Properties

Label 3150.2.bp.d.1349.1
Level 3150
Weight 2
Character 3150.1349
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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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: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.1
Root \(0.965926 + 0.258819i\)
Character \(\chi\) = 3150.1349
Dual form 3150.2.bp.d.899.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.63896 - 0.189469i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.63896 - 0.189469i) q^{7} -1.00000 q^{8} +(-3.44829 + 1.99087i) q^{11} -0.0681483 q^{13} +(-1.48356 + 2.19067i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(6.34607 - 3.66390i) q^{17} +(1.76260 + 1.01764i) q^{19} +3.98174i q^{22} +(-1.86603 + 3.23205i) q^{23} +(-0.0340742 + 0.0590182i) q^{26} +(1.15539 + 2.38014i) q^{28} -0.898979i q^{29} +(-4.18154 + 2.41421i) q^{31} +(0.500000 + 0.866025i) q^{32} -7.32780i q^{34} +(3.52312 + 2.03407i) q^{37} +(1.76260 - 1.01764i) q^{38} -1.68921 q^{41} +0.964724i q^{43} +(3.44829 + 1.99087i) q^{44} +(1.86603 + 3.23205i) q^{46} +(1.43890 + 0.830749i) q^{47} +(6.92820 + 1.00000i) q^{49} +(0.0340742 + 0.0590182i) q^{52} +(6.61339 + 11.4547i) q^{53} +(2.63896 + 0.189469i) q^{56} +(-0.778539 - 0.449490i) q^{58} +(-5.32112 - 9.21645i) q^{59} +(6.51299 + 3.76028i) q^{61} +4.82843i q^{62} +1.00000 q^{64} +(9.23435 - 5.33145i) q^{67} +(-6.34607 - 3.66390i) q^{68} +9.93426i q^{71} +(5.82843 + 10.0951i) q^{73} +(3.52312 - 2.03407i) q^{74} -2.03528i q^{76} +(9.47710 - 4.60048i) q^{77} +(8.77489 - 15.1986i) q^{79} +(-0.844605 + 1.46290i) q^{82} -14.3490i q^{83} +(0.835475 + 0.482362i) q^{86} +(3.44829 - 1.99087i) q^{88} +(-0.913956 + 1.58302i) q^{89} +(0.179841 + 0.0129120i) q^{91} +3.73205 q^{92} +(1.43890 - 0.830749i) q^{94} +17.1502 q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} + O(q^{10}) \) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} - 24q^{11} - 16q^{13} - 4q^{16} + 24q^{17} - 8q^{23} - 8q^{26} + 4q^{32} - 32q^{41} + 24q^{44} + 8q^{46} + 12q^{47} + 8q^{52} + 4q^{53} - 24q^{59} + 8q^{64} - 48q^{67} - 24q^{68} + 24q^{73} - 4q^{77} + 24q^{79} - 16q^{82} + 24q^{88} - 16q^{89} - 20q^{91} + 16q^{92} + 12q^{94} + 48q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.63896 0.189469i −0.997433 0.0716124i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −3.44829 + 1.99087i −1.03970 + 0.600270i −0.919748 0.392510i \(-0.871607\pi\)
−0.119950 + 0.992780i \(0.538273\pi\)
\(12\) 0 0
\(13\) −0.0681483 −0.0189010 −0.00945048 0.999955i \(-0.503008\pi\)
−0.00945048 + 0.999955i \(0.503008\pi\)
\(14\) −1.48356 + 2.19067i −0.396499 + 0.585481i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.34607 3.66390i 1.53915 0.888627i 0.540258 0.841499i \(-0.318327\pi\)
0.998889 0.0471274i \(-0.0150067\pi\)
\(18\) 0 0
\(19\) 1.76260 + 1.01764i 0.404368 + 0.233462i 0.688367 0.725362i \(-0.258328\pi\)
−0.283999 + 0.958825i \(0.591661\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.98174i 0.848910i
\(23\) −1.86603 + 3.23205i −0.389093 + 0.673929i −0.992328 0.123635i \(-0.960545\pi\)
0.603235 + 0.797564i \(0.293878\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −0.0340742 + 0.0590182i −0.00668250 + 0.0115744i
\(27\) 0 0
\(28\) 1.15539 + 2.38014i 0.218349 + 0.449804i
\(29\) 0.898979i 0.166936i −0.996510 0.0834681i \(-0.973400\pi\)
0.996510 0.0834681i \(-0.0265997\pi\)
\(30\) 0 0
\(31\) −4.18154 + 2.41421i −0.751027 + 0.433606i −0.826065 0.563575i \(-0.809426\pi\)
0.0750380 + 0.997181i \(0.476092\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 7.32780i 1.25671i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.52312 + 2.03407i 0.579197 + 0.334400i 0.760814 0.648970i \(-0.224800\pi\)
−0.181617 + 0.983369i \(0.558133\pi\)
\(38\) 1.76260 1.01764i 0.285932 0.165083i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.68921 −0.263810 −0.131905 0.991262i \(-0.542109\pi\)
−0.131905 + 0.991262i \(0.542109\pi\)
\(42\) 0 0
\(43\) 0.964724i 0.147119i 0.997291 + 0.0735595i \(0.0234359\pi\)
−0.997291 + 0.0735595i \(0.976564\pi\)
\(44\) 3.44829 + 1.99087i 0.519849 + 0.300135i
\(45\) 0 0
\(46\) 1.86603 + 3.23205i 0.275130 + 0.476540i
\(47\) 1.43890 + 0.830749i 0.209885 + 0.121177i 0.601258 0.799055i \(-0.294666\pi\)
−0.391373 + 0.920232i \(0.628000\pi\)
\(48\) 0 0
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.0340742 + 0.0590182i 0.00472524 + 0.00818435i
