Properties

Label 3150.2.bp.b.899.3
Level 3150
Weight 2
Character 3150.899
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 899.3
Root \(-0.965926 + 0.258819i\)
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.b.1349.3

$q$-expansion

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

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.358719 2.62132i 0.135583 0.990766i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −2.59808 1.50000i −0.783349 0.452267i 0.0542666 0.998526i \(-0.482718\pi\)
−0.837616 + 0.546259i \(0.816051\pi\)
\(12\) 0 0
\(13\) −2.44949 −0.679366 −0.339683 0.940540i \(-0.610320\pi\)
−0.339683 + 0.940540i \(0.610320\pi\)
\(14\) −2.44949 + 1.00000i −0.654654 + 0.267261i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 5.12132 + 2.95680i 1.24210 + 0.717128i 0.969522 0.245005i \(-0.0787895\pi\)
0.272581 + 0.962133i \(0.412123\pi\)
\(18\) 0 0
\(19\) 5.12132 2.95680i 1.17491 0.678335i 0.220080 0.975482i \(-0.429368\pi\)
0.954832 + 0.297146i \(0.0960350\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000i 0.639602i
\(23\) 2.12132 + 3.67423i 0.442326 + 0.766131i 0.997862 0.0653618i \(-0.0208201\pi\)
−0.555536 + 0.831493i \(0.687487\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.22474 + 2.12132i 0.240192 + 0.416025i
\(27\) 0 0
\(28\) 2.09077 + 1.62132i 0.395118 + 0.306401i
\(29\) 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 −0.416794 0.909001i \(-0.636846\pi\)
−0.995615 + 0.0935461i \(0.970180\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 5.91359i 1.01417i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.210133 0.121320i 0.0345457 0.0199449i −0.482628 0.875826i \(-0.660318\pi\)
0.517173 + 0.855881i \(0.326984\pi\)
\(38\) −5.12132 2.95680i −0.830788 0.479656i
\(39\) 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
\(43\) 0.242641i 0.0370024i −0.999829 0.0185012i \(-0.994111\pi\)
0.999829 0.0185012i \(-0.00588944\pi\)
\(44\) 2.59808 1.50000i 0.391675 0.226134i
\(45\) 0 0
\(46\) 2.12132 3.67423i 0.312772 0.541736i
\(47\) −5.12132 + 2.95680i −0.747021 + 0.431293i −0.824617 0.565692i \(-0.808609\pi\)
0.0775953 + 0.996985i \(0.475276\pi\)
\(48\) 0 0
\(49\) −6.74264 1.88064i −0.963234 0.268662i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.22474 2.12132i 0.169842 0.294174i
\(53\) 3.62132 6.27231i 0.497427 0.861568i −0.502569 0.864537i \(-0.667612\pi\)
0.999996 + 0.00296896i \(0.000945050\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.358719 2.62132i 0.0479359 0.350289i
\(57\) 0 0
\(58\) −6.27231 + 3.62132i −0.823595 + 0.475503i
\(59\) −4.03295 + 6.98528i −0.525046 + 0.909406i 0.474529 + 0.880240i \(0.342619\pi\)
−0.999575 + 0.0291661i \(0.990715\pi\)
\(60\) 0 0
\(61\) 0.878680 0.507306i 0.112503 0.0649539i −0.442692 0.896674i \(-0.645977\pi\)
0.555196 + 0.831720i \(0.312643\pi\)
\(62\) 9.08052i 1.15323i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −8.66025 5.00000i −1.05802 0.610847i −0.133135 0.991098i \(-0.542504\pi\)
−0.924883 + 0.380251i \(0.875838\pi\)
\(68\) −5.12132 + 2.95680i −0.621051 + 0.358564i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.75736i 0.208560i −0.994548 0.104280i \(-0.966746\pi\)
0.994548 0.104280i \(-0.0332538\pi\)
\(72\) 0 0
\(73\) 0.717439 1.24264i 0.0839699 0.145440i −0.820982 0.570954i \(-0.806573\pi\)
0.904952 + 0.425514i \(0.139907\pi\)
\(74\) −0.210133 0.121320i −0.0244275 0.0141032i
\(75\) 0 0
\(76\) 5.91359i 0.678335i
\(77\) −4.86396 + 6.27231i −0.554300 + 0.714796i
\(78\) 0 0
\(79\) −1.37868 2.38794i −0.155114 0.268665i 0.777987 0.628281i \(-0.216241\pi\)
−0.933100 + 0.359616i \(0.882908\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −5.91359 10.2426i −0.653047 1.13111i
\(83\) 6.63103i 0.727850i 0.931428 + 0.363925i \(0.118564\pi\)
−0.931428 + 0.363925i \(0.881436\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.210133 + 0.121320i −0.0226592 + 0.0130823i
\(87\) 0 0
\(88\) −2.59808 1.50000i −0.276956 0.159901i
