Properties

Label 912.2.bo.e.625.1
Level $912$
Weight $2$
Character 912.625
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 228)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 625.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 912.625
Dual form 912.2.bo.e.769.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.766044 - 0.642788i) q^{3} +(0.826352 - 0.300767i) q^{5} +(-1.09240 - 1.89209i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\) \(q+(-0.766044 - 0.642788i) q^{3} +(0.826352 - 0.300767i) q^{5} +(-1.09240 - 1.89209i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-0.0812519 + 0.140732i) q^{11} +(0.581252 - 0.487728i) q^{13} +(-0.826352 - 0.300767i) q^{15} +(0.539363 - 3.05888i) q^{17} +(-2.77719 - 3.35965i) q^{19} +(-0.379385 + 2.15160i) q^{21} +(1.21301 + 0.441500i) q^{23} +(-3.23783 + 2.71686i) q^{25} +(0.500000 - 0.866025i) q^{27} +(-1.13176 - 6.41852i) q^{29} +(0.479055 + 0.829748i) q^{31} +(0.152704 - 0.0555796i) q^{33} +(-1.47178 - 1.23497i) q^{35} -1.16250 q^{37} -0.758770 q^{39} +(-8.11721 - 6.81115i) q^{41} +(-0.166374 + 0.0605553i) q^{43} +(0.439693 + 0.761570i) q^{45} +(0.602196 + 3.41523i) q^{47} +(1.11334 - 1.92836i) q^{49} +(-2.37939 + 1.99654i) q^{51} +(-7.83022 - 2.84997i) q^{53} +(-0.0248149 + 0.140732i) q^{55} +(-0.0320889 + 4.35878i) q^{57} +(0.482926 - 2.73881i) q^{59} +(-6.79086 - 2.47167i) q^{61} +(1.67365 - 1.40436i) q^{63} +(0.333626 - 0.577857i) q^{65} +(-0.184793 - 1.04801i) q^{67} +(-0.645430 - 1.11792i) q^{69} +(4.77719 - 1.73875i) q^{71} +(1.72281 + 1.44561i) q^{73} +4.22668 q^{75} +0.355037 q^{77} +(4.01501 + 3.36900i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(-8.55690 - 14.8210i) q^{83} +(-0.474308 - 2.68993i) q^{85} +(-3.25877 + 5.64436i) q^{87} +(11.9684 - 10.0427i) q^{89} +(-1.55778 - 0.566986i) q^{91} +(0.166374 - 0.943555i) q^{93} +(-3.30541 - 1.94096i) q^{95} +(-1.63563 + 9.27612i) q^{97} +(-0.152704 - 0.0555796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{5} - 3 q^{7} + O(q^{10}) \) \( 6 q + 6 q^{5} - 3 q^{7} - 3 q^{11} + 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 9 q^{21} + 15 q^{23} + 3 q^{27} - 12 q^{29} + 6 q^{31} + 3 q^{33} + 6 q^{35} - 12 q^{37} + 18 q^{39} - 18 q^{41} + 18 q^{43} - 3 q^{45} + 3 q^{47} - 3 q^{51} - 24 q^{53} + 27 q^{55} + 9 q^{57} - 18 q^{59} - 9 q^{61} + 9 q^{63} + 21 q^{65} + 6 q^{67} + 12 q^{69} + 18 q^{71} + 21 q^{73} + 12 q^{75} - 48 q^{77} - 6 q^{79} - 15 q^{83} + 27 q^{85} + 3 q^{87} + 15 q^{89} - 30 q^{91} - 18 q^{93} - 24 q^{95} + 9 q^{97} - 3 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.766044 0.642788i −0.442276 0.371114i
\(4\) 0 0
\(5\) 0.826352 0.300767i 0.369556 0.134507i −0.150565 0.988600i \(-0.548109\pi\)
0.520121 + 0.854093i \(0.325887\pi\)
\(6\) 0 0
\(7\) −1.09240 1.89209i −0.412887 0.715141i 0.582317 0.812962i \(-0.302146\pi\)
−0.995204 + 0.0978205i \(0.968813\pi\)
\(8\) 0 0
\(9\) 0.173648 + 0.984808i 0.0578827 + 0.328269i
\(10\) 0 0
\(11\) −0.0812519 + 0.140732i −0.0244984 + 0.0424324i −0.878015 0.478634i \(-0.841132\pi\)
0.853516 + 0.521066i \(0.174466\pi\)
\(12\) 0 0
\(13\) 0.581252 0.487728i 0.161210 0.135271i −0.558614 0.829428i \(-0.688667\pi\)
0.719824 + 0.694156i \(0.244222\pi\)
\(14\) 0 0
\(15\) −0.826352 0.300767i −0.213363 0.0776578i
\(16\) 0 0
\(17\) 0.539363 3.05888i 0.130815 0.741887i −0.846868 0.531802i \(-0.821515\pi\)
0.977683 0.210085i \(-0.0673740\pi\)
\(18\) 0 0
\(19\) −2.77719 3.35965i −0.637131 0.770756i
\(20\) 0 0
\(21\) −0.379385 + 2.15160i −0.0827886 + 0.469518i
\(22\) 0 0
\(23\) 1.21301 + 0.441500i 0.252930 + 0.0920591i 0.465374 0.885114i \(-0.345920\pi\)
−0.212443 + 0.977173i \(0.568142\pi\)
\(24\) 0 0
\(25\) −3.23783 + 2.71686i −0.647565 + 0.543372i
\(26\) 0 0
\(27\) 0.500000 0.866025i 0.0962250 0.166667i
\(28\) 0 0
\(29\) −1.13176 6.41852i −0.210162 1.19189i −0.889107 0.457700i \(-0.848673\pi\)
0.678944 0.734190i \(-0.262438\pi\)
\(30\) 0 0
\(31\) 0.479055 + 0.829748i 0.0860409 + 0.149027i 0.905834 0.423632i \(-0.139245\pi\)
−0.819793 + 0.572659i \(0.805912\pi\)
\(32\) 0 0
\(33\) 0.152704 0.0555796i 0.0265823 0.00967516i
\(34\) 0 0
\(35\) −1.47178 1.23497i −0.248776 0.208748i
\(36\) 0 0
\(37\) −1.16250 −0.191114 −0.0955572 0.995424i \(-0.530463\pi\)
−0.0955572 + 0.995424i \(0.530463\pi\)
\(38\) 0 0
\(39\) −0.758770 −0.121501
\(40\) 0 0
\(41\) −8.11721 6.81115i −1.26770 1.06372i −0.994818 0.101674i \(-0.967580\pi\)
−0.272878 0.962049i \(-0.587975\pi\)
\(42\) 0 0
