Properties

Label 378.2.f.c.253.1
Level 378
Weight 2
Character 378.253
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 253.1
Root \(-1.18614 + 1.26217i\)
Character \(\chi\) = 378.253
Dual form 378.2.f.c.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.686141 + 1.18843i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.686141 + 1.18843i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +1.37228 q^{10} +(2.18614 + 3.78651i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.37228 q^{17} +5.00000 q^{19} +(-0.686141 - 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(-3.68614 + 6.38458i) q^{23} +(1.55842 + 2.69927i) q^{25} +2.00000 q^{26} +1.00000 q^{28} +(1.37228 + 2.37686i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.18614 - 3.78651i) q^{34} +1.37228 q^{35} +2.00000 q^{37} +(-2.50000 - 4.33013i) q^{38} +(-0.686141 + 1.18843i) q^{40} +(5.18614 - 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} -4.37228 q^{44} +7.37228 q^{46} +(-0.500000 + 0.866025i) q^{49} +(1.55842 - 2.69927i) q^{50} +(-1.00000 - 1.73205i) q^{52} -2.74456 q^{53} -6.00000 q^{55} +(-0.500000 - 0.866025i) q^{56} +(1.37228 - 2.37686i) q^{58} +(3.55842 - 6.16337i) q^{59} +(7.05842 + 12.2255i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-1.37228 - 2.37686i) q^{65} +(-7.55842 + 13.0916i) q^{67} +(-2.18614 + 3.78651i) q^{68} +(-0.686141 - 1.18843i) q^{70} -10.1168 q^{71} -5.11684 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(2.18614 - 3.78651i) q^{77} +(-6.05842 - 10.4935i) q^{79} +1.37228 q^{80} -10.3723 q^{82} +(-2.74456 - 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.55842 + 7.89542i) q^{86} +(2.18614 + 3.78651i) q^{88} -3.25544 q^{89} +2.00000 q^{91} +(-3.68614 - 6.38458i) q^{92} +(-3.43070 + 5.94215i) q^{95} +(-4.55842 - 7.89542i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} + 3q^{5} - 2q^{7} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} + 3q^{5} - 2q^{7} + 4q^{8} - 6q^{10} + 3q^{11} - 4q^{13} - 2q^{14} - 2q^{16} + 6q^{17} + 20q^{19} + 3q^{20} + 3q^{22} - 9q^{23} - 11q^{25} + 8q^{26} + 4q^{28} - 6q^{29} - 4q^{31} - 2q^{32} - 3q^{34} - 6q^{35} + 8q^{37} - 10q^{38} + 3q^{40} + 15q^{41} - q^{43} - 6q^{44} + 18q^{46} - 2q^{49} - 11q^{50} - 4q^{52} + 12q^{53} - 24q^{55} - 2q^{56} - 6q^{58} - 3q^{59} + 11q^{61} + 8q^{62} + 4q^{64} + 6q^{65} - 13q^{67} - 3q^{68} + 3q^{70} - 6q^{71} + 14q^{73} - 4q^{74} - 10q^{76} + 3q^{77} - 7q^{79} - 6q^{80} - 30q^{82} + 12q^{83} - 12q^{85} - q^{86} + 3q^{88} - 36q^{89} + 8q^{91} - 9q^{92} + 15q^{95} - q^{97} + 4q^{98} + O(q^{100}) \)

Character values

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

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

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
\(5\) −0.686141 + 1.18843i −0.306851 + 0.531482i −0.977672 0.210138i \(-0.932609\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.37228 0.433953
\(11\) 2.18614 + 3.78651i 0.659146 + 1.14167i 0.980837 + 0.194830i \(0.0624155\pi\)
−0.321691 + 0.946845i \(0.604251\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.37228 1.06043 0.530217 0.847862i \(-0.322110\pi\)
0.530217 + 0.847862i \(0.322110\pi\)
\(18\) 0 0
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) −0.686141 1.18843i −0.153426 0.265741i
\(21\) 0 0
\(22\) 2.18614 3.78651i 0.466087 0.807286i
\(23\) −3.68614 + 6.38458i −0.768613 + 1.33128i 0.169701 + 0.985496i \(0.445720\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) 0 0
\(25\) 1.55842 + 2.69927i 0.311684 + 0.539853i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 1.37228 + 2.37686i 0.254826 + 0.441372i 0.964848 0.262807i \(-0.0846484\pi\)
−0.710022 + 0.704179i \(0.751315\pi\)
\(30\) 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
\(34\) −2.18614 3.78651i −0.374920 0.649381i
\(35\) 1.37228 0.231958
\(36\) 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
\(40\) −0.686141 + 1.18843i −0.108488 + 0.187907i
\(41\) 5.18614 8.98266i 0.809939 1.40286i −0.102966 0.994685i \(-0.532833\pi\)
0.912906 0.408171i \(-0.133833\pi\)
\(42\) 0 0
\(43\) −4.55842 7.89542i −0.695153 1.20404i −0.970129 0.242589i \(-0.922003\pi\)
0.274976 0.961451i \(-0.411330\pi\)
\(44\) −4.37228 −0.659146
\(45\) 0 0
\(46\) 7.37228 1.08698
