Properties

Label 1050.3.h.a.349.7
Level $1050$
Weight $3$
Character 1050.349
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.7
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1050.349
Dual form 1050.3.h.a.349.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +2.44949i q^{6} +(-3.16693 - 6.24264i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +2.44949i q^{6} +(-3.16693 - 6.24264i) q^{7} -2.82843i q^{8} +3.00000 q^{9} -1.75736 q^{11} -3.46410 q^{12} -18.7554 q^{13} +(8.82843 - 4.47871i) q^{14} +4.00000 q^{16} +23.4803 q^{17} +4.24264i q^{18} +23.0600i q^{19} +(-5.48528 - 10.8126i) q^{21} -2.48528i q^{22} +18.7279i q^{23} -4.89898i q^{24} -26.5241i q^{26} +5.19615 q^{27} +(6.33386 + 12.4853i) q^{28} -30.0000 q^{29} +8.60927i q^{31} +5.65685i q^{32} -3.04384 q^{33} +33.2061i q^{34} -6.00000 q^{36} +70.9117i q^{37} -32.6118 q^{38} -32.4853 q^{39} +41.3951i q^{41} +(15.2913 - 7.75736i) q^{42} +10.4264i q^{43} +3.51472 q^{44} -26.4853 q^{46} +38.6995 q^{47} +6.92820 q^{48} +(-28.9411 + 39.5400i) q^{49} +40.6690 q^{51} +37.5108 q^{52} -37.0294i q^{53} +7.34847i q^{54} +(-17.6569 + 8.95743i) q^{56} +39.9411i q^{57} -42.4264i q^{58} +97.4872i q^{59} +16.7262i q^{61} -12.1753 q^{62} +(-9.50079 - 18.7279i) q^{63} -8.00000 q^{64} -4.30463i q^{66} -60.9706i q^{67} -46.9606 q^{68} +32.4377i q^{69} -110.610 q^{71} -8.48528i q^{72} +56.7585 q^{73} -100.284 q^{74} -46.1200i q^{76} +(5.56543 + 10.9706i) q^{77} -45.9411i q^{78} +69.8234 q^{79} +9.00000 q^{81} -58.5416 q^{82} -6.43583 q^{83} +(10.9706 + 21.6251i) q^{84} -14.7452 q^{86} -51.9615 q^{87} +4.97056i q^{88} +42.0915i q^{89} +(59.3970 + 117.083i) q^{91} -37.4558i q^{92} +14.9117i q^{93} +54.7293i q^{94} +9.79796i q^{96} +51.7153 q^{97} +(-55.9180 - 40.9289i) q^{98} -5.27208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 16 q^{4} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 16 q^{4} + 24 q^{9} - 48 q^{11} + 48 q^{14} + 32 q^{16} + 24 q^{21} - 240 q^{29} - 48 q^{36} - 192 q^{39} + 96 q^{44} - 144 q^{46} + 40 q^{49} - 48 q^{51} - 96 q^{56} - 64 q^{64} - 240 q^{71} - 576 q^{74} - 256 q^{79} + 72 q^{81} - 48 q^{84} - 480 q^{86} - 144 q^{99}+O(q^{100}) \) 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
\(3\) 1.73205 0.577350
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −3.16693 6.24264i −0.452418 0.891806i
\(8\) 2.82843i 0.353553i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) −1.75736 −0.159760 −0.0798800 0.996804i \(-0.525454\pi\)
−0.0798800 + 0.996804i \(0.525454\pi\)
\(12\) −3.46410 −0.288675
\(13\) −18.7554 −1.44272 −0.721361 0.692559i \(-0.756483\pi\)
−0.721361 + 0.692559i \(0.756483\pi\)
\(14\) 8.82843 4.47871i 0.630602 0.319908i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 23.4803 1.38119 0.690597 0.723240i \(-0.257348\pi\)
0.690597 + 0.723240i \(0.257348\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 23.0600i 1.21369i 0.794822 + 0.606843i \(0.207564\pi\)
−0.794822 + 0.606843i \(0.792436\pi\)
\(20\) 0 0
\(21\) −5.48528 10.8126i −0.261204 0.514884i
\(22\) 2.48528i 0.112967i
\(23\) 18.7279i 0.814257i 0.913371 + 0.407129i \(0.133470\pi\)
−0.913371 + 0.407129i \(0.866530\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) 26.5241i 1.02016i
\(27\) 5.19615 0.192450
\(28\) 6.33386 + 12.4853i 0.226209 + 0.445903i
\(29\) −30.0000 −1.03448 −0.517241 0.855840i \(-0.673041\pi\)
−0.517241 + 0.855840i \(0.673041\pi\)
\(30\) 0 0
\(31\) 8.60927i 0.277718i 0.990312 + 0.138859i \(0.0443435\pi\)
−0.990312 + 0.138859i \(0.955656\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −3.04384 −0.0922374
\(34\) 33.2061i 0.976651i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 70.9117i 1.91653i 0.285878 + 0.958266i \(0.407715\pi\)
−0.285878 + 0.958266i \(0.592285\pi\)
\(38\) −32.6118 −0.858205
\(39\) −32.4853 −0.832956
\(40\) 0 0
\(41\) 41.3951i 1.00964i 0.863225 + 0.504819i \(0.168441\pi\)
−0.863225 + 0.504819i \(0.831559\pi\)
\(42\) 15.2913 7.75736i 0.364078 0.184699i
\(43\) 10.4264i 0.242475i 0.992624 + 0.121237i \(0.0386862\pi\)
−0.992624 + 0.121237i \(0.961314\pi\)
\(44\) 3.51472 0.0798800
\(45\) 0 0
\(46\) −26.4853 −0.575767
