Properties

Label 668.2.e.a.21.6
Level $668$
Weight $2$
Character 668.21
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 21.6
Character \(\chi\) \(=\) 668.21
Dual form 668.2.e.a.509.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.537235 - 0.0819657i) q^{3} +(-1.19475 - 1.41779i) q^{5} +(0.821536 - 1.13980i) q^{7} +(-2.58161 - 0.806524i) q^{9} +O(q^{10})\) \(q+(-0.537235 - 0.0819657i) q^{3} +(-1.19475 - 1.41779i) q^{5} +(0.821536 - 1.13980i) q^{7} +(-2.58161 - 0.806524i) q^{9} +(-0.0156941 + 0.0148274i) q^{11} +(-0.255201 + 1.91510i) q^{13} +(0.525653 + 0.859613i) q^{15} +(-2.08237 + 3.13251i) q^{17} +(-5.72303 - 1.32253i) q^{19} +(-0.534782 + 0.545000i) q^{21} +(1.10797 + 5.24513i) q^{23} +(0.264842 - 1.53983i) q^{25} +(2.78587 + 1.36021i) q^{27} +(0.217852 - 1.03131i) q^{29} +(-8.62801 + 1.65265i) q^{31} +(0.00964676 - 0.00667943i) q^{33} +(-2.59752 + 0.197011i) q^{35} +(-5.97084 + 1.86536i) q^{37} +(0.294075 - 1.00794i) q^{39} +(-0.246121 + 0.0978776i) q^{41} +(-9.13328 - 3.23751i) q^{43} +(1.94091 + 4.62377i) q^{45} +(2.82948 - 11.2676i) q^{47} +(1.58924 + 4.76806i) q^{49} +(1.37548 - 1.51221i) q^{51} +(3.05790 + 2.29323i) q^{53} +(0.0397728 + 0.00453577i) q^{55} +(2.96621 + 1.17960i) q^{57} +(-4.22102 - 6.34967i) q^{59} +(-0.243249 - 0.311885i) q^{61} +(-3.04016 + 2.27992i) q^{63} +(3.02010 - 1.92625i) q^{65} +(-3.18850 + 3.78372i) q^{67} +(-0.165320 - 2.90868i) q^{69} +(0.352493 + 3.71398i) q^{71} +(0.568238 - 1.01354i) q^{73} +(-0.268496 + 0.805544i) q^{75} +(0.00400696 + 0.0300694i) q^{77} +(-16.4267 - 0.622057i) q^{79} +(5.28578 + 3.65988i) q^{81} +(3.72234 - 1.00999i) q^{83} +(6.92915 - 0.790215i) q^{85} +(-0.201569 + 0.536198i) q^{87} +(6.11244 - 9.99581i) q^{89} +(1.97316 + 1.86420i) q^{91} +(4.77073 - 0.180661i) q^{93} +(4.96254 + 9.69413i) q^{95} +(8.19386 + 1.56949i) q^{97} +(0.0524748 - 0.0256210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{23}{83}\right)\) \(1\)

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
\(3\) −0.537235 0.0819657i −0.310173 0.0473229i −0.00612953 0.999981i \(-0.501951\pi\)
−0.304043 + 0.952658i \(0.598337\pi\)
\(4\) 0 0
\(5\) −1.19475 1.41779i −0.534310 0.634054i 0.428723 0.903436i \(-0.358964\pi\)
−0.963033 + 0.269382i \(0.913180\pi\)
\(6\) 0 0
\(7\) 0.821536 1.13980i 0.310512 0.430802i −0.626861 0.779131i \(-0.715661\pi\)
0.937372 + 0.348329i \(0.113251\pi\)
\(8\) 0 0
\(9\) −2.58161 0.806524i −0.860537 0.268841i
\(10\) 0 0
\(11\) −0.0156941 + 0.0148274i −0.00473195 + 0.00447064i −0.689114 0.724653i \(-0.742000\pi\)
0.684382 + 0.729124i \(0.260072\pi\)
\(12\) 0 0
\(13\) −0.255201 + 1.91510i −0.0707800 + 0.531153i 0.919608 + 0.392837i \(0.128506\pi\)
−0.990388 + 0.138316i \(0.955831\pi\)
\(14\) 0 0
\(15\) 0.525653 + 0.859613i 0.135723 + 0.221951i
\(16\) 0 0
\(17\) −2.08237 + 3.13251i −0.505050 + 0.759745i −0.993620 0.112780i \(-0.964025\pi\)
0.488570 + 0.872525i \(0.337519\pi\)
\(18\) 0 0
\(19\) −5.72303 1.32253i −1.31295 0.303410i −0.490101 0.871666i \(-0.663040\pi\)
−0.822852 + 0.568256i \(0.807618\pi\)
\(20\) 0 0
\(21\) −0.534782 + 0.545000i −0.116699 + 0.118929i
\(22\) 0 0
\(23\) 1.10797 + 5.24513i 0.231028 + 1.09369i 0.926839 + 0.375460i \(0.122515\pi\)
−0.695811 + 0.718225i \(0.744955\pi\)
\(24\) 0 0
\(25\) 0.264842 1.53983i 0.0529684 0.307967i
\(26\) 0 0
\(27\) 2.78587 + 1.36021i 0.536142 + 0.261773i
\(28\) 0 0
\(29\) 0.217852 1.03131i 0.0404540 0.191509i −0.953485 0.301440i \(-0.902533\pi\)
0.993939 + 0.109931i \(0.0350629\pi\)
\(30\) 0 0
\(31\) −8.62801 + 1.65265i −1.54964 + 0.296825i −0.890424 0.455132i \(-0.849592\pi\)
−0.659212 + 0.751957i \(0.729110\pi\)
\(32\) 0 0
\(33\) 0.00964676 0.00667943i 0.00167929 0.00116274i
\(34\) 0 0
\(35\) −2.59752 + 0.197011i −0.439061 + 0.0333010i
\(36\) 0 0
\(37\) −5.97084 + 1.86536i −0.981600 + 0.306663i −0.746556 0.665322i \(-0.768294\pi\)
−0.235043 + 0.971985i \(0.575523\pi\)
\(38\) 0 0
\(39\) 0.294075 1.00794i 0.0470897 0.161399i
\(40\) 0 0
\(41\) −0.246121 + 0.0978776i −0.0384377 + 0.0152859i −0.388672 0.921376i \(-0.627066\pi\)
0.350234 + 0.936662i \(0.386102\pi\)
\(42\) 0 0
\(43\) −9.13328 3.23751i −1.39281 0.493715i −0.471269 0.881990i \(-0.656204\pi\)
−0.921544 + 0.388274i \(0.873071\pi\)
\(44\) 0 0
\(45\) 1.94091 + 4.62377i 0.289334 + 0.689271i
\(46\) 0 0
\(47\) 2.82948 11.2676i 0.412722 1.64355i −0.308773 0.951136i \(-0.599918\pi\)
0.721495 0.692419i \(-0.243455\pi\)
\(48\) 0 0
\(49\) 1.58924 + 4.76806i 0.227035 + 0.681152i
\(50\) 0 0
\(51\) 1.37548 1.51221i 0.192606 0.211752i
\(52\) 0 0