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 1.55842 2.69927i 0.220394 0.381734i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −2.74456 −0.376995 −0.188497 0.982074i \(-0.560362\pi\)
−0.188497 + 0.982074i \(0.560362\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) 1.37228 2.37686i 0.180189 0.312097i
\(59\) 3.55842 6.16337i 0.463267 0.802402i −0.535854 0.844310i \(-0.680010\pi\)
0.999121 + 0.0419083i \(0.0133437\pi\)
\(60\) 0 0
\(61\) 7.05842 + 12.2255i 0.903738 + 1.56532i 0.822602 + 0.568618i \(0.192522\pi\)
0.0811364 + 0.996703i \(0.474145\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.37228 2.37686i −0.170211 0.294813i
\(66\) 0 0
\(67\) −7.55842 + 13.0916i −0.923408 + 1.59939i −0.129307 + 0.991605i \(0.541275\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) −2.18614 + 3.78651i −0.265108 + 0.459181i
\(69\) 0 0
\(70\) −0.686141 1.18843i −0.0820095 0.142045i
\(71\) −10.1168 −1.20065 −0.600324 0.799757i \(-0.704962\pi\)
−0.600324 + 0.799757i \(0.704962\pi\)
\(72\) 0 0
\(73\) −5.11684 −0.598881 −0.299441 0.954115i \(-0.596800\pi\)
−0.299441 + 0.954115i \(0.596800\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) −2.50000 + 4.33013i −0.286770 + 0.496700i
\(77\) 2.18614 3.78651i 0.249134 0.431512i
\(78\) 0 0
\(79\) −6.05842 10.4935i −0.681626 1.18061i −0.974485 0.224455i \(-0.927940\pi\)
0.292859 0.956156i \(-0.405393\pi\)
\(80\) 1.37228 0.153426
\(81\) 0 0
\(82\) −10.3723 −1.14543
\(83\) −2.74456 4.75372i −0.301255 0.521789i 0.675166 0.737666i \(-0.264072\pi\)
−0.976420 + 0.215877i \(0.930739\pi\)
\(84\) 0 0
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) −4.55842 + 7.89542i −0.491547 + 0.851385i
\(87\) 0 0
\(88\) 2.18614 + 3.78651i 0.233043 + 0.403643i
\(89\) −3.25544 −0.345076 −0.172538 0.985003i \(-0.555197\pi\)
−0.172538 + 0.985003i \(0.555197\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) −3.68614 6.38458i −0.384307 0.665639i
\(93\) 0 0
\(94\) 0 0
\(95\) −3.43070 + 5.94215i −0.351983 + 0.609652i
\(96\) 0 0
\(97\) −4.55842 7.89542i −0.462838 0.801658i 0.536263 0.844051i \(-0.319835\pi\)
−0.999101 + 0.0423924i \(0.986502\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) −3.11684 −0.311684
\(101\) 3.68614 + 6.38458i 0.366785 + 0.635290i 0.989061 0.147508i \(-0.0471252\pi\)
−0.622276 + 0.782798i \(0.713792\pi\)
\(102\) 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
\(106\) 1.37228 + 2.37686i 0.133288 + 0.230861i
\(107\) 1.62772 0.157358 0.0786788 0.996900i \(-0.474930\pi\)
0.0786788 + 0.996900i \(0.474930\pi\)
\(108\) 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
\(113\) 0.686141 1.18843i 0.0645467 0.111798i −0.831946 0.554856i \(-0.812773\pi\)
0.896493 + 0.443058i \(0.146107\pi\)
\(114\) 0 0
\(115\) −5.05842 8.76144i −0.471700 0.817009i
\(116\) −2.74456 −0.254826
\(117\) 0 0
\(118\) −7.11684 −0.655159
\(119\) −2.18614 3.78651i −0.200403 0.347108i
\(120\) 0 0
\(121\) −4.05842 + 7.02939i −0.368947 + 0.639036i
\(122\) 7.05842 12.2255i 0.639040 1.10685i
\(123\) 0 0
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) −11.1386 −0.996266
\(126\) 0 0
\(127\) −14.1168 −1.25267 −0.626334 0.779555i \(-0.715445\pi\)
−0.626334 + 0.779555i \(0.715445\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −1.37228 + 2.37686i −0.120357 + 0.208464i
\(131\) −3.68614 + 6.38458i −0.322060 + 0.557824i −0.980913 0.194448i \(-0.937708\pi\)
0.658853 + 0.752271i \(0.271042\pi\)
\(132\) 0 0
\(133\) −2.50000 4.33013i −0.216777 0.375470i
\(134\) 15.1168 1.30590
\(135\) 0 0
\(136\) 4.37228 0.374920
\(137\) 8.18614 + 14.1788i 0.699389 + 1.21138i 0.968678 + 0.248318i \(0.0798779\pi\)
−0.269289 + 0.963059i \(0.586789\pi\)
\(138\) 0 0
\(139\) 10.6168 18.3889i 0.900509 1.55973i 0.0736742 0.997282i \(-0.476528\pi\)
0.826835 0.562445i \(-0.190139\pi\)
\(140\) −0.686141 + 1.18843i −0.0579895 + 0.100441i
\(141\) 0 0
\(142\) 5.05842 + 8.76144i 0.424493 + 0.735244i
\(143\) −8.74456 −0.731257
\(144\) 0 0
\(145\) −3.76631 −0.312775
\(146\) 2.55842 + 4.43132i 0.211737 + 0.366738i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) 7.37228 12.7692i 0.603961 1.04609i −0.388254 0.921552i \(-0.626922\pi\)
0.992215 0.124538i \(-0.0397450\pi\)
\(150\) 0 0
\(151\) 4.05842 + 7.02939i 0.330270 + 0.572044i 0.982565 0.185921i \(-0.0595270\pi\)
−0.652295 + 0.757965i \(0.726194\pi\)
\(152\) 5.00000 0.405554
\(153\) 0 0
\(154\) −4.37228 −0.352328
