Properties

Label 400.2.l.g.301.5
Level $400$
Weight $2$
Character 400.301
Analytic conductor $3.194$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 301.5
Root \(1.22306 - 0.710021i\) of defining polynomial
Character \(\chi\) \(=\) 400.301
Dual form 400.2.l.g.101.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22306 - 0.710021i) q^{2} +(-1.09156 - 1.09156i) q^{3} +(0.991741 - 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} +0.973926i q^{7} +(-0.0202025 - 2.82835i) q^{8} -0.616985i q^{9} +O(q^{10})\) \(q+(1.22306 - 0.710021i) q^{2} +(-1.09156 - 1.09156i) q^{3} +(0.991741 - 1.73679i) q^{4} +(-2.11008 - 0.560012i) q^{6} +0.973926i q^{7} +(-0.0202025 - 2.82835i) q^{8} -0.616985i q^{9} +(1.40810 - 1.40810i) q^{11} +(-2.97836 + 0.813270i) q^{12} +(-4.60317 - 4.60317i) q^{13} +(0.691508 + 1.19117i) q^{14} +(-2.03290 - 3.44490i) q^{16} +0.490104 q^{17} +(-0.438072 - 0.754608i) q^{18} +(4.54863 + 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +(0.722406 - 2.72196i) q^{22} +1.94308i q^{23} +(-3.06527 + 3.10938i) q^{24} +(-8.89828 - 2.36159i) q^{26} +(-3.94816 + 3.94816i) q^{27} +(1.69151 + 0.965882i) q^{28} +(-3.74613 - 3.74613i) q^{29} +4.29021 q^{31} +(-4.93230 - 2.76991i) q^{32} -3.07405 q^{33} +(0.599426 - 0.347984i) q^{34} +(-1.07157 - 0.611889i) q^{36} +(4.55320 - 4.55320i) q^{37} +(8.79286 + 2.33362i) q^{38} +10.0493i q^{39} +10.1542i q^{41} +(0.545410 - 2.05506i) q^{42} +(-1.79055 + 1.79055i) q^{43} +(-1.04911 - 3.84204i) q^{44} +(1.37963 + 2.37650i) q^{46} +10.0162 q^{47} +(-1.54128 + 5.97936i) q^{48} +6.05147 q^{49} +(-0.534979 - 0.534979i) q^{51} +(-12.5599 + 3.42960i) q^{52} +(5.61412 - 5.61412i) q^{53} +(-2.02555 + 7.63211i) q^{54} +(2.75461 - 0.0196757i) q^{56} -9.93022i q^{57} +(-7.24157 - 1.92191i) q^{58} +(8.44185 - 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} +(5.24718 - 3.04614i) q^{62} +0.600897 q^{63} +(-7.99918 + 0.114280i) q^{64} +(-3.75974 + 2.18264i) q^{66} +(7.07504 + 7.07504i) q^{67} +(0.486056 - 0.851209i) q^{68} +(2.12099 - 2.12099i) q^{69} -0.897891i q^{71} +(-1.74505 + 0.0124646i) q^{72} +9.71555i q^{73} +(2.33596 - 8.80170i) q^{74} +(12.4111 - 3.38897i) q^{76} +(1.37138 + 1.37138i) q^{77} +(7.13520 + 12.2909i) q^{78} -14.7857 q^{79} +6.76838 q^{81} +(7.20968 + 12.4192i) q^{82} +(0.815000 + 0.815000i) q^{83} +(-0.792065 - 2.90071i) q^{84} +(-0.918620 + 3.46128i) q^{86} +8.17827i q^{87} +(-4.01105 - 3.95415i) q^{88} -1.12404i q^{89} +(4.48314 - 4.48314i) q^{91} +(3.37472 + 1.92703i) q^{92} +(-4.68303 - 4.68303i) q^{93} +(12.2504 - 7.11174i) q^{94} +(2.36039 + 8.40744i) q^{96} -7.54442 q^{97} +(7.40130 - 4.29667i) q^{98} +(-0.868775 - 0.868775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} + O(q^{10}) \) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} - 2q^{11} + 8q^{12} - 4q^{13} + 14q^{14} + 2q^{16} - 8q^{17} + 18q^{18} - 14q^{19} - 20q^{21} + 2q^{22} - 14q^{24} - 16q^{26} - 10q^{27} + 26q^{28} - 4q^{31} - 16q^{32} + 28q^{33} - 6q^{34} + 2q^{36} + 8q^{37} + 10q^{38} + 10q^{42} - 44q^{44} - 10q^{46} + 8q^{47} - 28q^{48} + 4q^{49} + 10q^{51} - 12q^{52} - 16q^{53} + 10q^{54} + 6q^{56} - 60q^{58} + 20q^{59} + 4q^{61} - 18q^{62} - 8q^{63} + 38q^{64} + 32q^{66} + 50q^{67} - 60q^{68} - 14q^{72} + 10q^{74} + 60q^{76} - 8q^{77} + 4q^{78} + 12q^{79} - 8q^{81} + 42q^{82} - 2q^{83} + 34q^{84} + 6q^{86} + 30q^{88} - 2q^{92} - 44q^{93} + 32q^{94} - 34q^{96} + 64q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22306 0.710021i 0.864832 0.502061i
\(3\) −1.09156 1.09156i −0.630214 0.630214i 0.317908 0.948122i \(-0.397020\pi\)
−0.948122 + 0.317908i \(0.897020\pi\)
\(4\) 0.991741 1.73679i 0.495870 0.868396i
\(5\) 0 0
\(6\) −2.11008 0.560012i −0.861435 0.228624i
\(7\) 0.973926i 0.368109i 0.982916 + 0.184055i \(0.0589224\pi\)
−0.982916 + 0.184055i \(0.941078\pi\)
\(8\) −0.0202025 2.82835i −0.00714267 0.999974i
\(9\) 0.616985i 0.205662i
\(10\) 0 0
\(11\) 1.40810 1.40810i 0.424558 0.424558i −0.462212 0.886769i \(-0.652944\pi\)
0.886769 + 0.462212i \(0.152944\pi\)
\(12\) −2.97836 + 0.813270i −0.859780 + 0.234771i
\(13\) −4.60317 4.60317i −1.27669 1.27669i −0.942510 0.334179i \(-0.891541\pi\)
−0.334179 0.942510i \(-0.608459\pi\)
\(14\) 0.691508 + 1.19117i 0.184813 + 0.318353i
\(15\) 0 0
\(16\) −2.03290 3.44490i −0.508225 0.861224i
\(17\) 0.490104 0.118868 0.0594338 0.998232i \(-0.481070\pi\)
0.0594338 + 0.998232i \(0.481070\pi\)
\(18\) −0.438072 0.754608i −0.103255 0.177863i
\(19\) 4.54863 + 4.54863i 1.04353 + 1.04353i 0.999009 + 0.0445187i \(0.0141754\pi\)
0.0445187 + 0.999009i \(0.485825\pi\)
\(20\) 0 0
\(21\) 1.06310 1.06310i 0.231988 0.231988i
\(22\) 0.722406 2.72196i 0.154018 0.580325i
\(23\) 1.94308i 0.405160i 0.979266 + 0.202580i \(0.0649325\pi\)
−0.979266 + 0.202580i \(0.935067\pi\)
\(24\) −3.06527 + 3.10938i −0.625696 + 0.634699i
\(25\) 0 0
\(26\) −8.89828 2.36159i −1.74510 0.463147i
\(27\) −3.94816 + 3.94816i −0.759824 + 0.759824i
\(28\) 1.69151 + 0.965882i 0.319665 + 0.182535i
\(29\) −3.74613 3.74613i −0.695640 0.695640i 0.267827 0.963467i \(-0.413694\pi\)
−0.963467 + 0.267827i \(0.913694\pi\)
\(30\) 0 0
\(31\) 4.29021 0.770545 0.385272 0.922803i \(-0.374107\pi\)
0.385272 + 0.922803i \(0.374107\pi\)
\(32\) −4.93230 2.76991i −0.871916 0.489655i
