Properties

Label 252.2.w.a.5.1
Level $252$
Weight $2$
Character 252.5
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.w (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.1
Root \(1.08696 + 1.34852i\) of defining polynomial
Character \(\chi\) \(=\) 252.5
Dual form 252.2.w.a.101.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.63336 + 0.576322i) q^{3} +(0.0382122 + 0.0661855i) q^{5} +(0.232935 - 2.63548i) q^{7} +(2.33571 - 1.88268i) q^{9} +O(q^{10})\) \(q+(-1.63336 + 0.576322i) q^{3} +(0.0382122 + 0.0661855i) q^{5} +(0.232935 - 2.63548i) q^{7} +(2.33571 - 1.88268i) q^{9} +(4.66300 + 2.69219i) q^{11} +(4.60313 + 2.65762i) q^{13} +(-0.100558 - 0.0860820i) q^{15} +(1.89092 + 3.27516i) q^{17} +(-4.33939 - 2.50535i) q^{19} +(1.13842 + 4.43892i) q^{21} +(-2.02463 + 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} +(-2.73001 + 4.42120i) q^{27} +(8.84430 - 5.10626i) q^{29} -5.74620i q^{31} +(-9.16791 - 1.70991i) q^{33} +(0.183331 - 0.0852905i) q^{35} +(0.354486 - 0.613988i) q^{37} +(-9.05019 - 1.68795i) q^{39} +(-3.29910 + 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(0.213859 + 0.0826487i) q^{45} -2.92385 q^{47} +(-6.89148 - 1.22779i) q^{49} +(-4.97609 - 4.25973i) q^{51} +(-10.4835 + 6.05264i) q^{53} +0.411498i q^{55} +(8.53166 + 1.59124i) q^{57} -0.579903 q^{59} -2.77868i q^{61} +(-4.41768 - 6.59424i) q^{63} +0.406214i q^{65} +5.27185 q^{67} +(2.63327 - 3.07610i) q^{69} +3.32103i q^{71} +(-6.17326 + 3.56413i) q^{73} +(-1.58599 + 8.50350i) q^{75} +(8.18137 - 11.6621i) q^{77} +0.938245 q^{79} +(1.91105 - 8.79476i) q^{81} +(6.49790 + 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(-11.5031 + 13.4375i) q^{87} +(1.51794 - 2.62915i) q^{89} +(8.07632 - 11.5124i) q^{91} +(3.31166 + 9.38560i) q^{93} -0.382940i q^{95} +(-6.18183 + 3.56908i) q^{97} +(15.9599 - 2.49077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{7} + 6 q^{9} + O(q^{10}) \) \( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.63336 + 0.576322i −0.943019 + 0.332739i
\(4\) 0 0
\(5\) 0.0382122 + 0.0661855i 0.0170890 + 0.0295991i 0.874443 0.485127i \(-0.161227\pi\)
−0.857354 + 0.514727i \(0.827893\pi\)
\(6\) 0 0
\(7\) 0.232935 2.63548i 0.0880412 0.996117i
\(8\) 0 0
\(9\) 2.33571 1.88268i 0.778569 0.627559i
\(10\) 0 0
\(11\) 4.66300 + 2.69219i 1.40595 + 0.811725i 0.994994 0.0999316i \(-0.0318624\pi\)
0.410954 + 0.911656i \(0.365196\pi\)
\(12\) 0 0
\(13\) 4.60313 + 2.65762i 1.27668 + 0.737091i 0.976236 0.216709i \(-0.0695324\pi\)
0.300442 + 0.953800i \(0.402866\pi\)
\(14\) 0 0
\(15\) −0.100558 0.0860820i −0.0259641 0.0222263i
\(16\) 0 0
\(17\) 1.89092 + 3.27516i 0.458615 + 0.794344i 0.998888 0.0471458i \(-0.0150125\pi\)
−0.540273 + 0.841490i \(0.681679\pi\)
\(18\) 0 0
\(19\) −4.33939 2.50535i −0.995525 0.574767i −0.0886040 0.996067i \(-0.528241\pi\)
−0.906921 + 0.421300i \(0.861574\pi\)
\(20\) 0 0
\(21\) 1.13842 + 4.43892i 0.248423 + 0.968652i
\(22\) 0 0
\(23\) −2.02463 + 1.16892i −0.422164 + 0.243737i −0.696003 0.718039i \(-0.745040\pi\)
0.273839 + 0.961776i \(0.411707\pi\)
\(24\) 0 0
\(25\) 2.49708 4.32507i 0.499416 0.865014i
\(26\) 0 0
\(27\) −2.73001 + 4.42120i −0.525392 + 0.850861i
\(28\) 0 0
\(29\) 8.84430 5.10626i 1.64235 0.948209i 0.662349 0.749196i \(-0.269560\pi\)
0.979997 0.199013i \(-0.0637736\pi\)
\(30\) 0 0
\(31\) 5.74620i 1.03205i −0.856574 0.516024i \(-0.827411\pi\)
0.856574 0.516024i \(-0.172589\pi\)
\(32\) 0 0
\(33\) −9.16791 1.70991i −1.59593 0.297657i
\(34\) 0 0
\(35\) 0.183331 0.0852905i 0.0309887 0.0144167i
\(36\) 0 0
\(37\) 0.354486 0.613988i 0.0582771 0.100939i −0.835415 0.549620i \(-0.814773\pi\)
0.893692 + 0.448681i \(0.148106\pi\)
\(38\) 0 0
\(39\) −9.05019 1.68795i −1.44919 0.270289i
\(40\) 0 0
\(41\) −3.29910 + 5.71422i −0.515234 + 0.892411i 0.484610 + 0.874730i \(0.338961\pi\)
−0.999844 + 0.0176805i \(0.994372\pi\)
\(42\) 0 0
\(43\) 0.716520 + 1.24105i 0.109268 + 0.189258i 0.915474 0.402377i \(-0.131816\pi\)
−0.806206 + 0.591635i \(0.798483\pi\)
\(44\) 0 0
\(45\) 0.213859 + 0.0826487i 0.0318802 + 0.0123205i
\(46\) 0 0
\(47\) −2.92385 −0.426487 −0.213244 0.976999i \(-0.568403\pi\)
−0.213244 + 0.976999i \(0.568403\pi\)
\(48\) 0 0
\(49\) −6.89148 1.22779i −0.984497 0.175399i
\(50\) 0 0
\(51\) −4.97609 4.25973i −0.696792 0.596482i
\(52\) 0 0
