Properties

Label 931.2.x.a.814.1
Level $931$
Weight $2$
Character 931.814
Analytic conductor $7.434$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.x (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.43407242818\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 814.1
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 931.814
Dual form 931.2.x.a.557.1

$q$-expansion

\(f(q)\) \(=\) \(q+(2.37939 - 0.866025i) q^{2} +(-0.500000 - 0.419550i) q^{3} +(3.37939 - 2.83564i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(-1.55303 - 0.565258i) q^{6} +(3.05303 - 5.28801i) q^{8} +(-0.446967 - 2.53487i) q^{9} +O(q^{10})\) \(q+(2.37939 - 0.866025i) q^{2} +(-0.500000 - 0.419550i) q^{3} +(3.37939 - 2.83564i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(-1.55303 - 0.565258i) q^{6} +(3.05303 - 5.28801i) q^{8} +(-0.446967 - 2.53487i) q^{9} +(-3.20574 - 1.16679i) q^{10} -1.18479 q^{11} -2.87939 q^{12} +(-2.55303 - 0.929228i) q^{13} +(0.152704 + 0.866025i) q^{15} +(1.15270 - 6.53731i) q^{16} +(0.673648 - 3.82045i) q^{17} +(-3.25877 - 5.64436i) q^{18} +(3.29813 + 2.84997i) q^{19} -5.94356 q^{20} +(-2.81908 + 1.02606i) q^{22} +(4.75877 + 1.73205i) q^{23} +(-3.74510 + 1.36310i) q^{24} +(-0.553033 - 3.13641i) q^{25} -6.87939 q^{26} +(-1.81908 + 3.15074i) q^{27} +(-3.56418 + 2.99070i) q^{29} +(1.11334 + 1.92836i) q^{30} +(1.91875 - 3.32337i) q^{31} +(-0.798133 - 4.52644i) q^{32} +(0.592396 + 0.497079i) q^{33} +(-1.70574 - 9.67372i) q^{34} +(-8.69846 - 7.29888i) q^{36} +(2.05303 - 3.55596i) q^{37} +(10.3157 + 3.92490i) q^{38} +(0.886659 + 1.53574i) q^{39} +(-7.73055 + 2.81369i) q^{40} +(9.38326 - 3.41523i) q^{41} +(-1.51114 + 8.57013i) q^{43} +(-4.00387 + 3.35965i) q^{44} +(-1.73396 + 3.00330i) q^{45} +12.8229 q^{46} +(0.0996702 + 0.565258i) q^{47} +(-3.31908 + 2.78504i) q^{48} +(-4.03209 - 6.98378i) q^{50} +(-1.93969 + 1.62760i) q^{51} +(-11.2626 + 4.09927i) q^{52} +(2.25490 - 1.89209i) q^{53} +(-1.59967 + 9.07218i) q^{54} +(1.22281 + 1.02606i) q^{55} +(-0.453363 - 2.80872i) q^{57} +(-5.89053 + 10.2027i) q^{58} +(-0.683448 + 3.87603i) q^{59} +(2.97178 + 2.49362i) q^{60} +(4.24510 + 1.54509i) q^{61} +(1.68732 - 9.56926i) q^{62} +(0.819078 + 1.41868i) q^{64} +(1.83022 + 3.17004i) q^{65} +(1.84002 + 0.669713i) q^{66} +(3.65270 + 1.32948i) q^{67} +(-8.55690 - 14.8210i) q^{68} +(-1.65270 - 2.86257i) q^{69} +(-1.20439 + 6.83045i) q^{71} +(-14.7690 - 5.37549i) q^{72} +(4.69459 + 3.93923i) q^{73} +(1.80541 - 10.2390i) q^{74} +(-1.03936 + 1.80023i) q^{75} +(19.2271 + 0.278817i) q^{76} +(3.43969 + 2.88624i) q^{78} +(1.70321 - 9.65939i) q^{79} +(-6.85117 + 5.74881i) q^{80} +(-5.02481 + 1.82888i) q^{81} +(19.3687 - 16.2523i) q^{82} +(-6.15910 - 10.6679i) q^{83} +(-4.00387 + 3.35965i) q^{85} +(3.82635 + 21.7003i) q^{86} +3.03684 q^{87} +(-3.61721 + 6.26519i) q^{88} +(-1.85844 + 1.55942i) q^{89} +(-1.52481 + 8.64766i) q^{90} +(20.9932 - 7.64090i) q^{92} +(-2.35369 + 0.856674i) q^{93} +(0.726682 + 1.25865i) q^{94} +(-0.935822 - 5.79769i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(5.64543 + 4.73708i) q^{97} +(0.529563 + 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} - 9 q^{10} - 6 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{23} - 21 q^{24} + 9 q^{25} - 30 q^{26} + 6 q^{27} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 24 q^{36} + 3 q^{38} + 12 q^{39} - 9 q^{40} + 21 q^{41} - 3 q^{43} - 15 q^{45} + 36 q^{46} + 15 q^{47} - 3 q^{48} - 15 q^{50} - 6 q^{51} - 21 q^{52} + 15 q^{53} - 24 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 12 q^{62} - 12 q^{64} - 12 q^{65} - 9 q^{66} + 24 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 15 q^{79} - 15 q^{80} - 3 q^{81} + 45 q^{82} + 24 q^{86} + 42 q^{87} + 9 q^{88} - 3 q^{89} + 18 q^{90} + 42 q^{92} + 27 q^{93} - 9 q^{94} - 24 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).

\(n\) \(248\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.37939 0.866025i 1.68248 0.612372i 0.688833 0.724920i \(-0.258123\pi\)
0.993646 + 0.112548i \(0.0359011\pi\)
\(3\) −0.500000 0.419550i −0.288675 0.242227i 0.486937 0.873437i \(-0.338114\pi\)
−0.775612 + 0.631210i \(0.782559\pi\)
\(4\) 3.37939 2.83564i 1.68969 1.41782i
\(5\) −1.03209 0.866025i −0.461564 0.387298i 0.382142 0.924104i \(-0.375187\pi\)
−0.843706 + 0.536805i \(0.819631\pi\)
\(6\) −1.55303 0.565258i −0.634023 0.230766i
\(7\) 0 0
\(8\) 3.05303 5.28801i 1.07941 1.86959i
\(9\) −0.446967 2.53487i −0.148989 0.844958i
\(10\) −3.20574 1.16679i −1.01374 0.368972i
\(11\) −1.18479 −0.357228 −0.178614 0.983919i \(-0.557161\pi\)
−0.178614 + 0.983919i \(0.557161\pi\)
\(12\) −2.87939 −0.831207
\(13\) −2.55303 0.929228i −0.708084 0.257722i −0.0372256 0.999307i \(-0.511852\pi\)
−0.670859 + 0.741585i \(0.734074\pi\)
\(14\) 0 0
\(15\) 0.152704 + 0.866025i 0.0394279 + 0.223607i
\(16\) 1.15270 6.53731i 0.288176 1.63433i
\(17\) 0.673648 3.82045i 0.163384 0.926595i −0.787332 0.616530i \(-0.788538\pi\)
0.950715 0.310065i \(-0.100351\pi\)
\(18\) −3.25877 5.64436i −0.768100 1.33039i
\(19\) 3.29813 + 2.84997i 0.756644 + 0.653827i
\(20\) −5.94356 −1.32902
\(21\) 0 0
\(22\) −2.81908 + 1.02606i −0.601029 + 0.218757i
\(23\) 4.75877 + 1.73205i 0.992272 + 0.361158i 0.786600 0.617463i \(-0.211840\pi\)
0.205673 + 0.978621i \(0.434062\pi\)
\(24\) −3.74510 + 1.36310i −0.764465 + 0.278243i
\(25\) −0.553033 3.13641i −0.110607 0.627282i
\(26\) −6.87939 −1.34916
\(27\) −1.81908 + 3.15074i −0.350082 + 0.606359i
\(28\) 0 0
\(29\) −3.56418 + 2.99070i −0.661851 + 0.555359i −0.910641 0.413198i \(-0.864412\pi\)
0.248790 + 0.968557i \(0.419967\pi\)
\(30\) 1.11334 + 1.92836i 0.203267 + 0.352069i
