Properties

Label 819.2.n.d.172.3
Level $819$
Weight $2$
Character 819.172
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 172.3
Root \(0.756174 + 1.30973i\) of defining polynomial
Character \(\chi\) \(=\) 819.172
Dual form 819.2.n.d.100.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.425563 + 0.737096i) q^{2} +(0.637793 + 1.10469i) q^{4} +(1.72074 + 2.98041i) q^{5} +(1.82097 + 1.91940i) q^{7} -2.78793 q^{8} +O(q^{10})\) \(q+(-0.425563 + 0.737096i) q^{2} +(0.637793 + 1.10469i) q^{4} +(1.72074 + 2.98041i) q^{5} +(1.82097 + 1.91940i) q^{7} -2.78793 q^{8} -2.92913 q^{10} +0.897986 q^{11} +(-3.07517 + 1.88237i) q^{13} +(-2.18972 + 0.525403i) q^{14} +(-0.0891447 + 0.154403i) q^{16} +(0.968404 + 1.67733i) q^{17} +1.03804 q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} +(2.82506 - 4.89315i) q^{23} +(-3.42189 + 5.92688i) q^{25} +(-0.0788077 - 3.06776i) q^{26} +(-0.958938 + 3.23578i) q^{28} +(-0.917969 - 1.58997i) q^{29} +(4.56692 - 7.91014i) q^{31} +(-2.86381 - 4.96026i) q^{32} -1.64847 q^{34} +(-2.58718 + 8.73000i) q^{35} +(5.30001 - 9.17989i) q^{37} +(-0.441751 + 0.765135i) q^{38} +(-4.79731 - 8.30918i) q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +(0.572729 + 0.991996i) q^{44} +(2.40448 + 4.16469i) q^{46} +(3.59565 + 6.22784i) q^{47} +(-0.368167 + 6.99031i) q^{49} +(-2.91246 - 5.04452i) q^{50} +(-4.04076 - 2.19655i) q^{52} +(-4.69324 + 8.12893i) q^{53} +(1.54520 + 2.67637i) q^{55} +(-5.07673 - 5.35115i) q^{56} +1.56261 q^{58} +(-0.255259 - 0.442121i) q^{59} +1.43619 q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(-10.9018 - 5.92620i) q^{65} -8.44932 q^{67} +(-1.23528 + 2.13957i) q^{68} +(-5.33385 - 5.62216i) q^{70} +(-1.72419 + 2.98638i) q^{71} +(-5.45026 + 9.44013i) q^{73} +(4.51097 + 7.81324i) q^{74} +(0.662054 + 1.14671i) q^{76} +(1.63520 + 1.72359i) q^{77} +(6.04589 + 10.4718i) q^{79} -0.613579 q^{80} +4.53771 q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +(1.66593 + 2.88547i) q^{86} -2.50353 q^{88} +(6.80391 - 11.7847i) q^{89} +(-9.21280 - 2.47475i) q^{91} +7.20722 q^{92} -6.12069 q^{94} +(1.78619 + 3.09378i) q^{95} +(-0.253120 + 0.438417i) q^{97} +(-4.99585 - 3.24619i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} + O(q^{10}) \) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} - 8q^{10} + 8q^{11} - 2q^{13} + 2q^{14} + 8q^{16} - 5q^{17} + 2q^{19} + q^{20} - 5q^{22} + q^{23} + 7q^{25} - 5q^{26} - 7q^{28} - 3q^{29} + 16q^{31} - 8q^{32} + 32q^{34} - 8q^{35} - 13q^{37} + 17q^{38} - 5q^{40} + 8q^{41} - 11q^{43} - 21q^{44} + 16q^{46} + q^{47} - 3q^{49} - 6q^{50} - 25q^{52} + 2q^{53} + 9q^{55} + 18q^{56} + 16q^{58} - 13q^{59} + 10q^{61} - 5q^{62} - 30q^{64} - 19q^{65} + 22q^{67} - 29q^{68} - 39q^{70} - 6q^{71} - 30q^{73} + 3q^{74} - 9q^{76} - 11q^{77} + 7q^{79} - 14q^{80} - 2q^{82} + 54q^{83} - q^{85} + 7q^{86} - 4q^{89} - 20q^{91} - 54q^{92} - 90q^{94} + 6q^{95} - 35q^{97} - 62q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.425563 + 0.737096i −0.300918 + 0.521206i −0.976344 0.216222i \(-0.930626\pi\)
0.675426 + 0.737428i \(0.263960\pi\)
\(3\) 0 0
\(4\) 0.637793 + 1.10469i 0.318896 + 0.552345i
\(5\) 1.72074 + 2.98041i 0.769538 + 1.33288i 0.937814 + 0.347139i \(0.112847\pi\)
−0.168276 + 0.985740i \(0.553820\pi\)
\(6\) 0 0
\(7\) 1.82097 + 1.91940i 0.688260 + 0.725464i
\(8\) −2.78793 −0.985684
\(9\) 0 0
\(10\) −2.92913 −0.926272
\(11\) 0.897986 0.270753 0.135377 0.990794i \(-0.456776\pi\)
0.135377 + 0.990794i \(0.456776\pi\)
\(12\) 0 0
\(13\) −3.07517 + 1.88237i −0.852900 + 0.522075i
\(14\) −2.18972 + 0.525403i −0.585226 + 0.140420i
\(15\) 0 0
\(16\) −0.0891447 + 0.154403i −0.0222862 + 0.0386008i
\(17\) 0.968404 + 1.67733i 0.234873 + 0.406811i 0.959236 0.282607i \(-0.0911994\pi\)
−0.724363 + 0.689419i \(0.757866\pi\)
\(18\) 0 0
\(19\) 1.03804 0.238142 0.119071 0.992886i \(-0.462008\pi\)
0.119071 + 0.992886i \(0.462008\pi\)
\(20\) −2.19495 + 3.80177i −0.490806 + 0.850101i
\(21\) 0 0
\(22\) −0.382150 + 0.661902i −0.0814745 + 0.141118i
\(23\) 2.82506 4.89315i 0.589067 1.02029i −0.405288 0.914189i \(-0.632829\pi\)
0.994355 0.106104i \(-0.0338378\pi\)
\(24\) 0 0
\(25\) −3.42189 + 5.92688i −0.684378 + 1.18538i
\(26\) −0.0788077 3.06776i −0.0154555 0.601638i
\(27\) 0 0
\(28\) −0.958938 + 3.23578i −0.181222 + 0.611505i
\(29\) −0.917969 1.58997i −0.170463 0.295250i 0.768119 0.640307i \(-0.221193\pi\)
−0.938582 + 0.345057i \(0.887860\pi\)
\(30\) 0 0
\(31\) 4.56692 7.91014i 0.820244 1.42070i −0.0852573 0.996359i \(-0.527171\pi\)
0.905501 0.424345i \(-0.139495\pi\)
\(32\) −2.86381 4.96026i −0.506254 0.876858i
\(33\) 0 0
\(34\) −1.64847 −0.282710
\(35\) −2.58718 + 8.73000i −0.437313 + 1.47564i
\(36\) 0 0
\(37\) 5.30001 9.17989i 0.871316 1.50916i 0.0106808 0.999943i \(-0.496600\pi\)
0.860636 0.509221i \(-0.170067\pi\)
