Properties

Label 378.2.f.c.127.2
Level 378
Weight 2
Character 378.127
Analytic conductor 3.018
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 378.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
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 127.2
Root \(1.68614 + 0.396143i\)
Character \(\chi\) = 378.127
Dual form 378.2.f.c.253.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.18614 + 3.78651i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.18614 + 3.78651i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} -4.37228 q^{10} +(-0.686141 + 1.18843i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.37228 q^{17} +5.00000 q^{19} +(2.18614 - 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} +(-0.813859 - 1.40965i) q^{23} +(-7.05842 + 12.2255i) q^{25} +2.00000 q^{26} +1.00000 q^{28} +(-4.37228 + 7.57301i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.686141 - 1.18843i) q^{34} -4.37228 q^{35} +2.00000 q^{37} +(-2.50000 + 4.33013i) q^{38} +(2.18614 + 3.78651i) q^{40} +(2.31386 + 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +1.37228 q^{44} +1.62772 q^{46} +(-0.500000 - 0.866025i) q^{49} +(-7.05842 - 12.2255i) q^{50} +(-1.00000 + 1.73205i) q^{52} +8.74456 q^{53} -6.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-4.37228 - 7.57301i) q^{58} +(-5.05842 - 8.76144i) q^{59} +(-1.55842 + 2.69927i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(4.37228 - 7.57301i) q^{65} +(1.05842 + 1.83324i) q^{67} +(0.686141 + 1.18843i) q^{68} +(2.18614 - 3.78651i) q^{70} +7.11684 q^{71} +12.1168 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.50000 - 4.33013i) q^{76} +(-0.686141 - 1.18843i) q^{77} +(2.55842 - 4.43132i) q^{79} -4.37228 q^{80} -4.62772 q^{82} +(8.74456 - 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(4.05842 + 7.02939i) q^{86} +(-0.686141 + 1.18843i) q^{88} -14.7446 q^{89} +2.00000 q^{91} +(-0.813859 + 1.40965i) q^{92} +(10.9307 + 18.9325i) q^{95} +(4.05842 - 7.02939i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} + 3q^{5} - 2q^{7} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} + 3q^{5} - 2q^{7} + 4q^{8} - 6q^{10} + 3q^{11} - 4q^{13} - 2q^{14} - 2q^{16} + 6q^{17} + 20q^{19} + 3q^{20} + 3q^{22} - 9q^{23} - 11q^{25} + 8q^{26} + 4q^{28} - 6q^{29} - 4q^{31} - 2q^{32} - 3q^{34} - 6q^{35} + 8q^{37} - 10q^{38} + 3q^{40} + 15q^{41} - q^{43} - 6q^{44} + 18q^{46} - 2q^{49} - 11q^{50} - 4q^{52} + 12q^{53} - 24q^{55} - 2q^{56} - 6q^{58} - 3q^{59} + 11q^{61} + 8q^{62} + 4q^{64} + 6q^{65} - 13q^{67} - 3q^{68} + 3q^{70} - 6q^{71} + 14q^{73} - 4q^{74} - 10q^{76} + 3q^{77} - 7q^{79} - 6q^{80} - 30q^{82} + 12q^{83} - 12q^{85} - q^{86} + 3q^{88} - 36q^{89} + 8q^{91} - 9q^{92} + 15q^{95} - q^{97} + 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) 2.18614 + 3.78651i 0.977672 + 1.69338i 0.670820 + 0.741620i \(0.265942\pi\)
0.306851 + 0.951757i \(0.400725\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −4.37228 −1.38264
\(11\) −0.686141 + 1.18843i −0.206879 + 0.358325i −0.950730 0.310021i \(-0.899664\pi\)
0.743851 + 0.668346i \(0.232997\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.37228 −0.332827 −0.166414 0.986056i \(-0.553219\pi\)
−0.166414 + 0.986056i \(0.553219\pi\)
\(18\) 0 0
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 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 0.768613 0.639713i \(-0.220947\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) 0 0
