Properties

Label 400.2.l.f.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 \(-0.507829 + 1.31989i\) of defining polynomial
Character \(\chi\) \(=\) 400.301
Dual form 400.2.l.f.101.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.507829 - 1.31989i) q^{2} +(-0.0623209 - 0.0623209i) q^{3} +(-1.48422 - 1.34056i) q^{4} +(-0.113905 + 0.0506084i) q^{6} -0.375877i q^{7} +(-2.52312 + 1.27824i) q^{8} -2.99223i q^{9} +O(q^{10})\) \(q+(0.507829 - 1.31989i) q^{2} +(-0.0623209 - 0.0623209i) q^{3} +(-1.48422 - 1.34056i) q^{4} +(-0.113905 + 0.0506084i) q^{6} -0.375877i q^{7} +(-2.52312 + 1.27824i) q^{8} -2.99223i q^{9} +(2.36756 - 2.36756i) q^{11} +(0.00895328 + 0.176043i) q^{12} +(-1.76442 - 1.76442i) q^{13} +(-0.496116 - 0.190881i) q^{14} +(0.405819 + 3.97936i) q^{16} -4.64955 q^{17} +(-3.94942 - 1.51954i) q^{18} +(-2.34965 - 2.34965i) q^{19} +(-0.0234250 + 0.0234250i) q^{21} +(-1.92260 - 4.32723i) q^{22} -2.07779i q^{23} +(0.236904 + 0.0775821i) q^{24} +(-3.22487 + 1.43282i) q^{26} +(-0.373441 + 0.373441i) q^{27} +(-0.503884 + 0.557884i) q^{28} +(2.55422 + 2.55422i) q^{29} +8.51714 q^{31} +(5.45841 + 1.48520i) q^{32} -0.295096 q^{33} +(-2.36118 + 6.13690i) q^{34} +(-4.01125 + 4.44113i) q^{36} +(-7.62613 + 7.62613i) q^{37} +(-4.29450 + 1.90806i) q^{38} +0.219921i q^{39} -3.77709i q^{41} +(0.0190225 + 0.0428143i) q^{42} +(6.21191 - 6.21191i) q^{43} +(-6.68782 + 0.340133i) q^{44} +(-2.74246 - 1.05516i) q^{46} +9.71696 q^{47} +(0.222706 - 0.273288i) q^{48} +6.85872 q^{49} +(0.289764 + 0.289764i) q^{51} +(0.253484 + 4.98410i) q^{52} +(3.03609 - 3.03609i) q^{53} +(0.303257 + 0.682545i) q^{54} +(0.480459 + 0.948381i) q^{56} +0.292864i q^{57} +(4.66840 - 2.07418i) q^{58} +(-8.11663 + 8.11663i) q^{59} +(0.728329 + 0.728329i) q^{61} +(4.32525 - 11.2417i) q^{62} -1.12471 q^{63} +(4.73223 - 6.45027i) q^{64} +(-0.149858 + 0.389495i) q^{66} +(-0.969239 - 0.969239i) q^{67} +(6.90096 + 6.23299i) q^{68} +(-0.129490 + 0.129490i) q^{69} -9.14230i q^{71} +(3.82478 + 7.54975i) q^{72} +7.56793i q^{73} +(6.19289 + 13.9384i) q^{74} +(0.337561 + 6.63723i) q^{76} +(-0.889909 - 0.889909i) q^{77} +(0.290271 + 0.111682i) q^{78} +11.8065 q^{79} -8.93015 q^{81} +(-4.98534 - 1.91811i) q^{82} +(10.6393 + 10.6393i) q^{83} +(0.0661703 - 0.00336533i) q^{84} +(-5.04445 - 11.3536i) q^{86} -0.318363i q^{87} +(-2.94733 + 8.99991i) q^{88} -15.7111i q^{89} +(-0.663205 + 0.663205i) q^{91} +(-2.78540 + 3.08390i) q^{92} +(-0.530796 - 0.530796i) q^{93} +(4.93455 - 12.8253i) q^{94} +(-0.247614 - 0.432731i) q^{96} -3.86020 q^{97} +(3.48305 - 9.05275i) q^{98} +(-7.08428 - 7.08428i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.507829 1.31989i 0.359089 0.933303i
\(3\) −0.0623209 0.0623209i −0.0359810 0.0359810i 0.688887 0.724868i \(-0.258099\pi\)
−0.724868 + 0.688887i \(0.758099\pi\)
\(4\) −1.48422 1.34056i −0.742110 0.670278i
\(5\) 0 0
\(6\) −0.113905 + 0.0506084i −0.0465015 + 0.0206608i
\(7\) 0.375877i 0.142068i −0.997474 0.0710340i \(-0.977370\pi\)
0.997474 0.0710340i \(-0.0226299\pi\)
\(8\) −2.52312 + 1.27824i −0.892056 + 0.451924i
\(9\) 2.99223i 0.997411i
\(10\) 0 0
\(11\) 2.36756 2.36756i 0.713845 0.713845i −0.253492 0.967337i \(-0.581579\pi\)
0.967337 + 0.253492i \(0.0815793\pi\)
\(12\) 0.00895328 + 0.176043i 0.00258459 + 0.0508191i
\(13\) −1.76442 1.76442i −0.489363 0.489363i 0.418742 0.908105i \(-0.362471\pi\)
−0.908105 + 0.418742i \(0.862471\pi\)
\(14\) −0.496116 0.190881i −0.132593 0.0510151i
\(15\) 0 0
\(16\) 0.405819 + 3.97936i 0.101455 + 0.994840i
\(17\) −4.64955 −1.12768 −0.563841 0.825883i \(-0.690677\pi\)
−0.563841 + 0.825883i \(0.690677\pi\)
\(18\) −3.94942 1.51954i −0.930887 0.358159i
\(19\) −2.34965 2.34965i −0.539047 0.539047i 0.384202 0.923249i \(-0.374476\pi\)
−0.923249 + 0.384202i \(0.874476\pi\)
\(20\) 0 0
\(21\) −0.0234250 + 0.0234250i −0.00511175 + 0.00511175i
\(22\) −1.92260 4.32723i −0.409900 0.922568i
\(23\) 2.07779i 0.433250i −0.976255 0.216625i \(-0.930495\pi\)
0.976255 0.216625i \(-0.0695048\pi\)
\(24\) 0.236904 + 0.0775821i 0.0483577 + 0.0158364i
\(25\) 0 0
\(26\) −3.22487 + 1.43282i −0.632449 + 0.280999i
\(27\) −0.373441 + 0.373441i −0.0718688 + 0.0718688i
\(28\) −0.503884 + 0.557884i −0.0952251 + 0.105430i
\(29\) 2.55422 + 2.55422i 0.474307 + 0.474307i 0.903305 0.428998i \(-0.141133\pi\)
−0.428998 + 0.903305i \(0.641133\pi\)
\(30\) 0 0
\(31\) 8.51714 1.52972 0.764862 0.644194i \(-0.222807\pi\)
0.764862 + 0.644194i \(0.222807\pi\)
\(32\) 5.45841 + 1.48520i 0.964919 + 0.262548i
\(33\) −0.295096 −0.0513697
\(34\) −2.36118 + 6.13690i −0.404938 + 1.05247i
\(35\) 0 0
\(36\) −4.01125 + 4.44113i −0.668542 + 0.740189i
\(37\) −7.62613 + 7.62613i −1.25373 + 1.25373i −0.299691 + 0.954036i \(0.596884\pi\)
−0.954036 + 0.299691i \(0.903116\pi\)
\(38\) −4.29450 + 1.90806i −0.696660 + 0.309528i
\(39\) 0.219921i 0.0352155i
\(40\) 0 0
\(41\) 3.77709i 0.589882i −0.955515 0.294941i \(-0.904700\pi\)
0.955515 0.294941i \(-0.0953001\pi\)
\(42\) 0.0190225 + 0.0428143i 0.00293524 + 0.00660638i
\(43\) 6.21191 6.21191i 0.947307 0.947307i −0.0513725 0.998680i \(-0.516360\pi\)
0.998680 + 0.0513725i \(0.0163596\pi\)
\(44\) −6.68782 + 0.340133i −1.00823 + 0.0512770i
\(45\) 0 0
\(46\) −2.74246 1.05516i −0.404353 0.155575i