\(155\) −1.37228 2.37686i −0.110224 0.190914i
\(156\) 0 0
\(157\) 4.05842 7.02939i 0.323897 0.561007i −0.657391 0.753549i \(-0.728340\pi\)
0.981289 + 0.192543i \(0.0616734\pi\)
\(158\) −6.05842 + 10.4935i −0.481982 + 0.834818i
\(159\) 0 0
\(160\) −0.686141 1.18843i −0.0542442 0.0939537i
\(161\) 7.37228 0.581017
\(162\) 0 0
\(163\) 16.2337 1.27152 0.635760 0.771887i \(-0.280687\pi\)
0.635760 + 0.771887i \(0.280687\pi\)
\(164\) 5.18614 + 8.98266i 0.404970 + 0.701428i
\(165\) 0 0
\(166\) −2.74456 + 4.75372i −0.213019 + 0.368960i
\(167\) 8.74456 15.1460i 0.676675 1.17203i −0.299302 0.954158i \(-0.596754\pi\)
0.975976 0.217876i \(-0.0699129\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 6.00000 0.460179
\(171\) 0 0
\(172\) 9.11684 0.695153
\(173\) −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
\(175\) 1.55842 2.69927i 0.117806 0.204045i
\(176\) 2.18614 3.78651i 0.164787 0.285419i
\(177\) 0 0
\(178\) 1.62772 + 2.81929i 0.122003 + 0.211315i
\(179\) −14.7446 −1.10206 −0.551030 0.834485i \(-0.685765\pi\)
−0.551030 + 0.834485i \(0.685765\pi\)
\(180\) 0 0
\(181\) 18.1168 1.34661 0.673307 0.739363i \(-0.264873\pi\)
0.673307 + 0.739363i \(0.264873\pi\)
\(182\) −1.00000 1.73205i −0.0741249 0.128388i
\(183\) 0 0
\(184\) −3.68614 + 6.38458i −0.271746 + 0.470678i
\(185\) −1.37228 + 2.37686i −0.100892 + 0.174750i
\(186\) 0 0
\(187\) 9.55842 + 16.5557i 0.698981 + 1.21067i
\(188\) 0 0
\(189\) 0 0
\(190\) 6.86141 0.497779
\(191\) −0.941578 1.63086i −0.0681302 0.118005i 0.829948 0.557841i \(-0.188370\pi\)
−0.898078 + 0.439836i \(0.855037\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) −4.55842 + 7.89542i −0.327276 + 0.566858i
\(195\) 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 \(0.615329\pi\)
\(200\) 1.55842 + 2.69927i 0.110197 + 0.190867i
\(201\) 0 0
\(202\) 3.68614 6.38458i 0.259356 0.449218i
\(203\) 1.37228 2.37686i 0.0963153 0.166823i
\(204\) 0 0
\(205\) 7.11684 + 12.3267i 0.497062 + 0.860937i
\(206\) −10.0000 −0.696733
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 10.9307 + 18.9325i 0.756093 + 1.30959i
\(210\) 0 0
\(211\) 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) 1.37228 2.37686i 0.0942487 0.163243i
\(213\) 0 0
\(214\) −0.813859 1.40965i −0.0556343 0.0963614i
\(215\) 12.5109 0.853235
\(216\) 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
\(221\) −4.37228 + 7.57301i −0.294111 + 0.509416i
\(222\) 0 0
\(223\) 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i \(-0.123907\pi\)
−0.791258 + 0.611482i \(0.790574\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −1.37228 −0.0912828
\(227\) −11.8723 20.5634i −0.787991 1.36484i −0.927196 0.374577i \(-0.877788\pi\)
0.139205 0.990264i \(-0.455545\pi\)
\(228\) 0 0
\(229\) 10.0584 17.4217i 0.664679 1.15126i −0.314693 0.949194i \(-0.601902\pi\)
0.979372 0.202065i \(-0.0647651\pi\)
\(230\) −5.05842 + 8.76144i −0.333542 + 0.577713i
\(231\) 0 0
\(232\) 1.37228 + 2.37686i 0.0900947 + 0.156049i
\(233\) 11.7446 0.769412 0.384706 0.923039i \(-0.374303\pi\)
0.384706 + 0.923039i \(0.374303\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.55842 + 6.16337i 0.231634 + 0.401201i
\(237\) 0 0
\(238\) −2.18614 + 3.78651i −0.141706 + 0.245443i
\(239\) −9.43070 + 16.3345i −0.610021 + 1.05659i 0.381215 + 0.924487i \(0.375506\pi\)
−0.991236 + 0.132102i \(0.957827\pi\)
\(240\) 0 0
\(241\) −0.441578 0.764836i −0.0284445 0.0492674i 0.851453 0.524431i \(-0.175722\pi\)
−0.879897 + 0.475164i \(0.842389\pi\)
\(242\) 8.11684 0.521770
\(243\) 0 0
\(244\) −14.1168 −0.903738
\(245\) −0.686141 1.18843i −0.0438359 0.0759260i
\(246\) 0 0
\(247\) −5.00000 + 8.66025i −0.318142 + 0.551039i
\(248\) −1.00000 + 1.73205i −0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 5.56930 + 9.64630i 0.352233 + 0.610086i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) −32.2337 −2.02651
\(254\) 7.05842 + 12.2255i 0.442885 + 0.767099i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.9307 18.9325i 0.681839 1.18098i −0.292581 0.956241i \(-0.594514\pi\)
0.974419 0.224738i \(-0.0721527\pi\)
\(258\) 0 0
\(259\) −1.00000 1.73205i −0.0621370 0.107624i
\(260\) 2.74456 0.170211
\(261\) 0 0
\(262\) 7.37228 0.455461
\(263\) 6.68614 + 11.5807i 0.412285 + 0.714099i 0.995139 0.0984781i \(-0.0313974\pi\)
−0.582854 + 0.812577i \(0.698064\pi\)
\(264\) 0 0
