Properties

Label 3150.2.bf.a.1151.4
Level 3150
Weight 2
Character 3150.1151
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 1151.4
Root \(-0.258819 - 0.965926i\)
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.a.1601.4

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 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 \(-0.183949\pi\)
−0.0542666 + 0.998526i \(0.517282\pi\)
\(12\) 0 0
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) 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 \(-0.872598\pi\)
0.797925 + 0.602756i \(0.205931\pi\)
\(18\) 0 0
\(19\) −0.878680 + 0.507306i −0.201583 + 0.116384i −0.597394 0.801948i \(-0.703797\pi\)
0.395811 + 0.918332i \(0.370464\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) −3.67423 + 2.12132i −0.766131 + 0.442326i −0.831493 0.555536i \(-0.812513\pi\)
0.0653618 + 0.997862i \(0.479180\pi\)
\(24\) 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 0.868541 0.495618i \(-0.165058\pi\)
0.00505256 + 0.999987i \(0.498392\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 1.01461i 0.174005i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.12132 + 7.13834i 0.677541 + 1.17354i 0.975719 + 0.219025i \(0.0702877\pi\)
−0.298178 + 0.954510i \(0.596379\pi\)
\(38\) −0.507306 + 0.878680i −0.0822959 + 0.142541i
\(39\) 0 0
\(40\) 0 0
\(41\) −2.02922 −0.316912 −0.158456 0.987366i \(-0.550652\pi\)
−0.158456 + 0.987366i \(0.550652\pi\)
\(42\) 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 \(-0.190243\pi\)
−0.900650 + 0.434545i \(0.856909\pi\)
\(48\) 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 \(-0.306134\pi\)
−0.424265 + 0.905538i \(0.639467\pi\)
\(54\) 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 −0.197022 0.980399i \(-0.563127\pi\)
0.947561 0.319574i \(-0.103540\pi\)
\(60\) 0 0
\(61\) 5.12132 2.95680i 0.655718 0.378579i −0.134926 0.990856i \(-0.543080\pi\)
0.790643 + 0.612277i \(0.209746\pi\)
\(62\) 5.61642 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 0.380251 + 0.924883i \(0.375838\pi\)
−0.991098 + 0.133135i \(0.957496\pi\)
\(68\) 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 0.0121828 0.999926i \(-0.496122\pi\)
−0.859870 + 0.510513i \(0.829455\pi\)
\(74\) 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 0.987050 + 0.160415i \(0.0512831\pi\)
−0.354602 + 0.935017i \(0.615384\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.75736 + 1.01461i −0.194068 + 0.112045i
\(83\) −3.16693 −0.347616 −0.173808 0.984780i \(-0.555607\pi\)
−0.173808 + 0.984780i \(0.555607\pi\)
\(84\) 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 −0.998218 0.0596775i \(-0.980993\pi\)
0.447427 0.894321i \(-0.352341\pi\)
\(90\) 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 \(0.0611568\pi\)
−0.981600 + 0.190950i \(0.938843\pi\)
\(98\) 1.88064 + 6.74264i 0.189973 + 0.681110i
\(99\) 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
\(103\) 13.2426 7.64564i 1.30484 0.753348i 0.323607 0.946192i \(-0.395105\pi\)
0.981229 + 0.192844i \(0.0617712\pi\)
\(104\) 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 \(-0.581248\pi\)
0.711724 + 0.702459i \(0.247915\pi\)
\(108\) 0 0
\(109\) −0.757359 + 1.31178i −0.0725419 + 0.125646i −0.900015 0.435860i \(-0.856444\pi\)
0.827473 + 0.561506i \(0.189778\pi\)
\(110\) 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 \(-0.0937766\pi\)
−0.729921 + 0.683531i \(0.760443\pi\)
\(132\) 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 \(-0.120960\pi\)
0.143098 + 0.989709i \(0.454294\pi\)
\(138\) 0 0
\(139\) 20.1903i 1.71252i 0.516549 + 0.856258i \(0.327217\pi\)
−0.516549 + 0.856258i \(0.672783\pi\)
\(140\) 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 \(-0.349743\pi\)
0.998671 + 0.0515300i \(0.0164098\pi\)
