Properties

Label 3150.2.bf.a.1601.1
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 1601.1
Root \(-0.965926 - 0.258819i\)
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.a.1151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.62132 + 0.358719i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.62132 + 0.358719i) q^{7} -1.00000i q^{8} +(-2.59808 + 1.50000i) q^{11} +2.44949i q^{13} +(2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.95680 + 5.12132i) q^{17} +(-5.12132 - 2.95680i) q^{19} +3.00000 q^{22} +(-3.67423 - 2.12132i) q^{23} +(1.22474 - 2.12132i) q^{26} +(-1.62132 - 2.09077i) q^{28} -7.24264i q^{29} +(-7.86396 + 4.54026i) q^{31} +(0.866025 - 0.500000i) q^{32} -5.91359i q^{34} +(-0.121320 + 0.210133i) q^{37} +(2.95680 + 5.12132i) q^{38} +11.8272 q^{41} +0.242641 q^{43} +(-2.59808 - 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} +(2.95680 - 5.12132i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-2.12132 + 1.22474i) q^{52} +(6.27231 - 3.62132i) q^{53} +(0.358719 + 2.62132i) q^{56} +(-3.62132 + 6.27231i) q^{58} +(4.03295 + 6.98528i) q^{59} +(0.878680 + 0.507306i) q^{61} +9.08052 q^{62} -1.00000 q^{64} +(-5.00000 - 8.66025i) q^{67} +(-2.95680 + 5.12132i) q^{68} +1.75736i q^{71} +(1.24264 - 0.717439i) q^{73} +(0.210133 - 0.121320i) q^{74} -5.91359i q^{76} +(6.27231 - 4.86396i) q^{77} +(1.37868 - 2.38794i) q^{79} +(-10.2426 - 5.91359i) q^{82} -6.63103 q^{83} +(-0.210133 - 0.121320i) q^{86} +(1.50000 + 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-0.878680 - 6.42090i) q^{91} -4.24264i q^{92} +(-5.12132 + 2.95680i) q^{94} -13.5592i q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{7} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{7} - 4q^{16} - 24q^{19} + 24q^{22} + 4q^{28} - 12q^{31} + 16q^{37} - 32q^{43} + 20q^{49} - 12q^{58} + 24q^{61} - 8q^{64} - 40q^{67} - 24q^{73} + 28q^{79} - 48q^{82} + 12q^{88} - 24q^{91} - 24q^{94} + O(q^{100}) \)

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
\(7\) −2.62132 + 0.358719i −0.990766 + 0.135583i
\(8\) 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 \(0.110320\pi\)
−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
\(17\) 2.95680 + 5.12132i 0.717128 + 1.24210i 0.962133 + 0.272581i \(0.0878772\pi\)
−0.245005 + 0.969522i \(0.578789\pi\)
\(18\) 0 0
\(19\) −5.12132 2.95680i −1.17491 0.678335i −0.220080 0.975482i \(-0.570632\pi\)
−0.954832 + 0.297146i \(0.903965\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) −3.67423 2.12132i −0.766131 0.442326i 0.0653618 0.997862i \(-0.479180\pi\)
−0.831493 + 0.555536i \(0.812513\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.22474 2.12132i 0.240192 0.416025i
\(27\) 0 0
\(28\) −1.62132 2.09077i −0.306401 0.395118i
\(29\) 7.24264i 1.34492i −0.740131 0.672462i \(-0.765237\pi\)
0.740131 0.672462i \(-0.234763\pi\)
\(30\) 0 0
\(31\) −7.86396 + 4.54026i −1.41241 + 0.815455i −0.995615 0.0935461i \(-0.970180\pi\)
−0.416794 + 0.909001i \(0.636846\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 5.91359i 1.01417i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.121320 + 0.210133i −0.0199449 + 0.0345457i −0.875826 0.482628i \(-0.839682\pi\)
0.855881 + 0.517173i \(0.173016\pi\)
\(38\) 2.95680 + 5.12132i 0.479656 + 0.830788i
\(39\) 0 0
\(40\) 0 0
\(41\) 11.8272 1.84710 0.923548 0.383483i \(-0.125276\pi\)
0.923548 + 0.383483i \(0.125276\pi\)
\(42\) 0 0
\(43\) 0.242641 0.0370024 0.0185012 0.999829i \(-0.494111\pi\)
0.0185012 + 0.999829i \(0.494111\pi\)
\(44\) −2.59808 1.50000i −0.391675 0.226134i
\(45\) 0 0
\(46\) 2.12132 + 3.67423i 0.312772 + 0.541736i
\(47\) 2.95680 5.12132i 0.431293 0.747021i −0.565692 0.824617i \(-0.691391\pi\)
0.996985 + 0.0775953i \(0.0247242\pi\)
\(48\) 0 0
\(49\) 6.74264 1.88064i 0.963234 0.268662i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.12132 + 1.22474i −0.294174 + 0.169842i
\(53\) 6.27231 3.62132i 0.861568 0.497427i −0.00296896 0.999996i \(-0.500945\pi\)
0.864537 + 0.502569i \(0.167612\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.358719 + 2.62132i 0.0479359 + 0.350289i