\(89\) −5.19615 9.00000i −0.550791 0.953998i −0.998218 0.0596775i \(-0.980993\pi\)
0.447427 0.894321i \(-0.352341\pi\)
\(90\) 0 0
\(91\) −0.878680 + 6.42090i −0.0921107 + 0.673093i
\(92\) −4.24264 −0.442326
\(93\) 0 0
\(94\) 5.12132 + 2.95680i 0.528224 + 0.304970i
\(95\) 0 0
\(96\) 0 0
\(97\) −13.5592 −1.37673 −0.688366 0.725364i \(-0.741672\pi\)
−0.688366 + 0.725364i \(0.741672\pi\)
\(98\) 1.74264 + 6.77962i 0.176033 + 0.684845i
\(99\) 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
\(103\) −2.74666 4.75736i −0.270637 0.468757i 0.698388 0.715719i \(-0.253901\pi\)
−0.969025 + 0.246963i \(0.920568\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) −7.24264 −0.703467
\(107\) 5.74264 + 9.94655i 0.555162 + 0.961569i 0.997891 + 0.0649133i \(0.0206771\pi\)
−0.442729 + 0.896656i \(0.645990\pi\)
\(108\) 0 0
\(109\) 9.24264 16.0087i 0.885284 1.53336i 0.0398971 0.999204i \(-0.487297\pi\)
0.845387 0.534154i \(-0.179370\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.44949 + 1.00000i −0.231455 + 0.0944911i
\(113\) −8.48528 −0.798228 −0.399114 0.916901i \(-0.630682\pi\)
−0.399114 + 0.916901i \(0.630682\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.27231 + 3.62132i 0.582369 + 0.336231i
\(117\) 0 0
\(118\) 8.06591 0.742527
\(119\) 9.58783 12.3640i 0.878915 1.13340i
\(120\) 0 0
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) −0.878680 0.507306i −0.0795519 0.0459293i
\(123\) 0 0
\(124\) 7.86396 4.54026i 0.706205 0.407727i
\(125\) 0 0
\(126\) 0 0
\(127\) 3.24264i 0.287738i −0.989597 0.143869i \(-0.954046\pi\)
0.989597 0.143869i \(-0.0459544\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −2.59808 4.50000i −0.226995 0.393167i 0.729921 0.683531i \(-0.239557\pi\)
−0.956916 + 0.290365i \(0.906223\pi\)
\(132\) 0 0
\(133\) −5.91359 14.4853i −0.512773 1.25603i
\(134\) 10.0000i 0.863868i
\(135\) 0 0
\(136\) 5.12132 + 2.95680i 0.439150 + 0.253543i
\(137\) −1.24264 + 2.15232i −0.106166 + 0.183885i −0.914214 0.405232i \(-0.867191\pi\)
0.808048 + 0.589117i \(0.200524\pi\)
\(138\) 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
\(142\) −1.52192 + 0.878680i −0.127717 + 0.0737372i
\(143\) 6.36396 + 3.67423i 0.532181 + 0.307255i
\(144\) 0 0
\(145\) 0 0
\(146\) −1.43488 −0.118751
\(147\) 0 0
\(148\) 0.242641i 0.0199449i
\(149\) 3.04384 1.75736i 0.249361 0.143968i −0.370111 0.928988i \(-0.620680\pi\)
0.619472 + 0.785019i \(0.287347\pi\)
\(150\) 0 0
\(151\) −2.62132 + 4.54026i −0.213320 + 0.369481i −0.952752 0.303751i \(-0.901761\pi\)
0.739432 + 0.673232i \(0.235094\pi\)
\(152\) 5.12132 2.95680i 0.415394 0.239828i
\(153\) 0 0
\(154\) 7.86396 + 1.07616i 0.633696 + 0.0867193i
\(155\) 0 0
\(156\) 0 0
\(157\) 7.34847 12.7279i 0.586472 1.01580i −0.408219 0.912884i \(-0.633850\pi\)
0.994690 0.102915i \(-0.0328168\pi\)
\(158\) −1.37868 + 2.38794i −0.109682 + 0.189975i
\(159\) 0 0
\(160\) 0 0
\(161\) 10.3923 4.24264i 0.819028 0.334367i
\(162\) 0 0
\(163\) −1.94218 + 1.12132i −0.152124 + 0.0878286i −0.574130 0.818764i \(-0.694659\pi\)
0.422006 + 0.906593i \(0.361326\pi\)
\(164\) −5.91359 + 10.2426i −0.461774 + 0.799816i
\(165\) 0 0
\(166\) 5.74264 3.31552i 0.445715 0.257334i
\(167\) 16.1318i 1.24832i 0.781298 + 0.624159i \(0.214558\pi\)
−0.781298 + 0.624159i \(0.785442\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) 0.210133 + 0.121320i 0.0160225 + 0.00925059i
\(173\) 18.0000 10.3923i 1.36851 0.790112i 0.377776 0.925897i \(-0.376689\pi\)
0.990738 + 0.135785i \(0.0433555\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) 0 0
\(178\) −5.19615 + 9.00000i −0.389468 + 0.674579i
\(179\) −22.9369 13.2426i −1.71439 0.989801i −0.928420 0.371532i \(-0.878833\pi\)
−0.785966 0.618269i \(-0.787834\pi\)
\(180\) 0 0
\(181\) 11.8272i 0.879108i −0.898216 0.439554i \(-0.855137\pi\)
0.898216 0.439554i \(-0.144863\pi\)
\(182\) 6.00000 2.44949i 0.444750 0.181568i
\(183\) 0 0
\(184\) 2.12132 + 3.67423i 0.156386 + 0.270868i
\(185\) 0 0
\(186\) 0 0
