Properties

Label 252.2.w.a.101.1
Level $252$
Weight $2$
Character 252.101
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 101.1
Root \(1.08696 - 1.34852i\) of defining polynomial
Character \(\chi\) \(=\) 252.101
Dual form 252.2.w.a.5.1

$q$-expansion

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

Character values

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

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

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 0
\(3\) −1.63336 0.576322i −0.943019 0.332739i
\(4\) 0 0
\(5\) 0.0382122 0.0661855i 0.0170890 0.0295991i −0.857354 0.514727i \(-0.827893\pi\)
0.874443 + 0.485127i \(0.161227\pi\)
\(6\) 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 0.410954 0.911656i \(-0.365196\pi\)
0.994994 + 0.0999316i \(0.0318624\pi\)
\(12\) 0 0
\(13\) 4.60313 2.65762i 1.27668 0.737091i 0.300442 0.953800i \(-0.402866\pi\)
0.976236 + 0.216709i \(0.0695324\pi\)
\(14\) 0 0
\(15\) −0.100558 + 0.0860820i −0.0259641 + 0.0222263i
\(16\) 0 0
\(17\) 1.89092 3.27516i 0.458615 0.794344i −0.540273 0.841490i \(-0.681679\pi\)
0.998888 + 0.0471458i \(0.0150125\pi\)
\(18\) 0 0
\(19\) −4.33939 + 2.50535i −0.995525 + 0.574767i −0.906921 0.421300i \(-0.861574\pi\)
−0.0886040 + 0.996067i \(0.528241\pi\)
\(20\) 0 0
\(21\) 1.13842 4.43892i 0.248423 0.968652i
\(22\) 0 0
\(23\) −2.02463 1.16892i −0.422164 0.243737i 0.273839 0.961776i \(-0.411707\pi\)
−0.696003 + 0.718039i \(0.745040\pi\)
\(24\) 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 0.979997 + 0.199013i \(0.0637736\pi\)
0.662349 + 0.749196i \(0.269560\pi\)
\(30\) 0 0
\(31\) 5.74620i 1.03205i 0.856574 + 0.516024i \(0.172589\pi\)
−0.856574 + 0.516024i \(0.827411\pi\)
\(32\) 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 0.893692 0.448681i \(-0.148106\pi\)
−0.835415 + 0.549620i \(0.814773\pi\)
\(38\) 0 0
\(39\) −9.05019 + 1.68795i −1.44919 + 0.270289i
\(40\) 0 0
\(41\) −3.29910 5.71422i −0.515234 0.892411i −0.999844 0.0176805i \(-0.994372\pi\)
0.484610 0.874730i \(-0.338961\pi\)
\(42\) 0 0
\(43\) 0.716520 1.24105i 0.109268 0.189258i −0.806206 0.591635i \(-0.798483\pi\)
0.915474 + 0.402377i \(0.131816\pi\)
\(44\) 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 −0.442167 0.896933i \(-0.645790\pi\)
−0.997850 + 0.0655390i \(0.979123\pi\)
\(54\) 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 \(0.0569261\pi\)
−0.984051 + 0.177887i \(0.943074\pi\)
\(62\) 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 \(-0.936858\pi\)
0.980390 0.197067i \(-0.0631416\pi\)
\(72\) 0 0
\(73\) −6.17326 3.56413i −0.722525 0.417150i 0.0931564 0.995651i \(-0.470304\pi\)
−0.815681 + 0.578502i \(0.803638\pi\)
\(74\) 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 −0.250398 0.968143i \(-0.580561\pi\)
0.963635 0.267221i \(-0.0861053\pi\)
\(84\) 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 0.935192 0.354141i \(-0.115227\pi\)
−0.774291 + 0.632830i \(0.781893\pi\)
\(90\) 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 0.152179 0.988353i \(-0.451371\pi\)
−0.779849 + 0.625967i \(0.784704\pi\)
\(98\) 0 0
\(99\) 15.9599 + 2.49077i 1.60403 + 0.250332i
\(100\) 0 0
\(101\) 4.08628 + 7.07765i 0.406600 + 0.704252i 0.994506 0.104677i \(-0.0333808\pi\)
−0.587906 + 0.808929i \(0.700048\pi\)
\(102\) 0 0
\(103\) −6.46599 3.73314i −0.637113 0.367837i 0.146389 0.989227i \(-0.453235\pi\)
−0.783502 + 0.621390i \(0.786568\pi\)
\(104\) 0 0
