Properties

Label 1456.2.cc.c.225.1
Level $1456$
Weight $2$
Character 1456.225
Analytic conductor $11.626$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.cc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 225.1
Root \(0.759479 + 1.19298i\) of defining polynomial
Character \(\chi\) \(=\) 1456.225
Dual form 1456.2.cc.c.673.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41289 + 2.44719i) q^{3} +0.518957i q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.49250 - 4.31714i) q^{9} +O(q^{10})\) \(q+(-1.41289 + 2.44719i) q^{3} +0.518957i q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.49250 - 4.31714i) q^{9} +(-1.40656 - 0.812080i) q^{11} +(1.42641 - 3.31140i) q^{13} +(-1.26999 - 0.733228i) q^{15} +(0.974127 + 1.68724i) q^{17} +(-2.15740 + 1.24558i) q^{19} +2.82577i q^{21} +(4.57029 - 7.91598i) q^{23} +4.73068 q^{25} +5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} -5.79391i q^{31} +(3.97463 - 2.29475i) q^{33} +(0.259479 + 0.449430i) q^{35} +(-8.85879 - 5.11463i) q^{37} +(6.08826 + 8.16934i) q^{39} +(3.64513 + 2.10452i) q^{41} +(0.498655 + 0.863697i) q^{43} +(2.24041 - 1.29350i) q^{45} -4.51725i q^{47} +(0.500000 - 0.866025i) q^{49} -5.50532 q^{51} -8.89651 q^{53} +(0.421434 - 0.729946i) q^{55} -7.03944i q^{57} +(5.37392 - 3.10263i) q^{59} +(6.73536 + 11.6660i) q^{61} +(-4.31714 - 2.49250i) q^{63} +(1.71847 + 0.740247i) q^{65} +(7.25094 + 4.18633i) q^{67} +(12.9146 + 22.3688i) q^{69} +(4.50168 - 2.59905i) q^{71} +11.8395i q^{73} +(-6.68392 + 11.5769i) q^{75} -1.62416 q^{77} -0.982310 q^{79} +(-0.447609 + 0.775281i) q^{81} +8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(7.38934 + 12.7987i) q^{87} +(-10.4087 - 6.00949i) q^{89} +(-0.420388 - 3.58096i) q^{91} +(14.1788 + 8.18614i) q^{93} +(-0.646401 - 1.11960i) q^{95} +(3.82981 - 2.21114i) q^{97} +8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −1.41289 + 2.44719i −0.815731 + 1.41289i 0.0930713 + 0.995659i \(0.470332\pi\)
−0.908802 + 0.417228i \(0.863002\pi\)
\(4\) 0 0
\(5\) 0.518957i 0.232085i 0.993244 + 0.116042i \(0.0370208\pi\)
−0.993244 + 0.116042i \(0.962979\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 0 0
\(9\) −2.49250 4.31714i −0.830833 1.43905i
\(10\) 0 0
\(11\) −1.40656 0.812080i −0.424095 0.244851i 0.272733 0.962090i \(-0.412072\pi\)
−0.696828 + 0.717239i \(0.745406\pi\)
\(12\) 0 0
\(13\) 1.42641 3.31140i 0.395616 0.918416i
\(14\) 0 0
\(15\) −1.26999 0.733228i −0.327909 0.189319i
\(16\) 0 0
\(17\) 0.974127 + 1.68724i 0.236260 + 0.409215i 0.959638 0.281237i \(-0.0907448\pi\)
−0.723378 + 0.690452i \(0.757411\pi\)
\(18\) 0 0
\(19\) −2.15740 + 1.24558i −0.494942 + 0.285755i −0.726622 0.687037i \(-0.758911\pi\)
0.231680 + 0.972792i \(0.425578\pi\)
\(20\) 0 0
\(21\) 2.82577i 0.616634i
\(22\) 0 0
\(23\) 4.57029 7.91598i 0.952971 1.65059i 0.214028 0.976828i \(-0.431342\pi\)
0.738943 0.673767i \(-0.235325\pi\)
\(24\) 0 0
\(25\) 4.73068 0.946137
\(26\) 0 0
\(27\) 5.60916 1.07948
\(28\) 0 0
\(29\) 2.61498 4.52928i 0.485589 0.841065i −0.514274 0.857626i \(-0.671938\pi\)
0.999863 + 0.0165608i \(0.00527172\pi\)
\(30\) 0 0
\(31\) 5.79391i 1.04062i −0.853978 0.520308i \(-0.825817\pi\)
0.853978 0.520308i \(-0.174183\pi\)
\(32\) 0 0
\(33\) 3.97463 2.29475i 0.691894 0.399465i
\(34\) 0 0
\(35\) 0.259479 + 0.449430i 0.0438599 + 0.0759675i
\(36\) 0 0
\(37\) −8.85879 5.11463i −1.45638 0.840840i −0.457546 0.889186i \(-0.651272\pi\)
−0.998831 + 0.0483462i \(0.984605\pi\)
\(38\) 0 0
\(39\) 6.08826 + 8.16934i 0.974902 + 1.30814i
\(40\) 0 0
\(41\) 3.64513 + 2.10452i 0.569273 + 0.328670i 0.756859 0.653578i \(-0.226733\pi\)
−0.187586 + 0.982248i \(0.560066\pi\)
\(42\) 0 0
\(43\) 0.498655 + 0.863697i 0.0760442 + 0.131712i 0.901540 0.432696i \(-0.142438\pi\)
−0.825496 + 0.564408i \(0.809104\pi\)
\(44\) 0 0
\(45\) 2.24041 1.29350i 0.333980 0.192824i
\(46\) 0 0
\(47\) 4.51725i 0.658909i −0.944171 0.329455i \(-0.893135\pi\)
0.944171 0.329455i \(-0.106865\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 0 0
\(51\) −5.50532 −0.770899
\(52\) 0 0
\(53\) −8.89651 −1.22203 −0.611015 0.791619i \(-0.709238\pi\)
−0.611015 + 0.791619i \(0.709238\pi\)
