Properties

Label 384.3.i.c.353.4
Level $384$
Weight $3$
Character 384.353
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 353.4
Root \(-1.28499 + 1.53258i\) of defining polynomial
Character \(\chi\) \(=\) 384.353
Dual form 384.3.i.c.161.4

$q$-expansion

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

Character values

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

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

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
\(3\) −2.06336 + 2.17774i −0.687785 + 0.725914i
\(4\) 0 0
\(5\) 3.17955 3.17955i 0.635909 0.635909i −0.313634 0.949544i \(-0.601547\pi\)
0.949544 + 0.313634i \(0.101547\pi\)
\(6\) 0 0
\(7\) 6.03979i 0.862827i −0.902154 0.431414i \(-0.858015\pi\)
0.902154 0.431414i \(-0.141985\pi\)
\(8\) 0 0
\(9\) −0.485128 8.98692i −0.0539031 0.998546i
\(10\) 0 0
\(11\) −13.0097 + 13.0097i −1.18270 + 1.18270i −0.203657 + 0.979042i \(0.565283\pi\)
−0.979042 + 0.203657i \(0.934717\pi\)
\(12\) 0 0
\(13\) −6.39520 + 6.39520i −0.491939 + 0.491939i −0.908917 0.416978i \(-0.863089\pi\)
0.416978 + 0.908917i \(0.363089\pi\)
\(14\) 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 −0.786534 0.617547i \(-0.788126\pi\)
0.617547 + 0.786534i \(0.288126\pi\)
\(20\) 0 0
\(21\) 13.1531 + 12.4622i 0.626339 + 0.593440i
\(22\) 0 0
\(23\) −34.0396 −1.47998 −0.739992 0.672616i \(-0.765171\pi\)
−0.739992 + 0.672616i \(0.765171\pi\)
\(24\) 0 0
\(25\) 4.78097i 0.191239i
\(26\) 0 0
\(27\) 20.5722 + 17.4867i 0.761933 + 0.647656i
\(28\) 0 0
\(29\) −27.9597 27.9597i −0.964128 0.964128i 0.0352510 0.999378i \(-0.488777\pi\)
−0.999378 + 0.0352510i \(0.988777\pi\)
\(30\) 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 0.382301 0.924038i \(-0.375132\pi\)
−0.924038 + 0.382301i \(0.875132\pi\)
\(38\) 0 0
\(39\) −0.731530 27.1227i −0.0187572 0.695453i
\(40\) 0 0
\(41\) −45.1067 −1.10016 −0.550081 0.835111i \(-0.685403\pi\)
−0.550081 + 0.835111i \(0.685403\pi\)
\(42\) 0 0
\(43\) −36.0095 36.0095i −0.837431 0.837431i 0.151089 0.988520i \(-0.451722\pi\)
−0.988520 + 0.151089i \(0.951722\pi\)
\(44\) 0 0
\(45\) −30.1168 27.0318i −0.669262 0.600707i
\(46\) 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
\(51\) 9.57876 + 9.07563i 0.187819 + 0.177953i
\(52\) 0 0
\(53\) −20.7687 + 20.7687i −0.391863 + 0.391863i −0.875351 0.483488i \(-0.839370\pi\)
0.483488 + 0.875351i \(0.339370\pi\)
\(54\) 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 \(-0.905096\pi\)
0.293753 + 0.955881i \(0.405096\pi\)
\(60\) 0 0
\(61\) 49.8322 49.8322i 0.816921 0.816921i −0.168739 0.985661i \(-0.553970\pi\)
0.985661 + 0.168739i \(0.0539696\pi\)
\(62\) 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 −0.287416 0.957806i \(-0.592796\pi\)
0.957806 + 0.287416i \(0.0927961\pi\)
\(68\) 0 0
\(69\) 70.2358 74.1295i 1.01791 1.07434i
\(70\) 0 0
\(71\) −46.6947 −0.657672 −0.328836 0.944387i \(-0.606656\pi\)
−0.328836 + 0.944387i \(0.606656\pi\)
\(72\) 0 0