\(43\) −0.166374 + 0.0605553i −0.0253718 + 0.00923459i −0.354675 0.934990i \(-0.615408\pi\)
0.329303 + 0.944224i \(0.393186\pi\)
\(44\) 0 0
\(45\) 0.439693 + 0.761570i 0.0655455 + 0.113528i
\(46\) 0 0
\(47\) 0.602196 + 3.41523i 0.0878394 + 0.498162i 0.996708 + 0.0810787i \(0.0258365\pi\)
−0.908868 + 0.417083i \(0.863052\pi\)
\(48\) 0 0
\(49\) 1.11334 1.92836i 0.159049 0.275480i
\(50\) 0 0
\(51\) −2.37939 + 1.99654i −0.333181 + 0.279572i
\(52\) 0 0
\(53\) −7.83022 2.84997i −1.07556 0.391473i −0.257309 0.966329i \(-0.582836\pi\)
−0.818255 + 0.574856i \(0.805058\pi\)
\(54\) 0 0
\(55\) −0.0248149 + 0.140732i −0.00334604 + 0.0189764i
\(56\) 0 0
\(57\) −0.0320889 + 4.35878i −0.00425028 + 0.577335i
\(58\) 0 0
\(59\) 0.482926 2.73881i 0.0628716 0.356563i −0.937100 0.349060i \(-0.886501\pi\)
0.999972 0.00750222i \(-0.00238805\pi\)
\(60\) 0 0
\(61\) −6.79086 2.47167i −0.869480 0.316465i −0.131524 0.991313i \(-0.541987\pi\)
−0.737957 + 0.674848i \(0.764209\pi\)
\(62\) 0 0
\(63\) 1.67365 1.40436i 0.210860 0.176932i
\(64\) 0 0
\(65\) 0.333626 0.577857i 0.0413812 0.0716743i
\(66\) 0 0
\(67\) −0.184793 1.04801i −0.0225760 0.128035i 0.971437 0.237298i \(-0.0762619\pi\)
−0.994013 + 0.109263i \(0.965151\pi\)
\(68\) 0 0
\(69\) −0.645430 1.11792i −0.0777006 0.134581i
\(70\) 0 0
\(71\) 4.77719 1.73875i 0.566948 0.206352i −0.0426126 0.999092i \(-0.513568\pi\)
0.609561 + 0.792739i \(0.291346\pi\)
\(72\) 0 0
\(73\) 1.72281 + 1.44561i 0.201640 + 0.169196i 0.738016 0.674783i \(-0.235763\pi\)
−0.536376 + 0.843979i \(0.680207\pi\)
\(74\) 0 0
\(75\) 4.22668 0.488055
\(76\) 0 0
\(77\) 0.355037 0.0404602
\(78\) 0 0
\(79\) 4.01501 + 3.36900i 0.451724 + 0.379042i 0.840075 0.542470i \(-0.182511\pi\)
−0.388351 + 0.921512i \(0.626955\pi\)
\(80\) 0 0
\(81\) −0.939693 + 0.342020i −0.104410 + 0.0380022i
\(82\) 0 0
\(83\) −8.55690 14.8210i −0.939242 1.62682i −0.766889 0.641780i \(-0.778196\pi\)
−0.172353 0.985035i \(-0.555137\pi\)
\(84\) 0 0
\(85\) −0.474308 2.68993i −0.0514459 0.291764i
\(86\) 0 0
\(87\) −3.25877 + 5.64436i −0.349377 + 0.605138i
\(88\) 0 0
\(89\) 11.9684 10.0427i 1.26865 1.06452i 0.273941 0.961747i \(-0.411673\pi\)
0.994705 0.102773i \(-0.0327717\pi\)
\(90\) 0 0
\(91\) −1.55778 0.566986i −0.163300 0.0594363i
\(92\) 0 0
\(93\) 0.166374 0.943555i 0.0172522 0.0978421i
\(94\) 0 0
\(95\) −3.30541 1.94096i −0.339128 0.199138i
\(96\) 0 0
\(97\) −1.63563 + 9.27612i −0.166073 + 0.941847i 0.781878 + 0.623431i \(0.214262\pi\)
−0.947951 + 0.318416i \(0.896849\pi\)
\(98\) 0 0
\(99\) −0.152704 0.0555796i −0.0153473 0.00558596i
\(100\) 0 0
\(101\) −4.83022 + 4.05304i −0.480625 + 0.403292i −0.850652 0.525729i \(-0.823793\pi\)
0.370027 + 0.929021i \(0.379348\pi\)
\(102\) 0 0
\(103\) −4.30793 + 7.46156i −0.424473 + 0.735209i −0.996371 0.0851156i \(-0.972874\pi\)
0.571898 + 0.820325i \(0.306207\pi\)
\(104\) 0 0
\(105\) 0.333626 + 1.89209i 0.0325585 + 0.184649i
\(106\) 0 0
\(107\) −6.57398 11.3865i −0.635530 1.10077i −0.986402 0.164348i \(-0.947448\pi\)
0.350872 0.936423i \(-0.385885\pi\)
\(108\) 0 0
\(109\) 9.44356 3.43718i 0.904529 0.329222i 0.152463 0.988309i \(-0.451280\pi\)
0.752066 + 0.659087i \(0.229057\pi\)
\(110\) 0 0
\(111\) 0.890530 + 0.747243i 0.0845253 + 0.0709252i
\(112\) 0 0
\(113\) 8.04458 0.756770 0.378385 0.925648i \(-0.376480\pi\)
0.378385 + 0.925648i \(0.376480\pi\)
\(114\) 0 0
\(115\) 1.13516 0.105854
\(116\) 0 0
\(117\) 0.581252 + 0.487728i 0.0537368 + 0.0450905i
\(118\) 0 0
\(119\) −6.37686 + 2.32099i −0.584566 + 0.212765i
\(120\) 0 0
\(121\) 5.48680 + 9.50341i 0.498800 + 0.863946i
\(122\) 0 0
\(123\) 1.84002 + 10.4353i 0.165909 + 0.940918i
\(124\) 0 0
\(125\) −4.05690 + 7.02676i −0.362861 + 0.628493i
\(126\) 0 0
\(127\) −15.3589 + 12.8877i −1.36288 + 1.14359i −0.387802 + 0.921743i \(0.626766\pi\)
−0.975080 + 0.221852i \(0.928790\pi\)
\(128\) 0 0
\(129\) 0.166374 + 0.0605553i 0.0146484 + 0.00533159i
\(130\) 0 0
\(131\) 2.76264 15.6677i 0.241373 1.36889i −0.587394 0.809301i \(-0.699846\pi\)
0.828767 0.559594i \(-0.189043\pi\)
\(132\) 0 0
\(133\) −3.32295 + 8.92474i −0.288136 + 0.773873i
\(134\) 0 0
\(135\) 0.152704 0.866025i 0.0131426 0.0745356i
\(136\) 0 0
\(137\) 4.74035 + 1.72535i 0.404996 + 0.147406i 0.536482 0.843912i \(-0.319753\pi\)
−0.131487 + 0.991318i \(0.541975\pi\)
\(138\) 0 0
\(139\) 8.08512 6.78422i 0.685771 0.575430i −0.231915 0.972736i \(-0.574499\pi\)
0.917686 + 0.397306i \(0.130055\pi\)
\(140\) 0 0
\(141\) 1.73396 3.00330i 0.146025 0.252923i
\(142\) 0 0
