Properties

Label 1050.3.e.a.701.3
Level $1050$
Weight $3$
Character 1050.701
Analytic conductor $28.610$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{7})\)
Defining polynomial: \( x^{4} + 8x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 701.3
Root \(-2.57794i\) of defining polynomial
Character \(\chi\) \(=\) 1050.701
Dual form 1050.3.e.a.701.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(-2.64575 + 1.41421i) q^{3} -2.00000 q^{4} +(-2.00000 - 3.74166i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(5.00000 - 7.48331i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(-2.64575 + 1.41421i) q^{3} -2.00000 q^{4} +(-2.00000 - 3.74166i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(5.00000 - 7.48331i) q^{9} +14.5544i q^{11} +(5.29150 - 2.82843i) q^{12} +0.583005 q^{13} +3.74166i q^{14} +4.00000 q^{16} -21.5367i q^{17} +(10.5830 + 7.07107i) q^{18} -16.0000 q^{19} +(-7.00000 + 3.74166i) q^{21} -20.5830 q^{22} +38.8308i q^{23} +(4.00000 + 7.48331i) q^{24} +0.824494i q^{26} +(-2.64575 + 26.8701i) q^{27} -5.29150 q^{28} -35.7676i q^{29} -58.4575 q^{31} +5.65685i q^{32} +(-20.5830 - 38.5073i) q^{33} +30.4575 q^{34} +(-10.0000 + 14.9666i) q^{36} -20.0000 q^{37} -22.6274i q^{38} +(-1.54249 + 0.824494i) q^{39} +8.75149i q^{41} +(-5.29150 - 9.89949i) q^{42} +11.7490 q^{43} -29.1088i q^{44} -54.9150 q^{46} -8.48528i q^{47} +(-10.5830 + 5.65685i) q^{48} +7.00000 q^{49} +(30.4575 + 56.9808i) q^{51} -1.16601 q^{52} -50.9117i q^{53} +(-38.0000 - 3.74166i) q^{54} -7.48331i q^{56} +(42.3320 - 22.6274i) q^{57} +50.5830 q^{58} -58.2175i q^{59} +38.9150 q^{61} -82.6714i q^{62} +(13.2288 - 19.7990i) q^{63} -8.00000 q^{64} +(54.4575 - 29.1088i) q^{66} -70.5830 q^{67} +43.0734i q^{68} +(-54.9150 - 102.737i) q^{69} +17.0279i q^{71} +(-21.1660 - 14.1421i) q^{72} -72.3320 q^{73} -28.2843i q^{74} +32.0000 q^{76} +38.5073i q^{77} +(-1.16601 - 2.18141i) q^{78} +20.9150 q^{79} +(-31.0000 - 74.8331i) q^{81} -12.3765 q^{82} -145.544i q^{83} +(14.0000 - 7.48331i) q^{84} +16.6156i q^{86} +(50.5830 + 94.6321i) q^{87} +41.1660 q^{88} -53.6514i q^{89} +1.54249 q^{91} -77.6616i q^{92} +(154.664 - 82.6714i) q^{93} +12.0000 q^{94} +(-8.00000 - 14.9666i) q^{96} +111.166 q^{97} +9.89949i q^{98} +(108.915 + 72.7719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{4} - 8 q^{6} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{4} - 8 q^{6} + 20 q^{9} - 40 q^{13} + 16 q^{16} - 64 q^{19} - 28 q^{21} - 40 q^{22} + 16 q^{24} - 128 q^{31} - 40 q^{33} + 16 q^{34} - 40 q^{36} - 80 q^{37} - 112 q^{39} - 80 q^{43} - 8 q^{46} + 28 q^{49} + 16 q^{51} + 80 q^{52} - 152 q^{54} + 160 q^{58} - 56 q^{61} - 32 q^{64} + 112 q^{66} - 240 q^{67} - 8 q^{69} - 120 q^{73} + 128 q^{76} + 80 q^{78} - 128 q^{79} - 124 q^{81} - 240 q^{82} + 56 q^{84} + 160 q^{87} + 80 q^{88} + 112 q^{91} + 280 q^{93} + 48 q^{94} - 32 q^{96} + 360 q^{97} + 224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −2.64575 + 1.41421i −0.881917 + 0.471405i
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) −2.00000 3.74166i −0.333333 0.623610i
\(7\) 2.64575 0.377964
\(8\) 2.82843i 0.353553i
\(9\) 5.00000 7.48331i 0.555556 0.831479i
\(10\) 0 0
\(11\) 14.5544i 1.32313i 0.749890 + 0.661563i \(0.230107\pi\)
−0.749890 + 0.661563i \(0.769893\pi\)
\(12\) 5.29150 2.82843i 0.440959 0.235702i
\(13\) 0.583005 0.0448466 0.0224233 0.999749i \(-0.492862\pi\)
0.0224233 + 0.999749i \(0.492862\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 21.5367i 1.26687i −0.773798 0.633433i \(-0.781645\pi\)
0.773798 0.633433i \(-0.218355\pi\)
\(18\) 10.5830 + 7.07107i 0.587945 + 0.392837i
\(19\) −16.0000 −0.842105 −0.421053 0.907036i \(-0.638339\pi\)
−0.421053 + 0.907036i \(0.638339\pi\)
\(20\) 0 0
\(21\) −7.00000 + 3.74166i −0.333333 + 0.178174i
\(22\) −20.5830 −0.935591
\(23\) 38.8308i 1.68830i 0.536111 + 0.844148i \(0.319893\pi\)
−0.536111 + 0.844148i \(0.680107\pi\)
\(24\) 4.00000 + 7.48331i 0.166667 + 0.311805i
\(25\) 0 0
\(26\) 0.824494i 0.0317113i
\(27\) −2.64575 + 26.8701i −0.0979908 + 0.995187i
\(28\) −5.29150 −0.188982
\(29\) 35.7676i 1.23337i −0.787212 0.616683i \(-0.788476\pi\)
0.787212 0.616683i \(-0.211524\pi\)
\(30\) 0 0
\(31\) −58.4575 −1.88573 −0.942863 0.333180i \(-0.891878\pi\)
−0.942863 + 0.333180i \(0.891878\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −20.5830 38.5073i −0.623727 1.16689i
\(34\) 30.4575 0.895809
\(35\) 0 0
\(36\) −10.0000 + 14.9666i −0.277778 + 0.415740i
\(37\) −20.0000 −0.540541 −0.270270 0.962784i \(-0.587113\pi\)
