Properties

Label 252.2.w.a.5.7
Level $252$
Weight $2$
Character 252.5
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 5.7
Root \(-0.811340 + 1.53027i\) of defining polynomial
Character \(\chi\) \(=\) 252.5
Dual form 252.2.w.a.101.7

$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.990659 + 0.136365i \(0.0435419\pi\)
−0.377234 + 0.926118i \(0.623125\pi\)
\(6\) 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 0.444385 0.895836i \(-0.353422\pi\)
−0.553624 + 0.832767i \(0.686756\pi\)
\(12\) 0 0
\(13\) 1.32512 + 0.765056i 0.367521 + 0.212188i 0.672375 0.740211i \(-0.265274\pi\)
−0.304854 + 0.952399i \(0.598608\pi\)
\(14\) 0 0
\(15\) 1.31241 + 4.56672i 0.338862 + 1.17912i
\(16\) 0 0
\(17\) −1.95291 3.38253i −0.473649 0.820385i 0.525896 0.850549i \(-0.323730\pi\)
−0.999545 + 0.0301645i \(0.990397\pi\)
\(18\) 0 0
\(19\) −5.11994 2.95600i −1.17459 0.678152i −0.219836 0.975537i \(-0.570552\pi\)
−0.954758 + 0.297385i \(0.903886\pi\)
\(20\) 0 0
\(21\) −4.57214 0.309039i −0.997723 0.0674379i
\(22\) 0 0
\(23\) 7.72884 4.46225i 1.61157 0.930443i 0.622569 0.782565i \(-0.286089\pi\)
0.989006 0.147878i \(-0.0472444\pi\)
\(24\) 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 0.174787 0.984606i \(-0.444076\pi\)
0.940088 + 0.340933i \(0.110743\pi\)
\(30\) 0 0
\(31\) 3.52907i 0.633839i 0.948452 + 0.316920i \(0.102649\pi\)
−0.948452 + 0.316920i \(0.897351\pi\)
\(32\) 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 0.201095 + 0.979572i \(0.435550\pi\)
−0.948881 + 0.315633i \(0.897783\pi\)
\(38\) 0 0
\(39\) 1.90751 + 1.83988i 0.305445 + 0.294616i
\(40\) 0 0
\(41\) 1.06236 1.84006i 0.165913 0.287370i −0.771066 0.636755i \(-0.780276\pi\)
0.936979 + 0.349385i \(0.113610\pi\)
\(42\) 0 0
\(43\) −5.77846 10.0086i −0.881208 1.52630i −0.850000 0.526783i \(-0.823398\pi\)
−0.0312079 0.999513i \(-0.509935\pi\)
\(44\) 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 −0.714721 0.699410i \(-0.753446\pi\)
0.248346 + 0.968671i \(0.420113\pi\)
\(54\) 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 \(-0.961918\pi\)
0.992852 0.119354i \(-0.0380823\pi\)
\(62\) 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 \(-0.831497\pi\)
0.863126 0.504988i \(-0.168503\pi\)
\(72\) 0 0
\(73\) 1.65059 0.952971i 0.193187 0.111537i −0.400286 0.916390i \(-0.631089\pi\)
0.593474 + 0.804853i \(0.297756\pi\)
\(74\) 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 0.991012 0.133775i \(-0.0427100\pi\)
−0.611359 + 0.791354i \(0.709377\pi\)
\(84\) 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 0.481581 + 0.876401i \(0.340063\pi\)
−0.999777 + 0.0211389i \(0.993271\pi\)
\(90\) 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 −0.489791 0.871840i \(-0.662927\pi\)
0.510140 + 0.860091i \(0.329594\pi\)
\(98\) 0 0
\(99\) −0.666342 1.06357i −0.0669699 0.106893i
\(100\) 0 0
\(101\) −7.14031 + 12.3674i −0.710487 + 1.23060i 0.254187 + 0.967155i \(0.418192\pi\)
−0.964674 + 0.263445i \(0.915141\pi\)
\(102\) 0 0
\(103\) −9.30617 + 5.37292i −0.916964 + 0.529410i −0.882665 0.470002i \(-0.844253\pi\)
−0.0342991 + 0.999412i \(0.510920\pi\)
\(104\) 0 0
\(105\) −5.53721 11.2863i −0.540376 1.10143i
\(106\) 0 0
\(107\) −5.50534 3.17851i −0.532221 0.307278i 0.209699 0.977766i \(-0.432751\pi\)
−0.741920 + 0.670488i \(0.766085\pi\)
\(108\) 0 0
\(109\) 2.58036 + 4.46932i 0.247154 + 0.428083i 0.962735 0.270447i \(-0.0871714\pi\)
