Properties

Label 384.2.j.a.289.4
Level $384$
Weight $2$
Character 384.289
Analytic conductor $3.066$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 289.4
Root \(0.500000 - 0.691860i\) of defining polynomial
Character \(\chi\) \(=\) 384.289
Dual form 384.2.j.a.97.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{3} +(2.68554 - 2.68554i) q^{5} +2.15894i q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{3} +(2.68554 - 2.68554i) q^{5} +2.15894i q^{7} +1.00000i q^{9} +(1.79793 - 1.79793i) q^{11} +(-1.38372 - 1.38372i) q^{13} +3.79793 q^{15} -0.224777 q^{17} +(0.158942 + 0.158942i) q^{19} +(-1.52660 + 1.52660i) q^{21} +2.82843i q^{23} -9.42429i q^{25} +(-0.707107 + 0.707107i) q^{27} +(1.85712 + 1.85712i) q^{29} -1.84106 q^{31} +2.54266 q^{33} +(5.79793 + 5.79793i) q^{35} +(3.66949 - 3.66949i) q^{37} -1.95687i q^{39} +5.88163i q^{41} +(-7.75481 + 7.75481i) q^{43} +(2.68554 + 2.68554i) q^{45} +2.82843 q^{47} +2.33897 q^{49} +(-0.158942 - 0.158942i) q^{51} +(-7.51397 + 7.51397i) q^{53} -9.65685i q^{55} +0.224777i q^{57} +(4.00000 - 4.00000i) q^{59} +(-5.98737 - 5.98737i) q^{61} -2.15894 q^{63} -7.43208 q^{65} +(-10.4243 - 10.4243i) q^{67} +(-2.00000 + 2.00000i) q^{69} -4.31788i q^{71} +5.97474i q^{73} +(6.66398 - 6.66398i) q^{75} +(3.88163 + 3.88163i) q^{77} -15.0075 q^{79} -1.00000 q^{81} +(-10.1158 - 10.1158i) q^{83} +(-0.603650 + 0.603650i) q^{85} +2.62636i q^{87} +1.42847i q^{89} +(2.98737 - 2.98737i) q^{91} +(-1.30182 - 1.30182i) q^{93} +0.853690 q^{95} -16.3990 q^{97} +(1.79793 + 1.79793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 8q^{11} + 8q^{15} - 8q^{19} + 16q^{29} - 24q^{31} + 24q^{35} + 16q^{37} - 8q^{43} - 8q^{49} + 8q^{51} - 16q^{53} + 32q^{59} - 16q^{61} - 8q^{63} - 16q^{65} - 16q^{67} - 16q^{69} + 16q^{75} - 16q^{77} + 24q^{79} - 8q^{81} - 40q^{83} + 16q^{85} - 8q^{91} + 48q^{95} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 0 0
\(5\) 2.68554 2.68554i 1.20101 1.20101i 0.227153 0.973859i \(-0.427058\pi\)
0.973859 0.227153i \(-0.0729416\pi\)
\(6\) 0 0
\(7\) 2.15894i 0.816003i 0.912981 + 0.408002i \(0.133774\pi\)
−0.912981 + 0.408002i \(0.866226\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 1.79793 1.79793i 0.542097 0.542097i −0.382046 0.924143i \(-0.624780\pi\)
0.924143 + 0.382046i \(0.124780\pi\)
\(12\) 0 0
\(13\) −1.38372 1.38372i −0.383775 0.383775i 0.488685 0.872460i \(-0.337477\pi\)
−0.872460 + 0.488685i \(0.837477\pi\)
\(14\) 0 0
\(15\) 3.79793 0.980622
\(16\) 0 0
\(17\) −0.224777 −0.0545165 −0.0272583 0.999628i \(-0.508678\pi\)
−0.0272583 + 0.999628i \(0.508678\pi\)
\(18\) 0 0
\(19\) 0.158942 + 0.158942i 0.0364637 + 0.0364637i 0.725104 0.688640i \(-0.241792\pi\)
−0.688640 + 0.725104i \(0.741792\pi\)
\(20\) 0 0
\(21\) −1.52660 + 1.52660i −0.333132 + 0.333132i
\(22\) 0 0
\(23\) 2.82843i 0.589768i 0.955533 + 0.294884i \(0.0952810\pi\)
−0.955533 + 0.294884i \(0.904719\pi\)
\(24\) 0 0
\(25\) 9.42429i 1.88486i
\(26\) 0 0
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) 1.85712 + 1.85712i 0.344858 + 0.344858i 0.858190 0.513332i \(-0.171589\pi\)
−0.513332 + 0.858190i \(0.671589\pi\)
\(30\) 0 0
\(31\) −1.84106 −0.330664 −0.165332 0.986238i \(-0.552870\pi\)
−0.165332 + 0.986238i \(0.552870\pi\)
\(32\) 0 0
\(33\) 2.54266 0.442620
\(34\) 0 0
\(35\) 5.79793 + 5.79793i 0.980029 + 0.980029i
\(36\) 0 0
\(37\) 3.66949 3.66949i 0.603260 0.603260i −0.337916 0.941176i \(-0.609722\pi\)
0.941176 + 0.337916i \(0.109722\pi\)
\(38\) 0 0
\(39\) 1.95687i 0.313351i
\(40\) 0 0
\(41\) 5.88163i 0.918557i 0.888292 + 0.459278i \(0.151892\pi\)
−0.888292 + 0.459278i \(0.848108\pi\)
\(42\) 0 0
\(43\) −7.75481 + 7.75481i −1.18260 + 1.18260i −0.203528 + 0.979069i \(0.565241\pi\)
−0.979069 + 0.203528i \(0.934759\pi\)
\(44\) 0 0
\(45\) 2.68554 + 2.68554i 0.400337 + 0.400337i
\(46\) 0 0
\(47\) 2.82843 0.412568 0.206284 0.978492i \(-0.433863\pi\)
0.206284 + 0.978492i \(0.433863\pi\)
\(48\) 0 0
\(49\) 2.33897 0.334139
\(50\) 0 0
