Properties

Label 819.2.j.c.235.1
Level $819$
Weight $2$
Character 819.235
Analytic conductor $6.540$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(1\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.1
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 819.235
Dual form 819.2.j.c.352.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30902 - 2.26728i) q^{2} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} +(-2.00000 + 1.73205i) q^{7} +7.47214 q^{8} +O(q^{10})\) \(q+(-1.30902 - 2.26728i) q^{2} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} +(-2.00000 + 1.73205i) q^{7} +7.47214 q^{8} +(2.92705 - 5.06980i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(6.54508 + 2.26728i) q^{14} +(-4.92705 - 8.53390i) q^{16} +(0.736068 - 1.27491i) q^{17} +(-1.50000 - 2.59808i) q^{19} -10.8541 q^{20} +7.85410 q^{22} +(-4.11803 - 7.13264i) q^{23} +(1.30902 + 2.26728i) q^{26} +(-2.42705 - 12.6113i) q^{28} -4.47214 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-5.42705 + 9.39993i) q^{32} -3.85410 q^{34} +(-5.59017 - 1.93649i) q^{35} +(-2.35410 - 4.07742i) q^{37} +(-3.92705 + 6.80185i) q^{38} +(8.35410 + 14.4697i) q^{40} +4.47214 q^{41} -8.00000 q^{43} +(-7.28115 - 12.6113i) q^{44} +(-10.7812 + 18.6735i) q^{46} +(-3.73607 - 6.47106i) q^{47} +(1.00000 - 6.92820i) q^{49} +(2.42705 - 4.20378i) q^{52} +(-3.73607 + 6.47106i) q^{53} -6.70820 q^{55} +(-14.9443 + 12.9421i) q^{56} +(5.85410 + 10.1396i) q^{58} +(-0.736068 + 1.27491i) q^{59} +(-1.50000 - 2.59808i) q^{61} +13.0902 q^{62} +8.70820 q^{64} +(-1.11803 - 1.93649i) q^{65} +(1.50000 - 2.59808i) q^{67} +(3.57295 + 6.18853i) q^{68} +(2.92705 + 15.2094i) q^{70} +8.94427 q^{71} +(1.35410 - 2.34537i) q^{73} +(-6.16312 + 10.6748i) q^{74} +14.5623 q^{76} +(-1.50000 - 7.79423i) q^{77} +(1.35410 + 2.34537i) q^{79} +(11.0172 - 19.0824i) q^{80} +(-5.85410 - 10.1396i) q^{82} +3.29180 q^{85} +(10.4721 + 18.1383i) q^{86} +(-11.2082 + 19.4132i) q^{88} +(1.11803 + 1.93649i) q^{89} +(2.00000 - 1.73205i) q^{91} +39.9787 q^{92} +(-9.78115 + 16.9415i) q^{94} +(3.35410 - 5.80948i) q^{95} +9.41641 q^{97} +(-17.0172 + 6.80185i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + O(q^{10}) \) \( 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + 5 q^{10} - 6 q^{11} - 4 q^{13} + 15 q^{14} - 13 q^{16} - 6 q^{17} - 6 q^{19} - 30 q^{20} + 18 q^{22} - 12 q^{23} + 3 q^{26} - 3 q^{28} - 10 q^{31} - 15 q^{32} - 2 q^{34} + 4 q^{37} - 9 q^{38} + 20 q^{40} - 32 q^{43} - 9 q^{44} - 23 q^{46} - 6 q^{47} + 4 q^{49} + 3 q^{52} - 6 q^{53} - 24 q^{56} + 10 q^{58} + 6 q^{59} - 6 q^{61} + 30 q^{62} + 8 q^{64} + 6 q^{67} + 21 q^{68} + 5 q^{70} - 8 q^{73} - 9 q^{74} + 18 q^{76} - 6 q^{77} - 8 q^{79} + 15 q^{80} - 10 q^{82} + 40 q^{85} + 24 q^{86} - 18 q^{88} + 8 q^{91} + 66 q^{92} - 19 q^{94} - 16 q^{97} - 39 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30902 2.26728i −0.925615 1.60321i −0.790569 0.612372i \(-0.790215\pi\)
−0.135045 0.990839i \(-0.543118\pi\)
\(3\) 0 0
\(4\) −2.42705 + 4.20378i −1.21353 + 2.10189i
\(5\) 1.11803 + 1.93649i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 7.47214 2.64180
\(9\) 0 0
\(10\) 2.92705 5.06980i 0.925615 1.60321i
\(11\) −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
\(14\) 6.54508 + 2.26728i 1.74925 + 0.605957i
\(15\) 0 0
\(16\) −4.92705 8.53390i −1.23176 2.13348i
\(17\) 0.736068 1.27491i 0.178523 0.309210i −0.762852 0.646573i \(-0.776202\pi\)
0.941375 + 0.337363i \(0.109535\pi\)
\(18\) 0 0
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) −10.8541 −2.42705
\(21\) 0 0
\(22\) 7.85410 1.67450
\(23\) −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
\(26\) 1.30902 + 2.26728i 0.256719 + 0.444651i
\(27\) 0 0
\(28\) −2.42705 12.6113i −0.458670 2.38332i
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) −5.42705 + 9.39993i −0.959376 + 1.66169i
