Properties

Label 3150.2.bf.e.1151.3
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.3
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.e.1601.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.295801 + 2.62916i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.295801 + 2.62916i) q^{7} +1.00000i q^{8} +(0.570938 + 0.329631i) q^{11} -6.13514i q^{13} +(-1.05841 - 2.42482i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.43678 - 4.22062i) q^{17} +(-6.30208 + 3.63851i) q^{19} -0.659263 q^{22} +(3.98266 - 2.29939i) q^{23} +(3.06757 + 5.31319i) q^{26} +(2.12902 + 1.57075i) q^{28} +8.09526i q^{29} +(0.759345 + 0.438408i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.87356i q^{34} +(-5.05533 - 8.75609i) q^{37} +(3.63851 - 6.30208i) q^{38} -6.25234 q^{41} -9.03582 q^{43} +(0.570938 - 0.329631i) q^{44} +(-2.29939 + 3.98266i) q^{46} +(6.00136 + 10.3947i) q^{47} +(-6.82500 - 1.55542i) q^{49} +(-5.31319 - 3.06757i) q^{52} +(-10.5749 - 6.10540i) q^{53} +(-2.62916 - 0.295801i) q^{56} +(-4.04763 - 7.01070i) q^{58} +(4.06613 - 7.04274i) q^{59} +(-0.0618764 + 0.0357243i) q^{61} -0.876816 q^{62} -1.00000 q^{64} +(-0.666965 + 1.15522i) q^{67} +(-2.43678 - 4.22062i) q^{68} +2.60701i q^{71} +(-2.44571 - 1.41203i) q^{73} +(8.75609 + 5.05533i) q^{74} +7.27702i q^{76} +(-1.03554 + 1.40359i) q^{77} +(-2.88837 - 5.00280i) q^{79} +(5.41468 - 3.12617i) q^{82} +7.44660 q^{83} +(7.82525 - 4.51791i) q^{86} +(-0.329631 + 0.570938i) q^{88} +(-2.66489 - 4.61572i) q^{89} +(16.1303 + 1.81478i) q^{91} -4.59878i q^{92} +(-10.3947 - 6.00136i) q^{94} +11.4792i q^{97} +(6.68833 - 2.06547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{4} + 4q^{7} + O(q^{10}) \) \( 24q + 12q^{4} + 4q^{7} - 12q^{16} + 12q^{19} - 4q^{28} - 28q^{37} - 96q^{43} - 8q^{46} - 52q^{49} + 12q^{52} - 8q^{58} - 12q^{61} - 24q^{64} + 4q^{67} + 12q^{73} + 4q^{79} + 68q^{91} - 24q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.295801 + 2.62916i −0.111802 + 0.993730i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.570938 + 0.329631i 0.172144 + 0.0993876i 0.583597 0.812044i \(-0.301645\pi\)
−0.411452 + 0.911431i \(0.634978\pi\)
\(12\) 0 0
\(13\) 6.13514i 1.70158i −0.525504 0.850791i \(-0.676123\pi\)
0.525504 0.850791i \(-0.323877\pi\)
\(14\) −1.05841 2.42482i −0.282872 0.648061i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.43678 4.22062i 0.591005 1.02365i −0.403092 0.915160i \(-0.632064\pi\)
0.994097 0.108492i \(-0.0346022\pi\)
\(18\) 0 0
\(19\) −6.30208 + 3.63851i −1.44580 + 0.834732i −0.998227 0.0595173i \(-0.981044\pi\)
−0.447570 + 0.894249i \(0.647711\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.659263 −0.140555
\(23\) 3.98266 2.29939i 0.830442 0.479456i −0.0235617 0.999722i \(-0.507501\pi\)
0.854004 + 0.520266i \(0.174167\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.06757 + 5.31319i 0.601600 + 1.04200i
\(27\) 0 0
\(28\) 2.12902 + 1.57075i 0.402347 + 0.296844i
\(29\) 8.09526i 1.50325i 0.659589 + 0.751626i \(0.270730\pi\)
−0.659589 + 0.751626i \(0.729270\pi\)
\(30\) 0 0
\(31\) 0.759345 + 0.438408i 0.136382 + 0.0787404i 0.566639 0.823966i \(-0.308243\pi\)
−0.430256 + 0.902707i \(0.641577\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.87356i 0.835808i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.05533 8.75609i −0.831092 1.43949i −0.897173 0.441679i \(-0.854383\pi\)
0.0660818 0.997814i \(-0.478950\pi\)
\(38\) 3.63851 6.30208i 0.590244 1.02233i
\(39\) 0 0
\(40\) 0 0
\(41\) −6.25234 −0.976451 −0.488226 0.872717i \(-0.662356\pi\)
−0.488226 + 0.872717i \(0.662356\pi\)
\(42\) 0 0
\(43\) −9.03582 −1.37795 −0.688975 0.724785i \(-0.741939\pi\)
−0.688975 + 0.724785i \(0.741939\pi\)
\(44\) 0.570938 0.329631i 0.0860722 0.0496938i
\(45\) 0 0
\(46\) −2.29939 + 3.98266i −0.339027 + 0.587211i
\(47\) 6.00136 + 10.3947i 0.875388 + 1.51622i 0.856349 + 0.516397i \(0.172727\pi\)
0.0190383 + 0.999819i \(0.493940\pi\)
\(48\) 0 0
\(49\) −6.82500 1.55542i −0.975001 0.222202i
\(50\) 0 0
\(51\) 0 0
\(52\) −5.31319 3.06757i −0.736807 0.425396i
\(53\) −10.5749 6.10540i −1.45257 0.838641i −0.453943 0.891031i \(-0.649983\pi\)
−0.998627 + 0.0523897i \(0.983316\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.62916 0.295801i −0.351337 0.0395280i
\(57\) 0 0
\(58\) −4.04763 7.01070i −0.531480 0.920550i
