Properties

Label 3150.2.bp.e.899.1
Level 3150
Weight 2
Character 3150.899
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bp (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 899.1
Root \(0.258819 + 0.965926i\)
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.e.1349.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.09077 + 1.62132i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.09077 + 1.62132i) q^{7} -1.00000 q^{8} +(2.59808 + 1.50000i) q^{11} +2.44949 q^{13} +(-2.44949 - 1.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.878680 - 0.507306i) q^{17} +(0.878680 - 0.507306i) q^{19} +3.00000i q^{22} +(2.12132 + 3.67423i) q^{23} +(1.22474 + 2.12132i) q^{26} +(-0.358719 - 2.62132i) q^{28} -1.24264i q^{29} +(4.86396 + 2.80821i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.01461i q^{34} +(-7.13834 + 4.12132i) q^{37} +(0.878680 + 0.507306i) q^{38} -2.02922 q^{41} +8.24264i q^{43} +(-2.59808 + 1.50000i) q^{44} +(-2.12132 + 3.67423i) q^{46} +(0.878680 - 0.507306i) q^{47} +(1.74264 - 6.77962i) q^{49} +(-1.22474 + 2.12132i) q^{52} +(0.621320 - 1.07616i) q^{53} +(2.09077 - 1.62132i) q^{56} +(1.07616 - 0.621320i) q^{58} +(-5.76500 + 9.98528i) q^{59} +(5.12132 - 2.95680i) q^{61} +5.61642i q^{62} +1.00000 q^{64} +(-8.66025 - 5.00000i) q^{67} +(0.878680 - 0.507306i) q^{68} +10.2426i q^{71} +(-4.18154 + 7.24264i) q^{73} +(-7.13834 - 4.12132i) q^{74} +1.01461i q^{76} +(-7.86396 + 1.07616i) q^{77} +(-5.62132 - 9.73641i) q^{79} +(-1.01461 - 1.75736i) q^{82} +3.16693i q^{83} +(-7.13834 + 4.12132i) q^{86} +(-2.59808 - 1.50000i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-5.12132 + 3.97141i) q^{91} -4.24264 q^{92} +(0.878680 + 0.507306i) q^{94} -3.76127 q^{97} +(6.74264 - 1.88064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} + O(q^{10}) \) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} - 4q^{16} - 24q^{17} + 24q^{19} - 12q^{31} + 4q^{32} + 24q^{38} + 24q^{47} - 20q^{49} - 12q^{53} + 24q^{61} + 8q^{64} + 24q^{68} - 12q^{77} - 28q^{79} - 24q^{91} + 24q^{94} + 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.09077 + 1.62132i −0.790237 + 0.612801i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 2.59808 + 1.50000i 0.783349 + 0.452267i 0.837616 0.546259i \(-0.183949\pi\)
−0.0542666 + 0.998526i \(0.517282\pi\)
\(12\) 0 0
\(13\) 2.44949 0.679366 0.339683 0.940540i \(-0.389680\pi\)
0.339683 + 0.940540i \(0.389680\pi\)
\(14\) −2.44949 1.00000i −0.654654 0.267261i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.878680 0.507306i −0.213111 0.123040i 0.389645 0.920965i \(-0.372598\pi\)
−0.602756 + 0.797925i \(0.705931\pi\)
\(18\) 0 0
\(19\) 0.878680 0.507306i 0.201583 0.116384i −0.395811 0.918332i \(-0.629536\pi\)
0.597394 + 0.801948i \(0.296203\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000i 0.639602i
\(23\) 2.12132 + 3.67423i 0.442326 + 0.766131i 0.997862 0.0653618i \(-0.0208201\pi\)
−0.555536 + 0.831493i \(0.687487\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.22474 + 2.12132i 0.240192 + 0.416025i
\(27\) 0 0
\(28\) −0.358719 2.62132i −0.0677916 0.495383i
\(29\) 1.24264i 0.230753i −0.993322 0.115376i \(-0.963193\pi\)
0.993322 0.115376i \(-0.0368074\pi\)
\(30\) 0 0
\(31\) 4.86396 + 2.80821i 0.873593 + 0.504369i 0.868541 0.495618i \(-0.165058\pi\)
0.00505256 + 0.999987i \(0.498392\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.01461i 0.174005i
\(35\) 0 0
\(36\) 0 0
\(37\) −7.13834 + 4.12132i −1.17354 + 0.677541i −0.954510 0.298178i \(-0.903621\pi\)
−0.219025 + 0.975719i \(0.570288\pi\)
\(38\) 0.878680 + 0.507306i 0.142541 + 0.0822959i
\(39\) 0 0
\(40\) 0 0
\(41\) −2.02922 −0.316912 −0.158456 0.987366i \(-0.550652\pi\)
−0.158456 + 0.987366i \(0.550652\pi\)
\(42\) 0 0
\(43\) 8.24264i 1.25699i 0.777813 + 0.628495i \(0.216329\pi\)
−0.777813 + 0.628495i \(0.783671\pi\)
\(44\) −2.59808 + 1.50000i −0.391675 + 0.226134i
\(45\) 0 0
\(46\) −2.12132 + 3.67423i −0.312772 + 0.541736i
\(47\) 0.878680 0.507306i 0.128169 0.0739982i −0.434545 0.900650i \(-0.643091\pi\)
0.562713 + 0.826652i \(0.309757\pi\)
\(48\) 0 0
\(49\) 1.74264 6.77962i 0.248949 0.968517i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.22474 + 2.12132i −0.169842 + 0.294174i
\(53\) 0.621320 1.07616i 0.0853449 0.147822i −0.820193 0.572087i \(-0.806134\pi\)
