Properties

Label 804.2.q.b.265.1
Level 804
Weight 2
Character 804.265
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 265.1
Character \(\chi\) = 804.265
Dual form 804.2.q.b.625.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.142315 - 0.989821i) q^{3} +(-1.42271 - 3.11530i) q^{5} +(2.11496 + 0.621007i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\) \(q+(0.142315 - 0.989821i) q^{3} +(-1.42271 - 3.11530i) q^{5} +(2.11496 + 0.621007i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-0.794441 - 1.73958i) q^{11} +(0.629292 - 0.726242i) q^{13} +(-3.28606 + 0.964876i) q^{15} +(5.57190 - 3.58084i) q^{17} +(-7.43980 + 2.18452i) q^{19} +(0.915676 - 2.00505i) q^{21} +(0.573090 - 3.98593i) q^{23} +(-4.40669 + 5.08559i) q^{25} +(-0.415415 + 0.909632i) q^{27} -0.158121 q^{29} +(-0.313948 - 0.362315i) q^{31} +(-1.83494 + 0.538786i) q^{33} +(-1.07435 - 7.47224i) q^{35} -4.87640 q^{37} +(-0.629292 - 0.726242i) q^{39} +(-6.45260 + 4.14683i) q^{41} +(-0.750192 + 0.482119i) q^{43} +(0.487399 + 3.38993i) q^{45} +(-0.408040 + 2.83798i) q^{47} +(-1.80138 - 1.15768i) q^{49} +(-2.75143 - 6.02479i) q^{51} +(-0.988260 - 0.635116i) q^{53} +(-4.28906 + 4.94984i) q^{55} +(1.10349 + 7.67497i) q^{57} +(-4.69850 - 5.42236i) q^{59} +(3.47016 - 7.59859i) q^{61} +(-1.85433 - 1.19170i) q^{63} +(-3.15776 - 0.927203i) q^{65} +(8.18240 - 0.219983i) q^{67} +(-3.86380 - 1.13451i) q^{69} +(7.18046 + 4.61460i) q^{71} +(4.82513 - 10.5656i) q^{73} +(4.40669 + 5.08559i) q^{75} +(-0.599914 - 4.17250i) q^{77} +(-5.28952 + 6.10443i) q^{79} +(0.841254 + 0.540641i) q^{81} +(3.65286 + 7.99865i) q^{83} +(-19.0826 - 12.2636i) q^{85} +(-0.0225030 + 0.156512i) q^{87} +(-1.53875 - 10.7022i) q^{89} +(1.78193 - 1.14518i) q^{91} +(-0.403307 + 0.259190i) q^{93} +(17.3901 + 20.0693i) q^{95} +15.3671 q^{97} +(0.272163 + 1.89294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{11}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.142315 0.989821i 0.0821655 0.571474i
\(4\) 0 0
\(5\) −1.42271 3.11530i −0.636255 1.39320i −0.903085 0.429461i \(-0.858703\pi\)
0.266830 0.963744i \(-0.414024\pi\)
\(6\) 0 0
\(7\) 2.11496 + 0.621007i 0.799379 + 0.234719i 0.655814 0.754922i \(-0.272325\pi\)
0.143564 + 0.989641i \(0.454144\pi\)
\(8\) 0 0
\(9\) −0.959493 0.281733i −0.319831 0.0939109i
\(10\) 0 0
\(11\) −0.794441 1.73958i −0.239533 0.524504i 0.751241 0.660028i \(-0.229456\pi\)
−0.990774 + 0.135524i \(0.956728\pi\)
\(12\) 0 0
\(13\) 0.629292 0.726242i 0.174534 0.201423i −0.661742 0.749732i \(-0.730183\pi\)
0.836276 + 0.548308i \(0.184728\pi\)
\(14\) 0 0
\(15\) −3.28606 + 0.964876i −0.848458 + 0.249130i
\(16\) 0 0
\(17\) 5.57190 3.58084i 1.35138 0.868482i 0.353624 0.935388i \(-0.384949\pi\)
0.997759 + 0.0669060i \(0.0213128\pi\)
\(18\) 0 0
\(19\) −7.43980 + 2.18452i −1.70681 + 0.501164i −0.982175 0.187971i \(-0.939809\pi\)
−0.724633 + 0.689135i \(0.757991\pi\)
\(20\) 0 0
\(21\) 0.915676 2.00505i 0.199817 0.437538i
\(22\) 0 0
\(23\) 0.573090 3.98593i 0.119497 0.831123i −0.838614 0.544727i \(-0.816633\pi\)
0.958111 0.286396i \(-0.0924575\pi\)
\(24\) 0 0
\(25\) −4.40669 + 5.08559i −0.881338 + 1.01712i
\(26\) 0 0
\(27\) −0.415415 + 0.909632i −0.0799467 + 0.175059i
\(28\) 0 0
\(29\) −0.158121 −0.0293624 −0.0146812 0.999892i \(-0.504673\pi\)
−0.0146812 + 0.999892i \(0.504673\pi\)
\(30\) 0 0
\(31\) −0.313948 0.362315i −0.0563867 0.0650738i 0.726855 0.686790i \(-0.240981\pi\)
−0.783242 + 0.621717i \(0.786436\pi\)
\(32\) 0 0
\(33\) −1.83494 + 0.538786i −0.319422 + 0.0937906i
\(34\) 0 0
\(35\) −1.07435 7.47224i −0.181598 1.26304i
\(36\) 0 0
\(37\) −4.87640 −0.801675 −0.400837 0.916149i \(-0.631281\pi\)
−0.400837 + 0.916149i \(0.631281\pi\)
\(38\) 0 0
\(39\) −0.629292 0.726242i −0.100767 0.116292i
\(40\) 0 0
\(41\) −6.45260 + 4.14683i −1.00773 + 0.647627i −0.936804 0.349855i \(-0.886231\pi\)
−0.0709230 + 0.997482i \(0.522594\pi\)
\(42\) 0 0
\(43\) −0.750192 + 0.482119i −0.114403 + 0.0735225i −0.596591 0.802545i \(-0.703479\pi\)
0.482188 + 0.876068i \(0.339842\pi\)
\(44\) 0 0
\(45\) 0.487399 + 3.38993i 0.0726571 + 0.505341i
\(46\) 0 0
\(47\) −0.408040 + 2.83798i −0.0595187 + 0.413962i 0.938179 + 0.346149i \(0.112511\pi\)
−0.997698 + 0.0678123i \(0.978398\pi\)
\(48\) 0 0
\(49\) −1.80138 1.15768i −0.257340 0.165383i
\(50\) 0 0
\(51\) −2.75143 6.02479i −0.385277 0.843639i
\(52\) 0 0
