Properties

Label 2646.2.h.k.667.1
Level $2646$
Weight $2$
Character 2646.667
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.h (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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.k.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -4.37228 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -4.37228 q^{5} +1.00000 q^{8} +(2.18614 + 3.78651i) q^{10} +1.37228 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(0.686141 + 1.18843i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(2.18614 - 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} +1.62772 q^{23} +14.1168 q^{25} +(-1.00000 + 1.73205i) q^{26} +(-4.37228 + 7.57301i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.686141 - 1.18843i) q^{34} +(-1.00000 + 1.73205i) q^{37} +5.00000 q^{38} -4.37228 q^{40} +(2.31386 + 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +(-0.686141 + 1.18843i) q^{44} +(-0.813859 - 1.40965i) q^{46} +(-7.05842 - 12.2255i) q^{50} +2.00000 q^{52} +(-4.37228 - 7.57301i) q^{53} -6.00000 q^{55} +8.74456 q^{58} +(-5.05842 + 8.76144i) q^{59} +(-1.55842 - 2.69927i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(4.37228 + 7.57301i) q^{65} +(1.05842 - 1.83324i) q^{67} -1.37228 q^{68} +7.11684 q^{71} +(-6.05842 - 10.4935i) q^{73} +2.00000 q^{74} +(-2.50000 - 4.33013i) q^{76} +(2.55842 + 4.43132i) q^{79} +(2.18614 + 3.78651i) q^{80} +(2.31386 - 4.00772i) q^{82} +(8.74456 - 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} -8.11684 q^{86} +1.37228 q^{88} +(7.37228 - 12.7692i) q^{89} +(-0.813859 + 1.40965i) q^{92} +(10.9307 - 18.9325i) q^{95} +(4.05842 - 7.02939i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} - 6q^{5} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} - 6q^{5} + 4q^{8} + 3q^{10} - 6q^{11} - 4q^{13} - 2q^{16} - 3q^{17} - 10q^{19} + 3q^{20} + 3q^{22} + 18q^{23} + 22q^{25} - 4q^{26} - 6q^{29} - 4q^{31} - 2q^{32} - 3q^{34} - 4q^{37} + 20q^{38} - 6q^{40} + 15q^{41} - q^{43} + 3q^{44} - 9q^{46} - 11q^{50} + 8q^{52} - 6q^{53} - 24q^{55} + 12q^{58} - 3q^{59} + 11q^{61} + 8q^{62} + 4q^{64} + 6q^{65} - 13q^{67} + 6q^{68} - 6q^{71} - 7q^{73} + 8q^{74} - 10q^{76} - 7q^{79} + 3q^{80} + 15q^{82} + 12q^{83} - 12q^{85} + 2q^{86} - 6q^{88} + 18q^{89} - 9q^{92} + 15q^{95} - q^{97} + O(q^{100}) \)

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
\(5\) −4.37228 −1.95534 −0.977672 0.210138i \(-0.932609\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.18614 + 3.78651i 0.691318 + 1.19740i
\(11\) 1.37228 0.413758 0.206879 0.978366i \(-0.433669\pi\)
0.206879 + 0.978366i \(0.433669\pi\)
\(12\) 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
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.686141 + 1.18843i 0.166414 + 0.288237i 0.937156 0.348910i \(-0.113448\pi\)
−0.770743 + 0.637146i \(0.780115\pi\)
\(18\) 0 0
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 2.18614 3.78651i 0.488836 0.846689i
\(21\) 0 0
\(22\) −0.686141 1.18843i −0.146286 0.253374i
\(23\) 1.62772 0.339403 0.169701 0.985496i \(-0.445720\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 0 0
\(25\) 14.1168 2.82337
\(26\) −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
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 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 −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 5.00000 0.811107
\(39\) 0 0
\(40\) −4.37228 −0.691318
\(41\) 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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −7.05842 12.2255i −0.998212 1.72895i
