Properties

Label 804.2.s.b.5.13
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.13
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.429842 - 1.67787i) q^{3} +(-3.03558 + 0.891328i) q^{5} +(-1.25477 - 1.08727i) q^{7} +(-2.63047 - 1.44244i) q^{9} +O(q^{10})\) \(q+(0.429842 - 1.67787i) q^{3} +(-3.03558 + 0.891328i) q^{5} +(-1.25477 - 1.08727i) q^{7} +(-2.63047 - 1.44244i) q^{9} +(1.88696 - 0.554063i) q^{11} +(-0.265744 - 0.413506i) q^{13} +(0.190706 + 5.47644i) q^{15} +(-2.11532 - 0.304138i) q^{17} +(4.38841 + 5.06450i) q^{19} +(-2.36364 + 1.63799i) q^{21} +(-5.82102 + 2.65837i) q^{23} +(4.21404 - 2.70820i) q^{25} +(-3.55090 + 3.79356i) q^{27} +9.06475i q^{29} +(-3.35609 + 5.22218i) q^{31} +(-0.118546 - 3.40423i) q^{33} +(4.77808 + 2.18207i) q^{35} -7.61322 q^{37} +(-0.808036 + 0.268141i) q^{39} +(-0.191141 + 1.32941i) q^{41} +(-3.41972 - 0.491681i) q^{43} +(9.27070 + 2.03402i) q^{45} +(-4.53234 + 2.06985i) q^{47} +(-0.603899 - 4.20021i) q^{49} +(-1.41956 + 3.41850i) q^{51} +(-0.353730 - 2.46024i) q^{53} +(-5.23419 + 3.36381i) q^{55} +(10.3839 - 5.18623i) q^{57} +(1.69949 - 2.64446i) q^{59} +(2.44051 - 8.31163i) q^{61} +(1.73233 + 4.66995i) q^{63} +(1.17526 + 1.01837i) q^{65} +(-8.02999 + 1.58723i) q^{67} +(1.95827 + 10.9096i) q^{69} +(15.3838 - 2.21185i) q^{71} +(5.08429 + 1.49288i) q^{73} +(-2.73262 - 8.23470i) q^{75} +(-2.97012 - 1.35641i) q^{77} +(-1.14758 - 1.78567i) q^{79} +(4.83876 + 7.58857i) q^{81} +(-2.84309 - 9.68269i) q^{83} +(6.69233 - 0.962212i) q^{85} +(15.2094 + 3.89641i) q^{87} +(4.82981 + 2.20570i) q^{89} +(-0.116143 + 0.807790i) q^{91} +(7.31953 + 7.87579i) q^{93} +(-17.8355 - 11.4622i) q^{95} +13.2013i q^{97} +(-5.76280 - 1.26438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

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 0
\(3\) 0.429842 1.67787i 0.248170 0.968717i
\(4\) 0 0
\(5\) −3.03558 + 0.891328i −1.35755 + 0.398614i −0.877900 0.478843i \(-0.841056\pi\)
−0.479655 + 0.877457i \(0.659238\pi\)
\(6\) 0 0
\(7\) −1.25477 1.08727i −0.474259 0.410948i 0.384661 0.923058i \(-0.374318\pi\)
−0.858920 + 0.512110i \(0.828864\pi\)
\(8\) 0 0
\(9\) −2.63047 1.44244i −0.876824 0.480812i
\(10\) 0 0
\(11\) 1.88696 0.554063i 0.568941 0.167056i 0.0154049 0.999881i \(-0.495096\pi\)
0.553536 + 0.832825i \(0.313278\pi\)
\(12\) 0 0
\(13\) −0.265744 0.413506i −0.0737042 0.114686i 0.802445 0.596726i \(-0.203532\pi\)
−0.876149 + 0.482040i \(0.839896\pi\)
\(14\) 0 0
\(15\) 0.190706 + 5.47644i 0.0492402 + 1.41401i
\(16\) 0 0
\(17\) −2.11532 0.304138i −0.513042 0.0737642i −0.119068 0.992886i \(-0.537991\pi\)
−0.393973 + 0.919122i \(0.628900\pi\)
\(18\) 0 0
\(19\) 4.38841 + 5.06450i 1.00677 + 1.16188i 0.986778 + 0.162076i \(0.0518189\pi\)
0.0199928 + 0.999800i \(0.493636\pi\)
\(20\) 0 0
\(21\) −2.36364 + 1.63799i −0.515789 + 0.357438i
\(22\) 0 0
\(23\) −5.82102 + 2.65837i −1.21377 + 0.554309i −0.916327 0.400432i \(-0.868860\pi\)
−0.297440 + 0.954740i \(0.596133\pi\)
\(24\) 0 0
\(25\) 4.21404 2.70820i 0.842809 0.541640i
\(26\) 0 0
\(27\) −3.55090 + 3.79356i −0.683372 + 0.730071i
\(28\) 0 0
\(29\) 9.06475i 1.68328i 0.540038 + 0.841641i \(0.318410\pi\)
−0.540038 + 0.841641i \(0.681590\pi\)
\(30\) 0 0
\(31\) −3.35609 + 5.22218i −0.602772 + 0.937931i 0.397026 + 0.917808i \(0.370042\pi\)
−0.999797 + 0.0201238i \(0.993594\pi\)
\(32\) 0 0
\(33\) −0.118546 3.40423i −0.0206362 0.592601i
\(34\) 0 0
\(35\) 4.77808 + 2.18207i 0.807642 + 0.368838i
\(36\) 0 0
\(37\) −7.61322 −1.25161 −0.625803 0.779981i \(-0.715228\pi\)
−0.625803 + 0.779981i \(0.715228\pi\)
\(38\) 0 0
\(39\) −0.808036 + 0.268141i −0.129389 + 0.0429369i
\(40\) 0 0
\(41\) −0.191141 + 1.32941i −0.0298512 + 0.207619i −0.999288 0.0377203i \(-0.987990\pi\)
0.969437 + 0.245340i \(0.0788995\pi\)
\(42\) 0 0
\(43\) −3.41972 0.491681i −0.521502 0.0749807i −0.123463 0.992349i \(-0.539400\pi\)
−0.398039 + 0.917369i \(0.630309\pi\)
\(44\) 0 0
\(45\) 9.27070 + 2.03402i 1.38199 + 0.303215i
\(46\) 0 0
\(47\) −4.53234 + 2.06985i −0.661110 + 0.301919i −0.717570 0.696486i \(-0.754746\pi\)
0.0564606 + 0.998405i \(0.482018\pi\)
\(48\) 0 0
\(49\) −0.603899 4.20021i −0.0862713 0.600030i
\(50\) 0 0
\(51\) −1.41956 + 3.41850i −0.198778 + 0.478686i
\(52\) 0 0
\(53\) −0.353730 2.46024i −0.0485885 0.337941i −0.999587 0.0287444i \(-0.990849\pi\)