\(31\) 1.91875 3.32337i 0.344617 0.596895i −0.640667 0.767819i \(-0.721342\pi\)
0.985284 + 0.170924i \(0.0546753\pi\)
\(32\) −0.798133 4.52644i −0.141091 0.800169i
\(33\) 0.592396 + 0.497079i 0.103123 + 0.0865304i
\(34\) −1.70574 9.67372i −0.292531 1.65903i
\(35\) 0 0
\(36\) −8.69846 7.29888i −1.44974 1.21648i
\(37\) 2.05303 3.55596i 0.337517 0.584596i −0.646448 0.762958i \(-0.723746\pi\)
0.983965 + 0.178362i \(0.0570798\pi\)
\(38\) 10.3157 + 3.92490i 1.67342 + 0.636704i
\(39\) 0.886659 + 1.53574i 0.141979 + 0.245915i
\(40\) −7.73055 + 2.81369i −1.22231 + 0.444884i
\(41\) 9.38326 3.41523i 1.46542 0.533369i 0.518566 0.855038i \(-0.326466\pi\)
0.946852 + 0.321669i \(0.104244\pi\)
\(42\) 0 0
\(43\) −1.51114 + 8.57013i −0.230447 + 1.30693i 0.621545 + 0.783378i \(0.286505\pi\)
−0.851993 + 0.523554i \(0.824606\pi\)
\(44\) −4.00387 + 3.35965i −0.603606 + 0.506486i
\(45\) −1.73396 + 3.00330i −0.258483 + 0.447705i
\(46\) 12.8229 1.89064
\(47\) 0.0996702 + 0.565258i 0.0145384 + 0.0824513i 0.991214 0.132270i \(-0.0422267\pi\)
−0.976675 + 0.214722i \(0.931116\pi\)
\(48\) −3.31908 + 2.78504i −0.479068 + 0.401985i
\(49\) 0 0
\(50\) −4.03209 6.98378i −0.570223 0.987656i
\(51\) −1.93969 + 1.62760i −0.271611 + 0.227909i
\(52\) −11.2626 + 4.09927i −1.56185 + 0.568466i
\(53\) 2.25490 1.89209i 0.309734 0.259898i −0.474648 0.880176i \(-0.657425\pi\)
0.784382 + 0.620278i \(0.212980\pi\)
\(54\) −1.59967 + 9.07218i −0.217688 + 1.23457i
\(55\) 1.22281 + 1.02606i 0.164884 + 0.138354i
\(56\) 0 0
\(57\) −0.453363 2.80872i −0.0600494 0.372023i
\(58\) −5.89053 + 10.2027i −0.773464 + 1.33968i
\(59\) −0.683448 + 3.87603i −0.0889774 + 0.504616i 0.907450 + 0.420160i \(0.138026\pi\)
−0.996427 + 0.0844555i \(0.973085\pi\)
\(60\) 2.97178 + 2.49362i 0.383655 + 0.321925i
\(61\) 4.24510 + 1.54509i 0.543529 + 0.197829i 0.599169 0.800622i \(-0.295498\pi\)
−0.0556399 + 0.998451i \(0.517720\pi\)
\(62\) 1.68732 9.56926i 0.214290 1.21530i
\(63\) 0 0
\(64\) 0.819078 + 1.41868i 0.102385 + 0.177336i
\(65\) 1.83022 + 3.17004i 0.227011 + 0.393195i
\(66\) 1.84002 + 0.669713i 0.226491 + 0.0824360i
\(67\) 3.65270 + 1.32948i 0.446249 + 0.162421i 0.555363 0.831608i \(-0.312579\pi\)
−0.109114 + 0.994029i \(0.534801\pi\)
\(68\) −8.55690 14.8210i −1.03768 1.79731i
\(69\) −1.65270 2.86257i −0.198962 0.344613i
\(70\) 0 0
\(71\) −1.20439 + 6.83045i −0.142935 + 0.810625i 0.826067 + 0.563572i \(0.190573\pi\)
−0.969002 + 0.247053i \(0.920538\pi\)
\(72\) −14.7690 5.37549i −1.74055 0.633508i
\(73\) 4.69459 + 3.93923i 0.549461 + 0.461052i 0.874758 0.484560i \(-0.161020\pi\)
−0.325298 + 0.945612i \(0.605465\pi\)
\(74\) 1.80541 10.2390i 0.209874 1.19026i
\(75\) −1.03936 + 1.80023i −0.120015 + 0.207873i
\(76\) 19.2271 + 0.278817i 2.20551 + 0.0319825i
\(77\) 0 0
\(78\) 3.43969 + 2.88624i 0.389468 + 0.326803i
\(79\) 1.70321 9.65939i 0.191626 1.08677i −0.725516 0.688206i \(-0.758399\pi\)
0.917142 0.398561i \(-0.130490\pi\)
\(80\) −6.85117 + 5.74881i −0.765984 + 0.642737i
\(81\) −5.02481 + 1.82888i −0.558313 + 0.203209i
\(82\) 19.3687 16.2523i 2.13892 1.79476i
\(83\) −6.15910 10.6679i −0.676049 1.17095i −0.976161 0.217047i \(-0.930357\pi\)
0.300112 0.953904i \(-0.402976\pi\)
\(84\) 0 0
\(85\) −4.00387 + 3.35965i −0.434281 + 0.364405i
\(86\) 3.82635 + 21.7003i 0.412606 + 2.34001i
\(87\) 3.03684 0.325583
\(88\) −3.61721 + 6.26519i −0.385596 + 0.667872i
\(89\) −1.85844 + 1.55942i −0.196994 + 0.165298i −0.735949 0.677037i \(-0.763264\pi\)
0.538955 + 0.842335i \(0.318819\pi\)
\(90\) −1.52481 + 8.64766i −0.160730 + 0.911543i
\(91\) 0 0
\(92\) 20.9932 7.64090i 2.18869 0.796619i
\(93\) −2.35369 + 0.856674i −0.244067 + 0.0888330i
\(94\) 0.726682 + 1.25865i 0.0749515 + 0.129820i
\(95\) −0.935822 5.79769i −0.0960133 0.594830i
\(96\) −1.50000 + 2.59808i −0.153093 + 0.265165i
\(97\) 5.64543 + 4.73708i 0.573207 + 0.480977i 0.882708 0.469922i \(-0.155718\pi\)
−0.309502 + 0.950899i \(0.600162\pi\)
\(98\) 0 0
\(99\) 0.529563 + 3.00330i 0.0532231 + 0.301843i
\(100\) −10.7626 9.03093i −1.07626 0.903093i
\(101\) 0.376859 + 2.13727i 0.0374989 + 0.212667i 0.997800 0.0662996i \(-0.0211193\pi\)
−0.960301 + 0.278966i \(0.910008\pi\)
\(102\) −3.20574 + 5.55250i −0.317415 + 0.549779i
\(103\) 6.23783 + 10.8042i 0.614631 + 1.06457i 0.990449 + 0.137879i \(0.0440285\pi\)
−0.375818 + 0.926694i \(0.622638\pi\)
\(104\) −12.7083 + 10.6635i −1.24615 + 1.04564i
\(105\) 0 0
\(106\) 3.72668 6.45480i 0.361967 0.626946i
\(107\) −6.68004 −0.645784 −0.322892 0.946436i \(-0.604655\pi\)
−0.322892 + 0.946436i \(0.604655\pi\)
\(108\) 2.78699 + 15.8058i 0.268178 + 1.52091i
\(109\) −8.88326 + 3.23324i −0.850862 + 0.309688i −0.730392 0.683029i \(-0.760662\pi\)
−0.120470 + 0.992717i \(0.538440\pi\)
\(110\) 3.79813 + 1.38241i 0.362138 + 0.131807i
\(111\) −2.51842 + 0.916629i −0.239038 + 0.0870026i
\(112\) 0 0
\(113\) 1.31046 0.123278 0.0616388 0.998099i \(-0.480367\pi\)
0.0616388 + 0.998099i \(0.480367\pi\)
\(114\) −3.51114 6.29039i −0.328849 0.589149i
\(115\) −3.41147 5.90885i −0.318122 0.551003i
\(116\) −3.56418 + 20.2135i −0.330926 + 1.87677i
\(117\) −1.21436 + 6.88695i −0.112267 + 0.636699i
\(118\) 1.73055 + 9.81445i 0.159310 + 0.903493i
\(119\) 0 0
\(120\) 5.04576 + 1.83651i 0.460613 + 0.167649i
\(121\) −9.59627 −0.872388
\(122\) 11.4388 1.03562
\(123\) −6.12449 2.22913i −0.552226 0.200994i
\(124\) −2.93969 16.6718i −0.263992 1.49717i
\(125\) −5.51367 + 9.54996i −0.493158 + 0.854174i
\(126\) 0 0
\(127\) 13.6284 + 4.96032i 1.20932 + 0.440157i 0.866468 0.499232i \(-0.166385\pi\)
0.342853 + 0.939389i \(0.388607\pi\)
\(128\) 10.2194 + 8.57510i 0.903277 + 0.757939i
\(129\) 4.35117 3.65106i 0.383099 0.321458i
\(130\) 7.10014 + 5.95772i 0.622723 + 0.522527i
