Properties

Label 1050.2.bc.h.607.1
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.1
Root \(0.792206 + 1.03242i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.h.493.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-2.15951 + 1.52856i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-2.15951 + 1.52856i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.883028 + 1.52945i) q^{11} +(0.258819 + 0.965926i) q^{12} +(2.71395 + 2.71395i) q^{13} +(1.69031 - 2.03540i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.14529 + 0.574830i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-0.886994 + 1.53632i) q^{19} +(-0.917556 - 2.48155i) q^{21} +(-1.24879 - 1.24879i) q^{22} +(-1.04741 - 3.90900i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.32389 - 1.91905i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.10591 + 2.40353i) q^{28} -3.84628i q^{29} +(-8.94554 + 5.16471i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.70588 + 0.457089i) q^{33} -2.22097 q^{34} -1.00000 q^{36} +(-3.21516 + 0.861499i) q^{37} +(0.459142 - 1.71354i) q^{38} +(-3.32389 + 1.91905i) q^{39} +11.8993i q^{41} +(1.52856 + 2.15951i) q^{42} +(-3.46335 + 3.46335i) q^{43} +(1.52945 + 0.883028i) q^{44} +(2.02344 + 3.50471i) q^{46} +(-1.59118 - 5.93837i) q^{47} +(0.707107 + 0.707107i) q^{48} +(2.32699 - 6.60190i) q^{49} +(-1.11049 + 1.92342i) q^{51} +(3.70732 + 0.993373i) q^{52} +(0.396561 + 0.106258i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.446149 - 2.60786i) q^{56} +(-1.25440 - 1.25440i) q^{57} +(0.995491 + 3.71522i) q^{58} +(-5.18379 - 8.97859i) q^{59} +(-5.87936 - 3.39445i) q^{61} +(7.30401 - 7.30401i) q^{62} +(2.63447 - 0.244018i) q^{63} -1.00000i q^{64} +(1.52945 - 0.883028i) q^{66} +(-1.97702 + 7.37834i) q^{67} +(2.14529 - 0.574830i) q^{68} +4.04689 q^{69} -10.7193 q^{71} +(0.965926 - 0.258819i) q^{72} +(-2.75198 + 10.2705i) q^{73} +(2.88263 - 1.66429i) q^{74} +1.77399i q^{76} +(-4.24477 - 1.95310i) q^{77} +(2.71395 - 2.71395i) q^{78} +(10.9907 + 6.34546i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-3.07978 - 11.4939i) q^{82} +(-1.94227 - 1.94227i) q^{83} +(-2.03540 - 1.69031i) q^{84} +(2.44896 - 4.24172i) q^{86} +(3.71522 + 0.995491i) q^{87} +(-1.70588 - 0.457089i) q^{88} +(0.558127 - 0.966705i) q^{89} +(-10.0092 - 1.71236i) q^{91} +(-2.86158 - 2.86158i) q^{92} +(-2.67345 - 9.97746i) q^{93} +(3.07393 + 5.32419i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(-7.26720 + 7.26720i) q^{97} +(-0.539001 + 6.97922i) q^{98} -1.76606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 4q^{11} + 16q^{13} + 16q^{14} + 8q^{16} + 12q^{17} - 8q^{19} + 8q^{21} - 4q^{22} - 32q^{23} - 8q^{24} - 12q^{26} + 8q^{28} - 24q^{31} - 8q^{33} + 16q^{34} - 16q^{36} + 8q^{37} + 28q^{38} - 12q^{39} + 4q^{42} + 24q^{43} - 4q^{46} + 24q^{47} + 52q^{49} + 8q^{51} + 8q^{52} - 44q^{53} - 8q^{54} + 8q^{56} + 8q^{57} - 48q^{58} + 8q^{59} + 24q^{61} - 8q^{62} - 4q^{63} - 36q^{67} + 12q^{68} - 8q^{69} - 32q^{71} + 40q^{73} - 24q^{74} + 44q^{77} + 16q^{78} + 12q^{79} + 8q^{81} - 12q^{82} + 16q^{83} + 4q^{84} - 8q^{86} - 12q^{87} - 8q^{88} - 16q^{89} + 8q^{91} - 8q^{92} - 40q^{93} + 8q^{94} - 44q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) −2.15951 + 1.52856i −0.816219 + 0.577743i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) 0.883028 + 1.52945i 0.266243 + 0.461147i 0.967889 0.251380i \(-0.0808843\pi\)
−0.701645 + 0.712526i \(0.747551\pi\)
\(12\) 0.258819 + 0.965926i 0.0747146 + 0.278839i
\(13\) 2.71395 + 2.71395i 0.752713 + 0.752713i 0.974985 0.222272i \(-0.0713472\pi\)
−0.222272 + 0.974985i \(0.571347\pi\)
\(14\) 1.69031 2.03540i 0.451754 0.543984i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 2.14529 + 0.574830i 0.520310 + 0.139417i 0.509410 0.860524i \(-0.329864\pi\)
0.0109000 + 0.999941i \(0.496530\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) −0.886994 + 1.53632i −0.203490 + 0.352456i −0.949651 0.313311i \(-0.898562\pi\)
0.746160 + 0.665766i \(0.231895\pi\)
\(20\) 0 0
\(21\) −0.917556 2.48155i −0.200227 0.541519i
\(22\) −1.24879 1.24879i −0.266243 0.266243i
\(23\) −1.04741 3.90900i −0.218401 0.815082i −0.984942 0.172887i \(-0.944691\pi\)
0.766541 0.642195i \(-0.221976\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) −3.32389 1.91905i −0.651869 0.376356i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −1.10591 + 2.40353i −0.208998 + 0.454225i
\(29\) 3.84628i 0.714236i −0.934059 0.357118i \(-0.883759\pi\)
0.934059 0.357118i \(-0.116241\pi\)
\(30\) 0 0
\(31\) −8.94554 + 5.16471i −1.60667 + 0.927610i −0.616558 + 0.787310i \(0.711473\pi\)
−0.990109 + 0.140300i \(0.955193\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) −1.70588 + 0.457089i −0.296956 + 0.0795690i
\(34\) −2.22097 −0.380893
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −3.21516 + 0.861499i −0.528569 + 0.141630i −0.513227 0.858253i \(-0.671550\pi\)
−0.0153416 + 0.999882i \(0.504884\pi\)
\(38\) 0.459142 1.71354i 0.0744827 0.277973i
\(39\) −3.32389 + 1.91905i −0.532248 + 0.307294i
\(40\) 0 0
\(41\) 11.8993i 1.85836i 0.369622 + 0.929182i \(0.379487\pi\)
−0.369622 + 0.929182i \(0.620513\pi\)
\(42\) 1.52856 + 2.15951i 0.235862 + 0.333220i
\(43\) −3.46335 + 3.46335i −0.528155 + 0.528155i −0.920022 0.391867i \(-0.871829\pi\)
0.391867 + 0.920022i \(0.371829\pi\)
\(44\) 1.52945 + 0.883028i 0.230573 + 0.133122i
