Properties

Label 392.3.k.l.67.6
Level 392
Weight 3
Character 392.67
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 67.6
Root \(0.907369 + 0.0534805i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.l.275.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.98615 - 0.234945i) q^{2} +(2.66613 - 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})\) \(q+(1.98615 - 0.234945i) q^{2} +(2.66613 - 4.61787i) q^{3} +(3.88960 - 0.933271i) 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} +(3.45667 - 2.58086i) q^{10} +(-2.62956 + 4.55453i) q^{11} +(6.06045 - 20.4499i) q^{12} +21.4116i q^{13} -11.5013i q^{15} +(14.2580 - 7.26011i) q^{16} +(0.463429 - 0.802683i) q^{17} +(-23.2524 - 31.1430i) 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} +(7.23239 - 42.0405i) q^{24} +(-10.1738 + 17.6216i) q^{25} +(5.03053 + 42.5266i) q^{26} -55.6311 q^{27} +9.42223i q^{29} +(-2.70217 - 22.8434i) q^{30} +(29.8813 + 17.2520i) q^{31} +(26.6129 - 17.7695i) 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} +(-7.09562 - 9.50349i) q^{38} +(98.8758 + 57.0860i) q^{39} +(11.0364 - 13.2645i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(-5.97732 + 20.1694i) q^{44} +(-36.2999 - 20.9578i) q^{45} +(-13.9252 + 10.3970i) 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} +(19.9828 + 83.2825i) q^{52} +(-64.5031 - 37.2409i) q^{53} +(-110.492 + 13.0702i) q^{54} +11.3436i q^{55} -31.6208 q^{57} +(2.21370 + 18.7140i) q^{58} +(26.8367 - 46.4825i) q^{59} +(-10.7338 - 44.7355i) 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} +(33.5546 + 44.9412i) q^{66} +(39.2453 - 67.9749i) q^{67} +(1.05343 - 3.55462i) q^{68} +46.3330i q^{69} +74.5100i q^{71} +(-119.507 - 99.4329i) q^{72} +(16.8020 - 29.1020i) q^{73} +(20.5134 - 15.3160i) 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} +(18.8036 - 28.9384i) q^{80} +(-60.8713 + 105.432i) q^{81} +(-85.6705 + 10.1341i) q^{82} +72.9274 q^{83} -1.99917i q^{85} +(-82.8984 + 9.80616i) q^{86} +(43.5106 + 25.1209i) q^{87} +(-7.13318 + 41.4638i) 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} +(73.7162 - 55.0390i) q^{94} +(-11.0772 - 6.39541i) q^{95} +(-11.1040 - 170.270i) 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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.98615 0.234945i 0.993076 0.117472i
\(3\) 2.66613 4.61787i 0.888709 1.53929i 0.0473064 0.998880i \(-0.484936\pi\)
0.841403 0.540409i \(-0.181730\pi\)
\(4\) 3.88960 0.933271i 0.972401 0.233318i
\(5\) 1.86796 1.07847i 0.373592 0.215693i −0.301435 0.953487i \(-0.597466\pi\)
0.675026 + 0.737794i \(0.264132\pi\)
\(6\) 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
\(10\) 3.45667 2.58086i 0.345667 0.258086i
\(11\) −2.62956 + 4.55453i −0.239051 + 0.414048i −0.960442 0.278480i \(-0.910170\pi\)
0.721392 + 0.692527i \(0.243503\pi\)
\(12\) 6.06045 20.4499i 0.505038 1.70416i
\(13\) 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
\(16\) 14.2580 7.26011i 0.891126 0.453757i
\(17\) 0.463429 0.802683i 0.0272606 0.0472167i −0.852073 0.523423i \(-0.824655\pi\)
0.879334 + 0.476206i \(0.157988\pi\)
\(18\) −23.2524 31.1430i −1.29180 1.73016i
\(19\) −2.96505 5.13561i −0.156055 0.270295i 0.777388 0.629022i \(-0.216544\pi\)
−0.933443 + 0.358726i \(0.883211\pi\)
\(20\) 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 \(-0.727157\pi\)
0.327410 + 0.944882i \(0.393824\pi\)
\(24\) 7.23239 42.0405i 0.301350 1.75169i
\(25\) −10.1738 + 17.6216i −0.406953 + 0.704863i
\(26\) 5.03053 + 42.5266i 0.193482 + 1.63564i
\(27\) −55.6311 −2.06041
\(28\) 0 0
\(29\) 9.42223i 0.324904i 0.986716 + 0.162452i \(0.0519403\pi\)
−0.986716 + 0.162452i \(0.948060\pi\)
\(30\) −2.70217 22.8434i −0.0900723 0.761445i
\(31\) 29.8813 + 17.2520i 0.963912 + 0.556515i 0.897375 0.441269i \(-0.145471\pi\)
0.0665375 + 0.997784i \(0.478805\pi\)
\(32\) 26.6129 17.7695i 0.831652 0.555298i
\(33\) 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 \(-0.611328\pi\)
0.642265 + 0.766483i \(0.277995\pi\)
\(38\) −7.09562 9.50349i −0.186727 0.250092i
\(39\) 98.8758 + 57.0860i 2.53528 + 1.46374i
\(40\) 11.0364 13.2645i 0.275911 0.331614i
\(41\) −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 \(0.661300\pi\)
\(44\) −5.97732 + 20.1694i −0.135848 + 0.458395i
\(45\) −36.2999 20.9578i −0.806665 0.465728i
