(q^{10}) \) \( 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + 3 q^{10} + 3 q^{11} - 4 q^{13} + 4 q^{16} - 3 q^{17} - 10 q^{19} + 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} - 4 q^{26} - 6 q^{29} + 8 q^{31} + 4 q^{32} - 3 q^{34} - 4 q^{37} - 10 q^{38} + 3 q^{40} + 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} - 4 q^{52} - 6 q^{53} - 24 q^{55} - 6 q^{58} + 6 q^{59} - 22 q^{61} + 8 q^{62} + 4 q^{64} - 12 q^{65} + 26 q^{67} - 3 q^{68} - 6 q^{71} - 7 q^{73} - 4 q^{74} - 10 q^{76} + 14 q^{79} + 3 q^{80} + 15 q^{82} + 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} + 18 q^{89} - 9 q^{92} - 30 q^{95} - q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 2.18614 3.78651i 0.977672 1.69338i 0.306851 0.951757i \(-0.400725\pi\)
0.670820 0.741620i \(-0.265942\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.18614 3.78651i 0.691318 1.19740i
\(11\) −0.686141 1.18843i −0.206879 0.358325i 0.743851 0.668346i \(-0.232997\pi\)
−0.950730 + 0.310021i \(0.899664\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.686141 1.18843i 0.166414 0.288237i −0.770743 0.637146i \(-0.780115\pi\)
0.937156 + 0.348910i \(0.113448\pi\)
\(18\) 0 0
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) 2.18614 3.78651i 0.488836 0.846689i
\(21\) 0 0
\(22\) −0.686141 1.18843i −0.146286 0.253374i
\(23\) −0.813859 + 1.40965i −0.169701 + 0.293931i −0.938315 0.345782i \(-0.887614\pi\)
0.768613 + 0.639713i \(0.220947\pi\)
\(24\) 0 0
\(25\) −7.05842 12.2255i −1.41168 2.44511i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.37228 + 7.57301i −0.811912 + 1.40627i 0.0996117 + 0.995026i \(0.468240\pi\)
−0.911524 + 0.411247i \(0.865093\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0.686141 1.18843i 0.117672 0.203814i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) −2.50000 4.33013i −0.405554 0.702439i
\(39\) 0 0
\(40\) 2.18614 3.78651i 0.345659 0.598699i
\(41\) 2.31386 + 4.00772i 0.361364 + 0.625901i 0.988186 0.153262i \(-0.0489778\pi\)
−0.626821 + 0.779163i \(0.715644\pi\)
\(42\) 0 0
\(43\) 4.05842 7.02939i 0.618904 1.07197i −0.370783 0.928720i \(-0.620910\pi\)
0.989686 0.143253i \(-0.0457562\pi\)
\(44\) −0.686141 1.18843i −0.103440 0.179163i
\(45\) 0 0
\(46\) −0.813859 + 1.40965i −0.119997 + 0.207841i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −7.05842 12.2255i −0.998212 1.72895i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −4.37228 + 7.57301i −0.600579 + 1.04023i 0.392154 + 0.919899i \(0.371730\pi\)
−0.992733 + 0.120334i \(0.961603\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 0 0
\(58\) −4.37228 + 7.57301i −0.574109 + 0.994385i
\(59\) 10.1168 1.31710 0.658550 0.752537i \(-0.271170\pi\)
0.658550 + 0.752537i \(0.271170\pi\)
\(60\) 0 0
\(61\) 3.11684 0.399071 0.199535 0.979891i \(-0.436057\pi\)
0.199535 + 0.979891i \(0.436057\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −8.74456 −1.08463
\(66\) 0 0
\(67\) −2.11684 −0.258614 −0.129307 0.991605i \(-0.541275\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 0.686141 1.18843i 0.0832068 0.144118i
\(69\) 0 0
\(70\) 0 0
\(71\) 7.11684 0.844614 0.422307 0.906453i \(-0.361220\pi\)
0.422307 + 0.906453i \(0.361220\pi\)
\(72\) 0 0
\(73\) −6.05842 + 10.4935i −0.709085 + 1.22817i 0.256112 + 0.966647i \(0.417558\pi\)
−0.965197 + 0.261524i \(0.915775\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) 0 0
\(78\) 0 0
\(79\) −5.11684 −0.575690 −0.287845 0.957677i \(-0.592939\pi\)
−0.287845 + 0.957677i \(0.592939\pi\)
\(80\) 2.18614 3.78651i 0.244418 0.423344i
\(81\) 0 0
\(82\) 2.31386 + 4.00772i 0.255523 + 0.442579i
\(83\) 8.74456 15.1460i 0.959840 1.66249i 0.236960 0.971519i \(-0.423849\pi\)
0.722881 0.690973i \(-0.242818\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 4.05842 7.02939i 0.437631 0.757999i
\(87\) 0 0
\(88\) −0.686141 1.18843i −0.0731428 0.126687i