\(45\) 0 0
\(46\) 2.02344 + 3.50471i 0.298341 + 0.516741i
\(47\) −1.59118 5.93837i −0.232098 0.866200i −0.979436 0.201756i \(-0.935335\pi\)
0.747338 0.664444i \(-0.231332\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 2.32699 6.60190i 0.332427 0.943129i
\(50\) 0 0
\(51\) −1.11049 + 1.92342i −0.155499 + 0.269332i
\(52\) 3.70732 + 0.993373i 0.514113 + 0.137756i
\(53\) 0.396561 + 0.106258i 0.0544719 + 0.0145957i 0.285952 0.958244i \(-0.407690\pi\)
−0.231480 + 0.972840i \(0.574357\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 0.446149 2.60786i 0.0596191 0.348490i
\(57\) −1.25440 1.25440i −0.166149 0.166149i
\(58\) 0.995491 + 3.71522i 0.130714 + 0.487833i
\(59\) −5.18379 8.97859i −0.674872 1.16891i −0.976506 0.215489i \(-0.930865\pi\)
0.301634 0.953424i \(-0.402468\pi\)
\(60\) 0 0
\(61\) −5.87936 3.39445i −0.752775 0.434615i 0.0739204 0.997264i \(-0.476449\pi\)
−0.826696 + 0.562649i \(0.809782\pi\)
\(62\) 7.30401 7.30401i 0.927610 0.927610i
\(63\) 2.63447 0.244018i 0.331913 0.0307434i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 1.52945 0.883028i 0.188262 0.108693i
\(67\) −1.97702 + 7.37834i −0.241532 + 0.901408i 0.733563 + 0.679621i \(0.237856\pi\)
−0.975095 + 0.221787i \(0.928811\pi\)
\(68\) 2.14529 0.574830i 0.260155 0.0697083i
\(69\) 4.04689 0.487188
\(70\) 0 0
\(71\) −10.7193 −1.27214 −0.636072 0.771629i \(-0.719442\pi\)
−0.636072 + 0.771629i \(0.719442\pi\)
\(72\) 0.965926 0.258819i 0.113835 0.0305021i
\(73\) −2.75198 + 10.2705i −0.322095 + 1.20207i 0.595106 + 0.803647i \(0.297110\pi\)
−0.917200 + 0.398426i \(0.869556\pi\)
\(74\) 2.88263 1.66429i 0.335099 0.193470i
\(75\) 0 0
\(76\) 1.77399i 0.203490i
\(77\) −4.24477 1.95310i −0.483737 0.222577i
\(78\) 2.71395 2.71395i 0.307294 0.307294i
\(79\) 10.9907 + 6.34546i 1.23655 + 0.713920i 0.968386 0.249455i \(-0.0802515\pi\)
0.268159 + 0.963375i \(0.413585\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −3.07978 11.4939i −0.340104 1.26929i
\(83\) −1.94227 1.94227i −0.213191 0.213191i 0.592430 0.805622i \(-0.298169\pi\)
−0.805622 + 0.592430i \(0.798169\pi\)
\(84\) −2.03540 1.69031i −0.222081 0.184428i
\(85\) 0 0
\(86\) 2.44896 4.24172i 0.264078 0.457396i
\(87\) 3.71522 + 0.995491i 0.398314 + 0.106728i
\(88\) −1.70588 0.457089i −0.181847 0.0487259i
\(89\) 0.558127 0.966705i 0.0591614 0.102471i −0.834928 0.550359i \(-0.814491\pi\)
0.894089 + 0.447889i \(0.147824\pi\)
\(90\) 0 0
\(91\) −10.0092 1.71236i −1.04925 0.179504i
\(92\) −2.86158 2.86158i −0.298341 0.298341i
\(93\) −2.67345 9.97746i −0.277224 1.03461i
\(94\) 3.07393 + 5.32419i 0.317051 + 0.549149i
\(95\) 0 0
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) −7.26720 + 7.26720i −0.737872 + 0.737872i −0.972166 0.234293i \(-0.924722\pi\)
0.234293 + 0.972166i \(0.424722\pi\)
\(98\) −0.539001 + 6.97922i −0.0544473 + 0.705007i
\(99\) 1.76606i 0.177495i
\(100\) 0 0
\(101\) 15.8887 9.17333i 1.58098 0.912780i 0.586265 0.810119i \(-0.300598\pi\)
0.994716 0.102661i \(-0.0327358\pi\)
\(102\) 0.574830 2.14529i 0.0569166 0.212416i
\(103\) −8.80911 + 2.36040i −0.867988 + 0.232577i −0.665217 0.746650i \(-0.731661\pi\)
−0.202770 + 0.979226i \(0.564994\pi\)
\(104\) −3.83810 −0.376356
\(105\) 0 0
\(106\) −0.410550 −0.0398762
\(107\) −14.2519 + 3.81880i −1.37779 + 0.369177i −0.870317 0.492492i \(-0.836086\pi\)
−0.507471 + 0.861669i \(0.669419\pi\)
\(108\) 0.258819 0.965926i 0.0249049 0.0929463i
\(109\) −17.4494 + 10.0744i −1.67135 + 0.964955i −0.704467 + 0.709736i \(0.748814\pi\)
−0.966883 + 0.255218i \(0.917853\pi\)
\(110\) 0 0
\(111\) 3.32858i 0.315935i
\(112\) 0.244018 + 2.63447i 0.0230576 + 0.248934i
\(113\) 6.54677 6.54677i 0.615869 0.615869i −0.328600 0.944469i \(-0.606577\pi\)
0.944469 + 0.328600i \(0.106577\pi\)
\(114\) 1.53632 + 0.886994i 0.143889 + 0.0830746i
\(115\) 0 0
\(116\) −1.92314 3.33098i −0.178559 0.309273i
\(117\) −0.993373 3.70732i −0.0918374 0.342742i
\(118\) 7.33099 + 7.33099i 0.674872 + 0.674872i
\(119\) −5.51145 + 2.03786i −0.505234 + 0.186811i
\(120\) 0 0
\(121\) 3.94052 6.82518i 0.358229 0.620471i
\(122\) 6.55758 + 1.75710i 0.593695 + 0.159080i
\(123\) −11.4939 3.07978i −1.03637 0.277694i
\(124\) −5.16471 + 8.94554i −0.463805 + 0.803333i
\(125\) 0 0
\(126\) −2.48155 + 0.917556i −0.221074 + 0.0817424i
\(127\) −12.5444 12.5444i −1.11313 1.11313i −0.992724 0.120409i \(-0.961579\pi\)
−0.120409 0.992724i \(-0.538421\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −2.44896 4.24172i −0.215619 0.373462i
\(130\) 0 0
\(131\) 0.830756 + 0.479637i 0.0725835 + 0.0419061i 0.535853 0.844312i \(-0.319990\pi\)
−0.463269 + 0.886218i \(0.653324\pi\)
\(132\) −1.24879 + 1.24879i −0.108693 + 0.108693i
\(133\) −0.432886 4.67353i −0.0375359 0.405246i
\(134\) 7.63862i 0.659877i
\(135\) 0 0
\(136\) −1.92342 + 1.11049i −0.164932 + 0.0952233i
\(137\) −2.88499 + 10.7669i −0.246481 + 0.919880i 0.726152 + 0.687534i \(0.241307\pi\)
−0.972633 + 0.232346i \(0.925360\pi\)
\(138\) −3.90900 + 1.04741i −0.332756 + 0.0891616i
\(139\) 13.5695 1.15095 0.575477 0.817818i \(-0.304816\pi\)
0.575477 + 0.817818i \(0.304816\pi\)
\(140\) 0 0
\(141\) 6.14785 0.517742
\(142\) 10.3540 2.77435i 0.868891 0.232819i
\(143\) −1.75435 + 6.54733i −0.146706 + 0.547516i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 10.6328i 0.879979i
\(147\) 5.77468 + 3.95640i 0.476288 + 0.326318i