−0.270270 + 0.962784i \(0.587113\pi\)
\(38\) 22.6274i 0.595458i
\(39\) −1.54249 + 0.824494i −0.0395509 + 0.0211409i
\(40\) 0 0
\(41\) 8.75149i 0.213451i 0.994289 + 0.106725i \(0.0340366\pi\)
−0.994289 + 0.106725i \(0.965963\pi\)
\(42\) −5.29150 9.89949i −0.125988 0.235702i
\(43\) 11.7490 0.273233 0.136616 0.990624i \(-0.456377\pi\)
0.136616 + 0.990624i \(0.456377\pi\)
\(44\) 29.1088i 0.661563i
\(45\) 0 0
\(46\) −54.9150 −1.19380
\(47\) 8.48528i 0.180538i −0.995917 0.0902690i \(-0.971227\pi\)
0.995917 0.0902690i \(-0.0287727\pi\)
\(48\) −10.5830 + 5.65685i −0.220479 + 0.117851i
\(49\) 7.00000 0.142857
\(50\) 0 0
\(51\) 30.4575 + 56.9808i 0.597206 + 1.11727i
\(52\) −1.16601 −0.0224233
\(53\) 50.9117i 0.960598i −0.877105 0.480299i \(-0.840528\pi\)
0.877105 0.480299i \(-0.159472\pi\)
\(54\) −38.0000 3.74166i −0.703704 0.0692900i
\(55\) 0 0
\(56\) 7.48331i 0.133631i
\(57\) 42.3320 22.6274i 0.742667 0.396972i
\(58\) 50.5830 0.872121
\(59\) 58.2175i 0.986738i −0.869820 0.493369i \(-0.835765\pi\)
0.869820 0.493369i \(-0.164235\pi\)
\(60\) 0 0
\(61\) 38.9150 0.637951 0.318976 0.947763i \(-0.396661\pi\)
0.318976 + 0.947763i \(0.396661\pi\)
\(62\) 82.6714i 1.33341i
\(63\) 13.2288 19.7990i 0.209980 0.314270i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 54.4575 29.1088i 0.825114 0.441042i
\(67\) −70.5830 −1.05348 −0.526739 0.850027i \(-0.676585\pi\)
−0.526739 + 0.850027i \(0.676585\pi\)
\(68\) 43.0734i 0.633433i
\(69\) −54.9150 102.737i −0.795870 1.48894i
\(70\) 0 0
\(71\) 17.0279i 0.239829i 0.992784 + 0.119915i \(0.0382621\pi\)
−0.992784 + 0.119915i \(0.961738\pi\)
\(72\) −21.1660 14.1421i −0.293972 0.196419i
\(73\) −72.3320 −0.990850 −0.495425 0.868651i \(-0.664988\pi\)
−0.495425 + 0.868651i \(0.664988\pi\)
\(74\) 28.2843i 0.382220i
\(75\) 0 0
\(76\) 32.0000 0.421053
\(77\) 38.5073i 0.500095i
\(78\) −1.16601 2.18141i −0.0149489 0.0279667i
\(79\) 20.9150 0.264747 0.132374 0.991200i \(-0.457740\pi\)
0.132374 + 0.991200i \(0.457740\pi\)
\(80\) 0 0
\(81\) −31.0000 74.8331i −0.382716 0.923866i
\(82\) −12.3765 −0.150933
\(83\) 145.544i 1.75354i −0.480910 0.876770i \(-0.659694\pi\)
0.480910 0.876770i \(-0.340306\pi\)
\(84\) 14.0000 7.48331i 0.166667 0.0890871i
\(85\) 0 0
\(86\) 16.6156i 0.193205i
\(87\) 50.5830 + 94.6321i 0.581414 + 1.08773i
\(88\) 41.1660 0.467796
\(89\) 53.6514i 0.602824i −0.953494 0.301412i \(-0.902542\pi\)
0.953494 0.301412i \(-0.0974580\pi\)
\(90\) 0 0
\(91\) 1.54249 0.0169504
\(92\) 77.6616i 0.844148i
\(93\) 154.664 82.6714i 1.66305 0.888940i
\(94\) 12.0000 0.127660
\(95\) 0 0
\(96\) −8.00000 14.9666i −0.0833333 0.155902i
\(97\) 111.166 1.14604 0.573021 0.819541i \(-0.305771\pi\)
0.573021 + 0.819541i \(0.305771\pi\)
\(98\) 9.89949i 0.101015i
\(99\) 108.915 + 72.7719i 1.10015 + 0.735070i
\(100\) 0 0
\(101\) 57.8367i 0.572641i 0.958134 + 0.286320i \(0.0924322\pi\)
−0.958134 + 0.286320i \(0.907568\pi\)
\(102\) −80.5830 + 43.0734i −0.790029 + 0.422289i
\(103\) 119.373 1.15896 0.579478 0.814988i \(-0.303256\pi\)
0.579478 + 0.814988i \(0.303256\pi\)
\(104\) 1.64899i 0.0158557i
\(105\) 0 0
\(106\) 72.0000 0.679245
\(107\) 116.492i 1.08871i −0.838854 0.544357i \(-0.816774\pi\)
0.838854 0.544357i \(-0.183226\pi\)
\(108\) 5.29150 53.7401i 0.0489954 0.497594i
\(109\) 87.8301 0.805780 0.402890 0.915248i \(-0.368006\pi\)
0.402890 + 0.915248i \(0.368006\pi\)
\(110\) 0 0
\(111\) 52.9150 28.2843i 0.476712 0.254813i
\(112\) 10.5830 0.0944911
\(113\) 69.1763i 0.612180i 0.952003 + 0.306090i \(0.0990208\pi\)
−0.952003 + 0.306090i \(0.900979\pi\)
\(114\) 32.0000 + 59.8665i 0.280702 + 0.525145i
\(115\) 0 0
\(116\) 71.5352i 0.616683i
\(117\) 2.91503 4.36281i 0.0249148 0.0372890i
\(118\) 82.3320 0.697729
\(119\) 56.9808i 0.478830i
\(120\) 0 0
\(121\) −90.8301 −0.750662
\(122\) 55.0342i 0.451100i
\(123\) −12.3765 23.1543i −0.100622 0.188246i
\(124\) 116.915 0.942863
\(125\) 0 0
\(126\) 28.0000 + 18.7083i 0.222222 + 0.148478i
\(127\) 27.0850 0.213268 0.106634 0.994298i \(-0.465993\pi\)
0.106634 + 0.994298i \(0.465993\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −31.0850 + 16.6156i −0.240969 + 0.128803i
\(130\) 0 0
\(131\) 145.544i 1.11102i −0.831509 0.555511i \(-0.812523\pi\)
0.831509 0.555511i \(-0.187477\pi\)
\(132\) 41.1660 + 77.0146i 0.311864 + 0.583444i
\(133\) −42.3320 −0.318286
\(134\) 99.8194i 0.744921i
\(135\) 0 0
\(136\) −60.9150 −0.447905
\(137\) 24.8088i 0.181086i 0.995893 + 0.0905431i \(0.0288603\pi\)
−0.995893 + 0.0905431i \(0.971140\pi\)
