Properties

Label 384.3.i.c.161.3
Level $384$
Weight $3$
Character 384.161
Analytic conductor $10.463$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{23} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 161.3
Root \(1.28499 + 1.53258i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.c.353.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.17774 - 2.06336i) q^{3} +(-3.17955 - 3.17955i) q^{5} +6.03979i q^{7} +(0.485128 + 8.98692i) q^{9} +O(q^{10})\) \(q+(-2.17774 - 2.06336i) q^{3} +(-3.17955 - 3.17955i) q^{5} +6.03979i q^{7} +(0.485128 + 8.98692i) q^{9} +(13.0097 + 13.0097i) q^{11} +(-6.39520 - 6.39520i) q^{13} +(0.363700 + 13.4848i) q^{15} -4.39848i q^{17} +(-3.21075 - 3.21075i) q^{19} +(12.4622 - 13.1531i) q^{21} +34.0396 q^{23} -4.78097i q^{25} +(17.4867 - 20.5722i) q^{27} +(27.9597 - 27.9597i) q^{29} +7.90993 q^{31} +(-1.48814 - 55.1754i) q^{33} +(19.2038 - 19.2038i) q^{35} +(-20.0443 + 20.0443i) q^{37} +(0.731530 + 27.1227i) q^{39} +45.1067 q^{41} +(-36.0095 + 36.0095i) q^{43} +(27.0318 - 30.1168i) q^{45} -5.08935i q^{47} +12.5209 q^{49} +(-9.07563 + 9.57876i) q^{51} +(20.7687 + 20.7687i) q^{53} -82.7299i q^{55} +(0.367268 + 13.6171i) q^{57} +(39.0656 + 39.0656i) q^{59} +(49.8322 + 49.8322i) q^{61} +(-54.2791 + 2.93007i) q^{63} +40.6677i q^{65} +(44.9162 + 44.9162i) q^{67} +(-74.1295 - 70.2358i) q^{69} +46.6947 q^{71} -97.3523i q^{73} +(-9.86483 + 10.4117i) q^{75} +(-78.5758 + 78.5758i) q^{77} +40.1637 q^{79} +(-80.5293 + 8.71960i) q^{81} +(35.5451 - 35.5451i) q^{83} +(-13.9852 + 13.9852i) q^{85} +(-118.580 + 3.19823i) q^{87} -69.6795 q^{89} +(38.6257 - 38.6257i) q^{91} +(-17.2258 - 16.3210i) q^{93} +20.4174i q^{95} +61.0939 q^{97} +(-110.606 + 123.228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 6q^{3} + O(q^{10}) \) \( 20q - 6q^{3} - 92q^{13} + 116q^{15} - 52q^{19} - 48q^{21} + 18q^{27} + 80q^{31} + 60q^{33} + 116q^{37} + 172q^{43} - 60q^{45} - 364q^{49} + 128q^{51} + 244q^{61} - 296q^{63} + 356q^{67} + 20q^{69} - 146q^{75} - 384q^{79} - 188q^{81} - 48q^{85} + 136q^{91} + 132q^{93} + 472q^{97} - 452q^{99} + O(q^{100}) \)

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
\(3\) −2.17774 2.06336i −0.725914 0.687785i
\(4\) 0 0
\(5\) −3.17955 3.17955i −0.635909 0.635909i 0.313634 0.949544i \(-0.398453\pi\)
−0.949544 + 0.313634i \(0.898453\pi\)
\(6\) 0 0
\(7\) 6.03979i 0.862827i 0.902154 + 0.431414i \(0.141985\pi\)
−0.902154 + 0.431414i \(0.858015\pi\)
\(8\) 0 0
\(9\) 0.485128 + 8.98692i 0.0539031 + 0.998546i
\(10\) 0 0
\(11\) 13.0097 + 13.0097i 1.18270 + 1.18270i 0.979042 + 0.203657i \(0.0652828\pi\)
0.203657 + 0.979042i \(0.434717\pi\)
\(12\) 0 0
\(13\) −6.39520 6.39520i −0.491939 0.491939i 0.416978 0.908917i \(-0.363089\pi\)
−0.908917 + 0.416978i \(0.863089\pi\)
\(14\) 0 0
\(15\) 0.363700 + 13.4848i 0.0242466 + 0.898985i
\(16\) 0 0
\(17\) 4.39848i 0.258734i −0.991597 0.129367i \(-0.958705\pi\)
0.991597 0.129367i \(-0.0412945\pi\)
\(18\) 0 0
\(19\) −3.21075 3.21075i −0.168987 0.168987i 0.617547 0.786534i \(-0.288126\pi\)
−0.786534 + 0.617547i \(0.788126\pi\)
\(20\) 0 0
\(21\) 12.4622 13.1531i 0.593440 0.626339i
\(22\) 0 0
\(23\) 34.0396 1.47998 0.739992 0.672616i \(-0.234829\pi\)
0.739992 + 0.672616i \(0.234829\pi\)
\(24\) 0 0
\(25\) 4.78097i 0.191239i
\(26\) 0 0
\(27\) 17.4867 20.5722i 0.647656 0.761933i
\(28\) 0 0
\(29\) 27.9597 27.9597i 0.964128 0.964128i −0.0352510 0.999378i \(-0.511223\pi\)
0.999378 + 0.0352510i \(0.0112231\pi\)
\(30\) 0 0
\(31\) 7.90993 0.255159 0.127580 0.991828i \(-0.459279\pi\)
0.127580 + 0.991828i \(0.459279\pi\)
\(32\) 0 0
\(33\) −1.48814 55.1754i −0.0450952 1.67198i
\(34\) 0 0
\(35\) 19.2038 19.2038i 0.548680 0.548680i
\(36\) 0 0
\(37\) −20.0443 + 20.0443i −0.541736 + 0.541736i −0.924038 0.382301i \(-0.875132\pi\)
0.382301 + 0.924038i \(0.375132\pi\)
\(38\) 0 0
\(39\) 0.731530 + 27.1227i 0.0187572 + 0.695453i
\(40\) 0 0
\(41\) 45.1067 1.10016 0.550081 0.835111i \(-0.314597\pi\)
0.550081 + 0.835111i \(0.314597\pi\)
\(42\) 0 0
\(43\) −36.0095 + 36.0095i −0.837431 + 0.837431i −0.988520 0.151089i \(-0.951722\pi\)
0.151089 + 0.988520i \(0.451722\pi\)
\(44\) 0 0