\(38\) −0.441751 + 0.765135i −0.0716614 + 0.124121i
\(39\) 0 0
\(40\) −4.79731 8.30918i −0.758521 1.31380i
\(41\) −2.66571 4.61715i −0.416314 0.721078i 0.579251 0.815149i \(-0.303345\pi\)
−0.995565 + 0.0940715i \(0.970012\pi\)
\(42\) 0 0
\(43\) 1.95732 3.39018i 0.298489 0.516998i −0.677302 0.735706i \(-0.736851\pi\)
0.975790 + 0.218708i \(0.0701841\pi\)
\(44\) 0.572729 + 0.991996i 0.0863422 + 0.149549i
\(45\) 0 0
\(46\) 2.40448 + 4.16469i 0.354522 + 0.614050i
\(47\) 3.59565 + 6.22784i 0.524479 + 0.908424i 0.999594 + 0.0285004i \(0.00907317\pi\)
−0.475115 + 0.879924i \(0.657593\pi\)
\(48\) 0 0
\(49\) −0.368167 + 6.99031i −0.0525953 + 0.998616i
\(50\) −2.91246 5.04452i −0.411883 0.713403i
\(51\) 0 0
\(52\) −4.04076 2.19655i −0.560352 0.304607i
\(53\) −4.69324 + 8.12893i −0.644666 + 1.11659i 0.339712 + 0.940529i \(0.389670\pi\)
−0.984378 + 0.176065i \(0.943663\pi\)
\(54\) 0 0
\(55\) 1.54520 + 2.67637i 0.208355 + 0.360881i
\(56\) −5.07673 5.35115i −0.678407 0.715078i
\(57\) 0 0
\(58\) 1.56261 0.205181
\(59\) −0.255259 0.442121i −0.0332318 0.0575592i 0.848931 0.528503i \(-0.177247\pi\)
−0.882163 + 0.470944i \(0.843913\pi\)
\(60\) 0 0
\(61\) 1.43619 0.183885 0.0919426 0.995764i \(-0.470692\pi\)
0.0919426 + 0.995764i \(0.470692\pi\)
\(62\) 3.88702 + 6.73252i 0.493653 + 0.855031i
\(63\) 0 0
\(64\) 4.51834 0.564792
\(65\) −10.9018 5.92620i −1.35220 0.735055i
\(66\) 0 0
\(67\) −8.44932 −1.03225 −0.516124 0.856514i \(-0.672626\pi\)
−0.516124 + 0.856514i \(0.672626\pi\)
\(68\) −1.23528 + 2.13957i −0.149800 + 0.259461i
\(69\) 0 0
\(70\) −5.33385 5.62216i −0.637516 0.671977i
\(71\) −1.72419 + 2.98638i −0.204623 + 0.354418i −0.950013 0.312211i \(-0.898930\pi\)
0.745389 + 0.666629i \(0.232264\pi\)
\(72\) 0 0
\(73\) −5.45026 + 9.44013i −0.637905 + 1.10488i 0.347987 + 0.937499i \(0.386865\pi\)
−0.985892 + 0.167384i \(0.946468\pi\)
\(74\) 4.51097 + 7.81324i 0.524390 + 0.908270i
\(75\) 0 0
\(76\) 0.662054 + 1.14671i 0.0759428 + 0.131537i
\(77\) 1.63520 + 1.72359i 0.186349 + 0.196422i
\(78\) 0 0
\(79\) 6.04589 + 10.4718i 0.680216 + 1.17817i 0.974915 + 0.222578i \(0.0714472\pi\)
−0.294699 + 0.955590i \(0.595219\pi\)
\(80\) −0.613579 −0.0686002
\(81\) 0 0
\(82\) 4.53771 0.501107
\(83\) −1.51669 −0.166479 −0.0832393 0.996530i \(-0.526527\pi\)
−0.0832393 + 0.996530i \(0.526527\pi\)
\(84\) 0 0
\(85\) −3.33274 + 5.77248i −0.361487 + 0.626113i
\(86\) 1.66593 + 2.88547i 0.179642 + 0.311148i
\(87\) 0 0
\(88\) −2.50353 −0.266877
\(89\) 6.80391 11.7847i 0.721213 1.24918i −0.239301 0.970945i \(-0.576918\pi\)
0.960514 0.278232i \(-0.0897484\pi\)
\(90\) 0 0
\(91\) −9.21280 2.47475i −0.965763 0.259424i
\(92\) 7.20722 0.751405
\(93\) 0 0
\(94\) −6.12069 −0.631301
\(95\) 1.78619 + 3.09378i 0.183260 + 0.317415i
\(96\) 0 0
\(97\) −0.253120 + 0.438417i −0.0257005 + 0.0445145i −0.878590 0.477578i \(-0.841515\pi\)
0.852889 + 0.522092i \(0.174848\pi\)
\(98\) −4.99585 3.24619i −0.504657 0.327915i
\(99\) 0 0
\(100\) −8.72982 −0.872982
\(101\) 5.98654 0.595683 0.297842 0.954615i \(-0.403733\pi\)
0.297842 + 0.954615i \(0.403733\pi\)
\(102\) 0 0
\(103\) 2.06651 + 3.57930i 0.203619 + 0.352679i 0.949692 0.313186i \(-0.101396\pi\)
−0.746073 + 0.665865i \(0.768063\pi\)
\(104\) 8.57338 5.24792i 0.840689 0.514601i
\(105\) 0 0
\(106\) −3.99454 6.91874i −0.387984 0.672008i
\(107\) −7.06169 + 12.2312i −0.682679 + 1.18243i 0.291481 + 0.956577i \(0.405852\pi\)
−0.974160 + 0.225858i \(0.927481\pi\)
\(108\) 0 0
\(109\) 2.10119 3.63936i 0.201257 0.348588i −0.747677 0.664063i \(-0.768831\pi\)
0.948934 + 0.315475i \(0.102164\pi\)
\(110\) −2.63032 −0.250791
\(111\) 0 0
\(112\) −0.458690 + 0.110059i −0.0433421 + 0.0103996i
\(113\) 6.88472 11.9247i 0.647660 1.12178i −0.336020 0.941855i \(-0.609081\pi\)
0.983680 0.179926i \(-0.0575857\pi\)
\(114\) 0 0
\(115\) 19.4448 1.81324
\(116\) 1.17095 2.02814i 0.108720 0.188308i
\(117\) 0 0
\(118\) 0.434514 0.0400003
\(119\) −1.45602 + 4.91310i −0.133473 + 0.450384i
\(120\) 0 0
\(121\) −10.1936 −0.926693
\(122\) −0.611189 + 1.05861i −0.0553344 + 0.0958420i
\(123\) 0 0
\(124\) 11.6510 1.04629
\(125\) −6.34531 −0.567542
\(126\) 0 0
\(127\) −0.972482 1.68439i −0.0862938 0.149465i 0.819648 0.572868i \(-0.194169\pi\)
−0.905942 + 0.423402i \(0.860836\pi\)
\(128\) 3.80478 6.59007i 0.336298 0.582485i
\(129\) 0 0
\(130\) 9.00758 5.51370i 0.790017 0.483584i
\(131\) −6.01770 10.4230i −0.525769 0.910659i −0.999549 0.0300158i \(-0.990444\pi\)
0.473780 0.880643i \(-0.342889\pi\)
\(132\) 0 0
\(133\) 1.89023 + 1.99241i 0.163904 + 0.172764i
\(134\) 3.59571 6.22796i 0.310622 0.538014i
\(135\) 0 0
\(136\) −2.69985 4.67627i −0.231510 0.400987i
\(137\) 4.35857 + 7.54927i 0.372378 + 0.644978i 0.989931 0.141552i \(-0.0452092\pi\)
−0.617553 + 0.786529i \(0.711876\pi\)
\(138\) 0 0
\(139\) −2.10625 + 3.64813i −0.178650 + 0.309430i −0.941418 0.337241i \(-0.890506\pi\)
