Properties

Label 432.2.be.a.239.1
Level $432$
Weight $2$
Character 432.239
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 239.1
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.a.47.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.72868 - 0.107984i) q^{3} +(0.902279 + 0.159096i) q^{5} +(-2.30964 - 2.75253i) q^{7} +(2.97668 + 0.373339i) q^{9} +O(q^{10})\) \(q+(-1.72868 - 0.107984i) q^{3} +(0.902279 + 0.159096i) q^{5} +(-2.30964 - 2.75253i) q^{7} +(2.97668 + 0.373339i) q^{9} +(0.316002 + 1.79214i) q^{11} +(-4.18526 + 1.52331i) q^{13} +(-1.54257 - 0.372458i) q^{15} +(-3.92200 - 2.26437i) q^{17} +(0.794277 - 0.458576i) q^{19} +(3.69541 + 5.00764i) q^{21} +(-5.68258 - 4.76825i) q^{23} +(-3.90967 - 1.42300i) q^{25} +(-5.10542 - 0.966817i) q^{27} +(3.02791 - 8.31913i) q^{29} +(-3.84549 + 4.58288i) q^{31} +(-0.352746 - 3.13216i) q^{33} +(-1.64603 - 2.85100i) q^{35} +(-3.15380 + 5.46255i) q^{37} +(7.39948 - 2.18138i) q^{39} +(-1.16283 - 3.19486i) q^{41} +(0.919062 - 0.162055i) q^{43} +(2.62640 + 0.810434i) q^{45} +(0.999632 - 0.838791i) q^{47} +(-1.02641 + 5.82105i) q^{49} +(6.53538 + 4.33789i) q^{51} -2.53299i q^{53} +1.66728i q^{55} +(-1.42257 + 0.706963i) q^{57} +(-2.13801 + 12.1253i) q^{59} +(-2.66045 + 2.23238i) q^{61} +(-5.84744 - 9.05567i) q^{63} +(-4.01863 + 0.708592i) q^{65} +(0.986708 + 2.71096i) q^{67} +(9.30847 + 8.85641i) q^{69} +(4.44194 - 7.69367i) q^{71} +(-0.528554 - 0.915482i) q^{73} +(6.60491 + 2.88210i) q^{75} +(4.20306 - 5.00901i) q^{77} +(3.99634 - 10.9798i) q^{79} +(8.72124 + 2.22262i) q^{81} +(15.7994 + 5.75052i) q^{83} +(-3.17849 - 2.66707i) q^{85} +(-6.13263 + 14.0542i) q^{87} +(13.1352 - 7.58359i) q^{89} +(13.8594 + 8.00174i) q^{91} +(7.14251 - 7.50709i) q^{93} +(0.789617 - 0.287397i) q^{95} +(1.86037 + 10.5507i) q^{97} +(0.271563 + 5.45260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 6 q^{5} - 12 q^{9} + O(q^{10}) \) \( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.72868 0.107984i −0.998055 0.0623444i
\(4\) 0 0
\(5\) 0.902279 + 0.159096i 0.403511 + 0.0711499i 0.371721 0.928345i \(-0.378768\pi\)
0.0317906 + 0.999495i \(0.489879\pi\)
\(6\) 0 0
\(7\) −2.30964 2.75253i −0.872963 1.04036i −0.998832 0.0483102i \(-0.984616\pi\)
0.125869 0.992047i \(-0.459828\pi\)
\(8\) 0 0
\(9\) 2.97668 + 0.373339i 0.992226 + 0.124446i
\(10\) 0 0
\(11\) 0.316002 + 1.79214i 0.0952783 + 0.540350i 0.994662 + 0.103189i \(0.0329048\pi\)
−0.899383 + 0.437161i \(0.855984\pi\)
\(12\) 0 0
\(13\) −4.18526 + 1.52331i −1.16078 + 0.422491i −0.849377 0.527786i \(-0.823022\pi\)
−0.311406 + 0.950277i \(0.600800\pi\)
\(14\) 0 0
\(15\) −1.54257 0.372458i −0.398290 0.0961682i
\(16\) 0 0
\(17\) −3.92200 2.26437i −0.951226 0.549190i −0.0577643 0.998330i \(-0.518397\pi\)
−0.893461 + 0.449140i \(0.851731\pi\)
\(18\) 0 0
\(19\) 0.794277 0.458576i 0.182220 0.105205i −0.406115 0.913822i \(-0.633117\pi\)
0.588335 + 0.808617i \(0.299784\pi\)
\(20\) 0 0
\(21\) 3.69541 + 5.00764i 0.806405 + 1.09276i
\(22\) 0 0
\(23\) −5.68258 4.76825i −1.18490 0.994248i −0.999934 0.0115034i \(-0.996338\pi\)
−0.184965 0.982745i \(-0.559217\pi\)
\(24\) 0 0
\(25\) −3.90967 1.42300i −0.781934 0.284601i
\(26\) 0 0
\(27\) −5.10542 0.966817i −0.982538 0.186064i
\(28\) 0 0
\(29\) 3.02791 8.31913i 0.562270 1.54482i −0.254031 0.967196i \(-0.581757\pi\)
0.816301 0.577627i \(-0.196021\pi\)
\(30\) 0 0
\(31\) −3.84549 + 4.58288i −0.690671 + 0.823110i −0.991437 0.130588i \(-0.958313\pi\)
0.300766 + 0.953698i \(0.402758\pi\)
\(32\) 0 0
\(33\) −0.352746 3.13216i −0.0614052 0.545239i
\(34\) 0 0
\(35\) −1.64603 2.85100i −0.278229 0.481907i
\(36\) 0 0
\(37\) −3.15380 + 5.46255i −0.518482 + 0.898037i 0.481287 + 0.876563i \(0.340169\pi\)
−0.999769 + 0.0214743i \(0.993164\pi\)
\(38\) 0 0
\(39\) 7.39948 2.18138i 1.18487 0.349300i
\(40\) 0 0
\(41\) −1.16283 3.19486i −0.181604 0.498953i 0.815169 0.579223i \(-0.196644\pi\)
−0.996773 + 0.0802698i \(0.974422\pi\)
\(42\) 0 0
\(43\) 0.919062 0.162055i 0.140156 0.0247132i −0.103130 0.994668i \(-0.532886\pi\)
0.243286 + 0.969955i \(0.421775\pi\)
\(44\) 0 0
\(45\) 2.62640 + 0.810434i 0.391520 + 0.120812i
\(46\) 0 0
\(47\) 0.999632 0.838791i 0.145811 0.122350i −0.566964 0.823742i \(-0.691882\pi\)
0.712776 + 0.701392i \(0.247438\pi\)
\(48\) 0 0
\(49\) −1.02641 + 5.82105i −0.146630 + 0.831579i
\(50\) 0 0
\(51\) 6.53538 + 4.33789i 0.915136 + 0.607426i
\(52\) 0 0
