Properties

Label 252.2.w.a.101.7
Level $252$
Weight $2$
Character 252.101
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.w (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.7
Root \(-0.811340 - 1.53027i\) of defining polynomial
Character \(\chi\) \(=\) 252.101
Dual form 252.2.w.a.5.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.68085 - 0.418028i) q^{3} +(1.37166 - 2.37578i) q^{5} +(-2.60476 - 0.463945i) q^{7} +(2.65051 - 1.40528i) q^{9} +O(q^{10})\) \(q+(1.68085 - 0.418028i) q^{3} +(1.37166 - 2.37578i) q^{5} +(-2.60476 - 0.463945i) q^{7} +(2.65051 - 1.40528i) q^{9} +(-0.362306 + 0.209178i) q^{11} +(1.32512 - 0.765056i) q^{13} +(1.31241 - 4.56672i) q^{15} +(-1.95291 + 3.38253i) q^{17} +(-5.11994 + 2.95600i) q^{19} +(-4.57214 + 0.309039i) q^{21} +(7.72884 + 4.46225i) q^{23} +(-1.26290 - 2.18740i) q^{25} +(3.86765 - 3.47005i) q^{27} +(6.00378 + 3.46629i) q^{29} -3.52907i q^{31} +(-0.521540 + 0.503050i) q^{33} +(-4.67507 + 5.55196i) q^{35} +(-4.54861 - 7.87842i) q^{37} +(1.90751 - 1.83988i) q^{39} +(1.06236 + 1.84006i) q^{41} +(-5.77846 + 10.0086i) q^{43} +(0.296944 - 8.22460i) q^{45} -1.77075 q^{47} +(6.56951 + 2.41692i) q^{49} +(-1.86855 + 6.50189i) q^{51} +(-3.39526 - 1.96025i) q^{53} +1.14768i q^{55} +(-7.37015 + 7.10886i) q^{57} -4.05456 q^{59} +1.86437i q^{61} +(-7.55590 + 2.43073i) q^{63} -4.19758i q^{65} -12.7688 q^{67} +(14.8564 + 4.26950i) q^{69} +8.51021i q^{71} +(1.65059 + 0.952971i) q^{73} +(-3.03713 - 3.14877i) q^{75} +(1.04077 - 0.376767i) q^{77} -0.867266 q^{79} +(5.05036 - 7.44942i) q^{81} +(3.45880 - 5.99082i) q^{83} +(5.35744 + 9.27936i) q^{85} +(11.5405 + 3.31656i) q^{87} +(-4.88864 - 8.46738i) q^{89} +(-3.80655 + 1.37800i) q^{91} +(-1.47525 - 5.93183i) q^{93} +16.2185i q^{95} +(0.200411 + 0.115707i) q^{97} +(-0.666342 + 1.06357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + 6q^{9} + O(q^{10}) \) \( 16q - q^{7} + 6q^{9} - 6q^{11} - 3q^{13} - 3q^{15} + 9q^{17} + 6q^{21} + 21q^{23} - 8q^{25} + 9q^{27} + 6q^{29} - 15q^{35} + q^{37} - 3q^{39} - 6q^{41} - 2q^{43} - 30q^{45} - 36q^{47} - 5q^{49} - 33q^{51} + 15q^{57} - 30q^{59} - 15q^{63} + 14q^{67} + 21q^{69} - 57q^{75} + 3q^{77} + 2q^{79} + 18q^{81} + 6q^{85} + 48q^{87} + 21q^{89} + 9q^{91} + 21q^{93} - 3q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.68085 0.418028i 0.970439 0.241348i
\(4\) 0 0
\(5\) 1.37166 2.37578i 0.613425 1.06248i −0.377234 0.926118i \(-0.623125\pi\)
0.990659 0.136365i \(-0.0435419\pi\)
\(6\) 0 0
\(7\) −2.60476 0.463945i −0.984505 0.175355i
\(8\) 0 0
\(9\) 2.65051 1.40528i 0.883502 0.468427i
\(10\) 0 0
\(11\) −0.362306 + 0.209178i −0.109240 + 0.0630695i −0.553624 0.832767i \(-0.686756\pi\)
0.444385 + 0.895836i \(0.353422\pi\)
\(12\) 0 0
\(13\) 1.32512 0.765056i 0.367521 0.212188i −0.304854 0.952399i \(-0.598608\pi\)
0.672375 + 0.740211i \(0.265274\pi\)
\(14\) 0 0
\(15\) 1.31241 4.56672i 0.338862 1.17912i
\(16\) 0 0
\(17\) −1.95291 + 3.38253i −0.473649 + 0.820385i −0.999545 0.0301645i \(-0.990397\pi\)
0.525896 + 0.850549i \(0.323730\pi\)
\(18\) 0 0
\(19\) −5.11994 + 2.95600i −1.17459 + 0.678152i −0.954758 0.297385i \(-0.903886\pi\)
−0.219836 + 0.975537i \(0.570552\pi\)
\(20\) 0 0
\(21\) −4.57214 + 0.309039i −0.997723 + 0.0674379i
\(22\) 0 0
\(23\) 7.72884 + 4.46225i 1.61157 + 0.930443i 0.989006 + 0.147878i \(0.0472444\pi\)
0.622569 + 0.782565i \(0.286089\pi\)
\(24\) 0 0
\(25\) −1.26290 2.18740i −0.252579 0.437480i
\(26\) 0 0
\(27\) 3.86765 3.47005i 0.744330 0.667812i
\(28\) 0 0
\(29\) 6.00378 + 3.46629i 1.11487 + 0.643673i 0.940088 0.340933i \(-0.110743\pi\)
0.174787 + 0.984606i \(0.444076\pi\)
\(30\) 0 0
\(31\) 3.52907i 0.633839i −0.948452 0.316920i \(-0.897351\pi\)
0.948452 0.316920i \(-0.102649\pi\)
\(32\) 0 0
\(33\) −0.521540 + 0.503050i −0.0907885 + 0.0875698i
\(34\) 0 0
\(35\) −4.67507 + 5.55196i −0.790231 + 0.938453i
\(36\) 0 0
\(37\) −4.54861 7.87842i −0.747787 1.29520i −0.948881 0.315633i \(-0.897783\pi\)
0.201095 0.979572i \(-0.435550\pi\)
\(38\) 0 0
\(39\) 1.90751 1.83988i 0.305445 0.294616i
\(40\) 0 0
\(41\) 1.06236 + 1.84006i 0.165913 + 0.287370i 0.936979 0.349385i \(-0.113610\pi\)
−0.771066 + 0.636755i \(0.780276\pi\)
\(42\) 0 0
\(43\) −5.77846 + 10.0086i −0.881208 + 1.52630i −0.0312079 + 0.999513i \(0.509935\pi\)
−0.850000 + 0.526783i \(0.823398\pi\)
\(44\) 0 0
