Properties

Label 392.3.k.l.275.2
Level 392
Weight 3
Character 392.275
Analytic conductor 10.681
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.2
Root \(-0.407369 - 0.812545i\) of defining polynomial
Character \(\chi\) \(=\) 392.275
Dual form 392.3.k.l.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19654 - 1.60259i) q^{2} +(2.66613 + 4.61787i) q^{3} +(-1.13656 + 3.83513i) q^{4} +(-1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 + 16.8294i) q^{9} +O(q^{10})\) \(q+(-1.19654 - 1.60259i) q^{2} +(2.66613 + 4.61787i) q^{3} +(-1.13656 + 3.83513i) q^{4} +(-1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 + 16.8294i) q^{9} +(0.506759 + 4.28400i) q^{10} +(-2.62956 - 4.55453i) q^{11} +(-20.7403 + 4.97644i) q^{12} +21.4116i q^{13} -11.5013i q^{15} +(-13.4164 - 8.71774i) q^{16} +(0.463429 + 0.802683i) q^{17} +(38.5968 - 4.56566i) q^{18} +(-2.96505 + 5.13561i) q^{19} +(6.25911 - 5.93812i) q^{20} +(-4.15264 + 9.66378i) q^{22} +(7.52507 + 4.34460i) q^{23} +(32.7919 + 27.2837i) q^{24} +(-10.1738 - 17.6216i) q^{25} +(34.3139 - 25.6199i) q^{26} -55.6311 q^{27} +9.42223i q^{29} +(-18.4318 + 13.7618i) q^{30} +(-29.8813 + 17.2520i) q^{31} +(2.08243 + 31.9322i) q^{32} +(14.0215 - 24.2859i) q^{33} +(0.731855 - 1.70313i) q^{34} +(-53.4996 - 56.3916i) q^{36} +(-11.0853 - 6.40011i) q^{37} +(11.7781 - 1.39324i) q^{38} +(-98.8758 + 57.0860i) q^{39} +(-17.0056 - 2.92555i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(20.4559 - 4.90818i) q^{44} +(36.2999 - 20.9578i) q^{45} +(-2.04148 - 17.2581i) q^{46} +(-39.8357 - 22.9991i) q^{47} +(4.48745 - 85.1980i) q^{48} +(-16.0667 + 37.3894i) q^{50} +(-2.47112 + 4.28011i) q^{51} +(-82.1161 - 24.3356i) q^{52} +(64.5031 - 37.2409i) q^{53} +(66.5650 + 89.1536i) q^{54} +11.3436i q^{55} -31.6208 q^{57} +(15.0999 - 11.2741i) q^{58} +(26.8367 + 46.4825i) q^{59} +(44.1090 + 13.0720i) q^{60} +(24.0893 + 13.9080i) q^{61} +(63.4020 + 27.2446i) q^{62} +(48.6823 - 41.5455i) q^{64} +(23.0916 - 39.9959i) q^{65} +(-55.6975 + 6.58853i) q^{66} +(39.2453 + 67.9749i) q^{67} +(-3.60511 + 0.865011i) q^{68} +46.3330i q^{69} +74.5100i q^{71} +(-26.3578 + 153.213i) q^{72} +(16.8020 + 29.1020i) q^{73} +(3.00734 + 25.4232i) q^{74} +(54.2494 - 93.9627i) q^{75} +(-16.3258 - 17.2083i) q^{76} +(209.794 + 90.1511i) q^{78} +(-26.1642 - 15.1059i) q^{79} +(15.6596 + 30.7536i) q^{80} +(-60.8713 - 105.432i) q^{81} +(51.6116 + 69.1258i) q^{82} +72.9274 q^{83} -1.99917i q^{85} +(49.9416 + 66.8891i) q^{86} +(-43.5106 + 25.1209i) q^{87} +(-32.3421 - 26.9094i) q^{88} +(-27.4198 + 47.4925i) q^{89} +(-77.0211 - 33.0968i) q^{90} +(-25.2148 + 23.9217i) q^{92} +(-159.335 - 91.9919i) q^{93} +(10.8070 + 91.3596i) q^{94} +(11.0772 - 6.39541i) q^{95} +(-141.907 + 94.7516i) q^{96} +53.7125 q^{97} +102.200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + O(q^{10}) \) \( 12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + 6q^{10} + 30q^{11} - 32q^{12} + 16q^{16} - 30q^{17} - 16q^{18} - 78q^{19} - 48q^{20} + 24q^{22} + 76q^{24} - 92q^{25} + 128q^{26} - 156q^{27} - 16q^{30} + 112q^{32} + 78q^{33} - 76q^{34} - 248q^{36} - 80q^{38} - 44q^{40} + 232q^{41} - 200q^{43} + 132q^{44} - 156q^{46} - 176q^{48} + 48q^{50} + 10q^{51} - 132q^{52} + 36q^{54} + 332q^{57} + 4q^{58} + 110q^{59} + 84q^{60} + 96q^{62} - 160q^{64} - 32q^{65} + 138q^{66} + 434q^{67} - 96q^{68} - 328q^{72} - 102q^{73} - 34q^{74} + 60q^{75} + 168q^{76} + 720q^{78} + 256q^{80} - 82q^{81} + 24q^{82} + 536q^{83} + 240q^{86} - 204q^{88} - 214q^{89} - 440q^{90} + 160q^{92} + 16q^{94} - 48q^{96} + 152q^{97} + 504q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19654 1.60259i −0.598272 0.801293i
\(3\) 2.66613 + 4.61787i 0.888709 + 1.53929i 0.841403 + 0.540409i \(0.181730\pi\)
0.0473064 + 0.998880i \(0.484936\pi\)
\(4\) −1.13656 + 3.83513i −0.284141 + 0.958782i
\(5\) −1.86796 1.07847i −0.373592 0.215693i 0.301435 0.953487i \(-0.402534\pi\)
−0.675026 + 0.737794i \(0.735868\pi\)
\(6\) 4.21039 9.79818i 0.701732 1.63303i
\(7\) 0 0
\(8\) 7.50608 2.76746i 0.938259 0.345932i
\(9\) −9.71647 + 16.8294i −1.07961 + 1.86993i
\(10\) 0.506759 + 4.28400i 0.0506759 + 0.428400i
\(11\) −2.62956 4.55453i −0.239051 0.414048i 0.721392 0.692527i \(-0.243503\pi\)
−0.960442 + 0.278480i \(0.910170\pi\)
\(12\) −20.7403 + 4.97644i −1.72836 + 0.414703i
\(13\) 21.4116i 1.64704i 0.567285 + 0.823522i \(0.307994\pi\)
−0.567285 + 0.823522i \(0.692006\pi\)
\(14\) 0 0
\(15\) 11.5013i 0.766754i
\(16\) −13.4164 8.71774i −0.838528 0.544859i
\(17\) 0.463429 + 0.802683i 0.0272606 + 0.0472167i 0.879334 0.476206i \(-0.157988\pi\)
−0.852073 + 0.523423i \(0.824655\pi\)
\(18\) 38.5968 4.56566i 2.14426 0.253648i
\(19\) −2.96505 + 5.13561i −0.156055 + 0.270295i −0.933443 0.358726i \(-0.883211\pi\)
0.777388 + 0.629022i \(0.216544\pi\)
\(20\) 6.25911 5.93812i 0.312956 0.296906i
\(21\) 0 0
\(22\) −4.15264 + 9.66378i −0.188756 + 0.439263i
\(23\) 7.52507 + 4.34460i 0.327177 + 0.188896i 0.654587 0.755987i \(-0.272843\pi\)
−0.327410 + 0.944882i \(0.606176\pi\)
\(24\) 32.7919 + 27.2837i 1.36633 + 1.13682i
\(25\) −10.1738 17.6216i −0.406953 0.704863i
\(26\) 34.3139 25.6199i 1.31976 0.985380i
\(27\) −55.6311 −2.06041
\(28\) 0 0
\(29\) 9.42223i 0.324904i 0.986716 + 0.162452i \(0.0519403\pi\)
−0.986716 + 0.162452i \(0.948060\pi\)
\(30\) −18.4318 + 13.7618i −0.614395 + 0.458728i
\(31\) −29.8813 + 17.2520i −0.963912 + 0.556515i −0.897375 0.441269i \(-0.854529\pi\)
−0.0665375 + 0.997784i \(0.521195\pi\)
\(32\) 2.08243 + 31.9322i 0.0650759 + 0.997880i
\(33\) 14.0215 24.2859i 0.424893 0.735936i