\(25\) −7.05842 + 12.2255i −1.41168 + 2.44511i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −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 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 0.686141 1.18843i 0.117672 0.203814i
\(35\) −4.37228 −0.739050
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −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 \(-0.0457562\pi\)
\(44\) 1.37228 0.206879
\(45\) 0 0
\(46\) 1.62772 0.239994
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −7.05842 12.2255i −0.998212 1.72895i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 8.74456 1.20116 0.600579 0.799565i \(-0.294937\pi\)
0.600579 + 0.799565i \(0.294937\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) −4.37228 7.57301i −0.574109 0.994385i
\(59\) −5.05842 8.76144i −0.658550 1.14064i −0.980991 0.194053i \(-0.937837\pi\)
0.322441 0.946590i \(-0.395497\pi\)
\(60\) 0 0
\(61\) −1.55842 + 2.69927i −0.199535 + 0.345606i −0.948378 0.317142i \(-0.897277\pi\)
0.748842 + 0.662748i \(0.230610\pi\)
\(62\) 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 0.923408 0.383819i \(-0.125391\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) 0.686141 + 1.18843i 0.0832068 + 0.144118i
\(69\) 0 0
\(70\) 2.18614 3.78651i 0.261294 0.452574i
\(71\) 7.11684 0.844614 0.422307 0.906453i \(-0.361220\pi\)
0.422307 + 0.906453i \(0.361220\pi\)
\(72\) 0 0
\(73\) 12.1168 1.41817 0.709085 0.705123i \(-0.249108\pi\)
0.709085 + 0.705123i \(0.249108\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0 0
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) −0.686141 1.18843i −0.0781930 0.135434i
\(78\) 0 0
\(79\) 2.55842 4.43132i 0.287845 0.498562i −0.685450 0.728120i \(-0.740395\pi\)
0.973295 + 0.229557i \(0.0737279\pi\)
\(80\) −4.37228 −0.488836
\(81\) 0 0
\(82\) −4.62772 −0.511046
\(83\) 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
\(89\) −14.7446 −1.56292 −0.781460 0.623955i \(-0.785525\pi\)
−0.781460 + 0.623955i \(0.785525\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) −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 \(0.0314725\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 14.1168 1.41168
\(101\) 0.813859 1.40965i 0.0809820 0.140265i −0.822690 0.568490i \(-0.807528\pi\)
0.903672 + 0.428225i \(0.140861\pi\)
\(102\) 0 0
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) −4.37228 + 7.57301i −0.424674 + 0.735556i
\(107\) 7.37228 0.712705 0.356353 0.934352i \(-0.384020\pi\)
0.356353 + 0.934352i \(0.384020\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 3.00000 5.19615i 0.286039 0.495434i
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −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
\(116\) 8.74456 0.811912
\(117\) 0 0
\(118\) 10.1168 0.931331
\(119\) 0.686141 1.18843i 0.0628984 0.108943i
\(120\) 0 0
\(121\) 4.55842 + 7.89542i 0.414402 + 0.717765i
\(122\) −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
\(131\) −0.813859 1.40965i −0.0711072 0.123161i 0.828280 0.560315i \(-0.189320\pi\)
−0.899387 + 0.437154i \(0.855987\pi\)
\(132\) 0 0
\(133\) −2.50000 + 4.33013i −0.216777 + 0.375470i
\(134\) −2.11684 −0.182867
\(135\) 0 0
\(136\) −1.37228 −0.117672
\(137\) 5.31386 9.20387i 0.453994 0.786340i −0.544636 0.838672i \(-0.683332\pi\)
0.998630 + 0.0523324i \(0.0166655\pi\)
\(138\) 0 0
\(139\) −6.61684 11.4607i −0.561233 0.972085i −0.997389 0.0722136i \(-0.976994\pi\)