\(45\) 27.0318 30.1168i 0.600707 0.669262i
\(46\) 0 0
\(47\) 5.08935i 0.108284i −0.998533 0.0541421i \(-0.982758\pi\)
0.998533 0.0541421i \(-0.0172424\pi\)
\(48\) 0 0
\(49\) 12.5209 0.255529
\(50\) 0 0
\(51\) −9.07563 + 9.57876i −0.177953 + 0.187819i
\(52\) 0 0
\(53\) 20.7687 + 20.7687i 0.391863 + 0.391863i 0.875351 0.483488i \(-0.160630\pi\)
−0.483488 + 0.875351i \(0.660630\pi\)
\(54\) 0 0
\(55\) 82.7299i 1.50418i
\(56\) 0 0
\(57\) 0.367268 + 13.6171i 0.00644331 + 0.238896i
\(58\) 0 0
\(59\) 39.0656 + 39.0656i 0.662129 + 0.662129i 0.955881 0.293753i \(-0.0949043\pi\)
−0.293753 + 0.955881i \(0.594904\pi\)
\(60\) 0 0
\(61\) 49.8322 + 49.8322i 0.816921 + 0.816921i 0.985661 0.168739i \(-0.0539696\pi\)
−0.168739 + 0.985661i \(0.553970\pi\)
\(62\) 0 0
\(63\) −54.2791 + 2.93007i −0.861573 + 0.0465090i
\(64\) 0 0
\(65\) 40.6677i 0.625657i
\(66\) 0 0
\(67\) 44.9162 + 44.9162i 0.670390 + 0.670390i 0.957806 0.287416i \(-0.0927961\pi\)
−0.287416 + 0.957806i \(0.592796\pi\)
\(68\) 0 0
\(69\) −74.1295 70.2358i −1.07434 1.01791i
\(70\) 0 0
\(71\) 46.6947 0.657672 0.328836 0.944387i \(-0.393344\pi\)
0.328836 + 0.944387i \(0.393344\pi\)
\(72\) 0 0
\(73\) 97.3523i 1.33359i −0.745240 0.666797i \(-0.767665\pi\)
0.745240 0.666797i \(-0.232335\pi\)
\(74\) 0 0
\(75\) −9.86483 + 10.4117i −0.131531 + 0.138823i
\(76\) 0 0
\(77\) −78.5758 + 78.5758i −1.02047 + 1.02047i
\(78\) 0 0
\(79\) 40.1637 0.508402 0.254201 0.967151i \(-0.418188\pi\)
0.254201 + 0.967151i \(0.418188\pi\)
\(80\) 0 0
\(81\) −80.5293 + 8.71960i −0.994189 + 0.107649i
\(82\) 0 0
\(83\) 35.5451 35.5451i 0.428254 0.428254i −0.459779 0.888033i \(-0.652071\pi\)
0.888033 + 0.459779i \(0.152071\pi\)
\(84\) 0 0
\(85\) −13.9852 + 13.9852i −0.164531 + 0.164531i
\(86\) 0 0
\(87\) −118.580 + 3.19823i −1.36299 + 0.0367613i
\(88\) 0 0
\(89\) −69.6795 −0.782916 −0.391458 0.920196i \(-0.628029\pi\)
−0.391458 + 0.920196i \(0.628029\pi\)
\(90\) 0 0
\(91\) 38.6257 38.6257i 0.424458 0.424458i
\(92\) 0 0
\(93\) −17.2258 16.3210i −0.185224 0.175495i
\(94\) 0 0
\(95\) 20.4174i 0.214920i
\(96\) 0 0
\(97\) 61.0939 0.629834 0.314917 0.949119i \(-0.398023\pi\)
0.314917 + 0.949119i \(0.398023\pi\)
\(98\) 0 0
\(99\) −110.606 + 123.228i −1.11723 + 1.24473i
\(100\) 0 0
\(101\) 104.036 + 104.036i 1.03006 + 1.03006i 0.999534 + 0.0305280i \(0.00971886\pi\)
0.0305280 + 0.999534i \(0.490281\pi\)
\(102\) 0 0
\(103\) 57.2961i 0.556272i 0.960542 + 0.278136i \(0.0897167\pi\)
−0.960542 + 0.278136i \(0.910283\pi\)
\(104\) 0 0
\(105\) −81.4452 + 2.19667i −0.775668 + 0.0209207i
\(106\) 0 0
\(107\) −92.4468 92.4468i −0.863989 0.863989i 0.127810 0.991799i \(-0.459205\pi\)
−0.991799 + 0.127810i \(0.959205\pi\)
\(108\) 0 0
\(109\) −75.3749 75.3749i −0.691513 0.691513i 0.271052 0.962565i \(-0.412629\pi\)
−0.962565 + 0.271052i \(0.912629\pi\)
\(110\) 0 0
\(111\) 85.0096 2.29281i 0.765853 0.0206559i
\(112\) 0 0
\(113\) 112.254i 0.993401i 0.867922 + 0.496701i \(0.165455\pi\)
−0.867922 + 0.496701i \(0.834545\pi\)
\(114\) 0 0
\(115\) −108.231 108.231i −0.941135 0.941135i
\(116\) 0 0
\(117\) 54.3707 60.5756i 0.464706 0.517740i
\(118\) 0 0
\(119\) 26.5659 0.223243
\(120\) 0 0
\(121\) 217.504i 1.79756i
\(122\) 0 0
\(123\) −98.2307 93.0711i −0.798624 0.756676i
\(124\) 0 0
\(125\) −94.6900 + 94.6900i −0.757520 + 0.757520i
\(126\) 0 0
\(127\) −93.6335 −0.737272 −0.368636 0.929574i \(-0.620175\pi\)
−0.368636 + 0.929574i \(0.620175\pi\)
\(128\) 0 0
\(129\) 152.720 4.11903i 1.18388 0.0319305i
\(130\) 0 0
\(131\) 81.5208 81.5208i 0.622296 0.622296i −0.323822 0.946118i \(-0.604968\pi\)
0.946118 + 0.323822i \(0.104968\pi\)
\(132\) 0 0
\(133\) 19.3922 19.3922i 0.145806 0.145806i
\(134\) 0 0
\(135\) −121.010 + 9.81037i −0.896371 + 0.0726694i
\(136\) 0 0
\(137\) 24.5510 0.179205 0.0896023 0.995978i \(-0.471440\pi\)
0.0896023 + 0.995978i \(0.471440\pi\)
\(138\) 0 0
\(139\) 3.06917 3.06917i 0.0220804 0.0220804i −0.695980 0.718061i \(-0.745030\pi\)
0.718061 + 0.695980i \(0.245030\pi\)
\(140\) 0 0
\(141\) −10.5011 + 11.0833i −0.0744762 + 0.0786050i
\(142\) 0 0
\(143\) 166.399i 1.16363i
\(144\) 0 0
\(145\) −177.798 −1.22620
\(146\) 0 0
\(147\) −27.2674 25.8351i −0.185492 0.175749i