0.762769 + 0.646672i \(0.223840\pi\)
\(140\) −11.2940 + 2.70990i −0.954519 + 0.229029i
\(141\) 0 0
\(142\) −1.46750 2.54178i −0.123150 0.213302i
\(143\) −2.76146 + 1.69034i −0.230925 + 0.141353i
\(144\) 0 0
\(145\) 3.15917 5.47184i 0.262355 0.454412i
\(146\) −4.63885 8.03473i −0.383914 0.664959i
\(147\) 0 0
\(148\) 13.5212 1.11144
\(149\) −5.86484 −0.480466 −0.240233 0.970715i \(-0.577224\pi\)
−0.240233 + 0.970715i \(0.577224\pi\)
\(150\) 0 0
\(151\) 8.42840 14.5984i 0.685893 1.18800i −0.287262 0.957852i \(-0.592745\pi\)
0.973155 0.230150i \(-0.0739216\pi\)
\(152\) −2.89398 −0.234733
\(153\) 0 0
\(154\) −1.96633 + 0.471805i −0.158452 + 0.0380191i
\(155\) 31.4339 2.52483
\(156\) 0 0
\(157\) 0.969500 1.67922i 0.0773746 0.134017i −0.824742 0.565509i \(-0.808680\pi\)
0.902116 + 0.431493i \(0.142013\pi\)
\(158\) −10.2916 −0.818757
\(159\) 0 0
\(160\) 9.85573 17.0706i 0.779164 1.34955i
\(161\) 14.5362 3.48785i 1.14562 0.274881i
\(162\) 0 0
\(163\) −11.8959 −0.931762 −0.465881 0.884847i \(-0.654262\pi\)
−0.465881 + 0.884847i \(0.654262\pi\)
\(164\) 3.40035 5.88957i 0.265522 0.459898i
\(165\) 0 0
\(166\) 0.645448 1.11795i 0.0500965 0.0867696i
\(167\) 8.28801 + 14.3553i 0.641346 + 1.11084i 0.985133 + 0.171796i \(0.0549569\pi\)
−0.343787 + 0.939048i \(0.611710\pi\)
\(168\) 0 0
\(169\) 5.91338 11.5772i 0.454875 0.890555i
\(170\) −2.83658 4.91310i −0.217556 0.376818i
\(171\) 0 0
\(172\) 4.99346 0.380748
\(173\) 9.98656 0.759264 0.379632 0.925138i \(-0.376051\pi\)
0.379632 + 0.925138i \(0.376051\pi\)
\(174\) 0 0
\(175\) −17.6072 + 4.22469i −1.33098 + 0.319357i
\(176\) −0.0800507 + 0.138652i −0.00603405 + 0.0104513i
\(177\) 0 0
\(178\) 5.79098 + 10.0303i 0.434052 + 0.751801i
\(179\) −9.17657 −0.685889 −0.342945 0.939356i \(-0.611424\pi\)
−0.342945 + 0.939356i \(0.611424\pi\)
\(180\) 0 0
\(181\) 6.00489 0.446340 0.223170 0.974780i \(-0.428360\pi\)
0.223170 + 0.974780i \(0.428360\pi\)
\(182\) 5.74475 5.73756i 0.425829 0.425296i
\(183\) 0 0
\(184\) −7.87609 + 13.6418i −0.580633 + 1.00569i
\(185\) 36.4797 2.68204
\(186\) 0 0
\(187\) 0.869614 + 1.50622i 0.0635925 + 0.110145i
\(188\) −4.58655 + 7.94415i −0.334509 + 0.579386i
\(189\) 0 0
\(190\) −3.04055 −0.220585
\(191\) −1.31612 −0.0952313 −0.0476156 0.998866i \(-0.515162\pi\)
−0.0476156 + 0.998866i \(0.515162\pi\)
\(192\) 0 0
\(193\) −16.4254 −1.18233 −0.591163 0.806552i \(-0.701331\pi\)
−0.591163 + 0.806552i \(0.701331\pi\)
\(194\) −0.215437 0.373148i −0.0154675 0.0267905i
\(195\) 0 0
\(196\) −7.95694 + 4.05166i −0.568353 + 0.289404i
\(197\) −12.7938 22.1594i −0.911517 1.57879i −0.811922 0.583766i \(-0.801579\pi\)
−0.0995951 0.995028i \(-0.531755\pi\)
\(198\) 0 0
\(199\) 12.6894 + 21.9787i 0.899528 + 1.55803i 0.828099 + 0.560582i \(0.189422\pi\)
0.0714284 + 0.997446i \(0.477244\pi\)
\(200\) 9.54000 16.5238i 0.674580 1.16841i
\(201\) 0 0
\(202\) −2.54765 + 4.41266i −0.179252 + 0.310473i
\(203\) 1.38019 4.65723i 0.0968704 0.326873i
\(204\) 0 0
\(205\) 9.17399 15.8898i 0.640740 1.10979i
\(206\) −3.51772 −0.245091
\(207\) 0 0
\(208\) −0.0165082 0.642619i −0.00114464 0.0445576i
\(209\) 0.932145 0.0644778
\(210\) 0 0
\(211\) 2.84824 + 4.93330i 0.196081 + 0.339622i 0.947254 0.320483i \(-0.103845\pi\)
−0.751173 + 0.660105i \(0.770512\pi\)
\(212\) −11.9733 −0.822327
\(213\) 0 0
\(214\) −6.01038 10.4103i −0.410861 0.711633i
\(215\) 13.4722 0.918794
\(216\) 0 0
\(217\) 23.4989 5.63836i 1.59521 0.382757i
\(218\) 1.78837 + 3.09755i 0.121124 + 0.209793i
\(219\) 0 0
\(220\) −1.97104 + 3.41393i −0.132887 + 0.230167i
\(221\) −6.13536 3.33517i −0.412709 0.224348i
\(222\) 0 0
\(223\) −1.17906 2.04219i −0.0789558 0.136755i 0.823844 0.566817i \(-0.191825\pi\)
−0.902800 + 0.430061i \(0.858492\pi\)
\(224\) 4.30581 14.5292i 0.287694 0.970776i
\(225\) 0 0
\(226\) 5.85976 + 10.1494i 0.389786 + 0.675129i
\(227\) 13.1463 + 22.7701i 0.872551 + 1.51130i 0.859349 + 0.511390i \(0.170869\pi\)
0.0132022 + 0.999913i \(0.495797\pi\)
\(228\) 0 0
\(229\) −0.0342777 0.0593708i −0.00226514 0.00392333i 0.864891 0.501960i \(-0.167388\pi\)
−0.867156 + 0.498037i \(0.834054\pi\)
\(230\) −8.27498 + 14.3327i −0.545636 + 0.945069i
\(231\) 0 0
\(232\) 2.55924 + 4.43273i 0.168022 + 0.291023i
\(233\) 7.33514 + 12.7048i 0.480541 + 0.832322i 0.999751 0.0223253i \(-0.00710694\pi\)
−0.519210 + 0.854647i \(0.673774\pi\)
\(234\) 0 0
\(235\) −12.3743 + 21.4330i −0.807213 + 1.39813i
\(236\) 0.325604 0.563963i 0.0211950 0.0367109i
\(237\) 0 0
\(238\) −3.00180 3.16406i −0.194578 0.205096i
\(239\) −3.35434 −0.216974 −0.108487 0.994098i \(-0.534601\pi\)
−0.108487 + 0.994098i \(0.534601\pi\)
\(240\) 0 0
\(241\) 4.28989 + 7.43031i 0.276336 + 0.478628i 0.970471 0.241216i \(-0.0775464\pi\)
−0.694135 + 0.719845i \(0.744213\pi\)
\(242\) 4.33802 7.51368i 0.278859 0.482998i
