Properties

Label 168.2.u.a.89.6
Level 168
Weight 2
Character 168.89
Analytic conductor 1.341
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.6
Root \(0.247636 - 1.71426i\) of \(x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} - 13122 x + 6561\)
Character \(\chi\) \(=\) 168.89
Dual form 168.2.u.a.17.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.642670 - 1.60841i) q^{3} +(1.28955 - 2.23357i) q^{5} +(-0.203402 + 2.63792i) q^{7} +(-2.17395 - 2.06735i) q^{9} +O(q^{10})\) \(q+(0.642670 - 1.60841i) q^{3} +(1.28955 - 2.23357i) q^{5} +(-0.203402 + 2.63792i) q^{7} +(-2.17395 - 2.06735i) q^{9} +(-1.43199 + 0.826762i) q^{11} -5.71177i q^{13} +(-2.76373 - 3.50957i) q^{15} +(3.79313 + 6.56990i) q^{17} +(2.58961 + 1.49511i) q^{19} +(4.11213 + 2.02247i) q^{21} +(-0.249340 - 0.143957i) q^{23} +(-0.825879 - 1.43046i) q^{25} +(-4.72227 + 2.16798i) q^{27} +2.05856i q^{29} +(-5.21209 + 3.00920i) q^{31} +(0.409472 + 2.83457i) q^{33} +(5.62967 + 3.85604i) q^{35} +(-0.877523 + 1.51991i) q^{37} +(-9.18685 - 3.67078i) q^{39} +4.28635 q^{41} +2.46537 q^{43} +(-7.42098 + 2.18971i) q^{45} +(-0.186586 + 0.323176i) q^{47} +(-6.91726 - 1.07312i) q^{49} +(13.0048 - 1.87863i) q^{51} +(-6.73264 + 3.88709i) q^{53} +4.26461i q^{55} +(4.06901 - 3.20429i) q^{57} +(4.89610 + 8.48029i) q^{59} +(0.889794 + 0.513723i) q^{61} +(5.89569 - 5.31421i) q^{63} +(-12.7576 - 7.36561i) q^{65} +(-1.18281 - 2.04868i) q^{67} +(-0.391784 + 0.308524i) q^{69} -15.6655i q^{71} +(-3.30170 + 1.90624i) q^{73} +(-2.83154 + 0.409034i) q^{75} +(-1.88966 - 3.94565i) q^{77} +(4.56033 - 7.89872i) q^{79} +(0.452128 + 8.98864i) q^{81} -6.65166 q^{83} +19.5657 q^{85} +(3.31101 + 1.32298i) q^{87} +(7.25723 - 12.5699i) q^{89} +(15.0672 + 1.16179i) q^{91} +(1.49037 + 10.3171i) q^{93} +(6.67886 - 3.85604i) q^{95} +4.43739i q^{97} +(4.82229 + 1.16309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q + 4q^{7} + 2q^{9} + 8q^{15} - 6q^{19} + 14q^{21} - 18q^{25} - 48q^{31} - 12q^{33} - 2q^{37} - 22q^{39} + 20q^{43} - 42q^{45} - 28q^{49} + 6q^{51} - 8q^{57} + 36q^{61} - 32q^{63} + 14q^{67} + 30q^{73} + 54q^{75} + 28q^{79} + 30q^{81} + 16q^{85} + 78q^{87} + 66q^{91} + 16q^{93} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

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
\(3\) 0.642670 1.60841i 0.371046 0.928615i
\(4\) 0 0
\(5\) 1.28955 2.23357i 0.576704 0.998881i −0.419150 0.907917i \(-0.637672\pi\)
0.995854 0.0909641i \(-0.0289949\pi\)
\(6\) 0 0
\(7\) −0.203402 + 2.63792i −0.0768787 + 0.997040i
\(8\) 0 0
\(9\) −2.17395 2.06735i −0.724650 0.689117i
\(10\) 0 0
\(11\) −1.43199 + 0.826762i −0.431763 + 0.249278i −0.700097 0.714048i \(-0.746860\pi\)
0.268335 + 0.963326i \(0.413527\pi\)
\(12\) 0 0
\(13\) 5.71177i 1.58416i −0.610418 0.792080i \(-0.708998\pi\)
0.610418 0.792080i \(-0.291002\pi\)
\(14\) 0 0
\(15\) −2.76373 3.50957i −0.713592 0.906167i
\(16\) 0 0
\(17\) 3.79313 + 6.56990i 0.919970 + 1.59343i 0.799458 + 0.600722i \(0.205120\pi\)
0.120512 + 0.992712i \(0.461547\pi\)
\(18\) 0 0
\(19\) 2.58961 + 1.49511i 0.594097 + 0.343002i 0.766716 0.641987i \(-0.221890\pi\)
−0.172619 + 0.984989i \(0.555223\pi\)
\(20\) 0 0
\(21\) 4.11213 + 2.02247i 0.897341 + 0.441338i
\(22\) 0 0
\(23\) −0.249340 0.143957i −0.0519910 0.0300170i 0.473779 0.880644i \(-0.342889\pi\)
−0.525770 + 0.850627i \(0.676223\pi\)
\(24\) 0 0
\(25\) −0.825879 1.43046i −0.165176 0.286093i
\(26\) 0 0
\(27\) −4.72227 + 2.16798i −0.908802 + 0.417227i
\(28\) 0 0
\(29\) 2.05856i 0.382265i 0.981564 + 0.191133i \(0.0612161\pi\)
−0.981564 + 0.191133i \(0.938784\pi\)
\(30\) 0 0
\(31\) −5.21209 + 3.00920i −0.936118 + 0.540468i −0.888741 0.458409i \(-0.848420\pi\)
−0.0473770 + 0.998877i \(0.515086\pi\)
\(32\) 0 0
\(33\) 0.409472 + 2.83457i 0.0712798 + 0.493435i
\(34\) 0 0
\(35\) 5.62967 + 3.85604i 0.951589 + 0.651790i
\(36\) 0 0
\(37\) −0.877523 + 1.51991i −0.144264 + 0.249872i −0.929098 0.369833i \(-0.879415\pi\)
0.784834 + 0.619706i \(0.212748\pi\)
\(38\) 0 0
\(39\) −9.18685 3.67078i −1.47107 0.587795i
\(40\) 0 0
\(41\) 4.28635 0.669415 0.334708 0.942322i \(-0.391362\pi\)
0.334708 + 0.942322i \(0.391362\pi\)
\(42\) 0 0
\(43\) 2.46537 0.375965 0.187982 0.982172i \(-0.439805\pi\)
0.187982 + 0.982172i \(0.439805\pi\)
\(44\) 0 0
\(45\) −7.42098 + 2.18971i −1.10625 + 0.326423i