0.436156 0.899871i \(-0.356340\pi\)
\(140\) 2.18614 + 3.78651i 0.184763 + 0.320018i
\(141\) 0 0
\(142\) −3.55842 + 6.16337i −0.298616 + 0.517218i
\(143\) 2.74456 0.229512
\(144\) 0 0
\(145\) −38.2337 −3.17513
\(146\) −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 0.924965 0.380052i \(-0.124094\pi\)
−0.791617 + 0.611017i \(0.790761\pi\)
\(150\) 0 0
\(151\) −4.55842 + 7.89542i −0.370959 + 0.642520i −0.989713 0.143065i \(-0.954304\pi\)
0.618754 + 0.785585i \(0.287638\pi\)
\(152\) 5.00000 0.405554
\(153\) 0 0
\(154\) 1.37228 0.110582
\(155\) 4.37228 7.57301i 0.351190 0.608279i
\(156\) 0 0
\(157\) −4.55842 7.89542i −0.363802 0.630123i 0.624781 0.780800i \(-0.285188\pi\)
−0.988583 + 0.150677i \(0.951855\pi\)
\(158\) 2.55842 + 4.43132i 0.203537 + 0.352537i
\(159\) 0 0
\(160\) 2.18614 3.78651i 0.172830 0.299350i
\(161\) 1.62772 0.128282
\(162\) 0 0
\(163\) −18.2337 −1.42817 −0.714086 0.700058i \(-0.753158\pi\)
−0.714086 + 0.700058i \(0.753158\pi\)
\(164\) 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
\(170\) 6.00000 0.460179
\(171\) 0 0
\(172\) −8.11684 −0.618904
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) −7.05842 12.2255i −0.533567 0.924164i
\(176\) −0.686141 1.18843i −0.0517198 0.0895813i
\(177\) 0 0
\(178\) 7.37228 12.7692i 0.552576 0.957089i
\(179\) −3.25544 −0.243323 −0.121661 0.992572i \(-0.538822\pi\)
−0.121661 + 0.992572i \(0.538822\pi\)
\(180\) 0 0
\(181\) 0.883156 0.0656445 0.0328222 0.999461i \(-0.489550\pi\)
0.0328222 + 0.999461i \(0.489550\pi\)
\(182\) −1.00000 + 1.73205i −0.0741249 + 0.128388i
\(183\) 0 0
\(184\) −0.813859 1.40965i −0.0599985 0.103920i
\(185\) 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 0.279683 + 0.960092i \(0.409771\pi\)
−0.971306 + 0.237834i \(0.923563\pi\)
\(192\) 0 0
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) 4.05842 + 7.02939i 0.291378 + 0.504681i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) −7.05842 + 12.2255i −0.499106 + 0.864477i
\(201\) 0 0
\(202\) 0.813859 + 1.40965i 0.0572629 + 0.0991823i
\(203\) −4.37228 7.57301i −0.306874 0.531521i
\(204\) 0 0
\(205\) −10.1168 + 17.5229i −0.706591 + 1.22385i
\(206\) −10.0000 −0.696733
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) −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
\(215\) 35.4891 2.42034
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) −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 \(0.123907\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 4.37228 0.290840
\(227\) −6.12772 + 10.6135i −0.406711 + 0.704444i −0.994519 0.104556i \(-0.966658\pi\)
0.587808 + 0.809000i \(0.299991\pi\)
\(228\) 0 0
\(229\) 1.44158 + 2.49689i 0.0952622 + 0.164999i 0.909718 0.415227i \(-0.136298\pi\)
−0.814456 + 0.580226i \(0.802964\pi\)
\(230\) 3.55842 + 6.16337i 0.234635 + 0.406400i
\(231\) 0 0
\(232\) −4.37228 + 7.57301i −0.287054 + 0.497193i
\(233\) 0.255437 0.0167343 0.00836713 0.999965i \(-0.497337\pi\)
0.00836713 + 0.999965i \(0.497337\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.05842 + 8.76144i −0.329275 + 0.570321i
\(237\) 0 0
\(238\) 0.686141 + 1.18843i 0.0444759 + 0.0770345i
\(239\) 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 0.411556 + 0.911385i \(0.364986\pi\)
−0.995060 + 0.0992745i \(0.968348\pi\)
\(242\) −9.11684 −0.586053
\(243\) 0 0
\(244\) 3.11684 0.199535
\(245\) 2.18614 3.78651i 0.139667 0.241911i
