Properties

Label 378.2.k.d.269.2
Level $378$
Weight $2$
Character 378.269
Analytic conductor $3.018$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.2
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 378.269
Dual form 378.2.k.d.215.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(-1.00000 - 2.44949i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(-1.00000 - 2.44949i) q^{7} +1.00000i q^{8} +(-2.12132 - 1.22474i) q^{10} +(3.67423 + 2.12132i) q^{11} +4.18154i q^{13} +(2.09077 + 1.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.22474 - 2.12132i) q^{17} +(4.24264 - 2.44949i) q^{19} +2.44949 q^{20} -4.24264 q^{22} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.09077 - 3.62132i) q^{26} +(-2.62132 - 0.358719i) q^{28} +10.2426i q^{29} +(4.86396 + 2.80821i) q^{31} +(0.866025 + 0.500000i) q^{32} +2.44949i q^{34} +(3.97141 - 5.12132i) q^{35} +(1.62132 + 2.80821i) q^{37} +(-2.44949 + 4.24264i) q^{38} +(-2.12132 + 1.22474i) q^{40} +2.44949 q^{41} +7.00000 q^{43} +(3.67423 - 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-3.97141 - 6.87868i) q^{47} +(-5.00000 + 4.89898i) q^{49} -1.00000i q^{50} +(3.62132 + 2.09077i) q^{52} +(-2.15232 - 1.24264i) q^{53} +10.3923i q^{55} +(2.44949 - 1.00000i) q^{56} +(-5.12132 - 8.87039i) q^{58} +(-1.22474 + 2.12132i) q^{59} +(-0.621320 + 0.358719i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(-8.87039 + 5.12132i) q^{65} +(1.74264 - 3.01834i) q^{67} +(-1.22474 - 2.12132i) q^{68} +(-0.878680 + 6.42090i) q^{70} -12.7279i q^{71} +(-13.2426 - 7.64564i) q^{73} +(-2.80821 - 1.62132i) q^{74} -4.89898i q^{76} +(1.52192 - 11.1213i) q^{77} +(-4.62132 - 8.00436i) q^{79} +(1.22474 - 2.12132i) q^{80} +(-2.12132 + 1.22474i) q^{82} +5.49333 q^{83} +6.00000 q^{85} +(-6.06218 + 3.50000i) q^{86} +(-2.12132 + 3.67423i) q^{88} +(-8.87039 - 15.3640i) q^{89} +(10.2426 - 4.18154i) q^{91} +6.00000i q^{92} +(6.87868 + 3.97141i) q^{94} +(10.3923 + 6.00000i) q^{95} -6.63103i q^{97} +(1.88064 - 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 8 q^{7} - 4 q^{16} - 4 q^{25} - 4 q^{28} - 12 q^{31} - 4 q^{37} + 56 q^{43} + 24 q^{46} - 40 q^{49} + 12 q^{52} - 24 q^{58} + 12 q^{61} - 8 q^{64} - 20 q^{67} - 24 q^{70} - 72 q^{73} - 20 q^{79} + 48 q^{85} + 48 q^{91} + 72 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.22474 + 2.12132i 0.547723 + 0.948683i 0.998430 + 0.0560116i \(0.0178384\pi\)
−0.450708 + 0.892672i \(0.648828\pi\)
\(6\) 0 0
\(7\) −1.00000 2.44949i −0.377964 0.925820i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.12132 1.22474i −0.670820 0.387298i
\(11\) 3.67423 + 2.12132i 1.10782 + 0.639602i 0.938265 0.345918i \(-0.112432\pi\)
0.169559 + 0.985520i \(0.445766\pi\)
\(12\) 0 0
\(13\) 4.18154i 1.15975i 0.814705 + 0.579875i \(0.196899\pi\)
−0.814705 + 0.579875i \(0.803101\pi\)
\(14\) 2.09077 + 1.62132i 0.558782 + 0.433316i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.22474 2.12132i 0.297044 0.514496i −0.678414 0.734680i \(-0.737332\pi\)
0.975458 + 0.220184i \(0.0706658\pi\)
\(18\) 0 0
\(19\) 4.24264 2.44949i 0.973329 0.561951i 0.0730792 0.997326i \(-0.476717\pi\)
0.900249 + 0.435375i \(0.143384\pi\)
\(20\) 2.44949 0.547723
\(21\) 0 0
\(22\) −4.24264 −0.904534
\(23\) −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −2.09077 3.62132i −0.410034 0.710199i
\(27\) 0 0
\(28\) −2.62132 0.358719i −0.495383 0.0677916i
\(29\) 10.2426i 1.90201i 0.309175 + 0.951005i \(0.399947\pi\)
−0.309175 + 0.951005i \(0.600053\pi\)
\(30\) 0 0
\(31\) 4.86396 + 2.80821i 0.873593 + 0.504369i 0.868541 0.495618i \(-0.165058\pi\)
0.00505256 + 0.999987i \(0.498392\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 2.44949i 0.420084i
\(35\) 3.97141 5.12132i 0.671290 0.865661i
\(36\) 0 0
\(37\) 1.62132 + 2.80821i 0.266543 + 0.461667i 0.967967 0.251078i \(-0.0807851\pi\)
−0.701423 + 0.712745i \(0.747452\pi\)
\(38\) −2.44949 + 4.24264i −0.397360 + 0.688247i
\(39\) 0 0
\(40\) −2.12132 + 1.22474i −0.335410 + 0.193649i
\(41\) 2.44949 0.382546 0.191273 0.981537i \(-0.438738\pi\)
0.191273 + 0.981537i \(0.438738\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) 3.67423 2.12132i 0.553912 0.319801i
\(45\) 0 0
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) −3.97141 6.87868i −0.579289 1.00336i −0.995561 0.0941183i \(-0.969997\pi\)
0.416272 0.909240i \(-0.363337\pi\)
\(48\) 0 0
\(49\) −5.00000 + 4.89898i −0.714286 + 0.699854i
\(50\) 1.00000i 0.141421i
\(51\) 0 0
\(52\) 3.62132 + 2.09077i 0.502187 + 0.289938i
\(53\) −2.15232 1.24264i −0.295643 0.170690i 0.344841 0.938661i \(-0.387933\pi\)