0.905538 + 0.424265i \(0.139467\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.09077 1.62132i 0.279391 0.216658i
\(57\) 0 0
\(58\) 1.07616 0.621320i 0.141307 0.0815834i
\(59\) −5.76500 + 9.98528i −0.750540 + 1.29997i 0.197022 + 0.980399i \(0.436873\pi\)
−0.947561 + 0.319574i \(0.896460\pi\)
\(60\) 0 0
\(61\) 5.12132 2.95680i 0.655718 0.378579i −0.134926 0.990856i \(-0.543080\pi\)
0.790643 + 0.612277i \(0.209746\pi\)
\(62\) 5.61642i 0.713286i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −8.66025 5.00000i −1.05802 0.610847i −0.133135 0.991098i \(-0.542504\pi\)
−0.924883 + 0.380251i \(0.875838\pi\)
\(68\) 0.878680 0.507306i 0.106556 0.0615199i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.2426i 1.21558i 0.794099 + 0.607789i \(0.207943\pi\)
−0.794099 + 0.607789i \(0.792057\pi\)
\(72\) 0 0
\(73\) −4.18154 + 7.24264i −0.489412 + 0.847687i −0.999926 0.0121828i \(-0.996122\pi\)
0.510513 + 0.859870i \(0.329455\pi\)
\(74\) −7.13834 4.12132i −0.829815 0.479094i
\(75\) 0 0
\(76\) 1.01461i 0.116384i
\(77\) −7.86396 + 1.07616i −0.896182 + 0.122640i
\(78\) 0 0
\(79\) −5.62132 9.73641i −0.632448 1.09543i −0.987050 0.160415i \(-0.948717\pi\)
0.354602 0.935017i \(-0.384616\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.01461 1.75736i −0.112045 0.194068i
\(83\) 3.16693i 0.347616i 0.984780 + 0.173808i \(0.0556071\pi\)
−0.984780 + 0.173808i \(0.944393\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −7.13834 + 4.12132i −0.769747 + 0.444413i
\(87\) 0 0
\(88\) −2.59808 1.50000i −0.276956 0.159901i
\(89\) 5.19615 + 9.00000i 0.550791 + 0.953998i 0.998218 + 0.0596775i \(0.0190072\pi\)
−0.447427 + 0.894321i \(0.647659\pi\)
\(90\) 0 0
\(91\) −5.12132 + 3.97141i −0.536860 + 0.416317i
\(92\) −4.24264 −0.442326
\(93\) 0 0
\(94\) 0.878680 + 0.507306i 0.0906289 + 0.0523246i
\(95\) 0 0
\(96\) 0 0
\(97\) −3.76127 −0.381900 −0.190950 0.981600i \(-0.561157\pi\)
−0.190950 + 0.981600i \(0.561157\pi\)
\(98\) 6.74264 1.88064i 0.681110 0.189973i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −7.64564 13.2426i −0.753348 1.30484i −0.946192 0.323607i \(-0.895105\pi\)
0.192844 0.981229i \(-0.438229\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) 1.24264 0.120696
\(107\) 2.74264 + 4.75039i 0.265141 + 0.459238i 0.967601 0.252486i \(-0.0812481\pi\)
−0.702459 + 0.711724i \(0.747915\pi\)
\(108\) 0 0
\(109\) 0.757359 1.31178i 0.0725419 0.125646i −0.827473 0.561506i \(-0.810222\pi\)
0.900015 + 0.435860i \(0.143556\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.44949 + 1.00000i 0.231455 + 0.0944911i
\(113\) −8.48528 −0.798228 −0.399114 0.916901i \(-0.630682\pi\)
−0.399114 + 0.916901i \(0.630682\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.07616 + 0.621320i 0.0999188 + 0.0576881i
\(117\) 0 0
\(118\) −11.5300 −1.06142
\(119\) 2.65962 0.363961i 0.243807 0.0333643i
\(120\) 0 0
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) 5.12132 + 2.95680i 0.463663 + 0.267696i
\(123\) 0 0
\(124\) −4.86396 + 2.80821i −0.436797 + 0.252185i
\(125\) 0 0
\(126\) 0 0
\(127\) 5.24264i 0.465209i 0.972571 + 0.232605i \(0.0747248\pi\)
−0.972571 + 0.232605i \(0.925275\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 2.59808 + 4.50000i 0.226995 + 0.393167i 0.956916 0.290365i \(-0.0937766\pi\)
−0.729921 + 0.683531i \(0.760443\pi\)
\(132\) 0 0
\(133\) −1.01461 + 2.48528i −0.0879780 + 0.215501i
\(134\) 10.0000i 0.863868i
\(135\) 0 0
\(136\) 0.878680 + 0.507306i 0.0753462 + 0.0435011i
\(137\) −7.24264 + 12.5446i −0.618781 + 1.07176i 0.370928 + 0.928662i \(0.379040\pi\)
−0.989709 + 0.143098i \(0.954294\pi\)
\(138\) 0 0
\(139\) 20.1903i 1.71252i −0.516549 0.856258i \(-0.672783\pi\)
0.516549 0.856258i \(-0.327217\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.87039 + 5.12132i −0.744386 + 0.429772i
\(143\) 6.36396 + 3.67423i 0.532181 + 0.307255i
\(144\) 0 0
\(145\) 0 0
\(146\) −8.36308 −0.692134
\(147\) 0 0
\(148\) 8.24264i 0.677541i
\(149\) −17.7408 + 10.2426i −1.45338 + 0.839110i −0.998671 0.0515300i \(-0.983590\pi\)
−0.454709 + 0.890640i \(0.650257\pi\)
\(150\) 0 0
\(151\) 1.62132 2.80821i 0.131941 0.228529i −0.792484 0.609893i \(-0.791212\pi\)
0.924425 + 0.381364i \(0.124546\pi\)
\(152\) −0.878680 + 0.507306i −0.0712703 + 0.0411479i
\(153\) 0 0
\(154\) −4.86396 6.27231i −0.391949 0.505437i