\(33\) 0 0
\(34\) −3.85410 −0.660973
\(35\) −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 \(0.959826\pi\)
\(38\) −3.92705 + 6.80185i −0.637052 + 1.10341i
\(39\) 0 0
\(40\) 8.35410 + 14.4697i 1.32090 + 2.28787i
\(41\) 4.47214 0.698430 0.349215 0.937043i \(-0.386448\pi\)
0.349215 + 0.937043i \(0.386448\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −7.28115 12.6113i −1.09768 1.90123i
\(45\) 0 0
\(46\) −10.7812 + 18.6735i −1.58959 + 2.75326i
\(47\) −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
\(51\) 0 0
\(52\) 2.42705 4.20378i 0.336571 0.582959i
\(53\) −3.73607 + 6.47106i −0.513188 + 0.888868i 0.486695 + 0.873572i \(0.338202\pi\)
−0.999883 + 0.0152962i \(0.995131\pi\)
\(54\) 0 0
\(55\) −6.70820 −0.904534
\(56\) −14.9443 + 12.9421i −1.99701 + 1.72946i
\(57\) 0 0
\(58\) 5.85410 + 10.1396i 0.768681 + 1.33139i
\(59\) −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 \(0.894849\pi\)
\(62\) 13.0902 1.66245
\(63\) 0 0
\(64\) 8.70820 1.08853
\(65\) −1.11803 1.93649i −0.138675 0.240192i
\(66\) 0 0
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) 3.57295 + 6.18853i 0.433284 + 0.750469i
\(69\) 0 0
\(70\) 2.92705 + 15.2094i 0.349850 + 1.81787i
\(71\) 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 \(0.116006\pi\)
\(74\) −6.16312 + 10.6748i −0.716448 + 1.24092i
\(75\) 0 0
\(76\) 14.5623 1.67041
\(77\) −1.50000 7.79423i −0.170941 0.888235i
\(78\) 0 0
\(79\) 1.35410 + 2.34537i 0.152348 + 0.263875i 0.932090 0.362226i \(-0.117983\pi\)
−0.779742 + 0.626101i \(0.784650\pi\)
\(80\) 11.0172 19.0824i 1.23176 2.13348i
\(81\) 0 0
\(82\) −5.85410 10.1396i −0.646477 1.11973i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 3.29180 0.357045
\(86\) 10.4721 + 18.1383i 1.12924 + 1.95590i
\(87\) 0 0
\(88\) −11.2082 + 19.4132i −1.19480 + 2.06945i
\(89\) 1.11803 + 1.93649i 0.118511 + 0.205268i 0.919178 0.393842i \(-0.128854\pi\)
−0.800667 + 0.599110i \(0.795521\pi\)
\(90\) 0 0
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) 39.9787 4.16807
\(93\) 0 0
\(94\) −9.78115 + 16.9415i −1.00885 + 1.74738i
\(95\) 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 \(0.341345\pi\)
\(98\) −17.0172 + 6.80185i −1.71900 + 0.687091i
\(99\) 0 0
\(100\) 0 0
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 0 0
\(103\) 1.35410 + 2.34537i 0.133424 + 0.231097i 0.924994 0.379981i \(-0.124070\pi\)
−0.791571 + 0.611078i \(0.790736\pi\)
\(104\) −7.47214 −0.732703
\(105\) 0 0
\(106\) 19.5623 1.90006
\(107\) −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 \(0.125265\pi\)
\(110\) 8.78115 + 15.2094i 0.837250 + 1.45016i
\(111\) 0 0
\(112\) 24.6353 + 8.53390i 2.32781 + 0.806378i
\(113\) −2.94427 −0.276974 −0.138487 0.990364i \(-0.544224\pi\)
−0.138487 + 0.990364i \(0.544224\pi\)
\(114\) 0 0
\(115\) 9.20820 15.9491i 0.858669 1.48726i
\(116\) 10.8541 18.7999i 1.00778 1.74552i
\(117\) 0 0
\(118\) 3.85410 0.354799
\(119\) 0.736068 + 3.82472i 0.0674752 + 0.350612i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −3.92705 + 6.80185i −0.355538 + 0.615811i
\(123\) 0 0
\(124\) −12.1353 21.0189i −1.08978 1.88755i
\(125\) 11.1803 1.00000
\(126\) 0 0
\(127\) −11.4164 −1.01304 −0.506521 0.862228i \(-0.669069\pi\)
−0.506521 + 0.862228i \(0.669069\pi\)
\(128\) −0.545085 0.944115i −0.0481792 0.0834488i
\(129\) 0 0
\(130\) −2.92705 + 5.06980i −0.256719 + 0.444651i
\(131\) −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
\(134\) −7.85410 −0.678491
\(135\) 0 0
\(136\) 5.50000 9.52628i 0.471621 0.816872i
\(137\) −4.11803 + 7.13264i −0.351827 + 0.609383i −0.986570 0.163341i \(-0.947773\pi\)
0.634742 + 0.772724i \(0.281106\pi\)
\(138\) 0 0
\(139\) −23.4164 −1.98615 −0.993077 0.117466i \(-0.962523\pi\)
−0.993077 + 0.117466i \(0.962523\pi\)
\(140\) 21.7082 18.7999i 1.83468 1.58888i
\(141\) 0 0