\(53\) 2.53299i 0.347934i −0.984752 0.173967i \(-0.944341\pi\)
0.984752 0.173967i \(-0.0556585\pi\)
\(54\) 0 0
\(55\) 1.66728i 0.224816i
\(56\) 0 0
\(57\) −1.42257 + 0.706963i −0.188424 + 0.0936395i
\(58\) 0 0
\(59\) −2.13801 + 12.1253i −0.278346 + 1.57858i 0.449785 + 0.893137i \(0.351501\pi\)
−0.728130 + 0.685439i \(0.759610\pi\)
\(60\) 0 0
\(61\) −2.66045 + 2.23238i −0.340636 + 0.285827i −0.797017 0.603957i \(-0.793590\pi\)
0.456381 + 0.889784i \(0.349145\pi\)
\(62\) 0 0
\(63\) −5.84744 9.05567i −0.736709 1.14091i
\(64\) 0 0
\(65\) −4.01863 + 0.708592i −0.498449 + 0.0878901i
\(66\) 0 0
\(67\) 0.986708 + 2.71096i 0.120546 + 0.331196i 0.985259 0.171069i \(-0.0547222\pi\)
−0.864713 + 0.502266i \(0.832500\pi\)
\(68\) 0 0
\(69\) 9.30847 + 8.85641i 1.12061 + 1.06619i
\(70\) 0 0
\(71\) 4.44194 7.69367i 0.527161 0.913070i −0.472337 0.881418i \(-0.656590\pi\)
0.999499 0.0316527i \(-0.0100770\pi\)
\(72\) 0 0
\(73\) −0.528554 0.915482i −0.0618625 0.107149i 0.833435 0.552617i \(-0.186371\pi\)
−0.895298 + 0.445468i \(0.853037\pi\)
\(74\) 0 0
\(75\) 6.60491 + 2.88210i 0.762669 + 0.332796i
\(76\) 0 0
\(77\) 4.20306 5.00901i 0.478983 0.570829i
\(78\) 0 0
\(79\) 3.99634 10.9798i 0.449623 1.23533i −0.483364 0.875420i \(-0.660585\pi\)
0.932987 0.359910i \(-0.117193\pi\)
\(80\) 0 0
\(81\) 8.72124 + 2.22262i 0.969026 + 0.246958i
\(82\) 0 0
\(83\) 15.7994 + 5.75052i 1.73421 + 0.631201i 0.998916 0.0465461i \(-0.0148214\pi\)
0.735295 + 0.677747i \(0.237044\pi\)
\(84\) 0 0
\(85\) −3.17849 2.66707i −0.344755 0.289284i
\(86\) 0 0
\(87\) −6.13263 + 14.0542i −0.657487 + 1.50676i
\(88\) 0 0
\(89\) 13.1352 7.58359i 1.39232 0.803859i 0.398752 0.917059i \(-0.369444\pi\)
0.993572 + 0.113200i \(0.0361102\pi\)
\(90\) 0 0
\(91\) 13.8594 + 8.00174i 1.45286 + 0.838811i
\(92\) 0 0
\(93\) 7.14251 7.50709i 0.740644 0.778449i
\(94\) 0 0
\(95\) 0.789617 0.287397i 0.0810130 0.0294863i
\(96\) 0 0
\(97\) 1.86037 + 10.5507i 0.188892 + 1.07126i 0.920852 + 0.389912i \(0.127495\pi\)
−0.731960 + 0.681347i \(0.761394\pi\)
\(98\) 0 0
\(99\) 0.271563 + 5.45260i 0.0272931 + 0.548007i
\(100\) 0 0
\(101\) −2.54770 3.03623i −0.253506 0.302116i 0.624250 0.781225i \(-0.285405\pi\)
−0.877756 + 0.479108i \(0.840960\pi\)
\(102\) 0 0
\(103\) −2.32334 0.409667i −0.228925 0.0403657i 0.0580087 0.998316i \(-0.481525\pi\)
−0.286934 + 0.957950i \(0.592636\pi\)
\(104\) 0 0
\(105\) 2.53759 + 5.10622i 0.247644 + 0.498316i
\(106\) 0 0
\(107\) 7.73225 0.747504 0.373752 0.927529i \(-0.378071\pi\)
0.373752 + 0.927529i \(0.378071\pi\)
\(108\) 0 0
\(109\) −15.5672 −1.49107 −0.745533 0.666469i \(-0.767805\pi\)
−0.745533 + 0.666469i \(0.767805\pi\)
\(110\) 0 0
\(111\) 6.04179 9.10244i 0.573461 0.863966i
\(112\) 0 0
\(113\) −9.66087 1.70347i −0.908818 0.160249i −0.300352 0.953829i \(-0.597104\pi\)
−0.608467 + 0.793579i \(0.708215\pi\)
\(114\) 0 0
\(115\) −4.36866 5.20636i −0.407379 0.485496i
\(116\) 0 0
\(117\) −13.0269 + 2.97189i −1.20434 + 0.274751i
\(118\) 0 0
\(119\) 2.82569 + 16.0253i 0.259031 + 1.46904i
\(120\) 0 0
\(121\) 7.22471 2.62958i 0.656792 0.239053i
\(122\) 0 0
\(123\) 1.66518 + 5.64846i 0.150144 + 0.509305i
\(124\) 0 0
\(125\) −7.26847 4.19645i −0.650112 0.375342i
\(126\) 0 0
\(127\) 16.7402 9.66498i 1.48546 0.857628i 0.485593 0.874185i \(-0.338604\pi\)
0.999863 + 0.0165567i \(0.00527040\pi\)
\(128\) 0 0
\(129\) −1.60627 + 0.180899i −0.141424 + 0.0159272i
\(130\) 0 0
\(131\) −13.4142 11.2558i −1.17200 0.983427i −0.172004 0.985096i \(-0.555024\pi\)
−0.999999 + 0.00166932i \(0.999469\pi\)
\(132\) 0 0
\(133\) −3.09674 1.12712i −0.268521 0.0977338i
\(134\) 0 0
\(135\) −4.45269 1.68459i −0.383227 0.144986i
\(136\) 0 0
\(137\) −5.50764 + 15.1321i −0.470549 + 1.29282i 0.446762 + 0.894653i \(0.352577\pi\)
−0.917312 + 0.398170i \(0.869645\pi\)
\(138\) 0 0
\(139\) −10.6052 + 12.6388i −0.899525 + 1.07201i 0.0975235 + 0.995233i \(0.468908\pi\)
−0.997048 + 0.0767785i \(0.975537\pi\)
\(140\) 0 0
\(141\) −1.81862 + 1.34206i −0.153156 + 0.113022i
\(142\) 0 0
\(143\) −4.05254 7.01921i −0.338890 0.586975i
\(144\) 0 0
\(145\) 4.05556 7.02444i 0.336796 0.583348i
\(146\) 0 0
\(147\) 2.40291 9.95191i 0.198189 0.820820i
\(148\) 0 0
\(149\) −2.32731 6.39423i −0.190661 0.523836i 0.807123 0.590384i \(-0.201024\pi\)
−0.997783 + 0.0665481i \(0.978801\pi\)
\(150\) 0 0
\(151\) −14.6770 + 2.58795i −1.19440 + 0.210604i −0.735275 0.677769i \(-0.762947\pi\)
−0.459121 + 0.888374i \(0.651836\pi\)
\(152\) 0 0
