Properties

Label 384.2.k.b.95.1
Level $384$
Weight $2$
Character 384.95
Analytic conductor $3.066$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.k (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.163368480538624.2
Defining polynomial: \(x^{12} - 2 x^{10} - 2 x^{8} + 16 x^{6} - 8 x^{4} - 32 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 95.1
Root \(1.27715 + 0.607364i\) of defining polynomial
Character \(\chi\) \(=\) 384.95
Dual form 384.2.k.b.287.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73003 + 0.0835731i) q^{3} +(0.431733 + 0.431733i) q^{5} -3.10278 q^{7} +(2.98603 - 0.289169i) q^{9} +O(q^{10})\) \(q+(-1.73003 + 0.0835731i) q^{3} +(0.431733 + 0.431733i) q^{5} -3.10278 q^{7} +(2.98603 - 0.289169i) q^{9} +(2.98603 - 2.98603i) q^{11} +(-2.10278 - 2.10278i) q^{13} +(-0.782994 - 0.710831i) q^{15} -2.42945i q^{17} +(0.710831 - 0.710831i) q^{19} +(5.36790 - 0.259309i) q^{21} -5.97206i q^{23} -4.62721i q^{25} +(-5.14177 + 0.749823i) q^{27} +(2.86119 - 2.86119i) q^{29} +0.524438i q^{31} +(-4.91638 + 5.41549i) q^{33} +(-1.33957 - 1.33957i) q^{35} +(-1.52444 + 1.52444i) q^{37} +(3.81361 + 3.46214i) q^{39} -1.81568 q^{41} +(-0.710831 - 0.710831i) q^{43} +(1.41401 + 1.16432i) q^{45} +7.53805 q^{47} +2.62721 q^{49} +(0.203037 + 4.20304i) q^{51} +(-8.83325 - 8.83325i) q^{53} +2.57834 q^{55} +(-1.17036 + 1.28917i) q^{57} +(-0.0804722 + 0.0804722i) q^{59} +(5.72999 + 5.72999i) q^{61} +(-9.26498 + 0.897225i) q^{63} -1.81568i q^{65} +(0.391944 - 0.391944i) q^{67} +(0.499104 + 10.3319i) q^{69} +5.01985i q^{71} +13.4600i q^{73} +(0.386711 + 8.00523i) q^{75} +(-9.26498 + 9.26498i) q^{77} +3.47556i q^{79} +(8.83276 - 1.72693i) q^{81} +(4.55202 + 4.55202i) q^{83} +(1.04888 - 1.04888i) q^{85} +(-4.71083 + 5.18907i) q^{87} -12.5579 q^{89} +(6.52444 + 6.52444i) q^{91} +(-0.0438289 - 0.907295i) q^{93} +0.613779 q^{95} -8.67609 q^{97} +(8.05292 - 9.77985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{3} - 8q^{7} + O(q^{10}) \) \( 12q + 2q^{3} - 8q^{7} + 4q^{13} + 12q^{19} + 8q^{21} - 10q^{27} - 4q^{33} + 4q^{37} + 20q^{39} - 12q^{43} + 12q^{45} - 20q^{49} - 24q^{51} + 24q^{55} - 12q^{61} - 28q^{67} - 4q^{69} + 34q^{75} - 4q^{81} - 32q^{85} - 60q^{87} + 56q^{91} - 28q^{93} - 8q^{97} + 52q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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 0
\(3\) −1.73003 + 0.0835731i −0.998835 + 0.0482510i
\(4\) 0 0
\(5\) 0.431733 + 0.431733i 0.193077 + 0.193077i 0.797024 0.603947i \(-0.206406\pi\)
−0.603947 + 0.797024i \(0.706406\pi\)
\(6\) 0 0
\(7\) −3.10278 −1.17274 −0.586369 0.810044i \(-0.699443\pi\)
−0.586369 + 0.810044i \(0.699443\pi\)
\(8\) 0 0
\(9\) 2.98603 0.289169i 0.995344 0.0963895i
\(10\) 0 0
\(11\) 2.98603 2.98603i 0.900322 0.900322i −0.0951415 0.995464i \(-0.530330\pi\)
0.995464 + 0.0951415i \(0.0303304\pi\)
\(12\) 0 0
\(13\) −2.10278 2.10278i −0.583205 0.583205i 0.352578 0.935783i \(-0.385305\pi\)
−0.935783 + 0.352578i \(0.885305\pi\)
\(14\) 0 0
\(15\) −0.782994 0.710831i −0.202168 0.183536i
\(16\) 0 0
\(17\) 2.42945i 0.589229i −0.955616 0.294615i \(-0.904809\pi\)
0.955616 0.294615i \(-0.0951913\pi\)
\(18\) 0 0
\(19\) 0.710831 0.710831i 0.163076 0.163076i −0.620852 0.783928i \(-0.713213\pi\)
0.783928 + 0.620852i \(0.213213\pi\)
\(20\) 0 0
\(21\) 5.36790 0.259309i 1.17137 0.0565858i
\(22\) 0 0
\(23\) 5.97206i 1.24526i −0.782516 0.622631i \(-0.786064\pi\)
0.782516 0.622631i \(-0.213936\pi\)
\(24\) 0 0
\(25\) 4.62721i 0.925443i
\(26\) 0 0
\(27\) −5.14177 + 0.749823i −0.989533 + 0.144304i
\(28\) 0 0
\(29\) 2.86119 2.86119i 0.531309 0.531309i −0.389653 0.920962i \(-0.627405\pi\)
0.920962 + 0.389653i \(0.127405\pi\)
\(30\) 0 0
\(31\) 0.524438i 0.0941918i 0.998890 + 0.0470959i \(0.0149966\pi\)
−0.998890 + 0.0470959i \(0.985003\pi\)
\(32\) 0 0
\(33\) −4.91638 + 5.41549i −0.855832 + 0.942715i
\(34\) 0 0
\(35\) −1.33957 1.33957i −0.226429 0.226429i
\(36\) 0 0
\(37\) −1.52444 + 1.52444i −0.250616 + 0.250616i −0.821223 0.570607i \(-0.806708\pi\)
0.570607 + 0.821223i \(0.306708\pi\)
\(38\) 0 0
\(39\) 3.81361 + 3.46214i 0.610666 + 0.554385i
\(40\) 0 0
\(41\) −1.81568 −0.283561 −0.141780 0.989898i \(-0.545283\pi\)
−0.141780 + 0.989898i \(0.545283\pi\)