\(53\) 6.61339 + 11.4547i 0.908419 + 1.57343i 0.816260 + 0.577684i \(0.196043\pi\)
0.0921588 + 0.995744i \(0.470623\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.63896 + 0.189469i 0.352646 + 0.0253188i
\(57\) 0 0
\(58\) −0.778539 0.449490i −0.102227 0.0590209i
\(59\) −5.32112 9.21645i −0.692751 1.19988i −0.970933 0.239352i \(-0.923065\pi\)
0.278182 0.960528i \(-0.410268\pi\)
\(60\) 0 0
\(61\) 6.51299 + 3.76028i 0.833903 + 0.481454i 0.855187 0.518319i \(-0.173442\pi\)
−0.0212839 + 0.999773i \(0.506775\pi\)
\(62\) 4.82843i 0.613211i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 9.23435 5.33145i 1.12816 0.651341i 0.184685 0.982798i \(-0.440874\pi\)
0.943470 + 0.331457i \(0.107540\pi\)
\(68\) −6.34607 3.66390i −0.769573 0.444313i
\(69\) 0 0
\(70\) 0 0
\(71\) 9.93426i 1.17898i 0.807776 + 0.589490i \(0.200671\pi\)
−0.807776 + 0.589490i \(0.799329\pi\)
\(72\) 0 0
\(73\) 5.82843 + 10.0951i 0.682166 + 1.18155i 0.974319 + 0.225174i \(0.0722951\pi\)
−0.292153 + 0.956372i \(0.594372\pi\)
\(74\) 3.52312 2.03407i 0.409554 0.236456i
\(75\) 0 0
\(76\) 2.03528i 0.233462i
\(77\) 9.47710 4.60048i 1.08002 0.524273i
\(78\) 0 0
\(79\) 8.77489 15.1986i 0.987252 1.70997i 0.355787 0.934567i \(-0.384213\pi\)
0.631465 0.775404i \(-0.282454\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.844605 + 1.46290i −0.0932711 + 0.161550i
\(83\) 14.3490i 1.57501i −0.616311 0.787503i \(-0.711374\pi\)
0.616311 0.787503i \(-0.288626\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.835475 + 0.482362i 0.0900916 + 0.0520144i
\(87\) 0 0
\(88\) 3.44829 1.99087i 0.367589 0.212227i
\(89\) −0.913956 + 1.58302i −0.0968791 + 0.167800i −0.910391 0.413748i \(-0.864219\pi\)
0.813512 + 0.581548i \(0.197553\pi\)
\(90\) 0 0
\(91\) 0.179841 + 0.0129120i 0.0188524 + 0.00135354i
\(92\) 3.73205 0.389093
\(93\) 0 0
\(94\) 1.43890 0.830749i 0.148411 0.0856852i
\(95\) 0 0
\(96\) 0 0
\(97\) 17.1502 1.74134 0.870668 0.491870i \(-0.163687\pi\)
0.870668 + 0.491870i \(0.163687\pi\)
\(98\) 4.33013 5.50000i 0.437409 0.555584i
\(99\) 0 0
\(100\) 0 0
\(101\) 3.36773 + 5.83307i 0.335101 + 0.580412i 0.983504 0.180885i \(-0.0578962\pi\)
−0.648403 + 0.761297i \(0.724563\pi\)
\(102\) 0 0
\(103\) 0.260021 0.450370i 0.0256206 0.0443762i −0.852931 0.522024i \(-0.825177\pi\)
0.878551 + 0.477648i \(0.158510\pi\)
\(104\) 0.0681483 0.00668250
\(105\) 0 0
\(106\) 13.2268 1.28470
\(107\) 3.06350 5.30614i 0.296160 0.512964i −0.679094 0.734051i \(-0.737627\pi\)
0.975254 + 0.221087i \(0.0709605\pi\)
\(108\) 0 0
\(109\) 6.77729 + 11.7386i 0.649147 + 1.12436i 0.983327 + 0.181846i \(0.0582074\pi\)
−0.334180 + 0.942509i \(0.608459\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.48356 2.19067i 0.140184 0.206999i
\(113\) 11.6982 1.10047 0.550236 0.835009i \(-0.314538\pi\)
0.550236 + 0.835009i \(0.314538\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.778539 + 0.449490i −0.0722855 + 0.0417341i
\(117\) 0 0
\(118\) −10.6422 −0.979698
\(119\) −17.4412 + 8.46651i −1.59883 + 0.776123i
\(120\) 0 0
\(121\) 2.42713 4.20390i 0.220648 0.382173i
\(122\) 6.51299 3.76028i 0.589659 0.340440i
\(123\) 0 0
\(124\) 4.18154 + 2.41421i 0.375513 + 0.216803i
\(125\) 0 0
\(126\) 0 0
\(127\) 10.7530i 0.954173i 0.878856 + 0.477086i \(0.158307\pi\)
−0.878856 + 0.477086i \(0.841693\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.85457 + 3.21221i −0.162035 + 0.280653i −0.935598 0.353066i \(-0.885139\pi\)
0.773564 + 0.633719i \(0.218472\pi\)
\(132\) 0 0
\(133\) −4.45862 3.01946i −0.386611 0.261821i
\(134\) 10.6629i 0.921135i
\(135\) 0 0
\(136\) −6.34607 + 3.66390i −0.544171 + 0.314177i
\(137\) −6.76028 11.7091i −0.577570 1.00038i −0.995757 0.0920192i \(-0.970668\pi\)
0.418188 0.908361i \(-0.362665\pi\)
\(138\) 0 0
\(139\) 9.06251i 0.768672i 0.923193 + 0.384336i \(0.125570\pi\)
−0.923193 + 0.384336i \(0.874430\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.60332 + 4.96713i 0.721974 + 0.416832i
\(143\) 0.234995 0.135674i 0.0196513 0.0113457i
\(144\) 0 0
\(145\) 0 0
\(146\) 11.6569 0.964728
\(147\) 0 0
\(148\) 4.06815i 0.334400i
\(149\) −13.2385 7.64324i −1.08454 0.626158i −0.152421 0.988316i \(-0.548707\pi\)
−0.932117 + 0.362157i \(0.882040\pi\)
\(150\) 0 0
\(151\) 4.93942 + 8.55532i 0.401964 + 0.696222i 0.993963 0.109717i \(-0.0349944\pi\)
−0.591999 + 0.805939i \(0.701661\pi\)
\(152\) −1.76260 1.01764i −0.142966 0.0825413i
