Properties

Label 585.2.bs.a.289.6
Level $585$
Weight $2$
Character 585.289
Analytic conductor $4.671$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 8 x^{10} + 54 x^{8} - 78 x^{6} + 92 x^{4} - 10 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.6
Root \(2.20467 + 1.27287i\) of defining polynomial
Character \(\chi\) \(=\) 585.289
Dual form 585.2.bs.a.334.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.20467 - 1.27287i) q^{2} +(2.24039 - 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(2.54486 + 1.46928i) q^{7} -6.31544i q^{8} +O(q^{10})\) \(q+(2.20467 - 1.27287i) q^{2} +(2.24039 - 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(2.54486 + 1.46928i) q^{7} -6.31544i q^{8} +(4.45158 + 3.54786i) q^{10} +(-0.317544 - 0.550003i) q^{11} +(-3.60484 - 0.0716710i) q^{13} +7.48079 q^{14} +(-3.55794 - 6.16253i) q^{16} +(-1.05998 - 0.611979i) q^{17} +(0.682456 - 1.18205i) q^{19} +(9.90788 + 1.49037i) q^{20} +(-1.40016 - 0.808385i) q^{22} +(1.86449 - 1.07646i) q^{23} +(-3.66324 + 3.40304i) q^{25} +(-8.03872 + 4.43048i) q^{26} +(11.4030 - 6.58351i) q^{28} +(-1.50000 - 2.59808i) q^{29} -8.96157 q^{31} +(-4.74954 - 2.74215i) q^{32} -3.11588 q^{34} +(-0.977401 + 6.49770i) q^{35} +(1.05998 - 0.611979i) q^{37} -3.47471i q^{38} +(13.1440 - 5.16315i) q^{40} +(-4.98079 - 8.62698i) q^{41} +(-1.18412 - 0.683650i) q^{43} -2.84570 q^{44} +(2.74039 - 4.74650i) q^{46} +6.16379i q^{47} +(0.817544 + 1.41603i) q^{49} +(-3.74464 + 12.1654i) q^{50} +(-8.35437 + 13.8279i) q^{52} +0.642285i q^{53} +(0.885090 - 1.11054i) q^{55} +(9.27912 - 16.0719i) q^{56} +(-6.61402 - 3.81861i) q^{58} +(-3.79833 + 6.57890i) q^{59} +(1.13509 - 1.96603i) q^{61} +(-19.7574 + 11.4069i) q^{62} +0.270178 q^{64} +(-2.79795 - 7.56118i) q^{65} +(6.95421 - 4.01502i) q^{67} +(-4.74954 + 2.74215i) q^{68} +(6.11588 + 15.5694i) q^{70} +(1.31754 - 2.28205i) q^{71} +10.3263i q^{73} +(1.55794 - 2.69843i) q^{74} +(-3.05794 - 5.29650i) q^{76} -1.86624i q^{77} -1.03843 q^{79} +(9.91702 - 12.4431i) q^{80} +(-21.9620 - 12.6798i) q^{82} +11.8452i q^{83} +(0.407104 - 2.70640i) q^{85} -3.48079 q^{86} +(-3.47351 + 2.00543i) q^{88} +(6.27912 + 10.8758i) q^{89} +(-9.06851 - 5.47890i) q^{91} -9.64680i q^{92} +(7.84570 + 13.5891i) q^{94} +(3.01808 + 0.453987i) q^{95} +(12.8031 + 7.39190i) q^{97} +(3.60484 + 2.08125i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 6 q^{5} + O(q^{10}) \) \( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.20467 1.27287i 1.55894 0.900055i 0.561582 0.827421i \(-0.310193\pi\)
0.997359 0.0726333i \(-0.0231403\pi\)
\(3\) 0 0
\(4\) 2.24039 3.88048i 1.12020 1.94024i
\(5\) 0.817544 + 2.08125i 0.365617 + 0.930765i
\(6\) 0 0
\(7\) 2.54486 + 1.46928i 0.961867 + 0.555334i 0.896747 0.442543i \(-0.145924\pi\)
0.0651198 + 0.997877i \(0.479257\pi\)
\(8\) 6.31544i 2.23284i
\(9\) 0 0
\(10\) 4.45158 + 3.54786i 1.40771 + 1.12193i
\(11\) −0.317544 0.550003i −0.0957433 0.165832i 0.814175 0.580619i \(-0.197189\pi\)
−0.909919 + 0.414787i \(0.863856\pi\)
\(12\) 0 0
\(13\) −3.60484 0.0716710i −0.999802 0.0198779i
\(14\) 7.48079 1.99932
\(15\) 0 0
\(16\) −3.55794 6.16253i −0.889484 1.54063i
\(17\) −1.05998 0.611979i −0.257082 0.148427i 0.365920 0.930646i \(-0.380754\pi\)
−0.623003 + 0.782220i \(0.714088\pi\)
\(18\) 0 0
\(19\) 0.682456 1.18205i 0.156566 0.271180i −0.777062 0.629424i \(-0.783291\pi\)
0.933628 + 0.358244i \(0.116624\pi\)
\(20\) 9.90788 + 1.49037i 2.21547 + 0.333256i
\(21\) 0 0
\(22\) −1.40016 0.808385i −0.298516 0.172348i
\(23\) 1.86449 1.07646i 0.388773 0.224458i −0.292856 0.956157i \(-0.594606\pi\)
0.681628 + 0.731699i \(0.261272\pi\)
\(24\) 0 0
\(25\) −3.66324 + 3.40304i −0.732648 + 0.680607i
\(26\) −8.03872 + 4.43048i −1.57652 + 0.868888i
\(27\) 0 0
\(28\) 11.4030 6.58351i 2.15496 1.24417i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) −8.96157 −1.60955 −0.804773 0.593583i \(-0.797713\pi\)
−0.804773 + 0.593583i \(0.797713\pi\)
\(32\) −4.74954 2.74215i −0.839607 0.484747i
\(33\) 0 0
\(34\) −3.11588 −0.534368
\(35\) −0.977401 + 6.49770i −0.165211 + 1.09831i
\(36\) 0 0
\(37\) 1.05998 0.611979i 0.174259 0.100609i −0.410333 0.911936i \(-0.634588\pi\)
0.584593 + 0.811327i \(0.301254\pi\)
\(38\) 3.47471i 0.563672i
\(39\) 0 0
\(40\) 13.1440 5.16315i 2.07825 0.816366i
\(41\) −4.98079 8.62698i −0.777868 1.34731i −0.933168 0.359440i \(-0.882968\pi\)
0.155300 0.987867i \(-0.450366\pi\)
\(42\) 0 0
\(43\) −1.18412 0.683650i −0.180576 0.104256i 0.406987 0.913434i \(-0.366579\pi\)
−0.587563 + 0.809178i \(0.699913\pi\)
\(44\) −2.84570 −0.429005
\(45\) 0 0
\(46\) 2.74039 4.74650i 0.404049 0.699833i
\(47\) 6.16379i 0.899081i 0.893260 + 0.449540i \(0.148412\pi\)
−0.893260 + 0.449540i \(0.851588\pi\)
\(48\) 0 0