\(46\) −13.9252 + 10.3970i −0.302721 + 0.226022i
\(47\) 39.8357 22.9991i 0.847567 0.489343i −0.0122620 0.999925i \(-0.503903\pi\)
0.859829 + 0.510582i \(0.170570\pi\)
\(48\) 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
\(52\) 19.9828 + 83.2825i 0.384285 + 1.60159i
\(53\) −64.5031 37.2409i −1.21704 0.702658i −0.252756 0.967530i \(-0.581337\pi\)
−0.964284 + 0.264872i \(0.914670\pi\)
\(54\) −110.492 + 13.0702i −2.04614 + 0.242041i
\(55\) 11.3436i 0.206246i
\(56\) 0 0
\(57\) −31.6208 −0.554751
\(58\) 2.21370 + 18.7140i 0.0381672 + 0.322655i
\(59\) 26.8367 46.4825i 0.454860 0.787840i −0.543821 0.839201i \(-0.683023\pi\)
0.998680 + 0.0513617i \(0.0163561\pi\)
\(60\) −10.7338 44.7355i −0.178897 0.745592i
\(61\) −24.0893 + 13.9080i −0.394907 + 0.228000i −0.684284 0.729215i \(-0.739885\pi\)
0.289377 + 0.957215i \(0.406552\pi\)
\(62\) 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
\(66\) 33.5546 + 44.9412i 0.508403 + 0.680927i
\(67\) 39.2453 67.9749i 0.585751 1.01455i −0.409030 0.912521i \(-0.634133\pi\)
0.994781 0.102030i \(-0.0325338\pi\)
\(68\) 1.05343 3.55462i 0.0154917 0.0522739i
\(69\) 46.3330i 0.671493i
\(70\) 0 0
\(71\) 74.5100i 1.04944i 0.851276 + 0.524719i \(0.175829\pi\)
−0.851276 + 0.524719i \(0.824171\pi\)
\(72\) −119.507 99.4329i −1.65982 1.38101i
\(73\) 16.8020 29.1020i 0.230165 0.398657i −0.727692 0.685904i \(-0.759407\pi\)
0.957857 + 0.287247i \(0.0927401\pi\)
\(74\) 20.5134 15.3160i 0.277209 0.206973i
\(75\) 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 \(-0.605424\pi\)
0.656370 + 0.754439i \(0.272091\pi\)
\(80\) 18.8036 28.9384i 0.235045 0.361730i
\(81\) −60.8713 + 105.432i −0.751497 + 1.30163i
\(82\) −85.6705 + 10.1341i −1.04476 + 0.123586i
\(83\) 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
\(86\) −82.8984 + 9.80616i −0.963935 + 0.114025i
\(87\) 43.5106 + 25.1209i 0.500122 + 0.288745i
\(88\) −7.13318 + 41.4638i −0.0810589 + 0.471180i
\(89\) −27.4198 47.4925i −0.308088 0.533624i 0.669856 0.742491i \(-0.266356\pi\)
−0.977944 + 0.208867i \(0.933022\pi\)
\(90\) −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
\(94\) 73.7162 55.0390i 0.784215 0.585521i
\(95\) −11.0772 6.39541i −0.116602 0.0673201i
\(96\) −11.1040 170.270i −0.115667 1.77365i
\(97\) 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
\(100\) −23.1264 + 78.0359i −0.231264 + 0.780359i
\(101\) −78.2037 45.1509i −0.774294 0.447039i 0.0601103 0.998192i \(-0.480855\pi\)
−0.834404 + 0.551153i \(0.814188\pi\)
\(102\) −5.91362 7.92038i −0.0579766 0.0776508i
\(103\) −97.6980 + 56.4060i −0.948525 + 0.547631i −0.892622 0.450805i \(-0.851137\pi\)
−0.0559023 + 0.998436i \(0.517804\pi\)
\(104\) 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 0.977092 + 0.212817i \(0.0682637\pi\)
−0.304241 + 0.952595i \(0.598403\pi\)
\(108\) −216.383 + 51.9189i −2.00354 + 0.480730i
\(109\) 57.7477 + 33.3406i 0.529795 + 0.305877i 0.740933 0.671579i \(-0.234384\pi\)
−0.211138 + 0.977456i \(0.567717\pi\)
\(110\) 2.66511 + 22.5300i 0.0242282 + 0.204818i
\(111\) 68.2540i 0.614901i
\(112\) 0 0
\(113\) 7.16467 0.0634042 0.0317021 0.999497i \(-0.489907\pi\)
0.0317021 + 0.999497i \(0.489907\pi\)
\(114\) −62.8037 + 7.42913i −0.550910 + 0.0651678i
\(115\) −9.37101 + 16.2311i −0.0814870 + 0.141140i
\(116\) 8.79349 + 36.6487i 0.0758060 + 0.315937i
\(117\) 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
\(122\) −44.5775 + 33.2830i −0.365389 + 0.272812i
\(123\) −115.000 + 199.187i −0.934963 + 1.61940i
\(124\) 132.327 + 39.2159i 1.06715 + 0.316258i
\(125\) 97.8118i 0.782494i
\(126\) 0 0
\(127\) 131.492i 1.03537i 0.855572 + 0.517684i \(0.173206\pi\)
−0.855572 + 0.517684i \(0.826794\pi\)
\(128\) 86.9296 93.9534i 0.679138 0.734011i
\(129\) −111.279 + 192.742i −0.862631 + 1.49412i
\(130\) 55.2604 + 74.0127i 0.425080 + 0.569329i
\(131\) −4.38060 7.58742i −0.0334397 0.0579193i 0.848821 0.528680i \(-0.177313\pi\)
−0.882261 + 0.470761i \(0.843980\pi\)
\(132\) 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
\(136\) 1.25714 7.30752i 0.00924370 0.0537318i
\(137\) 118.420 205.110i 0.864381 1.49715i −0.00327850 0.999995i \(-0.501044\pi\)
0.867660 0.497158i \(-0.165623\pi\)
\(138\) 10.8857 + 92.0244i 0.0788818 + 0.666844i
\(139\) −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
\(142\) 17.5057 + 147.988i 0.123280 + 1.04217i
