Properties

Label 637.2.x.b.19.5
Level $637$
Weight $2$
Character 637.19
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 19.5
Character \(\chi\) \(=\) 637.19
Dual form 637.2.x.b.570.6

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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 0.697366 0.716715i \(-0.254355\pi\)
0.245579 + 0.969377i \(0.421022\pi\)
\(3\) 1.07207i 0.618958i −0.950906 0.309479i \(-0.899845\pi\)
0.950906 0.309479i \(-0.100155\pi\)
\(4\) −0.0814361 0.0470171i −0.0407180 0.0235086i
\(5\) −2.77200 + 0.742756i −1.23968 + 0.332171i −0.818341 0.574734i \(-0.805106\pi\)
−0.421337 + 0.906904i \(0.638439\pi\)
\(6\) 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 0.538293 0.842758i \(-0.319069\pi\)
−0.842758 + 0.538293i \(0.819069\pi\)
\(12\) −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 0.490840 + 0.871250i \(0.336690\pi\)
−0.999944 + 0.0105451i \(0.996643\pi\)
\(18\) 2.46792 + 0.661277i 0.581694 + 0.155864i
\(19\) −4.35974 4.35974i −1.00019 1.00019i −1.00000 0.000191931i \(-0.999939\pi\)
−0.000191931 1.00000i \(-0.500061\pi\)
\(20\) 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 −0.995671 0.0929436i \(-0.970372\pi\)
−0.417344 + 0.908748i \(0.637039\pi\)
\(24\) −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 −0.822119 0.569315i \(-0.807208\pi\)
0.904101 + 0.427319i \(0.140542\pi\)
\(30\) 4.24746i 0.775477i
\(31\) 0.237463 0.886225i 0.0426497 0.159171i −0.941317 0.337524i \(-0.890410\pi\)
0.983966 + 0.178354i \(0.0570771\pi\)
\(32\) 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 −0.605358 0.795953i \(-0.706970\pi\)
0.922232 0.386637i \(-0.126363\pi\)
\(38\) −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 0.798933 0.601421i \(-0.205398\pi\)
0.992606 + 0.121379i \(0.0387317\pi\)
\(42\) 0 0
\(43\) 0.809734 0.467500i 0.123483 0.0712931i −0.436986 0.899468i \(-0.643954\pi\)
0.560469 + 0.828175i \(0.310621\pi\)
\(44\) 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 0.881533 0.472122i \(-0.156512\pi\)
−0.999491 + 0.0318968i \(0.989845\pi\)
\(48\) −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 0.766201 0.642601i \(-0.222145\pi\)
−0.939609 + 0.342249i \(0.888811\pi\)
\(54\) 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 0.991681 + 0.128720i \(0.0410869\pi\)
−0.794461 + 0.607315i \(0.792246\pi\)
\(60\) 0.0748780 0.279449i 0.00966671 0.0360767i
\(61\) 0.0854082i 0.0109354i 0.999985 + 0.00546770i \(0.00174043\pi\)
−0.999985 + 0.00546770i \(0.998260\pi\)
\(62\) 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 −0.661199 0.750211i \(-0.729952\pi\)
0.750211 + 0.661199i \(0.229952\pi\)
\(68\) 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 0.421109 0.907010i \(-0.361641\pi\)
−0.0888143 + 0.996048i \(0.528308\pi\)
\(72\) −3.78317 3.78317i −0.445851 0.445851i
\(73\) 2.75156 + 0.737278i 0.322046 + 0.0862919i 0.416220 0.909264i \(-0.363355\pi\)
−0.0941746 + 0.995556i \(0.530021\pi\)
\(74\) 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 0.468849 + 0.883279i \(0.344669\pi\)
−0.999366 + 0.0356045i \(0.988664\pi\)
\(80\) 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 0.617494 0.786575i \(-0.288148\pi\)
−0.786575 + 0.617494i \(0.788148\pi\)
\(84\) 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 0.501977 0.864881i \(-0.332606\pi\)
0.00228491 + 0.999997i \(0.499273\pi\)
\(90\) −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 −0.733758 0.679411i \(-0.762235\pi\)
0.975158 0.221509i \(-0.0710981\pi\)
\(98\) 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 −0.999862 0.0166161i \(-0.994711\pi\)