\(89\) 7.37228 + 12.7692i 0.781460 + 1.35353i 0.931091 + 0.364787i \(0.118858\pi\)
−0.149631 + 0.988742i \(0.547808\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.813859 + 1.40965i −0.0848507 + 0.146966i
\(93\) 0 0
\(94\) 0 0
\(95\) −21.8614 −2.24293
\(96\) 0 0
\(97\) 4.05842 7.02939i 0.412070 0.713727i −0.583046 0.812439i \(-0.698139\pi\)
0.995116 + 0.0987127i \(0.0314725\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −7.05842 12.2255i −0.705842 1.22255i
\(101\) 0.813859 + 1.40965i 0.0809820 + 0.140265i 0.903672 0.428225i \(-0.140861\pi\)
−0.822690 + 0.568490i \(0.807528\pi\)
\(102\) 0 0
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) −4.37228 + 7.57301i −0.424674 + 0.735556i
\(107\) −3.68614 6.38458i −0.356353 0.617221i 0.630996 0.775786i \(-0.282646\pi\)
−0.987348 + 0.158565i \(0.949313\pi\)
\(108\) 0 0
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) −6.00000 −0.572078
\(111\) 0 0
\(112\) 0 0
\(113\) −2.18614 3.78651i −0.205655 0.356205i 0.744686 0.667415i \(-0.232599\pi\)
−0.950341 + 0.311210i \(0.899266\pi\)
\(114\) 0 0
\(115\) 3.55842 + 6.16337i 0.331825 + 0.574737i
\(116\) −4.37228 + 7.57301i −0.405956 + 0.703137i
\(117\) 0 0
\(118\) 10.1168 0.931331
\(119\) 0 0
\(120\) 0 0
\(121\) 4.55842 7.89542i 0.414402 0.717765i
\(122\) 3.11684 0.282186
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) −39.8614 −3.56531
\(126\) 0 0
\(127\) 3.11684 0.276575 0.138288 0.990392i \(-0.455840\pi\)
0.138288 + 0.990392i \(0.455840\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −8.74456 −0.766949
\(131\) −0.813859 + 1.40965i −0.0711072 + 0.123161i −0.899387 0.437154i \(-0.855987\pi\)
0.828280 + 0.560315i \(0.189320\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −2.11684 −0.182867
\(135\) 0 0
\(136\) 0.686141 1.18843i 0.0588361 0.101907i
\(137\) 5.31386 + 9.20387i 0.453994 + 0.786340i 0.998630 0.0523324i \(-0.0166655\pi\)
−0.544636 + 0.838672i \(0.683332\pi\)
\(138\) 0 0
\(139\) −6.61684 11.4607i −0.561233 0.972085i −0.997389 0.0722136i \(-0.976994\pi\)
0.436156 0.899871i \(-0.356340\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.11684 0.597232
\(143\) −1.37228 + 2.37686i −0.114756 + 0.198763i
\(144\) 0 0
\(145\) 19.1168 + 33.1113i 1.58757 + 2.74975i
\(146\) −6.05842 + 10.4935i −0.501399 + 0.868448i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 1.62772 2.81929i 0.133348 0.230965i −0.791617 0.611017i \(-0.790761\pi\)
0.924965 + 0.380052i \(0.124094\pi\)
\(150\) 0 0
\(151\) −4.55842 7.89542i −0.370959 0.642520i 0.618754 0.785585i \(-0.287638\pi\)
−0.989713 + 0.143065i \(0.954304\pi\)
\(152\) −2.50000 4.33013i −0.202777 0.351220i
\(153\) 0 0
\(154\) 0 0
\(155\) 4.37228 7.57301i 0.351190 0.608279i
\(156\) 0 0
\(157\) 9.11684 0.727603 0.363802 0.931476i \(-0.381479\pi\)
0.363802 + 0.931476i \(0.381479\pi\)
\(158\) −5.11684 −0.407074
\(159\) 0 0
\(160\) 2.18614 3.78651i 0.172830 0.299350i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.11684 + 15.7908i 0.714086 + 1.23683i 0.963311 + 0.268388i \(0.0864909\pi\)
−0.249225 + 0.968446i \(0.580176\pi\)
\(164\) 2.31386 + 4.00772i 0.180682 + 0.312951i
\(165\) 0 0
\(166\) 8.74456 15.1460i 0.678710 1.17556i
\(167\) −2.74456 4.75372i −0.212381 0.367854i 0.740078 0.672521i \(-0.234788\pi\)
−0.952459 + 0.304666i \(0.901455\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) 0 0
\(172\) 4.05842 7.02939i 0.309452 0.535986i
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.686141 1.18843i −0.0517198 0.0895813i
\(177\) 0 0
\(178\) 7.37228 + 12.7692i 0.552576 + 0.957089i
\(179\) 1.62772 2.81929i 0.121661 0.210724i −0.798762 0.601648i \(-0.794511\pi\)
0.920423 + 0.390924i \(0.127844\pi\)
\(180\) 0 0
\(181\) 0.883156 0.0656445 0.0328222 0.999461i \(-0.489550\pi\)
0.0328222 + 0.999461i \(0.489550\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.813859 + 1.40965i −0.0599985 + 0.103920i