\(53\) −0.988260 0.635116i −0.135748 0.0872399i 0.471004 0.882131i \(-0.343892\pi\)
−0.606752 + 0.794891i \(0.707528\pi\)
\(54\) 0 0
\(55\) −4.28906 + 4.94984i −0.578337 + 0.667437i
\(56\) 0 0
\(57\) 1.10349 + 7.67497i 0.146161 + 1.01657i
\(58\) 0 0
\(59\) −4.69850 5.42236i −0.611693 0.705932i 0.362414 0.932017i \(-0.381953\pi\)
−0.974107 + 0.226086i \(0.927407\pi\)
\(60\) 0 0
\(61\) 3.47016 7.59859i 0.444308 0.972899i −0.546479 0.837473i \(-0.684032\pi\)
0.990787 0.135427i \(-0.0432405\pi\)
\(62\) 0 0
\(63\) −1.85433 1.19170i −0.233623 0.150141i
\(64\) 0 0
\(65\) −3.15776 0.927203i −0.391672 0.115005i
\(66\) 0 0
\(67\) 8.18240 0.219983i 0.999639 0.0268752i
\(68\) 0 0
\(69\) −3.86380 1.13451i −0.465146 0.136579i
\(70\) 0 0
\(71\) 7.18046 + 4.61460i 0.852163 + 0.547652i 0.892249 0.451544i \(-0.149127\pi\)
−0.0400854 + 0.999196i \(0.512763\pi\)
\(72\) 0 0
\(73\) 4.82513 10.5656i 0.564739 1.23661i −0.384813 0.922995i \(-0.625734\pi\)
0.949552 0.313611i \(-0.101539\pi\)
\(74\) 0 0
\(75\) 4.40669 + 5.08559i 0.508841 + 0.587234i
\(76\) 0 0
\(77\) −0.599914 4.17250i −0.0683666 0.475500i
\(78\) 0 0
\(79\) −5.28952 + 6.10443i −0.595118 + 0.686802i −0.970785 0.239952i \(-0.922868\pi\)
0.375667 + 0.926755i \(0.377414\pi\)
\(80\) 0 0
\(81\) 0.841254 + 0.540641i 0.0934726 + 0.0600712i
\(82\) 0 0
\(83\) 3.65286 + 7.99865i 0.400954 + 0.877966i 0.997173 + 0.0751442i \(0.0239417\pi\)
−0.596219 + 0.802822i \(0.703331\pi\)
\(84\) 0 0
\(85\) −19.0826 12.2636i −2.06980 1.33018i
\(86\) 0 0
\(87\) −0.0225030 + 0.156512i −0.00241258 + 0.0167798i
\(88\) 0 0
\(89\) −1.53875 10.7022i −0.163107 1.13443i −0.892732 0.450587i \(-0.851215\pi\)
0.729625 0.683847i \(-0.239695\pi\)
\(90\) 0 0
\(91\) 1.78193 1.14518i 0.186797 0.120047i
\(92\) 0 0
\(93\) −0.403307 + 0.259190i −0.0418210 + 0.0268767i
\(94\) 0 0
\(95\) 17.3901 + 20.0693i 1.78419 + 2.05906i
\(96\) 0 0
\(97\) 15.3671 1.56029 0.780145 0.625599i \(-0.215145\pi\)
0.780145 + 0.625599i \(0.215145\pi\)
\(98\) 0 0
\(99\) 0.272163 + 1.89294i 0.0273534 + 0.190247i
\(100\) 0 0
\(101\) 10.7238 3.14879i 1.06706 0.313316i 0.299367 0.954138i \(-0.403224\pi\)
0.767690 + 0.640822i \(0.221406\pi\)
\(102\) 0 0
\(103\) 6.89880 + 7.96163i 0.679759 + 0.784483i 0.985870 0.167513i \(-0.0535735\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(104\) 0 0
\(105\) −7.54908 −0.736715
\(106\) 0 0
\(107\) 4.88768 10.7025i 0.472510 1.03465i −0.511946 0.859018i \(-0.671075\pi\)
0.984455 0.175634i \(-0.0561976\pi\)
\(108\) 0 0
\(109\) −2.43495 + 2.81008i −0.233226 + 0.269157i −0.860284 0.509816i \(-0.829714\pi\)
0.627058 + 0.778973i \(0.284259\pi\)
\(110\) 0 0
\(111\) −0.693984 + 4.82676i −0.0658700 + 0.458136i
\(112\) 0 0
\(113\) 6.21204 13.6025i 0.584379 1.27961i −0.354400 0.935094i \(-0.615315\pi\)
0.938780 0.344519i \(-0.111958\pi\)
\(114\) 0 0
\(115\) −13.2327 + 3.88547i −1.23396 + 0.362322i
\(116\) 0 0
\(117\) −0.808407 + 0.519532i −0.0747373 + 0.0480307i
\(118\) 0 0
\(119\) 14.0081 4.11314i 1.28412 0.377050i
\(120\) 0 0
\(121\) 4.80846 5.54925i 0.437132 0.504478i
\(122\) 0 0
\(123\) 3.18632 + 6.97708i 0.287301 + 0.629102i
\(124\) 0 0
\(125\) 5.68227 + 1.66847i 0.508238 + 0.149232i
\(126\) 0 0
\(127\) 3.81987 + 1.12162i 0.338959 + 0.0995273i 0.446782 0.894643i \(-0.352570\pi\)
−0.107823 + 0.994170i \(0.534388\pi\)
\(128\) 0 0
\(129\) 0.370448 + 0.811169i 0.0326162 + 0.0714194i
\(130\) 0 0
\(131\) 0.441724 3.07226i 0.0385936 0.268425i −0.961383 0.275213i \(-0.911252\pi\)
0.999977 + 0.00678825i \(0.00216078\pi\)
\(132\) 0 0
\(133\) −17.0915 −1.48202
\(134\) 0 0
\(135\) 3.42479 0.294759
\(136\) 0 0
\(137\) −2.15316 + 14.9756i −0.183957 + 1.27945i 0.663336 + 0.748322i \(0.269140\pi\)
−0.847293 + 0.531126i \(0.821769\pi\)
\(138\) 0 0
\(139\) 4.54419 + 9.95039i 0.385433 + 0.843981i 0.998542 + 0.0539825i \(0.0171915\pi\)
−0.613109 + 0.789999i \(0.710081\pi\)
\(140\) 0 0
\(141\) 2.75102 + 0.807773i 0.231678 + 0.0680268i
\(142\) 0 0
\(143\) −1.76329 0.517750i −0.147454 0.0432964i
\(144\) 0 0
\(145\) 0.224961 + 0.492595i 0.0186820 + 0.0409078i
\(146\) 0 0
\(147\) −1.40226 + 1.61829i −0.115656 + 0.133474i
\(148\) 0 0
\(149\) −18.5426 + 5.44459i −1.51907 + 0.446039i −0.931684 0.363270i \(-0.881660\pi\)
−0.587384 + 0.809309i \(0.699842\pi\)
\(150\) 0 0
\(151\) −9.22887 + 5.93104i −0.751035 + 0.482661i −0.859307 0.511460i \(-0.829105\pi\)