0.950998 0.309196i \(-0.100060\pi\)
\(54\) 0 0
\(55\) −5.23419 + 3.36381i −0.705778 + 0.453576i
\(56\) 0 0
\(57\) 10.3839 5.18623i 1.37538 0.686934i
\(58\) 0 0
\(59\) 1.69949 2.64446i 0.221255 0.344280i −0.712826 0.701341i \(-0.752585\pi\)
0.934081 + 0.357061i \(0.116221\pi\)
\(60\) 0 0
\(61\) 2.44051 8.31163i 0.312476 1.06419i −0.642197 0.766539i \(-0.721977\pi\)
0.954673 0.297656i \(-0.0962047\pi\)
\(62\) 0 0
\(63\) 1.73233 + 4.66995i 0.218253 + 0.588358i
\(64\) 0 0
\(65\) 1.17526 + 1.01837i 0.145773 + 0.126313i
\(66\) 0 0
\(67\) −8.02999 + 1.58723i −0.981019 + 0.193911i
\(68\) 0 0
\(69\) 1.95827 + 10.9096i 0.235748 + 1.31336i
\(70\) 0 0
\(71\) 15.3838 2.21185i 1.82572 0.262499i 0.857840 0.513917i \(-0.171806\pi\)
0.967878 + 0.251419i \(0.0808971\pi\)
\(72\) 0 0
\(73\) 5.08429 + 1.49288i 0.595071 + 0.174729i 0.565380 0.824830i \(-0.308729\pi\)
0.0296911 + 0.999559i \(0.490548\pi\)
\(74\) 0 0
\(75\) −2.73262 8.23470i −0.315536 0.950861i
\(76\) 0 0
\(77\) −2.97012 1.35641i −0.338477 0.154577i
\(78\) 0 0
\(79\) −1.14758 1.78567i −0.129113 0.200904i 0.770678 0.637225i \(-0.219918\pi\)
−0.899791 + 0.436321i \(0.856281\pi\)
\(80\) 0 0
\(81\) 4.83876 + 7.58857i 0.537639 + 0.843175i
\(82\) 0 0
\(83\) −2.84309 9.68269i −0.312070 1.06281i −0.954930 0.296830i \(-0.904071\pi\)
0.642860 0.765984i \(-0.277748\pi\)
\(84\) 0 0
\(85\) 6.69233 0.962212i 0.725886 0.104367i
\(86\) 0 0
\(87\) 15.2094 + 3.89641i 1.63062 + 0.417739i
\(88\) 0 0
\(89\) 4.82981 + 2.20570i 0.511959 + 0.233804i 0.654607 0.755970i \(-0.272834\pi\)
−0.142647 + 0.989774i \(0.545562\pi\)
\(90\) 0 0
\(91\) −0.116143 + 0.807790i −0.0121751 + 0.0846794i
\(92\) 0 0
\(93\) 7.31953 + 7.87579i 0.759000 + 0.816681i
\(94\) 0 0
\(95\) −17.8355 11.4622i −1.82989 1.17600i
\(96\) 0 0
\(97\) 13.2013i 1.34039i 0.742186 + 0.670194i \(0.233789\pi\)
−0.742186 + 0.670194i \(0.766211\pi\)
\(98\) 0 0
\(99\) −5.76280 1.26438i −0.579184 0.127075i
\(100\) 0 0
\(101\) −7.61191 8.78461i −0.757413 0.874102i 0.237852 0.971302i \(-0.423557\pi\)
−0.995265 + 0.0971999i \(0.969011\pi\)
\(102\) 0 0
\(103\) −11.4173 7.33743i −1.12498 0.722978i −0.160471 0.987041i \(-0.551301\pi\)
−0.964506 + 0.264062i \(0.914938\pi\)
\(104\) 0 0
\(105\) 5.71505 7.07903i 0.557732 0.690842i
\(106\) 0 0
\(107\) −0.0498318 + 0.169712i −0.00481742 + 0.0164066i −0.961867 0.273519i \(-0.911812\pi\)
0.957049 + 0.289926i \(0.0936306\pi\)
\(108\) 0 0
\(109\) −8.55064 13.3050i −0.819002 1.27439i −0.958763 0.284207i \(-0.908270\pi\)
0.139761 0.990185i \(-0.455367\pi\)
\(110\) 0 0
\(111\) −3.27248 + 12.7740i −0.310610 + 1.21245i
\(112\) 0 0
\(113\) −2.48008 0.728216i −0.233306 0.0685048i 0.162990 0.986628i \(-0.447886\pi\)
−0.396296 + 0.918123i \(0.629704\pi\)
\(114\) 0 0
\(115\) 15.3007 13.2582i 1.42680 1.23633i
\(116\) 0 0
\(117\) 0.102576 + 1.47103i 0.00948318 + 0.135997i
\(118\) 0 0
\(119\) 2.32357 + 2.68154i 0.213001 + 0.245817i
\(120\) 0 0
\(121\) −6.00014 + 3.85606i −0.545467 + 0.350551i
\(122\) 0 0
\(123\) 2.14842 + 0.892147i 0.193716 + 0.0804422i
\(124\) 0 0
\(125\) −0.0191479 + 0.0220978i −0.00171264 + 0.00197649i
\(126\) 0 0
\(127\) −8.82859 + 10.1887i −0.783411 + 0.904104i −0.997351 0.0727426i \(-0.976825\pi\)
0.213940 + 0.976847i \(0.431370\pi\)
\(128\) 0 0
\(129\) −2.29491 + 5.52648i −0.202056 + 0.486580i
\(130\) 0 0
\(131\) −6.01060 + 2.74495i −0.525149 + 0.239827i −0.660306 0.750997i \(-0.729573\pi\)
0.135157 + 0.990824i \(0.456846\pi\)
\(132\) 0 0
\(133\) 11.1262i 0.964761i
\(134\) 0 0
\(135\) 7.39776 14.6807i 0.636698 1.26351i
\(136\) 0 0
\(137\) 4.98287 + 10.9110i 0.425716 + 0.932187i 0.994003 + 0.109357i \(0.0348791\pi\)
−0.568287 + 0.822830i \(0.692394\pi\)
\(138\) 0 0
\(139\) −1.49570 5.09389i −0.126864 0.432058i 0.871426 0.490528i \(-0.163196\pi\)
−0.998289 + 0.0584699i \(0.981378\pi\)
\(140\) 0 0
\(141\) 1.52474 + 8.49437i 0.128406 + 0.715355i
\(142\) 0 0
\(143\) −0.730558 0.633032i −0.0610923 0.0529368i
\(144\) 0 0
\(145\) −8.07966 27.5168i −0.670980 2.28515i
\(146\) 0 0
\(147\) −7.30697 0.792167i −0.602669 0.0653368i
\(148\) 0 0
\(149\) −6.69588 + 5.80202i −0.548548 + 0.475320i −0.884487 0.466564i \(-0.845492\pi\)
0.335939 + 0.941884i \(0.390946\pi\)
\(150\) 0 0
\(151\) 0.234723 1.63254i 0.0191015 0.132854i −0.978039 0.208421i \(-0.933168\pi\)
0.997141 + 0.0755670i \(0.0240767\pi\)
\(152\) 0 0