\(143\) −97.5195 56.3029i −0.681955 0.393727i
\(144\) −260.721 169.411i −1.81056 1.17647i
\(145\) 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 \(-0.948507\pi\)
−0.353985 + 0.935251i \(0.615174\pi\)
\(150\) 129.824 + 173.879i 0.865491 + 1.15919i
\(151\) −128.077 73.9452i −0.848190 0.489703i 0.0118494 0.999930i \(-0.496228\pi\)
−0.860040 + 0.510227i \(0.829561\pi\)
\(152\) −36.4685 30.3427i −0.239924 0.199623i
\(153\) −18.0116 −0.117723
\(154\) 0 0
\(155\) 74.4227 0.480146
\(156\) 437.864 + 129.764i 2.80682 + 0.831819i
\(157\) −99.4450 57.4146i −0.633407 0.365698i 0.148663 0.988888i \(-0.452503\pi\)
−0.782070 + 0.623190i \(0.785836\pi\)
\(158\) 48.4170 36.1498i 0.306437 0.228796i
\(159\) −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 0.780434 0.625238i \(-0.214998\pi\)
−0.931689 + 0.363257i \(0.881665\pi\)
\(164\) −167.774 + 40.2556i −1.02301 + 0.245461i
\(165\) 52.3830 + 30.2433i 0.317473 + 0.183293i
\(166\) 144.845 17.1339i 0.872560 0.103216i
\(167\) 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
\(170\) −0.469695 3.97066i −0.00276291 0.0233568i
\(171\) −57.6196 + 99.8001i −0.336957 + 0.583626i
\(172\) −162.345 + 38.9531i −0.943867 + 0.226471i
\(173\) 47.1300 27.2105i 0.272428 0.157286i −0.357563 0.933889i \(-0.616392\pi\)
0.629990 + 0.776603i \(0.283059\pi\)
\(174\) 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
\(178\) −65.6180 87.8852i −0.368641 0.493737i
\(179\) 63.5100 110.003i 0.354805 0.614540i −0.632280 0.774740i \(-0.717881\pi\)
0.987084 + 0.160200i \(0.0512141\pi\)
\(180\) −160.751 47.6397i −0.893064 0.264665i
\(181\) 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
\(184\) −44.4602 + 53.4362i −0.241632 + 0.290414i
\(185\) 13.8046 23.9103i 0.0746194 0.129245i
\(186\) 294.850 220.145i 1.58521 1.18357i
\(187\) 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 \(-0.700507\pi\)
0.405282 + 0.914192i \(0.367174\pi\)
\(192\) −62.0584 335.574i −0.323221 1.74778i
\(193\) −141.153 + 244.485i −0.731364 + 1.26676i 0.224936 + 0.974374i \(0.427783\pi\)
−0.956300 + 0.292387i \(0.905551\pi\)
\(194\) 106.681 12.6195i 0.549904 0.0650488i
\(195\) 246.261 1.26288
\(196\) 0 0
\(197\) 261.806i 1.32896i −0.747304 0.664482i \(-0.768652\pi\)
0.747304 0.664482i \(-0.231348\pi\)
\(198\) 202.985 24.0113i 1.02518 0.121269i
\(199\) 278.968 + 161.062i 1.40185 + 0.809357i 0.994582 0.103953i \(-0.0331492\pi\)
0.407265 + 0.913310i \(0.366482\pi\)
\(200\) −27.5985 + 160.425i −0.137992 + 0.802123i
\(201\) −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
\(206\) −180.791 + 134.984i −0.877626 + 0.655265i
\(207\) 146.234 + 84.4283i 0.706445 + 0.407866i
\(208\) 155.450 + 305.286i 0.747357 + 1.46772i
\(209\) 31.1870 0.149220
\(210\) 0 0
\(211\) 169.792 0.804702 0.402351 0.915485i \(-0.368193\pi\)
0.402351 + 0.915485i \(0.368193\pi\)
\(212\) −285.647 84.6533i −1.34739 0.399308i
\(213\) 344.077 + 198.653i 1.61539 + 0.932644i
\(214\) 172.290 + 230.756i 0.805096 + 1.07830i
\(215\) −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
\(220\) 10.5866 + 44.1219i 0.0481210 + 0.200554i
\(221\) 17.1867 + 9.92275i 0.0777679 + 0.0448993i
\(222\) −16.0359 135.563i −0.0722338 0.610643i
\(223\) 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
\(226\) 14.2301 1.68330i 0.0629652 0.00744823i
\(227\) 92.5653 160.328i 0.407777 0.706290i −0.586864 0.809686i \(-0.699637\pi\)
0.994640 + 0.103396i \(0.0329708\pi\)
\(228\) −122.992 + 29.5108i −0.539440 + 0.129433i
\(229\) −160.173 + 92.4759i −0.699445 + 0.403825i −0.807141 0.590359i \(-0.798986\pi\)
0.107695 + 0.994184i \(0.465653\pi\)
\(230\) −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 0.743418 0.668827i \(-0.233203\pi\)
−0.950930 + 0.309405i \(0.899870\pi\)
\(234\) 666.819 497.869i 2.84966 2.12765i
\(235\) 49.6076 85.9228i 0.211096 0.365629i
\(236\) 61.0033 205.845i 0.258489 0.872223i
\(237\) 161.097i 0.679734i
\(238\) 0 0
\(239\) 163.185i 0.682782i 0.939921 + 0.341391i \(0.110898\pi\)
−0.939921 + 0.341391i \(0.889102\pi\)
\(240\) −83.5008 163.986i −0.347920 0.683274i
\(241\) 102.745 177.960i 0.426330 0.738424i −0.570214 0.821496i \(-0.693140\pi\)
0.996544 + 0.0830718i \(0.0264731\pi\)
\(242\) 111.687 + 149.588i 0.461519 + 0.618133i
\(243\) 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
\(248\) 272.035 + 46.7993i 1.09692 + 0.188707i
