Properties

Label 3150.2.bp.g.899.1
Level 3150
Weight 2
Character 3150.899
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bp (of order \(6\), degree \(2\), not 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 899.1
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.g.1349.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.62916 - 0.295801i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.62916 - 0.295801i) q^{7} +1.00000 q^{8} +(0.570938 + 0.329631i) q^{11} -6.13514 q^{13} +(1.05841 + 2.42482i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.22062 + 2.43678i) q^{17} +(6.30208 - 3.63851i) q^{19} -0.659263i q^{22} +(-2.29939 - 3.98266i) q^{23} +(3.06757 + 5.31319i) q^{26} +(1.57075 - 2.12902i) q^{28} -8.09526i q^{29} +(0.759345 + 0.438408i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.87356i q^{34} +(8.75609 - 5.05533i) q^{37} +(-6.30208 - 3.63851i) q^{38} -6.25234 q^{41} +9.03582i q^{43} +(-0.570938 + 0.329631i) q^{44} +(-2.29939 + 3.98266i) q^{46} +(-10.3947 + 6.00136i) q^{47} +(6.82500 + 1.55542i) q^{49} +(3.06757 - 5.31319i) q^{52} +(-6.10540 + 10.5749i) q^{53} +(-2.62916 - 0.295801i) q^{56} +(-7.01070 + 4.04763i) q^{58} +(-4.06613 + 7.04274i) q^{59} +(-0.0618764 + 0.0357243i) q^{61} -0.876816i q^{62} +1.00000 q^{64} +(-1.15522 - 0.666965i) q^{67} +(-4.22062 + 2.43678i) q^{68} +2.60701i q^{71} +(-1.41203 + 2.44571i) q^{73} +(-8.75609 - 5.05533i) q^{74} +7.27702i q^{76} +(-1.40359 - 1.03554i) q^{77} +(2.88837 + 5.00280i) q^{79} +(3.12617 + 5.41468i) q^{82} -7.44660i q^{83} +(7.82525 - 4.51791i) q^{86} +(0.570938 + 0.329631i) q^{88} +(2.66489 + 4.61572i) q^{89} +(16.1303 + 1.81478i) q^{91} +4.59878 q^{92} +(10.3947 + 6.00136i) q^{94} -11.4792 q^{97} +(-2.06547 - 6.68833i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 12q^{2} - 12q^{4} + 24q^{8} - 12q^{16} + 24q^{17} - 12q^{19} - 8q^{23} - 12q^{32} + 12q^{38} - 8q^{46} - 24q^{47} + 52q^{49} - 32q^{53} - 12q^{61} + 24q^{64} - 24q^{68} - 16q^{77} - 4q^{79} + 68q^{91} + 16q^{92} + 24q^{94} - 20q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.62916 0.295801i −0.993730 0.111802i
\(8\) 1.00000 0.353553
\(9\) 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
\(13\) −6.13514 −1.70158 −0.850791 0.525504i \(-0.823877\pi\)
−0.850791 + 0.525504i \(0.823877\pi\)
\(14\) 1.05841 + 2.42482i 0.282872 + 0.648061i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.22062 + 2.43678i 1.02365 + 0.591005i 0.915160 0.403092i \(-0.132064\pi\)
0.108492 + 0.994097i \(0.465398\pi\)
\(18\) 0 0
\(19\) 6.30208 3.63851i 1.44580 0.834732i 0.447570 0.894249i \(-0.352289\pi\)
0.998227 + 0.0595173i \(0.0189562\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.659263i 0.140555i
\(23\) −2.29939 3.98266i −0.479456 0.830442i 0.520266 0.854004i \(-0.325833\pi\)
−0.999722 + 0.0235617i \(0.992499\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.06757 + 5.31319i 0.601600 + 1.04200i
\(27\) 0 0
\(28\) 1.57075 2.12902i 0.296844 0.402347i
\(29\) 8.09526i 1.50325i −0.659589 0.751626i \(-0.729270\pi\)
0.659589 0.751626i \(-0.270730\pi\)
\(30\) 0 0
\(31\) 0.759345 + 0.438408i 0.136382 + 0.0787404i 0.566639 0.823966i \(-0.308243\pi\)
−0.430256 + 0.902707i \(0.641577\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 4.87356i 0.835808i
\(35\) 0 0
\(36\) 0 0
\(37\) 8.75609 5.05533i 1.43949 0.831092i 0.441679 0.897173i \(-0.354383\pi\)
0.997814 + 0.0660818i \(0.0210498\pi\)
\(38\) −6.30208 3.63851i −1.02233 0.590244i
\(39\) 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
\(43\) 9.03582i 1.37795i 0.724785 + 0.688975i \(0.241939\pi\)
−0.724785 + 0.688975i \(0.758061\pi\)
\(44\) −0.570938 + 0.329631i −0.0860722 + 0.0496938i
\(45\) 0 0
\(46\) −2.29939 + 3.98266i −0.339027 + 0.587211i
\(47\) −10.3947 + 6.00136i −1.51622 + 0.875388i −0.516397 + 0.856349i \(0.672727\pi\)
−0.999819 + 0.0190383i \(0.993940\pi\)
\(48\) 0 0
\(49\) 6.82500 + 1.55542i 0.975001 + 0.222202i
\(50\) 0 0
\(51\) 0 0
\(52\) 3.06757 5.31319i 0.425396 0.736807i
