Properties

Label 784.2.bb.b.111.15
Level $784$
Weight $2$
Character 784.111
Analytic conductor $6.260$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.bb (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 111.15
Character \(\chi\) \(=\) 784.111
Dual form 784.2.bb.b.671.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.977383 + 1.22560i) q^{3} +(-0.470082 + 0.374878i) q^{5} +(-1.48039 - 2.19281i) q^{7} +(0.120747 - 0.529025i) q^{9} +O(q^{10})\) \(q+(0.977383 + 1.22560i) q^{3} +(-0.470082 + 0.374878i) q^{5} +(-1.48039 - 2.19281i) q^{7} +(0.120747 - 0.529025i) q^{9} +(5.53257 - 1.26277i) q^{11} +(0.517931 - 0.118214i) q^{13} +(-0.918900 - 0.209733i) q^{15} +(0.00663338 - 0.0137744i) q^{17} +4.54052 q^{19} +(1.24060 - 3.95759i) q^{21} +(-0.102508 - 0.212861i) q^{23} +(-1.03216 + 4.52219i) q^{25} +(5.00346 - 2.40954i) q^{27} +(-3.07949 - 1.48300i) q^{29} +5.84992 q^{31} +(6.95509 + 5.54650i) q^{33} +(1.51794 + 0.475836i) q^{35} +(5.35144 + 2.57712i) q^{37} +(0.651100 + 0.519235i) q^{39} +(1.23297 - 0.983262i) q^{41} +(-5.47172 - 4.36355i) q^{43} +(0.141559 + 0.293950i) q^{45} +(0.699308 + 3.06387i) q^{47} +(-2.61688 + 6.49245i) q^{49} +(0.0233652 - 0.00533296i) q^{51} +(-10.7318 + 5.16818i) q^{53} +(-2.12738 + 2.66764i) q^{55} +(4.43782 + 5.56486i) q^{57} +(6.17584 - 7.74426i) q^{59} +(-3.48363 + 7.23382i) q^{61} +(-1.33881 + 0.518390i) q^{63} +(-0.199154 + 0.249731i) q^{65} -5.76147i q^{67} +(0.160692 - 0.333681i) q^{69} +(-1.23326 - 2.56090i) q^{71} +(3.26962 + 0.746269i) q^{73} +(-6.55121 + 3.15490i) q^{75} +(-10.9594 - 10.2625i) q^{77} -7.84700i q^{79} +(6.37675 + 3.07088i) q^{81} +(-3.22440 + 14.1270i) q^{83} +(0.00204547 + 0.00896179i) q^{85} +(-1.19227 - 5.22368i) q^{87} +(-4.67524 - 1.06709i) q^{89} +(-1.02596 - 0.960723i) q^{91} +(5.71761 + 7.16966i) q^{93} +(-2.13442 + 1.70214i) q^{95} -13.2524i q^{97} -3.07934i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q - 24q^{9} + O(q^{10}) \) \( 120q - 24q^{9} - 14q^{17} + 16q^{21} + 40q^{25} + 32q^{29} - 62q^{37} - 28q^{41} - 60q^{49} + 14q^{53} - 34q^{57} - 112q^{61} - 32q^{65} + 112q^{69} + 42q^{73} + 66q^{77} - 44q^{81} - 12q^{85} + 28q^{89} - 58q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{11}{14}\right)\)

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
\(3\) 0.977383 + 1.22560i 0.564292 + 0.707600i 0.979345 0.202197i \(-0.0648083\pi\)
−0.415053 + 0.909797i \(0.636237\pi\)
\(4\) 0 0
\(5\) −0.470082 + 0.374878i −0.210227 + 0.167650i −0.722943 0.690908i \(-0.757211\pi\)
0.512716 + 0.858558i \(0.328640\pi\)
\(6\) 0 0
\(7\) −1.48039 2.19281i −0.559536 0.828806i
\(8\) 0 0
\(9\) 0.120747 0.529025i 0.0402488 0.176342i
\(10\) 0 0
\(11\) 5.53257 1.26277i 1.66813 0.380740i 0.718850 0.695165i \(-0.244669\pi\)
0.949282 + 0.314425i \(0.101812\pi\)
\(12\) 0 0
\(13\) 0.517931 0.118214i 0.143648 0.0327868i −0.150092 0.988672i \(-0.547957\pi\)
0.293740 + 0.955885i \(0.405100\pi\)
\(14\) 0 0
\(15\) −0.918900 0.209733i −0.237259 0.0541528i
\(16\) 0 0
\(17\) 0.00663338 0.0137744i 0.00160883 0.00334077i −0.900163 0.435553i \(-0.856553\pi\)
0.901772 + 0.432213i \(0.142267\pi\)
\(18\) 0 0
\(19\) 4.54052 1.04167 0.520833 0.853658i \(-0.325621\pi\)
0.520833 + 0.853658i \(0.325621\pi\)
\(20\) 0 0
\(21\) 1.24060 3.95759i 0.270722 0.863616i
\(22\) 0 0
\(23\) −0.102508 0.212861i −0.0213745 0.0443846i 0.890008 0.455944i \(-0.150698\pi\)
−0.911383 + 0.411560i \(0.864984\pi\)
\(24\) 0 0
\(25\) −1.03216 + 4.52219i −0.206432 + 0.904439i
\(26\) 0 0
\(27\) 5.00346 2.40954i 0.962917 0.463717i
\(28\) 0 0
\(29\) −3.07949 1.48300i −0.571846 0.275387i 0.125532 0.992090i \(-0.459936\pi\)
−0.697379 + 0.716703i \(0.745650\pi\)
\(30\) 0 0
\(31\) 5.84992 1.05068 0.525338 0.850893i \(-0.323939\pi\)
0.525338 + 0.850893i \(0.323939\pi\)
\(32\) 0 0
\(33\) 6.95509 + 5.54650i 1.21073 + 0.965522i
\(34\) 0 0
\(35\) 1.51794 + 0.475836i 0.256579 + 0.0804310i
\(36\) 0 0
\(37\) 5.35144 + 2.57712i 0.879772 + 0.423676i 0.818541 0.574448i \(-0.194783\pi\)
0.0612307 + 0.998124i \(0.480497\pi\)
\(38\) 0 0
\(39\) 0.651100 + 0.519235i 0.104259 + 0.0831442i
\(40\) 0 0
\(41\) 1.23297 0.983262i 0.192558 0.153560i −0.522465 0.852661i \(-0.674988\pi\)
0.715023 + 0.699101i \(0.246416\pi\)
\(42\) 0 0
\(43\) −5.47172 4.36355i −0.834429 0.665435i 0.110079 0.993923i \(-0.464890\pi\)
−0.944508 + 0.328488i \(0.893461\pi\)
\(44\) 0 0
\(45\) 0.141559 + 0.293950i 0.0211024 + 0.0438195i
\(46\) 0 0
