Properties

Label 400.2.l.f.301.2
Level $400$
Weight $2$
Character 400.301
Analytic conductor $3.194$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 301.2
Root \(1.22306 - 0.710021i\) of defining polynomial
Character \(\chi\) \(=\) 400.301
Dual form 400.2.l.f.101.2

$q$-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 0.948122 0.317908i \(-0.102980\pi\)
−0.317908 + 0.948122i \(0.602980\pi\)
\(4\) 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 \(-0.941078\pi\)
0.982916 0.184055i \(-0.0589224\pi\)
\(8\) 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 \(0.108459\pi\)
0.334179 + 0.942510i \(0.391541\pi\)
\(14\) 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 \(-0.518930\pi\)
−0.0594338 + 0.998232i \(0.518930\pi\)
\(18\) 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 \(-0.935067\pi\)
0.979266 0.202580i \(-0.0649325\pi\)
\(24\) −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 −0.974205 0.225663i \(-0.927545\pi\)
0.225663 + 0.974205i \(0.427545\pi\)
\(38\) −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 −0.557273 0.830329i \(-0.688152\pi\)
0.830329 + 0.557273i \(0.188152\pi\)
\(44\) −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 \(-0.760717\pi\)
−0.730510 + 0.682902i \(0.760717\pi\)
\(48\) 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 −0.978309 0.207151i \(-0.933581\pi\)
0.207151 + 0.978309i \(0.433581\pi\)
\(54\) −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 0.127486 0.991840i \(-0.459309\pi\)
−0.991840 + 0.127486i \(0.959309\pi\)
\(68\) −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 \(-0.807501\pi\)
0.822642 0.568559i \(-0.192499\pi\)
\(74\) 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 0.660962 0.750420i \(-0.270149\pi\)
−0.750420 + 0.660962i \(0.770149\pi\)
\(84\) −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 \(-0.374888\pi\)
0.383010 + 0.923744i \(0.374888\pi\)
\(98\) −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 \(-0.761720\pi\)
0.732657 0.680598i \(-0.238280\pi\)
\(104\) −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 −0.0428589 0.999081i \(-0.513647\pi\)
0.999081 + 0.0428589i \(0.0136466\pi\)
\(108\) −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 \(-0.800146\pi\)
−0.809286 + 0.587415i \(0.800146\pi\)
\(114\) −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 \(-0.480554\pi\)
0.0610535 + 0.998134i \(0.480554\pi\)
\(128\) 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 \(0.226835\pi\)
−0.756649 + 0.653822i \(0.773165\pi\)
\(138\) −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 0.814402 0.580301i \(-0.197065\pi\)
−0.580301 + 0.814402i \(0.697065\pi\)
\(158\) 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 0.445263 0.895400i \(-0.353110\pi\)
−0.895400 + 0.445263i \(0.853110\pi\)
\(164\) 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 \(0.0798470\pi\)
−0.968703 + 0.248224i \(0.920153\pi\)
\(168\) 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 0.686057 0.727548i \(-0.259340\pi\)
−0.727548 + 0.686057i \(0.759340\pi\)
\(174\) 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 \(-0.500931\pi\)
−0.00292498 + 0.999996i \(0.500931\pi\)
\(194\) −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 −0.655202 0.755454i \(-0.727416\pi\)
0.755454 + 0.655202i \(0.227416\pi\)
\(198\) 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 \(-0.416104\pi\)
0.260525 + 0.965467i \(0.416104\pi\)
\(224\) 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 0.774980 0.631986i \(-0.217760\pi\)
−0.631986 + 0.774980i \(0.717760\pi\)
\(228\) 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 \(0.0791699\pi\)
−0.969228 + 0.246163i \(0.920830\pi\)
\(234\) −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 \(-0.746955\pi\)
−0.700311 + 0.713838i \(0.746955\pi\)
\(258\) −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 \(0.0817294\pi\)
−0.967218 + 0.253948i \(0.918271\pi\)
\(264\) 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 −0.328234 0.944597i \(-0.606453\pi\)
0.944597 + 0.328234i \(0.106453\pi\)
\(278\) 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 −0.891900 0.452232i \(-0.850628\pi\)
0.452232 + 0.891900i \(0.350628\pi\)
\(284\) −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 −0.723182 0.690658i \(-0.757321\pi\)
0.690658 + 0.723182i \(0.257321\pi\)
\(294\) −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 0.928600 0.371082i \(-0.121013\pi\)
−0.371082 + 0.928600i \(0.621013\pi\)
\(308\) −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 \(0.0154006\pi\)
−0.998830 + 0.0483634i \(0.984599\pi\)