\(46\) 0 0
\(47\) −0.186586 + 0.323176i −0.0272163 + 0.0471401i −0.879313 0.476245i \(-0.841998\pi\)
0.852096 + 0.523385i \(0.175331\pi\)
\(48\) 0 0
\(49\) −6.91726 1.07312i −0.988179 0.153302i
\(50\) 0 0
\(51\) 13.0048 1.87863i 1.82104 0.263061i
\(52\) 0 0
\(53\) −6.73264 + 3.88709i −0.924799 + 0.533933i −0.885163 0.465281i \(-0.845953\pi\)
−0.0396361 + 0.999214i \(0.512620\pi\)
\(54\) 0 0
\(55\) 4.26461i 0.575039i
\(56\) 0 0
\(57\) 4.06901 3.20429i 0.538954 0.424418i
\(58\) 0 0
\(59\) 4.89610 + 8.48029i 0.637417 + 1.10404i 0.985997 + 0.166760i \(0.0533306\pi\)
−0.348580 + 0.937279i \(0.613336\pi\)
\(60\) 0 0
\(61\) 0.889794 + 0.513723i 0.113926 + 0.0657755i 0.555880 0.831262i \(-0.312381\pi\)
−0.441954 + 0.897038i \(0.645715\pi\)
\(62\) 0 0
\(63\) 5.89569 5.31421i 0.742787 0.669527i
\(64\) 0 0
\(65\) −12.7576 7.36561i −1.58239 0.913592i
\(66\) 0 0
\(67\) −1.18281 2.04868i −0.144503 0.250286i 0.784685 0.619895i \(-0.212825\pi\)
−0.929187 + 0.369609i \(0.879492\pi\)
\(68\) 0 0
\(69\) −0.391784 + 0.308524i −0.0471653 + 0.0371419i
\(70\) 0 0
\(71\) 15.6655i 1.85915i −0.368631 0.929576i \(-0.620174\pi\)
0.368631 0.929576i \(-0.379826\pi\)
\(72\) 0 0
\(73\) −3.30170 + 1.90624i −0.386434 + 0.223108i −0.680614 0.732642i \(-0.738287\pi\)
0.294180 + 0.955750i \(0.404954\pi\)
\(74\) 0 0
\(75\) −2.83154 + 0.409034i −0.326958 + 0.0472312i
\(76\) 0 0
\(77\) −1.88966 3.94565i −0.215347 0.449649i
\(78\) 0 0
\(79\) 4.56033 7.89872i 0.513077 0.888676i −0.486808 0.873509i \(-0.661839\pi\)
0.999885 0.0151665i \(-0.00482783\pi\)
\(80\) 0 0
\(81\) 0.452128 + 8.98864i 0.0502364 + 0.998737i
\(82\) 0 0
\(83\) −6.65166 −0.730114 −0.365057 0.930985i \(-0.618951\pi\)
−0.365057 + 0.930985i \(0.618951\pi\)
\(84\) 0 0
\(85\) 19.5657 2.12220
\(86\) 0 0
\(87\) 3.31101 + 1.32298i 0.354977 + 0.141838i
\(88\) 0 0
\(89\) 7.25723 12.5699i 0.769265 1.33241i −0.168697 0.985668i \(-0.553956\pi\)
0.937962 0.346738i \(-0.112711\pi\)
\(90\) 0 0
\(91\) 15.0672 + 1.16179i 1.57947 + 0.121788i
\(92\) 0 0
\(93\) 1.49037 + 10.3171i 0.154544 + 1.06983i
\(94\) 0 0
\(95\) 6.67886 3.85604i 0.685237 0.395622i
\(96\) 0 0
\(97\) 4.43739i 0.450548i 0.974295 + 0.225274i \(0.0723278\pi\)
−0.974295 + 0.225274i \(0.927672\pi\)
\(98\) 0 0
\(99\) 4.82229 + 1.16309i 0.484659 + 0.116895i
\(100\) 0 0
\(101\) −2.03628 3.52694i −0.202617 0.350943i 0.746754 0.665101i \(-0.231611\pi\)
−0.949371 + 0.314157i \(0.898278\pi\)
\(102\) 0 0
\(103\) −7.30346 4.21666i −0.719632 0.415479i 0.0949855 0.995479i \(-0.469720\pi\)
−0.814617 + 0.579999i \(0.803053\pi\)
\(104\) 0 0
\(105\) 9.82011 6.57665i 0.958345 0.641815i
\(106\) 0 0
\(107\) −12.6334 7.29389i −1.22132 0.705127i −0.256118 0.966646i \(-0.582444\pi\)
−0.965199 + 0.261518i \(0.915777\pi\)
\(108\) 0 0
\(109\) −8.64994 14.9821i −0.828514 1.43503i −0.899204 0.437530i \(-0.855853\pi\)
0.0706901 0.997498i \(-0.477480\pi\)
\(110\) 0 0
\(111\) 1.88068 + 2.38822i 0.178507 + 0.226680i
\(112\) 0 0
\(113\) 4.00000i 0.376288i 0.982141 + 0.188144i \(0.0602472\pi\)
−0.982141 + 0.188144i \(0.939753\pi\)
\(114\) 0 0
\(115\) −0.643073 + 0.371279i −0.0599669 + 0.0346219i
\(116\) 0 0
\(117\) −11.8082 + 12.4171i −1.09167 + 1.14796i
\(118\) 0 0
\(119\) −18.1024 + 8.66965i −1.65944 + 0.794746i
\(120\) 0 0
\(121\) −4.13293 + 7.15844i −0.375721 + 0.650767i
\(122\) 0 0
\(123\) 2.75471 6.89420i 0.248384 0.621629i
\(124\) 0 0
\(125\) 8.63545 0.772378
\(126\) 0 0
\(127\) −16.6481 −1.47728 −0.738641 0.674099i \(-0.764532\pi\)
−0.738641 + 0.674099i \(0.764532\pi\)
\(128\) 0 0
\(129\) 1.58442 3.96531i 0.139500 0.349126i
\(130\) 0 0
\(131\) 8.29744 14.3716i 0.724951 1.25565i −0.234043 0.972226i \(-0.575196\pi\)
0.958994 0.283426i \(-0.0914709\pi\)
\(132\) 0 0
\(133\) −4.47072 + 6.52708i −0.387660 + 0.565969i
\(134\) 0 0
\(135\) −1.24729 + 13.3432i −0.107350 + 1.14840i
\(136\) 0 0
\(137\) −8.61684 + 4.97493i −0.736186 + 0.425037i −0.820681 0.571387i \(-0.806406\pi\)
0.0844948 + 0.996424i \(0.473072\pi\)
\(138\) 0 0
\(139\) 3.11952i 0.264594i 0.991210 + 0.132297i \(0.0422353\pi\)
−0.991210 + 0.132297i \(0.957765\pi\)
\(140\) 0 0
\(141\) 0.399886 + 0.507801i 0.0336765 + 0.0427646i
\(142\) 0 0
\(143\) 4.72227 + 8.17922i 0.394896 + 0.683981i
\(144\) 0 0
\(145\) 4.59794 + 2.65462i 0.381838 + 0.220454i
\(146\) 0 0