\(47\) 38.6995 0.823393 0.411696 0.911321i \(-0.364936\pi\)
0.411696 + 0.911321i \(0.364936\pi\)
\(48\) 6.92820 0.144338
\(49\) −28.9411 + 39.5400i −0.590635 + 0.806939i
\(50\) 0 0
\(51\) 40.6690 0.797432
\(52\) 37.5108 0.721361
\(53\) 37.0294i 0.698669i −0.936998 0.349334i \(-0.886408\pi\)
0.936998 0.349334i \(-0.113592\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) −17.6569 + 8.95743i −0.315301 + 0.159954i
\(57\) 39.9411i 0.700721i
\(58\) 42.4264i 0.731490i
\(59\) 97.4872i 1.65233i 0.563431 + 0.826163i \(0.309481\pi\)
−0.563431 + 0.826163i \(0.690519\pi\)
\(60\) 0 0
\(61\) 16.7262i 0.274199i 0.990557 + 0.137100i \(0.0437781\pi\)
−0.990557 + 0.137100i \(0.956222\pi\)
\(62\) −12.1753 −0.196376
\(63\) −9.50079 18.7279i −0.150806 0.297269i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 4.30463i 0.0652217i
\(67\) 60.9706i 0.910008i −0.890489 0.455004i \(-0.849638\pi\)
0.890489 0.455004i \(-0.150362\pi\)
\(68\) −46.9606 −0.690597
\(69\) 32.4377i 0.470112i
\(70\) 0 0
\(71\) −110.610 −1.55789 −0.778945 0.627092i \(-0.784245\pi\)
−0.778945 + 0.627092i \(0.784245\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 56.7585 0.777514 0.388757 0.921340i \(-0.372905\pi\)
0.388757 + 0.921340i \(0.372905\pi\)
\(74\) −100.284 −1.35519
\(75\) 0 0
\(76\) 46.1200i 0.606843i
\(77\) 5.56543 + 10.9706i 0.0722783 + 0.142475i
\(78\) 45.9411i 0.588989i
\(79\) 69.8234 0.883840 0.441920 0.897054i \(-0.354297\pi\)
0.441920 + 0.897054i \(0.354297\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −58.5416 −0.713922
\(83\) −6.43583 −0.0775401 −0.0387701 0.999248i \(-0.512344\pi\)
−0.0387701 + 0.999248i \(0.512344\pi\)
\(84\) 10.9706 + 21.6251i 0.130602 + 0.257442i
\(85\) 0 0
\(86\) −14.7452 −0.171455
\(87\) −51.9615 −0.597259
\(88\) 4.97056i 0.0564837i
\(89\) 42.0915i 0.472938i 0.971639 + 0.236469i \(0.0759901\pi\)
−0.971639 + 0.236469i \(0.924010\pi\)
\(90\) 0 0
\(91\) 59.3970 + 117.083i 0.652714 + 1.28663i
\(92\) 37.4558i 0.407129i
\(93\) 14.9117i 0.160341i
\(94\) 54.7293i 0.582227i
\(95\) 0 0
\(96\) 9.79796i 0.102062i
\(97\) 51.7153 0.533148 0.266574 0.963814i \(-0.414108\pi\)
0.266574 + 0.963814i \(0.414108\pi\)
\(98\) −55.9180 40.9289i −0.570592 0.417642i
\(99\) −5.27208 −0.0532533
\(100\) 0 0
\(101\) 6.60991i 0.0654447i 0.999464 + 0.0327223i \(0.0104177\pi\)
−0.999464 + 0.0327223i \(0.989582\pi\)
\(102\) 57.5147i 0.563870i
\(103\) −175.871 −1.70748 −0.853742 0.520696i \(-0.825673\pi\)
−0.853742 + 0.520696i \(0.825673\pi\)
\(104\) 53.0482i 0.510079i
\(105\) 0 0
\(106\) 52.3675 0.494033
\(107\) 46.2426i 0.432174i 0.976374 + 0.216087i \(0.0693295\pi\)
−0.976374 + 0.216087i \(0.930670\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 35.9411 0.329735 0.164868 0.986316i \(-0.447280\pi\)
0.164868 + 0.986316i \(0.447280\pi\)
\(110\) 0 0
\(111\) 122.823i 1.10651i
\(112\) −12.6677 24.9706i −0.113105 0.222951i
\(113\) 73.0294i 0.646278i −0.946351 0.323139i \(-0.895262\pi\)
0.946351 0.323139i \(-0.104738\pi\)
\(114\) −56.4853 −0.495485
\(115\) 0 0
\(116\) 60.0000 0.517241
\(117\) −56.2662 −0.480907
\(118\) −137.868 −1.16837
\(119\) −74.3604 146.579i −0.624877 1.23176i
\(120\) 0 0
\(121\) −117.912 −0.974477
\(122\) −23.6544 −0.193888
\(123\) 71.6985i 0.582915i
\(124\) 17.2185i 0.138859i
\(125\) 0 0
\(126\) 26.4853 13.4361i 0.210201 0.106636i
\(127\) 89.9411i 0.708198i −0.935208 0.354099i \(-0.884788\pi\)
0.935208 0.354099i \(-0.115212\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 18.0591i 0.139993i
\(130\) 0 0
\(131\) 12.1753i 0.0929415i 0.998920 + 0.0464708i \(0.0147974\pi\)
−0.998920 + 0.0464708i \(0.985203\pi\)
\(132\) 6.08767 0.0461187
\(133\) 143.955 73.0294i 1.08237 0.549094i
\(134\) 86.2254 0.643473
\(135\) 0 0
\(136\) 66.4123i 0.488326i
\(137\) 165.765i 1.20996i −0.796241 0.604980i \(-0.793181\pi\)
0.796241 0.604980i \(-0.206819\pi\)
\(138\) −45.8739 −0.332419
\(139\) 220.514i 1.58643i 0.608941 + 0.793215i \(0.291594\pi\)
−0.608941 + 0.793215i \(0.708406\pi\)
\(140\) 0 0
\(141\) 67.0294 0.475386
\(142\) 156.426i 1.10159i
\(143\) 32.9600 0.230489
\(144\) 12.0000 0.0833333
\(145\) 0 0
\(146\) 80.2687i 0.549786i
