Properties

Label 637.2.x.b.570.6
Level $637$
Weight $2$
Character 637.570
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 570.6
Character \(\chi\) \(=\) 637.570
Dual form 637.2.x.b.19.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.33353 - 0.357317i) q^{2} +1.07207i q^{3} +(-0.0814361 + 0.0470171i) q^{4} +(-2.77200 - 0.742756i) q^{5} +(0.383068 + 1.42963i) q^{6} +(-2.04421 + 2.04421i) q^{8} +1.85067 q^{9} +O(q^{10})\) \(q+(1.33353 - 0.357317i) q^{2} +1.07207i q^{3} +(-0.0814361 + 0.0470171i) q^{4} +(-2.77200 - 0.742756i) q^{5} +(0.383068 + 1.42963i) q^{6} +(-2.04421 + 2.04421i) q^{8} +1.85067 q^{9} -3.96194 q^{10} +(-1.00979 + 1.00979i) q^{11} +(-0.0504055 - 0.0873049i) q^{12} +(-3.54926 + 0.634621i) q^{13} +(0.796284 - 2.97177i) q^{15} +(-1.90154 + 3.29357i) q^{16} +(-2.09909 - 3.63573i) q^{17} +(2.46792 - 0.661277i) q^{18} +(-4.35974 + 4.35974i) q^{19} +(0.260663 - 0.0698445i) q^{20} +(-0.985770 + 1.70740i) q^{22} +(-6.77658 - 3.91246i) q^{23} +(-2.19153 - 2.19153i) q^{24} +(2.80219 + 1.61784i) q^{25} +(-4.50627 + 2.11449i) q^{26} +5.20025i q^{27} +(0.441485 + 0.764674i) q^{29} -4.24746i q^{30} +(0.237463 + 0.886225i) q^{31} +(0.137560 - 0.513380i) q^{32} +(-1.08257 - 1.08257i) q^{33} +(-4.09830 - 4.09830i) q^{34} +(-0.150711 + 0.0870133i) q^{36} +(1.92747 + 7.19341i) q^{37} +(-4.25601 + 7.37163i) q^{38} +(-0.680356 - 3.80505i) q^{39} +(7.18492 - 4.14822i) q^{40} +(11.4714 + 3.07376i) q^{41} +(0.809734 + 0.467500i) q^{43} +(0.0347561 - 0.129711i) q^{44} +(-5.13007 - 1.37460i) q^{45} +(-10.4347 - 2.79598i) q^{46} +(-0.808679 + 3.01803i) q^{47} +(-3.53093 - 2.03858i) q^{48} +(4.31487 + 1.15617i) q^{50} +(3.89775 - 2.25037i) q^{51} +(0.259200 - 0.218557i) q^{52} +(-1.26243 + 2.18659i) q^{53} +(1.85814 + 6.93466i) q^{54} +(3.54919 - 2.04912i) q^{55} +(-4.67393 - 4.67393i) q^{57} +(0.861962 + 0.861962i) q^{58} +(1.51488 - 5.65360i) q^{59} +(0.0748780 + 0.279449i) q^{60} -0.0854082i q^{61} +(0.633327 + 1.09695i) q^{62} -8.33994i q^{64} +(10.3099 + 0.877064i) q^{65} +(-1.83045 - 1.05681i) q^{66} +(0.728594 + 0.728594i) q^{67} +(0.341884 + 0.197387i) q^{68} +(4.19442 - 7.26495i) q^{69} +(2.79996 - 0.750247i) q^{71} +(-3.78317 + 3.78317i) q^{72} +(2.75156 - 0.737278i) q^{73} +(5.14066 + 8.90388i) q^{74} +(-1.73444 + 3.00414i) q^{75} +(0.150057 - 0.560022i) q^{76} +(-2.26688 - 4.83102i) q^{78} +(-4.71534 - 8.16721i) q^{79} +(7.71741 - 7.71741i) q^{80} -0.0229961 q^{81} +16.3958 q^{82} +(-1.54040 + 1.54040i) q^{83} +(3.11823 + 11.6374i) q^{85} +(1.24685 + 0.334092i) q^{86} +(-0.819782 + 0.473301i) q^{87} -4.12847i q^{88} +(4.75720 - 1.27469i) q^{89} -7.33225 q^{90} +0.735811 q^{92} +(-0.950093 + 0.254577i) q^{93} +4.31358i q^{94} +(15.3234 - 8.84698i) q^{95} +(0.550378 + 0.147473i) q^{96} +(2.37752 + 8.87303i) q^{97} +(-1.86880 + 1.86880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33353 0.357317i 0.942945 0.252661i 0.245579 0.969377i \(-0.421022\pi\)
0.697366 + 0.716715i \(0.254355\pi\)
\(3\) 1.07207i 0.618958i 0.950906 + 0.309479i \(0.100155\pi\)
−0.950906 + 0.309479i \(0.899845\pi\)
\(4\) −0.0814361 + 0.0470171i −0.0407180 + 0.0235086i
\(5\) −2.77200 0.742756i −1.23968 0.332171i −0.421337 0.906904i \(-0.638439\pi\)
−0.818341 + 0.574734i \(0.805106\pi\)
\(6\) 0.383068 + 1.42963i 0.156387 + 0.583644i
\(7\) 0 0
\(8\) −2.04421 + 2.04421i −0.722739 + 0.722739i
\(9\) 1.85067 0.616891
\(10\) −3.96194 −1.25287
\(11\) −1.00979 + 1.00979i −0.304465 + 0.304465i −0.842758 0.538293i \(-0.819069\pi\)
0.538293 + 0.842758i \(0.319069\pi\)
\(12\) −0.0504055 0.0873049i −0.0145508 0.0252028i
\(13\) −3.54926 + 0.634621i −0.984388 + 0.176012i
\(14\) 0 0
\(15\) 0.796284 2.97177i 0.205600 0.767309i
\(16\) −1.90154 + 3.29357i −0.475386 + 0.823393i
\(17\) −2.09909 3.63573i −0.509105 0.881795i −0.999944 0.0105451i \(-0.996643\pi\)
0.490840 0.871250i \(-0.336690\pi\)
\(18\) 2.46792 0.661277i 0.581694 0.155864i
\(19\) −4.35974 + 4.35974i −1.00019 + 1.00019i −0.000191931 1.00000i \(0.500061\pi\)
−1.00000 0.000191931i \(0.999939\pi\)
\(20\) 0.260663 0.0698445i 0.0582861 0.0156177i
\(21\) 0 0
\(22\) −0.985770 + 1.70740i −0.210167 + 0.364020i
\(23\) −6.77658 3.91246i −1.41302 0.815805i −0.417344 0.908748i \(-0.637039\pi\)
−0.995671 + 0.0929436i \(0.970372\pi\)
\(24\) −2.19153 2.19153i −0.447345 0.447345i
\(25\) 2.80219 + 1.61784i 0.560438 + 0.323569i
\(26\) −4.50627 + 2.11449i −0.883752 + 0.414687i
\(27\) 5.20025i 1.00079i
\(28\) 0 0
\(29\) 0.441485 + 0.764674i 0.0819817 + 0.141996i 0.904101 0.427319i \(-0.140542\pi\)
−0.822119 + 0.569315i \(0.807208\pi\)
\(30\) 4.24746i 0.775477i
\(31\) 0.237463 + 0.886225i 0.0426497 + 0.159171i 0.983966 0.178354i \(-0.0570771\pi\)
−0.941317 + 0.337524i \(0.890410\pi\)
\(32\) 0.137560 0.513380i 0.0243174 0.0907536i
\(33\) −1.08257 1.08257i −0.188451 0.188451i
\(34\) −4.09830 4.09830i −0.702853 0.702853i
\(35\) 0 0
\(36\) −0.150711 + 0.0870133i −0.0251186 + 0.0145022i
\(37\) 1.92747 + 7.19341i 0.316874 + 1.18259i 0.922232 + 0.386637i \(0.126363\pi\)
−0.605358 + 0.795953i \(0.706970\pi\)
\(38\) −4.25601 + 7.37163i −0.690416 + 1.19584i
\(39\) −0.680356 3.80505i −0.108944 0.609295i
\(40\) 7.18492 4.14822i 1.13604 0.655890i
\(41\) 11.4714 + 3.07376i 1.79154 + 0.480041i 0.992606 0.121379i \(-0.0387317\pi\)
0.798933 + 0.601421i \(0.205398\pi\)
\(42\) 0 0
\(43\) 0.809734 + 0.467500i 0.123483 + 0.0712931i 0.560469 0.828175i \(-0.310621\pi\)
−0.436986 + 0.899468i \(0.643954\pi\)
\(44\) 0.0347561 0.129711i 0.00523967 0.0195547i
\(45\) −5.13007 1.37460i −0.764746 0.204913i
\(46\) −10.4347 2.79598i −1.53852 0.412245i
