Properties

Label 1050.3.e.e.701.2
Level $1050$
Weight $3$
Character 1050.701
Analytic conductor $28.610$
Analytic rank $0$
Dimension $24$
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.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 701.2
Character \(\chi\) \(=\) 1050.701
Dual form 1050.3.e.e.701.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(1.28756 - 2.70965i) q^{3} -2.00000 q^{4} +(-3.83202 - 1.82088i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-5.68438 - 6.97766i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(1.28756 - 2.70965i) q^{3} -2.00000 q^{4} +(-3.83202 - 1.82088i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-5.68438 - 6.97766i) q^{9} +10.4698i q^{11} +(-2.57512 + 5.41930i) q^{12} +11.9937 q^{13} -3.74166i q^{14} +4.00000 q^{16} -29.1133i q^{17} +(-9.86791 + 8.03893i) q^{18} -20.3176 q^{19} +(3.40656 - 7.16905i) q^{21} +14.8066 q^{22} -7.71572i q^{23} +(7.66404 + 3.64177i) q^{24} -16.9617i q^{26} +(-26.2260 + 6.41851i) q^{27} -5.29150 q^{28} -47.4046i q^{29} -35.5084 q^{31} -5.65685i q^{32} +(28.3695 + 13.4805i) q^{33} -41.1724 q^{34} +(11.3688 + 13.9553i) q^{36} -58.0907 q^{37} +28.7334i q^{38} +(15.4426 - 32.4988i) q^{39} -52.5850i q^{41} +(-10.1386 - 4.81761i) q^{42} -15.7629 q^{43} -20.9396i q^{44} -10.9117 q^{46} +85.2023i q^{47} +(5.15024 - 10.8386i) q^{48} +7.00000 q^{49} +(-78.8867 - 37.4850i) q^{51} -23.9875 q^{52} -42.7649i q^{53} +(9.07715 + 37.0892i) q^{54} +7.48331i q^{56} +(-26.1601 + 55.0535i) q^{57} -67.0403 q^{58} +37.9769i q^{59} +53.5108 q^{61} +50.2165i q^{62} +(-15.0395 - 18.4612i) q^{63} -8.00000 q^{64} +(19.0643 - 40.1206i) q^{66} +27.6366 q^{67} +58.2265i q^{68} +(-20.9069 - 9.93444i) q^{69} -58.0688i q^{71} +(19.7358 - 16.0779i) q^{72} -67.8080 q^{73} +82.1526i q^{74} +40.6352 q^{76} +27.7005i q^{77} +(-45.9602 - 21.8392i) q^{78} -19.2994 q^{79} +(-16.3756 + 79.3274i) q^{81} -74.3664 q^{82} -33.6998i q^{83} +(-6.81312 + 14.3381i) q^{84} +22.2920i q^{86} +(-128.450 - 61.0363i) q^{87} -29.6131 q^{88} +46.8325i q^{89} +31.7324 q^{91} +15.4314i q^{92} +(-45.7192 + 96.2153i) q^{93} +120.494 q^{94} +(-15.3281 - 7.28354i) q^{96} +65.1337 q^{97} -9.89949i q^{98} +(73.0549 - 59.5145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) \) 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
\(3\) 1.28756 2.70965i 0.429186 0.903216i
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) −3.83202 1.82088i −0.638670 0.303481i
\(7\) 2.64575 0.377964
\(8\) 2.82843i 0.353553i
\(9\) −5.68438 6.97766i −0.631598 0.775296i
\(10\) 0 0
\(11\) 10.4698i 0.951802i 0.879499 + 0.475901i \(0.157878\pi\)
−0.879499 + 0.475901i \(0.842122\pi\)
\(12\) −2.57512 + 5.41930i −0.214593 + 0.451608i
\(13\) 11.9937 0.922595 0.461297 0.887246i \(-0.347384\pi\)
0.461297 + 0.887246i \(0.347384\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 29.1133i 1.71254i −0.516525 0.856272i \(-0.672775\pi\)
0.516525 0.856272i \(-0.327225\pi\)
\(18\) −9.86791 + 8.03893i −0.548217 + 0.446607i
\(19\) −20.3176 −1.06935 −0.534673 0.845059i \(-0.679565\pi\)
−0.534673 + 0.845059i \(0.679565\pi\)
\(20\) 0 0
\(21\) 3.40656 7.16905i 0.162217 0.341384i
\(22\) 14.8066 0.673026
\(23\) 7.71572i 0.335466i −0.985832 0.167733i \(-0.946355\pi\)
0.985832 0.167733i \(-0.0536446\pi\)
\(24\) 7.66404 + 3.64177i 0.319335 + 0.151740i
\(25\) 0 0
\(26\) 16.9617i 0.652373i
\(27\) −26.2260 + 6.41851i −0.971333 + 0.237723i
\(28\) −5.29150 −0.188982
\(29\) 47.4046i 1.63464i −0.576182 0.817321i \(-0.695458\pi\)
0.576182 0.817321i \(-0.304542\pi\)
\(30\) 0 0
\(31\) −35.5084 −1.14543 −0.572717 0.819753i \(-0.694110\pi\)
−0.572717 + 0.819753i \(0.694110\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 28.3695 + 13.4805i 0.859683 + 0.408501i
\(34\) −41.1724 −1.21095
\(35\) 0 0
\(36\) 11.3688 + 13.9553i 0.315799 + 0.387648i
\(37\) −58.0907 −1.57002 −0.785009 0.619485i \(-0.787342\pi\)
−0.785009 + 0.619485i \(0.787342\pi\)
\(38\) 28.7334i 0.756142i
\(39\) 15.4426 32.4988i 0.395965 0.833302i
\(40\) 0 0
\(41\) 52.5850i 1.28256i −0.767307 0.641280i \(-0.778404\pi\)
0.767307 0.641280i \(-0.221596\pi\)
\(42\) −10.1386 4.81761i −0.241395 0.114705i
\(43\) −15.7629 −0.366578 −0.183289 0.983059i \(-0.558674\pi\)
−0.183289 + 0.983059i \(0.558674\pi\)
\(44\) 20.9396i 0.475901i
\(45\) 0 0
\(46\) −10.9117 −0.237210
\(47\) 85.2023i 1.81281i 0.422405 + 0.906407i \(0.361186\pi\)
−0.422405 + 0.906407i \(0.638814\pi\)