\(33\) −3.07405 −0.535124
\(34\) 0.599426 0.347984i 0.102801 0.0596788i
\(35\) 0 0
\(36\) −1.07157 0.611889i −0.178596 0.101982i
\(37\) 4.55320 4.55320i 0.748542 0.748542i −0.225663 0.974205i \(-0.572455\pi\)
0.974205 + 0.225663i \(0.0724549\pi\)
\(38\) 8.79286 + 2.33362i 1.42639 + 0.378562i
\(39\) 10.0493i 1.60917i
\(40\) 0 0
\(41\) 10.1542i 1.58582i 0.609341 + 0.792908i \(0.291434\pi\)
−0.609341 + 0.792908i \(0.708566\pi\)
\(42\) 0.545410 2.05506i 0.0841586 0.317102i
\(43\) −1.79055 + 1.79055i −0.273057 + 0.273057i −0.830329 0.557273i \(-0.811848\pi\)
0.557273 + 0.830329i \(0.311848\pi\)
\(44\) −1.04911 3.84204i −0.158159 0.579210i
\(45\) 0 0
\(46\) 1.37963 + 2.37650i 0.203415 + 0.350395i
\(47\) 10.0162 1.46102 0.730510 0.682902i \(-0.239283\pi\)
0.730510 + 0.682902i \(0.239283\pi\)
\(48\) −1.54128 + 5.97936i −0.222465 + 0.863046i
\(49\) 6.05147 0.864495
\(50\) 0 0
\(51\) −0.534979 0.534979i −0.0749120 0.0749120i
\(52\) −12.5599 + 3.42960i −1.74174 + 0.475600i
\(53\) 5.61412 5.61412i 0.771158 0.771158i −0.207151 0.978309i \(-0.566419\pi\)
0.978309 + 0.207151i \(0.0664190\pi\)
\(54\) −2.02555 + 7.63211i −0.275643 + 1.03860i
\(55\) 0 0
\(56\) 2.75461 0.0196757i 0.368100 0.00262928i
\(57\) 9.93022i 1.31529i
\(58\) −7.24157 1.92191i −0.950865 0.252359i
\(59\) 8.44185 8.44185i 1.09904 1.09904i 0.104512 0.994524i \(-0.466672\pi\)
0.994524 0.104512i \(-0.0333281\pi\)
\(60\) 0 0
\(61\) 3.01095 + 3.01095i 0.385513 + 0.385513i 0.873084 0.487571i \(-0.162117\pi\)
−0.487571 + 0.873084i \(0.662117\pi\)
\(62\) 5.24718 3.04614i 0.666392 0.386860i
\(63\) 0.600897 0.0757060
\(64\) −7.99918 + 0.114280i −0.999898 + 0.0142850i
\(65\) 0 0
\(66\) −3.75974 + 2.18264i −0.462793 + 0.268665i
\(67\) 7.07504 + 7.07504i 0.864354 + 0.864354i 0.991840 0.127486i \(-0.0406908\pi\)
−0.127486 + 0.991840i \(0.540691\pi\)
\(68\) 0.486056 0.851209i 0.0589430 0.103224i
\(69\) 2.12099 2.12099i 0.255337 0.255337i
\(70\) 0 0
\(71\) 0.897891i 0.106560i −0.998580 0.0532800i \(-0.983032\pi\)
0.998580 0.0532800i \(-0.0169676\pi\)
\(72\) −1.74505 + 0.0124646i −0.205656 + 0.00146897i
\(73\) 9.71555i 1.13712i 0.822642 + 0.568559i \(0.192499\pi\)
−0.822642 + 0.568559i \(0.807501\pi\)
\(74\) 2.33596 8.80170i 0.271550 1.02318i
\(75\) 0 0
\(76\) 12.4111 3.38897i 1.42365 0.388741i
\(77\) 1.37138 + 1.37138i 0.156284 + 0.156284i
\(78\) 7.13520 + 12.2909i 0.807902 + 1.39166i
\(79\) −14.7857 −1.66352 −0.831760 0.555135i \(-0.812666\pi\)
−0.831760 + 0.555135i \(0.812666\pi\)
\(80\) 0 0
\(81\) 6.76838 0.752042
\(82\) 7.20968 + 12.4192i 0.796176 + 1.37147i
\(83\) 0.815000 + 0.815000i 0.0894579 + 0.0894579i 0.750420 0.660962i \(-0.229851\pi\)
−0.660962 + 0.750420i \(0.729851\pi\)
\(84\) −0.792065 2.90071i −0.0864214 0.316493i
\(85\) 0 0
\(86\) −0.918620 + 3.46128i −0.0990573 + 0.373239i
\(87\) 8.17827i 0.876803i
\(88\) −4.01105 3.95415i −0.427579 0.421514i
\(89\) 1.12404i 0.119148i −0.998224 0.0595739i \(-0.981026\pi\)
0.998224 0.0595739i \(-0.0189742\pi\)
\(90\) 0 0
\(91\) 4.48314 4.48314i 0.469961 0.469961i
\(92\) 3.37472 + 1.92703i 0.351839 + 0.200907i
\(93\) −4.68303 4.68303i −0.485608 0.485608i
\(94\) 12.2504 7.11174i 1.26354 0.733520i
\(95\) 0 0
\(96\) 2.36039 + 8.40744i 0.240906 + 0.858081i
\(97\) −7.54442 −0.766019 −0.383010 0.923744i \(-0.625112\pi\)
−0.383010 + 0.923744i \(0.625112\pi\)
\(98\) 7.40130 4.29667i 0.747644 0.434029i
\(99\) −0.868775 0.868775i −0.0873152 0.0873152i
\(100\) 0 0
\(101\) −2.60535 + 2.60535i −0.259242 + 0.259242i −0.824746 0.565504i \(-0.808682\pi\)
0.565504 + 0.824746i \(0.308682\pi\)
\(102\) −1.03416 0.274464i −0.102397 0.0271760i
\(103\) 13.8146i 1.36120i 0.732657 + 0.680598i \(0.238280\pi\)
−0.732657 + 0.680598i \(0.761720\pi\)
\(104\) −12.9264 + 13.1124i −1.26754 + 1.28577i
\(105\) 0 0
\(106\) 2.88025 10.8525i 0.279755 1.05409i
\(107\) −9.89124 + 9.89124i −0.956222 + 0.956222i −0.999081 0.0428589i \(-0.986353\pi\)
0.0428589 + 0.999081i \(0.486353\pi\)
\(108\) 2.94159 + 10.7727i 0.283054 + 1.03660i
\(109\) −11.5454 11.5454i −1.10584 1.10584i −0.993691 0.112154i \(-0.964225\pi\)
−0.112154 0.993691i \(-0.535775\pi\)
\(110\) 0 0
\(111\) −9.94021 −0.943483
\(112\) 3.35507 1.97989i 0.317025 0.187082i
\(113\) 17.2057 1.61857 0.809286 0.587415i \(-0.199854\pi\)
0.809286 + 0.587415i \(0.199854\pi\)
\(114\) −7.05066 12.1452i −0.660355 1.13751i
\(115\) 0 0
\(116\) −10.2215 + 2.79106i −0.949038 + 0.259144i
\(117\) −2.84008 + 2.84008i −0.262566 + 0.262566i
\(118\) 4.33098 16.3188i 0.398699 1.50226i
\(119\) 0.477325i 0.0437563i
\(120\) 0 0
\(121\) 7.03452i 0.639502i
\(122\) 5.82041 + 1.54473i 0.526955 + 0.139853i
\(123\) 11.0839 11.0839i 0.999403 0.999403i
\(124\) 4.25478 7.45121i 0.382091 0.669139i
\(125\) 0 0
\(126\) 0.734932 0.426650i 0.0654730 0.0380090i
\(127\) −1.37608 −0.122107 −0.0610535 0.998134i \(-0.519446\pi\)
−0.0610535 + 0.998134i \(0.519446\pi\)
\(128\) −9.70232 + 5.81936i −0.857572 + 0.514363i
\(129\) 3.90900 0.344168
\(130\) 0 0
\(131\) −9.03973 9.03973i −0.789804 0.789804i 0.191657 0.981462i \(-0.438614\pi\)
−0.981462 + 0.191657i \(0.938614\pi\)
\(132\) −3.04866 + 5.33899i −0.265352 + 0.464700i
\(133\) −4.43003 + 4.43003i −0.384132 + 0.384132i
\(134\) 13.6766 + 3.62976i 1.18148 + 0.313563i
\(135\) 0 0
\(136\) −0.00990133 1.38619i −0.000849032 0.118865i
