Properties

Label 585.2.c.b.469.5
Level $585$
Weight $2$
Character 585.469
Analytic conductor $4.671$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 469.5
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 585.469
Dual form 585.2.c.b.469.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.53919i q^{2} -0.369102 q^{4} +(-0.539189 + 2.17009i) q^{5} +1.70928i q^{7} +2.51026i q^{8} +O(q^{10})\) \(q+1.53919i q^{2} -0.369102 q^{4} +(-0.539189 + 2.17009i) q^{5} +1.70928i q^{7} +2.51026i q^{8} +(-3.34017 - 0.829914i) q^{10} +2.53919 q^{11} -1.00000i q^{13} -2.63090 q^{14} -4.60197 q^{16} +0.921622i q^{17} +0.539189 q^{19} +(0.199016 - 0.800984i) q^{20} +3.90829i q^{22} -2.82991i q^{23} +(-4.41855 - 2.34017i) q^{25} +1.53919 q^{26} -0.630898i q^{28} -5.12783 q^{29} +0.879362 q^{31} -2.06278i q^{32} -1.41855 q^{34} +(-3.70928 - 0.921622i) q^{35} +6.04945i q^{37} +0.829914i q^{38} +(-5.44748 - 1.35350i) q^{40} -1.26180 q^{41} +6.43188i q^{43} -0.937221 q^{44} +4.35577 q^{46} +5.70928i q^{47} +4.07838 q^{49} +(3.60197 - 6.80098i) q^{50} +0.369102i q^{52} -8.49693i q^{53} +(-1.36910 + 5.51026i) q^{55} -4.29072 q^{56} -7.89269i q^{58} -4.72261 q^{59} +8.04945 q^{61} +1.35350i q^{62} -6.02893 q^{64} +(2.17009 + 0.539189i) q^{65} -7.86603i q^{67} -0.340173i q^{68} +(1.41855 - 5.70928i) q^{70} +14.4813 q^{71} -1.95055i q^{73} -9.31124 q^{74} -0.199016 q^{76} +4.34017i q^{77} -0.496928 q^{79} +(2.48133 - 9.98667i) q^{80} -1.94214i q^{82} -8.63090i q^{83} +(-2.00000 - 0.496928i) q^{85} -9.89988 q^{86} +6.37402i q^{88} +12.8371 q^{89} +1.70928 q^{91} +1.04453i q^{92} -8.78765 q^{94} +(-0.290725 + 1.17009i) q^{95} -5.91548i q^{97} +6.27739i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 10 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50} - 16 q^{55} - 40 q^{56} - 16 q^{59} + 12 q^{61} - 66 q^{64} + 2 q^{65} - 20 q^{70} + 24 q^{71} - 4 q^{74} - 20 q^{76} + 32 q^{79} - 48 q^{80} - 12 q^{85} + 32 q^{86} + 20 q^{89} - 4 q^{91} - 32 q^{94} - 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.53919i 1.08837i 0.838965 + 0.544185i \(0.183161\pi\)
−0.838965 + 0.544185i \(0.816839\pi\)
\(3\) 0 0
\(4\) −0.369102 −0.184551
\(5\) −0.539189 + 2.17009i −0.241133 + 0.970492i
\(6\) 0 0
\(7\) 1.70928i 0.646045i 0.946391 + 0.323023i \(0.104699\pi\)
−0.946391 + 0.323023i \(0.895301\pi\)
\(8\) 2.51026i 0.887511i
\(9\) 0 0
\(10\) −3.34017 0.829914i −1.05626 0.262442i
\(11\) 2.53919 0.765594 0.382797 0.923832i \(-0.374961\pi\)
0.382797 + 0.923832i \(0.374961\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) −2.63090 −0.703137
\(15\) 0 0
\(16\) −4.60197 −1.15049
\(17\) 0.921622i 0.223526i 0.993735 + 0.111763i \(0.0356498\pi\)
−0.993735 + 0.111763i \(0.964350\pi\)
\(18\) 0 0
\(19\) 0.539189 0.123698 0.0618492 0.998086i \(-0.480300\pi\)
0.0618492 + 0.998086i \(0.480300\pi\)
\(20\) 0.199016 0.800984i 0.0445013 0.179105i
\(21\) 0 0
\(22\) 3.90829i 0.833250i
\(23\) 2.82991i 0.590078i −0.955485 0.295039i \(-0.904667\pi\)
0.955485 0.295039i \(-0.0953326\pi\)
\(24\) 0 0
\(25\) −4.41855 2.34017i −0.883710 0.468035i
\(26\) 1.53919 0.301860
\(27\) 0 0
\(28\) 0.630898i 0.119228i
\(29\) −5.12783 −0.952213 −0.476107 0.879388i \(-0.657952\pi\)
−0.476107 + 0.879388i \(0.657952\pi\)
\(30\) 0 0
\(31\) 0.879362 0.157938 0.0789690 0.996877i \(-0.474837\pi\)
0.0789690 + 0.996877i \(0.474837\pi\)
\(32\) 2.06278i 0.364651i
\(33\) 0 0
\(34\) −1.41855 −0.243279
\(35\) −3.70928 0.921622i −0.626982 0.155783i
\(36\) 0 0
\(37\) 6.04945i 0.994523i 0.867601 + 0.497262i \(0.165661\pi\)
−0.867601 + 0.497262i \(0.834339\pi\)
\(38\) 0.829914i 0.134630i
\(39\) 0 0
\(40\) −5.44748 1.35350i −0.861322 0.214008i
\(41\) −1.26180 −0.197059 −0.0985297 0.995134i \(-0.531414\pi\)
−0.0985297 + 0.995134i \(0.531414\pi\)
\(42\) 0 0
\(43\) 6.43188i 0.980853i 0.871483 + 0.490426i \(0.163159\pi\)
−0.871483 + 0.490426i \(0.836841\pi\)
\(44\) −0.937221 −0.141291
\(45\) 0 0
\(46\) 4.35577 0.642223