\(53\) 3.05790 + 2.29323i 0.420035 + 0.314999i 0.788942 0.614468i \(-0.210629\pi\)
−0.368907 + 0.929466i \(0.620268\pi\)
\(54\) 0 0
\(55\) 0.0397728 + 0.00453577i 0.00536296 + 0.000611603i
\(56\) 0 0
\(57\) 2.96621 + 1.17960i 0.392883 + 0.156242i
\(58\) 0 0
\(59\) −4.22102 6.34967i −0.549530 0.826657i 0.448204 0.893931i \(-0.352064\pi\)
−0.997735 + 0.0672745i \(0.978570\pi\)
\(60\) 0 0
\(61\) −0.243249 0.311885i −0.0311448 0.0399328i 0.772703 0.634768i \(-0.218904\pi\)
−0.803848 + 0.594835i \(0.797217\pi\)
\(62\) 0 0
\(63\) −3.04016 + 2.27992i −0.383024 + 0.287243i
\(64\) 0 0
\(65\) 3.02010 1.92625i 0.374598 0.238922i
\(66\) 0 0
\(67\) −3.18850 + 3.78372i −0.389538 + 0.462255i −0.923694 0.383130i \(-0.874846\pi\)
0.534157 + 0.845385i \(0.320629\pi\)
\(68\) 0 0
\(69\) −0.165320 2.90868i −0.0199022 0.350164i
\(70\) 0 0
\(71\) 0.352493 + 3.71398i 0.0418332 + 0.440768i 0.991743 + 0.128243i \(0.0409338\pi\)
−0.949910 + 0.312525i \(0.898825\pi\)
\(72\) 0 0
\(73\) 0.568238 1.01354i 0.0665072 0.118625i −0.836992 0.547215i \(-0.815688\pi\)
0.903499 + 0.428589i \(0.140989\pi\)
\(74\) 0 0
\(75\) −0.268496 + 0.805544i −0.0310032 + 0.0930162i
\(76\) 0 0
\(77\) 0.00400696 + 0.0300694i 0.000456635 + 0.00342672i
\(78\) 0 0
\(79\) −16.4267 0.622057i −1.84815 0.0699869i −0.909673 0.415326i \(-0.863668\pi\)
−0.938478 + 0.345339i \(0.887764\pi\)
\(80\) 0 0
\(81\) 5.28578 + 3.65988i 0.587309 + 0.406654i
\(82\) 0 0
\(83\) 3.72234 1.00999i 0.408580 0.110861i −0.0516405 0.998666i \(-0.516445\pi\)
0.460221 + 0.887805i \(0.347770\pi\)
\(84\) 0 0
\(85\) 6.92915 0.790215i 0.751572 0.0857109i
\(86\) 0 0
\(87\) −0.201569 + 0.536198i −0.0216105 + 0.0574864i
\(88\) 0 0
\(89\) 6.11244 9.99581i 0.647917 1.05955i −0.344752 0.938694i \(-0.612037\pi\)
0.992670 0.120860i \(-0.0385653\pi\)
\(90\) 0 0
\(91\) 1.97316 + 1.86420i 0.206844 + 0.195421i
\(92\) 0 0
\(93\) 4.77073 0.180661i 0.494701 0.0187336i
\(94\) 0 0
\(95\) 4.96254 + 9.69413i 0.509146 + 0.994597i
\(96\) 0 0
\(97\) 8.19386 + 1.56949i 0.831961 + 0.159358i 0.586398 0.810023i \(-0.300545\pi\)
0.245563 + 0.969381i \(0.421027\pi\)
\(98\) 0 0
\(99\) 0.0524748 0.0256210i 0.00527391 0.00257501i
\(100\) 0 0
\(101\) −0.669183 + 0.237208i −0.0665862 + 0.0236030i −0.367189 0.930146i \(-0.619680\pi\)
0.300603 + 0.953749i \(0.402812\pi\)
\(102\) 0 0
\(103\) −0.0234315 + 1.23796i −0.00230877 + 0.121980i 0.996805 + 0.0798787i \(0.0254533\pi\)
−0.999113 + 0.0421009i \(0.986595\pi\)
\(104\) 0 0
\(105\) 1.41163 + 0.107066i 0.137761 + 0.0104486i
\(106\) 0 0
\(107\) −0.210171 11.1040i −0.0203180 1.07347i −0.853699 0.520767i \(-0.825646\pi\)
0.833381 0.552699i \(-0.186402\pi\)
\(108\) 0 0
\(109\) 9.00852 17.5978i 0.862860 1.68556i 0.144939 0.989441i \(-0.453701\pi\)
0.717921 0.696124i \(-0.245094\pi\)
\(110\) 0 0
\(111\) 3.36064 0.512731i 0.318977 0.0486663i
\(112\) 0 0
\(113\) 12.1953 + 10.6780i 1.14724 + 1.00450i 0.999881 + 0.0154191i \(0.00490824\pi\)
0.147358 + 0.989083i \(0.452923\pi\)
\(114\) 0 0
\(115\) 6.11272 7.83751i 0.570014 0.730851i
\(116\) 0 0
\(117\) 2.20340 4.73821i 0.203705 0.438048i
\(118\) 0 0
\(119\) 1.85967 + 4.94695i 0.170476 + 0.453486i
\(120\) 0 0
\(121\) −0.624172 + 10.9818i −0.0567429 + 0.998346i
\(122\) 0 0
\(123\) 0.140247 0.0324098i 0.0126457 0.00292229i
\(124\) 0 0
\(125\) −10.4985 + 6.14995i −0.939016 + 0.550068i
\(126\) 0 0
\(127\) 0.110867 1.16813i 0.00983783 0.103655i −0.989257 0.146184i \(-0.953301\pi\)
0.999095 + 0.0425297i \(0.0135417\pi\)
\(128\) 0 0
\(129\) 4.64135 + 2.48792i 0.408648 + 0.219049i
\(130\) 0 0
\(131\) −0.775050 0.852092i −0.0677164 0.0744476i 0.704963 0.709244i \(-0.250964\pi\)
−0.772680 + 0.634796i \(0.781084\pi\)
\(132\) 0 0
\(133\) −6.20909 + 5.43657i −0.538396 + 0.471410i
\(134\) 0 0
\(135\) −1.39994 5.57490i −0.120488 0.479811i
\(136\) 0 0
\(137\) −1.69616 5.81356i −0.144912 0.496686i 0.854841 0.518890i \(-0.173655\pi\)
−0.999753 + 0.0222039i \(0.992932\pi\)
\(138\) 0 0
\(139\) −4.76339 + 2.10641i −0.404025 + 0.178664i −0.596454 0.802648i \(-0.703424\pi\)
0.192428 + 0.981311i \(0.438364\pi\)
\(140\) 0 0
\(141\) −2.44365 + 5.82145i −0.205793 + 0.490254i
\(142\) 0 0
\(143\) −0.0243909 0.0338397i −0.00203967 0.00282982i
\(144\) 0 0
\(145\) −1.72245 + 0.923291i −0.143042 + 0.0766752i
\(146\) 0 0
\(147\) −0.462978 2.69183i −0.0381858 0.222019i
\(148\) 0 0
\(149\) 15.1733 + 9.67765i 1.24304 + 0.792824i 0.984873 0.173276i \(-0.0554352\pi\)
0.258169 + 0.966100i \(0.416881\pi\)
\(150\) 0 0
\(151\) 2.56035 + 4.56676i 0.208358 + 0.371638i 0.956421 0.291990i \(-0.0943173\pi\)