−0.640484 + 0.767971i \(0.721266\pi\)
\(54\) 0 0
\(55\) 10.3923i 1.40130i
\(56\) 2.44949 1.00000i 0.327327 0.133631i
\(57\) 0 0
\(58\) −5.12132 8.87039i −0.672462 1.16474i
\(59\) −1.22474 + 2.12132i −0.159448 + 0.276172i −0.934670 0.355517i \(-0.884305\pi\)
0.775222 + 0.631689i \(0.217638\pi\)
\(60\) 0 0
\(61\) −0.621320 + 0.358719i −0.0795519 + 0.0459293i −0.539248 0.842147i \(-0.681292\pi\)
0.459696 + 0.888076i \(0.347958\pi\)
\(62\) −5.61642 −0.713286
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −8.87039 + 5.12132i −1.10024 + 0.635222i
\(66\) 0 0
\(67\) 1.74264 3.01834i 0.212897 0.368749i −0.739723 0.672912i \(-0.765043\pi\)
0.952620 + 0.304163i \(0.0983766\pi\)
\(68\) −1.22474 2.12132i −0.148522 0.257248i
\(69\) 0 0
\(70\) −0.878680 + 6.42090i −0.105022 + 0.767444i
\(71\) 12.7279i 1.51053i −0.655422 0.755263i \(-0.727509\pi\)
0.655422 0.755263i \(-0.272491\pi\)
\(72\) 0 0
\(73\) −13.2426 7.64564i −1.54993 0.894855i −0.998146 0.0608704i \(-0.980612\pi\)
−0.551788 0.833984i \(-0.686054\pi\)
\(74\) −2.80821 1.62132i −0.326448 0.188475i
\(75\) 0 0
\(76\) 4.89898i 0.561951i
\(77\) 1.52192 11.1213i 0.173439 1.26739i
\(78\) 0 0
\(79\) −4.62132 8.00436i −0.519939 0.900561i −0.999731 0.0231789i \(-0.992621\pi\)
0.479792 0.877382i \(-0.340712\pi\)
\(80\) 1.22474 2.12132i 0.136931 0.237171i
\(81\) 0 0
\(82\) −2.12132 + 1.22474i −0.234261 + 0.135250i
\(83\) 5.49333 0.602971 0.301485 0.953471i \(-0.402518\pi\)
0.301485 + 0.953471i \(0.402518\pi\)
\(84\) 0 0
\(85\) 6.00000 0.650791
\(86\) −6.06218 + 3.50000i −0.653701 + 0.377415i
\(87\) 0 0
\(88\) −2.12132 + 3.67423i −0.226134 + 0.391675i
\(89\) −8.87039 15.3640i −0.940259 1.62858i −0.764976 0.644059i \(-0.777249\pi\)
−0.175283 0.984518i \(-0.556084\pi\)
\(90\) 0 0
\(91\) 10.2426 4.18154i 1.07372 0.438345i
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 6.87868 + 3.97141i 0.709482 + 0.409619i
\(95\) 10.3923 + 6.00000i 1.06623 + 0.615587i
\(96\) 0 0
\(97\) 6.63103i 0.673279i −0.941634 0.336640i \(-0.890710\pi\)
0.941634 0.336640i \(-0.109290\pi\)
\(98\) 1.88064 6.74264i 0.189973 0.681110i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 3.67423 6.36396i 0.365600 0.633238i −0.623272 0.782005i \(-0.714197\pi\)
0.988872 + 0.148767i \(0.0475305\pi\)
\(102\) 0 0
\(103\) 5.37868 3.10538i 0.529977 0.305982i −0.211030 0.977480i \(-0.567682\pi\)
0.741007 + 0.671497i \(0.234348\pi\)
\(104\) −4.18154 −0.410034
\(105\) 0 0
\(106\) 2.48528 0.241392
\(107\) −12.5446 + 7.24264i −1.21273 + 0.700173i −0.963354 0.268233i \(-0.913560\pi\)
−0.249380 + 0.968406i \(0.580227\pi\)
\(108\) 0 0
\(109\) −3.86396 + 6.69258i −0.370100 + 0.641033i −0.989581 0.143980i \(-0.954010\pi\)
0.619480 + 0.785012i \(0.287343\pi\)
\(110\) −5.19615 9.00000i −0.495434 0.858116i
\(111\) 0 0
\(112\) −1.62132 + 2.09077i −0.153200 + 0.197559i
\(113\) 1.75736i 0.165318i −0.996578 0.0826592i \(-0.973659\pi\)
0.996578 0.0826592i \(-0.0263413\pi\)
\(114\) 0 0
\(115\) −12.7279 7.34847i −1.18688 0.685248i
\(116\) 8.87039 + 5.12132i 0.823595 + 0.475503i
\(117\) 0 0
\(118\) 2.44949i 0.225494i
\(119\) −6.42090 0.878680i −0.588603 0.0805484i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0.358719 0.621320i 0.0324769 0.0562517i
\(123\) 0 0
\(124\) 4.86396 2.80821i 0.436797 0.252185i
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 17.7279 1.57310 0.786549 0.617527i \(-0.211866\pi\)
0.786549 + 0.617527i \(0.211866\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 5.12132 8.87039i 0.449170 0.777984i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) −10.2426 7.94282i −0.888150 0.688729i
\(134\) 3.48528i 0.301082i
\(135\) 0 0
\(136\) 2.12132 + 1.22474i 0.181902 + 0.105021i
\(137\) 5.19615 + 3.00000i 0.443937 + 0.256307i 0.705266 0.708942i \(-0.250827\pi\)
−0.261329 + 0.965250i \(0.584161\pi\)
\(138\) 0 0
\(139\) 11.5300i 0.977963i −0.872294 0.488981i \(-0.837369\pi\)
0.872294 0.488981i \(-0.162631\pi\)
\(140\) −2.44949 6.00000i −0.207020 0.507093i
\(141\) 0 0
\(142\) 6.36396 + 11.0227i 0.534052 + 0.925005i
\(143\) −8.87039 + 15.3640i −0.741779 + 1.28480i
\(144\) 0 0
\(145\) −21.7279 + 12.5446i −1.80441 + 1.04177i
\(146\) 15.2913 1.26552
\(147\) 0 0
\(148\) 3.24264 0.266543
\(149\) −6.71807 + 3.87868i −0.550366 + 0.317754i −0.749270 0.662265i \(-0.769595\pi\)
0.198904 + 0.980019i \(0.436262\pi\)
\(150\) 0 0
\(151\) −8.62132 + 14.9326i −0.701593 + 1.21519i 0.266314 + 0.963886i \(0.414194\pi\)
−0.967907 + 0.251309i \(0.919139\pi\)
\(152\) 2.44949 + 4.24264i 0.198680 + 0.344124i
\(153\) 0 0
\(154\) 4.24264 + 10.3923i 0.341882 + 0.837436i
