Properties

Label 637.2.x.b.19.6
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 19.6
Character \(\chi\) \(=\) 637.19
Dual form 637.2.x.b.570.5

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

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

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 \(0.100155\pi\)
−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 \(-0.361561\pi\)
0.818341 + 0.574734i \(0.194894\pi\)
\(6\) −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 \(-0.663310\pi\)
0.999944 0.0105451i \(-0.00335669\pi\)
\(18\) 2.46792 + 0.661277i 0.581694 + 0.155864i
\(19\) 4.35974 + 4.35974i 1.00019 + 1.00019i 1.00000 0.000191931i \(6.10936e-5\pi\)
0.000191931 1.00000i \(0.499939\pi\)
\(20\) −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 −0.983966 0.178354i \(-0.942923\pi\)
0.941317 + 0.337524i \(0.109590\pi\)
\(32\) 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 −0.992606 0.121379i \(-0.961268\pi\)
−0.798933 + 0.601421i \(0.794602\pi\)
\(42\) 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 0.999491 0.0318968i \(-0.0101548\pi\)
−0.881533 + 0.472122i \(0.843488\pi\)
\(48\) 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 \(-0.958913\pi\)
0.794461 0.607315i \(-0.207754\pi\)
\(60\) 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 −0.661199 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 0.0941746 0.995556i \(-0.469979\pi\)
−0.416220 + 0.909264i \(0.636645\pi\)
\(74\) 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 0.786575 0.617494i \(-0.211852\pi\)
−0.617494 + 0.786575i \(0.711852\pi\)
\(84\) 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 \(-0.500727\pi\)
−0.501977 + 0.864881i \(0.667394\pi\)
\(90\) 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 \(0.237765\pi\)
−0.975158 + 0.221509i \(0.928902\pi\)
\(98\) 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 \(-0.605655\pi\)
−0.325863 + 0.945417i \(0.605655\pi\)
\(102\) 4.39366 + 4.39366i 0.435037 + 0.435037i
\(103\) 4.92770 8.53503i 0.485541 0.840982i −0.514321 0.857598i \(-0.671956\pi\)
0.999862 + 0.0166161i \(0.00528932\pi\)
\(104\) −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 0.408340 0.912830i \(-0.366108\pi\)
−0.586364 + 0.810047i \(0.699441\pi\)
\(132\) −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 −0.256524 0.966538i \(-0.582577\pi\)
0.708784 + 0.705425i \(0.249244\pi\)
\(140\) 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 −0.715649 0.698460i \(-0.753869\pi\)
0.247059 + 0.969000i \(0.420536\pi\)
\(158\) −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 \(0.165577\pi\)
−0.502962 + 0.864308i \(0.667756\pi\)
\(168\) 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 \(-0.222209\pi\)
0.766070 + 0.642757i \(0.222209\pi\)
\(174\) 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 \(-0.330099\pi\)
0.508774 + 0.860900i \(0.330099\pi\)
\(182\) 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 −0.998420 0.0561884i \(-0.982105\pi\)
0.547871 + 0.836563i \(0.315439\pi\)
\(200\) −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 0.590423 0.807094i \(-0.298961\pi\)
0.914868 + 0.403752i \(0.132294\pi\)
\(224\) 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 \(-0.695768\pi\)
−0.0912961 + 0.995824i \(0.529101\pi\)
\(228\) 0.600381 0.160872i 0.0397612 0.0106540i
\(229\) 0.499191 + 1.86301i 0.0329875 + 0.123111i 0.980456 0.196738i \(-0.0630347\pi\)
−0.947469 + 0.319848i \(0.896368\pi\)
\(230\) −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 0.992714 0.120495i \(-0.0384482\pi\)
−0.919963 + 0.392005i \(0.871782\pi\)
\(242\) 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 \(-0.120708\pi\)
−0.785073 + 0.619403i \(0.787375\pi\)
\(252\) 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 \(-0.253448\pi\)
−0.968672 + 0.248342i \(0.920114\pi\)
\(258\) 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 \(-0.208280\pi\)
−0.130360 + 0.991467i \(0.541613\pi\)
\(270\) 20.6030i 1.25386i
\(271\) −4.45677 1.19419i −0.270730 0.0725418i 0.120900 0.992665i \(-0.461422\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(272\) −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 \(-0.0627336\pi\)
0.980642 + 0.195810i \(0.0627336\pi\)
\(284\) −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 \(-0.638341\pi\)
−0.818163 + 0.574986i \(0.805007\pi\)
\(294\) 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 \(-0.937760\pi\)
0.194289 + 0.980944i \(0.437760\pi\)
\(308\) 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 \(-0.905138\pi\)
