Properties

Label 2646.2.h.o.667.2
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.o.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +0.593579 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +0.593579 q^{5} +1.00000 q^{8} +(-0.296790 - 0.514055i) q^{10} +0.593579 q^{11} +(1.25729 + 2.17770i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(1.46050 + 2.52967i) q^{17} +(-2.69076 + 4.66053i) q^{19} +(-0.296790 + 0.514055i) q^{20} +(-0.296790 - 0.514055i) q^{22} -4.46050 q^{23} -4.64766 q^{25} +(1.25729 - 2.17770i) q^{26} +(3.09718 - 5.36447i) q^{29} +(-3.93346 + 6.81296i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.46050 - 2.52967i) q^{34} +(0.500000 - 0.866025i) q^{37} +5.38151 q^{38} +0.593579 q^{40} +(-0.136673 - 0.236725i) q^{41} +(-5.58113 + 9.66679i) q^{43} +(-0.296790 + 0.514055i) q^{44} +(2.23025 + 3.86291i) q^{46} +(-6.08113 - 10.5328i) q^{47} +(2.32383 + 4.02499i) q^{50} -2.51459 q^{52} +(-4.02704 - 6.97504i) q^{53} +0.352336 q^{55} -6.19436 q^{58} +(-4.32383 + 7.48910i) q^{59} +(-3.32383 - 5.75705i) q^{61} +7.86693 q^{62} +1.00000 q^{64} +(0.746304 + 1.29264i) q^{65} +(0.956906 - 1.65741i) q^{67} -2.92101 q^{68} +14.4107 q^{71} +(-3.95691 - 6.85356i) q^{73} -1.00000 q^{74} +(-2.69076 - 4.66053i) q^{76} +(4.62422 + 8.00938i) q^{79} +(-0.296790 - 0.514055i) q^{80} +(-0.136673 + 0.236725i) q^{82} +(3.85087 - 6.66991i) q^{83} +(0.866926 + 1.50156i) q^{85} +11.1623 q^{86} +0.593579 q^{88} +(-6.21780 + 10.7695i) q^{89} +(2.23025 - 3.86291i) q^{92} +(-6.08113 + 10.5328i) q^{94} +(-1.59718 + 2.76639i) q^{95} +(-5.86693 + 10.1618i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + O(q^{10}) \) \( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + q^{10} - 2 q^{11} - 8 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} - 14 q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} + 3 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} - 9 q^{47} + 2 q^{50} + 16 q^{52} - 15 q^{53} + 26 q^{55} - 10 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 8 q^{68} - 14 q^{71} - 19 q^{73} - 6 q^{74} + 3 q^{76} + 5 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} - 9 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.593579 0.265457 0.132728 0.991152i \(-0.457626\pi\)
0.132728 + 0.991152i \(0.457626\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.296790 0.514055i −0.0938531 0.162558i
\(11\) 0.593579 0.178971 0.0894855 0.995988i \(-0.471478\pi\)
0.0894855 + 0.995988i \(0.471478\pi\)
\(12\) 0 0
\(13\) 1.25729 + 2.17770i 0.348711 + 0.603985i 0.986021 0.166623i \(-0.0532862\pi\)
−0.637310 + 0.770608i \(0.719953\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.46050 + 2.52967i 0.354224 + 0.613535i 0.986985 0.160813i \(-0.0514116\pi\)
−0.632760 + 0.774348i \(0.718078\pi\)
\(18\) 0 0
\(19\) −2.69076 + 4.66053i −0.617302 + 1.06920i 0.372674 + 0.927962i \(0.378441\pi\)
−0.989976 + 0.141236i \(0.954892\pi\)
\(20\) −0.296790 + 0.514055i −0.0663642 + 0.114946i
\(21\) 0 0
\(22\) −0.296790 0.514055i −0.0632758 0.109597i
\(23\) −4.46050 −0.930080 −0.465040 0.885290i \(-0.653960\pi\)
−0.465040 + 0.885290i \(0.653960\pi\)
\(24\) 0 0
\(25\) −4.64766 −0.929533
\(26\) 1.25729 2.17770i 0.246576 0.427082i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.09718 5.36447i 0.575132 0.996157i −0.420896 0.907109i \(-0.638284\pi\)
0.996027 0.0890480i \(-0.0283825\pi\)
\(30\) 0 0
\(31\) −3.93346 + 6.81296i −0.706471 + 1.22364i 0.259687 + 0.965693i \(0.416380\pi\)
−0.966158 + 0.257951i \(0.916953\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 1.46050 2.52967i 0.250475 0.433835i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 5.38151 0.872997
\(39\) 0 0
\(40\) 0.593579 0.0938531
\(41\) −0.136673 0.236725i −0.0213448 0.0369702i 0.855156 0.518371i \(-0.173461\pi\)
−0.876500 + 0.481401i \(0.840128\pi\)
\(42\) 0 0
\(43\) −5.58113 + 9.66679i −0.851114 + 1.47417i 0.0290902 + 0.999577i \(0.490739\pi\)
−0.880204 + 0.474596i \(0.842594\pi\)
\(44\) −0.296790 + 0.514055i −0.0447427 + 0.0774967i
\(45\) 0 0
\(46\) 2.23025 + 3.86291i 0.328833 + 0.569555i
\(47\) −6.08113 10.5328i −0.887023 1.53637i −0.843377 0.537323i \(-0.819436\pi\)
−0.0436467 0.999047i \(-0.513898\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.32383 + 4.02499i 0.328639 + 0.569220i
\(51\) 0 0
\(52\) −2.51459 −0.348711
\(53\) −4.02704 6.97504i −0.553157 0.958096i −0.998044 0.0625092i \(-0.980090\pi\)