\(246\) 0 0
\(247\) −5.00000 8.66025i −0.318142 0.551039i
\(248\) −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
\(257\) −3.43070 5.94215i −0.214001 0.370661i 0.738962 0.673747i \(-0.235316\pi\)
−0.952963 + 0.303086i \(0.901983\pi\)
\(258\) 0 0
\(259\) −1.00000 + 1.73205i −0.0621370 + 0.107624i
\(260\) −8.74456 −0.542315
\(261\) 0 0
\(262\) 1.62772 0.100561
\(263\) 3.81386 6.60580i 0.235173 0.407331i −0.724150 0.689642i \(-0.757768\pi\)
0.959323 + 0.282311i \(0.0911011\pi\)
\(264\) 0 0
\(265\) 19.1168 + 33.1113i 1.17434 + 2.03401i
\(266\) −2.50000 4.33013i −0.153285 0.265497i
\(267\) 0 0
\(268\) 1.05842 1.83324i 0.0646534 0.111983i
\(269\) 1.62772 0.0992438 0.0496219 0.998768i \(-0.484198\pi\)
0.0496219 + 0.998768i \(0.484198\pi\)
\(270\) 0 0
\(271\) 16.2337 0.986126 0.493063 0.869994i \(-0.335877\pi\)
0.493063 + 0.869994i \(0.335877\pi\)
\(272\) 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 −0.621652 0.783293i \(-0.713538\pi\)
0.989178 + 0.146720i \(0.0468717\pi\)
\(278\) 13.2337 0.793704
\(279\) 0 0
\(280\) −4.37228 −0.261294
\(281\) 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 −0.915638 0.402004i \(-0.868314\pi\)
0.109673 0.993968i \(-0.465019\pi\)
\(284\) −3.55842 6.16337i −0.211153 0.365729i
\(285\) 0 0
\(286\) −1.37228 + 2.37686i −0.0811447 + 0.140547i
\(287\) −4.62772 −0.273166
\(288\) 0 0
\(289\) −15.1168 −0.889226
\(290\) 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
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) −3.25544 −0.188582
\(299\) −1.62772 + 2.81929i −0.0941334 + 0.163044i
\(300\) 0 0
\(301\) 4.05842 + 7.02939i 0.233924 + 0.405167i
\(302\) −4.55842 7.89542i −0.262308 0.454330i
\(303\) 0 0
\(304\) −2.50000 + 4.33013i −0.143385 + 0.248350i
\(305\) −13.6277 −0.780321
\(306\) 0 0
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) −0.686141 + 1.18843i −0.0390965 + 0.0677171i
\(309\) 0 0
\(310\) 4.37228 + 7.57301i 0.248329 + 0.430118i
\(311\) 4.11684 + 7.13058i 0.233445 + 0.404338i 0.958820 0.284016i \(-0.0916668\pi\)
−0.725375 + 0.688354i \(0.758334\pi\)
\(312\) 0 0
\(313\) 10.0584 17.4217i 0.568536 0.984733i −0.428175 0.903696i \(-0.640843\pi\)
0.996711 0.0810370i \(-0.0258232\pi\)
\(314\) 9.11684 0.514493
\(315\) 0 0
\(316\) −5.11684 −0.287845
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) −6.00000 10.3923i −0.335936 0.581857i
\(320\) 2.18614 + 3.78651i 0.122209 + 0.211672i
\(321\) 0 0
\(322\) −0.813859 + 1.40965i −0.0453546 + 0.0785565i
\(323\) −6.86141 −0.381779
\(324\) 0 0
\(325\) 28.2337 1.56612
\(326\) 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
\(331\) −11.1168 + 19.2549i −0.611037 + 1.05835i 0.380029 + 0.924975i \(0.375914\pi\)
−0.991066 + 0.133373i \(0.957419\pi\)
\(332\) −17.4891 −0.959840
\(333\) 0 0
\(334\) 5.48913 0.300352
\(335\) −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
\(341\) 2.74456 0.148626
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 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 0.697709 0.716382i \(-0.254203\pi\)
−0.969259 + 0.246043i \(0.920870\pi\)
\(348\) 0 0
\(349\) 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i \(-0.632927\pi\)
0.994388 0.105797i \(-0.0337393\pi\)
\(350\) 14.1168 0.754577
\(351\) 0 0
\(352\) 1.37228 0.0731428
\(353\) −6.68614 + 11.5807i −0.355867 + 0.616380i −0.987266 0.159078i \(-0.949148\pi\)
0.631399 + 0.775458i \(0.282481\pi\)
