Properties

Label 585.2.bs.a.289.1
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: \( x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 \) Copy content Toggle raw display
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 289.1
Root \(-2.20467 - 1.27287i\) of defining polynomial
Character \(\chi\) \(=\) 585.289
Dual form 585.2.bs.a.334.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.20467 + 1.27287i) q^{2} +(2.24039 - 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(-2.54486 - 1.46928i) q^{7} +6.31544i q^{8} +O(q^{10})\) \(q+(-2.20467 + 1.27287i) q^{2} +(2.24039 - 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(-2.54486 - 1.46928i) q^{7} +6.31544i q^{8} +(0.846746 + 5.62912i) q^{10} +(-0.317544 - 0.550003i) q^{11} +(3.60484 + 0.0716710i) q^{13} +7.48079 q^{14} +(-3.55794 - 6.16253i) q^{16} +(1.05998 + 0.611979i) q^{17} +(0.682456 - 1.18205i) q^{19} +(-6.24464 - 7.83529i) q^{20} +(1.40016 + 0.808385i) q^{22} +(-1.86449 + 1.07646i) q^{23} +(-3.66324 - 3.40304i) q^{25} +(-8.03872 + 4.43048i) q^{26} +(-11.4030 + 6.58351i) q^{28} +(-1.50000 - 2.59808i) q^{29} -8.96157 q^{31} +(4.74954 + 2.74215i) q^{32} -3.11588 q^{34} +(-5.13847 + 4.09531i) q^{35} +(-1.05998 + 0.611979i) q^{37} +3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +(-4.98079 - 8.62698i) q^{41} +(1.18412 + 0.683650i) q^{43} -2.84570 q^{44} +(2.74039 - 4.74650i) q^{46} -6.16379i q^{47} +(0.817544 + 1.41603i) q^{49} +(12.4079 + 2.83976i) q^{50} +(8.35437 - 13.8279i) q^{52} -0.642285i q^{53} +(-1.40430 + 0.211239i) q^{55} +(9.27912 - 16.0719i) q^{56} +(6.61402 + 3.81861i) q^{58} +(-3.79833 + 6.57890i) q^{59} +(1.13509 - 1.96603i) q^{61} +(19.7574 - 11.4069i) q^{62} +0.270178 q^{64} +(3.09628 - 7.44399i) q^{65} +(-6.95421 + 4.01502i) q^{67} +(4.74954 - 2.74215i) q^{68} +(6.11588 - 15.5694i) q^{70} +(1.31754 - 2.28205i) q^{71} -10.3263i q^{73} +(1.55794 - 2.69843i) q^{74} +(-3.05794 - 5.29650i) q^{76} +1.86624i q^{77} -1.03843 q^{79} +(-15.7346 + 2.36683i) q^{80} +(21.9620 + 12.6798i) q^{82} -11.8452i q^{83} +(2.14026 - 1.70576i) q^{85} -3.48079 q^{86} +(3.47351 - 2.00543i) q^{88} +(6.27912 + 10.8758i) q^{89} +(-9.06851 - 5.47890i) q^{91} +9.64680i q^{92} +(7.84570 + 13.5891i) q^{94} +(-1.90220 - 2.38674i) q^{95} +(-12.8031 - 7.39190i) q^{97} +(-3.60484 - 2.08125i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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 \(0.689807\pi\)
−0.997359 + 0.0726333i \(0.976860\pi\)
\(3\) 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 −0.0651198 0.997877i \(-0.520743\pi\)
−0.896747 + 0.442543i \(0.854076\pi\)
\(8\) 6.31544i 2.23284i
\(9\) 0 0
\(10\) 0.846746 + 5.62912i 0.267765 + 1.78008i
\(11\) −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 0.623003 0.782220i \(-0.285912\pi\)
−0.365920 + 0.930646i \(0.619246\pi\)
\(18\) 0 0
\(19\) 0.682456 1.18205i 0.156566 0.271180i −0.777062 0.629424i \(-0.783291\pi\)
0.933628 + 0.358244i \(0.116624\pi\)
\(20\) −6.24464 7.83529i −1.39634 1.75202i
\(21\) 0 0
\(22\) 1.40016 + 0.808385i 0.298516 + 0.172348i
\(23\) −1.86449 + 1.07646i −0.388773 + 0.224458i −0.681628 0.731699i \(-0.738728\pi\)
0.292856 + 0.956157i \(0.405394\pi\)
\(24\) 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
\(35\) −5.13847 + 4.09531i −0.868561 + 0.692233i
\(36\) 0 0