\(249\) 194.434 336.769i 0.780859 1.35249i
\(250\) 22.9803 + 194.269i 0.0919214 + 0.777077i
\(251\) 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
\(254\) 30.8932 + 261.162i 0.121627 + 1.02820i
\(255\) −9.23191 5.33005i −0.0362036 0.0209021i
\(256\) 150.582 207.029i 0.588210 0.808708i
\(257\) 107.889 + 186.868i 0.419800 + 0.727114i 0.995919 0.0902512i \(-0.0287670\pi\)
−0.576119 + 0.817366i \(0.695434\pi\)
\(258\) −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
\(262\) −10.4832 14.0406i −0.0400121 0.0535900i
\(263\) −285.059 164.579i −1.08387 0.625775i −0.151935 0.988391i \(-0.548550\pi\)
−0.931939 + 0.362616i \(0.881884\pi\)
\(264\) 172.456 + 143.488i 0.653244 + 0.543515i
\(265\) −160.652 −0.606234
\(266\) 0 0
\(267\) −292.419 −1.09520
\(268\) 89.2097 301.022i 0.332872 1.12322i
\(269\) −253.803 146.533i −0.943507 0.544734i −0.0524492 0.998624i \(-0.516703\pi\)
−0.891058 + 0.453889i \(0.850036\pi\)
\(270\) −192.298 + 143.576i −0.712216 + 0.531764i
\(271\) −23.2529 + 13.4251i −0.0858042 + 0.0495391i −0.542288 0.840193i \(-0.682442\pi\)
0.456484 + 0.889732i \(0.349109\pi\)
\(272\) 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
\(276\) 43.2413 + 180.217i 0.156671 + 0.652960i
\(277\) −289.925 167.389i −1.04666 0.604291i −0.124949 0.992163i \(-0.539877\pi\)
−0.921713 + 0.387872i \(0.873210\pi\)
\(278\) −341.860 + 40.4390i −1.22971 + 0.145464i
\(279\) 670.513i 2.40327i
\(280\) 0 0
\(281\) −123.357 −0.438994 −0.219497 0.975613i \(-0.570442\pi\)
−0.219497 + 0.975613i \(0.570442\pi\)
\(282\) −57.6259 487.152i −0.204347 1.72749i
\(283\) −0.309453 + 0.535988i −0.00109347 + 0.00189395i −0.866572 0.499053i \(-0.833681\pi\)
0.865478 + 0.500947i \(0.167015\pi\)
\(284\) 69.5381 + 289.814i 0.244852 + 1.02047i
\(285\) −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
\(290\) 24.3175 + 32.5695i 0.0838534 + 0.112309i
\(291\) 143.204 248.037i 0.492112 0.852362i
\(292\) 38.1932 128.876i 0.130799 0.441356i
\(293\) 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
\(296\) 65.4951 78.7178i 0.221267 0.265939i
\(297\) 146.285 253.373i 0.492542 0.853108i
\(298\) −369.728 + 276.051i −1.24070 + 0.926347i
\(299\) −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
\(304\) −79.5608 51.6971i −0.261713 0.170056i
\(305\) −29.9986 + 51.9591i −0.0983560 + 0.170358i
\(306\) −35.7738 + 4.23172i −0.116908 + 0.0138292i
\(307\) −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
\(310\) 147.815 17.4852i 0.476822 0.0564039i
\(311\) −140.492 81.1132i −0.451743 0.260814i 0.256823 0.966459i \(-0.417324\pi\)
−0.708566 + 0.705644i \(0.750658\pi\)
\(312\) 900.152 + 154.857i 2.88510 + 0.496336i
\(313\) −133.123 230.576i −0.425313 0.736664i 0.571137 0.820855i \(-0.306503\pi\)
−0.996450 + 0.0841913i \(0.973169\pi\)
\(314\) −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 \(-0.427456\pi\)
0.956600 + 0.291405i \(0.0941228\pi\)
\(318\) −636.476 + 475.214i −2.00150 + 1.49438i
\(319\) −42.9138 24.7763i −0.134526 0.0776686i
\(320\) 46.1311 130.108i 0.144160 0.406586i
\(321\) 767.792 2.39187
\(322\) 0 0
\(323\) −5.49636 −0.0170166
\(324\) −138.368 + 466.898i −0.427062 + 1.44104i
\(325\) −377.305 217.837i −1.16094 0.670269i
\(326\) −59.0005 79.0220i −0.180983 0.242399i
\(327\) 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 0.798108 0.602514i \(-0.205834\pi\)
−0.920847 + 0.389925i \(0.872501\pi\)
\(332\) 283.659 68.0611i 0.854394 0.205003i
\(333\) −215.420 124.373i −0.646907 0.373492i
\(334\) 56.7290 + 479.571i 0.169847 + 1.43584i
\(335\) 169.299i 0.505370i
\(336\) 0 0
\(337\) −69.4941 −0.206214 −0.103107 0.994670i \(-0.532878\pi\)
−0.103107 + 0.994670i \(0.532878\pi\)
\(338\) −574.902 + 68.0059i −1.70089 + 0.201201i
\(339\) 19.1019 33.0855i 0.0563479 0.0975974i
\(340\) −1.86577 7.77598i −0.00548756 0.0228705i
\(341\) −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
\(346\) 87.2145 65.1172i 0.252065 0.188200i
\(347\) 174.677 302.549i 0.503391 0.871899i −0.496601 0.867979i \(-0.665419\pi\)
0.999992 0.00392020i \(-0.00124784\pi\)
\(348\) 192.683 + 57.1029i 0.553688 + 0.164089i
\(349\) 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
\(352\) 10.9517 + 167.935i 0.0311129 + 0.477088i
\(353\) −235.858 + 408.519i −0.668154 + 1.15728i 0.310266 + 0.950650i \(0.399582\pi\)
