Properties

Label 2646.2.h.p.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.p.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.460505 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.460505 q^{5} -1.00000 q^{8} +(-0.230252 - 0.398809i) q^{10} +3.64766 q^{11} +(-0.730252 - 1.26483i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.86693 - 3.23361i) q^{17} +(2.02704 - 3.51094i) q^{19} +(0.230252 - 0.398809i) q^{20} +(1.82383 + 3.15897i) q^{22} -1.13307 q^{23} -4.78794 q^{25} +(0.730252 - 1.26483i) q^{26} +(4.48755 - 7.77266i) q^{29} +(-0.257295 + 0.445647i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.86693 - 3.23361i) q^{34} +(-4.55408 + 7.88791i) q^{37} +4.05408 q^{38} +0.460505 q^{40} +(-0.472958 - 0.819187i) q^{41} +(4.66372 - 8.07779i) q^{43} +(-1.82383 + 3.15897i) q^{44} +(-0.566537 - 0.981271i) q^{46} +(-1.16372 - 2.01561i) q^{47} +(-2.39397 - 4.14647i) q^{50} +1.46050 q^{52} +(-6.21780 - 10.7695i) q^{53} -1.67977 q^{55} +8.97509 q^{58} +(6.44805 - 11.1684i) q^{59} +(6.04163 + 10.4644i) q^{61} -0.514589 q^{62} +1.00000 q^{64} +(0.336285 + 0.582462i) q^{65} +(1.16012 - 2.00938i) q^{67} +3.73385 q^{68} -1.67977 q^{71} +(6.62062 + 11.4673i) q^{73} -9.10817 q^{74} +(2.02704 + 3.51094i) q^{76} +(2.50360 + 4.33636i) q^{79} +(0.230252 + 0.398809i) q^{80} +(0.472958 - 0.819187i) q^{82} +(3.32383 - 5.75705i) q^{83} +(0.859728 + 1.48909i) q^{85} +9.32743 q^{86} -3.64766 q^{88} +(-1.36333 + 2.36135i) q^{89} +(0.566537 - 0.981271i) q^{92} +(1.16372 - 2.01561i) q^{94} +(-0.933463 + 1.61680i) q^{95} +(5.59358 - 9.68836i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + O(q^{10}) \) \( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} - 9 q^{37} + 6 q^{38} - 10 q^{40} - 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 3 q^{47} + 2 q^{50} - 4 q^{52} - 9 q^{53} - 14 q^{55} + 10 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} + 8 q^{68} - 14 q^{71} + 25 q^{73} - 18 q^{74} + 3 q^{76} + 7 q^{79} - 5 q^{80} + 12 q^{82} + 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} - 9 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.460505 −0.205944 −0.102972 0.994684i \(-0.532835\pi\)
−0.102972 + 0.994684i \(0.532835\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.230252 0.398809i −0.0728122 0.126114i
\(11\) 3.64766 1.09981 0.549906 0.835227i \(-0.314664\pi\)
0.549906 + 0.835227i \(0.314664\pi\)
\(12\) 0 0
\(13\) −0.730252 1.26483i −0.202536 0.350802i 0.746809 0.665038i \(-0.231585\pi\)
−0.949345 + 0.314236i \(0.898252\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.86693 3.23361i −0.452796 0.784266i 0.545763 0.837940i \(-0.316240\pi\)
−0.998558 + 0.0536743i \(0.982907\pi\)
\(18\) 0 0
\(19\) 2.02704 3.51094i 0.465035 0.805465i −0.534168 0.845378i \(-0.679375\pi\)
0.999203 + 0.0399136i \(0.0127083\pi\)
\(20\) 0.230252 0.398809i 0.0514860 0.0891764i
\(21\) 0 0
\(22\) 1.82383 + 3.15897i 0.388842 + 0.673495i
\(23\) −1.13307 −0.236262 −0.118131 0.992998i \(-0.537690\pi\)
−0.118131 + 0.992998i \(0.537690\pi\)
\(24\) 0 0
\(25\) −4.78794 −0.957587
\(26\) 0.730252 1.26483i 0.143214 0.248054i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.48755 7.77266i 0.833317 1.44335i −0.0620772 0.998071i \(-0.519772\pi\)
0.895394 0.445275i \(-0.146894\pi\)
\(30\) 0 0
\(31\) −0.257295 + 0.445647i −0.0462115 + 0.0800406i −0.888206 0.459446i \(-0.848048\pi\)
0.841994 + 0.539486i \(0.181381\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.86693 3.23361i 0.320175 0.554560i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.55408 + 7.88791i −0.748687 + 1.29676i 0.199765 + 0.979844i \(0.435982\pi\)
−0.948452 + 0.316920i \(0.897351\pi\)
\(38\) 4.05408 0.657659
\(39\) 0 0
\(40\) 0.460505 0.0728122
\(41\) −0.472958 0.819187i −0.0738636 0.127936i 0.826728 0.562602i \(-0.190200\pi\)
−0.900592 + 0.434666i \(0.856866\pi\)
\(42\) 0 0
\(43\) 4.66372 8.07779i 0.711210 1.23185i −0.253193 0.967416i \(-0.581481\pi\)
0.964403 0.264436i \(-0.0851858\pi\)
\(44\) −1.82383 + 3.15897i −0.274953 + 0.476233i
\(45\) 0 0
\(46\) −0.566537 0.981271i −0.0835314 0.144681i
\(47\) −1.16372 2.01561i −0.169745 0.294007i 0.768585 0.639748i \(-0.220961\pi\)
−0.938330 + 0.345740i \(0.887628\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.39397 4.14647i −0.338558 0.586400i
\(51\) 0 0
\(52\) 1.46050 0.202536
\(53\) −6.21780 10.7695i −0.854080 1.47931i −0.877495 0.479585i \(-0.840787\pi\)