\(138\) 145.292 77.6616i 1.05284 0.562765i
\(139\) 146.458 1.05365 0.526826 0.849973i \(-0.323382\pi\)
0.526826 + 0.849973i \(0.323382\pi\)
\(140\) 0 0
\(141\) 12.0000 + 22.4499i 0.0851064 + 0.159219i
\(142\) −24.0810 −0.169585
\(143\) 8.48528i 0.0593376i
\(144\) 20.0000 29.9333i 0.138889 0.207870i
\(145\) 0 0
\(146\) 102.293i 0.700636i
\(147\) −18.5203 + 9.89949i −0.125988 + 0.0673435i
\(148\) 40.0000 0.270270
\(149\) 219.552i 1.47351i −0.676162 0.736753i \(-0.736358\pi\)
0.676162 0.736753i \(-0.263642\pi\)
\(150\) 0 0
\(151\) −211.660 −1.40172 −0.700861 0.713298i \(-0.747201\pi\)
−0.700861 + 0.713298i \(0.747201\pi\)
\(152\) 45.2548i 0.297729i
\(153\) −161.166 107.684i −1.05337 0.703814i
\(154\) −54.4575 −0.353620
\(155\) 0 0
\(156\) 3.08497 1.64899i 0.0197755 0.0105704i
\(157\) −208.745 −1.32959 −0.664793 0.747027i \(-0.731480\pi\)
−0.664793 + 0.747027i \(0.731480\pi\)
\(158\) 29.5783i 0.187205i
\(159\) 72.0000 + 134.700i 0.452830 + 0.847168i
\(160\) 0 0
\(161\) 102.737i 0.638116i
\(162\) 105.830 43.8406i 0.653272 0.270621i
\(163\) −266.996 −1.63801 −0.819006 0.573784i \(-0.805475\pi\)
−0.819006 + 0.573784i \(0.805475\pi\)
\(164\) 17.5030i 0.106725i
\(165\) 0 0
\(166\) 205.830 1.23994
\(167\) 7.19124i 0.0430613i −0.999768 0.0215307i \(-0.993146\pi\)
0.999768 0.0215307i \(-0.00685395\pi\)
\(168\) 10.5830 + 19.7990i 0.0629941 + 0.117851i
\(169\) −168.660 −0.997989
\(170\) 0 0
\(171\) −80.0000 + 119.733i −0.467836 + 0.700193i
\(172\) −23.4980 −0.136616
\(173\) 192.536i 1.11293i −0.830872 0.556464i \(-0.812158\pi\)
0.830872 0.556464i \(-0.187842\pi\)
\(174\) −133.830 + 71.5352i −0.769138 + 0.411122i
\(175\) 0 0
\(176\) 58.2175i 0.330781i
\(177\) 82.3320 + 154.029i 0.465153 + 0.870221i
\(178\) 75.8745 0.426261
\(179\) 43.6631i 0.243928i 0.992535 + 0.121964i \(0.0389193\pi\)
−0.992535 + 0.121964i \(0.961081\pi\)
\(180\) 0 0
\(181\) −81.0850 −0.447983 −0.223992 0.974591i \(-0.571909\pi\)
−0.223992 + 0.974591i \(0.571909\pi\)
\(182\) 2.18141i 0.0119857i
\(183\) −102.959 + 55.0342i −0.562620 + 0.300733i
\(184\) 109.830 0.596902
\(185\) 0 0
\(186\) 116.915 + 218.728i 0.628575 + 1.17596i
\(187\) 313.454 1.67622
\(188\) 16.9706i 0.0902690i
\(189\) −7.00000 + 71.0915i −0.0370370 + 0.376145i
\(190\) 0 0
\(191\) 53.5571i 0.280404i −0.990123 0.140202i \(-0.955225\pi\)
0.990123 0.140202i \(-0.0447751\pi\)
\(192\) 21.1660 11.3137i 0.110240 0.0589256i
\(193\) 110.494 0.572508 0.286254 0.958154i \(-0.407590\pi\)
0.286254 + 0.958154i \(0.407590\pi\)
\(194\) 157.212i 0.810374i
\(195\) 0 0
\(196\) −14.0000 −0.0714286
\(197\) 86.1469i 0.437294i −0.975804 0.218647i \(-0.929836\pi\)
0.975804 0.218647i \(-0.0701643\pi\)
\(198\) −102.915 + 154.029i −0.519773 + 0.777925i
\(199\) −88.0000 −0.442211 −0.221106 0.975250i \(-0.570967\pi\)
−0.221106 + 0.975250i \(0.570967\pi\)
\(200\) 0 0
\(201\) 186.745 99.8194i 0.929080 0.496614i
\(202\) −81.7935 −0.404918
\(203\) 94.6321i 0.466168i
\(204\) −60.9150 113.962i −0.298603 0.558635i
\(205\) 0 0
\(206\) 168.818i 0.819506i
\(207\) 290.583 + 194.154i 1.40378 + 0.937942i
\(208\) 2.33202 0.0112116
\(209\) 232.870i 1.11421i
\(210\) 0 0
\(211\) −61.2549 −0.290308 −0.145154 0.989409i \(-0.546368\pi\)
−0.145154 + 0.989409i \(0.546368\pi\)
\(212\) 101.823i 0.480299i
\(213\) −24.0810 45.0515i −0.113057 0.211509i
\(214\) 164.745 0.769837
\(215\) 0 0
\(216\) 76.0000 + 7.48331i 0.351852 + 0.0346450i
\(217\) −154.664 −0.712738
\(218\) 124.210i 0.569773i
\(219\) 191.373 102.293i 0.873847 0.467091i
\(220\) 0 0
\(221\) 12.5560i 0.0568146i
\(222\) 40.0000 + 74.8331i 0.180180 + 0.337086i
\(223\) −150.494 −0.674861 −0.337431 0.941350i \(-0.609558\pi\)
−0.337431 + 0.941350i \(0.609558\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) −97.8301 −0.432876
\(227\) 190.558i 0.839464i −0.907648 0.419732i \(-0.862124\pi\)
0.907648 0.419732i \(-0.137876\pi\)
\(228\) −84.6640 + 45.2548i −0.371334 + 0.198486i
\(229\) −142.915 −0.624083 −0.312042 0.950068i \(-0.601013\pi\)
−0.312042 + 0.950068i \(0.601013\pi\)
\(230\) 0 0
\(231\) −54.4575 101.881i −0.235747 0.441042i
\(232\) −101.166 −0.436060
\(233\) 7.83826i 0.0336406i −0.999859 0.0168203i \(-0.994646\pi\)
0.999859 0.0168203i \(-0.00535432\pi\)
\(234\) 6.16995 + 4.12247i 0.0263673 + 0.0176174i
\(235\) 0 0
\(236\) 116.435i 0.493369i
\(237\) −55.3360 + 29.5783i −0.233485 + 0.124803i
\(238\) 80.5830 0.338584
\(239\) 213.369i 0.892756i 0.894844 + 0.446378i \(0.147286\pi\)
−0.894844 + 0.446378i \(0.852714\pi\)
\(240\) 0 0
