Properties

Label 224.3.s.a.33.5
Level 224
Weight 3
Character 224.33
Analytic conductor 6.104
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 33.5
Root \(0.707107 + 0.358323i\) of \(x^{16} + 36 x^{14} + 522 x^{12} + 3644 x^{10} + 12219 x^{8} + 15156 x^{6} + 15478 x^{4} - 10992 x^{2} + 11025\)
Character \(\chi\) \(=\) 224.33
Dual form 224.3.s.a.129.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.438854 - 0.253372i) q^{3} +(-4.59219 - 2.65130i) q^{5} +(-5.27770 - 4.59846i) q^{7} +(-4.37160 + 7.57184i) q^{9} +O(q^{10})\) \(q+(0.438854 - 0.253372i) q^{3} +(-4.59219 - 2.65130i) q^{5} +(-5.27770 - 4.59846i) q^{7} +(-4.37160 + 7.57184i) q^{9} +(8.54498 + 14.8003i) q^{11} +21.4744i q^{13} -2.68707 q^{15} +(-20.7992 + 12.0084i) q^{17} +(-10.5831 - 6.11016i) q^{19} +(-3.48126 - 0.680829i) q^{21} +(20.1464 - 34.8946i) q^{23} +(1.55882 + 2.69996i) q^{25} +8.99128i q^{27} -26.0770 q^{29} +(-21.8789 + 12.6318i) q^{31} +(7.50000 + 4.33013i) q^{33} +(12.0443 + 35.1098i) q^{35} +(-6.48126 + 11.2259i) q^{37} +(5.44101 + 9.42411i) q^{39} -33.8721i q^{41} +29.9958 q^{43} +(40.1505 - 23.1809i) q^{45} +(-48.2788 - 27.8738i) q^{47} +(6.70828 + 48.5386i) q^{49} +(-6.08521 + 10.5399i) q^{51} +(4.36362 + 7.55801i) q^{53} -90.6214i q^{55} -6.19259 q^{57} +(-43.2893 + 24.9931i) q^{59} +(3.40886 + 1.96811i) q^{61} +(57.8909 - 19.8593i) q^{63} +(56.9351 - 98.6144i) q^{65} +(52.9426 + 91.6994i) q^{67} -20.4182i q^{69} -35.0232 q^{71} +(40.3712 - 23.3083i) q^{73} +(1.36819 + 0.789926i) q^{75} +(22.9610 - 117.406i) q^{77} +(-43.4998 + 75.3438i) q^{79} +(-37.0663 - 64.2007i) q^{81} -64.0079i q^{83} +127.352 q^{85} +(-11.4440 + 6.60721i) q^{87} +(37.2272 + 21.4932i) q^{89} +(98.7491 - 113.335i) q^{91} +(-6.40109 + 11.0870i) q^{93} +(32.3998 + 56.1181i) q^{95} +28.7493i q^{97} -149.421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{9} + O(q^{10}) \) \( 16q + 8q^{9} + 48q^{17} + 56q^{21} + 16q^{25} + 112q^{29} + 120q^{33} + 8q^{37} - 72q^{45} - 128q^{49} - 24q^{53} - 528q^{57} - 360q^{61} - 8q^{65} + 72q^{73} + 32q^{81} + 720q^{85} + 408q^{89} - 232q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.438854 0.253372i 0.146285 0.0844575i −0.425071 0.905160i \(-0.639751\pi\)
0.571356 + 0.820702i \(0.306418\pi\)
\(4\) 0 0
\(5\) −4.59219 2.65130i −0.918439 0.530261i −0.0353020 0.999377i \(-0.511239\pi\)
−0.883137 + 0.469116i \(0.844573\pi\)
\(6\) 0 0
\(7\) −5.27770 4.59846i −0.753957 0.656923i
\(8\) 0 0
\(9\) −4.37160 + 7.57184i −0.485734 + 0.841316i
\(10\) 0 0
\(11\) 8.54498 + 14.8003i 0.776817 + 1.34549i 0.933768 + 0.357880i \(0.116500\pi\)
−0.156951 + 0.987606i \(0.550167\pi\)
\(12\) 0 0
\(13\) 21.4744i 1.65187i 0.563762 + 0.825937i \(0.309353\pi\)
−0.563762 + 0.825937i \(0.690647\pi\)
\(14\) 0 0
\(15\) −2.68707 −0.179138
\(16\) 0 0
\(17\) −20.7992 + 12.0084i −1.22348 + 0.706378i −0.965659 0.259814i \(-0.916339\pi\)
−0.257824 + 0.966192i \(0.583005\pi\)
\(18\) 0 0
\(19\) −10.5831 6.11016i −0.557006 0.321588i 0.194937 0.980816i \(-0.437550\pi\)
−0.751943 + 0.659228i \(0.770883\pi\)
\(20\) 0 0
\(21\) −3.48126 0.680829i −0.165775 0.0324205i
\(22\) 0 0
\(23\) 20.1464 34.8946i 0.875932 1.51716i 0.0201644 0.999797i \(-0.493581\pi\)
0.855767 0.517361i \(-0.173086\pi\)
\(24\) 0 0
\(25\) 1.55882 + 2.69996i 0.0623530 + 0.107998i
\(26\) 0 0
\(27\) 8.99128i 0.333010i
\(28\) 0 0
\(29\) −26.0770 −0.899209 −0.449604 0.893228i \(-0.648435\pi\)
−0.449604 + 0.893228i \(0.648435\pi\)
\(30\) 0 0
\(31\) −21.8789 + 12.6318i −0.705770 + 0.407477i −0.809493 0.587130i \(-0.800258\pi\)
0.103723 + 0.994606i \(0.466925\pi\)
\(32\) 0 0
\(33\) 7.50000 + 4.33013i 0.227273 + 0.131216i
\(34\) 0 0
\(35\) 12.0443 + 35.1098i 0.344123 + 1.00314i
\(36\) 0 0
\(37\) −6.48126 + 11.2259i −0.175169 + 0.303402i −0.940220 0.340568i \(-0.889381\pi\)
0.765051 + 0.643970i \(0.222714\pi\)
\(38\) 0 0
\(39\) 5.44101 + 9.42411i 0.139513 + 0.241644i
\(40\) 0 0
\(41\) 33.8721i 0.826150i −0.910697 0.413075i \(-0.864455\pi\)
0.910697 0.413075i \(-0.135545\pi\)
\(42\) 0 0
\(43\) 29.9958 0.697576 0.348788 0.937202i \(-0.386593\pi\)
0.348788 + 0.937202i \(0.386593\pi\)
\(44\) 0 0
\(45\) 40.1505 23.1809i 0.892233 0.515131i
\(46\) 0 0