\(147\) −6.17152 + 10.4361i −0.509018 + 0.860756i
\(148\) 0 0
\(149\) 0.987090 + 0.569897i 0.0808655 + 0.0466877i 0.539888 0.841737i \(-0.318467\pi\)
−0.459022 + 0.888425i \(0.651800\pi\)
\(150\) 0 0
\(151\) 6.38621 + 11.0612i 0.519702 + 0.900151i 0.999738 + 0.0229016i \(0.00729044\pi\)
−0.480036 + 0.877249i \(0.659376\pi\)
\(152\) 0 0
\(153\) 5.33619 22.1244i 0.431406 1.78865i
\(154\) 0 0
\(155\) 15.5221i 1.24676i
\(156\) 0 0
\(157\) 7.82053 4.51518i 0.624146 0.360351i −0.154335 0.988019i \(-0.549324\pi\)
0.778481 + 0.627668i \(0.215990\pi\)
\(158\) 0 0
\(159\) 1.92516 + 13.3269i 0.152675 + 1.05690i
\(160\) 0 0
\(161\) 0.430463 0.628459i 0.0339252 0.0495295i
\(162\) 0 0
\(163\) −0.0498774 + 0.0863903i −0.00390670 + 0.00676661i −0.867972 0.496613i \(-0.834577\pi\)
0.864065 + 0.503379i \(0.167910\pi\)
\(164\) 0 0
\(165\) 6.85922 + 2.74073i 0.533990 + 0.213366i
\(166\) 0 0
\(167\) 3.08612 0.238811 0.119406 0.992846i \(-0.461901\pi\)
0.119406 + 0.992846i \(0.461901\pi\)
\(168\) 0 0
\(169\) −19.6243 −1.50956
\(170\) 0 0
\(171\) −2.53877 8.60393i −0.194144 0.657959i
\(172\) 0 0
\(173\) −3.73038 + 6.46120i −0.283615 + 0.491236i −0.972272 0.233851i \(-0.924867\pi\)
0.688657 + 0.725087i \(0.258201\pi\)
\(174\) 0 0
\(175\) 3.94144 1.88764i 0.297945 0.142693i
\(176\) 0 0
\(177\) 16.7863 2.42490i 1.26174 0.182266i
\(178\) 0 0
\(179\) 2.61465 1.50957i 0.195428 0.112830i −0.399093 0.916910i \(-0.630675\pi\)
0.594521 + 0.804080i \(0.297342\pi\)
\(180\) 0 0
\(181\) 0.762552i 0.0566801i −0.999598 0.0283400i \(-0.990978\pi\)
0.999598 0.0283400i \(-0.00902212\pi\)
\(182\) 0 0
\(183\) 1.39812 1.10100i 0.103352 0.0813881i
\(184\) 0 0
\(185\) 2.26322 + 3.92001i 0.166395 + 0.288205i
\(186\) 0 0
\(187\) −10.8635 6.27204i −0.794417 0.458657i
\(188\) 0 0
\(189\) −4.75843 12.8980i −0.346125 0.938188i
\(190\) 0 0
\(191\) 1.05844 + 0.611089i 0.0765859 + 0.0442169i 0.537804 0.843070i \(-0.319254\pi\)
−0.461218 + 0.887287i \(0.652587\pi\)
\(192\) 0 0
\(193\) 11.7587 + 20.3666i 0.846409 + 1.46602i 0.884392 + 0.466744i \(0.154573\pi\)
−0.0379837 + 0.999278i \(0.512093\pi\)
\(194\) 0 0
\(195\) −20.0458 + 15.7858i −1.43551 + 1.13044i
\(196\) 0 0
\(197\) 14.7312i 1.04956i 0.851239 + 0.524778i \(0.175852\pi\)
−0.851239 + 0.524778i \(0.824148\pi\)
\(198\) 0 0
\(199\) 5.96032 3.44119i 0.422516 0.243940i −0.273637 0.961833i \(-0.588227\pi\)
0.696153 + 0.717893i \(0.254893\pi\)
\(200\) 0 0
\(201\) −4.05527 + 0.585810i −0.286036 + 0.0413198i
\(202\) 0 0
\(203\) −5.43032 0.418716i −0.381134 0.0293881i
\(204\) 0 0
\(205\) 5.52746 9.57384i 0.386055 0.668666i
\(206\) 0 0
\(207\) 0.244445 + 0.828428i 0.0169901 + 0.0575797i
\(208\) 0 0
\(209\) −4.94441 −0.342012
\(210\) 0 0
\(211\) −19.0897 −1.31419 −0.657093 0.753809i \(-0.728214\pi\)
−0.657093 + 0.753809i \(0.728214\pi\)
\(212\) 0 0
\(213\) −25.1965 10.0677i −1.72644 0.689830i
\(214\) 0 0
\(215\) 3.17921 5.50656i 0.216821 0.375544i
\(216\) 0 0
\(217\) −6.87788 14.3612i −0.466901 0.974898i
\(218\) 0 0
\(219\) 0.944103 + 6.53555i 0.0637966 + 0.441632i
\(220\) 0 0
\(221\) 37.5257 21.6655i 2.52425 1.45738i
\(222\) 0 0
\(223\) 10.9876i 0.735785i −0.929868 0.367892i \(-0.880079\pi\)
0.929868 0.367892i \(-0.119921\pi\)
\(224\) 0 0
\(225\) −1.16185 + 4.81714i −0.0774567 + 0.321143i
\(226\) 0 0
\(227\) −9.45418 16.3751i −0.627496 1.08686i −0.988052 0.154118i \(-0.950746\pi\)
0.360556 0.932737i \(-0.382587\pi\)
\(228\) 0 0
\(229\) 14.9744 + 8.64545i 0.989533 + 0.571307i 0.905135 0.425125i \(-0.139770\pi\)
0.0843986 + 0.996432i \(0.473103\pi\)
\(230\) 0 0
\(231\) −7.56065 + 0.503597i −0.497454 + 0.0331343i
\(232\) 0 0
\(233\) 4.45119 + 2.56990i 0.291607 + 0.168360i 0.638666 0.769484i \(-0.279486\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(234\) 0 0
\(235\) 0.481223 + 0.833503i 0.0313916 + 0.0543718i
\(236\) 0 0
\(237\) −9.77358 12.4111i −0.634862 0.806190i
\(238\) 0 0
\(239\) 5.67983i 0.367398i 0.982983 + 0.183699i \(0.0588071\pi\)
−0.982983 + 0.183699i \(0.941193\pi\)
\(240\) 0 0
\(241\) 20.1604 11.6396i 1.29864 0.749773i 0.318475 0.947931i \(-0.396829\pi\)
0.980170 + 0.198158i \(0.0634960\pi\)
\(242\) 0 0
\(243\) 14.7480 + 5.04952i 0.946082 + 0.323927i
\(244\) 0 0
\(245\) −11.3170 + 14.0663i −0.723018 + 0.898664i
\(246\) 0 0
\(247\) 8.53973 14.7913i 0.543370 0.941145i
\(248\) 0 0