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) −4.37228 7.57301i −0.600579 1.04023i −0.992733 0.120334i \(-0.961603\pi\)
0.392154 0.919899i \(-0.371730\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 0 0
\(58\) 8.74456 1.14822
\(59\) −5.05842 + 8.76144i −0.658550 + 1.14064i 0.322441 + 0.946590i \(0.395497\pi\)
−0.980991 + 0.194053i \(0.937837\pi\)
\(60\) 0 0
\(61\) −1.55842 2.69927i −0.199535 0.345606i 0.748842 0.662748i \(-0.230610\pi\)
−0.948378 + 0.317142i \(0.897277\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.37228 + 7.57301i 0.542315 + 0.939317i
\(66\) 0 0
\(67\) 1.05842 1.83324i 0.129307 0.223966i −0.794101 0.607785i \(-0.792058\pi\)
0.923408 + 0.383819i \(0.125391\pi\)
\(68\) −1.37228 −0.166414
\(69\) 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 −0.965197 0.261524i \(-0.915775\pi\)
0.256112 0.966647i \(-0.417558\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.55842 + 4.43132i 0.287845 + 0.498562i 0.973295 0.229557i \(-0.0737279\pi\)
−0.685450 + 0.728120i \(0.740395\pi\)
\(80\) 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
\(86\) −8.11684 −0.875262
\(87\) 0 0
\(88\) 1.37228 0.146286
\(89\) 7.37228 12.7692i 0.781460 1.35353i −0.149631 0.988742i \(-0.547808\pi\)
0.931091 0.364787i \(-0.118858\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.813859 + 1.40965i −0.0848507 + 0.146966i
\(93\) 0 0
\(94\) 0 0
\(95\) 10.9307 18.9325i 1.12147 1.94244i
\(96\) 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
\(101\) −1.62772 −0.161964 −0.0809820 0.996716i \(-0.525806\pi\)
−0.0809820 + 0.996716i \(0.525806\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) −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 −0.987348 0.158565i \(-0.949313\pi\)
0.630996 + 0.775786i \(0.282646\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 3.00000 + 5.19615i 0.286039 + 0.495434i
\(111\) 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
\(115\) −7.11684 −0.663649
\(116\) −4.37228 7.57301i −0.405956 0.703137i
\(117\) 0 0
\(118\) 10.1168 0.931331
\(119\) 0 0
\(120\) 0 0
\(121\) −9.11684 −0.828804
\(122\) −1.55842 + 2.69927i −0.141093 + 0.244380i
\(123\) 0 0
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) −39.8614 −3.56531
\(126\) 0 0
\(127\) 3.11684 0.276575 0.138288 0.990392i \(-0.455840\pi\)
0.138288 + 0.990392i \(0.455840\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 4.37228 7.57301i 0.383474 0.664197i
\(131\) 1.62772 0.142214 0.0711072 0.997469i \(-0.477347\pi\)
0.0711072 + 0.997469i \(0.477347\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −2.11684 −0.182867
\(135\) 0 0
\(136\) 0.686141 + 1.18843i 0.0588361 + 0.101907i
\(137\) −10.6277 −0.907987 −0.453994 0.891005i \(-0.650001\pi\)
−0.453994 + 0.891005i \(0.650001\pi\)
\(138\) 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
\(142\) −3.55842 6.16337i −0.298616 0.517218i
\(143\) −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
\(149\) −3.25544 −0.266696 −0.133348 0.991069i \(-0.542573\pi\)
−0.133348 + 0.991069i \(0.542573\pi\)
\(150\) 0 0
\(151\) 9.11684 0.741918 0.370959 0.928649i \(-0.379029\pi\)
0.370959 + 0.928649i \(0.379029\pi\)
\(152\) −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
\(157\) −4.55842 + 7.89542i −0.363802 + 0.630123i −0.988583 0.150677i \(-0.951855\pi\)
0.624781 + 0.780800i \(0.285188\pi\)
\(158\) 2.55842 4.43132i 0.203537 0.352537i
\(159\) 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 −0.249225 0.968446i \(-0.580176\pi\)
0.963311 0.268388i \(-0.0864909\pi\)
\(164\) −4.62772 −0.361364
\(165\) 0 0
\(166\) −17.4891 −1.35742
\(167\) −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