\(131\) 18.6138 6.77487i 1.62630 0.591923i 0.641729 0.766932i \(-0.278217\pi\)
0.984567 + 0.175008i \(0.0559952\pi\)
\(132\) 3.41147 0.296931
\(133\) 0 0
\(134\) 9.84255 0.850267
\(135\) 4.60607 1.67647i 0.396427 0.144288i
\(136\) −18.1459 15.2262i −1.55600 1.30564i
\(137\) 7.81702 6.55926i 0.667853 0.560395i −0.244576 0.969630i \(-0.578649\pi\)
0.912429 + 0.409235i \(0.134204\pi\)
\(138\) −6.41147 5.37987i −0.545781 0.457965i
\(139\) 1.56031 + 0.567905i 0.132344 + 0.0481691i 0.407343 0.913275i \(-0.366455\pi\)
−0.274999 + 0.961444i \(0.588678\pi\)
\(140\) 0 0
\(141\) 0.187319 0.324446i 0.0157751 0.0273232i
\(142\) 3.04963 + 17.2953i 0.255919 + 1.45139i
\(143\) 3.02481 + 1.10094i 0.252948 + 0.0920654i
\(144\) −17.0865 −1.42387
\(145\) 6.26857 0.520576
\(146\) 14.5817 + 5.30731i 1.20679 + 0.439236i
\(147\) 0 0
\(148\) −3.14543 17.8386i −0.258553 1.46633i
\(149\) 1.94609 11.0368i 0.159430 0.904172i −0.795194 0.606356i \(-0.792631\pi\)
0.954623 0.297816i \(-0.0962581\pi\)
\(150\) −0.914000 + 5.18355i −0.0746278 + 0.423235i
\(151\) 5.52094 + 9.56256i 0.449288 + 0.778190i 0.998340 0.0575986i \(-0.0183443\pi\)
−0.549052 + 0.835788i \(0.685011\pi\)
\(152\) 25.1400 8.73951i 2.03912 0.708868i
\(153\) −9.98545 −0.807276
\(154\) 0 0
\(155\) −4.85844 + 1.76833i −0.390239 + 0.142036i
\(156\) 7.35117 + 2.67561i 0.588564 + 0.214220i
\(157\) −10.3302 + 3.75989i −0.824441 + 0.300072i −0.719576 0.694414i \(-0.755664\pi\)
−0.104866 + 0.994486i \(0.533441\pi\)
\(158\) −4.31268 24.4584i −0.343098 1.94581i
\(159\) −1.92127 −0.152367
\(160\) −3.09627 + 5.36289i −0.244781 + 0.423974i
\(161\) 0 0
\(162\) −10.3721 + 8.70323i −0.814910 + 0.683791i
\(163\) 3.16637 + 5.48432i 0.248010 + 0.429565i 0.962973 0.269596i \(-0.0868902\pi\)
−0.714964 + 0.699161i \(0.753557\pi\)
\(164\) 22.0253 38.1489i 1.71989 2.97893i
\(165\) −0.180922 1.02606i −0.0140848 0.0798787i
\(166\) −23.8935 20.0490i −1.85450 1.55611i
\(167\) −2.39259 13.5690i −0.185144 1.05000i −0.925770 0.378087i \(-0.876582\pi\)
0.740626 0.671917i \(-0.234529\pi\)
\(168\) 0 0
\(169\) −4.30406 3.61154i −0.331082 0.277811i
\(170\) −6.61721 + 11.4613i −0.507517 + 0.879045i
\(171\) 5.75015 9.63419i 0.439725 0.736745i
\(172\) 19.1951 + 33.2468i 1.46361 + 2.53505i
\(173\) −23.7246 + 8.63506i −1.80375 + 0.656511i −0.805822 + 0.592157i \(0.798276\pi\)
−0.997927 + 0.0643540i \(0.979501\pi\)
\(174\) 7.22580 2.62998i 0.547787 0.199378i
\(175\) 0 0
\(176\) −1.36571 + 7.74535i −0.102945 + 0.583828i
\(177\) 1.96791 1.65127i 0.147917 0.124117i
\(178\) −3.07145 + 5.31991i −0.230215 + 0.398744i
\(179\) 5.83069 0.435806 0.217903 0.975970i \(-0.430078\pi\)
0.217903 + 0.975970i \(0.430078\pi\)
\(180\) 2.65657 + 15.0662i 0.198009 + 1.12297i
\(181\) 10.3892 8.71756i 0.772222 0.647971i −0.169055 0.985607i \(-0.554072\pi\)
0.941277 + 0.337635i \(0.109627\pi\)
\(182\) 0 0
\(183\) −1.47431 2.55358i −0.108984 0.188766i
\(184\) 23.6878 19.8764i 1.74629 1.46531i
\(185\) −5.19846 + 1.89209i −0.382199 + 0.139109i
\(186\) −4.85844 + 4.07672i −0.356238 + 0.298919i
\(187\) −0.798133 + 4.52644i −0.0583653 + 0.331006i
\(188\) 1.93969 + 1.62760i 0.141467 + 0.118705i
\(189\) 0 0
\(190\) −7.24763 12.9845i −0.525798 0.941994i
\(191\) 5.14203 8.90625i 0.372064 0.644434i −0.617819 0.786320i \(-0.711984\pi\)
0.989883 + 0.141887i \(0.0453169\pi\)
\(192\) 0.185670 1.05299i 0.0133996 0.0759927i
\(193\) 10.5719 + 8.87089i 0.760983 + 0.638541i 0.938383 0.345598i \(-0.112324\pi\)
−0.177399 + 0.984139i \(0.556768\pi\)
\(194\) 17.5351 + 6.38225i 1.25895 + 0.458219i
\(195\) 0.414878 2.35289i 0.0297100 0.168494i
\(196\) 0 0
\(197\) 3.97044 + 6.87700i 0.282882 + 0.489966i 0.972093 0.234594i \(-0.0753762\pi\)
−0.689211 + 0.724560i \(0.742043\pi\)
\(198\) 3.86097 + 6.68739i 0.274387 + 0.475252i
\(199\) −25.4047 9.24654i −1.80089 0.655470i −0.998258 0.0589938i \(-0.981211\pi\)
−0.802631 0.596476i \(-0.796567\pi\)
\(200\) −18.2738 6.65111i −1.29215 0.470305i
\(201\) −1.26857 2.19723i −0.0894781 0.154981i
\(202\) 2.74763 + 4.75903i 0.193322 + 0.334844i
\(203\) 0 0
\(204\) −1.93969 + 11.0005i −0.135806 + 0.770192i
\(205\) −12.6420 4.60132i −0.882957 0.321370i
\(206\) 24.1989 + 20.3053i 1.68602 + 1.41474i
\(207\) 2.26352 12.8370i 0.157325 0.892237i
\(208\) −9.01754 + 15.6188i −0.625254 + 1.08297i
\(209\) −3.90760 3.37662i −0.270295 0.233566i
\(210\) 0 0
\(211\) −6.18345 5.18853i −0.425686 0.357193i 0.404635 0.914478i \(-0.367399\pi\)
−0.830321 + 0.557285i \(0.811843\pi\)
\(212\) 2.25490 12.7882i 0.154867 0.878295i
\(213\) 3.46791 2.90992i 0.237617 0.199385i
\(214\) −15.8944 + 5.78509i −1.08652 + 0.395461i
\(215\) 8.98158 7.53644i 0.612539 0.513981i
\(216\) 11.1074 + 19.2386i 0.755764 + 1.30902i
\(217\) 0 0
\(218\) −18.3366 + 15.3863i −1.24191 + 1.04209i
\(219\) −0.694593 3.93923i −0.0469362 0.266189i
\(220\) 7.04189 0.474764
\(221\) −5.26991 + 9.12776i −0.354493 + 0.614000i
\(222\) −5.19846 + 4.36203i −0.348898 + 0.292760i
\(223\) −2.68732 + 15.2405i −0.179956 + 1.02058i 0.752310 + 0.658809i \(0.228940\pi\)
−0.932266 + 0.361773i \(0.882172\pi\)
\(224\) 0 0
\(225\) −7.70321 + 2.80374i −0.513547 + 0.186916i
\(226\) 3.11809 1.13489i 0.207412 0.0754919i
\(227\) −4.93629 8.54990i −0.327633 0.567477i 0.654409 0.756141i \(-0.272918\pi\)
−0.982042 + 0.188664i \(0.939584\pi\)
\(228\) −9.49660 8.20616i −0.628927 0.543466i
\(229\) −10.0594 + 17.4234i −0.664746 + 1.15137i 0.314608 + 0.949222i \(0.398127\pi\)
−0.979354 + 0.202152i \(0.935206\pi\)
\(230\) −13.2344 11.1050i −0.872652 0.732242i
\(231\) 0 0
\(232\) 4.93330 + 27.9781i 0.323887 + 1.83685i
\(233\) 2.70780 + 2.27211i 0.177394 + 0.148851i 0.727161 0.686467i \(-0.240839\pi\)
−0.549768 + 0.835318i \(0.685284\pi\)