\(137\) 15.3056i 1.30764i −0.756649 0.653822i \(-0.773165\pi\)
0.756649 0.653822i \(-0.226835\pi\)
\(138\) 1.08815 4.10004i 0.0926291 0.349018i
\(139\) −0.346824 + 0.346824i −0.0294173 + 0.0294173i −0.721662 0.692245i \(-0.756622\pi\)
0.692245 + 0.721662i \(0.256622\pi\)
\(140\) 0 0
\(141\) −10.9334 10.9334i −0.920754 0.920754i
\(142\) −0.637521 1.09817i −0.0534996 0.0921566i
\(143\) −12.9634 −1.08406
\(144\) −2.12545 + 1.25427i −0.177121 + 0.104522i
\(145\) 0 0
\(146\) 6.89824 + 11.8827i 0.570902 + 0.983417i
\(147\) −6.60555 6.60555i −0.544817 0.544817i
\(148\) −3.39237 12.4236i −0.278851 1.02121i
\(149\) 4.30028 4.30028i 0.352293 0.352293i −0.508669 0.860962i \(-0.669862\pi\)
0.860962 + 0.508669i \(0.169862\pi\)
\(150\) 0 0
\(151\) 2.02102i 0.164468i −0.996613 0.0822341i \(-0.973794\pi\)
0.996613 0.0822341i \(-0.0262055\pi\)
\(152\) 12.7732 12.9570i 1.03605 1.05095i
\(153\) 0.302387i 0.0244465i
\(154\) 2.65099 + 0.703570i 0.213623 + 0.0566953i
\(155\) 0 0
\(156\) 17.4535 + 9.96628i 1.39740 + 0.797941i
\(157\) −2.93327 2.93327i −0.234101 0.234101i 0.580301 0.814402i \(-0.302935\pi\)
−0.814402 + 0.580301i \(0.802935\pi\)
\(158\) −18.0838 + 10.4981i −1.43867 + 0.835188i
\(159\) −12.2563 −0.971989
\(160\) 0 0
\(161\) −1.89241 −0.149143
\(162\) 8.27811 4.80569i 0.650390 0.377570i
\(163\) 5.74697 + 5.74697i 0.450137 + 0.450137i 0.895400 0.445263i \(-0.146890\pi\)
−0.445263 + 0.895400i \(0.646890\pi\)
\(164\) 17.6357 + 10.0703i 1.37712 + 0.786360i
\(165\) 0 0
\(166\) 1.57546 + 0.418125i 0.122279 + 0.0324528i
\(167\) 6.41553i 0.496449i −0.968703 0.248224i \(-0.920153\pi\)
0.968703 0.248224i \(-0.0798470\pi\)
\(168\) −3.02830 2.98535i −0.233639 0.230325i
\(169\) 29.3783i 2.25987i
\(170\) 0 0
\(171\) 2.80644 2.80644i 0.214613 0.214613i
\(172\) 1.33405 + 4.88558i 0.101721 + 0.372522i
\(173\) 0.545724 + 0.545724i 0.0414907 + 0.0414907i 0.727548 0.686057i \(-0.240660\pi\)
−0.686057 + 0.727548i \(0.740660\pi\)
\(174\) 5.80674 + 10.0025i 0.440208 + 0.758288i
\(175\) 0 0
\(176\) −7.71328 1.98823i −0.581410 0.149869i
\(177\) −18.4296 −1.38525
\(178\) −0.798090 1.37476i −0.0598194 0.103043i
\(179\) −3.57757 3.57757i −0.267400 0.267400i 0.560652 0.828052i \(-0.310551\pi\)
−0.828052 + 0.560652i \(0.810551\pi\)
\(180\) 0 0
\(181\) −1.64176 + 1.64176i −0.122031 + 0.122031i −0.765485 0.643454i \(-0.777501\pi\)
0.643454 + 0.765485i \(0.277501\pi\)
\(182\) 2.30002 8.66627i 0.170489 0.642386i
\(183\) 6.57328i 0.485911i
\(184\) 5.49571 0.0392550i 0.405149 0.00289392i
\(185\) 0 0
\(186\) −9.05267 2.40257i −0.663774 0.176165i
\(187\) 0.690114 0.690114i 0.0504662 0.0504662i
\(188\) 9.93352 17.3961i 0.724476 1.26874i
\(189\) −3.84522 3.84522i −0.279698 0.279698i
\(190\) 0 0
\(191\) −15.3359 −1.10967 −0.554835 0.831960i \(-0.687219\pi\)
−0.554835 + 0.831960i \(0.687219\pi\)
\(192\) 8.85635 + 8.60686i 0.639152 + 0.621147i
\(193\) 0.0812703 0.00584996 0.00292498 0.999996i \(-0.499069\pi\)
0.00292498 + 0.999996i \(0.499069\pi\)
\(194\) −9.22726 + 5.35669i −0.662478 + 0.384588i
\(195\) 0 0
\(196\) 6.00149 10.5101i 0.428678 0.750725i
\(197\) −1.40711 + 1.40711i −0.100252 + 0.100252i −0.755454 0.655202i \(-0.772584\pi\)
0.655202 + 0.755454i \(0.272584\pi\)
\(198\) −1.67941 0.445714i −0.119351 0.0316755i
\(199\) 14.3046i 1.01402i 0.861939 + 0.507011i \(0.169250\pi\)
−0.861939 + 0.507011i \(0.830750\pi\)
\(200\) 0 0
\(201\) 15.4457i 1.08946i
\(202\) −1.33664 + 5.03635i −0.0940458 + 0.354356i
\(203\) 3.64846 3.64846i 0.256071 0.256071i
\(204\) −1.45971 + 0.398587i −0.102200 + 0.0279067i
\(205\) 0 0
\(206\) 9.80868 + 16.8961i 0.683403 + 1.17721i
\(207\) 1.19885 0.0833258
\(208\) −6.49966 + 25.2152i −0.450670 + 1.74836i
\(209\) 12.8098 0.886075
\(210\) 0 0
\(211\) 8.70115 + 8.70115i 0.599012 + 0.599012i 0.940050 0.341038i \(-0.110778\pi\)
−0.341038 + 0.940050i \(0.610778\pi\)
\(212\) −4.18281 15.3183i −0.287277 1.05207i
\(213\) −0.980103 + 0.980103i −0.0671556 + 0.0671556i
\(214\) −5.07457 + 19.1205i −0.346891 + 1.30705i
\(215\) 0 0
\(216\) 11.2466 + 11.0870i 0.765232 + 0.754378i
\(217\) 4.17835i 0.283645i
\(218\) −22.3181 5.92320i −1.51157 0.401169i
\(219\) 10.6051 10.6051i 0.716628 0.716628i
\(220\) 0 0
\(221\) −2.25603 2.25603i −0.151757 0.151757i
\(222\) −12.1575 + 7.05776i −0.815955 + 0.473686i
\(223\) −7.78095 −0.521051 −0.260525 0.965467i \(-0.583896\pi\)
−0.260525 + 0.965467i \(0.583896\pi\)
\(224\) 2.69769 4.80370i 0.180247 0.320961i
\(225\) 0 0
\(226\) 21.0435 12.2164i 1.39979 0.812621i
\(227\) −2.15443 2.15443i −0.142995 0.142995i 0.631986 0.774980i \(-0.282240\pi\)
−0.774980 + 0.631986i \(0.782240\pi\)
\(228\) −17.2467 9.84821i −1.14219 0.652214i
\(229\) −7.63865 + 7.63865i −0.504776 + 0.504776i −0.912918 0.408142i \(-0.866177\pi\)
0.408142 + 0.912918i \(0.366177\pi\)
\(230\) 0 0
\(231\) 2.99390i 0.196984i
\(232\) −10.5197 + 10.6711i −0.690653 + 0.700591i
\(233\) 7.51503i 0.492326i −0.969228 0.246163i \(-0.920830\pi\)
0.969228 0.246163i \(-0.0791699\pi\)
\(234\) −1.45707 + 5.49010i −0.0952515 + 0.358899i
\(235\) 0 0
\(236\) −6.28962 23.0339i −0.409419 1.49938i
\(237\) 16.1395 + 16.1395i 1.04837 + 1.04837i
\(238\) 0.338911 + 0.583796i 0.0219683 + 0.0378419i
\(239\) 20.5776 1.33105 0.665526 0.746375i \(-0.268207\pi\)
