Properties

Label 1050.2.bc.g.943.4
Level $1050$
Weight $2$
Character 1050.943
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 943.4
Root \(0.792206 + 1.03242i\) of defining polynomial
Character \(\chi\) \(=\) 1050.943
Dual form 1050.2.bc.g.157.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.52856 + 2.15951i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.52856 + 2.15951i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(0.883028 + 1.52945i) q^{11} +(0.965926 - 0.258819i) q^{12} +(-2.71395 + 2.71395i) q^{13} +(-1.69031 + 2.03540i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.574830 - 2.14529i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(0.886994 - 1.53632i) q^{19} +(-0.917556 - 2.48155i) q^{21} +(-1.24879 + 1.24879i) q^{22} +(3.90900 - 1.04741i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.32389 - 1.91905i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.40353 - 1.10591i) q^{28} +3.84628i q^{29} +(-8.94554 + 5.16471i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.457089 - 1.70588i) q^{33} +2.22097 q^{34} -1.00000 q^{36} +(0.861499 + 3.21516i) q^{37} +(1.71354 + 0.459142i) q^{38} +(3.32389 - 1.91905i) q^{39} +11.8993i q^{41} +(2.15951 - 1.52856i) q^{42} +(-3.46335 - 3.46335i) q^{43} +(-1.52945 - 0.883028i) q^{44} +(2.02344 + 3.50471i) q^{46} +(-5.93837 + 1.59118i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-2.32699 + 6.60190i) q^{49} +(-1.11049 + 1.92342i) q^{51} +(0.993373 - 3.70732i) q^{52} +(-0.106258 + 0.396561i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.446149 - 2.60786i) q^{56} +(-1.25440 + 1.25440i) q^{57} +(-3.71522 + 0.995491i) q^{58} +(5.18379 + 8.97859i) q^{59} +(-5.87936 - 3.39445i) q^{61} +(-7.30401 - 7.30401i) q^{62} +(0.244018 + 2.63447i) q^{63} +1.00000i q^{64} +(1.52945 - 0.883028i) q^{66} +(7.37834 + 1.97702i) q^{67} +(0.574830 + 2.14529i) q^{68} -4.04689 q^{69} -10.7193 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-10.2705 - 2.75198i) q^{73} +(-2.88263 + 1.66429i) q^{74} +1.77399i q^{76} +(-1.95310 + 4.24477i) q^{77} +(2.71395 + 2.71395i) q^{78} +(-10.9907 - 6.34546i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-11.4939 + 3.07978i) q^{82} +(1.94227 - 1.94227i) q^{83} +(2.03540 + 1.69031i) q^{84} +(2.44896 - 4.24172i) q^{86} +(0.995491 - 3.71522i) q^{87} +(0.457089 - 1.70588i) q^{88} +(-0.558127 + 0.966705i) q^{89} +(-10.0092 - 1.71236i) q^{91} +(-2.86158 + 2.86158i) q^{92} +(9.97746 - 2.67345i) q^{93} +(-3.07393 - 5.32419i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(7.26720 + 7.26720i) q^{97} +(-6.97922 - 0.539001i) q^{98} +1.76606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + O(q^{10}) \) \( 16q + 4q^{7} + 4q^{11} - 16q^{13} - 16q^{14} + 8q^{16} - 12q^{17} + 8q^{19} + 8q^{21} - 4q^{22} + 40q^{23} + 8q^{24} - 12q^{26} + 4q^{28} - 24q^{31} - 4q^{33} - 16q^{34} - 16q^{36} + 8q^{37} + 20q^{38} + 12q^{39} - 8q^{42} + 24q^{43} - 4q^{46} - 52q^{49} + 8q^{51} - 8q^{52} + 28q^{53} + 8q^{54} + 8q^{56} + 8q^{57} + 12q^{58} - 8q^{59} + 24q^{61} + 8q^{62} + 4q^{63} + 84q^{67} - 12q^{68} + 8q^{69} - 32q^{71} - 16q^{73} + 24q^{74} - 44q^{77} + 16q^{78} - 12q^{79} + 8q^{81} - 36q^{82} - 16q^{83} - 4q^{84} - 8q^{86} - 48q^{87} + 4q^{88} + 16q^{89} + 8q^{91} - 8q^{92} + 32q^{93} - 8q^{94} + 44q^{97} - 24q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 + 0.965926i 0.183013 + 0.683013i
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 1.52856 + 2.15951i 0.577743 + 0.816219i
\(8\) −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 \(0.747551\pi\)
\(12\) 0.965926 0.258819i 0.278839 0.0747146i
\(13\) −2.71395 + 2.71395i −0.752713 + 0.752713i −0.974985 0.222272i \(-0.928653\pi\)
0.222272 + 0.974985i \(0.428653\pi\)
\(14\) −1.69031 + 2.03540i −0.451754 + 0.543984i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.574830 2.14529i 0.139417 0.520310i −0.860524 0.509410i \(-0.829864\pi\)
0.999941 0.0109000i \(-0.00346965\pi\)
\(18\) −0.258819 + 0.965926i −0.0610042 + 0.227671i
\(19\) 0.886994 1.53632i 0.203490 0.352456i −0.746160 0.665766i \(-0.768105\pi\)
0.949651 + 0.313311i \(0.101438\pi\)
\(20\) 0 0
\(21\) −0.917556 2.48155i −0.200227 0.541519i
\(22\) −1.24879 + 1.24879i −0.266243 + 0.266243i
\(23\) 3.90900 1.04741i 0.815082 0.218401i 0.172887 0.984942i \(-0.444691\pi\)
0.642195 + 0.766541i \(0.278024\pi\)
\(24\) 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
\(28\) −2.40353 1.10591i −0.454225 0.208998i
\(29\) 3.84628i 0.714236i 0.934059 + 0.357118i \(0.116241\pi\)
