Properties

Label 637.2.e.j.79.1
Level $637$
Weight $2$
Character 637.79
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
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.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.2696112.1
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} + 18 x^{2} - 8 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(1.17146 - 2.02903i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.j.508.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.17146 + 2.02903i) q^{2} +(0.573183 + 0.992782i) q^{3} +(-1.74464 - 3.02181i) q^{4} +(0.671462 - 1.16301i) q^{5} -2.68585 q^{6} +3.48929 q^{8} +(0.842923 - 1.45999i) q^{9} +O(q^{10})\) \(q+(-1.17146 + 2.02903i) q^{2} +(0.573183 + 0.992782i) q^{3} +(-1.74464 - 3.02181i) q^{4} +(0.671462 - 1.16301i) q^{5} -2.68585 q^{6} +3.48929 q^{8} +(0.842923 - 1.45999i) q^{9} +(1.57318 + 2.72483i) q^{10} +(-0.573183 - 0.992782i) q^{11} +(2.00000 - 3.46410i) q^{12} +1.00000 q^{13} +1.53948 q^{15} +(-0.598279 + 1.03625i) q^{16} +(-2.91611 - 5.05084i) q^{17} +(1.97490 + 3.42063i) q^{18} +(1.67146 - 2.89506i) q^{19} -4.68585 q^{20} +2.68585 q^{22} +(1.58757 - 2.74975i) q^{23} +(2.00000 + 3.46410i) q^{24} +(1.59828 + 2.76830i) q^{25} +(-1.17146 + 2.02903i) q^{26} +5.37169 q^{27} +10.4893 q^{29} +(-1.80344 + 3.12365i) q^{30} +(-0.817827 - 1.41652i) q^{31} +(2.08757 + 3.61577i) q^{32} +(0.657077 - 1.13809i) q^{33} +13.6644 q^{34} -5.88240 q^{36} +(-4.25903 + 7.37685i) q^{37} +(3.91611 + 6.78289i) q^{38} +(0.573183 + 0.992782i) q^{39} +(2.34292 - 4.05806i) q^{40} -0.292731 q^{41} -8.15371 q^{43} +(-2.00000 + 3.46410i) q^{44} +(-1.13198 - 1.96065i) q^{45} +(3.71955 + 6.44245i) q^{46} +(5.30712 - 9.19219i) q^{47} -1.37169 q^{48} -7.48929 q^{50} +(3.34292 - 5.79011i) q^{51} +(-1.74464 - 3.02181i) q^{52} +(0.391010 + 0.677249i) q^{53} +(-6.29273 + 10.8993i) q^{54} -1.53948 q^{55} +3.83221 q^{57} +(-12.2878 + 21.2831i) q^{58} +(-6.32150 - 10.9492i) q^{59} +(-2.68585 - 4.65202i) q^{60} +(1.00000 - 1.73205i) q^{61} +3.83221 q^{62} -12.1751 q^{64} +(0.671462 - 1.16301i) q^{65} +(1.53948 + 2.66646i) q^{66} +(3.05019 + 5.28309i) q^{67} +(-10.1751 + 17.6239i) q^{68} +3.63986 q^{69} +1.53948 q^{71} +(2.94120 - 5.09431i) q^{72} +(7.65004 + 13.2503i) q^{73} +(-9.97858 - 17.2834i) q^{74} +(-1.83221 + 3.17348i) q^{75} -11.6644 q^{76} -2.68585 q^{78} +(-0.441202 + 0.764184i) q^{79} +(0.803442 + 1.39160i) q^{80} +(0.550192 + 0.952961i) q^{81} +(0.342923 - 0.593960i) q^{82} -12.1292 q^{83} -7.83221 q^{85} +(9.55176 - 16.5441i) q^{86} +(6.01228 + 10.4136i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-2.86802 + 4.96755i) q^{89} +5.30429 q^{90} -11.0790 q^{92} +(0.937529 - 1.62385i) q^{93} +(12.4342 + 21.5366i) q^{94} +(-2.24464 - 3.88784i) q^{95} +(-2.39312 + 4.14500i) q^{96} -5.34292 q^{97} -1.93260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + 2q^{3} - 3q^{4} - 2q^{5} + 8q^{6} + 6q^{8} - 7q^{9} + O(q^{10}) \) \( 6q - q^{2} + 2q^{3} - 3q^{4} - 2q^{5} + 8q^{6} + 6q^{8} - 7q^{9} + 8q^{10} - 2q^{11} + 12q^{12} + 6q^{13} - 12q^{15} + q^{16} - 4q^{17} + 15q^{18} + 4q^{19} - 4q^{20} - 8q^{22} - 10q^{23} + 12q^{24} + 5q^{25} - q^{26} - 16q^{27} + 48q^{29} - 20q^{30} + 4q^{31} - 7q^{32} + 16q^{33} + 28q^{34} - 2q^{36} + 10q^{38} + 2q^{39} + 2q^{40} + 4q^{41} + 20q^{43} - 12q^{44} - 22q^{45} + 18q^{46} + 8q^{47} + 40q^{48} - 30q^{50} + 8q^{51} - 3q^{52} - 8q^{53} - 32q^{54} + 12q^{55} - 4q^{57} - 12q^{58} + 4q^{59} + 8q^{60} + 6q^{61} - 4q^{62} - 34q^{64} - 2q^{65} - 12q^{66} + 12q^{67} - 22q^{68} - 12q^{69} - 12q^{71} + q^{72} + 10q^{73} - 30q^{74} + 16q^{75} - 16q^{76} + 8q^{78} + 14q^{79} + 14q^{80} - 3q^{81} - 10q^{82} - 24q^{83} - 20q^{85} + 26q^{86} + 26q^{87} - 12q^{88} - 2q^{89} - 56q^{90} - 24q^{92} + 22q^{93} + 10q^{94} - 6q^{95} + 4q^{96} - 20q^{97} + 28q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17146 + 2.02903i −0.828348 + 1.43474i 0.0709847 + 0.997477i \(0.477386\pi\)
−0.899333 + 0.437264i \(0.855947\pi\)
\(3\) 0.573183 + 0.992782i 0.330927 + 0.573183i 0.982694 0.185237i \(-0.0593052\pi\)
−0.651767 + 0.758420i \(0.725972\pi\)
\(4\) −1.74464 3.02181i −0.872322 1.51091i
\(5\) 0.671462 1.16301i 0.300287 0.520112i −0.675914 0.736980i \(-0.736251\pi\)
0.976201 + 0.216869i \(0.0695843\pi\)
\(6\) −2.68585 −1.09649
\(7\) 0 0
\(8\) 3.48929 1.23365
\(9\) 0.842923 1.45999i 0.280974 0.486662i
\(10\) 1.57318 + 2.72483i 0.497484 + 0.861668i
\(11\) −0.573183 0.992782i −0.172821 0.299335i 0.766584 0.642144i \(-0.221955\pi\)
−0.939405 + 0.342809i \(0.888622\pi\)
\(12\) 2.00000 3.46410i 0.577350 1.00000i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.53948 0.397492
\(16\) −0.598279 + 1.03625i −0.149570 + 0.259062i
\(17\) −2.91611 5.05084i −0.707260 1.22501i −0.965870 0.259028i \(-0.916598\pi\)
0.258610 0.965982i \(-0.416735\pi\)
\(18\) 1.97490 + 3.42063i 0.465489 + 0.806251i
\(19\) 1.67146 2.89506i 0.383460 0.664171i −0.608095 0.793865i \(-0.708066\pi\)
0.991554 + 0.129693i \(0.0413992\pi\)
\(20\) −4.68585 −1.04779
\(21\) 0 0
\(22\) 2.68585 0.572624
\(23\) 1.58757 2.74975i 0.331031 0.573362i −0.651684 0.758491i \(-0.725937\pi\)
0.982714 + 0.185129i \(0.0592703\pi\)
\(24\) 2.00000 + 3.46410i 0.408248 + 0.707107i
\(25\) 1.59828 + 2.76830i 0.319656 + 0.553660i