\(49\) 0.817544 + 1.41603i 0.116792 + 0.202290i
\(50\) −3.74464 + 12.1654i −0.529571 + 1.72045i
\(51\) 0 0
\(52\) −8.35437 + 13.8279i −1.15854 + 1.91759i
\(53\) 0.642285i 0.0882246i 0.999027 + 0.0441123i \(0.0140459\pi\)
−0.999027 + 0.0441123i \(0.985954\pi\)
\(54\) 0 0
\(55\) 0.885090 1.11054i 0.119345 0.149746i
\(56\) 9.27912 16.0719i 1.23997 2.14770i
\(57\) 0 0
\(58\) −6.61402 3.81861i −0.868464 0.501408i
\(59\) −3.79833 + 6.57890i −0.494501 + 0.856500i −0.999980 0.00633858i \(-0.997982\pi\)
0.505479 + 0.862839i \(0.331316\pi\)
\(60\) 0 0
\(61\) 1.13509 1.96603i 0.145333 0.251725i −0.784164 0.620554i \(-0.786908\pi\)
0.929497 + 0.368829i \(0.120241\pi\)
\(62\) −19.7574 + 11.4069i −2.50919 + 1.44868i
\(63\) 0 0
\(64\) 0.270178 0.0337722
\(65\) −2.79795 7.56118i −0.347043 0.937849i
\(66\) 0 0
\(67\) 6.95421 4.01502i 0.849592 0.490512i −0.0109212 0.999940i \(-0.503476\pi\)
0.860513 + 0.509428i \(0.170143\pi\)
\(68\) −4.74954 + 2.74215i −0.575966 + 0.332534i
\(69\) 0 0
\(70\) 6.11588 + 15.5694i 0.730987 + 1.86090i
\(71\) 1.31754 2.28205i 0.156364 0.270830i −0.777191 0.629265i \(-0.783356\pi\)
0.933555 + 0.358435i \(0.116689\pi\)
\(72\) 0 0
\(73\) 10.3263i 1.20860i 0.796756 + 0.604301i \(0.206547\pi\)
−0.796756 + 0.604301i \(0.793453\pi\)
\(74\) 1.55794 2.69843i 0.181107 0.313686i
\(75\) 0 0
\(76\) −3.05794 5.29650i −0.350770 0.607551i
\(77\) 1.86624i 0.212678i
\(78\) 0 0
\(79\) −1.03843 −0.116832 −0.0584161 0.998292i \(-0.518605\pi\)
−0.0584161 + 0.998292i \(0.518605\pi\)
\(80\) 9.91702 12.4431i 1.10876 1.39118i
\(81\) 0 0
\(82\) −21.9620 12.6798i −2.42530 1.40025i
\(83\) 11.8452i 1.30018i 0.759855 + 0.650092i \(0.225270\pi\)
−0.759855 + 0.650092i \(0.774730\pi\)
\(84\) 0 0
\(85\) 0.407104 2.70640i 0.0441566 0.293551i
\(86\) −3.48079 −0.375343
\(87\) 0 0
\(88\) −3.47351 + 2.00543i −0.370277 + 0.213780i
\(89\) 6.27912 + 10.8758i 0.665585 + 1.15283i 0.979126 + 0.203253i \(0.0651513\pi\)
−0.313541 + 0.949575i \(0.601515\pi\)
\(90\) 0 0
\(91\) −9.06851 5.47890i −0.950638 0.574344i
\(92\) 9.64680i 1.00575i
\(93\) 0 0
\(94\) 7.84570 + 13.5891i 0.809222 + 1.40161i
\(95\) 3.01808 + 0.453987i 0.309648 + 0.0465781i
\(96\) 0 0
\(97\) 12.8031 + 7.39190i 1.29996 + 0.750534i 0.980397 0.197031i \(-0.0631299\pi\)
0.319565 + 0.947564i \(0.396463\pi\)
\(98\) 3.60484 + 2.08125i 0.364144 + 0.210238i
\(99\) 0 0
\(100\) 4.99829 + 21.8393i 0.499829 + 2.18393i
\(101\) 6.61588 + 11.4590i 0.658304 + 1.14022i 0.981054 + 0.193732i \(0.0620593\pi\)
−0.322750 + 0.946484i \(0.604607\pi\)
\(102\) 0 0
\(103\) 10.9686i 1.08077i −0.841419 0.540383i \(-0.818279\pi\)
0.841419 0.540383i \(-0.181721\pi\)
\(104\) −0.452633 + 22.7661i −0.0443843 + 2.23240i
\(105\) 0 0
\(106\) 0.817544 + 1.41603i 0.0794069 + 0.137537i
\(107\) 9.24360 5.33680i 0.893613 0.515928i 0.0184903 0.999829i \(-0.494114\pi\)
0.875123 + 0.483901i \(0.160781\pi\)
\(108\) 0 0
\(109\) 3.27018 0.313226 0.156613 0.987660i \(-0.449942\pi\)
0.156613 + 0.987660i \(0.449942\pi\)
\(110\) 0.537759 3.57499i 0.0512733 0.340862i
\(111\) 0 0
\(112\) 20.9104i 1.97584i
\(113\) 4.78895 + 2.76490i 0.450507 + 0.260100i 0.708044 0.706168i \(-0.249578\pi\)
−0.257537 + 0.966268i \(0.582911\pi\)
\(114\) 0 0
\(115\) 3.76470 + 3.00042i 0.351060 + 0.279790i
\(116\) −13.4424 −1.24809
\(117\) 0 0
\(118\) 19.3391i 1.78031i
\(119\) −1.79833 3.11480i −0.164853 0.285533i
\(120\) 0 0
\(121\) 5.29833 9.17698i 0.481666 0.834271i
\(122\) 5.77928i 0.523231i
\(123\) 0 0
\(124\) −20.0774 + 34.7752i −1.80301 + 3.12290i
\(125\) −10.0774 4.84201i −0.901354 0.433082i
\(126\) 0 0
\(127\) −14.9231 + 8.61586i −1.32421 + 0.764534i −0.984397 0.175959i \(-0.943697\pi\)
−0.339813 + 0.940493i \(0.610364\pi\)
\(128\) 10.0947 5.82819i 0.892256 0.515144i
\(129\) 0 0
\(130\) −15.7930 13.1085i −1.38513 1.14969i
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) 3.47351 2.00543i 0.301191 0.173893i
\(134\) 10.2212 17.7036i 0.882975 1.52936i
\(135\) 0 0
\(136\) −3.86491 + 6.69422i −0.331413 + 0.574025i
\(137\) −7.51044 4.33616i −0.641661 0.370463i 0.143593 0.989637i \(-0.454134\pi\)
−0.785254 + 0.619174i \(0.787468\pi\)
\(138\) 0 0
\(139\) 7.16324 12.4071i 0.607578 1.05236i −0.384060 0.923308i \(-0.625474\pi\)
0.991638 0.129048i \(-0.0411922\pi\)
\(140\) 23.0244 + 18.3502i 1.94592 + 1.55087i
\(141\) 0 0
\(142\) 6.70825i 0.562944i
\(143\) 1.10528 + 2.00543i 0.0924279 + 0.167703i
\(144\) 0 0
\(145\) 4.18094 5.24592i 0.347208 0.435650i
\(146\) 13.1440 + 22.7661i 1.08781 + 1.88414i
\(147\) 0 0
\(148\) 5.48429i 0.450806i
\(149\) 8.57745 14.8566i 0.702692 1.21710i −0.264826 0.964296i \(-0.585315\pi\)
0.967518 0.252802i \(-0.0813521\pi\)
\(150\) 0 0
\(151\) −21.3828 −1.74011 −0.870053 0.492957i \(-0.835916\pi\)
