Properties

Label 378.2.k.d.215.2
Level $378$
Weight $2$
Character 378.215
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 215.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 378.215
Dual form 378.2.k.d.269.2

$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 −0.450708 0.892672i \(-0.648828\pi\)
0.998430 0.0560116i \(-0.0178384\pi\)
\(6\) 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 0.169559 0.985520i \(-0.445766\pi\)
0.938265 + 0.345918i \(0.112432\pi\)
\(12\) 0 0
\(13\) 4.18154i 1.15975i −0.814705 0.579875i \(-0.803101\pi\)
0.814705 0.579875i \(-0.196899\pi\)
\(14\) 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 0.975458 0.220184i \(-0.0706658\pi\)
−0.678414 + 0.734680i \(0.737332\pi\)
\(18\) 0 0
\(19\) 4.24264 + 2.44949i 0.973329 + 0.561951i 0.900249 0.435375i \(-0.143384\pi\)
0.0730792 + 0.997326i \(0.476717\pi\)
\(20\) 2.44949 0.547723
\(21\) 0 0
\(22\) −4.24264 −0.904534
\(23\) −5.19615 3.00000i −1.08347 0.625543i −0.151642 0.988436i \(-0.548456\pi\)
−0.931831 + 0.362892i \(0.881789\pi\)
\(24\) 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 \(-0.600053\pi\)
0.309175 0.951005i \(-0.399947\pi\)
\(30\) 0 0
\(31\) 4.86396 2.80821i 0.873593 0.504369i 0.00505256 0.999987i \(-0.498392\pi\)
0.868541 + 0.495618i \(0.165058\pi\)
\(32\) 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 −0.701423 0.712745i \(-0.747452\pi\)
0.967967 + 0.251078i \(0.0807851\pi\)
\(38\) −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 0.416272 + 0.909240i \(0.363337\pi\)
−0.995561 + 0.0941183i \(0.969997\pi\)
\(48\) 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 −0.640484 0.767971i \(-0.721266\pi\)
0.344841 + 0.938661i \(0.387933\pi\)
\(54\) 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 0.775222 0.631689i \(-0.217638\pi\)
−0.934670 + 0.355517i \(0.884305\pi\)
\(60\) 0 0
\(61\) −0.621320 0.358719i −0.0795519 0.0459293i 0.459696 0.888076i \(-0.347958\pi\)
−0.539248 + 0.842147i \(0.681292\pi\)
\(62\) −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 0.952620 0.304163i \(-0.0983766\pi\)
−0.739723 + 0.672912i \(0.765043\pi\)
\(68\) −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 \(0.272491\pi\)
−0.655422 + 0.755263i \(0.727509\pi\)
\(72\) 0 0
\(73\) −13.2426 + 7.64564i −1.54993 + 0.894855i −0.551788 + 0.833984i \(0.686054\pi\)
−0.998146 + 0.0608704i \(0.980612\pi\)
\(74\) −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 0.479792 + 0.877382i \(0.340712\pi\)
−0.999731 + 0.0231789i \(0.992621\pi\)
\(80\) 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 −0.175283 + 0.984518i \(0.556084\pi\)
−0.764976 + 0.644059i \(0.777249\pi\)
\(90\) 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 \(0.109290\pi\)
−0.941634 + 0.336640i \(0.890710\pi\)
\(98\) 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 0.988872 0.148767i \(-0.0475305\pi\)
−0.623272 + 0.782005i \(0.714197\pi\)
\(102\) 0 0
\(103\) 5.37868 + 3.10538i 0.529977 + 0.305982i 0.741007 0.671497i \(-0.234348\pi\)
−0.211030 + 0.977480i \(0.567682\pi\)
\(104\) −4.18154 −0.410034
\(105\) 0 0
\(106\) 2.48528 0.241392
\(107\) −12.5446 7.24264i −1.21273 0.700173i −0.249380 0.968406i \(-0.580227\pi\)
−0.963354 + 0.268233i \(0.913560\pi\)
\(108\) 0 0
\(109\) −3.86396 6.69258i −0.370100 0.641033i 0.619480 0.785012i \(-0.287343\pi\)
−0.989581 + 0.143980i \(0.954010\pi\)
\(110\) −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 \(0.0263413\pi\)
−0.996578 + 0.0826592i \(0.973659\pi\)
\(114\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 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 −0.261329 0.965250i \(-0.584161\pi\)
0.705266 + 0.708942i \(0.250827\pi\)
\(138\) 0 0
\(139\) 11.5300i 0.977963i 0.872294 + 0.488981i \(0.162631\pi\)
−0.872294 + 0.488981i \(0.837369\pi\)
\(140\) −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 0.198904 0.980019i \(-0.436262\pi\)
−0.749270 + 0.662265i \(0.769595\pi\)
\(150\) 0 0
