Properties

Label 392.3.k.l.275.6
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 275.6
Root \(0.907369 - 0.0534805i\) of defining polynomial
Character \(\chi\) \(=\) 392.275
Dual form 392.3.k.l.67.6

$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.98615 + 0.234945i 0.993076 + 0.117472i
\(3\) 2.66613 + 4.61787i 0.888709 + 1.53929i 0.841403 + 0.540409i \(0.181730\pi\)
0.0473064 + 0.998880i \(0.484936\pi\)
\(4\) 3.88960 + 0.933271i 0.972401 + 0.233318i
\(5\) 1.86796 + 1.07847i 0.373592 + 0.215693i 0.675026 0.737794i \(-0.264132\pi\)
−0.301435 + 0.953487i \(0.597466\pi\)
\(6\) 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 0.721392 0.692527i \(-0.243503\pi\)
−0.960442 + 0.278480i \(0.910170\pi\)
\(12\) 6.06045 + 20.4499i 0.505038 + 1.70416i
\(13\) 21.4116i 1.64704i −0.567285 0.823522i \(-0.692006\pi\)
0.567285 0.823522i \(-0.307994\pi\)
\(14\) 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 0.879334 0.476206i \(-0.157988\pi\)
−0.852073 + 0.523423i \(0.824655\pi\)
\(18\) −23.2524 + 31.1430i −1.29180 + 1.73016i
\(19\) −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 0.327410 0.944882i \(-0.393824\pi\)
−0.654587 + 0.755987i \(0.727157\pi\)
\(24\) 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 \(-0.948060\pi\)
0.986716 0.162452i \(-0.0519403\pi\)
\(30\) −2.70217 + 22.8434i −0.0900723 + 0.761445i
\(31\) 29.8813 17.2520i 0.963912 0.556515i 0.0665375 0.997784i \(-0.478805\pi\)
0.897375 + 0.441269i \(0.145471\pi\)
\(32\) 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 0.642265 0.766483i \(-0.277995\pi\)
−0.342662 + 0.939459i \(0.611328\pi\)
\(38\) −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 0.859829 0.510582i \(-0.170570\pi\)
−0.0122620 + 0.999925i \(0.503903\pi\)
\(48\) 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 −0.964284 0.264872i \(-0.914670\pi\)
−0.252756 + 0.967530i \(0.581337\pi\)
\(54\) −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 0.998680 0.0513617i \(-0.0163561\pi\)
−0.543821 + 0.839201i \(0.683023\pi\)
\(60\) −10.7338 + 44.7355i −0.178897 + 0.745592i
\(61\) −24.0893 13.9080i −0.394907 0.228000i 0.289377 0.957215i \(-0.406552\pi\)
−0.684284 + 0.729215i \(0.739885\pi\)
\(62\) 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 0.994781 + 0.102030i \(0.0325338\pi\)
−0.409030 + 0.912521i \(0.634133\pi\)
\(68\) 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 \(-0.824171\pi\)
0.851276 0.524719i \(-0.175829\pi\)
\(72\) −119.507 + 99.4329i −1.65982 + 1.38101i
\(73\) 16.8020 + 29.1020i 0.230165 + 0.398657i 0.957857 0.287247i \(-0.0927401\pi\)
−0.727692 + 0.685904i \(0.759407\pi\)
\(74\) 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 0.656370 0.754439i \(-0.272091\pi\)
−0.325178 + 0.945653i \(0.605424\pi\)
\(80\) 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 −0.977944 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
\(94\) 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 −0.834404 0.551153i \(-0.814188\pi\)
0.0601103 + 0.998192i \(0.480855\pi\)
\(102\) −5.91362 + 7.92038i −0.0579766 + 0.0776508i
\(103\) −97.6980 56.4060i −0.948525 0.547631i −0.0559023 0.998436i \(-0.517804\pi\)
−0.892622 + 0.450805i \(0.851137\pi\)
\(104\) 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 \(-0.0682637\pi\)
\(108\) −216.383 51.9189i −2.00354 0.480730i
\(109\) 57.7477 33.3406i 0.529795 0.305877i −0.211138 0.977456i \(-0.567717\pi\)
0.740933 + 0.671579i \(0.234384\pi\)
\(110\) 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 \(-0.826794\pi\)
0.855572 0.517684i \(-0.173206\pi\)
\(128\) 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 −0.882261 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
\(136\) 1.25714 + 7.30752i 0.00924370 + 0.0537318i
\(137\) 118.420 + 205.110i 0.864381 + 1.49715i 0.867660 + 0.497158i \(0.165623\pi\)
