Properties

Label 3150.2.bf.a.1601.2
Level 3150
Weight 2
Character 3150.1601
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.bf (of order \(6\), degree \(2\), 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: \(\Z[a_1, \ldots, a_{7}]\)
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 1601.2
Root \(0.965926 + 0.258819i\)
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.a.1151.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +(-2.59808 + 1.50000i) q^{11} -2.44949i q^{13} +(-2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.507306 + 0.878680i) q^{17} +(-0.878680 - 0.507306i) q^{19} +3.00000 q^{22} +(3.67423 + 2.12132i) q^{23} +(-1.22474 + 2.12132i) q^{26} +(2.62132 + 0.358719i) q^{28} +1.24264i q^{29} +(4.86396 - 2.80821i) q^{31} +(0.866025 - 0.500000i) q^{32} -1.01461i q^{34} +(4.12132 - 7.13834i) q^{37} +(0.507306 + 0.878680i) q^{38} +2.02922 q^{41} -8.24264 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(0.507306 - 0.878680i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(2.12132 - 1.22474i) q^{52} +(-1.07616 + 0.621320i) q^{53} +(-2.09077 - 1.62132i) q^{56} +(0.621320 - 1.07616i) q^{58} +(-5.76500 - 9.98528i) q^{59} +(5.12132 + 2.95680i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(-5.00000 - 8.66025i) q^{67} +(-0.507306 + 0.878680i) q^{68} +10.2426i q^{71} +(-7.24264 + 4.18154i) q^{73} +(-7.13834 + 4.12132i) q^{74} -1.01461i q^{76} +(-1.07616 + 7.86396i) q^{77} +(5.62132 - 9.73641i) q^{79} +(-1.75736 - 1.01461i) q^{82} +3.16693 q^{83} +(7.13834 + 4.12132i) q^{86} +(1.50000 + 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-5.12132 - 3.97141i) q^{91} +4.24264i q^{92} +(-0.878680 + 0.507306i) q^{94} -3.76127i q^{97} +(-1.88064 + 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{7} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{7} - 4q^{16} - 24q^{19} + 24q^{22} + 4q^{28} - 12q^{31} + 16q^{37} - 32q^{43} + 20q^{49} - 12q^{58} + 24q^{61} - 8q^{64} - 40q^{67} - 24q^{73} + 28q^{79} - 48q^{82} + 12q^{88} - 24q^{91} - 24q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 1.62132 2.09077i 0.612801 0.790237i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −2.59808 + 1.50000i −0.783349 + 0.452267i −0.837616 0.546259i \(-0.816051\pi\)
0.0542666 + 0.998526i \(0.482718\pi\)
\(12\) 0 0
\(13\) 2.44949i 0.679366i −0.940540 0.339683i \(-0.889680\pi\)
0.940540 0.339683i \(-0.110320\pi\)
\(14\) −2.44949 + 1.00000i −0.654654 + 0.267261i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.507306 + 0.878680i 0.123040 + 0.213111i 0.920965 0.389645i \(-0.127402\pi\)
−0.797925 + 0.602756i \(0.794069\pi\)
\(18\) 0 0
\(19\) −0.878680 0.507306i −0.201583 0.116384i 0.395811 0.918332i \(-0.370464\pi\)
−0.597394 + 0.801948i \(0.703797\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) 3.67423 + 2.12132i 0.766131 + 0.442326i 0.831493 0.555536i \(-0.187487\pi\)
−0.0653618 + 0.997862i \(0.520820\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.22474 + 2.12132i −0.240192 + 0.416025i
\(27\) 0 0
\(28\) 2.62132 + 0.358719i 0.495383 + 0.0677916i
\(29\) 1.24264i 0.230753i 0.993322 + 0.115376i \(0.0368074\pi\)
−0.993322 + 0.115376i \(0.963193\pi\)
\(30\) 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
\(34\) 1.01461i 0.174005i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.12132 7.13834i 0.677541 1.17354i −0.298178 0.954510i \(-0.596379\pi\)
0.975719 0.219025i \(-0.0702877\pi\)
\(38\) 0.507306 + 0.878680i 0.0822959 + 0.142541i
\(39\) 0 0
\(40\) 0 0
\(41\) 2.02922 0.316912 0.158456 0.987366i \(-0.449348\pi\)
0.158456 + 0.987366i \(0.449348\pi\)
\(42\) 0 0
\(43\) −8.24264 −1.25699 −0.628495 0.777813i \(-0.716329\pi\)
−0.628495 + 0.777813i \(0.716329\pi\)
\(44\) −2.59808 1.50000i −0.391675 0.226134i
\(45\) 0 0
\(46\) −2.12132 3.67423i −0.312772 0.541736i
\(47\) 0.507306 0.878680i 0.0739982 0.128169i −0.826652 0.562713i \(-0.809757\pi\)
0.900650 + 0.434545i \(0.143091\pi\)
\(48\) 0 0
\(49\) −1.74264 6.77962i −0.248949 0.968517i
\(50\) 0 0
\(51\) 0 0
\(52\) 2.12132 1.22474i 0.294174 0.169842i
\(53\) −1.07616 + 0.621320i −0.147822 + 0.0853449i −0.572087 0.820193i \(-0.693866\pi\)