\(148\) −2.35366 + 2.35366i −0.193470 + 0.193470i
\(149\) −8.74565 5.04930i −0.716471 0.413655i 0.0969812 0.995286i \(-0.469081\pi\)
−0.813453 + 0.581631i \(0.802415\pi\)
\(150\) 0 0
\(151\) 7.15497 + 12.3928i 0.582263 + 1.00851i 0.995211 + 0.0977541i \(0.0311659\pi\)
−0.412948 + 0.910755i \(0.635501\pi\)
\(152\) −0.459142 1.71354i −0.0372413 0.138987i
\(153\) −1.57046 1.57046i −0.126964 0.126964i
\(154\) 4.60563 + 0.787924i 0.371133 + 0.0634927i
\(155\) 0 0
\(156\) −1.91905 + 3.32389i −0.153647 + 0.266124i
\(157\) 9.25683 + 2.48036i 0.738776 + 0.197954i 0.608534 0.793528i \(-0.291758\pi\)
0.130242 + 0.991482i \(0.458425\pi\)
\(158\) −12.2585 3.28465i −0.975233 0.261313i
\(159\) −0.205275 + 0.355547i −0.0162794 + 0.0281967i
\(160\) 0 0
\(161\) 8.23705 + 6.84049i 0.649170 + 0.539106i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) −3.06537 11.4401i −0.240098 0.896058i −0.975784 0.218736i \(-0.929807\pi\)
0.735686 0.677323i \(-0.236860\pi\)
\(164\) 5.94967 + 10.3051i 0.464591 + 0.804695i
\(165\) 0 0
\(166\) 2.37878 + 1.37339i 0.184629 + 0.106596i
\(167\) 6.95883 6.95883i 0.538490 0.538490i −0.384595 0.923085i \(-0.625659\pi\)
0.923085 + 0.384595i \(0.125659\pi\)
\(168\) 2.40353 + 1.10591i 0.185436 + 0.0853229i
\(169\) 1.73100i 0.133154i
\(170\) 0 0
\(171\) 1.53632 0.886994i 0.117485 0.0678301i
\(172\) −1.26767 + 4.73102i −0.0966592 + 0.360737i
\(173\) 8.37084 2.24296i 0.636423 0.170529i 0.0738403 0.997270i \(-0.476474\pi\)
0.562583 + 0.826741i \(0.309808\pi\)
\(174\) −3.84628 −0.291586
\(175\) 0 0
\(176\) 1.76606 0.133122
\(177\) 10.0143 2.68333i 0.752722 0.201691i
\(178\) −0.288908 + 1.07822i −0.0216546 + 0.0808160i
\(179\) −11.5646 + 6.67682i −0.864378 + 0.499049i −0.865476 0.500951i \(-0.832984\pi\)
0.00109809 + 0.999999i \(0.499650\pi\)
\(180\) 0 0
\(181\) 8.73922i 0.649581i 0.945786 + 0.324791i \(0.105294\pi\)
−0.945786 + 0.324791i \(0.894706\pi\)
\(182\) 10.1114 0.936566i 0.749505 0.0694229i
\(183\) 4.80048 4.80048i 0.354862 0.354862i
\(184\) 3.50471 + 2.02344i 0.258371 + 0.149170i
\(185\) 0 0
\(186\) 5.16471 + 8.94554i 0.378695 + 0.655919i
\(187\) 1.01518 + 3.78871i 0.0742374 + 0.277058i
\(188\) −4.34719 4.34719i −0.317051 0.317051i
\(189\) −0.446149 + 2.60786i −0.0324525 + 0.189694i
\(190\) 0 0
\(191\) 5.43796 9.41883i 0.393477 0.681523i −0.599428 0.800429i \(-0.704605\pi\)
0.992906 + 0.118906i \(0.0379386\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) 10.8195 + 2.89908i 0.778806 + 0.208680i 0.626258 0.779616i \(-0.284586\pi\)
0.152548 + 0.988296i \(0.451252\pi\)
\(194\) 5.13869 8.90047i 0.368936 0.639016i
\(195\) 0 0
\(196\) −1.28572 6.88091i −0.0918371 0.491494i
\(197\) 10.3775 + 10.3775i 0.739367 + 0.739367i 0.972456 0.233088i \(-0.0748831\pi\)
−0.233088 + 0.972456i \(0.574883\pi\)
\(198\) 0.457089 + 1.70588i 0.0324839 + 0.121232i
\(199\) 9.28152 + 16.0761i 0.657949 + 1.13960i 0.981146 + 0.193270i \(0.0619092\pi\)
−0.323197 + 0.946332i \(0.604757\pi\)
\(200\) 0 0
\(201\) −6.61524 3.81931i −0.466603 0.269394i
\(202\) −12.9730 + 12.9730i −0.912780 + 0.912780i
\(203\) 5.87928 + 8.30609i 0.412645 + 0.582973i
\(204\) 2.22097i 0.155499i
\(205\) 0 0
\(206\) 7.89804 4.55993i 0.550282 0.317706i
\(207\) −1.04741 + 3.90900i −0.0728002 + 0.271694i
\(208\) 3.70732 0.993373i 0.257056 0.0688780i
\(209\) −3.13296 −0.216712
\(210\) 0 0
\(211\) −0.453133 −0.0311950 −0.0155975 0.999878i \(-0.504965\pi\)
−0.0155975 + 0.999878i \(0.504965\pi\)
\(212\) 0.396561 0.106258i 0.0272359 0.00729784i
\(213\) 2.77435 10.3540i 0.190096 0.709446i
\(214\) 12.7779 7.37735i 0.873483 0.504305i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 11.4234 24.8271i 0.775473 1.68537i
\(218\) 14.2474 14.2474i 0.964955 0.964955i
\(219\) −9.20830 5.31641i −0.622239 0.359250i
\(220\) 0 0
\(221\) 4.26215 + 7.38226i 0.286703 + 0.496585i
\(222\) 0.861499 + 3.21516i 0.0578201 + 0.215787i
\(223\) 4.67260 + 4.67260i 0.312901 + 0.312901i 0.846032 0.533132i \(-0.178985\pi\)
−0.533132 + 0.846032i \(0.678985\pi\)
\(224\) −0.917556 2.48155i −0.0613068 0.165806i
\(225\) 0 0
\(226\) −4.62927 + 8.01813i −0.307934 + 0.533358i
\(227\) 16.0416 + 4.29835i 1.06472 + 0.285291i 0.748323 0.663335i \(-0.230860\pi\)
0.316399 + 0.948626i \(0.397526\pi\)
\(228\) −1.71354 0.459142i −0.113482 0.0304074i
\(229\) 6.77075 11.7273i 0.447423 0.774960i −0.550794 0.834641i \(-0.685675\pi\)
0.998217 + 0.0596810i \(0.0190084\pi\)
\(230\) 0 0
\(231\) 2.98518 3.59463i 0.196410 0.236510i
\(232\) 2.71973 + 2.71973i 0.178559 + 0.178559i
\(233\) −2.99668 11.1838i −0.196319 0.732672i −0.991922 0.126853i \(-0.959512\pi\)
0.795603 0.605819i \(-0.207154\pi\)
\(234\) 1.91905 + 3.32389i 0.125452 + 0.217290i
\(235\) 0 0
\(236\) −8.97859 5.18379i −0.584456 0.337436i
\(237\) −8.97383 + 8.97383i −0.582913 + 0.582913i
\(238\) 4.79621 3.39489i 0.310892 0.220058i
\(239\) 17.0264i 1.10135i 0.834721 + 0.550673i \(0.185629\pi\)
−0.834721 + 0.550673i \(0.814371\pi\)
\(240\) 0 0
\(241\) 16.3866 9.46081i 1.05555 0.609424i 0.131355 0.991335i \(-0.458067\pi\)
0.924199 + 0.381911i \(0.124734\pi\)
\(242\) −2.03976 + 7.61250i −0.131121 + 0.489350i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) −6.78891 −0.434615
\(245\) 0 0
\(246\) 11.8993 0.758674
\(247\) −6.57674 + 1.76223i −0.418468 + 0.112128i
\(248\) 2.67345 9.97746i 0.169764 0.633569i
\(249\) 2.37878 1.37339i 0.150749 0.0870350i