\(42\) 0 0
\(43\) −0.710831 0.710831i −0.108401 0.108401i 0.650826 0.759227i \(-0.274423\pi\)
−0.759227 + 0.650826i \(0.774423\pi\)
\(44\) 0 0
\(45\) 1.41401 + 1.16432i 0.210788 + 0.173567i
\(46\) 0 0
\(47\) 7.53805 1.09954 0.549769 0.835317i \(-0.314716\pi\)
0.549769 + 0.835317i \(0.314716\pi\)
\(48\) 0 0
\(49\) 2.62721 0.375316
\(50\) 0 0
\(51\) 0.203037 + 4.20304i 0.0284309 + 0.588543i
\(52\) 0 0
\(53\) −8.83325 8.83325i −1.21334 1.21334i −0.969921 0.243419i \(-0.921731\pi\)
−0.243419 0.969921i \(-0.578269\pi\)
\(54\) 0 0
\(55\) 2.57834 0.347663
\(56\) 0 0
\(57\) −1.17036 + 1.28917i −0.155017 + 0.170755i
\(58\) 0 0
\(59\) −0.0804722 + 0.0804722i −0.0104766 + 0.0104766i −0.712326 0.701849i \(-0.752358\pi\)
0.701849 + 0.712326i \(0.252358\pi\)
\(60\) 0 0
\(61\) 5.72999 + 5.72999i 0.733650 + 0.733650i 0.971341 0.237691i \(-0.0763906\pi\)
−0.237691 + 0.971341i \(0.576391\pi\)
\(62\) 0 0
\(63\) −9.26498 + 0.897225i −1.16728 + 0.113040i
\(64\) 0 0
\(65\) 1.81568i 0.225207i
\(66\) 0 0
\(67\) 0.391944 0.391944i 0.0478835 0.0478835i −0.682760 0.730643i \(-0.739220\pi\)
0.730643 + 0.682760i \(0.239220\pi\)
\(68\) 0 0
\(69\) 0.499104 + 10.3319i 0.0600850 + 1.24381i
\(70\) 0 0
\(71\) 5.01985i 0.595747i 0.954605 + 0.297873i \(0.0962774\pi\)
−0.954605 + 0.297873i \(0.903723\pi\)
\(72\) 0 0
\(73\) 13.4600i 1.57537i 0.616078 + 0.787686i \(0.288721\pi\)
−0.616078 + 0.787686i \(0.711279\pi\)
\(74\) 0 0
\(75\) 0.386711 + 8.00523i 0.0446535 + 0.924365i
\(76\) 0 0
\(77\) −9.26498 + 9.26498i −1.05584 + 1.05584i
\(78\) 0 0
\(79\) 3.47556i 0.391031i 0.980701 + 0.195516i \(0.0626380\pi\)
−0.980701 + 0.195516i \(0.937362\pi\)
\(80\) 0 0
\(81\) 8.83276 1.72693i 0.981418 0.191881i
\(82\) 0 0
\(83\) 4.55202 + 4.55202i 0.499649 + 0.499649i 0.911329 0.411680i \(-0.135058\pi\)
−0.411680 + 0.911329i \(0.635058\pi\)
\(84\) 0 0
\(85\) 1.04888 1.04888i 0.113767 0.113767i
\(86\) 0 0
\(87\) −4.71083 + 5.18907i −0.505054 + 0.556326i
\(88\) 0 0
\(89\) −12.5579 −1.33114 −0.665568 0.746338i \(-0.731810\pi\)
−0.665568 + 0.746338i \(0.731810\pi\)
\(90\) 0 0
\(91\) 6.52444 + 6.52444i 0.683947 + 0.683947i
\(92\) 0 0
\(93\) −0.0438289 0.907295i −0.00454485 0.0940821i
\(94\) 0 0
\(95\) 0.613779 0.0629724
\(96\) 0 0
\(97\) −8.67609 −0.880923 −0.440462 0.897771i \(-0.645185\pi\)
−0.440462 + 0.897771i \(0.645185\pi\)
\(98\) 0 0
\(99\) 8.05292 9.77985i 0.809348 0.982912i
\(100\) 0 0
\(101\) 0.182046 + 0.182046i 0.0181142 + 0.0181142i 0.716106 0.697992i \(-0.245923\pi\)
−0.697992 + 0.716106i \(0.745923\pi\)
\(102\) 0 0
\(103\) 6.35720 0.626394 0.313197 0.949688i \(-0.398600\pi\)
0.313197 + 0.949688i \(0.398600\pi\)
\(104\) 0 0
\(105\) 2.42945 + 2.20555i 0.237090 + 0.215240i
\(106\) 0 0
\(107\) 1.64646 1.64646i 0.159169 0.159169i −0.623029 0.782199i \(-0.714098\pi\)
0.782199 + 0.623029i \(0.214098\pi\)
\(108\) 0 0
\(109\) −6.57331 6.57331i −0.629609 0.629609i 0.318360 0.947970i \(-0.396868\pi\)
−0.947970 + 0.318360i \(0.896868\pi\)
\(110\) 0 0
\(111\) 2.50993 2.76473i 0.238232 0.262417i
\(112\) 0 0
\(113\) 8.31277i 0.782000i −0.920391 0.391000i \(-0.872129\pi\)
0.920391 0.391000i \(-0.127871\pi\)
\(114\) 0 0
\(115\) 2.57834 2.57834i 0.240431 0.240431i
\(116\) 0 0
\(117\) −6.88701 5.67090i −0.636704 0.524274i
\(118\) 0 0
\(119\) 7.53805i 0.691012i
\(120\) 0 0
\(121\) 6.83276i 0.621160i
\(122\) 0 0
\(123\) 3.14118 0.151742i 0.283231 0.0136821i
\(124\) 0 0
\(125\) 4.15639 4.15639i 0.371759 0.371759i
\(126\) 0 0
\(127\) 15.7789i 1.40015i −0.714070 0.700074i \(-0.753150\pi\)
0.714070 0.700074i \(-0.246850\pi\)
\(128\) 0 0
\(129\) 1.28917 + 1.17036i 0.113505 + 0.103044i
\(130\) 0 0
\(131\) 0.0804722 + 0.0804722i 0.00703089 + 0.00703089i 0.710613 0.703583i \(-0.248417\pi\)
−0.703583 + 0.710613i \(0.748417\pi\)
\(132\) 0 0
\(133\) −2.20555 + 2.20555i −0.191245 + 0.191245i
\(134\) 0 0
\(135\) −2.54359 1.89615i −0.218918 0.163194i
\(136\) 0 0
\(137\) 13.2604 1.13291 0.566457 0.824091i \(-0.308314\pi\)
0.566457 + 0.824091i \(0.308314\pi\)
\(138\) 0 0
\(139\) −8.39194 8.39194i −0.711795 0.711795i 0.255115 0.966911i \(-0.417887\pi\)
−0.966911 + 0.255115i \(0.917887\pi\)
\(140\) 0 0
\(141\) −13.0411 + 0.629978i −1.09826 + 0.0530537i
\(142\) 0 0