\(53\) −10.4835 + 6.05264i −1.44002 + 0.831394i −0.997850 0.0655390i \(-0.979123\pi\)
−0.442167 + 0.896933i \(0.645790\pi\)
\(54\) 0 0
\(55\) 0.411498i 0.0554863i
\(56\) 0 0
\(57\) 8.53166 + 1.59124i 1.13005 + 0.210765i
\(58\) 0 0
\(59\) −0.579903 −0.0754969 −0.0377484 0.999287i \(-0.512019\pi\)
−0.0377484 + 0.999287i \(0.512019\pi\)
\(60\) 0 0
\(61\) 2.77868i 0.355773i −0.984051 0.177887i \(-0.943074\pi\)
0.984051 0.177887i \(-0.0569261\pi\)
\(62\) 0 0
\(63\) −4.41768 6.59424i −0.556576 0.830797i
\(64\) 0 0
\(65\) 0.406214i 0.0503847i
\(66\) 0 0
\(67\) 5.27185 0.644059 0.322030 0.946730i \(-0.395635\pi\)
0.322030 + 0.946730i \(0.395635\pi\)
\(68\) 0 0
\(69\) 2.63327 3.07610i 0.317008 0.370319i
\(70\) 0 0
\(71\) 3.32103i 0.394134i 0.980390 + 0.197067i \(0.0631416\pi\)
−0.980390 + 0.197067i \(0.936858\pi\)
\(72\) 0 0
\(73\) −6.17326 + 3.56413i −0.722525 + 0.417150i −0.815681 0.578502i \(-0.803638\pi\)
0.0931564 + 0.995651i \(0.470304\pi\)
\(74\) 0 0
\(75\) −1.58599 + 8.50350i −0.183134 + 0.981900i
\(76\) 0 0
\(77\) 8.18137 11.6621i 0.932354 1.32902i
\(78\) 0 0
\(79\) 0.938245 0.105561 0.0527804 0.998606i \(-0.483192\pi\)
0.0527804 + 0.998606i \(0.483192\pi\)
\(80\) 0 0
\(81\) 1.91105 8.79476i 0.212339 0.977196i
\(82\) 0 0
\(83\) 6.49790 + 11.2547i 0.713238 + 1.23536i 0.963635 + 0.267221i \(0.0861053\pi\)
−0.250398 + 0.968143i \(0.580561\pi\)
\(84\) 0 0
\(85\) −0.144512 + 0.250303i −0.0156746 + 0.0271491i
\(86\) 0 0
\(87\) −11.5031 + 13.4375i −1.23326 + 1.44065i
\(88\) 0 0
\(89\) 1.51794 2.62915i 0.160901 0.278689i −0.774291 0.632830i \(-0.781893\pi\)
0.935192 + 0.354141i \(0.115227\pi\)
\(90\) 0 0
\(91\) 8.07632 11.5124i 0.846629 1.20683i
\(92\) 0 0
\(93\) 3.31166 + 9.38560i 0.343403 + 0.973241i
\(94\) 0 0
\(95\) 0.382940i 0.0392888i
\(96\) 0 0
\(97\) −6.18183 + 3.56908i −0.627670 + 0.362385i −0.779849 0.625967i \(-0.784704\pi\)
0.152179 + 0.988353i \(0.451371\pi\)
\(98\) 0 0
\(99\) 15.9599 2.49077i 1.60403 0.250332i
\(100\) 0 0
\(101\) 4.08628 7.07765i 0.406600 0.704252i −0.587906 0.808929i \(-0.700048\pi\)
0.994506 + 0.104677i \(0.0333808\pi\)
\(102\) 0 0
\(103\) −6.46599 + 3.73314i −0.637113 + 0.367837i −0.783502 0.621390i \(-0.786568\pi\)
0.146389 + 0.989227i \(0.453235\pi\)
\(104\) 0 0
\(105\) −0.250291 + 0.244968i −0.0244259 + 0.0239064i
\(106\) 0 0
\(107\) −3.99991 2.30935i −0.386686 0.223253i 0.294037 0.955794i \(-0.405001\pi\)
−0.680723 + 0.732541i \(0.738334\pi\)
\(108\) 0 0
\(109\) 5.22792 + 9.05503i 0.500744 + 0.867314i 1.00000 0.000859385i \(0.000273551\pi\)
−0.499256 + 0.866455i \(0.666393\pi\)
\(110\) 0 0
\(111\) −0.225148 + 1.20716i −0.0213701 + 0.114578i
\(112\) 0 0
\(113\) −16.6379 9.60591i −1.56516 0.903648i −0.996720 0.0809270i \(-0.974212\pi\)
−0.568445 0.822721i \(-0.692455\pi\)
\(114\) 0 0
\(115\) −0.154731 0.0893340i −0.0144287 0.00833044i
\(116\) 0 0
\(117\) 15.7550 2.45879i 1.45655 0.227315i
\(118\) 0 0
\(119\) 9.07208 4.22057i 0.831636 0.386899i
\(120\) 0 0
\(121\) 8.99573 + 15.5811i 0.817793 + 1.41646i
\(122\) 0 0
\(123\) 2.09539 11.2347i 0.188935 1.01300i
\(124\) 0 0
\(125\) 0.763798 0.0683162
\(126\) 0 0
\(127\) 1.26488 0.112240 0.0561198 0.998424i \(-0.482127\pi\)
0.0561198 + 0.998424i \(0.482127\pi\)
\(128\) 0 0
\(129\) −1.88558 1.61413i −0.166016 0.142116i
\(130\) 0 0
\(131\) −7.24394 12.5469i −0.632906 1.09623i −0.986955 0.160998i \(-0.948529\pi\)
0.354049 0.935227i \(-0.384805\pi\)
\(132\) 0 0
\(133\) −7.61359 + 10.8528i −0.660182 + 0.941056i
\(134\) 0 0
\(135\) −0.396940 0.0117435i −0.0341631 0.00101072i
\(136\) 0 0
\(137\) −13.3414 7.70264i −1.13983 0.658081i −0.193442 0.981112i \(-0.561965\pi\)
−0.946389 + 0.323030i \(0.895298\pi\)
\(138\) 0 0
\(139\) 0.374701 + 0.216333i 0.0317817 + 0.0183492i 0.515807 0.856705i \(-0.327492\pi\)
−0.484025 + 0.875054i \(0.660826\pi\)
\(140\) 0 0
\(141\) 4.77569 1.68508i 0.402185 0.141909i
\(142\) 0 0
\(143\) 14.3096 + 24.7850i 1.19663 + 2.07262i
\(144\) 0 0
\(145\) 0.675921 + 0.390243i 0.0561322 + 0.0324079i
\(146\) 0 0
\(147\) 11.9639 1.96629i 0.986762 0.162177i
\(148\) 0 0
\(149\) −4.04535 + 2.33558i −0.331408 + 0.191338i −0.656466 0.754356i \(-0.727949\pi\)
0.325058 + 0.945694i \(0.394616\pi\)
\(150\) 0 0
\(151\) 4.12276 7.14083i 0.335506 0.581113i −0.648076 0.761575i \(-0.724426\pi\)
0.983582 + 0.180463i \(0.0577595\pi\)
\(152\) 0 0