−0.748063 + 0.663627i \(0.769016\pi\)
\(152\) 0 0
\(153\) 7.90232 6.40743i 0.638865 0.518010i
\(154\) 0 0
\(155\) 12.6515 + 10.2582i 1.01619 + 0.823956i
\(156\) 0 0
\(157\) −8.36277 17.9834i −0.667422 1.43523i −0.887993 0.459857i \(-0.847901\pi\)
0.220571 0.975371i \(-0.429208\pi\)
\(158\) 0 0
\(159\) −1.45485 1.48264i −0.115377 0.117581i
\(160\) 0 0
\(161\) 6.88861 + 3.04620i 0.542899 + 0.240074i
\(162\) 0 0
\(163\) −13.9693 8.18311i −1.09416 0.640950i −0.156211 0.987724i \(-0.549928\pi\)
−0.937949 + 0.346773i \(0.887277\pi\)
\(164\) 0 0
\(165\) −0.0209955 0.00569677i −0.00163450 0.000443493i
\(166\) 0 0
\(167\) 6.11298 11.3856i 0.473036 0.881043i
\(168\) 0 0
\(169\) 8.94389 + 2.42677i 0.687991 + 0.186675i
\(170\) 0 0
\(171\) 13.7080 + 8.03002i 1.04827 + 0.614071i
\(172\) 0 0
\(173\) −20.1801 8.92382i −1.53427 0.678465i −0.546940 0.837172i \(-0.684207\pi\)
−0.987326 + 0.158707i \(0.949267\pi\)
\(174\) 0 0
\(175\) −1.53752 1.56689i −0.116225 0.118446i
\(176\) 0 0
\(177\) 1.74722 + 3.75724i 0.131329 + 0.282411i
\(178\) 0 0
\(179\) 8.73479 + 7.08242i 0.652869 + 0.529365i 0.897928 0.440143i \(-0.145072\pi\)
−0.245059 + 0.969508i \(0.578807\pi\)
\(180\) 0 0
\(181\) 7.82730 6.34661i 0.581799 0.471739i −0.293076 0.956089i \(-0.594679\pi\)
0.874874 + 0.484350i \(0.160944\pi\)
\(182\) 0 0
\(183\) 0.105118 + 0.187493i 0.00777054 + 0.0138599i
\(184\) 0 0
\(185\) 9.77836 + 6.23673i 0.718919 + 0.458534i
\(186\) 0 0
\(187\) −0.0137661 0.0800382i −0.00100668 0.00585297i
\(188\) 0 0
\(189\) 3.83906 2.05786i 0.279251 0.149687i
\(190\) 0 0
\(191\) −11.9954 16.6423i −0.867954 1.20419i −0.977652 0.210230i \(-0.932579\pi\)
0.109698 0.993965i \(-0.465012\pi\)
\(192\) 0 0
\(193\) −2.31222 + 5.50833i −0.166437 + 0.396498i −0.983712 0.179749i \(-0.942471\pi\)
0.817275 + 0.576247i \(0.195483\pi\)
\(194\) 0 0
\(195\) −1.78039 + 0.787304i −0.127496 + 0.0563800i
\(196\) 0 0
\(197\) −1.24039 4.25144i −0.0883745 0.302903i 0.903767 0.428025i \(-0.140791\pi\)
−0.992141 + 0.125122i \(0.960068\pi\)
\(198\) 0 0
\(199\) 1.82807 + 7.27979i 0.129588 + 0.516051i 0.999730 + 0.0232485i \(0.00740089\pi\)
−0.870141 + 0.492802i \(0.835973\pi\)
\(200\) 0 0
\(201\) 2.02311 1.77140i 0.142699 0.124945i
\(202\) 0 0
\(203\) −0.996506 1.09556i −0.0699410 0.0768934i
\(204\) 0 0
\(205\) 0.432824 + 0.232008i 0.0302297 + 0.0162041i
\(206\) 0 0
\(207\) 1.36997 14.4345i 0.0952197 1.00327i
\(208\) 0 0
\(209\) 0.109428 0.0641018i 0.00756926 0.00443402i
\(210\) 0 0
\(211\) 14.9184 3.44750i 1.02703 0.237335i 0.322168 0.946683i \(-0.395588\pi\)
0.704859 + 0.709347i \(0.251010\pi\)
\(212\) 0 0
\(213\) 0.115047 2.02417i 0.00788292 0.138694i
\(214\) 0 0
\(215\) 6.32193 + 16.8171i 0.431152 + 1.14692i
\(216\) 0 0
\(217\) −5.20454 + 11.1919i −0.353307 + 0.759754i
\(218\) 0 0
\(219\) −0.388352 + 0.497931i −0.0262424 + 0.0336470i
\(220\) 0 0
\(221\) −5.46764 4.78737i −0.367793 0.322033i
\(222\) 0 0
\(223\) 3.36103 0.512790i 0.225071 0.0343390i −0.0373084 0.999304i \(-0.511878\pi\)
0.262379 + 0.964965i \(0.415493\pi\)
\(224\) 0 0
\(225\) −1.92563 + 3.76165i −0.128375 + 0.250776i
\(226\) 0 0
\(227\) 0.102663 + 5.42403i 0.00681401 + 0.360006i 0.986891 + 0.161388i \(0.0515970\pi\)
−0.980077 + 0.198618i \(0.936355\pi\)
\(228\) 0 0
\(229\) −3.72243 0.282331i −0.245985 0.0186570i −0.0479412 0.998850i \(-0.515266\pi\)
−0.198044 + 0.980193i \(0.563459\pi\)
\(230\) 0 0
\(231\) 0.000311977 0.0164827i 2.05266e−5 0.00108448i
\(232\) 0 0
\(233\) 15.6115 5.53386i 1.02274 0.362535i 0.230716 0.973021i \(-0.425893\pi\)
0.792027 + 0.610486i \(0.209026\pi\)
\(234\) 0 0
\(235\) −19.3557 + 9.45046i −1.26262 + 0.616480i
\(236\) 0 0
\(237\) 8.77402 + 1.68062i 0.569934 + 0.109168i
\(238\) 0 0
\(239\) −1.75138 3.42126i −0.113287 0.221303i 0.826598 0.562793i \(-0.190273\pi\)
−0.939885 + 0.341490i \(0.889068\pi\)
\(240\) 0 0
\(241\) −5.18330 + 0.196284i −0.333886 + 0.0126438i −0.204252 0.978918i \(-0.565476\pi\)
−0.129633 + 0.991562i \(0.541380\pi\)
\(242\) 0 0
\(243\) −9.30027 8.78668i −0.596612 0.563666i
\(244\) 0 0
\(245\) 4.86135 7.94987i 0.310580 0.507899i
\(246\) 0 0
\(247\) 3.99330 10.6226i 0.254088 0.675903i
\(248\) 0 0
\(249\) −2.08256 + 0.237499i −0.131977 + 0.0150509i
\(250\) 0 0
\(251\) −13.0665 + 3.54536i −0.824748 + 0.223781i −0.649130 0.760677i \(-0.724867\pi\)
−0.175618 + 0.984458i \(0.556192\pi\)
\(252\) 0 0
\(253\) −0.0951605 0.0658893i −0.00598269 0.00414242i
\(254\) 0 0
\(255\) −3.78735 0.143422i −0.237173 0.00898142i
\(256\) 0 0
\(257\) −0.479864 3.60104i −0.0299331 0.224626i 0.969888 0.243552i \(-0.0783127\pi\)