\(143\) −12.5579 −1.05014
\(144\) 0 0
\(145\) 2.47054 0.205167
\(146\) 0 0
\(147\) −4.54517 + 0.219564i −0.374879 + 0.0181094i
\(148\) 0 0
\(149\) 5.79002 + 5.79002i 0.474337 + 0.474337i 0.903315 0.428978i \(-0.141126\pi\)
−0.428978 + 0.903315i \(0.641126\pi\)
\(150\) 0 0
\(151\) 9.94610 0.809402 0.404701 0.914449i \(-0.367376\pi\)
0.404701 + 0.914449i \(0.367376\pi\)
\(152\) 0 0
\(153\) −0.702522 7.25443i −0.0567955 0.586486i
\(154\) 0 0
\(155\) −0.226417 + 0.226417i −0.0181863 + 0.0181863i
\(156\) 0 0
\(157\) 9.15165 + 9.15165i 0.730381 + 0.730381i 0.970695 0.240314i \(-0.0772504\pi\)
−0.240314 + 0.970695i \(0.577250\pi\)
\(158\) 0 0
\(159\) 16.0200 + 14.5436i 1.27047 + 1.15338i
\(160\) 0 0
\(161\) 18.5300i 1.46037i
\(162\) 0 0
\(163\) −15.7003 + 15.7003i −1.22974 + 1.22974i −0.265678 + 0.964062i \(0.585596\pi\)
−0.964062 + 0.265678i \(0.914404\pi\)
\(164\) 0 0
\(165\) −4.46061 + 0.215480i −0.347258 + 0.0167751i
\(166\) 0 0
\(167\) 19.1437i 1.48139i −0.671843 0.740694i \(-0.734497\pi\)
0.671843 0.740694i \(-0.265503\pi\)
\(168\) 0 0
\(169\) 4.15667i 0.319744i
\(170\) 0 0
\(171\) 1.91701 2.32811i 0.146598 0.178035i
\(172\) 0 0
\(173\) 13.3281 13.3281i 1.01331 1.01331i 0.0134040 0.999910i \(-0.495733\pi\)
0.999910 0.0134040i \(-0.00426674\pi\)
\(174\) 0 0
\(175\) 14.3572i 1.08530i
\(176\) 0 0
\(177\) 0.132494 0.145945i 0.00995889 0.0109699i
\(178\) 0 0
\(179\) −9.18451 9.18451i −0.686483 0.686483i 0.274970 0.961453i \(-0.411332\pi\)
−0.961453 + 0.274970i \(0.911332\pi\)
\(180\) 0 0
\(181\) 16.5139 16.5139i 1.22747 1.22747i 0.262548 0.964919i \(-0.415437\pi\)
0.964919 0.262548i \(-0.0845627\pi\)
\(182\) 0 0
\(183\) −10.3919 9.43420i −0.768195 0.697396i
\(184\) 0 0
\(185\) −1.31630 −0.0967764
\(186\) 0 0
\(187\) −7.25443 7.25443i −0.530496 0.530496i
\(188\) 0 0
\(189\) 15.9537 2.32653i 1.16046 0.169230i
\(190\) 0 0
\(191\) 3.17852 0.229989 0.114995 0.993366i \(-0.463315\pi\)
0.114995 + 0.993366i \(0.463315\pi\)
\(192\) 0 0
\(193\) −11.4600 −0.824907 −0.412454 0.910979i \(-0.635328\pi\)
−0.412454 + 0.910979i \(0.635328\pi\)
\(194\) 0 0
\(195\) 0.151742 + 3.14118i 0.0108664 + 0.224944i
\(196\) 0 0
\(197\) 14.8053 + 14.8053i 1.05483 + 1.05483i 0.998407 + 0.0564281i \(0.0179712\pi\)
0.0564281 + 0.998407i \(0.482029\pi\)
\(198\) 0 0
\(199\) −24.4550 −1.73357 −0.866783 0.498686i \(-0.833816\pi\)
−0.866783 + 0.498686i \(0.833816\pi\)
\(200\) 0 0
\(201\) −0.645320 + 0.710831i −0.0455173 + 0.0501382i
\(202\) 0 0
\(203\) −8.87762 + 8.87762i −0.623087 + 0.623087i
\(204\) 0 0
\(205\) −0.783887 0.783887i −0.0547491 0.0547491i
\(206\) 0 0
\(207\) −1.72693 17.8328i −0.120030 1.23946i
\(208\) 0 0
\(209\) 4.24513i 0.293642i
\(210\) 0 0
\(211\) 6.18639 6.18639i 0.425889 0.425889i −0.461336 0.887225i \(-0.652630\pi\)
0.887225 + 0.461336i \(0.152630\pi\)
\(212\) 0 0
\(213\) −0.419525 8.68451i −0.0287454 0.595053i
\(214\) 0 0
\(215\) 0.613779i 0.0418594i
\(216\) 0 0
\(217\) 1.62721i 0.110462i
\(218\) 0 0
\(219\) −1.12489 23.2862i −0.0760132 1.57354i
\(220\) 0 0
\(221\) −5.10860 + 5.10860i −0.343641 + 0.343641i
\(222\) 0 0
\(223\) 8.18996i 0.548441i 0.961667 + 0.274220i \(0.0884197\pi\)
−0.961667 + 0.274220i \(0.911580\pi\)
\(224\) 0 0
\(225\) −1.33804 13.8170i −0.0892030 0.921133i
\(226\) 0 0
\(227\) 9.91030 + 9.91030i 0.657770 + 0.657770i 0.954852 0.297082i \(-0.0960135\pi\)
−0.297082 + 0.954852i \(0.596014\pi\)
\(228\) 0 0
\(229\) −7.15165 + 7.15165i −0.472594 + 0.472594i −0.902753 0.430159i \(-0.858458\pi\)
0.430159 + 0.902753i \(0.358458\pi\)
\(230\) 0 0
\(231\) 15.2544 16.8030i 1.00367 1.10556i
\(232\) 0 0
\(233\) 19.6431 1.28686 0.643432 0.765503i \(-0.277510\pi\)
0.643432 + 0.765503i \(0.277510\pi\)
\(234\) 0 0
\(235\) 3.25443 + 3.25443i 0.212295 + 0.212295i
\(236\) 0 0
\(237\) −0.290464 6.01284i −0.0188676 0.390576i
\(238\) 0 0
\(239\) −9.44247 −0.610782 −0.305391 0.952227i \(-0.598787\pi\)
−0.305391 + 0.952227i \(0.598787\pi\)
\(240\) 0 0
\(241\) 16.6167 1.07037 0.535186 0.844734i \(-0.320241\pi\)
0.535186 + 0.844734i \(0.320241\pi\)
\(242\) 0 0
\(243\) −15.1366 + 3.72583i −0.971017 + 0.239012i
\(244\) 0 0
\(245\) 1.13425 + 1.13425i 0.0724649 + 0.0724649i
\(246\) 0 0
\(247\) −2.98944 −0.190213
\(248\) 0 0