\(54\) 0 0
\(55\) 0.421434 0.729946i 0.0568262 0.0984259i
\(56\) 0 0
\(57\) 7.03944i 0.932397i
\(58\) 0 0
\(59\) 5.37392 3.10263i 0.699624 0.403928i −0.107583 0.994196i \(-0.534311\pi\)
0.807207 + 0.590268i \(0.200978\pi\)
\(60\) 0 0
\(61\) 6.73536 + 11.6660i 0.862375 + 1.49368i 0.869630 + 0.493703i \(0.164357\pi\)
−0.00725571 + 0.999974i \(0.502310\pi\)
\(62\) 0 0
\(63\) −4.31714 2.49250i −0.543908 0.314025i
\(64\) 0 0
\(65\) 1.71847 + 0.740247i 0.213150 + 0.0918164i
\(66\) 0 0
\(67\) 7.25094 + 4.18633i 0.885843 + 0.511442i 0.872580 0.488470i \(-0.162445\pi\)
0.0132624 + 0.999912i \(0.495778\pi\)
\(68\) 0 0
\(69\) 12.9146 + 22.3688i 1.55474 + 2.69288i
\(70\) 0 0
\(71\) 4.50168 2.59905i 0.534251 0.308450i −0.208495 0.978023i \(-0.566856\pi\)
0.742746 + 0.669573i \(0.233523\pi\)
\(72\) 0 0
\(73\) 11.8395i 1.38571i 0.721076 + 0.692856i \(0.243648\pi\)
−0.721076 + 0.692856i \(0.756352\pi\)
\(74\) 0 0
\(75\) −6.68392 + 11.5769i −0.771793 + 1.33678i
\(76\) 0 0
\(77\) −1.62416 −0.185090
\(78\) 0 0
\(79\) −0.982310 −0.110518 −0.0552592 0.998472i \(-0.517599\pi\)
−0.0552592 + 0.998472i \(0.517599\pi\)
\(80\) 0 0
\(81\) −0.447609 + 0.775281i −0.0497343 + 0.0861423i
\(82\) 0 0
\(83\) 8.91851i 0.978934i 0.872022 + 0.489467i \(0.162809\pi\)
−0.872022 + 0.489467i \(0.837191\pi\)
\(84\) 0 0
\(85\) −0.875603 + 0.505530i −0.0949725 + 0.0548324i
\(86\) 0 0
\(87\) 7.38934 + 12.7987i 0.792220 + 1.37217i
\(88\) 0 0
\(89\) −10.4087 6.00949i −1.10332 0.637005i −0.166233 0.986087i \(-0.553160\pi\)
−0.937092 + 0.349082i \(0.886494\pi\)
\(90\) 0 0
\(91\) −0.420388 3.58096i −0.0440686 0.375387i
\(92\) 0 0
\(93\) 14.1788 + 8.18614i 1.47027 + 0.848863i
\(94\) 0 0
\(95\) −0.646401 1.11960i −0.0663194 0.114869i
\(96\) 0 0
\(97\) 3.82981 2.21114i 0.388858 0.224507i −0.292807 0.956172i \(-0.594589\pi\)
0.681665 + 0.731664i \(0.261256\pi\)
\(98\) 0 0
\(99\) 8.09643i 0.813722i
\(100\) 0 0
\(101\) 9.15132 15.8506i 0.910591 1.57719i 0.0973594 0.995249i \(-0.468960\pi\)
0.813231 0.581940i \(-0.197706\pi\)
\(102\) 0 0
\(103\) 5.02046 0.494680 0.247340 0.968929i \(-0.420444\pi\)
0.247340 + 0.968929i \(0.420444\pi\)
\(104\) 0 0
\(105\) −1.46646 −0.143111
\(106\) 0 0
\(107\) 3.07228 5.32134i 0.297008 0.514434i −0.678442 0.734654i \(-0.737344\pi\)
0.975450 + 0.220221i \(0.0706777\pi\)
\(108\) 0 0
\(109\) 11.8962i 1.13945i 0.821834 + 0.569727i \(0.192951\pi\)
−0.821834 + 0.569727i \(0.807049\pi\)
\(110\) 0 0
\(111\) 25.0330 14.4528i 2.37602 1.37180i
\(112\) 0 0
\(113\) −1.77806 3.07969i −0.167266 0.289713i 0.770192 0.637812i \(-0.220161\pi\)
−0.937458 + 0.348099i \(0.886827\pi\)
\(114\) 0 0
\(115\) 4.10805 + 2.37178i 0.383078 + 0.221170i
\(116\) 0 0
\(117\) −17.8511 + 2.09563i −1.65033 + 0.193741i
\(118\) 0 0
\(119\) 1.68724 + 0.974127i 0.154669 + 0.0892980i
\(120\) 0 0
\(121\) −4.18105 7.24180i −0.380096 0.658345i
\(122\) 0 0
\(123\) −10.3003 + 5.94689i −0.928748 + 0.536213i
\(124\) 0 0
\(125\) 5.04981i 0.451668i
\(126\) 0 0
\(127\) 0.711749 1.23279i 0.0631575 0.109392i −0.832718 0.553698i \(-0.813216\pi\)
0.895875 + 0.444306i \(0.146550\pi\)
\(128\) 0 0
\(129\) −2.81818 −0.248127
\(130\) 0 0
\(131\) −8.67374 −0.757828 −0.378914 0.925432i \(-0.623702\pi\)
−0.378914 + 0.925432i \(0.623702\pi\)
\(132\) 0 0
\(133\) −1.24558 + 2.15740i −0.108005 + 0.187071i
\(134\) 0 0
\(135\) 2.91091i 0.250531i
\(136\) 0 0
\(137\) 7.37667 4.25892i 0.630231 0.363864i −0.150611 0.988593i \(-0.548124\pi\)
0.780842 + 0.624729i \(0.214791\pi\)
\(138\) 0 0
\(139\) −2.51922 4.36342i −0.213677 0.370100i 0.739185 0.673502i \(-0.235211\pi\)
−0.952863 + 0.303402i \(0.901877\pi\)
\(140\) 0 0
\(141\) 11.0546 + 6.38237i 0.930964 + 0.537493i
\(142\) 0 0
\(143\) −4.69546 + 3.49933i −0.392654 + 0.292628i
\(144\) 0 0
\(145\) 2.35050 + 1.35706i 0.195198 + 0.112698i
\(146\) 0 0
\(147\) 1.41289 + 2.44719i 0.116533 + 0.201841i
\(148\) 0 0
\(149\) 2.91409 1.68245i 0.238732 0.137832i −0.375862 0.926676i \(-0.622653\pi\)
0.614594 + 0.788844i \(0.289320\pi\)
\(150\) 0 0
\(151\) 12.6566i 1.02998i 0.857196 + 0.514991i \(0.172205\pi\)
−0.857196 + 0.514991i \(0.827795\pi\)
\(152\) 0 0