\(155\) 13.7574i 1.10502i
\(156\) 0 0
\(157\) −9.00000 5.19615i −0.718278 0.414698i 0.0958404 0.995397i \(-0.469446\pi\)
−0.814119 + 0.580699i \(0.802779\pi\)
\(158\) 8.00436 + 4.62132i 0.636793 + 0.367653i
\(159\) 0 0
\(160\) 2.44949i 0.193649i
\(161\) 12.5446 + 9.72792i 0.988655 + 0.766668i
\(162\) 0 0
\(163\) −3.74264 6.48244i −0.293146 0.507744i 0.681406 0.731906i \(-0.261369\pi\)
−0.974552 + 0.224162i \(0.928036\pi\)
\(164\) 1.22474 2.12132i 0.0956365 0.165647i
\(165\) 0 0
\(166\) −4.75736 + 2.74666i −0.369243 + 0.213182i
\(167\) −20.1903 −1.56237 −0.781185 0.624300i \(-0.785384\pi\)
−0.781185 + 0.624300i \(0.785384\pi\)
\(168\) 0 0
\(169\) −4.48528 −0.345022
\(170\) −5.19615 + 3.00000i −0.398527 + 0.230089i
\(171\) 0 0
\(172\) 3.50000 6.06218i 0.266872 0.462237i
\(173\) −10.3923 18.0000i −0.790112 1.36851i −0.925897 0.377776i \(-0.876689\pi\)
0.135785 0.990738i \(-0.456644\pi\)
\(174\) 0 0
\(175\) 2.62132 + 0.358719i 0.198153 + 0.0271166i
\(176\) 4.24264i 0.319801i
\(177\) 0 0
\(178\) 15.3640 + 8.87039i 1.15158 + 0.664864i
\(179\) 16.2189 + 9.36396i 1.21225 + 0.699895i 0.963250 0.268607i \(-0.0865633\pi\)
0.249004 + 0.968502i \(0.419897\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i 0.931345 + 0.364138i \(0.118636\pi\)
−0.931345 + 0.364138i \(0.881364\pi\)
\(182\) −6.77962 + 8.74264i −0.502539 + 0.648048i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) −3.97141 + 6.87868i −0.291984 + 0.505731i
\(186\) 0 0
\(187\) 9.00000 5.19615i 0.658145 0.379980i
\(188\) −7.94282 −0.579289
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 18.3712 10.6066i 1.32929 0.767467i 0.344101 0.938933i \(-0.388184\pi\)
0.985190 + 0.171466i \(0.0548503\pi\)
\(192\) 0 0
\(193\) −7.74264 + 13.4106i −0.557327 + 0.965319i 0.440391 + 0.897806i \(0.354840\pi\)
−0.997718 + 0.0675134i \(0.978493\pi\)
\(194\) 3.31552 + 5.74264i 0.238040 + 0.412298i
\(195\) 0 0
\(196\) 1.74264 + 6.77962i 0.124474 + 0.484258i
\(197\) 16.9706i 1.20910i 0.796566 + 0.604551i \(0.206648\pi\)
−0.796566 + 0.604551i \(0.793352\pi\)
\(198\) 0 0
\(199\) 3.10660 + 1.79360i 0.220221 + 0.127145i 0.606053 0.795425i \(-0.292752\pi\)
−0.385832 + 0.922569i \(0.626085\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) 0 0
\(202\) 7.34847i 0.517036i
\(203\) 25.0892 10.2426i 1.76092 0.718892i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) −3.10538 + 5.37868i −0.216362 + 0.374750i
\(207\) 0 0
\(208\) 3.62132 2.09077i 0.251093 0.144969i
\(209\) 20.7846 1.43770
\(210\) 0 0
\(211\) −13.4853 −0.928365 −0.464183 0.885740i \(-0.653652\pi\)
−0.464183 + 0.885740i \(0.653652\pi\)
\(212\) −2.15232 + 1.24264i −0.147822 + 0.0853449i
\(213\) 0 0
\(214\) 7.24264 12.5446i 0.495097 0.857533i
\(215\) 8.57321 + 14.8492i 0.584688 + 1.01271i
\(216\) 0 0
\(217\) 2.01472 14.7224i 0.136768 0.999424i
\(218\) 7.72792i 0.523401i
\(219\) 0 0
\(220\) 9.00000 + 5.19615i 0.606780 + 0.350325i
\(221\) 8.87039 + 5.12132i 0.596687 + 0.344497i
\(222\) 0 0
\(223\) 10.3923i 0.695920i −0.937509 0.347960i \(-0.886874\pi\)
0.937509 0.347960i \(-0.113126\pi\)
\(224\) 0.358719 2.62132i 0.0239680 0.175144i
\(225\) 0 0
\(226\) 0.878680 + 1.52192i 0.0584489 + 0.101236i
\(227\) −2.15232 + 3.72792i −0.142854 + 0.247431i −0.928570 0.371156i \(-0.878961\pi\)
0.785716 + 0.618587i \(0.212295\pi\)
\(228\) 0 0
\(229\) 7.86396 4.54026i 0.519665 0.300029i −0.217132 0.976142i \(-0.569670\pi\)
0.736798 + 0.676113i \(0.236337\pi\)
\(230\) 14.6969 0.969087
\(231\) 0 0
\(232\) −10.2426 −0.672462
\(233\) −3.04384 + 1.75736i −0.199408 + 0.115128i −0.596379 0.802703i \(-0.703395\pi\)
0.396971 + 0.917831i \(0.370061\pi\)
\(234\) 0 0
\(235\) 9.72792 16.8493i 0.634580 1.09912i
\(236\) 1.22474 + 2.12132i 0.0797241 + 0.138086i
\(237\) 0 0
\(238\) 6.00000 2.44949i 0.388922 0.158777i
\(239\) 7.75736i 0.501782i −0.968015 0.250891i \(-0.919276\pi\)
0.968015 0.250891i \(-0.0807236\pi\)
\(240\) 0 0
\(241\) 15.9853 + 9.22911i 1.02970 + 0.594499i 0.916899 0.399118i \(-0.130684\pi\)
0.112803 + 0.993617i \(0.464017\pi\)
\(242\) −6.06218 3.50000i −0.389692 0.224989i
\(243\) 0 0
\(244\) 0.717439i 0.0459293i
\(245\) −16.5160 4.60660i −1.05517 0.294305i
\(246\) 0 0
\(247\) 10.2426 + 17.7408i 0.651724 + 1.12882i
\(248\) −2.80821 + 4.86396i −0.178321 + 0.308862i
\(249\) 0 0
\(250\) −8.48528 + 4.89898i −0.536656 + 0.309839i
\(251\) −5.49333 −0.346736 −0.173368 0.984857i \(-0.555465\pi\)
−0.173368 + 0.984857i \(0.555465\pi\)
\(252\) 0 0
\(253\) −25.4558 −1.60040
\(254\) −15.3528 + 8.86396i −0.963322 + 0.556174i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.15232 3.72792i −0.134258 0.232541i 0.791056 0.611744i \(-0.209532\pi\)