−0.934059 + 0.357118i \(0.883759\pi\)
\(30\) 0 0
\(31\) −8.94554 + 5.16471i −1.60667 + 0.927610i −0.616558 + 0.787310i \(0.711473\pi\)
−0.990109 + 0.140300i \(0.955193\pi\)
\(32\) 0.965926 + 0.258819i 0.170753 + 0.0457532i
\(33\) −0.457089 1.70588i −0.0795690 0.296956i
\(34\) 2.22097 0.380893
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 0.861499 + 3.21516i 0.141630 + 0.528569i 0.999882 + 0.0153416i \(0.00488357\pi\)
−0.858253 + 0.513227i \(0.828450\pi\)
\(38\) 1.71354 + 0.459142i 0.277973 + 0.0744827i
\(39\) 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 \(0.620513\pi\)
\(42\) 2.15951 1.52856i 0.333220 0.235862i
\(43\) −3.46335 3.46335i −0.528155 0.528155i 0.391867 0.920022i \(-0.371829\pi\)
−0.920022 + 0.391867i \(0.871829\pi\)
\(44\) −1.52945 0.883028i −0.230573 0.133122i
\(45\) 0 0
\(46\) 2.02344 + 3.50471i 0.298341 + 0.516741i
\(47\) −5.93837 + 1.59118i −0.866200 + 0.232098i −0.664444 0.747338i \(-0.731332\pi\)
−0.201756 + 0.979436i \(0.564665\pi\)
\(48\) −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
\(52\) 0.993373 3.70732i 0.137756 0.514113i
\(53\) −0.106258 + 0.396561i −0.0145957 + 0.0544719i −0.972840 0.231480i \(-0.925643\pi\)
0.958244 + 0.285952i \(0.0923098\pi\)
\(54\) 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
\(58\) −3.71522 + 0.995491i −0.487833 + 0.130714i
\(59\) 5.18379 + 8.97859i 0.674872 + 1.16891i 0.976506 + 0.215489i \(0.0691346\pi\)
−0.301634 + 0.953424i \(0.597532\pi\)
\(60\) 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
\(63\) 0.244018 + 2.63447i 0.0307434 + 0.331913i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 1.52945 0.883028i 0.188262 0.108693i
\(67\) 7.37834 + 1.97702i 0.901408 + 0.241532i 0.679621 0.733563i \(-0.262144\pi\)
0.221787 + 0.975095i \(0.428811\pi\)
\(68\) 0.574830 + 2.14529i 0.0697083 + 0.260155i
\(69\) −4.04689 −0.487188
\(70\) 0 0
\(71\) −10.7193 −1.27214 −0.636072 0.771629i \(-0.719442\pi\)
−0.636072 + 0.771629i \(0.719442\pi\)
\(72\) −0.258819 0.965926i −0.0305021 0.113835i
\(73\) −10.2705 2.75198i −1.20207 0.322095i −0.398426 0.917200i \(-0.630444\pi\)
−0.803647 + 0.595106i \(0.797110\pi\)
\(74\) −2.88263 + 1.66429i −0.335099 + 0.193470i
\(75\) 0 0
\(76\) 1.77399i 0.203490i
\(77\) −1.95310 + 4.24477i −0.222577 + 0.483737i
\(78\) 2.71395 + 2.71395i 0.307294 + 0.307294i
\(79\) −10.9907 6.34546i −1.23655 0.713920i −0.268159 0.963375i \(-0.586415\pi\)
−0.968386 + 0.249455i \(0.919749\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −11.4939 + 3.07978i −1.26929 + 0.340104i
\(83\) 1.94227 1.94227i 0.213191 0.213191i −0.592430 0.805622i \(-0.701831\pi\)
0.805622 + 0.592430i \(0.201831\pi\)
\(84\) 2.03540 + 1.69031i 0.222081 + 0.184428i
\(85\) 0 0
\(86\) 2.44896 4.24172i 0.264078 0.457396i
\(87\) 0.995491 3.71522i 0.106728 0.398314i
\(88\) 0.457089 1.70588i 0.0487259 0.181847i
\(89\) −0.558127 + 0.966705i −0.0591614 + 0.102471i −0.894089 0.447889i \(-0.852176\pi\)
0.834928 + 0.550359i \(0.185509\pi\)
\(90\) 0 0
\(91\) −10.0092 1.71236i −1.04925 0.179504i
\(92\) −2.86158 + 2.86158i −0.298341 + 0.298341i
\(93\) 9.97746 2.67345i 1.03461 0.277224i
\(94\) −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 \(-0.0752777\pi\)
−0.234293 + 0.972166i \(0.575278\pi\)
\(98\) −6.97922 0.539001i −0.705007 0.0544473i
\(99\) 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 \(-0.0327358\pi\)
\(102\) −2.14529 0.574830i −0.212416 0.0569166i
\(103\) −2.36040 8.80911i −0.232577 0.867988i −0.979226 0.202770i \(-0.935006\pi\)
0.746650 0.665217i \(-0.231661\pi\)
\(104\) 3.83810 0.376356
\(105\) 0 0
\(106\) −0.410550 −0.0398762
\(107\) 3.81880 + 14.2519i 0.369177 + 1.37779i 0.861669 + 0.507471i \(0.169419\pi\)
−0.492492 + 0.870317i \(0.663914\pi\)
\(108\) 0.965926 + 0.258819i 0.0929463 + 0.0249049i
\(109\) 17.4494 10.0744i 1.67135 0.964955i 0.704467 0.709736i \(-0.251186\pi\)
0.966883 0.255218i \(-0.0821474\pi\)
\(110\) 0 0
\(111\) 3.32858i 0.315935i
\(112\) 2.63447 0.244018i 0.248934 0.0230576i
\(113\) 6.54677 + 6.54677i 0.615869 + 0.615869i 0.944469 0.328600i \(-0.106577\pi\)
−0.328600 + 0.944469i \(0.606577\pi\)
\(114\) −1.53632 0.886994i −0.143889 0.0830746i
\(115\) 0 0
\(116\) −1.92314 3.33098i −0.178559 0.309273i
\(117\) −3.70732 + 0.993373i −0.342742 + 0.0918374i
\(118\) −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
\(122\) 1.75710 6.55758i 0.159080 0.593695i
\(123\) 3.07978 11.4939i 0.277694 1.03637i
\(124\) 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 −0.120409 + 0.992724i \(0.538421\pi\)
−0.992724 + 0.120409i \(0.961579\pi\)
