Properties

Label 637.2.k.i.459.5
Level $637$
Weight $2$
Character 637.459
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 459.5
Root \(0.874681 - 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 637.459
Dual form 637.2.k.i.569.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.34523i q^{2} +(1.02505 + 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +O(q^{10})\) \(q+1.34523i q^{2} +(1.02505 + 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +(-2.39973 - 4.15646i) q^{10} +(-1.10736 + 0.639336i) q^{11} +(0.195135 + 0.337984i) q^{12} +(-3.57420 - 0.474474i) q^{13} +(-6.33438 - 3.65716i) q^{15} -3.58303 q^{16} +7.73920 q^{17} +(-1.40141 - 0.809103i) q^{18} +(-0.817422 - 0.471939i) q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} -1.64727 q^{23} +(-5.23141 + 3.02035i) q^{24} +(3.86451 - 6.69354i) q^{25} +(0.638275 - 4.80810i) q^{26} +3.68419 q^{27} +(-2.02242 + 3.50293i) q^{29} +(4.91970 - 8.52117i) q^{30} +(-4.46193 - 2.57610i) q^{31} +1.07309i q^{32} +(-2.27021 - 1.31071i) q^{33} +10.4110i q^{34} +(-0.114498 + 0.198317i) q^{36} +1.05608i q^{37} +(0.634865 - 1.09962i) q^{38} +(-2.82133 - 6.83214i) q^{39} +(-5.25629 - 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(-0.210805 + 0.121708i) q^{44} -4.29176i q^{45} -2.21596i q^{46} +(-0.774415 + 0.447109i) q^{47} +(-3.67279 - 6.36146i) q^{48} +(9.00432 + 5.19865i) q^{50} +(7.93308 + 13.7405i) q^{51} +(-0.680407 - 0.0903239i) q^{52} +(0.0399961 - 0.0692754i) q^{53} +4.95607i q^{54} +(2.28101 - 3.95082i) q^{55} -1.93505i q^{57} +(-4.71224 - 2.72061i) q^{58} +11.1847i q^{59} +(-1.20585 - 0.696200i) q^{60} +(-3.81196 + 6.60251i) q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(11.8899 - 4.90994i) q^{65} +(1.76319 - 3.05394i) q^{66} +(5.47418 - 3.16052i) q^{67} +1.47328 q^{68} +(-1.68854 - 2.92464i) q^{69} +(9.89346 - 5.71199i) q^{71} +(-3.06959 - 1.77223i) q^{72} +(-0.658617 - 0.380253i) q^{73} -1.42067 q^{74} +15.8453 q^{75} +(-0.155610 - 0.0898413i) q^{76} +(9.19077 - 3.79533i) q^{78} +(1.42765 + 2.47277i) q^{79} +(11.0708 - 6.39172i) q^{80} +(5.58087 + 9.66636i) q^{81} +(-2.82418 + 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(-4.46270 + 2.57654i) q^{86} -8.29233 q^{87} +(-1.88383 - 3.26289i) q^{88} -7.57626i q^{89} +5.77339 q^{90} -0.313586 q^{92} -10.5625i q^{93} +(-0.601462 - 1.04176i) q^{94} +3.36755 q^{95} +(-1.90522 + 1.09998i) q^{96} +(0.414443 - 0.239279i) q^{97} -1.53815i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} + O(q^{10}) \) \( 12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} - 12q^{10} + 12q^{11} + q^{12} + 2q^{13} - 12q^{15} + 16q^{16} + 34q^{17} + 3q^{18} - 9q^{19} + 3q^{20} - 15q^{22} - 6q^{23} - 15q^{24} - 5q^{25} + 6q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{31} + 6q^{33} - 13q^{36} - 19q^{38} - 4q^{39} + q^{40} + 6q^{41} + 11q^{43} - 33q^{44} + 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} + 7q^{52} - 8q^{53} + 15q^{55} - 24q^{58} - 30q^{60} - 5q^{61} - 41q^{62} + 2q^{64} + 21q^{65} + 34q^{66} + 15q^{67} - 22q^{68} - 7q^{69} + 30q^{71} + 57q^{72} - 42q^{73} + 66q^{74} + 2q^{75} + 45q^{76} + 44q^{78} - 35q^{79} + 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 57q^{86} + 20q^{87} - 14q^{88} - 66q^{92} - q^{94} - 4q^{95} - 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34523i 0.951219i 0.879657 + 0.475609i \(0.157772\pi\)
−0.879657 + 0.475609i \(0.842228\pi\)
\(3\) 1.02505 + 1.77544i 0.591814 + 1.02505i 0.993988 + 0.109489i \(0.0349213\pi\)
−0.402174 + 0.915563i \(0.631745\pi\)
\(4\) 0.190366 0.0951832
\(5\) −3.08979 + 1.78389i −1.38179 + 0.797779i −0.992372 0.123280i \(-0.960659\pi\)
−0.389422 + 0.921059i \(0.627325\pi\)
\(6\) −2.38837 + 1.37893i −0.975048 + 0.562944i
\(7\) 0 0
\(8\) 2.94654i 1.04176i
\(9\) −0.601462 + 1.04176i −0.200487 + 0.347254i
\(10\) −2.39973 4.15646i −0.758862 1.31439i
\(11\) −1.10736 + 0.639336i −0.333882 + 0.192767i −0.657563 0.753399i \(-0.728413\pi\)
0.323681 + 0.946166i \(0.395080\pi\)
\(12\) 0.195135 + 0.337984i 0.0563307 + 0.0975677i
\(13\) −3.57420 0.474474i −0.991304 0.131595i
\(14\) 0 0
\(15\) −6.33438 3.65716i −1.63553 0.944273i
\(16\) −3.58303 −0.895757
\(17\) 7.73920 1.87703 0.938515 0.345238i \(-0.112202\pi\)
0.938515 + 0.345238i \(0.112202\pi\)
\(18\) −1.40141 0.809103i −0.330315 0.190707i
\(19\) −0.817422 0.471939i −0.187530 0.108270i 0.403296 0.915070i \(-0.367865\pi\)
−0.590826 + 0.806799i \(0.701198\pi\)
\(20\) −0.588191 + 0.339592i −0.131524 + 0.0759352i
\(21\) 0 0
\(22\) −0.860052 1.48965i −0.183364 0.317595i
\(23\) −1.64727 −0.343481 −0.171740 0.985142i \(-0.554939\pi\)
−0.171740 + 0.985142i \(0.554939\pi\)
\(24\) −5.23141 + 3.02035i −1.06786 + 0.616527i
\(25\) 3.86451 6.69354i 0.772903 1.33871i
\(26\) 0.638275 4.80810i 0.125176 0.942946i
\(27\) 3.68419 0.709023
\(28\) 0 0
\(29\) −2.02242 + 3.50293i −0.375554 + 0.650478i −0.990410 0.138161i \(-0.955881\pi\)
0.614856 + 0.788639i \(0.289214\pi\)
\(30\) 4.91970 8.52117i 0.898210 1.55575i
\(31\) −4.46193 2.57610i −0.801387 0.462681i 0.0425691 0.999094i \(-0.486446\pi\)
−0.843956 + 0.536413i \(0.819779\pi\)
\(32\) 1.07309i 0.189698i
\(33\) −2.27021 1.31071i −0.395192 0.228164i
\(34\) 10.4110i 1.78547i
\(35\) 0 0
\(36\) −0.114498 + 0.198317i −0.0190830 + 0.0330528i
\(37\) 1.05608i 0.173619i 0.996225 + 0.0868094i \(0.0276671\pi\)