\(148\) 0 0
\(149\) 5.86344 + 5.86344i 0.0393519 + 0.0393519i 0.726509 0.687157i \(-0.241142\pi\)
−0.687157 + 0.726509i \(0.741142\pi\)
\(150\) 0 0
\(151\) 179.561i 1.18914i 0.804043 + 0.594571i \(0.202678\pi\)
−0.804043 + 0.594571i \(0.797322\pi\)
\(152\) 0 0
\(153\) 39.5288 2.13382i 0.258358 0.0139466i
\(154\) 0 0
\(155\) −25.1500 25.1500i −0.162258 0.162258i
\(156\) 0 0
\(157\) 14.8689 + 14.8689i 0.0947067 + 0.0947067i 0.752873 0.658166i \(-0.228668\pi\)
−0.658166 + 0.752873i \(0.728668\pi\)
\(158\) 0 0
\(159\) −2.37568 88.0822i −0.0149414 0.553976i
\(160\) 0 0
\(161\) 205.592i 1.27697i
\(162\) 0 0
\(163\) 66.1190 + 66.1190i 0.405638 + 0.405638i 0.880214 0.474577i \(-0.157399\pi\)
−0.474577 + 0.880214i \(0.657399\pi\)
\(164\) 0 0
\(165\) −170.701 + 180.164i −1.03455 + 1.09191i
\(166\) 0 0
\(167\) −158.709 −0.950353 −0.475176 0.879891i \(-0.657616\pi\)
−0.475176 + 0.879891i \(0.657616\pi\)
\(168\) 0 0
\(169\) 87.2028i 0.515993i
\(170\) 0 0
\(171\) 27.2971 30.4123i 0.159632 0.177850i
\(172\) 0 0
\(173\) 76.9955 76.9955i 0.445061 0.445061i −0.448648 0.893709i \(-0.648094\pi\)
0.893709 + 0.448648i \(0.148094\pi\)
\(174\) 0 0
\(175\) 28.8760 0.165006
\(176\) 0 0
\(177\) −4.46861 165.681i −0.0252464 0.936051i
\(178\) 0 0
\(179\) −101.360 + 101.360i −0.566257 + 0.566257i −0.931078 0.364821i \(-0.881130\pi\)
0.364821 + 0.931078i \(0.381130\pi\)
\(180\) 0 0
\(181\) 212.373 212.373i 1.17333 1.17333i 0.191920 0.981411i \(-0.438529\pi\)
0.981411 0.191920i \(-0.0614714\pi\)
\(182\) 0 0
\(183\) −5.70017 211.343i −0.0311485 1.15488i
\(184\) 0 0
\(185\) 127.463 0.688991
\(186\) 0 0
\(187\) 57.2229 57.2229i 0.306005 0.306005i
\(188\) 0 0
\(189\) 124.252 + 105.616i 0.657416 + 0.558815i
\(190\) 0 0
\(191\) 36.3314i 0.190217i −0.995467 0.0951083i \(-0.969680\pi\)
0.995467 0.0951083i \(-0.0303197\pi\)
\(192\) 0 0
\(193\) 47.1090 0.244088 0.122044 0.992525i \(-0.461055\pi\)
0.122044 + 0.992525i \(0.461055\pi\)
\(194\) 0 0
\(195\) 83.9119 88.5638i 0.430317 0.454173i
\(196\) 0 0
\(197\) −32.2783 32.2783i −0.163849 0.163849i 0.620420 0.784269i \(-0.286962\pi\)
−0.784269 + 0.620420i \(0.786962\pi\)
\(198\) 0 0
\(199\) 118.181i 0.593874i −0.954897 0.296937i \(-0.904035\pi\)
0.954897 0.296937i \(-0.0959651\pi\)
\(200\) 0 0
\(201\) −5.13784 190.494i −0.0255614 0.947731i
\(202\) 0 0
\(203\) 168.871 + 168.871i 0.831875 + 0.831875i
\(204\) 0 0
\(205\) −143.419 143.419i −0.699604 0.699604i
\(206\) 0 0
\(207\) 16.5136 + 305.911i 0.0797756 + 1.47783i
\(208\) 0 0
\(209\) 83.5416i 0.399721i
\(210\) 0 0
\(211\) 63.8884 + 63.8884i 0.302789 + 0.302789i 0.842104 0.539315i \(-0.181317\pi\)
−0.539315 + 0.842104i \(0.681317\pi\)
\(212\) 0 0
\(213\) −101.689 96.3478i −0.477413 0.452337i
\(214\) 0 0
\(215\) 228.988 1.06506
\(216\) 0 0
\(217\) 47.7743i 0.220158i
\(218\) 0 0
\(219\) −200.872 + 212.008i −0.917226 + 0.968075i
\(220\) 0 0
\(221\) −28.1292 + 28.1292i −0.127281 + 0.127281i
\(222\) 0 0
\(223\) 42.8886 0.192326 0.0961628 0.995366i \(-0.469343\pi\)
0.0961628 + 0.995366i \(0.469343\pi\)
\(224\) 0 0
\(225\) 42.9661 2.31938i 0.190961 0.0103084i
\(226\) 0 0
\(227\) −23.0035 + 23.0035i −0.101337 + 0.101337i −0.755958 0.654621i \(-0.772828\pi\)
0.654621 + 0.755958i \(0.272828\pi\)
\(228\) 0 0
\(229\) −241.282 + 241.282i −1.05363 + 1.05363i −0.0551571 + 0.998478i \(0.517566\pi\)
−0.998478 + 0.0551571i \(0.982434\pi\)
\(230\) 0 0
\(231\) 333.248 8.98807i 1.44263 0.0389094i
\(232\) 0 0
\(233\) −240.310 −1.03137 −0.515687 0.856777i \(-0.672463\pi\)
−0.515687 + 0.856777i \(0.672463\pi\)
\(234\) 0 0
\(235\) −16.1818 + 16.1818i −0.0688589 + 0.0688589i
\(236\) 0 0
\(237\) −87.4663 82.8721i −0.369056 0.349671i
\(238\) 0 0
\(239\) 218.171i 0.912851i 0.889762 + 0.456425i \(0.150870\pi\)
−0.889762 + 0.456425i \(0.849130\pi\)
\(240\) 0 0
\(241\) −88.9611 −0.369133 −0.184567 0.982820i \(-0.559088\pi\)
−0.184567 + 0.982820i \(0.559088\pi\)
\(242\) 0 0
\(243\) 193.364 + 147.172i 0.795736 + 0.605644i
\(244\) 0 0
\(245\) −39.8109 39.8109i −0.162493 0.162493i
\(246\) 0 0
\(247\) 41.0667i 0.166262i
\(248\) 0 0
\(249\) −150.750 + 4.06591i −0.605423 + 0.0163289i
\(250\) 0 0
