Properties

Label 1323.2.g.c.361.1
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.c.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23025 + 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +2.59358 q^{5} +5.05408 q^{8} +O(q^{10})\) \(q+(-1.23025 + 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +2.59358 q^{5} +5.05408 q^{8} +(-3.19076 + 5.52655i) q^{10} -4.51459 q^{11} +(-0.500000 + 0.866025i) q^{13} +(-2.16372 + 3.74766i) q^{16} +(-0.472958 + 0.819187i) q^{17} +(2.02704 + 3.51094i) q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +0.273346 q^{23} +1.72665 q^{25} +(-1.23025 - 2.13086i) q^{26} +(1.23025 + 2.13086i) q^{29} +(-1.16372 - 2.01561i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(-1.16372 - 2.01561i) q^{34} +(-0.890369 - 1.54216i) q^{37} -9.97509 q^{38} +13.1082 q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(9.15126 + 15.8505i) q^{44} +(-0.336285 + 0.582462i) q^{46} +(-6.08113 + 10.5328i) q^{47} +(-2.12422 + 3.67926i) q^{50} +4.05408 q^{52} +(-3.13667 + 5.43288i) q^{53} -11.7089 q^{55} -6.05408 q^{58} +(-1.36333 - 2.36135i) q^{59} +(1.13667 - 1.96878i) q^{61} +5.72665 q^{62} -7.32743 q^{64} +(-1.29679 + 2.24611i) q^{65} +(7.90856 + 13.6980i) q^{67} +3.83482 q^{68} -3.27335 q^{71} +(0.753696 - 1.30544i) q^{73} +4.38151 q^{74} +(8.21780 - 14.2336i) q^{76} +(-7.35447 + 12.7383i) q^{79} +(-5.61177 + 9.71987i) q^{80} +(-7.88151 - 13.6512i) q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} -25.6768 q^{86} -22.8171 q^{88} +(-7.17830 - 12.4332i) q^{89} +(-0.554084 - 0.959702i) q^{92} +(-14.9626 - 25.9161i) q^{94} +(5.25729 + 9.10590i) q^{95} +(5.74484 + 9.95036i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{4} + 10q^{5} + 12q^{8} + O(q^{10}) \) \( 6q - q^{2} - 3q^{4} + 10q^{5} + 12q^{8} + 4q^{11} - 3q^{13} - 3q^{16} - 12q^{17} + 3q^{19} - 16q^{20} + 15q^{22} + 12q^{25} - q^{26} + q^{29} + 3q^{31} - 8q^{32} + 3q^{34} + 3q^{37} - 16q^{38} + 42q^{40} - 22q^{41} + 3q^{43} + 23q^{44} - 12q^{46} - 9q^{47} + 10q^{50} + 6q^{52} - 18q^{53} - 12q^{55} - 18q^{58} - 9q^{59} + 6q^{61} + 36q^{62} - 24q^{64} - 5q^{65} - 12q^{68} - 18q^{71} - 3q^{73} - 12q^{74} + 21q^{76} - 15q^{79} + 11q^{80} - 9q^{82} - 12q^{83} - 9q^{85} - 68q^{86} - 42q^{88} - 2q^{89} + 15q^{92} - 24q^{94} + 16q^{95} - 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23025 + 2.13086i −0.869920 + 1.50675i −0.00784213 + 0.999969i \(0.502496\pi\)
−0.862078 + 0.506776i \(0.830837\pi\)
\(3\) 0 0
\(4\) −2.02704 3.51094i −1.01352 1.75547i
\(5\) 2.59358 1.15988 0.579942 0.814658i \(-0.303075\pi\)
0.579942 + 0.814658i \(0.303075\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 5.05408 1.78689
\(9\) 0 0
\(10\) −3.19076 + 5.52655i −1.00901 + 1.74765i
\(11\) −4.51459 −1.36120 −0.680600 0.732655i \(-0.738281\pi\)
−0.680600 + 0.732655i \(0.738281\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.16372 + 3.74766i −0.540929 + 0.936916i
\(17\) −0.472958 + 0.819187i −0.114709 + 0.198682i −0.917663 0.397359i \(-0.869927\pi\)
0.802954 + 0.596041i \(0.203260\pi\)
\(18\) 0 0
\(19\) 2.02704 + 3.51094i 0.465035 + 0.805465i 0.999203 0.0399136i \(-0.0127083\pi\)
−0.534168 + 0.845378i \(0.679375\pi\)
\(20\) −5.25729 9.10590i −1.17557 2.03614i
\(21\) 0 0
\(22\) 5.55408 9.61996i 1.18413 2.05098i
\(23\) 0.273346 0.0569966 0.0284983 0.999594i \(-0.490927\pi\)
0.0284983 + 0.999594i \(0.490927\pi\)
\(24\) 0 0
\(25\) 1.72665 0.345331
\(26\) −1.23025 2.13086i −0.241272 0.417896i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.23025 + 2.13086i 0.228452 + 0.395691i 0.957350 0.288932i \(-0.0933002\pi\)
−0.728897 + 0.684623i \(0.759967\pi\)
\(30\) 0 0
\(31\) −1.16372 2.01561i −0.209009 0.362015i 0.742393 0.669964i \(-0.233691\pi\)
−0.951403 + 0.307949i \(0.900357\pi\)
\(32\) −0.269748 0.467216i −0.0476851 0.0825930i
\(33\) 0 0
\(34\) −1.16372 2.01561i −0.199576 0.345675i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.890369 1.54216i −0.146376 0.253530i 0.783510 0.621380i \(-0.213428\pi\)
−0.929885 + 0.367849i \(0.880094\pi\)
\(38\) −9.97509 −1.61817
\(39\) 0 0
\(40\) 13.1082 2.07258
\(41\) −3.20321 + 5.54812i −0.500257 + 0.866471i 0.499743 + 0.866174i \(0.333428\pi\)
−1.00000 0.000297253i \(0.999905\pi\)
\(42\) 0 0
\(43\) 5.21780 + 9.03749i 0.795707 + 1.37820i 0.922389 + 0.386262i \(0.126234\pi\)
−0.126682 + 0.991943i \(0.540433\pi\)
\(44\) 9.15126 + 15.8505i 1.37960 + 2.38955i