0.444888 0.895586i \(-0.353244\pi\)
\(54\) 0 0
\(55\) 0.352336 0.0475090
\(56\) 0 0
\(57\) 0 0
\(58\) −6.19436 −0.813359
\(59\) −4.32383 + 7.48910i −0.562915 + 0.974997i 0.434325 + 0.900756i \(0.356987\pi\)
−0.997240 + 0.0742412i \(0.976347\pi\)
\(60\) 0 0
\(61\) −3.32383 5.75705i −0.425573 0.737114i 0.570901 0.821019i \(-0.306594\pi\)
−0.996474 + 0.0839050i \(0.973261\pi\)
\(62\) 7.86693 0.999101
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.746304 + 1.29264i 0.0925676 + 0.160332i
\(66\) 0 0
\(67\) 0.956906 1.65741i 0.116905 0.202485i −0.801635 0.597814i \(-0.796036\pi\)
0.918540 + 0.395329i \(0.129369\pi\)
\(68\) −2.92101 −0.354224
\(69\) 0 0
\(70\) 0 0
\(71\) 14.4107 1.71023 0.855117 0.518435i \(-0.173485\pi\)
0.855117 + 0.518435i \(0.173485\pi\)
\(72\) 0 0
\(73\) −3.95691 6.85356i −0.463121 0.802149i 0.535994 0.844222i \(-0.319937\pi\)
−0.999115 + 0.0420732i \(0.986604\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) −2.69076 4.66053i −0.308651 0.534599i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.62422 + 8.00938i 0.520265 + 0.901126i 0.999722 + 0.0235607i \(0.00750031\pi\)
−0.479457 + 0.877565i \(0.659166\pi\)
\(80\) −0.296790 0.514055i −0.0331821 0.0574731i
\(81\) 0 0
\(82\) −0.136673 + 0.236725i −0.0150930 + 0.0261419i
\(83\) 3.85087 6.66991i 0.422688 0.732118i −0.573513 0.819196i \(-0.694420\pi\)
0.996201 + 0.0870787i \(0.0277532\pi\)
\(84\) 0 0
\(85\) 0.866926 + 1.50156i 0.0940313 + 0.162867i
\(86\) 11.1623 1.20366
\(87\) 0 0
\(88\) 0.593579 0.0632758
\(89\) −6.21780 + 10.7695i −0.659085 + 1.14157i 0.321767 + 0.946819i \(0.395723\pi\)
−0.980853 + 0.194751i \(0.937610\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.23025 3.86291i 0.232520 0.402736i
\(93\) 0 0
\(94\) −6.08113 + 10.5328i −0.627220 + 1.08638i
\(95\) −1.59718 + 2.76639i −0.163867 + 0.283826i
\(96\) 0 0
\(97\) −5.86693 + 10.1618i −0.595696 + 1.03178i 0.397752 + 0.917493i \(0.369790\pi\)
−0.993448 + 0.114283i \(0.963543\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.32383 4.02499i 0.232383 0.402499i
\(101\) −1.62276 −0.161470 −0.0807352 0.996736i \(-0.525727\pi\)
−0.0807352 + 0.996736i \(0.525727\pi\)
\(102\) 0 0
\(103\) −6.38151 −0.628789 −0.314395 0.949292i \(-0.601802\pi\)
−0.314395 + 0.949292i \(0.601802\pi\)
\(104\) 1.25729 + 2.17770i 0.123288 + 0.213541i
\(105\) 0 0
\(106\) −4.02704 + 6.97504i −0.391141 + 0.677476i
\(107\) −9.35447 + 16.2024i −0.904331 + 1.56635i −0.0825182 + 0.996590i \(0.526296\pi\)
−0.821813 + 0.569758i \(0.807037\pi\)
\(108\) 0 0
\(109\) −1.43346 2.48283i −0.137301 0.237812i 0.789173 0.614171i \(-0.210509\pi\)
−0.926474 + 0.376359i \(0.877176\pi\)
\(110\) −0.176168 0.305132i −0.0167970 0.0290932i
\(111\) 0 0
\(112\) 0 0
\(113\) 6.16012 + 10.6696i 0.579495 + 1.00371i 0.995537 + 0.0943695i \(0.0300835\pi\)
−0.416042 + 0.909345i \(0.636583\pi\)
\(114\) 0 0
\(115\) −2.64766 −0.246896
\(116\) 3.09718 + 5.36447i 0.287566 + 0.498078i
\(117\) 0 0
\(118\) 8.64766 0.796082
\(119\) 0 0
\(120\) 0 0
\(121\) −10.6477 −0.967969
\(122\) −3.32383 + 5.75705i −0.300926 + 0.521218i
\(123\) 0 0
\(124\) −3.93346 6.81296i −0.353235 0.611822i
\(125\) −5.72665 −0.512207
\(126\) 0 0
\(127\) 12.3346 1.09452 0.547261 0.836962i \(-0.315671\pi\)
0.547261 + 0.836962i \(0.315671\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0.746304 1.29264i 0.0654552 0.113372i
\(131\) −1.18716 −0.103723 −0.0518613 0.998654i \(-0.516515\pi\)
−0.0518613 + 0.998654i \(0.516515\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.91381 −0.165328
\(135\) 0 0
\(136\) 1.46050 + 2.52967i 0.125237 + 0.216917i
\(137\) −2.52179 −0.215451 −0.107725 0.994181i \(-0.534357\pi\)
−0.107725 + 0.994181i \(0.534357\pi\)
\(138\) 0 0
\(139\) −2.45691 4.25549i −0.208392 0.360946i 0.742816 0.669496i \(-0.233490\pi\)
−0.951208 + 0.308550i \(0.900156\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −7.20535 12.4800i −0.604659 1.04730i
\(143\) 0.746304 + 1.29264i 0.0624091 + 0.108096i
\(144\) 0 0
\(145\) 1.83842 3.18424i 0.152673 0.264437i
\(146\) −3.95691 + 6.85356i −0.327476 + 0.567205i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) −18.0512 −1.47881 −0.739404 0.673262i \(-0.764893\pi\)
−0.739404 + 0.673262i \(0.764893\pi\)
\(150\) 0 0
\(151\) 1.64766 0.134085 0.0670425 0.997750i \(-0.478644\pi\)
0.0670425 + 0.997750i \(0.478644\pi\)
