Properties

Label 3150.2.bf.c.1601.2
Level 3150
Weight 2
Character 3150.1601
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1601.2
Root \(-0.965926 - 0.258819i\)
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.c.1151.2

$q$-expansion

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

Character values

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

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

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
\(7\) 0.189469 2.63896i 0.0716124 0.997433i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 3.44829 1.99087i 1.03970 0.600270i 0.119950 0.992780i \(-0.461727\pi\)
0.919748 + 0.392510i \(0.128393\pi\)
\(12\) 0 0
\(13\) 0.0681483i 0.0189010i 0.999955 + 0.00945048i \(0.00300822\pi\)
−0.999955 + 0.00945048i \(0.996992\pi\)
\(14\) −1.48356 + 2.19067i −0.396499 + 0.585481i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.66390 6.34607i −0.888627 1.53915i −0.841499 0.540258i \(-0.818327\pi\)
−0.0471274 0.998889i \(-0.515007\pi\)
\(18\) 0 0
\(19\) −1.76260 1.01764i −0.404368 0.233462i 0.283999 0.958825i \(-0.408339\pi\)
−0.688367 + 0.725362i \(0.741672\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −3.98174 −0.848910
\(23\) −3.23205 1.86603i −0.673929 0.389093i 0.123635 0.992328i \(-0.460545\pi\)
−0.797564 + 0.603235i \(0.793878\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.0340742 0.0590182i 0.00668250 0.0115744i
\(27\) 0 0
\(28\) 2.38014 1.15539i 0.449804 0.218349i
\(29\) 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 \(0.476092\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 7.32780i 1.25671i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.03407 + 3.52312i −0.334400 + 0.579197i −0.983369 0.181617i \(-0.941867\pi\)
0.648970 + 0.760814i \(0.275200\pi\)
\(38\) 1.01764 + 1.76260i 0.165083 + 0.285932i
\(39\) 0 0
\(40\) 0 0
\(41\) 1.68921 0.263810 0.131905 0.991262i \(-0.457891\pi\)
0.131905 + 0.991262i \(0.457891\pi\)
\(42\) 0 0
\(43\) 0.964724 0.147119 0.0735595 0.997291i \(-0.476564\pi\)
0.0735595 + 0.997291i \(0.476564\pi\)
\(44\) 3.44829 + 1.99087i 0.519849 + 0.300135i
\(45\) 0 0
\(46\) 1.86603 + 3.23205i 0.275130 + 0.476540i
\(47\) 0.830749 1.43890i 0.121177 0.209885i −0.799055 0.601258i \(-0.794666\pi\)
0.920232 + 0.391373i \(0.128000\pi\)
\(48\) 0 0
\(49\) −6.92820 1.00000i −0.989743 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.0590182 + 0.0340742i −0.00818435 + 0.00472524i
\(53\) −11.4547 + 6.61339i −1.57343 + 0.908419i −0.577684 + 0.816260i \(0.696043\pi\)
−0.995744 + 0.0921588i \(0.970623\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.63896 0.189469i −0.352646 0.0253188i
\(57\) 0 0
\(58\) −0.449490 + 0.778539i −0.0590209 + 0.102227i
\(59\) −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 \(0.506775\pi\)
\(62\) 4.82843 0.613211
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 5.33145 + 9.23435i 0.651341 + 1.12816i 0.982798 + 0.184685i \(0.0591264\pi\)
−0.331457 + 0.943470i \(0.607540\pi\)
\(68\) 3.66390 6.34607i 0.444313 0.769573i
\(69\) 0 0
\(70\) 0 0
\(71\) 9.93426i 1.17898i −0.807776 0.589490i \(-0.799329\pi\)
0.807776 0.589490i \(-0.200671\pi\)
\(72\) 0 0
\(73\) 10.0951 5.82843i 1.18155 0.682166i 0.225174 0.974319i \(-0.427705\pi\)
0.956372 + 0.292153i \(0.0943716\pi\)
\(74\) 3.52312 2.03407i 0.409554 0.236456i
\(75\) 0 0
\(76\) 2.03528i 0.233462i
\(77\) −4.60048 9.47710i −0.524273 1.08002i
\(78\) 0 0
\(79\) −8.77489 + 15.1986i −0.987252 + 1.70997i −0.355787 + 0.934567i \(0.615787\pi\)
−0.631465 + 0.775404i \(0.717546\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.46290 0.844605i −0.161550 0.0932711i
\(83\) 14.3490 1.57501 0.787503 0.616311i \(-0.211374\pi\)
0.787503 + 0.616311i \(0.211374\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.835475 0.482362i −0.0900916 0.0520144i