\(105\) −0.250291 0.244968i −0.0244259 0.0239064i
\(106\) 0 0
\(107\) −3.99991 + 2.30935i −0.386686 + 0.223253i −0.680723 0.732541i \(-0.738334\pi\)
0.294037 + 0.955794i \(0.405001\pi\)
\(108\) 0 0
\(109\) 5.22792 9.05503i 0.500744 0.867314i −0.499256 0.866455i \(-0.666393\pi\)
1.00000 0.000859385i \(-0.000273551\pi\)
\(110\) 0 0
\(111\) −0.225148 1.20716i −0.0213701 0.114578i
\(112\) 0 0
\(113\) −16.6379 + 9.60591i −1.56516 + 0.903648i −0.568445 + 0.822721i \(0.692455\pi\)
−0.996720 + 0.0809270i \(0.974212\pi\)
\(114\) 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 0.354049 + 0.935227i \(0.384805\pi\)
−0.986955 + 0.160998i \(0.948529\pi\)
\(132\) 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 −0.946389 0.323030i \(-0.895298\pi\)
−0.193442 + 0.981112i \(0.561965\pi\)
\(138\) 0 0
\(139\) 0.374701 0.216333i 0.0317817 0.0183492i −0.484025 0.875054i \(-0.660826\pi\)
0.515807 + 0.856705i \(0.327492\pi\)
\(140\) 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 0.325058 0.945694i \(-0.394616\pi\)
−0.656466 + 0.754356i \(0.727949\pi\)
\(150\) 0 0
\(151\) 4.12276 + 7.14083i 0.335506 + 0.581113i 0.983582 0.180463i \(-0.0577595\pi\)
−0.648076 + 0.761575i \(0.724426\pi\)
\(152\) 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 \(0.247672\pi\)
−0.712258 + 0.701917i \(0.752328\pi\)
\(158\) 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 0.582346 0.812941i \(-0.302135\pi\)
−0.995201 + 0.0978563i \(0.968801\pi\)
\(164\) 0 0
\(165\) −0.237155 + 0.672123i −0.0184625 + 0.0523247i
\(166\) 0 0
\(167\) 4.59146 + 7.95265i 0.355298 + 0.615395i 0.987169 0.159679i \(-0.0510460\pi\)
−0.631871 + 0.775074i \(0.717713\pi\)
\(168\) 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 0.299041 0.954240i \(-0.403333\pi\)
−0.676876 + 0.736097i \(0.736667\pi\)
\(180\) 0 0
\(181\) 16.0704i 1.19451i −0.802053 0.597253i \(-0.796259\pi\)
0.802053 0.597253i \(-0.203741\pi\)
\(182\) 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 \(-0.906868\pi\)
0.957502 0.288425i \(-0.0931316\pi\)
\(192\) 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 \(0.159741\pi\)
−0.876698 + 0.481042i \(0.840259\pi\)
\(198\) 0 0
\(199\) 21.2568 + 12.2726i 1.50685 + 0.869983i 0.999968 + 0.00796947i \(0.00253679\pi\)
0.506886 + 0.862013i \(0.330797\pi\)
\(200\) 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 −0.912005 0.410178i \(-0.865467\pi\)
0.100778 0.994909i \(-0.467867\pi\)
\(212\) 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 0.700875 0.713284i \(-0.252793\pi\)
−0.267285 + 0.963618i \(0.586126\pi\)
\(224\) 0 0
\(225\) −2.31026 + 14.8033i −0.154017 + 0.986886i
\(226\) 0 0
\(227\) 0.318701 + 0.552006i 0.0211529 + 0.0366379i 0.876408 0.481569i \(-0.159933\pi\)
−0.855255 + 0.518207i \(0.826600\pi\)
\(228\) 0 0
\(229\) −1.58351 0.914239i −0.104641 0.0604146i 0.446766 0.894651i \(-0.352576\pi\)
−0.551407 + 0.834236i \(0.685909\pi\)
\(230\) 0 0
\(231\) −6.64196 23.7635i −0.437009 1.56352i
\(232\) 0 0
\(233\) −17.4232 + 10.0593i −1.14143 + 0.659007i −0.946785 0.321866i \(-0.895690\pi\)
−0.194649 + 0.980873i \(0.562357\pi\)
\(234\) 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 −0.576055 0.817411i \(-0.695409\pi\)
0.419871 + 0.907584i \(0.362075\pi\)
\(240\) 0 0
\(241\) −20.0304 + 11.5645i −1.29027 + 0.744938i −0.978702 0.205286i \(-0.934187\pi\)
−0.311568 + 0.950224i \(0.600854\pi\)
\(242\) 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 −0.645129 0.764074i \(-0.723196\pi\)