\(187\) −8.87039 15.3640i −0.648667 1.12352i
\(188\) 5.91359i 0.431293i
\(189\) 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
\(193\) −8.21449 4.74264i −0.591292 0.341383i 0.174316 0.984690i \(-0.444229\pi\)
−0.765608 + 0.643307i \(0.777562\pi\)
\(194\) 6.77962 + 11.7426i 0.486748 + 0.843072i
\(195\) 0 0
\(196\) 5.00000 4.89898i 0.357143 0.349927i
\(197\) −26.4853 −1.88700 −0.943499 0.331375i \(-0.892487\pi\)
−0.943499 + 0.331375i \(0.892487\pi\)
\(198\) 0 0
\(199\) −19.9706 11.5300i −1.41568 0.817341i −0.419761 0.907635i \(-0.637886\pi\)
−0.995915 + 0.0902942i \(0.971219\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −18.9853 2.59808i −1.33251 0.182349i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.74666 + 4.75736i −0.191369 + 0.331461i
\(207\) 0 0
\(208\) 1.22474 + 2.12132i 0.0849208 + 0.147087i
\(209\) −17.7408 −1.22716
\(210\) 0 0
\(211\) −0.242641 −0.0167041 −0.00835204 0.999965i \(-0.502659\pi\)
−0.00835204 + 0.999965i \(0.502659\pi\)
\(212\) 3.62132 + 6.27231i 0.248713 + 0.430784i
\(213\) 0 0
\(214\) 5.74264 9.94655i 0.392559 0.679932i
\(215\) 0 0
\(216\) 0 0
\(217\) −14.7224 + 18.9853i −0.999424 + 1.28880i
\(218\) −18.4853 −1.25198
\(219\) 0 0
\(220\) 0 0
\(221\) −12.5446 7.24264i −0.843843 0.487193i
\(222\) 0 0
\(223\) 2.15232 0.144130 0.0720649 0.997400i \(-0.477041\pi\)
0.0720649 + 0.997400i \(0.477041\pi\)
\(224\) 2.09077 + 1.62132i 0.139695 + 0.108329i
\(225\) 0 0
\(226\) 4.24264 + 7.34847i 0.282216 + 0.488813i
\(227\) −13.5000 7.79423i −0.896026 0.517321i −0.0201176 0.999798i \(-0.506404\pi\)
−0.875909 + 0.482476i \(0.839737\pi\)
\(228\) 0 0
\(229\) 12.0000 6.92820i 0.792982 0.457829i −0.0480291 0.998846i \(-0.515294\pi\)
0.841011 + 0.541017i \(0.181961\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 7.24264i 0.475503i
\(233\) 9.36396 + 16.2189i 0.613453 + 1.06253i 0.990654 + 0.136401i \(0.0435535\pi\)
−0.377200 + 0.926132i \(0.623113\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.03295 6.98528i −0.262523 0.454703i
\(237\) 0 0
\(238\) −15.5014 2.12132i −1.00481 0.137505i
\(239\) 12.7279i 0.823301i −0.911342 0.411650i \(-0.864952\pi\)
0.911342 0.411650i \(-0.135048\pi\)
\(240\) 0 0
\(241\) 6.25736 + 3.61269i 0.403072 + 0.232714i 0.687809 0.725892i \(-0.258573\pi\)
−0.284737 + 0.958606i \(0.591906\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 0 0
\(244\) 1.01461i 0.0649539i
\(245\) 0 0
\(246\) 0 0
\(247\) −12.5446 + 7.24264i −0.798195 + 0.460838i
\(248\) −7.86396 4.54026i −0.499362 0.288307i
\(249\) 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
\(253\) 12.7279i 0.800198i
\(254\) −2.80821 + 1.62132i −0.176203 + 0.101731i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.72792 2.15232i 0.232541 0.134258i −0.379203 0.925314i \(-0.623802\pi\)
0.611744 + 0.791056i \(0.290468\pi\)
\(258\) 0 0
\(259\) −0.242641 0.594346i −0.0150770 0.0369309i
\(260\) 0 0
\(261\) 0 0
\(262\) −2.59808 + 4.50000i −0.160510 + 0.278011i
\(263\) −7.60660 + 13.1750i −0.469043 + 0.812407i −0.999374 0.0353843i \(-0.988734\pi\)
0.530331 + 0.847791i \(0.322068\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −9.58783 + 12.3640i −0.587867 + 0.758083i
\(267\) 0 0
\(268\) 8.66025 5.00000i 0.529009 0.305424i
\(269\) 6.98975 12.1066i 0.426173 0.738153i −0.570357 0.821397i \(-0.693195\pi\)
0.996529 + 0.0832447i \(0.0265283\pi\)
\(270\) 0 0
\(271\) −5.37868 + 3.10538i −0.326732 + 0.188639i −0.654389 0.756158i \(-0.727074\pi\)
0.327658 + 0.944797i \(0.393741\pi\)
\(272\) 5.91359i 0.358564i
\(273\) 0 0
\(274\) 2.48528 0.150141
\(275\) 0 0
\(276\) 0 0
\(277\) 11.2328 + 6.48528i 0.674916 + 0.389663i 0.797937 0.602741i \(-0.205925\pi\)
−0.123021 + 0.992404i \(0.539258\pi\)
\(278\) −0.514719 + 0.297173i −0.0308708 + 0.0178232i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000i 0.357930i 0.983855 + 0.178965i \(0.0572749\pi\)
−0.983855 + 0.178965i \(0.942725\pi\)
\(282\) 0 0
\(283\) 10.6024 18.3640i 0.630250 1.09162i −0.357251 0.934008i \(-0.616286\pi\)