0.665526 + 0.746375i \(0.268207\pi\)
\(240\) 0 0
\(241\) −23.2914 −1.50033 −0.750166 0.661250i \(-0.770026\pi\)
−0.750166 + 0.661250i \(0.770026\pi\)
\(242\) 4.99466 + 8.60362i 0.321069 + 0.553062i
\(243\) 4.45639 + 4.45639i 0.285877 + 0.285877i
\(244\) 8.21549 2.24332i 0.525943 0.143614i
\(245\) 0 0
\(246\) 5.68646 21.4261i 0.362556 1.36608i
\(247\) 41.8762i 2.66452i
\(248\) −0.0866731 12.1342i −0.00550375 0.770525i
\(249\) 1.77925i 0.112755i
\(250\) 0 0
\(251\) −3.34230 + 3.34230i −0.210964 + 0.210964i −0.804677 0.593713i \(-0.797661\pi\)
0.593713 + 0.804677i \(0.297661\pi\)
\(252\) 0.595935 1.04363i 0.0375404 0.0657428i
\(253\) 2.73604 + 2.73604i 0.172014 + 0.172014i
\(254\) −1.68302 + 0.977043i −0.105602 + 0.0613051i
\(255\) 0 0
\(256\) −7.73464 + 14.0063i −0.483415 + 0.875391i
\(257\) 22.4537 1.40062 0.700311 0.713838i \(-0.253045\pi\)
0.700311 + 0.713838i \(0.253045\pi\)
\(258\) 4.78093 2.77547i 0.297648 0.172793i
\(259\) 4.43448 + 4.43448i 0.275545 + 0.275545i
\(260\) 0 0
\(261\) −2.31131 + 2.31131i −0.143066 + 0.143066i
\(262\) −17.4745 4.63771i −1.07958 0.286519i
\(263\) 8.23670i 0.507897i −0.967218 0.253948i \(-0.918271\pi\)
0.967218 0.253948i \(-0.0817294\pi\)
\(264\) 0.0621036 + 8.69451i 0.00382221 + 0.535110i
\(265\) 0 0
\(266\) −2.27277 + 8.56359i −0.139352 + 0.525068i
\(267\) −1.22696 + 1.22696i −0.0750885 + 0.0750885i
\(268\) 19.3045 5.27128i 1.17921 0.321994i
\(269\) −17.2960 17.2960i −1.05455 1.05455i −0.998423 0.0561306i \(-0.982124\pi\)
−0.0561306 0.998423i \(-0.517876\pi\)
\(270\) 0 0
\(271\) −12.4753 −0.757822 −0.378911 0.925433i \(-0.623701\pi\)
−0.378911 + 0.925433i \(0.623701\pi\)
\(272\) −0.996332 1.68836i −0.0604115 0.102372i
\(273\) −9.78726 −0.592352
\(274\) −10.8673 18.7196i −0.656516 1.13089i
\(275\) 0 0
\(276\) −1.58025 5.78719i −0.0951197 0.348348i
\(277\) −10.2583 + 10.2583i −0.616363 + 0.616363i −0.944597 0.328234i \(-0.893547\pi\)
0.328234 + 0.944597i \(0.393547\pi\)
\(278\) −0.177934 + 0.670439i −0.0106718 + 0.0402103i
\(279\) 2.64700i 0.158472i
\(280\) 0 0
\(281\) 21.4066i 1.27701i −0.769618 0.638505i \(-0.779553\pi\)
0.769618 0.638505i \(-0.220447\pi\)
\(282\) −21.1350 5.60922i −1.25857 0.334024i
\(283\) 7.39635 7.39635i 0.439668 0.439668i −0.452232 0.891900i \(-0.649372\pi\)
0.891900 + 0.452232i \(0.149372\pi\)
\(284\) −1.55945 0.890475i −0.0925363 0.0528400i
\(285\) 0 0
\(286\) −15.8550 + 9.20430i −0.937526 + 0.544261i
\(287\) −9.88942 −0.583754
\(288\) −1.70899 + 3.04316i −0.100703 + 0.179320i
\(289\) −16.7598 −0.985870
\(290\) 0 0
\(291\) 8.23520 + 8.23520i 0.482756 + 0.482756i
\(292\) 16.8739 + 9.63531i 0.987470 + 0.563864i
\(293\) 0.556728 0.556728i 0.0325244 0.0325244i −0.690658 0.723182i \(-0.742679\pi\)
0.723182 + 0.690658i \(0.242679\pi\)
\(294\) −12.7691 3.38889i −0.744706 0.197644i
\(295\) 0 0
\(296\) −12.9701 12.7861i −0.753870 0.743177i
\(297\) 11.1188i 0.645178i
\(298\) 2.20620 8.31278i 0.127802 0.481546i
\(299\) 8.94430 8.94430i 0.517263 0.517263i
\(300\) 0 0
\(301\) −1.74387 1.74387i −0.100515 0.100515i
\(302\) −1.43497 2.47182i −0.0825730 0.142238i
\(303\) 5.68781 0.326756
\(304\) 6.42266 24.9165i 0.368365 1.42906i
\(305\) 0 0
\(306\) −0.214701 0.369836i −0.0122736 0.0211421i
\(307\) −9.76852 9.76852i −0.557519 0.557519i 0.371082 0.928600i \(-0.378987\pi\)
−0.928600 + 0.371082i \(0.878987\pi\)
\(308\) 3.74187 1.02175i 0.213213 0.0582197i
\(309\) 15.0795 15.0795i 0.857844 0.857844i
\(310\) 0 0
\(311\) 30.6874i 1.74013i 0.492941 + 0.870063i \(0.335922\pi\)
−0.492941 + 0.870063i \(0.664078\pi\)
\(312\) 28.4229 0.203021i 1.60913 0.0114938i
\(313\) 1.71127i 0.0967268i −0.998830 0.0483634i \(-0.984599\pi\)
0.998830 0.0483634i \(-0.0154006\pi\)
\(314\) −5.67024 1.50488i −0.319990 0.0849251i
\(315\) 0 0
\(316\) −14.6636 + 25.6797i −0.824891 + 1.44460i
\(317\) 10.0380 + 10.0380i 0.563790 + 0.563790i 0.930382 0.366592i \(-0.119476\pi\)
−0.366592 + 0.930382i \(0.619476\pi\)
\(318\) −14.9902 + 8.70224i −0.840608 + 0.487997i
\(319\) −10.5498 −0.590678
\(320\) 0 0
\(321\) 21.5938 1.20525
\(322\) −2.31453 + 1.34365i −0.128984 + 0.0748788i
\(323\) 2.22930 + 2.22930i 0.124042 + 0.124042i
\(324\) 6.71248 11.7553i 0.372915 0.653070i
\(325\) 0 0
\(326\) 11.1093 + 2.94841i 0.615290 + 0.163297i
\(327\) 25.2049i 1.39384i
\(328\) 28.7196 0.205140i 1.58578 0.0113270i
\(329\) 9.75508i 0.537815i
\(330\) 0 0
\(331\) 7.89713 7.89713i 0.434066 0.434066i −0.455943 0.890009i \(-0.650698\pi\)
0.890009 + 0.455943i \(0.150698\pi\)
\(332\) 2.22376 0.607218i 0.122044 0.0333254i
\(333\) −2.80926 2.80926i −0.153946 0.153946i
\(334\) −4.55516 7.84656i −0.249247 0.429345i
\(335\) 0 0
\(336\) −5.82345 1.50110i −0.317695 0.0818915i
\(337\) 3.46077 0.188520 0.0942601 0.995548i \(-0.469951\pi\)
0.0942601 + 0.995548i \(0.469951\pi\)
\(338\) 20.8592 + 35.9313i 1.13459 + 1.95441i
\(339\) −18.7810 18.7810i −1.02005 1.02005i
\(340\) 0 0
\(341\) 6.04104 6.04104i 0.327141 0.327141i
\(342\) 1.43981 5.42506i 0.0778558 0.293354i
\(343\) 12.7112i 0.686338i
\(344\) 5.10049 + 5.02814i 0.275000 + 0.271099i
\(345\) 0 0
\(346\) 1.05493 + 0.279977i 0.0567133 + 0.0150516i
\(347\) 17.4637 17.4637i 0.937498 0.937498i −0.0606600 0.998158i \(-0.519321\pi\)
0.998158 + 0.0606600i \(0.0193205\pi\)
\(348\) 14.2040 + 8.11073i 0.761413 + 0.434781i