\(265\) 1.88316 3.26172i 0.115681 0.200366i
\(266\) −2.50000 + 4.33013i −0.153285 + 0.265497i
\(267\) 0 0
\(268\) −7.55842 13.0916i −0.461704 0.799695i
\(269\) 7.37228 0.449496 0.224748 0.974417i \(-0.427844\pi\)
0.224748 + 0.974417i \(0.427844\pi\)
\(270\) 0 0
\(271\) −18.2337 −1.10762 −0.553809 0.832644i \(-0.686826\pi\)
−0.553809 + 0.832644i \(0.686826\pi\)
\(272\) −2.18614 3.78651i −0.132554 0.229591i
\(273\) 0 0
\(274\) 8.18614 14.1788i 0.494543 0.856573i
\(275\) −6.81386 + 11.8020i −0.410891 + 0.711684i
\(276\) 0 0
\(277\) −11.1168 19.2549i −0.667946 1.15692i −0.978477 0.206354i \(-0.933840\pi\)
0.310531 0.950563i \(-0.399493\pi\)
\(278\) −21.2337 −1.27351
\(279\) 0 0
\(280\) 1.37228 0.0820095
\(281\) 5.31386 + 9.20387i 0.316998 + 0.549057i 0.979860 0.199685i \(-0.0639917\pi\)
−0.662862 + 0.748742i \(0.730658\pi\)
\(282\) 0 0
\(283\) −4.94158 + 8.55906i −0.293746 + 0.508784i −0.974692 0.223550i \(-0.928235\pi\)
0.680946 + 0.732333i \(0.261569\pi\)
\(284\) 5.05842 8.76144i 0.300162 0.519896i
\(285\) 0 0
\(286\) 4.37228 + 7.57301i 0.258538 + 0.447802i
\(287\) −10.3723 −0.612256
\(288\) 0 0
\(289\) 2.11684 0.124520
\(290\) 1.88316 + 3.26172i 0.110583 + 0.191535i
\(291\) 0 0
\(292\) 2.55842 4.43132i 0.149720 0.259323i
\(293\) −2.31386 + 4.00772i −0.135177 + 0.234134i −0.925665 0.378344i \(-0.876494\pi\)
0.790488 + 0.612478i \(0.209827\pi\)
\(294\) 0 0
\(295\) 4.88316 + 8.45787i 0.284308 + 0.492436i
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) −14.7446 −0.854130
\(299\) −7.37228 12.7692i −0.426350 0.738460i
\(300\) 0 0
\(301\) −4.55842 + 7.89542i −0.262743 + 0.455084i
\(302\) 4.05842 7.02939i 0.233536 0.404496i
\(303\) 0 0
\(304\) −2.50000 4.33013i −0.143385 0.248350i
\(305\) −19.3723 −1.10925
\(306\) 0 0
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 2.18614 + 3.78651i 0.124567 + 0.215756i
\(309\) 0 0
\(310\) −1.37228 + 2.37686i −0.0779403 + 0.134997i
\(311\) −13.1168 + 22.7190i −0.743788 + 1.28828i 0.206971 + 0.978347i \(0.433639\pi\)
−0.950759 + 0.309931i \(0.899694\pi\)
\(312\) 0 0
\(313\) 1.44158 + 2.49689i 0.0814828 + 0.141132i 0.903887 0.427771i \(-0.140701\pi\)
−0.822404 + 0.568904i \(0.807368\pi\)
\(314\) −8.11684 −0.458060
\(315\) 0 0
\(316\) 12.1168 0.681626
\(317\) −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
\(320\) −0.686141 + 1.18843i −0.0383564 + 0.0664353i
\(321\) 0 0
\(322\) −3.68614 6.38458i −0.205421 0.355799i
\(323\) 21.8614 1.21640
\(324\) 0 0
\(325\) −6.23369 −0.345783
\(326\) −8.11684 14.0588i −0.449550 0.778644i
\(327\) 0 0
\(328\) 5.18614 8.98266i 0.286357 0.495984i
\(329\) 0 0
\(330\) 0 0
\(331\) 6.11684 + 10.5947i 0.336212 + 0.582337i 0.983717 0.179725i \(-0.0575207\pi\)
−0.647505 + 0.762061i \(0.724187\pi\)
\(332\) 5.48913 0.301255
\(333\) 0 0
\(334\) −17.4891 −0.956962
\(335\) −10.3723 17.9653i −0.566698 0.981550i
\(336\) 0 0
\(337\) −4.55842 + 7.89542i −0.248313 + 0.430091i −0.963058 0.269294i \(-0.913210\pi\)
0.714745 + 0.699385i \(0.246543\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 0 0
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) −8.74456 −0.473545
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.55842 7.89542i −0.245774 0.425692i
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 3.55842 6.16337i 0.191026 0.330867i −0.754564 0.656226i \(-0.772152\pi\)
0.945591 + 0.325359i \(0.105485\pi\)
\(348\) 0 0
\(349\) 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i \(0.0337393\pi\)
−0.405571 + 0.914063i \(0.632927\pi\)
\(350\) −3.11684 −0.166602
\(351\) 0 0
\(352\) −4.37228 −0.233043
\(353\) −3.81386 6.60580i −0.202991 0.351591i 0.746500 0.665386i \(-0.231733\pi\)
−0.949491 + 0.313795i \(0.898400\pi\)
\(354\) 0 0
\(355\) 6.94158 12.0232i 0.368421 0.638123i
\(356\) 1.62772 2.81929i 0.0862689 0.149422i
\(357\) 0 0
\(358\) 7.37228 + 12.7692i 0.389637 + 0.674871i
\(359\) 6.86141 0.362131 0.181066 0.983471i \(-0.442045\pi\)
0.181066 + 0.983471i \(0.442045\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −9.05842 15.6896i −0.476100 0.824630i
\(363\) 0 0
\(364\) −1.00000 + 1.73205i −0.0524142 + 0.0907841i
\(365\) 3.51087 6.08101i 0.183768 0.318295i
\(366\) 0 0
\(367\) −11.1168 19.2549i −0.580295 1.00510i −0.995444 0.0953465i \(-0.969604\pi\)
0.415150 0.909753i \(-0.363729\pi\)
\(368\) 7.37228 0.384307