\(45\) 0.296944 8.22460i 0.0442659 1.22605i
\(46\) 0 0
\(47\) −1.77075 −0.258290 −0.129145 0.991626i \(-0.541223\pi\)
−0.129145 + 0.991626i \(0.541223\pi\)
\(48\) 0 0
\(49\) 6.56951 + 2.41692i 0.938502 + 0.345275i
\(50\) 0 0
\(51\) −1.86855 + 6.50189i −0.261649 + 0.910447i
\(52\) 0 0
\(53\) −3.39526 1.96025i −0.466374 0.269261i 0.248346 0.968671i \(-0.420113\pi\)
−0.714721 + 0.699410i \(0.753446\pi\)
\(54\) 0 0
\(55\) 1.14768i 0.154753i
\(56\) 0 0
\(57\) −7.37015 + 7.10886i −0.976200 + 0.941591i
\(58\) 0 0
\(59\) −4.05456 −0.527859 −0.263929 0.964542i \(-0.585019\pi\)
−0.263929 + 0.964542i \(0.585019\pi\)
\(60\) 0 0
\(61\) 1.86437i 0.238708i 0.992852 + 0.119354i \(0.0380823\pi\)
−0.992852 + 0.119354i \(0.961918\pi\)
\(62\) 0 0
\(63\) −7.55590 + 2.43073i −0.951953 + 0.306243i
\(64\) 0 0
\(65\) 4.19758i 0.520646i
\(66\) 0 0
\(67\) −12.7688 −1.55996 −0.779979 0.625805i \(-0.784770\pi\)
−0.779979 + 0.625805i \(0.784770\pi\)
\(68\) 0 0
\(69\) 14.8564 + 4.26950i 1.78850 + 0.513987i
\(70\) 0 0
\(71\) 8.51021i 1.00998i 0.863126 + 0.504988i \(0.168503\pi\)
−0.863126 + 0.504988i \(0.831497\pi\)
\(72\) 0 0
\(73\) 1.65059 + 0.952971i 0.193187 + 0.111537i 0.593474 0.804853i \(-0.297756\pi\)
−0.400286 + 0.916390i \(0.631089\pi\)
\(74\) 0 0
\(75\) −3.03713 3.14877i −0.350698 0.363588i
\(76\) 0 0
\(77\) 1.04077 0.376767i 0.118606 0.0429366i
\(78\) 0 0
\(79\) −0.867266 −0.0975750 −0.0487875 0.998809i \(-0.515536\pi\)
−0.0487875 + 0.998809i \(0.515536\pi\)
\(80\) 0 0
\(81\) 5.05036 7.44942i 0.561151 0.827713i
\(82\) 0 0
\(83\) 3.45880 5.99082i 0.379653 0.657578i −0.611359 0.791354i \(-0.709377\pi\)
0.991012 + 0.133775i \(0.0427100\pi\)
\(84\) 0 0
\(85\) 5.35744 + 9.27936i 0.581096 + 1.00649i
\(86\) 0 0
\(87\) 11.5405 + 3.31656i 1.23727 + 0.355572i
\(88\) 0 0
\(89\) −4.88864 8.46738i −0.518195 0.897540i −0.999777 0.0211389i \(-0.993271\pi\)
0.481581 0.876401i \(-0.340063\pi\)
\(90\) 0 0
\(91\) −3.80655 + 1.37800i −0.399035 + 0.144454i
\(92\) 0 0
\(93\) −1.47525 5.93183i −0.152976 0.615102i
\(94\) 0 0
\(95\) 16.2185i 1.66398i
\(96\) 0 0
\(97\) 0.200411 + 0.115707i 0.0203486 + 0.0117483i 0.510140 0.860091i \(-0.329594\pi\)
−0.489791 + 0.871840i \(0.662927\pi\)
\(98\) 0 0
\(99\) −0.666342 + 1.06357i −0.0669699 + 0.106893i
\(100\) 0 0
\(101\) −7.14031 12.3674i −0.710487 1.23060i −0.964674 0.263445i \(-0.915141\pi\)
0.254187 0.967155i \(-0.418192\pi\)
\(102\) 0 0
\(103\) −9.30617 5.37292i −0.916964 0.529410i −0.0342991 0.999412i \(-0.510920\pi\)
−0.882665 + 0.470002i \(0.844253\pi\)
\(104\) 0 0
\(105\) −5.53721 + 11.2863i −0.540376 + 1.10143i
\(106\) 0 0
\(107\) −5.50534 + 3.17851i −0.532221 + 0.307278i −0.741920 0.670488i \(-0.766085\pi\)
0.209699 + 0.977766i \(0.432751\pi\)
\(108\) 0 0
\(109\) 2.58036 4.46932i 0.247154 0.428083i −0.715581 0.698530i \(-0.753838\pi\)
0.962735 + 0.270447i \(0.0871714\pi\)
\(110\) 0 0
\(111\) −10.9389 11.3410i −1.03828 1.07644i
\(112\) 0 0
\(113\) 9.19186 5.30692i 0.864697 0.499233i −0.000885276 1.00000i \(-0.500282\pi\)
0.865582 + 0.500766i \(0.166948\pi\)
\(114\) 0 0
\(115\) 21.2027 12.2414i 1.97716 1.14151i
\(116\) 0 0
\(117\) 2.43711 3.88995i 0.225311 0.359626i
\(118\) 0 0
\(119\) 6.65615 7.90463i 0.610168 0.724616i
\(120\) 0 0
\(121\) −5.41249 + 9.37471i −0.492044 + 0.852246i
\(122\) 0 0
\(123\) 2.55487 + 2.64877i 0.230365 + 0.238832i
\(124\) 0 0
\(125\) 6.78753 0.607096
\(126\) 0 0
\(127\) 10.2909 0.913169 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(128\) 0 0
\(129\) −5.52886 + 19.2385i −0.486789 + 1.69385i
\(130\) 0 0
\(131\) 9.83048 17.0269i 0.858893 1.48765i −0.0140928 0.999901i \(-0.504486\pi\)
0.872986 0.487746i \(-0.162181\pi\)
\(132\) 0 0
\(133\) 14.7076 5.32428i 1.27531 0.461674i
\(134\) 0 0
\(135\) −2.93899 13.9484i −0.252948 1.20049i
\(136\) 0 0
\(137\) −4.66411 + 2.69282i −0.398481 + 0.230063i −0.685829 0.727763i \(-0.740560\pi\)
0.287347 + 0.957827i \(0.407227\pi\)
\(138\) 0 0
\(139\) 14.7839 8.53549i 1.25395 0.723971i 0.282062 0.959396i \(-0.408982\pi\)
0.971892 + 0.235425i \(0.0756484\pi\)
\(140\) 0 0
\(141\) −2.97636 + 0.740221i −0.250655 + 0.0623379i
\(142\) 0 0
\(143\) −0.320065 + 0.554369i −0.0267652 + 0.0463587i
\(144\) 0 0
\(145\) 16.4703 9.50912i 1.36778 0.789690i
\(146\) 0 0
\(147\) 12.0527 + 1.31625i 0.994090 + 0.108562i
\(148\) 0 0