\(153\) 5.12560 + 3.85125i 0.414380 + 0.311355i
\(154\) 0 0
\(155\) 5.53302 18.8438i 0.444423 1.51357i
\(156\) 0 0
\(157\) 3.06444 + 6.71020i 0.244569 + 0.535532i 0.991613 0.129243i \(-0.0412547\pi\)
−0.747044 + 0.664775i \(0.768527\pi\)
\(158\) 0 0
\(159\) −4.28001 0.464006i −0.339427 0.0367981i
\(160\) 0 0
\(161\) 10.1944 + 2.99335i 0.803432 + 0.235909i
\(162\) 0 0
\(163\) −18.5314 −1.45149 −0.725745 0.687963i \(-0.758505\pi\)
−0.725745 + 0.687963i \(0.758505\pi\)
\(164\) 0 0
\(165\) 3.39414 + 10.2282i 0.264234 + 0.796262i
\(166\) 0 0
\(167\) −0.789841 + 0.684402i −0.0611198 + 0.0529606i −0.684885 0.728651i \(-0.740148\pi\)
0.623765 + 0.781612i \(0.285602\pi\)
\(168\) 0 0
\(169\) 5.30003 11.6054i 0.407694 0.892726i
\(170\) 0 0
\(171\) −4.23838 19.6520i −0.324117 1.50283i
\(172\) 0 0
\(173\) 5.09001 7.92020i 0.386986 0.602162i −0.592037 0.805911i \(-0.701676\pi\)
0.979023 + 0.203749i \(0.0653125\pi\)
\(174\) 0 0
\(175\) −8.23219 1.18361i −0.622295 0.0894726i
\(176\) 0 0
\(177\) −3.70654 3.98823i −0.278601 0.299773i
\(178\) 0 0
\(179\) −1.21859 + 2.66834i −0.0910818 + 0.199441i −0.949690 0.313191i \(-0.898602\pi\)
0.858609 + 0.512632i \(0.171329\pi\)
\(180\) 0 0
\(181\) 3.89978 + 8.53932i 0.289868 + 0.634723i 0.997408 0.0719506i \(-0.0229224\pi\)
−0.707540 + 0.706673i \(0.750195\pi\)
\(182\) 0 0
\(183\) −12.8968 7.66755i −0.953356 0.566801i
\(184\) 0 0
\(185\) 23.1106 6.78587i 1.69912 0.498907i
\(186\) 0 0
\(187\) −4.16005 + 0.598125i −0.304213 + 0.0437392i
\(188\) 0 0
\(189\) 8.58018 0.899274i 0.624116 0.0654126i
\(190\) 0 0
\(191\) −0.522401 + 1.14390i −0.0377996 + 0.0827696i −0.927590 0.373600i \(-0.878123\pi\)
0.889790 + 0.456370i \(0.150851\pi\)
\(192\) 0 0
\(193\) −2.79049 1.79334i −0.200864 0.129087i 0.436342 0.899781i \(-0.356274\pi\)
−0.637206 + 0.770693i \(0.719910\pi\)
\(194\) 0 0
\(195\) 2.21386 1.53419i 0.158538 0.109866i
\(196\) 0 0
\(197\) 2.73971 + 19.0551i 0.195197 + 1.35762i 0.817989 + 0.575235i \(0.195089\pi\)
−0.622792 + 0.782388i \(0.714002\pi\)
\(198\) 0 0
\(199\) −15.6841 + 18.1004i −1.11181 + 1.28310i −0.156444 + 0.987687i \(0.550003\pi\)
−0.955369 + 0.295414i \(0.904542\pi\)
\(200\) 0 0
\(201\) −0.788472 + 14.1555i −0.0556145 + 0.998452i
\(202\) 0 0
\(203\) 9.85579 11.3742i 0.691741 0.798311i
\(204\) 0 0
\(205\) −0.604719 4.20592i −0.0422354 0.293754i
\(206\) 0 0
\(207\) 19.1466 + 1.40368i 1.33078 + 0.0975627i
\(208\) 0 0
\(209\) 11.0868 + 7.12507i 0.766892 + 0.492851i
\(210\) 0 0
\(211\) 5.24189 11.4781i 0.360867 0.790188i −0.638915 0.769278i \(-0.720616\pi\)
0.999781 0.0209101i \(-0.00665639\pi\)
\(212\) 0 0
\(213\) 2.90141 26.7627i 0.198801 1.83375i
\(214\) 0 0
\(215\) 10.8191 1.55555i 0.737856 0.106088i
\(216\) 0 0
\(217\) 9.88903 2.90368i 0.671311 0.197115i
\(218\) 0 0
\(219\) 4.69030 7.88906i 0.316941 0.533093i
\(220\) 0 0
\(221\) 0.436372 + 0.955522i 0.0293536 + 0.0642754i
\(222\) 0 0
\(223\) −8.49959 + 18.6115i −0.569175 + 1.24632i 0.378061 + 0.925781i \(0.376591\pi\)
−0.947236 + 0.320538i \(0.896136\pi\)
\(224\) 0 0
\(225\) −14.9913 + 1.04536i −0.999422 + 0.0696904i
\(226\) 0 0
\(227\) −0.499215 0.0717763i −0.0331341 0.00476396i 0.125728 0.992065i \(-0.459873\pi\)
−0.158862 + 0.987301i \(0.550782\pi\)
\(228\) 0 0
\(229\) 9.32943 14.5169i 0.616506 0.959302i −0.382864 0.923805i \(-0.625062\pi\)
0.999370 0.0354972i \(-0.0113015\pi\)
\(230\) 0 0
\(231\) −3.55256 + 4.40042i −0.233741 + 0.289527i
\(232\) 0 0
\(233\) 3.47909 7.61814i 0.227923 0.499081i −0.760773 0.649018i \(-0.775180\pi\)
0.988696 + 0.149937i \(0.0479072\pi\)
\(234\) 0 0
\(235\) 11.9134 10.3230i 0.777144 0.673399i
\(236\) 0 0
\(237\) −3.48940 + 1.15793i −0.226661 + 0.0752157i
\(238\) 0 0
\(239\) −22.3180 −1.44363 −0.721814 0.692087i \(-0.756692\pi\)
−0.721814 + 0.692087i \(0.756692\pi\)
\(240\) 0 0
\(241\) 6.56454 + 1.92752i 0.422859 + 0.124163i 0.486237 0.873827i \(-0.338369\pi\)
−0.0633779 + 0.997990i \(0.520187\pi\)
\(242\) 0 0
\(243\) 14.8125 4.85689i 0.950223 0.311570i
\(244\) 0 0
\(245\) 5.57695 + 12.2118i 0.356298 + 0.780185i
\(246\) 0 0
\(247\) 0.928005 3.16050i 0.0590476 0.201098i
\(248\) 0 0
\(249\) −17.4683 + 0.608302i −1.10701 + 0.0385495i
\(250\) 0 0
\(251\) 1.72705 12.0119i 0.109010 0.758183i −0.859845 0.510555i \(-0.829440\pi\)
0.968855 0.247628i \(-0.0796509\pi\)
\(252\) 0 0