0.108272 + 0.994121i \(0.465468\pi\)
\(152\) 0 0
\(153\) −6.35504 + 1.86601i −0.513774 + 0.150858i
\(154\) 0 0
\(155\) −0.682064 + 1.49351i −0.0547847 + 0.119962i
\(156\) 0 0
\(157\) 0.578114 4.02087i 0.0461385 0.320900i −0.953661 0.300883i \(-0.902719\pi\)
0.999800 0.0200175i \(-0.00637219\pi\)
\(158\) 0 0
\(159\) −0.769296 + 0.887815i −0.0610091 + 0.0704083i
\(160\) 0 0
\(161\) 3.68735 8.07417i 0.290604 0.636334i
\(162\) 0 0
\(163\) 13.1972 1.03368 0.516841 0.856081i \(-0.327108\pi\)
0.516841 + 0.856081i \(0.327108\pi\)
\(164\) 0 0
\(165\) 4.28906 + 4.94984i 0.333903 + 0.385345i
\(166\) 0 0
\(167\) 20.1799 5.92535i 1.56157 0.458518i 0.617035 0.786936i \(-0.288334\pi\)
0.944532 + 0.328418i \(0.106515\pi\)
\(168\) 0 0
\(169\) 1.71867 + 11.9536i 0.132206 + 0.919511i
\(170\) 0 0
\(171\) 7.75389 0.592955
\(172\) 0 0
\(173\) −4.42395 5.10550i −0.336346 0.388164i 0.562231 0.826981i \(-0.309943\pi\)
−0.898577 + 0.438816i \(0.855398\pi\)
\(174\) 0 0
\(175\) −12.4782 + 8.01922i −0.943260 + 0.606196i
\(176\) 0 0
\(177\) −6.03584 + 3.87900i −0.453681 + 0.291563i
\(178\) 0 0
\(179\) −2.02075 14.0546i −0.151038 1.05049i −0.914484 0.404622i \(-0.867403\pi\)
0.763446 0.645872i \(-0.223506\pi\)
\(180\) 0 0
\(181\) 0.856199 5.95499i 0.0636408 0.442631i −0.932942 0.360027i \(-0.882767\pi\)
0.996582 0.0826038i \(-0.0263236\pi\)
\(182\) 0 0
\(183\) −7.02739 4.51623i −0.519480 0.333849i
\(184\) 0 0
\(185\) 6.93770 + 15.1914i 0.510070 + 1.11690i
\(186\) 0 0
\(187\) −10.6557 6.84801i −0.779223 0.500776i
\(188\) 0 0
\(189\) −1.44347 + 1.66586i −0.104997 + 0.121173i
\(190\) 0 0
\(191\) 1.05446 + 7.33396i 0.0762983 + 0.530666i 0.991745 + 0.128227i \(0.0409286\pi\)
−0.915447 + 0.402440i \(0.868162\pi\)
\(192\) 0 0
\(193\) 1.94581 + 2.24558i 0.140062 + 0.161640i 0.821447 0.570285i \(-0.193167\pi\)
−0.681385 + 0.731926i \(0.738622\pi\)
\(194\) 0 0
\(195\) −1.36716 + 2.99367i −0.0979045 + 0.214381i
\(196\) 0 0
\(197\) −11.6008 7.45539i −0.826524 0.531175i 0.0576477 0.998337i \(-0.481640\pi\)
−0.884172 + 0.467162i \(0.845276\pi\)
\(198\) 0 0
\(199\) 25.8803 + 7.59915i 1.83461 + 0.538690i 0.999927 0.0120447i \(-0.00383403\pi\)
0.834681 + 0.550734i \(0.185652\pi\)
\(200\) 0 0
\(201\) 0.946733 8.13042i 0.0667774 0.573475i
\(202\) 0 0
\(203\) −0.334420 0.0981945i −0.0234717 0.00689190i
\(204\) 0 0
\(205\) 22.0988 + 14.2020i 1.54345 + 0.991914i
\(206\) 0 0
\(207\) −1.67284 + 3.66301i −0.116270 + 0.254597i
\(208\) 0 0
\(209\) 9.71064 + 11.2067i 0.671699 + 0.775182i
\(210\) 0 0
\(211\) 0.754514 + 5.24776i 0.0519429 + 0.361271i 0.999171 + 0.0407104i \(0.0129621\pi\)
−0.947228 + 0.320560i \(0.896129\pi\)
\(212\) 0 0
\(213\) 5.58951 6.45064i 0.382987 0.441991i
\(214\) 0 0
\(215\) 2.56925 + 1.65116i 0.175222 + 0.112608i
\(216\) 0 0
\(217\) −0.438986 0.961246i −0.0298003 0.0652536i
\(218\) 0 0
\(219\) −9.77133 6.27965i −0.660285 0.424340i
\(220\) 0 0
\(221\) 0.905795 6.29994i 0.0609304 0.423780i
\(222\) 0 0
\(223\) −0.565255 3.93144i −0.0378523 0.263269i 0.962103 0.272685i \(-0.0879117\pi\)
−0.999956 + 0.00941646i \(0.997003\pi\)
\(224\) 0 0
\(225\) 5.66097 3.63808i 0.377398 0.242539i
\(226\) 0 0
\(227\) −2.54308 + 1.63434i −0.168790 + 0.108475i −0.622308 0.782772i \(-0.713805\pi\)
0.453518 + 0.891247i \(0.350169\pi\)
\(228\) 0 0
\(229\) 14.4345 + 16.6583i 0.953856 + 1.10081i 0.994820 + 0.101648i \(0.0324117\pi\)
−0.0409639 + 0.999161i \(0.513043\pi\)
\(230\) 0 0
\(231\) −4.21540 −0.277353
\(232\) 0 0
\(233\) −0.902244 6.27524i −0.0591080 0.411105i −0.997797 0.0663401i \(-0.978868\pi\)
0.938689 0.344765i \(-0.112041\pi\)
\(234\) 0 0
\(235\) 9.42168 2.76645i 0.614603 0.180464i
\(236\) 0 0
\(237\) 5.28952 + 6.10443i 0.343591 + 0.396526i
\(238\) 0 0
\(239\) 13.0625 0.844945 0.422473 0.906376i \(-0.361162\pi\)
0.422473 + 0.906376i \(0.361162\pi\)
\(240\) 0 0
\(241\) 7.93320 17.3713i 0.511022 1.11898i −0.461706 0.887033i \(-0.652762\pi\)
0.972728 0.231949i \(-0.0745104\pi\)
\(242\) 0 0
\(243\) 0.654861 0.755750i 0.0420093 0.0484814i
\(244\) 0 0
\(245\) −1.04367 + 7.25889i −0.0666777 + 0.463753i
\(246\) 0 0
\(247\) −3.09532 + 6.77780i −0.196950 + 0.431261i
\(248\) 0 0
\(249\) 8.43709 2.47735i 0.534679 0.156996i
\(250\) 0 0
\(251\) 17.6620 11.3507i 1.11482 0.716450i 0.152481 0.988306i \(-0.451274\pi\)
0.962338 + 0.271856i \(0.0876375\pi\)
\(252\) 0 0