\(155\) 0 0
\(156\) 0 0
\(157\) −7.34847 + 12.7279i −0.586472 + 1.01580i 0.408219 + 0.912884i \(0.366150\pi\)
−0.994690 + 0.102915i \(0.967183\pi\)
\(158\) 5.62132 9.73641i 0.447208 0.774587i
\(159\) 0 0
\(160\) 0 0
\(161\) −10.3923 4.24264i −0.819028 0.334367i
\(162\) 0 0
\(163\) 5.40629 3.12132i 0.423453 0.244481i −0.273101 0.961985i \(-0.588049\pi\)
0.696554 + 0.717505i \(0.254716\pi\)
\(164\) 1.01461 1.75736i 0.0792279 0.137227i
\(165\) 0 0
\(166\) −2.74264 + 1.58346i −0.212870 + 0.122901i
\(167\) 23.0600i 1.78444i 0.451603 + 0.892219i \(0.350852\pi\)
−0.451603 + 0.892219i \(0.649148\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) −7.13834 4.12132i −0.544293 0.314248i
\(173\) −18.0000 + 10.3923i −1.36851 + 0.790112i −0.990738 0.135785i \(-0.956644\pi\)
−0.377776 + 0.925897i \(0.623311\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) 0 0
\(178\) −5.19615 + 9.00000i −0.389468 + 0.674579i
\(179\) 8.23999 + 4.75736i 0.615886 + 0.355582i 0.775265 0.631636i \(-0.217616\pi\)
−0.159380 + 0.987217i \(0.550949\pi\)
\(180\) 0 0
\(181\) 2.02922i 0.150831i −0.997152 0.0754155i \(-0.975972\pi\)
0.997152 0.0754155i \(-0.0240283\pi\)
\(182\) −6.00000 2.44949i −0.444750 0.181568i
\(183\) 0 0
\(184\) −2.12132 3.67423i −0.156386 0.270868i
\(185\) 0 0
\(186\) 0 0
\(187\) −1.52192 2.63604i −0.111294 0.192766i
\(188\) 1.01461i 0.0739982i
\(189\) 0 0
\(190\) 0 0
\(191\) 7.34847 4.24264i 0.531717 0.306987i −0.209999 0.977702i \(-0.567346\pi\)
0.741715 + 0.670715i \(0.234013\pi\)
\(192\) 0 0
\(193\) 6.48244 + 3.74264i 0.466617 + 0.269401i 0.714822 0.699306i \(-0.246508\pi\)
−0.248206 + 0.968707i \(0.579841\pi\)
\(194\) −1.88064 3.25736i −0.135022 0.233865i
\(195\) 0 0
\(196\) 5.00000 + 4.89898i 0.357143 + 0.349927i
\(197\) 9.51472 0.677896 0.338948 0.940805i \(-0.389929\pi\)
0.338948 + 0.940805i \(0.389929\pi\)
\(198\) 0 0
\(199\) 13.9706 + 8.06591i 0.990347 + 0.571777i 0.905378 0.424607i \(-0.139588\pi\)
0.0849690 + 0.996384i \(0.472921\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.01472 + 2.59808i 0.141406 + 0.182349i
\(204\) 0 0
\(205\) 0 0
\(206\) 7.64564 13.2426i 0.532697 0.922658i
\(207\) 0 0
\(208\) −1.22474 2.12132i −0.0849208 0.147087i
\(209\) 3.04384 0.210547
\(210\) 0 0
\(211\) 8.24264 0.567447 0.283723 0.958906i \(-0.408430\pi\)
0.283723 + 0.958906i \(0.408430\pi\)
\(212\) 0.621320 + 1.07616i 0.0426725 + 0.0739109i
\(213\) 0 0
\(214\) −2.74264 + 4.75039i −0.187483 + 0.324730i
\(215\) 0 0
\(216\) 0 0
\(217\) −14.7224 + 2.01472i −0.999424 + 0.136768i
\(218\) 1.51472 0.102590
\(219\) 0 0
\(220\) 0 0
\(221\) −2.15232 1.24264i −0.144780 0.0835891i
\(222\) 0 0
\(223\) −12.5446 −0.840050 −0.420025 0.907513i \(-0.637979\pi\)
−0.420025 + 0.907513i \(0.637979\pi\)
\(224\) 0.358719 + 2.62132i 0.0239680 + 0.175144i
\(225\) 0 0
\(226\) −4.24264 7.34847i −0.282216 0.488813i
\(227\) 13.5000 + 7.79423i 0.896026 + 0.517321i 0.875909 0.482476i \(-0.160263\pi\)
0.0201176 + 0.999798i \(0.493596\pi\)
\(228\) 0 0
\(229\) 12.0000 6.92820i 0.792982 0.457829i −0.0480291 0.998846i \(-0.515294\pi\)
0.841011 + 0.541017i \(0.181961\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.24264i 0.0815834i
\(233\) 3.36396 + 5.82655i 0.220380 + 0.381710i 0.954924 0.296852i \(-0.0959368\pi\)
−0.734543 + 0.678562i \(0.762603\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.76500 9.98528i −0.375270 0.649986i
\(237\) 0 0
\(238\) 1.64501 + 2.12132i 0.106630 + 0.137505i
\(239\) 12.7279i 0.823301i −0.911342 0.411650i \(-0.864952\pi\)
0.911342 0.411650i \(-0.135048\pi\)
\(240\) 0 0
\(241\) 14.7426 + 8.51167i 0.949657 + 0.548285i 0.892974 0.450108i \(-0.148614\pi\)
0.0566826 + 0.998392i \(0.481948\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 0 0
\(244\) 5.91359i 0.378579i
\(245\) 0 0
\(246\) 0 0
\(247\) 2.15232 1.24264i 0.136949 0.0790673i
\(248\) −4.86396 2.80821i −0.308862 0.178321i
\(249\) 0 0
\(250\) 0 0
\(251\) 17.6177 1.11202 0.556009 0.831176i \(-0.312332\pi\)
0.556009 + 0.831176i \(0.312332\pi\)
\(252\) 0 0
\(253\) 12.7279i 0.800198i
\(254\) −4.54026 + 2.62132i −0.284881 + 0.164476i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 21.7279 12.5446i 1.35535 0.782512i 0.366358 0.930474i \(-0.380605\pi\)
0.988993 + 0.147962i \(0.0472714\pi\)
\(258\) 0 0
\(259\) 8.24264 20.1903i 0.512173 1.25456i