\(53\) −6.10540 + 10.5749i −0.838641 + 1.45257i 0.0523897 + 0.998627i \(0.483316\pi\)
−0.891031 + 0.453943i \(0.850017\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.62916 0.295801i −0.351337 0.0395280i
\(57\) 0 0
\(58\) −7.01070 + 4.04763i −0.920550 + 0.531480i
\(59\) −4.06613 + 7.04274i −0.529365 + 0.916887i 0.470049 + 0.882640i \(0.344236\pi\)
−0.999413 + 0.0342461i \(0.989097\pi\)
\(60\) 0 0
\(61\) −0.0618764 + 0.0357243i −0.00792246 + 0.00457403i −0.503956 0.863729i \(-0.668123\pi\)
0.496034 + 0.868303i \(0.334789\pi\)
\(62\) 0.876816i 0.111356i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.15522 0.666965i −0.141132 0.0814827i 0.427771 0.903887i \(-0.359299\pi\)
−0.568903 + 0.822404i \(0.692632\pi\)
\(68\) −4.22062 + 2.43678i −0.511826 + 0.295503i
\(69\) 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
\(73\) −1.41203 + 2.44571i −0.165266 + 0.286249i −0.936750 0.350000i \(-0.886181\pi\)
0.771484 + 0.636249i \(0.219515\pi\)
\(74\) −8.75609 5.05533i −1.01788 0.587670i
\(75\) 0 0
\(76\) 7.27702i 0.834732i
\(77\) −1.40359 1.03554i −0.159953 0.118011i
\(78\) 0 0
\(79\) 2.88837 + 5.00280i 0.324967 + 0.562859i 0.981506 0.191433i \(-0.0613136\pi\)
−0.656539 + 0.754292i \(0.727980\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 3.12617 + 5.41468i 0.345228 + 0.597952i
\(83\) 7.44660i 0.817370i −0.912675 0.408685i \(-0.865987\pi\)
0.912675 0.408685i \(-0.134013\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.82525 4.51791i 0.843819 0.487179i
\(87\) 0 0
\(88\) 0.570938 + 0.329631i 0.0608622 + 0.0351388i
\(89\) 2.66489 + 4.61572i 0.282478 + 0.489266i 0.971994 0.235004i \(-0.0755104\pi\)
−0.689517 + 0.724270i \(0.742177\pi\)
\(90\) 0 0
\(91\) 16.1303 + 1.81478i 1.69091 + 0.190241i
\(92\) 4.59878 0.479456
\(93\) 0 0
\(94\) 10.3947 + 6.00136i 1.07213 + 0.618993i
\(95\) 0 0
\(96\) 0 0
\(97\) −11.4792 −1.16553 −0.582766 0.812640i \(-0.698030\pi\)
−0.582766 + 0.812640i \(0.698030\pi\)
\(98\) −2.06547 6.68833i −0.208644 0.675624i
\(99\) 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
\(103\) 1.03422 + 1.79131i 0.101904 + 0.176503i 0.912469 0.409145i \(-0.134173\pi\)
−0.810565 + 0.585649i \(0.800840\pi\)
\(104\) −6.13514 −0.601600
\(105\) 0 0
\(106\) 12.2108 1.18602
\(107\) 5.44632 + 9.43331i 0.526516 + 0.911953i 0.999523 + 0.0308937i \(0.00983533\pi\)
−0.473007 + 0.881059i \(0.656831\pi\)
\(108\) 0 0
\(109\) −7.17254 + 12.4232i −0.687005 + 1.18993i 0.285797 + 0.958290i \(0.407742\pi\)
−0.972802 + 0.231637i \(0.925592\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.05841 + 2.42482i 0.100010 + 0.229124i
\(113\) −11.9081 −1.12022 −0.560108 0.828420i \(-0.689240\pi\)
−0.560108 + 0.828420i \(0.689240\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.01070 + 4.04763i 0.650927 + 0.375813i
\(117\) 0 0
\(118\) 8.13225 0.748635
\(119\) −10.3759 7.65515i −0.951158 0.701747i
\(120\) 0 0
\(121\) −5.28269 9.14988i −0.480244 0.831807i
\(122\) 0.0618764 + 0.0357243i 0.00560202 + 0.00323433i
\(123\) 0 0
\(124\) −0.759345 + 0.438408i −0.0681912 + 0.0393702i
\(125\) 0 0
\(126\) 0 0
\(127\) 14.6264i 1.29788i −0.760839 0.648941i \(-0.775212\pi\)
0.760839 0.648941i \(-0.224788\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 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
\(133\) −17.6455 + 7.70208i −1.53006 + 0.667855i
\(134\) 1.33393i 0.115234i
\(135\) 0 0
\(136\) 4.22062 + 2.43678i 0.361915 + 0.208952i
\(137\) 1.75034 3.03168i 0.149542 0.259014i −0.781516 0.623885i \(-0.785553\pi\)
0.931058 + 0.364871i \(0.118887\pi\)
\(138\) 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
\(142\) 2.25773 1.30350i 0.189465 0.109388i
\(143\) −3.50279 2.02234i −0.292918 0.169116i
\(144\) 0 0
\(145\) 0 0
\(146\) 2.82406 0.233721
\(147\) 0 0
\(148\) 10.1107i 0.831092i
\(149\) −7.14910 + 4.12754i −0.585677 + 0.338141i −0.763386 0.645942i \(-0.776465\pi\)
0.177709 + 0.984083i \(0.443131\pi\)
\(150\) 0 0
\(151\) −0.463545 + 0.802883i −0.0377227 + 0.0653377i −0.884270 0.466975i \(-0.845344\pi\)
0.846548 + 0.532313i \(0.178677\pi\)