−0.00327850 + 0.999995i \(0.501044\pi\)
\(138\) 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 −0.353985 0.935251i \(-0.615174\pi\)
−0.986944 + 0.161066i \(0.948507\pi\)
\(150\) 129.824 173.879i 0.865491 1.15919i
\(151\) −128.077 + 73.9452i −0.848190 + 0.489703i −0.860040 0.510227i \(-0.829561\pi\)
0.0118494 + 0.999930i \(0.496228\pi\)
\(152\) −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 −0.782070 0.623190i \(-0.785836\pi\)
0.148663 + 0.988888i \(0.452503\pi\)
\(158\) 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 −0.931689 0.363257i \(-0.881665\pi\)
0.780434 + 0.625238i \(0.214998\pi\)
\(164\) −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 \(-0.742797\pi\)
0.690926 0.722926i \(-0.257203\pi\)
\(168\) 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 0.629990 0.776603i \(-0.283059\pi\)
−0.357563 + 0.933889i \(0.616392\pi\)
\(174\) 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 0.987084 0.160200i \(-0.0512141\pi\)
−0.632280 + 0.774740i \(0.717881\pi\)
\(180\) −160.751 + 47.6397i −0.893064 + 0.264665i
\(181\) 212.704i 1.17516i 0.809165 + 0.587581i \(0.199920\pi\)
−0.809165 + 0.587581i \(0.800080\pi\)
\(182\) 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 0.405282 0.914192i \(-0.367174\pi\)
−0.589073 + 0.808080i \(0.700507\pi\)
\(192\) −62.0584 + 335.574i −0.323221 + 1.74778i
\(193\) −141.153 244.485i −0.731364 1.26676i −0.956300 0.292387i \(-0.905551\pi\)
0.224936 0.974374i \(-0.427783\pi\)
\(194\) 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 \(0.231348\pi\)
−0.747304 + 0.664482i \(0.768652\pi\)
\(198\) 202.985 + 24.0113i 1.02518 + 0.121269i
\(199\) 278.968 161.062i 1.40185 0.809357i 0.407265 0.913310i \(-0.366482\pi\)
0.994582 + 0.103953i \(0.0331492\pi\)
\(200\) −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 \(0.0325031\pi\)
−0.994791 + 0.101934i \(0.967497\pi\)
\(224\) 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 0.994640 0.103396i \(-0.0329708\pi\)
−0.586864 + 0.809686i \(0.699637\pi\)
\(228\) −122.992 29.5108i −0.539440 0.129433i
\(229\) −160.173 92.4759i −0.699445 0.403825i 0.107695 0.994184i \(-0.465653\pi\)
−0.807141 + 0.590359i \(0.798986\pi\)
\(230\) −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 \(0.233203\pi\)
\(234\) 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 \(-0.889102\pi\)
0.939921 0.341391i \(-0.110898\pi\)
\(240\) −83.5008 + 163.986i −0.347920 + 0.683274i
\(241\) 102.745 + 177.960i 0.426330 + 0.738424i 0.996544 0.0830718i \(-0.0264731\pi\)
−0.570214 + 0.821496i \(0.693140\pi\)
\(242\) 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 −0.576119 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
\(262\) −10.4832 + 14.0406i −0.0400121 + 0.0535900i
\(263\) −285.059 + 164.579i −1.08387 + 0.625775i −0.931939 0.362616i \(-0.881884\pi\)
−0.151935 + 0.988391i \(0.548550\pi\)
\(264\) 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 −0.891058 0.453889i \(-0.850036\pi\)
−0.0524492 + 0.998624i \(0.516703\pi\)
\(270\) −192.298 143.576i −0.712216 0.531764i
\(271\) −23.2529 13.4251i −0.0858042 0.0495391i 0.456484 0.889732i \(-0.349109\pi\)
−0.542288 + 0.840193i \(0.682442\pi\)
\(272\) 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 −0.921713 0.387872i \(-0.873210\pi\)
−0.124949 + 0.992163i \(0.539877\pi\)
\(278\) −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 0.865478 0.500947i \(-0.167015\pi\)
−0.866572 + 0.499053i \(0.833681\pi\)
\(284\) 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 \(0.0153671\pi\)
−0.998835 + 0.0482584i \(0.984633\pi\)
\(294\) 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 −0.708566 0.705644i \(-0.750658\pi\)
0.256823 + 0.966459i \(0.417324\pi\)
\(312\) 900.152 154.857i 2.88510 0.496336i
\(313\) −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 0.956600 0.291405i \(-0.0941228\pi\)