−0.996225 + 0.0868094i \(0.972333\pi\)
\(38\) 0.634865 1.09962i 0.102989 0.178382i
\(39\) −2.82133 6.83214i −0.451775 1.09402i
\(40\) −5.25629 9.10417i −0.831093 1.43950i
\(41\) 3.63629 + 2.09941i 0.567893 + 0.327873i 0.756307 0.654217i \(-0.227002\pi\)
−0.188415 + 0.982090i \(0.560335\pi\)
\(42\) 0 0
\(43\) 1.91532 + 3.31744i 0.292084 + 0.505904i 0.974302 0.225244i \(-0.0723180\pi\)
−0.682218 + 0.731148i \(0.738985\pi\)
\(44\) −0.210805 + 0.121708i −0.0317800 + 0.0183482i
\(45\) 4.29176i 0.639778i
\(46\) 2.21596i 0.326725i
\(47\) −0.774415 + 0.447109i −0.112960 + 0.0652175i −0.555416 0.831573i \(-0.687441\pi\)
0.442456 + 0.896790i \(0.354107\pi\)
\(48\) −3.67279 6.36146i −0.530121 0.918197i
\(49\) 0 0
\(50\) 9.00432 + 5.19865i 1.27340 + 0.735200i
\(51\) 7.93308 + 13.7405i 1.11085 + 1.92405i
\(52\) −0.680407 0.0903239i −0.0943554 0.0125257i
\(53\) 0.0399961 0.0692754i 0.00549389 0.00951570i −0.863265 0.504750i \(-0.831585\pi\)
0.868759 + 0.495235i \(0.164918\pi\)
\(54\) 4.95607i 0.674436i
\(55\) 2.28101 3.95082i 0.307571 0.532729i
\(56\) 0 0
\(57\) 1.93505i 0.256303i
\(58\) −4.71224 2.72061i −0.618747 0.357234i
\(59\) 11.1847i 1.45613i 0.685509 + 0.728064i \(0.259580\pi\)
−0.685509 + 0.728064i \(0.740420\pi\)
\(60\) −1.20585 0.696200i −0.155675 0.0898790i
\(61\) −3.81196 + 6.60251i −0.488072 + 0.845365i −0.999906 0.0137195i \(-0.995633\pi\)
0.511834 + 0.859084i \(0.328966\pi\)
\(62\) 3.46543 6.00231i 0.440111 0.762294i
\(63\) 0 0
\(64\) −8.60961 −1.07620
\(65\) 11.8899 4.90994i 1.47476 0.609003i
\(66\) 1.76319 3.05394i 0.217034 0.375914i
\(67\) 5.47418 3.16052i 0.668777 0.386119i −0.126836 0.991924i \(-0.540482\pi\)
0.795613 + 0.605805i \(0.207149\pi\)
\(68\) 1.47328 0.178662
\(69\) −1.68854 2.92464i −0.203277 0.352085i
\(70\) 0 0
\(71\) 9.89346 5.71199i 1.17414 0.677889i 0.219487 0.975616i \(-0.429562\pi\)
0.954651 + 0.297727i \(0.0962285\pi\)
\(72\) −3.06959 1.77223i −0.361755 0.208859i
\(73\) −0.658617 0.380253i −0.0770853 0.0445052i 0.460962 0.887420i \(-0.347504\pi\)
−0.538047 + 0.842915i \(0.680838\pi\)
\(74\) −1.42067 −0.165149
\(75\) 15.8453 1.82966
\(76\) −0.155610 0.0898413i −0.0178497 0.0103055i
\(77\) 0 0
\(78\) 9.19077 3.79533i 1.04065 0.429737i
\(79\) 1.42765 + 2.47277i 0.160624 + 0.278208i 0.935093 0.354404i \(-0.115316\pi\)
−0.774469 + 0.632612i \(0.781983\pi\)
\(80\) 11.0708 6.39172i 1.23775 0.714616i
\(81\) 5.58087 + 9.66636i 0.620097 + 1.07404i
\(82\) −2.82418 + 4.89163i −0.311879 + 0.540190i
\(83\) 2.32483i 0.255183i 0.991827 + 0.127591i \(0.0407246\pi\)
−0.991827 + 0.127591i \(0.959275\pi\)
\(84\) 0 0
\(85\) −23.9125 + 13.8059i −2.59367 + 1.49746i
\(86\) −4.46270 + 2.57654i −0.481226 + 0.277836i
\(87\) −8.29233 −0.889032
\(88\) −1.88383 3.26289i −0.200817 0.347825i
\(89\) 7.57626i 0.803082i −0.915841 0.401541i \(-0.868475\pi\)
0.915841 0.401541i \(-0.131525\pi\)
\(90\) 5.77339 0.608569
\(91\) 0 0
\(92\) −0.313586 −0.0326936
\(93\) 10.5625i 1.09528i
\(94\) −0.601462 1.04176i −0.0620361 0.107450i
\(95\) 3.36755 0.345503
\(96\) −1.90522 + 1.09998i −0.194450 + 0.112266i
\(97\) 0.414443 0.239279i 0.0420803 0.0242951i −0.478812 0.877917i \(-0.658933\pi\)
0.520893 + 0.853622i \(0.325599\pi\)
\(98\) 0 0
\(99\) 1.53815i 0.154589i
\(100\) 0.735674 1.27422i 0.0735674 0.127422i
\(101\) −1.43918 2.49273i −0.143204 0.248036i 0.785498 0.618865i \(-0.212407\pi\)
−0.928701 + 0.370829i \(0.879074\pi\)
\(102\) −18.4841 + 10.6718i −1.83020 + 1.05666i
\(103\) 5.66755 + 9.81649i 0.558441 + 0.967248i 0.997627 + 0.0688516i \(0.0219335\pi\)
−0.439186 + 0.898396i \(0.644733\pi\)
\(104\) 1.39806 10.5315i 0.137091 1.03270i
\(105\) 0 0
\(106\) 0.0931910 + 0.0538039i 0.00905151 + 0.00522589i
\(107\) −6.57206 −0.635345 −0.317673 0.948200i \(-0.602901\pi\)
−0.317673 + 0.948200i \(0.602901\pi\)
\(108\) 0.701346 0.0674871
\(109\) −5.05684 2.91957i −0.484358 0.279644i 0.237873 0.971296i \(-0.423550\pi\)
−0.722231 + 0.691652i \(0.756883\pi\)
\(110\) 5.31475 + 3.06847i 0.506741 + 0.292567i
\(111\) −1.87501 + 1.08254i −0.177968 + 0.102750i
\(112\) 0 0
\(113\) −3.26617 5.65717i −0.307255 0.532181i 0.670506 0.741904i \(-0.266077\pi\)
−0.977761 + 0.209723i \(0.932744\pi\)
\(114\) 2.60308 0.243800
\(115\) 5.08973 2.93855i 0.474619 0.274022i
\(116\) −0.385001 + 0.666841i −0.0357464 + 0.0619146i
\(117\) 2.64403 3.43809i 0.244441 0.317851i
\(118\) −15.0460 −1.38510
\(119\) 0 0
\(120\) 10.7759 18.6645i 0.983705 1.70383i
\(121\) −4.68250 + 8.11033i −0.425682 + 0.737302i
\(122\) −8.88187 5.12795i −0.804127 0.464263i
\(123\) 8.60802i 0.776159i
\(124\) −0.849402 0.490402i −0.0762786 0.0440394i
\(125\) 9.73656i 0.870865i
\(126\) 0 0
\(127\) 7.35818 12.7447i 0.652932 1.13091i −0.329475 0.944164i \(-0.606872\pi\)
0.982408 0.186748i \(-0.0597948\pi\)
\(128\) 9.43568i 0.834005i
\(129\) −3.92661 + 6.80109i −0.345719 + 0.598802i
\(130\) 6.60498 + 15.9946i 0.579295 + 1.40282i
\(131\) 5.59335 + 9.68796i 0.488693 + 0.846441i 0.999915 0.0130074i \(-0.00414049\pi\)
−0.511222 + 0.859448i \(0.670807\pi\)
\(132\) −0.432171 0.249514i −0.0376157 0.0217174i
\(133\) 0 0
\(134\) 4.25161 + 7.36400i 0.367283 + 0.636153i
\(135\) −11.3834 + 6.57219i −0.979724 + 0.565644i
\(136\) 22.8038i 1.95541i
\(137\) 17.6308i 1.50630i 0.657848 + 0.753151i \(0.271467\pi\)
