Properties

Label 224.3.s.a.129.4
Level 224
Weight 3
Character 224.129
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 129.4
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 \(\chi\) \(=\) 224.129
Dual form 224.3.s.a.33.4

$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

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

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 \(-0.360249\pi\)
−0.571356 + 0.820702i \(0.693582\pi\)
\(4\) 0 0
\(5\) −4.59219 + 2.65130i −0.918439 + 0.530261i −0.883137 0.469116i \(-0.844573\pi\)
−0.0353020 + 0.999377i \(0.511239\pi\)
\(6\) 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 0.156951 + 0.987606i \(0.449833\pi\)
−0.933768 + 0.357880i \(0.883500\pi\)
\(12\) 0 0
\(13\) 21.4744i 1.65187i −0.563762 0.825937i \(-0.690647\pi\)
0.563762 0.825937i \(-0.309353\pi\)
\(14\) 0 0
\(15\) 2.68707 0.179138
\(16\) 0 0
\(17\) −20.7992 12.0084i −1.22348 0.706378i −0.257824 0.966192i \(-0.583005\pi\)
−0.965659 + 0.259814i \(0.916339\pi\)
\(18\) 0 0
\(19\) 10.5831 6.11016i 0.557006 0.321588i −0.194937 0.980816i \(-0.562450\pi\)
0.751943 + 0.659228i \(0.229117\pi\)
\(20\) 0 0
\(21\) −3.48126 + 0.680829i −0.165775 + 0.0324205i
\(22\) 0 0
\(23\) −20.1464 34.8946i −0.875932 1.51716i −0.855767 0.517361i \(-0.826914\pi\)
−0.0201644 0.999797i \(-0.506419\pi\)
\(24\) 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 \(-0.199742\pi\)
−0.103723 + 0.994606i \(0.533075\pi\)
\(32\) 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 0.765051 0.643970i \(-0.222714\pi\)
−0.940220 + 0.340568i \(0.889381\pi\)
\(38\) 0 0
\(39\) −5.44101 + 9.42411i −0.139513 + 0.241644i
\(40\) 0 0
\(41\) 33.8721i 0.826150i 0.910697 + 0.413075i \(0.135545\pi\)
−0.910697 + 0.413075i \(0.864455\pi\)
\(42\) 0 0
\(43\) −29.9958 −0.697576 −0.348788 0.937202i \(-0.613407\pi\)
−0.348788 + 0.937202i \(0.613407\pi\)
\(44\) 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 \(-0.464587\pi\)
0.916184 + 0.400758i \(0.131253\pi\)
\(48\) 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 −0.821919 0.569604i \(-0.807096\pi\)
0.904251 + 0.427001i \(0.140430\pi\)
\(54\) 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 \(-0.194095\pi\)
−0.0860631 + 0.996290i \(0.527429\pi\)
\(60\) 0 0
\(61\) 3.40886 1.96811i 0.0558829 0.0322640i −0.471798 0.881707i \(-0.656395\pi\)
0.527681 + 0.849443i \(0.323062\pi\)
\(62\) 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 0.135661 + 0.990755i \(0.456684\pi\)
−0.925850 + 0.377892i \(0.876649\pi\)
\(68\) 0 0
\(69\) 20.4182i 0.295916i
\(70\) 0 0
\(71\) 35.0232 0.493285 0.246642 0.969107i \(-0.420673\pi\)
0.246642 + 0.969107i \(0.420673\pi\)
\(72\) 0 0
\(73\) 40.3712 + 23.3083i 0.553030 + 0.319292i 0.750343 0.661049i \(-0.229888\pi\)
−0.197313 + 0.980340i \(0.563222\pi\)
\(74\) 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 0.998229 + 0.0594846i \(0.0189457\pi\)
−0.447599 + 0.894234i \(0.647721\pi\)
\(80\) 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 −0.276059 0.961141i \(-0.589029\pi\)
0.694343 + 0.719645i \(0.255695\pi\)
\(90\) 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 \(-0.952655\pi\)
0.988959 0.148192i \(-0.0473454\pi\)
\(98\) 0 0
\(99\) 149.421 1.50930
\(100\) 0 0
\(101\) −53.2337 30.7345i −0.527067 0.304302i 0.212754 0.977106i \(-0.431757\pi\)
−0.739821 + 0.672804i \(0.765090\pi\)
\(102\) 0 0
\(103\) −51.7263 + 29.8642i −0.502197 + 0.289944i −0.729620 0.683852i \(-0.760303\pi\)
0.227423 + 0.973796i \(0.426970\pi\)
\(104\) 0 0
\(105\) 14.1816 12.3564i 0.135062 0.117680i
\(106\) 0 0
\(107\) −65.8380 114.035i −0.615308 1.06574i −0.990330 0.138729i \(-0.955698\pi\)
0.375022 0.927016i \(-0.377635\pi\)
\(108\) 0 0
\(109\) 18.9045 32.7436i 0.173436 0.300400i −0.766183 0.642623i \(-0.777846\pi\)
0.939619 + 0.342222i \(0.111180\pi\)
\(110\) 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 \(-0.516024\pi\)