\(153\) 4.85602 8.41087i 0.392586 0.679979i
\(154\) 0 0
\(155\) 3.00679 0.241511
\(156\) 0 0
\(157\) 10.3691 0.827547 0.413773 0.910380i \(-0.364211\pi\)
0.413773 + 0.910380i \(0.364211\pi\)
\(158\) 0 0
\(159\) 12.5698 21.7715i 0.996847 1.72659i
\(160\) 0 0
\(161\) 9.14058i 0.720379i
\(162\) 0 0
\(163\) −13.6428 + 7.87669i −1.06859 + 0.616950i −0.927796 0.373089i \(-0.878299\pi\)
−0.140794 + 0.990039i \(0.544965\pi\)
\(164\) 0 0
\(165\) 1.19088 + 2.06266i 0.0927098 + 0.160578i
\(166\) 0 0
\(167\) 14.2016 + 8.19930i 1.09895 + 0.634481i 0.935946 0.352144i \(-0.114547\pi\)
0.163007 + 0.986625i \(0.447881\pi\)
\(168\) 0 0
\(169\) −8.93069 9.44684i −0.686976 0.726680i
\(170\) 0 0
\(171\) 10.7547 + 6.20920i 0.822429 + 0.474830i
\(172\) 0 0
\(173\) −0.150677 0.260981i −0.0114558 0.0198420i 0.860241 0.509888i \(-0.170313\pi\)
−0.871696 + 0.490046i \(0.836980\pi\)
\(174\) 0 0
\(175\) 4.09689 2.36534i 0.309696 0.178803i
\(176\) 0 0
\(177\) 17.5347i 1.31799i
\(178\) 0 0
\(179\) 4.90791 8.50075i 0.366834 0.635376i −0.622234 0.782831i \(-0.713775\pi\)
0.989069 + 0.147455i \(0.0471083\pi\)
\(180\) 0 0
\(181\) 12.4320 0.924062 0.462031 0.886864i \(-0.347121\pi\)
0.462031 + 0.886864i \(0.347121\pi\)
\(182\) 0 0
\(183\) −38.0652 −2.81386
\(184\) 0 0
\(185\) 2.65427 4.59733i 0.195146 0.338003i
\(186\) 0 0
\(187\) 3.16427i 0.231395i
\(188\) 0 0
\(189\) 4.85767 2.80458i 0.353344 0.204003i
\(190\) 0 0
\(191\) −6.12346 10.6061i −0.443078 0.767434i 0.554838 0.831958i \(-0.312780\pi\)
−0.997916 + 0.0645248i \(0.979447\pi\)
\(192\) 0 0
\(193\) −10.0752 5.81692i −0.725229 0.418711i 0.0914452 0.995810i \(-0.470851\pi\)
−0.816674 + 0.577099i \(0.804185\pi\)
\(194\) 0 0
\(195\) −4.23953 + 3.15955i −0.303599 + 0.226260i
\(196\) 0 0
\(197\) −1.55984 0.900572i −0.111134 0.0641631i 0.443403 0.896322i \(-0.353771\pi\)
−0.554537 + 0.832159i \(0.687104\pi\)
\(198\) 0 0
\(199\) −3.29657 5.70982i −0.233687 0.404759i 0.725203 0.688535i \(-0.241746\pi\)
−0.958890 + 0.283777i \(0.908413\pi\)
\(200\) 0 0
\(201\) −20.4895 + 11.8296i −1.44522 + 0.834397i
\(202\) 0 0
\(203\) 5.22996i 0.367071i
\(204\) 0 0
\(205\) −1.09215 + 1.89166i −0.0762793 + 0.132120i
\(206\) 0 0
\(207\) −45.5658 −3.16704
\(208\) 0 0
\(209\) 4.04603 0.279870
\(210\) 0 0
\(211\) 5.35996 9.28373i 0.368995 0.639118i −0.620414 0.784275i \(-0.713035\pi\)
0.989409 + 0.145157i \(0.0463686\pi\)
\(212\) 0 0
\(213\) 14.6886i 1.00645i
\(214\) 0 0
\(215\) −0.448221 + 0.258781i −0.0305684 + 0.0176487i
\(216\) 0 0
\(217\) −2.89695 5.01767i −0.196658 0.340622i
\(218\) 0 0
\(219\) −28.9736 16.7279i −1.95785 1.13037i
\(220\) 0 0
\(221\) 6.97662 0.819021i 0.469298 0.0550933i
\(222\) 0 0
\(223\) 11.1612 + 6.44392i 0.747409 + 0.431517i 0.824757 0.565487i \(-0.191312\pi\)
−0.0773480 + 0.997004i \(0.524645\pi\)
\(224\) 0 0
\(225\) −11.7912 20.4230i −0.786082 1.36153i
\(226\) 0 0
\(227\) 0.605486 0.349577i 0.0401875 0.0232023i −0.479772 0.877393i \(-0.659280\pi\)
0.519959 + 0.854191i \(0.325947\pi\)
\(228\) 0 0
\(229\) 18.2868i 1.20843i −0.796822 0.604214i \(-0.793487\pi\)
0.796822 0.604214i \(-0.206513\pi\)
\(230\) 0 0
\(231\) 2.29475 3.97463i 0.150984 0.261511i
\(232\) 0 0
\(233\) −26.7796 −1.75439 −0.877194 0.480137i \(-0.840587\pi\)
−0.877194 + 0.480137i \(0.840587\pi\)
\(234\) 0 0
\(235\) 2.34426 0.152923
\(236\) 0 0
\(237\) 1.38789 2.40390i 0.0901533 0.156150i
\(238\) 0 0
\(239\) 16.6177i 1.07491i 0.843293 + 0.537454i \(0.180614\pi\)
−0.843293 + 0.537454i \(0.819386\pi\)
\(240\) 0 0
\(241\) 15.0800 8.70643i 0.971387 0.560830i 0.0717279 0.997424i \(-0.477149\pi\)
0.899659 + 0.436594i \(0.143815\pi\)
\(242\) 0 0
\(243\) 7.14890 + 12.3823i 0.458602 + 0.794322i
\(244\) 0 0
\(245\) 0.449430 + 0.259479i 0.0287130 + 0.0165775i
\(246\) 0 0
\(247\) 1.04725 + 8.92073i 0.0666350 + 0.567612i
\(248\) 0 0
\(249\) −21.8253 12.6008i −1.38312 0.798546i
\(250\) 0 0
\(251\) 3.22491 + 5.58571i 0.203554 + 0.352567i 0.949671 0.313249i \(-0.101417\pi\)
−0.746117 + 0.665815i \(0.768084\pi\)
\(252\) 0 0
\(253\) −12.8568 + 7.42288i −0.808300 + 0.466672i
\(254\) 0 0
\(255\) 2.85703i 0.178914i
\(256\) 0 0