0.984272 + 0.176661i \(0.0565297\pi\)
\(258\) 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 0.101972 0.994787i \(-0.467485\pi\)
0.912497 + 0.409083i \(0.134151\pi\)
\(264\) 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 −0.704739 0.709467i \(-0.748936\pi\)
0.966786 + 0.255589i \(0.0822693\pi\)
\(270\) 0 0
\(271\) 1.58706 0.916292i 0.0964073 0.0556608i −0.451021 0.892513i \(-0.648940\pi\)
0.547429 + 0.836852i \(0.315607\pi\)
\(272\) 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 0.524373 0.851489i \(-0.324300\pi\)
−0.999597 + 0.0283760i \(0.990966\pi\)
\(278\) 0 0
\(279\) −10.8182 + 13.4214i −0.647671 + 0.803521i
\(280\) 0 0
\(281\) −9.95916 5.74992i −0.594114 0.343012i 0.172609 0.984990i \(-0.444780\pi\)
−0.766722 + 0.641979i \(0.778114\pi\)
\(282\) 0 0
\(283\) 9.92818i 0.590169i −0.955471 0.295085i \(-0.904652\pi\)
0.955471 0.295085i \(-0.0953478\pi\)
\(284\) 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 −0.999986 0.00522664i \(-0.998336\pi\)
0.495467 0.868627i \(-0.334997\pi\)
\(294\) 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 \(0.211896\pi\)
−0.786490 + 0.617602i \(0.788104\pi\)
\(308\) 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 \(0.211755\pi\)
−0.786764 + 0.617254i \(0.788245\pi\)
\(314\) 0 0
\(315\) 0.267634 + 0.544368i 0.0150795 + 0.0306716i
\(316\) 0 0
\(317\) 24.8594i 1.39624i −0.715981 0.698120i \(-0.754020\pi\)
0.715981 0.698120i \(-0.245980\pi\)
\(318\) 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 0.570765 0.821113i \(-0.306647\pi\)
−0.996488 + 0.0837408i \(0.973313\pi\)
\(338\) 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 \(-0.664631\pi\)
0.494451 0.869206i \(-0.335369\pi\)
\(348\) 0 0
\(349\) 26.0421 + 15.0354i 1.39400 + 0.804827i 0.993755 0.111581i \(-0.0355915\pi\)
0.400246 + 0.916408i \(0.368925\pi\)
\(350\) 0 0
\(351\) −24.3165 13.0960i −1.29792 0.699014i
\(352\) 0 0
\(353\) 8.50607 + 14.7329i 0.452733 + 0.784156i 0.998555 0.0537453i \(-0.0171159\pi\)
−0.545822 + 0.837901i \(0.683783\pi\)
\(354\) 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 −0.985858 0.167583i \(-0.946404\pi\)
−0.347798 + 0.937570i \(0.613070\pi\)
\(360\) 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 −0.850221 0.526426i \(-0.823532\pi\)
0.0307880 + 0.999526i \(0.490198\pi\)
\(368\) 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 −0.472278 0.881450i \(-0.656568\pi\)
0.999497 0.0317200i \(-0.0100985\pi\)
\(374\) 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 −0.0616774 0.998096i \(-0.519645\pi\)
0.895215 0.445634i \(-0.147022\pi\)
\(384\) 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 −0.804201 0.594357i \(-0.797407\pi\)
0.112628 + 0.993637i \(0.464073\pi\)
\(390\) 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 −0.572404 0.819972i \(-0.693989\pi\)
0.423914 + 0.905702i \(0.360656\pi\)
\(398\) 0 0
\(399\) 6.18101 + 22.1144i 0.309438 + 1.10710i
\(400\) 0 0
\(401\) −0.851348 0.491526i −0.0425143 0.0245456i 0.478592 0.878037i \(-0.341147\pi\)
−0.521106 + 0.853492i \(0.674481\pi\)
\(402\) 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 \(0.253237\pi\)
−0.699880 + 0.714260i \(0.746763\pi\)
\(410\) 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 0.670509 0.741901i \(-0.266076\pi\)
−0.977760 + 0.209727i \(0.932742\pi\)
\(420\) 0 0
\(421\) −13.0232 + 22.5568i −0.634710 + 1.09935i 0.351866 + 0.936050i \(0.385547\pi\)
−0.986576 + 0.163300i \(0.947786\pi\)