\(26\) −1.17146 + 2.02903i −0.229743 + 0.397926i
\(27\) 5.37169 1.03378
\(28\) 0 0
\(29\) 10.4893 1.94781 0.973906 0.226952i \(-0.0728760\pi\)
0.973906 + 0.226952i \(0.0728760\pi\)
\(30\) −1.80344 + 3.12365i −0.329262 + 0.570299i
\(31\) −0.817827 1.41652i −0.146886 0.254414i 0.783189 0.621784i \(-0.213592\pi\)
−0.930075 + 0.367370i \(0.880258\pi\)
\(32\) 2.08757 + 3.61577i 0.369033 + 0.639184i
\(33\) 0.657077 1.13809i 0.114382 0.198116i
\(34\) 13.6644 2.34343
\(35\) 0 0
\(36\) −5.88240 −0.980401
\(37\) −4.25903 + 7.37685i −0.700180 + 1.21275i 0.268223 + 0.963357i \(0.413564\pi\)
−0.968403 + 0.249391i \(0.919770\pi\)
\(38\) 3.91611 + 6.78289i 0.635276 + 1.10033i
\(39\) 0.573183 + 0.992782i 0.0917827 + 0.158972i
\(40\) 2.34292 4.05806i 0.370449 0.641636i
\(41\) −0.292731 −0.0457169 −0.0228584 0.999739i \(-0.507277\pi\)
−0.0228584 + 0.999739i \(0.507277\pi\)
\(42\) 0 0
\(43\) −8.15371 −1.24343 −0.621715 0.783244i \(-0.713564\pi\)
−0.621715 + 0.783244i \(0.713564\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) −1.13198 1.96065i −0.168746 0.292276i
\(46\) 3.71955 + 6.44245i 0.548417 + 0.949887i
\(47\) 5.30712 9.19219i 0.774122 1.34082i −0.161164 0.986928i \(-0.551525\pi\)
0.935286 0.353892i \(-0.115142\pi\)
\(48\) −1.37169 −0.197987
\(49\) 0 0
\(50\) −7.48929 −1.05915
\(51\) 3.34292 5.79011i 0.468103 0.810778i
\(52\) −1.74464 3.02181i −0.241939 0.419050i
\(53\) 0.391010 + 0.677249i 0.0537093 + 0.0930273i 0.891630 0.452765i \(-0.149562\pi\)
−0.837921 + 0.545792i \(0.816229\pi\)
\(54\) −6.29273 + 10.8993i −0.856332 + 1.48321i
\(55\) −1.53948 −0.207584
\(56\) 0 0
\(57\) 3.83221 0.507589
\(58\) −12.2878 + 21.2831i −1.61347 + 2.79461i
\(59\) −6.32150 10.9492i −0.822989 1.42546i −0.903446 0.428701i \(-0.858971\pi\)
0.0804572 0.996758i \(-0.474362\pi\)
\(60\) −2.68585 4.65202i −0.346741 0.600573i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 3.83221 0.486691
\(63\) 0 0
\(64\) −12.1751 −1.52189
\(65\) 0.671462 1.16301i 0.0832846 0.144253i
\(66\) 1.53948 + 2.66646i 0.189497 + 0.328218i
\(67\) 3.05019 + 5.28309i 0.372640 + 0.645432i 0.989971 0.141272i \(-0.0451192\pi\)
−0.617331 + 0.786704i \(0.711786\pi\)
\(68\) −10.1751 + 17.6239i −1.23392 + 2.13721i
\(69\) 3.63986 0.438188
\(70\) 0 0
\(71\) 1.53948 0.182703 0.0913514 0.995819i \(-0.470881\pi\)
0.0913514 + 0.995819i \(0.470881\pi\)
\(72\) 2.94120 5.09431i 0.346624 0.600370i
\(73\) 7.65004 + 13.2503i 0.895369 + 1.55083i 0.833347 + 0.552750i \(0.186422\pi\)
0.0620224 + 0.998075i \(0.480245\pi\)
\(74\) −9.97858 17.2834i −1.15999 2.00915i
\(75\) −1.83221 + 3.17348i −0.211566 + 0.366442i
\(76\) −11.6644 −1.33800
\(77\) 0 0
\(78\) −2.68585 −0.304112
\(79\) −0.441202 + 0.764184i −0.0496391 + 0.0859774i −0.889777 0.456395i \(-0.849140\pi\)
0.840138 + 0.542372i \(0.182474\pi\)
\(80\) 0.803442 + 1.39160i 0.0898276 + 0.155586i
\(81\) 0.550192 + 0.952961i 0.0611325 + 0.105885i
\(82\) 0.342923 0.593960i 0.0378695 0.0655919i
\(83\) −12.1292 −1.33135 −0.665674 0.746243i \(-0.731856\pi\)
−0.665674 + 0.746243i \(0.731856\pi\)
\(84\) 0 0
\(85\) −7.83221 −0.849523
\(86\) 9.55176 16.5441i 1.02999 1.78400i
\(87\) 6.01228 + 10.4136i 0.644584 + 1.11645i
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) −2.86802 + 4.96755i −0.304009 + 0.526560i −0.977040 0.213055i \(-0.931659\pi\)
0.673031 + 0.739614i \(0.264992\pi\)
\(90\) 5.30429 0.559121
\(91\) 0 0
\(92\) −11.0790 −1.15506
\(93\) 0.937529 1.62385i 0.0972172 0.168385i
\(94\) 12.4342 + 21.5366i 1.28249 + 2.22133i
\(95\) −2.24464 3.88784i −0.230296 0.398884i
\(96\) −2.39312 + 4.14500i −0.244246 + 0.423047i
\(97\) −5.34292 −0.542492 −0.271246 0.962510i \(-0.587436\pi\)
−0.271246 + 0.962510i \(0.587436\pi\)
\(98\) 0 0
\(99\) −1.93260 −0.194233
\(100\) 5.57686 9.65940i 0.557686 0.965940i
\(101\) −5.57318 9.65304i −0.554552 0.960513i −0.997938 0.0641821i \(-0.979556\pi\)
0.443386 0.896331i \(-0.353777\pi\)
\(102\) 7.83221 + 13.5658i 0.775505 + 1.34321i
\(103\) 1.70727 2.95708i 0.168222 0.291369i −0.769573 0.638559i \(-0.779531\pi\)
0.937795 + 0.347190i \(0.112864\pi\)
\(104\) 3.48929 0.342153
\(105\) 0 0
\(106\) −1.83221 −0.177960
\(107\) −2.48929 + 4.31157i −0.240649 + 0.416816i −0.960899 0.276898i \(-0.910693\pi\)
0.720251 + 0.693714i \(0.244027\pi\)
\(108\) −9.37169 16.2322i −0.901792 1.56195i
\(109\) 6.74832 + 11.6884i 0.646372 + 1.11955i 0.983983 + 0.178263i \(0.0570477\pi\)
−0.337611 + 0.941286i \(0.609619\pi\)
\(110\) 1.80344 3.12365i 0.171951 0.297829i
\(111\) −9.76481 −0.926835
\(112\) 0 0
\(113\) 16.4464 1.54715 0.773576 0.633704i \(-0.218466\pi\)
0.773576 + 0.633704i \(0.218466\pi\)
\(114\) −4.48929 + 7.77568i −0.420460 + 0.728259i
\(115\) −2.13198 3.69270i −0.198808 0.344346i
\(116\) −18.3001 31.6967i −1.69912 2.94296i
\(117\) 0.842923 1.45999i 0.0779283 0.134976i
\(118\) 29.6216 2.72689
\(119\) 0 0
\(120\) 5.37169 0.490366
\(121\) 4.84292 8.38819i 0.440266 0.762563i
\(122\) 2.34292 + 4.05806i 0.212118 + 0.367400i
\(123\) −0.167788 0.290618i −0.0151290 0.0262041i
\(124\) −2.85363 + 4.94264i −0.256264 + 0.443862i
\(125\) 11.0073 0.984527
\(126\) 0 0
\(127\) 12.0575 1.06993 0.534967 0.844873i \(-0.320324\pi\)
0.534967 + 0.844873i \(0.320324\pi\)
\(128\) 10.0876 17.4722i 0.891623 1.54434i
\(129\) −4.67357 8.09486i −0.411485 0.712712i
\(130\) 1.57318 + 2.72483i 0.137977 + 0.238984i