\(152\) 6.30208 3.63851i 0.511167 0.295122i
\(153\) 0 0
\(154\) −0.195010 + 1.73331i −0.0157144 + 0.139674i
\(155\) 0 0
\(156\) 0 0
\(157\) 4.17124 7.22480i 0.332901 0.576602i −0.650178 0.759782i \(-0.725306\pi\)
0.983079 + 0.183180i \(0.0586391\pi\)
\(158\) 2.88837 5.00280i 0.229786 0.398001i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.86740 + 11.1512i 0.383605 + 0.878840i
\(162\) 0 0
\(163\) −21.0488 + 12.1525i −1.64867 + 0.951858i −0.671064 + 0.741400i \(0.734162\pi\)
−0.977603 + 0.210458i \(0.932504\pi\)
\(164\) 3.12617 5.41468i 0.244113 0.422816i
\(165\) 0 0
\(166\) −6.44894 + 3.72330i −0.500535 + 0.288984i
\(167\) 7.48724i 0.579380i 0.957120 + 0.289690i \(0.0935523\pi\)
−0.957120 + 0.289690i \(0.906448\pi\)
\(168\) 0 0
\(169\) 24.6400 1.89538
\(170\) 0 0
\(171\) 0 0
\(172\) −7.82525 4.51791i −0.596670 0.344487i
\(173\) −12.3328 + 7.12036i −0.937647 + 0.541351i −0.889222 0.457476i \(-0.848754\pi\)
−0.0484252 + 0.998827i \(0.515420\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.659263i 0.0496938i
\(177\) 0 0
\(178\) 2.66489 4.61572i 0.199742 0.345963i
\(179\) 11.3826 + 6.57176i 0.850777 + 0.491196i 0.860913 0.508752i \(-0.169893\pi\)
−0.0101362 + 0.999949i \(0.503226\pi\)
\(180\) 0 0
\(181\) 6.34537i 0.471648i 0.971796 + 0.235824i \(0.0757788\pi\)
−0.971796 + 0.235824i \(0.924221\pi\)
\(182\) −6.49350 14.8766i −0.481331 1.10273i
\(183\) 0 0
\(184\) −2.29939 3.98266i −0.169513 0.293606i
\(185\) 0 0
\(186\) 0 0
\(187\) 1.60648 + 2.78250i 0.117477 + 0.203477i
\(188\) 12.0027i 0.875388i
\(189\) 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
\(193\) 2.09462 + 1.20933i 0.150774 + 0.0870495i 0.573489 0.819213i \(-0.305589\pi\)
−0.422715 + 0.906263i \(0.638923\pi\)
\(194\) 5.73958 + 9.94125i 0.412078 + 0.713740i
\(195\) 0 0
\(196\) −4.75953 + 5.13292i −0.339967 + 0.366637i
\(197\) −6.24457 −0.444907 −0.222454 0.974943i \(-0.571407\pi\)
−0.222454 + 0.974943i \(0.571407\pi\)
\(198\) 0 0
\(199\) 4.38388 + 2.53103i 0.310765 + 0.179420i 0.647269 0.762262i \(-0.275911\pi\)
−0.336504 + 0.941682i \(0.609244\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 15.4975 1.09040
\(203\) −2.39458 + 21.2838i −0.168067 + 1.49383i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.03422 1.79131i 0.0720572 0.124807i
\(207\) 0 0
\(208\) 3.06757 + 5.31319i 0.212698 + 0.368403i
\(209\) 4.79747 0.331848
\(210\) 0 0
\(211\) 5.72168 0.393896 0.196948 0.980414i \(-0.436897\pi\)
0.196948 + 0.980414i \(0.436897\pi\)
\(212\) −6.10540 10.5749i −0.419321 0.726285i
\(213\) 0 0
\(214\) 5.44632 9.43331i 0.372303 0.644848i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.86676 1.37726i −0.126724 0.0934946i
\(218\) 14.3451 0.971572
\(219\) 0 0
\(220\) 0 0
\(221\) −25.8941 14.9500i −1.74183 1.00564i
\(222\) 0 0
\(223\) 6.61006 0.442642 0.221321 0.975201i \(-0.428963\pi\)
0.221321 + 0.975201i \(0.428963\pi\)
\(224\) 1.57075 2.12902i 0.104950 0.142251i
\(225\) 0 0
\(226\) 5.95403 + 10.3127i 0.396056 + 0.685989i
\(227\) 20.8328 + 12.0278i 1.38272 + 0.798314i 0.992481 0.122400i \(-0.0390590\pi\)
0.390239 + 0.920714i \(0.372392\pi\)
\(228\) 0 0
\(229\) 4.39811 2.53925i 0.290635 0.167798i −0.347593 0.937645i \(-0.613001\pi\)
0.638228 + 0.769847i \(0.279668\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.09526i 0.531480i
\(233\) −11.0386 19.1195i −0.723165 1.25256i −0.959725 0.280941i \(-0.909353\pi\)
0.236560 0.971617i \(-0.423980\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.06613 7.04274i −0.264682 0.458443i
\(237\) 0 0
\(238\) −1.44160 + 12.8134i −0.0934451 + 0.830568i
\(239\) 17.8556i 1.15498i 0.816398 + 0.577490i \(0.195968\pi\)
−0.816398 + 0.577490i \(0.804032\pi\)
\(240\) 0 0
\(241\) 18.8401 + 10.8773i 1.21360 + 0.700670i 0.963541 0.267562i \(-0.0862179\pi\)
0.250055 + 0.968232i \(0.419551\pi\)
\(242\) −5.28269 + 9.14988i −0.339584 + 0.588177i
\(243\) 0 0
\(244\) 0.0714487i 0.00457403i
\(245\) 0 0
\(246\) 0 0
\(247\) −38.6642 + 22.3228i −2.46014 + 1.42036i
\(248\) 0.759345 + 0.438408i 0.0482185 + 0.0278390i