\(47\) 0.699308 + 3.06387i 0.102005 + 0.446911i 0.999976 + 0.00685856i \(0.00218316\pi\)
−0.897972 + 0.440053i \(0.854960\pi\)
\(48\) 0 0
\(49\) −2.61688 + 6.49245i −0.373839 + 0.927493i
\(50\) 0 0
\(51\) 0.0233652 0.00533296i 0.00327178 0.000746763i
\(52\) 0 0
\(53\) −10.7318 + 5.16818i −1.47413 + 0.709904i −0.986593 0.163198i \(-0.947819\pi\)
−0.487537 + 0.873102i \(0.662105\pi\)
\(54\) 0 0
\(55\) −2.12738 + 2.66764i −0.286855 + 0.359705i
\(56\) 0 0
\(57\) 4.43782 + 5.56486i 0.587804 + 0.737083i
\(58\) 0 0
\(59\) 6.17584 7.74426i 0.804026 1.00822i −0.195595 0.980685i \(-0.562664\pi\)
0.999621 0.0275323i \(-0.00876491\pi\)
\(60\) 0 0
\(61\) −3.48363 + 7.23382i −0.446033 + 0.926196i 0.549826 + 0.835279i \(0.314694\pi\)
−0.995858 + 0.0909169i \(0.971020\pi\)
\(62\) 0 0
\(63\) −1.33881 + 0.518390i −0.168674 + 0.0653110i
\(64\) 0 0
\(65\) −0.199154 + 0.249731i −0.0247020 + 0.0309754i
\(66\) 0 0
\(67\) 5.76147i 0.703875i −0.936024 0.351937i \(-0.885523\pi\)
0.936024 0.351937i \(-0.114477\pi\)
\(68\) 0 0
\(69\) 0.160692 0.333681i 0.0193451 0.0401705i
\(70\) 0 0
\(71\) −1.23326 2.56090i −0.146362 0.303923i 0.814880 0.579629i \(-0.196803\pi\)
−0.961242 + 0.275706i \(0.911088\pi\)
\(72\) 0 0
\(73\) 3.26962 + 0.746269i 0.382680 + 0.0873442i 0.409533 0.912295i \(-0.365692\pi\)
−0.0268533 + 0.999639i \(0.508549\pi\)
\(74\) 0 0
\(75\) −6.55121 + 3.15490i −0.756469 + 0.364296i
\(76\) 0 0
\(77\) −10.9594 10.2625i −1.24894 1.16952i
\(78\) 0 0
\(79\) 7.84700i 0.882856i −0.897297 0.441428i \(-0.854472\pi\)
0.897297 0.441428i \(-0.145528\pi\)
\(80\) 0 0
\(81\) 6.37675 + 3.07088i 0.708528 + 0.341209i
\(82\) 0 0
\(83\) −3.22440 + 14.1270i −0.353924 + 1.55064i 0.414106 + 0.910229i \(0.364094\pi\)
−0.768030 + 0.640414i \(0.778763\pi\)
\(84\) 0 0
\(85\) 0.00204547 + 0.00896179i 0.000221862 + 0.000972043i
\(86\) 0 0
\(87\) −1.19227 5.22368i −0.127825 0.560037i
\(88\) 0 0
\(89\) −4.67524 1.06709i −0.495575 0.113112i −0.0325735 0.999469i \(-0.510370\pi\)
−0.463001 + 0.886358i \(0.653227\pi\)
\(90\) 0 0
\(91\) −1.02596 0.960723i −0.107550 0.100711i
\(92\) 0 0
\(93\) 5.71761 + 7.16966i 0.592889 + 0.743459i
\(94\) 0 0
\(95\) −2.13442 + 1.70214i −0.218986 + 0.174636i
\(96\) 0 0
\(97\) 13.2524i 1.34558i −0.739833 0.672791i \(-0.765095\pi\)
0.739833 0.672791i \(-0.234905\pi\)
\(98\) 0 0
\(99\) 3.07934i 0.309486i
\(100\) 0 0
\(101\) 10.2089 8.14136i 1.01583 0.810095i 0.0339137 0.999425i \(-0.489203\pi\)
0.981914 + 0.189330i \(0.0606314\pi\)
\(102\) 0 0
\(103\) 5.97069 + 7.48701i 0.588310 + 0.737717i 0.983505 0.180880i \(-0.0578946\pi\)
−0.395195 + 0.918597i \(0.629323\pi\)
\(104\) 0 0
\(105\) 0.900427 + 2.32546i 0.0878727 + 0.226942i
\(106\) 0 0
\(107\) 4.83564 + 1.10370i 0.467479 + 0.106699i 0.449770 0.893144i \(-0.351506\pi\)
0.0177083 + 0.999843i \(0.494363\pi\)
\(108\) 0 0
\(109\) −4.07697 17.8624i −0.390503 1.71090i −0.662891 0.748716i \(-0.730671\pi\)
0.272388 0.962187i \(-0.412187\pi\)
\(110\) 0 0
\(111\) 2.07189 + 9.07756i 0.196655 + 0.861604i
\(112\) 0 0
\(113\) −1.48222 + 6.49402i −0.139435 + 0.610906i 0.856124 + 0.516770i \(0.172866\pi\)
−0.995559 + 0.0941358i \(0.969991\pi\)
\(114\) 0 0
\(115\) 0.127984 + 0.0616340i 0.0119346 + 0.00574740i
\(116\) 0 0
\(117\) 0.288272i 0.0266508i
\(118\) 0 0
\(119\) −0.0400246 + 0.00584568i −0.00366905 + 0.000535873i
\(120\) 0 0
\(121\) 19.1041 9.20003i 1.73673 0.836367i
\(122\) 0 0
\(123\) 2.41017 + 0.550105i 0.217318 + 0.0496013i
\(124\) 0 0
\(125\) −2.51445 5.22131i −0.224899 0.467008i
\(126\) 0 0
\(127\) −0.726717 + 1.50904i −0.0644857 + 0.133906i −0.930721 0.365731i \(-0.880819\pi\)
0.866235 + 0.499637i \(0.166533\pi\)
\(128\) 0 0
\(129\) 10.9710i 0.965942i
\(130\) 0 0
\(131\) −11.1098 + 13.9313i −0.970669 + 1.21718i 0.00545948 + 0.999985i \(0.498262\pi\)
−0.976128 + 0.217195i \(0.930309\pi\)
\(132\) 0 0
\(133\) −6.72175 9.95652i −0.582850 0.863340i
\(134\) 0 0
\(135\) −1.44875 + 3.00837i −0.124689 + 0.258919i
\(136\) 0 0
\(137\) −11.5875 + 14.5302i −0.989983 + 1.24140i −0.0196056 + 0.999808i \(0.506241\pi\)
−0.970378 + 0.241592i \(0.922330\pi\)
\(138\) 0 0
\(139\) −0.243306 0.305096i −0.0206370 0.0258779i 0.771406 0.636343i \(-0.219554\pi\)
−0.792043 + 0.610465i \(0.790982\pi\)
\(140\) 0 0
\(141\) −3.07158 + 3.85165i −0.258674 + 0.324367i
\(142\) 0 0
\(143\) 2.71621 1.30806i 0.227141 0.109385i
\(144\) 0 0
\(145\) 2.00356 0.457299i 0.166386 0.0379766i
\(146\) 0 0
\(147\) −10.5148 + 3.13837i −0.867249 + 0.258849i