\(48\) 5.15024 10.8386i 0.107297 0.225804i
\(49\) 7.00000 0.142857
\(50\) 0 0
\(51\) −78.8867 37.4850i −1.54680 0.735001i
\(52\) −23.9875 −0.461297
\(53\) 42.7649i 0.806885i −0.915005 0.403443i \(-0.867813\pi\)
0.915005 0.403443i \(-0.132187\pi\)
\(54\) 9.07715 + 37.0892i 0.168095 + 0.686836i
\(55\) 0 0
\(56\) 7.48331i 0.133631i
\(57\) −26.1601 + 55.0535i −0.458949 + 0.965850i
\(58\) −67.0403 −1.15587
\(59\) 37.9769i 0.643676i 0.946795 + 0.321838i \(0.104301\pi\)
−0.946795 + 0.321838i \(0.895699\pi\)
\(60\) 0 0
\(61\) 53.5108 0.877226 0.438613 0.898676i \(-0.355470\pi\)
0.438613 + 0.898676i \(0.355470\pi\)
\(62\) 50.2165i 0.809944i
\(63\) −15.0395 18.4612i −0.238722 0.293034i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 19.0643 40.1206i 0.288854 0.607888i
\(67\) 27.6366 0.412487 0.206243 0.978501i \(-0.433876\pi\)
0.206243 + 0.978501i \(0.433876\pi\)
\(68\) 58.2265i 0.856272i
\(69\) −20.9069 9.93444i −0.302998 0.143977i
\(70\) 0 0
\(71\) 58.0688i 0.817871i −0.912563 0.408935i \(-0.865900\pi\)
0.912563 0.408935i \(-0.134100\pi\)
\(72\) 19.7358 16.0779i 0.274109 0.223304i
\(73\) −67.8080 −0.928877 −0.464438 0.885605i \(-0.653744\pi\)
−0.464438 + 0.885605i \(0.653744\pi\)
\(74\) 82.1526i 1.11017i
\(75\) 0 0
\(76\) 40.6352 0.534673
\(77\) 27.7005i 0.359747i
\(78\) −45.9602 21.8392i −0.589234 0.279990i
\(79\) −19.2994 −0.244296 −0.122148 0.992512i \(-0.538978\pi\)
−0.122148 + 0.992512i \(0.538978\pi\)
\(80\) 0 0
\(81\) −16.3756 + 79.3274i −0.202168 + 0.979351i
\(82\) −74.3664 −0.906907
\(83\) 33.6998i 0.406021i −0.979177 0.203011i \(-0.934927\pi\)
0.979177 0.203011i \(-0.0650726\pi\)
\(84\) −6.81312 + 14.3381i −0.0811086 + 0.170692i
\(85\) 0 0
\(86\) 22.2920i 0.259210i
\(87\) −128.450 61.0363i −1.47643 0.701566i
\(88\) −29.6131 −0.336513
\(89\) 46.8325i 0.526208i 0.964768 + 0.263104i \(0.0847462\pi\)
−0.964768 + 0.263104i \(0.915254\pi\)
\(90\) 0 0
\(91\) 31.7324 0.348708
\(92\) 15.4314i 0.167733i
\(93\) −45.7192 + 96.2153i −0.491604 + 1.03457i
\(94\) 120.494 1.28185
\(95\) 0 0
\(96\) −15.3281 7.28354i −0.159668 0.0758702i
\(97\) 65.1337 0.671482 0.335741 0.941954i \(-0.391013\pi\)
0.335741 + 0.941954i \(0.391013\pi\)
\(98\) 9.89949i 0.101015i
\(99\) 73.0549 59.5145i 0.737928 0.601156i
\(100\) 0 0
\(101\) 171.169i 1.69474i −0.531000 0.847372i \(-0.678184\pi\)
0.531000 0.847372i \(-0.321816\pi\)
\(102\) −53.0119 + 111.563i −0.519724 + 1.09375i
\(103\) 129.879 1.26096 0.630481 0.776205i \(-0.282858\pi\)
0.630481 + 0.776205i \(0.282858\pi\)
\(104\) 33.9234i 0.326186i
\(105\) 0 0
\(106\) −60.4787 −0.570554
\(107\) 29.1627i 0.272549i −0.990671 0.136274i \(-0.956487\pi\)
0.990671 0.136274i \(-0.0435128\pi\)
\(108\) 52.4520 12.8370i 0.485667 0.118861i
\(109\) −19.3296 −0.177336 −0.0886680 0.996061i \(-0.528261\pi\)
−0.0886680 + 0.996061i \(0.528261\pi\)
\(110\) 0 0
\(111\) −74.7952 + 157.405i −0.673830 + 1.41807i
\(112\) 10.5830 0.0944911
\(113\) 28.5568i 0.252715i −0.991985 0.126358i \(-0.959671\pi\)
0.991985 0.126358i \(-0.0403287\pi\)
\(114\) 77.8574 + 36.9959i 0.682959 + 0.324526i
\(115\) 0 0
\(116\) 94.8092i 0.817321i
\(117\) −68.1769 83.6882i −0.582709 0.715284i
\(118\) 53.7074 0.455148
\(119\) 77.0264i 0.647281i
\(120\) 0 0
\(121\) 11.3828 0.0940727
\(122\) 75.6757i 0.620292i
\(123\) −142.487 67.7063i −1.15843 0.550457i
\(124\) 71.0169 0.572717
\(125\) 0 0
\(126\) −26.1080 + 21.2690i −0.207207 + 0.168802i
\(127\) −162.116 −1.27650 −0.638252 0.769828i \(-0.720342\pi\)
−0.638252 + 0.769828i \(0.720342\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −20.2956 + 42.7118i −0.157330 + 0.331099i
\(130\) 0 0
\(131\) 49.5756i 0.378440i 0.981935 + 0.189220i \(0.0605959\pi\)
−0.981935 + 0.189220i \(0.939404\pi\)
\(132\) −56.7391 26.9610i −0.429841 0.204250i
\(133\) −53.7553 −0.404175
\(134\) 39.0840i 0.291672i
\(135\) 0 0
\(136\) 82.3447 0.605476
\(137\) 212.721i 1.55271i 0.630297 + 0.776354i \(0.282933\pi\)
−0.630297 + 0.776354i \(0.717067\pi\)
\(138\) −14.0494 + 29.5668i −0.101807 + 0.214252i
\(139\) −74.1650 −0.533561 −0.266780 0.963757i \(-0.585960\pi\)
−0.266780 + 0.963757i \(0.585960\pi\)
\(140\) 0 0
\(141\) 230.868 + 109.703i 1.63736 + 0.778036i
\(142\) −82.1217 −0.578322
\(143\) 125.572i 0.878128i
\(144\) −22.7375 27.9107i −0.157899 0.193824i
\(145\) 0 0
\(146\) 95.8950i 0.656815i
\(147\) 9.01292 18.9675i 0.0613124 0.129031i
\(148\) 116.181 0.785009
\(149\) 23.1598i 0.155435i 0.996975 + 0.0777176i \(0.0247632\pi\)