\(250\) 0 0
\(251\) 18.1527i 1.14579i 0.819629 + 0.572894i \(0.194179\pi\)
−0.819629 + 0.572894i \(0.805821\pi\)
\(252\) 2.15951 1.52856i 0.136037 0.0962904i
\(253\) 5.05372 5.05372i 0.317725 0.317725i
\(254\) 15.3637 + 8.87021i 0.964002 + 0.556567i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.22983 + 23.2500i 0.388606 + 1.45030i 0.832403 + 0.554170i \(0.186964\pi\)
−0.443797 + 0.896127i \(0.646369\pi\)
\(258\) 3.46335 + 3.46335i 0.215619 + 0.215619i
\(259\) 5.62632 6.77499i 0.349603 0.420978i
\(260\) 0 0
\(261\) −1.92314 + 3.33098i −0.119039 + 0.206182i
\(262\) −0.926588 0.248279i −0.0572448 0.0153387i
\(263\) 13.5576 + 3.63274i 0.835995 + 0.224004i 0.651328 0.758797i \(-0.274212\pi\)
0.184668 + 0.982801i \(0.440879\pi\)
\(264\) 0.883028 1.52945i 0.0543466 0.0941311i
\(265\) 0 0
\(266\) 1.62773 + 4.40224i 0.0998027 + 0.269919i
\(267\) 0.789311 + 0.789311i 0.0483051 + 0.0483051i
\(268\) 1.97702 + 7.37834i 0.120766 + 0.450704i
\(269\) 13.2762 + 22.9951i 0.809466 + 1.40204i 0.913234 + 0.407435i \(0.133577\pi\)
−0.103768 + 0.994602i \(0.533090\pi\)
\(270\) 0 0
\(271\) 10.3582 + 5.98031i 0.629216 + 0.363278i 0.780448 0.625220i \(-0.214991\pi\)
−0.151232 + 0.988498i \(0.548324\pi\)
\(272\) 1.57046 1.57046i 0.0952233 0.0952233i
\(273\) 4.24460 9.22499i 0.256895 0.558322i
\(274\) 11.1467i 0.673399i
\(275\) 0 0
\(276\) 3.50471 2.02344i 0.210959 0.121797i
\(277\) 0.611241 2.28118i 0.0367259 0.137063i −0.945129 0.326698i \(-0.894064\pi\)
0.981855 + 0.189635i \(0.0607306\pi\)
\(278\) −13.1072 + 3.51206i −0.786116 + 0.210639i
\(279\) 10.3294 0.618406
\(280\) 0 0
\(281\) −11.0306 −0.658033 −0.329017 0.944324i \(-0.606717\pi\)
−0.329017 + 0.944324i \(0.606717\pi\)
\(282\) −5.93837 + 1.59118i −0.353625 + 0.0947534i
\(283\) −6.05917 + 22.6131i −0.360180 + 1.34421i 0.513658 + 0.857995i \(0.328290\pi\)
−0.873838 + 0.486217i \(0.838377\pi\)
\(284\) −9.28317 + 5.35964i −0.550855 + 0.318036i
\(285\) 0 0
\(286\) 6.77830i 0.400809i
\(287\) −18.1889 25.6968i −1.07366 1.51683i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) −10.4506 6.03364i −0.614740 0.354920i
\(290\) 0 0
\(291\) −5.13869 8.90047i −0.301235 0.521755i
\(292\) 2.75198 + 10.2705i 0.161047 + 0.601037i
\(293\) −15.4837 15.4837i −0.904565 0.904565i 0.0912620 0.995827i \(-0.470910\pi\)
−0.995827 + 0.0912620i \(0.970910\pi\)
\(294\) −6.60190 2.32699i −0.385031 0.135713i
\(295\) 0 0
\(296\) 1.66429 2.88263i 0.0967348 0.167550i
\(297\) 1.70588 + 0.457089i 0.0989852 + 0.0265230i
\(298\) 9.75450 + 2.61371i 0.565063 + 0.151408i
\(299\) 7.76618 13.4514i 0.449130 0.777916i
\(300\) 0 0
\(301\) 2.18520 12.7731i 0.125953 0.736228i
\(302\) −10.1186 10.1186i −0.582263 0.582263i
\(303\) 4.74846 + 17.7215i 0.272792 + 1.01807i
\(304\) 0.886994 + 1.53632i 0.0508726 + 0.0881139i
\(305\) 0 0
\(306\) 1.92342 + 1.11049i 0.109954 + 0.0634822i
\(307\) 2.12149 2.12149i 0.121080 0.121080i −0.643971 0.765050i \(-0.722714\pi\)
0.765050 + 0.643971i \(0.222714\pi\)
\(308\) −4.65263 + 0.430950i −0.265108 + 0.0245557i
\(309\) 9.11987i 0.518811i
\(310\) 0 0
\(311\) 13.0082 7.51027i 0.737626 0.425868i −0.0835796 0.996501i \(-0.526635\pi\)
0.821205 + 0.570633i \(0.193302\pi\)
\(312\) 0.993373 3.70732i 0.0562387 0.209886i
\(313\) 12.8644 3.44701i 0.727139 0.194836i 0.123784 0.992309i \(-0.460497\pi\)
0.603355 + 0.797473i \(0.293830\pi\)
\(314\) −9.58338 −0.540821
\(315\) 0 0
\(316\) 12.6909 0.713920
\(317\) 13.4280 3.59802i 0.754192 0.202085i 0.138815 0.990318i \(-0.455671\pi\)
0.615377 + 0.788233i \(0.289004\pi\)
\(318\) 0.106258 0.396561i 0.00595867 0.0222380i
\(319\) 5.88269 3.39638i 0.329368 0.190160i
\(320\) 0 0
\(321\) 14.7547i 0.823527i
\(322\) −9.72682 4.47550i −0.542055 0.249410i
\(323\) −2.78598 + 2.78598i −0.155016 + 0.155016i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) 5.92183 + 10.2569i 0.327980 + 0.568078i
\(327\) −5.21491 19.4623i −0.288385 1.07627i
\(328\) −8.41410 8.41410i −0.464591 0.464591i
\(329\) 12.5133 + 10.3918i 0.689883 + 0.572916i
\(330\) 0 0
\(331\) 9.31631 16.1363i 0.512071 0.886932i −0.487832 0.872938i \(-0.662212\pi\)
0.999902 0.0139944i \(-0.00445470\pi\)
\(332\) −2.65318 0.710918i −0.145612 0.0390167i
\(333\) 3.21516 + 0.861499i 0.176190 + 0.0472099i
\(334\) −4.92063 + 8.52279i −0.269245 + 0.466346i
\(335\) 0 0
\(336\) −2.60786 0.446149i −0.142271 0.0243394i
\(337\) −9.63568 9.63568i −0.524889 0.524889i 0.394155 0.919044i \(-0.371037\pi\)
−0.919044 + 0.394155i \(0.871037\pi\)
\(338\) −0.448015 1.67202i −0.0243688 0.0909456i
\(339\) 4.62927 + 8.01813i 0.251427 + 0.435485i
\(340\) 0 0
\(341\) −15.7983 9.12117i −0.855528 0.493939i
\(342\) −1.25440 + 1.25440i −0.0678301 + 0.0678301i
\(343\) 5.06626 + 17.8138i 0.273552 + 0.961857i
\(344\) 4.89791i 0.264078i
\(345\) 0 0
\(346\) −7.50509 + 4.33306i −0.403476 + 0.232947i
\(347\) −9.02693 + 33.6890i −0.484591 + 1.80852i 0.0973042 + 0.995255i \(0.468978\pi\)
−0.581895 + 0.813264i \(0.697689\pi\)
\(348\) 3.71522 0.995491i 0.199157 0.0533639i
\(349\) 1.49727 0.0801469 0.0400735 0.999197i \(-0.487241\pi\)
0.0400735 + 0.999197i \(0.487241\pi\)
\(350\) 0 0
\(351\) 3.83810 0.204863
\(352\) −1.70588 + 0.457089i −0.0909237 + 0.0243629i
\(353\) 1.54431 5.76343i 0.0821951 0.306756i −0.912573 0.408913i \(-0.865908\pi\)
0.994768 + 0.102157i \(0.0325745\pi\)
\(354\) −8.97859 + 5.18379i −0.477207 + 0.275515i