−0.925314 + 0.379203i \(0.876198\pi\)
\(258\) 0 0
\(259\) 5.25736 6.77962i 0.326676 0.421265i
\(260\) 10.2426i 0.635222i
\(261\) 0 0
\(262\) 0 0
\(263\) −16.2189 9.36396i −1.00010 0.577407i −0.0918204 0.995776i \(-0.529269\pi\)
−0.908277 + 0.418369i \(0.862602\pi\)
\(264\) 0 0
\(265\) 6.08767i 0.373963i
\(266\) 12.8418 + 1.75736i 0.787381 + 0.107751i
\(267\) 0 0
\(268\) −1.74264 3.01834i −0.106449 0.184375i
\(269\) −4.89898 + 8.48528i −0.298696 + 0.517357i −0.975838 0.218496i \(-0.929885\pi\)
0.677142 + 0.735853i \(0.263218\pi\)
\(270\) 0 0
\(271\) 13.3492 7.70719i 0.810909 0.468178i −0.0363626 0.999339i \(-0.511577\pi\)
0.847271 + 0.531160i \(0.178244\pi\)
\(272\) −2.44949 −0.148522
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −3.67423 + 2.12132i −0.221565 + 0.127920i
\(276\) 0 0
\(277\) 0.863961 1.49642i 0.0519104 0.0899114i −0.838903 0.544282i \(-0.816802\pi\)
0.890813 + 0.454370i \(0.150136\pi\)
\(278\) 5.76500 + 9.98528i 0.345762 + 0.598877i
\(279\) 0 0
\(280\) 5.12132 + 3.97141i 0.306057 + 0.237337i
\(281\) 22.2426i 1.32688i 0.748227 + 0.663442i \(0.230905\pi\)
−0.748227 + 0.663442i \(0.769095\pi\)
\(282\) 0 0
\(283\) −20.2279 11.6786i −1.20243 0.694220i −0.241331 0.970443i \(-0.577584\pi\)
−0.961094 + 0.276222i \(0.910917\pi\)
\(284\) −11.0227 6.36396i −0.654077 0.377632i
\(285\) 0 0
\(286\) 17.7408i 1.04903i
\(287\) −2.44949 6.00000i −0.144589 0.354169i
\(288\) 0 0
\(289\) 5.50000 + 9.52628i 0.323529 + 0.560369i
\(290\) 12.5446 21.7279i 0.736646 1.27591i
\(291\) 0 0
\(292\) −13.2426 + 7.64564i −0.774967 + 0.447427i
\(293\) −7.94282 −0.464024 −0.232012 0.972713i \(-0.574531\pi\)
−0.232012 + 0.972713i \(0.574531\pi\)
\(294\) 0 0
\(295\) −6.00000 −0.349334
\(296\) −2.80821 + 1.62132i −0.163224 + 0.0942373i
\(297\) 0 0
\(298\) 3.87868 6.71807i 0.224686 0.389167i
\(299\) −12.5446 21.7279i −0.725474 1.25656i
\(300\) 0 0
\(301\) −7.00000 17.1464i −0.403473 0.988304i
\(302\) 17.2426i 0.992202i
\(303\) 0 0
\(304\) −4.24264 2.44949i −0.243332 0.140488i
\(305\) −1.52192 0.878680i −0.0871448 0.0503131i
\(306\) 0 0
\(307\) 2.57258i 0.146825i −0.997302 0.0734125i \(-0.976611\pi\)
0.997302 0.0734125i \(-0.0233890\pi\)
\(308\) −8.87039 6.87868i −0.505437 0.391949i
\(309\) 0 0
\(310\) −6.87868 11.9142i −0.390683 0.676682i
\(311\) 8.57321 14.8492i 0.486142 0.842023i −0.513731 0.857951i \(-0.671737\pi\)
0.999873 + 0.0159282i \(0.00507031\pi\)
\(312\) 0 0
\(313\) −0.514719 + 0.297173i −0.0290936 + 0.0167972i −0.514476 0.857505i \(-0.672014\pi\)
0.485383 + 0.874302i \(0.338680\pi\)
\(314\) 10.3923 0.586472
\(315\) 0 0
\(316\) −9.24264 −0.519939
\(317\) 11.9142 6.87868i 0.669169 0.386345i −0.126592 0.991955i \(-0.540404\pi\)
0.795762 + 0.605610i \(0.207071\pi\)
\(318\) 0 0
\(319\) −21.7279 + 37.6339i −1.21653 + 2.10709i
\(320\) −1.22474 2.12132i −0.0684653 0.118585i
\(321\) 0 0
\(322\) −15.7279 2.15232i −0.876483 0.119944i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) −3.62132 2.09077i −0.200875 0.115975i
\(326\) 6.48244 + 3.74264i 0.359029 + 0.207286i
\(327\) 0 0
\(328\) 2.44949i 0.135250i
\(329\) −12.8778 + 16.6066i −0.709979 + 0.915552i
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) 2.74666 4.75736i 0.150743 0.261094i
\(333\) 0 0
\(334\) 17.4853 10.0951i 0.956752 0.552381i
\(335\) 8.53716 0.466435
\(336\) 0 0
\(337\) 29.4558 1.60456 0.802281 0.596947i \(-0.203620\pi\)
0.802281 + 0.596947i \(0.203620\pi\)
\(338\) 3.88437 2.24264i 0.211282 0.121984i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) 11.9142 + 20.6360i 0.645191 + 1.11750i
\(342\) 0 0
\(343\) 17.0000 + 7.34847i 0.917914 + 0.396780i
\(344\) 7.00000i 0.377415i
\(345\) 0 0
\(346\) 18.0000 + 10.3923i 0.967686 + 0.558694i
\(347\) −25.0892 14.4853i −1.34686 0.777611i −0.359058 0.933315i \(-0.616902\pi\)
−0.987804 + 0.155705i \(0.950235\pi\)
\(348\) 0 0
\(349\) 24.3718i 1.30459i 0.757964 + 0.652296i \(0.226194\pi\)
−0.757964 + 0.652296i \(0.773806\pi\)
\(350\) −2.44949 + 1.00000i −0.130931 + 0.0534522i
\(351\) 0 0
\(352\) 2.12132 + 3.67423i 0.113067 + 0.195837i
\(353\) 15.2913 26.4853i 0.813873 1.40967i −0.0962614 0.995356i \(-0.530688\pi\)
0.910134 0.414313i \(-0.135978\pi\)
\(354\) 0 0
\(355\) 27.0000 15.5885i 1.43301 0.827349i
\(356\) −17.7408 −0.940259
\(357\) 0 0
\(358\) −18.7279 −0.989801
\(359\) −2.15232 + 1.24264i −0.113595 + 0.0655841i −0.555721 0.831369i \(-0.687558\pi\)
0.442126 + 0.896953i \(0.354224\pi\)
\(360\) 0 0
\(361\) 2.50000 4.33013i 0.131579 0.227901i
