Properties

Label 3150.2.bp.h.899.12
Level 3150
Weight 2
Character 3150.899
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.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 899.12
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.h.1349.12

$q$-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 \(-0.176123\pi\)
0.850791 + 0.525504i \(0.176123\pi\)
\(14\) 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 −0.108492 0.994097i \(-0.534602\pi\)
−0.915160 + 0.403092i \(0.867936\pi\)
\(18\) 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 0.999722 0.0235617i \(-0.00750062\pi\)
−0.520266 + 0.854004i \(0.674167\pi\)
\(24\) 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 −0.997814 0.0660818i \(-0.978950\pi\)
−0.441679 + 0.897173i \(0.645617\pi\)
\(38\) 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 \(-0.758061\pi\)
0.724785 0.688975i \(-0.241939\pi\)
\(44\) −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 \(-0.327273\pi\)
0.999819 0.0190383i \(-0.00606045\pi\)
\(48\) 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 \(-0.516684\pi\)
0.891031 0.453943i \(-0.149983\pi\)
\(54\) 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 0.568903 0.822404i \(-0.307368\pi\)
−0.427771 + 0.903887i \(0.640701\pi\)
\(68\) 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 −0.771484 0.636249i \(-0.780485\pi\)
0.936750 + 0.350000i \(0.113819\pi\)
\(74\) −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 \(0.134013\pi\)
−0.912675 + 0.408685i \(0.865987\pi\)
\(84\) 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 \(-0.301970\pi\)
0.582766 + 0.812640i \(0.301970\pi\)
\(98\) 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 0.810565 0.585649i \(-0.199160\pi\)
−0.912469 + 0.409145i \(0.865827\pi\)
\(104\) −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 \(-0.990165\pi\)
0.473007 0.881059i \(-0.343169\pi\)
\(108\) 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 \(-0.310760\pi\)
0.560108 + 0.828420i \(0.310760\pi\)
\(114\) 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 \(0.224788\pi\)
−0.760839 + 0.648941i \(0.775212\pi\)
\(128\) 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 −0.931058 0.364871i \(-0.881113\pi\)
0.781516 + 0.623885i \(0.214447\pi\)
\(138\) 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 −0.983079 0.183180i \(-0.941361\pi\)
0.650178 + 0.759782i \(0.274694\pi\)
\(158\) −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 \(-0.265838\pi\)
0.977603 0.210458i \(-0.0674956\pi\)
\(164\) 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 \(-0.906448\pi\)
0.957120 0.289690i \(-0.0935523\pi\)
\(168\) 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 0.0484252 0.998827i \(-0.484580\pi\)
0.889222 + 0.457476i \(0.151246\pi\)
\(174\) 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 0.422715 0.906263i \(-0.361077\pi\)
−0.573489 + 0.819213i \(0.694411\pi\)
\(194\) 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 \(-0.428593\pi\)
0.222454 + 0.974943i \(0.428593\pi\)
\(198\) 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 \(-0.571037\pi\)
−0.221321 + 0.975201i \(0.571037\pi\)
\(224\) 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 −0.390239 0.920714i \(-0.627608\pi\)
−0.992481 + 0.122400i \(0.960941\pi\)
\(228\) 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 \(0.0906465\pi\)
−0.236560 + 0.971617i \(0.576020\pi\)
\(234\) 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 −0.873818 0.486253i \(-0.838363\pi\)
−0.0158016 + 0.999875i \(0.505030\pi\)
\(258\) 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 −0.939569 0.342361i \(-0.888773\pi\)
0.766278 + 0.642510i \(0.222107\pi\)
\(264\) 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 −0.360415 0.932792i \(-0.617365\pi\)
−0.988029 + 0.154267i \(0.950698\pi\)
\(278\) −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 −0.741092 0.671404i \(-0.765692\pi\)
0.951999 + 0.306103i \(0.0990251\pi\)
\(284\) −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 \(0.0841617\pi\)
−0.965249 + 0.261332i \(0.915838\pi\)
\(294\) 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 \(-0.569828\pi\)
−0.217615 + 0.976035i \(0.569828\pi\)
\(308\) −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 0.709191 0.705016i \(-0.249060\pi\)
−0.965157 + 0.261670i \(0.915727\pi\)
\(314\) −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 \(0.128793\pi\)
−0.118702 + 0.992930i \(0.537873\pi\)
\(318\) 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 \(0.00416970\pi\)