0.0234151 0.999726i \(-0.492546\pi\)
\(54\) 0 0
\(55\) −1.67977 −0.226500
\(56\) 0 0
\(57\) 0 0
\(58\) 8.97509 1.17849
\(59\) 6.44805 11.1684i 0.839465 1.45400i −0.0508779 0.998705i \(-0.516202\pi\)
0.890343 0.455291i \(-0.150465\pi\)
\(60\) 0 0
\(61\) 6.04163 + 10.4644i 0.773552 + 1.33983i 0.935605 + 0.353049i \(0.114855\pi\)
−0.162053 + 0.986782i \(0.551812\pi\)
\(62\) −0.514589 −0.0653529
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.336285 + 0.582462i 0.0417110 + 0.0722456i
\(66\) 0 0
\(67\) 1.16012 2.00938i 0.141731 0.245485i −0.786418 0.617695i \(-0.788067\pi\)
0.928148 + 0.372210i \(0.121400\pi\)
\(68\) 3.73385 0.452796
\(69\) 0 0
\(70\) 0 0
\(71\) −1.67977 −0.199352 −0.0996758 0.995020i \(-0.531781\pi\)
−0.0996758 + 0.995020i \(0.531781\pi\)
\(72\) 0 0
\(73\) 6.62062 + 11.4673i 0.774885 + 1.34214i 0.934859 + 0.355019i \(0.115526\pi\)
−0.159974 + 0.987121i \(0.551141\pi\)
\(74\) −9.10817 −1.05880
\(75\) 0 0
\(76\) 2.02704 + 3.51094i 0.232518 + 0.402732i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.50360 + 4.33636i 0.281677 + 0.487879i 0.971798 0.235815i \(-0.0757761\pi\)
−0.690121 + 0.723694i \(0.742443\pi\)
\(80\) 0.230252 + 0.398809i 0.0257430 + 0.0445882i
\(81\) 0 0
\(82\) 0.472958 0.819187i 0.0522295 0.0904641i
\(83\) 3.32383 5.75705i 0.364838 0.631918i −0.623912 0.781494i \(-0.714458\pi\)
0.988750 + 0.149577i \(0.0477911\pi\)
\(84\) 0 0
\(85\) 0.859728 + 1.48909i 0.0932506 + 0.161515i
\(86\) 9.32743 1.00580
\(87\) 0 0
\(88\) −3.64766 −0.388842
\(89\) −1.36333 + 2.36135i −0.144512 + 0.250303i −0.929191 0.369600i \(-0.879495\pi\)
0.784679 + 0.619903i \(0.212828\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.566537 0.981271i 0.0590656 0.102305i
\(93\) 0 0
\(94\) 1.16372 2.01561i 0.120028 0.207895i
\(95\) −0.933463 + 1.61680i −0.0957713 + 0.165881i
\(96\) 0 0
\(97\) 5.59358 9.68836i 0.567942 0.983704i −0.428827 0.903386i \(-0.641073\pi\)
0.996769 0.0803178i \(-0.0255935\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.39397 4.14647i 0.239397 0.414647i
\(101\) 13.7558 1.36876 0.684378 0.729127i \(-0.260074\pi\)
0.684378 + 0.729127i \(0.260074\pi\)
\(102\) 0 0
\(103\) −11.1623 −1.09985 −0.549925 0.835214i \(-0.685344\pi\)
−0.549925 + 0.835214i \(0.685344\pi\)
\(104\) 0.730252 + 1.26483i 0.0716071 + 0.124027i
\(105\) 0 0
\(106\) 6.21780 10.7695i 0.603926 1.04603i
\(107\) 3.89037 6.73832i 0.376096 0.651418i −0.614394 0.788999i \(-0.710600\pi\)
0.990490 + 0.137581i \(0.0439329\pi\)
\(108\) 0 0
\(109\) −3.75729 6.50783i −0.359884 0.623337i 0.628058 0.778167i \(-0.283850\pi\)
−0.987941 + 0.154830i \(0.950517\pi\)
\(110\) −0.839883 1.45472i −0.0800797 0.138702i
\(111\) 0 0
\(112\) 0 0
\(113\) −3.03064 5.24922i −0.285099 0.493805i 0.687534 0.726152i \(-0.258693\pi\)
−0.972633 + 0.232346i \(0.925360\pi\)
\(114\) 0 0
\(115\) 0.521786 0.0486568
\(116\) 4.48755 + 7.77266i 0.416658 + 0.721673i
\(117\) 0 0
\(118\) 12.8961 1.18718
\(119\) 0 0
\(120\) 0 0
\(121\) 2.30545 0.209586
\(122\) −6.04163 + 10.4644i −0.546984 + 0.947403i
\(123\) 0 0
\(124\) −0.257295 0.445647i −0.0231057 0.0400203i
\(125\) 4.50739 0.403153
\(126\) 0 0
\(127\) 8.80992 0.781754 0.390877 0.920443i \(-0.372172\pi\)
0.390877 + 0.920443i \(0.372172\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.336285 + 0.582462i −0.0294941 + 0.0510853i
\(131\) 21.1373 1.84678 0.923389 0.383865i \(-0.125407\pi\)
0.923389 + 0.383865i \(0.125407\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.32023 0.200438
\(135\) 0 0
\(136\) 1.86693 + 3.23361i 0.160088 + 0.277280i
\(137\) 4.40642 0.376466 0.188233 0.982124i \(-0.439724\pi\)
0.188233 + 0.982124i \(0.439724\pi\)
\(138\) 0 0
\(139\) 1.01245 + 1.75362i 0.0858751 + 0.148740i 0.905764 0.423783i \(-0.139298\pi\)
−0.819889 + 0.572523i \(0.805965\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.839883 1.45472i −0.0704815 0.122077i
\(143\) −2.66372 4.61369i −0.222751 0.385816i
\(144\) 0 0
\(145\) −2.06654 + 3.57935i −0.171617 + 0.297249i
\(146\) −6.62062 + 11.4673i −0.547927 + 0.949037i
\(147\) 0 0
\(148\) −4.55408 7.88791i −0.374343 0.648382i
\(149\) 9.16225 0.750601 0.375300 0.926903i \(-0.377540\pi\)
0.375300 + 0.926903i \(0.377540\pi\)
\(150\) 0 0
\(151\) −0.103896 −0.00845496 −0.00422748 0.999991i \(-0.501346\pi\)
−0.00422748 + 0.999991i \(0.501346\pi\)
\(152\) −2.02704 + 3.51094i −0.164415 + 0.284775i
\(153\) 0 0
\(154\) 0 0
\(155\) 0.118485 0.205223i 0.00951698 0.0164839i