\(47\) −0.808679 + 3.01803i −0.117958 + 0.440225i −0.999491 0.0318968i \(-0.989845\pi\)
0.881533 + 0.472122i \(0.156512\pi\)
\(48\) −3.53093 2.03858i −0.509646 0.294244i
\(49\) 0 0
\(50\) 4.31487 + 1.15617i 0.610215 + 0.163507i
\(51\) 3.89775 2.25037i 0.545794 0.315114i
\(52\) 0.259200 0.218557i 0.0359446 0.0303084i
\(53\) −1.26243 + 2.18659i −0.173408 + 0.300351i −0.939609 0.342249i \(-0.888811\pi\)
0.766201 + 0.642601i \(0.222145\pi\)
\(54\) 1.85814 + 6.93466i 0.252860 + 0.943688i
\(55\) 3.54919 2.04912i 0.478572 0.276304i
\(56\) 0 0
\(57\) −4.67393 4.67393i −0.619077 0.619077i
\(58\) 0.861962 + 0.861962i 0.113181 + 0.113181i
\(59\) 1.51488 5.65360i 0.197220 0.736035i −0.794461 0.607315i \(-0.792246\pi\)
0.991681 0.128720i \(-0.0410869\pi\)
\(60\) 0.0748780 + 0.279449i 0.00966671 + 0.0360767i
\(61\) 0.0854082i 0.0109354i −0.999985 0.00546770i \(-0.998260\pi\)
0.999985 0.00546770i \(-0.00174043\pi\)
\(62\) 0.633327 + 1.09695i 0.0804326 + 0.139313i
\(63\) 0 0
\(64\) 8.33994i 1.04249i
\(65\) 10.3099 + 0.877064i 1.27879 + 0.108786i
\(66\) −1.83045 1.05681i −0.225313 0.130085i
\(67\) 0.728594 + 0.728594i 0.0890119 + 0.0890119i 0.750211 0.661199i \(-0.229952\pi\)
−0.661199 + 0.750211i \(0.729952\pi\)
\(68\) 0.341884 + 0.197387i 0.0414595 + 0.0239366i
\(69\) 4.19442 7.26495i 0.504949 0.874598i
\(70\) 0 0
\(71\) 2.79996 0.750247i 0.332294 0.0890380i −0.0888143 0.996048i \(-0.528308\pi\)
0.421109 + 0.907010i \(0.361641\pi\)
\(72\) −3.78317 + 3.78317i −0.445851 + 0.445851i
\(73\) 2.75156 0.737278i 0.322046 0.0862919i −0.0941746 0.995556i \(-0.530021\pi\)
0.416220 + 0.909264i \(0.363355\pi\)
\(74\) 5.14066 + 8.90388i 0.597589 + 1.03506i
\(75\) −1.73444 + 3.00414i −0.200276 + 0.346888i
\(76\) 0.150057 0.560022i 0.0172128 0.0642389i
\(77\) 0 0
\(78\) −2.26688 4.83102i −0.256674 0.547006i
\(79\) −4.71534 8.16721i −0.530517 0.918883i −0.999366 0.0356045i \(-0.988664\pi\)
0.468849 0.883279i \(-0.344669\pi\)
\(80\) 7.71741 7.71741i 0.862832 0.862832i
\(81\) −0.0229961 −0.00255513
\(82\) 16.3958 1.81061
\(83\) −1.54040 + 1.54040i −0.169081 + 0.169081i −0.786575 0.617494i \(-0.788148\pi\)
0.617494 + 0.786575i \(0.288148\pi\)
\(84\) 0 0
\(85\) 3.11823 + 11.6374i 0.338219 + 1.26225i
\(86\) 1.24685 + 0.334092i 0.134451 + 0.0360260i
\(87\) −0.819782 + 0.473301i −0.0878898 + 0.0507432i
\(88\) 4.12847i 0.440097i
\(89\) 4.75720 1.27469i 0.504262 0.135117i 0.00228491 0.999997i \(-0.499273\pi\)
0.501977 + 0.864881i \(0.332606\pi\)
\(90\) −7.33225 −0.772887
\(91\) 0 0
\(92\) 0.735811 0.0767136
\(93\) −0.950093 + 0.254577i −0.0985201 + 0.0263984i
\(94\) 4.31358i 0.444912i
\(95\) 15.3234 8.84698i 1.57215 0.907681i
\(96\) 0.550378 + 0.147473i 0.0561727 + 0.0150514i
\(97\) 2.37752 + 8.87303i 0.241401 + 0.900920i 0.975158 + 0.221509i \(0.0710981\pi\)
−0.733758 + 0.679411i \(0.762235\pi\)
\(98\) 0 0
\(99\) −1.86880 + 1.86880i −0.187821 + 0.187821i
\(100\) −0.304266 −0.0304266
\(101\) 6.54977 0.651726 0.325863 0.945417i \(-0.394345\pi\)
0.325863 + 0.945417i \(0.394345\pi\)
\(102\) 4.39366 4.39366i 0.435037 0.435037i
\(103\) −4.92770 8.53503i −0.485541 0.840982i 0.514321 0.857598i \(-0.328044\pi\)
−0.999862 + 0.0166161i \(0.994711\pi\)
\(104\) 5.95815 8.55275i 0.584245 0.838666i
\(105\) 0 0
\(106\) −0.902174 + 3.36696i −0.0876269 + 0.327028i
\(107\) −5.29678 + 9.17430i −0.512059 + 0.886913i 0.487843 + 0.872931i \(0.337784\pi\)
−0.999902 + 0.0139814i \(0.995549\pi\)
\(108\) −0.244501 0.423488i −0.0235271 0.0407501i
\(109\) −15.9403 + 4.27118i −1.52680 + 0.409105i −0.921974 0.387252i \(-0.873424\pi\)
−0.604827 + 0.796357i \(0.706758\pi\)
\(110\) 4.00074 4.00074i 0.381456 0.381456i
\(111\) −7.71182 + 2.06638i −0.731974 + 0.196132i
\(112\) 0 0
\(113\) −0.322118 + 0.557925i −0.0303023 + 0.0524851i −0.880779 0.473528i \(-0.842980\pi\)
0.850477 + 0.526013i \(0.176314\pi\)
\(114\) −7.90288 4.56273i −0.740172 0.427339i
\(115\) 15.8787 + 15.8787i 1.48070 + 1.48070i
\(116\) −0.0719056 0.0415147i −0.00667627 0.00385454i
\(117\) −6.56852 + 1.17448i −0.607260 + 0.108580i
\(118\) 8.08051i 0.743871i
\(119\) 0 0
\(120\) 4.44717 + 7.70272i 0.405969 + 0.703159i
\(121\) 8.96063i 0.814603i
\(122\) −0.0305178 0.113894i −0.00276295 0.0103115i
\(123\) −3.29528 + 12.2982i −0.297126 + 1.10889i
\(124\) −0.0610059 0.0610059i −0.00547849 0.00547849i
\(125\) 3.58022 + 3.58022i 0.320225 + 0.320225i
\(126\) 0 0
\(127\) −14.1284 + 8.15702i −1.25369 + 0.723819i −0.971841 0.235640i \(-0.924282\pi\)
−0.281850 + 0.959458i \(0.590948\pi\)
\(128\) −2.70488 10.0948i −0.239080 0.892259i
\(129\) −0.501191 + 0.868089i −0.0441274 + 0.0764310i
\(130\) 14.0619 2.51433i 1.23331 0.220521i
\(131\) 2.03759 1.17640i 0.178025 0.102783i −0.408340 0.912830i \(-0.633892\pi\)
0.586364 + 0.810047i \(0.300559\pi\)
\(132\) 0.139059 + 0.0372608i 0.0121036 + 0.00324314i
\(133\) 0 0
\(134\) 1.23194 + 0.711259i 0.106423 + 0.0614435i
\(135\) 3.86251 14.4151i 0.332432 1.24065i
\(136\) 11.7232 + 3.14122i 1.00526 + 0.269358i
\(137\) −10.0332 2.68838i −0.857190 0.229683i −0.196650 0.980474i \(-0.563006\pi\)
−0.660541 + 0.750790i \(0.729673\pi\)
\(138\) 2.99748 11.1867i 0.255162 0.952278i
\(139\) −5.33208 3.07848i −0.452261 0.261113i 0.256524 0.966538i \(-0.417423\pi\)
−0.708784 + 0.705425i \(0.750756\pi\)
\(140\) 0 0
\(141\) −3.23553 0.866959i −0.272481 0.0730111i
\(142\) 3.46574 2.00095i 0.290839 0.167916i
\(143\) 2.94319 4.22486i 0.246122 0.353301i
\(144\) −3.51914 + 6.09532i −0.293261 + 0.507943i
\(145\) −0.655831 2.44759i −0.0544638 0.203262i
\(146\) 3.40583 1.96636i 0.281869 0.162737i