0.514321 + 0.857598i \(0.328044\pi\)
\(104\) 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 −0.999902 0.0139814i \(-0.995549\pi\)
0.487843 0.872931i \(-0.337784\pi\)
\(108\) −0.244501 + 0.423488i −0.0235271 + 0.0407501i
\(109\) −15.9403 4.27118i −1.52680 0.409105i −0.604827 0.796357i \(-0.706758\pi\)
−0.921974 + 0.387252i \(0.873424\pi\)
\(110\) 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 0.850477 0.526013i \(-0.176314\pi\)
−0.880779 + 0.473528i \(0.842980\pi\)
\(114\) −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 −0.281850 0.959458i \(-0.590948\pi\)
−0.971841 + 0.235640i \(0.924282\pi\)
\(128\) −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 0.586364 0.810047i \(-0.300559\pi\)
−0.408340 + 0.912830i \(0.633892\pi\)
\(132\) 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 −0.660541 0.750790i \(-0.729673\pi\)
−0.196650 + 0.980474i \(0.563006\pi\)
\(138\) 2.99748 + 11.1867i 0.255162 + 0.952278i
\(139\) −5.33208 + 3.07848i −0.452261 + 0.261113i −0.708784 0.705425i \(-0.750756\pi\)
0.256524 + 0.966538i \(0.417423\pi\)
\(140\) 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 −0.408442 0.912784i \(-0.633928\pi\)
0.912784 + 0.408442i \(0.133928\pi\)
\(150\) −1.23949 4.62584i −0.101204 0.377698i
\(151\) 3.49627 13.0482i 0.284522 1.06185i −0.664665 0.747141i \(-0.731426\pi\)
0.949188 0.314710i \(-0.101907\pi\)
\(152\) 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 −0.247059 0.969000i \(-0.579464\pi\)
0.715649 + 0.698460i \(0.246131\pi\)
\(158\) −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 0.336588 0.941652i \(-0.390727\pi\)
−0.941652 + 0.336588i \(0.890727\pi\)
\(164\) −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 −0.867732 0.497032i \(-0.834423\pi\)
0.502962 0.864308i \(-0.332244\pi\)
\(168\) 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 \(0.211991\pi\)
−0.786306 + 0.617837i \(0.788009\pi\)
\(180\) 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 0.869499 + 0.493935i \(0.164442\pi\)
0.493935 + 0.869499i \(0.335558\pi\)
\(194\) 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 0.898490 + 0.438995i \(0.144665\pi\)
−0.558617 + 0.829426i \(0.688668\pi\)
\(198\) −1.82434 3.15985i −0.129650 0.224560i
\(199\) 6.35578 11.0085i 0.450550 0.780375i −0.547871 0.836563i \(-0.684561\pi\)
0.998420 + 0.0561884i \(0.0178947\pi\)
\(200\) −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 −0.933387 0.358872i \(-0.883161\pi\)
0.777486 + 0.628900i \(0.216495\pi\)
\(212\) 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 −0.914868 0.403752i \(-0.867706\pi\)
−0.590423 + 0.807094i \(0.701039\pi\)
\(224\) 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 0.0912961 0.995824i \(-0.470899\pi\)
0.576977 + 0.816761i \(0.304232\pi\)
\(228\) 0.600381 0.160872i 0.0397612 0.0106540i
\(229\) −0.499191 1.86301i −0.0329875 0.123111i 0.947469 0.319848i \(-0.103632\pi\)
−0.980456 + 0.196738i \(0.936965\pi\)
\(230\) 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 0.723602 0.690217i \(-0.242485\pi\)
−0.235945 + 0.971766i \(0.575818\pi\)
\(234\) −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 −0.884278 0.466960i \(-0.845349\pi\)
0.466960 + 0.884278i \(0.345349\pi\)
\(240\) 8.27358 8.27358i 0.534057 0.534057i
\(241\) −1.12940 4.21497i −0.0727509 0.271510i 0.919963 0.392005i \(-0.128218\pi\)
−0.992714 + 0.120495i \(0.961552\pi\)
\(242\) 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 0.785073 0.619403i \(-0.212625\pi\)
−0.928956 + 0.370191i \(0.879292\pi\)
\(252\) 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 0.968672 0.248342i \(-0.0798857\pi\)