\(47\) 5.70928i 0.832783i 0.909185 + 0.416392i \(0.136705\pi\)
−0.909185 + 0.416392i \(0.863295\pi\)
\(48\) 0 0
\(49\) 4.07838 0.582625
\(50\) 3.60197 6.80098i 0.509395 0.961804i
\(51\) 0 0
\(52\) 0.369102i 0.0511853i
\(53\) 8.49693i 1.16714i −0.812062 0.583571i \(-0.801655\pi\)
0.812062 0.583571i \(-0.198345\pi\)
\(54\) 0 0
\(55\) −1.36910 + 5.51026i −0.184610 + 0.743003i
\(56\) −4.29072 −0.573372
\(57\) 0 0
\(58\) 7.89269i 1.03636i
\(59\) −4.72261 −0.614831 −0.307415 0.951575i \(-0.599464\pi\)
−0.307415 + 0.951575i \(0.599464\pi\)
\(60\) 0 0
\(61\) 8.04945 1.03063 0.515313 0.857002i \(-0.327676\pi\)
0.515313 + 0.857002i \(0.327676\pi\)
\(62\) 1.35350i 0.171895i
\(63\) 0 0
\(64\) −6.02893 −0.753616
\(65\) 2.17009 + 0.539189i 0.269166 + 0.0668781i
\(66\) 0 0
\(67\) 7.86603i 0.960989i −0.876998 0.480494i \(-0.840457\pi\)
0.876998 0.480494i \(-0.159543\pi\)
\(68\) 0.340173i 0.0412520i
\(69\) 0 0
\(70\) 1.41855 5.70928i 0.169549 0.682389i
\(71\) 14.4813 1.71862 0.859309 0.511457i \(-0.170894\pi\)
0.859309 + 0.511457i \(0.170894\pi\)
\(72\) 0 0
\(73\) 1.95055i 0.228295i −0.993464 0.114147i \(-0.963586\pi\)
0.993464 0.114147i \(-0.0364136\pi\)
\(74\) −9.31124 −1.08241
\(75\) 0 0
\(76\) −0.199016 −0.0228287
\(77\) 4.34017i 0.494609i
\(78\) 0 0
\(79\) −0.496928 −0.0559088 −0.0279544 0.999609i \(-0.508899\pi\)
−0.0279544 + 0.999609i \(0.508899\pi\)
\(80\) 2.48133 9.98667i 0.277421 1.11654i
\(81\) 0 0
\(82\) 1.94214i 0.214474i
\(83\) 8.63090i 0.947364i −0.880696 0.473682i \(-0.842925\pi\)
0.880696 0.473682i \(-0.157075\pi\)
\(84\) 0 0
\(85\) −2.00000 0.496928i −0.216930 0.0538995i
\(86\) −9.89988 −1.06753
\(87\) 0 0
\(88\) 6.37402i 0.679473i
\(89\) 12.8371 1.36073 0.680365 0.732873i \(-0.261821\pi\)
0.680365 + 0.732873i \(0.261821\pi\)
\(90\) 0 0
\(91\) 1.70928 0.179181
\(92\) 1.04453i 0.108900i
\(93\) 0 0
\(94\) −8.78765 −0.906377
\(95\) −0.290725 + 1.17009i −0.0298277 + 0.120048i
\(96\) 0 0
\(97\) 5.91548i 0.600626i −0.953841 0.300313i \(-0.902909\pi\)
0.953841 0.300313i \(-0.0970911\pi\)
\(98\) 6.27739i 0.634113i
\(99\) 0 0
\(100\) 1.63090 + 0.863763i 0.163090 + 0.0863763i
\(101\) 16.4391 1.63575 0.817874 0.575397i \(-0.195152\pi\)
0.817874 + 0.575397i \(0.195152\pi\)
\(102\) 0 0
\(103\) 10.1906i 1.00411i −0.864836 0.502055i \(-0.832577\pi\)
0.864836 0.502055i \(-0.167423\pi\)
\(104\) 2.51026 0.246151
\(105\) 0 0
\(106\) 13.0784 1.27028
\(107\) 9.75154i 0.942717i 0.881942 + 0.471358i \(0.156236\pi\)
−0.881942 + 0.471358i \(0.843764\pi\)
\(108\) 0 0
\(109\) 16.8638 1.61526 0.807628 0.589693i \(-0.200751\pi\)
0.807628 + 0.589693i \(0.200751\pi\)
\(110\) −8.48133 2.10731i −0.808663 0.200924i
\(111\) 0 0
\(112\) 7.86603i 0.743270i
\(113\) 11.7587i 1.10617i 0.833126 + 0.553084i \(0.186549\pi\)
−0.833126 + 0.553084i \(0.813451\pi\)
\(114\) 0 0
\(115\) 6.14116 + 1.52586i 0.572666 + 0.142287i
\(116\) 1.89269 0.175732
\(117\) 0 0
\(118\) 7.26898i 0.669164i
\(119\) −1.57531 −0.144408
\(120\) 0 0
\(121\) −4.55252 −0.413865
\(122\) 12.3896i 1.12170i
\(123\) 0 0
\(124\) −0.324575 −0.0291477
\(125\) 7.46081 8.32684i 0.667315 0.744775i
\(126\) 0 0
\(127\) 18.0072i 1.59788i 0.601411 + 0.798940i \(0.294605\pi\)
−0.601411 + 0.798940i \(0.705395\pi\)
\(128\) 13.4052i 1.18487i
\(129\) 0 0
\(130\) −0.829914 + 3.34017i −0.0727882 + 0.292953i
\(131\) −14.2557 −1.24552 −0.622761 0.782412i \(-0.713989\pi\)
−0.622761 + 0.782412i \(0.713989\pi\)
\(132\) 0 0
\(133\) 0.921622i 0.0799148i
\(134\) 12.1073 1.04591
\(135\) 0 0
\(136\) −2.31351 −0.198382
\(137\) 13.7854i 1.17776i 0.808219 + 0.588882i \(0.200432\pi\)
−0.808219 + 0.588882i \(0.799568\pi\)
\(138\) 0 0
\(139\) 6.65368 0.564358 0.282179 0.959362i \(-0.408943\pi\)
0.282179 + 0.959362i \(0.408943\pi\)
\(140\) 1.36910 + 0.340173i 0.115710 + 0.0287499i
\(141\) 0 0
\(142\) 22.2895i 1.87049i
\(143\) 2.53919i 0.212338i
\(144\) 0 0
\(145\) 2.76487 11.1278i 0.229610 0.924116i
\(146\) 3.00227 0.248469
\(147\) 0 0
\(148\) 2.23287i 0.183540i