0.424265 + 0.905538i \(0.360533\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.09077 1.62132i −0.279391 0.216658i
\(57\) 0 0
\(58\) 0.621320 1.07616i 0.0815834 0.141307i
\(59\) −5.76500 9.98528i −0.750540 1.29997i −0.947561 0.319574i \(-0.896460\pi\)
0.197022 0.980399i \(-0.436873\pi\)
\(60\) 0 0
\(61\) 5.12132 + 2.95680i 0.655718 + 0.378579i 0.790643 0.612277i \(-0.209746\pi\)
−0.134926 + 0.990856i \(0.543080\pi\)
\(62\) −5.61642 −0.713286
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.00000 8.66025i −0.610847 1.05802i −0.991098 0.133135i \(-0.957496\pi\)
0.380251 0.924883i \(-0.375838\pi\)
\(68\) −0.507306 + 0.878680i −0.0615199 + 0.106556i
\(69\) 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
\(73\) −7.24264 + 4.18154i −0.847687 + 0.489412i −0.859870 0.510513i \(-0.829455\pi\)
0.0121828 + 0.999926i \(0.496122\pi\)
\(74\) −7.13834 + 4.12132i −0.829815 + 0.479094i
\(75\) 0 0
\(76\) 1.01461i 0.116384i
\(77\) −1.07616 + 7.86396i −0.122640 + 0.896182i
\(78\) 0 0
\(79\) 5.62132 9.73641i 0.632448 1.09543i −0.354602 0.935017i \(-0.615384\pi\)
0.987050 0.160415i \(-0.0512831\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.75736 1.01461i −0.194068 0.112045i
\(83\) 3.16693 0.347616 0.173808 0.984780i \(-0.444393\pi\)
0.173808 + 0.984780i \(0.444393\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.13834 + 4.12132i 0.769747 + 0.444413i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 5.19615 9.00000i 0.550791 0.953998i −0.447427 0.894321i \(-0.647659\pi\)
0.998218 0.0596775i \(-0.0190072\pi\)
\(90\) 0 0
\(91\) −5.12132 3.97141i −0.536860 0.416317i
\(92\) 4.24264i 0.442326i
\(93\) 0 0
\(94\) −0.878680 + 0.507306i −0.0906289 + 0.0523246i
\(95\) 0 0
\(96\) 0 0
\(97\) 3.76127i 0.381900i −0.981600 0.190950i \(-0.938843\pi\)
0.981600 0.190950i \(-0.0611568\pi\)
\(98\) −1.88064 + 6.74264i −0.189973 + 0.681110i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 13.2426 + 7.64564i 1.30484 + 0.753348i 0.981229 0.192844i \(-0.0617712\pi\)
0.323607 + 0.946192i \(0.395105\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) 1.24264 0.120696
\(107\) −4.75039 2.74264i −0.459238 0.265141i 0.252486 0.967601i \(-0.418752\pi\)
−0.711724 + 0.702459i \(0.752085\pi\)
\(108\) 0 0
\(109\) −0.757359 1.31178i −0.0725419 0.125646i 0.827473 0.561506i \(-0.189778\pi\)
−0.900015 + 0.435860i \(0.856444\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 + 2.44949i 0.0944911 + 0.231455i
\(113\) 8.48528i 0.798228i −0.916901 0.399114i \(-0.869318\pi\)
0.916901 0.399114i \(-0.130682\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.07616 + 0.621320i −0.0999188 + 0.0576881i
\(117\) 0 0
\(118\) 11.5300i 1.06142i
\(119\) 2.65962 + 0.363961i 0.243807 + 0.0333643i
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) −2.95680 5.12132i −0.267696 0.463663i
\(123\) 0 0
\(124\) 4.86396 + 2.80821i 0.436797 + 0.252185i
\(125\) 0 0
\(126\) 0 0
\(127\) 5.24264 0.465209 0.232605 0.972571i \(-0.425275\pi\)
0.232605 + 0.972571i \(0.425275\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −2.59808 + 4.50000i −0.226995 + 0.393167i −0.956916 0.290365i \(-0.906223\pi\)
0.729921 + 0.683531i \(0.239557\pi\)
\(132\) 0 0
\(133\) −2.48528 + 1.01461i −0.215501 + 0.0879780i
\(134\) 10.0000i 0.863868i
\(135\) 0 0
\(136\) 0.878680 0.507306i 0.0753462 0.0435011i
\(137\) −12.5446 + 7.24264i −1.07176 + 0.618781i −0.928662 0.370928i \(-0.879040\pi\)
−0.143098 + 0.989709i \(0.545706\pi\)
\(138\) 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
\(142\) 5.12132 8.87039i 0.429772 0.744386i
\(143\) 3.67423 + 6.36396i 0.307255 + 0.532181i
\(144\) 0 0
\(145\) 0 0
\(146\) 8.36308 0.692134
\(147\) 0 0
\(148\) 8.24264 0.677541
\(149\) −17.7408 10.2426i −1.45338 0.839110i −0.454709 0.890640i \(-0.650257\pi\)
−0.998671 + 0.0515300i \(0.983590\pi\)
\(150\) 0 0
\(151\) 1.62132 + 2.80821i 0.131941 + 0.228529i 0.924425 0.381364i \(-0.124546\pi\)
−0.792484 + 0.609893i \(0.791212\pi\)
\(152\) −0.507306 + 0.878680i −0.0411479 + 0.0712703i
\(153\) 0 0
\(154\) 4.86396 6.27231i 0.391949 0.505437i
\(155\) 0 0
\(156\) 0 0
\(157\) 12.7279 7.34847i 1.01580 0.586472i 0.102915 0.994690i \(-0.467183\pi\)
0.912884 + 0.408219i \(0.133850\pi\)