\(87\) 0 0
\(88\) −1.99087 3.44829i −0.212227 0.367589i
\(89\) −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
\(92\) 3.73205i 0.389093i
\(93\) 0 0
\(94\) −1.43890 + 0.830749i −0.148411 + 0.0856852i
\(95\) 0 0
\(96\) 0 0
\(97\) 17.1502i 1.74134i 0.491870 + 0.870668i \(0.336313\pi\)
−0.491870 + 0.870668i \(0.663687\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) 0 0
\(100\) 0 0
\(101\) −3.36773 5.83307i −0.335101 0.580412i 0.648403 0.761297i \(-0.275437\pi\)
−0.983504 + 0.180885i \(0.942104\pi\)
\(102\) 0 0
\(103\) −0.450370 0.260021i −0.0443762 0.0256206i 0.477648 0.878551i \(-0.341490\pi\)
−0.522024 + 0.852931i \(0.674823\pi\)
\(104\) 0.0681483 0.00668250
\(105\) 0 0
\(106\) 13.2268 1.28470
\(107\) −5.30614 3.06350i −0.512964 0.296160i 0.221087 0.975254i \(-0.429040\pi\)
−0.734051 + 0.679094i \(0.762373\pi\)
\(108\) 0 0
\(109\) −6.77729 11.7386i −0.649147 1.12436i −0.983327 0.181846i \(-0.941793\pi\)
0.334180 0.942509i \(-0.391541\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.19067 + 1.48356i 0.206999 + 0.140184i
\(113\) 11.6982i 1.10047i 0.835009 + 0.550236i \(0.185462\pi\)
−0.835009 + 0.550236i \(0.814538\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.778539 0.449490i 0.0722855 0.0417341i
\(117\) 0 0
\(118\) 10.6422i 0.979698i
\(119\) −17.4412 + 8.46651i −1.59883 + 0.776123i
\(120\) 0 0
\(121\) 2.42713 4.20390i 0.220648 0.382173i
\(122\) −3.76028 6.51299i −0.340440 0.589659i
\(123\) 0 0
\(124\) −4.18154 2.41421i −0.375513 0.216803i
\(125\) 0 0
\(126\) 0 0
\(127\) −10.7530 −0.954173 −0.477086 0.878856i \(-0.658307\pi\)
−0.477086 + 0.878856i \(0.658307\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 1.85457 3.21221i 0.162035 0.280653i −0.773564 0.633719i \(-0.781528\pi\)
0.935598 + 0.353066i \(0.114861\pi\)
\(132\) 0 0
\(133\) −3.01946 + 4.45862i −0.261821 + 0.386611i
\(134\) 10.6629i 0.921135i
\(135\) 0 0
\(136\) −6.34607 + 3.66390i −0.544171 + 0.314177i
\(137\) −11.7091 + 6.76028i −1.00038 + 0.577570i −0.908361 0.418188i \(-0.862665\pi\)
−0.0920192 + 0.995757i \(0.529332\pi\)
\(138\) 0 0
\(139\) 9.06251i 0.768672i −0.923193 0.384336i \(-0.874430\pi\)
0.923193 0.384336i \(-0.125570\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.96713 + 8.60332i −0.416832 + 0.721974i
\(143\) 0.135674 + 0.234995i 0.0113457 + 0.0196513i
\(144\) 0 0
\(145\) 0 0
\(146\) −11.6569 −0.964728
\(147\) 0 0
\(148\) −4.06815 −0.334400
\(149\) −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 \(0.701661\pi\)
\(152\) −1.01764 + 1.76260i −0.0825413 + 0.142966i
\(153\) 0 0
\(154\) −0.754415 + 10.5076i −0.0607925 + 0.846730i
\(155\) 0 0
\(156\) 0 0
\(157\) −12.3741 + 7.14418i −0.987560 + 0.570168i −0.904544 0.426380i \(-0.859788\pi\)
−0.0830157 + 0.996548i \(0.526455\pi\)
\(158\) 15.1986 8.77489i 1.20913 0.698093i
\(159\) 0 0
\(160\) 0 0
\(161\) −5.53674 + 8.17569i −0.436356 + 0.644335i
\(162\) 0 0
\(163\) 4.98879 8.64083i 0.390752 0.676802i −0.601797 0.798649i \(-0.705548\pi\)
0.992549 + 0.121847i \(0.0388817\pi\)
\(164\) 0.844605 + 1.46290i 0.0659526 + 0.114233i
\(165\) 0 0
\(166\) −12.4266 7.17449i −0.964490 0.556849i
\(167\) 13.7778 1.06616 0.533079 0.846065i \(-0.321035\pi\)
0.533079 + 0.846065i \(0.321035\pi\)
\(168\) 0 0
\(169\) 12.9954 0.999643
\(170\) 0 0
\(171\) 0 0
\(172\) 0.482362 + 0.835475i 0.0367798 + 0.0637044i
\(173\) 4.13638 7.16442i 0.314483 0.544701i −0.664844 0.746982i \(-0.731502\pi\)
0.979327 + 0.202281i \(0.0648355\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.98174i 0.300135i
\(177\) 0 0
\(178\) 1.58302 0.913956i 0.118652 0.0685039i
\(179\) −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 \(-0.211511\pi\)
\(182\) −0.149291 0.101102i −0.0110662 0.00749421i
\(183\) 0 0
\(184\) −1.86603 + 3.23205i −0.137565 + 0.238270i