\(148\) 0 0
\(149\) −0.0316917 0.138850i −0.00259629 0.0113751i 0.973613 0.228205i \(-0.0732855\pi\)
−0.976209 + 0.216830i \(0.930428\pi\)
\(150\) 0 0
\(151\) −8.20129 17.0302i −0.667412 1.38589i −0.909526 0.415647i \(-0.863555\pi\)
0.242114 0.970248i \(-0.422159\pi\)
\(152\) 0 0
\(153\) −0.00648603 0.00517243i −0.000524364 0.000418166i
\(154\) 0 0
\(155\) −2.74994 + 2.19301i −0.220881 + 0.176146i
\(156\) 0 0
\(157\) −17.4714 13.9330i −1.39437 1.11198i −0.979352 0.202164i \(-0.935203\pi\)
−0.415022 0.909812i \(-0.636226\pi\)
\(158\) 0 0
\(159\) −16.8232 8.10164i −1.33417 0.642502i
\(160\) 0 0
\(161\) −0.315012 + 0.539900i −0.0248264 + 0.0425501i
\(162\) 0 0
\(163\) −3.05602 2.43709i −0.239366 0.190888i 0.496458 0.868061i \(-0.334634\pi\)
−0.735824 + 0.677173i \(0.763205\pi\)
\(164\) 0 0
\(165\) −5.34872 −0.416397
\(166\) 0 0
\(167\) 8.61377 + 4.14817i 0.666554 + 0.320995i 0.736384 0.676564i \(-0.236532\pi\)
−0.0698306 + 0.997559i \(0.522246\pi\)
\(168\) 0 0
\(169\) −11.4583 + 5.51803i −0.881409 + 0.424464i
\(170\) 0 0
\(171\) 0.548252 2.40205i 0.0419259 0.183689i
\(172\) 0 0
\(173\) 4.07147 + 8.45450i 0.309548 + 0.642784i 0.996470 0.0839475i \(-0.0267528\pi\)
−0.686922 + 0.726731i \(0.741039\pi\)
\(174\) 0 0
\(175\) 11.4443 4.43128i 0.865110 0.334974i
\(176\) 0 0
\(177\) 15.5275 1.16712
\(178\) 0 0
\(179\) −3.27697 + 6.80471i −0.244933 + 0.508608i −0.986801 0.161938i \(-0.948226\pi\)
0.741868 + 0.670545i \(0.233940\pi\)
\(180\) 0 0
\(181\) 1.86582 + 0.425860i 0.138685 + 0.0316539i 0.291300 0.956632i \(-0.405912\pi\)
−0.152615 + 0.988286i \(0.548769\pi\)
\(182\) 0 0
\(183\) −12.2706 + 2.80069i −0.907069 + 0.207033i
\(184\) 0 0
\(185\) −3.48172 + 0.794680i −0.255981 + 0.0584261i
\(186\) 0 0
\(187\) 0.0193058 0.0845841i 0.00141178 0.00618540i
\(188\) 0 0
\(189\) −12.6908 7.40460i −0.923118 0.538606i
\(190\) 0 0
\(191\) −20.6249 + 16.4478i −1.49237 + 1.19012i −0.560063 + 0.828450i \(0.689223\pi\)
−0.932305 + 0.361673i \(0.882206\pi\)
\(192\) 0 0
\(193\) 3.82962 + 4.80219i 0.275662 + 0.345669i 0.900319 0.435230i \(-0.143333\pi\)
−0.624658 + 0.780899i \(0.714761\pi\)
\(194\) 0 0
\(195\) −0.500720 −0.0358573
\(196\) 0 0
\(197\) 0.465162 0.0331414 0.0165707 0.999863i \(-0.494725\pi\)
0.0165707 + 0.999863i \(0.494725\pi\)
\(198\) 0 0
\(199\) 11.6098 + 14.5582i 0.822995 + 1.03200i 0.998867 + 0.0475898i \(0.0151540\pi\)
−0.175872 + 0.984413i \(0.556275\pi\)
\(200\) 0 0
\(201\) 7.06125 5.63116i 0.498062 0.397191i
\(202\) 0 0
\(203\) 1.30690 + 8.94817i 0.0917263 + 0.628039i
\(204\) 0 0
\(205\) −0.210994 + 0.924427i −0.0147365 + 0.0645648i
\(206\) 0 0
\(207\) −0.124986 + 0.0285273i −0.00868715 + 0.00198279i
\(208\) 0 0
\(209\) 25.1207 5.73364i 1.73764 0.396604i
\(210\) 0 0
\(211\) −20.9566 4.78320i −1.44271 0.329289i −0.571663 0.820489i \(-0.693702\pi\)
−0.871047 + 0.491199i \(0.836559\pi\)
\(212\) 0 0
\(213\) 1.93327 4.01447i 0.132465 0.275067i
\(214\) 0 0
\(215\) 4.20795 0.286980
\(216\) 0 0
\(217\) −8.66018 12.8278i −0.587891 0.870808i
\(218\) 0 0
\(219\) 2.28104 + 4.73663i 0.154139 + 0.320072i
\(220\) 0 0
\(221\) 0.00180731 0.00791833i 0.000121573 0.000532645i
\(222\) 0 0
\(223\) −9.57519 + 4.61117i −0.641202 + 0.308787i −0.726086 0.687604i \(-0.758662\pi\)
0.0848835 + 0.996391i \(0.472948\pi\)
\(224\) 0 0
\(225\) 2.26772 + 1.09208i 0.151182 + 0.0728052i
\(226\) 0 0
\(227\) −10.0968 −0.670150 −0.335075 0.942192i \(-0.608762\pi\)
−0.335075 + 0.942192i \(0.608762\pi\)
\(228\) 0 0
\(229\) 16.1208 + 12.8559i 1.06529 + 0.849542i 0.989055 0.147548i \(-0.0471380\pi\)
0.0762369 + 0.997090i \(0.475709\pi\)
\(230\) 0 0
\(231\) 1.86618 23.4622i 0.122786 1.54370i
\(232\) 0 0
\(233\) −18.6175 8.96571i −1.21967 0.587363i −0.290452 0.956890i \(-0.593806\pi\)
−0.929220 + 0.369527i \(0.879520\pi\)
\(234\) 0 0
\(235\) −1.47731 1.17812i −0.0963690 0.0768518i
\(236\) 0 0
\(237\) 9.61727 7.66952i 0.624709 0.498189i
\(238\) 0 0
\(239\) 1.90732 + 1.52104i 0.123374 + 0.0983876i 0.683233 0.730200i \(-0.260573\pi\)
−0.559859 + 0.828588i \(0.689145\pi\)
\(240\) 0 0
\(241\) 5.37926 + 11.1701i 0.346508 + 0.719532i 0.999277 0.0380255i \(-0.0121068\pi\)
−0.652768 + 0.757558i \(0.726393\pi\)
\(242\) 0 0
\(243\) −1.23840 5.42580i −0.0794436 0.348065i
\(244\) 0 0
\(245\) −1.20373 4.03299i −0.0769036 0.257659i
\(246\) 0 0
\(247\) 2.35168 0.536755i 0.149634 0.0341529i
\(248\) 0 0
\(249\) −20.4656 + 9.85569i −1.29695 + 0.624579i
\(250\) 0 0