\(173\) −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
\(176\) −0.686141 1.18843i −0.0517198 0.0895813i
\(177\) 0 0
\(178\) −14.7446 −1.10515
\(179\) 1.62772 + 2.81929i 0.121661 + 0.210724i 0.920423 0.390924i \(-0.127844\pi\)
−0.798762 + 0.601648i \(0.794511\pi\)
\(180\) 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
\(184\) 1.62772 0.119997
\(185\) 4.37228 7.57301i 0.321457 0.556779i
\(186\) 0 0
\(187\) 0.941578 + 1.63086i 0.0688550 + 0.119260i
\(188\) 0 0
\(189\) 0 0
\(190\) −21.8614 −1.58599
\(191\) −9.55842 16.5557i −0.691623 1.19793i −0.971306 0.237834i \(-0.923563\pi\)
0.279683 0.960092i \(-0.409771\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) −8.11684 −0.582755
\(195\) 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 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 14.1168 0.998212
\(201\) 0 0
\(202\) 0.813859 + 1.40965i 0.0572629 + 0.0991823i
\(203\) 0 0
\(204\) 0 0
\(205\) −10.1168 17.5229i −0.706591 1.22385i
\(206\) 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 \(0.647678\pi\)
\(212\) 8.74456 0.600579
\(213\) 0 0
\(214\) 7.37228 0.503959
\(215\) −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
\(220\) 3.00000 5.19615i 0.202260 0.350325i
\(221\) 1.37228 2.37686i 0.0923096 0.159885i
\(222\) 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
\(227\) 12.2554 0.813422 0.406711 0.913557i \(-0.366676\pi\)
0.406711 + 0.913557i \(0.366676\pi\)
\(228\) 0 0
\(229\) −2.88316 −0.190524 −0.0952622 0.995452i \(-0.530369\pi\)
−0.0952622 + 0.995452i \(0.530369\pi\)
\(230\) 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 −0.870179 0.492736i \(-0.835997\pi\)
0.861812 + 0.507229i \(0.169330\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.05842 8.76144i −0.329275 0.570321i
\(237\) 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
\(241\) 18.1168 1.16701 0.583504 0.812110i \(-0.301681\pi\)
0.583504 + 0.812110i \(0.301681\pi\)
\(242\) 4.55842 + 7.89542i 0.293026 + 0.507537i
\(243\) 0 0
\(244\) 3.11684 0.199535
\(245\) 0 0
\(246\) 0 0
\(247\) 10.0000 0.636285
\(248\) −1.00000 + 1.73205i −0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 19.9307 + 34.5210i 1.26053 + 2.18330i
\(251\) 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
\(254\) −1.55842 2.69927i −0.0977841 0.169367i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.86141 0.428003 0.214001 0.976833i \(-0.431350\pi\)
0.214001 + 0.976833i \(0.431350\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −8.74456 −0.542315
\(261\) 0 0
\(262\) −0.813859 1.40965i −0.0502804 0.0870882i
\(263\) −7.62772 −0.470345 −0.235173 0.971954i \(-0.575566\pi\)
−0.235173 + 0.971954i \(0.575566\pi\)
\(264\) 0 0
\(265\) 19.1168 + 33.1113i 1.17434 + 2.03401i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.05842 + 1.83324i 0.0646534 + 0.111983i
\(269\) −0.813859 1.40965i −0.0496219 0.0859476i 0.840148 0.542358i \(-0.182468\pi\)
−0.889769 + 0.456410i \(0.849135\pi\)
\(270\) 0 0
\(271\) −8.11684 + 14.0588i −0.493063 + 0.854010i −0.999968 0.00799154i \(-0.997456\pi\)
0.506905 + 0.862002i \(0.330790\pi\)
\(272\) 0.686141 1.18843i 0.0416034 0.0720592i
\(273\) 0 0
\(274\) 5.31386 + 9.20387i 0.321022 + 0.556026i
\(275\) 19.3723 1.16819
\(276\) 0 0
\(277\) −12.2337 −0.735051 −0.367526 0.930013i \(-0.619795\pi\)
−0.367526 + 0.930013i \(0.619795\pi\)
\(278\) −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
\(283\) −13.5584 + 23.4839i −0.805965 + 1.39597i 0.109673 + 0.993968i \(0.465019\pi\)
−0.915638 + 0.402004i \(0.868314\pi\)
\(284\) −3.55842 + 6.16337i −0.211153 + 0.365729i
\(285\) 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
