Properties

Label 1456.2.r.j.417.1
Level $1456$
Weight $2$
Character 1456.417
Analytic conductor $11.626$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 417.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 1456.417
Dual form 1456.2.r.j.625.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.11803 + 1.93649i) q^{3} +(-1.11803 - 1.93649i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-1.11803 + 1.93649i) q^{3} +(-1.11803 - 1.93649i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +5.00000 q^{15} +(-0.736068 + 1.27491i) q^{17} +(1.50000 + 2.59808i) q^{19} +(1.11803 + 5.80948i) q^{21} +(-4.11803 - 7.13264i) q^{23} -2.23607 q^{27} +4.47214 q^{29} +(2.50000 - 4.33013i) q^{31} +(-3.35410 - 5.80948i) q^{33} +(-5.59017 - 1.93649i) q^{35} +(-2.35410 - 4.07742i) q^{37} +(1.11803 - 1.93649i) q^{39} -4.47214 q^{41} +8.00000 q^{43} +(-2.23607 + 3.87298i) q^{45} +(-3.73607 - 6.47106i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-1.64590 - 2.85078i) q^{51} +(3.73607 - 6.47106i) q^{53} +6.70820 q^{55} -6.70820 q^{57} +(-0.736068 + 1.27491i) q^{59} +(-1.50000 - 2.59808i) q^{61} +(-5.00000 - 1.73205i) q^{63} +(1.11803 + 1.93649i) q^{65} +(-1.50000 + 2.59808i) q^{67} +18.4164 q^{69} +8.94427 q^{71} +(1.35410 - 2.34537i) q^{73} +(1.50000 + 7.79423i) q^{77} +(-1.35410 - 2.34537i) q^{79} +(5.50000 - 9.52628i) q^{81} +3.29180 q^{85} +(-5.00000 + 8.66025i) q^{87} +(-1.11803 - 1.93649i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(5.59017 + 9.68246i) q^{93} +(3.35410 - 5.80948i) q^{95} +9.41641 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q + 8 q^{7} - 4 q^{9} - 6 q^{11} - 4 q^{13} + 20 q^{15} + 6 q^{17} + 6 q^{19} - 12 q^{23} + 10 q^{31} + 4 q^{37} + 32 q^{43} - 6 q^{47} + 4 q^{49} - 20 q^{51} + 6 q^{53} + 6 q^{59} - 6 q^{61} - 20 q^{63} - 6 q^{67} + 20 q^{69} - 8 q^{73} + 6 q^{77} + 8 q^{79} + 22 q^{81} + 40 q^{85} - 20 q^{87} - 8 q^{91} - 16 q^{97} + 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) −1.11803 + 1.93649i −0.645497 + 1.11803i 0.338689 + 0.940898i \(0.390016\pi\)
−0.984186 + 0.177136i \(0.943317\pi\)
\(4\) 0 0
\(5\) −1.11803 1.93649i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 0 0
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 5.00000 1.29099
\(16\) 0 0
\(17\) −0.736068 + 1.27491i −0.178523 + 0.309210i −0.941375 0.337363i \(-0.890465\pi\)
0.762852 + 0.646573i \(0.223798\pi\)
\(18\) 0 0
\(19\) 1.50000 + 2.59808i 0.344124 + 0.596040i 0.985194 0.171442i \(-0.0548427\pi\)
−0.641071 + 0.767482i \(0.721509\pi\)
\(20\) 0 0
\(21\) 1.11803 + 5.80948i 0.243975 + 1.26773i
\(22\) 0 0
\(23\) −4.11803 7.13264i −0.858669 1.48726i −0.873199 0.487365i \(-0.837958\pi\)
0.0145291 0.999894i \(-0.495375\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) 0 0
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 0 0
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) 0 0
\(33\) −3.35410 5.80948i −0.583874 1.01130i
\(34\) 0 0
\(35\) −5.59017 1.93649i −0.944911 0.327327i
\(36\) 0 0
\(37\) −2.35410 4.07742i −0.387012 0.670324i 0.605034 0.796200i \(-0.293159\pi\)
−0.992046 + 0.125875i \(0.959826\pi\)
\(38\) 0 0
\(39\) 1.11803 1.93649i 0.179029 0.310087i
\(40\) 0 0
\(41\) −4.47214 −0.698430 −0.349215 0.937043i \(-0.613552\pi\)
−0.349215 + 0.937043i \(0.613552\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −2.23607 + 3.87298i −0.333333 + 0.577350i
\(46\) 0 0
\(47\) −3.73607 6.47106i −0.544962 0.943901i −0.998609 0.0527200i \(-0.983211\pi\)
0.453648 0.891181i \(-0.350122\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) −1.64590 2.85078i −0.230472 0.399189i
\(52\) 0 0
\(53\) 3.73607 6.47106i 0.513188 0.888868i −0.486695 0.873572i \(-0.661798\pi\)
0.999883 0.0152962i \(-0.00486912\pi\)
\(54\) 0 0
\(55\) 6.70820 0.904534
\(56\) 0 0
\(57\) −6.70820 −0.888523
\(58\) 0 0
\(59\) −0.736068 + 1.27491i −0.0958279 + 0.165979i −0.909954 0.414710i \(-0.863883\pi\)