\(251\) 169.225 + 169.225i 0.674205 + 0.674205i 0.958683 0.284478i \(-0.0918201\pi\)
−0.284478 + 0.958683i \(0.591820\pi\)
\(252\) 0 0
\(253\) 442.845 + 442.845i 1.75038 + 1.75038i
\(254\) 0 0
\(255\) 59.3125 1.59973i 0.232598 0.00627343i
\(256\) 0 0
\(257\) 393.109i 1.52961i −0.644262 0.764804i \(-0.722836\pi\)
0.644262 0.764804i \(-0.277164\pi\)
\(258\) 0 0
\(259\) −121.063 121.063i −0.467425 0.467425i
\(260\) 0 0
\(261\) 264.835 + 237.707i 1.01470 + 0.910756i
\(262\) 0 0
\(263\) 179.865 0.683897 0.341948 0.939719i \(-0.388913\pi\)
0.341948 + 0.939719i \(0.388913\pi\)
\(264\) 0 0
\(265\) 132.070i 0.498378i
\(266\) 0 0
\(267\) 151.744 + 143.774i 0.568330 + 0.538478i
\(268\) 0 0
\(269\) 290.530 290.530i 1.08004 1.08004i 0.0835324 0.996505i \(-0.473380\pi\)
0.996505 0.0835324i \(-0.0266202\pi\)
\(270\) 0 0
\(271\) −496.550 −1.83229 −0.916144 0.400849i \(-0.868715\pi\)
−0.916144 + 0.400849i \(0.868715\pi\)
\(272\) 0 0
\(273\) −163.815 + 4.41829i −0.600056 + 0.0161842i
\(274\) 0 0
\(275\) 62.1989 62.1989i 0.226178 0.226178i
\(276\) 0 0
\(277\) 93.0101 93.0101i 0.335776 0.335776i −0.518999 0.854775i \(-0.673695\pi\)
0.854775 + 0.518999i \(0.173695\pi\)
\(278\) 0 0
\(279\) 3.83733 + 71.0859i 0.0137539 + 0.254788i
\(280\) 0 0
\(281\) 300.875 1.07073 0.535365 0.844621i \(-0.320174\pi\)
0.535365 + 0.844621i \(0.320174\pi\)
\(282\) 0 0
\(283\) 101.469 101.469i 0.358549 0.358549i −0.504729 0.863278i \(-0.668408\pi\)
0.863278 + 0.504729i \(0.168408\pi\)
\(284\) 0 0
\(285\) 42.1284 44.4639i 0.147819 0.156014i
\(286\) 0 0
\(287\) 272.435i 0.949250i
\(288\) 0 0
\(289\) 269.653 0.933057
\(290\) 0 0
\(291\) −133.047 126.058i −0.457205 0.433190i
\(292\) 0 0
\(293\) −321.104 321.104i −1.09592 1.09592i −0.994883 0.101037i \(-0.967784\pi\)
−0.101037 0.994883i \(-0.532216\pi\)
\(294\) 0 0
\(295\) 248.422i 0.842107i
\(296\) 0 0
\(297\) 495.135 40.1409i 1.66712 0.135155i
\(298\) 0 0
\(299\) −217.690 217.690i −0.728061 0.728061i
\(300\) 0 0
\(301\) −217.490 217.490i −0.722558 0.722558i
\(302\) 0 0
\(303\) −11.9004 441.228i −0.0392753 1.45620i
\(304\) 0 0
\(305\) 316.888i 1.03898i
\(306\) 0 0
\(307\) 94.2282 + 94.2282i 0.306932 + 0.306932i 0.843718 0.536786i \(-0.180362\pi\)
−0.536786 + 0.843718i \(0.680362\pi\)
\(308\) 0 0
\(309\) 118.222 124.776i 0.382596 0.403806i
\(310\) 0 0
\(311\) −245.712 −0.790070 −0.395035 0.918666i \(-0.629268\pi\)
−0.395035 + 0.918666i \(0.629268\pi\)
\(312\) 0 0
\(313\) 353.841i 1.13048i 0.824925 + 0.565242i \(0.191217\pi\)
−0.824925 + 0.565242i \(0.808783\pi\)
\(314\) 0 0
\(315\) 181.899 + 163.267i 0.577458 + 0.518307i
\(316\) 0 0
\(317\) 234.024 234.024i 0.738245 0.738245i −0.233994 0.972238i \(-0.575179\pi\)
0.972238 + 0.233994i \(0.0751795\pi\)
\(318\) 0 0
\(319\) 727.494 2.28055
\(320\) 0 0
\(321\) 10.5747 + 392.076i 0.0329431 + 1.22142i
\(322\) 0 0
\(323\) −14.1224 + 14.1224i −0.0437226 + 0.0437226i
\(324\) 0 0
\(325\) −30.5752 + 30.5752i −0.0940777 + 0.0940777i
\(326\) 0 0
\(327\) 8.62193 + 319.673i 0.0263668 + 0.977592i
\(328\) 0 0
\(329\) 30.7386 0.0934305
\(330\) 0 0
\(331\) −32.5392 + 32.5392i −0.0983058 + 0.0983058i −0.754549 0.656243i \(-0.772144\pi\)
0.656243 + 0.754549i \(0.272144\pi\)
\(332\) 0 0
\(333\) −189.860 170.412i −0.570150 0.511748i
\(334\) 0 0
\(335\) 285.626i 0.852615i
\(336\) 0 0
\(337\) −185.573 −0.550660 −0.275330 0.961350i \(-0.588787\pi\)
−0.275330 + 0.961350i \(0.588787\pi\)
\(338\) 0 0
\(339\) 231.621 244.461i 0.683247 0.721124i
\(340\) 0 0
\(341\) 102.906 + 102.906i 0.301776 + 0.301776i
\(342\) 0 0
\(343\) 371.574i 1.08330i
\(344\) 0 0
\(345\) 12.3802 + 459.016i 0.0358846 + 1.33048i
\(346\) 0 0
\(347\) −51.9585 51.9585i −0.149736 0.149736i 0.628264 0.778000i \(-0.283766\pi\)
−0.778000 + 0.628264i \(0.783766\pi\)
\(348\) 0 0
\(349\) −378.719 378.719i −1.08515 1.08515i −0.996020 0.0891344i \(-0.971590\pi\)
−0.0891344 0.996020i \(-0.528410\pi\)
\(350\) 0 0
\(351\) −243.394 + 19.7322i −0.693431 + 0.0562170i
\(352\) 0 0
\(353\) 326.435i 0.924744i −0.886686 0.462372i \(-0.846998\pi\)
0.886686 0.462372i \(-0.153002\pi\)
\(354\) 0 0
\(355\) −148.468 148.468i −0.418220 0.418220i
\(356\) 0 0