\(369\) 0 0
\(370\) 2.74456 0.142683
\(371\) 1.37228 + 2.37686i 0.0712453 + 0.123400i
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 9.55842 16.5557i 0.494254 0.856073i
\(375\) 0 0
\(376\) 0 0
\(377\) −5.48913 −0.282704
\(378\) 0 0
\(379\) 9.11684 0.468301 0.234150 0.972200i \(-0.424769\pi\)
0.234150 + 0.972200i \(0.424769\pi\)
\(380\) −3.43070 5.94215i −0.175991 0.304826i
\(381\) 0 0
\(382\) −0.941578 + 1.63086i −0.0481753 + 0.0834421i
\(383\) −10.6277 + 18.4077i −0.543051 + 0.940592i 0.455676 + 0.890146i \(0.349398\pi\)
−0.998727 + 0.0504462i \(0.983936\pi\)
\(384\) 0 0
\(385\) 3.00000 + 5.19615i 0.152894 + 0.264820i
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) 9.11684 0.462838
\(389\) −17.4891 30.2921i −0.886734 1.53587i −0.843713 0.536794i \(-0.819635\pi\)
−0.0430204 0.999074i \(-0.513698\pi\)
\(390\) 0 0
\(391\) −16.1168 + 27.9152i −0.815064 + 1.41173i
\(392\) −0.500000 + 0.866025i −0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) 16.6277 0.836631
\(396\) 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
\(400\) 1.55842 2.69927i 0.0779211 0.134963i
\(401\) −0.127719 + 0.221215i −0.00637797 + 0.0110470i −0.869197 0.494466i \(-0.835364\pi\)
0.862819 + 0.505513i \(0.168697\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) −7.37228 −0.366785
\(405\) 0 0
\(406\) −2.74456 −0.136210
\(407\) 4.37228 + 7.57301i 0.216726 + 0.375380i
\(408\) 0 0
\(409\) −14.6753 + 25.4183i −0.725645 + 1.25685i 0.233063 + 0.972462i \(0.425125\pi\)
−0.958708 + 0.284393i \(0.908208\pi\)
\(410\) 7.11684 12.3267i 0.351476 0.608774i
\(411\) 0 0
\(412\) 5.00000 + 8.66025i 0.246332 + 0.426660i
\(413\) −7.11684 −0.350197
\(414\) 0 0
\(415\) 7.53262 0.369762
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 0 0
\(418\) 10.9307 18.9325i 0.534638 0.926020i
\(419\) 13.8030 23.9075i 0.674320 1.16796i −0.302347 0.953198i \(-0.597770\pi\)
0.976667 0.214759i \(-0.0688964\pi\)
\(420\) 0 0
\(421\) 0.116844 + 0.202380i 0.00569463 + 0.00986338i 0.868859 0.495060i \(-0.164854\pi\)
−0.863164 + 0.504924i \(0.831521\pi\)
\(422\) −16.0000 −0.778868
\(423\) 0 0
\(424\) −2.74456 −0.133288
\(425\) 6.81386 + 11.8020i 0.330521 + 0.572479i
\(426\) 0 0
\(427\) 7.05842 12.2255i 0.341581 0.591636i
\(428\) −0.813859 + 1.40965i −0.0393394 + 0.0681378i
\(429\) 0 0
\(430\) −6.25544 10.8347i −0.301664 0.522497i
\(431\) 29.4891 1.42044 0.710221 0.703979i \(-0.248595\pi\)
0.710221 + 0.703979i \(0.248595\pi\)
\(432\) 0 0
\(433\) −2.88316 −0.138556 −0.0692778 0.997597i \(-0.522069\pi\)
−0.0692778 + 0.997597i \(0.522069\pi\)
\(434\) −1.00000 1.73205i −0.0480015 0.0831411i
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) −18.4307 + 31.9229i −0.881660 + 1.52708i
\(438\) 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
\(442\) 8.74456 0.415936
\(443\) −11.4416 19.8174i −0.543606 0.941553i −0.998693 0.0511061i \(-0.983725\pi\)
0.455087 0.890447i \(-0.349608\pi\)
\(444\) 0 0
\(445\) 2.23369 3.86886i 0.105887 0.183402i
\(446\) 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
\(451\) 45.3505 2.13547
\(452\) 0.686141 + 1.18843i 0.0322733 + 0.0558991i
\(453\) 0 0
\(454\) −11.8723 + 20.5634i −0.557194 + 0.965088i
\(455\) −1.37228 + 2.37686i −0.0643335 + 0.111429i
\(456\) 0 0
\(457\) −16.7337 28.9836i −0.782769 1.35580i −0.930323 0.366742i \(-0.880473\pi\)
0.147554 0.989054i \(-0.452860\pi\)
\(458\) −20.1168 −0.939998
\(459\) 0 0
\(460\) 10.1168 0.471700
\(461\) 15.4307 + 26.7268i 0.718680 + 1.24479i 0.961523 + 0.274724i \(0.0885865\pi\)
−0.242844 + 0.970065i \(0.578080\pi\)
\(462\) 0 0
\(463\) 2.94158 5.09496i 0.136707 0.236783i −0.789541 0.613697i \(-0.789682\pi\)
0.926248 + 0.376914i \(0.123015\pi\)
\(464\) 1.37228 2.37686i 0.0637066 0.110343i
\(465\) 0 0
\(466\) −5.87228 10.1711i −0.272028 0.471167i
\(467\) 30.0951 1.39263 0.696317 0.717734i \(-0.254821\pi\)
0.696317 + 0.717734i \(0.254821\pi\)
\(468\) 0 0
\(469\) 15.1168 0.698031
\(470\) 0 0
\(471\) 0 0
\(472\) 3.55842 6.16337i 0.163790 0.283692i
\(473\) 19.9307 34.5210i 0.916415 1.58728i
\(474\) 0 0
\(475\) 7.79211 + 13.4963i 0.357527 + 0.619254i
\(476\) 4.37228 0.200403
\(477\) 0 0
\(478\) 18.8614 0.862701
\(479\) 10.6277 + 18.4077i 0.485593 + 0.841072i 0.999863 0.0165568i \(-0.00527043\pi\)
−0.514270 + 0.857628i \(0.671937\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −0.441578 + 0.764836i −0.0201133 + 0.0348373i