\(422\) 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 0.340947 0.940083i \(-0.389252\pi\)
−0.643662 + 0.765310i \(0.722586\pi\)
\(432\) 0 0
\(433\) 8.29113i 0.398446i 0.979954 + 0.199223i \(0.0638419\pi\)
−0.979954 + 0.199223i \(0.936158\pi\)
\(434\) 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 \(0.0248790\pi\)
−0.996947 + 0.0780802i \(0.975121\pi\)
\(440\) 0 0
\(441\) −18.4080 10.1067i −0.876572 0.481270i
\(442\) 0 0
\(443\) 2.84907i 0.135363i 0.997707 + 0.0676817i \(0.0215602\pi\)
−0.997707 + 0.0676817i \(0.978440\pi\)
\(444\) 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 \(-0.843726\pi\)
0.881886 0.471463i \(-0.156274\pi\)
\(450\) 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 −0.952016 0.306049i \(-0.900993\pi\)
0.741054 + 0.671445i \(0.234326\pi\)
\(462\) 0 0
\(463\) 10.8227 + 18.7455i 0.502974 + 0.871176i 0.999994 + 0.00343694i \(0.00109401\pi\)
−0.497021 + 0.867739i \(0.665573\pi\)
\(464\) 0 0
\(465\) −0.494645 0.577829i −0.0229386 0.0267962i
\(466\) 0 0
\(467\) 13.7761 + 23.8610i 0.637484 + 1.10415i 0.985983 + 0.166845i \(0.0533580\pi\)
−0.348500 + 0.937309i \(0.613309\pi\)
\(468\) 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 0.916981 0.398931i \(-0.130619\pi\)
−0.803975 + 0.594663i \(0.797285\pi\)
\(480\) 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 −0.953847 0.300293i \(-0.902916\pi\)
0.736985 + 0.675909i \(0.236249\pi\)
\(488\) 0 0
\(489\) 3.34780 + 17.9496i 0.151393 + 0.811711i
\(490\) 0 0
\(491\) −33.0010 + 19.0531i −1.48931 + 0.859855i −0.999925 0.0122119i \(-0.996113\pi\)
−0.489387 + 0.872067i \(0.662779\pi\)
\(492\) 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 −0.441868 0.897080i \(-0.645684\pi\)
0.997828 0.0658709i \(-0.0209825\pi\)
\(500\) 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 0.135420 0.990788i \(-0.456762\pi\)
0.790338 0.612671i \(-0.209905\pi\)
\(510\) 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 −0.818220 0.574906i \(-0.805039\pi\)
0.906993 + 0.421146i \(0.138372\pi\)
\(522\) 0 0
\(523\) 26.2429 15.1514i 1.14752 0.662523i 0.199241 0.979951i \(-0.436152\pi\)
0.948282 + 0.317428i \(0.102819\pi\)
\(524\) 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 0.990989 0.133946i \(-0.0427647\pi\)
−0.611495 + 0.791249i \(0.709431\pi\)
\(542\) 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 −0.908917 0.416976i \(-0.863090\pi\)
0.815571 + 0.578657i \(0.196423\pi\)
\(548\) 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 0.778849 0.627211i \(-0.215804\pi\)
−0.153756 + 0.988109i \(0.549137\pi\)
\(558\) 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 \(-0.849385\pi\)
0.890128 0.455710i \(-0.150615\pi\)
\(570\) 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 0.738109 0.674682i \(-0.235719\pi\)
−0.215237 + 0.976562i \(0.569052\pi\)
\(578\) 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 0.328322 + 0.944566i \(0.393517\pi\)
−0.982179 + 0.187948i \(0.939816\pi\)
\(588\) 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 0.929526 0.368755i \(-0.120216\pi\)
−0.784115 + 0.620616i \(0.786883\pi\)
\(594\) 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 \(0.0391583\pi\)
−0.992443 + 0.122709i \(0.960842\pi\)
\(600\) 0 0
\(601\) 0.530083 + 0.306043i 0.0216225 + 0.0124838i 0.510772 0.859716i \(-0.329360\pi\)
−0.489150 + 0.872200i \(0.662693\pi\)
\(602\) 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 0.535590 0.844478i \(-0.320089\pi\)