\(143\) 0.0214114 + 0.121430i 0.00179051 + 0.0101545i
\(144\) 0 0
\(145\) −2.86571 4.96356i −0.237985 0.412202i
\(146\) 0 0
\(147\) −2.09240 + 0.761570i −0.172578 + 0.0628132i
\(148\) 0 0
\(149\) 10.5680 + 8.86765i 0.865768 + 0.726466i 0.963203 0.268776i \(-0.0866192\pi\)
−0.0974344 + 0.995242i \(0.531064\pi\)
\(150\) 0 0
\(151\) 20.2841 1.65069 0.825346 0.564627i \(-0.190980\pi\)
0.825346 + 0.564627i \(0.190980\pi\)
\(152\) 0 0
\(153\) 3.10607 0.251111
\(154\) 0 0
\(155\) 0.645430 + 0.541580i 0.0518422 + 0.0435007i
\(156\) 0 0
\(157\) 12.3807 4.50622i 0.988090 0.359635i 0.203110 0.979156i \(-0.434895\pi\)
0.784980 + 0.619521i \(0.212673\pi\)
\(158\) 0 0
\(159\) 4.16637 + 7.21637i 0.330415 + 0.572296i
\(160\) 0 0
\(161\) −0.489733 2.77741i −0.0385964 0.218891i
\(162\) 0 0
\(163\) −8.74510 + 15.1470i −0.684969 + 1.18640i 0.288477 + 0.957487i \(0.406851\pi\)
−0.973447 + 0.228915i \(0.926482\pi\)
\(164\) 0 0
\(165\) 0.109470 0.0918566i 0.00852226 0.00715102i
\(166\) 0 0
\(167\) 14.0077 + 5.09840i 1.08395 + 0.394526i 0.821377 0.570386i \(-0.193206\pi\)
0.262574 + 0.964912i \(0.415428\pi\)
\(168\) 0 0
\(169\) −2.15745 + 12.2355i −0.165958 + 0.941193i
\(170\) 0 0
\(171\) 2.82635 3.31839i 0.216137 0.253764i
\(172\) 0 0
\(173\) 0.311804 1.76833i 0.0237060 0.134443i −0.970658 0.240465i \(-0.922700\pi\)
0.994364 + 0.106021i \(0.0338112\pi\)
\(174\) 0 0
\(175\) 8.67752 + 3.15836i 0.655959 + 0.238749i
\(176\) 0 0
\(177\) −2.13041 + 1.78763i −0.160132 + 0.134367i
\(178\) 0 0
\(179\) 3.91740 6.78514i 0.292801 0.507145i −0.681670 0.731659i \(-0.738746\pi\)
0.974471 + 0.224514i \(0.0720795\pi\)
\(180\) 0 0
\(181\) −0.0727959 0.412846i −0.00541088 0.0306866i 0.981983 0.188970i \(-0.0605150\pi\)
−0.987394 + 0.158284i \(0.949404\pi\)
\(182\) 0 0
\(183\) 3.61334 + 6.25849i 0.267106 + 0.462641i
\(184\) 0 0
\(185\) −0.960637 + 0.349643i −0.0706274 + 0.0257063i
\(186\) 0 0
\(187\) 0.386659 + 0.324446i 0.0282753 + 0.0237258i
\(188\) 0 0
\(189\) −2.18479 −0.158920
\(190\) 0 0
\(191\) 19.5398 1.41385 0.706926 0.707287i \(-0.250081\pi\)
0.706926 + 0.707287i \(0.250081\pi\)
\(192\) 0 0
\(193\) −12.7476 10.6965i −0.917594 0.769953i 0.0559543 0.998433i \(-0.482180\pi\)
−0.973549 + 0.228480i \(0.926624\pi\)
\(194\) 0 0
\(195\) −0.627011 + 0.228213i −0.0449012 + 0.0163427i
\(196\) 0 0
\(197\) 10.9979 + 19.0490i 0.783571 + 1.35718i 0.929849 + 0.367941i \(0.119937\pi\)
−0.146278 + 0.989243i \(0.546730\pi\)
\(198\) 0 0
\(199\) 3.77584 + 21.4139i 0.267663 + 1.51799i 0.761345 + 0.648347i \(0.224539\pi\)
−0.493682 + 0.869642i \(0.664349\pi\)
\(200\) 0 0
\(201\) −0.532089 + 0.921605i −0.0375307 + 0.0650050i
\(202\) 0 0
\(203\) −10.9081 + 9.15296i −0.765596 + 0.642412i
\(204\) 0 0
\(205\) −8.75624 3.18701i −0.611563 0.222591i
\(206\) 0 0
\(207\) −0.224155 + 1.27125i −0.0155799 + 0.0883579i
\(208\) 0 0
\(209\) 0.698463 0.117863i 0.0483137 0.00815275i
\(210\) 0 0
\(211\) 1.49794 8.49524i 0.103122 0.584837i −0.888831 0.458235i \(-0.848482\pi\)
0.991954 0.126602i \(-0.0404070\pi\)
\(212\) 0 0
\(213\) −4.77719 1.73875i −0.327328 0.119137i
\(214\) 0 0
\(215\) −0.119271 + 0.100080i −0.00813419 + 0.00682539i
\(216\) 0 0
\(217\) 1.04664 1.81283i 0.0710503 0.123063i
\(218\) 0 0
\(219\) −0.390530 2.21480i −0.0263895 0.149663i
\(220\) 0 0
\(221\) −1.17840 2.04104i −0.0792675 0.137295i
\(222\) 0 0
\(223\) 14.2442 5.18447i 0.953864 0.347178i 0.182238 0.983255i \(-0.441666\pi\)
0.771626 + 0.636077i \(0.219444\pi\)
\(224\) 0 0
\(225\) −3.23783 2.71686i −0.215855 0.181124i
\(226\) 0 0
\(227\) 5.71419 0.379264 0.189632 0.981855i \(-0.439270\pi\)
0.189632 + 0.981855i \(0.439270\pi\)
\(228\) 0 0
\(229\) 22.1634 1.46460 0.732301 0.680982i \(-0.238447\pi\)
0.732301 + 0.680982i \(0.238447\pi\)
\(230\) 0 0
\(231\) −0.271974 0.228213i −0.0178946 0.0150153i
\(232\) 0 0
\(233\) 10.1750 3.70339i 0.666586 0.242617i 0.0135087 0.999909i \(-0.495700\pi\)
0.653077 + 0.757291i \(0.273478\pi\)
\(234\) 0 0
\(235\) 1.52481 + 2.64106i 0.0994680 + 0.172284i
\(236\) 0 0
\(237\) −0.910130 5.16160i −0.0591193 0.335282i
\(238\) 0 0
\(239\) −4.93107 + 8.54087i −0.318965 + 0.552463i −0.980272 0.197652i \(-0.936668\pi\)
0.661308 + 0.750115i \(0.270002\pi\)
\(240\) 0 0
\(241\) −5.29086 + 4.43956i −0.340814 + 0.285977i −0.797089 0.603862i \(-0.793628\pi\)
0.456275 + 0.889839i \(0.349183\pi\)
\(242\) 0 0
\(243\) 0.939693 + 0.342020i 0.0602813 + 0.0219406i
\(244\) 0 0
\(245\) 0.340022 1.92836i 0.0217232 0.123199i
\(246\) 0 0