0.987501 0.157616i \(-0.0503807\pi\)
\(284\) 1.52192 + 0.878680i 0.0903092 + 0.0521400i
\(285\) 0 0
\(286\) 7.34847i 0.434524i
\(287\) 4.24264 31.0028i 0.250435 1.83004i
\(288\) 0 0
\(289\) 8.98528 + 15.5630i 0.528546 + 0.915468i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.717439 + 1.24264i 0.0419849 + 0.0727200i
\(293\) 0.717439i 0.0419132i −0.999780 0.0209566i \(-0.993329\pi\)
0.999780 0.0209566i \(-0.00667119\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.210133 0.121320i 0.0122137 0.00705160i
\(297\) 0 0
\(298\) −3.04384 1.75736i −0.176325 0.101801i
\(299\) −5.19615 9.00000i −0.300501 0.520483i
\(300\) 0 0
\(301\) −0.636039 0.0870399i −0.0366607 0.00501690i
\(302\) 5.24264 0.301680
\(303\) 0 0
\(304\) −5.12132 2.95680i −0.293728 0.169584i
\(305\) 0 0
\(306\) 0 0
\(307\) 9.97204 0.569134 0.284567 0.958656i \(-0.408150\pi\)
0.284567 + 0.958656i \(0.408150\pi\)
\(308\) −3.00000 7.34847i −0.170941 0.418718i
\(309\) 0 0
\(310\) 0 0
\(311\) −4.47871 + 7.75736i −0.253965 + 0.439879i −0.964614 0.263667i \(-0.915068\pi\)
0.710649 + 0.703547i \(0.248401\pi\)
\(312\) 0 0
\(313\) 9.22911 + 15.9853i 0.521660 + 0.903542i 0.999683 + 0.0251940i \(0.00802035\pi\)
−0.478023 + 0.878348i \(0.658646\pi\)
\(314\) −14.6969 −0.829396
\(315\) 0 0
\(316\) 2.75736 0.155114
\(317\) −0.621320 1.07616i −0.0348968 0.0604431i 0.848050 0.529917i \(-0.177777\pi\)
−0.882946 + 0.469474i \(0.844444\pi\)
\(318\) 0 0
\(319\) −10.8640 + 18.8169i −0.608265 + 1.05355i
\(320\) 0 0
\(321\) 0 0
\(322\) −8.87039 6.87868i −0.494327 0.383334i
\(323\) 34.9706 1.94581
\(324\) 0 0
\(325\) 0 0
\(326\) 1.94218 + 1.12132i 0.107568 + 0.0621042i
\(327\) 0 0
\(328\) 11.8272 0.653047
\(329\) 5.91359 + 14.4853i 0.326027 + 0.798599i
\(330\) 0 0
\(331\) 16.7279 + 28.9736i 0.919450 + 1.59253i 0.800253 + 0.599663i \(0.204699\pi\)
0.119197 + 0.992871i \(0.461968\pi\)
\(332\) −5.74264 3.31552i −0.315168 0.181963i
\(333\) 0 0
\(334\) 13.9706 8.06591i 0.764435 0.441347i
\(335\) 0 0
\(336\) 0 0
\(337\) 5.00000i 0.272367i 0.990684 + 0.136184i \(0.0434837\pi\)
−0.990684 + 0.136184i \(0.956516\pi\)
\(338\) 3.50000 + 6.06218i 0.190375 + 0.329739i
\(339\) 0 0
\(340\) 0 0
\(341\) 13.6208 + 23.5919i 0.737607 + 1.27757i
\(342\) 0 0
\(343\) −7.34847 + 17.0000i −0.396780 + 0.917914i
\(344\) 0.242641i 0.0130823i
\(345\) 0 0
\(346\) −18.0000 10.3923i −0.967686 0.558694i
\(347\) 1.24264 2.15232i 0.0667084 0.115542i −0.830742 0.556657i \(-0.812084\pi\)
0.897451 + 0.441115i \(0.145417\pi\)
\(348\) 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
\(352\) 2.59808 1.50000i 0.138478 0.0799503i
\(353\) −7.75736 4.47871i −0.412883 0.238378i 0.279145 0.960249i \(-0.409949\pi\)
−0.692028 + 0.721871i \(0.743282\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.3923 0.550791
\(357\) 0 0
\(358\) 26.4853i 1.39979i
\(359\) 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
\(361\) 7.98528 13.8309i 0.420278 0.727943i
\(362\) −10.2426 + 5.91359i −0.538341 + 0.310811i
\(363\) 0 0
\(364\) −5.12132 3.97141i −0.268430 0.208158i
\(365\) 0 0
\(366\) 0 0
\(367\) −7.70719 + 13.3492i −0.402312 + 0.696825i −0.994005 0.109339i \(-0.965127\pi\)
0.591693 + 0.806164i \(0.298460\pi\)
\(368\) 2.12132 3.67423i 0.110581 0.191533i
\(369\) 0 0
\(370\) 0 0
\(371\) −15.1427 11.7426i −0.786170 0.609648i
\(372\) 0 0
\(373\) −25.5095 + 14.7279i −1.32083 + 0.762583i −0.983861 0.178932i \(-0.942736\pi\)
−0.336971 + 0.941515i \(0.609402\pi\)
\(374\) −8.87039 + 15.3640i −0.458677 + 0.794452i
\(375\) 0 0
\(376\) −5.12132 + 2.95680i −0.264112 + 0.152485i
\(377\) 17.7408i 0.913696i
\(378\) 0 0
\(379\) −12.4853 −0.641326 −0.320663 0.947193i \(-0.603906\pi\)
−0.320663 + 0.947193i \(0.603906\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −7.34847 4.24264i −0.375980 0.217072i
\(383\) 19.2426 11.1097i 0.983253 0.567681i 0.0800023 0.996795i \(-0.474507\pi\)
0.903251 + 0.429113i \(0.141174\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.48528i 0.482788i