\(57\) 0 0
\(58\) −3.62132 + 6.27231i −0.475503 + 0.823595i
\(59\) 4.03295 + 6.98528i 0.525046 + 0.909406i 0.999575 + 0.0291661i \(0.00928518\pi\)
−0.474529 + 0.880240i \(0.657381\pi\)
\(60\) 0 0
\(61\) 0.878680 + 0.507306i 0.112503 + 0.0649539i 0.555196 0.831720i \(-0.312643\pi\)
−0.442692 + 0.896674i \(0.645977\pi\)
\(62\) 9.08052 1.15323
\(63\) 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 \(-0.375838\pi\)
\(68\) −2.95680 + 5.12132i −0.358564 + 0.621051i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.75736i 0.208560i 0.994548 + 0.104280i \(0.0332538\pi\)
−0.994548 + 0.104280i \(0.966746\pi\)
\(72\) 0 0
\(73\) 1.24264 0.717439i 0.145440 0.0839699i −0.425514 0.904952i \(-0.639907\pi\)
0.570954 + 0.820982i \(0.306573\pi\)
\(74\) 0.210133 0.121320i 0.0244275 0.0141032i
\(75\) 0 0
\(76\) 5.91359i 0.678335i
\(77\) 6.27231 4.86396i 0.714796 0.554300i
\(78\) 0 0
\(79\) 1.37868 2.38794i 0.155114 0.268665i −0.777987 0.628281i \(-0.783759\pi\)
0.933100 + 0.359616i \(0.117092\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −10.2426 5.91359i −1.13111 0.653047i
\(83\) −6.63103 −0.727850 −0.363925 0.931428i \(-0.618564\pi\)
−0.363925 + 0.931428i \(0.618564\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.210133 0.121320i −0.0226592 0.0130823i
\(87\) 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
\(91\) −0.878680 6.42090i −0.0921107 0.673093i
\(92\) 4.24264i 0.442326i
\(93\) 0 0
\(94\) −5.12132 + 2.95680i −0.528224 + 0.304970i
\(95\) 0 0
\(96\) 0 0
\(97\) 13.5592i 1.37673i −0.725364 0.688366i \(-0.758328\pi\)
0.725364 0.688366i \(-0.241672\pi\)
\(98\) −6.77962 1.74264i −0.684845 0.176033i
\(99\) 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
\(103\) 4.75736 + 2.74666i 0.468757 + 0.270637i 0.715719 0.698388i \(-0.246099\pi\)
−0.246963 + 0.969025i \(0.579432\pi\)
\(104\) 2.44949 0.240192
\(105\) 0 0
\(106\) −7.24264 −0.703467
\(107\) 9.94655 + 5.74264i 0.961569 + 0.555162i 0.896656 0.442729i \(-0.145990\pi\)
0.0649133 + 0.997891i \(0.479323\pi\)
\(108\) 0 0
\(109\) −9.24264 16.0087i −0.885284 1.53336i −0.845387 0.534154i \(-0.820630\pi\)
−0.0398971 0.999204i \(-0.512703\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 2.44949i 0.0944911 0.231455i
\(113\) 8.48528i 0.798228i 0.916901 + 0.399114i \(0.130682\pi\)
−0.916901 + 0.399114i \(0.869318\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.27231 3.62132i 0.582369 0.336231i
\(117\) 0 0
\(118\) 8.06591i 0.742527i
\(119\) −9.58783 12.3640i −0.878915 1.13340i
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) −0.507306 0.878680i −0.0459293 0.0795519i
\(123\) 0 0
\(124\) −7.86396 4.54026i −0.706205 0.407727i
\(125\) 0 0
\(126\) 0 0
\(127\) −3.24264 −0.287738 −0.143869 0.989597i \(-0.545954\pi\)
−0.143869 + 0.989597i \(0.545954\pi\)
\(128\) 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
\(133\) 14.4853 + 5.91359i 1.25603 + 0.512773i
\(134\) 10.0000i 0.863868i
\(135\) 0 0
\(136\) 5.12132 2.95680i 0.439150 0.253543i
\(137\) 2.15232 1.24264i 0.183885 0.106166i −0.405232 0.914214i \(-0.632809\pi\)
0.589117 + 0.808048i \(0.299476\pi\)
\(138\) 0 0
\(139\) 0.594346i 0.0504118i −0.999682 0.0252059i \(-0.991976\pi\)
0.999682 0.0252059i \(-0.00802413\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.878680 1.52192i 0.0737372 0.127717i
\(143\) −3.67423 6.36396i −0.307255 0.532181i
\(144\) 0 0
\(145\) 0 0
\(146\) −1.43488 −0.118751
\(147\) 0 0
\(148\) −0.242641 −0.0199449
\(149\) −3.04384 1.75736i −0.249361 0.143968i 0.370111 0.928988i \(-0.379320\pi\)
−0.619472 + 0.785019i \(0.712653\pi\)
\(150\) 0 0
\(151\) −2.62132 4.54026i −0.213320 0.369481i 0.739432 0.673232i \(-0.235094\pi\)
−0.952752 + 0.303751i \(0.901761\pi\)
\(152\) −2.95680 + 5.12132i −0.239828 + 0.415394i
\(153\) 0 0
\(154\) −7.86396 + 1.07616i −0.633696 + 0.0867193i
\(155\) 0 0
\(156\) 0 0
\(157\) −12.7279 + 7.34847i −1.01580 + 0.586472i −0.912884 0.408219i \(-0.866150\pi\)
−0.102915 + 0.994690i \(0.532817\pi\)
\(158\) −2.38794 + 1.37868i −0.189975 + 0.109682i
\(159\) 0 0
\(160\) 0 0
\(161\) 10.3923 + 4.24264i 0.819028 + 0.334367i