\(152\) −2.69076 + 4.66053i −0.218249 + 0.378019i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.33482 + 4.04403i −0.187537 + 0.324824i
\(156\) 0 0
\(157\) −3.30039 + 5.71644i −0.263400 + 0.456222i −0.967143 0.254233i \(-0.918177\pi\)
0.703743 + 0.710454i \(0.251510\pi\)
\(158\) 4.62422 8.00938i 0.367883 0.637192i
\(159\) 0 0
\(160\) −0.296790 + 0.514055i −0.0234633 + 0.0406396i
\(161\) 0 0
\(162\) 0 0
\(163\) −2.99115 + 5.18082i −0.234285 + 0.405793i −0.959065 0.283188i \(-0.908608\pi\)
0.724780 + 0.688980i \(0.241941\pi\)
\(164\) 0.273346 0.0213448
\(165\) 0 0
\(166\) −7.70175 −0.597772
\(167\) 3.73025 + 6.46099i 0.288656 + 0.499966i 0.973489 0.228733i \(-0.0734584\pi\)
−0.684833 + 0.728700i \(0.740125\pi\)
\(168\) 0 0
\(169\) 3.33842 5.78231i 0.256802 0.444793i
\(170\) 0.866926 1.50156i 0.0664902 0.115164i
\(171\) 0 0
\(172\) −5.58113 9.66679i −0.425557 0.737086i
\(173\) 12.8296 + 22.2215i 0.975414 + 1.68947i 0.678562 + 0.734543i \(0.262603\pi\)
0.296851 + 0.954924i \(0.404063\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.296790 0.514055i −0.0223714 0.0387483i
\(177\) 0 0
\(178\) 12.4356 0.932088
\(179\) −7.51819 13.0219i −0.561936 0.973301i −0.997328 0.0730602i \(-0.976723\pi\)
0.435392 0.900241i \(-0.356610\pi\)
\(180\) 0 0
\(181\) 0.0861875 0.00640627 0.00320313 0.999995i \(-0.498980\pi\)
0.00320313 + 0.999995i \(0.498980\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.46050 −0.328833
\(185\) 0.296790 0.514055i 0.0218204 0.0377941i
\(186\) 0 0
\(187\) 0.866926 + 1.50156i 0.0633959 + 0.109805i
\(188\) 12.1623 0.887023
\(189\) 0 0
\(190\) 3.19436 0.231743
\(191\) 1.99115 + 3.44877i 0.144074 + 0.249544i 0.929027 0.370011i \(-0.120646\pi\)
−0.784953 + 0.619555i \(0.787313\pi\)
\(192\) 0 0
\(193\) −3.39037 + 5.87229i −0.244044 + 0.422697i −0.961862 0.273534i \(-0.911808\pi\)
0.717818 + 0.696230i \(0.245141\pi\)
\(194\) 11.7339 0.842441
\(195\) 0 0
\(196\) 0 0
\(197\) −11.0584 −0.787875 −0.393938 0.919137i \(-0.628887\pi\)
−0.393938 + 0.919137i \(0.628887\pi\)
\(198\) 0 0
\(199\) −2.80924 4.86575i −0.199142 0.344924i 0.749109 0.662447i \(-0.230482\pi\)
−0.948250 + 0.317523i \(0.897149\pi\)
\(200\) −4.64766 −0.328639
\(201\) 0 0
\(202\) 0.811379 + 1.40535i 0.0570884 + 0.0988800i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.0811263 0.140515i −0.00566611 0.00981399i
\(206\) 3.19076 + 5.52655i 0.222311 + 0.385053i
\(207\) 0 0
\(208\) 1.25729 2.17770i 0.0871777 0.150996i
\(209\) −1.59718 + 2.76639i −0.110479 + 0.191355i
\(210\) 0 0
\(211\) 9.66225 + 16.7355i 0.665177 + 1.15212i 0.979237 + 0.202717i \(0.0649772\pi\)
−0.314060 + 0.949403i \(0.601689\pi\)
\(212\) 8.05408 0.553157
\(213\) 0 0
\(214\) 18.7089 1.27892
\(215\) −3.31284 + 5.73801i −0.225934 + 0.391329i
\(216\) 0 0
\(217\) 0 0
\(218\) −1.43346 + 2.48283i −0.0970863 + 0.168158i
\(219\) 0 0
\(220\) −0.176168 + 0.305132i −0.0118773 + 0.0205720i
\(221\) −3.67257 + 6.36108i −0.247044 + 0.427892i
\(222\) 0 0
\(223\) −12.6623 + 21.9317i −0.847927 + 1.46865i 0.0351275 + 0.999383i \(0.488816\pi\)
−0.883055 + 0.469270i \(0.844517\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 6.16012 10.6696i 0.409765 0.709734i
\(227\) 4.81711 0.319723 0.159862 0.987139i \(-0.448895\pi\)
0.159862 + 0.987139i \(0.448895\pi\)
\(228\) 0 0
\(229\) 9.29533 0.614253 0.307126 0.951669i \(-0.400633\pi\)
0.307126 + 0.951669i \(0.400633\pi\)
\(230\) 1.32383 + 2.29294i 0.0872909 + 0.151192i
\(231\) 0 0
\(232\) 3.09718 5.36447i 0.203340 0.352195i
\(233\) −0.0971780 + 0.168317i −0.00636634 + 0.0110268i −0.869191 0.494476i \(-0.835360\pi\)
0.862825 + 0.505503i \(0.168693\pi\)
\(234\) 0 0
\(235\) −3.60963 6.25206i −0.235466 0.407840i
\(236\) −4.32383 7.48910i −0.281457 0.487499i
\(237\) 0 0
\(238\) 0 0
\(239\) 6.82743 + 11.8255i 0.441630 + 0.764925i 0.997811 0.0661361i \(-0.0210672\pi\)
−0.556181 + 0.831061i \(0.687734\pi\)
\(240\) 0 0
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) 5.32383 + 9.22115i 0.342229 + 0.592758i
\(243\) 0 0
\(244\) 6.64766 0.425573
\(245\) 0 0
\(246\) 0 0
\(247\) −13.5323 −0.861039
\(248\) −3.93346 + 6.81296i −0.249775 + 0.432623i
\(249\) 0 0
\(250\) 2.86333 + 4.95943i 0.181093 + 0.313662i
\(251\) −19.5438 −1.23359 −0.616796 0.787123i \(-0.711570\pi\)
−0.616796 + 0.787123i \(0.711570\pi\)
\(252\) 0 0
\(253\) −2.64766 −0.166457
\(254\) −6.16731 10.6821i −0.386972 0.670255i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.32743 0.519451 0.259725 0.965683i \(-0.416368\pi\)