\(156\) 0 0
\(157\) 10.4911 18.1712i 0.837285 1.45022i −0.0548721 0.998493i \(-0.517475\pi\)
0.892157 0.451726i \(-0.149192\pi\)
\(158\) −2.50360 + 4.33636i −0.199176 + 0.344982i
\(159\) 0 0
\(160\) −0.230252 + 0.398809i −0.0182031 + 0.0315286i
\(161\) 0 0
\(162\) 0 0
\(163\) −11.5182 + 19.9501i −0.902174 + 1.56261i −0.0775078 + 0.996992i \(0.524696\pi\)
−0.824666 + 0.565620i \(0.808637\pi\)
\(164\) 0.945916 0.0738636
\(165\) 0 0
\(166\) 6.64766 0.515959
\(167\) −5.31498 9.20581i −0.411285 0.712367i 0.583745 0.811937i \(-0.301587\pi\)
−0.995031 + 0.0995698i \(0.968253\pi\)
\(168\) 0 0
\(169\) 5.43346 9.41103i 0.417959 0.723926i
\(170\) −0.859728 + 1.48909i −0.0659382 + 0.114208i
\(171\) 0 0
\(172\) 4.66372 + 8.07779i 0.355605 + 0.615926i
\(173\) −1.46936 2.54500i −0.111713 0.193493i 0.804748 0.593617i \(-0.202301\pi\)
−0.916461 + 0.400124i \(0.868967\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.82383 3.15897i −0.137476 0.238116i
\(177\) 0 0
\(178\) −2.72665 −0.204371
\(179\) 4.58113 + 7.93474i 0.342409 + 0.593071i 0.984880 0.173240i \(-0.0554237\pi\)
−0.642470 + 0.766311i \(0.722090\pi\)
\(180\) 0 0
\(181\) −22.4284 −1.66709 −0.833545 0.552452i \(-0.813692\pi\)
−0.833545 + 0.552452i \(0.813692\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.13307 0.0835314
\(185\) 2.09718 3.63242i 0.154188 0.267061i
\(186\) 0 0
\(187\) −6.80992 11.7951i −0.497990 0.862545i
\(188\) 2.32743 0.169745
\(189\) 0 0
\(190\) −1.86693 −0.135441
\(191\) 1.24484 + 2.15613i 0.0900736 + 0.156012i 0.907542 0.419962i \(-0.137956\pi\)
−0.817468 + 0.575974i \(0.804623\pi\)
\(192\) 0 0
\(193\) −2.24484 + 3.88818i −0.161587 + 0.279877i −0.935438 0.353491i \(-0.884995\pi\)
0.773851 + 0.633368i \(0.218328\pi\)
\(194\) 11.1872 0.803191
\(195\) 0 0
\(196\) 0 0
\(197\) −12.7339 −0.907249 −0.453625 0.891193i \(-0.649869\pi\)
−0.453625 + 0.891193i \(0.649869\pi\)
\(198\) 0 0
\(199\) 1.47296 + 2.55124i 0.104415 + 0.180852i 0.913499 0.406841i \(-0.133370\pi\)
−0.809084 + 0.587693i \(0.800036\pi\)
\(200\) 4.78794 0.338558
\(201\) 0 0
\(202\) 6.87792 + 11.9129i 0.483928 + 0.838189i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.217799 + 0.377240i 0.0152118 + 0.0263476i
\(206\) −5.58113 9.66679i −0.388855 0.673517i
\(207\) 0 0
\(208\) −0.730252 + 1.26483i −0.0506339 + 0.0877005i
\(209\) 7.39397 12.8067i 0.511451 0.885860i
\(210\) 0 0
\(211\) −0.608168 1.05338i −0.0418680 0.0725176i 0.844332 0.535820i \(-0.179998\pi\)
−0.886200 + 0.463303i \(0.846664\pi\)
\(212\) 12.4356 0.854080
\(213\) 0 0
\(214\) 7.78074 0.531880
\(215\) −2.14766 + 3.71986i −0.146469 + 0.253693i
\(216\) 0 0
\(217\) 0 0
\(218\) 3.75729 6.50783i 0.254476 0.440766i
\(219\) 0 0
\(220\) 0.839883 1.45472i 0.0566249 0.0980773i
\(221\) −2.72665 + 4.72270i −0.183415 + 0.317683i
\(222\) 0 0
\(223\) 0.445916 0.772349i 0.0298607 0.0517203i −0.850709 0.525637i \(-0.823827\pi\)
0.880570 + 0.473917i \(0.157160\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3.03064 5.24922i 0.201595 0.349173i
\(227\) −14.6519 −0.972483 −0.486242 0.873824i \(-0.661632\pi\)
−0.486242 + 0.873824i \(0.661632\pi\)
\(228\) 0 0
\(229\) 9.57587 0.632791 0.316396 0.948627i \(-0.397527\pi\)
0.316396 + 0.948627i \(0.397527\pi\)
\(230\) 0.260893 + 0.451880i 0.0172028 + 0.0297961i
\(231\) 0 0
\(232\) −4.48755 + 7.77266i −0.294622 + 0.510300i
\(233\) −7.21420 + 12.4954i −0.472618 + 0.818598i −0.999509 0.0313345i \(-0.990024\pi\)
0.526891 + 0.849933i \(0.323358\pi\)
\(234\) 0 0
\(235\) 0.535897 + 0.928200i 0.0349580 + 0.0605491i
\(236\) 6.44805 + 11.1684i 0.419732 + 0.726998i
\(237\) 0 0
\(238\) 0 0
\(239\) 9.15486 + 15.8567i 0.592179 + 1.02568i 0.993938 + 0.109938i \(0.0350654\pi\)
−0.401760 + 0.915745i \(0.631601\pi\)
\(240\) 0 0
\(241\) −0.0933847 −0.00601544 −0.00300772 0.999995i \(-0.500957\pi\)
−0.00300772 + 0.999995i \(0.500957\pi\)
\(242\) 1.15272 + 1.99658i 0.0741000 + 0.128345i
\(243\) 0 0
\(244\) −12.0833 −0.773552
\(245\) 0 0
\(246\) 0 0
\(247\) −5.92101 −0.376745
\(248\) 0.257295 0.445647i 0.0163382 0.0282986i
\(249\) 0 0
\(250\) 2.25370 + 3.90352i 0.142536 + 0.246880i
\(251\) −18.2733 −1.15340 −0.576702 0.816955i \(-0.695661\pi\)
−0.576702 + 0.816955i \(0.695661\pi\)
\(252\) 0 0
\(253\) −4.13307 −0.259844
\(254\) 4.40496 + 7.62961i 0.276392 + 0.478724i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −21.0512 −1.31314 −0.656568 0.754267i \(-0.727992\pi\)