\(153\) 10.5827 + 4.08984i 0.855561 + 0.330644i
\(154\) 0 0
\(155\) 0.380316 0.219575i 0.0305477 0.0176367i
\(156\) 0 0
\(157\) 17.5900i 1.40383i −0.712258 0.701917i \(-0.752328\pi\)
0.712258 0.701917i \(-0.247672\pi\)
\(158\) 0 0
\(159\) 13.6350 15.9280i 1.08133 1.26317i
\(160\) 0 0
\(161\) 2.60905 + 5.60814i 0.205622 + 0.441984i
\(162\) 0 0
\(163\) −5.27097 + 9.12959i −0.412854 + 0.715085i −0.995201 0.0978563i \(-0.968801\pi\)
0.582346 + 0.812941i \(0.302135\pi\)
\(164\) 0 0
\(165\) −0.237155 0.672123i −0.0184625 0.0523247i
\(166\) 0 0
\(167\) 4.59146 7.95265i 0.355298 0.615395i −0.631871 0.775074i \(-0.717713\pi\)
0.987169 + 0.159679i \(0.0510460\pi\)
\(168\) 0 0
\(169\) 7.62587 + 13.2084i 0.586605 + 1.01603i
\(170\) 0 0
\(171\) −14.8523 + 2.31791i −1.13579 + 0.177255i
\(172\) 0 0
\(173\) −2.44717 −0.186055 −0.0930274 0.995664i \(-0.529654\pi\)
−0.0930274 + 0.995664i \(0.529654\pi\)
\(174\) 0 0
\(175\) −10.8170 7.58846i −0.817686 0.573633i
\(176\) 0 0
\(177\) 0.947188 0.334210i 0.0711950 0.0251208i
\(178\) 0 0
\(179\) −5.05509 + 2.91856i −0.377835 + 0.218143i −0.676876 0.736097i \(-0.736667\pi\)
0.299041 + 0.954240i \(0.403333\pi\)
\(180\) 0 0
\(181\) 16.0704i 1.19451i 0.802053 + 0.597253i \(0.203741\pi\)
−0.802053 + 0.597253i \(0.796259\pi\)
\(182\) 0 0
\(183\) 1.60141 + 4.53857i 0.118380 + 0.335501i
\(184\) 0 0
\(185\) 0.0541828 0.00398360
\(186\) 0 0
\(187\) 20.3628i 1.48907i
\(188\) 0 0
\(189\) 11.0161 + 8.22475i 0.801300 + 0.598262i
\(190\) 0 0
\(191\) 7.97223i 0.576850i 0.957502 + 0.288425i \(0.0931316\pi\)
−0.957502 + 0.288425i \(0.906868\pi\)
\(192\) 0 0
\(193\) 0.718054 0.0516867 0.0258433 0.999666i \(-0.491773\pi\)
0.0258433 + 0.999666i \(0.491773\pi\)
\(194\) 0 0
\(195\) −0.234110 0.663492i −0.0167650 0.0475137i
\(196\) 0 0
\(197\) 13.5035i 0.962083i −0.876698 0.481042i \(-0.840259\pi\)
0.876698 0.481042i \(-0.159741\pi\)
\(198\) 0 0
\(199\) 21.2568 12.2726i 1.50685 0.869983i 0.506886 0.862013i \(-0.330797\pi\)
0.999968 0.00796947i \(-0.00253679\pi\)
\(200\) 0 0
\(201\) −8.61081 + 3.03828i −0.607360 + 0.214304i
\(202\) 0 0
\(203\) −11.3973 24.4984i −0.799932 1.71945i
\(204\) 0 0
\(205\) −0.504265 −0.0352194
\(206\) 0 0
\(207\) −2.52824 + 6.54197i −0.175725 + 0.454699i
\(208\) 0 0
\(209\) −13.4897 23.3649i −0.933105 1.61618i
\(210\) 0 0
\(211\) −11.7838 + 20.4101i −0.811227 + 1.40509i 0.100778 + 0.994909i \(0.467867\pi\)
−0.912005 + 0.410178i \(0.865467\pi\)
\(212\) 0 0
\(213\) −1.91398 5.42443i −0.131144 0.371676i
\(214\) 0 0
\(215\) −0.0547597 + 0.0948465i −0.00373458 + 0.00646848i
\(216\) 0 0
\(217\) −15.1440 1.33849i −1.02804 0.0908628i
\(218\) 0 0
\(219\) 8.02904 9.37928i 0.542552 0.633793i
\(220\) 0 0
\(221\) 20.1013i 1.35216i
\(222\) 0 0
\(223\) 6.47489 3.73828i 0.433590 0.250334i −0.267285 0.963618i \(-0.586126\pi\)
0.700875 + 0.713284i \(0.252793\pi\)
\(224\) 0 0
\(225\) −2.31026 14.8033i −0.154017 0.986886i
\(226\) 0 0
\(227\) 0.318701 0.552006i 0.0211529 0.0366379i −0.855255 0.518207i \(-0.826600\pi\)
0.876408 + 0.481569i \(0.159933\pi\)
\(228\) 0 0
\(229\) −1.58351 + 0.914239i −0.104641 + 0.0604146i −0.551407 0.834236i \(-0.685909\pi\)
0.446766 + 0.894651i \(0.352576\pi\)
\(230\) 0 0
\(231\) −6.64196 + 23.7635i −0.437009 + 1.56352i
\(232\) 0 0
\(233\) −17.4232 10.0593i −1.14143 0.659007i −0.194649 0.980873i \(-0.562357\pi\)
−0.946785 + 0.321866i \(0.895690\pi\)
\(234\) 0 0
\(235\) −0.111727 0.193516i −0.00728825 0.0126236i
\(236\) 0 0
\(237\) −1.53249 + 0.540731i −0.0995458 + 0.0351242i
\(238\) 0 0
\(239\) −2.41455 1.39404i −0.156184 0.0901730i 0.419871 0.907584i \(-0.362075\pi\)
−0.576055 + 0.817411i \(0.695409\pi\)
\(240\) 0 0
\(241\) −20.0304 11.5645i −1.29027 0.744938i −0.311568 0.950224i \(-0.600854\pi\)
−0.978702 + 0.205286i \(0.934187\pi\)
\(242\) 0 0
\(243\) 1.94718 + 15.4664i 0.124912 + 0.992168i
\(244\) 0 0
\(245\) −0.182077 0.503033i −0.0116325 0.0321376i
\(246\) 0 0
\(247\) −13.3165 23.0649i −0.847310 1.46758i
\(248\) 0 0
\(249\) −17.0997 14.6381i −1.08365 0.927649i
\(250\) 0 0
\(251\) −18.6541 −1.17743 −0.588717 0.808339i \(-0.700367\pi\)
−0.588717 + 0.808339i \(0.700367\pi\)
\(252\) 0 0
\(253\) −12.5878 −0.791388
\(254\) 0 0
\(255\) 0.0917853 0.492119i 0.00574782 0.0308177i
\(256\) 0 0
\(257\) 5.43687 + 9.41694i 0.339143 + 0.587413i 0.984272 0.176661i \(-0.0565297\pi\)