\(251\) 6.62267 8.30457i 0.418019 0.524180i −0.527583 0.849503i \(-0.676902\pi\)
0.945603 + 0.325323i \(0.105473\pi\)
\(252\) 0 0
\(253\) −0.835930 1.04822i −0.0525545 0.0659012i
\(254\) 0 0
\(255\) −0.00898435 + 0.0112660i −0.000562622 + 0.000705506i
\(256\) 0 0
\(257\) −11.0392 + 22.9231i −0.688604 + 1.42990i 0.203959 + 0.978979i \(0.434619\pi\)
−0.892563 + 0.450922i \(0.851095\pi\)
\(258\) 0 0
\(259\) −2.27109 15.5499i −0.141119 0.966222i
\(260\) 0 0
\(261\) −1.15638 + 1.45006i −0.0715783 + 0.0897563i
\(262\) 0 0
\(263\) 15.3223i 0.944812i 0.881381 + 0.472406i \(0.156614\pi\)
−0.881381 + 0.472406i \(0.843386\pi\)
\(264\) 0 0
\(265\) 3.10741 6.45259i 0.190886 0.396380i
\(266\) 0 0
\(267\) −3.26167 6.77293i −0.199611 0.414497i
\(268\) 0 0
\(269\) −31.4742 7.18379i −1.91902 0.438003i −0.998928 0.0462989i \(-0.985257\pi\)
−0.920091 0.391705i \(-0.871886\pi\)
\(270\) 0 0
\(271\) −2.89788 + 1.39555i −0.176034 + 0.0847734i −0.519825 0.854273i \(-0.674003\pi\)
0.343792 + 0.939046i \(0.388289\pi\)
\(272\) 0 0
\(273\) 0.174703 2.19641i 0.0105735 0.132933i
\(274\) 0 0
\(275\) 26.3227i 1.58732i
\(276\) 0 0
\(277\) −11.9688 5.76386i −0.719134 0.346317i 0.0382663 0.999268i \(-0.487816\pi\)
−0.757400 + 0.652951i \(0.773531\pi\)
\(278\) 0 0
\(279\) 0.706358 3.09475i 0.0422885 0.185278i
\(280\) 0 0
\(281\) 4.33185 + 18.9791i 0.258417 + 1.13220i 0.922944 + 0.384934i \(0.125776\pi\)
−0.664527 + 0.747264i \(0.731367\pi\)
\(282\) 0 0
\(283\) 0.177804 + 0.779009i 0.0105693 + 0.0463073i 0.979938 0.199305i \(-0.0638683\pi\)
−0.969368 + 0.245612i \(0.921011\pi\)
\(284\) 0 0
\(285\) −4.17228 0.952296i −0.247145 0.0564092i
\(286\) 0 0
\(287\) −3.98139 1.24806i −0.235014 0.0736709i
\(288\) 0 0
\(289\) 10.5992 + 13.2910i 0.623481 + 0.781821i
\(290\) 0 0
\(291\) 16.2422 12.9527i 0.952134 0.759301i
\(292\) 0 0
\(293\) 0.330751i 0.0193227i 0.999953 + 0.00966134i \(0.00307535\pi\)
−0.999953 + 0.00966134i \(0.996925\pi\)
\(294\) 0 0
\(295\) 5.95563i 0.346750i
\(296\) 0 0
\(297\) 24.6393 19.6492i 1.42972 1.14016i
\(298\) 0 0
\(299\) −0.0782556 0.0981294i −0.00452564 0.00567497i
\(300\) 0 0
\(301\) −1.46816 + 18.4582i −0.0846236 + 1.06391i
\(302\) 0 0
\(303\) 19.9561 + 4.55484i 1.14645 + 0.261669i
\(304\) 0 0
\(305\) −1.07421 4.70642i −0.0615091 0.269489i
\(306\) 0 0
\(307\) −6.19856 27.1577i −0.353770 1.54997i −0.768395 0.639976i \(-0.778944\pi\)
0.414624 0.909993i \(-0.363913\pi\)
\(308\) 0 0
\(309\) −3.34042 + 14.6353i −0.190030 + 0.832576i
\(310\) 0 0
\(311\) 18.7589 + 9.03380i 1.06372 + 0.512260i 0.882077 0.471105i \(-0.156145\pi\)
0.181642 + 0.983365i \(0.441859\pi\)
\(312\) 0 0
\(313\) 8.00551i 0.452498i 0.974069 + 0.226249i \(0.0726464\pi\)
−0.974069 + 0.226249i \(0.927354\pi\)
\(314\) 0 0
\(315\) 0.435016 0.745575i 0.0245104 0.0420084i
\(316\) 0 0
\(317\) 12.4573 5.99912i 0.699671 0.336944i −0.0500047 0.998749i \(-0.515924\pi\)
0.749676 + 0.661805i \(0.230209\pi\)
\(318\) 0 0
\(319\) −18.9102 4.31612i −1.05877 0.241656i
\(320\) 0 0
\(321\) 3.37357 + 7.00529i 0.188294 + 0.390997i
\(322\) 0 0
\(323\) 0.0301190 0.0625428i 0.00167587 0.00347997i
\(324\) 0 0
\(325\) 2.46420i 0.136689i
\(326\) 0 0
\(327\) 17.9073 22.4551i 0.990278 1.24177i
\(328\) 0 0
\(329\) 5.68325 6.06919i 0.313328 0.334605i
\(330\) 0 0
\(331\) −7.92697 + 16.4605i −0.435706 + 0.904752i 0.561314 + 0.827603i \(0.310296\pi\)
−0.997020 + 0.0771491i \(0.975418\pi\)
\(332\) 0 0
\(333\) 2.00953 2.51987i 0.110121 0.138088i
\(334\) 0 0
\(335\) 2.15985 + 2.70836i 0.118005 + 0.147974i
\(336\) 0 0
\(337\) −9.72562 + 12.1955i −0.529788 + 0.664333i −0.972655 0.232254i \(-0.925390\pi\)
0.442867 + 0.896587i \(0.353961\pi\)
\(338\) 0 0
\(339\) −9.40776 + 4.53054i −0.510960 + 0.246065i
\(340\) 0 0
\(341\) 32.3651 7.38712i 1.75267 0.400035i
\(342\) 0 0
\(343\) 18.1108 3.87306i 0.977889 0.209126i
\(344\) 0 0
\(345\) 0.0495511 + 0.217097i 0.00266774 + 0.0116881i
\(346\) 0 0
\(347\) −6.93676 14.4043i −0.372385 0.773265i 0.627601 0.778535i \(-0.284037\pi\)
−0.999986 + 0.00527002i \(0.998322\pi\)
\(348\) 0 0
\(349\) 7.39975 + 5.90111i 0.396100 + 0.315879i 0.801204 0.598392i \(-0.204193\pi\)
−0.405104 + 0.914271i \(0.632765\pi\)
\(350\) 0 0
\(351\) 2.30661 1.83946i 0.123118 0.0981830i
\(352\) 0 0
\(353\) −10.1340 8.08158i −0.539377 0.430139i 0.315533 0.948915i \(-0.397817\pi\)
−0.854911 + 0.518775i \(0.826388\pi\)
\(354\) 0 0
\(355\) 1.53976 + 0.741510i 0.0817220 + 0.0393552i
\(356\) 0 0