\(357\) −57.8537 54.8149i −0.162055 0.153543i
\(358\) 0 0
\(359\) −254.927 −0.710103 −0.355051 0.934847i \(-0.615537\pi\)
−0.355051 + 0.934847i \(0.615537\pi\)
\(360\) 0 0
\(361\) 340.382i 0.942887i
\(362\) 0 0
\(363\) 448.789 473.668i 1.23633 1.30487i
\(364\) 0 0
\(365\) −309.536 + 309.536i −0.848045 + 0.848045i
\(366\) 0 0
\(367\) 124.247 0.338548 0.169274 0.985569i \(-0.445858\pi\)
0.169274 + 0.985569i \(0.445858\pi\)
\(368\) 0 0
\(369\) 21.8825 + 405.370i 0.0593021 + 1.09856i
\(370\) 0 0
\(371\) −125.439 + 125.439i −0.338110 + 0.338110i
\(372\) 0 0
\(373\) 201.674 201.674i 0.540680 0.540680i −0.383048 0.923728i \(-0.625126\pi\)
0.923728 + 0.383048i \(0.125126\pi\)
\(374\) 0 0
\(375\) 401.589 10.8313i 1.07091 0.0288835i
\(376\) 0 0
\(377\) −357.616 −0.948583
\(378\) 0 0
\(379\) −227.541 + 227.541i −0.600372 + 0.600372i −0.940411 0.340040i \(-0.889560\pi\)
0.340040 + 0.940411i \(0.389560\pi\)
\(380\) 0 0
\(381\) 203.910 + 193.199i 0.535196 + 0.507084i
\(382\) 0 0
\(383\) 128.933i 0.336641i 0.985732 + 0.168320i \(0.0538343\pi\)
−0.985732 + 0.168320i \(0.946166\pi\)
\(384\) 0 0
\(385\) 499.671 1.29785
\(386\) 0 0
\(387\) −341.084 306.145i −0.881353 0.791073i
\(388\) 0 0
\(389\) 107.474 + 107.474i 0.276283 + 0.276283i 0.831623 0.555340i \(-0.187412\pi\)
−0.555340 + 0.831623i \(0.687412\pi\)
\(390\) 0 0
\(391\) 149.723i 0.382922i
\(392\) 0 0
\(393\) −345.738 + 9.32494i −0.879739 + 0.0237276i
\(394\) 0 0
\(395\) −127.702 127.702i −0.323297 0.323297i
\(396\) 0 0
\(397\) 259.306 + 259.306i 0.653163 + 0.653163i 0.953753 0.300591i \(-0.0971837\pi\)
−0.300591 + 0.953753i \(0.597184\pi\)
\(398\) 0 0
\(399\) −82.2444 + 2.21822i −0.206126 + 0.00555946i
\(400\) 0 0
\(401\) 335.810i 0.837431i 0.908117 + 0.418716i \(0.137520\pi\)
−0.908117 + 0.418716i \(0.862480\pi\)
\(402\) 0 0
\(403\) −50.5856 50.5856i −0.125523 0.125523i
\(404\) 0 0
\(405\) 283.771 + 228.322i 0.700669 + 0.563759i
\(406\) 0 0
\(407\) −521.539 −1.28142
\(408\) 0 0
\(409\) 66.3618i 0.162254i −0.996704 0.0811269i \(-0.974148\pi\)
0.996704 0.0811269i \(-0.0258519\pi\)
\(410\) 0 0
\(411\) −53.4658 50.6575i −0.130087 0.123254i
\(412\) 0 0
\(413\) −235.948 + 235.948i −0.571303 + 0.571303i
\(414\) 0 0
\(415\) −226.035 −0.544662
\(416\) 0 0
\(417\) −13.0167 + 0.351074i −0.0312150 + 0.000841904i
\(418\) 0 0
\(419\) −371.566 + 371.566i −0.886792 + 0.886792i −0.994214 0.107422i \(-0.965740\pi\)
0.107422 + 0.994214i \(0.465740\pi\)
\(420\) 0 0
\(421\) −487.629 + 487.629i −1.15826 + 1.15826i −0.173416 + 0.984849i \(0.555481\pi\)
−0.984849 + 0.173416i \(0.944519\pi\)
\(422\) 0 0
\(423\) 45.7376 2.46899i 0.108127 0.00583685i
\(424\) 0 0
\(425\) −21.0290 −0.0494800
\(426\) 0 0
\(427\) −300.976 + 300.976i −0.704862 + 0.704862i
\(428\) 0 0
\(429\) −343.341 + 362.375i −0.800328 + 0.844696i
\(430\) 0 0
\(431\) 505.901i 1.17378i 0.809665 + 0.586892i \(0.199649\pi\)
−0.809665 + 0.586892i \(0.800351\pi\)
\(432\) 0 0
\(433\) −758.226 −1.75110 −0.875550 0.483128i \(-0.839500\pi\)
−0.875550 + 0.483128i \(0.839500\pi\)
\(434\) 0 0
\(435\) 387.199 + 366.861i 0.890113 + 0.843359i
\(436\) 0 0
\(437\) −109.293 109.293i −0.250097 0.250097i
\(438\) 0 0
\(439\) 145.760i 0.332026i −0.986124 0.166013i \(-0.946911\pi\)
0.986124 0.166013i \(-0.0530895\pi\)
\(440\) 0 0
\(441\) 6.07425 + 112.525i 0.0137738 + 0.255158i
\(442\) 0 0
\(443\) −607.046 607.046i −1.37031 1.37031i −0.859983 0.510323i \(-0.829526\pi\)
−0.510323 0.859983i \(-0.670474\pi\)
\(444\) 0 0
\(445\) 221.549 + 221.549i 0.497864 + 0.497864i
\(446\) 0 0
\(447\) −0.670702 24.8674i −0.00150045 0.0556318i
\(448\) 0 0
\(449\) 190.654i 0.424620i 0.977202 + 0.212310i \(0.0680986\pi\)
−0.977202 + 0.212310i \(0.931901\pi\)
\(450\) 0 0
\(451\) 586.824 + 586.824i 1.30116 + 1.30116i
\(452\) 0 0
\(453\) 370.497 391.037i 0.817875 0.863216i
\(454\) 0 0
\(455\) −245.624 −0.539834
\(456\) 0 0
\(457\) 128.091i 0.280287i −0.990131 0.140143i \(-0.955244\pi\)
0.990131 0.140143i \(-0.0447563\pi\)
\(458\) 0 0
\(459\) −90.4863 76.9150i −0.197138 0.167571i
\(460\) 0 0
\(461\) −74.2060 + 74.2060i −0.160968 + 0.160968i −0.782995 0.622028i \(-0.786309\pi\)
0.622028 + 0.782995i \(0.286309\pi\)
