Properties

Label 336.2.bc.f.257.3
Level 336
Weight 2
Character 336.257
Analytic conductor 2.683
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
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: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.3
Root \(1.60841 + 0.642670i\)
Character \(\chi\) = 336.257
Dual form 336.2.bc.f.17.3

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.268335 0.963326i \(-0.586473\pi\)
0.700097 + 0.714048i \(0.253140\pi\)
\(12\) 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 0.172619 0.984989i \(-0.444777\pi\)
−0.766716 + 0.641987i \(0.778110\pi\)
\(20\) 0 0
\(21\) 4.11213 + 2.02247i 0.897341 + 0.441338i
\(22\) 0 0
\(23\) 0.249340 + 0.143957i 0.0519910 + 0.0300170i 0.525770 0.850627i \(-0.323777\pi\)
−0.473779 + 0.880644i \(0.657111\pi\)
\(24\) 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 0.0473770 0.998877i \(-0.484914\pi\)
0.888741 + 0.458409i \(0.151580\pi\)
\(32\) 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 \(-0.560195\pi\)
−0.187982 + 0.982172i \(0.560195\pi\)
\(44\) 0 0
\(45\) −7.42098 + 2.18971i −1.10625 + 0.326423i
\(46\) 0 0
\(47\) 0.186586 0.323176i 0.0272163 0.0471401i −0.852096 0.523385i \(-0.824669\pi\)
0.879313 + 0.476245i \(0.158002\pi\)
\(48\) 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 \(-0.946669\pi\)
0.348580 0.937279i \(-0.386664\pi\)
\(60\) 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 0.929187 0.369609i \(-0.120508\pi\)
−0.784685 + 0.619895i \(0.787175\pi\)
\(68\) 0 0
\(69\) −0.391784 + 0.308524i −0.0471653 + 0.0371419i
\(70\) 0 0
\(71\) 15.6655i 1.85915i 0.368631 + 0.929576i \(0.379826\pi\)
−0.368631 + 0.929576i \(0.620174\pi\)
\(72\) 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 \(0.338161\pi\)
−0.999885 + 0.0151665i \(0.995172\pi\)
\(80\) 0 0
\(81\) 0.452128 + 8.98864i 0.0502364 + 0.998737i
\(82\) 0 0
\(83\) 6.65166 0.730114 0.365057 0.930985i \(-0.381049\pi\)
0.365057 + 0.930985i \(0.381049\pi\)
\(84\) 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 0.814617 0.579999i \(-0.196947\pi\)
−0.0949855 + 0.995479i \(0.530280\pi\)
\(104\) 0 0
\(105\) 9.82011 6.57665i 0.958345 0.641815i
\(106\) 0 0
\(107\) 12.6334 + 7.29389i 1.22132 + 0.705127i 0.965199 0.261518i \(-0.0842231\pi\)
0.256118 + 0.966646i \(0.417556\pi\)
\(108\) 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 \(-0.235468\pi\)
0.738641 + 0.674099i \(0.235468\pi\)
\(128\) 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 \(0.424804\pi\)
−0.958994 + 0.283426i \(0.908529\pi\)
\(132\) 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 \(-0.957765\pi\)
0.991210 0.132297i \(-0.0422353\pi\)
\(140\) 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 \(-0.992710\pi\)
0.480036 0.877249i \(-0.340624\pi\)
\(152\) 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 −0.864065 0.503379i \(-0.832090\pi\)
0.867972 + 0.496613i \(0.165423\pi\)
\(164\) 0 0
\(165\) 6.85922 + 2.74073i 0.533990 + 0.213366i
\(166\) 0 0
\(167\) −3.08612 −0.238811 −0.119406 0.992846i \(-0.538099\pi\)
−0.119406 + 0.992846i \(0.538099\pi\)
\(168\) 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 −0.594521 0.804080i \(-0.702658\pi\)
0.399093 + 0.916910i \(0.369325\pi\)
\(180\) 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 0.461218 0.887287i \(-0.347413\pi\)
−0.537804 + 0.843070i \(0.680746\pi\)
\(192\) 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 −0.696153 0.717893i \(-0.745107\pi\)
0.273637 + 0.961833i \(0.411773\pi\)
\(200\) 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 \(-0.271786\pi\)
0.657093 + 0.753809i \(0.271786\pi\)
\(212\) 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 \(0.119921\pi\)
−0.929868 + 0.367892i \(0.880079\pi\)
\(224\) 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 \(0.0492535\pi\)
−0.360556 + 0.932737i \(0.617413\pi\)
\(228\) 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 \(-0.941193\pi\)
0.982983 0.183699i \(-0.0588071\pi\)
\(240\) 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 \(-0.735746\pi\)
−0.674744 + 0.738052i \(0.735746\pi\)
\(252\) 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 −0.440052 0.897973i \(-0.645040\pi\)
0.557641 + 0.830082i \(0.311707\pi\)
\(264\) 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 −0.144217 0.989546i \(-0.546066\pi\)
−0.929081 + 0.369877i \(0.879400\pi\)
\(272\) 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 −0.397285 0.917695i \(-0.630048\pi\)
0.596105 + 0.802907i \(0.296714\pi\)
\(284\) 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 \(0.238951\pi\)
−0.731221 + 0.682140i \(0.761049\pi\)
\(308\) 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 \(-0.961884\pi\)
0.392965 0.919553i \(-0.371449\pi\)
\(312\) 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 \(-0.658665\pi\)
0.999684 0.0251350i \(-0.00800157\pi\)
\(332\) 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 −0.777880 0.628412i \(-0.783705\pi\)