\(47\) 9.71696 1.41736 0.708682 0.705528i \(-0.249290\pi\)
0.708682 + 0.705528i \(0.249290\pi\)
\(48\) 0.222706 0.273288i 0.0321449 0.0394458i
\(49\) 6.85872 0.979817
\(50\) 0 0
\(51\) 0.289764 + 0.289764i 0.0405751 + 0.0405751i
\(52\) 0.253484 + 4.98410i 0.0351520 + 0.691170i
\(53\) 3.03609 3.03609i 0.417040 0.417040i −0.467143 0.884182i \(-0.654717\pi\)
0.884182 + 0.467143i \(0.154717\pi\)
\(54\) 0.303257 + 0.682545i 0.0412681 + 0.0928827i
\(55\) 0 0
\(56\) 0.480459 + 0.948381i 0.0642040 + 0.126733i
\(57\) 0.292864i 0.0387908i
\(58\) 4.66840 2.07418i 0.612991 0.272354i
\(59\) −8.11663 + 8.11663i −1.05670 + 1.05670i −0.0584019 + 0.998293i \(0.518600\pi\)
−0.998293 + 0.0584019i \(0.981400\pi\)
\(60\) 0 0
\(61\) 0.728329 + 0.728329i 0.0932529 + 0.0932529i 0.752194 0.658941i \(-0.228995\pi\)
−0.658941 + 0.752194i \(0.728995\pi\)
\(62\) 4.32525 11.2417i 0.549307 1.42770i
\(63\) −1.12471 −0.141700
\(64\) 4.73223 6.45027i 0.591529 0.806284i
\(65\) 0 0
\(66\) −0.149858 + 0.389495i −0.0184463 + 0.0479435i
\(67\) −0.969239 0.969239i −0.118411 0.118411i 0.645418 0.763829i \(-0.276683\pi\)
−0.763829 + 0.645418i \(0.776683\pi\)
\(68\) 6.90096 + 6.23299i 0.836864 + 0.755860i
\(69\) −0.129490 + 0.129490i −0.0155887 + 0.0155887i
\(70\) 0 0
\(71\) 9.14230i 1.08499i −0.840058 0.542496i \(-0.817479\pi\)
0.840058 0.542496i \(-0.182521\pi\)
\(72\) 3.82478 + 7.54975i 0.450754 + 0.889747i
\(73\) 7.56793i 0.885759i 0.896581 + 0.442879i \(0.146043\pi\)
−0.896581 + 0.442879i \(0.853957\pi\)
\(74\) 6.19289 + 13.9384i 0.719908 + 1.62031i
\(75\) 0 0
\(76\) 0.337561 + 6.63723i 0.0387209 + 0.761343i
\(77\) −0.889909 0.889909i −0.101415 0.101415i
\(78\) 0.290271 + 0.111682i 0.0328667 + 0.0126455i
\(79\) 11.8065 1.32834 0.664169 0.747583i \(-0.268786\pi\)
0.664169 + 0.747583i \(0.268786\pi\)
\(80\) 0 0
\(81\) −8.93015 −0.992239
\(82\) −4.98534 1.91811i −0.550539 0.211820i
\(83\) 10.6393 + 10.6393i 1.16782 + 1.16782i 0.982720 + 0.185101i \(0.0592611\pi\)
0.185101 + 0.982720i \(0.440739\pi\)
\(84\) 0.0661703 0.00336533i 0.00721977 0.000367188i
\(85\) 0 0
\(86\) −5.04445 11.3536i −0.543957 1.22429i
\(87\) 0.318363i 0.0341320i
\(88\) −2.94733 + 8.99991i −0.314186 + 0.959394i
\(89\) 15.7111i 1.66538i −0.553741 0.832689i \(-0.686800\pi\)
0.553741 0.832689i \(-0.313200\pi\)
\(90\) 0 0
\(91\) −0.663205 + 0.663205i −0.0695228 + 0.0695228i
\(92\) −2.78540 + 3.08390i −0.290398 + 0.321519i
\(93\) −0.530796 0.530796i −0.0550410 0.0550410i
\(94\) 4.93455 12.8253i 0.508960 1.32283i
\(95\) 0 0
\(96\) −0.247614 0.432731i −0.0252720 0.0441655i
\(97\) −3.86020 −0.391943 −0.195972 0.980610i \(-0.562786\pi\)
−0.195972 + 0.980610i \(0.562786\pi\)
\(98\) 3.48305 9.05275i 0.351841 0.914466i
\(99\) −7.08428 7.08428i −0.711997 0.711997i
\(100\) 0 0
\(101\) −6.87437 + 6.87437i −0.684026 + 0.684026i −0.960905 0.276879i \(-0.910700\pi\)
0.276879 + 0.960905i \(0.410700\pi\)
\(102\) 0.529607 0.235306i 0.0524390 0.0232988i
\(103\) 1.15407i 0.113714i 0.998382 + 0.0568571i \(0.0181079\pi\)
−0.998382 + 0.0568571i \(0.981892\pi\)
\(104\) 6.70719 + 2.19650i 0.657694 + 0.215384i
\(105\) 0 0
\(106\) −2.46549 5.54913i −0.239470 0.538979i
\(107\) 5.70435 5.70435i 0.551460 0.551460i −0.375402 0.926862i \(-0.622495\pi\)
0.926862 + 0.375402i \(0.122495\pi\)
\(108\) 1.05489 0.0536502i 0.101507 0.00516249i
\(109\) 11.1863 + 11.1863i 1.07145 + 1.07145i 0.997243 + 0.0742092i \(0.0236433\pi\)
0.0742092 + 0.997243i \(0.476357\pi\)
\(110\) 0 0
\(111\) 0.950534 0.0902207
\(112\) 1.49575 0.152538i 0.141335 0.0144135i
\(113\) −4.08163 −0.383967 −0.191984 0.981398i \(-0.561492\pi\)
−0.191984 + 0.981398i \(0.561492\pi\)
\(114\) 0.386549 + 0.148725i 0.0362036 + 0.0139294i
\(115\) 0 0
\(116\) −0.366950 7.21510i −0.0340705 0.669905i
\(117\) −5.27956 + 5.27956i −0.488096 + 0.488096i
\(118\) 6.59120 + 14.8349i 0.606769 + 1.36566i
\(119\) 1.74766i 0.160208i
\(120\) 0 0
\(121\) 0.210643i 0.0191493i
\(122\) 1.33118 0.591448i 0.120519 0.0535472i
\(123\) −0.235392 + 0.235392i −0.0212245 + 0.0212245i
\(124\) −12.6413 11.4177i −1.13522 1.02534i
\(125\) 0 0
\(126\) −0.571160 + 1.48449i −0.0508830 + 0.132249i
\(127\) 17.0918 1.51665 0.758326 0.651876i \(-0.226018\pi\)
0.758326 + 0.651876i \(0.226018\pi\)
\(128\) −6.11049 9.52166i −0.540096 0.841603i
\(129\) −0.774263 −0.0681701
\(130\) 0 0
\(131\) −3.56424 3.56424i −0.311409 0.311409i 0.534046 0.845455i \(-0.320671\pi\)
−0.845455 + 0.534046i \(0.820671\pi\)
\(132\) 0.437988 + 0.395593i 0.0381220 + 0.0344320i
\(133\) −0.883179 + 0.883179i −0.0765813 + 0.0765813i
\(134\) −1.77150 + 0.787081i −0.153034 + 0.0679935i
\(135\) 0 0
\(136\) 11.7314 5.94322i 1.00596 0.509627i
\(137\) 16.6995i 1.42673i −0.700792 0.713366i \(-0.747170\pi\)
0.700792 0.713366i \(-0.252830\pi\)
\(138\) 0.105154 + 0.236671i 0.00895128 + 0.0201468i
\(139\) −7.56455 + 7.56455i −0.641616 + 0.641616i −0.950953 0.309336i \(-0.899893\pi\)
0.309336 + 0.950953i \(0.399893\pi\)
\(140\) 0 0
\(141\) −0.605569 0.605569i −0.0509982 0.0509982i
\(142\) −12.0668 4.64272i −1.01263 0.389609i
\(143\) −8.35474 −0.698658
\(144\) 11.9072 1.21431i 0.992264 0.101192i
\(145\) 0 0
\(146\) 9.98883 + 3.84321i 0.826682 + 0.318066i
\(147\) −0.427441 0.427441i −0.0352548 0.0352548i