−0.0503211 + 0.998733i \(0.516024\pi\)
\(128\) 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 \(-0.667970\pi\)
0.496449 + 0.868066i \(0.334637\pi\)
\(132\) 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 −0.717824 0.696225i \(-0.754862\pi\)
0.961860 + 0.273541i \(0.0881951\pi\)
\(138\) 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 0.924686 0.380730i \(-0.124327\pi\)
−0.792065 + 0.610437i \(0.790994\pi\)
\(150\) 0 0
\(151\) −111.362 + 192.885i −0.737499 + 1.27739i 0.216119 + 0.976367i \(0.430660\pi\)
−0.953618 + 0.301019i \(0.902673\pi\)
\(152\) 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 −0.175002 0.984568i \(-0.555993\pi\)
−0.940162 + 0.340728i \(0.889327\pi\)
\(158\) 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 \(-0.164099\pi\)
−0.861963 + 0.506971i \(0.830765\pi\)
\(164\) 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 −0.236911 0.971531i \(-0.576135\pi\)
0.722915 + 0.690937i \(0.242802\pi\)
\(174\) 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 \(-0.908757\pi\)
0.724457 + 0.689320i \(0.242091\pi\)
\(180\) 0 0
\(181\) 214.347i 1.18424i −0.805851 0.592119i \(-0.798292\pi\)
0.805851 0.592119i \(-0.201708\pi\)
\(182\) 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 \(-0.212435\pi\)
−0.928734 + 0.370746i \(0.879102\pi\)
\(192\) 0 0
\(193\) 174.150 301.637i 0.902332 1.56289i 0.0778732 0.996963i \(-0.475187\pi\)
0.824459 0.565922i \(-0.191480\pi\)
\(194\) 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 \(-0.445722\pi\)
−0.768618 + 0.639707i \(0.779056\pi\)
\(200\) 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 \(-0.422633\pi\)
0.240670 + 0.970607i \(0.422633\pi\)
\(212\) 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 \(-0.297706\pi\)
−0.400143 + 0.916453i \(0.631040\pi\)
\(228\) 0 0
\(229\) −172.801 + 99.7665i −0.754588 + 0.435661i −0.827349 0.561688i \(-0.810152\pi\)
0.0727614 + 0.997349i \(0.476819\pi\)
\(230\) 0 0
\(231\) 19.6708 57.3416i 0.0851551 0.248232i
\(232\) 0 0
\(233\) 88.5790 + 153.423i 0.380167 + 0.658469i 0.991086 0.133224i \(-0.0425330\pi\)
−0.610919 + 0.791693i \(0.709200\pi\)
\(234\) 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 \(-0.408379\pi\)
0.283878 + 0.958860i \(0.408379\pi\)
\(240\) 0 0
\(241\) 273.872 + 158.120i 1.13640 + 0.656101i 0.945537 0.325516i \(-0.105538\pi\)
0.190863 + 0.981617i \(0.438871\pi\)
\(242\) 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 −0.763211 0.646149i \(-0.776378\pi\)
0.177976 + 0.984035i \(0.443045\pi\)
\(258\) 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 −0.277690 0.960671i \(-0.589569\pi\)
0.970810 0.239848i \(-0.0770977\pi\)
\(264\) 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 0.527781 0.849380i \(-0.323024\pi\)
−0.471694 + 0.881762i \(0.656357\pi\)
\(270\) 0 0
\(271\) 112.812 65.1322i 0.416281 0.240340i −0.277204 0.960811i \(-0.589408\pi\)
0.693485 + 0.720471i \(0.256074\pi\)
\(272\) 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 −0.548572 0.836103i \(-0.684828\pi\)
0.998373 + 0.0570258i \(0.0181617\pi\)
\(278\) 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 \(-0.209713\pi\)
−0.134823 + 0.990870i \(0.543047\pi\)
\(284\) 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 \(-0.960880\pi\)
0.992457 0.122591i \(-0.0391204\pi\)
\(294\) 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 \(-0.166833\pi\)
−0.000524087 1.00000i \(0.500167\pi\)
\(312\) 0 0
\(313\) 475.367 274.453i 1.51875 0.876848i 0.518989 0.854781i \(-0.326309\pi\)
0.999756 0.0220674i \(-0.00702483\pi\)
\(314\) 0 0
\(315\) 318.499 62.2887i 1.01111 0.197742i
\(316\) 0 0
\(317\) −70.9651 122.915i −0.223865 0.387745i 0.732113 0.681183i \(-0.238534\pi\)
−0.955978 + 0.293437i \(0.905201\pi\)
\(318\) 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 \(-0.148932\pi\)
−0.836838 + 0.547451i \(0.815598\pi\)