\(34\) 0.731855 1.70313i 0.0215252 0.0500921i
\(35\) 0 0
\(36\) −53.4996 56.3916i −1.48610 1.56643i
\(37\) −11.0853 6.40011i −0.299603 0.172976i 0.342662 0.939459i \(-0.388672\pi\)
−0.642265 + 0.766483i \(0.722005\pi\)
\(38\) 11.7781 1.39324i 0.309949 0.0366643i
\(39\) −98.8758 + 57.0860i −2.53528 + 1.46374i
\(40\) −17.0056 2.92555i −0.425141 0.0731387i
\(41\) −43.1339 −1.05205 −0.526023 0.850470i \(-0.676317\pi\)
−0.526023 + 0.850470i \(0.676317\pi\)
\(42\) 0 0
\(43\) −41.7382 −0.970656 −0.485328 0.874332i \(-0.661300\pi\)
−0.485328 + 0.874332i \(0.661300\pi\)
\(44\) 20.4559 4.90818i 0.464906 0.111550i
\(45\) 36.2999 20.9578i 0.806665 0.465728i
\(46\) −2.04148 17.2581i −0.0443800 0.375175i
\(47\) −39.8357 22.9991i −0.847567 0.489343i 0.0122620 0.999925i \(-0.496097\pi\)
−0.859829 + 0.510582i \(0.829430\pi\)
\(48\) 4.48745 85.1980i 0.0934885 1.77496i
\(49\) 0 0
\(50\) −16.0667 + 37.3894i −0.321333 + 0.747788i
\(51\) −2.47112 + 4.28011i −0.0484534 + 0.0839238i
\(52\) −82.1161 24.3356i −1.57916 0.467993i
\(53\) 64.5031 37.2409i 1.21704 0.702658i 0.252756 0.967530i \(-0.418663\pi\)
0.964284 + 0.264872i \(0.0853297\pi\)
\(54\) 66.5650 + 89.1536i 1.23269 + 1.65099i
\(55\) 11.3436i 0.206246i
\(56\) 0 0
\(57\) −31.6208 −0.554751
\(58\) 15.0999 11.2741i 0.260344 0.194381i
\(59\) 26.8367 + 46.4825i 0.454860 + 0.787840i 0.998680 0.0513617i \(-0.0163561\pi\)
−0.543821 + 0.839201i \(0.683023\pi\)
\(60\) 44.1090 + 13.0720i 0.735150 + 0.217866i
\(61\) 24.0893 + 13.9080i 0.394907 + 0.228000i 0.684284 0.729215i \(-0.260115\pi\)
−0.289377 + 0.957215i \(0.593448\pi\)
\(62\) 63.4020 + 27.2446i 1.02261 + 0.439429i
\(63\) 0 0
\(64\) 48.6823 41.5455i 0.760661 0.649149i
\(65\) 23.0916 39.9959i 0.355256 0.615322i
\(66\) −55.6975 + 6.58853i −0.843902 + 0.0998262i
\(67\) 39.2453 + 67.9749i 0.585751 + 1.01455i 0.994781 + 0.102030i \(0.0325338\pi\)
−0.409030 + 0.912521i \(0.634133\pi\)
\(68\) −3.60511 + 0.865011i −0.0530164 + 0.0127207i
\(69\) 46.3330i 0.671493i
\(70\) 0 0
\(71\) 74.5100i 1.04944i 0.851276 + 0.524719i \(0.175829\pi\)
−0.851276 + 0.524719i \(0.824171\pi\)
\(72\) −26.3578 + 153.213i −0.366081 + 2.12796i
\(73\) 16.8020 + 29.1020i 0.230165 + 0.398657i 0.957857 0.287247i \(-0.0927401\pi\)
−0.727692 + 0.685904i \(0.759407\pi\)
\(74\) 3.00734 + 25.4232i 0.0406397 + 0.343556i
\(75\) 54.2494 93.9627i 0.723325 1.25284i
\(76\) −16.3258 17.2083i −0.214813 0.226425i
\(77\) 0 0
\(78\) 209.794 + 90.1511i 2.68967 + 1.15578i
\(79\) −26.1642 15.1059i −0.331192 0.191214i 0.325178 0.945653i \(-0.394576\pi\)
−0.656370 + 0.754439i \(0.727909\pi\)
\(80\) 15.6596 + 30.7536i 0.195745 + 0.384420i
\(81\) −60.8713 105.432i −0.751497 1.30163i
\(82\) 51.6116 + 69.1258i 0.629410 + 0.842997i
\(83\) 72.9274 0.878644 0.439322 0.898330i \(-0.355219\pi\)
0.439322 + 0.898330i \(0.355219\pi\)
\(84\) 0 0
\(85\) 1.99917i 0.0235197i
\(86\) 49.9416 + 66.8891i 0.580716 + 0.777780i
\(87\) −43.5106 + 25.1209i −0.500122 + 0.288745i
\(88\) −32.3421 26.9094i −0.367524 0.305789i
\(89\) −27.4198 + 47.4925i −0.308088 + 0.533624i −0.977944 0.208867i \(-0.933022\pi\)
0.669856 + 0.742491i \(0.266356\pi\)
\(90\) −77.0211 33.0968i −0.855790 0.367743i
\(91\) 0 0
\(92\) −25.2148 + 23.9217i −0.274074 + 0.260018i
\(93\) −159.335 91.9919i −1.71328 0.989160i
\(94\) 10.8070 + 91.3596i 0.114969 + 0.971910i
\(95\) 11.0772 6.39541i 0.116602 0.0673201i
\(96\) −141.907 + 94.7516i −1.47819 + 0.986996i
\(97\) 53.7125 0.553738 0.276869 0.960908i \(-0.410703\pi\)
0.276869 + 0.960908i \(0.410703\pi\)
\(98\) 0 0
\(99\) 102.200 1.03232
\(100\) 79.1442 18.9899i 0.791442 0.189899i
\(101\) 78.2037 45.1509i 0.774294 0.447039i −0.0601103 0.998192i \(-0.519145\pi\)
0.834404 + 0.551153i \(0.185812\pi\)
\(102\) 9.81606 1.16115i 0.0962358 0.0113839i
\(103\) 97.6980 + 56.4060i 0.948525 + 0.547631i 0.892622 0.450805i \(-0.148863\pi\)
0.0559023 + 0.998436i \(0.482196\pi\)
\(104\) 59.2556 + 160.717i 0.569766 + 1.54535i
\(105\) 0 0
\(106\) −136.863 58.8114i −1.29116 0.554825i
\(107\) 71.9950 124.699i 0.672851 1.16541i −0.304241 0.952595i \(-0.598403\pi\)
0.977092 0.212817i \(-0.0682637\pi\)
\(108\) 63.2283 213.352i 0.585447 1.97548i
\(109\) −57.7477 + 33.3406i −0.529795 + 0.305877i −0.740933 0.671579i \(-0.765616\pi\)
0.211138 + 0.977456i \(0.432283\pi\)
\(110\) 18.1790 13.5731i 0.165264 0.123391i
\(111\) 68.2540i 0.614901i
\(112\) 0 0
\(113\) 7.16467 0.0634042 0.0317021 0.999497i \(-0.489907\pi\)
0.0317021 + 0.999497i \(0.489907\pi\)
\(114\) 37.8357 + 50.6750i 0.331892 + 0.444518i
\(115\) −9.37101 16.2311i −0.0814870 0.141140i
\(116\) −36.1355 10.7090i −0.311513 0.0923187i
\(117\) −360.344 208.045i −3.07986 1.77816i
\(118\) 42.3810 98.6266i 0.359161 0.835818i
\(119\) 0 0
\(120\) −31.8294 86.3297i −0.265245 0.719414i
\(121\) 46.6709 80.8363i 0.385710 0.668069i
\(122\) −6.53521 55.2468i −0.0535673 0.452842i
\(123\) −115.000 199.187i −0.934963 1.61940i
\(124\) −32.2015 134.207i −0.259690 1.08231i
\(125\) 97.8118i 0.782494i
\(126\) 0 0
\(127\) 131.492i 1.03537i 0.855572 + 0.517684i \(0.173206\pi\)
−0.855572 + 0.517684i \(0.826794\pi\)
\(128\) −124.831 28.3066i −0.975241 0.221145i
\(129\) −111.279 192.742i −0.862631 1.49412i
\(130\) −91.7271 + 10.8505i −0.705593 + 0.0834655i
\(131\) −4.38060 + 7.58742i −0.0334397 + 0.0579193i −0.882261 0.470761i \(-0.843980\pi\)
0.848821 + 0.528680i \(0.177313\pi\)
\(132\) 77.2032 + 81.3766i 0.584873 + 0.616489i
\(133\) 0 0
\(134\) 61.9769 144.229i 0.462514 1.07634i
\(135\) 103.916 + 59.9962i 0.769752 + 0.444416i