\(51\) −0.158942 0.158942i −0.0222563 0.0222563i
\(52\) 0 0
\(53\) −7.51397 + 7.51397i −1.03212 + 1.03212i −0.0326567 + 0.999467i \(0.510397\pi\)
−0.999467 + 0.0326567i \(0.989603\pi\)
\(54\) 0 0
\(55\) 9.65685i 1.30213i
\(56\) 0 0
\(57\) 0.224777i 0.0297725i
\(58\) 0 0
\(59\) 4.00000 4.00000i 0.520756 0.520756i −0.397044 0.917800i \(-0.629964\pi\)
0.917800 + 0.397044i \(0.129964\pi\)
\(60\) 0 0
\(61\) −5.98737 5.98737i −0.766604 0.766604i 0.210903 0.977507i \(-0.432360\pi\)
−0.977507 + 0.210903i \(0.932360\pi\)
\(62\) 0 0
\(63\) −2.15894 −0.272001
\(64\) 0 0
\(65\) −7.43208 −0.921836
\(66\) 0 0
\(67\) −10.4243 10.4243i −1.27353 1.27353i −0.944223 0.329307i \(-0.893185\pi\)
−0.329307 0.944223i \(-0.606815\pi\)
\(68\) 0 0
\(69\) −2.00000 + 2.00000i −0.240772 + 0.240772i
\(70\) 0 0
\(71\) 4.31788i 0.512438i −0.966619 0.256219i \(-0.917523\pi\)
0.966619 0.256219i \(-0.0824769\pi\)
\(72\) 0 0
\(73\) 5.97474i 0.699290i 0.936882 + 0.349645i \(0.113698\pi\)
−0.936882 + 0.349645i \(0.886302\pi\)
\(74\) 0 0
\(75\) 6.66398 6.66398i 0.769490 0.769490i
\(76\) 0 0
\(77\) 3.88163 + 3.88163i 0.442353 + 0.442353i
\(78\) 0 0
\(79\) −15.0075 −1.68848 −0.844239 0.535966i \(-0.819947\pi\)
−0.844239 + 0.535966i \(0.819947\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −10.1158 10.1158i −1.11036 1.11036i −0.993102 0.117253i \(-0.962591\pi\)
−0.117253 0.993102i \(-0.537409\pi\)
\(84\) 0 0
\(85\) −0.603650 + 0.603650i −0.0654750 + 0.0654750i
\(86\) 0 0
\(87\) 2.62636i 0.281575i
\(88\) 0 0
\(89\) 1.42847i 0.151417i 0.997130 + 0.0757086i \(0.0241219\pi\)
−0.997130 + 0.0757086i \(0.975878\pi\)
\(90\) 0 0
\(91\) 2.98737 2.98737i 0.313161 0.313161i
\(92\) 0 0
\(93\) −1.30182 1.30182i −0.134993 0.134993i
\(94\) 0 0
\(95\) 0.853690 0.0875867
\(96\) 0 0
\(97\) −16.3990 −1.66507 −0.832535 0.553973i \(-0.813111\pi\)
−0.832535 + 0.553973i \(0.813111\pi\)
\(98\) 0 0
\(99\) 1.79793 + 1.79793i 0.180699 + 0.180699i
\(100\) 0 0
\(101\) −0.0818942 + 0.0818942i −0.00814878 + 0.00814878i −0.711169 0.703021i \(-0.751834\pi\)
0.703021 + 0.711169i \(0.251834\pi\)
\(102\) 0 0
\(103\) 13.3507i 1.31548i 0.753245 + 0.657740i \(0.228488\pi\)
−0.753245 + 0.657740i \(0.771512\pi\)
\(104\) 0 0
\(105\) 8.19951i 0.800191i
\(106\) 0 0
\(107\) −7.27798 + 7.27798i −0.703589 + 0.703589i −0.965179 0.261590i \(-0.915753\pi\)
0.261590 + 0.965179i \(0.415753\pi\)
\(108\) 0 0
\(109\) 7.04057 + 7.04057i 0.674365 + 0.674365i 0.958719 0.284355i \(-0.0917793\pi\)
−0.284355 + 0.958719i \(0.591779\pi\)
\(110\) 0 0
\(111\) 5.18944 0.492559
\(112\) 0 0
\(113\) 18.8486 1.77313 0.886563 0.462608i \(-0.153086\pi\)
0.886563 + 0.462608i \(0.153086\pi\)
\(114\) 0 0
\(115\) 7.59587 + 7.59587i 0.708318 + 0.708318i
\(116\) 0 0
\(117\) 1.38372 1.38372i 0.127925 0.127925i
\(118\) 0 0
\(119\) 0.485281i 0.0444857i
\(120\) 0 0
\(121\) 4.53488i 0.412261i
\(122\) 0 0
\(123\) −4.15894 + 4.15894i −0.374999 + 0.374999i
\(124\) 0 0
\(125\) −11.8816 11.8816i −1.06273 1.06273i
\(126\) 0 0
\(127\) 3.81580 0.338597 0.169299 0.985565i \(-0.445850\pi\)
0.169299 + 0.985565i \(0.445850\pi\)
\(128\) 0 0
\(129\) −10.9670 −0.965586
\(130\) 0 0
\(131\) −0.767438 0.767438i −0.0670514 0.0670514i 0.672786 0.739837i \(-0.265098\pi\)
−0.739837 + 0.672786i \(0.765098\pi\)
\(132\) 0 0
\(133\) −0.343146 + 0.343146i −0.0297545 + 0.0297545i
\(134\) 0 0
\(135\) 3.79793i 0.326874i
\(136\) 0 0
\(137\) 5.31010i 0.453672i −0.973933 0.226836i \(-0.927162\pi\)
0.973933 0.226836i \(-0.0728382\pi\)
\(138\) 0 0
\(139\) 8.76744 8.76744i 0.743644 0.743644i −0.229633 0.973277i \(-0.573753\pi\)
0.973277 + 0.229633i \(0.0737526\pi\)
\(140\) 0 0
\(141\) 2.00000 + 2.00000i 0.168430 + 0.168430i
\(142\) 0 0
\(143\) −4.97567 −0.416086
\(144\) 0 0
\(145\) 9.97474 0.828357
\(146\) 0 0
\(147\) 1.65390 + 1.65390i 0.136412 + 0.136412i
\(148\) 0 0
\(149\) 1.02869 1.02869i 0.0842735 0.0842735i −0.663713 0.747987i \(-0.731021\pi\)
0.747987 + 0.663713i \(0.231021\pi\)
\(150\) 0 0