\(149\) 9.31162 + 5.37607i 0.762838 + 0.440425i 0.830314 0.557296i \(-0.188161\pi\)
−0.0674758 + 0.997721i \(0.521495\pi\)
\(150\) 0 0
\(151\) −3.78223 6.55102i −0.307794 0.533115i 0.670086 0.742284i \(-0.266257\pi\)
−0.977879 + 0.209169i \(0.932924\pi\)
\(152\) 0 0
\(153\) −0.422776 + 11.7098i −0.0341794 + 0.946682i
\(154\) 0 0
\(155\) −8.38430 4.84068i −0.673443 0.388812i
\(156\) 0 0
\(157\) 12.2764i 0.979763i −0.871789 0.489882i \(-0.837040\pi\)
0.871789 0.489882i \(-0.162960\pi\)
\(158\) 0 0
\(159\) −6.52635 1.87558i −0.517573 0.148743i
\(160\) 0 0
\(161\) −18.0615 15.2088i −1.42345 1.19862i
\(162\) 0 0
\(163\) 5.91745 + 10.2493i 0.463490 + 0.802789i 0.999132 0.0416566i \(-0.0132635\pi\)
−0.535642 + 0.844445i \(0.679930\pi\)
\(164\) 0 0
\(165\) 0.479763 + 1.92908i 0.0373495 + 0.150179i
\(166\) 0 0
\(167\) 6.78854 + 11.7581i 0.525313 + 0.909869i 0.999565 + 0.0294798i \(0.00938508\pi\)
−0.474252 + 0.880389i \(0.657282\pi\)
\(168\) 0 0
\(169\) −5.32938 + 9.23075i −0.409952 + 0.710058i
\(170\) 0 0
\(171\) −9.41641 + 15.0298i −0.720091 + 1.14936i
\(172\) 0 0
\(173\) −16.6217 −1.26372 −0.631862 0.775081i \(-0.717709\pi\)
−0.631862 + 0.775081i \(0.717709\pi\)
\(174\) 0 0
\(175\) 2.27471 + 6.28356i 0.171952 + 0.474993i
\(176\) 0 0
\(177\) −6.81510 + 1.69492i −0.512254 + 0.127398i
\(178\) 0 0
\(179\) 14.8080 + 8.54942i 1.10680 + 0.639014i 0.938000 0.346636i \(-0.112676\pi\)
0.168805 + 0.985650i \(0.446009\pi\)
\(180\) 0 0
\(181\) 18.2171i 1.35407i 0.735952 + 0.677034i \(0.236735\pi\)
−0.735952 + 0.677034i \(0.763265\pi\)
\(182\) 0 0
\(183\) 0.779357 + 3.13372i 0.0576117 + 0.231651i
\(184\) 0 0
\(185\) −24.9566 −1.83484
\(186\) 0 0
\(187\) 1.63402i 0.119491i
\(188\) 0 0
\(189\) −11.6842 + 7.24426i −0.849901 + 0.526943i
\(190\) 0 0
\(191\) 20.9994i 1.51946i −0.650239 0.759730i \(-0.725331\pi\)
0.650239 0.759730i \(-0.274669\pi\)
\(192\) 0 0
\(193\) −6.97483 −0.502059 −0.251030 0.967979i \(-0.580769\pi\)
−0.251030 + 0.967979i \(0.580769\pi\)
\(194\) 0 0
\(195\) −1.75471 7.05550i −0.125657 0.505255i
\(196\) 0 0
\(197\) 16.0756i 1.14534i −0.819786 0.572670i \(-0.805908\pi\)
0.819786 0.572670i \(-0.194092\pi\)
\(198\) 0 0
\(199\) −5.44956 3.14630i −0.386309 0.223036i 0.294251 0.955728i \(-0.404930\pi\)
−0.680560 + 0.732693i \(0.738263\pi\)
\(200\) 0 0
\(201\) −21.4624 + 5.33772i −1.51384 + 0.376493i
\(202\) 0 0
\(203\) −14.0302 11.8143i −0.984729 0.829198i
\(204\) 0 0
\(205\) 5.82879 0.407100
\(206\) 0 0
\(207\) 26.7561 + 0.966012i 1.85967 + 0.0671425i
\(208\) 0 0
\(209\) 1.23666 2.14195i 0.0855414 0.148162i
\(210\) 0 0
\(211\) −1.29814 2.24844i −0.0893674 0.154789i 0.817876 0.575394i \(-0.195151\pi\)
−0.907244 + 0.420605i \(0.861818\pi\)
\(212\) 0 0
\(213\) 3.55750 + 14.3044i 0.243756 + 0.980120i
\(214\) 0 0
\(215\) 15.8522 + 27.4568i 1.08111 + 1.87254i
\(216\) 0 0
\(217\) −1.63729 + 9.19236i −0.111147 + 0.624018i
\(218\) 0 0
\(219\) 3.17277 + 0.911807i 0.214396 + 0.0616142i
\(220\) 0 0
\(221\) 5.97633i 0.402011i
\(222\) 0 0
\(223\) −20.7215 11.9636i −1.38762 0.801141i −0.394571 0.918866i \(-0.629107\pi\)
−0.993046 + 0.117725i \(0.962440\pi\)
\(224\) 0 0
\(225\) −6.42123 4.02299i −0.428082 0.268200i
\(226\) 0 0
\(227\) −1.86609 3.23216i −0.123857 0.214526i 0.797429 0.603413i \(-0.206193\pi\)
−0.921285 + 0.388887i \(0.872860\pi\)
\(228\) 0 0
\(229\) 18.2455 + 10.5341i 1.20570 + 0.696111i 0.961817 0.273694i \(-0.0882457\pi\)
0.243882 + 0.969805i \(0.421579\pi\)
\(230\) 0 0
\(231\) 1.59187 1.06836i 0.104738 0.0702928i
\(232\) 0 0
\(233\) −11.0542 + 6.38215i −0.724186 + 0.418109i −0.816291 0.577640i \(-0.803974\pi\)
0.0921057 + 0.995749i \(0.470640\pi\)
\(234\) 0 0
\(235\) −2.42886 + 4.20691i −0.158441 + 0.274429i
\(236\) 0 0
\(237\) −1.45774 + 0.362541i −0.0946905 + 0.0235496i
\(238\) 0 0
\(239\) 11.0521 6.38091i 0.714899 0.412747i −0.0979736 0.995189i \(-0.531236\pi\)
0.812872 + 0.582442i \(0.197903\pi\)
\(240\) 0 0
\(241\) −2.63438 + 1.52096i −0.169695 + 0.0979737i −0.582442 0.812872i \(-0.697903\pi\)
0.412747 + 0.910846i \(0.364569\pi\)
\(242\) 0 0
\(243\) 5.37484 14.6325i 0.344796 0.938678i
\(244\) 0 0
\(245\) 14.7532 12.2925i 0.942549 0.785341i
\(246\) 0 0
\(247\) −4.52301 + 7.83408i −0.287792 + 0.498470i
\(248\) 0 0
\(249\) 3.30940 11.5155i 0.209725 0.729768i
\(250\) 0 0
\(251\) −6.32067 −0.398957 −0.199478 0.979902i \(-0.563925\pi\)