\(59\) 4.06613 7.04274i 0.529365 0.916887i −0.470049 0.882640i \(-0.655764\pi\)
0.999413 0.0342461i \(-0.0109030\pi\)
\(60\) 0 0
\(61\) −0.0618764 + 0.0357243i −0.00792246 + 0.00457403i −0.503956 0.863729i \(-0.668123\pi\)
0.496034 + 0.868303i \(0.334789\pi\)
\(62\) −0.876816 −0.111356
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −0.666965 + 1.15522i −0.0814827 + 0.141132i −0.903887 0.427771i \(-0.859299\pi\)
0.822404 + 0.568903i \(0.192632\pi\)
\(68\) −2.43678 4.22062i −0.295503 0.511826i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.60701i 0.309395i 0.987962 + 0.154697i \(0.0494402\pi\)
−0.987962 + 0.154697i \(0.950560\pi\)
\(72\) 0 0
\(73\) −2.44571 1.41203i −0.286249 0.165266i 0.350000 0.936750i \(-0.386181\pi\)
−0.636249 + 0.771484i \(0.719515\pi\)
\(74\) 8.75609 + 5.05533i 1.01788 + 0.587670i
\(75\) 0 0
\(76\) 7.27702i 0.834732i
\(77\) −1.03554 + 1.40359i −0.118011 + 0.159953i
\(78\) 0 0
\(79\) −2.88837 5.00280i −0.324967 0.562859i 0.656539 0.754292i \(-0.272020\pi\)
−0.981506 + 0.191433i \(0.938686\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 5.41468 3.12617i 0.597952 0.345228i
\(83\) 7.44660 0.817370 0.408685 0.912675i \(-0.365987\pi\)
0.408685 + 0.912675i \(0.365987\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.82525 4.51791i 0.843819 0.487179i
\(87\) 0 0
\(88\) −0.329631 + 0.570938i −0.0351388 + 0.0608622i
\(89\) −2.66489 4.61572i −0.282478 0.489266i 0.689517 0.724270i \(-0.257823\pi\)
−0.971994 + 0.235004i \(0.924490\pi\)
\(90\) 0 0
\(91\) 16.1303 + 1.81478i 1.69091 + 0.190241i
\(92\) 4.59878i 0.479456i
\(93\) 0 0
\(94\) −10.3947 6.00136i −1.07213 0.618993i
\(95\) 0 0
\(96\) 0 0
\(97\) 11.4792i 1.16553i 0.812640 + 0.582766i \(0.198030\pi\)
−0.812640 + 0.582766i \(0.801970\pi\)
\(98\) 6.68833 2.06547i 0.675624 0.208644i
\(99\) 0 0
\(100\) 0 0
\(101\) −7.74874 + 13.4212i −0.771029 + 1.33546i 0.165971 + 0.986131i \(0.446924\pi\)
−0.937000 + 0.349330i \(0.886409\pi\)
\(102\) 0 0
\(103\) −1.79131 + 1.03422i −0.176503 + 0.101904i −0.585649 0.810565i \(-0.699160\pi\)
0.409145 + 0.912469i \(0.365827\pi\)
\(104\) 6.13514 0.601600
\(105\) 0 0
\(106\) 12.2108 1.18602
\(107\) 9.43331 5.44632i 0.911953 0.526516i 0.0308937 0.999523i \(-0.490165\pi\)
0.881059 + 0.473007i \(0.156831\pi\)
\(108\) 0 0
\(109\) 7.17254 12.4232i 0.687005 1.18993i −0.285797 0.958290i \(-0.592258\pi\)
0.972802 0.231637i \(-0.0744082\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.42482 1.05841i 0.229124 0.100010i
\(113\) 11.9081i 1.12022i −0.828420 0.560108i \(-0.810760\pi\)
0.828420 0.560108i \(-0.189240\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.01070 + 4.04763i 0.650927 + 0.375813i
\(117\) 0 0
\(118\) 8.13225i 0.748635i
\(119\) 10.3759 + 7.65515i 0.951158 + 0.701747i
\(120\) 0 0
\(121\) −5.28269 9.14988i −0.480244 0.831807i
\(122\) 0.0357243 0.0618764i 0.00323433 0.00560202i
\(123\) 0 0
\(124\) 0.759345 0.438408i 0.0681912 0.0393702i
\(125\) 0 0
\(126\) 0 0
\(127\) −14.6264 −1.29788 −0.648941 0.760839i \(-0.724788\pi\)
−0.648941 + 0.760839i \(0.724788\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.64037 2.84120i −0.143320 0.248237i 0.785425 0.618957i \(-0.212444\pi\)
−0.928745 + 0.370720i \(0.879111\pi\)
\(132\) 0 0
\(133\) −7.70208 17.6455i −0.667855 1.53006i
\(134\) 1.33393i 0.115234i
\(135\) 0 0
\(136\) 4.22062 + 2.43678i 0.361915 + 0.208952i
\(137\) −3.03168 1.75034i −0.259014 0.149542i 0.364871 0.931058i \(-0.381113\pi\)
−0.623885 + 0.781516i \(0.714447\pi\)
\(138\) 0 0
\(139\) 1.78031i 0.151004i −0.997146 0.0755021i \(-0.975944\pi\)
0.997146 0.0755021i \(-0.0240560\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.30350 2.25773i −0.109388 0.189465i
\(143\) 2.02234 3.50279i 0.169116 0.292918i
\(144\) 0 0
\(145\) 0 0
\(146\) 2.82406 0.233721
\(147\) 0 0
\(148\) −10.1107 −0.831092
\(149\) 7.14910 4.12754i 0.585677 0.338141i −0.177709 0.984083i \(-0.556869\pi\)
0.763386 + 0.645942i \(0.223535\pi\)
\(150\) 0 0
\(151\) −0.463545 + 0.802883i −0.0377227 + 0.0653377i −0.884270 0.466975i \(-0.845344\pi\)
0.846548 + 0.532313i \(0.178677\pi\)
\(152\) −3.63851 6.30208i −0.295122 0.511167i
\(153\) 0 0
\(154\) 0.195010 1.73331i 0.0157144 0.139674i
\(155\) 0 0
\(156\) 0 0
\(157\) −7.22480 4.17124i −0.576602 0.332901i 0.183180 0.983079i \(-0.441361\pi\)