\(131\) 1.83221 3.17348i 0.160081 0.277269i −0.774816 0.632186i \(-0.782158\pi\)
0.934898 + 0.354918i \(0.115491\pi\)
\(132\) −4.58546 −0.399113
\(133\) 0 0
\(134\) −14.2927 −1.23470
\(135\) 3.60688 6.24731i 0.310431 0.537683i
\(136\) −10.1751 17.6239i −0.872511 1.51123i
\(137\) 6.55176 + 11.3480i 0.559755 + 0.969523i 0.997517 + 0.0704325i \(0.0224379\pi\)
−0.437762 + 0.899091i \(0.644229\pi\)
\(138\) −4.26396 + 7.38540i −0.362973 + 0.628687i
\(139\) 7.49663 0.635856 0.317928 0.948115i \(-0.397013\pi\)
0.317928 + 0.948115i \(0.397013\pi\)
\(140\) 0 0
\(141\) 12.1678 1.02471
\(142\) −1.80344 + 3.12365i −0.151342 + 0.262131i
\(143\) −0.573183 0.992782i −0.0479319 0.0830206i
\(144\) 1.00861 + 1.74696i 0.0840505 + 0.145580i
\(145\) 7.04315 12.1991i 0.584902 1.01308i
\(146\) −35.8469 −2.96671
\(147\) 0 0
\(148\) 29.7220 2.44313
\(149\) −1.08389 + 1.87736i −0.0887961 + 0.153799i −0.907002 0.421125i \(-0.861635\pi\)
0.818206 + 0.574925i \(0.194969\pi\)
\(150\) −4.29273 7.43523i −0.350500 0.607084i
\(151\) −7.45559 12.9135i −0.606727 1.05088i −0.991776 0.127986i \(-0.959149\pi\)
0.385049 0.922896i \(-0.374185\pi\)
\(152\) 5.83221 10.1017i 0.473055 0.819355i
\(153\) −9.83221 −0.794887
\(154\) 0 0
\(155\) −2.19656 −0.176432
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) −11.4342 19.8046i −0.912546 1.58058i −0.810456 0.585800i \(-0.800780\pi\)
−0.102090 0.994775i \(-0.532553\pi\)
\(158\) −1.03370 1.79042i −0.0822369 0.142439i
\(159\) −0.448240 + 0.776375i −0.0355478 + 0.0615705i
\(160\) 5.60688 0.443263
\(161\) 0 0
\(162\) −2.57812 −0.202556
\(163\) −3.53948 + 6.13056i −0.277234 + 0.480183i −0.970696 0.240310i \(-0.922751\pi\)
0.693463 + 0.720493i \(0.256084\pi\)
\(164\) 0.510711 + 0.884578i 0.0398799 + 0.0690739i
\(165\) −0.882404 1.52837i −0.0686950 0.118983i
\(166\) 14.2088 24.6104i 1.10282 1.91014i
\(167\) 2.61423 0.202295 0.101148 0.994871i \(-0.467749\pi\)
0.101148 + 0.994871i \(0.467749\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 9.17513 15.8918i 0.703701 1.21885i
\(171\) −2.81783 4.88062i −0.215485 0.373230i
\(172\) 14.2253 + 24.6390i 1.08467 + 1.87871i
\(173\) −5.50157 + 9.52899i −0.418276 + 0.724476i −0.995766 0.0919219i \(-0.970699\pi\)
0.577490 + 0.816398i \(0.304032\pi\)
\(174\) −28.1726 −2.13576
\(175\) 0 0
\(176\) 1.37169 0.103395
\(177\) 7.24675 12.5517i 0.544699 0.943446i
\(178\) −6.71955 11.6386i −0.503651 0.872350i
\(179\) −11.9807 20.7512i −0.895478 1.55101i −0.833212 0.552954i \(-0.813500\pi\)
−0.0622667 0.998060i \(-0.519833\pi\)
\(180\) −3.94981 + 6.84127i −0.294401 + 0.509918i
\(181\) 6.56090 0.487668 0.243834 0.969817i \(-0.421595\pi\)
0.243834 + 0.969817i \(0.421595\pi\)
\(182\) 0 0
\(183\) 2.29273 0.169484
\(184\) 5.53948 9.59466i 0.408376 0.707328i
\(185\) 5.71955 + 9.90655i 0.420510 + 0.728344i
\(186\) 2.19656 + 3.80455i 0.161059 + 0.278963i
\(187\) −3.34292 + 5.79011i −0.244459 + 0.423415i
\(188\) −37.0361 −2.70114
\(189\) 0 0
\(190\) 10.5181 0.763060
\(191\) 2.19656 3.80455i 0.158937 0.275288i −0.775548 0.631288i \(-0.782527\pi\)
0.934486 + 0.356001i \(0.115860\pi\)
\(192\) −6.97858 12.0873i −0.503635 0.872322i
\(193\) 4.14637 + 7.18172i 0.298462 + 0.516951i 0.975784 0.218735i \(-0.0701931\pi\)
−0.677322 + 0.735686i \(0.736860\pi\)
\(194\) 6.25903 10.8410i 0.449372 0.778335i
\(195\) 1.53948 0.110245
\(196\) 0 0
\(197\) −3.17092 −0.225919 −0.112959 0.993600i \(-0.536033\pi\)
−0.112959 + 0.993600i \(0.536033\pi\)
\(198\) 2.26396 3.92130i 0.160893 0.278674i
\(199\) 6.79851 + 11.7754i 0.481934 + 0.834733i 0.999785 0.0207372i \(-0.00660132\pi\)
−0.517851 + 0.855471i \(0.673268\pi\)
\(200\) 5.57686 + 9.65940i 0.394343 + 0.683023i
\(201\) −3.49663 + 6.05635i −0.246634 + 0.427182i
\(202\) 26.1151 1.83745
\(203\) 0 0
\(204\) −23.3288 −1.63335
\(205\) −0.196558 + 0.340448i −0.0137282 + 0.0237779i
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) −2.67639 4.63565i −0.186022 0.322200i
\(208\) −0.598279 + 1.03625i −0.0414832 + 0.0718510i
\(209\) −3.83221 −0.265080
\(210\) 0 0
\(211\) 9.27552 0.638553 0.319277 0.947662i \(-0.396560\pi\)
0.319277 + 0.947662i \(0.396560\pi\)
\(212\) 1.36435 2.36312i 0.0937037 0.162300i
\(213\) 0.882404 + 1.52837i 0.0604613 + 0.104722i
\(214\) −5.83221 10.1017i −0.398682 0.690537i
\(215\) −5.47490 + 9.48281i −0.373385 + 0.646722i
\(216\) 18.7434 1.27533
\(217\) 0 0
\(218\) −31.6216 −2.14168
\(219\) −8.76974 + 15.1896i −0.592604 + 1.02642i
\(220\) 2.68585 + 4.65202i 0.181080 + 0.313639i
\(221\) −2.91611 5.05084i −0.196159 0.339756i
\(222\) 11.4391 19.8131i 0.767742 1.32977i
\(223\) −19.5928 −1.31203 −0.656016 0.754747i \(-0.727760\pi\)
−0.656016 + 0.754747i \(0.727760\pi\)
\(224\) 0 0
\(225\) 5.38890 0.359260
\(226\) −19.2664 + 33.3703i −1.28158 + 2.21976i
\(227\) 9.83221 + 17.0299i 0.652587 + 1.13031i 0.982493 + 0.186300i \(0.0596496\pi\)
−0.329906 + 0.944014i \(0.607017\pi\)
\(228\) −6.68585 11.5802i −0.442781 0.766919i
\(229\) −3.88240 + 6.72452i −0.256556 + 0.444369i −0.965317 0.261080i \(-0.915921\pi\)
0.708761 + 0.705449i \(0.249255\pi\)
\(230\) 9.99013 0.658730
\(231\) 0 0
\(232\) 36.6002 2.40292
\(233\) −6.09828 + 10.5625i −0.399512 + 0.691974i −0.993666 0.112377i \(-0.964154\pi\)
0.594154 + 0.804351i \(0.297487\pi\)
\(234\) 1.97490 + 3.42063i 0.129104 + 0.223614i