\(150\) 0 0
\(151\) 1.62132 2.80821i 0.131941 0.228529i −0.792484 0.609893i \(-0.791212\pi\)
0.924425 + 0.381364i \(0.124546\pi\)
\(152\) 0.507306 + 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 0.912884 0.408219i \(-0.133850\pi\)
0.102915 + 0.994690i \(0.467183\pi\)
\(158\) 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 0.961985 0.273101i \(-0.0880492\pi\)
−0.717505 + 0.696554i \(0.754716\pi\)
\(164\) −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 \(-0.149148\pi\)
0.892219 + 0.451603i \(0.149148\pi\)
\(168\) 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 −0.925897 0.377776i \(-0.876689\pi\)
0.135785 0.990738i \(-0.456644\pi\)
\(174\) 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 \(-0.449051\pi\)
−0.775265 + 0.631636i \(0.782384\pi\)
\(180\) 0 0
\(181\) 2.02922i 0.150831i −0.997152 0.0754155i \(-0.975972\pi\)
0.997152 0.0754155i \(-0.0240283\pi\)
\(182\) −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 \(-0.567346\pi\)
0.741715 + 0.670715i \(0.234013\pi\)
\(192\) 0 0
\(193\) −3.74264 + 6.48244i −0.269401 + 0.466617i −0.968707 0.248206i \(-0.920159\pi\)
0.699306 + 0.714822i \(0.253492\pi\)
\(194\) 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 −0.0849690 0.996384i \(-0.527079\pi\)
−0.905378 + 0.424607i \(0.860412\pi\)
\(200\) 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 \(-0.862021\pi\)
0.907513 0.420025i \(-0.137979\pi\)
\(224\) −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 −0.482476 0.875909i \(-0.660263\pi\)
0.999798 0.0201176i \(-0.00640405\pi\)
\(228\) 0 0
\(229\) −12.0000 + 6.92820i −0.792982 + 0.457829i −0.841011 0.541017i \(-0.818039\pi\)
0.0480291 + 0.998846i \(0.484706\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.24264 0.0815834
\(233\) −5.82655 + 3.36396i −0.381710 + 0.220380i −0.678562 0.734543i \(-0.737397\pi\)
0.296852 + 0.954924i \(0.404063\pi\)
\(234\) 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 0.892974 0.450108i \(-0.148614\pi\)
0.0566826 + 0.998392i \(0.481948\pi\)
\(242\) −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 \(-0.312332\pi\)
0.556009 + 0.831176i \(0.312332\pi\)
\(252\) 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 −0.930474 0.366358i \(-0.880605\pi\)
0.147962 0.988993i \(-0.452729\pi\)
\(258\) 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 \(-0.650204\pi\)
−0.998663 + 0.0516967i \(0.983537\pi\)
\(264\) 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 \(-0.937207\pi\)
0.660038 + 0.751232i \(0.270540\pi\)
\(270\) 0 0
\(271\) −9.62132 + 5.55487i −0.584454 + 0.337434i −0.762901 0.646515i \(-0.776226\pi\)
0.178448 + 0.983949i \(0.442892\pi\)
\(272\) 1.01461 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 0.357552 + 0.933893i \(0.383612\pi\)
−0.987551 + 0.157298i \(0.949722\pi\)
\(278\) 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 0.658071 0.752956i \(-0.271373\pi\)
−0.323043 + 0.946384i \(0.604706\pi\)
\(284\) 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 \(-0.461023\pi\)
0.122144 + 0.992512i \(0.461023\pi\)
\(294\) 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 \(-0.751411\pi\)
0.710233 0.703966i \(-0.248589\pi\)
\(308\) 7.34847 + 3.00000i 0.418718 + 0.170941i
\(309\) 0 0
\(310\) 0 0
\(311\) 9.37769 16.2426i 0.531760 0.921036i −0.467552 0.883965i \(-0.654864\pi\)
0.999313 0.0370703i \(-0.0118026\pi\)
\(312\) 0 0
\(313\) 0.985281 0.568852i 0.0556914 0.0321534i −0.471896 0.881654i \(-0.656430\pi\)
0.527587 + 0.849501i \(0.323097\pi\)
\(314\) 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 \(-0.731864\pi\)
0.313404 + 0.949620i \(0.398530\pi\)
\(318\) 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 0.520000 0.854166i \(-0.325932\pi\)
−0.999730 + 0.0232497i \(0.992599\pi\)