\(253\) −9.51115 + 8.24146i −0.597961 + 0.518136i
\(254\) 0 0
\(255\) 1.26219 11.6424i 0.0790411 0.729078i
\(256\) 0 0
\(257\) 4.41723 + 15.0437i 0.275539 + 0.938400i 0.974715 + 0.223451i \(0.0717322\pi\)
−0.699176 + 0.714950i \(0.746450\pi\)
\(258\) 0 0
\(259\) 9.55285 + 8.27759i 0.593585 + 0.514344i
\(260\) 0 0
\(261\) 13.0753 23.8446i 0.809342 1.47594i
\(262\) 0 0
\(263\) 5.74550 + 19.5674i 0.354282 + 1.20658i 0.923245 + 0.384212i \(0.125527\pi\)
−0.568963 + 0.822363i \(0.692655\pi\)
\(264\) 0 0
\(265\) 3.26666 + 7.15299i 0.200669 + 0.439405i
\(266\) 0 0
\(267\) 5.77693 7.15568i 0.353543 0.437920i
\(268\) 0 0
\(269\) 13.4572i 0.820497i −0.911974 0.410249i \(-0.865442\pi\)
0.911974 0.410249i \(-0.134558\pi\)
\(270\) 0 0
\(271\) 29.4231 13.4371i 1.78733 0.816245i 0.816168 0.577815i \(-0.196095\pi\)
0.971160 0.238430i \(-0.0766326\pi\)
\(272\) 0 0
\(273\) 1.30544 + 0.542094i 0.0790089 + 0.0328090i
\(274\) 0 0
\(275\) 6.45123 7.44512i 0.389024 0.448958i
\(276\) 0 0
\(277\) 11.6975 13.4996i 0.702834 0.811114i −0.286298 0.958141i \(-0.592425\pi\)
0.989133 + 0.147026i \(0.0469702\pi\)
\(278\) 0 0
\(279\) 16.3608 8.89585i 0.979493 0.532580i
\(280\) 0 0
\(281\) 19.2147 12.3486i 1.14626 0.736654i 0.177366 0.984145i \(-0.443242\pi\)
0.968890 + 0.247491i \(0.0796061\pi\)
\(282\) 0 0
\(283\) −2.67257 3.08431i −0.158868 0.183343i 0.670735 0.741697i \(-0.265979\pi\)
−0.829603 + 0.558354i \(0.811433\pi\)
\(284\) 0 0
\(285\) −26.8985 + 24.9987i −1.59333 + 1.48080i
\(286\) 0 0
\(287\) 1.68526 1.46029i 0.0994779 0.0861981i
\(288\) 0 0
\(289\) −11.9293 3.50275i −0.701722 0.206044i
\(290\) 0 0
\(291\) 22.1500 + 5.67448i 1.29846 + 0.332644i
\(292\) 0 0
\(293\) −5.44028 8.46524i −0.317825 0.494545i 0.645180 0.764031i \(-0.276782\pi\)
−0.963004 + 0.269486i \(0.913146\pi\)
\(294\) 0 0
\(295\) −2.80187 + 9.54230i −0.163131 + 0.555574i
\(296\) 0 0
\(297\) −4.59856 + 9.12573i −0.266835 + 0.529529i
\(298\) 0 0
\(299\) 2.64615 + 1.70058i 0.153031 + 0.0983471i
\(300\) 0 0
\(301\) 3.75638 + 4.33509i 0.216514 + 0.249870i
\(302\) 0 0
\(303\) −18.0113 + 8.99577i −1.03472 + 0.516793i
\(304\) 0 0
\(305\) 27.4060i 1.56926i
\(306\) 0 0
\(307\) −11.2516 7.23094i −0.642161 0.412692i 0.178633 0.983916i \(-0.442832\pi\)
−0.820794 + 0.571224i \(0.806469\pi\)
\(308\) 0 0
\(309\) −17.2189 + 16.0027i −0.979546 + 0.910362i
\(310\) 0 0
\(311\) −3.74884 + 26.0738i −0.212577 + 1.47851i 0.551928 + 0.833892i \(0.313892\pi\)
−0.764506 + 0.644617i \(0.777017\pi\)
\(312\) 0 0
\(313\) 8.46340 + 3.86511i 0.478380 + 0.218469i 0.639986 0.768387i \(-0.278940\pi\)
−0.161606 + 0.986855i \(0.551667\pi\)
\(314\) 0 0
\(315\) −9.42109 12.6320i −0.530818 0.711730i
\(316\) 0 0
\(317\) −29.9478 + 4.30584i −1.68203 + 0.241840i −0.916063 0.401035i \(-0.868651\pi\)
−0.765971 + 0.642875i \(0.777741\pi\)
\(318\) 0 0
\(319\) 5.02244 + 17.1048i 0.281202 + 0.957688i
\(320\) 0 0
\(321\) 0.263334 + 0.156560i 0.0146978 + 0.00873835i
\(322\) 0 0
\(323\) −7.74261 12.0477i −0.430811 0.670354i
\(324\) 0 0
\(325\) −2.23971 1.02284i −0.124237 0.0567371i
\(326\) 0 0
\(327\) −25.9995 + 8.62775i −1.43778 + 0.477116i
\(328\) 0 0
\(329\) 7.93753 + 2.33067i 0.437610 + 0.128494i
\(330\) 0 0
\(331\) −24.4599 + 3.51681i −1.34444 + 0.193301i −0.776681 0.629894i \(-0.783098\pi\)
−0.567758 + 0.823195i \(0.692189\pi\)
\(332\) 0 0
\(333\) 20.0263 + 10.9816i 1.09744 + 0.601787i
\(334\) 0 0
\(335\) 22.9610 11.9755i 1.25449 0.654293i
\(336\) 0 0
\(337\) −6.09098 5.27786i −0.331797 0.287503i 0.472990 0.881068i \(-0.343175\pi\)
−0.804786 + 0.593565i \(0.797720\pi\)
\(338\) 0 0
\(339\) −2.28789 + 3.84822i −0.124261 + 0.209007i
\(340\) 0 0
\(341\) −3.43941 + 11.7135i −0.186254 + 0.634324i
\(342\) 0 0
\(343\) −10.0924 + 15.7040i −0.544937 + 0.847938i
\(344\) 0 0
\(345\) −15.6685 31.3715i −0.843564 1.68898i
\(346\) 0 0
\(347\) −18.3774 + 11.8104i −0.986551 + 0.634018i −0.931223 0.364450i \(-0.881257\pi\)
−0.0553285 + 0.998468i \(0.517621\pi\)
\(348\) 0 0
\(349\) 3.30080 + 22.9575i 0.176688 + 1.22889i 0.864362 + 0.502870i \(0.167723\pi\)
−0.687674 + 0.726019i \(0.741368\pi\)
\(350\) 0 0
\(351\) 2.51229 + 0.460204i 0.134096 + 0.0245639i
\(352\) 0 0
\(353\) −4.36249 30.3418i −0.232192 1.61493i −0.688588 0.725152i \(-0.741769\pi\)
0.456397 0.889776i \(-0.349140\pi\)
\(354\) 0 0
\(355\) −44.7273 + 20.4263i −2.37388 + 1.08411i