\(151\) 2.03696i 0.165766i −0.996559 0.0828829i \(-0.973587\pi\)
0.996559 0.0828829i \(-0.0264127\pi\)
\(152\) 0 0
\(153\) 0.224777i 0.0181722i
\(154\) 0 0
\(155\) −4.94424 + 4.94424i −0.397131 + 0.397131i
\(156\) 0 0
\(157\) −6.09378 6.09378i −0.486336 0.486336i 0.420812 0.907148i \(-0.361745\pi\)
−0.907148 + 0.420812i \(0.861745\pi\)
\(158\) 0 0
\(159\) −10.6264 −0.842725
\(160\) 0 0
\(161\) −6.10641 −0.481252
\(162\) 0 0
\(163\) 3.43692 + 3.43692i 0.269201 + 0.269201i 0.828778 0.559577i \(-0.189037\pi\)
−0.559577 + 0.828778i \(0.689037\pi\)
\(164\) 0 0
\(165\) 6.82843 6.82843i 0.531592 0.531592i
\(166\) 0 0
\(167\) 21.7023i 1.67937i −0.543072 0.839686i \(-0.682739\pi\)
0.543072 0.839686i \(-0.317261\pi\)
\(168\) 0 0
\(169\) 9.17064i 0.705434i
\(170\) 0 0
\(171\) −0.158942 + 0.158942i −0.0121546 + 0.0121546i
\(172\) 0 0
\(173\) 8.74653 + 8.74653i 0.664987 + 0.664987i 0.956551 0.291565i \(-0.0941758\pi\)
−0.291565 + 0.956551i \(0.594176\pi\)
\(174\) 0 0
\(175\) 20.3465 1.53805
\(176\) 0 0
\(177\) 5.65685 0.425195
\(178\) 0 0
\(179\) 8.23163 + 8.23163i 0.615261 + 0.615261i 0.944312 0.329051i \(-0.106729\pi\)
−0.329051 + 0.944312i \(0.606729\pi\)
\(180\) 0 0
\(181\) −6.72269 + 6.72269i −0.499694 + 0.499694i −0.911343 0.411649i \(-0.864953\pi\)
0.411649 + 0.911343i \(0.364953\pi\)
\(182\) 0 0
\(183\) 8.46742i 0.625930i
\(184\) 0 0
\(185\) 19.7091i 1.44904i
\(186\) 0 0
\(187\) −0.404135 + 0.404135i −0.0295533 + 0.0295533i
\(188\) 0 0
\(189\) −1.52660 1.52660i −0.111044 0.111044i
\(190\) 0 0
\(191\) 20.8032 1.50526 0.752632 0.658441i \(-0.228784\pi\)
0.752632 + 0.658441i \(0.228784\pi\)
\(192\) 0 0
\(193\) 14.1454 1.01821 0.509103 0.860705i \(-0.329977\pi\)
0.509103 + 0.860705i \(0.329977\pi\)
\(194\) 0 0
\(195\) −5.25527 5.25527i −0.376338 0.376338i
\(196\) 0 0
\(197\) 2.42865 2.42865i 0.173034 0.173034i −0.615277 0.788311i \(-0.710956\pi\)
0.788311 + 0.615277i \(0.210956\pi\)
\(198\) 0 0
\(199\) 0.306182i 0.0217047i 0.999941 + 0.0108523i \(0.00345447\pi\)
−0.999941 + 0.0108523i \(0.996546\pi\)
\(200\) 0 0
\(201\) 14.7422i 1.03983i
\(202\) 0 0
\(203\) −4.00941 + 4.00941i −0.281405 + 0.281405i
\(204\) 0 0
\(205\) 15.7954 + 15.7954i 1.10320 + 1.10320i
\(206\) 0 0
\(207\) −2.82843 −0.196589
\(208\) 0 0
\(209\) 0.571533 0.0395337
\(210\) 0 0
\(211\) 7.23256 + 7.23256i 0.497910 + 0.497910i 0.910787 0.412877i \(-0.135476\pi\)
−0.412877 + 0.910787i \(0.635476\pi\)
\(212\) 0 0
\(213\) 3.05320 3.05320i 0.209202 0.209202i
\(214\) 0 0
\(215\) 41.6517i 2.84063i
\(216\) 0 0
\(217\) 3.97474i 0.269823i
\(218\) 0 0
\(219\) −4.22478 + 4.22478i −0.285484 + 0.285484i
\(220\) 0 0
\(221\) 0.311029 + 0.311029i 0.0209221 + 0.0209221i
\(222\) 0 0
\(223\) 1.71908 0.115118 0.0575591 0.998342i \(-0.481668\pi\)
0.0575591 + 0.998342i \(0.481668\pi\)
\(224\) 0 0
\(225\) 9.42429 0.628286
\(226\) 0 0
\(227\) 10.1158 + 10.1158i 0.671410 + 0.671410i 0.958041 0.286631i \(-0.0925353\pi\)
−0.286631 + 0.958041i \(0.592535\pi\)
\(228\) 0 0
\(229\) 12.0195 12.0195i 0.794270 0.794270i −0.187915 0.982185i \(-0.560173\pi\)
0.982185 + 0.187915i \(0.0601730\pi\)
\(230\) 0 0
\(231\) 5.48946i 0.361180i
\(232\) 0 0
\(233\) 13.3779i 0.876418i 0.898873 + 0.438209i \(0.144387\pi\)
−0.898873 + 0.438209i \(0.855613\pi\)
\(234\) 0 0
\(235\) 7.59587 7.59587i 0.495500 0.495500i
\(236\) 0 0
\(237\) −10.6119 10.6119i −0.689319 0.689319i
\(238\) 0 0
\(239\) −13.3675 −0.864670 −0.432335 0.901713i \(-0.642310\pi\)
−0.432335 + 0.901713i \(0.642310\pi\)
\(240\) 0 0
\(241\) 0.211474 0.0136222 0.00681112 0.999977i \(-0.497832\pi\)
0.00681112 + 0.999977i \(0.497832\pi\)
\(242\) 0 0
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 0 0
\(245\) 6.28141 6.28141i 0.401305 0.401305i
\(246\) 0 0
\(247\) 0.439861i 0.0279877i
\(248\) 0 0
\(249\) 14.3059i 0.906601i
\(250\) 0 0
\(251\) 10.4337 10.4337i 0.658569 0.658569i −0.296472 0.955041i \(-0.595810\pi\)
0.955041 + 0.296472i \(0.0958102\pi\)
\(252\) 0 0
\(253\) 5.08532 + 5.08532i 0.319711 + 0.319711i
\(254\) 0 0