−0.996975 + 0.0777176i \(0.975237\pi\)
\(150\) 0 0
\(151\) 75.1469 0.497661 0.248831 0.968547i \(-0.419954\pi\)
0.248831 + 0.968547i \(0.419954\pi\)
\(152\) 57.4668i 0.378071i
\(153\) −203.143 + 165.491i −1.32773 + 1.08164i
\(154\) 39.1745 0.254380
\(155\) 0 0
\(156\) −30.8853 + 64.9976i −0.197983 + 0.416651i
\(157\) −66.6968 −0.424820 −0.212410 0.977181i \(-0.568131\pi\)
−0.212410 + 0.977181i \(0.568131\pi\)
\(158\) 27.2934i 0.172743i
\(159\) −115.878 55.0624i −0.728792 0.346304i
\(160\) 0 0
\(161\) 20.4139i 0.126794i
\(162\) 112.186 + 23.1586i 0.692506 + 0.142954i
\(163\) 248.817 1.52648 0.763241 0.646114i \(-0.223607\pi\)
0.763241 + 0.646114i \(0.223607\pi\)
\(164\) 105.170i 0.641280i
\(165\) 0 0
\(166\) −47.6587 −0.287100
\(167\) 92.0222i 0.551031i −0.961297 0.275516i \(-0.911151\pi\)
0.961297 0.275516i \(-0.0888485\pi\)
\(168\) 20.2771 + 9.63521i 0.120697 + 0.0573525i
\(169\) −25.1504 −0.148819
\(170\) 0 0
\(171\) 115.493 + 141.769i 0.675397 + 0.829060i
\(172\) 31.5257 0.183289
\(173\) 233.473i 1.34956i 0.738021 + 0.674778i \(0.235761\pi\)
−0.738021 + 0.674778i \(0.764239\pi\)
\(174\) −86.3183 + 181.655i −0.496082 + 1.04400i
\(175\) 0 0
\(176\) 41.8793i 0.237951i
\(177\) 102.904 + 48.8975i 0.581379 + 0.276257i
\(178\) 66.2311 0.372085
\(179\) 185.252i 1.03493i −0.855705 0.517465i \(-0.826876\pi\)
0.855705 0.517465i \(-0.173124\pi\)
\(180\) 0 0
\(181\) −146.372 −0.808684 −0.404342 0.914608i \(-0.632499\pi\)
−0.404342 + 0.914608i \(0.632499\pi\)
\(182\) 44.8764i 0.246574i
\(183\) 68.8983 144.995i 0.376493 0.792324i
\(184\) 21.8233 0.118605
\(185\) 0 0
\(186\) 136.069 + 64.6567i 0.731554 + 0.347617i
\(187\) 304.811 1.63000
\(188\) 170.405i 0.906407i
\(189\) −69.3875 + 16.9818i −0.367129 + 0.0898507i
\(190\) 0 0
\(191\) 83.4780i 0.437057i −0.975831 0.218529i \(-0.929874\pi\)
0.975831 0.218529i \(-0.0701257\pi\)
\(192\) −10.3005 + 21.6772i −0.0536483 + 0.112902i
\(193\) −88.5046 −0.458573 −0.229287 0.973359i \(-0.573639\pi\)
−0.229287 + 0.973359i \(0.573639\pi\)
\(194\) 92.1130i 0.474809i
\(195\) 0 0
\(196\) −14.0000 −0.0714286
\(197\) 36.9343i 0.187484i −0.995597 0.0937419i \(-0.970117\pi\)
0.995597 0.0937419i \(-0.0298828\pi\)
\(198\) −84.1662 103.315i −0.425082 0.521794i
\(199\) 205.101 1.03066 0.515330 0.856992i \(-0.327669\pi\)
0.515330 + 0.856992i \(0.327669\pi\)
\(200\) 0 0
\(201\) 35.5838 74.8854i 0.177034 0.372564i
\(202\) −242.070 −1.19836
\(203\) 125.421i 0.617837i
\(204\) 157.773 + 74.9701i 0.773399 + 0.367500i
\(205\) 0 0
\(206\) 183.677i 0.891634i
\(207\) −53.8377 + 43.8591i −0.260085 + 0.211880i
\(208\) 47.9749 0.230649
\(209\) 212.721i 1.01781i
\(210\) 0 0
\(211\) 49.4829 0.234516 0.117258 0.993101i \(-0.462590\pi\)
0.117258 + 0.993101i \(0.462590\pi\)
\(212\) 85.5298i 0.403443i
\(213\) −157.346 74.7670i −0.738714 0.351019i
\(214\) −41.2423 −0.192721
\(215\) 0 0
\(216\) −18.1543 74.1783i −0.0840477 0.343418i
\(217\) −93.9465 −0.432933
\(218\) 27.3362i 0.125395i
\(219\) −87.3069 + 183.736i −0.398661 + 0.838976i
\(220\) 0 0
\(221\) 349.177i 1.57998i
\(222\) 222.605 + 105.776i 1.00272 + 0.476470i
\(223\) 1.69928 0.00762011 0.00381005 0.999993i \(-0.498787\pi\)
0.00381005 + 0.999993i \(0.498787\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) −40.3855 −0.178697
\(227\) 206.970i 0.911762i −0.890041 0.455881i \(-0.849324\pi\)
0.890041 0.455881i \(-0.150676\pi\)
\(228\) 52.3202 110.107i 0.229474 0.482925i
\(229\) 7.02543 0.0306787 0.0153394 0.999882i \(-0.495117\pi\)
0.0153394 + 0.999882i \(0.495117\pi\)
\(230\) 0 0
\(231\) 75.0587 + 35.6661i 0.324930 + 0.154399i
\(232\) 134.081 0.577933
\(233\) 116.672i 0.500738i −0.968151 0.250369i \(-0.919448\pi\)
0.968151 0.250369i \(-0.0805519\pi\)
\(234\) −118.353 + 96.4168i −0.505782 + 0.412037i
\(235\) 0 0
\(236\) 75.9538i 0.321838i
\(237\) −24.8491 + 52.2945i −0.104848 + 0.220652i
\(238\) −108.932 −0.457697
\(239\) 157.119i 0.657400i −0.944434 0.328700i \(-0.893389\pi\)
0.944434 0.328700i \(-0.106611\pi\)
\(240\) 0 0
\(241\) −287.032 −1.19101 −0.595503 0.803353i \(-0.703047\pi\)
−0.595503 + 0.803353i \(0.703047\pi\)
\(242\) 16.0977i 0.0665194i
\(243\) 193.865 + 146.511i 0.797797 + 0.602926i
\(244\) −107.022 −0.438613
\(245\) 0 0
\(246\) −95.7511 + 201.507i −0.389232 + 0.819133i
\(247\) −243.684 −0.986573
\(248\) 100.433i 0.404972i
\(249\) −91.3145 43.3905i −0.366725 0.174259i
\(250\) 0 0
\(251\) 161.056i 0.641658i 0.947137 + 0.320829i \(0.103961\pi\)