\(47\) −48.2788 27.8738i −1.02721 0.593060i −0.111025 0.993818i \(-0.535413\pi\)
−0.916184 + 0.400758i \(0.868747\pi\)
\(48\) 0 0
\(49\) 6.70828 + 48.5386i 0.136904 + 0.990584i
\(50\) 0 0
\(51\) −6.08521 + 10.5399i −0.119318 + 0.206665i
\(52\) 0 0
\(53\) 4.36362 + 7.55801i 0.0823324 + 0.142604i 0.904251 0.427001i \(-0.140430\pi\)
−0.821919 + 0.569604i \(0.807096\pi\)
\(54\) 0 0
\(55\) 90.6214i 1.64766i
\(56\) 0 0
\(57\) −6.19259 −0.108642
\(58\) 0 0
\(59\) −43.2893 + 24.9931i −0.733718 + 0.423612i −0.819781 0.572678i \(-0.805905\pi\)
0.0860631 + 0.996290i \(0.472571\pi\)
\(60\) 0 0
\(61\) 3.40886 + 1.96811i 0.0558829 + 0.0322640i 0.527681 0.849443i \(-0.323062\pi\)
−0.471798 + 0.881707i \(0.656395\pi\)
\(62\) 0 0
\(63\) 57.8909 19.8593i 0.918903 0.315226i
\(64\) 0 0
\(65\) 56.9351 98.6144i 0.875924 1.51715i
\(66\) 0 0
\(67\) 52.9426 + 91.6994i 0.790189 + 1.36865i 0.925850 + 0.377892i \(0.123351\pi\)
−0.135661 + 0.990755i \(0.543316\pi\)
\(68\) 0 0
\(69\) 20.4182i 0.295916i
\(70\) 0 0
\(71\) −35.0232 −0.493285 −0.246642 0.969107i \(-0.579327\pi\)
−0.246642 + 0.969107i \(0.579327\pi\)
\(72\) 0 0
\(73\) 40.3712 23.3083i 0.553030 0.319292i −0.197313 0.980340i \(-0.563222\pi\)
0.750343 + 0.661049i \(0.229888\pi\)
\(74\) 0 0
\(75\) 1.36819 + 0.789926i 0.0182426 + 0.0105323i
\(76\) 0 0
\(77\) 22.9610 117.406i 0.298194 1.52475i
\(78\) 0 0
\(79\) −43.4998 + 75.3438i −0.550630 + 0.953719i 0.447599 + 0.894234i \(0.352279\pi\)
−0.998229 + 0.0594846i \(0.981054\pi\)
\(80\) 0 0
\(81\) −37.0663 64.2007i −0.457609 0.792601i
\(82\) 0 0
\(83\) 64.0079i 0.771180i −0.922670 0.385590i \(-0.873998\pi\)
0.922670 0.385590i \(-0.126002\pi\)
\(84\) 0 0
\(85\) 127.352 1.49826
\(86\) 0 0
\(87\) −11.4440 + 6.60721i −0.131540 + 0.0759449i
\(88\) 0 0
\(89\) 37.2272 + 21.4932i 0.418284 + 0.241496i 0.694343 0.719645i \(-0.255695\pi\)
−0.276059 + 0.961141i \(0.589029\pi\)
\(90\) 0 0
\(91\) 98.7491 113.335i 1.08515 1.24544i
\(92\) 0 0
\(93\) −6.40109 + 11.0870i −0.0688289 + 0.119215i
\(94\) 0 0
\(95\) 32.3998 + 56.1181i 0.341051 + 0.590717i
\(96\) 0 0
\(97\) 28.7493i 0.296384i 0.988959 + 0.148192i \(0.0473454\pi\)
−0.988959 + 0.148192i \(0.952655\pi\)
\(98\) 0 0
\(99\) −149.421 −1.50930
\(100\) 0 0
\(101\) −53.2337 + 30.7345i −0.527067 + 0.304302i −0.739821 0.672804i \(-0.765090\pi\)
0.212754 + 0.977106i \(0.431757\pi\)
\(102\) 0 0
\(103\) 51.7263 + 29.8642i 0.502197 + 0.289944i 0.729620 0.683852i \(-0.239697\pi\)
−0.227423 + 0.973796i \(0.573030\pi\)
\(104\) 0 0
\(105\) 14.1816 + 12.3564i 0.135062 + 0.117680i
\(106\) 0 0
\(107\) 65.8380 114.035i 0.615308 1.06574i −0.375022 0.927016i \(-0.622365\pi\)
0.990330 0.138729i \(-0.0443017\pi\)
\(108\) 0 0
\(109\) 18.9045 + 32.7436i 0.173436 + 0.300400i 0.939619 0.342222i \(-0.111180\pi\)
−0.766183 + 0.642623i \(0.777846\pi\)
\(110\) 0 0
\(111\) 6.56870i 0.0591774i
\(112\) 0 0
\(113\) −46.4443 −0.411012 −0.205506 0.978656i \(-0.565884\pi\)
−0.205506 + 0.978656i \(0.565884\pi\)
\(114\) 0 0
\(115\) −185.033 + 106.829i −1.60898 + 0.928944i
\(116\) 0 0
\(117\) −162.601 93.8774i −1.38975 0.802371i
\(118\) 0 0
\(119\) 164.992 + 32.2675i 1.38649 + 0.271155i
\(120\) 0 0
\(121\) −85.5335 + 148.148i −0.706888 + 1.22437i
\(122\) 0 0
\(123\) −8.58227 14.8649i −0.0697745 0.120853i
\(124\) 0 0
\(125\) 116.034i 0.928268i
\(126\) 0 0
\(127\) 12.7816 0.100642 0.0503211 0.998733i \(-0.483976\pi\)
0.0503211 + 0.998733i \(0.483976\pi\)
\(128\) 0 0
\(129\) 13.1638 7.60010i 0.102045 0.0589155i
\(130\) 0 0
\(131\) 0.929338 + 0.536554i 0.00709418 + 0.00409583i 0.503543 0.863970i \(-0.332030\pi\)
−0.496449 + 0.868066i \(0.665363\pi\)
\(132\) 0 0
\(133\) 27.7572 + 80.9137i 0.208700 + 0.608374i
\(134\) 0 0
\(135\) 23.8386 41.2897i 0.176582 0.305850i
\(136\) 0 0
\(137\) 33.4330 + 57.9076i 0.244036 + 0.422683i 0.961860 0.273541i \(-0.0881951\pi\)
−0.717824 + 0.696225i \(0.754862\pi\)
\(138\) 0 0
\(139\) 221.071i 1.59044i −0.606322 0.795219i \(-0.707356\pi\)
0.606322 0.795219i \(-0.292644\pi\)
\(140\) 0 0
\(141\) −28.2498 −0.200353
\(142\) 0 0
\(143\) −317.828 + 183.498i −2.22257 + 1.28320i
\(144\) 0 0
\(145\) 119.751 + 69.1382i 0.825868 + 0.476815i
\(146\) 0 0
\(147\) 15.2423 + 19.6017i 0.103689 + 0.133345i