\(128\) −0.965926 + 0.258819i −0.0853766 + 0.0228766i
\(129\) 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
\(133\) 4.67353 0.432886i 0.405246 0.0375359i
\(134\) 7.63862i 0.659877i
\(135\) 0 0
\(136\) −1.92342 + 1.11049i −0.164932 + 0.0952233i
\(137\) 10.7669 + 2.88499i 0.919880 + 0.246481i 0.687534 0.726152i \(-0.258693\pi\)
0.232346 + 0.972633i \(0.425360\pi\)
\(138\) −1.04741 3.90900i −0.0891616 0.332756i
\(139\) −13.5695 −1.15095 −0.575477 0.817818i \(-0.695184\pi\)
−0.575477 + 0.817818i \(0.695184\pi\)
\(140\) 0 0
\(141\) 6.14785 0.517742
\(142\) −2.77435 10.3540i −0.232819 0.868891i
\(143\) −6.54733 1.75435i −0.547516 0.146706i
\(144\) 0.866025 0.500000i 0.0721688 0.0416667i
\(145\) 0 0
\(146\) 10.6328i 0.879979i
\(147\) 3.95640 5.77468i 0.326318 0.476288i
\(148\) −2.35366 2.35366i −0.193470 0.193470i
\(149\) 8.74565 + 5.04930i 0.716471 + 0.413655i 0.813453 0.581631i \(-0.197585\pi\)
−0.0969812 + 0.995286i \(0.530919\pi\)
\(150\) 0 0
\(151\) 7.15497 + 12.3928i 0.582263 + 1.00851i 0.995211 + 0.0977541i \(0.0311659\pi\)
−0.412948 + 0.910755i \(0.635501\pi\)
\(152\) −1.71354 + 0.459142i −0.138987 + 0.0372413i
\(153\) 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
\(157\) 2.48036 9.25683i 0.197954 0.738776i −0.793528 0.608534i \(-0.791758\pi\)
0.991482 0.130242i \(-0.0415754\pi\)
\(158\) 3.28465 12.2585i 0.261313 0.975233i
\(159\) 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
\(163\) 11.4401 3.06537i 0.896058 0.240098i 0.218736 0.975784i \(-0.429807\pi\)
0.677323 + 0.735686i \(0.263140\pi\)
\(164\) −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 \(-0.374341\pi\)
−0.923085 + 0.384595i \(0.874341\pi\)
\(168\) −1.10591 + 2.40353i −0.0853229 + 0.185436i
\(169\) 1.73100i 0.133154i
\(170\) 0 0
\(171\) 1.53632 0.886994i 0.117485 0.0678301i
\(172\) 4.73102 + 1.26767i 0.360737 + 0.0966592i
\(173\) 2.24296 + 8.37084i 0.170529 + 0.636423i 0.997270 + 0.0738403i \(0.0235255\pi\)
−0.826741 + 0.562583i \(0.809808\pi\)
\(174\) 3.84628 0.291586
\(175\) 0 0
\(176\) 1.76606 0.133122
\(177\) −2.68333 10.0143i −0.201691 0.752722i
\(178\) −1.07822 0.288908i −0.0808160 0.0216546i
\(179\) 11.5646 6.67682i 0.864378 0.499049i −0.00109809 0.999999i \(-0.500350\pi\)
0.865476 + 0.500951i \(0.167016\pi\)
\(180\) 0 0
\(181\) 8.73922i 0.649581i 0.945786 + 0.324791i \(0.105294\pi\)
−0.945786 + 0.324791i \(0.894706\pi\)
\(182\) −0.936566 10.1114i −0.0694229 0.749505i
\(183\) 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
\(187\) 3.78871 1.01518i 0.277058 0.0742374i
\(188\) 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 \(0.0379386\pi\)
\(192\) 0.258819 0.965926i 0.0186787 0.0697097i
\(193\) −2.89908 + 10.8195i −0.208680 + 0.778806i 0.779616 + 0.626258i \(0.215414\pi\)
−0.988296 + 0.152548i \(0.951252\pi\)
\(194\) −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 −0.233088 0.972456i \(-0.574883\pi\)
0.972456 + 0.233088i \(0.0748831\pi\)
\(198\) −1.70588 + 0.457089i −0.121232 + 0.0324839i
\(199\) −9.28152 16.0761i −0.657949 1.13960i −0.981146 0.193270i \(-0.938091\pi\)
0.323197 0.946332i \(-0.395243\pi\)
\(200\) 0 0
\(201\) −6.61524 3.81931i −0.466603 0.269394i
\(202\) 12.9730 + 12.9730i 0.912780 + 0.912780i
\(203\) −8.30609 + 5.87928i −0.582973 + 0.412645i
\(204\) 2.22097i 0.155499i
\(205\) 0 0
\(206\) 7.89804 4.55993i 0.550282 0.317706i
\(207\) 3.90900 + 1.04741i 0.271694 + 0.0728002i
\(208\) 0.993373 + 3.70732i 0.0688780 + 0.257056i
\(209\) 3.13296 0.216712
\(210\) 0 0
\(211\) −0.453133 −0.0311950 −0.0155975 0.999878i \(-0.504965\pi\)
−0.0155975 + 0.999878i \(0.504965\pi\)
\(212\) −0.106258 0.396561i −0.00729784 0.0272359i
\(213\) 10.3540 + 2.77435i 0.709446 + 0.190096i
\(214\) −12.7779 + 7.37735i −0.873483 + 0.504305i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −24.8271 11.4234i −1.68537 0.775473i
\(218\) 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
\(222\) 3.21516 0.861499i 0.215787 0.0578201i
\(223\) −4.67260 + 4.67260i −0.312901 + 0.312901i −0.846032 0.533132i \(-0.821015\pi\)
0.533132 + 0.846032i \(0.321015\pi\)
\(224\) 0.917556 + 2.48155i 0.0613068 + 0.165806i
\(225\) 0 0
\(226\) −4.62927 + 8.01813i −0.307934 + 0.533358i
\(227\) 4.29835 16.0416i 0.285291 1.06472i −0.663335 0.748323i \(-0.730860\pi\)
0.948626 0.316399i \(-0.102474\pi\)
\(228\) 0.459142 1.71354i 0.0304074 0.113482i
\(229\) −6.77075 + 11.7273i −0.447423 + 0.774960i −0.998217 0.0596810i \(-0.980992\pi\)
0.550794 + 0.834641i \(0.314325\pi\)
\(230\) 0 0
\(231\) 2.98518 3.59463i 0.196410 0.236510i