\(147\) −50.1275 + 68.4853i −0.341003 + 0.465886i
\(148\) 141.823i 0.958266i
\(149\) −210.853 −1.41512 −0.707560 0.706653i \(-0.750204\pi\)
−0.707560 + 0.706653i \(0.750204\pi\)
\(150\) 0 0
\(151\) −72.3675 −0.479255 −0.239628 0.970865i \(-0.577025\pi\)
−0.239628 + 0.970865i \(0.577025\pi\)
\(152\) 65.2236 0.429103
\(153\) 70.4409 0.460398
\(154\) −15.5147 + 7.87071i −0.100745 + 0.0511085i
\(155\) 0 0
\(156\) 64.9706 0.416478
\(157\) 233.674 1.48837 0.744184 0.667974i \(-0.232838\pi\)
0.744184 + 0.667974i \(0.232838\pi\)
\(158\) 98.7452i 0.624969i
\(159\) 64.1369i 0.403377i
\(160\) 0 0
\(161\) 116.912 59.3100i 0.726160 0.368385i
\(162\) 12.7279i 0.0785674i
\(163\) 73.0883i 0.448395i −0.974544 0.224197i \(-0.928024\pi\)
0.974544 0.224197i \(-0.0719760\pi\)
\(164\) 82.7903i 0.504819i
\(165\) 0 0
\(166\) 9.10164i 0.0548292i
\(167\) −39.3958 −0.235903 −0.117951 0.993019i \(-0.537633\pi\)
−0.117951 + 0.993019i \(0.537633\pi\)
\(168\) −30.5826 + 15.5147i −0.182039 + 0.0923495i
\(169\) 182.765 1.08145
\(170\) 0 0
\(171\) 69.1801i 0.404562i
\(172\) 20.8528i 0.121237i
\(173\) −23.8284 −0.137737 −0.0688683 0.997626i \(-0.521939\pi\)
−0.0688683 + 0.997626i \(0.521939\pi\)
\(174\) 73.4847i 0.422326i
\(175\) 0 0
\(176\) −7.02944 −0.0399400
\(177\) 168.853i 0.953971i
\(178\) −59.5263 −0.334417
\(179\) 12.9045 0.0720924 0.0360462 0.999350i \(-0.488524\pi\)
0.0360462 + 0.999350i \(0.488524\pi\)
\(180\) 0 0
\(181\) 65.3678i 0.361148i 0.983561 + 0.180574i \(0.0577955\pi\)
−0.983561 + 0.180574i \(0.942204\pi\)
\(182\) −165.581 + 84.0000i −0.909783 + 0.461538i
\(183\) 28.9706i 0.158309i
\(184\) 52.9706 0.287883
\(185\) 0 0
\(186\) −21.0883 −0.113378
\(187\) −41.2633 −0.220659
\(188\) −77.3989 −0.411696
\(189\) −16.4558 32.4377i −0.0870680 0.171628i
\(190\) 0 0
\(191\) −100.066 −0.523906 −0.261953 0.965081i \(-0.584367\pi\)
−0.261953 + 0.965081i \(0.584367\pi\)
\(192\) −13.8564 −0.0721688
\(193\) 78.9117i 0.408869i 0.978880 + 0.204434i \(0.0655355\pi\)
−0.978880 + 0.204434i \(0.934464\pi\)
\(194\) 73.1365i 0.376992i
\(195\) 0 0
\(196\) 57.8823 79.0800i 0.295318 0.403469i
\(197\) 183.941i 0.933711i 0.884334 + 0.466856i \(0.154613\pi\)
−0.884334 + 0.466856i \(0.845387\pi\)
\(198\) 7.45584i 0.0376558i
\(199\) 170.029i 0.854419i −0.904153 0.427210i \(-0.859497\pi\)
0.904153 0.427210i \(-0.140503\pi\)
\(200\) 0 0
\(201\) 105.604i 0.525394i
\(202\) −9.34783 −0.0462764
\(203\) 95.0079 + 187.279i 0.468019 + 0.922558i
\(204\) −81.3381 −0.398716
\(205\) 0 0
\(206\) 248.719i 1.20737i
\(207\) 56.1838i 0.271419i
\(208\) −75.0215 −0.360680
\(209\) 40.5247i 0.193898i
\(210\) 0 0
\(211\) 21.5736 0.102245 0.0511223 0.998692i \(-0.483720\pi\)
0.0511223 + 0.998692i \(0.483720\pi\)
\(212\) 74.0589i 0.349334i
\(213\) −191.582 −0.899448
\(214\) −65.3970 −0.305593
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 53.7446 27.2649i 0.247671 0.125645i
\(218\) 50.8284i 0.233158i
\(219\) 98.3087 0.448898
\(220\) 0 0
\(221\) −440.382 −1.99268
\(222\) −173.697 −0.782421
\(223\) 119.359 0.535240 0.267620 0.963525i \(-0.413763\pi\)
0.267620 + 0.963525i \(0.413763\pi\)
\(224\) 35.3137 17.9149i 0.157650 0.0799770i
\(225\) 0 0
\(226\) 103.279 0.456988
\(227\) −169.843 −0.748207 −0.374103 0.927387i \(-0.622049\pi\)
−0.374103 + 0.927387i \(0.622049\pi\)
\(228\) 79.8823i 0.350361i
\(229\) 110.011i 0.480396i 0.970724 + 0.240198i \(0.0772124\pi\)
−0.970724 + 0.240198i \(0.922788\pi\)
\(230\) 0 0
\(231\) 9.63961 + 19.0016i 0.0417299 + 0.0822579i
\(232\) 84.8528i 0.365745i
\(233\) 57.2649i 0.245772i 0.992421 + 0.122886i \(0.0392150\pi\)
−0.992421 + 0.122886i \(0.960785\pi\)
\(234\) 79.5724i 0.340053i
\(235\) 0 0
\(236\) 194.974i 0.826163i
\(237\) 120.938 0.510285
\(238\) 207.294 105.161i 0.870983 0.441855i
\(239\) −281.522 −1.17792 −0.588958 0.808164i \(-0.700462\pi\)
−0.588958 + 0.808164i \(0.700462\pi\)
\(240\) 0 0
\(241\) 168.306i 0.698366i 0.937055 + 0.349183i \(0.113541\pi\)
−0.937055 + 0.349183i \(0.886459\pi\)
\(242\) 166.752i 0.689059i
\(243\) 15.5885 0.0641500
\(244\) 33.4523i 0.137100i
\(245\) 0 0
\(246\) −101.397 −0.412183
\(247\) 432.500i 1.75101i
\(248\) 24.3507 0.0981882