−0.978420 + 0.206627i \(0.933751\pi\)
\(354\) −342.451 458.661i −0.967377 1.29565i
\(355\) 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 0.590731 0.806869i \(-0.298839\pi\)
0.994134 0.108154i \(-0.0344939\pi\)
\(360\) −330.470 56.8520i −0.917971 0.157922i
\(361\) 162.917 282.180i 0.451294 0.781663i
\(362\) −49.9737 422.463i −0.138049 1.16703i
\(363\) 497.722 1.37113
\(364\) 0 0
\(365\) 72.4817i 0.198580i
\(366\) 34.8474 + 294.590i 0.0952115 + 0.804890i
\(367\) 307.850 + 177.737i 0.838829 + 0.484298i 0.856866 0.515539i \(-0.172408\pi\)
−0.0180371 + 0.999837i \(0.505742\pi\)
\(368\) −75.7502 + 116.578i −0.205843 + 0.316788i
\(369\) 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 \(-0.805897\pi\)
0.0860872 + 0.996288i \(0.472564\pi\)
\(374\) 5.83250 + 7.81173i 0.0155949 + 0.0208870i
\(375\) 451.682 + 260.779i 1.20449 + 0.695410i
\(376\) 235.360 282.877i 0.625958 0.752332i
\(377\) −201.745 −0.535132
\(378\) 0 0
\(379\) −178.404 −0.470723 −0.235361 0.971908i \(-0.575627\pi\)
−0.235361 + 0.971908i \(0.575627\pi\)
\(380\) −49.0544 14.5376i −0.129091 0.0382568i
\(381\) 607.211 + 350.574i 1.59373 + 0.920140i
\(382\) −64.9604 + 48.5016i −0.170053 + 0.126968i
\(383\) 604.832 349.200i 1.57920 0.911750i 0.584225 0.811591i \(-0.301398\pi\)
0.994972 0.100158i \(-0.0319349\pi\)
\(384\) −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
\(388\) 208.920 50.1284i 0.538455 0.129197i
\(389\) −151.865 87.6790i −0.390397 0.225396i 0.291935 0.956438i \(-0.405701\pi\)
−0.682332 + 0.731042i \(0.739034\pi\)
\(390\) 489.112 57.8577i 1.25413 0.148353i
\(391\) 8.05366i 0.0205976i
\(392\) 0 0
\(393\) −46.7170 −0.118873
\(394\) −61.5099 519.987i −0.156117 1.31976i
\(395\) 32.5824 56.4344i 0.0824871 0.142872i
\(396\) 397.517 95.3803i 1.00383 0.240859i
\(397\) −334.033 + 192.854i −0.841393 + 0.485778i −0.857737 0.514088i \(-0.828130\pi\)
0.0163447 + 0.999866i \(0.494797\pi\)
\(398\) 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 −0.981330 0.192330i \(-0.938396\pi\)
0.324103 0.946022i \(-0.394938\pi\)
\(402\) −500.792 670.734i −1.24575 1.66849i
\(403\) −369.392 + 639.805i −0.916605 + 1.58761i
\(404\) −346.319 102.634i −0.857226 0.254044i
\(405\) 262.590i 0.648371i
\(406\) 0 0
\(407\) 67.3178i 0.165400i
\(408\) −30.3935 25.2881i −0.0744938 0.0619807i
\(409\) −211.872 + 366.973i −0.518025 + 0.897245i 0.481756 + 0.876305i \(0.339999\pi\)
−0.999781 + 0.0209399i \(0.993334\pi\)
\(410\) −149.100 + 111.323i −0.363658 + 0.271519i
\(411\) −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
\(416\) 380.473 + 569.823i 0.914599 + 1.36977i
\(417\) −458.898 + 794.834i −1.10047 + 1.90608i
\(418\) 61.9422 7.32723i 0.148187 0.0175292i
\(419\) −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 \(0.952088\pi\)
\(422\) 337.233 39.8917i 0.799131 0.0945302i
\(423\) −774.124 446.941i −1.83008 1.05660i
\(424\) −587.228 101.023i −1.38497 0.238262i
\(425\) 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
\(430\) −144.275 + 107.721i −0.335524 + 0.250513i
\(431\) 220.198 + 127.131i 0.510900 + 0.294968i 0.733204 0.680009i \(-0.238024\pi\)
−0.222303 + 0.974978i \(0.571358\pi\)
\(432\) −793.188 + 403.887i −1.83608 + 0.934925i
\(433\) −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
\(436\) 255.731 + 75.7876i 0.586540 + 0.173825i
\(437\) 44.6244 + 25.7639i 0.102115 + 0.0589563i
\(438\) −214.403 287.160i −0.489505 0.655617i
\(439\) 236.715 136.667i 0.539214 0.311315i −0.205546 0.978647i \(-0.565897\pi\)
0.744760 + 0.667332i \(0.232564\pi\)
\(440\) 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 −0.999121 0.0419124i \(-0.986655\pi\)
0.463263 0.886221i \(-0.346678\pi\)
\(444\) −63.6995 265.481i −0.143467 0.597930i
\(445\) −102.438 59.1427i −0.230198 0.132905i
\(446\) −10.6812 90.2957i −0.0239489 0.202457i
\(447\) 1230.19i 2.75210i
\(448\) 0 0
\(449\) 782.101 1.74187 0.870936 0.491396i \(-0.163513\pi\)
0.870936 + 0.491396i \(0.163513\pi\)
\(450\) 785.353 92.9004i 1.74523 0.206445i
\(451\) 113.423 196.454i 0.251492 0.435597i
\(452\) 27.8677 6.68658i 0.0616542 0.0147933i
\(453\) −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 0.950893 0.309520i \(-0.100168\pi\)
−0.743498 + 0.668738i \(0.766835\pi\)
\(458\) −296.401 + 221.303i −0.647164 + 0.483194i
\(459\) −25.7811 + 44.6541i −0.0561679 + 0.0972857i