\(153\) 0 0
\(154\) 0.754415 10.5076i 0.0607925 0.846730i
\(155\) 0 0
\(156\) 0 0
\(157\) 7.14418 + 12.3741i 0.570168 + 0.987560i 0.996548 + 0.0830157i \(0.0264552\pi\)
−0.426380 + 0.904544i \(0.640212\pi\)
\(158\) −8.77489 15.1986i −0.698093 1.20913i
\(159\) 0 0
\(160\) 0 0
\(161\) 5.53674 8.17569i 0.436356 0.644335i
\(162\) 0 0
\(163\) 8.64083 + 4.98879i 0.676802 + 0.390752i 0.798649 0.601797i \(-0.205548\pi\)
−0.121847 + 0.992549i \(0.538882\pi\)
\(164\) 0.844605 + 1.46290i 0.0659526 + 0.114233i
\(165\) 0 0
\(166\) −12.4266 7.17449i −0.964490 0.556849i
\(167\) 13.7778i 1.06616i 0.846065 + 0.533079i \(0.178965\pi\)
−0.846065 + 0.533079i \(0.821035\pi\)
\(168\) 0 0
\(169\) −12.9954 −0.999643
\(170\) 0 0
\(171\) 0 0
\(172\) 0.835475 0.482362i 0.0637044 0.0367798i
\(173\) −7.16442 4.13638i −0.544701 0.314483i 0.202281 0.979327i \(-0.435164\pi\)
−0.746982 + 0.664844i \(0.768498\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.98174i 0.300135i
\(177\) 0 0
\(178\) 0.913956 + 1.58302i 0.0685039 + 0.118652i
\(179\) −9.97501 + 5.75908i −0.745568 + 0.430454i −0.824090 0.566459i \(-0.808313\pi\)
0.0785226 + 0.996912i \(0.474980\pi\)
\(180\) 0 0
\(181\) 16.5924i 1.23330i −0.787237 0.616650i \(-0.788489\pi\)
0.787237 0.616650i \(-0.211511\pi\)
\(182\) 0.101102 0.149291i 0.00749421 0.0110662i
\(183\) 0 0
\(184\) 1.86603 3.23205i 0.137565 0.238270i
\(185\) 0 0
\(186\) 0 0
\(187\) −14.5887 + 25.2684i −1.06683 + 1.84781i
\(188\) 1.66150i 0.121177i
\(189\) 0 0
\(190\) 0 0
\(191\) −15.9640 9.21682i −1.15511 0.666905i −0.204986 0.978765i \(-0.565715\pi\)
−0.950128 + 0.311859i \(0.899048\pi\)
\(192\) 0 0
\(193\) 5.50643 3.17914i 0.396361 0.228839i −0.288552 0.957464i \(-0.593174\pi\)
0.684913 + 0.728625i \(0.259840\pi\)
\(194\) 8.57509 14.8525i 0.615656 1.06635i
\(195\) 0 0
\(196\) −2.59808 6.50000i −0.185577 0.464286i
\(197\) 12.8389 0.914734 0.457367 0.889278i \(-0.348792\pi\)
0.457367 + 0.889278i \(0.348792\pi\)
\(198\) 0 0
\(199\) 8.33950 4.81481i 0.591171 0.341313i −0.174389 0.984677i \(-0.555795\pi\)
0.765561 + 0.643364i \(0.222462\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 6.73545 0.473905
\(203\) −0.170328 + 2.37237i −0.0119547 + 0.166508i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.260021 0.450370i −0.0181165 0.0313787i
\(207\) 0 0
\(208\) 0.0340742 0.0590182i 0.00236262 0.00409218i
\(209\) −8.10394 −0.560561
\(210\) 0 0
\(211\) −14.5619 −1.00248 −0.501241 0.865308i \(-0.667123\pi\)
−0.501241 + 0.865308i \(0.667123\pi\)
\(212\) 6.61339 11.4547i 0.454210 0.786714i
\(213\) 0 0
\(214\) −3.06350 5.30614i −0.209417 0.362721i
\(215\) 0 0
\(216\) 0 0
\(217\) 11.4923 5.57874i 0.780150 0.378709i
\(218\) 13.5546 0.918033
\(219\) 0 0
\(220\) 0 0
\(221\) −0.432474 + 0.249689i −0.0290913 + 0.0167959i
\(222\) 0 0
\(223\) 23.6609 1.58445 0.792227 0.610227i \(-0.208922\pi\)
0.792227 + 0.610227i \(0.208922\pi\)
\(224\) −1.15539 2.38014i −0.0771980 0.159030i
\(225\) 0 0
\(226\) 5.84909 10.1309i 0.389076 0.673899i
\(227\) −7.48288 + 4.32024i −0.496656 + 0.286744i −0.727332 0.686286i \(-0.759240\pi\)
0.230676 + 0.973031i \(0.425906\pi\)
\(228\) 0 0
\(229\) 12.1896 + 7.03768i 0.805513 + 0.465063i 0.845395 0.534141i \(-0.179365\pi\)
−0.0398824 + 0.999204i \(0.512698\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.898979i 0.0590209i
\(233\) −10.0988 + 17.4916i −0.661593 + 1.14591i 0.318604 + 0.947888i \(0.396786\pi\)
−0.980197 + 0.198025i \(0.936547\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.32112 + 9.21645i −0.346375 + 0.599940i
\(237\) 0 0
\(238\) −1.38839 + 19.3378i −0.0899959 + 1.25348i
\(239\) 23.5040i 1.52035i −0.649721 0.760173i \(-0.725114\pi\)
0.649721 0.760173i \(-0.274886\pi\)
\(240\) 0 0
\(241\) −12.8765 + 7.43426i −0.829449 + 0.478883i −0.853664 0.520824i \(-0.825625\pi\)
0.0242151 + 0.999707i \(0.492291\pi\)
\(242\) −2.42713 4.20390i −0.156022 0.270237i
\(243\) 0 0
\(244\) 7.52056i 0.481454i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.120118 0.0693504i −0.00764295 0.00441266i
\(248\) 4.18154 2.41421i 0.265528 0.153303i
\(249\) 0 0
\(250\) 0 0
\(251\) 4.31736 0.272509 0.136255 0.990674i \(-0.456493\pi\)
0.136255 + 0.990674i \(0.456493\pi\)
\(252\) 0 0
\(253\) 14.8601i 0.934244i
\(254\) 9.31236 + 5.37649i 0.584309 + 0.337351i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.18570 2.41662i −0.261097 0.150744i 0.363738 0.931501i \(-0.381500\pi\)
