Properties

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

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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.b.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 \(-0.696925\pi\)
−0.579942 + 0.814658i \(0.696925\pi\)
\(6\) 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 −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.16372 + 3.74766i −0.540929 + 0.936916i
\(17\) 0.472958 0.819187i 0.114709 0.198682i −0.802954 0.596041i \(-0.796740\pi\)
0.917663 + 0.397359i \(0.130073\pi\)
\(18\) 0 0
\(19\) −2.02704 3.51094i −0.465035 0.805465i 0.534168 0.845378i \(-0.320625\pi\)
−0.999203 + 0.0399136i \(0.987292\pi\)
\(20\) 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 0.951403 0.307949i \(-0.0996427\pi\)
−0.742393 + 0.669964i \(0.766309\pi\)
\(32\) −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 \(-0.666572\pi\)
1.00000 0.000297253i \(-9.46187e-5\pi\)
\(42\) 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 \(-0.486102\pi\)
0.843377 0.537323i \(-0.180564\pi\)
\(48\) 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 0.941020 0.338350i \(-0.109869\pi\)
−0.763530 + 0.645772i \(0.776536\pi\)
\(60\) 0 0
\(61\) −1.13667 + 1.96878i −0.145536 + 0.252076i −0.929573 0.368639i \(-0.879824\pi\)
0.784037 + 0.620714i \(0.213157\pi\)
\(62\) −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 −0.906756 0.421656i \(-0.861449\pi\)
0.818543 + 0.574446i \(0.194782\pi\)
\(74\) 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 0.890815 0.454367i \(-0.150135\pi\)
−0.838901 + 0.544285i \(0.816801\pi\)
\(84\) 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 \(0.108575\pi\)
−0.181489 + 0.983393i \(0.558092\pi\)
\(90\) 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 \(-0.968428\pi\)
0.411785 0.911281i \(-0.364906\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) −3.67977 −0.366150 −0.183075 0.983099i \(-0.558605\pi\)
−0.183075 + 0.983099i \(0.558605\pi\)
\(102\) 0 0
\(103\) 9.72665 0.958396 0.479198 0.877707i \(-0.340928\pi\)
0.479198 + 0.877707i \(0.340928\pi\)
\(104\) 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 \(-0.387636\pi\)
0.345717 + 0.938339i \(0.387636\pi\)
\(132\) 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 −0.906289 0.422658i \(-0.861097\pi\)
0.819177 + 0.573541i \(0.194431\pi\)
\(140\) 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 0.961166 0.275972i \(-0.0889996\pi\)
−0.719581 + 0.694408i \(0.755666\pi\)
\(158\) −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 −0.654415 0.756136i \(-0.727085\pi\)
0.982040 + 0.188672i \(0.0604183\pi\)
\(168\) 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 \(0.396025\pi\)
−0.980667 + 0.195682i \(0.937308\pi\)
\(174\) 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 \(-0.802438\pi\)
−0.813495 + 0.581572i \(0.802438\pi\)
\(182\) 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 \(-0.535609\pi\)
0.916430 0.400194i \(-0.131057\pi\)
\(200\) 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 0.998131 0.0611159i \(-0.0194659\pi\)
−0.551993 + 0.833849i \(0.686133\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.7807 + 22.1369i 0.850162 + 1.47252i
\(227\) 1.38151 0.0916943 0.0458472 0.998948i \(-0.485401\pi\)
0.0458472 + 0.998948i \(0.485401\pi\)
\(228\) 0 0
\(229\) 17.9794 1.18811 0.594055 0.804424i \(-0.297526\pi\)
0.594055 + 0.804424i \(0.297526\pi\)
\(230\) 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 \(-0.181062\pi\)
0.842535 + 0.538641i \(0.181062\pi\)
\(242\) −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 \(-0.302068\pi\)
0.582516 + 0.812819i \(0.302068\pi\)
\(252\) 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 \(-0.619262\pi\)
−0.365969 + 0.930627i \(0.619262\pi\)
\(258\) 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 \(-0.638651\pi\)
0.996129 0.0879017i \(-0.0280161\pi\)
\(270\) 0 0
\(271\) −11.9911 20.7693i −0.728410 1.26164i −0.957555 0.288251i \(-0.906926\pi\)
0.229145 0.973392i \(-0.426407\pi\)
\(272\) 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 \(0.0359245\pi\)
−0.399287 + 0.916826i \(0.630742\pi\)
\(284\) 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 −0.997694 0.0678705i \(-0.978380\pi\)
0.557625 + 0.830093i \(0.311713\pi\)
\(294\) 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 \(-0.216132\pi\)
0.778203 + 0.628013i \(0.216132\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 14.8525 0.843567
\(311\) 7.99115 + 13.8411i 0.453136 + 0.784855i 0.998579 0.0532931i \(-0.0169718\pi\)
−0.545443 + 0.838148i \(0.683638\pi\)
\(312\) 0 0