\(158\) −9.73641 + 5.62132i −0.774587 + 0.447208i
\(159\) 0 0
\(160\) 0 0
\(161\) 10.3923 4.24264i 0.819028 0.334367i
\(162\) 0 0
\(163\) 3.12132 5.40629i 0.244481 0.423453i −0.717505 0.696554i \(-0.754716\pi\)
0.961985 + 0.273101i \(0.0880492\pi\)
\(164\) 1.01461 + 1.75736i 0.0792279 + 0.137227i
\(165\) 0 0
\(166\) −2.74264 1.58346i −0.212870 0.122901i
\(167\) −23.0600 −1.78444 −0.892219 0.451603i \(-0.850852\pi\)
−0.892219 + 0.451603i \(0.850852\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) −4.12132 7.13834i −0.314248 0.544293i
\(173\) 10.3923 18.0000i 0.790112 1.36851i −0.135785 0.990738i \(-0.543356\pi\)
0.925897 0.377776i \(-0.123311\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) 0 0
\(178\) −9.00000 + 5.19615i −0.674579 + 0.389468i
\(179\) 8.23999 4.75736i 0.615886 0.355582i −0.159380 0.987217i \(-0.550949\pi\)
0.775265 + 0.631636i \(0.217616\pi\)
\(180\) 0 0
\(181\) 2.02922i 0.150831i 0.997152 + 0.0754155i \(0.0240283\pi\)
−0.997152 + 0.0754155i \(0.975972\pi\)
\(182\) 2.44949 + 6.00000i 0.181568 + 0.444750i
\(183\) 0 0
\(184\) 2.12132 3.67423i 0.156386 0.270868i
\(185\) 0 0
\(186\) 0 0
\(187\) −2.63604 1.52192i −0.192766 0.111294i
\(188\) 1.01461 0.0739982
\(189\) 0 0
\(190\) 0 0
\(191\) −7.34847 4.24264i −0.531717 0.306987i 0.209999 0.977702i \(-0.432654\pi\)
−0.741715 + 0.670715i \(0.765987\pi\)
\(192\) 0 0
\(193\) −3.74264 6.48244i −0.269401 0.466617i 0.699306 0.714822i \(-0.253492\pi\)
−0.968707 + 0.248206i \(0.920159\pi\)
\(194\) −1.88064 + 3.25736i −0.135022 + 0.233865i
\(195\) 0 0
\(196\) 5.00000 4.89898i 0.357143 0.349927i
\(197\) 9.51472i 0.677896i −0.940805 0.338948i \(-0.889929\pi\)
0.940805 0.338948i \(-0.110071\pi\)
\(198\) 0 0
\(199\) −13.9706 + 8.06591i −0.990347 + 0.571777i −0.905378 0.424607i \(-0.860412\pi\)
−0.0849690 + 0.996384i \(0.527079\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.59808 + 2.01472i 0.182349 + 0.141406i
\(204\) 0 0
\(205\) 0 0
\(206\) −7.64564 13.2426i −0.532697 0.922658i
\(207\) 0 0
\(208\) 2.12132 + 1.22474i 0.147087 + 0.0849208i
\(209\) 3.04384 0.210547
\(210\) 0 0
\(211\) 8.24264 0.567447 0.283723 0.958906i \(-0.408430\pi\)
0.283723 + 0.958906i \(0.408430\pi\)
\(212\) −1.07616 0.621320i −0.0739109 0.0426725i
\(213\) 0 0
\(214\) 2.74264 + 4.75039i 0.187483 + 0.324730i
\(215\) 0 0
\(216\) 0 0
\(217\) 2.01472 14.7224i 0.136768 0.999424i
\(218\) 1.51472i 0.102590i
\(219\) 0 0
\(220\) 0 0
\(221\) 2.15232 1.24264i 0.144780 0.0835891i
\(222\) 0 0
\(223\) 12.5446i 0.840050i 0.907513 + 0.420025i \(0.137979\pi\)
−0.907513 + 0.420025i \(0.862021\pi\)
\(224\) 0.358719 2.62132i 0.0239680 0.175144i
\(225\) 0 0
\(226\) −4.24264 + 7.34847i −0.282216 + 0.488813i
\(227\) −7.79423 13.5000i −0.517321 0.896026i −0.999798 0.0201176i \(-0.993596\pi\)
0.482476 0.875909i \(-0.339737\pi\)
\(228\) 0 0
\(229\) −12.0000 6.92820i −0.792982 0.457829i 0.0480291 0.998846i \(-0.484706\pi\)
−0.841011 + 0.541017i \(0.818039\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.24264 0.0815834
\(233\) 5.82655 + 3.36396i 0.381710 + 0.220380i 0.678562 0.734543i \(-0.262603\pi\)
−0.296852 + 0.954924i \(0.595937\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5.76500 9.98528i 0.375270 0.649986i
\(237\) 0 0
\(238\) −2.12132 1.64501i −0.137505 0.106630i
\(239\) 12.7279i 0.823301i 0.911342 + 0.411650i \(0.135048\pi\)
−0.911342 + 0.411650i \(0.864952\pi\)
\(240\) 0 0
\(241\) 14.7426 8.51167i 0.949657 0.548285i 0.0566826 0.998392i \(-0.481948\pi\)
0.892974 + 0.450108i \(0.148614\pi\)
\(242\) 1.73205 1.00000i 0.111340 0.0642824i
\(243\) 0 0
\(244\) 5.91359i 0.378579i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.24264 + 2.15232i −0.0790673 + 0.136949i
\(248\) −2.80821 4.86396i −0.178321 0.308862i
\(249\) 0 0
\(250\) 0 0
\(251\) −17.6177 −1.11202 −0.556009 0.831176i \(-0.687668\pi\)
−0.556009 + 0.831176i \(0.687668\pi\)
\(252\) 0 0
\(253\) −12.7279 −0.800198
\(254\) −4.54026 2.62132i −0.284881 0.164476i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 12.5446 21.7279i 0.782512 1.35535i −0.147962 0.988993i \(-0.547271\pi\)
0.930474 0.366358i \(-0.119395\pi\)
\(258\) 0 0
\(259\) −8.24264 20.1903i −0.512173 1.25456i