\(147\) 0 0
\(148\) −0.495179 0.495179i −0.0407035 0.0407035i
\(149\) 6.15629 + 6.15629i 0.504343 + 0.504343i 0.912784 0.408442i \(-0.133928\pi\)
−0.408442 + 0.912784i \(0.633928\pi\)
\(150\) −1.23949 + 4.62584i −0.101204 + 0.377698i
\(151\) 3.49627 + 13.0482i 0.284522 + 1.06185i 0.949188 + 0.314710i \(0.101907\pi\)
−0.664665 + 0.747141i \(0.731426\pi\)
\(152\) 17.8245i 1.44575i
\(153\) −3.88473 6.72855i −0.314062 0.543971i
\(154\) 0 0
\(155\) 2.63300i 0.211487i
\(156\) 0.234308 + 0.277880i 0.0187597 + 0.0222482i
\(157\) 5.87142 + 3.38986i 0.468590 + 0.270541i 0.715649 0.698460i \(-0.246131\pi\)
−0.247059 + 0.969000i \(0.579464\pi\)
\(158\) −9.20631 9.20631i −0.732415 0.732415i
\(159\) −2.34417 1.35341i −0.185905 0.107332i
\(160\) −0.762632 + 1.32092i −0.0602914 + 0.104428i
\(161\) 0 0
\(162\) −0.0306659 + 0.00821691i −0.00240934 + 0.000645582i
\(163\) −7.72493 + 7.72493i −0.605063 + 0.605063i −0.941652 0.336588i \(-0.890727\pi\)
0.336588 + 0.941652i \(0.390727\pi\)
\(164\) −1.07871 + 0.289039i −0.0842330 + 0.0225702i
\(165\) 2.19680 + 3.80497i 0.171020 + 0.296216i
\(166\) −1.50375 + 2.60458i −0.116714 + 0.202155i
\(167\) −4.71387 + 17.5924i −0.364770 + 1.36134i 0.502962 + 0.864308i \(0.332244\pi\)
−0.867732 + 0.497032i \(0.834423\pi\)
\(168\) 0 0
\(169\) 12.1945 4.50487i 0.938039 0.346529i
\(170\) 8.31647 + 14.4045i 0.637844 + 1.10478i
\(171\) −8.06844 + 8.06844i −0.617009 + 0.617009i
\(172\) −0.0879221 −0.00670400
\(173\) −20.1522 −1.53214 −0.766070 0.642757i \(-0.777791\pi\)
−0.766070 + 0.642757i \(0.777791\pi\)
\(174\) −0.924081 + 0.924081i −0.0700544 + 0.0700544i
\(175\) 0 0
\(176\) −1.40566 5.24600i −0.105956 0.395432i
\(177\) 6.06103 + 1.62405i 0.455575 + 0.122071i
\(178\) 5.88838 3.39966i 0.441353 0.254815i
\(179\) 16.5322i 1.23567i −0.786306 0.617837i \(-0.788009\pi\)
0.786306 0.617837i \(-0.211991\pi\)
\(180\) 0.482402 0.129259i 0.0359562 0.00963442i
\(181\) −13.6897 −1.01755 −0.508774 0.860900i \(-0.669901\pi\)
−0.508774 + 0.860900i \(0.669901\pi\)
\(182\) 0 0
\(183\) 0.0915633 0.00676855
\(184\) 21.8507 5.85488i 1.61085 0.431627i
\(185\) 21.3718i 1.57129i
\(186\) −1.17601 + 0.678969i −0.0862292 + 0.0497844i
\(187\) 5.79100 + 1.55169i 0.423480 + 0.113471i
\(188\) −0.0760436 0.283799i −0.00554605 0.0206981i
\(189\) 0 0
\(190\) 17.2730 17.2730i 1.25311 1.25311i
\(191\) −8.14890 −0.589633 −0.294817 0.955554i \(-0.595259\pi\)
−0.294817 + 0.955554i \(0.595259\pi\)
\(192\) 8.94097 0.645259
\(193\) 18.9414 18.9414i 1.36343 1.36343i 0.493935 0.869499i \(-0.335558\pi\)
0.869499 0.493935i \(-0.164442\pi\)
\(194\) 6.34097 + 10.9829i 0.455255 + 0.788525i
\(195\) −0.940271 + 11.0529i −0.0673342 + 0.791517i
\(196\) 0 0
\(197\) 4.77033 17.8031i 0.339872 1.26842i −0.558617 0.829426i \(-0.688668\pi\)
0.898490 0.438995i \(-0.144665\pi\)
\(198\) −1.82434 + 3.15985i −0.129650 + 0.224560i
\(199\) 6.35578 + 11.0085i 0.450550 + 0.780375i 0.998420 0.0561884i \(-0.0178947\pi\)
−0.547871 + 0.836563i \(0.684561\pi\)
\(200\) −9.03550 + 2.42105i −0.638906 + 0.171194i
\(201\) −0.781101 + 0.781101i −0.0550947 + 0.0550947i
\(202\) 8.73428 2.34034i 0.614542 0.164666i
\(203\) 0 0
\(204\) −0.211612 + 0.366522i −0.0148158 + 0.0256617i
\(205\) −29.5158 17.0410i −2.06147 1.19019i
\(206\) −9.62093 9.62093i −0.670322 0.670322i
\(207\) −12.5412 7.24069i −0.871676 0.503262i
\(208\) 4.65891 12.8965i 0.323037 0.894212i
\(209\) 8.80488i 0.609046i
\(210\) 0 0
\(211\) −2.26459 3.92239i −0.155901 0.270028i 0.777486 0.628900i \(-0.216495\pi\)
−0.933387 + 0.358872i \(0.883161\pi\)
\(212\) 0.237423i 0.0163063i
\(213\) 0.804316 + 3.00175i 0.0551108 + 0.205676i
\(214\) −3.78526 + 14.1268i −0.258755 + 0.965688i
\(215\) −1.89735 1.89735i −0.129398 0.129398i
\(216\) −10.6304 10.6304i −0.723308 0.723308i
\(217\) 0 0
\(218\) −19.7306 + 11.3915i −1.33632 + 0.771527i
\(219\) 0.790412 + 2.94986i 0.0534111 + 0.199333i
\(220\) −0.192688 + 0.333745i −0.0129910 + 0.0225011i
\(221\) 9.75754 + 11.5720i 0.656363 + 0.778420i
\(222\) −9.54556 + 5.51113i −0.640656 + 0.369883i
\(223\) −22.4788 6.02318i −1.50529 0.403342i −0.590423 0.807094i \(-0.701039\pi\)
−0.914868 + 0.403752i \(0.867706\pi\)
\(224\) 0 0
\(225\) 5.18593 + 2.99410i 0.345729 + 0.199607i
\(226\) −0.230197 + 0.859105i −0.0153124 + 0.0571468i
\(227\) 10.0685 + 2.69786i 0.668273 + 0.179063i 0.576977 0.816761i \(-0.304232\pi\)
0.0912961 + 0.995824i \(0.470899\pi\)
\(228\) 0.600381 + 0.160872i 0.0397612 + 0.0106540i
\(229\) −0.499191 + 1.86301i −0.0329875 + 0.123111i −0.980456 0.196738i \(-0.936965\pi\)
0.947469 + 0.319848i \(0.103632\pi\)
\(230\) 26.8484 + 15.5009i 1.77033 + 1.02210i
\(231\) 0 0
\(232\) −2.46565 0.660668i −0.161878 0.0433750i
\(233\) 7.44377 4.29766i 0.487657 0.281549i −0.235945 0.971766i \(-0.575818\pi\)
0.723602 + 0.690217i \(0.242485\pi\)
\(234\) −8.33963 + 3.91324i −0.545179 + 0.255816i
\(235\) 4.48332 7.76535i 0.292460 0.506555i
\(236\) 0.142450 + 0.531632i 0.00927273 + 0.0346063i
\(237\) 8.75580 5.05516i 0.568750 0.328368i
\(238\) 0 0
\(239\) −6.45158 6.45158i −0.417318 0.417318i 0.466960 0.884278i \(-0.345349\pi\)
−0.884278 + 0.466960i \(0.845349\pi\)
\(240\) 8.27358 + 8.27358i 0.534057 + 0.534057i
\(241\) −1.12940 + 4.21497i −0.0727509 + 0.271510i −0.992714 0.120495i \(-0.961552\pi\)
0.919963 + 0.392005i \(0.128218\pi\)
\(242\) 3.20179 + 11.9492i 0.205819 + 0.768125i
\(243\) 15.5761i 0.999206i
\(244\) 0.00401565 + 0.00695531i 0.000257076 + 0.000445268i
\(245\) 0 0
\(246\) 17.5774i 1.12069i
\(247\) 12.7071 18.2406i 0.808531 1.16062i
\(248\) −2.29706 1.32621i −0.145863 0.0842143i