\(149\) −9.07838 −0.743730 −0.371865 0.928287i \(-0.621282\pi\)
−0.371865 + 0.928287i \(0.621282\pi\)
\(150\) 0 0
\(151\) 3.27739 0.266711 0.133355 0.991068i \(-0.457425\pi\)
0.133355 + 0.991068i \(0.457425\pi\)
\(152\) 1.35350i 0.109784i
\(153\) 0 0
\(154\) −6.68035 −0.538318
\(155\) −0.474142 + 1.90829i −0.0380840 + 0.153278i
\(156\) 0 0
\(157\) 12.8371i 1.02451i −0.858833 0.512256i \(-0.828810\pi\)
0.858833 0.512256i \(-0.171190\pi\)
\(158\) 0.764867i 0.0608495i
\(159\) 0 0
\(160\) 4.47641 + 1.11223i 0.353891 + 0.0879293i
\(161\) 4.83710 0.381217
\(162\) 0 0
\(163\) 12.0494i 0.943786i 0.881656 + 0.471893i \(0.156429\pi\)
−0.881656 + 0.471893i \(0.843571\pi\)
\(164\) 0.465732 0.0363675
\(165\) 0 0
\(166\) 13.2846 1.03108
\(167\) 8.72979i 0.675532i 0.941230 + 0.337766i \(0.109671\pi\)
−0.941230 + 0.337766i \(0.890329\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0.764867 3.07838i 0.0586626 0.236101i
\(171\) 0 0
\(172\) 2.37402i 0.181018i
\(173\) 0.863763i 0.0656707i −0.999461 0.0328354i \(-0.989546\pi\)
0.999461 0.0328354i \(-0.0104537\pi\)
\(174\) 0 0
\(175\) 4.00000 7.55252i 0.302372 0.570917i
\(176\) −11.6853 −0.880810
\(177\) 0 0
\(178\) 19.7587i 1.48098i
\(179\) 19.9155 1.48855 0.744276 0.667872i \(-0.232795\pi\)
0.744276 + 0.667872i \(0.232795\pi\)
\(180\) 0 0
\(181\) 14.3896 1.06957 0.534786 0.844987i \(-0.320392\pi\)
0.534786 + 0.844987i \(0.320392\pi\)
\(182\) 2.63090i 0.195015i
\(183\) 0 0
\(184\) 7.10382 0.523700
\(185\) −13.1278 3.26180i −0.965177 0.239812i
\(186\) 0 0
\(187\) 2.34017i 0.171130i
\(188\) 2.10731i 0.153691i
\(189\) 0 0
\(190\) −1.80098 0.447480i −0.130657 0.0324636i
\(191\) −1.47641 −0.106829 −0.0534146 0.998572i \(-0.517010\pi\)
−0.0534146 + 0.998572i \(0.517010\pi\)
\(192\) 0 0
\(193\) 17.7321i 1.27638i −0.769878 0.638191i \(-0.779683\pi\)
0.769878 0.638191i \(-0.220317\pi\)
\(194\) 9.10504 0.653704
\(195\) 0 0
\(196\) −1.50534 −0.107524
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 0 0
\(199\) 5.39189 0.382221 0.191110 0.981569i \(-0.438791\pi\)
0.191110 + 0.981569i \(0.438791\pi\)
\(200\) 5.87444 11.0917i 0.415386 0.784302i
\(201\) 0 0
\(202\) 25.3028i 1.78030i
\(203\) 8.76487i 0.615173i
\(204\) 0 0
\(205\) 0.680346 2.73820i 0.0475174 0.191245i
\(206\) 15.6853 1.09284
\(207\) 0 0
\(208\) 4.60197i 0.319089i
\(209\) 1.36910 0.0947028
\(210\) 0 0
\(211\) −22.7526 −1.56635 −0.783176 0.621800i \(-0.786402\pi\)
−0.783176 + 0.621800i \(0.786402\pi\)
\(212\) 3.13624i 0.215398i
\(213\) 0 0
\(214\) −15.0095 −1.02603
\(215\) −13.9577 3.46800i −0.951910 0.236516i
\(216\) 0 0
\(217\) 1.50307i 0.102035i
\(218\) 25.9565i 1.75800i
\(219\) 0 0
\(220\) 0.505339 2.03385i 0.0340699 0.137122i
\(221\) 0.921622 0.0619950
\(222\) 0 0
\(223\) 8.76099i 0.586679i 0.956008 + 0.293340i \(0.0947667\pi\)
−0.956008 + 0.293340i \(0.905233\pi\)
\(224\) 3.52586 0.235581
\(225\) 0 0
\(226\) −18.0989 −1.20392
\(227\) 17.2267i 1.14338i −0.820470 0.571689i \(-0.806288\pi\)
0.820470 0.571689i \(-0.193712\pi\)
\(228\) 0 0
\(229\) −3.07838 −0.203425 −0.101712 0.994814i \(-0.532432\pi\)
−0.101712 + 0.994814i \(0.532432\pi\)
\(230\) −2.34858 + 9.45240i −0.154861 + 0.623273i
\(231\) 0 0
\(232\) 12.8722i 0.845100i
\(233\) 18.9360i 1.24054i −0.784389 0.620269i \(-0.787023\pi\)
0.784389 0.620269i \(-0.212977\pi\)
\(234\) 0 0
\(235\) −12.3896 3.07838i −0.808210 0.200811i
\(236\) 1.74313 0.113468
\(237\) 0 0
\(238\) 2.42469i 0.157170i
\(239\) 6.63809 0.429382 0.214691 0.976682i \(-0.431126\pi\)
0.214691 + 0.976682i \(0.431126\pi\)
\(240\) 0 0
\(241\) −9.47641 −0.610429 −0.305215 0.952284i \(-0.598728\pi\)
−0.305215 + 0.952284i \(0.598728\pi\)
\(242\) 7.00719i 0.450439i
\(243\) 0 0
\(244\) −2.97107 −0.190203
\(245\) −2.19902 + 8.85043i −0.140490 + 0.565433i
\(246\) 0 0
\(247\) 0.539189i 0.0343078i
\(248\) 2.20743i 0.140172i
\(249\) 0 0
\(250\) 12.8166 + 11.4836i 0.810592 + 0.726286i
\(251\) −29.4596 −1.85947 −0.929736 0.368226i \(-0.879965\pi\)