\(249\) −4.27482 + 10.6986i −0.270906 + 0.677995i
\(250\) 0 0
\(251\) 21.3799 1.34949 0.674744 0.738052i \(-0.264254\pi\)
0.674744 + 0.738052i \(0.264254\pi\)
\(252\) 0 0
\(253\) 0.476072 0.0299304
\(254\) 0 0
\(255\) 12.5743 31.4697i 0.787433 1.97071i
\(256\) 0 0
\(257\) −7.09305 + 12.2855i −0.442452 + 0.766349i −0.997871 0.0652214i \(-0.979225\pi\)
0.555419 + 0.831571i \(0.312558\pi\)
\(258\) 0 0
\(259\) −3.83092 2.62399i −0.238042 0.163047i
\(260\) 0 0
\(261\) 4.25577 4.47521i 0.263425 0.277009i
\(262\) 0 0
\(263\) −1.90698 + 1.10100i −0.117590 + 0.0678904i −0.557641 0.830082i \(-0.688293\pi\)
0.440052 + 0.897973i \(0.354960\pi\)
\(264\) 0 0
\(265\) 20.0504i 1.23169i
\(266\) 0 0
\(267\) −15.5535 19.7509i −0.951860 1.20873i
\(268\) 0 0
\(269\) −7.33275 12.7007i −0.447086 0.774375i 0.551109 0.834433i \(-0.314205\pi\)
−0.998195 + 0.0600579i \(0.980871\pi\)
\(270\) 0 0
\(271\) 17.6687 + 10.2010i 1.07330 + 0.619669i 0.929081 0.369877i \(-0.120600\pi\)
0.144217 + 0.989546i \(0.453934\pi\)
\(272\) 0 0
\(273\) 11.5519 23.4875i 0.699150 1.42153i
\(274\) 0 0
\(275\) 2.36531 + 1.36561i 0.142633 + 0.0823495i
\(276\) 0 0
\(277\) −0.00535275 0.00927123i −0.000321615 0.000557054i 0.865865 0.500279i \(-0.166769\pi\)
−0.866186 + 0.499721i \(0.833436\pi\)
\(278\) 0 0
\(279\) 17.5519 + 4.23335i 1.05080 + 0.253444i
\(280\) 0 0
\(281\) 8.11712i 0.484227i −0.970248 0.242114i \(-0.922159\pi\)
0.970248 0.242114i \(-0.0778406\pi\)
\(282\) 0 0
\(283\) −3.34466 + 1.93104i −0.198819 + 0.114788i −0.596105 0.802907i \(-0.703286\pi\)
0.397285 + 0.917695i \(0.369952\pi\)
\(284\) 0 0
\(285\) −1.90979 13.2205i −0.113126 0.783115i
\(286\) 0 0
\(287\) −0.871852 + 11.3070i −0.0514638 + 0.667434i
\(288\) 0 0
\(289\) −20.2757 + 35.1185i −1.19269 + 2.06580i
\(290\) 0 0
\(291\) 7.13713 + 2.85177i 0.418386 + 0.167174i
\(292\) 0 0
\(293\) 5.75351 0.336123 0.168062 0.985776i \(-0.446249\pi\)
0.168062 + 0.985776i \(0.446249\pi\)
\(294\) 0 0
\(295\) 25.2550 1.47041
\(296\) 0 0
\(297\) 4.96987 7.00873i 0.288381 0.406688i
\(298\) 0 0
\(299\) −0.822247 + 1.42417i −0.0475518 + 0.0823621i
\(300\) 0 0
\(301\) −0.501460 + 6.50344i −0.0289037 + 0.374852i
\(302\) 0 0
\(303\) −6.98141 + 1.00851i −0.401071 + 0.0579374i
\(304\) 0 0
\(305\) 2.29487 1.32494i 0.131404 0.0758660i
\(306\) 0 0
\(307\) 23.9041i 1.36428i −0.731221 0.682140i \(-0.761049\pi\)
0.731221 0.682140i \(-0.238951\pi\)
\(308\) 0 0
\(309\) −11.4758 + 9.03703i −0.652836 + 0.514099i
\(310\) 0 0
\(311\) 10.5789 + 18.3232i 0.599874 + 1.03901i 0.992839 + 0.119459i \(0.0381159\pi\)
−0.392965 + 0.919553i \(0.628551\pi\)
\(312\) 0 0
\(313\) −18.2861 10.5575i −1.03359 0.596746i −0.115582 0.993298i \(-0.536873\pi\)
−0.918012 + 0.396552i \(0.870207\pi\)
\(314\) 0 0
\(315\) −4.26685 20.0214i −0.240410 1.12808i
\(316\) 0 0
\(317\) −13.8698 8.00775i −0.779007 0.449760i 0.0570712 0.998370i \(-0.481824\pi\)
−0.836078 + 0.548610i \(0.815157\pi\)
\(318\) 0 0
\(319\) −1.70194 2.94785i −0.0952904 0.165048i
\(320\) 0 0
\(321\) −19.8507 + 15.6321i −1.10796 + 0.872498i
\(322\) 0 0
\(323\) 22.6846i 1.26221i
\(324\) 0 0
\(325\) −8.17048 + 4.71723i −0.453217 + 0.261665i
\(326\) 0 0
\(327\) −29.6564 + 4.28406i −1.64000 + 0.236909i
\(328\) 0 0
\(329\) −0.814561 0.557933i −0.0449082 0.0307599i
\(330\) 0 0
\(331\) −9.48985 + 16.4369i −0.521610 + 0.903454i 0.478074 + 0.878319i \(0.341335\pi\)
−0.999684 + 0.0251350i \(0.991998\pi\)
\(332\) 0 0
\(333\) 5.04989 1.49007i 0.276732 0.0816555i
\(334\) 0 0
\(335\) −6.10115 −0.333341
\(336\) 0 0
\(337\) 0.151144 0.00823337 0.00411668 0.999992i \(-0.498690\pi\)
0.00411668 + 0.999992i \(0.498690\pi\)
\(338\) 0 0
\(339\) 6.43363 + 2.57068i 0.349427 + 0.139620i
\(340\) 0 0
\(341\) 4.97579 8.61831i 0.269454 0.466708i
\(342\) 0 0
\(343\) 4.23778 18.0289i 0.228819 0.973469i
\(344\) 0 0
\(345\) 0.183884 + 1.27293i 0.00989996 + 0.0685325i
\(346\) 0 0
\(347\) 11.5977 6.69596i 0.622599 0.359458i −0.155281 0.987870i \(-0.549628\pi\)
0.777880 + 0.628412i \(0.216295\pi\)
\(348\) 0 0
\(349\) 13.4025i 0.717421i 0.933449 + 0.358710i \(0.116783\pi\)
−0.933449 + 0.358710i \(0.883217\pi\)
\(350\) 0 0
\(351\) 12.3830 + 26.9725i 0.660955 + 1.43969i
\(352\) 0 0
\(353\) 10.7469 + 18.6141i 0.571998 + 0.990729i 0.996361 + 0.0852371i \(0.0271648\pi\)
−0.424363 + 0.905492i \(0.639502\pi\)