\(73\) 97.3523i 1.33359i 0.745240 + 0.666797i \(0.232335\pi\)
−0.745240 + 0.666797i \(0.767665\pi\)
\(74\) 0 0
\(75\) −10.4117 9.86483i −0.138823 0.131531i
\(76\) 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 \(-0.347929\pi\)
−0.888033 + 0.459779i \(0.847929\pi\)
\(84\) 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 \(-0.371971\pi\)
0.391458 + 0.920196i \(0.371971\pi\)
\(90\) 0 0
\(91\) 38.6257 + 38.6257i 0.424458 + 0.424458i
\(92\) 0 0
\(93\) −16.3210 + 17.2258i −0.175495 + 0.185224i
\(94\) 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
\(99\) 123.228 + 110.606i 1.24473 + 1.11723i
\(100\) 0 0
\(101\) −104.036 + 104.036i −1.03006 + 1.03006i −0.0305280 + 0.999534i \(0.509719\pi\)
−0.999534 + 0.0305280i \(0.990281\pi\)
\(102\) 0 0
\(103\) 57.2961i 0.556272i −0.960542 0.278136i \(-0.910283\pi\)
0.960542 0.278136i \(-0.0897167\pi\)
\(104\) 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 \(-0.540795\pi\)
0.991799 + 0.127810i \(0.0407947\pi\)
\(108\) 0 0
\(109\) −75.3749 + 75.3749i −0.691513 + 0.691513i −0.962565 0.271052i \(-0.912629\pi\)
0.271052 + 0.962565i \(0.412629\pi\)
\(110\) 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
\(117\) 60.5756 + 54.3707i 0.517740 + 0.464706i
\(118\) 0 0
\(119\) −26.5659 −0.223243
\(120\) 0 0
\(121\) 217.504i 1.79756i
\(122\) 0 0
\(123\) 93.0711 98.2307i 0.756676 0.798624i
\(124\) 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 \(-0.395032\pi\)
−0.946118 + 0.323822i \(0.895032\pi\)
\(132\) 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 \(-0.528560\pi\)
−0.0896023 + 0.995978i \(0.528560\pi\)
\(138\) 0 0
\(139\) 3.06917 + 3.06917i 0.0220804 + 0.0220804i 0.718061 0.695980i \(-0.245030\pi\)
−0.695980 + 0.718061i \(0.745030\pi\)
\(140\) 0 0
\(141\) 11.0833 + 10.5011i 0.0786050 + 0.0744762i
\(142\) 0 0
\(143\) 166.399i 1.16363i
\(144\) 0 0
\(145\) −177.798 −1.22620
\(146\) 0 0
\(147\) −25.8351 + 27.2674i −0.175749 + 0.185492i
\(148\) 0 0
\(149\) −5.86344 + 5.86344i −0.0393519 + 0.0393519i −0.726509 0.687157i \(-0.758858\pi\)
0.687157 + 0.726509i \(0.258858\pi\)
\(150\) 0 0
\(151\) 179.561i 1.18914i −0.804043 0.594571i \(-0.797322\pi\)
0.804043 0.594571i \(-0.202678\pi\)
\(152\) 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 −0.658166 0.752873i \(-0.728668\pi\)
0.752873 + 0.658166i \(0.228668\pi\)
\(158\) 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 −0.474577 0.880214i \(-0.657399\pi\)
0.880214 + 0.474577i \(0.157399\pi\)
\(164\) 0 0
\(165\) −180.164 170.701i −1.09191 1.03455i
\(166\) 0 0
\(167\) 158.709 0.950353 0.475176 0.879891i \(-0.342384\pi\)
0.475176 + 0.879891i \(0.342384\pi\)
\(168\) 0 0
\(169\) 87.2028i 0.515993i
\(170\) 0 0
\(171\) 30.4123 + 27.2971i 0.177850 + 0.159632i
\(172\) 0 0
\(173\) −76.9955 76.9955i −0.445061 0.445061i 0.448648 0.893709i \(-0.351906\pi\)
−0.893709 + 0.448648i \(0.851906\pi\)
\(174\) 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 \(-0.118870\pi\)