\(153\) −10.8292 8.20454i −0.875487 0.663298i
\(154\) 0 0
\(155\) −4.19882 + 3.52323i −0.337258 + 0.282993i
\(156\) 0 0
\(157\) 1.99263 11.3007i 0.159029 0.901897i −0.795981 0.605322i \(-0.793044\pi\)
0.955009 0.296575i \(-0.0958446\pi\)
\(158\) 0 0
\(159\) −0.273522 + 4.37874i −0.0216917 + 0.347257i
\(160\) 0 0
\(161\) 26.6544i 2.10066i
\(162\) 0 0
\(163\) 3.48604i 0.273047i 0.990637 + 0.136524i \(0.0435930\pi\)
−0.990637 + 0.136524i \(0.956407\pi\)
\(164\) 0 0
\(165\) 0.180039 2.88220i 0.0140160 0.224379i
\(166\) 0 0
\(167\) −0.759638 + 4.30812i −0.0587826 + 0.333372i −0.999990 0.00445650i \(-0.998581\pi\)
0.941208 + 0.337829i \(0.109693\pi\)
\(168\) 0 0
\(169\) 5.23738 4.39469i 0.402876 0.338053i
\(170\) 0 0
\(171\) 2.53551 1.06850i 0.193895 0.0817102i
\(172\) 0 0
\(173\) 10.3347 1.82229i 0.785732 0.138546i 0.233634 0.972325i \(-0.424938\pi\)
0.552098 + 0.833779i \(0.313827\pi\)
\(174\) 0 0
\(175\) 5.11309 + 14.0481i 0.386513 + 1.06194i
\(176\) 0 0
\(177\) 5.00527 20.7299i 0.376219 1.55815i
\(178\) 0 0
\(179\) 12.6163 21.8521i 0.942988 1.63330i 0.183257 0.983065i \(-0.441336\pi\)
0.759731 0.650238i \(-0.225331\pi\)
\(180\) 0 0
\(181\) 1.92076 + 3.32686i 0.142769 + 0.247283i 0.928538 0.371236i \(-0.121066\pi\)
−0.785769 + 0.618520i \(0.787733\pi\)
\(182\) 0 0
\(183\) 4.84013 3.57179i 0.357793 0.264034i
\(184\) 0 0
\(185\) −3.71468 + 4.42698i −0.273109 + 0.325478i
\(186\) 0 0
\(187\) 2.81870 7.74432i 0.206124 0.566321i
\(188\) 0 0
\(189\) 9.13050 + 16.2858i 0.664146 + 1.18462i
\(190\) 0 0
\(191\) −9.28905 3.38094i −0.672132 0.244636i −0.0166663 0.999861i \(-0.505305\pi\)
−0.655465 + 0.755225i \(0.727528\pi\)
\(192\) 0 0
\(193\) 7.95376 + 6.67400i 0.572524 + 0.480405i 0.882482 0.470345i \(-0.155871\pi\)
−0.309958 + 0.950750i \(0.600315\pi\)
\(194\) 0 0
\(195\) 7.02344 0.790984i 0.502959 0.0566436i
\(196\) 0 0
\(197\) 11.0769 6.39528i 0.789200 0.455645i −0.0504809 0.998725i \(-0.516075\pi\)
0.839681 + 0.543080i \(0.182742\pi\)
\(198\) 0 0
\(199\) 6.79765 + 3.92463i 0.481873 + 0.278209i 0.721197 0.692730i \(-0.243592\pi\)
−0.239324 + 0.970940i \(0.576926\pi\)
\(200\) 0 0
\(201\) −1.41296 4.79293i −0.0996628 0.338067i
\(202\) 0 0
\(203\) −29.8920 + 10.8798i −2.09801 + 0.763613i
\(204\) 0 0
\(205\) −0.540911 3.06766i −0.0377788 0.214254i
\(206\) 0 0
\(207\) −15.1350 16.3151i −1.05196 1.13398i
\(208\) 0 0
\(209\) 1.07283 + 1.27854i 0.0742089 + 0.0884387i
\(210\) 0 0
\(211\) −28.3624 5.00106i −1.95255 0.344287i −0.999084 0.0427907i \(-0.986375\pi\)
−0.953467 0.301497i \(-0.902514\pi\)
\(212\) 0 0
\(213\) −8.50949 + 12.8202i −0.583061 + 0.878429i
\(214\) 0 0
\(215\) 0.855033 0.0583127
\(216\) 0 0
\(217\) 21.4962 1.45926
\(218\) 0 0
\(219\) 0.814844 + 1.63965i 0.0550620 + 0.110797i
\(220\) 0 0
\(221\) 19.8640 + 3.50255i 1.33620 + 0.235607i
\(222\) 0 0
\(223\) −15.0617 17.9499i −1.00861 1.20201i −0.979294 0.202443i \(-0.935112\pi\)
−0.0293149 0.999570i \(-0.509333\pi\)
\(224\) 0 0
\(225\) −11.1066 5.69545i −0.740438 0.379697i
\(226\) 0 0
\(227\) 0.871006 + 4.93972i 0.0578107 + 0.327861i 0.999973 0.00729519i \(-0.00232215\pi\)
−0.942163 + 0.335156i \(0.891211\pi\)
\(228\) 0 0
\(229\) −9.01670 + 3.28181i −0.595840 + 0.216868i −0.622296 0.782782i \(-0.713800\pi\)
0.0264559 + 0.999650i \(0.491578\pi\)
\(230\) 0 0
\(231\) −7.80664 + 8.20512i −0.513639 + 0.539857i
\(232\) 0 0
\(233\) −18.7009 10.7969i −1.22513 0.707332i −0.259126 0.965843i \(-0.583435\pi\)
−0.966008 + 0.258512i \(0.916768\pi\)
\(234\) 0 0
\(235\) 1.03540 0.597786i 0.0675417 0.0389952i
\(236\) 0 0
\(237\) −8.09404 + 18.5491i −0.525764 + 1.20490i
\(238\) 0 0
\(239\) 8.27842 + 6.94642i 0.535486 + 0.449326i 0.869991 0.493068i \(-0.164125\pi\)
−0.334505 + 0.942394i \(0.608569\pi\)
\(240\) 0 0
\(241\) 12.1965 + 4.43917i 0.785646 + 0.285952i 0.703525 0.710670i \(-0.251608\pi\)
0.0821214 + 0.996622i \(0.473830\pi\)
\(242\) 0 0
\(243\) −14.8362 4.78395i −0.951745 0.306891i
\(244\) 0 0
\(245\) −1.85221 + 5.08891i −0.118334 + 0.325119i
\(246\) 0 0
\(247\) −2.62571 + 3.12919i −0.167070 + 0.199106i
\(248\) 0 0
\(249\) −26.6912 11.6469i −1.69149 0.738092i
\(250\) 0 0
\(251\) −9.36454 16.2199i −0.591085 1.02379i −0.994087 0.108590i \(-0.965367\pi\)
0.403002 0.915199i \(-0.367967\pi\)
\(252\) 0 0
\(253\) 6.74965 11.6907i 0.424347 0.734991i
\(254\) 0 0
\(255\) 5.20659 + 4.95374i 0.326050 + 0.310215i
\(256\) 0 0