\(355\) 0 0
\(356\) 1.11625i 0.0591614i
\(357\) −0.541957 5.85109i −0.0286834 0.309673i
\(358\) 9.44244 9.44244i 0.499049 0.499049i
\(359\) −14.9989 8.65964i −0.791613 0.457038i 0.0489170 0.998803i \(-0.484423\pi\)
−0.840530 + 0.541765i \(0.817756\pi\)
\(360\) 0 0
\(361\) 7.92648 + 13.7291i 0.417183 + 0.722583i
\(362\) −2.26188 8.44144i −0.118882 0.443672i
\(363\) 5.57274 + 5.57274i 0.292493 + 0.292493i
\(364\) −9.52443 + 3.52167i −0.499216 + 0.184586i
\(365\) 0 0
\(366\) −3.39445 + 5.87936i −0.177431 + 0.307319i
\(367\) −5.29802 1.41960i −0.276554 0.0741025i 0.117876 0.993028i \(-0.462391\pi\)
−0.394430 + 0.918926i \(0.629058\pi\)
\(368\) −3.90900 1.04741i −0.203770 0.0546001i
\(369\) 5.94967 10.3051i 0.309727 0.536464i
\(370\) 0 0
\(371\) −1.01880 + 0.376703i −0.0528935 + 0.0195574i
\(372\) −7.30401 7.30401i −0.378695 0.378695i
\(373\) −7.98224 29.7901i −0.413305 1.54247i −0.788207 0.615410i \(-0.788991\pi\)
0.374903 0.927064i \(-0.377676\pi\)
\(374\) −1.96118 3.39686i −0.101410 0.175648i
\(375\) 0 0
\(376\) 5.32419 + 3.07393i 0.274574 + 0.158526i
\(377\) 10.4386 10.4386i 0.537615 0.537615i
\(378\) −0.244018 2.63447i −0.0125509 0.135503i
\(379\) 12.9203i 0.663670i 0.943337 + 0.331835i \(0.107668\pi\)
−0.943337 + 0.331835i \(0.892332\pi\)
\(380\) 0 0
\(381\) 15.3637 8.87021i 0.787104 0.454435i
\(382\) −2.81490 + 10.5053i −0.144023 + 0.537500i
\(383\) 1.14948 0.308002i 0.0587356 0.0157382i −0.229332 0.973348i \(-0.573654\pi\)
0.288067 + 0.957610i \(0.406987\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −11.2012 −0.570126
\(387\) 4.73102 1.26767i 0.240491 0.0644394i
\(388\) −2.65998 + 9.92718i −0.135040 + 0.503976i
\(389\) 8.25213 4.76437i 0.418400 0.241563i −0.275993 0.961160i \(-0.589007\pi\)
0.694392 + 0.719597i \(0.255673\pi\)
\(390\) 0 0
\(391\) 8.98802i 0.454544i
\(392\) 3.02282 + 6.31368i 0.152675 + 0.318889i
\(393\) −0.678310 + 0.678310i −0.0342162 + 0.0342162i
\(394\) −12.7098 7.33801i −0.640311 0.369684i
\(395\) 0 0
\(396\) −0.883028 1.52945i −0.0443738 0.0768578i
\(397\) 7.38494 + 27.5610i 0.370639 + 1.38324i 0.859613 + 0.510946i \(0.170705\pi\)
−0.488974 + 0.872299i \(0.662629\pi\)
\(398\) −13.1260 13.1260i −0.657949 0.657949i
\(399\) 4.62632 + 0.791463i 0.231606 + 0.0396227i
\(400\) 0 0
\(401\) −19.6150 + 33.9741i −0.979526 + 1.69659i −0.315415 + 0.948954i \(0.602144\pi\)
−0.664111 + 0.747634i \(0.731190\pi\)
\(402\) 7.37834 + 1.97702i 0.367998 + 0.0986049i
\(403\) −38.2945 10.2610i −1.90758 0.511135i
\(404\) 9.17333 15.8887i 0.456390 0.790491i
\(405\) 0 0
\(406\) −7.82873 6.50140i −0.388533 0.322659i
\(407\) −4.15670 4.15670i −0.206040 0.206040i
\(408\) −0.574830 2.14529i −0.0284583 0.106208i
\(409\) −4.32912 7.49826i −0.214061 0.370765i 0.738920 0.673793i \(-0.235336\pi\)
−0.952982 + 0.303028i \(0.902003\pi\)
\(410\) 0 0
\(411\) −9.65336 5.57337i −0.476165 0.274914i
\(412\) −6.44872 + 6.44872i −0.317706 + 0.317706i
\(413\) 24.9188 + 11.4656i 1.22617 + 0.564187i
\(414\) 4.04689i 0.198894i
\(415\) 0 0
\(416\) −3.32389 + 1.91905i −0.162967 + 0.0940891i
\(417\) −3.51206 + 13.1072i −0.171986 + 0.641861i
\(418\) 3.02621 0.810871i 0.148017 0.0396610i
\(419\) −4.29623 −0.209884 −0.104942 0.994478i \(-0.533466\pi\)
−0.104942 + 0.994478i \(0.533466\pi\)
\(420\) 0 0
\(421\) −18.8346 −0.917945 −0.458972 0.888451i \(-0.651782\pi\)
−0.458972 + 0.888451i \(0.651782\pi\)
\(422\) 0.437693 0.117279i 0.0213066 0.00570907i
\(423\) −1.59118 + 5.93837i −0.0773659 + 0.288733i
\(424\) −0.355547 + 0.205275i −0.0172669 + 0.00996904i
\(425\) 0 0
\(426\) 10.7193i 0.519351i
\(427\) 17.8852 1.65662i 0.865525 0.0801693i
\(428\) −10.4332 + 10.4332i −0.504305 + 0.504305i
\(429\) −5.87018 3.38915i −0.283415 0.163630i
\(430\) 0 0
\(431\) −3.46231 5.99690i −0.166774 0.288860i 0.770510 0.637428i \(-0.220002\pi\)
−0.937284 + 0.348567i \(0.886668\pi\)
\(432\) −0.258819 0.965926i −0.0124524 0.0464731i
\(433\) 11.5154 + 11.5154i 0.553393 + 0.553393i 0.927419 0.374025i \(-0.122023\pi\)
−0.374025 + 0.927419i \(0.622023\pi\)
\(434\) −4.60846 + 26.9377i −0.221213 + 1.29305i
\(435\) 0 0
\(436\) −10.0744 + 17.4494i −0.482477 + 0.835675i
\(437\) 6.93451 + 1.85810i 0.331723 + 0.0888848i
\(438\) 10.2705 + 2.75198i 0.490745 + 0.131495i
\(439\) −9.11194 + 15.7823i −0.434889 + 0.753250i −0.997287 0.0736169i \(-0.976546\pi\)
0.562397 + 0.826867i \(0.309879\pi\)
\(440\) 0 0
\(441\) −5.31618 + 4.55392i −0.253152 + 0.216853i
\(442\) −6.02759 6.02759i −0.286703 0.286703i
\(443\) 8.49765 + 31.7136i 0.403735 + 1.50676i 0.806376 + 0.591403i \(0.201426\pi\)
−0.402641 + 0.915358i \(0.631908\pi\)
\(444\) −1.66429 2.88263i −0.0789837 0.136804i
\(445\) 0 0
\(446\) −5.72275 3.30403i −0.270980 0.156450i
\(447\) 7.14079 7.14079i 0.337748 0.337748i
\(448\) 1.52856 + 2.15951i 0.0722178 + 0.102027i
\(449\) 8.14032i 0.384165i 0.981379 + 0.192083i \(0.0615242\pi\)
−0.981379 + 0.192083i \(0.938476\pi\)
\(450\) 0 0
\(451\) −18.1994 + 10.5075i −0.856978 + 0.494777i
\(452\) 2.39629 8.94306i 0.112712 0.420646i
\(453\) −13.8223 + 3.70368i −0.649430 + 0.174014i
\(454\) −16.6075 −0.779430
\(455\) 0 0
\(456\) 1.77399 0.0830746
\(457\) 4.41041 1.18177i 0.206310 0.0552806i −0.154184 0.988042i \(-0.549275\pi\)
0.360494 + 0.932762i \(0.382608\pi\)
\(458\) −3.50480 + 13.0801i −0.163768 + 0.611192i
\(459\) 1.92342 1.11049i 0.0897774 0.0518330i