\(232\) 2.71973 2.71973i 0.178559 0.178559i
\(233\) 11.1838 2.99668i 0.732672 0.196319i 0.126853 0.991922i \(-0.459512\pi\)
0.605819 + 0.795603i \(0.292846\pi\)
\(234\) −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
\(238\) 3.39489 + 4.79621i 0.220058 + 0.310892i
\(239\) 17.0264i 1.10135i −0.834721 0.550673i \(-0.814371\pi\)
0.834721 0.550673i \(-0.185629\pi\)
\(240\) 0 0
\(241\) 16.3866 9.46081i 1.05555 0.609424i 0.131355 0.991335i \(-0.458067\pi\)
0.924199 + 0.381911i \(0.124734\pi\)
\(242\) 7.61250 + 2.03976i 0.489350 + 0.131121i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 6.78891 0.434615
\(245\) 0 0
\(246\) 11.8993 0.758674
\(247\) 1.76223 + 6.57674i 0.112128 + 0.418468i
\(248\) 9.97746 + 2.67345i 0.633569 + 0.169764i
\(249\) −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 \(0.805821\pi\)
\(252\) −1.52856 2.15951i −0.0962904 0.136037i
\(253\) 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
\(257\) 23.2500 6.22983i 1.45030 0.388606i 0.554170 0.832403i \(-0.313036\pi\)
0.896127 + 0.443797i \(0.146369\pi\)
\(258\) −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
\(262\) −0.248279 + 0.926588i −0.0153387 + 0.0572448i
\(263\) −3.63274 + 13.5576i −0.224004 + 0.835995i 0.758797 + 0.651328i \(0.225788\pi\)
−0.982801 + 0.184668i \(0.940879\pi\)
\(264\) −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
\(268\) −7.37834 + 1.97702i −0.450704 + 0.120766i
\(269\) −13.2762 22.9951i −0.809466 1.40204i −0.913234 0.407435i \(-0.866423\pi\)
0.103768 0.994602i \(-0.466910\pi\)
\(270\) 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
\(273\) 9.22499 + 4.24460i 0.558322 + 0.256895i
\(274\) 11.1467i 0.673399i
\(275\) 0 0
\(276\) 3.50471 2.02344i 0.210959 0.121797i
\(277\) −2.28118 0.611241i −0.137063 0.0367259i 0.189635 0.981855i \(-0.439269\pi\)
−0.326698 + 0.945129i \(0.605936\pi\)
\(278\) −3.51206 13.1072i −0.210639 0.786116i
\(279\) −10.3294 −0.618406
\(280\) 0 0
\(281\) −11.0306 −0.658033 −0.329017 0.944324i \(-0.606717\pi\)
−0.329017 + 0.944324i \(0.606717\pi\)
\(282\) 1.59118 + 5.93837i 0.0947534 + 0.353625i
\(283\) −22.6131 6.05917i −1.34421 0.360180i −0.486217 0.873838i \(-0.661623\pi\)
−0.857995 + 0.513658i \(0.828290\pi\)
\(284\) 9.28317 5.35964i 0.550855 0.318036i
\(285\) 0 0
\(286\) 6.77830i 0.400809i
\(287\) −25.6968 + 18.1889i −1.51683 + 1.07366i
\(288\) 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
\(292\) 10.2705 2.75198i 0.601037 0.161047i
\(293\) 15.4837 15.4837i 0.904565 0.904565i −0.0912620 0.995827i \(-0.529090\pi\)
0.995827 + 0.0912620i \(0.0290901\pi\)
\(294\) 6.60190 + 2.32699i 0.385031 + 0.135713i
\(295\) 0 0
\(296\) 1.66429 2.88263i 0.0967348 0.167550i
\(297\) 0.457089 1.70588i 0.0265230 0.0989852i
\(298\) −2.61371 + 9.75450i −0.151408 + 0.565063i
\(299\) −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
\(303\) −17.7215 + 4.74846i −1.01807 + 0.272792i
\(304\) −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 \(-0.277286\pi\)
−0.765050 + 0.643971i \(0.777286\pi\)
\(308\) −0.430950 4.65263i −0.0245557 0.265108i
\(309\) 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 \(0.193302\pi\)
\(312\) −3.70732 0.993373i −0.209886 0.0562387i
\(313\) 3.44701 + 12.8644i 0.194836 + 0.727139i 0.992309 + 0.123784i \(0.0395031\pi\)
−0.797473 + 0.603355i \(0.793830\pi\)
\(314\) 9.58338 0.540821
\(315\) 0 0
\(316\) 12.6909 0.713920
\(317\) −3.59802 13.4280i −0.202085 0.754192i −0.990318 0.138815i \(-0.955671\pi\)
0.788233 0.615377i \(-0.210996\pi\)
\(318\) 0.396561 + 0.106258i 0.0222380 + 0.00595867i
\(319\) −5.88269 + 3.39638i −0.329368 + 0.190160i
\(320\) 0 0
\(321\) 14.7547i 0.823527i
\(322\) −4.47550 + 9.72682i −0.249410 + 0.542055i
\(323\) −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
\(327\) −19.4623 + 5.21491i −1.07627 + 0.288385i
\(328\) 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 \(-0.00445470\pi\)
\(332\) −0.710918 + 2.65318i −0.0390167 + 0.145612i
\(333\) −0.861499 + 3.21516i −0.0472099 + 0.176190i
\(334\) 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 −0.919044 0.394155i \(-0.871037\pi\)
0.394155 + 0.919044i \(0.371037\pi\)
\(338\) 1.67202 0.448015i 0.0909456 0.0243688i
\(339\) −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
\(343\) −17.8138 + 5.06626i −0.961857 + 0.273552i
\(344\) 4.89791i 0.264078i
\(345\) 0 0
\(346\) −7.50509 + 4.33306i −0.403476 + 0.232947i
\(347\) 33.6890 + 9.02693i 1.80852 + 0.484591i 0.995255 0.0973042i \(-0.0310220\pi\)
0.813264 + 0.581895i \(0.197689\pi\)