−0.364821 + 0.931078i \(0.618870\pi\)
\(180\) 0 0
\(181\) 212.373 + 212.373i 1.17333 + 1.17333i 0.981411 + 0.191920i \(0.0614714\pi\)
0.191920 + 0.981411i \(0.438529\pi\)
\(182\) 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
\(189\) 105.616 124.252i 0.558815 0.657416i
\(190\) 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
\(195\) −88.5638 83.9119i −0.454173 0.430317i
\(196\) 0 0
\(197\) 32.2783 32.2783i 0.163849 0.163849i −0.620420 0.784269i \(-0.713038\pi\)
0.784269 + 0.620420i \(0.213038\pi\)
\(198\) 0 0
\(199\) 118.181i 0.593874i 0.954897 + 0.296937i \(0.0959651\pi\)
−0.954897 + 0.296937i \(0.904035\pi\)
\(200\) 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 −0.539315 0.842104i \(-0.681317\pi\)
0.842104 + 0.539315i \(0.181317\pi\)
\(212\) 0 0
\(213\) 96.3478 101.689i 0.452337 0.477413i
\(214\) 0 0
\(215\) −228.988 −1.06506
\(216\) 0 0
\(217\) 47.7743i 0.220158i
\(218\) 0 0
\(219\) −212.008 200.872i −0.968075 0.917226i
\(220\) 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 \(-0.227172\pi\)
−0.654621 + 0.755958i \(0.727172\pi\)
\(228\) 0 0
\(229\) −241.282 241.282i −1.05363 1.05363i −0.998478 0.0551571i \(-0.982434\pi\)
−0.0551571 0.998478i \(-0.517566\pi\)
\(230\) 0 0
\(231\) −333.248 + 8.98807i −1.44263 + 0.0389094i
\(232\) 0 0
\(233\) 240.310 1.03137 0.515687 0.856777i \(-0.327537\pi\)
0.515687 + 0.856777i \(0.327537\pi\)
\(234\) 0 0
\(235\) −16.1818 16.1818i −0.0688589 0.0688589i
\(236\) 0 0
\(237\) −82.8721 + 87.4663i −0.349671 + 0.369056i
\(238\) 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
\(243\) 147.172 193.364i 0.605644 0.795736i
\(244\) 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 \(-0.908180\pi\)
0.284478 + 0.958683i \(0.408180\pi\)
\(252\) 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
\(261\) −237.707 + 264.835i −0.910756 + 1.01470i
\(262\) 0 0
\(263\) −179.865 −0.683897 −0.341948 0.939719i \(-0.611087\pi\)
−0.341948 + 0.939719i \(0.611087\pi\)
\(264\) 0 0
\(265\) 132.070i 0.498378i
\(266\) 0 0
\(267\) −143.774 + 151.744i −0.538478 + 0.568330i
\(268\) 0 0
\(269\) −290.530 290.530i −1.08004 1.08004i −0.996505 0.0835324i \(-0.973380\pi\)
−0.0835324 0.996505i \(-0.526620\pi\)
\(270\) 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 0.854775 0.518999i \(-0.173695\pi\)
−0.518999 + 0.854775i \(0.673695\pi\)
\(278\) 0 0
\(279\) −3.83733 71.0859i −0.0137539 0.254788i
\(280\) 0 0
\(281\) −300.875 −1.07073 −0.535365 0.844621i \(-0.679826\pi\)
−0.535365 + 0.844621i \(0.679826\pi\)
\(282\) 0 0
\(283\) 101.469 + 101.469i 0.358549 + 0.358549i 0.863278 0.504729i \(-0.168408\pi\)
−0.504729 + 0.863278i \(0.668408\pi\)
\(284\) 0 0
\(285\) −44.4639 42.1284i −0.156014 0.147819i
\(286\) 0 0
\(287\) 272.435i 0.949250i
\(288\) 0 0
\(289\) 269.653 0.933057
\(290\) 0 0
\(291\) −126.058 + 133.047i −0.433190 + 0.457205i
\(292\) 0 0
\(293\) 321.104 321.104i 1.09592 1.09592i 0.101037 0.994883i \(-0.467784\pi\)