\(354\) 0 0
\(355\) −34.9899 20.2014i −1.85707 1.07218i
\(356\) 0 0
\(357\) 2.31047 + 34.6878i 0.122283 + 1.83587i
\(358\) 0 0
\(359\) 24.4173 + 14.0974i 1.28870 + 0.744030i 0.978422 0.206616i \(-0.0662452\pi\)
0.310276 + 0.950647i \(0.399579\pi\)
\(360\) 0 0
\(361\) −5.02928 8.71097i −0.264699 0.458472i
\(362\) 0 0
\(363\) 8.85759 + 11.2479i 0.464903 + 0.590364i
\(364\) 0 0
\(365\) 9.83274i 0.514669i
\(366\) 0 0
\(367\) −19.6810 + 11.3628i −1.02734 + 0.593135i −0.916221 0.400673i \(-0.868776\pi\)
−0.111118 + 0.993807i \(0.535443\pi\)
\(368\) 0 0
\(369\) −9.31831 8.86138i −0.485092 0.461305i
\(370\) 0 0
\(371\) −8.88441 18.5508i −0.461255 0.963110i
\(372\) 0 0
\(373\) 6.95699 12.0499i 0.360219 0.623918i −0.627778 0.778393i \(-0.716035\pi\)
0.987997 + 0.154475i \(0.0493686\pi\)
\(374\) 0 0
\(375\) 5.54974 13.8893i 0.286588 0.717242i
\(376\) 0 0
\(377\) 11.7580 0.605569
\(378\) 0 0
\(379\) 20.8656 1.07179 0.535897 0.844283i \(-0.319973\pi\)
0.535897 + 0.844283i \(0.319973\pi\)
\(380\) 0 0
\(381\) −10.6992 + 26.7770i −0.548139 + 1.37183i
\(382\) 0 0
\(383\) −1.23577 + 2.14042i −0.0631451 + 0.109371i −0.895870 0.444317i \(-0.853446\pi\)
0.832725 + 0.553687i \(0.186780\pi\)
\(384\) 0 0
\(385\) −11.2497 0.867429i −0.573337 0.0442083i
\(386\) 0 0
\(387\) −5.35959 5.09677i −0.272443 0.259084i
\(388\) 0 0
\(389\) −20.4245 + 11.7921i −1.03556 + 0.597882i −0.918573 0.395251i \(-0.870658\pi\)
−0.116989 + 0.993133i \(0.537324\pi\)
\(390\) 0 0
\(391\) 2.18419i 0.110459i
\(392\) 0 0
\(393\) −17.7829 22.5819i −0.897027 1.13910i
\(394\) 0 0
\(395\) −11.7615 20.3716i −0.591788 1.02501i
\(396\) 0 0
\(397\) −1.79160 1.03438i −0.0899181 0.0519142i 0.454367 0.890815i \(-0.349866\pi\)
−0.544285 + 0.838901i \(0.683199\pi\)
\(398\) 0 0
\(399\) 7.62501 + 11.3855i 0.381728 + 0.569988i
\(400\) 0 0
\(401\) −6.46052 3.72998i −0.322623 0.186266i 0.329938 0.944003i \(-0.392972\pi\)
−0.652561 + 0.757736i \(0.726305\pi\)
\(402\) 0 0
\(403\) 17.1879 + 29.7702i 0.856188 + 1.48296i
\(404\) 0 0
\(405\) 20.6598 + 10.5814i 1.02659 + 0.525796i
\(406\) 0 0
\(407\) 2.90201i 0.143847i
\(408\) 0 0
\(409\) 29.2897 16.9104i 1.44828 0.836166i 0.449902 0.893078i \(-0.351459\pi\)
0.998379 + 0.0569122i \(0.0181255\pi\)
\(410\) 0 0
\(411\) 2.46394 + 17.0566i 0.121537 + 0.841342i
\(412\) 0 0
\(413\) −23.3662 + 11.1906i −1.14978 + 0.550654i
\(414\) 0 0
\(415\) −8.57764 + 14.8569i −0.421060 + 0.729297i
\(416\) 0 0
\(417\) 5.01746 + 2.00482i 0.245706 + 0.0981765i
\(418\) 0 0
\(419\) −15.2980 −0.747358 −0.373679 0.927558i \(-0.621904\pi\)
−0.373679 + 0.927558i \(0.621904\pi\)
\(420\) 0 0
\(421\) 11.8931 0.579633 0.289816 0.957082i \(-0.406406\pi\)
0.289816 + 0.957082i \(0.406406\pi\)
\(422\) 0 0
\(423\) 1.07375 0.316831i 0.0522073 0.0154048i
\(424\) 0 0
\(425\) 6.26534 10.8519i 0.303913 0.526393i
\(426\) 0 0
\(427\) −1.53615 + 2.24271i −0.0743393 + 0.108533i
\(428\) 0 0
\(429\) 16.1904 2.33881i 0.781679 0.112919i
\(430\) 0 0
\(431\) −14.9148 + 8.61109i −0.718423 + 0.414782i −0.814172 0.580624i \(-0.802809\pi\)
0.0957491 + 0.995405i \(0.469475\pi\)
\(432\) 0 0
\(433\) 1.55093i 0.0745329i 0.999305 + 0.0372664i \(0.0118650\pi\)
−0.999305 + 0.0372664i \(0.988135\pi\)
\(434\) 0 0
\(435\) 7.22466 5.68931i 0.346396 0.272782i
\(436\) 0 0
\(437\) −0.430463 0.745583i −0.0205918 0.0356661i
\(438\) 0 0
\(439\) 16.8278 + 9.71551i 0.803145 + 0.463696i 0.844570 0.535446i \(-0.179856\pi\)
−0.0414249 + 0.999142i \(0.513190\pi\)
\(440\) 0 0
\(441\) 12.8193 + 16.6333i 0.610441 + 0.792062i
\(442\) 0 0
\(443\) −3.08964 1.78380i −0.146793 0.0847510i 0.424805 0.905285i \(-0.360343\pi\)
−0.571598 + 0.820534i \(0.693676\pi\)
\(444\) 0 0
\(445\) −18.7171 32.4190i −0.887277 1.53681i
\(446\) 0 0
\(447\) 1.55100 1.22139i 0.0733597 0.0577697i
\(448\) 0 0
\(449\) 29.5796i 1.39595i −0.716124 0.697973i \(-0.754085\pi\)
0.716124 0.697973i \(-0.245915\pi\)
\(450\) 0 0
\(451\) −6.13803 + 3.54379i −0.289028 + 0.166871i
\(452\) 0 0
\(453\) 21.8952 3.16290i 1.02873 0.148606i
\(454\) 0 0
\(455\) 22.0248 32.1554i 1.03254 1.50747i
\(456\) 0 0
\(457\) 11.2312 19.4530i 0.525374 0.909975i −0.474189 0.880423i \(-0.657259\pi\)
0.999563 0.0295520i \(-0.00940807\pi\)
\(458\) 0 0
\(459\) −32.1556 22.8014i −1.50089 1.06428i
\(460\) 0 0
\(461\) −9.31904 −0.434031 −0.217015 0.976168i \(-0.569632\pi\)