−0.645129 + 0.764074i \(0.723196\pi\)
\(258\) 0 0
\(259\) −1.53558 1.07726i −0.0954162 0.0669376i
\(260\) 0 0
\(261\) 11.0443 28.5777i 0.683622 1.76891i
\(262\) 0 0
\(263\) 16.4519 + 9.49852i 1.01447 + 0.585704i 0.912497 0.409083i \(-0.134151\pi\)
0.101972 + 0.994787i \(0.467485\pi\)
\(264\) 0 0
\(265\) −0.801194 0.462570i −0.0492170 0.0284154i
\(266\) 0 0
\(267\) −0.964101 + 5.16915i −0.0590020 + 0.316347i
\(268\) 0 0
\(269\) 4.29788 + 7.44415i 0.262046 + 0.453878i 0.966786 0.255589i \(-0.0822693\pi\)
−0.704739 + 0.709467i \(0.748936\pi\)
\(270\) 0 0
\(271\) 1.58706 + 0.916292i 0.0964073 + 0.0556608i 0.547429 0.836852i \(-0.315607\pi\)
−0.451021 + 0.892513i \(0.648940\pi\)
\(272\) 0 0
\(273\) −6.55668 + 23.4584i −0.396828 + 1.41977i
\(274\) 0 0
\(275\) 23.2878 13.4452i 1.40431 0.810776i
\(276\) 0 0
\(277\) −7.90931 + 13.6993i −0.475224 + 0.823113i −0.999597 0.0283760i \(-0.990966\pi\)
0.524373 + 0.851489i \(0.324300\pi\)
\(278\) 0 0
\(279\) −10.8182 13.4214i −0.647671 0.803521i
\(280\) 0 0
\(281\) −9.95916 + 5.74992i −0.594114 + 0.343012i −0.766722 0.641979i \(-0.778114\pi\)
0.172609 + 0.984990i \(0.444780\pi\)
\(282\) 0 0
\(283\) 9.92818i 0.590169i 0.955471 + 0.295085i \(0.0953478\pi\)
−0.955471 + 0.295085i \(0.904652\pi\)
\(284\) 0 0
\(285\) 0.220697 + 0.625478i 0.0130729 + 0.0370501i
\(286\) 0 0
\(287\) 14.2912 + 10.0258i 0.843584 + 0.591802i
\(288\) 0 0
\(289\) 1.34887 2.33631i 0.0793454 0.137430i
\(290\) 0 0
\(291\) 8.04020 9.39231i 0.471325 0.550587i
\(292\) 0 0
\(293\) −8.63598 + 14.9580i −0.504520 + 0.873854i 0.495467 + 0.868627i \(0.334997\pi\)
−0.999986 + 0.00522664i \(0.998336\pi\)
\(294\) 0 0
\(295\) −0.0221594 0.0383812i −0.00129017 0.00223464i
\(296\) 0 0
\(297\) −24.6328 + 13.2664i −1.42934 + 0.769793i
\(298\) 0 0
\(299\) −12.4262 −0.718624
\(300\) 0 0
\(301\) 3.43766 1.59929i 0.198143 0.0921815i
\(302\) 0 0
\(303\) −2.59535 + 13.9153i −0.149099 + 0.799415i
\(304\) 0 0
\(305\) 0.183908 0.106180i 0.0105306 0.00607982i
\(306\) 0 0
\(307\) 21.6425i 1.23520i −0.786490 0.617602i \(-0.788104\pi\)
0.786490 0.617602i \(-0.211896\pi\)
\(308\) 0 0
\(309\) 8.40978 9.82404i 0.478416 0.558870i
\(310\) 0 0
\(311\) 20.2032 1.14562 0.572808 0.819690i \(-0.305854\pi\)
0.572808 + 0.819690i \(0.305854\pi\)
\(312\) 0 0
\(313\) 21.8407i 1.23451i −0.786764 0.617254i \(-0.788245\pi\)
0.786764 0.617254i \(-0.211755\pi\)
\(314\) 0 0
\(315\) 0.267634 0.544368i 0.0150795 0.0306716i
\(316\) 0 0
\(317\) 24.8594i 1.39624i 0.715981 + 0.698120i \(0.245980\pi\)
−0.715981 + 0.698120i \(0.754020\pi\)
\(318\) 0 0
\(319\) 54.9880 3.07874
\(320\) 0 0
\(321\) 7.86421 + 1.46676i 0.438938 + 0.0818664i
\(322\) 0 0
\(323\) 18.9496i 1.05439i
\(324\) 0 0
\(325\) 22.9888 13.2726i 1.27519 0.736230i
\(326\) 0 0
\(327\) −13.7577 11.7771i −0.760801 0.651276i
\(328\) 0 0
\(329\) −0.681067 + 7.70574i −0.0375484 + 0.424831i
\(330\) 0 0
\(331\) 16.1444 0.887375 0.443688 0.896181i \(-0.353670\pi\)
0.443688 + 0.896181i \(0.353670\pi\)
\(332\) 0 0
\(333\) −0.327965 2.10148i −0.0179724 0.115160i
\(334\) 0 0
\(335\) 0.201449 + 0.348920i 0.0110063 + 0.0190635i
\(336\) 0 0
\(337\) −7.81522 + 13.5364i −0.425722 + 0.737372i −0.996488 0.0837408i \(-0.973313\pi\)
0.570765 + 0.821113i \(0.306647\pi\)
\(338\) 0 0
\(339\) 32.7118 + 6.10108i 1.77666 + 0.331365i
\(340\) 0 0
\(341\) 15.4698 26.7946i 0.837739 1.45101i
\(342\) 0 0
\(343\) −4.84108 + 17.8764i −0.261394 + 0.965232i
\(344\) 0 0
\(345\) 0.304216 + 0.0567395i 0.0163784 + 0.00305475i
\(346\) 0 0
\(347\) 32.3830i 1.73841i 0.494451 + 0.869206i \(0.335369\pi\)
−0.494451 + 0.869206i \(0.664631\pi\)
\(348\) 0 0
\(349\) 26.0421 15.0354i 1.39400 0.804827i 0.400246 0.916408i \(-0.368925\pi\)
0.993755 + 0.111581i \(0.0355915\pi\)
\(350\) 0 0
\(351\) −24.3165 + 13.0960i −1.29792 + 0.699014i
\(352\) 0 0
\(353\) 8.50607 14.7329i 0.452733 0.784156i −0.545822 0.837901i \(-0.683783\pi\)
0.998555 + 0.0537453i \(0.0171159\pi\)
\(354\) 0 0
\(355\) −0.219804 + 0.126904i −0.0116660 + 0.00673537i
\(356\) 0 0
\(357\) −12.3855 + 12.1221i −0.655512 + 0.641571i
\(358\) 0 0
\(359\) −25.2692 14.5892i −1.33366 0.769987i −0.347798 0.937570i \(-0.613070\pi\)
−0.985858 + 0.167583i \(0.946404\pi\)
\(360\) 0 0
\(361\) 3.05356 + 5.28892i 0.160714 + 0.278364i
\(362\) 0 0