0.994883 0.101037i \(-0.0322160\pi\)
\(294\) 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 −0.536786 0.843718i \(-0.680362\pi\)
0.843718 + 0.536786i \(0.180362\pi\)
\(308\) 0 0
\(309\) 124.776 + 118.222i 0.403806 + 0.382596i
\(310\) 0 0
\(311\) 245.712 0.790070 0.395035 0.918666i \(-0.370732\pi\)
0.395035 + 0.918666i \(0.370732\pi\)
\(312\) 0 0
\(313\) 353.841i 1.13048i −0.824925 0.565242i \(-0.808783\pi\)
0.824925 0.565242i \(-0.191217\pi\)
\(314\) 0 0
\(315\) −163.267 + 181.899i −0.518307 + 0.577458i
\(316\) 0 0
\(317\) −234.024 234.024i −0.738245 0.738245i 0.233994 0.972238i \(-0.424821\pi\)
−0.972238 + 0.233994i \(0.924821\pi\)
\(318\) 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 0.656243 0.754549i \(-0.272144\pi\)
−0.754549 + 0.656243i \(0.772144\pi\)
\(332\) 0 0
\(333\) −170.412 + 189.860i −0.511748 + 0.570150i
\(334\) 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
\(339\) −244.461 231.621i −0.721124 0.683247i
\(340\) 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 \(-0.716234\pi\)
0.778000 + 0.628264i \(0.216234\pi\)
\(348\) 0 0
\(349\) −378.719 + 378.719i −1.08515 + 1.08515i −0.0891344 + 0.996020i \(0.528410\pi\)
−0.996020 + 0.0891344i \(0.971590\pi\)
\(350\) 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
\(357\) 54.8149 57.8537i 0.153543 0.162055i
\(358\) 0 0
\(359\) 254.927 0.710103 0.355051 0.934847i \(-0.384463\pi\)
0.355051 + 0.934847i \(0.384463\pi\)
\(360\) 0 0
\(361\) 340.382i 0.942887i
\(362\) 0 0
\(363\) 473.668 + 448.789i 1.30487 + 1.23633i
\(364\) 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 0.923728 0.383048i \(-0.125126\pi\)
−0.383048 + 0.923728i \(0.625126\pi\)
\(374\) 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 0.340040 0.940411i \(-0.389560\pi\)
−0.940411 + 0.340040i \(0.889560\pi\)
\(380\) 0 0
\(381\) 193.199 203.910i 0.507084 0.535196i
\(382\) 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
\(387\) −306.145 + 341.084i −0.791073 + 0.881353i
\(388\) 0 0
\(389\) −107.474 + 107.474i −0.276283 + 0.276283i −0.831623 0.555340i \(-0.812588\pi\)
0.555340 + 0.831623i \(0.312588\pi\)
\(390\) 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 −0.300591 0.953753i \(-0.597184\pi\)
0.953753 + 0.300591i \(0.0971837\pi\)
\(398\) 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
\(405\) −228.322 + 283.771i −0.563759 + 0.700669i
\(406\) 0 0
\(407\) 521.539 1.28142
\(408\) 0 0
\(409\) 66.3618i 0.162254i 0.996704 + 0.0811269i \(0.0258519\pi\)
−0.996704 + 0.0811269i \(0.974148\pi\)
\(410\) 0 0
\(411\) 50.6575 53.4658i 0.123254 0.130087i
\(412\) 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 \(-0.0342596\pi\)
−0.107422 + 0.994214i \(0.534260\pi\)
\(420\) 0 0
\(421\) −487.629 487.629i −1.15826 1.15826i −0.984849 0.173416i \(-0.944519\pi\)
−0.173416 0.984849i \(-0.555481\pi\)
\(422\) 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
\(429\) 362.375 + 343.341i 0.844696 + 0.800328i