−0.217015 + 0.976168i \(0.569632\pi\)
\(462\) 0 0
\(463\) −16.6243 −0.772597 −0.386298 0.922374i \(-0.626246\pi\)
−0.386298 + 0.922374i \(0.626246\pi\)
\(464\) 0 0
\(465\) 24.9658 + 9.97556i 1.15776 + 0.462605i
\(466\) 0 0
\(467\) −6.06560 + 10.5059i −0.280683 + 0.486156i −0.971553 0.236822i \(-0.923894\pi\)
0.690871 + 0.722979i \(0.257227\pi\)
\(468\) 0 0
\(469\) 5.64484 2.70344i 0.260654 0.124833i
\(470\) 0 0
\(471\) −2.23624 15.4804i −0.103040 0.713298i
\(472\) 0 0
\(473\) −3.53039 + 2.03827i −0.162328 + 0.0937198i
\(474\) 0 0
\(475\) 4.93913i 0.226623i
\(476\) 0 0
\(477\) 22.6724 + 5.46838i 1.03810 + 0.250380i
\(478\) 0 0
\(479\) −13.2594 22.9660i −0.605839 1.04934i −0.991918 0.126878i \(-0.959504\pi\)
0.386080 0.922465i \(-0.373829\pi\)
\(480\) 0 0
\(481\) 8.68140 + 5.01221i 0.395838 + 0.228537i
\(482\) 0 0
\(483\) −0.734173 1.09625i −0.0334060 0.0498811i
\(484\) 0 0
\(485\) 9.91120 + 5.72223i 0.450044 + 0.259833i
\(486\) 0 0
\(487\) 17.5986 + 30.4817i 0.797469 + 1.38126i 0.921260 + 0.388948i \(0.127161\pi\)
−0.123791 + 0.992308i \(0.539505\pi\)
\(488\) 0 0
\(489\) 0.106896 + 0.135744i 0.00483401 + 0.00613854i
\(490\) 0 0
\(491\) 32.5795i 1.47029i −0.677910 0.735145i \(-0.737114\pi\)
0.677910 0.735145i \(-0.262886\pi\)
\(492\) 0 0
\(493\) −13.5245 + 7.80840i −0.609115 + 0.351673i
\(494\) 0 0
\(495\) 8.81643 9.27104i 0.396269 0.416702i
\(496\) 0 0
\(497\) 41.3243 + 3.18639i 1.85365 + 0.142929i
\(498\) 0 0
\(499\) −2.46895 + 4.27635i −0.110525 + 0.191436i −0.915982 0.401219i \(-0.868587\pi\)
0.805457 + 0.592655i \(0.201920\pi\)
\(500\) 0 0
\(501\) 1.98336 4.96374i 0.0886099 0.221764i
\(502\) 0 0
\(503\) −16.7907 −0.748661 −0.374331 0.927295i \(-0.622127\pi\)
−0.374331 + 0.927295i \(0.622127\pi\)
\(504\) 0 0
\(505\) −10.5035 −0.467401
\(506\) 0 0
\(507\) −12.6119 + 31.5639i −0.560116 + 1.40180i
\(508\) 0 0
\(509\) −0.631490 + 1.09377i −0.0279903 + 0.0484806i −0.879681 0.475564i \(-0.842244\pi\)
0.851691 + 0.524044i \(0.175577\pi\)
\(510\) 0 0
\(511\) −4.35693 9.09735i −0.192739 0.402443i
\(512\) 0 0
\(513\) −15.4702 1.44611i −0.683027 0.0638475i
\(514\) 0 0
\(515\) −18.8364 + 10.8752i −0.830029 + 0.479218i
\(516\) 0 0
\(517\) 0.617048i 0.0271378i
\(518\) 0 0
\(519\) 7.99485 + 10.1524i 0.350935 + 0.445640i
\(520\) 0 0
\(521\) −14.9945 25.9713i −0.656922 1.13782i −0.981408 0.191932i \(-0.938525\pi\)
0.324486 0.945891i \(-0.394809\pi\)
\(522\) 0 0
\(523\) 30.7587 + 17.7586i 1.34499 + 0.776528i 0.987534 0.157404i \(-0.0503125\pi\)
0.357451 + 0.933932i \(0.383646\pi\)
\(524\) 0 0
\(525\) −0.503059 7.55257i −0.0219553 0.329621i
\(526\) 0 0
\(527\) −39.5403 22.8286i −1.72240 0.994429i
\(528\) 0 0
\(529\) −11.4586 19.8468i −0.498198 0.862904i
\(530\) 0 0
\(531\) 6.88785 28.5577i 0.298907 1.23930i
\(532\) 0 0
\(533\) 24.4826i 1.06046i
\(534\) 0 0
\(535\) −32.5828 + 18.8117i −1.40868 + 0.813300i
\(536\) 0 0
\(537\) −0.747645 5.17557i −0.0322633 0.223343i
\(538\) 0 0
\(539\) 10.7927 4.18223i 0.464874 0.180141i
\(540\) 0 0
\(541\) 11.9158 20.6388i 0.512300 0.887330i −0.487598 0.873068i \(-0.662127\pi\)
0.999898 0.0142616i \(-0.00453975\pi\)
\(542\) 0 0
\(543\) −1.22649 0.490069i −0.0526339 0.0210309i
\(544\) 0 0
\(545\) −44.6181 −1.91123
\(546\) 0 0
\(547\) 21.1040 0.902342 0.451171 0.892437i \(-0.351006\pi\)
0.451171 + 0.892437i \(0.351006\pi\)
\(548\) 0 0
\(549\) −0.872324 2.95632i −0.0372299 0.126173i
\(550\) 0 0
\(551\) −3.07778 + 5.33087i −0.131118 + 0.227103i
\(552\) 0 0
\(553\) 19.9086 + 13.6364i 0.846601 + 0.579879i
\(554\) 0 0
\(555\) 7.75948 1.12091i 0.329372 0.0475799i
\(556\) 0 0
\(557\) 19.3020 11.1440i 0.817852 0.472187i −0.0318235 0.999494i \(-0.510131\pi\)
0.849675 + 0.527307i \(0.176798\pi\)
\(558\) 0 0
\(559\) 14.0816i 0.595588i
\(560\) 0 0
\(561\) −17.0696 + 13.4421i −0.720680 + 0.567525i
\(562\) 0 0
\(563\) 20.2197 + 35.0215i 0.852157 + 1.47598i 0.879258 + 0.476347i \(0.158039\pi\)
−0.0271005 + 0.999633i \(0.508627\pi\)
\(564\) 0 0
\(565\) 8.93427 + 5.15820i 0.375867 + 0.217007i
\(566\) 0 0
\(567\) −23.8033 0.635629i −0.999644 0.0266939i
\(568\) 0 0
\(569\) 21.7717 + 12.5699i 0.912717 + 0.526957i 0.881304 0.472549i \(-0.156666\pi\)
0.0314127 + 0.999506i \(0.489999\pi\)
\(570\) 0 0
\(571\) −0.655344 1.13509i −0.0274253 0.0475020i 0.851987 0.523563i \(-0.175398\pi\)