\(257\) 9.97322 + 27.4012i 0.622113 + 1.70924i 0.701756 + 0.712417i \(0.252399\pi\)
−0.0796439 + 0.996823i \(0.525378\pi\)
\(258\) 0 0
\(259\) 22.3200 3.93561i 1.38689 0.244547i
\(260\) 0 0
\(261\) 12.1190 23.6329i 0.750146 1.46284i
\(262\) 0 0
\(263\) 6.74060 5.65604i 0.415643 0.348766i −0.410859 0.911699i \(-0.634771\pi\)
0.826503 + 0.562932i \(0.190327\pi\)
\(264\) 0 0
\(265\) 0.402989 2.28547i 0.0247554 0.140395i
\(266\) 0 0
\(267\) −23.5254 + 11.6912i −1.43973 + 0.715491i
\(268\) 0 0
\(269\) 20.0940i 1.22515i 0.790412 + 0.612575i \(0.209866\pi\)
−0.790412 + 0.612575i \(0.790134\pi\)
\(270\) 0 0
\(271\) 9.14240i 0.555361i −0.960673 0.277681i \(-0.910434\pi\)
0.960673 0.277681i \(-0.0895657\pi\)
\(272\) 0 0
\(273\) −23.0945 15.3291i −1.39774 0.927757i
\(274\) 0 0
\(275\) 1.31475 7.45634i 0.0792826 0.449634i
\(276\) 0 0
\(277\) 11.2006 9.39839i 0.672977 0.564694i −0.240968 0.970533i \(-0.577465\pi\)
0.913945 + 0.405839i \(0.133021\pi\)
\(278\) 0 0
\(279\) −13.1578 + 12.2061i −0.787735 + 0.730760i
\(280\) 0 0
\(281\) 4.33423 0.764241i 0.258558 0.0455908i −0.0428663 0.999081i \(-0.513649\pi\)
0.301425 + 0.953490i \(0.402538\pi\)
\(282\) 0 0
\(283\) −4.34262 11.9313i −0.258142 0.709239i −0.999282 0.0378888i \(-0.987937\pi\)
0.741140 0.671351i \(-0.234285\pi\)
\(284\) 0 0
\(285\) −1.39603 + 0.411552i −0.0826937 + 0.0243782i
\(286\) 0 0
\(287\) −6.10820 + 10.5797i −0.360556 + 0.624501i
\(288\) 0 0
\(289\) 1.75474 + 3.03931i 0.103220 + 0.178783i
\(290\) 0 0
\(291\) −2.07669 18.4397i −0.121737 1.08095i
\(292\) 0 0
\(293\) −13.6489 + 16.2661i −0.797376 + 0.950276i −0.999577 0.0290682i \(-0.990746\pi\)
0.202201 + 0.979344i \(0.435190\pi\)
\(294\) 0 0
\(295\) −3.85817 + 10.6002i −0.224631 + 0.617169i
\(296\) 0 0
\(297\) 0.119346 9.45513i 0.00692517 0.548642i
\(298\) 0 0
\(299\) 31.0466 + 11.3000i 1.79547 + 0.653498i
\(300\) 0 0
\(301\) −2.56877 2.15545i −0.148061 0.124238i
\(302\) 0 0
\(303\) 4.07630 + 5.52379i 0.234177 + 0.317333i
\(304\) 0 0
\(305\) −2.75563 + 1.59096i −0.157787 + 0.0910983i
\(306\) 0 0
\(307\) 1.24710 + 0.720015i 0.0711759 + 0.0410934i 0.535166 0.844747i \(-0.320249\pi\)
−0.463990 + 0.885841i \(0.653583\pi\)
\(308\) 0 0
\(309\) 3.97207 + 0.959066i 0.225963 + 0.0545594i
\(310\) 0 0
\(311\) −8.32511 + 3.03009i −0.472073 + 0.171821i −0.567091 0.823655i \(-0.691931\pi\)
0.0950180 + 0.995476i \(0.469709\pi\)
\(312\) 0 0
\(313\) −5.38779 30.5557i −0.304536 1.72711i −0.625681 0.780079i \(-0.715179\pi\)
0.321145 0.947030i \(-0.395932\pi\)
\(314\) 0 0
\(315\) −3.83530 9.10104i −0.216095 0.512785i
\(316\) 0 0
\(317\) 1.05369 + 1.25574i 0.0591813 + 0.0705295i 0.794823 0.606841i \(-0.207564\pi\)
−0.735642 + 0.677371i \(0.763119\pi\)
\(318\) 0 0
\(319\) 15.8659 + 2.79758i 0.888318 + 0.156634i
\(320\) 0 0
\(321\) −13.3666 0.834957i −0.746050 0.0466027i
\(322\) 0 0
\(323\) −4.15354 −0.231109
\(324\) 0 0
\(325\) 18.5307 1.02790
\(326\) 0 0
\(327\) 26.9107 + 1.68100i 1.48817 + 0.0929597i
\(328\) 0 0
\(329\) −4.61759 0.814205i −0.254576 0.0448886i
\(330\) 0 0
\(331\) −4.17455 4.97503i −0.229454 0.273452i 0.639017 0.769193i \(-0.279341\pi\)
−0.868471 + 0.495740i \(0.834897\pi\)
\(332\) 0 0
\(333\) −11.4272 + 15.0828i −0.626209 + 0.826533i
\(334\) 0 0
\(335\) 0.458983 + 2.60302i 0.0250769 + 0.142218i
\(336\) 0 0
\(337\) 19.8793 7.23548i 1.08290 0.394142i 0.261911 0.965092i \(-0.415647\pi\)
0.820985 + 0.570950i \(0.193425\pi\)
\(338\) 0 0
\(339\) 16.5166 + 3.98798i 0.897060 + 0.216597i
\(340\) 0 0
\(341\) −9.42834 5.44346i −0.510573 0.294780i
\(342\) 0 0
\(343\) −3.38918 + 1.95675i −0.182999 + 0.105654i
\(344\) 0 0
\(345\) 6.98981 + 9.47189i 0.376319 + 0.509949i
\(346\) 0 0
\(347\) 7.60026 + 6.37737i 0.408003 + 0.342355i 0.823577 0.567204i \(-0.191975\pi\)
−0.415574 + 0.909559i \(0.636419\pi\)
\(348\) 0 0
\(349\) −10.6407 3.87290i −0.569583 0.207311i 0.0411427 0.999153i \(-0.486900\pi\)
−0.610726 + 0.791842i \(0.709122\pi\)
\(350\) 0 0
\(351\) 22.8403 3.73075i 1.21912 0.199133i
\(352\) 0 0
\(353\) 3.15842 8.67769i 0.168106 0.461867i −0.826821 0.562464i \(-0.809853\pi\)
0.994927 + 0.100598i \(0.0320755\pi\)
\(354\) 0 0
\(355\) 5.23190 6.23514i 0.277680 0.330927i
\(356\) 0 0
\(357\) −3.15425 28.0078i −0.166941 1.48233i
\(358\) 0 0
\(359\) 8.31565 + 14.4031i 0.438883 + 0.760168i 0.997604 0.0691878i \(-0.0220408\pi\)
−0.558720 + 0.829356i \(0.688707\pi\)
\(360\) 0 0
\(361\) −9.07942 + 15.7260i −0.477864 + 0.827685i
\(362\) 0 0