\(387\) 0 0
\(388\) 6.77962 11.7426i 0.344183 0.596142i
\(389\) 27.2416 + 15.7279i 1.38120 + 0.797437i 0.992302 0.123843i \(-0.0395218\pi\)
0.388900 + 0.921280i \(0.372855\pi\)
\(390\) 0 0
\(391\) 25.0892i 1.26882i
\(392\) −6.74264 1.88064i −0.340555 0.0949865i
\(393\) 0 0
\(394\) 13.2426 + 22.9369i 0.667155 + 1.15555i
\(395\) 0 0
\(396\) 0 0
\(397\) −6.92820 12.0000i −0.347717 0.602263i 0.638127 0.769931i \(-0.279710\pi\)
−0.985843 + 0.167668i \(0.946376\pi\)
\(398\) 23.0600i 1.15589i
\(399\) 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
\(403\) 19.2627 + 11.1213i 0.959543 + 0.553992i
\(404\) 0 0
\(405\) 0 0
\(406\) 7.24264 + 17.7408i 0.359446 + 0.880460i
\(407\) −0.727922 −0.0360818
\(408\) 0 0
\(409\) −12.9853 7.49706i −0.642081 0.370706i 0.143335 0.989674i \(-0.454217\pi\)
−0.785416 + 0.618969i \(0.787551\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 5.49333 0.270637
\(413\) 16.8640 + 13.0774i 0.829821 + 0.643498i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.22474 2.12132i 0.0600481 0.104006i
\(417\) 0 0
\(418\) 8.87039 + 15.3640i 0.433865 + 0.751476i
\(419\) −23.6544 −1.15559 −0.577796 0.816181i \(-0.696087\pi\)
−0.577796 + 0.816181i \(0.696087\pi\)
\(420\) 0 0
\(421\) −14.2426 −0.694144 −0.347072 0.937839i \(-0.612824\pi\)
−0.347072 + 0.937839i \(0.612824\pi\)
\(422\) 0.121320 + 0.210133i 0.00590578 + 0.0102291i
\(423\) 0 0
\(424\) 3.62132 6.27231i 0.175867 0.304610i
\(425\) 0 0
\(426\) 0 0
\(427\) −1.01461 2.48528i −0.0491005 0.120271i
\(428\) −11.4853 −0.555162
\(429\) 0 0
\(430\) 0 0
\(431\) −3.04384 1.75736i −0.146616 0.0846490i 0.424897 0.905242i \(-0.360310\pi\)
−0.571514 + 0.820593i \(0.693644\pi\)
\(432\) 0 0
\(433\) −3.46410 −0.166474 −0.0832370 0.996530i \(-0.526526\pi\)
−0.0832370 + 0.996530i \(0.526526\pi\)
\(434\) 23.8030 + 3.25736i 1.14258 + 0.156358i
\(435\) 0 0
\(436\) 9.24264 + 16.0087i 0.442642 + 0.766679i
\(437\) 21.7279 + 12.5446i 1.03939 + 0.600091i
\(438\) 0 0
\(439\) 14.5919 8.42463i 0.696433 0.402086i −0.109585 0.993977i \(-0.534952\pi\)
0.806017 + 0.591892i \(0.201619\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 14.4853i 0.688995i
\(443\) −8.22792 14.2512i −0.390920 0.677094i 0.601651 0.798759i \(-0.294510\pi\)
−0.992571 + 0.121665i \(0.961177\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.07616 1.86396i −0.0509576 0.0882611i
\(447\) 0 0
\(448\) 0.358719 2.62132i 0.0169479 0.123846i
\(449\) 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
\(452\) 4.24264 7.34847i 0.199557 0.345643i
\(453\) 0 0
\(454\) 15.5885i 0.731603i
\(455\) 0 0
\(456\) 0 0
\(457\) 19.9186 11.5000i 0.931752 0.537947i 0.0443868 0.999014i \(-0.485867\pi\)
0.887365 + 0.461067i \(0.152533\pi\)
\(458\) −12.0000 6.92820i −0.560723 0.323734i
\(459\) 0 0
\(460\) 0 0
\(461\) 32.6118 1.51888 0.759441 0.650576i \(-0.225472\pi\)
0.759441 + 0.650576i \(0.225472\pi\)
\(462\) 0 0
\(463\) 29.4558i 1.36893i −0.729046 0.684465i \(-0.760036\pi\)
0.729046 0.684465i \(-0.239964\pi\)
\(464\) −6.27231 + 3.62132i −0.291185 + 0.168116i
\(465\) 0 0
\(466\) 9.36396 16.2189i 0.433777 0.751324i
\(467\) 34.4558 19.8931i 1.59443 0.920542i 0.601892 0.798578i \(-0.294414\pi\)
0.992534 0.121965i \(-0.0389195\pi\)
\(468\) 0 0
\(469\) −16.2132 + 20.9077i −0.748656 + 0.965428i
\(470\) 0 0
\(471\) 0 0
\(472\) −4.03295 + 6.98528i −0.185632 + 0.321524i
\(473\) −0.363961 + 0.630399i −0.0167349 + 0.0289858i
\(474\) 0 0
\(475\) 0 0
\(476\) 5.91359 + 14.4853i 0.271049 + 0.663932i
\(477\) 0 0
\(478\) −11.0227 + 6.36396i −0.504167 + 0.291081i
\(479\) −6.00063 + 10.3934i −0.274176 + 0.474886i −0.969927 0.243397i \(-0.921738\pi\)
0.695751 + 0.718283i \(0.255072\pi\)
\(480\) 0 0
\(481\) −0.514719 + 0.297173i −0.0234691 + 0.0135499i
\(482\) 7.22538i 0.329107i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 0 0
\(487\) −12.3090 7.10660i −0.557774 0.322031i 0.194478 0.980907i \(-0.437699\pi\)