\(235\) −7.12705 12.3444i −0.464917 0.805260i
\(236\) −22.0575 + 38.2048i −1.43582 + 2.48692i
\(237\) −1.01156 −0.0657077
\(238\) 0 0
\(239\) −10.2927 −0.665781 −0.332891 0.942965i \(-0.608024\pi\)
−0.332891 + 0.942965i \(0.608024\pi\)
\(240\) −0.921039 + 1.59529i −0.0594528 + 0.102975i
\(241\) 2.01438 + 3.48902i 0.129758 + 0.224747i 0.923583 0.383399i \(-0.125247\pi\)
−0.793825 + 0.608147i \(0.791913\pi\)
\(242\) 11.3466 + 19.6529i 0.729387 + 1.26334i
\(243\) 7.42682 12.8636i 0.476431 0.825202i
\(244\) −6.97858 −0.446758
\(245\) 0 0
\(246\) 0.786230 0.0501282
\(247\) 1.67146 2.89506i 0.106353 0.184208i
\(248\) −2.85363 4.94264i −0.181206 0.313858i
\(249\) −6.95222 12.0416i −0.440579 0.763105i
\(250\) −12.8947 + 22.3342i −0.815531 + 1.41254i
\(251\) 2.91117 0.183752 0.0918758 0.995770i \(-0.470714\pi\)
0.0918758 + 0.995770i \(0.470714\pi\)
\(252\) 0 0
\(253\) −3.63986 −0.228836
\(254\) −14.1249 + 24.4651i −0.886278 + 1.53508i
\(255\) −4.48929 7.77568i −0.281130 0.486932i
\(256\) 11.4593 + 19.8480i 0.716204 + 1.24050i
\(257\) 9.79851 16.9715i 0.611214 1.05865i −0.379822 0.925060i \(-0.624015\pi\)
0.991036 0.133594i \(-0.0426520\pi\)
\(258\) 21.8996 1.36341
\(259\) 0 0
\(260\) −4.68585 −0.290604
\(261\) 8.84166 15.3142i 0.547285 0.947926i
\(262\) 4.29273 + 7.43523i 0.265206 + 0.459350i
\(263\) −3.78412 6.55430i −0.233339 0.404155i 0.725450 0.688275i \(-0.241632\pi\)
−0.958789 + 0.284120i \(0.908299\pi\)
\(264\) 2.29273 3.97113i 0.141108 0.244406i
\(265\) 1.05019 0.0645128
\(266\) 0 0
\(267\) −6.57560 −0.402420
\(268\) 10.6430 18.4342i 0.650125 1.12605i
\(269\) 4.73604 + 8.20306i 0.288761 + 0.500149i 0.973514 0.228626i \(-0.0734233\pi\)
−0.684753 + 0.728775i \(0.740090\pi\)
\(270\) 8.45065 + 14.6370i 0.514290 + 0.890777i
\(271\) −14.6858 + 25.4366i −0.892102 + 1.54517i −0.0547504 + 0.998500i \(0.517436\pi\)
−0.837351 + 0.546665i \(0.815897\pi\)
\(272\) 6.97858 0.423138
\(273\) 0 0
\(274\) −30.7005 −1.85469
\(275\) 1.83221 3.17348i 0.110487 0.191368i
\(276\) −6.35027 10.9990i −0.382241 0.662061i
\(277\) 0.951913 + 1.64876i 0.0571949 + 0.0990645i 0.893205 0.449649i \(-0.148451\pi\)
−0.836010 + 0.548714i \(0.815118\pi\)
\(278\) −8.78202 + 15.2109i −0.526711 + 0.912289i
\(279\) −2.75746 −0.165085
\(280\) 0 0
\(281\) −20.5756 −1.22744 −0.613719 0.789525i \(-0.710327\pi\)
−0.613719 + 0.789525i \(0.710327\pi\)
\(282\) −14.2541 + 24.6888i −0.848819 + 1.47020i
\(283\) 13.4966 + 23.3769i 0.802292 + 1.38961i 0.918104 + 0.396339i \(0.129719\pi\)
−0.115813 + 0.993271i \(0.536947\pi\)
\(284\) −2.68585 4.65202i −0.159376 0.276047i
\(285\) 2.57318 4.45688i 0.152422 0.264003i
\(286\) 2.68585 0.158817
\(287\) 0 0
\(288\) 7.03863 0.414756
\(289\) −8.50735 + 14.7352i −0.500432 + 0.866774i
\(290\) 16.5016 + 28.5816i 0.969005 + 1.67837i
\(291\) −3.06247 5.30436i −0.179525 0.310947i
\(292\) 26.6932 46.2340i 1.56210 2.70564i
\(293\) −14.9070 −0.870874 −0.435437 0.900219i \(-0.643406\pi\)
−0.435437 + 0.900219i \(0.643406\pi\)
\(294\) 0 0
\(295\) −16.9786 −0.988531
\(296\) −14.8610 + 25.7400i −0.863777 + 1.49611i
\(297\) −3.07896 5.33292i −0.178659 0.309447i
\(298\) −2.53948 4.39851i −0.147108 0.254799i
\(299\) 1.58757 2.74975i 0.0918114 0.159022i
\(300\) 12.7862 0.738213
\(301\) 0 0
\(302\) 34.9357 2.01033
\(303\) 6.38890 11.0659i 0.367033 0.635720i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) −1.34292 2.32601i −0.0768956 0.133187i
\(306\) 11.5181 19.9499i 0.658444 1.14046i
\(307\) 26.0288 1.48554 0.742770 0.669546i \(-0.233512\pi\)
0.742770 + 0.669546i \(0.233512\pi\)
\(308\) 0 0
\(309\) 3.91431 0.222677
\(310\) 2.57318 4.45688i 0.146147 0.253134i
\(311\) −9.74832 16.8846i −0.552776 0.957437i −0.998073 0.0620536i \(-0.980235\pi\)
0.445296 0.895383i \(-0.353098\pi\)
\(312\) 2.00000 + 3.46410i 0.113228 + 0.196116i
\(313\) 1.74097 3.01545i 0.0984055 0.170443i −0.812619 0.582795i \(-0.801959\pi\)
0.911025 + 0.412352i \(0.135292\pi\)
\(314\) 53.5787 3.02362
\(315\) 0 0
\(316\) 3.07896 0.173205
\(317\) −2.51071 + 4.34868i −0.141016 + 0.244246i −0.927879 0.372881i \(-0.878370\pi\)
0.786864 + 0.617127i \(0.211703\pi\)
\(318\) −1.05019 1.81899i −0.0588918 0.102004i
\(319\) −6.01228 10.4136i −0.336623 0.583048i
\(320\) −8.17513 + 14.1597i −0.457004 + 0.791554i
\(321\) −5.70727 −0.318549
\(322\) 0 0
\(323\) −19.4966 −1.08482
\(324\) 1.91978 3.32515i 0.106654 0.184731i
\(325\) 1.59828 + 2.76830i 0.0886566 + 0.153558i
\(326\) −8.29273 14.3634i −0.459292 0.795517i
\(327\) −7.73604 + 13.3992i −0.427804 + 0.740978i
\(328\) −1.02142 −0.0563986
\(329\) 0 0
\(330\) 4.13481 0.227614
\(331\) 3.07475 5.32562i 0.169004 0.292723i −0.769066 0.639169i \(-0.779278\pi\)
0.938070 + 0.346446i \(0.112612\pi\)
\(332\) 21.1611 + 36.6520i 1.16136 + 2.01154i
\(333\) 7.18007 + 12.4362i 0.393465 + 0.681502i
\(334\) −3.06247 + 5.30436i −0.167571 + 0.290241i
\(335\) 8.19235 0.447596
\(336\) 0 0
\(337\) −25.6258 −1.39593 −0.697963 0.716134i \(-0.745910\pi\)
−0.697963 + 0.716134i \(0.745910\pi\)
\(338\) −1.17146 + 2.02903i −0.0637191 + 0.110365i
\(339\) 9.42682 + 16.3277i 0.511994 + 0.886800i
\(340\) 13.6644 + 23.6675i 0.741057 + 1.28355i
\(341\) −0.937529 + 1.62385i −0.0507700 + 0.0879363i
\(342\) 13.2039 0.713985
\(343\) 0 0
\(344\) −28.4507 −1.53396
\(345\) 2.44403 4.23318i 0.131582 0.227907i