\(260\) 0 0
\(261\) 0 0
\(262\) −2.59808 + 4.50000i −0.160510 + 0.278011i
\(263\) −13.6066 + 23.5673i −0.839019 + 1.45322i 0.0516967 + 0.998663i \(0.483537\pi\)
−0.890716 + 0.454561i \(0.849796\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.65962 + 0.363961i −0.163072 + 0.0223159i
\(267\) 0 0
\(268\) 8.66025 5.00000i 0.529009 0.305424i
\(269\) 5.25770 9.10660i 0.320568 0.555239i −0.660038 0.751232i \(-0.729460\pi\)
0.980605 + 0.195993i \(0.0627930\pi\)
\(270\) 0 0
\(271\) −9.62132 + 5.55487i −0.584454 + 0.337434i −0.762901 0.646515i \(-0.776226\pi\)
0.178448 + 0.983949i \(0.442892\pi\)
\(272\) 1.01461i 0.0615199i
\(273\) 0 0
\(274\) −14.4853 −0.875088
\(275\) 0 0
\(276\) 0 0
\(277\) −18.1610 10.4853i −1.09119 0.630000i −0.157298 0.987551i \(-0.550278\pi\)
−0.933893 + 0.357552i \(0.883612\pi\)
\(278\) 17.4853 10.0951i 1.04870 0.605466i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000i 0.357930i −0.983855 0.178965i \(-0.942725\pi\)
0.983855 0.178965i \(-0.0572749\pi\)
\(282\) 0 0
\(283\) 3.25397 5.63604i 0.193428 0.335028i −0.752956 0.658071i \(-0.771373\pi\)
0.946384 + 0.323043i \(0.104706\pi\)
\(284\) −8.87039 5.12132i −0.526361 0.303894i
\(285\) 0 0
\(286\) 7.34847i 0.434524i
\(287\) 4.24264 3.29002i 0.250435 0.194204i
\(288\) 0 0
\(289\) −7.98528 13.8309i −0.469722 0.813583i
\(290\) 0 0
\(291\) 0 0
\(292\) −4.18154 7.24264i −0.244706 0.423843i
\(293\) 4.18154i 0.244288i −0.992512 0.122144i \(-0.961023\pi\)
0.992512 0.122144i \(-0.0389770\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 7.13834 4.12132i 0.414907 0.239547i
\(297\) 0 0
\(298\) −17.7408 10.2426i −1.02770 0.593340i
\(299\) 5.19615 + 9.00000i 0.300501 + 0.520483i
\(300\) 0 0
\(301\) −13.3640 17.2335i −0.770286 0.993321i
\(302\) 3.24264 0.186593
\(303\) 0 0
\(304\) −0.878680 0.507306i −0.0503957 0.0290960i
\(305\) 0 0
\(306\) 0 0
\(307\) 24.6690 1.40793 0.703966 0.710233i \(-0.251411\pi\)
0.703966 + 0.710233i \(0.251411\pi\)
\(308\) 3.00000 7.34847i 0.170941 0.418718i
\(309\) 0 0
\(310\) 0 0
\(311\) 9.37769 16.2426i 0.531760 0.921036i −0.467552 0.883965i \(-0.654864\pi\)
0.999313 0.0370703i \(-0.0118026\pi\)
\(312\) 0 0
\(313\) −0.568852 0.985281i −0.0321534 0.0556914i 0.849501 0.527587i \(-0.176903\pi\)
−0.881654 + 0.471896i \(0.843570\pi\)
\(314\) −14.6969 −0.829396
\(315\) 0 0
\(316\) 11.2426 0.632448
\(317\) −3.62132 6.27231i −0.203394 0.352288i 0.746226 0.665693i \(-0.231864\pi\)
−0.949620 + 0.313404i \(0.898530\pi\)
\(318\) 0 0
\(319\) 1.86396 3.22848i 0.104362 0.180760i
\(320\) 0 0
\(321\) 0 0
\(322\) −1.52192 11.1213i −0.0848132 0.619767i
\(323\) −1.02944 −0.0572794
\(324\) 0 0
\(325\) 0 0
\(326\) 5.40629 + 3.12132i 0.299426 + 0.172874i
\(327\) 0 0
\(328\) 2.02922 0.112045
\(329\) −1.01461 + 2.48528i −0.0559374 + 0.137018i
\(330\) 0 0
\(331\) −8.72792 15.1172i −0.479730 0.830917i 0.520000 0.854166i \(-0.325932\pi\)
−0.999730 + 0.0232497i \(0.992599\pi\)
\(332\) −2.74264 1.58346i −0.150522 0.0869039i
\(333\) 0 0
\(334\) −19.9706 + 11.5300i −1.09274 + 0.630894i
\(335\) 0 0
\(336\) 0 0
\(337\) 5.00000i 0.272367i 0.990684 + 0.136184i \(0.0434837\pi\)
−0.990684 + 0.136184i \(0.956516\pi\)
\(338\) −3.50000 6.06218i −0.190375 0.329739i
\(339\) 0 0
\(340\) 0 0
\(341\) 8.42463 + 14.5919i 0.456219 + 0.790195i
\(342\) 0 0
\(343\) 7.34847 + 17.0000i 0.396780 + 0.917914i
\(344\) 8.24264i 0.444413i
\(345\) 0 0
\(346\) −18.0000 10.3923i −0.967686 0.558694i
\(347\) 7.24264 12.5446i 0.388805 0.673431i −0.603484 0.797375i \(-0.706221\pi\)
0.992289 + 0.123945i \(0.0395545\pi\)
\(348\) 0 0
\(349\) 36.9164i 1.97609i 0.154163 + 0.988045i \(0.450732\pi\)
−0.154163 + 0.988045i \(0.549268\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.59808 1.50000i 0.138478 0.0799503i
\(353\) 16.2426 + 9.37769i 0.864509 + 0.499124i 0.865519 0.500875i \(-0.166988\pi\)
−0.00101095 + 0.999999i \(0.500322\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −10.3923 −0.550791
\(357\) 0 0
\(358\) 9.51472i 0.502869i
\(359\) −15.5885 + 9.00000i −0.822727 + 0.475002i −0.851356 0.524588i \(-0.824219\pi\)
0.0286287 + 0.999590i \(0.490886\pi\)
\(360\) 0 0
\(361\) −8.98528 + 15.5630i −0.472910 + 0.819103i
\(362\) 1.75736 1.01461i 0.0923648 0.0533268i
\(363\) 0 0
\(364\) −0.878680 6.42090i −0.0460553 0.336546i
\(365\) 0 0
\(366\) 0 0