\(357\) −0.0462839 0.0433407i −0.00244960 0.00229383i
\(358\) 0 0
\(359\) 2.16713 + 1.72823i 0.114377 + 0.0912123i 0.679008 0.734131i \(-0.262410\pi\)
−0.564631 + 0.825343i \(0.690982\pi\)
\(360\) 0 0
\(361\) 1.61631 0.0850690
\(362\) 0 0
\(363\) 29.9475 + 14.4220i 1.57184 + 0.756957i
\(364\) 0 0
\(365\) −1.81675 + 0.874900i −0.0950930 + 0.0457944i
\(366\) 0 0
\(367\) 2.28986 10.0325i 0.119530 0.523693i −0.879342 0.476191i \(-0.842017\pi\)
0.998871 0.0475016i \(-0.0151259\pi\)
\(368\) 0 0
\(369\) −0.371293 0.770998i −0.0193287 0.0401365i
\(370\) 0 0
\(371\) 27.2202 + 15.8820i 1.41320 + 0.824552i
\(372\) 0 0
\(373\) 11.9550 0.619005 0.309502 0.950899i \(-0.399838\pi\)
0.309502 + 0.950899i \(0.399838\pi\)
\(374\) 0 0
\(375\) 3.94165 8.18492i 0.203546 0.422668i
\(376\) 0 0
\(377\) −1.77027 0.404054i −0.0911738 0.0208098i
\(378\) 0 0
\(379\) 10.9222 2.49293i 0.561038 0.128053i 0.0674081 0.997725i \(-0.478527\pi\)
0.493629 + 0.869672i \(0.335670\pi\)
\(380\) 0 0
\(381\) −2.55976 + 0.584249i −0.131141 + 0.0299320i
\(382\) 0 0
\(383\) −3.70012 + 16.2113i −0.189067 + 0.828357i 0.788043 + 0.615621i \(0.211095\pi\)
−0.977110 + 0.212736i \(0.931763\pi\)
\(384\) 0 0
\(385\) 8.99900 + 0.715779i 0.458632 + 0.0364795i
\(386\) 0 0
\(387\) −2.96912 + 2.36779i −0.150929 + 0.120362i
\(388\) 0 0
\(389\) 7.77214 + 9.74595i 0.394063 + 0.494139i 0.938798 0.344469i \(-0.111941\pi\)
−0.544735 + 0.838608i \(0.683370\pi\)
\(390\) 0 0
\(391\) −0.00361200 −0.000182667
\(392\) 0 0
\(393\) −27.9327 −1.40902
\(394\) 0 0
\(395\) 2.94167 + 3.68873i 0.148011 + 0.185600i
\(396\) 0 0
\(397\) −2.53902 + 2.02480i −0.127430 + 0.101622i −0.685131 0.728420i \(-0.740255\pi\)
0.557701 + 0.830042i \(0.311684\pi\)
\(398\) 0 0
\(399\) 5.63298 17.9695i 0.282002 0.899600i
\(400\) 0 0
\(401\) 0.282584 1.23808i 0.0141116 0.0618269i −0.967382 0.253322i \(-0.918477\pi\)
0.981493 + 0.191496i \(0.0613338\pi\)
\(402\) 0 0
\(403\) 3.02986 0.691545i 0.150928 0.0344483i
\(404\) 0 0
\(405\) −4.14880 + 0.946937i −0.206156 + 0.0470537i
\(406\) 0 0
\(407\) 32.8615 + 7.50043i 1.62889 + 0.371783i
\(408\) 0 0
\(409\) 12.4653 25.8844i 0.616369 1.27990i −0.326014 0.945365i \(-0.605706\pi\)
0.942382 0.334538i \(-0.108580\pi\)
\(410\) 0 0
\(411\) −29.1336 −1.43705
\(412\) 0 0
\(413\) −26.1244 2.07793i −1.28550 0.102248i
\(414\) 0 0
\(415\) −3.78018 7.84962i −0.185562 0.385323i
\(416\) 0 0
\(417\) 0.136122 0.596391i 0.00666595 0.0292054i
\(418\) 0 0
\(419\) 31.6865 15.2594i 1.54799 0.745471i 0.551905 0.833907i \(-0.313901\pi\)
0.996082 + 0.0884361i \(0.0281869\pi\)
\(420\) 0 0
\(421\) 23.4369 + 11.2866i 1.14225 + 0.550077i 0.906696 0.421785i \(-0.138596\pi\)
0.235551 + 0.971862i \(0.424311\pi\)
\(422\) 0 0
\(423\) 1.70530 0.0829147
\(424\) 0 0
\(425\) 0.0554436 + 0.0442148i 0.00268941 + 0.00214473i
\(426\) 0 0
\(427\) 21.0196 3.06995i 1.01721 0.148565i
\(428\) 0 0
\(429\) 4.25793 + 2.05051i 0.205575 + 0.0989997i
\(430\) 0 0
\(431\) −17.5563 14.0007i −0.845659 0.674390i 0.101612 0.994824i \(-0.467600\pi\)
−0.947271 + 0.320434i \(0.896171\pi\)
\(432\) 0 0
\(433\) 23.3517 18.6224i 1.12221 0.894935i 0.126927 0.991912i \(-0.459489\pi\)
0.995287 + 0.0969770i \(0.0309173\pi\)
\(434\) 0 0
\(435\) 2.51871 + 2.00860i 0.120763 + 0.0963050i
\(436\) 0 0
\(437\) −0.465442 0.966500i −0.0222651 0.0462339i
\(438\) 0 0
\(439\) −4.30520 18.8623i −0.205476 0.900249i −0.967534 0.252740i \(-0.918668\pi\)
0.762058 0.647509i \(-0.224189\pi\)
\(440\) 0 0
\(441\) 3.11869 + 2.16833i 0.148509 + 0.103254i
\(442\) 0 0
\(443\) 26.9869 6.15958i 1.28218 0.292650i 0.473448 0.880822i \(-0.343009\pi\)
0.808736 + 0.588171i \(0.200152\pi\)
\(444\) 0 0
\(445\) 2.59778 1.25102i 0.123146 0.0593042i
\(446\) 0 0
\(447\) 0.139200 0.174551i 0.00658394 0.00825600i
\(448\) 0 0
\(449\) 1.34377 + 1.68504i 0.0634166 + 0.0795219i 0.812528 0.582922i \(-0.198091\pi\)
−0.749111 + 0.662444i \(0.769519\pi\)
\(450\) 0 0
\(451\) 5.57986 6.99692i 0.262745 0.329472i
\(452\) 0 0
\(453\) 12.8563 26.6965i 0.604044 1.25431i
\(454\) 0 0
\(455\) 0.842441 + 0.0670076i 0.0394942 + 0.00314137i
\(456\) 0 0
\(457\) −17.0661 + 21.4002i −0.798319 + 1.00106i 0.201448 + 0.979499i \(0.435435\pi\)
−0.999768 + 0.0215614i \(0.993136\pi\)
\(458\) 0 0
\(459\) 0.0849030i 0.00396293i
\(460\) 0 0
\(461\) −0.184354 + 0.382815i −0.00858622 + 0.0178295i −0.905218 0.424948i \(-0.860292\pi\)
0.896632 + 0.442777i \(0.146007\pi\)
\(462\) 0 0
\(463\) 10.7832 + 22.3916i 0.501139 + 1.04063i 0.986110 + 0.166096i \(0.0531160\pi\)