\(45\) 0 0
\(46\) −0.336285 + 0.582462i −0.0495825 + 0.0858794i
\(47\) −6.08113 + 10.5328i −0.887023 + 1.53637i −0.0436467 + 0.999047i \(0.513898\pi\)
−0.843377 + 0.537323i \(0.819436\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.12422 + 3.67926i −0.300410 + 0.520326i
\(51\) 0 0
\(52\) 4.05408 0.562200
\(53\) −3.13667 + 5.43288i −0.430855 + 0.746263i −0.996947 0.0780790i \(-0.975121\pi\)
0.566092 + 0.824342i \(0.308455\pi\)
\(54\) 0 0
\(55\) −11.7089 −1.57883
\(56\) 0 0
\(57\) 0 0
\(58\) −6.05408 −0.794940
\(59\) −1.36333 2.36135i −0.177490 0.307422i 0.763530 0.645772i \(-0.223464\pi\)
−0.941020 + 0.338350i \(0.890131\pi\)
\(60\) 0 0
\(61\) 1.13667 1.96878i 0.145536 0.252076i −0.784037 0.620714i \(-0.786843\pi\)
0.929573 + 0.368639i \(0.120176\pi\)
\(62\) 5.72665 0.727286
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) −1.29679 + 2.24611i −0.160847 + 0.278595i
\(66\) 0 0
\(67\) 7.90856 + 13.6980i 0.966184 + 1.67348i 0.706400 + 0.707813i \(0.250318\pi\)
0.259784 + 0.965667i \(0.416349\pi\)
\(68\) 3.83482 0.465041
\(69\) 0 0
\(70\) 0 0
\(71\) −3.27335 −0.388475 −0.194237 0.980955i \(-0.562223\pi\)
−0.194237 + 0.980955i \(0.562223\pi\)
\(72\) 0 0
\(73\) 0.753696 1.30544i 0.0882134 0.152790i −0.818543 0.574446i \(-0.805218\pi\)
0.906756 + 0.421656i \(0.138551\pi\)
\(74\) 4.38151 0.509341
\(75\) 0 0
\(76\) 8.21780 14.2336i 0.942646 1.63271i
\(77\) 0 0
\(78\) 0 0
\(79\) −7.35447 + 12.7383i −0.827443 + 1.43317i 0.0725952 + 0.997361i \(0.476872\pi\)
−0.900038 + 0.435811i \(0.856461\pi\)
\(80\) −5.61177 + 9.71987i −0.627415 + 1.08671i
\(81\) 0 0
\(82\) −7.88151 13.6512i −0.870368 1.50752i
\(83\) −0.472958 0.819187i −0.0519139 0.0899175i 0.838901 0.544285i \(-0.183199\pi\)
−0.890815 + 0.454367i \(0.849865\pi\)
\(84\) 0 0
\(85\) −1.22665 + 2.12463i −0.133049 + 0.230448i
\(86\) −25.6768 −2.76881
\(87\) 0 0
\(88\) −22.8171 −2.43231
\(89\) −7.17830 12.4332i −0.760899 1.31792i −0.942388 0.334522i \(-0.891425\pi\)
0.181489 0.983393i \(-0.441908\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.554084 0.959702i −0.0577673 0.100056i
\(93\) 0 0
\(94\) −14.9626 25.9161i −1.54328 2.67304i
\(95\) 5.25729 + 9.10590i 0.539387 + 0.934246i
\(96\) 0 0
\(97\) 5.74484 + 9.95036i 0.583300 + 1.01031i 0.995085 + 0.0990246i \(0.0315722\pi\)
−0.411785 + 0.911281i \(0.635094\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) 3.67977 0.366150 0.183075 0.983099i \(-0.441395\pi\)
0.183075 + 0.983099i \(0.441395\pi\)
\(102\) 0 0
\(103\) −9.72665 −0.958396 −0.479198 0.877707i \(-0.659072\pi\)
−0.479198 + 0.877707i \(0.659072\pi\)
\(104\) −2.52704 + 4.37697i −0.247797 + 0.429197i
\(105\) 0 0
\(106\) −7.71780 13.3676i −0.749619 1.29838i
\(107\) −0.687159 1.19019i −0.0664301 0.115060i 0.830897 0.556426i \(-0.187828\pi\)
−0.897327 + 0.441365i \(0.854494\pi\)
\(108\) 0 0
\(109\) 1.69961 2.94381i 0.162793 0.281966i −0.773076 0.634313i \(-0.781283\pi\)
0.935869 + 0.352347i \(0.114616\pi\)
\(110\) 14.4050 24.9501i 1.37346 2.37890i
\(111\) 0 0
\(112\) 0 0
\(113\) 5.19436 8.99689i 0.488644 0.846356i −0.511271 0.859420i \(-0.670825\pi\)
0.999915 + 0.0130636i \(0.00415840\pi\)
\(114\) 0 0
\(115\) 0.708945 0.0661095
\(116\) 4.98755 8.63868i 0.463082 0.802082i
\(117\) 0 0
\(118\) 6.70895 0.617608
\(119\) 0 0
\(120\) 0 0
\(121\) 9.38151 0.852865
\(122\) 2.79679 + 4.84418i 0.253209 + 0.438572i
\(123\) 0 0
\(124\) −4.71780 + 8.17147i −0.423671 + 0.733820i
\(125\) −8.48968 −0.759340
\(126\) 0 0
\(127\) 0.672570 0.0596809 0.0298405 0.999555i \(-0.490500\pi\)
0.0298405 + 0.999555i \(0.490500\pi\)
\(128\) 9.55408 16.5482i 0.844470 1.46266i
\(129\) 0 0
\(130\) −3.19076 5.52655i −0.279848 0.484711i
\(131\) −7.91381 −0.691433 −0.345717 0.938339i \(-0.612364\pi\)
−0.345717 + 0.938339i \(0.612364\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −38.9181 −3.36201
\(135\) 0 0
\(136\) −2.39037 + 4.14024i −0.204972 + 0.355023i
\(137\) 3.67257 0.313769 0.156884 0.987617i \(-0.449855\pi\)
0.156884 + 0.987617i \(0.449855\pi\)
\(138\) 0 0
\(139\) 1.02704 1.77889i 0.0871126 0.150883i −0.819177 0.573541i \(-0.805569\pi\)
0.906289 + 0.422658i \(0.138903\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.02704 6.97504i 0.337942 0.585332i
\(143\) 2.25729 3.90975i 0.188764 0.326950i
\(144\) 0 0
\(145\) 3.19076 + 5.52655i 0.264978 + 0.458955i
\(146\) 1.85447 + 3.21204i 0.153477 + 0.265830i
\(147\) 0 0