\(142\) −11.7082 20.2792i −0.982531 1.70179i
\(143\) 1.50000 2.59808i 0.125436 0.217262i
\(144\) 0 0
\(145\) −5.00000 8.66025i −0.415227 0.719195i
\(146\) −7.09017 −0.586787
\(147\) 0 0
\(148\) 22.8541 1.87860
\(149\) 0.354102 + 0.613323i 0.0290092 + 0.0502453i 0.880166 0.474667i \(-0.157431\pi\)
−0.851156 + 0.524912i \(0.824098\pi\)
\(150\) 0 0
\(151\) −10.2082 + 17.6811i −0.830732 + 1.43887i 0.0667268 + 0.997771i \(0.478744\pi\)
−0.897459 + 0.441098i \(0.854589\pi\)
\(152\) −11.2082 19.4132i −0.909105 1.57462i
\(153\) 0 0
\(154\) −15.7082 + 13.6037i −1.26580 + 1.09622i
\(155\) −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 \(0.256779\pi\)
\(158\) 3.54508 6.14027i 0.282032 0.488493i
\(159\) 0 0
\(160\) −24.2705 −1.91875
\(161\) 20.5902 + 7.13264i 1.62273 + 0.562131i
\(162\) 0 0
\(163\) 8.20820 + 14.2170i 0.642916 + 1.11356i 0.984779 + 0.173813i \(0.0556090\pi\)
−0.341862 + 0.939750i \(0.611058\pi\)
\(164\) −10.8541 + 18.7999i −0.847563 + 1.46802i
\(165\) 0 0
\(166\) 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
\(170\) −4.30902 7.46344i −0.330487 0.572419i
\(171\) 0 0
\(172\) 19.4164 33.6302i 1.48049 2.56428i
\(173\) −8.20820 14.2170i −0.624058 1.08090i −0.988722 0.149761i \(-0.952149\pi\)
0.364664 0.931139i \(-0.381184\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 29.5623 2.22834
\(177\) 0 0
\(178\) 2.92705 5.06980i 0.219392 0.379998i
\(179\) −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 \(0.893544\pi\)
\(182\) −6.54508 2.26728i −0.485154 0.168062i
\(183\) 0 0
\(184\) −30.7705 53.2961i −2.26843 3.92904i
\(185\) 5.26393 9.11740i 0.387012 0.670324i
\(186\) 0 0
\(187\) 2.20820 + 3.82472i 0.161480 + 0.279691i
\(188\) 36.2705 2.64530
\(189\) 0 0
\(190\) −17.5623 −1.27410
\(191\) 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 \(0.174781\pi\)
\(194\) −12.3262 21.3497i −0.884972 1.53282i
\(195\) 0 0
\(196\) 26.6976 + 21.0189i 1.90697 + 1.50135i
\(197\) 9.05573 0.645194 0.322597 0.946536i \(-0.395444\pi\)
0.322597 + 0.946536i \(0.395444\pi\)
\(198\) 0 0
\(199\) 10.3541 17.9338i 0.733983 1.27130i −0.221185 0.975232i \(-0.570993\pi\)
0.955168 0.296064i \(-0.0956741\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 23.5623 1.65784
\(203\) 8.94427 7.74597i 0.627765 0.543660i
\(204\) 0 0
\(205\) 5.00000 + 8.66025i 0.349215 + 0.604858i
\(206\) 3.54508 6.14027i 0.246998 0.427813i
\(207\) 0 0
\(208\) 4.92705 + 8.53390i 0.341630 + 0.591720i
\(209\) 9.00000 0.622543
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −18.1353 31.4112i −1.24553 2.15733i
\(213\) 0 0
\(214\) −12.7812 + 22.1376i −0.873702 + 1.51330i
\(215\) −8.94427 15.4919i −0.609994 1.05654i
\(216\) 0 0
\(217\) −2.50000 12.9904i −0.169711 0.881845i
\(218\) −7.09017 −0.480207
\(219\) 0 0
\(220\) 16.2812 28.1998i 1.09768 1.90123i
\(221\) −0.736068 + 1.27491i −0.0495133 + 0.0857595i
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −5.42705 28.1998i −0.362610 1.88418i
\(225\) 0 0
\(226\) 3.85410 + 6.67550i 0.256371 + 0.444048i
\(227\) 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 \(-0.460300\pi\)
\(230\) −48.2148 −3.17919
\(231\) 0 0
\(232\) −33.4164 −2.19389
\(233\) 5.97214 + 10.3440i 0.391248 + 0.677661i 0.992614 0.121312i \(-0.0387103\pi\)
−0.601367 + 0.798973i \(0.705377\pi\)
\(234\) 0 0
\(235\) 8.35410 14.4697i 0.544962 0.943901i
\(236\) −3.57295 6.18853i −0.232579 0.402839i
\(237\) 0 0
\(238\) 7.70820 6.67550i 0.499649 0.432708i
\(239\) −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 \(0.215122\pi\)
\(242\) 2.61803 4.53457i 0.168294 0.291493i
\(243\) 0 0
\(244\) 14.5623 0.932256
\(245\) 14.5344 5.80948i 0.928571 0.371154i
\(246\) 0 0
\(247\) 1.50000 + 2.59808i 0.0954427 + 0.165312i
\(248\) −18.6803 + 32.3553i −1.18620 + 2.05456i
\(249\) 0 0
\(250\) −14.6353 25.3490i −0.925615 1.60321i
\(251\) −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