−0.715581 + 0.698530i \(0.753838\pi\)
\(110\) 0 0
\(111\) −10.9389 + 11.3410i −1.03828 + 1.07644i
\(112\) 0 0
\(113\) 9.19186 + 5.30692i 0.864697 + 0.499233i 0.865582 0.500766i \(-0.166948\pi\)
−0.000885276 1.00000i \(0.500282\pi\)
\(114\) 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 0.872986 + 0.487746i \(0.162181\pi\)
−0.0140928 + 0.999901i \(0.504486\pi\)
\(132\) 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 0.287347 0.957827i \(-0.407227\pi\)
−0.685829 + 0.727763i \(0.740560\pi\)
\(138\) 0 0
\(139\) 14.7839 + 8.53549i 1.25395 + 0.723971i 0.971892 0.235425i \(-0.0756484\pi\)
0.282062 + 0.959396i \(0.408982\pi\)
\(140\) 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 −0.0674758 0.997721i \(-0.521495\pi\)
0.830314 + 0.557296i \(0.188161\pi\)
\(150\) 0 0
\(151\) −3.78223 + 6.55102i −0.307794 + 0.533115i −0.977879 0.209169i \(-0.932924\pi\)
0.670086 + 0.742284i \(0.266257\pi\)
\(152\) 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 \(0.162960\pi\)
−0.871789 + 0.489882i \(0.837040\pi\)
\(158\) 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 −0.535642 0.844445i \(-0.679930\pi\)
0.999132 + 0.0416566i \(0.0132635\pi\)
\(164\) 0 0
\(165\) 0.479763 1.92908i 0.0373495 0.150179i
\(166\) 0 0
\(167\) 6.78854 11.7581i 0.525313 0.909869i −0.474252 0.880389i \(-0.657282\pi\)
0.999565 0.0294798i \(-0.00938508\pi\)
\(168\) 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 0.168805 0.985650i \(-0.446009\pi\)
0.938000 + 0.346636i \(0.112676\pi\)
\(180\) 0 0
\(181\) 18.2171i 1.35407i −0.735952 0.677034i \(-0.763265\pi\)
0.735952 0.677034i \(-0.236735\pi\)
\(182\) 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 \(0.274669\pi\)
−0.650239 + 0.759730i \(0.725331\pi\)
\(192\) 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 \(0.194092\pi\)
−0.819786 + 0.572670i \(0.805908\pi\)
\(198\) 0 0
\(199\) −5.44956 + 3.14630i −0.386309 + 0.223036i −0.680560 0.732693i \(-0.738263\pi\)
0.294251 + 0.955728i \(0.404930\pi\)
\(200\) 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 −0.907244 0.420605i \(-0.861818\pi\)
0.817876 + 0.575394i \(0.195151\pi\)
\(212\) 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 −0.993046 0.117725i \(-0.962440\pi\)
−0.394571 + 0.918866i \(0.629107\pi\)
\(224\) 0 0
\(225\) −6.42123 + 4.02299i −0.428082 + 0.268200i
\(226\) 0 0
\(227\) −1.86609 + 3.23216i −0.123857 + 0.214526i −0.921285 0.388887i \(-0.872860\pi\)
0.797429 + 0.603413i \(0.206193\pi\)
\(228\) 0 0
\(229\) 18.2455 10.5341i 1.20570 0.696111i 0.243882 0.969805i \(-0.421579\pi\)
0.961817 + 0.273694i \(0.0882457\pi\)
\(230\) 0 0
\(231\) 1.59187 + 1.06836i 0.104738 + 0.0702928i
\(232\) 0 0
\(233\) −11.0542 6.38215i −0.724186 0.418109i 0.0921057 0.995749i \(-0.470640\pi\)
−0.816291 + 0.577640i \(0.803974\pi\)
\(234\) 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 0.812872 0.582442i \(-0.197903\pi\)
−0.0979736 + 0.995189i \(0.531236\pi\)
\(240\) 0 0
\(241\) −2.63438 1.52096i −0.169695 0.0979737i 0.412747 0.910846i \(-0.364569\pi\)
−0.582442 + 0.812872i \(0.697903\pi\)
\(242\) 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 −0.940578 0.339577i \(-0.889716\pi\)
0.176206 0.984353i \(-0.443617\pi\)
\(258\) 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 −0.321323 0.946970i \(-0.604128\pi\)
−0.980761 + 0.195211i \(0.937461\pi\)