\(249\) −1.65142 1.65142i −0.104654 0.104654i
\(250\) 6.05359 + 3.49504i 0.382863 + 0.221046i
\(251\) −2.27953 + 3.94826i −0.143883 + 0.249212i −0.928956 0.370191i \(-0.879292\pi\)
0.785073 + 0.619403i \(0.212625\pi\)
\(252\) 0 0
\(253\) 10.7937 2.89218i 0.678597 0.181830i
\(254\) −15.9259 + 15.9259i −0.999280 + 0.999280i
\(255\) −12.4761 + 3.34295i −0.781281 + 0.209344i
\(256\) 1.12588 + 1.95008i 0.0703674 + 0.121880i
\(257\) 4.31666 7.47667i 0.269266 0.466382i −0.699407 0.714724i \(-0.746552\pi\)
0.968672 + 0.248342i \(0.0798857\pi\)
\(258\) −0.358169 + 1.33670i −0.0222986 + 0.0832195i
\(259\) 0 0
\(260\) −0.880838 + 0.413319i −0.0546272 + 0.0256330i
\(261\) 0.817044 + 1.41516i 0.0505737 + 0.0875963i
\(262\) 2.29683 2.29683i 0.141898 0.141898i
\(263\) −13.0629 −0.805491 −0.402745 0.915312i \(-0.631944\pi\)
−0.402745 + 0.915312i \(0.631944\pi\)
\(264\) 4.42600 0.272402
\(265\) 5.12356 5.12356i 0.314738 0.314738i
\(266\) 0 0
\(267\) 1.36655 + 5.10004i 0.0836316 + 0.312117i
\(268\) −0.0935902 0.0250774i −0.00571693 0.00153185i
\(269\) −10.8756 + 6.27901i −0.663095 + 0.382838i −0.793455 0.608629i \(-0.791720\pi\)
0.130360 + 0.991467i \(0.458387\pi\)
\(270\) 20.6030i 1.25386i
\(271\) 4.45677 1.19419i 0.270730 0.0725418i −0.120900 0.992665i \(-0.538578\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(272\) 15.9661 0.968085
\(273\) 0 0
\(274\) −14.3401 −0.866315
\(275\) −4.46333 + 1.19595i −0.269149 + 0.0721182i
\(276\) 0.788839i 0.0474825i
\(277\) 1.44840 0.836232i 0.0870257 0.0502443i −0.455856 0.890054i \(-0.650667\pi\)
0.542881 + 0.839809i \(0.317333\pi\)
\(278\) −8.21045 2.19998i −0.492430 0.131946i
\(279\) 0.439467 + 1.64011i 0.0263102 + 0.0981910i
\(280\) 0 0
\(281\) −13.9259 + 13.9259i −0.830749 + 0.830749i −0.987619 0.156870i \(-0.949860\pi\)
0.156870 + 0.987619i \(0.449860\pi\)
\(282\) −4.62445 −0.275382
\(283\) −32.9939 −1.96128 −0.980642 0.195810i \(-0.937266\pi\)
−0.980642 + 0.195810i \(0.937266\pi\)
\(284\) −0.192743 + 0.192743i −0.0114372 + 0.0114372i
\(285\) 9.48456 + 16.4277i 0.561817 + 0.973095i
\(286\) 2.41520 6.68561i 0.142814 0.395329i
\(287\) 0 0
\(288\) 0.254578 0.950098i 0.0150012 0.0559851i
\(289\) −0.312374 + 0.541047i −0.0183749 + 0.0318263i
\(290\) −1.74913 3.02959i −0.102713 0.177904i
\(291\) −9.51249 + 2.54886i −0.557632 + 0.149417i
\(292\) −0.189412 + 0.189412i −0.0110845 + 0.0110845i
\(293\) 21.2120 5.68375i 1.23922 0.332048i 0.421057 0.907034i \(-0.361659\pi\)
0.818163 + 0.574986i \(0.194993\pi\)
\(294\) 0 0
\(295\) −8.39849 + 14.5466i −0.488979 + 0.846936i
\(296\) −18.6450 10.7647i −1.08372 0.625686i
\(297\) −5.25118 5.25118i −0.304704 0.304704i
\(298\) 10.4093 + 6.00982i 0.602996 + 0.348140i
\(299\) 26.5348 + 9.58579i 1.53455 + 0.554361i
\(300\) 0.326193i 0.0188328i
\(301\) 0 0
\(302\) 9.32472 + 16.1509i 0.536578 + 0.929380i
\(303\) 7.02179i 0.403391i
\(304\) −6.06887 22.6493i −0.348074 1.29903i
\(305\) −0.0634374 + 0.236752i −0.00363242 + 0.0135564i
\(306\) −7.58461 7.58461i −0.433584 0.433584i
\(307\) 13.7833 + 13.7833i 0.786656 + 0.786656i 0.980944 0.194289i \(-0.0622399\pi\)
−0.194289 + 0.980944i \(0.562240\pi\)
\(308\) 0 0
\(309\) 9.15013 5.28283i 0.520533 0.300530i
\(310\) −0.940815 3.51117i −0.0534347 0.199421i
\(311\) 12.9133 22.3666i 0.732248 1.26829i −0.223672 0.974664i \(-0.571804\pi\)
0.955920 0.293627i \(-0.0948622\pi\)
\(312\) 9.16912 + 6.38753i 0.519099 + 0.361623i
\(313\) −24.8257 + 14.3331i −1.40323 + 0.810155i −0.994723 0.102600i \(-0.967284\pi\)
−0.408507 + 0.912755i \(0.633950\pi\)
\(314\) 9.04094 + 2.42251i 0.510210 + 0.136710i
\(315\) 0 0
\(316\) 0.767998 + 0.443404i 0.0432033 + 0.0249434i
\(317\) 3.22651 12.0415i 0.181219 0.676317i −0.814190 0.580599i \(-0.802819\pi\)
0.995408 0.0957183i \(-0.0305148\pi\)
\(318\) −3.60961 0.967191i −0.202417 0.0542374i
\(319\) −1.21797 0.326355i −0.0681934 0.0182724i
\(320\) −6.19454 + 23.1183i −0.346285 + 1.29235i
\(321\) −9.83546 5.67851i −0.548962 0.316943i
\(322\) 0 0
\(323\) 25.0023 + 6.69935i 1.39117 + 0.372762i
\(324\) 0.00187272 0.00108121i 0.000104040 6.00674e-5i
\(325\) −10.9724 3.96383i −0.608640 0.219873i
\(326\) −7.54114 + 13.0616i −0.417665 + 0.723418i
\(327\) −4.57899 17.0890i −0.253219 0.945026i
\(328\) −29.7335 + 17.1667i −1.64176 + 0.947870i
\(329\) 0 0
\(330\) 4.28907 + 4.28907i 0.236105 + 0.236105i
\(331\) 21.1797 + 21.1797i 1.16414 + 1.16414i 0.983561 + 0.180578i \(0.0577970\pi\)
0.180578 + 0.983561i \(0.442203\pi\)
\(332\) 0.0530190 0.197870i 0.00290980 0.0108595i
\(333\) 3.56711 + 13.3126i 0.195477 + 0.729529i
\(334\) 25.1443i 1.37583i
\(335\) −1.47850 2.56083i −0.0807789 0.139913i
\(336\) 0 0
\(337\) 13.4402i 0.732137i −0.930588 0.366068i \(-0.880704\pi\)
0.930588 0.366068i \(-0.119296\pi\)
\(338\) 14.6520 10.3647i 0.796965 0.563764i
\(339\) −0.598133 0.345332i −0.0324861 0.0187559i
\(340\) −0.801093 0.801093i −0.0434453 0.0434453i
\(341\) −1.13470 0.655117i −0.0614472 0.0354766i
\(342\) −7.87648 + 13.6425i −0.425911 + 0.737700i
\(343\) 0 0
\(344\) −2.61094 + 0.699599i −0.140772 + 0.0377199i
\(345\) −17.0230 + 17.0230i −0.916490 + 0.916490i
\(346\) −26.8734 + 7.20071i −1.44472 + 0.387113i
\(347\) 7.24936 + 12.5563i 0.389166 + 0.674055i 0.992338 0.123556i \(-0.0394299\pi\)
−0.603172 + 0.797611i \(0.706097\pi\)
\(348\) 0.0445066 0.0770876i 0.00238580 0.00413233i
\(349\) 5.68220 21.2063i 0.304161 1.13515i −0.629504 0.776998i \(-0.716742\pi\)
0.933665 0.358148i \(-0.116592\pi\)
\(350\) 0 0
\(351\) −3.30019 18.4570i −0.176151 0.985163i
\(352\) 0.379501 + 0.657316i 0.0202275 + 0.0350351i