0.814126 + 0.580688i \(0.197217\pi\)
\(60\) 0 0
\(61\) −1.50000 2.59808i −0.192055 0.332650i 0.753876 0.657017i \(-0.228182\pi\)
−0.945931 + 0.324367i \(0.894849\pi\)
\(62\) 0 0
\(63\) −5.00000 1.73205i −0.629941 0.218218i
\(64\) 0 0
\(65\) 1.11803 + 1.93649i 0.138675 + 0.240192i
\(66\) 0 0
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) 0 0
\(69\) 18.4164 2.21707
\(70\) 0 0
\(71\) 8.94427 1.06149 0.530745 0.847532i \(-0.321912\pi\)
0.530745 + 0.847532i \(0.321912\pi\)
\(72\) 0 0
\(73\) 1.35410 2.34537i 0.158486 0.274505i −0.775837 0.630933i \(-0.782672\pi\)
0.934323 + 0.356428i \(0.116006\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) 0 0
\(79\) −1.35410 2.34537i −0.152348 0.263875i 0.779742 0.626101i \(-0.215350\pi\)
−0.932090 + 0.362226i \(0.882017\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 3.29180 0.357045
\(86\) 0 0
\(87\) −5.00000 + 8.66025i −0.536056 + 0.928477i
\(88\) 0 0
\(89\) −1.11803 1.93649i −0.118511 0.205268i 0.800667 0.599110i \(-0.204479\pi\)
−0.919178 + 0.393842i \(0.871146\pi\)
\(90\) 0 0
\(91\) −2.00000 + 1.73205i −0.209657 + 0.181568i
\(92\) 0 0
\(93\) 5.59017 + 9.68246i 0.579674 + 1.00402i
\(94\) 0 0
\(95\) 3.35410 5.80948i 0.344124 0.596040i
\(96\) 0 0
\(97\) 9.41641 0.956091 0.478046 0.878335i \(-0.341345\pi\)
0.478046 + 0.878335i \(0.341345\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 0 0
\(103\) −1.35410 2.34537i −0.133424 0.231097i 0.791571 0.611078i \(-0.209264\pi\)
−0.924994 + 0.379981i \(0.875930\pi\)
\(104\) 0 0
\(105\) 10.0000 8.66025i 0.975900 0.845154i
\(106\) 0 0
\(107\) −4.88197 8.45581i −0.471957 0.817454i 0.527528 0.849538i \(-0.323119\pi\)
−0.999485 + 0.0320835i \(0.989786\pi\)
\(108\) 0 0
\(109\) 1.35410 2.34537i 0.129699 0.224646i −0.793861 0.608100i \(-0.791932\pi\)
0.923560 + 0.383454i \(0.125265\pi\)
\(110\) 0 0
\(111\) 10.5279 0.999261
\(112\) 0 0
\(113\) 2.94427 0.276974 0.138487 0.990364i \(-0.455776\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(114\) 0 0
\(115\) −9.20820 + 15.9491i −0.858669 + 1.48726i
\(116\) 0 0
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 0 0
\(119\) 0.736068 + 3.82472i 0.0674752 + 0.350612i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 5.00000 8.66025i 0.450835 0.780869i
\(124\) 0 0
\(125\) −11.1803 −1.00000
\(126\) 0 0
\(127\) 11.4164 1.01304 0.506521 0.862228i \(-0.330931\pi\)
0.506521 + 0.862228i \(0.330931\pi\)
\(128\) 0 0
\(129\) −8.94427 + 15.4919i −0.787499 + 1.36399i
\(130\) 0 0
\(131\) −4.11803 7.13264i −0.359794 0.623182i 0.628132 0.778107i \(-0.283820\pi\)
−0.987926 + 0.154925i \(0.950486\pi\)
\(132\) 0 0
\(133\) 7.50000 + 2.59808i 0.650332 + 0.225282i
\(134\) 0 0
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) 4.11803 7.13264i 0.351827 0.609383i −0.634742 0.772724i \(-0.718894\pi\)
0.986570 + 0.163341i \(0.0522271\pi\)
\(138\) 0 0
\(139\) 23.4164 1.98615 0.993077 0.117466i \(-0.0374771\pi\)
0.993077 + 0.117466i \(0.0374771\pi\)
\(140\) 0 0
\(141\) 16.7082 1.40708
\(142\) 0 0
\(143\) 1.50000 2.59808i 0.125436 0.217262i
\(144\) 0 0
\(145\) −5.00000 8.66025i −0.415227 0.719195i
\(146\) 0 0
\(147\) 12.2984 + 9.68246i 1.01435 + 0.798596i
\(148\) 0 0
\(149\) −0.354102 0.613323i −0.0290092 0.0502453i 0.851156 0.524912i \(-0.175902\pi\)
−0.880166 + 0.474667i \(0.842569\pi\)
\(150\) 0 0
\(151\) 10.2082 17.6811i 0.830732 1.43887i −0.0667268 0.997771i \(-0.521256\pi\)
0.897459 0.441098i \(-0.145411\pi\)
\(152\) 0 0
\(153\) 2.94427 0.238030
\(154\) 0 0
\(155\) −11.1803 −0.898027
\(156\) 0 0
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) 0 0
\(159\) 8.35410 + 14.4697i 0.662523 + 1.14752i
\(160\) 0 0
\(161\) −20.5902 7.13264i −1.62273 0.562131i
\(162\) 0 0
\(163\) −8.20820 14.2170i −0.642916 1.11356i −0.984779 0.173813i \(-0.944391\pi\)
0.341862 0.939750i \(-0.388942\pi\)
\(164\) 0 0
\(165\) −7.50000 + 12.9904i −0.583874 + 1.01130i
\(166\) 0 0