\(363\) −23.6729 20.2650i −1.24251 1.06364i
\(364\) 0 0
\(365\) −0.471788 0.272387i −0.0246945 0.0142574i
\(366\) 0 0
\(367\) −15.6981 9.06329i −0.819433 0.473100i 0.0307880 0.999526i \(-0.490198\pi\)
−0.850221 + 0.526426i \(0.823532\pi\)
\(368\) 0 0
\(369\) 3.05228 + 19.5579i 0.158896 + 1.01814i
\(370\) 0 0
\(371\) 13.5096 + 29.0388i 0.701385 + 1.50762i
\(372\) 0 0
\(373\) 10.1823 + 17.6362i 0.527219 + 0.913170i 0.999497 + 0.0317200i \(0.0100985\pi\)
−0.472278 + 0.881450i \(0.656568\pi\)
\(374\) 0 0
\(375\) −1.24755 + 0.440193i −0.0644235 + 0.0227315i
\(376\) 0 0
\(377\) 54.2820 2.79566
\(378\) 0 0
\(379\) −21.9961 −1.12986 −0.564931 0.825138i \(-0.691097\pi\)
−0.564931 + 0.825138i \(0.691097\pi\)
\(380\) 0 0
\(381\) −2.06599 + 0.728975i −0.105844 + 0.0373465i
\(382\) 0 0
\(383\) 16.3127 + 28.2544i 0.833538 + 1.44373i 0.895215 + 0.445634i \(0.147022\pi\)
−0.0616774 + 0.998096i \(0.519645\pi\)
\(384\) 0 0
\(385\) 1.08449 + 0.0958523i 0.0552709 + 0.00488509i
\(386\) 0 0
\(387\) 4.01008 + 1.54975i 0.203844 + 0.0787783i
\(388\) 0 0
\(389\) −13.6400 7.87504i −0.691574 0.399280i 0.112628 0.993637i \(-0.464073\pi\)
−0.804201 + 0.594357i \(0.797407\pi\)
\(390\) 0 0
\(391\) −7.65680 4.42066i −0.387221 0.223562i
\(392\) 0 0
\(393\) 19.0630 + 16.3187i 0.961600 + 0.823168i
\(394\) 0 0
\(395\) 0.0358524 + 0.0620983i 0.00180393 + 0.00312450i
\(396\) 0 0
\(397\) −2.95864 1.70817i −0.148490 0.0857308i 0.423914 0.905702i \(-0.360656\pi\)
−0.572404 + 0.819972i \(0.693989\pi\)
\(398\) 0 0
\(399\) 6.18101 22.1144i 0.309438 1.10710i
\(400\) 0 0
\(401\) −0.851348 + 0.491526i −0.0425143 + 0.0245456i −0.521106 0.853492i \(-0.674481\pi\)
0.478592 + 0.878037i \(0.341147\pi\)
\(402\) 0 0
\(403\) 15.2712 26.4505i 0.760713 1.31759i
\(404\) 0 0
\(405\) 0.655112 0.209583i 0.0325528 0.0104143i
\(406\) 0 0
\(407\) 3.30594 1.90868i 0.163869 0.0946099i
\(408\) 0 0
\(409\) 28.8900i 1.42852i −0.699880 0.714260i \(-0.746763\pi\)
0.699880 0.714260i \(-0.253237\pi\)
\(410\) 0 0
\(411\) 26.2304 + 4.89224i 1.29385 + 0.241317i
\(412\) 0 0
\(413\) −0.135080 + 1.52832i −0.00664684 + 0.0752037i
\(414\) 0 0
\(415\) −0.496599 + 0.860135i −0.0243771 + 0.0422223i
\(416\) 0 0
\(417\) −0.736697 0.137402i −0.0360762 0.00672859i
\(418\) 0 0
\(419\) −6.28926 + 10.8933i −0.307251 + 0.532174i −0.977760 0.209727i \(-0.932742\pi\)
0.670509 + 0.741901i \(0.266076\pi\)
\(420\) 0 0
\(421\) −13.0232 22.5568i −0.634710 1.09935i −0.986576 0.163300i \(-0.947786\pi\)
0.351866 0.936050i \(-0.385547\pi\)
\(422\) 0 0
\(423\) −6.82925 + 5.50466i −0.332050 + 0.267646i
\(424\) 0 0
\(425\) 18.8871 0.916158
\(426\) 0 0
\(427\) −7.32315 0.647252i −0.354392 0.0313227i
\(428\) 0 0
\(429\) −37.6568 32.2357i −1.81809 1.55636i
\(430\) 0 0
\(431\) −6.28454 + 3.62838i −0.302716 + 0.174773i −0.643662 0.765310i \(-0.722586\pi\)
0.340947 + 0.940083i \(0.389252\pi\)
\(432\) 0 0
\(433\) 8.29113i 0.398446i −0.979954 0.199223i \(-0.936158\pi\)
0.979954 0.199223i \(-0.0638419\pi\)
\(434\) 0 0
\(435\) −1.32893 0.247858i −0.0637171 0.0118839i
\(436\) 0 0
\(437\) 11.7142 0.560367
\(438\) 0 0
\(439\) 3.27192i 0.156160i −0.996947 0.0780802i \(-0.975121\pi\)
0.996947 0.0780802i \(-0.0248790\pi\)
\(440\) 0 0
\(441\) −18.4080 + 10.1067i −0.876572 + 0.481270i
\(442\) 0 0
\(443\) 2.84907i 0.135363i −0.997707 0.0676817i \(-0.978440\pi\)
0.997707 0.0676817i \(-0.0215602\pi\)
\(444\) 0 0
\(445\) 0.232015 0.0109986
\(446\) 0 0
\(447\) 5.26145 6.14626i 0.248858 0.290708i
\(448\) 0 0
\(449\) 19.9802i 0.942925i 0.881886 + 0.471463i \(0.156274\pi\)
−0.881886 + 0.471463i \(0.843726\pi\)
\(450\) 0 0
\(451\) −30.7675 + 17.7636i −1.44878 + 0.836455i
\(452\) 0 0
\(453\) −2.61852 + 14.0396i −0.123029 + 0.659636i
\(454\) 0 0
\(455\) 1.07057 + 0.0946216i 0.0501890 + 0.00443593i
\(456\) 0 0
\(457\) 18.3002 0.856046 0.428023 0.903768i \(-0.359210\pi\)
0.428023 + 0.903768i \(0.359210\pi\)
\(458\) 0 0
\(459\) −19.6424 0.581123i −0.916828 0.0271245i
\(460\) 0 0
\(461\) −4.52954 7.84539i −0.210962 0.365396i 0.741054 0.671445i \(-0.234326\pi\)
−0.952016 + 0.306049i \(0.900993\pi\)
\(462\) 0 0
\(463\) 10.8227 18.7455i 0.502974 0.871176i −0.497021 0.867739i \(-0.665573\pi\)
0.999994 0.00343694i \(-0.00109401\pi\)
\(464\) 0 0
\(465\) −0.494645 + 0.577829i −0.0229386 + 0.0267962i
\(466\) 0 0