\(37\) −1.05998 + 0.611979i −0.174259 + 0.100609i −0.584593 0.811327i \(-0.698746\pi\)
0.410333 + 0.911936i \(0.365412\pi\)
\(38\) 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 0.587563 0.809178i \(-0.300087\pi\)
−0.406987 + 0.913434i \(0.633421\pi\)
\(44\) −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 \(-0.851588\pi\)
0.893260 0.449540i \(-0.148412\pi\)
\(48\) 0 0
\(49\) 0.817544 + 1.41603i 0.116792 + 0.202290i
\(50\) 12.4079 + 2.83976i 1.75474 + 0.401603i
\(51\) 0 0
\(52\) 8.35437 13.8279i 1.15854 1.91759i
\(53\) 0.642285i 0.0882246i −0.999027 0.0441123i \(-0.985954\pi\)
0.999027 0.0441123i \(-0.0140459\pi\)
\(54\) 0 0
\(55\) −1.40430 + 0.211239i −0.189356 + 0.0284834i
\(56\) 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
\(65\) 3.09628 7.44399i 0.384046 0.923314i
\(66\) 0 0
\(67\) −6.95421 + 4.01502i −0.849592 + 0.490512i −0.860513 0.509428i \(-0.829857\pi\)
0.0109212 + 0.999940i \(0.496524\pi\)
\(68\) 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 \(-0.793453\pi\)
0.796756 0.604301i \(-0.206547\pi\)
\(74\) 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 \(0.518605\pi\)
\(80\) −15.7346 + 2.36683i −1.75918 + 0.264620i
\(81\) 0 0
\(82\) 21.9620 + 12.6798i 2.42530 + 1.40025i
\(83\) 11.8452i 1.30018i −0.759855 0.650092i \(-0.774730\pi\)
0.759855 0.650092i \(-0.225270\pi\)
\(84\) 0 0
\(85\) 2.14026 1.70576i 0.232144 0.185016i
\(86\) −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
\(95\) −1.90220 2.38674i −0.195162 0.244874i
\(96\) 0 0
\(97\) −12.8031 7.39190i −1.29996 0.750534i −0.319565 0.947564i \(-0.603537\pi\)
−0.980397 + 0.197031i \(0.936870\pi\)
\(98\) −3.60484 2.08125i −0.364144 0.210238i
\(99\) 0 0
\(100\) −21.4125 + 6.59098i −2.14125 + 0.659098i
\(101\) 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 \(0.181721\pi\)
−0.841419 + 0.540383i \(0.818279\pi\)
\(104\) −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 −0.875123 0.483901i \(-0.839219\pi\)
−0.0184903 + 0.999829i \(0.505886\pi\)
\(108\) 0 0
\(109\) 3.27018 0.313226 0.156613 0.987660i \(-0.449942\pi\)
0.156613 + 0.987660i \(0.449942\pi\)
\(110\) 2.82715 2.25321i 0.269558 0.214835i
\(111\) 0 0
\(112\) 20.9104i 1.97584i
\(113\) −4.78895 2.76490i −0.450507 0.260100i 0.257537 0.966268i \(-0.417089\pi\)
−0.708044 + 0.706168i \(0.750422\pi\)
\(114\) 0 0
\(115\) 0.716091 + 4.76053i 0.0667759 + 0.443922i
\(116\) −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 0.339813 0.940493i \(-0.389636\pi\)
0.984397 + 0.175959i \(0.0563027\pi\)
\(128\) −10.0947 + 5.82819i −0.892256 + 0.515144i
\(129\) 0 0
\(130\) 2.64894 + 20.3527i 0.232327 + 1.78505i
\(131\) −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 0.785254 0.619174i \(-0.212532\pi\)
−0.143593 + 0.989637i \(0.545866\pi\)
\(138\) 0 0
\(139\) 7.16324 12.4071i 0.607578 1.05236i −0.384060 0.923308i \(-0.625474\pi\)
0.991638 0.129048i \(-0.0411922\pi\)
\(140\) 4.37953 + 29.1148i 0.370137 + 2.46065i
\(141\) 0 0
\(142\) 6.70825i 0.562944i
\(143\) −1.10528 2.00543i −0.0924279 0.167703i
\(144\) 0 0
\(145\) −6.63357 + 0.997839i −0.550888 + 0.0828660i
\(146\) 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 \(0.261800\pi\)
−0.680413 + 0.732829i \(0.738200\pi\)
\(158\) 2.28939 1.32178i 0.182134 0.105155i
\(159\) 0 0
\(160\) 9.59006 7.64317i 0.758161 0.604245i