\(356\) 0 0
\(357\) 5.49804 2.74600i 0.290987 0.145334i
\(358\) 0 0
\(359\) −32.0809 4.61254i −1.69317 0.243441i −0.772843 0.634597i \(-0.781166\pi\)
−0.920324 + 0.391156i \(0.872075\pi\)
\(360\) 0 0
\(361\) −3.68700 + 25.6436i −0.194052 + 1.34966i
\(362\) 0 0
\(363\) 3.89083 + 11.7249i 0.204216 + 0.615399i
\(364\) 0 0
\(365\) −16.7644 −0.877491
\(366\) 0 0
\(367\) 20.5231 + 9.37259i 1.07130 + 0.489245i 0.871401 0.490571i \(-0.163212\pi\)
0.199897 + 0.979817i \(0.435939\pi\)
\(368\) 0 0
\(369\) 2.42038 3.22127i 0.126000 0.167693i
\(370\) 0 0
\(371\) −2.23109 + 3.47164i −0.115832 + 0.180239i
\(372\) 0 0
\(373\) 27.4560i 1.42162i −0.703386 0.710808i \(-0.748330\pi\)
0.703386 0.710808i \(-0.251670\pi\)
\(374\) 0 0
\(375\) 0.0288466 + 0.0416262i 0.00148963 + 0.00214957i
\(376\) 0 0
\(377\) 3.74833 2.40890i 0.193049 0.124065i
\(378\) 0 0
\(379\) 24.4741 11.1769i 1.25715 0.574121i 0.328298 0.944574i \(-0.393525\pi\)
0.928851 + 0.370454i \(0.120798\pi\)
\(380\) 0 0
\(381\) 13.3004 + 19.1927i 0.681402 + 0.983274i
\(382\) 0 0
\(383\) −1.40639 1.62306i −0.0718631 0.0829344i 0.718680 0.695341i \(-0.244747\pi\)
−0.790543 + 0.612407i \(0.790201\pi\)
\(384\) 0 0
\(385\) 10.2251 + 1.47014i 0.521117 + 0.0749254i
\(386\) 0 0
\(387\) 8.28625 + 6.22608i 0.421214 + 0.316489i
\(388\) 0 0
\(389\) 13.8927 + 21.6175i 0.704388 + 1.09605i 0.990455 + 0.137839i \(0.0440158\pi\)
−0.286066 + 0.958210i \(0.592348\pi\)
\(390\) 0 0
\(391\) 13.1219 3.85293i 0.663601 0.194851i
\(392\) 0 0
\(393\) 2.02205 + 11.2649i 0.101999 + 0.568238i
\(394\) 0 0
\(395\) 5.07520 + 4.39769i 0.255361 + 0.221272i
\(396\) 0 0
\(397\) −18.8203 + 5.52612i −0.944561 + 0.277348i −0.717521 0.696537i \(-0.754723\pi\)
−0.227041 + 0.973885i \(0.572905\pi\)
\(398\) 0 0
\(399\) −18.6682 4.78250i −0.934580 0.239424i
\(400\) 0 0
\(401\) −35.2908 −1.76234 −0.881169 0.472801i \(-0.843243\pi\)
−0.881169 + 0.472801i \(0.843243\pi\)
\(402\) 0 0
\(403\) 3.05126 0.151994
\(404\) 0 0
\(405\) −21.4524 18.7228i −1.06598 0.930345i
\(406\) 0 0
\(407\) −14.3659 + 4.21820i −0.712089 + 0.209088i
\(408\) 0 0
\(409\) 17.4769 + 15.1438i 0.864178 + 0.748815i 0.969362 0.245638i \(-0.0789975\pi\)
−0.105183 + 0.994453i \(0.533543\pi\)
\(410\) 0 0
\(411\) 20.4490 3.67060i 1.00867 0.181057i
\(412\) 0 0
\(413\) −5.00771 + 1.47040i −0.246413 + 0.0723535i
\(414\) 0 0
\(415\) 17.2609 + 26.8585i 0.847305 + 1.31843i
\(416\) 0 0
\(417\) −9.18978 + 0.320016i −0.450025 + 0.0156713i
\(418\) 0 0
\(419\) −3.08530 0.443600i −0.150727 0.0216713i 0.0665382 0.997784i \(-0.478805\pi\)
−0.217265 + 0.976113i \(0.569714\pi\)
\(420\) 0 0
\(421\) 5.87434 + 6.77935i 0.286298 + 0.330406i 0.880621 0.473821i \(-0.157126\pi\)
−0.594323 + 0.804226i \(0.702580\pi\)
\(422\) 0 0
\(423\) 14.9078 + 1.09293i 0.724843 + 0.0531401i
\(424\) 0 0
\(425\) −9.73773 + 4.44707i −0.472350 + 0.215715i
\(426\) 0 0
\(427\) −12.0992 + 7.77571i −0.585523 + 0.376293i
\(428\) 0 0
\(429\) −1.37617 + 0.953674i −0.0664420 + 0.0460438i
\(430\) 0 0
\(431\) 9.40488i 0.453017i −0.974009 0.226508i \(-0.927269\pi\)
0.974009 0.226508i \(-0.0727311\pi\)
\(432\) 0 0
\(433\) 8.59786 13.3785i 0.413187 0.642931i −0.570817 0.821077i \(-0.693374\pi\)
0.984004 + 0.178146i \(0.0570100\pi\)
\(434\) 0 0
\(435\) −49.6425 + 1.72870i −2.38018 + 0.0828851i
\(436\) 0 0
\(437\) −39.0084 17.8145i −1.86602 0.852184i
\(438\) 0 0
\(439\) 33.0069 1.57533 0.787667 0.616101i \(-0.211289\pi\)
0.787667 + 0.616101i \(0.211289\pi\)
\(440\) 0 0
\(441\) −4.47000 + 11.9196i −0.212857 + 0.567601i
\(442\) 0 0
\(443\) −4.12806 + 28.7113i −0.196130 + 1.36411i 0.619252 + 0.785192i \(0.287436\pi\)
−0.815382 + 0.578923i \(0.803473\pi\)
\(444\) 0 0
\(445\) −16.6273 2.39065i −0.788210 0.113328i
\(446\) 0 0
\(447\) 6.85683 + 13.7287i 0.324317 + 0.649348i
\(448\) 0 0
\(449\) −5.06841 + 2.31467i −0.239193 + 0.109236i −0.531405 0.847118i \(-0.678336\pi\)
0.292212 + 0.956353i \(0.405609\pi\)
\(450\) 0 0
\(451\) 0.375902 + 2.61446i 0.0177005 + 0.123110i
\(452\) 0 0
\(453\) −2.63829 1.09557i −0.123957 0.0514743i
\(454\) 0 0
\(455\) −0.367445 2.55564i −0.0172261 0.119810i
\(456\) 0 0
\(457\) 27.5754 17.7216i 1.28992 0.828982i 0.297844 0.954615i \(-0.403732\pi\)
0.992077 + 0.125633i \(0.0400961\pi\)
\(458\) 0 0
\(459\) 8.66508 6.94464i 0.404451 0.324148i
\(460\) 0 0