−0.624835 + 0.780757i \(0.714834\pi\)
\(258\) 0 0
\(259\) −8.91197 6.03536i −0.553763 0.375019i
\(260\) 0 0
\(261\) 0 0
\(262\) 1.85457 + 3.21221i 0.114576 + 0.198451i
\(263\) 3.33245 + 5.77197i 0.205488 + 0.355915i 0.950288 0.311372i \(-0.100789\pi\)
−0.744800 + 0.667287i \(0.767455\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.84424 + 2.35155i −0.297019 + 0.144183i
\(267\) 0 0
\(268\) −9.23435 5.33145i −0.564078 0.325670i
\(269\) 15.8700 + 27.4877i 0.967612 + 1.67595i 0.702426 + 0.711757i \(0.252100\pi\)
0.265186 + 0.964197i \(0.414567\pi\)
\(270\) 0 0
\(271\) 15.1244 + 8.73205i 0.918739 + 0.530434i 0.883233 0.468935i \(-0.155362\pi\)
0.0355066 + 0.999369i \(0.488696\pi\)
\(272\) 7.32780i 0.444313i
\(273\) 0 0
\(274\) −13.5206 −0.816807
\(275\) 0 0
\(276\) 0 0
\(277\) −20.3557 + 11.7524i −1.22305 + 0.706130i −0.965568 0.260152i \(-0.916227\pi\)
−0.257486 + 0.966282i \(0.582894\pi\)
\(278\) 7.84836 + 4.53125i 0.470714 + 0.271767i
\(279\) 0 0
\(280\) 0 0
\(281\) 15.4159i 0.919635i 0.888013 + 0.459817i \(0.152085\pi\)
−0.888013 + 0.459817i \(0.847915\pi\)
\(282\) 0 0
\(283\) 13.8554 + 23.9983i 0.823619 + 1.42655i 0.902970 + 0.429703i \(0.141382\pi\)
−0.0793517 + 0.996847i \(0.525285\pi\)
\(284\) 8.60332 4.96713i 0.510513 0.294745i
\(285\) 0 0
\(286\) 0.271349i 0.0160452i
\(287\) 4.45776 + 0.320053i 0.263133 + 0.0188921i
\(288\) 0 0
\(289\) 18.3484 31.7803i 1.07932 1.86943i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.82843 10.0951i 0.341083 0.590773i
\(293\) 2.84377i 0.166135i 0.996544 + 0.0830673i \(0.0264717\pi\)
−0.996544 + 0.0830673i \(0.973528\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −3.52312 2.03407i −0.204777 0.118228i
\(297\) 0 0
\(298\) −13.2385 + 7.64324i −0.766884 + 0.442761i
\(299\) 0.127167 0.220259i 0.00735423 0.0127379i
\(300\) 0 0
\(301\) 0.182785 2.54587i 0.0105355 0.146741i
\(302\) 9.87883 0.568463
\(303\) 0 0
\(304\) −1.76260 + 1.01764i −0.101092 + 0.0583655i
\(305\) 0 0
\(306\) 0 0
\(307\) −2.52180 −0.143927 −0.0719634 0.997407i \(-0.522926\pi\)
−0.0719634 + 0.997407i \(0.522926\pi\)
\(308\) −8.72268 5.90717i −0.497021 0.336592i
\(309\) 0 0
\(310\) 0 0
\(311\) −5.49697 9.52104i −0.311705 0.539889i 0.667027 0.745034i \(-0.267567\pi\)
−0.978732 + 0.205145i \(0.934233\pi\)
\(312\) 0 0
\(313\) 12.4731 21.6040i 0.705020 1.22113i −0.261665 0.965159i \(-0.584271\pi\)
0.966684 0.255971i \(-0.0823952\pi\)
\(314\) 14.2884 0.806339
\(315\) 0 0
\(316\) −17.5498 −0.987252
\(317\) 7.53465 13.0504i 0.423188 0.732984i −0.573061 0.819513i \(-0.694244\pi\)
0.996249 + 0.0865290i \(0.0275775\pi\)
\(318\) 0 0
\(319\) 1.78975 + 3.09994i 0.100207 + 0.173563i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.31199 8.88280i −0.240298 0.495019i
\(323\) 14.9141 0.829843
\(324\) 0 0
\(325\) 0 0
\(326\) 8.64083 4.98879i 0.478572 0.276303i
\(327\) 0 0
\(328\) 1.68921 0.0932711
\(329\) −3.63980 2.46494i −0.200668 0.135896i
\(330\) 0 0
\(331\) −15.0904 + 26.1373i −0.829444 + 1.43664i 0.0690315 + 0.997614i \(0.478009\pi\)
−0.898475 + 0.439024i \(0.855324\pi\)
\(332\) −12.4266 + 7.17449i −0.681997 + 0.393751i
\(333\) 0 0
\(334\) 11.9319 + 6.88891i 0.652886 + 0.376944i
\(335\) 0 0
\(336\) 0 0
\(337\) 21.5911i 1.17614i −0.808809 0.588071i \(-0.799887\pi\)
0.808809 0.588071i \(-0.200113\pi\)
\(338\) −6.49768 + 11.2543i −0.353427 + 0.612154i
\(339\) 0 0
\(340\) 0 0
\(341\) 9.61277 16.6498i 0.520561 0.901638i
\(342\) 0 0
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 0.964724i 0.0520144i
\(345\) 0 0
\(346\) −7.16442 + 4.13638i −0.385161 + 0.222373i
\(347\) −11.5921 20.0781i −0.622297 1.07785i −0.989057 0.147534i \(-0.952866\pi\)
0.366760 0.930316i \(-0.380467\pi\)
\(348\) 0 0
\(349\) 10.7287i 0.574292i 0.957887 + 0.287146i \(0.0927064\pi\)
−0.957887 + 0.287146i \(0.907294\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.44829 1.99087i −0.183794 0.106114i
\(353\) −7.57561 + 4.37378i −0.403209 + 0.232793i −0.687868 0.725836i \(-0.741453\pi\)
0.284659 + 0.958629i \(0.408120\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.82791 0.0968791
\(357\) 0 0
\(358\) 11.5182i 0.608753i
\(359\) −22.3059 12.8783i −1.17726 0.679691i −0.221881 0.975074i \(-0.571220\pi\)
−0.955379 + 0.295382i \(0.904553\pi\)
\(360\) 0 0
\(361\) −7.42883 12.8671i −0.390991 0.677216i
\(362\) −14.3694 8.29618i −0.755239 0.436037i
\(363\) 0 0