\(253\) −7.38913 + 2.16965i −0.464551 + 0.136404i
\(254\) 0 0
\(255\) −14.8545 + 17.1431i −0.930228 + 1.07354i
\(256\) 0 0
\(257\) −9.27322 20.3055i −0.578448 1.26662i −0.942176 0.335119i \(-0.891224\pi\)
0.363728 0.931505i \(-0.381504\pi\)
\(258\) 0 0
\(259\) −10.3134 3.02828i −0.640842 0.188168i
\(260\) 0 0
\(261\) 0.151716 + 0.0445479i 0.00939100 + 0.00275745i
\(262\) 0 0
\(263\) 4.98816 + 10.9225i 0.307583 + 0.673513i 0.998792 0.0491424i \(-0.0156488\pi\)
−0.691209 + 0.722655i \(0.742922\pi\)
\(264\) 0 0
\(265\) −0.572570 + 3.98231i −0.0351727 + 0.244632i
\(266\) 0 0
\(267\) −10.8123 −0.661701
\(268\) 0 0
\(269\) 22.3231 1.36107 0.680533 0.732717i \(-0.261748\pi\)
0.680533 + 0.732717i \(0.261748\pi\)
\(270\) 0 0
\(271\) −2.21991 + 15.4398i −0.134850 + 0.937903i 0.804258 + 0.594280i \(0.202563\pi\)
−0.939108 + 0.343622i \(0.888346\pi\)
\(272\) 0 0
\(273\) −0.879924 1.92677i −0.0532554 0.116613i
\(274\) 0 0
\(275\) 12.3477 + 3.62560i 0.744592 + 0.218632i
\(276\) 0 0
\(277\) 4.77077 + 1.40082i 0.286648 + 0.0841674i 0.421896 0.906644i \(-0.361365\pi\)
−0.135248 + 0.990812i \(0.543183\pi\)
\(278\) 0 0
\(279\) 0.199155 + 0.436089i 0.0119231 + 0.0261079i
\(280\) 0 0
\(281\) −13.0457 + 15.0555i −0.778241 + 0.898137i −0.996981 0.0776456i \(-0.975260\pi\)
0.218741 + 0.975783i \(0.429805\pi\)
\(282\) 0 0
\(283\) −21.2358 + 6.23540i −1.26234 + 0.370656i −0.843364 0.537343i \(-0.819428\pi\)
−0.418974 + 0.907998i \(0.637610\pi\)
\(284\) 0 0
\(285\) 22.3399 14.3570i 1.32330 0.850433i
\(286\) 0 0
\(287\) −16.2222 + 4.76326i −0.957565 + 0.281167i
\(288\) 0 0
\(289\) 11.1616 24.4404i 0.656563 1.43767i
\(290\) 0 0
\(291\) 2.18696 15.2107i 0.128202 0.891665i
\(292\) 0 0
\(293\) 6.08199 7.01899i 0.355314 0.410054i −0.549751 0.835329i \(-0.685277\pi\)
0.905064 + 0.425275i \(0.139823\pi\)
\(294\) 0 0
\(295\) −10.2077 + 22.3517i −0.594314 + 1.30137i
\(296\) 0 0
\(297\) 1.91240 0.110969
\(298\) 0 0
\(299\) −2.53411 2.92451i −0.146551 0.169129i
\(300\) 0 0
\(301\) −1.88602 + 0.553787i −0.108709 + 0.0319197i
\(302\) 0 0
\(303\) −1.59058 11.0628i −0.0913766 0.635539i
\(304\) 0 0
\(305\) −28.6089 −1.63814
\(306\) 0 0
\(307\) 12.6743 + 14.6269i 0.723362 + 0.834804i 0.991707 0.128519i \(-0.0410222\pi\)
−0.268345 + 0.963323i \(0.586477\pi\)
\(308\) 0 0
\(309\) 8.86240 5.69552i 0.504164 0.324007i
\(310\) 0 0
\(311\) −1.44196 + 0.926695i −0.0817663 + 0.0525480i −0.580885 0.813986i \(-0.697293\pi\)
0.499119 + 0.866534i \(0.333657\pi\)
\(312\) 0 0
\(313\) 2.06229 + 14.3435i 0.116568 + 0.810745i 0.961290 + 0.275540i \(0.0888566\pi\)
−0.844722 + 0.535205i \(0.820234\pi\)
\(314\) 0 0
\(315\) −1.07435 + 7.47224i −0.0605325 + 0.421013i
\(316\) 0 0
\(317\) −19.7280 12.6784i −1.10803 0.712089i −0.147169 0.989111i \(-0.547016\pi\)
−0.960863 + 0.277022i \(0.910652\pi\)
\(318\) 0 0
\(319\) 0.125618 + 0.275065i 0.00703326 + 0.0154007i
\(320\) 0 0
\(321\) −9.89800 6.36106i −0.552452 0.355040i
\(322\) 0 0
\(323\) −33.6314 + 38.8127i −1.87130 + 2.15960i
\(324\) 0 0
\(325\) 0.920274 + 6.40065i 0.0510476 + 0.355044i
\(326\) 0 0
\(327\) 2.43495 + 2.81008i 0.134653 + 0.155398i
\(328\) 0 0
\(329\) −2.62539 + 5.74881i −0.144743 + 0.316942i
\(330\) 0 0
\(331\) −22.3351 14.3539i −1.22765 0.788963i −0.244126 0.969743i \(-0.578501\pi\)
−0.983523 + 0.180781i \(0.942138\pi\)
\(332\) 0 0
\(333\) 4.67887 + 1.37384i 0.256400 + 0.0752860i
\(334\) 0 0
\(335\) −12.3265 25.1777i −0.673468 1.37560i
\(336\) 0 0
\(337\) −12.5146 3.67462i −0.681715 0.200170i −0.0775017 0.996992i \(-0.524694\pi\)
−0.604213 + 0.796823i \(0.706512\pi\)
\(338\) 0 0
\(339\) −12.5799 8.08464i −0.683249 0.439097i
\(340\) 0 0
\(341\) −0.380865 + 0.833977i −0.0206250 + 0.0451624i
\(342\) 0 0
\(343\) −13.1952 15.2281i −0.712475 0.822241i
\(344\) 0 0
\(345\) 1.96271 + 13.6510i 0.105669 + 0.734943i
\(346\) 0 0
\(347\) 19.5624 22.5762i 1.05016 1.21195i 0.0734721 0.997297i \(-0.476592\pi\)
0.976690 0.214654i \(-0.0688625\pi\)
\(348\) 0 0
\(349\) −2.63684 1.69459i −0.141147 0.0907095i 0.468162 0.883643i \(-0.344916\pi\)
−0.609308 + 0.792933i \(0.708553\pi\)
\(350\) 0 0
\(351\) 0.399195 + 0.874116i 0.0213075 + 0.0466569i
\(352\) 0 0
\(353\) 15.2350 + 9.79094i 0.810877 + 0.521119i 0.879149 0.476548i \(-0.158112\pi\)
−0.0682717 + 0.997667i \(0.521748\pi\)
\(354\) 0 0
\(355\) 4.16016 28.9345i 0.220798 1.53568i