\(167\) −22.4721 −1.73895 −0.869473 0.493980i \(-0.835541\pi\)
−0.869473 + 0.493980i \(0.835541\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 3.00000 5.19615i 0.229416 0.397360i
\(172\) 0 0
\(173\) 8.20820 + 14.2170i 0.624058 + 1.08090i 0.988722 + 0.149761i \(0.0478505\pi\)
−0.364664 + 0.931139i \(0.618816\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.64590 2.85078i −0.123713 0.214278i
\(178\) 0 0
\(179\) −10.0623 + 17.4284i −0.752092 + 1.30266i 0.194715 + 0.980860i \(0.437622\pi\)
−0.946807 + 0.321802i \(0.895712\pi\)
\(180\) 0 0
\(181\) −25.4164 −1.88919 −0.944593 0.328243i \(-0.893544\pi\)
−0.944593 + 0.328243i \(0.893544\pi\)
\(182\) 0 0
\(183\) 6.70820 0.495885
\(184\) 0 0
\(185\) −5.26393 + 9.11740i −0.387012 + 0.670324i
\(186\) 0 0
\(187\) −2.20820 3.82472i −0.161480 0.279691i
\(188\) 0 0
\(189\) −4.47214 + 3.87298i −0.325300 + 0.281718i
\(190\) 0 0
\(191\) 5.59017 + 9.68246i 0.404491 + 0.700598i 0.994262 0.106972i \(-0.0341155\pi\)
−0.589772 + 0.807570i \(0.700782\pi\)
\(192\) 0 0
\(193\) −0.354102 + 0.613323i −0.0254888 + 0.0441479i −0.878488 0.477764i \(-0.841448\pi\)
0.853000 + 0.521912i \(0.174781\pi\)
\(194\) 0 0
\(195\) −5.00000 −0.358057
\(196\) 0 0
\(197\) −9.05573 −0.645194 −0.322597 0.946536i \(-0.604556\pi\)
−0.322597 + 0.946536i \(0.604556\pi\)
\(198\) 0 0
\(199\) −10.3541 + 17.9338i −0.733983 + 1.27130i 0.221185 + 0.975232i \(0.429007\pi\)
−0.955168 + 0.296064i \(0.904326\pi\)
\(200\) 0 0
\(201\) −3.35410 5.80948i −0.236580 0.409769i
\(202\) 0 0
\(203\) 8.94427 7.74597i 0.627765 0.543660i
\(204\) 0 0
\(205\) 5.00000 + 8.66025i 0.349215 + 0.604858i
\(206\) 0 0
\(207\) −8.23607 + 14.2653i −0.572446 + 0.991506i
\(208\) 0 0
\(209\) −9.00000 −0.622543
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −10.0000 + 17.3205i −0.685189 + 1.18678i
\(214\) 0 0
\(215\) −8.94427 15.4919i −0.609994 1.05654i
\(216\) 0 0
\(217\) −2.50000 12.9904i −0.169711 0.881845i
\(218\) 0 0
\(219\) 3.02786 + 5.24441i 0.204604 + 0.354385i
\(220\) 0 0
\(221\) 0.736068 1.27491i 0.0495133 0.0857595i
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.97214 5.14789i 0.197268 0.341677i −0.750374 0.661014i \(-0.770127\pi\)
0.947642 + 0.319336i \(0.103460\pi\)
\(228\) 0 0
\(229\) −12.0623 20.8925i −0.797100 1.38062i −0.921497 0.388385i \(-0.873033\pi\)
0.124398 0.992232i \(-0.460300\pi\)
\(230\) 0 0
\(231\) −16.7705 5.80948i −1.10342 0.382235i
\(232\) 0 0
\(233\) −5.97214 10.3440i −0.391248 0.677661i 0.601367 0.798973i \(-0.294623\pi\)
−0.992614 + 0.121312i \(0.961290\pi\)
\(234\) 0 0
\(235\) −8.35410 + 14.4697i −0.544962 + 0.943901i
\(236\) 0 0
\(237\) 6.05573 0.393362
\(238\) 0 0
\(239\) −19.4164 −1.25594 −0.627972 0.778236i \(-0.716115\pi\)
−0.627972 + 0.778236i \(0.716115\pi\)
\(240\) 0 0
\(241\) −2.35410 + 4.07742i −0.151641 + 0.262650i −0.931831 0.362893i \(-0.881789\pi\)
0.780190 + 0.625543i \(0.215122\pi\)
\(242\) 0 0
\(243\) 8.94427 + 15.4919i 0.573775 + 0.993808i
\(244\) 0 0
\(245\) −14.5344 + 5.80948i −0.928571 + 0.371154i
\(246\) 0 0
\(247\) −1.50000 2.59808i −0.0954427 0.165312i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.52786 −0.0964379 −0.0482190 0.998837i \(-0.515355\pi\)
−0.0482190 + 0.998837i \(0.515355\pi\)
\(252\) 0 0
\(253\) 24.7082 1.55339
\(254\) 0 0
\(255\) −3.68034 + 6.37454i −0.230472 + 0.399189i
\(256\) 0 0
\(257\) 0.0278640 + 0.0482619i 0.00173811 + 0.00301050i 0.866893 0.498494i \(-0.166113\pi\)
−0.865155 + 0.501504i \(0.832780\pi\)
\(258\) 0 0
\(259\) −11.7705 4.07742i −0.731384 0.253359i
\(260\) 0 0
\(261\) −4.47214 7.74597i −0.276818 0.479463i
\(262\) 0 0
\(263\) 13.0623 22.6246i 0.805456 1.39509i −0.110526 0.993873i \(-0.535254\pi\)
0.915983 0.401218i \(-0.131413\pi\)
\(264\) 0 0
\(265\) −16.7082 −1.02638
\(266\) 0 0
\(267\) 5.00000 0.305995
\(268\) 0 0
\(269\) −6.73607 + 11.6672i −0.410705 + 0.711362i −0.994967 0.100203i \(-0.968051\pi\)
0.584262 + 0.811565i \(0.301384\pi\)