\(162\) 0 0
\(163\) −1.12132 + 1.94218i −0.0878286 + 0.152124i −0.906593 0.422006i \(-0.861326\pi\)
0.818764 + 0.574130i \(0.194659\pi\)
\(164\) 5.91359 + 10.2426i 0.461774 + 0.799816i
\(165\) 0 0
\(166\) 5.74264 + 3.31552i 0.445715 + 0.257334i
\(167\) 16.1318 1.24832 0.624159 0.781298i \(-0.285442\pi\)
0.624159 + 0.781298i \(0.285442\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) 0.121320 + 0.210133i 0.00925059 + 0.0160225i
\(173\) 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
\(179\) 22.9369 13.2426i 1.71439 0.989801i 0.785966 0.618269i \(-0.212166\pi\)
0.928420 0.371532i \(-0.121167\pi\)
\(180\) 0 0
\(181\) 11.8272i 0.879108i 0.898216 + 0.439554i \(0.144863\pi\)
−0.898216 + 0.439554i \(0.855137\pi\)
\(182\) −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
\(187\) −15.3640 8.87039i −1.12352 0.648667i
\(188\) 5.91359 0.431293
\(189\) 0 0
\(190\) 0 0
\(191\) 7.34847 + 4.24264i 0.531717 + 0.306987i 0.741715 0.670715i \(-0.234013\pi\)
−0.209999 + 0.977702i \(0.567346\pi\)
\(192\) 0 0
\(193\) 4.74264 + 8.21449i 0.341383 + 0.591292i 0.984690 0.174316i \(-0.0557714\pi\)
−0.643307 + 0.765608i \(0.722438\pi\)
\(194\) −6.77962 + 11.7426i −0.486748 + 0.843072i
\(195\) 0 0
\(196\) 5.00000 + 4.89898i 0.357143 + 0.349927i
\(197\) 26.4853i 1.88700i −0.331375 0.943499i \(-0.607513\pi\)
0.331375 0.943499i \(-0.392487\pi\)
\(198\) 0 0
\(199\) 19.9706 11.5300i 1.41568 0.817341i 0.419761 0.907635i \(-0.362114\pi\)
0.995915 + 0.0902942i \(0.0287807\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.59808 + 18.9853i 0.182349 + 1.33251i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.74666 4.75736i −0.191369 0.331461i
\(207\) 0 0
\(208\) −2.12132 1.22474i −0.147087 0.0849208i
\(209\) 17.7408 1.22716
\(210\) 0 0
\(211\) −0.242641 −0.0167041 −0.00835204 0.999965i \(-0.502659\pi\)
−0.00835204 + 0.999965i \(0.502659\pi\)
\(212\) 6.27231 + 3.62132i 0.430784 + 0.248713i
\(213\) 0 0
\(214\) −5.74264 9.94655i −0.392559 0.679932i
\(215\) 0 0
\(216\) 0 0
\(217\) 18.9853 14.7224i 1.28880 0.999424i
\(218\) 18.4853i 1.25198i
\(219\) 0 0
\(220\) 0 0
\(221\) −12.5446 + 7.24264i −0.843843 + 0.487193i
\(222\) 0 0
\(223\) 2.15232i 0.144130i −0.997400 0.0720649i \(-0.977041\pi\)
0.997400 0.0720649i \(-0.0229589\pi\)
\(224\) −2.09077 + 1.62132i −0.139695 + 0.108329i
\(225\) 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
\(232\) −7.24264 −0.475503
\(233\) −16.2189 9.36396i −1.06253 0.613453i −0.136401 0.990654i \(-0.543554\pi\)
−0.926132 + 0.377200i \(0.876887\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.03295 + 6.98528i −0.262523 + 0.454703i
\(237\) 0 0
\(238\) 2.12132 + 15.5014i 0.137505 + 1.00481i
\(239\) 12.7279i 0.823301i −0.911342 0.411650i \(-0.864952\pi\)
0.911342 0.411650i \(-0.135048\pi\)
\(240\) 0 0
\(241\) 6.25736 3.61269i 0.403072 0.232714i −0.284737 0.958606i \(-0.591906\pi\)
0.687809 + 0.725892i \(0.258573\pi\)
\(242\) 1.73205 1.00000i 0.111340 0.0642824i
\(243\) 0 0
\(244\) 1.01461i 0.0649539i
\(245\) 0 0
\(246\) 0 0
\(247\) 7.24264 12.5446i 0.460838 0.798195i
\(248\) 4.54026 + 7.86396i 0.288307 + 0.499362i
\(249\) 0 0
\(250\) 0 0
\(251\) −27.4156 −1.73046 −0.865230 0.501375i \(-0.832828\pi\)
−0.865230 + 0.501375i \(0.832828\pi\)
\(252\) 0 0
\(253\) 12.7279 0.800198
\(254\) 2.80821 + 1.62132i 0.176203 + 0.101731i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.15232 + 3.72792i −0.134258 + 0.232541i −0.925314 0.379203i \(-0.876198\pi\)
0.791056 + 0.611744i \(0.209532\pi\)
\(258\) 0 0
\(259\) 0.242641 0.594346i 0.0150770 0.0369309i
\(260\) 0 0
\(261\) 0 0
\(262\) 4.50000 2.59808i 0.278011 0.160510i
\(263\) −13.1750 + 7.60660i −0.812407 + 0.469043i −0.847791 0.530331i \(-0.822068\pi\)
0.0353843 + 0.999374i \(0.488734\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −9.58783 12.3640i −0.587867 0.758083i
\(267\) 0 0
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) −6.98975 12.1066i −0.426173 0.738153i 0.570357 0.821397i \(-0.306805\pi\)
−0.996529 + 0.0832447i \(0.973472\pi\)
\(270\) 0 0