0.225936 + 0.974142i \(0.427456\pi\)
\(318\) −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 −0.920847 0.389925i \(-0.872501\pi\)
0.798108 + 0.602514i \(0.205834\pi\)
\(332\) 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 0.999992 + 0.00392020i \(0.00124784\pi\)
−0.496601 + 0.867979i \(0.665419\pi\)
\(348\) 192.683 57.1029i 0.553688 0.164089i
\(349\) 165.836i 0.475174i −0.971366 0.237587i \(-0.923643\pi\)
0.971366 0.237587i \(-0.0763566\pi\)
\(350\) 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 −0.978420 0.206627i \(-0.933751\pi\)
0.310266 0.950650i \(-0.399582\pi\)
\(354\) −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 0.994134 + 0.108154i \(0.0344939\pi\)
0.590731 + 0.806869i \(0.298839\pi\)
\(360\) −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 −0.0180371 0.999837i \(-0.505742\pi\)
0.856866 + 0.515539i \(0.172408\pi\)
\(368\) −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 0.0860872 0.996288i \(-0.472564\pi\)
−0.819767 + 0.572698i \(0.805897\pi\)
\(374\) 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 0.994972 + 0.100158i \(0.0319349\pi\)
0.584225 + 0.811591i \(0.301398\pi\)
\(384\) −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 −0.682332 0.731042i \(-0.739034\pi\)
0.291935 + 0.956438i \(0.405701\pi\)
\(390\) 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 0.0163447 0.999866i \(-0.494797\pi\)
−0.857737 + 0.514088i \(0.828130\pi\)
\(398\) 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 \(0.938396\pi\)
\(402\) −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 −0.999781 0.0209399i \(-0.993334\pi\)
0.481756 0.876305i \(-0.339999\pi\)
\(410\) −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 \(-0.952088\pi\)
0.988693 0.149952i \(-0.0479119\pi\)
\(422\) 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 −0.222303 0.974978i \(-0.571358\pi\)
0.733204 + 0.680009i \(0.238024\pi\)
\(432\) −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 0.744760 0.667332i \(-0.232564\pi\)
−0.205546 + 0.978647i \(0.565897\pi\)
\(440\) 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 \(0.986655\pi\)
\(444\) −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 −0.743498 0.668738i \(-0.766835\pi\)
0.950893 + 0.309520i \(0.100168\pi\)
\(458\) −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 \(0.0704972\pi\)
−0.975575 + 0.219667i \(0.929503\pi\)
\(462\) 0 0
\(463\) 652.927i 1.41021i −0.709103 0.705105i \(-0.750900\pi\)
0.709103 0.705105i \(-0.249100\pi\)
\(464\) 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 −0.411008 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
\(472\) 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 −0.398317 0.917248i \(-0.630405\pi\)
0.595202 + 0.803576i \(0.297072\pi\)
\(480\) −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 −0.0670428 0.997750i \(-0.521356\pi\)
0.830556 + 0.556936i \(0.188023\pi\)
\(488\) −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 −0.983305 0.181967i \(-0.941754\pi\)
0.649240 + 0.760583i \(0.275087\pi\)
\(500\) 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 \(-0.804336\pi\)
0.816949 0.576710i \(-0.195664\pi\)
\(504\) 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 0.738213 0.674568i \(-0.235670\pi\)
−0.215087 + 0.976595i \(0.569003\pi\)
\(510\) −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 0.971215 + 0.238205i \(0.0765591\pi\)
−0.279316 + 0.960199i \(0.590108\pi\)
\(522\) 293.436 + 219.089i 0.562138 + 0.419711i
\(523\) −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
\(528\) 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 −0.453689 0.891160i \(-0.649892\pi\)
−0.998612 + 0.0526734i \(0.983226\pi\)
\(542\) −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 0.346352 0.938105i \(-0.387420\pi\)
0.985598 + 0.169103i \(0.0540869\pi\)