\(254\) 14.9443 + 25.8842i 0.937687 + 1.62412i
\(255\) 0 0
\(256\) 7.28115 12.6113i 0.455072 0.788208i
\(257\) −0.0278640 0.0482619i −0.00173811 0.00301050i 0.865155 0.501504i \(-0.167220\pi\)
−0.866893 + 0.498494i \(0.833887\pi\)
\(258\) 0 0
\(259\) 11.7705 + 4.07742i 0.731384 + 0.253359i
\(260\) 10.8541 0.673143
\(261\) 0 0
\(262\) −10.7812 + 18.6735i −0.666062 + 1.15365i
\(263\) 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
\(266\) −3.92705 20.4056i −0.240783 1.25114i
\(267\) 0 0
\(268\) 7.28115 + 12.6113i 0.444767 + 0.770359i
\(269\) 6.73607 11.6672i 0.410705 0.711362i −0.584262 0.811565i \(-0.698616\pi\)
0.994967 + 0.100203i \(0.0319492\pi\)
\(270\) 0 0
\(271\) 10.2082 + 17.6811i 0.620104 + 1.07405i 0.989466 + 0.144766i \(0.0462430\pi\)
−0.369362 + 0.929286i \(0.620424\pi\)
\(272\) −14.5066 −0.879590
\(273\) 0 0
\(274\) 21.5623 1.30263
\(275\) 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 \(0.162685\pi\)
\(278\) 30.6525 + 53.0916i 1.83841 + 3.18423i
\(279\) 0 0
\(280\) −41.7705 14.4697i −2.49627 0.864732i
\(281\) −26.9443 −1.60736 −0.803680 0.595061i \(-0.797128\pi\)
−0.803680 + 0.595061i \(0.797128\pi\)
\(282\) 0 0
\(283\) −13.0623 + 22.6246i −0.776473 + 1.34489i 0.157489 + 0.987521i \(0.449660\pi\)
−0.933963 + 0.357371i \(0.883673\pi\)
\(284\) −21.7082 + 37.5997i −1.28814 + 2.23113i
\(285\) 0 0
\(286\) −7.85410 −0.464423
\(287\) −8.94427 + 7.74597i −0.527964 + 0.457230i
\(288\) 0 0
\(289\) 7.41641 + 12.8456i 0.436259 + 0.755623i
\(290\) −13.0902 + 22.6728i −0.768681 + 1.33139i
\(291\) 0 0
\(292\) 6.57295 + 11.3847i 0.384653 + 0.666238i
\(293\) 14.9443 0.873054 0.436527 0.899691i \(-0.356208\pi\)
0.436527 + 0.899691i \(0.356208\pi\)
\(294\) 0 0
\(295\) −3.29180 −0.191656
\(296\) −17.5902 30.4671i −1.02241 1.77086i
\(297\) 0 0
\(298\) 0.927051 1.60570i 0.0537026 0.0930157i
\(299\) 4.11803 + 7.13264i 0.238152 + 0.412491i
\(300\) 0 0
\(301\) 16.0000 13.8564i 0.922225 0.798670i
\(302\) 53.4508 3.07575
\(303\) 0 0
\(304\) −14.7812 + 25.6017i −0.847757 + 1.46836i
\(305\) 3.35410 5.80948i 0.192055 0.332650i
\(306\) 0 0
\(307\) 19.4164 1.10815 0.554076 0.832466i \(-0.313072\pi\)
0.554076 + 0.832466i \(0.313072\pi\)
\(308\) 36.4058 + 12.6113i 2.07441 + 0.718597i
\(309\) 0 0
\(310\) 14.6353 + 25.3490i 0.831227 + 1.43973i
\(311\) −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 \(0.782893\pi\)
\(314\) 18.3262 1.03421
\(315\) 0 0
\(316\) −13.1459 −0.739515
\(317\) −4.11803 7.13264i −0.231292 0.400609i 0.726897 0.686747i \(-0.240962\pi\)
−0.958189 + 0.286138i \(0.907629\pi\)
\(318\) 0 0
\(319\) 6.70820 11.6190i 0.375587 0.650536i
\(320\) 9.73607 + 16.8634i 0.544263 + 0.942691i
\(321\) 0 0
\(322\) −10.7812 56.0205i −0.600810 3.12190i
\(323\) −4.41641 −0.245736
\(324\) 0 0
\(325\) 0 0
\(326\) 21.4894 37.2207i 1.19019 2.06146i
\(327\) 0 0
\(328\) 33.4164 1.84511
\(329\) 18.6803 + 6.47106i 1.02988 + 0.356761i
\(330\) 0 0
\(331\) 0.791796 + 1.37143i 0.0435210 + 0.0753807i 0.886965 0.461836i \(-0.152809\pi\)
−0.843444 + 0.537217i \(0.819476\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 29.4164 + 50.9507i 1.60959 + 2.78790i
\(335\) 6.70820 0.366508
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) −1.30902 2.26728i −0.0712011 0.123324i
\(339\) 0 0
\(340\) −7.98936 + 13.8380i −0.433284 + 0.750469i
\(341\) −7.50000 12.9904i −0.406148 0.703469i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −59.7771 −3.22296
\(345\) 0 0
\(346\) −21.4894 + 37.2207i −1.15527 + 2.00099i
\(347\) 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
\(351\) 0 0
\(352\) −16.2812 28.1998i −0.867788 1.50305i
\(353\) 8.64590 14.9751i 0.460175 0.797046i −0.538795 0.842437i \(-0.681120\pi\)
0.998969 + 0.0453912i \(0.0144534\pi\)
\(354\) 0 0
\(355\) 10.0000 + 17.3205i 0.530745 + 0.919277i