\(290\) −38.2337 −2.24516
\(291\) 0 0
\(292\) 12.1168 0.709085
\(293\) −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
\(299\) −1.62772 2.81929i −0.0941334 0.163044i
\(300\) 0 0
\(301\) 0 0
\(302\) −4.55842 7.89542i −0.262308 0.454330i
\(303\) 0 0
\(304\) 5.00000 0.286770
\(305\) 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
\(310\) −8.74456 −0.496658
\(311\) 4.11684 7.13058i 0.233445 0.404338i −0.725375 0.688354i \(-0.758334\pi\)
0.958820 + 0.284016i \(0.0916668\pi\)
\(312\) 0 0
\(313\) 10.0584 + 17.4217i 0.568536 + 0.984733i 0.996711 + 0.0810370i \(0.0258232\pi\)
−0.428175 + 0.903696i \(0.640843\pi\)
\(314\) 9.11684 0.514493
\(315\) 0 0
\(316\) −5.11684 −0.287845
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) −4.37228 −0.244418
\(321\) 0 0
\(322\) 0 0
\(323\) −6.86141 −0.381779
\(324\) 0 0
\(325\) −14.1168 24.4511i −0.783062 1.35630i
\(326\) −18.2337 −1.00987
\(327\) 0 0
\(328\) 2.31386 + 4.00772i 0.127762 + 0.221289i
\(329\) 0 0
\(330\) 0 0
\(331\) −11.1168 19.2549i −0.611037 1.05835i −0.991066 0.133373i \(-0.957419\pi\)
0.380029 0.924975i \(-0.375914\pi\)
\(332\) 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 \(0.762376\pi\)
\(338\) −9.00000 −0.489535
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) −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
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) −5.05842 + 8.76144i −0.271550 + 0.470339i −0.969259 0.246043i \(-0.920870\pi\)
0.697709 + 0.716382i \(0.254203\pi\)
\(348\) 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
\(353\) 13.3723 0.711735 0.355867 0.934536i \(-0.384185\pi\)
0.355867 + 0.934536i \(0.384185\pi\)
\(354\) 0 0
\(355\) −31.1168 −1.65151
\(356\) 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 −0.418932 0.908018i \(-0.637595\pi\)
0.995832 0.0912032i \(-0.0290713\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −0.441578 0.764836i −0.0232088 0.0401989i
\(363\) 0 0
\(364\) 0 0
\(365\) 26.4891 + 45.8805i 1.38650 + 2.40150i
\(366\) 0 0
\(367\) −12.2337 −0.638593 −0.319297 0.947655i \(-0.603447\pi\)
−0.319297 + 0.947655i \(0.603447\pi\)
\(368\) −0.813859 1.40965i −0.0424254 0.0734829i
\(369\) 0 0
\(370\) −8.74456 −0.454608
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0.941578 1.63086i 0.0486878 0.0843298i
\(375\) 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 \(0.566847\pi\)
\(380\) 10.9307 + 18.9325i 0.560733 + 0.971218i
\(381\) 0 0
\(382\) −9.55842 + 16.5557i −0.489051 + 0.847062i
\(383\) 32.7446 1.67317 0.836584 0.547838i \(-0.184549\pi\)
0.836584 + 0.547838i \(0.184549\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) 4.05842 + 7.02939i 0.206035 + 0.356863i
\(389\) −10.9783 −0.556619 −0.278310 0.960491i \(-0.589774\pi\)
−0.278310 + 0.960491i \(0.589774\pi\)
\(390\) 0 0
\(391\) 1.11684 + 1.93443i 0.0564812 + 0.0978284i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) −11.1861 19.3750i −0.562836 0.974860i
\(396\) 0 0
\(397\) 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i \(-0.647170\pi\)
0.998125 0.0612128i \(-0.0194968\pi\)
\(398\) 5.00000 8.66025i 0.250627 0.434099i
\(399\) 0 0
\(400\) −7.05842 12.2255i −0.352921 0.611277i
\(401\) 11.7446 0.586495 0.293248 0.956036i \(-0.405264\pi\)
0.293248 + 0.956036i \(0.405264\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) 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
\(409\) 11.1753 19.3561i 0.552581 0.957099i −0.445506 0.895279i \(-0.646976\pi\)
0.998087 0.0618200i \(-0.0196905\pi\)
\(410\) −10.1168 + 17.5229i −0.499635 + 0.865394i
\(411\) 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