\(460\) −21.3015 + 71.8781i −0.0463076 + 0.156257i
\(461\) 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 \(0.750900\pi\)
\(464\) 68.4064 + 134.342i 0.147428 + 0.289531i
\(465\) 198.420 343.674i 0.426710 0.739084i
\(466\) −115.707 154.971i −0.248298 0.332556i
\(467\) 272.725 + 472.373i 0.583993 + 1.01150i 0.995000 + 0.0998730i \(0.0318437\pi\)
−0.411008 + 0.911632i \(0.634823\pi\)
\(468\) 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
\(472\) 72.7998 423.171i 0.154237 0.896549i
\(473\) 109.753 190.098i 0.232036 0.401898i
\(474\) −37.8489 319.963i −0.0798499 0.675028i
\(475\) 120.663 0.254028
\(476\) 0 0
\(477\) 1447.40i 3.03438i
\(478\) 38.3394 + 324.110i 0.0802079 + 0.678054i
\(479\) 94.3079 + 54.4487i 0.196885 + 0.113672i 0.595202 0.803576i \(-0.297072\pi\)
−0.398317 + 0.917248i \(0.630405\pi\)
\(480\) −204.373 306.083i −0.425777 0.637672i
\(481\) 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
\(486\) 177.666 + 237.956i 0.365568 + 0.489622i
\(487\) 371.831 + 214.677i 0.763513 + 0.440814i 0.830556 0.556936i \(-0.188023\pi\)
−0.0670428 + 0.997750i \(0.521356\pi\)
\(488\) −142.327 + 171.061i −0.291653 + 0.350534i
\(489\) −262.929 −0.537686
\(490\) 0 0
\(491\) 453.887 0.924413 0.462206 0.886772i \(-0.347058\pi\)
0.462206 + 0.886772i \(0.347058\pi\)
\(492\) −261.411 + 882.083i −0.531323 + 1.79285i
\(493\) 7.56306 + 4.36654i 0.0153409 + 0.00885707i
\(494\) 203.485 151.928i 0.411912 0.307547i
\(495\) 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 0.649240 0.760583i \(-0.275087\pi\)
−0.983305 + 0.181967i \(0.941754\pi\)
\(500\) 91.2849 + 380.449i 0.182570 + 0.760898i
\(501\) 1115.02 + 643.755i 2.22558 + 1.28494i
\(502\) 316.392 37.4265i 0.630264 0.0745547i
\(503\) 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
\(506\) −10.7364 90.7621i −0.0212181 0.179372i
\(507\) −771.724 + 1336.67i −1.52214 + 2.63642i
\(508\) 122.717 + 511.450i 0.241570 + 1.00679i
\(509\) 266.271 153.732i 0.523126 0.302027i −0.215087 0.976595i \(-0.569003\pi\)
0.738213 + 0.674568i \(0.235670\pi\)
\(510\) −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
\(514\) 258.187 + 345.801i 0.502309 + 0.672765i
\(515\) −121.664 + 210.728i −0.236241 + 0.409181i
\(516\) −252.952 + 853.542i −0.490218 + 1.65415i
\(517\) 241.910i 0.467911i
\(518\) 0 0
\(519\) 290.187i 0.559127i
\(520\) 284.015 + 236.307i 0.546182 + 0.454437i
\(521\) 360.480 624.369i 0.691899 1.19840i −0.279316 0.960199i \(-0.590108\pi\)
0.971215 0.238205i \(-0.0765591\pi\)
\(522\) 293.436 219.089i 0.562138 0.419711i
\(523\) −134.988 233.807i −0.258104 0.447049i 0.707630 0.706583i \(-0.249764\pi\)
−0.965734 + 0.259534i \(0.916431\pi\)
\(524\) −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
\(528\) 376.236 + 244.471i 0.712569 + 0.463013i
\(529\) −226.749 + 392.741i −0.428637 + 0.742421i
\(530\) −319.080 + 37.7443i −0.602037 + 0.0712157i
\(531\) −1043.03 −1.96428
\(532\) 0 0
\(533\) 923.564i 1.73277i
\(534\) −580.788 + 68.7022i −1.08762 + 0.128656i
\(535\) 268.967 + 155.288i 0.502743 + 0.290259i
\(536\) 106.461 618.835i 0.198621 1.15454i
\(537\) −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 \(-0.983226\pi\)
−0.453689 + 0.891160i \(0.649892\pi\)
\(542\) −43.0297 + 32.1274i −0.0793907 + 0.0592757i
\(543\) −982.241 567.097i −1.80891 1.04438i
\(544\) −1.93012 29.5966i −0.00354801 0.0544055i
\(545\) 143.827 0.263903
\(546\) 0 0
\(547\) −557.327 −1.01888 −0.509439 0.860506i \(-0.670147\pi\)
−0.509439 + 0.860506i \(0.670147\pi\)
\(548\) 269.185 908.314i 0.491213 1.65751i
\(549\) 468.127 + 270.273i 0.852690 + 0.492301i
\(550\) −128.043 171.494i −0.232805 0.311807i
\(551\) 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
\(556\) −669.484 + 160.636i −1.20411 + 0.288914i
\(557\) 741.896 + 428.334i 1.33195 + 0.769002i 0.985598 0.169103i \(-0.0540869\pi\)
0.346352 + 0.938105i \(0.387420\pi\)
\(558\) −157.533 1331.74i −0.282318 2.38663i
\(559\) 893.680i 1.59871i
\(560\) 0 0
\(561\) 25.9918 0.0463313
\(562\) −245.006 + 28.9821i −0.435954 + 0.0515696i
\(563\) 6.84436 11.8548i 0.0121569 0.0210564i −0.859883 0.510491i \(-0.829464\pi\)
0.872040 + 0.489435i \(0.162797\pi\)
\(564\) −228.908 954.020i −0.405865 1.69152i
\(565\) 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 0.723563 + 0.690258i \(0.242503\pi\)