\(247\) −3.25284 0.598287i −0.206973 0.0380681i
\(248\) 0 0
\(249\) −2.97178 + 16.8538i −0.188329 + 1.06807i
\(250\) 0 0
\(251\) 23.3910 + 8.51363i 1.47643 + 0.537375i 0.949837 0.312744i \(-0.101248\pi\)
0.526589 + 0.850120i \(0.323471\pi\)
\(252\) 0 0
\(253\) −0.160693 + 0.134837i −0.0101027 + 0.00847715i
\(254\) 0 0
\(255\) −1.36571 + 2.36549i −0.0855244 + 0.148133i
\(256\) 0 0
\(257\) −2.47565 14.0401i −0.154427 0.875799i −0.959308 0.282362i \(-0.908882\pi\)
0.804881 0.593436i \(-0.202229\pi\)
\(258\) 0 0
\(259\) 1.26991 + 2.19956i 0.0789087 + 0.136674i
\(260\) 0 0
\(261\) 6.12449 2.22913i 0.379096 0.137980i
\(262\) 0 0
\(263\) −16.5594 13.8950i −1.02110 0.856803i −0.0313331 0.999509i \(-0.509975\pi\)
−0.989765 + 0.142706i \(0.954420\pi\)
\(264\) 0 0
\(265\) −7.32770 −0.450137
\(266\) 0 0
\(267\) −15.6236 −0.956149
\(268\) 0 0
\(269\) −8.14022 6.83045i −0.496318 0.416460i 0.359966 0.932965i \(-0.382788\pi\)
−0.856284 + 0.516505i \(0.827233\pi\)
\(270\) 0 0
\(271\) −11.4179 + 4.15577i −0.693586 + 0.252445i −0.664670 0.747137i \(-0.731428\pi\)
−0.0289163 + 0.999582i \(0.509206\pi\)
\(272\) 0 0
\(273\) 0.828878 + 1.43566i 0.0501660 + 0.0868900i
\(274\) 0 0
\(275\) −0.119271 0.676417i −0.00719229 0.0407895i
\(276\) 0 0
\(277\) −4.90760 + 8.50022i −0.294869 + 0.510729i −0.974954 0.222404i \(-0.928609\pi\)
0.680085 + 0.733133i \(0.261943\pi\)
\(278\) 0 0
\(279\) −0.733956 + 0.615862i −0.0439408 + 0.0368707i
\(280\) 0 0
\(281\) −26.5133 9.65004i −1.58165 0.575673i −0.606087 0.795399i \(-0.707262\pi\)
−0.975562 + 0.219726i \(0.929484\pi\)
\(282\) 0 0
\(283\) 2.67752 15.1850i 0.159162 0.902652i −0.795720 0.605665i \(-0.792907\pi\)
0.954882 0.296987i \(-0.0959818\pi\)
\(284\) 0 0
\(285\) 1.28446 + 3.61154i 0.0760850 + 0.213929i
\(286\) 0 0
\(287\) −4.02007 + 22.7989i −0.237297 + 1.34578i
\(288\) 0 0
\(289\) 6.90895 + 2.51465i 0.406409 + 0.147921i
\(290\) 0 0
\(291\) 7.21554 6.05455i 0.422982 0.354924i
\(292\) 0 0
\(293\) −13.8885 + 24.0555i −0.811373 + 1.40534i 0.100530 + 0.994934i \(0.467946\pi\)
−0.911903 + 0.410405i \(0.865387\pi\)
\(294\) 0 0
\(295\) −0.424678 2.40847i −0.0247257 0.140226i
\(296\) 0 0
\(297\) 0.0812519 + 0.140732i 0.00471471 + 0.00816612i
\(298\) 0 0
\(299\) 0.920397 0.334997i 0.0532279 0.0193734i
\(300\) 0 0
\(301\) 0.296322 + 0.248644i 0.0170797 + 0.0143316i
\(302\) 0 0
\(303\) 6.30541 0.362236
\(304\) 0 0
\(305\) −6.35504 −0.363888
\(306\) 0 0
\(307\) −20.8293 17.4779i −1.18879 0.997516i −0.999880 0.0155226i \(-0.995059\pi\)
−0.188914 0.981994i \(-0.560497\pi\)
\(308\) 0 0
\(309\) 8.09627 2.94680i 0.460581 0.167638i
\(310\) 0 0
\(311\) −2.97178 5.14728i −0.168514 0.291875i 0.769383 0.638787i \(-0.220564\pi\)
−0.937898 + 0.346912i \(0.887230\pi\)
\(312\) 0 0
\(313\) 1.24170 + 7.04201i 0.0701848 + 0.398038i 0.999581 + 0.0289536i \(0.00921752\pi\)
−0.929396 + 0.369084i \(0.879671\pi\)
\(314\) 0 0
\(315\) 0.960637 1.66387i 0.0541258 0.0937486i
\(316\) 0 0
\(317\) 17.0758 14.3283i 0.959072 0.804757i −0.0217300 0.999764i \(-0.506917\pi\)
0.980802 + 0.195007i \(0.0624730\pi\)
\(318\) 0 0
\(319\) 0.995252 + 0.362242i 0.0557234 + 0.0202817i
\(320\) 0 0
\(321\) −2.28312 + 12.9482i −0.127431 + 0.722699i
\(322\) 0 0
\(323\) −11.7747 + 6.68302i −0.655160 + 0.371853i
\(324\) 0 0
\(325\) −0.556904 + 3.15836i −0.0308915 + 0.175194i
\(326\) 0 0
\(327\) −9.44356 3.43718i −0.522230 0.190076i
\(328\) 0 0
\(329\) 5.80406 4.87019i 0.319988 0.268502i
\(330\) 0 0
\(331\) 3.15183 5.45912i 0.173240 0.300061i −0.766311 0.642470i \(-0.777910\pi\)
0.939551 + 0.342410i \(0.111243\pi\)
\(332\) 0 0
\(333\) −0.201867 1.14484i −0.0110622 0.0627370i
\(334\) 0 0
\(335\) −0.467911 0.810446i −0.0255647 0.0442794i
\(336\) 0 0
\(337\) 24.3123 8.84894i 1.32437 0.482033i 0.419517 0.907748i \(-0.362200\pi\)
0.904857 + 0.425715i \(0.139977\pi\)
\(338\) 0 0
\(339\) −6.16250 5.17095i −0.334701 0.280848i
\(340\) 0 0
\(341\) −0.155697 −0.00843145
\(342\) 0 0
\(343\) −20.1584 −1.08845
\(344\) 0 0
\(345\) −0.869585 0.729669i −0.0468169 0.0392840i
\(346\) 0 0
\(347\) −17.4820 + 6.36295i −0.938486 + 0.341581i −0.765568 0.643355i \(-0.777542\pi\)
−0.172918 + 0.984936i \(0.555320\pi\)
\(348\) 0 0
\(349\) 0.871644 + 1.50973i 0.0466581 + 0.0808141i 0.888411 0.459048i \(-0.151810\pi\)
−0.841753 + 0.539863i \(0.818476\pi\)
\(350\) 0 0
\(351\) −0.131759 0.747243i −0.00703278 0.0398849i
\(352\) 0 0
\(353\) 5.33615 9.24249i 0.284015 0.491928i −0.688355 0.725374i \(-0.741667\pi\)
0.972370 + 0.233446i \(0.0750002\pi\)
