Properties

Label 168.2.u.a.17.8
Level 168
Weight 2
Character 168.17
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 17.8
Root \(1.60841 - 0.642670i\) 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 \(\chi\) \(=\) 168.17
Dual form 168.2.u.a.89.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.71426 - 0.247636i) q^{3} +(-1.28955 - 2.23357i) q^{5} +(-0.203402 - 2.63792i) q^{7} +(2.87735 - 0.849022i) q^{9} +O(q^{10})\) \(q+(1.71426 - 0.247636i) q^{3} +(-1.28955 - 2.23357i) q^{5} +(-0.203402 - 2.63792i) q^{7} +(2.87735 - 0.849022i) q^{9} +(1.43199 + 0.826762i) q^{11} +5.71177i q^{13} +(-2.76373 - 3.50957i) q^{15} +(-3.79313 + 6.56990i) q^{17} +(2.58961 - 1.49511i) q^{19} +(-1.00193 - 4.47170i) q^{21} +(0.249340 - 0.143957i) q^{23} +(-0.825879 + 1.43046i) q^{25} +(4.72227 - 2.16798i) q^{27} +2.05856i q^{29} +(-5.21209 - 3.00920i) q^{31} +(2.65954 + 1.06267i) q^{33} +(-5.62967 + 3.85604i) q^{35} +(-0.877523 - 1.51991i) q^{37} +(1.41444 + 9.79144i) q^{39} -4.28635 q^{41} +2.46537 q^{43} +(-5.60684 - 5.33190i) q^{45} +(0.186586 + 0.323176i) q^{47} +(-6.91726 + 1.07312i) q^{49} +(-4.87546 + 12.2018i) q^{51} +(6.73264 + 3.88709i) q^{53} -4.26461i q^{55} +(4.06901 - 3.20429i) q^{57} +(-4.89610 + 8.48029i) q^{59} +(0.889794 - 0.513723i) q^{61} +(-2.82491 - 7.41754i) q^{63} +(12.7576 - 7.36561i) q^{65} +(-1.18281 + 2.04868i) q^{67} +(0.391784 - 0.308524i) q^{69} -15.6655i q^{71} +(-3.30170 - 1.90624i) q^{73} +(-1.06153 + 2.65670i) q^{75} +(1.88966 - 3.94565i) q^{77} +(4.56033 + 7.89872i) q^{79} +(7.55832 - 4.88587i) q^{81} +6.65166 q^{83} +19.5657 q^{85} +(0.509773 + 3.52890i) q^{87} +(-7.25723 - 12.5699i) q^{89} +(15.0672 - 1.16179i) q^{91} +(-9.68004 - 3.86784i) q^{93} +(-6.67886 - 3.85604i) q^{95} -4.43739i q^{97} +(4.82229 + 1.16309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q + 4q^{7} + 2q^{9} + 8q^{15} - 6q^{19} + 14q^{21} - 18q^{25} - 48q^{31} - 12q^{33} - 2q^{37} - 22q^{39} + 20q^{43} - 42q^{45} - 28q^{49} + 6q^{51} - 8q^{57} + 36q^{61} - 32q^{63} + 14q^{67} + 30q^{73} + 54q^{75} + 28q^{79} + 30q^{81} + 16q^{85} + 78q^{87} + 66q^{91} + 16q^{93} + 20q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 1.71426 0.247636i 0.989727 0.142972i
\(4\) 0 0
\(5\) −1.28955 2.23357i −0.576704 0.998881i −0.995854 0.0909641i \(-0.971005\pi\)
0.419150 0.907917i \(-0.362328\pi\)
\(6\) 0 0
\(7\) −0.203402 2.63792i −0.0768787 0.997040i
\(8\) 0 0
\(9\) 2.87735 0.849022i 0.959118 0.283007i
\(10\) 0 0
\(11\) 1.43199 + 0.826762i 0.431763 + 0.249278i 0.700097 0.714048i \(-0.253140\pi\)
−0.268335 + 0.963326i \(0.586473\pi\)
\(12\) 0 0
\(13\) 5.71177i 1.58416i 0.610418 + 0.792080i \(0.291002\pi\)
−0.610418 + 0.792080i \(0.708998\pi\)
\(14\) 0 0
\(15\) −2.76373 3.50957i −0.713592 0.906167i
\(16\) 0 0
\(17\) −3.79313 + 6.56990i −0.919970 + 1.59343i −0.120512 + 0.992712i \(0.538453\pi\)
−0.799458 + 0.600722i \(0.794880\pi\)
\(18\) 0 0
\(19\) 2.58961 1.49511i 0.594097 0.343002i −0.172619 0.984989i \(-0.555223\pi\)
0.766716 + 0.641987i \(0.221890\pi\)
\(20\) 0 0
\(21\) −1.00193 4.47170i −0.218638 0.975806i
\(22\) 0 0
\(23\) 0.249340 0.143957i 0.0519910 0.0300170i −0.473779 0.880644i \(-0.657111\pi\)