−0.879412 + 0.476061i \(0.842064\pi\)
\(572\) 0 0
\(573\) 1.66311 1.30967i 0.0694773 0.0547123i
\(574\) 0 0
\(575\) 0.475563i 0.0198324i
\(576\) 0 0
\(577\) 5.21739 3.01226i 0.217203 0.125402i −0.387452 0.921890i \(-0.626645\pi\)
0.604654 + 0.796488i \(0.293311\pi\)
\(578\) 0 0
\(579\) 40.3148 5.82374i 1.67543 0.242026i
\(580\) 0 0
\(581\) 1.35296 17.5465i 0.0561303 0.727953i
\(582\) 0 0
\(583\) 6.42740 11.1326i 0.266196 0.461065i
\(584\) 0 0
\(585\) 12.5071 + 42.3869i 0.517106 + 1.75248i
\(586\) 0 0
\(587\) 39.5131 1.63088 0.815439 0.578843i \(-0.196496\pi\)
0.815439 + 0.578843i \(0.196496\pi\)
\(588\) 0 0
\(589\) −17.9964 −0.741527
\(590\) 0 0
\(591\) 23.6938 + 9.46731i 0.974633 + 0.389433i
\(592\) 0 0
\(593\) −6.75855 + 11.7062i −0.277540 + 0.480714i −0.970773 0.240000i \(-0.922853\pi\)
0.693232 + 0.720714i \(0.256186\pi\)
\(594\) 0 0
\(595\) −3.97971 + 51.6129i −0.163152 + 2.11592i
\(596\) 0 0
\(597\) −1.70432 11.7982i −0.0697533 0.482867i
\(598\) 0 0
\(599\) −5.68762 + 3.28375i −0.232390 + 0.134170i −0.611674 0.791110i \(-0.709504\pi\)
0.379284 + 0.925280i \(0.376170\pi\)
\(600\) 0 0
\(601\) 10.0499i 0.409946i −0.978768 0.204973i \(-0.934289\pi\)
0.978768 0.204973i \(-0.0657106\pi\)
\(602\) 0 0
\(603\) −1.66398 + 6.89900i −0.0677623 + 0.280949i
\(604\) 0 0
\(605\) 10.6592 + 18.4623i 0.433360 + 0.750601i
\(606\) 0 0
\(607\) −0.673920 0.389088i −0.0273536 0.0157926i 0.486261 0.873814i \(-0.338360\pi\)
−0.513614 + 0.858021i \(0.671694\pi\)
\(608\) 0 0
\(609\) −4.16337 + 8.46508i −0.168708 + 0.343022i
\(610\) 0 0
\(611\) 1.84591 + 1.06573i 0.0746774 + 0.0431150i
\(612\) 0 0
\(613\) −19.3349 33.4890i −0.780928 1.35261i −0.931402 0.363993i \(-0.881413\pi\)
0.150474 0.988614i \(-0.451920\pi\)
\(614\) 0 0
\(615\) −11.8463 15.0432i −0.477689 0.606602i
\(616\) 0 0
\(617\) 7.83523i 0.315434i −0.987484 0.157717i \(-0.949587\pi\)
0.987484 0.157717i \(-0.0504134\pi\)
\(618\) 0 0
\(619\) 17.9235 10.3481i 0.720407 0.415927i −0.0944957 0.995525i \(-0.530124\pi\)
0.814902 + 0.579598i \(0.196791\pi\)
\(620\) 0 0
\(621\) 1.48955 + 0.139239i 0.0597735 + 0.00558747i
\(622\) 0 0
\(623\) 31.6823 + 21.7008i 1.26932 + 0.869422i
\(624\) 0 0
\(625\) 15.2652 26.4402i 0.610610 1.05761i
\(626\) 0 0
\(627\) −3.17762 + 7.95263i −0.126902 + 0.317597i
\(628\) 0 0
\(629\) −13.3142 −0.530874
\(630\) 0 0
\(631\) −7.21022 −0.287034 −0.143517 0.989648i \(-0.545841\pi\)
−0.143517 + 0.989648i \(0.545841\pi\)
\(632\) 0 0
\(633\) −12.2683 + 30.7040i −0.487623 + 1.22037i
\(634\) 0 0
\(635\) −21.4686 + 37.1847i −0.851955 + 1.47563i
\(636\) 0 0
\(637\) −6.12940 + 39.5098i −0.242855 + 1.56543i
\(638\) 0 0
\(639\) −32.3860 + 34.0560i −1.28117 + 1.34723i
\(640\) 0 0
\(641\) −31.9156 + 18.4265i −1.26059 + 0.727802i −0.973189 0.230009i \(-0.926124\pi\)
−0.287401 + 0.957810i \(0.592791\pi\)
\(642\) 0 0
\(643\) 10.5183i 0.414801i −0.978256 0.207400i \(-0.933500\pi\)
0.978256 0.207400i \(-0.0665003\pi\)
\(644\) 0 0
\(645\) −6.81361 8.65237i −0.268286 0.340687i
\(646\) 0 0
\(647\) −10.2057 17.6768i −0.401228 0.694948i 0.592646 0.805463i \(-0.298083\pi\)
−0.993874 + 0.110515i \(0.964750\pi\)
\(648\) 0 0
\(649\) −14.0224 8.09581i −0.550426 0.317789i
\(650\) 0 0
\(651\) −27.5188 + 1.83296i −1.07855 + 0.0718395i
\(652\) 0 0
\(653\) 28.7382 + 16.5920i 1.12461 + 0.649295i 0.942574 0.333996i \(-0.108397\pi\)
0.182038 + 0.983291i \(0.441731\pi\)
\(654\) 0 0
\(655\) −21.3999 37.0658i −0.836165 1.44828i
\(656\) 0 0
\(657\) 11.1186 + 2.68170i 0.433777 + 0.104623i
\(658\) 0 0
\(659\) 7.18286i 0.279804i 0.990165 + 0.139902i \(0.0446788\pi\)
−0.990165 + 0.139902i \(0.955321\pi\)
\(660\) 0 0
\(661\) −18.2360 + 10.5285i −0.709297 + 0.409513i −0.810801 0.585323i \(-0.800968\pi\)
0.101504 + 0.994835i \(0.467635\pi\)
\(662\) 0 0
\(663\) −10.7303 74.2804i −0.416730 2.88481i
\(664\) 0 0
\(665\) 8.81344 + 18.4026i 0.341771 + 0.713624i
\(666\) 0 0
\(667\) 0.296344 0.513282i 0.0114745 0.0198744i
\(668\) 0 0
\(669\) −17.6726 7.06140i −0.683261 0.273010i
\(670\) 0 0
\(671\) −1.69891 −0.0655856
\(672\) 0 0
\(673\) −21.5441 −0.830464 −0.415232 0.909715i \(-0.636300\pi\)
−0.415232 + 0.909715i \(0.636300\pi\)
\(674\) 0 0
\(675\) 7.00124 + 4.96456i 0.269478 + 0.191086i
\(676\) 0 0
\(677\) 2.69876 4.67439i 0.103722 0.179651i −0.809493 0.587129i \(-0.800258\pi\)