\(364\) −0.0787382 0.162203i −0.00412700 0.00850172i
\(365\) 0 0
\(366\) 0 0
\(367\) 9.96885 + 17.2665i 0.520369 + 0.901306i 0.999720 + 0.0236826i \(0.00753911\pi\)
−0.479350 + 0.877624i \(0.659128\pi\)
\(368\) −1.86603 3.23205i −0.0972733 0.168482i
\(369\) 0 0
\(370\) 0 0
\(371\) −15.2822 31.4816i −0.793410 1.63444i
\(372\) 0 0
\(373\) 0.893327 + 0.515762i 0.0462547 + 0.0267052i 0.522949 0.852364i \(-0.324832\pi\)
−0.476694 + 0.879069i \(0.658165\pi\)
\(374\) 14.5887 + 25.2684i 0.754364 + 1.30660i
\(375\) 0 0
\(376\) −1.43890 0.830749i −0.0742056 0.0428426i
\(377\) 0.0612640i 0.00315525i
\(378\) 0 0
\(379\) −5.09497 −0.261711 −0.130855 0.991401i \(-0.541772\pi\)
−0.130855 + 0.991401i \(0.541772\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −15.9640 + 9.21682i −0.816789 + 0.471573i
\(383\) −7.33307 4.23375i −0.374702 0.216335i 0.300808 0.953685i \(-0.402744\pi\)
−0.675511 + 0.737350i \(0.736077\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.35827i 0.323628i
\(387\) 0 0
\(388\) −8.57509 14.8525i −0.435334 0.754021i
\(389\) 4.97229 2.87075i 0.252105 0.145553i −0.368623 0.929579i \(-0.620171\pi\)
0.620728 + 0.784026i \(0.286837\pi\)
\(390\) 0 0
\(391\) 27.3477i 1.38303i
\(392\) −6.92820 1.00000i −0.349927 0.0505076i
\(393\) 0 0
\(394\) 6.41946 11.1188i 0.323407 0.560158i
\(395\) 0 0
\(396\) 0 0
\(397\) −8.43791 + 14.6149i −0.423487 + 0.733501i −0.996278 0.0862009i \(-0.972527\pi\)
0.572791 + 0.819701i \(0.305861\pi\)
\(398\) 9.62962i 0.482689i
\(399\) 0 0
\(400\) 0 0
\(401\) 1.63572 + 0.944382i 0.0816838 + 0.0471602i 0.540286 0.841482i \(-0.318316\pi\)
−0.458602 + 0.888642i \(0.651650\pi\)
\(402\) 0 0
\(403\) 0.284965 0.164525i 0.0141951 0.00819556i
\(404\) 3.36773 5.83307i 0.167551 0.290206i
\(405\) 0 0
\(406\) 1.96937 + 1.33369i 0.0977381 + 0.0661901i
\(407\) −16.1983 −0.802920
\(408\) 0 0
\(409\) −28.5617 + 16.4901i −1.41228 + 0.815382i −0.995603 0.0936705i \(-0.970140\pi\)
−0.416681 + 0.909053i \(0.636807\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.520042 −0.0256206
\(413\) 12.2960 + 25.3300i 0.605046 + 1.24641i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.0340742 0.0590182i −0.00167062 0.00289361i
\(417\) 0 0
\(418\) −4.05197 + 7.01822i −0.198188 + 0.343272i
\(419\) 0.300470 0.0146789 0.00733945 0.999973i \(-0.497664\pi\)
0.00733945 + 0.999973i \(0.497664\pi\)
\(420\) 0 0
\(421\) 28.8625 1.40667 0.703335 0.710858i \(-0.251693\pi\)
0.703335 + 0.710858i \(0.251693\pi\)
\(422\) −7.28094 + 12.6110i −0.354431 + 0.613892i
\(423\) 0 0
\(424\) −6.61339 11.4547i −0.321175 0.556291i
\(425\) 0 0
\(426\) 0 0
\(427\) −16.4751 11.1572i −0.797284 0.539936i
\(428\) −6.12701 −0.296160
\(429\) 0 0
\(430\) 0 0
\(431\) 29.0895 16.7948i 1.40119 0.808978i 0.406677 0.913572i \(-0.366688\pi\)
0.994515 + 0.104594i \(0.0333543\pi\)
\(432\) 0 0
\(433\) −11.2207 −0.539234 −0.269617 0.962968i \(-0.586897\pi\)
−0.269617 + 0.962968i \(0.586897\pi\)
\(434\) 0.914836 12.7420i 0.0439135 0.611636i
\(435\) 0 0
\(436\) 6.77729 11.7386i 0.324574 0.562178i
\(437\) −6.57812 + 3.79788i −0.314674 + 0.181677i
\(438\) 0 0
\(439\) 14.6075 + 8.43363i 0.697177 + 0.402515i 0.806295 0.591513i \(-0.201469\pi\)
−0.109118 + 0.994029i \(0.534803\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0.499378i 0.0237530i
\(443\) 1.02823 1.78094i 0.0488526 0.0846152i −0.840565 0.541711i \(-0.817777\pi\)
0.889418 + 0.457095i \(0.151110\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 11.8305 20.4910i 0.560189 0.970276i
\(447\) 0 0
\(448\) −2.63896 0.189469i −0.124679 0.00895155i
\(449\) 12.5892i 0.594122i −0.954858 0.297061i \(-0.903994\pi\)
0.954858 0.297061i \(-0.0960065\pi\)
\(450\) 0 0
\(451\) 5.82489 3.36300i 0.274283 0.158357i
\(452\) −5.84909 10.1309i −0.275118 0.476519i
\(453\) 0 0
\(454\) 8.64048i 0.405518i
\(455\) 0 0
\(456\) 0 0
\(457\) −30.2701 17.4765i −1.41598 0.817515i −0.420035 0.907508i \(-0.637982\pi\)
−0.995942 + 0.0899930i \(0.971316\pi\)
\(458\) 12.1896 7.03768i 0.569584 0.328849i
\(459\) 0 0
\(460\) 0 0
\(461\) −23.3750 −1.08868 −0.544341 0.838864i \(-0.683220\pi\)
−0.544341 + 0.838864i \(0.683220\pi\)
\(462\) 0 0
\(463\) 6.35693i 0.295431i 0.989030 + 0.147716i \(0.0471921\pi\)
−0.989030 + 0.147716i \(0.952808\pi\)
\(464\) 0.778539 + 0.449490i 0.0361428 + 0.0208670i
\(465\) 0 0
\(466\) 10.0988 + 17.4916i 0.467817 + 0.810283i