0.259725 + 0.965683i \(0.416368\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.49261 −0.0925676
\(261\) 0 0
\(262\) 0.593579 + 1.02811i 0.0366715 + 0.0635168i
\(263\) 17.0905 1.05384 0.526921 0.849914i \(-0.323346\pi\)
0.526921 + 0.849914i \(0.323346\pi\)
\(264\) 0 0
\(265\) −2.39037 4.14024i −0.146839 0.254333i
\(266\) 0 0
\(267\) 0 0
\(268\) 0.956906 + 1.65741i 0.0584524 + 0.101242i
\(269\) −5.00720 8.67272i −0.305294 0.528785i 0.672033 0.740522i \(-0.265421\pi\)
−0.977327 + 0.211737i \(0.932088\pi\)
\(270\) 0 0
\(271\) −5.10457 + 8.84137i −0.310081 + 0.537075i −0.978380 0.206818i \(-0.933689\pi\)
0.668299 + 0.743893i \(0.267023\pi\)
\(272\) 1.46050 2.52967i 0.0885561 0.153384i
\(273\) 0 0
\(274\) 1.26089 + 2.18393i 0.0761733 + 0.131936i
\(275\) −2.75876 −0.166359
\(276\) 0 0
\(277\) 19.3422 1.16216 0.581081 0.813846i \(-0.302630\pi\)
0.581081 + 0.813846i \(0.302630\pi\)
\(278\) −2.45691 + 4.25549i −0.147355 + 0.255227i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.40136 11.0875i 0.381873 0.661424i −0.609457 0.792819i \(-0.708612\pi\)
0.991330 + 0.131396i \(0.0419458\pi\)
\(282\) 0 0
\(283\) −8.17617 + 14.1615i −0.486023 + 0.841816i −0.999871 0.0160650i \(-0.994886\pi\)
0.513848 + 0.857881i \(0.328219\pi\)
\(284\) −7.20535 + 12.4800i −0.427559 + 0.740553i
\(285\) 0 0
\(286\) 0.746304 1.29264i 0.0441299 0.0764352i
\(287\) 0 0
\(288\) 0 0
\(289\) 4.23385 7.33325i 0.249050 0.431367i
\(290\) −3.67684 −0.215912
\(291\) 0 0
\(292\) 7.91381 0.463121
\(293\) −10.3889 17.9941i −0.606926 1.05123i −0.991744 0.128235i \(-0.959069\pi\)
0.384817 0.922993i \(-0.374264\pi\)
\(294\) 0 0
\(295\) −2.56654 + 4.44537i −0.149430 + 0.258820i
\(296\) 0.500000 0.866025i 0.0290619 0.0503367i
\(297\) 0 0
\(298\) 9.02558 + 15.6328i 0.522838 + 0.905582i
\(299\) −5.60817 9.71363i −0.324329 0.561754i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.823832 1.42692i −0.0474062 0.0821099i
\(303\) 0 0
\(304\) 5.38151 0.308651
\(305\) −1.97296 3.41726i −0.112971 0.195672i
\(306\) 0 0
\(307\) 22.6768 1.29424 0.647118 0.762390i \(-0.275974\pi\)
0.647118 + 0.762390i \(0.275974\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.66964 0.265218
\(311\) 3.25729 5.64180i 0.184704 0.319917i −0.758773 0.651356i \(-0.774201\pi\)
0.943477 + 0.331439i \(0.107534\pi\)
\(312\) 0 0
\(313\) 0.133074 + 0.230492i 0.00752181 + 0.0130282i 0.869762 0.493472i \(-0.164272\pi\)
−0.862240 + 0.506500i \(0.830939\pi\)
\(314\) 6.60078 0.372503
\(315\) 0 0
\(316\) −9.24844 −0.520265
\(317\) 7.86186 + 13.6171i 0.441566 + 0.764815i 0.997806 0.0662067i \(-0.0210897\pi\)
−0.556240 + 0.831022i \(0.687756\pi\)
\(318\) 0 0
\(319\) 1.83842 3.18424i 0.102932 0.178283i
\(320\) 0.593579 0.0331821
\(321\) 0 0
\(322\) 0 0
\(323\) −15.7195 −0.874654
\(324\) 0 0
\(325\) −5.84348 10.1212i −0.324138 0.561424i
\(326\) 5.98229 0.331328
\(327\) 0 0
\(328\) −0.136673 0.236725i −0.00754651 0.0130709i
\(329\) 0 0
\(330\) 0 0
\(331\) 12.5811 + 21.7912i 0.691521 + 1.19775i 0.971339 + 0.237697i \(0.0763925\pi\)
−0.279818 + 0.960053i \(0.590274\pi\)
\(332\) 3.85087 + 6.66991i 0.211344 + 0.366059i
\(333\) 0 0
\(334\) 3.73025 6.46099i 0.204110 0.353529i
\(335\) 0.568000 0.983804i 0.0310331 0.0537510i
\(336\) 0 0
\(337\) −9.36693 16.2240i −0.510249 0.883777i −0.999929 0.0118752i \(-0.996220\pi\)
0.489681 0.871902i \(-0.337113\pi\)
\(338\) −6.67684 −0.363172
\(339\) 0 0
\(340\) −1.73385 −0.0940313
\(341\) −2.33482 + 4.04403i −0.126438 + 0.218997i
\(342\) 0 0
\(343\) 0 0
\(344\) −5.58113 + 9.66679i −0.300914 + 0.521199i
\(345\) 0 0
\(346\) 12.8296 22.2215i 0.689722 1.19463i
\(347\) 11.2719 19.5235i 0.605106 1.04808i −0.386928 0.922110i \(-0.626464\pi\)
0.992035 0.125965i \(-0.0402028\pi\)
\(348\) 0 0
\(349\) −1.89543 + 3.28298i −0.101460 + 0.175734i −0.912286 0.409553i \(-0.865685\pi\)
0.810826 + 0.585287i \(0.199018\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.296790 + 0.514055i −0.0158189 + 0.0273992i
\(353\) 6.83482 0.363781 0.181890 0.983319i \(-0.441778\pi\)
0.181890 + 0.983319i \(0.441778\pi\)
\(354\) 0 0
\(355\) 8.55389 0.453993
\(356\) −6.21780 10.7695i −0.329543 0.570785i
\(357\) 0 0
\(358\) −7.51819 + 13.0219i −0.397349 + 0.688228i
\(359\) 6.32237 10.9507i 0.333682 0.577954i −0.649549 0.760320i \(-0.725042\pi\)
0.983231 + 0.182366i \(0.0583755\pi\)
\(360\) 0 0