\(185\) −8.74456 −0.642913
\(186\) 0 0
\(187\) −1.88316 −0.137710
\(188\) 0 0
\(189\) 0 0
\(190\) −21.8614 −1.58599
\(191\) 19.1168 1.38325 0.691623 0.722259i \(-0.256896\pi\)
0.691623 + 0.722259i \(0.256896\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 4.05842 7.02939i 0.291378 0.504681i
\(195\) 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
\(199\) 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) −7.05842 12.2255i −0.499106 0.864477i
\(201\) 0 0
\(202\) 0.813859 + 1.40965i 0.0572629 + 0.0991823i
\(203\) 0 0
\(204\) 0 0
\(205\) 20.2337 1.41318
\(206\) 5.00000 8.66025i 0.348367 0.603388i
\(207\) 0 0
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) −3.43070 + 5.94215i −0.237307 + 0.411027i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −4.37228 + 7.57301i −0.300290 + 0.520117i
\(213\) 0 0
\(214\) −3.68614 6.38458i −0.251979 0.436441i
\(215\) −17.7446 30.7345i −1.21017 2.09607i
\(216\) 0 0
\(217\) 0 0
\(218\) −7.00000 + 12.1244i −0.474100 + 0.821165i
\(219\) 0 0
\(220\) −6.00000 −0.404520
\(221\) −2.74456 −0.184619
\(222\) 0 0
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.18614 3.78651i −0.145420 0.251875i
\(227\) −6.12772 10.6135i −0.406711 0.704444i 0.587808 0.809000i \(-0.299991\pi\)
−0.994519 + 0.104556i \(0.966658\pi\)
\(228\) 0 0
\(229\) 1.44158 2.49689i 0.0952622 0.164999i −0.814456 0.580226i \(-0.802964\pi\)
0.909718 + 0.415227i \(0.136298\pi\)
\(230\) 3.55842 + 6.16337i 0.234635 + 0.406400i
\(231\) 0 0
\(232\) −4.37228 + 7.57301i −0.287054 + 0.497193i
\(233\) −0.127719 0.221215i −0.00836713 0.0144923i 0.861812 0.507229i \(-0.169330\pi\)
−0.870179 + 0.492736i \(0.835997\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 10.1168 0.658550
\(237\) 0 0
\(238\) 0 0
\(239\) 4.93070 + 8.54023i 0.318941 + 0.552421i 0.980267 0.197677i \(-0.0633396\pi\)
−0.661327 + 0.750098i \(0.730006\pi\)
\(240\) 0 0
\(241\) −9.05842 15.6896i −0.583504 1.01066i −0.995060 0.0992745i \(-0.968348\pi\)
0.411556 0.911385i \(-0.364986\pi\)
\(242\) 4.55842 7.89542i 0.293026 0.507537i
\(243\) 0 0
\(244\) 3.11684 0.199535
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 + 8.66025i −0.318142 + 0.551039i
\(248\) 2.00000 0.127000
\(249\) 0 0
\(250\) −39.8614 −2.52106
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) 2.23369 0.140431
\(254\) 3.11684 0.195568
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −3.43070 + 5.94215i −0.214001 + 0.370661i −0.952963 0.303086i \(-0.901983\pi\)
0.738962 + 0.673747i \(0.235316\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −8.74456 −0.542315
\(261\) 0 0
\(262\) −0.813859 + 1.40965i −0.0502804 + 0.0870882i
\(263\) 3.81386 + 6.60580i 0.235173 + 0.407331i 0.959323 0.282311i \(-0.0911011\pi\)
−0.724150 + 0.689642i \(0.757768\pi\)
\(264\) 0 0
\(265\) 19.1168 + 33.1113i 1.17434 + 2.03401i
\(266\) 0 0
\(267\) 0 0
\(268\) −2.11684 −0.129307
\(269\) −0.813859 + 1.40965i −0.0496219 + 0.0859476i −0.889769 0.456410i \(-0.849135\pi\)
0.840148 + 0.542358i \(0.182468\pi\)
\(270\) 0 0
\(271\) −8.11684 14.0588i −0.493063 0.854010i 0.506905 0.862002i \(-0.330790\pi\)
−0.999968 + 0.00799154i \(0.997456\pi\)
\(272\) 0.686141 1.18843i 0.0416034 0.0720592i
\(273\) 0 0
\(274\) 5.31386 + 9.20387i 0.321022 + 0.556026i
\(275\) −9.68614 + 16.7769i −0.584096 + 1.01168i
\(276\) 0 0
\(277\) 6.11684 + 10.5947i 0.367526 + 0.636573i 0.989178 0.146720i \(-0.0468717\pi\)
−0.621652 + 0.783293i \(0.713538\pi\)
\(278\) −6.61684 11.4607i −0.396852 0.687368i
\(279\) 0 0
\(280\) 0 0
\(281\) 8.18614 14.1788i 0.488344 0.845837i −0.511566 0.859244i \(-0.670934\pi\)
0.999910 + 0.0134071i \(0.00426773\pi\)
\(282\) 0 0
\(283\) 27.1168 1.61193 0.805965 0.591964i \(-0.201647\pi\)
0.805965 + 0.591964i \(0.201647\pi\)
\(284\) 7.11684 0.422307
\(285\) 0 0
\(286\) −1.37228 + 2.37686i −0.0811447 + 0.140547i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.55842 + 13.0916i 0.444613 + 0.770092i