−0.999914 + 0.0130991i \(0.995830\pi\)
\(338\) 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 −0.815588 0.578633i \(-0.803586\pi\)
0.908905 + 0.417004i \(0.136920\pi\)
\(348\) 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 −0.0946235 0.995513i \(-0.530165\pi\)
−0.909451 + 0.415810i \(0.863498\pi\)
\(354\) 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 \(0.349881\pi\)
−0.998649 + 0.0519641i \(0.983452\pi\)
\(368\) 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 −0.531169 0.847266i \(-0.678247\pi\)
0.468169 + 0.883639i \(0.344914\pi\)
\(374\) 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 \(-0.322413\pi\)
0.999412 0.0343009i \(-0.0109205\pi\)
\(384\) 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 0.929588 0.368600i \(-0.120163\pi\)
−0.784011 + 0.620747i \(0.786829\pi\)
\(398\) 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 \(-0.821708\pi\)
−0.847190 + 0.531289i \(0.821708\pi\)
\(434\) −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 \(-0.920006\pi\)
0.268937 0.963158i \(-0.413328\pi\)
\(444\) 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 −0.329720 0.944079i \(-0.606954\pi\)
0.652737 + 0.757585i \(0.273621\pi\)
\(458\) 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 \(-0.865350\pi\)
0.911856 0.410511i \(-0.134650\pi\)
\(464\) −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 0.00913924 0.999958i \(-0.497091\pi\)
0.870559 + 0.492064i \(0.163758\pi\)
\(468\) 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 0.179476 0.983762i \(-0.442560\pi\)
−0.762225 + 0.647312i \(0.775893\pi\)
\(488\) 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 \(-0.961157\pi\)
0.992564 0.121726i \(-0.0388430\pi\)
\(504\) 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 0.863536 0.504288i \(-0.168245\pi\)
−0.868494 + 0.495700i \(0.834912\pi\)
\(524\) 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 \(-0.901503\pi\)
0.952505 0.304524i \(-0.0984972\pi\)
\(548\) −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 −0.593183 0.805068i \(-0.702129\pi\)
0.993801 + 0.111177i \(0.0354622\pi\)
\(558\) 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 −0.437202 0.899363i \(-0.644031\pi\)
−0.997472 + 0.0710537i \(0.977364\pi\)
\(564\) 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 −0.952987 0.303010i \(-0.902008\pi\)
0.738908 + 0.673806i \(0.235342\pi\)
\(578\) −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 \(0.173506\pi\)
−0.855083 + 0.518490i \(0.826494\pi\)
\(588\) 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 −0.309339 0.950952i \(-0.600108\pi\)
0.668879 + 0.743371i \(0.266774\pi\)
\(594\) 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 \(-0.870768\pi\)
0.117334 0.993093i \(-0.462565\pi\)
\(608\) 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 0.768573 0.639762i \(-0.220967\pi\)
−0.169764 + 0.985485i \(0.554301\pi\)
\(614\) −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 \(-0.462740\pi\)
0.116790 + 0.993157i \(0.462740\pi\)
\(618\) 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 \(-0.504153\pi\)
−0.0130470 + 0.999915i \(0.504153\pi\)
\(644\) −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 0.153219 0.988192i \(-0.451036\pi\)
−0.779190 + 0.626787i \(0.784369\pi\)
\(648\) 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 0.984468 0.175562i \(-0.0561744\pi\)
−0.644276 + 0.764793i \(0.722841\pi\)
\(654\) 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 \(0.139356\pi\)
−0.905686 + 0.423949i \(0.860644\pi\)
\(674\) −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 −0.279901 0.960029i \(-0.590302\pi\)
0.691459 + 0.722416i \(0.256968\pi\)
\(678\) 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 \(-0.638901\pi\)
0.996198 0.0871187i \(-0.0277659\pi\)
\(684\) 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 \(-0.314600\pi\)
0.550074 + 0.835116i \(0.314600\pi\)
\(728\) −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 0.996452 0.0841657i \(-0.0268225\pi\)
−0.571116 + 0.820870i \(0.693489\pi\)
\(734\) −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 \(-0.767600\pi\)
−0.745103 + 0.666950i \(0.767600\pi\)
\(744\) 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 \(0.374050\pi\)
−0.385440 + 0.922733i \(0.625950\pi\)
\(758\) −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 \(0.0156425\pi\)
0.541938 + 0.840419i \(0.317691\pi\)
\(774\) 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 −0.939303 0.343090i \(-0.888526\pi\)
0.766776