\(356\) 0 0
\(357\) −2.07772 14.4508i −0.109964 0.764819i
\(358\) 0 0
\(359\) −25.4151 + 16.3333i −1.34136 + 0.862037i −0.997045 0.0768181i \(-0.975524\pi\)
−0.344311 + 0.938856i \(0.611888\pi\)
\(360\) 0 0
\(361\) 34.5947 22.2327i 1.82077 1.17014i
\(362\) 0 0
\(363\) −4.80846 5.54925i −0.252378 0.291260i
\(364\) 0 0
\(365\) −39.7797 −2.08216
\(366\) 0 0
\(367\) −0.404403 2.81269i −0.0211097 0.146821i 0.976541 0.215333i \(-0.0690838\pi\)
−0.997650 + 0.0685124i \(0.978175\pi\)
\(368\) 0 0
\(369\) 7.35952 2.16095i 0.383121 0.112495i
\(370\) 0 0
\(371\) −1.69572 1.95696i −0.0880372 0.101600i
\(372\) 0 0
\(373\) −33.0527 −1.71140 −0.855701 0.517471i \(-0.826874\pi\)
−0.855701 + 0.517471i \(0.826874\pi\)
\(374\) 0 0
\(375\) 2.46015 5.38699i 0.127042 0.278183i
\(376\) 0 0
\(377\) −0.0995045 + 0.114834i −0.00512474 + 0.00591427i
\(378\) 0 0
\(379\) 5.17838 36.0164i 0.265995 1.85004i −0.219261 0.975666i \(-0.570365\pi\)
0.485256 0.874372i \(-0.338726\pi\)
\(380\) 0 0
\(381\) 1.65382 3.62137i 0.0847280 0.185528i
\(382\) 0 0
\(383\) −23.8331 + 6.99803i −1.21782 + 0.357583i −0.826639 0.562733i \(-0.809750\pi\)
−0.391177 + 0.920316i \(0.627932\pi\)
\(384\) 0 0
\(385\) −12.1451 + 7.80517i −0.618970 + 0.397788i
\(386\) 0 0
\(387\) 0.855633 0.251236i 0.0434943 0.0127711i
\(388\) 0 0
\(389\) −2.58105 + 2.97869i −0.130864 + 0.151025i −0.817400 0.576071i \(-0.804585\pi\)
0.686535 + 0.727096i \(0.259131\pi\)
\(390\) 0 0
\(391\) −11.0798 24.2613i −0.560328 1.22695i
\(392\) 0 0
\(393\) −2.97812 0.874456i −0.150226 0.0441105i
\(394\) 0 0
\(395\) 26.5426 + 7.79361i 1.33550 + 0.392139i
\(396\) 0 0
\(397\) 15.2373 + 33.3651i 0.764740 + 1.67455i 0.737904 + 0.674906i \(0.235816\pi\)
0.0268359 + 0.999640i \(0.491457\pi\)
\(398\) 0 0
\(399\) −2.43237 + 16.9175i −0.121771 + 0.846934i
\(400\) 0 0
\(401\) −19.9008 −0.993798 −0.496899 0.867808i \(-0.665528\pi\)
−0.496899 + 0.867808i \(0.665528\pi\)
\(402\) 0 0
\(403\) −0.460694 −0.0229488
\(404\) 0 0
\(405\) 0.487399 3.38993i 0.0242190 0.168447i
\(406\) 0 0
\(407\) 3.87401 + 8.48290i 0.192028 + 0.420482i
\(408\) 0 0
\(409\) −11.8899 3.49118i −0.587916 0.172628i −0.0257731 0.999668i \(-0.508205\pi\)
−0.562143 + 0.827040i \(0.690023\pi\)
\(410\) 0 0
\(411\) 14.5167 + 4.26249i 0.716056 + 0.210253i
\(412\) 0 0
\(413\) −6.56981 14.3859i −0.323279 0.707882i
\(414\) 0 0
\(415\) 19.7212 22.7595i 0.968078 1.11722i
\(416\) 0 0
\(417\) 10.4958 3.08185i 0.513982 0.150919i
\(418\) 0 0
\(419\) 15.3890 9.88989i 0.751800 0.483153i −0.107766 0.994176i \(-0.534370\pi\)
0.859567 + 0.511023i \(0.170733\pi\)
\(420\) 0 0
\(421\) 36.6203 10.7527i 1.78476 0.524054i 0.788868 0.614563i \(-0.210668\pi\)
0.995896 + 0.0905091i \(0.0288494\pi\)
\(422\) 0 0
\(423\) 1.19106 2.60806i 0.0579114 0.126808i
\(424\) 0 0
\(425\) −6.34293 + 44.1161i −0.307677 + 2.13994i
\(426\) 0 0
\(427\) 12.0580 13.9157i 0.583528 0.673428i
\(428\) 0 0
\(429\) −0.763423 + 1.67166i −0.0368584 + 0.0807086i
\(430\) 0 0
\(431\) 11.9112 0.573744 0.286872 0.957969i \(-0.407385\pi\)
0.286872 + 0.957969i \(0.407385\pi\)
\(432\) 0 0
\(433\) −17.0461 19.6722i −0.819182 0.945386i 0.180086 0.983651i \(-0.442363\pi\)
−0.999268 + 0.0382645i \(0.987817\pi\)
\(434\) 0 0
\(435\) 0.519597 0.152567i 0.0249128 0.00731505i
\(436\) 0 0
\(437\) 4.44367 + 30.9064i 0.212570 + 1.47846i
\(438\) 0 0
\(439\) −20.7749 −0.991530 −0.495765 0.868457i \(-0.665112\pi\)
−0.495765 + 0.868457i \(0.665112\pi\)
\(440\) 0 0
\(441\) 1.40226 + 1.61829i 0.0667742 + 0.0770615i
\(442\) 0 0
\(443\) −0.105792 + 0.0679881i −0.00502631 + 0.00323021i −0.543152 0.839635i \(-0.682769\pi\)
0.538125 + 0.842865i \(0.319133\pi\)
\(444\) 0 0
\(445\) −31.1515 + 20.0198i −1.47672 + 0.949032i
\(446\) 0 0
\(447\) 2.75029 + 19.1287i 0.130084 + 0.904756i
\(448\) 0 0
\(449\) 3.61922 25.1722i 0.170801 1.18795i −0.706395 0.707818i \(-0.749680\pi\)
0.877196 0.480132i \(-0.159411\pi\)
\(450\) 0 0
\(451\) 12.3400 + 7.93042i 0.581067 + 0.373429i
\(452\) 0 0
\(453\) 4.55726 + 9.97901i 0.214119 + 0.468855i
\(454\) 0 0
\(455\) −6.10273 3.92199i −0.286100 0.183866i
\(456\) 0 0
\(457\) 19.5482 22.5599i 0.914429 1.05531i −0.0838396 0.996479i \(-0.526718\pi\)
0.998268 0.0588275i \(-0.0187362\pi\)
\(458\) 0 0
\(459\) 0.942598 + 6.55591i 0.0439967 + 0.306004i
\(460\) 0 0
\(461\) −7.14512 8.24591i −0.332781 0.384050i 0.564556 0.825394i \(-0.309047\pi\)