\(243\) 0 0
\(244\) 0.915991 + 1.58654i 0.0586403 + 0.101568i
\(245\) −21.4675 + 10.9312i −1.37151 + 0.698370i
\(246\) 0 0
\(247\) −3.19215 + 1.95397i −0.203112 + 0.124328i
\(248\) −12.7323 + 22.0530i −0.808501 + 1.40036i
\(249\) 0 0
\(250\) 2.70033 4.67711i 0.170784 0.295806i
\(251\) 10.7575 18.6326i 0.679010 1.17608i −0.296270 0.955104i \(-0.595743\pi\)
0.975280 0.220975i \(-0.0709238\pi\)
\(252\) 0 0
\(253\) 2.53687 4.39399i 0.159492 0.276248i
\(254\) 1.65541 0.103870
\(255\) 0 0
\(256\) 7.75668 + 13.4350i 0.484793 + 0.839686i
\(257\) 2.46896 4.27636i 0.154010 0.266752i −0.778688 0.627411i \(-0.784115\pi\)
0.932698 + 0.360659i \(0.117448\pi\)
\(258\) 0 0
\(259\) 27.2710 6.54344i 1.69454 0.406590i
\(260\) −0.406471 15.8228i −0.0252083 0.981288i
\(261\) 0 0
\(262\) 10.2436 0.632854
\(263\) 8.95439 0.552151 0.276076 0.961136i \(-0.410966\pi\)
0.276076 + 0.961136i \(0.410966\pi\)
\(264\) 0 0
\(265\) −32.3034 −1.98438
\(266\) −2.27301 + 0.545389i −0.139367 + 0.0334400i
\(267\) 0 0
\(268\) −5.38891 9.33387i −0.329180 0.570157i
\(269\) −2.41172 4.17723i −0.147045 0.254690i 0.783089 0.621910i \(-0.213643\pi\)
−0.930134 + 0.367220i \(0.880310\pi\)
\(270\) 0 0
\(271\) 3.71072 6.42715i 0.225410 0.390422i −0.731032 0.682343i \(-0.760961\pi\)
0.956442 + 0.291921i \(0.0942945\pi\)
\(272\) −0.345312 −0.0209376
\(273\) 0 0
\(274\) −7.41938 −0.448221
\(275\) −3.07281 + 5.32226i −0.185297 + 0.320944i
\(276\) 0 0
\(277\) −1.90816 3.30503i −0.114650 0.198580i 0.802990 0.595993i \(-0.203241\pi\)
−0.917640 + 0.397413i \(0.869908\pi\)
\(278\) −1.79268 3.10502i −0.107518 0.186226i
\(279\) 0 0
\(280\) 7.21288 24.3387i 0.431052 1.45451i
\(281\) −8.54978 −0.510037 −0.255019 0.966936i \(-0.582082\pi\)
−0.255019 + 0.966936i \(0.582082\pi\)
\(282\) 0 0
\(283\) 15.2643 0.907371 0.453686 0.891162i \(-0.350109\pi\)
0.453686 + 0.891162i \(0.350109\pi\)
\(284\) −4.39870 −0.261015
\(285\) 0 0
\(286\) −0.0707683 2.75481i −0.00418461 0.162895i
\(287\) 4.00797 13.5242i 0.236583 0.798310i
\(288\) 0 0
\(289\) 6.62439 11.4738i 0.389670 0.674928i
\(290\) 2.68885 + 4.65723i 0.157895 + 0.273482i
\(291\) 0 0
\(292\) −13.9045 −0.813702
\(293\) −2.96982 + 5.14388i −0.173499 + 0.300509i −0.939641 0.342163i \(-0.888841\pi\)
0.766142 + 0.642671i \(0.222174\pi\)
\(294\) 0 0
\(295\) 0.878467 1.52155i 0.0511463 0.0885881i
\(296\) −14.7761 + 25.5929i −0.858842 + 1.48756i
\(297\) 0 0
\(298\) 2.49586 4.32295i 0.144581 0.250422i
\(299\) 0.523159 + 20.3651i 0.0302551 + 1.17774i
\(300\) 0 0
\(301\) 10.0713 2.41653i 0.580501 0.139286i
\(302\) 7.17362 + 12.4251i 0.412796 + 0.714983i
\(303\) 0 0
\(304\) −0.0925356 + 0.160276i −0.00530728 + 0.00919248i
\(305\) 2.47131 + 4.28043i 0.141507 + 0.245097i
\(306\) 0 0
\(307\) 22.2133 1.26778 0.633891 0.773422i \(-0.281457\pi\)
0.633891 + 0.773422i \(0.281457\pi\)
\(308\) −0.861114 + 2.90569i −0.0490665 + 0.165567i
\(309\) 0 0
\(310\) −13.3771 + 23.1698i −0.759769 + 1.31596i
\(311\) 4.92130 8.52394i 0.279061 0.483348i −0.692091 0.721811i \(-0.743310\pi\)
0.971152 + 0.238463i \(0.0766435\pi\)
\(312\) 0 0
\(313\) 10.4563 + 18.1108i 0.591023 + 1.02368i 0.994095 + 0.108513i \(0.0346090\pi\)
−0.403072 + 0.915168i \(0.632058\pi\)
\(314\) 0.825166 + 1.42923i 0.0465668 + 0.0806561i
\(315\) 0 0
\(316\) −7.71205 + 13.3577i −0.433837 + 0.751427i
\(317\) −12.6801 21.9626i −0.712188 1.23355i −0.964034 0.265778i \(-0.914371\pi\)
0.251847 0.967767i \(-0.418962\pi\)
\(318\) 0 0
\(319\) −0.824324 1.42777i −0.0461533 0.0799398i
\(320\) 7.77489 + 13.4665i 0.434629 + 0.752800i
\(321\) 0 0
\(322\) −3.61521 + 12.1989i −0.201468 + 0.679819i
\(323\) 1.00524 + 1.74113i 0.0559331 + 0.0968790i
\(324\) 0 0
\(325\) −0.633681 24.6674i −0.0351503 1.36830i
\(326\) 5.06247 8.76845i 0.280384 0.485640i
\(327\) 0 0
\(328\) 7.43183 + 12.8723i 0.410354 + 0.710755i
\(329\) −5.40615 + 18.2422i −0.298051 + 1.00572i
\(330\) 0 0
\(331\) 1.78283 0.0979935 0.0489967 0.998799i \(-0.484398\pi\)
0.0489967 + 0.998799i \(0.484398\pi\)
\(332\) −0.967335 1.67547i −0.0530894 0.0919536i
\(333\) 0 0
\(334\) −14.1083 −0.771971
\(335\) −14.5391 25.1824i −0.794354 1.37586i
\(336\) 0 0
\(337\) 9.56149 0.520848 0.260424 0.965494i \(-0.416138\pi\)
0.260424 + 0.965494i \(0.416138\pi\)
\(338\) 6.01701 + 9.28556i 0.327282 + 0.505068i
\(339\) 0 0
\(340\) −8.50240 −0.461107
\(341\) 4.10103 7.10320i 0.222083 0.384660i
\(342\) 0 0
\(343\) −14.0876 + 12.0225i −0.760659 + 0.649152i
\(344\) −5.45689 + 9.45160i −0.294216 + 0.509596i
\(345\) 0 0
\(346\) −4.24991 + 7.36106i −0.228477 + 0.395733i
\(347\) 0.316694 + 0.548531i 0.0170010 + 0.0294467i 0.874401 0.485204i \(-0.161255\pi\)
−0.857400 + 0.514651i \(0.827921\pi\)
\(348\) 0 0
\(349\) −15.2994 26.4994i −0.818960 1.41848i −0.906449 0.422315i \(-0.861217\pi\)
0.0874885 0.996166i \(-0.472116\pi\)