\(234\) 3.07486 + 17.4384i 0.201010 + 1.13998i
\(235\) 0.386659 0.669713i 0.0252229 0.0436873i
\(236\) 8.68139 + 15.0366i 0.565110 + 0.978800i
\(237\) −4.90420 + 4.11511i −0.318562 + 0.267305i
\(238\) 0 0
\(239\) −5.98680 + 10.3694i −0.387254 + 0.670743i −0.992079 0.125615i \(-0.959910\pi\)
0.604825 + 0.796358i \(0.293243\pi\)
\(240\) 5.83750 0.376809
\(241\) 2.24035 + 12.7057i 0.144314 + 0.818444i 0.967916 + 0.251276i \(0.0808500\pi\)
−0.823602 + 0.567168i \(0.808039\pi\)
\(242\) −22.8332 + 8.31061i −1.46777 + 0.534226i
\(243\) 13.5360 + 4.92669i 0.868332 + 0.316047i
\(244\) 18.7271 6.81612i 1.19888 0.436358i
\(245\) 0 0
\(246\) −16.5030 −1.05219
\(247\) −5.77197 10.3408i −0.367262 0.657968i
\(248\) −11.7160 20.2927i −0.743967 1.28859i
\(249\) −1.39615 + 7.91799i −0.0884777 + 0.501782i
\(250\) −4.84864 + 27.4980i −0.306655 + 1.73913i
\(251\) 2.49407 + 14.1446i 0.157424 + 0.892798i 0.956536 + 0.291615i \(0.0941925\pi\)
−0.799112 + 0.601183i \(0.794696\pi\)
\(252\) 0 0
\(253\) −5.63816 2.05212i −0.354468 0.129016i
\(254\) 36.7229 2.30420
\(255\) 3.41147 0.213635
\(256\) 28.6634 + 10.4326i 1.79146 + 0.652040i
\(257\) 0.864370 + 4.90209i 0.0539180 + 0.305784i 0.999826 0.0186508i \(-0.00593707\pi\)
−0.945908 + 0.324435i \(0.894826\pi\)
\(258\) 7.19119 12.4555i 0.447704 0.775446i
\(259\) 0 0
\(260\) 15.1741 + 5.52293i 0.941059 + 0.342517i
\(261\) 9.17412 + 7.69800i 0.567863 + 0.476494i
\(262\) 38.4222 32.2401i 2.37373 1.99180i
\(263\) −18.4179 15.4544i −1.13569 0.952961i −0.136405 0.990653i \(-0.543555\pi\)
−0.999289 + 0.0376922i \(0.987999\pi\)
\(264\) 4.43717 1.61500i 0.273089 0.0993962i
\(265\) −3.96585 −0.243620
\(266\) 0 0
\(267\) 1.58347 0.0969070
\(268\) 16.1138 5.86495i 0.984307 0.358259i
\(269\) −10.0437 8.42767i −0.612375 0.513844i 0.283021 0.959114i \(-0.408663\pi\)
−0.895396 + 0.445270i \(0.853108\pi\)
\(270\) 9.50774 7.97794i 0.578623 0.485522i
\(271\) −20.3537 17.0788i −1.23640 1.03746i −0.997797 0.0663443i \(-0.978866\pi\)
−0.238602 0.971117i \(-0.576689\pi\)
\(272\) −24.1989 8.80769i −1.46728 0.534045i
\(273\) 0 0
\(274\) 12.9192 22.3767i 0.780478 1.35183i
\(275\) 0.655230 + 3.71599i 0.0395118 + 0.224083i
\(276\) −13.7023 4.98724i −0.824784 0.300197i
\(277\) −16.5107 −0.992034 −0.496017 0.868313i \(-0.665205\pi\)
−0.496017 + 0.868313i \(0.665205\pi\)
\(278\) 4.20439 0.252163
\(279\) −9.28194 3.37835i −0.555695 0.202256i
\(280\) 0 0
\(281\) −3.36706 19.0955i −0.200862 1.13914i −0.903820 0.427913i \(-0.859249\pi\)
0.702958 0.711231i \(-0.251862\pi\)
\(282\) 0.164725 0.934204i 0.00980925 0.0556310i
\(283\) −1.96404 + 11.1386i −0.116750 + 0.662123i 0.869119 + 0.494604i \(0.164687\pi\)
−0.985869 + 0.167519i \(0.946424\pi\)
\(284\) 15.2986 + 26.4980i 0.907805 + 1.57236i
\(285\) −1.96451 + 3.29147i −0.116367 + 0.194970i
\(286\) 8.15064 0.481958
\(287\) 0 0
\(288\) −11.1172 + 4.04633i −0.655088 + 0.238433i
\(289\) 1.83275 + 0.667066i 0.107809 + 0.0392392i
\(290\) 14.9153 5.42874i 0.875859 0.318787i
\(291\) −0.835275 4.73708i −0.0489647 0.277692i
\(292\) 27.0351 1.58211
\(293\) −1.94949 + 3.37662i −0.113891 + 0.197264i −0.917336 0.398115i \(-0.869665\pi\)
0.803445 + 0.595379i \(0.202998\pi\)
\(294\) 0 0
\(295\) 4.06212 3.40852i 0.236506 0.198452i
\(296\) −12.5360 21.7129i −0.728638 1.26204i
\(297\) 2.15523 3.73297i 0.125059 0.216609i
\(298\) −4.92767 27.9462i −0.285452 1.61888i
\(299\) −10.5398 8.84397i −0.609534 0.511460i
\(300\) 1.59240 + 9.03093i 0.0919370 + 0.521401i
\(301\) 0 0
\(302\) 21.4179 + 17.9717i 1.23246 + 1.03416i
\(303\) 0.708263 1.22675i 0.0406887 0.0704748i
\(304\) 22.4329 18.2757i 1.28661 1.04819i
\(305\) −3.04323 5.27103i −0.174255 0.301819i
\(306\) −23.7592 + 8.64766i −1.35823 + 0.494354i
\(307\) −21.7777 + 7.92642i −1.24292 + 0.452385i −0.878002 0.478657i \(-0.841124\pi\)
−0.364914 + 0.931041i \(0.618902\pi\)
\(308\) 0 0
\(309\) 1.41400 8.01919i 0.0804397 0.456196i
\(310\) −10.0287 + 8.41507i −0.569591 + 0.477944i
\(311\) 1.73055 2.99740i 0.0981306 0.169967i −0.812780 0.582570i \(-0.802047\pi\)
0.910911 + 0.412603i \(0.135380\pi\)
\(312\) 10.8280 0.613015
\(313\) −3.97477 22.5421i −0.224668 1.27415i −0.863320 0.504657i \(-0.831619\pi\)
0.638652 0.769496i \(-0.279492\pi\)
\(314\) −21.3234 + 17.8925i −1.20335 + 1.00973i
\(315\) 0 0
\(316\) −21.6348 37.4725i −1.21705 2.10799i
\(317\) 20.0096 16.7900i 1.12385 0.943021i 0.125056 0.992150i \(-0.460089\pi\)
0.998792 + 0.0491289i \(0.0156445\pi\)
\(318\) −4.57145 + 1.66387i −0.256354 + 0.0933053i
\(319\) 4.22281 3.54336i 0.236432 0.198390i
\(320\) 0.383256 2.17355i 0.0214246 0.121505i
\(321\) 3.34002 + 2.80261i 0.186422 + 0.156427i
\(322\) 0 0
\(323\) 13.1099 10.6805i 0.729456 0.594277i
\(324\) −11.7947 + 20.4291i −0.655263 + 1.13495i
\(325\) −1.50253 + 8.52125i −0.0833452 + 0.472674i
\(326\) 12.2836 + 10.3072i 0.680325 + 0.570860i
\(327\) 5.79813 + 2.11035i 0.320638 + 0.116703i
\(328\) 10.5876 60.0455i 0.584605 3.31546i
\(329\) 0 0
\(330\) −1.31908 2.28471i −0.0726128 0.125769i
\(331\) −9.52229 16.4931i −0.523392 0.906542i −0.999629 0.0272251i \(-0.991333\pi\)
0.476237 0.879317i \(-0.342000\pi\)
\(332\) −51.0642 18.5859i −2.80251 1.02003i
\(333\) −9.93154 3.61479i −0.544245 0.198089i
\(334\) −17.4440 30.2139i −0.954495 1.65323i
\(335\) −2.61856 4.53547i −0.143067 0.247799i
\(336\) 0 0
\(337\) 0.295445 1.67555i 0.0160939 0.0912731i −0.975703 0.219098i \(-0.929688\pi\)
0.991797 + 0.127825i \(0.0407996\pi\)
\(338\) −13.3687 4.86581i −0.727162 0.264665i
\(339\) −0.655230 0.549803i −0.0355872 0.0298612i
\(340\) −4.00387 + 22.7071i −0.217140 + 1.23146i
\(341\) −2.27332 + 3.93750i −0.123107 + 0.213228i
\(342\) 5.33837 27.9032i 0.288666 1.50883i