\(290\) 19.1168 + 33.1113i 1.12258 + 1.94437i
\(291\) 0 0
\(292\) −6.05842 + 10.4935i −0.354542 + 0.614085i
\(293\) −5.18614 8.98266i −0.302978 0.524773i 0.673831 0.738885i \(-0.264647\pi\)
−0.976809 + 0.214113i \(0.931314\pi\)
\(294\) 0 0
\(295\) 22.1168 38.3075i 1.28769 2.23035i
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 0 0
\(298\) 1.62772 2.81929i 0.0942912 0.163317i
\(299\) 3.25544 0.188267
\(300\) 0 0
\(301\) 0 0
\(302\) −4.55842 7.89542i −0.262308 0.454330i
\(303\) 0 0
\(304\) −2.50000 4.33013i −0.143385 0.248350i
\(305\) 6.81386 11.8020i 0.390160 0.675778i
\(306\) 0 0
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.37228 7.57301i 0.248329 0.430118i
\(311\) −8.23369 −0.466890 −0.233445 0.972370i \(-0.575000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(312\) 0 0
\(313\) −20.1168 −1.13707 −0.568536 0.822659i \(-0.692490\pi\)
−0.568536 + 0.822659i \(0.692490\pi\)
\(314\) 9.11684 0.514493
\(315\) 0 0
\(316\) −5.11684 −0.287845
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 2.18614 3.78651i 0.122209 0.211672i
\(321\) 0 0
\(322\) 0 0
\(323\) −6.86141 −0.381779
\(324\) 0 0
\(325\) −14.1168 + 24.4511i −0.783062 + 1.35630i
\(326\) 9.11684 + 15.7908i 0.504935 + 0.874574i
\(327\) 0 0
\(328\) 2.31386 + 4.00772i 0.127762 + 0.221289i
\(329\) 0 0
\(330\) 0 0
\(331\) 22.2337 1.22207 0.611037 0.791602i \(-0.290753\pi\)
0.611037 + 0.791602i \(0.290753\pi\)
\(332\) 8.74456 15.1460i 0.479920 0.831246i
\(333\) 0 0
\(334\) −2.74456 4.75372i −0.150176 0.260112i
\(335\) −4.62772 + 8.01544i −0.252839 + 0.437930i
\(336\) 0 0
\(337\) 4.05842 + 7.02939i 0.221076 + 0.382915i 0.955135 0.296171i \(-0.0957097\pi\)
−0.734059 + 0.679086i \(0.762376\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 0 0
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) −1.37228 2.37686i −0.0743132 0.128714i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.05842 7.02939i 0.218815 0.378999i
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 10.1168 0.543101 0.271550 0.962424i \(-0.412464\pi\)
0.271550 + 0.962424i \(0.412464\pi\)
\(348\) 0 0
\(349\) 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i \(-0.632927\pi\)
0.994388 0.105797i \(-0.0337393\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.686141 1.18843i −0.0365714 0.0633436i
\(353\) −6.68614 11.5807i −0.355867 0.616380i 0.631399 0.775458i \(-0.282481\pi\)
−0.987266 + 0.159078i \(0.949148\pi\)
\(354\) 0 0
\(355\) 15.5584 26.9480i 0.825755 1.43025i
\(356\) 7.37228 + 12.7692i 0.390730 + 0.676764i
\(357\) 0 0
\(358\) 1.62772 2.81929i 0.0860276 0.149004i
\(359\) 10.9307 + 18.9325i 0.576900 + 0.999221i 0.995832 + 0.0912032i \(0.0290713\pi\)
−0.418932 + 0.908018i \(0.637595\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0.883156 0.0464177
\(363\) 0 0
\(364\) 0 0
\(365\) 26.4891 + 45.8805i 1.38650 + 2.40150i
\(366\) 0 0
\(367\) 6.11684 + 10.5947i 0.319297 + 0.553038i 0.980341 0.197308i \(-0.0632200\pi\)
−0.661045 + 0.750346i \(0.729887\pi\)
\(368\) −0.813859 + 1.40965i −0.0424254 + 0.0734829i
\(369\) 0 0
\(370\) −8.74456 −0.454608
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) −1.88316 −0.0973757
\(375\) 0 0
\(376\) 0 0
\(377\) 17.4891 0.900736
\(378\) 0 0
\(379\) −8.11684 −0.416934 −0.208467 0.978029i \(-0.566847\pi\)
−0.208467 + 0.978029i \(0.566847\pi\)
\(380\) −21.8614 −1.12147
\(381\) 0 0
\(382\) 19.1168 0.978103
\(383\) −16.3723 + 28.3576i −0.836584 + 1.44901i 0.0561493 + 0.998422i \(0.482118\pi\)
−0.892734 + 0.450584i \(0.851216\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) 4.05842 7.02939i 0.206035 0.356863i
\(389\) 5.48913 + 9.50744i 0.278310 + 0.482047i 0.970965 0.239222i \(-0.0768925\pi\)
−0.692655 + 0.721269i \(0.743559\pi\)
\(390\) 0 0
\(391\) 1.11684 + 1.93443i 0.0564812 + 0.0978284i
\(392\) 0 0
\(393\) 0 0