\(350\) 4.37895 14.7761i 0.234065 0.789813i
\(351\) 0 0
\(352\) −2.57166 4.45425i −0.137070 0.237412i
\(353\) 1.10035 0.0585655 0.0292828 0.999571i \(-0.490678\pi\)
0.0292828 + 0.999571i \(0.490678\pi\)
\(354\) 0 0
\(355\) −11.8675 −0.629862
\(356\) 17.3579 0.919969
\(357\) 0 0
\(358\) 3.90521 6.76402i 0.206397 0.357489i
\(359\) −4.88693 8.46441i −0.257922 0.446734i 0.707763 0.706450i \(-0.249705\pi\)
−0.965685 + 0.259716i \(0.916371\pi\)
\(360\) 0 0
\(361\) −17.9225 −0.943288
\(362\) −2.55546 + 4.42618i −0.134312 + 0.232635i
\(363\) 0 0
\(364\) −3.14203 11.7557i −0.164687 0.616164i
\(365\) −37.5139 −1.96357
\(366\) 0 0
\(367\) −11.1473 −0.581882 −0.290941 0.956741i \(-0.593968\pi\)
−0.290941 + 0.956741i \(0.593968\pi\)
\(368\) 0.503679 + 0.872397i 0.0262561 + 0.0454769i
\(369\) 0 0
\(370\) −15.5244 + 26.8891i −0.807076 + 1.39790i
\(371\) −24.1489 + 5.79432i −1.25375 + 0.300826i
\(372\) 0 0
\(373\) −30.7301 −1.59115 −0.795573 0.605858i \(-0.792830\pi\)
−0.795573 + 0.605858i \(0.792830\pi\)
\(374\) −1.48030 −0.0765445
\(375\) 0 0
\(376\) −10.0244 17.3628i −0.516970 0.895419i
\(377\) 5.81582 + 3.16147i 0.299530 + 0.162824i
\(378\) 0 0
\(379\) −11.3286 19.6217i −0.581912 1.00790i −0.995253 0.0973246i \(-0.968972\pi\)
0.413341 0.910576i \(-0.364362\pi\)
\(380\) −2.27844 + 3.94638i −0.116882 + 0.202445i
\(381\) 0 0
\(382\) 0.560093 0.970109i 0.0286568 0.0496351i
\(383\) 0.589263 0.0301099 0.0150550 0.999887i \(-0.495208\pi\)
0.0150550 + 0.999887i \(0.495208\pi\)
\(384\) 0 0
\(385\) −2.32325 + 7.83942i −0.118404 + 0.399534i
\(386\) 6.99004 12.1071i 0.355783 0.616235i
\(387\) 0 0
\(388\) −0.645753 −0.0327832
\(389\) 2.84973 4.93587i 0.144487 0.250259i −0.784695 0.619883i \(-0.787180\pi\)
0.929181 + 0.369624i \(0.120514\pi\)
\(390\) 0 0
\(391\) 10.9432 0.553422
\(392\) 1.02643 19.4885i 0.0518423 0.984319i
\(393\) 0 0
\(394\) 21.7782 1.09717
\(395\) −20.8068 + 36.0384i −1.04690 + 1.81329i
\(396\) 0 0
\(397\) −25.5283 −1.28123 −0.640614 0.767863i \(-0.721320\pi\)
−0.640614 + 0.767863i \(0.721320\pi\)
\(398\) −21.6005 −1.08274
\(399\) 0 0
\(400\) −0.610086 1.05670i −0.0305043 0.0528350i
\(401\) 12.7506 22.0846i 0.636733 1.10285i −0.349413 0.936969i \(-0.613619\pi\)
0.986145 0.165884i \(-0.0530478\pi\)
\(402\) 0 0
\(403\) 0.845724 + 32.9217i 0.0421285 + 1.63995i
\(404\) 3.81817 + 6.61327i 0.189961 + 0.329022i
\(405\) 0 0
\(406\) 2.84547 + 2.99928i 0.141218 + 0.148852i
\(407\) 4.75934 8.24341i 0.235912 0.408611i
\(408\) 0 0
\(409\) −0.0734938 0.127295i −0.00363403 0.00629433i 0.864203 0.503144i \(-0.167823\pi\)
−0.867837 + 0.496850i \(0.834490\pi\)
\(410\) 7.80822 + 13.5242i 0.385621 + 0.667914i
\(411\) 0 0
\(412\) −2.63601 + 4.56570i −0.129867 + 0.224936i
\(413\) 0.383788 1.29503i 0.0188850 0.0637242i
\(414\) 0 0
\(415\) −2.60983 4.52036i −0.128112 0.221896i
\(416\) 18.1437 + 9.86292i 0.889570 + 0.483569i
\(417\) 0 0
\(418\) −0.396686 + 0.687080i −0.0194026 + 0.0336062i
\(419\) 6.84795 + 11.8610i 0.334544 + 0.579447i 0.983397 0.181466i \(-0.0580844\pi\)
−0.648853 + 0.760914i \(0.724751\pi\)
\(420\) 0 0
\(421\) 3.44169 0.167738 0.0838688 0.996477i \(-0.473272\pi\)
0.0838688 + 0.996477i \(0.473272\pi\)
\(422\) −4.84842 −0.236017
\(423\) 0 0
\(424\) 13.0844 22.6629i 0.635437 1.10061i
\(425\) −13.2551 −0.642966
\(426\) 0 0
\(427\) 2.61525 + 2.75662i 0.126561 + 0.133402i
\(428\) −18.0156 −0.870816
\(429\) 0 0
\(430\) −5.73325 + 9.93028i −0.276482 + 0.478881i
\(431\) −22.2910 −1.07372 −0.536861 0.843671i \(-0.680390\pi\)
−0.536861 + 0.843671i \(0.680390\pi\)
\(432\) 0 0
\(433\) 12.9481 22.4268i 0.622247 1.07776i −0.366819 0.930292i \(-0.619553\pi\)
0.989066 0.147472i \(-0.0471136\pi\)
\(434\) −5.84424 + 19.7204i −0.280533 + 0.946611i
\(435\) 0 0
\(436\) 5.36049 0.256721
\(437\) 2.93253 5.07929i 0.140282 0.242975i
\(438\) 0 0
\(439\) 13.9919 24.2347i 0.667798 1.15666i −0.310721 0.950501i \(-0.600570\pi\)
0.978519 0.206159i \(-0.0660963\pi\)
\(440\) −4.30792 7.46153i −0.205372 0.355715i
\(441\) 0 0
\(442\) 5.06932 3.10302i 0.241123 0.147596i
\(443\) 16.6044 + 28.7597i 0.788900 + 1.36642i 0.926641 + 0.375947i \(0.122683\pi\)
−0.137741 + 0.990468i \(0.543984\pi\)
\(444\) 0 0
\(445\) 46.8310 2.22000
\(446\) 2.00706 0.0950370
\(447\) 0 0
\(448\) 8.22774 + 8.67249i 0.388724 + 0.409736i
\(449\) 9.84320 17.0489i 0.464529 0.804589i −0.534651 0.845073i \(-0.679557\pi\)
0.999180 + 0.0404845i \(0.0128901\pi\)
\(450\) 0 0
\(451\) −2.39377 4.14614i −0.112718 0.195234i
\(452\) 17.5641 0.826146
\(453\) 0 0
\(454\) −22.3783 −1.05027
\(455\) −8.47706 31.7163i −0.397411 1.48688i
\(456\) 0 0
\(457\) 0.373471 0.646871i 0.0174702 0.0302593i −0.857158 0.515053i \(-0.827772\pi\)
0.874628 + 0.484794i \(0.161105\pi\)
\(458\) 0.0583493 0.00272648
\(459\) 0 0
\(460\) 12.4017 + 21.4805i 0.578235 + 1.00153i