\(136\) 5.69993 + 4.74248i 0.0419113 + 0.0348712i
\(137\) 118.420 + 205.110i 0.864381 + 1.49715i 0.867660 + 0.497158i \(0.165623\pi\)
−0.00327850 + 0.999995i \(0.501044\pi\)
\(138\) 74.2526 55.4395i 0.538063 0.401735i
\(139\) −172.122 −1.23828 −0.619142 0.785279i \(-0.712520\pi\)
−0.619142 + 0.785279i \(0.712520\pi\)
\(140\) 0 0
\(141\) 245.274i 1.73954i
\(142\) 119.409 89.1545i 0.840907 0.627849i
\(143\) 97.5195 56.3029i 0.681955 0.393727i
\(144\) 277.075 141.085i 1.92413 0.979758i
\(145\) 10.1616 17.6003i 0.0700797 0.121382i
\(146\) 26.5341 61.7485i 0.181740 0.422935i
\(147\) 0 0
\(148\) 37.1444 35.2395i 0.250976 0.238105i
\(149\) 199.798 + 115.354i 1.34093 + 0.774186i 0.986944 0.161066i \(-0.0514931\pi\)
0.353985 + 0.935251i \(0.384826\pi\)
\(150\) −215.495 + 25.4912i −1.43663 + 0.169941i
\(151\) 128.077 73.9452i 0.848190 0.489703i −0.0118494 0.999930i \(-0.503772\pi\)
0.860040 + 0.510227i \(0.170439\pi\)
\(152\) −8.04327 + 46.7540i −0.0529163 + 0.307592i
\(153\) −18.0116 −0.117723
\(154\) 0 0
\(155\) 74.4227 0.480146
\(156\) −106.553 444.083i −0.683034 2.84669i
\(157\) 99.4450 57.4146i 0.633407 0.365698i −0.148663 0.988888i \(-0.547497\pi\)
0.782070 + 0.623190i \(0.214164\pi\)
\(158\) 7.09810 + 60.0052i 0.0449247 + 0.379780i
\(159\) 343.947 + 198.578i 2.16319 + 1.24892i
\(160\) 30.5479 61.8938i 0.190924 0.386836i
\(161\) 0 0
\(162\) −96.1289 + 223.706i −0.593388 + 1.38090i
\(163\) −24.6545 + 42.7029i −0.151255 + 0.261981i −0.931689 0.363257i \(-0.881665\pi\)
0.780434 + 0.625238i \(0.214998\pi\)
\(164\) 49.0245 165.424i 0.298930 1.00868i
\(165\) −52.3830 + 30.2433i −0.317473 + 0.183293i
\(166\) −87.2609 116.872i −0.525668 0.704051i
\(167\) 241.457i 1.44585i 0.690926 + 0.722926i \(0.257203\pi\)
−0.690926 + 0.722926i \(0.742797\pi\)
\(168\) 0 0
\(169\) −289.455 −1.71275
\(170\) −3.20385 + 2.39210i −0.0188461 + 0.0140712i
\(171\) −57.6196 99.8001i −0.336957 0.583626i
\(172\) 47.4382 160.071i 0.275803 0.930648i
\(173\) −47.1300 27.2105i −0.272428 0.157286i 0.357563 0.933889i \(-0.383608\pi\)
−0.629990 + 0.776603i \(0.716941\pi\)
\(174\) 92.3207 + 39.6713i 0.530579 + 0.227996i
\(175\) 0 0
\(176\) −4.42590 + 84.0293i −0.0251471 + 0.477439i
\(177\) −143.100 + 247.857i −0.808475 + 1.40032i
\(178\) 108.920 12.8843i 0.611909 0.0723836i
\(179\) 63.5100 + 110.003i 0.354805 + 0.614540i 0.987084 0.160200i \(-0.0512141\pi\)
−0.632280 + 0.774740i \(0.717881\pi\)
\(180\) 39.1186 + 163.035i 0.217325 + 0.905748i
\(181\) 212.704i 1.17516i −0.809165 0.587581i \(-0.800080\pi\)
0.809165 0.587581i \(-0.199920\pi\)
\(182\) 0 0
\(183\) 148.322i 0.810502i
\(184\) 68.5072 + 11.7856i 0.372322 + 0.0640520i
\(185\) 13.8046 + 23.9103i 0.0746194 + 0.129245i
\(186\) 43.2260 + 365.420i 0.232398 + 1.96462i
\(187\) 2.43723 4.22140i 0.0130333 0.0225743i
\(188\) 133.480 126.635i 0.710002 0.673590i
\(189\) 0 0
\(190\) −23.5035 10.0997i −0.123703 0.0531565i
\(191\) 35.1041 + 20.2674i 0.183791 + 0.106112i 0.589073 0.808080i \(-0.299493\pi\)
−0.405282 + 0.914192i \(0.632826\pi\)
\(192\) 321.645 + 114.043i 1.67523 + 0.593974i
\(193\) −141.153 244.485i −0.731364 1.26676i −0.956300 0.292387i \(-0.905551\pi\)
0.224936 0.974374i \(-0.427783\pi\)
\(194\) −64.2694 86.0790i −0.331286 0.443706i
\(195\) 246.261 1.26288
\(196\) 0 0
\(197\) 261.806i 1.32896i −0.747304 0.664482i \(-0.768652\pi\)
0.747304 0.664482i \(-0.231348\pi\)
\(198\) −122.287 163.784i −0.617610 0.827193i
\(199\) −278.968 + 161.062i −1.40185 + 0.809357i −0.994582 0.103953i \(-0.966851\pi\)
−0.407265 + 0.913310i \(0.633518\pi\)
\(200\) −125.132 104.113i −0.625662 0.520566i
\(201\) −209.266 + 362.460i −1.04113 + 1.80328i
\(202\) −165.932 71.3031i −0.821448 0.352986i
\(203\) 0 0
\(204\) −13.6062 14.3417i −0.0666970 0.0703025i
\(205\) 80.5723 + 46.5184i 0.393036 + 0.226919i
\(206\) −26.5046 224.062i −0.128663 1.08768i
\(207\) −146.234 + 84.4283i −0.706445 + 0.407866i
\(208\) 186.661 287.267i 0.897406 1.38109i
\(209\) 31.1870 0.149220
\(210\) 0 0
\(211\) 169.792 0.804702 0.402351 0.915485i \(-0.368193\pi\)
0.402351 + 0.915485i \(0.368193\pi\)
\(212\) 69.5117 + 289.704i 0.327885 + 1.36653i
\(213\) −344.077 + 198.653i −1.61539 + 0.932644i
\(214\) −285.986 + 33.8297i −1.33638 + 0.158083i
\(215\) 77.9652 + 45.0133i 0.362629 + 0.209364i
\(216\) −417.571 + 153.957i −1.93320 + 0.712763i
\(217\) 0 0
\(218\) 122.529 + 52.6521i 0.562059 + 0.241523i
\(219\) −89.5927 + 155.179i −0.409099 + 0.708581i
\(220\) −43.5040 12.8927i −0.197745 0.0586031i
\(221\) −17.1867 + 9.92275i −0.0777679 + 0.0448993i
\(222\) −109.383 + 81.6689i −0.492716 + 0.367878i
\(223\) 45.4626i 0.203868i −0.994791 0.101934i \(-0.967497\pi\)
0.994791 0.101934i \(-0.0325031\pi\)
\(224\) 0 0
\(225\) 395.414 1.75740
\(226\) −8.57285 11.4820i −0.0379329 0.0508053i
\(227\) 92.5653 + 160.328i 0.407777 + 0.706290i 0.994640 0.103396i \(-0.0329708\pi\)
−0.586864 + 0.809686i \(0.699637\pi\)
\(228\) 35.9391 121.270i 0.157627 0.531885i
\(229\) 160.173 + 92.4759i 0.699445 + 0.403825i 0.807141 0.590359i \(-0.201014\pi\)
−0.107695 + 0.994184i \(0.534347\pi\)
\(230\) −14.7988 + 34.4390i −0.0643428 + 0.149735i
\(231\) 0 0
\(232\) 26.0756 + 70.7239i 0.112395 + 0.304845i
\(233\) −48.3504 + 83.7453i −0.207512 + 0.359422i −0.950930 0.309405i \(-0.899870\pi\)
0.743418 + 0.668827i \(0.233203\pi\)
\(234\) 97.7580 + 826.417i 0.417769 + 3.53170i
\(235\) 49.6076 + 85.9228i 0.211096 + 0.365629i
\(236\) −208.768 + 50.0919i −0.884611 + 0.212254i
\(237\) 161.097i 0.679734i
\(238\) 0 0
\(239\) 163.185i 0.682782i 0.939921 + 0.341391i \(0.110898\pi\)