\(270\) 0 0
\(271\) −10.2082 17.6811i −0.620104 1.07405i −0.989466 0.144766i \(-0.953757\pi\)
0.369362 0.929286i \(-0.379576\pi\)
\(272\) 0 0
\(273\) −1.11803 5.80948i −0.0676665 0.351605i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.208204 0.360620i 0.0125098 0.0216675i −0.859703 0.510795i \(-0.829351\pi\)
0.872213 + 0.489127i \(0.162685\pi\)
\(278\) 0 0
\(279\) −10.0000 −0.598684
\(280\) 0 0
\(281\) 26.9443 1.60736 0.803680 0.595061i \(-0.202872\pi\)
0.803680 + 0.595061i \(0.202872\pi\)
\(282\) 0 0
\(283\) 13.0623 22.6246i 0.776473 1.34489i −0.157489 0.987521i \(-0.550340\pi\)
0.933963 0.357371i \(-0.116327\pi\)
\(284\) 0 0
\(285\) 7.50000 + 12.9904i 0.444262 + 0.769484i
\(286\) 0 0
\(287\) −8.94427 + 7.74597i −0.527964 + 0.457230i
\(288\) 0 0
\(289\) 7.41641 + 12.8456i 0.436259 + 0.755623i
\(290\) 0 0
\(291\) −10.5279 + 18.2348i −0.617154 + 1.06894i
\(292\) 0 0
\(293\) −14.9443 −0.873054 −0.436527 0.899691i \(-0.643792\pi\)
−0.436527 + 0.899691i \(0.643792\pi\)
\(294\) 0 0
\(295\) 3.29180 0.191656
\(296\) 0 0
\(297\) 3.35410 5.80948i 0.194625 0.337100i
\(298\) 0 0
\(299\) 4.11803 + 7.13264i 0.238152 + 0.412491i
\(300\) 0 0
\(301\) 16.0000 13.8564i 0.922225 0.798670i
\(302\) 0 0
\(303\) 10.0623 + 17.4284i 0.578064 + 1.00124i
\(304\) 0 0
\(305\) −3.35410 + 5.80948i −0.192055 + 0.332650i
\(306\) 0 0
\(307\) −19.4164 −1.10815 −0.554076 0.832466i \(-0.686928\pi\)
−0.554076 + 0.832466i \(0.686928\pi\)
\(308\) 0 0
\(309\) 6.05573 0.344498
\(310\) 0 0
\(311\) −13.8820 + 24.0443i −0.787174 + 1.36343i 0.140518 + 0.990078i \(0.455123\pi\)
−0.927692 + 0.373347i \(0.878210\pi\)
\(312\) 0 0
\(313\) 2.79180 + 4.83553i 0.157802 + 0.273320i 0.934076 0.357075i \(-0.116226\pi\)
−0.776274 + 0.630396i \(0.782893\pi\)
\(314\) 0 0
\(315\) 2.23607 + 11.6190i 0.125988 + 0.654654i
\(316\) 0 0
\(317\) 4.11803 + 7.13264i 0.231292 + 0.400609i 0.958189 0.286138i \(-0.0923714\pi\)
−0.726897 + 0.686747i \(0.759038\pi\)
\(318\) 0 0
\(319\) −6.70820 + 11.6190i −0.375587 + 0.650536i
\(320\) 0 0
\(321\) 21.8328 1.21859
\(322\) 0 0
\(323\) −4.41641 −0.245736
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 3.02786 + 5.24441i 0.167441 + 0.290017i
\(328\) 0 0
\(329\) −18.6803 6.47106i −1.02988 0.356761i
\(330\) 0 0
\(331\) −0.791796 1.37143i −0.0435210 0.0753807i 0.843444 0.537217i \(-0.180524\pi\)
−0.886965 + 0.461836i \(0.847191\pi\)
\(332\) 0 0
\(333\) −4.70820 + 8.15485i −0.258008 + 0.446883i
\(334\) 0 0
\(335\) 6.70820 0.366508
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) −3.29180 + 5.70156i −0.178786 + 0.309666i
\(340\) 0 0
\(341\) 7.50000 + 12.9904i 0.406148 + 0.703469i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) −20.5902 35.6632i −1.10854 1.92004i
\(346\) 0 0
\(347\) 11.5344 19.9782i 0.619201 1.07249i −0.370430 0.928860i \(-0.620790\pi\)
0.989632 0.143628i \(-0.0458768\pi\)
\(348\) 0 0
\(349\) −29.4164 −1.57462 −0.787312 0.616555i \(-0.788528\pi\)
−0.787312 + 0.616555i \(0.788528\pi\)
\(350\) 0 0
\(351\) 2.23607 0.119352
\(352\) 0 0
\(353\) −8.64590 + 14.9751i −0.460175 + 0.797046i −0.998969 0.0453912i \(-0.985547\pi\)
0.538795 + 0.842437i \(0.318880\pi\)
\(354\) 0 0
\(355\) −10.0000 17.3205i −0.530745 0.919277i
\(356\) 0 0
\(357\) −8.22949 2.85078i −0.435551 0.150879i
\(358\) 0 0
\(359\) 5.97214 + 10.3440i 0.315197 + 0.545938i 0.979479 0.201544i \(-0.0645960\pi\)
−0.664282 + 0.747482i \(0.731263\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) 0 0
\(363\) −4.47214 −0.234726
\(364\) 0 0
\(365\) −6.05573 −0.316971
\(366\) 0 0
\(367\) −6.35410 + 11.0056i −0.331681 + 0.574489i −0.982842 0.184451i \(-0.940949\pi\)
0.651160 + 0.758940i \(0.274283\pi\)
\(368\) 0 0
\(369\) 4.47214 + 7.74597i 0.232810 + 0.403239i
\(370\) 0 0
\(371\) −3.73607 19.4132i −0.193967 1.00788i
\(372\) 0 0
\(373\) 0.791796 + 1.37143i 0.0409976 + 0.0710100i 0.885796 0.464075i \(-0.153613\pi\)