−0.929736 + 0.368226i \(0.879965\pi\)
\(252\) 0 0
\(253\) 7.18568i 0.451760i
\(254\) −27.7165 −1.73909
\(255\) 0 0
\(256\) 8.57531 0.535957
\(257\) 20.4657i 1.27662i −0.769781 0.638309i \(-0.779634\pi\)
0.769781 0.638309i \(-0.220366\pi\)
\(258\) 0 0
\(259\) −10.3402 −0.642507
\(260\) −0.800984 0.199016i −0.0496749 0.0123424i
\(261\) 0 0
\(262\) 21.9421i 1.35559i
\(263\) 9.14342i 0.563808i −0.959443 0.281904i \(-0.909034\pi\)
0.959443 0.281904i \(-0.0909659\pi\)
\(264\) 0 0
\(265\) 18.4391 + 4.58145i 1.13270 + 0.281436i
\(266\) −1.41855 −0.0869769
\(267\) 0 0
\(268\) 2.90337i 0.177352i
\(269\) 11.3919 0.694576 0.347288 0.937759i \(-0.387103\pi\)
0.347288 + 0.937759i \(0.387103\pi\)
\(270\) 0 0
\(271\) −21.1350 −1.28386 −0.641930 0.766763i \(-0.721866\pi\)
−0.641930 + 0.766763i \(0.721866\pi\)
\(272\) 4.24128i 0.257165i
\(273\) 0 0
\(274\) −21.2183 −1.28185
\(275\) −11.2195 5.94214i −0.676563 0.358325i
\(276\) 0 0
\(277\) 13.0784i 0.785804i 0.919580 + 0.392902i \(0.128529\pi\)
−0.919580 + 0.392902i \(0.871471\pi\)
\(278\) 10.2413i 0.614231i
\(279\) 0 0
\(280\) 2.31351 9.31124i 0.138259 0.556453i
\(281\) 0.680346 0.0405860 0.0202930 0.999794i \(-0.493540\pi\)
0.0202930 + 0.999794i \(0.493540\pi\)
\(282\) 0 0
\(283\) 19.2956i 1.14701i −0.819203 0.573504i \(-0.805584\pi\)
0.819203 0.573504i \(-0.194416\pi\)
\(284\) −5.34509 −0.317173
\(285\) 0 0
\(286\) 3.90829 0.231102
\(287\) 2.15676i 0.127309i
\(288\) 0 0
\(289\) 16.1506 0.950036
\(290\) 17.1278 + 4.25565i 1.00578 + 0.249900i
\(291\) 0 0
\(292\) 0.719953i 0.0421321i
\(293\) 9.46800i 0.553126i 0.960996 + 0.276563i \(0.0891955\pi\)
−0.960996 + 0.276563i \(0.910804\pi\)
\(294\) 0 0
\(295\) 2.54638 10.2485i 0.148256 0.596689i
\(296\) −15.1857 −0.882650
\(297\) 0 0
\(298\) 13.9733i 0.809454i
\(299\) −2.82991 −0.163658
\(300\) 0 0
\(301\) −10.9939 −0.633675
\(302\) 5.04453i 0.290280i
\(303\) 0 0
\(304\) −2.48133 −0.142314
\(305\) −4.34017 + 17.4680i −0.248518 + 1.00021i
\(306\) 0 0
\(307\) 0.264063i 0.0150709i 0.999972 + 0.00753543i \(0.00239862\pi\)
−0.999972 + 0.00753543i \(0.997601\pi\)
\(308\) 1.60197i 0.0912806i
\(309\) 0 0
\(310\) −2.93722 0.729794i −0.166823 0.0414495i
\(311\) −13.0472 −0.739838 −0.369919 0.929064i \(-0.620615\pi\)
−0.369919 + 0.929064i \(0.620615\pi\)
\(312\) 0 0
\(313\) 33.7009i 1.90489i −0.304718 0.952443i \(-0.598562\pi\)
0.304718 0.952443i \(-0.401438\pi\)
\(314\) 19.7587 1.11505
\(315\) 0 0
\(316\) 0.183417 0.0103180
\(317\) 13.9506i 0.783541i −0.920063 0.391771i \(-0.871863\pi\)
0.920063 0.391771i \(-0.128137\pi\)
\(318\) 0 0
\(319\) −13.0205 −0.729009
\(320\) 3.25073 13.0833i 0.181721 0.731379i
\(321\) 0 0
\(322\) 7.44521i 0.414905i
\(323\) 0.496928i 0.0276498i
\(324\) 0 0
\(325\) −2.34017 + 4.41855i −0.129809 + 0.245097i
\(326\) −18.5464 −1.02719
\(327\) 0 0
\(328\) 3.16743i 0.174892i
\(329\) −9.75872 −0.538016
\(330\) 0 0
\(331\) −18.4547 −1.01436 −0.507180 0.861840i \(-0.669312\pi\)
−0.507180 + 0.861840i \(0.669312\pi\)
\(332\) 3.18568i 0.174837i
\(333\) 0 0
\(334\) −13.4368 −0.735229
\(335\) 17.0700 + 4.24128i 0.932632 + 0.231726i
\(336\) 0 0
\(337\) 15.8576i 0.863820i 0.901917 + 0.431910i \(0.142160\pi\)
−0.901917 + 0.431910i \(0.857840\pi\)
\(338\) 1.53919i 0.0837208i
\(339\) 0 0
\(340\) 0.738205 + 0.183417i 0.0400348 + 0.00994721i
\(341\) 2.23287 0.120916
\(342\) 0 0
\(343\) 18.9360i 1.02245i
\(344\) −16.1457 −0.870517
\(345\) 0 0
\(346\) 1.32950 0.0714741
\(347\) 9.72487i 0.522059i 0.965331 + 0.261029i \(0.0840619\pi\)
−0.965331 + 0.261029i \(0.915938\pi\)
\(348\) 0 0
\(349\) 30.9093 1.65454 0.827269 0.561805i \(-0.189893\pi\)
0.827269 + 0.561805i \(0.189893\pi\)
\(350\) 11.6248 + 6.15676i 0.621369 + 0.329092i
\(351\) 0 0
\(352\) 5.23779i 0.279175i
\(353\) 5.95055i 0.316716i −0.987382 0.158358i \(-0.949380\pi\)
0.987382 0.158358i \(-0.0506200\pi\)
\(354\) 0 0
\(355\) −7.80817 + 31.4257i −0.414415 + 1.66791i
\(356\) −4.73820 −0.251124
\(357\) 0 0
\(358\) 30.6537i 1.62010i
