Properties

Label 168.2.u.a.89.8
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 89.8
Root \(1.60841 + 0.642670i\)
Character \(\chi\) = 168.89
Dual form 168.2.u.a.17.8

$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

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

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
\(3\) 1.71426 + 0.247636i 0.989727 + 0.142972i
\(4\) 0 0
\(5\) −1.28955 + 2.23357i −0.576704 + 0.998881i 0.419150 + 0.907917i \(0.362328\pi\)
−0.995854 + 0.0909641i \(0.971005\pi\)
\(6\) 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 −0.268335 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 \(-0.794880\pi\)
−0.120512 0.992712i \(-0.538453\pi\)
\(18\) 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
\(21\) −1.00193 + 4.47170i −0.218638 + 0.975806i
\(22\) 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 \(-0.938784\pi\)
0.981564 0.191133i \(-0.0612161\pi\)
\(30\) 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
\(33\) 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 −0.929098 0.369833i \(-0.879415\pi\)
0.784834 + 0.619706i \(0.212748\pi\)
\(38\) 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 −0.852096 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
\(51\) −4.87546 12.2018i −0.682701 1.70859i
\(52\) 0 0
\(53\) 6.73264 3.88709i 0.924799 0.533933i 0.0396361 0.999214i \(-0.487380\pi\)
0.885163 + 0.465281i \(0.154047\pi\)
\(54\) 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
\(63\) −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 0.784685 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 \(0.379826\pi\)
−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
\(75\) −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 −0.486808 0.873509i \(-0.661839\pi\)
0.999885 0.0151665i \(-0.00482783\pi\)
\(80\) 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 0.168697 + 0.985668i \(0.446044\pi\)
−0.937962 + 0.346738i \(0.887289\pi\)
\(90\) 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 \(0.0723278\pi\)
−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 0.949371 0.314157i \(-0.101722\pi\)
−0.746754 + 0.665101i \(0.768389\pi\)
\(102\) 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
\(105\) −8.69581 8.00436i −0.848625 0.781145i
\(106\) 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 \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 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 0.234043 + 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
\(135\) −10.9319 + 7.75180i −0.940871 + 0.667169i
\(136\) 0 0
\(137\) 8.61684 4.97493i 0.736186 0.425037i −0.0844948 0.996424i \(-0.526928\pi\)
0.820681 + 0.571387i \(0.193594\pi\)
\(138\) 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
\(147\) −11.5922 3.55256i −0.956109 0.293010i
\(148\) 0 0
\(149\) −0.987090 0.569897i −0.0808655 0.0466877i 0.459022 0.888425i \(-0.348200\pi\)
−0.539888 + 0.841737i \(0.681533\pi\)
\(150\) 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
\(159\) 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 −0.867972 0.496613i \(-0.834577\pi\)
0.864065 + 0.503379i \(0.167910\pi\)
\(164\) 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 −0.688657 0.725087i \(-0.741799\pi\)
0.972272 + 0.233851i \(0.0751328\pi\)
\(174\) 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 −0.594521 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
\(189\) −6.67947 + 12.0160i −0.485860 + 0.874037i
\(190\) 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 \(-0.824148\pi\)
0.851239 0.524778i \(-0.175852\pi\)
\(198\) 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
\(201\) −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 \(-0.880079\pi\)
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 \(0.0492535\pi\)
−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
\(231\) 2.26228 + 7.23181i 0.148847 + 0.475818i
\(232\) 0 0
\(233\) −4.45119 2.56990i −0.291607 0.168360i 0.347059 0.937843i \(-0.387180\pi\)
−0.638666 + 0.769484i \(0.720514\pi\)
\(234\) 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
\(243\) 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 −0.555419 0.831571i \(-0.687442\pi\)
0.997871 + 0.0652214i \(0.0207753\pi\)
\(258\) 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 −0.440052 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 0.998195 0.0600579i \(-0.0191285\pi\)
−0.551109 + 0.834433i \(0.685795\pi\)
\(270\) 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
\(273\) 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 0.865865 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 \(0.0778406\pi\)
−0.970248 + 0.242114i \(0.922159\pi\)
\(282\) 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
\(285\) −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 \(-0.761049\pi\)
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 \(-0.961884\pi\)
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
\(315\) −12.9247 15.8749i −0.728224 0.894450i
\(316\) 0 0
\(317\) 13.8698 + 8.00775i 0.779007 + 0.449760i 0.836078 0.548610i \(-0.184843\pi\)
−0.0570712 + 0.998370i \(0.518176\pi\)
\(318\) 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 0.478074 + 0.878319i \(0.341335\pi\)
−0.999684 + 0.0251350i \(0.991998\pi\)
\(332\) 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 −0.777880 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 \(-0.972835\pi\)
0.424363 0.905492i \(-0.360498\pi\)
\(354\) 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 −0.310276 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 −0.916221 0.400673i \(-0.868776\pi\)
−0.111118 + 0.993807i \(0.535443\pi\)
\(368\) 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 −0.627778 0.778393i \(-0.716035\pi\)