\(249\) −8.25557 7.49472i −0.523176 0.474958i
\(250\) 0 0
\(251\) 2.03382 2.03382i 0.128374 0.128374i −0.640001 0.768374i \(-0.721066\pi\)
0.768374 + 0.640001i \(0.221066\pi\)
\(252\) 0 0
\(253\) −17.8328 17.8328i −1.12114 1.12114i
\(254\) 0 0
\(255\) −1.72693 + 1.90225i −0.108145 + 0.119123i
\(256\) 0 0
\(257\) 15.0761i 0.940421i 0.882554 + 0.470211i \(0.155822\pi\)
−0.882554 + 0.470211i \(0.844178\pi\)
\(258\) 0 0
\(259\) 4.72999 4.72999i 0.293907 0.293907i
\(260\) 0 0
\(261\) 7.71623 9.37096i 0.477623 0.580048i
\(262\) 0 0
\(263\) 29.8138i 1.83840i 0.393796 + 0.919198i \(0.371162\pi\)
−0.393796 + 0.919198i \(0.628838\pi\)
\(264\) 0 0
\(265\) 7.62721i 0.468536i
\(266\) 0 0
\(267\) 21.7256 1.04950i 1.32958 0.0642285i
\(268\) 0 0
\(269\) −16.3713 + 16.3713i −0.998176 + 0.998176i −0.999998 0.00182258i \(-0.999420\pi\)
0.00182258 + 0.999998i \(0.499420\pi\)
\(270\) 0 0
\(271\) 13.3466i 0.810751i −0.914150 0.405375i \(-0.867141\pi\)
0.914150 0.405375i \(-0.132859\pi\)
\(272\) 0 0
\(273\) −11.8328 10.7422i −0.716151 0.650149i
\(274\) 0 0
\(275\) −13.8170 13.8170i −0.833197 0.833197i
\(276\) 0 0
\(277\) −10.6811 + 10.6811i −0.641766 + 0.641766i −0.950989 0.309224i \(-0.899931\pi\)
0.309224 + 0.950989i \(0.399931\pi\)
\(278\) 0 0
\(279\) 0.151651 + 1.56599i 0.00907911 + 0.0937533i
\(280\) 0 0
\(281\) 17.5943 1.04959 0.524794 0.851229i \(-0.324142\pi\)
0.524794 + 0.851229i \(0.324142\pi\)
\(282\) 0 0
\(283\) 17.1758 + 17.1758i 1.02100 + 1.02100i 0.999775 + 0.0212224i \(0.00675580\pi\)
0.0212224 + 0.999775i \(0.493244\pi\)
\(284\) 0 0
\(285\) −1.06186 + 0.0512954i −0.0628990 + 0.00303848i
\(286\) 0 0
\(287\) 5.63363 0.332543
\(288\) 0 0
\(289\) 11.0978 0.652809
\(290\) 0 0
\(291\) 15.0099 0.725088i 0.879897 0.0425054i
\(292\) 0 0
\(293\) −3.72465 3.72465i −0.217597 0.217597i 0.589888 0.807485i \(-0.299172\pi\)
−0.807485 + 0.589888i \(0.799172\pi\)
\(294\) 0 0
\(295\) −0.0694851 −0.00404558
\(296\) 0 0
\(297\) −13.1145 + 17.5925i −0.760979 + 1.02082i
\(298\) 0 0
\(299\) −12.5579 + 12.5579i −0.726242 + 0.726242i
\(300\) 0 0
\(301\) 2.20555 + 2.20555i 0.127126 + 0.127126i
\(302\) 0 0
\(303\) −0.330160 0.299731i −0.0189672 0.0172191i
\(304\) 0 0
\(305\) 4.94765i 0.283302i
\(306\) 0 0
\(307\) 13.4408 13.4408i 0.767108 0.767108i −0.210488 0.977596i \(-0.567505\pi\)
0.977596 + 0.210488i \(0.0675054\pi\)
\(308\) 0 0
\(309\) −10.9982 + 0.531291i −0.625664 + 0.0302241i
\(310\) 0 0
\(311\) 13.8320i 0.784341i 0.919893 + 0.392170i \(0.128276\pi\)
−0.919893 + 0.392170i \(0.871724\pi\)
\(312\) 0 0
\(313\) 3.94056i 0.222734i 0.993779 + 0.111367i \(0.0355229\pi\)
−0.993779 + 0.111367i \(0.964477\pi\)
\(314\) 0 0
\(315\) −4.38736 3.61264i −0.247200 0.203549i
\(316\) 0 0
\(317\) 8.92199 8.92199i 0.501109 0.501109i −0.410673 0.911782i \(-0.634706\pi\)
0.911782 + 0.410673i \(0.134706\pi\)
\(318\) 0 0
\(319\) 17.0872i 0.956699i
\(320\) 0 0
\(321\) −2.71083 + 2.98603i −0.151304 + 0.166664i
\(322\) 0 0
\(323\) −1.72693 1.72693i −0.0960891 0.0960891i
\(324\) 0 0
\(325\) −9.72999 + 9.72999i −0.539723 + 0.539723i
\(326\) 0 0
\(327\) 11.9214 + 10.8227i 0.659255 + 0.598497i
\(328\) 0 0
\(329\) −23.3889 −1.28947
\(330\) 0 0
\(331\) −9.44082 9.44082i −0.518914 0.518914i 0.398328 0.917243i \(-0.369590\pi\)
−0.917243 + 0.398328i \(0.869590\pi\)
\(332\) 0 0
\(333\) −4.11120 + 4.99284i −0.225292 + 0.273606i
\(334\) 0 0
\(335\) 0.338430 0.0184904
\(336\) 0 0
\(337\) 5.94056 0.323603 0.161801 0.986823i \(-0.448270\pi\)
0.161801 + 0.986823i \(0.448270\pi\)
\(338\) 0 0
\(339\) 0.694724 + 14.3814i 0.0377322 + 0.781089i
\(340\) 0 0
\(341\) 1.56599 + 1.56599i 0.0848030 + 0.0848030i
\(342\) 0 0
\(343\) 13.5678 0.732591
\(344\) 0 0
\(345\) −4.24513 + 4.67609i −0.228550 + 0.251752i
\(346\) 0 0
\(347\) −4.09918 + 4.09918i −0.220056 + 0.220056i −0.808522 0.588466i \(-0.799732\pi\)
0.588466 + 0.808522i \(0.299732\pi\)
\(348\) 0 0
\(349\) 8.10278 + 8.10278i 0.433732 + 0.433732i 0.889896 0.456164i \(-0.150777\pi\)
−0.456164 + 0.889896i \(0.650777\pi\)
\(350\) 0 0
\(351\) 12.3887 + 9.23527i 0.661259 + 0.492942i
\(352\) 0 0
\(353\) 29.2465i 1.55664i −0.627870 0.778318i \(-0.716073\pi\)
0.627870 0.778318i \(-0.283927\pi\)
\(354\) 0 0