−0.656568 + 0.754267i \(0.727992\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.672570 −0.0417110
\(261\) 0 0
\(262\) 10.5687 + 18.3055i 0.652935 + 1.13092i
\(263\) 5.16518 0.318499 0.159249 0.987238i \(-0.449093\pi\)
0.159249 + 0.987238i \(0.449093\pi\)
\(264\) 0 0
\(265\) 2.86333 + 4.95943i 0.175893 + 0.304655i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.16012 + 2.00938i 0.0708654 + 0.122742i
\(269\) 8.42840 + 14.5984i 0.513889 + 0.890081i 0.999870 + 0.0161123i \(0.00512891\pi\)
−0.485981 + 0.873969i \(0.661538\pi\)
\(270\) 0 0
\(271\) −12.5562 + 21.7480i −0.762736 + 1.32110i 0.178699 + 0.983904i \(0.442811\pi\)
−0.941435 + 0.337194i \(0.890522\pi\)
\(272\) −1.86693 + 3.23361i −0.113199 + 0.196066i
\(273\) 0 0
\(274\) 2.20321 + 3.81607i 0.133101 + 0.230537i
\(275\) −17.4648 −1.05317
\(276\) 0 0
\(277\) 3.38151 0.203176 0.101588 0.994827i \(-0.467608\pi\)
0.101588 + 0.994827i \(0.467608\pi\)
\(278\) −1.01245 + 1.75362i −0.0607229 + 0.105175i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.1388 17.5609i 0.604831 1.04760i −0.387248 0.921976i \(-0.626574\pi\)
0.992078 0.125622i \(-0.0400925\pi\)
\(282\) 0 0
\(283\) 8.67471 15.0250i 0.515658 0.893145i −0.484177 0.874970i \(-0.660881\pi\)
0.999835 0.0181754i \(-0.00578571\pi\)
\(284\) 0.839883 1.45472i 0.0498379 0.0863218i
\(285\) 0 0
\(286\) 2.66372 4.61369i 0.157509 0.272813i
\(287\) 0 0
\(288\) 0 0
\(289\) 1.52918 2.64861i 0.0899517 0.155801i
\(290\) −4.13307 −0.242702
\(291\) 0 0
\(292\) −13.2412 −0.774885
\(293\) −4.93560 8.54871i −0.288341 0.499421i 0.685073 0.728474i \(-0.259770\pi\)
−0.973414 + 0.229054i \(0.926437\pi\)
\(294\) 0 0
\(295\) −2.96936 + 5.14308i −0.172883 + 0.299442i
\(296\) 4.55408 7.88791i 0.264701 0.458475i
\(297\) 0 0
\(298\) 4.58113 + 7.93474i 0.265378 + 0.459647i
\(299\) 0.827430 + 1.43315i 0.0478515 + 0.0828813i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.0519482 0.0899768i −0.00298928 0.00517759i
\(303\) 0 0
\(304\) −4.05408 −0.232518
\(305\) −2.78220 4.81891i −0.159308 0.275930i
\(306\) 0 0
\(307\) −7.78794 −0.444481 −0.222240 0.974992i \(-0.571337\pi\)
−0.222240 + 0.974992i \(0.571337\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.236971 0.0134590
\(311\) −7.70535 + 13.3461i −0.436930 + 0.756785i −0.997451 0.0713552i \(-0.977268\pi\)
0.560521 + 0.828140i \(0.310601\pi\)
\(312\) 0 0
\(313\) 4.24844 + 7.35851i 0.240136 + 0.415928i 0.960753 0.277406i \(-0.0894746\pi\)
−0.720617 + 0.693334i \(0.756141\pi\)
\(314\) 20.9823 1.18410
\(315\) 0 0
\(316\) −5.00720 −0.281677
\(317\) −7.05262 12.2155i −0.396115 0.686091i 0.597128 0.802146i \(-0.296308\pi\)
−0.993243 + 0.116055i \(0.962975\pi\)
\(318\) 0 0
\(319\) 16.3691 28.3520i 0.916491 1.58741i
\(320\) −0.460505 −0.0257430
\(321\) 0 0
\(322\) 0 0
\(323\) −15.1373 −0.842264
\(324\) 0 0
\(325\) 3.49640 + 6.05594i 0.193945 + 0.335923i
\(326\) −23.0364 −1.27587
\(327\) 0 0
\(328\) 0.472958 + 0.819187i 0.0261147 + 0.0452320i
\(329\) 0 0
\(330\) 0 0
\(331\) −13.7719 23.8536i −0.756971 1.31111i −0.944388 0.328832i \(-0.893345\pi\)
0.187417 0.982280i \(-0.439988\pi\)
\(332\) 3.32383 + 5.75705i 0.182419 + 0.315959i
\(333\) 0 0
\(334\) 5.31498 9.20581i 0.290823 0.503720i
\(335\) −0.534239 + 0.925330i −0.0291886 + 0.0505562i
\(336\) 0 0
\(337\) 0.748440 + 1.29634i 0.0407701 + 0.0706159i 0.885690 0.464276i \(-0.153686\pi\)
−0.844920 + 0.534892i \(0.820352\pi\)
\(338\) 10.8669 0.591083
\(339\) 0 0
\(340\) −1.71946 −0.0932506
\(341\) −0.938524 + 1.62557i −0.0508239 + 0.0880296i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.66372 + 8.07779i −0.251451 + 0.435525i
\(345\) 0 0
\(346\) 1.46936 2.54500i 0.0789932 0.136820i
\(347\) −9.14406 + 15.8380i −0.490879 + 0.850228i −0.999945 0.0105001i \(-0.996658\pi\)
0.509066 + 0.860728i \(0.329991\pi\)
\(348\) 0 0
\(349\) 3.90136 6.75735i 0.208835 0.361713i −0.742513 0.669832i \(-0.766366\pi\)
0.951348 + 0.308119i \(0.0996995\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.82383 3.15897i 0.0972106 0.168374i
\(353\) 26.9253 1.43309 0.716544 0.697542i \(-0.245723\pi\)
0.716544 + 0.697542i \(0.245723\pi\)
\(354\) 0 0
\(355\) 0.773541 0.0410553
\(356\) −1.36333 2.36135i −0.0722562 0.125151i
\(357\) 0 0
\(358\) −4.58113 + 7.93474i −0.242120 + 0.419364i
\(359\) 3.13161 5.42411i 0.165280 0.286274i −0.771475 0.636260i \(-0.780481\pi\)
0.936755 + 0.349987i \(0.113814\pi\)
\(360\) 0 0