\(353\) −8.16512 + 8.16512i −0.434585 + 0.434585i −0.890185 0.455600i \(-0.849425\pi\)
0.455600 + 0.890185i \(0.349425\pi\)
\(354\) 8.66284 0.460425
\(355\) −8.31875 −0.441514
\(356\) −0.327476 + 0.327476i −0.0173562 + 0.0173562i
\(357\) 0 0
\(358\) −5.90723 22.0461i −0.312207 1.16517i
\(359\) 0.861987 + 0.230969i 0.0454939 + 0.0121901i 0.281494 0.959563i \(-0.409170\pi\)
−0.236000 + 0.971753i \(0.575837\pi\)
\(360\) 13.2969 7.67699i 0.700810 0.404613i
\(361\) 19.0146i 1.00077i
\(362\) −18.2556 + 4.89156i −0.959491 + 0.257095i
\(363\) −9.60639 −0.504205
\(364\) 0 0
\(365\) −8.17495 −0.427897
\(366\) 0.122102 0.0327171i 0.00638237 0.00171015i
\(367\) 14.4731i 0.755489i 0.925910 + 0.377744i \(0.123300\pi\)
−0.925910 + 0.377744i \(0.876700\pi\)
\(368\) 25.7720 14.8794i 1.34346 0.775645i
\(369\) 21.2299 + 5.68853i 1.10518 + 0.296133i
\(370\) −7.63651 28.4998i −0.397003 1.48164i
\(371\) 0 0
\(372\) 0.0654024 0.0654024i 0.00339096 0.00339096i
\(373\) 20.9269 1.08356 0.541778 0.840522i \(-0.317751\pi\)
0.541778 + 0.840522i \(0.317751\pi\)
\(374\) 8.27689 0.427988
\(375\) −3.83824 + 3.83824i −0.198206 + 0.198206i
\(376\) −4.51639 7.82262i −0.232915 0.403421i
\(377\) −2.05222 2.43385i −0.105695 0.125350i
\(378\) 0 0
\(379\) −5.53128 + 20.6430i −0.284123 + 1.06036i 0.665355 + 0.746527i \(0.268280\pi\)
−0.949478 + 0.313834i \(0.898387\pi\)
\(380\) −0.831920 + 1.44093i −0.0426766 + 0.0739180i
\(381\) −8.74488 15.1466i −0.448014 0.775982i
\(382\) −10.8668 + 2.91174i −0.555992 + 0.148978i
\(383\) 12.6750 12.6750i 0.647662 0.647662i −0.304765 0.952427i \(-0.598578\pi\)
0.952427 + 0.304765i \(0.0985781\pi\)
\(384\) 10.8223 2.89981i 0.552271 0.147981i
\(385\) 0 0
\(386\) 18.4908 32.0270i 0.941156 1.63013i
\(387\) 1.49855 + 0.865189i 0.0761757 + 0.0439800i
\(388\) −0.610801 0.610801i −0.0310087 0.0310087i
\(389\) 4.21022 + 2.43077i 0.213467 + 0.123245i 0.602921 0.797801i \(-0.294003\pi\)
−0.389455 + 0.921046i \(0.627337\pi\)
\(390\) 2.69553 + 15.0754i 0.136493 + 0.763370i
\(391\) 32.8505i 1.66132i
\(392\) 0 0
\(393\) 1.26118 + 2.18443i 0.0636182 + 0.110190i
\(394\) 25.4454i 1.28192i
\(395\) 7.00470 + 26.1419i 0.352445 + 1.31534i
\(396\) 0.0643221 0.240053i 0.00323231 0.0120631i
\(397\) 13.8333 + 13.8333i 0.694275 + 0.694275i 0.963170 0.268895i \(-0.0866584\pi\)
−0.268895 + 0.963170i \(0.586658\pi\)
\(398\) 12.4091 + 12.4091i 0.622014 + 0.622014i
\(399\) 0 0
\(400\) −10.6570 + 6.15281i −0.532849 + 0.307640i
\(401\) −1.11204 4.15019i −0.0555327 0.207251i 0.932585 0.360951i \(-0.117548\pi\)
−0.988118 + 0.153700i \(0.950881\pi\)
\(402\) −0.762518 + 1.32072i −0.0380309 + 0.0658715i
\(403\) −1.40524 2.99475i −0.0699998 0.149179i
\(404\) −0.533387 + 0.307951i −0.0265370 + 0.0153212i
\(405\) 0.0637454 + 0.0170805i 0.00316753 + 0.000848738i
\(406\) 0 0
\(407\) −9.21022 5.31752i −0.456534 0.263580i
\(408\) −3.36760 + 12.5681i −0.166721 + 0.622212i
\(409\) −29.2989 7.85062i −1.44874 0.388188i −0.553154 0.833079i \(-0.686576\pi\)
−0.895585 + 0.444891i \(0.853242\pi\)
\(410\) −45.4491 12.1781i −2.24457 0.601432i
\(411\) 2.88212 10.7562i 0.142164 0.530565i
\(412\) 0.802586 + 0.463373i 0.0395406 + 0.0228288i
\(413\) 0 0
\(414\) −19.3113 5.17444i −0.949098 0.254310i
\(415\) 5.41415 3.12586i 0.265770 0.153442i
\(416\) −0.162434 + 1.90942i −0.00796397 + 0.0936170i
\(417\) 3.30033 5.71634i 0.161618 0.279930i
\(418\) −3.14613 11.7415i −0.153882 0.574297i
\(419\) 6.87240 3.96778i 0.335739 0.193839i −0.322647 0.946519i \(-0.604573\pi\)
0.658386 + 0.752680i \(0.271239\pi\)
\(420\) 0 0
\(421\) −5.98090 5.98090i −0.291491 0.291491i 0.546178 0.837669i \(-0.316082\pi\)
−0.837669 + 0.546178i \(0.816082\pi\)
\(422\) −4.42143 4.42143i −0.215232 0.215232i
\(423\) −1.49660 + 5.58539i −0.0727672 + 0.271571i
\(424\) −1.88918 7.05053i −0.0917469 0.342404i
\(425\) 13.5840i 0.658922i
\(426\) 2.14515 + 3.71551i 0.103933 + 0.180017i
\(427\) 0 0
\(428\) 0.996159i 0.0481511i
\(429\) 4.52934 + 3.15530i 0.218678 + 0.152339i
\(430\) −3.20811 1.85221i −0.154709 0.0893213i
\(431\) 0.409100 + 0.409100i 0.0197057 + 0.0197057i 0.716891 0.697185i \(-0.245565\pi\)
−0.697185 + 0.716891i \(0.745565\pi\)
\(432\) −17.1274 9.88850i −0.824042 0.475761i
\(433\) −4.11334 + 7.12452i −0.197675 + 0.342382i −0.947774 0.318943i \(-0.896672\pi\)
0.750099 + 0.661325i \(0.230006\pi\)
\(434\) 0 0
\(435\) 2.62399 0.703095i 0.125810 0.0337108i
\(436\) 1.09729 1.09729i 0.0525509 0.0525509i
\(437\) 46.6014 12.4868i 2.22925 0.597325i
\(438\) 2.10807 + 3.65128i 0.100727 + 0.174465i
\(439\) −6.36168 + 11.0188i −0.303626 + 0.525896i −0.976955 0.213447i \(-0.931531\pi\)
0.673328 + 0.739344i \(0.264864\pi\)
\(440\) −3.06645 + 11.4441i −0.146187 + 0.545578i
\(441\) 0 0
\(442\) 17.1468 + 11.9451i 0.815591 + 0.568169i
\(443\) 1.11534 + 1.93182i 0.0529912 + 0.0917834i 0.891304 0.453406i \(-0.149791\pi\)
−0.838313 + 0.545189i \(0.816458\pi\)
\(444\) 0.530865 0.530865i 0.0251938 0.0251938i
\(445\) −14.1338 −0.670005
\(446\) −32.1282 −1.52132
\(447\) −6.59996 + 6.59996i −0.312167 + 0.312167i
\(448\) 0 0
\(449\) 10.0883 + 37.6500i 0.476096 + 1.77682i 0.617184 + 0.786819i \(0.288273\pi\)
−0.141088 + 0.989997i \(0.545060\pi\)
\(450\) 7.98542 + 2.13969i 0.376436 + 0.100866i
\(451\) −14.6877 + 8.47994i −0.691616 + 0.399305i
\(452\) 0.0605803i 0.00284946i
\(453\) −13.9886 + 3.74823i −0.657242 + 0.176107i
\(454\) 14.3906 0.675387
\(455\) 0 0
\(456\) 19.1090 0.894862
\(457\) −22.2431 + 5.96003i −1.04049 + 0.278798i −0.738316 0.674455i \(-0.764379\pi\)
−0.302174 + 0.953253i \(0.597712\pi\)
\(458\) 2.66273i 0.124421i