\(467\) −6.74907 3.89658i −0.312310 0.180312i 0.335650 0.941987i \(-0.391044\pi\)
−0.647960 + 0.761675i \(0.724377\pi\)
\(468\) 0 0
\(469\) −25.3792 + 12.3199i −1.17190 + 0.568878i
\(470\) 0 0
\(471\) 0 0
\(472\) 5.32112 + 9.21645i 0.244924 + 0.424222i
\(473\) −1.92064 3.32665i −0.0883111 0.152959i
\(474\) 0 0
\(475\) 0 0
\(476\) 16.0528 + 10.8713i 0.735779 + 0.498284i
\(477\) 0 0
\(478\) −20.3550 11.7520i −0.931018 0.537523i
\(479\) 13.7520 + 23.8191i 0.628344 + 1.08832i 0.987884 + 0.155194i \(0.0496004\pi\)
−0.359540 + 0.933130i \(0.617066\pi\)
\(480\) 0 0
\(481\) −0.240095 0.138619i −0.0109474 0.00632047i
\(482\) 14.8685i 0.677242i
\(483\) 0 0
\(484\) −4.85425 −0.220648
\(485\) 0 0
\(486\) 0 0
\(487\) 30.6978 17.7234i 1.39105 0.803124i 0.397619 0.917551i \(-0.369836\pi\)
0.993432 + 0.114427i \(0.0365032\pi\)
\(488\) −6.51299 3.76028i −0.294829 0.170220i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.64349i 0.0741695i 0.999312 + 0.0370848i \(0.0118072\pi\)
−0.999312 + 0.0370848i \(0.988193\pi\)
\(492\) 0 0
\(493\) −3.29377 5.70498i −0.148344 0.256939i
\(494\) −0.120118 + 0.0693504i −0.00540438 + 0.00312022i
\(495\) 0 0
\(496\) 4.82843i 0.216803i
\(497\) 1.88223 26.2161i 0.0844296 1.17595i
\(498\) 0 0
\(499\) −17.3665 + 30.0796i −0.777430 + 1.34655i 0.155988 + 0.987759i \(0.450144\pi\)
−0.933418 + 0.358790i \(0.883189\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 2.15868 3.73894i 0.0963465 0.166877i
\(503\) 28.9613i 1.29132i 0.763625 + 0.645660i \(0.223418\pi\)
−0.763625 + 0.645660i \(0.776582\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −12.8692 7.43003i −0.572105 0.330305i
\(507\) 0 0
\(508\) 9.31236 5.37649i 0.413169 0.238543i
\(509\) −10.7311 + 18.5867i −0.475646 + 0.823842i −0.999611 0.0278973i \(-0.991119\pi\)
0.523965 + 0.851740i \(0.324452\pi\)
\(510\) 0 0
\(511\) −13.4683 27.7449i −0.595801 1.22736i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −4.18570 + 2.41662i −0.184624 + 0.106592i
\(515\) 0 0
\(516\) 0 0
\(517\) −6.61565 −0.290956
\(518\) −9.68276 + 4.70032i −0.425436 + 0.206520i
\(519\) 0 0
\(520\) 0 0
\(521\) 20.1218 + 34.8520i 0.881552 + 1.52689i 0.849616 + 0.527403i \(0.176834\pi\)
0.0319362 + 0.999490i \(0.489833\pi\)
\(522\) 0 0
\(523\) 14.8444 25.7113i 0.649102 1.12428i −0.334235 0.942490i \(-0.608478\pi\)
0.983338 0.181789i \(-0.0581887\pi\)
\(524\) 3.70915 0.162035
\(525\) 0 0
\(526\) 6.66490 0.290603
\(527\) −17.6909 + 30.6415i −0.770627 + 1.33477i
\(528\) 0 0
\(529\) 4.53590 + 7.85641i 0.197213 + 0.341583i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.385621 + 5.37101i −0.0167188 + 0.232863i
\(533\) 0.115117 0.00498627
\(534\) 0 0
\(535\) 0 0
\(536\) −9.23435 + 5.33145i −0.398863 + 0.230284i
\(537\) 0 0
\(538\) 31.7400 1.36841
\(539\) −25.8813 + 10.3449i −1.11479 + 0.445585i
\(540\) 0 0
\(541\) 8.62914 14.9461i 0.370996 0.642584i −0.618723 0.785609i \(-0.712350\pi\)
0.989719 + 0.143026i \(0.0456831\pi\)
\(542\) 15.1244 8.73205i 0.649647 0.375074i
\(543\) 0 0
\(544\) 6.34607 + 3.66390i 0.272085 + 0.157089i
\(545\) 0 0
\(546\) 0 0
\(547\) 17.9703i 0.768354i −0.923260 0.384177i \(-0.874485\pi\)
0.923260 0.384177i \(-0.125515\pi\)
\(548\) −6.76028 + 11.7091i −0.288785 + 0.500190i
\(549\) 0 0
\(550\) 0 0
\(551\) 0.914836 1.58454i 0.0389733 0.0675038i
\(552\) 0 0
\(553\) −26.0362 + 38.4458i −1.10717 + 1.63488i
\(554\) 23.5047i 0.998619i
\(555\) 0 0
\(556\) 7.84836 4.53125i 0.332845 0.192168i
\(557\) 22.6273 + 39.1916i 0.958748 + 1.66060i 0.725547 + 0.688172i \(0.241587\pi\)
0.233201 + 0.972428i \(0.425080\pi\)
\(558\) 0 0
\(559\) 0.0657443i 0.00278069i
\(560\) 0 0
\(561\) 0 0
\(562\) 13.3506 + 7.70794i 0.563159 + 0.325140i
\(563\) 13.7410 7.93336i 0.579114 0.334351i −0.181667 0.983360i \(-0.558149\pi\)
0.760781 + 0.649009i \(0.224816\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 27.7108 1.16477
\(567\) 0 0
\(568\) 9.93426i 0.416832i
\(569\) −0.0524375 0.0302748i −0.00219829 0.00126918i 0.498900 0.866659i \(-0.333737\pi\)
−0.501099 + 0.865390i \(0.667071\pi\)
\(570\) 0 0
\(571\) 6.78245 + 11.7476i 0.283837 + 0.491620i 0.972326 0.233626i \(-0.0750592\pi\)
−0.688490 + 0.725246i \(0.741726\pi\)
\(572\) −0.234995 0.135674i −0.00982564 0.00567284i
\(573\) 0 0
\(574\) 2.50605 3.70050i 0.104601 0.154456i
\(575\) 0 0
\(576\) 0 0
\(577\) −21.8384 37.8252i −0.909144 1.57468i −0.815256 0.579101i \(-0.803404\pi\)
−0.0938887 0.995583i \(-0.529930\pi\)