\(467\) 13.7761 23.8610i 0.637484 1.10415i −0.348500 0.937309i \(-0.613309\pi\)
0.985983 0.166845i \(-0.0533580\pi\)
\(468\) 0 0
\(469\) 1.22800 13.8938i 0.0567038 0.641558i
\(470\) 0 0
\(471\) 10.1375 + 28.7307i 0.467111 + 1.32384i
\(472\) 0 0
\(473\) 7.71602i 0.354783i
\(474\) 0 0
\(475\) −21.6716 + 12.5121i −0.994362 + 0.574095i
\(476\) 0 0
\(477\) −13.0912 + 33.8742i −0.599403 + 1.55099i
\(478\) 0 0
\(479\) 2.47325 4.28380i 0.113006 0.195732i −0.803975 0.594663i \(-0.797285\pi\)
0.916981 + 0.398931i \(0.130619\pi\)
\(480\) 0 0
\(481\) 3.26349 1.88418i 0.148802 0.0859110i
\(482\) 0 0
\(483\) −7.49361 7.65644i −0.340971 0.348380i
\(484\) 0 0
\(485\) −0.472443 0.272765i −0.0214525 0.0123856i
\(486\) 0 0
\(487\) −4.78573 8.28913i −0.216862 0.375616i 0.736985 0.675909i \(-0.236249\pi\)
−0.953847 + 0.300293i \(0.902916\pi\)
\(488\) 0 0
\(489\) 3.34780 17.9496i 0.151393 0.811711i
\(490\) 0 0
\(491\) −33.0010 19.0531i −1.48931 0.859855i −0.489387 0.872067i \(-0.662779\pi\)
−0.999925 + 0.0122119i \(0.996113\pi\)
\(492\) 0 0
\(493\) 33.4477 + 19.3110i 1.50641 + 0.869725i
\(494\) 0 0
\(495\) 0.774717 + 0.961138i 0.0348210 + 0.0431999i
\(496\) 0 0
\(497\) 8.75250 + 0.773585i 0.392603 + 0.0347000i
\(498\) 0 0
\(499\) 12.4192 + 21.5107i 0.555960 + 0.962951i 0.997828 + 0.0658709i \(0.0209825\pi\)
−0.441868 + 0.897080i \(0.645684\pi\)
\(500\) 0 0
\(501\) −2.91622 + 15.6357i −0.130287 + 0.698550i
\(502\) 0 0
\(503\) −27.2820 −1.21645 −0.608223 0.793766i \(-0.708117\pi\)
−0.608223 + 0.793766i \(0.708117\pi\)
\(504\) 0 0
\(505\) 0.624584 0.0277936
\(506\) 0 0
\(507\) −20.0680 17.1791i −0.891253 0.762949i
\(508\) 0 0
\(509\) 20.8860 + 36.1757i 0.925758 + 1.60346i 0.790338 + 0.612671i \(0.209905\pi\)
0.135420 + 0.990788i \(0.456762\pi\)
\(510\) 0 0
\(511\) 7.95522 + 17.0997i 0.351918 + 0.756446i
\(512\) 0 0
\(513\) 22.9233 12.3457i 1.01209 0.545076i
\(514\) 0 0
\(515\) −0.494160 0.285303i −0.0217753 0.0125720i
\(516\) 0 0
\(517\) −13.6339 7.87154i −0.599619 0.346190i
\(518\) 0 0
\(519\) 3.99710 1.41036i 0.175453 0.0619078i
\(520\) 0 0
\(521\) 2.02629 + 3.50963i 0.0887732 + 0.153760i 0.906993 0.421146i \(-0.138372\pi\)
−0.818220 + 0.574906i \(0.805039\pi\)
\(522\) 0 0
\(523\) 26.2429 + 15.1514i 1.14752 + 0.662523i 0.948282 0.317428i \(-0.102819\pi\)
0.199241 + 0.979951i \(0.436152\pi\)
\(524\) 0 0
\(525\) 22.0413 + 6.16061i 0.961963 + 0.268871i
\(526\) 0 0
\(527\) 18.8198 10.8656i 0.819801 0.473312i
\(528\) 0 0
\(529\) −8.76726 + 15.1853i −0.381185 + 0.660232i
\(530\) 0 0
\(531\) −1.35448 + 1.09177i −0.0587795 + 0.0473788i
\(532\) 0 0
\(533\) −30.3724 + 17.5355i −1.31558 + 0.759548i
\(534\) 0 0
\(535\) 0.352982i 0.0152607i
\(536\) 0 0
\(537\) 6.57474 7.68041i 0.283721 0.331434i
\(538\) 0 0
\(539\) −28.8296 24.2783i −1.24178 1.04574i
\(540\) 0 0
\(541\) 8.82681 15.2885i 0.379494 0.657303i −0.611495 0.791249i \(-0.709431\pi\)
0.990989 + 0.133946i \(0.0427647\pi\)
\(542\) 0 0
\(543\) −9.26174 26.2488i −0.397459 1.12644i
\(544\) 0 0
\(545\) −0.399541 + 0.692026i −0.0171145 + 0.0296431i
\(546\) 0 0
\(547\) −2.18319 3.78140i −0.0933466 0.161681i 0.815571 0.578657i \(-0.196423\pi\)
−0.908917 + 0.416976i \(0.863090\pi\)
\(548\) 0 0
\(549\) −5.23135 6.49018i −0.223269 0.276994i
\(550\) 0 0
\(551\) −51.1719 −2.18000
\(552\) 0 0
\(553\) 0.218550 2.47272i 0.00929371 0.105151i
\(554\) 0 0
\(555\) −0.0884998 + 0.0312267i −0.00375661 + 0.00132550i
\(556\) 0 0
\(557\) 14.7527 8.51750i 0.625094 0.360898i −0.153756 0.988109i \(-0.549137\pi\)
0.778849 + 0.627211i \(0.215804\pi\)
\(558\) 0 0
\(559\) 7.61695i 0.322163i
\(560\) 0 0
\(561\) −11.7355 33.2597i −0.495474 1.40423i
\(562\) 0 0
\(563\) −12.9198 −0.544507 −0.272253 0.962226i \(-0.587769\pi\)
−0.272253 + 0.962226i \(0.587769\pi\)
\(564\) 0 0
\(565\) 1.46825i 0.0617699i
\(566\) 0 0
\(567\) −22.7332 7.08515i −0.954707 0.297548i
\(568\) 0 0
\(569\) 21.7408i 0.911420i 0.890128 + 0.455710i \(0.150615\pi\)
−0.890128 + 0.455710i \(0.849385\pi\)
\(570\) 0 0
\(571\) −33.6508 −1.40824 −0.704122 0.710079i \(-0.748659\pi\)
−0.704122 + 0.710079i \(0.748659\pi\)
\(572\) 0 0
\(573\) −4.59457 13.0215i −0.191941 0.543980i
\(574\) 0 0
\(575\) 11.6755i 0.486904i
\(576\) 0 0
\(577\) 12.5598 7.25141i 0.522871 0.301880i −0.215237 0.976562i \(-0.569052\pi\)
0.738109 + 0.674682i \(0.235719\pi\)
\(578\) 0 0