−0.844798 + 0.535085i \(0.820280\pi\)
\(374\) 0 0
\(375\) 12.5000 21.6506i 0.645497 1.11803i
\(376\) 0 0
\(377\) −4.47214 −0.230327
\(378\) 0 0
\(379\) 15.4164 0.791888 0.395944 0.918275i \(-0.370417\pi\)
0.395944 + 0.918275i \(0.370417\pi\)
\(380\) 0 0
\(381\) −12.7639 + 22.1078i −0.653916 + 1.13262i
\(382\) 0 0
\(383\) 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) 0 0
\(385\) 13.4164 11.6190i 0.683763 0.592157i
\(386\) 0 0
\(387\) −8.00000 13.8564i −0.406663 0.704361i
\(388\) 0 0
\(389\) −0.736068 + 1.27491i −0.0373201 + 0.0646404i −0.884082 0.467332i \(-0.845215\pi\)
0.846762 + 0.531972i \(0.178549\pi\)
\(390\) 0 0
\(391\) 12.1246 0.613168
\(392\) 0 0
\(393\) 18.4164 0.928985
\(394\) 0 0
\(395\) −3.02786 + 5.24441i −0.152348 + 0.263875i
\(396\) 0 0
\(397\) 13.0623 + 22.6246i 0.655578 + 1.13549i 0.981748 + 0.190184i \(0.0609084\pi\)
−0.326170 + 0.945311i \(0.605758\pi\)
\(398\) 0 0
\(399\) −13.4164 + 11.6190i −0.671660 + 0.581675i
\(400\) 0 0
\(401\) −7.11803 12.3288i −0.355458 0.615671i 0.631739 0.775182i \(-0.282342\pi\)
−0.987196 + 0.159511i \(0.949008\pi\)
\(402\) 0 0
\(403\) −2.50000 + 4.33013i −0.124534 + 0.215699i
\(404\) 0 0
\(405\) −24.5967 −1.22222
\(406\) 0 0
\(407\) 14.1246 0.700131
\(408\) 0 0
\(409\) −4.35410 + 7.54153i −0.215296 + 0.372904i −0.953364 0.301822i \(-0.902405\pi\)
0.738068 + 0.674727i \(0.235738\pi\)
\(410\) 0 0
\(411\) 9.20820 + 15.9491i 0.454207 + 0.786710i
\(412\) 0 0
\(413\) 0.736068 + 3.82472i 0.0362195 + 0.188202i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −26.1803 + 45.3457i −1.28206 + 2.22059i
\(418\) 0 0
\(419\) −32.9443 −1.60943 −0.804717 0.593659i \(-0.797683\pi\)
−0.804717 + 0.593659i \(0.797683\pi\)
\(420\) 0 0
\(421\) 13.4164 0.653876 0.326938 0.945046i \(-0.393983\pi\)
0.326938 + 0.945046i \(0.393983\pi\)
\(422\) 0 0
\(423\) −7.47214 + 12.9421i −0.363308 + 0.629267i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7.50000 2.59808i −0.362950 0.125730i
\(428\) 0 0
\(429\) 3.35410 + 5.80948i 0.161938 + 0.280484i
\(430\) 0 0
\(431\) −15.6803 + 27.1591i −0.755295 + 1.30821i 0.189932 + 0.981797i \(0.439173\pi\)
−0.945227 + 0.326413i \(0.894160\pi\)
\(432\) 0 0
\(433\) 29.4164 1.41366 0.706831 0.707382i \(-0.250124\pi\)
0.706831 + 0.707382i \(0.250124\pi\)
\(434\) 0 0
\(435\) 22.3607 1.07211
\(436\) 0 0
\(437\) 12.3541 21.3979i 0.590977 1.02360i
\(438\) 0 0
\(439\) 12.0623 + 20.8925i 0.575702 + 0.997146i 0.995965 + 0.0897433i \(0.0286047\pi\)
−0.420262 + 0.907403i \(0.638062\pi\)
\(440\) 0 0
\(441\) −13.0000 + 5.19615i −0.619048 + 0.247436i
\(442\) 0 0
\(443\) 1.11803 + 1.93649i 0.0531194 + 0.0920055i 0.891362 0.453291i \(-0.149750\pi\)
−0.838243 + 0.545297i \(0.816417\pi\)
\(444\) 0 0
\(445\) −2.50000 + 4.33013i −0.118511 + 0.205268i
\(446\) 0 0
\(447\) 1.58359 0.0749013
\(448\) 0 0
\(449\) −34.3607 −1.62158 −0.810790 0.585337i \(-0.800962\pi\)
−0.810790 + 0.585337i \(0.800962\pi\)
\(450\) 0 0
\(451\) 6.70820 11.6190i 0.315877 0.547115i
\(452\) 0 0
\(453\) 22.8262 + 39.5362i 1.07247 + 1.85757i
\(454\) 0 0
\(455\) 5.59017 + 1.93649i 0.262071 + 0.0907841i
\(456\) 0 0
\(457\) 3.06231 + 5.30407i 0.143249 + 0.248114i 0.928718 0.370786i \(-0.120912\pi\)
−0.785470 + 0.618900i \(0.787578\pi\)
\(458\) 0 0
\(459\) 1.64590 2.85078i 0.0768239 0.133063i
\(460\) 0 0
\(461\) 34.3607 1.60034 0.800168 0.599776i \(-0.204744\pi\)
0.800168 + 0.599776i \(0.204744\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 0 0
\(465\) 12.5000 21.6506i 0.579674 1.00402i
\(466\) 0 0
\(467\) 4.82624 + 8.35929i 0.223332 + 0.386822i 0.955818 0.293960i \(-0.0949734\pi\)
−0.732486 + 0.680782i \(0.761640\pi\)
\(468\) 0 0
\(469\) 1.50000 + 7.79423i 0.0692636 + 0.359904i
\(470\) 0 0
\(471\) −7.82624 13.5554i −0.360614 0.624602i
\(472\) 0 0
\(473\) −12.0000 + 20.7846i −0.551761 + 0.955677i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −14.9443 −0.684251
\(478\) 0 0