−0.699407 + 0.714724i \(0.746552\pi\)
\(258\) −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 0.130360 0.991467i \(-0.458387\pi\)
−0.793455 + 0.608629i \(0.791720\pi\)
\(270\) 20.6030i 1.25386i
\(271\) 4.45677 + 1.19419i 0.270730 + 0.0725418i 0.391630 0.920123i \(-0.371911\pi\)
−0.120900 + 0.992665i \(0.538578\pi\)
\(272\) 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 0.542881 0.839809i \(-0.317333\pi\)
−0.455856 + 0.890054i \(0.650667\pi\)
\(278\) −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 0.156870 0.987619i \(-0.449860\pi\)
−0.987619 + 0.156870i \(0.949860\pi\)
\(282\) −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 0.818163 0.574986i \(-0.194993\pi\)
0.421057 + 0.907034i \(0.361659\pi\)
\(294\) 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 −0.194289 0.980944i \(-0.562240\pi\)
0.980944 + 0.194289i \(0.0622399\pi\)
\(308\) 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 0.955920 + 0.293627i \(0.0948622\pi\)
−0.223672 + 0.974664i \(0.571804\pi\)
\(312\) 9.16912 6.38753i 0.519099 0.361623i
\(313\) −24.8257 14.3331i −1.40323 0.810155i −0.408507 0.912755i \(-0.633950\pi\)
−0.994723 + 0.102600i \(0.967284\pi\)
\(314\) 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 0.995408 + 0.0957183i \(0.0305148\pi\)
−0.814190 + 0.580599i \(0.802819\pi\)
\(318\) −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 0.180578 0.983561i \(-0.442203\pi\)
0.983561 0.180578i \(-0.0577970\pi\)
\(332\) 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 \(0.119296\pi\)
−0.930588 + 0.366068i \(0.880704\pi\)
\(338\) 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 −0.603172 0.797611i \(-0.706097\pi\)
0.992338 + 0.123556i \(0.0394299\pi\)
\(348\) 0.0445066 + 0.0770876i 0.00238580 + 0.00413233i
\(349\) 5.68220 + 21.2063i 0.304161 + 1.13515i 0.933665 + 0.358148i \(0.116592\pi\)
−0.629504 + 0.776998i \(0.716742\pi\)
\(350\) 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 0.455600 0.890185i \(-0.349425\pi\)
−0.890185 + 0.455600i \(0.849425\pi\)
\(354\) 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 −0.236000 0.971753i \(-0.575837\pi\)
0.281494 + 0.959563i \(0.409170\pi\)
\(360\) 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 \(-0.876700\pi\)
0.925910 0.377744i \(-0.123300\pi\)
\(368\) 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 −0.949478 0.313834i \(-0.898387\pi\)
0.665355 0.746527i \(-0.268280\pi\)
\(380\) −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 0.952427 0.304765i \(-0.0985781\pi\)
−0.304765 + 0.952427i \(0.598578\pi\)
\(384\) 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 −0.389455 0.921046i \(-0.627337\pi\)
0.602921 + 0.797801i \(0.294003\pi\)
\(390\) 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 −0.268895 0.963170i \(-0.586658\pi\)
0.963170 + 0.268895i \(0.0866584\pi\)
\(398\) 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 −0.988118 0.153700i \(-0.950881\pi\)
0.932585 + 0.360951i \(0.117548\pi\)
\(402\) −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 −0.895585 0.444891i \(-0.853242\pi\)
−0.553154 + 0.833079i \(0.686576\pi\)
\(410\) −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 0.658386 0.752680i \(-0.271239\pi\)
−0.322647 + 0.946519i \(0.604573\pi\)
\(420\) 0 0
\(421\) −5.98090 + 5.98090i −0.291491 + 0.291491i −0.837669 0.546178i \(-0.816082\pi\)
0.546178 + 0.837669i \(0.316082\pi\)
\(422\) −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 −0.697185 0.716891i \(-0.745565\pi\)
0.716891 + 0.697185i \(0.245565\pi\)