\(255\) −0.853690 −0.0534601
\(256\) 0 0
\(257\) −0.742176 −0.0462957 −0.0231478 0.999732i \(-0.507369\pi\)
−0.0231478 + 0.999732i \(0.507369\pi\)
\(258\) 0 0
\(259\) 7.92221 + 7.92221i 0.492262 + 0.492262i
\(260\) 0 0
\(261\) −1.85712 + 1.85712i −0.114953 + 0.114953i
\(262\) 0 0
\(263\) 5.48435i 0.338180i 0.985601 + 0.169090i \(0.0540828\pi\)
−0.985601 + 0.169090i \(0.945917\pi\)
\(264\) 0 0
\(265\) 40.3582i 2.47918i
\(266\) 0 0
\(267\) −1.01008 + 1.01008i −0.0618158 + 0.0618158i
\(268\) 0 0
\(269\) −14.4741 14.4741i −0.882500 0.882500i 0.111289 0.993788i \(-0.464502\pi\)
−0.993788 + 0.111289i \(0.964502\pi\)
\(270\) 0 0
\(271\) 14.0370 0.852685 0.426342 0.904562i \(-0.359802\pi\)
0.426342 + 0.904562i \(0.359802\pi\)
\(272\) 0 0
\(273\) 4.22478 0.255695
\(274\) 0 0
\(275\) −16.9442 16.9442i −1.02178 1.02178i
\(276\) 0 0
\(277\) −9.49013 + 9.49013i −0.570207 + 0.570207i −0.932186 0.361980i \(-0.882101\pi\)
0.361980 + 0.932186i \(0.382101\pi\)
\(278\) 0 0
\(279\) 1.84106i 0.110221i
\(280\) 0 0
\(281\) 3.89359i 0.232272i −0.993233 0.116136i \(-0.962949\pi\)
0.993233 0.116136i \(-0.0370509\pi\)
\(282\) 0 0
\(283\) −12.4853 + 12.4853i −0.742173 + 0.742173i −0.972996 0.230823i \(-0.925858\pi\)
0.230823 + 0.972996i \(0.425858\pi\)
\(284\) 0 0
\(285\) 0.603650 + 0.603650i 0.0357571 + 0.0357571i
\(286\) 0 0
\(287\) −12.6981 −0.749545
\(288\) 0 0
\(289\) −16.9495 −0.997028
\(290\) 0 0
\(291\) −11.5959 11.5959i −0.679762 0.679762i
\(292\) 0 0
\(293\) 11.1553 11.1553i 0.651697 0.651697i −0.301704 0.953402i \(-0.597556\pi\)
0.953402 + 0.301704i \(0.0975556\pi\)
\(294\) 0 0
\(295\) 21.4844i 1.25087i
\(296\) 0 0
\(297\) 2.54266i 0.147540i
\(298\) 0 0
\(299\) 3.91375 3.91375i 0.226338 0.226338i
\(300\) 0 0
\(301\) −16.7422 16.7422i −0.965003 0.965003i
\(302\) 0 0
\(303\) −0.115816 −0.00665345
\(304\) 0 0
\(305\) −32.1587 −1.84140
\(306\) 0 0
\(307\) −5.40320 5.40320i −0.308377 0.308377i 0.535903 0.844280i \(-0.319971\pi\)
−0.844280 + 0.535903i \(0.819971\pi\)
\(308\) 0 0
\(309\) −9.44035 + 9.44035i −0.537043 + 0.537043i
\(310\) 0 0
\(311\) 24.1623i 1.37012i −0.728488 0.685059i \(-0.759776\pi\)
0.728488 0.685059i \(-0.240224\pi\)
\(312\) 0 0
\(313\) 16.6105i 0.938881i 0.882964 + 0.469441i \(0.155544\pi\)
−0.882964 + 0.469441i \(0.844456\pi\)
\(314\) 0 0
\(315\) −5.79793 + 5.79793i −0.326676 + 0.326676i
\(316\) 0 0
\(317\) −1.81170 1.81170i −0.101755 0.101755i 0.654397 0.756152i \(-0.272923\pi\)
−0.756152 + 0.654397i \(0.772923\pi\)
\(318\) 0 0
\(319\) 6.67794 0.373893
\(320\) 0 0
\(321\) −10.2926 −0.574478
\(322\) 0 0
\(323\) −0.0357265 0.0357265i −0.00198788 0.00198788i
\(324\) 0 0
\(325\) −13.0406 + 13.0406i −0.723361 + 0.723361i
\(326\) 0 0
\(327\) 9.95687i 0.550616i
\(328\) 0 0
\(329\) 6.10641i 0.336657i
\(330\) 0 0
\(331\) 13.5252 13.5252i 0.743411 0.743411i −0.229822 0.973233i \(-0.573814\pi\)
0.973233 + 0.229822i \(0.0738142\pi\)
\(332\) 0 0
\(333\) 3.66949 + 3.66949i 0.201087 + 0.201087i
\(334\) 0 0
\(335\) −55.9898 −3.05905
\(336\) 0 0
\(337\) −1.12615 −0.0613454 −0.0306727 0.999529i \(-0.509765\pi\)
−0.0306727 + 0.999529i \(0.509765\pi\)
\(338\) 0 0
\(339\) 13.3280 + 13.3280i 0.723876 + 0.723876i
\(340\) 0 0
\(341\) −3.31010 + 3.31010i −0.179252 + 0.179252i
\(342\) 0 0
\(343\) 20.1623i 1.08866i
\(344\) 0 0
\(345\) 10.7422i 0.578339i
\(346\) 0 0
\(347\) 20.7938 20.7938i 1.11627 1.11627i 0.123983 0.992284i \(-0.460433\pi\)
0.992284 0.123983i \(-0.0395669\pi\)
\(348\) 0 0
\(349\) 19.2855 + 19.2855i 1.03233 + 1.03233i 0.999460 + 0.0328700i \(0.0104647\pi\)
0.0328700 + 0.999460i \(0.489535\pi\)
\(350\) 0 0
\(351\) 1.95687 0.104450
\(352\) 0 0
\(353\) 25.5908 1.36206 0.681029 0.732256i \(-0.261533\pi\)
0.681029 + 0.732256i \(0.261533\pi\)
\(354\) 0 0
\(355\) −11.5959 11.5959i −0.615445 0.615445i
\(356\) 0 0
\(357\) 0.343146 0.343146i 0.0181612 0.0181612i
\(358\) 0 0
\(359\) 3.77296i 0.199129i 0.995031 + 0.0995645i \(0.0317450\pi\)
−0.995031 + 0.0995645i \(0.968255\pi\)