−0.657848 + 0.753151i \(0.728533\pi\)
\(138\) 3.93430 2.27147i 0.334910 0.193360i
\(139\) −2.92855 5.07240i −0.248396 0.430235i 0.714685 0.699447i \(-0.246570\pi\)
−0.963081 + 0.269212i \(0.913237\pi\)
\(140\) 0 0
\(141\) −1.58763 0.916619i −0.133703 0.0771932i
\(142\) 7.68392 + 13.3089i 0.644820 + 1.11686i
\(143\) 4.26128 1.75970i 0.356346 0.147153i
\(144\) 2.15506 3.73267i 0.179588 0.311055i
\(145\) 14.4311i 1.19844i
\(146\) 0.511526 0.885989i 0.0423342 0.0733250i
\(147\) 0 0
\(148\) 0.201043i 0.0165256i
\(149\) 9.07505 + 5.23948i 0.743457 + 0.429235i 0.823325 0.567570i \(-0.192116\pi\)
−0.0798677 + 0.996805i \(0.525450\pi\)
\(150\) 21.3155i 1.74041i
\(151\) −4.08249 2.35703i −0.332229 0.191812i 0.324602 0.945851i \(-0.394770\pi\)
−0.656830 + 0.754039i \(0.728103\pi\)
\(152\) 1.39059 2.40857i 0.112791 0.195361i
\(153\) −4.65483 + 8.06241i −0.376321 + 0.651807i
\(154\) 0 0
\(155\) 18.3819 1.47647
\(156\) −0.537087 1.30061i −0.0430014 0.104132i
\(157\) 4.50105 7.79604i 0.359223 0.622192i −0.628608 0.777722i \(-0.716375\pi\)
0.987831 + 0.155530i \(0.0497085\pi\)
\(158\) −3.32643 + 1.92052i −0.264637 + 0.152788i
\(159\) 0.163992 0.0130054
\(160\) −1.91428 3.31563i −0.151337 0.262123i
\(161\) 0 0
\(162\) −13.0034 + 7.50754i −1.02165 + 0.589848i
\(163\) 10.4203 + 6.01619i 0.816185 + 0.471224i 0.849099 0.528234i \(-0.177146\pi\)
−0.0329144 + 0.999458i \(0.510479\pi\)
\(164\) 0.692227 + 0.399657i 0.0540538 + 0.0312080i
\(165\) 9.35261 0.728099
\(166\) −3.12742 −0.242735
\(167\) 16.8199 + 9.71099i 1.30157 + 0.751459i 0.980672 0.195657i \(-0.0626838\pi\)
0.320893 + 0.947116i \(0.396017\pi\)
\(168\) 0 0
\(169\) 12.5497 + 3.39173i 0.965365 + 0.260902i
\(170\) −18.5720 32.1677i −1.42441 2.46715i
\(171\) 0.983297 0.567707i 0.0751946 0.0434136i
\(172\) 0.364613 + 0.631528i 0.0278015 + 0.0481536i
\(173\) −7.18976 + 12.4530i −0.546627 + 0.946786i 0.451875 + 0.892081i \(0.350755\pi\)
−0.998503 + 0.0547049i \(0.982578\pi\)
\(174\) 11.1551i 0.845663i
\(175\) 0 0
\(176\) 3.96771 2.29076i 0.299077 0.172672i
\(177\) −19.8578 + 11.4649i −1.49261 + 0.861757i
\(178\) 10.1918 0.763907
\(179\) 2.71303 + 4.69911i 0.202781 + 0.351228i 0.949424 0.313998i \(-0.101669\pi\)
−0.746642 + 0.665226i \(0.768335\pi\)
\(180\) 0.817008i 0.0608962i
\(181\) 15.4902 1.15138 0.575688 0.817669i \(-0.304734\pi\)
0.575688 + 0.817669i \(0.304734\pi\)
\(182\) 0 0
\(183\) −15.6298 −1.15539
\(184\) 4.85376i 0.357824i
\(185\) −1.88393 3.26307i −0.138509 0.239905i
\(186\) 14.2090 1.04185
\(187\) −8.57010 + 4.94795i −0.626707 + 0.361830i
\(188\) −0.147423 + 0.0851144i −0.0107519 + 0.00620761i
\(189\) 0 0
\(190\) 4.53011i 0.328649i
\(191\) −2.37311 + 4.11035i −0.171712 + 0.297414i −0.939019 0.343866i \(-0.888263\pi\)
0.767306 + 0.641281i \(0.221597\pi\)
\(192\) −8.82529 15.2859i −0.636911 1.10316i
\(193\) 18.2204 10.5196i 1.31154 0.757215i 0.329185 0.944266i \(-0.393226\pi\)
0.982350 + 0.187050i \(0.0598928\pi\)
\(194\) 0.321884 + 0.557519i 0.0231099 + 0.0400276i
\(195\) 20.9051 + 16.0769i 1.49704 + 1.15129i
\(196\) 0 0
\(197\) 5.03342 + 2.90604i 0.358616 + 0.207047i 0.668474 0.743736i \(-0.266948\pi\)
−0.309857 + 0.950783i \(0.600281\pi\)
\(198\) 2.06915 0.147048
\(199\) 10.6182 0.752703 0.376352 0.926477i \(-0.377179\pi\)
0.376352 + 0.926477i \(0.377179\pi\)
\(200\) 19.7228 + 11.3869i 1.39461 + 0.805178i
\(201\) 11.2226 + 6.47939i 0.791583 + 0.457021i
\(202\) 3.35329 1.93602i 0.235936 0.136218i
\(203\) 0 0
\(204\) 1.51019 + 2.61573i 0.105735 + 0.183138i
\(205\) −14.9805 −1.04628
\(206\) −13.2054 + 7.62414i −0.920064 + 0.531199i
\(207\) 0.990773 1.71607i 0.0688635 0.119275i
\(208\) 12.8064 + 1.70005i 0.887967 + 0.117877i
\(209\) 1.20691 0.0834837
\(210\) 0 0
\(211\) 2.33275 4.04043i 0.160593 0.278155i −0.774489 0.632588i \(-0.781993\pi\)
0.935081 + 0.354433i \(0.115326\pi\)
\(212\) 0.00761392 0.0131877i 0.000522926 0.000905735i
\(213\) 20.2826 + 11.7102i 1.38974 + 0.802368i
\(214\) 8.84091i 0.604352i
\(215\) −11.8359 6.83344i −0.807200 0.466037i
\(216\) 10.8556i 0.738631i
\(217\) 0 0
\(218\) 3.92748 6.80260i 0.266003 0.460730i
\(219\) 1.55912i 0.105355i
\(220\) 0.434227 0.752104i 0.0292756 0.0507068i
\(221\) −27.6614 3.67205i −1.86071 0.247009i
\(222\) −1.45626 2.52232i −0.0977377 0.169287i
\(223\) −20.9798 12.1127i −1.40491 0.811126i −0.410020 0.912076i \(-0.634478\pi\)
−0.994891 + 0.100950i \(0.967812\pi\)
\(224\) 0 0
\(225\) 4.64872 + 8.05182i 0.309915 + 0.536788i
\(226\) 7.61017 4.39373i 0.506221 0.292267i
\(227\) 15.3753i 1.02049i −0.860028 0.510247i \(-0.829554\pi\)
0.860028 0.510247i \(-0.170446\pi\)
\(228\) 0.368368i 0.0243958i
\(229\) 14.1608 8.17573i 0.935771 0.540268i 0.0471389 0.998888i \(-0.484990\pi\)
0.888632 + 0.458621i \(0.151656\pi\)
\(230\) 3.95302 + 6.84683i 0.260654 + 0.451467i
\(231\) 0 0
\(232\) −10.3215 5.95913i −0.677641 0.391236i
\(233\) −14.5554 25.2106i −0.953554 1.65160i −0.737643 0.675191i \(-0.764061\pi\)
−0.215911 0.976413i \(-0.569272\pi\)
\(234\) 4.62500 + 3.55682i 0.302346 + 0.232517i
\(235\) 1.59518 2.76294i 0.104058 0.180234i
\(236\) 2.12920i 0.138599i
\(237\) −2.92684 + 5.06943i −0.190119 + 0.329295i
\(238\) 0 0
\(239\) 8.65409i 0.559787i 0.960031 + 0.279893i \(0.0902991\pi\)
−0.960031 + 0.279893i \(0.909701\pi\)
\(240\) 22.6963 + 13.1037i 1.46504 + 0.845840i