\(148\) 0 0
\(149\) 19.7606 34.2264i 0.132621 0.229707i −0.792065 0.610437i \(-0.790994\pi\)
0.924686 + 0.380730i \(0.124327\pi\)
\(150\) 0 0
\(151\) 111.362 + 192.885i 0.737499 + 1.27739i 0.953618 + 0.301019i \(0.0973269\pi\)
−0.216119 + 0.976367i \(0.569340\pi\)
\(152\) 0 0
\(153\) 209.984i 1.37245i
\(154\) 0 0
\(155\) 133.963 0.864275
\(156\) 0 0
\(157\) −175.081 + 101.083i −1.11516 + 0.643840i −0.940162 0.340728i \(-0.889327\pi\)
−0.175002 + 0.984568i \(0.555993\pi\)
\(158\) 0 0
\(159\) 3.82998 + 2.21124i 0.0240879 + 0.0139072i
\(160\) 0 0
\(161\) −266.789 + 91.5209i −1.65707 + 0.568453i
\(162\) 0 0
\(163\) −1.31509 + 2.27780i −0.00806802 + 0.0139742i −0.870031 0.492997i \(-0.835901\pi\)
0.861963 + 0.506971i \(0.169235\pi\)
\(164\) 0 0
\(165\) −22.9610 39.7696i −0.139157 0.241028i
\(166\) 0 0
\(167\) 133.004i 0.796434i −0.917291 0.398217i \(-0.869629\pi\)
0.917291 0.398217i \(-0.130371\pi\)
\(168\) 0 0
\(169\) −292.148 −1.72869
\(170\) 0 0
\(171\) 92.5304 53.4224i 0.541113 0.312412i
\(172\) 0 0
\(173\) 84.0786 + 48.5428i 0.486004 + 0.280594i 0.722915 0.690937i \(-0.242802\pi\)
−0.236911 + 0.971531i \(0.576135\pi\)
\(174\) 0 0
\(175\) 4.18867 21.4178i 0.0239352 0.122387i
\(176\) 0 0
\(177\) −12.6651 + 21.9367i −0.0715544 + 0.123936i
\(178\) 0 0
\(179\) 42.0185 + 72.7782i 0.234740 + 0.406582i 0.959197 0.282738i \(-0.0912427\pi\)
−0.724457 + 0.689320i \(0.757909\pi\)
\(180\) 0 0
\(181\) 214.347i 1.18424i 0.805851 + 0.592119i \(0.201708\pi\)
−0.805851 + 0.592119i \(0.798292\pi\)
\(182\) 0 0
\(183\) 1.99466 0.0108998
\(184\) 0 0
\(185\) 59.5264 34.3676i 0.321765 0.185771i
\(186\) 0 0
\(187\) −355.458 205.224i −1.90084 1.09745i
\(188\) 0 0
\(189\) 41.3461 47.4533i 0.218762 0.251076i
\(190\) 0 0
\(191\) 27.3687 47.4040i 0.143292 0.248188i −0.785443 0.618934i \(-0.787565\pi\)
0.928734 + 0.370746i \(0.120898\pi\)
\(192\) 0 0
\(193\) 174.150 + 301.637i 0.902332 + 1.56289i 0.824459 + 0.565922i \(0.191480\pi\)
0.0778732 + 0.996963i \(0.475187\pi\)
\(194\) 0 0
\(195\) 57.7031i 0.295913i
\(196\) 0 0
\(197\) 161.606 0.820337 0.410169 0.912010i \(-0.365470\pi\)
0.410169 + 0.912010i \(0.365470\pi\)
\(198\) 0 0
\(199\) 119.186 68.8121i 0.598925 0.345789i −0.169694 0.985497i \(-0.554278\pi\)
0.768618 + 0.639707i \(0.220944\pi\)
\(200\) 0 0
\(201\) 46.4682 + 26.8284i 0.231185 + 0.133475i
\(202\) 0 0
\(203\) 137.627 + 119.914i 0.677965 + 0.590711i
\(204\) 0 0
\(205\) −89.8053 + 155.547i −0.438075 + 0.758768i
\(206\) 0 0
\(207\) 176.144 + 305.091i 0.850939 + 1.47387i
\(208\) 0 0
\(209\) 208.845i 0.999258i
\(210\) 0 0
\(211\) −101.563 −0.481341 −0.240670 0.970607i \(-0.577367\pi\)
−0.240670 + 0.970607i \(0.577367\pi\)
\(212\) 0 0
\(213\) −15.3701 + 8.87392i −0.0721600 + 0.0416616i
\(214\) 0 0
\(215\) −137.746 79.5279i −0.640681 0.369897i
\(216\) 0 0
\(217\) 173.557 + 33.9425i 0.799802 + 0.156417i
\(218\) 0 0
\(219\) 11.8114 20.4579i 0.0539332 0.0934150i
\(220\) 0 0
\(221\) −257.873 446.650i −1.16685 2.02104i
\(222\) 0 0
\(223\) 180.573i 0.809744i 0.914373 + 0.404872i \(0.132684\pi\)
−0.914373 + 0.404872i \(0.867316\pi\)
\(224\) 0 0
\(225\) −27.2582 −0.121148
\(226\) 0 0
\(227\) −43.9146 + 25.3541i −0.193456 + 0.111692i −0.593600 0.804761i \(-0.702294\pi\)
0.400143 + 0.916453i \(0.368960\pi\)
\(228\) 0 0
\(229\) −172.801 99.7665i −0.754588 0.435661i 0.0727614 0.997349i \(-0.476819\pi\)
−0.827349 + 0.561688i \(0.810152\pi\)
\(230\) 0 0
\(231\) −19.6708 57.3416i −0.0851551 0.248232i
\(232\) 0 0
\(233\) 88.5790 153.423i 0.380167 0.658469i −0.610919 0.791693i \(-0.709200\pi\)
0.991086 + 0.133224i \(0.0425330\pi\)
\(234\) 0 0
\(235\) 147.804 + 256.004i 0.628952 + 1.08938i
\(236\) 0 0
\(237\) 44.0866i 0.186019i
\(238\) 0 0
\(239\) −135.694 −0.567756 −0.283878 0.958860i \(-0.591621\pi\)
−0.283878 + 0.958860i \(0.591621\pi\)
\(240\) 0 0
\(241\) 273.872 158.120i 1.13640 0.656101i 0.190863 0.981617i \(-0.438871\pi\)
0.945537 + 0.325516i \(0.105538\pi\)
\(242\) 0 0
\(243\) −102.613 59.2439i −0.422278 0.243802i
\(244\) 0 0
\(245\) 97.8850 240.684i 0.399530 0.982386i
\(246\) 0 0
\(247\) 131.212 227.266i 0.531222 0.920104i
\(248\) 0 0
\(249\) −16.2179 28.0901i −0.0651319 0.112812i