\(332\) −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 \(-0.460445\pi\)
−0.797375 + 0.603484i \(0.793779\pi\)
\(348\) 0 0
\(349\) 36.9164i 1.97609i −0.154163 0.988045i \(-0.549268\pi\)
0.154163 0.988045i \(-0.450732\pi\)
\(350\) 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 \(-0.999678\pi\)
0.500875 + 0.865519i \(0.333012\pi\)
\(354\) 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 \(-0.509114\pi\)
0.851356 + 0.524588i \(0.175781\pi\)
\(360\) 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 0.00838099 0.999965i \(-0.497332\pi\)
−0.861804 + 0.507241i \(0.830666\pi\)
\(368\) 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 0.997867 + 0.0652837i \(0.0207952\pi\)
−0.442396 + 0.896820i \(0.645871\pi\)
\(374\) −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 \(-0.269461\pi\)
−0.979935 + 0.199316i \(0.936128\pi\)
\(384\) 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 \(-0.497515\pi\)
−0.862096 + 0.506744i \(0.830849\pi\)
\(390\) 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 −0.769931 0.638127i \(-0.779710\pi\)
0.167668 + 0.985843i \(0.446376\pi\)
\(398\) −16.1318 −0.808615
\(399\) 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
\(403\) −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 0.398224 0.917288i \(-0.369627\pi\)
−0.595283 + 0.803516i \(0.702960\pi\)
\(410\) 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 \(-0.531607\pi\)
−0.0991341 + 0.995074i \(0.531607\pi\)
\(420\) 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 \(-0.169098\pi\)
−0.00763808 + 0.999971i \(0.502431\pi\)
\(432\) 0 0
\(433\) 3.46410i 0.166474i −0.996530 0.0832370i \(-0.973474\pi\)
0.996530 0.0832370i \(-0.0265259\pi\)
\(434\) 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 0.183059 0.983102i \(-0.441400\pi\)
0.942921 + 0.333018i \(0.108067\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −2.48528 −0.118213
\(443\) 29.8396 17.2279i 1.41772 0.818523i 0.421625 0.906770i \(-0.361460\pi\)
0.996099 + 0.0882469i \(0.0281264\pi\)
\(444\) 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 −0.999014 0.0443868i \(-0.985867\pi\)
0.461067 0.887365i \(-0.347467\pi\)
\(458\) −6.92820 + 12.0000i −0.323734 + 0.560723i
\(459\) 0 0
\(460\) 0 0
\(461\) −22.8138 −1.06255 −0.531273 0.847201i \(-0.678286\pi\)
−0.531273 + 0.847201i \(0.678286\pi\)
\(462\) 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 \(-0.311562\pi\)
−0.997662 + 0.0683432i \(0.978229\pi\)
\(468\) 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 0.0612470 + 0.998123i \(0.480492\pi\)
−0.895023 + 0.446020i \(0.852841\pi\)
\(480\) 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 −0.346371 0.938098i \(-0.612586\pi\)
0.985602 0.169083i \(-0.0540806\pi\)
\(488\) −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 0.916646 + 0.399699i \(0.130885\pi\)
−0.112173 + 0.993689i \(0.535781\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 15.2574 8.80884i 0.680969 0.393158i
\(503\) 3.29002 0.146695 0.0733474 0.997306i \(-0.476632\pi\)
0.0733474 + 0.997306i \(0.476632\pi\)
\(504\) 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 −0.793178 0.608990i \(-0.791575\pi\)
−0.130812 0.991407i \(-0.541758\pi\)
\(510\) 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 \(-0.977810\pi\)
0.559109 + 0.829094i \(0.311143\pi\)
\(522\) 0 0
\(523\) 23.8492 13.7694i 1.04285 0.602092i 0.122214 0.992504i \(-0.461001\pi\)
0.920641 + 0.390411i \(0.127667\pi\)
\(524\) 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 0.957989 0.286804i \(-0.0925930\pi\)
−0.727374 + 0.686241i \(0.759260\pi\)
\(542\) −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 \(-0.441464\pi\)
−0.759992 + 0.649932i \(0.774797\pi\)