\(260\) 0 0
\(261\) 0 0
\(262\) 4.50000 2.59808i 0.278011 0.160510i
\(263\) 23.5673 13.6066i 1.45322 0.839019i 0.454561 0.890716i \(-0.349796\pi\)
0.998663 + 0.0516967i \(0.0164629\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.65962 + 0.363961i 0.163072 + 0.0223159i
\(267\) 0 0
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) 5.25770 + 9.10660i 0.320568 + 0.555239i 0.980605 0.195993i \(-0.0627930\pi\)
−0.660038 + 0.751232i \(0.729460\pi\)
\(270\) 0 0
\(271\) −9.62132 5.55487i −0.584454 0.337434i 0.178448 0.983949i \(-0.442892\pi\)
−0.762901 + 0.646515i \(0.776226\pi\)
\(272\) −1.01461 −0.0615199
\(273\) 0 0
\(274\) 14.4853 0.875088
\(275\) 0 0
\(276\) 0 0
\(277\) −10.4853 18.1610i −0.630000 1.09119i −0.987551 0.157298i \(-0.949722\pi\)
0.357552 0.933893i \(-0.383612\pi\)
\(278\) −10.0951 + 17.4853i −0.605466 + 1.04870i
\(279\) 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
\(283\) 5.63604 3.25397i 0.335028 0.193428i −0.323043 0.946384i \(-0.604706\pi\)
0.658071 + 0.752956i \(0.271373\pi\)
\(284\) −8.87039 + 5.12132i −0.526361 + 0.303894i
\(285\) 0 0
\(286\) 7.34847i 0.434524i
\(287\) 3.29002 4.24264i 0.194204 0.250435i
\(288\) 0 0
\(289\) 7.98528 13.8309i 0.469722 0.813583i
\(290\) 0 0
\(291\) 0 0
\(292\) −7.24264 4.18154i −0.423843 0.244706i
\(293\) −4.18154 −0.244288 −0.122144 0.992512i \(-0.538977\pi\)
−0.122144 + 0.992512i \(0.538977\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −7.13834 4.12132i −0.414907 0.239547i
\(297\) 0 0
\(298\) 10.2426 + 17.7408i 0.593340 + 1.02770i
\(299\) 5.19615 9.00000i 0.300501 0.520483i
\(300\) 0 0
\(301\) −13.3640 + 17.2335i −0.770286 + 0.993321i
\(302\) 3.24264i 0.186593i
\(303\) 0 0
\(304\) 0.878680 0.507306i 0.0503957 0.0290960i
\(305\) 0 0
\(306\) 0 0
\(307\) 24.6690i 1.40793i 0.710233 + 0.703966i \(0.248589\pi\)
−0.710233 + 0.703966i \(0.751411\pi\)
\(308\) −7.34847 + 3.00000i −0.418718 + 0.170941i
\(309\) 0 0
\(310\) 0 0
\(311\) −9.37769 16.2426i −0.531760 0.921036i −0.999313 0.0370703i \(-0.988197\pi\)
0.467552 0.883965i \(-0.345136\pi\)
\(312\) 0 0
\(313\) 0.985281 + 0.568852i 0.0556914 + 0.0321534i 0.527587 0.849501i \(-0.323097\pi\)
−0.471896 + 0.881654i \(0.656430\pi\)
\(314\) −14.6969 −0.829396
\(315\) 0 0
\(316\) 11.2426 0.632448
\(317\) 6.27231 + 3.62132i 0.352288 + 0.203394i 0.665693 0.746226i \(-0.268136\pi\)
−0.313404 + 0.949620i \(0.601470\pi\)
\(318\) 0 0
\(319\) −1.86396 3.22848i −0.104362 0.180760i
\(320\) 0 0
\(321\) 0 0
\(322\) −11.1213 1.52192i −0.619767 0.0848132i
\(323\) 1.02944i 0.0572794i
\(324\) 0 0
\(325\) 0 0
\(326\) −5.40629 + 3.12132i −0.299426 + 0.172874i
\(327\) 0 0
\(328\) 2.02922i 0.112045i
\(329\) −1.01461 2.48528i −0.0559374 0.137018i
\(330\) 0 0
\(331\) −8.72792 + 15.1172i −0.479730 + 0.830917i −0.999730 0.0232497i \(-0.992599\pi\)
0.520000 + 0.854166i \(0.325932\pi\)
\(332\) 1.58346 + 2.74264i 0.0869039 + 0.150522i
\(333\) 0 0
\(334\) 19.9706 + 11.5300i 1.09274 + 0.630894i
\(335\) 0 0
\(336\) 0 0
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) −6.06218 3.50000i −0.329739 0.190375i
\(339\) 0 0
\(340\) 0 0
\(341\) −8.42463 + 14.5919i −0.456219 + 0.790195i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 8.24264i 0.444413i
\(345\) 0 0
\(346\) −18.0000 + 10.3923i −0.967686 + 0.558694i
\(347\) 12.5446 7.24264i 0.673431 0.388805i −0.123945 0.992289i \(-0.539555\pi\)
0.797375 + 0.603484i \(0.206221\pi\)
\(348\) 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
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 9.37769 + 16.2426i 0.499124 + 0.864509i 0.999999 0.00101095i \(-0.000321796\pi\)
−0.500875 + 0.865519i \(0.666988\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.3923 0.550791
\(357\) 0 0
\(358\) −9.51472 −0.502869
\(359\) −15.5885 9.00000i −0.822727 0.475002i 0.0286287 0.999590i \(-0.490886\pi\)
−0.851356 + 0.524588i \(0.824219\pi\)
\(360\) 0 0
\(361\) −8.98528 15.5630i −0.472910 0.819103i
\(362\) 1.01461 1.75736i 0.0533268 0.0923648i
\(363\) 0 0
\(364\) 0.878680 6.42090i 0.0460553 0.336546i
\(365\) 0 0
\(366\) 0 0
\(367\) −16.3492 + 9.43924i −0.853424 + 0.492724i −0.861804 0.507241i \(-0.830666\pi\)