\(257\) −1.83578 + 3.17966i −0.114513 + 0.198342i −0.917585 0.397540i \(-0.869864\pi\)
0.803072 + 0.595882i \(0.203197\pi\)
\(258\) 0 0
\(259\) −10.2293 −0.635615
\(260\) 0 0
\(261\) −26.0713 −1.61377
\(262\) 0 0
\(263\) 9.15964 15.8650i 0.564807 0.978275i −0.432260 0.901749i \(-0.642284\pi\)
0.997068 0.0765263i \(-0.0243829\pi\)
\(264\) 0 0
\(265\) 4.61690i 0.283614i
\(266\) 0 0
\(267\) 29.4128 16.9815i 1.80003 1.03925i
\(268\) 0 0
\(269\) −13.7715 23.8529i −0.839661 1.45434i −0.890178 0.455613i \(-0.849420\pi\)
0.0505171 0.998723i \(-0.483913\pi\)
\(270\) 0 0
\(271\) −5.64582 3.25961i −0.342959 0.198007i 0.318621 0.947882i \(-0.396780\pi\)
−0.661580 + 0.749875i \(0.730114\pi\)
\(272\) 0 0
\(273\) 9.35726 + 4.03072i 0.566327 + 0.243950i
\(274\) 0 0
\(275\) −6.65401 3.84169i −0.401252 0.231663i
\(276\) 0 0
\(277\) 2.72093 + 4.71279i 0.163485 + 0.283164i 0.936116 0.351691i \(-0.114393\pi\)
−0.772631 + 0.634855i \(0.781060\pi\)
\(278\) 0 0
\(279\) −25.0131 + 14.4413i −1.49749 + 0.864579i
\(280\) 0 0
\(281\) 3.54237i 0.211320i −0.994402 0.105660i \(-0.966304\pi\)
0.994402 0.105660i \(-0.0336955\pi\)
\(282\) 0 0
\(283\) 7.06956 12.2448i 0.420242 0.727880i −0.575721 0.817646i \(-0.695279\pi\)
0.995963 + 0.0897658i \(0.0286119\pi\)
\(284\) 0 0
\(285\) 3.65317 0.216395
\(286\) 0 0
\(287\) 4.20903 0.248451
\(288\) 0 0
\(289\) 6.60215 11.4353i 0.388362 0.672663i
\(290\) 0 0
\(291\) 12.4964i 0.732551i
\(292\) 0 0
\(293\) −7.23071 + 4.17465i −0.422423 + 0.243886i −0.696113 0.717932i \(-0.745089\pi\)
0.273691 + 0.961818i \(0.411756\pi\)
\(294\) 0 0
\(295\) 1.61013 + 2.78883i 0.0937455 + 0.162372i
\(296\) 0 0
\(297\) −7.88964 4.55508i −0.457803 0.264313i
\(298\) 0 0
\(299\) −19.6938 26.4255i −1.13892 1.52823i
\(300\) 0 0
\(301\) 0.863697 + 0.498655i 0.0497826 + 0.0287420i
\(302\) 0 0
\(303\) 25.8596 + 44.7901i 1.48559 + 2.57312i
\(304\) 0 0
\(305\) −6.05415 + 3.49536i −0.346659 + 0.200144i
\(306\) 0 0
\(307\) 8.33362i 0.475625i −0.971311 0.237813i \(-0.923570\pi\)
0.971311 0.237813i \(-0.0764304\pi\)
\(308\) 0 0
\(309\) −7.09334 + 12.2860i −0.403526 + 0.698927i
\(310\) 0 0
\(311\) −14.6227 −0.829176 −0.414588 0.910009i \(-0.636074\pi\)
−0.414588 + 0.910009i \(0.636074\pi\)
\(312\) 0 0
\(313\) 17.1328 0.968404 0.484202 0.874956i \(-0.339110\pi\)
0.484202 + 0.874956i \(0.339110\pi\)
\(314\) 0 0
\(315\) 1.29350 2.24041i 0.0728805 0.126233i
\(316\) 0 0
\(317\) 14.0000i 0.786320i −0.919470 0.393160i \(-0.871382\pi\)
0.919470 0.393160i \(-0.128618\pi\)
\(318\) 0 0
\(319\) −7.35627 + 4.24714i −0.411872 + 0.237794i
\(320\) 0 0
\(321\) 8.68157 + 15.0369i 0.484558 + 0.839279i
\(322\) 0 0
\(323\) −4.20317 2.42670i −0.233871 0.135025i
\(324\) 0 0
\(325\) 6.74791 15.6652i 0.374307 0.868947i
\(326\) 0 0
\(327\) −29.1124 16.8081i −1.60992 0.929487i
\(328\) 0 0
\(329\) −2.25863 3.91206i −0.124522 0.215679i
\(330\) 0 0
\(331\) −5.99286 + 3.45998i −0.329397 + 0.190178i −0.655574 0.755131i \(-0.727573\pi\)
0.326176 + 0.945309i \(0.394240\pi\)
\(332\) 0 0
\(333\) 50.9928i 2.79439i
\(334\) 0 0
\(335\) −2.17253 + 3.76292i −0.118698 + 0.205591i
\(336\) 0 0
\(337\) 11.1559 0.607703 0.303852 0.952719i \(-0.401727\pi\)
0.303852 + 0.952719i \(0.401727\pi\)
\(338\) 0 0
\(339\) 10.0488 0.545776
\(340\) 0 0
\(341\) −4.70512 + 8.14950i −0.254796 + 0.441320i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) −11.6084 + 6.70213i −0.624977 + 0.360830i
\(346\) 0 0
\(347\) −2.46255 4.26527i −0.132197 0.228971i 0.792326 0.610097i \(-0.208870\pi\)
−0.924523 + 0.381126i \(0.875536\pi\)
\(348\) 0 0
\(349\) 1.31926 + 0.761675i 0.0706183 + 0.0407715i 0.534893 0.844920i \(-0.320352\pi\)
−0.464275 + 0.885691i \(0.653685\pi\)
\(350\) 0 0
\(351\) 8.00098 18.5741i 0.427061 0.991415i
\(352\) 0 0
\(353\) 15.5261 + 8.96401i 0.826372 + 0.477106i 0.852609 0.522550i \(-0.175019\pi\)
−0.0262367 + 0.999656i \(0.508352\pi\)
\(354\) 0 0
\(355\) 1.34879 + 2.33618i 0.0715865 + 0.123991i
\(356\) 0 0
\(357\) −4.76775 + 2.75266i −0.252336 + 0.145686i
\(358\) 0 0
\(359\) 20.0014i 1.05563i −0.849359 0.527816i \(-0.823011\pi\)
0.849359 0.527816i \(-0.176989\pi\)
\(360\) 0 0
\(361\) −6.39707 + 11.0801i −0.336688 + 0.583161i