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) 6.86141 0.335602
\(419\) −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
\(425\) 9.68614 + 16.7769i 0.469847 + 0.813799i
\(426\) 0 0
\(427\) 0 0
\(428\) −3.68614 6.38458i −0.178176 0.308610i
\(429\) 0 0
\(430\) 35.4891 1.71144
\(431\) −3.25544 5.63858i −0.156809 0.271601i 0.776907 0.629615i \(-0.216787\pi\)
−0.933716 + 0.358014i \(0.883454\pi\)
\(432\) 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
\(436\) 14.0000 0.670478
\(437\) −4.06930 + 7.04823i −0.194661 + 0.337162i
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) −2.74456 −0.130546
\(443\) −20.0584 34.7422i −0.953004 1.65065i −0.738870 0.673848i \(-0.764640\pi\)
−0.214134 0.976804i \(-0.568693\pi\)
\(444\) 0 0
\(445\) −32.2337 + 55.8304i −1.52802 + 2.64661i
\(446\) −4.00000 −0.189405
\(447\) 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
\(452\) 4.37228 0.205655
\(453\) 0 0
\(454\) −6.12772 10.6135i −0.287588 0.498117i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.7337 + 30.7156i 0.829547 + 1.43682i 0.898394 + 0.439190i \(0.144735\pi\)
−0.0688472 + 0.997627i \(0.521932\pi\)
\(458\) 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 \(0.652828\pi\)
\(464\) 8.74456 0.405956
\(465\) 0 0
\(466\) 0.255437 0.0118329
\(467\) 16.5475 28.6612i 0.765729 1.32628i −0.174131 0.984722i \(-0.555712\pi\)
0.939860 0.341559i \(-0.110955\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −5.05842 + 8.76144i −0.232833 + 0.403278i
\(473\) 5.56930 9.64630i 0.256077 0.443538i
\(474\) 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
\(479\) −32.7446 −1.49614 −0.748069 0.663621i \(-0.769019\pi\)
−0.748069 + 0.663621i \(0.769019\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) −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 −0.918996 0.394266i \(-0.870999\pi\)
0.118053 0.993007i \(-0.462335\pi\)
\(488\) −1.55842 2.69927i −0.0705464 0.122190i
\(489\) 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
\(493\) −12.0000 −0.540453
\(494\) −5.00000 8.66025i −0.224961 0.389643i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) 18.1168 0.811021 0.405511 0.914090i \(-0.367094\pi\)
0.405511 + 0.914090i \(0.367094\pi\)
\(500\) 19.9307 34.5210i 0.891328 1.54383i
\(501\) 0 0
\(502\) −4.50000 7.79423i −0.200845 0.347873i
\(503\) 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
\(506\) −1.11684 1.93443i −0.0496498 0.0859959i
\(507\) 0 0
\(508\) −1.55842 + 2.69927i −0.0691438 + 0.119761i
\(509\) 28.9783 1.28444 0.642219 0.766521i \(-0.278014\pi\)
0.642219 + 0.766521i \(0.278014\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.43070 5.94215i −0.151322 0.262097i
\(515\) 43.7228 1.92666
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 4.37228 + 7.57301i 0.191737 + 0.332099i
\(521\) −12.4307 21.5306i −0.544599 0.943273i −0.998632 0.0522883i \(-0.983349\pi\)
0.454033 0.890985i \(-0.349985\pi\)
\(522\) 0 0
\(523\) 17.5584 30.4121i 0.767776 1.32983i −0.170990 0.985273i \(-0.554697\pi\)
0.938766 0.344555i \(-0.111970\pi\)
\(524\) −0.813859 + 1.40965i −0.0355536 + 0.0615807i
\(525\) 0 0
\(526\) 3.81386 + 6.60580i 0.166292 + 0.288026i
\(527\) −2.74456 −0.119555
\(528\) 0 0
\(529\) −20.3505 −0.884806
\(530\) 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
\(535\) 16.1168 27.9152i 0.696792 1.20688i
\(536\) 1.05842 1.83324i 0.0457169 0.0791839i
\(537\) 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 −0.791213 0.611541i \(-0.790550\pi\)
0.925216 + 0.379440i \(0.123883\pi\)
\(542\) 16.2337 0.697297
\(543\) 0 0
\(544\) −1.37228 −0.0588361
\(545\) 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