\(185\) 0 0
\(186\) 0 0
\(187\) −25.2684 14.5887i −1.84781 1.06683i
\(188\) 1.66150 0.121177
\(189\) 0 0
\(190\) 0 0
\(191\) 15.9640 + 9.21682i 1.15511 + 0.666905i 0.950128 0.311859i \(-0.100952\pi\)
0.204986 + 0.978765i \(0.434285\pi\)
\(192\) 0 0
\(193\) −3.17914 5.50643i −0.228839 0.396361i 0.728625 0.684913i \(-0.240160\pi\)
−0.957464 + 0.288552i \(0.906826\pi\)
\(194\) 8.57509 14.8525i 0.615656 1.06635i
\(195\) 0 0
\(196\) −2.59808 6.50000i −0.185577 0.464286i
\(197\) 12.8389i 0.914734i −0.889278 0.457367i \(-0.848792\pi\)
0.889278 0.457367i \(-0.151208\pi\)
\(198\) 0 0
\(199\) −8.33950 + 4.81481i −0.591171 + 0.341313i −0.765561 0.643364i \(-0.777538\pi\)
0.174389 + 0.984677i \(0.444205\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 6.73545i 0.473905i
\(203\) −2.37237 0.170328i −0.166508 0.0119547i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.260021 + 0.450370i 0.0181165 + 0.0313787i
\(207\) 0 0
\(208\) −0.0590182 0.0340742i −0.00409218 0.00236262i
\(209\) −8.10394 −0.560561
\(210\) 0 0
\(211\) −14.5619 −1.00248 −0.501241 0.865308i \(-0.667123\pi\)
−0.501241 + 0.865308i \(0.667123\pi\)
\(212\) −11.4547 6.61339i −0.786714 0.454210i
\(213\) 0 0
\(214\) 3.06350 + 5.30614i 0.209417 + 0.362721i
\(215\) 0 0
\(216\) 0 0
\(217\) 5.57874 + 11.4923i 0.378709 + 0.780150i
\(218\) 13.5546i 0.918033i
\(219\) 0 0
\(220\) 0 0
\(221\) 0.432474 0.249689i 0.0290913 0.0167959i
\(222\) 0 0
\(223\) 23.6609i 1.58445i −0.610227 0.792227i \(-0.708922\pi\)
0.610227 0.792227i \(-0.291078\pi\)
\(224\) −1.15539 2.38014i −0.0771980 0.159030i
\(225\) 0 0
\(226\) 5.84909 10.1309i 0.389076 0.673899i
\(227\) 4.32024 + 7.48288i 0.286744 + 0.496656i 0.973031 0.230676i \(-0.0740936\pi\)
−0.686286 + 0.727332i \(0.740760\pi\)
\(228\) 0 0
\(229\) −12.1896 7.03768i −0.805513 0.465063i 0.0398824 0.999204i \(-0.487302\pi\)
−0.845395 + 0.534141i \(0.820635\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.898979 −0.0590209
\(233\) −17.4916 10.0988i −1.14591 0.661593i −0.198025 0.980197i \(-0.563453\pi\)
−0.947888 + 0.318604i \(0.896786\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5.32112 9.21645i 0.346375 0.599940i
\(237\) 0 0
\(238\) 19.3378 + 1.38839i 1.25348 + 0.0899959i
\(239\) 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 \(0.492291\pi\)
\(242\) −4.20390 + 2.42713i −0.270237 + 0.156022i
\(243\) 0 0
\(244\) 7.52056i 0.481454i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.0693504 0.120118i 0.00441266 0.00764295i
\(248\) 2.41421 + 4.18154i 0.153303 + 0.265528i
\(249\) 0 0
\(250\) 0 0
\(251\) −4.31736 −0.272509 −0.136255 0.990674i \(-0.543507\pi\)
−0.136255 + 0.990674i \(0.543507\pi\)
\(252\) 0 0
\(253\) −14.8601 −0.934244
\(254\) 9.31236 + 5.37649i 0.584309 + 0.337351i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.41662 + 4.18570i −0.150744 + 0.261097i −0.931501 0.363738i \(-0.881500\pi\)
0.780757 + 0.624835i \(0.214834\pi\)
\(258\) 0 0
\(259\) 8.91197 + 6.03536i 0.553763 + 0.375019i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.21221 + 1.85457i −0.198451 + 0.114576i
\(263\) −5.77197 + 3.33245i −0.355915 + 0.205488i −0.667287 0.744800i \(-0.732545\pi\)
0.311372 + 0.950288i \(0.399211\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.84424 2.35155i 0.297019 0.144183i
\(267\) 0 0
\(268\) −5.33145 + 9.23435i −0.325670 + 0.564078i
\(269\) 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 \(0.488696\pi\)
\(272\) 7.32780 0.444313
\(273\) 0 0
\(274\) 13.5206 0.816807
\(275\) 0 0
\(276\) 0 0
\(277\) −11.7524 20.3557i −0.706130 1.22305i −0.966282 0.257486i \(-0.917106\pi\)
0.260152 0.965568i \(-0.416227\pi\)
\(278\) −4.53125 + 7.84836i −0.271767 + 0.470714i
\(279\) 0 0
\(280\) 0 0
\(281\) 15.4159i 0.919635i −0.888013 0.459817i \(-0.847915\pi\)
0.888013 0.459817i \(-0.152085\pi\)