\(367\) 9.43924 16.3492i 0.492724 0.853424i −0.507241 0.861804i \(-0.669334\pi\)
0.999965 + 0.00838099i \(0.00266778\pi\)
\(368\) 2.12132 3.67423i 0.110581 0.191533i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.445759 + 3.25736i 0.0231427 + 0.169114i
\(372\) 0 0
\(373\) 18.5813 10.7279i 0.962104 0.555471i 0.0652837 0.997867i \(-0.479205\pi\)
0.896820 + 0.442396i \(0.145871\pi\)
\(374\) 1.52192 2.63604i 0.0786965 0.136306i
\(375\) 0 0
\(376\) −0.878680 + 0.507306i −0.0453144 + 0.0261623i
\(377\) 3.04384i 0.156766i
\(378\) 0 0
\(379\) 4.48528 0.230393 0.115197 0.993343i \(-0.463250\pi\)
0.115197 + 0.993343i \(0.463250\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 7.34847 + 4.24264i 0.375980 + 0.217072i
\(383\) −10.7574 + 6.21076i −0.549675 + 0.317355i −0.748991 0.662580i \(-0.769461\pi\)
0.199316 + 0.979935i \(0.436128\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 7.48528i 0.380991i
\(387\) 0 0
\(388\) 1.88064 3.25736i 0.0954749 0.165367i
\(389\) 16.8493 + 9.72792i 0.854291 + 0.493225i 0.862096 0.506744i \(-0.169151\pi\)
−0.00780525 + 0.999970i \(0.502485\pi\)
\(390\) 0 0
\(391\) 4.30463i 0.217695i
\(392\) −1.74264 + 6.77962i −0.0880166 + 0.342422i
\(393\) 0 0
\(394\) 4.75736 + 8.23999i 0.239672 + 0.415125i
\(395\) 0 0
\(396\) 0 0
\(397\) −6.92820 12.0000i −0.347717 0.602263i 0.638127 0.769931i \(-0.279710\pi\)
−0.985843 + 0.167668i \(0.946376\pi\)
\(398\) 16.1318i 0.808615i
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 11.9142 + 6.87868i 0.593490 + 0.342651i
\(404\) 0 0
\(405\) 0 0
\(406\) −1.24264 + 3.04384i −0.0616712 + 0.151063i
\(407\) −24.7279 −1.22572
\(408\) 0 0
\(409\) 3.98528 + 2.30090i 0.197059 + 0.113772i 0.595283 0.803516i \(-0.297040\pi\)
−0.398224 + 0.917288i \(0.630373\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 15.2913 0.753348
\(413\) −4.13604 30.2238i −0.203521 1.48722i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.22474 2.12132i 0.0600481 0.104006i
\(417\) 0 0
\(418\) 1.52192 + 2.63604i 0.0744394 + 0.128933i
\(419\) 4.05845 0.198268 0.0991341 0.995074i \(-0.468393\pi\)
0.0991341 + 0.995074i \(0.468393\pi\)
\(420\) 0 0
\(421\) −5.75736 −0.280597 −0.140298 0.990109i \(-0.544806\pi\)
−0.140298 + 0.990109i \(0.544806\pi\)
\(422\) 4.12132 + 7.13834i 0.200623 + 0.347489i
\(423\) 0 0
\(424\) −0.621320 + 1.07616i −0.0301740 + 0.0522629i
\(425\) 0 0
\(426\) 0 0
\(427\) −5.91359 + 14.4853i −0.286179 + 0.700992i
\(428\) −5.48528 −0.265141
\(429\) 0 0
\(430\) 0 0
\(431\) 17.7408 + 10.2426i 0.854543 + 0.493371i 0.862181 0.506600i \(-0.169098\pi\)
−0.00763808 + 0.999971i \(0.502431\pi\)
\(432\) 0 0
\(433\) −3.46410 −0.166474 −0.0832370 0.996530i \(-0.526526\pi\)
−0.0832370 + 0.996530i \(0.526526\pi\)
\(434\) −9.10601 11.7426i −0.437103 0.563665i
\(435\) 0 0
\(436\) 0.757359 + 1.31178i 0.0362709 + 0.0628231i
\(437\) 3.72792 + 2.15232i 0.178331 + 0.102959i
\(438\) 0 0
\(439\) −23.5919 + 13.6208i −1.12598 + 0.650084i −0.942921 0.333018i \(-0.891933\pi\)
−0.183059 + 0.983102i \(0.558600\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 2.48528i 0.118213i
\(443\) −17.2279 29.8396i −0.818523 1.41772i −0.906770 0.421625i \(-0.861460\pi\)
0.0882469 0.996099i \(-0.471874\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −6.27231 10.8640i −0.297003 0.514423i
\(447\) 0 0
\(448\) −2.09077 + 1.62132i −0.0987796 + 0.0766002i
\(449\) 10.2426i 0.483380i −0.970354 0.241690i \(-0.922298\pi\)
0.970354 0.241690i \(-0.0777017\pi\)
\(450\) 0 0
\(451\) −5.27208 3.04384i −0.248252 0.143329i
\(452\) 4.24264 7.34847i 0.199557 0.345643i
\(453\) 0 0
\(454\) 15.5885i 0.731603i
\(455\) 0 0
\(456\) 0 0
\(457\) 19.9186 11.5000i 0.931752 0.537947i 0.0443868 0.999014i \(-0.485867\pi\)
0.887365 + 0.461067i \(0.152533\pi\)
\(458\) 12.0000 + 6.92820i 0.560723 + 0.323734i
\(459\) 0 0
\(460\) 0 0
\(461\) −22.8138 −1.06255 −0.531273 0.847201i \(-0.678286\pi\)
−0.531273 + 0.847201i \(0.678286\pi\)
\(462\) 0 0
\(463\) 21.4558i 0.997138i 0.866850 + 0.498569i \(0.166141\pi\)
−0.866850 + 0.498569i \(0.833859\pi\)
\(464\) −1.07616 + 0.621320i −0.0499594 + 0.0288441i
\(465\) 0 0
\(466\) −3.36396 + 5.82655i −0.155832 + 0.269910i
\(467\) 16.4558 9.50079i 0.761486 0.439644i −0.0683432 0.997662i \(-0.521771\pi\)
0.829829 + 0.558018i \(0.188438\pi\)
\(468\) 0 0