\(394\) 6.00000 0.302276
\(395\) −11.1861 + 19.3750i −0.562836 + 0.974860i
\(396\) 0 0
\(397\) 11.0000 + 19.0526i 0.552074 + 0.956221i 0.998125 + 0.0612128i \(0.0194968\pi\)
−0.446051 + 0.895008i \(0.647170\pi\)
\(398\) 5.00000 8.66025i 0.250627 0.434099i
\(399\) 0 0
\(400\) −7.05842 12.2255i −0.352921 0.611277i
\(401\) −5.87228 + 10.1711i −0.293248 + 0.507920i −0.974576 0.224058i \(-0.928069\pi\)
0.681328 + 0.731978i \(0.261403\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 0.813859 + 1.40965i 0.0404910 + 0.0701325i
\(405\) 0 0
\(406\) 0 0
\(407\) −1.37228 + 2.37686i −0.0680215 + 0.117817i
\(408\) 0 0
\(409\) −22.3505 −1.10516 −0.552581 0.833459i \(-0.686357\pi\)
−0.552581 + 0.833459i \(0.686357\pi\)
\(410\) 20.2337 0.999271
\(411\) 0 0
\(412\) 5.00000 8.66025i 0.246332 0.426660i
\(413\) 0 0
\(414\) 0 0
\(415\) −38.2337 66.2227i −1.87682 3.25074i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 0 0
\(418\) −3.43070 + 5.94215i −0.167801 + 0.290640i
\(419\) −6.30298 10.9171i −0.307921 0.533335i 0.669986 0.742373i \(-0.266300\pi\)
−0.977907 + 0.209039i \(0.932967\pi\)
\(420\) 0 0
\(421\) −17.1168 + 29.6472i −0.834224 + 1.44492i 0.0604368 + 0.998172i \(0.480751\pi\)
−0.894661 + 0.446746i \(0.852583\pi\)
\(422\) 8.00000 + 13.8564i 0.389434 + 0.674519i
\(423\) 0 0
\(424\) −4.37228 + 7.57301i −0.212337 + 0.367778i
\(425\) −19.3723 −0.939694
\(426\) 0 0
\(427\) 0 0
\(428\) −3.68614 6.38458i −0.178176 0.308610i
\(429\) 0 0
\(430\) −17.7446 30.7345i −0.855719 1.48215i
\(431\) −3.25544 + 5.63858i −0.156809 + 0.271601i −0.933716 0.358014i \(-0.883454\pi\)
0.776907 + 0.629615i \(0.216787\pi\)
\(432\) 0 0
\(433\) −20.1168 −0.966754 −0.483377 0.875412i \(-0.660590\pi\)
−0.483377 + 0.875412i \(0.660590\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 8.13859 0.389322
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) −2.74456 −0.130546
\(443\) 40.1168 1.90601 0.953004 0.302956i \(-0.0979737\pi\)
0.953004 + 0.302956i \(0.0979737\pi\)
\(444\) 0 0
\(445\) 64.4674 3.05605
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) 0 0
\(448\) 0 0
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0 0
\(451\) 3.17527 5.49972i 0.149517 0.258972i
\(452\) −2.18614 3.78651i −0.102827 0.178102i
\(453\) 0 0
\(454\) −6.12772 10.6135i −0.287588 0.498117i
\(455\) 0 0
\(456\) 0 0
\(457\) −35.4674 −1.65909 −0.829547 0.558437i \(-0.811401\pi\)
−0.829547 + 0.558437i \(0.811401\pi\)
\(458\) 1.44158 2.49689i 0.0673605 0.116672i
\(459\) 0 0
\(460\) 3.55842 + 6.16337i 0.165912 + 0.287368i
\(461\) 1.06930 1.85208i 0.0498021 0.0862598i −0.840050 0.542509i \(-0.817474\pi\)
0.889852 + 0.456250i \(0.150808\pi\)
\(462\) 0 0
\(463\) 11.5584 + 20.0198i 0.537165 + 0.930398i 0.999055 + 0.0434604i \(0.0138382\pi\)
−0.461890 + 0.886937i \(0.652828\pi\)
\(464\) −4.37228 + 7.57301i −0.202978 + 0.351568i
\(465\) 0 0
\(466\) −0.127719 0.221215i −0.00591645 0.0102476i
\(467\) 16.5475 + 28.6612i 0.765729 + 1.32628i 0.939860 + 0.341559i \(0.110955\pi\)
−0.174131 + 0.984722i \(0.555712\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 10.1168 0.465665
\(473\) −11.1386 −0.512153
\(474\) 0 0
\(475\) −35.2921 + 61.1277i −1.61931 + 2.80473i
\(476\) 0 0
\(477\) 0 0
\(478\) 4.93070 + 8.54023i 0.225525 + 0.390621i
\(479\) 16.3723 + 28.3576i 0.748069 + 1.29569i 0.948747 + 0.316036i \(0.102352\pi\)
−0.200679 + 0.979657i \(0.564315\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −9.05842 15.6896i −0.412600 0.714644i
\(483\) 0 0
\(484\) 4.55842 7.89542i 0.207201 0.358883i
\(485\) −17.7446 30.7345i −0.805739 1.39558i
\(486\) 0 0
\(487\) −17.6753 + 30.6145i −0.800943 + 1.38727i 0.118053 + 0.993007i \(0.462335\pi\)
−0.918996 + 0.394266i \(0.870999\pi\)
\(488\) 3.11684 0.141093
\(489\) 0 0
\(490\) 0 0
\(491\) −12.6861 21.9730i −0.572518 0.991629i −0.996306 0.0858685i \(-0.972634\pi\)
