Properties

Label 400.2.l.g.301.2
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 301.2
Root \(-0.507829 + 1.31989i\) of defining polynomial
Character \(\chi\) \(=\) 400.301
Dual form 400.2.l.g.101.2

$q$-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 0.724868 0.688887i \(-0.241901\pi\)
−0.688887 + 0.724868i \(0.741901\pi\)
\(4\) −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 \(0.0226299\pi\)
−0.997474 + 0.0710340i \(0.977370\pi\)
\(8\) 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 0.908105 0.418742i \(-0.137529\pi\)
−0.418742 + 0.908105i \(0.637529\pi\)
\(14\) −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 \(-0.309323\pi\)
0.563841 + 0.825883i \(0.309323\pi\)
\(18\) 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 \(0.0695048\pi\)
−0.976255 + 0.216625i \(0.930495\pi\)
\(24\) 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 \(-0.403116\pi\)
0.954036 0.299691i \(-0.0968837\pi\)
\(38\) 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 −0.998680 0.0513725i \(-0.983640\pi\)
0.0513725 + 0.998680i \(0.483640\pi\)
\(44\) −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 \(-0.750710\pi\)
−0.708682 + 0.705528i \(0.750710\pi\)
\(48\) −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 −0.884182 0.467143i \(-0.845283\pi\)
0.467143 + 0.884182i \(0.345283\pi\)
\(54\) 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 0.763829 0.645418i \(-0.223317\pi\)
−0.645418 + 0.763829i \(0.723317\pi\)
\(68\) −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 \(-0.853957\pi\)
0.896581 0.442879i \(-0.146043\pi\)
\(74\) 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 \(-0.940739\pi\)
−0.185101 0.982720i \(-0.559261\pi\)
\(84\) 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 \(-0.437214\pi\)
0.195972 + 0.980610i \(0.437214\pi\)
\(98\) −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 \(-0.981892\pi\)
0.998382 0.0568571i \(-0.0181079\pi\)
\(104\) 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 −0.926862 0.375402i \(-0.877505\pi\)
0.375402 + 0.926862i \(0.377505\pi\)
\(108\) −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 \(-0.438508\pi\)
0.191984 + 0.981398i \(0.438508\pi\)
\(114\) 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 \(-0.773982\pi\)
−0.758326 + 0.651876i \(0.773982\pi\)
\(128\) 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 \(0.252830\pi\)
−0.700792 + 0.713366i \(0.747170\pi\)
\(138\) −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 0.175702 0.984443i \(-0.443780\pi\)
−0.984443 + 0.175702i \(0.943780\pi\)
\(158\) −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 0.933823 0.357735i \(-0.116451\pi\)
−0.357735 + 0.933823i \(0.616451\pi\)
\(164\) −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 \(0.100552\pi\)
−0.950519 + 0.310665i \(0.899448\pi\)
\(168\) −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 0.982009 0.188832i \(-0.0604702\pi\)
−0.188832 + 0.982009i \(0.560470\pi\)
\(174\) −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 \(-0.481499\pi\)
0.0580903 + 0.998311i \(0.481499\pi\)
\(194\) −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 −0.865133 0.501543i \(-0.832766\pi\)
0.501543 + 0.865133i \(0.332766\pi\)
\(198\) 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 \(-0.249703\pi\)
0.707765 + 0.706448i \(0.249703\pi\)
\(224\) 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 0.999291 0.0376566i \(-0.0119893\pi\)
−0.0376566 + 0.999291i \(0.511989\pi\)
\(228\) −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 \(0.0360482\pi\)
−0.993594 + 0.113007i \(0.963952\pi\)
\(234\) 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 \(-0.669637\pi\)
−0.508061 + 0.861321i \(0.669637\pi\)
\(258\) 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 \(-0.895169\pi\)
0.946257 0.323416i \(-0.104831\pi\)
\(264\) 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 −0.930058 0.367412i \(-0.880244\pi\)
0.367412 + 0.930058i \(0.380244\pi\)
\(278\) −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 −0.642801 0.766033i \(-0.722228\pi\)
0.766033 + 0.642801i \(0.222228\pi\)
\(284\) −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 −0.968943 0.247284i \(-0.920462\pi\)
0.247284 + 0.968943i \(0.420462\pi\)
\(294\) −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 0.336916 0.941535i \(-0.390616\pi\)
−0.941535 + 0.336916i \(0.890616\pi\)
\(308\) −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 \(0.0231012\pi\)
−0.997368 + 0.0725108i \(0.976899\pi\)