\(354\) 0 0
\(355\) 3.42468 2.87365i 0.181763 0.152517i
\(356\) 0 0
\(357\) 6.37686 + 2.32099i 0.337499 + 0.122840i
\(358\) 0 0
\(359\) 1.18298 6.70902i 0.0624354 0.354089i −0.937545 0.347863i \(-0.886907\pi\)
0.999981 0.00622527i \(-0.00198158\pi\)
\(360\) 0 0
\(361\) −3.57444 + 18.6607i −0.188129 + 0.982144i
\(362\) 0 0
\(363\) 1.90554 10.8069i 0.100015 0.567214i
\(364\) 0 0
\(365\) 1.85844 + 0.676417i 0.0972752 + 0.0354053i
\(366\) 0 0
\(367\) 13.7815 11.5641i 0.719390 0.603640i −0.207827 0.978166i \(-0.566639\pi\)
0.927216 + 0.374526i \(0.122195\pi\)
\(368\) 0 0
\(369\) 5.29813 9.17664i 0.275810 0.477717i
\(370\) 0 0
\(371\) 3.16132 + 17.9287i 0.164128 + 0.930814i
\(372\) 0 0
\(373\) −1.68004 2.90992i −0.0869894 0.150670i 0.819248 0.573440i \(-0.194391\pi\)
−0.906237 + 0.422770i \(0.861058\pi\)
\(374\) 0 0
\(375\) 7.62449 2.77509i 0.393727 0.143305i
\(376\) 0 0
\(377\) −3.78833 3.17879i −0.195109 0.163716i
\(378\) 0 0
\(379\) −15.1584 −0.778634 −0.389317 0.921104i \(-0.627289\pi\)
−0.389317 + 0.921104i \(0.627289\pi\)
\(380\) 0 0
\(381\) 20.0496 1.02717
\(382\) 0 0
\(383\) −5.46585 4.58639i −0.279292 0.234354i 0.492371 0.870385i \(-0.336130\pi\)
−0.771663 + 0.636032i \(0.780575\pi\)
\(384\) 0 0
\(385\) 0.293386 0.106784i 0.0149523 0.00544220i
\(386\) 0 0
\(387\) −0.0885259 0.153331i −0.00450002 0.00779427i
\(388\) 0 0
\(389\) 4.33006 + 24.5570i 0.219543 + 1.24509i 0.872847 + 0.487994i \(0.162271\pi\)
−0.653304 + 0.757095i \(0.726618\pi\)
\(390\) 0 0
\(391\) 2.00475 3.47232i 0.101384 0.175603i
\(392\) 0 0
\(393\) −12.1873 + 10.2264i −0.614769 + 0.515852i
\(394\) 0 0
\(395\) 4.33110 + 1.57639i 0.217921 + 0.0793169i
\(396\) 0 0
\(397\) 3.58647 20.3399i 0.180000 1.02083i −0.752214 0.658919i \(-0.771014\pi\)
0.932213 0.361909i \(-0.117875\pi\)
\(398\) 0 0
\(399\) 8.28224 4.70080i 0.414631 0.235334i
\(400\) 0 0
\(401\) 6.30722 35.7700i 0.314967 1.78627i −0.257434 0.966296i \(-0.582877\pi\)
0.572402 0.819973i \(-0.306012\pi\)
\(402\) 0 0
\(403\) 0.683144 + 0.248644i 0.0340298 + 0.0123858i
\(404\) 0 0
\(405\) −0.673648 + 0.565258i −0.0334738 + 0.0280879i
\(406\) 0 0
\(407\) 0.0944557 0.163602i 0.00468199 0.00810945i
\(408\) 0 0
\(409\) 0.860662 + 4.88106i 0.0425570 + 0.241353i 0.998665 0.0516631i \(-0.0164522\pi\)
−0.956108 + 0.293016i \(0.905341\pi\)
\(410\) 0 0
\(411\) −2.52229 4.36873i −0.124415 0.215494i
\(412\) 0 0
\(413\) −5.70961 + 2.07813i −0.280951 + 0.102258i
\(414\) 0 0
\(415\) −11.5287 9.67372i −0.565921 0.474864i
\(416\) 0 0
\(417\) −10.5544 −0.516850
\(418\) 0 0
\(419\) 35.0966 1.71458 0.857290 0.514834i \(-0.172146\pi\)
0.857290 + 0.514834i \(0.172146\pi\)
\(420\) 0 0
\(421\) −14.0967 11.8286i −0.687033 0.576489i 0.231019 0.972949i \(-0.425794\pi\)
−0.918052 + 0.396460i \(0.870238\pi\)
\(422\) 0 0
\(423\) −3.25877 + 1.18610i −0.158447 + 0.0576699i
\(424\) 0 0
\(425\) 6.56418 + 11.3695i 0.318409 + 0.551501i
\(426\) 0 0
\(427\) 2.74170 + 15.5489i 0.132680 + 0.752466i
\(428\) 0 0
\(429\) 0.0616516 0.106784i 0.00297657 0.00515556i
\(430\) 0 0
\(431\) −6.73648 + 5.65258i −0.324485 + 0.272275i −0.790448 0.612529i \(-0.790152\pi\)
0.465963 + 0.884804i \(0.345708\pi\)
\(432\) 0 0
\(433\) −16.3614 5.95507i −0.786280 0.286183i −0.0824914 0.996592i \(-0.526288\pi\)
−0.703789 + 0.710409i \(0.748510\pi\)
\(434\) 0 0
\(435\) −0.995252 + 5.64436i −0.0477187 + 0.270626i
\(436\) 0 0
\(437\) −1.88548 5.30142i −0.0901946 0.253601i
\(438\) 0 0
\(439\) 4.94743 28.0583i 0.236128 1.33915i −0.604097 0.796911i \(-0.706466\pi\)
0.840225 0.542238i \(-0.182423\pi\)
\(440\) 0 0
\(441\) 2.09240 + 0.761570i 0.0996379 + 0.0362652i
\(442\) 0 0
\(443\) −13.8216 + 11.5977i −0.656684 + 0.551023i −0.909091 0.416598i \(-0.863222\pi\)
0.252407 + 0.967621i \(0.418778\pi\)
\(444\) 0 0
\(445\) 6.86959 11.8985i 0.325650 0.564042i
\(446\) 0 0
\(447\) −2.39558 13.5860i −0.113307 0.642597i
\(448\) 0 0
\(449\) −4.76739 8.25736i −0.224987 0.389689i 0.731329 0.682025i \(-0.238901\pi\)
−0.956316 + 0.292336i \(0.905567\pi\)
\(450\) 0 0
\(451\) 1.61809 0.588936i 0.0761928 0.0277319i
\(452\) 0 0
\(453\) −15.5385 13.0383i −0.730062 0.612595i
\(454\) 0 0
\(455\) −1.45781 −0.0683430
\(456\) 0 0
\(457\) 10.4584 0.489224 0.244612 0.969621i \(-0.421339\pi\)
0.244612 + 0.969621i \(0.421339\pi\)
\(458\) 0 0
\(459\) −2.37939 1.99654i −0.111060 0.0931906i
\(460\) 0 0
\(461\) −39.1489 + 14.2490i −1.82335 + 0.663644i −0.828775 + 0.559583i \(0.810961\pi\)
−0.994571 + 0.104061i \(0.966816\pi\)
\(462\) 0 0