0.423789 0.905761i \(-0.360700\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) −5.00000 + 8.66025i −0.224961 + 0.389643i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) −9.05842 + 15.6896i −0.405511 + 0.702365i −0.994381 0.105863i \(-0.966240\pi\)
0.588870 + 0.808228i \(0.299573\pi\)
\(500\) −39.8614 −1.78266
\(501\) 0 0
\(502\) 9.00000 0.401690
\(503\) 32.2337 1.43723 0.718615 0.695409i \(-0.244777\pi\)
0.718615 + 0.695409i \(0.244777\pi\)
\(504\) 0 0
\(505\) 7.11684 0.316695
\(506\) 2.23369 0.0992995
\(507\) 0 0
\(508\) 3.11684 0.138288
\(509\) −14.4891 + 25.0959i −0.642219 + 1.11236i 0.342717 + 0.939439i \(0.388653\pi\)
−0.984936 + 0.172918i \(0.944681\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.43070 + 5.94215i −0.151322 + 0.262097i
\(515\) −21.8614 37.8651i −0.963329 1.66853i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −8.74456 −0.383474
\(521\) −12.4307 + 21.5306i −0.544599 + 0.943273i 0.454033 + 0.890985i \(0.349985\pi\)
−0.998632 + 0.0522883i \(0.983349\pi\)
\(522\) 0 0
\(523\) 17.5584 + 30.4121i 0.767776 + 1.32983i 0.938766 + 0.344555i \(0.111970\pi\)
−0.170990 + 0.985273i \(0.554697\pi\)
\(524\) −0.813859 + 1.40965i −0.0355536 + 0.0615807i
\(525\) 0 0
\(526\) 3.81386 + 6.60580i 0.166292 + 0.288026i
\(527\) 1.37228 2.37686i 0.0597775 0.103538i
\(528\) 0 0
\(529\) 10.1753 + 17.6241i 0.442403 + 0.766264i
\(530\) 19.1168 + 33.1113i 0.830383 + 1.43826i
\(531\) 0 0
\(532\) 0 0
\(533\) 4.62772 8.01544i 0.200449 0.347187i
\(534\) 0 0
\(535\) −32.2337 −1.39358
\(536\) −2.11684 −0.0914337
\(537\) 0 0
\(538\) −0.813859 + 1.40965i −0.0350880 + 0.0607741i
\(539\) 0 0
\(540\) 0 0
\(541\) 3.11684 + 5.39853i 0.134004 + 0.232101i 0.925216 0.379440i \(-0.123883\pi\)
−0.791213 + 0.611541i \(0.790550\pi\)
\(542\) −8.11684 14.0588i −0.348648 0.603877i
\(543\) 0 0
\(544\) 0.686141 1.18843i 0.0294180 0.0509535i
\(545\) 30.6060 + 53.0111i 1.31102 + 2.27075i
\(546\) 0 0
\(547\) −9.05842 + 15.6896i −0.387310 + 0.670841i −0.992087 0.125554i \(-0.959929\pi\)
0.604777 + 0.796395i \(0.293262\pi\)
\(548\) 5.31386 + 9.20387i 0.226997 + 0.393170i
\(549\) 0 0
\(550\) −9.68614 + 16.7769i −0.413018 + 0.715369i
\(551\) 43.7228 1.86265
\(552\) 0 0
\(553\) 0 0
\(554\) 6.11684 + 10.5947i 0.259880 + 0.450125i
\(555\) 0 0
\(556\) −6.61684 11.4607i −0.280617 0.486042i
\(557\) 14.7446 25.5383i 0.624747 1.08209i −0.363843 0.931460i \(-0.618535\pi\)
0.988590 0.150633i \(-0.0481313\pi\)
\(558\) 0 0
\(559\) −16.2337 −0.686612
\(560\) 0 0
\(561\) 0 0
\(562\) 8.18614 14.1788i 0.345312 0.598097i
\(563\) −3.00000 −0.126435 −0.0632175 0.998000i \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) 0 0
\(565\) −19.1168 −0.804252
\(566\) 27.1168 1.13981
\(567\) 0 0
\(568\) 7.11684 0.298616
\(569\) −16.1168 −0.675653 −0.337827 0.941208i \(-0.609692\pi\)
−0.337827 + 0.941208i \(0.609692\pi\)
\(570\) 0 0
\(571\) −22.3505 −0.935341 −0.467670 0.883903i \(-0.654907\pi\)
−0.467670 + 0.883903i \(0.654907\pi\)
\(572\) −1.37228 + 2.37686i −0.0573780 + 0.0993815i
\(573\) 0 0
\(574\) 0 0
\(575\) 22.9783 0.958259
\(576\) 0 0
\(577\) −4.94158 + 8.55906i −0.205721 + 0.356319i −0.950362 0.311146i \(-0.899287\pi\)
0.744641 + 0.667465i \(0.232620\pi\)
\(578\) 7.55842 + 13.0916i 0.314389 + 0.544538i
\(579\) 0 0
\(580\) 19.1168 + 33.1113i 0.793784 + 1.37487i
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 0.496989
\(584\) −6.05842 + 10.4935i −0.250699 + 0.434224i
\(585\) 0 0
\(586\) −5.18614 8.98266i −0.214237 0.371070i
\(587\) 7.24456 12.5480i 0.299015 0.517909i −0.676896 0.736079i \(-0.736675\pi\)
0.975911 + 0.218170i \(0.0700086\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) 22.1168 38.3075i 0.910536 1.57709i
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 7.37228 + 12.7692i 0.302743 + 0.524367i 0.976756 0.214353i \(-0.0687642\pi\)