\(148\) 21.5421 1.09560i 1.77075 0.0900579i
\(149\) −10.2542 + 10.2542i −0.840056 + 0.840056i −0.988866 0.148810i \(-0.952456\pi\)
0.148810 + 0.988866i \(0.452456\pi\)
\(150\) 0 0
\(151\) 19.0430i 1.54970i 0.632147 + 0.774849i \(0.282174\pi\)
−0.632147 + 0.774849i \(0.717826\pi\)
\(152\) 8.93184 + 2.92503i 0.724468 + 0.237252i
\(153\) 13.9125i 1.12476i
\(154\) −1.62650 + 0.722661i −0.131067 + 0.0582337i
\(155\) 0 0
\(156\) 0.294816 0.326411i 0.0236042 0.0261338i
\(157\) 10.1335 + 10.1335i 0.808741 + 0.808741i 0.984443 0.175702i \(-0.0562196\pi\)
−0.175702 + 0.984443i \(0.556220\pi\)
\(158\) 5.99569 15.5833i 0.476991 1.23974i
\(159\) −0.378424 −0.0300110
\(160\) 0 0
\(161\) −0.780994 −0.0615509
\(162\) −4.53499 + 11.7868i −0.356302 + 0.926060i
\(163\) −7.35501 7.35501i −0.576089 0.576089i 0.357735 0.933823i \(-0.383549\pi\)
−0.933823 + 0.357735i \(0.883549\pi\)
\(164\) −5.06340 + 5.60603i −0.395385 + 0.437758i
\(165\) 0 0
\(166\) 19.4457 8.63981i 1.50928 0.670579i
\(167\) 8.02936i 0.621331i −0.950519 0.310665i \(-0.899448\pi\)
0.950519 0.310665i \(-0.100552\pi\)
\(168\) 0.0291613 0.0890465i 0.00224984 0.00687009i
\(169\) 6.77363i 0.521048i
\(170\) 0 0
\(171\) −7.03070 + 7.03070i −0.537651 + 0.537651i
\(172\) −17.5472 + 0.892429i −1.33797 + 0.0680471i
\(173\) −10.4326 10.4326i −0.793177 0.793177i 0.188832 0.982009i \(-0.439530\pi\)
−0.982009 + 0.188832i \(0.939530\pi\)
\(174\) −0.420204 0.161674i −0.0318556 0.0122564i
\(175\) 0 0
\(176\) 10.3822 + 8.46056i 0.782585 + 0.637739i
\(177\) 1.01167 0.0760418
\(178\) −20.7370 7.97857i −1.55430 0.598019i
\(179\) −8.30280 8.30280i −0.620580 0.620580i 0.325099 0.945680i \(-0.394602\pi\)
−0.945680 + 0.325099i \(0.894602\pi\)
\(180\) 0 0
\(181\) −10.4772 + 10.4772i −0.778765 + 0.778765i −0.979621 0.200856i \(-0.935628\pi\)
0.200856 + 0.979621i \(0.435628\pi\)
\(182\) 0.538564 + 1.21215i 0.0399210 + 0.0898508i
\(183\) 0.0907802i 0.00671066i
\(184\) 2.65591 + 5.24251i 0.195796 + 0.386483i
\(185\) 0 0
\(186\) −0.970145 + 0.431039i −0.0711345 + 0.0316053i
\(187\) −11.0081 + 11.0081i −0.804990 + 0.804990i
\(188\) −14.4221 13.0261i −1.05184 0.950028i
\(189\) 0.140368 + 0.140368i 0.0102103 + 0.0102103i
\(190\) 0 0
\(191\) 1.68079 0.121618 0.0608089 0.998149i \(-0.480632\pi\)
0.0608089 + 0.998149i \(0.480632\pi\)
\(192\) −0.696903 + 0.107070i −0.0502947 + 0.00772710i
\(193\) −1.61403 −0.116181 −0.0580903 0.998311i \(-0.518501\pi\)
−0.0580903 + 0.998311i \(0.518501\pi\)
\(194\) −1.96032 + 5.09503i −0.140743 + 0.365802i
\(195\) 0 0
\(196\) −10.1798 9.19449i −0.727132 0.656750i
\(197\) 5.10322 5.10322i 0.363589 0.363589i −0.501543 0.865133i \(-0.667234\pi\)
0.865133 + 0.501543i \(0.167234\pi\)
\(198\) −12.9481 + 5.75287i −0.920179 + 0.408839i
\(199\) 11.1545i 0.790725i 0.918525 + 0.395362i \(0.129381\pi\)
−0.918525 + 0.395362i \(0.870619\pi\)
\(200\) 0 0
\(201\) 0.120808i 0.00852111i
\(202\) 5.58241 + 12.5644i 0.392777 + 0.884030i
\(203\) 0.960072 0.960072i 0.0673839 0.0673839i
\(204\) −0.0416288 0.818519i −0.00291460 0.0573078i
\(205\) 0 0
\(206\) 1.52325 + 0.586072i 0.106130 + 0.0408335i
\(207\) −6.21724 −0.432128
\(208\) 6.30524 7.73731i 0.437189 0.536486i
\(209\) −11.1259 −0.769591
\(210\) 0 0
\(211\) −2.48377 2.48377i −0.170989 0.170989i 0.616425 0.787414i \(-0.288581\pi\)
−0.787414 + 0.616425i \(0.788581\pi\)
\(212\) −8.57628 + 0.436178i −0.589022 + 0.0299568i
\(213\) −0.569756 + 0.569756i −0.0390391 + 0.0390391i
\(214\) −4.63228 10.4259i −0.316656 0.712703i
\(215\) 0 0
\(216\) 0.464890 1.41958i 0.0316317 0.0965903i
\(217\) 3.20140i 0.217325i
\(218\) 20.4454 9.08395i 1.38474 0.615243i
\(219\) 0.471640 0.471640i 0.0318705 0.0318705i
\(220\) 0 0
\(221\) 8.20377 + 8.20377i 0.551846 + 0.551846i
\(222\) 0.482708 1.25460i 0.0323973 0.0842033i
\(223\) −21.1384 −1.41553 −0.707765 0.706448i \(-0.750297\pi\)
−0.707765 + 0.706448i \(0.750297\pi\)
\(224\) 0.558251 2.05169i 0.0372997 0.137084i
\(225\) 0 0
\(226\) −2.07277 + 5.38730i −0.137878 + 0.358358i
\(227\) −14.4885 14.4885i −0.961634 0.961634i 0.0376566 0.999291i \(-0.488011\pi\)
−0.999291 + 0.0376566i \(0.988011\pi\)
\(228\) 0.392601 0.434675i 0.0260006 0.0287871i
\(229\) −10.0956 + 10.0956i −0.667138 + 0.667138i −0.957053 0.289914i \(-0.906373\pi\)
0.289914 + 0.957053i \(0.406373\pi\)
\(230\) 0 0
\(231\) 0.110920i 0.00729799i
\(232\) −9.70949 3.17970i −0.637459 0.208758i
\(233\) 3.44995i 0.226014i −0.993594 0.113007i \(-0.963952\pi\)
0.993594 0.113007i \(-0.0360482\pi\)
\(234\) 4.28733 + 9.64955i 0.280271 + 0.630811i
\(235\) 0 0
\(236\) 22.9277 1.16607i 1.49246 0.0759047i
\(237\) −0.735793 0.735793i −0.0477949 0.0477949i
\(238\) 2.30672 + 0.887511i 0.149522 + 0.0575288i
\(239\) 18.0060 1.16471 0.582354 0.812935i \(-0.302132\pi\)
0.582354 + 0.812935i \(0.302132\pi\)
\(240\) 0 0
\(241\) 12.6235 0.813154 0.406577 0.913617i \(-0.366722\pi\)
0.406577 + 0.913617i \(0.366722\pi\)
\(242\) −0.278025 0.106970i −0.0178721 0.00687632i
\(243\) 1.67686 + 1.67686i 0.107571 + 0.107571i
\(244\) −0.104635 2.05737i −0.00669856 0.131709i
\(245\) 0 0
\(246\) 0.191152 + 0.430230i 0.0121874 + 0.0274304i
\(247\) 8.29155i 0.527578i
\(248\) −21.4897 + 10.8869i −1.36460 + 0.691320i