\(250\) 0 0
\(251\) 40.1231i 0.159853i −0.996801 0.0799265i \(-0.974531\pi\)
0.996801 0.0799265i \(-0.0254686\pi\)
\(252\) 0 0
\(253\) 688.603 2.72175
\(254\) 0 0
\(255\) 55.8889 32.2675i 0.219172 0.126539i
\(256\) 0 0
\(257\) −150.405 86.8366i −0.585235 0.337886i 0.177976 0.984035i \(-0.443045\pi\)
−0.763211 + 0.646149i \(0.776378\pi\)
\(258\) 0 0
\(259\) 85.8280 29.4430i 0.331382 0.113680i
\(260\) 0 0
\(261\) 113.999 197.451i 0.436776 0.756518i
\(262\) 0 0
\(263\) −182.291 315.737i −0.693120 1.20052i −0.970810 0.239848i \(-0.922902\pi\)
0.277690 0.960671i \(-0.410431\pi\)
\(264\) 0 0
\(265\) 46.2771i 0.174631i
\(266\) 0 0
\(267\) 21.7831 0.0815846
\(268\) 0 0
\(269\) 15.0874 8.71074i 0.0560871 0.0323819i −0.471694 0.881762i \(-0.656357\pi\)
0.527781 + 0.849380i \(0.323024\pi\)
\(270\) 0 0
\(271\) −112.812 65.1322i −0.416281 0.240340i 0.277204 0.960811i \(-0.410592\pi\)
−0.693485 + 0.720471i \(0.743926\pi\)
\(272\) 0 0
\(273\) 14.6204 74.7580i 0.0535545 0.273839i
\(274\) 0 0
\(275\) −26.6402 + 46.1423i −0.0968736 + 0.167790i
\(276\) 0 0
\(277\) 124.595 + 215.804i 0.449801 + 0.779077i 0.998373 0.0570258i \(-0.0181617\pi\)
−0.548572 + 0.836103i \(0.684828\pi\)
\(278\) 0 0
\(279\) 220.885i 0.791701i
\(280\) 0 0
\(281\) −197.454 −0.702684 −0.351342 0.936247i \(-0.614275\pi\)
−0.351342 + 0.936247i \(0.614275\pi\)
\(282\) 0 0
\(283\) −185.615 + 107.165i −0.655884 + 0.378675i −0.790707 0.612195i \(-0.790287\pi\)
0.134823 + 0.990870i \(0.456953\pi\)
\(284\) 0 0
\(285\) 28.4376 + 16.4184i 0.0997809 + 0.0576085i
\(286\) 0 0
\(287\) −155.760 + 178.767i −0.542717 + 0.622882i
\(288\) 0 0
\(289\) 143.904 249.250i 0.497939 0.862456i
\(290\) 0 0
\(291\) 7.28427 + 12.6167i 0.0250319 + 0.0433565i
\(292\) 0 0
\(293\) 71.8385i 0.245182i 0.992457 + 0.122591i \(0.0391204\pi\)
−0.992457 + 0.122591i \(0.960880\pi\)
\(294\) 0 0
\(295\) 265.057 0.898499
\(296\) 0 0
\(297\) −133.074 + 76.8304i −0.448061 + 0.258688i
\(298\) 0 0
\(299\) 749.340 + 432.632i 2.50615 + 1.44693i
\(300\) 0 0
\(301\) −158.309 137.934i −0.525943 0.458254i
\(302\) 0 0
\(303\) −15.5746 + 26.9759i −0.0514012 + 0.0890295i
\(304\) 0 0
\(305\) −10.4361 18.0758i −0.0342167 0.0592651i
\(306\) 0 0
\(307\) 507.046i 1.65162i 0.563951 + 0.825808i \(0.309281\pi\)
−0.563951 + 0.825808i \(0.690719\pi\)
\(308\) 0 0
\(309\) 30.2671 0.0979516
\(310\) 0 0
\(311\) −269.089 + 155.359i −0.865239 + 0.499546i −0.865763 0.500454i \(-0.833167\pi\)
0.000524087 1.00000i \(0.499833\pi\)
\(312\) 0 0
\(313\) 475.367 + 274.453i 1.51875 + 0.876848i 0.999756 + 0.0220674i \(0.00702483\pi\)
0.518989 + 0.854781i \(0.326309\pi\)
\(314\) 0 0
\(315\) −318.499 62.2887i −1.01111 0.197742i
\(316\) 0 0
\(317\) −70.9651 + 122.915i −0.223865 + 0.387745i −0.955978 0.293437i \(-0.905201\pi\)
0.732113 + 0.681183i \(0.238534\pi\)
\(318\) 0 0
\(319\) −222.828 385.949i −0.698520 1.20987i
\(320\) 0 0
\(321\) 66.7261i 0.207869i
\(322\) 0 0
\(323\) 293.494 0.908649
\(324\) 0 0
\(325\) −57.9800 + 33.4748i −0.178400 + 0.102999i
\(326\) 0 0
\(327\) 16.5927 + 9.57978i 0.0507421 + 0.0292960i
\(328\) 0 0
\(329\) 126.625 + 369.118i 0.384877 + 1.12194i
\(330\) 0 0
\(331\) −18.4325 + 31.9260i −0.0556873 + 0.0964533i −0.892525 0.450997i \(-0.851068\pi\)
0.836838 + 0.547451i \(0.184402\pi\)
\(332\) 0 0
\(333\) −56.6671 98.1502i −0.170171 0.294745i
\(334\) 0 0
\(335\) 561.468i 1.67602i
\(336\) 0 0
\(337\) −541.604 −1.60713 −0.803567 0.595214i \(-0.797067\pi\)
−0.803567 + 0.595214i \(0.797067\pi\)
\(338\) 0 0
\(339\) −20.3823 + 11.7677i −0.0601247 + 0.0347130i
\(340\) 0 0
\(341\) −373.909 215.877i −1.09651 0.633069i
\(342\) 0 0
\(343\) 187.799 287.020i 0.547518 0.836794i
\(344\) 0 0
\(345\) −54.1348 + 93.7643i −0.156913 + 0.271781i
\(346\) 0 0
\(347\) −122.201 211.658i −0.352164 0.609966i 0.634464 0.772952i \(-0.281221\pi\)
−0.986628 + 0.162986i \(0.947887\pi\)
\(348\) 0 0
\(349\) 190.205i 0.545001i 0.962156 + 0.272501i \(0.0878507\pi\)
−0.962156 + 0.272501i \(0.912149\pi\)
\(350\) 0 0
\(351\) −193.082 −0.550091
\(352\) 0 0
\(353\) 341.878 197.383i 0.968493 0.559160i 0.0697166 0.997567i \(-0.477791\pi\)
0.898777 + 0.438407i \(0.144457\pi\)
\(354\) 0 0
\(355\) 160.833 + 92.8572i 0.453052 + 0.261570i