\(361\) 1.28220 + 2.22084i 0.0674842 + 0.116886i
\(362\) −11.2142 19.4236i −0.589405 1.02088i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.04883 5.28073i −0.159583 0.276406i
\(366\) 0 0
\(367\) −29.2733 −1.52806 −0.764028 0.645183i \(-0.776781\pi\)
−0.764028 + 0.645183i \(0.776781\pi\)
\(368\) 0.566537 + 0.981271i 0.0295328 + 0.0511523i
\(369\) 0 0
\(370\) 4.19436 0.218054
\(371\) 0 0
\(372\) 0 0
\(373\) 17.8597 0.924742 0.462371 0.886687i \(-0.346999\pi\)
0.462371 + 0.886687i \(0.346999\pi\)
\(374\) 6.80992 11.7951i 0.352132 0.609911i
\(375\) 0 0
\(376\) 1.16372 + 2.01561i 0.0600140 + 0.103947i
\(377\) −13.1082 −0.675105
\(378\) 0 0
\(379\) −22.4255 −1.15192 −0.575960 0.817478i \(-0.695371\pi\)
−0.575960 + 0.817478i \(0.695371\pi\)
\(380\) −0.933463 1.61680i −0.0478856 0.0829403i
\(381\) 0 0
\(382\) −1.24484 + 2.15613i −0.0636916 + 0.110317i
\(383\) −14.1403 −0.722534 −0.361267 0.932462i \(-0.617656\pi\)
−0.361267 + 0.932462i \(0.617656\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4.48968 −0.228519
\(387\) 0 0
\(388\) 5.59358 + 9.68836i 0.283971 + 0.491852i
\(389\) 23.1301 1.17275 0.586373 0.810041i \(-0.300555\pi\)
0.586373 + 0.810041i \(0.300555\pi\)
\(390\) 0 0
\(391\) 2.11537 + 3.66392i 0.106979 + 0.185292i
\(392\) 0 0
\(393\) 0 0
\(394\) −6.36693 11.0278i −0.320761 0.555574i
\(395\) −1.15292 1.99691i −0.0580097 0.100476i
\(396\) 0 0
\(397\) 5.13307 8.89075i 0.257622 0.446214i −0.707983 0.706230i \(-0.750395\pi\)
0.965604 + 0.260016i \(0.0837279\pi\)
\(398\) −1.47296 + 2.55124i −0.0738327 + 0.127882i
\(399\) 0 0
\(400\) 2.39397 + 4.14647i 0.119698 + 0.207324i
\(401\) −34.0335 −1.69955 −0.849775 0.527146i \(-0.823262\pi\)
−0.849775 + 0.527146i \(0.823262\pi\)
\(402\) 0 0
\(403\) 0.751560 0.0374379
\(404\) −6.87792 + 11.9129i −0.342189 + 0.592689i
\(405\) 0 0
\(406\) 0 0
\(407\) −16.6118 + 28.7724i −0.823415 + 1.42620i
\(408\) 0 0
\(409\) −1.74484 + 3.02215i −0.0862769 + 0.149436i −0.905935 0.423418i \(-0.860830\pi\)
0.819658 + 0.572854i \(0.194164\pi\)
\(410\) −0.217799 + 0.377240i −0.0107563 + 0.0186305i
\(411\) 0 0
\(412\) 5.58113 9.66679i 0.274962 0.476249i
\(413\) 0 0
\(414\) 0 0
\(415\) −1.53064 + 2.65115i −0.0751362 + 0.130140i
\(416\) −1.46050 −0.0716071
\(417\) 0 0
\(418\) 14.7879 0.723302
\(419\) 14.4897 + 25.0969i 0.707867 + 1.22606i 0.965647 + 0.259858i \(0.0836759\pi\)
−0.257779 + 0.966204i \(0.582991\pi\)
\(420\) 0 0
\(421\) −1.06128 + 1.83819i −0.0517237 + 0.0895881i −0.890728 0.454537i \(-0.849805\pi\)
0.839004 + 0.544125i \(0.183138\pi\)
\(422\) 0.608168 1.05338i 0.0296052 0.0512777i
\(423\) 0 0
\(424\) 6.21780 + 10.7695i 0.301963 + 0.523015i
\(425\) 8.93872 + 15.4823i 0.433592 + 0.751003i
\(426\) 0 0
\(427\) 0 0
\(428\) 3.89037 + 6.73832i 0.188048 + 0.325709i
\(429\) 0 0
\(430\) −4.29533 −0.207139
\(431\) −10.9356 18.9410i −0.526749 0.912356i −0.999514 0.0311679i \(-0.990077\pi\)
0.472765 0.881189i \(-0.343256\pi\)
\(432\) 0 0
\(433\) 13.0512 0.627199 0.313599 0.949555i \(-0.398465\pi\)
0.313599 + 0.949555i \(0.398465\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.51459 0.359884
\(437\) −2.29679 + 3.97816i −0.109870 + 0.190301i
\(438\) 0 0
\(439\) 2.43200 + 4.21235i 0.116073 + 0.201044i 0.918208 0.396098i \(-0.129636\pi\)
−0.802135 + 0.597143i \(0.796303\pi\)
\(440\) 1.67977 0.0800797
\(441\) 0 0
\(442\) −5.45331 −0.259387
\(443\) −5.76975 9.99350i −0.274129 0.474805i 0.695786 0.718249i \(-0.255056\pi\)
−0.969915 + 0.243444i \(0.921723\pi\)
\(444\) 0 0
\(445\) 0.627819 1.08741i 0.0297615 0.0515484i
\(446\) 0.891832 0.0422294
\(447\) 0 0
\(448\) 0 0
\(449\) 26.4251 1.24708 0.623538 0.781793i \(-0.285694\pi\)
0.623538 + 0.781793i \(0.285694\pi\)
\(450\) 0 0
\(451\) −1.72519 2.98812i −0.0812361 0.140705i
\(452\) 6.06128 0.285099
\(453\) 0 0
\(454\) −7.32597 12.6889i −0.343825 0.595522i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.86906 + 3.23731i 0.0874310 + 0.151435i 0.906425 0.422368i \(-0.138801\pi\)
−0.818994 + 0.573803i \(0.805468\pi\)
\(458\) 4.78794 + 8.29295i 0.223726 + 0.387504i
\(459\) 0 0
\(460\) −0.260893 + 0.451880i −0.0121642 + 0.0210690i
\(461\) −7.90496 + 13.6918i −0.368171 + 0.637690i −0.989280 0.146034i \(-0.953349\pi\)
0.621109 + 0.783724i \(0.286682\pi\)
\(462\) 0 0
\(463\) 19.1965 + 33.2493i 0.892137 + 1.54523i 0.837309 + 0.546730i \(0.184128\pi\)
0.0548278 + 0.998496i \(0.482539\pi\)
\(464\) −8.97509 −0.416658
\(465\) 0 0