\(356\) −10.8541 −0.575266
\(357\) 0 0
\(358\) 52.6869 2.78459
\(359\) 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
\(362\) 33.2705 + 57.6262i 1.74866 + 3.02877i
\(363\) 0 0
\(364\) 2.42705 + 12.6113i 0.127212 + 0.661013i
\(365\) 6.05573 0.316971
\(366\) 0 0
\(367\) 6.35410 11.0056i 0.331681 0.574489i −0.651160 0.758940i \(-0.725717\pi\)
0.982842 + 0.184451i \(0.0590508\pi\)
\(368\) −40.5795 + 70.2858i −2.11535 + 3.66390i
\(369\) 0 0
\(370\) −27.5623 −1.43290
\(371\) −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 \(0.820280\pi\)
\(374\) 5.78115 10.0133i 0.298936 0.517773i
\(375\) 0 0
\(376\) −27.9164 48.3526i −1.43968 2.49360i
\(377\) 4.47214 0.230327
\(378\) 0 0
\(379\) −15.4164 −0.791888 −0.395944 0.918275i \(-0.629583\pi\)
−0.395944 + 0.918275i \(0.629583\pi\)
\(380\) 16.2812 + 28.1998i 0.835206 + 1.44662i
\(381\) 0 0
\(382\) 14.6353 25.3490i 0.748805 1.29697i
\(383\) 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
\(386\) 1.85410 0.0943713
\(387\) 0 0
\(388\) −22.8541 + 39.5845i −1.16024 + 2.00960i
\(389\) 0.736068 1.27491i 0.0373201 0.0646404i −0.846762 0.531972i \(-0.821451\pi\)
0.884082 + 0.467332i \(0.154785\pi\)
\(390\) 0 0
\(391\) −12.1246 −0.613168
\(392\) 7.47214 51.7685i 0.377400 2.61470i
\(393\) 0 0
\(394\) −11.8541 20.5319i −0.597201 1.03438i
\(395\) −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 \(0.605758\pi\)
\(398\) −54.2148 −2.71754
\(399\) 0 0
\(400\) 0 0
\(401\) 7.11803 + 12.3288i 0.355458 + 0.615671i 0.987196 0.159511i \(-0.0509917\pi\)
−0.631739 + 0.775182i \(0.717658\pi\)
\(402\) 0 0
\(403\) 2.50000 4.33013i 0.124534 0.215699i
\(404\) −21.8435 37.8340i −1.08675 1.88231i
\(405\) 0 0
\(406\) −29.2705 10.1396i −1.45267 0.503220i
\(407\) 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 \(0.235738\pi\)
\(410\) 13.0902 22.6728i 0.646477 1.11973i
\(411\) 0 0
\(412\) −13.1459 −0.647652
\(413\) −0.736068 3.82472i −0.0362195 0.188202i
\(414\) 0 0
\(415\) 0 0
\(416\) 5.42705 9.39993i 0.266083 0.460869i
\(417\) 0 0
\(418\) −11.7812 20.4056i −0.576235 0.998068i
\(419\) −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 \(0.393983\pi\)
\(422\) −5.23607 9.06914i −0.254888 0.441479i
\(423\) 0 0
\(424\) −27.9164 + 48.3526i −1.35574 + 2.34821i
\(425\) 0 0
\(426\) 0 0
\(427\) 7.50000 + 2.59808i 0.362950 + 0.125730i
\(428\) 47.3951 2.29093
\(429\) 0 0
\(430\) −23.4164 + 40.5584i −1.12924 + 1.95590i
\(431\) −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 \(0.250124\pi\)
\(434\) −26.1803 + 22.6728i −1.25670 + 1.08833i
\(435\) 0 0
\(436\) 6.57295 + 11.3847i 0.314787 + 0.545227i
\(437\) −12.3541 + 21.3979i −0.590977 + 1.02360i
\(438\) 0 0
\(439\) −12.0623 20.8925i −0.575702 0.997146i −0.995965 0.0897433i \(-0.971395\pi\)
0.420262 0.907403i \(-0.361938\pi\)
\(440\) −50.1246 −2.38960
\(441\) 0 0
\(442\) 3.85410 0.183321
\(443\) 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
\(446\) 5.23607 + 9.06914i 0.247935 + 0.429436i
\(447\) 0 0
\(448\) −17.4164 + 15.0831i −0.822848 + 0.712607i
\(449\) 34.3607 1.62158 0.810790 0.585337i \(-0.199038\pi\)
0.810790 + 0.585337i \(0.199038\pi\)
\(450\) 0 0
\(451\) −6.70820 + 11.6190i −0.315877 + 0.547115i
\(452\) 7.14590 12.3771i 0.336115 0.582168i
\(453\) 0 0
\(454\) −15.5623 −0.730375
\(455\) 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 \(0.787578\pi\)
\(458\) −31.5795 + 54.6973i −1.47561 + 2.55584i
\(459\) 0 0
\(460\) 44.6976 + 77.4184i 2.08403 + 3.60965i
\(461\) −34.3607 −1.60034 −0.800168 0.599776i \(-0.795256\pi\)
−0.800168 + 0.599776i \(0.795256\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 22.0344 + 38.1648i 1.02292 + 1.77176i
\(465\) 0 0
\(466\) 15.6353 27.0811i 0.724289 1.25451i
\(467\) 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
\(470\) −43.7426 −2.01770
\(471\) 0 0
\(472\) −5.50000 + 9.52628i −0.253158 + 0.438483i