\(332\) 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 \(-0.718779\pi\)
0.986628 + 0.162986i \(0.0521126\pi\)
\(348\) 0 0
\(349\) 190.205i 0.545001i −0.962156 0.272501i \(-0.912149\pi\)
0.962156 0.272501i \(-0.0878507\pi\)
\(350\) 0 0
\(351\) 193.082 0.550091
\(352\) 0 0
\(353\) 341.878 + 197.383i 0.968493 + 0.559160i 0.898777 0.438407i \(-0.144457\pi\)
0.0697166 + 0.997567i \(0.477791\pi\)
\(354\) 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 \(-0.0312494\pi\)
−0.582476 + 0.812848i \(0.697916\pi\)
\(360\) 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 \(-0.639904\pi\)
−0.996468 + 0.0839772i \(0.973238\pi\)
\(368\) 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 0.785355 0.619045i \(-0.212480\pi\)
−0.928787 + 0.370615i \(0.879147\pi\)
\(374\) 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 \(-0.247667\pi\)
0.712270 + 0.701906i \(0.247667\pi\)
\(380\) 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 \(-0.722478\pi\)
0.341265 + 0.939967i \(0.389145\pi\)
\(384\) 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 −0.220787 0.975322i \(-0.570862\pi\)
0.955047 0.296454i \(-0.0958043\pi\)
\(390\) 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 −0.701439 0.712730i \(-0.747459\pi\)
0.266523 + 0.963829i \(0.414125\pi\)
\(398\) 0 0
\(399\) −32.6826 + 28.4764i −0.0819114 + 0.0713694i
\(400\) 0 0
\(401\) −317.211 549.426i −0.791050 1.37014i −0.925317 0.379194i \(-0.876201\pi\)
0.134267 0.990945i \(-0.457132\pi\)
\(402\) 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 −0.461602 0.887087i \(-0.652725\pi\)
−0.999041 + 0.0437846i \(0.986058\pi\)
\(410\) 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 \(-0.725479\pi\)
0.982979 + 0.183716i \(0.0588127\pi\)
\(432\) 0 0
\(433\) 407.880i 0.941986i −0.882137 0.470993i \(-0.843896\pi\)
0.882137 0.470993i \(-0.156104\pi\)
\(434\) 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 \(-0.647052\pi\)
0.552382 + 0.833591i \(0.313719\pi\)
\(440\) 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 \(-0.0501997\pi\)
−0.629808 + 0.776751i \(0.716866\pi\)
\(444\) 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 0.946805 + 0.321808i \(0.104291\pi\)
−0.194709 + 0.980861i \(0.562376\pi\)
\(458\) 0 0
\(459\) 107.971 187.011i 0.235231 0.407432i
\(460\) 0 0
\(461\) 676.260i 1.46694i −0.679721 0.733470i \(-0.737899\pi\)
0.679721 0.733470i \(-0.262101\pi\)
\(462\) 0 0
\(463\) −559.738 −1.20894 −0.604469 0.796629i \(-0.706615\pi\)
−0.604469 + 0.796629i \(0.706615\pi\)
\(464\) 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 \(-0.537247\pi\)
0.801729 + 0.597687i \(0.203914\pi\)
\(468\) 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 \(-0.438992\pi\)
−0.754922 + 0.655815i \(0.772325\pi\)
\(480\) 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 \(-0.740385\pi\)
0.973302 + 0.229528i \(0.0737182\pi\)
\(488\) 0 0
\(489\) 1.33283i 0.00272562i
\(490\) 0 0
\(491\) −423.804 −0.863145 −0.431573 0.902078i \(-0.642041\pi\)
−0.431573 + 0.902078i \(0.642041\pi\)
\(492\) 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 \(-0.219875\pi\)
−0.937145 + 0.348940i \(0.886542\pi\)
\(500\) 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 −0.740443 0.672119i \(-0.765384\pi\)
0.211851 + 0.977302i \(0.432051\pi\)
\(510\) 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 0.554681 0.832063i \(-0.312840\pi\)
−0.443247 + 0.896399i \(0.646174\pi\)
\(522\) 0 0
\(523\) 462.718 267.150i 0.884738 0.510804i 0.0125204 0.999922i \(-0.496015\pi\)
0.872218 + 0.489118i \(0.162681\pi\)
\(524\) 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 0.787576 0.616217i \(-0.211336\pi\)
−0.927448 + 0.373952i \(0.878002\pi\)
\(542\) 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 \(-0.750811\pi\)
−0.708906 + 0.705303i \(0.750811\pi\)
\(548\) 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 −0.893498 0.449067i \(-0.851756\pi\)