\(348\) 0.995491 + 3.71522i 0.0533639 + 0.199157i
\(349\) −1.49727 −0.0801469 −0.0400735 0.999197i \(-0.512759\pi\)
−0.0400735 + 0.999197i \(0.512759\pi\)
\(350\) 0 0
\(351\) 3.83810 0.204863
\(352\) 0.457089 + 1.70588i 0.0243629 + 0.0909237i
\(353\) 5.76343 + 1.54431i 0.306756 + 0.0821951i 0.408913 0.912573i \(-0.365908\pi\)
−0.102157 + 0.994768i \(0.532574\pi\)
\(354\) 8.97859 5.18379i 0.477207 0.275515i
\(355\) 0 0
\(356\) 1.11625i 0.0591614i
\(357\) −5.85109 + 0.541957i −0.309673 + 0.0286834i
\(358\) 9.44244 + 9.44244i 0.499049 + 0.499049i
\(359\) 14.9989 + 8.65964i 0.791613 + 0.457038i 0.840530 0.541765i \(-0.182244\pi\)
−0.0489170 + 0.998803i \(0.515577\pi\)
\(360\) 0 0
\(361\) 7.92648 + 13.7291i 0.417183 + 0.722583i
\(362\) −8.44144 + 2.26188i −0.443672 + 0.118882i
\(363\) −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
\(367\) −1.41960 + 5.29802i −0.0741025 + 0.276554i −0.993028 0.117876i \(-0.962391\pi\)
0.918926 + 0.394430i \(0.129058\pi\)
\(368\) 1.04741 3.90900i 0.0546001 0.203770i
\(369\) −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
\(373\) 29.7901 7.98224i 1.54247 0.413305i 0.615410 0.788207i \(-0.288991\pi\)
0.927064 + 0.374903i \(0.122324\pi\)
\(374\) 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
\(378\) 2.63447 0.244018i 0.135503 0.0125509i
\(379\) 12.9203i 0.663670i −0.943337 0.331835i \(-0.892332\pi\)
0.943337 0.331835i \(-0.107668\pi\)
\(380\) 0 0
\(381\) 15.3637 8.87021i 0.787104 0.454435i
\(382\) 10.5053 + 2.81490i 0.537500 + 0.144023i
\(383\) 0.308002 + 1.14948i 0.0157382 + 0.0587356i 0.973348 0.229332i \(-0.0736540\pi\)
−0.957610 + 0.288067i \(0.906987\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −11.2012 −0.570126
\(387\) −1.26767 4.73102i −0.0644394 0.240491i
\(388\) −9.92718 2.65998i −0.503976 0.135040i
\(389\) −8.25213 + 4.76437i −0.418400 + 0.241563i −0.694392 0.719597i \(-0.744327\pi\)
0.275993 + 0.961160i \(0.410993\pi\)
\(390\) 0 0
\(391\) 8.98802i 0.454544i
\(392\) 6.31368 3.02282i 0.318889 0.152675i
\(393\) −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
\(397\) 27.5610 7.38494i 1.38324 0.370639i 0.510946 0.859613i \(-0.329295\pi\)
0.872299 + 0.488974i \(0.162629\pi\)
\(398\) 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 \(0.731190\pi\)
\(402\) 1.97702 7.37834i 0.0986049 0.367998i
\(403\) 10.2610 38.2945i 0.511135 1.90758i
\(404\) −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
\(408\) 2.14529 0.574830i 0.106208 0.0284583i
\(409\) 4.32912 + 7.49826i 0.214061 + 0.370765i 0.952982 0.303028i \(-0.0979974\pi\)
−0.738920 + 0.673793i \(0.764664\pi\)
\(410\) 0 0
\(411\) −9.65336 5.57337i −0.476165 0.274914i
\(412\) 6.44872 + 6.44872i 0.317706 + 0.317706i
\(413\) −11.4656 + 24.9188i −0.564187 + 1.22617i
\(414\) 4.04689i 0.198894i
\(415\) 0 0
\(416\) −3.32389 + 1.91905i −0.162967 + 0.0940891i
\(417\) 13.1072 + 3.51206i 0.641861 + 0.171986i
\(418\) 0.810871 + 3.02621i 0.0396610 + 0.148017i
\(419\) 4.29623 0.209884 0.104942 0.994478i \(-0.466534\pi\)
0.104942 + 0.994478i \(0.466534\pi\)
\(420\) 0 0
\(421\) −18.8346 −0.917945 −0.458972 0.888451i \(-0.651782\pi\)
−0.458972 + 0.888451i \(0.651782\pi\)
\(422\) −0.117279 0.437693i −0.00570907 0.0213066i
\(423\) −5.93837 1.59118i −0.288733 0.0773659i
\(424\) 0.355547 0.205275i 0.0172669 0.00996904i
\(425\) 0 0
\(426\) 10.7193i 0.519351i
\(427\) −1.65662 17.8852i −0.0801693 0.865525i
\(428\) −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 \(0.886668\pi\)
\(432\) −0.965926 + 0.258819i −0.0464731 + 0.0124524i
\(433\) −11.5154 + 11.5154i −0.553393 + 0.553393i −0.927419 0.374025i \(-0.877977\pi\)
0.374025 + 0.927419i \(0.377977\pi\)
\(434\) 4.60846 26.9377i 0.221213 1.29305i
\(435\) 0 0
\(436\) −10.0744 + 17.4494i −0.482477 + 0.835675i
\(437\) 1.85810 6.93451i 0.0888848 0.331723i
\(438\) −2.75198 + 10.2705i −0.131495 + 0.490745i
\(439\) 9.11194 15.7823i 0.434889 0.753250i −0.562397 0.826867i \(-0.690121\pi\)
0.997287 + 0.0736169i \(0.0234542\pi\)
\(440\) 0 0
\(441\) −5.31618 + 4.55392i −0.253152 + 0.216853i
\(442\) −6.02759 + 6.02759i −0.286703 + 0.286703i
\(443\) −31.7136 + 8.49765i −1.50676 + 0.403735i −0.915358 0.402641i \(-0.868092\pi\)
−0.591403 + 0.806376i \(0.701426\pi\)
\(444\) 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
\(448\) −2.15951 + 1.52856i −0.102027 + 0.0722178i
\(449\) 8.14032i 0.384165i −0.981379 0.192083i \(-0.938476\pi\)
0.981379 0.192083i \(-0.0615242\pi\)
\(450\) 0 0
\(451\) −18.1994 + 10.5075i −0.856978 + 0.494777i
\(452\) −8.94306 2.39629i −0.420646 0.112712i