\(354\) 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
\(359\) −21.8614 −1.15380 −0.576900 0.816814i \(-0.695738\pi\)
−0.576900 + 0.816814i \(0.695738\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −0.441578 + 0.764836i −0.0232088 + 0.0401989i
\(363\) 0 0
\(364\) −1.00000 1.73205i −0.0524142 0.0907841i
\(365\) 26.4891 + 45.8805i 1.38650 + 2.40150i
\(366\) 0 0
\(367\) 6.11684 10.5947i 0.319297 0.553038i −0.661045 0.750346i \(-0.729887\pi\)
0.980341 + 0.197308i \(0.0632200\pi\)
\(368\) 1.62772 0.0848507
\(369\) 0 0
\(370\) −8.74456 −0.454608
\(371\) −4.37228 + 7.57301i −0.226998 + 0.393171i
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 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
\(383\) −16.3723 28.3576i −0.836584 1.44901i −0.892734 0.450584i \(-0.851216\pi\)
0.0561493 0.998422i \(-0.482118\pi\)
\(384\) 0 0
\(385\) 3.00000 5.19615i 0.152894 0.264820i
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) −8.11684 −0.412070
\(389\) 5.48913 9.50744i 0.278310 0.482047i −0.692655 0.721269i \(-0.743559\pi\)
0.970965 + 0.239222i \(0.0768925\pi\)
\(390\) 0 0
\(391\) 1.11684 + 1.93443i 0.0564812 + 0.0978284i
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 0 0
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) 22.3723 1.12567
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 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 0.681328 0.731978i \(-0.261403\pi\)
−0.974576 + 0.224058i \(0.928069\pi\)
\(402\) 0 0
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) −1.62772 −0.0809820
\(405\) 0 0
\(406\) 8.74456 0.433985
\(407\) −1.37228 + 2.37686i −0.0680215 + 0.117817i
\(408\) 0 0
\(409\) 11.1753 + 19.3561i 0.552581 + 0.957099i 0.998087 + 0.0618200i \(0.0196905\pi\)
−0.445506 + 0.895279i \(0.646976\pi\)
\(410\) −10.1168 17.5229i −0.499635 0.865394i
\(411\) 0 0
\(412\) 5.00000 8.66025i 0.246332 0.426660i
\(413\) 10.1168 0.497817
\(414\) 0 0
\(415\) 76.4674 3.75364
\(416\) −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 \(0.852583\pi\)
\(422\) −16.0000 −0.778868
\(423\) 0 0
\(424\) 8.74456 0.424674
\(425\) 9.68614 16.7769i 0.469847 0.813799i
\(426\) 0 0
\(427\) −1.55842 2.69927i −0.0754173 0.130627i
\(428\) −3.68614 6.38458i −0.178176 0.308610i
\(429\) 0 0
\(430\) −17.7446 + 30.7345i −0.855719 + 1.48215i
\(431\) 6.51087 0.313618 0.156809 0.987629i \(-0.449879\pi\)
0.156809 + 0.987629i \(0.449879\pi\)
\(432\) 0 0
\(433\) −20.1168 −0.966754 −0.483377 0.875412i \(-0.660590\pi\)
−0.483377 + 0.875412i \(0.660590\pi\)
\(434\) −1.00000 + 1.73205i −0.0480015 + 0.0831411i
\(435\) 0 0
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) −4.06930 7.04823i −0.194661 0.337162i
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) −2.74456 −0.130546
\(443\) −20.0584 + 34.7422i −0.953004 + 1.65065i −0.214134 + 0.976804i \(0.568693\pi\)
−0.738870 + 0.673848i \(0.764640\pi\)
\(444\) 0 0
\(445\) −32.2337 55.8304i −1.52802 2.64661i
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) 0 0
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0 0
\(451\) −6.35053 −0.299035
\(452\) −2.18614 + 3.78651i −0.102827 + 0.178102i
\(453\) 0 0
\(454\) −6.12772 10.6135i −0.287588 0.498117i
\(455\) 4.37228 + 7.57301i 0.204976 + 0.355028i
\(456\) 0 0
\(457\) 17.7337 30.7156i 0.829547 1.43682i −0.0688472 0.997627i \(-0.521932\pi\)
0.898394 0.439190i \(-0.144735\pi\)
\(458\) −2.88316 −0.134721
\(459\) 0 0
\(460\) −7.11684 −0.331825