\(241\) 18.1982i 1.17225i 0.810222 + 0.586124i \(0.199347\pi\)
−0.810222 + 0.586124i \(0.800653\pi\)
\(242\) −10.9102 6.29902i −0.701336 0.404916i
\(243\) −5.91508 + 10.2452i −0.379453 + 0.657231i
\(244\) −0.725669 + 1.25690i −0.0464562 + 0.0804645i
\(245\) 0 0
\(246\) −11.5797 −0.738297
\(247\) 2.69770 + 2.07465i 0.171651 + 0.132007i
\(248\) 7.59057 13.1473i 0.482002 0.834851i
\(249\) −4.12759 + 2.38307i −0.261576 + 0.151021i
\(250\) −13.0979 −0.828383
\(251\) −7.93598 13.7455i −0.500915 0.867610i −0.999999 0.00105678i \(-0.999664\pi\)
0.499085 0.866553i \(-0.333670\pi\)
\(252\) 0 0
\(253\) 1.82413 1.05316i 0.114682 0.0662117i
\(254\) 17.1446 + 9.89841i 1.07574 + 0.621082i
\(255\) −49.0230 28.3034i −3.06994 1.77243i
\(256\) −4.52609 −0.282880
\(257\) −24.3267 −1.51746 −0.758730 0.651406i \(-0.774180\pi\)
−0.758730 + 0.651406i \(0.774180\pi\)
\(258\) −9.14900 5.28218i −0.569592 0.328854i
\(259\) 0 0
\(260\) 2.26344 0.934688i 0.140372 0.0579669i
\(261\) −2.43282 4.21376i −0.150588 0.260825i
\(262\) −13.0325 + 7.52432i −0.805150 + 0.464854i
\(263\) −7.71727 13.3667i −0.475867 0.824226i 0.523751 0.851872i \(-0.324532\pi\)
−0.999618 + 0.0276456i \(0.991199\pi\)
\(264\) 3.86204 6.68925i 0.237692 0.411695i
\(265\) 0.285395i 0.0175317i
\(266\) 0 0
\(267\) 13.4512 7.76606i 0.823201 0.475275i
\(268\) 1.04210 0.601656i 0.0636563 0.0367520i
\(269\) 13.0407 0.795106 0.397553 0.917579i \(-0.369859\pi\)
0.397553 + 0.917579i \(0.369859\pi\)
\(270\) −8.84108 15.3132i −0.538051 0.931931i
\(271\) 26.9706i 1.63835i −0.573544 0.819174i \(-0.694432\pi\)
0.573544 0.819174i \(-0.305568\pi\)
\(272\) −27.7298 −1.68136
\(273\) 0 0
\(274\) −23.7174 −1.43282
\(275\) 9.88289i 0.595961i
\(276\) −0.321442 0.556753i −0.0193485 0.0335126i
\(277\) −12.7015 −0.763156 −0.381578 0.924337i \(-0.624619\pi\)
−0.381578 + 0.924337i \(0.624619\pi\)
\(278\) 6.82352 3.93956i 0.409248 0.236279i
\(279\) 5.36737 3.09885i 0.321336 0.185523i
\(280\) 0 0
\(281\) 26.7216i 1.59408i 0.603930 + 0.797038i \(0.293601\pi\)
−0.603930 + 0.797038i \(0.706399\pi\)
\(282\) 1.23306 2.13572i 0.0734276 0.127180i
\(283\) −7.37113 12.7672i −0.438168 0.758929i 0.559380 0.828911i \(-0.311039\pi\)
−0.997548 + 0.0699819i \(0.977706\pi\)
\(284\) 1.88338 1.08737i 0.111758 0.0645236i
\(285\) 3.45191 + 5.97888i 0.204473 + 0.354158i
\(286\) 2.36719 + 5.73238i 0.139975 + 0.338963i
\(287\) 0 0
\(288\) −1.11791 0.645425i −0.0658734 0.0380320i
\(289\) 42.8952 2.52324
\(290\) 19.4131 1.13997
\(291\) 0.849651 + 0.490546i 0.0498074 + 0.0287563i
\(292\) −0.125379 0.0723874i −0.00733723 0.00423615i
\(293\) 10.0312 5.79153i 0.586030 0.338345i −0.177496 0.984121i \(-0.556800\pi\)
0.763526 + 0.645777i \(0.223466\pi\)
\(294\) 0 0
\(295\) −19.9523 34.5584i −1.16167 2.01207i
\(296\) −3.11179 −0.180869
\(297\) −4.07974 + 2.35544i −0.236730 + 0.136676i
\(298\) −7.04829 + 12.2080i −0.408297 + 0.707190i
\(299\) 5.88768 + 0.781589i 0.340493 + 0.0452005i
\(300\) 3.01641 0.174153
\(301\) 0 0
\(302\) 3.17074 5.49188i 0.182455 0.316022i
\(303\) 2.95047 5.11036i 0.169500 0.293582i
\(304\) 2.92885 + 1.69097i 0.167981 + 0.0969838i
\(305\) 27.2004i 1.55749i
\(306\) −10.8458 6.26180i −0.620011 0.357963i
\(307\) 29.3335i 1.67415i −0.547086 0.837076i \(-0.684263\pi\)
0.547086 0.837076i \(-0.315737\pi\)
\(308\) 0 0
\(309\) −11.6191 + 20.1248i −0.660986 + 1.14486i
\(310\) 24.7278i 1.40444i
\(311\) 0.0753271 0.130470i 0.00427141 0.00739830i −0.863882 0.503695i \(-0.831974\pi\)
0.868153 + 0.496296i \(0.165307\pi\)
\(312\) 20.1312 8.31317i 1.13970 0.470641i
\(313\) −5.26057 9.11157i −0.297345 0.515016i 0.678183 0.734893i \(-0.262768\pi\)
−0.975528 + 0.219877i \(0.929434\pi\)
\(314\) 10.4874 + 6.05493i 0.591841 + 0.341699i
\(315\) 0 0
\(316\) 0.271777 + 0.470732i 0.0152887 + 0.0264808i
\(317\) 1.30489 0.753380i 0.0732901 0.0423140i −0.462907 0.886407i \(-0.653194\pi\)
0.536197 + 0.844093i \(0.319860\pi\)
\(318\) 0.220607i 0.0123710i
\(319\) 5.17202i 0.289578i
\(320\) 26.6018 15.3586i 1.48709 0.858571i
\(321\) −6.73671 11.6683i −0.376006 0.651262i
\(322\) 0 0
\(323\) −6.32619 3.65243i −0.351999 0.203227i
\(324\) 1.06241 + 1.84015i 0.0590228 + 0.102231i
\(325\) −16.9884 + 22.0904i −0.942349 + 1.22535i
\(326\) −8.09314 + 14.0177i −0.448237 + 0.776370i
\(327\) 11.9708i 0.661989i
\(328\) −6.18600 + 10.7145i −0.341565 + 0.591607i
\(329\) 0 0
\(330\) 12.5814i 0.692582i
\(331\) −21.8679 12.6254i −1.20197 0.693957i −0.240976 0.970531i \(-0.577467\pi\)
−0.960993 + 0.276574i \(0.910801\pi\)
\(332\) 0.442569i 0.0242891i
\(333\) −1.10019 0.635193i −0.0602899 0.0348084i
\(334\) −13.0635 + 22.6266i −0.714802 + 1.23807i
\(335\) −11.2760 + 19.5306i −0.616075 + 1.06707i
\(336\) 0 0
\(337\) 32.1811 1.75302 0.876509 0.481386i \(-0.159866\pi\)
0.876509 + 0.481386i \(0.159866\pi\)
\(338\) −4.56264 + 16.8823i −0.248175 + 0.918273i
\(339\) 6.69598 11.5978i 0.363676 0.629905i
\(340\) −4.55213 + 2.62817i −0.246874 + 0.142533i
\(341\) 6.58797 0.356759
\(342\) 0.763694 + 1.32276i 0.0412959 + 0.0715265i
\(343\) 0 0
\(344\) −9.77495 + 5.64357i −0.527030 + 0.304281i
\(345\) 10.4345 + 6.02434i 0.561773 + 0.324340i
\(346\) −16.7521 9.67185i −0.900600 0.519962i
\(347\) 24.7638 1.32939 0.664695 0.747115i \(-0.268562\pi\)
0.664695 + 0.747115i \(0.268562\pi\)
\(348\) −1.57858 −0.0846209