\(461\) −16.5855 + 28.7269i −0.772464 + 1.33795i 0.163744 + 0.986503i \(0.447643\pi\)
−0.936209 + 0.351445i \(0.885691\pi\)
\(462\) 0 0
\(463\) −30.7521 −1.42917 −0.714586 0.699548i \(-0.753385\pi\)
−0.714586 + 0.699548i \(0.753385\pi\)
\(464\) 0.327328 0.0151958
\(465\) 0 0
\(466\) −12.4863 −0.578414
\(467\) −14.8033 25.6400i −0.685013 1.18648i −0.973433 0.228973i \(-0.926463\pi\)
0.288420 0.957504i \(-0.406870\pi\)
\(468\) 0 0
\(469\) −15.3859 16.2176i −0.710456 0.748859i
\(470\) −10.5321 18.2422i −0.485810 0.841448i
\(471\) 0 0
\(472\) 0.711644 + 1.23260i 0.0327561 + 0.0567352i
\(473\) 1.75765 3.04434i 0.0808168 0.139979i
\(474\) 0 0
\(475\) −3.55205 + 6.15234i −0.162979 + 0.282289i
\(476\) −6.35609 + 1.52509i −0.291331 + 0.0699024i
\(477\) 0 0
\(478\) 1.42748 2.47247i 0.0652915 0.113088i
\(479\) −14.0905 −0.643813 −0.321907 0.946771i \(-0.604324\pi\)
−0.321907 + 0.946771i \(0.604324\pi\)
\(480\) 0 0
\(481\) 0.981481 + 38.2063i 0.0447517 + 1.74206i
\(482\) −7.30247 −0.332618
\(483\) 0 0
\(484\) −6.50142 11.2608i −0.295519 0.511854i
\(485\) −1.74222 −0.0791100
\(486\) 0 0
\(487\) 8.39773 + 14.5453i 0.380537 + 0.659110i 0.991139 0.132828i \(-0.0424057\pi\)
−0.610602 + 0.791938i \(0.709072\pi\)
\(488\) −4.00400 −0.181253
\(489\) 0 0
\(490\) 1.07841 20.4755i 0.0487176 0.924990i
\(491\) 10.8345 + 18.7659i 0.488954 + 0.846893i 0.999919 0.0127081i \(-0.00404524\pi\)
−0.510965 + 0.859601i \(0.670712\pi\)
\(492\) 0 0
\(493\) 1.77793 3.07947i 0.0800740 0.138692i
\(494\) −0.0818055 3.18446i −0.00368060 0.143276i
\(495\) 0 0
\(496\) 0.814234 + 1.41029i 0.0365602 + 0.0633241i
\(497\) −8.87173 + 2.12870i −0.397952 + 0.0954851i
\(498\) 0 0
\(499\) 11.6524 + 20.1825i 0.521633 + 0.903495i 0.999683 + 0.0251622i \(0.00801023\pi\)
−0.478051 + 0.878332i \(0.658656\pi\)
\(500\) −4.04699 7.00960i −0.180987 0.313479i
\(501\) 0 0
\(502\) 9.15601 + 15.8587i 0.408653 + 0.707807i
\(503\) −21.9415 + 38.0037i −0.978322 + 1.69450i −0.309816 + 0.950796i \(0.600268\pi\)
−0.668506 + 0.743707i \(0.733066\pi\)
\(504\) 0 0
\(505\) 10.3013 + 17.8423i 0.458401 + 0.793974i
\(506\) 2.15919 + 3.73983i 0.0959879 + 0.166256i
\(507\) 0 0
\(508\) 1.24048 2.14858i 0.0550376 0.0953279i
\(509\) 9.96210 17.2549i 0.441563 0.764809i −0.556243 0.831020i \(-0.687758\pi\)
0.997806 + 0.0662109i \(0.0210910\pi\)
\(510\) 0 0
\(511\) −28.0441 + 6.72894i −1.24060 + 0.297671i
\(512\) 2.01529 0.0890641
\(513\) 0 0
\(514\) 2.10139 + 3.63972i 0.0926886 + 0.160541i
\(515\) −7.11185 + 12.3181i −0.313386 + 0.542800i
\(516\) 0 0
\(517\) 3.22884 + 5.59252i 0.142004 + 0.245959i
\(518\) −6.78237 + 22.8860i −0.298000 + 1.00555i
\(519\) 0 0
\(520\) 30.3935 + 16.5219i 1.33284 + 0.724532i
\(521\) −8.26204 + 14.3103i −0.361967 + 0.626944i −0.988284 0.152623i \(-0.951228\pi\)
0.626318 + 0.779568i \(0.284561\pi\)
\(522\) 0 0
\(523\) 5.99809 10.3890i 0.262278 0.454279i −0.704569 0.709636i \(-0.748860\pi\)
0.966847 + 0.255357i \(0.0821929\pi\)
\(524\) 7.67609 13.2954i 0.335332 0.580812i
\(525\) 0 0
\(526\) −3.81065 + 6.60024i −0.166152 + 0.287784i
\(527\) 17.6905 0.770611
\(528\) 0 0
\(529\) −4.46197 7.72837i −0.193999 0.336016i
\(530\) 13.7471 23.8107i 0.597137 1.03427i
\(531\) 0 0
\(532\) −0.995416 + 3.35886i −0.0431567 + 0.145625i
\(533\) 16.8887 + 9.18068i 0.731531 + 0.397660i
\(534\) 0 0
\(535\) −48.6053 −2.10139
\(536\) 23.5561 1.01747
\(537\) 0 0
\(538\) 4.10536 0.176995
\(539\) −0.330609 + 6.27720i −0.0142403 + 0.270378i
\(540\) 0 0
\(541\) −18.1158 31.3775i −0.778860 1.34903i −0.932599 0.360914i \(-0.882465\pi\)
0.153739 0.988112i \(-0.450869\pi\)
\(542\) 3.15829 + 5.47031i 0.135660 + 0.234970i
\(543\) 0 0
\(544\) 5.54665 9.60707i 0.237811 0.411900i
\(545\) 14.4624 0.619500
\(546\) 0 0
\(547\) −7.34857 −0.314202 −0.157101 0.987583i \(-0.550215\pi\)
−0.157101 + 0.987583i \(0.550215\pi\)
\(548\) −5.55973 + 9.62974i −0.237500 + 0.411362i
\(549\) 0 0
\(550\) −2.61535 4.52991i −0.111519 0.193156i
\(551\) −0.952888 1.65045i −0.0405944 0.0703115i
\(552\) 0 0
\(553\) −9.09016 + 30.6732i −0.386553 + 1.30436i
\(554\) 3.24816 0.138001
\(555\) 0 0
\(556\) −5.37340 −0.227883
\(557\) −10.8280 −0.458796 −0.229398 0.973333i \(-0.573676\pi\)
−0.229398 + 0.973333i \(0.573676\pi\)
\(558\) 0 0
\(559\) 0.362466 + 14.1098i 0.0153307 + 0.596781i
\(560\) −1.11731 1.17770i −0.0472148 0.0497670i
\(561\) 0 0
\(562\) 3.63847 6.30201i 0.153480 0.265834i
\(563\) −6.92997 12.0031i −0.292064 0.505869i 0.682234 0.731134i \(-0.261009\pi\)
−0.974298 + 0.225265i \(0.927675\pi\)
\(564\) 0 0
\(565\) 47.3873 1.99360
\(566\) −6.49594 + 11.2513i −0.273045 + 0.472927i
\(567\) 0 0
\(568\) 4.80692 8.32583i 0.201694 0.349344i
\(569\) 13.7060 23.7395i 0.574586 0.995212i −0.421500 0.906828i \(-0.638496\pi\)
0.996086 0.0883842i \(-0.0281703\pi\)
\(570\) 0 0