0.525770 + 0.850627i \(0.323777\pi\)
\(24\) 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 \(-0.515086\pi\)
−0.888741 + 0.458409i \(0.848420\pi\)
\(32\) 0 0
\(33\) 2.65954 + 1.06267i 0.462967 + 0.184987i
\(34\) 0 0
\(35\) −5.62967 + 3.85604i −0.951589 + 0.651790i
\(36\) 0 0
\(37\) −0.877523 1.51991i −0.144264 0.249872i 0.784834 0.619706i \(-0.212748\pi\)
−0.929098 + 0.369833i \(0.879415\pi\)
\(38\) 0 0
\(39\) 1.41444 + 9.79144i 0.226491 + 1.56788i
\(40\) 0 0
\(41\) −4.28635 −0.669415 −0.334708 0.942322i \(-0.608638\pi\)
−0.334708 + 0.942322i \(0.608638\pi\)
\(42\) 0 0
\(43\) 2.46537 0.375965 0.187982 0.982172i \(-0.439805\pi\)
0.187982 + 0.982172i \(0.439805\pi\)
\(44\) 0 0
\(45\) −5.60684 5.33190i −0.835818 0.794833i
\(46\) 0 0
\(47\) 0.186586 + 0.323176i 0.0272163 + 0.0471401i 0.879313 0.476245i \(-0.158002\pi\)
−0.852096 + 0.523385i \(0.824669\pi\)
\(48\) 0 0
\(49\) −6.91726 + 1.07312i −0.988179 + 0.153302i
\(50\) 0 0
\(51\) −4.87546 + 12.2018i −0.682701 + 1.70859i
\(52\) 0 0
\(53\) 6.73264 + 3.88709i 0.924799 + 0.533933i 0.885163 0.465281i \(-0.154047\pi\)
0.0396361 + 0.999214i \(0.487380\pi\)
\(54\) 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 0.348580 + 0.937279i \(0.386664\pi\)
−0.985997 + 0.166760i \(0.946669\pi\)
\(60\) 0 0
\(61\) 0.889794 0.513723i 0.113926 0.0657755i −0.441954 0.897038i \(-0.645715\pi\)
0.555880 + 0.831262i \(0.312381\pi\)
\(62\) 0 0
\(63\) −2.82491 7.41754i −0.355906 0.934522i
\(64\) 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 \(-0.879492\pi\)
0.784685 + 0.619895i \(0.212825\pi\)
\(68\) 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 0.294180 0.955750i \(-0.404954\pi\)
−0.680614 + 0.732642i \(0.738287\pi\)
\(74\) 0 0
\(75\) −1.06153 + 2.65670i −0.122575 + 0.306769i
\(76\) 0 0
\(77\) 1.88966 3.94565i 0.215347 0.449649i
\(78\) 0 0
\(79\) 4.56033 + 7.89872i 0.513077 + 0.888676i 0.999885 + 0.0151665i \(0.00482783\pi\)
−0.486808 + 0.873509i \(0.661839\pi\)
\(80\) 0 0
\(81\) 7.55832 4.88587i 0.839814 0.542875i
\(82\) 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
\(87\) 0.509773 + 3.52890i 0.0546534 + 0.378338i
\(88\) 0 0
\(89\) −7.25723 12.5699i −0.769265 1.33241i −0.937962 0.346738i \(-0.887289\pi\)
0.168697 0.985668i \(-0.446044\pi\)
\(90\) 0 0
\(91\) 15.0672 1.16179i 1.57947 0.121788i
\(92\) 0 0
\(93\) −9.68004 3.86784i −1.00377 0.401077i
\(94\) 0 0
\(95\) −6.67886 3.85604i −0.685237 0.395622i
\(96\) 0 0
\(97\) 4.43739i 0.450548i −0.974295 0.225274i \(-0.927672\pi\)
0.974295 0.225274i \(-0.0723278\pi\)
\(98\) 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 \(-0.768389\pi\)
0.949371 + 0.314157i \(0.101722\pi\)
\(102\) 0 0
\(103\) −7.30346 + 4.21666i −0.719632 + 0.415479i −0.814617 0.579999i \(-0.803053\pi\)
0.0949855 + 0.995479i \(0.469720\pi\)
\(104\) 0 0
\(105\) −8.69581 + 8.00436i −0.848625 + 0.781145i
\(106\) 0 0
\(107\) 12.6334 7.29389i 1.22132 0.705127i 0.256118 0.966646i \(-0.417556\pi\)
0.965199 + 0.261518i \(0.0842231\pi\)
\(108\) 0 0
\(109\) −8.64994 + 14.9821i −0.828514 + 1.43503i 0.0706901 + 0.997498i \(0.477480\pi\)
−0.899204 + 0.437530i \(0.855853\pi\)