\(355\) −2.16724 + 2.16724i −0.115025 + 0.115025i
\(356\) 0 0
\(357\) −0.629978 13.0411i −0.0333420 0.690207i
\(358\) 0 0
\(359\) 21.3235i 1.12541i −0.826657 0.562706i \(-0.809760\pi\)
0.826657 0.562706i \(-0.190240\pi\)
\(360\) 0 0
\(361\) 17.9894i 0.946812i
\(362\) 0 0
\(363\) 0.571035 + 11.8209i 0.0299716 + 0.620437i
\(364\) 0 0
\(365\) −5.81112 + 5.81112i −0.304168 + 0.304168i
\(366\) 0 0
\(367\) 32.8277i 1.71359i 0.515654 + 0.856797i \(0.327549\pi\)
−0.515654 + 0.856797i \(0.672451\pi\)
\(368\) 0 0
\(369\) −5.42166 + 0.525036i −0.282240 + 0.0273323i
\(370\) 0 0
\(371\) 27.4076 + 27.4076i 1.42293 + 1.42293i
\(372\) 0 0
\(373\) −1.35720 + 1.35720i −0.0702732 + 0.0702732i −0.741370 0.671097i \(-0.765824\pi\)
0.671097 + 0.741370i \(0.265824\pi\)
\(374\) 0 0
\(375\) −6.84333 + 7.53805i −0.353388 + 0.389263i
\(376\) 0 0
\(377\) −12.0329 −0.619724
\(378\) 0 0
\(379\) 17.3869 + 17.3869i 0.893106 + 0.893106i 0.994814 0.101708i \(-0.0324308\pi\)
−0.101708 + 0.994814i \(0.532431\pi\)
\(380\) 0 0
\(381\) 1.31869 + 27.2980i 0.0675585 + 1.39852i
\(382\) 0 0
\(383\) −32.9757 −1.68498 −0.842491 0.538711i \(-0.818912\pi\)
−0.842491 + 0.538711i \(0.818912\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 0 0
\(387\) −2.32811 1.91701i −0.118345 0.0974473i
\(388\) 0 0
\(389\) −3.97434 3.97434i −0.201507 0.201507i 0.599138 0.800645i \(-0.295510\pi\)
−0.800645 + 0.599138i \(0.795510\pi\)
\(390\) 0 0
\(391\) −14.5089 −0.733744
\(392\) 0 0
\(393\) −0.145945 0.132494i −0.00736195 0.00668346i
\(394\) 0 0
\(395\) −1.50052 + 1.50052i −0.0754991 + 0.0754991i
\(396\) 0 0
\(397\) 15.9355 + 15.9355i 0.799782 + 0.799782i 0.983061 0.183279i \(-0.0586712\pi\)
−0.183279 + 0.983061i \(0.558671\pi\)
\(398\) 0 0
\(399\) 3.63135 4.00000i 0.181795 0.200250i
\(400\) 0 0
\(401\) 29.7716i 1.48672i 0.668891 + 0.743361i \(0.266769\pi\)
−0.668891 + 0.743361i \(0.733231\pi\)
\(402\) 0 0
\(403\) 1.10278 1.10278i 0.0549331 0.0549331i
\(404\) 0 0
\(405\) 4.55897 + 3.06782i 0.226537 + 0.152441i
\(406\) 0 0
\(407\) 9.10404i 0.451270i
\(408\) 0 0
\(409\) 15.6655i 0.774610i 0.921952 + 0.387305i \(0.126594\pi\)
−0.921952 + 0.387305i \(0.873406\pi\)
\(410\) 0 0
\(411\) −22.9410 + 1.10821i −1.13159 + 0.0546642i
\(412\) 0 0
\(413\) 0.249687 0.249687i 0.0122863 0.0122863i
\(414\) 0 0
\(415\) 3.93051i 0.192941i
\(416\) 0 0
\(417\) 15.2197 + 13.8170i 0.745311 + 0.676621i
\(418\) 0 0
\(419\) −14.1554 14.1554i −0.691538 0.691538i 0.271032 0.962570i \(-0.412635\pi\)
−0.962570 + 0.271032i \(0.912635\pi\)
\(420\) 0 0
\(421\) 7.35720 7.35720i 0.358568 0.358568i −0.504717 0.863285i \(-0.668403\pi\)
0.863285 + 0.504717i \(0.168403\pi\)
\(422\) 0 0
\(423\) 22.5089 2.17977i 1.09442 0.105984i
\(424\) 0 0
\(425\) −11.2416 −0.545298
\(426\) 0 0
\(427\) −17.7789 17.7789i −0.860380 0.860380i
\(428\) 0 0
\(429\) 21.7256 1.04950i 1.04892 0.0506705i
\(430\) 0 0
\(431\) 20.7097 0.997553 0.498776 0.866731i \(-0.333783\pi\)
0.498776 + 0.866731i \(0.333783\pi\)
\(432\) 0 0
\(433\) −23.4005 −1.12456 −0.562279 0.826948i \(-0.690075\pi\)
−0.562279 + 0.826948i \(0.690075\pi\)
\(434\) 0 0
\(435\) −4.27411 + 0.206471i −0.204928 + 0.00989951i
\(436\) 0 0
\(437\) −4.24513 4.24513i −0.203072 0.203072i
\(438\) 0 0
\(439\) 20.2594 0.966931 0.483465 0.875363i \(-0.339378\pi\)
0.483465 + 0.875363i \(0.339378\pi\)
\(440\) 0 0
\(441\) 7.84494 0.759707i 0.373569 0.0361765i
\(442\) 0 0
\(443\) −4.05264 + 4.05264i −0.192547 + 0.192547i −0.796796 0.604249i \(-0.793473\pi\)
0.604249 + 0.796796i \(0.293473\pi\)
\(444\) 0 0
\(445\) −5.42166 5.42166i −0.257011 0.257011i
\(446\) 0 0
\(447\) −10.5008 9.53303i −0.496671 0.450897i
\(448\) 0 0
\(449\) 5.38394i 0.254084i −0.991897 0.127042i \(-0.959452\pi\)
0.991897 0.127042i \(-0.0405483\pi\)
\(450\) 0 0
\(451\) −5.42166 + 5.42166i −0.255296 + 0.255296i
\(452\) 0 0
\(453\) −17.2071 + 0.831227i −0.808459 + 0.0390544i
\(454\) 0 0
\(455\) 5.63363i 0.264109i
\(456\) 0 0
\(457\) 28.0766i 1.31337i −0.754165 0.656685i \(-0.771958\pi\)
0.754165 0.656685i \(-0.228042\pi\)
\(458\) 0 0
\(459\) 1.82166 + 12.4917i 0.0850279 + 0.583062i
\(460\) 0 0
\(461\) 22.7962 22.7962i 1.06172 1.06172i 0.0637594 0.997965i \(-0.479691\pi\)
0.997965 0.0637594i \(-0.0203090\pi\)