\(359\) 10.9783 0.579410 0.289705 0.957116i \(-0.406443\pi\)
0.289705 + 0.957116i \(0.406443\pi\)
\(360\) 0 0
\(361\) −18.7093 −0.984699
\(362\) 22.1483i 1.16409i
\(363\) 0 0
\(364\) −0.630898 −0.0330680
\(365\) 4.23287 + 1.05172i 0.221558 + 0.0550493i
\(366\) 0 0
\(367\) 10.3740i 0.541520i −0.962647 0.270760i \(-0.912725\pi\)
0.962647 0.270760i \(-0.0872749\pi\)
\(368\) 13.0232i 0.678880i
\(369\) 0 0
\(370\) 5.02052 20.2062i 0.261004 1.05047i
\(371\) 14.5236 0.754027
\(372\) 0 0
\(373\) 23.9877i 1.24204i 0.783796 + 0.621018i \(0.213281\pi\)
−0.783796 + 0.621018i \(0.786719\pi\)
\(374\) −3.60197 −0.186253
\(375\) 0 0
\(376\) −14.3318 −0.739104
\(377\) 5.12783i 0.264096i
\(378\) 0 0
\(379\) −29.7575 −1.52854 −0.764270 0.644896i \(-0.776901\pi\)
−0.764270 + 0.644896i \(0.776901\pi\)
\(380\) 0.107307 0.431882i 0.00550474 0.0221551i
\(381\) 0 0
\(382\) 2.27247i 0.116270i
\(383\) 12.4163i 0.634442i −0.948352 0.317221i \(-0.897250\pi\)
0.948352 0.317221i \(-0.102750\pi\)
\(384\) 0 0
\(385\) −9.41855 2.34017i −0.480014 0.119266i
\(386\) 27.2930 1.38918
\(387\) 0 0
\(388\) 2.18342i 0.110846i
\(389\) −16.8371 −0.853675 −0.426837 0.904328i \(-0.640372\pi\)
−0.426837 + 0.904328i \(0.640372\pi\)
\(390\) 0 0
\(391\) 2.60811 0.131898
\(392\) 10.2378i 0.517086i
\(393\) 0 0
\(394\) −3.07838 −0.155086
\(395\) 0.267938 1.07838i 0.0134814 0.0542591i
\(396\) 0 0
\(397\) 3.89269i 0.195369i 0.995217 + 0.0976843i \(0.0311436\pi\)
−0.995217 + 0.0976843i \(0.968856\pi\)
\(398\) 8.29914i 0.415998i
\(399\) 0 0
\(400\) 20.3340 + 10.7694i 1.01670 + 0.538470i
\(401\) 9.10504 0.454684 0.227342 0.973815i \(-0.426996\pi\)
0.227342 + 0.973815i \(0.426996\pi\)
\(402\) 0 0
\(403\) 0.879362i 0.0438041i
\(404\) −6.06770 −0.301879
\(405\) 0 0
\(406\) 13.4908 0.669536
\(407\) 15.3607i 0.761401i
\(408\) 0 0
\(409\) 19.4186 0.960186 0.480093 0.877218i \(-0.340603\pi\)
0.480093 + 0.877218i \(0.340603\pi\)
\(410\) 4.21461 + 1.04718i 0.208145 + 0.0517166i
\(411\) 0 0
\(412\) 3.76138i 0.185310i
\(413\) 8.07223i 0.397209i
\(414\) 0 0
\(415\) 18.7298 + 4.65368i 0.919409 + 0.228440i
\(416\) −2.06278 −0.101136
\(417\) 0 0
\(418\) 2.10731i 0.103072i
\(419\) −16.7792 −0.819720 −0.409860 0.912149i \(-0.634422\pi\)
−0.409860 + 0.912149i \(0.634422\pi\)
\(420\) 0 0
\(421\) −19.0205 −0.927003 −0.463502 0.886096i \(-0.653407\pi\)
−0.463502 + 0.886096i \(0.653407\pi\)
\(422\) 35.0205i 1.70477i
\(423\) 0 0
\(424\) 21.3295 1.03585
\(425\) 2.15676 4.07223i 0.104618 0.197532i
\(426\) 0 0
\(427\) 13.7587i 0.665831i
\(428\) 3.59932i 0.173979i
\(429\) 0 0
\(430\) 5.33791 21.4836i 0.257417 1.03603i
\(431\) −8.02997 −0.386790 −0.193395 0.981121i \(-0.561950\pi\)
−0.193395 + 0.981121i \(0.561950\pi\)
\(432\) 0 0
\(433\) 13.0472i 0.627008i 0.949587 + 0.313504i \(0.101503\pi\)
−0.949587 + 0.313504i \(0.898497\pi\)
\(434\) −2.31351 −0.111052
\(435\) 0 0
\(436\) −6.22446 −0.298097
\(437\) 1.52586i 0.0729917i
\(438\) 0 0
\(439\) 7.70086 0.367542 0.183771 0.982969i \(-0.441169\pi\)
0.183771 + 0.982969i \(0.441169\pi\)
\(440\) −13.8322 3.43680i −0.659423 0.163843i
\(441\) 0 0
\(442\) 1.41855i 0.0674736i
\(443\) 6.39084i 0.303638i −0.988408 0.151819i \(-0.951487\pi\)
0.988408 0.151819i \(-0.0485131\pi\)
\(444\) 0 0
\(445\) −6.92162 + 27.8576i −0.328116 + 1.32058i
\(446\) −13.4848 −0.638525
\(447\) 0 0
\(448\) 10.3051i 0.486870i
\(449\) 31.6163 1.49207 0.746034 0.665908i \(-0.231956\pi\)
0.746034 + 0.665908i \(0.231956\pi\)
\(450\) 0 0
\(451\) −3.20394 −0.150867
\(452\) 4.34017i 0.204145i
\(453\) 0 0
\(454\) 26.5152 1.24442
\(455\) −0.921622 + 3.70928i −0.0432063 + 0.173894i
\(456\) 0 0
\(457\) 35.6430i 1.66731i −0.552286 0.833655i \(-0.686244\pi\)
0.552286 0.833655i \(-0.313756\pi\)
\(458\) 4.73820i 0.221402i
\(459\) 0 0
\(460\) −2.26672 0.563198i −0.105686 0.0262592i
\(461\) 14.9795 0.697664 0.348832 0.937185i \(-0.386578\pi\)
0.348832 + 0.937185i \(0.386578\pi\)
\(462\) 0 0
\(463\) 9.09663i 0.422756i 0.977404 + 0.211378i \(0.0677951\pi\)