\(461\) 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
\(467\) −33.0951 −1.53146 −0.765729 0.643163i \(-0.777622\pi\)
−0.765729 + 0.643163i \(0.777622\pi\)
\(468\) 0 0
\(469\) −2.11684 −0.0977468
\(470\) 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
\(476\) −1.37228 −0.0628984
\(477\) 0 0
\(478\) −9.86141 −0.451050
\(479\) 16.3723 28.3576i 0.748069 1.29569i −0.200679 0.979657i \(-0.564315\pi\)
0.948747 0.316036i \(-0.102352\pi\)
\(480\) 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
\(485\) 35.4891 1.61148
\(486\) 0 0
\(487\) 35.3505 1.60189 0.800943 0.598741i \(-0.204332\pi\)
0.800943 + 0.598741i \(0.204332\pi\)
\(488\) −1.55842 + 2.69927i −0.0705464 + 0.122190i
\(489\) 0 0
\(490\) 2.18614 + 3.78651i 0.0987598 + 0.171057i
\(491\) −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
\(494\) 10.0000 0.449921
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −3.55842 + 6.16337i −0.159617 + 0.276465i
\(498\) 0 0
\(499\) −9.05842 15.6896i −0.405511 0.702365i 0.588870 0.808228i \(-0.299573\pi\)
−0.994381 + 0.105863i \(0.966240\pi\)
\(500\) 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
\(509\) −14.4891 25.0959i −0.642219 1.11236i −0.984936 0.172918i \(-0.944681\pi\)
0.342717 0.939439i \(-0.388653\pi\)
\(510\) 0 0
\(511\) −6.05842 + 10.4935i −0.268009 + 0.464205i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.86141 0.302644
\(515\) −21.8614 + 37.8651i −0.963329 + 1.66853i
\(516\) 0 0
\(517\) 0 0
\(518\) −1.00000 1.73205i −0.0439375 0.0761019i
\(519\) 0 0
\(520\) 4.37228 7.57301i 0.191737 0.332099i
\(521\) 24.8614 1.08920 0.544599 0.838697i \(-0.316682\pi\)
0.544599 + 0.838697i \(0.316682\pi\)
\(522\) 0 0
\(523\) −35.1168 −1.53555 −0.767776 0.640718i \(-0.778637\pi\)
−0.767776 + 0.640718i \(0.778637\pi\)
\(524\) −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
\(530\) −38.2337 −1.66077
\(531\) 0 0
\(532\) 5.00000 0.216777
\(533\) 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
\(539\) 1.37228 0.0591083
\(540\) 0 0
\(541\) −6.23369 −0.268007 −0.134004 0.990981i \(-0.542783\pi\)
−0.134004 + 0.990981i \(0.542783\pi\)
\(542\) −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 \(0.293262\pi\)
\(548\) −10.6277 −0.453994
\(549\) 0 0
\(550\) 19.3723 0.826037
\(551\) −21.8614 + 37.8651i −0.931327 + 1.61311i
\(552\) 0 0
\(553\) 2.55842 + 4.43132i 0.108795 + 0.188439i
\(554\) 6.11684 + 10.5947i 0.259880 + 0.450125i
\(555\) 0 0
\(556\) −6.61684 + 11.4607i −0.280617 + 0.486042i
\(557\) −29.4891 −1.24949 −0.624747 0.780827i \(-0.714798\pi\)
−0.624747 + 0.780827i \(0.714798\pi\)
\(558\) 0 0
\(559\) −16.2337 −0.686612
\(560\) 2.18614 3.78651i 0.0923813 0.160009i
\(561\) 0 0
\(562\) 8.18614 + 14.1788i 0.345312 + 0.598097i
\(563\) 1.50000 + 2.59808i 0.0632175 + 0.109496i 0.895902 0.444252i \(-0.146530\pi\)
−0.832684 + 0.553748i \(0.813197\pi\)
\(564\) 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 −0.646197 0.763171i \(-0.723642\pi\)
0.984024 + 0.178038i \(0.0569749\pi\)
\(570\) 0 0
\(571\) 11.1753 + 19.3561i 0.467670 + 0.810029i 0.999318 0.0369371i \(-0.0117601\pi\)
−0.531647 + 0.846966i \(0.678427\pi\)
\(572\) −1.37228 2.37686i −0.0573780 0.0993815i
\(573\) 0 0
\(574\) 2.31386 4.00772i 0.0965786 0.167279i
\(575\) 22.9783 0.958259
\(576\) 0 0
\(577\) 9.88316 0.411441 0.205721 0.978611i \(-0.434046\pi\)
0.205721 + 0.978611i \(0.434046\pi\)
\(578\) 7.55842 13.0916i 0.314389 0.544538i