\(356\) 0 0
\(357\) 80.5832 27.6438i 0.225723 0.0774336i
\(358\) 0 0
\(359\) −148.162 + 256.625i −0.412709 + 0.714833i −0.995185 0.0980151i \(-0.968751\pi\)
0.582476 + 0.812848i \(0.302084\pi\)
\(360\) 0 0
\(361\) −105.832 183.306i −0.293163 0.507773i
\(362\) 0 0
\(363\) 86.6873i 0.238808i
\(364\) 0 0
\(365\) −247.190 −0.677232
\(366\) 0 0
\(367\) 521.865 301.299i 1.42198 0.820978i 0.425507 0.904955i \(-0.360096\pi\)
0.996468 + 0.0839772i \(0.0267623\pi\)
\(368\) 0 0
\(369\) 256.474 + 148.076i 0.695053 + 0.401289i
\(370\) 0 0
\(371\) 11.7253 59.9548i 0.0316047 0.161603i
\(372\) 0 0
\(373\) −53.4998 + 92.6644i −0.143431 + 0.248430i −0.928787 0.370615i \(-0.879147\pi\)
0.785355 + 0.619045i \(0.212480\pi\)
\(374\) 0 0
\(375\) 29.3997 + 50.9218i 0.0783992 + 0.135791i
\(376\) 0 0
\(377\) 559.988i 1.48538i
\(378\) 0 0
\(379\) −539.901 −1.42454 −0.712270 0.701906i \(-0.752333\pi\)
−0.712270 + 0.701906i \(0.752333\pi\)
\(380\) 0 0
\(381\) 5.60924 3.23849i 0.0147224 0.00849998i
\(382\) 0 0
\(383\) 115.719 + 66.8102i 0.302137 + 0.174439i 0.643403 0.765528i \(-0.277522\pi\)
−0.341265 + 0.939967i \(0.610855\pi\)
\(384\) 0 0
\(385\) −416.719 + 478.273i −1.08239 + 1.24227i
\(386\) 0 0
\(387\) −131.130 + 227.123i −0.338836 + 0.586882i
\(388\) 0 0
\(389\) 285.627 + 494.721i 0.734260 + 1.27178i 0.955047 + 0.296454i \(0.0958043\pi\)
−0.220787 + 0.975322i \(0.570862\pi\)
\(390\) 0 0
\(391\) 967.707i 2.47495i
\(392\) 0 0
\(393\) 0.543792 0.00138369
\(394\) 0 0
\(395\) 399.518 230.662i 1.01144 0.583955i
\(396\) 0 0
\(397\) −172.662 99.6863i −0.434916 0.251099i 0.266523 0.963829i \(-0.414125\pi\)
−0.701439 + 0.712730i \(0.747459\pi\)
\(398\) 0 0
\(399\) 32.6826 + 28.4764i 0.0819114 + 0.0713694i
\(400\) 0 0
\(401\) −317.211 + 549.426i −0.791050 + 1.37014i 0.134267 + 0.990945i \(0.457132\pi\)
−0.925317 + 0.379194i \(0.876201\pi\)
\(402\) 0 0
\(403\) −271.259 469.835i −0.673100 1.16584i
\(404\) 0 0
\(405\) 393.096i 0.970608i
\(406\) 0 0
\(407\) −221.529 −0.544298
\(408\) 0 0
\(409\) −597.403 + 344.911i −1.46064 + 0.843303i −0.999041 0.0437846i \(-0.986058\pi\)
−0.461602 + 0.887087i \(0.652725\pi\)
\(410\) 0 0
\(411\) 29.3444 + 16.9420i 0.0713975 + 0.0412214i
\(412\) 0 0
\(413\) 343.398 + 67.1582i 0.831472 + 0.162611i
\(414\) 0 0
\(415\) −169.704 + 293.937i −0.408926 + 0.708281i
\(416\) 0 0
\(417\) −56.0133 97.0179i −0.134324 0.232657i
\(418\) 0 0
\(419\) 43.8224i 0.104588i 0.998632 + 0.0522940i \(0.0166533\pi\)
−0.998632 + 0.0522940i \(0.983347\pi\)
\(420\) 0 0
\(421\) −357.611 −0.849433 −0.424717 0.905326i \(-0.639626\pi\)
−0.424717 + 0.905326i \(0.639626\pi\)
\(422\) 0 0
\(423\) 422.112 243.706i 0.997901 0.576138i
\(424\) 0 0
\(425\) −64.8446 37.4380i −0.152575 0.0880895i
\(426\) 0 0
\(427\) −8.94068 26.0626i −0.0209384 0.0610365i
\(428\) 0 0
\(429\) −92.9867 + 161.058i −0.216752 + 0.375426i
\(430\) 0 0
\(431\) −143.259 248.131i −0.332387 0.575711i 0.650592 0.759427i \(-0.274521\pi\)
−0.982979 + 0.183716i \(0.941187\pi\)
\(432\) 0 0
\(433\) 407.880i 0.941986i 0.882137 + 0.470993i \(0.156104\pi\)
−0.882137 + 0.470993i \(0.843896\pi\)
\(434\) 0 0
\(435\) 70.0708 0.161082
\(436\) 0 0
\(437\) −426.424 + 246.196i −0.975798 + 0.563377i
\(438\) 0 0
\(439\) −46.8249 27.0344i −0.106663 0.0615817i 0.445720 0.895173i \(-0.352948\pi\)
−0.552382 + 0.833591i \(0.686281\pi\)
\(440\) 0 0
\(441\) −396.853 161.398i −0.899893 0.365981i
\(442\) 0 0
\(443\) −158.497 + 274.526i −0.357782 + 0.619697i −0.987590 0.157054i \(-0.949800\pi\)
0.629808 + 0.776751i \(0.283134\pi\)
\(444\) 0 0
\(445\) −113.970 197.401i −0.256112 0.443599i
\(446\) 0 0
\(447\) 20.0272i 0.0448035i
\(448\) 0 0
\(449\) 544.261 1.21216 0.606081 0.795403i \(-0.292741\pi\)
0.606081 + 0.795403i \(0.292741\pi\)
\(450\) 0 0
\(451\) 501.319 289.437i 1.11157 0.641767i
\(452\) 0 0
\(453\) 97.7437 + 56.4323i 0.215770 + 0.124575i
\(454\) 0 0
\(455\) −753.961 + 258.644i −1.65706 + 0.568448i
\(456\) 0 0
\(457\) 343.708 595.320i 0.752096 1.30267i −0.194709 0.980861i \(-0.562376\pi\)
0.946805 0.321808i \(-0.104291\pi\)
\(458\) 0 0
\(459\) −107.971 187.011i −0.235231 0.407432i
\(460\) 0 0
\(461\) 676.260i 1.46694i 0.679721 + 0.733470i \(0.262101\pi\)