\(453\) −3.70368 13.8223i −0.174014 0.649430i
\(454\) 16.6075 0.779430
\(455\) 0 0
\(456\) 1.77399 0.0830746
\(457\) −1.18177 4.41041i −0.0552806 0.206310i 0.932762 0.360494i \(-0.117392\pi\)
−0.988042 + 0.154184i \(0.950725\pi\)
\(458\) −13.0801 3.50480i −0.611192 0.163768i
\(459\) −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 \(-0.0562495\pi\)
\(462\) 4.24477 + 1.95310i 0.197485 + 0.0908665i
\(463\) 8.87647 + 8.87647i 0.412525 + 0.412525i 0.882617 0.470092i \(-0.155779\pi\)
−0.470092 + 0.882617i \(0.655779\pi\)
\(464\) 3.33098 + 1.92314i 0.154637 + 0.0892796i
\(465\) 0 0
\(466\) 5.78914 + 10.0271i 0.268177 + 0.464495i
\(467\) −11.1162 + 2.97858i −0.514397 + 0.137832i −0.506674 0.862138i \(-0.669125\pi\)
−0.00772331 + 0.999970i \(0.502458\pi\)
\(468\) 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
\(472\) 2.68333 10.0143i 0.123510 0.460946i
\(473\) 2.23878 8.35525i 0.102939 0.384175i
\(474\) −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
\(478\) 16.4462 4.40676i 0.752233 0.201560i
\(479\) 6.17379 + 10.6933i 0.282088 + 0.488590i 0.971899 0.235399i \(-0.0756398\pi\)
−0.689811 + 0.723989i \(0.742306\pi\)
\(480\) 0 0
\(481\) −11.0638 6.38770i −0.504467 0.291254i
\(482\) 13.3796 + 13.3796i 0.609424 + 0.609424i
\(483\) −6.18593 8.73931i −0.281469 0.397652i
\(484\) 7.88104i 0.358229i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) −15.0556 4.03414i −0.682235 0.182804i −0.0989752 0.995090i \(-0.531556\pi\)
−0.583260 + 0.812286i \(0.698223\pi\)
\(488\) 1.75710 + 6.55758i 0.0795401 + 0.296848i
\(489\) −11.8437 −0.535589
\(490\) 0 0
\(491\) −2.67474 −0.120709 −0.0603547 0.998177i \(-0.519223\pi\)
−0.0603547 + 0.998177i \(0.519223\pi\)
\(492\) 3.07978 + 11.4939i 0.138847 + 0.518184i
\(493\) 8.25140 + 2.21096i 0.371624 + 0.0995764i
\(494\) −5.89654 + 3.40437i −0.265298 + 0.153170i
\(495\) 0 0
\(496\) 10.3294i 0.463805i
\(497\) −16.3851 23.1484i −0.734972 1.03835i
\(498\) −1.94227 1.94227i −0.0870350 0.0870350i
\(499\) −15.7413 9.08825i −0.704678 0.406846i 0.104410 0.994534i \(-0.466705\pi\)
−0.809087 + 0.587688i \(0.800038\pi\)
\(500\) 0 0
\(501\) 4.92063 + 8.52279i 0.219838 + 0.380770i
\(502\) −17.5342 + 4.69827i −0.782588 + 0.209694i
\(503\) 3.59630 3.59630i 0.160351 0.160351i −0.622371 0.782722i \(-0.713831\pi\)
0.782722 + 0.622371i \(0.213831\pi\)
\(504\) 1.69031 2.03540i 0.0752923 0.0906640i
\(505\) 0 0
\(506\) −3.57352 + 6.18952i −0.158862 + 0.275158i
\(507\) −0.448015 + 1.67202i −0.0198971 + 0.0742568i
\(508\) 4.59156 17.1359i 0.203718 0.760284i
\(509\) 2.40629 4.16782i 0.106657 0.184735i −0.807757 0.589516i \(-0.799319\pi\)
0.914414 + 0.404780i \(0.132652\pi\)
\(510\) 0 0
\(511\) −9.75621 26.3859i −0.431589 1.16724i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −1.71354 + 0.459142i −0.0756547 + 0.0202716i
\(514\) 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
\(518\) −8.00034 3.68111i −0.351515 0.161739i
\(519\) 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 \(0.296093\pi\)
\(522\) −3.71522 0.995491i −0.162611 0.0435714i
\(523\) −1.58561 5.91757i −0.0693338 0.258757i 0.922555 0.385866i \(-0.126097\pi\)
−0.991889 + 0.127108i \(0.959430\pi\)
\(524\) −0.959275 −0.0419061
\(525\) 0 0
\(526\) −14.0358 −0.611991
\(527\) 5.93766 + 22.1596i 0.258648 + 0.965289i
\(528\) −1.70588 0.457089i −0.0742389 0.0198923i
\(529\) −5.73541 + 3.31134i −0.249366 + 0.143971i
\(530\) 0 0
\(531\) 10.3676i 0.449915i
\(532\) −3.83095 + 2.71165i −0.166093 + 0.117565i
\(533\) −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
\(537\) −12.8986 + 3.45617i −0.556617 + 0.149145i
\(538\) 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 \(0.0720506\pi\)
\(542\) −3.09564 + 11.5531i −0.132969 + 0.496247i
\(543\) 2.26188 8.44144i 0.0970664 0.362257i
\(544\) 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 −0.315037 0.949079i \(-0.602017\pi\)
0.949079 + 0.315037i \(0.102017\pi\)
\(548\) −10.7669 + 2.88499i −0.459940 + 0.123241i
\(549\) −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
\(553\) −3.09681 33.4339i −0.131690 1.42175i
\(554\) 2.36165i 0.100337i
\(555\) 0 0
\(556\) 11.7516 6.78477i 0.498378 0.287738i
\(557\) 0.0387479 + 0.0103825i 0.00164180 + 0.000439920i 0.259640 0.965706i \(-0.416396\pi\)
−0.257998 + 0.966145i \(0.583063\pi\)
\(558\) −2.67345 9.97746i −0.113176 0.422379i
\(559\) 18.7987 0.795099
\(560\) 0 0
\(561\) −3.92236 −0.165602
\(562\) −2.85494 10.6548i −0.120428 0.449445i
\(563\) −13.4327 3.59929i −0.566122 0.151692i −0.0356047 0.999366i \(-0.511336\pi\)