\(264\) 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 0.976480 0.215609i \(-0.0691737\pi\)
−0.674963 + 0.737852i \(0.735840\pi\)
\(270\) 0 0
\(271\) −5.10505 2.94740i −0.310110 0.179042i 0.336866 0.941553i \(-0.390633\pi\)
−0.646976 + 0.762511i \(0.723966\pi\)
\(272\) 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 0.268741 + 0.963213i \(0.413392\pi\)
−0.968537 + 0.248870i \(0.919941\pi\)
\(278\) 0 0
\(279\) −4.95933 + 9.35381i −0.296908 + 0.559998i
\(280\) 0 0
\(281\) 21.7962 12.5840i 1.30025 0.750700i 0.319803 0.947484i \(-0.396383\pi\)
0.980447 + 0.196784i \(0.0630499\pi\)
\(282\) 0 0
\(283\) 9.96439i 0.592322i 0.955138 + 0.296161i \(0.0957064\pi\)
−0.955138 + 0.296161i \(0.904294\pi\)
\(284\) 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 −0.993318 0.115406i \(-0.963183\pi\)
0.596604 + 0.802536i \(0.296516\pi\)
\(294\) 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 \(0.161068\pi\)
−0.874686 + 0.484691i \(0.838932\pi\)
\(308\) 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 \(-0.887398\pi\)
0.938080 0.346419i \(-0.112602\pi\)
\(314\) 0 0
\(315\) −4.58922 21.2853i −0.258573 1.19929i
\(316\) 0 0
\(317\) 23.0950i 1.29714i −0.761154 0.648571i \(-0.775367\pi\)
0.761154 0.648571i \(-0.224633\pi\)
\(318\) 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 −0.999995 0.00305455i \(-0.999028\pi\)
0.502643 + 0.864494i \(0.332361\pi\)
\(338\) 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 \(-0.954225\pi\)
0.989678 0.143311i \(-0.0457749\pi\)
\(348\) 0 0
\(349\) −0.0136817 + 0.00789914i −0.000732365 + 0.000422831i −0.500366 0.865814i \(-0.666801\pi\)
0.499634 + 0.866237i \(0.333468\pi\)
\(350\) 0 0
\(351\) 2.47030 + 7.55719i 0.131855 + 0.403373i
\(352\) 0 0
\(353\) 17.1543 29.7121i 0.913029 1.58141i 0.103268 0.994654i \(-0.467070\pi\)
0.809761 0.586760i \(-0.199597\pi\)
\(354\) 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 0.349887 0.936792i \(-0.386220\pi\)
−0.636342 + 0.771407i \(0.719553\pi\)
\(360\) 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 0.864250 0.503062i \(-0.167793\pi\)
−0.00353959 + 0.999994i \(0.501127\pi\)
\(368\) 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 0.690943 0.722909i \(-0.257195\pi\)
−0.971529 + 0.236920i \(0.923862\pi\)
\(374\) 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 0.689327 + 0.724451i \(0.257906\pi\)
0.282729 + 0.959200i \(0.408760\pi\)
\(384\) 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 0.859473 0.511182i \(-0.170792\pi\)
−0.0129603 + 0.999916i \(0.504125\pi\)
\(390\) 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 −0.00353639 0.999994i \(-0.501126\pi\)
−0.867788 + 0.496934i \(0.834459\pi\)
\(398\) 0 0
\(399\) 22.4956 + 15.0975i 1.12619 + 0.755820i
\(400\) 0 0
\(401\) 26.4232 15.2554i 1.31951 0.761820i 0.335861 0.941912i \(-0.390973\pi\)
0.983650 + 0.180092i \(0.0576395\pi\)
\(402\) 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 \(0.00136881\pi\)
−0.999991 + 0.00430023i \(0.998631\pi\)
\(410\) 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 0.285387 + 0.958412i \(0.407878\pi\)
−0.972703 + 0.232054i \(0.925455\pi\)
\(420\) 0 0
\(421\) −1.56130 2.70424i −0.0760929 0.131797i 0.825468 0.564449i \(-0.190911\pi\)
−0.901561 + 0.432652i \(0.857578\pi\)
\(422\) 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 −0.278675 0.960385i \(-0.589895\pi\)