−0.679721 + 0.733470i \(0.737899\pi\)
\(462\) 0 0
\(463\) 559.738 1.20894 0.604469 0.796629i \(-0.293385\pi\)
0.604469 + 0.796629i \(0.293385\pi\)
\(464\) 0 0
\(465\) 58.7901 33.9425i 0.126430 0.0729945i
\(466\) 0 0
\(467\) −319.886 184.686i −0.684981 0.395474i 0.116748 0.993162i \(-0.462753\pi\)
−0.801729 + 0.597687i \(0.796086\pi\)
\(468\) 0 0
\(469\) 142.261 727.417i 0.303327 1.55100i
\(470\) 0 0
\(471\) −51.2233 + 88.7213i −0.108754 + 0.188368i
\(472\) 0 0
\(473\) 256.313 + 443.948i 0.541889 + 0.938579i
\(474\) 0 0
\(475\) 38.0987i 0.0802077i
\(476\) 0 0
\(477\) −76.3040 −0.159967
\(478\) 0 0
\(479\) 270.362 156.094i 0.564430 0.325874i −0.190492 0.981689i \(-0.561008\pi\)
0.754922 + 0.655815i \(0.227675\pi\)
\(480\) 0 0
\(481\) −241.069 139.181i −0.501182 0.289358i
\(482\) 0 0
\(483\) −93.8923 + 107.761i −0.194394 + 0.223108i
\(484\) 0 0
\(485\) 76.2231 132.022i 0.157161 0.272211i
\(486\) 0 0
\(487\) −140.195 242.824i −0.287874 0.498613i 0.685428 0.728140i \(-0.259615\pi\)
−0.973302 + 0.229528i \(0.926282\pi\)
\(488\) 0 0
\(489\) 1.33283i 0.00272562i
\(490\) 0 0
\(491\) 423.804 0.863145 0.431573 0.902078i \(-0.357959\pi\)
0.431573 + 0.902078i \(0.357959\pi\)
\(492\) 0 0
\(493\) 542.382 313.144i 1.10017 0.635181i
\(494\) 0 0
\(495\) 686.171 + 396.161i 1.38620 + 0.800325i
\(496\) 0 0
\(497\) 184.842 + 161.053i 0.371916 + 0.324050i
\(498\) 0 0
\(499\) 83.0243 143.802i 0.166381 0.288181i −0.770764 0.637121i \(-0.780125\pi\)
0.937145 + 0.348940i \(0.113458\pi\)
\(500\) 0 0
\(501\) −33.6997 58.3695i −0.0672648 0.116506i
\(502\) 0 0
\(503\) 632.164i 1.25679i 0.777896 + 0.628393i \(0.216287\pi\)
−0.777896 + 0.628393i \(0.783713\pi\)
\(504\) 0 0
\(505\) 325.946 0.645438
\(506\) 0 0
\(507\) −128.211 + 74.0224i −0.252881 + 0.146001i
\(508\) 0 0
\(509\) −269.053 155.338i −0.528592 0.305183i 0.211851 0.977302i \(-0.432051\pi\)
−0.740443 + 0.672119i \(0.765384\pi\)
\(510\) 0 0
\(511\) −320.249 62.6310i −0.626711 0.122566i
\(512\) 0 0
\(513\) 54.9382 95.1558i 0.107092 0.185489i
\(514\) 0 0
\(515\) −158.358 274.284i −0.307491 0.532591i
\(516\) 0 0
\(517\) 952.725i 1.84279i
\(518\) 0 0
\(519\) 49.1977 0.0947932
\(520\) 0 0
\(521\) 58.0568 33.5191i 0.111433 0.0643361i −0.443247 0.896399i \(-0.646174\pi\)
0.554681 + 0.832063i \(0.312840\pi\)
\(522\) 0 0
\(523\) −462.718 267.150i −0.884738 0.510804i −0.0125204 0.999922i \(-0.503985\pi\)
−0.872218 + 0.489118i \(0.837319\pi\)
\(524\) 0 0
\(525\) −3.58846 10.4606i −0.00683517 0.0199249i
\(526\) 0 0
\(527\) 303.375 525.462i 0.575665 0.997081i
\(528\) 0 0
\(529\) −547.257 947.877i −1.03451 1.79183i
\(530\) 0 0
\(531\) 437.040i 0.823051i
\(532\) 0 0
\(533\) 727.383 1.36470
\(534\) 0 0
\(535\) −604.681 + 349.113i −1.13025 + 0.652547i
\(536\) 0 0
\(537\) 36.8800 + 21.2927i 0.0686778 + 0.0396512i
\(538\) 0 0
\(539\) −661.066 + 514.047i −1.22647 + 0.953704i
\(540\) 0 0
\(541\) −75.6707 + 131.065i −0.139872 + 0.242265i −0.927448 0.373952i \(-0.878002\pi\)
0.787576 + 0.616217i \(0.211336\pi\)
\(542\) 0 0
\(543\) 54.3096 + 94.0670i 0.100018 + 0.173236i
\(544\) 0 0
\(545\) 200.487i 0.367865i
\(546\) 0 0
\(547\) 775.543 1.41781 0.708906 0.705303i \(-0.249189\pi\)
0.708906 + 0.705303i \(0.249189\pi\)
\(548\) 0 0
\(549\) −29.8044 + 17.2076i −0.0542885 + 0.0313435i
\(550\) 0 0
\(551\) 275.976 + 159.335i 0.500865 + 0.289174i
\(552\) 0 0
\(553\) 576.044 197.610i 1.04167 0.357342i
\(554\) 0 0
\(555\) 17.4156 30.1647i 0.0313795 0.0543508i
\(556\) 0 0
\(557\) −32.2200 55.8066i −0.0578455 0.100191i 0.835653 0.549258i \(-0.185090\pi\)
−0.893498 + 0.449067i \(0.851756\pi\)
\(558\) 0 0
\(559\) 644.140i 1.15231i
\(560\) 0 0
\(561\) −207.992 −0.370752
\(562\) 0 0
\(563\) 789.688 455.927i 1.40264 0.809816i 0.407980 0.912991i \(-0.366233\pi\)
0.994663 + 0.103175i \(0.0329000\pi\)
\(564\) 0 0
\(565\) 213.281 + 123.138i 0.377489 + 0.217943i
\(566\) 0 0
\(567\) −99.5997 + 509.280i −0.175661 + 0.898201i
\(568\) 0 0
\(569\) −118.002 + 204.386i −0.207385 + 0.359201i −0.950890 0.309529i \(-0.899829\pi\)
0.743505 + 0.668730i \(0.233162\pi\)
\(570\) 0 0
\(571\) −414.770 718.403i −0.726392 1.25815i −0.958398 0.285434i \(-0.907862\pi\)
0.232006 0.972714i \(-0.425471\pi\)