−0.939921 + 0.341391i \(0.889102\pi\)
\(240\) −100.266 + 154.307i −0.417773 + 0.642945i
\(241\) 102.745 + 177.960i 0.426330 + 0.738424i 0.996544 0.0830718i \(-0.0264731\pi\)
−0.570214 + 0.821496i \(0.693140\pi\)
\(242\) −185.391 + 21.9301i −0.766078 + 0.0906204i
\(243\) 74.2413 128.590i 0.305520 0.529176i
\(244\) −80.7180 + 76.5784i −0.330812 + 0.313846i
\(245\) 0 0
\(246\) −181.611 + 422.634i −0.738254 + 1.71802i
\(247\) −109.962 63.4863i −0.445188 0.257030i
\(248\) −176.547 + 212.190i −0.711883 + 0.855604i
\(249\) 194.434 + 336.769i 0.780859 + 1.35249i
\(250\) 156.752 117.036i 0.627007 0.468145i
\(251\) 159.299 0.634658 0.317329 0.948316i \(-0.397214\pi\)
0.317329 + 0.948316i \(0.397214\pi\)
\(252\) 0 0
\(253\) 45.6975i 0.180622i
\(254\) 210.727 157.336i 0.829633 0.619431i
\(255\) 9.23191 5.33005i 0.0362036 0.0209021i
\(256\) 104.002 + 233.922i 0.406257 + 0.913759i
\(257\) 107.889 186.868i 0.419800 0.727114i −0.576119 0.817366i \(-0.695434\pi\)
0.995919 + 0.0902512i \(0.0287670\pi\)
\(258\) −175.734 + 408.959i −0.681140 + 1.58511i
\(259\) 0 0
\(260\) 127.144 + 134.017i 0.489017 + 0.515452i
\(261\) −158.571 91.5507i −0.607550 0.350769i
\(262\) 17.4011 2.05840i 0.0664163 0.00785647i
\(263\) 285.059 164.579i 1.08387 0.625775i 0.151935 0.988391i \(-0.451450\pi\)
0.931939 + 0.362616i \(0.118116\pi\)
\(264\) 38.0360 221.096i 0.144076 0.837483i
\(265\) −160.652 −0.606234
\(266\) 0 0
\(267\) −292.419 −1.09520
\(268\) −305.298 + 73.2531i −1.13917 + 0.273332i
\(269\) 253.803 146.533i 0.943507 0.544734i 0.0524492 0.998624i \(-0.483297\pi\)
0.891058 + 0.453889i \(0.149964\pi\)
\(270\) −28.1916 238.323i −0.104413 0.882679i
\(271\) 23.2529 + 13.4251i 0.0858042 + 0.0495391i 0.542288 0.840193i \(-0.317558\pi\)
−0.456484 + 0.889732i \(0.650891\pi\)
\(272\) 0.780014 14.8092i 0.00286770 0.0544456i
\(273\) 0 0
\(274\) 187.011 435.202i 0.682523 1.58833i
\(275\) −53.5053 + 92.6739i −0.194565 + 0.336996i
\(276\) −177.693 52.6605i −0.643816 0.190799i
\(277\) 289.925 167.389i 1.04666 0.604291i 0.124949 0.992163i \(-0.460123\pi\)
0.921713 + 0.387872i \(0.126790\pi\)
\(278\) 205.951 + 275.840i 0.740831 + 0.992229i
\(279\) 670.513i 2.40327i
\(280\) 0 0
\(281\) −123.357 −0.438994 −0.219497 0.975613i \(-0.570442\pi\)
−0.219497 + 0.975613i \(0.570442\pi\)
\(282\) −393.073 + 293.482i −1.39388 + 1.04072i
\(283\) −0.309453 0.535988i −0.00109347 0.00189395i 0.865478 0.500947i \(-0.167015\pi\)
−0.866572 + 0.499053i \(0.833681\pi\)
\(284\) −285.756 84.6855i −1.00618 0.298188i
\(285\) 59.0663 + 34.1019i 0.207250 + 0.119656i
\(286\) −206.917 88.9145i −0.723485 0.310890i
\(287\) 0 0
\(288\) −557.634 275.222i −1.93623 0.955631i
\(289\) 144.070 249.537i 0.498514 0.863451i
\(290\) −40.3648 + 4.77480i −0.139189 + 0.0164648i
\(291\) 143.204 + 248.037i 0.492112 + 0.852362i
\(292\) −130.707 + 31.3617i −0.447625 + 0.107403i
\(293\) 28.2794i 0.0965169i −0.998835 0.0482584i \(-0.984633\pi\)
0.998835 0.0482584i \(-0.0153671\pi\)
\(294\) 0 0
\(295\) 115.770i 0.392440i
\(296\) −100.919 17.3615i −0.340943 0.0586538i
\(297\) 146.285 + 253.373i 0.492542 + 0.853108i
\(298\) −54.2034 458.220i −0.181891 1.53765i
\(299\) −93.0247 + 161.123i −0.311119 + 0.538874i
\(300\) 298.701 + 314.848i 0.995671 + 1.04949i
\(301\) 0 0
\(302\) −271.753 116.775i −0.899844 0.386674i
\(303\) 417.002 + 240.756i 1.37624 + 0.794575i
\(304\) 84.5514 43.0531i 0.278130 0.141622i
\(305\) −29.9986 51.9591i −0.0983560 0.170358i
\(306\) 21.5517 + 28.8651i 0.0704303 + 0.0943305i
\(307\) −400.893 −1.30584 −0.652921 0.757426i \(-0.726457\pi\)
−0.652921 + 0.757426i \(0.726457\pi\)
\(308\) 0 0
\(309\) 601.542i 1.94674i
\(310\) −89.0500 119.269i −0.287258 0.384738i
\(311\) 140.492 81.1132i 0.451743 0.260814i −0.256823 0.966459i \(-0.582676\pi\)
0.708566 + 0.705644i \(0.249342\pi\)
\(312\) −584.186 + 702.126i −1.87239 + 2.25040i
\(313\) −133.123 + 230.576i −0.425313 + 0.736664i −0.996450 0.0841913i \(-0.973169\pi\)
0.571137 + 0.820855i \(0.306503\pi\)
\(314\) −211.002 90.6700i −0.671981 0.288758i
\(315\) 0 0
\(316\) 87.6704 83.1742i 0.277438 0.263210i
\(317\) −374.864 216.428i −1.18254 0.682737i −0.225936 0.974142i \(-0.572544\pi\)
−0.956600 + 0.291405i \(0.905877\pi\)
\(318\) −93.3096 788.812i −0.293426 2.48054i
\(319\) 42.9138 24.7763i 0.134526 0.0776686i
\(320\) −135.742 + 25.1030i −0.424194 + 0.0784470i
\(321\) 767.792 2.39187
\(322\) 0 0
\(323\) −5.49636 −0.0170166
\(324\) 473.530 113.619i 1.46151 0.350675i
\(325\) 377.305 217.837i 1.16094 0.670269i
\(326\) 97.9353 11.5849i 0.300415 0.0355365i
\(327\) −307.925 177.781i −0.941668 0.543672i
\(328\) −323.766 + 119.371i −0.987092 + 0.363937i
\(329\) 0 0
\(330\) 111.146 + 47.7608i 0.336807 + 0.144730i
\(331\) −40.6264 + 70.3671i −0.122738 + 0.212589i −0.920847 0.389925i \(-0.872501\pi\)
0.798108 + 0.602514i \(0.205834\pi\)
\(332\) −82.8867 + 279.686i −0.249659 + 0.842428i
\(333\) 215.420 124.373i 0.646907 0.373492i
\(334\) 386.956 288.914i 1.15855 0.865012i
\(335\) 169.299i 0.505370i
\(336\) 0 0
\(337\) −69.4941 −0.206214 −0.103107 0.994670i \(-0.532878\pi\)
−0.103107 + 0.994670i \(0.532878\pi\)
\(338\) 346.346 + 463.877i 1.02469 + 1.37242i
\(339\) 19.1019 + 33.0855i 0.0563479 + 0.0975974i
\(340\) 7.66708 + 2.27219i 0.0225502 + 0.00668291i
\(341\) 157.149 + 90.7300i 0.460848 + 0.266071i
\(342\) −90.9938 + 211.756i −0.266064 + 0.619168i
\(343\) 0 0
\(344\) −313.290 + 115.509i −0.910727 + 0.335781i
\(345\) 49.9686 86.5481i 0.144836 0.250864i
\(346\) 12.7859 + 108.089i 0.0369536 + 0.312395i