\(430\) 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
\(435\) 366.861 387.199i 0.843359 0.890113i
\(436\) 0 0
\(437\) 109.293 109.293i 0.250097 0.250097i
\(438\) 0 0
\(439\) 145.760i 0.332026i 0.986124 + 0.166013i \(0.0530895\pi\)
−0.986124 + 0.166013i \(0.946911\pi\)
\(440\) 0 0
\(441\) −6.07425 112.525i −0.0137738 0.255158i
\(442\) 0 0
\(443\) 607.046 607.046i 1.37031 1.37031i 0.510323 0.859983i \(-0.329526\pi\)
0.859983 0.510323i \(-0.170474\pi\)
\(444\) 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
\(453\) 391.037 + 370.497i 0.863216 + 0.817875i
\(454\) 0 0
\(455\) 245.624 0.539834
\(456\) 0 0
\(457\) 128.091i 0.280287i 0.990131 + 0.140143i \(0.0447563\pi\)
−0.990131 + 0.140143i \(0.955244\pi\)
\(458\) 0 0
\(459\) 76.9150 90.4863i 0.167571 0.197138i
\(460\) 0 0
\(461\) 74.2060 + 74.2060i 0.160968 + 0.160968i 0.782995 0.622028i \(-0.213691\pi\)
−0.622028 + 0.782995i \(0.713691\pi\)
\(462\) 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 \(-0.0825038\pi\)
−0.256301 + 0.966597i \(0.582504\pi\)
\(468\) 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
\(477\) 196.722 + 176.571i 0.412415 + 0.370170i
\(478\) 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
\(483\) −447.727 424.210i −0.926970 0.878281i
\(484\) 0 0
\(485\) 194.251 194.251i 0.400517 0.400517i
\(486\) 0 0
\(487\) 815.778i 1.67511i 0.546354 + 0.837554i \(0.316015\pi\)
−0.546354 + 0.837554i \(0.683985\pi\)
\(488\) 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 \(-0.911690\pi\)
0.273888 + 0.961762i \(0.411690\pi\)
\(492\) 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 −0.0331940 + 0.999449i \(0.510568\pi\)
−0.999449 + 0.0331940i \(0.989432\pi\)
\(500\) 0 0
\(501\) −327.473 + 345.627i −0.653639 + 0.689875i
\(502\) 0 0
\(503\) 196.781 0.391215 0.195607 0.980682i \(-0.437332\pi\)
0.195607 + 0.980682i \(0.437332\pi\)
\(504\) 0 0
\(505\) 661.576i 1.31005i
\(506\) 0 0
\(507\) −189.905 179.930i −0.374567 0.354892i
\(508\) 0 0
\(509\) −29.3054 29.3054i −0.0575744 0.0575744i 0.677733 0.735308i \(-0.262962\pi\)
−0.735308 + 0.677733i \(0.762962\pi\)
\(510\) 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 \(-0.764975\pi\)
−0.739578 + 0.673071i \(0.764975\pi\)
\(522\) 0 0
\(523\) 258.725 + 258.725i 0.494694 + 0.494694i 0.909782 0.415087i \(-0.136249\pi\)
−0.415087 + 0.909782i \(0.636249\pi\)
\(524\) 0 0
\(525\) −59.5815 + 62.8846i −0.113489 + 0.119780i
\(526\) 0 0
\(527\) 34.7917i 0.0660183i
\(528\) 0 0
\(529\) 629.695 1.19035
\(530\) 0 0
\(531\) 370.031 + 332.127i 0.696857 + 0.625475i
\(532\) 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 −0.584588 0.811330i \(-0.698744\pi\)
0.811330 + 0.584588i \(0.198744\pi\)
\(542\) 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 −0.332399 0.943139i \(-0.607858\pi\)
0.943139 + 0.332399i \(0.107858\pi\)
\(548\) 0 0
\(549\) −472.013 423.663i −0.859768 0.771699i
\(550\) 0 0
\(551\) 179.543 0.325849
\(552\) 0 0
\(553\) 242.581i 0.438663i
\(554\) 0 0