−0.759782 + 0.650178i \(0.774694\pi\)
\(158\) 5.00280 + 2.88837i 0.398001 + 0.229786i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.86740 + 11.1512i 0.383605 + 0.878840i
\(162\) 0 0
\(163\) −12.1525 21.0488i −0.951858 1.64867i −0.741400 0.671064i \(-0.765838\pi\)
−0.210458 0.977603i \(-0.567496\pi\)
\(164\) −3.12617 + 5.41468i −0.244113 + 0.422816i
\(165\) 0 0
\(166\) −6.44894 + 3.72330i −0.500535 + 0.288984i
\(167\) 7.48724 0.579380 0.289690 0.957120i \(-0.406448\pi\)
0.289690 + 0.957120i \(0.406448\pi\)
\(168\) 0 0
\(169\) −24.6400 −1.89538
\(170\) 0 0
\(171\) 0 0
\(172\) −4.51791 + 7.82525i −0.344487 + 0.596670i
\(173\) −7.12036 12.3328i −0.541351 0.937647i −0.998827 0.0484252i \(-0.984580\pi\)
0.457476 0.889222i \(-0.348754\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.659263i 0.0496938i
\(177\) 0 0
\(178\) 4.61572 + 2.66489i 0.345963 + 0.199742i
\(179\) −11.3826 6.57176i −0.850777 0.491196i 0.0101362 0.999949i \(-0.496774\pi\)
−0.860913 + 0.508752i \(0.830107\pi\)
\(180\) 0 0
\(181\) 6.34537i 0.471648i 0.971796 + 0.235824i \(0.0757788\pi\)
−0.971796 + 0.235824i \(0.924221\pi\)
\(182\) −14.8766 + 6.49350i −1.10273 + 0.481331i
\(183\) 0 0
\(184\) 2.29939 + 3.98266i 0.169513 + 0.293606i
\(185\) 0 0
\(186\) 0 0
\(187\) 2.78250 1.60648i 0.203477 0.117477i
\(188\) 12.0027 0.875388
\(189\) 0 0
\(190\) 0 0
\(191\) −18.8926 + 10.9077i −1.36702 + 0.789251i −0.990547 0.137175i \(-0.956198\pi\)
−0.376477 + 0.926426i \(0.622865\pi\)
\(192\) 0 0
\(193\) −1.20933 + 2.09462i −0.0870495 + 0.150774i −0.906263 0.422715i \(-0.861077\pi\)
0.819213 + 0.573489i \(0.194411\pi\)
\(194\) −5.73958 9.94125i −0.412078 0.713740i
\(195\) 0 0
\(196\) −4.75953 + 5.13292i −0.339967 + 0.366637i
\(197\) 6.24457i 0.444907i 0.974943 + 0.222454i \(0.0714066\pi\)
−0.974943 + 0.222454i \(0.928593\pi\)
\(198\) 0 0
\(199\) −4.38388 2.53103i −0.310765 0.179420i 0.336504 0.941682i \(-0.390756\pi\)
−0.647269 + 0.762262i \(0.724089\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 15.4975i 1.09040i
\(203\) −21.2838 2.39458i −1.49383 0.168067i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.03422 1.79131i 0.0720572 0.124807i
\(207\) 0 0
\(208\) −5.31319 + 3.06757i −0.368403 + 0.212698i
\(209\) −4.79747 −0.331848
\(210\) 0 0
\(211\) 5.72168 0.393896 0.196948 0.980414i \(-0.436897\pi\)
0.196948 + 0.980414i \(0.436897\pi\)
\(212\) −10.5749 + 6.10540i −0.726285 + 0.419321i
\(213\) 0 0
\(214\) −5.44632 + 9.43331i −0.372303 + 0.644848i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.37726 + 1.86676i −0.0934946 + 0.126724i
\(218\) 14.3451i 0.971572i
\(219\) 0 0
\(220\) 0 0
\(221\) −25.8941 14.9500i −1.74183 1.00564i
\(222\) 0 0
\(223\) 6.61006i 0.442642i 0.975201 + 0.221321i \(0.0710369\pi\)
−0.975201 + 0.221321i \(0.928963\pi\)
\(224\) −1.57075 + 2.12902i −0.104950 + 0.142251i
\(225\) 0 0
\(226\) 5.95403 + 10.3127i 0.396056 + 0.685989i
\(227\) 12.0278 20.8328i 0.798314 1.38272i −0.122400 0.992481i \(-0.539059\pi\)
0.920714 0.390239i \(-0.127608\pi\)
\(228\) 0 0
\(229\) −4.39811 + 2.53925i −0.290635 + 0.167798i −0.638228 0.769847i \(-0.720332\pi\)
0.347593 + 0.937645i \(0.386999\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −8.09526 −0.531480
\(233\) 19.1195 11.0386i 1.25256 0.723165i 0.280941 0.959725i \(-0.409353\pi\)
0.971617 + 0.236560i \(0.0760201\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.06613 7.04274i −0.264682 0.458443i
\(237\) 0 0
\(238\) −12.8134 1.44160i −0.830568 0.0934451i
\(239\) 17.8556i 1.15498i −0.816398 0.577490i \(-0.804032\pi\)
0.816398 0.577490i \(-0.195968\pi\)
\(240\) 0 0
\(241\) 18.8401 + 10.8773i 1.21360 + 0.700670i 0.963541 0.267562i \(-0.0862179\pi\)
0.250055 + 0.968232i \(0.419551\pi\)
\(242\) 9.14988 + 5.28269i 0.588177 + 0.339584i
\(243\) 0 0
\(244\) 0.0714487i 0.00457403i
\(245\) 0 0
\(246\) 0 0
\(247\) 22.3228 + 38.6642i 1.42036 + 2.46014i
\(248\) −0.438408 + 0.759345i −0.0278390 + 0.0482185i
\(249\) 0 0
\(250\) 0 0
\(251\) −16.0445 −1.01272 −0.506361 0.862321i \(-0.669010\pi\)
−0.506361 + 0.862321i \(0.669010\pi\)
\(252\) 0 0
\(253\) 3.03181 0.190608
\(254\) 12.6668 7.31319i 0.794787 0.458870i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.23399 14.2617i −0.513622 0.889620i −0.999875 0.0158016i \(-0.994970\pi\)