\(432\) −17.1274 + 9.88850i −0.824042 + 0.475761i
\(433\) −4.11334 7.12452i −0.197675 0.342382i 0.750099 0.661325i \(-0.230006\pi\)
−0.947774 + 0.318943i \(0.896672\pi\)
\(434\) 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 0.673328 0.739344i \(-0.264864\pi\)
−0.976955 + 0.213447i \(0.931531\pi\)
\(440\) −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 −0.838313 0.545189i \(-0.816458\pi\)
0.891304 + 0.453406i \(0.149791\pi\)
\(444\) 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 −0.141088 0.989997i \(-0.545060\pi\)
0.617184 0.786819i \(-0.288273\pi\)
\(450\) 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 −0.302174 0.953253i \(-0.597712\pi\)
−0.738316 + 0.674455i \(0.764379\pi\)
\(458\) 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 0.504859 + 0.863202i \(0.331544\pi\)
−0.868822 + 0.495125i \(0.835122\pi\)
\(462\) 0 0
\(463\) 2.19856 + 2.19856i 0.102176 + 0.102176i 0.756347 0.654171i \(-0.226982\pi\)
−0.654171 + 0.756347i \(0.726982\pi\)
\(464\) −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 −0.999932 0.0116879i \(-0.996280\pi\)
0.510088 + 0.860122i \(0.329613\pi\)
\(468\) 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 −0.979126 0.203255i \(-0.934848\pi\)
0.203255 + 0.979126i \(0.434848\pi\)
\(480\) −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 −0.813694 0.581294i \(-0.802547\pi\)
0.414032 0.910262i \(-0.364120\pi\)
\(488\) 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 0.750605 0.660751i \(-0.229762\pi\)
−0.196924 + 0.980419i \(0.563095\pi\)
\(492\) −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 −0.892032 0.451972i \(-0.850721\pi\)
0.546536 0.837436i \(-0.315946\pi\)
\(500\) −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 −0.739709 0.672927i \(-0.765037\pi\)
0.212918 + 0.977070i \(0.431703\pi\)
\(504\) 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 −0.948921 0.315515i \(-0.897823\pi\)
0.979547 + 0.201216i \(0.0644895\pi\)
\(510\) −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 −0.175182 0.984536i \(-0.556052\pi\)
0.765042 + 0.643980i \(0.222718\pi\)
\(522\) 1.59521 1.59521i 0.0698204 0.0698204i
\(523\) −0.102601 + 0.0592367i −0.00448643 + 0.00259024i −0.502242 0.864727i \(-0.667491\pi\)
0.497755 + 0.867318i \(0.334158\pi\)
\(524\) −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 −0.161432 0.986884i \(-0.551611\pi\)
0.353638 + 0.935382i \(0.384945\pi\)
\(542\) 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 0.727137 0.686492i \(-0.240850\pi\)
−0.686492 + 0.727137i \(0.740850\pi\)
\(558\) 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 −0.279995 0.960001i \(-0.590333\pi\)
0.971383 0.237517i \(-0.0763337\pi\)
\(564\) 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 0.152552 0.988296i \(-0.451251\pi\)
0.932165 + 0.362034i \(0.117918\pi\)
\(570\) 18.5178 18.5178i 0.775626 0.775626i
\(571\) −0.640877 + 0.370010i −0.0268198 + 0.0154844i −0.513350 0.858179i \(-0.671596\pi\)
0.486530 + 0.873664i \(0.338262\pi\)
\(572\) −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 0.496454 + 0.868063i \(0.334635\pi\)
−0.863973 + 0.503538i \(0.832031\pi\)
\(578\) −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 −0.497316 0.867569i \(-0.665681\pi\)
0.00309648 + 0.999995i \(0.499014\pi\)
\(588\) 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 0.974405 + 0.224800i \(0.0721728\pi\)
−0.731460 + 0.681885i \(0.761161\pi\)
\(594\) −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 0.839425 0.543476i \(-0.182892\pi\)
−0.890376 + 0.455225i \(0.849559\pi\)
\(600\) −2.59553 + 9.68666i −0.105962 + 0.395456i