\(148\) −3.60963 + 6.25206i −0.296710 + 0.513917i
\(149\) 13.5438 1.10955 0.554774 0.832001i \(-0.312805\pi\)
0.554774 + 0.832001i \(0.312805\pi\)
\(150\) 0 0
\(151\) 9.92821 0.807946 0.403973 0.914771i \(-0.367629\pi\)
0.403973 + 0.914771i \(0.367629\pi\)
\(152\) 10.2448 + 17.7446i 0.830966 + 1.43928i
\(153\) 0 0
\(154\) 0 0
\(155\) −3.01819 5.22765i −0.242427 0.419895i
\(156\) 0 0
\(157\) −3.02704 5.24299i −0.241584 0.418436i 0.719581 0.694408i \(-0.244334\pi\)
−0.961166 + 0.275972i \(0.911000\pi\)
\(158\) −18.0957 31.3427i −1.43962 2.49349i
\(159\) 0 0
\(160\) −0.699612 1.21176i −0.0553092 0.0957983i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.90856 15.4301i −0.697772 1.20858i −0.969237 0.246128i \(-0.920842\pi\)
0.271465 0.962448i \(-0.412492\pi\)
\(164\) 25.9722 2.02809
\(165\) 0 0
\(166\) 2.32743 0.180644
\(167\) −4.23385 + 7.33325i −0.327625 + 0.567464i −0.982040 0.188672i \(-0.939582\pi\)
0.654415 + 0.756136i \(0.272915\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) −3.01819 5.22765i −0.231484 0.400943i
\(171\) 0 0
\(172\) 21.1534 36.6388i 1.61293 2.79368i
\(173\) 8.67830 15.0313i 0.659799 1.14281i −0.320868 0.947124i \(-0.603975\pi\)
0.980667 0.195682i \(-0.0626920\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.76829 16.9192i 0.736312 1.27533i
\(177\) 0 0
\(178\) 35.3245 2.64768
\(179\) −5.67471 + 9.82888i −0.424147 + 0.734645i −0.996340 0.0854741i \(-0.972759\pi\)
0.572193 + 0.820119i \(0.306093\pi\)
\(180\) 0 0
\(181\) 21.8889 1.62699 0.813495 0.581572i \(-0.197562\pi\)
0.813495 + 0.581572i \(0.197562\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.38151 0.101847
\(185\) −2.30924 3.99973i −0.169779 0.294066i
\(186\) 0 0
\(187\) 2.13521 3.69829i 0.156142 0.270446i
\(188\) 49.3068 3.59607
\(189\) 0 0
\(190\) −25.8712 −1.87689
\(191\) −0.350874 + 0.607731i −0.0253883 + 0.0439739i −0.878440 0.477852i \(-0.841416\pi\)
0.853052 + 0.521826i \(0.174749\pi\)
\(192\) 0 0
\(193\) −6.07227 10.5175i −0.437092 0.757065i 0.560372 0.828241i \(-0.310658\pi\)
−0.997464 + 0.0711760i \(0.977325\pi\)
\(194\) −28.2704 −2.02970
\(195\) 0 0
\(196\) 0 0
\(197\) 16.4107 1.16921 0.584607 0.811317i \(-0.301249\pi\)
0.584607 + 0.811317i \(0.301249\pi\)
\(198\) 0 0
\(199\) −11.3530 + 19.6640i −0.804794 + 1.39394i 0.111637 + 0.993749i \(0.464391\pi\)
−0.916430 + 0.400194i \(0.868943\pi\)
\(200\) 8.72665 0.617068
\(201\) 0 0
\(202\) −4.52704 + 7.84107i −0.318522 + 0.551696i
\(203\) 0 0
\(204\) 0 0
\(205\) −8.30778 + 14.3895i −0.580241 + 1.00501i
\(206\) 11.9662 20.7261i 0.833727 1.44406i
\(207\) 0 0
\(208\) −2.16372 3.74766i −0.150027 0.259854i
\(209\) −9.15126 15.8505i −0.633006 1.09640i
\(210\) 0 0
\(211\) −2.28074 + 3.95035i −0.157012 + 0.271954i −0.933790 0.357822i \(-0.883520\pi\)
0.776778 + 0.629775i \(0.216853\pi\)
\(212\) 25.4327 1.74672
\(213\) 0 0
\(214\) 3.38151 0.231156
\(215\) 13.5328 + 23.4395i 0.922928 + 1.59856i
\(216\) 0 0
\(217\) 0 0
\(218\) 4.18190 + 7.24327i 0.283234 + 0.490576i
\(219\) 0 0
\(220\) 23.7345 + 41.1094i 1.60018 + 2.77160i
\(221\) −0.472958 0.819187i −0.0318146 0.0551045i
\(222\) 0 0
\(223\) −6.66225 11.5394i −0.446137 0.772733i 0.551993 0.833849i \(-0.313867\pi\)
−0.998131 + 0.0611159i \(0.980534\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.7807 + 22.1369i 0.850162 + 1.47252i
\(227\) −1.38151 −0.0916943 −0.0458472 0.998948i \(-0.514599\pi\)
−0.0458472 + 0.998948i \(0.514599\pi\)
\(228\) 0 0
\(229\) −17.9794 −1.18811 −0.594055 0.804424i \(-0.702474\pi\)
−0.594055 + 0.804424i \(0.702474\pi\)
\(230\) −0.872181 + 1.51066i −0.0575099 + 0.0996101i
\(231\) 0 0
\(232\) 6.21780 + 10.7695i 0.408219 + 0.707055i
\(233\) −9.49115 16.4391i −0.621786 1.07696i −0.989153 0.146888i \(-0.953074\pi\)
0.367367 0.930076i \(-0.380259\pi\)
\(234\) 0 0
\(235\) −15.7719 + 27.3177i −1.02884 + 1.78201i
\(236\) −5.52704 + 9.57312i −0.359780 + 0.623157i
\(237\) 0 0
\(238\) 0 0
\(239\) 2.44592 4.23645i 0.158213 0.274033i −0.776011 0.630719i \(-0.782760\pi\)
0.934224 + 0.356686i \(0.116093\pi\)
\(240\) 0 0
\(241\) −26.1593 −1.68507 −0.842535 0.538641i \(-0.818938\pi\)
−0.842535 + 0.538641i \(0.818938\pi\)
\(242\) −11.5416 + 19.9907i −0.741924 + 1.28505i
\(243\) 0 0
\(244\) −9.21634 −0.590016
\(245\) 0 0
\(246\) 0 0
\(247\) −4.05408 −0.257955
\(248\) −5.88151 10.1871i −0.373477 0.646880i
\(249\) 0 0
\(250\) 10.4445 18.0903i 0.660565 1.14413i