\(571\) 0.103879 0.179923i 0.00434719 0.00752956i −0.863844 0.503760i \(-0.831950\pi\)
0.868191 + 0.496230i \(0.165283\pi\)
\(572\) −3.62854 1.97247i −0.151717 0.0824732i
\(573\) 0 0
\(574\) 8.26302 + 8.70967i 0.344892 + 0.363535i
\(575\) 19.3341 + 33.4876i 0.806288 + 1.39653i
\(576\) 0 0
\(577\) 1.66328 2.88089i 0.0692434 0.119933i −0.829325 0.558766i \(-0.811275\pi\)
0.898568 + 0.438833i \(0.144608\pi\)
\(578\) 5.63818 + 9.76562i 0.234518 + 0.406196i
\(579\) 0 0
\(580\) 8.05959 0.334656
\(581\) −2.76184 2.91113i −0.114581 0.120774i
\(582\) 0 0
\(583\) −4.21447 + 7.29967i −0.174545 + 0.302321i
\(584\) 15.1950 26.3185i 0.628772 1.08907i
\(585\) 0 0
\(586\) −2.52769 4.37809i −0.104418 0.180857i
\(587\) −7.54051 13.0606i −0.311230 0.539067i 0.667399 0.744701i \(-0.267408\pi\)
−0.978629 + 0.205634i \(0.934074\pi\)
\(588\) 0 0
\(589\) 4.74064 8.21104i 0.195335 0.338330i
\(590\) 0.747686 + 1.29503i 0.0307817 + 0.0533155i
\(591\) 0 0
\(592\) 0.944935 + 1.63668i 0.0388366 + 0.0672670i
\(593\) 12.9245 + 22.3859i 0.530747 + 0.919281i 0.999356 + 0.0358751i \(0.0114218\pi\)
−0.468609 + 0.883405i \(0.655245\pi\)
\(594\) 0 0
\(595\) −17.1485 + 4.11463i −0.703020 + 0.168684i
\(596\) −3.74055 6.47882i −0.153219 0.265383i
\(597\) 0 0
\(598\) −15.2337 8.28101i −0.622952 0.338636i
\(599\) −17.7734 + 30.7845i −0.726203 + 1.25782i 0.232274 + 0.972650i \(0.425383\pi\)
−0.958477 + 0.285170i \(0.907950\pi\)
\(600\) 0 0
\(601\) 13.6474 + 23.6379i 0.556688 + 0.964212i 0.997770 + 0.0667449i \(0.0212614\pi\)
−0.441082 + 0.897467i \(0.645405\pi\)
\(602\) −2.50477 + 8.45192i −0.102087 + 0.344474i
\(603\) 0 0
\(604\) 21.5023 0.874915
\(605\) −17.5406 30.3811i −0.713125 1.23517i
\(606\) 0 0
\(607\) −38.9258 −1.57995 −0.789976 0.613138i \(-0.789907\pi\)
−0.789976 + 0.613138i \(0.789907\pi\)
\(608\) −2.97274 5.14894i −0.120561 0.208817i
\(609\) 0 0
\(610\) −4.20679 −0.170328
\(611\) −22.7803 12.3834i −0.921593 0.500977i
\(612\) 0 0
\(613\) 0.886645 0.0358113 0.0179056 0.999840i \(-0.494300\pi\)
0.0179056 + 0.999840i \(0.494300\pi\)
\(614\) −9.45317 + 16.3734i −0.381499 + 0.660775i
\(615\) 0 0
\(616\) −4.55884 4.80526i −0.183681 0.193609i
\(617\) 17.3944 30.1280i 0.700272 1.21291i −0.268099 0.963391i \(-0.586395\pi\)
0.968371 0.249515i \(-0.0802712\pi\)
\(618\) 0 0
\(619\) −1.02781 + 1.78021i −0.0413111 + 0.0715529i −0.885942 0.463797i \(-0.846487\pi\)
0.844631 + 0.535350i \(0.179820\pi\)
\(620\) 20.0483 + 34.7247i 0.805161 + 1.39458i
\(621\) 0 0
\(622\) 4.18864 + 7.25494i 0.167949 + 0.290897i
\(623\) 35.0092 8.40016i 1.40262 0.336545i
\(624\) 0 0
\(625\) 6.19081 + 10.7228i 0.247632 + 0.428912i
\(626\) −17.7992 −0.711398
\(627\) 0 0
\(628\) 2.47336 0.0986979
\(629\) 20.5302 0.818593
\(630\) 0 0
\(631\) 22.6169 39.1736i 0.900363 1.55947i 0.0733401 0.997307i \(-0.476634\pi\)
0.827023 0.562168i \(-0.190033\pi\)
\(632\) −16.8555 29.1946i −0.670477 1.16130i
\(633\) 0 0
\(634\) 21.5848 0.857241
\(635\) 3.34678 5.79679i 0.132813 0.230038i
\(636\) 0 0
\(637\) −12.0262 22.1894i −0.476494 0.879178i
\(638\) 1.40321 0.0555534
\(639\) 0 0
\(640\) 26.1881 1.03518
\(641\) −9.53097 16.5081i −0.376451 0.652032i 0.614092 0.789234i \(-0.289522\pi\)
−0.990543 + 0.137202i \(0.956189\pi\)
\(642\) 0 0
\(643\) 5.26755 9.12367i 0.207732 0.359802i −0.743268 0.668994i \(-0.766725\pi\)
0.951000 + 0.309192i \(0.100058\pi\)
\(644\) 13.1241 + 13.8335i 0.517162 + 0.545117i
\(645\) 0 0
\(646\) −1.71117 −0.0673252
\(647\) 24.1608 0.949860 0.474930 0.880024i \(-0.342473\pi\)
0.474930 + 0.880024i \(0.342473\pi\)
\(648\) 0 0
\(649\) −0.229219 0.397019i −0.00899762 0.0155843i
\(650\) 18.4520 + 10.0305i 0.723745 + 0.393427i
\(651\) 0 0
\(652\) −7.58714 13.1413i −0.297135 0.514654i
\(653\) −16.8445 + 29.1755i −0.659176 + 1.14173i 0.321653 + 0.946858i \(0.395762\pi\)
−0.980829 + 0.194869i \(0.937572\pi\)
\(654\) 0 0
\(655\) 20.7098 35.8704i 0.809199 1.40157i
\(656\) 0.950537 0.0371122
\(657\) 0 0
\(658\) −11.1456 11.7480i −0.434500 0.457986i
\(659\) −2.10030 + 3.63782i −0.0818159 + 0.141709i −0.904030 0.427469i \(-0.859405\pi\)
0.822214 + 0.569178i \(0.192739\pi\)
\(660\) 0 0
\(661\) 17.6726 0.687385 0.343693 0.939082i \(-0.388322\pi\)
0.343693 + 0.939082i \(0.388322\pi\)
\(662\) −0.758708 + 1.31412i −0.0294880 + 0.0510748i
\(663\) 0 0
\(664\) 4.22844 0.164095
\(665\) −2.68559 + 9.06208i −0.104143 + 0.351413i
\(666\) 0 0
\(667\) −10.3733 −0.401655
\(668\) −10.5721 + 18.3114i −0.409046 + 0.708488i
\(669\) 0 0
\(670\) 24.7491 0.956143
\(671\) 1.28968 0.0497875
\(672\) 0 0
\(673\) 10.3052 + 17.8491i 0.397235 + 0.688031i 0.993384 0.114843i \(-0.0366366\pi\)
−0.596149 + 0.802874i \(0.703303\pi\)
\(674\) −4.06901 + 7.04774i −0.156733 + 0.271469i
\(675\) 0 0
\(676\) 16.5607 0.851419i 0.636952 0.0327469i
\(677\) −10.6537 18.4527i −0.409455 0.709196i 0.585374 0.810763i \(-0.300948\pi\)