\(466\) −14.4284 −0.668383
\(467\) 3.15652 5.46725i 0.146066 0.252994i −0.783704 0.621134i \(-0.786672\pi\)
0.929770 + 0.368140i \(0.120005\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.535897 + 0.928200i −0.0247191 + 0.0428147i
\(471\) 0 0
\(472\) −6.44805 + 11.1684i −0.296796 + 0.514065i
\(473\) 17.0117 29.4651i 0.782197 1.35481i
\(474\) 0 0
\(475\) −9.70535 + 16.8102i −0.445312 + 0.771303i
\(476\) 0 0
\(477\) 0 0
\(478\) −9.15486 + 15.8567i −0.418734 + 0.725268i
\(479\) −20.4136 −0.932722 −0.466361 0.884594i \(-0.654435\pi\)
−0.466361 + 0.884594i \(0.654435\pi\)
\(480\) 0 0
\(481\) 13.3025 0.606543
\(482\) −0.0466924 0.0808735i −0.00212678 0.00368369i
\(483\) 0 0
\(484\) −1.15272 + 1.99658i −0.0523966 + 0.0907535i
\(485\) −2.57587 + 4.46154i −0.116964 + 0.202588i
\(486\) 0 0
\(487\) 6.18190 + 10.7074i 0.280129 + 0.485197i 0.971416 0.237383i \(-0.0762895\pi\)
−0.691287 + 0.722580i \(0.742956\pi\)
\(488\) −6.04163 10.4644i −0.273492 0.473702i
\(489\) 0 0
\(490\) 0 0
\(491\) −0.207004 0.358541i −0.00934194 0.0161807i 0.861317 0.508069i \(-0.169640\pi\)
−0.870659 + 0.491888i \(0.836307\pi\)
\(492\) 0 0
\(493\) −33.5117 −1.50929
\(494\) −2.96050 5.12774i −0.133199 0.230708i
\(495\) 0 0
\(496\) 0.514589 0.0231057
\(497\) 0 0
\(498\) 0 0
\(499\) −0.923935 −0.0413610 −0.0206805 0.999786i \(-0.506583\pi\)
−0.0206805 + 0.999786i \(0.506583\pi\)
\(500\) −2.25370 + 3.90352i −0.100788 + 0.174571i
\(501\) 0 0
\(502\) −9.13667 15.8252i −0.407790 0.706312i
\(503\) −23.8142 −1.06182 −0.530911 0.847428i \(-0.678150\pi\)
−0.530911 + 0.847428i \(0.678150\pi\)
\(504\) 0 0
\(505\) −6.33463 −0.281887
\(506\) −2.06654 3.57935i −0.0918688 0.159121i
\(507\) 0 0
\(508\) −4.40496 + 7.62961i −0.195438 + 0.338509i
\(509\) −30.6342 −1.35784 −0.678919 0.734213i \(-0.737551\pi\)
−0.678919 + 0.734213i \(0.737551\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −10.5256 18.2308i −0.464263 0.804128i
\(515\) 5.14027 0.226507
\(516\) 0 0
\(517\) −4.24484 7.35228i −0.186688 0.323353i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.336285 0.582462i −0.0147471 0.0255427i
\(521\) −13.4518 23.2993i −0.589336 1.02076i −0.994320 0.106436i \(-0.966056\pi\)
0.404984 0.914324i \(-0.367277\pi\)
\(522\) 0 0
\(523\) 7.85301 13.6018i 0.343388 0.594766i −0.641671 0.766980i \(-0.721759\pi\)
0.985060 + 0.172214i \(0.0550920\pi\)
\(524\) −10.5687 + 18.3055i −0.461695 + 0.799679i
\(525\) 0 0
\(526\) 2.58259 + 4.47318i 0.112606 + 0.195040i
\(527\) 1.92140 0.0836975
\(528\) 0 0
\(529\) −21.7161 −0.944180
\(530\) −2.86333 + 4.95943i −0.124375 + 0.215424i
\(531\) 0 0
\(532\) 0 0
\(533\) −0.690757 + 1.19643i −0.0299200 + 0.0518230i
\(534\) 0 0
\(535\) −1.79153 + 3.10303i −0.0774548 + 0.134156i
\(536\) −1.16012 + 2.00938i −0.0501094 + 0.0867920i
\(537\) 0 0
\(538\) −8.42840 + 14.5984i −0.363374 + 0.629383i
\(539\) 0 0
\(540\) 0 0
\(541\) −2.05934 + 3.56688i −0.0885379 + 0.153352i −0.906893 0.421360i \(-0.861553\pi\)
0.818355 + 0.574713i \(0.194886\pi\)
\(542\) −25.1124 −1.07867
\(543\) 0 0
\(544\) −3.73385 −0.160088
\(545\) 1.73025 + 2.99689i 0.0741159 + 0.128372i
\(546\) 0 0
\(547\) −11.8602 + 20.5425i −0.507106 + 0.878333i 0.492860 + 0.870108i \(0.335951\pi\)
−0.999966 + 0.00822465i \(0.997382\pi\)
\(548\) −2.20321 + 3.81607i −0.0941165 + 0.163015i
\(549\) 0 0
\(550\) −8.73239 15.1249i −0.372350 0.644930i
\(551\) −18.1929 31.5110i −0.775043 1.34241i
\(552\) 0 0
\(553\) 0 0
\(554\) 1.69076 + 2.92848i 0.0718334 + 0.124419i
\(555\) 0 0
\(556\) −2.02491 −0.0858751
\(557\) 21.0313 + 36.4273i 0.891125 + 1.54347i 0.838528 + 0.544859i \(0.183417\pi\)
0.0525975 + 0.998616i \(0.483250\pi\)
\(558\) 0 0
\(559\) −13.6228 −0.576181
\(560\) 0 0
\(561\) 0 0
\(562\) 20.2776 0.855360
\(563\) −5.91216 + 10.2402i −0.249168 + 0.431571i −0.963295 0.268445i \(-0.913490\pi\)
0.714127 + 0.700016i \(0.246824\pi\)
\(564\) 0 0
\(565\) 1.39562 + 2.41729i 0.0587144 + 0.101696i
\(566\) 17.3494 0.729250
\(567\) 0 0
\(568\) 1.67977 0.0704815
\(569\) 7.10078 + 12.2989i 0.297680 + 0.515597i 0.975605 0.219534i \(-0.0704538\pi\)
−0.677925 + 0.735131i \(0.737120\pi\)
\(570\) 0 0
\(571\) −5.97869 + 10.3554i −0.250200 + 0.433360i −0.963581 0.267417i \(-0.913830\pi\)
0.713380 + 0.700777i \(0.247163\pi\)
\(572\) 5.32743 0.222751
\(573\) 0 0
\(574\) 0 0
\(575\) 5.42509 0.226242
\(576\) 0 0
\(577\) −21.3135 36.9161i −0.887293 1.53684i −0.843062 0.537816i \(-0.819250\pi\)