\(572\) 0 0
\(573\) 27.7379i 0.0484082i
\(574\) 0 0
\(575\) 125.619 0.218468
\(576\) 0 0
\(577\) 380.226 219.524i 0.658971 0.380457i −0.132914 0.991128i \(-0.542433\pi\)
0.791885 + 0.610671i \(0.209100\pi\)
\(578\) 0 0
\(579\) 152.853 + 88.2497i 0.263995 + 0.152417i
\(580\) 0 0
\(581\) −294.338 + 337.815i −0.506606 + 0.581437i
\(582\) 0 0
\(583\) −74.5741 + 129.166i −0.127914 + 0.221554i
\(584\) 0 0
\(585\) 497.795 + 862.207i 0.850932 + 1.47386i
\(586\) 0 0
\(587\) 871.738i 1.48507i 0.669805 + 0.742537i \(0.266378\pi\)
−0.669805 + 0.742537i \(0.733622\pi\)
\(588\) 0 0
\(589\) 308.729 0.524158
\(590\) 0 0
\(591\) 70.9216 40.9466i 0.120003 0.0692836i
\(592\) 0 0
\(593\) 662.637 + 382.574i 1.11743 + 0.645149i 0.940744 0.339117i \(-0.110128\pi\)
0.176688 + 0.984267i \(0.443462\pi\)
\(594\) 0 0
\(595\) −672.125 585.623i −1.12962 0.984240i
\(596\) 0 0
\(597\) 34.8702 60.3969i 0.0584090 0.101167i
\(598\) 0 0
\(599\) 146.400 + 253.571i 0.244407 + 0.423325i 0.961965 0.273174i \(-0.0880735\pi\)
−0.717558 + 0.696499i \(0.754740\pi\)
\(600\) 0 0
\(601\) 748.440i 1.24532i −0.782491 0.622662i \(-0.786051\pi\)
0.782491 0.622662i \(-0.213949\pi\)
\(602\) 0 0
\(603\) −925.777 −1.53529
\(604\) 0 0
\(605\) 785.572 453.550i 1.29847 0.749670i
\(606\) 0 0
\(607\) −53.7404 31.0270i −0.0885344 0.0511154i 0.455079 0.890451i \(-0.349611\pi\)
−0.543614 + 0.839336i \(0.682944\pi\)
\(608\) 0 0
\(609\) 90.7811 + 17.7540i 0.149066 + 0.0291527i
\(610\) 0 0
\(611\) 598.572 1036.76i 0.979660 1.69682i
\(612\) 0 0
\(613\) −22.3280 38.6732i −0.0364241 0.0630884i 0.847239 0.531212i \(-0.178263\pi\)
−0.883663 + 0.468124i \(0.844930\pi\)
\(614\) 0 0
\(615\) 91.0168i 0.147995i
\(616\) 0 0
\(617\) −832.160 −1.34872 −0.674360 0.738403i \(-0.735580\pi\)
−0.674360 + 0.738403i \(0.735580\pi\)
\(618\) 0 0
\(619\) 216.394 124.935i 0.349586 0.201834i −0.314917 0.949119i \(-0.601977\pi\)
0.664503 + 0.747285i \(0.268643\pi\)
\(620\) 0 0
\(621\) 313.747 + 181.142i 0.505229 + 0.291694i
\(622\) 0 0
\(623\) −97.6388 284.623i −0.156724 0.456858i
\(624\) 0 0
\(625\) 346.611 600.347i 0.554577 0.960556i
\(626\) 0 0
\(627\) −52.9156 91.6525i −0.0843948 0.146176i
\(628\) 0 0
\(629\) 311.319i 0.494943i
\(630\) 0 0
\(631\) 26.0372 0.0412634 0.0206317 0.999787i \(-0.493432\pi\)
0.0206317 + 0.999787i \(0.493432\pi\)
\(632\) 0 0
\(633\) −44.5713 + 25.7332i −0.0704128 + 0.0406528i
\(634\) 0 0
\(635\) −58.6954 33.8878i −0.0924336 0.0533666i
\(636\) 0 0
\(637\) −1042.34 + 144.056i −1.63632 + 0.226148i
\(638\) 0 0
\(639\) 153.108 265.190i 0.239605 0.415008i
\(640\) 0 0
\(641\) −235.195 407.370i −0.366920 0.635523i 0.622163 0.782888i \(-0.286254\pi\)
−0.989082 + 0.147365i \(0.952921\pi\)
\(642\) 0 0
\(643\) 668.123i 1.03907i 0.854449 + 0.519536i \(0.173895\pi\)
−0.854449 + 0.519536i \(0.826105\pi\)
\(644\) 0 0
\(645\) −80.6007 −0.124962
\(646\) 0 0
\(647\) 925.107 534.111i 1.42984 0.825519i 0.432733 0.901522i \(-0.357549\pi\)
0.997108 + 0.0760031i \(0.0242159\pi\)
\(648\) 0 0
\(649\) −739.813 427.131i −1.13993 0.658138i
\(650\) 0 0
\(651\) 84.7662 29.0788i 0.130209 0.0446678i
\(652\) 0 0
\(653\) 389.917 675.357i 0.597117 1.03424i −0.396128 0.918195i \(-0.629646\pi\)
0.993244 0.116041i \(-0.0370204\pi\)
\(654\) 0 0
\(655\) −2.84513 4.92792i −0.00434371 0.00752353i
\(656\) 0 0
\(657\) 407.579i 0.620363i
\(658\) 0 0
\(659\) −1017.20 −1.54355 −0.771774 0.635897i \(-0.780630\pi\)
−0.771774 + 0.635897i \(0.780630\pi\)
\(660\) 0 0
\(661\) −819.200 + 472.966i −1.23934 + 0.715530i −0.968958 0.247224i \(-0.920482\pi\)
−0.270377 + 0.962755i \(0.587148\pi\)
\(662\) 0 0
\(663\) −226.337 130.676i −0.341384 0.197098i
\(664\) 0 0
\(665\) 87.0605 445.164i 0.130918 0.669419i
\(666\) 0 0
\(667\) −525.359 + 909.949i −0.787645 + 1.36424i
\(668\) 0 0
\(669\) 45.7522 + 79.2452i 0.0683890 + 0.118453i
\(670\) 0 0
\(671\) 67.2697i 0.100253i
\(672\) 0 0
\(673\) −76.8911 −0.114251 −0.0571256 0.998367i \(-0.518194\pi\)
−0.0571256 + 0.998367i \(0.518194\pi\)
\(674\) 0 0
\(675\) −24.2761 + 14.0158i −0.0359646 + 0.0207642i
\(676\) 0 0
\(677\) 555.161 + 320.523i 0.820031 + 0.473445i 0.850427 0.526093i \(-0.176343\pi\)
−0.0303959 + 0.999538i \(0.509677\pi\)