\(463\) 6.90895 + 11.9666i 0.321086 + 0.556137i 0.980712 0.195456i \(-0.0626188\pi\)
−0.659626 + 0.751594i \(0.729285\pi\)
\(464\) 0 0
\(465\) −0.146307 0.829748i −0.00678483 0.0384787i
\(466\) 0 0
\(467\) −3.72668 + 6.45480i −0.172450 + 0.298693i −0.939276 0.343163i \(-0.888502\pi\)
0.766826 + 0.641855i \(0.221835\pi\)
\(468\) 0 0
\(469\) −1.78106 + 1.49449i −0.0822417 + 0.0690090i
\(470\) 0 0
\(471\) −12.3807 4.50622i −0.570474 0.207636i
\(472\) 0 0
\(473\) 0.00499613 0.0283345i 0.000229722 0.00130282i
\(474\) 0 0
\(475\) 18.1197 + 3.33272i 0.831391 + 0.152916i
\(476\) 0 0
\(477\) 1.44697 8.20616i 0.0662520 0.375734i
\(478\) 0 0
\(479\) 22.3525 + 8.13565i 1.02131 + 0.371727i 0.797767 0.602966i \(-0.206015\pi\)
0.223546 + 0.974693i \(0.428237\pi\)
\(480\) 0 0
\(481\) −0.675708 + 0.566986i −0.0308096 + 0.0258523i
\(482\) 0 0
\(483\) −1.41013 + 2.44242i −0.0641631 + 0.111134i
\(484\) 0 0
\(485\) 1.43835 + 8.15728i 0.0653120 + 0.370403i
\(486\) 0 0
\(487\) 2.42855 + 4.20637i 0.110048 + 0.190609i 0.915789 0.401659i \(-0.131566\pi\)
−0.805741 + 0.592268i \(0.798233\pi\)
\(488\) 0 0
\(489\) 16.4354 5.98200i 0.743235 0.270515i
\(490\) 0 0
\(491\) 2.29632 + 1.92684i 0.103632 + 0.0869572i 0.693131 0.720811i \(-0.256231\pi\)
−0.589500 + 0.807769i \(0.700675\pi\)
\(492\) 0 0
\(493\) −20.2439 −0.911740
\(494\) 0 0
\(495\) −0.142903 −0.00642303
\(496\) 0 0
\(497\) −8.50846 7.13944i −0.381656 0.320248i
\(498\) 0 0
\(499\) 2.37211 0.863378i 0.106190 0.0386501i −0.288379 0.957516i \(-0.593116\pi\)
0.394569 + 0.918866i \(0.370894\pi\)
\(500\) 0 0
\(501\) −7.45336 12.9096i −0.332992 0.576759i
\(502\) 0 0
\(503\) −3.18614 18.0695i −0.142063 0.805678i −0.969679 0.244383i \(-0.921414\pi\)
0.827616 0.561295i \(-0.189697\pi\)
\(504\) 0 0
\(505\) −2.77244 + 4.80201i −0.123372 + 0.213687i
\(506\) 0 0
\(507\) 9.51754 7.98617i 0.422689 0.354678i
\(508\) 0 0
\(509\) −15.2922 5.56591i −0.677815 0.246704i −0.0199059 0.999802i \(-0.506337\pi\)
−0.657909 + 0.753097i \(0.728559\pi\)
\(510\) 0 0
\(511\) 0.853226 4.83889i 0.0377445 0.214060i
\(512\) 0 0
\(513\) −4.29813 + 0.725293i −0.189767 + 0.0320225i
\(514\) 0 0
\(515\) −1.31567 + 7.46156i −0.0579755 + 0.328796i
\(516\) 0 0
\(517\) −0.529563 0.192745i −0.0232901 0.00847692i
\(518\) 0 0
\(519\) −1.37551 + 1.15419i −0.0603784 + 0.0506635i
\(520\) 0 0
\(521\) −14.1454 + 24.5006i −0.619723 + 1.07339i 0.369814 + 0.929106i \(0.379422\pi\)
−0.989536 + 0.144285i \(0.953912\pi\)
\(522\) 0 0
\(523\) −0.841833 4.77427i −0.0368108 0.208764i 0.960855 0.277052i \(-0.0893575\pi\)
−0.997666 + 0.0682878i \(0.978246\pi\)
\(524\) 0 0
\(525\) −4.61721 7.99724i −0.201512 0.349028i
\(526\) 0 0
\(527\) 2.79648 1.01784i 0.121817 0.0443377i
\(528\) 0 0
\(529\) −16.3425 13.7130i −0.710546 0.596219i
\(530\) 0 0
\(531\) 2.78106 0.120688
\(532\) 0 0
\(533\) −8.04013 −0.348257
\(534\) 0 0
\(535\) −8.85710 7.43199i −0.382926 0.321313i
\(536\) 0 0
\(537\) −7.36231 + 2.67966i −0.317707 + 0.115636i
\(538\) 0 0
\(539\) 0.180922 + 0.313366i 0.00779287 + 0.0134976i
\(540\) 0 0
\(541\) −4.22193 23.9438i −0.181515 1.02942i −0.930352 0.366669i \(-0.880498\pi\)
0.748837 0.662755i \(-0.230613\pi\)
\(542\) 0 0
\(543\) −0.209607 + 0.363051i −0.00899512 + 0.0155800i
\(544\) 0 0
\(545\) 6.76991 5.68063i 0.289991 0.243332i
\(546\) 0 0
\(547\) −21.3999 7.78893i −0.914994 0.333031i −0.158749 0.987319i \(-0.550746\pi\)
−0.756245 + 0.654288i \(0.772968\pi\)
\(548\) 0 0
\(549\) 1.25490 7.11689i 0.0535578 0.303742i
\(550\) 0 0
\(551\) −18.4209 + 21.6278i −0.784755 + 0.921374i
\(552\) 0 0
\(553\) 1.98845 11.2770i 0.0845573 0.479548i
\(554\) 0 0
\(555\) 0.960637 + 0.349643i 0.0407768 + 0.0148415i
\(556\) 0 0
\(557\) 14.6578 12.2993i 0.621069 0.521139i −0.277070 0.960850i \(-0.589364\pi\)
0.898139 + 0.439711i \(0.144919\pi\)
\(558\) 0 0
\(559\) −0.0671708 + 0.116343i −0.00284102 + 0.00492080i
\(560\) 0 0
\(561\) −0.0876485 0.497079i −0.00370052 0.0209867i
\(562\) 0 0
\(563\) −10.6741 18.4881i −0.449860 0.779181i 0.548516 0.836140i \(-0.315193\pi\)
−0.998377 + 0.0569590i \(0.981860\pi\)
\(564\) 0 0
\(565\) 6.64765 2.41955i 0.279669 0.101791i
\(566\) 0 0
\(567\) 1.67365 + 1.40436i 0.0702866 + 0.0589775i
\(568\) 0 0
\(569\) 39.2121 1.64386 0.821929 0.569590i \(-0.192898\pi\)
0.821929 + 0.569590i \(0.192898\pi\)
\(570\) 0 0
\(571\) 7.27900 0.304617 0.152308 0.988333i \(-0.451329\pi\)
0.152308 + 0.988333i \(0.451329\pi\)
\(572\) 0 0
\(573\) −14.9684 12.5600i −0.625313 0.524700i
\(574\) 0 0