\(469\) 26.2132 3.58719i 1.21041 0.165641i
\(470\) 0 0
\(471\) 0 0
\(472\) 5.76500 9.98528i 0.265356 0.459610i
\(473\) −12.3640 + 21.4150i −0.568496 + 0.984663i
\(474\) 0 0
\(475\) 0 0
\(476\) −1.01461 + 2.48528i −0.0465047 + 0.113913i
\(477\) 0 0
\(478\) 11.0227 6.36396i 0.504167 0.291081i
\(479\) 18.2481 31.6066i 0.833776 1.44414i −0.0612470 0.998123i \(-0.519508\pi\)
0.895023 0.446020i \(-0.147159\pi\)
\(480\) 0 0
\(481\) −17.4853 + 10.0951i −0.797260 + 0.460298i
\(482\) 17.0233i 0.775392i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 0 0
\(487\) 24.4334 + 14.1066i 1.10718 + 0.639231i 0.938098 0.346371i \(-0.112586\pi\)
0.169083 + 0.985602i \(0.445919\pi\)
\(488\) −5.12132 + 2.95680i −0.231831 + 0.133848i
\(489\) 0 0
\(490\) 0 0
\(491\) 19.9706i 0.901259i −0.892711 0.450629i \(-0.851200\pi\)
0.892711 0.450629i \(-0.148800\pi\)
\(492\) 0 0
\(493\) −0.630399 + 1.09188i −0.0283917 + 0.0491759i
\(494\) 2.15232 + 1.24264i 0.0968373 + 0.0559090i
\(495\) 0 0
\(496\) 5.61642i 0.252185i
\(497\) −16.6066 21.4150i −0.744908 0.960594i
\(498\) 0 0
\(499\) −17.9706 31.1259i −0.804473 1.39339i −0.916646 0.399699i \(-0.869115\pi\)
0.112173 0.993689i \(-0.464219\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 8.80884 + 15.2574i 0.393158 + 0.680969i
\(503\) 3.29002i 0.146695i −0.997306 0.0733474i \(-0.976632\pi\)
0.997306 0.0733474i \(-0.0233682\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −11.0227 + 6.36396i −0.490019 + 0.282913i
\(507\) 0 0
\(508\) −4.54026 2.62132i −0.201441 0.116302i
\(509\) 20.8462 + 36.1066i 0.923990 + 1.60040i 0.793178 + 0.608990i \(0.208425\pi\)
0.130812 + 0.991407i \(0.458242\pi\)
\(510\) 0 0
\(511\) −3.00000 21.9223i −0.132712 0.969786i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 21.7279 + 12.5446i 0.958378 + 0.553320i
\(515\) 0 0
\(516\) 0 0
\(517\) 3.04384 0.133868
\(518\) 21.6066 2.95680i 0.949340 0.129914i
\(519\) 0 0
\(520\) 0 0
\(521\) −10.0081 + 17.3345i −0.438462 + 0.759439i −0.997571 0.0696551i \(-0.977810\pi\)
0.559109 + 0.829094i \(0.311143\pi\)
\(522\) 0 0
\(523\) −13.7694 23.8492i −0.602092 1.04285i −0.992504 0.122214i \(-0.961001\pi\)
0.390411 0.920641i \(-0.372333\pi\)
\(524\) −5.19615 −0.226995
\(525\) 0 0
\(526\) −27.2132 −1.18655
\(527\) −2.84924 4.93503i −0.124115 0.214973i
\(528\) 0 0
\(529\) 2.50000 4.33013i 0.108696 0.188266i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.64501 2.12132i −0.0713203 0.0919709i
\(533\) −4.97056 −0.215299
\(534\) 0 0
\(535\) 0 0
\(536\) 8.66025 + 5.00000i 0.374066 + 0.215967i
\(537\) 0 0
\(538\) 10.5154 0.453351
\(539\) 14.6969 15.0000i 0.633042 0.646096i
\(540\) 0 0
\(541\) 5.36396 + 9.29065i 0.230615 + 0.399436i 0.957989 0.286804i \(-0.0925930\pi\)
−0.727374 + 0.686241i \(0.759260\pi\)
\(542\) −9.62132 5.55487i −0.413271 0.238602i
\(543\) 0 0
\(544\) −0.878680 + 0.507306i −0.0376731 + 0.0217506i
\(545\) 0 0
\(546\) 0 0
\(547\) 19.6985i 0.842246i −0.907003 0.421123i \(-0.861636\pi\)
0.907003 0.421123i \(-0.138364\pi\)
\(548\) −7.24264 12.5446i −0.309390 0.535880i
\(549\) 0 0
\(550\) 0 0
\(551\) −0.630399 1.09188i −0.0268559 0.0465158i
\(552\) 0 0
\(553\) 27.5387 + 11.2426i 1.17107 + 0.478086i
\(554\) 20.9706i 0.890954i
\(555\) 0 0
\(556\) 17.4853 + 10.0951i 0.741541 + 0.428129i
\(557\) 7.86396 13.6208i 0.333207 0.577131i −0.649932 0.759992i \(-0.725203\pi\)
0.983139 + 0.182861i \(0.0585360\pi\)
\(558\) 0 0
\(559\) 20.1903i 0.853957i
\(560\) 0 0
\(561\) 0 0
\(562\) 5.19615 3.00000i 0.219186 0.126547i
\(563\) 20.9558 + 12.0989i 0.883184 + 0.509906i 0.871707 0.490028i \(-0.163013\pi\)
0.0114768 + 0.999934i \(0.496347\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 6.50794 0.273549
\(567\) 0 0
\(568\) 10.2426i 0.429772i
\(569\) −1.52192 + 0.878680i −0.0638021 + 0.0368362i −0.531562 0.847020i \(-0.678395\pi\)
0.467760 + 0.883856i \(0.345061\pi\)
\(570\) 0 0
\(571\) 8.36396 14.4868i 0.350021 0.606254i −0.636232 0.771498i \(-0.719508\pi\)
0.986253 + 0.165244i \(0.0528412\pi\)
\(572\) −6.36396 + 3.67423i −0.266091 + 0.153627i
\(573\) 0 0
\(574\) 4.97056 + 2.02922i 0.207467 + 0.0846982i
\(575\) 0 0
\(576\) 0 0
\(577\) 10.2437 17.7426i 0.426452 0.738636i −0.570103 0.821573i \(-0.693097\pi\)
0.996555 + 0.0829373i \(0.0264301\pi\)
\(578\) 7.98528 13.8309i 0.332144 0.575290i
\(579\) 0 0
\(580\) 0 0