\(362\) −4.89898 8.48528i −0.257485 0.445976i
\(363\) 0 0
\(364\) 1.50000 10.9612i 0.0786214 0.574521i
\(365\) 37.4558i 1.96053i
\(366\) 0 0
\(367\) 7.97056 + 4.60181i 0.416060 + 0.240212i 0.693390 0.720562i \(-0.256116\pi\)
−0.277330 + 0.960775i \(0.589450\pi\)
\(368\) 5.19615 + 3.00000i 0.270868 + 0.156386i
\(369\) 0 0
\(370\) 7.94282i 0.412927i
\(371\) −0.891519 + 6.51472i −0.0462854 + 0.338227i
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) −5.19615 + 9.00000i −0.268687 + 0.465379i
\(375\) 0 0
\(376\) 6.87868 3.97141i 0.354741 0.204810i
\(377\) −42.8300 −2.20586
\(378\) 0 0
\(379\) 9.48528 0.487226 0.243613 0.969872i \(-0.421667\pi\)
0.243613 + 0.969872i \(0.421667\pi\)
\(380\) 10.3923 6.00000i 0.533114 0.307794i
\(381\) 0 0
\(382\) −10.6066 + 18.3712i −0.542681 + 0.939951i
\(383\) 7.64564 + 13.2426i 0.390674 + 0.676667i 0.992539 0.121931i \(-0.0389086\pi\)
−0.601865 + 0.798598i \(0.705575\pi\)
\(384\) 0 0
\(385\) 25.4558 10.3923i 1.29735 0.529641i
\(386\) 15.4853i 0.788180i
\(387\) 0 0
\(388\) −5.74264 3.31552i −0.291538 0.168320i
\(389\) −28.1331 16.2426i −1.42640 0.823535i −0.429569 0.903034i \(-0.641334\pi\)
−0.996835 + 0.0794995i \(0.974668\pi\)
\(390\) 0 0
\(391\) 14.6969i 0.743256i
\(392\) −4.89898 5.00000i −0.247436 0.252538i
\(393\) 0 0
\(394\) −8.48528 14.6969i −0.427482 0.740421i
\(395\) 11.3199 19.6066i 0.569565 0.986515i
\(396\) 0 0
\(397\) −25.8640 + 14.9326i −1.29807 + 0.749444i −0.980071 0.198646i \(-0.936346\pi\)
−0.318004 + 0.948090i \(0.603012\pi\)
\(398\) −3.58719 −0.179810
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 24.4588 14.1213i 1.22142 0.705185i 0.256197 0.966625i \(-0.417531\pi\)
0.965220 + 0.261440i \(0.0841972\pi\)
\(402\) 0 0
\(403\) −11.7426 + 20.3389i −0.584943 + 1.01315i
\(404\) −3.67423 6.36396i −0.182800 0.316619i
\(405\) 0 0
\(406\) −16.6066 + 21.4150i −0.824172 + 1.06281i
\(407\) 13.7574i 0.681927i
\(408\) 0 0
\(409\) −11.7426 6.77962i −0.580636 0.335230i 0.180750 0.983529i \(-0.442148\pi\)
−0.761386 + 0.648299i \(0.775481\pi\)
\(410\) −5.19615 3.00000i −0.256620 0.148159i
\(411\) 0 0
\(412\) 6.21076i 0.305982i
\(413\) 6.42090 + 0.878680i 0.315952 + 0.0432370i
\(414\) 0 0
\(415\) 6.72792 + 11.6531i 0.330261 + 0.572028i
\(416\) −2.09077 + 3.62132i −0.102508 + 0.177550i
\(417\) 0 0
\(418\) −18.0000 + 10.3923i −0.880409 + 0.508304i
\(419\) −12.8418 −0.627363 −0.313681 0.949528i \(-0.601562\pi\)
−0.313681 + 0.949528i \(0.601562\pi\)
\(420\) 0 0
\(421\) 27.4558 1.33812 0.669058 0.743210i \(-0.266698\pi\)
0.669058 + 0.743210i \(0.266698\pi\)
\(422\) 11.6786 6.74264i 0.568505 0.328227i
\(423\) 0 0
\(424\) 1.24264 2.15232i 0.0603480 0.104526i
\(425\) 1.22474 + 2.12132i 0.0594089 + 0.102899i
\(426\) 0 0
\(427\) 1.50000 + 1.16320i 0.0725901 + 0.0562911i
\(428\) 14.4853i 0.700173i
\(429\) 0 0
\(430\) −14.8492 8.57321i −0.716094 0.413437i
\(431\) −8.87039 5.12132i −0.427272 0.246685i 0.270912 0.962604i \(-0.412675\pi\)
−0.698184 + 0.715919i \(0.746008\pi\)
\(432\) 0 0
\(433\) 26.8213i 1.28895i −0.764626 0.644475i \(-0.777076\pi\)
0.764626 0.644475i \(-0.222924\pi\)
\(434\) 5.61642 + 13.7574i 0.269597 + 0.660374i
\(435\) 0 0
\(436\) 3.86396 + 6.69258i 0.185050 + 0.320516i
\(437\) −14.6969 + 25.4558i −0.703050 + 1.21772i
\(438\) 0 0
\(439\) −21.7279 + 12.5446i −1.03702 + 0.598722i −0.918987 0.394288i \(-0.870991\pi\)
−0.118030 + 0.993010i \(0.537658\pi\)
\(440\) −10.3923 −0.495434
\(441\) 0 0
\(442\) −10.2426 −0.487193
\(443\) −22.0454 + 12.7279i −1.04741 + 0.604722i −0.921923 0.387374i \(-0.873382\pi\)
−0.125486 + 0.992095i \(0.540049\pi\)
\(444\) 0 0
\(445\) 21.7279 37.6339i 1.03000 1.78402i
\(446\) 5.19615 + 9.00000i 0.246045 + 0.426162i
\(447\) 0 0
\(448\) 1.00000 + 2.44949i 0.0472456 + 0.115728i
\(449\) 30.7279i 1.45014i −0.688675 0.725070i \(-0.741807\pi\)
0.688675 0.725070i \(-0.258193\pi\)
\(450\) 0 0
\(451\) 9.00000 + 5.19615i 0.423793 + 0.244677i
\(452\) −1.52192 0.878680i −0.0715850 0.0413296i
\(453\) 0 0
\(454\) 4.30463i 0.202026i
\(455\) 21.4150 + 16.6066i 1.00395 + 0.778529i
\(456\) 0 0
\(457\) 11.5000 + 19.9186i 0.537947 + 0.931752i 0.999014 + 0.0443868i \(0.0141334\pi\)
−0.461067 + 0.887365i \(0.652533\pi\)
\(458\) −4.54026 + 7.86396i −0.212152 + 0.367459i
\(459\) 0 0
\(460\) −12.7279 + 7.34847i −0.593442 + 0.342624i
\(461\) 42.2357 1.96711 0.983556 0.180605i \(-0.0578056\pi\)
0.983556 + 0.180605i \(0.0578056\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 8.87039 5.12132i 0.411797 0.237751i
\(465\) 0 0
\(466\) 1.75736 3.04384i 0.0814081 0.141003i