\(479\) 11.9164 20.6398i 0.544475 0.943058i −0.454165 0.890917i \(-0.650062\pi\)
0.998640 0.0521401i \(-0.0166043\pi\)
\(480\) 0 0
\(481\) 2.35410 + 4.07742i 0.107338 + 0.185915i
\(482\) 0 0
\(483\) 36.8328 31.8982i 1.67595 1.45142i
\(484\) 0 0
\(485\) −10.5279 18.2348i −0.478046 0.827999i
\(486\) 0 0
\(487\) −10.9164 + 18.9078i −0.494670 + 0.856793i −0.999981 0.00614405i \(-0.998044\pi\)
0.505311 + 0.862937i \(0.331378\pi\)
\(488\) 0 0
\(489\) 36.7082 1.66000
\(490\) 0 0
\(491\) 25.5279 1.15206 0.576028 0.817430i \(-0.304602\pi\)
0.576028 + 0.817430i \(0.304602\pi\)
\(492\) 0 0
\(493\) −3.29180 + 5.70156i −0.148255 + 0.256785i
\(494\) 0 0
\(495\) −6.70820 11.6190i −0.301511 0.522233i
\(496\) 0 0
\(497\) 17.8885 15.4919i 0.802411 0.694908i
\(498\) 0 0
\(499\) 13.2082 + 22.8773i 0.591280 + 1.02413i 0.994060 + 0.108831i \(0.0347107\pi\)
−0.402780 + 0.915297i \(0.631956\pi\)
\(500\) 0 0
\(501\) 25.1246 43.5171i 1.12248 1.94420i
\(502\) 0 0
\(503\) −20.9443 −0.933859 −0.466929 0.884295i \(-0.654640\pi\)
−0.466929 + 0.884295i \(0.654640\pi\)
\(504\) 0 0
\(505\) −20.1246 −0.895533
\(506\) 0 0
\(507\) −1.11803 + 1.93649i −0.0496536 + 0.0860026i
\(508\) 0 0
\(509\) 10.1180 + 17.5249i 0.448474 + 0.776780i 0.998287 0.0585081i \(-0.0186343\pi\)
−0.549813 + 0.835288i \(0.685301\pi\)
\(510\) 0 0
\(511\) −1.35410 7.03612i −0.0599019 0.311260i
\(512\) 0 0
\(513\) −3.35410 5.80948i −0.148087 0.256495i
\(514\) 0 0
\(515\) −3.02786 + 5.24441i −0.133424 + 0.231097i
\(516\) 0 0
\(517\) 22.4164 0.985872
\(518\) 0 0
\(519\) −36.7082 −1.61131
\(520\) 0 0
\(521\) 8.97214 15.5402i 0.393076 0.680828i −0.599777 0.800167i \(-0.704744\pi\)
0.992854 + 0.119339i \(0.0380775\pi\)
\(522\) 0 0
\(523\) 16.3541 + 28.3261i 0.715115 + 1.23862i 0.962915 + 0.269804i \(0.0869590\pi\)
−0.247800 + 0.968811i \(0.579708\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.68034 + 6.37454i 0.160318 + 0.277679i
\(528\) 0 0
\(529\) −22.4164 + 38.8264i −0.974626 + 1.68810i
\(530\) 0 0
\(531\) 2.94427 0.127771
\(532\) 0 0
\(533\) 4.47214 0.193710
\(534\) 0 0
\(535\) −10.9164 + 18.9078i −0.471957 + 0.817454i
\(536\) 0 0
\(537\) −22.5000 38.9711i −0.970947 1.68173i
\(538\) 0 0
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 0 0
\(541\) −0.645898 1.11873i −0.0277693 0.0480979i 0.851807 0.523856i \(-0.175507\pi\)
−0.879576 + 0.475758i \(0.842174\pi\)
\(542\) 0 0
\(543\) 28.4164 49.2187i 1.21946 2.11217i
\(544\) 0 0
\(545\) −6.05573 −0.259399
\(546\) 0 0
\(547\) 4.58359 0.195980 0.0979901 0.995187i \(-0.468759\pi\)
0.0979901 + 0.995187i \(0.468759\pi\)
\(548\) 0 0
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 0 0
\(551\) 6.70820 + 11.6190i 0.285779 + 0.494984i
\(552\) 0 0
\(553\) −6.77051 2.34537i −0.287911 0.0997354i
\(554\) 0 0
\(555\) −11.7705 20.3871i −0.499630 0.865385i
\(556\) 0 0
\(557\) 9.35410 16.2018i 0.396346 0.686491i −0.596926 0.802296i \(-0.703611\pi\)
0.993272 + 0.115805i \(0.0369447\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 9.87539 0.416939
\(562\) 0 0
\(563\) 6.29837 10.9091i 0.265445 0.459764i −0.702235 0.711945i \(-0.747815\pi\)
0.967680 + 0.252181i \(0.0811479\pi\)
\(564\) 0 0
\(565\) −3.29180 5.70156i −0.138487 0.239866i
\(566\) 0 0
\(567\) −5.50000 28.5788i −0.230978 1.20020i
\(568\) 0 0
\(569\) −12.7361 22.0595i −0.533924 0.924783i −0.999215 0.0396252i \(-0.987384\pi\)
0.465291 0.885158i \(-0.345950\pi\)
\(570\) 0 0
\(571\) −18.0623 + 31.2848i −0.755884 + 1.30923i 0.189050 + 0.981968i \(0.439459\pi\)
−0.944934 + 0.327262i \(0.893874\pi\)
\(572\) 0 0
\(573\) −25.0000 −1.04439
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 9.64590 16.7072i 0.401564 0.695529i −0.592351 0.805680i \(-0.701800\pi\)
0.993915 + 0.110151i \(0.0351334\pi\)
\(578\) 0 0
\(579\) −0.791796 1.37143i −0.0329059 0.0569947i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 11.2082 + 19.4132i 0.464196 + 0.804012i
\(584\) 0 0