\(249\) 1.32611i 0.0840386i
\(250\) 0 0
\(251\) −9.17919 + 9.17919i −0.579386 + 0.579386i −0.934734 0.355348i \(-0.884362\pi\)
0.355348 + 0.934734i \(0.384362\pi\)
\(252\) 1.66932 + 1.50774i 0.105157 + 0.0949785i
\(253\) −4.91929 4.91929i −0.309273 0.309273i
\(254\) 8.67970 22.5593i 0.544613 1.41550i
\(255\) 0 0
\(256\) −15.6706 + 3.22980i −0.979414 + 0.201863i
\(257\) 16.2897 1.01612 0.508061 0.861321i \(-0.330363\pi\)
0.508061 + 0.861321i \(0.330363\pi\)
\(258\) −0.393193 + 1.02194i −0.0244791 + 0.0636233i
\(259\) 2.86648 + 2.86648i 0.178115 + 0.178115i
\(260\) 0 0
\(261\) 7.64282 7.64282i 0.473079 0.473079i
\(262\) −6.51442 + 2.89438i −0.402462 + 0.178815i
\(263\) 10.4898i 0.646831i 0.946257 + 0.323416i \(0.104831\pi\)
−0.946257 + 0.323416i \(0.895169\pi\)
\(264\) 0.744562 0.377202i 0.0458246 0.0232152i
\(265\) 0 0
\(266\) 0.717196 + 1.61420i 0.0439741 + 0.0989731i
\(267\) −0.979132 + 0.979132i −0.0599219 + 0.0599219i
\(268\) 0.139245 + 2.73788i 0.00850574 + 0.167243i
\(269\) −8.46636 8.46636i −0.516203 0.516203i 0.400217 0.916420i \(-0.368935\pi\)
−0.916420 + 0.400217i \(0.868935\pi\)
\(270\) 0 0
\(271\) −8.92117 −0.541923 −0.270961 0.962590i \(-0.587342\pi\)
−0.270961 + 0.962590i \(0.587342\pi\)
\(272\) −1.88688 18.5022i −0.114409 1.12186i
\(273\) 0.0826631 0.00500300
\(274\) −22.0415 8.48047i −1.33157 0.512324i
\(275\) 0 0
\(276\) 0.365780 0.0186031i 0.0220174 0.00111977i
\(277\) 9.36430 9.36430i 0.562646 0.562646i −0.367412 0.930058i \(-0.619756\pi\)
0.930058 + 0.367412i \(0.119756\pi\)
\(278\) 6.14288 + 13.8259i 0.368425 + 0.829220i
\(279\) 25.4853i 1.52576i
\(280\) 0 0
\(281\) 3.12921i 0.186673i −0.995635 0.0933365i \(-0.970247\pi\)
0.995635 0.0933365i \(-0.0297532\pi\)
\(282\) −1.10681 + 0.491760i −0.0659096 + 0.0292839i
\(283\) −2.07308 + 2.07308i −0.123232 + 0.123232i −0.766033 0.642801i \(-0.777772\pi\)
0.642801 + 0.766033i \(0.277772\pi\)
\(284\) −12.2558 + 13.5692i −0.727246 + 0.805183i
\(285\) 0 0
\(286\) −4.24277 + 11.0273i −0.250880 + 0.652060i
\(287\) −1.41972 −0.0838035
\(288\) 4.44405 16.3328i 0.261868 0.962420i
\(289\) 4.61834 0.271667
\(290\) 0 0
\(291\) 0.240571 + 0.240571i 0.0141025 + 0.0141025i
\(292\) 10.1452 11.2325i 0.593705 0.657331i
\(293\) 12.3528 12.3528i 0.721659 0.721659i −0.247284 0.968943i \(-0.579538\pi\)
0.968943 + 0.247284i \(0.0795382\pi\)
\(294\) −0.781242 + 0.347109i −0.0455630 + 0.0202438i
\(295\) 0 0
\(296\) 9.49362 28.9896i 0.551806 1.68499i
\(297\) 1.76829i 0.102606i
\(298\) 8.32703 + 18.7418i 0.482372 + 1.08568i
\(299\) −3.66610 + 3.66610i −0.212016 + 0.212016i
\(300\) 0 0
\(301\) −2.33491 2.33491i −0.134582 0.134582i
\(302\) 25.1347 + 9.67058i 1.44634 + 0.556479i
\(303\) 0.856834 0.0492238
\(304\) 8.39657 10.3036i 0.481576 0.590954i
\(305\) 0 0
\(306\) 18.3630 + 7.06519i 1.04974 + 0.403890i
\(307\) 10.5938 + 10.5938i 0.604619 + 0.604619i 0.941535 0.336916i \(-0.109384\pi\)
−0.336916 + 0.941535i \(0.609384\pi\)
\(308\) 0.127848 + 2.51379i 0.00728483 + 0.143237i
\(309\) 0.0719229 0.0719229i 0.00409155 0.00409155i
\(310\) 0 0
\(311\) 19.4153i 1.10094i −0.834854 0.550471i \(-0.814448\pi\)
0.834854 0.550471i \(-0.185552\pi\)
\(312\) −0.281110 0.554885i −0.0159147 0.0314142i
\(313\) 2.56569i 0.145022i −0.997368 0.0725108i \(-0.976899\pi\)
0.997368 0.0725108i \(-0.0231012\pi\)
\(314\) 18.5212 8.22902i 1.04521 0.464391i
\(315\) 0 0
\(316\) −17.5235 15.8273i −0.985773 0.890355i
\(317\) −7.32418 7.32418i −0.411367 0.411367i 0.470848 0.882215i \(-0.343948\pi\)
−0.882215 + 0.470848i \(0.843948\pi\)
\(318\) −0.192175 + 0.499478i −0.0107766 + 0.0280093i
\(319\) 12.0945 0.677163
\(320\) 0 0
\(321\) −0.711000 −0.0396842
\(322\) −0.396611 + 1.03083i −0.0221023 + 0.0574457i
\(323\) 10.9248 + 10.9248i 0.607873 + 0.607873i
\(324\) 13.2543 + 11.9714i 0.736351 + 0.665076i
\(325\) 0 0
\(326\) −13.4429 + 5.97272i −0.744533 + 0.330798i
\(327\) 1.39428i 0.0771038i
\(328\) 4.82801 + 9.53004i 0.266582 + 0.526208i
\(329\) 3.65238i 0.201362i
\(330\) 0 0
\(331\) 4.17652 4.17652i 0.229562 0.229562i −0.582948 0.812510i \(-0.698101\pi\)
0.812510 + 0.582948i \(0.198101\pi\)
\(332\) −1.52849 30.0538i −0.0838870 1.64942i
\(333\) 22.8191 + 22.8191i 1.25048 + 1.25048i
\(334\) −10.5979 4.07754i −0.579890 0.223113i
\(335\) 0 0
\(336\) −0.102723 0.0837101i −0.00560398 0.00456676i
\(337\) 12.4540 0.678410 0.339205 0.940712i \(-0.389842\pi\)
0.339205 + 0.940712i \(0.389842\pi\)
\(338\) −8.94045 3.43984i −0.486296 0.187103i
\(339\) 0.254371 + 0.254371i 0.0138155 + 0.0138155i
\(340\) 0 0
\(341\) 20.1648 20.1648i 1.09199 1.09199i
\(342\) 5.70936 + 12.8501i 0.308727 + 0.694856i
\(343\) 5.20917i 0.281269i
\(344\) −7.73309 + 23.6136i −0.416940 + 1.27316i
\(345\) 0 0
\(346\) −19.0679 + 8.47193i −1.02510 + 0.455454i
\(347\) −17.5107 + 17.5107i −0.940024 + 0.940024i −0.998300 0.0582766i \(-0.981439\pi\)
0.0582766 + 0.998300i \(0.481439\pi\)
\(348\) −0.426783 + 0.472520i −0.0228780 + 0.0253297i
\(349\) 8.42042 + 8.42042i 0.450735 + 0.450735i 0.895598 0.444863i \(-0.146748\pi\)
−0.444863 + 0.895598i \(0.646748\pi\)
\(350\) 0 0
\(351\) 1.31782 0.0703398
\(352\) 16.4394 9.40680i 0.876221 0.501384i
\(353\) 9.71293 0.516967 0.258484 0.966016i \(-0.416777\pi\)
0.258484 + 0.966016i \(0.416777\pi\)