−0.897338 + 0.441344i \(0.854502\pi\)
\(462\) 0 0
\(463\) −1.06410 + 2.33004i −0.0494527 + 0.108286i −0.932746 0.360535i \(-0.882594\pi\)
0.883293 + 0.468822i \(0.155321\pi\)
\(464\) 0 0
\(465\) 1.38124 + 0.887671i 0.0640536 + 0.0411648i
\(466\) 0 0
\(467\) −5.06121 1.48610i −0.234205 0.0687687i 0.162524 0.986705i \(-0.448036\pi\)
−0.396729 + 0.917936i \(0.629855\pi\)
\(468\) 0 0
\(469\) 17.4420 + 4.61607i 0.805398 + 0.213151i
\(470\) 0 0
\(471\) −3.89767 1.14446i −0.179595 0.0527339i
\(472\) 0 0
\(473\) 1.43467 + 0.922006i 0.0659662 + 0.0423939i
\(474\) 0 0
\(475\) 21.6753 47.4623i 0.994532 2.17772i
\(476\) 0 0
\(477\) 0.769296 + 0.887815i 0.0352236 + 0.0406502i
\(478\) 0 0
\(479\) 3.86971 + 26.9144i 0.176812 + 1.22975i 0.864082 + 0.503351i \(0.167900\pi\)
−0.687271 + 0.726402i \(0.741191\pi\)
\(480\) 0 0
\(481\) −3.06868 + 3.54144i −0.139920 + 0.161476i
\(482\) 0 0
\(483\) −7.46722 4.79889i −0.339770 0.218357i
\(484\) 0 0
\(485\) −21.8629 47.8731i −0.992743 2.17380i
\(486\) 0 0
\(487\) −19.0757 12.2592i −0.864402 0.555518i 0.0316335 0.999500i \(-0.489929\pi\)
−0.896036 + 0.443982i \(0.853565\pi\)
\(488\) 0 0
\(489\) 1.87815 13.0628i 0.0849331 0.590722i
\(490\) 0 0
\(491\) −2.58484 17.9779i −0.116652 0.811333i −0.961200 0.275853i \(-0.911040\pi\)
0.844548 0.535480i \(-0.179869\pi\)
\(492\) 0 0
\(493\) −0.881036 + 0.566207i −0.0396798 + 0.0255007i
\(494\) 0 0
\(495\) 5.50986 3.54097i 0.247650 0.159155i
\(496\) 0 0
\(497\) 12.3207 + 14.2188i 0.552657 + 0.637800i
\(498\) 0 0
\(499\) 2.76799 0.123912 0.0619562 0.998079i \(-0.480266\pi\)
0.0619562 + 0.998079i \(0.480266\pi\)
\(500\) 0 0
\(501\) −2.99314 20.8178i −0.133724 0.930069i
\(502\) 0 0
\(503\) −19.8030 + 5.81467i −0.882971 + 0.259264i −0.691623 0.722259i \(-0.743104\pi\)
−0.191348 + 0.981522i \(0.561286\pi\)
\(504\) 0 0
\(505\) −25.0663 28.9280i −1.11543 1.28728i
\(506\) 0 0
\(507\) 12.0766 0.536339
\(508\) 0 0
\(509\) −4.88784 + 10.7029i −0.216650 + 0.474396i −0.986486 0.163845i \(-0.947610\pi\)
0.769837 + 0.638241i \(0.220338\pi\)
\(510\) 0 0
\(511\) 16.7662 19.3493i 0.741694 0.855961i
\(512\) 0 0
\(513\) 1.10349 7.67497i 0.0487204 0.338858i
\(514\) 0 0
\(515\) 14.9879 32.8189i 0.660446 1.44617i
\(516\) 0 0
\(517\) 5.26106 1.54479i 0.231381 0.0679397i
\(518\) 0 0
\(519\) −5.68313 + 3.65233i −0.249462 + 0.160319i
\(520\) 0 0
\(521\) 14.5384 4.26886i 0.636940 0.187022i 0.0527088 0.998610i \(-0.483214\pi\)
0.584231 + 0.811588i \(0.301396\pi\)
\(522\) 0 0
\(523\) −0.714748 + 0.824863i −0.0312537 + 0.0360687i −0.771161 0.636640i \(-0.780324\pi\)
0.739908 + 0.672709i \(0.234869\pi\)
\(524\) 0 0
\(525\) 6.16177 + 13.4924i 0.268922 + 0.588856i
\(526\) 0 0
\(527\) −3.04668 0.894586i −0.132715 0.0389688i
\(528\) 0 0
\(529\) 6.50916 + 1.91126i 0.283007 + 0.0830984i
\(530\) 0 0
\(531\) 2.98053 + 6.52644i 0.129344 + 0.283223i
\(532\) 0 0
\(533\) −1.04897 + 7.29572i −0.0454358 + 0.316013i
\(534\) 0 0
\(535\) −40.2953 −1.74212
\(536\) 0 0
\(537\) −14.1992 −0.612739
\(538\) 0 0
\(539\) −0.582785 + 4.05336i −0.0251023 + 0.174591i
\(540\) 0 0
\(541\) 14.4457 + 31.6316i 0.621068 + 1.35995i 0.914740 + 0.404043i \(0.132395\pi\)
−0.293672 + 0.955906i \(0.594877\pi\)
\(542\) 0 0
\(543\) −5.77253 1.69497i −0.247723 0.0727380i
\(544\) 0 0
\(545\) 12.2185 + 3.58767i 0.523382 + 0.153679i
\(546\) 0 0
\(547\) 13.6256 + 29.8358i 0.582587 + 1.27569i 0.939820 + 0.341671i \(0.110993\pi\)
−0.357233 + 0.934015i \(0.616280\pi\)
\(548\) 0 0
\(549\) −5.47036 + 6.31313i −0.233469 + 0.269438i
\(550\) 0 0
\(551\) 1.17639 0.345420i 0.0501160 0.0147154i
\(552\) 0 0
\(553\) −14.9780 + 9.62578i −0.636930 + 0.409330i
\(554\) 0 0
\(555\) 16.0242 4.70512i 0.680188 0.199721i
\(556\) 0 0
\(557\) −2.89730 + 6.34420i −0.122763 + 0.268812i −0.961029 0.276449i \(-0.910842\pi\)
0.838266 + 0.545261i \(0.183570\pi\)
\(558\) 0 0
\(559\) −0.121955 + 0.848215i −0.00515814 + 0.0358757i
\(560\) 0 0
\(561\) −8.29477 + 9.57268i −0.350206 + 0.404159i
\(562\) 0 0
\(563\) −12.6424 + 27.6829i −0.532812 + 1.16670i 0.431544 + 0.902092i \(0.357969\pi\)
−0.964357 + 0.264605i \(0.914758\pi\)
\(564\) 0 0
\(565\) −51.2137 −2.15458
\(566\) 0 0
\(567\) 1.44347 + 1.66586i 0.0606202 + 0.0699594i
\(568\) 0 0
\(569\) −22.1342 + 6.49920i −0.927915 + 0.272460i −0.710564 0.703633i \(-0.751560\pi\)
−0.217351 + 0.976093i \(0.569742\pi\)