−0.199478 + 0.979902i \(0.563925\pi\)
\(252\) 0 0
\(253\) −3.73361 −0.234730
\(254\) 0 0
\(255\) 12.8841 + 13.3576i 0.806832 + 0.836488i
\(256\) 0 0
\(257\) −12.2538 + 21.2242i −0.764372 + 1.32393i 0.176206 + 0.984353i \(0.443617\pi\)
−0.940578 + 0.339577i \(0.889716\pi\)
\(258\) 0 0
\(259\) 8.19287 + 22.6317i 0.509080 + 1.40626i
\(260\) 0 0
\(261\) 20.7842 + 0.750401i 1.28651 + 0.0464486i
\(262\) 0 0
\(263\) −21.1163 + 12.1915i −1.30208 + 0.751759i −0.980761 0.195211i \(-0.937461\pi\)
−0.321323 + 0.946970i \(0.604128\pi\)
\(264\) 0 0
\(265\) −9.31427 + 5.37760i −0.572171 + 0.330343i
\(266\) 0 0
\(267\) −11.7567 12.1888i −0.719496 0.745942i
\(268\) 0 0
\(269\) 4.94525 8.56542i 0.301517 0.522243i −0.674963 0.737852i \(-0.735840\pi\)
0.976480 + 0.215609i \(0.0691737\pi\)
\(270\) 0 0
\(271\) −5.10505 + 2.94740i −0.310110 + 0.179042i −0.646976 0.762511i \(-0.723966\pi\)
0.336866 + 0.941553i \(0.390633\pi\)
\(272\) 0 0
\(273\) −5.82219 + 3.90746i −0.352375 + 0.236490i
\(274\) 0 0
\(275\) 0.915111 + 0.528340i 0.0551833 + 0.0318601i
\(276\) 0 0
\(277\) −11.6469 20.1731i −0.699796 1.21208i −0.968537 0.248870i \(-0.919941\pi\)
0.268741 0.963213i \(-0.413392\pi\)
\(278\) 0 0
\(279\) −4.95933 9.35381i −0.296908 0.559998i
\(280\) 0 0
\(281\) 21.7962 + 12.5840i 1.30025 + 0.750700i 0.980447 0.196784i \(-0.0630499\pi\)
0.319803 + 0.947484i \(0.396383\pi\)
\(282\) 0 0
\(283\) 9.96439i 0.592322i −0.955138 0.296161i \(-0.904294\pi\)
0.955138 0.296161i \(-0.0957064\pi\)
\(284\) 0 0
\(285\) 6.77977 + 27.2608i 0.401599 + 1.61479i
\(286\) 0 0
\(287\) −1.91350 5.28579i −0.112951 0.312011i
\(288\) 0 0
\(289\) 0.872317 + 1.51090i 0.0513128 + 0.0888764i
\(290\) 0 0
\(291\) 0.385229 + 0.110709i 0.0225825 + 0.00648989i
\(292\) 0 0
\(293\) −6.79065 11.7618i −0.396714 0.687129i 0.596604 0.802536i \(-0.296516\pi\)
−0.993318 + 0.115406i \(0.963183\pi\)
\(294\) 0 0
\(295\) −5.56147 + 9.63275i −0.323801 + 0.560841i
\(296\) 0 0
\(297\) −0.675418 + 2.06625i −0.0391917 + 0.119896i
\(298\) 0 0
\(299\) 13.6555 0.789717
\(300\) 0 0
\(301\) 19.6949 23.3891i 1.13520 1.34812i
\(302\) 0 0
\(303\) −17.1717 17.8028i −0.986487 1.02275i
\(304\) 0 0
\(305\) 4.42933 + 2.55728i 0.253623 + 0.146429i
\(306\) 0 0
\(307\) 16.9849i 0.969381i −0.874686 0.484691i \(-0.838932\pi\)
0.874686 0.484691i \(-0.161068\pi\)
\(308\) 0 0
\(309\) −17.8883 5.14083i −1.01763 0.292452i
\(310\) 0 0
\(311\) 0.00297881 0.000168913 8.44563e−5 1.00000i \(-0.499973\pi\)
8.44563e−5 1.00000i \(0.499973\pi\)
\(312\) 0 0
\(313\) 12.2576i 0.692838i 0.938080 + 0.346419i \(0.112602\pi\)
−0.938080 + 0.346419i \(0.887398\pi\)
\(314\) 0 0
\(315\) −4.58922 + 21.2853i −0.258573 + 1.19929i
\(316\) 0 0
\(317\) 23.0950i 1.29714i 0.761154 + 0.648571i \(0.224633\pi\)
−0.761154 + 0.648571i \(0.775367\pi\)
\(318\) 0 0
\(319\) −2.90028 −0.162384
\(320\) 0 0
\(321\) −7.92494 + 7.64397i −0.442327 + 0.426645i
\(322\) 0 0
\(323\) 23.0911i 1.28482i
\(324\) 0 0
\(325\) −3.34697 1.93237i −0.185656 0.107189i
\(326\) 0 0
\(327\) 2.46890 8.59091i 0.136530 0.475078i
\(328\) 0 0
\(329\) 4.61236 + 0.821528i 0.254288 + 0.0452923i
\(330\) 0 0
\(331\) −3.46213 −0.190296 −0.0951479 0.995463i \(-0.530332\pi\)
−0.0951479 + 0.995463i \(0.530332\pi\)
\(332\) 0 0
\(333\) −23.1275 14.4897i −1.26738 0.794032i
\(334\) 0 0
\(335\) −17.5145 + 30.3359i −0.956917 + 1.65743i
\(336\) 0 0
\(337\) −9.13018 15.8139i −0.497352 0.861440i 0.502643 0.864494i \(-0.332361\pi\)
−0.999995 + 0.00305455i \(0.999028\pi\)
\(338\) 0 0
\(339\) 13.2317 12.7626i 0.718646 0.693168i
\(340\) 0 0
\(341\) 0.738202 + 1.27860i 0.0399759 + 0.0692403i
\(342\) 0 0
\(343\) −15.9907 9.34339i −0.863414 0.504496i
\(344\) 0 0
\(345\) 30.5213 29.4392i 1.64321 1.58495i
\(346\) 0 0
\(347\) 5.33917i 0.286622i 0.989678 + 0.143311i \(0.0457749\pi\)
−0.989678 + 0.143311i \(0.954225\pi\)
\(348\) 0 0
\(349\) −0.0136817 0.00789914i −0.000732365 0.000422831i 0.499634 0.866237i \(-0.333468\pi\)
−0.500366 + 0.865814i \(0.666801\pi\)
\(350\) 0 0
\(351\) 2.47030 7.55719i 0.131855 0.403373i
\(352\) 0 0
\(353\) 17.1543 + 29.7121i 0.913029 + 1.58141i 0.809761 + 0.586760i \(0.199597\pi\)
0.103268 + 0.994654i \(0.467070\pi\)
\(354\) 0 0
\(355\) 20.2184 + 11.6731i 1.07308 + 0.619544i
\(356\) 0 0
\(357\) 7.88363 16.0689i 0.417246 0.850459i
\(358\) 0 0
\(359\) −5.42754 + 3.13359i −0.286454 + 0.165385i −0.636342 0.771407i \(-0.719553\pi\)