\(461\) 10.4093 16.1972i 0.484810 0.754379i −0.509549 0.860441i \(-0.670188\pi\)
0.994360 + 0.106062i \(0.0338242\pi\)
\(462\) 0 0
\(463\) 3.57771 12.1846i 0.166270 0.566265i −0.833632 0.552320i \(-0.813743\pi\)
0.999903 0.0139452i \(-0.00443904\pi\)
\(464\) 0 0
\(465\) −29.2390 17.3835i −1.35592 0.806141i
\(466\) 0 0
\(467\) −9.15972 7.93694i −0.423861 0.367278i 0.416654 0.909065i \(-0.363203\pi\)
−0.840516 + 0.541787i \(0.817748\pi\)
\(468\) 0 0
\(469\) 11.8015 + 6.73912i 0.544944 + 0.311184i
\(470\) 0 0
\(471\) 12.5760 2.25740i 0.579473 0.104016i
\(472\) 0 0
\(473\) −6.72530 + 0.966953i −0.309230 + 0.0444605i
\(474\) 0 0
\(475\) 32.2086 + 9.45731i 1.47783 + 0.433931i
\(476\) 0 0
\(477\) −2.61827 + 6.98184i −0.119882 + 0.319676i
\(478\) 0 0
\(479\) −10.5795 4.83151i −0.483391 0.220757i 0.158787 0.987313i \(-0.449242\pi\)
−0.642178 + 0.766556i \(0.721969\pi\)
\(480\) 0 0
\(481\) 2.02317 + 3.14811i 0.0922485 + 0.143541i
\(482\) 0 0
\(483\) 9.40443 15.8182i 0.427916 0.719752i
\(484\) 0 0
\(485\) −11.7667 40.0736i −0.534298 1.81965i
\(486\) 0 0
\(487\) 19.4795 2.80073i 0.882702 0.126913i 0.313967 0.949434i \(-0.398342\pi\)
0.568735 + 0.822521i \(0.307433\pi\)
\(488\) 0 0
\(489\) −7.96558 + 31.0932i −0.360216 + 1.40608i
\(490\) 0 0
\(491\) 13.2953 + 6.07174i 0.600006 + 0.274014i 0.692175 0.721730i \(-0.256653\pi\)
−0.0921686 + 0.995743i \(0.529380\pi\)
\(492\) 0 0
\(493\) 2.75693 19.1749i 0.124166 0.863593i
\(494\) 0 0
\(495\) 18.6205 1.29842i 0.836927 0.0583595i
\(496\) 0 0
\(497\) −21.7080 13.9509i −0.973737 0.625783i
\(498\) 0 0
\(499\) 28.0049i 1.25367i 0.779152 + 0.626835i \(0.215650\pi\)
−0.779152 + 0.626835i \(0.784350\pi\)
\(500\) 0 0
\(501\) 0.808827 + 1.61943i 0.0361357 + 0.0723509i
\(502\) 0 0
\(503\) 19.7335 + 22.7737i 0.879874 + 1.01543i 0.999744 + 0.0226388i \(0.00720677\pi\)
−0.119870 + 0.992790i \(0.538248\pi\)
\(504\) 0 0
\(505\) 30.9366 + 19.8817i 1.37666 + 0.884725i
\(506\) 0 0
\(507\) −17.1942 13.8812i −0.763621 0.616488i
\(508\) 0 0
\(509\) 9.53776 32.4826i 0.422754 1.43977i −0.422969 0.906144i \(-0.639012\pi\)
0.845723 0.533622i \(-0.179170\pi\)
\(510\) 0 0
\(511\) −4.75646 7.40120i −0.210414 0.327410i
\(512\) 0 0
\(513\) −34.7953 1.33584i −1.53625 0.0589789i
\(514\) 0 0
\(515\) 41.1981 + 12.0969i 1.81541 + 0.533051i
\(516\) 0 0
\(517\) −7.40553 + 6.41693i −0.325695 + 0.282216i
\(518\) 0 0
\(519\) −11.1011 11.9448i −0.487286 0.524318i
\(520\) 0 0
\(521\) 1.50801 + 1.74034i 0.0660672 + 0.0762457i 0.787821 0.615904i \(-0.211209\pi\)
−0.721754 + 0.692150i \(0.756664\pi\)
\(522\) 0 0
\(523\) −17.2890 + 11.1110i −0.755994 + 0.485848i −0.860988 0.508625i \(-0.830154\pi\)
0.104994 + 0.994473i \(0.466518\pi\)
\(524\) 0 0
\(525\) −5.52449 + 13.3038i −0.241108 + 0.580624i
\(526\) 0 0
\(527\) 8.68749 10.0259i 0.378433 0.436735i
\(528\) 0 0
\(529\) 11.7555 13.5666i 0.511111 0.589853i
\(530\) 0 0
\(531\) −8.28494 + 4.50477i −0.359536 + 0.195491i
\(532\) 0 0
\(533\) 0.600515 0.274246i 0.0260112 0.0118789i
\(534\) 0 0
\(535\) 0.559590i 0.0241932i
\(536\) 0 0
\(537\) 3.95332 + 3.19160i 0.170598 + 0.137728i
\(538\) 0 0
\(539\) −3.46671 7.59105i −0.149322 0.326969i
\(540\) 0 0
\(541\) 4.57439 + 15.5790i 0.196669 + 0.669792i 0.997485 + 0.0708815i \(0.0225812\pi\)
−0.800816 + 0.598910i \(0.795601\pi\)
\(542\) 0 0
\(543\) 16.0041 2.87274i 0.686803 0.123281i
\(544\) 0 0
\(545\) 37.8153 + 32.7672i 1.61983 + 1.40359i
\(546\) 0 0
\(547\) −0.529705 1.80401i −0.0226485 0.0771338i 0.947393 0.320072i \(-0.103707\pi\)
−0.970042 + 0.242938i \(0.921889\pi\)
\(548\) 0 0
\(549\) −18.4087 + 18.3432i −0.785664 + 0.782869i
\(550\) 0 0
\(551\) −45.9084 + 39.7799i −1.95576 + 1.69468i
\(552\) 0 0
\(553\) −0.501547 + 3.48834i −0.0213280 + 0.148339i
\(554\) 0 0
\(555\) −1.45189 41.6933i −0.0616293 1.76978i
\(556\) 0 0
\(557\) 6.93447 23.6166i 0.293823 1.00067i −0.671802 0.740731i \(-0.734479\pi\)
0.965625 0.259939i \(-0.0837024\pi\)
\(558\) 0 0
\(559\) 0.705457 + 1.54473i 0.0298376 + 0.0653353i
\(560\) 0 0
\(561\) −0.784593 + 7.23711i −0.0331255 + 0.305551i
\(562\) 0 0
\(563\) 33.1018 + 9.71955i 1.39507 + 0.409630i 0.890989 0.454025i \(-0.150012\pi\)
0.504083 + 0.863655i \(0.331830\pi\)
\(564\) 0 0
\(565\) 8.17756 0.344033
\(566\) 0 0
\(567\) 2.17926 14.7829i 0.0915204 0.620825i
\(568\) 0 0