−0.463545 + 0.886073i \(0.653423\pi\)
\(608\) 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 −0.948265 0.317479i \(-0.897164\pi\)
0.749077 + 0.662482i \(0.230497\pi\)
\(614\) 0 0
\(615\) 0.823644 + 0.290619i 0.0332125 + 0.0117189i
\(616\) 0 0
\(617\) 23.2143 13.4028i 0.934571 0.539575i 0.0463170 0.998927i \(-0.485252\pi\)
0.888254 + 0.459352i \(0.151918\pi\)
\(618\) 0 0
\(619\) 0.0603011 0.0348148i 0.00242370 0.00139933i −0.498788 0.866724i \(-0.666221\pi\)
0.501211 + 0.865325i \(0.332888\pi\)
\(620\) 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 −0.808005 0.589176i \(-0.799453\pi\)
0.106239 + 0.994341i \(0.466119\pi\)
\(642\) 0 0
\(643\) 15.6081 9.01132i 0.615522 0.355372i −0.159602 0.987182i \(-0.551021\pi\)
0.775123 + 0.631810i \(0.217688\pi\)
\(644\) 0 0
\(645\) 0.0347800 + 0.186477i 0.00136946 + 0.00734254i
\(646\) 0 0
\(647\) 9.11827 15.7933i 0.358476 0.620899i −0.629230 0.777219i \(-0.716630\pi\)
0.987706 + 0.156320i \(0.0499631\pi\)
\(648\) 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 0.339651 0.940552i \(-0.389691\pi\)
−0.644716 + 0.764422i \(0.723024\pi\)
\(654\) 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 0.957704 0.287754i \(-0.0929086\pi\)
0.229650 + 0.973273i \(0.426242\pi\)
\(660\) 0 0
\(661\) 12.5628i 0.488637i −0.969695 0.244318i \(-0.921436\pi\)
0.969695 0.244318i \(-0.0785642\pi\)
\(662\) 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 0.122982 0.992409i \(-0.460754\pi\)
0.797960 0.602710i \(-0.205913\pi\)
\(674\) 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 0.853761 0.520665i \(-0.174316\pi\)
−0.0240289 + 0.999711i \(0.507649\pi\)
\(684\) 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 \(-0.654589\pi\)
0.466787 0.884370i \(-0.345411\pi\)
\(692\) 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 \(0.237989\pi\)
−0.733279 + 0.679928i \(0.762011\pi\)
\(702\) 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 0.949310 + 0.314342i \(0.101784\pi\)
−0.202427 + 0.979297i \(0.564883\pi\)
\(720\) 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 0.561588 0.827417i \(-0.310191\pi\)
−0.435770 + 0.900058i \(0.643524\pi\)
\(728\) 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 0.827273 0.561800i \(-0.189891\pi\)
−0.0728971 + 0.997339i \(0.523224\pi\)
\(734\) 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 −0.369065 0.929404i \(-0.620322\pi\)
0.989420 0.145083i \(-0.0463448\pi\)
\(740\) 0 0
\(741\) 35.0434 29.9986i 1.28735 1.10203i
\(742\) 0 0
\(743\) 29.4003 16.9743i 1.07859 0.622725i 0.148076 0.988976i \(-0.452692\pi\)
0.930516 + 0.366251i \(0.119359\pi\)
\(744\) 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 −0.895347 0.445369i \(-0.853072\pi\)
0.833375 + 0.552709i \(0.186406\pi\)
\(752\) 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 −0.673694 0.739010i \(-0.735294\pi\)
0.976849 + 0.213931i \(0.0686269\pi\)
\(762\) 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 0.00158643 0.999999i \(-0.499495\pi\)
0.866818 + 0.498625i \(0.166162\pi\)
\(770\) 0 0
\(771\) −14.3075 + 12.2478i −0.515273 + 0.441095i
\(772\) 0 0
\(773\) 6.42238 11.1239i 0.230997 0.400098i −0.727105 0.686526i \(-0.759135\pi\)
0.958102 + 0.286428i \(0.0924679\pi\)
\(774\) 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 \(0.0430556\pi\)
−0.990866 + 0.134851i \(0.956944\pi\)
\(788\) 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
\(796\)