−0.999821 + 0.0189258i \(0.993975\pi\)
\(258\) 0 0
\(259\) −2.77913 + 8.33799i −0.172687 + 0.518097i
\(260\) 0 0
\(261\) −1.39418 + 2.48673i −0.0862977 + 0.153925i
\(262\) 0 0
\(263\) 0.0374928 + 0.395037i 0.00231191 + 0.0243590i 0.996608 0.0822986i \(-0.0262261\pi\)
−0.994296 + 0.106658i \(0.965985\pi\)
\(264\) 0 0
\(265\) −0.402138 7.07530i −0.0247031 0.434632i
\(266\) 0 0
\(267\) −4.10313 + 4.86909i −0.251107 + 0.297983i
\(268\) 0 0
\(269\) −23.0591 + 14.7073i −1.40594 + 0.896722i −0.999854 0.0171121i \(-0.994553\pi\)
−0.406087 + 0.913834i \(0.633107\pi\)
\(270\) 0 0
\(271\) −7.79534 + 5.84599i −0.473533 + 0.355118i −0.809856 0.586628i \(-0.800455\pi\)
0.336323 + 0.941747i \(0.390816\pi\)
\(272\) 0 0
\(273\) −0.907251 1.16324i −0.0549093 0.0704027i
\(274\) 0 0
\(275\) 0.0186753 + 0.0280932i 0.00112616 + 0.00169409i
\(276\) 0 0
\(277\) −23.3664 9.29234i −1.40395 0.558323i −0.459853 0.887995i \(-0.652098\pi\)
−0.944095 + 0.329672i \(0.893062\pi\)
\(278\) 0 0
\(279\) 23.6071 + 2.69220i 1.41332 + 0.161178i
\(280\) 0 0
\(281\) 19.3178 + 14.4870i 1.15240 + 0.864224i 0.992420 0.122896i \(-0.0392182\pi\)
0.159981 + 0.987120i \(0.448857\pi\)
\(282\) 0 0
\(283\) 3.52158 3.87163i 0.209336 0.230145i −0.626086 0.779754i \(-0.715344\pi\)
0.835422 + 0.549610i \(0.185224\pi\)
\(284\) 0 0
\(285\) −1.87146 5.61478i −0.110856 0.332591i
\(286\) 0 0
\(287\) −0.0906371 + 0.360938i −0.00535014 + 0.0213055i
\(288\) 0 0
\(289\) 1.10352 + 2.62889i 0.0649131 + 0.154641i
\(290\) 0 0
\(291\) −4.27338 1.51480i −0.250510 0.0887992i
\(292\) 0 0
\(293\) −18.8458 + 7.49460i −1.10098 + 0.437839i −0.848196 0.529683i \(-0.822311\pi\)
−0.252787 + 0.967522i \(0.581347\pi\)
\(294\) 0 0
\(295\) −3.95940 + 13.5708i −0.230525 + 0.790123i
\(296\) 0 0
\(297\) −0.0638903 + 0.0199601i −0.00370729 + 0.00115820i
\(298\) 0 0
\(299\) −10.3277 + 0.783314i −0.597266 + 0.0453002i
\(300\) 0 0
\(301\) −11.1934 + 7.75034i −0.645178 + 0.446722i
\(302\) 0 0
\(303\) 0.378951 0.0725861i 0.0217702 0.00416997i
\(304\) 0 0
\(305\) −0.151564 + 0.717501i −0.00867851 + 0.0410840i
\(306\) 0 0
\(307\) −22.7174 11.0918i −1.29655 0.633045i −0.344442 0.938807i \(-0.611932\pi\)
−0.952108 + 0.305762i \(0.901089\pi\)
\(308\) 0 0
\(309\) 0.114058 0.663153i 0.00648855 0.0377255i
\(310\) 0 0
\(311\) −0.168612 0.798207i −0.00956110 0.0452622i 0.973367 0.229253i \(-0.0736284\pi\)
−0.982928 + 0.183991i \(0.941098\pi\)
\(312\) 0 0
\(313\) −21.3324 + 21.7400i −1.20578 + 1.22882i −0.239621 + 0.970867i \(0.577023\pi\)
−0.966158 + 0.257951i \(0.916953\pi\)
\(314\) 0 0
\(315\) 6.86468 + 1.58636i 0.386781 + 0.0893811i
\(316\) 0 0
\(317\) −0.832361 + 1.25212i −0.0467500 + 0.0703260i −0.855414 0.517945i \(-0.826697\pi\)
0.808664 + 0.588271i \(0.200191\pi\)
\(318\) 0 0
\(319\) 0.0118727 + 0.0194156i 0.000664741 + 0.00108707i
\(320\) 0 0
\(321\) −0.797237 + 5.98269i −0.0444974 + 0.333921i
\(322\) 0 0
\(323\) 16.0603 15.1734i 0.893620 0.844272i
\(324\) 0 0
\(325\) 2.88134 + 0.900165i 0.159828 + 0.0499321i
\(326\) 0 0
\(327\) −6.28211 + 8.71576i −0.347401 + 0.481983i
\(328\) 0 0
\(329\) −10.5183 12.4818i −0.579892 0.688144i
\(330\) 0 0
\(331\) −20.4856 3.12548i −1.12599 0.171792i −0.439020 0.898477i \(-0.644674\pi\)
−0.686971 + 0.726685i \(0.741060\pi\)
\(332\) 0 0
\(333\) 16.9188 0.927146
\(334\) 0 0
\(335\) 9.17399 0.501229
\(336\) 0 0
\(337\) −15.0449 2.29540i −0.819548 0.125038i −0.272518 0.962151i \(-0.587856\pi\)
−0.547031 + 0.837113i \(0.684242\pi\)
\(338\) 0 0
\(339\) −5.67652 6.73619i −0.308306 0.365860i
\(340\) 0 0
\(341\) 0.110904 0.153868i 0.00600581 0.00833243i
\(342\) 0 0
\(343\) 16.1279 + 5.03852i 0.870822 + 0.272055i
\(344\) 0 0
\(345\) −3.92637 + 3.70955i −0.211389 + 0.199715i
\(346\) 0 0
\(347\) −0.598016 + 4.48768i −0.0321032 + 0.240911i −0.999943 0.0106551i \(-0.996608\pi\)
0.967840 + 0.251566i \(0.0809457\pi\)
\(348\) 0 0
\(349\) −7.14101 11.6779i −0.382249 0.625101i 0.602695 0.797971i \(-0.294093\pi\)
−0.984945 + 0.172870i \(0.944696\pi\)
\(350\) 0 0
\(351\) −3.31590 + 4.98810i −0.176990 + 0.266245i
\(352\) 0 0
\(353\) −7.83684 1.81101i −0.417113 0.0963905i 0.0113808 0.999935i \(-0.496377\pi\)
−0.428494 + 0.903545i \(0.640956\pi\)
\(354\) 0 0
\(355\) 4.84449 4.93705i 0.257119 0.262031i
\(356\) 0 0
\(357\) −0.593601 2.81010i −0.0314167 0.148726i
\(358\) 0 0
\(359\) 1.35446 7.87505i 0.0714857 0.415629i −0.927627 0.373508i \(-0.878155\pi\)
0.999113 0.0421211i \(-0.0134115\pi\)
\(360\) 0 0
\(361\) 13.9304 + 6.80154i 0.733176 + 0.357976i
