Properties

Label 1152.2.r.h.193.4
Level $1152$
Weight $2$
Character 1152.193
Analytic conductor $9.199$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 193.4
Character \(\chi\) \(=\) 1152.193
Dual form 1152.2.r.h.961.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.29861 - 1.14613i) q^{3} +(2.41023 + 1.39154i) q^{5} +(-0.551569 - 0.955345i) q^{7} +(0.372790 + 2.97675i) q^{9} +O(q^{10})\) \(q+(-1.29861 - 1.14613i) q^{3} +(2.41023 + 1.39154i) q^{5} +(-0.551569 - 0.955345i) q^{7} +(0.372790 + 2.97675i) q^{9} +(-2.58435 + 1.49208i) q^{11} +(0.220334 + 0.127210i) q^{13} +(-1.53506 - 4.56950i) q^{15} +3.78309 q^{17} +6.46552i q^{19} +(-0.378672 + 1.87279i) q^{21} +(-2.63820 + 4.56950i) q^{23} +(1.37279 + 2.37774i) q^{25} +(2.92762 - 4.29291i) q^{27} +(-8.06422 + 4.65588i) q^{29} +(3.74134 - 6.48019i) q^{31} +(5.06618 + 1.02436i) q^{33} -3.07013i q^{35} +2.52867i q^{37} +(-0.140330 - 0.417727i) q^{39} +(-0.764334 + 1.32387i) q^{41} +(-4.85118 + 2.80083i) q^{43} +(-3.24377 + 7.69339i) q^{45} +(5.13607 + 8.89594i) q^{47} +(2.89154 - 5.00830i) q^{49} +(-4.91277 - 4.33590i) q^{51} +0.962492i q^{53} -8.30515 q^{55} +(7.41030 - 8.39620i) q^{57} +(6.76187 + 3.90397i) q^{59} +(-11.5283 + 6.65588i) q^{61} +(2.63820 - 1.99802i) q^{63} +(0.354036 + 0.613209i) q^{65} +(6.55465 + 3.78433i) q^{67} +(8.66322 - 2.91030i) q^{69} +4.17327 q^{71} +5.34926 q^{73} +(0.942470 - 4.66116i) q^{75} +(2.85089 + 1.64596i) q^{77} +(-1.94630 - 3.37110i) q^{79} +(-8.72205 + 2.21940i) q^{81} +(14.4208 - 8.32584i) q^{83} +(9.11809 + 5.26433i) q^{85} +(15.8085 + 3.19643i) q^{87} +10.0948 q^{89} -0.280660i q^{91} +(-12.2857 + 4.12721i) q^{93} +(-8.99705 + 15.5834i) q^{95} +(7.54742 + 13.0725i) q^{97} +(-5.40495 - 7.13673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{9} + O(q^{10}) \) \( 24 q + 4 q^{9} + 8 q^{17} + 28 q^{25} - 44 q^{33} + 28 q^{41} + 28 q^{49} + 100 q^{57} + 40 q^{65} - 120 q^{73} + 44 q^{81} - 16 q^{89} + 52 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) −1.29861 1.14613i −0.749754 0.661716i
\(4\) 0 0
\(5\) 2.41023 + 1.39154i 1.07789 + 0.622317i 0.930325 0.366736i \(-0.119525\pi\)
0.147560 + 0.989053i \(0.452858\pi\)
\(6\) 0 0
\(7\) −0.551569 0.955345i −0.208473 0.361086i 0.742760 0.669557i \(-0.233516\pi\)
−0.951234 + 0.308471i \(0.900183\pi\)
\(8\) 0 0
\(9\) 0.372790 + 2.97675i 0.124263 + 0.992249i
\(10\) 0 0
\(11\) −2.58435 + 1.49208i −0.779211 + 0.449878i −0.836151 0.548500i \(-0.815199\pi\)
0.0569396 + 0.998378i \(0.481866\pi\)
\(12\) 0 0
\(13\) 0.220334 + 0.127210i 0.0611096 + 0.0352817i 0.530244 0.847845i \(-0.322101\pi\)
−0.469134 + 0.883127i \(0.655434\pi\)
\(14\) 0 0
\(15\) −1.53506 4.56950i −0.396352 1.17984i
\(16\) 0 0
\(17\) 3.78309 0.917534 0.458767 0.888557i \(-0.348291\pi\)
0.458767 + 0.888557i \(0.348291\pi\)
\(18\) 0 0
\(19\) 6.46552i 1.48329i 0.670792 + 0.741646i \(0.265954\pi\)
−0.670792 + 0.741646i \(0.734046\pi\)
\(20\) 0 0
\(21\) −0.378672 + 1.87279i −0.0826329 + 0.408676i
\(22\) 0 0
\(23\) −2.63820 + 4.56950i −0.550103 + 0.952806i 0.448164 + 0.893952i \(0.352078\pi\)
−0.998267 + 0.0588548i \(0.981255\pi\)
\(24\) 0 0
\(25\) 1.37279 + 2.37774i 0.274558 + 0.475548i
\(26\) 0 0
\(27\) 2.92762 4.29291i 0.563420 0.826170i
\(28\) 0 0
\(29\) −8.06422 + 4.65588i −1.49749 + 0.864575i −0.999996 0.00289371i \(-0.999079\pi\)
−0.497492 + 0.867469i \(0.665746\pi\)
\(30\) 0 0
\(31\) 3.74134 6.48019i 0.671964 1.16388i −0.305382 0.952230i \(-0.598784\pi\)
0.977346 0.211646i \(-0.0678825\pi\)
\(32\) 0 0
\(33\) 5.06618 + 1.02436i 0.881908 + 0.178319i
\(34\) 0 0
\(35\) 3.07013i 0.518946i
\(36\) 0 0
\(37\) 2.52867i 0.415711i 0.978160 + 0.207855i \(0.0666483\pi\)
−0.978160 + 0.207855i \(0.933352\pi\)
\(38\) 0 0
\(39\) −0.140330 0.417727i −0.0224708 0.0668898i
\(40\) 0 0
\(41\) −0.764334 + 1.32387i −0.119369 + 0.206753i −0.919518 0.393048i \(-0.871420\pi\)
0.800149 + 0.599802i \(0.204754\pi\)
\(42\) 0 0
\(43\) −4.85118 + 2.80083i −0.739798 + 0.427123i −0.821996 0.569493i \(-0.807139\pi\)
0.0821976 + 0.996616i \(0.473806\pi\)
\(44\) 0 0
\(45\) −3.24377 + 7.69339i −0.483552 + 1.14686i
\(46\) 0 0
\(47\) 5.13607 + 8.89594i 0.749173 + 1.29761i 0.948219 + 0.317616i \(0.102882\pi\)
−0.199046 + 0.979990i \(0.563784\pi\)
\(48\) 0 0
\(49\) 2.89154 5.00830i 0.413078 0.715472i