\(282\) 0 0
\(283\) 23.9983 13.8554i 1.42655 0.823619i 0.429703 0.902970i \(-0.358618\pi\)
0.996847 + 0.0793517i \(0.0252850\pi\)
\(284\) 8.60332 4.96713i 0.510513 0.294745i
\(285\) 0 0
\(286\) 0.271349i 0.0160452i
\(287\) 0.320053 4.45776i 0.0188921 0.263133i
\(288\) 0 0
\(289\) −18.3484 + 31.7803i −1.07932 + 1.86943i
\(290\) 0 0
\(291\) 0 0
\(292\) 10.0951 + 5.82843i 0.590773 + 0.341083i
\(293\) −2.84377 −0.166135 −0.0830673 0.996544i \(-0.526472\pi\)
−0.0830673 + 0.996544i \(0.526472\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.52312 + 2.03407i 0.204777 + 0.118228i
\(297\) 0 0
\(298\) 7.64324 + 13.2385i 0.442761 + 0.766884i
\(299\) 0.127167 0.220259i 0.00735423 0.0127379i
\(300\) 0 0
\(301\) 0.182785 2.54587i 0.0105355 0.146741i
\(302\) 9.87883i 0.568463i
\(303\) 0 0
\(304\) 1.76260 1.01764i 0.101092 0.0583655i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.52180i 0.143927i −0.997407 0.0719634i \(-0.977074\pi\)
0.997407 0.0719634i \(-0.0229265\pi\)
\(308\) 5.90717 8.72268i 0.336592 0.497021i
\(309\) 0 0
\(310\) 0 0
\(311\) 5.49697 + 9.52104i 0.311705 + 0.539889i 0.978732 0.205145i \(-0.0657667\pi\)
−0.667027 + 0.745034i \(0.732433\pi\)
\(312\) 0 0
\(313\) −21.6040 12.4731i −1.22113 0.705020i −0.255971 0.966684i \(-0.582395\pi\)
−0.965159 + 0.261665i \(0.915729\pi\)
\(314\) 14.2884 0.806339
\(315\) 0 0
\(316\) −17.5498 −0.987252
\(317\) −13.0504 7.53465i −0.732984 0.423188i 0.0865290 0.996249i \(-0.472422\pi\)
−0.819513 + 0.573061i \(0.805756\pi\)
\(318\) 0 0
\(319\) −1.78975 3.09994i −0.100207 0.173563i
\(320\) 0 0
\(321\) 0 0
\(322\) 8.88280 4.31199i 0.495019 0.240298i
\(323\) 14.9141i 0.829843i
\(324\) 0 0
\(325\) 0 0
\(326\) −8.64083 + 4.98879i −0.478572 + 0.276303i
\(327\) 0 0
\(328\) 1.68921i 0.0932711i
\(329\) −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 \(0.855324\pi\)
\(332\) 7.17449 + 12.4266i 0.393751 + 0.681997i
\(333\) 0 0
\(334\) −11.9319 6.88891i −0.652886 0.376944i
\(335\) 0 0
\(336\) 0 0
\(337\) 21.5911 1.17614 0.588071 0.808809i \(-0.299887\pi\)
0.588071 + 0.808809i \(0.299887\pi\)
\(338\) −11.2543 6.49768i −0.612154 0.353427i
\(339\) 0 0
\(340\) 0 0
\(341\) −9.61277 + 16.6498i −0.520561 + 0.901638i
\(342\) 0 0
\(343\) −3.95164 + 18.0938i −0.213368 + 0.976972i
\(344\) 0.964724i 0.0520144i
\(345\) 0 0
\(346\) −7.16442 + 4.13638i −0.385161 + 0.222373i
\(347\) −20.0781 + 11.5921i −1.07785 + 0.622297i −0.930316 0.366760i \(-0.880467\pi\)
−0.147534 + 0.989057i \(0.547134\pi\)
\(348\) 0 0
\(349\) 10.7287i 0.574292i −0.957887 0.287146i \(-0.907294\pi\)
0.957887 0.287146i \(-0.0927064\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.99087 3.44829i 0.106114 0.183794i
\(353\) −4.37378 7.57561i −0.232793 0.403209i 0.725836 0.687868i \(-0.241453\pi\)
−0.958629 + 0.284659i \(0.908120\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.82791 −0.0968791
\(357\) 0 0
\(358\) 11.5182 0.608753
\(359\) −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
\(362\) −8.29618 + 14.3694i −0.436037 + 0.755239i
\(363\) 0 0
\(364\) 0.0787382 + 0.162203i 0.00412700 + 0.00850172i
\(365\) 0 0
\(366\) 0 0
\(367\) −17.2665 + 9.96885i −0.901306 + 0.520369i −0.877624 0.479350i \(-0.840872\pi\)
−0.0236826 + 0.999720i \(0.507539\pi\)
\(368\) 3.23205 1.86603i 0.168482 0.0972733i
\(369\) 0 0
\(370\) 0 0
\(371\) 15.2822 + 31.4816i 0.793410 + 1.63444i
\(372\) 0 0
\(373\) 0.515762 0.893327i 0.0267052 0.0462547i −0.852364 0.522949i \(-0.824832\pi\)
0.879069 + 0.476694i \(0.158165\pi\)
\(374\) 14.5887 + 25.2684i 0.754364 + 1.30660i
\(375\) 0 0
\(376\) −1.43890 0.830749i −0.0742056 0.0428426i
\(377\) 0.0612640 0.00315525
\(378\) 0 0
\(379\) 5.09497 0.261711 0.130855 0.991401i \(-0.458228\pi\)
0.130855 + 0.991401i \(0.458228\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −9.21682 15.9640i −0.471573 0.816789i