\(251\) −18.4576 −1.16503 −0.582516 0.812819i \(-0.697932\pi\)
−0.582516 + 0.812819i \(0.697932\pi\)
\(252\) 0 0
\(253\) −1.23405 −0.0775838
\(254\) −0.827430 + 1.43315i −0.0519176 + 0.0899239i
\(255\) 0 0
\(256\) 16.1804 + 28.0253i 1.01128 + 1.75158i
\(257\) 11.7339 0.731938 0.365969 0.930627i \(-0.380738\pi\)
0.365969 + 0.930627i \(0.380738\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 10.5146 0.652087
\(261\) 0 0
\(262\) 9.73599 16.8632i 0.601491 1.04181i
\(263\) 7.52179 0.463813 0.231907 0.972738i \(-0.425504\pi\)
0.231907 + 0.972738i \(0.425504\pi\)
\(264\) 0 0
\(265\) −8.13521 + 14.0906i −0.499742 + 0.865579i
\(266\) 0 0
\(267\) 0 0
\(268\) 32.0620 55.5329i 1.95850 3.39221i
\(269\) −9.41741 + 16.3114i −0.574190 + 0.994526i 0.421939 + 0.906624i \(0.361349\pi\)
−0.996129 + 0.0879017i \(0.971984\pi\)
\(270\) 0 0
\(271\) 11.9911 + 20.7693i 0.728410 + 1.26164i 0.957555 + 0.288251i \(0.0930738\pi\)
−0.229145 + 0.973392i \(0.573593\pi\)
\(272\) −2.04669 3.54498i −0.124099 0.214946i
\(273\) 0 0
\(274\) −4.51819 + 7.82573i −0.272954 + 0.472770i
\(275\) −7.79513 −0.470064
\(276\) 0 0
\(277\) 7.16225 0.430338 0.215169 0.976577i \(-0.430970\pi\)
0.215169 + 0.976577i \(0.430970\pi\)
\(278\) 2.52704 + 4.37697i 0.151562 + 0.262513i
\(279\) 0 0
\(280\) 0 0
\(281\) 7.44085 + 12.8879i 0.443884 + 0.768830i 0.997974 0.0636271i \(-0.0202668\pi\)
−0.554090 + 0.832457i \(0.686933\pi\)
\(282\) 0 0
\(283\) −9.99854 17.3180i −0.594351 1.02945i −0.993638 0.112621i \(-0.964076\pi\)
0.399287 0.916826i \(-0.369258\pi\)
\(284\) 6.63521 + 11.4925i 0.393727 + 0.681956i
\(285\) 0 0
\(286\) 5.55408 + 9.61996i 0.328420 + 0.568840i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.05262 + 13.9475i 0.473684 + 0.820444i
\(290\) −15.7017 −0.922038
\(291\) 0 0
\(292\) −6.11109 −0.357625
\(293\) 7.53278 13.0472i 0.440070 0.762223i −0.557625 0.830093i \(-0.688287\pi\)
0.997694 + 0.0678705i \(0.0216205\pi\)
\(294\) 0 0
\(295\) −3.53590 6.12435i −0.205868 0.356574i
\(296\) −4.50000 7.79423i −0.261557 0.453030i
\(297\) 0 0
\(298\) −16.6623 + 28.8599i −0.965218 + 1.67181i
\(299\) −0.136673 + 0.236725i −0.00790401 + 0.0136901i
\(300\) 0 0
\(301\) 0 0
\(302\) −12.2142 + 21.1556i −0.702848 + 1.21737i
\(303\) 0 0
\(304\) −17.5438 −1.00620
\(305\) 2.94805 5.10618i 0.168805 0.292379i
\(306\) 0 0
\(307\) −27.2704 −1.55641 −0.778203 0.628013i \(-0.783868\pi\)
−0.778203 + 0.628013i \(0.783868\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 14.8525 0.843567
\(311\) −7.99115 13.8411i −0.453136 0.784855i 0.545443 0.838148i \(-0.316362\pi\)
−0.998579 + 0.0532931i \(0.983028\pi\)
\(312\) 0 0
\(313\) −5.79893 + 10.0440i −0.327775 + 0.567722i −0.982070 0.188517i \(-0.939632\pi\)
0.654295 + 0.756239i \(0.272965\pi\)
\(314\) 14.8961 0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) −1.00885 + 1.74739i −0.0566629 + 0.0981430i −0.892965 0.450125i \(-0.851379\pi\)
0.836303 + 0.548268i \(0.184713\pi\)
\(318\) 0 0
\(319\) −5.55408 9.61996i −0.310969 0.538614i
\(320\) −19.0043 −1.06237
\(321\) 0 0
\(322\) 0 0
\(323\) −3.83482 −0.213375
\(324\) 0 0
\(325\) −0.863327 + 1.49533i −0.0478888 + 0.0829458i
\(326\) 43.8391 2.42802
\(327\) 0 0
\(328\) −16.1893 + 28.0407i −0.893904 + 1.54829i
\(329\) 0 0
\(330\) 0 0
\(331\) 9.85447 17.0684i 0.541651 0.938167i −0.457159 0.889385i \(-0.651133\pi\)
0.998809 0.0487815i \(-0.0155338\pi\)
\(332\) −1.91741 + 3.32105i −0.105232 + 0.182266i
\(333\) 0 0
\(334\) −10.4174 18.0435i −0.570015 0.987296i
\(335\) 20.5115 + 35.5269i 1.12066 + 1.94104i
\(336\) 0 0
\(337\) 14.5256 25.1590i 0.791259 1.37050i −0.133929 0.990991i \(-0.542759\pi\)
0.925188 0.379509i \(-0.123907\pi\)
\(338\) −29.5261 −1.60601
\(339\) 0 0
\(340\) 9.94592 0.539393
\(341\) 5.25370 + 9.09967i 0.284504 + 0.492775i
\(342\) 0 0
\(343\) 0 0
\(344\) 26.3712 + 45.6763i 1.42184 + 2.46270i
\(345\) 0 0
\(346\) 21.3530 + 36.9845i 1.14794 + 1.98830i
\(347\) 14.5416 + 25.1868i 0.780636 + 1.35210i 0.931572 + 0.363557i \(0.118438\pi\)
−0.150936 + 0.988544i \(0.548229\pi\)
\(348\) 0 0
\(349\) −12.3815 21.4454i −0.662767 1.14795i −0.979885 0.199561i \(-0.936049\pi\)
0.317118 0.948386i \(-0.397285\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.21780 + 2.10929i 0.0649089 + 0.112426i
\(353\) 33.3025 1.77251 0.886257 0.463193i \(-0.153296\pi\)
0.886257 + 0.463193i \(0.153296\pi\)
\(354\) 0 0
\(355\) −8.48968 −0.450586