\(343\) 0 0
\(344\) 40.7053 + 34.1558i 2.19468 + 1.84156i
\(345\) −0.773318 + 4.38571i −0.0416341 + 0.236119i
\(346\) −48.9718 + 41.0923i −2.63274 + 2.20913i
\(347\) 4.60607 1.67647i 0.247267 0.0899977i −0.215414 0.976523i \(-0.569110\pi\)
0.462680 + 0.886525i \(0.346888\pi\)
\(348\) 10.2626 8.61138i 0.550135 0.461618i
\(349\) 14.0646 + 24.3607i 0.752863 + 1.30400i 0.946430 + 0.322910i \(0.104661\pi\)
−0.193566 + 0.981087i \(0.562006\pi\)
\(350\) 0 0
\(351\) 7.57192 6.35359i 0.404159 0.339130i
\(352\) 0.945622 + 5.36289i 0.0504018 + 0.285843i
\(353\) −8.31996 −0.442827 −0.221413 0.975180i \(-0.571067\pi\)
−0.221413 + 0.975180i \(0.571067\pi\)
\(354\) 3.25237 5.63328i 0.172862 0.299405i
\(355\) 7.15839 6.00660i 0.379928 0.318797i
\(356\) −1.85844 + 10.5397i −0.0984972 + 0.558605i
\(357\) 0 0
\(358\) 13.8735 5.04952i 0.733235 0.266876i
\(359\) −23.4256 + 8.52623i −1.23636 + 0.449997i −0.875770 0.482729i \(-0.839646\pi\)
−0.360587 + 0.932726i \(0.617423\pi\)
\(360\) 10.5876 + 18.3383i 0.558018 + 0.966516i
\(361\) 2.75537 + 18.7991i 0.145019 + 0.989429i
\(362\) 17.1702 29.7397i 0.902448 1.56309i
\(363\) 4.79813 + 4.02611i 0.251837 + 0.211316i
\(364\) 0 0
\(365\) −1.43376 8.13127i −0.0750466 0.425610i
\(366\) −5.71941 4.79915i −0.298958 0.250856i
\(367\) −0.449026 2.54655i −0.0234390 0.132929i 0.970843 0.239717i \(-0.0770546\pi\)
−0.994282 + 0.106788i \(0.965943\pi\)
\(368\) 16.8084 29.1130i 0.876198 1.51762i
\(369\) −12.8512 22.2589i −0.669005 1.15875i
\(370\) −10.7306 + 9.00400i −0.557855 + 0.468096i
\(371\) 0 0
\(372\) −5.52481 + 9.56926i −0.286448 + 0.496143i
\(373\) −23.3833 −1.21074 −0.605371 0.795943i \(-0.706975\pi\)
−0.605371 + 0.795943i \(0.706975\pi\)
\(374\) 2.02094 + 11.4613i 0.104501 + 0.592652i
\(375\) 6.76352 2.46172i 0.349267 0.127123i
\(376\) 3.29339 + 1.19869i 0.169843 + 0.0618179i
\(377\) 11.8785 4.32342i 0.611774 0.222668i
\(378\) 0 0
\(379\) 25.4388 1.30670 0.653352 0.757054i \(-0.273362\pi\)
0.653352 + 0.757054i \(0.273362\pi\)
\(380\) −19.6027 16.9390i −1.00560 0.868950i
\(381\) −4.73308 8.19793i −0.242483 0.419993i
\(382\) 4.52182 25.6445i 0.231357 1.31209i
\(383\) −4.77197 + 27.0632i −0.243836 + 1.38287i 0.579343 + 0.815084i \(0.303309\pi\)
−0.823179 + 0.567781i \(0.807802\pi\)
\(384\) −1.51202 8.57510i −0.0771600 0.437596i
\(385\) 0 0
\(386\) 32.8371 + 11.9517i 1.67136 + 0.608327i
\(387\) 22.3996 1.13864
\(388\) 32.5107 1.65048
\(389\) 3.14068 + 1.14311i 0.159239 + 0.0579582i 0.420410 0.907334i \(-0.361886\pi\)
−0.261171 + 0.965293i \(0.584109\pi\)
\(390\) −1.05051 5.95772i −0.0531945 0.301681i
\(391\) 9.82295 17.0138i 0.496768 0.860427i
\(392\) 0 0
\(393\) −12.1493 4.42198i −0.612851 0.223060i
\(394\) 15.4029 + 12.9245i 0.775985 + 0.651128i
\(395\) −10.1231 + 8.49432i −0.509351 + 0.427396i
\(396\) 10.3059 + 8.64766i 0.517890 + 0.434561i
\(397\) 12.3319 4.48843i 0.618919 0.225268i −0.0134823 0.999909i \(-0.504292\pi\)
0.632401 + 0.774641i \(0.282069\pi\)
\(398\) −68.4552 −3.43135
\(399\) 0 0
\(400\) −21.1411 −1.05706
\(401\) −16.0817 + 5.85327i −0.803083 + 0.292298i −0.710763 0.703431i \(-0.751650\pi\)
−0.0923194 + 0.995729i \(0.529428\pi\)
\(402\) −4.92127 4.12944i −0.245451 0.205958i
\(403\) −7.98680 + 6.70172i −0.397851 + 0.333836i
\(404\) 7.33409 + 6.15403i 0.364885 + 0.306175i
\(405\) 6.76991 + 2.46405i 0.336400 + 0.122440i
\(406\) 0 0
\(407\) −2.43242 + 4.21307i −0.120571 + 0.208834i
\(408\) 2.68479 + 15.2262i 0.132917 + 0.753810i
\(409\) 8.26739 + 3.00908i 0.408796 + 0.148790i 0.538229 0.842799i \(-0.319094\pi\)
−0.129433 + 0.991588i \(0.541316\pi\)
\(410\) −34.0651 −1.68236
\(411\) −6.66044 −0.328535
\(412\) 51.7169 + 18.8234i 2.54791 + 0.927364i
\(413\) 0 0
\(414\) −5.73143 32.5046i −0.281684 1.59751i
\(415\) −2.88191 + 16.3441i −0.141467 + 0.802302i
\(416\) −2.16843 + 12.2978i −0.106316 + 0.602949i
\(417\) −0.541889 0.938579i −0.0265364 0.0459624i
\(418\) −12.2219 4.65020i −0.597794 0.227449i
\(419\) 6.84018 0.334165 0.167082 0.985943i \(-0.446565\pi\)
0.167082 + 0.985943i \(0.446565\pi\)
\(420\) 0 0
\(421\) 4.53209 1.64955i 0.220880 0.0803939i −0.229210 0.973377i \(-0.573614\pi\)
0.450090 + 0.892983i \(0.351392\pi\)
\(422\) −19.2062 6.99049i −0.934943 0.340292i
\(423\) 1.38831 0.505303i 0.0675018 0.0245687i
\(424\) −3.12108 17.7005i −0.151573 0.859614i
\(425\) −12.3550 −0.599307
\(426\) 5.73143 9.92713i 0.277689 0.480971i
\(427\) 0 0
\(428\) −22.5744 + 18.9422i −1.09118 + 0.915606i
\(429\) −1.05051 1.81953i −0.0507190 0.0878478i
\(430\) 14.8439 25.7104i 0.715836 1.23986i
\(431\) 0.226377 + 1.28385i 0.0109042 + 0.0618407i 0.989774 0.142642i \(-0.0455598\pi\)
−0.978870 + 0.204483i \(0.934449\pi\)
\(432\) 18.5005 + 15.5237i 0.890104 + 0.746886i
\(433\) 3.44238 + 19.5227i 0.165430 + 0.938202i 0.948620 + 0.316419i \(0.102480\pi\)
−0.783189 + 0.621783i \(0.786409\pi\)
\(434\) 0 0
\(435\) −3.13429 2.62998i −0.150277 0.126098i
\(436\) −20.8516 + 36.1161i −0.998612 + 1.72965i
\(437\) 10.7588 + 19.2749i 0.514662 + 0.922042i
\(438\) −5.06418 8.77141i −0.241976 0.419114i
\(439\) 32.4825 11.8227i 1.55031 0.564265i 0.581817 0.813320i \(-0.302342\pi\)
0.968489 + 0.249055i \(0.0801200\pi\)
\(440\) 9.15910 3.33364i 0.436643 0.158925i
\(441\) 0 0
\(442\) −4.63429 + 26.2823i −0.220430 + 1.25012i
\(443\) 13.0305 10.9339i 0.619098 0.519485i −0.278422 0.960459i \(-0.589811\pi\)
0.897520 + 0.440974i \(0.145367\pi\)
\(444\) −5.91147 + 10.2390i −0.280546 + 0.485920i
\(445\) 3.26857 0.154945
\(446\) 6.80453 + 38.5904i 0.322204 + 1.82731i
\(447\) −5.60354 + 4.70193i −0.265038 + 0.222394i
\(448\) 0 0
\(449\) −18.7049 32.3978i −0.882737 1.52895i −0.848286 0.529539i \(-0.822365\pi\)