−0.752251 + 0.658876i \(0.771032\pi\)
\(488\) 0.878680 0.507306i 0.0397760 0.0229647i
\(489\) 0 0
\(490\) 0 0
\(491\) 13.9706i 0.630483i −0.949012 0.315241i \(-0.897915\pi\)
0.949012 0.315241i \(-0.102085\pi\)
\(492\) 0 0
\(493\) 21.4150 37.0919i 0.964483 1.67053i
\(494\) 12.5446 + 7.24264i 0.564409 + 0.325862i
\(495\) 0 0
\(496\) 9.08052i 0.407727i
\(497\) −4.60660 0.630399i −0.206634 0.0282773i
\(498\) 0 0
\(499\) 15.9706 + 27.6618i 0.714941 + 1.23831i 0.962982 + 0.269564i \(0.0868796\pi\)
−0.248042 + 0.968749i \(0.579787\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 13.7078 + 23.7426i 0.611810 + 1.05969i
\(503\) 31.0028i 1.38235i −0.722688 0.691174i \(-0.757094\pi\)
0.722688 0.691174i \(-0.242906\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −11.0227 + 6.36396i −0.490019 + 0.282913i
\(507\) 0 0
\(508\) 2.80821 + 1.62132i 0.124594 + 0.0719345i
\(509\) −8.59871 14.8934i −0.381131 0.660138i 0.610093 0.792330i \(-0.291132\pi\)
−0.991224 + 0.132191i \(0.957799\pi\)
\(510\) 0 0
\(511\) −3.00000 2.32640i −0.132712 0.102914i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.72792 2.15232i −0.164432 0.0949346i
\(515\) 0 0
\(516\) 0 0
\(517\) 17.7408 0.780238
\(518\) −0.393398 + 0.507306i −0.0172849 + 0.0222897i
\(519\) 0 0
\(520\) 0 0
\(521\) −16.9363 + 29.3345i −0.741993 + 1.28517i 0.209594 + 0.977788i \(0.432786\pi\)
−0.951587 + 0.307380i \(0.900548\pi\)
\(522\) 0 0
\(523\) 3.37706 + 5.84924i 0.147669 + 0.255770i 0.930365 0.366634i \(-0.119490\pi\)
−0.782697 + 0.622403i \(0.786156\pi\)
\(524\) 5.19615 0.226995
\(525\) 0 0
\(526\) 15.2132 0.663327
\(527\) −26.8492 46.5043i −1.16957 2.02576i
\(528\) 0 0
\(529\) 2.50000 4.33013i 0.108696 0.188266i
\(530\) 0 0
\(531\) 0 0
\(532\) 15.5014 + 2.12132i 0.672072 + 0.0919709i
\(533\) −28.9706 −1.25485
\(534\) 0 0
\(535\) 0 0
\(536\) −8.66025 5.00000i −0.374066 0.215967i
\(537\) 0 0
\(538\) −13.9795 −0.602699
\(539\) 14.6969 + 15.0000i 0.633042 + 0.646096i
\(540\) 0 0
\(541\) −7.36396 12.7548i −0.316601 0.548370i 0.663175 0.748464i \(-0.269208\pi\)
−0.979777 + 0.200094i \(0.935875\pi\)
\(542\) 5.37868 + 3.10538i 0.231034 + 0.133388i
\(543\) 0 0
\(544\) −5.12132 + 2.95680i −0.219575 + 0.126772i
\(545\) 0 0
\(546\) 0 0
\(547\) 39.6985i 1.69738i 0.528887 + 0.848692i \(0.322610\pi\)
−0.528887 + 0.848692i \(0.677390\pi\)
\(548\) −1.24264 2.15232i −0.0530830 0.0919424i
\(549\) 0 0
\(550\) 0 0
\(551\) −21.4150 37.0919i −0.912310 1.58017i
\(552\) 0 0
\(553\) −6.75412 + 2.75736i −0.287215 + 0.117255i
\(554\) 12.9706i 0.551066i
\(555\) 0 0
\(556\) 0.514719 + 0.297173i 0.0218289 + 0.0126029i
\(557\) 4.86396 8.42463i 0.206093 0.356963i −0.744388 0.667748i \(-0.767259\pi\)
0.950480 + 0.310785i \(0.100592\pi\)
\(558\) 0 0
\(559\) 0.594346i 0.0251382i
\(560\) 0 0
\(561\) 0 0
\(562\) 5.19615 3.00000i 0.219186 0.126547i
\(563\) 29.9558 + 17.2950i 1.26249 + 0.728898i 0.973555 0.228451i \(-0.0733662\pi\)
0.288933 + 0.957349i \(0.406700\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −21.2049 −0.891307
\(567\) 0 0
\(568\) 1.75736i 0.0737372i
\(569\) 8.87039 5.12132i 0.371866 0.214697i −0.302407 0.953179i \(-0.597790\pi\)
0.674273 + 0.738482i \(0.264457\pi\)
\(570\) 0 0
\(571\) −4.36396 + 7.55860i −0.182626 + 0.316318i −0.942774 0.333432i \(-0.891793\pi\)
0.760148 + 0.649750i \(0.225126\pi\)
\(572\) −6.36396 + 3.67423i −0.266091 + 0.153627i
\(573\) 0 0
\(574\) −28.9706 + 11.8272i −1.20921 + 0.493657i
\(575\) 0 0
\(576\) 0 0
\(577\) 5.34474 9.25736i 0.222504 0.385389i −0.733063 0.680160i \(-0.761910\pi\)
0.955568 + 0.294771i \(0.0952435\pi\)
\(578\) 8.98528 15.5630i 0.373738 0.647334i
\(579\) 0 0
\(580\) 0 0
\(581\) 17.3821 + 2.37868i 0.721129 + 0.0986843i
\(582\) 0 0
\(583\) −18.8169 + 10.8640i −0.779318 + 0.449939i
\(584\) 0.717439 1.24264i 0.0296878 0.0514208i
\(585\) 0 0
\(586\) −0.621320 + 0.358719i −0.0256665 + 0.0148186i
\(587\) 5.19615i 0.214468i −0.994234 0.107234i \(-0.965801\pi\)
0.994234 0.107234i \(-0.0341994\pi\)