\(569\) 24.9932 21.6567i 1.04777 0.907897i 0.0518959 0.998653i \(-0.483474\pi\)
0.995873 + 0.0907554i \(0.0289282\pi\)
\(570\) 0 0
\(571\) −14.8373 + 32.4892i −0.620922 + 1.35963i 0.293925 + 0.955828i \(0.405038\pi\)
−0.914847 + 0.403800i \(0.867689\pi\)
\(572\) 0 0
\(573\) 1.69476 + 1.36821i 0.0707995 + 0.0571580i
\(574\) 0 0
\(575\) −17.3306 + 26.9670i −0.722737 + 1.12460i
\(576\) 0 0
\(577\) 9.17105 + 1.31860i 0.381796 + 0.0548940i 0.330541 0.943792i \(-0.392769\pi\)
0.0512549 + 0.998686i \(0.483678\pi\)
\(578\) 0 0
\(579\) −4.20846 + 3.91122i −0.174898 + 0.162545i
\(580\) 0 0
\(581\) −6.96022 + 15.2408i −0.288759 + 0.632294i
\(582\) 0 0
\(583\) −2.03060 4.44640i −0.0840991 0.184151i
\(584\) 0 0
\(585\) −1.62255 4.37402i −0.0670843 0.180843i
\(586\) 0 0
\(587\) −16.8520 + 4.94820i −0.695557 + 0.204234i −0.610353 0.792130i \(-0.708972\pi\)
−0.0852039 + 0.996364i \(0.527154\pi\)
\(588\) 0 0
\(589\) −41.1756 + 5.92016i −1.69661 + 0.243936i
\(590\) 0 0
\(591\) 33.1496 + 3.59383i 1.36359 + 0.147830i
\(592\) 0 0
\(593\) 1.40647 3.07974i 0.0577569 0.126470i −0.878553 0.477645i \(-0.841491\pi\)
0.936310 + 0.351175i \(0.114218\pi\)
\(594\) 0 0
\(595\) −9.44353 6.06899i −0.387147 0.248804i
\(596\) 0 0
\(597\) 23.6283 + 34.0961i 0.967043 + 1.39546i
\(598\) 0 0
\(599\) 1.19705 + 8.32568i 0.0489102 + 0.340178i 0.999553 + 0.0298910i \(0.00951603\pi\)
−0.950643 + 0.310287i \(0.899575\pi\)
\(600\) 0 0
\(601\) 6.82435 7.87571i 0.278371 0.321257i −0.599297 0.800527i \(-0.704553\pi\)
0.877668 + 0.479270i \(0.159098\pi\)
\(602\) 0 0
\(603\) 23.4121 + 7.40759i 0.953415 + 0.301660i
\(604\) 0 0
\(605\) 14.7769 17.0535i 0.600768 0.693323i
\(606\) 0 0
\(607\) 3.16796 + 22.0337i 0.128584 + 0.894319i 0.947352 + 0.320194i \(0.103748\pi\)
−0.818768 + 0.574124i \(0.805343\pi\)
\(608\) 0 0
\(609\) −14.8479 21.4258i −0.601668 0.868217i
\(610\) 0 0
\(611\) 2.06034 + 1.32410i 0.0833523 + 0.0535673i
\(612\) 0 0
\(613\) −4.49055 + 9.83293i −0.181372 + 0.397148i −0.978379 0.206822i \(-0.933688\pi\)
0.797007 + 0.603970i \(0.206415\pi\)
\(614\) 0 0
\(615\) −7.31690 0.793243i −0.295046 0.0319866i
\(616\) 0 0
\(617\) 26.6415 3.83047i 1.07255 0.154209i 0.416655 0.909065i \(-0.363202\pi\)
0.655891 + 0.754856i \(0.272293\pi\)
\(618\) 0 0
\(619\) 10.5222 3.08959i 0.422922 0.124181i −0.0633442 0.997992i \(-0.520177\pi\)
0.486266 + 0.873811i \(0.338358\pi\)
\(620\) 0 0
\(621\) 10.5852 31.5220i 0.424769 1.26493i
\(622\) 0 0
\(623\) −3.66213 8.01894i −0.146720 0.321272i
\(624\) 0 0
\(625\) −10.3661 + 22.6987i −0.414646 + 0.907948i
\(626\) 0 0
\(627\) 16.7205 15.5396i 0.667753 0.620590i
\(628\) 0 0
\(629\) 16.1044 + 2.31547i 0.642126 + 0.0923237i
\(630\) 0 0
\(631\) 3.61806 5.62981i 0.144033 0.224119i −0.761740 0.647882i \(-0.775655\pi\)
0.905773 + 0.423763i \(0.139291\pi\)
\(632\) 0 0
\(633\) −17.0056 13.7290i −0.675912 0.545678i
\(634\) 0 0
\(635\) 17.7184 38.7979i 0.703134 1.53965i
\(636\) 0 0
\(637\) −1.57633 + 1.36590i −0.0624564 + 0.0541188i
\(638\) 0 0
\(639\) −43.6570 16.3719i −1.72705 0.647662i
\(640\) 0 0
\(641\) −38.4911 −1.52031 −0.760153 0.649744i \(-0.774876\pi\)
−0.760153 + 0.649744i \(0.774876\pi\)
\(642\) 0 0
\(643\) −17.8153 5.23103i −0.702565 0.206292i −0.0891106 0.996022i \(-0.528402\pi\)
−0.613455 + 0.789730i \(0.710221\pi\)
\(644\) 0 0
\(645\) 2.04050 18.8216i 0.0803445 0.741101i
\(646\) 0 0
\(647\) 6.81847 + 14.9304i 0.268062 + 0.586973i 0.995016 0.0997123i \(-0.0317923\pi\)
−0.726955 + 0.686685i \(0.759065\pi\)
\(648\) 0 0
\(649\) 1.74168 5.93163i 0.0683671 0.232837i
\(650\) 0 0
\(651\) −0.621264 17.8406i −0.0243493 0.699228i
\(652\) 0 0
\(653\) 2.92846 20.3679i 0.114599 0.797056i −0.848748 0.528798i \(-0.822643\pi\)
0.963347 0.268258i \(-0.0864480\pi\)
\(654\) 0 0
\(655\) 15.7990 13.6899i 0.617320 0.534911i
\(656\) 0 0
\(657\) −11.2207 11.2608i −0.437761 0.439324i
\(658\) 0 0
\(659\) 7.65218 + 26.0609i 0.298087 + 1.01519i 0.963276 + 0.268515i \(0.0865328\pi\)
−0.665189 + 0.746675i \(0.731649\pi\)
\(660\) 0 0
\(661\) −0.502433 0.435361i −0.0195424 0.0169336i 0.645035 0.764153i \(-0.276843\pi\)
−0.664577 + 0.747220i \(0.731388\pi\)
\(662\) 0 0
\(663\) 1.79081 0.321451i 0.0695493 0.0124841i
\(664\) 0 0
\(665\) 9.91706 + 33.7744i 0.384567 + 1.30972i
\(666\) 0 0
\(667\) −24.0975 52.7661i −0.933057 2.04311i
\(668\) 0 0
\(669\) 27.5741 + 22.2612i 1.06608 + 0.860667i