−0.484971 + 0.874530i \(0.661170\pi\)
\(464\) 0 0
\(465\) −5.37549 1.22692i −0.249283 0.0568971i
\(466\) 0 0
\(467\) −15.1510 + 7.29634i −0.701105 + 0.337634i −0.750247 0.661157i \(-0.770066\pi\)
0.0491422 + 0.998792i \(0.484351\pi\)
\(468\) 0 0
\(469\) −12.6338 + 8.52923i −0.583376 + 0.393843i
\(470\) 0 0
\(471\) 35.0309i 1.61414i
\(472\) 0 0
\(473\) −35.7828 17.2321i −1.64530 0.792333i
\(474\) 0 0
\(475\) −4.68655 + 20.5331i −0.215034 + 0.942123i
\(476\) 0 0
\(477\) 1.43826 + 6.30145i 0.0658536 + 0.288523i
\(478\) 0 0
\(479\) 1.99233 + 8.72898i 0.0910320 + 0.398837i 0.999831 0.0183974i \(-0.00585641\pi\)
−0.908799 + 0.417235i \(0.862999\pi\)
\(480\) 0 0
\(481\) 3.07633 + 0.702153i 0.140269 + 0.0320154i
\(482\) 0 0
\(483\) −0.969588 + 0.141610i −0.0441178 + 0.00644350i
\(484\) 0 0
\(485\) 4.96805 + 6.22974i 0.225587 + 0.282878i
\(486\) 0 0
\(487\) −18.2801 + 14.5779i −0.828350 + 0.660587i −0.942990 0.332820i \(-0.892000\pi\)
0.114640 + 0.993407i \(0.463428\pi\)
\(488\) 0 0
\(489\) 6.12743i 0.277092i
\(490\) 0 0
\(491\) 23.0316i 1.03940i −0.854348 0.519701i \(-0.826043\pi\)
0.854348 0.519701i \(-0.173957\pi\)
\(492\) 0 0
\(493\) −0.0408548 + 0.0325806i −0.00184001 + 0.00146736i
\(494\) 0 0
\(495\) 1.15438 + 1.44754i 0.0518854 + 0.0650622i
\(496\) 0 0
\(497\) −3.78987 + 6.49546i −0.169999 + 0.291361i
\(498\) 0 0
\(499\) 25.2438 + 5.76173i 1.13007 + 0.257930i 0.746372 0.665529i \(-0.231794\pi\)
0.383695 + 0.923460i \(0.374651\pi\)
\(500\) 0 0
\(501\) 3.33495 + 14.6114i 0.148995 + 0.652788i
\(502\) 0 0
\(503\) 1.46034 + 6.39816i 0.0651133 + 0.285280i 0.996993 0.0774865i \(-0.0246895\pi\)
−0.931880 + 0.362766i \(0.881832\pi\)
\(504\) 0 0
\(505\) −1.74702 + 7.65421i −0.0777415 + 0.340608i
\(506\) 0 0
\(507\) −17.9621 8.65007i −0.797723 0.384163i
\(508\) 0 0
\(509\) 28.9425i 1.28286i 0.767183 + 0.641428i \(0.221658\pi\)
−0.767183 + 0.641428i \(0.778342\pi\)
\(510\) 0 0
\(511\) −3.20389 8.27444i −0.141732 0.366040i
\(512\) 0 0
\(513\) 22.7183 10.9406i 1.00304 0.483038i
\(514\) 0 0
\(515\) −5.61343 1.28123i −0.247357 0.0564577i
\(516\) 0 0
\(517\) 7.73794 + 16.0680i 0.340314 + 0.706670i
\(518\) 0 0
\(519\) −6.38244 + 13.2533i −0.280158 + 0.581754i
\(520\) 0 0
\(521\) 28.1910i 1.23507i 0.786543 + 0.617536i \(0.211869\pi\)
−0.786543 + 0.617536i \(0.788131\pi\)
\(522\) 0 0
\(523\) −3.51846 + 4.41201i −0.153852 + 0.192924i −0.852784 0.522264i \(-0.825088\pi\)
0.698932 + 0.715188i \(0.253659\pi\)
\(524\) 0 0
\(525\) 16.6165 + 9.69511i 0.725202 + 0.423129i
\(526\) 0 0
\(527\) 0.0388048 0.0805790i 0.00169036 0.00351007i
\(528\) 0 0
\(529\) 14.3055 17.9385i 0.621977 0.779934i
\(530\) 0 0
\(531\) −3.35120 4.20227i −0.145430 0.182363i
\(532\) 0 0
\(533\) 0.522358 0.655017i 0.0226259 0.0283719i
\(534\) 0 0
\(535\) −2.68690 + 1.29394i −0.116165 + 0.0559420i
\(536\) 0 0
\(537\) −11.5427 + 2.63455i −0.498104 + 0.113689i
\(538\) 0 0
\(539\) −6.27955 + 39.2245i −0.270479 + 1.68952i
\(540\) 0 0
\(541\) −2.16996 9.50722i −0.0932939 0.408747i 0.906619 0.421950i \(-0.138654\pi\)
−0.999913 + 0.0132031i \(0.995797\pi\)
\(542\) 0 0
\(543\) 1.30168 + 2.70297i 0.0558605 + 0.115996i
\(544\) 0 0
\(545\) 8.61271 + 6.86841i 0.368928 + 0.294210i
\(546\) 0 0
\(547\) 20.8866 16.6565i 0.893045 0.712179i −0.0652781 0.997867i \(-0.520793\pi\)
0.958323 + 0.285688i \(0.0922220\pi\)
\(548\) 0 0
\(549\) 3.40624 + 2.71638i 0.145375 + 0.115932i
\(550\) 0 0
\(551\) −13.9825 6.73360i −0.595673 0.286861i
\(552\) 0 0
\(553\) −17.2070 + 11.6166i −0.731716 + 0.493990i
\(554\) 0 0
\(555\) −4.37693 3.49049i −0.185791 0.148163i
\(556\) 0 0
\(557\) 16.1878 0.685900 0.342950 0.939354i \(-0.388574\pi\)
0.342950 + 0.939354i \(0.388574\pi\)
\(558\) 0 0
\(559\) −3.34981 1.61318i −0.141682 0.0682303i
\(560\) 0 0
\(561\) 0.122535 0.0590099i 0.00517344 0.00249140i
\(562\) 0 0
\(563\) 2.82099 12.3596i 0.118891 0.520894i −0.880050 0.474881i \(-0.842491\pi\)
0.998941 0.0460134i \(-0.0146517\pi\)
\(564\) 0 0
\(565\) −1.73770 3.60837i −0.0731056 0.151805i
\(566\) 0 0
\(567\) −2.70622 18.5292i −0.113651 0.778151i
\(568\) 0 0
\(569\) −15.3269 −0.642535 −0.321268 0.946988i \(-0.604109\pi\)
−0.321268 + 0.946988i \(0.604109\pi\)
\(570\) 0 0
\(571\) 12.4813 25.9177i 0.522327 1.08462i −0.458311 0.888792i \(-0.651545\pi\)
0.980638 0.195831i \(-0.0627404\pi\)
\(572\) 0 0
\(573\) −40.3169 9.20207i −1.68426 0.384422i
\(574\) 0 0
\(575\) 1.06840 0.243856i 0.0445555 0.0101695i