\(362\) 0 0
\(363\) 1.23546 5.84865i 0.0648447 0.306974i
\(364\) 0 0
\(365\) −2.11588 + 0.405286i −0.110750 + 0.0212137i
\(366\) 0 0
\(367\) 0.167156 0.115739i 0.00872545 0.00604152i −0.564891 0.825165i \(-0.691082\pi\)
0.573617 + 0.819124i \(0.305540\pi\)
\(368\) 0 0
\(369\) 0.714330 0.0541790i 0.0371865 0.00282045i
\(370\) 0 0
\(371\) 5.12599 1.60142i 0.266128 0.0831414i
\(372\) 0 0
\(373\) 3.03599 10.4058i 0.157197 0.538793i −0.842802 0.538223i \(-0.819096\pi\)
1.00000 0.000569571i \(-0.000181300\pi\)
\(374\) 0 0
\(375\) 6.14425 2.44345i 0.317288 0.126179i
\(376\) 0 0
\(377\) 1.91946 + 0.680398i 0.0988572 + 0.0350423i
\(378\) 0 0
\(379\) −7.43388 17.7095i −0.381853 0.909676i −0.992995 0.118156i \(-0.962302\pi\)
0.611142 0.791521i \(-0.290710\pi\)
\(380\) 0 0
\(381\) −0.155308 + 0.618471i −0.00795666 + 0.0316852i
\(382\) 0 0
\(383\) 1.51416 + 4.54280i 0.0773700 + 0.232126i 0.980249 0.197769i \(-0.0633696\pi\)
−0.902879 + 0.429896i \(0.858550\pi\)
\(384\) 0 0
\(385\) 0.0378446 0.0416065i 0.00192874 0.00212046i
\(386\) 0 0
\(387\) 20.9674 + 15.7242i 1.06584 + 0.799306i
\(388\) 0 0
\(389\) −0.815848 0.0930411i −0.0413652 0.00471737i 0.0926005 0.995703i \(-0.470482\pi\)
−0.133966 + 0.990986i \(0.542771\pi\)
\(390\) 0 0
\(391\) −18.7376 7.45159i −0.947603 0.376843i
\(392\) 0 0
\(393\) 0.346541 + 0.521301i 0.0174807 + 0.0262961i
\(394\) 0 0
\(395\) 18.7440 + 24.0328i 0.943110 + 1.20922i
\(396\) 0 0
\(397\) 22.2756 16.7052i 1.11798 0.838411i 0.129774 0.991544i \(-0.458575\pi\)
0.988206 + 0.153133i \(0.0489362\pi\)
\(398\) 0 0
\(399\) 3.78135 2.41178i 0.189304 0.120740i
\(400\) 0 0
\(401\) −24.6170 + 29.2124i −1.22931 + 1.45880i −0.385027 + 0.922905i \(0.625808\pi\)
−0.844286 + 0.535893i \(0.819975\pi\)
\(402\) 0 0
\(403\) −0.963114 16.9452i −0.0479761 0.844103i
\(404\) 0 0
\(405\) −1.12627 11.8668i −0.0559649 0.589665i
\(406\) 0 0
\(407\) 0.0660485 0.117807i 0.00327390 0.00583949i
\(408\) 0 0
\(409\) −4.44758 + 13.3437i −0.219918 + 0.659802i 0.779523 + 0.626374i \(0.215462\pi\)
−0.999441 + 0.0334280i \(0.989358\pi\)
\(410\) 0 0
\(411\) 0.434722 + 3.26227i 0.0214432 + 0.160916i
\(412\) 0 0
\(413\) −10.7050 0.405385i −0.526761 0.0199477i
\(414\) 0 0
\(415\) −5.87924 4.07080i −0.288600 0.199827i
\(416\) 0 0
\(417\) 2.73171 0.741203i 0.133772 0.0362969i
\(418\) 0 0
\(419\) −16.4949 + 1.88111i −0.805828 + 0.0918983i −0.506487 0.862248i \(-0.669056\pi\)
−0.299341 + 0.954146i \(0.596767\pi\)
\(420\) 0 0
\(421\) −6.56422 + 17.4616i −0.319920 + 0.851026i 0.673777 + 0.738934i \(0.264671\pi\)
−0.993698 + 0.112092i \(0.964245\pi\)
\(422\) 0 0
\(423\) −16.3922 + 26.8066i −0.797018 + 1.30338i
\(424\) 0 0
\(425\) 4.27204 + 4.03613i 0.207224 + 0.195781i
\(426\) 0 0
\(427\) −0.555323 + 0.0210293i −0.0268739 + 0.00101768i
\(428\) 0 0
\(429\) 0.0103299 + 0.0201791i 0.000498733 + 0.000974256i
\(430\) 0 0
\(431\) 1.93652 + 0.370930i 0.0932788 + 0.0178671i 0.234552 0.972104i \(-0.424638\pi\)
−0.141273 + 0.989971i \(0.545120\pi\)
\(432\) 0 0
\(433\) 27.7595 13.5537i 1.33404 0.651349i 0.373018 0.927824i \(-0.378323\pi\)
0.961021 + 0.276476i \(0.0891665\pi\)
\(434\) 0 0
\(435\) 1.00104 0.354842i 0.0479962 0.0170134i
\(436\) 0 0
\(437\) 0.595902 31.4833i 0.0285058 1.50605i
\(438\) 0 0
\(439\) −20.3343 1.54227i −0.970501 0.0736086i −0.419181 0.907903i \(-0.637683\pi\)
−0.551320 + 0.834294i \(0.685876\pi\)
\(440\) 0 0
\(441\) −0.257245 13.5910i −0.0122497 0.647192i
\(442\) 0 0
\(443\) −7.63294 + 14.9107i −0.362652 + 0.708427i −0.997961 0.0638314i \(-0.979668\pi\)
0.635309 + 0.772258i \(0.280873\pi\)
\(444\) 0 0
\(445\) −21.4748 + 3.27640i −1.01800 + 0.155316i
\(446\) 0 0
\(447\) −7.35836 6.44285i −0.348039 0.304737i
\(448\) 0 0
\(449\) 2.78414 3.56973i 0.131392 0.168466i −0.718320 0.695712i \(-0.755089\pi\)
0.849712 + 0.527247i \(0.176776\pi\)
\(450\) 0 0
\(451\) 0.00241138 0.00518545i 0.000113548 0.000244173i
\(452\) 0 0
\(453\) −1.00119 2.66328i −0.0470400 0.125132i
\(454\) 0 0
\(455\) 0.285593 5.02478i 0.0133888 0.235566i
\(456\) 0 0
\(457\) −10.3615 + 2.39443i −0.484690 + 0.112007i −0.460425 0.887699i \(-0.652303\pi\)
−0.0242651 + 0.999706i \(0.507725\pi\)
\(458\) 0 0
\(459\) −10.0621 + 5.89431i −0.469659 + 0.275123i
\(460\) 0 0
\(461\) −0.927989 + 9.77759i −0.0432208 + 0.455388i 0.947527 + 0.319675i \(0.103574\pi\)
−0.990748 + 0.135713i \(0.956667\pi\)
\(462\) 0 0
\(463\) −25.8051 13.8324i −1.19927 0.642846i −0.253387 0.967365i \(-0.581545\pi\)
−0.945879 + 0.324519i \(0.894798\pi\)
\(464\) 0 0
\(465\) −5.95598 6.54803i −0.276202 0.303658i