\(271\) −5.37868 3.10538i −0.326732 0.188639i 0.327658 0.944797i \(-0.393741\pi\)
−0.654389 + 0.756158i \(0.727074\pi\)
\(272\) −5.91359 −0.358564
\(273\) 0 0
\(274\) −2.48528 −0.150141
\(275\) 0 0
\(276\) 0 0
\(277\) 6.48528 + 11.2328i 0.389663 + 0.674916i 0.992404 0.123021i \(-0.0392582\pi\)
−0.602741 + 0.797937i \(0.705925\pi\)
\(278\) −0.297173 + 0.514719i −0.0178232 + 0.0308708i
\(279\) 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
\(283\) 18.3640 10.6024i 1.09162 0.630250i 0.157616 0.987501i \(-0.449619\pi\)
0.934008 + 0.357251i \(0.116286\pi\)
\(284\) −1.52192 + 0.878680i −0.0903092 + 0.0521400i
\(285\) 0 0
\(286\) 7.34847i 0.434524i
\(287\) −31.0028 + 4.24264i −1.83004 + 0.250435i
\(288\) 0 0
\(289\) −8.98528 + 15.5630i −0.528546 + 0.915468i
\(290\) 0 0
\(291\) 0 0
\(292\) 1.24264 + 0.717439i 0.0727200 + 0.0419849i
\(293\) 0.717439 0.0419132 0.0209566 0.999780i \(-0.493329\pi\)
0.0209566 + 0.999780i \(0.493329\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.210133 + 0.121320i 0.0122137 + 0.00705160i
\(297\) 0 0
\(298\) 1.75736 + 3.04384i 0.101801 + 0.176325i
\(299\) 5.19615 9.00000i 0.300501 0.520483i
\(300\) 0 0
\(301\) −0.636039 + 0.0870399i −0.0366607 + 0.00501690i
\(302\) 5.24264i 0.301680i
\(303\) 0 0
\(304\) 5.12132 2.95680i 0.293728 0.169584i
\(305\) 0 0
\(306\) 0 0
\(307\) 9.97204i 0.569134i 0.958656 + 0.284567i \(0.0918499\pi\)
−0.958656 + 0.284567i \(0.908150\pi\)
\(308\) 7.34847 + 3.00000i 0.418718 + 0.170941i
\(309\) 0 0
\(310\) 0 0
\(311\) −4.47871 7.75736i −0.253965 0.439879i 0.710649 0.703547i \(-0.248401\pi\)
−0.964614 + 0.263667i \(0.915068\pi\)
\(312\) 0 0
\(313\) −15.9853 9.22911i −0.903542 0.521660i −0.0251940 0.999683i \(-0.508020\pi\)
−0.878348 + 0.478023i \(0.841354\pi\)
\(314\) 14.6969 0.829396
\(315\) 0 0
\(316\) 2.75736 0.155114
\(317\) −1.07616 0.621320i −0.0604431 0.0348968i 0.469474 0.882946i \(-0.344444\pi\)
−0.529917 + 0.848050i \(0.677777\pi\)
\(318\) 0 0
\(319\) 10.8640 + 18.8169i 0.608265 + 1.05355i
\(320\) 0 0
\(321\) 0 0
\(322\) −6.87868 8.87039i −0.383334 0.494327i
\(323\) 34.9706i 1.94581i
\(324\) 0 0
\(325\) 0 0
\(326\) 1.94218 1.12132i 0.107568 0.0621042i
\(327\) 0 0
\(328\) 11.8272i 0.653047i
\(329\) −5.91359 + 14.4853i −0.326027 + 0.798599i
\(330\) 0 0
\(331\) 16.7279 28.9736i 0.919450 1.59253i 0.119197 0.992871i \(-0.461968\pi\)
0.800253 0.599663i \(-0.204699\pi\)
\(332\) −3.31552 5.74264i −0.181963 0.315168i
\(333\) 0 0
\(334\) −13.9706 8.06591i −0.764435 0.441347i
\(335\) 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
\(341\) 13.6208 23.5919i 0.737607 1.27757i
\(342\) 0 0
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 0.242641i 0.0130823i
\(345\) 0 0
\(346\) −18.0000 + 10.3923i −0.967686 + 0.558694i
\(347\) −2.15232 + 1.24264i −0.115542 + 0.0667084i −0.556657 0.830742i \(-0.687916\pi\)
0.441115 + 0.897451i \(0.354583\pi\)
\(348\) 0 0
\(349\) 2.27541i 0.121800i −0.998144 0.0608999i \(-0.980603\pi\)
0.998144 0.0608999i \(-0.0193971\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 4.47871 + 7.75736i 0.238378 + 0.412883i 0.960249 0.279145i \(-0.0900510\pi\)
−0.721871 + 0.692028i \(0.756718\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.3923 0.550791
\(357\) 0 0
\(358\) −26.4853 −1.39979
\(359\) −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
\(361\) 7.98528 + 13.8309i 0.420278 + 0.727943i
\(362\) 5.91359 10.2426i 0.310811 0.538341i
\(363\) 0 0
\(364\) 5.12132 3.97141i 0.268430 0.208158i
\(365\) 0 0
\(366\) 0 0
\(367\) 13.3492 7.70719i 0.696825 0.402312i −0.109339 0.994005i \(-0.534873\pi\)
0.806164 + 0.591693i \(0.201540\pi\)
\(368\) 3.67423 2.12132i 0.191533 0.110581i
\(369\) 0 0
\(370\) 0 0
\(371\) −15.1427 + 11.7426i −0.786170 + 0.609648i
\(372\) 0 0
\(373\) −14.7279 + 25.5095i −0.762583 + 1.32083i 0.178932 + 0.983861i \(0.442736\pi\)
−0.941515 + 0.336971i \(0.890598\pi\)
\(374\) 8.87039 + 15.3640i 0.458677 + 0.794452i
\(375\) 0 0
\(376\) −5.12132 2.95680i −0.264112 0.152485i
\(377\) 17.7408 0.913696
\(378\) 0 0
\(379\) 12.4853 0.641326 0.320663 0.947193i \(-0.396094\pi\)