\(314\) −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 0.366592 0.930382i \(-0.380524\pi\)
−0.930382 + 0.366592i \(0.880524\pi\)
\(318\) 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 \(-0.530049\pi\)
−0.0942601 + 0.995548i \(0.530049\pi\)
\(338\) −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 −0.998158 0.0606600i \(-0.980679\pi\)
0.0606600 + 0.998158i \(0.480679\pi\)
\(348\) −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 \(-0.591935\pi\)
−0.284825 + 0.958580i \(0.591935\pi\)
\(354\) −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 \(-0.616777\pi\)
−0.358693 + 0.933456i \(0.616777\pi\)
\(368\) −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 −0.0427313 0.999087i \(-0.513606\pi\)
0.999087 + 0.0427313i \(0.0136059\pi\)
\(374\) 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 \(-0.298800\pi\)
0.590830 + 0.806796i \(0.298800\pi\)
\(384\) 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 0.599540 0.800345i \(-0.295350\pi\)
−0.800345 + 0.599540i \(0.795350\pi\)
\(398\) −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 \(-0.494828\pi\)
0.0162461 + 0.999868i \(0.494828\pi\)
\(434\) 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 \(-0.356142\pi\)
0.899600 0.436714i \(-0.143858\pi\)
\(444\) −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 \(0.0423046\pi\)
−0.991181 + 0.132513i \(0.957695\pi\)
\(458\) 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 \(-0.920019\pi\)
−0.968598 + 0.248631i \(0.920019\pi\)
\(464\) −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 0.775397 0.631474i \(-0.217550\pi\)
−0.631474 + 0.775397i \(0.717550\pi\)
\(468\) −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 \(-0.947140\pi\)
0.986243 0.165301i \(-0.0528597\pi\)
\(488\) −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 \(0.227312\pi\)
−0.755670 + 0.654953i \(0.772688\pi\)
\(504\) −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 −0.255380 0.966841i \(-0.582201\pi\)
0.966841 + 0.255380i \(0.0822006\pi\)
\(524\) −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 0.0590579 0.998255i \(-0.481190\pi\)
−0.998255 + 0.0590579i \(0.981190\pi\)
\(548\) 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 0.973199 0.229965i \(-0.0738612\pi\)
−0.229965 + 0.973199i \(0.573861\pi\)
\(558\) 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 \(0.0573833\pi\)
0.179300 + 0.983794i \(0.442617\pi\)
\(564\) −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 \(-0.524512\pi\)
−0.0769302 + 0.997036i \(0.524512\pi\)
\(578\) 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 \(-0.460641\pi\)
0.992365 0.123335i \(-0.0393590\pi\)
\(588\) 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 \(-0.529815\pi\)
−0.0935306 + 0.995616i \(0.529815\pi\)
\(594\) 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 \(-0.466094\pi\)
0.106319 + 0.994332i \(0.466094\pi\)
\(608\) 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 −0.151541 0.988451i \(-0.548424\pi\)
0.988451 + 0.151541i \(0.0484235\pi\)
\(614\) −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 \(-0.985881\pi\)
0.999016 0.0443419i \(-0.0141191\pi\)
\(618\) −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 0.696342 0.717710i \(-0.254810\pi\)
−0.717710 + 0.696342i \(0.754810\pi\)
\(644\) −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 \(-0.778276\pi\)
0.767049 0.641588i \(-0.221724\pi\)
\(648\) 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 0.871491 0.490412i \(-0.163154\pi\)
−0.490412 + 0.871491i \(0.663154\pi\)
\(654\) 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 \(-0.477972\pi\)
0.0691469 + 0.997606i \(0.477972\pi\)
\(674\) 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 −0.484608 0.874731i \(-0.661038\pi\)
0.874731 + 0.484608i \(0.161038\pi\)
\(678\) 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 −0.311866 0.950126i \(-0.600954\pi\)
0.950126 + 0.311866i \(0.100954\pi\)
\(684\) −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 \(0.104978\pi\)
−0.946108 + 0.323852i \(0.895022\pi\)
\(728\) 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 0.837744 0.546063i \(-0.183874\pi\)
−0.546063 + 0.837744i \(0.683874\pi\)
\(734\) 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 \(-0.633862\pi\)
0.408254 0.912868i \(-0.366138\pi\)
\(744\) −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 −0.930127 0.367237i \(-0.880304\pi\)
0.367237 + 0.930127i \(0.380304\pi\)
\(758\) 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 −0.730533 0.682878i \(-0.760728\pi\)
0.682878 + 0.730533i \(0.260728\pi\)
\(774\) 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