\(346\) −12.8898 22.3257i −0.692957 1.20024i
\(347\) 8.35027 + 14.4631i 0.448266 + 0.776419i 0.998273 0.0587404i \(-0.0187084\pi\)
−0.550007 + 0.835160i \(0.685375\pi\)
\(348\) 20.9786 36.3360i 1.12457 1.94781i
\(349\) −23.5500 −1.26060 −0.630300 0.776351i \(-0.717068\pi\)
−0.630300 + 0.776351i \(0.717068\pi\)
\(350\) 0 0
\(351\) 5.37169 0.286720
\(352\) 2.39312 4.14500i 0.127553 0.220929i
\(353\) 3.82487 + 6.62486i 0.203577 + 0.352606i 0.949678 0.313227i \(-0.101410\pi\)
−0.746101 + 0.665832i \(0.768077\pi\)
\(354\) 16.9786 + 29.4078i 0.902401 + 1.56300i
\(355\) 1.03370 1.79042i 0.0548632 0.0950259i
\(356\) 20.0147 1.06078
\(357\) 0 0
\(358\) 56.1396 2.96707
\(359\) −9.18741 + 15.9131i −0.484893 + 0.839860i −0.999849 0.0173569i \(-0.994475\pi\)
0.514956 + 0.857216i \(0.327808\pi\)
\(360\) −3.94981 6.84127i −0.208173 0.360566i
\(361\) 3.91243 + 6.77653i 0.205918 + 0.356660i
\(362\) −7.68585 + 13.3123i −0.403959 + 0.699678i
\(363\) 11.1035 0.582784
\(364\) 0 0
\(365\) 20.5468 1.07547
\(366\) −2.68585 + 4.65202i −0.140391 + 0.243165i
\(367\) −2.66936 4.62346i −0.139339 0.241343i 0.787907 0.615794i \(-0.211165\pi\)
−0.927247 + 0.374451i \(0.877831\pi\)
\(368\) 1.89962 + 3.29023i 0.0990243 + 0.171515i
\(369\) −0.246750 + 0.427383i −0.0128453 + 0.0222487i
\(370\) −26.8009 −1.39331
\(371\) 0 0
\(372\) −6.54262 −0.339219
\(373\) −10.7606 + 18.6379i −0.557163 + 0.965034i 0.440569 + 0.897719i \(0.354777\pi\)
−0.997732 + 0.0673152i \(0.978557\pi\)
\(374\) −7.83221 13.5658i −0.404994 0.701470i
\(375\) 6.30922 + 10.9279i 0.325807 + 0.564314i
\(376\) 18.5181 32.0742i 0.954996 1.65410i
\(377\) 10.4893 0.540226
\(378\) 0 0
\(379\) 4.61002 0.236801 0.118400 0.992966i \(-0.462223\pi\)
0.118400 + 0.992966i \(0.462223\pi\)
\(380\) −7.83221 + 13.5658i −0.401784 + 0.695910i
\(381\) 6.91117 + 11.9705i 0.354070 + 0.613267i
\(382\) 5.14637 + 8.91377i 0.263311 + 0.456068i
\(383\) 4.16779 7.21882i 0.212964 0.368865i −0.739677 0.672962i \(-0.765022\pi\)
0.952641 + 0.304098i \(0.0983549\pi\)
\(384\) 23.1281 1.18025
\(385\) 0 0
\(386\) −19.4292 −0.988922
\(387\) −6.87295 + 11.9043i −0.349372 + 0.605130i
\(388\) 9.32150 + 16.1453i 0.473227 + 0.819654i
\(389\) 3.22112 + 5.57914i 0.163317 + 0.282873i 0.936056 0.351850i \(-0.114447\pi\)
−0.772739 + 0.634724i \(0.781114\pi\)
\(390\) −1.80344 + 3.12365i −0.0913209 + 0.158172i
\(391\) −18.5181 −0.936498
\(392\) 0 0
\(393\) 4.20077 0.211901
\(394\) 3.71462 6.43390i 0.187140 0.324135i
\(395\) 0.592500 + 1.02624i 0.0298119 + 0.0516358i
\(396\) 3.37169 + 5.83994i 0.169434 + 0.293468i
\(397\) −0.700231 + 1.21284i −0.0351436 + 0.0608705i −0.883062 0.469256i \(-0.844522\pi\)
0.847919 + 0.530126i \(0.177856\pi\)
\(398\) −31.8568 −1.59684
\(399\) 0 0
\(400\) −3.82487 −0.191243
\(401\) 3.48929 6.04363i 0.174247 0.301804i −0.765654 0.643253i \(-0.777584\pi\)
0.939900 + 0.341449i \(0.110918\pi\)
\(402\) −8.19235 14.1896i −0.408597 0.707711i
\(403\) −0.817827 1.41652i −0.0407389 0.0705618i
\(404\) −19.4464 + 33.6822i −0.967497 + 1.67575i
\(405\) 1.47773 0.0734291
\(406\) 0 0
\(407\) 9.76481 0.484024
\(408\) 11.6644 20.2034i 0.577475 1.00022i
\(409\) 9.18952 + 15.9167i 0.454392 + 0.787031i 0.998653 0.0518854i \(-0.0165230\pi\)
−0.544261 + 0.838916i \(0.683190\pi\)
\(410\) −0.460519 0.797643i −0.0227434 0.0393928i
\(411\) −7.51071 + 13.0089i −0.370476 + 0.641683i
\(412\) −11.9143 −0.586976
\(413\) 0 0
\(414\) 12.5412 0.616365
\(415\) −8.14426 + 14.1063i −0.399786 + 0.692450i
\(416\) 2.08757 + 3.61577i 0.102351 + 0.177278i
\(417\) 4.29694 + 7.44252i 0.210422 + 0.364462i
\(418\) 4.48929 7.77568i 0.219578 0.380321i
\(419\) −30.0393 −1.46751 −0.733757 0.679412i \(-0.762235\pi\)
−0.733757 + 0.679412i \(0.762235\pi\)
\(420\) 0 0
\(421\) −8.31729 −0.405360 −0.202680 0.979245i \(-0.564965\pi\)
−0.202680 + 0.979245i \(0.564965\pi\)
\(422\) −10.8659 + 18.8203i −0.528944 + 0.916159i
\(423\) −8.94698 15.4966i −0.435017 0.753472i
\(424\) 1.36435 + 2.36312i 0.0662585 + 0.114763i
\(425\) 9.32150 16.1453i 0.452159 0.783163i
\(426\) −4.13481 −0.200332
\(427\) 0 0
\(428\) 17.3717 0.839692
\(429\) 0.657077 1.13809i 0.0317240 0.0549475i
\(430\) −12.8273 22.2175i −0.618586 1.07142i
\(431\) −4.82487 8.35691i −0.232406 0.402538i 0.726110 0.687579i \(-0.241326\pi\)
−0.958516 + 0.285040i \(0.907993\pi\)
\(432\) −3.21377 + 5.56641i −0.154623 + 0.267814i
\(433\) 26.3074 1.26425 0.632127 0.774865i \(-0.282182\pi\)
0.632127 + 0.774865i \(0.282182\pi\)
\(434\) 0 0
\(435\) 16.1481 0.774240
\(436\) 23.5468 40.7843i 1.12769 1.95321i
\(437\) −5.30712 9.19219i −0.253874 0.439722i
\(438\) −20.5468 35.5881i −0.981765 1.70047i
\(439\) −16.9070 + 29.2837i −0.806925 + 1.39764i 0.108058 + 0.994145i \(0.465537\pi\)
−0.914984 + 0.403491i \(0.867797\pi\)
\(440\) −5.37169 −0.256085
\(441\) 0 0
\(442\) 13.6644 0.649950
\(443\) −13.2232 + 22.9033i −0.628254 + 1.08817i 0.359648 + 0.933088i \(0.382897\pi\)
−0.987902 + 0.155080i \(0.950436\pi\)
\(444\) 17.0361 + 29.5074i 0.808498 + 1.40036i
\(445\) 3.85153 + 6.67104i 0.182580 + 0.316238i
\(446\) 22.9522 39.7544i 1.08682 1.88243i
\(447\) −2.48508 −0.117540
\(448\) 0 0
\(449\) 2.64300 0.124731 0.0623655 0.998053i \(-0.480136\pi\)
0.0623655 + 0.998053i \(0.480136\pi\)
\(450\) −6.31289 + 10.9343i −0.297593 + 0.515446i
\(451\) 0.167788 + 0.290618i 0.00790084 + 0.0136847i