−0.870053 + 0.492957i \(0.835916\pi\)
\(152\) −7.46515 4.31000i −0.605503 0.349587i
\(153\) 0 0
\(154\) −2.37548 4.11446i −0.191422 0.331552i
\(155\) −7.32648 18.6513i −0.588477 1.49811i
\(156\) 0 0
\(157\) 18.3646i 1.46566i −0.680413 0.732829i \(-0.738200\pi\)
0.680413 0.732829i \(-0.261800\pi\)
\(158\) −2.28939 + 1.32178i −0.182134 + 0.105155i
\(159\) 0 0
\(160\) 1.82415 12.1268i 0.144211 0.958709i
\(161\) 6.32648 0.498597
\(162\) 0 0
\(163\) −3.47351 2.00543i −0.272066 0.157078i 0.357760 0.933814i \(-0.383541\pi\)
−0.629826 + 0.776736i \(0.716874\pi\)
\(164\) −44.6357 −3.48546
\(165\) 0 0
\(166\) 15.0774 + 26.1149i 1.17024 + 2.02691i
\(167\) −2.54486 + 1.46928i −0.196927 + 0.113696i −0.595221 0.803562i \(-0.702936\pi\)
0.398294 + 0.917258i \(0.369602\pi\)
\(168\) 0 0
\(169\) 12.9897 + 0.516725i 0.999210 + 0.0397480i
\(170\) −2.54737 6.48493i −0.195374 0.497371i
\(171\) 0 0
\(172\) −5.30577 + 3.06329i −0.404561 + 0.233574i
\(173\) −1.18412 0.683650i −0.0900267 0.0519769i 0.454311 0.890843i \(-0.349886\pi\)
−0.544337 + 0.838866i \(0.683219\pi\)
\(174\) 0 0
\(175\) −14.3224 + 3.27794i −1.08267 + 0.247789i
\(176\) −2.25961 + 3.91375i −0.170324 + 0.295010i
\(177\) 0 0
\(178\) 27.6868 + 15.9850i 2.07522 + 1.19813i
\(179\) −3.89306 6.74299i −0.290981 0.503994i 0.683061 0.730362i \(-0.260648\pi\)
−0.974042 + 0.226367i \(0.927315\pi\)
\(180\) 0 0
\(181\) −3.86684 −0.287420 −0.143710 0.989620i \(-0.545903\pi\)
−0.143710 + 0.989620i \(0.545903\pi\)
\(182\) −26.9670 0.536155i −1.99893 0.0397425i
\(183\) 0 0
\(184\) −6.79833 11.7751i −0.501180 0.868069i
\(185\) 2.14026 + 1.70576i 0.157355 + 0.125410i
\(186\) 0 0
\(187\) 0.777322i 0.0568434i
\(188\) 23.9184 + 13.8093i 1.74443 + 1.00715i
\(189\) 0 0
\(190\) 7.23175 2.84073i 0.524646 0.206088i
\(191\) 2.47185 4.28136i 0.178857 0.309789i −0.762633 0.646832i \(-0.776094\pi\)
0.941489 + 0.337043i \(0.109427\pi\)
\(192\) 0 0
\(193\) −4.29240 + 2.47822i −0.308974 + 0.178386i −0.646467 0.762942i \(-0.723754\pi\)
0.337493 + 0.941328i \(0.390421\pi\)
\(194\) 37.6357 2.70208
\(195\) 0 0
\(196\) 7.32648 0.523320
\(197\) −5.84174 + 3.37273i −0.416207 + 0.240297i −0.693453 0.720502i \(-0.743912\pi\)
0.277246 + 0.960799i \(0.410578\pi\)
\(198\) 0 0
\(199\) 2.58772 4.48207i 0.183439 0.317725i −0.759611 0.650378i \(-0.774610\pi\)
0.943049 + 0.332653i \(0.107944\pi\)
\(200\) 21.4917 + 23.1350i 1.51969 + 1.63589i
\(201\) 0 0
\(202\) 29.1717 + 16.8423i 2.05251 + 1.18502i
\(203\) 8.81566i 0.618738i
\(204\) 0 0
\(205\) 13.8829 17.4192i 0.969625 1.21661i
\(206\) −13.9616 24.1822i −0.972749 1.68485i
\(207\) 0 0
\(208\) 12.3841 + 22.4699i 0.858684 + 1.55801i
\(209\) −0.866840 −0.0599606
\(210\) 0 0
\(211\) 7.00894 + 12.1398i 0.482515 + 0.835741i 0.999799 0.0200732i \(-0.00638994\pi\)
−0.517283 + 0.855814i \(0.673057\pi\)
\(212\) 2.49237 + 1.43897i 0.171177 + 0.0988289i
\(213\) 0 0
\(214\) 13.5861 23.5318i 0.928726 1.60860i
\(215\) 0.454782 3.02336i 0.0310158 0.206191i
\(216\) 0 0
\(217\) −22.8060 13.1670i −1.54817 0.893836i
\(218\) 7.20968 4.16251i 0.488301 0.281921i
\(219\) 0 0
\(220\) −2.32648 5.92262i −0.156852 0.399303i
\(221\) 3.77719 + 2.28205i 0.254081 + 0.153508i
\(222\) 0 0
\(223\) 0.00719226 0.00415245i 0.000481629 0.000278069i −0.499759 0.866164i \(-0.666578\pi\)
0.500241 + 0.865886i \(0.333245\pi\)
\(224\) −8.05794 13.9568i −0.538394 0.932525i
\(225\) 0 0
\(226\) 14.0774 0.936418
\(227\) 9.75454 + 5.63179i 0.647431 + 0.373795i 0.787471 0.616351i \(-0.211390\pi\)
−0.140040 + 0.990146i \(0.544723\pi\)
\(228\) 0 0
\(229\) 16.5404 1.09302 0.546509 0.837453i \(-0.315957\pi\)
0.546509 + 0.837453i \(0.315957\pi\)
\(230\) 12.1191 + 1.82298i 0.799108 + 0.120204i
\(231\) 0 0
\(232\) −16.4080 + 9.47315i −1.07724 + 0.621943i
\(233\) 6.94941i 0.455271i 0.973746 + 0.227636i \(0.0730995\pi\)
−0.973746 + 0.227636i \(0.926900\pi\)
\(234\) 0 0
\(235\) −12.8284 + 5.03917i −0.836833 + 0.328719i
\(236\) 17.0195 + 29.4787i 1.10788 + 1.91890i
\(237\) 0 0
\(238\) −7.92947 4.57808i −0.513991 0.296753i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −9.88605 + 17.1231i −0.636817 + 1.10300i 0.349310 + 0.937007i \(0.386416\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(242\) 26.9763i 1.73410i
\(243\) 0 0
\(244\) −5.08609 8.80937i −0.325604 0.563962i
\(245\) −2.27874 + 2.85918i −0.145583 + 0.182667i
\(246\) 0 0
\(247\) −2.54486 + 4.21218i −0.161926 + 0.268015i
\(248\) 56.5962i 3.59386i
\(249\) 0 0
\(250\) −28.3807 + 2.15223i −1.79496 + 0.136119i
\(251\) 1.83676 3.18136i 0.115935 0.200806i −0.802218 0.597031i \(-0.796347\pi\)
0.918153 + 0.396226i \(0.129680\pi\)
\(252\) 0 0
\(253\) −1.18412 0.683650i −0.0744447 0.0429807i
\(254\) −21.9337 + 37.9903i −1.37624 + 2.38372i
