Properties

Label 3150.2.bf.d.1601.3
Level 3150
Weight 2
Character 3150.1601
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 1601.3
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.d.1151.3

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 \(-0.698355\pi\)
0.411452 + 0.911431i \(0.365022\pi\)
\(12\) 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 0.994097 + 0.108492i \(0.0346022\pi\)
−0.403092 + 0.915160i \(0.632064\pi\)
\(18\) 0 0
\(19\) −6.30208 3.63851i −1.44580 0.834732i −0.447570 0.894249i \(-0.647711\pi\)
−0.998227 + 0.0595173i \(0.981044\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.659263 0.140555
\(23\) 3.98266 + 2.29939i 0.830442 + 0.479456i 0.854004 0.520266i \(-0.174167\pi\)
−0.0235617 + 0.999722i \(0.507501\pi\)
\(24\) 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 −0.430256 0.902707i \(-0.641577\pi\)
0.566639 + 0.823966i \(0.308243\pi\)
\(32\) 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 −0.0660818 0.997814i \(-0.521050\pi\)
0.897173 0.441679i \(-0.145617\pi\)
\(38\) 3.63851 + 6.30208i 0.590244 + 1.02233i
\(39\) 0 0
\(40\) 0 0
\(41\) 6.25234 0.976451 0.488226 0.872717i \(-0.337644\pi\)
0.488226 + 0.872717i \(0.337644\pi\)
\(42\) 0 0
\(43\) 9.03582 1.37795 0.688975 0.724785i \(-0.258061\pi\)
0.688975 + 0.724785i \(0.258061\pi\)
\(44\) −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 0.0190383 0.999819i \(-0.493940\pi\)
0.856349 0.516397i \(-0.172727\pi\)
\(48\) 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 −0.998627 0.0523897i \(-0.983316\pi\)
−0.453943 + 0.891031i \(0.649983\pi\)
\(54\) 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 −0.999413 0.0342461i \(-0.989097\pi\)
0.470049 0.882640i \(-0.344236\pi\)
\(60\) 0 0
\(61\) −0.0618764 0.0357243i −0.00792246 0.00457403i 0.496034 0.868303i \(-0.334789\pi\)
−0.503956 + 0.863729i \(0.668123\pi\)
\(62\) −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 \(-0.140701\pi\)
−0.822404 + 0.568903i \(0.807368\pi\)
\(68\) −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 \(-0.613819\pi\)
0.636249 + 0.771484i \(0.280485\pi\)
\(74\) −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 −0.981506 0.191433i \(-0.938686\pi\)
0.656539 + 0.754292i \(0.272020\pi\)
\(80\) 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 \(-0.742177\pi\)
0.971994 + 0.235004i \(0.0755104\pi\)
\(90\) 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 0.937000 + 0.349330i \(0.113591\pi\)
−0.165971 + 0.986131i \(0.553076\pi\)
\(102\) 0 0
\(103\) 1.79131 + 1.03422i 0.176503 + 0.101904i 0.585649 0.810565i \(-0.300840\pi\)
−0.409145 + 0.912469i \(0.634173\pi\)
\(104\) −6.13514 −0.601600
\(105\) 0 0
\(106\) 12.2108 1.18602
\(107\) 9.43331 + 5.44632i 0.911953 + 0.526516i 0.881059 0.473007i \(-0.156831\pi\)
0.0308937 + 0.999523i \(0.490165\pi\)
\(108\) 0 0
\(109\) 7.17254 + 12.4232i 0.687005 + 1.18993i 0.972802 + 0.231637i \(0.0744082\pi\)
−0.285797 + 0.958290i \(0.592258\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.42482 1.05841i −0.229124 0.100010i
\(113\) 11.9081i 1.12022i 0.828420 + 0.560108i \(0.189240\pi\)
−0.828420 + 0.560108i \(0.810760\pi\)
\(114\) 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 \(-0.275212\pi\)
0.648941 + 0.760839i \(0.275212\pi\)
\(128\) 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 \(-0.787556\pi\)
0.928745 + 0.370720i \(0.120889\pi\)
\(132\) 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 −0.623885 0.781516i \(-0.714447\pi\)
0.364871 + 0.931058i \(0.381113\pi\)
\(138\) 0 0
\(139\) 1.78031i 0.151004i 0.997146 + 0.0755021i \(0.0240560\pi\)
−0.997146 + 0.0755021i \(0.975944\pi\)
\(140\) 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 \(-0.443131\pi\)
−0.763386 + 0.645942i \(0.776465\pi\)
\(150\) 0 0