\(570\) 0 0
\(571\) 6.41722 + 44.6328i 0.268552 + 1.86782i 0.462233 + 0.886759i \(0.347048\pi\)
−0.193680 + 0.981065i \(0.562042\pi\)
\(572\) 0 0
\(573\) 7.40937 0.309531
\(574\) 0 0
\(575\) 17.7454 + 20.4792i 0.740033 + 0.854043i
\(576\) 0 0
\(577\) 16.0558 10.3184i 0.668411 0.429562i −0.161941 0.986800i \(-0.551775\pi\)
0.830352 + 0.557239i \(0.188139\pi\)
\(578\) 0 0
\(579\) 2.49964 1.60642i 0.103881 0.0667606i
\(580\) 0 0
\(581\) 2.75842 + 19.1853i 0.114439 + 0.795938i
\(582\) 0 0
\(583\) −0.319723 + 2.22372i −0.0132416 + 0.0920972i
\(584\) 0 0
\(585\) 2.76863 + 1.77929i 0.114469 + 0.0735645i
\(586\) 0 0
\(587\) 14.0970 + 30.8681i 0.581845 + 1.27406i 0.940246 + 0.340495i \(0.110595\pi\)
−0.358401 + 0.933568i \(0.616678\pi\)
\(588\) 0 0
\(589\) 3.12720 + 2.00973i 0.128854 + 0.0828094i
\(590\) 0 0
\(591\) −9.03047 + 10.4217i −0.371464 + 0.428692i
\(592\) 0 0
\(593\) 2.66185 + 18.5135i 0.109309 + 0.760260i 0.968573 + 0.248728i \(0.0800126\pi\)
−0.859264 + 0.511532i \(0.829078\pi\)
\(594\) 0 0
\(595\) −32.7431 37.7875i −1.34233 1.54914i
\(596\) 0 0
\(597\) 11.2050 24.5354i 0.458588 1.00417i
\(598\) 0 0
\(599\) −24.3301 15.6360i −0.994100 0.638869i −0.0608688 0.998146i \(-0.519387\pi\)
−0.933231 + 0.359277i \(0.883023\pi\)
\(600\) 0 0
\(601\) 14.4010 + 4.22851i 0.587429 + 0.172485i 0.561922 0.827190i \(-0.310062\pi\)
0.0255066 + 0.999675i \(0.491880\pi\)
\(602\) 0 0
\(603\) −7.91293 2.09418i −0.322239 0.0852814i
\(604\) 0 0
\(605\) −24.1286 7.08481i −0.980968 0.288038i
\(606\) 0 0
\(607\) 21.2316 + 13.6447i 0.861764 + 0.553822i 0.895223 0.445618i \(-0.147016\pi\)
−0.0334593 + 0.999440i \(0.510652\pi\)
\(608\) 0 0
\(609\) −0.144788 + 0.317041i −0.00586710 + 0.0128472i
\(610\) 0 0
\(611\) 1.80428 + 2.08225i 0.0729935 + 0.0842390i
\(612\) 0 0
\(613\) 5.45981 + 37.9738i 0.220520 + 1.53375i 0.736080 + 0.676895i \(0.236675\pi\)
−0.515560 + 0.856854i \(0.672416\pi\)
\(614\) 0 0
\(615\) 17.2025 19.8527i 0.693671 0.800539i
\(616\) 0 0
\(617\) 4.79741 + 3.08311i 0.193136 + 0.124121i 0.633635 0.773632i \(-0.281562\pi\)
−0.440499 + 0.897753i \(0.645198\pi\)
\(618\) 0 0
\(619\) −0.450694 0.986882i −0.0181149 0.0396661i 0.900358 0.435149i \(-0.143304\pi\)
−0.918473 + 0.395483i \(0.870577\pi\)
\(620\) 0 0
\(621\) 3.38766 + 2.17711i 0.135942 + 0.0873646i
\(622\) 0 0
\(623\) 3.39178 23.5903i 0.135889 0.945127i
\(624\) 0 0
\(625\) 1.90187 + 13.2278i 0.0760749 + 0.529113i
\(626\) 0 0
\(627\) 12.4746 8.01693i 0.498187 0.320165i
\(628\) 0 0
\(629\) −27.1708 + 17.4616i −1.08337 + 0.696240i
\(630\) 0 0
\(631\) −12.4877 14.4116i −0.497127 0.573716i 0.450629 0.892711i \(-0.351200\pi\)
−0.947756 + 0.318996i \(0.896654\pi\)
\(632\) 0 0
\(633\) 5.30172 0.210725
\(634\) 0 0
\(635\) −1.94040 13.4958i −0.0770025 0.535564i
\(636\) 0 0
\(637\) −1.97435 + 0.579721i −0.0782266 + 0.0229694i
\(638\) 0 0
\(639\) −5.58951 6.45064i −0.221118 0.255184i
\(640\) 0 0
\(641\) −0.0564206 −0.00222848 −0.00111424 0.999999i \(-0.500355\pi\)
−0.00111424 + 0.999999i \(0.500355\pi\)
\(642\) 0 0
\(643\) 12.5242 27.4243i 0.493908 1.08151i −0.484494 0.874795i \(-0.660996\pi\)
0.978402 0.206713i \(-0.0662765\pi\)
\(644\) 0 0
\(645\) 1.99999 2.30812i 0.0787497 0.0908820i
\(646\) 0 0
\(647\) 1.70621 11.8670i 0.0670781 0.466538i −0.928403 0.371575i \(-0.878818\pi\)
0.995481 0.0949627i \(-0.0302732\pi\)
\(648\) 0 0
\(649\) −5.69997 + 12.4812i −0.223743 + 0.489929i
\(650\) 0 0
\(651\) −1.01394 + 0.297718i −0.0397393 + 0.0116685i
\(652\) 0 0
\(653\) −39.2864 + 25.2478i −1.53739 + 0.988024i −0.549050 + 0.835789i \(0.685011\pi\)
−0.988344 + 0.152234i \(0.951353\pi\)
\(654\) 0 0
\(655\) −10.1995 + 2.99483i −0.398526 + 0.117018i
\(656\) 0 0
\(657\) −7.60634 + 8.77819i −0.296752 + 0.342470i
\(658\) 0 0
\(659\) −14.7641 32.3288i −0.575127 1.25935i −0.944023 0.329881i \(-0.892991\pi\)
0.368896 0.929471i \(-0.379736\pi\)
\(660\) 0 0
\(661\) 10.8736 + 3.19279i 0.422936 + 0.124185i 0.486273 0.873807i \(-0.338356\pi\)
−0.0633371 + 0.997992i \(0.520174\pi\)
\(662\) 0 0
\(663\) −6.10691 1.79315i −0.237173 0.0696402i
\(664\) 0 0
\(665\) 24.3162 + 53.2451i 0.942942 + 2.06476i
\(666\) 0 0
\(667\) −0.0906177 + 0.630260i −0.00350873 + 0.0244038i
\(668\) 0 0
\(669\) −3.97187 −0.153561
\(670\) 0 0
\(671\) −15.9752 −0.616716
\(672\) 0 0
\(673\) 3.48972 24.2716i 0.134519 0.935600i −0.805042 0.593218i \(-0.797857\pi\)