\(241\) −130.000 −0.539419 −0.269710 0.962942i \(-0.586928\pi\)
−0.269710 + 0.962942i \(0.586928\pi\)
\(242\) 128.453i 0.530798i
\(243\) 187.848 + 154.149i 0.773038 + 0.634359i
\(244\) −77.8301 −0.318976
\(245\) 0 0
\(246\) 32.7451 17.5030i 0.133110 0.0711503i
\(247\) −9.32808 −0.0377655
\(248\) 165.343i 0.666705i
\(249\) 205.830 + 385.073i 0.826627 + 1.54648i
\(250\) 0 0
\(251\) 389.258i 1.55083i −0.631453 0.775415i \(-0.717541\pi\)
0.631453 0.775415i \(-0.282459\pi\)
\(252\) −26.4575 + 39.5980i −0.104990 + 0.157135i
\(253\) −565.158 −2.23383
\(254\) 38.3039i 0.150803i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 336.139i 1.30793i −0.756523 0.653967i \(-0.773103\pi\)
0.756523 0.653967i \(-0.226897\pi\)
\(258\) −23.4980 43.9608i −0.0910776 0.170391i
\(259\) −52.9150 −0.204305
\(260\) 0 0
\(261\) −267.660 178.838i −1.02552 0.685203i
\(262\) 205.830 0.785611
\(263\) 438.933i 1.66895i 0.551048 + 0.834473i \(0.314228\pi\)
−0.551048 + 0.834473i \(0.685772\pi\)
\(264\) −108.915 + 58.2175i −0.412557 + 0.220521i
\(265\) 0 0
\(266\) 59.8665i 0.225062i
\(267\) 75.8745 + 141.948i 0.284174 + 0.531641i
\(268\) 141.166 0.526739
\(269\) 14.4601i 0.0537549i −0.999639 0.0268775i \(-0.991444\pi\)
0.999639 0.0268775i \(-0.00855639\pi\)
\(270\) 0 0
\(271\) 61.5425 0.227094 0.113547 0.993533i \(-0.463779\pi\)
0.113547 + 0.993533i \(0.463779\pi\)
\(272\) 86.1469i 0.316716i
\(273\) −4.08104 + 2.18141i −0.0149489 + 0.00799050i
\(274\) −35.0850 −0.128047
\(275\) 0 0
\(276\) 109.830 + 205.473i 0.397935 + 0.744468i
\(277\) −150.494 −0.543300 −0.271650 0.962396i \(-0.587569\pi\)
−0.271650 + 0.962396i \(0.587569\pi\)
\(278\) 207.122i 0.745044i
\(279\) −292.288 + 437.456i −1.04763 + 1.56794i
\(280\) 0 0
\(281\) 300.220i 1.06840i 0.845359 + 0.534199i \(0.179387\pi\)
−0.845359 + 0.534199i \(0.820613\pi\)
\(282\) −31.7490 + 16.9706i −0.112585 + 0.0601793i
\(283\) −98.8340 −0.349237 −0.174618 0.984636i \(-0.555869\pi\)
−0.174618 + 0.984636i \(0.555869\pi\)
\(284\) 34.0557i 0.119915i
\(285\) 0 0
\(286\) −12.0000 −0.0419580
\(287\) 23.1543i 0.0806769i
\(288\) 42.3320 + 28.2843i 0.146986 + 0.0982093i
\(289\) −174.830 −0.604948
\(290\) 0 0
\(291\) −294.118 + 157.212i −1.01071 + 0.540249i
\(292\) 144.664 0.495425
\(293\) 7.15424i 0.0244172i −0.999925 0.0122086i \(-0.996114\pi\)
0.999925 0.0122086i \(-0.00388621\pi\)
\(294\) −14.0000 26.1916i −0.0476190 0.0890871i
\(295\) 0 0
\(296\) 56.5685i 0.191110i
\(297\) −391.077 38.5073i −1.31676 0.129654i
\(298\) 310.494 1.04193
\(299\) 22.6386i 0.0757142i
\(300\) 0 0
\(301\) 31.0850 0.103272
\(302\) 299.333i 0.991168i
\(303\) −81.7935 153.022i −0.269945 0.505022i
\(304\) −64.0000 −0.210526
\(305\) 0 0
\(306\) 152.288 227.923i 0.497672 0.744847i
\(307\) −105.830 −0.344723 −0.172362 0.985034i \(-0.555140\pi\)
−0.172362 + 0.985034i \(0.555140\pi\)
\(308\) 77.0146i 0.250047i
\(309\) −315.830 + 168.818i −1.02210 + 0.546337i
\(310\) 0 0
\(311\) 265.403i 0.853385i −0.904397 0.426692i \(-0.859679\pi\)
0.904397 0.426692i \(-0.140321\pi\)
\(312\) 2.33202 + 4.36281i 0.00747443 + 0.0139834i
\(313\) −259.328 −0.828524 −0.414262 0.910158i \(-0.635960\pi\)
−0.414262 + 0.910158i \(0.635960\pi\)
\(314\) 295.210i 0.940160i
\(315\) 0 0
\(316\) −41.8301 −0.132374
\(317\) 37.8233i 0.119316i −0.998219 0.0596581i \(-0.980999\pi\)
0.998219 0.0596581i \(-0.0190011\pi\)
\(318\) −190.494 + 101.823i −0.599038 + 0.320199i
\(319\) 520.575 1.63190
\(320\) 0 0
\(321\) 164.745 + 308.210i 0.513225 + 0.960155i
\(322\) −145.292 −0.451216
\(323\) 344.587i 1.06683i
\(324\) 62.0000 + 149.666i 0.191358 + 0.461933i
\(325\) 0 0
\(326\) 377.589i 1.15825i
\(327\) −232.376 + 124.210i −0.710631 + 0.379848i
\(328\) 24.7530 0.0754663
\(329\) 22.4499i 0.0682369i
\(330\) 0 0
\(331\) 145.490 0.439547 0.219774 0.975551i \(-0.429468\pi\)
0.219774 + 0.975551i \(0.429468\pi\)
\(332\) 291.088i 0.876770i
\(333\) −100.000 + 149.666i −0.300300 + 0.449448i
\(334\) 10.1699 0.0304489
\(335\) 0 0
\(336\) −28.0000 + 14.9666i −0.0833333 + 0.0445435i
\(337\) 600.316 1.78135 0.890677 0.454637i \(-0.150231\pi\)
0.890677 + 0.454637i \(0.150231\pi\)
\(338\) 238.521i 0.705685i
\(339\) −97.8301 183.023i −0.288584 0.539892i
\(340\) 0 0
\(341\) 850.813i 2.49505i
\(342\) −169.328 113.137i −0.495111 0.330810i
\(343\) 18.5203 0.0539949
\(344\) 33.2312i 0.0966024i
\(345\) 0 0
\(346\) 272.288 0.786958
\(347\) 31.6395i 0.0911803i −0.998960 0.0455901i \(-0.985483\pi\)
0.998960 0.0455901i \(-0.0145168\pi\)
\(348\) −101.166 189.264i −0.290707 0.543863i