\(50\) 0 0
\(51\) −4.91277 4.33590i −0.687925 0.607147i
\(52\) 0 0
\(53\) 0.962492i 0.132208i 0.997813 + 0.0661042i \(0.0210570\pi\)
−0.997813 + 0.0661042i \(0.978943\pi\)
\(54\) 0 0
\(55\) −8.30515 −1.11987
\(56\) 0 0
\(57\) 7.41030 8.39620i 0.981518 1.11210i
\(58\) 0 0
\(59\) 6.76187 + 3.90397i 0.880321 + 0.508253i 0.870764 0.491701i \(-0.163625\pi\)
0.00955667 + 0.999954i \(0.496958\pi\)
\(60\) 0 0
\(61\) −11.5283 + 6.65588i −1.47605 + 0.852198i −0.999635 0.0270225i \(-0.991397\pi\)
−0.476415 + 0.879220i \(0.658064\pi\)
\(62\) 0 0
\(63\) 2.63820 1.99802i 0.332382 0.251727i
\(64\) 0 0
\(65\) 0.354036 + 0.613209i 0.0439128 + 0.0760592i
\(66\) 0 0
\(67\) 6.55465 + 3.78433i 0.800778 + 0.462329i 0.843743 0.536747i \(-0.180347\pi\)
−0.0429654 + 0.999077i \(0.513681\pi\)
\(68\) 0 0
\(69\) 8.66322 2.91030i 1.04293 0.350359i
\(70\) 0 0
\(71\) 4.17327 0.495275 0.247638 0.968853i \(-0.420346\pi\)
0.247638 + 0.968853i \(0.420346\pi\)
\(72\) 0 0
\(73\) 5.34926 0.626084 0.313042 0.949739i \(-0.398652\pi\)
0.313042 + 0.949739i \(0.398652\pi\)
\(74\) 0 0
\(75\) 0.942470 4.66116i 0.108827 0.538224i
\(76\) 0 0
\(77\) 2.85089 + 1.64596i 0.324889 + 0.187575i
\(78\) 0 0
\(79\) −1.94630 3.37110i −0.218976 0.379278i 0.735519 0.677504i \(-0.236938\pi\)
−0.954495 + 0.298226i \(0.903605\pi\)
\(80\) 0 0
\(81\) −8.72205 + 2.21940i −0.969117 + 0.246601i
\(82\) 0 0
\(83\) 14.4208 8.32584i 1.58289 0.913880i 0.588451 0.808533i \(-0.299738\pi\)
0.994436 0.105347i \(-0.0335954\pi\)
\(84\) 0 0
\(85\) 9.11809 + 5.26433i 0.988996 + 0.570997i
\(86\) 0 0
\(87\) 15.8085 + 3.19643i 1.69485 + 0.342693i
\(88\) 0 0
\(89\) 10.0948 1.07005 0.535026 0.844836i \(-0.320302\pi\)
0.535026 + 0.844836i \(0.320302\pi\)
\(90\) 0 0
\(91\) 0.280660i 0.0294211i
\(92\) 0 0
\(93\) −12.2857 + 4.12721i −1.27396 + 0.427972i
\(94\) 0 0
\(95\) −8.99705 + 15.5834i −0.923078 + 1.59882i
\(96\) 0 0
\(97\) 7.54742 + 13.0725i 0.766325 + 1.32731i 0.939543 + 0.342430i \(0.111250\pi\)
−0.173219 + 0.984883i \(0.555417\pi\)
\(98\) 0 0
\(99\) −5.40495 7.13673i −0.543218 0.717268i
\(100\) 0 0
\(101\) 4.51798 2.60846i 0.449556 0.259551i −0.258087 0.966122i \(-0.583092\pi\)
0.707643 + 0.706571i \(0.249759\pi\)
\(102\) 0 0
\(103\) −8.20620 + 14.2136i −0.808581 + 1.40050i 0.105266 + 0.994444i \(0.466431\pi\)
−0.913847 + 0.406059i \(0.866903\pi\)
\(104\) 0 0
\(105\) −3.51875 + 3.98691i −0.343395 + 0.389082i
\(106\) 0 0
\(107\) 4.08729i 0.395133i 0.980289 + 0.197567i \(0.0633038\pi\)
−0.980289 + 0.197567i \(0.936696\pi\)
\(108\) 0 0
\(109\) 0.962492i 0.0921900i −0.998937 0.0460950i \(-0.985322\pi\)
0.998937 0.0460950i \(-0.0146777\pi\)
\(110\) 0 0
\(111\) 2.89817 3.28376i 0.275082 0.311681i
\(112\) 0 0
\(113\) −3.91030 + 6.77283i −0.367850 + 0.637135i −0.989229 0.146375i \(-0.953239\pi\)
0.621379 + 0.783510i \(0.286573\pi\)
\(114\) 0 0
\(115\) −12.7173 + 7.34235i −1.18590 + 0.684677i
\(116\) 0 0
\(117\) −0.296533 + 0.703301i −0.0274145 + 0.0650202i
\(118\) 0 0
\(119\) −2.08663 3.61415i −0.191281 0.331309i
\(120\) 0 0
\(121\) −1.04742 + 1.81419i −0.0952202 + 0.164926i
\(122\) 0 0
\(123\) 2.50989 0.843166i 0.226309 0.0760257i
\(124\) 0 0
\(125\) 6.27425i 0.561186i
\(126\) 0 0
\(127\) −8.34653 −0.740635 −0.370317 0.928905i \(-0.620751\pi\)
−0.370317 + 0.928905i \(0.620751\pi\)
\(128\) 0 0
\(129\) 9.50991 + 1.92287i 0.837301 + 0.169299i
\(130\) 0 0
\(131\) 12.5101 + 7.22271i 1.09301 + 0.631051i 0.934377 0.356287i \(-0.115957\pi\)
0.158635 + 0.987337i \(0.449291\pi\)
\(132\) 0 0
\(133\) 6.17680 3.56618i 0.535596 0.309227i
\(134\) 0 0
\(135\) 13.0300 6.27296i 1.12144 0.539891i
\(136\) 0 0
\(137\) −3.54742 6.14432i −0.303077 0.524944i 0.673755 0.738955i \(-0.264681\pi\)
−0.976831 + 0.214011i \(0.931347\pi\)
\(138\) 0 0
\(139\) −6.04959 3.49273i −0.513119 0.296250i 0.220996 0.975275i \(-0.429069\pi\)
−0.734115 + 0.679025i \(0.762403\pi\)
\(140\) 0 0
\(141\) 3.52610 17.4390i 0.296951 1.46863i
\(142\) 0 0
\(143\) −0.759227 −0.0634897
\(144\) 0 0
\(145\) −25.9154 −2.15216
\(146\) 0 0
\(147\) −9.49514 + 3.18977i −0.783146 + 0.263088i
\(148\) 0 0
\(149\) 4.15945 + 2.40146i 0.340755 + 0.196735i 0.660606 0.750733i \(-0.270299\pi\)
−0.319851 + 0.947468i \(0.603633\pi\)
\(150\) 0 0
\(151\) −11.2240 19.4406i −0.913397 1.58205i −0.809231 0.587491i \(-0.800116\pi\)