\(151\) −8.62132 14.9326i −0.701593 1.21519i −0.967907 0.251309i \(-0.919139\pi\)
0.266314 0.963886i \(-0.414194\pi\)
\(152\) 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 −0.814119 0.580699i \(-0.802779\pi\)
0.0958404 + 0.995397i \(0.469446\pi\)
\(158\) 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 −0.974552 0.224162i \(-0.928036\pi\)
0.681406 + 0.731906i \(0.261369\pi\)
\(164\) 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 0.135785 + 0.990738i \(0.456644\pi\)
−0.925897 + 0.377776i \(0.876689\pi\)
\(174\) 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 0.249004 0.968502i \(-0.419897\pi\)
0.963250 + 0.268607i \(0.0865633\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i −0.931345 0.364138i \(-0.881364\pi\)
0.931345 0.364138i \(-0.118636\pi\)
\(182\) −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 0.985190 0.171466i \(-0.0548503\pi\)
0.344101 + 0.938933i \(0.388184\pi\)
\(192\) 0 0
\(193\) −7.74264 13.4106i −0.557327 0.965319i −0.997718 0.0675134i \(-0.978493\pi\)
0.440391 0.897806i \(-0.354840\pi\)
\(194\) 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 \(-0.793352\pi\)
0.796566 0.604551i \(-0.206648\pi\)
\(198\) 0 0
\(199\) 3.10660 1.79360i 0.220221 0.127145i −0.385832 0.922569i \(-0.626085\pi\)
0.606053 + 0.795425i \(0.292752\pi\)
\(200\) −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 \(0.113126\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) 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 0.785716 0.618587i \(-0.212295\pi\)
−0.928570 + 0.371156i \(0.878961\pi\)
\(228\) 0 0
\(229\) 7.86396 + 4.54026i 0.519665 + 0.300029i 0.736798 0.676113i \(-0.236337\pi\)
−0.217132 + 0.976142i \(0.569670\pi\)
\(230\) 14.6969 0.969087
\(231\) 0 0
\(232\) −10.2426 −0.672462
\(233\) −3.04384 1.75736i −0.199408 0.115128i 0.396971 0.917831i \(-0.370061\pi\)
−0.596379 + 0.802703i \(0.703395\pi\)
\(234\) 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 \(0.0807236\pi\)
−0.968015 + 0.250891i \(0.919276\pi\)
\(240\) 0 0
\(241\) 15.9853 9.22911i 1.02970 0.594499i 0.112803 0.993617i \(-0.464017\pi\)
0.916899 + 0.399118i \(0.130684\pi\)
\(242\) −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 −0.925314 0.379203i \(-0.876198\pi\)
0.791056 + 0.611744i \(0.209532\pi\)
\(258\) 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 −0.908277 0.418369i \(-0.862602\pi\)
−0.0918204 + 0.995776i \(0.529269\pi\)
\(264\) 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 0.677142 0.735853i \(-0.263218\pi\)
−0.975838 + 0.218496i \(0.929885\pi\)
\(270\) 0 0
\(271\) 13.3492 + 7.70719i 0.810909 + 0.468178i 0.847271 0.531160i \(-0.178244\pi\)
−0.0363626 + 0.999339i \(0.511577\pi\)
\(272\) −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 0.890813 0.454370i \(-0.150136\pi\)
−0.838903 + 0.544282i \(0.816802\pi\)
\(278\) 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 \(-0.769095\pi\)
0.748227 0.663442i \(-0.230905\pi\)
\(282\) 0 0
\(283\) −20.2279 + 11.6786i −1.20243 + 0.694220i −0.961094 0.276222i \(-0.910917\pi\)
−0.241331 + 0.970443i \(0.577584\pi\)
\(284\) −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 \(0.0233890\pi\)
−0.997302 + 0.0734125i \(0.976611\pi\)
\(308\) −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 0.999873 0.0159282i \(-0.00507031\pi\)
−0.513731 + 0.857951i \(0.671737\pi\)
\(312\) 0 0
\(313\) −0.514719 0.297173i −0.0290936 0.0167972i 0.485383 0.874302i \(-0.338680\pi\)
−0.514476 + 0.857505i \(0.672014\pi\)
\(314\) 10.3923 0.586472
\(315\) 0 0
\(316\) −9.24264 −0.519939
\(317\) 11.9142 + 6.87868i 0.669169 + 0.386345i 0.795762 0.605610i \(-0.207071\pi\)
−0.126592 + 0.991955i \(0.540404\pi\)
\(318\) 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 −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) 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 −0.987804 0.155705i \(-0.950235\pi\)
−0.359058 + 0.933315i \(0.616902\pi\)
\(348\) 0 0