\(579\) −1.17284 + 0.413830i −0.0487415 + 0.0171982i
\(580\) 0 0
\(581\) 31.1751 14.5035i 1.29336 0.601705i
\(582\) 0 0
\(583\) −65.1793 −2.69945
\(584\) 0 0
\(585\) 0.764770 + 0.948797i 0.0316193 + 0.0392279i
\(586\) 0 0
\(587\) −15.8417 27.4386i −0.653857 1.13251i −0.982179 0.187948i \(-0.939816\pi\)
0.328322 0.944566i \(-0.393517\pi\)
\(588\) 0 0
\(589\) −14.3963 + 24.9350i −0.593187 + 1.02743i
\(590\) 0 0
\(591\) 7.78235 + 22.0560i 0.320123 + 0.907263i
\(592\) 0 0
\(593\) 3.54101 6.13320i 0.145412 0.251860i −0.784115 0.620616i \(-0.786883\pi\)
0.929526 + 0.368755i \(0.120216\pi\)
\(594\) 0 0
\(595\) 0.626005 + 0.439163i 0.0256637 + 0.0180039i
\(596\) 0 0
\(597\) −27.6469 + 32.2963i −1.13151 + 1.32180i
\(598\) 0 0
\(599\) 6.00650i 0.245419i −0.992443 0.122709i \(-0.960842\pi\)
0.992443 0.122709i \(-0.0391583\pi\)
\(600\) 0 0
\(601\) 0.530083 0.306043i 0.0216225 0.0124838i −0.489150 0.872200i \(-0.662693\pi\)
0.510772 + 0.859716i \(0.329360\pi\)
\(602\) 0 0
\(603\) 12.3135 9.92519i 0.501444 0.404185i
\(604\) 0 0
\(605\) −0.687494 + 1.19077i −0.0279506 + 0.0484119i
\(606\) 0 0
\(607\) 1.77500 1.02480i 0.0720450 0.0415952i −0.463545 0.886073i \(-0.653423\pi\)
0.535590 + 0.844478i \(0.320089\pi\)
\(608\) 0 0
\(609\) 32.7348 + 33.4461i 1.32648 + 1.35530i
\(610\) 0 0
\(611\) −13.4588 7.77047i −0.544487 0.314360i
\(612\) 0 0
\(613\) −4.93166 8.54189i −0.199188 0.345003i 0.749077 0.662482i \(-0.230497\pi\)
−0.948265 + 0.317479i \(0.897164\pi\)
\(614\) 0 0
\(615\) 0.823644 0.290619i 0.0332125 0.0117189i
\(616\) 0 0
\(617\) 23.2143 + 13.4028i 0.934571 + 0.539575i 0.888254 0.459352i \(-0.151918\pi\)
0.0463170 + 0.998927i \(0.485252\pi\)
\(618\) 0 0
\(619\) 0.0603011 + 0.0348148i 0.00242370 + 0.00139933i 0.501211 0.865325i \(-0.332888\pi\)
−0.498788 + 0.866724i \(0.666221\pi\)
\(620\) 0 0
\(621\) 0.359236 12.1425i 0.0144157 0.487260i
\(622\) 0 0
\(623\) −6.57547 4.61291i −0.263441 0.184812i
\(624\) 0 0
\(625\) −12.4562 21.5748i −0.498248 0.862992i
\(626\) 0 0
\(627\) 35.4992 + 30.3888i 1.41770 + 1.21361i
\(628\) 0 0
\(629\) 2.68121 0.106907
\(630\) 0 0
\(631\) 11.8214 0.470603 0.235301 0.971922i \(-0.424392\pi\)
0.235301 + 0.971922i \(0.424392\pi\)
\(632\) 0 0
\(633\) 7.48432 40.1282i 0.297475 1.59495i
\(634\) 0 0
\(635\) 0.0483338 + 0.0837165i 0.00191807 + 0.00332219i
\(636\) 0 0
\(637\) −28.4594 23.9666i −1.12760 0.949592i
\(638\) 0 0
\(639\) 6.25243 + 7.75696i 0.247342 + 0.306860i
\(640\) 0 0
\(641\) −17.7673 10.2580i −0.701766 0.405165i 0.106239 0.994341i \(-0.466119\pi\)
−0.808005 + 0.589176i \(0.799453\pi\)
\(642\) 0 0
\(643\) 15.6081 + 9.01132i 0.615522 + 0.355372i 0.775123 0.631810i \(-0.217688\pi\)
−0.159602 + 0.987182i \(0.551021\pi\)
\(644\) 0 0
\(645\) 0.0347800 0.186477i 0.00136946 0.00734254i
\(646\) 0 0
\(647\) 9.11827 + 15.7933i 0.358476 + 0.620899i 0.987706 0.156320i \(-0.0499631\pi\)
−0.629230 + 0.777219i \(0.716630\pi\)
\(648\) 0 0
\(649\) −2.70409 1.56121i −0.106145 0.0612827i
\(650\) 0 0
\(651\) 25.5069 6.54157i 0.999696 0.256384i
\(652\) 0 0
\(653\) −7.79559 + 4.50079i −0.305065 + 0.176129i −0.644716 0.764422i \(-0.723024\pi\)
0.339651 + 0.940552i \(0.389691\pi\)
\(654\) 0 0
\(655\) 0.553614 0.958888i 0.0216315 0.0374669i
\(656\) 0 0
\(657\) −7.70881 + 19.9470i −0.300749 + 0.778207i
\(658\) 0 0
\(659\) 30.4806 17.5980i 1.18735 0.685519i 0.229650 0.973273i \(-0.426242\pi\)
0.957704 + 0.287754i \(0.0929086\pi\)
\(660\) 0 0
\(661\) 12.5628i 0.488637i 0.969695 + 0.244318i \(0.0785642\pi\)
−0.969695 + 0.244318i \(0.921436\pi\)
\(662\) 0 0
\(663\) −11.5848 32.8326i −0.449918 1.27511i
\(664\) 0 0
\(665\) −1.00923 0.0892002i −0.0391363 0.00345904i
\(666\) 0 0
\(667\) −11.9376 + 20.6765i −0.462226 + 0.800599i
\(668\) 0 0
\(669\) −8.42135 + 9.83756i −0.325588 + 0.380342i
\(670\) 0 0
\(671\) 7.48072 12.9570i 0.288790 0.500199i
\(672\) 0 0
\(673\) 23.8913 + 41.3810i 0.920942 + 1.59512i 0.797960 + 0.602710i \(0.205913\pi\)
0.122982 + 0.992409i \(0.460754\pi\)
\(674\) 0 0
\(675\) 12.3049 + 22.8476i 0.473617 + 0.879404i
\(676\) 0 0
\(677\) −37.0471 −1.42384 −0.711918 0.702263i \(-0.752173\pi\)
−0.711918 + 0.702263i \(0.752173\pi\)
\(678\) 0 0
\(679\) 7.96627 + 17.1234i 0.305717 + 0.657137i
\(680\) 0 0
\(681\) −0.202419 + 1.08530i −0.00775672 + 0.0415887i
\(682\) 0 0