−0.104167 0.994560i \(-0.533218\pi\)
\(152\) 0 0
\(153\) 1.41030 + 11.2613i 0.114016 + 0.910422i
\(154\) 0 0
\(155\) 18.0349 10.4125i 1.44860 0.836350i
\(156\) 0 0
\(157\) 1.05388 + 0.608456i 0.0841085 + 0.0485601i 0.541464 0.840724i \(-0.317870\pi\)
−0.457356 + 0.889284i \(0.651203\pi\)
\(158\) 0 0
\(159\) 1.10314 1.24990i 0.0874845 0.0991239i
\(160\) 0 0
\(161\) 5.82060 0.458727
\(162\) 0 0
\(163\) 3.02875i 0.237230i 0.992940 + 0.118615i \(0.0378455\pi\)
−0.992940 + 0.118615i \(0.962155\pi\)
\(164\) 0 0
\(165\) 10.7852 + 9.51875i 0.839625 + 0.741034i
\(166\) 0 0
\(167\) 11.1044 19.2333i 0.859282 1.48832i −0.0133323 0.999911i \(-0.504244\pi\)
0.872615 0.488409i \(-0.162423\pi\)
\(168\) 0 0
\(169\) −6.46764 11.2023i −0.497510 0.861713i
\(170\) 0 0
\(171\) −19.2462 + 2.41028i −1.47179 + 0.184319i
\(172\) 0 0
\(173\) −9.77910 + 5.64596i −0.743491 + 0.429255i −0.823337 0.567553i \(-0.807890\pi\)
0.0798463 + 0.996807i \(0.474557\pi\)
\(174\) 0 0
\(175\) 1.51438 2.62298i 0.114476 0.198278i
\(176\) 0 0
\(177\) −4.30661 12.8197i −0.323705 0.963588i
\(178\) 0 0
\(179\) 3.59007i 0.268335i 0.990959 + 0.134167i \(0.0428359\pi\)
−0.990959 + 0.134167i \(0.957164\pi\)
\(180\) 0 0
\(181\) 25.6610i 1.90737i −0.300809 0.953684i \(-0.597257\pi\)
0.300809 0.953684i \(-0.402743\pi\)
\(182\) 0 0
\(183\) 22.5993 + 4.56950i 1.67059 + 0.337787i
\(184\) 0 0
\(185\) −3.51875 + 6.09466i −0.258704 + 0.448088i
\(186\) 0 0
\(187\) −9.77683 + 5.64465i −0.714952 + 0.412778i
\(188\) 0 0
\(189\) −5.71599 0.429052i −0.415777 0.0312089i
\(190\) 0 0
\(191\) 10.8237 + 18.7472i 0.783176 + 1.35650i 0.930082 + 0.367351i \(0.119735\pi\)
−0.146906 + 0.989150i \(0.546931\pi\)
\(192\) 0 0
\(193\) 10.5849 18.3336i 0.761920 1.31968i −0.179940 0.983678i \(-0.557590\pi\)
0.941860 0.336006i \(-0.109076\pi\)
\(194\) 0 0
\(195\) 0.243059 1.20209i 0.0174058 0.0860835i
\(196\) 0 0
\(197\) 5.56618i 0.396574i −0.980144 0.198287i \(-0.936462\pi\)
0.980144 0.198287i \(-0.0635378\pi\)
\(198\) 0 0
\(199\) −26.9238 −1.90858 −0.954290 0.298883i \(-0.903386\pi\)
−0.954290 + 0.298883i \(0.903386\pi\)
\(200\) 0 0
\(201\) −4.17463 12.4268i −0.294456 0.876521i
\(202\) 0 0
\(203\) 8.89594 + 5.13607i 0.624373 + 0.360482i
\(204\) 0 0
\(205\) −3.68444 + 2.12721i −0.257332 + 0.148571i
\(206\) 0 0
\(207\) −14.5857 6.14980i −1.01378 0.427440i
\(208\) 0 0
\(209\) −9.64704 16.7092i −0.667300 1.15580i
\(210\) 0 0
\(211\) −15.8264 9.13738i −1.08954 0.629043i −0.156082 0.987744i \(-0.549887\pi\)
−0.933453 + 0.358701i \(0.883220\pi\)
\(212\) 0 0
\(213\) −5.41946 4.78309i −0.371335 0.327732i
\(214\) 0 0
\(215\) −15.5899 −1.06322
\(216\) 0 0
\(217\) −8.25442 −0.560347
\(218\) 0 0
\(219\) −6.94662 6.13093i −0.469409 0.414290i
\(220\) 0 0
\(221\) 0.833543 + 0.481246i 0.0560701 + 0.0323721i
\(222\) 0 0
\(223\) −5.13607 8.89594i −0.343937 0.595716i 0.641223 0.767354i \(-0.278427\pi\)
−0.985160 + 0.171638i \(0.945094\pi\)
\(224\) 0 0
\(225\) −6.56618 + 4.97285i −0.437745 + 0.331523i
\(226\) 0 0
\(227\) −4.64396 + 2.68119i −0.308230 + 0.177957i −0.646134 0.763224i \(-0.723615\pi\)
0.337904 + 0.941181i \(0.390282\pi\)
\(228\) 0 0
\(229\) 4.07731 + 2.35404i 0.269436 + 0.155559i 0.628631 0.777703i \(-0.283615\pi\)
−0.359195 + 0.933262i \(0.616949\pi\)
\(230\) 0 0
\(231\) −1.81572 5.40495i −0.119466 0.355620i
\(232\) 0 0
\(233\) −17.8779 −1.17122 −0.585611 0.810592i \(-0.699145\pi\)
−0.585611 + 0.810592i \(0.699145\pi\)
\(234\) 0 0
\(235\) 28.5883i 1.86489i
\(236\) 0 0
\(237\) −1.33621 + 6.60846i −0.0867959 + 0.429265i
\(238\) 0 0
\(239\) −9.84022 + 17.0438i −0.636511 + 1.10247i 0.349682 + 0.936868i \(0.386290\pi\)
−0.986193 + 0.165601i \(0.947044\pi\)
\(240\) 0 0
\(241\) 4.79193 + 8.29986i 0.308675 + 0.534641i 0.978073 0.208263i \(-0.0667811\pi\)
−0.669398 + 0.742904i \(0.733448\pi\)
\(242\) 0 0
\(243\) 13.8703 + 7.11443i 0.889779 + 0.456391i
\(244\) 0 0
\(245\) 13.9385 8.04742i 0.890501 0.514131i
\(246\) 0 0
\(247\) −0.822477 + 1.42457i −0.0523330 + 0.0906434i
\(248\) 0 0
\(249\) −28.2695 5.71599i −1.79151 0.362236i
\(250\) 0 0
\(251\) 13.2563i 0.836730i −0.908279 0.418365i \(-0.862603\pi\)
0.908279 0.418365i \(-0.137397\pi\)
\(252\) 0 0
\(253\) 15.7456i 0.989916i
\(254\) 0 0
\(255\) −5.80728 17.2868i −0.363666 1.08254i