\(349\) 24.2159 + 24.2159i 1.29625 + 1.29625i 0.930852 + 0.365397i \(0.119067\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(350\) 0 0
\(351\) 36.3481 1.94012
\(352\) −10.8455 + 3.04486i −0.578065 + 0.162292i
\(353\) 10.7028 0.569650 0.284825 0.958580i \(-0.408065\pi\)
0.284825 + 0.958580i \(0.408065\pi\)
\(354\) −22.5405 + 13.0854i −1.19801 + 0.695482i
\(355\) 0 0
\(356\) −1.95222 1.11475i −0.103467 0.0590818i
\(357\) 0.521030 0.521030i 0.0275758 0.0275758i
\(358\) −6.91573 1.83543i −0.365507 0.0970053i
\(359\) 23.6390i 1.24762i −0.781577 0.623809i \(-0.785584\pi\)
0.781577 0.623809i \(-0.214416\pi\)
\(360\) 0 0
\(361\) 22.3801i 1.17790i
\(362\) −0.842282 + 3.17364i −0.0442693 + 0.166803i
\(363\) 7.67861 7.67861i 0.403023 0.403023i
\(364\) −3.34017 12.2324i −0.175073 0.641152i
\(365\) 0 0
\(366\) −4.66717 8.03950i −0.243957 0.420232i
\(367\) 13.7431 0.717386 0.358693 0.933456i \(-0.383223\pi\)
0.358693 + 0.933456i \(0.383223\pi\)
\(368\) 6.69370 3.95008i 0.348933 0.205912i
\(369\) 6.26498 0.326142
\(370\) 0 0
\(371\) 5.46773 + 5.46773i 0.283871 + 0.283871i
\(372\) −12.7778 + 3.48910i −0.662499 + 0.180902i
\(373\) −18.4703 + 18.4703i −0.956355 + 0.956355i −0.999087 0.0427313i \(-0.986394\pi\)
0.0427313 + 0.999087i \(0.486394\pi\)
\(374\) 0.354054 1.33405i 0.0183077 0.0689819i
\(375\) 0 0
\(376\) −0.202353 28.3295i −0.0104356 1.46098i
\(377\) 34.4881i 1.77623i
\(378\) −7.43311 1.97274i −0.382318 0.101467i
\(379\) −16.1028 + 16.1028i −0.827143 + 0.827143i −0.987121 0.159978i \(-0.948858\pi\)
0.159978 + 0.987121i \(0.448858\pi\)
\(380\) 0 0
\(381\) 1.50207 + 1.50207i 0.0769535 + 0.0769535i
\(382\) −18.7568 + 10.8888i −0.959679 + 0.557122i
\(383\) −23.1255 −1.18166 −0.590830 0.806796i \(-0.701200\pi\)
−0.590830 + 0.806796i \(0.701200\pi\)
\(384\) 16.9429 + 4.23850i 0.864613 + 0.216295i
\(385\) 0 0
\(386\) 0.0993983 0.0577036i 0.00505924 0.00293704i
\(387\) 1.10474 + 1.10474i 0.0561573 + 0.0561573i
\(388\) −7.48211 + 13.1031i −0.379846 + 0.665209i
\(389\) −19.4044 + 19.4044i −0.983842 + 0.983842i −0.999872 0.0160295i \(-0.994897\pi\)
0.0160295 + 0.999872i \(0.494897\pi\)
\(390\) 0 0
\(391\) 0.952310i 0.0481604i
\(392\) −0.122255 17.1157i −0.00617480 0.864473i
\(393\) 19.7348i 0.995491i
\(394\) −0.721898 + 2.72005i −0.0363687 + 0.137034i
\(395\) 0 0
\(396\) −2.37048 + 0.647283i −0.119121 + 0.0325272i
\(397\) 4.00102 + 4.00102i 0.200806 + 0.200806i 0.800345 0.599540i \(-0.204650\pi\)
−0.599540 + 0.800345i \(0.704650\pi\)
\(398\) 10.1565 + 17.4953i 0.509101 + 0.876960i
\(399\) 9.67130 0.484171
\(400\) 0 0
\(401\) 38.9287 1.94401 0.972003 0.234967i \(-0.0754980\pi\)
0.972003 + 0.234967i \(0.0754980\pi\)
\(402\) −10.9668 18.8910i −0.546973 0.942197i
\(403\) −19.7486 19.7486i −0.983746 0.983746i
\(404\) 1.94112 + 7.10879i 0.0965745 + 0.353676i
\(405\) 0 0
\(406\) 1.87179 7.05275i 0.0928955 0.350022i
\(407\) 12.8227i 0.635598i
\(408\) −1.50230 + 1.52392i −0.0743750 + 0.0754452i
\(409\) 4.59845i 0.227379i −0.993516 0.113689i \(-0.963733\pi\)
0.993516 0.113689i \(-0.0362669\pi\)
\(410\) 0 0
\(411\) −16.7070 + 16.7070i −0.824095 + 0.824095i
\(412\) 23.9932 + 13.7005i 1.18206 + 0.674977i
\(413\) 8.22174 + 8.22174i 0.404565 + 0.404565i
\(414\) 1.46626 0.851208i 0.0720628 0.0418346i
\(415\) 0 0
\(416\) 9.95386 + 35.4546i 0.488028 + 1.73830i
\(417\) 0.757161 0.0370783
\(418\) 15.6672 9.09525i 0.766306 0.444863i
\(419\) 16.6774 + 16.6774i 0.814746 + 0.814746i 0.985341 0.170595i \(-0.0545689\pi\)
−0.170595 + 0.985341i \(0.554569\pi\)
\(420\) 0 0
\(421\) 15.4169 15.4169i 0.751372 0.751372i −0.223364 0.974735i \(-0.571704\pi\)
0.974735 + 0.223364i \(0.0717037\pi\)
\(422\) 16.8200 + 4.46401i 0.818786 + 0.217305i
\(423\) 6.17987i 0.300476i
\(424\) −15.9921 15.7653i −0.776647 0.765631i
\(425\) 0 0
\(426\) −0.502829 + 1.89462i −0.0243622 + 0.0917945i
\(427\) −2.93244 + 2.93244i −0.141911 + 0.141911i
\(428\) 7.36949 + 26.9886i 0.356218 + 1.30454i
\(429\) 14.1504 + 14.1504i 0.683186 + 0.683186i
\(430\) 0 0
\(431\) 20.2234 0.974126 0.487063 0.873367i \(-0.338068\pi\)
0.487063 + 0.873367i \(0.338068\pi\)
\(432\) 21.6272 + 5.57480i 1.04054 + 0.268218i
\(433\) −0.676118 −0.0324922 −0.0162461 0.999868i \(-0.505172\pi\)
−0.0162461 + 0.999868i \(0.505172\pi\)
\(434\) 2.96671 + 5.11036i 0.142407 + 0.245305i
\(435\) 0 0
\(436\) −31.5019 + 8.60189i −1.50867 + 0.411956i
\(437\) −8.83834 + 8.83834i −0.422795 + 0.422795i
\(438\) 5.44082 20.5005i 0.259972 0.979553i
\(439\) 13.3550i 0.637400i −0.947856 0.318700i \(-0.896754\pi\)
0.947856 0.318700i \(-0.103246\pi\)
\(440\) 0 0
\(441\) 3.73366i 0.177794i
\(442\) −4.36108 1.15743i −0.207436 0.0550532i
\(443\) −28.1262 + 28.1262i −1.33631 + 1.33631i −0.436714 + 0.899600i \(0.643858\pi\)
−0.899600 + 0.436714i \(0.856142\pi\)
\(444\) −9.85811 + 17.2641i −0.467845 + 0.819317i
\(445\) 0 0
\(446\) −9.51655 + 5.52464i −0.450622 + 0.261599i
\(447\) −9.38805 −0.444039
\(448\) −0.111300 7.79061i −0.00525843 0.368072i
\(449\) −8.37972 −0.395464 −0.197732 0.980256i \(-0.563358\pi\)
−0.197732 + 0.980256i \(0.563358\pi\)
\(450\) 0 0
\(451\) 14.2981 + 14.2981i 0.673271 + 0.673271i
\(452\) 17.0635 29.8827i 0.802602 1.40556i
\(453\) −2.20607 + 2.20607i −0.103650 + 0.103650i
\(454\) −4.16469 1.10530i −0.195458 0.0518745i