−0.977404 + 0.211378i \(0.932205\pi\)
\(464\) 23.5981 1.09551
\(465\) 0 0
\(466\) 29.1461 1.35017
\(467\) 1.87709i 0.0868616i −0.999056 0.0434308i \(-0.986171\pi\)
0.999056 0.0434308i \(-0.0138288\pi\)
\(468\) 0 0
\(469\) 13.4452 0.620842
\(470\) 4.73820 19.0700i 0.218557 0.879632i
\(471\) 0 0
\(472\) 11.8550i 0.545669i
\(473\) 16.3318i 0.750935i
\(474\) 0 0
\(475\) −2.38243 1.26180i −0.109314 0.0578951i
\(476\) 0.581449 0.0266507
\(477\) 0 0
\(478\) 10.2173i 0.467327i
\(479\) −15.7431 −0.719322 −0.359661 0.933083i \(-0.617108\pi\)
−0.359661 + 0.933083i \(0.617108\pi\)
\(480\) 0 0
\(481\) 6.04945 0.275831
\(482\) 14.5860i 0.664373i
\(483\) 0 0
\(484\) 1.68035 0.0763794
\(485\) 12.8371 + 3.18956i 0.582903 + 0.144830i
\(486\) 0 0
\(487\) 4.94441i 0.224053i 0.993705 + 0.112026i \(0.0357341\pi\)
−0.993705 + 0.112026i \(0.964266\pi\)
\(488\) 20.2062i 0.914692i
\(489\) 0 0
\(490\) −13.6225 3.38470i −0.615401 0.152905i
\(491\) −39.4863 −1.78199 −0.890995 0.454014i \(-0.849992\pi\)
−0.890995 + 0.454014i \(0.849992\pi\)
\(492\) 0 0
\(493\) 4.72592i 0.212845i
\(494\) 0.829914 0.0373396
\(495\) 0 0
\(496\) −4.04680 −0.181706
\(497\) 24.7526i 1.11030i
\(498\) 0 0
\(499\) −1.67089 −0.0747993 −0.0373997 0.999300i \(-0.511907\pi\)
−0.0373997 + 0.999300i \(0.511907\pi\)
\(500\) −2.75380 + 3.07346i −0.123154 + 0.137449i
\(501\) 0 0
\(502\) 45.3439i 2.02380i
\(503\) 9.08557i 0.405105i 0.979271 + 0.202553i \(0.0649237\pi\)
−0.979271 + 0.202553i \(0.935076\pi\)
\(504\) 0 0
\(505\) −8.86376 + 35.6742i −0.394432 + 1.58748i
\(506\) 11.0601 0.491683
\(507\) 0 0
\(508\) 6.64650i 0.294891i
\(509\) −19.5441 −0.866277 −0.433139 0.901327i \(-0.642594\pi\)
−0.433139 + 0.901327i \(0.642594\pi\)
\(510\) 0 0
\(511\) 3.33403 0.147489
\(512\) 13.6114i 0.601546i
\(513\) 0 0
\(514\) 31.5006 1.38943
\(515\) 22.1145 + 5.49466i 0.974481 + 0.242124i
\(516\) 0 0
\(517\) 14.4969i 0.637574i
\(518\) 15.9155i 0.699286i
\(519\) 0 0
\(520\) −1.35350 + 5.44748i −0.0593551 + 0.238888i
\(521\) −6.50534 −0.285004 −0.142502 0.989795i \(-0.545515\pi\)
−0.142502 + 0.989795i \(0.545515\pi\)
\(522\) 0 0
\(523\) 36.5452i 1.59801i −0.601326 0.799004i \(-0.705361\pi\)
0.601326 0.799004i \(-0.294639\pi\)
\(524\) 5.26180 0.229863
\(525\) 0 0
\(526\) 14.0735 0.613632
\(527\) 0.810439i 0.0353033i
\(528\) 0 0
\(529\) 14.9916 0.651808
\(530\) −7.05172 + 28.3812i −0.306307 + 1.23280i
\(531\) 0 0
\(532\) 0.340173i 0.0147484i
\(533\) 1.26180i 0.0546544i
\(534\) 0 0
\(535\) −21.1617 5.25792i −0.914899 0.227320i
\(536\) 19.7458 0.852888
\(537\) 0 0
\(538\) 17.5343i 0.755956i
\(539\) 10.3558 0.446055
\(540\) 0 0
\(541\) 20.3402 0.874492 0.437246 0.899342i \(-0.355954\pi\)
0.437246 + 0.899342i \(0.355954\pi\)
\(542\) 32.5308i 1.39732i
\(543\) 0 0
\(544\) 1.90110 0.0815091
\(545\) −9.09275 + 36.5958i −0.389491 + 1.56759i
\(546\) 0 0
\(547\) 11.5948i 0.495757i −0.968791 0.247879i \(-0.920267\pi\)
0.968791 0.247879i \(-0.0797334\pi\)
\(548\) 5.08822i 0.217358i
\(549\) 0 0
\(550\) 9.14608 17.2690i 0.389990 0.736352i
\(551\) −2.76487 −0.117787
\(552\) 0 0
\(553\) 0.849388i 0.0361196i
\(554\) −20.1301 −0.855246
\(555\) 0 0
\(556\) −2.45589 −0.104153
\(557\) 10.7298i 0.454636i −0.973821 0.227318i \(-0.927004\pi\)
0.973821 0.227318i \(-0.0729957\pi\)
\(558\) 0 0
\(559\) 6.43188 0.272040
\(560\) 17.0700 + 4.24128i 0.721338 + 0.179227i
\(561\) 0 0
\(562\) 1.04718i 0.0441727i
\(563\) 10.2485i 0.431921i 0.976402 + 0.215961i \(0.0692883\pi\)
−0.976402 + 0.215961i \(0.930712\pi\)
\(564\) 0 0
\(565\) −25.5174 6.34017i −1.07353 0.266733i
\(566\) 29.6996 1.24837
\(567\) 0 0
\(568\) 36.3519i 1.52529i
\(569\) −8.84551 −0.370823 −0.185412 0.982661i \(-0.559362\pi\)
−0.185412 + 0.982661i \(0.559362\pi\)
\(570\) 0 0
\(571\) 9.29299 0.388900 0.194450 0.980912i \(-0.437708\pi\)
0.194450 + 0.980912i \(0.437708\pi\)
\(572\) 0.937221i 0.0391872i
\(573\) 0 0
\(574\) 3.31965 0.138560
\(575\) −6.62249 + 12.5041i −0.276177 + 0.521458i