\(349\) −592.405 −1.69744 −0.848718 0.528846i \(-0.822625\pi\)
−0.848718 + 0.528846i \(0.822625\pi\)
\(350\) 0 0
\(351\) −1.54249 + 15.6654i −0.00439455 + 0.0446307i
\(352\) −82.3320 −0.233898
\(353\) 621.977i 1.76197i 0.473141 + 0.880987i \(0.343120\pi\)
−0.473141 + 0.880987i \(0.656880\pi\)
\(354\) −217.830 + 116.435i −0.615339 + 0.328913i
\(355\) 0 0
\(356\) 107.303i 0.301412i
\(357\) 80.5830 + 150.757i 0.225723 + 0.422289i
\(358\) −61.7490 −0.172483
\(359\) 499.509i 1.39139i 0.718337 + 0.695696i \(0.244904\pi\)
−0.718337 + 0.695696i \(0.755096\pi\)
\(360\) 0 0
\(361\) −105.000 −0.290859
\(362\) 114.671i 0.316772i
\(363\) 240.314 128.453i 0.662021 0.353865i
\(364\) −3.08497 −0.00847520
\(365\) 0 0
\(366\) −77.8301 145.607i −0.212650 0.397833i
\(367\) −73.0039 −0.198921 −0.0994604 0.995042i \(-0.531712\pi\)
−0.0994604 + 0.995042i \(0.531712\pi\)
\(368\) 155.323i 0.422074i
\(369\) 65.4902 + 43.7575i 0.177480 + 0.118584i
\(370\) 0 0
\(371\) 134.700i 0.363072i
\(372\) −309.328 + 165.343i −0.831527 + 0.444470i
\(373\) 474.664 1.27256 0.636279 0.771459i \(-0.280473\pi\)
0.636279 + 0.771459i \(0.280473\pi\)
\(374\) 443.290i 1.18527i
\(375\) 0 0
\(376\) −24.0000 −0.0638298
\(377\) 20.8527i 0.0553122i
\(378\) −100.539 9.89949i −0.265975 0.0261891i
\(379\) −223.660 −0.590132 −0.295066 0.955477i \(-0.595342\pi\)
−0.295066 + 0.955477i \(0.595342\pi\)
\(380\) 0 0
\(381\) −71.6601 + 38.3039i −0.188084 + 0.100535i
\(382\) 75.7411 0.198275
\(383\) 518.175i 1.35294i −0.736471 0.676469i \(-0.763509\pi\)
0.736471 0.676469i \(-0.236491\pi\)
\(384\) 16.0000 + 29.9333i 0.0416667 + 0.0779512i
\(385\) 0 0
\(386\) 156.262i 0.404824i
\(387\) 58.7451 87.9216i 0.151796 0.227188i
\(388\) −222.332 −0.573021
\(389\) 44.1383i 0.113466i 0.998389 + 0.0567330i \(0.0180684\pi\)
−0.998389 + 0.0567330i \(0.981932\pi\)
\(390\) 0 0
\(391\) 836.288 2.13884
\(392\) 19.7990i 0.0505076i
\(393\) 205.830 + 385.073i 0.523741 + 0.979829i
\(394\) 121.830 0.309213
\(395\) 0 0
\(396\) −217.830 145.544i −0.550076 0.367535i
\(397\) −299.417 −0.754199 −0.377099 0.926173i \(-0.623079\pi\)
−0.377099 + 0.926173i \(0.623079\pi\)
\(398\) 124.451i 0.312690i
\(399\) 112.000 59.8665i 0.280702 0.150041i
\(400\) 0 0
\(401\) 277.008i 0.690794i 0.938457 + 0.345397i \(0.112256\pi\)
−0.938457 + 0.345397i \(0.887744\pi\)
\(402\) 141.166 + 264.097i 0.351159 + 0.656959i
\(403\) −34.0810 −0.0845683
\(404\) 115.673i 0.286320i
\(405\) 0 0
\(406\) 133.830 0.329631
\(407\) 291.088i 0.715203i
\(408\) 161.166 86.1469i 0.395015 0.211144i
\(409\) −740.980 −1.81169 −0.905844 0.423612i \(-0.860762\pi\)
−0.905844 + 0.423612i \(0.860762\pi\)
\(410\) 0 0
\(411\) −35.0850 65.6380i −0.0853649 0.159703i
\(412\) −238.745 −0.579478
\(413\) 154.029i 0.372952i
\(414\) −274.575 + 410.946i −0.663225 + 0.992624i
\(415\) 0 0
\(416\) 3.29798i 0.00792783i
\(417\) −387.490 + 207.122i −0.929233 + 0.496696i
\(418\) 329.328 0.787866
\(419\) 89.7998i 0.214319i 0.994242 + 0.107160i \(0.0341756\pi\)
−0.994242 + 0.107160i \(0.965824\pi\)
\(420\) 0 0
\(421\) 281.150 0.667815 0.333908 0.942606i \(-0.391633\pi\)
0.333908 + 0.942606i \(0.391633\pi\)
\(422\) 86.6275i 0.205279i
\(423\) −63.4980 42.4264i −0.150114 0.100299i
\(424\) −144.000 −0.339623
\(425\) 0 0
\(426\) 63.7124 34.0557i 0.149560 0.0799430i
\(427\) 102.959 0.241123
\(428\) 232.985i 0.544357i
\(429\) −12.0000 22.4499i −0.0279720 0.0523309i
\(430\) 0 0
\(431\) 560.200i 1.29977i 0.760033 + 0.649885i \(0.225183\pi\)
−0.760033 + 0.649885i \(0.774817\pi\)
\(432\) −10.5830 + 107.480i −0.0244977 + 0.248797i
\(433\) 543.004 1.25405 0.627025 0.778999i \(-0.284272\pi\)
0.627025 + 0.778999i \(0.284272\pi\)
\(434\) 218.728i 0.503982i
\(435\) 0 0
\(436\) −175.660 −0.402890
\(437\) 621.293i 1.42172i
\(438\) 144.664 + 270.642i 0.330283 + 0.617903i
\(439\) 342.170 0.779430 0.389715 0.920935i \(-0.372573\pi\)
0.389715 + 0.920935i \(0.372573\pi\)
\(440\) 0 0
\(441\) 35.0000 52.3832i 0.0793651 0.118783i
\(442\) 17.7569 0.0401740
\(443\) 399.816i 0.902519i 0.892393 + 0.451259i \(0.149025\pi\)
−0.892393 + 0.451259i \(0.850975\pi\)
\(444\) −105.830 + 56.5685i −0.238356 + 0.127407i
\(445\) 0 0
\(446\) 212.831i 0.477199i
\(447\) 310.494 + 580.881i 0.694618 + 1.29951i
\(448\) −21.1660 −0.0472456
\(449\) 737.040i 1.64151i −0.571277 0.820757i \(-0.693552\pi\)
0.571277 0.820757i \(-0.306448\pi\)
\(450\) 0 0
\(451\) −127.373 −0.282422
\(452\) 138.353i 0.306090i
\(453\) 560.000 299.333i 1.23620 0.660778i
\(454\) 269.490 0.593591
\(455\) 0 0