\(349\) 24.3718i 1.30459i −0.757964 0.652296i \(-0.773806\pi\)
0.757964 0.652296i \(-0.226194\pi\)
\(350\) −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 0.910134 + 0.414313i \(0.135978\pi\)
−0.0962614 + 0.995356i \(0.530688\pi\)
\(354\) 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 0.442126 0.896953i \(-0.354224\pi\)
−0.555721 + 0.831369i \(0.687558\pi\)
\(360\) 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 −0.277330 0.960775i \(-0.589450\pi\)
0.693390 + 0.720562i \(0.256116\pi\)
\(368\) 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 −0.427051 0.904227i \(-0.640448\pi\)
0.996610 0.0822766i \(-0.0262191\pi\)
\(374\) −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 −0.601865 0.798598i \(-0.705575\pi\)
0.992539 + 0.121931i \(0.0389086\pi\)
\(384\) 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 −0.996835 0.0794995i \(-0.974668\pi\)
−0.429569 + 0.903034i \(0.641334\pi\)
\(390\) 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 −0.318004 0.948090i \(-0.603012\pi\)
−0.980071 + 0.198646i \(0.936346\pi\)
\(398\) −3.58719 −0.179810
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 24.4588 + 14.1213i 1.22142 + 0.705185i 0.965220 0.261440i \(-0.0841972\pi\)
0.256197 + 0.966625i \(0.417531\pi\)
\(402\) 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 −0.761386 0.648299i \(-0.775481\pi\)
0.180750 + 0.983529i \(0.442148\pi\)
\(410\) −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 −0.698184 0.715919i \(-0.746008\pi\)
0.270912 + 0.962604i \(0.412675\pi\)
\(432\) 0 0
\(433\) 26.8213i 1.28895i 0.764626 + 0.644475i \(0.222924\pi\)
−0.764626 + 0.644475i \(0.777076\pi\)
\(434\) 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 −0.118030 0.993010i \(-0.537658\pi\)
−0.918987 + 0.394288i \(0.870991\pi\)
\(440\) −10.3923 −0.495434
\(441\) 0 0
\(442\) −10.2426 −0.487193
\(443\) −22.0454 12.7279i −1.04741 0.604722i −0.125486 0.992095i \(-0.540049\pi\)
−0.921923 + 0.387374i \(0.873382\pi\)
\(444\) 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 \(0.258193\pi\)
−0.688675 + 0.725070i \(0.741807\pi\)
\(450\) 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 −0.461067 0.887365i \(-0.652533\pi\)
0.999014 0.0443868i \(-0.0141334\pi\)
\(458\) −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 −0.828662 0.559749i \(-0.810897\pi\)
0.899088 + 0.437768i \(0.144231\pi\)
\(468\) 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 0.836688 0.547679i \(-0.184489\pi\)
−0.892648 + 0.450754i \(0.851155\pi\)
\(480\) 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 0.501541 0.865134i \(-0.332767\pi\)
−0.999998 + 0.00178012i \(0.999433\pi\)
\(488\) −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 \(0.00739466\pi\)
−0.999730 + 0.0232289i \(0.992605\pi\)
\(492\) 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 0.401777 + 0.915737i \(0.368393\pi\)
−0.993941 + 0.109919i \(0.964941\pi\)
\(500\) 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 −0.314791 0.949161i \(-0.601934\pi\)
0.979393 0.201964i \(-0.0647323\pi\)
\(510\) 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 0.949047 0.315135i \(-0.102050\pi\)
−0.747438 + 0.664331i \(0.768716\pi\)
\(522\) 0 0
\(523\) 15.2574 + 8.80884i 0.667158 + 0.385184i 0.794999 0.606611i \(-0.207471\pi\)
−0.127841 + 0.991795i \(0.540805\pi\)
\(524\) 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 −0.304499 + 0.952513i \(0.598489\pi\)
−0.672651 + 0.739960i \(0.734844\pi\)
\(542\) −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 −0.835867 0.548932i \(-0.815035\pi\)
0.0574555 + 0.998348i \(0.481701\pi\)
\(558\) 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 0.638490 0.769630i \(-0.279559\pi\)
−0.985764 + 0.168134i \(0.946226\pi\)
\(564\) 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 0.531562 0.847020i \(-0.321605\pi\)
−0.467760 + 0.883856i \(0.654939\pi\)
\(570\) 0 0
\(571\) 11.0000 + 19.0526i 0.460336 + 0.797325i 0.998978 0.0452101i \(-0.0143957\pi\)