0.223672 0.974664i \(-0.428196\pi\)
\(312\) 9.16912 6.38753i 0.519099 0.361623i
\(313\) 24.8257 + 14.3331i 1.40323 + 0.810155i 0.994723 0.102600i \(-0.0327162\pi\)
0.408507 + 0.912755i \(0.366050\pi\)
\(314\) −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 \(-0.883408\pi\)
0.629504 0.776998i \(-0.283258\pi\)
\(350\) 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 \(-0.150575\pi\)
−0.455600 + 0.890185i \(0.650575\pi\)
\(354\) 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 \(0.123300\pi\)
−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 −0.949478 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 0.304765 0.952427i \(-0.401422\pi\)
−0.952427 + 0.304765i \(0.901422\pi\)
\(384\) −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 −0.963170 0.268895i \(-0.913342\pi\)
0.268895 + 0.963170i \(0.413342\pi\)
\(398\) −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 0.553154 0.833079i \(-0.313424\pi\)
0.895585 + 0.444891i \(0.146758\pi\)
\(410\) −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 \(-0.395427\pi\)
−0.658386 + 0.752680i \(0.728761\pi\)
\(420\) 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 0.947774 0.318943i \(-0.103328\pi\)
−0.750099 + 0.661325i \(0.769994\pi\)
\(434\) 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 \(-0.0684692\pi\)
−0.673328 + 0.739344i \(0.735136\pi\)
\(440\) 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 \(-0.668456\pi\)
0.868822 0.495125i \(-0.164878\pi\)
\(462\) 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 −0.510088 0.860122i \(-0.670387\pi\)
0.999932 + 0.0116879i \(0.00372046\pi\)
\(468\) −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 \(-0.565152\pi\)
0.979126 + 0.203255i \(0.0651521\pi\)
\(480\) −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 −0.212918 0.977070i \(-0.568297\pi\)
0.739709 + 0.672927i \(0.234963\pi\)
\(504\) 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 \(-0.935511\pi\)
0.948921 + 0.315515i \(0.102177\pi\)
\(510\) 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 \(-0.777282\pi\)
0.175182 + 0.984536i \(0.443948\pi\)
\(522\) 1.59521 1.59521i 0.0698204 0.0698204i
\(523\) 0.102601 0.0592367i 0.00448643 0.00259024i −0.497755 0.867318i \(-0.665842\pi\)
0.502242 + 0.864727i \(0.332509\pi\)
\(524\) 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 \(0.409667\pi\)
−0.971383 + 0.237517i \(0.923666\pi\)
\(564\) 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 \(-0.665365\pi\)
0.863973 0.503538i \(-0.167969\pi\)
\(578\) −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 \(-0.500986\pi\)
0.497316 + 0.867569i \(0.334319\pi\)
\(588\) 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 \(-0.927827\pi\)
0.731460 0.681885i \(-0.238839\pi\)
\(594\) 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 0.0704537 0.997515i \(-0.477555\pi\)
−0.828647 + 0.559772i \(0.810889\pi\)
\(602\) 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 −0.798901 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 −0.0205475 0.999789i \(-0.506541\pi\)
−0.517689 + 0.855569i \(0.673208\pi\)
\(620\) 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 \(0.245503\pi\)
−0.969486 + 0.245147i \(0.921164\pi\)
\(644\) 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 \(-0.738279\pi\)
−0.680595 + 0.732660i \(0.738279\pi\)
\(648\) 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 −0.884652 0.466252i \(-0.845604\pi\)
0.466252 + 0.884652i \(0.345604\pi\)
\(662\) 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 −0.255562 0.966793i \(-0.582261\pi\)
−0.965048 + 0.262073i \(0.915594\pi\)
\(678\) 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 \(0.194994\pi\)
−0.996043 + 0.0888748i \(0.971673\pi\)
\(692\) −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 \(-0.830384\pi\)
−0.861355 + 0.508004i \(0.830384\pi\)
\(720\) −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 \(-0.480657\pi\)
0.0607318 + 0.998154i \(0.480657\pi\)
\(728\) 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 \(-0.369139\pi\)
0.804428 + 0.594050i \(0.202472\pi\)
\(734\) −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 −0.728629 0.684908i \(-0.759842\pi\)
0.684908 + 0.728629i \(0.259842\pi\)
\(762\) 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 \(-0.562546\pi\)
0.321304 + 0.946976i \(0.395879\pi\)
\(770\) 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 \(-0.423741\pi\)
0.691219 + 0.722645i \(0.257074\pi\)
\(774\) 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