−0.947137 + 0.320829i \(0.896039\pi\)
\(252\) 30.0789 + 36.9223i 0.119361 + 0.146517i
\(253\) 80.7822 0.319297
\(254\) 229.267i 0.902625i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 356.900i 1.38871i 0.719630 + 0.694357i \(0.244311\pi\)
−0.719630 + 0.694357i \(0.755689\pi\)
\(258\) 60.4036 + 28.7023i 0.234122 + 0.111249i
\(259\) −153.693 −0.593411
\(260\) 0 0
\(261\) −330.774 + 269.466i −1.26733 + 1.03244i
\(262\) 70.1105 0.267597
\(263\) 126.259i 0.480071i −0.970764 0.240036i \(-0.922841\pi\)
0.970764 0.240036i \(-0.0771591\pi\)
\(264\) −38.1287 + 80.2412i −0.144427 + 0.303944i
\(265\) 0 0
\(266\) 76.0214i 0.285795i
\(267\) 126.900 + 60.2996i 0.475279 + 0.225841i
\(268\) −55.2732 −0.206243
\(269\) 356.319i 1.32461i −0.749236 0.662304i \(-0.769579\pi\)
0.749236 0.662304i \(-0.230421\pi\)
\(270\) 0 0
\(271\) −422.588 −1.55937 −0.779683 0.626175i \(-0.784620\pi\)
−0.779683 + 0.626175i \(0.784620\pi\)
\(272\) 116.453i 0.428136i
\(273\) 40.8574 85.9837i 0.149661 0.314959i
\(274\) 300.833 1.09793
\(275\) 0 0
\(276\) 41.8137 + 19.8689i 0.151499 + 0.0719887i
\(277\) 267.379 0.965266 0.482633 0.875823i \(-0.339680\pi\)
0.482633 + 0.875823i \(0.339680\pi\)
\(278\) 104.885i 0.377284i
\(279\) 201.843 + 247.766i 0.723453 + 0.888050i
\(280\) 0 0
\(281\) 417.470i 1.48566i −0.669480 0.742830i \(-0.733483\pi\)
0.669480 0.742830i \(-0.266517\pi\)
\(282\) 155.143 326.497i 0.550154 1.15779i
\(283\) 56.1781 0.198509 0.0992546 0.995062i \(-0.468354\pi\)
0.0992546 + 0.995062i \(0.468354\pi\)
\(284\) 116.138i 0.408935i
\(285\) 0 0
\(286\) 177.586 0.620930
\(287\) 139.127i 0.484762i
\(288\) −39.4716 + 32.1557i −0.137054 + 0.111652i
\(289\) −558.582 −1.93281
\(290\) 0 0
\(291\) 83.8635 176.489i 0.288191 0.606493i
\(292\) 135.616 0.464438
\(293\) 35.8668i 0.122412i −0.998125 0.0612062i \(-0.980505\pi\)
0.998125 0.0612062i \(-0.0194947\pi\)
\(294\) −26.8241 12.7462i −0.0912386 0.0433544i
\(295\) 0 0
\(296\) 164.305i 0.555085i
\(297\) −67.2007 274.582i −0.226265 0.924517i
\(298\) 32.7530 0.109909
\(299\) 92.5402i 0.309499i
\(300\) 0 0
\(301\) −41.7046 −0.138553
\(302\) 106.274i 0.351900i
\(303\) −463.808 220.390i −1.53072 0.727361i
\(304\) −81.2703 −0.267337
\(305\) 0 0
\(306\) 234.039 + 287.287i 0.764835 + 0.938846i
\(307\) 496.572 1.61750 0.808749 0.588154i \(-0.200145\pi\)
0.808749 + 0.588154i \(0.200145\pi\)
\(308\) 55.4011i 0.179874i
\(309\) 167.227 351.926i 0.541188 1.13892i
\(310\) 0 0
\(311\) 49.5016i 0.159169i 0.996828 + 0.0795846i \(0.0253594\pi\)
−0.996828 + 0.0795846i \(0.974641\pi\)
\(312\) 91.9204 + 43.6784i 0.294617 + 0.139995i
\(313\) 219.172 0.700229 0.350114 0.936707i \(-0.386143\pi\)
0.350114 + 0.936707i \(0.386143\pi\)
\(314\) 94.3235i 0.300393i
\(315\) 0 0
\(316\) 38.5987 0.122148
\(317\) 96.3016i 0.303791i 0.988397 + 0.151895i \(0.0485377\pi\)
−0.988397 + 0.151895i \(0.951462\pi\)
\(318\) −77.8700 + 163.876i −0.244874 + 0.515333i
\(319\) 496.318 1.55586
\(320\) 0 0
\(321\) −79.0206 37.5487i −0.246170 0.116974i
\(322\) −28.8696 −0.0896570
\(323\) 591.511i 1.83130i
\(324\) 32.7512 158.655i 0.101084 0.489675i
\(325\) 0 0
\(326\) 351.880i 1.07939i
\(327\) −24.8880 + 52.3764i −0.0761102 + 0.160173i
\(328\) 148.733 0.453453
\(329\) 225.424i 0.685180i
\(330\) 0 0
\(331\) 538.706 1.62751 0.813755 0.581208i \(-0.197420\pi\)
0.813755 + 0.581208i \(0.197420\pi\)
\(332\) 67.3995i 0.203011i
\(333\) 330.209 + 405.337i 0.991620 + 1.21723i
\(334\) −130.139 −0.389638
\(335\) 0 0
\(336\) 13.6262 28.6762i 0.0405543 0.0853459i
\(337\) 202.735 0.601589 0.300794 0.953689i \(-0.402748\pi\)
0.300794 + 0.953689i \(0.402748\pi\)
\(338\) 35.5681i 0.105231i
\(339\) −77.3790 36.7686i −0.228257 0.108462i
\(340\) 0 0
\(341\) 371.767i 1.09023i
\(342\) 200.492 163.332i 0.586234 0.477578i
\(343\) 18.5203 0.0539949
\(344\) 44.5841i 0.129605i
\(345\) 0 0
\(346\) 330.181 0.954280
\(347\) 139.011i 0.400607i −0.979734 0.200304i \(-0.935807\pi\)
0.979734 0.200304i \(-0.0641928\pi\)
\(348\) 256.900 + 122.073i 0.738217 + 0.350783i
\(349\) −452.984 −1.29795 −0.648974 0.760811i \(-0.724801\pi\)
−0.648974 + 0.760811i \(0.724801\pi\)
\(350\) 0 0
\(351\) −314.547 + 76.9819i −0.896147 + 0.219322i
\(352\) 59.2263 0.168256
\(353\) 453.499i 1.28470i −0.766412 0.642349i \(-0.777960\pi\)
0.766412 0.642349i \(-0.222040\pi\)
\(354\) 69.1515 145.528i 0.195343 0.411097i
\(355\) 0 0
\(356\) 93.6650i 0.263104i
\(357\) −208.715 99.1761i −0.584635 0.277804i