\(349\) 10.0075 + 5.77782i 0.535688 + 0.309280i 0.743330 0.668925i \(-0.233245\pi\)
−0.207642 + 0.978205i \(0.566579\pi\)
\(350\) 0 0
\(351\) −13.1680 1.74805i −0.702857 0.0933042i
\(352\) −0.686067 1.18830i −0.0365675 0.0633368i
\(353\) 17.3971 10.0442i 0.925953 0.534599i 0.0404237 0.999183i \(-0.487129\pi\)
0.885529 + 0.464583i \(0.153796\pi\)
\(354\) −15.4229 26.7133i −0.819719 1.41980i
\(355\) −20.3791 + 35.2977i −1.08161 + 1.87340i
\(356\) 1.44227i 0.0764399i
\(357\) 0 0
\(358\) −6.32136 + 3.64964i −0.334094 + 0.192890i
\(359\) 13.0346 7.52551i 0.687938 0.397181i −0.114901 0.993377i \(-0.536655\pi\)
0.802839 + 0.596196i \(0.203322\pi\)
\(360\) 12.6458 0.666495
\(361\) −9.05455 15.6829i −0.476555 0.825418i
\(362\) 20.8378i 1.09521i
\(363\) −19.1992 −1.00770
\(364\) 0 0
\(365\) 2.71331 0.142021
\(366\) 21.0257i 1.09903i
\(367\) 4.50178 + 7.79731i 0.234991 + 0.407016i 0.959270 0.282491i \(-0.0911607\pi\)
−0.724279 + 0.689507i \(0.757827\pi\)
\(368\) 5.90223 0.307675
\(369\) −4.37418 + 2.52543i −0.227711 + 0.131469i
\(370\) 4.38956 2.53431i 0.228202 0.131753i
\(371\) 0 0
\(372\) 2.01075i 0.104253i
\(373\) 8.06953 13.9768i 0.417824 0.723693i −0.577896 0.816110i \(-0.696126\pi\)
0.995720 + 0.0924174i \(0.0294594\pi\)
\(374\) −6.65611 11.5287i −0.344179 0.596136i
\(375\) −17.2867 + 9.98048i −0.892681 + 0.515390i
\(376\) −1.31742 2.28184i −0.0679409 0.117677i
\(377\) 8.89057 11.5606i 0.457888 0.595400i
\(378\) 0 0
\(379\) −13.5668 7.83277i −0.696878 0.402342i 0.109306 0.994008i \(-0.465137\pi\)
−0.806183 + 0.591666i \(0.798471\pi\)
\(380\) 0.641068 0.0328861
\(381\) 30.1700 1.54566
\(382\) −5.52935 3.19237i −0.282906 0.163336i
\(383\) −21.3327 12.3164i −1.09005 0.629339i −0.156459 0.987685i \(-0.550008\pi\)
−0.933589 + 0.358345i \(0.883341\pi\)
\(384\) 16.7525 9.67207i 0.854898 0.493576i
\(385\) 0 0
\(386\) 14.1512 + 24.5106i 0.720277 + 1.24756i
\(387\) −4.60798 −0.234237
\(388\) 0.0788960 0.0455506i 0.00400534 0.00231248i
\(389\) −9.42834 + 16.3304i −0.478036 + 0.827982i −0.999683 0.0251791i \(-0.991984\pi\)
0.521647 + 0.853161i \(0.325318\pi\)
\(390\) −21.6270 + 28.1221i −1.09513 + 1.42402i
\(391\) −12.7486 −0.644724
\(392\) 0 0
\(393\) −11.4669 + 19.8613i −0.578431 + 1.00187i
\(394\) −3.90929 + 6.77108i −0.196947 + 0.341122i
\(395\) −8.82229 5.09355i −0.443897 0.256284i
\(396\) 0.292811i 0.0147143i
\(397\) 12.5600 + 7.25149i 0.630366 + 0.363942i 0.780894 0.624664i \(-0.214764\pi\)
−0.150528 + 0.988606i \(0.548097\pi\)
\(398\) 14.2839i 0.715985i
\(399\) 0 0
\(400\) −13.8467 + 23.9831i −0.692333 + 1.19916i
\(401\) 20.9889i 1.04814i 0.851676 + 0.524069i \(0.175587\pi\)
−0.851676 + 0.524069i \(0.824413\pi\)
\(402\) −8.71624 + 15.0970i −0.434727 + 0.752968i
\(403\) 14.7255 + 11.3245i 0.733531 + 0.564116i
\(404\) −0.273971 0.474532i −0.0136306 0.0236089i
\(405\) −34.4874 19.9113i −1.71369 0.989401i
\(406\) 0 0
\(407\) −0.675191 1.16947i −0.0334680 0.0579683i
\(408\) −40.4869 + 23.3751i −2.00440 + 1.15724i
\(409\) 21.4276i 1.05953i −0.848146 0.529763i \(-0.822281\pi\)
0.848146 0.529763i \(-0.177719\pi\)
\(410\) 20.1521i 0.995242i
\(411\) −31.3025 + 18.0725i −1.54404 + 0.891451i
\(412\) 1.07891 + 1.86873i 0.0531542 + 0.0920657i
\(413\) 0 0
\(414\) 2.30850 + 1.33281i 0.113457 + 0.0655043i
\(415\) −4.14723 7.18321i −0.203580 0.352610i
\(416\) 0.509155 3.83545i 0.0249634 0.188048i
\(417\) 6.00383 10.3989i 0.294009 0.509238i
\(418\) 1.62357i 0.0794113i
\(419\) 3.98203 6.89708i 0.194535 0.336944i −0.752213 0.658920i \(-0.771014\pi\)
0.946748 + 0.321976i \(0.104347\pi\)
\(420\) 0 0
\(421\) 2.81786i 0.137334i −0.997640 0.0686670i \(-0.978125\pi\)
0.997640 0.0686670i \(-0.0218746\pi\)
\(422\) 5.43530 + 3.13807i 0.264586 + 0.152759i
\(423\) 1.07568i 0.0523011i
\(424\) 0.204122 + 0.117850i 0.00991306 + 0.00572331i
\(425\) 29.9082 51.8026i 1.45076 2.51279i
\(426\) −15.7528 + 27.2847i −0.763227 + 1.32195i
\(427\) 0 0
\(428\) −1.25110 −0.0604742
\(429\) 7.49227 + 5.76187i 0.361730 + 0.278186i
\(430\) 9.19253 15.9219i 0.443303 0.767823i
\(431\) 4.96775 2.86813i 0.239288 0.138153i −0.375561 0.926797i \(-0.622550\pi\)
0.614849 + 0.788645i \(0.289217\pi\)
\(432\) −13.2006 −0.635112
\(433\) 12.2628 + 21.2398i 0.589314 + 1.02072i 0.994322 + 0.106409i \(0.0339351\pi\)
−0.405009 + 0.914313i \(0.632732\pi\)
\(434\) 0 0
\(435\) 25.6215 14.7926i 1.22846 0.709251i
\(436\) −0.962653 0.555788i −0.0461027 0.0266174i
\(437\) 1.34652 + 0.777413i 0.0644128 + 0.0371887i
\(438\) 2.09736 0.100216
\(439\) 36.6423 1.74884 0.874420 0.485169i \(-0.161242\pi\)
0.874420 + 0.485169i \(0.161242\pi\)
\(440\) 11.6412 + 6.72108i 0.554975 + 0.320415i
\(441\) 0 0
\(442\) 4.93973 37.2108i 0.234959 1.76994i
\(443\) −13.5467 23.4635i −0.643622 1.11479i −0.984618 0.174721i \(-0.944098\pi\)
0.340996 0.940065i \(-0.389236\pi\)
\(444\) −0.356939 + 0.206079i −0.0169396 + 0.00978008i
\(445\) 13.5152 + 23.4090i 0.640682 + 1.10969i
\(446\) 16.2943 28.2226i 0.771558 1.33638i
\(447\) 21.4830i 1.01611i
\(448\) 0 0
\(449\) 23.7571 13.7162i 1.12117 0.647307i 0.179470 0.983764i \(-0.442562\pi\)
0.941699 + 0.336456i \(0.109228\pi\)
\(450\) −10.8315 + 6.25358i −0.510602 + 0.294796i
\(451\) −5.36892 −0.252812
\(452\) −0.621768 1.07693i −0.0292455 0.0506547i
\(453\) 9.66431i 0.454069i
\(454\) 20.6832 0.970712
\(455\) 0 0
\(456\) 5.70169 0.267006