\(579\) 0 0
\(580\) 19.1168 + 33.1113i 0.793784 + 1.37487i
\(581\) 8.74456 + 15.1460i 0.362786 + 0.628363i
\(582\) 0 0
\(583\) −6.00000 + 10.3923i −0.248495 + 0.430405i
\(584\) 12.1168 0.501399
\(585\) 0 0
\(586\) 10.3723 0.428475
\(587\) 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
\(593\) −14.7446 −0.605487 −0.302743 0.953072i \(-0.597902\pi\)
−0.302743 + 0.953072i \(0.597902\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 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 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 0 0
\(601\) −12.0584 + 20.8858i −0.491873 + 0.851950i −0.999956 0.00935863i \(-0.997021\pi\)
0.508083 + 0.861308i \(0.330354\pi\)
\(602\) −8.11684 −0.330818
\(603\) 0 0
\(604\) 9.11684 0.370959
\(605\) −19.9307 + 34.5210i −0.810298 + 1.40348i
\(606\) 0 0
\(607\) −11.1168 19.2549i −0.451219 0.781534i 0.547243 0.836974i \(-0.315677\pi\)
−0.998462 + 0.0554398i \(0.982344\pi\)
\(608\) −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
\(613\) −36.2337 −1.46346 −0.731732 0.681592i \(-0.761288\pi\)
−0.731732 + 0.681592i \(0.761288\pi\)
\(614\) 6.50000 11.2583i 0.262319 0.454349i
\(615\) 0 0
\(616\) −0.686141 1.18843i −0.0276454 0.0478832i
\(617\) 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 −0.105014 + 0.994471i \(0.533489\pi\)
−0.808730 + 0.588180i \(0.799844\pi\)
\(620\) −8.74456 −0.351190
\(621\) 0 0
\(622\) −8.23369 −0.330141
\(623\) 7.37228 12.7692i 0.295364 0.511586i
\(624\) 0 0
\(625\) −51.8505 89.8078i −2.07402 3.59231i
\(626\) 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
\(635\) 6.81386 + 11.8020i 0.270400 + 0.468346i
\(636\) 0 0
\(637\) −1.00000 + 1.73205i −0.0396214 + 0.0686264i
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) −4.37228 −0.172830
\(641\) 17.1060 29.6284i 0.675645 1.17025i −0.300635 0.953739i \(-0.597198\pi\)
0.976280 0.216512i \(-0.0694682\pi\)
\(642\) 0 0
\(643\) −13.1753 22.8202i −0.519582 0.899942i −0.999741 0.0227606i \(-0.992754\pi\)
0.480159 0.877181i \(-0.340579\pi\)
\(644\) −0.813859 1.40965i −0.0320706 0.0555478i
\(645\) 0 0
\(646\) 3.43070 5.94215i 0.134979 0.233791i
\(647\) −5.48913 −0.215800 −0.107900 0.994162i \(-0.534413\pi\)
−0.107900 + 0.994162i \(0.534413\pi\)
\(648\) 0 0
\(649\) 13.8832 0.544962
\(650\) −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 −0.999632 0.0271143i \(-0.991368\pi\)
0.476335 0.879264i \(-0.341965\pi\)
\(654\) 0 0
\(655\) 3.55842 6.16337i 0.139039 0.240823i
\(656\) −4.62772 −0.180682
\(657\) 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 −0.999491 0.0318879i \(-0.989848\pi\)
0.472130 0.881529i \(-0.343485\pi\)
\(662\) −11.1168 19.2549i −0.432068 0.748364i
\(663\) 0 0
\(664\) 8.74456 15.1460i 0.339355 0.587780i
\(665\) −21.8614 −0.847749
\(666\) 0 0
\(667\) 14.2337 0.551131
\(668\) −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 \(0.148969\pi\)
\(674\) −8.11684 −0.312649
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 17.2337 29.8496i 0.662344 1.14721i −0.317654 0.948207i \(-0.602895\pi\)
0.979998 0.199007i \(-0.0637718\pi\)
\(678\) 0 0
\(679\) 4.05842 + 7.02939i 0.155748 + 0.269763i
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 0 0
\(682\) −1.37228 + 2.37686i −0.0525474 + 0.0910147i
\(683\) −29.8397 −1.14178 −0.570891 0.821026i \(-0.693402\pi\)
−0.570891 + 0.821026i \(0.693402\pi\)
\(684\) 0 0
\(685\) 46.4674 1.77543