\(581\) −5.13461 6.62132i −0.213019 0.274699i
\(582\) 0 0
\(583\) 3.22848 1.86396i 0.133710 0.0771974i
\(584\) 4.18154 7.24264i 0.173033 0.299703i
\(585\) 0 0
\(586\) 3.62132 2.09077i 0.149595 0.0863689i
\(587\) 5.19615i 0.214468i 0.994234 + 0.107234i \(0.0341994\pi\)
−0.994234 + 0.107234i \(0.965801\pi\)
\(588\) 0 0
\(589\) 5.69848 0.234802
\(590\) 0 0
\(591\) 0 0
\(592\) 7.13834 + 4.12132i 0.293384 + 0.169385i
\(593\) 26.3345 15.2042i 1.08143 0.624363i 0.150148 0.988664i \(-0.452025\pi\)
0.931282 + 0.364300i \(0.118692\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.4853i 0.839110i
\(597\) 0 0
\(598\) −5.19615 + 9.00000i −0.212486 + 0.368037i
\(599\) 37.6339 + 21.7279i 1.53768 + 0.887779i 0.998974 + 0.0452836i \(0.0144192\pi\)
0.538704 + 0.842495i \(0.318914\pi\)
\(600\) 0 0
\(601\) 6.03668i 0.246241i 0.992392 + 0.123121i \(0.0392902\pi\)
−0.992392 + 0.123121i \(0.960710\pi\)
\(602\) 8.24264 20.1903i 0.335945 0.822894i
\(603\) 0 0
\(604\) 1.62132 + 2.80821i 0.0659706 + 0.114264i
\(605\) 0 0
\(606\) 0 0
\(607\) 12.4831 + 21.6213i 0.506672 + 0.877582i 0.999970 + 0.00772182i \(0.00245796\pi\)
−0.493298 + 0.869860i \(0.664209\pi\)
\(608\) 1.01461i 0.0411479i
\(609\) 0 0
\(610\) 0 0
\(611\) 2.15232 1.24264i 0.0870734 0.0502719i
\(612\) 0 0
\(613\) −4.51477 2.60660i −0.182350 0.105280i 0.406046 0.913852i \(-0.366907\pi\)
−0.588396 + 0.808573i \(0.700240\pi\)
\(614\) 12.3345 + 21.3640i 0.497779 + 0.862179i
\(615\) 0 0
\(616\) 7.86396 1.07616i 0.316848 0.0433597i
\(617\) −41.6985 −1.67872 −0.839359 0.543578i \(-0.817069\pi\)
−0.839359 + 0.543578i \(0.817069\pi\)
\(618\) 0 0
\(619\) 41.3345 + 23.8645i 1.66137 + 0.959195i 0.972060 + 0.234733i \(0.0754217\pi\)
0.689315 + 0.724462i \(0.257912\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 18.7554 0.752022
\(623\) −25.4558 10.3923i −1.01987 0.416359i
\(624\) 0 0
\(625\) 0 0
\(626\) 0.568852 0.985281i 0.0227359 0.0393798i
\(627\) 0 0
\(628\) −7.34847 12.7279i −0.293236 0.507899i
\(629\) 8.36308 0.333458
\(630\) 0 0
\(631\) 33.2426 1.32337 0.661684 0.749783i \(-0.269842\pi\)
0.661684 + 0.749783i \(0.269842\pi\)
\(632\) 5.62132 + 9.73641i 0.223604 + 0.387294i
\(633\) 0 0
\(634\) 3.62132 6.27231i 0.143821 0.249105i
\(635\) 0 0
\(636\) 0 0
\(637\) 4.26858 16.6066i 0.169127 0.657978i
\(638\) 3.72792 0.147590
\(639\) 0 0
\(640\) 0 0
\(641\) −36.1119 20.8492i −1.42634 0.823496i −0.429507 0.903064i \(-0.641313\pi\)
−0.996829 + 0.0795681i \(0.974646\pi\)
\(642\) 0 0
\(643\) 2.62357 0.103463 0.0517317 0.998661i \(-0.483526\pi\)
0.0517317 + 0.998661i \(0.483526\pi\)
\(644\) 8.87039 6.87868i 0.349542 0.271058i
\(645\) 0 0
\(646\) −0.514719 0.891519i −0.0202513 0.0350763i
\(647\) 10.0919 + 5.82655i 0.396753 + 0.229065i 0.685082 0.728466i \(-0.259766\pi\)
−0.288329 + 0.957531i \(0.593100\pi\)
\(648\) 0 0
\(649\) −29.9558 + 17.2950i −1.17587 + 0.678889i
\(650\) 0 0
\(651\) 0 0
\(652\) 6.24264i 0.244481i
\(653\) −5.37868 9.31615i −0.210484 0.364569i 0.741382 0.671083i \(-0.234171\pi\)
−0.951866 + 0.306514i \(0.900837\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.01461 + 1.75736i 0.0396139 + 0.0686134i
\(657\) 0 0
\(658\) −2.65962 + 0.363961i −0.103683 + 0.0141887i
\(659\) 6.00000i 0.233727i 0.993148 + 0.116863i \(0.0372840\pi\)
−0.993148 + 0.116863i \(0.962716\pi\)
\(660\) 0 0
\(661\) 35.1213 + 20.2773i 1.36606 + 0.788696i 0.990422 0.138071i \(-0.0440901\pi\)
0.375639 + 0.926766i \(0.377423\pi\)
\(662\) 8.72792 15.1172i 0.339220 0.587547i
\(663\) 0 0
\(664\) 3.16693i 0.122901i
\(665\) 0 0
\(666\) 0 0
\(667\) 4.56575 2.63604i 0.176787 0.102068i
\(668\) −19.9706 11.5300i −0.772684 0.446109i
\(669\) 0 0
\(670\) 0 0
\(671\) 17.7408 0.684875
\(672\) 0 0
\(673\) 15.9706i 0.615620i −0.951448 0.307810i \(-0.900404\pi\)
0.951448 0.307810i \(-0.0995961\pi\)
\(674\) −4.33013 + 2.50000i −0.166790 + 0.0962964i
\(675\) 0 0
\(676\) 3.50000 6.06218i 0.134615 0.233161i
\(677\) 10.8640 6.27231i 0.417536 0.241064i −0.276487 0.961018i \(-0.589170\pi\)
0.694023 + 0.719953i \(0.255837\pi\)
\(678\) 0 0
\(679\) 7.86396 6.09823i 0.301791 0.234029i
\(680\) 0 0
\(681\) 0 0
\(682\) −8.42463 + 14.5919i −0.322596 + 0.558752i
\(683\) 12.9853 22.4912i 0.496868 0.860601i −0.503125 0.864213i \(-0.667817\pi\)