\(360\) 0 0
\(361\) 18.9495i 0.997341i
\(362\) 0 0
\(363\) −3.20664 + 3.20664i −0.168305 + 0.168305i
\(364\) 0 0
\(365\) 16.0454 + 16.0454i 0.839856 + 0.839856i
\(366\) 0 0
\(367\) 27.4474 1.43274 0.716371 0.697720i \(-0.245802\pi\)
0.716371 + 0.697720i \(0.245802\pi\)
\(368\) 0 0
\(369\) −5.88163 −0.306186
\(370\) 0 0
\(371\) −16.2222 16.2222i −0.842216 0.842216i
\(372\) 0 0
\(373\) −12.6231 + 12.6231i −0.653601 + 0.653601i −0.953858 0.300257i \(-0.902928\pi\)
0.300257 + 0.953858i \(0.402928\pi\)
\(374\) 0 0
\(375\) 16.8032i 0.867712i
\(376\) 0 0
\(377\) 5.13946i 0.264695i
\(378\) 0 0
\(379\) −11.6686 + 11.6686i −0.599373 + 0.599373i −0.940146 0.340772i \(-0.889311\pi\)
0.340772 + 0.940146i \(0.389311\pi\)
\(380\) 0 0
\(381\) 2.69818 + 2.69818i 0.138232 + 0.138232i
\(382\) 0 0
\(383\) 17.1885 0.878291 0.439145 0.898416i \(-0.355281\pi\)
0.439145 + 0.898416i \(0.355281\pi\)
\(384\) 0 0
\(385\) 20.8486 1.06254
\(386\) 0 0
\(387\) −7.75481 7.75481i −0.394199 0.394199i
\(388\) 0 0
\(389\) 1.88238 1.88238i 0.0954404 0.0954404i −0.657774 0.753215i \(-0.728502\pi\)
0.753215 + 0.657774i \(0.228502\pi\)
\(390\) 0 0
\(391\) 0.635767i 0.0321521i
\(392\) 0 0
\(393\) 1.08532i 0.0547472i
\(394\) 0 0
\(395\) −40.3034 + 40.3034i −2.02788 + 2.02788i
\(396\) 0 0
\(397\) −8.41166 8.41166i −0.422169 0.422169i 0.463781 0.885950i \(-0.346493\pi\)
−0.885950 + 0.463781i \(0.846493\pi\)
\(398\) 0 0
\(399\) −0.485281 −0.0242945
\(400\) 0 0
\(401\) 1.12389 0.0561242 0.0280621 0.999606i \(-0.491066\pi\)
0.0280621 + 0.999606i \(0.491066\pi\)
\(402\) 0 0
\(403\) 2.54751 + 2.54751i 0.126900 + 0.126900i
\(404\) 0 0
\(405\) −2.68554 + 2.68554i −0.133446 + 0.133446i
\(406\) 0 0
\(407\) 13.1950i 0.654051i
\(408\) 0 0
\(409\) 13.7211i 0.678464i −0.940703 0.339232i \(-0.889833\pi\)
0.940703 0.339232i \(-0.110167\pi\)
\(410\) 0 0
\(411\) 3.75481 3.75481i 0.185211 0.185211i
\(412\) 0 0
\(413\) 8.63577 + 8.63577i 0.424938 + 0.424938i
\(414\) 0 0
\(415\) −54.3329 −2.66710
\(416\) 0 0
\(417\) 12.3990 0.607183
\(418\) 0 0
\(419\) −9.30755 9.30755i −0.454703 0.454703i 0.442209 0.896912i \(-0.354195\pi\)
−0.896912 + 0.442209i \(0.854195\pi\)
\(420\) 0 0
\(421\) −8.44378 + 8.44378i −0.411525 + 0.411525i −0.882269 0.470745i \(-0.843985\pi\)
0.470745 + 0.882269i \(0.343985\pi\)
\(422\) 0 0
\(423\) 2.82843i 0.137523i
\(424\) 0 0
\(425\) 2.11837i 0.102756i
\(426\) 0 0
\(427\) 12.9264 12.9264i 0.625551 0.625551i
\(428\) 0 0
\(429\) −3.51833 3.51833i −0.169866 0.169866i
\(430\) 0 0
\(431\) 30.6054 1.47421 0.737105 0.675778i \(-0.236192\pi\)
0.737105 + 0.675778i \(0.236192\pi\)
\(432\) 0 0
\(433\) −15.3137 −0.735930 −0.367965 0.929840i \(-0.619945\pi\)
−0.367965 + 0.929840i \(0.619945\pi\)
\(434\) 0 0
\(435\) 7.05320 + 7.05320i 0.338175 + 0.338175i
\(436\) 0 0
\(437\) −0.449555 + 0.449555i −0.0215051 + 0.0215051i
\(438\) 0 0
\(439\) 33.3676i 1.59255i −0.604936 0.796274i \(-0.706801\pi\)
0.604936 0.796274i \(-0.293199\pi\)
\(440\) 0 0
\(441\) 2.33897i 0.111380i
\(442\) 0 0
\(443\) 2.28832 2.28832i 0.108721 0.108721i −0.650653 0.759375i \(-0.725505\pi\)
0.759375 + 0.650653i \(0.225505\pi\)
\(444\) 0 0
\(445\) 3.83621 + 3.83621i 0.181854 + 0.181854i
\(446\) 0 0
\(447\) 1.45479 0.0688091
\(448\) 0 0
\(449\) −27.4165 −1.29387 −0.646933 0.762547i \(-0.723948\pi\)
−0.646933 + 0.762547i \(0.723948\pi\)
\(450\) 0 0
\(451\) 10.5748 + 10.5748i 0.497947 + 0.497947i
\(452\) 0 0
\(453\) 1.44035 1.44035i 0.0676736 0.0676736i
\(454\) 0 0
\(455\) 16.0454i 0.752221i
\(456\) 0 0
\(457\) 10.9147i 0.510567i −0.966866 0.255284i \(-0.917831\pi\)
0.966866 0.255284i \(-0.0821688\pi\)
\(458\) 0 0
\(459\) 0.158942 0.158942i 0.00741876 0.00741876i
\(460\) 0 0
\(461\) −17.8319 17.8319i −0.830512 0.830512i 0.157075 0.987587i \(-0.449794\pi\)
−0.987587 + 0.157075i \(0.949794\pi\)
\(462\) 0 0
\(463\) −22.4937 −1.04537 −0.522686 0.852525i \(-0.675070\pi\)
−0.522686 + 0.852525i \(0.675070\pi\)
\(464\) 0 0
\(465\) −6.99222 −0.324256
\(466\) 0 0