0.913215 + 0.407477i \(0.133592\pi\)
\(678\) 0 0
\(679\) −11.7055 0.902573i −0.449215 0.0346376i
\(680\) 0 0
\(681\) −32.4138 + 4.68238i −1.24210 + 0.179429i
\(682\) 0 0
\(683\) −28.9007 + 16.6858i −1.10585 + 0.638465i −0.937752 0.347305i \(-0.887097\pi\)
−0.168101 + 0.985770i \(0.553764\pi\)
\(684\) 0 0
\(685\) 25.6617i 0.980483i
\(686\) 0 0
\(687\) 23.5290 18.5287i 0.897686 0.706914i
\(688\) 0 0
\(689\) 22.2022 + 38.4553i 0.845835 + 1.46503i
\(690\) 0 0
\(691\) −34.4696 19.9010i −1.31128 0.757070i −0.328975 0.944339i \(-0.606703\pi\)
−0.982309 + 0.187268i \(0.940037\pi\)
\(692\) 0 0
\(693\) −4.04901 + 12.4843i −0.153809 + 0.474238i
\(694\) 0 0
\(695\) 6.96765 + 4.02278i 0.264298 + 0.152593i
\(696\) 0 0
\(697\) 16.2587 + 28.1609i 0.615842 + 1.06667i
\(698\) 0 0
\(699\) 6.99409 5.50774i 0.264541 0.208322i
\(700\) 0 0
\(701\) 10.6583i 0.402559i 0.979534 + 0.201280i \(0.0645100\pi\)
−0.979534 + 0.201280i \(0.935490\pi\)
\(702\) 0 0
\(703\) −4.54488 + 2.62399i −0.171414 + 0.0989657i
\(704\) 0 0
\(705\) 1.64988 0.238336i 0.0621381 0.00897626i
\(706\) 0 0
\(707\) 9.71797 4.65416i 0.365482 0.175038i
\(708\) 0 0
\(709\) −17.5727 + 30.4367i −0.659955 + 1.14308i 0.320672 + 0.947190i \(0.396091\pi\)
−0.980627 + 0.195885i \(0.937242\pi\)
\(710\) 0 0
\(711\) −26.2434 + 7.74364i −0.984203 + 0.290409i
\(712\) 0 0
\(713\) 1.73278 0.0648930
\(714\) 0 0
\(715\) 24.3584 0.910954
\(716\) 0 0
\(717\) 9.13549 + 3.65026i 0.341171 + 0.136321i
\(718\) 0 0
\(719\) 15.6309 27.0734i 0.582932 1.00967i −0.412197 0.911095i \(-0.635239\pi\)
0.995130 0.0985739i \(-0.0314281\pi\)
\(720\) 0 0
\(721\) 12.6087 18.4083i 0.469574 0.685560i
\(722\) 0 0
\(723\) −5.76476 39.9066i −0.214394 1.48414i
\(724\) 0 0
\(725\) 2.94470 1.70012i 0.109363 0.0631410i
\(726\) 0 0
\(727\) 39.7975i 1.47601i 0.674797 + 0.738003i \(0.264231\pi\)
−0.674797 + 0.738003i \(0.735769\pi\)
\(728\) 0 0
\(729\) 17.5998 20.4756i 0.651843 0.758354i
\(730\) 0 0
\(731\) 9.35146 + 16.1972i 0.345876 + 0.599075i
\(732\) 0 0
\(733\) 10.5878 + 6.11289i 0.391071 + 0.225785i 0.682624 0.730770i \(-0.260839\pi\)
−0.291553 + 0.956555i \(0.594172\pi\)
\(734\) 0 0
\(735\) 15.3513 + 27.2424i 0.566240 + 1.00485i
\(736\) 0 0
\(737\) 3.38754 + 1.95580i 0.124782 + 0.0720428i
\(738\) 0 0
\(739\) −14.5001 25.1148i −0.533393 0.923864i −0.999239 0.0389981i \(-0.987583\pi\)
0.465846 0.884866i \(-0.345750\pi\)
\(740\) 0 0
\(741\) −18.3021 23.2413i −0.672346 0.853789i
\(742\) 0 0
\(743\) 33.4864i 1.22850i 0.789113 + 0.614248i \(0.210541\pi\)
−0.789113 + 0.614248i \(0.789459\pi\)
\(744\) 0 0
\(745\) 2.54580 1.46982i 0.0932710 0.0538501i
\(746\) 0 0
\(747\) 14.4604 + 13.7513i 0.529078 + 0.503134i
\(748\) 0 0
\(749\) 21.8104 31.8423i 0.796934 1.16349i
\(750\) 0 0
\(751\) −5.86021 + 10.1502i −0.213842 + 0.370385i −0.952914 0.303242i \(-0.901931\pi\)
0.739072 + 0.673627i \(0.235264\pi\)
\(752\) 0 0
\(753\) 13.7402 34.3876i 0.500722 1.25315i
\(754\) 0 0
\(755\) 32.9413 1.19886
\(756\) 0 0
\(757\) 11.2688 0.409571 0.204785 0.978807i \(-0.434350\pi\)
0.204785 + 0.978807i \(0.434350\pi\)
\(758\) 0 0
\(759\) 0.305957 0.765717i 0.0111055 0.0277938i
\(760\) 0 0
\(761\) −10.0633 + 17.4301i −0.364793 + 0.631841i −0.988743 0.149624i \(-0.952194\pi\)
0.623950 + 0.781465i \(0.285527\pi\)
\(762\) 0 0
\(763\) 41.2811 19.7705i 1.49448 0.715739i
\(764\) 0 0
\(765\) −42.5349 40.4492i −1.53785 1.46244i
\(766\) 0 0
\(767\) 48.4374 27.9654i 1.74897 1.00977i
\(768\) 0 0
\(769\) 7.95157i 0.286741i 0.989669 + 0.143370i \(0.0457940\pi\)
−0.989669 + 0.143370i \(0.954206\pi\)
\(770\) 0 0
\(771\) 15.2016 + 19.3040i 0.547473 + 0.695218i
\(772\) 0 0
\(773\) −15.8927 27.5269i −0.571620 0.990075i −0.996400 0.0847784i \(-0.972982\pi\)
0.424780 0.905297i \(-0.360352\pi\)
\(774\) 0 0
\(775\) 8.60911 + 4.97047i 0.309248 + 0.178545i
\(776\) 0 0
\(777\) −6.68246 + 4.47533i −0.239732 + 0.160552i
\(778\) 0 0
\(779\) 11.1000 + 6.40857i 0.397698 + 0.229611i
\(780\) 0 0
\(781\) 12.9516 + 22.4329i 0.463446 + 0.802712i
\(782\) 0 0
\(783\) −4.46291 9.72110i −0.159492 0.347404i
\(784\) 0 0
\(785\) 23.2902i 0.831264i
\(786\) 0 0
\(787\) 26.3569 15.2172i 0.939523 0.542434i 0.0497122 0.998764i \(-0.484170\pi\)
0.889811 + 0.456330i \(0.150836\pi\)
\(788\) 0 0
\(789\) 0.545292 + 3.77478i 0.0194129 + 0.134386i