0.320663 + 0.947193i \(0.396094\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.24264 7.34847i −0.217072 0.375980i
\(383\) 11.1097 19.2426i 0.567681 0.983253i −0.429113 0.903251i \(-0.641174\pi\)
0.996795 0.0800023i \(-0.0254928\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.48528i 0.482788i
\(387\) 0 0
\(388\) 11.7426 6.77962i 0.596142 0.344183i
\(389\) −27.2416 + 15.7279i −1.38120 + 0.797437i −0.992302 0.123843i \(-0.960478\pi\)
−0.388900 + 0.921280i \(0.627145\pi\)
\(390\) 0 0
\(391\) 25.0892i 1.26882i
\(392\) −1.88064 6.74264i −0.0949865 0.340555i
\(393\) 0 0
\(394\) −13.2426 + 22.9369i −0.667155 + 1.15555i
\(395\) 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 \(0.779710\pi\)
\(398\) −23.0600 −1.15589
\(399\) 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
\(403\) −11.1213 19.2627i −0.553992 0.959543i
\(404\) 0 0
\(405\) 0 0
\(406\) 7.24264 17.7408i 0.359446 0.880460i
\(407\) 0.727922i 0.0360818i
\(408\) 0 0
\(409\) 12.9853 7.49706i 0.642081 0.370706i −0.143335 0.989674i \(-0.545783\pi\)
0.785416 + 0.618969i \(0.212449\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 5.49333i 0.270637i
\(413\) −13.0774 16.8640i −0.643498 0.829821i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.22474 + 2.12132i 0.0600481 + 0.104006i
\(417\) 0 0
\(418\) −15.3640 8.87039i −0.751476 0.433865i
\(419\) 23.6544 1.15559 0.577796 0.816181i \(-0.303913\pi\)
0.577796 + 0.816181i \(0.303913\pi\)
\(420\) 0 0
\(421\) −14.2426 −0.694144 −0.347072 0.937839i \(-0.612824\pi\)
−0.347072 + 0.937839i \(0.612824\pi\)
\(422\) 0.210133 + 0.121320i 0.0102291 + 0.00590578i
\(423\) 0 0
\(424\) −3.62132 6.27231i −0.175867 0.304610i
\(425\) 0 0
\(426\) 0 0
\(427\) −2.48528 1.01461i −0.120271 0.0491005i
\(428\) 11.4853i 0.555162i
\(429\) 0 0
\(430\) 0 0
\(431\) −3.04384 + 1.75736i −0.146616 + 0.0846490i −0.571514 0.820593i \(-0.693644\pi\)
0.424897 + 0.905242i \(0.360310\pi\)
\(432\) 0 0
\(433\) 3.46410i 0.166474i 0.996530 + 0.0832370i \(0.0265259\pi\)
−0.996530 + 0.0832370i \(0.973474\pi\)
\(434\) −23.8030 + 3.25736i −1.14258 + 0.156358i
\(435\) 0 0
\(436\) 9.24264 16.0087i 0.442642 0.766679i
\(437\) 12.5446 + 21.7279i 0.600091 + 1.03939i
\(438\) 0 0
\(439\) −14.5919 8.42463i −0.696433 0.402086i 0.109585 0.993977i \(-0.465048\pi\)
−0.806017 + 0.591892i \(0.798381\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 14.4853 0.688995
\(443\) 14.2512 + 8.22792i 0.677094 + 0.390920i 0.798759 0.601651i \(-0.205490\pi\)
−0.121665 + 0.992571i \(0.538823\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.07616 + 1.86396i −0.0509576 + 0.0882611i
\(447\) 0 0
\(448\) 2.62132 0.358719i 0.123846 0.0169479i
\(449\) 1.75736i 0.0829349i 0.999140 + 0.0414675i \(0.0132033\pi\)
−0.999140 + 0.0414675i \(0.986797\pi\)
\(450\) 0 0
\(451\) −30.7279 + 17.7408i −1.44692 + 0.835380i
\(452\) −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
\(461\) 32.6118 1.51888 0.759441 0.650576i \(-0.225472\pi\)
0.759441 + 0.650576i \(0.225472\pi\)
\(462\) 0 0
\(463\) 29.4558 1.36893 0.684465 0.729046i \(-0.260036\pi\)
0.684465 + 0.729046i \(0.260036\pi\)
\(464\) 6.27231 + 3.62132i 0.291185 + 0.168116i
\(465\) 0 0
\(466\) 9.36396 + 16.2189i 0.433777 + 0.751324i
\(467\) −19.8931 + 34.4558i −0.920542 + 1.59443i −0.121965 + 0.992534i \(0.538920\pi\)
−0.798578 + 0.601892i \(0.794414\pi\)
\(468\) 0 0
\(469\) 16.2132 + 20.9077i 0.748656 + 0.965428i
\(470\) 0 0
\(471\) 0 0
\(472\) 6.98528 4.03295i 0.321524 0.185632i
\(473\) −0.630399 + 0.363961i −0.0289858 + 0.0167349i
\(474\) 0 0
\(475\) 0 0
\(476\) 5.91359 14.4853i 0.271049 0.663932i
\(477\) 0 0
\(478\) −6.36396 + 11.0227i −0.291081 + 0.504167i
\(479\) 6.00063 + 10.3934i 0.274176 + 0.474886i 0.969927 0.243397i \(-0.0782616\pi\)
−0.695751 + 0.718283i \(0.744928\pi\)
\(480\) 0 0
\(481\) −0.514719 0.297173i −0.0234691 0.0135499i
\(482\) −7.22538 −0.329107
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 0 0
\(487\) −7.10660 12.3090i −0.322031 0.557774i 0.658876 0.752251i \(-0.271032\pi\)
−0.980907 + 0.194478i \(0.937699\pi\)
\(488\) 0.507306 0.878680i 0.0229647 0.0397760i