\(362\) 0 0
\(363\) 23.6294 1.24022
\(364\) 0 0
\(365\) −6.14421 −0.321602
\(366\) 0 0
\(367\) 13.7078 23.7427i 0.715544 1.23936i −0.247206 0.968963i \(-0.579512\pi\)
0.962749 0.270395i \(-0.0871543\pi\)
\(368\) 0 0
\(369\) 20.9820i 1.09228i
\(370\) 0 0
\(371\) −7.70460 + 4.44825i −0.400003 + 0.230942i
\(372\) 0 0
\(373\) 7.94643 + 13.7636i 0.411451 + 0.712653i 0.995049 0.0993893i \(-0.0316889\pi\)
−0.583598 + 0.812043i \(0.698356\pi\)
\(374\) 0 0
\(375\) −12.3578 7.13481i −0.638156 0.368440i
\(376\) 0 0
\(377\) −11.2682 15.1199i −0.580341 0.778712i
\(378\) 0 0
\(379\) −7.60284 4.38950i −0.390532 0.225474i 0.291859 0.956461i \(-0.405726\pi\)
−0.682390 + 0.730988i \(0.739060\pi\)
\(380\) 0 0
\(381\) 2.01124 + 3.48357i 0.103039 + 0.178469i
\(382\) 0 0
\(383\) −6.89562 + 3.98119i −0.352349 + 0.203429i −0.665720 0.746202i \(-0.731875\pi\)
0.313370 + 0.949631i \(0.398542\pi\)
\(384\) 0 0
\(385\) 0.842869i 0.0429566i
\(386\) 0 0
\(387\) 2.48580 4.30553i 0.126360 0.218862i
\(388\) 0 0
\(389\) −32.0434 −1.62467 −0.812333 0.583194i \(-0.801803\pi\)
−0.812333 + 0.583194i \(0.801803\pi\)
\(390\) 0 0
\(391\) 17.8082 0.900598
\(392\) 0 0
\(393\) 12.2550 21.2263i 0.618184 1.07073i
\(394\) 0 0
\(395\) 0.509777i 0.0256496i
\(396\) 0 0
\(397\) 5.57251 3.21729i 0.279676 0.161471i −0.353601 0.935396i \(-0.615043\pi\)
0.633277 + 0.773925i \(0.281710\pi\)
\(398\) 0 0
\(399\) −3.51972 6.09633i −0.176206 0.305198i
\(400\) 0 0
\(401\) −0.462092 0.266789i −0.0230758 0.0133228i 0.488418 0.872610i \(-0.337574\pi\)
−0.511494 + 0.859287i \(0.670908\pi\)
\(402\) 0 0
\(403\) −19.1859 8.26451i −0.955719 0.411685i
\(404\) 0 0
\(405\) −0.402337 0.232290i −0.0199923 0.0115426i
\(406\) 0 0
\(407\) 8.30697 + 14.3881i 0.411761 + 0.713191i
\(408\) 0 0
\(409\) −34.4269 + 19.8764i −1.70230 + 0.982824i −0.758877 + 0.651234i \(0.774252\pi\)
−0.943424 + 0.331590i \(0.892415\pi\)
\(410\) 0 0
\(411\) 24.0695i 1.18726i
\(412\) 0 0
\(413\) 3.10263 5.37392i 0.152671 0.264433i
\(414\) 0 0
\(415\) −4.62832 −0.227195
\(416\) 0 0
\(417\) 14.2375 0.697213
\(418\) 0 0
\(419\) 11.9088 20.6266i 0.581783 1.00768i −0.413485 0.910511i \(-0.635689\pi\)
0.995268 0.0971665i \(-0.0309779\pi\)
\(420\) 0 0
\(421\) 23.2419i 1.13274i 0.824151 + 0.566370i \(0.191653\pi\)
−0.824151 + 0.566370i \(0.808347\pi\)
\(422\) 0 0
\(423\) −19.5016 + 11.2593i −0.948200 + 0.547444i
\(424\) 0 0
\(425\) 4.60828 + 7.98178i 0.223535 + 0.387173i
\(426\) 0 0
\(427\) 11.6660 + 6.73536i 0.564557 + 0.325947i
\(428\) 0 0
\(429\) −1.92937 16.4348i −0.0931510 0.793482i
\(430\) 0 0
\(431\) 2.34424 + 1.35345i 0.112918 + 0.0651932i 0.555395 0.831586i \(-0.312567\pi\)
−0.442477 + 0.896780i \(0.645900\pi\)
\(432\) 0 0
\(433\) −2.90945 5.03932i −0.139819 0.242174i 0.787609 0.616176i \(-0.211319\pi\)
−0.927428 + 0.374002i \(0.877985\pi\)
\(434\) 0 0
\(435\) −6.64198 + 3.83475i −0.318459 + 0.183862i
\(436\) 0 0
\(437\) 22.7706i 1.08927i
\(438\) 0 0
\(439\) −19.0851 + 33.0563i −0.910882 + 1.57769i −0.0980599 + 0.995181i \(0.531264\pi\)
−0.812822 + 0.582513i \(0.802070\pi\)
\(440\) 0 0
\(441\) −4.98500 −0.237381
\(442\) 0 0
\(443\) 31.6740 1.50488 0.752440 0.658661i \(-0.228877\pi\)
0.752440 + 0.658661i \(0.228877\pi\)
\(444\) 0 0
\(445\) 3.11867 5.40169i 0.147839 0.256065i
\(446\) 0 0
\(447\) 9.50845i 0.449734i
\(448\) 0 0
\(449\) 27.1975 15.7025i 1.28353 0.741045i 0.306036 0.952020i \(-0.400997\pi\)
0.977491 + 0.210975i \(0.0676638\pi\)
\(450\) 0 0
\(451\) −3.41807 5.92027i −0.160951 0.278775i
\(452\) 0 0
\(453\) −30.9732 17.8824i −1.45525 0.840187i
\(454\) 0 0
\(455\) 1.85836 0.218163i 0.0871215 0.0102276i
\(456\) 0 0
\(457\) 27.5640 + 15.9141i 1.28939 + 0.744429i 0.978545 0.206032i \(-0.0660551\pi\)
0.310844 + 0.950461i \(0.399388\pi\)
\(458\) 0 0
\(459\) 5.46403 + 9.46398i 0.255039 + 0.441741i
\(460\) 0 0
\(461\) 1.01005 0.583153i 0.0470427 0.0271601i −0.476294 0.879286i \(-0.658020\pi\)
0.523337 + 0.852126i \(0.324687\pi\)
\(462\) 0 0
\(463\) 20.3441i 0.945469i 0.881205 + 0.472734i \(0.156733\pi\)
−0.881205 + 0.472734i \(0.843267\pi\)
\(464\) 0 0
\(465\) −4.24825 + 7.35819i −0.197008 + 0.341228i
\(466\) 0 0