\(356\) −29.1015 + 50.4052i −1.54237 + 2.67147i
\(357\) 0 0
\(358\) −13.9626 24.1840i −0.737949 1.27816i
\(359\) 12.7683 + 22.1153i 0.673884 + 1.16720i 0.976794 + 0.214182i \(0.0687087\pi\)
−0.302909 + 0.953019i \(0.597958\pi\)
\(360\) 0 0
\(361\) 1.28220 2.22084i 0.0674842 0.116886i
\(362\) −26.9289 + 46.6422i −1.41535 + 2.45146i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.95477 3.38576i 0.102317 0.177219i
\(366\) 0 0
\(367\) 27.4504 1.43290 0.716449 0.697639i \(-0.245766\pi\)
0.716449 + 0.697639i \(0.245766\pi\)
\(368\) −0.591443 + 1.02441i −0.0308311 + 0.0534011i
\(369\) 0 0
\(370\) 11.3638 0.590776
\(371\) 0 0
\(372\) 0 0
\(373\) 16.3274 0.845402 0.422701 0.906269i \(-0.361082\pi\)
0.422701 + 0.906269i \(0.361082\pi\)
\(374\) 5.25370 + 9.09967i 0.271662 + 0.470533i
\(375\) 0 0
\(376\) −30.7345 + 53.2338i −1.58501 + 2.74532i
\(377\) −2.46050 −0.126722
\(378\) 0 0
\(379\) 12.0364 0.618267 0.309134 0.951019i \(-0.399961\pi\)
0.309134 + 0.951019i \(0.399961\pi\)
\(380\) 21.3135 36.9161i 1.09336 1.89376i
\(381\) 0 0
\(382\) −0.863327 1.49533i −0.0441716 0.0765075i
\(383\) 12.4356 0.635429 0.317715 0.948186i \(-0.397085\pi\)
0.317715 + 0.948186i \(0.397085\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 29.8817 1.52094
\(387\) 0 0
\(388\) 23.2901 40.3396i 1.18237 2.04793i
\(389\) −20.6008 −1.04450 −0.522250 0.852792i \(-0.674907\pi\)
−0.522250 + 0.852792i \(0.674907\pi\)
\(390\) 0 0
\(391\) −0.129281 + 0.223922i −0.00653803 + 0.0113242i
\(392\) 0 0
\(393\) 0 0
\(394\) −20.1893 + 34.9689i −1.01712 + 1.76171i
\(395\) −19.0744 + 33.0378i −0.959738 + 1.66231i
\(396\) 0 0
\(397\) 11.8186 + 20.4704i 0.593157 + 1.02738i 0.993804 + 0.111146i \(0.0354521\pi\)
−0.400647 + 0.916233i \(0.631215\pi\)
\(398\) −27.9341 48.3833i −1.40021 2.42524i
\(399\) 0 0
\(400\) −3.73599 + 6.47092i −0.186799 + 0.323546i
\(401\) 2.56440 0.128060 0.0640300 0.997948i \(-0.479605\pi\)
0.0640300 + 0.997948i \(0.479605\pi\)
\(402\) 0 0
\(403\) 2.32743 0.115938
\(404\) −7.45904 12.9194i −0.371101 0.642766i
\(405\) 0 0
\(406\) 0 0
\(407\) 4.01965 + 6.96224i 0.199247 + 0.345105i
\(408\) 0 0
\(409\) 17.1623 + 29.7259i 0.848619 + 1.46985i 0.882441 + 0.470423i \(0.155899\pi\)
−0.0338223 + 0.999428i \(0.510768\pi\)
\(410\) −20.4413 35.4054i −1.00953 1.74855i
\(411\) 0 0
\(412\) 19.7163 + 34.1497i 0.971354 + 1.68243i
\(413\) 0 0
\(414\) 0 0
\(415\) −1.22665 2.12463i −0.0602141 0.104294i
\(416\) 0.539495 0.0264509
\(417\) 0 0
\(418\) 45.0335 2.20266
\(419\) 2.02850 3.51347i 0.0990989 0.171644i −0.812213 0.583361i \(-0.801737\pi\)
0.911312 + 0.411717i \(0.135071\pi\)
\(420\) 0 0
\(421\) 10.5344 + 18.2462i 0.513417 + 0.889264i 0.999879 + 0.0155624i \(0.00495387\pi\)
−0.486462 + 0.873702i \(0.661713\pi\)
\(422\) −5.61177 9.71987i −0.273177 0.473156i
\(423\) 0 0
\(424\) −15.8530 + 27.4582i −0.769890 + 1.33349i
\(425\) −0.816635 + 1.41445i −0.0396126 + 0.0686110i
\(426\) 0 0
\(427\) 0 0
\(428\) −2.78580 + 4.82515i −0.134657 + 0.233232i
\(429\) 0 0
\(430\) −66.5949 −3.21149
\(431\) 11.3092 19.5882i 0.544747 0.943530i −0.453876 0.891065i \(-0.649959\pi\)
0.998623 0.0524646i \(-0.0167077\pi\)
\(432\) 0 0
\(433\) 2.41789 0.116196 0.0580982 0.998311i \(-0.481496\pi\)
0.0580982 + 0.998311i \(0.481496\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −13.7807 −0.659978
\(437\) 0.554084 + 0.959702i 0.0265054 + 0.0459088i
\(438\) 0 0
\(439\) 11.7448 20.3427i 0.560551 0.970902i −0.436898 0.899511i \(-0.643923\pi\)
0.997448 0.0713911i \(-0.0227438\pi\)
\(440\) −59.1780 −2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) −6.70895 + 11.6202i −0.318752 + 0.552094i −0.980228 0.197872i \(-0.936597\pi\)
0.661476 + 0.749966i \(0.269930\pi\)
\(444\) 0 0
\(445\) −18.6175 32.2465i −0.882554 1.52863i
\(446\) 32.7850 1.55242
\(447\) 0 0
\(448\) 0 0
\(449\) 9.16225 0.432393 0.216197 0.976350i \(-0.430635\pi\)
0.216197 + 0.976350i \(0.430635\pi\)
\(450\) 0 0
\(451\) 14.4612 25.0475i 0.680950 1.17944i
\(452\) −42.1167 −1.98100
\(453\) 0 0
\(454\) 1.69961 2.94381i 0.0797667 0.138160i
\(455\) 0 0
\(456\) 0 0
\(457\) −4.40856 + 7.63584i −0.206224 + 0.357190i −0.950522 0.310658i \(-0.899451\pi\)
0.744298 + 0.667847i \(0.232784\pi\)
\(458\) 22.1192 38.3115i 1.03356 1.79018i
\(459\) 0 0
\(460\) −1.43706 2.48906i −0.0670033 0.116053i
\(461\) −2.82957 4.90095i −0.131786 0.228260i 0.792579 0.609769i \(-0.208738\pi\)
−0.924365 + 0.381509i \(0.875405\pi\)