\(473\) 12.0000 20.7846i 0.551761 0.955677i
\(474\) 0 0
\(475\) 0 0
\(476\) −17.8647 6.18853i −0.818829 0.283651i
\(477\) 0 0
\(478\) 25.4164 + 44.0225i 1.16252 + 2.01354i
\(479\) 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
\(482\) 12.3262 0.561445
\(483\) 0 0
\(484\) −9.70820 −0.441282
\(485\) 10.5279 + 18.2348i 0.478046 + 0.827999i
\(486\) 0 0
\(487\) 10.9164 18.9078i 0.494670 0.856793i −0.505311 0.862937i \(-0.668622\pi\)
0.999981 + 0.00614405i \(0.00195572\pi\)
\(488\) −11.2082 19.4132i −0.507372 0.878793i
\(489\) 0 0
\(490\) −32.1976 25.3490i −1.45454 1.14515i
\(491\) 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
\(494\) 3.92705 6.80185i 0.176686 0.306030i
\(495\) 0 0
\(496\) 49.2705 2.21231
\(497\) −17.8885 + 15.4919i −0.802411 + 0.694908i
\(498\) 0 0
\(499\) −13.2082 22.8773i −0.591280 1.02413i −0.994060 0.108831i \(-0.965289\pi\)
0.402780 0.915297i \(-0.368044\pi\)
\(500\) −27.1353 + 46.9996i −1.21353 + 2.10189i
\(501\) 0 0
\(502\) 2.00000 + 3.46410i 0.0892644 + 0.154610i
\(503\) −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
\(506\) −32.3435 56.0205i −1.43784 2.49042i
\(507\) 0 0
\(508\) 27.7082 47.9920i 1.22935 2.12930i
\(509\) −10.1180 17.5249i −0.448474 0.776780i 0.549813 0.835288i \(-0.314699\pi\)
−0.998287 + 0.0585081i \(0.981366\pi\)
\(510\) 0 0
\(511\) 1.35410 + 7.03612i 0.0599019 + 0.311260i
\(512\) −40.3050 −1.78124
\(513\) 0 0
\(514\) −0.0729490 + 0.126351i −0.00321764 + 0.00557312i
\(515\) −3.02786 + 5.24441i −0.133424 + 0.231097i
\(516\) 0 0
\(517\) 22.4164 0.985872
\(518\) −6.16312 32.0245i −0.270792 1.40708i
\(519\) 0 0
\(520\) −8.35410 14.4697i −0.366352 0.634540i
\(521\) −8.97214 + 15.5402i −0.393076 + 0.680828i −0.992854 0.119339i \(-0.961923\pi\)
0.599777 + 0.800167i \(0.295256\pi\)
\(522\) 0 0
\(523\) −16.3541 28.3261i −0.715115 1.23862i −0.962915 0.269804i \(-0.913041\pi\)
0.247800 0.968811i \(-0.420292\pi\)
\(524\) 39.9787 1.74648
\(525\) 0 0
\(526\) −68.3951 −2.98217
\(527\) 3.68034 + 6.37454i 0.160318 + 0.277679i
\(528\) 0 0
\(529\) −22.4164 + 38.8264i −0.974626 + 1.68810i
\(530\) 21.8713 + 37.8822i 0.950030 + 1.64550i
\(531\) 0 0
\(532\) −29.1246 + 25.2227i −1.26271 + 1.09354i
\(533\) −4.47214 −0.193710
\(534\) 0 0
\(535\) 10.9164 18.9078i 0.471957 0.817454i
\(536\) 11.2082 19.4132i 0.484121 0.838522i
\(537\) 0 0
\(538\) −35.2705 −1.52062
\(539\) 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 \(0.842174\pi\)
\(542\) 26.7254 46.2898i 1.14796 1.98832i
\(543\) 0 0
\(544\) 7.98936 + 13.8380i 0.342541 + 0.593298i
\(545\) 6.05573 0.259399
\(546\) 0 0
\(547\) −4.58359 −0.195980 −0.0979901 0.995187i \(-0.531241\pi\)
−0.0979901 + 0.995187i \(0.531241\pi\)
\(548\) −19.9894 34.6226i −0.853903 1.47900i
\(549\) 0 0
\(550\) 0 0
\(551\) 6.70820 + 11.6190i 0.285779 + 0.494984i
\(552\) 0 0
\(553\) −6.77051 2.34537i −0.287911 0.0997354i
\(554\) −1.09017 −0.0463169
\(555\) 0 0
\(556\) 56.8328 98.4373i 2.41025 4.17467i
\(557\) −9.35410 + 16.2018i −0.396346 + 0.686491i −0.993272 0.115805i \(-0.963055\pi\)
0.596926 + 0.802296i \(0.296389\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 11.0172 + 57.2472i 0.465563 + 2.41913i
\(561\) 0 0
\(562\) 35.2705 + 61.0903i 1.48780 + 2.57694i
\(563\) 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
\(566\) 68.3951 2.87486
\(567\) 0 0
\(568\) 66.8328 2.80424
\(569\) 12.7361 + 22.0595i 0.533924 + 0.924783i 0.999215 + 0.0396252i \(0.0126164\pi\)
−0.465291 + 0.885158i \(0.654050\pi\)
\(570\) 0 0
\(571\) 18.0623 31.2848i 0.755884 1.30923i −0.189050 0.981968i \(-0.560541\pi\)
0.944934 0.327262i \(-0.106126\pi\)
\(572\) 7.28115 + 12.6113i 0.304440 + 0.527306i
\(573\) 0 0
\(574\) 29.2705 + 10.1396i 1.22173 + 0.423219i
\(575\) 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 \(0.0351334\pi\)
\(578\) 19.4164 33.6302i 0.807616 1.39883i