\(363\) −12.7732 + 3.76556i −0.670418 + 0.197640i
\(364\) 0 0
\(365\) −0.331253 0.910110i −0.0173386 0.0476374i
\(366\) 0 0
\(367\) −15.0549 + 2.65459i −0.785860 + 0.138568i −0.552158 0.833740i \(-0.686195\pi\)
−0.233703 + 0.972308i \(0.575084\pi\)
\(368\) 0 0
\(369\) −2.26862 9.94420i −0.118100 0.517675i
\(370\) 0 0
\(371\) −6.97213 + 5.85032i −0.361975 + 0.303733i
\(372\) 0 0
\(373\) −3.27227 + 18.5580i −0.169432 + 0.960896i 0.774945 + 0.632029i \(0.217778\pi\)
−0.944376 + 0.328866i \(0.893333\pi\)
\(374\) 0 0
\(375\) 12.1117 + 8.03920i 0.625446 + 0.415143i
\(376\) 0 0
\(377\) 39.4302i 2.03076i
\(378\) 0 0
\(379\) 27.7620i 1.42604i 0.701144 + 0.713019i \(0.252673\pi\)
−0.701144 + 0.713019i \(0.747327\pi\)
\(380\) 0 0
\(381\) −29.9822 + 14.9000i −1.53603 + 0.763350i
\(382\) 0 0
\(383\) 5.46348 30.9849i 0.279171 1.58325i −0.446224 0.894921i \(-0.647231\pi\)
0.725394 0.688333i \(-0.241657\pi\)
\(384\) 0 0
\(385\) 4.58924 3.85083i 0.233889 0.196256i
\(386\) 0 0
\(387\) 2.79626 0.139265i 0.142142 0.00707926i
\(388\) 0 0
\(389\) −9.58341 + 1.68981i −0.485898 + 0.0856769i −0.411230 0.911532i \(-0.634901\pi\)
−0.0746678 + 0.997208i \(0.523790\pi\)
\(390\) 0 0
\(391\) 11.4900 + 31.5685i 0.581075 + 1.59649i
\(392\) 0 0
\(393\) 21.9734 + 20.9063i 1.10841 + 1.05458i
\(394\) 0 0
\(395\) 5.35266 9.27108i 0.269322 0.466479i
\(396\) 0 0
\(397\) −8.72266 15.1081i −0.437778 0.758253i 0.559740 0.828668i \(-0.310901\pi\)
−0.997518 + 0.0704151i \(0.977568\pi\)
\(398\) 0 0
\(399\) 5.23156 + 2.28283i 0.261906 + 0.114284i
\(400\) 0 0
\(401\) 6.59597 7.86077i 0.329387 0.392548i −0.575780 0.817605i \(-0.695301\pi\)
0.905167 + 0.425057i \(0.139746\pi\)
\(402\) 0 0
\(403\) 9.11325 25.0385i 0.453963 1.24725i
\(404\) 0 0
\(405\) 7.51537 + 3.39294i 0.373442 + 0.168596i
\(406\) 0 0
\(407\) −10.7863 3.92587i −0.534655 0.194598i
\(408\) 0 0
\(409\) −5.65802 4.74764i −0.279771 0.234756i 0.492094 0.870542i \(-0.336232\pi\)
−0.771865 + 0.635786i \(0.780676\pi\)
\(410\) 0 0
\(411\) 11.1550 25.5639i 0.550234 1.26097i
\(412\) 0 0
\(413\) 38.3132 22.1201i 1.88527 1.08846i
\(414\) 0 0
\(415\) 13.3406 + 7.70219i 0.654864 + 0.378086i
\(416\) 0 0
\(417\) 19.6979 20.7033i 0.964609 1.01385i
\(418\) 0 0
\(419\) −15.7103 + 5.71807i −0.767496 + 0.279346i −0.695949 0.718091i \(-0.745016\pi\)
−0.0715474 + 0.997437i \(0.522794\pi\)
\(420\) 0 0
\(421\) 1.99066 + 11.2896i 0.0970187 + 0.550221i 0.994110 + 0.108375i \(0.0345648\pi\)
−0.897091 + 0.441845i \(0.854324\pi\)
\(422\) 0 0
\(423\) 3.28874 2.12361i 0.159904 0.103253i
\(424\) 0 0
\(425\) 12.1115 + 14.4340i 0.587495 + 0.700150i
\(426\) 0 0
\(427\) 12.2894 + 2.16695i 0.594725 + 0.104866i
\(428\) 0 0
\(429\) 6.24759 + 12.5716i 0.301637 + 0.606961i
\(430\) 0 0
\(431\) 16.5555 0.797449 0.398724 0.917071i \(-0.369453\pi\)
0.398724 + 0.917071i \(0.369453\pi\)
\(432\) 0 0
\(433\) −4.88427 −0.234723 −0.117361 0.993089i \(-0.537444\pi\)
−0.117361 + 0.993089i \(0.537444\pi\)
\(434\) 0 0
\(435\) −7.76930 + 11.7051i −0.372509 + 0.561216i
\(436\) 0 0
\(437\) −6.70014 1.18142i −0.320511 0.0565148i
\(438\) 0 0
\(439\) 19.5417 + 23.2889i 0.932677 + 1.11152i 0.993552 + 0.113375i \(0.0361662\pi\)
−0.0608757 + 0.998145i \(0.519389\pi\)
\(440\) 0 0
\(441\) −5.22851 + 16.9442i −0.248977 + 0.806867i
\(442\) 0 0
\(443\) −0.340783 1.93268i −0.0161911 0.0918243i 0.975641 0.219372i \(-0.0704007\pi\)
−0.991832 + 0.127547i \(0.959290\pi\)
\(444\) 0 0
\(445\) 13.0581 4.75276i 0.619013 0.225302i
\(446\) 0 0
\(447\) 3.33270 + 11.3049i 0.157631 + 0.534703i
\(448\) 0 0
\(449\) −25.2445 14.5749i −1.19136 0.687834i −0.232747 0.972537i \(-0.574771\pi\)
−0.958616 + 0.284704i \(0.908105\pi\)
\(450\) 0 0
\(451\) 5.35817 3.09354i 0.252307 0.145669i
\(452\) 0 0
\(453\) 25.6513 2.88886i 1.20520 0.135731i
\(454\) 0 0
\(455\) 11.2320 + 9.42478i 0.526565 + 0.441841i
\(456\) 0 0
\(457\) 28.2232 + 10.2724i 1.32023 + 0.480523i 0.903531 0.428523i \(-0.140966\pi\)
0.416695 + 0.909046i \(0.363188\pi\)
\(458\) 0 0
\(459\) 17.8342 + 15.3524i 0.832431 + 0.716589i
\(460\) 0 0
\(461\) −0.669179 + 1.83856i −0.0311668 + 0.0856301i −0.954300 0.298850i \(-0.903397\pi\)
0.923133 + 0.384480i \(0.125619\pi\)
\(462\) 0 0
\(463\) −13.0605 + 15.5649i −0.606974 + 0.723363i −0.978772 0.204950i \(-0.934297\pi\)
0.371799 + 0.928313i \(0.378741\pi\)
\(464\) 0 0
\(465\) 7.63888 5.63714i 0.354245 0.261416i
\(466\) 0 0