−0.0344512 0.999406i \(-0.510968\pi\)
\(450\) −15.9008 + 13.3424i −0.749571 + 0.628965i
\(451\) −11.1172 + 4.04633i −0.523489 + 0.190534i
\(452\) 4.42855 3.71599i 0.208301 0.174786i
\(453\) 1.25150 7.09759i 0.0588004 0.333474i
\(454\) −19.1498 16.0686i −0.898743 0.754135i
\(455\) 0 0
\(456\) −16.2366 6.17771i −0.760351 0.289298i
\(457\) −4.55556 + 7.89046i −0.213100 + 0.369100i −0.952683 0.303965i \(-0.901689\pi\)
0.739583 + 0.673065i \(0.235023\pi\)
\(458\) −8.84611 + 50.1688i −0.413352 + 2.34423i
\(459\) 10.8118 + 9.07218i 0.504652 + 0.423453i
\(460\) −28.2841 10.2946i −1.31875 0.479986i
\(461\) −4.24540 + 24.0769i −0.197728 + 1.12137i 0.710751 + 0.703443i \(0.248355\pi\)
−0.908480 + 0.417929i \(0.862756\pi\)
\(462\) 0 0
\(463\) 0.125362 + 0.217134i 0.00582609 + 0.0100911i 0.868924 0.494946i \(-0.164812\pi\)
−0.863098 + 0.505037i \(0.831479\pi\)
\(464\) 15.4427 + 26.7475i 0.716909 + 1.24172i
\(465\) 3.17112 + 1.15419i 0.147057 + 0.0535245i
\(466\) 8.41060 + 3.06121i 0.389613 + 0.141808i
\(467\) −7.68092 13.3037i −0.355431 0.615624i 0.631761 0.775163i \(-0.282332\pi\)
−0.987192 + 0.159539i \(0.948999\pi\)
\(468\) 15.4251 + 26.7171i 0.713028 + 1.23500i
\(469\) 0 0
\(470\) 0.340022 1.92836i 0.0156841 0.0889487i
\(471\) 6.74257 + 2.45410i 0.310681 + 0.113079i
\(472\) 18.4099 + 15.4477i 0.847383 + 0.711039i
\(473\) 1.79039 10.1538i 0.0823223 0.466873i
\(474\) −8.10519 + 14.0386i −0.372284 + 0.644814i
\(475\) 7.11468 11.9204i 0.326444 0.546946i
\(476\) 0 0
\(477\) −5.80406 4.87019i −0.265750 0.222991i
\(478\) −5.26470 + 29.8576i −0.240802 + 1.36565i
\(479\) −0.550974 + 0.462322i −0.0251746 + 0.0211240i −0.655288 0.755379i \(-0.727453\pi\)
0.630114 + 0.776503i \(0.283008\pi\)
\(480\) 3.79813 1.38241i 0.173360 0.0630980i
\(481\) −8.54576 + 7.17074i −0.389653 + 0.326958i
\(482\) 16.3341 + 28.2915i 0.743998 + 1.28864i
\(483\) 0 0
\(484\) −32.4295 + 27.2116i −1.47407 + 1.23689i
\(485\) −1.72416 9.77817i −0.0782899 0.444004i
\(486\) 36.4739 1.65449
\(487\) −5.87346 + 10.1731i −0.266152 + 0.460988i −0.967865 0.251471i \(-0.919086\pi\)
0.701713 + 0.712460i \(0.252419\pi\)
\(488\) 21.1309 17.7309i 0.956550 0.802641i
\(489\) 0.717759 4.07061i 0.0324582 0.184079i
\(490\) 0 0
\(491\) −0.0834734 + 0.0303818i −0.00376710 + 0.00137111i −0.343903 0.939005i \(-0.611749\pi\)
0.340136 + 0.940376i \(0.389527\pi\)
\(492\) −27.0180 + 9.83375i −1.21807 + 0.443340i
\(493\) 9.02481 + 15.6314i 0.406457 + 0.704005i
\(494\) −22.6891 19.6060i −1.02083 0.882117i
\(495\) 2.05438 3.55829i 0.0923374 0.159933i
\(496\) −19.5141 16.3743i −0.876211 0.735228i
\(497\) 0 0
\(498\) 3.53519 + 20.0490i 0.158416 + 0.898419i
\(499\) 11.2536 + 9.44285i 0.503778 + 0.422720i 0.858934 0.512087i \(-0.171128\pi\)
−0.355155 + 0.934807i \(0.615572\pi\)
\(500\) 8.44743 + 47.9078i 0.377781 + 2.14250i
\(501\) −4.49660 + 7.78833i −0.200893 + 0.347957i
\(502\) 18.1839 + 31.4955i 0.811588 + 1.40571i
\(503\) −3.75671 + 3.15225i −0.167503 + 0.140552i −0.722686 0.691176i \(-0.757093\pi\)
0.555183 + 0.831728i \(0.312648\pi\)
\(504\) 0 0
\(505\) 1.46198 2.53223i 0.0650573 0.112683i
\(506\) −15.1925 −0.675390
\(507\) 0.636812 + 3.61154i 0.0282818 + 0.160394i
\(508\) 60.1211 21.8823i 2.66744 0.970870i
\(509\) −6.02704 2.19366i −0.267144 0.0972324i 0.204975 0.978767i \(-0.434289\pi\)
−0.472119 + 0.881535i \(0.656511\pi\)
\(510\) 8.11721 2.95442i 0.359436 0.130824i
\(511\) 0 0
\(512\) 50.5553 2.23425
\(513\) −14.9791 + 5.20723i −0.661341 + 0.229905i
\(514\) 6.30200 + 10.9154i 0.277969 + 0.481457i
\(515\) 2.91875 16.5530i 0.128615 0.729414i
\(516\) 4.35117 24.6767i 0.191549 1.08633i
\(517\) −0.118089 0.669713i −0.00519353 0.0294540i
\(518\) 0 0
\(519\) 15.4851 + 5.63613i 0.679723 + 0.247399i
\(520\) 22.3509 0.980153
\(521\) −35.8135 −1.56902 −0.784508 0.620119i \(-0.787084\pi\)
−0.784508 + 0.620119i \(0.787084\pi\)
\(522\) 28.4954 + 10.3715i 1.24721 + 0.453947i
\(523\) 6.73277 + 38.1835i 0.294404 + 1.66965i 0.669616 + 0.742707i \(0.266459\pi\)
−0.375213 + 0.926939i \(0.622430\pi\)
\(524\) 43.6921 75.6770i 1.90870 3.30596i
\(525\) 0 0
\(526\) −57.2071 20.8217i −2.49435 0.907869i
\(527\) −11.4042 9.56926i −0.496775 0.416844i
\(528\) 3.93242 3.29969i 0.171137 0.143601i
\(529\) 2.02687 + 1.70075i 0.0881250 + 0.0739456i
\(530\) −9.43629 + 3.43453i −0.409886 + 0.149186i
\(531\) 10.1307 0.439636
\(532\) 0 0
\(533\) −27.1293 −1.17510
\(534\) 3.76769 1.37133i 0.163044 0.0593432i
\(535\) 6.89440 + 5.78509i 0.298071 + 0.250111i
\(536\) 18.1821 15.2566i 0.785347 0.658985i
\(537\) −2.91534 2.44626i −0.125806 0.105564i
\(538\) −31.1964 11.3546i −1.34497 0.489530i
\(539\) 0 0
\(540\) 10.8118 18.7266i 0.465266 0.805864i
\(541\) 1.64796 + 9.34602i 0.0708512 + 0.401817i 0.999522 + 0.0309122i \(0.00984123\pi\)
−0.928671 + 0.370905i \(0.879048\pi\)
\(542\) −63.2199 23.0102i −2.71553 0.988372i
\(543\) −8.85204 −0.379878
\(544\) −17.8307 −0.764484
\(545\) 11.9684 + 4.35613i 0.512669 + 0.186596i
\(546\) 0 0
\(547\) 2.46791 + 13.9962i 0.105520 + 0.598435i 0.991011 + 0.133779i \(0.0427111\pi\)
−0.885491 + 0.464657i \(0.846178\pi\)
\(548\) 7.81702 44.3325i 0.333926 1.89379i
\(549\) 2.01919 11.4514i 0.0861769 0.488734i
\(550\) 4.77719 + 8.27433i 0.203700 + 0.352819i
\(551\) −20.2785 0.294064i −0.863895 0.0125275i
\(552\) −20.1830 −0.859047
\(553\) 0 0
\(554\) −39.2854 + 14.2987i −1.66908 + 0.607494i
\(555\) 3.39306 + 1.23497i 0.144027 + 0.0524216i
\(556\) 6.88326 2.50530i 0.291915 0.106248i
\(557\) 3.91400 + 22.1974i 0.165842 + 0.940534i 0.948193 + 0.317696i \(0.102909\pi\)
−0.782351 + 0.622838i \(0.785980\pi\)
\(558\) −25.0110 −1.05880
\(559\) 11.8216 20.4756i 0.500001 0.866026i
\(560\) 0 0