0.486253 0.873818i \(-0.338363\pi\)
\(258\) 0 0
\(259\) 24.5166 10.7012i 1.52339 0.664943i
\(260\) 0 0
\(261\) 0 0
\(262\) 2.84120 + 1.64037i 0.175530 + 0.101342i
\(263\) 4.86760 + 2.81031i 0.300149 + 0.173291i 0.642510 0.766278i \(-0.277893\pi\)
−0.342361 + 0.939569i \(0.611227\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 15.4929 + 11.4304i 0.949933 + 0.700843i
\(267\) 0 0
\(268\) 0.666965 + 1.15522i 0.0407414 + 0.0705661i
\(269\) 3.27081 5.66521i 0.199425 0.345414i −0.748917 0.662664i \(-0.769426\pi\)
0.948342 + 0.317249i \(0.102759\pi\)
\(270\) 0 0
\(271\) −16.0238 + 9.25135i −0.973377 + 0.561980i −0.900264 0.435344i \(-0.856627\pi\)
−0.0731130 + 0.997324i \(0.523293\pi\)
\(272\) −4.87356 −0.295503
\(273\) 0 0
\(274\) 3.50069 0.211484
\(275\) 0 0
\(276\) 0 0
\(277\) 12.9572 22.4426i 0.778525 1.34844i −0.154267 0.988029i \(-0.549302\pi\)
0.932792 0.360415i \(-0.117365\pi\)
\(278\) 0.890157 + 1.54180i 0.0533881 + 0.0924708i
\(279\) 0 0
\(280\) 0 0
\(281\) 9.24160i 0.551308i −0.961257 0.275654i \(-0.911106\pi\)
0.961257 0.275654i \(-0.0888943\pi\)
\(282\) 0 0
\(283\) −6.14531 3.54800i −0.365301 0.210907i 0.306103 0.951999i \(-0.400975\pi\)
−0.671404 + 0.741092i \(0.734308\pi\)
\(284\) 2.25773 + 1.30350i 0.133972 + 0.0773486i
\(285\) 0 0
\(286\) 4.04467i 0.239166i
\(287\) 1.84944 16.4384i 0.109169 0.970329i
\(288\) 0 0
\(289\) −3.37577 5.84701i −0.198575 0.343942i
\(290\) 0 0
\(291\) 0 0
\(292\) −2.44571 + 1.41203i −0.143124 + 0.0826328i
\(293\) 8.94657 0.522664 0.261332 0.965249i \(-0.415838\pi\)
0.261332 + 0.965249i \(0.415838\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 8.75609 5.05533i 0.508938 0.293835i
\(297\) 0 0
\(298\) −4.12754 + 7.14910i −0.239102 + 0.414136i
\(299\) −14.1071 24.4342i −0.815834 1.41307i
\(300\) 0 0
\(301\) 2.67280 23.7567i 0.154058 1.36931i
\(302\) 0.927090i 0.0533480i
\(303\) 0 0
\(304\) 6.30208 + 3.63851i 0.361449 + 0.208683i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.62584i 0.435230i −0.976035 0.217615i \(-0.930172\pi\)
0.976035 0.217615i \(-0.0698276\pi\)
\(308\) 0.697771 + 1.59860i 0.0397592 + 0.0910884i
\(309\) 0 0
\(310\) 0 0
\(311\) −3.20348 + 5.54859i −0.181653 + 0.314632i −0.942443 0.334366i \(-0.891478\pi\)
0.760791 + 0.648997i \(0.224811\pi\)
\(312\) 0 0
\(313\) −7.84360 + 4.52850i −0.443346 + 0.255966i −0.705016 0.709191i \(-0.749060\pi\)
0.261670 + 0.965157i \(0.415727\pi\)
\(314\) 8.34248 0.470793
\(315\) 0 0
\(316\) −5.77674 −0.324967
\(317\) −24.6876 + 14.2534i −1.38660 + 0.800552i −0.992930 0.118702i \(-0.962127\pi\)
−0.393666 + 0.919253i \(0.628793\pi\)
\(318\) 0 0
\(319\) −2.66845 + 4.62189i −0.149405 + 0.258776i
\(320\) 0 0
\(321\) 0 0
\(322\) −9.79091 7.22355i −0.545626 0.402553i
\(323\) 35.4650i 1.97332i
\(324\) 0 0
\(325\) 0 0
\(326\) 21.0488 + 12.1525i 1.16578 + 0.673065i
\(327\) 0 0
\(328\) 6.25234i 0.345228i
\(329\) −29.1044 + 12.7038i −1.60458 + 0.700383i
\(330\) 0 0
\(331\) −7.53535 13.0516i −0.414180 0.717381i 0.581162 0.813788i \(-0.302598\pi\)
−0.995342 + 0.0964068i \(0.969265\pi\)
\(332\) 3.72330 6.44894i 0.204343 0.353932i
\(333\) 0 0
\(334\) −6.48414 + 3.74362i −0.354797 + 0.204842i
\(335\) 0 0
\(336\) 0 0
\(337\) −0.480936 −0.0261983 −0.0130991 0.999914i \(-0.504170\pi\)
−0.0130991 + 0.999914i \(0.504170\pi\)
\(338\) 21.3389 12.3200i 1.16068 0.670119i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.289026 + 0.500608i 0.0156516 + 0.0271094i
\(342\) 0 0
\(343\) 6.10828 17.4840i 0.329816 0.944045i
\(344\) 9.03582i 0.487179i
\(345\) 0 0
\(346\) 12.3328 + 7.12036i 0.663017 + 0.382793i
\(347\) 3.01081 + 1.73829i 0.161629 + 0.0933165i 0.578633 0.815588i \(-0.303586\pi\)
−0.417004 + 0.908905i \(0.636920\pi\)
\(348\) 0 0
\(349\) 0.611574i 0.0327368i −0.999866 0.0163684i \(-0.994790\pi\)
0.999866 0.0163684i \(-0.00521046\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.329631 + 0.570938i 0.0175694 + 0.0304311i
\(353\) −10.8916 + 18.8649i −0.579703 + 1.00407i 0.415810 + 0.909451i \(0.363498\pi\)
−0.995513 + 0.0946235i \(0.969835\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −5.32978 −0.282478
\(357\) 0 0
\(358\) 13.1435 0.694656
\(359\) −14.0413 + 8.10672i −0.741069 + 0.427857i −0.822458 0.568826i \(-0.807398\pi\)
0.0813887 + 0.996682i \(0.474064\pi\)
\(360\) 0 0