\(462\) 0 0
\(463\) 0.740035i 0.0343923i 0.999852 + 0.0171962i \(0.00547398\pi\)
−0.999852 + 0.0171962i \(0.994526\pi\)
\(464\) 0 0
\(465\) 0.372787 0.410632i 0.0172876 0.0190426i
\(466\) 0 0
\(467\) 9.73282 + 9.73282i 0.450381 + 0.450381i 0.895481 0.445100i \(-0.146832\pi\)
−0.445100 + 0.895481i \(0.646832\pi\)
\(468\) 0 0
\(469\) −1.21611 + 1.21611i −0.0561549 + 0.0561549i
\(470\) 0 0
\(471\) −16.5975 15.0678i −0.764772 0.694289i
\(472\) 0 0
\(473\) −4.24513 −0.195191
\(474\) 0 0
\(475\) −3.28917 3.28917i −0.150917 0.150917i
\(476\) 0 0
\(477\) −28.9307 23.8221i −1.32464 1.09074i
\(478\) 0 0
\(479\) 28.2478 1.29067 0.645337 0.763898i \(-0.276717\pi\)
0.645337 + 0.763898i \(0.276717\pi\)
\(480\) 0 0
\(481\) 6.41110 0.292321
\(482\) 0 0
\(483\) −1.54861 32.0575i −0.0704641 1.45866i
\(484\) 0 0
\(485\) −3.74576 3.74576i −0.170086 0.170086i
\(486\) 0 0
\(487\) 19.7094 0.893117 0.446559 0.894754i \(-0.352649\pi\)
0.446559 + 0.894754i \(0.352649\pi\)
\(488\) 0 0
\(489\) 25.8499 28.4741i 1.16897 1.28764i
\(490\) 0 0
\(491\) 29.4414 29.4414i 1.32867 1.32867i 0.422143 0.906529i \(-0.361278\pi\)
0.906529 0.422143i \(-0.138722\pi\)
\(492\) 0 0
\(493\) −6.95112 6.95112i −0.313063 0.313063i
\(494\) 0 0
\(495\) 7.69899 0.745574i 0.346044 0.0335111i
\(496\) 0 0
\(497\) 15.5755i 0.698656i
\(498\) 0 0
\(499\) −4.43026 + 4.43026i −0.198326 + 0.198326i −0.799282 0.600956i \(-0.794787\pi\)
0.600956 + 0.799282i \(0.294787\pi\)
\(500\) 0 0
\(501\) 1.59990 + 33.1193i 0.0714784 + 1.47966i
\(502\) 0 0
\(503\) 27.6805i 1.23421i −0.786879 0.617107i \(-0.788304\pi\)
0.786879 0.617107i \(-0.211696\pi\)
\(504\) 0 0
\(505\) 0.157190i 0.00699488i
\(506\) 0 0
\(507\) 0.347386 + 7.19119i 0.0154280 + 0.319372i
\(508\) 0 0
\(509\) −17.3235 + 17.3235i −0.767851 + 0.767851i −0.977728 0.209877i \(-0.932694\pi\)
0.209877 + 0.977728i \(0.432694\pi\)
\(510\) 0 0
\(511\) 41.7633i 1.84750i
\(512\) 0 0
\(513\) −3.12193 + 4.18793i −0.137837 + 0.184902i
\(514\) 0 0
\(515\) 2.74461 + 2.74461i 0.120942 + 0.120942i
\(516\) 0 0
\(517\) 22.5089 22.5089i 0.989938 0.989938i
\(518\) 0 0
\(519\) −21.9441 + 24.1719i −0.963240 + 1.06103i
\(520\) 0 0
\(521\) −10.1284 −0.443735 −0.221868 0.975077i \(-0.571215\pi\)
−0.221868 + 0.975077i \(0.571215\pi\)
\(522\) 0 0
\(523\) −1.45641 1.45641i −0.0636842 0.0636842i 0.674547 0.738232i \(-0.264339\pi\)
−0.738232 + 0.674547i \(0.764339\pi\)
\(524\) 0 0
\(525\) −1.19988 24.8384i −0.0523669 1.08404i
\(526\) 0 0
\(527\) 1.27410 0.0555006
\(528\) 0 0
\(529\) −12.6655 −0.550675
\(530\) 0 0
\(531\) −0.217023 + 0.263563i −0.00941798 + 0.0114376i
\(532\) 0 0
\(533\) 3.81796 + 3.81796i 0.165374 + 0.165374i
\(534\) 0 0
\(535\) 1.42166 0.0614638
\(536\) 0 0
\(537\) 16.6571 + 15.1219i 0.718806 + 0.652560i
\(538\) 0 0
\(539\) 7.84494 7.84494i 0.337905 0.337905i
\(540\) 0 0
\(541\) −5.18996 5.18996i −0.223134 0.223134i 0.586683 0.809817i \(-0.300434\pi\)
−0.809817 + 0.586683i \(0.800434\pi\)
\(542\) 0 0
\(543\) −27.1894 + 29.9497i −1.16681 + 1.28526i
\(544\) 0 0
\(545\) 5.67583i 0.243126i
\(546\) 0 0
\(547\) −12.6413 + 12.6413i −0.540505 + 0.540505i −0.923677 0.383172i \(-0.874832\pi\)
0.383172 + 0.923677i \(0.374832\pi\)
\(548\) 0 0
\(549\) 18.7669 + 15.4530i 0.800950 + 0.659518i
\(550\) 0 0
\(551\) 4.06764i 0.173287i
\(552\) 0 0
\(553\) 10.7839i 0.458578i
\(554\) 0 0
\(555\) 2.27724 0.110007i 0.0966636 0.00466955i
\(556\) 0 0
\(557\) −6.90317 + 6.90317i −0.292497 + 0.292497i −0.838066 0.545569i \(-0.816314\pi\)
0.545569 + 0.838066i \(0.316314\pi\)
\(558\) 0 0
\(559\) 2.98944i 0.126440i
\(560\) 0 0
\(561\) 13.1567 + 11.9441i 0.555475 + 0.504281i
\(562\) 0 0
\(563\) −18.3840 18.3840i −0.774794 0.774794i 0.204146 0.978940i \(-0.434558\pi\)
−0.978940 + 0.204146i \(0.934558\pi\)
\(564\) 0 0
\(565\) 3.58890 3.58890i 0.150986 0.150986i
\(566\) 0 0
\(567\) −27.4061 + 5.35828i −1.15095 + 0.225027i
\(568\) 0 0
\(569\) 43.5570 1.82601 0.913003 0.407953i \(-0.133757\pi\)
0.913003 + 0.407953i \(0.133757\pi\)
\(570\) 0 0
\(571\) −7.00859 7.00859i −0.293301 0.293301i 0.545082 0.838383i \(-0.316498\pi\)
−0.838383 + 0.545082i \(0.816498\pi\)
\(572\) 0 0
\(573\) −5.49894 + 0.265638i −0.229721 + 0.0110972i
\(574\) 0 0
\(575\) −27.6340 −1.15242