\(347\) 174.677 + 302.549i 0.503391 + 0.871899i 0.999992 + 0.00392020i \(0.00124784\pi\)
−0.496601 + 0.867979i \(0.665419\pi\)
\(348\) −46.8891 195.420i −0.134739 0.561552i
\(349\) 165.836i 0.475174i 0.971366 + 0.237587i \(0.0763566\pi\)
−0.971366 + 0.237587i \(0.923643\pi\)
\(350\) 0 0
\(351\) 1191.15i 3.39358i
\(352\) 139.960 93.4519i 0.397614 0.265488i
\(353\) −235.858 408.519i −0.668154 1.15728i −0.978420 0.206627i \(-0.933751\pi\)
0.310266 0.950650i \(-0.399582\pi\)
\(354\) 568.437 67.2412i 1.60576 0.189947i
\(355\) 80.3566 139.182i 0.226356 0.392061i
\(356\) −150.976 159.137i −0.424089 0.447014i
\(357\) 0 0
\(358\) 100.296 233.403i 0.280157 0.651964i
\(359\) −568.967 328.493i −1.58487 0.915022i −0.994134 0.108154i \(-0.965506\pi\)
−0.590731 0.806869i \(1.29884\pi\)
\(360\) 214.470 257.769i 0.595750 0.716025i
\(361\) 162.917 + 282.180i 0.451294 + 0.781663i
\(362\) −340.877 + 254.510i −0.941649 + 0.703067i
\(363\) 497.722 1.37113
\(364\) 0 0
\(365\) 72.4817i 0.198580i
\(366\) 237.699 177.474i 0.649450 0.484901i
\(367\) −307.850 + 177.737i −0.838829 + 0.484298i −0.856866 0.515539i \(-0.827592\pi\)
0.0180371 + 0.999837i \(0.494258\pi\)
\(368\) −63.0845 123.891i −0.171425 0.336659i
\(369\) 419.109 725.918i 1.13580 1.96726i
\(370\) 21.8004 50.7327i 0.0589201 0.137116i
\(371\) 0 0
\(372\) 533.895 506.514i 1.43520 1.36160i
\(373\) 273.662 + 157.999i 0.733680 + 0.423590i 0.819767 0.572698i \(-0.194103\pi\)
−0.0860872 + 0.996288i \(0.527436\pi\)
\(374\) −9.68141 + 1.14523i −0.0258861 + 0.00306210i
\(375\) −451.682 + 260.779i −1.20449 + 0.695410i
\(376\) −362.659 62.3896i −0.964518 0.165930i
\(377\) −201.745 −0.535132
\(378\) 0 0
\(379\) −178.404 −0.470723 −0.235361 0.971908i \(-0.575627\pi\)
−0.235361 + 0.971908i \(0.575627\pi\)
\(380\) 11.9373 + 49.7512i 0.0314140 + 0.130924i
\(381\) −607.211 + 350.574i −1.59373 + 0.920140i
\(382\) −9.52341 80.5082i −0.0249304 0.210754i
\(383\) −604.832 349.200i −1.57920 0.911750i −0.994972 0.100158i \(-0.968065\pi\)
−0.584225 0.811591i \(1.30140\pi\)
\(384\) −202.099 651.921i −0.526299 1.69771i
\(385\) 0 0
\(386\) −222.912 + 518.747i −0.577491 + 1.34390i
\(387\) 405.548 702.430i 1.04793 1.81506i
\(388\) −61.0478 + 205.995i −0.157340 + 0.530914i
\(389\) 151.865 87.6790i 0.390397 0.225396i −0.291935 0.956438i \(-0.594299\pi\)
0.682332 + 0.731042i \(0.260966\pi\)
\(390\) −294.662 394.655i −0.755544 1.01193i
\(391\) 8.05366i 0.0205976i
\(392\) 0 0
\(393\) −46.7170 −0.118873
\(394\) −419.567 + 313.263i −1.06489 + 0.795083i
\(395\) 32.5824 + 56.4344i 0.0824871 + 0.142872i
\(396\) −116.157 + 391.950i −0.293325 + 0.989773i
\(397\) 334.033 + 192.854i 0.841393 + 0.485778i 0.857737 0.514088i \(-0.171870\pi\)
−0.0163447 + 0.999866i \(0.505203\pi\)
\(398\) 591.913 + 254.352i 1.48722 + 0.639075i
\(399\) 0 0
\(400\) −17.1239 + 325.112i −0.0428098 + 0.812779i
\(401\) −263.548 + 456.479i −0.657228 + 1.13835i 0.324103 + 0.946022i \(0.394938\pi\)
−0.981330 + 0.192330i \(0.938396\pi\)
\(402\) 831.269 98.3319i 2.06783 0.244607i
\(403\) −369.392 639.805i −0.916605 1.58761i
\(404\) 84.2761 + 351.238i 0.208604 + 0.869402i
\(405\) 262.590i 0.648371i
\(406\) 0 0
\(407\) 67.3178i 0.165400i
\(408\) −6.70340 + 38.9656i −0.0164299 + 0.0955039i
\(409\) −211.872 366.973i −0.518025 0.897245i −0.999781 0.0209399i \(-0.993334\pi\)
0.481756 0.876305i \(-0.339999\pi\)
\(410\) −21.8585 184.785i −0.0533134 0.450696i
\(411\) −631.447 + 1093.70i −1.53637 + 2.66107i
\(412\) −327.364 + 310.576i −0.794574 + 0.753824i
\(413\) 0 0
\(414\) 310.279 + 133.331i 0.749467 + 0.322055i
\(415\) −136.225 78.6498i −0.328254 0.189517i
\(416\) −683.718 + 44.5881i −1.64355 + 0.107183i
\(417\) −458.898 794.834i −1.10047 1.90608i
\(418\) −37.3167 49.9799i −0.0892743 0.119569i
\(419\) −295.598 −0.705485 −0.352742 0.935721i \(-0.614751\pi\)
−0.352742 + 0.935721i \(0.614751\pi\)
\(420\) 0 0
\(421\) 126.260i 0.299904i 0.988693 + 0.149952i \(0.0479119\pi\)
−0.988693 + 0.149952i \(0.952088\pi\)
\(422\) −203.164 272.107i −0.481431 0.644802i
\(423\) 774.124 446.941i 1.83008 1.05660i
\(424\) 381.102 458.043i 0.898827 1.08029i
\(425\) 9.42970 16.3327i 0.0221875 0.0384299i
\(426\) 730.063 + 313.716i 1.71376 + 0.736424i
\(427\) 0 0
\(428\) 396.410 + 417.839i 0.926192 + 0.976259i
\(429\) 519.999 + 300.221i 1.21212 + 0.699817i
\(430\) −21.1512 178.806i −0.0491889 0.415829i
\(431\) −220.198 + 127.131i −0.510900 + 0.294968i −0.733204 0.680009i \(-0.761976\pi\)
0.222303 + 0.974978i \(0.428642\pi\)
\(432\) 746.371 + 484.977i 1.72771 + 1.12263i
\(433\) −546.301 −1.26167 −0.630833 0.775919i \(-0.717287\pi\)
−0.630833 + 0.775919i \(0.717287\pi\)
\(434\) 0 0
\(435\) 108.368 0.249122
\(436\) −62.2317 259.364i −0.142733 0.594871i
\(437\) −44.6244 + 25.7639i −0.102115 + 0.0589563i
\(438\) 355.890 42.0987i 0.812534 0.0961156i
\(439\) −236.715 136.667i −0.539214 0.311315i 0.205546 0.978647i \(-0.434103\pi\)
−0.744760 + 0.667332i \(0.767436\pi\)
\(440\) 31.3928 + 85.1456i 0.0713473 + 0.193513i
\(441\) 0 0
\(442\) 36.4667 + 15.6702i 0.0825039 + 0.0354529i
\(443\) −237.385 + 411.163i −0.535858 + 0.928133i 0.463263 + 0.886221i \(0.346678\pi\)
−0.999121 + 0.0419124i \(0.986655\pi\)
\(444\) 261.763 + 77.5751i 0.589556 + 0.174719i
\(445\) 102.438 59.1427i 0.230198 0.132905i
\(446\) −72.8578 + 54.3981i −0.163358 + 0.121969i
\(447\) 1230.19i 2.75210i
\(448\) 0 0
\(449\) 782.101 1.74187 0.870936 0.491396i \(-0.163513\pi\)
0.870936 + 0.491396i \(0.163513\pi\)
\(450\) −473.131 633.686i −1.05140 1.40819i
\(451\) 113.423 + 196.454i 0.251492 + 0.435597i