\(460\) 0 0
\(461\) 7.54894i 0.351589i −0.984427 0.175795i \(-0.943751\pi\)
0.984427 0.175795i \(-0.0562495\pi\)
\(462\) −1.95310 + 4.24477i −0.0908665 + 0.197485i
\(463\) 8.87647 8.87647i 0.412525 0.412525i −0.470092 0.882617i \(-0.655779\pi\)
0.882617 + 0.470092i \(0.155779\pi\)
\(464\) −3.33098 1.92314i −0.154637 0.0892796i
\(465\) 0 0
\(466\) 5.78914 + 10.0271i 0.268177 + 0.464495i
\(467\) −2.97858 11.1162i −0.137832 0.514397i −0.999970 0.00772331i \(-0.997542\pi\)
0.862138 0.506674i \(-0.169125\pi\)
\(468\) −2.71395 2.71395i −0.125452 0.125452i
\(469\) −7.00886 18.9556i −0.323639 0.875290i
\(470\) 0 0
\(471\) −4.79169 + 8.29945i −0.220789 + 0.382418i
\(472\) 10.0143 + 2.68333i 0.460946 + 0.123510i
\(473\) −8.35525 2.23878i −0.384175 0.102939i
\(474\) 6.34546 10.9907i 0.291457 0.504817i
\(475\) 0 0
\(476\) −3.75412 + 4.52057i −0.172070 + 0.207200i
\(477\) −0.290303 0.290303i −0.0132921 0.0132921i
\(478\) −4.40676 16.4462i −0.201560 0.752233i
\(479\) −6.17379 10.6933i −0.282088 0.488590i 0.689811 0.723989i \(-0.257694\pi\)
−0.971899 + 0.235399i \(0.924360\pi\)
\(480\) 0 0
\(481\) −11.0638 6.38770i −0.504467 0.291254i
\(482\) −13.3796 + 13.3796i −0.609424 + 0.609424i
\(483\) −8.73931 + 6.18593i −0.397652 + 0.281469i
\(484\) 7.88104i 0.358229i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 4.03414 15.0556i 0.182804 0.682235i −0.812286 0.583260i \(-0.801777\pi\)
0.995090 0.0989752i \(-0.0315565\pi\)
\(488\) 6.55758 1.75710i 0.296848 0.0795401i
\(489\) 11.8437 0.535589
\(490\) 0 0
\(491\) −2.67474 −0.120709 −0.0603547 0.998177i \(-0.519223\pi\)
−0.0603547 + 0.998177i \(0.519223\pi\)
\(492\) −11.4939 + 3.07978i −0.518184 + 0.138847i
\(493\) 2.21096 8.25140i 0.0995764 0.371624i
\(494\) 5.89654 3.40437i 0.265298 0.153170i
\(495\) 0 0
\(496\) 10.3294i 0.463805i
\(497\) 23.1484 16.3851i 1.03835 0.734972i
\(498\) −1.94227 + 1.94227i −0.0870350 + 0.0870350i
\(499\) 15.7413 + 9.08825i 0.704678 + 0.406846i 0.809087 0.587688i \(-0.199962\pi\)
−0.104410 + 0.994534i \(0.533295\pi\)
\(500\) 0 0
\(501\) 4.92063 + 8.52279i 0.219838 + 0.380770i
\(502\) −4.69827 17.5342i −0.209694 0.782588i
\(503\) −3.59630 3.59630i −0.160351 0.160351i 0.622371 0.782722i \(-0.286169\pi\)
−0.782722 + 0.622371i \(0.786169\pi\)
\(504\) −1.69031 + 2.03540i −0.0752923 + 0.0906640i
\(505\) 0 0
\(506\) −3.57352 + 6.18952i −0.158862 + 0.275158i
\(507\) −1.67202 0.448015i −0.0742568 0.0198971i
\(508\) −17.1359 4.59156i −0.760284 0.203718i
\(509\) −2.40629 + 4.16782i −0.106657 + 0.184735i −0.914414 0.404780i \(-0.867348\pi\)
0.807757 + 0.589516i \(0.200681\pi\)
\(510\) 0 0
\(511\) −9.75621 26.3859i −0.431589 1.16724i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0.459142 + 1.71354i 0.0202716 + 0.0756547i
\(514\) −12.0351 20.8454i −0.530846 0.919452i
\(515\) 0 0
\(516\) −4.24172 2.44896i −0.186731 0.107809i
\(517\) 7.67738 7.67738i 0.337651 0.337651i
\(518\) −3.68111 + 8.00034i −0.161739 + 0.351515i
\(519\) 8.66613i 0.380401i
\(520\) 0 0
\(521\) 4.61481 2.66436i 0.202178 0.116728i −0.395493 0.918469i \(-0.629426\pi\)
0.597671 + 0.801741i \(0.296093\pi\)
\(522\) 0.995491 3.71522i 0.0435714 0.162611i
\(523\) −5.91757 + 1.58561i −0.258757 + 0.0693338i −0.385866 0.922555i \(-0.626097\pi\)
0.127108 + 0.991889i \(0.459430\pi\)
\(524\) 0.959275 0.0419061
\(525\) 0 0
\(526\) −14.0358 −0.611991
\(527\) −22.1596 + 5.93766i −0.965289 + 0.258648i
\(528\) −0.457089 + 1.70588i −0.0198923 + 0.0742389i
\(529\) 5.73541 3.31134i 0.249366 0.143971i
\(530\) 0 0
\(531\) 10.3676i 0.449915i
\(532\) −2.71165 3.83095i −0.117565 0.166093i
\(533\) −32.2942 + 32.2942i −1.39881 + 1.39881i
\(534\) −0.966705 0.558127i −0.0418334 0.0241525i
\(535\) 0 0
\(536\) −3.81931 6.61524i −0.164969 0.285735i
\(537\) −3.45617 12.8986i −0.149145 0.556617i
\(538\) −18.7754 18.7754i −0.809466 0.809466i
\(539\) 12.1521 2.27065i 0.523427 0.0978040i
\(540\) 0 0
\(541\) 6.81239 11.7994i 0.292887 0.507296i −0.681604 0.731721i \(-0.738717\pi\)
0.974491 + 0.224426i \(0.0720506\pi\)
\(542\) −11.5531 3.09564i −0.496247 0.132969i
\(543\) −8.44144 2.26188i −0.362257 0.0970664i
\(544\) −1.11049 + 1.92342i −0.0476117 + 0.0824658i
\(545\) 0 0
\(546\) −1.71236 + 10.0092i −0.0732823 + 0.428356i
\(547\) 14.8290 + 14.8290i 0.634042 + 0.634042i 0.949079 0.315037i \(-0.102017\pi\)
−0.315037 + 0.949079i \(0.602017\pi\)
\(548\) 2.88499 + 10.7669i 0.123241 + 0.459940i
\(549\) 3.39445 + 5.87936i 0.144872 + 0.250925i
\(550\) 0 0
\(551\) 5.90911 + 3.41163i 0.251737 + 0.145340i
\(552\) −2.86158 + 2.86158i −0.121797 + 0.121797i
\(553\) −33.4339 + 3.09681i −1.42175 + 0.131690i
\(554\) 2.36165i 0.100337i
\(555\) 0 0
\(556\) 11.7516 6.78477i 0.498378 0.287738i
\(557\) −0.0103825 + 0.0387479i −0.000439920 + 0.00164180i −0.966145 0.257998i \(-0.916937\pi\)
0.965706 + 0.259640i \(0.0836039\pi\)
\(558\) −9.97746 + 2.67345i −0.422379 + 0.113176i
\(559\) −18.7987 −0.795099
\(560\) 0 0
\(561\) −3.92236 −0.165602
\(562\) 10.6548 2.85494i 0.449445 0.120428i
\(563\) −3.59929 + 13.4327i −0.151692 + 0.566122i 0.847674 + 0.530518i \(0.178002\pi\)
−0.999366 + 0.0356047i \(0.988664\pi\)
\(564\) 5.32419 3.07393i 0.224189 0.129436i
\(565\) 0 0
\(566\) 23.4108i 0.984031i
\(567\) −2.40353 1.10591i −0.100939 0.0464439i
\(568\) 7.57968 7.57968i 0.318036 0.318036i
\(569\) −17.1817 9.91984i −0.720293 0.415861i 0.0945677 0.995518i \(-0.469853\pi\)