\(555\) 263.002 277.582i 0.473878 0.500148i
\(556\) 0 0
\(557\) −159.480 159.480i −0.286320 0.286320i 0.549303 0.835623i \(-0.314893\pi\)
−0.835623 + 0.549303i \(0.814893\pi\)
\(558\) 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 \(-0.390982\pi\)
−0.941921 + 0.335835i \(0.890982\pi\)
\(564\) 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 \(-0.782704\pi\)
−0.775901 + 0.630855i \(0.782704\pi\)
\(570\) 0 0
\(571\) 370.112 + 370.112i 0.648181 + 0.648181i 0.952553 0.304372i \(-0.0984466\pi\)
−0.304372 + 0.952553i \(0.598447\pi\)
\(572\) 0 0
\(573\) 79.1204 + 74.9645i 0.138081 + 0.130828i
\(574\) 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
\(579\) −97.2025 + 102.591i −0.167880 + 0.177187i
\(580\) 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 \(-0.674101\pi\)
0.854112 + 0.520088i \(0.174101\pi\)
\(588\) 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
\(597\) −257.368 243.849i −0.431102 0.408458i
\(598\) 0 0
\(599\) −783.533 −1.30807 −0.654034 0.756465i \(-0.726925\pi\)
−0.654034 + 0.756465i \(0.726925\pi\)
\(600\) 0 0
\(601\) 797.210i 1.32647i −0.748410 0.663236i \(-0.769182\pi\)
0.748410 0.663236i \(-0.230818\pi\)
\(602\) 0 0
\(603\) −425.448 381.868i −0.705552 0.633280i
\(604\) 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 0.983917 0.178628i \(-0.0571658\pi\)
−0.178628 + 0.983917i \(0.557166\pi\)
\(614\) 0 0
\(615\) −16.4053 608.253i −0.0266752 0.989029i
\(616\) 0 0
\(617\) 685.069 1.11032 0.555161 0.831743i \(-0.312657\pi\)
0.555161 + 0.831743i \(0.312657\pi\)
\(618\) 0 0
\(619\) −379.995 379.995i −0.613885 0.613885i 0.330071 0.943956i \(-0.392927\pi\)
−0.943956 + 0.330071i \(0.892927\pi\)
\(620\) 0 0
\(621\) −700.269 595.241i −1.12765 0.958520i
\(622\) 0 0
\(623\) 420.850i 0.675521i
\(624\) 0 0
\(625\) 482.618 0.772189
\(626\) 0 0
\(627\) 181.932 + 172.376i 0.290163 + 0.274922i
\(628\) 0 0
\(629\) −88.1642 + 88.1642i −0.140166 + 0.140166i
\(630\) 0 0
\(631\) 489.285i 0.775412i 0.921783 + 0.387706i \(0.126732\pi\)
−0.921783 + 0.387706i \(0.873268\pi\)
\(632\) 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 −0.826823 0.562462i \(-0.809854\pi\)
0.562462 + 0.826823i \(0.309854\pi\)
\(644\) 0 0
\(645\) 472.483 498.677i 0.732532 0.773142i
\(646\) 0 0
\(647\) −1003.50 −1.55101 −0.775503 0.631343i \(-0.782504\pi\)
−0.775503 + 0.631343i \(0.782504\pi\)
\(648\) 0 0
\(649\) 1016.46i 1.56620i
\(650\) 0 0
\(651\) 104.040 + 98.5754i 0.159816 + 0.151422i
\(652\) 0 0
\(653\) 407.090 + 407.090i 0.623415 + 0.623415i 0.946403 0.322988i \(-0.104687\pi\)
−0.322988 + 0.946403i \(0.604687\pi\)
\(654\) 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 \(-0.488774\pi\)
−0.999378 + 0.0352587i \(0.988774\pi\)
\(660\) 0 0
\(661\) 196.325 + 196.325i 0.297013 + 0.297013i 0.839843 0.542830i \(-0.182647\pi\)
−0.542830 + 0.839843i \(0.682647\pi\)
\(662\) 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
\(669\) −88.4944 + 93.4003i −0.132279 + 0.139612i