\(249\) −11.1472 −0.0447678
\(250\) 0 0
\(251\) 106.096i 0.422695i 0.977411 + 0.211348i \(0.0677852\pi\)
−0.977411 + 0.211348i \(0.932215\pi\)
\(252\) 19.0016 + 37.4558i 0.0754031 + 0.148634i
\(253\) 32.9117i 0.130086i
\(254\) 127.196 0.500771
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) −290.462 −1.13020 −0.565102 0.825021i \(-0.691163\pi\)
−0.565102 + 0.825021i \(0.691163\pi\)
\(258\) −25.5394 −0.0989898
\(259\) 442.676 224.572i 1.70917 0.867074i
\(260\) 0 0
\(261\) −90.0000 −0.344828
\(262\) −17.2185 −0.0657196
\(263\) 89.0223i 0.338488i −0.985574 0.169244i \(-0.945867\pi\)
0.985574 0.169244i \(-0.0541326\pi\)
\(264\) 8.60927i 0.0326109i
\(265\) 0 0
\(266\) 103.279 + 203.584i 0.388268 + 0.765352i
\(267\) 72.9045i 0.273051i
\(268\) 121.941i 0.455004i
\(269\) 191.498i 0.711888i −0.934507 0.355944i \(-0.884159\pi\)
0.934507 0.355944i \(-0.115841\pi\)
\(270\) 0 0
\(271\) 217.440i 0.802362i −0.915999 0.401181i \(-0.868600\pi\)
0.915999 0.401181i \(-0.131400\pi\)
\(272\) 93.9211 0.345298
\(273\) 102.879 + 202.794i 0.376845 + 0.742835i
\(274\) 234.426 0.855571
\(275\) 0 0
\(276\) 64.8754i 0.235056i
\(277\) 290.676i 1.04937i −0.851296 0.524686i \(-0.824183\pi\)
0.851296 0.524686i \(-0.175817\pi\)
\(278\) −311.854 −1.12178
\(279\) 25.8278i 0.0925728i
\(280\) 0 0
\(281\) 18.8528 0.0670919 0.0335459 0.999437i \(-0.489320\pi\)
0.0335459 + 0.999437i \(0.489320\pi\)
\(282\) 94.7939i 0.336149i
\(283\) 401.734 1.41955 0.709777 0.704426i \(-0.248796\pi\)
0.709777 + 0.704426i \(0.248796\pi\)
\(284\) 221.220 0.778945
\(285\) 0 0
\(286\) 46.6124i 0.162980i
\(287\) 258.415 131.095i 0.900401 0.456779i
\(288\) 16.9706i 0.0589256i
\(289\) 262.324 0.907695
\(290\) 0 0
\(291\) 89.5736 0.307813
\(292\) −113.517 −0.388757
\(293\) 280.893 0.958679 0.479340 0.877629i \(-0.340876\pi\)
0.479340 + 0.877629i \(0.340876\pi\)
\(294\) −96.8528 70.8910i −0.329431 0.241126i
\(295\) 0 0
\(296\) 200.569 0.677596
\(297\) −9.13151 −0.0307458
\(298\) 298.191i 1.00064i
\(299\) 351.249i 1.17475i
\(300\) 0 0
\(301\) 65.0883 33.0197i 0.216240 0.109700i
\(302\) 102.343i 0.338885i
\(303\) 11.4487i 0.0377845i
\(304\) 92.2401i 0.303421i
\(305\) 0 0
\(306\) 99.6184i 0.325550i
\(307\) 152.318 0.496151 0.248076 0.968741i \(-0.420202\pi\)
0.248076 + 0.968741i \(0.420202\pi\)
\(308\) −11.1309 21.9411i −0.0361392 0.0712374i
\(309\) −304.617 −0.985817
\(310\) 0 0
\(311\) 283.156i 0.910470i −0.890371 0.455235i \(-0.849555\pi\)
0.890371 0.455235i \(-0.150445\pi\)
\(312\) 91.8823i 0.294494i
\(313\) −48.5819 −0.155214 −0.0776069 0.996984i \(-0.524728\pi\)
−0.0776069 + 0.996984i \(0.524728\pi\)
\(314\) 330.465i 1.05244i
\(315\) 0 0
\(316\) −139.647 −0.441920
\(317\) 578.029i 1.82343i 0.410819 + 0.911717i \(0.365243\pi\)
−0.410819 + 0.911717i \(0.634757\pi\)
\(318\) 90.7032 0.285230
\(319\) 52.7208 0.165269
\(320\) 0 0
\(321\) 80.0946i 0.249516i
\(322\) 83.8770 + 165.338i 0.260488 + 0.513472i
\(323\) 541.456i 1.67633i
\(324\) −18.0000 −0.0555556
\(325\) 0 0
\(326\) 103.362 0.317063
\(327\) 62.2519 0.190373
\(328\) 117.083 0.356961
\(329\) −122.558 241.587i −0.372518 0.734307i
\(330\) 0 0
\(331\) 332.368 1.00413 0.502066 0.864829i \(-0.332574\pi\)
0.502066 + 0.864829i \(0.332574\pi\)
\(332\) 12.8717 0.0387701
\(333\) 212.735i 0.638844i
\(334\) 55.7141i 0.166809i
\(335\) 0 0
\(336\) −21.9411 43.2503i −0.0653010 0.128721i
\(337\) 88.1766i 0.261652i −0.991405 0.130826i \(-0.958237\pi\)
0.991405 0.130826i \(-0.0417629\pi\)
\(338\) 258.468i 0.764698i
\(339\) 126.491i 0.373129i
\(340\) 0 0
\(341\) 15.1296i 0.0443683i
\(342\) −97.8354 −0.286068
\(343\) 338.488 + 55.4487i 0.986847 + 0.161658i
\(344\) 29.4903 0.0857277
\(345\) 0 0
\(346\) 33.6985i 0.0973945i
\(347\) 320.080i 0.922422i 0.887291 + 0.461211i \(0.152585\pi\)
−0.887291 + 0.461211i \(0.847415\pi\)
\(348\) 103.923 0.298629
\(349\) 333.046i 0.954287i 0.878825 + 0.477143i \(0.158328\pi\)
−0.878825 + 0.477143i \(0.841672\pi\)
\(350\) 0 0
\(351\) −97.4558 −0.277652
\(352\) 9.94113i 0.0282418i
\(353\) 655.712 1.85754 0.928771 0.370654i \(-0.120866\pi\)
0.928771 + 0.370654i \(0.120866\pi\)
\(354\) −238.794 −0.674559
\(355\) 0 0