\(249\) 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
\(253\) 3.03181i 0.190608i
\(254\) −12.6668 + 7.31319i −0.794787 + 0.458870i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 14.2617 8.23399i 0.889620 0.513622i 0.0158016 0.999875i \(-0.494970\pi\)
0.873818 + 0.486253i \(0.161637\pi\)
\(258\) 0 0
\(259\) −24.5166 + 10.7012i −1.52339 + 0.664943i
\(260\) 0 0
\(261\) 0 0
\(262\) −1.64037 + 2.84120i −0.101342 + 0.175530i
\(263\) 2.81031 4.86760i 0.173291 0.300149i −0.766278 0.642510i \(-0.777893\pi\)
0.939569 + 0.342361i \(0.111227\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 15.4929 + 11.4304i 0.949933 + 0.700843i
\(267\) 0 0
\(268\) 1.15522 0.666965i 0.0705661 0.0407414i
\(269\) −3.27081 + 5.66521i −0.199425 + 0.345414i −0.948342 0.317249i \(-0.897241\pi\)
0.748917 + 0.662664i \(0.230574\pi\)
\(270\) 0 0
\(271\) −16.0238 + 9.25135i −0.973377 + 0.561980i −0.900264 0.435344i \(-0.856627\pi\)
−0.0731130 + 0.997324i \(0.523293\pi\)
\(272\) 4.87356i 0.295503i
\(273\) 0 0
\(274\) −3.50069 −0.211484
\(275\) 0 0
\(276\) 0 0
\(277\) 22.4426 + 12.9572i 1.34844 + 0.778525i 0.988029 0.154267i \(-0.0493016\pi\)
0.360415 + 0.932792i \(0.382635\pi\)
\(278\) 1.54180 0.890157i 0.0924708 0.0533881i
\(279\) 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
\(283\) −3.54800 + 6.14531i −0.210907 + 0.365301i −0.951999 0.306103i \(-0.900975\pi\)
0.741092 + 0.671404i \(0.234308\pi\)
\(284\) −2.25773 1.30350i −0.133972 0.0773486i
\(285\) 0 0
\(286\) 4.04467i 0.239166i
\(287\) 16.4384 + 1.84944i 0.970329 + 0.109169i
\(288\) 0 0
\(289\) 3.37577 + 5.84701i 0.198575 + 0.343942i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.41203 2.44571i −0.0826328 0.143124i
\(293\) 8.94657i 0.522664i −0.965249 0.261332i \(-0.915838\pi\)
0.965249 0.261332i \(-0.0841617\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 8.75609 5.05533i 0.508938 0.293835i
\(297\) 0 0
\(298\) 7.14910 + 4.12754i 0.414136 + 0.239102i
\(299\) 14.1071 + 24.4342i 0.815834 + 1.41307i
\(300\) 0 0
\(301\) 2.67280 23.7567i 0.154058 1.36931i
\(302\) 0.927090 0.0533480
\(303\) 0 0
\(304\) −6.30208 3.63851i −0.361449 0.208683i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.62584 0.435230 0.217615 0.976035i \(-0.430172\pi\)
0.217615 + 0.976035i \(0.430172\pi\)
\(308\) 1.59860 0.697771i 0.0910884 0.0397592i
\(309\) 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
\(313\) 4.52850 + 7.84360i 0.255966 + 0.443346i 0.965157 0.261670i \(-0.0842731\pi\)
−0.709191 + 0.705016i \(0.750940\pi\)
\(314\) −8.34248 −0.470793
\(315\) 0 0
\(316\) −5.77674 −0.324967
\(317\) −14.2534 24.6876i −0.800552 1.38660i −0.919253 0.393666i \(-0.871207\pi\)
0.118702 0.992930i \(-0.462127\pi\)
\(318\) 0 0
\(319\) 2.66845 4.62189i 0.149405 0.258776i
\(320\) 0 0
\(321\) 0 0
\(322\) 7.22355 9.79091i 0.402553 0.545626i
\(323\) 35.4650 1.97332
\(324\) 0 0
\(325\) 0 0
\(326\) 21.0488 + 12.1525i 1.16578 + 0.673065i
\(327\) 0 0
\(328\) −6.25234 −0.345228
\(329\) 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 \(0.969265\pi\)
\(332\) 6.44894 + 3.72330i 0.353932 + 0.204343i
\(333\) 0 0
\(334\) 6.48414 3.74362i 0.354797 0.204842i
\(335\) 0 0
\(336\) 0 0
\(337\) 0.480936i 0.0261983i −0.999914 0.0130991i \(-0.995830\pi\)
0.999914 0.0130991i \(-0.00416970\pi\)
\(338\) −12.3200 21.3389i −0.670119 1.16068i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.289026 + 0.500608i 0.0156516 + 0.0271094i
\(342\) 0 0
\(343\) −17.4840 6.10828i −0.944045 0.329816i
\(344\) 9.03582i 0.487179i
\(345\) 0 0
\(346\) 12.3328 + 7.12036i 0.663017 + 0.382793i
\(347\) −1.73829 + 3.01081i −0.0933165 + 0.161629i −0.908905 0.417004i \(-0.863080\pi\)
0.815588 + 0.578633i \(0.196414\pi\)
\(348\) 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
\(352\) −0.570938 + 0.329631i −0.0304311 + 0.0175694i
\(353\) 18.8649 + 10.8916i 1.00407 + 0.579703i 0.909451 0.415810i \(-0.136502\pi\)
0.0946235 + 0.995513i \(0.469835\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −5.32978 −0.282478
\(357\) 0 0