\(452\) −8.14311 + 27.4774i −0.0180157 + 0.0607908i
\(453\) 682.938 + 394.294i 1.50759 + 0.870407i
\(454\) 146.181 340.183i 0.321984 0.749302i
\(455\) 0 0
\(456\) −237.348 + 87.5092i −0.520500 + 0.191906i
\(457\) 94.7793 164.163i 0.207395 0.359218i −0.743498 0.668738i \(-0.766835\pi\)
0.950893 + 0.309520i \(0.100168\pi\)
\(458\) −43.4534 367.343i −0.0948765 0.802058i
\(459\) −25.7811 44.6541i −0.0561679 0.0972857i
\(460\) 72.8990 17.4914i 0.158476 0.0380247i
\(461\) 202.533i 0.439335i −0.975575 0.219667i \(-0.929503\pi\)
0.975575 0.219667i \(-0.0704972\pi\)
\(462\) 0 0
\(463\) 652.927i 1.41021i 0.709103 + 0.705105i \(0.249100\pi\)
−0.709103 + 0.705105i \(0.750900\pi\)
\(464\) 82.1406 126.413i 0.177027 0.272441i
\(465\) 198.420 + 343.674i 0.426710 + 0.739084i
\(466\) 192.062 22.7193i 0.412151 0.0487539i
\(467\) 272.725 472.373i 0.583993 1.01150i −0.411008 0.911632i \(-0.634823\pi\)
0.995000 0.0998730i \(-0.0318437\pi\)
\(468\) 1207.43 1145.51i 2.57998 2.44767i
\(469\) 0 0
\(470\) 78.3411 182.311i 0.166683 0.387895i
\(471\) 530.266 + 306.149i 1.12583 + 0.649998i
\(472\) 330.077 + 274.632i 0.699316 + 0.581847i
\(473\) 109.753 + 190.098i 0.232036 + 0.401898i
\(474\) −258.172 + 192.760i −0.544666 + 0.406666i
\(475\) 120.663 0.254028
\(476\) 0 0
\(477\) 1447.40i 3.03438i
\(478\) 261.518 195.258i 0.547108 0.408489i
\(479\) −94.3079 + 54.4487i −0.196885 + 0.113672i −0.595202 0.803576i \(-0.702928\pi\)
0.398317 + 0.917248i \(0.369595\pi\)
\(480\) 367.262 23.9507i 0.765129 0.0498972i
\(481\) 137.036 237.354i 0.284899 0.493459i
\(482\) 162.257 377.596i 0.336633 0.783394i
\(483\) 0 0
\(484\) 256.973 + 270.865i 0.530937 + 0.559637i
\(485\) −100.333 57.9272i −0.206872 0.119437i
\(486\) −294.909 + 34.8852i −0.606809 + 0.0717802i
\(487\) −371.831 + 214.677i −0.763513 + 0.440814i −0.830556 0.556936i \(-0.811977\pi\)
0.0670428 + 0.997750i \(0.478644\pi\)
\(488\) 219.306 + 37.7281i 0.449398 + 0.0773117i
\(489\) −262.929 −0.537686
\(490\) 0 0
\(491\) 453.887 0.924413 0.462206 0.886772i \(-0.347058\pi\)
0.462206 + 0.886772i \(0.347058\pi\)
\(492\) 894.612 214.653i 1.81832 0.436287i
\(493\) −7.56306 + 4.36654i −0.0153409 + 0.00885707i
\(494\) 29.8315 + 252.187i 0.0603877 + 0.510500i
\(495\) −190.905 110.219i −0.385667 0.222665i
\(496\) 551.299 + 29.0374i 1.11149 + 0.0585431i
\(497\) 0 0
\(498\) 307.053 714.556i 0.616572 1.43485i
\(499\) −166.698 + 288.730i −0.334064 + 0.578617i −0.983305 0.181967i \(-0.941754\pi\)
0.649240 + 0.760583i \(0.275087\pi\)
\(500\) −375.121 111.169i −0.750242 0.222339i
\(501\) −1115.02 + 643.755i −2.22558 + 1.28494i
\(502\) −190.608 255.291i −0.379698 0.508547i
\(503\) 580.170i 1.15342i 0.816949 + 0.576710i \(0.195664\pi\)
−0.816949 + 0.576710i \(0.804336\pi\)
\(504\) 0 0
\(505\) −194.775 −0.385693
\(506\) −73.2341 + 54.6790i −0.144731 + 0.108061i
\(507\) −771.724 1336.67i −1.52214 2.63642i
\(508\) −504.288 149.449i −0.992692 0.294190i
\(509\) −266.271 153.732i −0.523126 0.302027i 0.215087 0.976595i \(-0.430997\pi\)
−0.738213 + 0.674568i \(0.764330\pi\)
\(510\) −19.5882 8.41730i −0.0384083 0.0165045i
\(511\) 0 0
\(512\) 250.438 446.570i 0.489136 0.872207i
\(513\) 164.949 285.700i 0.321538 0.556919i
\(514\) −428.566 + 50.6956i −0.833786 + 0.0986296i
\(515\) −121.664 210.728i −0.236241 0.409181i
\(516\) 865.665 207.708i 1.67765 0.402534i
\(517\) 241.910i 0.467911i
\(518\) 0 0
\(519\) 290.187i 0.559127i
\(520\) 62.6406 364.118i 0.120463 0.700226i
\(521\) 360.480 + 624.369i 0.691899 + 1.19840i 0.971215 + 0.238205i \(0.0765591\pi\)
−0.279316 + 0.960199i \(0.590108\pi\)
\(522\) 43.0187 + 363.667i 0.0824113 + 0.696681i
\(523\) −134.988 + 233.807i −0.258104 + 0.447049i −0.965734 0.259534i \(-0.916431\pi\)
0.707630 + 0.706583i \(0.249764\pi\)
\(524\) −24.1199 25.4238i −0.0460304 0.0485186i
\(525\) 0 0
\(526\) −604.837 259.905i −1.14988 0.494117i
\(527\) −27.6957 15.9901i −0.0525536 0.0303418i
\(528\) −399.836 + 203.595i −0.757266 + 0.385596i
\(529\) −226.749 392.741i −0.428637 0.742421i
\(530\) 192.227 + 257.459i 0.362693 + 0.485771i
\(531\) −1043.03 −1.96428
\(532\) 0 0
\(533\) 923.564i 1.73277i
\(534\) 349.892 + 468.626i 0.655229 + 0.877578i
\(535\) −268.967 + 155.288i −0.502743 + 0.290259i
\(536\) 482.696 + 401.615i 0.900553 + 0.749282i
\(537\) −338.652 + 586.562i −0.630636 + 1.09229i
\(538\) −538.520 231.408i −1.00097 0.430127i
\(539\) 0 0
\(540\) −348.201 + 330.344i −0.644817 + 0.611748i
\(541\) 785.695 + 453.621i 1.45230 + 0.838486i 0.998612 0.0526734i \(-0.0167742\pi\)
0.453689 + 0.891160i \(0.350108\pi\)
\(542\) −6.30831 53.3286i −0.0116389 0.0983922i
\(543\) 982.241 567.097i 1.80891 1.04438i
\(544\) −24.6664 + 16.4698i −0.0453426 + 0.0302754i
\(545\) 143.827 0.263903
\(546\) 0 0
\(547\) −557.327 −1.01888 −0.509439 0.860506i \(-0.670147\pi\)
−0.509439 + 0.860506i \(0.670147\pi\)
\(548\) −921.215 + 221.036i −1.68105 + 0.403351i
\(549\) −468.127 + 270.273i −0.852690 + 0.492301i
\(550\) 212.539 25.1415i 0.386435 0.0457119i
\(551\) −48.3889 27.9374i −0.0878202 0.0507030i
\(552\) 128.225 + 347.779i 0.232291 + 0.630035i
\(553\) 0 0
\(554\) −615.163 264.343i −1.11040 0.477153i
\(555\) −73.6096 + 127.496i −0.132630 + 0.229722i
\(556\) 195.627 660.108i 0.351847 1.18725i
\(557\) −741.896 + 428.334i −1.33195 + 0.769002i −0.985598 0.169103i \(-0.945913\pi\)
−0.346352 + 0.938105i \(0.612580\pi\)
\(558\) −1074.55 + 802.298i −1.92572 + 1.43781i
\(559\) 893.680i 1.59871i
\(560\) 0 0
\(561\) 25.9918 0.0463313
\(562\) 147.602 + 197.691i 0.262638 + 0.351763i