\(361\) −4.98035 8.62622i −0.262124 0.454012i
\(362\) −0.0430937 0.0746406i −0.00226496 0.00392302i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.34874 4.06813i −0.122939 0.212936i
\(366\) 0 0
\(367\) −6.54377 −0.341582 −0.170791 0.985307i \(-0.554632\pi\)
−0.170791 + 0.985307i \(0.554632\pi\)
\(368\) 2.23025 + 3.86291i 0.116260 + 0.201368i
\(369\) 0 0
\(370\) −0.593579 −0.0308587
\(371\) 0 0
\(372\) 0 0
\(373\) 9.42840 0.488184 0.244092 0.969752i \(-0.421510\pi\)
0.244092 + 0.969752i \(0.421510\pi\)
\(374\) 0.866926 1.50156i 0.0448277 0.0776438i
\(375\) 0 0
\(376\) −6.08113 10.5328i −0.313610 0.543189i
\(377\) 15.5763 0.802218
\(378\) 0 0
\(379\) −7.27762 −0.373826 −0.186913 0.982376i \(-0.559848\pi\)
−0.186913 + 0.982376i \(0.559848\pi\)
\(380\) −1.59718 2.76639i −0.0819335 0.141913i
\(381\) 0 0
\(382\) 1.99115 3.44877i 0.101876 0.176454i
\(383\) −24.0833 −1.23060 −0.615299 0.788294i \(-0.710965\pi\)
−0.615299 + 0.788294i \(0.710965\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.78074 0.345130
\(387\) 0 0
\(388\) −5.86693 10.1618i −0.297848 0.515888i
\(389\) 16.2983 0.826354 0.413177 0.910651i \(-0.364419\pi\)
0.413177 + 0.910651i \(0.364419\pi\)
\(390\) 0 0
\(391\) −6.51459 11.2836i −0.329457 0.570636i
\(392\) 0 0
\(393\) 0 0
\(394\) 5.52918 + 9.57682i 0.278556 + 0.482473i
\(395\) 2.74484 + 4.75420i 0.138108 + 0.239210i
\(396\) 0 0
\(397\) 6.08619 10.5416i 0.305457 0.529067i −0.671906 0.740636i \(-0.734524\pi\)
0.977363 + 0.211569i \(0.0678574\pi\)
\(398\) −2.80924 + 4.86575i −0.140815 + 0.243898i
\(399\) 0 0
\(400\) 2.32383 + 4.02499i 0.116192 + 0.201250i
\(401\) 33.3609 1.66596 0.832981 0.553301i \(-0.186632\pi\)
0.832981 + 0.553301i \(0.186632\pi\)
\(402\) 0 0
\(403\) −19.7821 −0.985416
\(404\) 0.811379 1.40535i 0.0403676 0.0699187i
\(405\) 0 0
\(406\) 0 0
\(407\) 0.296790 0.514055i 0.0147113 0.0254808i
\(408\) 0 0
\(409\) −2.89037 + 5.00627i −0.142920 + 0.247544i −0.928595 0.371095i \(-0.878982\pi\)
0.785675 + 0.618639i \(0.212316\pi\)
\(410\) −0.0811263 + 0.140515i −0.00400654 + 0.00693954i
\(411\) 0 0
\(412\) 3.19076 5.52655i 0.157197 0.272274i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.28580 3.95912i 0.112205 0.194346i
\(416\) −2.51459 −0.123288
\(417\) 0 0
\(418\) 3.19436 0.156241
\(419\) 15.4356 + 26.7352i 0.754078 + 1.30610i 0.945831 + 0.324659i \(0.105249\pi\)
−0.191753 + 0.981443i \(0.561417\pi\)
\(420\) 0 0
\(421\) −1.86693 + 3.23361i −0.0909884 + 0.157597i −0.907927 0.419128i \(-0.862336\pi\)
0.816939 + 0.576724i \(0.195669\pi\)
\(422\) 9.66225 16.7355i 0.470351 0.814672i
\(423\) 0 0
\(424\) −4.02704 6.97504i −0.195570 0.338738i
\(425\) −6.78794 11.7570i −0.329263 0.570301i
\(426\) 0 0
\(427\) 0 0
\(428\) −9.35447 16.2024i −0.452165 0.783174i
\(429\) 0 0
\(430\) 6.62568 0.319519
\(431\) 14.0979 + 24.4182i 0.679070 + 1.17618i 0.975261 + 0.221055i \(0.0709499\pi\)
−0.296192 + 0.955128i \(0.595717\pi\)
\(432\) 0 0
\(433\) −12.5438 −0.602815 −0.301407 0.953495i \(-0.597456\pi\)
−0.301407 + 0.953495i \(0.597456\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.86693 0.137301
\(437\) 12.0021 20.7883i 0.574140 0.994440i
\(438\) 0 0
\(439\) 13.0203 + 22.5519i 0.621426 + 1.07634i 0.989220 + 0.146434i \(0.0467797\pi\)
−0.367794 + 0.929907i \(0.619887\pi\)
\(440\) 0.352336 0.0167970
\(441\) 0 0
\(442\) 7.34514 0.349373
\(443\) −11.7865 20.4148i −0.559992 0.969935i −0.997496 0.0707186i \(-0.977471\pi\)
0.437504 0.899216i \(-0.355863\pi\)
\(444\) 0 0
\(445\) −3.69076 + 6.39258i −0.174959 + 0.303037i
\(446\) 25.3245 1.19915
\(447\) 0 0
\(448\) 0 0
\(449\) −13.6870 −0.645928 −0.322964 0.946411i \(-0.604679\pi\)
−0.322964 + 0.946411i \(0.604679\pi\)
\(450\) 0 0
\(451\) −0.0811263 0.140515i −0.00382009 0.00661659i
\(452\) −12.3202 −0.579495
\(453\) 0 0
\(454\) −2.40856 4.17174i −0.113039 0.195790i
\(455\) 0 0
\(456\) 0 0
\(457\) 11.1762 + 19.3577i 0.522799 + 0.905515i 0.999648 + 0.0265293i \(0.00844554\pi\)
−0.476849 + 0.878985i \(0.658221\pi\)
\(458\) −4.64766 8.04999i −0.217171 0.376151i
\(459\) 0 0
\(460\) 1.32383 2.29294i 0.0617240 0.106909i
\(461\) −3.98755 + 6.90663i −0.185719 + 0.321674i −0.943818 0.330464i \(-0.892795\pi\)
0.758100 + 0.652138i \(0.226128\pi\)
\(462\) 0 0
\(463\) −14.3676 24.8854i −0.667719 1.15652i −0.978540 0.206055i \(-0.933937\pi\)
0.310821 0.950468i \(-0.399396\pi\)
\(464\) −6.19436 −0.287566
\(465\) 0 0
\(466\) 0.194356 0.00900336