0.987997 + 0.154475i \(0.0493686\pi\)
\(374\) 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 −0.832725 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
\(387\) 7.09373 + 2.09315i 0.360595 + 0.106401i
\(388\) 0 0
\(389\) 20.4245 11.7921i 1.03556 0.597882i 0.116989 0.993133i \(-0.462676\pi\)
0.918573 + 0.395251i \(0.129342\pi\)
\(390\) 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
\(399\) −9.28030 + 10.0820i −0.464596 + 0.504730i
\(400\) 0 0
\(401\) 6.46052 + 3.72998i 0.322623 + 0.186266i 0.652561 0.757736i \(-0.273695\pi\)
−0.329938 + 0.944003i \(0.607028\pi\)
\(402\) 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
\(411\) 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 −0.0957491 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 0.844570 0.535446i \(-0.179856\pi\)
−0.0414249 + 0.999142i \(0.513190\pi\)
\(440\) 0 0
\(441\) −18.9923 8.96064i −0.904395 0.426697i
\(442\) 0 0
\(443\) 3.08964 + 1.78380i 0.146793 + 0.0847510i 0.571598 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 \(0.245915\pi\)
−0.716124 + 0.697973i \(0.754085\pi\)
\(450\) 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 −0.474189 0.880423i \(-0.657259\pi\)
0.999563 0.0295520i \(-0.00940807\pi\)
\(458\) 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 −0.690871 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
\(471\) 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 0.991918 + 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
\(483\) −0.893552 + 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 0.921260 + 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 \(0.262886\pi\)
−0.677910 + 0.735145i \(0.737114\pi\)
\(492\) 0 0
\(493\) −13.5245 + 7.80840i −0.609115 + 0.351673i
\(494\) 0 0
\(495\) −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 −0.915982 0.401219i \(-0.868587\pi\)
0.805457 + 0.592655i \(0.201920\pi\)
\(500\) 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 −0.851691 0.524044i \(-0.824423\pi\)
0.879681 + 0.475564i \(0.157756\pi\)
\(510\) 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 0.981408 + 0.191932i \(0.0614755\pi\)
−0.324486 + 0.945891i \(0.605191\pi\)
\(522\) 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
\(525\) 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 −0.487598 0.873068i \(-0.662127\pi\)
0.999898 0.0142616i \(-0.00453975\pi\)
\(542\) 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 −0.849675 0.527307i \(-0.823202\pi\)
0.0318235 + 0.999494i \(0.489869\pi\)
\(558\) 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
\(567\) −14.4259 + 18.9445i −0.605832 + 0.795593i
\(568\) 0 0
\(569\) −21.7717 12.5699i −0.912717 0.526957i −0.0314127 0.999506i \(-0.510001\pi\)
−0.881304 + 0.472549i \(0.843334\pi\)
\(570\) 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
\(579\) 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 −0.693232 0.720714i \(-0.743814\pi\)
0.970773 + 0.240000i \(0.0771474\pi\)
\(594\) 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 −0.379284 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 0.486261 0.873814i \(-0.338360\pi\)
−0.513614 + 0.858021i \(0.671694\pi\)
\(608\) 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 −0.931402 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 \(0.0504134\pi\)
−0.987484 + 0.157717i \(0.949587\pi\)
\(618\) 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
\(621\) 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 0.287401 0.957810i \(-0.407209\pi\)
0.973189 + 0.230009i \(0.0738755\pi\)
\(642\) 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 0.993874 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
\(651\) −8.23413 26.3219i −0.322721 1.03164i
\(652\) 0 0
\(653\) −28.7382 16.5920i −1.12461 0.649295i −0.182038 0.983291i \(-0.558269\pi\)
−0.942574 + 0.333996i \(0.891603\pi\)
\(654\) 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
\(663\) −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 −0.913215 0.407477i \(-0.866408\pi\)
0.809493 + 0.587129i \(0.199742\pi\)
\(678\) 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 0.168101 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 −0.328975 0.944339i \(-0.606703\pi\)
−0.982309 + 0.187268i \(0.940037\pi\)
\(692\) 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 \(-0.935490\pi\)
0.979534 0.201280i \(-0.0645100\pi\)
\(702\) 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 0.320672 + 0.947190i \(0.396091\pi\)
−0.980627 + 0.195885i \(0.937242\pi\)
\(710\) 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 0.412197 + 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
\(723\) 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 \(0.264231\pi\)
−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
\(735\) 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 −0.999239 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 \(-0.789459\pi\)
0.789113 0.614248i \(-0.210541\pi\)
\(744\) 0 0
\(745\) 2.54580 1.46982i 0.0932710 0.0538501i
\(746\) 0 0
\(747\) 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 −0.952914 0.303242i \(-0.901931\pi\)
0.739072 + 0.673627i \(0.235264\pi\)
\(752\) 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 −0.623950 0.781465i \(-0.714473\pi\)
0.988743 + 0.149624i \(0.0478063\pi\)
\(762\) 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 \(0.0457940\pi\)
−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 \(0.0270182\pi\)
−0.424780 + 0.905297i \(0.639648\pi\)
\(774\) 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 0.0497122 0.998764i \(-0.484170\pi\)
0.889811 + 0.456330i \(0.150836\pi\)
\(788\) 0 0
\(789\) 3.54171 1.41516i 0.126088 0.0503809i