0.349887 + 0.936792i \(0.386220\pi\)
\(360\) 0 0
\(361\) 7.97583 13.8145i 0.419781 0.727081i
\(362\) 0 0
\(363\) −5.17869 + 18.0200i −0.271811 + 0.945807i
\(364\) 0 0
\(365\) 4.52811 2.61430i 0.237012 0.136839i
\(366\) 0 0
\(367\) 16.4888 9.51984i 0.860711 0.496931i −0.00353959 0.999994i \(-0.501127\pi\)
0.864250 + 0.503062i \(0.167793\pi\)
\(368\) 0 0
\(369\) 5.40160 + 3.38418i 0.281196 + 0.176174i
\(370\) 0 0
\(371\) 7.93437 + 6.68119i 0.411932 + 0.346870i
\(372\) 0 0
\(373\) −5.41901 + 9.38600i −0.280586 + 0.485989i −0.971529 0.236920i \(-0.923862\pi\)
0.690943 + 0.722909i \(0.257195\pi\)
\(374\) 0 0
\(375\) 11.4088 2.83738i 0.589149 0.146521i
\(376\) 0 0
\(377\) 10.6076 0.546320
\(378\) 0 0
\(379\) 0.700312 0.0359726 0.0179863 0.999838i \(-0.494274\pi\)
0.0179863 + 0.999838i \(0.494274\pi\)
\(380\) 0 0
\(381\) 17.2974 4.30188i 0.886174 0.220392i
\(382\) 0 0
\(383\) 19.0235 32.9497i 0.972056 1.68365i 0.282729 0.959200i \(-0.408760\pi\)
0.689327 0.724451i \(-0.257906\pi\)
\(384\) 0 0
\(385\) 0.532461 2.98943i 0.0271367 0.152356i
\(386\) 0 0
\(387\) −1.25095 + 34.6482i −0.0635896 + 1.76127i
\(388\) 0 0
\(389\) 16.6958 9.63934i 0.846512 0.488734i −0.0129603 0.999916i \(-0.504125\pi\)
0.859473 + 0.511182i \(0.170792\pi\)
\(390\) 0 0
\(391\) −30.1874 + 17.4287i −1.52664 + 0.881407i
\(392\) 0 0
\(393\) 9.40584 32.7290i 0.474462 1.65096i
\(394\) 0 0
\(395\) −1.18959 + 2.06044i −0.0598549 + 0.103672i
\(396\) 0 0
\(397\) −17.3610 + 10.0234i −0.871325 + 0.503059i −0.867788 0.496934i \(-0.834459\pi\)
−0.00353639 + 0.999994i \(0.501126\pi\)
\(398\) 0 0
\(399\) 22.4956 15.0975i 1.12619 0.755820i
\(400\) 0 0
\(401\) 26.4232 + 15.2554i 1.31951 + 0.761820i 0.983650 0.180092i \(-0.0576395\pi\)
0.335861 + 0.941912i \(0.390973\pi\)
\(402\) 0 0
\(403\) −2.69993 4.67642i −0.134493 0.232949i
\(404\) 0 0
\(405\) −10.7708 22.2166i −0.535207 1.10395i
\(406\) 0 0
\(407\) 3.29598 + 1.90294i 0.163376 + 0.0943250i
\(408\) 0 0
\(409\) 0.173933i 0.00860045i −0.999991 0.00430023i \(-0.998631\pi\)
0.999991 0.00430023i \(-0.00136881\pi\)
\(410\) 0 0
\(411\) −6.71398 + 6.47595i −0.331176 + 0.319435i
\(412\) 0 0
\(413\) 10.5611 + 1.88109i 0.519680 + 0.0925624i
\(414\) 0 0
\(415\) −9.48860 16.4347i −0.465777 0.806749i
\(416\) 0 0
\(417\) 21.2814 20.5269i 1.04216 1.00521i
\(418\) 0 0
\(419\) −14.0690 24.3682i −0.687316 1.19047i −0.972703 0.232054i \(-0.925455\pi\)
0.285387 0.958412i \(-0.407878\pi\)
\(420\) 0 0
\(421\) −1.56130 + 2.70424i −0.0760929 + 0.131797i −0.901561 0.432652i \(-0.857578\pi\)
0.825468 + 0.564449i \(0.190911\pi\)
\(422\) 0 0
\(423\) −4.69337 + 2.48840i −0.228200 + 0.120990i
\(424\) 0 0
\(425\) 9.86527 0.478536
\(426\) 0 0
\(427\) 0.864963 4.85622i 0.0418585 0.235009i
\(428\) 0 0
\(429\) −0.306240 + 1.06561i −0.0147854 + 0.0514480i
\(430\) 0 0
\(431\) 8.58876 + 4.95872i 0.413706 + 0.238853i 0.692381 0.721532i \(-0.256562\pi\)
−0.278675 + 0.960385i \(0.589895\pi\)
\(432\) 0 0
\(433\) 17.1274i 0.823092i −0.911389 0.411546i \(-0.864989\pi\)
0.911389 0.411546i \(-0.135011\pi\)
\(434\) 0 0
\(435\) 23.7090 22.8684i 1.13676 1.09646i
\(436\) 0 0
\(437\) −52.7616 −2.52393
\(438\) 0 0
\(439\) 21.4537i 1.02393i 0.859006 + 0.511965i \(0.171082\pi\)
−0.859006 + 0.511965i \(0.828918\pi\)
\(440\) 0 0
\(441\) 20.8090 2.82594i 0.990904 0.134569i
\(442\) 0 0
\(443\) 6.74738i 0.320578i −0.987070 0.160289i \(-0.948757\pi\)
0.987070 0.160289i \(-0.0512425\pi\)
\(444\) 0 0
\(445\) −26.8222 −1.27149
\(446\) 0 0
\(447\) 17.8988 + 5.14384i 0.846583 + 0.243295i
\(448\) 0 0
\(449\) 5.81624i 0.274485i −0.990537 0.137243i \(-0.956176\pi\)
0.990537 0.137243i \(-0.0438240\pi\)
\(450\) 0 0
\(451\) −0.769801 0.444445i −0.0362485 0.0209281i
\(452\) 0 0
\(453\) −9.09587 9.43020i −0.427361 0.443069i
\(454\) 0 0
\(455\) −1.94745 + 10.9337i −0.0912977 + 0.512579i
\(456\) 0 0
\(457\) −33.3898 −1.56191 −0.780954 0.624588i \(-0.785267\pi\)
−0.780954 + 0.624588i \(0.785267\pi\)
\(458\) 0 0
\(459\) 4.18440 + 19.8591i 0.195311 + 0.926946i
\(460\) 0 0
\(461\) −18.5154 + 32.0696i −0.862347 + 1.49363i 0.00730959 + 0.999973i \(0.497673\pi\)
−0.869657 + 0.493656i \(0.835660\pi\)
\(462\) 0 0
\(463\) 10.5618 + 18.2935i 0.490848 + 0.850173i 0.999944 0.0105362i \(-0.00335383\pi\)
−0.509097 + 0.860709i \(0.670020\pi\)
\(464\) 0 0