\(361\) 16.9775 29.4059i 0.893553 1.54768i
\(362\) −3.17268 5.49525i −0.166753 0.288824i
\(363\) 0 0
\(364\) 9.63679 13.0619i 0.505105 0.684627i
\(365\) 0 0
\(366\) 0 0
\(367\) −18.0615 10.4278i −0.942802 0.544327i −0.0519641 0.998649i \(-0.516548\pi\)
−0.890837 + 0.454322i \(0.849881\pi\)
\(368\) −3.98266 2.29939i −0.207611 0.119864i
\(369\) 0 0
\(370\) 0 0
\(371\) 19.1801 25.9971i 0.995784 1.34970i
\(372\) 0 0
\(373\) 0.702477 + 1.21673i 0.0363729 + 0.0629997i 0.883639 0.468169i \(-0.155086\pi\)
−0.847266 + 0.531169i \(0.821753\pi\)
\(374\) −1.60648 + 2.78250i −0.0830689 + 0.143880i
\(375\) 0 0
\(376\) −10.3947 + 6.00136i −0.536063 + 0.309496i
\(377\) 49.6656 2.55791
\(378\) 0 0
\(379\) 21.8729 1.12353 0.561766 0.827296i \(-0.310122\pi\)
0.561766 + 0.827296i \(0.310122\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 10.9077 18.8926i 0.558085 0.966632i
\(383\) −17.2741 29.9197i −0.882666 1.52882i −0.848365 0.529411i \(-0.822413\pi\)
−0.0343009 0.999412i \(-0.510920\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.41866i 0.123107i
\(387\) 0 0
\(388\) 9.94125 + 5.73958i 0.504690 + 0.291383i
\(389\) 10.0406 + 5.79694i 0.509078 + 0.293916i 0.732455 0.680816i \(-0.238375\pi\)
−0.223376 + 0.974732i \(0.571708\pi\)
\(390\) 0 0
\(391\) 22.4124i 1.13344i
\(392\) 1.55542 6.82500i 0.0785604 0.344715i
\(393\) 0 0
\(394\) −3.12229 5.40796i −0.157299 0.272449i
\(395\) 0 0
\(396\) 0 0
\(397\) −5.02400 + 2.90061i −0.252147 + 0.145577i −0.620747 0.784011i \(-0.713171\pi\)
0.368600 + 0.929588i \(0.379837\pi\)
\(398\) 5.06207 0.253739
\(399\) 0 0
\(400\) 0 0
\(401\) 17.7829 10.2670i 0.888036 0.512708i 0.0147366 0.999891i \(-0.495309\pi\)
0.873300 + 0.487183i \(0.161976\pi\)
\(402\) 0 0
\(403\) 2.68970 4.65869i 0.133983 0.232066i
\(404\) 7.74874 + 13.4212i 0.385514 + 0.667730i
\(405\) 0 0
\(406\) 19.6296 8.56811i 0.974199 0.425228i
\(407\) 6.66558i 0.330401i
\(408\) 0 0
\(409\) 7.85765 + 4.53662i 0.388536 + 0.224321i 0.681526 0.731794i \(-0.261317\pi\)
−0.292990 + 0.956116i \(0.594650\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 2.06843i 0.101904i
\(413\) 17.3138 + 12.7738i 0.851954 + 0.628556i
\(414\) 0 0
\(415\) 0 0
\(416\) 3.06757 5.31319i 0.150400 0.260501i
\(417\) 0 0
\(418\) 4.15473 2.39873i 0.203214 0.117326i
\(419\) 5.30162 0.259001 0.129501 0.991579i \(-0.458663\pi\)
0.129501 + 0.991579i \(0.458663\pi\)
\(420\) 0 0
\(421\) 21.8234 1.06361 0.531804 0.846867i \(-0.321514\pi\)
0.531804 + 0.846867i \(0.321514\pi\)
\(422\) −4.95512 + 2.86084i −0.241211 + 0.139263i
\(423\) 0 0
\(424\) 6.10540 10.5749i 0.296504 0.513561i
\(425\) 0 0
\(426\) 0 0
\(427\) −0.0756221 0.173250i −0.00365961 0.00838417i
\(428\) 10.8926i 0.526516i
\(429\) 0 0
\(430\) 0 0
\(431\) 12.9922 + 7.50107i 0.625814 + 0.361314i 0.779129 0.626864i \(-0.215662\pi\)
−0.153315 + 0.988177i \(0.548995\pi\)
\(432\) 0 0
\(433\) 35.2578i 1.69438i 0.531289 + 0.847190i \(0.321708\pi\)
−0.531289 + 0.847190i \(0.678292\pi\)
\(434\) 0.259363 2.30529i 0.0124498 0.110658i
\(435\) 0 0
\(436\) −7.17254 12.4232i −0.343502 0.594964i
\(437\) −16.7327 + 28.9819i −0.800434 + 1.38639i
\(438\) 0 0
\(439\) 25.4755 14.7083i 1.21588 0.701988i 0.251846 0.967767i \(-0.418962\pi\)
0.964034 + 0.265779i \(0.0856291\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 29.9000 1.42220
\(443\) −25.5061 + 14.7259i −1.21183 + 0.699651i −0.963158 0.268937i \(-0.913328\pi\)
−0.248673 + 0.968588i \(0.579994\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −3.30503 5.72448i −0.156498 0.271062i
\(447\) 0 0
\(448\) 0.295801 2.62916i 0.0139753 0.124216i
\(449\) 29.2408i 1.37996i 0.723829 + 0.689980i \(0.242381\pi\)
−0.723829 + 0.689980i \(0.757619\pi\)
\(450\) 0 0
\(451\) −3.56970 2.06097i −0.168091 0.0970471i
\(452\) −10.3127 5.95403i −0.485067 0.280054i
\(453\) 0 0
\(454\) 24.0556i 1.12899i
\(455\) 0 0
\(456\) 0 0
\(457\) 3.98679 + 6.90532i 0.186494 + 0.323017i 0.944079 0.329720i \(-0.106954\pi\)
−0.757585 + 0.652737i \(0.773621\pi\)
\(458\) 2.53925 4.39811i 0.118651 0.205510i
\(459\) 0 0
\(460\) 0 0
\(461\) −39.9112 −1.85885 −0.929425 0.369012i \(-0.879696\pi\)
−0.929425 + 0.369012i \(0.879696\pi\)
\(462\) 0 0
\(463\) −17.6663 −0.821021 −0.410511 0.911856i \(-0.634650\pi\)
−0.410511 + 0.911856i \(0.634650\pi\)
\(464\) 7.01070 4.04763i 0.325464 0.187907i