\(467\) 1.52192 + 2.63604i 0.0704260 + 0.121981i 0.899088 0.437768i \(-0.144231\pi\)
−0.828662 + 0.559749i \(0.810897\pi\)
\(468\) 0 0
\(469\) −9.13604 1.25024i −0.421863 0.0577306i
\(470\) 19.4558i 0.897431i
\(471\) 0 0
\(472\) −2.12132 1.22474i −0.0976417 0.0563735i
\(473\) 25.7196 + 14.8492i 1.18259 + 0.682769i
\(474\) 0 0
\(475\) 4.89898i 0.224781i
\(476\) −3.97141 + 5.12132i −0.182029 + 0.234735i
\(477\) 0 0
\(478\) 3.87868 + 6.71807i 0.177407 + 0.307277i
\(479\) −1.22474 + 2.12132i −0.0559600 + 0.0969256i −0.892648 0.450754i \(-0.851155\pi\)
0.836688 + 0.547679i \(0.184489\pi\)
\(480\) 0 0
\(481\) −11.7426 + 6.77962i −0.535418 + 0.309124i
\(482\) −18.4582 −0.840749
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) 14.0665 8.12132i 0.638729 0.368770i
\(486\) 0 0
\(487\) −11.0000 + 19.0526i −0.498458 + 0.863354i −0.999998 0.00178012i \(-0.999433\pi\)
0.501541 + 0.865134i \(0.332767\pi\)
\(488\) −0.358719 0.621320i −0.0162385 0.0281259i
\(489\) 0 0
\(490\) 16.6066 4.26858i 0.750210 0.192835i
\(491\) 1.02944i 0.0464579i −0.999730 0.0232289i \(-0.992605\pi\)
0.999730 0.0232289i \(-0.00739466\pi\)
\(492\) 0 0
\(493\) 21.7279 + 12.5446i 0.978576 + 0.564981i
\(494\) −17.7408 10.2426i −0.798195 0.460838i
\(495\) 0 0
\(496\) 5.61642i 0.252185i
\(497\) −31.1769 + 12.7279i −1.39848 + 0.570925i
\(498\) 0 0
\(499\) −13.2279 22.9114i −0.592163 1.02566i −0.993941 0.109919i \(-0.964941\pi\)
0.401777 0.915737i \(-0.368393\pi\)
\(500\) 4.89898 8.48528i 0.219089 0.379473i
\(501\) 0 0
\(502\) 4.75736 2.74666i 0.212331 0.122590i
\(503\) 20.1903 0.900239 0.450120 0.892968i \(-0.351381\pi\)
0.450120 + 0.892968i \(0.351381\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 22.0454 12.7279i 0.980038 0.565825i
\(507\) 0 0
\(508\) 8.86396 15.3528i 0.393275 0.681172i
\(509\) 14.9941 + 25.9706i 0.664602 + 1.15112i 0.979393 + 0.201964i \(0.0647323\pi\)
−0.314791 + 0.949161i \(0.601934\pi\)
\(510\) 0 0
\(511\) −5.48528 + 40.0834i −0.242655 + 1.77318i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.72792 + 2.15232i 0.164432 + 0.0949346i
\(515\) 13.1750 + 7.60660i 0.580561 + 0.335187i
\(516\) 0 0
\(517\) 33.6985i 1.48206i
\(518\) −1.16320 + 8.50000i −0.0511080 + 0.373469i
\(519\) 0 0
\(520\) −5.12132 8.87039i −0.224585 0.388992i
\(521\) 4.60181 7.97056i 0.201609 0.349197i −0.747438 0.664331i \(-0.768716\pi\)
0.949047 + 0.315135i \(0.102050\pi\)
\(522\) 0 0
\(523\) 15.2574 8.80884i 0.667158 0.385184i −0.127841 0.991795i \(-0.540805\pi\)
0.794999 + 0.606611i \(0.207471\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 18.7279 0.816576
\(527\) 11.9142 6.87868i 0.518992 0.299640i
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 3.04384 + 5.27208i 0.132216 + 0.229004i
\(531\) 0 0
\(532\) −12.0000 + 4.89898i −0.520266 + 0.212398i
\(533\) 10.2426i 0.443658i
\(534\) 0 0
\(535\) −30.7279 17.7408i −1.32848 0.767001i
\(536\) 3.01834 + 1.74264i 0.130373 + 0.0752706i
\(537\) 0 0
\(538\) 9.79796i 0.422420i
\(539\) −28.7635 + 7.39340i −1.23893 + 0.318456i
\(540\) 0 0
\(541\) −22.7279 39.3659i −0.977150 1.69247i −0.672651 0.739960i \(-0.734844\pi\)
−0.304499 0.952513i \(-0.598489\pi\)
\(542\) −7.70719 + 13.3492i −0.331052 + 0.573399i
\(543\) 0 0
\(544\) 2.12132 1.22474i 0.0909509 0.0525105i
\(545\) −18.9295 −0.810849
\(546\) 0 0
\(547\) 6.02944 0.257800 0.128900 0.991658i \(-0.458855\pi\)
0.128900 + 0.991658i \(0.458855\pi\)
\(548\) 5.19615 3.00000i 0.221969 0.128154i
\(549\) 0 0
\(550\) 2.12132 3.67423i 0.0904534 0.156670i
\(551\) 25.0892 + 43.4558i 1.06884 + 1.85128i
\(552\) 0 0
\(553\) −14.9853 + 19.3242i −0.637239 + 0.821750i
\(554\) 1.72792i 0.0734124i
\(555\) 0 0
\(556\) −9.98528 5.76500i −0.423470 0.244491i
\(557\) −18.3712 10.6066i −0.778412 0.449416i 0.0574555 0.998348i \(-0.481701\pi\)
−0.835867 + 0.548932i \(0.815035\pi\)
\(558\) 0 0
\(559\) 29.2708i 1.23802i
\(560\) −6.42090 0.878680i −0.271332 0.0371310i
\(561\) 0 0
\(562\) −11.1213 19.2627i −0.469125 0.812548i
\(563\) −8.23999 + 14.2721i −0.347274 + 0.601496i −0.985764 0.168134i \(-0.946226\pi\)
0.638490 + 0.769630i \(0.279559\pi\)
\(564\) 0 0
\(565\) 3.72792 2.15232i 0.156835 0.0905486i
\(566\) 23.3572 0.981776
\(567\) 0 0
\(568\) 12.7279 0.534052
\(569\) 1.52192 0.878680i 0.0638021 0.0368362i −0.467760 0.883856i \(-0.654939\pi\)
0.531562 + 0.847020i \(0.321605\pi\)
\(570\) 0 0
\(571\) 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i \(-0.681062\pi\)
0.998978 + 0.0452101i \(0.0143957\pi\)
\(572\) 8.87039 + 15.3640i 0.370890 + 0.642399i
\(573\) 0 0
\(574\) 5.12132 + 3.97141i 0.213760 + 0.165763i
\(575\) 6.00000i 0.250217i