0.00838099 + 0.999965i \(0.497332\pi\)
\(368\) −3.67423 + 2.12132i −0.191533 + 0.110581i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.445759 + 3.25736i −0.0231427 + 0.169114i
\(372\) 0 0
\(373\) 10.7279 18.5813i 0.555471 0.962104i −0.442396 0.896820i \(-0.645871\pi\)
0.997867 0.0652837i \(-0.0207952\pi\)
\(374\) 1.52192 + 2.63604i 0.0786965 + 0.136306i
\(375\) 0 0
\(376\) −0.878680 0.507306i −0.0453144 0.0261623i
\(377\) 3.04384 0.156766
\(378\) 0 0
\(379\) −4.48528 −0.230393 −0.115197 0.993343i \(-0.536750\pi\)
−0.115197 + 0.993343i \(0.536750\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 4.24264 + 7.34847i 0.217072 + 0.375980i
\(383\) 6.21076 10.7574i 0.317355 0.549675i −0.662580 0.748991i \(-0.730539\pi\)
0.979935 + 0.199316i \(0.0638719\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 7.48528i 0.380991i
\(387\) 0 0
\(388\) 3.25736 1.88064i 0.165367 0.0954749i
\(389\) 16.8493 9.72792i 0.854291 0.493225i −0.00780525 0.999970i \(-0.502485\pi\)
0.862096 + 0.506744i \(0.169151\pi\)
\(390\) 0 0
\(391\) 4.30463i 0.217695i
\(392\) −6.77962 + 1.74264i −0.342422 + 0.0880166i
\(393\) 0 0
\(394\) −4.75736 + 8.23999i −0.239672 + 0.415125i
\(395\) 0 0
\(396\) 0 0
\(397\) −12.0000 6.92820i −0.602263 0.347717i 0.167668 0.985843i \(-0.446376\pi\)
−0.769931 + 0.638127i \(0.779710\pi\)
\(398\) 16.1318 0.808615
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) −6.87868 11.9142i −0.342651 0.593490i
\(404\) 0 0
\(405\) 0 0
\(406\) −1.24264 3.04384i −0.0616712 0.151063i
\(407\) 24.7279i 1.22572i
\(408\) 0 0
\(409\) −3.98528 + 2.30090i −0.197059 + 0.113772i −0.595283 0.803516i \(-0.702960\pi\)
0.398224 + 0.917288i \(0.369627\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 15.2913i 0.753348i
\(413\) −30.2238 4.13604i −1.48722 0.203521i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.22474 2.12132i −0.0600481 0.104006i
\(417\) 0 0
\(418\) −2.63604 1.52192i −0.128933 0.0744394i
\(419\) 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 \(0.544806\pi\)
\(422\) −7.13834 4.12132i −0.347489 0.200623i
\(423\) 0 0
\(424\) 0.621320 + 1.07616i 0.0301740 + 0.0522629i
\(425\) 0 0
\(426\) 0 0
\(427\) 14.4853 5.91359i 0.700992 0.286179i
\(428\) 5.48528i 0.265141i
\(429\) 0 0
\(430\) 0 0
\(431\) −17.7408 + 10.2426i −0.854543 + 0.493371i −0.862181 0.506600i \(-0.830902\pi\)
0.00763808 + 0.999971i \(0.497569\pi\)
\(432\) 0 0
\(433\) 3.46410i 0.166474i 0.996530 + 0.0832370i \(0.0265259\pi\)
−0.996530 + 0.0832370i \(0.973474\pi\)
\(434\) −9.10601 + 11.7426i −0.437103 + 0.563665i
\(435\) 0 0
\(436\) 0.757359 1.31178i 0.0362709 0.0628231i
\(437\) −2.15232 3.72792i −0.102959 0.178331i
\(438\) 0 0
\(439\) 23.5919 + 13.6208i 1.12598 + 0.650084i 0.942921 0.333018i \(-0.108067\pi\)
0.183059 + 0.983102i \(0.441400\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −2.48528 −0.118213
\(443\) −29.8396 17.2279i −1.41772 0.818523i −0.421625 0.906770i \(-0.638540\pi\)
−0.996099 + 0.0882469i \(0.971874\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 6.27231 10.8640i 0.297003 0.514423i
\(447\) 0 0
\(448\) −1.62132 + 2.09077i −0.0766002 + 0.0987796i
\(449\) 10.2426i 0.483380i 0.970354 + 0.241690i \(0.0777017\pi\)
−0.970354 + 0.241690i \(0.922298\pi\)
\(450\) 0 0
\(451\) −5.27208 + 3.04384i −0.248252 + 0.143329i
\(452\) 7.34847 4.24264i 0.345643 0.199557i
\(453\) 0 0
\(454\) 15.5885i 0.731603i
\(455\) 0 0
\(456\) 0 0
\(457\) −11.5000 + 19.9186i −0.537947 + 0.931752i 0.461067 + 0.887365i \(0.347467\pi\)
−0.999014 + 0.0443868i \(0.985867\pi\)
\(458\) 6.92820 + 12.0000i 0.323734 + 0.560723i
\(459\) 0 0
\(460\) 0 0
\(461\) 22.8138 1.06255 0.531273 0.847201i \(-0.321714\pi\)
0.531273 + 0.847201i \(0.321714\pi\)
\(462\) 0 0
\(463\) −21.4558 −0.997138 −0.498569 0.866850i \(-0.666141\pi\)
−0.498569 + 0.866850i \(0.666141\pi\)
\(464\) −1.07616 0.621320i −0.0499594 0.0288441i
\(465\) 0 0
\(466\) −3.36396 5.82655i −0.155832 0.269910i
\(467\) 9.50079 16.4558i 0.439644 0.761486i −0.558018 0.829829i \(-0.688438\pi\)
0.997662 + 0.0683432i \(0.0217713\pi\)
\(468\) 0 0
\(469\) −26.2132 3.58719i −1.21041 0.165641i
\(470\) 0 0
\(471\) 0 0
\(472\) −9.98528 + 5.76500i −0.459610 + 0.265356i