\(551\) −21.8614 37.8651i −0.931327 1.61311i
\(552\) 0 0
\(553\) 0 0
\(554\) 6.11684 + 10.5947i 0.259880 + 0.450125i
\(555\) 0 0
\(556\) 13.2337 0.561233
\(557\) 14.7446 + 25.5383i 0.624747 + 1.08209i 0.988590 + 0.150633i \(0.0481313\pi\)
−0.363843 + 0.931460i \(0.618535\pi\)
\(558\) 0 0
\(559\) −16.2337 −0.686612
\(560\) 0 0
\(561\) 0 0
\(562\) −16.3723 −0.690623
\(563\) 1.50000 2.59808i 0.0632175 0.109496i −0.832684 0.553748i \(-0.813197\pi\)
0.895902 + 0.444252i \(0.146530\pi\)
\(564\) 0 0
\(565\) 9.55842 + 16.5557i 0.402126 + 0.696502i
\(566\) 27.1168 1.13981
\(567\) 0 0
\(568\) 7.11684 0.298616
\(569\) 8.05842 + 13.9576i 0.337827 + 0.585133i 0.984024 0.178038i \(-0.0569749\pi\)
−0.646197 + 0.763171i \(0.723642\pi\)
\(570\) 0 0
\(571\) 11.1753 19.3561i 0.467670 0.810029i −0.531647 0.846966i \(-0.678427\pi\)
0.999318 + 0.0369371i \(0.0117601\pi\)
\(572\) 2.74456 0.114756
\(573\) 0 0
\(574\) 0 0
\(575\) 22.9783 0.958259
\(576\) 0 0
\(577\) −4.94158 8.55906i −0.205721 0.356319i 0.744641 0.667465i \(-0.232620\pi\)
−0.950362 + 0.311146i \(0.899287\pi\)
\(578\) −15.1168 −0.628778
\(579\) 0 0
\(580\) 19.1168 + 33.1113i 0.793784 + 1.37487i
\(581\) 0 0
\(582\) 0 0
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −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
\(590\) −44.2337 −1.82107
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) 7.37228 12.7692i 0.302743 0.524367i −0.674013 0.738719i \(-0.735431\pi\)
0.976756 + 0.214353i \(0.0687642\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.62772 2.81929i 0.0666740 0.115483i
\(597\) 0 0
\(598\) −1.62772 + 2.81929i −0.0665624 + 0.115289i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 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
\(605\) 39.8614 1.62060
\(606\) 0 0
\(607\) 22.2337 0.902438 0.451219 0.892413i \(-0.350989\pi\)
0.451219 + 0.892413i \(0.350989\pi\)
\(608\) −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 0.956142 + 0.292903i \(0.0946213\pi\)
−0.224410 + 0.974495i \(0.572045\pi\)
\(614\) 6.50000 + 11.2583i 0.262319 + 0.454349i
\(615\) 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
\(619\) 45.4674 1.82749 0.913744 0.406290i \(-0.133178\pi\)
0.913744 + 0.406290i \(0.133178\pi\)
\(620\) 4.37228 + 7.57301i 0.175595 + 0.304140i
\(621\) 0 0
\(622\) −8.23369 −0.330141
\(623\) 0 0
\(624\) 0 0
\(625\) 103.701 4.14804
\(626\) 10.0584 17.4217i 0.402015 0.696311i
\(627\) 0 0
\(628\) −4.55842 7.89542i −0.181901 0.315061i
\(629\) −2.74456 −0.109433
\(630\) 0 0
\(631\) −37.3505 −1.48690 −0.743451 0.668791i \(-0.766812\pi\)
−0.743451 + 0.668791i \(0.766812\pi\)
\(632\) 2.55842 + 4.43132i 0.101769 + 0.176268i
\(633\) 0 0
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) −13.6277 −0.540800
\(636\) 0 0
\(637\) 0 0
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) 2.18614 + 3.78651i 0.0864148 + 0.149675i
\(641\) −34.2119 −1.35129 −0.675645 0.737227i \(-0.736135\pi\)
−0.675645 + 0.737227i \(0.736135\pi\)
\(642\) 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
\(646\) 3.43070 + 5.94215i 0.134979 + 0.233791i
\(647\) 2.74456 + 4.75372i 0.107900 + 0.186888i 0.914919 0.403637i \(-0.132254\pi\)
−0.807019 + 0.590525i \(0.798921\pi\)
\(648\) 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
\(653\) 26.7446 1.04660 0.523298 0.852150i \(-0.324702\pi\)
0.523298 + 0.852150i \(0.324702\pi\)
\(654\) 0 0
\(655\) −7.11684 −0.278078
\(656\) 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
\(661\) −13.5584 + 23.4839i −0.527361 + 0.913417i 0.472130 + 0.881529i \(0.343485\pi\)
−0.999491 + 0.0318879i \(0.989848\pi\)
\(662\) −11.1168 + 19.2549i −0.432068 + 0.748364i