\(561\) 2.29813 1.92836i 0.0970273 0.0814155i
\(562\) −24.5488 42.5197i −1.03553 1.79358i
\(563\) 21.4859 37.2147i 0.905524 1.56841i 0.0853106 0.996354i \(-0.472812\pi\)
0.820213 0.572058i \(-0.193855\pi\)
\(564\) −0.286989 1.62760i −0.0120844 0.0685341i
\(565\) −1.35251 1.13489i −0.0569006 0.0477452i
\(566\) 4.97313 + 28.2040i 0.209036 + 1.18550i
\(567\) 0 0
\(568\) 32.4424 + 27.2224i 1.36125 + 1.14223i
\(569\) −3.71348 + 6.43193i −0.155677 + 0.269641i −0.933305 0.359084i \(-0.883089\pi\)
0.777628 + 0.628724i \(0.216423\pi\)
\(570\) −1.82383 + 9.53298i −0.0763916 + 0.399293i
\(571\) −2.02229 3.50271i −0.0846301 0.146584i 0.820603 0.571498i \(-0.193638\pi\)
−0.905234 + 0.424914i \(0.860304\pi\)
\(572\) 13.3439 4.85678i 0.557936 0.203072i
\(573\) −6.30763 + 2.29579i −0.263505 + 0.0959080i
\(574\) 0 0
\(575\) 2.80066 15.8833i 0.116796 0.662381i
\(576\) 3.23009 2.71036i 0.134587 0.112932i
\(577\) −1.61721 + 2.80109i −0.0673254 + 0.116611i −0.897723 0.440560i \(-0.854780\pi\)
0.830398 + 0.557171i \(0.188113\pi\)
\(578\) 4.93851 0.205415
\(579\) −1.56418 8.87089i −0.0650050 0.368662i
\(580\) 21.1839 17.7754i 0.879614 0.738084i
\(581\) 0 0
\(582\) −6.08987 10.5480i −0.252433 0.437227i
\(583\) −2.67159 + 2.24173i −0.110646 + 0.0928429i
\(584\) 35.1634 12.7984i 1.45507 0.529603i
\(585\) 7.21760 6.05628i 0.298411 0.250396i
\(586\) −1.71436 + 9.72259i −0.0708194 + 0.401637i
\(587\) −31.2610 26.2311i −1.29028 1.08267i −0.991738 0.128279i \(-0.959055\pi\)
−0.298543 0.954396i \(-0.596501\pi\)
\(588\) 0 0
\(589\) 15.7998 5.49254i 0.651019 0.226316i
\(590\) 6.71348 11.6281i 0.276390 0.478721i
\(591\) 0.900025 5.10430i 0.0370221 0.209963i
\(592\) −20.8799 17.5203i −0.858157 0.720079i
\(593\) 10.3969 + 3.78417i 0.426951 + 0.155397i 0.546553 0.837425i \(-0.315940\pi\)
−0.119602 + 0.992822i \(0.538162\pi\)
\(594\) 1.89528 10.7487i 0.0777642 0.441023i
\(595\) 0 0
\(596\) −24.7199 42.8161i −1.01257 1.75381i
\(597\) 8.82295 + 15.2818i 0.361099 + 0.625442i
\(598\) −32.7374 11.9154i −1.33873 0.487259i
\(599\) 41.8705 + 15.2396i 1.71078 + 0.622674i 0.996979 0.0776714i \(-0.0247485\pi\)
0.713804 + 0.700346i \(0.246971\pi\)
\(600\) 6.34642 + 10.9923i 0.259091 + 0.448760i
\(601\) 2.49953 + 4.32932i 0.101958 + 0.176597i 0.912491 0.409096i \(-0.134156\pi\)
−0.810533 + 0.585693i \(0.800823\pi\)
\(602\) 0 0
\(603\) 1.73742 9.85337i 0.0707530 0.401260i
\(604\) 45.7734 + 16.6601i 1.86249 + 0.677892i
\(605\) 9.90420 + 8.31061i 0.402663 + 0.337874i
\(606\) 0.622836 3.53228i 0.0253010 0.143489i
\(607\) 15.5940 27.0097i 0.632943 1.09629i −0.354004 0.935244i \(-0.615180\pi\)
0.986947 0.161045i \(-0.0514865\pi\)
\(608\) 10.2679 17.2035i 0.416417 0.697692i
\(609\) 0 0
\(610\) −11.8059 9.90630i −0.478006 0.401095i
\(611\) 0.270792 1.53574i 0.0109551 0.0621293i
\(612\) −33.7447 + 28.3152i −1.36405 + 1.14457i
\(613\) −15.3824 + 5.59873i −0.621288 + 0.226130i −0.633435 0.773796i \(-0.718356\pi\)
0.0121468 + 0.999926i \(0.496133\pi\)
\(614\) −44.9530 + 37.7200i −1.81415 + 1.52226i
\(615\) 4.39053 + 7.60462i 0.177043 + 0.306648i
\(616\) 0 0
\(617\) 12.3014 10.3221i 0.495235 0.415551i −0.360663 0.932696i \(-0.617450\pi\)
0.855898 + 0.517145i \(0.173005\pi\)
\(618\) −3.58037 20.3053i −0.144024 0.816799i
\(619\) 23.8425 0.958313 0.479156 0.877730i \(-0.340943\pi\)
0.479156 + 0.877730i \(0.340943\pi\)
\(620\) −11.4042 + 19.7527i −0.458004 + 0.793286i
\(621\) −14.1138 + 11.8429i −0.566368 + 0.475239i
\(622\) 1.52182 8.63068i 0.0610195 0.346059i
\(623\) 0 0
\(624\) 11.0617 4.02611i 0.442820 0.161173i
\(625\) −1.00253 + 0.364890i −0.0401010 + 0.0145956i
\(626\) −28.9795 50.1940i −1.15825 2.00616i
\(627\) 0.537141 + 3.32774i 0.0214514 + 0.132897i
\(628\) −24.2481 + 41.9989i −0.967604 + 1.67594i
\(629\) −12.2023 10.2390i −0.486539 0.408255i
\(630\) 0 0
\(631\) 3.72874 + 21.1467i 0.148439 + 0.841838i 0.964541 + 0.263931i \(0.0850193\pi\)
−0.816103 + 0.577907i \(0.803870\pi\)
\(632\) −45.8790 38.4970i −1.82497 1.53133i
\(633\) 0.914878 + 5.18853i 0.0363631 + 0.206226i
\(634\) 33.0699 57.2787i 1.31337 2.27483i
\(635\) −9.76991 16.9220i −0.387707 0.671529i
\(636\) −6.49273 + 5.44804i −0.257453 + 0.216029i
\(637\) 0 0
\(638\) 6.97906 12.0881i 0.276303 0.478572i
\(639\) 17.8527 0.706240
\(640\) −3.12108 17.7005i −0.123372 0.699675i
\(641\) −11.9846 + 4.36203i −0.473362 + 0.172290i −0.567675 0.823253i \(-0.692157\pi\)
0.0943126 + 0.995543i \(0.469935\pi\)
\(642\) 10.3743 + 3.77595i 0.409442 + 0.149025i
\(643\) −26.8828 + 9.78456i −1.06016 + 0.385865i −0.812487 0.582979i \(-0.801887\pi\)
−0.247669 + 0.968845i \(0.579665\pi\)
\(644\) 0 0
\(645\) −7.65270 −0.301325
\(646\) 21.9440 36.7665i 0.863376 1.44656i
\(647\) −8.35638 14.4737i −0.328523 0.569019i 0.653696 0.756757i \(-0.273218\pi\)
−0.982219 + 0.187738i \(0.939884\pi\)
\(648\) −5.66978 + 32.1549i −0.222730 + 1.26316i
\(649\) 0.809745 4.59229i 0.0317853 0.180263i
\(650\) 3.80453 + 21.5766i 0.149226 + 0.846302i
\(651\) 0 0
\(652\) 26.2520 + 9.55493i 1.02811 + 0.374200i
\(653\) 27.0000 1.05659 0.528296 0.849060i \(-0.322831\pi\)
0.528296 + 0.849060i \(0.322831\pi\)
\(654\) 15.6236 0.610931
\(655\) −25.0783 9.12776i −0.979891 0.356651i
\(656\) −11.5103 65.2780i −0.449400 2.54868i
\(657\) 7.88713 13.6609i 0.307706 0.532963i
\(658\) 0 0
\(659\) 41.2533 + 15.0150i 1.60700 + 0.584900i 0.980844 0.194797i \(-0.0624047\pi\)
0.626157 + 0.779697i \(0.284627\pi\)
\(660\) −3.52094 2.95442i −0.137053 0.115001i
\(661\) −8.23964 + 6.91388i −0.320485 + 0.268919i −0.788809 0.614638i \(-0.789302\pi\)
0.468325 + 0.883556i \(0.344858\pi\)
\(662\) −36.9406 30.9969i −1.43574 1.20473i
\(663\) 6.46451 2.35289i 0.251061 0.0913786i
\(664\) −75.2158 −2.91894
\(665\) 0 0