\(579\) 0 0
\(580\) 48.5410 2.01556
\(581\) 0 0
\(582\) 0 0
\(583\) −11.2082 19.4132i −0.464196 0.804012i
\(584\) 10.1180 17.5249i 0.418687 0.725188i
\(585\) 0 0
\(586\) −19.5623 33.8829i −0.808111 1.39969i
\(587\) 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
\(590\) 4.30902 + 7.46344i 0.177399 + 0.307265i
\(591\) 0 0
\(592\) −23.1976 + 40.1794i −0.953414 + 1.65136i
\(593\) 13.8820 + 24.0443i 0.570064 + 0.987380i 0.996559 + 0.0828898i \(0.0264149\pi\)
−0.426495 + 0.904490i \(0.640252\pi\)
\(594\) 0 0
\(595\) −6.58359 + 5.70156i −0.269901 + 0.233741i
\(596\) −3.43769 −0.140813
\(597\) 0 0
\(598\) 10.7812 18.6735i 0.440874 0.763616i
\(599\) −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 \(0.648113\pi\)
\(602\) −52.3607 18.1383i −2.13406 0.739261i
\(603\) 0 0
\(604\) −49.5517 85.8260i −2.01623 3.49221i
\(605\) −2.23607 + 3.87298i −0.0909091 + 0.157459i
\(606\) 0 0
\(607\) −12.0623 20.8925i −0.489594 0.848001i 0.510334 0.859976i \(-0.329522\pi\)
−0.999928 + 0.0119745i \(0.996188\pi\)
\(608\) 32.5623 1.32058
\(609\) 0 0
\(610\) −17.5623 −0.711077
\(611\) 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 \(0.0473858\pi\)
\(614\) −25.4164 44.0225i −1.02572 1.77660i
\(615\) 0 0
\(616\) −11.2082 58.2395i −0.451591 2.34654i
\(617\) 4.47214 0.180041 0.0900207 0.995940i \(-0.471307\pi\)
0.0900207 + 0.995940i \(0.471307\pi\)
\(618\) 0 0
\(619\) −8.50000 + 14.7224i −0.341644 + 0.591744i −0.984738 0.174042i \(-0.944317\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) 27.1353 46.9996i 1.08978 1.88755i
\(621\) 0 0
\(622\) 72.6869 2.91448
\(623\) −5.59017 1.93649i −0.223965 0.0775839i
\(624\) 0 0
\(625\) 12.5000 + 21.6506i 0.500000 + 0.866025i
\(626\) 7.30902 12.6596i 0.292127 0.505979i
\(627\) 0 0
\(628\) −16.9894 29.4264i −0.677949 1.17424i
\(629\) −6.93112 −0.276362
\(630\) 0 0
\(631\) 22.8328 0.908960 0.454480 0.890757i \(-0.349825\pi\)
0.454480 + 0.890757i \(0.349825\pi\)
\(632\) 10.1180 + 17.5249i 0.402474 + 0.697105i
\(633\) 0 0
\(634\) −10.7812 + 18.6735i −0.428174 + 0.741620i
\(635\) −12.7639 22.1078i −0.506521 0.877320i
\(636\) 0 0
\(637\) −1.00000 + 6.92820i −0.0396214 + 0.274505i
\(638\) −35.1246 −1.39060
\(639\) 0 0
\(640\) 1.21885 2.11111i 0.0481792 0.0834488i
\(641\) 5.97214 10.3440i 0.235885 0.408565i −0.723644 0.690173i \(-0.757534\pi\)
0.959530 + 0.281608i \(0.0908677\pi\)
\(642\) 0 0
\(643\) 34.8328 1.37367 0.686836 0.726812i \(-0.258999\pi\)
0.686836 + 0.726812i \(0.258999\pi\)
\(644\) −79.9574 + 69.2452i −3.15076 + 2.72864i
\(645\) 0 0
\(646\) 5.78115 + 10.0133i 0.227456 + 0.393966i
\(647\) 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
\(651\) 0 0
\(652\) −79.6869 −3.12078
\(653\) 2.26393 + 3.92125i 0.0885945 + 0.153450i 0.906917 0.421309i \(-0.138429\pi\)
−0.818323 + 0.574759i \(0.805096\pi\)
\(654\) 0 0
\(655\) 9.20820 15.9491i 0.359794 0.623182i
\(656\) −22.0344 38.1648i −0.860300 1.49008i
\(657\) 0 0
\(658\) −9.78115 50.8244i −0.381309 1.98134i
\(659\) 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 \(0.125021\pi\)
\(662\) 2.07295 3.59045i 0.0805675 0.139547i
\(663\) 0 0
\(664\) 0 0
\(665\) 3.35410 + 17.4284i 0.130066 + 0.675845i
\(666\) 0 0
\(667\) 18.4164 + 31.8982i 0.713086 + 1.23510i
\(668\) 54.5410 94.4678i 2.11026 3.65507i
\(669\) 0 0
\(670\) −8.78115 15.2094i −0.339246 0.587591i
\(671\) 9.00000 0.347441
\(672\) 0 0
\(673\) −9.41641 −0.362976 −0.181488 0.983393i \(-0.558091\pi\)
−0.181488 + 0.983393i \(0.558091\pi\)
\(674\) −23.5623 40.8111i −0.907586 1.57199i
\(675\) 0 0
\(676\) −2.42705 + 4.20378i −0.0933481 + 0.161684i
\(677\) −1.44427 2.50155i −0.0555079 0.0961425i 0.836936 0.547300i \(-0.184344\pi\)
−0.892444 + 0.451158i \(0.851011\pi\)
\(678\) 0 0
\(679\) −18.8328 + 16.3097i −0.722737 + 0.625909i
\(680\) 24.5967 0.943242
\(681\) 0 0