\(663\) 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
\(668\) 5.48913 0.212381
\(669\) 0 0
\(670\) 9.25544 0.357569
\(671\) −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
\(677\) 17.2337 + 29.8496i 0.662344 + 1.14721i 0.979998 + 0.199007i \(0.0637718\pi\)
−0.317654 + 0.948207i \(0.602895\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 0 0
\(682\) 2.74456 0.105095
\(683\) 14.9198 + 25.8419i 0.570891 + 0.988813i 0.996475 + 0.0838936i \(0.0267356\pi\)
−0.425583 + 0.904919i \(0.639931\pi\)
\(684\) 0 0
\(685\) 46.4674 1.77543
\(686\) 0 0
\(687\) 0 0
\(688\) −8.11684 −0.309452
\(689\) −8.74456 + 15.1460i −0.333141 + 0.577018i
\(690\) 0 0
\(691\) 11.5584 + 20.0198i 0.439703 + 0.761588i 0.997666 0.0682775i \(-0.0217503\pi\)
−0.557963 + 0.829866i \(0.688417\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 10.1168 0.384030
\(695\) 28.9307 + 50.1094i 1.09740 + 1.90076i
\(696\) 0 0
\(697\) −3.17527 + 5.49972i −0.120272 + 0.208317i
\(698\) −22.0000 −0.832712
\(699\) 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
\(704\) 1.37228 0.0517198
\(705\) 0 0
\(706\) −6.68614 11.5807i −0.251636 0.435847i
\(707\) 0 0
\(708\) 0 0
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) 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
\(716\) −3.25544 −0.121661
\(717\) 0 0
\(718\) −21.8614 −0.815860
\(719\) 1.37228 2.37686i 0.0511775 0.0886420i −0.839302 0.543666i \(-0.817036\pi\)
0.890479 + 0.455024i \(0.150369\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3.00000 + 5.19615i −0.111648 + 0.193381i
\(723\) 0 0
\(724\) −0.441578 + 0.764836i −0.0164111 + 0.0284249i
\(725\) −61.7228 + 106.907i −2.29233 + 3.97043i
\(726\) 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
\(731\) 11.1386 0.411976
\(732\) 0 0
\(733\) −41.1168 −1.51869 −0.759343 0.650691i \(-0.774479\pi\)
−0.759343 + 0.650691i \(0.774479\pi\)
\(734\) 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 0.930966 0.365106i \(-0.118967\pi\)
−0.781674 + 0.623687i \(0.785634\pi\)
\(740\) 4.37228 + 7.57301i 0.160728 + 0.278390i
\(741\) 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
\(745\) 14.2337 0.521482
\(746\) 5.00000 + 8.66025i 0.183063 + 0.317074i
\(747\) 0 0
\(748\) −1.88316 −0.0688550
\(749\) 0 0
\(750\) 0 0
\(751\) −17.1168 −0.624603 −0.312301 0.949983i \(-0.601100\pi\)
−0.312301 + 0.949983i \(0.601100\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −8.74456 15.1460i −0.318458 0.551586i
\(755\) −39.8614 −1.45071
\(756\) 0 0
\(757\) 46.2337 1.68039 0.840196 0.542283i \(-0.182440\pi\)
0.840196 + 0.542283i \(0.182440\pi\)
\(758\) 4.05842 + 7.02939i 0.147409 + 0.255319i
\(759\) 0 0
\(760\) 10.9307 18.9325i 0.396498 0.686755i
\(761\) −35.4891 −1.28648 −0.643240 0.765665i \(-0.722410\pi\)
−0.643240 + 0.765665i \(0.722410\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 19.1168 0.691623
\(765\) 0 0
\(766\) −16.3723 28.3576i −0.591555 1.02460i
\(767\) 20.2337 0.730596
\(768\) 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
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) −19.9307 34.5210i −0.716858 1.24163i −0.962239 0.272207i \(-0.912246\pi\)
0.245381 0.969427i \(-0.421087\pi\)
\(774\) 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
\(779\) −23.1386 −0.829026
\(780\) 0 0
\(781\) 9.76631 0.349466
\(782\) 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
\(787\) 2.00000 3.46410i 0.0712923 0.123482i −0.828176 0.560469i \(-0.810621\pi\)
0.899468 + 0.436987i \(0.143954\pi\)
\(788\) −3.00000 + 5.19615i −0.106871 + 0.185105i
\(789\) 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
\(794\) −22.0000 −0.780751