\(455\) 0 0
\(456\) −28.0862 + 0.200615i −1.31526 + 0.00939468i
\(457\) 5.66561i 0.265026i −0.991181 0.132513i \(-0.957695\pi\)
0.991181 0.132513i \(-0.0423046\pi\)
\(458\) −3.91891 + 14.7661i −0.183119 + 0.689975i
\(459\) −1.93501 + 1.93501i −0.0903186 + 0.0903186i
\(460\) 0 0
\(461\) 16.6375 + 16.6375i 0.774887 + 0.774887i 0.978956 0.204069i \(-0.0654168\pi\)
−0.204069 + 0.978956i \(0.565417\pi\)
\(462\) −2.12573 3.66171i −0.0988979 0.170358i
\(463\) 41.6835 1.93720 0.968598 0.248631i \(-0.0799808\pi\)
0.968598 + 0.248631i \(0.0799808\pi\)
\(464\) −5.28953 + 20.5206i −0.245560 + 0.952643i
\(465\) 0 0
\(466\) −5.33583 9.19132i −0.247178 0.425780i
\(467\) −3.11020 3.11020i −0.143923 0.143923i 0.631474 0.775397i \(-0.282450\pi\)
−0.775397 + 0.631474i \(0.782450\pi\)
\(468\) 2.11601 + 7.74926i 0.0978126 + 0.358210i
\(469\) −6.89057 + 6.89057i −0.318177 + 0.318177i
\(470\) 0 0
\(471\) 6.40370i 0.295067i
\(472\) −24.0471 23.7060i −1.10686 1.09116i
\(473\) 5.04255i 0.231857i
\(474\) 31.1989 + 8.28016i 1.43301 + 0.380320i
\(475\) 0 0
\(476\) 0.829015 + 0.473383i 0.0379978 + 0.0216975i
\(477\) −3.46383 3.46383i −0.158598 0.158598i
\(478\) 25.1675 14.6105i 1.15114 0.668268i
\(479\) −8.32325 −0.380299 −0.190149 0.981755i \(-0.560897\pi\)
−0.190149 + 0.981755i \(0.560897\pi\)
\(480\) 0 0
\(481\) −41.9183 −1.91131
\(482\) −28.4868 + 16.5374i −1.29754 + 0.753257i
\(483\) 2.06569 + 2.06569i 0.0939920 + 0.0939920i
\(484\) 12.2175 + 6.97642i 0.555341 + 0.317110i
\(485\) 0 0
\(486\) 8.61455 + 2.28629i 0.390764 + 0.103708i
\(487\) 7.29577i 0.330603i 0.986243 + 0.165301i \(0.0528597\pi\)
−0.986243 + 0.165301i \(0.947140\pi\)
\(488\) 8.45521 8.57687i 0.382750 0.388257i
\(489\) 12.5463i 0.567365i
\(490\) 0 0
\(491\) 3.57528 3.57528i 0.161350 0.161350i −0.621815 0.783165i \(-0.713604\pi\)
0.783165 + 0.621815i \(0.213604\pi\)
\(492\) −8.25810 30.2429i −0.372304 1.36345i
\(493\) −1.83600 1.83600i −0.0826891 0.0826891i
\(494\) −29.7330 51.2170i −1.33775 2.30436i
\(495\) 0 0
\(496\) −8.72157 14.7793i −0.391610 0.663612i
\(497\) 0.874479 0.0392257
\(498\) −1.26330 2.17612i −0.0566099 0.0975143i
\(499\) −10.8833 10.8833i −0.487203 0.487203i 0.420220 0.907422i \(-0.361953\pi\)
−0.907422 + 0.420220i \(0.861953\pi\)
\(500\) 0 0
\(501\) −7.00295 + 7.00295i −0.312869 + 0.312869i
\(502\) −1.71472 + 6.46093i −0.0765318 + 0.288365i
\(503\) 29.3781i 1.30991i −0.755670 0.654953i \(-0.772688\pi\)
0.755670 0.654953i \(-0.227312\pi\)
\(504\) −0.0121396 1.69955i −0.000540742 0.0757040i
\(505\) 0 0
\(506\) 5.28899 + 1.40369i 0.235124 + 0.0624017i
\(507\) 32.0682 32.0682i 1.42420 1.42420i
\(508\) −1.36471 + 2.38996i −0.0605493 + 0.106037i
\(509\) 17.4592 + 17.4592i 0.773863 + 0.773863i 0.978780 0.204916i \(-0.0656922\pi\)
−0.204916 + 0.978780i \(0.565692\pi\)
\(510\) 0 0
\(511\) −9.46222 −0.418584
\(512\) 0.484827 + 22.6222i 0.0214265 + 0.999770i
\(513\) −35.9175 −1.58579
\(514\) 27.4621 15.9426i 1.21130 0.703197i
\(515\) 0 0
\(516\) 3.87671 6.78912i 0.170663 0.298874i
\(517\) 14.1039 14.1039i 0.620287 0.620287i
\(518\) 8.57221 + 2.27505i 0.376641 + 0.0999602i
\(519\) 1.19138i 0.0522959i
\(520\) 0 0
\(521\) 9.48578i 0.415580i −0.978174 0.207790i \(-0.933373\pi\)
0.978174 0.207790i \(-0.0666270\pi\)
\(522\) −1.18579 + 4.46794i −0.0519005 + 0.195556i
\(523\) −16.2705 + 16.2705i −0.711460 + 0.711460i −0.966841 0.255380i \(-0.917799\pi\)
0.255380 + 0.966841i \(0.417799\pi\)
\(524\) −24.6652 + 6.73507i −1.07750 + 0.294223i
\(525\) 0 0
\(526\) −5.84823 10.0740i −0.254995 0.439246i
\(527\) 2.10265 0.0915929
\(528\) 6.24924 + 10.5898i 0.271963 + 0.460862i
\(529\) 19.2245 0.835846
\(530\) 0 0
\(531\) −5.20849 5.20849i −0.226029 0.226029i
\(532\) 3.30060 + 12.0875i 0.143099 + 0.524059i
\(533\) 46.7414 46.7414i 2.02459 2.02459i
\(534\) −0.629474 + 2.37180i −0.0272400 + 0.102638i
\(535\) 0 0
\(536\) 19.8678 20.1537i 0.858158 0.870506i
\(537\) 7.81028i 0.337039i
\(538\) −33.4345 8.87348i −1.44146 0.382563i
\(539\) 8.52106 8.52106i 0.367028 0.367028i
\(540\) 0 0
\(541\) −2.55686 2.55686i −0.109928 0.109928i 0.650003 0.759931i \(-0.274767\pi\)
−0.759931 + 0.650003i \(0.774767\pi\)
\(542\) −15.2580 + 8.85774i −0.655389 + 0.380472i
\(543\) 3.58416 0.153811
\(544\) −2.41734 1.35754i −0.103643 0.0582042i
\(545\) 0 0
\(546\) −11.9704 + 6.94915i −0.512285 + 0.297396i
\(547\) 21.9660 + 21.9660i 0.939197 + 0.939197i 0.998255 0.0590579i \(-0.0188097\pi\)
−0.0590579 + 0.998255i \(0.518810\pi\)
\(548\) −26.5826 15.1792i −1.13555 0.648422i
\(549\) 1.85771 1.85771i 0.0792852 0.0792852i
\(550\) 0 0
\(551\) 34.0796i 1.45184i
\(552\) −6.04176 5.95606i −0.257154 0.253507i
\(553\) 14.4002i 0.612357i
\(554\) −5.26290 + 19.8301i −0.223599 + 0.842502i
\(555\) 0 0
\(556\) 0.258402 + 0.946322i 0.0109587 + 0.0401330i
\(557\) −17.5409 17.5409i −0.743234 0.743234i 0.229965 0.973199i \(-0.426139\pi\)
−0.973199 + 0.229965i \(0.926139\pi\)
\(558\) −1.87942 3.23743i −0.0795623 0.137051i
\(559\) 16.4844 0.697217
\(560\) 0 0
\(561\) −1.50661 −0.0636089
\(562\) −15.1991 26.1815i −0.641136 1.10440i
\(563\) −27.5975 27.5975i −1.16309 1.16309i −0.983794 0.179300i \(-0.942617\pi\)
−0.179300 0.983794i \(-0.557383\pi\)
\(564\) −29.8320 + 8.14592i −1.25615 + 0.343005i
\(565\) 0 0