\(558\) −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 0.872040 0.489435i \(-0.162797\pi\)
−0.859883 + 0.510491i \(0.829464\pi\)
\(564\) −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 0.235999 0.971753i \(-0.424164\pi\)
0.723563 0.690258i \(-0.242503\pi\)
\(570\) −109.303 81.6090i −0.191759 0.143174i
\(571\) −359.549 622.757i −0.629683 1.09064i −0.987615 0.156895i \(-0.949852\pi\)
0.357932 0.933747i \(-0.383482\pi\)
\(572\) −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 −0.835628 0.549296i \(-0.814896\pi\)
−0.0578905 0.998323i \(-0.518437\pi\)
\(578\) 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 −0.677308 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
\(598\) −222.616 + 298.160i −0.372268 + 0.498595i
\(599\) −983.923 + 568.068i −1.64261 + 0.948361i −0.662708 + 0.748878i \(0.730593\pi\)
−0.979901 + 0.199484i \(0.936074\pi\)
\(600\) 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 0.146490 0.989212i \(-0.453202\pi\)
−0.783438 + 0.621470i \(0.786536\pi\)
\(608\) −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 0.0271583 0.999631i \(-0.491354\pi\)
0.879285 + 0.476296i \(0.158021\pi\)
\(614\) −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 0.986205 0.165530i \(-0.0529336\pi\)
−0.636456 + 0.771313i \(0.719600\pi\)
\(620\) 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 \(0.0606373\pi\)
−0.981910 + 0.189348i \(0.939363\pi\)
\(632\) 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 0.869114 0.494612i \(-0.164690\pi\)
−0.862904 + 0.505368i \(0.831357\pi\)
\(642\) 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 −0.258225 0.966085i \(-0.583138\pi\)
0.707541 + 0.706672i \(0.249804\pi\)
\(648\) −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 0.531833 0.846849i \(-0.321503\pi\)
−0.467476 + 0.884006i \(0.654837\pi\)
\(654\) 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 −0.935690 0.352823i \(-0.885222\pi\)
−0.162291 + 0.986743i \(0.551888\pi\)
\(662\) −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 0.928437 0.371490i \(-0.121153\pi\)
0.142499 + 0.989795i \(0.454486\pi\)
\(678\) 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 0.888648 0.458591i \(-0.151646\pi\)
−0.841475 + 0.540296i \(0.818312\pi\)
\(684\) −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 −0.991227 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
\(696\) 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 \(0.165223\pi\)
−0.868284 + 0.496067i \(0.834777\pi\)
\(702\) −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 −0.188168 0.982137i \(-0.560255\pi\)
−0.944640 + 0.328110i \(0.893588\pi\)
\(710\) 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 0.991493 + 0.130163i \(0.0415501\pi\)
0.608471 + 0.793576i \(0.291783\pi\)
\(720\) −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 \(-0.879023\pi\)
0.928642 0.370977i \(-0.120977\pi\)
\(728\) 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 0.737883 0.674929i \(-0.235826\pi\)
−0.215564 + 0.976490i \(0.569159\pi\)
\(734\) 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 0.933730 + 0.357977i \(0.116533\pi\)
−0.156848 + 0.987623i \(0.550133\pi\)
\(740\) 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 \(0.129656\pi\)
−0.918183 + 0.396156i \(0.870344\pi\)
\(744\) 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 0.891133 0.453742i \(-0.149911\pi\)
0.0526140 + 0.998615i \(0.483245\pi\)
\(752\) 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 \(-0.977885\pi\)
0.997588 0.0694192i \(-0.0221146\pi\)
\(758\) −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 −0.312527 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
\(766\) 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 −0.307205 0.951643i \(-0.599394\pi\)
0.670545 + 0.741869i \(0.266060\pi\)
\(774\) 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 0