−0.674013 + 0.738719i \(0.735431\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.62772 2.81929i 0.0666740 0.115483i
\(597\) 0 0
\(598\) 3.25544 0.133125
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −12.0584 + 20.8858i −0.491873 + 0.851950i −0.999956 0.00935863i \(-0.997021\pi\)
0.508083 + 0.861308i \(0.330354\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4.55842 7.89542i −0.185480 0.321260i
\(605\) −19.9307 34.5210i −0.810298 1.40348i
\(606\) 0 0
\(607\) −11.1168 + 19.2549i −0.451219 + 0.781534i −0.998462 0.0554398i \(-0.982344\pi\)
0.547243 + 0.836974i \(0.315677\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 0 0
\(610\) 6.81386 11.8020i 0.275885 0.477847i
\(611\) 0 0
\(612\) 0 0
\(613\) 18.1168 31.3793i 0.731732 1.26740i −0.224410 0.974495i \(-0.572045\pi\)
0.956142 0.292903i \(-0.0946213\pi\)
\(614\) −13.0000 −0.524637
\(615\) 0 0
\(616\) 0 0
\(617\) 9.43070 + 16.3345i 0.379666 + 0.657600i 0.991014 0.133762i \(-0.0427056\pi\)
−0.611348 + 0.791362i \(0.709372\pi\)
\(618\) 0 0
\(619\) −22.7337 39.3759i −0.913744 1.58265i −0.808730 0.588180i \(-0.799844\pi\)
−0.105014 0.994471i \(-0.533489\pi\)
\(620\) 4.37228 7.57301i 0.175595 0.304140i
\(621\) 0 0
\(622\) −8.23369 −0.330141
\(623\) 0 0
\(624\) 0 0
\(625\) −51.8505 + 89.8078i −2.07402 + 3.59231i
\(626\) −20.1168 −0.804031
\(627\) 0 0
\(628\) 9.11684 0.363802
\(629\) −2.74456 −0.109433
\(630\) 0 0
\(631\) −37.3505 −1.48690 −0.743451 0.668791i \(-0.766812\pi\)
−0.743451 + 0.668791i \(0.766812\pi\)
\(632\) −5.11684 −0.203537
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) 6.81386 11.8020i 0.270400 0.468346i
\(636\) 0 0
\(637\) 0 0
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) 2.18614 3.78651i 0.0864148 0.149675i
\(641\) 17.1060 + 29.6284i 0.675645 + 1.17025i 0.976280 + 0.216512i \(0.0694682\pi\)
−0.300635 + 0.953739i \(0.597198\pi\)
\(642\) 0 0
\(643\) −13.1753 22.8202i −0.519582 0.899942i −0.999741 0.0227606i \(-0.992754\pi\)
0.480159 0.877181i \(-0.340579\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.86141 −0.269958
\(647\) 2.74456 4.75372i 0.107900 0.186888i −0.807019 0.590525i \(-0.798921\pi\)
0.914919 + 0.403637i \(0.132254\pi\)
\(648\) 0 0
\(649\) −6.94158 12.0232i −0.272481 0.471951i
\(650\) −14.1168 + 24.4511i −0.553708 + 0.959051i
\(651\) 0 0
\(652\) 9.11684 + 15.7908i 0.357043 + 0.618417i
\(653\) −13.3723 + 23.1615i −0.523298 + 0.906378i 0.476335 + 0.879264i \(0.341965\pi\)
−0.999632 + 0.0271143i \(0.991368\pi\)
\(654\) 0 0
\(655\) 3.55842 + 6.16337i 0.139039 + 0.240823i
\(656\) 2.31386 + 4.00772i 0.0903410 + 0.156475i
\(657\) 0 0
\(658\) 0 0
\(659\) −10.3723 + 17.9653i −0.404047 + 0.699829i −0.994210 0.107454i \(-0.965730\pi\)
0.590163 + 0.807284i \(0.299063\pi\)
\(660\) 0 0
\(661\) 27.1168 1.05472 0.527361 0.849641i \(-0.323181\pi\)
0.527361 + 0.849641i \(0.323181\pi\)
\(662\) 22.2337 0.864137
\(663\) 0 0
\(664\) 8.74456 15.1460i 0.339355 0.587780i
\(665\) 0 0
\(666\) 0 0
\(667\) −7.11684 12.3267i −0.275565 0.477293i
\(668\) −2.74456 4.75372i −0.106190 0.183927i
\(669\) 0 0
\(670\) −4.62772 + 8.01544i −0.178784 + 0.309664i
\(671\) −2.13859 3.70415i −0.0825595 0.142997i
\(672\) 0 0
\(673\) 1.44158 2.49689i 0.0555687 0.0962479i −0.836903 0.547351i \(-0.815636\pi\)
0.892472 + 0.451103i \(0.148969\pi\)
\(674\) 4.05842 + 7.02939i 0.156325 + 0.270762i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −34.4674 −1.32469 −0.662344 0.749199i \(-0.730438\pi\)
−0.662344 + 0.749199i \(0.730438\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 0 0
\(682\) −1.37228 2.37686i −0.0525474 0.0910147i
\(683\) 14.9198 25.8419i 0.570891 0.988813i −0.425583 0.904919i \(-0.639931\pi\)
0.996475 0.0838936i \(-0.0267356\pi\)
\(684\) 0 0
\(685\) 46.4674 1.77543
\(686\) 0 0
\(687\) 0 0
\(688\) 4.05842 7.02939i 0.154726 0.267993i
\(689\) 17.4891 0.666283
\(690\) 0 0
\(691\) −23.1168 −0.879406 −0.439703 0.898143i \(-0.644916\pi\)