\(110\) 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
\(117\) 4.84942 + 16.4348i 0.448329 + 1.51940i
\(118\) 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
\(123\) −7.34790 + 1.06145i −0.662538 + 0.0957079i
\(124\) 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
\(129\) 4.22627 0.610512i 0.372102 0.0537526i
\(130\) 0 0
\(131\) −8.29744 14.3716i −0.724951 1.25565i −0.958994 0.283426i \(-0.908529\pi\)
0.234043 0.972226i \(-0.424804\pi\)
\(132\) 0 0
\(133\) −4.47072 6.52708i −0.387660 0.565969i
\(134\) 0 0
\(135\) −10.9319 7.75180i −0.940871 0.667169i
\(136\) 0 0
\(137\) 8.61684 + 4.97493i 0.736186 + 0.425037i 0.820681 0.571387i \(-0.193594\pi\)
−0.0844948 + 0.996424i \(0.526928\pi\)
\(138\) 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
\(147\) −11.5922 + 3.55256i −0.956109 + 0.293010i
\(148\) 0 0
\(149\) −0.987090 + 0.569897i −0.0808655 + 0.0466877i −0.539888 0.841737i \(-0.681533\pi\)
0.459022 + 0.888425i \(0.348200\pi\)
\(150\) 0 0
\(151\) 6.38621 11.0612i 0.519702 0.900151i −0.480036 0.877249i \(-0.659376\pi\)
0.999738 0.0229016i \(-0.00729044\pi\)
\(152\) 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 0.778481 0.627668i \(-0.215990\pi\)
−0.154335 + 0.988019i \(0.549324\pi\)
\(158\) 0 0
\(159\) 12.5041 + 4.99623i 0.991636 + 0.396227i
\(160\) 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 \(-0.167910\pi\)
−0.867972 + 0.496613i \(0.834577\pi\)
\(164\) 0 0
\(165\) −1.05607 7.31063i −0.0822148 0.569132i
\(166\) 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
\(171\) 6.18184 6.50060i 0.472737 0.497113i
\(172\) 0 0
\(173\) 3.73038 + 6.46120i 0.283615 + 0.491236i 0.972272 0.233851i \(-0.0751328\pi\)
−0.688657 + 0.725087i \(0.741799\pi\)
\(174\) 0 0
\(175\) 3.94144 + 1.88764i 0.297945 + 0.142693i
\(176\) 0 0
\(177\) −6.29315 + 15.7498i −0.473022 + 1.18383i
\(178\) 0 0
\(179\) −2.61465 1.50957i −0.195428 0.112830i 0.399093 0.916910i \(-0.369325\pi\)
−0.594521 + 0.804080i \(0.702658\pi\)
\(180\) 0 0
\(181\) 0.762552i 0.0566801i 0.999598 + 0.0283400i \(0.00902212\pi\)
−0.999598 + 0.0283400i \(0.990978\pi\)
\(182\) 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
\(189\) −6.67947 12.0160i −0.485860 0.874037i
\(190\) 0 0
\(191\) −1.05844 + 0.611089i −0.0765859 + 0.0442169i −0.537804 0.843070i \(-0.680746\pi\)
0.461218 + 0.887287i \(0.347413\pi\)
\(192\) 0 0
\(193\) 11.7587 20.3666i 0.846409 1.46602i −0.0379837 0.999278i \(-0.512093\pi\)
0.884392 0.466744i \(-0.154573\pi\)
\(194\) 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 \(-0.254893\pi\)
−0.273637 + 0.961833i \(0.588227\pi\)
\(200\) 0 0
\(201\) −1.52031 + 3.80487i −0.107234 + 0.268375i
\(202\) 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
\(207\) 0.595218 0.625909i 0.0413705 0.0435037i
\(208\) 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
\(213\) −3.87933 26.8547i −0.265807 1.84005i
\(214\) 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
\(219\) −6.13201 2.45016i −0.414363 0.165566i
\(220\) 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 −0.360556 0.932737i \(-0.617413\pi\)
0.988052 0.154118i \(-0.0492535\pi\)
\(228\) 0 0