\(356\) 84.1829i 0.236469i
\(357\) −128.796 253.882i −0.360773 0.711155i
\(358\) 18.2498i 0.0509770i
\(359\) 97.7574 0.272305 0.136152 0.990688i \(-0.456526\pi\)
0.136152 + 0.990688i \(0.456526\pi\)
\(360\) 0 0
\(361\) −170.765 −0.473032
\(362\) −92.4440 −0.255370
\(363\) −204.229 −0.562614
\(364\) −118.794 234.166i −0.326357 0.643314i
\(365\) 0 0
\(366\) −40.9706 −0.111941
\(367\) −321.057 −0.874815 −0.437408 0.899263i \(-0.644103\pi\)
−0.437408 + 0.899263i \(0.644103\pi\)
\(368\) 74.9117i 0.203564i
\(369\) 124.185i 0.336546i
\(370\) 0 0
\(371\) −231.161 + 117.270i −0.623077 + 0.316091i
\(372\) 29.8234i 0.0801704i
\(373\) 187.470i 0.502601i 0.967909 + 0.251300i \(0.0808582\pi\)
−0.967909 + 0.251300i \(0.919142\pi\)
\(374\) 58.3551i 0.156030i
\(375\) 0 0
\(376\) 109.459i 0.291113i
\(377\) 562.662 1.49247
\(378\) 45.8739 23.2721i 0.121359 0.0615663i
\(379\) 357.103 0.942223 0.471112 0.882074i \(-0.343853\pi\)
0.471112 + 0.882074i \(0.343853\pi\)
\(380\) 0 0
\(381\) 155.783i 0.408878i
\(382\) 141.515i 0.370457i
\(383\) −622.230 −1.62462 −0.812311 0.583225i \(-0.801791\pi\)
−0.812311 + 0.583225i \(0.801791\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −111.598 −0.289114
\(387\) 31.2792i 0.0808249i
\(388\) −103.431 −0.266574
\(389\) −227.470 −0.584756 −0.292378 0.956303i \(-0.594447\pi\)
−0.292378 + 0.956303i \(0.594447\pi\)
\(390\) 0 0
\(391\) 439.737i 1.12465i
\(392\) 111.836 + 81.8579i 0.285296 + 0.208821i
\(393\) 21.0883i 0.0536598i
\(394\) −260.132 −0.660234
\(395\) 0 0
\(396\) 10.5442 0.0266267
\(397\) 720.329 1.81443 0.907216 0.420666i \(-0.138204\pi\)
0.907216 + 0.420666i \(0.138204\pi\)
\(398\) 240.458 0.604166
\(399\) 249.338 126.491i 0.624908 0.317019i
\(400\) 0 0
\(401\) 697.176 1.73859 0.869296 0.494291i \(-0.164572\pi\)
0.869296 + 0.494291i \(0.164572\pi\)
\(402\) 149.347 0.371509
\(403\) 161.470i 0.400670i
\(404\) 13.2198i 0.0327223i
\(405\) 0 0
\(406\) −264.853 + 134.361i −0.652347 + 0.330939i
\(407\) 124.617i 0.306185i
\(408\) 115.029i 0.281935i
\(409\) 102.386i 0.250333i −0.992136 0.125166i \(-0.960053\pi\)
0.992136 0.125166i \(-0.0399465\pi\)
\(410\) 0 0
\(411\) 287.113i 0.698571i
\(412\) 351.742 0.853742
\(413\) 608.578 308.735i 1.47355 0.747543i
\(414\) −79.4558 −0.191922
\(415\) 0 0
\(416\) 106.096i 0.255040i
\(417\) 381.941i 0.915926i
\(418\) 57.3106 0.137107
\(419\) 391.426i 0.934191i −0.884207 0.467095i \(-0.845300\pi\)
0.884207 0.467095i \(-0.154700\pi\)
\(420\) 0 0
\(421\) 354.441 0.841902 0.420951 0.907083i \(-0.361696\pi\)
0.420951 + 0.907083i \(0.361696\pi\)
\(422\) 30.5097i 0.0722978i
\(423\) 116.098 0.274464
\(424\) −104.735 −0.247017
\(425\) 0 0
\(426\) 270.938i 0.636006i
\(427\) 104.415 52.9706i 0.244533 0.124053i
\(428\) 92.4853i 0.216087i
\(429\) 57.0883 0.133073
\(430\) 0 0
\(431\) 585.286 1.35797 0.678987 0.734151i \(-0.262419\pi\)
0.678987 + 0.734151i \(0.262419\pi\)
\(432\) 20.7846 0.0481125
\(433\) 392.207 0.905789 0.452895 0.891564i \(-0.350391\pi\)
0.452895 + 0.891564i \(0.350391\pi\)
\(434\) 38.5584 + 76.0063i 0.0888443 + 0.175130i
\(435\) 0 0
\(436\) −71.8823 −0.164868
\(437\) −431.866 −0.988252
\(438\) 139.029i 0.317419i
\(439\) 392.513i 0.894106i 0.894507 + 0.447053i \(0.147527\pi\)
−0.894507 + 0.447053i \(0.852473\pi\)
\(440\) 0 0
\(441\) −86.8234 + 118.620i −0.196878 + 0.268980i
\(442\) 622.794i 1.40904i
\(443\) 814.742i 1.83915i −0.392918 0.919574i \(-0.628534\pi\)
0.392918 0.919574i \(-0.371466\pi\)
\(444\) 245.645i 0.553255i
\(445\) 0 0
\(446\) 168.798i 0.378472i
\(447\) −365.208 −0.817020
\(448\) 25.3354 + 49.9411i 0.0565523 + 0.111476i
\(449\) −180.323 −0.401610 −0.200805 0.979631i \(-0.564356\pi\)
−0.200805 + 0.979631i \(0.564356\pi\)
\(450\) 0 0
\(451\) 72.7461i 0.161300i
\(452\) 146.059i 0.323139i
\(453\) −125.344 −0.276698
\(454\) 240.194i 0.529062i
\(455\) 0 0
\(456\) 112.971 0.247742
\(457\) 280.177i 0.613078i −0.951858 0.306539i \(-0.900829\pi\)
0.951858 0.306539i \(-0.0991710\pi\)
\(458\) −155.579 −0.339691
\(459\) 122.007 0.265811
\(460\) 0 0
\(461\) 406.297i 0.881338i 0.897670 + 0.440669i \(0.145259\pi\)
−0.897670 + 0.440669i \(0.854741\pi\)