\(255\) 0 0
\(256\) 14.5669 25.2306i 0.910430 1.57691i
\(257\) 11.4877 6.63242i 0.716583 0.413719i −0.0969108 0.995293i \(-0.530896\pi\)
0.813494 + 0.581574i \(0.197563\pi\)
\(258\) 0 0
\(259\) 3.59666 0.223486
\(260\) −35.6095 6.08264i −2.20841 0.377230i
\(261\) 0 0
\(262\) −22.0467 + 12.7287i −1.36205 + 0.786381i
\(263\) −26.2150 + 15.1352i −1.61649 + 0.933279i −0.628667 + 0.777674i \(0.716399\pi\)
−0.987819 + 0.155605i \(0.950267\pi\)
\(264\) 0 0
\(265\) −1.33676 + 0.525096i −0.0821164 + 0.0322564i
\(266\) 5.10530 8.84265i 0.313026 0.542177i
\(267\) 0 0
\(268\) 35.9809i 2.19788i
\(269\) 11.1248 19.2687i 0.678292 1.17484i −0.297203 0.954814i \(-0.596054\pi\)
0.975495 0.220022i \(-0.0706129\pi\)
\(270\) 0 0
\(271\) 5.91421 + 10.2437i 0.359262 + 0.622261i 0.987838 0.155488i \(-0.0496950\pi\)
−0.628575 + 0.777749i \(0.716362\pi\)
\(272\) 8.70953i 0.528093i
\(273\) 0 0
\(274\) −22.0774 −1.33375
\(275\) 3.03492 + 0.934179i 0.183013 + 0.0563331i
\(276\) 0 0
\(277\) 14.5363 + 8.39254i 0.873402 + 0.504259i 0.868477 0.495729i \(-0.165099\pi\)
0.00492452 + 0.999988i \(0.498432\pi\)
\(278\) 36.4715i 2.18741i
\(279\) 0 0
\(280\) 41.0358 + 6.17271i 2.45236 + 0.368890i
\(281\) 10.5967 0.632144 0.316072 0.948735i \(-0.397636\pi\)
0.316072 + 0.948735i \(0.397636\pi\)
\(282\) 0 0
\(283\) −7.63458 + 4.40783i −0.453829 + 0.262018i −0.709446 0.704760i \(-0.751055\pi\)
0.255617 + 0.966778i \(0.417721\pi\)
\(284\) −5.90364 10.2254i −0.350316 0.606766i
\(285\) 0 0
\(286\) 4.98943 + 3.01445i 0.295031 + 0.178248i
\(287\) 29.2726i 1.72791i
\(288\) 0 0
\(289\) −7.75096 13.4251i −0.455939 0.789710i
\(290\) 2.54024 16.8873i 0.149168 0.991659i
\(291\) 0 0
\(292\) 40.0709 + 23.1350i 2.34497 + 1.35387i
\(293\) −24.4675 14.1263i −1.42940 0.825267i −0.432331 0.901715i \(-0.642309\pi\)
−0.997074 + 0.0764476i \(0.975642\pi\)
\(294\) 0 0
\(295\) −16.7977 2.52675i −0.977999 0.147113i
\(296\) −3.86491 6.69422i −0.224643 0.389094i
\(297\) 0 0
\(298\) 43.6719i 2.52984i
\(299\) −6.79833 + 3.74685i −0.393158 + 0.216686i
\(300\) 0 0
\(301\) −2.00894 3.47959i −0.115793 0.200560i
\(302\) −47.1421 + 27.2175i −2.71272 + 1.56619i
\(303\) 0 0
\(304\) −9.71254 −0.557052
\(305\) 5.01980 + 0.755091i 0.287433 + 0.0432364i
\(306\) 0 0
\(307\) 12.7219i 0.726077i −0.931774 0.363039i \(-0.881739\pi\)
0.931774 0.363039i \(-0.118261\pi\)
\(308\) −7.24190 4.18112i −0.412646 0.238241i
\(309\) 0 0
\(310\) −39.8932 31.7944i −2.26578 1.80580i
\(311\) −27.9231 −1.58338 −0.791688 0.610925i \(-0.790798\pi\)
−0.791688 + 0.610925i \(0.790798\pi\)
\(312\) 0 0
\(313\) 24.5807i 1.38938i 0.719307 + 0.694692i \(0.244460\pi\)
−0.719307 + 0.694692i \(0.755540\pi\)
\(314\) −23.3758 40.4880i −1.31917 2.28487i
\(315\) 0 0
\(316\) −2.32648 + 4.02959i −0.130875 + 0.226682i
\(317\) 0.234377i 0.0131639i −0.999978 0.00658196i \(-0.997905\pi\)
0.999978 0.00658196i \(-0.00209512\pi\)
\(318\) 0 0
\(319\) −0.952633 + 1.65001i −0.0533372 + 0.0923828i
\(320\) 0.220882 + 0.562309i 0.0123477 + 0.0314340i
\(321\) 0 0
\(322\) 13.9478 8.05279i 0.777283 0.448764i
\(323\) −1.44678 + 0.835296i −0.0805008 + 0.0464771i
\(324\) 0 0
\(325\) 13.4493 12.0048i 0.746033 0.665909i
\(326\) −10.2106 −0.565513
\(327\) 0 0
\(328\) −54.4831 + 31.4558i −3.00833 + 1.73686i
\(329\) −9.05631 + 15.6860i −0.499290 + 0.864796i
\(330\) 0 0
\(331\) 9.16324 15.8712i 0.503657 0.872360i −0.496334 0.868132i \(-0.665321\pi\)
0.999991 0.00422829i \(-0.00134591\pi\)
\(332\) 45.9652 + 26.5380i 2.52267 + 1.45646i
\(333\) 0 0
\(334\) −3.74039 + 6.47855i −0.204665 + 0.354491i
\(335\) 14.0416 + 11.1910i 0.767177 + 0.611431i
\(336\) 0 0
\(337\) 21.2949i 1.16001i 0.814614 + 0.580003i \(0.196949\pi\)
−0.814614 + 0.580003i \(0.803051\pi\)
\(338\) 29.2958 15.3950i 1.59348 0.837379i
\(339\) 0 0
\(340\) −9.59006 7.64317i −0.520094 0.414509i
\(341\) 2.84570 + 4.92889i 0.154103 + 0.266915i
\(342\) 0 0
\(343\) 15.7651i 0.851234i
\(344\) −4.31754 + 7.47821i −0.232786 + 0.403198i
\(345\) 0 0
\(346\) −3.48079 −0.187128
\(347\) 3.30407 + 1.90761i 0.177372 + 0.102406i 0.586057 0.810270i \(-0.300679\pi\)
−0.408685 + 0.912675i \(0.634013\pi\)
\(348\) 0 0
\(349\) 12.1632 + 21.0674i 0.651083 + 1.12771i 0.982860 + 0.184352i \(0.0590185\pi\)
−0.331777 + 0.943358i \(0.607648\pi\)
\(350\) −27.4039 + 25.4574i −1.46480 + 1.36075i
\(351\) 0 0
\(352\) 3.48301i 0.185645i
\(353\) 23.4338 13.5295i 1.24726 0.720104i 0.276696 0.960958i \(-0.410761\pi\)
0.970562 + 0.240853i \(0.0774272\pi\)
\(354\) 0 0
\(355\) 5.82669 + 0.876465i 0.309248 + 0.0465179i
\(356\) 56.2708 2.98235
\(357\) 0 0
\(358\) −17.1659 9.91073i −0.907245 0.523798i
\(359\) 27.0039 1.42521 0.712605 0.701566i \(-0.247515\pi\)
0.712605 + 0.701566i \(0.247515\pi\)