\(467\) −1.56939 −0.0726229 −0.0363114 0.999341i \(-0.511561\pi\)
−0.0363114 + 0.999341i \(0.511561\pi\)
\(468\) 0 0
\(469\) 8.37266 0.386614
\(470\) 0 0
\(471\) −14.6504 + 25.3753i −0.675055 + 1.16923i
\(472\) 0 0
\(473\) 1.61979i 0.0744781i
\(474\) 0 0
\(475\) −10.2060 + 5.89243i −0.468283 + 0.270363i
\(476\) 0 0
\(477\) 22.1745 + 38.4074i 1.01530 + 1.75856i
\(478\) 0 0
\(479\) −6.68501 3.85959i −0.305446 0.176349i 0.339441 0.940627i \(-0.389762\pi\)
−0.644887 + 0.764278i \(0.723095\pi\)
\(480\) 0 0
\(481\) −29.5729 + 22.0394i −1.34841 + 1.00491i
\(482\) 0 0
\(483\) 22.3688 + 12.9146i 1.01781 + 0.587635i
\(484\) 0 0
\(485\) 1.14749 + 1.98751i 0.0521047 + 0.0902481i
\(486\) 0 0
\(487\) 0.0659739 0.0380900i 0.00298956 0.00172602i −0.498504 0.866887i \(-0.666117\pi\)
0.501494 + 0.865161i \(0.332784\pi\)
\(488\) 0 0
\(489\) 44.5155i 2.01306i
\(490\) 0 0
\(491\) −0.893574 + 1.54772i −0.0403264 + 0.0698474i −0.885484 0.464670i \(-0.846173\pi\)
0.845158 + 0.534517i \(0.179506\pi\)
\(492\) 0 0
\(493\) 10.1893 0.458902
\(494\) 0 0
\(495\) −4.20170 −0.188852
\(496\) 0 0
\(497\) 2.59905 4.50168i 0.116583 0.201928i
\(498\) 0 0
\(499\) 8.33493i 0.373123i −0.982443 0.186561i \(-0.940266\pi\)
0.982443 0.186561i \(-0.0597343\pi\)
\(500\) 0 0
\(501\) −40.1305 + 23.1694i −1.79290 + 1.03513i
\(502\) 0 0
\(503\) 0.720238 + 1.24749i 0.0321138 + 0.0556228i 0.881636 0.471931i \(-0.156443\pi\)
−0.849522 + 0.527554i \(0.823109\pi\)
\(504\) 0 0
\(505\) 8.22576 + 4.74914i 0.366041 + 0.211334i
\(506\) 0 0
\(507\) 35.7363 8.50779i 1.58710 0.377844i
\(508\) 0 0
\(509\) 12.8394 + 7.41282i 0.569096 + 0.328568i 0.756788 0.653660i \(-0.226767\pi\)
−0.187692 + 0.982228i \(0.560101\pi\)
\(510\) 0 0
\(511\) 5.91976 + 10.2533i 0.261875 + 0.453581i
\(512\) 0 0
\(513\) −12.1012 + 6.98664i −0.534282 + 0.308468i
\(514\) 0 0
\(515\) 2.60540i 0.114808i
\(516\) 0 0
\(517\) −3.66837 + 6.35380i −0.161335 + 0.279440i
\(518\) 0 0
\(519\) 0.851561 0.0373794
\(520\) 0 0
\(521\) −0.334388 −0.0146498 −0.00732489 0.999973i \(-0.502332\pi\)
−0.00732489 + 0.999973i \(0.502332\pi\)
\(522\) 0 0
\(523\) −16.2533 + 28.1515i −0.710705 + 1.23098i 0.253887 + 0.967234i \(0.418291\pi\)
−0.964593 + 0.263744i \(0.915043\pi\)
\(524\) 0 0
\(525\) 13.3678i 0.583420i
\(526\) 0 0
\(527\) 9.77570 5.64400i 0.425836 0.245857i
\(528\) 0 0
\(529\) −30.2751 52.4380i −1.31631 2.27991i
\(530\) 0 0
\(531\) −26.7890 15.4666i −1.16254 0.671194i
\(532\) 0 0
\(533\) 12.1683 9.06855i 0.527070 0.392803i
\(534\) 0 0
\(535\) 2.76155 + 1.59438i 0.119392 + 0.0689311i
\(536\) 0 0
\(537\) 13.8686 + 24.0212i 0.598476 + 1.03659i
\(538\) 0 0
\(539\) −1.40656 + 0.812080i −0.0605850 + 0.0349787i
\(540\) 0 0
\(541\) 10.6015i 0.455796i −0.973685 0.227898i \(-0.926815\pi\)
0.973685 0.227898i \(-0.0731852\pi\)
\(542\) 0 0
\(543\) −17.5650 + 30.4235i −0.753786 + 1.30560i
\(544\) 0 0
\(545\) −6.17364 −0.264450
\(546\) 0 0
\(547\) −10.2327 −0.437519 −0.218760 0.975779i \(-0.570201\pi\)
−0.218760 + 0.975779i \(0.570201\pi\)
\(548\) 0 0
\(549\) 33.5758 58.1549i 1.43298 2.48199i
\(550\) 0 0
\(551\) 13.0286i 0.555038i
\(552\) 0 0
\(553\) −0.850705 + 0.491155i −0.0361757 + 0.0208860i
\(554\) 0 0
\(555\) 7.50037 + 12.9910i 0.318373 + 0.551438i
\(556\) 0 0
\(557\) 27.7067 + 15.9965i 1.17397 + 0.677793i 0.954612 0.297851i \(-0.0962700\pi\)
0.219359 + 0.975644i \(0.429603\pi\)
\(558\) 0 0
\(559\) 3.57133 0.419257i 0.151051 0.0177327i
\(560\) 0 0
\(561\) 7.74359 + 4.47076i 0.326934 + 0.188756i
\(562\) 0 0
\(563\) −5.39566 9.34556i −0.227400 0.393868i 0.729637 0.683835i \(-0.239689\pi\)
−0.957037 + 0.289967i \(0.906356\pi\)
\(564\) 0 0
\(565\) 1.59823 0.922737i 0.0672380 0.0388199i
\(566\) 0 0
\(567\) 0.895217i 0.0375956i
\(568\) 0 0
\(569\) −12.3007 + 21.3054i −0.515672 + 0.893170i 0.484163 + 0.874978i \(0.339124\pi\)
−0.999835 + 0.0181917i \(0.994209\pi\)
\(570\) 0 0
\(571\) 16.5724 0.693534 0.346767 0.937951i \(-0.387279\pi\)
0.346767 + 0.937951i \(0.387279\pi\)
\(572\) 0 0
\(573\) 34.6070 1.44573
\(574\) 0 0
\(575\) 21.6206 37.4480i 0.901641 1.56169i
\(576\) 0 0
\(577\) 14.6611i 0.610348i 0.952297 + 0.305174i \(0.0987147\pi\)