\(229\) 14.9744 8.64545i 0.989533 0.571307i 0.0843986 0.996432i \(-0.473103\pi\)
0.905135 + 0.425125i \(0.139770\pi\)
\(230\) 0 0
\(231\) 2.26228 7.23181i 0.148847 0.475818i
\(232\) 0 0
\(233\) −4.45119 + 2.56990i −0.291607 + 0.168360i −0.638666 0.769484i \(-0.720514\pi\)
0.347059 + 0.937843i \(0.387180\pi\)
\(234\) 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 0.980170 0.198158i \(-0.0634960\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(242\) 0 0
\(243\) 11.7470 10.2473i 0.753570 0.657368i
\(244\) 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
\(249\) 11.4026 1.64719i 0.722613 0.104386i
\(250\) 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
\(255\) 33.5407 4.84517i 2.10040 0.303416i
\(256\) 0 0
\(257\) 7.09305 + 12.2855i 0.442452 + 0.766349i 0.997871 0.0652214i \(-0.0207753\pi\)
−0.555419 + 0.831571i \(0.687442\pi\)
\(258\) 0 0
\(259\) −3.83092 + 2.62399i −0.238042 + 0.163047i
\(260\) 0 0
\(261\) 1.74776 + 5.92321i 0.108184 + 0.366638i
\(262\) 0 0
\(263\) 1.90698 + 1.10100i 0.117590 + 0.0678904i 0.557641 0.830082i \(-0.311707\pi\)
−0.440052 + 0.897973i \(0.645040\pi\)
\(264\) 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 \(-0.685795\pi\)
0.998195 + 0.0600579i \(0.0191285\pi\)
\(270\) 0 0
\(271\) 17.6687 10.2010i 1.07330 0.619669i 0.144217 0.989546i \(-0.453934\pi\)
0.929081 + 0.369877i \(0.120600\pi\)
\(272\) 0 0
\(273\) 25.5413 5.72277i 1.54583 0.346358i
\(274\) 0 0
\(275\) −2.36531 + 1.36561i −0.142633 + 0.0823495i
\(276\) 0 0
\(277\) −0.00535275 + 0.00927123i −0.000321615 + 0.000557054i −0.866186 0.499721i \(-0.833436\pi\)
0.865865 + 0.500279i \(0.166769\pi\)
\(278\) 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 \(-0.369952\pi\)
−0.596105 + 0.802907i \(0.703286\pi\)
\(284\) 0 0
\(285\) −12.4042 4.95632i −0.734760 0.293587i
\(286\) 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
\(291\) −1.09885 7.60682i −0.0644160 0.445920i
\(292\) 0 0
\(293\) −5.75351 −0.336123 −0.168062 0.985776i \(-0.553751\pi\)
−0.168062 + 0.985776i \(0.553751\pi\)
\(294\) 0 0
\(295\) 25.2550 1.47041
\(296\) 0 0
\(297\) 8.55467 + 0.799668i 0.496392 + 0.0464015i
\(298\) 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
\(303\) 2.61731 6.55033i 0.150360 0.376307i
\(304\) 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 0.392965 + 0.919553i \(0.371449\pi\)
−0.992839 + 0.119459i \(0.961884\pi\)
\(312\) 0 0
\(313\) −18.2861 + 10.5575i −1.03359 + 0.596746i −0.918012 0.396552i \(-0.870207\pi\)
−0.115582 + 0.993298i \(0.536873\pi\)
\(314\) 0 0
\(315\) −12.9247 + 15.8749i −0.728224 + 0.894450i
\(316\) 0 0
\(317\) 13.8698 8.00775i 0.779007 0.449760i −0.0570712 0.998370i \(-0.518176\pi\)
0.836078 + 0.548610i \(0.184843\pi\)
\(318\) 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
\(327\) −11.1181 + 27.8253i −0.614833 + 1.53874i
\(328\) 0 0
\(329\) 0.814561 0.557933i 0.0449082 0.0307599i
\(330\) 0 0
\(331\) −9.48985 16.4369i −0.521610 0.903454i −0.999684 0.0251350i \(-0.991998\pi\)
0.478074 0.878319i \(-0.341335\pi\)
\(332\) 0 0
\(333\) −3.81538 3.62829i −0.209082 0.198829i
\(334\) 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