\(467\) 0.632284 + 1.09515i 0.0292586 + 0.0506774i 0.880284 0.474447i \(-0.157352\pi\)
−0.851025 + 0.525125i \(0.824019\pi\)
\(468\) 0 0
\(469\) 5.18304 8.97729i 0.239330 0.414533i
\(470\) 0 0
\(471\) −4.66491 + 19.3202i −0.214948 + 0.890228i
\(472\) 0 0
\(473\) 0.580852 + 1.59588i 0.0267076 + 0.0733785i
\(474\) 0 0
\(475\) −3.75791 + 0.662622i −0.172425 + 0.0304032i
\(476\) 0 0
\(477\) 0.945665 7.53991i 0.0432990 0.345229i
\(478\) 0 0
\(479\) 5.46294 4.58395i 0.249608 0.209446i −0.509395 0.860533i \(-0.670131\pi\)
0.759004 + 0.651086i \(0.225686\pi\)
\(480\) 0 0
\(481\) 4.87834 27.6664i 0.222433 1.26148i
\(482\) 0 0
\(483\) 2.87824 46.0770i 0.130964 2.09657i
\(484\) 0 0
\(485\) 9.81563i 0.445705i
\(486\) 0 0
\(487\) 35.3831i 1.60336i −0.597752 0.801681i \(-0.703939\pi\)
0.597752 0.801681i \(-0.296061\pi\)
\(488\) 0 0
\(489\) 0.376435 6.02625i 0.0170230 0.272516i
\(490\) 0 0
\(491\) −0.202915 + 1.15079i −0.00915741 + 0.0519343i −0.989044 0.147621i \(-0.952839\pi\)
0.979887 + 0.199555i \(0.0639496\pi\)
\(492\) 0 0
\(493\) −30.7131 + 25.7713i −1.38325 + 1.16068i
\(494\) 0 0
\(495\) −0.622462 + 4.96297i −0.0279776 + 0.223069i
\(496\) 0 0
\(497\) −31.4363 + 5.54307i −1.41011 + 0.248641i
\(498\) 0 0
\(499\) −9.12958 25.0833i −0.408696 1.12288i −0.957877 0.287180i \(-0.907282\pi\)
0.549180 0.835704i \(-0.314940\pi\)
\(500\) 0 0
\(501\) 1.77838 7.36534i 0.0794521 0.329059i
\(502\) 0 0
\(503\) −11.9257 + 20.6560i −0.531742 + 0.921005i 0.467571 + 0.883956i \(0.345129\pi\)
−0.999313 + 0.0370494i \(0.988204\pi\)
\(504\) 0 0
\(505\) −1.81568 3.14486i −0.0807969 0.139944i
\(506\) 0 0
\(507\) −9.52832 + 7.03146i −0.423168 + 0.312278i
\(508\) 0 0
\(509\) 13.0480 15.5500i 0.578343 0.689242i −0.394978 0.918691i \(-0.629248\pi\)
0.973321 + 0.229449i \(0.0736923\pi\)
\(510\) 0 0
\(511\) −1.29912 + 3.56929i −0.0574695 + 0.157896i
\(512\) 0 0
\(513\) −4.49847 + 1.57330i −0.198612 + 0.0694629i
\(514\) 0 0
\(515\) −2.03112 0.739267i −0.0895018 0.0325760i
\(516\) 0 0
\(517\) 1.81912 + 1.52642i 0.0800046 + 0.0671319i
\(518\) 0 0
\(519\) −18.0622 + 2.03417i −0.792841 + 0.0892902i
\(520\) 0 0
\(521\) 28.4047 16.3995i 1.24443 0.718474i 0.274439 0.961604i \(-0.411508\pi\)
0.969993 + 0.243131i \(0.0781745\pi\)
\(522\) 0 0
\(523\) −30.4619 17.5872i −1.33201 0.769034i −0.346399 0.938087i \(-0.612596\pi\)
−0.985607 + 0.169053i \(0.945929\pi\)
\(524\) 0 0
\(525\) −7.32193 24.8368i −0.319555 1.08397i
\(526\) 0 0
\(527\) 25.4594 9.26646i 1.10903 0.403653i
\(528\) 0 0
\(529\) 5.56158 + 31.5413i 0.241808 + 1.37136i
\(530\) 0 0
\(531\) −10.8910 + 35.2948i −0.472630 + 1.53167i
\(532\) 0 0
\(533\) 9.73354 + 11.6000i 0.421606 + 0.502451i
\(534\) 0 0
\(535\) 6.97664 + 1.23017i 0.301626 + 0.0531849i
\(536\) 0 0
\(537\) −24.1693 + 36.4130i −1.04298 + 1.57134i
\(538\) 0 0
\(539\) −10.7565 −0.463315
\(540\) 0 0
\(541\) −35.1137 −1.50965 −0.754827 0.655924i \(-0.772279\pi\)
−0.754827 + 0.655924i \(0.772279\pi\)
\(542\) 0 0
\(543\) −2.96114 5.95849i −0.127075 0.255703i
\(544\) 0 0
\(545\) −14.0459 2.47668i −0.601662 0.106089i
\(546\) 0 0
\(547\) 9.15157 + 10.9064i 0.391293 + 0.466324i 0.925345 0.379127i \(-0.123776\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(548\) 0 0
\(549\) −8.75274 + 5.65184i −0.373558 + 0.241214i
\(550\) 0 0
\(551\) −1.40995 7.99622i −0.0600659 0.340650i
\(552\) 0 0
\(553\) −39.4524 + 14.3595i −1.67769 + 0.610629i
\(554\) 0 0
\(555\) 6.89954 7.25172i 0.292869 0.307818i
\(556\) 0 0
\(557\) −21.0603 12.1592i −0.892352 0.515200i −0.0176411 0.999844i \(-0.505616\pi\)
−0.874711 + 0.484645i \(0.838949\pi\)
\(558\) 0 0
\(559\) −3.59966 + 2.07826i −0.152249 + 0.0879012i
\(560\) 0 0
\(561\) −5.70890 + 13.0831i −0.241030 + 0.552369i
\(562\) 0 0
\(563\) 5.33375 + 4.47555i 0.224791 + 0.188622i 0.748227 0.663443i \(-0.230906\pi\)
−0.523436 + 0.852065i \(0.675350\pi\)
\(564\) 0 0
\(565\) −8.44578 3.07401i −0.355317 0.129325i
\(566\) 0 0
\(567\) −14.0251 29.1389i −0.589000 1.22372i
\(568\) 0 0
\(569\) 6.42509 17.6528i 0.269354 0.740043i −0.729098 0.684410i \(-0.760060\pi\)
0.998451 0.0556334i \(-0.0177178\pi\)
\(570\) 0 0
\(571\) 17.2113 20.5116i 0.720269 0.858383i −0.274388 0.961619i \(-0.588475\pi\)
0.994657 + 0.103236i \(0.0329197\pi\)
\(572\) 0 0
\(573\) 15.6927 + 6.84763i 0.655573 + 0.286064i
\(574\) 0 0
\(575\) 15.4318 + 26.7286i 0.643549 + 1.11466i
\(576\) 0 0
\(577\) −4.84104 + 8.38493i −0.201535 + 0.349069i −0.949023 0.315206i \(-0.897926\pi\)