\(566\) 3.79460 14.2977i 0.159499 0.600979i
\(567\) 6.59190i 0.276834i
\(568\) −2.53955 + 0.0181396i −0.106557 + 0.000761123i
\(569\) 23.6390i 0.990998i −0.868608 0.495499i \(-0.834985\pi\)
0.868608 0.495499i \(-0.165015\pi\)
\(570\) 0 0
\(571\) −21.7518 + 21.7518i −0.910284 + 0.910284i −0.996294 0.0860105i \(-0.972588\pi\)
0.0860105 + 0.996294i \(0.472588\pi\)
\(572\) −12.8564 + 22.5148i −0.537551 + 0.941390i
\(573\) 16.7401 + 16.7401i 0.699329 + 0.699329i
\(574\) −12.0953 + 7.02169i −0.504850 + 0.293080i
\(575\) 0 0
\(576\) 0.0705089 + 4.93537i 0.00293787 + 0.205641i
\(577\) 3.69585 0.153860 0.0769302 0.997036i \(-0.475488\pi\)
0.0769302 + 0.997036i \(0.475488\pi\)
\(578\) −20.4982 + 11.8998i −0.852613 + 0.494967i
\(579\) −0.0887116 0.0887116i −0.00368673 0.00368673i
\(580\) 0 0
\(581\) −0.793750 + 0.793750i −0.0329303 + 0.0329303i
\(582\) 15.9193 + 4.22496i 0.659876 + 0.175130i
\(583\) 15.8105i 0.654802i
\(584\) 27.4790 0.196278i 1.13709 0.00812206i
\(585\) 0 0
\(586\) 0.285622 1.07620i 0.0117989 0.0444573i
\(587\) −27.0313 + 27.0313i −1.11570 + 1.11570i −0.123335 + 0.992365i \(0.539359\pi\)
−0.992365 + 0.123335i \(0.960641\pi\)
\(588\) −18.0235 + 4.92148i −0.743276 + 0.202958i
\(589\) 19.5146 + 19.5146i 0.804085 + 0.804085i
\(590\) 0 0
\(591\) 3.07189 0.126361
\(592\) −24.9415 6.42912i −1.02509 0.264235i
\(593\) 4.55524 0.187061 0.0935306 0.995616i \(-0.470185\pi\)
0.0935306 + 0.995616i \(0.470185\pi\)
\(594\) 7.89458 + 13.5989i 0.323919 + 0.557971i
\(595\) 0 0
\(596\) −3.20393 11.7335i −0.131238 0.480621i
\(597\) 15.6143 15.6143i 0.639051 0.639051i
\(598\) 4.58876 17.2900i 0.187648 0.707043i
\(599\) 7.46846i 0.305153i −0.988292 0.152576i \(-0.951243\pi\)
0.988292 0.152576i \(-0.0487570\pi\)
\(600\) 0 0
\(601\) 12.2638i 0.500250i 0.968214 + 0.250125i \(0.0804717\pi\)
−0.968214 + 0.250125i \(0.919528\pi\)
\(602\) −3.37103 0.894668i −0.137393 0.0364639i
\(603\) 4.36519 4.36519i 0.177764 0.177764i
\(604\) −3.51009 2.00433i −0.142824 0.0815550i
\(605\) 0 0
\(606\) 6.95652 4.03846i 0.282589 0.164051i
\(607\) −5.23884 −0.212638 −0.106319 0.994332i \(-0.533906\pi\)
−0.106319 + 0.994332i \(0.533906\pi\)
\(608\) −9.83593 35.0345i −0.398900 1.42084i
\(609\) −7.96503 −0.322759
\(610\) 0 0
\(611\) −46.1064 46.1064i −1.86527 1.86527i
\(612\) −0.525183 0.299889i −0.0212293 0.0121223i
\(613\) −20.7209 + 20.7209i −0.836910 + 0.836910i −0.988451 0.151541i \(-0.951576\pi\)
0.151541 + 0.988451i \(0.451576\pi\)
\(614\) −18.8833 5.01161i −0.762068 0.202252i
\(615\) 0 0
\(616\) 3.85105 3.90646i 0.155163 0.157396i
\(617\) 2.20286i 0.0886838i 0.999016 + 0.0443419i \(0.0141191\pi\)
−0.999016 + 0.0443419i \(0.985881\pi\)
\(618\) 7.73636 29.1499i 0.311202 1.17258i
\(619\) −31.4569 + 31.4569i −1.26436 + 1.26436i −0.315404 + 0.948958i \(0.602140\pi\)
−0.948958 + 0.315404i \(0.897860\pi\)
\(620\) 0 0
\(621\) −7.67158 7.67158i −0.307850 0.307850i
\(622\) 21.7887 + 37.5325i 0.873648 + 1.50492i
\(623\) 1.09473 0.0438594
\(624\) 34.6187 20.4292i 1.38586 0.817822i
\(625\) 0 0
\(626\) −1.21504 2.09298i −0.0485627 0.0836525i
\(627\) −13.9827 13.9827i −0.558416 0.558416i
\(628\) −8.00353 + 2.18544i −0.319376 + 0.0872085i
\(629\) 2.23154 2.23154i 0.0889775 0.0889775i
\(630\) 0 0
\(631\) 16.8215i 0.669655i −0.942279 0.334828i \(-0.891322\pi\)
0.942279 0.334828i \(-0.108678\pi\)
\(632\) 0.298708 + 41.8192i 0.0118820 + 1.66348i
\(633\) 18.9957i 0.755011i
\(634\) 19.4042 + 5.14986i 0.770640 + 0.204527i
\(635\) 0 0
\(636\) −12.1551 + 21.2867i −0.481981 + 0.844072i
\(637\) −27.8559 27.8559i −1.10369 1.10369i
\(638\) −12.9031 + 7.49061i −0.510838 + 0.296556i
\(639\) −0.553985 −0.0219153
\(640\) 0 0
\(641\) −14.9208 −0.589336 −0.294668 0.955600i \(-0.595209\pi\)
−0.294668 + 0.955600i \(0.595209\pi\)
\(642\) 26.4105 15.3320i 1.04234 0.605108i
\(643\) 0.541845 + 0.541845i 0.0213683 + 0.0213683i 0.717710 0.696342i \(-0.245190\pi\)
−0.696342 + 0.717710i \(0.745190\pi\)
\(644\) −1.87678 + 3.28673i −0.0739556 + 0.129515i
\(645\) 0 0
\(646\) 4.30942 + 1.14371i 0.169552 + 0.0449988i
\(647\) 32.6391i 1.28318i 0.767049 + 0.641588i \(0.221724\pi\)
−0.767049 + 0.641588i \(0.778276\pi\)
\(648\) −0.136738 19.1434i −0.00537158 0.752023i
\(649\) 23.7739i 0.933208i
\(650\) 0 0
\(651\) 4.56093 4.56093i 0.178757 0.178757i
\(652\) 15.6808 4.28179i 0.614108 0.167688i
\(653\) −9.73805 9.73805i −0.381079 0.381079i 0.490412 0.871491i \(-0.336846\pi\)
−0.871491 + 0.490412i \(0.836846\pi\)
\(654\) 17.8960 + 30.8271i 0.699790 + 1.20544i
\(655\) 0 0
\(656\) 34.9801 20.6424i 1.36574 0.805952i
\(657\) 5.99434 0.233862
\(658\) 6.92631 + 11.9310i 0.270016 + 0.465120i
\(659\) 1.26445 + 1.26445i 0.0492560 + 0.0492560i 0.731306 0.682050i \(-0.238911\pi\)
−0.682050 + 0.731306i \(0.738911\pi\)
\(660\) 0 0
\(661\) 22.6701 22.6701i 0.881763 0.881763i −0.111951 0.993714i \(-0.535710\pi\)
0.993714 + 0.111951i \(0.0357099\pi\)
\(662\) 4.05152 15.2658i 0.157467 0.593321i
\(663\) 4.92519i 0.191279i
\(664\) 2.28865 2.32158i 0.0888167 0.0900946i
\(665\) 0 0
\(666\) −5.43052 1.44125i −0.210428 0.0558474i
\(667\) 7.27903 7.27903i 0.281845 0.281845i
\(668\) −11.1424 6.36254i −0.431114 0.246174i
\(669\) 8.49339 + 8.49339i 0.328373 + 0.328373i
\(670\) 0 0
\(671\) 8.47943 0.327345
\(672\) −8.18822 + 2.29884i −0.315868 + 0.0886798i