0.692381 + 0.721532i \(0.256562\pi\)
\(432\) 0 0
\(433\) 17.1274i 0.823092i 0.911389 + 0.411546i \(0.135011\pi\)
−0.911389 + 0.411546i \(0.864989\pi\)
\(434\) 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 \(-0.828918\pi\)
0.859006 0.511965i \(-0.171082\pi\)
\(440\) 0 0
\(441\) 20.8090 + 2.82594i 0.990904 + 0.134569i
\(442\) 0 0
\(443\) 6.74738i 0.320578i 0.987070 + 0.160289i \(0.0512425\pi\)
−0.987070 + 0.160289i \(0.948757\pi\)
\(444\) 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 \(0.0438240\pi\)
−0.990537 + 0.137243i \(0.956176\pi\)
\(450\) 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 −0.869657 0.493656i \(-0.835660\pi\)
0.00730959 0.999973i \(-0.497673\pi\)
\(462\) 0 0
\(463\) 10.5618 18.2935i 0.490848 0.850173i −0.509097 0.860709i \(-0.670020\pi\)
0.999944 + 0.0105362i \(0.00335383\pi\)
\(464\) 0 0
\(465\) −16.1163 + 4.63158i −0.747374 + 0.214784i
\(466\) 0 0
\(467\) 9.30470 16.1162i 0.430570 0.745770i −0.566352 0.824163i \(-0.691646\pi\)
0.996922 + 0.0783937i \(0.0249791\pi\)
\(468\) 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 −0.654539 0.756028i \(-0.727137\pi\)
0.982009 + 0.188834i \(0.0604707\pi\)
\(480\) 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 0.709204 0.705003i \(-0.249054\pi\)
−0.965153 + 0.261687i \(0.915721\pi\)
\(488\) 0 0
\(489\) 14.2308 14.7539i 0.643541 0.667195i
\(490\) 0 0
\(491\) −8.84097 5.10434i −0.398988 0.230356i 0.287059 0.957913i \(-0.407322\pi\)
−0.686047 + 0.727557i \(0.740656\pi\)
\(492\) 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 0.996719 0.0809379i \(-0.0257915\pi\)
−0.568454 + 0.822715i \(0.692458\pi\)
\(500\) 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 0.999853 0.0171449i \(-0.00545767\pi\)
−0.514774 + 0.857326i \(0.672124\pi\)
\(510\) 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 0.884169 0.467168i \(-0.154726\pi\)
−0.846663 + 0.532129i \(0.821392\pi\)
\(522\) 0 0
\(523\) 7.16320 + 4.13568i 0.313225 + 0.180841i 0.648369 0.761326i \(-0.275452\pi\)
−0.335144 + 0.942167i \(0.608785\pi\)
\(524\) 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 −0.997575 0.0695932i \(-0.977830\pi\)
0.559057 + 0.829129i \(0.311163\pi\)
\(542\) 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 0.912304 + 0.409513i \(0.134301\pi\)
−0.101503 + 0.994835i \(0.532365\pi\)
\(548\) 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 −0.157920 0.987452i \(-0.550479\pi\)
0.776198 + 0.630489i \(0.217146\pi\)
\(558\) 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 \(0.0424886\pi\)
−0.991104 + 0.133086i \(0.957511\pi\)
\(570\) 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 −0.144651 0.989483i \(-0.546206\pi\)
0.784592 + 0.620013i \(0.212873\pi\)
\(578\) 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 0.942589 0.333955i \(-0.108383\pi\)
−0.760508 + 0.649329i \(0.775050\pi\)
\(588\) 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 −0.765511 0.643422i \(-0.777514\pi\)
0.939976 + 0.341241i \(0.110847\pi\)
\(594\) 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 \(-0.975861\pi\)
0.997126 0.0757609i \(-0.0241386\pi\)
\(600\) 0 0
\(601\) 6.14043 3.54518i 0.250473 0.144611i −0.369508 0.929228i \(-0.620474\pi\)
0.619981 + 0.784617i \(0.287140\pi\)
\(602\) 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 −0.959418 0.281988i \(-0.909006\pi\)
−0.235500 + 0.971874i \(0.575673\pi\)