\(576\) 0 0
\(577\) 18.9234 4.31915i 0.787793 0.179809i 0.190346 0.981717i \(-0.439039\pi\)
0.597447 + 0.801908i \(0.296182\pi\)
\(578\) 0 0
\(579\) −2.14256 + 9.38715i −0.0890415 + 0.390117i
\(580\) 0 0
\(581\) 35.7513 13.8430i 1.48322 0.574306i
\(582\) 0 0
\(583\) −52.8484 + 42.1452i −2.18876 + 1.74547i
\(584\) 0 0
\(585\) 0.108067 + 0.135512i 0.00446802 + 0.00560272i
\(586\) 0 0
\(587\) −46.2068 −1.90716 −0.953580 0.301141i \(-0.902633\pi\)
−0.953580 + 0.301141i \(0.902633\pi\)
\(588\) 0 0
\(589\) 26.5617 1.09445
\(590\) 0 0
\(591\) 0.454641 + 0.570102i 0.0187015 + 0.0234509i
\(592\) 0 0
\(593\) −26.5710 + 21.1896i −1.09114 + 0.870154i −0.992165 0.124936i \(-0.960127\pi\)
−0.0989739 + 0.995090i \(0.531556\pi\)
\(594\) 0 0
\(595\) 0.0166234 0.0177523i 0.000681495 0.000727774i
\(596\) 0 0
\(597\) −6.49532 + 28.4578i −0.265836 + 1.16470i
\(598\) 0 0
\(599\) −20.6554 + 4.71446i −0.843957 + 0.192628i −0.622576 0.782560i \(-0.713914\pi\)
−0.221382 + 0.975187i \(0.571057\pi\)
\(600\) 0 0
\(601\) −16.2174 + 3.70152i −0.661521 + 0.150988i −0.540084 0.841611i \(-0.681608\pi\)
−0.121437 + 0.992599i \(0.538750\pi\)
\(602\) 0 0
\(603\) −3.04796 0.695677i −0.124122 0.0283301i
\(604\) 0 0
\(605\) −5.53159 + 11.4865i −0.224891 + 0.466991i
\(606\) 0 0
\(607\) 39.8869 1.61896 0.809479 0.587149i \(-0.199750\pi\)
0.809479 + 0.587149i \(0.199750\pi\)
\(608\) 0 0
\(609\) −9.68953 + 10.3475i −0.392640 + 0.419303i
\(610\) 0 0
\(611\) 0.724387 + 1.50421i 0.0293056 + 0.0608536i
\(612\) 0 0
\(613\) −3.58047 + 15.6871i −0.144614 + 0.633594i 0.849715 + 0.527243i \(0.176774\pi\)
−0.994329 + 0.106352i \(0.966083\pi\)
\(614\) 0 0
\(615\) −1.33920 + 0.644924i −0.0540017 + 0.0260059i
\(616\) 0 0
\(617\) −40.1516 19.3360i −1.61644 0.778437i −0.616481 0.787370i \(-0.711442\pi\)
−0.999960 + 0.00893318i \(0.997156\pi\)
\(618\) 0 0
\(619\) −21.5643 −0.866743 −0.433371 0.901215i \(-0.642676\pi\)
−0.433371 + 0.901215i \(0.642676\pi\)
\(620\) 0 0
\(621\) −1.02580 0.818044i −0.0411637 0.0328270i
\(622\) 0 0
\(623\) 4.58126 + 11.8317i 0.183544 + 0.474025i
\(624\) 0 0
\(625\) −17.7563 8.55099i −0.710253 0.342040i
\(626\) 0 0
\(627\) 31.5797 + 25.1840i 1.26117 + 1.00575i
\(628\) 0 0
\(629\) 0.0709964 0.0566177i 0.00283081 0.00225750i
\(630\) 0 0
\(631\) −27.6690 22.0653i −1.10148 0.878405i −0.108203 0.994129i \(-0.534510\pi\)
−0.993281 + 0.115724i \(0.963081\pi\)
\(632\) 0 0
\(633\) −14.6203 30.3594i −0.581105 1.20668i
\(634\) 0 0
\(635\) −0.224090 0.981804i −0.00889275 0.0389617i
\(636\) 0 0
\(637\) −0.587859 + 3.67200i −0.0232918 + 0.145490i
\(638\) 0 0
\(639\) −1.50369 + 0.343208i −0.0594852 + 0.0135771i
\(640\) 0 0
\(641\) 0.149827 0.0721528i 0.00591781 0.00284987i −0.430922 0.902389i \(-0.641812\pi\)
0.436840 + 0.899539i \(0.356097\pi\)
\(642\) 0 0
\(643\) 26.6992 33.4797i 1.05291 1.32031i 0.107582 0.994196i \(-0.465689\pi\)
0.945331 0.326114i \(-0.105739\pi\)
\(644\) 0 0
\(645\) 4.11278 + 5.15726i 0.161941 + 0.203067i
\(646\) 0 0
\(647\) −3.44553 + 4.32055i −0.135458 + 0.169858i −0.844934 0.534871i \(-0.820360\pi\)
0.709476 + 0.704729i \(0.248932\pi\)
\(648\) 0 0
\(649\) 24.3890 50.6444i 0.957353 1.98796i
\(650\) 0 0
\(651\) 7.25742 23.1516i 0.284441 0.907382i
\(652\) 0 0
\(653\) −15.9289 + 19.9742i −0.623344 + 0.781649i −0.988811 0.149175i \(-0.952338\pi\)
0.365466 + 0.930825i \(0.380910\pi\)
\(654\) 0 0
\(655\) 10.7137i 0.418617i
\(656\) 0 0
\(657\) 0.789590 1.63960i 0.0308048 0.0639669i
\(658\) 0 0
\(659\) −3.91741 8.13459i −0.152601 0.316878i 0.810628 0.585561i \(-0.199126\pi\)
−0.963229 + 0.268683i \(0.913412\pi\)
\(660\) 0 0
\(661\) −3.38856 0.773416i −0.131800 0.0300824i 0.156112 0.987739i \(-0.450104\pi\)
−0.287912 + 0.957657i \(0.592961\pi\)
\(662\) 0 0
\(663\) 0.0114711 0.00552421i 0.000445502 0.000214542i
\(664\) 0 0
\(665\) 6.89225 + 2.16054i 0.267270 + 0.0837823i
\(666\) 0 0
\(667\) 0.807523i 0.0312674i
\(668\) 0 0
\(669\) −15.0101 7.22847i −0.580323 0.279469i
\(670\) 0 0
\(671\) −10.1387 + 44.4207i −0.391401 + 1.71484i
\(672\) 0 0
\(673\) −3.03339 13.2901i −0.116929 0.512297i −0.999141 0.0414454i \(-0.986804\pi\)
0.882212 0.470852i \(-0.156053\pi\)
\(674\) 0 0
\(675\) 5.73203 + 25.1137i 0.220626 + 0.966626i
\(676\) 0 0
\(677\) 30.4123 + 6.94141i 1.16884 + 0.266780i 0.762528 0.646955i \(-0.223958\pi\)
0.406311 + 0.913735i \(0.366815\pi\)
\(678\) 0 0
\(679\) −29.0602 + 19.6188i −1.11523 + 0.752901i
\(680\) 0 0