\(151\) −0.463545 0.802883i −0.0377227 0.0653377i 0.846548 0.532313i \(-0.178677\pi\)
−0.884270 + 0.466975i \(0.845344\pi\)
\(152\) −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 \(-0.558639\pi\)
0.759782 + 0.650178i \(0.225306\pi\)
\(158\) 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 0.210458 0.977603i \(-0.432504\pi\)
0.741400 0.671064i \(-0.234162\pi\)
\(164\) 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 0.457476 + 0.889222i \(0.348754\pi\)
−0.998827 + 0.0484252i \(0.984580\pi\)
\(174\) 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 \(-0.503226\pi\)
0.860913 + 0.508752i \(0.169893\pi\)
\(180\) 0 0
\(181\) 6.34537i 0.471648i −0.971796 0.235824i \(-0.924221\pi\)
0.971796 0.235824i \(-0.0757788\pi\)
\(182\) −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 \(-0.0438022\pi\)
0.376477 + 0.926426i \(0.377135\pi\)
\(192\) 0 0
\(193\) 1.20933 + 2.09462i 0.0870495 + 0.150774i 0.906263 0.422715i \(-0.138923\pi\)
−0.819213 + 0.573489i \(0.805589\pi\)
\(194\) 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 \(-0.928593\pi\)
0.974943 0.222454i \(-0.0714066\pi\)
\(198\) 0 0
\(199\) −4.38388 + 2.53103i −0.310765 + 0.179420i −0.647269 0.762262i \(-0.724089\pi\)
0.336504 + 0.941682i \(0.390756\pi\)
\(200\) 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 0.920714 + 0.390239i \(0.127608\pi\)
−0.122400 + 0.992481i \(0.539059\pi\)
\(228\) 0 0
\(229\) −4.39811 2.53925i −0.290635 0.167798i 0.347593 0.937645i \(-0.386999\pi\)
−0.638228 + 0.769847i \(0.720332\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.09526 0.531480
\(233\) 19.1195 + 11.0386i 1.25256 + 0.723165i 0.971617 0.236560i \(-0.0760201\pi\)
0.280941 + 0.959725i \(0.409353\pi\)
\(234\) 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 0.250055 0.968232i \(-0.419551\pi\)
0.963541 + 0.267562i \(0.0862179\pi\)
\(242\) 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 \(-0.330990\pi\)
0.506361 + 0.862321i \(0.330990\pi\)
\(252\) 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 0.486253 + 0.873818i \(0.338363\pi\)
−0.999875 + 0.0158016i \(0.994970\pi\)
\(258\) 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 −0.342361 0.939569i \(-0.611227\pi\)
0.642510 + 0.766278i \(0.277893\pi\)
\(264\) 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 \(-0.230574\pi\)
−0.948342 + 0.317249i \(0.897241\pi\)
\(270\) 0 0
\(271\) −16.0238 9.25135i −0.973377 0.561980i −0.0731130 0.997324i \(-0.523293\pi\)
−0.900264 + 0.435344i \(0.856627\pi\)
\(272\) −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 −0.932792 0.360415i \(-0.882635\pi\)
0.154267 0.988029i \(-0.450698\pi\)
\(278\) 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 \(-0.599025\pi\)
0.671404 + 0.741092i \(0.265692\pi\)
\(284\) −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 \(-0.108522\pi\)
−0.760791 + 0.648997i \(0.775189\pi\)
\(312\) 0 0
\(313\) 7.84360 + 4.52850i 0.443346 + 0.255966i 0.705016 0.709191i \(-0.250940\pi\)
−0.261670 + 0.965157i \(0.584273\pi\)
\(314\) −8.34248 −0.470793
\(315\) 0 0
\(316\) −5.77674 −0.324967
\(317\) −24.6876 14.2534i −1.38660 0.800552i −0.393666 0.919253i \(-0.628793\pi\)
−0.992930 + 0.118702i \(0.962127\pi\)
\(318\) 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 −0.995342 0.0964068i \(-0.969265\pi\)
0.581162 + 0.813788i \(0.302598\pi\)
\(332\) 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 \(-0.495830\pi\)
0.0130991 + 0.999914i \(0.495830\pi\)
\(338\) 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 −0.417004 0.908905i \(-0.636920\pi\)
0.578633 + 0.815588i \(0.303586\pi\)
\(348\) 0 0
\(349\) 0.611574i 0.0327368i 0.999866 + 0.0163684i \(0.00521046\pi\)
−0.999866 + 0.0163684i \(0.994790\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.329631 + 0.570938i −0.0175694 + 0.0304311i