−0.952297 + 0.305174i \(0.901285\pi\)
\(578\) 0 0
\(579\) 28.4702 16.4373i 1.18318 0.683111i
\(580\) 0 0
\(581\) 4.45926 + 7.72366i 0.185001 + 0.320431i
\(582\) 0 0
\(583\) 12.5135 + 7.22467i 0.518256 + 0.299215i
\(584\) 0 0
\(585\) −1.08754 9.26394i −0.0449644 0.383017i
\(586\) 0 0
\(587\) −30.5998 17.6668i −1.26299 0.729186i −0.289336 0.957227i \(-0.593435\pi\)
−0.973652 + 0.228041i \(0.926768\pi\)
\(588\) 0 0
\(589\) 7.21676 + 12.4998i 0.297362 + 0.515045i
\(590\) 0 0
\(591\) 4.40775 2.54481i 0.181310 0.104680i
\(592\) 0 0
\(593\) 16.4294i 0.674675i −0.941384 0.337338i \(-0.890474\pi\)
0.941384 0.337338i \(-0.109526\pi\)
\(594\) 0 0
\(595\) −0.505530 + 0.875603i −0.0207247 + 0.0358962i
\(596\) 0 0
\(597\) 18.6307 0.762504
\(598\) 0 0
\(599\) −12.0819 −0.493653 −0.246826 0.969060i \(-0.579388\pi\)
−0.246826 + 0.969060i \(0.579388\pi\)
\(600\) 0 0
\(601\) −3.90743 + 6.76787i −0.159387 + 0.276067i −0.934648 0.355574i \(-0.884285\pi\)
0.775261 + 0.631642i \(0.217619\pi\)
\(602\) 0 0
\(603\) 41.7377i 1.69969i
\(604\) 0 0
\(605\) 3.75818 2.16979i 0.152792 0.0882144i
\(606\) 0 0
\(607\) 17.7825 + 30.8001i 0.721768 + 1.25014i 0.960291 + 0.279002i \(0.0900035\pi\)
−0.238523 + 0.971137i \(0.576663\pi\)
\(608\) 0 0
\(609\) 12.7987 + 7.38934i 0.518630 + 0.299431i
\(610\) 0 0
\(611\) −14.9584 6.44347i −0.605153 0.260675i
\(612\) 0 0
\(613\) −10.3376 5.96839i −0.417530 0.241061i 0.276490 0.961017i \(-0.410829\pi\)
−0.694020 + 0.719956i \(0.744162\pi\)
\(614\) 0 0
\(615\) −3.08618 5.34542i −0.124447 0.215548i
\(616\) 0 0
\(617\) −20.4124 + 11.7851i −0.821772 + 0.474450i −0.851027 0.525122i \(-0.824020\pi\)
0.0292550 + 0.999572i \(0.490687\pi\)
\(618\) 0 0
\(619\) 28.5571i 1.14781i 0.818923 + 0.573904i \(0.194572\pi\)
−0.818923 + 0.573904i \(0.805428\pi\)
\(620\) 0 0
\(621\) 25.6355 44.4020i 1.02872 1.78179i
\(622\) 0 0
\(623\) −12.0190 −0.481530
\(624\) 0 0
\(625\) 21.0328 0.841311
\(626\) 0 0
\(627\) −5.71659 + 9.90142i −0.228298 + 0.395425i
\(628\) 0 0
\(629\) 19.9292i 0.794628i
\(630\) 0 0
\(631\) 38.9646 22.4962i 1.55116 0.895561i 0.553109 0.833109i \(-0.313441\pi\)
0.998048 0.0624526i \(-0.0198922\pi\)
\(632\) 0 0
\(633\) 15.1460 + 26.2337i 0.602001 + 1.04270i
\(634\) 0 0
\(635\) 0.639763 + 0.369367i 0.0253882 + 0.0146579i
\(636\) 0 0
\(637\) −2.15455 2.89101i −0.0853662 0.114546i
\(638\) 0 0
\(639\) −22.4409 12.9562i −0.887747 0.512541i
\(640\) 0 0
\(641\) −1.26650 2.19364i −0.0500238 0.0866437i 0.839929 0.542696i \(-0.182596\pi\)
−0.889953 + 0.456052i \(0.849263\pi\)
\(642\) 0 0
\(643\) −15.9150 + 9.18853i −0.627627 + 0.362360i −0.779832 0.625988i \(-0.784696\pi\)
0.152206 + 0.988349i \(0.451362\pi\)
\(644\) 0 0
\(645\) 1.46251i 0.0575863i
\(646\) 0 0
\(647\) −10.4643 + 18.1248i −0.411396 + 0.712558i −0.995043 0.0994494i \(-0.968292\pi\)
0.583647 + 0.812008i \(0.301625\pi\)
\(648\) 0 0
\(649\) −10.0783 −0.395609
\(650\) 0 0
\(651\) 16.3723 0.641680
\(652\) 0 0
\(653\) 24.0580 41.6696i 0.941461 1.63066i 0.178775 0.983890i \(-0.442786\pi\)
0.762686 0.646769i \(-0.223880\pi\)
\(654\) 0 0
\(655\) 4.50130i 0.175880i
\(656\) 0 0
\(657\) 51.1129 29.5100i 1.99410 1.15130i
\(658\) 0 0
\(659\) −1.10819 1.91944i −0.0431690 0.0747708i 0.843634 0.536919i \(-0.180412\pi\)
−0.886803 + 0.462148i \(0.847079\pi\)
\(660\) 0 0
\(661\) −0.552034 0.318717i −0.0214716 0.0123966i 0.489226 0.872157i \(-0.337279\pi\)
−0.510697 + 0.859761i \(0.670613\pi\)
\(662\) 0 0
\(663\) −7.85287 + 18.2303i −0.304980 + 0.708006i
\(664\) 0 0
\(665\) −1.11960 0.646401i −0.0434162 0.0250664i
\(666\) 0 0
\(667\) −23.9024 41.4002i −0.925506 1.60302i
\(668\) 0 0
\(669\) −31.5390 + 18.2091i −1.21937 + 0.704003i
\(670\) 0 0
\(671\) 21.8786i 0.844614i
\(672\) 0 0
\(673\) 7.70343 13.3427i 0.296945 0.514324i −0.678490 0.734609i \(-0.737365\pi\)
0.975436 + 0.220285i \(0.0706988\pi\)
\(674\) 0 0
\(675\) 26.5352 1.02134
\(676\) 0 0
\(677\) −11.6812 −0.448945 −0.224473 0.974480i \(-0.572066\pi\)
−0.224473 + 0.974480i \(0.572066\pi\)
\(678\) 0 0
\(679\) 2.21114 3.82981i 0.0848559 0.146975i
\(680\) 0 0
\(681\) 1.97565i 0.0757072i
\(682\) 0 0