\(256\) 0 0
\(257\) 4.75442 8.23490i 0.296573 0.513679i −0.678777 0.734345i \(-0.737490\pi\)
0.975349 + 0.220666i \(0.0708230\pi\)
\(258\) 0 0
\(259\) 2.41575 1.39473i 0.150107 0.0866646i
\(260\) 0 0
\(261\) −16.8656 22.2695i −1.04396 1.37845i
\(262\) 0 0
\(263\) 0.0206882 + 0.0358330i 0.00127569 + 0.00220956i 0.866663 0.498895i \(-0.166261\pi\)
−0.865387 + 0.501104i \(0.832927\pi\)
\(264\) 0 0
\(265\) −1.33935 + 2.31982i −0.0822756 + 0.142506i
\(266\) 0 0
\(267\) −13.1093 11.5700i −0.802276 0.708070i
\(268\) 0 0
\(269\) 15.5463i 0.947878i −0.880558 0.473939i \(-0.842832\pi\)
0.880558 0.473939i \(-0.157168\pi\)
\(270\) 0 0
\(271\) 19.3779 1.17712 0.588562 0.808452i \(-0.299694\pi\)
0.588562 + 0.808452i \(0.299694\pi\)
\(272\) 0 0
\(273\) −0.321672 + 0.364468i −0.0194684 + 0.0220586i
\(274\) 0 0
\(275\) −7.09554 4.09661i −0.427877 0.247035i
\(276\) 0 0
\(277\) −20.7763 + 11.9952i −1.24833 + 0.720723i −0.970776 0.239987i \(-0.922857\pi\)
−0.277553 + 0.960710i \(0.589524\pi\)
\(278\) 0 0
\(279\) 20.6846 + 8.72127i 1.23836 + 0.522129i
\(280\) 0 0
\(281\) 2.92021 + 5.05796i 0.174205 + 0.301732i 0.939886 0.341488i \(-0.110931\pi\)
−0.765681 + 0.643221i \(0.777598\pi\)
\(282\) 0 0
\(283\) 12.9962 + 7.50337i 0.772544 + 0.446029i 0.833782 0.552094i \(-0.186171\pi\)
−0.0612371 + 0.998123i \(0.519505\pi\)
\(284\) 0 0
\(285\) 29.5442 9.92498i 1.75005 0.587905i
\(286\) 0 0
\(287\) 1.68633 0.0995410
\(288\) 0 0
\(289\) −2.68824 −0.158132
\(290\) 0 0
\(291\) 5.18158 25.6264i 0.303749 1.50225i
\(292\) 0 0
\(293\) −20.6464 11.9202i −1.20618 0.696386i −0.244255 0.969711i \(-0.578543\pi\)
−0.961922 + 0.273325i \(0.911877\pi\)
\(294\) 0 0
\(295\) 10.8651 + 18.8189i 0.632590 + 1.09568i
\(296\) 0 0
\(297\) −1.16065 + 15.4626i −0.0673477 + 0.897231i
\(298\) 0 0
\(299\) −1.16257 + 0.671210i −0.0672332 + 0.0388171i
\(300\) 0 0
\(301\) 5.35152 + 3.08970i 0.308457 + 0.178087i
\(302\) 0 0
\(303\) −8.85672 1.79080i −0.508805 0.102879i
\(304\) 0 0
\(305\) −37.0478 −2.12135
\(306\) 0 0
\(307\) 0.497216i 0.0283776i 0.999899 + 0.0141888i \(0.00451659\pi\)
−0.999899 + 0.0141888i \(0.995483\pi\)
\(308\) 0 0
\(309\) 26.9472 9.05257i 1.53297 0.514982i
\(310\) 0 0
\(311\) −1.12383 + 1.94652i −0.0637263 + 0.110377i −0.896128 0.443795i \(-0.853632\pi\)
0.832402 + 0.554172i \(0.186965\pi\)
\(312\) 0 0
\(313\) 6.50000 + 11.2583i 0.367402 + 0.636358i 0.989158 0.146852i \(-0.0469141\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 9.13900 1.14451i 0.514924 0.0644860i
\(316\) 0 0
\(317\) 9.86123 5.69339i 0.553862 0.319772i −0.196816 0.980440i \(-0.563060\pi\)
0.750678 + 0.660668i \(0.229727\pi\)
\(318\) 0 0
\(319\) 13.8938 24.0648i 0.777906 1.34737i
\(320\) 0 0
\(321\) 4.68455 5.30780i 0.261466 0.296253i
\(322\) 0 0
\(323\) 24.4596i 1.36097i
\(324\) 0 0
\(325\) 0.698530i 0.0387475i
\(326\) 0 0
\(327\) −1.10314 + 1.24990i −0.0610036 + 0.0691199i
\(328\) 0 0
\(329\) 5.66579 9.81344i 0.312365 0.541033i
\(330\) 0 0
\(331\) 15.8264 9.13738i 0.869898 0.502236i 0.00258383 0.999997i \(-0.499178\pi\)
0.867314 + 0.497761i \(0.165844\pi\)
\(332\) 0 0
\(333\) −7.52721 + 0.942663i −0.412488 + 0.0516576i
\(334\) 0 0
\(335\) 10.5321 + 18.2422i 0.575431 + 0.996676i
\(336\) 0 0
\(337\) 1.20807 2.09244i 0.0658079 0.113983i −0.831244 0.555907i \(-0.812371\pi\)
0.897052 + 0.441925i \(0.145704\pi\)
\(338\) 0 0
\(339\) 12.8405 4.31360i 0.697399 0.234282i
\(340\) 0 0
\(341\) 22.3294i 1.20921i
\(342\) 0 0
\(343\) −14.1015 −0.761409
\(344\) 0 0
\(345\) 24.9301 + 5.04078i 1.34219 + 0.271387i
\(346\) 0 0
\(347\) −6.55465 3.78433i −0.351872 0.203153i 0.313638 0.949543i \(-0.398452\pi\)
−0.665509 + 0.746389i \(0.731786\pi\)
\(348\) 0 0
\(349\) 17.7873 10.2695i 0.952130 0.549713i 0.0583881 0.998294i \(-0.481404\pi\)
0.893742 + 0.448581i \(0.148071\pi\)
\(350\) 0 0
\(351\) 1.19115 0.573451i 0.0635791 0.0306086i
\(352\) 0 0
\(353\) 16.1136 + 27.9096i 0.857640 + 1.48548i 0.874174 + 0.485613i \(0.161404\pi\)
−0.0165334 + 0.999863i \(0.505263\pi\)
\(354\) 0 0
\(355\) 10.0585 + 5.80728i 0.533850 + 0.308219i
\(356\) 0 0
\(357\) −1.43255 + 7.08493i −0.0758185 + 0.374974i
\(358\) 0 0
\(359\) 14.1429 0.746432 0.373216 0.927744i \(-0.378255\pi\)
0.373216 + 0.927744i \(0.378255\pi\)
\(360\) 0 0
\(361\) −22.8029 −1.20015