\(457\) 39.6639i 1.85540i −0.373327 0.927700i \(-0.621783\pi\)
0.373327 0.927700i \(-0.378217\pi\)
\(458\) 10.9982 + 19.0495i 0.513913 + 0.890123i
\(459\) 28.5127 1.33086
\(460\) 0.968913 0.559402i 0.0451758 0.0260823i
\(461\) 4.23988 2.44790i 0.197471 0.114010i −0.398004 0.917384i \(-0.630297\pi\)
0.595475 + 0.803374i \(0.296964\pi\)
\(462\) 0 0
\(463\) 4.71193i 0.218982i 0.993988 + 0.109491i \(0.0349221\pi\)
−0.993988 + 0.109491i \(0.965078\pi\)
\(464\) 7.24638 12.5511i 0.336405 0.582670i
\(465\) 18.8424 + 32.6360i 0.873794 + 1.51346i
\(466\) 33.9140 19.5803i 1.57104 0.907038i
\(467\) −16.0081 27.7268i −0.740765 1.28304i −0.952147 0.305639i \(-0.901130\pi\)
0.211383 0.977403i \(-0.432203\pi\)
\(468\) 0.503335 0.654496i 0.0232667 0.0302541i
\(469\) 0 0
\(470\) 3.71678 + 2.14588i 0.171442 + 0.0989822i
\(471\) 18.4552 0.850372
\(472\) −32.9563 −1.51693
\(473\) −4.24191 2.44907i −0.195043 0.112608i
\(474\) −6.81953 3.93726i −0.313232 0.180844i
\(475\) −6.31788 + 3.64763i −0.289884 + 0.167365i
\(476\) 0 0
\(477\) 0.0481123 + 0.0833330i 0.00220291 + 0.00381556i
\(478\) −11.6417 −0.532480
\(479\) −15.6097 + 9.01224i −0.713224 + 0.411780i −0.812254 0.583305i \(-0.801759\pi\)
0.0990298 + 0.995084i \(0.468426\pi\)
\(480\) 3.92447 6.79738i 0.179127 0.310257i
\(481\) 0.501083 3.77464i 0.0228474 0.172109i
\(482\) −24.4807 −1.11506
\(483\) 0 0
\(484\) −0.891390 + 1.54393i −0.0405177 + 0.0701788i
\(485\) −0.853693 + 1.47864i −0.0387642 + 0.0671416i
\(486\) −13.7821 7.95712i −0.625170 0.360942i
\(487\) 17.6004i 0.797550i 0.917049 + 0.398775i \(0.130565\pi\)
−0.917049 + 0.398775i \(0.869435\pi\)
\(488\) −19.4545 11.2321i −0.880666 0.508453i
\(489\) 24.6676i 1.11551i
\(490\) 0 0
\(491\) 1.93180 3.34598i 0.0871810 0.151002i −0.819138 0.573597i \(-0.805547\pi\)
0.906318 + 0.422595i \(0.138881\pi\)
\(492\) 1.63868i 0.0738773i
\(493\) −15.6519 + 27.1099i −0.704926 + 1.22097i
\(494\) −2.79087 + 3.62902i −0.125567 + 0.163277i
\(495\) 2.74388 + 4.75254i 0.123328 + 0.213611i
\(496\) 15.9872 + 9.23023i 0.717848 + 0.414450i
\(497\) 0 0
\(498\) −3.20576 5.55255i −0.143654 0.248816i
\(499\) −10.9528 + 6.32363i −0.490317 + 0.283084i −0.724706 0.689058i \(-0.758024\pi\)
0.234389 + 0.972143i \(0.424691\pi\)
\(500\) 1.85351i 0.0828917i
\(501\) 39.8171i 1.77890i
\(502\) 18.4908 10.6757i 0.825287 0.476480i
\(503\) 11.0180 + 19.0837i 0.491268 + 0.850902i 0.999949 0.0100533i \(-0.00320011\pi\)
−0.508681 + 0.860955i \(0.669867\pi\)
\(504\) 0 0
\(505\) 8.89351 + 5.13467i 0.395756 + 0.228490i
\(506\) 1.41674 + 2.45387i 0.0629818 + 0.109088i
\(507\) 6.84233 + 25.7580i 0.303879 + 1.14395i
\(508\) 1.40075 2.42617i 0.0621482 0.107644i
\(509\) 15.6702i 0.694568i 0.937760 + 0.347284i \(0.112896\pi\)
−0.937760 + 0.347284i \(0.887104\pi\)
\(510\) 38.0745 65.9470i 1.68597 2.92018i
\(511\) 0 0
\(512\) 24.9600i 1.10309i
\(513\) −3.01154 1.73871i −0.132963 0.0767661i
\(514\) 32.7249i 1.44344i
\(515\) −35.0230 20.2206i −1.54330 0.891025i
\(516\) −0.747495 + 1.29470i −0.0329066 + 0.0569959i
\(517\) 0.571705 0.990222i 0.0251436 0.0435499i
\(518\) 0 0
\(519\) −29.4795 −1.29401
\(520\) 14.4673 + 35.0341i 0.634435 + 1.53635i
\(521\) −12.6207 + 21.8598i −0.552925 + 0.957694i 0.445137 + 0.895463i \(0.353155\pi\)
−0.998062 + 0.0622317i \(0.980178\pi\)
\(522\) 5.66846 3.27269i 0.248102 0.143242i
\(523\) 13.2477 0.579279 0.289640 0.957136i \(-0.406465\pi\)
0.289640 + 0.957136i \(0.406465\pi\)
\(524\) 1.06479 + 1.84426i 0.0465154 + 0.0805670i
\(525\) 0 0
\(526\) 17.9812 10.3815i 0.784019 0.452654i
\(527\) −34.5318 19.9369i −1.50423 0.868466i
\(528\) 8.13422 + 4.69629i 0.353996 + 0.204380i
\(529\) −20.2865 −0.882021
\(530\) −0.383920 −0.0166764
\(531\) −11.6518 6.72720i −0.505647 0.291935i
\(532\) 0 0
\(533\) −12.0007 9.22903i −0.519807 0.399754i
\(534\) 10.4471 + 18.0949i 0.452091 + 0.783044i
\(535\) 20.3063 11.7238i 0.877916 0.506865i
\(536\) 9.31258 + 16.1299i 0.402242 + 0.696704i
\(537\) −5.56200 + 9.63366i −0.240018 + 0.415723i
\(538\) 17.5427i 0.756320i
\(539\) 0 0
\(540\) −2.16701 + 1.25112i −0.0932532 + 0.0538398i
\(541\) −12.4737 + 7.20170i −0.536287 + 0.309625i −0.743573 0.668655i \(-0.766870\pi\)
0.207286 + 0.978280i \(0.433537\pi\)
\(542\) 36.2816 1.55843
\(543\) 15.8782 + 27.5019i 0.681401 + 1.18022i
\(544\) 8.30488i 0.356069i
\(545\) 20.8328 0.892377
\(546\) 0 0
\(547\) 2.00679 0.0858042 0.0429021 0.999079i \(-0.486340\pi\)
0.0429021 + 0.999079i \(0.486340\pi\)
\(548\) 3.35631i 0.143375i
\(549\) −4.58550 7.94232i −0.195704 0.338970i
\(550\) −13.2947 −0.566889
\(551\) 3.30634 1.90892i 0.140855 0.0813226i
\(552\) 8.61757 4.97535i 0.366788 0.211765i
\(553\) 0 0
\(554\) 17.0863i 0.725928i
\(555\) 3.86226 6.68962i 0.163944 0.283959i
\(556\) −0.557497 0.965614i −0.0236432 0.0409512i
\(557\) −7.42977 + 4.28958i −0.314810 + 0.181755i −0.649077 0.760723i \(-0.724845\pi\)
0.334267 + 0.942478i \(0.391511\pi\)
\(558\) 4.16865 + 7.22032i 0.176473 + 0.305661i
\(559\) −5.27170 12.7659i −0.222969 0.539942i
\(560\) 0 0
\(561\) −17.5696 10.1438i −0.741788 0.428272i
\(562\) −35.9466 −1.51631
\(563\) −12.7744 −0.538375 −0.269188 0.963088i \(-0.586755\pi\)
−0.269188 + 0.963088i \(0.586755\pi\)
\(564\) −0.302231 0.174493i −0.0127262 0.00734750i
\(565\) 20.1835 + 11.6530i 0.849126 + 0.490243i
\(566\) 17.1747 9.91583i 0.721908 0.416794i