\(576\) 0 0
\(577\) 28.4494 1.18436 0.592182 0.805804i \(-0.298267\pi\)
0.592182 + 0.805804i \(0.298267\pi\)
\(578\) 0 0
\(579\) 19.8261 0.957746i 0.823946 0.0398026i
\(580\) 0 0
\(581\) −14.1239 14.1239i −0.585958 0.585958i
\(582\) 0 0
\(583\) −52.7527 −2.18479
\(584\) 0 0
\(585\) −0.525036 5.42166i −0.0217076 0.224158i
\(586\) 0 0
\(587\) 19.9011 19.9011i 0.821405 0.821405i −0.164904 0.986310i \(-0.552732\pi\)
0.986310 + 0.164904i \(0.0527315\pi\)
\(588\) 0 0
\(589\) 0.372787 + 0.372787i 0.0153604 + 0.0153604i
\(590\) 0 0
\(591\) −26.8510 24.3764i −1.10450 1.00271i
\(592\) 0 0
\(593\) 20.4344i 0.839140i −0.907723 0.419570i \(-0.862181\pi\)
0.907723 0.419570i \(-0.137819\pi\)
\(594\) 0 0
\(595\) −3.25443 + 3.25443i −0.133418 + 0.133418i
\(596\) 0 0
\(597\) 42.3079 2.04378i 1.73155 0.0836462i
\(598\) 0 0
\(599\) 32.6704i 1.33488i −0.744665 0.667438i \(-0.767391\pi\)
0.744665 0.667438i \(-0.232609\pi\)
\(600\) 0 0
\(601\) 6.73553i 0.274748i 0.990519 + 0.137374i \(0.0438662\pi\)
−0.990519 + 0.137374i \(0.956134\pi\)
\(602\) 0 0
\(603\) 1.05702 1.28369i 0.0430451 0.0522760i
\(604\) 0 0
\(605\) 2.94993 2.94993i 0.119932 0.119932i
\(606\) 0 0
\(607\) 21.2388i 0.862058i 0.902338 + 0.431029i \(0.141849\pi\)
−0.902338 + 0.431029i \(0.858151\pi\)
\(608\) 0 0
\(609\) 14.6167 16.1005i 0.592297 0.652426i
\(610\) 0 0
\(611\) −15.8508 15.8508i −0.641256 0.641256i
\(612\) 0 0
\(613\) 9.62219 9.62219i 0.388637 0.388637i −0.485564 0.874201i \(-0.661386\pi\)
0.874201 + 0.485564i \(0.161386\pi\)
\(614\) 0 0
\(615\) 1.42166 + 1.29064i 0.0573270 + 0.0520436i
\(616\) 0 0
\(617\) −3.74576 −0.150798 −0.0753992 0.997153i \(-0.524023\pi\)
−0.0753992 + 0.997153i \(0.524023\pi\)
\(618\) 0 0
\(619\) 13.0680 + 13.0680i 0.525249 + 0.525249i 0.919152 0.393903i \(-0.128876\pi\)
−0.393903 + 0.919152i \(0.628876\pi\)
\(620\) 0 0
\(621\) 4.47799 + 30.7070i 0.179696 + 1.23223i
\(622\) 0 0
\(623\) 38.9643 1.56107
\(624\) 0 0
\(625\) −19.5472 −0.781887
\(626\) 0 0
\(627\) 0.354779 + 7.34422i 0.0141685 + 0.293300i
\(628\) 0 0
\(629\) 3.70355 + 3.70355i 0.147670 + 0.147670i
\(630\) 0 0
\(631\) −7.51388 −0.299123 −0.149561 0.988752i \(-0.547786\pi\)
−0.149561 + 0.988752i \(0.547786\pi\)
\(632\) 0 0
\(633\) −10.1857 + 11.2197i −0.404843 + 0.445942i
\(634\) 0 0
\(635\) 6.81226 6.81226i 0.270336 0.270336i
\(636\) 0 0
\(637\) −5.52444 5.52444i −0.218886 0.218886i
\(638\) 0 0
\(639\) 1.45158 + 14.9894i 0.0574238 + 0.592973i
\(640\) 0 0
\(641\) 27.7227i 1.09498i −0.836811 0.547491i \(-0.815583\pi\)
0.836811 0.547491i \(-0.184417\pi\)
\(642\) 0 0
\(643\) −19.7003 + 19.7003i −0.776903 + 0.776903i −0.979303 0.202400i \(-0.935126\pi\)
0.202400 + 0.979303i \(0.435126\pi\)
\(644\) 0 0
\(645\) 0.0512954 + 1.06186i 0.00201976 + 0.0418106i
\(646\) 0 0
\(647\) 5.29520i 0.208176i 0.994568 + 0.104088i \(0.0331923\pi\)
−0.994568 + 0.104088i \(0.966808\pi\)
\(648\) 0 0
\(649\) 0.480585i 0.0188646i
\(650\) 0 0
\(651\) 0.135991 + 2.81513i 0.00532992 + 0.110334i
\(652\) 0 0
\(653\) 29.7039 29.7039i 1.16240 1.16240i 0.178457 0.983948i \(-0.442890\pi\)
0.983948 0.178457i \(-0.0571104\pi\)
\(654\) 0 0
\(655\) 0.0694851i 0.00271501i
\(656\) 0 0
\(657\) 3.89220 + 40.1919i 0.151849 + 1.56804i
\(658\) 0 0
\(659\) 1.03268 + 1.03268i 0.0402276 + 0.0402276i 0.726934 0.686707i \(-0.240944\pi\)
−0.686707 + 0.726934i \(0.740944\pi\)
\(660\) 0 0
\(661\) −29.8277 + 29.8277i −1.16016 + 1.16016i −0.175725 + 0.984439i \(0.556227\pi\)
−0.984439 + 0.175725i \(0.943773\pi\)
\(662\) 0 0
\(663\) 8.41110 9.26498i 0.326660 0.359822i
\(664\) 0 0
\(665\) −1.90442 −0.0738502
\(666\) 0 0
\(667\) −17.0872 17.0872i −0.661619 0.661619i
\(668\) 0 0
\(669\) −0.684461 14.1689i −0.0264628 0.547802i
\(670\) 0 0
\(671\) 34.2198 1.32104
\(672\) 0 0
\(673\) −0.891685 −0.0343719 −0.0171860 0.999852i \(-0.505471\pi\)
−0.0171860 + 0.999852i \(0.505471\pi\)
\(674\) 0 0
\(675\) 3.46959 + 23.7920i 0.133545 + 0.915756i
\(676\) 0 0
\(677\) −8.13073 8.13073i −0.312489 0.312489i 0.533384 0.845873i \(-0.320920\pi\)
−0.845873 + 0.533384i \(0.820920\pi\)
\(678\) 0 0
\(679\) 26.9200 1.03309
\(680\) 0 0
\(681\) −17.9734 16.3169i −0.688742 0.625266i
\(682\) 0 0