\(489\) 0 0
\(490\) 0 0
\(491\) 13.9706i 0.630483i 0.949012 + 0.315241i \(0.102085\pi\)
−0.949012 + 0.315241i \(0.897915\pi\)
\(492\) 0 0
\(493\) 37.0919 21.4150i 1.67053 0.964483i
\(494\) −12.5446 + 7.24264i −0.564409 + 0.325862i
\(495\) 0 0
\(496\) 9.08052i 0.407727i
\(497\) −0.630399 4.60660i −0.0282773 0.206634i
\(498\) 0 0
\(499\) −15.9706 + 27.6618i −0.714941 + 1.23831i 0.248042 + 0.968749i \(0.420213\pi\)
−0.962982 + 0.269564i \(0.913120\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 23.7426 + 13.7078i 1.05969 + 0.611810i
\(503\) 31.0028 1.38235 0.691174 0.722688i \(-0.257094\pi\)
0.691174 + 0.722688i \(0.257094\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −11.0227 6.36396i −0.490019 0.282913i
\(507\) 0 0
\(508\) −1.62132 2.80821i −0.0719345 0.124594i
\(509\) 8.59871 14.8934i 0.381131 0.660138i −0.610093 0.792330i \(-0.708868\pi\)
0.991224 + 0.132191i \(0.0422013\pi\)
\(510\) 0 0
\(511\) −3.00000 + 2.32640i −0.132712 + 0.102914i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.72792 2.15232i 0.164432 0.0949346i
\(515\) 0 0
\(516\) 0 0
\(517\) 17.7408i 0.780238i
\(518\) −0.507306 + 0.393398i −0.0222897 + 0.0172849i
\(519\) 0 0
\(520\) 0 0
\(521\) −16.9363 29.3345i −0.741993 1.28517i −0.951587 0.307380i \(-0.900548\pi\)
0.209594 0.977788i \(-0.432786\pi\)
\(522\) 0 0
\(523\) −5.84924 3.37706i −0.255770 0.147669i 0.366634 0.930365i \(-0.380510\pi\)
−0.622403 + 0.782697i \(0.713844\pi\)
\(524\) −5.19615 −0.226995
\(525\) 0 0
\(526\) 15.2132 0.663327
\(527\) −46.5043 26.8492i −2.02576 1.16957i
\(528\) 0 0
\(529\) −2.50000 4.33013i −0.108696 0.188266i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.12132 + 15.5014i 0.0919709 + 0.672072i
\(533\) 28.9706i 1.25485i
\(534\) 0 0
\(535\) 0 0
\(536\) −8.66025 + 5.00000i −0.374066 + 0.215967i
\(537\) 0 0
\(538\) 13.9795i 0.602699i
\(539\) −14.6969 + 15.0000i −0.633042 + 0.646096i
\(540\) 0 0
\(541\) −7.36396 + 12.7548i −0.316601 + 0.548370i −0.979777 0.200094i \(-0.935875\pi\)
0.663175 + 0.748464i \(0.269208\pi\)
\(542\) 3.10538 + 5.37868i 0.133388 + 0.231034i
\(543\) 0 0
\(544\) 5.12132 + 2.95680i 0.219575 + 0.126772i
\(545\) 0 0
\(546\) 0 0
\(547\) 39.6985 1.69738 0.848692 0.528887i \(-0.177390\pi\)
0.848692 + 0.528887i \(0.177390\pi\)
\(548\) 2.15232 + 1.24264i 0.0919424 + 0.0530830i
\(549\) 0 0
\(550\) 0 0
\(551\) −21.4150 + 37.0919i −0.912310 + 1.58017i
\(552\) 0 0
\(553\) −2.75736 + 6.75412i −0.117255 + 0.287215i
\(554\) 12.9706i 0.551066i
\(555\) 0 0
\(556\) 0.514719 0.297173i 0.0218289 0.0126029i
\(557\) −8.42463 + 4.86396i −0.356963 + 0.206093i −0.667748 0.744388i \(-0.732741\pi\)
0.310785 + 0.950480i \(0.399408\pi\)
\(558\) 0 0
\(559\) 0.594346i 0.0251382i
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 + 5.19615i −0.126547 + 0.219186i
\(563\) −17.2950 29.9558i −0.728898 1.26249i −0.957349 0.288933i \(-0.906700\pi\)
0.228451 0.973555i \(-0.426634\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −21.2049 −0.891307
\(567\) 0 0
\(568\) 1.75736 0.0737372
\(569\) −8.87039 5.12132i −0.371866 0.214697i 0.302407 0.953179i \(-0.402210\pi\)
−0.674273 + 0.738482i \(0.735543\pi\)
\(570\) 0 0
\(571\) −4.36396 7.55860i −0.182626 0.316318i 0.760148 0.649750i \(-0.225126\pi\)
−0.942774 + 0.333432i \(0.891793\pi\)
\(572\) 3.67423 6.36396i 0.153627 0.266091i
\(573\) 0 0
\(574\) 28.9706 + 11.8272i 1.20921 + 0.493657i
\(575\) 0 0
\(576\) 0 0
\(577\) −9.25736 + 5.34474i −0.385389 + 0.222504i −0.680160 0.733063i \(-0.738090\pi\)
0.294771 + 0.955568i \(0.404757\pi\)
\(578\) 15.5630 8.98528i 0.647334 0.373738i
\(579\) 0 0
\(580\) 0 0
\(581\) 17.3821 2.37868i 0.721129 0.0986843i
\(582\) 0 0
\(583\) −10.8640 + 18.8169i −0.449939 + 0.779318i
\(584\) −0.717439 1.24264i −0.0296878 0.0514208i
\(585\) 0 0
\(586\) −0.621320 0.358719i −0.0256665 0.0148186i
\(587\) −5.19615 −0.214468 −0.107234 0.994234i \(-0.534199\pi\)
−0.107234 + 0.994234i \(0.534199\pi\)
\(588\) 0 0
\(589\) 53.6985 2.21261
\(590\) 0 0
\(591\) 0 0
\(592\) −0.121320 0.210133i −0.00498624 0.00863641i
\(593\) 11.7401 20.3345i 0.482110 0.835039i −0.517679 0.855575i \(-0.673204\pi\)