\(465\) −16.1163 4.63158i −0.747374 0.214784i
\(466\) 0 0
\(467\) 9.30470 + 16.1162i 0.430570 + 0.745770i 0.996922 0.0783937i \(-0.0249791\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(468\) 0 0
\(469\) 33.2596 + 5.92402i 1.53579 + 0.273546i
\(470\) 0 0
\(471\) −5.13187 20.6348i −0.236464 0.950800i
\(472\) 0 0
\(473\) 4.83490i 0.222309i
\(474\) 0 0
\(475\) 12.9319 + 7.46624i 0.593356 + 0.342574i
\(476\) 0 0
\(477\) −11.7539 0.424366i −0.538172 0.0194304i
\(478\) 0 0
\(479\) 7.16703 + 12.4137i 0.327470 + 0.567194i 0.982009 0.188834i \(-0.0604707\pi\)
−0.654539 + 0.756028i \(0.727137\pi\)
\(480\) 0 0
\(481\) −12.0549 6.95988i −0.549655 0.317343i
\(482\) 0 0
\(483\) −36.7164 18.0135i −1.67065 0.819644i
\(484\) 0 0
\(485\) 0.549791 0.317422i 0.0249647 0.0144134i
\(486\) 0 0
\(487\) −5.64829 + 9.78313i −0.255949 + 0.443316i −0.965153 0.261687i \(-0.915721\pi\)
0.709204 + 0.705003i \(0.249054\pi\)
\(488\) 0 0
\(489\) 14.2308 + 14.7539i 0.643541 + 0.667195i
\(490\) 0 0
\(491\) −8.84097 + 5.10434i −0.398988 + 0.230356i −0.686047 0.727557i \(-0.740656\pi\)
0.287059 + 0.957913i \(0.407322\pi\)
\(492\) 0 0
\(493\) −23.4496 + 13.5387i −1.05612 + 0.609751i
\(494\) 0 0
\(495\) 1.61282 + 3.04194i 0.0724907 + 0.136725i
\(496\) 0 0
\(497\) 3.94827 22.1670i 0.177104 0.994327i
\(498\) 0 0
\(499\) 9.56672 16.5701i 0.428265 0.741777i −0.568454 0.822715i \(-0.692458\pi\)
0.996719 + 0.0809379i \(0.0257915\pi\)
\(500\) 0 0
\(501\) 16.3257 + 16.9258i 0.729379 + 0.756188i
\(502\) 0 0
\(503\) 0.268917 0.0119904 0.00599520 0.999982i \(-0.498092\pi\)
0.00599520 + 0.999982i \(0.498092\pi\)
\(504\) 0 0
\(505\) −39.1763 −1.74332
\(506\) 0 0
\(507\) −5.09917 + 17.7433i −0.226462 + 0.788009i
\(508\) 0 0
\(509\) 10.9439 18.9553i 0.485079 0.840181i −0.514774 0.857326i \(-0.672124\pi\)
0.999853 + 0.0171449i \(0.00545767\pi\)
\(510\) 0 0
\(511\) −3.85727 3.24804i −0.170636 0.143685i
\(512\) 0 0
\(513\) −9.54468 + 29.1992i −0.421408 + 1.28918i
\(514\) 0 0
\(515\) −25.5298 + 14.7396i −1.12498 + 0.649506i
\(516\) 0 0
\(517\) 0.641553 0.370401i 0.0282155 0.0162902i
\(518\) 0 0
\(519\) −27.9386 + 6.94833i −1.22637 + 0.304998i
\(520\) 0 0
\(521\) 0.856074 1.48276i 0.0375053 0.0649610i −0.846663 0.532129i \(-0.821392\pi\)
0.884169 + 0.467168i \(0.154726\pi\)
\(522\) 0 0
\(523\) 7.16320 4.13568i 0.313225 0.180841i −0.335144 0.942167i \(-0.608785\pi\)
0.648369 + 0.761326i \(0.275452\pi\)
\(524\) 0 0
\(525\) 6.45014 + 9.61083i 0.281507 + 0.419451i
\(526\) 0 0
\(527\) 11.9372 + 6.89193i 0.519992 + 0.300217i
\(528\) 0 0
\(529\) 28.3233 + 49.0574i 1.23145 + 2.13293i
\(530\) 0 0
\(531\) −10.7466 + 5.69780i −0.466364 + 0.247263i
\(532\) 0 0
\(533\) 2.81550 + 1.62553i 0.121953 + 0.0704096i
\(534\) 0 0
\(535\) 17.4393i 0.753967i
\(536\) 0 0
\(537\) 28.4640 + 8.18012i 1.22831 + 0.352998i
\(538\) 0 0
\(539\) −2.88574 + 0.498528i −0.124298 + 0.0214731i
\(540\) 0 0
\(541\) −10.1997 17.6664i −0.438518 0.759536i 0.559057 0.829129i \(-0.311163\pi\)
−0.997575 + 0.0695932i \(0.977830\pi\)
\(542\) 0 0
\(543\) 7.61526 + 30.6202i 0.326802 + 1.31404i
\(544\) 0 0
\(545\) −7.07875 12.2608i −0.303220 0.525193i
\(546\) 0 0
\(547\) 18.9630 32.8449i 0.810801 1.40435i −0.101503 0.994835i \(-0.532365\pi\)
0.912304 0.409513i \(-0.134301\pi\)
\(548\) 0 0
\(549\) 2.61996 + 4.94152i 0.111817 + 0.210899i
\(550\) 0 0
\(551\) −40.9853 −1.74603
\(552\) 0 0
\(553\) 2.25902 + 0.402363i 0.0960631 + 0.0171102i
\(554\) 0 0
\(555\) −41.9482 + 10.4325i −1.78060 + 0.442836i
\(556\) 0 0
\(557\) 14.5919 + 8.42463i 0.618278 + 0.356963i 0.776198 0.630489i \(-0.217146\pi\)
−0.157920 + 0.987452i \(0.550479\pi\)
\(558\) 0 0
\(559\) 17.6834i 0.747928i
\(560\) 0 0
\(561\) −0.683064 2.74654i −0.0288390 0.115959i
\(562\) 0 0
\(563\) −16.5607 −0.697950 −0.348975 0.937132i \(-0.613470\pi\)
−0.348975 + 0.937132i \(0.613470\pi\)
\(564\) 0 0
\(565\) 29.1171i 1.22497i
\(566\) 0 0
\(567\) −16.6111 + 17.0608i −0.697600 + 0.716488i
\(568\) 0 0
\(569\) 6.34919i 0.266172i −0.991104 0.133086i \(-0.957511\pi\)
0.991104 0.133086i \(-0.0424886\pi\)
\(570\) 0 0
\(571\) 45.7406 1.91418 0.957092 0.289785i \(-0.0935838\pi\)
0.957092 + 0.289785i \(0.0935838\pi\)
\(572\) 0 0
\(573\) −8.77831 35.2967i −0.366719 1.47454i
\(574\) 0 0
\(575\) 22.5414i 0.940043i
\(576\) 0 0
\(577\) 15.3719 + 8.87497i 0.639940 + 0.369470i 0.784592 0.620013i \(-0.212873\pi\)