\(558\) 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 0.490028 + 0.871707i \(0.336987\pi\)
−0.999934 + 0.0114768i \(0.996347\pi\)
\(564\) 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 \(-0.654939\pi\)
0.531562 + 0.847020i \(0.321605\pi\)
\(570\) 0 0
\(571\) 8.36396 14.4868i 0.350021 0.606254i −0.636232 0.771498i \(-0.719508\pi\)
0.986253 + 0.165244i \(0.0528412\pi\)
\(572\) 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 0.0829373 0.996555i \(-0.473570\pi\)
−0.821573 + 0.570103i \(0.806903\pi\)
\(578\) 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 \(-0.465801\pi\)
0.107234 + 0.994234i \(0.465801\pi\)
\(588\) 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 0.988664 + 0.150148i \(0.0479749\pi\)
−0.364300 + 0.931282i \(0.618692\pi\)
\(594\) 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 −0.998974 0.0452836i \(-0.985581\pi\)
−0.538704 0.842495i \(-0.681086\pi\)
\(600\) 0 0
\(601\) 6.03668i 0.246241i 0.992392 + 0.123121i \(0.0392902\pi\)
−0.992392 + 0.123121i \(0.960710\pi\)
\(602\) −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 0.00772182 0.999970i \(-0.497542\pi\)
0.869860 + 0.493298i \(0.164209\pi\)
\(608\) 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 −0.808573 0.588396i \(-0.799760\pi\)
0.913852 + 0.406046i \(0.133093\pi\)
\(614\) −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 −0.972060 0.234733i \(-0.924578\pi\)
−0.689315 0.724462i \(-0.742088\pi\)
\(620\) 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 \(-0.641313\pi\)
−0.996829 + 0.0795681i \(0.974646\pi\)
\(642\) 0 0
\(643\) 2.62357i 0.103463i 0.998661 + 0.0517317i \(0.0164741\pi\)
−0.998661 + 0.0517317i \(0.983526\pi\)
\(644\) −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 \(-0.759766\pi\)
0.957531 + 0.288329i \(0.0930997\pi\)
\(648\) 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 \(-0.599163\pi\)
0.671083 + 0.741382i \(0.265829\pi\)
\(654\) 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 0.990422 0.138071i \(-0.0440901\pi\)
0.375639 + 0.926766i \(0.377423\pi\)
\(662\) −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 \(-0.244163\pi\)
−0.961018 + 0.276487i \(0.910830\pi\)
\(678\) 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 \(-0.167817\pi\)
−0.00361277 + 0.999993i \(0.501150\pi\)
\(684\) 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 −0.513782 0.857921i \(-0.671756\pi\)
0.486090 + 0.873909i \(0.338423\pi\)
\(692\) −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 0.924021 0.382342i \(-0.124882\pi\)
−0.793128 + 0.609055i \(0.791549\pi\)
\(710\) 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 \(-0.308152\pi\)
−0.996872 + 0.0790270i \(0.974819\pi\)
\(720\) 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 \(-0.837150\pi\)
0.871958 0.489580i \(-0.162850\pi\)
\(728\) 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 0.286291 0.958143i \(-0.407578\pi\)
0.972921 + 0.231136i \(0.0742443\pi\)
\(734\) −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 −0.330472 0.943816i \(-0.607208\pi\)
0.982605 0.185710i \(-0.0594586\pi\)
\(740\) 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 0.511713 0.859157i \(-0.329011\pi\)
−0.999908 + 0.0135781i \(0.995678\pi\)
\(752\) −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 \(-0.137357\pi\)
−0.816382 + 0.577512i \(0.804024\pi\)
\(762\) 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 \(-0.654685\pi\)
0.467056 0.884228i \(-0.345315\pi\)
\(770\) 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 \(-0.969449\pi\)
0.580692 + 0.814123i \(0.302782\pi\)
\(774\) 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 −0.197337 0.980336i \(-0.563229\pi\)
−0.947664 + 0.319269i \(0.896563\pi\)
\(788\) −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