\(462\) 0 0
\(463\) −7.86333 + 13.6197i −0.365440 + 0.632960i −0.988847 0.148937i \(-0.952415\pi\)
0.623407 + 0.781898i \(0.285748\pi\)
\(464\) −10.6477 −0.494305
\(465\) 0 0
\(466\) 46.7060 2.16361
\(467\) −10.9985 19.0500i −0.508952 0.881530i −0.999946 0.0103675i \(-0.996700\pi\)
0.490995 0.871163i \(-0.336633\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −38.8068 67.2153i −1.79002 3.10041i
\(471\) 0 0
\(472\) −6.89037 11.9345i −0.317155 0.549328i
\(473\) −23.5562 40.8006i −1.08312 1.87601i
\(474\) 0 0
\(475\) 3.50000 + 6.06218i 0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.01819 + 10.4238i 0.275265 + 0.476774i
\(479\) −24.9751 −1.14114 −0.570571 0.821249i \(-0.693278\pi\)
−0.570571 + 0.821249i \(0.693278\pi\)
\(480\) 0 0
\(481\) 1.78074 0.0811947
\(482\) 32.1826 55.7419i 1.46588 2.53897i
\(483\) 0 0
\(484\) −19.0167 32.9379i −0.864397 1.49718i
\(485\) 14.8997 + 25.8070i 0.676561 + 1.17184i
\(486\) 0 0
\(487\) 8.79893 15.2402i 0.398717 0.690599i −0.594851 0.803836i \(-0.702789\pi\)
0.993568 + 0.113238i \(0.0361221\pi\)
\(488\) 5.74484 9.95036i 0.260057 0.450432i
\(489\) 0 0
\(490\) 0 0
\(491\) 6.89757 11.9469i 0.311283 0.539158i −0.667358 0.744737i \(-0.732575\pi\)
0.978640 + 0.205580i \(0.0659080\pi\)
\(492\) 0 0
\(493\) −2.32743 −0.104822
\(494\) 4.98755 8.63868i 0.224400 0.388673i
\(495\) 0 0
\(496\) 10.0718 0.452237
\(497\) 0 0
\(498\) 0 0
\(499\) 13.0875 0.585879 0.292939 0.956131i \(-0.405367\pi\)
0.292939 + 0.956131i \(0.405367\pi\)
\(500\) 17.2089 + 29.8068i 0.769607 + 1.33300i
\(501\) 0 0
\(502\) 22.7075 39.3305i 1.01348 1.75541i
\(503\) 22.3068 0.994611 0.497305 0.867576i \(-0.334323\pi\)
0.497305 + 0.867576i \(0.334323\pi\)
\(504\) 0 0
\(505\) 9.54377 0.424692
\(506\) 1.51819 2.62958i 0.0674917 0.116899i
\(507\) 0 0
\(508\) −1.36333 2.36135i −0.0604879 0.104768i
\(509\) 15.8932 0.704453 0.352226 0.935915i \(-0.385425\pi\)
0.352226 + 0.935915i \(0.385425\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −41.4078 −1.82998
\(513\) 0 0
\(514\) −14.4356 + 25.0032i −0.636727 + 1.10284i
\(515\) −25.2268 −1.11163
\(516\) 0 0
\(517\) 27.4538 47.5514i 1.20742 2.09131i
\(518\) 0 0
\(519\) 0 0
\(520\) −6.55408 + 11.3520i −0.287416 + 0.497818i
\(521\) 2.20895 3.82600i 0.0967756 0.167620i −0.813573 0.581463i \(-0.802480\pi\)
0.910348 + 0.413843i \(0.135814\pi\)
\(522\) 0 0
\(523\) −12.6367 21.8874i −0.552563 0.957067i −0.998089 0.0617982i \(-0.980316\pi\)
0.445526 0.895269i \(-0.353017\pi\)
\(524\) 16.0416 + 27.7849i 0.700782 + 1.21379i
\(525\) 0 0
\(526\) −9.25370 + 16.0279i −0.403480 + 0.698848i
\(527\) 2.20155 0.0959012
\(528\) 0 0
\(529\) −22.9253 −0.996751
\(530\) −20.0167 34.6700i −0.869471 1.50597i
\(531\) 0 0
\(532\) 0 0
\(533\) −3.20321 5.54812i −0.138746 0.240316i
\(534\) 0 0
\(535\) −1.78220 3.08686i −0.0770513 0.133457i
\(536\) 39.9705 + 69.2310i 1.72646 + 2.99032i
\(537\) 0 0
\(538\) −23.1716 40.1344i −0.998998 1.73032i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.71926 + 2.97785i 0.0739168 + 0.128028i 0.900615 0.434618i \(-0.143117\pi\)
−0.826698 + 0.562646i \(0.809783\pi\)
\(542\) −59.0085 −2.53463
\(543\) 0 0
\(544\) 0.510317 0.0218797
\(545\) 4.40808 7.63501i 0.188821 0.327048i
\(546\) 0 0
\(547\) 3.46410 + 6.00000i 0.148114 + 0.256542i 0.930531 0.366214i \(-0.119346\pi\)
−0.782416 + 0.622756i \(0.786013\pi\)
\(548\) −7.44445 12.8942i −0.318011 0.550812i
\(549\) 0 0
\(550\) 9.58998 16.6103i 0.408918 0.708267i
\(551\) −4.98755 + 8.63868i −0.212477 + 0.368020i
\(552\) 0 0
\(553\) 0 0
\(554\) −8.81138 + 15.2618i −0.374360 + 0.648410i
\(555\) 0 0
\(556\) −8.32743 −0.353162
\(557\) 16.7917 29.0841i 0.711488 1.23233i −0.252810 0.967516i \(-0.581355\pi\)
0.964298 0.264818i \(-0.0853119\pi\)
\(558\) 0 0
\(559\) −10.4356 −0.441379
\(560\) 0 0
\(561\) 0 0
\(562\) −36.6165 −1.54457
\(563\) 21.2396 + 36.7880i 0.895142 + 1.55043i 0.833629 + 0.552325i \(0.186259\pi\)
0.0615128 + 0.998106i \(0.480407\pi\)
\(564\) 0 0
\(565\) 13.4720 23.3341i 0.566770 0.981675i
\(566\) 49.2029 2.06815
\(567\) 0 0
\(568\) −16.5438 −0.694161
\(569\) 5.20175 9.00969i 0.218069 0.377706i −0.736149 0.676820i \(-0.763358\pi\)
0.954217 + 0.299114i \(0.0966910\pi\)
\(570\) 0 0
\(571\) −8.92480 15.4582i −0.373491 0.646906i 0.616609 0.787270i \(-0.288506\pi\)
−0.990100 + 0.140364i \(0.955173\pi\)
\(572\) −18.3025 −0.765267
\(573\) 0 0
\(574\) 0 0
\(575\) 0.471974 0.0196827