\(358\) −261.986 −0.731806
\(359\) 150.308i 0.418686i −0.977842 0.209343i \(-0.932868\pi\)
0.977842 0.209343i \(-0.0671324\pi\)
\(360\) 0 0
\(361\) 51.8039 0.143501
\(362\) 207.001i 0.571826i
\(363\) 14.6560 30.8434i 0.0403747 0.0849680i
\(364\) −63.4649 −0.174354
\(365\) 0 0
\(366\) −205.054 97.4369i −0.560258 0.266221i
\(367\) 382.992 1.04357 0.521787 0.853076i \(-0.325265\pi\)
0.521787 + 0.853076i \(0.325265\pi\)
\(368\) 30.8629i 0.0838665i
\(369\) −366.920 + 298.913i −0.994364 + 0.810062i
\(370\) 0 0
\(371\) 113.145i 0.304974i
\(372\) 91.4384 192.431i 0.245802 0.517287i
\(373\) 80.3409 0.215391 0.107696 0.994184i \(-0.465653\pi\)
0.107696 + 0.994184i \(0.465653\pi\)
\(374\) 431.067i 1.15259i
\(375\) 0 0
\(376\) −240.988 −0.640927
\(377\) 568.558i 1.50811i
\(378\) 24.0159 + 98.1287i 0.0635341 + 0.259600i
\(379\) 636.088 1.67833 0.839166 0.543875i \(-0.183044\pi\)
0.839166 + 0.543875i \(0.183044\pi\)
\(380\) 0 0
\(381\) −208.734 + 439.277i −0.547858 + 1.15296i
\(382\) −118.056 −0.309046
\(383\) 343.675i 0.897323i −0.893702 0.448661i \(-0.851901\pi\)
0.893702 0.448661i \(-0.148099\pi\)
\(384\) 30.6562 + 14.5671i 0.0798338 + 0.0379351i
\(385\) 0 0
\(386\) 125.164i 0.324260i
\(387\) 89.6021 + 109.988i 0.231530 + 0.284207i
\(388\) −130.267 −0.335741
\(389\) 520.410i 1.33782i −0.743345 0.668908i \(-0.766762\pi\)
0.743345 0.668908i \(-0.233238\pi\)
\(390\) 0 0
\(391\) −224.630 −0.574500
\(392\) 19.7990i 0.0505076i
\(393\) 134.333 + 63.8316i 0.341813 + 0.162421i
\(394\) −52.2330 −0.132571
\(395\) 0 0
\(396\) −146.110 + 119.029i −0.368964 + 0.300578i
\(397\) 184.320 0.464281 0.232140 0.972682i \(-0.425427\pi\)
0.232140 + 0.972682i \(0.425427\pi\)
\(398\) 290.057i 0.728787i
\(399\) −69.2131 + 145.658i −0.173466 + 0.365057i
\(400\) 0 0
\(401\) 10.1322i 0.0252674i −0.999920 0.0126337i \(-0.995978\pi\)
0.999920 0.0126337i \(-0.00402154\pi\)
\(402\) −105.904 50.3230i −0.263443 0.125182i
\(403\) −425.879 −1.05677
\(404\) 342.338i 0.847372i
\(405\) 0 0
\(406\) −177.372 −0.436876
\(407\) 608.199i 1.49435i
\(408\) 106.024 223.125i 0.259862 0.546876i
\(409\) 802.483 1.96206 0.981031 0.193853i \(-0.0620985\pi\)
0.981031 + 0.193853i \(0.0620985\pi\)
\(410\) 0 0
\(411\) 576.399 + 273.891i 1.40243 + 0.666402i
\(412\) −259.758 −0.630481
\(413\) 100.477i 0.243287i
\(414\) 62.0261 + 76.1380i 0.149822 + 0.183908i
\(415\) 0 0
\(416\) 67.8468i 0.163093i
\(417\) −95.4918 + 200.961i −0.228997 + 0.481921i
\(418\) −300.834 −0.719697
\(419\) 27.2524i 0.0650414i 0.999471 + 0.0325207i \(0.0103535\pi\)
−0.999471 + 0.0325207i \(0.989647\pi\)
\(420\) 0 0
\(421\) 792.513 1.88245 0.941227 0.337775i \(-0.109674\pi\)
0.941227 + 0.337775i \(0.109674\pi\)
\(422\) 69.9793i 0.165828i
\(423\) 594.513 484.322i 1.40547 1.14497i
\(424\) 120.957 0.285277
\(425\) 0 0
\(426\) −105.737 + 222.521i −0.248208 + 0.522349i
\(427\) 141.576 0.331560
\(428\) 58.3254i 0.136274i
\(429\) 340.257 + 161.682i 0.793139 + 0.376880i
\(430\) 0 0
\(431\) 483.889i 1.12271i 0.827574 + 0.561357i \(0.189720\pi\)
−0.827574 + 0.561357i \(0.810280\pi\)
\(432\) −104.904 + 25.6741i −0.242833 + 0.0594307i
\(433\) 567.937 1.31163 0.655816 0.754920i \(-0.272325\pi\)
0.655816 + 0.754920i \(0.272325\pi\)
\(434\) 132.860i 0.306130i
\(435\) 0 0
\(436\) 38.6592 0.0886680
\(437\) 156.765i 0.358729i
\(438\) 259.842 + 123.471i 0.593246 + 0.281896i
\(439\) −834.645 −1.90124 −0.950621 0.310355i \(-0.899552\pi\)
−0.950621 + 0.310355i \(0.899552\pi\)
\(440\) 0 0
\(441\) −39.7907 48.8437i −0.0902283 0.110757i
\(442\) −493.810 −1.11722
\(443\) 543.969i 1.22792i 0.789337 + 0.613960i \(0.210424\pi\)
−0.789337 + 0.613960i \(0.789576\pi\)
\(444\) 149.590 314.810i 0.336915 0.709033i
\(445\) 0 0
\(446\) 2.40315i 0.00538823i
\(447\) 62.7550 + 29.8197i 0.140392 + 0.0667107i
\(448\) −21.1660 −0.0472456
\(449\) 308.306i 0.686649i 0.939217 + 0.343325i \(0.111553\pi\)
−0.939217 + 0.343325i \(0.888447\pi\)
\(450\) 0 0
\(451\) 550.555 1.22074
\(452\) 57.1137i 0.126358i
\(453\) 96.7560 203.622i 0.213589 0.449496i
\(454\) −292.700 −0.644713
\(455\) 0 0
\(456\) −155.715 73.9919i −0.341480 0.162263i
\(457\) 475.765 1.04106 0.520530 0.853843i \(-0.325734\pi\)
0.520530 + 0.853843i \(0.325734\pi\)
\(458\) 9.93545i 0.0216931i
\(459\) 186.864 + 763.524i 0.407111 + 1.66345i
\(460\) 0 0
\(461\) 764.494i 1.65834i −0.558998 0.829169i \(-0.688814\pi\)
0.558998 0.829169i \(-0.311186\pi\)
\(462\) 50.4395 106.149i 0.109176 0.229760i