\(585\) 2.23607 3.87298i 0.0924500 0.160128i
\(586\) 0 0
\(587\) 6.11146 0.252247 0.126123 0.992015i \(-0.459746\pi\)
0.126123 + 0.992015i \(0.459746\pi\)
\(588\) 0 0
\(589\) 15.0000 0.618064
\(590\) 0 0
\(591\) 10.1246 17.5363i 0.416471 0.721349i
\(592\) 0 0
\(593\) −13.8820 24.0443i −0.570064 0.987380i −0.996559 0.0828898i \(-0.973585\pi\)
0.426495 0.904490i \(-0.359748\pi\)
\(594\) 0 0
\(595\) 6.58359 5.70156i 0.269901 0.233741i
\(596\) 0 0
\(597\) −23.1525 40.1013i −0.947568 1.64124i
\(598\) 0 0
\(599\) −8.53444 + 14.7821i −0.348708 + 0.603980i −0.986020 0.166626i \(-0.946713\pi\)
0.637312 + 0.770606i \(0.280046\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 6.00000 0.244339
\(604\) 0 0
\(605\) 2.23607 3.87298i 0.0909091 0.157459i
\(606\) 0 0
\(607\) 12.0623 + 20.8925i 0.489594 + 0.848001i 0.999928 0.0119745i \(-0.00381171\pi\)
−0.510334 + 0.859976i \(0.670478\pi\)
\(608\) 0 0
\(609\) 5.00000 + 25.9808i 0.202610 + 1.05279i
\(610\) 0 0
\(611\) 3.73607 + 6.47106i 0.151145 + 0.261791i
\(612\) 0 0
\(613\) 9.06231 15.6964i 0.366023 0.633971i −0.622917 0.782288i \(-0.714052\pi\)
0.988940 + 0.148318i \(0.0473858\pi\)
\(614\) 0 0
\(615\) −22.3607 −0.901670
\(616\) 0 0
\(617\) −4.47214 −0.180041 −0.0900207 0.995940i \(-0.528693\pi\)
−0.0900207 + 0.995940i \(0.528693\pi\)
\(618\) 0 0
\(619\) 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i \(-0.722350\pi\)
0.984738 + 0.174042i \(0.0556830\pi\)
\(620\) 0 0
\(621\) 9.20820 + 15.9491i 0.369512 + 0.640014i
\(622\) 0 0
\(623\) −5.59017 1.93649i −0.223965 0.0775839i
\(624\) 0 0
\(625\) 12.5000 + 21.6506i 0.500000 + 0.866025i
\(626\) 0 0
\(627\) 10.0623 17.4284i 0.401850 0.696024i
\(628\) 0 0
\(629\) 6.93112 0.276362
\(630\) 0 0
\(631\) −22.8328 −0.908960 −0.454480 0.890757i \(-0.650175\pi\)
−0.454480 + 0.890757i \(0.650175\pi\)
\(632\) 0 0
\(633\) 4.47214 7.74597i 0.177751 0.307875i
\(634\) 0 0
\(635\) −12.7639 22.1078i −0.506521 0.877320i
\(636\) 0 0
\(637\) −1.00000 + 6.92820i −0.0396214 + 0.274505i
\(638\) 0 0
\(639\) −8.94427 15.4919i −0.353830 0.612851i
\(640\) 0 0
\(641\) −5.97214 + 10.3440i −0.235885 + 0.408565i −0.959530 0.281608i \(-0.909132\pi\)
0.723644 + 0.690173i \(0.242466\pi\)
\(642\) 0 0
\(643\) −34.8328 −1.37367 −0.686836 0.726812i \(-0.741001\pi\)
−0.686836 + 0.726812i \(0.741001\pi\)
\(644\) 0 0
\(645\) 40.0000 1.57500
\(646\) 0 0
\(647\) 10.1180 17.5249i 0.397781 0.688977i −0.595671 0.803229i \(-0.703114\pi\)
0.993452 + 0.114252i \(0.0364471\pi\)
\(648\) 0 0
\(649\) −2.20820 3.82472i −0.0866796 0.150133i
\(650\) 0 0
\(651\) 27.9508 + 9.68246i 1.09548 + 0.379485i
\(652\) 0 0
\(653\) −2.26393 3.92125i −0.0885945 0.153450i 0.818323 0.574759i \(-0.194904\pi\)
−0.906917 + 0.421309i \(0.861571\pi\)
\(654\) 0 0
\(655\) −9.20820 + 15.9491i −0.359794 + 0.623182i
\(656\) 0 0
\(657\) −5.41641 −0.211314
\(658\) 0 0
\(659\) 8.94427 0.348419 0.174210 0.984709i \(-0.444263\pi\)
0.174210 + 0.984709i \(0.444263\pi\)
\(660\) 0 0
\(661\) 3.35410 5.80948i 0.130459 0.225962i −0.793394 0.608708i \(-0.791688\pi\)
0.923854 + 0.382746i \(0.125021\pi\)
\(662\) 0 0
\(663\) 1.64590 + 2.85078i 0.0639214 + 0.110715i
\(664\) 0 0
\(665\) −3.35410 17.4284i −0.130066 0.675845i
\(666\) 0 0
\(667\) −18.4164 31.8982i −0.713086 1.23510i
\(668\) 0 0
\(669\) −4.47214 + 7.74597i −0.172903 + 0.299476i
\(670\) 0 0
\(671\) 9.00000 0.347441
\(672\) 0 0
\(673\) −9.41641 −0.362976 −0.181488 0.983393i \(-0.558091\pi\)
−0.181488 + 0.983393i \(0.558091\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.44427 + 2.50155i 0.0555079 + 0.0961425i 0.892444 0.451158i \(-0.148989\pi\)
−0.836936 + 0.547300i \(0.815656\pi\)
\(678\) 0 0
\(679\) 18.8328 16.3097i 0.722737 0.625909i
\(680\) 0 0
\(681\) 6.64590 + 11.5110i 0.254671 + 0.441104i
\(682\) 0 0
\(683\) −6.73607 + 11.6672i −0.257748 + 0.446433i −0.965638 0.259889i \(-0.916314\pi\)
0.707890 + 0.706323i \(0.249647\pi\)
\(684\) 0 0