\(383\) 4.23375 7.33307i 0.216335 0.374702i −0.737350 0.675511i \(-0.763923\pi\)
0.953685 + 0.300808i \(0.0972565\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.35827i 0.323628i
\(387\) 0 0
\(388\) −14.8525 + 8.57509i −0.754021 + 0.435334i
\(389\) 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
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 0 0
\(394\) −6.41946 + 11.1188i −0.323407 + 0.560158i
\(395\) 0 0
\(396\) 0 0
\(397\) −14.6149 8.43791i −0.733501 0.423487i 0.0862009 0.996278i \(-0.472527\pi\)
−0.819701 + 0.572791i \(0.805861\pi\)
\(398\) 9.62962 0.482689
\(399\) 0 0
\(400\) 0 0
\(401\) −1.63572 0.944382i −0.0816838 0.0471602i 0.458602 0.888642i \(-0.348350\pi\)
−0.540286 + 0.841482i \(0.681684\pi\)
\(402\) 0 0
\(403\) −0.164525 0.284965i −0.00819556 0.0141951i
\(404\) 3.36773 5.83307i 0.167551 0.290206i
\(405\) 0 0
\(406\) 1.96937 + 1.33369i 0.0977381 + 0.0661901i
\(407\) 16.1983i 0.802920i
\(408\) 0 0
\(409\) 28.5617 16.4901i 1.41228 0.815382i 0.416681 0.909053i \(-0.363193\pi\)
0.995603 + 0.0936705i \(0.0298600\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.520042i 0.0256206i
\(413\) −25.3300 + 12.2960i −1.24641 + 0.605046i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.0340742 + 0.0590182i 0.00167062 + 0.00289361i
\(417\) 0 0
\(418\) 7.01822 + 4.05197i 0.343272 + 0.198188i
\(419\) 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 \(0.251693\pi\)
\(422\) 12.6110 + 7.28094i 0.613892 + 0.354431i
\(423\) 0 0
\(424\) 6.61339 + 11.4547i 0.321175 + 0.556291i
\(425\) 0 0
\(426\) 0 0
\(427\) 11.1572 16.4751i 0.539936 0.797284i
\(428\) 6.12701i 0.296160i
\(429\) 0 0
\(430\) 0 0
\(431\) −29.0895 + 16.7948i −1.40119 + 0.808978i −0.994515 0.104594i \(-0.966646\pi\)
−0.406677 + 0.913572i \(0.633312\pi\)
\(432\) 0 0
\(433\) 11.2207i 0.539234i 0.962968 + 0.269617i \(0.0868971\pi\)
−0.962968 + 0.269617i \(0.913103\pi\)
\(434\) 0.914836 12.7420i 0.0439135 0.611636i
\(435\) 0 0
\(436\) 6.77729 11.7386i 0.324574 0.562178i
\(437\) 3.79788 + 6.57812i 0.181677 + 0.314674i
\(438\) 0 0
\(439\) −14.6075 8.43363i −0.697177 0.402515i 0.109118 0.994029i \(-0.465197\pi\)
−0.806295 + 0.591513i \(0.798531\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −0.499378 −0.0237530
\(443\) 1.78094 + 1.02823i 0.0846152 + 0.0488526i 0.541711 0.840565i \(-0.317777\pi\)
−0.457095 + 0.889418i \(0.651110\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −11.8305 + 20.4910i −0.560189 + 0.970276i
\(447\) 0 0
\(448\) −0.189469 + 2.63896i −0.00895155 + 0.124679i
\(449\) 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
\(452\) −10.1309 + 5.84909i −0.476519 + 0.275118i
\(453\) 0 0
\(454\) 8.64048i 0.405518i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.4765 30.2701i 0.817515 1.41598i −0.0899930 0.995942i \(-0.528684\pi\)
0.907508 0.420035i \(-0.137982\pi\)
\(458\) 7.03768 + 12.1896i 0.328849 + 0.569584i
\(459\) 0 0
\(460\) 0 0
\(461\) 23.3750 1.08868 0.544341 0.838864i \(-0.316780\pi\)
0.544341 + 0.838864i \(0.316780\pi\)
\(462\) 0 0
\(463\) 6.35693 0.295431 0.147716 0.989030i \(-0.452808\pi\)
0.147716 + 0.989030i \(0.452808\pi\)
\(464\) 0.778539 + 0.449490i 0.0361428 + 0.0208670i
\(465\) 0 0
\(466\) 10.0988 + 17.4916i 0.467817 + 0.810283i
\(467\) −3.89658 + 6.74907i −0.180312 + 0.312310i −0.941987 0.335650i \(-0.891044\pi\)
0.761675 + 0.647960i \(0.224377\pi\)
\(468\) 0 0
\(469\) 25.3792 12.3199i 1.17190 0.568878i
\(470\) 0 0
\(471\) 0 0
\(472\) −9.21645 + 5.32112i −0.424222 + 0.244924i
\(473\) 3.32665 1.92064i 0.152959 0.0883111i
\(474\) 0 0
\(475\) 0 0
\(476\) −16.0528 10.8713i −0.735779 0.498284i
\(477\) 0 0
\(478\) −11.7520 + 20.3550i −0.537523 + 0.931018i
\(479\) 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
\(482\) 14.8685 0.677242
\(483\) 0 0