\(462\) 0 0
\(463\) −620.192 −1.33951 −0.669753 0.742584i \(-0.733600\pi\)
−0.669753 + 0.742584i \(0.733600\pi\)
\(464\) 0 0
\(465\) 2.87684 + 106.664i 0.00618675 + 0.229384i
\(466\) 0 0
\(467\) −331.708 + 331.708i −0.710296 + 0.710296i −0.966597 0.256301i \(-0.917496\pi\)
0.256301 + 0.966597i \(0.417496\pi\)
\(468\) 0 0
\(469\) −271.284 + 271.284i −0.578431 + 0.578431i
\(470\) 0 0
\(471\) −1.70082 63.0607i −0.00361108 0.133887i
\(472\) 0 0
\(473\) −936.946 −1.98086
\(474\) 0 0
\(475\) −15.3505 + 15.3505i −0.0323168 + 0.0323168i
\(476\) 0 0
\(477\) −176.571 + 196.722i −0.370170 + 0.412415i
\(478\) 0 0
\(479\) 867.941i 1.81198i −0.423294 0.905992i \(-0.639126\pi\)
0.423294 0.905992i \(-0.360874\pi\)
\(480\) 0 0
\(481\) 256.374 0.533002
\(482\) 0 0
\(483\) 424.210 447.727i 0.878281 0.926970i
\(484\) 0 0
\(485\) −194.251 194.251i −0.400517 0.400517i
\(486\) 0 0
\(487\) 815.778i 1.67511i −0.546354 0.837554i \(-0.683985\pi\)
0.546354 0.837554i \(-0.316015\pi\)
\(488\) 0 0
\(489\) −7.56317 280.417i −0.0154666 0.573450i
\(490\) 0 0
\(491\) 337.746 + 337.746i 0.687874 + 0.687874i 0.961762 0.273888i \(-0.0883098\pi\)
−0.273888 + 0.961762i \(0.588310\pi\)
\(492\) 0 0
\(493\) −122.980 122.980i −0.249453 0.249453i
\(494\) 0 0
\(495\) 743.486 40.1345i 1.50199 0.0810799i
\(496\) 0 0
\(497\) 282.026i 0.567457i
\(498\) 0 0
\(499\) −515.289 515.289i −1.03264 1.03264i −0.999449 0.0331940i \(-0.989432\pi\)
−0.0331940 0.999449i \(-0.510568\pi\)
\(500\) 0 0
\(501\) 345.627 + 327.473i 0.689875 + 0.653639i
\(502\) 0 0
\(503\) −196.781 −0.391215 −0.195607 0.980682i \(-0.562668\pi\)
−0.195607 + 0.980682i \(0.562668\pi\)
\(504\) 0 0
\(505\) 661.576i 1.31005i
\(506\) 0 0
\(507\) −179.930 + 189.905i −0.354892 + 0.374567i
\(508\) 0 0
\(509\) 29.3054 29.3054i 0.0575744 0.0575744i −0.677733 0.735308i \(-0.737038\pi\)
0.735308 + 0.677733i \(0.237038\pi\)
\(510\) 0 0
\(511\) 587.988 1.15066
\(512\) 0 0
\(513\) −122.197 + 9.90664i −0.238202 + 0.0193112i
\(514\) 0 0
\(515\) 182.175 182.175i 0.353739 0.353739i
\(516\) 0 0
\(517\) 66.2109 66.2109i 0.128068 0.128068i
\(518\) 0 0
\(519\) −326.546 + 8.80731i −0.629182 + 0.0169698i
\(520\) 0 0
\(521\) 770.641 1.47916 0.739578 0.673071i \(-0.235025\pi\)
0.739578 + 0.673071i \(0.235025\pi\)
\(522\) 0 0
\(523\) 258.725 258.725i 0.494694 0.494694i −0.415087 0.909782i \(-0.636249\pi\)
0.909782 + 0.415087i \(0.136249\pi\)
\(524\) 0 0
\(525\) −62.8846 59.5815i −0.119780 0.113489i
\(526\) 0 0
\(527\) 34.7917i 0.0660183i
\(528\) 0 0
\(529\) 629.695 1.19035
\(530\) 0 0
\(531\) −332.127 + 370.031i −0.625475 + 0.696857i
\(532\) 0 0
\(533\) −288.466 288.466i −0.541212 0.541212i
\(534\) 0 0
\(535\) 587.878i 1.09884i
\(536\) 0 0
\(537\) 429.878 11.5943i 0.800517 0.0215909i
\(538\) 0 0
\(539\) 162.894 + 162.894i 0.302214 + 0.302214i
\(540\) 0 0
\(541\) 122.667 + 122.667i 0.226742 + 0.226742i 0.811330 0.584588i \(-0.198744\pi\)
−0.584588 + 0.811330i \(0.698744\pi\)
\(542\) 0 0
\(543\) −900.694 + 24.2927i −1.65874 + 0.0447380i
\(544\) 0 0
\(545\) 479.316i 0.879479i
\(546\) 0 0
\(547\) 334.075 + 334.075i 0.610740 + 0.610740i 0.943139 0.332399i \(-0.107858\pi\)
−0.332399 + 0.943139i \(0.607858\pi\)
\(548\) 0 0
\(549\) −423.663 + 472.013i −0.771699 + 0.859768i
\(550\) 0 0
\(551\) −179.543 −0.325849
\(552\) 0 0
\(553\) 242.581i 0.438663i
\(554\) 0 0
\(555\) −277.582 263.002i −0.500148 0.473878i
\(556\) 0 0
\(557\) 159.480 159.480i 0.286320 0.286320i −0.549303 0.835623i \(-0.685107\pi\)
0.835623 + 0.549303i \(0.185107\pi\)
\(558\) 0 0
\(559\) 460.576 0.823929
\(560\) 0 0
\(561\) −242.688 + 6.54557i −0.432599 + 0.0116677i
\(562\) 0 0
\(563\) 341.226 341.226i 0.606086 0.606086i −0.335835 0.941921i \(-0.609018\pi\)
0.941921 + 0.335835i \(0.109018\pi\)
\(564\) 0 0
\(565\) 356.918 356.918i 0.631713 0.631713i
\(566\) 0 0
\(567\) −52.6646 486.380i −0.0928828 0.857813i
\(568\) 0 0
\(569\) 882.975 1.55180 0.775901 0.630855i \(-0.217296\pi\)
0.775901 + 0.630855i \(0.217296\pi\)
\(570\) 0 0
\(571\) 370.112 370.112i 0.648181 0.648181i −0.304372 0.952553i \(-0.598447\pi\)
0.952553 + 0.304372i \(0.0984466\pi\)
\(572\) 0 0