\(358\) 13.1435i 0.694656i
\(359\) 14.0413 8.10672i 0.741069 0.427857i −0.0813887 0.996682i \(-0.525936\pi\)
0.822458 + 0.568826i \(0.192602\pi\)
\(360\) 0 0
\(361\) 16.9775 29.4059i 0.893553 1.54768i
\(362\) 5.49525 3.17268i 0.288824 0.166753i
\(363\) 0 0
\(364\) −9.63679 + 13.0619i −0.505105 + 0.684627i
\(365\) 0 0
\(366\) 0 0
\(367\) 10.4278 18.0615i 0.544327 0.942802i −0.454322 0.890837i \(-0.650119\pi\)
0.998649 0.0519641i \(-0.0165481\pi\)
\(368\) −2.29939 + 3.98266i −0.119864 + 0.207611i
\(369\) 0 0
\(370\) 0 0
\(371\) 19.1801 25.9971i 0.995784 1.34970i
\(372\) 0 0
\(373\) 1.21673 0.702477i 0.0629997 0.0363729i −0.468169 0.883639i \(-0.655086\pi\)
0.531169 + 0.847266i \(0.321753\pi\)
\(374\) 1.60648 2.78250i 0.0830689 0.143880i
\(375\) 0 0
\(376\) −10.3947 + 6.00136i −0.536063 + 0.309496i
\(377\) 49.6656i 2.55791i
\(378\) 0 0
\(379\) −21.8729 −1.12353 −0.561766 0.827296i \(-0.689878\pi\)
−0.561766 + 0.827296i \(0.689878\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 18.8926 + 10.9077i 0.966632 + 0.558085i
\(383\) −29.9197 + 17.2741i −1.52882 + 0.882666i −0.529411 + 0.848365i \(0.677587\pi\)
−0.999412 + 0.0343009i \(0.989080\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.41866i 0.123107i
\(387\) 0 0
\(388\) 5.73958 9.94125i 0.291383 0.504690i
\(389\) −10.0406 5.79694i −0.509078 0.293916i 0.223376 0.974732i \(-0.428292\pi\)
−0.732455 + 0.680816i \(0.761625\pi\)
\(390\) 0 0
\(391\) 22.4124i 1.13344i
\(392\) 6.82500 + 1.55542i 0.344715 + 0.0785604i
\(393\) 0 0
\(394\) 3.12229 + 5.40796i 0.157299 + 0.272449i
\(395\) 0 0
\(396\) 0 0
\(397\) −2.90061 5.02400i −0.145577 0.252147i 0.784011 0.620747i \(-0.213171\pi\)
−0.929588 + 0.368600i \(0.879837\pi\)
\(398\) 5.06207i 0.253739i
\(399\) 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
\(403\) −4.65869 2.68970i −0.232066 0.133983i
\(404\) −7.74874 13.4212i −0.385514 0.667730i
\(405\) 0 0
\(406\) 19.6296 8.56811i 0.974199 0.425228i
\(407\) 6.66558 0.330401
\(408\) 0 0
\(409\) −7.85765 4.53662i −0.388536 0.224321i 0.292990 0.956116i \(-0.405350\pi\)
−0.681526 + 0.731794i \(0.738683\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.06843 −0.101904
\(413\) 12.7738 17.3138i 0.628556 0.851954i
\(414\) 0 0
\(415\) 0 0
\(416\) 3.06757 5.31319i 0.150400 0.260501i
\(417\) 0 0
\(418\) −2.39873 4.15473i −0.117326 0.203214i
\(419\) −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 \(0.321514\pi\)
\(422\) −2.86084 4.95512i −0.139263 0.241211i
\(423\) 0 0
\(424\) −6.10540 + 10.5749i −0.296504 + 0.513561i
\(425\) 0 0
\(426\) 0 0
\(427\) 0.173250 0.0756221i 0.00838417 0.00365961i
\(428\) −10.8926 −0.526516
\(429\) 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
\(433\) 35.2578 1.69438 0.847190 0.531289i \(-0.178292\pi\)
0.847190 + 0.531289i \(0.178292\pi\)
\(434\) −0.259363 + 2.30529i −0.0124498 + 0.110658i
\(435\) 0 0
\(436\) −7.17254 12.4232i −0.343502 0.594964i
\(437\) −28.9819 16.7327i −1.38639 0.800434i
\(438\) 0 0
\(439\) −25.4755 + 14.7083i −1.21588 + 0.701988i −0.964034 0.265779i \(-0.914371\pi\)
−0.251846 + 0.967767i \(0.581038\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 29.9000i 1.42220i
\(443\) 14.7259 + 25.5061i 0.699651 + 1.21183i 0.968588 + 0.248673i \(0.0799943\pi\)
−0.268937 + 0.963158i \(0.586672\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −3.30503 5.72448i −0.156498 0.271062i
\(447\) 0 0
\(448\) −2.62916 0.295801i −0.124216 0.0139753i
\(449\) 29.2408i 1.37996i −0.723829 0.689980i \(-0.757619\pi\)
0.723829 0.689980i \(-0.242381\pi\)
\(450\) 0 0
\(451\) −3.56970 2.06097i −0.168091 0.0970471i
\(452\) 5.95403 10.3127i 0.280054 0.485067i
\(453\) 0 0
\(454\) 24.0556i 1.12899i
\(455\) 0 0
\(456\) 0 0
\(457\) −6.90532 + 3.98679i −0.323017 + 0.186494i −0.652737 0.757585i \(-0.726379\pi\)
0.329720 + 0.944079i \(0.393046\pi\)
\(458\) −4.39811 2.53925i −0.205510 0.118651i
\(459\) 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
\(463\) 17.6663i 0.821021i 0.911856 + 0.410511i \(0.134650\pi\)