\(484\) 4.85425 0.220648
\(485\) 0 0
\(486\) 0 0
\(487\) 17.7234 + 30.6978i 0.803124 + 1.39105i 0.917551 + 0.397619i \(0.130164\pi\)
−0.114427 + 0.993432i \(0.536503\pi\)
\(488\) 3.76028 6.51299i 0.170220 0.294829i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.64349i 0.0741695i −0.999312 0.0370848i \(-0.988193\pi\)
0.999312 0.0370848i \(-0.0118072\pi\)
\(492\) 0 0
\(493\) −5.70498 + 3.29377i −0.256939 + 0.148344i
\(494\) −0.120118 + 0.0693504i −0.00540438 + 0.00312022i
\(495\) 0 0
\(496\) 4.82843i 0.216803i
\(497\) −26.2161 1.88223i −1.17595 0.0844296i
\(498\) 0 0
\(499\) 17.3665 30.0796i 0.777430 1.34655i −0.155988 0.987759i \(-0.549856\pi\)
0.933418 0.358790i \(-0.116811\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 3.73894 + 2.15868i 0.166877 + 0.0963465i
\(503\) −28.9613 −1.29132 −0.645660 0.763625i \(-0.723418\pi\)
−0.645660 + 0.763625i \(0.723418\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 12.8692 + 7.43003i 0.572105 + 0.330305i
\(507\) 0 0
\(508\) −5.37649 9.31236i −0.238543 0.413169i
\(509\) −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
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 4.18570 2.41662i 0.184624 0.106592i
\(515\) 0 0
\(516\) 0 0
\(517\) 6.61565i 0.290956i
\(518\) −4.70032 9.68276i −0.206520 0.425436i
\(519\) 0 0
\(520\) 0 0
\(521\) −20.1218 34.8520i −0.881552 1.52689i −0.849616 0.527403i \(-0.823166\pi\)
−0.0319362 0.999490i \(-0.510167\pi\)
\(522\) 0 0
\(523\) −25.7113 14.8444i −1.12428 0.649102i −0.181789 0.983338i \(-0.558189\pi\)
−0.942490 + 0.334235i \(0.891522\pi\)
\(524\) 3.70915 0.162035
\(525\) 0 0
\(526\) 6.66490 0.290603
\(527\) 30.6415 + 17.6909i 1.33477 + 0.770627i
\(528\) 0 0
\(529\) −4.53590 7.85641i −0.197213 0.341583i
\(530\) 0 0
\(531\) 0 0
\(532\) −5.37101 0.385621i −0.232863 0.0167188i
\(533\) 0.115117i 0.00498627i
\(534\) 0 0
\(535\) 0 0
\(536\) 9.23435 5.33145i 0.398863 0.230284i
\(537\) 0 0
\(538\) 31.7400i 1.36841i
\(539\) −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 \(0.0456831\pi\)
\(542\) −8.73205 15.1244i −0.375074 0.649647i
\(543\) 0 0
\(544\) −6.34607 3.66390i −0.272085 0.157089i
\(545\) 0 0
\(546\) 0 0
\(547\) 17.9703 0.768354 0.384177 0.923260i \(-0.374485\pi\)
0.384177 + 0.923260i \(0.374485\pi\)
\(548\) −11.7091 6.76028i −0.500190 0.288785i
\(549\) 0 0
\(550\) 0 0
\(551\) −0.914836 + 1.58454i −0.0389733 + 0.0675038i
\(552\) 0 0
\(553\) 38.4458 + 26.0362i 1.63488 + 1.10717i
\(554\) 23.5047i 0.998619i
\(555\) 0 0
\(556\) 7.84836 4.53125i 0.332845 0.192168i
\(557\) 39.1916 22.6273i 1.66060 0.958748i 0.688172 0.725547i \(-0.258413\pi\)
0.972428 0.233201i \(-0.0749201\pi\)
\(558\) 0 0
\(559\) 0.0657443i 0.00278069i
\(560\) 0 0
\(561\) 0 0
\(562\) −7.70794 + 13.3506i −0.325140 + 0.563159i
\(563\) 7.93336 + 13.7410i 0.334351 + 0.579114i 0.983360 0.181667i \(-0.0581494\pi\)
−0.649009 + 0.760781i \(0.724816\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −27.7108 −1.16477
\(567\) 0 0
\(568\) −9.93426 −0.416832
\(569\) −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 \(0.741726\pi\)
\(572\) −0.135674 + 0.234995i −0.00567284 + 0.00982564i
\(573\) 0 0
\(574\) −2.50605 + 3.70050i −0.104601 + 0.154456i
\(575\) 0 0
\(576\) 0 0
\(577\) 37.8252 21.8384i 1.57468 0.909144i 0.579101 0.815256i \(-0.303404\pi\)
0.995583 0.0938887i \(-0.0299298\pi\)
\(578\) 31.7803 18.3484i 1.32189 0.763191i
\(579\) 0 0
\(580\) 0 0
\(581\) 2.71868 37.8664i 0.112790 1.57096i
\(582\) 0 0
\(583\) −26.3328 + 45.6098i −1.09059 + 1.88896i
\(584\) −5.82843 10.0951i −0.241182 0.417740i
\(585\) 0 0
\(586\) 2.46278 + 1.42188i 0.101736 + 0.0587375i
\(587\) 45.4100 1.87427 0.937135 0.348967i \(-0.113468\pi\)
0.937135 + 0.348967i \(0.113468\pi\)
\(588\) 0 0
\(589\) 9.82718 0.404922
\(590\) 0 0
\(591\) 0 0
\(592\) −2.03407 3.52312i −0.0835999 0.144799i