−0.814860 + 0.579657i \(0.803186\pi\)
\(570\) 0 0
\(571\) 2.94454 + 5.10010i 0.123225 + 0.213432i 0.921038 0.389473i \(-0.127343\pi\)
−0.797813 + 0.602906i \(0.794010\pi\)
\(572\) 1.75435 + 6.54733i 0.0733532 + 0.273758i
\(573\) 7.69044 + 7.69044i 0.321273 + 0.321273i
\(574\) 24.2199 + 20.1135i 1.01092 + 0.839523i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −14.4051 3.85984i −0.599692 0.160687i −0.0538132 0.998551i \(-0.517138\pi\)
−0.545879 + 0.837864i \(0.683804\pi\)
\(578\) 11.6561 + 3.12324i 0.484830 + 0.129910i
\(579\) −5.60060 + 9.70052i −0.232753 + 0.403140i
\(580\) 0 0
\(581\) 7.16322 + 1.22547i 0.297180 + 0.0508411i
\(582\) 7.26720 + 7.26720i 0.301235 + 0.301235i
\(583\) 0.187658 + 0.700349i 0.00777200 + 0.0290055i
\(584\) −5.31641 9.20830i −0.219995 0.381042i
\(585\) 0 0
\(586\) 18.9635 + 10.9486i 0.783376 + 0.452282i
\(587\) −4.86057 + 4.86057i −0.200617 + 0.200617i −0.800264 0.599647i \(-0.795308\pi\)
0.599647 + 0.800264i \(0.295308\pi\)
\(588\) 6.97922 + 0.539001i 0.287818 + 0.0222280i
\(589\) 18.3243i 0.755039i
\(590\) 0 0
\(591\) −12.7098 + 7.33801i −0.522812 + 0.301846i
\(592\) −0.861499 + 3.21516i −0.0354074 + 0.132142i
\(593\) 20.4715 5.48532i 0.840664 0.225255i 0.187304 0.982302i \(-0.440025\pi\)
0.653361 + 0.757047i \(0.273359\pi\)
\(594\) −1.76606 −0.0724622
\(595\) 0 0
\(596\) −10.0986 −0.413655
\(597\) −17.9305 + 4.80447i −0.733847 + 0.196634i
\(598\) −4.02007 + 15.0031i −0.164393 + 0.613523i
\(599\) −10.0409 + 5.79712i −0.410260 + 0.236864i −0.690902 0.722949i \(-0.742786\pi\)
0.280641 + 0.959813i \(0.409453\pi\)
\(600\) 0 0
\(601\) 15.3561i 0.626387i 0.949689 + 0.313193i \(0.101399\pi\)
−0.949689 + 0.313193i \(0.898601\pi\)
\(602\) 1.19518 + 12.9034i 0.0487119 + 0.525904i
\(603\) 5.40132 5.40132i 0.219959 0.219959i
\(604\) 12.3928 + 7.15497i 0.504254 + 0.291131i
\(605\) 0 0
\(606\) −9.17333 15.8887i −0.372641 0.645433i
\(607\) −5.83734 21.7853i −0.236931 0.884237i −0.977269 0.212003i \(-0.932001\pi\)
0.740339 0.672234i \(-0.234665\pi\)
\(608\) −1.25440 1.25440i −0.0508726 0.0508726i
\(609\) −9.54474 + 3.52918i −0.386772 + 0.143009i
\(610\) 0 0
\(611\) 11.7980 20.4348i 0.477297 0.826703i
\(612\) −2.14529 0.574830i −0.0867183 0.0232361i
\(613\) −4.62200 1.23846i −0.186681 0.0500209i 0.164267 0.986416i \(-0.447474\pi\)
−0.350948 + 0.936395i \(0.614141\pi\)
\(614\) −1.50012 + 2.59828i −0.0605399 + 0.104858i
\(615\) 0 0
\(616\) 4.38256 1.62046i 0.176578 0.0652900i
\(617\) −17.3498 17.3498i −0.698475 0.698475i 0.265606 0.964082i \(-0.414428\pi\)
−0.964082 + 0.265606i \(0.914428\pi\)
\(618\) 2.36040 + 8.80911i 0.0949490 + 0.354355i
\(619\) −10.4801 18.1521i −0.421232 0.729596i 0.574828 0.818274i \(-0.305069\pi\)
−0.996060 + 0.0886786i \(0.971736\pi\)
\(620\) 0 0
\(621\) −3.50471 2.02344i −0.140639 0.0811980i
\(622\) −10.6211 + 10.6211i −0.425868 + 0.425868i
\(623\) 0.272387 + 2.94074i 0.0109129 + 0.117818i
\(624\) 3.83810i 0.153647i
\(625\) 0 0
\(626\) −11.5339 + 6.65911i −0.460988 + 0.266152i
\(627\) 0.810871 3.02621i 0.0323831 0.120855i
\(628\) 9.25683 2.48036i 0.369388 0.0989772i
\(629\) −7.39267 −0.294765
\(630\) 0 0
\(631\) −48.7823 −1.94199 −0.970996 0.239095i \(-0.923149\pi\)
−0.970996 + 0.239095i \(0.923149\pi\)
\(632\) −12.2585 + 3.28465i −0.487616 + 0.130656i
\(633\) 0.117279 0.437693i 0.00466144 0.0173967i
\(634\) −12.0392 + 6.95084i −0.478138 + 0.276053i
\(635\) 0 0
\(636\) 0.410550i 0.0162794i
\(637\) 24.2325 11.6019i 0.960128 0.459683i
\(638\) −4.80320 + 4.80320i −0.190160 + 0.190160i
\(639\) 9.28317 + 5.35964i 0.367237 + 0.212024i
\(640\) 0 0
\(641\) −6.03196 10.4477i −0.238248 0.412658i 0.721964 0.691931i \(-0.243240\pi\)
−0.960212 + 0.279273i \(0.909906\pi\)
\(642\) 3.81880 + 14.2519i 0.150716 + 0.562480i
\(643\) 15.5935 + 15.5935i 0.614947 + 0.614947i 0.944231 0.329284i \(-0.106807\pi\)
−0.329284 + 0.944231i \(0.606807\pi\)
\(644\) 10.5537 + 1.80551i 0.415875 + 0.0711472i
\(645\) 0 0
\(646\) 1.96999 3.41212i 0.0775082 0.134248i
\(647\) 6.33226 + 1.69672i 0.248947 + 0.0667051i 0.381135 0.924520i \(-0.375533\pi\)
−0.132188 + 0.991225i \(0.542200\pi\)
\(648\) −0.965926 0.258819i −0.0379452 0.0101674i
\(649\) 9.15487 15.8567i 0.359360 0.622430i
\(650\) 0 0
\(651\) 21.0245 + 17.4599i 0.824016 + 0.684308i
\(652\) −8.37474 8.37474i −0.327980 0.327980i
\(653\) 5.97625 + 22.3037i 0.233869 + 0.872811i 0.978655 + 0.205508i \(0.0658846\pi\)
−0.744787 + 0.667303i \(0.767449\pi\)
\(654\) 10.0744 + 17.4494i 0.393941 + 0.682326i
\(655\) 0 0
\(656\) 10.3051 + 5.94967i 0.402348 + 0.232296i
\(657\) 7.51854 7.51854i 0.293326 0.293326i
\(658\) −14.7765 6.79898i −0.576050 0.265052i
\(659\) 8.89429i 0.346472i 0.984880 + 0.173236i \(0.0554224\pi\)
−0.984880 + 0.173236i \(0.944578\pi\)
\(660\) 0 0
\(661\) 7.24046 4.18028i 0.281621 0.162594i −0.352536 0.935798i \(-0.614681\pi\)
0.634157 + 0.773204i \(0.281347\pi\)
\(662\) −4.82248 + 17.9977i −0.187431 + 0.699501i
\(663\) −8.23385 + 2.20625i −0.319776 + 0.0856837i
\(664\) 2.74678 0.106596
\(665\) 0 0
\(666\) −3.32858 −0.128980
\(667\) −15.0351 + 4.02864i −0.582161 + 0.155990i
\(668\) 2.54711 9.50594i 0.0985506 0.367796i
\(669\) −5.72275 + 3.30403i −0.221254 + 0.127741i
\(670\) 0 0
\(671\) 11.9896i 0.462853i
\(672\) 2.63447 0.244018i 0.101627 0.00941321i
\(673\) 11.1305 11.1305i 0.429048 0.429048i −0.459256 0.888304i \(-0.651884\pi\)