−0.530518 + 0.847674i \(0.678002\pi\)
\(564\) −5.32419 + 3.07393i −0.224189 + 0.129436i
\(565\) 0 0
\(566\) 23.4108i 0.984031i
\(567\) −1.10591 + 2.40353i −0.0464439 + 0.100939i
\(568\) 7.57968 + 7.57968i 0.318036 + 0.318036i
\(569\) 17.1817 + 9.91984i 0.720293 + 0.415861i 0.814860 0.579657i \(-0.196814\pi\)
−0.0945677 + 0.995518i \(0.530147\pi\)
\(570\) 0 0
\(571\) 2.94454 + 5.10010i 0.123225 + 0.213432i 0.921038 0.389473i \(-0.127343\pi\)
−0.797813 + 0.602906i \(0.794010\pi\)
\(572\) 6.54733 1.75435i 0.273758 0.0733532i
\(573\) −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
\(577\) −3.85984 + 14.4051i −0.160687 + 0.599692i 0.837864 + 0.545879i \(0.183804\pi\)
−0.998551 + 0.0538132i \(0.982862\pi\)
\(578\) −3.12324 + 11.6561i −0.129910 + 0.484830i
\(579\) 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
\(583\) −0.700349 + 0.187658i −0.0290055 + 0.00777200i
\(584\) 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 \(-0.204692\pi\)
−0.599647 + 0.800264i \(0.704692\pi\)
\(588\) −0.539001 + 6.97922i −0.0222280 + 0.287818i
\(589\) 18.3243i 0.755039i
\(590\) 0 0
\(591\) −12.7098 + 7.33801i −0.522812 + 0.301846i
\(592\) 3.21516 + 0.861499i 0.132142 + 0.0354074i
\(593\) 5.48532 + 20.4715i 0.225255 + 0.840664i 0.982302 + 0.187304i \(0.0599748\pi\)
−0.757047 + 0.653361i \(0.773359\pi\)
\(594\) 1.76606 0.0724622
\(595\) 0 0
\(596\) −10.0986 −0.413655
\(597\) 4.80447 + 17.9305i 0.196634 + 0.733847i
\(598\) −15.0031 4.02007i −0.613523 0.164393i
\(599\) 10.0409 5.79712i 0.410260 0.236864i −0.280641 0.959813i \(-0.590547\pi\)
0.690902 + 0.722949i \(0.257214\pi\)
\(600\) 0 0
\(601\) 15.3561i 0.626387i 0.949689 + 0.313193i \(0.101399\pi\)
−0.949689 + 0.313193i \(0.898601\pi\)
\(602\) 12.9034 1.19518i 0.525904 0.0487119i
\(603\) 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
\(607\) −21.7853 + 5.83734i −0.884237 + 0.236931i −0.672234 0.740339i \(-0.734665\pi\)
−0.212003 + 0.977269i \(0.567999\pi\)
\(608\) 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
\(612\) −0.574830 + 2.14529i −0.0232361 + 0.0867183i
\(613\) 1.23846 4.62200i 0.0500209 0.186681i −0.936395 0.350948i \(-0.885859\pi\)
0.986416 + 0.164267i \(0.0525260\pi\)
\(614\) 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 −0.964082 0.265606i \(-0.914428\pi\)
0.265606 + 0.964082i \(0.414428\pi\)
\(618\) −8.80911 + 2.36040i −0.354355 + 0.0949490i
\(619\) 10.4801 + 18.1521i 0.421232 + 0.729596i 0.996060 0.0886786i \(-0.0282644\pi\)
−0.574828 + 0.818274i \(0.694931\pi\)
\(620\) 0 0
\(621\) −3.50471 2.02344i −0.140639 0.0811980i
\(622\) 10.6211 + 10.6211i 0.425868 + 0.425868i
\(623\) −2.94074 + 0.272387i −0.117818 + 0.0109129i
\(624\) 3.83810i 0.153647i
\(625\) 0 0
\(626\) −11.5339 + 6.65911i −0.460988 + 0.266152i
\(627\) −3.02621 0.810871i −0.120855 0.0323831i
\(628\) 2.48036 + 9.25683i 0.0989772 + 0.369388i
\(629\) 7.39267 0.294765
\(630\) 0 0
\(631\) −48.7823 −1.94199 −0.970996 0.239095i \(-0.923149\pi\)
−0.970996 + 0.239095i \(0.923149\pi\)
\(632\) 3.28465 + 12.2585i 0.130656 + 0.487616i
\(633\) 0.437693 + 0.117279i 0.0173967 + 0.00466144i
\(634\) 12.0392 6.95084i 0.478138 0.276053i
\(635\) 0 0
\(636\) 0.410550i 0.0162794i
\(637\) −11.6019 24.2325i −0.459683 0.960128i
\(638\) −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 \(0.909906\pi\)
\(642\) 14.2519 3.81880i 0.562480 0.150716i
\(643\) −15.5935 + 15.5935i −0.614947 + 0.614947i −0.944231 0.329284i \(-0.893193\pi\)
0.329284 + 0.944231i \(0.393193\pi\)
\(644\) −10.5537 1.80551i −0.415875 0.0711472i
\(645\) 0 0
\(646\) 1.96999 3.41212i 0.0775082 0.134248i
\(647\) 1.69672 6.33226i 0.0667051 0.248947i −0.924520 0.381135i \(-0.875533\pi\)
0.991225 + 0.132188i \(0.0422001\pi\)
\(648\) 0.258819 0.965926i 0.0101674 0.0379452i
\(649\) −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
\(653\) −22.3037 + 5.97625i −0.872811 + 0.233869i −0.667303 0.744787i \(-0.732551\pi\)
−0.205508 + 0.978655i \(0.565885\pi\)
\(654\) −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
\(658\) 6.79898 14.7765i 0.265052 0.576050i
\(659\) 8.89429i 0.346472i −0.984880 0.173236i \(-0.944578\pi\)
0.984880 0.173236i \(-0.0554224\pi\)
\(660\) 0 0
\(661\) 7.24046 4.18028i 0.281621 0.162594i −0.352536 0.935798i \(-0.614681\pi\)
0.634157 + 0.773204i \(0.281347\pi\)
\(662\) 17.9977 + 4.82248i 0.699501 + 0.187431i
\(663\) −2.20625 8.23385i −0.0856837 0.319776i
\(664\) −2.74678 −0.106596
\(665\) 0 0
\(666\) −3.32858 −0.128980
\(667\) 4.02864 + 15.0351i 0.155990 + 0.582161i