\(682\) −19.6353 + 34.0093i −0.751873 + 1.30228i
\(683\) −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
\(686\) 22.2533 43.0784i 0.849635 1.64474i
\(687\) 0 0
\(688\) 39.4164 + 68.2712i 1.50274 + 2.60282i
\(689\) 3.73607 6.47106i 0.142333 0.246528i
\(690\) 0 0
\(691\) 25.9164 + 44.8885i 0.985907 + 1.70764i 0.637836 + 0.770172i \(0.279830\pi\)
0.348070 + 0.937468i \(0.386837\pi\)
\(692\) 79.6869 3.02924
\(693\) 0 0
\(694\) −60.3951 −2.29257
\(695\) −26.1803 45.3457i −0.993077 1.72006i
\(696\) 0 0
\(697\) 3.29180 5.70156i 0.124686 0.215962i
\(698\) 38.5066 + 66.6953i 1.45750 + 2.52446i
\(699\) 0 0
\(700\) 0 0
\(701\) 22.3607 0.844551 0.422276 0.906467i \(-0.361231\pi\)
0.422276 + 0.906467i \(0.361231\pi\)
\(702\) 0 0
\(703\) −7.06231 + 12.2323i −0.266360 + 0.461349i
\(704\) −13.0623 + 22.6246i −0.492304 + 0.852696i
\(705\) 0 0
\(706\) −45.2705 −1.70378
\(707\) −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 \(0.443000\pi\)
\(710\) 26.1803 45.3457i 0.982531 1.70179i
\(711\) 0 0
\(712\) 8.35410 + 14.4697i 0.313083 + 0.542276i
\(713\) 41.1803 1.54222
\(714\) 0 0
\(715\) 6.70820 0.250873
\(716\) −48.8435 84.5994i −1.82537 3.16163i
\(717\) 0 0
\(718\) 15.6353 27.0811i 0.583503 1.01066i
\(719\) 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
\(722\) −26.1803 −0.974331
\(723\) 0 0
\(724\) 61.6869 106.845i 2.29258 3.97086i
\(725\) 0 0
\(726\) 0 0
\(727\) −38.8328 −1.44023 −0.720115 0.693855i \(-0.755911\pi\)
−0.720115 + 0.693855i \(0.755911\pi\)
\(728\) 14.9443 12.9421i 0.553872 0.479667i
\(729\) 0 0
\(730\) −7.92705 13.7301i −0.293393 0.508172i
\(731\) −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 \(-0.344543\pi\)
\(734\) −33.2705 −1.22804
\(735\) 0 0
\(736\) 89.3951 3.29515
\(737\) 4.50000 + 7.79423i 0.165760 + 0.287104i
\(738\) 0 0
\(739\) 8.91641 15.4437i 0.327995 0.568105i −0.654119 0.756392i \(-0.726960\pi\)
0.982114 + 0.188287i \(0.0602936\pi\)
\(740\) 25.5517 + 44.2568i 0.939298 + 1.62691i
\(741\) 0 0
\(742\) −39.1246 + 33.8829i −1.43631 + 1.24388i
\(743\) −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
\(746\) 2.07295 3.59045i 0.0758961 0.131456i
\(747\) 0 0
\(748\) −21.4377 −0.783840
\(749\) 24.4098 + 8.45581i 0.891916 + 0.308969i
\(750\) 0 0
\(751\) 5.06231 + 8.76817i 0.184726 + 0.319955i 0.943484 0.331417i \(-0.107527\pi\)
−0.758758 + 0.651373i \(0.774194\pi\)
\(752\) −36.8156 + 63.7665i −1.34253 + 2.32532i
\(753\) 0 0
\(754\) −5.85410 10.1396i −0.213194 0.369263i
\(755\) −45.6525 −1.66146
\(756\) 0 0
\(757\) −52.8328 −1.92024 −0.960121 0.279586i \(-0.909803\pi\)
−0.960121 + 0.279586i \(0.909803\pi\)
\(758\) 20.1803 + 34.9534i 0.732983 + 1.26956i
\(759\) 0 0
\(760\) 25.0623 43.4092i 0.909105 1.57462i
\(761\) −16.7705 29.0474i −0.607931 1.05297i −0.991581 0.129488i \(-0.958667\pi\)
0.383650 0.923478i \(-0.374667\pi\)
\(762\) 0 0
\(763\) 1.35410 + 7.03612i 0.0490218 + 0.254725i
\(764\) −54.2705 −1.96344
\(765\) 0 0
\(766\) 19.6353 34.0093i 0.709451 1.22880i
\(767\) 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 \(0.188682\pi\)
\(770\) −43.9058 15.2094i −1.58225 0.548109i
\(771\) 0 0
\(772\) −1.71885 2.97713i −0.0618627 0.107149i
\(773\) −23.5344 + 40.7628i −0.846475 + 1.46614i 0.0378590 + 0.999283i \(0.487946\pi\)
−0.884334 + 0.466855i \(0.845387\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 70.3607 2.52580
\(777\) 0 0
\(778\) −3.85410 −0.138176
\(779\) −6.70820 11.6190i −0.240346 0.416292i
\(780\) 0 0
\(781\) −13.4164 + 23.2379i −0.480077 + 0.831517i
\(782\) 15.8713 + 27.4899i 0.567557 + 0.983038i
\(783\) 0 0
\(784\) −64.0517 + 25.6017i −2.28756 + 0.914347i
\(785\) −15.6525 −0.558661
\(786\) 0 0
\(787\) −10.2082 + 17.6811i −0.363883 + 0.630264i −0.988596 0.150590i \(-0.951883\pi\)
0.624713 + 0.780854i \(0.285216\pi\)
\(788\) −21.9787 + 38.0682i −0.782959 + 1.35613i
\(789\) 0 0