\(339\) 0.990542 + 6.85703i 0.0537989 + 0.372423i
\(340\) 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
\(345\) −1.19433 0.477219i −0.0643008 0.0256926i
\(346\) 0 0
\(347\) −11.5977 6.69596i −0.622599 0.359458i 0.155281 0.987870i \(-0.450372\pi\)
−0.777880 + 0.628412i \(0.783705\pi\)
\(348\) 0 0
\(349\) 13.4025i 0.717421i −0.933449 0.358710i \(-0.883217\pi\)
0.933449 0.358710i \(-0.116783\pi\)
\(350\) 0 0
\(351\) 12.3830 + 26.9725i 0.660955 + 1.43969i
\(352\) 0 0
\(353\) −10.7469 + 18.6141i −0.571998 + 0.990729i 0.424363 + 0.905492i \(0.360498\pi\)
−0.996361 + 0.0852371i \(0.972835\pi\)
\(354\) 0 0
\(355\) −34.9899 + 20.2014i −1.85707 + 1.07218i
\(356\) 0 0
\(357\) 33.1791 + 10.3792i 1.75602 + 0.549326i
\(358\) 0 0
\(359\) −24.4173 + 14.0974i −1.28870 + 0.744030i −0.978422 0.206616i \(-0.933755\pi\)
−0.310276 + 0.950647i \(0.600421\pi\)
\(360\) 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 \(-0.535443\pi\)
−0.916221 + 0.400673i \(0.868776\pi\)
\(368\) 0 0
\(369\) −12.3333 + 3.63920i −0.642048 + 0.189449i
\(370\) 0 0
\(371\) 8.88441 18.5508i 0.461255 0.963110i
\(372\) 0 0
\(373\) 6.95699 + 12.0499i 0.360219 + 0.623918i 0.987997 0.154475i \(-0.0493686\pi\)
−0.627778 + 0.778393i \(0.716035\pi\)
\(374\) 0 0
\(375\) −14.8034 + 2.13845i −0.764443 + 0.110429i
\(376\) 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
\(381\) −28.5392 + 4.12267i −1.46211 + 0.211211i
\(382\) 0 0
\(383\) 1.23577 + 2.14042i 0.0631451 + 0.109371i 0.895870 0.444317i \(-0.146554\pi\)
−0.832725 + 0.553687i \(0.813220\pi\)
\(384\) 0 0
\(385\) −11.2497 + 0.867429i −0.573337 + 0.0442083i
\(386\) 0 0
\(387\) 7.09373 2.09315i 0.360595 0.106401i
\(388\) 0 0
\(389\) 20.4245 + 11.7921i 1.03556 + 0.597882i 0.918573 0.395251i \(-0.129342\pi\)
0.116989 + 0.993133i \(0.462676\pi\)
\(390\) 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 −0.544285 0.838901i \(-0.683199\pi\)
0.454367 + 0.890815i \(0.349866\pi\)
\(398\) 0 0
\(399\) −9.28030 10.0820i −0.464596 0.504730i
\(400\) 0 0
\(401\) 6.46052 3.72998i 0.322623 0.186266i −0.329938 0.944003i \(-0.607028\pi\)
0.652561 + 0.757736i \(0.273695\pi\)
\(402\) 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 0.998379 0.0569122i \(-0.0181255\pi\)
0.449902 + 0.893078i \(0.351459\pi\)
\(410\) 0 0
\(411\) 16.0034 + 6.39448i 0.789392 + 0.315416i
\(412\) 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
\(417\) −0.772504 5.34766i −0.0378297 0.261876i
\(418\) 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
\(423\) 0.811257 + 0.771476i 0.0394447 + 0.0375105i
\(424\) 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
\(429\) −6.06973 + 15.1907i −0.293049 + 0.733413i
\(430\) 0 0
\(431\) 14.9148 + 8.61109i 0.718423 + 0.414782i 0.814172 0.580624i \(-0.197191\pi\)
−0.0957491 + 0.995405i \(0.530525\pi\)
\(432\) 0 0
\(433\) 1.55093i 0.0745329i −0.999305 0.0372664i \(-0.988135\pi\)
0.999305 0.0372664i \(-0.0118650\pi\)
\(434\) 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 \(-0.513190\pi\)
0.844570 + 0.535446i \(0.179856\pi\)
\(440\) 0 0
\(441\) −18.9923 + 8.96064i −0.904395 + 0.426697i
\(442\) 0 0
\(443\) 3.08964 1.78380i 0.146793 0.0847510i −0.424805 0.905285i \(-0.639657\pi\)