\(473\) 21.4150 12.3640i 0.984663 0.568496i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.01461 + 2.48528i 0.0465047 + 0.113913i
\(477\) 0 0
\(478\) 6.36396 11.0227i 0.291081 0.504167i
\(479\) 18.2481 + 31.6066i 0.833776 + 1.44414i 0.895023 + 0.446020i \(0.147159\pi\)
−0.0612470 + 0.998123i \(0.519508\pi\)
\(480\) 0 0
\(481\) −17.4853 10.0951i −0.797260 0.460298i
\(482\) −17.0233 −0.775392
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 0 0
\(487\) 14.1066 + 24.4334i 0.639231 + 1.10718i 0.985602 + 0.169083i \(0.0540806\pi\)
−0.346371 + 0.938098i \(0.612586\pi\)
\(488\) 2.95680 5.12132i 0.133848 0.231831i
\(489\) 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
\(493\) −1.09188 + 0.630399i −0.0491759 + 0.0283917i
\(494\) 2.15232 1.24264i 0.0968373 0.0559090i
\(495\) 0 0
\(496\) 5.61642i 0.252185i
\(497\) 21.4150 + 16.6066i 0.960594 + 0.744908i
\(498\) 0 0
\(499\) 17.9706 31.1259i 0.804473 1.39339i −0.112173 0.993689i \(-0.535781\pi\)
0.916646 0.399699i \(-0.130885\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 15.2574 + 8.80884i 0.680969 + 0.393158i
\(503\) −3.29002 −0.146695 −0.0733474 0.997306i \(-0.523368\pi\)
−0.0733474 + 0.997306i \(0.523368\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 11.0227 + 6.36396i 0.490019 + 0.282913i
\(507\) 0 0
\(508\) 2.62132 + 4.54026i 0.116302 + 0.201441i
\(509\) 20.8462 36.1066i 0.923990 1.60040i 0.130812 0.991407i \(-0.458242\pi\)
0.793178 0.608990i \(-0.208425\pi\)
\(510\) 0 0
\(511\) −3.00000 + 21.9223i −0.132712 + 0.969786i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −21.7279 + 12.5446i −0.958378 + 0.553320i
\(515\) 0 0
\(516\) 0 0
\(517\) 3.04384i 0.133868i
\(518\) −2.95680 + 21.6066i −0.129914 + 0.949340i
\(519\) 0 0
\(520\) 0 0
\(521\) 10.0081 + 17.3345i 0.438462 + 0.759439i 0.997571 0.0696551i \(-0.0221899\pi\)
−0.559109 + 0.829094i \(0.688857\pi\)
\(522\) 0 0
\(523\) 23.8492 + 13.7694i 1.04285 + 0.602092i 0.920641 0.390411i \(-0.127667\pi\)
0.122214 + 0.992504i \(0.461001\pi\)
\(524\) −5.19615 −0.226995
\(525\) 0 0
\(526\) −27.2132 −1.18655
\(527\) 4.93503 + 2.84924i 0.214973 + 0.124115i
\(528\) 0 0
\(529\) −2.50000 4.33013i −0.108696 0.188266i
\(530\) 0 0
\(531\) 0 0
\(532\) −2.12132 1.64501i −0.0919709 0.0713203i
\(533\) 4.97056i 0.215299i
\(534\) 0 0
\(535\) 0 0
\(536\) −8.66025 + 5.00000i −0.374066 + 0.215967i
\(537\) 0 0
\(538\) 10.5154i 0.453351i
\(539\) 14.6969 + 15.0000i 0.633042 + 0.646096i
\(540\) 0 0
\(541\) 5.36396 9.29065i 0.230615 0.399436i −0.727374 0.686241i \(-0.759260\pi\)
0.957989 + 0.286804i \(0.0925930\pi\)
\(542\) 5.55487 + 9.62132i 0.238602 + 0.413271i
\(543\) 0 0
\(544\) 0.878680 + 0.507306i 0.0376731 + 0.0217506i
\(545\) 0 0
\(546\) 0 0
\(547\) −19.6985 −0.842246 −0.421123 0.907003i \(-0.638364\pi\)
−0.421123 + 0.907003i \(0.638364\pi\)
\(548\) −12.5446 7.24264i −0.535880 0.309390i
\(549\) 0 0
\(550\) 0 0
\(551\) 0.630399 1.09188i 0.0268559 0.0465158i
\(552\) 0 0
\(553\) −11.2426 27.5387i −0.478086 1.17107i
\(554\) 20.9706i 0.890954i
\(555\) 0 0
\(556\) 17.4853 10.0951i 0.741541 0.428129i
\(557\) 13.6208 7.86396i 0.577131 0.333207i −0.182861 0.983139i \(-0.558536\pi\)
0.759992 + 0.649932i \(0.225203\pi\)
\(558\) 0 0
\(559\) 20.1903i 0.853957i
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 + 5.19615i −0.126547 + 0.219186i
\(563\) 12.0989 + 20.9558i 0.509906 + 0.883184i 0.999934 + 0.0114768i \(0.00365325\pi\)
−0.490028 + 0.871707i \(0.663013\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −6.50794 −0.273549
\(567\) 0 0
\(568\) 10.2426 0.429772
\(569\) −1.52192 0.878680i −0.0638021 0.0368362i 0.467760 0.883856i \(-0.345061\pi\)
−0.531562 + 0.847020i \(0.678395\pi\)
\(570\) 0 0
\(571\) 8.36396 + 14.4868i 0.350021 + 0.606254i 0.986253 0.165244i \(-0.0528412\pi\)
−0.636232 + 0.771498i \(0.719508\pi\)
\(572\) −3.67423 + 6.36396i −0.153627 + 0.266091i
\(573\) 0 0
\(574\) −4.97056 + 2.02922i −0.207467 + 0.0846982i
\(575\) 0 0
\(576\) 0 0
\(577\) −17.7426 + 10.2437i −0.738636 + 0.426452i −0.821573 0.570103i \(-0.806903\pi\)
0.0829373 + 0.996555i \(0.473570\pi\)
\(578\) −13.8309 + 7.98528i −0.575290 + 0.332144i
\(579\) 0 0
\(580\) 0 0