\(360\) 0 0
\(361\) 8.56851 + 14.8411i 0.450974 + 0.781110i
\(362\) −8.52512 + 4.92198i −0.448071 + 0.258694i
\(363\) 0 0
\(364\) −41.5777 + 22.9152i −2.17927 + 1.20108i
\(365\) −21.4917 + 8.44221i −1.12492 + 0.441885i
\(366\) 0 0
\(367\) 6.01118 3.47055i 0.313781 0.181161i −0.334836 0.942276i \(-0.608681\pi\)
0.648617 + 0.761115i \(0.275348\pi\)
\(368\) −13.2675 7.65998i −0.691615 0.399304i
\(369\) 0 0
\(370\) 6.88980 + 1.03638i 0.358184 + 0.0538789i
\(371\) −0.943693 + 1.63452i −0.0489941 + 0.0848603i
\(372\) 0 0
\(373\) −2.00301 1.15644i −0.103712 0.0598781i 0.447247 0.894411i \(-0.352405\pi\)
−0.550959 + 0.834532i \(0.685738\pi\)
\(374\) 0.989429 + 1.71374i 0.0511622 + 0.0886154i
\(375\) 0 0
\(376\) 38.9270 2.00751
\(377\) 5.22105 + 9.47315i 0.268898 + 0.487892i
\(378\) 0 0
\(379\) 2.58772 + 4.48207i 0.132922 + 0.230228i 0.924802 0.380449i \(-0.124231\pi\)
−0.791880 + 0.610677i \(0.790897\pi\)
\(380\) 8.52337 10.6945i 0.437240 0.548615i
\(381\) 0 0
\(382\) 12.5854i 0.643923i
\(383\) −17.8929 10.3305i −0.914283 0.527861i −0.0324760 0.999473i \(-0.510339\pi\)
−0.881807 + 0.471611i \(0.843673\pi\)
\(384\) 0 0
\(385\) 3.88412 1.52574i 0.197953 0.0777587i
\(386\) −6.30890 + 10.9273i −0.321115 + 0.556187i
\(387\) 0 0
\(388\) 57.3682 33.1215i 2.91243 1.68149i
\(389\) 19.7477 1.00125 0.500624 0.865665i \(-0.333104\pi\)
0.500624 + 0.865665i \(0.333104\pi\)
\(390\) 0 0
\(391\) −2.63509 −0.133262
\(392\) 8.94284 5.16315i 0.451681 0.260778i
\(393\) 0 0
\(394\) −8.58609 + 14.8715i −0.432561 + 0.749218i
\(395\) −0.848960 2.16123i −0.0427158 0.108743i
\(396\) 0 0
\(397\) −8.13113 4.69451i −0.408090 0.235611i 0.281879 0.959450i \(-0.409042\pi\)
−0.689969 + 0.723839i \(0.742376\pi\)
\(398\) 13.1753i 0.660420i
\(399\) 0 0
\(400\) 34.0049 + 10.4670i 1.70024 + 0.523352i
\(401\) 12.2510 + 21.2193i 0.611784 + 1.05964i 0.990940 + 0.134308i \(0.0428812\pi\)
−0.379156 + 0.925333i \(0.623786\pi\)
\(402\) 0 0
\(403\) 32.3050 + 0.642285i 1.60923 + 0.0319945i
\(404\) 59.2887 2.94972
\(405\) 0 0
\(406\) −11.2212 19.4357i −0.556898 0.964575i
\(407\) −0.673180 0.388661i −0.0333683 0.0192652i
\(408\) 0 0
\(409\) 18.0582 31.2778i 0.892922 1.54659i 0.0565671 0.998399i \(-0.481985\pi\)
0.836355 0.548188i \(-0.184682\pi\)
\(410\) 8.43492 56.0749i 0.416571 2.76934i
\(411\) 0 0
\(412\) −42.5633 24.5739i −2.09694 1.21067i
\(413\) −19.3324 + 11.1616i −0.951288 + 0.549226i
\(414\) 0 0
\(415\) −24.6530 + 9.68401i −1.21017 + 0.475370i
\(416\) 16.9248 + 10.2254i 0.829805 + 0.501341i
\(417\) 0 0
\(418\) −1.91110 + 1.10337i −0.0934749 + 0.0539678i
\(419\) 3.43342 + 5.94686i 0.167734 + 0.290523i 0.937623 0.347655i \(-0.113022\pi\)
−0.769889 + 0.638178i \(0.779689\pi\)
\(420\) 0 0
\(421\) 33.9795 1.65606 0.828029 0.560686i \(-0.189462\pi\)
0.828029 + 0.560686i \(0.189462\pi\)
\(422\) 30.9049 + 17.8429i 1.50443 + 0.868580i
\(423\) 0 0
\(424\) 4.05631 0.196992
\(425\) 5.96554 1.36532i 0.289371 0.0662277i
\(426\) 0 0
\(427\) 5.77729 3.33552i 0.279582 0.161417i
\(428\) 47.8261i 2.31176i
\(429\) 0 0
\(430\) −2.84570 7.24440i −0.137232 0.349356i
\(431\) −8.12482 14.0726i −0.391359 0.677853i 0.601270 0.799046i \(-0.294661\pi\)
−0.992629 + 0.121193i \(0.961328\pi\)
\(432\) 0 0
\(433\) −0.221929 0.128130i −0.0106652 0.00615756i 0.494658 0.869088i \(-0.335293\pi\)
−0.505323 + 0.862930i \(0.668627\pi\)
\(434\) −67.0396 −3.21800
\(435\) 0 0
\(436\) 7.32648 12.6898i 0.350875 0.607733i
\(437\) 2.93855i 0.140570i
\(438\) 0 0
\(439\) −3.79833 6.57890i −0.181284 0.313994i 0.761034 0.648712i \(-0.224692\pi\)
−0.942318 + 0.334718i \(0.891359\pi\)
\(440\) −7.01356 5.58973i −0.334358 0.266480i
\(441\) 0 0
\(442\) 11.2322 + 0.223318i 0.534263 + 0.0106221i
\(443\) 4.32246i 0.205366i −0.994714 0.102683i \(-0.967257\pi\)
0.994714 0.102683i \(-0.0327428\pi\)
\(444\) 0 0
\(445\) −17.5017 + 21.9599i −0.829663 + 1.04100i
\(446\) 0.0105711 0.0183096i 0.000500554 0.000866986i
\(447\) 0 0
\(448\) 0.687565 + 0.396966i 0.0324844 + 0.0187549i
\(449\) −1.64403 + 2.84754i −0.0775865 + 0.134384i −0.902208 0.431301i \(-0.858055\pi\)
0.824622 + 0.565685i \(0.191388\pi\)
\(450\) 0 0
\(451\) −3.16324 + 5.47890i −0.148951 + 0.257991i
\(452\) 21.4583 12.3889i 1.00931 0.582727i
\(453\) 0 0
\(454\) 28.6741 1.34574
\(455\) 3.98907 23.3531i 0.187010 1.09481i
\(456\) 0 0
\(457\) 13.3594 7.71304i 0.624925 0.360801i −0.153859 0.988093i \(-0.549170\pi\)
0.778784 + 0.627292i \(0.215837\pi\)
\(458\) 36.4661 21.0537i 1.70395 0.983775i
\(459\) 0 0
\(460\) 20.0774 7.88669i 0.936116 0.367719i
\(461\) 12.9424 22.4168i 0.602786 1.04406i −0.389611 0.920979i \(-0.627391\pi\)
0.992397 0.123076i \(-0.0392760\pi\)
\(462\) 0 0
\(463\) 7.04045i 0.327197i 0.986527 + 0.163599i \(0.0523102\pi\)