\(161\) 6.32648 0.498597
\(162\) 0 0
\(163\) 3.47351 + 2.00543i 0.272066 + 0.157078i 0.629826 0.776736i \(-0.283126\pi\)
−0.357760 + 0.933814i \(0.616459\pi\)
\(164\) −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 −0.398294 0.917258i \(-0.630398\pi\)
0.595221 + 0.803562i \(0.297064\pi\)
\(168\) 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 0.544337 0.838866i \(-0.316781\pi\)
−0.454311 + 0.890843i \(0.650114\pi\)
\(174\) 0 0
\(175\) 4.32244 + 14.0426i 0.326746 + 1.06152i
\(176\) −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
\(185\) 0.407104 + 2.70640i 0.0299309 + 0.198979i
\(186\) 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 −0.337493 0.941328i \(-0.609579\pi\)
0.646467 + 0.762942i \(0.276246\pi\)
\(194\) 37.6357 2.70208
\(195\) 0 0
\(196\) 7.32648 0.523320
\(197\) 5.84174 3.37273i 0.416207 0.240297i −0.277246 0.960799i \(-0.589422\pi\)
0.693453 + 0.720502i \(0.256088\pi\)
\(198\) 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
\(205\) −22.0269 + 3.31335i −1.53843 + 0.231414i
\(206\) −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
\(215\) 2.39092 1.90553i 0.163059 0.129956i
\(216\) 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 −0.500241 0.865886i \(-0.666755\pi\)
0.499759 + 0.866164i \(0.333422\pi\)
\(224\) −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 0.140040 0.990146i \(-0.455277\pi\)
−0.787471 + 0.616351i \(0.788610\pi\)
\(228\) 0 0
\(229\) 16.5404 1.09302 0.546509 0.837453i \(-0.315957\pi\)
0.546509 + 0.837453i \(0.315957\pi\)
\(230\) −7.63828 9.58393i −0.503653 0.631946i
\(231\) 0 0
\(232\) 16.4080 9.47315i 1.07724 0.621943i
\(233\) 6.94941i 0.455271i −0.973746 0.227636i \(-0.926900\pi\)
0.973746 0.227636i \(-0.0730995\pi\)
\(234\) 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
\(245\) 3.61549 0.543852i 0.230985 0.0347454i
\(246\) 0 0
\(247\) 2.54486 4.21218i 0.161926 0.268015i
\(248\) 56.5962i 3.59386i
\(249\) 0 0
\(250\) 16.0543 23.5023i 1.01536 1.48642i
\(251\) 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 −0.813494 0.581574i \(-0.802437\pi\)
0.0969108 + 0.995293i \(0.469104\pi\)
\(258\) 0 0
\(259\) 3.59666 0.223486
\(260\) −21.9493 28.6925i −1.36124 1.77943i
\(261\) 0 0
\(262\) 22.0467 12.7287i 1.36205 0.786381i
\(263\) 26.2150 15.1352i 1.61649 0.933279i 0.628667 0.777674i \(-0.283601\pi\)
0.987819 0.155605i \(-0.0497327\pi\)
\(264\) 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
\(275\) −0.708438 + 3.09541i −0.0427204 + 0.186660i
\(276\) 0 0
\(277\) −14.5363 8.39254i −0.873402 0.504259i −0.00492452 0.999988i \(-0.501568\pi\)
−0.868477 + 0.495729i \(0.834901\pi\)
\(278\) 36.4715i 2.18741i
\(279\) 0 0
\(280\) −25.8636 32.4517i −1.54565 1.93936i
\(281\) 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 −0.255617 0.966778i \(-0.582279\pi\)
0.709446 + 0.704760i \(0.248945\pi\)
\(284\) −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
\(290\) 13.3548 10.6436i 0.784218 0.625013i
\(291\) 0 0
\(292\) −40.0709 23.1350i −2.34497 1.35387i
\(293\) 24.4675 + 14.1263i 1.42940 + 0.825267i 0.997074 0.0764476i \(-0.0243578\pi\)
0.432331 + 0.901715i \(0.357691\pi\)
\(294\) 0 0
\(295\) 10.5871 + 13.2838i 0.616403 + 0.773415i
\(296\) −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
\(305\) −3.16383 3.96973i −0.181160 0.227306i