−0.911856 + 0.410511i \(0.865350\pi\)
\(464\) −7.01070 + 4.04763i −0.325464 + 0.187907i
\(465\) 0 0
\(466\) −11.0386 + 19.1195i −0.511355 + 0.885692i
\(467\) −19.0104 + 10.9757i −0.879698 + 0.507894i −0.870559 0.492064i \(-0.836242\pi\)
−0.00913924 + 0.999958i \(0.502909\pi\)
\(468\) 0 0
\(469\) 2.83997 + 2.09527i 0.131137 + 0.0967507i
\(470\) 0 0
\(471\) 0 0
\(472\) −4.06613 + 7.04274i −0.187159 + 0.324168i
\(473\) −2.97849 + 5.15890i −0.136951 + 0.237206i
\(474\) 0 0
\(475\) 0 0
\(476\) 11.8175 5.15823i 0.541655 0.236427i
\(477\) 0 0
\(478\) 15.4634 8.92778i 0.707278 0.408347i
\(479\) −16.9834 + 29.4161i −0.775990 + 1.34405i 0.158246 + 0.987400i \(0.449416\pi\)
−0.934236 + 0.356655i \(0.883917\pi\)
\(480\) 0 0
\(481\) −53.7199 + 31.0152i −2.44942 + 1.41417i
\(482\) 21.7546i 0.990897i
\(483\) 0 0
\(484\) 10.5654 0.480244
\(485\) 0 0
\(486\) 0 0
\(487\) 12.8602 + 7.42482i 0.582750 + 0.336451i 0.762225 0.647312i \(-0.224107\pi\)
−0.179476 + 0.983762i \(0.557440\pi\)
\(488\) −0.0618764 + 0.0357243i −0.00280101 + 0.00161716i
\(489\) 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
\(493\) 19.7264 34.1670i 0.888430 1.53881i
\(494\) 38.6642 + 22.3228i 1.73958 + 1.00435i
\(495\) 0 0
\(496\) 0.876816i 0.0393702i
\(497\) 0.771153 6.85424i 0.0345910 0.307455i
\(498\) 0 0
\(499\) 9.23416 + 15.9940i 0.413378 + 0.715991i 0.995257 0.0972842i \(-0.0310156\pi\)
−0.581879 + 0.813275i \(0.697682\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 8.02227 + 13.8950i 0.358052 + 0.620164i
\(503\) 5.46007i 0.243452i 0.992564 + 0.121726i \(0.0388430\pi\)
−0.992564 + 0.121726i \(0.961157\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −2.62562 + 1.51590i −0.116723 + 0.0673901i
\(507\) 0 0
\(508\) 12.6668 + 7.31319i 0.561999 + 0.324470i
\(509\) −0.412125 0.713821i −0.0182671 0.0316396i 0.856747 0.515736i \(-0.172482\pi\)
−0.875014 + 0.484097i \(0.839148\pi\)
\(510\) 0 0
\(511\) 4.43590 6.01249i 0.196233 0.265977i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −14.2617 8.23399i −0.629056 0.363186i
\(515\) 0 0
\(516\) 0 0
\(517\) −7.91294 −0.348011
\(518\) 21.5258 + 15.8814i 0.945791 + 0.697787i
\(519\) 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
\(523\) 0.113392 + 0.196400i 0.00495828 + 0.00858799i 0.868494 0.495700i \(-0.165088\pi\)
−0.863536 + 0.504288i \(0.831755\pi\)
\(524\) 3.28074 0.143320
\(525\) 0 0
\(526\) −5.62062 −0.245070
\(527\) 2.13661 + 3.70071i 0.0930721 + 0.161206i
\(528\) 0 0
\(529\) 0.925602 1.60319i 0.0402436 0.0697039i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.15255 19.1325i 0.0933247 0.829498i
\(533\) 38.3590 1.66151
\(534\) 0 0
\(535\) 0 0
\(536\) −1.15522 0.666965i −0.0498978 0.0288085i
\(537\) 0 0
\(538\) 6.54163 0.282030
\(539\) 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 \(-0.460929\pi\)
\(542\) 16.0238 + 9.25135i 0.688282 + 0.397380i
\(543\) 0 0
\(544\) −4.22062 + 2.43678i −0.180958 + 0.104476i
\(545\) 0 0
\(546\) 0 0
\(547\) 14.2444i 0.609047i 0.952505 + 0.304524i \(0.0984972\pi\)
−0.952505 + 0.304524i \(0.901503\pi\)
\(548\) 1.75034 + 3.03168i 0.0747709 + 0.129507i
\(549\) 0 0
\(550\) 0 0
\(551\) −29.4547 51.0170i −1.25481 2.17340i
\(552\) 0 0
\(553\) −6.11416 14.0076i −0.260001 0.595662i
\(554\) 25.9145i 1.10100i
\(555\) 0 0
\(556\) −1.54180 0.890157i −0.0653867 0.0377511i
\(557\) −9.45492 + 16.3764i −0.400618 + 0.693890i −0.993801 0.111177i \(-0.964538\pi\)
0.593183 + 0.805068i \(0.297871\pi\)
\(558\) 0 0
\(559\) 55.4361i 2.34470i
\(560\) 0 0
\(561\) 0 0
\(562\) −8.00346 + 4.62080i −0.337606 + 0.194917i
\(563\) 34.0414 + 19.6538i 1.43467 + 0.828310i 0.997472 0.0710537i \(-0.0226362\pi\)
0.437202 + 0.899363i \(0.355969\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 7.09599 0.298267
\(567\) 0 0
\(568\) 2.60701i 0.109388i
\(569\) −0.768837 + 0.443888i −0.0322313 + 0.0186088i −0.516029 0.856571i \(-0.672590\pi\)
0.483798 + 0.875180i \(0.339257\pi\)
\(570\) 0 0
\(571\) −12.7120 + 22.0178i −0.531981 + 0.921418i 0.467322 + 0.884087i \(0.345219\pi\)
−0.999303 + 0.0373309i \(0.988114\pi\)