\(683\) −19.8419 + 11.4557i −0.759227 + 0.438340i −0.829018 0.559221i \(-0.811100\pi\)
0.0697909 + 0.997562i \(0.477767\pi\)
\(684\) 0 0
\(685\) 2.21020 + 3.82817i 0.0844473 + 0.146267i
\(686\) 0 0
\(687\) 44.7514 + 25.8372i 1.70737 + 0.985752i
\(688\) 0 0
\(689\) −12.6901 + 29.4599i −0.483454 + 1.12233i
\(690\) 0 0
\(691\) 40.9046 + 23.6163i 1.55608 + 0.898405i 0.997625 + 0.0688729i \(0.0219403\pi\)
0.558458 + 0.829533i \(0.311393\pi\)
\(692\) 0 0
\(693\) 4.04822 + 7.01172i 0.153779 + 0.266353i
\(694\) 0 0
\(695\) 2.26443 1.30737i 0.0858946 0.0495913i
\(696\) 0 0
\(697\) 8.20026i 0.310607i
\(698\) 0 0
\(699\) 37.8365 65.5347i 1.43111 2.47875i
\(700\) 0 0
\(701\) 12.2098 0.461158 0.230579 0.973054i \(-0.425938\pi\)
0.230579 + 0.973054i \(0.425938\pi\)
\(702\) 0 0
\(703\) 25.4827 0.961097
\(704\) 0 0
\(705\) −3.31218 + 5.73686i −0.124744 + 0.216063i
\(706\) 0 0
\(707\) 18.3026i 0.688342i
\(708\) 0 0
\(709\) −15.4910 + 8.94374i −0.581777 + 0.335889i −0.761839 0.647766i \(-0.775703\pi\)
0.180062 + 0.983655i \(0.442370\pi\)
\(710\) 0 0
\(711\) 2.44841 + 4.24076i 0.0918224 + 0.159041i
\(712\) 0 0
\(713\) −45.8644 26.4798i −1.71764 0.991678i
\(714\) 0 0
\(715\) −1.81600 2.43674i −0.0679146 0.0911290i
\(716\) 0 0
\(717\) −40.6667 23.4789i −1.51872 0.876836i
\(718\) 0 0
\(719\) −4.56317 7.90364i −0.170178 0.294756i 0.768304 0.640085i \(-0.221101\pi\)
−0.938482 + 0.345329i \(0.887767\pi\)
\(720\) 0 0
\(721\) 4.34784 2.51023i 0.161922 0.0934858i
\(722\) 0 0
\(723\) 49.2048i 1.82995i
\(724\) 0 0
\(725\) 12.3706 21.4266i 0.459434 0.795763i
\(726\) 0 0
\(727\) −33.6859 −1.24934 −0.624670 0.780889i \(-0.714767\pi\)
−0.624670 + 0.780889i \(0.714767\pi\)
\(728\) 0 0
\(729\) −43.0880 −1.59585
\(730\) 0 0
\(731\) −0.971507 + 1.68270i −0.0359325 + 0.0622369i
\(732\) 0 0
\(733\) 46.4344i 1.71509i 0.514406 + 0.857547i \(0.328013\pi\)
−0.514406 + 0.857547i \(0.671987\pi\)
\(734\) 0 0
\(735\) −1.26999 + 0.733228i −0.0468442 + 0.0270455i
\(736\) 0 0
\(737\) −6.79927 11.7767i −0.250454 0.433799i
\(738\) 0 0
\(739\) 1.60237 + 0.925127i 0.0589440 + 0.0340314i 0.529182 0.848508i \(-0.322499\pi\)
−0.470238 + 0.882539i \(0.655832\pi\)
\(740\) 0 0
\(741\) −23.3104 10.0412i −0.856328 0.368871i
\(742\) 0 0
\(743\) −28.7095 16.5755i −1.05325 0.608094i −0.129693 0.991554i \(-0.541399\pi\)
−0.923558 + 0.383460i \(0.874732\pi\)
\(744\) 0 0
\(745\) 0.873120 + 1.51229i 0.0319886 + 0.0554059i
\(746\) 0 0
\(747\) 38.5024 22.2294i 1.40873 0.813331i
\(748\) 0 0
\(749\) 6.14456i 0.224517i
\(750\) 0 0
\(751\) 10.3871 17.9910i 0.379032 0.656503i −0.611890 0.790943i \(-0.709590\pi\)
0.990922 + 0.134441i \(0.0429237\pi\)
\(752\) 0 0
\(753\) −18.2257 −0.664182
\(754\) 0 0
\(755\) −6.56824 −0.239043
\(756\) 0 0
\(757\) −21.8075 + 37.7717i −0.792607 + 1.37283i 0.131741 + 0.991284i \(0.457943\pi\)
−0.924348 + 0.381551i \(0.875390\pi\)
\(758\) 0 0
\(759\) 41.9508i 1.52272i
\(760\) 0 0
\(761\) 10.7302 6.19511i 0.388971 0.224573i −0.292743 0.956191i \(-0.594568\pi\)
0.681714 + 0.731619i \(0.261235\pi\)
\(762\) 0 0
\(763\) 5.94812 + 10.3025i 0.215337 + 0.372974i
\(764\) 0 0
\(765\) 4.36488 + 2.52007i 0.157813 + 0.0911132i
\(766\) 0 0
\(767\) −2.60862 22.2208i −0.0941917 0.802347i
\(768\) 0 0
\(769\) −4.80955 2.77680i −0.173437 0.100134i 0.410769 0.911740i \(-0.365260\pi\)
−0.584205 + 0.811606i \(0.698594\pi\)
\(770\) 0 0
\(771\) −5.18750 8.98501i −0.186823 0.323587i
\(772\) 0 0
\(773\) 37.9355 21.9021i 1.36445 0.787764i 0.374235 0.927334i \(-0.377905\pi\)
0.990212 + 0.139570i \(0.0445721\pi\)
\(774\) 0 0
\(775\) 27.4092i 0.984566i
\(776\) 0 0
\(777\) 14.4528 25.0330i 0.518491 0.898052i
\(778\) 0 0
\(779\) −10.4853 −0.375677
\(780\) 0 0
\(781\) −8.44253 −0.302098
\(782\) 0 0
\(783\) 14.6678 25.4054i 0.524185 0.907916i
\(784\) 0 0
\(785\) 5.38113i 0.192061i
\(786\) 0 0
\(787\) −21.4782 + 12.4005i −0.765616 + 0.442029i −0.831309 0.555811i \(-0.812408\pi\)
0.0656923 + 0.997840i \(0.479074\pi\)
\(788\) 0 0
\(789\) 25.8831 + 44.8308i 0.921462 + 1.59602i
\(790\) 0 0
\(791\) −3.07969 1.77806i −0.109501 0.0632206i
\(792\) 0 0
\(793\) 48.2381 5.66293i 1.71299 0.201096i
\(794\) 0 0
\(795\) 11.2985 + 6.52316i 0.400715 +