\(306\) 0 0
\(307\) 12.7219i 0.726077i 0.931774 + 0.363039i \(0.118261\pi\)
−0.931774 + 0.363039i \(0.881739\pi\)
\(308\) 7.24190 + 4.18112i 0.412646 + 0.238241i
\(309\) 0 0
\(310\) −7.58818 50.4457i −0.430980 2.86513i
\(311\) −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 \(-0.755540\pi\)
0.719307 0.694692i \(-0.244460\pi\)
\(314\) −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 \(0.00209512\pi\)
−0.999978 + 0.00658196i \(0.997905\pi\)
\(318\) 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
\(325\) −12.9615 12.5299i −0.718975 0.695036i
\(326\) −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
\(335\) 2.67089 + 17.7559i 0.145926 + 0.970110i
\(336\) 0 0
\(337\) 21.2949i 1.16001i −0.814614 0.580003i \(-0.803051\pi\)
0.814614 0.580003i \(-0.196949\pi\)
\(338\) −29.2958 + 15.3950i −1.59348 + 0.837379i
\(339\) 0 0
\(340\) −1.82415 12.1268i −0.0989283 0.657669i
\(341\) 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 0.408685 0.912675i \(-0.365987\pi\)
−0.586057 + 0.810270i \(0.699321\pi\)
\(348\) 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 −0.970562 0.240853i \(-0.922573\pi\)
−0.276696 + 0.960958i \(0.589239\pi\)
\(354\) 0 0
\(355\) −3.67238 4.60783i −0.194910 0.244558i
\(356\) 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 −0.648617 0.761115i \(-0.724652\pi\)
0.334836 + 0.942276i \(0.391319\pi\)
\(368\) 13.2675 + 7.65998i 0.691615 + 0.399304i
\(369\) 0 0
\(370\) −4.34243 5.44855i −0.225752 0.283257i
\(371\) −0.943693 + 1.63452i −0.0489941 + 0.0848603i
\(372\) 0 0
\(373\) 2.00301 + 1.15644i 0.103712 + 0.0598781i 0.550959 0.834532i \(-0.314262\pi\)
−0.447247 + 0.894411i \(0.647595\pi\)
\(374\) 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 \(0.790897\pi\)
\(380\) −13.5234 + 2.03422i −0.693734 + 0.104353i
\(381\) 0 0
\(382\) 12.5854i 0.643923i
\(383\) 17.8929 + 10.3305i 0.914283 + 0.527861i 0.881807 0.471611i \(-0.156327\pi\)
0.0324760 + 0.999473i \(0.489661\pi\)
\(384\) 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 0.689969 0.723839i \(-0.257624\pi\)
−0.281879 + 0.959450i \(0.590958\pi\)
\(398\) 13.1753i 0.660420i
\(399\) 0 0
\(400\) −7.93772 + 34.6826i −0.396886 + 1.73413i
\(401\) 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 \(-0.184682\pi\)
\(410\) 44.3448 35.3423i 2.19003 1.74543i
\(411\) 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
\(425\) −1.80037 5.84897i −0.0873308 0.283717i
\(426\) 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 0.505323 0.862930i \(-0.331373\pi\)
−0.494658 + 0.869088i \(0.664707\pi\)
\(434\) −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 \(0.891359\pi\)
\(440\) −1.33407 8.86879i −0.0635991 0.422803i
\(441\) 0 0
\(442\) −11.2322 0.223318i −0.534263 0.0106221i
\(443\) 4.32246i 0.205366i 0.994714 + 0.102683i \(0.0327428\pi\)
−0.994714 + 0.102683i \(0.967257\pi\)
\(444\) 0 0
\(445\) 27.7687 4.17703i 1.31636 0.198010i
\(446\) 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
\(455\) −18.8169 + 14.3946i −0.882149 + 0.674831i
\(456\) 0 0
\(457\) −13.3594 + 7.71304i −0.624925 + 0.360801i −0.778784 0.627292i \(-0.784163\pi\)
0.153859 + 0.988093i \(0.450830\pi\)
\(458\) −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 \(-0.947690\pi\)
0.986527 0.163599i \(-0.0523102\pi\)