\(578\) −18.3484 31.7803i −0.763191 1.32189i
\(579\) 0 0
\(580\) 0 0
\(581\) −2.71868 + 37.8664i −0.112790 + 1.57096i
\(582\) 0 0
\(583\) −45.6098 26.3328i −1.88896 1.09059i
\(584\) −5.82843 10.0951i −0.241182 0.417740i
\(585\) 0 0
\(586\) 2.46278 + 1.42188i 0.101736 + 0.0587375i
\(587\) 45.4100i 1.87427i 0.348967 + 0.937135i \(0.386532\pi\)
−0.348967 + 0.937135i \(0.613468\pi\)
\(588\) 0 0
\(589\) −9.82718 −0.404922
\(590\) 0 0
\(591\) 0 0
\(592\) −3.52312 + 2.03407i −0.144799 + 0.0835999i
\(593\) −22.2579 12.8506i −0.914022 0.527711i −0.0322991 0.999478i \(-0.510283\pi\)
−0.881723 + 0.471767i \(0.843616\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.2865i 0.626158i
\(597\) 0 0
\(598\) −0.127167 0.220259i −0.00520023 0.00900706i
\(599\) 23.0347 13.2991i 0.941173 0.543386i 0.0508450 0.998707i \(-0.483809\pi\)
0.890328 + 0.455320i \(0.150475\pi\)
\(600\) 0 0
\(601\) 12.9681i 0.528979i −0.964389 0.264489i \(-0.914797\pi\)
0.964389 0.264489i \(-0.0852034\pi\)
\(602\) −2.11339 1.43123i −0.0861354 0.0583326i
\(603\) 0 0
\(604\) 4.93942 8.55532i 0.200982 0.348111i
\(605\) 0 0
\(606\) 0 0
\(607\) 8.15576 14.1262i 0.331032 0.573364i −0.651682 0.758492i \(-0.725937\pi\)
0.982714 + 0.185128i \(0.0592698\pi\)
\(608\) 2.03528i 0.0825413i
\(609\) 0 0
\(610\) 0 0
\(611\) −0.0980586 0.0566142i −0.00396703 0.00229036i
\(612\) 0 0
\(613\) 12.4603 7.19395i 0.503267 0.290561i −0.226795 0.973943i \(-0.572825\pi\)
0.730062 + 0.683381i \(0.239491\pi\)
\(614\) −1.26090 + 2.18394i −0.0508858 + 0.0881368i
\(615\) 0 0
\(616\) −9.47710 + 4.60048i −0.381843 + 0.185359i
\(617\) 8.65760 0.348542 0.174271 0.984698i \(-0.444243\pi\)
0.174271 + 0.984698i \(0.444243\pi\)
\(618\) 0 0
\(619\) −38.8459 + 22.4277i −1.56135 + 0.901444i −0.564225 + 0.825621i \(0.690825\pi\)
−0.997121 + 0.0758230i \(0.975842\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −10.9939 −0.440817
\(623\) 2.71182 4.00435i 0.108647 0.160431i
\(624\) 0 0
\(625\) 0 0
\(626\) −12.4731 21.6040i −0.498524 0.863469i
\(627\) 0 0
\(628\) 7.14418 12.3741i 0.285084 0.493780i
\(629\) 29.8106 1.18863
\(630\) 0 0
\(631\) −38.1878 −1.52023 −0.760116 0.649788i \(-0.774858\pi\)
−0.760116 + 0.649788i \(0.774858\pi\)
\(632\) −8.77489 + 15.1986i −0.349046 + 0.604566i
\(633\) 0 0
\(634\) −7.53465 13.0504i −0.299239 0.518298i
\(635\) 0 0
\(636\) 0 0
\(637\) −0.472146 0.0681483i −0.0187071 0.00270014i
\(638\) 3.57950 0.141714
\(639\) 0 0
\(640\) 0 0
\(641\) −7.40533 + 4.27547i −0.292493 + 0.168871i −0.639066 0.769152i \(-0.720679\pi\)
0.346573 + 0.938023i \(0.387345\pi\)
\(642\) 0 0
\(643\) −2.75058 −0.108472 −0.0542361 0.998528i \(-0.517272\pi\)
−0.0542361 + 0.998528i \(0.517272\pi\)
\(644\) −9.84873 0.707107i −0.388094 0.0278639i
\(645\) 0 0
\(646\) 7.45705 12.9160i 0.293394 0.508173i
\(647\) −24.0431 + 13.8813i −0.945234 + 0.545731i −0.891597 0.452830i \(-0.850415\pi\)
−0.0536365 + 0.998561i \(0.517081\pi\)
\(648\) 0 0
\(649\) 36.6975 + 21.1873i 1.44050 + 0.831675i
\(650\) 0 0
\(651\) 0 0
\(652\) 9.97758i 0.390752i
\(653\) 7.05994 12.2282i 0.276277 0.478525i −0.694180 0.719802i \(-0.744233\pi\)
0.970456 + 0.241276i \(0.0775660\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.844605 1.46290i 0.0329763 0.0571166i
\(657\) 0 0
\(658\) −3.95460 + 1.91969i −0.154166 + 0.0748372i
\(659\) 9.92570i 0.386650i 0.981135 + 0.193325i \(0.0619272\pi\)
−0.981135 + 0.193325i \(0.938073\pi\)
\(660\) 0 0
\(661\) 15.9029 9.18154i 0.618551 0.357121i −0.157754 0.987478i \(-0.550425\pi\)
0.776305 + 0.630358i \(0.217092\pi\)
\(662\) 15.0904 + 26.1373i 0.586505 + 1.01586i
\(663\) 0 0
\(664\) 14.3490i 0.556849i
\(665\) 0 0
\(666\) 0 0
\(667\) 2.90555 + 1.67752i 0.112503 + 0.0649538i
\(668\) 11.9319 6.88891i 0.461660 0.266540i
\(669\) 0 0
\(670\) 0 0
\(671\) −29.9449 −1.15601
\(672\) 0 0
\(673\) 32.6050i 1.25683i 0.777878 + 0.628415i \(0.216296\pi\)
−0.777878 + 0.628415i \(0.783704\pi\)
\(674\) −18.6984 10.7956i −0.720237 0.415829i
\(675\) 0 0
\(676\) 6.49768 + 11.2543i 0.249911 + 0.432858i
\(677\) −15.8816 9.16923i −0.610378 0.352402i 0.162735 0.986670i \(-0.447968\pi\)
−0.773113 + 0.634268i \(0.781302\pi\)
\(678\) 0 0
\(679\) −45.2586 3.24942i −1.73687 0.124701i
\(680\) 0 0
\(681\) 0 0
\(682\) −9.61277 16.6498i −0.368092 0.637554i
\(683\) 12.2385 + 21.1977i 0.468294 + 0.811108i 0.999343 0.0362323i \(-0.0115356\pi\)