\(465\) 0 0
\(466\) −11.0386 + 19.1195i −0.511355 + 0.885692i
\(467\) 10.9757 + 19.0104i 0.507894 + 0.879698i 0.999958 + 0.00913924i \(0.00290915\pi\)
−0.492064 + 0.870559i \(0.663758\pi\)
\(468\) 0 0
\(469\) −2.83997 2.09527i −0.131137 0.0967507i
\(470\) 0 0
\(471\) 0 0
\(472\) 7.04274 + 4.06613i 0.324168 + 0.187159i
\(473\) −5.15890 2.97849i −0.237206 0.136951i
\(474\) 0 0
\(475\) 0 0
\(476\) 11.8175 5.15823i 0.541655 0.236427i
\(477\) 0 0
\(478\) 8.92778 + 15.4634i 0.408347 + 0.707278i
\(479\) 16.9834 29.4161i 0.775990 1.34405i −0.158246 0.987400i \(-0.550584\pi\)
0.934236 0.356655i \(-0.116083\pi\)
\(480\) 0 0
\(481\) −53.7199 + 31.0152i −2.44942 + 1.41417i
\(482\) −21.7546 −0.990897
\(483\) 0 0
\(484\) −10.5654 −0.480244
\(485\) 0 0
\(486\) 0 0
\(487\) 7.42482 12.8602i 0.336451 0.582750i −0.647312 0.762225i \(-0.724107\pi\)
0.983762 + 0.179476i \(0.0574401\pi\)
\(488\) −0.0357243 0.0618764i −0.00161716 0.00280101i
\(489\) 0 0
\(490\) 0 0
\(491\) 15.6224i 0.705029i 0.935806 + 0.352515i \(0.114673\pi\)
−0.935806 + 0.352515i \(0.885327\pi\)
\(492\) 0 0
\(493\) 34.1670 + 19.7264i 1.53881 + 0.888430i
\(494\) −38.6642 22.3228i −1.73958 1.00435i
\(495\) 0 0
\(496\) 0.876816i 0.0393702i
\(497\) −6.85424 0.771153i −0.307455 0.0345910i
\(498\) 0 0
\(499\) −9.23416 15.9940i −0.413378 0.715991i 0.581879 0.813275i \(-0.302318\pi\)
−0.995257 + 0.0972842i \(0.968984\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 13.8950 8.02227i 0.620164 0.358052i
\(503\) −5.46007 −0.243452 −0.121726 0.992564i \(-0.538843\pi\)
−0.121726 + 0.992564i \(0.538843\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −2.62562 + 1.51590i −0.116723 + 0.0673901i
\(507\) 0 0
\(508\) −7.31319 + 12.6668i −0.324470 + 0.561999i
\(509\) 0.412125 + 0.713821i 0.0182671 + 0.0316396i 0.875014 0.484097i \(-0.160852\pi\)
−0.856747 + 0.515736i \(0.827518\pi\)
\(510\) 0 0
\(511\) 4.43590 6.01249i 0.196233 0.265977i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 14.2617 + 8.23399i 0.629056 + 0.363186i
\(515\) 0 0
\(516\) 0 0
\(517\) 7.91294i 0.348011i
\(518\) −15.8814 + 21.5258i −0.697787 + 0.945791i
\(519\) 0 0
\(520\) 0 0
\(521\) −15.2147 + 26.3526i −0.666566 + 1.15453i 0.312292 + 0.949986i \(0.398903\pi\)
−0.978858 + 0.204541i \(0.934430\pi\)
\(522\) 0 0
\(523\) −0.196400 + 0.113392i −0.00858799 + 0.00495828i −0.504288 0.863536i \(-0.668245\pi\)
0.495700 + 0.868494i \(0.334912\pi\)
\(524\) −3.28074 −0.143320
\(525\) 0 0
\(526\) −5.62062 −0.245070
\(527\) 3.70071 2.13661i 0.161206 0.0930721i
\(528\) 0 0
\(529\) −0.925602 + 1.60319i −0.0402436 + 0.0697039i
\(530\) 0 0
\(531\) 0 0
\(532\) −19.1325 2.15255i −0.829498 0.0933247i
\(533\) 38.3590i 1.66151i
\(534\) 0 0
\(535\) 0 0
\(536\) −1.15522 0.666965i −0.0498978 0.0288085i
\(537\) 0 0
\(538\) 6.54163i 0.282030i
\(539\) −3.38394 3.13778i −0.145757 0.135154i
\(540\) 0 0
\(541\) −18.5678 32.1603i −0.798290 1.38268i −0.920729 0.390204i \(-0.872405\pi\)
0.122438 0.992476i \(-0.460929\pi\)
\(542\) 9.25135 16.0238i 0.397380 0.688282i
\(543\) 0 0
\(544\) 4.22062 2.43678i 0.180958 0.104476i
\(545\) 0 0
\(546\) 0 0
\(547\) 14.2444 0.609047 0.304524 0.952505i \(-0.401503\pi\)
0.304524 + 0.952505i \(0.401503\pi\)
\(548\) −3.03168 + 1.75034i −0.129507 + 0.0747709i
\(549\) 0 0
\(550\) 0 0
\(551\) −29.4547 51.0170i −1.25481 2.17340i
\(552\) 0 0
\(553\) 14.0076 6.11416i 0.595662 0.260001i
\(554\) 25.9145i 1.10100i
\(555\) 0 0
\(556\) −1.54180 0.890157i −0.0653867 0.0377511i
\(557\) 16.3764 + 9.45492i 0.693890 + 0.400618i 0.805068 0.593183i \(-0.202129\pi\)
−0.111177 + 0.993801i \(0.535462\pi\)
\(558\) 0 0
\(559\) 55.4361i 2.34470i
\(560\) 0 0
\(561\) 0 0
\(562\) 4.62080 + 8.00346i 0.194917 + 0.337606i
\(563\) −19.6538 + 34.0414i −0.828310 + 1.43467i 0.0710537 + 0.997472i \(0.477364\pi\)
−0.899363 + 0.437202i \(0.855969\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 7.09599 0.298267
\(567\) 0 0
\(568\) −2.60701 −0.109388
\(569\) 0.768837 0.443888i 0.0322313 0.0186088i −0.483798 0.875180i \(-0.660743\pi\)
0.516029 + 0.856571i \(0.327410\pi\)
\(570\) 0 0
\(571\) −12.7120 + 22.0178i −0.531981 + 0.921418i 0.467322 + 0.884087i \(0.345219\pi\)
−0.999303 + 0.0373309i \(0.988114\pi\)
\(572\) −2.02234 3.50279i −0.0845581 0.146459i
\(573\) 0 0