0.835653 + 0.549258i \(0.185090\pi\)
\(558\) 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 \(-0.633767\pi\)
−0.994663 + 0.103175i \(0.967100\pi\)
\(564\) 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 0.743505 0.668730i \(-0.233162\pi\)
−0.950890 + 0.309529i \(0.899829\pi\)
\(570\) 0 0
\(571\) 414.770 718.403i 0.726392 1.25815i −0.232006 0.972714i \(-0.574529\pi\)
0.958398 0.285434i \(-0.0921377\pi\)
\(572\) 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 0.791885 0.610671i \(-0.209100\pi\)
−0.132914 + 0.991128i \(0.542433\pi\)
\(578\) 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 0.176688 0.984267i \(-0.443462\pi\)
0.940744 + 0.339117i \(0.110128\pi\)
\(594\) 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 \(-0.911926\pi\)
0.717558 + 0.696499i \(0.245260\pi\)
\(600\) 0 0
\(601\) 748.440i 1.24532i 0.782491 + 0.622662i \(0.213949\pi\)
−0.782491 + 0.622662i \(0.786051\pi\)
\(602\) 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 \(-0.650389\pi\)
0.543614 + 0.839336i \(0.317056\pi\)
\(608\) 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 −0.883663 0.468124i \(-0.844930\pi\)
0.847239 + 0.531212i \(0.178263\pi\)
\(614\) 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 \(-0.398023\pi\)
−0.664503 + 0.747285i \(0.731357\pi\)
\(620\) 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 \(-0.506568\pi\)
−0.0206317 + 0.999787i \(0.506568\pi\)
\(632\) 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 −0.989082 0.147365i \(-0.952921\pi\)
0.622163 + 0.782888i \(0.286254\pi\)
\(642\) 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 \(-0.642451\pi\)
−0.997108 + 0.0760031i \(0.975784\pi\)
\(648\) 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 0.993244 + 0.116041i \(0.0370204\pi\)
−0.396128 + 0.918195i \(0.629646\pi\)
\(654\) 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 \(-0.219370\pi\)
0.771774 + 0.635897i \(0.219370\pi\)
\(660\) 0 0
\(661\) −819.200 472.966i −1.23934 0.715530i −0.270377 0.962755i \(-0.587148\pi\)
−0.968958 + 0.247224i \(0.920482\pi\)
\(662\) 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 −0.0303959 0.999538i \(-0.509677\pi\)
0.850427 + 0.526093i \(0.176343\pi\)
\(678\) 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 0.199531 + 0.979891i \(0.436058\pi\)
−0.948377 + 0.317147i \(0.897275\pi\)
\(684\) 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 \(-0.833079\pi\)
0.000799666 1.00000i \(0.499745\pi\)
\(692\) 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 0.621205 0.783648i \(-0.286643\pi\)
−0.989262 + 0.146156i \(0.953310\pi\)
\(710\) 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 \(-0.514434\pi\)
0.842470 + 0.538743i \(0.181100\pi\)
\(720\) 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 −0.742853 0.669454i \(-0.766528\pi\)
0.208338 + 0.978057i \(0.433195\pi\)
\(734\) 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 \(-0.834519\pi\)
0.864156 + 0.503224i \(0.167853\pi\)
\(740\) 0 0
\(741\) 132.982i 0.179463i
\(742\) 0 0
\(743\) 866.020 1.16557 0.582786 0.812626i \(-0.301963\pi\)
0.582786 + 0.812626i \(0.301963\pi\)
\(744\) 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 \(-0.0674020\pi\)
−0.670846 + 0.741597i \(0.734069\pi\)
\(752\) 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 −0.999831 0.0183760i \(-0.994150\pi\)
−0.484002 + 0.875067i \(0.660817\pi\)
\(762\) 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 \(-0.832854\pi\)
0.865272 0.501303i \(-0.167146\pi\)
\(770\) 0 0
\(771\) 88.0080 0.114148
\(772\) 0 0
\(773\) −922.592 532.659i −1.19352 0.689080i −0.234418 0.972136i \(-0.575319\pi\)
−0.959104 + 0.283056i \(0.908652\pi\)
\(774\) 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 \(-0.128442\pi\)
0.119798 + 0.992798i \(0.461775\pi\)
\(788\) 0 0
\(789\) −159.998 + 92.3748i −0.202786 + 0.117078i
\(790\) 0 0
\(791\)