\(683\) −14.5917 + 14.5917i −0.558337 + 0.558337i −0.928834 0.370497i \(-0.879187\pi\)
0.370497 + 0.928834i \(0.379187\pi\)
\(684\) 0 0
\(685\) 5.72496 + 5.72496i 0.218740 + 0.218740i
\(686\) 0 0
\(687\) 11.7749 12.9703i 0.449241 0.494847i
\(688\) 0 0
\(689\) 37.1487i 1.41525i
\(690\) 0 0
\(691\) 11.2197 11.2197i 0.426817 0.426817i −0.460726 0.887543i \(-0.652411\pi\)
0.887543 + 0.460726i \(0.152411\pi\)
\(692\) 0 0
\(693\) −24.9864 + 30.3447i −0.949154 + 1.15270i
\(694\) 0 0
\(695\) 7.24616i 0.274863i
\(696\) 0 0
\(697\) 4.41110i 0.167082i
\(698\) 0 0
\(699\) −33.9833 + 1.64164i −1.28536 + 0.0620924i
\(700\) 0 0
\(701\) −14.7166 + 14.7166i −0.555837 + 0.555837i −0.928120 0.372282i \(-0.878575\pi\)
0.372282 + 0.928120i \(0.378575\pi\)
\(702\) 0 0
\(703\) 2.16724i 0.0817389i
\(704\) 0 0
\(705\) −5.90225 5.35828i −0.222292 0.201805i
\(706\) 0 0
\(707\) −0.564847 0.564847i −0.0212433 0.0212433i
\(708\) 0 0
\(709\) 23.2978 23.2978i 0.874966 0.874966i −0.118043 0.993009i \(-0.537662\pi\)
0.993009 + 0.118043i \(0.0376620\pi\)
\(710\) 0 0
\(711\) 1.00502 + 10.3781i 0.0376913 + 0.389211i
\(712\) 0 0
\(713\) 3.13198 0.117293
\(714\) 0 0
\(715\) −5.42166 5.42166i −0.202759 0.202759i
\(716\) 0 0
\(717\) 16.3358 0.789136i 0.610071 0.0294708i
\(718\) 0 0
\(719\) −27.3421 −1.01969 −0.509844 0.860267i \(-0.670297\pi\)
−0.509844 + 0.860267i \(0.670297\pi\)
\(720\) 0 0
\(721\) −19.7250 −0.734596
\(722\) 0 0
\(723\) −28.7474 + 1.38871i −1.06913 + 0.0516465i
\(724\) 0 0
\(725\) −13.2393 13.2393i −0.491696 0.491696i
\(726\) 0 0
\(727\) 24.1517 0.895735 0.447868 0.894100i \(-0.352184\pi\)
0.447868 + 0.894100i \(0.352184\pi\)
\(728\) 0 0
\(729\) 25.8755 7.71083i 0.958353 0.285586i
\(730\) 0 0
\(731\) −1.72693 + 1.72693i −0.0638729 + 0.0638729i
\(732\) 0 0
\(733\) 6.00502 + 6.00502i 0.221801 + 0.221801i 0.809256 0.587456i \(-0.199870\pi\)
−0.587456 + 0.809256i \(0.699870\pi\)
\(734\) 0 0
\(735\) −2.05709 1.86751i −0.0758770 0.0688840i
\(736\) 0 0
\(737\) 2.34071i 0.0862212i
\(738\) 0 0
\(739\) 10.9008 10.9008i 0.400992 0.400992i −0.477590 0.878583i \(-0.658490\pi\)
0.878583 + 0.477590i \(0.158490\pi\)
\(740\) 0 0
\(741\) 5.17183 0.249837i 0.189992 0.00917798i
\(742\) 0 0
\(743\) 1.29064i 0.0473490i 0.999720 + 0.0236745i \(0.00753652\pi\)
−0.999720 + 0.0236745i \(0.992463\pi\)
\(744\) 0 0
\(745\) 4.99948i 0.183167i
\(746\) 0 0
\(747\) 14.9088 + 12.2762i 0.545483 + 0.449162i
\(748\) 0 0
\(749\) −5.10860 + 5.10860i −0.186664 + 0.186664i
\(750\) 0 0
\(751\) 1.46552i 0.0534774i 0.999642 + 0.0267387i \(0.00851221\pi\)
−0.999642 + 0.0267387i \(0.991488\pi\)
\(752\) 0 0
\(753\) −3.34861 + 3.68855i −0.122030 + 0.134418i
\(754\) 0 0
\(755\) 4.29406 + 4.29406i 0.156277 + 0.156277i
\(756\) 0 0
\(757\) −4.71943 + 4.71943i −0.171530 + 0.171530i −0.787651 0.616121i \(-0.788703\pi\)
0.616121 + 0.787651i \(0.288703\pi\)
\(758\) 0 0
\(759\) 32.3416 + 29.3609i 1.17393 + 1.06573i
\(760\) 0 0
\(761\) −29.1578 −1.05697 −0.528485 0.848943i \(-0.677240\pi\)
−0.528485 + 0.848943i \(0.677240\pi\)
\(762\) 0 0
\(763\) 20.3955 + 20.3955i 0.738367 + 0.738367i
\(764\) 0 0
\(765\) 2.82867 3.43528i 0.102271 0.124203i
\(766\) 0 0
\(767\) 0.338430 0.0122200
\(768\) 0 0
\(769\) 20.8122 0.750505 0.375253 0.926923i \(-0.377556\pi\)
0.375253 + 0.926923i \(0.377556\pi\)
\(770\) 0 0
\(771\) −1.25996 26.0822i −0.0453762 0.939326i
\(772\) 0 0
\(773\) −26.6607 26.6607i −0.958918 0.958918i 0.0402703 0.999189i \(-0.487178\pi\)
−0.999189 + 0.0402703i \(0.987178\pi\)
\(774\) 0 0
\(775\) 2.42669 0.0871691
\(776\) 0 0
\(777\) −7.78774 + 8.57834i −0.279384 + 0.307746i
\(778\) 0 0
\(779\) −1.29064 + 1.29064i −0.0462419 + 0.0462419i
\(780\) 0 0
\(781\) 14.9894 + 14.9894i 0.536364 + 0.536364i
\(782\) 0 0
\(783\) −12.5662 + 16.8569i −0.449078 + 0.602418i
\(784\) 0 0
\(785\) 7.90214i 0.282040i
\(786\) 0 0
\(787\) 32.7875 32.7875i 1.16875 1.16875i 0.186243 0.982504i \(-0.440369\pi\)
0.982504 0.186243i \(-0.0596311\pi\)
\(788\) 0 0
\(789\) −2.49163 51.5788i −0.0887044 1.83625i
\(790\) 0 0
\(791\) 25.7927i 0.917082i
\(792\) 0 0
\(793\) 24.0978i 0.855736i
\(794\) 0 0
\(795\) 0.637430 + 13.1953i 0.0226073 + 0.467990i
\(796\) 0 0
\(797\) −11.2627 + 11.2627i −0.398945 + 0.398945i −0.877861 0.478916i \(-0.841030\pi\)