\(576\) 0 0
\(577\) −5.97150 + 10.3429i −0.248597 + 0.430582i −0.963137 0.269013i \(-0.913303\pi\)
0.714540 + 0.699595i \(0.246636\pi\)
\(578\) −39.6270 −1.64827
\(579\) 0 0
\(580\) 12.9356 22.4051i 0.537122 0.930322i
\(581\) 0 0
\(582\) 0 0
\(583\) 14.1608 24.5272i 0.586480 1.01581i
\(584\) 3.80924 6.59780i 0.157628 0.273019i
\(585\) 0 0
\(586\) 18.5344 + 32.1026i 0.765650 + 1.32615i
\(587\) 11.9299 + 20.6631i 0.492398 + 0.852859i 0.999962 0.00875568i \(-0.00278706\pi\)
−0.507563 + 0.861614i \(0.669454\pi\)
\(588\) 0 0
\(589\) 4.71780 8.17147i 0.194394 0.336699i
\(590\) 17.4002 0.716354
\(591\) 0 0
\(592\) 7.70602 0.316715
\(593\) 9.79007 + 16.9569i 0.402030 + 0.696336i 0.993971 0.109645i \(-0.0349714\pi\)
−0.591941 + 0.805981i \(0.701638\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −27.4538 47.5514i −1.12455 1.94778i
\(597\) 0 0
\(598\) −0.336285 0.582462i −0.0137517 0.0238187i
\(599\) 9.27335 + 16.0619i 0.378899 + 0.656272i 0.990902 0.134583i \(-0.0429696\pi\)
−0.612004 + 0.790855i \(0.709636\pi\)
\(600\) 0 0
\(601\) 9.09931 + 15.7605i 0.371169 + 0.642883i 0.989746 0.142841i \(-0.0456238\pi\)
−0.618577 + 0.785724i \(0.712290\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −20.1249 34.8573i −0.818870 1.41832i
\(605\) 24.3317 0.989224
\(606\) 0 0
\(607\) −22.3097 −0.905524 −0.452762 0.891631i \(-0.649561\pi\)
−0.452762 + 0.891631i \(0.649561\pi\)
\(608\) 1.09358 1.89413i 0.0443505 0.0768173i
\(609\) 0 0
\(610\) 7.25370 + 12.5638i 0.293694 + 0.508692i
\(611\) −6.08113 10.5328i −0.246016 0.426112i
\(612\) 0 0
\(613\) −5.11849 + 8.86548i −0.206734 + 0.358073i −0.950684 0.310162i \(-0.899617\pi\)
0.743950 + 0.668235i \(0.232950\pi\)
\(614\) 33.5495 58.1094i 1.35395 2.34511i
\(615\) 0 0
\(616\) 0 0
\(617\) −5.66372 + 9.80984i −0.228013 + 0.394929i −0.957219 0.289364i \(-0.906556\pi\)
0.729206 + 0.684294i \(0.239889\pi\)
\(618\) 0 0
\(619\) 8.63327 0.347000 0.173500 0.984834i \(-0.444492\pi\)
0.173500 + 0.984834i \(0.444492\pi\)
\(620\) −12.2360 + 21.1934i −0.491409 + 0.851145i
\(621\) 0 0
\(622\) 39.3245 1.57677
\(623\) 0 0
\(624\) 0 0
\(625\) −30.6519 −1.22608
\(626\) −14.2683 24.7134i −0.570275 0.987746i
\(627\) 0 0
\(628\) −12.2719 + 21.2555i −0.489701 + 0.848188i
\(629\) 1.68443 0.0671626
\(630\) 0 0
\(631\) −14.8535 −0.591308 −0.295654 0.955295i \(-0.595538\pi\)
−0.295654 + 0.955295i \(0.595538\pi\)
\(632\) −37.1701 + 64.3805i −1.47855 + 2.56092i
\(633\) 0 0
\(634\) −2.48229 4.29945i −0.0985844 0.170753i
\(635\) 1.74436 0.0692229
\(636\) 0 0
\(637\) 0 0
\(638\) 27.3317 1.08207
\(639\) 0 0
\(640\) 24.7793 42.9190i 0.979487 1.69652i
\(641\) 34.1593 1.34921 0.674606 0.738178i \(-0.264313\pi\)
0.674606 + 0.738178i \(0.264313\pi\)
\(642\) 0 0
\(643\) 5.41741 9.38323i 0.213642 0.370039i −0.739210 0.673475i \(-0.764801\pi\)
0.952852 + 0.303437i \(0.0981341\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.71780 8.17147i 0.185619 0.321502i
\(647\) 16.4846 28.5522i 0.648077 1.12250i −0.335504 0.942039i \(-0.608907\pi\)
0.983582 0.180464i \(-0.0577600\pi\)
\(648\) 0 0
\(649\) 6.15486 + 10.6605i 0.241599 + 0.418462i
\(650\) −2.12422 3.67926i −0.0833188 0.144312i
\(651\) 0 0
\(652\) −36.1160 + 62.5548i −1.41441 + 2.44984i
\(653\) 3.93113 0.153837 0.0769185 0.997037i \(-0.475492\pi\)
0.0769185 + 0.997037i \(0.475492\pi\)
\(654\) 0 0
\(655\) −20.5251 −0.801982
\(656\) −13.8617 24.0091i −0.541207 0.937399i
\(657\) 0 0
\(658\) 0 0
\(659\) 8.40856 + 14.5640i 0.327551 + 0.567335i 0.982025 0.188749i \(-0.0604434\pi\)
−0.654474 + 0.756084i \(0.727110\pi\)
\(660\) 0 0
\(661\) 8.51080 + 14.7411i 0.331032 + 0.573364i 0.982714 0.185128i \(-0.0592700\pi\)
−0.651683 + 0.758492i \(0.725937\pi\)
\(662\) 24.2470 + 41.9970i 0.942386 + 1.63226i
\(663\) 0 0
\(664\) −2.39037 4.14024i −0.0927643 0.160672i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.336285 + 0.582462i 0.0130210 + 0.0225530i
\(668\) 34.3288 1.32822
\(669\) 0 0
\(670\) −100.937 −3.89954
\(671\) −5.13161 + 8.88821i −0.198104 + 0.343126i
\(672\) 0 0
\(673\) −14.3727 24.8942i −0.554025 0.959600i −0.997979 0.0635501i \(-0.979758\pi\)
0.443953 0.896050i \(-0.353576\pi\)
\(674\) 35.7403 + 61.9039i 1.37666 + 2.38445i
\(675\) 0 0
\(676\) 24.3245 42.1313i 0.935558 1.62043i
\(677\) −3.01819 + 5.22765i −0.115998 + 0.200915i −0.918178 0.396167i \(-0.870340\pi\)