\(463\) 558.506 1.20628 0.603138 0.797637i \(-0.293917\pi\)
0.603138 + 0.797637i \(0.293917\pi\)
\(464\) 189.618i 0.408661i
\(465\) 0 0
\(466\) −164.999 −0.354075
\(467\) 251.321i 0.538160i −0.963118 0.269080i \(-0.913280\pi\)
0.963118 0.269080i \(-0.0867196\pi\)
\(468\) 136.354 + 167.376i 0.291354 + 0.357642i
\(469\) 73.1196 0.155905
\(470\) 0 0
\(471\) −85.8761 + 180.725i −0.182327 + 0.383705i
\(472\) −107.415 −0.227574
\(473\) 165.034i 0.348910i
\(474\) 73.9556 + 35.1419i 0.156024 + 0.0741391i
\(475\) 0 0
\(476\) 154.053i 0.323641i
\(477\) −298.399 + 243.092i −0.625575 + 0.509627i
\(478\) −222.199 −0.464852
\(479\) 343.617i 0.717363i 0.933460 + 0.358681i \(0.116774\pi\)
−0.933460 + 0.358681i \(0.883226\pi\)
\(480\) 0 0
\(481\) −696.724 −1.44849
\(482\) 405.925i 0.842169i
\(483\) −55.3144 26.2841i −0.114523 0.0544184i
\(484\) −22.7656 −0.0470363
\(485\) 0 0
\(486\) 207.198 274.166i 0.426333 0.564128i
\(487\) 909.858 1.86829 0.934146 0.356892i \(-0.116163\pi\)
0.934146 + 0.356892i \(0.116163\pi\)
\(488\) 151.351i 0.310146i
\(489\) 320.366 674.206i 0.655146 1.37874i
\(490\) 0 0
\(491\) 584.882i 1.19121i −0.803279 0.595603i \(-0.796913\pi\)
0.803279 0.595603i \(-0.203087\pi\)
\(492\) 284.973 + 135.413i 0.579214 + 0.275229i
\(493\) −1380.10 −2.79940
\(494\) 344.621i 0.697612i
\(495\) 0 0
\(496\) −142.034 −0.286358
\(497\) 153.636i 0.309126i
\(498\) −61.3634 + 129.138i −0.123220 + 0.259314i
\(499\) −903.199 −1.81002 −0.905009 0.425392i \(-0.860136\pi\)
−0.905009 + 0.425392i \(0.860136\pi\)
\(500\) 0 0
\(501\) −249.348 118.484i −0.497700 0.236495i
\(502\) 227.768 0.453720
\(503\) 188.576i 0.374903i 0.982274 + 0.187452i \(0.0600228\pi\)
−0.982274 + 0.187452i \(0.939977\pi\)
\(504\) 52.2161 42.5380i 0.103603 0.0844008i
\(505\) 0 0
\(506\) 114.243i 0.225777i
\(507\) −32.3827 + 68.1488i −0.0638711 + 0.134416i
\(508\) 324.232 0.638252
\(509\) 526.061i 1.03352i 0.856131 + 0.516759i \(0.172862\pi\)
−0.856131 + 0.516759i \(0.827138\pi\)
\(510\) 0 0
\(511\) −179.403 −0.351083
\(512\) 22.6274i 0.0441942i
\(513\) 532.849 130.409i 1.03869 0.254208i
\(514\) 504.732 0.981970
\(515\) 0 0
\(516\) 40.5912 85.4236i 0.0786652 0.165550i
\(517\) −892.053 −1.72544
\(518\) 217.355i 0.419605i
\(519\) 632.630 + 300.611i 1.21894 + 0.579211i
\(520\) 0 0
\(521\) 636.046i 1.22082i 0.792087 + 0.610408i \(0.208995\pi\)
−0.792087 + 0.610408i \(0.791005\pi\)
\(522\) 381.082 + 467.784i 0.730043 + 0.896139i
\(523\) −662.926 −1.26755 −0.633773 0.773519i \(-0.718494\pi\)
−0.633773 + 0.773519i \(0.718494\pi\)
\(524\) 99.1513i 0.189220i
\(525\) 0 0
\(526\) −178.557 −0.339461
\(527\) 1033.77i 1.96161i
\(528\) 113.478 + 53.9221i 0.214921 + 0.102125i
\(529\) 469.468 0.887463
\(530\) 0 0
\(531\) 264.990 215.875i 0.499040 0.406545i
\(532\) 107.511 0.202087
\(533\) 630.690i 1.18328i
\(534\) 85.2765 179.463i 0.159694 0.336073i
\(535\) 0 0
\(536\) 78.1681i 0.145836i
\(537\) −501.969 238.523i −0.934765 0.444178i
\(538\) −503.912 −0.936639
\(539\) 73.2888i 0.135972i
\(540\) 0 0
\(541\) −299.602 −0.553793 −0.276897 0.960900i \(-0.589306\pi\)
−0.276897 + 0.960900i \(0.589306\pi\)
\(542\) 597.630i 1.10264i
\(543\) −188.462 + 396.616i −0.347076 + 0.730416i
\(544\) −164.689 −0.302738
\(545\) 0 0
\(546\) −121.599 57.7811i −0.222709 0.105826i
\(547\) 177.699 0.324862 0.162431 0.986720i \(-0.448067\pi\)
0.162431 + 0.986720i \(0.448067\pi\)
\(548\) 425.442i 0.776354i
\(549\) −304.176 373.380i −0.554054 0.680110i
\(550\) 0 0
\(551\) 963.147i 1.74800i
\(552\) 28.0989 59.1336i 0.0509037 0.107126i
\(553\) −51.0613 −0.0923351
\(554\) 378.131i 0.682546i
\(555\) 0 0
\(556\) 148.330 0.266780
\(557\) 227.747i 0.408882i 0.978879 + 0.204441i \(0.0655377\pi\)
−0.978879 + 0.204441i \(0.934462\pi\)
\(558\) 350.394 285.450i 0.627946 0.511559i
\(559\) −189.055 −0.338203
\(560\) 0 0
\(561\) 392.462 825.930i 0.699575 1.47225i
\(562\) −590.392 −1.05052
\(563\) 271.221i 0.481742i −0.970557 0.240871i \(-0.922567\pi\)
0.970557 0.240871i \(-0.0774330\pi\)
\(564\) −461.736 219.406i −0.818682 0.389018i
\(565\) 0 0
\(566\) 79.4479i 0.140367i
\(567\) −43.3258 + 209.881i −0.0764123 + 0.370160i
\(568\) 164.243 0.289161
\(569\) 63.1031i 0.110902i −0.998461 0.0554509i \(-0.982340\pi\)
0.998461 0.0554509i \(-0.0176596\pi\)
\(570\) 0 0
\(571\) 130.175 0.227977 0.113988 0.993482i \(-0.463637\pi\)
0.113988 + 0.993482i \(0.463637\pi\)
\(572\) 251.144i 0.439064i
\(573\) −226.196 107.483i −0.394757 0.187579i