\(576\) 0 0
\(577\) 19.5259i 0.812872i −0.913679 0.406436i \(-0.866771\pi\)
0.913679 0.406436i \(-0.133229\pi\)
\(578\) 24.8588i 1.03399i
\(579\) 0 0
\(580\) −1.02052 + 4.10731i −0.0423747 + 0.170547i
\(581\) 14.7526 0.612040
\(582\) 0 0
\(583\) 21.5753i 0.893558i
\(584\) 4.89639 0.202614
\(585\) 0 0
\(586\) −14.5730 −0.602007
\(587\) 22.5029i 0.928794i −0.885627 0.464397i \(-0.846271\pi\)
0.885627 0.464397i \(-0.153729\pi\)
\(588\) 0 0
\(589\) 0.474142 0.0195367
\(590\) 15.7743 + 3.91935i 0.649419 + 0.161357i
\(591\) 0 0
\(592\) 27.8394i 1.14419i
\(593\) 4.43907i 0.182291i 0.995838 + 0.0911454i \(0.0290528\pi\)
−0.995838 + 0.0911454i \(0.970947\pi\)
\(594\) 0 0
\(595\) 0.849388 3.41855i 0.0348215 0.140147i
\(596\) 3.35085 0.137256
\(597\) 0 0
\(598\) 4.35577i 0.178121i
\(599\) 33.3607 1.36308 0.681540 0.731780i \(-0.261310\pi\)
0.681540 + 0.731780i \(0.261310\pi\)
\(600\) 0 0
\(601\) 13.3197 0.543320 0.271660 0.962393i \(-0.412427\pi\)
0.271660 + 0.962393i \(0.412427\pi\)
\(602\) 16.9216i 0.689674i
\(603\) 0 0
\(604\) −1.20969 −0.0492217
\(605\) 2.45467 9.87936i 0.0997964 0.401653i
\(606\) 0 0
\(607\) 14.1184i 0.573047i 0.958073 + 0.286523i \(0.0924996\pi\)
−0.958073 + 0.286523i \(0.907500\pi\)
\(608\) 1.11223i 0.0451068i
\(609\) 0 0
\(610\) −26.8865 6.68035i −1.08860 0.270479i
\(611\) 5.70928 0.230973
\(612\) 0 0
\(613\) 26.8104i 1.08286i 0.840745 + 0.541432i \(0.182118\pi\)
−0.840745 + 0.541432i \(0.817882\pi\)
\(614\) −0.406442 −0.0164027
\(615\) 0 0
\(616\) −10.8950 −0.438970
\(617\) 14.8950i 0.599649i −0.953994 0.299824i \(-0.903072\pi\)
0.953994 0.299824i \(-0.0969280\pi\)
\(618\) 0 0
\(619\) −45.3184 −1.82150 −0.910751 0.412956i \(-0.864496\pi\)
−0.910751 + 0.412956i \(0.864496\pi\)
\(620\) 0.175007 0.704355i 0.00702845 0.0282876i
\(621\) 0 0
\(622\) 20.0821i 0.805218i
\(623\) 21.9421i 0.879093i
\(624\) 0 0
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) 51.8720 2.07322
\(627\) 0 0
\(628\) 4.73820i 0.189075i
\(629\) −5.57531 −0.222302
\(630\) 0 0
\(631\) 37.8876 1.50828 0.754141 0.656713i \(-0.228054\pi\)
0.754141 + 0.656713i \(0.228054\pi\)
\(632\) 1.24742i 0.0496197i
\(633\) 0 0
\(634\) 21.4725 0.852783
\(635\) −39.0772 9.70928i −1.55073 0.385301i
\(636\) 0 0
\(637\) 4.07838i 0.161591i
\(638\) 20.0410i 0.793432i
\(639\) 0 0
\(640\) 29.0905 + 7.22795i 1.14990 + 0.285710i
\(641\) 8.47027 0.334555 0.167278 0.985910i \(-0.446502\pi\)
0.167278 + 0.985910i \(0.446502\pi\)
\(642\) 0 0
\(643\) 34.1750i 1.34773i −0.738854 0.673865i \(-0.764633\pi\)
0.738854 0.673865i \(-0.235367\pi\)
\(644\) −1.78539 −0.0703541
\(645\) 0 0
\(646\) −0.764867 −0.0300933
\(647\) 13.8238i 0.543468i 0.962372 + 0.271734i \(0.0875972\pi\)
−0.962372 + 0.271734i \(0.912403\pi\)
\(648\) 0 0
\(649\) −11.9916 −0.470711
\(650\) −6.80098 3.60197i −0.266757 0.141281i
\(651\) 0 0
\(652\) 4.44748i 0.174177i
\(653\) 42.8781i 1.67795i −0.544169 0.838976i \(-0.683155\pi\)
0.544169 0.838976i \(-0.316845\pi\)
\(654\) 0 0
\(655\) 7.68649 30.9360i 0.300336 1.20877i
\(656\) 5.80674 0.226715
\(657\) 0 0
\(658\) 15.0205i 0.585561i
\(659\) −23.2495 −0.905672 −0.452836 0.891594i \(-0.649588\pi\)
−0.452836 + 0.891594i \(0.649588\pi\)
\(660\) 0 0
\(661\) 27.0661 1.05275 0.526374 0.850253i \(-0.323551\pi\)
0.526374 + 0.850253i \(0.323551\pi\)
\(662\) 28.4052i 1.10400i
\(663\) 0 0
\(664\) 21.6658 0.840796
\(665\) −2.00000 0.496928i −0.0775567 0.0192701i
\(666\) 0 0
\(667\) 14.5113i 0.561880i
\(668\) 3.22219i 0.124670i
\(669\) 0 0
\(670\) −6.52813 + 26.2739i −0.252203 + 1.01505i
\(671\) 20.4391 0.789042
\(672\) 0 0
\(673\) 16.1711i 0.623351i −0.950189 0.311676i \(-0.899110\pi\)
0.950189 0.311676i \(-0.100890\pi\)
\(674\) −24.4079 −0.940156
\(675\) 0 0
\(676\) 0.369102 0.0141962
\(677\) 43.1194i 1.65721i −0.559831 0.828607i \(-0.689134\pi\)
0.559831 0.828607i \(-0.310866\pi\)
\(678\) 0 0
\(679\) 10.1112 0.388032
\(680\) 1.24742 5.02052i 0.0478363 0.192528i
\(681\) 0 0