−0.986527 + 0.163599i \(0.947690\pi\)
\(464\) −10.6738 + 18.4876i −0.495519 + 0.858265i
\(465\) 0 0
\(466\) 8.84570 + 15.3212i 0.409769 + 0.709741i
\(467\) 18.8113i 0.870482i 0.900314 + 0.435241i \(0.143337\pi\)
−0.900314 + 0.435241i \(0.856663\pi\)
\(468\) 0 0
\(469\) 23.5967 1.08959
\(470\) −21.8683 + 27.4386i −1.00871 + 1.26565i
\(471\) 0 0
\(472\) 41.5486 + 23.9881i 1.91243 + 1.10414i
\(473\) 0.868356i 0.0399271i
\(474\) 0 0
\(475\) 1.52255 + 6.65255i 0.0698594 + 0.305240i
\(476\) −16.1159 −0.738670
\(477\) 0 0
\(478\) 8.81870 5.09148i 0.403358 0.232879i
\(479\) 9.73876 + 16.8680i 0.444975 + 0.770720i 0.998051 0.0624114i \(-0.0198791\pi\)
−0.553075 + 0.833131i \(0.686546\pi\)
\(480\) 0 0
\(481\) −3.86491 + 2.13011i −0.176225 + 0.0971249i
\(482\) 50.3346i 2.29268i
\(483\) 0 0
\(484\) −23.7407 41.1201i −1.07912 1.86909i
\(485\) −4.91728 + 32.6898i −0.223282 + 1.48437i
\(486\) 0 0
\(487\) −27.9935 16.1620i −1.26851 0.732372i −0.293800 0.955867i \(-0.594920\pi\)
−0.974705 + 0.223495i \(0.928253\pi\)
\(488\) −12.4163 7.16858i −0.562062 0.324506i
\(489\) 0 0
\(490\) −1.38451 + 9.20411i −0.0625456 + 0.415799i
\(491\) 14.3354 + 24.8297i 0.646949 + 1.12055i 0.983848 + 0.179007i \(0.0572885\pi\)
−0.336899 + 0.941541i \(0.609378\pi\)
\(492\) 0 0
\(493\) 3.67187i 0.165373i
\(494\) −0.249036 + 12.5258i −0.0112046 + 0.563561i
\(495\) 0 0
\(496\) 31.8847 + 55.2260i 1.43167 + 2.47972i
\(497\) 6.70593 3.87167i 0.300802 0.173668i
\(498\) 0 0
\(499\) −28.9616 −1.29650 −0.648249 0.761428i \(-0.724498\pi\)
−0.648249 + 0.761428i \(0.724498\pi\)
\(500\) −41.3667 + 28.2573i −1.84998 + 1.26370i
\(501\) 0 0
\(502\) 9.35181i 0.417392i
\(503\) −24.3433 14.0546i −1.08542 0.626665i −0.153063 0.988216i \(-0.548914\pi\)
−0.932352 + 0.361551i \(0.882247\pi\)
\(504\) 0 0
\(505\) −18.4404 + 23.1376i −0.820587 + 1.02961i
\(506\) −3.48079 −0.154740
\(507\) 0 0
\(508\) 77.2116i 3.42571i
\(509\) −10.5563 18.2841i −0.467900 0.810427i 0.531427 0.847104i \(-0.321656\pi\)
−0.999327 + 0.0366773i \(0.988323\pi\)
\(510\) 0 0
\(511\) −15.1722 + 26.2790i −0.671178 + 1.16251i
\(512\) 50.8542i 2.24746i
\(513\) 0 0
\(514\) 16.8844 29.2447i 0.744740 1.28993i
\(515\) 22.8284 8.96730i 1.00594 0.395147i
\(516\) 0 0
\(517\) 3.39010 1.95728i 0.149097 0.0860809i
\(518\) 7.92947 4.57808i 0.348401 0.201149i
\(519\) 0 0
\(520\) −47.7522 + 17.6703i −2.09407 + 0.774893i
\(521\) −0.673516 −0.0295073 −0.0147536 0.999891i \(-0.504696\pi\)
−0.0147536 + 0.999891i \(0.504696\pi\)
\(522\) 0 0
\(523\) −25.8618 + 14.9313i −1.13086 + 0.652900i −0.944150 0.329516i \(-0.893114\pi\)
−0.186706 + 0.982416i \(0.559781\pi\)
\(524\) −22.4039 + 38.8048i −0.978720 + 1.69519i
\(525\) 0 0
\(526\) −38.5304 + 66.7366i −1.68000 + 2.90985i
\(527\) 9.49907 + 5.48429i 0.413786 + 0.238899i
\(528\) 0 0
\(529\) −9.18246 + 15.9045i −0.399237 + 0.691499i
\(530\) −2.27874 + 2.85918i −0.0989820 + 0.124195i
\(531\) 0 0
\(532\) 17.9718i 0.779177i
\(533\) 17.3366 + 31.4558i 0.750933 + 1.36250i
\(534\) 0 0
\(535\) 18.6643 + 14.8752i 0.806928 + 0.643112i
\(536\) −25.3566 43.9189i −1.09524 1.89701i
\(537\) 0 0
\(538\) 56.6418i 2.44200i
\(539\) 0.519213 0.899304i 0.0223641 0.0387358i
\(540\) 0 0
\(541\) 6.28806 0.270345 0.135172 0.990822i \(-0.456841\pi\)
0.135172 + 0.990822i \(0.456841\pi\)
\(542\) 26.0778 + 15.0560i 1.12014 + 0.646712i
\(543\) 0 0
\(544\) 3.35627 + 5.81323i 0.143899 + 0.249240i
\(545\) 2.67352 + 6.80607i 0.114521 + 0.291540i
\(546\) 0 0
\(547\) 3.03789i 0.129891i 0.997889 + 0.0649454i \(0.0206873\pi\)
−0.997889 + 0.0649454i \(0.979313\pi\)
\(548\) −33.6527 + 19.4294i −1.43757 + 0.829983i
\(549\) 0 0
\(550\) 7.88011 1.80350i 0.336009 0.0769015i
\(551\) −4.09473 −0.174442
\(552\) 0 0
\(553\) −2.64265 1.52574i −0.112377 0.0648809i
\(554\) 42.7304 1.81544
\(555\) 0 0
\(556\) −32.0970 55.5936i −1.36121 2.35769i
\(557\) 17.9264 10.3498i 0.759566 0.438536i −0.0695738 0.997577i \(-0.522164\pi\)
0.829140 + 0.559041i \(0.188831\pi\)
\(558\) 0 0
\(559\) 4.21955 + 2.54931i 0.178468 + 0.107824i
\(560\) 43.5198 17.0952i 1.83905 0.722402i
\(561\) 0 0
\(562\) 23.3622 13.4882i 0.985475 0.568964i
\(563\) 9.49188 + 5.48014i 0.400035 + 0.230960i 0.686499 0.727131i \(-0.259147\pi\)
−0.286464 + 0.958091i \(0.592480\pi\)
\(564\) 0 0
\(565\) −1.83929 + 12.2275i −0.0773794 + 0.514413i
\(566\) −11.2212 + 19.4357i −0.471661 + 0.816941i
\(567\) 0 0
\(568\) −14.4122 8.32087i −0.604721 0.349136i
\(569\) −21.3566 36.9907i −0.895314 1.55073i −0.833416 0.552647i \(-0.813618\pi\)
−0.0618981 0.998082i \(-0.519715\pi\)
\(570\) 0 0
\(571\) −23.6145 −0.988238 −0.494119 0.869394i \(-0.664509\pi\)
−0.494119 + 0.869394i \(0.664509\pi\)
\(572\) 10.2583 + 0.203954i 0.428920 + 0.00852774i