\(593\) 12.8506 22.2579i 0.527711 0.914022i −0.471767 0.881723i \(-0.656384\pi\)
0.999478 0.0322991i \(-0.0102829\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.2865i 0.626158i
\(597\) 0 0
\(598\) −0.220259 + 0.127167i −0.00900706 + 0.00520023i
\(599\) 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 \(-0.0852034\pi\)
\(602\) −1.43123 + 2.11339i −0.0583326 + 0.0861354i
\(603\) 0 0
\(604\) −4.93942 + 8.55532i −0.200982 + 0.348111i
\(605\) 0 0
\(606\) 0 0
\(607\) 14.1262 + 8.15576i 0.573364 + 0.331032i 0.758492 0.651682i \(-0.225937\pi\)
−0.185128 + 0.982714i \(0.559270\pi\)
\(608\) −2.03528 −0.0825413
\(609\) 0 0
\(610\) 0 0
\(611\) 0.0980586 + 0.0566142i 0.00396703 + 0.00229036i
\(612\) 0 0
\(613\) −7.19395 12.4603i −0.290561 0.503267i 0.683381 0.730062i \(-0.260509\pi\)
−0.973943 + 0.226795i \(0.927175\pi\)
\(614\) −1.26090 + 2.18394i −0.0508858 + 0.0881368i
\(615\) 0 0
\(616\) −9.47710 + 4.60048i −0.381843 + 0.185359i
\(617\) 8.65760i 0.348542i −0.984698 0.174271i \(-0.944243\pi\)
0.984698 0.174271i \(-0.0557569\pi\)
\(618\) 0 0
\(619\) 38.8459 22.4277i 1.56135 0.901444i 0.564225 0.825621i \(-0.309175\pi\)
0.997121 0.0758230i \(-0.0241584\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 10.9939i 0.440817i
\(623\) 4.00435 + 2.71182i 0.160431 + 0.108647i
\(624\) 0 0
\(625\) 0 0
\(626\) 12.4731 + 21.6040i 0.498524 + 0.863469i
\(627\) 0 0
\(628\) −12.3741 7.14418i −0.493780 0.285084i
\(629\) 29.8106 1.18863
\(630\) 0 0
\(631\) −38.1878 −1.52023 −0.760116 0.649788i \(-0.774858\pi\)
−0.760116 + 0.649788i \(0.774858\pi\)
\(632\) 15.1986 + 8.77489i 0.604566 + 0.349046i
\(633\) 0 0
\(634\) 7.53465 + 13.0504i 0.299239 + 0.518298i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.0681483 0.472146i 0.00270014 0.0187071i
\(638\) 3.57950i 0.141714i
\(639\) 0 0
\(640\) 0 0
\(641\) 7.40533 4.27547i 0.292493 0.168871i −0.346573 0.938023i \(-0.612655\pi\)
0.639066 + 0.769152i \(0.279321\pi\)
\(642\) 0 0
\(643\) 2.75058i 0.108472i 0.998528 + 0.0542361i \(0.0172724\pi\)
−0.998528 + 0.0542361i \(0.982728\pi\)
\(644\) −9.84873 0.707107i −0.388094 0.0278639i
\(645\) 0 0
\(646\) 7.45705 12.9160i 0.293394 0.508173i
\(647\) 13.8813 + 24.0431i 0.545731 + 0.945234i 0.998561 + 0.0536365i \(0.0170812\pi\)
−0.452830 + 0.891597i \(0.649585\pi\)
\(648\) 0 0
\(649\) −36.6975 21.1873i −1.44050 0.831675i
\(650\) 0 0
\(651\) 0 0
\(652\) 9.97758 0.390752
\(653\) 12.2282 + 7.05994i 0.478525 + 0.276277i 0.719802 0.694180i \(-0.244233\pi\)
−0.241276 + 0.970456i \(0.577566\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.844605 + 1.46290i −0.0329763 + 0.0571166i
\(657\) 0 0
\(658\) 1.91969 + 3.95460i 0.0748372 + 0.154166i
\(659\) 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 \(0.217092\pi\)
\(662\) 26.1373 15.0904i 1.01586 0.586505i
\(663\) 0 0
\(664\) 14.3490i 0.556849i
\(665\) 0 0
\(666\) 0 0
\(667\) −1.67752 + 2.90555i −0.0649538 + 0.112503i
\(668\) 6.88891 + 11.9319i 0.266540 + 0.461660i
\(669\) 0 0
\(670\) 0 0
\(671\) 29.9449 1.15601
\(672\) 0 0
\(673\) 32.6050 1.25683 0.628415 0.777878i \(-0.283704\pi\)
0.628415 + 0.777878i \(0.283704\pi\)
\(674\) −18.6984 10.7956i −0.720237 0.415829i
\(675\) 0 0
\(676\) 6.49768 + 11.2543i 0.249911 + 0.432858i
\(677\) −9.16923 + 15.8816i −0.352402 + 0.610378i −0.986670 0.162735i \(-0.947968\pi\)
0.634268 + 0.773113i \(0.281302\pi\)
\(678\) 0 0
\(679\) 45.2586 + 3.24942i 1.73687 + 0.124701i
\(680\) 0 0
\(681\) 0 0
\(682\) 16.6498 9.61277i 0.637554 0.368092i
\(683\) −21.1977 + 12.2385i −0.811108 + 0.468294i −0.847341 0.531050i \(-0.821798\pi\)
0.0362323 + 0.999343i \(0.488464\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 12.4691 13.6938i 0.476073 0.522834i
\(687\) 0 0
\(688\) −0.482362 + 0.835475i −0.0183899 + 0.0318522i