\(575\) −5.12701 + 1.86608i −0.213811 + 0.0778209i
\(576\) 0 0
\(577\) −7.49613 12.9837i −0.312068 0.540518i 0.666742 0.745289i \(-0.267688\pi\)
−0.978810 + 0.204771i \(0.934355\pi\)
\(578\) 0 0
\(579\) 2.88965 + 16.3880i 0.120090 + 0.681063i
\(580\) 0 0
\(581\) −18.6951 + 32.3808i −0.775602 + 1.34338i
\(582\) 0 0
\(583\) 1.03730 0.870401i 0.0429607 0.0360483i
\(584\) 0 0
\(585\) 0.627011 + 0.228213i 0.0259237 + 0.00943547i
\(586\) 0 0
\(587\) 2.08559 11.8280i 0.0860815 0.488192i −0.911037 0.412326i \(-0.864717\pi\)
0.997118 0.0758666i \(-0.0241723\pi\)
\(588\) 0 0
\(589\) 1.45723 3.91382i 0.0600443 0.161266i
\(590\) 0 0
\(591\) 3.81954 21.6617i 0.157115 0.891044i
\(592\) 0 0
\(593\) 34.1866 + 12.4429i 1.40388 + 0.510969i 0.929326 0.369260i \(-0.120389\pi\)
0.474549 + 0.880229i \(0.342611\pi\)
\(594\) 0 0
\(595\) −4.57145 + 3.83590i −0.187411 + 0.157257i
\(596\) 0 0
\(597\) 10.8721 18.8310i 0.444966 0.770704i
\(598\) 0 0
\(599\) −2.39739 13.5963i −0.0979548 0.555529i −0.993802 0.111167i \(-0.964541\pi\)
0.895847 0.444363i \(-0.146570\pi\)
\(600\) 0 0
\(601\) 0.483803 + 0.837972i 0.0197347 + 0.0341816i 0.875724 0.482812i \(-0.160384\pi\)
−0.855989 + 0.516993i \(0.827051\pi\)
\(602\) 0 0
\(603\) 1.00000 0.363970i 0.0407231 0.0148220i
\(604\) 0 0
\(605\) 7.39234 + 6.20291i 0.300541 + 0.252184i
\(606\) 0 0
\(607\) −1.53890 −0.0624619 −0.0312309 0.999512i \(-0.509943\pi\)
−0.0312309 + 0.999512i \(0.509943\pi\)
\(608\) 0 0
\(609\) 14.2395 0.577013
\(610\) 0 0
\(611\) 2.01573 + 1.69140i 0.0815477 + 0.0684266i
\(612\) 0 0
\(613\) −38.6921 + 14.0828i −1.56276 + 0.568798i −0.971367 0.237585i \(-0.923644\pi\)
−0.591393 + 0.806383i \(0.701422\pi\)
\(614\) 0 0
\(615\) 4.65910 + 8.06980i 0.187873 + 0.325406i
\(616\) 0 0
\(617\) 5.32857 + 30.2198i 0.214520 + 1.21660i 0.881737 + 0.471741i \(0.156374\pi\)
−0.667217 + 0.744864i \(0.732515\pi\)
\(618\) 0 0
\(619\) −5.97906 + 10.3560i −0.240319 + 0.416244i −0.960805 0.277225i \(-0.910585\pi\)
0.720486 + 0.693469i \(0.243919\pi\)
\(620\) 0 0
\(621\) 0.988856 0.829748i 0.0396814 0.0332967i
\(622\) 0 0
\(623\) −32.0758 11.6746i −1.28509 0.467734i
\(624\) 0 0
\(625\) 2.43077 13.7856i 0.0972308 0.551423i
\(626\) 0 0
\(627\) −0.610815 0.358675i −0.0243936 0.0143241i
\(628\) 0 0
\(629\) −0.627011 + 3.55596i −0.0250006 + 0.141785i
\(630\) 0 0
\(631\) −45.2708 16.4772i −1.80220 0.655949i −0.998110 0.0614459i \(-0.980429\pi\)
−0.804094 0.594503i \(-0.797349\pi\)
\(632\) 0 0
\(633\) −6.60813 + 5.54488i −0.262649 + 0.220389i
\(634\) 0 0
\(635\) −8.81567 + 15.2692i −0.349839 + 0.605940i
\(636\) 0 0
\(637\) −0.293386 1.66387i −0.0116244 0.0659250i
\(638\) 0 0
\(639\) 2.54189 + 4.40268i 0.100556 + 0.174167i
\(640\) 0 0
\(641\) −6.32383 + 2.30168i −0.249776 + 0.0909111i −0.463874 0.885901i \(-0.653541\pi\)
0.214098 + 0.976812i \(0.431319\pi\)
\(642\) 0 0
\(643\) 19.6819 + 16.5150i 0.776177 + 0.651290i 0.942283 0.334818i \(-0.108675\pi\)
−0.166106 + 0.986108i \(0.553119\pi\)
\(644\) 0 0
\(645\) 0.155697 0.00613055
\(646\) 0 0
\(647\) 50.4380 1.98292 0.991461 0.130403i \(-0.0416271\pi\)
0.991461 + 0.130403i \(0.0416271\pi\)
\(648\) 0 0
\(649\) 0.346201 + 0.290497i 0.0135896 + 0.0114030i
\(650\) 0 0
\(651\) −1.96703 + 0.715942i −0.0770941 + 0.0280600i
\(652\) 0 0
\(653\) 17.9304 + 31.0563i 0.701669 + 1.21533i 0.967880 + 0.251412i \(0.0808949\pi\)
−0.266211 + 0.963915i \(0.585772\pi\)
\(654\) 0 0
\(655\) −2.42943 13.7780i −0.0949255 0.538349i
\(656\) 0 0
\(657\) −1.12449 + 1.94767i −0.0438703 + 0.0759857i
\(658\) 0 0
\(659\) 9.66044 8.10608i 0.376317 0.315768i −0.434937 0.900461i \(-0.643229\pi\)
0.811255 + 0.584693i \(0.198785\pi\)
\(660\) 0 0
\(661\) 41.8820 + 15.2438i 1.62902 + 0.592915i 0.985070 0.172153i \(-0.0550724\pi\)
0.643950 + 0.765068i \(0.277295\pi\)
\(662\) 0 0
\(663\) −0.409253 + 2.32099i −0.0158941 + 0.0901397i
\(664\) 0 0
\(665\) −0.0616516 + 8.37441i −0.00239074 + 0.324746i
\(666\) 0 0
\(667\) 1.46094 8.28541i 0.0565679 0.320812i
\(668\) 0 0
\(669\) −14.2442 5.18447i −0.550713 0.200443i
\(670\) 0 0
\(671\) 0.899615 0.754866i 0.0347292 0.0291413i
\(672\) 0 0
\(673\) 6.41013 11.1027i 0.247092 0.427977i −0.715625 0.698484i \(-0.753858\pi\)
0.962718 + 0.270508i \(0.0871916\pi\)
\(674\) 0 0
\(675\) 0.733956 + 4.16247i 0.0282500 + 0.160213i
\(676\) 0 0
\(677\) 14.6844 + 25.4341i 0.564367 + 0.977512i 0.997108 + 0.0759937i \(0.0242129\pi\)
−0.432742 + 0.901518i \(0.642454\pi\)
\(678\) 0 0
\(679\) 19.3380 7.03844i 0.742123 0.270111i