\(483\) 0 0
\(484\) −4.05842 7.02939i −0.184474 0.319518i
\(485\) 12.5109 0.568090
\(486\) 0 0
\(487\) −16.3505 −0.740913 −0.370457 0.928850i \(-0.620799\pi\)
−0.370457 + 0.928850i \(0.620799\pi\)
\(488\) 7.05842 + 12.2255i 0.319520 + 0.553424i
\(489\) 0 0
\(490\) −0.686141 + 1.18843i −0.0309967 + 0.0536878i
\(491\) −9.81386 + 16.9981i −0.442893 + 0.767114i −0.997903 0.0647303i \(-0.979381\pi\)
0.555010 + 0.831844i \(0.312715\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) 10.0000 0.449921
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 5.05842 + 8.76144i 0.226901 + 0.393004i
\(498\) 0 0
\(499\) −0.441578 + 0.764836i −0.0197677 + 0.0342387i −0.875740 0.482783i \(-0.839626\pi\)
0.855972 + 0.517022i \(0.172959\pi\)
\(500\) 5.56930 9.64630i 0.249067 0.431396i
\(501\) 0 0
\(502\) −4.50000 7.79423i −0.200845 0.347873i
\(503\) −2.23369 −0.0995952 −0.0497976 0.998759i \(-0.515858\pi\)
−0.0497976 + 0.998759i \(0.515858\pi\)
\(504\) 0 0
\(505\) −10.1168 −0.450194
\(506\) 16.1168 + 27.9152i 0.716481 + 1.24098i
\(507\) 0 0
\(508\) 7.05842 12.2255i 0.313167 0.542421i
\(509\) 8.48913 14.7036i 0.376274 0.651725i −0.614243 0.789117i \(-0.710539\pi\)
0.990517 + 0.137392i \(0.0438718\pi\)
\(510\) 0 0
\(511\) 2.55842 + 4.43132i 0.113178 + 0.196030i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −21.8614 −0.964265
\(515\) 6.86141 + 11.8843i 0.302350 + 0.523685i
\(516\) 0 0
\(517\) 0 0
\(518\) −1.00000 + 1.73205i −0.0439375 + 0.0761019i
\(519\) 0 0
\(520\) −1.37228 2.37686i −0.0601785 0.104232i
\(521\) −3.86141 −0.169171 −0.0845856 0.996416i \(-0.526957\pi\)
−0.0845856 + 0.996416i \(0.526957\pi\)
\(522\) 0 0
\(523\) −17.8832 −0.781976 −0.390988 0.920396i \(-0.627867\pi\)
−0.390988 + 0.920396i \(0.627867\pi\)
\(524\) −3.68614 6.38458i −0.161030 0.278912i
\(525\) 0 0
\(526\) 6.68614 11.5807i 0.291530 0.504944i
\(527\) −4.37228 + 7.57301i −0.190460 + 0.329886i
\(528\) 0 0
\(529\) −15.6753 27.1504i −0.681533 1.18045i
\(530\) −3.76631 −0.163598
\(531\) 0 0
\(532\) 5.00000 0.216777
\(533\) 10.3723 + 17.9653i 0.449273 + 0.778164i
\(534\) 0 0
\(535\) −1.11684 + 1.93443i −0.0482854 + 0.0836327i
\(536\) −7.55842 + 13.0916i −0.326474 + 0.565470i
\(537\) 0 0
\(538\) −3.68614 6.38458i −0.158921 0.275259i
\(539\) −4.37228 −0.188327
\(540\) 0 0
\(541\) 28.2337 1.21386 0.606931 0.794755i \(-0.292401\pi\)
0.606931 + 0.794755i \(0.292401\pi\)
\(542\) 9.11684 + 15.7908i 0.391602 + 0.678275i
\(543\) 0 0
\(544\) −2.18614 + 3.78651i −0.0937300 + 0.162345i
\(545\) −9.60597 + 16.6380i −0.411475 + 0.712695i
\(546\) 0 0
\(547\) −0.441578 0.764836i −0.0188805 0.0327020i 0.856431 0.516262i \(-0.172677\pi\)
−0.875311 + 0.483560i \(0.839344\pi\)
\(548\) −16.3723 −0.699389
\(549\) 0 0
\(550\) 13.6277 0.581088
\(551\) 6.86141 + 11.8843i 0.292306 + 0.506288i
\(552\) 0 0
\(553\) −6.05842 + 10.4935i −0.257630 + 0.446229i
\(554\) −11.1168 + 19.2549i −0.472309 + 0.818064i
\(555\) 0 0
\(556\) 10.6168 + 18.3889i 0.450254 + 0.779864i
\(557\) −6.51087 −0.275875 −0.137937 0.990441i \(-0.544047\pi\)
−0.137937 + 0.990441i \(0.544047\pi\)
\(558\) 0 0
\(559\) 18.2337 0.771203
\(560\) −0.686141 1.18843i −0.0289947 0.0502204i
\(561\) 0 0
\(562\) 5.31386 9.20387i 0.224152 0.388242i
\(563\) 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
\(565\) 0.941578 + 1.63086i 0.0396125 + 0.0686108i
\(566\) 9.88316 0.415420
\(567\) 0 0
\(568\) −10.1168 −0.424493
\(569\) −0.558422 0.967215i −0.0234103 0.0405478i 0.854083 0.520137i \(-0.174119\pi\)
−0.877493 + 0.479589i \(0.840786\pi\)
\(570\) 0 0
\(571\) −14.6753 + 25.4183i −0.614141 + 1.06372i 0.376394 + 0.926460i \(0.377164\pi\)
−0.990535 + 0.137263i \(0.956169\pi\)
\(572\) 4.37228 7.57301i 0.182814 0.316644i
\(573\) 0 0
\(574\) 5.18614 + 8.98266i 0.216465 + 0.374929i
\(575\) −22.9783 −0.958259
\(576\) 0 0
\(577\) 27.1168 1.12889 0.564444 0.825471i \(-0.309090\pi\)
0.564444 + 0.825471i \(0.309090\pi\)
\(578\) −1.05842 1.83324i −0.0440246 0.0762528i
\(579\) 0 0
\(580\) 1.88316 3.26172i 0.0781938 0.135436i
\(581\) −2.74456 + 4.75372i −0.113864 + 0.197218i
\(582\) 0 0
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −5.11684 −0.211737
\(585\) 0 0
\(586\) 4.62772 0.191169
\(587\) −4.24456 7.35180i −0.175192 0.303441i 0.765036 0.643988i \(-0.222721\pi\)