−0.0442307 0.999021i \(-0.514084\pi\)
\(578\) 3.05836 0.127211
\(579\) 0 0
\(580\) −2.06654 3.57935i −0.0858083 0.148624i
\(581\) 0 0
\(582\) 0 0
\(583\) −22.6804 39.2837i −0.939328 1.62696i
\(584\) −6.62062 11.4673i −0.273963 0.474518i
\(585\) 0 0
\(586\) 4.93560 8.54871i 0.203888 0.353144i
\(587\) 20.5328 35.5638i 0.847478 1.46788i −0.0359730 0.999353i \(-0.511453\pi\)
0.883451 0.468523i \(-0.155214\pi\)
\(588\) 0 0
\(589\) 1.04309 + 1.80669i 0.0429799 + 0.0744434i
\(590\) −5.93872 −0.244493
\(591\) 0 0
\(592\) 9.10817 0.374343
\(593\) 16.1008 27.8874i 0.661180 1.14520i −0.319126 0.947712i \(-0.603389\pi\)
0.980306 0.197485i \(-0.0632772\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.58113 + 7.93474i −0.187650 + 0.325020i
\(597\) 0 0
\(598\) −0.827430 + 1.43315i −0.0338361 + 0.0586059i
\(599\) 9.53590 16.5167i 0.389626 0.674852i −0.602773 0.797913i \(-0.705938\pi\)
0.992399 + 0.123060i \(0.0392709\pi\)
\(600\) 0 0
\(601\) −4.27188 + 7.39912i −0.174254 + 0.301816i −0.939903 0.341442i \(-0.889085\pi\)
0.765649 + 0.643259i \(0.222418\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.0519482 0.0899768i 0.00211374 0.00366111i
\(605\) −1.06167 −0.0431631
\(606\) 0 0
\(607\) −38.0115 −1.54284 −0.771419 0.636328i \(-0.780453\pi\)
−0.771419 + 0.636328i \(0.780453\pi\)
\(608\) −2.02704 3.51094i −0.0822074 0.142387i
\(609\) 0 0
\(610\) 2.78220 4.81891i 0.112648 0.195112i
\(611\) −1.69961 + 2.94381i −0.0687589 + 0.119094i
\(612\) 0 0
\(613\) 11.3296 + 19.6234i 0.457597 + 0.792581i 0.998833 0.0482894i \(-0.0153770\pi\)
−0.541237 + 0.840870i \(0.682044\pi\)
\(614\) −3.89397 6.74455i −0.157148 0.272188i
\(615\) 0 0
\(616\) 0 0
\(617\) 10.1388 + 17.5609i 0.408173 + 0.706977i 0.994685 0.102964i \(-0.0328327\pi\)
−0.586512 + 0.809941i \(0.699499\pi\)
\(618\) 0 0
\(619\) −2.06128 −0.0828499 −0.0414249 0.999142i \(-0.513190\pi\)
−0.0414249 + 0.999142i \(0.513190\pi\)
\(620\) 0.118485 + 0.205223i 0.00475849 + 0.00824194i
\(621\) 0 0
\(622\) −15.4107 −0.617912
\(623\) 0 0
\(624\) 0 0
\(625\) 21.8640 0.874560
\(626\) −4.24844 + 7.35851i −0.169802 + 0.294105i
\(627\) 0 0
\(628\) 10.4911 + 18.1712i 0.418642 + 0.725110i
\(629\) 34.0085 1.35601
\(630\) 0 0
\(631\) 1.63715 0.0651740 0.0325870 0.999469i \(-0.489625\pi\)
0.0325870 + 0.999469i \(0.489625\pi\)
\(632\) −2.50360 4.33636i −0.0995878 0.172491i
\(633\) 0 0
\(634\) 7.05262 12.2155i 0.280095 0.485139i
\(635\) −4.05701 −0.160998
\(636\) 0 0
\(637\) 0 0
\(638\) 32.7381 1.29611
\(639\) 0 0
\(640\) −0.230252 0.398809i −0.00910153 0.0157643i
\(641\) −21.9325 −0.866281 −0.433140 0.901326i \(-0.642595\pi\)
−0.433140 + 0.901326i \(0.642595\pi\)
\(642\) 0 0
\(643\) 14.1819 + 24.5638i 0.559280 + 0.968701i 0.997557 + 0.0698609i \(0.0222555\pi\)
−0.438277 + 0.898840i \(0.644411\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7.56867 13.1093i −0.297785 0.515780i
\(647\) 17.3904 + 30.1210i 0.683686 + 1.18418i 0.973848 + 0.227201i \(0.0729575\pi\)
−0.290162 + 0.956978i \(0.593709\pi\)
\(648\) 0 0
\(649\) 23.5203 40.7384i 0.923253 1.59912i
\(650\) −3.49640 + 6.05594i −0.137140 + 0.237534i
\(651\) 0 0
\(652\) −11.5182 19.9501i −0.451087 0.781306i
\(653\) 3.19863 0.125172 0.0625860 0.998040i \(-0.480065\pi\)
0.0625860 + 0.998040i \(0.480065\pi\)
\(654\) 0 0
\(655\) −9.73385 −0.380333
\(656\) −0.472958 + 0.819187i −0.0184659 + 0.0319839i
\(657\) 0 0
\(658\) 0 0
\(659\) −5.30418 + 9.18711i −0.206622 + 0.357879i −0.950648 0.310271i \(-0.899580\pi\)
0.744027 + 0.668150i \(0.232914\pi\)
\(660\) 0 0
\(661\) 5.06507 8.77297i 0.197009 0.341229i −0.750549 0.660815i \(-0.770211\pi\)
0.947557 + 0.319586i \(0.103544\pi\)
\(662\) 13.7719 23.8536i 0.535259 0.927097i
\(663\) 0 0
\(664\) −3.32383 + 5.75705i −0.128990 + 0.223417i
\(665\) 0 0
\(666\) 0 0
\(667\) −5.08472 + 8.80700i −0.196881 + 0.341008i
\(668\) 10.6300 0.411285
\(669\) 0 0
\(670\) −1.06848 −0.0412789
\(671\) 22.0378 + 38.1707i 0.850761 + 1.47356i
\(672\) 0 0
\(673\) 1.60817 2.78543i 0.0619903 0.107370i −0.833365 0.552724i \(-0.813589\pi\)
0.895355 + 0.445353i \(0.146922\pi\)
\(674\) −0.748440 + 1.29634i −0.0288288 + 0.0499330i
\(675\) 0 0
\(676\) 5.43346 + 9.41103i 0.208979 + 0.361963i
\(677\) 14.6819 + 25.4298i 0.564271 + 0.977347i 0.997117 + 0.0758786i \(0.0241762\pi\)
−0.432846 + 0.901468i \(0.642491\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.859728 1.48909i −0.0329691 0.0571041i
\(681\) 0 0