0.747488 + 0.664275i \(0.231260\pi\)
\(578\) 0 0
\(579\) −13.0288 12.3961i −0.541460 0.515164i
\(580\) 0 0
\(581\) −20.6626 56.7699i −0.857228 2.35521i
\(582\) 0 0
\(583\) 4.53948 0.800433i 0.188006 0.0331505i
\(584\) 0 0
\(585\) −12.2267 + 0.608942i −0.505512 + 0.0251767i
\(586\) 0 0
\(587\) 6.78871 5.69641i 0.280200 0.235116i −0.491846 0.870682i \(-0.663678\pi\)
0.772046 + 0.635566i \(0.219233\pi\)
\(588\) 0 0
\(589\) −0.952788 + 5.40353i −0.0392589 + 0.222648i
\(590\) 0 0
\(591\) −19.8391 + 9.85927i −0.816072 + 0.405556i
\(592\) 0 0
\(593\) 6.46963i 0.265676i −0.991138 0.132838i \(-0.957591\pi\)
0.991138 0.132838i \(-0.0424090\pi\)
\(594\) 0 0
\(595\) 14.9088i 0.611203i
\(596\) 0 0
\(597\) −11.3272 7.51846i −0.463590 0.307710i
\(598\) 0 0
\(599\) −0.995333 + 5.64481i −0.0406682 + 0.230641i −0.998367 0.0571331i \(-0.981804\pi\)
0.957698 + 0.287774i \(0.0929152\pi\)
\(600\) 0 0
\(601\) −13.9437 + 11.7002i −0.568777 + 0.477260i −0.881240 0.472670i \(-0.843290\pi\)
0.312463 + 0.949930i \(0.398846\pi\)
\(602\) 0 0
\(603\) 1.92501 + 8.43803i 0.0783923 + 0.343623i
\(604\) 0 0
\(605\) 6.93706 1.22319i 0.282032 0.0497298i
\(606\) 0 0
\(607\) −12.4668 34.2523i −0.506012 1.39026i −0.885318 0.464985i \(-0.846060\pi\)
0.379307 0.925271i \(-0.376163\pi\)
\(608\) 0 0
\(609\) 52.8486 15.5799i 2.14153 0.631328i
\(610\) 0 0
\(611\) −2.90599 + 5.03331i −0.117564 + 0.203626i
\(612\) 0 0
\(613\) 9.95224 + 17.2378i 0.401967 + 0.696228i 0.993963 0.109713i \(-0.0349932\pi\)
−0.591996 + 0.805941i \(0.701660\pi\)
\(614\) 0 0
\(615\) 0.603805 + 5.36141i 0.0243478 + 0.216193i
\(616\) 0 0
\(617\) 10.3239 12.3036i 0.415625 0.495323i −0.517093 0.855929i \(-0.672986\pi\)
0.932718 + 0.360607i \(0.117430\pi\)
\(618\) 0 0
\(619\) −11.8156 + 32.4631i −0.474909 + 1.30480i 0.438855 + 0.898558i \(0.355384\pi\)
−0.913764 + 0.406245i \(0.866838\pi\)
\(620\) 0 0
\(621\) 24.4019 + 29.8379i 0.979214 + 1.19735i
\(622\) 0 0
\(623\) −51.2115 18.6395i −2.05175 0.746775i
\(624\) 0 0
\(625\) 10.0454 + 8.42910i 0.401816 + 0.337164i
\(626\) 0 0
\(627\) −1.71651 2.32604i −0.0685509 0.0928932i
\(628\) 0 0
\(629\) 24.7385 14.2828i 0.986387 0.569491i
\(630\) 0 0
\(631\) −26.9199 15.5422i −1.07166 0.618725i −0.143028 0.989719i \(-0.545684\pi\)
−0.928635 + 0.370994i \(0.879017\pi\)
\(632\) 0 0
\(633\) 48.4896 + 11.7079i 1.92729 + 0.465348i
\(634\) 0 0
\(635\) 16.6420 6.05720i 0.660418 0.240373i
\(636\) 0 0
\(637\) −4.57149 25.9262i −0.181129 1.02723i
\(638\) 0 0
\(639\) 16.0946 21.2432i 0.636692 0.840369i
\(640\) 0 0
\(641\) −23.7440 28.2970i −0.937831 1.11766i −0.992873 0.119179i \(-0.961974\pi\)
0.0550422 0.998484i \(-0.482471\pi\)
\(642\) 0 0
\(643\) −0.700721 0.123556i −0.0276337 0.00487257i 0.159814 0.987147i \(-0.448910\pi\)
−0.187448 + 0.982275i \(0.560022\pi\)
\(644\) 0 0
\(645\) −1.47808 0.0923296i −0.0581993 0.00363547i
\(646\) 0 0
\(647\) −33.2439 −1.30695 −0.653476 0.756947i \(-0.726690\pi\)
−0.653476 + 0.756947i \(0.726690\pi\)
\(648\) 0 0
\(649\) −22.4058 −0.879504
\(650\) 0 0
\(651\) −37.1601 2.32124i −1.45642 0.0909766i
\(652\) 0 0
\(653\) 5.33170 + 0.940122i 0.208645 + 0.0367898i 0.276994 0.960872i \(-0.410662\pi\)
−0.0683484 + 0.997662i \(0.521773\pi\)
\(654\) 0 0
\(655\) −10.3126 12.2900i −0.402945 0.480212i
\(656\) 0 0
\(657\) −1.23155 2.92242i −0.0480473 0.114015i
\(658\) 0 0
\(659\) −3.94718 22.3856i −0.153760 0.872017i −0.959911 0.280307i \(-0.909564\pi\)
0.806150 0.591711i \(-0.201547\pi\)
\(660\) 0 0
\(661\) 1.00411 0.365468i 0.0390555 0.0142150i −0.322419 0.946597i \(-0.604496\pi\)
0.361474 + 0.932382i \(0.382274\pi\)
\(662\) 0 0
\(663\) −33.9603 8.19978i −1.31891 0.318453i
\(664\) 0 0
\(665\) −2.61480 1.50966i −0.101398 0.0585419i
\(666\) 0 0
\(667\) −56.8740 + 32.8362i −2.20217 + 1.27142i
\(668\) 0 0
\(669\) 24.0987 + 32.6561i 0.931708 + 1.26256i
\(670\) 0 0
\(671\) −4.84145 4.06246i −0.186902 0.156829i
\(672\) 0 0
\(673\) −16.4390 5.98331i −0.633677 0.230640i 0.00515388 0.999987i \(-0.498359\pi\)
−0.638831 + 0.769347i \(0.720582\pi\)
\(674\) 0 0
\(675\) 18.5847 + 11.0450i 0.715325 + 0.425120i
\(676\) 0 0
\(677\) −0.164509 + 0.451985i −0.00632259 + 0.0173712i −0.942814 0.333320i \(-0.891831\pi\)
0.936491 + 0.350691i \(0.114053\pi\)
\(678\) 0 0
\(679\) 24.7442 29.4890i 0.949597 1.13169i
\(680\) 0 0
\(681\) −0.972282 8.63325i −0.0372579 0.330827i
\(682\) 0 0