\(467\) 24.2171 + 24.2171i 1.12063 + 1.12063i 0.991646 + 0.128989i \(0.0411731\pi\)
0.128989 + 0.991646i \(0.458827\pi\)
\(468\) 0 0
\(469\) 22.5054 22.5054i 1.03920 1.03920i
\(470\) 0 0
\(471\) 8.61790i 0.397092i
\(472\) 0 0
\(473\) 27.8852i 1.28216i
\(474\) 0 0
\(475\) 1.49791 1.49791i 0.0687289 0.0687289i
\(476\) 0 0
\(477\) −7.51397 7.51397i −0.344041 0.344041i
\(478\) 0 0
\(479\) 36.2362 1.65568 0.827838 0.560968i \(-0.189571\pi\)
0.827838 + 0.560968i \(0.189571\pi\)
\(480\) 0 0
\(481\) −10.1551 −0.463032
\(482\) 0 0
\(483\) −4.31788 4.31788i −0.196470 0.196470i
\(484\) 0 0
\(485\) −44.0403 + 44.0403i −1.99977 + 1.99977i
\(486\) 0 0
\(487\) 16.8200i 0.762186i 0.924537 + 0.381093i \(0.124452\pi\)
−0.924537 + 0.381093i \(0.875548\pi\)
\(488\) 0 0
\(489\) 4.86054i 0.219801i
\(490\) 0 0
\(491\) 6.10641 6.10641i 0.275578 0.275578i −0.555763 0.831341i \(-0.687574\pi\)
0.831341 + 0.555763i \(0.187574\pi\)
\(492\) 0 0
\(493\) −0.417438 0.417438i −0.0188005 0.0188005i
\(494\) 0 0
\(495\) 9.65685 0.434043
\(496\) 0 0
\(497\) 9.32206 0.418151
\(498\) 0 0
\(499\) −19.6770 19.6770i −0.880864 0.880864i 0.112758 0.993622i \(-0.464031\pi\)
−0.993622 + 0.112758i \(0.964031\pi\)
\(500\) 0 0
\(501\) 15.3458 15.3458i 0.685601 0.685601i
\(502\) 0 0
\(503\) 25.7308i 1.14728i 0.819108 + 0.573639i \(0.194469\pi\)
−0.819108 + 0.573639i \(0.805531\pi\)
\(504\) 0 0
\(505\) 0.439861i 0.0195736i
\(506\) 0 0
\(507\) 6.48462 6.48462i 0.287992 0.287992i
\(508\) 0 0
\(509\) −1.73514 1.73514i −0.0769087 0.0769087i 0.667606 0.744515i \(-0.267319\pi\)
−0.744515 + 0.667606i \(0.767319\pi\)
\(510\) 0 0
\(511\) −12.8991 −0.570623
\(512\) 0 0
\(513\) −0.224777 −0.00992417
\(514\) 0 0
\(515\) 35.8538 + 35.8538i 1.57991 + 1.57991i
\(516\) 0 0
\(517\) 5.08532 5.08532i 0.223652 0.223652i
\(518\) 0 0
\(519\) 12.3695i 0.542959i
\(520\) 0 0
\(521\) 33.5944i 1.47180i −0.677092 0.735898i \(-0.736760\pi\)
0.677092 0.735898i \(-0.263240\pi\)
\(522\) 0 0
\(523\) −21.8158 + 21.8158i −0.953938 + 0.953938i −0.998985 0.0450467i \(-0.985656\pi\)
0.0450467 + 0.998985i \(0.485656\pi\)
\(524\) 0 0
\(525\) 14.3871 + 14.3871i 0.627907 + 0.627907i
\(526\) 0 0
\(527\) 0.413828 0.0180266
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) 0 0
\(531\) 4.00000 + 4.00000i 0.173585 + 0.173585i
\(532\) 0 0
\(533\) 8.13853 8.13853i 0.352519 0.352519i
\(534\) 0 0
\(535\) 39.0907i 1.69004i
\(536\) 0 0
\(537\) 11.6413i 0.502359i
\(538\) 0 0
\(539\) 4.20531 4.20531i 0.181136 0.181136i
\(540\) 0 0
\(541\) −27.2112 27.2112i −1.16990 1.16990i −0.982232 0.187669i \(-0.939907\pi\)
−0.187669 0.982232i \(-0.560093\pi\)
\(542\) 0 0
\(543\) −9.50732 −0.407998
\(544\) 0 0
\(545\) 37.8155 1.61984
\(546\) 0 0
\(547\) −6.80116 6.80116i −0.290796 0.290796i 0.546598 0.837395i \(-0.315922\pi\)
−0.837395 + 0.546598i \(0.815922\pi\)
\(548\) 0 0
\(549\) 5.98737 5.98737i 0.255535 0.255535i
\(550\) 0 0
\(551\) 0.590346i 0.0251496i
\(552\) 0 0
\(553\) 32.4004i 1.37780i
\(554\) 0 0
\(555\) 13.9365 13.9365i 0.591570 0.591570i
\(556\) 0 0
\(557\) 4.29337 + 4.29337i 0.181916 + 0.181916i 0.792190 0.610274i \(-0.208941\pi\)
−0.610274 + 0.792190i \(0.708941\pi\)
\(558\) 0 0
\(559\) 21.4609 0.907701
\(560\) 0 0
\(561\) −0.571533 −0.0241301
\(562\) 0 0
\(563\) −10.0801 10.0801i −0.424825 0.424825i 0.462036 0.886861i \(-0.347119\pi\)
−0.886861 + 0.462036i \(0.847119\pi\)
\(564\) 0 0
\(565\) 50.6187 50.6187i 2.12954 2.12954i
\(566\) 0 0
\(567\) 2.15894i 0.0906670i
\(568\) 0 0
\(569\) 32.5018i 1.36255i 0.732029 + 0.681274i \(0.238574\pi\)
−0.732029 + 0.681274i \(0.761426\pi\)
\(570\) 0 0
\(571\) −9.17157 + 9.17157i −0.383818 + 0.383818i −0.872476 0.488657i \(-0.837487\pi\)
0.488657 + 0.872476i \(0.337487\pi\)
\(572\) 0 0
\(573\) 14.7101 + 14.7101i 0.614522 + 0.614522i
\(574\) 0 0
\(575\) 26.6559 1.11163
\(576\) 0 0
\(577\) 11.7536 0.489308 0.244654 0.969611i \(-0.421326\pi\)
0.244654 + 0.969611i \(0.421326\pi\)
\(578\) 0 0
\(579\) 10.0023 + 10.0023i 0.415681 + 0.415681i