\(354\) 0.513755 1.33529i 0.0273058 0.0709701i
\(355\) 0 0
\(356\) −21.0617 + 23.3188i −1.11627 + 1.23589i
\(357\) 0.108916 0.108916i 0.00576443 0.00576443i
\(358\) −15.1752 + 6.74238i −0.802033 + 0.356346i
\(359\) 6.77551i 0.357598i 0.983886 + 0.178799i \(0.0572212\pi\)
−0.983886 + 0.178799i \(0.942779\pi\)
\(360\) 0 0
\(361\) 7.95830i 0.418858i
\(362\) 8.50814 + 19.1494i 0.447178 + 1.00647i
\(363\) −0.0131274 + 0.0131274i −0.000689012 + 0.000689012i
\(364\) 1.87341 0.0952789i 0.0981932 0.00499397i
\(365\) 0 0
\(366\) −0.119820 0.0461008i −0.00626308 0.00240973i
\(367\) −34.4591 −1.79875 −0.899376 0.437176i \(-0.855979\pi\)
−0.899376 + 0.437176i \(0.855979\pi\)
\(368\) 8.26828 0.843208i 0.431014 0.0439553i
\(369\) −11.3019 −0.588355
\(370\) 0 0
\(371\) −1.14120 1.14120i −0.0592480 0.0592480i
\(372\) 0.0762564 + 1.49938i 0.00395371 + 0.0777392i
\(373\) 3.55187 3.55187i 0.183909 0.183909i −0.609148 0.793057i \(-0.708488\pi\)
0.793057 + 0.609148i \(0.208488\pi\)
\(374\) 8.93924 + 20.1197i 0.462237 + 1.04036i
\(375\) 0 0
\(376\) −24.5170 + 12.4206i −1.26437 + 0.640541i
\(377\) 9.01345i 0.464216i
\(378\) 0.256553 0.113987i 0.0131957 0.00586288i
\(379\) 26.4464 26.4464i 1.35846 1.35846i 0.482644 0.875817i \(-0.339677\pi\)
0.875817 0.482644i \(-0.160323\pi\)
\(380\) 0 0
\(381\) −1.06518 1.06518i −0.0545706 0.0545706i
\(382\) 0.853554 2.21846i 0.0436716 0.113506i
\(383\) 30.8614 1.57695 0.788473 0.615069i \(-0.210872\pi\)
0.788473 + 0.615069i \(0.210872\pi\)
\(384\) −0.212587 + 0.974209i −0.0108485 + 0.0497149i
\(385\) 0 0
\(386\) −0.819651 + 2.13034i −0.0417192 + 0.108432i
\(387\) −18.5875 18.5875i −0.944854 0.944854i
\(388\) 5.72938 + 5.17481i 0.290865 + 0.262711i
\(389\) 9.50959 9.50959i 0.482155 0.482155i −0.423664 0.905819i \(-0.639256\pi\)
0.905819 + 0.423664i \(0.139256\pi\)
\(390\) 0 0
\(391\) 9.66080i 0.488568i
\(392\) −17.3053 + 8.76705i −0.874052 + 0.442803i
\(393\) 0.444253i 0.0224096i
\(394\) −4.14413 9.32725i −0.208778 0.469900i
\(395\) 0 0
\(396\) 1.01776 + 20.0115i 0.0511442 + 1.00562i
\(397\) 24.8540 + 24.8540i 1.24739 + 1.24739i 0.956870 + 0.290518i \(0.0938276\pi\)
0.290518 + 0.956870i \(0.406172\pi\)
\(398\) 14.7228 + 5.66460i 0.737986 + 0.283941i
\(399\) 0.110081 0.00551094
\(400\) 0 0
\(401\) 4.69303 0.234359 0.117179 0.993111i \(-0.462615\pi\)
0.117179 + 0.993111i \(0.462615\pi\)
\(402\) 0.159453 + 0.0613496i 0.00795278 + 0.00305984i
\(403\) −15.0278 15.0278i −0.748590 0.748590i
\(404\) 19.4186 0.987602i 0.966110 0.0491350i
\(405\) 0 0
\(406\) −0.779638 1.75474i −0.0386928 0.0870864i
\(407\) 36.1106i 1.78993i
\(408\) −1.10150 0.360722i −0.0545322 0.0178584i
\(409\) 28.2641i 1.39757i 0.715331 + 0.698786i \(0.246276\pi\)
−0.715331 + 0.698786i \(0.753724\pi\)
\(410\) 0 0
\(411\) −1.04073 + 1.04073i −0.0513352 + 0.0513352i
\(412\) 1.54710 1.71290i 0.0762202 0.0843885i
\(413\) 3.05085 + 3.05085i 0.150123 + 0.150123i
\(414\) −3.15729 + 8.20607i −0.155172 + 0.403306i
\(415\) 0 0
\(416\) −7.01042 12.2514i −0.343714 0.600676i
\(417\) 0.942858 0.0461720
\(418\) −5.65003 + 14.6849i −0.276352 + 0.718262i
\(419\) 23.0355 + 23.0355i 1.12536 + 1.12536i 0.990923 + 0.134433i \(0.0429213\pi\)
0.134433 + 0.990923i \(0.457079\pi\)
\(420\) 0 0
\(421\) 5.40760 5.40760i 0.263550 0.263550i −0.562945 0.826495i \(-0.690332\pi\)
0.826495 + 0.562945i \(0.190332\pi\)
\(422\) −4.53962 + 2.01697i −0.220985 + 0.0981846i
\(423\) 29.0754i 1.41369i
\(424\) −3.77958 + 11.5413i −0.183552 + 0.560493i
\(425\) 0 0
\(426\) 0.462677 + 1.04135i 0.0224168 + 0.0504538i
\(427\) 0.273762 0.273762i 0.0132483 0.0132483i
\(428\) −16.1135 + 0.819511i −0.778876 + 0.0396126i
\(429\) 0.520675 + 0.520675i 0.0251384 + 0.0251384i
\(430\) 0 0
\(431\) −12.6839 −0.610961 −0.305481 0.952198i \(-0.598817\pi\)
−0.305481 + 0.952198i \(0.598817\pi\)
\(432\) −1.63761 1.33451i −0.0787894 0.0642065i
\(433\) 23.8511 1.14621 0.573104 0.819482i \(-0.305739\pi\)
0.573104 + 0.819482i \(0.305739\pi\)
\(434\) −4.22549 1.62576i −0.202830 0.0780390i
\(435\) 0 0
\(436\) −1.60707 31.5988i −0.0769647 1.51331i
\(437\) −4.88208 + 4.88208i −0.233542 + 0.233542i
\(438\) −0.383001 0.862025i −0.0183005 0.0411891i
\(439\) 4.65878i 0.222352i 0.993801 + 0.111176i \(0.0354617\pi\)
−0.993801 + 0.111176i \(0.964538\pi\)
\(440\) 0 0
\(441\) 20.5229i 0.977280i
\(442\) 14.9942 6.66197i 0.713201 0.316878i
\(443\) −8.74048 + 8.74048i −0.415273 + 0.415273i −0.883571 0.468298i \(-0.844867\pi\)
0.468298 + 0.883571i \(0.344867\pi\)
\(444\) −1.41080 1.27424i −0.0669537 0.0604729i
\(445\) 0 0
\(446\) −10.7347 + 27.9003i −0.508302 + 1.32112i
\(447\) 1.27810 0.0604520
\(448\) −2.42451 1.77874i −0.114547 0.0840374i
\(449\) −7.28525 −0.343812 −0.171906 0.985113i \(-0.554993\pi\)
−0.171906 + 0.985113i \(0.554993\pi\)
\(450\) 0 0
\(451\) −8.94247 8.94247i −0.421085 0.421085i
\(452\) 6.05803 + 5.47165i 0.284946 + 0.257365i
\(453\) 1.18678 1.18678i 0.0557596 0.0557596i
\(454\) −26.4809 + 11.7655i −1.24281 + 0.552184i
\(455\) 0 0
\(456\) −0.374350 0.738931i −0.0175305 0.0346036i
\(457\) 25.2194i 1.17971i 0.807508 + 0.589857i \(0.200816\pi\)
−0.807508 + 0.589857i \(0.799184\pi\)
\(458\) 8.19828 + 18.4520i 0.383080 + 0.862204i