−0.144651 + 0.989483i \(0.546206\pi\)
\(578\) 0 0
\(579\) −11.7236 + 2.91567i −0.487218 + 0.121171i
\(580\) 0 0
\(581\) −11.7888 + 13.9999i −0.489080 + 0.580815i
\(582\) 0 0
\(583\) 1.64016 0.0679287
\(584\) 0 0
\(585\) −5.89879 11.1257i −0.243885 0.459992i
\(586\) 0 0
\(587\) 4.41148 7.64091i 0.182081 0.315374i −0.760508 0.649329i \(-0.775050\pi\)
0.942589 + 0.333955i \(0.108383\pi\)
\(588\) 0 0
\(589\) 10.4319 + 18.0686i 0.429839 + 0.744503i
\(590\) 0 0
\(591\) −6.72005 27.0207i −0.276426 1.11148i
\(592\) 0 0
\(593\) 4.24849 + 7.35860i 0.174465 + 0.302181i 0.939976 0.341241i \(-0.110847\pi\)
−0.765511 + 0.643422i \(0.777514\pi\)
\(594\) 0 0
\(595\) −9.64972 26.6560i −0.395600 1.09279i
\(596\) 0 0
\(597\) −10.4751 3.01040i −0.428718 0.123207i
\(598\) 0 0
\(599\) 3.70842i 0.151522i 0.997126 + 0.0757609i \(0.0241386\pi\)
−0.997126 + 0.0757609i \(0.975861\pi\)
\(600\) 0 0
\(601\) 6.14043 + 3.54518i 0.250473 + 0.144611i 0.619981 0.784617i \(-0.287140\pi\)
−0.369508 + 0.929228i \(0.620474\pi\)
\(602\) 0 0
\(603\) −33.8438 + 17.9438i −1.37823 + 0.730727i
\(604\) 0 0
\(605\) 14.8482 + 25.7178i 0.603664 + 1.04558i
\(606\) 0 0
\(607\) −29.4396 16.9970i −1.19492 0.689886i −0.235500 0.971874i \(-0.575673\pi\)
−0.959418 + 0.281988i \(0.909006\pi\)
\(608\) 0 0
\(609\) −28.5214 13.9930i −1.15574 0.567023i
\(610\) 0 0
\(611\) −2.34644 + 1.35472i −0.0949270 + 0.0548061i
\(612\) 0 0
\(613\) −11.6761 + 20.2237i −0.471595 + 0.816827i −0.999472 0.0324944i \(-0.989655\pi\)
0.527877 + 0.849321i \(0.322988\pi\)
\(614\) 0 0
\(615\) 9.79732 2.43659i 0.395066 0.0982530i
\(616\) 0 0
\(617\) −39.0817 + 22.5638i −1.57337 + 0.908386i −0.577618 + 0.816307i \(0.696018\pi\)
−0.995752 + 0.0920787i \(0.970649\pi\)
\(618\) 0 0
\(619\) −7.97914 + 4.60676i −0.320709 + 0.185161i −0.651708 0.758470i \(-0.725947\pi\)
0.331000 + 0.943631i \(0.392614\pi\)
\(620\) 0 0
\(621\) 45.3767 9.56105i 1.82090 0.383672i
\(622\) 0 0
\(623\) 8.80533 + 24.3235i 0.352778 + 0.974501i
\(624\) 0 0
\(625\) 15.6247 27.0627i 0.624987 1.08251i
\(626\) 0 0
\(627\) 1.18324 4.11726i 0.0472540 0.164427i
\(628\) 0 0
\(629\) 35.5320 1.41675
\(630\) 0 0
\(631\) 17.6136 0.701188 0.350594 0.936528i \(-0.385980\pi\)
0.350594 + 0.936528i \(0.385980\pi\)
\(632\) 0 0
\(633\) −3.12188 3.23663i −0.124084 0.128644i
\(634\) 0 0
\(635\) 14.1156 24.4489i 0.560160 0.970226i
\(636\) 0 0
\(637\) 10.5544 1.82334i 0.418182 0.0722433i
\(638\) 0 0
\(639\) 11.9593 + 22.5564i 0.473101 + 0.892316i
\(640\) 0 0
\(641\) 16.5759 9.57009i 0.654708 0.377996i −0.135550 0.990771i \(-0.543280\pi\)
0.790258 + 0.612775i \(0.209947\pi\)
\(642\) 0 0
\(643\) −2.01129 + 1.16122i −0.0793177 + 0.0457941i −0.539134 0.842220i \(-0.681248\pi\)
0.459817 + 0.888014i \(0.347915\pi\)
\(644\) 0 0
\(645\) 38.1228 + 39.5240i 1.50108 + 1.55626i
\(646\) 0 0
\(647\) 12.9310 22.3971i 0.508370 0.880522i −0.491583 0.870831i \(-0.663582\pi\)
0.999953 0.00969167i \(-0.00308500\pi\)
\(648\) 0 0
\(649\) 1.46899 0.848123i 0.0576630 0.0332918i
\(650\) 0 0
\(651\) 1.09062 + 16.1354i 0.0427448 + 0.632396i
\(652\) 0 0
\(653\) −20.1140 11.6128i −0.787123 0.454446i 0.0518258 0.998656i \(-0.483496\pi\)
−0.838949 + 0.544211i \(0.816829\pi\)
\(654\) 0 0
\(655\) −26.9681 46.7102i −1.05373 1.82512i
\(656\) 0 0
\(657\) 5.71410 + 0.206305i 0.222928 + 0.00804871i
\(658\) 0 0
\(659\) 13.7002 + 7.90981i 0.533684 + 0.308122i 0.742515 0.669829i \(-0.233633\pi\)
−0.208832 + 0.977952i \(0.566966\pi\)
\(660\) 0 0
\(661\) 18.2450i 0.709647i −0.934933 0.354823i \(-0.884541\pi\)
0.934933 0.354823i \(-0.115459\pi\)
\(662\) 0 0
\(663\) 2.49827 + 10.0453i 0.0970248 + 0.390127i
\(664\) 0 0
\(665\) 7.52447 42.2452i 0.291787 1.63820i
\(666\) 0 0
\(667\) 30.9349 + 53.5807i 1.19780 + 2.07465i
\(668\) 0 0
\(669\) −39.8309 11.4468i −1.53995 0.442559i
\(670\) 0 0
\(671\) −0.389984 0.675472i −0.0150552 0.0260763i
\(672\) 0 0
\(673\) 14.4184 24.9733i 0.555787 0.962651i −0.442055 0.896988i \(-0.645750\pi\)
0.997842 0.0656633i \(-0.0209163\pi\)
\(674\) 0 0
\(675\) −12.4748 4.07779i −0.480157 0.156954i
\(676\) 0 0
\(677\) −33.5336 −1.28880 −0.644400 0.764689i \(-0.722893\pi\)
−0.644400 + 0.764689i \(0.722893\pi\)
\(678\) 0 0
\(679\) −0.468340 0.394369i −0.0179732 0.0151345i
\(680\) 0 0
\(681\) −4.48775 4.65270i −0.171971 0.178292i
\(682\) 0 0