\(689\) −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 \(0.780308\pi\)
\(692\) 8.27276 0.314483
\(693\) 0 0
\(694\) 23.1842 0.880061
\(695\) 0 0
\(696\) 0 0
\(697\) −6.18910 10.7198i −0.234429 0.406043i
\(698\) −5.36433 + 9.29128i −0.203043 + 0.351680i
\(699\) 0 0
\(700\) 0 0
\(701\) 14.2399i 0.537834i 0.963163 + 0.268917i \(0.0866658\pi\)
−0.963163 + 0.268917i \(0.913334\pi\)
\(702\) 0 0
\(703\) 7.17052 4.13990i 0.270441 0.156139i
\(704\) −3.44829 + 1.99087i −0.129962 + 0.0750337i
\(705\) 0 0
\(706\) 8.74756i 0.329219i
\(707\) −16.0313 + 7.78210i −0.602920 + 0.292676i
\(708\) 0 0
\(709\) −18.7586 + 32.4908i −0.704492 + 1.22022i 0.262382 + 0.964964i \(0.415492\pi\)
−0.966874 + 0.255252i \(0.917841\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.58302 + 0.913956i 0.0593261 + 0.0342519i
\(713\) 18.0199 0.674852
\(714\) 0 0
\(715\) 0 0
\(716\) −9.97501 5.75908i −0.372784 0.215227i
\(717\) 0 0
\(718\) 12.8783 + 22.3059i 0.480614 + 0.832449i
\(719\) 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
\(722\) 14.8577i 0.552945i
\(723\) 0 0
\(724\) 14.3694 8.29618i 0.534035 0.308325i
\(725\) 0 0
\(726\) 0 0
\(727\) 2.93413i 0.108821i −0.998519 0.0544104i \(-0.982672\pi\)
0.998519 0.0544104i \(-0.0173279\pi\)
\(728\) 0.0129120 0.179841i 0.000478550 0.00666534i
\(729\) 0 0
\(730\) 0 0
\(731\) −3.53465 6.12220i −0.130734 0.226438i
\(732\) 0 0
\(733\) −11.8197 6.82411i −0.436570 0.252054i 0.265571 0.964091i \(-0.414439\pi\)
−0.702142 + 0.712037i \(0.747773\pi\)
\(734\) 19.9377 0.735914
\(735\) 0 0
\(736\) −3.73205 −0.137565
\(737\) 36.7688 + 21.2285i 1.35440 + 0.781960i
\(738\) 0 0
\(739\) −15.6650 27.1325i −0.576246 0.998087i −0.995905 0.0904051i \(-0.971184\pi\)
0.419659 0.907682i \(-0.362149\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.50606 34.9049i 0.0920004 1.28140i
\(743\) 4.72061i 0.173182i −0.996244 0.0865911i \(-0.972403\pi\)
0.996244 0.0865911i \(-0.0275974\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.893327 + 0.515762i −0.0327070 + 0.0188834i
\(747\) 0 0
\(748\) 29.1774i 1.06683i
\(749\) −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 \(0.0114555\pi\)
\(752\) 0.830749 + 1.43890i 0.0302943 + 0.0524713i
\(753\) 0 0
\(754\) −0.0530562 0.0306320i −0.00193219 0.00111555i
\(755\) 0 0
\(756\) 0 0
\(757\) 37.8781 1.37670 0.688352 0.725377i \(-0.258335\pi\)
0.688352 + 0.725377i \(0.258335\pi\)
\(758\) −4.41237 2.54748i −0.160265 0.0925288i
\(759\) 0 0
\(760\) 0 0
\(761\) 10.3533 17.9325i 0.375308 0.650052i −0.615065 0.788476i \(-0.710870\pi\)
0.990373 + 0.138424i \(0.0442038\pi\)
\(762\) 0 0
\(763\) −32.2618 + 15.6609i −1.16796 + 0.566963i
\(764\) 18.4336i 0.666905i
\(765\) 0 0
\(766\) −7.33307 + 4.23375i −0.264955 + 0.152972i
\(767\) 0.628086 0.362626i 0.0226789 0.0130937i
\(768\) 0 0
\(769\) 3.34563i 0.120647i 0.998179 + 0.0603233i \(0.0192132\pi\)
−0.998179 + 0.0603233i \(0.980787\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.17914 5.50643i 0.114420 0.198181i
\(773\) −14.3632 24.8778i −0.516609 0.894793i −0.999814 0.0192861i \(-0.993861\pi\)
0.483205 0.875507i \(-0.339473\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 17.1502 0.615656
\(777\) 0 0
\(778\) −5.74150 −0.205843
\(779\) −2.97740 1.71901i −0.106677 0.0615898i
\(780\) 0 0
\(781\) −19.7778 34.2562i −0.707706 1.22578i
\(782\) 13.6739 23.6838i 0.488977 0.846932i
\(783\) 0 0
\(784\) 4.33013 5.50000i 0.154647 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) 4.75474 2.74515i 0.169488 0.0978541i −0.412856 0.910796i \(-0.635469\pi\)
0.582345 + 0.812942i \(0.302135\pi\)
\(788\) 11.1188 6.41946i 0.396092 0.228684i
\(789\) 0 0
\(790\) 0 0
\(791\) 30.8710 + 2.21644i 1.09765 + 0.0788075i
\(792\) 0 0
\(793\) −0.256257 + 0.443850i −0.00909995 + 0.0157616i
\(794\) 8.43791 + 14.6149i 0.299450 + 0.518663i
\(795\) 0 0
\(796\)