\(567\) 0 0
\(568\) 16.8306 + 29.1515i 0.706196 + 1.22317i
\(569\) 5.79116 0.242778 0.121389 0.992605i \(-0.461265\pi\)
0.121389 + 0.992605i \(0.461265\pi\)
\(570\) −8.04295 + 4.64360i −0.336882 + 0.194499i
\(571\) −22.0666 + 38.2204i −0.923458 + 1.59948i −0.129435 + 0.991588i \(0.541316\pi\)
−0.794023 + 0.607888i \(0.792017\pi\)
\(572\) 0.811204 0.334987i 0.0339182 0.0140065i
\(573\) −9.73025 −0.406487
\(574\) 0 0
\(575\) −6.36592 + 11.0261i −0.265477 + 0.459820i
\(576\) 5.17835 8.96917i 0.215765 0.373715i
\(577\) −10.3343 5.96649i −0.430221 0.248388i 0.269220 0.963079i \(-0.413234\pi\)
−0.699441 + 0.714691i \(0.746568\pi\)
\(578\) 57.7037i 2.40016i
\(579\) 37.3538 + 21.5662i 1.55237 + 0.896261i
\(580\) 2.74719i 0.114071i
\(581\) 0 0
\(582\) −0.659895 + 1.14297i −0.0273535 + 0.0473777i
\(583\) 0.102284i 0.00423617i
\(584\) 1.12043 1.94064i 0.0463637 0.0803043i
\(585\) −2.03633 + 15.3396i −0.0841919 + 0.634215i
\(586\) 7.79091 + 13.4943i 0.321840 + 0.557443i
\(587\) −17.6250 10.1758i −0.727462 0.420000i 0.0900312 0.995939i \(-0.471303\pi\)
−0.817493 + 0.575939i \(0.804637\pi\)
\(588\) 0 0
\(589\) 2.43152 + 4.21152i 0.100189 + 0.173533i
\(590\) 46.4889 26.8404i 1.91392 1.10500i
\(591\) 11.9154i 0.490133i
\(592\) 3.78397i 0.155520i
\(593\) −15.7443 + 9.09000i −0.646543 + 0.373282i −0.787130 0.616787i \(-0.788434\pi\)
0.140588 + 0.990068i \(0.455101\pi\)
\(594\) −3.16859 5.48817i −0.130009 0.225182i
\(595\) 0 0
\(596\) 1.72759 + 0.997422i 0.0707646 + 0.0408560i
\(597\) 10.8842 + 18.8520i 0.445460 + 0.771560i
\(598\) −1.05141 + 7.92026i −0.0429955 + 0.323884i
\(599\) 19.1341 33.1412i 0.781797 1.35411i −0.149096 0.988823i \(-0.547636\pi\)
0.930894 0.365290i \(-0.119030\pi\)
\(600\) 46.6888i 1.90606i
\(601\) −13.4360 + 23.2718i −0.548064 + 0.949275i 0.450343 + 0.892856i \(0.351302\pi\)
−0.998407 + 0.0564195i \(0.982032\pi\)
\(602\) 0 0
\(603\) 7.60372i 0.309648i
\(604\) −0.777170 0.448699i −0.0316226 0.0182573i
\(605\) 33.4122i 1.35840i
\(606\) 6.87459 + 3.96904i 0.279261 + 0.161231i
\(607\) −4.70105 + 8.14245i −0.190810 + 0.330492i −0.945519 0.325568i \(-0.894445\pi\)
0.754709 + 0.656059i \(0.227778\pi\)
\(608\) 0.506435 0.877171i 0.0205386 0.0355740i
\(609\) 0 0
\(610\) 36.5908 1.48152
\(611\) 2.98005 1.23061i 0.120560 0.0497853i
\(612\) −0.886124 + 1.53481i −0.0358194 + 0.0620411i
\(613\) 11.5089 6.64469i 0.464842 0.268376i −0.249236 0.968443i \(-0.580180\pi\)
0.714078 + 0.700066i \(0.246846\pi\)
\(614\) 39.4602 1.59248
\(615\) −15.3557 26.5969i −0.619204 1.07249i
\(616\) 0 0
\(617\) −9.72211 + 5.61306i −0.391397 + 0.225973i −0.682765 0.730638i \(-0.739223\pi\)
0.291368 + 0.956611i \(0.405890\pi\)
\(618\) −27.0724 15.6303i −1.08901 0.628742i
\(619\) 8.04109 + 4.64253i 0.323199 + 0.186599i 0.652817 0.757515i \(-0.273587\pi\)
−0.329619 + 0.944114i \(0.606920\pi\)
\(620\) 3.49929 0.140535
\(621\) −6.06888 −0.243536
\(622\) 0.175512 + 0.101332i 0.00703740 + 0.00406304i
\(623\) 0 0
\(624\) 10.1089 + 24.4797i 0.404681 + 0.979974i
\(625\) 1.95363 + 3.38379i 0.0781452 + 0.135351i
\(626\) 12.2571 7.07665i 0.489893 0.282840i
\(627\) 1.23715 + 2.14280i 0.0494068 + 0.0855752i
\(628\) 0.856848 1.48410i 0.0341920 0.0592222i
\(629\) 8.17322i 0.325888i
\(630\) 0 0
\(631\) 9.00894 5.20132i 0.358640 0.207061i −0.309844 0.950787i \(-0.600277\pi\)
0.668484 + 0.743726i \(0.266943\pi\)
\(632\) −7.28611 + 4.20664i −0.289826 + 0.167331i
\(633\) 9.56474 0.380164
\(634\) 1.01347 + 1.75538i 0.0402499 + 0.0697149i
\(635\) 52.5046i 2.08358i
\(636\) 0.0312187 0.00123790
\(637\) 0 0
\(638\) 6.95754 0.275452
\(639\) 13.7422i 0.543632i
\(640\) 16.8322 + 29.1542i 0.665351 + 1.15242i
\(641\) −14.8591 −0.586899 −0.293449 0.955975i \(-0.594803\pi\)
−0.293449 + 0.955975i \(0.594803\pi\)
\(642\) 15.6965 9.06239i 0.619492 0.357664i
\(643\) −1.98945 + 1.14861i −0.0784563 + 0.0452968i −0.538715 0.842488i \(-0.681090\pi\)
0.460259 + 0.887785i \(0.347757\pi\)
\(644\) 0 0
\(645\) 28.0185i 1.10323i
\(646\) 4.91334 8.51016i 0.193313 0.334828i
\(647\) −3.99932 6.92703i −0.157230 0.272330i 0.776639 0.629946i \(-0.216923\pi\)
−0.933869 + 0.357616i \(0.883590\pi\)
\(648\) −28.4823 + 16.4443i −1.11889 + 0.645991i
\(649\) −7.15081 12.3856i −0.280694 0.486176i
\(650\) −29.7166 22.8533i −1.16558 0.896380i
\(651\) 0 0
\(652\) 1.98368 + 1.14528i 0.0776871 + 0.0448526i
\(653\) 3.98444 0.155923 0.0779615 0.996956i \(-0.475159\pi\)
0.0779615 + 0.996956i \(0.475159\pi\)
\(654\) 16.1035 0.629696
\(655\) −34.5645 19.9558i −1.35055 0.779738i
\(656\) −13.0289 7.52225i −0.508694 0.293695i
\(657\) 0.792267 0.457415i 0.0309093 0.0178455i
\(658\) 0 0
\(659\) 13.7501 + 23.8159i 0.535629 + 0.927737i 0.999133 + 0.0416417i \(0.0132588\pi\)
−0.463504 + 0.886095i \(0.653408\pi\)
\(660\) 1.78042 0.0693028
\(661\) −6.05023 + 3.49310i −0.235327 + 0.135866i −0.613027 0.790062i \(-0.710048\pi\)
0.377700 + 0.925928i \(0.376715\pi\)
\(662\) 16.9841 29.4173i 0.660105 1.14333i
\(663\) −21.8349 52.8752i −0.847996 2.05350i
\(664\) −6.85019 −0.265839
\(665\) 0 0
\(666\) 0.854479 1.48000i 0.0331104 0.0573488i
\(667\) 3.33148 5.77029i 0.128995 0.223427i
\(668\) 3.20195 + 1.84865i 0.123887 + 0.0715263i
\(669\) 49.6646i 1.92014i
\(670\) −26.2731 15.1688i −1.01502 0.586022i
\(671\) 9.74849i 0.376336i
\(672\) 0 0