−0.439703 + 0.898143i \(0.644916\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 10.1168 0.384030
\(695\) −57.8614 −2.19481
\(696\) 0 0
\(697\) 6.35053 0.240544
\(698\) 11.0000 19.0526i 0.416356 0.721150i
\(699\) 0 0
\(700\) 0 0
\(701\) 38.2337 1.44407 0.722033 0.691858i \(-0.243208\pi\)
0.722033 + 0.691858i \(0.243208\pi\)
\(702\) 0 0
\(703\) −5.00000 + 8.66025i −0.188579 + 0.326628i
\(704\) −0.686141 1.18843i −0.0258599 0.0447907i
\(705\) 0 0
\(706\) −6.68614 11.5807i −0.251636 0.435847i
\(707\) 0 0
\(708\) 0 0
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) 15.5584 26.9480i 0.583897 1.01134i
\(711\) 0 0
\(712\) 7.37228 + 12.7692i 0.276288 + 0.478545i
\(713\) −1.62772 + 2.81929i −0.0609585 + 0.105583i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) 1.62772 2.81929i 0.0608307 0.105362i
\(717\) 0 0
\(718\) 10.9307 + 18.9325i 0.407930 + 0.706556i
\(719\) 1.37228 + 2.37686i 0.0511775 + 0.0886420i 0.890479 0.455024i \(-0.150369\pi\)
−0.839302 + 0.543666i \(0.817036\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3.00000 + 5.19615i −0.111648 + 0.193381i
\(723\) 0 0
\(724\) 0.883156 0.0328222
\(725\) 123.446 4.58466
\(726\) 0 0
\(727\) 18.1168 31.3793i 0.671917 1.16379i −0.305443 0.952210i \(-0.598805\pi\)
0.977360 0.211583i \(-0.0678620\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 26.4891 + 45.8805i 0.980407 + 1.69811i
\(731\) −5.56930 9.64630i −0.205988 0.356781i
\(732\) 0 0
\(733\) 20.5584 35.6082i 0.759343 1.31522i −0.183844 0.982956i \(-0.558854\pi\)
0.943186 0.332265i \(-0.107813\pi\)
\(734\) 6.11684 + 10.5947i 0.225777 + 0.391057i
\(735\) 0 0
\(736\) −0.813859 + 1.40965i −0.0299993 + 0.0519602i
\(737\) 1.45245 + 2.51572i 0.0535018 + 0.0926678i
\(738\) 0 0
\(739\) 4.05842 7.02939i 0.149291 0.258580i −0.781674 0.623687i \(-0.785634\pi\)
0.930966 + 0.365106i \(0.118967\pi\)
\(740\) −8.74456 −0.321457
\(741\) 0 0
\(742\) 0 0
\(743\) −6.86141 11.8843i −0.251721 0.435993i 0.712279 0.701896i \(-0.247663\pi\)
−0.964000 + 0.265904i \(0.914330\pi\)
\(744\) 0 0
\(745\) −7.11684 12.3267i −0.260741 0.451617i
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 0 0
\(748\) −1.88316 −0.0688550
\(749\) 0 0
\(750\) 0 0
\(751\) 8.55842 14.8236i 0.312301 0.540922i −0.666559 0.745452i \(-0.732234\pi\)
0.978860 + 0.204531i \(0.0655668\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 17.4891 0.636916
\(755\) −39.8614 −1.45071
\(756\) 0 0
\(757\) 46.2337 1.68039 0.840196 0.542283i \(-0.182440\pi\)
0.840196 + 0.542283i \(0.182440\pi\)
\(758\) −8.11684 −0.294817
\(759\) 0 0
\(760\) −21.8614 −0.792997
\(761\) 17.7446 30.7345i 0.643240 1.11412i −0.341465 0.939894i \(-0.610923\pi\)
0.984705 0.174230i \(-0.0557435\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 19.1168 0.691623
\(765\) 0 0
\(766\) −16.3723 + 28.3576i −0.591555 + 1.02460i
\(767\) −10.1168 17.5229i −0.365298 0.632715i
\(768\) 0 0
\(769\) 5.00000 + 8.66025i 0.180305 + 0.312297i 0.941984 0.335657i \(-0.108958\pi\)
−0.761680 + 0.647954i \(0.775625\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 −0.251936
\(773\) −19.9307 + 34.5210i −0.716858 + 1.24163i 0.245381 + 0.969427i \(0.421087\pi\)
−0.962239 + 0.272207i \(0.912246\pi\)
\(774\) 0 0
\(775\) −14.1168 24.4511i −0.507092 0.878309i
\(776\) 4.05842 7.02939i 0.145689 0.252341i
\(777\) 0 0
\(778\) 5.48913 + 9.50744i 0.196795 + 0.340858i
\(779\) 11.5693 20.0386i 0.414513 0.717958i
\(780\) 0 0
\(781\) −4.88316 8.45787i −0.174733 0.302647i
\(782\) 1.11684 + 1.93443i 0.0399383 + 0.0691751i
\(783\) 0 0
\(784\) 0 0
\(785\) 19.9307 34.5210i 0.711357 1.23211i
\(786\) 0 0
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 6.00000 0.213741
\(789\) 0 0
\(790\) −11.1861 + 19.3750i −0.397985 + 0.689330i
\(791\) 0 0
\(792\) 0 0
\(793\) −3.11684 5.39853i −0.110682 0.191707i
\(794\) 11.0000 + 19.0526i 0.390375 + 0.676150i