−0.940228 + 0.340547i \(0.889388\pi\)
\(588\) 0 0
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) 4.88316 8.45787i 0.201036 0.348205i
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) −3.25544 −0.133685 −0.0668424 0.997764i \(-0.521292\pi\)
−0.0668424 + 0.997764i \(0.521292\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 7.37228 + 12.7692i 0.301980 + 0.523045i
\(597\) 0 0
\(598\) −7.37228 + 12.7692i −0.301475 + 0.522170i
\(599\) 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
\(601\) −3.44158 5.96099i −0.140385 0.243154i 0.787257 0.616625i \(-0.211501\pi\)
−0.927642 + 0.373472i \(0.878167\pi\)
\(602\) 9.11684 0.371575
\(603\) 0 0
\(604\) −8.11684 −0.330270
\(605\) −5.56930 9.64630i −0.226424 0.392178i
\(606\) 0 0
\(607\) 6.11684 10.5947i 0.248275 0.430025i −0.714772 0.699357i \(-0.753470\pi\)
0.963047 + 0.269332i \(0.0868030\pi\)
\(608\) −2.50000 + 4.33013i −0.101388 + 0.175610i
\(609\) 0 0
\(610\) 9.68614 + 16.7769i 0.392180 + 0.679276i
\(611\) 0 0
\(612\) 0 0
\(613\) −1.76631 −0.0713407 −0.0356703 0.999364i \(-0.511357\pi\)
−0.0356703 + 0.999364i \(0.511357\pi\)
\(614\) 6.50000 + 11.2583i 0.262319 + 0.454349i
\(615\) 0 0
\(616\) 2.18614 3.78651i 0.0880821 0.152563i
\(617\) −4.93070 + 8.54023i −0.198503 + 0.343817i −0.948043 0.318142i \(-0.896941\pi\)
0.749540 + 0.661959i \(0.230275\pi\)
\(618\) 0 0
\(619\) 11.7337 + 20.3233i 0.471617 + 0.816864i 0.999473 0.0324697i \(-0.0103373\pi\)
−0.527856 + 0.849334i \(0.677004\pi\)
\(620\) 2.74456 0.110224
\(621\) 0 0
\(622\) 26.2337 1.05188
\(623\) 1.62772 + 2.81929i 0.0652132 + 0.112953i
\(624\) 0 0
\(625\) −0.149468 + 0.258886i −0.00597872 + 0.0103555i
\(626\) 1.44158 2.49689i 0.0576170 0.0997956i
\(627\) 0 0
\(628\) 4.05842 + 7.02939i 0.161949 + 0.280503i
\(629\) 8.74456 0.348669
\(630\) 0 0
\(631\) 14.3505 0.571286 0.285643 0.958336i \(-0.407793\pi\)
0.285643 + 0.958336i \(0.407793\pi\)
\(632\) −6.05842 10.4935i −0.240991 0.417409i
\(633\) 0 0
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) 9.68614 16.7769i 0.384383 0.665770i
\(636\) 0 0
\(637\) −1.00000 1.73205i −0.0396214 0.0686264i
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) 1.37228 0.0542442
\(641\) −23.1060 40.0207i −0.912631 1.58072i −0.810333 0.585969i \(-0.800714\pi\)
−0.102298 0.994754i \(-0.532619\pi\)
\(642\) 0 0
\(643\) 12.6753 21.9542i 0.499864 0.865789i −0.500136 0.865947i \(-0.666717\pi\)
1.00000 0.000157386i \(5.00974e-5\pi\)
\(644\) −3.68614 + 6.38458i −0.145254 + 0.251588i
\(645\) 0 0
\(646\) −10.9307 18.9325i −0.430063 0.744891i
\(647\) 17.4891 0.687568 0.343784 0.939049i \(-0.388291\pi\)
0.343784 + 0.939049i \(0.388291\pi\)
\(648\) 0 0
\(649\) 31.1168 1.22144
\(650\) 3.11684 + 5.39853i 0.122253 + 0.211748i
\(651\) 0 0
\(652\) −8.11684 + 14.0588i −0.317880 + 0.550585i
\(653\) −7.62772 + 13.2116i −0.298496 + 0.517010i −0.975792 0.218701i \(-0.929818\pi\)
0.677296 + 0.735710i \(0.263152\pi\)
\(654\) 0 0
\(655\) −5.05842 8.76144i −0.197649 0.342338i
\(656\) −10.3723 −0.404970
\(657\) 0 0
\(658\) 0 0
\(659\) −4.62772 8.01544i −0.180270 0.312237i 0.761702 0.647927i \(-0.224364\pi\)
−0.941973 + 0.335690i \(0.891031\pi\)
\(660\) 0 0
\(661\) −4.94158 + 8.55906i −0.192205 + 0.332909i −0.945981 0.324223i \(-0.894897\pi\)
0.753776 + 0.657132i \(0.228231\pi\)
\(662\) 6.11684 10.5947i 0.237738 0.411774i
\(663\) 0 0
\(664\) −2.74456 4.75372i −0.106510 0.184480i
\(665\) 6.86141 0.266074
\(666\) 0 0
\(667\) −20.2337 −0.783452
\(668\) 8.74456 + 15.1460i 0.338337 + 0.586017i
\(669\) 0 0
\(670\) −10.3723 + 17.9653i −0.400716 + 0.694061i
\(671\) −30.8614 + 53.4535i −1.19139 + 2.06355i
\(672\) 0 0
\(673\) 10.0584 + 17.4217i 0.387724 + 0.671557i 0.992143 0.125109i \(-0.0399281\pi\)
−0.604419 + 0.796666i \(0.706595\pi\)
\(674\) 9.11684 0.351168
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −17.2337 29.8496i −0.662344 1.14721i −0.979998 0.199007i \(-0.936228\pi\)
0.317654 0.948207i \(-0.397105\pi\)
\(678\) 0 0
\(679\) −4.55842 + 7.89542i −0.174936 + 0.302998i
\(680\) −3.00000 + 5.19615i −0.115045 + 0.199263i
\(681\) 0 0
\(682\) 4.37228 + 7.57301i 0.167423 + 0.289986i
\(683\) 44.8397 1.71574 0.857871 0.513865i \(-0.171787\pi\)
0.857871 + 0.513865i \(0.171787\pi\)
\(684\) 0 0
\(685\) −22.4674 −0.858434