\(467\) 16.7829 29.0688i 0.776619 1.34514i −0.157261 0.987557i \(-0.550267\pi\)
0.933880 0.357586i \(-0.116400\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −3.60963 + 6.25206i −0.166500 + 0.288386i
\(471\) 0 0
\(472\) −4.32383 + 7.48910i −0.199020 + 0.344714i
\(473\) −3.31284 + 5.73801i −0.152325 + 0.263834i
\(474\) 0 0
\(475\) 12.5057 21.6606i 0.573802 0.993855i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.82743 11.8255i 0.312279 0.540884i
\(479\) 0.367120 0.0167741 0.00838707 0.999965i \(-0.497330\pi\)
0.00838707 + 0.999965i \(0.497330\pi\)
\(480\) 0 0
\(481\) 2.51459 0.114655
\(482\) −6.50000 11.2583i −0.296067 0.512803i
\(483\) 0 0
\(484\) 5.32383 9.22115i 0.241992 0.419143i
\(485\) −3.48249 + 6.03184i −0.158132 + 0.273892i
\(486\) 0 0
\(487\) −14.9538 25.9007i −0.677621 1.17367i −0.975695 0.219131i \(-0.929678\pi\)
0.298075 0.954543i \(-0.403656\pi\)
\(488\) −3.32383 5.75705i −0.150463 0.260609i
\(489\) 0 0
\(490\) 0 0
\(491\) 0.255158 + 0.441947i 0.0115151 + 0.0199448i 0.871726 0.489994i \(-0.163001\pi\)
−0.860210 + 0.509939i \(0.829668\pi\)
\(492\) 0 0
\(493\) 18.0938 0.814903
\(494\) 6.76615 + 11.7193i 0.304423 + 0.527277i
\(495\) 0 0
\(496\) 7.86693 0.353235
\(497\) 0 0
\(498\) 0 0
\(499\) −19.0191 −0.851410 −0.425705 0.904862i \(-0.639974\pi\)
−0.425705 + 0.904862i \(0.639974\pi\)
\(500\) 2.86333 4.95943i 0.128052 0.221792i
\(501\) 0 0
\(502\) 9.77188 + 16.9254i 0.436141 + 0.755418i
\(503\) −37.7807 −1.68456 −0.842280 0.539040i \(-0.818787\pi\)
−0.842280 + 0.539040i \(0.818787\pi\)
\(504\) 0 0
\(505\) −0.963235 −0.0428634
\(506\) 1.32383 + 2.29294i 0.0588515 + 0.101934i
\(507\) 0 0
\(508\) −6.16731 + 10.6821i −0.273630 + 0.473942i
\(509\) −11.2163 −0.497155 −0.248578 0.968612i \(-0.579963\pi\)
−0.248578 + 0.968612i \(0.579963\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −4.16372 7.21177i −0.183654 0.318097i
\(515\) −3.78794 −0.166916
\(516\) 0 0
\(517\) −3.60963 6.25206i −0.158751 0.274965i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.746304 + 1.29264i 0.0327276 + 0.0566859i
\(521\) −13.7360 23.7914i −0.601785 1.04232i −0.992551 0.121831i \(-0.961123\pi\)
0.390766 0.920490i \(-0.372210\pi\)
\(522\) 0 0
\(523\) −11.0919 + 19.2118i −0.485016 + 0.840072i −0.999852 0.0172166i \(-0.994520\pi\)
0.514836 + 0.857289i \(0.327853\pi\)
\(524\) 0.593579 1.02811i 0.0259306 0.0449132i
\(525\) 0 0
\(526\) −8.54523 14.8008i −0.372590 0.645344i
\(527\) −22.9794 −1.00100
\(528\) 0 0
\(529\) −3.10390 −0.134952
\(530\) −2.39037 + 4.14024i −0.103831 + 0.179841i
\(531\) 0 0
\(532\) 0 0
\(533\) 0.343677 0.595265i 0.0148863 0.0257838i
\(534\) 0 0
\(535\) −5.55262 + 9.61742i −0.240061 + 0.415797i
\(536\) 0.956906 1.65741i 0.0413321 0.0715892i
\(537\) 0 0
\(538\) −5.00720 + 8.67272i −0.215876 + 0.373908i
\(539\) 0 0
\(540\) 0 0
\(541\) 14.9246 25.8502i 0.641659 1.11139i −0.343403 0.939188i \(-0.611580\pi\)
0.985062 0.172198i \(-0.0550869\pi\)
\(542\) 10.2091 0.438520
\(543\) 0 0
\(544\) −2.92101 −0.125237
\(545\) −0.850874 1.47376i −0.0364474 0.0631288i
\(546\) 0 0
\(547\) 8.84348 15.3174i 0.378120 0.654923i −0.612669 0.790340i \(-0.709904\pi\)
0.990789 + 0.135417i \(0.0432373\pi\)
\(548\) 1.26089 2.18393i 0.0538627 0.0932929i
\(549\) 0 0
\(550\) 1.37938 + 2.38915i 0.0588169 + 0.101874i
\(551\) 16.6675 + 28.8690i 0.710060 + 1.22986i
\(552\) 0 0
\(553\) 0 0
\(554\) −9.67111 16.7508i −0.410886 0.711675i
\(555\) 0 0
\(556\) 4.91381 0.208392
\(557\) −15.0651 26.0935i −0.638328 1.10562i −0.985800 0.167926i \(-0.946293\pi\)
0.347472 0.937690i \(-0.387040\pi\)
\(558\) 0 0
\(559\) −28.0685 −1.18717
\(560\) 0 0
\(561\) 0 0
\(562\) −12.8027 −0.540050
\(563\) −2.04883 + 3.54867i −0.0863478 + 0.149559i −0.905965 0.423353i \(-0.860853\pi\)
0.819617 + 0.572912i \(0.194186\pi\)
\(564\) 0 0
\(565\) 3.65652 + 6.33327i 0.153831 + 0.266443i
\(566\) 16.3523 0.687340
\(567\) 0 0
\(568\) 14.4107 0.604659
\(569\) 3.11849 + 5.40138i 0.130734 + 0.226437i 0.923960 0.382490i \(-0.124933\pi\)
−0.793226 + 0.608927i \(0.791600\pi\)
\(570\) 0 0
\(571\) −17.8011 + 30.8323i −0.744951 + 1.29029i 0.205266 + 0.978706i \(0.434194\pi\)
−0.950218 + 0.311587i \(0.899139\pi\)
\(572\) −1.49261 −0.0624091
\(573\) 0 0
\(574\) 0 0
\(575\) 20.7309 0.864539
\(576\) 0 0
\(577\) −23.1388 40.0776i −0.963281 1.66845i −0.714164 0.699979i \(-0.753193\pi\)
−0.249118 0.968473i \(-0.580141\pi\)