\(353\) −10.8916 18.8649i −0.579703 1.00407i −0.995513 0.0946235i \(-0.969835\pi\)
0.415810 0.909451i \(-0.363498\pi\)
\(354\) 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 \(-0.192602\pi\)
−0.0813887 + 0.996682i \(0.525936\pi\)
\(360\) 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 \(-0.483452\pi\)
0.890837 + 0.454322i \(0.150119\pi\)
\(368\) −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 \(-0.844914\pi\)
0.847266 + 0.531169i \(0.178247\pi\)
\(374\) 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 −0.0343009 + 0.999412i \(0.510920\pi\)
−0.848365 + 0.529411i \(0.822413\pi\)
\(384\) 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 \(-0.761625\pi\)
0.223376 + 0.974732i \(0.428292\pi\)
\(390\) 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 \(-0.286829\pi\)
−0.368600 + 0.929588i \(0.620163\pi\)
\(398\) 5.06207 0.253739
\(399\) 0 0
\(400\) 0 0
\(401\) −17.7829 10.2670i −0.888036 0.512708i −0.0147366 0.999891i \(-0.504691\pi\)
−0.873300 + 0.487183i \(0.838024\pi\)
\(402\) 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 −0.292990 0.956116i \(-0.594650\pi\)
0.681526 + 0.731794i \(0.261317\pi\)
\(410\) 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 \(-0.541337\pi\)
−0.129501 + 0.991579i \(0.541337\pi\)
\(420\) 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 \(-0.784338\pi\)
0.153315 + 0.988177i \(0.451005\pi\)
\(432\) 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 0.964034 0.265779i \(-0.0856291\pi\)
0.251846 + 0.967767i \(0.418962\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −29.9000 −1.42220
\(443\) −25.5061 14.7259i −1.21183 0.699651i −0.248673 0.968588i \(-0.579994\pi\)
−0.963158 + 0.268937i \(0.913328\pi\)
\(444\) 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 \(-0.893046\pi\)
0.757585 + 0.652737i \(0.226379\pi\)
\(458\) 2.53925 + 4.39811i 0.118651 + 0.205510i
\(459\) 0 0
\(460\) 0 0
\(461\) 39.9112 1.85885 0.929425 0.369012i \(-0.120304\pi\)
0.929425 + 0.369012i \(0.120304\pi\)
\(462\) 0 0
\(463\) 17.6663 0.821021 0.410511 0.911856i \(-0.365350\pi\)
0.410511 + 0.911856i \(0.365350\pi\)
\(464\) −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 −0.492064 0.870559i \(-0.663758\pi\)
0.999958 0.00913924i \(-0.00290915\pi\)
\(468\) 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 −0.934236 0.356655i \(-0.883917\pi\)
0.158246 0.987400i \(-0.449416\pi\)
\(480\) 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 \(-0.275893\pi\)
−0.983762 + 0.179476i \(0.942560\pi\)
\(488\) −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 −0.995257 0.0972842i \(-0.968984\pi\)
0.581879 + 0.813275i \(0.302318\pi\)
\(500\) 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 \(-0.839148\pi\)
0.856747 + 0.515736i \(0.172482\pi\)
\(510\) 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 0.978858 + 0.204541i \(0.0655701\pi\)
−0.312292 + 0.949986i \(0.601097\pi\)
\(522\) 0 0
\(523\) 0.196400 + 0.113392i 0.00858799 + 0.00495828i 0.504288 0.863536i \(-0.331755\pi\)
−0.495700 + 0.868494i \(0.665088\pi\)
\(524\) 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 0.122438 + 0.992476i \(0.460929\pi\)
−0.920729 + 0.390204i \(0.872405\pi\)
\(542\) 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 \(-0.598497\pi\)
−0.304524 + 0.952505i \(0.598497\pi\)
\(548\) −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 −0.111177 0.993801i \(-0.535462\pi\)
0.805068 + 0.593183i \(0.202129\pi\)
\(558\) 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 −0.899363 0.437202i \(-0.855969\pi\)
0.0710537 0.997472i \(-0.477364\pi\)
\(564\) 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 \(-0.339257\pi\)
−0.516029 + 0.856571i \(0.672590\pi\)
\(570\) 0 0