\(362\) 0 0
\(363\) 3.43949 1.15545i 0.180526 0.0606454i
\(364\) 0 0
\(365\) 12.8929 + 7.44374i 0.674847 + 0.389623i
\(366\) 0 0
\(367\) −2.22696 3.85721i −0.116247 0.201345i 0.802031 0.597283i \(-0.203753\pi\)
−0.918277 + 0.395938i \(0.870420\pi\)
\(368\) 0 0
\(369\) −4.22575 1.78171i −0.219984 0.0927519i
\(370\) 0 0
\(371\) 0.919512 0.530880i 0.0477387 0.0275619i
\(372\) 0 0
\(373\) 17.2301 + 9.94781i 0.892141 + 0.515078i 0.874642 0.484769i \(-0.161096\pi\)
0.0174988 + 0.999847i \(0.494430\pi\)
\(374\) 0 0
\(375\) −7.19108 + 8.14782i −0.371346 + 0.420752i
\(376\) 0 0
\(377\) −2.36909 −0.122015
\(378\) 0 0
\(379\) 2.46421i 0.126578i 0.997995 + 0.0632889i \(0.0201590\pi\)
−0.997995 + 0.0632889i \(0.979841\pi\)
\(380\) 0 0
\(381\) 10.8389 + 9.56618i 0.555294 + 0.490090i
\(382\) 0 0
\(383\) −12.2075 + 21.1440i −0.623775 + 1.08041i 0.365002 + 0.931007i \(0.381068\pi\)
−0.988776 + 0.149403i \(0.952265\pi\)
\(384\) 0 0
\(385\) 4.58086 + 7.93429i 0.233462 + 0.404369i
\(386\) 0 0
\(387\) −10.1458 13.3966i −0.515742 0.680989i
\(388\) 0 0
\(389\) 8.89776 5.13712i 0.451134 0.260463i −0.257175 0.966365i \(-0.582792\pi\)
0.708309 + 0.705902i \(0.249458\pi\)
\(390\) 0 0
\(391\) −9.98055 + 17.2868i −0.504738 + 0.874232i
\(392\) 0 0
\(393\) −7.96764 23.7176i −0.401914 1.19640i
\(394\) 0 0
\(395\) 10.8335i 0.545091i
\(396\) 0 0
\(397\) 28.2449i 1.41757i −0.705425 0.708785i \(-0.749244\pi\)
0.705425 0.708785i \(-0.250756\pi\)
\(398\) 0 0
\(399\) −12.1086 2.44831i −0.606186 0.122569i
\(400\) 0 0
\(401\) 2.33051 4.03656i 0.116380 0.201576i −0.801950 0.597391i \(-0.796204\pi\)
0.918331 + 0.395814i \(0.129538\pi\)
\(402\) 0 0
\(403\) 1.64869 0.951870i 0.0821270 0.0474160i
\(404\) 0 0
\(405\) −24.1105 6.78786i −1.19806 0.337291i
\(406\) 0 0
\(407\) −3.77296 6.53497i −0.187019 0.323926i
\(408\) 0 0
\(409\) 17.6324 30.5401i 0.871864 1.51011i 0.0117972 0.999930i \(-0.496245\pi\)
0.860067 0.510182i \(-0.170422\pi\)
\(410\) 0 0
\(411\) −2.43543 + 12.0449i −0.120131 + 0.594130i
\(412\) 0 0
\(413\) 8.61323i 0.423829i
\(414\) 0 0
\(415\) 46.3431 2.27489
\(416\) 0 0
\(417\) 3.85296 + 11.4693i 0.188680 + 0.561654i
\(418\) 0 0
\(419\) −6.68741 3.86098i −0.326702 0.188621i 0.327674 0.944791i \(-0.393735\pi\)
−0.654376 + 0.756170i \(0.727069\pi\)
\(420\) 0 0
\(421\) −19.2079 + 11.0897i −0.936137 + 0.540479i −0.888747 0.458397i \(-0.848424\pi\)
−0.0473898 + 0.998876i \(0.515090\pi\)
\(422\) 0 0
\(423\) −24.5663 + 18.6051i −1.19445 + 0.904612i
\(424\) 0 0
\(425\) 5.19339 + 8.99521i 0.251916 + 0.436332i
\(426\) 0 0
\(427\) 12.7173 + 7.34235i 0.615434 + 0.355321i
\(428\) 0 0
\(429\) 0.985941 + 0.870169i 0.0476017 + 0.0420122i
\(430\) 0 0
\(431\) 14.1429 0.681238 0.340619 0.940201i \(-0.389363\pi\)
0.340619 + 0.940201i \(0.389363\pi\)
\(432\) 0 0
\(433\) −27.8978 −1.34068 −0.670340 0.742054i \(-0.733852\pi\)
−0.670340 + 0.742054i \(0.733852\pi\)
\(434\) 0 0
\(435\) 33.6541 + 29.7024i 1.61359 + 1.42412i
\(436\) 0 0
\(437\) −29.5442 17.0573i −1.41329 0.815963i
\(438\) 0 0
\(439\) 1.53506 + 2.65881i 0.0732646 + 0.126898i 0.900330 0.435207i \(-0.143325\pi\)
−0.827066 + 0.562105i \(0.809992\pi\)
\(440\) 0 0
\(441\) 15.9864 + 6.74035i 0.761257 + 0.320969i
\(442\) 0 0
\(443\) −6.34742 + 3.66469i −0.301575 + 0.174114i −0.643150 0.765740i \(-0.722373\pi\)
0.341575 + 0.939854i \(0.389040\pi\)
\(444\) 0 0
\(445\) 24.3308 + 14.0474i 1.15339 + 0.665912i
\(446\) 0 0
\(447\) −2.64914 7.88582i −0.125300 0.372986i
\(448\) 0 0
\(449\) 29.3889 1.38695 0.693475 0.720481i \(-0.256079\pi\)
0.693475 + 0.720481i \(0.256079\pi\)
\(450\) 0 0
\(451\) 4.56178i 0.214806i
\(452\) 0 0
\(453\) −7.70569 + 38.1099i −0.362045 + 1.79056i
\(454\) 0 0
\(455\) 0.390551 0.676453i 0.0183093 0.0317126i
\(456\) 0 0
\(457\) 10.8217 + 18.7437i 0.506216 + 0.876793i 0.999974 + 0.00719307i \(0.00228964\pi\)
−0.493758 + 0.869600i \(0.664377\pi\)
\(458\) 0 0
\(459\) 11.0754 16.2404i 0.516957 0.758039i
\(460\) 0 0
\(461\) −4.43584 + 2.56103i −0.206598 + 0.119279i −0.599729 0.800203i \(-0.704725\pi\)
0.393132 + 0.919482i \(0.371392\pi\)
\(462\) 0 0
\(463\) 3.04944 5.28179i 0.141719 0.245465i −0.786425 0.617686i \(-0.788070\pi\)
0.928144 + 0.372221i \(0.121404\pi\)
\(464\) 0 0
\(465\) −35.3544 7.14854i −1.63952 0.331505i
\(466\) 0 0