\(670\) 0 0
\(671\) 17.0359i 0.657665i
\(672\) 0 0
\(673\) −25.8441 + 11.8026i −0.996218 + 0.454958i −0.845705 0.533650i \(-0.820820\pi\)
−0.150513 + 0.988608i \(0.548093\pi\)
\(674\) 0 0
\(675\) −4.68994 + 25.6028i −0.180516 + 0.985451i
\(676\) 0 0
\(677\) 16.5731 19.1264i 0.636956 0.735086i −0.341878 0.939744i \(-0.611063\pi\)
0.978834 + 0.204658i \(0.0656083\pi\)
\(678\) 0 0
\(679\) 14.3533 16.5646i 0.550830 0.635691i
\(680\) 0 0
\(681\) −0.335015 + 0.806763i −0.0128378 + 0.0309152i
\(682\) 0 0
\(683\) 8.34714 5.36438i 0.319395 0.205262i −0.371113 0.928588i \(-0.621024\pi\)
0.690507 + 0.723325i \(0.257387\pi\)
\(684\) 0 0
\(685\) −24.8512 28.6798i −0.949515 1.09580i
\(686\) 0 0
\(687\) −20.3472 21.8935i −0.776294 0.835289i
\(688\) 0 0
\(689\) −0.923324 + 0.800065i −0.0351758 + 0.0304800i
\(690\) 0 0
\(691\) 34.4370 + 10.1116i 1.31005 + 0.384664i 0.860891 0.508789i \(-0.169907\pi\)
0.449156 + 0.893454i \(0.351725\pi\)
\(692\) 0 0
\(693\) 5.85629 + 7.85221i 0.222462 + 0.298281i
\(694\) 0 0
\(695\) 9.08065 + 14.1298i 0.344449 + 0.535973i
\(696\) 0 0
\(697\) 0.808649 2.75401i 0.0306298 0.104315i
\(698\) 0 0
\(699\) −11.2868 9.11204i −0.426904 0.344649i
\(700\) 0 0
\(701\) 16.4770 + 10.5891i 0.622329 + 0.399946i 0.813462 0.581618i \(-0.197580\pi\)
−0.191134 + 0.981564i \(0.561216\pi\)
\(702\) 0 0
\(703\) −33.4099 38.5571i −1.26008 1.45421i
\(704\) 0 0
\(705\) −12.1997 24.4263i −0.459469 0.919949i
\(706\) 0 0
\(707\) 19.2989i 0.725808i
\(708\) 0 0
\(709\) −1.83525 1.17944i −0.0689242 0.0442949i 0.505725 0.862695i \(-0.331225\pi\)
−0.574649 + 0.818400i \(0.694861\pi\)
\(710\) 0 0
\(711\) 0.442963 + 6.35247i 0.0166124 + 0.238236i
\(712\) 0 0
\(713\) 5.65338 39.3202i 0.211721 1.47255i
\(714\) 0 0
\(715\) 2.78191 + 1.27046i 0.104037 + 0.0475123i
\(716\) 0 0
\(717\) −9.59320 + 37.4465i −0.358265 + 1.39847i
\(718\) 0 0
\(719\) −38.6622 + 5.55878i −1.44186 + 0.207308i −0.818444 0.574586i \(-0.805163\pi\)
−0.623412 + 0.781893i \(0.714254\pi\)
\(720\) 0 0
\(721\) 6.34832 + 21.6204i 0.236424 + 0.805186i
\(722\) 0 0
\(723\) 6.05584 10.1859i 0.225219 0.378817i
\(724\) 0 0
\(725\) 24.5492 + 38.1992i 0.911733 + 1.41868i
\(726\) 0 0
\(727\) 32.1464 + 14.6808i 1.19224 + 0.544480i 0.909898 0.414833i \(-0.136160\pi\)
0.282346 + 0.959313i \(0.408887\pi\)
\(728\) 0 0
\(729\) −1.78217 26.9411i −0.0660064 0.997819i
\(730\) 0 0
\(731\) 7.08427 + 2.08013i 0.262021 + 0.0769364i
\(732\) 0 0
\(733\) 38.3382 5.51219i 1.41605 0.203598i 0.608575 0.793496i \(-0.291742\pi\)
0.807477 + 0.589899i \(0.200832\pi\)
\(734\) 0 0
\(735\) 22.8870 4.10822i 0.844200 0.151534i
\(736\) 0 0
\(737\) −14.2729 + 7.44416i −0.525748 + 0.274209i
\(738\) 0 0
\(739\) −29.6209 25.6666i −1.08962 0.944162i −0.0909584 0.995855i \(-0.528993\pi\)
−0.998663 + 0.0516923i \(0.983538\pi\)
\(740\) 0 0
\(741\) −4.90399 2.91558i −0.180153 0.107107i
\(742\) 0 0
\(743\) 1.52119 5.18069i 0.0558070 0.190061i −0.926872 0.375378i \(-0.877513\pi\)
0.982679 + 0.185317i \(0.0593311\pi\)
\(744\) 0 0
\(745\) 15.1544 23.5807i 0.555215 0.863931i
\(746\) 0 0
\(747\) −6.48799 + 29.5710i −0.237383 + 1.08195i
\(748\) 0 0
\(749\) 0.247049 0.158769i 0.00902698 0.00580129i
\(750\) 0 0
\(751\) 1.94020 + 13.4944i 0.0707988 + 0.492416i 0.994111 + 0.108366i \(0.0345619\pi\)
−0.923312 + 0.384050i \(0.874529\pi\)
\(752\) 0 0
\(753\) −19.4120 8.06096i −0.707411 0.293758i
\(754\) 0 0
\(755\) 0.742604 + 5.16492i 0.0270261 + 0.187971i
\(756\) 0 0
\(757\) −25.7166 + 11.7444i −0.934685 + 0.426857i −0.823739 0.566970i \(-0.808116\pi\)
−0.110947 + 0.993826i \(0.535388\pi\)
\(758\) 0 0
\(759\) 9.73977 + 19.5010i 0.353531 + 0.707840i
\(760\) 0 0
\(761\) 23.0095 + 3.30826i 0.834093 + 0.119924i 0.546113 0.837712i \(-0.316107\pi\)
0.287980 + 0.957636i \(0.407016\pi\)
\(762\) 0 0
\(763\) −3.73703 + 25.9916i −0.135290 + 0.940959i
\(764\) 0 0
\(765\) −18.9919 7.12219i −0.686654 0.257503i
\(766\) 0 0
\(767\) −1.54513 −0.0557915
\(768\) 0 0
\(769\) 27.0155 + 12.3376i 0.974203 + 0.444904i 0.837936 0.545769i \(-0.183762\pi\)
0.136267 + 0.990672i \(0.456490\pi\)
\(770\) 0 0
\(771\) 27.1400 0.945100i 0.977424 0.0340369i
\(772\) 0 0
\(773\) 20.4015 31.7453i 0.733791 1.14180i −0.250988 0.967990i \(-0.580756\pi\)
0.984779 0.173811i \(-0.0556080\pi\)
\(774\) 0 0
\(775\) 31.0955i 1.11698i
\(776\) 0 0
\(777\)