\(588\) 0 0
\(589\) −53.6985 −2.21261
\(590\) 0 0
\(591\) 0 0
\(592\) −0.210133 0.121320i −0.00863641 0.00498624i
\(593\) 20.3345 11.7401i 0.835039 0.482110i −0.0205360 0.999789i \(-0.506537\pi\)
0.855575 + 0.517679i \(0.173204\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.51472i 0.143968i
\(597\) 0 0
\(598\) −5.19615 + 9.00000i −0.212486 + 0.368037i
\(599\) 6.45695 + 3.72792i 0.263824 + 0.152319i 0.626078 0.779761i \(-0.284659\pi\)
−0.362254 + 0.932079i \(0.617993\pi\)
\(600\) 0 0
\(601\) 23.3572i 0.952760i −0.879240 0.476380i \(-0.841949\pi\)
0.879240 0.476380i \(-0.158051\pi\)
\(602\) 0.242641 + 0.594346i 0.00988930 + 0.0242237i
\(603\) 0 0
\(604\) −2.62132 4.54026i −0.106660 0.184741i
\(605\) 0 0
\(606\) 0 0
\(607\) 10.0336 + 17.3787i 0.407251 + 0.705379i 0.994581 0.103969i \(-0.0331542\pi\)
−0.587330 + 0.809348i \(0.699821\pi\)
\(608\) 5.91359i 0.239828i
\(609\) 0 0
\(610\) 0 0
\(611\) 12.5446 7.24264i 0.507501 0.293006i
\(612\) 0 0
\(613\) 32.2276 + 18.6066i 1.30166 + 0.751514i 0.980689 0.195575i \(-0.0626575\pi\)
0.320971 + 0.947089i \(0.395991\pi\)
\(614\) −4.98602 8.63604i −0.201219 0.348522i
\(615\) 0 0
\(616\) −4.86396 + 6.27231i −0.195975 + 0.252719i
\(617\) −17.6985 −0.712514 −0.356257 0.934388i \(-0.615947\pi\)
−0.356257 + 0.934388i \(0.615947\pi\)
\(618\) 0 0
\(619\) −5.33452 3.07989i −0.214413 0.123791i 0.388948 0.921260i \(-0.372839\pi\)
−0.603360 + 0.797469i \(0.706172\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 8.95743 0.359160
\(623\) −25.4558 + 10.3923i −1.01987 + 0.416359i
\(624\) 0 0
\(625\) 0 0
\(626\) 9.22911 15.9853i 0.368869 0.638900i
\(627\) 0 0
\(628\) 7.34847 + 12.7279i 0.293236 + 0.507899i
\(629\) 1.43488 0.0572123
\(630\) 0 0
\(631\) 24.7574 0.985575 0.492787 0.870150i \(-0.335978\pi\)
0.492787 + 0.870150i \(0.335978\pi\)
\(632\) −1.37868 2.38794i −0.0548409 0.0949873i
\(633\) 0 0
\(634\) −0.621320 + 1.07616i −0.0246758 + 0.0427397i
\(635\) 0 0
\(636\) 0 0
\(637\) 16.5160 + 4.60660i 0.654389 + 0.182520i
\(638\) 21.7279 0.860217
\(639\) 0 0
\(640\) 0 0
\(641\) −15.3273 8.84924i −0.605393 0.349524i 0.165767 0.986165i \(-0.446990\pi\)
−0.771160 + 0.636641i \(0.780323\pi\)
\(642\) 0 0
\(643\) 32.0174 1.26264 0.631322 0.775520i \(-0.282512\pi\)
0.631322 + 0.775520i \(0.282512\pi\)
\(644\) −1.52192 + 11.1213i −0.0599720 + 0.438241i
\(645\) 0 0
\(646\) −17.4853 30.2854i −0.687949 1.19156i
\(647\) 28.0919 + 16.2189i 1.10441 + 0.637629i 0.937375 0.348323i \(-0.113249\pi\)
0.167031 + 0.985952i \(0.446582\pi\)
\(648\) 0 0
\(649\) 20.9558 12.0989i 0.822589 0.474922i
\(650\) 0 0
\(651\) 0 0
\(652\) 2.24264i 0.0878286i
\(653\) 9.62132 + 16.6646i 0.376511 + 0.652137i 0.990552 0.137138i \(-0.0437903\pi\)
−0.614041 + 0.789274i \(0.710457\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −5.91359 10.2426i −0.230887 0.399908i
\(657\) 0 0
\(658\) 9.58783 12.3640i 0.373772 0.481997i
\(659\) 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 0.960787 0.277288i \(-0.0894357\pi\)
0.240255 + 0.970710i \(0.422769\pi\)
\(662\) 16.7279 28.9736i 0.650149 1.12609i
\(663\) 0 0
\(664\) 6.63103i 0.257334i
\(665\) 0 0
\(666\) 0 0
\(667\) 26.6112 15.3640i 1.03039 0.594895i
\(668\) −13.9706 8.06591i −0.540537 0.312079i
\(669\) 0 0
\(670\) 0 0
\(671\) −3.04384 −0.117506
\(672\) 0 0
\(673\) 17.9706i 0.692714i 0.938103 + 0.346357i \(0.112581\pi\)
−0.938103 + 0.346357i \(0.887419\pi\)
\(674\) 4.33013 2.50000i 0.166790 0.0962964i
\(675\) 0 0
\(676\) 3.50000 6.06218i 0.134615 0.233161i
\(677\) 1.86396 1.07616i 0.0716378 0.0413601i −0.463753 0.885964i \(-0.653498\pi\)
0.535391 + 0.844604i \(0.320164\pi\)
\(678\) 0 0
\(679\) −4.86396 + 35.5431i −0.186662 + 1.36402i
\(680\) 0 0
\(681\) 0 0
\(682\) 13.6208 23.5919i 0.521567 0.903380i
\(683\) 3.98528 6.90271i 0.152493 0.264125i −0.779651 0.626215i \(-0.784603\pi\)
0.932143 + 0.362090i \(0.117937\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 18.3967 2.13604i 0.702388 0.0815543i