\(580\) 0 0
\(581\) 21.8395 21.8395i 0.906053 0.906053i
\(582\) 0 0
\(583\) 27.0192i 1.11902i
\(584\) 0 0
\(585\) 7.43208i 0.307279i
\(586\) 0 0
\(587\) 6.46002 6.46002i 0.266634 0.266634i −0.561109 0.827742i \(-0.689625\pi\)
0.827742 + 0.561109i \(0.189625\pi\)
\(588\) 0 0
\(589\) −0.292621 0.292621i −0.0120572 0.0120572i
\(590\) 0 0
\(591\) 3.43463 0.141282
\(592\) 0 0
\(593\) 5.49270 0.225558 0.112779 0.993620i \(-0.464025\pi\)
0.112779 + 0.993620i \(0.464025\pi\)
\(594\) 0 0
\(595\) −1.30324 1.30324i −0.0534278 0.0534278i
\(596\) 0 0
\(597\) −0.216503 + 0.216503i −0.00886089 + 0.00886089i
\(598\) 0 0
\(599\) 36.4348i 1.48868i 0.667799 + 0.744342i \(0.267237\pi\)
−0.667799 + 0.744342i \(0.732763\pi\)
\(600\) 0 0
\(601\) 9.97474i 0.406878i 0.979088 + 0.203439i \(0.0652119\pi\)
−0.979088 + 0.203439i \(0.934788\pi\)
\(602\) 0 0
\(603\) 10.4243 10.4243i 0.424510 0.424510i
\(604\) 0 0
\(605\) 12.1786 + 12.1786i 0.495131 + 0.495131i
\(606\) 0 0
\(607\) −4.51900 −0.183421 −0.0917103 0.995786i \(-0.529233\pi\)
−0.0917103 + 0.995786i \(0.529233\pi\)
\(608\) 0 0
\(609\) −5.67016 −0.229766
\(610\) 0 0
\(611\) −3.91375 3.91375i −0.158333 0.158333i
\(612\) 0 0
\(613\) 8.43692 8.43692i 0.340764 0.340764i −0.515890 0.856655i \(-0.672539\pi\)
0.856655 + 0.515890i \(0.172539\pi\)
\(614\) 0 0
\(615\) 22.3380i 0.900757i
\(616\) 0 0
\(617\) 32.1201i 1.29311i −0.762869 0.646554i \(-0.776210\pi\)
0.762869 0.646554i \(-0.223790\pi\)
\(618\) 0 0
\(619\) 15.0412 15.0412i 0.604559 0.604559i −0.336960 0.941519i \(-0.609399\pi\)
0.941519 + 0.336960i \(0.109399\pi\)
\(620\) 0 0
\(621\) −2.00000 2.00000i −0.0802572 0.0802572i
\(622\) 0 0
\(623\) −3.08398 −0.123557
\(624\) 0 0
\(625\) −16.6958 −0.667833
\(626\) 0 0
\(627\) 0.404135 + 0.404135i 0.0161396 + 0.0161396i
\(628\) 0 0
\(629\) −0.824818 + 0.824818i −0.0328876 + 0.0328876i
\(630\) 0 0
\(631\) 36.4685i 1.45179i −0.687807 0.725894i \(-0.741426\pi\)
0.687807 0.725894i \(-0.258574\pi\)
\(632\) 0 0
\(633\) 10.2284i 0.406542i
\(634\) 0 0
\(635\) 10.2475 10.2475i 0.406659 0.406659i
\(636\) 0 0
\(637\) −3.23648 3.23648i −0.128234 0.128234i
\(638\) 0 0
\(639\) 4.31788 0.170813
\(640\) 0 0
\(641\) 14.0036 0.553109 0.276555 0.960998i \(-0.410807\pi\)
0.276555 + 0.960998i \(0.410807\pi\)
\(642\) 0 0
\(643\) 16.6034 + 16.6034i 0.654774 + 0.654774i 0.954139 0.299365i \(-0.0967748\pi\)
−0.299365 + 0.954139i \(0.596775\pi\)
\(644\) 0 0
\(645\) −29.4522 + 29.4522i −1.15968 + 1.15968i
\(646\) 0 0
\(647\) 12.1908i 0.479270i −0.970863 0.239635i \(-0.922972\pi\)
0.970863 0.239635i \(-0.0770277\pi\)
\(648\) 0 0
\(649\) 14.3835i 0.564600i
\(650\) 0 0
\(651\) 2.81056 2.81056i 0.110155 0.110155i
\(652\) 0 0
\(653\) −0.983270 0.983270i −0.0384783 0.0384783i 0.687606 0.726084i \(-0.258662\pi\)
−0.726084 + 0.687606i \(0.758662\pi\)
\(654\) 0 0
\(655\) −4.12198 −0.161059
\(656\) 0 0
\(657\) −5.97474 −0.233097
\(658\) 0 0
\(659\) −18.0559 18.0559i −0.703357 0.703357i 0.261772 0.965130i \(-0.415693\pi\)
−0.965130 + 0.261772i \(0.915693\pi\)
\(660\) 0 0
\(661\) 4.55890 4.55890i 0.177321 0.177321i −0.612866 0.790187i \(-0.709983\pi\)
0.790187 + 0.612866i \(0.209983\pi\)
\(662\) 0 0
\(663\) 0.439861i 0.0170828i
\(664\) 0 0
\(665\) 1.84307i 0.0714710i
\(666\) 0 0
\(667\) −5.25272 + 5.25272i −0.203386 + 0.203386i
\(668\) 0 0
\(669\) 1.21557 + 1.21557i 0.0469968 + 0.0469968i
\(670\) 0 0
\(671\) −21.5298 −0.831148
\(672\) 0 0
\(673\) −10.8569 −0.418504 −0.209252 0.977862i \(-0.567103\pi\)
−0.209252 + 0.977862i \(0.567103\pi\)
\(674\) 0 0
\(675\) 6.66398 + 6.66398i 0.256497 + 0.256497i
\(676\) 0 0
\(677\) −23.7066 + 23.7066i −0.911120 + 0.911120i −0.996360 0.0852405i \(-0.972834\pi\)
0.0852405 + 0.996360i \(0.472834\pi\)
\(678\) 0 0
\(679\) 35.4045i 1.35870i
\(680\) 0 0
\(681\) 14.3059i 0.548204i
\(682\) 0 0
\(683\) −17.8337 + 17.8337i −0.682386 + 0.682386i −0.960537 0.278151i \(-0.910278\pi\)
0.278151 + 0.960537i \(0.410278\pi\)
\(684\) 0 0