0.802180 + 0.597082i \(0.203673\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6.19961 + 10.7380i −0.237744 + 0.411785i
\(681\) 0 0
\(682\) −25.8535 −0.989981
\(683\) 10.2556 17.7633i 0.392421 0.679693i −0.600347 0.799739i \(-0.704971\pi\)
0.992768 + 0.120046i \(0.0383043\pi\)
\(684\) 0 0
\(685\) 9.52510 0.363935
\(686\) 0 0
\(687\) 0 0
\(688\) −45.1593 −1.72168
\(689\) −3.13667 5.43288i −0.119498 0.206976i
\(690\) 0 0
\(691\) 7.50146 12.9929i 0.285369 0.494274i −0.687330 0.726346i \(-0.741217\pi\)
0.972699 + 0.232072i \(0.0745505\pi\)
\(692\) −70.3652 −2.67488
\(693\) 0 0
\(694\) −71.5595 −2.71636
\(695\) 2.66372 4.61369i 0.101040 0.175007i
\(696\) 0 0
\(697\) −3.02997 5.24806i −0.114768 0.198784i
\(698\) 60.9296 2.30622
\(699\) 0 0
\(700\) 0 0
\(701\) −38.5113 −1.45455 −0.727275 0.686346i \(-0.759214\pi\)
−0.727275 + 0.686346i \(0.759214\pi\)
\(702\) 0 0
\(703\) 3.60963 6.25206i 0.136140 0.235801i
\(704\) 33.0803 1.24676
\(705\) 0 0
\(706\) −40.9705 + 70.9630i −1.54195 + 2.67073i
\(707\) 0 0
\(708\) 0 0
\(709\) −3.82004 + 6.61650i −0.143465 + 0.248488i −0.928799 0.370584i \(-0.879158\pi\)
0.785334 + 0.619072i \(0.212491\pi\)
\(710\) 10.4445 18.0903i 0.391973 0.678918i
\(711\) 0 0
\(712\) −36.2798 62.8384i −1.35964 2.35497i
\(713\) −0.318097 0.550960i −0.0119128 0.0206336i
\(714\) 0 0
\(715\) 5.85447 10.1402i 0.218945 0.379224i
\(716\) 46.0115 1.71953
\(717\) 0 0
\(718\) −62.8329 −2.34490
\(719\) −15.0182 26.0123i −0.560084 0.970094i −0.997488 0.0708289i \(-0.977436\pi\)
0.437405 0.899265i \(-0.355898\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.15486 + 5.46438i 0.117412 + 0.203363i
\(723\) 0 0
\(724\) −44.3697 76.8506i −1.64899 2.85613i
\(725\) 2.12422 + 3.67926i 0.0788916 + 0.136644i
\(726\) 0 0
\(727\) −1.72812 2.99319i −0.0640923 0.111011i 0.832199 0.554478i \(-0.187082\pi\)
−0.896291 + 0.443466i \(0.853749\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 4.80972 + 8.33068i 0.178016 + 0.308332i
\(731\) −9.87120 −0.365099
\(732\) 0 0
\(733\) 38.5261 1.42299 0.711496 0.702690i \(-0.248018\pi\)
0.711496 + 0.702690i \(0.248018\pi\)
\(734\) −33.7709 + 58.4929i −1.24651 + 2.15901i
\(735\) 0 0
\(736\) −0.0737345 0.127712i −0.00271789 0.00470752i
\(737\) −35.7039 61.8409i −1.31517 2.27794i
\(738\) 0 0
\(739\) −22.5620 + 39.0785i −0.829955 + 1.43752i 0.0681179 + 0.997677i \(0.478301\pi\)
−0.898073 + 0.439847i \(0.855033\pi\)
\(740\) −9.36186 + 16.2152i −0.344149 + 0.596084i
\(741\) 0 0
\(742\) 0 0
\(743\) 4.74338 8.21577i 0.174018 0.301407i −0.765803 0.643075i \(-0.777658\pi\)
0.939821 + 0.341668i \(0.110992\pi\)
\(744\) 0 0
\(745\) 35.1268 1.28695
\(746\) −20.0869 + 34.7915i −0.735432 + 1.27381i
\(747\) 0 0
\(748\) −17.3126 −0.633013
\(749\) 0 0
\(750\) 0 0
\(751\) −9.83190 −0.358771 −0.179386 0.983779i \(-0.557411\pi\)
−0.179386 + 0.983779i \(0.557411\pi\)
\(752\) −26.3157 45.5800i −0.959633 1.66213i
\(753\) 0 0
\(754\) 3.02704 5.24299i 0.110238 0.190938i
\(755\) 25.7496 0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) −14.8078 + 25.6478i −0.537843 + 0.931571i
\(759\) 0 0
\(760\) 26.5708 + 46.0220i 0.963825 + 1.66939i
\(761\) −22.9794 −0.833001 −0.416501 0.909135i \(-0.636744\pi\)
−0.416501 + 0.909135i \(0.636744\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 2.84494 0.102926
\(765\) 0 0
\(766\) −15.2989 + 26.4985i −0.552773 + 0.957430i
\(767\) 2.72665 0.0984538
\(768\) 0 0
\(769\) −3.04329 + 5.27113i −0.109744 + 0.190082i −0.915666 0.401939i \(-0.868336\pi\)
0.805923 + 0.592021i \(0.201670\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −24.6175 + 42.6388i −0.886003 + 1.53460i
\(773\) −20.9107 + 36.2184i −0.752105 + 1.30268i 0.194695 + 0.980864i \(0.437628\pi\)
−0.946801 + 0.321821i \(0.895705\pi\)
\(774\) 0 0
\(775\) −2.00933 3.48027i −0.0721774 0.125015i
\(776\) 29.0349 + 50.2899i 1.04229 + 1.80530i
\(777\) 0 0
\(778\) 25.3442 43.8974i 0.908632 1.57380i
\(779\) −25.9722 −0.930550
\(780\) 0 0
\(781\) 14.7778 0.528792
\(782\) −0.318097 0.550960i −0.0113751 0.0197023i
\(783\) 0 0
\(784\) 0 0
\(785\) −7.85087 13.5981i −0.280210 0.485337i
\(786\) 0 0
\(787\) −16.1460 27.9657i −0.575543 0.996870i −0.995982 0.0895491i \(-0.971457\pi\)
0.420439 0.907321i \(-0.361876\pi\)
\(788\) −33.2652 57.6170i −1.18502 2.05252i
\(789\) 0 0
\(790\) −46.9327 81.2898i −1.66979 2.89216i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.13667 + 1.96878i 0.0403644 + 0.0699133i
\(794\) −58.1593 −2.06400