\(578\) −8.46770 −0.352210
\(579\) 0 0
\(580\) 1.83842 + 3.18424i 0.0763363 + 0.132218i
\(581\) 0 0
\(582\) 0 0
\(583\) −2.39037 4.14024i −0.0989990 0.171471i
\(584\) −3.95691 6.85356i −0.163738 0.283602i
\(585\) 0 0
\(586\) −10.3889 + 17.9941i −0.429162 + 0.743330i
\(587\) 1.13161 1.96001i 0.0467066 0.0808982i −0.841727 0.539903i \(-0.818461\pi\)
0.888434 + 0.459005i \(0.151794\pi\)
\(588\) 0 0
\(589\) −21.1680 36.6640i −0.872212 1.51072i
\(590\) 5.13307 0.211325
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) 23.0979 40.0067i 0.948515 1.64288i 0.199960 0.979804i \(-0.435919\pi\)
0.748555 0.663072i \(-0.230748\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.02558 15.6328i 0.369702 0.640343i
\(597\) 0 0
\(598\) −5.60817 + 9.71363i −0.229335 + 0.397220i
\(599\) −8.39037 + 14.5325i −0.342821 + 0.593784i −0.984955 0.172808i \(-0.944716\pi\)
0.642134 + 0.766592i \(0.278049\pi\)
\(600\) 0 0
\(601\) 5.69961 9.87202i 0.232492 0.402688i −0.726049 0.687643i \(-0.758645\pi\)
0.958541 + 0.284955i \(0.0919787\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.823832 + 1.42692i −0.0335212 + 0.0580605i
\(605\) −6.32023 −0.256954
\(606\) 0 0
\(607\) 14.4284 0.585631 0.292815 0.956169i \(-0.405408\pi\)
0.292815 + 0.956169i \(0.405408\pi\)
\(608\) −2.69076 4.66053i −0.109125 0.189009i
\(609\) 0 0
\(610\) −1.97296 + 3.41726i −0.0798827 + 0.138361i
\(611\) 15.2915 26.4857i 0.618629 1.07150i
\(612\) 0 0
\(613\) 12.2053 + 21.1403i 0.492969 + 0.853848i 0.999967 0.00809942i \(-0.00257815\pi\)
−0.506998 + 0.861947i \(0.669245\pi\)
\(614\) −11.3384 19.6387i −0.457581 0.792554i
\(615\) 0 0
\(616\) 0 0
\(617\) −24.4698 42.3830i −0.985119 1.70628i −0.641408 0.767200i \(-0.721650\pi\)
−0.343710 0.939076i \(-0.611684\pi\)
\(618\) 0 0
\(619\) 44.6591 1.79500 0.897501 0.441012i \(-0.145380\pi\)
0.897501 + 0.441012i \(0.145380\pi\)
\(620\) −2.33482 4.04403i −0.0937687 0.162412i
\(621\) 0 0
\(622\) −6.51459 −0.261211
\(623\) 0 0
\(624\) 0 0
\(625\) 19.8391 0.793564
\(626\) 0.133074 0.230492i 0.00531873 0.00921230i
\(627\) 0 0
\(628\) −3.30039 5.71644i −0.131700 0.228111i
\(629\) 2.92101 0.116468
\(630\) 0 0
\(631\) 33.2852 1.32506 0.662532 0.749034i \(-0.269482\pi\)
0.662532 + 0.749034i \(0.269482\pi\)
\(632\) 4.62422 + 8.00938i 0.183942 + 0.318596i
\(633\) 0 0
\(634\) 7.86186 13.6171i 0.312235 0.540806i
\(635\) 7.32158 0.290548
\(636\) 0 0
\(637\) 0 0
\(638\) −3.67684 −0.145568
\(639\) 0 0
\(640\) −0.296790 0.514055i −0.0117316 0.0203198i
\(641\) −30.7879 −1.21605 −0.608025 0.793918i \(-0.708038\pi\)
−0.608025 + 0.793918i \(0.708038\pi\)
\(642\) 0 0
\(643\) 13.7345 + 23.7889i 0.541637 + 0.938142i 0.998810 + 0.0487649i \(0.0155285\pi\)
−0.457174 + 0.889378i \(0.651138\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 7.85973 + 13.6134i 0.309237 + 0.535614i
\(647\) −6.63521 11.4925i −0.260857 0.451818i 0.705613 0.708598i \(-0.250672\pi\)
−0.966470 + 0.256780i \(0.917338\pi\)
\(648\) 0 0
\(649\) −2.56654 + 4.44537i −0.100745 + 0.174496i
\(650\) −5.84348 + 10.1212i −0.229200 + 0.396986i
\(651\) 0 0
\(652\) −2.99115 5.18082i −0.117142 0.202896i
\(653\) 17.1416 0.670803 0.335402 0.942075i \(-0.391128\pi\)
0.335402 + 0.942075i \(0.391128\pi\)
\(654\) 0 0
\(655\) −0.704673 −0.0275338
\(656\) −0.136673 + 0.236725i −0.00533619 + 0.00924255i
\(657\) 0 0
\(658\) 0 0
\(659\) −4.26089 + 7.38008i −0.165981 + 0.287487i −0.937003 0.349321i \(-0.886412\pi\)
0.771022 + 0.636808i \(0.219746\pi\)
\(660\) 0 0
\(661\) 17.1680 29.7358i 0.667757 1.15659i −0.310773 0.950484i \(-0.600588\pi\)
0.978530 0.206105i \(-0.0660789\pi\)
\(662\) 12.5811 21.7912i 0.488979 0.846937i
\(663\) 0 0
\(664\) 3.85087 6.66991i 0.149443 0.258843i
\(665\) 0 0
\(666\) 0 0
\(667\) −13.8150 + 23.9282i −0.534918 + 0.926505i
\(668\) −7.46050 −0.288656
\(669\) 0 0
\(670\) −1.13600 −0.0438875
\(671\) −1.97296 3.41726i −0.0761652 0.131922i
\(672\) 0 0
\(673\) −7.70155 + 13.3395i −0.296873 + 0.514199i −0.975419 0.220359i \(-0.929277\pi\)
0.678546 + 0.734558i \(0.262610\pi\)
\(674\) −9.36693 + 16.2240i −0.360800 + 0.624925i
\(675\) 0 0
\(676\) 3.33842 + 5.78231i 0.128401 + 0.222397i
\(677\) 3.69076 + 6.39258i 0.141847 + 0.245687i 0.928192 0.372101i \(-0.121362\pi\)
−0.786345 + 0.617788i \(0.788029\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.866926 + 1.50156i 0.0332451 + 0.0575822i
\(681\) 0 0
\(682\) 4.66964 0.178810