\(685\) −14.2605 14.2605i −0.544866 0.544866i
\(686\) 0 0
\(687\) 16.9981 0.648519
\(688\) 0 0
\(689\) 20.7945 0.792205
\(690\) 0 0
\(691\) 10.8557 + 10.8557i 0.412970 + 0.412970i 0.882772 0.469802i \(-0.155675\pi\)
−0.469802 + 0.882772i \(0.655675\pi\)
\(692\) 0 0
\(693\) −3.88163 + 3.88163i −0.147451 + 0.147451i
\(694\) 0 0
\(695\) 47.0907i 1.78625i
\(696\) 0 0
\(697\) 1.32206i 0.0500765i
\(698\) 0 0
\(699\) −9.45963 + 9.45963i −0.357796 + 0.357796i
\(700\) 0 0
\(701\) 6.08875 + 6.08875i 0.229969 + 0.229969i 0.812680 0.582711i \(-0.198008\pi\)
−0.582711 + 0.812680i \(0.698008\pi\)
\(702\) 0 0
\(703\) 1.16647 0.0439942
\(704\) 0 0
\(705\) 10.7422 0.404574
\(706\) 0 0
\(707\) −0.176805 0.176805i −0.00664943 0.00664943i
\(708\) 0 0
\(709\) −22.8836 + 22.8836i −0.859413 + 0.859413i −0.991269 0.131856i \(-0.957906\pi\)
0.131856 + 0.991269i \(0.457906\pi\)
\(710\) 0 0
\(711\) 15.0075i 0.562826i
\(712\) 0 0
\(713\) 5.20730i 0.195015i
\(714\) 0 0
\(715\) −13.3624 + 13.3624i −0.499724 + 0.499724i
\(716\) 0 0
\(717\) −9.45223 9.45223i −0.353000 0.353000i
\(718\) 0 0
\(719\) 1.46744 0.0547262 0.0273631 0.999626i \(-0.491289\pi\)
0.0273631 + 0.999626i \(0.491289\pi\)
\(720\) 0 0
\(721\) −28.8233 −1.07344
\(722\) 0 0
\(723\) 0.149535 + 0.149535i 0.00556126 + 0.00556126i
\(724\) 0 0
\(725\) 17.5020 17.5020i 0.650008 0.650008i
\(726\) 0 0
\(727\) 15.3928i 0.570889i 0.958395 + 0.285445i \(0.0921412\pi\)
−0.958395 + 0.285445i \(0.907859\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 1.74311 1.74311i 0.0644711 0.0644711i
\(732\) 0 0
\(733\) 12.4185 + 12.4185i 0.458688 + 0.458688i 0.898225 0.439536i \(-0.144857\pi\)
−0.439536 + 0.898225i \(0.644857\pi\)
\(734\) 0 0
\(735\) 8.88325 0.327664
\(736\) 0 0
\(737\) −37.4844 −1.38075
\(738\) 0 0
\(739\) −14.6559 14.6559i −0.539127 0.539127i 0.384146 0.923273i \(-0.374496\pi\)
−0.923273 + 0.384146i \(0.874496\pi\)
\(740\) 0 0
\(741\) 0.311029 0.311029i 0.0114259 0.0114259i
\(742\) 0 0
\(743\) 31.7821i 1.16597i −0.812482 0.582986i \(-0.801884\pi\)
0.812482 0.582986i \(-0.198116\pi\)
\(744\) 0 0
\(745\) 5.52518i 0.202427i
\(746\) 0 0
\(747\) 10.1158 10.1158i 0.370118 0.370118i
\(748\) 0 0
\(749\) −15.7127 15.7127i −0.574131 0.574131i
\(750\) 0 0
\(751\) −29.7594 −1.08594 −0.542968 0.839753i \(-0.682699\pi\)
−0.542968 + 0.839753i \(0.682699\pi\)
\(752\) 0 0
\(753\) 14.7555 0.537720
\(754\) 0 0
\(755\) −5.47036 5.47036i −0.199087 0.199087i
\(756\) 0 0
\(757\) −15.6355 + 15.6355i −0.568282 + 0.568282i −0.931647 0.363365i \(-0.881628\pi\)
0.363365 + 0.931647i \(0.381628\pi\)
\(758\) 0 0
\(759\) 7.19173i 0.261043i
\(760\) 0 0
\(761\) 4.55957i 0.165284i 0.996579 + 0.0826422i \(0.0263359\pi\)
−0.996579 + 0.0826422i \(0.973664\pi\)
\(762\) 0 0
\(763\) −15.2002 + 15.2002i −0.550284 + 0.550284i
\(764\) 0 0
\(765\) −0.603650 0.603650i −0.0218250 0.0218250i
\(766\) 0 0
\(767\) −11.0698 −0.399706
\(768\) 0 0
\(769\) 36.5794 1.31909 0.659543 0.751667i \(-0.270750\pi\)
0.659543 + 0.751667i \(0.270750\pi\)
\(770\) 0 0
\(771\) −0.524797 0.524797i −0.0189001 0.0189001i
\(772\) 0 0
\(773\) 18.7108 18.7108i 0.672981 0.672981i −0.285421 0.958402i \(-0.592133\pi\)
0.958402 + 0.285421i \(0.0921335\pi\)
\(774\) 0 0
\(775\) 17.3507i 0.623255i
\(776\) 0 0
\(777\) 11.2037i 0.401930i
\(778\) 0 0
\(779\) −0.934836 + 0.934836i −0.0334940 + 0.0334940i
\(780\) 0 0
\(781\) −7.76326 7.76326i −0.277791 0.277791i
\(782\) 0 0
\(783\) −2.62636 −0.0938584
\(784\) 0 0
\(785\) −32.7302 −1.16819
\(786\) 0 0
\(787\) 13.3759 + 13.3759i 0.476801 + 0.476801i 0.904107 0.427306i \(-0.140537\pi\)
−0.427306 + 0.904107i \(0.640537\pi\)
\(788\) 0 0
\(789\) −3.87802 + 3.87802i −0.138061 + 0.138061i
\(790\) 0 0
\(791\) 40.6930i 1.44688i
\(792\) 0 0
\(793\) 16.5697i 0.588406i
\(794\) 0 0
\(795\) −28.5376 + 28.5376i −1.01212 + 1.01212i
\(796\) 0 0
\(797\) 33.8043 + 33.8043i 1.19741 + 1.19741i 0.974939 + 0.222471i \(0.0714124\pi\)
0.222471 + 0.974939i \(0.428588\pi\)
\(798\) 0 0
\(799\) −0.635767