\(581\) 5.13461 6.62132i 0.213019 0.274699i
\(582\) 0 0
\(583\) 1.86396 3.22848i 0.0771974 0.133710i
\(584\) 4.18154 + 7.24264i 0.173033 + 0.299703i
\(585\) 0 0
\(586\) 3.62132 + 2.09077i 0.149595 + 0.0863689i
\(587\) −5.19615 −0.214468 −0.107234 0.994234i \(-0.534199\pi\)
−0.107234 + 0.994234i \(0.534199\pi\)
\(588\) 0 0
\(589\) −5.69848 −0.234802
\(590\) 0 0
\(591\) 0 0
\(592\) 4.12132 + 7.13834i 0.169385 + 0.293384i
\(593\) −15.2042 + 26.3345i −0.624363 + 1.08143i 0.364300 + 0.931282i \(0.381308\pi\)
−0.988664 + 0.150148i \(0.952025\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.4853i 0.839110i
\(597\) 0 0
\(598\) −9.00000 + 5.19615i −0.368037 + 0.212486i
\(599\) 37.6339 21.7279i 1.53768 0.887779i 0.538704 0.842495i \(-0.318914\pi\)
0.998974 0.0452836i \(-0.0144192\pi\)
\(600\) 0 0
\(601\) 6.03668i 0.246241i −0.992392 0.123121i \(-0.960710\pi\)
0.992392 0.123121i \(-0.0392902\pi\)
\(602\) 20.1903 8.24264i 0.822894 0.335945i
\(603\) 0 0
\(604\) −1.62132 + 2.80821i −0.0659706 + 0.114264i
\(605\) 0 0
\(606\) 0 0
\(607\) 21.6213 + 12.4831i 0.877582 + 0.506672i 0.869860 0.493298i \(-0.164209\pi\)
0.00772182 + 0.999970i \(0.497542\pi\)
\(608\) −1.01461 −0.0411479
\(609\) 0 0
\(610\) 0 0
\(611\) −2.15232 1.24264i −0.0870734 0.0502719i
\(612\) 0 0
\(613\) 2.60660 + 4.51477i 0.105280 + 0.182350i 0.913852 0.406046i \(-0.133093\pi\)
−0.808573 + 0.588396i \(0.799760\pi\)
\(614\) 12.3345 21.3640i 0.497779 0.862179i
\(615\) 0 0
\(616\) 7.86396 + 1.07616i 0.316848 + 0.0433597i
\(617\) 41.6985i 1.67872i 0.543578 + 0.839359i \(0.317069\pi\)
−0.543578 + 0.839359i \(0.682931\pi\)
\(618\) 0 0
\(619\) −41.3345 + 23.8645i −1.66137 + 0.959195i −0.689315 + 0.724462i \(0.742088\pi\)
−0.972060 + 0.234733i \(0.924578\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 18.7554i 0.752022i
\(623\) −10.3923 25.4558i −0.416359 1.01987i
\(624\) 0 0
\(625\) 0 0
\(626\) −0.568852 0.985281i −0.0227359 0.0393798i
\(627\) 0 0
\(628\) 12.7279 + 7.34847i 0.507899 + 0.293236i
\(629\) 8.36308 0.333458
\(630\) 0 0
\(631\) 33.2426 1.32337 0.661684 0.749783i \(-0.269842\pi\)
0.661684 + 0.749783i \(0.269842\pi\)
\(632\) −9.73641 5.62132i −0.387294 0.223604i
\(633\) 0 0
\(634\) −3.62132 6.27231i −0.143821 0.249105i
\(635\) 0 0
\(636\) 0 0
\(637\) −16.6066 + 4.26858i −0.657978 + 0.169127i
\(638\) 3.72792i 0.147590i
\(639\) 0 0
\(640\) 0 0
\(641\) 36.1119 20.8492i 1.42634 0.823496i 0.429507 0.903064i \(-0.358687\pi\)
0.996829 + 0.0795681i \(0.0253541\pi\)
\(642\) 0 0
\(643\) 2.62357i 0.103463i −0.998661 0.0517317i \(-0.983526\pi\)
0.998661 0.0517317i \(-0.0164741\pi\)
\(644\) 8.87039 + 6.87868i 0.349542 + 0.271058i
\(645\) 0 0
\(646\) −0.514719 + 0.891519i −0.0202513 + 0.0350763i
\(647\) −5.82655 10.0919i −0.229065 0.396753i 0.728466 0.685082i \(-0.240234\pi\)
−0.957531 + 0.288329i \(0.906900\pi\)
\(648\) 0 0
\(649\) 29.9558 + 17.2950i 1.17587 + 0.678889i
\(650\) 0 0
\(651\) 0 0
\(652\) 6.24264 0.244481
\(653\) −9.31615 5.37868i −0.364569 0.210484i 0.306514 0.951866i \(-0.400837\pi\)
−0.671083 + 0.741382i \(0.734171\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.01461 + 1.75736i −0.0396139 + 0.0686134i
\(657\) 0 0
\(658\) −0.363961 + 2.65962i −0.0141887 + 0.103683i
\(659\) 6.00000i 0.233727i −0.993148 0.116863i \(-0.962716\pi\)
0.993148 0.116863i \(-0.0372840\pi\)
\(660\) 0 0
\(661\) 35.1213 20.2773i 1.36606 0.788696i 0.375639 0.926766i \(-0.377423\pi\)
0.990422 + 0.138071i \(0.0440901\pi\)
\(662\) 15.1172 8.72792i 0.587547 0.339220i
\(663\) 0 0
\(664\) 3.16693i 0.122901i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.63604 + 4.56575i −0.102068 + 0.176787i
\(668\) −11.5300 19.9706i −0.446109 0.772684i
\(669\) 0 0
\(670\) 0 0
\(671\) −17.7408 −0.684875
\(672\) 0 0
\(673\) 15.9706 0.615620 0.307810 0.951448i \(-0.400404\pi\)
0.307810 + 0.951448i \(0.400404\pi\)
\(674\) −4.33013 2.50000i −0.166790 0.0962964i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) 6.27231 10.8640i 0.241064 0.417536i −0.719953 0.694023i \(-0.755837\pi\)
0.961018 + 0.276487i \(0.0891701\pi\)
\(678\) 0 0
\(679\) −7.86396 6.09823i −0.301791 0.234029i
\(680\) 0 0
\(681\) 0 0
\(682\) 14.5919 8.42463i 0.558752 0.322596i