\(683\) −4.79893 8.31198i −0.183626 0.318049i 0.759487 0.650523i \(-0.225450\pi\)
−0.943113 + 0.332474i \(0.892117\pi\)
\(684\) 0 0
\(685\) −1.49688 −0.0571929
\(686\) 0 0
\(687\) 0 0
\(688\) 11.1623 0.425557
\(689\) 10.1264 17.5394i 0.385783 0.668197i
\(690\) 0 0
\(691\) −7.07227 12.2495i −0.269042 0.465994i 0.699573 0.714561i \(-0.253374\pi\)
−0.968615 + 0.248567i \(0.920040\pi\)
\(692\) −25.6591 −0.975414
\(693\) 0 0
\(694\) −22.5438 −0.855750
\(695\) −1.45837 2.52597i −0.0553191 0.0958155i
\(696\) 0 0
\(697\) 0.399223 0.691475i 0.0151217 0.0261915i
\(698\) 3.79086 0.143486
\(699\) 0 0
\(700\) 0 0
\(701\) −37.3753 −1.41164 −0.705822 0.708389i \(-0.749422\pi\)
−0.705822 + 0.708389i \(0.749422\pi\)
\(702\) 0 0
\(703\) 2.69076 + 4.66053i 0.101484 + 0.175775i
\(704\) 0.593579 0.0223714
\(705\) 0 0
\(706\) −3.41741 5.91913i −0.128616 0.222769i
\(707\) 0 0
\(708\) 0 0
\(709\) 5.24338 + 9.08180i 0.196919 + 0.341074i 0.947528 0.319673i \(-0.103573\pi\)
−0.750609 + 0.660747i \(0.770240\pi\)
\(710\) −4.27694 7.40789i −0.160511 0.278013i
\(711\) 0 0
\(712\) −6.21780 + 10.7695i −0.233022 + 0.403606i
\(713\) 17.5452 30.3892i 0.657074 1.13809i
\(714\) 0 0
\(715\) 0.442991 + 0.767282i 0.0165669 + 0.0286947i
\(716\) 15.0364 0.561936
\(717\) 0 0
\(718\) −12.6447 −0.471897
\(719\) 1.11995 1.93981i 0.0417670 0.0723426i −0.844386 0.535735i \(-0.820035\pi\)
0.886153 + 0.463392i \(0.153368\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −4.98035 + 8.62622i −0.185349 + 0.321035i
\(723\) 0 0
\(724\) −0.0430937 + 0.0746406i −0.00160157 + 0.00277399i
\(725\) −14.3946 + 24.9322i −0.534604 + 0.925961i
\(726\) 0 0
\(727\) −0.185023 + 0.320469i −0.00686211 + 0.0118855i −0.869436 0.494045i \(-0.835518\pi\)
0.862574 + 0.505931i \(0.168851\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2.34874 + 4.06813i −0.0869307 + 0.150568i
\(731\) −32.6050 −1.20594
\(732\) 0 0
\(733\) −14.0191 −0.517806 −0.258903 0.965903i \(-0.583361\pi\)
−0.258903 + 0.965903i \(0.583361\pi\)
\(734\) 3.27188 + 5.66707i 0.120767 + 0.209175i
\(735\) 0 0
\(736\) 2.23025 3.86291i 0.0822082 0.142389i
\(737\) 0.568000 0.983804i 0.0209225 0.0362389i
\(738\) 0 0
\(739\) 13.3872 + 23.1874i 0.492458 + 0.852962i 0.999962 0.00868705i \(-0.00276521\pi\)
−0.507504 + 0.861649i \(0.669432\pi\)
\(740\) 0.296790 + 0.514055i 0.0109102 + 0.0188970i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.04669 + 8.74113i 0.185145 + 0.320681i 0.943625 0.331015i \(-0.107391\pi\)
−0.758480 + 0.651696i \(0.774058\pi\)
\(744\) 0 0
\(745\) −10.7148 −0.392560
\(746\) −4.71420 8.16524i −0.172599 0.298951i
\(747\) 0 0
\(748\) −1.73385 −0.0633959
\(749\) 0 0
\(750\) 0 0
\(751\) 11.5146 0.420173 0.210087 0.977683i \(-0.432625\pi\)
0.210087 + 0.977683i \(0.432625\pi\)
\(752\) −6.08113 + 10.5328i −0.221756 + 0.384092i
\(753\) 0 0
\(754\) −7.78813 13.4894i −0.283627 0.491256i
\(755\) 0.978019 0.0355938
\(756\) 0 0
\(757\) −15.2484 −0.554214 −0.277107 0.960839i \(-0.589376\pi\)
−0.277107 + 0.960839i \(0.589376\pi\)
\(758\) 3.63881 + 6.30260i 0.132168 + 0.228921i
\(759\) 0 0
\(760\) −1.59718 + 2.76639i −0.0579357 + 0.100348i
\(761\) −1.70175 −0.0616883 −0.0308442 0.999524i \(-0.509820\pi\)
−0.0308442 + 0.999524i \(0.509820\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.98229 −0.144074
\(765\) 0 0
\(766\) 12.0416 + 20.8567i 0.435082 + 0.753584i
\(767\) −21.7453 −0.785178
\(768\) 0 0
\(769\) −24.1211 41.7790i −0.869829 1.50659i −0.862171 0.506618i \(-0.830896\pi\)
−0.00765823 0.999971i \(-0.502438\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.39037 5.87229i −0.122022 0.211348i
\(773\) 3.10243 + 5.37357i 0.111587 + 0.193274i 0.916410 0.400240i \(-0.131073\pi\)
−0.804823 + 0.593514i \(0.797740\pi\)
\(774\) 0 0
\(775\) 18.2814 31.6643i 0.656688 1.13742i
\(776\) −5.86693 + 10.1618i −0.210610 + 0.364788i
\(777\) 0 0
\(778\) −8.14913 14.1147i −0.292160 0.506037i
\(779\) 1.47102 0.0527046
\(780\) 0 0
\(781\) 8.55389 0.306082
\(782\) −6.51459 + 11.2836i −0.232961 + 0.403501i
\(783\) 0 0
\(784\) 0 0
\(785\) −1.95904 + 3.39316i −0.0699212 + 0.121107i
\(786\) 0 0
\(787\) 3.04883 5.28073i 0.108679 0.188238i −0.806556 0.591157i \(-0.798671\pi\)
0.915235 + 0.402920i \(0.132005\pi\)
\(788\) 5.52918 9.57682i 0.196969 0.341160i
\(789\) 0 0
\(790\) 2.74484 4.75420i 0.0976571 0.169147i
\(791\) 0 0
\(792\) 0 0
\(793\) 8.35807 14.4766i 0.296804 0.514079i
\(794\) −12.1724 −0.431981