\(462\) −26.8723 + 13.6325i −0.0581651 + 0.0295075i
\(463\) 457.470i 0.988056i 0.869446 + 0.494028i \(0.164476\pi\)
−0.869446 + 0.494028i \(0.835524\pi\)
\(464\) −120.000 −0.258621
\(465\) 0 0
\(466\) −80.9848 −0.173787
\(467\) −643.711 −1.37840 −0.689198 0.724573i \(-0.742037\pi\)
−0.689198 + 0.724573i \(0.742037\pi\)
\(468\) 112.532 0.240454
\(469\) −380.617 + 193.089i −0.811551 + 0.411705i
\(470\) 0 0
\(471\) 404.735 0.859310
\(472\) 275.735 0.584185
\(473\) 18.3229i 0.0387377i
\(474\) 171.032i 0.360826i
\(475\) 0 0
\(476\) 148.721 + 293.158i 0.312439 + 0.615878i
\(477\) 111.088i 0.232890i
\(478\) 398.132i 0.832912i
\(479\) 168.535i 0.351847i −0.984404 0.175924i \(-0.943709\pi\)
0.984404 0.175924i \(-0.0562912\pi\)
\(480\) 0 0
\(481\) 1329.98i 2.76502i
\(482\) −238.021 −0.493819
\(483\) 202.497 102.728i 0.419248 0.212687i
\(484\) 235.823 0.487238
\(485\) 0 0
\(486\) 22.0454i 0.0453609i
\(487\) 2.77965i 0.00570771i 0.999996 + 0.00285385i \(0.000908411\pi\)
−0.999996 + 0.00285385i \(0.999092\pi\)
\(488\) 47.3087 0.0969441
\(489\) 126.593i 0.258881i
\(490\) 0 0
\(491\) −247.477 −0.504027 −0.252014 0.967724i \(-0.581093\pi\)
−0.252014 + 0.967724i \(0.581093\pi\)
\(492\) 143.397i 0.291457i
\(493\) −704.409 −1.42882
\(494\) 611.647 1.23815
\(495\) 0 0
\(496\) 34.4371i 0.0694296i
\(497\) 350.295 + 690.500i 0.704818 + 1.38934i
\(498\) 15.7645i 0.0316556i
\(499\) 483.426 0.968789 0.484394 0.874850i \(-0.339040\pi\)
0.484394 + 0.874850i \(0.339040\pi\)
\(500\) 0 0
\(501\) −68.2355 −0.136199
\(502\) −150.043 −0.298891
\(503\) −58.7033 −0.116706 −0.0583532 0.998296i \(-0.518585\pi\)
−0.0583532 + 0.998296i \(0.518585\pi\)
\(504\) −52.9706 + 26.8723i −0.105100 + 0.0533180i
\(505\) 0 0
\(506\) 46.5442 0.0919845
\(507\) 316.557 0.624374
\(508\) 179.882i 0.354099i
\(509\) 68.8793i 0.135323i −0.997708 0.0676614i \(-0.978446\pi\)
0.997708 0.0676614i \(-0.0215537\pi\)
\(510\) 0 0
\(511\) −179.750 354.323i −0.351762 0.693392i
\(512\) 22.6274i 0.0441942i
\(513\) 119.823i 0.233574i
\(514\) 410.776i 0.799175i
\(515\) 0 0
\(516\) 36.1181i 0.0699964i
\(517\) −68.0089 −0.131545
\(518\) 317.593 + 626.039i 0.613114 + 1.20857i
\(519\) −41.2721 −0.0795223
\(520\) 0 0
\(521\) 292.720i 0.561843i 0.959731 + 0.280922i \(0.0906401\pi\)
−0.959731 + 0.280922i \(0.909360\pi\)
\(522\) 127.279i 0.243830i
\(523\) −493.056 −0.942746 −0.471373 0.881934i \(-0.656241\pi\)
−0.471373 + 0.881934i \(0.656241\pi\)
\(524\) 24.3507i 0.0464708i
\(525\) 0 0
\(526\) 125.897 0.239347
\(527\) 202.148i 0.383583i
\(528\) −12.1753 −0.0230594
\(529\) 178.265 0.336985
\(530\) 0 0
\(531\) 292.462i 0.550775i
\(532\) −287.911 + 146.059i −0.541186 + 0.274547i
\(533\) 776.382i 1.45663i
\(534\) −103.103 −0.193076
\(535\) 0 0
\(536\) −172.451 −0.321737
\(537\) 22.3513 0.0416226
\(538\) 270.819 0.503381
\(539\) 50.8600 69.4860i 0.0943598 0.128916i
\(540\) 0 0
\(541\) −1037.85 −1.91840 −0.959198 0.282736i \(-0.908758\pi\)
−0.959198 + 0.282736i \(0.908758\pi\)
\(542\) 307.507 0.567356
\(543\) 113.220i 0.208509i
\(544\) 132.825i 0.244163i
\(545\) 0 0
\(546\) −286.794 + 145.492i −0.525264 + 0.266469i
\(547\) 130.530i 0.238629i 0.992857 + 0.119314i \(0.0380696\pi\)
−0.992857 + 0.119314i \(0.961930\pi\)
\(548\) 331.529i 0.604980i
\(549\) 50.1785i 0.0913998i
\(550\) 0 0
\(551\) 691.801i 1.25554i
\(552\) 91.7477 0.166210
\(553\) −221.126 435.882i −0.399866 0.788214i
\(554\) 411.078 0.742018
\(555\) 0 0
\(556\) 441.028i 0.793215i
\(557\) 665.147i 1.19416i −0.802182 0.597080i \(-0.796327\pi\)
0.802182 0.597080i \(-0.203673\pi\)
\(558\) −36.5260 −0.0654588
\(559\) 195.551i 0.349823i
\(560\) 0 0
\(561\) −71.4701 −0.127398
\(562\) 26.6619i 0.0474411i
\(563\) −829.295 −1.47299 −0.736497 0.676441i \(-0.763521\pi\)
−0.736497 + 0.676441i \(0.763521\pi\)
\(564\) −134.059 −0.237693
\(565\) 0 0
\(566\) 568.137i 1.00378i
\(567\) −28.5024 56.1838i −0.0502687 0.0990895i
\(568\) 312.853i 0.550797i
\(569\) −706.971 −1.24248 −0.621240 0.783621i \(-0.713371\pi\)
−0.621240 + 0.783621i \(0.713371\pi\)
\(570\) 0 0
\(571\) −366.912 −0.642577 −0.321289 0.946981i \(-0.604116\pi\)
−0.321289 + 0.946981i \(0.604116\pi\)
\(572\) −65.9199 −0.115245