\(314\) 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 0.882215 0.470848i \(-0.156052\pi\)
−0.470848 + 0.882215i \(0.656052\pi\)
\(318\) 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 \(-0.610158\pi\)
−0.339205 + 0.940712i \(0.610158\pi\)
\(338\) 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 −0.0582766 0.998300i \(-0.518561\pi\)
0.998300 + 0.0582766i \(0.0185605\pi\)
\(348\) 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 \(-0.583223\pi\)
−0.258484 + 0.966016i \(0.583223\pi\)
\(354\) 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 \(-0.144021\pi\)
0.899376 + 0.437176i \(0.144021\pi\)
\(368\) −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 −0.793057 0.609148i \(-0.791512\pi\)
0.609148 + 0.793057i \(0.291512\pi\)
\(374\) 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 \(-0.789128\pi\)
−0.788473 + 0.615069i \(0.789128\pi\)
\(384\) −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 \(-0.906172\pi\)
−0.290518 0.956870i \(-0.593828\pi\)
\(398\) −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 \(-0.694261\pi\)
−0.573104 + 0.819482i \(0.694261\pi\)
\(434\) −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 −0.468298 0.883571i \(-0.655133\pi\)
0.883571 + 0.468298i \(0.155133\pi\)
\(444\) −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 \(-0.799184\pi\)
0.807508 0.589857i \(-0.200816\pi\)
\(458\) −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 \(-0.479494\pi\)
0.0643768 + 0.997926i \(0.479494\pi\)
\(464\) −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 0.156627 0.987658i \(-0.449938\pi\)
−0.987658 + 0.156627i \(0.949938\pi\)
\(468\) −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 \(0.216534\pi\)
−0.777408 + 0.628997i \(0.783466\pi\)
\(488\) 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 \(-0.609913\pi\)
0.338482 0.940973i \(-0.390087\pi\)
\(504\) 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 −0.884840 0.465895i \(-0.845732\pi\)
0.465895 + 0.884840i \(0.345732\pi\)
\(524\) 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 0.441406 0.897308i \(-0.354480\pi\)
−0.897308 + 0.441406i \(0.854480\pi\)
\(548\) 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 0.999451 0.0331307i \(-0.0105477\pi\)
−0.0331307 + 0.999451i \(0.510548\pi\)
\(558\) 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 0.697080 0.716994i \(-0.254482\pi\)
−0.716994 + 0.697080i \(0.754482\pi\)
\(564\) 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 \(-0.293624\pi\)
0.603872 + 0.797081i \(0.293624\pi\)
\(578\) −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 −0.989172 0.146764i \(-0.953114\pi\)
0.146764 + 0.989172i \(0.453114\pi\)
\(588\) −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 \(-0.297709\pi\)
0.593592 + 0.804766i \(0.297709\pi\)
\(594\) 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 \(-0.675707\pi\)
−0.524392 + 0.851477i \(0.675707\pi\)
\(608\) 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 \(-0.392975\pi\)
0.944006 0.329929i \(-0.107025\pi\)
\(614\) 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 \(-0.901938\pi\)
0.952921 0.303220i \(-0.0980618\pi\)
\(618\) 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 \(0.0686027\pi\)
0.213857 + 0.976865i \(0.431397\pi\)
\(644\) 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 \(0.100178\pi\)
−0.950884 + 0.309548i \(0.899822\pi\)
\(648\) −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 0.584314 0.811528i \(-0.301364\pi\)
−0.811528 + 0.584314i \(0.801364\pi\)
\(654\) −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 \(-0.412323\pi\)
0.271975 + 0.962304i \(0.412323\pi\)
\(674\) 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 −0.529104 0.848557i \(-0.677472\pi\)
0.848557 + 0.529104i \(0.177472\pi\)
\(678\) −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 \(-0.447343\pi\)
0.986348 0.164673i \(-0.0526570\pi\)
\(684\) 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 \(0.100032\pi\)
−0.951025 + 0.309113i \(0.899968\pi\)
\(728\) −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 \(-0.995328\pi\)
−0.0146760 0.999892i \(-0.504672\pi\)
\(734\) −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 \(0.0978539\pi\)
−0.953118 + 0.302598i \(0.902146\pi\)
\(744\) 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 −0.674813 0.737989i \(-0.735776\pi\)
0.737989 + 0.674813i \(0.235776\pi\)
\(758\) 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 −0.802121 0.597161i \(-0.796295\pi\)
0.597161 + 0.802121i \(0.296295\pi\)
\(774\) −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
\(783\) 1.90770