\(666\) −26.7615 −1.03699
\(667\) −22.1411 + 8.05872i −0.857309 + 0.312035i
\(668\) −46.5624 39.0705i −1.80155 1.51168i
\(669\) 7.73783 6.49281i 0.299162 0.251026i
\(670\) −10.1584 8.52390i −0.392453 0.329307i
\(671\) −5.02956 1.83061i −0.194164 0.0706700i
\(672\) 0 0
\(673\) −2.32888 + 4.03374i −0.0897717 + 0.155489i −0.907415 0.420237i \(-0.861947\pi\)
0.817643 + 0.575726i \(0.195280\pi\)
\(674\) −0.748093 4.24265i −0.0288155 0.163421i
\(675\) 10.8880 + 3.96291i 0.419079 + 0.152532i
\(676\) −24.7861 −0.953312
\(677\) 3.26857 0.125621 0.0628107 0.998025i \(-0.479994\pi\)
0.0628107 + 0.998025i \(0.479994\pi\)
\(678\) −2.03519 0.740748i −0.0781609 0.0284482i
\(679\) 0 0
\(680\) 5.54189 + 31.4296i 0.212522 + 1.20527i
\(681\) −1.11897 + 6.34597i −0.0428789 + 0.243178i
\(682\) −1.99912 + 11.3376i −0.0765504 + 0.434139i
\(683\) −3.10947 5.38576i −0.118981 0.206080i 0.800383 0.599488i \(-0.204629\pi\)
−0.919364 + 0.393408i \(0.871296\pi\)
\(684\) −7.88713 48.8630i −0.301572 1.86832i
\(685\) −13.7483 −0.525297
\(686\) 0 0
\(687\) 12.3397 4.49129i 0.470790 0.171353i
\(688\) 54.2836 + 19.7576i 2.06954 + 0.753253i
\(689\) −7.51501 + 2.73524i −0.286299 + 0.104204i
\(690\) 1.95811 + 11.1050i 0.0745440 + 0.422760i
\(691\) 22.2175 0.845194 0.422597 0.906318i \(-0.361119\pi\)
0.422597 + 0.906318i \(0.361119\pi\)
\(692\) −55.6887 + 96.4557i −2.11697 + 3.66670i
\(693\) 0 0
\(694\) 9.50774 7.97794i 0.360909 0.302839i
\(695\) −1.11856 1.93739i −0.0424292 0.0734896i
\(696\) 9.27156 16.0588i 0.351438 0.608708i
\(697\) −6.72668 38.1489i −0.254791 1.44499i
\(698\) 54.5622 + 45.7831i 2.06521 + 1.73292i
\(699\) −0.400634 2.27211i −0.0151534 0.0859391i
\(700\) 0 0
\(701\) −21.2750 17.8518i −0.803544 0.674254i 0.145513 0.989356i \(-0.453517\pi\)
−0.949058 + 0.315102i \(0.897961\pi\)
\(702\) 12.5141 21.6751i 0.472316 0.818075i
\(703\) 16.9055 5.87695i 0.637605 0.221653i
\(704\) −0.970437 1.68085i −0.0365747 0.0633493i
\(705\) −0.474308 + 0.172634i −0.0178635 + 0.00650177i
\(706\) −19.7964 + 7.20529i −0.745047 + 0.271175i
\(707\) 0 0
\(708\) 1.96791 11.1606i 0.0739586 0.419440i
\(709\) −4.67886 + 3.92603i −0.175718 + 0.147445i −0.726405 0.687267i \(-0.758810\pi\)
0.550687 + 0.834712i \(0.314366\pi\)
\(710\) 11.8307 20.4914i 0.443998 0.769027i
\(711\) −25.2466 −0.946822
\(712\) 2.57233 + 14.5884i 0.0964021 + 0.546724i
\(713\) 14.8871 12.4918i 0.557527 0.467821i
\(714\) 0 0
\(715\) −2.16843 3.75584i −0.0810948 0.140460i
\(716\) 19.7041 16.5337i 0.736378 0.617895i
\(717\) 7.34389 2.67296i 0.274263 0.0998235i
\(718\) −48.3546 + 40.5743i −1.80458 + 1.51422i
\(719\) 6.72432 38.1355i 0.250775 1.42221i −0.555915 0.831239i \(-0.687632\pi\)
0.806690 0.590975i \(-0.201257\pi\)
\(720\) 17.6348 + 14.7973i 0.657208 + 0.551463i
\(721\) 0 0
\(722\) 22.8366 + 42.3442i 0.849891 + 1.57589i
\(723\) 4.21048 7.29277i 0.156590 0.271221i
\(724\) 10.3892 58.9200i 0.386111 2.18974i
\(725\) 11.3512 + 9.52476i 0.421572 + 0.353741i
\(726\) 14.9033 + 5.42437i 0.553114 + 0.201317i
\(727\) −1.92366 + 10.9096i −0.0713445 + 0.404615i 0.928132 + 0.372252i \(0.121414\pi\)
−0.999476 + 0.0323628i \(0.989697\pi\)
\(728\) 0 0
\(729\) 3.31996 + 5.75033i 0.122961 + 0.212975i
\(730\) −10.4534 18.1058i −0.386896 0.670124i
\(731\) 31.7237 + 11.5465i 1.17335 + 0.427063i
\(732\) −12.2233 4.44891i −0.451785 0.164436i
\(733\) 7.90373 + 13.6897i 0.291931 + 0.505639i 0.974266 0.225400i \(-0.0723689\pi\)
−0.682335 + 0.731039i \(0.739036\pi\)
\(734\) −3.27379 5.67036i −0.120838 0.209297i
\(735\) 0 0
\(736\) 4.04189 22.9227i 0.148986 0.844942i
\(737\) −4.32770 1.57515i −0.159413 0.0580215i
\(738\) −49.8546 41.8330i −1.83517 1.53989i
\(739\) 0.269037 1.52579i 0.00989670 0.0561270i −0.979459 0.201641i \(-0.935373\pi\)
0.989356 + 0.145514i \(0.0464836\pi\)
\(740\) −12.2023 + 21.1351i −0.448567 + 0.776940i
\(741\) −1.45249 + 7.59202i −0.0533584 + 0.278900i
\(742\) 0 0
\(743\) 29.2349 + 24.5310i 1.07252 + 0.899955i 0.995279 0.0970576i \(-0.0309431\pi\)
0.0772453 + 0.997012i \(0.475388\pi\)
\(744\) −2.65580 + 15.0618i −0.0973664 + 0.552193i
\(745\) −11.5667 + 9.70562i −0.423771 + 0.355586i
\(746\) −55.6379 + 20.2505i −2.03705 + 0.741425i
\(747\) −24.2888 + 20.3807i −0.888681 + 0.745692i
\(748\) 10.1382 + 17.5598i 0.370688 + 0.642050i
\(749\) 0 0
\(750\) 13.9611 11.7148i 0.509787 0.427762i
\(751\) −4.40167 24.9631i −0.160619 0.910918i −0.953467 0.301498i \(-0.902513\pi\)
0.792848 0.609420i \(-0.208598\pi\)
\(752\) 3.81016 0.138942
\(753\) 4.68732 8.11867i 0.170815 0.295861i
\(754\) 24.5194 20.5742i 0.892942 0.749267i
\(755\) 2.58331 14.6507i 0.0940163 0.533193i
\(756\) 0 0
\(757\) −39.8153 + 14.4916i −1.44711 + 0.526705i −0.941783 0.336222i \(-0.890851\pi\)
−0.505328 + 0.862927i \(0.668628\pi\)
\(758\) 60.5287 22.0307i 2.19850 0.800190i
\(759\) 1.95811 + 3.39155i 0.0710749 + 0.123105i
\(760\) −33.5153 12.7519i −1.21573 0.462560i
\(761\) 1.42855 2.47432i 0.0517848 0.0896940i −0.838971 0.544176i \(-0.816842\pi\)
0.890756 + 0.454482i \(0.150176\pi\)
\(762\) −18.3614 15.4071i −0.665165 0.558139i
\(763\) 0 0
\(764\) −7.87804 44.6786i −0.285018 1.61641i
\(765\) 10.3059 + 8.64766i 0.372610 + 0.312657i
\(766\) 12.0831 + 68.5265i 0.436579 + 2.47596i
\(767\) 5.34658 9.26055i 0.193054 0.334379i
\(768\) −9.95471 17.2421i −0.359210 0.622169i
\(769\) 14.6472 12.2905i 0.528193 0.443207i −0.339284 0.940684i \(-0.610185\pi\)
0.867477 + 0.497477i \(0.165740\pi\)
\(770\) 0 0
\(771\) 1.62449 2.81369i 0.0585044 0.101333i
\(772\) 60.8813 2.19116
\(773\) 0.436700 + 2.47665i 0.0157070 + 0.0890788i 0.991654 0.128931i \(-0.0411546\pi\)
−0.975947 + 0.218010i \(0.930043\pi\)
\(774\) 53.2973 19.3986i 1.91573 0.697270