\(608\) 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 0.527877 0.849321i \(-0.322988\pi\)
−0.999472 + 0.0324944i \(0.989655\pi\)
\(614\) 0 0
\(615\) 9.79732 + 2.43659i 0.395066 + 0.0982530i
\(616\) 0 0
\(617\) −39.0817 22.5638i −1.57337 0.908386i −0.995752 0.0920787i \(-0.970649\pi\)
−0.577618 0.816307i \(-0.696018\pi\)
\(618\) 0 0
\(619\) −7.97914 4.60676i −0.320709 0.185161i 0.331000 0.943631i \(-0.392614\pi\)
−0.651708 + 0.758470i \(0.725947\pi\)
\(620\) 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 0.790258 0.612775i \(-0.209947\pi\)
−0.135550 + 0.990771i \(0.543280\pi\)
\(642\) 0 0
\(643\) −2.01129 1.16122i −0.0793177 0.0457941i 0.459817 0.888014i \(-0.347915\pi\)
−0.539134 + 0.842220i \(0.681248\pi\)
\(644\) 0 0
\(645\) 38.1228 39.5240i 1.50108 1.55626i
\(646\) 0 0
\(647\) 12.9310 + 22.3971i 0.508370 + 0.880522i 0.999953 + 0.00969167i \(0.00308500\pi\)
−0.491583 + 0.870831i \(0.663582\pi\)
\(648\) 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 −0.838949 0.544211i \(-0.816829\pi\)
0.0518258 + 0.998656i \(0.483496\pi\)
\(654\) 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 −0.208832 0.977952i \(-0.566966\pi\)
0.742515 + 0.669829i \(0.233633\pi\)
\(660\) 0 0
\(661\) 18.2450i 0.709647i 0.934933 + 0.354823i \(0.115459\pi\)
−0.934933 + 0.354823i \(0.884541\pi\)
\(662\) 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 0.997842 + 0.0656633i \(0.0209163\pi\)
−0.442055 + 0.896988i \(0.645750\pi\)
\(674\) 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 −0.818649 0.574294i \(-0.805277\pi\)
0.0880282 + 0.996118i \(0.471943\pi\)
\(684\) 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 \(-0.832517\pi\)
0.864740 0.502219i \(-0.167483\pi\)
\(692\) 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 \(-0.873373\pi\)
0.921911 0.387402i \(-0.126627\pi\)
\(702\) 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 −0.997132 0.0756828i \(-0.975886\pi\)
0.564109 + 0.825700i \(0.309220\pi\)
\(720\) 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 −0.452732 0.891647i \(-0.649551\pi\)
0.545822 + 0.837901i \(0.316217\pi\)
\(728\) 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 −0.297647 0.954676i \(-0.596202\pi\)
0.677950 + 0.735108i \(0.262869\pi\)
\(734\) 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 0.986800 + 0.161945i \(0.0517767\pi\)
−0.353151 + 0.935566i \(0.614890\pi\)
\(740\) 0 0
\(741\) −4.32763 15.0586i −0.158979 0.553193i
\(742\) 0 0
\(743\) −2.44069 1.40913i −0.0895401 0.0516960i 0.454561 0.890715i \(-0.349796\pi\)
−0.544101 + 0.839019i \(0.683129\pi\)
\(744\) 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 0.786955 0.617011i \(-0.211657\pi\)
−0.927824 + 0.373017i \(0.878323\pi\)
\(752\) 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 0.836236 0.548369i \(-0.184751\pi\)
−0.893020 + 0.450017i \(0.851418\pi\)
\(762\) 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 0.596467 0.802637i \(-0.296571\pi\)
−0.396871 + 0.917874i \(0.629904\pi\)
\(770\) 0 0
\(771\) −11.7245 40.7971i −0.422247 1.46927i
\(772\) 0 0
\(773\) 23.9779 + 41.5309i 0.862425 + 1.49376i 0.869581 + 0.493790i \(0.164389\pi\)
−0.00715621 + 0.999974i \(0.502278\pi\)
\(774\) 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 \(-0.965663\pi\)
0.994187 0.107663i \(-0.0343368\pi\)
\(788\) 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
\(796\)