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) −4.55842 + 7.89542i −0.173788 + 0.301010i
\(689\) 2.74456 4.75372i 0.104560 0.181102i
\(690\) 0 0
\(691\) 2.94158 + 5.09496i 0.111903 + 0.193822i 0.916537 0.399949i \(-0.130972\pi\)
−0.804635 + 0.593770i \(0.797639\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −7.11684 −0.270152
\(695\) 14.5693 + 25.2348i 0.552645 + 0.957209i
\(696\) 0 0
\(697\) 22.6753 39.2747i 0.858887 1.48764i
\(698\) 11.0000 19.0526i 0.416356 0.721150i
\(699\) 0 0
\(700\) 1.55842 + 2.69927i 0.0589028 + 0.102023i
\(701\) 3.76631 0.142252 0.0711258 0.997467i \(-0.477341\pi\)
0.0711258 + 0.997467i \(0.477341\pi\)
\(702\) 0 0
\(703\) 10.0000 0.377157
\(704\) 2.18614 + 3.78651i 0.0823933 + 0.142709i
\(705\) 0 0
\(706\) −3.81386 + 6.60580i −0.143536 + 0.248612i
\(707\) 3.68614 6.38458i 0.138632 0.240117i
\(708\) 0 0
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) −13.8832 −0.521026
\(711\) 0 0
\(712\) −3.25544 −0.122003
\(713\) −7.37228 12.7692i −0.276094 0.478209i
\(714\) 0 0
\(715\) 6.00000 10.3923i 0.224387 0.388650i
\(716\) 7.37228 12.7692i 0.275515 0.477206i
\(717\) 0 0
\(718\) −3.43070 5.94215i −0.128033 0.221759i
\(719\) 8.74456 0.326117 0.163059 0.986616i \(-0.447864\pi\)
0.163059 + 0.986616i \(0.447864\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) −3.00000 5.19615i −0.111648 0.193381i
\(723\) 0 0
\(724\) −9.05842 + 15.6896i −0.336654 + 0.583101i
\(725\) −4.27719 + 7.40830i −0.158851 + 0.275138i
\(726\) 0 0
\(727\) 0.883156 + 1.52967i 0.0327544 + 0.0567324i 0.881938 0.471366i \(-0.156239\pi\)
−0.849183 + 0.528098i \(0.822905\pi\)
\(728\) 2.00000 0.0741249
\(729\) 0 0
\(730\) −7.02175 −0.259887
\(731\) −19.9307 34.5210i −0.737164 1.27680i
\(732\) 0 0
\(733\) 11.9416 20.6834i 0.441072 0.763960i −0.556697 0.830716i \(-0.687932\pi\)
0.997769 + 0.0667560i \(0.0212649\pi\)
\(734\) −11.1168 + 19.2549i −0.410330 + 0.710713i
\(735\) 0 0
\(736\) −3.68614 6.38458i −0.135873 0.235339i
\(737\) −66.0951 −2.43464
\(738\) 0 0
\(739\) 9.11684 0.335369 0.167684 0.985841i \(-0.446371\pi\)
0.167684 + 0.985841i \(0.446371\pi\)
\(740\) −1.37228 2.37686i −0.0504461 0.0873751i
\(741\) 0 0
\(742\) 1.37228 2.37686i 0.0503780 0.0872573i
\(743\) 21.8614 37.8651i 0.802017 1.38913i −0.116269 0.993218i \(-0.537094\pi\)
0.918286 0.395917i \(-0.129573\pi\)
\(744\) 0 0
\(745\) 10.1168 + 17.5229i 0.370652 + 0.641989i
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) −19.1168 −0.698981
\(749\) −0.813859 1.40965i −0.0297378 0.0515073i
\(750\) 0 0
\(751\) −0.0584220 + 0.101190i −0.00213185 + 0.00369247i −0.867089 0.498153i \(-0.834012\pi\)
0.864958 + 0.501845i \(0.167345\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 2.74456 + 4.75372i 0.0999511 + 0.173120i
\(755\) −11.1386 −0.405375
\(756\) 0 0
\(757\) 11.7663 0.427654 0.213827 0.976872i \(-0.431407\pi\)
0.213827 + 0.976872i \(0.431407\pi\)
\(758\) −4.55842 7.89542i −0.165569 0.286775i
\(759\) 0 0
\(760\) −3.43070 + 5.94215i −0.124445 + 0.215545i
\(761\) 6.25544 10.8347i 0.226759 0.392759i −0.730086 0.683355i \(-0.760520\pi\)
0.956846 + 0.290596i \(0.0938536\pi\)
\(762\) 0 0
\(763\) −7.00000 12.1244i −0.253417 0.438931i
\(764\) 1.88316 0.0681302
\(765\) 0 0
\(766\) 21.2554 0.767990
\(767\) 7.11684 + 12.3267i 0.256974 + 0.445093i
\(768\) 0 0
\(769\) 5.00000 8.66025i 0.180305 0.312297i −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 3.00000 5.19615i 0.108112 0.187256i
\(771\) 0 0
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) 11.1386 0.400627 0.200314 0.979732i \(-0.435804\pi\)
0.200314 + 0.979732i \(0.435804\pi\)
\(774\) 0 0
\(775\) −6.23369 −0.223921
\(776\) −4.55842 7.89542i −0.163638 0.283429i
\(777\) 0 0
\(778\) −17.4891 + 30.2921i −0.627016 + 1.08602i
\(779\) 25.9307 44.9133i 0.929064 1.60919i
\(780\) 0 0
\(781\) −22.1168 38.3075i −0.791403 1.37075i
\(782\) 32.2337 1.15267
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 5.56930 + 9.64630i 0.198777 + 0.344291i
\(786\) 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
\(790\) −8.31386 14.4000i −0.295794 0.512330i
\(791\) −1.37228 −0.0487927
\(792\) 0 0
\(793\) −28.2337 −1.00261
\(794\) 11.0000 + 19.0526i 0.390375 + 0.676150i
\(795\) 0 0
\(796\) 5.00000 8.66025i 0.177220 0.306955i
\(797\) −18.4307 + 31.9229i −0.652849 + 1.13077i 0.329579 + 0.944128i \(0.393093\pi\)