\(670\) 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
\(675\) −83.6034 + 98.3549i −0.123857 + 0.145711i
\(676\) 0 0
\(677\) −832.940 + 832.940i −1.23034 + 1.23034i −0.266507 + 0.963833i \(0.585869\pi\)
−0.963833 + 0.266507i \(0.914131\pi\)
\(678\) 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 −0.143264 + 0.989684i \(0.545760\pi\)
−0.989684 + 0.143264i \(0.954240\pi\)
\(684\) 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 −0.247077 + 0.968996i \(0.579470\pi\)
−0.968996 + 0.247077i \(0.920530\pi\)
\(692\) 0 0
\(693\) 668.035 744.274i 0.963975 1.07399i
\(694\) 0 0
\(695\) 19.5171 0.0280822
\(696\) 0 0
\(697\) 198.401i 0.284650i
\(698\) 0 0
\(699\) −495.845 + 523.334i −0.709364 + 0.748689i
\(700\) 0 0
\(701\) 529.432 + 529.432i 0.755253 + 0.755253i 0.975454 0.220201i \(-0.0706715\pi\)
−0.220201 + 0.975454i \(0.570671\pi\)
\(702\) 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 0.745641 0.666348i \(-0.232144\pi\)
−0.666348 + 0.745641i \(0.732144\pi\)
\(710\) 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
\(717\) −475.121 450.165i −0.662651 0.627845i
\(718\) 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
\(723\) 183.558 193.734i 0.253884 0.267959i
\(724\) 0 0
\(725\) 133.674 133.674i 0.184378 0.184378i
\(726\) 0 0
\(727\) 1338.18i 1.84069i −0.391110 0.920344i \(-0.627909\pi\)
0.391110 0.920344i \(-0.372091\pi\)
\(728\) 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 −0.0333615 + 0.999443i \(0.510621\pi\)
−0.999443 + 0.0333615i \(0.989379\pi\)
\(734\) 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 −0.287502 0.957780i \(-0.592825\pi\)
0.957780 + 0.287502i \(0.0928249\pi\)
\(740\) 0 0
\(741\) 89.4328 + 84.7353i 0.120692 + 0.114353i
\(742\) 0 0
\(743\) −1421.01 −1.91253 −0.956266 0.292500i \(-0.905513\pi\)
−0.956266 + 0.292500i \(0.905513\pi\)
\(744\) 0 0
\(745\) 37.2861i 0.0500485i
\(746\) 0 0
\(747\) −302.197 + 336.685i −0.404547 + 0.450716i
\(748\) 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 0.130331 0.991471i \(-0.458396\pi\)
−0.991471 + 0.130331i \(0.958396\pi\)
\(758\) 0 0
\(759\) 50.6558 + 1878.15i 0.0667402 + 2.47450i
\(760\) 0 0
\(761\) −434.623 −0.571122 −0.285561 0.958361i \(-0.592180\pi\)
−0.285561 + 0.958361i \(0.592180\pi\)
\(762\) 0 0
\(763\) 455.249 + 455.249i 0.596656 + 0.596656i
\(764\) 0 0
\(765\) −118.899 + 132.468i −0.155423 + 0.173161i
\(766\) 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
\(771\) 856.091 + 811.125i 1.11036 + 1.05204i
\(772\) 0 0
\(773\) 553.125 553.125i 0.715557 0.715557i −0.252135 0.967692i \(-0.581133\pi\)
0.967692 + 0.252135i \(0.0811328\pi\)
\(774\) 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 −0.510587 0.859826i \(-0.670572\pi\)
0.859826 + 0.510587i \(0.170572\pi\)
\(788\) 0 0
\(789\) 371.125 391.699i 0.470374 0.496450i
\(790\) 0 0
\(791\) 677.993 0.857134
\(792\) 0 0
\(793\) 637.374i 0.803750i
\(794\) 0 0
\(795\) −287.615 272.508i −0.361780 0.342777i