\(680\) 0 0
\(681\) −4.37733 3.67301i −0.167739 0.140750i
\(682\) 0 0
\(683\) −38.0033 −1.45416 −0.727078 0.686555i \(-0.759122\pi\)
−0.727078 + 0.686555i \(0.759122\pi\)
\(684\) 0 0
\(685\) 4.43613 0.169496
\(686\) 0 0
\(687\) −16.9782 14.2464i −0.647758 0.543533i
\(688\) 0 0
\(689\) −5.94134 + 2.16247i −0.226347 + 0.0823836i
\(690\) 0 0
\(691\) 16.1459 + 27.9655i 0.614219 + 1.06386i 0.990521 + 0.137361i \(0.0438621\pi\)
−0.376302 + 0.926497i \(0.622805\pi\)
\(692\) 0 0
\(693\) 0.0616516 + 0.349643i 0.00234195 + 0.0132819i
\(694\) 0 0
\(695\) 4.64068 8.03790i 0.176031 0.304895i
\(696\) 0 0
\(697\) −25.2126 + 21.1559i −0.954995 + 0.801336i
\(698\) 0 0
\(699\) −10.1750 3.70339i −0.384854 0.140075i
\(700\) 0 0
\(701\) 4.01367 22.7627i 0.151594 0.859734i −0.810239 0.586099i \(-0.800663\pi\)
0.961834 0.273635i \(-0.0882259\pi\)
\(702\) 0 0
\(703\) 3.22849 + 3.90560i 0.121765 + 0.147303i
\(704\) 0 0
\(705\) 0.529563 3.00330i 0.0199445 0.113111i
\(706\) 0 0
\(707\) 12.9452 + 4.71167i 0.486855 + 0.177201i
\(708\) 0 0
\(709\) 28.1589 23.6281i 1.05753 0.887371i 0.0636629 0.997971i \(-0.479722\pi\)
0.993865 + 0.110600i \(0.0352773\pi\)
\(710\) 0 0
\(711\) −2.62061 + 4.53904i −0.0982807 + 0.170227i
\(712\) 0 0
\(713\) 0.214766 + 1.21800i 0.00804304 + 0.0456143i
\(714\) 0 0
\(715\) 0.0542155 + 0.0939039i 0.00202754 + 0.00351181i
\(716\) 0 0
\(717\) 9.26739 3.37305i 0.346097 0.125969i
\(718\) 0 0
\(719\) −25.2414 21.1801i −0.941347 0.789884i 0.0364721 0.999335i \(-0.488388\pi\)
−0.977819 + 0.209451i \(0.932832\pi\)
\(720\) 0 0
\(721\) 18.8239 0.701038
\(722\) 0 0
\(723\) 6.90673 0.256864
\(724\) 0 0
\(725\) 21.1027 + 17.7072i 0.783733 + 0.657630i
\(726\) 0 0
\(727\) −7.44521 + 2.70984i −0.276128 + 0.100502i −0.476372 0.879244i \(-0.658049\pi\)
0.200245 + 0.979746i \(0.435826\pi\)
\(728\) 0 0
\(729\) −0.500000 0.866025i −0.0185185 0.0320750i
\(730\) 0 0
\(731\) 0.0954951 + 0.541580i 0.00353202 + 0.0200311i
\(732\) 0 0
\(733\) 3.71735 6.43864i 0.137303 0.237816i −0.789172 0.614173i \(-0.789490\pi\)
0.926475 + 0.376356i \(0.122823\pi\)
\(734\) 0 0
\(735\) −1.50000 + 1.25865i −0.0553283 + 0.0464260i
\(736\) 0 0
\(737\) 0.162504 + 0.0591466i 0.00598591 + 0.00217869i
\(738\) 0 0
\(739\) −3.36009 + 19.0560i −0.123603 + 0.700987i 0.858525 + 0.512772i \(0.171381\pi\)
−0.982128 + 0.188215i \(0.939730\pi\)
\(740\) 0 0
\(741\) 2.10725 + 2.54920i 0.0774117 + 0.0936472i
\(742\) 0 0
\(743\) −5.44965 + 30.9065i −0.199928 + 1.13385i 0.705295 + 0.708914i \(0.250815\pi\)
−0.905223 + 0.424936i \(0.860296\pi\)
\(744\) 0 0
\(745\) 11.4000 + 4.14927i 0.417665 + 0.152017i
\(746\) 0 0
\(747\) 13.1099 11.0005i 0.479668 0.402489i
\(748\) 0 0
\(749\) −14.3628 + 24.8771i −0.524804 + 0.908988i
\(750\) 0 0
\(751\) −0.906889 5.14322i −0.0330928 0.187679i 0.963780 0.266697i \(-0.0859324\pi\)
−0.996873 + 0.0790187i \(0.974821\pi\)
\(752\) 0 0
\(753\) −12.4461 21.5573i −0.453561 0.785590i
\(754\) 0 0
\(755\) 16.7618 6.10078i 0.610023 0.222030i
\(756\) 0 0
\(757\) −22.8063 19.1368i −0.828911 0.695539i 0.126130 0.992014i \(-0.459744\pi\)
−0.955041 + 0.296475i \(0.904189\pi\)
\(758\) 0 0
\(759\) 0.209770 0.00761415
\(760\) 0 0
\(761\) −9.35267 −0.339034 −0.169517 0.985527i \(-0.554221\pi\)
−0.169517 + 0.985527i \(0.554221\pi\)
\(762\) 0 0
\(763\) −16.8195 14.1133i −0.608908 0.510935i
\(764\) 0 0
\(765\) 2.56670 0.934204i 0.0927994 0.0337762i
\(766\) 0 0
\(767\) −1.05509 1.82747i −0.0380972 0.0659863i
\(768\) 0 0
\(769\) 6.74335 + 38.2434i 0.243171 + 1.37909i 0.824702 + 0.565568i \(0.191343\pi\)
−0.581530 + 0.813525i \(0.697546\pi\)
\(770\) 0 0
\(771\) −7.12836 + 12.3467i −0.256721 + 0.444655i
\(772\) 0 0
\(773\) −18.2069 + 15.2774i −0.654857 + 0.549491i −0.908540 0.417797i \(-0.862802\pi\)
0.253683 + 0.967287i \(0.418358\pi\)
\(774\) 0 0
\(775\) −3.80541 1.38505i −0.136694 0.0497526i
\(776\) 0 0
\(777\) 0.441037 2.50124i 0.0158221 0.0897316i
\(778\) 0 0
\(779\) −0.340022 + 46.1868i −0.0121826 + 1.65481i
\(780\) 0 0
\(781\) −0.143457 + 0.813583i −0.00513328 + 0.0291123i
\(782\) 0 0
\(783\) −6.12449 2.22913i −0.218871 0.0796626i
\(784\) 0 0
\(785\) 8.87551 7.44744i 0.316781 0.265811i
\(786\) 0 0
\(787\) −6.87804 + 11.9131i −0.245176 + 0.424657i −0.962181 0.272411i \(-0.912179\pi\)
0.717005 + 0.697068i \(0.245512\pi\)
\(788\) 0 0
\(789\) 3.75372 + 21.2884i 0.133636 + 0.757887i
\(790\) 0 0
\(791\) −8.78787 15.2210i −0.312461 0.541198i
\(792\) 0 0
\(793\) −5.15270 + 1.87543i −0.182978 + 0.0665985i