\(456\) −64.0000 119.733i −0.140351 0.262572i
\(457\) −665.336 −1.45588 −0.727939 0.685642i \(-0.759521\pi\)
−0.727939 + 0.685642i \(0.759521\pi\)
\(458\) 202.112i 0.441293i
\(459\) 578.693 + 56.9808i 1.26077 + 0.124141i
\(460\) 0 0
\(461\) 318.865i 0.691682i −0.938293 0.345841i \(-0.887594\pi\)
0.938293 0.345841i \(-0.112406\pi\)
\(462\) 144.081 77.0146i 0.311864 0.166698i
\(463\) −402.332 −0.868968 −0.434484 0.900680i \(-0.643069\pi\)
−0.434484 + 0.900680i \(0.643069\pi\)
\(464\) 143.070i 0.308341i
\(465\) 0 0
\(466\) 11.0850 0.0237875
\(467\) 697.087i 1.49269i 0.665558 + 0.746346i \(0.268194\pi\)
−0.665558 + 0.746346i \(0.731806\pi\)
\(468\) −5.83005 + 8.72562i −0.0124574 + 0.0186445i
\(469\) −186.745 −0.398177
\(470\) 0 0
\(471\) 552.288 295.210i 1.17259 0.626773i
\(472\) −164.664 −0.348864
\(473\) 171.000i 0.361522i
\(474\) −41.8301 78.2569i −0.0882491 0.165099i
\(475\) 0 0
\(476\) 113.962i 0.239415i
\(477\) −380.988 254.558i −0.798717 0.533665i
\(478\) −301.749 −0.631274
\(479\) 163.808i 0.341980i −0.985273 0.170990i \(-0.945303\pi\)
0.985273 0.170990i \(-0.0546966\pi\)
\(480\) 0 0
\(481\) −11.6601 −0.0242414
\(482\) 183.848i 0.381427i
\(483\) −145.292 271.816i −0.300811 0.562765i
\(484\) 181.660 0.375331
\(485\) 0 0
\(486\) −218.000 + 265.658i −0.448560 + 0.546621i
\(487\) 103.498 0.212522 0.106261 0.994338i \(-0.466112\pi\)
0.106261 + 0.994338i \(0.466112\pi\)
\(488\) 110.068i 0.225550i
\(489\) 706.405 377.589i 1.44459 0.772167i
\(490\) 0 0
\(491\) 570.094i 1.16109i 0.814229 + 0.580544i \(0.197160\pi\)
−0.814229 + 0.580544i \(0.802840\pi\)
\(492\) 24.7530 + 46.3085i 0.0503109 + 0.0941230i
\(493\) −770.316 −1.56251
\(494\) 13.1919i 0.0267043i
\(495\) 0 0
\(496\) −233.830 −0.471432
\(497\) 45.0515i 0.0906469i
\(498\) −544.575 + 291.088i −1.09352 + 0.584513i
\(499\) −487.660 −0.977275 −0.488637 0.872487i \(-0.662506\pi\)
−0.488637 + 0.872487i \(0.662506\pi\)
\(500\) 0 0
\(501\) 10.1699 + 19.0262i 0.0202993 + 0.0379765i
\(502\) 550.494 1.09660
\(503\) 97.9412i 0.194714i −0.995250 0.0973571i \(-0.968961\pi\)
0.995250 0.0973571i \(-0.0310389\pi\)
\(504\) −56.0000 37.4166i −0.111111 0.0742392i
\(505\) 0 0
\(506\) 799.254i 1.57955i
\(507\) 446.233 238.521i 0.880143 0.470456i
\(508\) −54.1699 −0.106634
\(509\) 318.104i 0.624958i 0.949925 + 0.312479i \(0.101159\pi\)
−0.949925 + 0.312479i \(0.898841\pi\)
\(510\) 0 0
\(511\) −191.373 −0.374506
\(512\) 22.6274i 0.0441942i
\(513\) 42.3320 429.921i 0.0825186 0.838052i
\(514\) 475.373 0.924849
\(515\) 0 0
\(516\) 62.1699 33.2312i 0.120484 0.0644016i
\(517\) 123.498 0.238874
\(518\) 74.8331i 0.144466i
\(519\) 272.288 + 509.403i 0.524639 + 0.981509i
\(520\) 0 0
\(521\) 727.150i 1.39568i 0.716253 + 0.697840i \(0.245856\pi\)
−0.716253 + 0.697840i \(0.754144\pi\)
\(522\) 252.915 378.529i 0.484512 0.725150i
\(523\) 207.624 0.396986 0.198493 0.980102i \(-0.436395\pi\)
0.198493 + 0.980102i \(0.436395\pi\)
\(524\) 291.088i 0.555511i
\(525\) 0 0
\(526\) −620.745 −1.18012
\(527\) 1258.98i 2.38896i
\(528\) −82.3320 154.029i −0.155932 0.291722i
\(529\) −978.830 −1.85034
\(530\) 0 0
\(531\) −435.660 291.088i −0.820452 0.548188i
\(532\) 84.6640 0.159143
\(533\) 5.10216i 0.00957254i
\(534\) −200.745 + 107.303i −0.375927 + 0.200941i
\(535\) 0 0
\(536\) 199.639i 0.372461i
\(537\) −61.7490 115.522i −0.114989 0.215124i
\(538\) 20.4496 0.0380105
\(539\) 101.881i 0.189018i
\(540\) 0 0
\(541\) 1025.15 1.89492 0.947459 0.319878i \(-0.103642\pi\)
0.947459 + 0.319878i \(0.103642\pi\)
\(542\) 87.0342i 0.160580i
\(543\) 214.531 114.671i 0.395084 0.211181i
\(544\) 121.830 0.223952
\(545\) 0 0
\(546\) −3.08497 5.77146i −0.00565014 0.0105704i
\(547\) 560.089 1.02393 0.511964 0.859007i \(-0.328918\pi\)
0.511964 + 0.859007i \(0.328918\pi\)
\(548\) 49.6176i 0.0905431i
\(549\) 194.575 291.213i 0.354417 0.530443i
\(550\) 0 0
\(551\) 572.281i 1.03862i
\(552\) −290.583 + 155.323i −0.526418 + 0.281383i
\(553\) 55.3360 0.100065
\(554\) 212.831i 0.384171i
\(555\) 0 0
\(556\) −292.915 −0.526826
\(557\) 575.705i 1.03358i −0.856112 0.516791i \(-0.827126\pi\)
0.856112 0.516791i \(-0.172874\pi\)
\(558\) −618.656 413.357i −1.10870 0.740783i
\(559\) 6.84974 0.0122536
\(560\) 0 0
\(561\) −829.320 + 443.290i −1.47829 + 0.790179i
\(562\) −424.575 −0.755472
\(563\) 468.558i 0.832251i 0.909307 + 0.416126i \(0.136612\pi\)
−0.909307 + 0.416126i \(0.863388\pi\)
\(564\) −24.0000 44.8999i −0.0425532 0.0796097i
\(565\) 0 0
\(566\) 139.772i 0.246948i
\(567\) −82.0183 197.990i −0.144653 0.349189i