0.571598 + 0.820534i \(0.306324\pi\)
\(444\) 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
\(453\) 8.20844 20.5433i 0.385666 0.965206i
\(454\) 0 0
\(455\) −22.0248 32.1554i −1.03254 1.50747i
\(456\) 0 0
\(457\) 11.2312 + 19.4530i 0.525374 + 0.909975i 0.999563 + 0.0295520i \(0.00940807\pi\)
−0.474189 + 0.880423i \(0.657259\pi\)
\(458\) 0 0
\(459\) −3.66883 + 39.2483i −0.171246 + 1.83195i
\(460\) 0 0
\(461\) 9.31904 0.434031 0.217015 0.976168i \(-0.430368\pi\)
0.217015 + 0.976168i \(0.430368\pi\)
\(462\) 0 0
\(463\) −16.6243 −0.772597 −0.386298 0.922374i \(-0.626246\pi\)
−0.386298 + 0.922374i \(0.626246\pi\)
\(464\) 0 0
\(465\) 3.84381 + 26.6088i 0.178253 + 1.23395i
\(466\) 0 0
\(467\) 6.06560 + 10.5059i 0.280683 + 0.486156i 0.971553 0.236822i \(-0.0761059\pi\)
−0.690871 + 0.722979i \(0.742773\pi\)
\(468\) 0 0
\(469\) 5.64484 + 2.70344i 0.260654 + 0.124833i
\(470\) 0 0
\(471\) 14.5245 + 5.80354i 0.669254 + 0.267413i
\(472\) 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 −0.386080 0.922465i \(-0.626171\pi\)
0.991918 0.126878i \(-0.0404956\pi\)
\(480\) 0 0
\(481\) 8.68140 5.01221i 0.395838 0.228537i
\(482\) 0 0
\(483\) −0.893552 0.970742i −0.0406580 0.0441703i
\(484\) 0 0
\(485\) −9.91120 + 5.72223i −0.450044 + 0.259833i
\(486\) 0 0
\(487\) 17.5986 30.4817i 0.797469 1.38126i −0.123791 0.992308i \(-0.539505\pi\)
0.921260 0.388948i \(-0.127161\pi\)
\(488\) 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
\(495\) −3.62074 12.2708i −0.162740 0.551530i
\(496\) 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 \(-0.201920\pi\)
−0.915982 + 0.401219i \(0.868587\pi\)
\(500\) 0 0
\(501\) −5.29041 + 0.764234i −0.236358 + 0.0341434i
\(502\) 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
\(507\) −33.6411 + 4.85967i −1.49405 + 0.215826i
\(508\) 0 0
\(509\) 0.631490 + 1.09377i 0.0279903 + 0.0484806i 0.879681 0.475564i \(-0.157756\pi\)
−0.851691 + 0.524044i \(0.824423\pi\)
\(510\) 0 0
\(511\) −4.35693 + 9.09735i −0.192739 + 0.402443i
\(512\) 0 0
\(513\) 8.98748 12.6745i 0.396807 0.559595i
\(514\) 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 −0.324486 0.945891i \(-0.605191\pi\)
0.981408 0.191932i \(-0.0614755\pi\)
\(522\) 0 0
\(523\) 30.7587 17.7586i 1.34499 0.776528i 0.357451 0.933932i \(-0.383646\pi\)
0.987534 + 0.157404i \(0.0503125\pi\)
\(524\) 0 0
\(525\) 7.22408 + 2.25987i 0.315285 + 0.0986287i
\(526\) 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
\(537\) −4.85600 1.94031i −0.209552 0.0837304i
\(538\) 0 0
\(539\) −10.7927 4.18223i −0.464874 0.180141i
\(540\) 0 0
\(541\) 11.9158 + 20.6388i 0.512300 + 0.887330i 0.999898 + 0.0142616i \(0.00453975\pi\)
−0.487598 + 0.873068i \(0.662127\pi\)
\(542\) 0 0
\(543\) 0.188835 + 1.30721i 0.00810369 + 0.0560978i
\(544\) 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
\(549\) 2.12409 2.23362i 0.0906539 0.0953284i
\(550\) 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
\(555\) −2.90901 + 7.28036i −0.123480 + 0.309034i
\(556\) 0 0
\(557\) −19.3020 11.1440i −0.817852 0.472187i 0.0318235 0.999494i \(-0.489869\pi\)
−0.849675 + 0.527307i \(0.823202\pi\)