\(452\) −28.6932 49.6981i −1.34961 2.33760i
\(453\) 8.54683 14.8035i 0.401565 0.695531i
\(454\) −46.0722 −2.16228
\(455\) 0 0
\(456\) 13.3717 0.626187
\(457\) 16.8445 29.1755i 0.787952 1.36477i −0.139268 0.990255i \(-0.544475\pi\)
0.927220 0.374518i \(-0.122192\pi\)
\(458\) −9.09617 15.7550i −0.425036 0.736184i
\(459\) −15.6644 27.1316i −0.731153 1.26639i
\(460\) −7.43910 + 12.8849i −0.346850 + 0.600761i
\(461\) 33.0790 1.54064 0.770320 0.637657i \(-0.220096\pi\)
0.770320 + 0.637657i \(0.220096\pi\)
\(462\) 0 0
\(463\) −2.51806 −0.117024 −0.0585120 0.998287i \(-0.518636\pi\)
−0.0585120 + 0.998287i \(0.518636\pi\)
\(464\) −6.27552 + 10.8695i −0.291334 + 0.504605i
\(465\) −1.25903 2.18070i −0.0583861 0.101128i
\(466\) −14.2878 24.7472i −0.661869 1.14639i
\(467\) −1.28780 + 2.23053i −0.0595922 + 0.103217i −0.894282 0.447503i \(-0.852313\pi\)
0.834690 + 0.550720i \(0.185647\pi\)
\(468\) −5.88240 −0.271914
\(469\) 0 0
\(470\) 33.3963 1.54045
\(471\) 13.1077 22.7033i 0.603972 1.04611i
\(472\) −22.0575 38.2048i −1.01528 1.75852i
\(473\) 4.67357 + 8.09486i 0.214891 + 0.372202i
\(474\) 1.18500 2.05248i 0.0544289 0.0942736i
\(475\) 10.6858 0.490300
\(476\) 0 0
\(477\) 1.31836 0.0603638
\(478\) 12.0575 20.8843i 0.551499 0.955224i
\(479\) −0.256923 0.445005i −0.0117391 0.0203328i 0.860096 0.510132i \(-0.170403\pi\)
−0.871835 + 0.489799i \(0.837070\pi\)
\(480\) 3.21377 + 5.56641i 0.146688 + 0.254071i
\(481\) −4.25903 + 7.37685i −0.194195 + 0.336356i
\(482\) −9.43910 −0.429939
\(483\) 0 0
\(484\) −33.7967 −1.53621
\(485\) −3.58757 + 6.21385i −0.162903 + 0.282156i
\(486\) 17.4005 + 30.1385i 0.789301 + 1.36711i
\(487\) −18.0288 31.2267i −0.816962 1.41502i −0.907911 0.419163i \(-0.862323\pi\)
0.0909493 0.995856i \(-0.471010\pi\)
\(488\) 3.48929 6.04363i 0.157953 0.273582i
\(489\) −8.11508 −0.366976
\(490\) 0 0
\(491\) −9.22846 −0.416475 −0.208237 0.978078i \(-0.566773\pi\)
−0.208237 + 0.978078i \(0.566773\pi\)
\(492\) −0.585462 + 1.01405i −0.0263947 + 0.0457169i
\(493\) −30.5879 52.9798i −1.37761 2.38609i
\(494\) 3.91611 + 6.78289i 0.176194 + 0.305177i
\(495\) −1.29766 + 2.24762i −0.0583257 + 0.101023i
\(496\) 1.95715 0.0878788
\(497\) 0 0
\(498\) 32.5770 1.45981
\(499\) −0.501568 + 0.868741i −0.0224533 + 0.0388902i −0.877034 0.480429i \(-0.840481\pi\)
0.854580 + 0.519319i \(0.173814\pi\)
\(500\) −19.2039 33.2621i −0.858825 1.48753i
\(501\) 1.49843 + 2.59536i 0.0669450 + 0.115952i
\(502\) −3.41033 + 5.90686i −0.152210 + 0.263636i
\(503\) −30.3503 −1.35325 −0.676626 0.736327i \(-0.736559\pi\)
−0.676626 + 0.736327i \(0.736559\pi\)
\(504\) 0 0
\(505\) −14.9687 −0.666099
\(506\) 4.26396 7.38540i 0.189556 0.328321i
\(507\) 0.573183 + 0.992782i 0.0254559 + 0.0440910i
\(508\) −21.0361 36.4356i −0.933327 1.61657i
\(509\) −5.29977 + 9.17947i −0.234908 + 0.406873i −0.959246 0.282572i \(-0.908812\pi\)
0.724338 + 0.689445i \(0.242146\pi\)
\(510\) 21.0361 0.931495
\(511\) 0 0
\(512\) −13.3461 −0.589818
\(513\) 8.97858 15.5514i 0.396414 0.686609i
\(514\) 22.9572 + 39.7630i 1.01260 + 1.75387i
\(515\) −2.29273 3.97113i −0.101030 0.174989i
\(516\) −16.3074 + 28.2453i −0.717894 + 1.24343i
\(517\) −12.1678 −0.535139
\(518\) 0 0
\(519\) −12.6136 −0.553676
\(520\) 2.34292 4.05806i 0.102744 0.177958i
\(521\) 8.13229 + 14.0855i 0.356282 + 0.617099i 0.987337 0.158640i \(-0.0507109\pi\)
−0.631054 + 0.775739i \(0.717378\pi\)
\(522\) 20.7153 + 35.8800i 0.906686 + 1.57043i
\(523\) −3.61110 + 6.25460i −0.157902 + 0.273495i −0.934112 0.356980i \(-0.883806\pi\)
0.776210 + 0.630475i \(0.217140\pi\)
\(524\) −12.7862 −0.558569
\(525\) 0 0
\(526\) 17.7318 0.773144
\(527\) −4.76974 + 8.26143i −0.207773 + 0.359874i
\(528\) 0.786230 + 1.36179i 0.0342163 + 0.0592643i
\(529\) 6.45926 + 11.1878i 0.280837 + 0.486425i
\(530\) −1.23026 + 2.13087i −0.0534391 + 0.0925592i
\(531\) −21.3142 −0.924955
\(532\) 0 0
\(533\) −0.292731 −0.0126796
\(534\) 7.70306 13.3421i 0.333344 0.577369i
\(535\) 3.34292 + 5.79011i 0.144527 + 0.250328i
\(536\) 10.6430 + 18.4342i 0.459708 + 0.796237i
\(537\) 13.7342 23.7884i 0.592676 1.02655i
\(538\) −22.1923 −0.956780
\(539\) 0 0
\(540\) −25.1709 −1.08318
\(541\) −8.67670 + 15.0285i −0.373041 + 0.646125i −0.990032 0.140845i \(-0.955018\pi\)
0.616991 + 0.786970i \(0.288351\pi\)
\(542\) −34.4078 59.5961i −1.47794 2.55987i
\(543\) 3.76060 + 6.51354i 0.161383 + 0.279523i
\(544\) 12.1751 21.0880i 0.522005 0.904138i
\(545\) 18.1249 0.776387
\(546\) 0 0
\(547\) −34.1109 −1.45848 −0.729238 0.684261i \(-0.760125\pi\)
−0.729238 + 0.684261i \(0.760125\pi\)
\(548\) 22.8610 39.5964i 0.976573 1.69147i
\(549\) −1.68585 2.91997i −0.0719502 0.124621i
\(550\) 4.29273 + 7.43523i 0.183043 + 0.317039i
\(551\) 17.5324 30.3671i 0.746907 1.29368i
\(552\) 12.7005 0.540571
\(553\) 0 0
\(554\) −4.46052 −0.189509
\(555\) −6.55669 + 11.3565i −0.278316 + 0.482058i
\(556\) −13.0790 22.6534i −0.554672 0.960719i
\(557\) 6.61110 + 11.4508i 0.280121 + 0.485184i 0.971414 0.237390i \(-0.0762920\pi\)
−0.691293 + 0.722574i \(0.742959\pi\)
\(558\) 3.23026 5.59497i 0.136748 0.236854i
\(559\) −8.15371 −0.344865
\(560\) 0 0
\(561\) −7.66442 −0.323592
\(562\) 24.1035 41.7485i 1.01675 1.76106i
\(563\) 20.6858 + 35.8289i 0.871804 + 1.51001i 0.860128 + 0.510078i \(0.170383\pi\)
0.0116762 + 0.999932i \(0.496283\pi\)