\(573\) 0 0
\(574\) −37.2602 64.5366i −1.55521 2.69370i
\(575\) −3.16683 + 10.2883i −0.132066 + 0.429050i
\(576\) 0 0
\(577\) 18.3646i 0.764530i 0.924053 + 0.382265i \(0.124856\pi\)
−0.924053 + 0.382265i \(0.875144\pi\)
\(578\) −34.1767 19.7319i −1.42156 0.820740i
\(579\) 0 0
\(580\) −10.9897 27.9770i −0.456324 1.16168i
\(581\) −17.4039 + 30.1445i −0.722037 + 1.25060i
\(582\) 0 0
\(583\) 0.353259 0.203954i 0.0146305 0.00844691i
\(584\) 65.2151 2.69862
\(585\) 0 0
\(586\) −71.9237 −2.97114
\(587\) −0.608726 + 0.351448i −0.0251248 + 0.0145058i −0.512510 0.858681i \(-0.671284\pi\)
0.487385 + 0.873187i \(0.337951\pi\)
\(588\) 0 0
\(589\) −6.11588 + 10.5930i −0.252000 + 0.436477i
\(590\) −40.2496 + 15.8106i −1.65705 + 0.650912i
\(591\) 0 0
\(592\) −7.54267 4.35476i −0.310002 0.178980i
\(593\) 37.1593i 1.52595i 0.646428 + 0.762975i \(0.276262\pi\)
−0.646428 + 0.762975i \(0.723738\pi\)
\(594\) 0 0
\(595\) 5.01248 6.28927i 0.205492 0.257835i
\(596\) −38.4337 66.5692i −1.57431 2.72678i
\(597\) 0 0
\(598\) −10.2189 + 16.9140i −0.417880 + 0.691663i
\(599\) −15.6914 −0.641133 −0.320567 0.947226i \(-0.603873\pi\)
−0.320567 + 0.947226i \(0.603873\pi\)
\(600\) 0 0
\(601\) −6.00193 10.3956i −0.244824 0.424047i 0.717258 0.696807i \(-0.245397\pi\)
−0.962082 + 0.272760i \(0.912063\pi\)
\(602\) −8.85812 5.11424i −0.361030 0.208441i
\(603\) 0 0
\(604\) −47.9059 + 82.9754i −1.94926 + 3.37622i
\(605\) 23.4313 + 3.52459i 0.952616 + 0.143295i
\(606\) 0 0
\(607\) 33.5035 + 19.3433i 1.35987 + 0.785119i 0.989606 0.143809i \(-0.0459350\pi\)
0.370261 + 0.928928i \(0.379268\pi\)
\(608\) −6.48269 + 3.74278i −0.262908 + 0.151790i
\(609\) 0 0
\(610\) 12.0282 4.72482i 0.487006 0.191302i
\(611\) 0.441765 22.2195i 0.0178719 0.898903i
\(612\) 0 0
\(613\) −14.9684 + 8.64201i −0.604568 + 0.349047i −0.770836 0.637033i \(-0.780161\pi\)
0.166269 + 0.986081i \(0.446828\pi\)
\(614\) −16.1933 28.0477i −0.653509 1.13191i
\(615\) 0 0
\(616\) −11.7861 −0.474877
\(617\) −22.9229 13.2345i −0.922841 0.532803i −0.0383009 0.999266i \(-0.512195\pi\)
−0.884540 + 0.466464i \(0.845528\pi\)
\(618\) 0 0
\(619\) 31.0039 1.24615 0.623075 0.782162i \(-0.285883\pi\)
0.623075 + 0.782162i \(0.285883\pi\)
\(620\) −88.7902 13.3560i −3.56590 0.536392i
\(621\) 0 0
\(622\) −61.5615 + 35.5425i −2.46839 + 1.42513i
\(623\) 36.9030i 1.47849i
\(624\) 0 0
\(625\) 1.83869 24.9323i 0.0735475 0.997292i
\(626\) 31.2881 + 54.1925i 1.25052 + 2.16597i
\(627\) 0 0
\(628\) −71.2635 41.1440i −2.84372 1.64182i
\(629\) −1.49807 −0.0597320
\(630\) 0 0
\(631\) 10.3566 17.9381i 0.412288 0.714104i −0.582851 0.812579i \(-0.698063\pi\)
0.995140 + 0.0984745i \(0.0313963\pi\)
\(632\) 6.55812i 0.260868i
\(633\) 0 0
\(634\) −0.298331 0.516725i −0.0118482 0.0205218i
\(635\) −30.1321 24.0149i −1.19576 0.953003i
\(636\) 0 0
\(637\) −2.84563 5.16315i −0.112748 0.204571i
\(638\) 4.85031i 0.192026i
\(639\) 0 0
\(640\) 20.3828 + 16.2449i 0.805702 + 0.642136i
\(641\) 10.5947 18.3506i 0.418467 0.724806i −0.577319 0.816519i \(-0.695901\pi\)
0.995785 + 0.0917132i \(0.0292343\pi\)
\(642\) 0 0
\(643\) 9.98843 + 5.76682i 0.393905 + 0.227421i 0.683851 0.729622i \(-0.260304\pi\)
−0.289946 + 0.957043i \(0.593637\pi\)
\(644\) 14.1738 24.5498i 0.558526 0.967396i
\(645\) 0 0
\(646\) −2.12645 + 3.68311i −0.0836639 + 0.144910i
\(647\) −30.1779 + 17.4232i −1.18641 + 0.684977i −0.957490 0.288467i \(-0.906854\pi\)
−0.228925 + 0.973444i \(0.573521\pi\)
\(648\) 0 0
\(649\) 4.82456 0.189380
\(650\) 14.3707 43.5860i 0.563666 1.70958i
\(651\) 0 0
\(652\) −15.5641 + 8.98591i −0.609535 + 0.351915i
\(653\) −19.3324 + 11.1616i −0.756537 + 0.436787i −0.828051 0.560653i \(-0.810550\pi\)
0.0715139 + 0.997440i \(0.477217\pi\)
\(654\) 0 0
\(655\) −8.17544 20.8125i −0.319441 0.813214i
\(656\) −35.4427 + 61.3885i −1.38380 + 2.39682i
\(657\) 0 0
\(658\) 46.1100i 1.79755i
\(659\) 0.433420 0.750705i 0.0168836 0.0292433i −0.857460 0.514550i \(-0.827959\pi\)
0.874344 + 0.485307i \(0.161292\pi\)
\(660\) 0 0
\(661\) −6.65430 11.5256i −0.258822 0.448293i 0.707104 0.707109i \(-0.250001\pi\)
−0.965927 + 0.258816i \(0.916668\pi\)
\(662\) 46.6544i 1.81328i
\(663\) 0 0
\(664\) 74.8079 2.90311
\(665\) 7.01356 + 5.58973i 0.271974 + 0.216760i
\(666\) 0 0
\(667\) −5.59346 3.22939i −0.216580 0.125042i
\(668\) 13.1670i 0.509448i
\(669\) 0 0
\(670\) 45.2020 + 6.79940i 1.74630 + 0.262684i
\(671\) −1.44176 −0.0556587
\(672\) 0 0
\(673\) −4.77457 + 2.75660i −0.184046 + 0.106259i −0.589192 0.807993i \(-0.700554\pi\)
0.405146 + 0.914252i \(0.367221\pi\)
\(674\) 27.1056 + 46.9483i 1.04407 + 1.80838i
\(675\) 0 0
\(676\) 31.1072 49.2486i 1.19643 1.89418i
\(677\) 4.80479i 0.184663i −0.995728 0.0923316i \(-0.970568\pi\)