\(563\) 6.84436 + 11.8548i 0.0121569 + 0.0210564i 0.872040 0.489435i \(-0.162797\pi\)
−0.859883 + 0.510491i \(0.829464\pi\)
\(564\) 940.659 + 278.770i 1.66784 + 0.494273i
\(565\) −13.3833 7.72686i −0.0236873 0.0136759i
\(566\) −0.488693 + 1.13726i −0.000863416 + 0.00200929i
\(567\) 0 0
\(568\) 206.204 + 559.278i 0.363034 + 0.984644i
\(569\) 545.991 945.684i 0.959563 1.66201i 0.235999 0.971753i \(-0.424164\pi\)
0.723563 0.690258i \(-0.242503\pi\)
\(570\) −16.0241 135.463i −0.0281125 0.237655i
\(571\) −359.549 622.757i −0.629683 1.09064i −0.987615 0.156895i \(-0.949852\pi\)
0.357932 0.933747i \(-0.383482\pi\)
\(572\) 105.092 + 437.992i 0.183727 + 0.765720i
\(573\) 216.142i 0.377210i
\(574\) 0 0
\(575\) 176.805i 0.307486i
\(576\) 226.166 + 1222.97i 0.392650 + 2.12321i
\(577\) −515.560 892.976i −0.893518 1.54762i −0.835628 0.549296i \(-0.814896\pi\)
−0.0578905 0.998323i \(-0.518437\pi\)
\(578\) −572.292 + 67.6971i −0.990124 + 0.117123i
\(579\) 752.665 1303.65i 1.29994 2.25156i
\(580\) 55.9503 + 58.9748i 0.0964660 + 0.101681i
\(581\) 0 0
\(582\) 226.151 526.285i 0.388575 0.904270i
\(583\) −339.229 195.854i −0.581868 0.335942i
\(584\) 206.656 + 171.943i 0.353863 + 0.294423i
\(585\) 448.738 + 777.238i 0.767074 + 1.32861i
\(586\) −45.3202 + 33.8376i −0.0773383 + 0.0577434i
\(587\) 671.907 1.14464 0.572322 0.820029i \(-0.306043\pi\)
0.572322 + 0.820029i \(0.306043\pi\)
\(588\) 0 0
\(589\) 204.612i 0.347388i
\(590\) −185.531 + 138.524i −0.314460 + 0.234786i
\(591\) 1208.99 698.008i 2.04566 1.18106i
\(592\) 92.9309 + 182.506i 0.156978 + 0.308286i
\(593\) 176.999 306.572i 0.298481 0.516984i −0.677308 0.735700i \(-0.736853\pi\)
0.975789 + 0.218716i \(0.0701867\pi\)
\(594\) 231.016 537.606i 0.388915 0.905061i
\(595\) 0 0
\(596\) −669.480 + 635.146i −1.12329 + 1.06568i
\(597\) −1487.53 858.824i −2.49167 1.43857i
\(598\) 369.522 43.7113i 0.617930 0.0730958i
\(599\) 983.923 568.068i 1.64261 0.948361i 0.662708 0.748878i \(-0.269407\pi\)
0.979901 0.199484i \(-0.0639265\pi\)
\(600\) 147.162 855.424i 0.245270 1.42571i
\(601\) 6.80783 0.0113275 0.00566375 0.999984i \(-0.498197\pi\)
0.00566375 + 0.999984i \(0.498197\pi\)
\(602\) 0 0
\(603\) −1525.30 −2.52953
\(604\) 138.022 + 575.234i 0.228513 + 0.952375i
\(605\) −174.358 + 100.666i −0.288196 + 0.166390i
\(606\) −113.129 956.357i −0.186681 1.57815i
\(607\) 386.628 + 223.220i 0.636948 + 0.367742i 0.783438 0.621470i \(-0.213464\pi\)
−0.146490 + 0.989212i \(0.546798\pi\)
\(608\) −170.166 83.9859i −0.279878 0.138135i
\(609\) 0 0
\(610\) −47.3743 + 110.247i −0.0776627 + 0.180732i
\(611\) 492.447 852.944i 0.805970 1.39598i
\(612\) 20.4713 69.0768i 0.0334499 0.112871i
\(613\) −555.650 + 320.805i −0.906443 + 0.523335i −0.879285 0.476296i \(-0.841979\pi\)
−0.0271583 + 0.999631i \(0.508646\pi\)
\(614\) 479.687 + 642.466i 0.781249 + 1.04636i
\(615\) 496.096i 0.806661i
\(616\) 0 0
\(617\) −502.890 −0.815057 −0.407528 0.913193i \(-0.633609\pi\)
−0.407528 + 0.913193i \(0.633609\pi\)
\(618\) 964.023 719.772i 1.55991 1.16468i
\(619\) 216.495 + 374.980i 0.349749 + 0.605783i 0.986205 0.165530i \(-0.0529336\pi\)
−0.636456 + 0.771313i \(0.719600\pi\)
\(620\) −84.5861 + 285.421i −0.136429 + 0.460356i
\(621\) −418.627 241.695i −0.674118 0.389202i
\(622\) −298.096 128.095i −0.479254 0.205941i
\(623\) 0 0
\(624\) 1824.22 + 96.0833i 2.92343 + 0.153980i
\(625\) −148.859 + 257.831i −0.238174 + 0.412530i
\(626\) 528.805 62.5530i 0.844736 0.0999250i
\(627\) 83.1486 + 144.018i 0.132613 + 0.229693i
\(628\) 107.167 + 446.640i 0.170648 + 0.711210i
\(629\) 11.8640i 0.0188617i
\(630\) 0 0
\(631\) 238.957i 0.378695i −0.981910 0.189348i \(-0.939363\pi\)
0.981910 0.189348i \(-0.0606373\pi\)
\(632\) −238.195 40.9777i −0.376891 0.0648381i
\(633\) 452.687 + 784.078i 0.715146 + 1.23867i
\(634\) 101.697 + 859.717i 0.160405 + 1.35602i
\(635\) 141.809 245.621i 0.223322 0.386805i
\(636\) −1152.49 + 1093.38i −1.81209 + 1.71916i
\(637\) 0 0
\(638\) −91.0543 39.1271i −0.142718 0.0613277i
\(639\) −1253.96 723.974i −1.96238 1.13298i
\(640\) 202.651 + 187.501i 0.316642 + 0.292971i
\(641\) 3.98065 + 6.89469i 0.00621006 + 0.0107561i 0.869114 0.494612i \(-0.164690\pi\)
−0.862904 + 0.505368i \(0.831357\pi\)
\(642\) −918.696 1230.45i −1.43099 1.91659i
\(643\) 584.919 0.909672 0.454836 0.890575i \(-0.349698\pi\)
0.454836 + 0.890575i \(0.349698\pi\)
\(644\) 0 0
\(645\) 480.044i 0.744255i
\(646\) 6.57664 + 8.80839i 0.0101806 + 0.0136353i
\(647\) −290.707 + 167.840i −0.449316 + 0.259413i −0.707541 0.706672i \(-0.750196\pi\)
0.258225 + 0.966085i \(0.416862\pi\)
\(648\) −748.683 622.923i −1.15538 0.961300i
\(649\) 141.137 244.457i 0.217469 0.376667i
\(650\) −800.566 344.012i −1.23164 0.529250i
\(651\) 0 0
\(652\) −135.750 143.088i −0.208205 0.219460i
\(653\) −42.0252 24.2632i −0.0643571 0.0371566i 0.467476 0.884006i \(-0.345163\pi\)
−0.531833 + 0.846849i \(0.678497\pi\)
\(654\) 83.5372 + 706.199i 0.127733 + 1.07982i
\(655\) 16.3656 9.44866i 0.0249856 0.0144254i
\(656\) 578.703 + 376.030i 0.882170 + 0.573217i
\(657\) −653.026 −0.993951
\(658\) 0 0
\(659\) 1224.65 1.85835 0.929176 0.369638i \(-0.120518\pi\)
0.929176 + 0.369638i \(0.120518\pi\)
\(660\) −56.4505 235.269i −0.0855311 0.356468i
\(661\) 725.765 419.021i 1.09798 0.633919i 0.162291 0.986743i \(-0.448112\pi\)
0.935690 + 0.352823i \(0.114778\pi\)
\(662\) 161.381 19.0899i 0.243777 0.0288367i
\(663\) −91.6439 52.9106i −0.138226 0.0798049i
\(664\) 547.399 201.824i 0.824396 0.303951i
\(665\) 0 0
\(666\) −457.078 196.412i −0.686303 0.294912i
\(667\) −40.9358 + 70.9029i −0.0613730 + 0.106301i