\(682\) −1.87705 −0.0718759
\(683\) −12.6278 21.8720i −0.483190 0.836910i 0.516624 0.856213i \(-0.327189\pi\)
−0.999814 + 0.0193029i \(0.993855\pi\)
\(684\) 0 0
\(685\) −2.02918 −0.0775309
\(686\) 0 0
\(687\) 0 0
\(688\) −9.32743 −0.355605
\(689\) −9.08113 + 15.7290i −0.345963 + 0.599226i
\(690\) 0 0
\(691\) −7.68190 13.3054i −0.292233 0.506163i 0.682104 0.731255i \(-0.261065\pi\)
−0.974338 + 0.225092i \(0.927732\pi\)
\(692\) 2.93872 0.111713
\(693\) 0 0
\(694\) −18.2881 −0.694208
\(695\) −0.466240 0.807551i −0.0176855 0.0306321i
\(696\) 0 0
\(697\) −1.76595 + 3.05872i −0.0668903 + 0.115857i
\(698\) 7.80272 0.295337
\(699\) 0 0
\(700\) 0 0
\(701\) 13.3700 0.504980 0.252490 0.967600i \(-0.418751\pi\)
0.252490 + 0.967600i \(0.418751\pi\)
\(702\) 0 0
\(703\) 18.4626 + 31.9782i 0.696332 + 1.20608i
\(704\) 3.64766 0.137476
\(705\) 0 0
\(706\) 13.4626 + 23.3180i 0.506673 + 0.877584i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.562939 + 0.975038i 0.0211416 + 0.0366183i 0.876403 0.481579i \(-0.159937\pi\)
−0.855261 + 0.518197i \(0.826603\pi\)
\(710\) 0.386770 + 0.669906i 0.0145152 + 0.0251411i
\(711\) 0 0
\(712\) 1.36333 2.36135i 0.0510928 0.0884954i
\(713\) 0.291534 0.504951i 0.0109180 0.0189106i
\(714\) 0 0
\(715\) 1.22665 + 2.12463i 0.0458743 + 0.0794565i
\(716\) −9.16225 −0.342409
\(717\) 0 0
\(718\) 6.26322 0.233741
\(719\) 9.13667 15.8252i 0.340740 0.590180i −0.643830 0.765169i \(-0.722656\pi\)
0.984570 + 0.174989i \(0.0559889\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.28220 + 2.22084i −0.0477186 + 0.0826510i
\(723\) 0 0
\(724\) 11.2142 19.4236i 0.416772 0.721871i
\(725\) −21.4861 + 37.2150i −0.797973 + 1.38213i
\(726\) 0 0
\(727\) 14.8478 25.7171i 0.550673 0.953793i −0.447553 0.894257i \(-0.647705\pi\)
0.998226 0.0595359i \(-0.0189621\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3.04883 5.28073i 0.112842 0.195448i
\(731\) −34.8272 −1.28813
\(732\) 0 0
\(733\) −19.2278 −0.710195 −0.355098 0.934829i \(-0.615552\pi\)
−0.355098 + 0.934829i \(0.615552\pi\)
\(734\) −14.6367 25.3515i −0.540249 0.935740i
\(735\) 0 0
\(736\) −0.566537 + 0.981271i −0.0208828 + 0.0361701i
\(737\) 4.23171 7.32955i 0.155877 0.269987i
\(738\) 0 0
\(739\) −15.1336 26.2121i −0.556697 0.964227i −0.997769 0.0667556i \(-0.978735\pi\)
0.441073 0.897471i \(-0.354598\pi\)
\(740\) 2.09718 + 3.63242i 0.0770938 + 0.133530i
\(741\) 0 0
\(742\) 0 0
\(743\) 11.8815 + 20.5794i 0.435890 + 0.754984i 0.997368 0.0725076i \(-0.0231002\pi\)
−0.561477 + 0.827492i \(0.689767\pi\)
\(744\) 0 0
\(745\) −4.21926 −0.154582
\(746\) 8.92986 + 15.4670i 0.326946 + 0.566286i
\(747\) 0 0
\(748\) 13.6198 0.497990
\(749\) 0 0
\(750\) 0 0
\(751\) 12.6683 0.462273 0.231136 0.972921i \(-0.425756\pi\)
0.231136 + 0.972921i \(0.425756\pi\)
\(752\) −1.16372 + 2.01561i −0.0424363 + 0.0735019i
\(753\) 0 0
\(754\) −6.55408 11.3520i −0.238686 0.413416i
\(755\) 0.0478448 0.00174125
\(756\) 0 0
\(757\) −29.0799 −1.05693 −0.528464 0.848955i \(-0.677232\pi\)
−0.528464 + 0.848955i \(0.677232\pi\)
\(758\) −11.2127 19.4210i −0.407265 0.705404i
\(759\) 0 0
\(760\) 0.933463 1.61680i 0.0338603 0.0586477i
\(761\) 29.2029 1.05860 0.529302 0.848433i \(-0.322454\pi\)
0.529302 + 0.848433i \(0.322454\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.48968 −0.0900736
\(765\) 0 0
\(766\) −7.07014 12.2458i −0.255454 0.442460i
\(767\) −18.8348 −0.680086
\(768\) 0 0
\(769\) −12.5869 21.8011i −0.453894 0.786167i 0.544730 0.838611i \(-0.316632\pi\)
−0.998624 + 0.0524443i \(0.983299\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.24484 3.88818i −0.0807936 0.139939i
\(773\) −0.752039 1.30257i −0.0270490 0.0468502i 0.852184 0.523242i \(-0.175278\pi\)
−0.879233 + 0.476392i \(0.841944\pi\)
\(774\) 0 0
\(775\) 1.23191 2.13373i 0.0442515 0.0766458i
\(776\) −5.59358 + 9.68836i −0.200798 + 0.347792i
\(777\) 0 0
\(778\) 11.5651 + 20.0313i 0.414628 + 0.718157i
\(779\) −3.83482 −0.137397
\(780\) 0 0
\(781\) −6.12722 −0.219249
\(782\) −2.11537 + 3.66392i −0.0756453 + 0.131022i
\(783\) 0 0
\(784\) 0 0
\(785\) −4.83122 + 8.36792i −0.172434 + 0.298664i
\(786\) 0 0
\(787\) −7.47656 + 12.9498i −0.266510 + 0.461610i −0.967958 0.251111i \(-0.919204\pi\)
0.701448 + 0.712721i \(0.252537\pi\)
\(788\) 6.36693 11.0278i 0.226812 0.392850i
\(789\) 0 0
\(790\) 1.15292 1.99691i 0.0410190 0.0710470i
\(791\) 0 0
\(792\) 0 0
\(793\) 8.82383 15.2833i 0.313343 0.542727i
\(794\) 10.2661