\(459\) 18.9067 10.9158i 0.882490 0.509506i
\(460\) −2.03967 0.546528i −0.0951002 0.0254820i
\(461\) −7.81461 29.1645i −0.363962 1.35833i −0.868822 0.495125i \(-0.835122\pi\)
0.504859 0.863202i \(-0.331544\pi\)
\(462\) 0 0
\(463\) 2.19856 2.19856i 0.102176 0.102176i −0.654171 0.756347i \(-0.726982\pi\)
0.756347 + 0.654171i \(0.226982\pi\)
\(464\) −3.35801 −0.155892
\(465\) 2.82275 0.130902
\(466\) 8.39083 8.39083i 0.388698 0.388698i
\(467\) −10.5856 18.3348i −0.489844 0.848434i 0.510088 0.860122i \(-0.329613\pi\)
−0.999932 + 0.0116879i \(0.996280\pi\)
\(468\) 0.479694 0.404478i 0.0221739 0.0186970i
\(469\) 0 0
\(470\) 3.20394 11.9573i 0.147787 0.551547i
\(471\) −3.63416 + 6.29455i −0.167453 + 0.290038i
\(472\) 8.46043 + 14.6539i 0.389423 + 0.674500i
\(473\) −1.28974 + 0.345586i −0.0593025 + 0.0158901i
\(474\) 9.86978 9.86978i 0.453334 0.453334i
\(475\) −19.2702 + 5.16343i −0.884176 + 0.236914i
\(476\) 0 0
\(477\) −2.33634 + 4.04666i −0.106974 + 0.185284i
\(478\) −10.9086 6.29809i −0.498948 0.288068i
\(479\) −16.9808 16.9808i −0.775871 0.775871i 0.203255 0.979126i \(-0.434848\pi\)
−0.979126 + 0.203255i \(0.934848\pi\)
\(480\) −1.41611 0.817593i −0.0646364 0.0373179i
\(481\) −11.4062 24.3081i −0.520077 1.10835i
\(482\) 6.02432i 0.274400i
\(483\) 0 0
\(484\) −0.421303 0.729719i −0.0191501 0.0331690i
\(485\) 26.3620i 1.19704i
\(486\) 5.56560 + 20.7711i 0.252461 + 0.942196i
\(487\) −8.81975 + 32.9158i −0.399661 + 1.49156i 0.414032 + 0.910262i \(0.364120\pi\)
−0.813694 + 0.581294i \(0.802547\pi\)
\(488\) 0.174593 + 0.174593i 0.00790344 + 0.00790344i
\(489\) −8.28165 8.28165i −0.374509 0.374509i
\(490\) 0 0
\(491\) 12.2688 7.08337i 0.553681 0.319668i −0.196924 0.980419i \(-0.563095\pi\)
0.750605 + 0.660751i \(0.229762\pi\)
\(492\) −0.309869 1.15645i −0.0139700 0.0521367i
\(493\) 1.85343 3.21024i 0.0834745 0.144582i
\(494\) 10.4275 28.8648i 0.469156 1.29869i
\(495\) 6.56838 3.79226i 0.295227 0.170449i
\(496\) −3.37039 0.903094i −0.151335 0.0405501i
\(497\) 0 0
\(498\) −2.79228 1.61213i −0.125125 0.0722411i
\(499\) −7.71779 + 28.8032i −0.345496 + 1.28941i 0.546536 + 0.837436i \(0.315946\pi\)
−0.892032 + 0.451972i \(0.850721\pi\)
\(500\) −0.459891 0.123227i −0.0205670 0.00551090i
\(501\) −18.8602 5.05358i −0.842613 0.225777i
\(502\) −1.62903 + 6.07962i −0.0727072 + 0.271347i
\(503\) −11.8147 6.82122i −0.526791 0.304143i 0.212918 0.977070i \(-0.431703\pi\)
−0.739709 + 0.672927i \(0.765037\pi\)
\(504\) 0 0
\(505\) −18.1560 4.86488i −0.807930 0.216484i
\(506\) 13.3603 7.71358i 0.593938 0.342910i
\(507\) 4.82952 + 13.0733i 0.214487 + 0.580607i
\(508\) 0.767040 1.32855i 0.0340319 0.0589450i
\(509\) 0.690957 + 2.57869i 0.0306261 + 0.114298i 0.979547 0.201216i \(-0.0644895\pi\)
−0.948921 + 0.315515i \(0.897823\pi\)
\(510\) −15.4426 + 8.91581i −0.683812 + 0.394799i
\(511\) 0 0
\(512\) 16.9779 + 16.9779i 0.750326 + 0.750326i
\(513\) −22.6717 22.6717i −1.00098 1.00098i
\(514\) 3.08483 11.5127i 0.136066 0.507806i
\(515\) 7.32016 + 27.3192i 0.322565 + 1.20383i
\(516\) 0.0942584i 0.00414949i
\(517\) −2.23099 3.86419i −0.0981190 0.169947i
\(518\) 0 0
\(519\) 21.6045i 0.948331i
\(520\) −22.8686 + 19.2828i −1.00286 + 0.845607i
\(521\) 13.4638 + 7.77333i 0.589860 + 0.340556i 0.765042 0.643980i \(-0.222718\pi\)
−0.175182 + 0.984536i \(0.556052\pi\)
\(522\) 1.59521 + 1.59521i 0.0698204 + 0.0698204i
\(523\) −0.102601 0.0592367i −0.00448643 0.00259024i 0.497755 0.867318i \(-0.334158\pi\)
−0.502242 + 0.864727i \(0.667491\pi\)
\(524\) −0.110622 + 0.191603i −0.00483255 + 0.00837022i
\(525\) 0 0
\(526\) −17.4197 + 4.66758i −0.759533 + 0.203516i
\(527\) 2.72362 2.72362i 0.118643 0.118643i
\(528\) 5.62407 1.50696i 0.244756 0.0655822i
\(529\) 19.1147 + 33.1077i 0.831075 + 1.43946i
\(530\) 5.00166 8.66313i 0.217258 0.376302i
\(531\) 2.80354 10.4630i 0.121663 0.454053i
\(532\) 0 0
\(533\) −42.6658 3.62957i −1.84806 0.157214i
\(534\) 3.64466 + 6.31274i 0.157720 + 0.273179i
\(535\) 21.4970 21.4970i 0.929395 0.929395i
\(536\) −2.97880 −0.128665
\(537\) 17.7236 0.764830
\(538\) −12.2592 + 12.2592i −0.528534 + 0.528534i
\(539\) 0 0
\(540\) 0.363209 + 1.35551i 0.0156300 + 0.0583320i
\(541\) 4.47060 + 1.19789i 0.192206 + 0.0515014i 0.353638 0.935382i \(-0.384945\pi\)
−0.161432 + 0.986884i \(0.551611\pi\)
\(542\) 5.51652 3.18496i 0.236955 0.136806i
\(543\) 14.6763i 0.629819i
\(544\) −2.15526 + 0.577501i −0.0924062 + 0.0247602i
\(545\) 47.3589 2.02863
\(546\) 0 0
\(547\) 29.4860 1.26073 0.630365 0.776299i \(-0.282905\pi\)
0.630365 + 0.776299i \(0.282905\pi\)
\(548\) 0.943461 0.252800i 0.0403026 0.0107991i
\(549\) 0.158063i 0.00674594i
\(550\) −5.52463 + 3.18965i −0.235571 + 0.136007i
\(551\) −5.25853 1.40902i −0.224021 0.0600263i
\(552\) 6.27682 + 23.4254i 0.267159 + 0.997052i
\(553\) 0 0
\(554\) 1.63267 1.63267i 0.0693657 0.0693657i
\(555\) 22.9120 0.972561
\(556\) 0.578964 0.0245536
\(557\) 0.959258 0.959258i 0.0406451 0.0406451i −0.686492 0.727137i \(-0.740850\pi\)
0.727137 + 0.686492i \(0.240850\pi\)
\(558\) 1.17208 + 2.03010i 0.0496181 + 0.0859411i
\(559\) −3.17064 1.14541i −0.134104 0.0484455i
\(560\) 0 0
\(561\) −1.66352 + 6.20834i −0.0702338 + 0.262116i
\(562\) −13.5946 + 23.5465i −0.573453 + 0.993249i
\(563\) 16.4050 + 28.4143i 0.691388 + 1.19752i 0.971383 + 0.237517i \(0.0763337\pi\)
−0.279995 + 0.960001i \(0.590333\pi\)
\(564\) 0.304251 0.0815238i 0.0128113 0.00343277i
\(565\) 1.30731 1.30731i 0.0549991 0.0549991i
\(566\) −43.9982 + 11.7893i −1.84938 + 0.495541i
\(567\) 0 0
\(568\) −4.19005 + 7.25739i −0.175811 + 0.304513i