\(668\) −926.019 274.432i −1.38626 0.410826i
\(669\) 209.940 121.209i 0.313812 0.181180i
\(670\) −271.316 + 202.574i −0.404950 + 0.302349i
\(671\) 146.287i 0.218014i
\(672\) 0 0
\(673\) 147.714 0.219486 0.109743 0.993960i \(-0.464997\pi\)
0.109743 + 0.993960i \(0.464997\pi\)
\(674\) 83.1528 + 111.370i 0.123372 + 0.165238i
\(675\) 565.980 + 980.307i 0.838490 + 1.45231i
\(676\) 328.984 1110.10i 0.486663 1.64216i
\(677\) −725.024 418.593i −1.07094 0.618305i −0.142499 0.989795i \(-0.545514\pi\)
−0.928437 + 0.371490i \(0.878847\pi\)
\(678\) 30.1661 70.2007i 0.0444927 0.103541i
\(679\) 0 0
\(680\) −5.53263 15.0059i −0.00813622 0.0220676i
\(681\) −493.582 + 854.909i −0.724790 + 1.25537i
\(682\) −42.6331 360.407i −0.0625118 0.528457i
\(683\) 32.2189 + 55.8047i 0.0471725 + 0.0817053i 0.888648 0.458591i \(-0.151646\pi\)
−0.841475 + 0.540296i \(0.818312\pi\)
\(684\) 448.235 107.549i 0.655314 0.157236i
\(685\) 510.849i 0.745765i
\(686\) 0 0
\(687\) 986.210i 1.43553i
\(688\) 559.978 + 363.863i 0.813922 + 0.528871i
\(689\) 797.385 + 1381.11i 1.15731 + 2.00452i
\(690\) −198.490 + 23.4797i −0.287667 + 0.0340285i
\(691\) −263.374 + 456.177i −0.381149 + 0.660169i −0.991227 0.132172i \(-0.957805\pi\)
0.610078 + 0.792341i \(0.291138\pi\)
\(692\) 157.922 149.823i 0.228211 0.216508i
\(693\) 0 0
\(694\) 275.852 641.948i 0.397482 0.924997i
\(695\) 321.516 + 185.627i 0.462613 + 0.267090i
\(696\) −257.073 + 308.973i −0.369358 + 0.443926i
\(697\) −19.9895 34.6229i −0.0286794 0.0496741i
\(698\) 265.766 198.430i 0.380754 0.284284i
\(699\) −515.633 −0.737672
\(700\) 0 0
\(701\) 695.486i 0.992134i −0.868284 0.496067i \(-0.834777\pi\)
0.868284 0.496067i \(-0.165223\pi\)
\(702\) −1908.92 + 1425.26i −2.71926 + 2.03029i
\(703\) 65.7370 37.9532i 0.0935092 0.0539875i
\(704\) −317.233 112.479i −0.450615 0.159771i
\(705\) −264.520 + 458.162i −0.375206 + 0.649876i
\(706\) −372.471 + 866.794i −0.527580 + 1.22775i
\(707\) 0 0
\(708\) −787.920 830.513i −1.11288 1.17304i
\(709\) 803.161 + 463.705i 1.13281 + 0.654027i 0.944640 0.328110i \(-0.106412\pi\)
0.188168 + 0.982137i \(0.439745\pi\)
\(710\) −319.201 + 37.7587i −0.449578 + 0.0531812i
\(711\) 508.447 293.552i 0.715115 0.412872i
\(712\) −74.3816 + 432.366i −0.104469 + 0.607255i
\(713\) −299.812 −0.420493
\(714\) 0 0
\(715\) −242.883 −0.339697
\(716\) −494.057 + 118.544i −0.690024 + 0.165564i
\(717\) −753.566 + 435.071i −1.05100 + 0.606794i
\(718\) 154.355 + 1304.87i 0.214979 + 1.81737i
\(719\) −1150.37 664.169i −1.59996 0.923739i −0.991493 0.130163i \(-0.958450\pi\)
−0.608471 0.793576i \(1.29178\pi\)
\(720\) −669.720 35.2747i −0.930167 0.0489927i
\(721\) 0 0
\(722\) 257.281 598.730i 0.356345 0.829266i
\(723\) −547.865 + 948.929i −0.757766 + 1.31249i
\(724\) 815.749 + 241.752i 1.12673 + 0.333912i
\(725\) 166.034 95.8600i 0.229013 0.132221i
\(726\) −595.546 797.642i −0.820311 1.09868i
\(727\) 539.401i 0.741954i 0.928642 + 0.370977i \(0.120977\pi\)
−0.928642 + 0.370977i \(0.879023\pi\)
\(728\) 0 0
\(729\) −303.936 −0.416922
\(730\) −116.158 + 86.7276i −0.159121 + 0.118805i
\(731\) −19.3427 33.5026i −0.0264606 0.0458311i
\(732\) −568.834 168.577i −0.777095 0.230297i
\(733\) −382.859 221.044i −0.522318 0.301561i 0.215564 0.976490i \(-0.430841\pi\)
−0.737883 + 0.674929i \(0.764174\pi\)
\(734\) 653.196 + 280.686i 0.889913 + 0.382406i
\(735\) 0 0
\(736\) −123.062 + 249.339i −0.167204 + 0.338776i
\(737\) 206.396 357.488i 0.280048 0.485058i
\(738\) −1664.83 + 196.935i −2.25587 + 0.266849i
\(739\) 574.116 + 994.398i 0.776882 + 1.34560i 0.933730 + 0.357977i \(0.116533\pi\)
−0.156848 + 0.987623i \(0.550133\pi\)
\(740\) −107.389 + 25.7669i −0.145120 + 0.0348201i
\(741\) 677.050i 0.913698i
\(742\) 0 0
\(743\) 588.688i 0.792313i −0.918183 0.396156i \(-0.870344\pi\)
0.918183 0.396156i \(-0.129656\pi\)
\(744\) −1450.56 249.546i −1.94968 0.335411i
\(745\) −248.810 430.952i −0.333973 0.578459i
\(746\) −74.2420 627.621i −0.0995202 0.841314i
\(747\) −708.597 + 1227.33i −0.948590 + 1.64301i
\(748\) 13.4196 + 14.1450i 0.0179406 + 0.0189104i
\(749\) 0 0
\(750\) 958.378 + 411.826i 1.27784 + 0.549101i
\(751\) −708.754 409.199i −0.943747 0.544873i −0.0526140 0.998615i \(-0.516755\pi\)
−0.891133 + 0.453742i \(0.850089\pi\)
\(752\) 333.952 + 655.844i 0.444086 + 0.872133i
\(753\) 424.712 + 735.622i 0.564026 + 0.976922i
\(754\) 241.396 + 323.313i 0.320154 + 0.428797i
\(755\) −318.989 −0.422503
\(756\) 0 0
\(757\) 105.101i 0.138838i 0.997588 + 0.0694192i \(0.0221146\pi\)
−0.997588 + 0.0694192i \(0.977885\pi\)
\(758\) 213.468 + 285.908i 0.281620 + 0.377187i
\(759\) 211.025 121.835i 0.278030 0.160521i
\(760\) 65.4471 78.6600i 0.0861146 0.103500i
\(761\) 507.117 878.352i 0.666382 1.15421i −0.312527 0.949909i \(-0.601175\pi\)
0.978909 0.204299i \(-0.0654913\pi\)
\(762\) 1288.38 + 553.631i 1.69079 + 0.726550i
\(763\) 0 0
\(764\) −117.626 + 111.594i −0.153961 + 0.146065i
\(765\) 33.6449 + 19.4249i 0.0439803 + 0.0253920i
\(766\) 164.085 + 1387.13i 0.214211 + 1.81087i
\(767\) −995.264 + 574.616i −1.29761 + 0.749173i
\(768\) −802.940 + 1103.93i −1.04549 + 1.43741i
\(769\) 1183.99 1.53964 0.769822 0.638258i \(-0.220345\pi\)
0.769822 + 0.638258i \(0.220345\pi\)
\(770\) 0 0
\(771\) 1150.58 1.49232
\(772\) 1098.06 263.469i 1.42236 0.341281i
\(773\) −280.862 + 162.156i −0.363340 + 0.209774i −0.670545 0.741869i \(-0.733940\pi\)
0.307205 + 0.951643i \(0.400606\pi\)
\(774\) −1610.96 + 190.563i −2.08134 + 0.246205i
\(775\) 608.014 + 351.037i 0.784534 + 0.452951i
\(776\) 403.170 148.647i 0.519550 0.191556i
\(777\) 0 0