0.888304 + 0.459256i \(0.151884\pi\)
\(674\) 11.8013 + 6.81346i 0.454567 + 0.262444i
\(675\) 0 0
\(676\) 0.865499 + 1.49909i 0.0332884 + 0.0576572i
\(677\) −11.2360 41.9335i −0.431836 1.61163i −0.748526 0.663106i \(-0.769238\pi\)
0.316690 0.948529i \(-0.397429\pi\)
\(678\) −6.54677 6.54677i −0.251427 0.251427i
\(679\) 4.58524 26.8020i 0.175965 1.02857i
\(680\) 0 0
\(681\) −8.30377 + 14.3825i −0.318201 + 0.551140i
\(682\) 17.6208 + 4.72147i 0.674734 + 0.180794i
\(683\) −17.2742 4.62860i −0.660977 0.177108i −0.0872904 0.996183i \(-0.527821\pi\)
−0.573687 + 0.819075i \(0.694487\pi\)
\(684\) 0.886994 1.53632i 0.0339151 0.0587426i
\(685\) 0 0
\(686\) −9.50420 15.8956i −0.362872 0.606897i
\(687\) 9.57528 + 9.57528i 0.365320 + 0.365320i
\(688\) 1.26767 + 4.73102i 0.0483296 + 0.180368i
\(689\) 0.787866 + 1.36462i 0.0300153 + 0.0519880i
\(690\) 0 0
\(691\) 30.5564 + 17.6417i 1.16242 + 0.671123i 0.951883 0.306463i \(-0.0991456\pi\)
0.210537 + 0.977586i \(0.432479\pi\)
\(692\) 6.12788 6.12788i 0.232947 0.232947i
\(693\) 2.69953 + 3.81382i 0.102547 + 0.144875i
\(694\) 34.8774i 1.32393i
\(695\) 0 0
\(696\) −3.33098 + 1.92314i −0.126260 + 0.0728964i
\(697\) −6.84009 + 25.5276i −0.259087 + 0.966926i
\(698\) −1.44625 + 0.387522i −0.0547414 + 0.0146679i
\(699\) 11.5783 0.437930
\(700\) 0 0
\(701\) −14.9862 −0.566020 −0.283010 0.959117i \(-0.591333\pi\)
−0.283010 + 0.959117i \(0.591333\pi\)
\(702\) −3.70732 + 0.993373i −0.139924 + 0.0374924i
\(703\) 1.52829 5.70366i 0.0576405 0.215117i
\(704\) 1.52945 0.883028i 0.0576433 0.0332804i
\(705\) 0 0
\(706\) 5.96674i 0.224561i
\(707\) −20.2898 + 44.0968i −0.763075 + 1.65843i
\(708\) 7.33099 7.33099i 0.275515 0.275515i
\(709\) −7.19605 4.15464i −0.270253 0.156031i 0.358750 0.933434i \(-0.383203\pi\)
−0.629003 + 0.777403i \(0.716537\pi\)
\(710\) 0 0
\(711\) −6.34546 10.9907i −0.237973 0.412182i
\(712\) 0.288908 + 1.07822i 0.0108273 + 0.0404080i
\(713\) 29.5585 + 29.5585i 1.10697 + 1.10697i
\(714\) 2.03786 + 5.51145i 0.0762652 + 0.206261i
\(715\) 0 0
\(716\) −6.67682 + 11.5646i −0.249524 + 0.432189i
\(717\) −16.4462 4.40676i −0.614196 0.164573i
\(718\) 16.7291 + 4.48256i 0.624326 + 0.167288i
\(719\) −7.07678 + 12.2574i −0.263920 + 0.457122i −0.967280 0.253711i \(-0.918349\pi\)
0.703360 + 0.710833i \(0.251682\pi\)
\(720\) 0 0
\(721\) 15.4154 18.5626i 0.574099 0.691307i
\(722\) −11.2097 11.2097i −0.417183 0.417183i
\(723\) 4.89728 + 18.2769i 0.182132 + 0.679725i
\(724\) 4.36961 + 7.56839i 0.162395 + 0.281277i
\(725\) 0 0
\(726\) −6.82518 3.94052i −0.253306 0.146246i
\(727\) 19.9622 19.9622i 0.740357 0.740357i −0.232290 0.972647i \(-0.574622\pi\)
0.972647 + 0.232290i \(0.0746217\pi\)
\(728\) 8.28842 5.86678i 0.307189 0.217437i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −9.42073 + 5.43906i −0.348438 + 0.201171i
\(732\) 1.75710 6.55758i 0.0649442 0.242375i
\(733\) 44.8290 12.0119i 1.65580 0.443670i 0.694570 0.719425i \(-0.255595\pi\)
0.961228 + 0.275755i \(0.0889279\pi\)
\(734\) 5.48491 0.202452
\(735\) 0 0
\(736\) 4.04689 0.149170
\(737\) −13.0306 + 3.49153i −0.479987 + 0.128612i
\(738\) −3.07978 + 11.4939i −0.113368 + 0.423095i
\(739\) −15.1424 + 8.74246i −0.557022 + 0.321597i −0.751949 0.659221i \(-0.770886\pi\)
0.194927 + 0.980818i \(0.437553\pi\)
\(740\) 0 0
\(741\) 6.80874i 0.250125i
\(742\) 0.886588 0.627552i 0.0325477 0.0230382i
\(743\) 12.2427 12.2427i 0.449143 0.449143i −0.445927 0.895069i \(-0.647126\pi\)
0.895069 + 0.445927i \(0.147126\pi\)
\(744\) 8.94554 + 5.16471i 0.327960 + 0.189348i
\(745\) 0 0
\(746\) 15.4205 + 26.7091i 0.564585 + 0.977889i
\(747\) 0.710918 + 2.65318i 0.0260111 + 0.0970749i
\(748\) 2.77353 + 2.77353i 0.101410 + 0.101410i
\(749\) 24.9400 30.0317i 0.911287 1.09734i
\(750\) 0 0
\(751\) 12.4732 21.6042i 0.455154 0.788350i −0.543543 0.839381i \(-0.682917\pi\)
0.998697 + 0.0510312i \(0.0162508\pi\)
\(752\) −5.93837 1.59118i −0.216550 0.0580244i
\(753\) −17.5342 4.69827i −0.638981 0.171214i
\(754\) −7.38120 + 12.7846i −0.268808 + 0.465588i
\(755\) 0 0
\(756\) 0.917556 + 2.48155i 0.0333712 + 0.0902531i
\(757\) 32.4637 + 32.4637i 1.17991 + 1.17991i 0.979765 + 0.200149i \(0.0641427\pi\)
0.200149 + 0.979765i \(0.435857\pi\)
\(758\) −3.34401 12.4800i −0.121460 0.453295i
\(759\) 3.57352 + 6.18952i 0.129711 + 0.224665i
\(760\) 0 0
\(761\) 28.5750 + 16.4978i 1.03584 + 0.598045i 0.918653 0.395065i \(-0.129278\pi\)
0.117191 + 0.993109i \(0.462611\pi\)
\(762\) −12.5444 + 12.5444i −0.454435 + 0.454435i
\(763\) 22.2828 48.4284i 0.806693 1.75322i
\(764\) 10.8759i 0.393477i
\(765\) 0 0
\(766\) −1.03059 + 0.595014i −0.0372369 + 0.0214987i
\(767\) 10.2989 38.4359i 0.371871 1.38784i
\(768\) 0.965926 0.258819i 0.0348548 0.00933933i
\(769\) −10.0980 −0.364144 −0.182072 0.983285i \(-0.558280\pi\)
−0.182072 + 0.983285i \(0.558280\pi\)
\(770\) 0 0
\(771\) −24.0702 −0.866867
\(772\) 10.8195 2.89908i 0.389403 0.104340i
\(773\) 3.06094 11.4236i 0.110094 0.410878i −0.888779 0.458336i \(-0.848446\pi\)
0.998873 + 0.0474585i \(0.0151122\pi\)
\(774\) −4.24172 + 2.44896i −0.152465 + 0.0880259i
\(775\) 0 0
\(776\) 10.2774i 0.368936i
\(777\) 5.08794 + 7.18811i 0.182529 + 0.257872i
\(778\) −6.73784 + 6.73784i −0.241563 + 0.241563i
\(779\) −18.2812 10.5546i −0.654991 0.378159i
\(780\) 0 0
\(781\) −9.46543 16.3946i −0.338700 0.586645i