\(601\) 18.5873 + 10.7314i 0.758193 + 0.437743i 0.828647 0.559772i \(-0.189111\pi\)
−0.0704537 + 0.997515i \(0.522445\pi\)
\(602\) 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 \(-0.894463\pi\)
0.945537 0.325514i \(-0.105537\pi\)
\(608\) 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 −0.798901 0.601462i \(-0.794585\pi\)
0.601462 + 0.798901i \(0.294585\pi\)
\(614\) 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 0.756223 0.654314i \(-0.227043\pi\)
0.327751 + 0.944764i \(0.393709\pi\)
\(618\) 10.3143 + 10.3143i 0.414901 + 0.414901i
\(619\) 13.3912 + 3.58815i 0.538237 + 0.144220i 0.517689 0.855569i \(-0.326792\pi\)
0.0205475 + 0.999789i \(0.493459\pi\)
\(620\) 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 −0.694764 0.719237i \(-0.744491\pi\)
0.961302 0.275496i \(-0.0888419\pi\)
\(632\) 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 0.699405 0.714726i \(-0.253449\pi\)
−0.269269 + 0.963065i \(0.586782\pi\)
\(642\) −15.1449 + 4.05806i −0.597720 + 0.160159i
\(643\) 6.40174 23.8916i 0.252460 0.942193i −0.717026 0.697046i \(-0.754497\pi\)
0.969486 0.245147i \(-0.0788361\pi\)
\(644\) 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 0.999108 + 0.0422314i \(0.0134467\pi\)
−0.462980 + 0.886368i \(0.653220\pi\)
\(654\) −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 0.904795 0.425847i \(-0.140024\pi\)
−0.821192 + 0.570652i \(0.806691\pi\)
\(660\) −0.357797 + 0.206574i −0.0139272 + 0.00804090i
\(661\) 10.7570 10.7570i 0.418399 0.418399i −0.466252 0.884652i \(-0.654396\pi\)
0.884652 + 0.466252i \(0.154396\pi\)
\(662\) 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 0.912314 0.409492i \(-0.134294\pi\)
0.101526 + 0.994833i \(0.467627\pi\)
\(674\) −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 0.965048 0.262073i \(-0.0844060\pi\)
0.255562 + 0.966793i \(0.417739\pi\)
\(678\) −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 −0.542219 0.840237i \(-0.682416\pi\)
−0.0494567 + 0.998776i \(0.515749\pi\)
\(684\) 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 −0.818161 0.574989i \(-0.805006\pi\)
0.996043 0.0888748i \(-0.0283271\pi\)
\(692\) 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 \(-0.748355\pi\)
0.703444 0.710751i \(-0.251645\pi\)
\(702\) −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 0.537252 0.843422i \(-0.319462\pi\)
−0.843422 + 0.537252i \(0.819462\pi\)
\(710\) −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 −0.804428 0.594050i \(-0.797528\pi\)
−0.399630 + 0.916676i \(0.630861\pi\)
\(734\) 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 0.679052 0.734090i \(-0.262391\pi\)
−0.734090 + 0.679052i \(0.762391\pi\)
\(740\) 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 −0.964058 0.265692i \(-0.914400\pi\)
0.702053 0.712125i \(-0.252267\pi\)
\(744\) 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 −0.376194 0.926541i \(-0.622767\pi\)
0.614311 + 0.789064i \(0.289434\pi\)
\(752\) −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 0.172512 + 0.985007i \(0.444812\pi\)
−0.939297 + 0.343104i \(0.888522\pi\)
\(758\) 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 −0.684908 0.728629i \(-0.740158\pi\)
0.728629 + 0.684908i \(0.240158\pi\)
\(762\) −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 −0.321304 0.946976i \(-0.604121\pi\)
0.195231 + 0.980757i \(0.437454\pi\)
\(770\) 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 −0.691219 0.722645i \(-0.742926\pi\)
−0.237291 + 0.971439i \(0.576259\pi\)
\(774\) 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