\(571\) −12.7120 22.0178i −0.531981 0.921418i −0.999303 0.0373309i \(-0.988114\pi\)
0.467322 0.884087i \(-0.345219\pi\)
\(572\) −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 \(-0.597992\pi\)
0.673806 + 0.738908i \(0.264658\pi\)
\(578\) 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 −0.950952 0.309339i \(-0.899892\pi\)
0.743371 + 0.668879i \(0.233226\pi\)
\(594\) 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 \(-0.837173\pi\)
−0.0120624 + 0.999927i \(0.503840\pi\)
\(600\) 0 0
\(601\) 15.2936i 0.623837i −0.950109 0.311919i \(-0.899028\pi\)
0.950109 0.311919i \(-0.100972\pi\)
\(602\) 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 \(-0.629232\pi\)
−0.993093 + 0.117334i \(0.962565\pi\)
\(608\) −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 \(-0.279033\pi\)
−0.985485 + 0.169764i \(0.945699\pi\)
\(614\) −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 \(-0.962740\pi\)
0.993157 0.116790i \(-0.0372605\pi\)
\(618\) 0 0
\(619\) 29.5344 17.0517i 1.18709 0.685366i 0.229445 0.973322i \(-0.426309\pi\)
0.957644 + 0.287956i \(0.0929756\pi\)
\(620\) 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 \(-0.679205\pi\)
0.465509 + 0.885043i \(0.345871\pi\)
\(642\) 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 0.988192 0.153219i \(-0.0489639\pi\)
−0.626787 + 0.779190i \(0.715631\pi\)
\(648\) 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 0.764793 0.644276i \(-0.222841\pi\)
−0.175562 + 0.984468i \(0.556174\pi\)
\(654\) 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 −0.943133 0.332417i \(-0.892136\pi\)
−0.183685 + 0.982985i \(0.558803\pi\)
\(662\) 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 \(-0.639356\pi\)
−0.423949 + 0.905686i \(0.639356\pi\)
\(674\) −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 −0.722416 0.691459i \(-0.756968\pi\)
0.960029 + 0.279901i \(0.0903018\pi\)
\(678\) 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 −0.906292 0.422652i \(-0.861099\pi\)
−0.0871187 + 0.996198i \(0.527766\pi\)
\(684\) 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 0.644027 0.765003i \(-0.277262\pi\)
−0.340498 + 0.940245i \(0.610596\pi\)
\(692\) −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 −0.890991 0.454021i \(-0.849989\pi\)
0.838689 + 0.544610i \(0.183322\pi\)
\(710\) 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 −0.497210 0.867630i \(-0.665642\pi\)
0.999995 0.00321841i \(-0.00102445\pi\)
\(720\) 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 \(-0.473177\pi\)
−0.820870 + 0.571116i \(0.806511\pi\)
\(734\) −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 −0.986972 0.160889i \(-0.948564\pi\)
0.354152 0.935188i \(-0.384770\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 3.61196 + 32.1042i 0.132599 + 1.17858i
\(743\) 40.6201i 1.49021i −0.666950 0.745103i \(-0.732400\pi\)
0.666950 0.745103i \(-0.267600\pi\)
\(744\) 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 0.0583658 + 0.998295i \(0.481411\pi\)
−0.893732 + 0.448601i \(0.851922\pi\)
\(752\) 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 \(-0.125950\pi\)
0.922733 + 0.385440i \(0.125950\pi\)
\(758\) −18.9424 10.9364i −0.688021 0.397229i
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0315 + 31.2316i −0.653643 + 1.13214i 0.328589 + 0.944473i \(0.393427\pi\)
−0.982232 + 0.187670i \(0.939906\pi\)
\(762\) 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 \(0.102666\pi\)
−0.948435 + 0.316971i \(0.897334\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.20933 + 2.09462i −0.0435248 + 0.0753871i
\(773\) 24.7318 + 42.8367i 0.889541 + 1.54073i 0.840419 + 0.541938i \(0.182309\pi\)
0.0491225 + 0.998793i \(0.484358\pi\)
\(774\) 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 \(-0.611474\pi\)
0.641915 + 0.766776i \(0.278140\pi\)