−0.538642 + 0.842535i \(0.681062\pi\)
\(572\) 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 −0.147580 0.989050i \(-0.547148\pi\)
0.782752 + 0.622333i \(0.213815\pi\)
\(578\) −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 −0.534343 0.845268i \(-0.679441\pi\)
0.999195 + 0.0401210i \(0.0127743\pi\)
\(594\) 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 −0.816542 0.577286i \(-0.804112\pi\)
0.0916735 + 0.995789i \(0.470778\pi\)
\(600\) 0 0
\(601\) 17.2695i 0.704438i 0.935918 + 0.352219i \(0.114573\pi\)
−0.935918 + 0.352219i \(0.885427\pi\)
\(602\) 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 0.884811 0.465950i \(-0.154287\pi\)
0.0388815 + 0.999244i \(0.487621\pi\)
\(608\) 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 0.686067 0.727538i \(-0.259336\pi\)
−0.973100 + 0.230383i \(0.926002\pi\)
\(614\) 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 \(-0.972783\pi\)
0.996347 0.0854011i \(-0.0272172\pi\)
\(618\) 0 0
\(619\) −27.9853 + 16.1573i −1.12482 + 0.649417i −0.942628 0.333845i \(-0.891654\pi\)
−0.182196 + 0.983262i \(0.558320\pi\)
\(620\) 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 −0.334081 0.942544i \(-0.608426\pi\)
0.649227 + 0.760595i \(0.275092\pi\)
\(642\) 0 0
\(643\) 1.73205i 0.0683054i 0.999417 + 0.0341527i \(0.0108733\pi\)
−0.999417 + 0.0341527i \(0.989127\pi\)
\(644\) 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 0.994729 0.102538i \(-0.0326965\pi\)
−0.586165 + 0.810191i \(0.699363\pi\)
\(648\) 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 0.234043 0.972226i \(-0.424805\pi\)
−0.724951 + 0.688800i \(0.758138\pi\)
\(654\) 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 \(0.0863480\pi\)
−0.963431 + 0.267955i \(0.913652\pi\)
\(660\) 0 0
\(661\) 4.24264 2.44949i 0.165020 0.0952741i −0.415216 0.909723i \(-0.636294\pi\)
0.580235 + 0.814449i \(0.302961\pi\)
\(662\) 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 −0.689557 0.724232i \(-0.742195\pi\)
0.971981 + 0.235058i \(0.0755280\pi\)
\(678\) 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 −0.528835 0.848725i \(-0.677371\pi\)
0.470600 + 0.882347i \(0.344037\pi\)
\(684\) 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 −0.0117776 0.999931i \(-0.503749\pi\)
−0.871854 + 0.489766i \(0.837082\pi\)
\(692\) −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 \(0.0211432\pi\)
−0.997795 + 0.0663745i \(0.978857\pi\)
\(702\) 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 −0.507731 0.861516i \(-0.669516\pi\)
0.999960 + 0.00895033i \(0.00284902\pi\)
\(710\) −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 −0.950518 0.310670i \(-0.899447\pi\)
0.744307 + 0.667838i \(0.232780\pi\)
\(720\) 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 \(-0.681411\pi\)
0.539564 0.841945i \(-0.318589\pi\)
\(728\) 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 0.733687 0.679488i \(-0.237798\pi\)
−0.221610 + 0.975135i \(0.571131\pi\)
\(734\) −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 −0.931429 0.363924i \(-0.881437\pi\)
0.150547 0.988603i \(-0.451897\pi\)
\(740\) 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 \(-0.960616\pi\)
0.992356 0.123412i \(-0.0393836\pi\)
\(744\) 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 −0.888301 0.459261i \(-0.848114\pi\)
0.841882 + 0.539661i \(0.181448\pi\)
\(752\) −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 −0.997980 0.0635319i \(-0.979764\pi\)
0.554010 + 0.832510i \(0.313097\pi\)
\(762\) 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 \(0.00682275\pi\)
−0.999770 + 0.0214327i \(0.993177\pi\)
\(770\) −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 0.940577 0.339580i \(-0.110285\pi\)
−0.764373 + 0.644774i \(0.776951\pi\)
\(774\) 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 −0.321616 0.946870i \(-0.604226\pi\)
0.659205 + 0.751963i \(0.270893\pi\)
\(788\) 14.6969 8.48528i 0.523557 0.302276i