0.235999 + 0.971753i \(0.424164\pi\)
\(570\) −109.303 + 81.6090i −0.191759 + 0.143174i
\(571\) −359.549 + 622.757i −0.629683 + 1.09064i 0.357932 + 0.933747i \(0.383482\pi\)
−0.987615 + 0.156895i \(0.949852\pi\)
\(572\) −431.858 127.984i −0.754997 0.223748i
\(573\) 216.142i 0.377210i
\(574\) 0 0
\(575\) 176.805i 0.307486i
\(576\) −1172.21 415.620i −2.03508 0.721562i
\(577\) −515.560 + 892.976i −0.893518 + 1.54762i −0.0578905 + 0.998323i \(0.518437\pi\)
−0.835628 + 0.549296i \(0.814896\pi\)
\(578\) 344.773 + 461.771i 0.596494 + 0.798911i
\(579\) 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
\(584\) 45.5788 264.941i 0.0780459 0.453666i
\(585\) 448.738 777.238i 0.767074 1.32861i
\(586\) −6.64410 56.1673i −0.0113381 0.0958486i
\(587\) 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
\(590\) −27.1995 229.937i −0.0461009 0.389723i
\(591\) −1208.99 698.008i −2.04566 1.18106i
\(592\) 111.589 171.733i 0.188495 0.290090i
\(593\) 176.999 + 306.572i 0.298481 + 0.516984i 0.975789 0.218716i \(-0.0701867\pi\)
−0.677308 + 0.735700i \(0.736853\pi\)
\(594\) 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
\(598\) −222.616 298.160i −0.372268 0.498595i
\(599\) −983.923 568.068i −1.64261 0.948361i −0.979901 0.199484i \(-0.936074\pi\)
−0.662708 0.748878i \(1.26941\pi\)
\(600\) 667.238 + 555.158i 1.11206 + 0.925264i
\(601\) 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
\(604\) −567.179 168.087i −0.939037 0.278290i
\(605\) 174.358 + 100.666i 0.288196 + 0.166390i
\(606\) −771.665 + 576.151i −1.27337 + 0.950744i
\(607\) −386.628 + 223.220i −0.636948 + 0.367742i −0.783438 0.621470i \(-0.786536\pi\)
0.146490 + 0.989212i \(0.453202\pi\)
\(608\) −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
\(612\) −70.0579 + 16.8097i −0.114474 + 0.0274668i
\(613\) 555.650 + 320.805i 0.906443 + 0.523335i 0.879285 0.476296i \(-0.158021\pi\)
0.0271583 + 0.999631i \(0.491354\pi\)
\(614\) −796.235 + 94.1877i −1.29680 + 0.153400i
\(615\) 496.096i 0.806661i
\(616\) 0 0
\(617\) −502.890 −0.815057 −0.407528 0.913193i \(-0.633609\pi\)
−0.407528 + 0.913193i \(0.633609\pi\)
\(618\) 141.329 + 1194.75i 0.228688 + 1.93326i
\(619\) 216.495 374.980i 0.349749 0.605783i −0.636456 0.771313i \(-0.719600\pi\)
0.986205 + 0.165530i \(0.0529336\pi\)
\(620\) 289.475 69.4565i 0.466894 0.112027i
\(621\) 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
\(626\) −318.575 426.682i −0.508906 0.681601i
\(627\) 83.1486 144.018i 0.132613 0.229693i
\(628\) −440.385 130.511i −0.701250 0.207820i
\(629\) 11.8640i 0.0188617i
\(630\) 0 0
\(631\) 238.957i 0.378695i −0.981910 0.189348i \(-0.939363\pi\)
0.981910 0.189348i \(-0.0606373\pi\)
\(632\) 154.585 185.794i 0.244597 0.293978i
\(633\) 452.687 784.078i 0.715146 1.23867i
\(634\) 693.688 517.930i 1.09414 0.816925i
\(635\) 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
\(640\) 61.0554 269.252i 0.0953991 0.420706i
\(641\) 3.98065 6.89469i 0.00621006 0.0107561i −0.862904 0.505368i \(-0.831357\pi\)
0.869114 + 0.494612i \(0.164690\pi\)
\(642\) 1524.95 180.388i 2.37531 0.280979i
\(643\) 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
\(646\) −10.9166 + 1.29134i −0.0168988 + 0.00199898i
\(647\) 290.707 + 167.840i 0.449316 + 0.259413i 0.707541 0.706672i \(-0.249804\pi\)
−0.258225 + 0.966085i \(0.583138\pi\)
\(648\) −165.125 + 959.840i −0.254823 + 1.48123i
\(649\) 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 \(-0.654837\pi\)
0.531833 + 0.846849i \(0.321503\pi\)
\(654\) 569.818 425.445i 0.871281 0.650528i
\(655\) −16.3656 9.44866i −0.0249856 0.0144254i
\(656\) −615.003 + 313.157i −0.937505 + 0.477373i
\(657\) −653.026 −0.993951
\(658\) 0 0
\(659\) 1224.65 1.85835 0.929176 0.369638i \(-0.120518\pi\)
0.929176 + 0.369638i \(0.120518\pi\)
\(660\) 231.974 + 68.7470i 0.351476 + 0.104162i
\(661\) −725.765 419.021i −1.09798 0.633919i −0.162291 0.986743i \(-0.551888\pi\)
−0.935690 + 0.352823i \(0.885222\pi\)
\(662\) −97.2226 130.215i −0.146862 0.196699i
\(663\) 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
\(668\) 225.345 + 939.172i 0.337343 + 1.40595i
\(669\) −209.940 121.209i −0.313812 0.181180i
\(670\) −39.7759 336.254i −0.0593670 0.501871i
\(671\) 146.287i 0.218014i
\(672\) 0 0
\(673\) 147.714 0.219486 0.109743 0.993960i \(-0.464997\pi\)
0.109743 + 0.993960i \(0.464997\pi\)