\(576\) 0 0
\(577\) 15.2574 + 8.80884i 0.635172 + 0.366717i 0.782752 0.622333i \(-0.213815\pi\)
−0.147580 + 0.989050i \(0.547148\pi\)
\(578\) −9.52628 5.50000i −0.396241 0.228770i
\(579\) 0 0
\(580\) 25.0892i 1.04177i
\(581\) −5.49333 13.4558i −0.227902 0.558242i
\(582\) 0 0
\(583\) −5.27208 9.13151i −0.218347 0.378188i
\(584\) 7.64564 13.2426i 0.316379 0.547984i
\(585\) 0 0
\(586\) 6.87868 3.97141i 0.284156 0.164057i
\(587\) 11.6531 0.480975 0.240488 0.970652i \(-0.422693\pi\)
0.240488 + 0.970652i \(0.422693\pi\)
\(588\) 0 0
\(589\) 27.5147 1.13372
\(590\) 5.19615 3.00000i 0.213922 0.123508i
\(591\) 0 0
\(592\) 1.62132 2.80821i 0.0666359 0.115417i
\(593\) 11.3199 + 19.6066i 0.464852 + 0.805147i 0.999195 0.0401210i \(-0.0127743\pi\)
−0.534343 + 0.845268i \(0.679441\pi\)
\(594\) 0 0
\(595\) −6.00000 14.6969i −0.245976 0.602516i
\(596\) 7.75736i 0.317754i
\(597\) 0 0
\(598\) 21.7279 + 12.5446i 0.888521 + 0.512988i
\(599\) −17.7408 10.2426i −0.724868 0.418503i 0.0916735 0.995789i \(-0.470778\pi\)
−0.816542 + 0.577286i \(0.804112\pi\)
\(600\) 0 0
\(601\) 17.2695i 0.704438i −0.935918 0.352219i \(-0.885427\pi\)
0.935918 0.352219i \(-0.114573\pi\)
\(602\) 14.6354 + 11.3492i 0.596494 + 0.462561i
\(603\) 0 0
\(604\) 8.62132 + 14.9326i 0.350797 + 0.607597i
\(605\) −8.57321 + 14.8492i −0.348551 + 0.603708i
\(606\) 0 0
\(607\) 22.7574 13.1390i 0.923693 0.533294i 0.0388815 0.999244i \(-0.487621\pi\)
0.884811 + 0.465950i \(0.154287\pi\)
\(608\) 4.89898 0.198680
\(609\) 0 0
\(610\) 1.75736 0.0711534
\(611\) 28.7635 16.6066i 1.16365 0.671831i
\(612\) 0 0
\(613\) −7.10660 + 12.3090i −0.287033 + 0.497156i −0.973100 0.230383i \(-0.926002\pi\)
0.686067 + 0.727538i \(0.259336\pi\)
\(614\) 1.28629 + 2.22792i 0.0519105 + 0.0899116i
\(615\) 0 0
\(616\) 11.1213 + 1.52192i 0.448091 + 0.0613198i
\(617\) 4.24264i 0.170802i 0.996347 + 0.0854011i \(0.0272172\pi\)
−0.996347 + 0.0854011i \(0.972783\pi\)
\(618\) 0 0
\(619\) −27.9853 16.1573i −1.12482 0.649417i −0.182196 0.983262i \(-0.558320\pi\)
−0.942628 + 0.333845i \(0.891654\pi\)
\(620\) 11.9142 + 6.87868i 0.478487 + 0.276254i
\(621\) 0 0
\(622\) 17.1464i 0.687509i
\(623\) −28.7635 + 37.0919i −1.15238 + 1.48605i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0.297173 0.514719i 0.0118774 0.0205723i
\(627\) 0 0
\(628\) −9.00000 + 5.19615i −0.359139 + 0.207349i
\(629\) 7.94282 0.316701
\(630\) 0 0
\(631\) −23.2426 −0.925275 −0.462637 0.886548i \(-0.653097\pi\)
−0.462637 + 0.886548i \(0.653097\pi\)
\(632\) 8.00436 4.62132i 0.318396 0.183826i
\(633\) 0 0
\(634\) −6.87868 + 11.9142i −0.273187 + 0.473174i
\(635\) 21.7122 + 37.6066i 0.861622 + 1.49237i
\(636\) 0 0
\(637\) −20.4853 20.9077i −0.811656 0.828393i
\(638\) 43.4558i 1.72043i
\(639\) 0 0
\(640\) 2.12132 + 1.22474i 0.0838525 + 0.0484123i
\(641\) 7.97887 + 4.60660i 0.315146 + 0.181950i 0.649227 0.760595i \(-0.275092\pi\)
−0.334081 + 0.942544i \(0.608426\pi\)
\(642\) 0 0
\(643\) 1.73205i 0.0683054i −0.999417 0.0341527i \(-0.989127\pi\)
0.999417 0.0341527i \(-0.0108733\pi\)
\(644\) 14.6969 6.00000i 0.579141 0.236433i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) 10.3923 18.0000i 0.408564 0.707653i −0.586165 0.810191i \(-0.699363\pi\)
0.994729 + 0.102538i \(0.0326965\pi\)
\(648\) 0 0
\(649\) −9.00000 + 5.19615i −0.353281 + 0.203967i
\(650\) 4.18154 0.164014
\(651\) 0 0
\(652\) −7.48528 −0.293146
\(653\) −12.5446 + 7.24264i −0.490909 + 0.283426i −0.724951 0.688800i \(-0.758138\pi\)
0.234043 + 0.972226i \(0.424805\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.22474 2.12132i −0.0478183 0.0828236i
\(657\) 0 0
\(658\) 2.84924 20.8207i 0.111075 0.811674i
\(659\) 13.7574i 0.535911i −0.963431 0.267955i \(-0.913652\pi\)
0.963431 0.267955i \(-0.0863480\pi\)
\(660\) 0 0
\(661\) 4.24264 + 2.44949i 0.165020 + 0.0952741i 0.580235 0.814449i \(-0.302961\pi\)
−0.415216 + 0.909723i \(0.636294\pi\)
\(662\) 8.66025 + 5.00000i 0.336590 + 0.194331i
\(663\) 0 0
\(664\) 5.49333i 0.213182i
\(665\) 4.30463 31.4558i 0.166927 1.21981i
\(666\) 0 0
\(667\) −30.7279 53.2223i −1.18979 2.06078i
\(668\) −10.0951 + 17.4853i −0.390592 + 0.676526i
\(669\) 0 0
\(670\) −7.39340 + 4.26858i −0.285632 + 0.164910i
\(671\) −3.04384 −0.117506
\(672\) 0 0
\(673\) 5.45584 0.210307 0.105154 0.994456i \(-0.466467\pi\)
0.105154 + 0.994456i \(0.466467\pi\)
\(674\) −25.5095 + 14.7279i −0.982590 + 0.567298i
\(675\) 0 0
\(676\) −2.24264 + 3.88437i −0.0862554 + 0.149399i
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) 0 0
\(679\) −16.2426 + 6.63103i −0.623335 + 0.254476i
\(680\) 6.00000i 0.230089i