\(574\) −196.755 −0.342779
\(575\) 0 0
\(576\) 45.4751 + 55.8213i 0.0789497 + 0.0969120i
\(577\) 371.832 0.644424 0.322212 0.946668i \(-0.395574\pi\)
0.322212 + 0.946668i \(0.395574\pi\)
\(578\) 789.954i 1.36670i
\(579\) −113.955 + 239.816i −0.196813 + 0.414190i
\(580\) 0 0
\(581\) 89.1612i 0.153462i
\(582\) −249.594 118.601i −0.428855 0.203782i
\(583\) 447.741 0.767995
\(584\) 191.790i 0.328408i
\(585\) 0 0
\(586\) −50.7233 −0.0865586
\(587\) 824.490i 1.40458i −0.711890 0.702291i \(-0.752160\pi\)
0.711890 0.702291i \(-0.247840\pi\)
\(588\) −18.0258 + 37.9351i −0.0306562 + 0.0645154i
\(589\) 721.445 1.22486
\(590\) 0 0
\(591\) −100.079 47.5551i −0.169338 0.0804655i
\(592\) −232.363 −0.392504
\(593\) 148.957i 0.251192i −0.992081 0.125596i \(-0.959916\pi\)
0.992081 0.125596i \(-0.0400843\pi\)
\(594\) −388.317 + 95.0361i −0.653732 + 0.159994i
\(595\) 0 0
\(596\) 46.3197i 0.0777176i
\(597\) 264.080 555.752i 0.442345 0.930909i
\(598\) −130.872 −0.218849
\(599\) 98.6062i 0.164618i 0.996607 + 0.0823090i \(0.0262294\pi\)
−0.996607 + 0.0823090i \(0.973771\pi\)
\(600\) 0 0
\(601\) 244.192 0.406310 0.203155 0.979147i \(-0.434880\pi\)
0.203155 + 0.979147i \(0.434880\pi\)
\(602\) 58.9792i 0.0979721i
\(603\) −157.097 192.839i −0.260526 0.319799i
\(604\) −150.294 −0.248831
\(605\) 0 0
\(606\) −311.679 + 655.924i −0.514322 + 1.08238i
\(607\) −504.707 −0.831478 −0.415739 0.909484i \(-0.636477\pi\)
−0.415739 + 0.909484i \(0.636477\pi\)
\(608\) 114.934i 0.189035i
\(609\) −339.846 161.487i −0.558040 0.265167i
\(610\) 0 0
\(611\) 1021.89i 1.67249i
\(612\) 406.285 330.982i 0.663865 0.540820i
\(613\) 416.536 0.679503 0.339752 0.940515i \(-0.389657\pi\)
0.339752 + 0.940515i \(0.389657\pi\)
\(614\) 702.259i 1.14374i
\(615\) 0 0
\(616\) −78.3490 −0.127190
\(617\) 132.241i 0.214330i −0.994241 0.107165i \(-0.965823\pi\)
0.994241 0.107165i \(-0.0341773\pi\)
\(618\) −497.699 236.495i −0.805338 0.382677i
\(619\) −669.449 −1.08150 −0.540751 0.841183i \(-0.681860\pi\)
−0.540751 + 0.841183i \(0.681860\pi\)
\(620\) 0 0
\(621\) 49.5234 + 202.352i 0.0797479 + 0.325849i
\(622\) 70.0059 0.112550
\(623\) 123.907i 0.198888i
\(624\) 61.7706 129.995i 0.0989913 0.208326i
\(625\) 0 0
\(626\) 309.955i 0.495137i
\(627\) −576.400 273.891i −0.919299 0.436829i
\(628\) 133.394 0.212410
\(629\) 1691.21i 2.68873i
\(630\) 0 0
\(631\) 590.546 0.935889 0.467944 0.883758i \(-0.344995\pi\)
0.467944 + 0.883758i \(0.344995\pi\)
\(632\) 54.5869i 0.0863716i
\(633\) 63.7121 134.081i 0.100651 0.211819i
\(634\) 136.191 0.214812
\(635\) 0 0
\(636\) 231.756 + 110.125i 0.364396 + 0.173152i
\(637\) 83.9561 0.131799
\(638\) 701.900i 1.10016i
\(639\) −405.185 + 330.085i −0.634092 + 0.516565i
\(640\) 0 0
\(641\) 542.271i 0.845977i −0.906135 0.422989i \(-0.860981\pi\)
0.906135 0.422989i \(-0.139019\pi\)
\(642\) −53.1019 + 111.752i −0.0827132 + 0.174069i
\(643\) −546.024 −0.849181 −0.424591 0.905385i \(-0.639582\pi\)
−0.424591 + 0.905385i \(0.639582\pi\)
\(644\) 40.8277i 0.0633971i
\(645\) 0 0
\(646\) 836.523 1.29493
\(647\) 801.011i 1.23804i 0.785376 + 0.619020i \(0.212470\pi\)
−0.785376 + 0.619020i \(0.787530\pi\)
\(648\) −224.372 46.3172i −0.346253 0.0714772i
\(649\) −397.611 −0.612652
\(650\) 0 0
\(651\) −120.962 + 254.562i −0.185809 + 0.391032i
\(652\) −497.633 −0.763241
\(653\) 1193.82i 1.82821i 0.405482 + 0.914103i \(0.367104\pi\)
−0.405482 + 0.914103i \(0.632896\pi\)
\(654\) 74.0715 + 35.1970i 0.113259 + 0.0538180i
\(655\) 0 0
\(656\) 210.340i 0.320640i
\(657\) 385.447 + 473.142i 0.586677 + 0.720155i
\(658\) 318.798 0.484495
\(659\) 1234.84i 1.87381i −0.349579 0.936907i \(-0.613675\pi\)
0.349579 0.936907i \(-0.386325\pi\)
\(660\) 0 0
\(661\) −660.309 −0.998954 −0.499477 0.866327i \(-0.666475\pi\)
−0.499477 + 0.866327i \(0.666475\pi\)
\(662\) 761.845i 1.15082i
\(663\) −946.146 449.586i −1.42707 0.678108i
\(664\) 95.3174 0.143550
\(665\) 0 0
\(666\) 573.233 466.987i 0.860711 0.701181i
\(667\) −365.761 −0.548367
\(668\) 184.044i 0.275516i
\(669\) 2.18793 4.60446i 0.00327045 0.00688260i
\(670\) 0 0
\(671\) 560.248i 0.834945i
\(672\) −40.5543 19.2704i −0.0603487 0.0286762i
\(673\) −372.706 −0.553798 −0.276899 0.960899i \(-0.589307\pi\)
−0.276899 + 0.960899i \(0.589307\pi\)
\(674\) 286.711i 0.425387i
\(675\) 0 0
\(676\) 50.3009 0.0744096
\(677\) 762.928i 1.12693i 0.826142 + 0.563463i \(0.190531\pi\)
−0.826142 + 0.563463i \(0.809469\pi\)
\(678\) −51.9987 + 109.430i −0.0766942 + 0.161402i