\(678\) 0 0
\(679\) 132.202 151.730i 0.194702 0.223461i
\(680\) 0 0
\(681\) −12.8481 + 22.2535i −0.0188665 + 0.0326777i
\(682\) 0 0
\(683\) 511.461 + 885.877i 0.748845 + 1.29704i 0.948377 + 0.317147i \(0.102725\pi\)
−0.199531 + 0.979891i \(0.563942\pi\)
\(684\) 0 0
\(685\) 354.564i 0.517611i
\(686\) 0 0
\(687\) −101.112 −0.147180
\(688\) 0 0
\(689\) −162.303 + 93.7059i −0.235564 + 0.136003i
\(690\) 0 0
\(691\) 597.595 + 345.021i 0.864826 + 0.499307i 0.865625 0.500692i \(-0.166921\pi\)
−0.000799666 1.00000i \(0.500255\pi\)
\(692\) 0 0
\(693\) 788.600 + 687.108i 1.13795 + 0.991497i
\(694\) 0 0
\(695\) −586.126 + 1015.20i −0.843347 + 1.46072i
\(696\) 0 0
\(697\) 406.751 + 704.513i 0.583574 + 1.01078i
\(698\) 0 0
\(699\) 89.7739i 0.128432i
\(700\) 0 0
\(701\) −361.922 −0.516294 −0.258147 0.966106i \(-0.583112\pi\)
−0.258147 + 0.966106i \(0.583112\pi\)
\(702\) 0 0
\(703\) 137.184 79.2032i 0.195141 0.112665i
\(704\) 0 0
\(705\) 129.729 + 74.8988i 0.184012 + 0.106239i
\(706\) 0 0
\(707\) 422.283 + 82.5858i 0.597289 + 0.116812i
\(708\) 0 0
\(709\) −260.952 + 451.982i −0.368056 + 0.637492i −0.989262 0.146156i \(-0.953310\pi\)
0.621205 + 0.783648i \(0.286643\pi\)
\(710\) 0 0
\(711\) −380.327 658.746i −0.534919 0.926507i
\(712\) 0 0
\(713\) 1017.94i 1.42769i
\(714\) 0 0
\(715\) 1946.04 2.72173
\(716\) 0 0
\(717\) −59.5497 + 34.3810i −0.0830540 + 0.0479513i
\(718\) 0 0
\(719\) −573.144 330.905i −0.797141 0.460230i 0.0453294 0.998972i \(-0.485566\pi\)
−0.842470 + 0.538743i \(0.818900\pi\)
\(720\) 0 0
\(721\) −135.667 395.476i −0.188164 0.548510i
\(722\) 0 0
\(723\) 80.1267 138.783i 0.110825 0.191955i
\(724\) 0 0
\(725\) −40.6495 70.4070i −0.0560683 0.0971132i
\(726\) 0 0
\(727\) 1169.62i 1.60882i −0.594071 0.804412i \(-0.702480\pi\)
0.594071 0.804412i \(-0.297520\pi\)
\(728\) 0 0
\(729\) 607.150 0.832854
\(730\) 0 0
\(731\) −623.888 + 360.202i −0.853472 + 0.492752i
\(732\) 0 0
\(733\) −391.800 226.206i −0.534516 0.308603i 0.208338 0.978057i \(-0.433195\pi\)
−0.742853 + 0.669454i \(0.766528\pi\)
\(734\) 0 0
\(735\) −18.0256 130.427i −0.0245246 0.177451i
\(736\) 0 0
\(737\) −904.788 + 1567.14i −1.22766 + 2.12638i
\(738\) 0 0
\(739\) 2.75378 + 4.76968i 0.00372636 + 0.00645424i 0.867883 0.496769i \(-0.165481\pi\)
−0.864156 + 0.503224i \(0.832147\pi\)
\(740\) 0 0
\(741\) 132.982i 0.179463i
\(742\) 0 0
\(743\) −866.020 −1.16557 −0.582786 0.812626i \(-0.698037\pi\)
−0.582786 + 0.812626i \(0.698037\pi\)
\(744\) 0 0
\(745\) −181.489 + 104.783i −0.243609 + 0.140648i
\(746\) 0 0
\(747\) 484.658 + 279.817i 0.648806 + 0.374588i
\(748\) 0 0
\(749\) −871.857 + 299.088i −1.16403 + 0.399316i
\(750\) 0 0
\(751\) −230.421 + 399.101i −0.306819 + 0.531426i −0.977665 0.210171i \(-0.932598\pi\)
0.670846 + 0.741597i \(0.265931\pi\)
\(752\) 0 0
\(753\) −10.1661 17.6082i −0.0135008 0.0233840i
\(754\) 0 0
\(755\) 1181.02i 1.56427i
\(756\) 0 0
\(757\) −547.987 −0.723893 −0.361946 0.932199i \(-0.617888\pi\)
−0.361946 + 0.932199i \(0.617888\pi\)
\(758\) 0 0
\(759\) 302.196 174.473i 0.398151 0.229872i
\(760\) 0 0
\(761\) −1129.20 651.942i −1.48383 0.856691i −0.484002 0.875067i \(-0.660817\pi\)
−0.999831 + 0.0183760i \(0.994150\pi\)
\(762\) 0 0
\(763\) 50.7978 259.743i 0.0665764 0.340423i
\(764\) 0 0
\(765\) −556.732 + 964.289i −0.727755 + 1.26051i
\(766\) 0 0
\(767\) −536.711 929.611i −0.699754 1.21201i
\(768\) 0 0
\(769\) 771.004i 1.00261i 0.865272 + 0.501303i \(0.167146\pi\)
−0.865272 + 0.501303i \(0.832854\pi\)
\(770\) 0 0
\(771\) −88.0080 −0.114148
\(772\) 0 0
\(773\) −922.592 + 532.659i −1.19352 + 0.689080i −0.959104 0.283056i \(-0.908652\pi\)
−0.234418 + 0.972136i \(0.575319\pi\)
\(774\) 0 0
\(775\) −68.2106 39.3814i −0.0880137 0.0508147i
\(776\) 0 0
\(777\) 30.2059 34.6676i 0.0388750 0.0446173i
\(778\) 0 0
\(779\) −206.964 + 358.473i −0.265679 + 0.460170i
\(780\) 0 0
\(781\) −299.273 518.356i −0.383192 0.663708i
\(782\) 0 0
\(783\) 234.466i 0.299446i
\(784\) 0 0
\(785\) 1072.01 1.36561
\(786\) 0 0
\(787\) −818.075 + 472.316i −1.03948 + 0.600147i −0.919687 0.392651i \(-0.871558\pi\)
−0.119798 + 0.992798i \(0.538225\pi\)
\(788\) 0 0
\(789\) −159.998 92.3748i −0.202786 0.117078i
\(790\) 0 0
\(791\) 245.119 +