\(683\) −20.5853 35.6548i −0.787675 1.36429i −0.927388 0.374101i \(-0.877951\pi\)
0.139713 0.990192i \(-0.455382\pi\)
\(684\) 0 0
\(685\) −7.37688 + 12.7771i −0.281856 + 0.488189i
\(686\) 0 0
\(687\) 15.9414 4.69955i 0.608202 0.179299i
\(688\) 0 0
\(689\) 3.85854 + 10.6013i 0.146999 + 0.403876i
\(690\) 0 0
\(691\) 10.6791 1.88301i 0.406251 0.0716330i 0.0332112 0.999448i \(-0.489427\pi\)
0.373040 + 0.927815i \(0.378315\pi\)
\(692\) 0 0
\(693\) 14.3812 13.3410i 0.546297 0.506784i
\(694\) 0 0
\(695\) −11.5797 + 9.71650i −0.439242 + 0.368568i
\(696\) 0 0
\(697\) −2.67371 + 15.1633i −0.101274 + 0.574353i
\(698\) 0 0
\(699\) 31.1619 + 20.6839i 1.17865 + 0.782336i
\(700\) 0 0
\(701\) 26.1415i 0.987349i 0.869647 + 0.493675i \(0.164347\pi\)
−0.869647 + 0.493675i \(0.835653\pi\)
\(702\) 0 0
\(703\) 5.78503i 0.218187i
\(704\) 0 0
\(705\) −1.85442 + 0.921575i −0.0698415 + 0.0347085i
\(706\) 0 0
\(707\) −2.47303 + 14.0252i −0.0930077 + 0.527473i
\(708\) 0 0
\(709\) 1.19849 1.00565i 0.0450101 0.0377680i −0.620005 0.784598i \(-0.712869\pi\)
0.665015 + 0.746830i \(0.268425\pi\)
\(710\) 0 0
\(711\) 15.9950 31.1915i 0.599860 1.16977i
\(712\) 0 0
\(713\) 43.7046 7.70630i 1.63675 0.288603i
\(714\) 0 0
\(715\) −2.53979 6.97802i −0.0949828 0.260963i
\(716\) 0 0
\(717\) −13.5606 12.9021i −0.506432 0.481837i
\(718\) 0 0
\(719\) −14.4301 + 24.9937i −0.538153 + 0.932109i 0.460850 + 0.887478i \(0.347545\pi\)
−0.999004 + 0.0446310i \(0.985789\pi\)
\(720\) 0 0
\(721\) 4.23846 + 7.34123i 0.157848 + 0.273402i
\(722\) 0 0
\(723\) −20.6045 8.99093i −0.766291 0.334376i
\(724\) 0 0
\(725\) −23.6763 + 28.2163i −0.879315 + 1.04793i
\(726\) 0 0
\(727\) −13.9968 + 38.4560i −0.519114 + 1.42625i 0.352385 + 0.935855i \(0.385371\pi\)
−0.871499 + 0.490398i \(0.836851\pi\)
\(728\) 0 0
\(729\) 25.1305 + 9.87200i 0.930760 + 0.365630i
\(730\) 0 0
\(731\) −3.97152 1.44552i −0.146892 0.0534643i
\(732\) 0 0
\(733\) 1.89373 + 1.58903i 0.0699466 + 0.0586922i 0.677091 0.735900i \(-0.263240\pi\)
−0.607144 + 0.794592i \(0.707685\pi\)
\(734\) 0 0
\(735\) 3.75141 8.59710i 0.138373 0.317109i
\(736\) 0 0
\(737\) −4.54661 + 2.62499i −0.167477 + 0.0966926i
\(738\) 0 0
\(739\) 9.69724 + 5.59870i 0.356719 + 0.205952i 0.667640 0.744484i \(-0.267304\pi\)
−0.310922 + 0.950436i \(0.600638\pi\)
\(740\) 0 0
\(741\) 4.87691 5.12585i 0.179158 0.188303i
\(742\) 0 0
\(743\) 41.9122 15.2548i 1.53761 0.559645i 0.572140 0.820156i \(-0.306113\pi\)
0.965471 + 0.260511i \(0.0838911\pi\)
\(744\) 0 0
\(745\) −1.08258 6.13964i −0.0396628 0.224939i
\(746\) 0 0
\(747\) 44.8829 + 23.0160i 1.64218 + 0.842111i
\(748\) 0 0
\(749\) −17.8587 21.2832i −0.652544 0.777671i
\(750\) 0 0
\(751\) 11.5655 + 2.03931i 0.422032 + 0.0744156i 0.380631 0.924727i \(-0.375707\pi\)
0.0414009 + 0.999143i \(0.486818\pi\)
\(752\) 0 0
\(753\) 14.4368 + 29.0502i 0.526107 + 1.05865i
\(754\) 0 0
\(755\) −13.6545 −0.496937
\(756\) 0 0
\(757\) 5.35502 0.194632 0.0973158 0.995254i \(-0.468974\pi\)
0.0973158 + 0.995254i \(0.468974\pi\)
\(758\) 0 0
\(759\) −12.9304 + 19.4807i −0.469344 + 0.707105i
\(760\) 0 0
\(761\) 13.3535 + 2.35458i 0.484064 + 0.0853536i 0.410354 0.911926i \(-0.365405\pi\)
0.0737099 + 0.997280i \(0.476516\pi\)
\(762\) 0 0
\(763\) 35.9547 + 42.8491i 1.30165 + 1.55124i
\(764\) 0 0
\(765\) −8.46562 9.12566i −0.306075 0.329939i
\(766\) 0 0
\(767\) −9.52242 54.0043i −0.343835 1.94998i
\(768\) 0 0
\(769\) −16.2757 + 5.92388i −0.586917 + 0.213620i −0.618373 0.785885i \(-0.712208\pi\)
0.0314556 + 0.999505i \(0.489986\pi\)
\(770\) 0 0
\(771\) −14.2816 48.4449i −0.514341 1.74470i
\(772\) 0 0
\(773\) −43.8577 25.3213i −1.57745 0.910743i −0.995213 0.0977249i \(-0.968843\pi\)
−0.582239 0.813018i \(-0.697823\pi\)
\(774\) 0 0
\(775\) 21.5561 12.4454i 0.774316 0.447052i
\(776\) 0 0
\(777\) −39.0091 + 4.39323i −1.39944 + 0.157606i
\(778\) 0 0
\(779\) −2.38870 2.00436i −0.0855840 0.0718135i
\(780\) 0 0
\(781\) 15.1918 + 5.52936i 0.543605 + 0.197856i
\(782\) 0 0
\(783\) −23.5018 + 39.5452i −0.839887 + 1.41323i
\(784\) 0 0
\(785\) 3.59581 9.87940i 0.128340 0.352611i
\(786\) 0 0
\(787\) −3.42817 + 4.08553i −0.122201 + 0.145634i −0.823676 0.567060i \(-0.808081\pi\)
0.701475 + 0.712694i \(0.252525\pi\)
\(788\) 0 0
\(789\) −12.2631 + 9.04961i −0.436579 + 0.322175i
\(790\) 0 0
\(791\) 17.6243 + 30.5262i 0.626649 + 1.08539i
\(792\) 0 0
\(793\) 7.73407 13.3958i 0.274645 0.475699i
\(794\) 0 0
\(795\) −0.943434 + 3.90733i −0.0334601 + 0.138579i