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) 4.05842 + 7.02939i 0.154726 + 0.267993i
\(689\) −8.74456 15.1460i −0.333141 0.577018i
\(690\) 0 0
\(691\) 11.5584 20.0198i 0.439703 0.761588i −0.557963 0.829866i \(-0.688417\pi\)
0.997666 + 0.0682775i \(0.0217503\pi\)
\(692\) 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
\(698\) 11.0000 + 19.0526i 0.416356 + 0.721150i
\(699\) 0 0
\(700\) −7.05842 + 12.2255i −0.266783 + 0.462082i
\(701\) 38.2337 1.44407 0.722033 0.691858i \(-0.243208\pi\)
0.722033 + 0.691858i \(0.243208\pi\)
\(702\) 0 0
\(703\) 10.0000 0.377157
\(704\) −0.686141 + 1.18843i −0.0258599 + 0.0447907i
\(705\) 0 0
\(706\) −6.68614 11.5807i −0.251636 0.435847i
\(707\) 0.813859 + 1.40965i 0.0306083 + 0.0530152i
\(708\) 0 0
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) −31.1168 −1.16779
\(711\) 0 0
\(712\) −14.7446 −0.552576
\(713\) −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
\(719\) −2.74456 −0.102355 −0.0511775 0.998690i \(-0.516297\pi\)
−0.0511775 + 0.998690i \(0.516297\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) −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 \(-0.0678620\pi\)
\(728\) 2.00000 0.0741249
\(729\) 0 0
\(730\) −52.9783 −1.96081
\(731\) −5.56930 + 9.64630i −0.205988 + 0.356781i
\(732\) 0 0
\(733\) 20.5584 + 35.6082i 0.759343 + 1.31522i 0.943186 + 0.332265i \(0.107813\pi\)
−0.183844 + 0.982956i \(0.558854\pi\)
\(734\) 6.11684 + 10.5947i 0.225777 + 0.391057i
\(735\) 0 0
\(736\) −0.813859 + 1.40965i −0.0299993 + 0.0519602i
\(737\) −2.90491 −0.107004
\(738\) 0 0
\(739\) −8.11684 −0.298583 −0.149291 0.988793i \(-0.547699\pi\)
−0.149291 + 0.988793i \(0.547699\pi\)
\(740\) 4.37228 7.57301i 0.160728 0.278390i
\(741\) 0 0
\(742\) −4.37228 7.57301i −0.160511 0.278014i
\(743\) −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
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) −1.88316 −0.0688550
\(749\) −3.68614 + 6.38458i −0.134689 + 0.233288i
\(750\) 0 0
\(751\) 8.55842 + 14.8236i 0.312301 + 0.540922i 0.978860 0.204531i \(-0.0655668\pi\)
−0.666559 + 0.745452i \(0.732234\pi\)
\(752\) 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
\(761\) 17.7446 + 30.7345i 0.643240 + 1.11412i 0.984705 + 0.174230i \(0.0557435\pi\)
−0.341465 + 0.939894i \(0.610923\pi\)
\(762\) 0 0
\(763\) −7.00000 + 12.1244i −0.253417 + 0.438931i
\(764\) 19.1168 0.691623
\(765\) 0 0
\(766\) 32.7446 1.18311
\(767\) −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 \(0.775625\pi\)
\(770\) 3.00000 + 5.19615i 0.108112 + 0.187256i
\(771\) 0 0
\(772\) 3.50000 6.06218i 0.125968 0.218183i
\(773\) 39.8614 1.43372 0.716858 0.697220i \(-0.245580\pi\)
0.716858 + 0.697220i \(0.245580\pi\)
\(774\) 0 0
\(775\) 28.2337 1.01418
\(776\) 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
\(782\) −2.23369 −0.0798765
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 19.9307 34.5210i 0.711357 1.23211i
\(786\) 0 0
\(787\) 2.00000 + 3.46410i 0.0712923 + 0.123482i 0.899468 0.436987i \(-0.143954\pi\)
−0.828176 + 0.560469i \(0.810621\pi\)
\(788\) −3.00000 5.19615i −0.106871 0.185105i
\(789\) 0 0
\(790\) −11.1861 + 19.3750i −0.397985 + 0.689330i
\(791\) 4.37228 0.155460
\(792\) 0 0
\(793\) 6.23369 0.221365
\(794\) 11.0000 19.0526i 0.390375 0.676150i
\(795\) 0 0
\(796\) 5.00000 + 8.66025i 0.177220 + 0.306955i
\(797\) −4.06930 7.04823i −0.144142 0.249661i 0.784911 0.619609i \(-0.212709\pi\)
−0.929052 + <