0.995728 0.0923316i \(-0.0294320\pi\)
\(678\) 0 0
\(679\) 21.7215 + 37.6227i 0.833594 + 1.44383i
\(680\) −17.0921 2.57104i −0.655453 0.0985949i
\(681\) 0 0
\(682\) 12.5477 + 7.24440i 0.480475 + 0.277403i
\(683\) 10.1866 + 5.88126i 0.389781 + 0.225040i 0.682065 0.731291i \(-0.261082\pi\)
−0.292284 + 0.956331i \(0.594415\pi\)
\(684\) 0 0
\(685\) 2.88453 19.1761i 0.110212 0.732683i
\(686\) −20.0669 34.7569i −0.766157 1.32702i
\(687\) 0 0
\(688\) 9.72953i 0.370935i
\(689\) 0.0460332 2.31533i 0.00175372 0.0882071i
\(690\) 0 0
\(691\) −2.43342 4.21481i −0.0925717 0.160339i 0.816021 0.578022i \(-0.196175\pi\)
−0.908593 + 0.417684i \(0.862842\pi\)
\(692\) −5.30577 + 3.06329i −0.201695 + 0.116449i
\(693\) 0 0
\(694\) 9.71254 0.368683
\(695\) 31.6786 + 4.76518i 1.20164 + 0.180753i
\(696\) 0 0
\(697\) 12.1925i 0.461825i
\(698\) 53.6320 + 30.9644i 2.03000 + 1.17202i
\(699\) 0 0
\(700\) −19.3679 + 62.9218i −0.732039 + 2.37822i
\(701\) −21.3828 −0.807617 −0.403808 0.914844i \(-0.632314\pi\)
−0.403808 + 0.914844i \(0.632314\pi\)
\(702\) 0 0
\(703\) 1.67059i 0.0630076i
\(704\) −0.0857934 0.148599i −0.00323346 0.00560052i
\(705\) 0 0
\(706\) 34.4427 59.6564i 1.29627 2.24520i
\(707\) 38.8822i 1.46232i
\(708\) 0 0
\(709\) −13.0582 + 22.6175i −0.490412 + 0.849419i −0.999939 0.0110357i \(-0.996487\pi\)
0.509527 + 0.860455i \(0.329820\pi\)
\(710\) 13.9616 5.48429i 0.523969 0.205822i
\(711\) 0 0
\(712\) 68.6851 39.6554i 2.57408 1.48615i
\(713\) −16.7087 + 9.64680i −0.625748 + 0.361276i
\(714\) 0 0
\(715\) −3.27020 + 3.93989i −0.122299 + 0.147344i
\(716\) −34.8880 −1.30383
\(717\) 0 0
\(718\) 59.5347 34.3724i 2.22182 1.28277i
\(719\) −18.3387 + 31.7635i −0.683918 + 1.18458i 0.289858 + 0.957070i \(0.406392\pi\)
−0.973776 + 0.227510i \(0.926941\pi\)
\(720\) 0 0
\(721\) 16.1159 27.9135i 0.600187 1.03955i
\(722\) 37.7815 + 21.8132i 1.40608 + 0.811803i
\(723\) 0 0
\(724\) −8.66324 + 15.0052i −0.321967 + 0.557663i
\(725\) 14.3362 + 4.41283i 0.532434 + 0.163888i
\(726\) 0 0
\(727\) 26.2596i 0.973916i 0.873425 + 0.486958i \(0.161893\pi\)
−0.873425 + 0.486958i \(0.838107\pi\)
\(728\) −34.6016 + 57.2716i −1.28242 + 2.12263i
\(729\) 0 0
\(730\) −36.6363 + 45.9684i −1.35597 + 1.70137i
\(731\) 0.836758 + 1.44931i 0.0309486 + 0.0536046i
\(732\) 0 0
\(733\) 31.7811i 1.17386i 0.809637 + 0.586931i \(0.199664\pi\)
−0.809637 + 0.586931i \(0.800336\pi\)
\(734\) 8.83513 15.3029i 0.326110 0.564840i
\(735\) 0 0
\(736\) −11.8073 −0.435222
\(737\) −4.41654 2.54989i −0.162685 0.0939265i
\(738\) 0 0
\(739\) −17.0685 29.5635i −0.627875 1.08751i −0.987977 0.154599i \(-0.950591\pi\)
0.360102 0.932913i \(-0.382742\pi\)
\(740\) 11.4142 4.48365i 0.419595 0.164822i
\(741\) 0 0
\(742\) 4.80479i 0.176390i
\(743\) −2.70254 + 1.56031i −0.0991465 + 0.0572423i −0.548753 0.835984i \(-0.684897\pi\)
0.449607 + 0.893227i \(0.351564\pi\)
\(744\) 0 0
\(745\) 37.9328 + 5.70594i 1.38975 + 0.209050i
\(746\) −5.88798 −0.215574
\(747\) 0 0
\(748\) 3.01638 + 1.74151i 0.110290 + 0.0636758i
\(749\) 31.3649 1.14605
\(750\) 0 0
\(751\) −0.742024 1.28522i −0.0270769 0.0468985i 0.852169 0.523266i \(-0.175287\pi\)
−0.879246 + 0.476367i \(0.841953\pi\)
\(752\) 37.9845 21.9304i 1.38515 0.799718i
\(753\) 0 0
\(754\) 23.5688 + 14.2395i 0.858325 + 0.518572i
\(755\) −17.4814 44.5030i −0.636213 1.61963i
\(756\) 0 0
\(757\) −4.41654 + 2.54989i −0.160522 + 0.0926774i −0.578109 0.815960i \(-0.696209\pi\)
0.417587 + 0.908637i \(0.362876\pi\)
\(758\) 11.4102 + 6.58767i 0.414436 + 0.239275i
\(759\) 0 0
\(760\) 2.86713 19.0605i 0.104002 0.691397i
\(761\) −14.8931 + 25.7955i −0.539873 + 0.935088i 0.459037 + 0.888417i \(0.348194\pi\)
−0.998910 + 0.0466707i \(0.985139\pi\)
\(762\) 0 0
\(763\) 8.32215 + 4.80479i 0.301282 + 0.173945i
\(764\) −11.0758 19.1839i −0.400709 0.694048i
\(765\) 0 0
\(766\) −52.5973 −1.90042
\(767\) 14.1639 23.4437i 0.511428 0.846501i
\(768\) 0 0
\(769\) 9.54930 + 16.5399i 0.344356 + 0.596443i 0.985237 0.171198i \(-0.0547638\pi\)
−0.640880 + 0.767641i \(0.721430\pi\)
\(770\) 6.62117 8.30773i 0.238610 0.299390i
\(771\) 0 0
\(772\) 22.2088i 0.799311i
\(773\) 42.6350 + 24.6153i 1.53347 + 0.885351i 0.999198 + 0.0400400i \(0.0127485\pi\)
0.534275 + 0.845311i \(0.320585\pi\)
\(774\) 0 0
\(775\) 32.8284 30.4966i 1.17923 1.09547i
\(776\) 46.6831 80.8574i 1.67582 2.90261i
\(777\) 0 0
\(778\) 43.5373 25.1362i 1.56089 0.901178i
\(779\) −13.5967 −0.487151
\(780\) 0 0
\(781\) −1.67352 −0.0598831
\(782\) −5.80951 + 3.35412i −0.207748 + 0.119943i
\(783\) 0 0
\(784\) 5.81754 10.0763i 0.207769 0.359867i
\(785\) 38.2215 15.0139i 1.36418 0.535869i
\(786\) 0 0
\(787\) −8.47263 4.89168i −0.302017 0.174369i 0.341332 0.939943i \(-0.389122\pi\)
−0.643349 + 0.765573i \(0.722455\pi\)
\(788\)