\(459\) 1.73633 1.73633i 0.0810451 0.0810451i
\(460\) 0 0
\(461\) 13.6698 + 13.6698i 0.636667 + 0.636667i 0.949732 0.313064i \(-0.101356\pi\)
−0.313064 + 0.949732i \(0.601356\pi\)
\(462\) 0.146402 + 0.0563283i 0.00681124 + 0.00262063i
\(463\) −2.77045 −0.128754 −0.0643768 0.997926i \(-0.520506\pi\)
−0.0643768 + 0.997926i \(0.520506\pi\)
\(464\) −9.12761 + 11.2007i −0.423739 + 0.519980i
\(465\) 0 0
\(466\) −4.55355 1.75198i −0.210939 0.0811590i
\(467\) 17.9587 + 17.9587i 0.831031 + 0.831031i 0.987658 0.156627i \(-0.0500621\pi\)
−0.156627 + 0.987658i \(0.550062\pi\)
\(468\) 14.9136 0.758484i 0.689380 0.0350609i
\(469\) −0.364314 + 0.364314i −0.0168225 + 0.0168225i
\(470\) 0 0
\(471\) 1.26306i 0.0581986i
\(472\) 10.1042 30.8542i 0.465085 1.42018i
\(473\) 29.4141i 1.35246i
\(474\) −1.34482 + 0.597509i −0.0617697 + 0.0274445i
\(475\) 0 0
\(476\) 2.34283 2.59391i 0.107384 0.118892i
\(477\) −9.08470 9.08470i −0.415960 0.415960i
\(478\) 9.14394 23.7659i 0.418234 1.08703i
\(479\) −22.4540 −1.02595 −0.512975 0.858403i \(-0.671457\pi\)
−0.512975 + 0.858403i \(0.671457\pi\)
\(480\) 0 0
\(481\) 26.9114 1.22705
\(482\) 6.41059 16.6617i 0.291995 0.758919i
\(483\) 0.0486722 + 0.0486722i 0.00221466 + 0.00221466i
\(484\) −0.282378 + 0.312640i −0.0128354 + 0.0142109i
\(485\) 0 0
\(486\) 3.06483 1.36171i 0.139023 0.0617685i
\(487\) 27.7615i 1.25799i −0.777408 0.628997i \(-0.783466\pi\)
0.777408 0.628997i \(-0.216534\pi\)
\(488\) −2.76863 0.906683i −0.125330 0.0410436i
\(489\) 0.916741i 0.0414565i
\(490\) 0 0
\(491\) 16.8993 16.8993i 0.762656 0.762656i −0.214146 0.976802i \(-0.568697\pi\)
0.976802 + 0.214146i \(0.0686968\pi\)
\(492\) 0.664929 0.0338174i 0.0299773 0.00152460i
\(493\) −11.8760 11.8760i −0.534867 0.534867i
\(494\) 10.9439 + 4.21068i 0.492391 + 0.189448i
\(495\) 0 0
\(496\) 3.45642 + 33.8928i 0.155198 + 1.52183i
\(497\) −3.43638 −0.154143
\(498\) −1.75032 0.673435i −0.0784335 0.0301773i
\(499\) −1.81950 1.81950i −0.0814520 0.0814520i 0.665207 0.746659i \(-0.268343\pi\)
−0.746659 + 0.665207i \(0.768343\pi\)
\(500\) 0 0
\(501\) −0.500397 + 0.500397i −0.0223561 + 0.0223561i
\(502\) 7.45407 + 16.7770i 0.332691 + 0.748794i
\(503\) 42.2076i 1.88195i 0.338482 + 0.940973i \(0.390087\pi\)
−0.338482 + 0.940973i \(0.609913\pi\)
\(504\) 2.83778 1.43764i 0.126405 0.0640378i
\(505\) 0 0
\(506\) −8.99108 + 3.99477i −0.399702 + 0.177589i
\(507\) −0.422139 + 0.422139i −0.0187478 + 0.0187478i
\(508\) −25.3680 22.9125i −1.12552 1.01658i
\(509\) −21.9831 21.9831i −0.974382 0.974382i 0.0252980 0.999680i \(-0.491947\pi\)
−0.999680 + 0.0252980i \(0.991947\pi\)
\(510\) 0 0
\(511\) 2.84461 0.125838
\(512\) −3.69500 + 22.3237i −0.163298 + 0.986577i
\(513\) 1.75491 0.0774812
\(514\) 8.27236 21.5006i 0.364878 0.948349i
\(515\) 0 0
\(516\) 1.14918 + 1.03794i 0.0505897 + 0.0456929i
\(517\) 23.0054 23.0054i 1.01178 1.01178i
\(518\) 5.23913 2.32776i 0.230194 0.102276i
\(519\) 1.30034i 0.0570786i
\(520\) 0 0
\(521\) 28.1418i 1.23291i 0.787388 + 0.616457i \(0.211433\pi\)
−0.787388 + 0.616457i \(0.788567\pi\)
\(522\) −6.20644 13.9689i −0.271649 0.611403i
\(523\) 9.58093 9.58093i 0.418945 0.418945i −0.465895 0.884840i \(-0.654268\pi\)
0.884840 + 0.465895i \(0.154268\pi\)
\(524\) 0.512054 + 10.0682i 0.0223692 + 0.439830i
\(525\) 0 0
\(526\) 13.8454 + 5.32704i 0.603690 + 0.232270i
\(527\) −39.6009 −1.72504
\(528\) −0.119756 1.17429i −0.00521170 0.0511046i
\(529\) 18.6828 0.812295
\(530\) 0 0
\(531\) 24.2868 + 24.2868i 1.05396 + 1.05396i
\(532\) 2.49478 0.126881i 0.108163 0.00550100i
\(533\) −6.66438 + 6.66438i −0.288666 + 0.288666i
\(534\) 0.795116 + 1.78958i 0.0344080 + 0.0774426i
\(535\) 0 0
\(536\) 3.68442 + 1.20659i 0.159143 + 0.0521166i
\(537\) 1.03488i 0.0446582i
\(538\) −15.4741 + 6.87521i −0.667137 + 0.296411i
\(539\) 16.2384 16.2384i 0.699437 0.699437i
\(540\) 0 0
\(541\) −26.9128 26.9128i −1.15707 1.15707i −0.985102 0.171972i \(-0.944986\pi\)
−0.171972 0.985102i \(-0.555014\pi\)
\(542\) −4.53043 + 11.7750i −0.194598 + 0.505778i
\(543\) 1.30590 0.0560415
\(544\) −25.3791 6.90550i −1.08812 0.296071i
\(545\) 0 0
\(546\) 0.0419787 0.109106i 0.00179652 0.00466931i
\(547\) 10.6627 + 10.6627i 0.455902 + 0.455902i 0.897308 0.441406i \(-0.145520\pi\)
−0.441406 + 0.897308i \(0.645520\pi\)
\(548\) −22.3866 + 24.7857i −0.956307 + 1.05879i
\(549\) 2.17933 2.17933i 0.0930115 0.0930115i
\(550\) 0 0
\(551\) 12.0030i 0.511347i
\(552\) 0.161199 0.492236i 0.00686110 0.0209510i
\(553\) 4.43780i 0.188714i
\(554\) −7.60439 17.1153i −0.323079 0.727159i
\(555\) 0 0
\(556\) 21.3681 1.08675i 0.906211 0.0460887i
\(557\) −22.8060 22.8060i −0.966320 0.966320i 0.0331307 0.999451i \(-0.489452\pi\)
−0.999451 + 0.0331307i \(0.989452\pi\)
\(558\) −33.6378 12.9421i −1.42400 0.547885i
\(559\) −21.9209 −0.927153
\(560\) 0 0
\(561\) 1.37207 0.0579287
\(562\) −4.13021 1.58910i −0.174223 0.0670322i
\(563\) 0.472513 + 0.472513i 0.0199140 + 0.0199140i 0.716994 0.697080i \(-0.245518\pi\)
−0.697080 + 0.716994i \(0.745518\pi\)
\(564\) 0.0869987 + 1.71060i 0.00366331 + 0.0720292i
\(565\) 0 0
\(566\) 1.68347 + 3.78900i 0.0707614 + 0.159264i
\(567\) 3.35664i 0.140965i
\(568\) 11.6860 + 23.0671i 0.490334 + 0.967874i
\(569\) 3.14792i 0.131967i 0.997821 + 0.0659837i \(0.0210185\pi\)