0.999789 + 0.0205360i \(0.00653726\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.51472i 0.143968i
\(597\) 0 0
\(598\) −9.00000 + 5.19615i −0.368037 + 0.212486i
\(599\) −6.45695 + 3.72792i −0.263824 + 0.152319i −0.626078 0.779761i \(-0.715341\pi\)
0.362254 + 0.932079i \(0.382007\pi\)
\(600\) 0 0
\(601\) 23.3572i 0.952760i 0.879240 + 0.476380i \(0.158051\pi\)
−0.879240 + 0.476380i \(0.841949\pi\)
\(602\) 0.594346 + 0.242641i 0.0242237 + 0.00988930i
\(603\) 0 0
\(604\) 2.62132 4.54026i 0.106660 0.184741i
\(605\) 0 0
\(606\) 0 0
\(607\) 17.3787 + 10.0336i 0.705379 + 0.407251i 0.809348 0.587330i \(-0.199821\pi\)
−0.103969 + 0.994581i \(0.533154\pi\)
\(608\) −5.91359 −0.239828
\(609\) 0 0
\(610\) 0 0
\(611\) 12.5446 + 7.24264i 0.507501 + 0.293006i
\(612\) 0 0
\(613\) −18.6066 32.2276i −0.751514 1.30166i −0.947089 0.320971i \(-0.895991\pi\)
0.195575 0.980689i \(-0.437343\pi\)
\(614\) 4.98602 8.63604i 0.201219 0.348522i
\(615\) 0 0
\(616\) −4.86396 6.27231i −0.195975 0.252719i
\(617\) 17.6985i 0.712514i −0.934388 0.356257i \(-0.884053\pi\)
0.934388 0.356257i \(-0.115947\pi\)
\(618\) 0 0
\(619\) 5.33452 3.07989i 0.214413 0.123791i −0.388948 0.921260i \(-0.627161\pi\)
0.603360 + 0.797469i \(0.293828\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 8.95743i 0.359160i
\(623\) −10.3923 + 25.4558i −0.416359 + 1.01987i
\(624\) 0 0
\(625\) 0 0
\(626\) 9.22911 + 15.9853i 0.368869 + 0.638900i
\(627\) 0 0
\(628\) −12.7279 7.34847i −0.507899 0.293236i
\(629\) −1.43488 −0.0572123
\(630\) 0 0
\(631\) 24.7574 0.985575 0.492787 0.870150i \(-0.335978\pi\)
0.492787 + 0.870150i \(0.335978\pi\)
\(632\) −2.38794 1.37868i −0.0949873 0.0548409i
\(633\) 0 0
\(634\) 0.621320 + 1.07616i 0.0246758 + 0.0427397i
\(635\) 0 0
\(636\) 0 0
\(637\) 4.60660 + 16.5160i 0.182520 + 0.654389i
\(638\) 21.7279i 0.860217i
\(639\) 0 0
\(640\) 0 0
\(641\) −15.3273 + 8.84924i −0.605393 + 0.349524i −0.771160 0.636641i \(-0.780323\pi\)
0.165767 + 0.986165i \(0.446990\pi\)
\(642\) 0 0
\(643\) 32.0174i 1.26264i −0.775520 0.631322i \(-0.782512\pi\)
0.775520 0.631322i \(-0.217488\pi\)
\(644\) 1.52192 + 11.1213i 0.0599720 + 0.438241i
\(645\) 0 0
\(646\) −17.4853 + 30.2854i −0.687949 + 1.19156i
\(647\) 16.2189 + 28.0919i 0.637629 + 1.10441i 0.985952 + 0.167031i \(0.0534180\pi\)
−0.348323 + 0.937375i \(0.613249\pi\)
\(648\) 0 0
\(649\) −20.9558 12.0989i −0.822589 0.474922i
\(650\) 0 0
\(651\) 0 0
\(652\) −2.24264 −0.0878286
\(653\) −16.6646 9.62132i −0.652137 0.376511i 0.137138 0.990552i \(-0.456210\pi\)
−0.789274 + 0.614041i \(0.789543\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −5.91359 + 10.2426i −0.230887 + 0.399908i
\(657\) 0 0
\(658\) 12.3640 9.58783i 0.481997 0.373772i
\(659\) 6.00000i 0.233727i −0.993148 0.116863i \(-0.962716\pi\)
0.993148 0.116863i \(-0.0372840\pi\)
\(660\) 0 0
\(661\) 30.8787 17.8278i 1.20104 0.693422i 0.240255 0.970710i \(-0.422769\pi\)
0.960787 + 0.277288i \(0.0894357\pi\)
\(662\) −28.9736 + 16.7279i −1.12609 + 0.650149i
\(663\) 0 0
\(664\) 6.63103i 0.257334i
\(665\) 0 0
\(666\) 0 0
\(667\) −15.3640 + 26.6112i −0.594895 + 1.03039i
\(668\) 8.06591 + 13.9706i 0.312079 + 0.540537i
\(669\) 0 0
\(670\) 0 0
\(671\) −3.04384 −0.117506
\(672\) 0 0
\(673\) −17.9706 −0.692714 −0.346357 0.938103i \(-0.612581\pi\)
−0.346357 + 0.938103i \(0.612581\pi\)
\(674\) −4.33013 2.50000i −0.166790 0.0962964i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) −1.07616 + 1.86396i −0.0413601 + 0.0716378i −0.885964 0.463753i \(-0.846502\pi\)
0.844604 + 0.535391i \(0.179836\pi\)
\(678\) 0 0
\(679\) 4.86396 + 35.5431i 0.186662 + 1.36402i
\(680\) 0 0
\(681\) 0 0
\(682\) −23.5919 + 13.6208i −0.903380 + 0.521567i
\(683\) 6.90271 3.98528i 0.264125 0.152493i −0.362090 0.932143i \(-0.617937\pi\)
0.626215 + 0.779651i \(0.284603\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 18.3967 + 2.13604i 0.702388 + 0.0815543i
\(687\) 0 0
\(688\) −0.121320 + 0.210133i −0.00462529 + 0.00801125i
\(689\) 8.87039 + 15.3640i 0.337935 + 0.585320i
\(690\) 0 0