\(467\) 28.8722i 1.33604i −0.744141 0.668022i \(-0.767141\pi\)
0.744141 0.668022i \(-0.232859\pi\)
\(468\) 0 0
\(469\) 8.34926i 0.385533i
\(470\) 0 0
\(471\) −0.671210 1.99802i −0.0309277 0.0920641i
\(472\) 0 0
\(473\) 8.35810 14.4767i 0.384306 0.665638i
\(474\) 0 0
\(475\) −15.3733 + 8.87580i −0.705377 + 0.407250i
\(476\) 0 0
\(477\) −2.86510 + 0.358808i −0.131184 + 0.0164287i
\(478\) 0 0
\(479\) −7.74265 13.4107i −0.353771 0.612749i 0.633136 0.774040i \(-0.281767\pi\)
−0.986907 + 0.161292i \(0.948434\pi\)
\(480\) 0 0
\(481\) −0.321672 + 0.557151i −0.0146670 + 0.0254039i
\(482\) 0 0
\(483\) −7.55870 6.67114i −0.343933 0.303547i
\(484\) 0 0
\(485\) 42.0103i 1.90759i
\(486\) 0 0
\(487\) 6.96273 0.315512 0.157756 0.987478i \(-0.449574\pi\)
0.157756 + 0.987478i \(0.449574\pi\)
\(488\) 0 0
\(489\) 3.47133 3.93318i 0.156979 0.177864i
\(490\) 0 0
\(491\) −5.56347 3.21207i −0.251076 0.144959i 0.369181 0.929358i \(-0.379638\pi\)
−0.620257 + 0.784399i \(0.712972\pi\)
\(492\) 0 0
\(493\) −30.5076 + 17.6136i −1.37400 + 0.793277i
\(494\) 0 0
\(495\) −3.09608 24.7224i −0.139158 1.11119i
\(496\) 0 0
\(497\) −2.30184 3.98691i −0.103252 0.178837i
\(498\) 0 0
\(499\) −17.3254 10.0028i −0.775593 0.447789i 0.0592729 0.998242i \(-0.481122\pi\)
−0.834866 + 0.550453i \(0.814455\pi\)
\(500\) 0 0
\(501\) −36.4641 + 12.2496i −1.62910 + 0.547274i
\(502\) 0 0
\(503\) −4.99574 −0.222749 −0.111375 0.993778i \(-0.535525\pi\)
−0.111375 + 0.993778i \(0.535525\pi\)
\(504\) 0 0
\(505\) 14.5191 0.646093
\(506\) 0 0
\(507\) −4.44026 + 21.9601i −0.197199 + 0.975284i
\(508\) 0 0
\(509\) 24.9441 + 14.4015i 1.10563 + 0.638333i 0.937693 0.347465i \(-0.112957\pi\)
0.167933 + 0.985798i \(0.446291\pi\)
\(510\) 0 0
\(511\) −2.95049 5.11039i −0.130522 0.226070i
\(512\) 0 0
\(513\) 27.7559 + 18.9286i 1.22545 + 0.835717i
\(514\) 0 0
\(515\) −39.5576 + 22.8386i −1.74312 + 1.00639i
\(516\) 0 0
\(517\) −26.5468 15.3268i −1.16753 0.674073i
\(518\) 0 0
\(519\) 19.1702 + 3.87616i 0.841480 + 0.170144i
\(520\) 0 0
\(521\) 3.44411 0.150889 0.0754446 0.997150i \(-0.475962\pi\)
0.0754446 + 0.997150i \(0.475962\pi\)
\(522\) 0 0
\(523\) 30.8578i 1.34932i −0.738130 0.674659i \(-0.764291\pi\)
0.738130 0.674659i \(-0.235709\pi\)
\(524\) 0 0
\(525\) −4.97285 + 1.67056i −0.217033 + 0.0729094i
\(526\) 0 0
\(527\) 14.1538 24.5151i 0.616550 1.06790i
\(528\) 0 0
\(529\) −2.42021 4.19193i −0.105227 0.182258i
\(530\) 0 0
\(531\) −9.10037 + 21.5838i −0.394922 + 0.936655i
\(532\) 0 0
\(533\) −0.336818 + 0.194462i −0.0145892 + 0.00842307i
\(534\) 0 0
\(535\) −5.68764 + 9.85128i −0.245898 + 0.425908i
\(536\) 0 0
\(537\) 4.11467 4.66211i 0.177561 0.201185i
\(538\) 0 0
\(539\) 17.2576i 0.743338i
\(540\) 0 0
\(541\) 30.8132i 1.32476i 0.749167 + 0.662382i \(0.230454\pi\)
−0.749167 + 0.662382i \(0.769546\pi\)
\(542\) 0 0
\(543\) −29.4108 + 33.3237i −1.26214 + 1.43006i
\(544\) 0 0
\(545\) 1.33935 2.31982i 0.0573715 0.0993703i
\(546\) 0 0
\(547\) 25.0588 14.4677i 1.07144 0.618595i 0.142864 0.989742i \(-0.454369\pi\)
0.928574 + 0.371148i \(0.121036\pi\)
\(548\) 0 0
\(549\) −24.1105 31.8357i −1.02901 1.35871i
\(550\) 0 0
\(551\) −30.1027 52.1393i −1.28242 2.22121i
\(552\) 0 0
\(553\) −2.14704 + 3.71878i −0.0913014 + 0.158139i
\(554\) 0 0
\(555\) 11.5547 3.88167i 0.490472 0.164768i
\(556\) 0 0
\(557\) 8.09485i 0.342990i 0.985185 + 0.171495i \(0.0548597\pi\)
−0.985185 + 0.171495i \(0.945140\pi\)
\(558\) 0 0
\(559\) −1.42517 −0.0602784
\(560\) 0 0
\(561\) 19.1658 + 3.87526i 0.809180 + 0.163613i
\(562\) 0 0
\(563\) 8.95145 + 5.16812i 0.377259 + 0.217810i 0.676625 0.736328i \(-0.263442\pi\)
−0.299366 + 0.954138i \(0.596775\pi\)
\(564\) 0 0
\(565\) −18.8494 + 10.8827i −0.793000 + 0.457839i
\(566\) 0 0
\(567\) 6.93111 + 7.10842i 0.291079 + 0.298525i
\(568\) 0 0
\(569\) −4.53751 7.85919i −0.190222 0.329475i 0.755102 0.655608i \(-0.227588\pi\)
−0.945324 + 0.326133i \(0.894254\pi\)
\(570\) 0 0
\(571\) −27.3067 15.7655i −1.14275 0.659767i −0.195640 0.980676i \(-0.562678\pi\)
−0.947110 + 0.320909i \(0.896012\pi\)
\(572\) 0 0
\(573\) 7.43087 36.7507i 0.310429 1.53528i
\(574\) 0 0
\(575\) −14.4868 −0.604141
\(576\) 0 0
\(577\) 29.4639 1.22660 0.613300 0.789850i \(-0.289842\pi\)
0.613300 + 0.789850i \(0.289842\pi\)
\(578\) 0 0
\(579\) −34.7584 + 11.6766i −1.44451 + 0.485264i