\(564\) −21.2285 36.7688i −0.893880 1.54824i
\(565\) 11.0432 19.1273i 0.464589 0.804692i
\(566\) −63.2432 −2.65831
\(567\) 0 0
\(568\) 5.37169 0.225391
\(569\) 1.34082 2.32236i 0.0562100 0.0973586i −0.836551 0.547889i \(-0.815432\pi\)
0.892761 + 0.450530i \(0.148765\pi\)
\(570\) 6.02877 + 10.4421i 0.252517 + 0.437373i
\(571\) 14.4658 + 25.0554i 0.605373 + 1.04854i 0.991992 + 0.126298i \(0.0403095\pi\)
−0.386619 + 0.922239i \(0.626357\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) 5.03612 0.210387
\(574\) 0 0
\(575\) 10.1495 0.423263
\(576\) −10.2627 + 17.7755i −0.427613 + 0.740647i
\(577\) −18.7648 32.5016i −0.781189 1.35306i −0.931249 0.364382i \(-0.881280\pi\)
0.150060 0.988677i \(-0.452053\pi\)
\(578\) −19.9321 34.5233i −0.829064 1.43598i
\(579\) −4.75325 + 8.23287i −0.197538 + 0.342146i
\(580\) −49.1512 −2.04089
\(581\) 0 0
\(582\) 14.3503 0.594838
\(583\) 0.448240 0.776375i 0.0185642 0.0321542i
\(584\) 26.6932 + 46.2340i 1.10457 + 1.91318i
\(585\) −1.13198 1.96065i −0.0468016 0.0810628i
\(586\) 17.4629 30.2467i 0.721387 1.24948i
\(587\) 23.0649 0.951990 0.475995 0.879448i \(-0.342088\pi\)
0.475995 + 0.879448i \(0.342088\pi\)
\(588\) 0 0
\(589\) −5.46787 −0.225299
\(590\) 19.8898 34.4501i 0.818848 1.41829i
\(591\) −1.81752 3.14804i −0.0747627 0.129493i
\(592\) −5.09617 8.82683i −0.209451 0.362781i
\(593\) 5.52510 9.56975i 0.226889 0.392982i −0.729996 0.683452i \(-0.760478\pi\)
0.956884 + 0.290469i \(0.0938114\pi\)
\(594\) 14.4275 0.591969
\(595\) 0 0
\(596\) 7.56404 0.309835
\(597\) −7.79358 + 13.4989i −0.318970 + 0.552472i
\(598\) 3.71955 + 6.44245i 0.152104 + 0.263451i
\(599\) 22.3022 + 38.6285i 0.911242 + 1.57832i 0.812311 + 0.583224i \(0.198209\pi\)
0.0989311 + 0.995094i \(0.468458\pi\)
\(600\) −6.39312 + 11.0732i −0.260998 + 0.452062i
\(601\) 47.8715 1.95272 0.976359 0.216156i \(-0.0693520\pi\)
0.976359 + 0.216156i \(0.0693520\pi\)
\(602\) 0 0
\(603\) 10.2843 0.418809
\(604\) −26.0147 + 45.0588i −1.05852 + 1.83342i
\(605\) −6.50367 11.2647i −0.264412 0.457975i
\(606\) 14.9687 + 25.9266i 0.608062 + 1.05319i
\(607\) −22.5345 + 39.0310i −0.914649 + 1.58422i −0.107235 + 0.994234i \(0.534200\pi\)
−0.807414 + 0.589985i \(0.799134\pi\)
\(608\) 13.9572 0.566037
\(609\) 0 0
\(610\) 6.29273 0.254785
\(611\) 5.30712 9.19219i 0.214703 0.371876i
\(612\) 17.1537 + 29.7111i 0.693398 + 1.20100i
\(613\) 12.7606 + 22.1020i 0.515396 + 0.892691i 0.999840 + 0.0178695i \(0.00568836\pi\)
−0.484445 + 0.874822i \(0.660978\pi\)
\(614\) −30.4917 + 52.8132i −1.23054 + 2.13137i
\(615\) −0.450654 −0.0181721
\(616\) 0 0
\(617\) 29.2432 1.17729 0.588643 0.808393i \(-0.299663\pi\)
0.588643 + 0.808393i \(0.299663\pi\)
\(618\) −4.58546 + 7.94225i −0.184454 + 0.319484i
\(619\) −2.39312 4.14500i −0.0961874 0.166601i 0.813916 0.580982i \(-0.197331\pi\)
−0.910104 + 0.414381i \(0.863998\pi\)
\(620\) 3.83221 + 6.63759i 0.153905 + 0.266572i
\(621\) 8.52792 14.7708i 0.342214 0.592732i
\(622\) 45.6791 1.83157
\(623\) 0 0
\(624\) −1.37169 −0.0549116
\(625\) −0.600384 + 1.03990i −0.0240154 + 0.0415958i
\(626\) 4.07896 + 7.06497i 0.163028 + 0.282373i
\(627\) −2.19656 3.80455i −0.0877221 0.151939i
\(628\) −39.8971 + 69.1038i −1.59207 + 2.75754i
\(629\) 49.6791 1.98084
\(630\) 0 0
\(631\) −28.3931 −1.13031 −0.565156 0.824984i \(-0.691184\pi\)
−0.565156 + 0.824984i \(0.691184\pi\)
\(632\) −1.53948 + 2.66646i −0.0612373 + 0.106066i
\(633\) 5.31657 + 9.20856i 0.211315 + 0.366008i
\(634\) −5.88240 10.1886i −0.233620 0.404642i
\(635\) 8.09617 14.0230i 0.321287 0.556485i
\(636\) 3.12808 0.124036
\(637\) 0 0
\(638\) 28.1726 1.11536
\(639\) 1.29766 2.24762i 0.0513348 0.0889145i
\(640\) −13.5468 23.4638i −0.535485 0.927488i
\(641\) −2.98068 5.16269i −0.117730 0.203914i 0.801138 0.598480i \(-0.204228\pi\)
−0.918868 + 0.394566i \(0.870895\pi\)
\(642\) 6.68585 11.5802i 0.263869 0.457035i
\(643\) 31.1940 1.23017 0.615086 0.788460i \(-0.289121\pi\)
0.615086 + 0.788460i \(0.289121\pi\)
\(644\) 0 0
\(645\) −12.5525 −0.494253
\(646\) 22.8396 39.5593i 0.898610 1.55644i
\(647\) −7.45559 12.9135i −0.293109 0.507680i 0.681434 0.731880i \(-0.261357\pi\)
−0.974543 + 0.224199i \(0.928023\pi\)
\(648\) 1.91978 + 3.32515i 0.0754160 + 0.130624i
\(649\) −7.24675 + 12.5517i −0.284460 + 0.492699i
\(650\) −7.48929 −0.293754
\(651\) 0 0
\(652\) 24.7005 0.967348
\(653\) 1.78623 3.09384i 0.0699006 0.121071i −0.828957 0.559313i \(-0.811065\pi\)
0.898857 + 0.438241i \(0.144398\pi\)
\(654\) −18.1249 31.3933i −0.708741 1.22758i
\(655\) −2.46052 4.26174i −0.0961404 0.166520i
\(656\) 0.175135 0.303342i 0.00683786 0.0118435i
\(657\) 25.7936 1.00630
\(658\) 0 0
\(659\) −3.90383 −0.152071 −0.0760357 0.997105i \(-0.524226\pi\)
−0.0760357 + 0.997105i \(0.524226\pi\)
\(660\) −3.07896 + 5.33292i −0.119848 + 0.207584i
\(661\) −6.89679 11.9456i −0.268254 0.464630i 0.700157 0.713989i \(-0.253113\pi\)
−0.968411 + 0.249359i \(0.919780\pi\)
\(662\) 7.20390 + 12.4775i 0.279988 + 0.484953i
\(663\) 3.34292 5.79011i 0.129828 0.224869i
\(664\) −42.3221 −1.64242
\(665\) 0 0
\(666\) −33.6447 −1.30371
\(667\) 16.6525 28.8429i 0.644786 1.11680i
\(668\) −4.56090 7.89972i −0.176467 0.305649i
\(669\) −11.2303 19.4514i −0.434187 0.752034i
\(670\) −9.59702 + 16.6225i −0.370765 + 0.642184i
\(671\) −2.29273 −0.0885099
\(672\) 0 0