\(573\) −74.9645 + 79.1204i −0.130828 + 0.138081i
\(574\) 0 0
\(575\) 162.742i 0.283030i
\(576\) 0 0
\(577\) −698.607 −1.21076 −0.605378 0.795938i \(-0.706978\pi\)
−0.605378 + 0.795938i \(0.706978\pi\)
\(578\) 0 0
\(579\) −102.591 97.2025i −0.177187 0.167880i
\(580\) 0 0
\(581\) 214.685 + 214.685i 0.369509 + 0.369509i
\(582\) 0 0
\(583\) 540.389i 0.926911i
\(584\) 0 0
\(585\) −365.477 + 19.7290i −0.624747 + 0.0337248i
\(586\) 0 0
\(587\) −196.072 196.072i −0.334024 0.334024i 0.520088 0.854112i \(-0.325899\pi\)
−0.854112 + 0.520088i \(0.825899\pi\)
\(588\) 0 0
\(589\) −25.3968 25.3968i −0.0431185 0.0431185i
\(590\) 0 0
\(591\) 3.69222 + 136.895i 0.00624742 + 0.231633i
\(592\) 0 0
\(593\) 774.011i 1.30525i −0.757683 0.652623i \(-0.773669\pi\)
0.757683 0.652623i \(-0.226331\pi\)
\(594\) 0 0
\(595\) −84.4675 84.4675i −0.141962 0.141962i
\(596\) 0 0
\(597\) −243.849 + 257.368i −0.408458 + 0.431102i
\(598\) 0 0
\(599\) 783.533 1.30807 0.654034 0.756465i \(-0.273075\pi\)
0.654034 + 0.756465i \(0.273075\pi\)
\(600\) 0 0
\(601\) 797.210i 1.32647i 0.748410 + 0.663236i \(0.230818\pi\)
−0.748410 + 0.663236i \(0.769182\pi\)
\(602\) 0 0
\(603\) −381.868 + 425.448i −0.633280 + 0.705552i
\(604\) 0 0
\(605\) 691.565 691.565i 1.14308 1.14308i
\(606\) 0 0
\(607\) −433.576 −0.714293 −0.357146 0.934048i \(-0.616250\pi\)
−0.357146 + 0.934048i \(0.616250\pi\)
\(608\) 0 0
\(609\) −19.3167 716.197i −0.0317186 1.17602i
\(610\) 0 0
\(611\) −32.5475 + 32.5475i −0.0532692 + 0.0532692i
\(612\) 0 0
\(613\) 493.642 493.642i 0.805289 0.805289i −0.178628 0.983917i \(-0.557166\pi\)
0.983917 + 0.178628i \(0.0571658\pi\)
\(614\) 0 0
\(615\) 16.4053 + 608.253i 0.0266752 + 0.989029i
\(616\) 0 0
\(617\) −685.069 −1.11032 −0.555161 0.831743i \(-0.687343\pi\)
−0.555161 + 0.831743i \(0.687343\pi\)
\(618\) 0 0
\(619\) −379.995 + 379.995i −0.613885 + 0.613885i −0.943956 0.330071i \(-0.892927\pi\)
0.330071 + 0.943956i \(0.392927\pi\)
\(620\) 0 0
\(621\) 595.241 700.269i 0.958520 1.12765i
\(622\) 0 0
\(623\) 420.850i 0.675521i
\(624\) 0 0
\(625\) 482.618 0.772189
\(626\) 0 0
\(627\) −172.376 + 181.932i −0.274922 + 0.290163i
\(628\) 0 0
\(629\) 88.1642 + 88.1642i 0.140166 + 0.140166i
\(630\) 0 0
\(631\) 489.285i 0.775412i −0.921783 0.387706i \(-0.873268\pi\)
0.921783 0.387706i \(-0.126732\pi\)
\(632\) 0 0
\(633\) −7.30802 270.957i −0.0115451 0.428052i
\(634\) 0 0
\(635\) 297.712 + 297.712i 0.468838 + 0.468838i
\(636\) 0 0
\(637\) −80.0739 80.0739i −0.125705 0.125705i
\(638\) 0 0
\(639\) 22.6529 + 419.641i 0.0354505 + 0.656716i
\(640\) 0 0
\(641\) 492.158i 0.767797i −0.923375 0.383898i \(-0.874581\pi\)
0.923375 0.383898i \(-0.125419\pi\)
\(642\) 0 0
\(643\) −169.985 169.985i −0.264362 0.264362i 0.562462 0.826823i \(-0.309854\pi\)
−0.826823 + 0.562462i \(0.809854\pi\)
\(644\) 0 0
\(645\) −498.677 472.483i −0.773142 0.732532i
\(646\) 0 0
\(647\) 1003.50 1.55101 0.775503 0.631343i \(-0.217496\pi\)
0.775503 + 0.631343i \(0.217496\pi\)
\(648\) 0 0
\(649\) 1016.46i 1.56620i
\(650\) 0 0
\(651\) 98.5754 104.040i 0.151422 0.159816i
\(652\) 0 0
\(653\) −407.090 + 407.090i −0.623415 + 0.623415i −0.946403 0.322988i \(-0.895313\pi\)
0.322988 + 0.946403i \(0.395313\pi\)
\(654\) 0 0
\(655\) −518.398 −0.791448
\(656\) 0 0
\(657\) 874.897 47.2283i 1.33165 0.0718848i
\(658\) 0 0
\(659\) 635.355 635.355i 0.964119 0.964119i −0.0352587 0.999378i \(-0.511226\pi\)
0.999378 + 0.0352587i \(0.0112255\pi\)
\(660\) 0 0
\(661\) 196.325 196.325i 0.297013 0.297013i −0.542830 0.839843i \(-0.682647\pi\)
0.839843 + 0.542830i \(0.182647\pi\)
\(662\) 0 0
\(663\) 119.299 3.21762i 0.179937 0.00485312i
\(664\) 0 0
\(665\) −123.317 −0.185439
\(666\) 0 0
\(667\) 951.737 951.737i 1.42689 1.42689i
\(668\) 0 0
\(669\) −93.4003 88.4944i −0.139612 0.132279i
\(670\) 0 0
\(671\) 1296.60i 1.93234i
\(672\) 0 0
\(673\) −489.653 −0.727568 −0.363784 0.931483i \(-0.618515\pi\)
−0.363784 + 0.931483i \(0.618515\pi\)
\(674\) 0 0
\(675\) −98.3549 83.6034i −0.145711 0.123857i
\(676\) 0 0
\(677\) 832.940 + 832.940i 1.23034 + 1.23034i 0.963833 + 0.266507i \(0.0858695\pi\)
0.266507 + 0.963833i \(0.414131\pi\)
\(678\) 0 0
\(679\) 368.994i 0.543438i