\(572\) 3.50279 2.02234i 0.146459 0.0845581i
\(573\) 0 0
\(574\) −6.61754 15.1608i −0.276211 0.632800i
\(575\) 0 0
\(576\) 0 0
\(577\) 5.14235 8.90681i 0.214079 0.370795i −0.738908 0.673806i \(-0.764658\pi\)
0.952987 + 0.303010i \(0.0979917\pi\)
\(578\) 3.37577 5.84701i 0.140414 0.243204i
\(579\) 0 0
\(580\) 0 0
\(581\) −2.20271 + 19.5783i −0.0913837 + 0.812246i
\(582\) 0 0
\(583\) −6.97161 + 4.02506i −0.288735 + 0.166701i
\(584\) −1.41203 + 2.44571i −0.0584302 + 0.101204i
\(585\) 0 0
\(586\) −7.74795 + 4.47328i −0.320065 + 0.184790i
\(587\) 25.1241i 1.03698i −0.855083 0.518490i \(-0.826494\pi\)
0.855083 0.518490i \(-0.173506\pi\)
\(588\) 0 0
\(589\) 6.38061 0.262909
\(590\) 0 0
\(591\) 0 0
\(592\) −8.75609 5.05533i −0.359873 0.207773i
\(593\) −8.75538 + 5.05492i −0.359540 + 0.207581i −0.668879 0.743371i \(-0.733226\pi\)
0.309339 + 0.950952i \(0.399892\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.25507i 0.338141i
\(597\) 0 0
\(598\) 14.1071 24.4342i 0.576882 0.999189i
\(599\) −21.6368 12.4920i −0.884056 0.510410i −0.0120624 0.999927i \(-0.503840\pi\)
−0.871994 + 0.489517i \(0.837173\pi\)
\(600\) 0 0
\(601\) 15.2936i 0.623837i 0.950109 + 0.311919i \(0.100972\pi\)
−0.950109 + 0.311919i \(0.899028\pi\)
\(602\) −21.9103 + 9.56361i −0.892996 + 0.389784i
\(603\) 0 0
\(604\) −0.463545 0.802883i −0.0188614 0.0326689i
\(605\) 0 0
\(606\) 0 0
\(607\) 19.7438 + 34.1973i 0.801377 + 1.38802i 0.918710 + 0.394932i \(0.129232\pi\)
−0.117334 + 0.993093i \(0.537435\pi\)
\(608\) 7.27702i 0.295122i
\(609\) 0 0
\(610\) 0 0
\(611\) 63.7727 36.8192i 2.57997 1.48954i
\(612\) 0 0
\(613\) −14.8258 8.55968i −0.598809 0.345722i 0.169764 0.985485i \(-0.445699\pi\)
−0.768573 + 0.639762i \(0.779033\pi\)
\(614\) −3.81292 6.60417i −0.153877 0.266523i
\(615\) 0 0
\(616\) −1.40359 1.03554i −0.0565521 0.0417230i
\(617\) −5.80201 −0.233580 −0.116790 0.993157i \(-0.537260\pi\)
−0.116790 + 0.993157i \(0.537260\pi\)
\(618\) 0 0
\(619\) −29.5344 17.0517i −1.18709 0.685366i −0.229445 0.973322i \(-0.573691\pi\)
−0.957644 + 0.287956i \(0.907024\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 6.40696 0.256896
\(623\) −5.64109 12.9238i −0.226006 0.517780i
\(624\) 0 0
\(625\) 0 0
\(626\) 4.52850 7.84360i 0.180995 0.313493i
\(627\) 0 0
\(628\) 4.17124 + 7.22480i 0.166451 + 0.288301i
\(629\) 49.2749 1.96472
\(630\) 0 0
\(631\) 33.1261 1.31873 0.659365 0.751823i \(-0.270825\pi\)
0.659365 + 0.751823i \(0.270825\pi\)
\(632\) 2.88837 + 5.00280i 0.114893 + 0.199001i
\(633\) 0 0
\(634\) −14.2534 + 24.6876i −0.566076 + 0.980472i
\(635\) 0 0
\(636\) 0 0
\(637\) −41.8724 9.54270i −1.65904 0.378096i
\(638\) −5.33690 −0.211290
\(639\) 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
\(643\) 0.661676 0.0260940 0.0130470 0.999915i \(-0.495847\pi\)
0.0130470 + 0.999915i \(0.495847\pi\)
\(644\) −12.0910 1.36032i −0.476450 0.0536042i
\(645\) 0 0
\(646\) −17.7325 30.7136i −0.697675 1.20841i
\(647\) 15.9223 + 9.19276i 0.625971 + 0.361405i 0.779190 0.626787i \(-0.215631\pi\)
−0.153219 + 0.988192i \(0.548964\pi\)
\(648\) 0 0
\(649\) −4.64302 + 2.68065i −0.182254 + 0.105225i
\(650\) 0 0
\(651\) 0 0
\(652\) 24.3050i 0.951858i
\(653\) −8.69323 15.0571i −0.340193 0.589231i 0.644276 0.764793i \(-0.277159\pi\)
−0.984468 + 0.175562i \(0.943826\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.12617 + 5.41468i 0.122056 + 0.211408i
\(657\) 0 0
\(658\) −25.5540 18.8533i −0.996200 0.734978i
\(659\) 35.4692i 1.38168i −0.723006 0.690841i \(-0.757240\pi\)
0.723006 0.690841i \(-0.242760\pi\)
\(660\) 0 0
\(661\) −28.9704 16.7261i −1.12682 0.650568i −0.183685 0.982985i \(-0.558803\pi\)
−0.943133 + 0.332417i \(0.892136\pi\)
\(662\) −7.53535 + 13.0516i −0.292870 + 0.507265i
\(663\) 0 0
\(664\) 7.44660i 0.288984i
\(665\) 0 0
\(666\) 0 0
\(667\) −32.2407 + 18.6142i −1.24836 + 0.720744i
\(668\) −6.48414 3.74362i −0.250879 0.144845i
\(669\) 0 0
\(670\) 0 0
\(671\) −0.0471035 −0.00181841
\(672\) 0 0
\(673\) 21.9964i 0.847898i −0.905686 0.423949i \(-0.860644\pi\)