−0.531050 + 0.847341i \(0.678202\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −12.4691 + 13.6938i −0.476073 + 0.522834i
\(687\) 0 0
\(688\) −0.835475 0.482362i −0.0318522 0.0183899i
\(689\) −0.450692 0.780621i −0.0171700 0.0297393i
\(690\) 0 0
\(691\) −15.9118 9.18670i −0.605315 0.349479i 0.165815 0.986157i \(-0.446975\pi\)
−0.771129 + 0.636678i \(0.780308\pi\)
\(692\) 8.27276i 0.314483i
\(693\) 0 0
\(694\) −23.1842 −0.880061
\(695\) 0 0
\(696\) 0 0
\(697\) −10.7198 + 6.18910i −0.406043 + 0.234429i
\(698\) 9.29128 + 5.36433i 0.351680 + 0.203043i
\(699\) 0 0
\(700\) 0 0
\(701\) 14.2399i 0.537834i −0.963163 0.268917i \(-0.913334\pi\)
0.963163 0.268917i \(-0.0866658\pi\)
\(702\) 0 0
\(703\) 4.13990 + 7.17052i 0.156139 + 0.270441i
\(704\) −3.44829 + 1.99087i −0.129962 + 0.0750337i
\(705\) 0 0
\(706\) 8.74756i 0.329219i
\(707\) −7.78210 16.0313i −0.292676 0.602920i
\(708\) 0 0
\(709\) 18.7586 32.4908i 0.704492 1.22022i −0.262382 0.964964i \(-0.584508\pi\)
0.966874 0.255252i \(-0.0821586\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.913956 1.58302i 0.0342519 0.0593261i
\(713\) 18.0199i 0.674852i
\(714\) 0 0
\(715\) 0 0
\(716\) 9.97501 + 5.75908i 0.372784 + 0.215227i
\(717\) 0 0
\(718\) −22.3059 + 12.8783i −0.832449 + 0.480614i
\(719\) 2.65733 4.60264i 0.0991019 0.171649i −0.812211 0.583363i \(-0.801736\pi\)
0.911313 + 0.411714i \(0.135070\pi\)
\(720\) 0 0
\(721\) −0.771516 + 1.13924i −0.0287327 + 0.0424276i
\(722\) −14.8577 −0.552945
\(723\) 0 0
\(724\) −14.3694 + 8.29618i −0.534035 + 0.308325i
\(725\) 0 0
\(726\) 0 0
\(727\) −2.93413 −0.108821 −0.0544104 0.998519i \(-0.517328\pi\)
−0.0544104 + 0.998519i \(0.517328\pi\)
\(728\) −0.179841 0.0129120i −0.00666534 0.000478550i
\(729\) 0 0
\(730\) 0 0
\(731\) 3.53465 + 6.12220i 0.130734 + 0.226438i
\(732\) 0 0
\(733\) 6.82411 11.8197i 0.252054 0.436570i −0.712037 0.702142i \(-0.752227\pi\)
0.964091 + 0.265571i \(0.0855606\pi\)
\(734\) 19.9377 0.735914
\(735\) 0 0
\(736\) −3.73205 −0.137565
\(737\) −21.2285 + 36.7688i −0.781960 + 1.35440i
\(738\) 0 0
\(739\) 15.6650 + 27.1325i 0.576246 + 0.998087i 0.995905 + 0.0904051i \(0.0288162\pi\)
−0.419659 + 0.907682i \(0.637851\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −34.9049 2.50606i −1.28140 0.0920004i
\(743\) −4.72061 −0.173182 −0.0865911 0.996244i \(-0.527597\pi\)
−0.0865911 + 0.996244i \(0.527597\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.893327 0.515762i 0.0327070 0.0188834i
\(747\) 0 0
\(748\) 29.1774 1.06683
\(749\) −9.08981 + 13.4223i −0.332134 + 0.490439i
\(750\) 0 0
\(751\) 12.8394 22.2385i 0.468516 0.811494i −0.530836 0.847474i \(-0.678122\pi\)
0.999352 + 0.0359807i \(0.0114555\pi\)
\(752\) −1.43890 + 0.830749i −0.0524713 + 0.0302943i
\(753\) 0 0
\(754\) 0.0530562 + 0.0306320i 0.00193219 + 0.00111555i
\(755\) 0 0
\(756\) 0 0
\(757\) 37.8781i 1.37670i −0.725377 0.688352i \(-0.758335\pi\)
0.725377 0.688352i \(-0.241665\pi\)
\(758\) −2.54748 + 4.41237i −0.0925288 + 0.160265i
\(759\) 0 0
\(760\) 0 0
\(761\) −10.3533 + 17.9325i −0.375308 + 0.650052i −0.990373 0.138424i \(-0.955796\pi\)
0.615065 + 0.788476i \(0.289130\pi\)
\(762\) 0 0
\(763\) −15.6609 32.2618i −0.566963 1.16796i
\(764\) 18.4336i 0.666905i
\(765\) 0 0
\(766\) −7.33307 + 4.23375i −0.264955 + 0.152972i
\(767\) 0.362626 + 0.628086i 0.0130937 + 0.0226789i
\(768\) 0 0
\(769\) 3.34563i 0.120647i −0.998179 0.0603233i \(-0.980787\pi\)
0.998179 0.0603233i \(-0.0192132\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.50643 3.17914i −0.198181 0.114420i
\(773\) −24.8778 + 14.3632i −0.894793 + 0.516609i −0.875507 0.483205i \(-0.839473\pi\)
−0.0192861 + 0.999814i \(0.506139\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −17.1502 −0.615656
\(777\) 0 0
\(778\) 5.74150i 0.205843i
\(779\) −2.97740 1.71901i −0.106677 0.0615898i
\(780\) 0 0
\(781\) −19.7778 34.2562i −0.707706 1.22578i
\(782\) 23.6838 + 13.6739i 0.846932 + 0.488977i
\(783\) 0 0
\(784\) −4.33013 + 5.50000i −0.154647 + 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) −2.74515 4.75474i −0.0978541 0.169488i 0.812942 0.582345i \(-0.197865\pi\)
−0.910796 + 0.412856i \(0.864531\pi\)
\(788\) −6.41946 11.1188i −0.228684 0.396092i
\(789\) 0 0
\(790\) 0 0
\(791\) −30.8710 2.21644i −1.09765 0.0788075i
\(792\) 0 0
\(793\) −0.443850 0.256257i −0.0157616 0.00909995i
\(794\) 8.43791 + 14.6149i 0.299450 + 0.518663i
\(795\) 0 0
\(796\) −8.33950 4.81481i &minus