−0.994829 + 0.101567i \(0.967614\pi\)
\(678\) 0 0
\(679\) −1.30242 + 0.312505i −0.0499823 + 0.0119928i
\(680\) 9.29147 16.0933i 0.356312 0.617150i
\(681\) 0 0
\(682\) 3.49049 + 6.04571i 0.133658 + 0.231502i
\(683\) −3.34878 5.80026i −0.128138 0.221941i 0.794817 0.606849i \(-0.207567\pi\)
−0.922955 + 0.384908i \(0.874233\pi\)
\(684\) 0 0
\(685\) −14.9999 + 25.9806i −0.573118 + 0.992670i
\(686\) −2.86655 15.5002i −0.109445 0.591801i
\(687\) 0 0
\(688\) 0.348970 + 0.604433i 0.0133043 + 0.0230438i
\(689\) −0.869117 33.8323i −0.0331107 1.28891i
\(690\) 0 0
\(691\) 12.4632 21.5868i 0.474121 0.821202i −0.525440 0.850831i \(-0.676099\pi\)
0.999561 + 0.0296291i \(0.00943262\pi\)
\(692\) 6.36936 + 11.0321i 0.242127 + 0.419376i
\(693\) 0 0
\(694\) −0.539093 −0.0204637
\(695\) −14.4972 −0.549911
\(696\) 0 0
\(697\) 5.16298 8.94254i 0.195562 0.338723i
\(698\) 26.0435 0.985761
\(699\) 0 0
\(700\) −15.8967 16.7560i −0.600839 0.633317i
\(701\) 4.94583 0.186801 0.0934007 0.995629i \(-0.470226\pi\)
0.0934007 + 0.995629i \(0.470226\pi\)
\(702\) 0 0
\(703\) 5.50162 9.52908i 0.207497 0.359396i
\(704\) 4.05741 0.152919
\(705\) 0 0
\(706\) −0.468266 + 0.811061i −0.0176234 + 0.0305247i
\(707\) 10.9013 + 11.4905i 0.409985 + 0.432147i
\(708\) 0 0
\(709\) −4.64497 −0.174446 −0.0872228 0.996189i \(-0.527799\pi\)
−0.0872228 + 0.996189i \(0.527799\pi\)
\(710\) 5.05037 8.74749i 0.189537 0.328288i
\(711\) 0 0
\(712\) −18.9688 + 32.8550i −0.710888 + 1.23129i
\(713\) −25.8037 44.6933i −0.966356 1.67378i
\(714\) 0 0
\(715\) −9.78966 5.32165i −0.366113 0.199018i
\(716\) −5.85275 10.1373i −0.218728 0.378847i
\(717\) 0 0
\(718\) 8.31878 0.310454
\(719\) −31.7413 −1.18375 −0.591875 0.806030i \(-0.701612\pi\)
−0.591875 + 0.806030i \(0.701612\pi\)
\(720\) 0 0
\(721\) −3.10705 + 10.4842i −0.115713 + 0.390453i
\(722\) 7.62714 13.2106i 0.283853 0.491647i
\(723\) 0 0
\(724\) 3.82987 + 6.63354i 0.142336 + 0.246533i
\(725\) 12.5647 0.466643
\(726\) 0 0
\(727\) 47.8755 1.77560 0.887801 0.460227i \(-0.152232\pi\)
0.887801 + 0.460227i \(0.152232\pi\)
\(728\) 25.6847 + 6.89944i 0.951937 + 0.255710i
\(729\) 0 0
\(730\) 15.9645 27.6514i 0.590873 1.02342i
\(731\) 7.58192 0.280427
\(732\) 0 0
\(733\) 3.80104 + 6.58359i 0.140395 + 0.243171i 0.927645 0.373463i \(-0.121830\pi\)
−0.787251 + 0.616633i \(0.788496\pi\)
\(734\) 4.74386 8.21660i 0.175099 0.303280i
\(735\) 0 0
\(736\) −32.3618 −1.19287
\(737\) −7.58737 −0.279484
\(738\) 0 0
\(739\) −33.4236 −1.22951 −0.614754 0.788719i \(-0.710745\pi\)
−0.614754 + 0.788719i \(0.710745\pi\)
\(740\) 23.2665 + 40.2988i 0.855294 + 1.48141i
\(741\) 0 0
\(742\) 6.00589 20.2659i 0.220483 0.743984i
\(743\) −1.46912 2.54458i −0.0538966 0.0933517i 0.837818 0.545949i \(-0.183831\pi\)
−0.891715 + 0.452597i \(0.850497\pi\)
\(744\) 0 0
\(745\) −10.0919 17.4796i −0.369737 0.640403i
\(746\) 13.0776 22.6511i 0.478805 0.829314i
\(747\) 0 0
\(748\) −1.10927 + 1.92131i −0.0405588 + 0.0702499i
\(749\) −36.3356 + 8.71842i −1.32767 + 0.318564i
\(750\) 0 0
\(751\) −0.598389 + 1.03644i −0.0218355 + 0.0378202i −0.876737 0.480971i \(-0.840284\pi\)
0.854901 + 0.518791i \(0.173618\pi\)
\(752\) −1.28213 −0.0467545
\(753\) 0 0
\(754\) −4.80531 + 2.94141i −0.174999 + 0.107120i
\(755\) 58.0123 2.11128
\(756\) 0 0
\(757\) −5.77321 9.99950i −0.209831 0.363438i 0.741830 0.670588i \(-0.233958\pi\)
−0.951661 + 0.307150i \(0.900625\pi\)
\(758\) 19.2841 0.700432
\(759\) 0 0
\(760\) −4.97979 8.62525i −0.180636 0.312871i
\(761\) −34.6497 −1.25605 −0.628026 0.778192i \(-0.716137\pi\)
−0.628026 + 0.778192i \(0.716137\pi\)
\(762\) 0 0
\(763\) 10.8116 2.59414i 0.391405 0.0939143i
\(764\) −0.839413 1.45391i −0.0303689 0.0526005i
\(765\) 0 0
\(766\) −0.250768 + 0.434344i −0.00906063 + 0.0156935i
\(767\) 1.61720 + 0.879108i 0.0583937 + 0.0317427i
\(768\) 0 0
\(769\) 3.27437 + 5.67138i 0.118077 + 0.204515i 0.919006 0.394245i \(-0.128994\pi\)
−0.800929 + 0.598760i \(0.795660\pi\)
\(770\) −4.78972 5.04862i −0.172610 0.181940i
\(771\) 0 0
\(772\) −10.4760 18.1450i −0.377039 0.653051i
\(773\) 16.9637 + 29.3821i 0.610143 + 1.05680i 0.991216 + 0.132254i \(0.0422214\pi\)
−0.381073 + 0.924545i \(0.624445\pi\)
\(774\) 0 0
\(775\) 31.2550 + 54.1352i 1.12271 + 1.94459i
\(776\) 0.705683 1.22228i 0.0253325 0.0438772i
\(777\) 0 0
\(778\) 2.42547 + 4.20104i 0.0869575 + 0.150615i
\(779\) −2.76711 4.79278i −0.0991422 0.171719i
\(780\) 0 0
\(781\) −1.54830 + 2.68173i −0.0554024 + 0.0959598i
\(782\) −4.65703 + 8.06620i −0.166535 + 0.288447i
\(783\) 0 0
\(784\) −1.04651 0.679995i −0.0373752 0.0242855i
\(785\) 6.67303 0.238171
\(786\) 0 0
\(787\) −6.48717 11.2361i −0.231243 0.400524i 0.726932 0.686710i \(-0.240946\pi\)
−0.958174 + 0.286186i \(0.907612\pi\)
\(788\) 16.3195 28.2662i 0.581359 1.00694i
\(789\) 0 0
\(790\) −17.7092 </