\(691\) 24.7279 + 14.2767i 0.940694 + 0.543110i 0.890178 0.455613i \(-0.150580\pi\)
0.0505165 + 0.998723i \(0.483913\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) 2.48528 0.0943400
\(695\) 0 0
\(696\) 0 0
\(697\) 34.9706 + 60.5708i 1.32460 + 2.29428i
\(698\) −1.13770 + 1.97056i −0.0430628 + 0.0745869i
\(699\) 0 0
\(700\) 0 0
\(701\) 20.6985i 0.781771i −0.920439 0.390885i \(-0.872169\pi\)
0.920439 0.390885i \(-0.127831\pi\)
\(702\) 0 0
\(703\) 1.24264 0.717439i 0.0468671 0.0270587i
\(704\) 2.59808 1.50000i 0.0979187 0.0565334i
\(705\) 0 0
\(706\) 8.95743i 0.337117i
\(707\) 0 0
\(708\) 0 0
\(709\) −13.4853 + 23.3572i −0.506450 + 0.877198i 0.493522 + 0.869733i \(0.335709\pi\)
−0.999972 + 0.00746433i \(0.997624\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.00000 5.19615i −0.337289 0.194734i
\(713\) 38.5254 1.44279
\(714\) 0 0
\(715\) 0 0
\(716\) 22.9369 + 13.2426i 0.857193 + 0.494901i
\(717\) 0 0
\(718\) 9.00000 + 15.5885i 0.335877 + 0.581756i
\(719\) −8.06591 + 13.9706i −0.300808 + 0.521014i −0.976319 0.216335i \(-0.930590\pi\)
0.675511 + 0.737349i \(0.263923\pi\)
\(720\) 0 0
\(721\) −13.4558 5.49333i −0.501122 0.204582i
\(722\) 15.9706i 0.594363i
\(723\) 0 0
\(724\) −10.2426 + 5.91359i −0.380665 + 0.219777i
\(725\) 0 0
\(726\) 0 0
\(727\) 11.7041i 0.434081i 0.976163 + 0.217040i \(0.0696403\pi\)
−0.976163 + 0.217040i \(0.930360\pi\)
\(728\) −6.42090 + 0.878680i −0.237974 + 0.0325660i
\(729\) 0 0
\(730\) 0 0
\(731\) 0.717439 + 1.24264i 0.0265354 + 0.0459607i
\(732\) 0 0
\(733\) −4.09188 2.36245i −0.151137 0.0872591i 0.422524 0.906352i \(-0.361144\pi\)
−0.573661 + 0.819093i \(0.694477\pi\)
\(734\) −15.4144 −0.568955
\(735\) 0 0
\(736\) −4.24264 −0.156386
\(737\) 25.9808 + 15.0000i 0.957014 + 0.552532i
\(738\) 0 0
\(739\) −7.72792 13.3852i −0.284276 0.492381i 0.688157 0.725562i \(-0.258420\pi\)
−0.972433 + 0.233181i \(0.925087\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 18.9853 2.59808i 0.696972 0.0953784i
\(743\) 38.4853i 1.41189i 0.708268 + 0.705944i \(0.249477\pi\)
−0.708268 + 0.705944i \(0.750523\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 25.5095 14.7279i 0.933969 0.539228i
\(747\) 0 0
\(748\) 17.7408i 0.648667i
\(749\) −28.1331 11.4853i −1.02796 0.419663i
\(750\) 0 0
\(751\) −17.6213 + 30.5210i −0.643011 + 1.11373i 0.341746 + 0.939792i \(0.388982\pi\)
−0.984757 + 0.173936i \(0.944352\pi\)
\(752\) 2.95680 + 5.12132i 0.107823 + 0.186755i
\(753\) 0 0
\(754\) −15.3640 8.87039i −0.559522 0.323040i
\(755\) 0 0
\(756\) 0 0
\(757\) 33.7574 1.22693 0.613466 0.789721i \(-0.289775\pi\)
0.613466 + 0.789721i \(0.289775\pi\)
\(758\) −10.8126 6.24264i −0.392730 0.226743i
\(759\) 0 0
\(760\) 0 0
\(761\) −14.7840 + 25.6066i −0.535919 + 0.928239i 0.463199 + 0.886254i \(0.346701\pi\)
−0.999118 + 0.0419845i \(0.986632\pi\)
\(762\) 0 0
\(763\) 29.9706 + 38.6485i 1.08501 + 1.39917i
\(764\) 8.48528i 0.306987i
\(765\) 0 0
\(766\) −19.2426 + 11.1097i −0.695265 + 0.401411i
\(767\) −17.1104 + 9.87868i −0.617820 + 0.356698i
\(768\) 0 0
\(769\) 9.84895i 0.355162i 0.984106 + 0.177581i \(0.0568272\pi\)
−0.984106 + 0.177581i \(0.943173\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.74264 + 8.21449i −0.170691 + 0.295646i
\(773\) −8.06591 13.9706i −0.290111 0.502486i 0.683725 0.729740i \(-0.260359\pi\)
−0.973836 + 0.227253i \(0.927025\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −13.5592 −0.486748
\(777\) 0 0
\(778\) 31.4558 1.12775
\(779\) −60.5708 34.9706i −2.17017 1.25295i
\(780\) 0 0
\(781\) −2.63604 4.56575i −0.0943249 0.163376i
\(782\) −12.5446 + 21.7279i −0.448595 + 0.776989i
\(783\) 0 0
\(784\) −1.74264 + 6.77962i −0.0622372 + 0.242129i
\(785\) 0 0
\(786\) 0 0
\(787\) −27.8787 + 16.0958i −0.993768 + 0.573752i −0.906398 0.422424i \(-0.861179\pi\)
−0.0873693 + 0.996176i \(0.527846\pi\)
\(788\) 22.9369 13.2426i 0.817094 0.471750i
\(789\) 0 0
\(790\) 0 0
\(791\) −3.04384 22.2426i −0.108226 0.790857i
\(792\) 0 0
\(793\) −1.24264 + 2.15232i −0.0441275 + 0.0764310i
\(794\) 6.92820 + 12.0000i 0.245873 + 0.425864i
\(795\) 0 0
\(796\) 19.9706 + 11.5300i 0.707838 + 0.408670i