\(580\) 0 0
\(581\) −15.9081 9.18455i −0.659979 0.381039i
\(582\) 0 0
\(583\) −1.43611 2.48742i −0.0594776 0.103018i
\(584\) 0 0
\(585\) −1.69339 + 1.28247i −0.0700129 + 0.0530238i
\(586\) 0 0
\(587\) −13.0896 + 7.55729i −0.540266 + 0.311923i −0.745187 0.666856i \(-0.767640\pi\)
0.204921 + 0.978779i \(0.434306\pi\)
\(588\) 0 0
\(589\) 41.8978 + 24.1897i 1.72637 + 0.996719i
\(590\) 0 0
\(591\) −6.37954 + 7.22831i −0.262419 + 0.297333i
\(592\) 0 0
\(593\) 9.54635 0.392021 0.196011 0.980602i \(-0.437201\pi\)
0.196011 + 0.980602i \(0.437201\pi\)
\(594\) 0 0
\(595\) 11.6146i 0.476151i
\(596\) 0 0
\(597\) 34.9636 + 30.8581i 1.43097 + 1.26294i
\(598\) 0 0
\(599\) 17.7232 30.6975i 0.724150 1.25426i −0.235173 0.971954i \(-0.575566\pi\)
0.959323 0.282311i \(-0.0911011\pi\)
\(600\) 0 0
\(601\) 10.7643 + 18.6444i 0.439086 + 0.760520i 0.997619 0.0689625i \(-0.0219689\pi\)
−0.558533 + 0.829482i \(0.688636\pi\)
\(602\) 0 0
\(603\) −8.82148 + 20.9223i −0.359238 + 0.852022i
\(604\) 0 0
\(605\) −5.04905 + 2.91507i −0.205273 + 0.118514i
\(606\) 0 0
\(607\) −12.8994 + 22.3424i −0.523571 + 0.906851i 0.476053 + 0.879417i \(0.342067\pi\)
−0.999624 + 0.0274346i \(0.991266\pi\)
\(608\) 0 0
\(609\) −5.66579 16.8656i −0.229590 0.683430i
\(610\) 0 0
\(611\) 2.61344i 0.105728i
\(612\) 0 0
\(613\) 9.11252i 0.368051i 0.982921 + 0.184026i \(0.0589130\pi\)
−0.982921 + 0.184026i \(0.941087\pi\)
\(614\) 0 0
\(615\) 7.22271 + 1.46041i 0.291248 + 0.0588892i
\(616\) 0 0
\(617\) −4.11360 + 7.12496i −0.165607 + 0.286840i −0.936871 0.349676i \(-0.886292\pi\)
0.771264 + 0.636516i \(0.219625\pi\)
\(618\) 0 0
\(619\) 23.0709 13.3200i 0.927297 0.535375i 0.0413410 0.999145i \(-0.486837\pi\)
0.885956 + 0.463770i \(0.153504\pi\)
\(620\) 0 0
\(621\) 11.8928 + 24.7033i 0.477241 + 0.991309i
\(622\) 0 0
\(623\) −5.56800 9.64406i −0.223077 0.386381i
\(624\) 0 0
\(625\) 15.5948 27.0111i 0.623794 1.08044i
\(626\) 0 0
\(627\) −6.62304 + 32.7555i −0.264499 + 1.30813i
\(628\) 0 0
\(629\) 9.56618i 0.381428i
\(630\) 0 0
\(631\) 3.02875 0.120573 0.0602864 0.998181i \(-0.480799\pi\)
0.0602864 + 0.998181i \(0.480799\pi\)
\(632\) 0 0
\(633\) 10.0798 + 30.0050i 0.400636 + 1.19259i
\(634\) 0 0
\(635\) −20.1170 11.6146i −0.798320 0.460910i
\(636\) 0 0
\(637\) 1.27421 0.735666i 0.0504861 0.0291481i
\(638\) 0 0
\(639\) 1.55575 + 12.4228i 0.0615446 + 0.491437i
\(640\) 0 0
\(641\) 6.30292 + 10.9170i 0.248950 + 0.431195i 0.963235 0.268661i \(-0.0865811\pi\)
−0.714285 + 0.699855i \(0.753248\pi\)
\(642\) 0 0
\(643\) 25.8105 + 14.9017i 1.01787 + 0.587665i 0.913485 0.406873i \(-0.133381\pi\)
0.104380 + 0.994537i \(0.466714\pi\)
\(644\) 0 0
\(645\) 20.2453 + 17.8680i 0.797157 + 0.703553i
\(646\) 0 0
\(647\) 11.8538 0.466023 0.233011 0.972474i \(-0.425142\pi\)
0.233011 + 0.972474i \(0.425142\pi\)
\(648\) 0 0
\(649\) −23.3001 −0.914607
\(650\) 0 0
\(651\) 10.7193 + 9.46061i 0.420122 + 0.370790i
\(652\) 0 0
\(653\) 3.29156 + 1.90038i 0.128809 + 0.0743678i 0.563020 0.826443i \(-0.309639\pi\)
−0.434211 + 0.900811i \(0.642973\pi\)
\(654\) 0 0
\(655\) 20.1014 + 34.8167i 0.785428 + 1.36040i
\(656\) 0 0
\(657\) 1.99415 + 15.9234i 0.0777993 + 0.621231i
\(658\) 0 0
\(659\) 30.2830 17.4839i 1.17966 0.681077i 0.223724 0.974653i \(-0.428179\pi\)
0.955936 + 0.293576i \(0.0948454\pi\)
\(660\) 0 0
\(661\) 15.2045 + 8.77832i 0.591386 + 0.341437i 0.765645 0.643263i \(-0.222420\pi\)
−0.174259 + 0.984700i \(0.555753\pi\)
\(662\) 0 0
\(663\) −0.530880 1.58030i −0.0206177 0.0613737i
\(664\) 0 0
\(665\) 19.8500 0.769749
\(666\) 0 0
\(667\) 49.1326i 1.90242i
\(668\) 0 0
\(669\) −3.52610 + 17.4390i −0.136327 + 0.674229i
\(670\) 0 0
\(671\) 19.8621 34.4022i 0.766770 1.32808i
\(672\) 0 0
\(673\) 20.7408 + 35.9241i 0.799499 + 1.38477i 0.919942 + 0.392053i \(0.128235\pi\)
−0.120443 + 0.992720i \(0.538432\pi\)
\(674\) 0 0
\(675\) 14.2264 + 1.06786i 0.547576 + 0.0411020i
\(676\) 0 0
\(677\) −4.99299 + 2.88270i −0.191896 + 0.110791i −0.592870 0.805298i \(-0.702005\pi\)
0.400974 + 0.916090i \(0.368672\pi\)
\(678\) 0 0
\(679\) 8.32584 14.4208i 0.319517 0.553419i
\(680\) 0 0
\(681\) 9.10368 + 1.84073i 0.348854 + 0.0705370i
\(682\) 0 0
\(683\) 39.1184i 1.49682i 0.663235 + 0.748411i \(0.269183\pi\)
−0.663235 + 0.748411i \(0.730817\pi\)
\(684\) 0 0