\(466\) 0 0
\(467\) 8.31584 7.28120i 0.384811 0.336934i −0.444441 0.895808i \(-0.646598\pi\)
0.829253 + 0.558874i \(0.188766\pi\)
\(468\) 0 0
\(469\) 1.69320 + 6.74270i 0.0781846 + 0.311349i
\(470\) 0 0
\(471\) 3.01875 + 10.3467i 0.139097 + 0.476753i
\(472\) 0 0
\(473\) 0.191343 0.0846134i 0.00879795 0.00389053i
\(474\) 0 0
\(475\) −3.55218 + 8.46224i −0.162985 + 0.388274i
\(476\) 0 0
\(477\) −6.04477 8.38649i −0.276771 0.383991i
\(478\) 0 0
\(479\) 16.8774 9.04682i 0.771146 0.413360i −0.0392594 0.999229i \(-0.512500\pi\)
0.810405 + 0.585869i \(0.199247\pi\)
\(480\) 0 0
\(481\) −2.04858 11.9108i −0.0934072 0.543085i
\(482\) 0 0
\(483\) −3.45112 2.20116i −0.157031 0.100156i
\(484\) 0 0
\(485\) −7.56444 13.4923i −0.343484 0.612654i
\(486\) 0 0
\(487\) 8.11520 6.58004i 0.367735 0.298170i −0.428044 0.903758i \(-0.640797\pi\)
0.795778 + 0.605588i \(0.207062\pi\)
\(488\) 0 0
\(489\) 6.83406 + 5.54125i 0.309047 + 0.250584i
\(490\) 0 0
\(491\) 13.9651 + 30.0307i 0.630238 + 1.35527i 0.917623 + 0.397452i \(0.130106\pi\)
−0.287385 + 0.957815i \(0.592786\pi\)
\(492\) 0 0
\(493\) 2.77693 + 2.82999i 0.125067 + 0.127456i
\(494\) 0 0
\(495\) −0.0990195 0.0437873i −0.00445060 0.00196809i
\(496\) 0 0
\(497\) 4.52276 + 2.64940i 0.202873 + 0.118842i
\(498\) 0 0
\(499\) 32.8170 + 8.90432i 1.46909 + 0.398612i 0.904398 0.426689i \(-0.140320\pi\)
0.564692 + 0.825302i \(0.308995\pi\)
\(500\) 0 0
\(501\) −4.21733 + 5.61567i −0.188416 + 0.250890i
\(502\) 0 0
\(503\) 36.5620 + 9.92046i 1.63022 + 0.442332i 0.955319 0.295578i \(-0.0955121\pi\)
0.674900 + 0.737909i \(0.264187\pi\)
\(504\) 0 0
\(505\) 1.13582 + 0.665354i 0.0505433 + 0.0296079i
\(506\) 0 0
\(507\) −4.60605 2.03684i −0.204562 0.0904591i
\(508\) 0 0
\(509\) −17.0594 17.3853i −0.756143 0.770590i 0.222770 0.974871i \(-0.428490\pi\)
−0.978912 + 0.204281i \(0.934514\pi\)
\(510\) 0 0
\(511\) −0.688396 1.48033i −0.0304528 0.0654860i
\(512\) 0 0
\(513\) −14.1447 11.4689i −0.624504 0.506366i
\(514\) 0 0
\(515\) 1.78316 1.44583i 0.0785752 0.0637111i
\(516\) 0 0
\(517\) 0.122664 + 0.218790i 0.00539476 + 0.00962236i
\(518\) 0 0
\(519\) 10.1100 + 6.44826i 0.443780 + 0.283047i
\(520\) 0 0
\(521\) 6.85805 + 39.8738i 0.300457 + 1.74690i 0.606682 + 0.794945i \(0.292500\pi\)
−0.306225 + 0.951959i \(0.599066\pi\)
\(522\) 0 0
\(523\) 18.2091 9.76067i 0.796228 0.426804i −0.0233820 0.999727i \(-0.507443\pi\)
0.819610 + 0.572922i \(0.194190\pi\)
\(524\) 0 0
\(525\) 0.697576 + 0.967813i 0.0304447 + 0.0422388i
\(526\) 0 0
\(527\) 12.7898 30.4688i 0.557132 1.32724i
\(528\) 0 0
\(529\) −5.24870 + 2.32102i −0.228204 + 0.100914i
\(530\) 0 0
\(531\) 5.77586 + 19.7967i 0.250651 + 0.859105i
\(532\) 0 0
\(533\) −0.124635 0.496325i −0.00539854 0.0214982i
\(534\) 0 0
\(535\) −15.4920 + 13.5645i −0.669779 + 0.586447i
\(536\) 0 0
\(537\) −4.11211 4.52087i −0.177451 0.195090i
\(538\) 0 0
\(539\) −0.0956399 0.0512661i −0.00411950 0.00220819i
\(540\) 0 0
\(541\) 0.211581 2.22929i 0.00909658 0.0958446i −0.989824 0.142298i \(-0.954551\pi\)
0.998920 + 0.0464533i \(0.0147919\pi\)
\(542\) 0 0
\(543\) −4.72530 + 2.76805i −0.202782 + 0.118788i
\(544\) 0 0
\(545\) −35.7129 + 8.25289i −1.52977 + 0.353515i
\(546\) 0 0
\(547\) −1.94052 + 34.1420i −0.0829708 + 1.45981i 0.639706 + 0.768620i \(0.279056\pi\)
−0.722676 + 0.691187i \(0.757088\pi\)
\(548\) 0 0
\(549\) 0.376431 + 1.00135i 0.0160657 + 0.0427366i
\(550\) 0 0
\(551\) −2.61071 + 5.61408i −0.111220 + 0.239168i
\(552\) 0 0
\(553\) −14.2042 + 18.2121i −0.604023 + 0.774455i
\(554\) 0 0
\(555\) −4.74208 4.15208i −0.201290 0.176246i
\(556\) 0 0
\(557\) 23.2366 3.54520i 0.984568 0.150215i 0.361491 0.932376i \(-0.382268\pi\)
0.623077 + 0.782161i \(0.285882\pi\)
\(558\) 0 0
\(559\) 8.53097 16.6649i 0.360821 0.704851i
\(560\) 0 0
\(561\) 0.000835227 0.0441276i 3.52633e−5 0.00186307i
\(562\) 0 0
\(563\) 21.7020 + 1.64601i 0.914629 + 0.0693709i 0.524520 0.851398i \(-0.324245\pi\)
0.390108 + 0.920769i \(0.372438\pi\)
\(564\) 0 0
\(565\) 0.568733 30.0480i 0.0239268 1.26413i
\(566\) 0 0
\(567\) 8.51398 3.01798i 0.357554 0.126743i
\(568\) 0 0
\(569\) 17.3526 8.47246i 0.727459 0.355184i −0.0374712 0.999298i \(-0.511930\pi\)
0.764930 + 0.644114i \(0.222774\pi\)
\(570\) 0 0
\(571\) 44.2094 + 8.46808i 1.85011 + 0.354378i 0.988259 0.152791i \(-0.0488262\pi\)
0.861847 + 0.507169i \(0.169308\pi\)
\(572\) 0 0
\(573\) 5.08022 + 9.92403i 0.212229 + 0.414582i
\(574\) 0 0
\(575\) 8.37006 0.316963i 0.349056 0.0132183i
\(576\) 0 0
\(577\) −3.73955 3.53304i −0.155679 0.147082i 0.604963 0.796254i \(-0.293188\pi\)