\(568\) 48.1621 0.0847924
\(569\) 506.455i 0.890079i −0.895511 0.445039i \(-0.853190\pi\)
0.895511 0.445039i \(-0.146810\pi\)
\(570\) 0 0
\(571\) 32.9150 0.0576445 0.0288223 0.999585i \(-0.490824\pi\)
0.0288223 + 0.999585i \(0.490824\pi\)
\(572\) 16.9706i 0.0296688i
\(573\) 75.7411 + 141.699i 0.132183 + 0.247293i
\(574\) −32.7451 −0.0570472
\(575\) 0 0
\(576\) −40.0000 + 59.8665i −0.0694444 + 0.103935i
\(577\) 252.154 0.437009 0.218505 0.975836i \(-0.429882\pi\)
0.218505 + 0.975836i \(0.429882\pi\)
\(578\) 247.247i 0.427763i
\(579\) −292.340 + 156.262i −0.504905 + 0.269883i
\(580\) 0 0
\(581\) 385.073i 0.662776i
\(582\) −222.332 415.945i −0.382014 0.714682i
\(583\) 740.988 1.27099
\(584\) 204.586i 0.350318i
\(585\) 0 0
\(586\) 10.1176 0.0172656
\(587\) 366.882i 0.625012i −0.949916 0.312506i \(-0.898832\pi\)
0.949916 0.312506i \(-0.101168\pi\)
\(588\) 37.0405 19.7990i 0.0629941 0.0336718i
\(589\) 935.320 1.58798
\(590\) 0 0
\(591\) 121.830 + 227.923i 0.206142 + 0.385657i
\(592\) −80.0000 −0.135135
\(593\) 620.757i 1.04681i 0.852085 + 0.523404i \(0.175338\pi\)
−0.852085 + 0.523404i \(0.824662\pi\)
\(594\) 54.4575 553.067i 0.0916793 0.931088i
\(595\) 0 0
\(596\) 439.105i 0.736753i
\(597\) 232.826 124.451i 0.389993 0.208460i
\(598\) −32.0157 −0.0535380
\(599\) 26.3488i 0.0439879i −0.999758 0.0219940i \(-0.992999\pi\)
0.999758 0.0219940i \(-0.00700146\pi\)
\(600\) 0 0
\(601\) 930.470 1.54820 0.774102 0.633061i \(-0.218202\pi\)
0.774102 + 0.633061i \(0.218202\pi\)
\(602\) 43.9608i 0.0730246i
\(603\) −352.915 + 528.195i −0.585265 + 0.875945i
\(604\) 423.320 0.700861
\(605\) 0 0
\(606\) 216.405 115.673i 0.357104 0.190880i
\(607\) −216.146 −0.356089 −0.178045 0.984022i \(-0.556977\pi\)
−0.178045 + 0.984022i \(0.556977\pi\)
\(608\) 90.5097i 0.148865i
\(609\) 133.830 + 250.373i 0.219754 + 0.411122i
\(610\) 0 0
\(611\) 4.94696i 0.00809650i
\(612\) 322.332 + 215.367i 0.526686 + 0.351907i
\(613\) 268.834 0.438555 0.219277 0.975663i \(-0.429630\pi\)
0.219277 + 0.975663i \(0.429630\pi\)
\(614\) 149.666i 0.243756i
\(615\) 0 0
\(616\) 108.915 0.176810
\(617\) 531.338i 0.861163i 0.902552 + 0.430582i \(0.141692\pi\)
−0.902552 + 0.430582i \(0.858308\pi\)
\(618\) −238.745 446.651i −0.386319 0.722736i
\(619\) 425.203 0.686919 0.343459 0.939168i \(-0.388401\pi\)
0.343459 + 0.939168i \(0.388401\pi\)
\(620\) 0 0
\(621\) −1043.39 102.737i −1.68017 0.165437i
\(622\) 375.336 0.603434
\(623\) 141.948i 0.227846i
\(624\) −6.16995 + 3.29798i −0.00988774 + 0.00528522i
\(625\) 0 0
\(626\) 366.745i 0.585855i
\(627\) 329.328 + 616.116i 0.525244 + 0.982642i
\(628\) 417.490 0.664793
\(629\) 430.734i 0.684792i
\(630\) 0 0
\(631\) −453.490 −0.718685 −0.359342 0.933206i \(-0.616999\pi\)
−0.359342 + 0.933206i \(0.616999\pi\)
\(632\) 59.1566i 0.0936023i
\(633\) 162.065 86.6275i 0.256027 0.136852i
\(634\) 53.4902 0.0843693
\(635\) 0 0
\(636\) −144.000 269.399i −0.226415 0.423584i
\(637\) 4.08104 0.00640665
\(638\) 736.204i 1.15393i
\(639\) 127.425 + 85.1393i 0.199413 + 0.133238i
\(640\) 0 0
\(641\) 463.455i 0.723019i −0.932368 0.361510i \(-0.882261\pi\)
0.932368 0.361510i \(-0.117739\pi\)
\(642\) −435.875 + 232.985i −0.678932 + 0.362905i
\(643\) −820.988 −1.27681 −0.638405 0.769701i \(-0.720405\pi\)
−0.638405 + 0.769701i \(0.720405\pi\)
\(644\) 205.473i 0.319058i
\(645\) 0 0
\(646\) −487.320 −0.754366
\(647\) 996.660i 1.54043i −0.637783 0.770216i \(-0.720148\pi\)
0.637783 0.770216i \(-0.279852\pi\)
\(648\) −211.660 + 87.6812i −0.326636 + 0.135311i
\(649\) 847.320 1.30558
\(650\) 0 0
\(651\) 409.203 218.728i 0.628575 0.335988i
\(652\) 533.992 0.819006
\(653\) 357.602i 0.547629i −0.961782 0.273815i \(-0.911715\pi\)
0.961782 0.273815i \(-0.0882855\pi\)
\(654\) −175.660 328.630i −0.268593 0.502492i
\(655\) 0 0
\(656\) 35.0060i 0.0533627i
\(657\) −361.660 + 541.283i −0.550472 + 0.823871i
\(658\) 31.7490 0.0482508
\(659\) 131.562i 0.199640i 0.995006 + 0.0998198i \(0.0318266\pi\)
−0.995006 + 0.0998198i \(0.968173\pi\)
\(660\) 0 0
\(661\) −250.915 −0.379599 −0.189800 0.981823i \(-0.560784\pi\)
−0.189800 + 0.981823i \(0.560784\pi\)
\(662\) 205.754i 0.310807i
\(663\) 17.7569 + 33.2201i 0.0267826 + 0.0501057i
\(664\) −411.660 −0.619970
\(665\) 0 0
\(666\) −211.660 141.421i −0.317808 0.212344i
\(667\) 1388.88 2.08228
\(668\) 14.3825i 0.0215307i
\(669\) 398.170 212.831i 0.595172 0.318133i
\(670\) 0 0
\(671\) 566.384i 0.844090i
\(672\) −21.1660 39.5980i −0.0314970 0.0589256i
\(673\) −196.502 −0.291979 −0.145990 0.989286i \(-0.546637\pi\)