0.155281 + 0.987870i \(0.450372\pi\)
\(348\) 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 −0.310276 0.950647i \(-0.600421\pi\)
−0.978422 + 0.206616i \(0.933755\pi\)
\(360\) 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 0.111118 0.993807i \(-0.464557\pi\)
0.916221 + 0.400673i \(0.131224\pi\)
\(368\) 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 \(-0.680027\pi\)
−0.535897 + 0.844283i \(0.680027\pi\)
\(380\) 0 0
\(381\) −10.6992 + 26.7770i −0.548139 + 1.37183i
\(382\) 0 0
\(383\) 1.23577 2.14042i 0.0631451 0.109371i −0.832725 0.553687i \(-0.813220\pi\)
0.895870 + 0.444317i \(0.146554\pi\)
\(384\) 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 \(-0.378096\pi\)
0.373679 + 0.927558i \(0.378096\pi\)
\(420\) 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 −0.0957491 0.995405i \(-0.530525\pi\)
0.814172 + 0.580624i \(0.197191\pi\)
\(432\) 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 0.0414249 0.999142i \(-0.486810\pi\)
−0.844570 + 0.535446i \(0.820144\pi\)
\(440\) 0 0
\(441\) 12.8193 + 16.6333i 0.610441 + 0.792062i
\(442\) 0 0
\(443\) 3.08964 + 1.78380i 0.146793 + 0.0847510i 0.571598 0.820534i \(-0.306324\pi\)
−0.424805 + 0.905285i \(0.639657\pi\)
\(444\) 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 \(-0.373754\pi\)
0.386298 + 0.922374i \(0.373754\pi\)
\(464\) 0 0
\(465\) 24.9658 + 9.97556i 1.15776 + 0.462605i
\(466\) 0 0
\(467\) 6.06560 10.5059i 0.280683 0.486156i −0.690871 0.722979i \(-0.742773\pi\)
0.971553 + 0.236822i \(0.0761059\pi\)
\(468\) 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 \(0.0404956\pi\)
−0.386080 + 0.922465i \(0.626171\pi\)
\(480\) 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 \(-0.872839\pi\)
0.123791 0.992308i \(-0.460495\pi\)
\(488\) 0 0
\(489\) 0.106896 + 0.135744i 0.00483401 + 0.00613854i
\(490\) 0 0
\(491\) 32.5795i 1.47029i 0.677910 + 0.735145i \(0.262886\pi\)
−0.677910 + 0.735145i \(0.737114\pi\)
\(492\) 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 −0.805457 0.592655i \(-0.798080\pi\)
0.915982 + 0.401219i \(0.131413\pi\)
\(500\) 0 0
\(501\) 1.98336 4.96374i 0.0886099 0.221764i
\(502\) 0 0
\(503\) 16.7907 0.748661 0.374331 0.927295i \(-0.377873\pi\)
0.374331 + 0.927295i \(0.377873\pi\)
\(504\) 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 −0.357451 0.933932i \(-0.616354\pi\)
−0.987534 + 0.157404i \(0.949688\pi\)
\(524\) 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 \(-0.648994\pi\)
−0.451171 + 0.892437i \(0.648994\pi\)
\(548\) 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 \(-0.841961\pi\)
0.0271005 0.999633i \(-0.491373\pi\)
\(564\) 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 0.879412 0.476061i \(-0.157936\pi\)
−0.851987 + 0.523563i \(0.824602\pi\)
\(572\) 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 \(-0.803504\pi\)
−0.815439 + 0.578843i \(0.803504\pi\)
\(588\) 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 −0.379284 0.925280i \(-0.623830\pi\)
0.611674 + 0.791110i \(0.290496\pi\)
\(600\) 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 0.513614 0.858021i \(-0.328306\pi\)
−0.486261 + 0.873814i \(0.661640\pi\)
\(608\) 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 −0.814902 0.579598i \(-0.803209\pi\)
0.0944957 + 0.995525i \(0.469876\pi\)
\(620\) 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 \(-0.454159\pi\)
0.143517 + 0.989648i \(0.454159\pi\)
\(632\) 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 \(0.0665003\pi\)
−0.978256 + 0.207400i \(0.933500\pi\)
\(644\) 0 0
\(645\) −6.81361 8.65237i −0.268286 0.340687i
\(646\) 0 0
\(647\) 10.2057 + 17.6768i 0.401228 + 0.694948i 0.993874 0.110515i \(-0.0352501\pi\)
−0.592646 + 0.805463i \(0.701917\pi\)
\(648\) 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 \(-0.955321\pi\)
0.990165 0.139902i \(-0.0446788\pi\)
\(660\) 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 0.168101 0.985770i \(-0.446236\pi\)
0.937752 + 0.347305i \(0.112903\pi\)
\(684\) 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 0.982309 0.187268i \(-0.0599634\pi\)
0.328975 + 0.944339i \(0.393297\pi\)
\(692\) 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 \(0.364761\pi\)
−0.995130 + 0.0985739i \(0.968572\pi\)
\(720\) 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 \(-0.735769\pi\)
0.674797 0.738003i \(-0.264231\pi\)
\(728\) 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 \(0.0124166\pi\)
−0.465846 + 0.884866i \(0.654250\pi\)
\(740\) 0 0
\(741\) −18.3021 23.2413i −0.672346 0.853789i
\(742\) 0 0
\(743\) 33.4864i 1.22850i −0.789113 0.614248i \(-0.789459\pi\)
0.789113 0.614248i \(-0.210541\pi\)
\(744\) 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 −0.739072 0.673627i \(-0.764736\pi\)
0.952914 + 0.303242i \(0.0980689\pi\)
\(752\) 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 −0.889811 0.456330i \(-0.849164\pi\)
−0.0497122 + 0.998764i \(0.515830\pi\)
\(788\) 0 0
\(789\) 0.545292 + 3.77478i 0.0194129 + 0.134386i