\(681\) −9.86846 12.3747i −0.378160 0.474198i
\(682\) 0 0
\(683\) −15.6111 + 12.4495i −0.597343 + 0.476365i −0.874874 0.484351i \(-0.839056\pi\)
0.277530 + 0.960717i \(0.410484\pi\)
\(684\) 0 0
\(685\) 11.1743i 0.426947i
\(686\) 0 0
\(687\) 32.3228i 1.23319i
\(688\) 0 0
\(689\) −4.94740 + 3.94542i −0.188481 + 0.150308i
\(690\) 0 0
\(691\) −0.808127 1.01336i −0.0307426 0.0385500i 0.766223 0.642575i \(-0.222134\pi\)
−0.796965 + 0.604025i \(0.793563\pi\)
\(692\) 0 0
\(693\) −6.75243 + 4.55864i −0.256504 + 0.173168i
\(694\) 0 0
\(695\) 0.228748 + 0.0522101i 0.00867689 + 0.00198044i
\(696\) 0 0
\(697\) −0.00536503 0.0235057i −0.000203215 0.000890344i
\(698\) 0 0
\(699\) −7.20804 31.5805i −0.272633 1.19448i
\(700\) 0 0
\(701\) 8.19084 35.8864i 0.309364 1.35541i −0.546175 0.837671i \(-0.683916\pi\)
0.855538 0.517740i \(-0.173226\pi\)
\(702\) 0 0
\(703\) 24.2983 + 11.7015i 0.916429 + 0.441329i
\(704\) 0 0
\(705\) 2.96206i 0.111558i
\(706\) 0 0
\(707\) −32.9657 10.3339i −1.23980 0.388647i
\(708\) 0 0
\(709\) 36.8366 17.7396i 1.38343 0.666223i 0.413699 0.910414i \(-0.364237\pi\)
0.969727 + 0.244191i \(0.0785223\pi\)
\(710\) 0 0
\(711\) −4.15126 0.947497i −0.155684 0.0355339i
\(712\) 0 0
\(713\) −0.599667 1.24522i −0.0224577 0.0466339i
\(714\) 0 0
\(715\) −0.786480 + 1.63314i −0.0294127 + 0.0610761i
\(716\) 0 0
\(717\) 3.82424i 0.142819i
\(718\) 0 0
\(719\) 20.5798 25.8063i 0.767497 0.962411i −0.232451 0.972608i \(-0.574674\pi\)
0.999948 + 0.0101970i \(0.00324586\pi\)
\(720\) 0 0
\(721\) 7.57866 24.1763i 0.282244 0.900374i
\(722\) 0 0
\(723\) −8.43252 + 17.5103i −0.313609 + 0.651216i
\(724\) 0 0
\(725\) 9.88495 12.3953i 0.367118 0.460351i
\(726\) 0 0
\(727\) −13.8787 17.4034i −0.514734 0.645456i 0.454747 0.890620i \(-0.349730\pi\)
−0.969482 + 0.245164i \(0.921158\pi\)
\(728\) 0 0
\(729\) 18.6780 23.4215i 0.691778 0.867463i
\(730\) 0 0
\(731\) −0.0964011 + 0.0464243i −0.00356552 + 0.00171707i
\(732\) 0 0
\(733\) −26.8704 + 6.13299i −0.992480 + 0.226527i −0.687778 0.725921i \(-0.741414\pi\)
−0.304702 + 0.952448i \(0.598557\pi\)
\(734\) 0 0
\(735\) 3.76633 5.41707i 0.138923 0.199812i
\(736\) 0 0
\(737\) −7.27542 31.8757i −0.267994 1.17416i
\(738\) 0 0
\(739\) 15.7143 + 32.6310i 0.578058 + 1.20035i 0.960992 + 0.276575i \(0.0891994\pi\)
−0.382934 + 0.923776i \(0.625086\pi\)
\(740\) 0 0
\(741\) 2.95633 + 2.35760i 0.108604 + 0.0866085i
\(742\) 0 0
\(743\) −29.2699 + 23.3419i −1.07381 + 0.856333i −0.990129 0.140160i \(-0.955238\pi\)
−0.0836785 + 0.996493i \(0.526667\pi\)
\(744\) 0 0
\(745\) 0.0669497 + 0.0533906i 0.00245285 + 0.00195608i
\(746\) 0 0
\(747\) 7.08422 + 3.41158i 0.259198 + 0.124823i
\(748\) 0 0
\(749\) −4.73843 12.2376i −0.173138 0.447151i
\(750\) 0 0
\(751\) −1.87218 1.49302i −0.0683169 0.0544809i 0.588736 0.808325i \(-0.299626\pi\)
−0.657053 + 0.753844i \(0.728197\pi\)
\(752\) 0 0
\(753\) 16.6510 0.606795
\(754\) 0 0
\(755\) 10.2395 + 4.93109i 0.372654 + 0.179461i
\(756\) 0 0
\(757\) 5.80434 2.79522i 0.210962 0.101594i −0.325419 0.945570i \(-0.605505\pi\)
0.536381 + 0.843976i \(0.319791\pi\)
\(758\) 0 0
\(759\) 0.467678 2.04903i 0.0169756 0.0743751i
\(760\) 0 0
\(761\) −4.63303 9.62059i −0.167947 0.348746i 0.799960 0.600053i \(-0.204854\pi\)
−0.967907 + 0.251307i \(0.919140\pi\)
\(762\) 0 0
\(763\) −33.1333 + 35.3833i −1.19951 + 1.28096i
\(764\) 0 0
\(765\) 0.00498799 0.000180341
\(766\) 0 0
\(767\) 2.28318 4.74107i 0.0824408 0.171190i
\(768\) 0 0
\(769\) −6.17361 1.40909i −0.222626 0.0508129i 0.109753 0.993959i \(-0.464994\pi\)
−0.332379 + 0.943146i \(0.607851\pi\)
\(770\) 0 0
\(771\) −38.8840 + 8.87501i −1.40037 + 0.319626i
\(772\) 0 0
\(773\) 14.0641 3.21005i 0.505852 0.115457i 0.0380238 0.999277i \(-0.487894\pi\)
0.467828 + 0.883819i \(0.345037\pi\)
\(774\) 0 0
\(775\) −6.03806 + 26.4545i −0.216894 + 0.950273i
\(776\) 0 0
\(777\) 16.8382 17.9816i 0.604067 0.645087i
\(778\) 0 0
\(779\) 5.59833 4.46452i 0.200581 0.159958i
\(780\) 0 0
\(781\) −10.0570 12.6110i −0.359866 0.451258i
\(782\) 0 0
\(783\) −18.9815 −0.678342
\(784\) 0 0
\(785\) 13.4362 0.479558
\(786\) 0 0
\(787\) −13.3793 16.7771i −0.476920 0.598039i 0.483930 0.875106i \(-0.339209\pi\)
−0.960850 + 0.277068i \(0.910637\pi\)
\(788\) 0 0
\(789\) −18.7790 + 14.9757i −0.668549 + 0.533150i
\(790\) 0 0
\(791\) 16.4345 6.36347i 0.584342 0.226259i
\(792\) 0 0
\(793\) −0.949136 + 4.15844i −0.0337048 + 0.147670i
\(794\) 0 0
\(795\) 10.9454 2.49822i 0.388194 0.0886028i
\(796\) 0 0