\(673\) −3.58765 −0.138294 −0.0691469 0.997606i \(-0.522028\pi\)
−0.0691469 + 0.997606i \(0.522028\pi\)
\(674\) 4.23273 2.45722i 0.163038 0.0946486i
\(675\) 0 0
\(676\) 51.0240 + 29.1356i 1.96246 + 1.12060i
\(677\) −10.1507 + 10.1507i −0.390124 + 0.390124i −0.874731 0.484608i \(-0.838962\pi\)
0.484608 + 0.874731i \(0.338962\pi\)
\(678\) −36.3052 9.63537i −1.39429 0.370044i
\(679\) 7.34770i 0.281979i
\(680\) 0 0
\(681\) 4.70339i 0.180234i
\(682\) 3.09928 11.6778i 0.118677 0.447166i
\(683\) −16.6805 + 16.6805i −0.638260 + 0.638260i −0.950126 0.311866i \(-0.899046\pi\)
0.311866 + 0.950126i \(0.399046\pi\)
\(684\) −2.09094 7.65745i −0.0799491 0.292790i
\(685\) 0 0
\(686\) 9.02519 + 15.5465i 0.344583 + 0.593568i
\(687\) 16.6761 0.636234
\(688\) 9.80828 + 2.52826i 0.373937 + 0.0963889i
\(689\) −51.6854 −1.96906
\(690\) 0 0
\(691\) 12.4781 + 12.4781i 0.474689 + 0.474689i 0.903428 0.428739i \(-0.141042\pi\)
−0.428739 + 0.903428i \(0.641042\pi\)
\(692\) 1.48903 0.406593i 0.0566043 0.0154563i
\(693\) 0.846123 0.846123i 0.0321415 0.0321415i
\(694\) 8.95951 33.7586i 0.340098 1.28146i
\(695\) 0 0
\(696\) 23.1311 0.165222i 0.876781 0.00626271i
\(697\) 4.97661i 0.188502i
\(698\) 46.8113 + 12.4237i 1.77183 + 0.470243i
\(699\) −8.20312 + 8.20312i −0.310271 + 0.310271i
\(700\) 0 0
\(701\) 6.40945 + 6.40945i 0.242082 + 0.242082i 0.817711 0.575629i \(-0.195243\pi\)
−0.575629 + 0.817711i \(0.695243\pi\)
\(702\) 44.4558 25.8079i 1.67788 0.974057i
\(703\) 41.4217 1.56225
\(704\) −11.1027 + 11.4246i −0.418449 + 0.430579i
\(705\) 0 0
\(706\) 13.0901 7.59918i 0.492652 0.285999i
\(707\) −2.53742 2.53742i −0.0954295 0.0954295i
\(708\) −18.2774 + 32.0084i −0.686907 + 1.20295i
\(709\) 8.78514 8.78514i 0.329933 0.329933i −0.522628 0.852561i \(-0.675048\pi\)
0.852561 + 0.522628i \(0.175048\pi\)
\(710\) 0 0
\(711\) 9.12255i 0.342122i
\(712\) −3.17918 + 0.0227084i −0.119145 + 0.000851033i
\(713\) 8.33621i 0.312194i
\(714\) 0.267308 1.00719i 0.0100037 0.0376932i
\(715\) 0 0
\(716\) −9.76152 + 2.66548i −0.364805 + 0.0996135i
\(717\) −22.4617 22.4617i −0.838847 0.838847i
\(718\) −16.7842 28.9119i −0.626380 1.07898i
\(719\) 46.2329 1.72420 0.862099 0.506740i \(-0.169150\pi\)
0.862099 + 0.506740i \(0.169150\pi\)
\(720\) 0 0
\(721\) −13.4544 −0.501069
\(722\) 15.8903 + 27.3721i 0.591376 + 1.01868i
\(723\) 25.4240 + 25.4240i 0.945530 + 0.945530i
\(724\) 1.22319 + 4.47959i 0.0454596 + 0.166483i
\(725\) 0 0
\(726\) 3.93941 14.8434i 0.146205 0.550889i
\(727\) 17.4640i 0.647703i −0.946108 0.323852i \(-0.895022\pi\)
0.946108 0.323852i \(-0.104978\pi\)
\(728\) −12.7705 12.5893i −0.473306 0.466592i
\(729\) 30.0340i 1.11237i
\(730\) 0 0
\(731\) −0.877557 + 0.877557i −0.0324576 + 0.0324576i
\(732\) −11.4164 6.51899i −0.421963 0.240949i
\(733\) −7.89695 7.89695i −0.291680 0.291680i 0.546063 0.837744i \(-0.316126\pi\)
−0.837744 + 0.546063i \(0.816126\pi\)
\(734\) 16.8086 9.75791i 0.620419 0.360171i
\(735\) 0 0
\(736\) 5.38214 9.58384i 0.198388 0.353265i
\(737\) 19.9247 0.733936
\(738\) 7.66243 4.44826i 0.282058 0.163743i
\(739\) 26.1724 + 26.1724i 0.962769 + 0.962769i 0.999331 0.0365624i \(-0.0116408\pi\)
−0.0365624 + 0.999331i \(0.511641\pi\)
\(740\) 0 0
\(741\) −45.7105 + 45.7105i −1.67922 + 1.67922i
\(742\) 10.5696 + 2.80515i 0.388021 + 0.102980i
\(743\) 49.7660i 1.82574i 0.408254 + 0.912868i \(0.366138\pi\)
−0.408254 + 0.912868i \(0.633862\pi\)
\(744\) −13.1507 + 13.3399i −0.482127 + 0.489064i
\(745\) 0 0
\(746\) −9.47594 + 35.7045i −0.346939 + 1.30724i
\(747\) 0.502843 0.502843i 0.0183981 0.0183981i
\(748\) −0.514171 1.88300i −0.0188000 0.0688493i
\(749\) −9.63333 9.63333i −0.351994 0.351994i
\(750\) 0 0
\(751\) −24.2379 −0.884454 −0.442227 0.896903i \(-0.645811\pi\)
−0.442227 + 0.896903i \(0.645811\pi\)
\(752\) −20.3620 34.5049i −0.742527 1.25827i
\(753\) 7.29665 0.265905
\(754\) 24.4873 + 42.1810i 0.891775 + 1.53614i
\(755\) 0 0
\(756\) −10.4918 + 2.86489i −0.381583 + 0.104195i
\(757\) 15.4872 15.4872i 0.562890 0.562890i −0.367237 0.930127i \(-0.619696\pi\)
0.930127 + 0.367237i \(0.119696\pi\)
\(758\) −8.26131 + 31.1279i −0.300064 + 1.13062i
\(759\) 5.97312i 0.216811i
\(760\) 0 0
\(761\) 25.9821i 0.941849i −0.882174 0.470924i \(-0.843920\pi\)
0.882174 0.470924i \(-0.156080\pi\)
\(762\) 2.90363 + 0.770619i 0.105187 + 0.0279166i
\(763\) 11.2443 11.2443i 0.407072 0.407072i
\(764\) −15.2093 + 26.6354i −0.550253 + 0.963634i
\(765\) 0 0
\(766\) −28.2839 + 16.4196i −1.02194 + 0.593265i
\(767\) −77.7185 −2.80625
\(768\) 23.7315 6.84587i 0.856338 0.247029i
\(769\) −24.9737 −0.900573 −0.450287 0.892884i \(-0.648678\pi\)
−0.450287 + 0.892884i \(0.648678\pi\)
\(770\) 0 0
\(771\) −24.5096 24.5096i −0.882691 0.882691i
\(772\) 0.0805991 0.141150i 0.00290082 0.00508009i
\(773\) 1.32495 1.32495i 0.0476550 0.0476550i −0.682878 0.730533i \(-0.739272\pi\)
0.730533 + 0.682878i \(0.239272\pi\)
\(774\) 2.13556 + 0.566775i 0.0767610 + 0.0203723i
\(775\) 0 0
\(776\) 0.152416 + 21.3383i 0.00547142 + 0.766000i
\(777\) 9.68103i 0.347305i
\(778\) −9.95518 + 37.5102i −0.356910 + 1.34481i
\(779\) −46.1876 + 46.1876i −1.65484 + 1.65484i
\(780\) 0 0
\(781\) −1.26432 1.26432i −0.0452409 0.0452409i
\(782\) 0.676160 + 1.16473i 0.0241794 + 0.0416507i
\(783\) 29.5807