\(687\) 0 0
\(688\) −0.210133 + 0.121320i −0.00801125 + 0.00462529i
\(689\) −8.87039 + 15.3640i −0.337935 + 0.585320i
\(690\) 0 0
\(691\) 24.7279 14.2767i 0.940694 0.543110i 0.0505165 0.998723i \(-0.483913\pi\)
0.890178 + 0.455613i \(0.150580\pi\)
\(692\) 20.7846i 0.790112i
\(693\) 0 0
\(694\) −2.48528 −0.0943400
\(695\) 0 0
\(696\) 0 0
\(697\) 60.5708 + 34.9706i 2.29428 + 1.32460i
\(698\) −1.97056 + 1.13770i −0.0745869 + 0.0430628i
\(699\) 0 0
\(700\) 0 0
\(701\) 20.6985i 0.781771i 0.920439 + 0.390885i \(0.127831\pi\)
−0.920439 + 0.390885i \(0.872169\pi\)
\(702\) 0 0
\(703\) 0.717439 1.24264i 0.0270587 0.0468671i
\(704\) −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 0.999972 + 0.00746433i \(0.00237599\pi\)
−0.493522 + 0.869733i \(0.664291\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −5.19615 9.00000i −0.194734 0.337289i
\(713\) 38.5254i 1.44279i
\(714\) 0 0
\(715\) 0 0
\(716\) 22.9369 13.2426i 0.857193 0.494901i
\(717\) 0 0
\(718\) −15.5885 9.00000i −0.581756 0.335877i
\(719\) 8.06591 + 13.9706i 0.300808 + 0.521014i 0.976319 0.216335i \(-0.0694105\pi\)
−0.675511 + 0.737349i \(0.736077\pi\)
\(720\) 0 0
\(721\) −13.4558 + 5.49333i −0.501122 + 0.204582i
\(722\) −15.9706 −0.594363
\(723\) 0 0
\(724\) 10.2426 + 5.91359i 0.380665 + 0.219777i
\(725\) 0 0
\(726\) 0 0
\(727\) 11.7041 0.434081 0.217040 0.976163i \(-0.430360\pi\)
0.217040 + 0.976163i \(0.430360\pi\)
\(728\) −0.878680 + 6.42090i −0.0325660 + 0.237974i
\(729\) 0 0
\(730\) 0 0
\(731\) 0.717439 1.24264i 0.0265354 0.0459607i
\(732\) 0 0
\(733\) 2.36245 + 4.09188i 0.0872591 + 0.151137i 0.906352 0.422524i \(-0.138856\pi\)
−0.819093 + 0.573661i \(0.805523\pi\)
\(734\) 15.4144 0.568955
\(735\) 0 0
\(736\) −4.24264 −0.156386
\(737\) 15.0000 + 25.9808i 0.552532 + 0.957014i
\(738\) 0 0
\(739\) 7.72792 13.3852i 0.284276 0.492381i −0.688157 0.725562i \(-0.741580\pi\)
0.972433 + 0.233181i \(0.0749134\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.59808 + 18.9853i −0.0953784 + 0.696972i
\(743\) −38.4853 −1.41189 −0.705944 0.708268i \(-0.749477\pi\)
−0.705944 + 0.708268i \(0.749477\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 25.5095 + 14.7279i 0.933969 + 0.539228i
\(747\) 0 0
\(748\) 17.7408 0.648667
\(749\) 28.1331 11.4853i 1.02796 0.419663i
\(750\) 0 0
\(751\) −17.6213 30.5210i −0.643011 1.11373i −0.984757 0.173936i \(-0.944352\pi\)
0.341746 0.939792i \(-0.388982\pi\)
\(752\) 5.12132 + 2.95680i 0.186755 + 0.107823i
\(753\) 0 0
\(754\) 15.3640 8.87039i 0.559522 0.323040i
\(755\) 0 0
\(756\) 0 0
\(757\) 33.7574i 1.22693i 0.789721 + 0.613466i \(0.210225\pi\)
−0.789721 + 0.613466i \(0.789775\pi\)
\(758\) 6.24264 + 10.8126i 0.226743 + 0.392730i
\(759\) 0 0
\(760\) 0 0
\(761\) −14.7840 25.6066i −0.535919 0.928239i −0.999118 0.0419845i \(-0.986632\pi\)
0.463199 0.886254i \(-0.346701\pi\)
\(762\) 0 0
\(763\) −38.6485 29.9706i −1.39917 1.08501i
\(764\) 8.48528i 0.306987i
\(765\) 0 0
\(766\) −19.2426 11.1097i −0.695265 0.401411i
\(767\) 9.87868 17.1104i 0.356698 0.617820i
\(768\) 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
\(772\) 8.21449 4.74264i 0.295646 0.170691i
\(773\) 13.9706 + 8.06591i 0.502486 + 0.290111i 0.729740 0.683725i \(-0.239641\pi\)
−0.227253 + 0.973836i \(0.572975\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −13.5592 −0.486748
\(777\) 0 0
\(778\) 31.4558i 1.12775i
\(779\) 60.5708 34.9706i 2.17017 1.25295i
\(780\) 0 0
\(781\) −2.63604 + 4.56575i −0.0943249 + 0.163376i
\(782\) 21.7279 12.5446i 0.776989 0.448595i
\(783\) 0 0
\(784\) 1.74264 + 6.77962i 0.0622372 + 0.242129i
\(785\) 0 0
\(786\) 0 0
\(787\) 16.0958 27.8787i 0.573752 0.993768i −0.422424 0.906398i \(-0.638821\pi\)
0.996176 0.0873693i \(-0.0278460\pi\)
\(788\) 13.2426 22.9369i 0.471750 0.817094i
\(789\) 0 0
\(790\) 0 0
\(791\) −3.04384 + 22.2426i −0.108226 + 0.790857i
\(792\) 0 0
\(793\) −2.15232 + 1.24264i −0.0764310 + 0.0441275i
\(794\) −6.92820 + 12.0000i −0.245873 + 0.425864i
\(795\) 0