\(668\) 9.50594 + 2.54711i 0.367796 + 0.0985506i
\(669\) 5.72275 3.30403i 0.221254 0.127741i
\(670\) 0 0
\(671\) 11.9896i 0.462853i
\(672\) −0.244018 2.63447i −0.00941321 0.101627i
\(673\) 11.1305 + 11.1305i 0.429048 + 0.429048i 0.888304 0.459256i \(-0.151884\pi\)
−0.459256 + 0.888304i \(0.651884\pi\)
\(674\) −11.8013 6.81346i −0.454567 0.262444i
\(675\) 0 0
\(676\) 0.865499 + 1.49909i 0.0332884 + 0.0576572i
\(677\) −41.9335 + 11.2360i −1.61163 + 0.431836i −0.948529 0.316690i \(-0.897429\pi\)
−0.663106 + 0.748526i \(0.730762\pi\)
\(678\) 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
\(682\) 4.72147 17.6208i 0.180794 0.674734i
\(683\) 4.62860 17.2742i 0.177108 0.660977i −0.819075 0.573687i \(-0.805513\pi\)
0.996183 0.0872904i \(-0.0278208\pi\)
\(684\) −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
\(688\) −4.73102 + 1.26767i −0.180368 + 0.0483296i
\(689\) −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
\(693\) −3.81382 + 2.69953i −0.144875 + 0.102547i
\(694\) 34.8774i 1.32393i
\(695\) 0 0
\(696\) −3.33098 + 1.92314i −0.126260 + 0.0728964i
\(697\) 25.5276 + 6.84009i 0.966926 + 0.259087i
\(698\) −0.387522 1.44625i −0.0146679 0.0547414i
\(699\) −11.5783 −0.437930
\(700\) 0 0
\(701\) −14.9862 −0.566020 −0.283010 0.959117i \(-0.591333\pi\)
−0.283010 + 0.959117i \(0.591333\pi\)
\(702\) 0.993373 + 3.70732i 0.0374924 + 0.139924i
\(703\) 5.70366 + 1.52829i 0.215117 + 0.0576405i
\(704\) −1.52945 + 0.883028i −0.0576433 + 0.0332804i
\(705\) 0 0
\(706\) 5.96674i 0.224561i
\(707\) 44.0968 + 20.2898i 1.65843 + 0.763075i
\(708\) 7.33099 + 7.33099i 0.275515 + 0.275515i
\(709\) 7.19605 + 4.15464i 0.270253 + 0.156031i 0.629003 0.777403i \(-0.283463\pi\)
−0.358750 + 0.933434i \(0.616797\pi\)
\(710\) 0 0
\(711\) −6.34546 10.9907i −0.237973 0.412182i
\(712\) 1.07822 0.288908i 0.0404080 0.0108273i
\(713\) −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
\(717\) −4.40676 + 16.4462i −0.164573 + 0.614196i
\(718\) −4.48256 + 16.7291i −0.167288 + 0.624326i
\(719\) 7.07678 12.2574i 0.263920 0.457122i −0.703360 0.710833i \(-0.748318\pi\)
0.967280 + 0.253711i \(0.0816513\pi\)
\(720\) 0 0
\(721\) 15.4154 18.5626i 0.574099 0.691307i
\(722\) −11.2097 + 11.2097i −0.417183 + 0.417183i
\(723\) −18.2769 + 4.89728i −0.679725 + 0.182132i
\(724\) −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 \(-0.425378\pi\)
−0.972647 + 0.232290i \(0.925378\pi\)
\(728\) 5.86678 + 8.28842i 0.217437 + 0.307189i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −9.42073 + 5.43906i −0.348438 + 0.201171i
\(732\) −6.55758 1.75710i −0.242375 0.0649442i
\(733\) 12.0119 + 44.8290i 0.443670 + 1.65580i 0.719425 + 0.694570i \(0.244405\pi\)
−0.275755 + 0.961228i \(0.588928\pi\)
\(734\) −5.48491 −0.202452
\(735\) 0 0
\(736\) 4.04689 0.149170
\(737\) 3.49153 + 13.0306i 0.128612 + 0.479987i
\(738\) −11.4939 3.07978i −0.423095 0.113368i
\(739\) 15.1424 8.74246i 0.557022 0.321597i −0.194927 0.980818i \(-0.562447\pi\)
0.751949 + 0.659221i \(0.229114\pi\)
\(740\) 0 0
\(741\) 6.80874i 0.250125i
\(742\) −0.627552 0.886588i −0.0230382 0.0325477i
\(743\) 12.2427 + 12.2427i 0.449143 + 0.449143i 0.895069 0.445927i \(-0.147126\pi\)
−0.445927 + 0.895069i \(0.647126\pi\)
\(744\) −8.94554 5.16471i −0.327960 0.189348i
\(745\) 0 0
\(746\) 15.4205 + 26.7091i 0.564585 + 0.977889i
\(747\) 2.65318 0.710918i 0.0970749 0.0260111i
\(748\) −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 \(0.0162508\pi\)
\(752\) −1.59118 + 5.93837i −0.0580244 + 0.216550i
\(753\) 4.69827 17.5342i 0.171214 0.638981i
\(754\) 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 0.200149 0.979765i \(-0.435857\pi\)
0.979765 0.200149i \(-0.0641427\pi\)
\(758\) 12.4800 3.34401i 0.453295 0.121460i
\(759\) −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
\(763\) 48.4284 + 22.2828i 1.75322 + 0.806693i
\(764\) 10.8759i 0.393477i
\(765\) 0 0
\(766\) −1.03059 + 0.595014i −0.0372369 + 0.0214987i
\(767\) −38.4359 10.2989i −1.38784 0.371871i
\(768\) 0.258819 + 0.965926i 0.00933933 + 0.0348548i
\(769\) 10.0980 0.364144 0.182072 0.983285i \(-0.441720\pi\)
0.182072 + 0.983285i \(0.441720\pi\)
\(770\) 0 0
\(771\) −24.0702 −0.866867
\(772\) −2.89908 10.8195i −0.104340 0.389403i
\(773\) 11.4236 + 3.06094i 0.410878 + 0.110094i 0.458336 0.888779i \(-0.348446\pi\)
−0.0474585 + 0.998873i \(0.515112\pi\)
\(774\) 4.24172 2.44896i 0.152465 0.0880259i
\(775\) 0 0
\(776\) 10.2774i 0.368936i
\(777\) 7.18811 5.08794i 0.257872 0.182529i
\(778\) −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