\(683\) 21.6844 12.5195i 0.829732 0.479046i −0.0240289 0.999711i \(-0.507649\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(684\) 0 0
\(685\) 1.17734i 0.0449839i
\(686\) 0 0
\(687\) 2.05954 2.40589i 0.0785763 0.0917904i
\(688\) 0 0
\(689\) −64.3424 −2.45125
\(690\) 0 0
\(691\) 46.4946i 1.76874i 0.466787 + 0.884370i \(0.345411\pi\)
−0.466787 + 0.884370i \(0.654589\pi\)
\(692\) 0 0
\(693\) −2.84674 42.6422i −0.108139 1.61984i
\(694\) 0 0
\(695\) 0.0330663i 0.00125428i
\(696\) 0 0
\(697\) −24.9533 −0.945174
\(698\) 0 0
\(699\) 34.2558 + 6.38905i 1.29567 + 0.241656i
\(700\) 0 0
\(701\) 36.0041i 1.35986i −0.733279 0.679928i \(-0.762011\pi\)
0.733279 0.679928i \(-0.237989\pi\)
\(702\) 0 0
\(703\) −3.07651 + 1.77622i −0.116033 + 0.0669915i
\(704\) 0 0
\(705\) 0.294017 + 0.251691i 0.0110733 + 0.00947922i
\(706\) 0 0
\(707\) −17.7011 12.4179i −0.665720 0.467025i
\(708\) 0 0
\(709\) 31.8316 1.19546 0.597731 0.801697i \(-0.296069\pi\)
0.597731 + 0.801697i \(0.296069\pi\)
\(710\) 0 0
\(711\) 2.19147 1.76641i 0.0821864 0.0662456i
\(712\) 0 0
\(713\) 6.71685 + 11.6339i 0.251548 + 0.435694i
\(714\) 0 0
\(715\) −1.09360 + 1.89418i −0.0408985 + 0.0708382i
\(716\) 0 0
\(717\) 4.74724 + 0.885409i 0.177289 + 0.0330662i
\(718\) 0 0
\(719\) 20.0271 34.6879i 0.746883 1.29364i −0.202427 0.979297i \(-0.564883\pi\)
0.949310 0.314342i \(-0.101784\pi\)
\(720\) 0 0
\(721\) 8.33245 + 17.9106i 0.310317 + 0.667024i
\(722\) 0 0
\(723\) 39.3816 + 7.34508i 1.46462 + 0.273167i
\(724\) 0 0
\(725\) 51.0030i 1.89420i
\(726\) 0 0
\(727\) 3.39242 1.95862i 0.125818 0.0726411i −0.435770 0.900058i \(-0.643524\pi\)
0.561588 + 0.827417i \(0.310191\pi\)
\(728\) 0 0
\(729\) −12.0940 24.1399i −0.447927 0.894070i
\(730\) 0 0
\(731\) −2.70976 + 4.69344i −0.100224 + 0.173593i
\(732\) 0 0
\(733\) 20.4239 11.7918i 0.754376 0.435539i −0.0728971 0.997339i \(-0.523224\pi\)
0.827273 + 0.561800i \(0.189891\pi\)
\(734\) 0 0
\(735\) 0.587305 + 0.716697i 0.0216631 + 0.0264358i
\(736\) 0 0
\(737\) 24.5827 + 14.1928i 0.905514 + 0.522798i
\(738\) 0 0
\(739\) 16.8641 + 29.2094i 0.620355 + 1.07449i 0.989420 + 0.145083i \(0.0463448\pi\)
−0.369065 + 0.929404i \(0.620322\pi\)
\(740\) 0 0
\(741\) 35.0434 + 29.9986i 1.28735 + 1.10203i
\(742\) 0 0
\(743\) 29.4003 + 16.9743i 1.07859 + 0.622725i 0.930516 0.366251i \(-0.119359\pi\)
0.148076 + 0.988976i \(0.452692\pi\)
\(744\) 0 0
\(745\) −0.309164 0.178496i −0.0113269 0.00653958i
\(746\) 0 0
\(747\) 36.3662 + 14.0542i 1.33057 + 0.514217i
\(748\) 0 0
\(749\) −7.01796 + 10.0038i −0.256431 + 0.365529i
\(750\) 0 0
\(751\) −1.69831 2.94157i −0.0619724 0.107339i 0.833375 0.552709i \(-0.186406\pi\)
−0.895347 + 0.445369i \(0.853072\pi\)
\(752\) 0 0
\(753\) 30.4687 10.7507i 1.11034 0.391779i
\(754\) 0 0
\(755\) 0.630160 0.0229339
\(756\) 0 0
\(757\) 29.1344 1.05891 0.529454 0.848339i \(-0.322397\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(758\) 0 0
\(759\) 20.5603 7.25461i 0.746293 0.263326i
\(760\) 0 0
\(761\) 8.36288 + 14.4849i 0.303154 + 0.525079i 0.976849 0.213931i \(-0.0686269\pi\)
−0.673694 + 0.739010i \(0.735294\pi\)
\(762\) 0 0
\(763\) 25.0821 11.6688i 0.908032 0.422440i
\(764\) 0 0
\(765\) 0.133701 + 0.856703i 0.00483396 + 0.0309742i
\(766\) 0 0
\(767\) −2.66937 1.54116i −0.0963852 0.0556480i
\(768\) 0 0
\(769\) 24.0816 + 13.9035i 0.868404 + 0.501373i 0.866818 0.498625i \(-0.166162\pi\)
0.00158643 + 0.999999i \(0.499495\pi\)
\(770\) 0 0
\(771\) −14.3075 12.2478i −0.515273 0.441095i
\(772\) 0 0
\(773\) 6.42238 + 11.1239i 0.230997 + 0.400098i 0.958102 0.286428i \(-0.0924679\pi\)
−0.727105 + 0.686526i \(0.759135\pi\)
\(774\) 0 0
\(775\) −24.8527 14.3487i −0.892736 0.515421i
\(776\) 0 0
\(777\) 3.12899 + 0.874561i 0.112252 + 0.0313747i
\(778\) 0 0
\(779\) 28.6322 16.5308i 1.02586 0.592278i
\(780\) 0 0
\(781\) −8.94083 + 15.4860i −0.319928 + 0.554132i
\(782\) 0 0
\(783\) −1.56927 + 53.0426i −0.0560812 + 1.89559i
\(784\) 0 0
\(785\) 1.16420 0.672153i 0.0415522 0.0239902i
\(786\) 0 0
\(787\) 7.56610i 0.269702i −0.990866 0.134851i \(-0.956944\pi\)
0.990866 0.134851i \(-0.0430556\pi\)
\(788\) 0 0
\(789\) −32.3461 6.03288i −1.15155 0.214776i
\(790\) 0 0
\(791\) −29.1917 + 41.6113i −1.03794 + 1.47953i
\(792\) 0 0
\(793\) 7.38467 12.7906i 0.262237 0.454208i
\(794\) 0 0
\(795\) 1.57522 + 0.293796i 0.0558675 + 0.0104199i