\(682\) 3.43680i 0.131602i
\(683\) 17.7093i 0.677627i −0.940854 0.338813i \(-0.889974\pi\)
0.940854 0.338813i \(-0.110026\pi\)
\(684\) 0 0
\(685\) −29.9155 7.43293i −1.14301 0.283998i
\(686\) −29.1461 −1.11280
\(687\) 0 0
\(688\) 29.5993i 1.12846i
\(689\) −8.49693 −0.323707
\(690\) 0 0
\(691\) −24.8794 −0.946456 −0.473228 0.880940i \(-0.656911\pi\)
−0.473228 + 0.880940i \(0.656911\pi\)
\(692\) 0.318817i 0.0121196i
\(693\) 0 0
\(694\) −14.9684 −0.568193
\(695\) −3.58759 + 14.4391i −0.136085 + 0.547705i
\(696\) 0 0
\(697\) 1.16290i 0.0440479i
\(698\) 47.5753i 1.80075i
\(699\) 0 0
\(700\) −1.47641 + 2.78765i −0.0558030 + 0.105363i
\(701\) −33.0661 −1.24889 −0.624445 0.781069i \(-0.714675\pi\)
−0.624445 + 0.781069i \(0.714675\pi\)
\(702\) 0 0
\(703\) 3.26180i 0.123021i
\(704\) −15.3086 −0.576964
\(705\) 0 0
\(706\) 9.15902 0.344704
\(707\) 28.0989i 1.05677i
\(708\) 0 0
\(709\) −2.18342 −0.0820000 −0.0410000 0.999159i \(-0.513054\pi\)
−0.0410000 + 0.999159i \(0.513054\pi\)
\(710\) −48.3701 12.0183i −1.81530 0.451037i
\(711\) 0 0
\(712\) 32.2245i 1.20766i
\(713\) 2.48852i 0.0931957i
\(714\) 0 0
\(715\) 5.51026 + 1.36910i 0.206072 + 0.0512015i
\(716\) −7.35085 −0.274714
\(717\) 0 0
\(718\) 16.8976i 0.630613i
\(719\) 5.20847 0.194243 0.0971216 0.995273i \(-0.469036\pi\)
0.0971216 + 0.995273i \(0.469036\pi\)
\(720\) 0 0
\(721\) 17.4186 0.648701
\(722\) 28.7971i 1.07172i
\(723\) 0 0
\(724\) −5.31124 −0.197391
\(725\) 22.6576 + 12.0000i 0.841481 + 0.445669i
\(726\) 0 0
\(727\) 3.52464i 0.130721i −0.997862 0.0653607i \(-0.979180\pi\)
0.997862 0.0653607i \(-0.0208198\pi\)
\(728\) 4.29072i 0.159025i
\(729\) 0 0
\(730\) −1.61879 + 6.51518i −0.0599141 + 0.241138i
\(731\) −5.92777 −0.219246
\(732\) 0 0
\(733\) 21.8310i 0.806345i 0.915124 + 0.403172i \(0.132093\pi\)
−0.915124 + 0.403172i \(0.867907\pi\)
\(734\) 15.9676 0.589374
\(735\) 0 0
\(736\) −5.83749 −0.215173
\(737\) 19.9733i 0.735727i
\(738\) 0 0
\(739\) −50.3533 −1.85228 −0.926139 0.377184i \(-0.876893\pi\)
−0.926139 + 0.377184i \(0.876893\pi\)
\(740\) 4.84551 + 1.20394i 0.178125 + 0.0442576i
\(741\) 0 0
\(742\) 22.3545i 0.820661i
\(743\) 30.7877i 1.12949i 0.825266 + 0.564745i \(0.191025\pi\)
−0.825266 + 0.564745i \(0.808975\pi\)
\(744\) 0 0
\(745\) 4.89496 19.7009i 0.179337 0.721784i
\(746\) −36.9216 −1.35180
\(747\) 0 0
\(748\) 0.863763i 0.0315823i
\(749\) −16.6681 −0.609038
\(750\) 0 0
\(751\) −10.6225 −0.387620 −0.193810 0.981039i \(-0.562085\pi\)
−0.193810 + 0.981039i \(0.562085\pi\)
\(752\) 26.2739i 0.958111i
\(753\) 0 0
\(754\) −7.89269 −0.287435
\(755\) −1.76713 + 7.11223i −0.0643126 + 0.258840i
\(756\) 0 0
\(757\) 7.98562i 0.290242i −0.989414 0.145121i \(-0.953643\pi\)
0.989414 0.145121i \(-0.0463572\pi\)
\(758\) 45.8024i 1.66362i
\(759\) 0 0
\(760\) −2.93722 0.729794i −0.106544 0.0264724i
\(761\) 48.9360 1.77393 0.886964 0.461838i \(-0.152810\pi\)
0.886964 + 0.461838i \(0.152810\pi\)
\(762\) 0 0
\(763\) 28.8248i 1.04353i
\(764\) 0.544946 0.0197155
\(765\) 0 0
\(766\) 19.1110 0.690509
\(767\) 4.72261i 0.170523i
\(768\) 0 0
\(769\) 7.99547 0.288324 0.144162 0.989554i \(-0.453951\pi\)
0.144162 + 0.989554i \(0.453951\pi\)
\(770\) 3.60197 14.4969i 0.129806 0.522433i
\(771\) 0 0
\(772\) 6.54495i 0.235558i
\(773\) 26.6141i 0.957242i 0.878022 + 0.478621i \(0.158863\pi\)
−0.878022 + 0.478621i \(0.841137\pi\)
\(774\) 0 0
\(775\) −3.88550 2.05786i −0.139571 0.0739205i
\(776\) 14.8494 0.533062
\(777\) 0 0
\(778\) 25.9155i 0.929115i
\(779\) −0.680346 −0.0243759
\(780\) 0 0
\(781\) 36.7708 1.31576
\(782\) 4.01438i 0.143554i
\(783\) 0 0
\(784\) −18.7686 −0.670306
\(785\) 27.8576 + 6.92162i 0.994281 + 0.247043i
\(786\) 0 0
\(787\) 9.25792i 0.330009i 0.986293 + 0.165005i \(0.0527639\pi\)
−0.986293 + 0.165005i \(0.947236\pi\)
\(788\) 0.738205i 0.0262975i
\(789\) 0 0
\(790\) 1.65983 + 0.412408i 0.0590540 + 0.0146728i
\(791\) −20.0989 −0.714634
\(792\) 0 0
\(793\) 8.04945i 0.285844i
\(794\) −5.99159 −0.212634
\(795\) 0 0