0.999993 + 0.00361277i \(0.00114998\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −11.0482 + 14.8640i −0.421822 + 0.567509i
\(687\) 0 0
\(688\) 7.13834 4.12132i 0.272147 0.157124i
\(689\) 1.52192 2.63604i 0.0579805 0.100425i
\(690\) 0 0
\(691\) −0.727922 + 0.420266i −0.0276915 + 0.0159877i −0.513782 0.857921i \(-0.671756\pi\)
0.486090 + 0.873909i \(0.338423\pi\)
\(692\) 20.7846i 0.790112i
\(693\) 0 0
\(694\) 14.4853 0.549854
\(695\) 0 0
\(696\) 0 0
\(697\) 1.78304 + 1.02944i 0.0675374 + 0.0389927i
\(698\) −31.9706 + 18.4582i −1.21010 + 0.698654i
\(699\) 0 0
\(700\) 0 0
\(701\) 38.6985i 1.46162i 0.682580 + 0.730811i \(0.260858\pi\)
−0.682580 + 0.730811i \(0.739142\pi\)
\(702\) 0 0
\(703\) −4.18154 + 7.24264i −0.157710 + 0.273161i
\(704\) 2.59808 + 1.50000i 0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) 18.7554i 0.705868i
\(707\) 0 0
\(708\) 0 0
\(709\) −3.48528 6.03668i −0.130892 0.226712i 0.793128 0.609055i \(-0.208451\pi\)
−0.924021 + 0.382342i \(0.875118\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −5.19615 9.00000i −0.194734 0.337289i
\(713\) 23.8284i 0.892382i
\(714\) 0 0
\(715\) 0 0
\(716\) −8.23999 + 4.75736i −0.307943 + 0.177791i
\(717\) 0 0
\(718\) −15.5885 9.00000i −0.581756 0.335877i
\(719\) 11.5300 + 19.9706i 0.429997 + 0.744776i 0.996872 0.0790270i \(-0.0251813\pi\)
−0.566876 + 0.823803i \(0.691848\pi\)
\(720\) 0 0
\(721\) 37.4558 + 15.2913i 1.39493 + 0.569477i
\(722\) −17.9706 −0.668795
\(723\) 0 0
\(724\) 1.75736 + 1.01461i 0.0653117 + 0.0377078i
\(725\) 0 0
\(726\) 0 0
\(727\) 26.4010 0.979160 0.489580 0.871958i \(-0.337150\pi\)
0.489580 + 0.871958i \(0.337150\pi\)
\(728\) 5.12132 3.97141i 0.189809 0.147190i
\(729\) 0 0
\(730\) 0 0
\(731\) 4.18154 7.24264i 0.154660 0.267879i
\(732\) 0 0
\(733\) −19.6830 34.0919i −0.727007 1.25921i −0.958143 0.286291i \(-0.907578\pi\)
0.231136 0.972921i \(-0.425756\pi\)
\(734\) 18.8785 0.696817
\(735\) 0 0
\(736\) 4.24264 0.156386
\(737\) −15.0000 25.9808i −0.552532 0.957014i
\(738\) 0 0
\(739\) −17.7279 + 30.7057i −0.652132 + 1.12953i 0.330472 + 0.943816i \(0.392792\pi\)
−0.982605 + 0.185710i \(0.940541\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.59808 + 2.01472i −0.0953784 + 0.0739626i
\(743\) 21.5147 0.789298 0.394649 0.918832i \(-0.370866\pi\)
0.394649 + 0.918832i \(0.370866\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 18.5813 + 10.7279i 0.680310 + 0.392777i
\(747\) 0 0
\(748\) 3.04384 0.111294
\(749\) −13.4361 5.48528i −0.490946 0.200428i
\(750\) 0 0
\(751\) −13.3787 23.1726i −0.488195 0.845578i 0.511713 0.859157i \(-0.329011\pi\)
−0.999908 + 0.0135781i \(0.995678\pi\)
\(752\) −0.878680 0.507306i −0.0320422 0.0184995i
\(753\) 0 0
\(754\) 2.63604 1.52192i 0.0959989 0.0554250i
\(755\) 0 0
\(756\) 0 0
\(757\) 42.2426i 1.53533i 0.640848 + 0.767667i \(0.278583\pi\)
−0.640848 + 0.767667i \(0.721417\pi\)
\(758\) 2.24264 + 3.88437i 0.0814564 + 0.141087i
\(759\) 0 0
\(760\) 0 0
\(761\) 2.53653 + 4.39340i 0.0919491 + 0.159261i 0.908331 0.418252i \(-0.137357\pi\)
−0.816382 + 0.577512i \(0.804024\pi\)
\(762\) 0 0
\(763\) 0.543359 + 3.97056i 0.0196709 + 0.143744i
\(764\) 8.48528i 0.306987i
\(765\) 0 0
\(766\) −10.7574 6.21076i −0.388679 0.224404i
\(767\) −14.1213 + 24.4588i −0.509891 + 0.883158i
\(768\) 0 0
\(769\) 49.0408i 1.76846i 0.467056 + 0.884228i \(0.345315\pi\)
−0.467056 + 0.884228i \(0.654685\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.48244 + 3.74264i −0.233308 + 0.134701i
\(773\) 19.9706 + 11.5300i 0.718291 + 0.414706i 0.814123 0.580692i \(-0.197218\pi\)
−0.0958322 + 0.995398i \(0.530551\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 3.76127 0.135022
\(777\) 0 0
\(778\) 19.4558i 0.697526i
\(779\) −1.78304 + 1.02944i −0.0638840 + 0.0368834i
\(780\) 0 0
\(781\) −15.3640 + 26.6112i −0.549766 + 0.952222i
\(782\) 3.72792 2.15232i 0.133310 0.0769667i
\(783\) 0 0
\(784\) −6.74264 + 1.88064i −0.240809 + 0.0671656i
\(785\) 0 0
\(786\) 0 0
\(787\) 18.5453 32.1213i 0.661067 1.14500i −0.319269 0.947664i \(-0.603437\pi\)
0.980336 0.197337i \(-0.0632294\pi\)
\(788\) −4.75736 + 8.23999i −0.169474 + 0.293537i
\(789\) 0 0
\(790\) 0 0
\(791\) 17.7408 13.7574i 0.630789 0.489155i
\(792\) 0 0
\(793\) 12.5446 7.24264i 0.445473 0.257194i
\(794\) 6.92820 12.0000i 0.245873 0.425864i
\(795\) 0 0
\(796\) −13.9706 + 8.06591i −0.495173 + 0.285889i
\(797\) 37.6339i