−0.997821 + 0.0659837i \(0.978981\pi\)
\(570\) 0 0
\(571\) 5.78162 5.78162i 0.241953 0.241953i −0.575704 0.817658i \(-0.695272\pi\)
0.817658 + 0.575704i \(0.195272\pi\)
\(572\) 12.4003 + 11.2000i 0.518481 + 0.468295i
\(573\) −0.104748 0.104748i −0.00437593 0.00437593i
\(574\) −0.720975 + 1.87388i −0.0300929 + 0.0782141i
\(575\) 0 0
\(576\) −19.3007 14.1599i −0.804196 0.589997i
\(577\) −29.0110 −1.20774 −0.603872 0.797081i \(-0.706376\pi\)
−0.603872 + 0.797081i \(0.706376\pi\)
\(578\) 2.34532 6.09570i 0.0975526 0.253548i
\(579\) 0.100588 + 0.100588i 0.00418029 + 0.00418029i
\(580\) 0 0
\(581\) 3.99908 3.99908i 0.165910 0.165910i
\(582\) 0.439696 0.195358i 0.0182260 0.00809786i
\(583\) 14.3762i 0.595403i
\(584\) −9.67359 19.0948i −0.400296 0.790147i
\(585\) 0 0
\(586\) −10.0312 22.5775i −0.414387 0.932666i
\(587\) 20.4099 20.4099i 0.842408 0.842408i −0.146764 0.989172i \(-0.546886\pi\)
0.989172 + 0.146764i \(0.0468857\pi\)
\(588\) 0.0614080 + 1.20743i 0.00253242 + 0.0497934i
\(589\) −20.0123 20.0123i −0.824592 0.824592i
\(590\) 0 0
\(591\) −0.636074 −0.0261646
\(592\) −33.4419 27.2523i −1.37446 1.12006i
\(593\) −28.9098 −1.18718 −0.593592 0.804766i \(-0.702291\pi\)
−0.593592 + 0.804766i \(0.702291\pi\)
\(594\) 2.33394 + 0.897986i 0.0957628 + 0.0368448i
\(595\) 0 0
\(596\) 28.9658 1.47316i 1.18648 0.0603430i
\(597\) 0.695161 0.695161i 0.0284511 0.0284511i
\(598\) 2.97710 + 6.70060i 0.121743 + 0.274008i
\(599\) 11.7893i 0.481696i −0.970563 0.240848i \(-0.922574\pi\)
0.970563 0.240848i \(-0.0774256\pi\)
\(600\) 0 0
\(601\) 17.7398i 0.723621i 0.932252 + 0.361810i \(0.117841\pi\)
−0.932252 + 0.361810i \(0.882159\pi\)
\(602\) −4.26756 + 1.89609i −0.173933 + 0.0772790i
\(603\) −2.90019 + 2.90019i −0.118105 + 0.118105i
\(604\) 25.5282 28.2640i 1.03873 1.15005i
\(605\) 0 0
\(606\) 0.435125 1.13093i 0.0176757 0.0459408i
\(607\) 25.8393 1.04878 0.524392 0.851477i \(-0.324293\pi\)
0.524392 + 0.851477i \(0.324293\pi\)
\(608\) −9.33565 16.3150i −0.378611 0.661662i
\(609\) −0.119665 −0.00484907
\(610\) 0 0
\(611\) −17.1448 17.1448i −0.693605 0.693605i
\(612\) 18.6505 20.6493i 0.753903 0.834697i
\(613\) −31.5411 + 31.5411i −1.27393 + 1.27393i −0.329929 + 0.944006i \(0.607025\pi\)
−0.944006 + 0.329929i \(0.892975\pi\)
\(614\) 19.3625 8.60280i 0.781405 0.347181i
\(615\) 0 0
\(616\) 3.38286 + 1.10783i 0.136299 + 0.0446358i
\(617\) 15.0637i 0.606440i 0.952921 + 0.303220i \(0.0980618\pi\)
−0.952921 + 0.303220i \(0.901938\pi\)
\(618\) −0.0584058 0.131455i −0.00234943 0.00528789i
\(619\) −10.4975 + 10.4975i −0.421929 + 0.421929i −0.885868 0.463938i \(-0.846436\pi\)
0.463938 + 0.885868i \(0.346436\pi\)
\(620\) 0 0
\(621\) 0.775933 + 0.775933i 0.0311371 + 0.0311371i
\(622\) −25.6261 9.85966i −1.02751 0.395336i
\(623\) −5.90545 −0.236597
\(624\) −0.875144 + 0.0892481i −0.0350338 + 0.00357278i
\(625\) 0 0
\(626\) −3.38644 1.30293i −0.135349 0.0520757i
\(627\) 0.693373 + 0.693373i 0.0276906 + 0.0276906i
\(628\) −1.45582 28.6249i −0.0580936 1.14226i
\(629\) 35.4581 35.4581i 1.41381 1.41381i
\(630\) 0 0
\(631\) 43.6349i 1.73708i 0.495621 + 0.868539i \(0.334940\pi\)
−0.495621 + 0.868539i \(0.665060\pi\)
\(632\) −29.7892 + 15.0915i −1.18495 + 0.600308i
\(633\) 0.309581i 0.0123047i
\(634\) −13.3865 + 5.94768i −0.531647 + 0.236213i
\(635\) 0 0
\(636\) 0.561665 + 0.507299i 0.0222714 + 0.0201157i
\(637\) −12.1017 12.1017i −0.479486 0.479486i
\(638\) 6.14194 15.9634i 0.243162 0.631999i
\(639\) −27.3559 −1.08218
\(640\) 0 0
\(641\) −34.2710 −1.35362 −0.676812 0.736156i \(-0.736639\pi\)
−0.676812 + 0.736156i \(0.736639\pi\)
\(642\) −0.361066 + 0.938442i −0.0142501 + 0.0370374i
\(643\) −30.1937 30.1937i −1.19072 1.19072i −0.976865 0.213857i \(-0.931397\pi\)
−0.213857 0.976865i \(-0.568603\pi\)
\(644\) 1.15917 + 1.04697i 0.0456776 + 0.0412562i
\(645\) 0 0
\(646\) 19.9675 8.87163i 0.785611 0.349049i
\(647\) 15.7474i 0.619096i −0.950884 0.309548i \(-0.899822\pi\)
0.950884 0.309548i \(-0.100178\pi\)
\(648\) 22.5318 11.4148i 0.885133 0.448417i
\(649\) 38.4331i 1.50863i
\(650\) 0 0
\(651\) −0.199514 + 0.199514i −0.00781956 + 0.00781956i
\(652\) 1.05665 + 20.7763i 0.0413817 + 0.813661i
\(653\) 5.80619 + 5.80619i 0.227214 + 0.227214i 0.811528 0.584314i \(-0.198636\pi\)
−0.584314 + 0.811528i \(0.698636\pi\)
\(654\) −1.84029 0.708054i −0.0719612 0.0276871i
\(655\) 0 0
\(656\) 15.0304 1.53282i 0.586839 0.0598464i
\(657\) 22.6450 0.883465
\(658\) −4.82074 1.85478i −0.187932 0.0723070i
\(659\) 1.76782 + 1.76782i 0.0688647 + 0.0688647i 0.740700 0.671836i \(-0.234494\pi\)
−0.671836 + 0.740700i \(0.734494\pi\)
\(660\) 0 0
\(661\) −12.4824 + 12.4824i −0.485509 + 0.485509i −0.906886 0.421377i \(-0.861547\pi\)
0.421377 + 0.906886i \(0.361547\pi\)
\(662\) −3.39159 7.63350i −0.131818 0.296685i
\(663\) 1.02253i 0.0397119i
\(664\) −40.4439 13.2447i −1.56953 0.513995i
\(665\) 0 0
\(666\) 41.7070 18.5306i 1.61611 0.718044i
\(667\) 5.30714 5.30714i 0.205493 0.205493i
\(668\) −10.7638 + 11.9173i −0.416464 + 0.461096i
\(669\) 1.31736 + 1.31736i 0.0509322 + 0.0509322i
\(670\) 0 0
\(671\) 3.44872 0.133136
\(672\) −0.162654 + 0.0930723i −0.00627450 + 0.00359034i
\(673\) −14.1113 −0.543950 −0.271975 0.962304i \(-0.587677\pi\)