\(573\) −173.319 −0.302477
\(574\) 185.397 + 365.454i 0.322991 + 0.636679i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) −390.357 −0.676528 −0.338264 0.941051i \(-0.609840\pi\)
−0.338264 + 0.941051i \(0.609840\pi\)
\(578\) 370.982i 0.641837i
\(579\) 136.679i 0.236061i
\(580\) 0 0
\(581\) 20.3818 + 40.1766i 0.0350806 + 0.0691507i
\(582\) 126.676i 0.217657i
\(583\) 65.0740i 0.111619i
\(584\) 160.537i 0.274893i
\(585\) 0 0
\(586\) 397.243i 0.677889i
\(587\) −702.499 −1.19676 −0.598381 0.801212i \(-0.704189\pi\)
−0.598381 + 0.801212i \(0.704189\pi\)
\(588\) 100.255 136.971i 0.170502 0.232943i
\(589\) −198.530 −0.337063
\(590\) 0 0
\(591\) 318.595i 0.539078i
\(592\) 283.647i 0.479133i
\(593\) −942.519 −1.58941 −0.794704 0.606997i \(-0.792374\pi\)
−0.794704 + 0.606997i \(0.792374\pi\)
\(594\) 12.9139i 0.0217406i
\(595\) 0 0
\(596\) 421.706 0.707560
\(597\) 294.500i 0.493299i
\(598\) 496.742 0.830672
\(599\) 952.109 1.58950 0.794749 0.606939i \(-0.207603\pi\)
0.794749 + 0.606939i \(0.207603\pi\)
\(600\) 0 0
\(601\) 729.804i 1.21432i 0.794581 + 0.607158i \(0.207690\pi\)
−0.794581 + 0.607158i \(0.792310\pi\)
\(602\) 46.6969 + 92.0488i 0.0775696 + 0.152905i
\(603\) 182.912i 0.303336i
\(604\) 144.735 0.239628
\(605\) 0 0
\(606\) −16.1909 −0.0267177
\(607\) −1006.34 −1.65789 −0.828944 0.559332i \(-0.811058\pi\)
−0.828944 + 0.559332i \(0.811058\pi\)
\(608\) −130.447 −0.214551
\(609\) 164.558 + 324.377i 0.270211 + 0.532639i
\(610\) 0 0
\(611\) −725.823 −1.18793
\(612\) −140.882 −0.230199
\(613\) 199.588i 0.325592i −0.986660 0.162796i \(-0.947949\pi\)
0.986660 0.162796i \(-0.0520512\pi\)
\(614\) 215.411i 0.350832i
\(615\) 0 0
\(616\) 31.0294 15.7414i 0.0503725 0.0255542i
\(617\) 353.294i 0.572599i 0.958140 + 0.286299i \(0.0924252\pi\)
−0.958140 + 0.286299i \(0.907575\pi\)
\(618\) 430.794i 0.697078i
\(619\) 56.2064i 0.0908020i 0.998969 + 0.0454010i \(0.0144566\pi\)
−0.998969 + 0.0454010i \(0.985543\pi\)
\(620\) 0 0
\(621\) 97.3131i 0.156704i
\(622\) 400.443 0.643799
\(623\) 262.762 133.301i 0.421769 0.213966i
\(624\) −129.941 −0.208239
\(625\) 0 0
\(626\) 68.7052i 0.109753i
\(627\) 70.1909i 0.111947i
\(628\) −467.348 −0.744184
\(629\) 1665.03i 2.64710i
\(630\) 0 0
\(631\) 807.322 1.27943 0.639716 0.768611i \(-0.279052\pi\)
0.639716 + 0.768611i \(0.279052\pi\)
\(632\) 197.490i 0.312485i
\(633\) 37.3666 0.0590309
\(634\) −817.456 −1.28936
\(635\) 0 0
\(636\) 128.274i 0.201688i
\(637\) 542.802 741.588i 0.852122 1.16419i
\(638\) 74.5584i 0.116863i
\(639\) −331.831 −0.519297
\(640\) 0 0
\(641\) 1016.35 1.58557 0.792786 0.609500i \(-0.208630\pi\)
0.792786 + 0.609500i \(0.208630\pi\)
\(642\) −113.271 −0.176434
\(643\) 404.688 0.629375 0.314687 0.949195i \(-0.398100\pi\)
0.314687 + 0.949195i \(0.398100\pi\)
\(644\) −233.823 + 118.620i −0.363080 + 0.184193i
\(645\) 0 0
\(646\) −765.734 −1.18535
\(647\) −940.604 −1.45379 −0.726896 0.686747i \(-0.759038\pi\)
−0.726896 + 0.686747i \(0.759038\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 171.320i 0.263975i
\(650\) 0 0
\(651\) 93.0883 47.2243i 0.142993 0.0725411i
\(652\) 146.177i 0.224197i
\(653\) 731.970i 1.12093i 0.828177 + 0.560467i \(0.189378\pi\)
−0.828177 + 0.560467i \(0.810622\pi\)
\(654\) 88.0374i 0.134614i
\(655\) 0 0
\(656\) 165.581i 0.252409i
\(657\) 170.276 0.259171
\(658\) 341.655 173.324i 0.519233 0.263410i
\(659\) −904.316 −1.37225 −0.686127 0.727481i \(-0.740691\pi\)
−0.686127 + 0.727481i \(0.740691\pi\)
\(660\) 0 0
\(661\) 335.881i 0.508141i −0.967186 0.254070i \(-0.918231\pi\)
0.967186 0.254070i \(-0.0817695\pi\)
\(662\) 470.039i 0.710028i
\(663\) −762.764 −1.15047
\(664\) 18.2033i 0.0274146i
\(665\) 0 0
\(666\) −300.853 −0.451731
\(667\) 561.838i 0.842335i
\(668\) 78.7916 0.117951
\(669\) 206.735 0.309021
\(670\) 0 0
\(671\) 29.3939i 0.0438061i
\(672\) 61.1651 31.0294i 0.0910195 0.0461748i
\(673\) 1191.44i 1.77034i 0.465266 + 0.885171i \(0.345959\pi\)
−0.465266 + 0.885171i \(0.654041\pi\)
\(674\) 124.701 0.185016
\(675\) 0 0
\(676\) −365.529 −0.540723
\(677\) 1211.07 1.78888 0.894441 0.447186i \(-0.147574\pi\)
0.894441 + 0.447186i \(0.147574\pi\)
\(678\) 178.885 0.263842