\(574\) 6.61754 + 15.1608i 0.276211 + 0.632800i
\(575\) 0 0
\(576\) 0 0
\(577\) −8.90681 5.14235i −0.370795 0.214079i 0.303010 0.952987i \(-0.402008\pi\)
−0.673806 + 0.738908i \(0.735342\pi\)
\(578\) 5.84701 + 3.37577i 0.243204 + 0.140414i
\(579\) 0 0
\(580\) 0 0
\(581\) −2.20271 + 19.5783i −0.0913837 + 0.812246i
\(582\) 0 0
\(583\) −4.02506 6.97161i −0.166701 0.288735i
\(584\) 1.41203 2.44571i 0.0584302 0.101204i
\(585\) 0 0
\(586\) −7.74795 + 4.47328i −0.320065 + 0.184790i
\(587\) −25.1241 −1.03698 −0.518490 0.855083i \(-0.673506\pi\)
−0.518490 + 0.855083i \(0.673506\pi\)
\(588\) 0 0
\(589\) −6.38061 −0.262909
\(590\) 0 0
\(591\) 0 0
\(592\) −5.05533 + 8.75609i −0.207773 + 0.359873i
\(593\) −5.05492 8.75538i −0.207581 0.359540i 0.743371 0.668879i \(-0.233226\pi\)
−0.950952 + 0.309339i \(0.899892\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.25507i 0.338141i
\(597\) 0 0
\(598\) 24.4342 + 14.1071i 0.999189 + 0.576882i
\(599\) 21.6368 + 12.4920i 0.884056 + 0.510410i 0.871994 0.489517i \(-0.162827\pi\)
0.0120624 + 0.999927i \(0.496160\pi\)
\(600\) 0 0
\(601\) 15.2936i 0.623837i 0.950109 + 0.311919i \(0.100972\pi\)
−0.950109 + 0.311919i \(0.899028\pi\)
\(602\) 9.56361 + 21.9103i 0.389784 + 0.892996i
\(603\) 0 0
\(604\) 0.463545 + 0.802883i 0.0188614 + 0.0326689i
\(605\) 0 0
\(606\) 0 0
\(607\) 34.1973 19.7438i 1.38802 0.801377i 0.394932 0.918710i \(-0.370768\pi\)
0.993093 + 0.117334i \(0.0374347\pi\)
\(608\) −7.27702 −0.295122
\(609\) 0 0
\(610\) 0 0
\(611\) 63.7727 36.8192i 2.57997 1.48954i
\(612\) 0 0
\(613\) 8.55968 14.8258i 0.345722 0.598809i −0.639762 0.768573i \(-0.720967\pi\)
0.985485 + 0.169764i \(0.0543006\pi\)
\(614\) 3.81292 + 6.60417i 0.153877 + 0.266523i
\(615\) 0 0
\(616\) −1.40359 1.03554i −0.0565521 0.0417230i
\(617\) 5.80201i 0.233580i 0.993157 + 0.116790i \(0.0372605\pi\)
−0.993157 + 0.116790i \(0.962740\pi\)
\(618\) 0 0
\(619\) 29.5344 + 17.0517i 1.18709 + 0.685366i 0.957644 0.287956i \(-0.0929756\pi\)
0.229445 + 0.973322i \(0.426309\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 6.40696i 0.256896i
\(623\) 12.9238 5.64109i 0.517780 0.226006i
\(624\) 0 0
\(625\) 0 0
\(626\) 4.52850 7.84360i 0.180995 0.313493i
\(627\) 0 0
\(628\) −7.22480 + 4.17124i −0.288301 + 0.166451i
\(629\) −49.2749 −1.96472
\(630\) 0 0
\(631\) 33.1261 1.31873 0.659365 0.751823i \(-0.270825\pi\)
0.659365 + 0.751823i \(0.270825\pi\)
\(632\) 5.00280 2.88837i 0.199001 0.114893i
\(633\) 0 0
\(634\) 14.2534 24.6876i 0.566076 0.980472i
\(635\) 0 0
\(636\) 0 0
\(637\) −9.54270 + 41.8724i −0.378096 + 1.65904i
\(638\) 5.33690i 0.211290i
\(639\) 0 0
\(640\) 0 0
\(641\) 1.72685 + 0.997000i 0.0682067 + 0.0393791i 0.533716 0.845664i \(-0.320795\pi\)
−0.465509 + 0.885043i \(0.654129\pi\)
\(642\) 0 0
\(643\) 0.661676i 0.0260940i 0.999915 + 0.0130470i \(0.00415310\pi\)
−0.999915 + 0.0130470i \(0.995847\pi\)
\(644\) 12.0910 + 1.36032i 0.476450 + 0.0536042i
\(645\) 0 0
\(646\) −17.7325 30.7136i −0.697675 1.20841i
\(647\) 9.19276 15.9223i 0.361405 0.625971i −0.626787 0.779190i \(-0.715631\pi\)
0.988192 + 0.153219i \(0.0489639\pi\)
\(648\) 0 0
\(649\) 4.64302 2.68065i 0.182254 0.105225i
\(650\) 0 0
\(651\) 0 0
\(652\) −24.3050 −0.951858
\(653\) 15.0571 8.69323i 0.589231 0.340193i −0.175562 0.984468i \(-0.556174\pi\)
0.764793 + 0.644276i \(0.222841\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.12617 + 5.41468i 0.122056 + 0.211408i
\(657\) 0 0
\(658\) 18.8533 25.5540i 0.734978 0.996200i
\(659\) 35.4692i 1.38168i 0.723006 + 0.690841i \(0.242760\pi\)
−0.723006 + 0.690841i \(0.757240\pi\)
\(660\) 0 0
\(661\) −28.9704 16.7261i −1.12682 0.650568i −0.183685 0.982985i \(-0.558803\pi\)
−0.943133 + 0.332417i \(0.892136\pi\)
\(662\) 13.0516 + 7.53535i 0.507265 + 0.292870i
\(663\) 0 0
\(664\) 7.44660i 0.288984i
\(665\) 0 0
\(666\) 0 0
\(667\) 18.6142 + 32.2407i 0.720744 + 1.24836i
\(668\) 3.74362 6.48414i 0.144845 0.250879i
\(669\) 0 0
\(670\) 0 0
\(671\) −0.0471035 −0.00181841
\(672\) 0 0
\(673\) 21.9964 0.847898 0.423949 0.905686i \(-0.360644\pi\)
0.423949 + 0.905686i \(0.360644\pi\)
\(674\) 0.416503 0.240468i 0.0160431 0.00926249i
\(675\) 0 0
\(676\) −12.3200 + 21.3389i −0.473846 + 0.820725i
\(677\) 6.18250 + 10.7084i 0.237613 + 0.411557i 0.960029 0.279901i \(-0.0903018\pi\)
−0.722416 + 0.691459i \(0.756968\pi\)