\(569\) 25.8745 + 14.9387i 1.08472 + 0.626261i 0.932165 0.362034i \(-0.117918\pi\)
0.152552 + 0.988296i \(0.451251\pi\)
\(570\) 18.5178 + 18.5178i 0.775626 + 0.775626i
\(571\) −0.640877 0.370010i −0.0268198 0.0154844i 0.486530 0.873664i \(-0.338262\pi\)
−0.513350 + 0.858179i \(0.671596\pi\)
\(572\) −0.0410408 + 0.482437i −0.00171600 + 0.0201717i
\(573\) 8.73616i 0.364958i
\(574\) 0 0
\(575\) −12.6595 21.9269i −0.527938 0.914416i
\(576\) 15.4345i 0.643104i
\(577\) −8.82812 32.9470i −0.367519 1.37160i −0.863973 0.503538i \(-0.832031\pi\)
0.496454 0.868063i \(-0.334635\pi\)
\(578\) −0.223233 + 0.833116i −0.00928526 + 0.0346531i
\(579\) 20.3065 + 20.3065i 0.843909 + 0.843909i
\(580\) 0.168487 + 0.168487i 0.00699605 + 0.00699605i
\(581\) 0 0
\(582\) −11.7744 + 6.79795i −0.488064 + 0.281784i
\(583\) −0.933213 3.48280i −0.0386498 0.144243i
\(584\) −4.11762 + 7.13193i −0.170388 + 0.295121i
\(585\) 19.0803 + 1.62316i 0.788874 + 0.0671093i
\(586\) 26.2559 15.1588i 1.08462 0.626206i
\(587\) −11.9740 3.20842i −0.494219 0.132426i 0.00309648 0.999995i \(-0.499014\pi\)
−0.497316 + 0.867569i \(0.665681\pi\)
\(588\) 0 0
\(589\) −4.89899 2.82843i −0.201859 0.116543i
\(590\) −6.00184 + 22.3992i −0.247092 + 0.922160i
\(591\) 19.0861 + 5.11412i 0.785099 + 0.210367i
\(592\) −27.3572 7.33034i −1.12437 0.301275i
\(593\) 5.91611 22.0792i 0.242945 0.906685i −0.731460 0.681885i \(-0.761161\pi\)
0.974405 0.224800i \(-0.0721728\pi\)
\(594\) −8.87892 5.12625i −0.364307 0.210333i
\(595\) 0 0
\(596\) −0.790795 0.211893i −0.0323922 0.00867948i
\(597\) −11.8019 + 6.81383i −0.483019 + 0.278871i
\(598\) 38.8100 + 3.30156i 1.58706 + 0.135011i
\(599\) −1.24701 + 2.15989i −0.0509516 + 0.0882508i −0.890376 0.455225i \(-0.849559\pi\)
0.839425 + 0.543476i \(0.182892\pi\)
\(600\) −2.59553 9.68666i −0.105962 0.395456i
\(601\) 18.5873 10.7314i 0.758193 0.437743i −0.0704537 0.997515i \(-0.522445\pi\)
0.828647 + 0.559772i \(0.189111\pi\)
\(602\) 0 0
\(603\) 1.34839 + 1.34839i 0.0549106 + 0.0549106i
\(604\) −0.898214 0.898214i −0.0365478 0.0365478i
\(605\) 6.65556 24.8389i 0.270587 1.00984i
\(606\) 2.50901 + 9.36374i 0.101921 + 0.380376i
\(607\) 16.0396i 0.651028i 0.945537 + 0.325514i \(0.105537\pi\)
−0.945537 + 0.325514i \(0.894463\pi\)
\(608\) 1.63848 + 2.83793i 0.0664490 + 0.115093i
\(609\) 0 0
\(610\) 0.338382i 0.0137007i
\(611\) 0.954908 11.2250i 0.0386314 0.454115i
\(612\) 0.632715 + 0.365298i 0.0255760 + 0.0147663i
\(613\) −4.88837 4.88837i −0.197440 0.197440i 0.601462 0.798901i \(-0.294585\pi\)
−0.798901 + 0.601462i \(0.794585\pi\)
\(614\) 23.3054 + 13.4554i 0.940530 + 0.543015i
\(615\) 18.2691 31.6429i 0.736680 1.27597i
\(616\) 0 0
\(617\) 26.9254 7.21463i 1.08397 0.290450i 0.327751 0.944764i \(-0.393709\pi\)
0.756223 + 0.654314i \(0.227043\pi\)
\(618\) 10.3143 10.3143i 0.414901 0.414901i
\(619\) 13.3912 3.58815i 0.538237 0.144220i 0.0205475 0.999789i \(-0.493459\pi\)
0.517689 + 0.855569i \(0.326792\pi\)
\(620\) 0.123796 + 0.214421i 0.00497177 + 0.00861136i
\(621\) 20.3458 35.2399i 0.816448 1.41413i
\(622\) 9.22831 34.4405i 0.370022 1.38094i
\(623\) 0 0
\(624\) 13.8259 + 4.99466i 0.553480 + 0.199947i
\(625\) −15.3544 26.5946i −0.614175 1.06378i
\(626\) −27.9842 + 27.9842i −1.11847 + 1.11847i
\(627\) 9.43942 0.376974
\(628\) −0.637527 −0.0254401
\(629\) 22.1074 22.1074i 0.881480 0.881480i
\(630\) 0 0
\(631\) 6.69536 + 24.9874i 0.266538 + 0.994733i 0.961302 + 0.275496i \(0.0888419\pi\)
−0.694764 + 0.719237i \(0.744491\pi\)
\(632\) 26.3347 + 7.05636i 1.04754 + 0.280687i
\(633\) 4.20506 2.42779i 0.167136 0.0964961i
\(634\) 17.2105i 0.683517i
\(635\) 45.2226 12.1174i 1.79460 0.480863i
\(636\) 0.254533 0.0100929
\(637\) 0 0
\(638\) −1.74081 −0.0689193
\(639\) 5.18181 1.38846i 0.204989 0.0549267i
\(640\) 29.9918i 1.18553i
\(641\) 10.8902 6.28745i 0.430136 0.248339i −0.269269 0.963065i \(-0.586782\pi\)
0.699405 + 0.714726i \(0.253449\pi\)
\(642\) −15.1449 4.05806i −0.597720 0.160159i
\(643\) 6.40174 + 23.8916i 0.252460 + 0.942193i 0.969486 + 0.245147i \(0.0788361\pi\)
−0.717026 + 0.697046i \(0.754497\pi\)
\(644\) 0 0
\(645\) 2.03408 2.03408i 0.0800919 0.0800919i
\(646\) 35.7350 1.40598
\(647\) 34.6235 1.36119 0.680595 0.732660i \(-0.261721\pi\)
0.680595 + 0.732660i \(0.261721\pi\)
\(648\) 0.0470090 0.0470090i 0.00184669 0.00184669i
\(649\) 4.17926 + 7.23869i 0.164050 + 0.284143i
\(650\) −16.0483 1.36523i −0.629468 0.0535487i
\(651\) 0 0
\(652\) 0.265884 0.992293i 0.0104128 0.0388612i
\(653\) 13.7001 23.7293i 0.536127 0.928600i −0.462980 0.886368i \(-0.653220\pi\)
0.999108 0.0422314i \(-0.0134467\pi\)
\(654\) −12.2124 21.1525i −0.477543 0.827129i
\(655\) −6.52198 + 1.74756i −0.254835 + 0.0682828i
\(656\) −31.9371 + 31.9371i −1.24694 + 1.24694i
\(657\) 5.09224 1.36446i 0.198667 0.0532327i
\(658\) 0 0
\(659\) 2.14617 3.71728i 0.0836031 0.144805i −0.821192 0.570652i \(-0.806691\pi\)
0.904795 + 0.425847i \(0.140024\pi\)
\(660\) −0.357797 0.206574i −0.0139272 0.00804090i
\(661\) 10.7570 + 10.7570i 0.418399 + 0.418399i 0.884652 0.466252i \(-0.154396\pi\)
−0.466252 + 0.884652i \(0.654396\pi\)
\(662\) 35.8115 + 20.6758i 1.39185 + 0.803586i
\(663\) −12.4060 + 10.4607i −0.481809 + 0.406261i
\(664\) 6.29783i 0.244403i
\(665\) 0 0
\(666\) 9.51367 + 16.4782i 0.368647 + 0.638516i
\(667\) 6.90917i 0.267524i
\(668\) −0.443265 1.65429i −0.0171504 0.0640063i
\(669\) 6.45725 24.0988i 0.249652 0.931713i
\(670\) −2.88664 2.88664i −0.111521 0.111521i
\(671\) 0.0862447 + 0.0862447i 0.00332944 + 0.00332944i
\(672\) 0 0
\(673\) 26.3013 15.1851i 1.01384 0.585341i 0.101526 0.994833i \(-0.467627\pi\)