\(313\) 5.79893 10.0440i 0.327775 0.567722i −0.654295 0.756239i \(-0.727035\pi\)
0.982070 + 0.188517i \(0.0603680\pi\)
\(314\) −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 \(0.0639515\pi\)
−0.317118 + 0.948386i \(0.602715\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.21780 + 2.10929i 0.0649089 + 0.112426i
\(353\) −33.3025 −1.77251 −0.886257 0.463193i \(-0.846704\pi\)
−0.886257 + 0.463193i \(0.846704\pi\)
\(354\) 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 \(-0.754234\pi\)
−0.716449 + 0.697639i \(0.754234\pi\)
\(368\) −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 \(-0.602915\pi\)
−0.317715 + 0.948186i \(0.602915\pi\)
\(384\) 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 \(-0.964548\pi\)
0.400647 0.916233i \(-0.368785\pi\)
\(398\) 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 \(-0.844101\pi\)
0.0338223 0.999428i \(-0.489232\pi\)
\(410\) −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 −0.911312 0.411717i \(-0.864929\pi\)
0.812213 + 0.583361i \(0.198263\pi\)
\(420\) 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 \(-0.518504\pi\)
−0.0580982 + 0.998311i \(0.518504\pi\)
\(434\) 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 \(0.356077\pi\)
−0.997448 + 0.0713911i \(0.977256\pi\)
\(440\) 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 0.924365 0.381509i \(-0.124595\pi\)
−0.792579 + 0.609769i \(0.791262\pi\)
\(462\) 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 \(0.00330013\pi\)
−0.490995 + 0.871163i \(0.663367\pi\)
\(468\) 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 \(-0.306722\pi\)
0.570571 + 0.821249i \(0.306722\pi\)
\(480\) 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 \(-0.665677\pi\)
−0.497305 + 0.867576i \(0.665677\pi\)
\(504\) 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 \(-0.614575\pi\)
−0.352226 + 0.935915i \(0.614575\pi\)
\(510\) 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 −0.910348 0.413843i \(-0.864186\pi\)
0.813573 + 0.581463i \(0.197520\pi\)
\(522\) 0 0
\(523\) 12.6367 + 21.8874i 0.552563 + 0.957067i 0.998089 + 0.0617982i \(0.0196835\pi\)
−0.445526 + 0.895269i \(0.646983\pi\)
\(524\) −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 \(-0.813741\pi\)
−0.0615128 0.998106i \(-0.519593\pi\)
\(564\) 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 −0.714540 0.699595i \(-0.753364\pi\)
0.963137 + 0.269013i \(0.0866973\pi\)
\(578\) −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 0.507563 0.861614i \(-0.330546\pi\)
−0.999962 + 0.00875568i \(0.997213\pi\)
\(588\) 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 0.591941 0.805981i \(-0.298362\pi\)
−0.993971 + 0.109645i \(0.965029\pi\)
\(594\) 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 0.618577 0.785724i \(-0.287710\pi\)
−0.989746 + 0.142841i \(0.954376\pi\)
\(602\) 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 \(-0.350439\pi\)
0.452762 + 0.891631i \(0.350439\pi\)
\(608\) −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 \(-0.555508\pi\)
−0.173500 + 0.984834i \(0.555508\pi\)
\(620\) −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 −0.952852 0.303437i \(-0.901866\pi\)
0.739210 + 0.673475i \(0.235199\pi\)
\(644\) 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 \(0.391093\pi\)
−0.983582 + 0.180464i \(0.942240\pi\)
\(648\) 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 0.651683 0.758492i \(-0.274063\pi\)
−0.982714 + 0.185128i \(0.940730\pi\)
\(662\) 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 −0.802180 0.597082i \(-0.796327\pi\)
0.918178 + 0.396167i \(0.129660\pi\)
\(678\) 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 −0.972699 0.232072i \(-0.925450\pi\)
0.687330 + 0.726346i \(0.258783\pi\)
\(692\) 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 \(0.0225644\pi\)
−0.437405 + 0.899265i \(0.644102\pi\)
\(720\) 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 0.896291 0.443466i \(-0.146251\pi\)
−0.832199 + 0.554478i \(0.812918\pi\)
\(728\) 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 \(-0.751982\pi\)
−0.711496 + 0.702690i \(0.751982\pi\)
\(734\) 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 \(-0.363256\pi\)
0.416501 + 0.909135i \(0.363256\pi\)
\(762\) 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 −0.805923 0.592021i \(-0.798330\pi\)
0.915666 + 0.401939i \(0.131664\pi\)
\(770\) 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 \(-0.562372\pi\)
0.946801 0.321821i \(-0.104295\pi\)
\(774\) 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 \(0.0285426\pi\)
−0.420439 + 0.907321i \(0.638124\pi\)
\(788\) −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