\(673\) 5.70306 0.219837 0.109918 0.993941i \(-0.464941\pi\)
0.109918 + 0.993941i \(0.464941\pi\)
\(674\) 30.0196 51.9955i 1.15631 2.00279i
\(675\) 8.58546 + 14.8705i 0.330455 + 0.572364i
\(676\) −1.74464 3.02181i −0.0671017 0.116224i
\(677\) −17.6307 + 30.5373i −0.677604 + 1.17364i 0.298097 + 0.954536i \(0.403648\pi\)
−0.975701 + 0.219108i \(0.929685\pi\)
\(678\) −44.1726 −1.69644
\(679\) 0 0
\(680\) −27.3288 −1.04801
\(681\) −11.2713 + 19.5225i −0.431917 + 0.748103i
\(682\) −2.19656 3.80455i −0.0841105 0.145684i
\(683\) −0.518058 0.897302i −0.0198229 0.0343343i 0.855944 0.517069i \(-0.172977\pi\)
−0.875767 + 0.482735i \(0.839644\pi\)
\(684\) −9.83221 + 17.0299i −0.375944 + 0.651154i
\(685\) 17.5970 0.672348
\(686\) 0 0
\(687\) −8.90131 −0.339606
\(688\) 4.87819 8.44928i 0.185979 0.322126i
\(689\) 0.391010 + 0.677249i 0.0148963 + 0.0258011i
\(690\) 5.72617 + 9.91802i 0.217992 + 0.377573i
\(691\) −1.83925 + 3.18567i −0.0699684 + 0.121189i −0.898887 0.438180i \(-0.855623\pi\)
0.828919 + 0.559369i \(0.188957\pi\)
\(692\) 38.3931 1.45949
\(693\) 0 0
\(694\) −39.1281 −1.48528
\(695\) 5.03370 8.71863i 0.190939 0.330716i
\(696\) 20.9786 + 36.3360i 0.795191 + 1.37731i
\(697\) 0.853635 + 1.47854i 0.0323337 + 0.0560036i
\(698\) 27.5879 47.7836i 1.04422 1.80864i
\(699\) −13.9817 −0.528837
\(700\) 0 0
\(701\) −0.0617493 −0.00233224 −0.00116612 0.999999i \(-0.500371\pi\)
−0.00116612 + 0.999999i \(0.500371\pi\)
\(702\) −6.29273 + 10.8993i −0.237504 + 0.411369i
\(703\) 14.2376 + 24.6603i 0.536981 + 0.930079i
\(704\) 6.97858 + 12.0873i 0.263015 + 0.455555i
\(705\) 8.17020 14.1512i 0.307708 0.532965i
\(706\) −17.9227 −0.674531
\(707\) 0 0
\(708\) −50.5720 −1.90061
\(709\) 21.4917 37.2247i 0.807138 1.39800i −0.107701 0.994183i \(-0.534349\pi\)
0.914838 0.403820i \(-0.132318\pi\)
\(710\) 2.42188 + 4.19483i 0.0908917 + 0.157429i
\(711\) 0.743798 + 1.28830i 0.0278946 + 0.0483149i
\(712\) −10.0073 + 17.3332i −0.375041 + 0.649590i
\(713\) −5.19342 −0.194495
\(714\) 0 0
\(715\) −1.53948 −0.0575733
\(716\) −41.8041 + 72.4068i −1.56229 + 2.70597i
\(717\) −5.89962 10.2184i −0.220325 0.381614i
\(718\) −21.5254 37.2831i −0.803321 1.39139i
\(719\) −8.82728 + 15.2893i −0.329202 + 0.570195i −0.982354 0.187033i \(-0.940113\pi\)
0.653152 + 0.757227i \(0.273446\pi\)
\(720\) 2.70896 0.100957
\(721\) 0 0
\(722\) −18.3331 −0.682286
\(723\) −2.30922 + 3.99969i −0.0858809 + 0.148750i
\(724\) −11.4464 19.8258i −0.425404 0.736821i
\(725\) 16.7648 + 29.0375i 0.622629 + 1.07843i
\(726\) −13.0073 + 22.5294i −0.482748 + 0.836144i
\(727\) −23.8077 −0.882977 −0.441488 0.897267i \(-0.645549\pi\)
−0.441488 + 0.897267i \(0.645549\pi\)
\(728\) 0 0
\(729\) 20.3288 0.752920
\(730\) −24.0698 + 41.6901i −0.890864 + 1.54302i
\(731\) 23.7771 + 41.1831i 0.879427 + 1.52321i
\(732\) −4.00000 6.92820i −0.147844 0.256074i
\(733\) −15.6746 + 27.1492i −0.578954 + 1.00278i 0.416645 + 0.909069i \(0.363206\pi\)
−0.995600 + 0.0937093i \(0.970128\pi\)
\(734\) 12.5082 0.461686
\(735\) 0 0
\(736\) 13.2566 0.488645
\(737\) 3.49663 6.05635i 0.128800 0.223088i
\(738\) −0.578116 1.00133i −0.0212807 0.0368593i
\(739\) 12.4054 + 21.4868i 0.456340 + 0.790404i 0.998764 0.0497009i \(-0.0158268\pi\)
−0.542424 + 0.840105i \(0.682493\pi\)
\(740\) 19.9572 34.5668i 0.733640 1.27070i
\(741\) 3.83221 0.140780
\(742\) 0 0
\(743\) 21.3717 0.784051 0.392026 0.919954i \(-0.371774\pi\)
0.392026 + 0.919954i \(0.371774\pi\)
\(744\) 3.27131 5.66607i 0.119932 0.207728i
\(745\) 1.45559 + 2.52115i 0.0533286 + 0.0923678i
\(746\) −25.2113 43.6672i −0.923049 1.59877i
\(747\) −10.2239 + 17.7084i −0.374075 + 0.647916i
\(748\) 23.3288 0.852987
\(749\) 0 0
\(750\) −29.5640 −1.07953
\(751\) −9.61213 + 16.6487i −0.350751 + 0.607519i −0.986381 0.164475i \(-0.947407\pi\)
0.635630 + 0.771994i \(0.280740\pi\)
\(752\) 6.35027 + 10.9990i 0.231571 + 0.401092i
\(753\) 1.66863 + 2.89016i 0.0608084 + 0.105323i
\(754\) −12.2878 + 21.2831i −0.447495 + 0.775084i
\(755\) −20.0246 −0.728768
\(756\) 0 0
\(757\) −19.8610 −0.721860 −0.360930 0.932593i \(-0.617541\pi\)
−0.360930 + 0.932593i \(0.617541\pi\)
\(758\) −5.40046 + 9.35387i −0.196154 + 0.339748i
\(759\) −2.08631 3.61359i −0.0757282 0.131165i
\(760\) −7.83221 13.5658i −0.284104 0.492083i
\(761\) −3.06037 + 5.30071i −0.110938 + 0.192151i −0.916149 0.400838i \(-0.868719\pi\)
0.805211 + 0.592989i \(0.202052\pi\)
\(762\) −32.3847 −1.17317
\(763\) 0 0
\(764\) −15.3288 −0.554578
\(765\) −6.60195 + 11.4349i −0.238694 + 0.413430i
\(766\) 9.76481 + 16.9131i 0.352817 + 0.611097i
\(767\) −6.32150 10.9492i −0.228256 0.395351i
\(768\) −13.1365 + 22.7531i −0.474023 + 0.821031i
\(769\) 3.82800 0.138041 0.0690206 0.997615i \(-0.478013\pi\)
0.0690206 + 0.997615i \(0.478013\pi\)
\(770\) 0 0
\(771\) 22.4653 0.809070
\(772\) 14.4679 25.0591i 0.520710 0.901896i
\(773\) 3.26817 + 5.66064i 0.117548 + 0.203599i 0.918795 0.394734i \(-0.129163\pi\)
−0.801247 + 0.598333i \(0.795830\pi\)
\(774\) −16.1028 27.8909i −0.578803 1.00252i
\(775\) 2.61423 4.52798i 0.0939060 0.162650i
\(776\) −18.6430 −0.669245
\(777\) 0 0
\(778\) −15.0937 −0.541134
\(779\) −0.489289 + 0.847473i −0.0175306 + 0.0303639i
\(780\) −2.68585 4.65202i −0.0961687 0.166569i
\(781\) −0.882404 1.52837i −0.0315749 0.0546893i
\(782\) 21.6932 37.5737i 0.775747 1.34363i
\(783\) 56.3452 2.01361
\(784\)