\(680\) 0 0
\(681\) 97.5600 2.63131i 0.143260 0.00386388i
\(682\) 0 0
\(683\) 773.804 + 773.804i 1.13295 + 1.13295i 0.989684 + 0.143264i \(0.0457599\pi\)
0.143264 + 0.989684i \(0.454240\pi\)
\(684\) 0 0
\(685\) −78.0611 78.0611i −0.113958 0.113958i
\(686\) 0 0
\(687\) 1023.30 27.5996i 1.48952 0.0401741i
\(688\) 0 0
\(689\) 265.640i 0.385545i
\(690\) 0 0
\(691\) −840.306 840.306i −1.21607 1.21607i −0.968996 0.247077i \(-0.920530\pi\)
−0.247077 0.968996i \(-0.579470\pi\)
\(692\) 0 0
\(693\) −744.274 668.035i −1.07399 0.963975i
\(694\) 0 0
\(695\) −19.5171 −0.0280822
\(696\) 0 0
\(697\) 198.401i 0.284650i
\(698\) 0 0
\(699\) 523.334 + 495.845i 0.748689 + 0.709364i
\(700\) 0 0
\(701\) −529.432 + 529.432i −0.755253 + 0.755253i −0.975454 0.220201i \(-0.929329\pi\)
0.220201 + 0.975454i \(0.429329\pi\)
\(702\) 0 0
\(703\) 128.714 0.183092
\(704\) 0 0
\(705\) 68.6288 1.85100i 0.0973458 0.00262553i
\(706\) 0 0
\(707\) −628.357 + 628.357i −0.888765 + 0.888765i
\(708\) 0 0
\(709\) 56.2182 56.2182i 0.0792923 0.0792923i −0.666348 0.745641i \(-0.732144\pi\)
0.745641 + 0.666348i \(0.232144\pi\)
\(710\) 0 0
\(711\) 19.4845 + 360.948i 0.0274044 + 0.507663i
\(712\) 0 0
\(713\) 269.251 0.377631
\(714\) 0 0
\(715\) −529.074 + 529.074i −0.739964 + 0.739964i
\(716\) 0 0
\(717\) 450.165 475.121i 0.627845 0.662651i
\(718\) 0 0
\(719\) 966.944i 1.34485i 0.740167 + 0.672423i \(0.234746\pi\)
−0.740167 + 0.672423i \(0.765254\pi\)
\(720\) 0 0
\(721\) −346.056 −0.479967
\(722\) 0 0
\(723\) 193.734 + 183.558i 0.267959 + 0.253884i
\(724\) 0 0
\(725\) −133.674 133.674i −0.184378 0.184378i
\(726\) 0 0
\(727\) 1338.18i 1.84069i 0.391110 + 0.920344i \(0.372091\pi\)
−0.391110 + 0.920344i \(0.627909\pi\)
\(728\) 0 0
\(729\) −117.429 719.480i −0.161083 0.986941i
\(730\) 0 0
\(731\) 158.387 + 158.387i 0.216672 + 0.216672i
\(732\) 0 0
\(733\) −757.046 757.046i −1.03280 1.03280i −0.999443 0.0333615i \(-0.989379\pi\)
−0.0333615 0.999443i \(-0.510621\pi\)
\(734\) 0 0
\(735\) 4.55386 + 168.842i 0.00619573 + 0.229717i
\(736\) 0 0
\(737\) 1168.69i 1.58574i
\(738\) 0 0
\(739\) 495.335 + 495.335i 0.670278 + 0.670278i 0.957780 0.287502i \(-0.0928249\pi\)
−0.287502 + 0.957780i \(0.592825\pi\)
\(740\) 0 0
\(741\) 84.7353 89.4328i 0.114353 0.120692i
\(742\) 0 0
\(743\) 1421.01 1.91253 0.956266 0.292500i \(-0.0944872\pi\)
0.956266 + 0.292500i \(0.0944872\pi\)
\(744\) 0 0
\(745\) 37.2861i 0.0500485i
\(746\) 0 0
\(747\) 336.685 + 302.197i 0.450716 + 0.404547i
\(748\) 0 0
\(749\) 558.359 558.359i 0.745473 0.745473i
\(750\) 0 0
\(751\) 143.509 0.191090 0.0955452 0.995425i \(-0.469541\pi\)
0.0955452 + 0.995425i \(0.469541\pi\)
\(752\) 0 0
\(753\) −19.3572 717.702i −0.0257068 0.953123i
\(754\) 0 0
\(755\) 570.921 570.921i 0.756187 0.756187i
\(756\) 0 0
\(757\) −651.883 + 651.883i −0.861140 + 0.861140i −0.991471 0.130331i \(-0.958396\pi\)
0.130331 + 0.991471i \(0.458396\pi\)
\(758\) 0 0
\(759\) −50.6558 1878.15i −0.0667402 2.47450i
\(760\) 0 0
\(761\) 434.623 0.571122 0.285561 0.958361i \(-0.407820\pi\)
0.285561 + 0.958361i \(0.407820\pi\)
\(762\) 0 0
\(763\) 455.249 455.249i 0.596656 0.596656i
\(764\) 0 0
\(765\) −132.468 118.899i −0.173161 0.155423i
\(766\) 0 0
\(767\) 499.665i 0.651453i
\(768\) 0 0
\(769\) 17.1894 0.0223529 0.0111764 0.999938i \(-0.496442\pi\)
0.0111764 + 0.999938i \(0.496442\pi\)
\(770\) 0 0
\(771\) −811.125 + 856.091i −1.05204 + 1.11036i
\(772\) 0 0
\(773\) −553.125 553.125i −0.715557 0.715557i 0.252135 0.967692i \(-0.418867\pi\)
−0.967692 + 0.252135i \(0.918867\pi\)
\(774\) 0 0
\(775\) 37.8171i 0.0487963i
\(776\) 0 0
\(777\) 13.8481 + 513.440i 0.0178225 + 0.660798i
\(778\) 0 0
\(779\) −144.826 144.826i −0.185913 0.185913i
\(780\) 0 0
\(781\) 607.484 + 607.484i 0.777828 + 0.777828i
\(782\) 0 0
\(783\) −86.2686 1064.12i −0.110177 1.35902i
\(784\) 0 0
\(785\) 94.5530i 0.120450i
\(786\) 0 0
\(787\) 274.851 + 274.851i 0.349239 + 0.349239i 0.859826 0.510587i \(-0.170572\pi\)
−0.510587 + 0.859826i \(0.670572\pi\)
\(788\) 0 0
\(789\) −391.699 371.125i −0.496450 0.470374i
\(790\) 0 0
\(791\) −677.993 −0.857134
\(792\) 0 0
\(793\) 637.374i 0.803750i
\(794\) 0 0
\(795\) −272.508 +