\(683\) −19.0943 11.0241i −0.730621 0.421824i 0.0880282 0.996118i \(-0.471943\pi\)
−0.818649 + 0.574294i \(0.805277\pi\)
\(684\) 0 0
\(685\) 14.7745i 0.564506i
\(686\) 0 0
\(687\) 35.0715 + 10.0790i 1.33806 + 0.384539i
\(688\) 0 0
\(689\) −5.99881 −0.228537
\(690\) 0 0
\(691\) 26.4036i 1.00444i 0.864740 + 0.502219i \(0.167483\pi\)
−0.864740 + 0.502219i \(0.832517\pi\)
\(692\) 0 0
\(693\) 2.22910 2.46119i 0.0846763 0.0934930i
\(694\) 0 0
\(695\) 46.8311i 1.77641i
\(696\) 0 0
\(697\) −8.29877 −0.314338
\(698\) 0 0
\(699\) −15.9125 + 15.3484i −0.601868 + 0.580530i
\(700\) 0 0
\(701\) 20.5140i 0.774804i 0.921911 + 0.387402i \(0.126627\pi\)
−0.921911 + 0.387402i \(0.873373\pi\)
\(702\) 0 0
\(703\) 46.5772 + 26.8913i 1.75669 + 1.01423i
\(704\) 0 0
\(705\) −2.32394 + 8.08651i −0.0875248 + 0.304556i
\(706\) 0 0
\(707\) 12.8610 + 35.5267i 0.483687 + 1.33612i
\(708\) 0 0
\(709\) −6.26109 −0.235140 −0.117570 0.993065i \(-0.537510\pi\)
−0.117570 + 0.993065i \(0.537510\pi\)
\(710\) 0 0
\(711\) −2.29869 + 1.21875i −0.0862077 + 0.0457068i
\(712\) 0 0
\(713\) 15.7476 27.2756i 0.589751 1.02148i
\(714\) 0 0
\(715\) 0.878041 + 1.52081i 0.0328369 + 0.0568751i
\(716\) 0 0
\(717\) 15.9095 15.3454i 0.594149 0.573085i
\(718\) 0 0
\(719\) −11.6111 20.1111i −0.433023 0.750017i 0.564109 0.825700i \(-0.309220\pi\)
−0.997132 + 0.0756828i \(0.975886\pi\)
\(720\) 0 0
\(721\) 21.7476 + 18.3127i 0.809922 + 0.682001i
\(722\) 0 0
\(723\) −3.79220 + 3.65775i −0.141033 + 0.136033i
\(724\) 0 0
\(725\) 17.5102i 0.650314i
\(726\) 0 0
\(727\) 2.50999 + 1.44914i 0.0930903 + 0.0537457i 0.545822 0.837901i \(-0.316217\pi\)
−0.452732 + 0.891647i \(0.649551\pi\)
\(728\) 0 0
\(729\) 2.91748 26.8419i 0.108055 0.994145i
\(730\) 0 0
\(731\) −22.5696 39.0917i −0.834767 1.44586i
\(732\) 0 0
\(733\) 10.2963 + 5.94457i 0.380302 + 0.219568i 0.677950 0.735108i \(-0.262869\pi\)
−0.297647 + 0.954676i \(0.596202\pi\)
\(734\) 0 0
\(735\) 19.6593 26.8291i 0.725145 0.989608i
\(736\) 0 0
\(737\) 4.62622 2.67095i 0.170409 0.0983858i
\(738\) 0 0
\(739\) 17.2254 29.8354i 0.633648 1.09751i −0.353151 0.935566i \(-0.614890\pi\)
0.986800 0.161945i \(-0.0517767\pi\)
\(740\) 0 0
\(741\) −4.32763 + 15.0586i −0.158979 + 0.553193i
\(742\) 0 0
\(743\) −2.44069 + 1.40913i −0.0895401 + 0.0516960i −0.544101 0.839019i \(-0.683129\pi\)
0.454561 + 0.890715i \(0.349796\pi\)
\(744\) 0 0
\(745\) 25.5447 14.7483i 0.935887 0.540335i
\(746\) 0 0
\(747\) 0.748781 20.7393i 0.0273965 0.758812i
\(748\) 0 0
\(749\) 15.8147 5.72507i 0.577857 0.209189i
\(750\) 0 0
\(751\) −3.86045 + 6.68649i −0.140870 + 0.243993i −0.927824 0.373017i \(-0.878323\pi\)
0.786955 + 0.617011i \(0.211657\pi\)
\(752\) 0 0
\(753\) −10.6241 + 2.64221i −0.387163 + 0.0962876i
\(754\) 0 0
\(755\) −20.7517 −0.755233
\(756\) 0 0
\(757\) 1.17924 0.0428603 0.0214302 0.999770i \(-0.493178\pi\)
0.0214302 + 0.999770i \(0.493178\pi\)
\(758\) 0 0
\(759\) −6.27564 + 1.56075i −0.227791 + 0.0566517i
\(760\) 0 0
\(761\) −1.56644 + 2.71316i −0.0567835 + 0.0983520i −0.893020 0.450017i \(-0.851418\pi\)
0.836236 + 0.548369i \(0.184751\pi\)
\(762\) 0 0
\(763\) −8.79473 + 10.4443i −0.318391 + 0.378110i
\(764\) 0 0
\(765\) 27.2401 + 17.0663i 0.984866 + 0.617033i
\(766\) 0 0
\(767\) −5.37276 + 3.10196i −0.193999 + 0.112005i
\(768\) 0 0
\(769\) 5.53497 3.19562i 0.199596 0.115237i −0.396871 0.917874i \(-0.629904\pi\)
0.596467 + 0.802637i \(0.296571\pi\)
\(770\) 0 0
\(771\) −11.7245 + 40.7971i −0.422247 + 1.46927i
\(772\) 0 0
\(773\) 23.9779 41.5309i 0.862425 1.49376i −0.00715621 0.999974i \(-0.502278\pi\)
0.869581 0.493790i \(-0.164389\pi\)
\(774\) 0 0
\(775\) −7.71948 + 4.45685i −0.277292 + 0.160095i
\(776\) 0 0
\(777\) 23.2316 + 34.6156i 0.833430 + 1.24183i
\(778\) 0 0
\(779\) −10.8784 6.28067i −0.389761 0.225028i
\(780\) 0 0
\(781\) −1.78015 3.08331i −0.0636987 0.110329i
\(782\) 0 0
\(783\) 35.2487 7.42705i 1.25969 0.265421i
\(784\) 0 0
\(785\) −29.1661 16.8390i −1.04098 0.601011i
\(786\) 0 0
\(787\) 6.04066i 0.215326i 0.994187 + 0.107663i \(0.0343368\pi\)
−0.994187 + 0.107663i \(0.965663\pi\)
\(788\) 0 0
\(789\) −30.3969 + 29.3192i −1.08216 + 1.04379i
\(790\) 0 0
\(791\) −26.4047 + 9.55872i −0.938842 + 0.339869i
\(792\) 0 0
\(793\) 1.42635 + 2.47050i 0.0506510 + 0.0877301i
\(794\) 0 0
\(795\) −13.4079 + 12.9325i −0.475529 + 0.458670i
\(796\)