\(673\) 2.72783 4.72474i 0.105150 0.182125i −0.808649 0.588291i \(-0.799801\pi\)
0.913800 + 0.406166i \(0.133134\pi\)
\(674\) 43.2909i 1.66750i
\(675\) 14.2376 24.6603i 0.548006 0.949174i
\(676\) 2.38905 + 0.645671i 0.0918866 + 0.0248335i
\(677\) 16.8961 + 29.2649i 0.649371 + 1.12474i 0.983273 + 0.182135i \(0.0583009\pi\)
−0.333903 + 0.942607i \(0.608366\pi\)
\(678\) 15.6016 + 9.00761i 0.599177 + 0.345935i
\(679\) 0 0
\(680\) −40.6795 70.4590i −1.55999 2.70198i
\(681\) 27.2979 15.7605i 1.04606 0.603942i
\(682\) 8.86231i 0.339355i
\(683\) 12.2988i 0.470602i 0.971923 + 0.235301i \(0.0756076\pi\)
−0.971923 + 0.235301i \(0.924392\pi\)
\(684\) 0.187187 0.108072i 0.00715726 0.00413225i
\(685\) −31.4514 54.4754i −1.20170 2.08140i
\(686\) 0 0
\(687\) 29.0311 + 16.7611i 1.10760 + 0.639476i
\(688\) −6.86265 11.8865i −0.261636 0.453167i
\(689\) −0.175823 + 0.228627i −0.00669834 + 0.00870998i
\(690\) −8.10410 + 14.0367i −0.308518 + 0.534369i
\(691\) 11.0897i 0.421871i −0.977500 0.210935i \(-0.932349\pi\)
0.977500 0.210935i \(-0.0676509\pi\)
\(692\) −1.36869 + 2.37064i −0.0520297 + 0.0901181i
\(693\) 0 0
\(694\) 33.3129i 1.26454i
\(695\) 18.0972 + 10.4484i 0.686465 + 0.396331i
\(696\) 24.4337i 0.926156i
\(697\) 28.1419 + 16.2478i 1.06595 + 0.615428i
\(698\) −7.77247 + 13.4623i −0.294193 + 0.509556i
\(699\) 29.8400 51.6844i 1.12865 1.95488i
\(700\) 0 0
\(701\) 10.6470 0.402133 0.201066 0.979578i \(-0.435559\pi\)
0.201066 + 0.979578i \(0.435559\pi\)
\(702\) 2.35153 17.7140i 0.0887526 0.668571i
\(703\) 0.498406 0.863265i 0.0187977 0.0325587i
\(704\) 9.53396 5.50443i 0.359325 0.207456i
\(705\) 6.54058 0.246333
\(706\) 13.5117 + 23.4030i 0.508521 + 0.880784i
\(707\) 0 0
\(708\) −3.78027 + 2.18254i −0.142071 + 0.0820248i
\(709\) 35.2532 + 20.3535i 1.32396 + 0.764391i 0.984358 0.176178i \(-0.0563733\pi\)
0.339605 + 0.940568i \(0.389707\pi\)
\(710\) −47.4833 27.4145i −1.78202 1.02885i
\(711\) −3.43472 −0.128812
\(712\) 22.3237 0.836618
\(713\) 7.35003 + 4.24354i 0.275261 + 0.158922i
\(714\) 0 0
\(715\) −10.0273 + 13.0387i −0.375001 + 0.487621i
\(716\) 0.516470 + 0.894552i 0.0193014 + 0.0334310i
\(717\) −15.3648 + 8.87089i −0.573810 + 0.331290i
\(718\) 10.1235 + 17.5344i 0.377806 + 0.654380i
\(719\) 4.88769 8.46572i 0.182280 0.315718i −0.760377 0.649482i \(-0.774986\pi\)
0.942657 + 0.333764i \(0.108319\pi\)
\(720\) 15.3775i 0.573086i
\(721\) 0 0
\(722\) 21.0971 12.1804i 0.785153 0.453308i
\(723\) −32.3098 + 18.6541i −1.20161 + 0.693752i
\(724\) 2.94881 0.109592
\(725\) 15.6313 + 27.0743i 0.580533 + 1.00551i
\(726\) 25.8273i 0.958540i
\(727\) 12.2091 0.452811 0.226406 0.974033i \(-0.427303\pi\)
0.226406 + 0.974033i \(0.427303\pi\)
\(728\) 0 0
\(729\) 9.23219 0.341933
\(730\) 3.65002i 0.135093i
\(731\) 14.8231 + 25.6743i 0.548251 + 0.949598i
\(732\) −2.97539 −0.109974
\(733\) 19.3256 11.1577i 0.713809 0.412118i −0.0986608 0.995121i \(-0.531456\pi\)
0.812470 + 0.583003i \(0.198123\pi\)
\(734\) −10.4891 + 6.05591i −0.387161 + 0.223528i
\(735\) 0 0
\(736\) 1.76768i 0.0651576i
\(737\) −4.04126 + 6.99968i −0.148862 + 0.257836i
\(738\) −3.39728 5.88426i −0.125056 0.216603i
\(739\) −36.6960 + 21.1865i −1.34989 + 0.779357i −0.988233 0.152956i \(-0.951121\pi\)
−0.361653 + 0.932313i \(0.617787\pi\)
\(740\) −0.358637 0.621178i −0.0131838 0.0228350i
\(741\) −0.918130 + 6.91624i −0.0337283 + 0.254074i
\(742\) 0 0
\(743\) −26.8296 15.4901i −0.984282 0.568276i −0.0807220 0.996737i \(-0.525723\pi\)
−0.903560 + 0.428461i \(0.859056\pi\)
\(744\) 31.1229 1.14102
\(745\) −37.3866 −1.36974
\(746\) 18.8020 + 10.8553i 0.688390 + 0.397442i
\(747\) −2.42192 1.39830i −0.0886133 0.0511609i
\(748\) −1.63146 + 0.941923i −0.0596520 + 0.0344401i
\(749\) 0 0
\(750\) −13.4260 23.2545i −0.490248 0.849135i
\(751\) −22.5660 −0.823444 −0.411722 0.911309i \(-0.635073\pi\)
−0.411722 + 0.911309i \(0.635073\pi\)
\(752\) 2.77475 1.60200i 0.101185 0.0584190i
\(753\) 16.2696 28.1798i 0.592897 1.02693i
\(754\) 15.5516 + 11.9598i 0.566356 + 0.435551i
\(755\) 16.8187 0.612095
\(756\) 0 0
\(757\) −16.1404 + 27.9560i −0.586633 + 1.01608i 0.408037 + 0.912965i \(0.366213\pi\)
−0.994670 + 0.103112i \(0.967120\pi\)
\(758\) 10.5368 18.2504i 0.382716 0.662883i
\(759\) 3.73966 + 2.15909i 0.135741 + 0.0783701i
\(760\) 9.92260i 0.359931i
\(761\) 25.7657 + 14.8758i 0.934006 + 0.539249i 0.888076 0.459696i \(-0.152042\pi\)
0.0459296 + 0.998945i \(0.485375\pi\)
\(762\) 40.5855i 1.47026i
\(763\) 0 0
\(764\) −0.451761 + 0.782473i −0.0163441 + 0.0283089i
\(765\) 33.2148i 1.20088i
\(766\) 16.5684 28.6972i 0.598639 1.03687i
\(767\) 5.30687 39.9764i 0.191620 1.44347i
\(768\) −4.63947 8.03581i −0.167413 0.289967i
\(769\) 36.2090 + 20.9053i 1.30573 + 0.753863i 0.981380 0.192075i \(-0.0615215\pi\)
0.324349 + 0.945938i \(0.394855\pi\)
\(770\) 0 0
\(771\) −24.9361 43.1907i −0.898053 1.55547i
\(772\) 3.46856 2.00257i 0.124836 0.0720742i
\(773\) 41.4336i 1.49026i 0.666917 + 0.745132i \(0.267613\pi\)
−0.666917 + 0.745132i \(0.732387\pi\)
\(774\) 6.19877i 0.222810i
\(775\) −34.4864 + 19.9107i −1.23879 + 0.715215i
\(776\) 0.705044 + 1.22117i 0.0253096 + 0.0438375i
\(777\) 0 0
\(778\) −21.9680 12.6832i −0.787592 0.454716i
\(779\) −1.98159 3.43221i −0.0709978 0.122972i
\(780\) 3.97963 + 3.06050i 0.142493 + 0.109583i
\(781\) −7.30376 + 12.6505i −0.261349 + 0.452670i
\(782\)