\(681\) 0 0
\(682\) −20.6360 11.9142i −0.790195 0.456219i
\(683\) −1.52192 0.878680i −0.0582346 0.0336217i 0.470600 0.882347i \(-0.344037\pi\)
−0.528835 + 0.848725i \(0.677371\pi\)
\(684\) 0 0
\(685\) 14.6969i 0.561541i
\(686\) −18.3967 + 2.13604i −0.702388 + 0.0815543i
\(687\) 0 0
\(688\) −3.50000 6.06218i −0.133436 0.231118i
\(689\) 5.19615 9.00000i 0.197958 0.342873i
\(690\) 0 0
\(691\) −23.2279 + 13.4106i −0.883632 + 0.510165i −0.871854 0.489766i \(-0.837082\pi\)
−0.0117776 + 0.999931i \(0.503749\pi\)
\(692\) −20.7846 −0.790112
\(693\) 0 0
\(694\) 28.9706 1.09971
\(695\) 24.4588 14.1213i 0.927777 0.535652i
\(696\) 0 0
\(697\) 3.00000 5.19615i 0.113633 0.196818i
\(698\) −12.1859 21.1066i −0.461243 0.798897i
\(699\) 0 0
\(700\) 1.62132 2.09077i 0.0612801 0.0790237i
\(701\) 3.51472i 0.132749i −0.997795 0.0663745i \(-0.978857\pi\)
0.997795 0.0663745i \(-0.0211432\pi\)
\(702\) 0 0
\(703\) 13.7574 + 7.94282i 0.518869 + 0.299569i
\(704\) −3.67423 2.12132i −0.138478 0.0799503i
\(705\) 0 0
\(706\) 30.5826i 1.15099i
\(707\) −19.2627 2.63604i −0.724448 0.0991384i
\(708\) 0 0
\(709\) 13.1066 + 22.7013i 0.492229 + 0.852565i 0.999960 0.00895033i \(-0.00284902\pi\)
−0.507731 + 0.861516i \(0.669516\pi\)
\(710\) −15.5885 + 27.0000i −0.585024 + 1.01329i
\(711\) 0 0
\(712\) 15.3640 8.87039i 0.575789 0.332432i
\(713\) −33.6985 −1.26202
\(714\) 0 0
\(715\) −43.4558 −1.62516
\(716\) 16.2189 9.36396i 0.606127 0.349948i
\(717\) 0 0
\(718\) 1.24264 2.15232i 0.0463749 0.0803237i
\(719\) −5.52938 9.57716i −0.206211 0.357168i 0.744307 0.667838i \(-0.232780\pi\)
−0.950518 + 0.310670i \(0.899447\pi\)
\(720\) 0 0
\(721\) −12.9853 10.0696i −0.483597 0.375013i
\(722\) 5.00000i 0.186081i
\(723\) 0 0
\(724\) 8.48528 + 4.89898i 0.315353 + 0.182069i
\(725\) −8.87039 5.12132i −0.329438 0.190201i
\(726\) 0 0
\(727\) 45.4026i 1.68389i 0.539564 + 0.841945i \(0.318589\pi\)
−0.539564 + 0.841945i \(0.681411\pi\)
\(728\) 4.18154 + 10.2426i 0.154978 + 0.379618i
\(729\) 0 0
\(730\) 18.7279 + 32.4377i 0.693151 + 1.20057i
\(731\) 8.57321 14.8492i 0.317092 0.549219i
\(732\) 0 0
\(733\) 13.8640 8.00436i 0.512077 0.295648i −0.221610 0.975135i \(-0.571131\pi\)
0.733687 + 0.679488i \(0.237798\pi\)
\(734\) −9.20361 −0.339712
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 12.8057 7.39340i 0.471706 0.272339i
\(738\) 0 0
\(739\) −21.2279 + 36.7678i −0.780882 + 1.35253i 0.150547 + 0.988603i \(0.451897\pi\)
−0.931429 + 0.363924i \(0.881437\pi\)
\(740\) 3.97141 + 6.87868i 0.145992 + 0.252865i
\(741\) 0 0
\(742\) −2.48528 6.08767i −0.0912375 0.223485i
\(743\) 6.72792i 0.246824i 0.992356 + 0.123412i \(0.0393836\pi\)
−0.992356 + 0.123412i \(0.960616\pi\)
\(744\) 0 0
\(745\) −16.4558 9.50079i −0.602895 0.348082i
\(746\) −19.0526 11.0000i −0.697564 0.402739i
\(747\) 0 0
\(748\) 10.3923i 0.379980i
\(749\) 30.2854 + 23.4853i 1.10660 + 0.858134i
\(750\) 0 0
\(751\) −1.27208 2.20330i −0.0464188 0.0803997i 0.841882 0.539661i \(-0.181448\pi\)
−0.888301 + 0.459261i \(0.848114\pi\)
\(752\) −3.97141 + 6.87868i −0.144822 + 0.250840i
\(753\) 0 0
\(754\) 37.0919 21.4150i 1.35081 0.779889i
\(755\) −42.2357 −1.53711
\(756\) 0 0
\(757\) 41.2426 1.49899 0.749495 0.662010i \(-0.230297\pi\)
0.749495 + 0.662010i \(0.230297\pi\)
\(758\) −8.21449 + 4.74264i −0.298364 + 0.172260i
\(759\) 0 0
\(760\) −6.00000 + 10.3923i −0.217643 + 0.376969i
\(761\) −12.2474 21.2132i −0.443970 0.768978i 0.554010 0.832510i \(-0.313097\pi\)
−0.997980 + 0.0635319i \(0.979764\pi\)
\(762\) 0 0
\(763\) 20.2574 + 2.77216i 0.733366 + 0.100359i
\(764\) 21.2132i 0.767467i
\(765\) 0 0
\(766\) −13.2426 7.64564i −0.478476 0.276248i
\(767\) −8.87039 5.12132i −0.320291 0.184920i
\(768\) 0 0
\(769\) 1.18869i 0.0428653i −0.999770 0.0214327i \(-0.993177\pi\)
0.999770 0.0214327i \(-0.00682275\pi\)
\(770\) −16.8493 + 21.7279i −0.607205 + 0.783020i
\(771\) 0 0
\(772\) 7.74264 + 13.4106i 0.278664 + 0.482660i
\(773\) 4.89898 8.48528i 0.176204 0.305194i −0.764373 0.644774i \(-0.776951\pi\)
0.940577 + 0.339580i \(0.110285\pi\)
\(774\) 0 0
\(775\) −4.86396 + 2.80821i −0.174719 + 0.100874i
\(776\) 6.63103 0.238040
\(777\) 0 0
\(778\) 32.4853 1.16465
\(779\) 10.3923 6.00000i 0.372343 0.214972i
\(780\) 0 0
\(781\) 27.0000 46.7654i 0.966136 1.67340i
\(782\) −7.34847 12.7279i −0.262781 0.455150i
\(783\) 0 0
\(784\) 6.74264 + 1.88064i 0.240809 + 0.0671656i
\(785\) 25.4558i 0.908558i
\(786\) 0 0
\(787\) 9.47056 + 5.46783i 0.337589 + 0.194907i 0.659205 0.751963i \(-0.270893\pi\)
−0.321616 + 0.946870i \(0.604226\pi\)
\(788\) 14.6969 + 8.48528i 0.523557 +