−0.145990 + 0.989286i \(0.546637\pi\)
\(674\) 848.975i 1.25961i
\(675\) 0 0
\(676\) 337.320 0.498994
\(677\) 54.1838i 0.0800352i 0.999199 + 0.0400176i \(0.0127414\pi\)
−0.999199 + 0.0400176i \(0.987259\pi\)
\(678\) 258.834 138.353i 0.381761 0.204060i
\(679\) 294.118 0.433163
\(680\) 0 0
\(681\) 269.490 + 504.170i 0.395727 + 0.740338i
\(682\) 1203.23 1.76427
\(683\) 749.006i 1.09664i −0.836268 0.548321i \(-0.815267\pi\)
0.836268 0.548321i \(-0.184733\pi\)
\(684\) 160.000 239.466i 0.233918 0.350097i
\(685\) 0 0
\(686\) 26.1916i 0.0381802i
\(687\) 378.118 202.112i 0.550390 0.294196i
\(688\) 46.9961 0.0683082
\(689\) 29.6818i 0.0430795i
\(690\) 0 0
\(691\) 475.137 0.687608 0.343804 0.939041i \(-0.388284\pi\)
0.343804 + 0.939041i \(0.388284\pi\)
\(692\) 385.073i 0.556464i
\(693\) 288.162 + 192.536i 0.415818 + 0.277830i
\(694\) 44.7451 0.0644742
\(695\) 0 0
\(696\) 267.660 143.070i 0.384569 0.205561i
\(697\) 188.478 0.270414
\(698\) 837.787i 1.20027i
\(699\) 11.0850 + 20.7381i 0.0158583 + 0.0296682i
\(700\) 0 0
\(701\) 1251.49i 1.78529i 0.450760 + 0.892645i \(0.351153\pi\)
−0.450760 + 0.892645i \(0.648847\pi\)
\(702\) −22.1542 2.18141i −0.0315587 0.00310742i
\(703\) 320.000 0.455192
\(704\) 116.435i 0.165391i
\(705\) 0 0
\(706\) −879.608 −1.24590
\(707\) 153.022i 0.216438i
\(708\) −164.664 308.058i −0.232576 0.435110i
\(709\) −16.5098 −0.0232861 −0.0116430 0.999932i \(-0.503706\pi\)
−0.0116430 + 0.999932i \(0.503706\pi\)
\(710\) 0 0
\(711\) 104.575 156.514i 0.147082 0.220132i
\(712\) −151.749 −0.213131
\(713\) 2269.95i 3.18366i
\(714\) −213.203 + 113.962i −0.298603 + 0.159610i
\(715\) 0 0
\(716\) 87.3263i 0.121964i
\(717\) −301.749 564.521i −0.420849 0.787337i
\(718\) −706.413 −0.983862
\(719\) 1327.59i 1.84643i −0.384279 0.923217i \(-0.625550\pi\)
0.384279 0.923217i \(-0.374450\pi\)
\(720\) 0 0
\(721\) 315.830 0.438044
\(722\) 148.492i 0.205668i
\(723\) 343.948 183.848i 0.475723 0.254285i
\(724\) 162.170 0.223992
\(725\) 0 0
\(726\) 181.660 + 339.855i 0.250221 + 0.468120i
\(727\) 202.782 0.278929 0.139465 0.990227i \(-0.455462\pi\)
0.139465 + 0.990227i \(0.455462\pi\)
\(728\) 4.36281i 0.00599287i
\(729\) −715.000 142.183i −0.980796 0.195038i
\(730\) 0 0
\(731\) 253.035i 0.346149i
\(732\) 205.919 110.068i 0.281310 0.150367i
\(733\) 582.559 0.794760 0.397380 0.917654i \(-0.369919\pi\)
0.397380 + 0.917654i \(0.369919\pi\)
\(734\) 103.243i 0.140658i
\(735\) 0 0
\(736\) −219.660 −0.298451
\(737\) 1027.29i 1.39388i
\(738\) −61.8824 + 92.6171i −0.0838515 + 0.125497i
\(739\) −256.810 −0.347511 −0.173755 0.984789i \(-0.555590\pi\)
−0.173755 + 0.984789i \(0.555590\pi\)
\(740\) 0 0
\(741\) 24.6798 13.1919i 0.0333061 0.0178028i
\(742\) 190.494 0.256731
\(743\) 573.256i 0.771542i 0.922595 + 0.385771i \(0.126064\pi\)
−0.922595 + 0.385771i \(0.873936\pi\)
\(744\) −233.830 437.456i −0.314288 0.587978i
\(745\) 0 0
\(746\) 671.276i 0.899834i
\(747\) −1089.15 727.719i −1.45803 0.974189i
\(748\) −626.907 −0.838111
\(749\) 308.210i 0.411495i
\(750\) 0 0
\(751\) −579.085 −0.771085 −0.385543 0.922690i \(-0.625986\pi\)
−0.385543 + 0.922690i \(0.625986\pi\)
\(752\) 33.9411i 0.0451345i
\(753\) 550.494 + 1029.88i 0.731068 + 1.36770i
\(754\) 29.4902 0.0391116
\(755\) 0 0
\(756\) 14.0000 142.183i 0.0185185 0.188073i
\(757\) −1167.13 −1.54179 −0.770895 0.636963i \(-0.780191\pi\)
−0.770895 + 0.636963i \(0.780191\pi\)
\(758\) 316.303i 0.417286i
\(759\) 1495.27 799.254i 1.97005 1.05304i
\(760\) 0 0
\(761\) 800.970i 1.05252i −0.850323 0.526261i \(-0.823593\pi\)
0.850323 0.526261i \(-0.176407\pi\)
\(762\) −54.1699 101.343i −0.0710892 0.132996i
\(763\) 232.376 0.304556
\(764\) 107.114i 0.140202i
\(765\) 0 0
\(766\) 732.810 0.956671
\(767\) 33.9411i 0.0442518i
\(768\) −42.3320 + 22.6274i −0.0551198 + 0.0294628i
\(769\) −242.680 −0.315578 −0.157789 0.987473i \(-0.550437\pi\)
−0.157789 + 0.987473i \(0.550437\pi\)
\(770\) 0 0
\(771\) 475.373 + 889.341i 0.616566 + 1.15349i
\(772\) −220.988 −0.286254
\(773\) 1262.83i 1.63367i 0.576870 + 0.816836i \(0.304274\pi\)
−0.576870 + 0.816836i \(0.695726\pi\)
\(774\) 124.340 + 83.0781i 0.160646 + 0.107336i
\(775\) 0 0
\(776\) 314.425i 0.405187i
\(777\) 140.000 74.8331i 0.180180 0.0963104i
\(778\) −62.4209 −0.0802326
\(779\) 140.024i 0.179748i
\(780\) 0 0
\(781\) −247.830 −0.317324
\(782\) 1182.69i 1.51239i
\(783\) 961.077 + 94.6321i 1.22743 + 0.120858i
\(784\) 28.0000 0.0357143
\(785\) 0 0
\(786\) −544.575 + 291.088i −0.692844 + 0.370341i
\(787\) −1347.00 −1.71156 −0.855782