\(678\) 0 0
\(679\) −30.1806 3.39554i −1.15823 0.130309i
\(680\) 0 0
\(681\) 0 0
\(682\) −0.500608 0.289026i −0.0191693 0.0110674i
\(683\) −25.9621 14.9892i −0.993411 0.573546i −0.0871187 0.996198i \(-0.527766\pi\)
−0.906292 + 0.422652i \(0.861099\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 3.45205 + 18.1957i 0.131800 + 0.694715i
\(687\) 0 0
\(688\) 4.51791 + 7.82525i 0.172244 + 0.298335i
\(689\) −37.4575 + 64.8783i −1.42702 + 2.47167i
\(690\) 0 0
\(691\) 7.97882 4.60657i 0.303529 0.175242i −0.340498 0.940245i \(-0.610596\pi\)
0.644027 + 0.765003i \(0.277262\pi\)
\(692\) −14.2407 −0.541351
\(693\) 0 0
\(694\) −3.47659 −0.131969
\(695\) 0 0
\(696\) 0 0
\(697\) −15.2356 + 26.3888i −0.577088 + 0.999546i
\(698\) 0.305787 + 0.529638i 0.0115742 + 0.0200471i
\(699\) 0 0
\(700\) 0 0
\(701\) 44.9022i 1.69593i −0.530050 0.847967i \(-0.677827\pi\)
0.530050 0.847967i \(-0.322173\pi\)
\(702\) 0 0
\(703\) 63.7183 + 36.7878i 2.40318 + 1.38748i
\(704\) −0.570938 0.329631i −0.0215180 0.0124234i
\(705\) 0 0
\(706\) 21.7833i 0.819824i
\(707\) −32.9945 24.3427i −1.24089 0.915502i
\(708\) 0 0
\(709\) −1.39264 2.41213i −0.0523019 0.0905895i 0.838689 0.544610i \(-0.183322\pi\)
−0.890991 + 0.454021i \(0.849989\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 4.61572 2.66489i 0.172981 0.0998709i
\(713\) 4.03229 0.151010
\(714\) 0 0
\(715\) 0 0
\(716\) −11.3826 + 6.57176i −0.425388 + 0.245598i
\(717\) 0 0
\(718\) 8.10672 14.0413i 0.302540 0.524015i
\(719\) −13.4818 23.3511i −0.502785 0.870849i −0.999995 0.00321841i \(-0.998976\pi\)
0.497210 0.867630i \(-0.334358\pi\)
\(720\) 0 0
\(721\) −2.18925 5.01558i −0.0815319 0.186790i
\(722\) 33.9550i 1.26368i
\(723\) 0 0
\(724\) 5.49525 + 3.17268i 0.204229 + 0.117912i
\(725\) 0 0
\(726\) 0 0
\(727\) 29.6632i 1.10015i 0.835116 + 0.550074i \(0.185400\pi\)
−0.835116 + 0.550074i \(0.814600\pi\)
\(728\) −1.81478 + 16.1303i −0.0672602 + 0.597829i
\(729\) 0 0
\(730\) 0 0
\(731\) −22.0183 + 38.1368i −0.814376 + 1.41054i
\(732\) 0 0
\(733\) 19.9455 11.5155i 0.736704 0.425336i −0.0841657 0.996452i \(-0.526823\pi\)
0.820870 + 0.571116i \(0.193489\pi\)
\(734\) 20.8556 0.769794
\(735\) 0 0
\(736\) 4.59878 0.169513
\(737\) −0.761591 + 0.439705i −0.0280536 + 0.0161967i
\(738\) 0 0
\(739\) −17.2029 + 29.7964i −0.632821 + 1.09608i 0.354152 + 0.935188i \(0.384770\pi\)
−0.986972 + 0.160889i \(0.948564\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.61196 + 32.1042i −0.132599 + 1.17858i
\(743\) 40.6201i 1.49021i 0.666950 + 0.745103i \(0.267600\pi\)
−0.666950 + 0.745103i \(0.732400\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.21673 0.702477i −0.0445475 0.0257195i
\(747\) 0 0
\(748\) 3.21295i 0.117477i
\(749\) 11.5289 + 26.4127i 0.421257 + 0.965101i
\(750\) 0 0
\(751\) −22.8927 39.6513i −0.835366 1.44690i −0.893732 0.448601i \(-0.851922\pi\)
0.0583658 0.998295i \(-0.481411\pi\)
\(752\) 6.00136 10.3947i 0.218847 0.379054i
\(753\) 0 0
\(754\) −43.0117 + 24.8328i −1.56639 + 0.904357i
\(755\) 0 0
\(756\) 0 0
\(757\) −50.7755 −1.84547 −0.922733 0.385440i \(-0.874050\pi\)
−0.922733 + 0.385440i \(0.874050\pi\)
\(758\) −18.9424 + 10.9364i −0.688021 + 0.397229i
\(759\) 0 0
\(760\) 0 0
\(761\) 18.0315 + 31.2316i 0.653643 + 1.13214i 0.982232 + 0.187670i \(0.0600935\pi\)
−0.328589 + 0.944473i \(0.606573\pi\)
\(762\) 0 0
\(763\) 30.5410 + 22.5326i 1.10566 + 0.815734i
\(764\) 21.8153i 0.789251i
\(765\) 0 0
\(766\) 29.9197 + 17.2741i 1.08104 + 0.624139i
\(767\) −43.2082 24.9463i −1.56016 0.900758i
\(768\) 0 0
\(769\) 17.5798i 0.633943i −0.948435 0.316971i \(-0.897334\pi\)
0.948435 0.316971i \(-0.102666\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.20933 + 2.09462i 0.0435248 + 0.0753871i
\(773\) 24.7318 42.8367i 0.889541 1.54073i 0.0491225 0.998793i \(-0.484358\pi\)
0.840419 0.541938i \(-0.182309\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −11.4792 −0.412078
\(777\) 0 0
\(778\) −11.5939 −0.415661
\(779\) 39.4028 22.7492i 1.41175 0.815074i
\(780\) 0 0
\(781\) −0.859351 + 1.48844i −0.0307500 + 0.0532605i
\(782\) 11.2062 + 19.4097i 0.400733 + 0.694090i
\(783\) 0 0
\(784\) 2.06547 + 6.68833i 0.0737669 + 0.238869i
\(785\) 0 0
\(786\) 0 0
\(787\) −8.38310 4.83998i −0.298825 0.172527i 0.343090 0.939303i \(-0.388526\pi\)
−0.641915 + 0.766776i