\(464\) −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 \(-0.856663\pi\)
0.900314 0.435241i \(-0.143337\pi\)
\(468\) 0 0
\(469\) 23.5967 1.08959
\(470\) 34.6967 5.21916i 1.60044 0.240742i
\(471\) 0 0
\(472\) −41.5486 23.9881i −1.91243 1.10414i
\(473\) 0.868356i 0.0399271i
\(474\) 0 0
\(475\) −6.52255 + 2.00771i −0.299275 + 0.0921199i
\(476\) −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
\(485\) −25.8516 + 20.6034i −1.17386 + 0.935552i
\(486\) 0 0
\(487\) 27.9935 + 16.1620i 1.26851 + 0.732372i 0.974705 0.223495i \(-0.0717467\pi\)
0.293800 + 0.955867i \(0.405080\pi\)
\(488\) 12.4163 + 7.16858i 0.562062 + 0.324506i
\(489\) 0 0
\(490\) −7.27874 + 5.80107i −0.328820 + 0.262066i
\(491\) 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 \(0.724498\pi\)
\(500\) −3.78816 + 49.9533i −0.169412 + 2.23398i
\(501\) 0 0
\(502\) 9.35181i 0.417392i
\(503\) 24.3433 + 14.0546i 1.08542 + 0.626665i 0.932352 0.361551i \(-0.117753\pi\)
0.153063 + 0.988216i \(0.451086\pi\)
\(504\) 0 0
\(505\) 29.2579 4.40105i 1.30196 0.195844i
\(506\) −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
\(520\) 47.0121 + 19.5544i 2.06162 + 0.857516i
\(521\) −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 0.186706 0.982416i \(-0.440219\pi\)
0.944150 + 0.329516i \(0.106886\pi\)
\(524\) −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
\(530\) 3.61549 0.543852i 0.157047 0.0236234i
\(531\) 0 0
\(532\) 17.9718i 0.779177i
\(533\) −17.3366 31.4558i −0.750933 1.36250i
\(534\) 0 0
\(535\) 3.55018 + 23.6014i 0.153488 + 1.02038i
\(536\) −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 \(-0.979313\pi\)
0.997889 0.0649454i \(-0.0206873\pi\)
\(548\) 33.6527 19.4294i 1.43757 0.829983i
\(549\) 0 0
\(550\) −2.37818 7.72612i −0.101406 0.329443i
\(551\) −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 −0.829140 0.559041i \(-0.811169\pi\)
0.0695738 + 0.997577i \(0.477836\pi\)
\(558\) 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 0.286464 0.958091i \(-0.407520\pi\)
−0.686499 + 0.727131i \(0.740853\pi\)
\(564\) 0 0
\(565\) −9.66965 + 7.70660i −0.406805 + 0.324219i
\(566\) −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
\(575\) 10.4933 + 2.40158i 0.437601 + 0.100153i
\(576\) 0 0
\(577\) 18.3646i 0.764530i −0.924053 0.382265i \(-0.875144\pi\)
0.924053 0.382265i \(-0.124856\pi\)
\(578\) 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 −0.487385 0.873187i \(-0.662049\pi\)
0.512510 + 0.858681i \(0.328716\pi\)
\(588\) 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 \(-0.723738\pi\)
0.646428 0.762975i \(-0.276262\pi\)
\(594\) 0 0
\(595\) −7.95291 + 1.19630i −0.326037 + 0.0490434i
\(596\) −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
\(605\) −14.7680 18.5298i −0.600405 0.753342i
\(606\) 0 0
\(607\) −33.5035 19.3433i −1.35987 0.785119i −0.370261 0.928928i \(-0.620732\pi\)
−0.989606 + 0.143809i \(0.954065\pi\)
\(608\) 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 −0.166269 0.986081i \(-0.553172\pi\)
0.770836 + 0.637033i \(0.219839\pi\)
\(614\) −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 0.884540 0.466464i \(-0.154472\pi\)
0.0383009 + 0.999266i \(0.487805\pi\)
\(618\) 0 0
\(619\) 31.0039 1.24615 0.623075 0.782162i \(-0.285883\pi\)
0.623075 + 0.782162i \(0.285883\pi\)
\(620\) 55.9618 + 70.2165i 2.24748 + 2.81996i