\(679\) 172.328 0.253796
\(680\) 0 0
\(681\) −560.816 266.486i −0.823518 0.391316i
\(682\) −525.758 −0.770906
\(683\) 28.2779i 0.0414024i −0.999786 0.0207012i \(-0.993410\pi\)
0.999786 0.0207012i \(-0.00658987\pi\)
\(684\) −230.986 283.538i −0.337698 0.414530i
\(685\) 0 0
\(686\) 26.1916i 0.0381802i
\(687\) 9.04565 19.0364i 0.0131669 0.0277095i
\(688\) −63.0514 −0.0916445
\(689\) 512.911i 0.744428i
\(690\) 0 0
\(691\) −587.034 −0.849543 −0.424771 0.905301i \(-0.639645\pi\)
−0.424771 + 0.905301i \(0.639645\pi\)
\(692\) 466.946i 0.674778i
\(693\) 193.285 157.460i 0.278911 0.227216i
\(694\) −196.591 −0.283272
\(695\) 0 0
\(696\) 172.637 363.311i 0.248041 0.521999i
\(697\) −1530.92 −2.19644
\(698\) 640.616i 0.917787i
\(699\) −316.140 150.222i −0.452274 0.214910i
\(700\) 0 0
\(701\) 221.461i 0.315922i 0.987445 + 0.157961i \(0.0504920\pi\)
−0.987445 + 0.157961i \(0.949508\pi\)
\(702\) 108.869 + 444.837i 0.155084 + 0.633671i
\(703\) 1180.26 1.67889
\(704\) 83.7586i 0.118975i
\(705\) 0 0
\(706\) −641.344 −0.908419
\(707\) 452.871i 0.640553i
\(708\) −205.808 97.7950i −0.290689 0.138129i
\(709\) 1187.65 1.67511 0.837553 0.546356i \(-0.183986\pi\)
0.837553 + 0.546356i \(0.183986\pi\)
\(710\) 0 0
\(711\) 109.705 + 134.665i 0.154297 + 0.189402i
\(712\) −132.462 −0.186043
\(713\) 273.973i 0.384254i
\(714\) −140.256 + 295.167i −0.196437 + 0.413399i
\(715\) 0 0
\(716\) 370.505i 0.517465i
\(717\) −425.736 202.300i −0.593774 0.282147i
\(718\) −212.568 −0.296055
\(719\) 611.937i 0.851095i 0.904936 + 0.425547i \(0.139918\pi\)
−0.904936 + 0.425547i \(0.860082\pi\)
\(720\) 0 0
\(721\) 343.628 0.476599
\(722\) 73.2618i 0.101471i
\(723\) −369.571 + 777.757i −0.511164 + 1.07574i
\(724\) 292.744 0.404342
\(725\) 0 0
\(726\) −43.6191 20.7268i −0.0600814 0.0285492i
\(727\) −1136.33 −1.56304 −0.781520 0.623881i \(-0.785555\pi\)
−0.781520 + 0.623881i \(0.785555\pi\)
\(728\) 89.7529i 0.123287i
\(729\) 646.605 336.664i 0.886976 0.461816i
\(730\) 0 0
\(731\) 458.908i 0.627781i
\(732\) −137.797 + 289.991i −0.188247 + 0.396162i
\(733\) −401.450 −0.547681 −0.273840 0.961775i \(-0.588294\pi\)
−0.273840 + 0.961775i \(0.588294\pi\)
\(734\) 541.632i 0.737919i
\(735\) 0 0
\(736\) −43.6467 −0.0593026
\(737\) 289.350i 0.392606i
\(738\) 422.727 + 518.904i 0.572801 + 0.703121i
\(739\) 75.9398 0.102760 0.0513801 0.998679i \(-0.483638\pi\)
0.0513801 + 0.998679i \(0.483638\pi\)
\(740\) 0 0
\(741\) −313.757 + 660.297i −0.423424 + 0.891088i
\(742\) −160.012 −0.215649
\(743\) 308.906i 0.415755i 0.978155 + 0.207877i \(0.0666555\pi\)
−0.978155 + 0.207877i \(0.933345\pi\)
\(744\) −272.138 129.313i −0.365777 0.173808i
\(745\) 0 0
\(746\) 113.619i 0.152305i
\(747\) −235.146 + 191.562i −0.314787 + 0.256442i
\(748\) −609.621 −0.815002
\(749\) 77.1572i 0.103014i
\(750\) 0 0
\(751\) 629.294 0.837941 0.418971 0.908000i \(-0.362391\pi\)
0.418971 + 0.908000i \(0.362391\pi\)
\(752\) 340.809i 0.453204i
\(753\) 436.405 + 207.369i 0.579555 + 0.275391i
\(754\) −804.063 −1.06640
\(755\) 0 0
\(756\) 138.775 33.9636i 0.183565 0.0449254i
\(757\) −526.381 −0.695351 −0.347676 0.937615i \(-0.613029\pi\)
−0.347676 + 0.937615i \(0.613029\pi\)
\(758\) 899.564i 1.18676i
\(759\) 104.012 218.891i 0.137038 0.288394i
\(760\) 0 0
\(761\) 955.908i 1.25612i 0.778164 + 0.628061i \(0.216151\pi\)
−0.778164 + 0.628061i \(0.783849\pi\)
\(762\) 621.232 + 295.194i 0.815265 + 0.387394i
\(763\) −51.1414 −0.0670267
\(764\) 166.956i 0.218529i
\(765\) 0 0
\(766\) −486.029 −0.634503
\(767\) 455.485i 0.593852i
\(768\) 20.6010 43.3544i 0.0268242 0.0564510i
\(769\) −1062.16 −1.38123 −0.690613 0.723225i \(-0.742659\pi\)
−0.690613 + 0.723225i \(0.742659\pi\)
\(770\) 0 0
\(771\) 967.072 + 459.530i 1.25431 + 0.596018i
\(772\) 177.009 0.229287
\(773\) 548.202i 0.709188i 0.935020 + 0.354594i \(0.115381\pi\)
−0.935020 + 0.354594i \(0.884619\pi\)
\(774\) 155.546 126.717i 0.200964 0.163716i
\(775\) 0 0
\(776\) 184.226i 0.237405i
\(777\) −197.889 + 416.455i −0.254684 + 0.535978i
\(778\) −735.971 −0.945979
\(779\) 1068.40i 1.37150i
\(780\) 0 0
\(781\) 607.970 0.778451
\(782\) 317.674i 0.406233i
\(783\) 304.267 + 1243.23i 0.388592 + 1.58778i
\(784\) 28.0000 0.0357143
\(785\) 0 0
\(786\) 90.2715 189.975i 0.114849 0.241698i
\(787\) −590.574 −0.750412 −0.375206 0.926942i \(-0.622428\pi\)
−0.375206 + 0.926942i \(0.622428\pi\)
\(788\) 73.8686i 0.0937419i
\(789\) −342.117 162.566i −0.433608 0.206040i