\(685\) 19.7456i 0.754440i
\(686\) 0 0
\(687\) −2.59682 7.73009i −0.0990751 0.294921i
\(688\) 0 0
\(689\) −0.122438 + 0.212070i −0.00466453 + 0.00807921i
\(690\) 0 0
\(691\) −21.6491 + 12.4991i −0.823570 + 0.475488i −0.851646 0.524117i \(-0.824395\pi\)
0.0280759 + 0.999606i \(0.491062\pi\)
\(692\) 0 0
\(693\) −3.83683 + 9.09999i −0.145749 + 0.345680i
\(694\) 0 0
\(695\) −9.72058 16.8365i −0.368723 0.638646i
\(696\) 0 0
\(697\) −2.89154 + 5.00830i −0.109525 + 0.189703i
\(698\) 0 0
\(699\) 23.2165 + 20.4904i 0.878129 + 0.775017i
\(700\) 0 0
\(701\) 7.54635i 0.285022i −0.989793 0.142511i \(-0.954482\pi\)
0.989793 0.142511i \(-0.0455176\pi\)
\(702\) 0 0
\(703\) −16.3492 −0.616620
\(704\) 0 0
\(705\) 32.7658 37.1251i 1.23403 1.39821i
\(706\) 0 0
\(707\) −4.98395 2.87748i −0.187441 0.108219i
\(708\) 0 0
\(709\) 8.42275 4.86288i 0.316323 0.182629i −0.333429 0.942775i \(-0.608206\pi\)
0.649752 + 0.760146i \(0.274873\pi\)
\(710\) 0 0
\(711\) 9.30934 7.05036i 0.349127 0.264409i
\(712\) 0 0
\(713\) 19.7408 + 34.1921i 0.739299 + 1.28050i
\(714\) 0 0
\(715\) −1.82991 1.05650i −0.0684346 0.0395108i
\(716\) 0 0
\(717\) 32.3129 10.8551i 1.20675 0.405392i
\(718\) 0 0
\(719\) −30.7532 −1.14690 −0.573450 0.819240i \(-0.694395\pi\)
−0.573450 + 0.819240i \(0.694395\pi\)
\(720\) 0 0
\(721\) 18.1051 0.674270
\(722\) 0 0
\(723\) 3.28983 16.2705i 0.122350 0.605105i
\(724\) 0 0
\(725\) −22.1410 12.7831i −0.822295 0.474752i
\(726\) 0 0
\(727\) 18.4260 + 31.9148i 0.683384 + 1.18366i 0.973942 + 0.226798i \(0.0728257\pi\)
−0.290558 + 0.956857i \(0.593841\pi\)
\(728\) 0 0
\(729\) −9.85810 25.1360i −0.365115 0.930962i
\(730\) 0 0
\(731\) −18.3525 + 10.5958i −0.678790 + 0.391900i
\(732\) 0 0
\(733\) −36.9869 21.3544i −1.36614 0.788743i −0.375710 0.926737i \(-0.622601\pi\)
−0.990433 + 0.137994i \(0.955934\pi\)
\(734\) 0 0
\(735\) −27.3241 5.52484i −1.00787 0.203787i
\(736\) 0 0
\(737\) −22.5860 −0.831966
\(738\) 0 0
\(739\) 15.7019i 0.577602i −0.957389 0.288801i \(-0.906743\pi\)
0.957389 0.288801i \(-0.0932566\pi\)
\(740\) 0 0
\(741\) 2.70082 0.907305i 0.0992171 0.0333307i
\(742\) 0 0
\(743\) 6.69183 11.5906i 0.245499 0.425217i −0.716773 0.697307i \(-0.754381\pi\)
0.962272 + 0.272090i \(0.0877148\pi\)
\(744\) 0 0
\(745\) 6.68347 + 11.5761i 0.244863 + 0.424116i
\(746\) 0 0
\(747\) 30.1599 + 39.8232i 1.10349 + 1.45706i
\(748\) 0 0
\(749\) 3.90477 2.25442i 0.142677 0.0823747i
\(750\) 0 0
\(751\) 6.69183 11.5906i 0.244188 0.422946i −0.717715 0.696337i \(-0.754812\pi\)
0.961903 + 0.273391i \(0.0881452\pi\)
\(752\) 0 0
\(753\) −15.1934 + 17.2148i −0.553678 + 0.627342i
\(754\) 0 0
\(755\) 62.4749i 2.27369i
\(756\) 0 0
\(757\) 0.867647i 0.0315352i −0.999876 0.0157676i \(-0.994981\pi\)
0.999876 0.0157676i \(-0.00501919\pi\)
\(758\) 0 0
\(759\) −18.0464 + 20.4474i −0.655044 + 0.742194i
\(760\) 0 0
\(761\) −18.6658 + 32.3301i −0.676634 + 1.17197i 0.299354 + 0.954142i \(0.403229\pi\)
−0.975988 + 0.217823i \(0.930104\pi\)
\(762\) 0 0
\(763\) −0.919512 + 0.530880i −0.0332886 + 0.0192192i
\(764\) 0 0
\(765\) −12.2715 + 29.1048i −0.443676 + 1.05228i
\(766\) 0 0
\(767\) 0.993247 + 1.72035i 0.0358641 + 0.0621184i
\(768\) 0 0
\(769\) −0.693386 + 1.20098i −0.0250042 + 0.0433085i −0.878257 0.478189i \(-0.841293\pi\)
0.853253 + 0.521498i \(0.174627\pi\)
\(770\) 0 0
\(771\) −15.6124 + 5.24478i −0.562266 + 0.188886i
\(772\) 0 0
\(773\) 27.3963i 0.985377i 0.870206 + 0.492688i \(0.163986\pi\)
−0.870206 + 0.492688i \(0.836014\pi\)
\(774\) 0 0
\(775\) 20.5443 0.737973
\(776\) 0 0
\(777\) −4.73567 0.957535i −0.169891 0.0343514i
\(778\) 0 0
\(779\) −8.55948 4.94182i −0.306675 0.177059i
\(780\) 0 0
\(781\) −10.7852 + 6.22683i −0.385924 + 0.222813i
\(782\) 0 0
\(783\) −3.62170 + 48.2496i −0.129429 + 1.72430i
\(784\) 0 0
\(785\) 1.69339 + 2.93303i 0.0604396 + 0.104684i
\(786\) 0 0
\(787\) −6.77802 3.91329i −0.241610 0.139494i 0.374306 0.927305i \(-0.377881\pi\)
−0.615917 + 0.787811i \(0.711214\pi\)
\(788\) 0 0
\(789\) 0.0142032 0.0702445i 0.000505647 0.00250077i
\(790\) 0 0
\(791\) 8.62719 0.306748
\(792\) 0 0
\(793\) −3.38677 −0.120268
\(794\) 0 0
\(795\) 4.39811 1.47749i 0.155985 0.0524011i
\(796\) 0 0
\(797\) 22.3613 + 12.9103i 0.792078 + 0.457306i 0.840693 0.541511i \(-0.182148\pi\)
−0.0486158 + 0.998818i \(0.515481\pi\)