−0.760642 + 0.649172i \(0.775116\pi\)
\(578\) 0 0
\(579\) 1.69370 2.76974i 0.0703876 0.115107i
\(580\) 0 0
\(581\) 1.90685 5.07245i 0.0791096 0.210441i
\(582\) 0 0
\(583\) −0.0819938 + 0.00935074i −0.00339583 + 0.000387268i
\(584\) 0 0
\(585\) −9.35030 + 2.53704i −0.386587 + 0.104894i
\(586\) 0 0
\(587\) −15.0266 10.4044i −0.620212 0.429436i 0.217109 0.976147i \(-0.430337\pi\)
−0.837321 + 0.546711i \(0.815880\pi\)
\(588\) 0 0
\(589\) 51.5640 + 1.95266i 2.12466 + 0.0804578i
\(590\) 0 0
\(591\) 0.317911 + 2.38569i 0.0130771 + 0.0981342i
\(592\) 0 0
\(593\) 11.9129 35.7413i 0.489205 1.46772i −0.356617 0.934251i \(-0.616070\pi\)
0.845821 0.533467i \(-0.179111\pi\)
\(594\) 0 0
\(595\) 4.79187 8.54701i 0.196447 0.350393i
\(596\) 0 0
\(597\) −0.385409 4.06079i −0.0157737 0.166197i
\(598\) 0 0
\(599\) 1.32497 + 23.3118i 0.0541368 + 0.952495i 0.904547 + 0.426374i \(0.140209\pi\)
−0.850410 + 0.526121i \(0.823646\pi\)
\(600\) 0 0
\(601\) −11.4615 + 13.6011i −0.467525 + 0.554802i −0.946364 0.323101i \(-0.895275\pi\)
0.478839 + 0.877903i \(0.341058\pi\)
\(602\) 0 0
\(603\) 11.2831 7.19649i 0.459485 0.293064i
\(604\) 0 0
\(605\) 16.3156 12.2356i 0.663323 0.497449i
\(606\) 0 0
\(607\) −10.6921 13.7091i −0.433981 0.556434i 0.520825 0.853663i \(-0.325624\pi\)
−0.954806 + 0.297229i \(0.903938\pi\)
\(608\) 0 0
\(609\) 0.445559 + 0.670253i 0.0180550 + 0.0271600i
\(610\) 0 0
\(611\) 20.8566 + 8.29425i 0.843766 + 0.335549i
\(612\) 0 0
\(613\) 16.0311 + 1.82822i 0.647492 + 0.0738413i 0.430870 0.902414i \(-0.358207\pi\)
0.216622 + 0.976256i \(0.430496\pi\)
\(614\) 0 0
\(615\) −0.213511 0.160119i −0.00860961 0.00645664i
\(616\) 0 0
\(617\) 25.9944 28.5784i 1.04650 1.15052i 0.0581493 0.998308i \(-0.481480\pi\)
0.988348 0.152214i \(-0.0486404\pi\)
\(618\) 0 0
\(619\) 1.86170 + 5.58551i 0.0748282 + 0.224501i 0.979440 0.201736i \(-0.0646584\pi\)
−0.904612 + 0.426237i \(0.859839\pi\)
\(620\) 0 0
\(621\) −4.04782 + 16.1193i −0.162433 + 0.646847i
\(622\) 0 0
\(623\) −6.37159 15.1789i −0.255272 0.608128i
\(624\) 0 0
\(625\) 13.8992 + 4.92689i 0.555967 + 0.197075i
\(626\) 0 0
\(627\) −0.0640424 + 0.0254684i −0.00255761 + 0.00101711i
\(628\) 0 0
\(629\) 6.59026 22.5881i 0.262771 0.900645i
\(630\) 0 0
\(631\) −39.4877 + 12.3364i −1.57198 + 0.491105i −0.955183 0.296016i \(-0.904342\pi\)
−0.616799 + 0.787121i \(0.711571\pi\)
\(632\) 0 0
\(633\) −8.29727 + 0.629315i −0.329787 + 0.0250130i
\(634\) 0 0
\(635\) −1.78861 + 1.23844i −0.0709790 + 0.0491460i
\(636\) 0 0
\(637\) −9.53689 + 1.82674i −0.377865 + 0.0723781i
\(638\) 0 0
\(639\) 2.08541 9.87233i 0.0824977 0.390544i
\(640\) 0 0
\(641\) 26.4512 + 12.9149i 1.04476 + 0.510106i 0.879378 0.476124i \(-0.157959\pi\)
0.165379 + 0.986230i \(0.447115\pi\)
\(642\) 0 0
\(643\) 2.95691 17.1919i 0.116609 0.677984i −0.867089 0.498154i \(-0.834011\pi\)
0.983698 0.179830i \(-0.0575548\pi\)
\(644\) 0 0
\(645\) −2.01794 9.55290i −0.0794562 0.376145i
\(646\) 0 0
\(647\) 5.74689 5.85670i 0.225934 0.230251i −0.591454 0.806339i \(-0.701446\pi\)
0.817387 + 0.576088i \(0.195422\pi\)
\(648\) 0 0
\(649\) 0.160395 + 0.0370655i 0.00629604 + 0.00145495i
\(650\) 0 0
\(651\) 3.71341 5.58607i 0.145540 0.218935i
\(652\) 0 0
\(653\) −16.8134 27.4953i −0.657959 1.07598i −0.991103 0.133099i \(-0.957507\pi\)
0.333144 0.942876i \(-0.391890\pi\)
\(654\) 0 0
\(655\) −0.282092 + 2.11690i −0.0110222 + 0.0827140i
\(656\) 0 0
\(657\) −2.28441 + 2.15826i −0.0891233 + 0.0842016i
\(658\) 0 0
\(659\) −14.9801 4.67994i −0.583540 0.182305i −0.00784528 0.999969i \(-0.502497\pi\)
−0.575695 + 0.817665i \(0.695268\pi\)
\(660\) 0 0
\(661\) −18.5016 + 25.6691i −0.719630 + 0.998410i 0.279637 + 0.960106i \(0.409786\pi\)
−0.999266 + 0.0383044i \(0.987804\pi\)
\(662\) 0 0
\(663\) 2.54500 + 3.02010i 0.0988398 + 0.117291i
\(664\) 0 0
\(665\) 15.1262 + 2.30780i 0.586570 + 0.0894928i
\(666\) 0 0
\(667\) 5.65071 0.218797
\(668\) 0 0
\(669\) −1.84769 −0.0714358
\(670\) 0 0
\(671\) 0.00844203 + 0.00128800i 0.000325901 + 4.97226e-5i
\(672\) 0 0
\(673\) 25.0036 + 29.6712i 0.963818 + 1.14374i 0.989567 + 0.144072i \(0.0460197\pi\)
−0.0257494 + 0.999668i \(0.508197\pi\)
\(674\) 0 0
\(675\) 2.83232 3.92954i 0.109016 0.151248i
\(676\) 0 0
\(677\) −1.21676 0.380129i −0.0467638 0.0146095i 0.274727 0.961522i \(-0.411413\pi\)
−0.321490 + 0.946913i \(0.604184\pi\)
\(678\) 0 0
\(679\) 8.52046 8.04993i 0.326985 0.308928i
\(680\) 0 0
\(681\) 0.389430 2.92239i 0.0149230 0.111986i
\(682\) 0 0
\(683\) 13.5056 + 22.0860i 0.516776 + 0.845096i 0.999530 0.0306599i \(-0.00976089\pi\)