\(679\) −163.779 322.840i −0.241206 0.475464i
\(680\) 0 0
\(681\) −294.177 −0.431977
\(682\) 21.3965 0.0313731
\(683\) 1233.89i 1.80657i −0.429038 0.903287i \(-0.641147\pi\)
0.429038 0.903287i \(-0.358853\pi\)
\(684\) 138.360i 0.202281i
\(685\) 0 0
\(686\) −78.4163 + 478.695i −0.114309 + 0.697806i
\(687\) 190.544i 0.277357i
\(688\) 41.7056i 0.0606186i
\(689\) 694.501i 1.00798i
\(690\) 0 0
\(691\) 86.7045i 0.125477i −0.998030 0.0627384i \(-0.980017\pi\)
0.998030 0.0627384i \(-0.0199834\pi\)
\(692\) 47.6569 0.0688683
\(693\) 16.6963 + 32.9117i 0.0240928 + 0.0474916i
\(694\) −452.662 −0.652251
\(695\) 0 0
\(696\) 146.969i 0.211163i
\(697\) 971.970i 1.39450i
\(698\) −470.998 −0.674783
\(699\) 99.1858i 0.141897i
\(700\) 0 0
\(701\) −149.147 −0.212763 −0.106382 0.994325i \(-0.533927\pi\)
−0.106382 + 0.994325i \(0.533927\pi\)
\(702\) 137.823i 0.196330i
\(703\) −1635.22 −2.32607
\(704\) 14.0589 0.0199700
\(705\) 0 0
\(706\) 927.317i 1.31348i
\(707\) 41.2633 20.9331i 0.0583639 0.0296084i
\(708\) 337.706i 0.476985i
\(709\) −189.647 −0.267485 −0.133742 0.991016i \(-0.542699\pi\)
−0.133742 + 0.991016i \(0.542699\pi\)
\(710\) 0 0
\(711\) 209.470 0.294613
\(712\) 119.053 0.167209
\(713\) −161.234 −0.226134
\(714\) 359.044 182.145i 0.502862 0.255105i
\(715\) 0 0
\(716\) −25.8091 −0.0360462
\(717\) −487.610 −0.680070
\(718\) 138.250i 0.192548i
\(719\) 12.0064i 0.0166987i 0.999965 + 0.00834937i \(0.00265772\pi\)
−0.999965 + 0.00834937i \(0.997342\pi\)
\(720\) 0 0
\(721\) 556.971 + 1097.90i 0.772497 + 1.52274i
\(722\) 241.497i 0.334484i
\(723\) 291.515i 0.403202i
\(724\) 130.736i 0.180574i
\(725\) 0 0
\(726\) 288.823i 0.397828i
\(727\) −417.169 −0.573823 −0.286911 0.957957i \(-0.592629\pi\)
−0.286911 + 0.957957i \(0.592629\pi\)
\(728\) 331.161 168.000i 0.454892 0.230769i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 244.815i 0.334904i
\(732\) 57.9411i 0.0791545i
\(733\) −1286.99 −1.75578 −0.877892 0.478859i \(-0.841051\pi\)
−0.877892 + 0.478859i \(0.841051\pi\)
\(734\) 454.043i 0.618588i
\(735\) 0 0
\(736\) −105.941 −0.143942
\(737\) 107.147i 0.145383i
\(738\) −175.625 −0.237974
\(739\) −1333.47 −1.80443 −0.902213 0.431292i \(-0.858058\pi\)
−0.902213 + 0.431292i \(0.858058\pi\)
\(740\) 0 0
\(741\) 749.111i 1.01095i
\(742\) −165.844 326.912i −0.223510 0.440582i
\(743\) 776.476i 1.04506i −0.852622 0.522528i \(-0.824989\pi\)
0.852622 0.522528i \(-0.175011\pi\)
\(744\) 42.1766 0.0566890
\(745\) 0 0
\(746\) −265.123 −0.355392
\(747\) −19.3075 −0.0258467
\(748\) 82.5266 0.110330
\(749\) 288.676 146.447i 0.385415 0.195524i
\(750\) 0 0
\(751\) 48.8385 0.0650313 0.0325157 0.999471i \(-0.489648\pi\)
0.0325157 + 0.999471i \(0.489648\pi\)
\(752\) 154.798 0.205848
\(753\) 183.765i 0.244043i
\(754\) 795.724i 1.05534i
\(755\) 0 0
\(756\) 32.9117 + 64.8754i 0.0435340 + 0.0858141i
\(757\) 1279.47i 1.69019i 0.534620 + 0.845093i \(0.320455\pi\)
−0.534620 + 0.845093i \(0.679545\pi\)
\(758\) 505.019i 0.666252i
\(759\) 57.0047i 0.0751050i
\(760\) 0 0
\(761\) 1316.12i 1.72947i −0.502231 0.864734i \(-0.667487\pi\)
0.502231 0.864734i \(-0.332513\pi\)
\(762\) 220.310 0.289121
\(763\) −113.823 224.368i −0.149178 0.294060i
\(764\) 200.132 0.261953
\(765\) 0 0
\(766\) 879.966i 1.14878i
\(767\) 1828.41i 2.38385i
\(768\) 27.7128 0.0360844
\(769\) 110.324i 0.143464i 0.997424 + 0.0717320i \(0.0228526\pi\)
−0.997424 + 0.0717320i \(0.977147\pi\)
\(770\) 0 0
\(771\) −503.095 −0.652523
\(772\) 157.823i 0.204434i
\(773\) 717.634 0.928375 0.464187 0.885737i \(-0.346346\pi\)
0.464187 + 0.885737i \(0.346346\pi\)
\(774\) −44.2355 −0.0571518
\(775\) 0 0
\(776\) 146.273i 0.188496i
\(777\) 766.738 388.971i 0.986792 0.500606i
\(778\) 321.691i 0.413485i
\(779\) −954.573 −1.22538
\(780\) 0 0
\(781\) 194.382 0.248888
\(782\) −621.882 −0.795245
\(783\) −155.885 −0.199086
\(784\) −115.765 + 158.160i −0.147659 + 0.201735i
\(785\) 0 0
\(786\) −29.8234 −0.0379432
\(787\) −347.191 −0.441158 −0.220579 0.975369i \(-0.570795\pi\)
−0.220579 + 0.975369i \(0.570795\pi\)
\(788\) 367.882i 0.466856i
\(789\) 154.191i 0.195426i
\(790\) 0 0
\(791\) −455.897 + 231.279i −0.576355 + 0.292388i