\(685\) −18.4164 −0.703655
\(686\) 0 0
\(687\) 53.9443 2.05810
\(688\) 0 0
\(689\) −3.73607 + 6.47106i −0.142333 + 0.246528i
\(690\) 0 0
\(691\) −25.9164 44.8885i −0.985907 1.70764i −0.637836 0.770172i \(-0.720170\pi\)
−0.348070 0.937468i \(-0.613163\pi\)
\(692\) 0 0
\(693\) 12.0000 10.3923i 0.455842 0.394771i
\(694\) 0 0
\(695\) −26.1803 45.3457i −0.993077 1.72006i
\(696\) 0 0
\(697\) 3.29180 5.70156i 0.124686 0.215962i
\(698\) 0 0
\(699\) 26.7082 1.01020
\(700\) 0 0
\(701\) −22.3607 −0.844551 −0.422276 0.906467i \(-0.638769\pi\)
−0.422276 + 0.906467i \(0.638769\pi\)
\(702\) 0 0
\(703\) 7.06231 12.2323i 0.266360 0.461349i
\(704\) 0 0
\(705\) −18.6803 32.3553i −0.703542 1.21857i
\(706\) 0 0
\(707\) −4.50000 23.3827i −0.169240 0.879396i
\(708\) 0 0
\(709\) 25.0623 + 43.4092i 0.941235 + 1.63027i 0.763120 + 0.646256i \(0.223666\pi\)
0.178114 + 0.984010i \(0.443000\pi\)
\(710\) 0 0
\(711\) −2.70820 + 4.69075i −0.101566 + 0.175917i
\(712\) 0 0
\(713\) −41.1803 −1.54222
\(714\) 0 0
\(715\) −6.70820 −0.250873
\(716\) 0 0
\(717\) 21.7082 37.5997i 0.810708 1.40419i
\(718\) 0 0
\(719\) 12.3541 + 21.3979i 0.460730 + 0.798008i 0.998998 0.0447660i \(-0.0142542\pi\)
−0.538267 + 0.842774i \(0.680921\pi\)
\(720\) 0 0
\(721\) −6.77051 2.34537i −0.252147 0.0873463i
\(722\) 0 0
\(723\) −5.26393 9.11740i −0.195768 0.339080i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 38.8328 1.44023 0.720115 0.693855i \(-0.244089\pi\)
0.720115 + 0.693855i \(0.244089\pi\)
\(728\) 0 0
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) −5.88854 + 10.1993i −0.217796 + 0.377233i
\(732\) 0 0
\(733\) −14.3541 24.8620i −0.530181 0.918300i −0.999380 0.0352078i \(-0.988791\pi\)
0.469199 0.883092i \(-0.344543\pi\)
\(734\) 0 0
\(735\) 5.00000 34.6410i 0.184428 1.27775i
\(736\) 0 0
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) 0 0
\(739\) −8.91641 + 15.4437i −0.327995 + 0.568105i −0.982114 0.188287i \(-0.939706\pi\)
0.654119 + 0.756392i \(0.273040\pi\)
\(740\) 0 0
\(741\) 6.70820 0.246432
\(742\) 0 0
\(743\) −32.9443 −1.20861 −0.604304 0.796754i \(-0.706549\pi\)
−0.604304 + 0.796754i \(0.706549\pi\)
\(744\) 0 0
\(745\) −0.791796 + 1.37143i −0.0290092 + 0.0502453i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −24.4098 8.45581i −0.891916 0.308969i
\(750\) 0 0
\(751\) −5.06231 8.76817i −0.184726 0.319955i 0.758758 0.651373i \(-0.225806\pi\)
−0.943484 + 0.331417i \(0.892473\pi\)
\(752\) 0 0
\(753\) 1.70820 2.95870i 0.0622504 0.107821i
\(754\) 0 0
\(755\) −45.6525 −1.66146
\(756\) 0 0
\(757\) −52.8328 −1.92024 −0.960121 0.279586i \(-0.909803\pi\)
−0.960121 + 0.279586i \(0.909803\pi\)
\(758\) 0 0
\(759\) −27.6246 + 47.8472i −1.00271 + 1.73674i
\(760\) 0 0
\(761\) 16.7705 + 29.0474i 0.607931 + 1.05297i 0.991581 + 0.129488i \(0.0413334\pi\)
−0.383650 + 0.923478i \(0.625333\pi\)
\(762\) 0 0
\(763\) −1.35410 7.03612i −0.0490218 0.254725i
\(764\) 0 0
\(765\) −3.29180 5.70156i −0.119015 0.206140i
\(766\) 0 0
\(767\) 0.736068 1.27491i 0.0265779 0.0460342i
\(768\) 0 0
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 0 0
\(771\) −0.124612 −0.00448778
\(772\) 0 0
\(773\) 23.5344 40.7628i 0.846475 1.46614i −0.0378590 0.999283i \(-0.512054\pi\)
0.884334 0.466855i \(-0.154613\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 21.0557 18.2348i 0.755370 0.654170i
\(778\) 0 0
\(779\) −6.70820 11.6190i −0.240346 0.416292i
\(780\) 0 0
\(781\) −13.4164 + 23.2379i −0.480077 + 0.831517i
\(782\) 0 0
\(783\) −10.0000 −0.357371
\(784\) 0 0
\(785\) 15.6525 0.558661
\(786\) 0 0
\(787\) 10.2082 17.6811i 0.363883 0.630264i −0.624713 0.780854i \(-0.714784\pi\)
0.988596 + 0.150590i \(0.0481174\pi\)
\(788\) 0 0
\(789\) 29.2082 + 50.5901i 1.03984 + 1.80106i
\(790\) 0 0
\(791\) 5.88854 5.09963i 0.209373 0.181322i
\(792\) 0 0
\(793\) 1.50000 + 2.59808i 0.0532666 + 0.0922604i
\(794\) 0 0
\(795\) 18.6803 32.3553i 0.662523 1.14752i
\(796\) 0 0
\(797\)