−0.482754 + 0.875756i \(0.660363\pi\)
\(684\) 0 0
\(685\) −6.21590 + 9.35057i −0.237497 + 0.357267i
\(686\) 0 0
\(687\) 1.97667 + 0.456789i 0.0754148 + 0.0174276i
\(688\) 0 0
\(689\) −5.17213 + 5.27095i −0.197043 + 0.200807i
\(690\) 0 0
\(691\) −6.11891 28.9669i −0.232774 1.10195i −0.924910 0.380185i \(-0.875860\pi\)
0.692136 0.721767i \(-0.256670\pi\)
\(692\) 0 0
\(693\) 0.0139073 0.0808590i 0.000528293 0.00307158i
\(694\) 0 0
\(695\) 8.67752 + 4.23683i 0.329157 + 0.160712i
\(696\) 0 0
\(697\) 0.205914 0.974795i 0.00779955 0.0369230i
\(698\) 0 0
\(699\) −8.84062 + 1.69338i −0.334383 + 0.0640494i
\(700\) 0 0
\(701\) −12.5728 + 8.70542i −0.474868 + 0.328799i −0.782440 0.622725i \(-0.786025\pi\)
0.307573 + 0.951525i \(0.400483\pi\)
\(702\) 0 0
\(703\) 36.6383 2.77886i 1.38184 0.104807i
\(704\) 0 0
\(705\) 11.1731 3.49062i 0.420805 0.131464i
\(706\) 0 0
\(707\) −0.279390 + 0.957606i −0.0105075 + 0.0360145i
\(708\) 0 0
\(709\) 23.3386 9.28129i 0.876498 0.348566i 0.112397 0.993663i \(-0.464147\pi\)
0.764100 + 0.645097i \(0.223183\pi\)
\(710\) 0 0
\(711\) 41.9057 + 14.8545i 1.57159 + 0.557086i
\(712\) 0 0
\(713\) −18.2280 43.4239i −0.682643 1.62624i
\(714\) 0 0
\(715\) −0.0188365 + 0.0750112i −0.000704445 + 0.00280526i
\(716\) 0 0
\(717\) 0.660477 + 1.98157i 0.0246660 + 0.0740031i
\(718\) 0 0
\(719\) −4.50640 + 4.95435i −0.168060 + 0.184766i −0.817997 0.575222i \(-0.804916\pi\)
0.649937 + 0.759988i \(0.274795\pi\)
\(720\) 0 0
\(721\) 1.39177 + 1.04373i 0.0518322 + 0.0388707i
\(722\) 0 0
\(723\) 2.80074 + 0.319402i 0.104160 + 0.0118787i
\(724\) 0 0
\(725\) −1.53035 0.608588i −0.0568356 0.0226024i
\(726\) 0 0
\(727\) −6.10499 9.18372i −0.226422 0.340605i 0.701972 0.712205i \(-0.252303\pi\)
−0.928393 + 0.371600i \(0.878809\pi\)
\(728\) 0 0
\(729\) −7.58557 9.72594i −0.280947 0.360220i
\(730\) 0 0
\(731\) 29.1604 21.8684i 1.07854 0.808832i
\(732\) 0 0
\(733\) 8.25612 5.26583i 0.304947 0.194498i −0.376403 0.926456i \(-0.622839\pi\)
0.681350 + 0.731958i \(0.261393\pi\)
\(734\) 0 0
\(735\) −3.26330 + 3.87248i −0.120369 + 0.142839i
\(736\) 0 0
\(737\) −0.00606219 0.106659i −0.000223304 0.00392885i
\(738\) 0 0
\(739\) 2.25248 + 23.7328i 0.0828587 + 0.873026i 0.936152 + 0.351595i \(0.114361\pi\)
−0.853293 + 0.521431i \(0.825398\pi\)
\(740\) 0 0
\(741\) −3.01603 + 5.37954i −0.110797 + 0.197622i
\(742\) 0 0
\(743\) −10.2220 + 30.6681i −0.375008 + 1.12510i 0.576399 + 0.817168i \(0.304457\pi\)
−0.951407 + 0.307935i \(0.900362\pi\)
\(744\) 0 0
\(745\) −4.40747 33.0749i −0.161477 1.21177i
\(746\) 0 0
\(747\) −10.4242 0.394751i −0.381402 0.0144432i
\(748\) 0 0
\(749\) −12.8290 8.88280i −0.468760 0.324570i
\(750\) 0 0
\(751\) 1.26310 0.342719i 0.0460910 0.0125060i −0.238744 0.971082i \(-0.576736\pi\)
0.284835 + 0.958576i \(0.408061\pi\)
\(752\) 0 0
\(753\) 7.31035 0.833688i 0.266404 0.0303813i
\(754\) 0 0
\(755\) 3.41571 9.08618i 0.124310 0.330680i
\(756\) 0 0
\(757\) −12.1114 + 19.8060i −0.440195 + 0.719861i −0.993588 0.113059i \(-0.963935\pi\)
0.553393 + 0.832920i \(0.313333\pi\)
\(758\) 0 0
\(759\) 0.0457228 + 0.0431979i 0.00165963 + 0.00156798i
\(760\) 0 0
\(761\) −17.6791 + 0.669481i −0.640865 + 0.0242687i −0.356276 0.934381i \(-0.615954\pi\)
−0.284589 + 0.958649i \(0.591857\pi\)
\(762\) 0 0
\(763\) −12.6571 24.7251i −0.458217 0.895109i
\(764\) 0 0
\(765\) −18.5257 3.54850i −0.669798 0.128296i
\(766\) 0 0
\(767\) 13.2374 6.46323i 0.477977 0.233374i
\(768\) 0 0
\(769\) −30.7385 + 10.8960i −1.10846 + 0.392919i −0.824469 0.565908i \(-0.808526\pi\)
−0.283990 + 0.958827i \(0.591658\pi\)
\(770\) 0 0
\(771\) −0.0373617 + 1.97393i −0.00134555 + 0.0710895i
\(772\) 0 0
\(773\) 27.3958 + 2.07786i 0.985358 + 0.0747354i 0.558431 0.829551i \(-0.311404\pi\)
0.426927 + 0.904286i \(0.359596\pi\)
\(774\) 0 0
\(775\) 0.259750 + 13.7234i 0.00933048 + 0.492959i
\(776\) 0 0
\(777\) 2.17648 4.25166i 0.0780806 0.152528i
\(778\) 0 0
\(779\) 1.53801 0.234653i 0.0551048 0.00840731i
\(780\) 0 0
\(781\) −0.0606008 0.0530610i −0.00216847 0.00189867i
\(782\) 0 0
\(783\) 2.00970 2.57677i 0.0718210 0.0920862i
\(784\) 0 0
\(785\) −15.5051 + 33.3423i −0.553401 + 1.19004i
\(786\) 0 0
\(787\) −8.94723 23.8007i −0.318934 0.848403i −0.993873 0.110529i \(-0.964746\pi\)
0.674939 0.737874i \(-0.264170\pi\)
\(788\) 0 0
\(789\) 0.0122370 0.215301i 0.000435649 0.00766490i
\(790\) 0 0
\(791\) 22.1896 5.12780i 0.788973 0.182323i
\(792\) 0 0
\(793\) 0.659367 0.386252i 0.0234148 0.0137162i
\(794\) 0 0
\(795\) −0.363889 + 3.83406i −0.0129058 + 0.135980i
\(796\) 0