0.939561 0.342382i \(-0.111234\pi\)
\(674\) 0 0
\(675\) −2.79541 6.12110i −0.107595 0.235601i
\(676\) 0 0
\(677\) −34.0653 10.0025i −1.30923 0.384426i −0.448638 0.893714i \(-0.648091\pi\)
−0.860596 + 0.509288i \(0.829909\pi\)
\(678\) 0 0
\(679\) 32.5007 + 9.54307i 1.24726 + 0.366229i
\(680\) 0 0
\(681\) 1.25578 + 2.74978i 0.0481218 + 0.105372i
\(682\) 0 0
\(683\) −20.3315 + 23.4638i −0.777964 + 0.897819i −0.996961 0.0779071i \(-0.975176\pi\)
0.218996 + 0.975726i \(0.429722\pi\)
\(684\) 0 0
\(685\) 49.7167 14.5981i 1.89958 0.557766i
\(686\) 0 0
\(687\) 18.5429 11.9168i 0.707457 0.454655i
\(688\) 0 0
\(689\) −1.08315 + 0.318042i −0.0412648 + 0.0121164i
\(690\) 0 0
\(691\) 0.266779 0.584165i 0.0101488 0.0222227i −0.904490 0.426495i \(-0.859748\pi\)
0.914639 + 0.404273i \(0.132475\pi\)
\(692\) 0 0
\(693\) −0.599914 + 4.17250i −0.0227889 + 0.158500i
\(694\) 0 0
\(695\) 24.5334 28.3130i 0.930605 1.07398i
\(696\) 0 0
\(697\) −21.1041 + 46.2115i −0.799374 + 1.75038i
\(698\) 0 0
\(699\) −6.33977 −0.239792
\(700\) 0 0
\(701\) 11.0617 + 12.7659i 0.417794 + 0.482160i 0.925164 0.379569i \(-0.123928\pi\)
−0.507370 + 0.861729i \(0.669382\pi\)
\(702\) 0 0
\(703\) 36.2794 10.6526i 1.36831 0.401771i
\(704\) 0 0
\(705\) −1.39745 9.71949i −0.0526311 0.366057i
\(706\) 0 0
\(707\) 24.6358 0.926523
\(708\) 0 0
\(709\) 18.7837 + 21.6775i 0.705436 + 0.814117i 0.989476 0.144696i \(-0.0462203\pi\)
−0.284040 + 0.958812i \(0.591675\pi\)
\(710\) 0 0
\(711\) 6.79508 4.36693i 0.254835 0.163773i
\(712\) 0 0
\(713\) −1.62408 + 1.04373i −0.0608224 + 0.0390882i
\(714\) 0 0
\(715\) 0.895710 + 6.22980i 0.0334976 + 0.232981i
\(716\) 0 0
\(717\) 1.85899 12.9296i 0.0694253 0.482864i
\(718\) 0 0
\(719\) 16.6441 + 10.6965i 0.620721 + 0.398913i 0.812864 0.582454i \(-0.197907\pi\)
−0.192143 + 0.981367i \(0.561544\pi\)
\(720\) 0 0
\(721\) 9.64642 + 21.1227i 0.359252 + 0.786651i
\(722\) 0 0
\(723\) −16.0655 10.3246i −0.597481 0.383978i
\(724\) 0 0
\(725\) 0.696792 0.804140i 0.0258782 0.0298650i
\(726\) 0 0
\(727\) 4.73697 + 32.9464i 0.175685 + 1.22191i 0.866610 + 0.498987i \(0.166294\pi\)
−0.690925 + 0.722926i \(0.742797\pi\)
\(728\) 0 0
\(729\) −0.654861 0.755750i −0.0242541 0.0279907i
\(730\) 0 0
\(731\) −2.45360 + 5.37264i −0.0907497 + 0.198714i
\(732\) 0 0
\(733\) 42.5947 + 27.3739i 1.57327 + 1.01108i 0.978265 + 0.207358i \(0.0664866\pi\)
0.595006 + 0.803721i \(0.297150\pi\)
\(734\) 0 0
\(735\) 7.03647 + 2.06609i 0.259544 + 0.0762091i
\(736\) 0 0
\(737\) −6.88311 14.0592i −0.253543 0.517877i
\(738\) 0 0
\(739\) 38.9458 + 11.4355i 1.43264 + 0.420663i 0.903763 0.428033i \(-0.140793\pi\)
0.528882 + 0.848695i \(0.322611\pi\)
\(740\) 0 0
\(741\) 6.26830 + 4.02839i 0.230272 + 0.147987i
\(742\) 0 0
\(743\) −21.5214 + 47.1254i −0.789545 + 1.72886i −0.111597 + 0.993754i \(0.535597\pi\)
−0.677948 + 0.735109i \(0.737131\pi\)
\(744\) 0 0
\(745\) 43.3423 + 50.0196i 1.58794 + 1.83258i
\(746\) 0 0
\(747\) −1.25141 8.70378i −0.0457869 0.318455i
\(748\) 0 0
\(749\) 16.9836 19.6001i 0.620566 0.716172i
\(750\) 0 0
\(751\) −2.50030 1.60685i −0.0912372 0.0586346i 0.494227 0.869333i \(-0.335451\pi\)
−0.585464 + 0.810698i \(0.699088\pi\)
\(752\) 0 0
\(753\) −8.72160 19.0976i −0.317833 0.695957i
\(754\) 0 0
\(755\) 31.6070 + 20.3126i 1.15030 + 0.739250i
\(756\) 0 0
\(757\) 3.50790 24.3980i 0.127497 0.886759i −0.821216 0.570618i \(-0.806704\pi\)
0.948712 0.316141i \(-0.102387\pi\)
\(758\) 0 0
\(759\) 1.09598 + 7.62270i 0.0397815 + 0.276686i
\(760\) 0 0
\(761\) 30.7105 19.7364i 1.11325 0.715445i 0.151254 0.988495i \(-0.451669\pi\)
0.962000 + 0.273050i \(0.0880324\pi\)
\(762\) 0 0
\(763\) −6.89489 + 4.43108i −0.249612 + 0.160416i
\(764\) 0 0
\(765\) 14.8545 + 17.1431i 0.537067 + 0.619809i
\(766\) 0 0
\(767\) −6.89468 −0.248952
\(768\) 0 0
\(769\) −7.04914 49.0278i −0.254198 1.76799i −0.572409 0.819968i \(-0.693991\pi\)
0.318210 0.948020i \(-0.396918\pi\)
\(770\) 0 0
\(771\) −21.4186 + 6.28906i −0.771371 + 0.226495i
\(772\) 0 0
\(773\) 32.4095 + 37.4026i 1.16569 + 1.34528i 0.927394 + 0.374085i \(0.122043\pi\)
0.238296 + 0.971193i \(0.423411\pi\)
\(774\) 0 0
\(775\) 3.22606 0.115884
\(776\) 0 0
\(777\) −4.46520 + 9.77743i −0.160188 + 0.350763i
\(778\) 0 0
\(779\) 38.9472 44.9475i 1.39543 1.61041i
\(780\) 0 0
\(781\) 2.32303 16.1570i 0.0831245 0.578144i
\(782\)