0.905686 0.423949i \(-0.139356\pi\)
\(674\) −0.416503 + 0.240468i −0.0160431 + 0.00926249i
\(675\) 0 0
\(676\) −12.3200 + 21.3389i −0.473846 + 0.820725i
\(677\) −10.7084 + 6.18250i −0.411557 + 0.237613i −0.691459 0.722416i \(-0.743032\pi\)
0.279901 + 0.960029i \(0.409698\pi\)
\(678\) 0 0
\(679\) 30.1806 + 3.39554i 1.15823 + 0.130309i
\(680\) 0 0
\(681\) 0 0
\(682\) 0.289026 0.500608i 0.0110674 0.0191693i
\(683\) −14.9892 + 25.9621i −0.573546 + 0.993411i 0.422652 + 0.906292i \(0.361099\pi\)
−0.996198 + 0.0871187i \(0.972234\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 3.45205 + 18.1957i 0.131800 + 0.694715i
\(687\) 0 0
\(688\) 7.82525 4.51791i 0.298335 0.172244i
\(689\) 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 \(0.277262\pi\)
\(692\) 14.2407i 0.541351i
\(693\) 0 0
\(694\) 3.47659 0.131969
\(695\) 0 0
\(696\) 0 0
\(697\) −26.3888 15.2356i −0.999546 0.577088i
\(698\) 0.529638 0.305787i 0.0200471 0.0115742i
\(699\) 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
\(703\) 36.7878 63.7183i 1.38748 2.40318i
\(704\) 0.570938 + 0.329631i 0.0215180 + 0.0124234i
\(705\) 0 0
\(706\) 21.7833i 0.819824i
\(707\) 24.3427 32.9945i 0.915502 1.24089i
\(708\) 0 0
\(709\) 1.39264 + 2.41213i 0.0523019 + 0.0905895i 0.890991 0.454021i \(-0.150011\pi\)
−0.838689 + 0.544610i \(0.816678\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 2.66489 + 4.61572i 0.0998709 + 0.172981i
\(713\) 4.03229i 0.151010i
\(714\) 0 0
\(715\) 0 0
\(716\) −11.3826 + 6.57176i −0.425388 + 0.245598i
\(717\) 0 0
\(718\) −14.0413 8.10672i −0.524015 0.302540i
\(719\) 13.4818 + 23.3511i 0.502785 + 0.870849i 0.999995 + 0.00321841i \(0.00102445\pi\)
−0.497210 + 0.867630i \(0.665642\pi\)
\(720\) 0 0
\(721\) −2.18925 5.01558i −0.0815319 0.186790i
\(722\) −33.9550 −1.26368
\(723\) 0 0
\(724\) −5.49525 3.17268i −0.204229 0.117912i
\(725\) 0 0
\(726\) 0 0
\(727\) −29.6632 −1.10015 −0.550074 0.835116i \(-0.685400\pi\)
−0.550074 + 0.835116i \(0.685400\pi\)
\(728\) 16.1303 + 1.81478i 0.597829 + 0.0672602i
\(729\) 0 0
\(730\) 0 0
\(731\) −22.0183 + 38.1368i −0.814376 + 1.41054i
\(732\) 0 0
\(733\) −11.5155 19.9455i −0.425336 0.736704i 0.571116 0.820870i \(-0.306511\pi\)
−0.996452 + 0.0841657i \(0.973177\pi\)
\(734\) −20.8556 −0.769794
\(735\) 0 0
\(736\) 4.59878 0.169513
\(737\) −0.439705 0.761591i −0.0161967 0.0280536i
\(738\) 0 0
\(739\) 17.2029 29.7964i 0.632821 1.09608i −0.354152 0.935188i \(-0.615230\pi\)
0.986972 0.160889i \(-0.0514363\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −32.1042 3.61196i −1.17858 0.132599i
\(743\) 40.6201 1.49021 0.745103 0.666950i \(-0.232400\pi\)
0.745103 + 0.666950i \(0.232400\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.21673 0.702477i −0.0445475 0.0257195i
\(747\) 0 0
\(748\) −3.21295 −0.117477
\(749\) −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 \(-0.481411\pi\)
\(752\) 10.3947 + 6.00136i 0.379054 + 0.218847i
\(753\) 0 0
\(754\) 43.0117 24.8328i 1.56639 0.904357i
\(755\) 0 0
\(756\) 0 0
\(757\) 50.7755i 1.84547i −0.385440 0.922733i \(-0.625950\pi\)
0.385440 0.922733i \(-0.374050\pi\)
\(758\) 10.9364 + 18.9424i 0.397229 + 0.688021i
\(759\) 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
\(763\) 22.5326 30.5410i 0.815734 1.10566i
\(764\) 21.8153i 0.789251i
\(765\) 0 0
\(766\) 29.9197 + 17.2741i 1.08104 + 0.624139i
\(767\) 24.9463 43.2082i 0.900758 1.56016i
\(768\) 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
\(772\) −2.09462 + 1.20933i −0.0753871 + 0.0435248i
\(773\) −42.8367 24.7318i −1.54073 0.889541i −0.998793 0.0491225i \(-0.984358\pi\)
−0.541938 0.840419i \(-0.682309\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −11.4792 −0.412078
\(777\) 0 0
\(778\) 11.5939i 0.415661i
\(779\) −39.4028 + 22.7492i −1.41175 + 0.815074i
\(780\) 0 0
\(781\) −0.859351 + 1.48844i −0.0307500 + 0.0532605i
\(782\) −19.4097 + 11.2062i −0.694090 + 0.400733i
\(783\) 0 0
\(784\) −2.06547 6.68833i −0.0737669 0.238869i
\(785\) 0 0
\(786\) 0 0
\(787\) 4.83998 8.38310i 0.172527 0.298825i