\(558\) 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 0.0271005 + 0.999633i \(0.491373\pi\)
−0.879258 + 0.476347i \(0.841961\pi\)
\(564\) 0 0
\(565\) 8.93427 5.15820i 0.375867 0.217007i
\(566\) 0 0
\(567\) −14.4259 18.9445i −0.605832 0.795593i
\(568\) 0 0
\(569\) −21.7717 + 12.5699i −0.912717 + 0.526957i −0.881304 0.472549i \(-0.843334\pi\)
−0.0314127 + 0.999506i \(0.510001\pi\)
\(570\) 0 0
\(571\) −0.655344 + 1.13509i −0.0274253 + 0.0475020i −0.879412 0.476061i \(-0.842064\pi\)
0.851987 + 0.523563i \(0.175398\pi\)
\(572\) 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 0.604654 0.796488i \(-0.293311\pi\)
−0.387452 + 0.921890i \(0.626645\pi\)
\(578\) 0 0
\(579\) 15.1139 37.8255i 0.628112 1.57197i
\(580\) 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
\(585\) 30.4546 32.0250i 1.25914 1.32407i
\(586\) 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
\(591\) 3.64797 + 25.2531i 0.150058 + 1.03877i
\(592\) 0 0
\(593\) 6.75855 + 11.7062i 0.277540 + 0.480714i 0.970773 0.240000i \(-0.0771474\pi\)
−0.693232 + 0.720714i \(0.743814\pi\)
\(594\) 0 0
\(595\) −3.97971 51.6129i −0.163152 2.11592i
\(596\) 0 0
\(597\) 11.0697 + 4.42310i 0.453052 + 0.181025i
\(598\) 0 0
\(599\) 5.68762 + 3.28375i 0.232390 + 0.134170i 0.611674 0.791110i \(-0.290496\pi\)
−0.379284 + 0.925280i \(0.623830\pi\)
\(600\) 0 0
\(601\) 10.0499i 0.409946i 0.978768 + 0.204973i \(0.0657106\pi\)
−0.978768 + 0.204973i \(0.934289\pi\)
\(602\) 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 \(-0.671694\pi\)
0.486261 + 0.873814i \(0.338360\pi\)
\(608\) 0 0
\(609\) 9.20528 2.06253i 0.373017 0.0835778i
\(610\) 0 0
\(611\) −1.84591 + 1.06573i −0.0746774 + 0.0431150i
\(612\) 0 0
\(613\) −19.3349 + 33.4890i −0.780928 + 1.35261i 0.150474 + 0.988614i \(0.451920\pi\)
−0.931402 + 0.363993i \(0.881413\pi\)
\(614\) 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 \(-0.196791\pi\)
−0.0944957 + 0.995525i \(0.530124\pi\)
\(620\) 0 0
\(621\) 0.865358 1.22037i 0.0347256 0.0489716i
\(622\) 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
\(627\) 8.47599 1.22441i 0.338498 0.0488983i
\(628\) 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
\(633\) −32.7246 + 4.72728i −1.30069 + 0.187892i
\(634\) 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
\(639\) −13.3003 45.0751i −0.526153 1.78315i
\(640\) 0 0
\(641\) 31.9156 + 18.4265i 1.26059 + 0.727802i 0.973189 0.230009i \(-0.0738755\pi\)
0.287401 + 0.957810i \(0.407209\pi\)
\(642\) 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 −0.592646 0.805463i \(-0.701917\pi\)
0.993874 + 0.110515i \(0.0352501\pi\)
\(648\) 0 0
\(649\) −14.0224 + 8.09581i −0.550426 + 0.317789i
\(650\) 0 0
\(651\) −8.23413 + 26.3219i −0.322721 + 1.03164i
\(652\) 0 0
\(653\) −28.7382 + 16.5920i −1.12461 + 0.649295i −0.942574 0.333996i \(-0.891603\pi\)
−0.182038 + 0.983291i \(0.558269\pi\)
\(654\) 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 0.101504 0.994835i \(-0.467635\pi\)
−0.810801 + 0.585323i \(0.800968\pi\)
\(662\) 0 0
\(663\) −69.6939 27.8475i −2.70669 1.08151i
\(664\) 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
\(669\) 2.72092 + 18.8356i 0.105197 + 0.728226i