\(621\) 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
\(635\) −5.73149 38.1026i −0.227447 1.51206i
\(636\) 0 0
\(637\) 2.84563 + 5.16315i 0.112748 + 0.204571i
\(638\) 4.85031i 0.192026i
\(639\) 0 0
\(640\) 3.87707 + 25.7745i 0.153254 + 1.01883i
\(641\) 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 0.289946 0.957043i \(-0.406363\pi\)
−0.683851 + 0.729622i \(0.739696\pi\)
\(644\) 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 0.228925 0.973444i \(-0.426479\pi\)
0.957490 + 0.288467i \(0.0931456\pi\)
\(648\) 0 0
\(649\) 4.82456 0.189380
\(650\) 44.5249 + 11.1262i 1.74641 + 0.436404i
\(651\) 0 0
\(652\) 15.5641 8.98591i 0.609535 0.351915i
\(653\) 19.3324 11.1616i 0.756537 0.436787i −0.0715139 0.997440i \(-0.522783\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(654\) 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
\(665\) 1.33407 + 8.86879i 0.0517328 + 0.343917i
\(666\) 0 0
\(667\) 5.59346 + 3.22939i 0.216580 + 0.125042i
\(668\) 13.1670i 0.509448i
\(669\) 0 0
\(670\) −28.4894 35.7464i −1.10064 1.38100i
\(671\) −1.44176 −0.0556587
\(672\) 0 0
\(673\) 4.77457 2.75660i 0.184046 0.106259i −0.405146 0.914252i \(-0.632779\pi\)
0.589192 + 0.807993i \(0.299446\pi\)
\(674\) 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 \(0.0294320\pi\)
−0.995728 + 0.0923316i \(0.970568\pi\)
\(678\) 0 0
\(679\) 21.7215 + 37.6227i 0.833594 + 1.44383i
\(680\) 10.7726 + 13.5167i 0.413112 + 0.518341i
\(681\) 0 0
\(682\) −12.5477 7.24440i −0.480475 0.277403i
\(683\) −10.1866 5.88126i −0.389781 0.225040i 0.292284 0.956331i \(-0.405585\pi\)
−0.682065 + 0.731291i \(0.738918\pi\)
\(684\) 0 0
\(685\) 15.1648 12.0861i 0.579416 0.461788i
\(686\) −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
\(695\) −19.9661 25.0519i −0.757356 0.950272i
\(696\) 0 0
\(697\) 12.1925i 0.461825i
\(698\) −53.6320 30.9644i −2.03000 1.17202i
\(699\) 0 0
\(700\) 64.1758 + 14.6877i 2.42562 + 0.555145i
\(701\) −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
\(715\) −5.07743 + 0.660834i −0.189885 + 0.0247138i
\(716\) −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
\(725\) −3.34648 + 14.6219i −0.124285 + 0.543045i
\(726\) 0 0
\(727\) 26.2596i 0.973916i −0.873425 0.486958i \(-0.838107\pi\)
0.873425 0.486958i \(-0.161893\pi\)
\(728\) 34.6016 57.2716i 1.28242 2.12263i
\(729\) 0 0
\(730\) 58.1279 8.74375i 2.15141 0.323621i
\(731\) 0.836758 + 1.44931i 0.0309486 + 0.0536046i
\(732\) 0 0
\(733\) 31.7811i 1.17386i −0.809637 0.586931i \(-0.800336\pi\)
0.809637 0.586931i \(-0.199664\pi\)
\(734\) 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 −0.449607 0.893227i \(-0.648436\pi\)
0.548753 + 0.835984i \(0.315103\pi\)
\(744\) 0 0
\(745\) −23.9079 29.9978i −0.875917 1.09903i
\(746\) −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 −0.417587 0.908637i \(-0.637124\pi\)
0.578109 + 0.815960i \(0.303791\pi\)
\(758\) −11.4102 6.58767i −0.414436 0.239275i
\(759\) 0 0
\(760\) 15.0733 12.0132i 0.546766 0.435766i
\(761\) −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 \(0.721430\pi\)
\(770\) −10.5053 + 1.58023i −0.378584 + 0.0569476i
\(771\) 0 0
\(772\) 22.2088i 0.799311i
\(773\) −42.6350 24.6153i −1.53347 0.885351i −0.999198 0.0400400i \(-0.987251\pi\)
−0.534275 0.845311i \(-0.679415\pi\)
\(774\) 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