\(674\) −138.026 + 16.3273i −0.204786 + 0.0242244i
\(675\) 565.980 980.307i 0.838490 1.45231i
\(676\) −1125.87 + 270.140i −1.66548 + 0.399616i
\(677\) 725.024 418.593i 1.07094 0.618305i 0.142499 0.989795i \(-0.454486\pi\)
0.928437 + 0.371490i \(0.121153\pi\)
\(678\) 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
\(682\) −290.805 + 217.125i −0.426401 + 0.318365i
\(683\) 32.2189 55.8047i 0.0471725 0.0817053i −0.841475 0.540296i \(-0.818312\pi\)
0.888648 + 0.458591i \(0.151646\pi\)
\(684\) −130.977 + 441.957i −0.191486 + 0.646136i
\(685\) 510.849i 0.745765i
\(686\) 0 0
\(687\) 986.210i 1.43553i
\(688\) −595.104 + 303.024i −0.864976 + 0.440442i
\(689\) 797.385 1381.11i 1.15731 2.00452i
\(690\) 119.579 + 160.158i 0.173303 + 0.232113i
\(691\) −263.374 456.177i −0.381149 0.660169i 0.610078 0.792341i \(-0.291138\pi\)
−0.991227 + 0.132172i \(0.957805\pi\)
\(692\) 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
\(696\) 396.115 + 68.1452i 0.569130 + 0.0979098i
\(697\) −19.9895 + 34.6229i −0.0286794 + 0.0496741i
\(698\) 38.9622 + 329.375i 0.0558198 + 0.471884i
\(699\) −515.633 −0.737672
\(700\) 0 0
\(701\) 695.486i 0.992134i −0.868284 0.496067i \(-0.834777\pi\)
0.868284 0.496067i \(-0.165223\pi\)
\(702\) −279.854 2365.80i −0.398652 3.37009i
\(703\) −65.7370 37.9532i −0.0935092 0.0539875i
\(704\) 61.2072 + 330.971i 0.0869420 + 0.470130i
\(705\) −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 \(-0.893588\pi\)
−0.188168 + 0.982137i \(0.560255\pi\)
\(710\) 192.300 + 257.557i 0.270846 + 0.362756i
\(711\) −508.447 293.552i −0.715115 0.412872i
\(712\) −337.249 280.599i −0.473664 0.394100i
\(713\) −299.812 −0.420493
\(714\) 0 0
\(715\) −242.883 −0.339697
\(716\) 144.366 487.138i 0.201629 0.680361i
\(717\) 753.566 + 435.071i 1.05100 + 0.606794i
\(718\) 1052.88 786.113i 1.46640 1.09486i
\(719\) 1150.37 664.169i 1.59996 0.923739i 0.608471 0.793576i \(-0.291783\pi\)
0.991493 0.130163i \(-0.0415501\pi\)
\(720\) −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
\(724\) −198.511 827.335i −0.274186 1.14273i
\(725\) −166.034 95.8600i −0.229013 0.132221i
\(726\) 988.551 116.937i 1.36164 0.161070i
\(727\) 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
\(730\) −17.0292 143.960i −0.0233277 0.197205i
\(731\) −19.3427 + 33.5026i −0.0264606 + 0.0458311i
\(732\) 138.425 + 576.913i 0.189105 + 0.788133i
\(733\) 382.859 221.044i 0.522318 0.301561i −0.215564 0.976490i \(-0.569159\pi\)
0.737883 + 0.674929i \(0.235826\pi\)
\(734\) 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
\(738\) 1002.96 + 1343.32i 1.35903 + 1.82021i
\(739\) 574.116 994.398i 0.776882 1.34560i −0.156848 0.987623i \(-0.550133\pi\)
0.933730 0.357977i \(-0.116533\pi\)
\(740\) 31.3796 105.885i 0.0424049 0.143088i
\(741\) 677.050i 0.913698i
\(742\) 0 0
\(743\) 588.688i 0.792313i −0.918183 0.396156i \(-0.870344\pi\)
0.918183 0.396156i \(-0.129656\pi\)
\(744\) 941.394 1131.45i 1.26531 1.52077i
\(745\) −248.810 + 430.952i −0.333973 + 0.578459i
\(746\) −506.414 + 378.106i −0.678840 + 0.506844i
\(747\) −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 \(-0.483245\pi\)
0.891133 + 0.453742i \(0.149911\pi\)
\(752\) 401.001 617.133i 0.533246 0.820656i
\(753\) 424.712 735.622i 0.564026 0.976922i
\(754\) −400.695 + 47.3988i −0.531426 + 0.0628631i
\(755\) −318.989 −0.422503
\(756\) 0 0
\(757\) 105.101i 0.138838i 0.997588 + 0.0694192i \(0.0221146\pi\)
−0.997588 + 0.0694192i \(0.977885\pi\)
\(758\) −354.337 + 41.9150i −0.467464 + 0.0552969i
\(759\) −211.025 121.835i −0.278030 0.160521i
\(760\) −100.845 17.3488i −0.132691 0.0228274i
\(761\) 507.117 + 878.352i 0.666382 + 1.15421i 0.978909 + 0.204299i \(0.0654913\pi\)
−0.312527 + 0.949909i \(0.601175\pi\)
\(762\) 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
\(766\) 1119.25 835.667i 1.46116 1.09095i
\(767\) 995.264 + 574.616i 1.29761 + 0.749173i
\(768\) −554.564 1247.33i −0.722089 1.62413i
\(769\) 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
\(772\) −320.860 + 1082.68i −0.415621 + 1.40244i
\(773\) 280.862 + 162.156i 0.363340 + 0.209774i 0.670545 0.741869i \(-0.266060\pi\)
−0.307205 + 0.951643i \(0.599394\pi\)
\(774\) 970.512 + 1299.85i 1.25389 + 1.67939i
\(775\) −608.014 + 351.037i −0.784534 + 0.452951i
\(776\) 403.170 148.647i 0.519550 0.191556i
\(777\) 0