\(670\) 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
\(675\) −0.798814 + 8.54553i −0.0307464 + 0.328918i
\(676\) 0 0
\(677\) −2.69876 4.67439i −0.103722 0.179651i 0.809493 0.587129i \(-0.199742\pi\)
−0.913215 + 0.407477i \(0.866408\pi\)
\(678\) 0 0
\(679\) −11.7055 + 0.902573i −0.449215 + 0.0346376i
\(680\) 0 0
\(681\) 12.1518 30.4124i 0.465659 1.16540i
\(682\) 0 0
\(683\) 28.9007 + 16.6858i 1.10585 + 0.638465i 0.937752 0.347305i \(-0.112903\pi\)
0.168101 + 0.985770i \(0.446236\pi\)
\(684\) 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 \(-0.940037\pi\)
−0.328975 + 0.944339i \(0.606703\pi\)
\(692\) 0 0
\(693\) 2.08728 12.9574i 0.0792893 0.492211i
\(694\) 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
\(705\) 0.618535 1.54801i 0.0232954 0.0583013i
\(706\) 0 0
\(707\) −9.71797 4.65416i −0.365482 0.175038i
\(708\) 0 0
\(709\) −17.5727 30.4367i −0.659955 1.14308i −0.980627 0.195885i \(-0.937242\pi\)
0.320672 0.947190i \(-0.396091\pi\)
\(710\) 0 0
\(711\) 19.8279 + 18.8556i 0.743603 + 0.707140i
\(712\) 0 0
\(713\) −1.73278 −0.0648930
\(714\) 0 0
\(715\) 24.3584 0.910954
\(716\) 0 0
\(717\) 1.40653 + 9.73669i 0.0525278 + 0.363623i
\(718\) 0 0
\(719\) −15.6309 27.0734i −0.582932 1.00967i −0.995130 0.0985739i \(-0.968572\pi\)
0.412197 0.911095i \(-0.364761\pi\)
\(720\) 0 0
\(721\) 12.6087 + 18.4083i 0.469574 + 0.685560i
\(722\) 0 0
\(723\) 37.4425 + 14.9608i 1.39250 + 0.556400i
\(724\) 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 −0.291553 0.956555i \(-0.594172\pi\)
0.682624 + 0.730770i \(0.260839\pi\)
\(734\) 0 0
\(735\) 22.8836 + 21.3108i 0.844075 + 0.786060i
\(736\) 0 0
\(737\) −3.38754 + 1.95580i −0.124782 + 0.0720428i
\(738\) 0 0
\(739\) −14.5001 + 25.1148i −0.533393 + 0.923864i 0.465846 + 0.884866i \(0.345750\pi\)
−0.999239 + 0.0389981i \(0.987583\pi\)
\(740\) 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
\(747\) 19.1392 5.64740i 0.700265 0.206628i
\(748\) 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 \(-0.235264\pi\)
−0.952914 + 0.303242i \(0.901931\pi\)
\(752\) 0 0
\(753\) −36.6507 + 5.29443i −1.33562 + 0.192940i
\(754\) 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
\(759\) 0.816109 0.117892i 0.0296229 0.00427922i
\(760\) 0 0
\(761\) 10.0633 + 17.4301i 0.364793 + 0.631841i 0.988743 0.149624i \(-0.0478063\pi\)
−0.623950 + 0.781465i \(0.714473\pi\)
\(762\) 0 0
\(763\) 41.2811 + 19.7705i 1.49448 + 0.715739i
\(764\) 0 0
\(765\) 56.2975 16.6117i 2.03544 0.600599i
\(766\) 0 0
\(767\) −48.4374 27.9654i −1.74897 1.00977i
\(768\) 0 0
\(769\) 7.95157i 0.286741i −0.989669 0.143370i \(-0.954206\pi\)
0.989669 0.143370i \(-0.0457940\pi\)
\(770\) 0 0
\(771\) 15.2016 + 19.3040i 0.547473 + 0.695218i
\(772\) 0 0
\(773\) 15.8927 27.5269i 0.571620 0.990075i −0.424780 0.905297i \(-0.639648\pi\)
0.996400 0.0847784i \(-0.0270182\pi\)
\(774\) 0 0
\(775\) 8.60911 4.97047i 0.309248 0.178545i
\(776\) 0 0
\(777\) −5.91739 + 5.44687i −0.212285 + 0.195405i
\(778\) 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 \(-0.150836\pi\)
0.0497122 + 0.998764i \(0.484170\pi\)
\(788\) 0 0
\(789\) 3.54171 + 1.41516i 0.126088 + 0.0503809i