−0.271975 + 0.962304i \(0.587677\pi\)
\(674\) 6.32447 16.4379i 0.243610 0.633162i
\(675\) 0 0
\(676\) −9.08043 + 10.0536i −0.349247 + 0.386675i
\(677\) −8.31191 + 8.31191i −0.319453 + 0.319453i −0.848557 0.529104i \(-0.822528\pi\)
0.529104 + 0.848557i \(0.322528\pi\)
\(678\) 0.464918 0.206565i 0.0178551 0.00793306i
\(679\) 1.45096i 0.0556827i
\(680\) 0 0
\(681\) 1.80587i 0.0692011i
\(682\) −16.3751 36.8556i −0.627034 1.41127i
\(683\) −30.0811 + 30.0811i −1.15102 + 1.15102i −0.164673 + 0.986348i \(0.552657\pi\)
−0.986348 + 0.164673i \(0.947343\pi\)
\(684\) 19.8601 1.01006i 0.759372 0.0386206i
\(685\) 0 0
\(686\) −6.87553 2.64537i −0.262509 0.101001i
\(687\) 1.25834 0.0480086
\(688\) 27.2403 + 22.1985i 1.03853 + 0.846310i
\(689\) −10.7139 −0.408167
\(690\) 0 0
\(691\) 24.0212 + 24.0212i 0.913810 + 0.913810i 0.996570 0.0827600i \(-0.0263735\pi\)
−0.0827600 + 0.996570i \(0.526373\pi\)
\(692\) 1.49879 + 29.4698i 0.0569756 + 1.12027i
\(693\) −2.66282 + 2.66282i −0.101152 + 0.101152i
\(694\) 14.2198 + 32.0046i 0.539775 + 1.21488i
\(695\) 0 0
\(696\) 0.406942 + 0.803266i 0.0154251 + 0.0304477i
\(697\) 17.5618i 0.665200i
\(698\) 15.3902 6.83790i 0.582526 0.258818i
\(699\) −0.215004 + 0.215004i −0.00813219 + 0.00813219i
\(700\) 0 0
\(701\) 10.0971 + 10.0971i 0.381363 + 0.381363i 0.871593 0.490230i \(-0.163087\pi\)
−0.490230 + 0.871593i \(0.663087\pi\)
\(702\) 0.669225 1.73937i 0.0252583 0.0656484i
\(703\) 35.8375 1.35164
\(704\) −4.06756 26.4752i −0.153302 0.997822i
\(705\) 0 0
\(706\) 4.93251 12.8200i 0.185637 0.482487i
\(707\) 2.58392 + 2.58392i 0.0971782 + 0.0971782i
\(708\) −1.50154 1.35620i −0.0564314 0.0509692i
\(709\) −4.67310 + 4.67310i −0.175502 + 0.175502i −0.789392 0.613890i \(-0.789604\pi\)
0.613890 + 0.789392i \(0.289604\pi\)
\(710\) 0 0
\(711\) 35.3279i 1.32490i
\(712\) 20.0825 + 39.6410i 0.752625 + 1.48561i
\(713\) 17.6968i 0.662752i
\(714\) −0.0884462 0.199067i −0.00331002 0.00744990i
\(715\) 0 0
\(716\) 1.19282 + 23.4536i 0.0445776 + 0.876500i
\(717\) −1.12215 1.12215i −0.0419074 0.0419074i
\(718\) 8.94293 + 3.44080i 0.333747 + 0.128409i
\(719\) −23.5339 −0.877667 −0.438833 0.898568i \(-0.644608\pi\)
−0.438833 + 0.898568i \(0.644608\pi\)
\(720\) 0 0
\(721\) 0.433789 0.0161552
\(722\) −10.5041 4.04145i −0.390921 0.150407i
\(723\) −0.786710 0.786710i −0.0292581 0.0292581i
\(724\) 29.5958 1.50520i 1.09992 0.0559404i
\(725\) 0 0
\(726\) 0.0106603 + 0.0239933i 0.000395641 + 0.000890474i
\(727\) 16.6692i 0.618226i −0.951025 0.309113i \(-0.899968\pi\)
0.951025 0.309113i \(-0.100032\pi\)
\(728\) 0.825612 2.52108i 0.0305992 0.0934373i
\(729\) 26.5814i 0.984498i
\(730\) 0 0
\(731\) −28.8826 + 28.8826i −1.06826 + 1.06826i
\(732\) −0.121696 + 0.134738i −0.00449801 + 0.00498005i
\(733\) 27.4684 + 27.4684i 1.01457 + 1.01457i 0.999892 + 0.0146760i \(0.00467168\pi\)
0.0146760 + 0.999892i \(0.495328\pi\)
\(734\) −17.4993 + 45.4823i −0.645912 + 1.67878i
\(735\) 0 0
\(736\) 3.08593 11.3414i 0.113749 0.418051i
\(737\) −4.58945 −0.169055
\(738\) −5.73944 + 14.9173i −0.211272 + 0.549114i
\(739\) 22.7939 + 22.7939i 0.838486 + 0.838486i 0.988660 0.150174i \(-0.0479832\pi\)
−0.150174 + 0.988660i \(0.547983\pi\)
\(740\) 0 0
\(741\) 0.516736 0.516736i 0.0189828 0.0189828i
\(742\) −2.08579 + 0.926722i −0.0765717 + 0.0340210i
\(743\) 16.4964i 0.605196i −0.953118 0.302598i \(-0.902146\pi\)
0.953118 0.302598i \(-0.0978539\pi\)
\(744\) 2.01774 + 0.660778i 0.0739740 + 0.0242253i
\(745\) 0 0
\(746\) −2.88434 6.49181i −0.105603 0.237682i
\(747\) 31.8354 31.8354i 1.16480 1.16480i
\(748\) 31.0954 1.58147i 1.13696 0.0578242i
\(749\) −2.14413 2.14413i −0.0783449 0.0783449i
\(750\) 0 0
\(751\) −21.6997 −0.791833 −0.395917 0.918286i \(-0.629573\pi\)
−0.395917 + 0.918286i \(0.629573\pi\)
\(752\) 3.94333 + 38.6673i 0.143798 + 1.41005i
\(753\) 1.14411 0.0416937
\(754\) −11.8968 4.57729i −0.433254 0.166695i
\(755\) 0 0
\(756\) −0.0201658 0.396508i −0.000733425 0.0144209i
\(757\) −1.73819 + 1.73819i −0.0631757 + 0.0631757i −0.737989 0.674813i \(-0.764224\pi\)
0.674813 + 0.737989i \(0.264224\pi\)
\(758\) −21.4761 48.3366i −0.780047 1.75566i
\(759\) 0.613149i 0.0222559i
\(760\) 0 0
\(761\) 46.5311i 1.68675i 0.537323 + 0.843376i \(0.319435\pi\)
−0.537323 + 0.843376i \(0.680565\pi\)
\(762\) −1.94684 + 0.864989i −0.0705266 + 0.0313352i
\(763\) 4.20467 4.20467i 0.152219 0.152219i
\(764\) −2.49467 2.25320i −0.0902538 0.0815178i
\(765\) 0 0
\(766\) 15.6723 40.7337i 0.566264 1.47177i
\(767\) 28.6423 1.03421
\(768\) 1.17789 + 0.775323i 0.0425035 + 0.0279770i
\(769\) 15.4731 0.557976 0.278988 0.960295i \(-0.410001\pi\)
0.278988 + 0.960295i \(0.410001\pi\)
\(770\) 0 0
\(771\) −1.01519 1.01519i −0.0365610 0.0365610i
\(772\) 2.39558 + 2.16370i 0.0862187 + 0.0778732i
\(773\) 5.69848 5.69848i 0.204960 0.204960i −0.597161 0.802121i \(-0.703705\pi\)
0.802121 + 0.597161i \(0.203705\pi\)
\(774\) −33.9727 + 15.0942i −1.22112 + 0.542549i
\(775\) 0 0
\(776\) 9.73972 4.93424i 0.349636 0.177129i
\(777\) 0.357284i 0.0128175i
\(778\) −7.72237 17.3808i −0.276860 0.623134i
\(779\) −8.87484 + 8.87484i −0.317974 + 0.317974i
\(780\) 0 0
\(781\) −21.6449 21.6449i −0.774516 0.774516i
\(782\) 12.7512 + 4.90603i 0.455982 + 0.175439i