\(683\) −22.4912 + 12.9853i −0.860601 + 0.496868i −0.864213 0.503125i \(-0.832183\pi\)
0.00361277 + 0.999993i \(0.498850\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 11.0482 + 14.8640i 0.421822 + 0.567509i
\(687\) 0 0
\(688\) 4.12132 7.13834i 0.157124 0.272147i
\(689\) 1.52192 + 2.63604i 0.0579805 + 0.100425i
\(690\) 0 0
\(691\) −0.727922 0.420266i −0.0276915 0.0159877i 0.486090 0.873909i \(-0.338423\pi\)
−0.513782 + 0.857921i \(0.671756\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) −14.4853 −0.549854
\(695\) 0 0
\(696\) 0 0
\(697\) 1.02944 + 1.78304i 0.0389927 + 0.0675374i
\(698\) 18.4582 31.9706i 0.698654 1.21010i
\(699\) 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
\(703\) −7.24264 + 4.18154i −0.273161 + 0.157710i
\(704\) 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 \(-0.791549\pi\)
0.924021 + 0.382342i \(0.124882\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.00000 5.19615i −0.337289 0.194734i
\(713\) 23.8284 0.892382
\(714\) 0 0
\(715\) 0 0
\(716\) 8.23999 + 4.75736i 0.307943 + 0.177791i
\(717\) 0 0
\(718\) 9.00000 + 15.5885i 0.335877 + 0.581756i
\(719\) 11.5300 19.9706i 0.429997 0.744776i −0.566876 0.823803i \(-0.691848\pi\)
0.996872 + 0.0790270i \(0.0251813\pi\)
\(720\) 0 0
\(721\) 37.4558 15.2913i 1.39493 0.569477i
\(722\) 17.9706i 0.668795i
\(723\) 0 0
\(724\) −1.75736 + 1.01461i −0.0653117 + 0.0377078i
\(725\) 0 0
\(726\) 0 0
\(727\) 26.4010i 0.979160i 0.871958 + 0.489580i \(0.162850\pi\)
−0.871958 + 0.489580i \(0.837150\pi\)
\(728\) −3.97141 + 5.12132i −0.147190 + 0.189809i
\(729\) 0 0
\(730\) 0 0
\(731\) −4.18154 7.24264i −0.154660 0.267879i
\(732\) 0 0
\(733\) 34.0919 + 19.6830i 1.25921 + 0.727007i 0.972921 0.231136i \(-0.0742443\pi\)
0.286291 + 0.958143i \(0.407578\pi\)
\(734\) 18.8785 0.696817
\(735\) 0 0
\(736\) 4.24264 0.156386
\(737\) 25.9808 + 15.0000i 0.957014 + 0.552532i
\(738\) 0 0
\(739\) 17.7279 + 30.7057i 0.652132 + 1.12953i 0.982605 + 0.185710i \(0.0594586\pi\)
−0.330472 + 0.943816i \(0.607208\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.01472 2.59808i 0.0739626 0.0953784i
\(743\) 21.5147i 0.789298i 0.918832 + 0.394649i \(0.129134\pi\)
−0.918832 + 0.394649i \(0.870866\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −18.5813 + 10.7279i −0.680310 + 0.392777i
\(747\) 0 0
\(748\) 3.04384i 0.111294i
\(749\) −13.4361 + 5.48528i −0.490946 + 0.200428i
\(750\) 0 0
\(751\) −13.3787 + 23.1726i −0.488195 + 0.845578i −0.999908 0.0135781i \(-0.995678\pi\)
0.511713 + 0.859157i \(0.329011\pi\)
\(752\) 0.507306 + 0.878680i 0.0184995 + 0.0320422i
\(753\) 0 0
\(754\) −2.63604 1.52192i −0.0959989 0.0554250i
\(755\) 0 0
\(756\) 0 0
\(757\) 42.2426 1.53533 0.767667 0.640848i \(-0.221417\pi\)
0.767667 + 0.640848i \(0.221417\pi\)
\(758\) 3.88437 + 2.24264i 0.141087 + 0.0814564i
\(759\) 0 0
\(760\) 0 0
\(761\) −2.53653 + 4.39340i −0.0919491 + 0.159261i −0.908331 0.418252i \(-0.862643\pi\)
0.816382 + 0.577512i \(0.195976\pi\)
\(762\) 0 0
\(763\) −3.97056 0.543359i −0.143744 0.0196709i
\(764\) 8.48528i 0.306987i
\(765\) 0 0
\(766\) −10.7574 + 6.21076i −0.388679 + 0.224404i
\(767\) −24.4588 + 14.1213i −0.883158 + 0.509891i
\(768\) 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
\(772\) 3.74264 6.48244i 0.134701 0.233308i
\(773\) 11.5300 + 19.9706i 0.414706 + 0.718291i 0.995398 0.0958322i \(-0.0305512\pi\)
−0.580692 + 0.814123i \(0.697218\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −3.76127 −0.135022
\(777\) 0 0
\(778\) −19.4558 −0.697526
\(779\) −1.78304 1.02944i −0.0638840 0.0368834i
\(780\) 0 0
\(781\) −15.3640 26.6112i −0.549766 0.952222i
\(782\) 2.15232 3.72792i 0.0769667 0.133310i
\(783\) 0 0
\(784\) 6.74264 + 1.88064i 0.240809 + 0.0671656i
\(785\) 0 0
\(786\) 0 0
\(787\) −32.1213 + 18.5453i −1.14500 + 0.661067i −0.947664 0.319269i \(-0.896563\pi\)
−0.197337 + 0.980336i \(0.563229\pi\)
\(788\) 8.23999 4.75736i 0.293537 0.169474i
\(789\) 0 0
\(790\) 0 0
\(791\) −17.7408 13.7574i −0.630789 0.489155i
\(792\) 0 0
\(793\) 7.24264 12.5446i 0.257194 0.445473i
\(794\) 6.92820 + 12.0000i 0.245873 + 0.425864i
\(795\) 0 0
\(796\) −13.9706 8.06591i −0.495173 0.285889i