0.912314 + 0.409492i \(0.134294\pi\)
\(674\) −4.80243 17.9229i −0.184983 0.690365i
\(675\) −8.41319 + 14.5721i −0.323824 + 0.560879i
\(676\) −0.781267 + 0.940210i −0.0300487 + 0.0361619i
\(677\) 31.7593 18.3363i 1.22061 0.704720i 0.255562 0.966793i \(-0.417739\pi\)
0.965048 + 0.262073i \(0.0844060\pi\)
\(678\) −0.921018 0.246786i −0.0353715 0.00947776i
\(679\) 0 0
\(680\) −30.1636 17.4150i −1.15672 0.667834i
\(681\) −2.89228 + 10.7942i −0.110833 + 0.413633i
\(682\) −1.74723 0.468169i −0.0669049 0.0179271i
\(683\) −15.4630 4.14330i −0.591676 0.158539i −0.0494567 0.998776i \(-0.515749\pi\)
−0.542219 + 0.840237i \(0.682416\pi\)
\(684\) 0.277707 1.03642i 0.0106184 0.0396284i
\(685\) 25.8151 + 14.9044i 0.986346 + 0.569467i
\(686\) 0 0
\(687\) −1.99727 0.535166i −0.0762005 0.0204179i
\(688\) −3.07949 + 1.77794i −0.117404 + 0.0677835i
\(689\) 3.09303 8.56194i 0.117835 0.326184i
\(690\) −16.6180 + 28.7833i −0.632638 + 1.09576i
\(691\) 4.67596 + 17.4509i 0.177882 + 0.663864i 0.996043 + 0.0888748i \(0.0283271\pi\)
−0.818161 + 0.574989i \(0.805006\pi\)
\(692\) 1.64111 0.947497i 0.0623858 0.0360184i
\(693\) 0 0
\(694\) 14.1538 + 14.1538i 0.537270 + 0.537270i
\(695\) 12.4940 + 12.4940i 0.473923 + 0.473923i
\(696\) 0.708280 2.64334i 0.0268473 0.100195i
\(697\) −12.9042 48.1592i −0.488783 1.82416i
\(698\) 30.3094i 1.14723i
\(699\) 4.60738 + 7.98022i 0.174267 + 0.301840i
\(700\) 0 0
\(701\) 37.6363i 1.42150i 0.703444 + 0.710751i \(0.251645\pi\)
−0.703444 + 0.710751i \(0.748355\pi\)
\(702\) −10.9959 23.4337i −0.415013 0.884448i
\(703\) −39.7646 22.9581i −1.49975 0.865882i
\(704\) 8.42163 + 8.42163i 0.317402 + 0.317402i
\(705\) 8.32497 + 4.80642i 0.313537 + 0.181020i
\(706\) −7.97086 + 13.8059i −0.299987 + 0.519593i
\(707\) 0 0
\(708\) −0.569945 + 0.152716i −0.0214198 + 0.00573943i
\(709\) −8.15239 + 8.15239i −0.306169 + 0.306169i −0.843422 0.537252i \(-0.819462\pi\)
0.537252 + 0.843422i \(0.319462\pi\)
\(710\) −11.0933 + 2.97243i −0.416323 + 0.111553i
\(711\) −8.72655 15.1148i −0.327271 0.566850i
\(712\) −7.11900 + 12.3305i −0.266796 + 0.462104i
\(713\) 1.85813 6.93465i 0.0695876 0.259705i
\(714\) 0 0
\(715\) −11.2966 + 9.52526i −0.422468 + 0.356225i
\(716\) 0.777296 + 1.34632i 0.0290489 + 0.0503142i
\(717\) 6.91652 6.91652i 0.258302 0.258302i
\(718\) 1.23201 0.0459782
\(719\) 46.1930 1.72271 0.861355 0.508004i \(-0.169616\pi\)
0.861355 + 0.508004i \(0.169616\pi\)
\(720\) 14.2824 14.2824i 0.532273 0.532273i
\(721\) 0 0
\(722\) −6.79424 25.3564i −0.252855 0.943669i
\(723\) −4.51873 1.21079i −0.168053 0.0450298i
\(724\) 1.11484 0.643651i 0.0414325 0.0239211i
\(725\) 2.85702i 0.106107i
\(726\) −12.8104 + 3.43253i −0.475438 + 0.127393i
\(727\) −3.27502 −0.121464 −0.0607318 0.998154i \(-0.519343\pi\)
−0.0607318 + 0.998154i \(0.519343\pi\)
\(728\) 0 0
\(729\) −16.7676 −0.621022
\(730\) −10.9015 + 2.92105i −0.403483 + 0.108113i
\(731\) 3.92530i 0.145183i
\(732\) −0.00745656 + 0.00430505i −0.000275602 + 0.000159119i
\(733\) −32.5986 8.73478i −1.20406 0.322626i −0.399630 0.916676i \(-0.630861\pi\)
−0.804428 + 0.594050i \(0.797528\pi\)
\(734\) 5.17148 + 19.3002i 0.190883 + 0.712384i
\(735\) 0 0
\(736\) −2.94077 + 2.94077i −0.108398 + 0.108398i
\(737\) −1.47146 −0.0542020
\(738\) 30.3432 1.11695
\(739\) −1.49619 + 1.49619i −0.0550382 + 0.0550382i −0.734090 0.679052i \(-0.762391\pi\)
0.679052 + 0.734090i \(0.262391\pi\)
\(740\) 1.00484 + 1.74044i 0.0369387 + 0.0639797i
\(741\) 19.5552 + 13.6228i 0.718377 + 0.500447i
\(742\) 0 0
\(743\) −7.14174 + 26.6533i −0.262005 + 0.977816i 0.702053 + 0.712125i \(0.252267\pi\)
−0.964058 + 0.265692i \(0.914400\pi\)
\(744\) 1.42178 2.46260i 0.0521251 0.0902834i
\(745\) −12.4926 21.6379i −0.457695 0.792751i
\(746\) 27.9066 7.47755i 1.02173 0.273773i
\(747\) −2.85078 + 2.85078i −0.104305 + 0.104305i
\(748\) −0.544552 + 0.145912i −0.0199108 + 0.00533508i
\(749\) 0 0
\(750\) −3.74692 + 6.48986i −0.136818 + 0.236976i
\(751\) 6.52544 + 3.76747i 0.238117 + 0.137477i 0.614311 0.789064i \(-0.289434\pi\)
−0.376194 + 0.926541i \(0.622767\pi\)
\(752\) −8.40237 8.40237i −0.306403 0.306403i
\(753\) −4.23280 2.44381i −0.154252 0.0890574i
\(754\) −3.60635 2.51231i −0.131335 0.0914929i
\(755\) 38.7667i 1.41086i
\(756\) 0 0
\(757\) −21.0971 36.5412i −0.766786 1.32811i −0.939297 0.343104i \(-0.888522\pi\)
0.172512 0.985007i \(-0.444812\pi\)
\(758\) 29.5044i 1.07165i
\(759\) 3.10061 + 11.5716i 0.112545 + 0.420023i
\(760\) −13.2392 + 49.4095i −0.480237 + 1.79227i
\(761\) 1.20610 + 1.20610i 0.0437212 + 0.0437212i 0.728629 0.684908i \(-0.240158\pi\)
−0.684908 + 0.728629i \(0.740158\pi\)
\(762\) −17.0736 17.0736i −0.618513 0.618513i
\(763\) 0 0
\(764\) 0.663614 0.383138i 0.0240087 0.0138614i
\(765\) 5.77082 + 21.5370i 0.208644 + 0.778671i
\(766\) 12.3734 21.4314i 0.447070 0.774349i
\(767\) −1.78880 + 21.0275i −0.0645899 + 0.759258i
\(768\) −2.09061 + 1.20702i −0.0754385 + 0.0435545i
\(769\) −3.49612 0.936782i −0.126073 0.0337812i 0.195231 0.980757i \(-0.437454\pi\)
−0.321304 + 0.946976i \(0.604121\pi\)
\(770\) 0 0
\(771\) 8.01550 + 4.62775i 0.288671 + 0.166664i
\(772\) −0.651944 + 2.43309i −0.0234640 + 0.0875688i
\(773\) −25.8153 6.91718i −0.928510 0.248794i −0.237291 0.971439i \(-0.576259\pi\)
−0.691219 + 0.722645i \(0.742926\pi\)
\(774\) 2.30750 + 0.618294i 0.0829415 + 0.0222241i
\(775\) −0.768358 + 2.86755i −0.0276002 + 0.103005i
\(776\) −22.9985 13.2782i −0.825600 0.476660i
\(777\) 0 0
\(778\) 6.48299 + 1.73711i 0.232426 + 0.0622785i
\(779\) −63.4133 + 36.6117i −2.27202 + 1.31175i
\(780\) −0.443106 0.944317i −0.0158657