Properties

Label 1050.2.bc.c.943.1
Level $1050$
Weight $2$
Character 1050.943
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 943.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1050.943
Dual form 1050.2.bc.c.157.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.19067 - 1.48356i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.19067 - 1.48356i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(0.366025 + 0.633975i) q^{11} +(0.965926 - 0.258819i) q^{12} +(-1.03528 + 1.03528i) q^{13} +(-0.866025 + 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.586988 - 2.19067i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-2.09808 + 3.63397i) q^{19} +(1.73205 + 2.00000i) q^{21} +(0.517638 - 0.517638i) q^{22} +(-3.60488 + 0.965926i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.26795 + 0.732051i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.63896 + 0.189469i) q^{28} +8.19615i q^{29} +(6.86603 - 3.96410i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.189469 - 0.707107i) q^{33} -2.26795 q^{34} -1.00000 q^{36} +(1.22474 + 4.57081i) q^{37} +(4.05317 + 1.08604i) q^{38} +(1.26795 - 0.732051i) q^{39} +2.46410i q^{41} +(1.48356 - 2.19067i) q^{42} +(0.138701 + 0.138701i) q^{43} +(-0.633975 - 0.366025i) q^{44} +(1.86603 + 3.23205i) q^{46} +(10.6252 - 2.84701i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.59808 + 6.50000i) q^{49} +(-1.13397 + 1.96410i) q^{51} +(0.378937 - 1.41421i) q^{52} +(-1.36345 + 5.08845i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(2.96713 - 2.96713i) q^{57} +(7.91688 - 2.12132i) q^{58} +(-0.267949 - 0.464102i) q^{59} +(10.5622 + 6.09808i) q^{61} +(-5.60609 - 5.60609i) q^{62} +(-1.15539 - 2.38014i) q^{63} +1.00000i q^{64} +(-0.633975 + 0.366025i) q^{66} +(3.86370 + 1.03528i) q^{67} +(0.586988 + 2.19067i) q^{68} +3.73205 q^{69} -12.8564 q^{71} +(0.258819 + 0.965926i) q^{72} +(7.72741 + 2.07055i) q^{73} +(4.09808 - 2.36603i) q^{74} -4.19615i q^{76} +(0.138701 - 1.93185i) q^{77} +(-1.03528 - 1.03528i) q^{78} +(7.03590 + 4.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.38014 - 0.637756i) q^{82} +(-8.24504 + 8.24504i) q^{83} +(-2.50000 - 0.866025i) q^{84} +(0.0980762 - 0.169873i) q^{86} +(2.12132 - 7.91688i) q^{87} +(-0.189469 + 0.707107i) q^{88} +(-3.23205 + 5.59808i) q^{89} +(3.80385 - 0.732051i) q^{91} +(2.63896 - 2.63896i) q^{92} +(-7.65806 + 2.05197i) q^{93} +(-5.50000 - 9.52628i) q^{94} +(0.866025 + 0.500000i) q^{96} +(4.94975 + 4.94975i) q^{97} +(5.60609 - 4.19187i) q^{98} +0.732051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 4q^{11} + 4q^{16} + 4q^{19} - 4q^{24} + 24q^{26} + 48q^{31} - 32q^{34} - 8q^{36} + 24q^{39} - 12q^{44} + 8q^{46} - 16q^{51} - 4q^{54} - 4q^{56} - 16q^{59} + 36q^{61} - 12q^{66} + 16q^{69} + 8q^{71} + 12q^{74} + 84q^{79} + 4q^{81} - 20q^{84} - 20q^{86} - 12q^{89} + 72q^{91} - 44q^{94} + O(q^{100}) \)

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
\(7\) −2.19067 1.48356i −0.827996 0.560734i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0 0
\(11\) 0.366025 + 0.633975i 0.110361 + 0.191151i 0.915916 0.401371i \(-0.131466\pi\)
−0.805555 + 0.592521i \(0.798133\pi\)
\(12\) 0.965926 0.258819i 0.278839 0.0747146i
\(13\) −1.03528 + 1.03528i −0.287134 + 0.287134i −0.835946 0.548812i \(-0.815080\pi\)
0.548812 + 0.835946i \(0.315080\pi\)
\(14\) −0.866025 + 2.50000i −0.231455 + 0.668153i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.586988 2.19067i 0.142366 0.531316i −0.857493 0.514496i \(-0.827979\pi\)
0.999859 0.0168199i \(-0.00535420\pi\)
\(18\) 0.258819 0.965926i 0.0610042 0.227671i
\(19\) −2.09808 + 3.63397i −0.481332 + 0.833691i −0.999770 0.0214238i \(-0.993180\pi\)
0.518439 + 0.855115i \(0.326513\pi\)
\(20\) 0 0
\(21\) 1.73205 + 2.00000i 0.377964 + 0.436436i
\(22\) 0.517638 0.517638i 0.110361 0.110361i
\(23\) −3.60488 + 0.965926i −0.751670 + 0.201409i −0.614259 0.789105i \(-0.710545\pi\)
−0.137411 + 0.990514i \(0.543878\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) 1.26795 + 0.732051i 0.248665 + 0.143567i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 2.63896 + 0.189469i 0.498716 + 0.0358062i
\(29\) 8.19615i 1.52199i 0.648759 + 0.760994i \(0.275288\pi\)
−0.648759 + 0.760994i \(0.724712\pi\)
\(30\) 0 0
\(31\) 6.86603 3.96410i 1.23317 0.711974i 0.265484 0.964115i \(-0.414468\pi\)
0.967690 + 0.252142i \(0.0811349\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) −0.189469 0.707107i −0.0329823 0.123091i
\(34\) −2.26795 −0.388950
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 1.22474 + 4.57081i 0.201347 + 0.751437i 0.990532 + 0.137281i \(0.0438364\pi\)
−0.789185 + 0.614155i \(0.789497\pi\)
\(38\) 4.05317 + 1.08604i 0.657511 + 0.176180i
\(39\) 1.26795 0.732051i 0.203034 0.117222i
\(40\) 0 0
\(41\) 2.46410i 0.384828i 0.981314 + 0.192414i \(0.0616316\pi\)
−0.981314 + 0.192414i \(0.938368\pi\)
\(42\) 1.48356 2.19067i 0.228919 0.338028i
\(43\) 0.138701 + 0.138701i 0.0211517 + 0.0211517i 0.717604 0.696452i \(-0.245239\pi\)
−0.696452 + 0.717604i \(0.745239\pi\)
\(44\) −0.633975 0.366025i −0.0955753 0.0551804i
\(45\) 0 0
\(46\) 1.86603 + 3.23205i 0.275130 + 0.476540i
\(47\) 10.6252 2.84701i 1.54984 0.415279i 0.620412 0.784276i \(-0.286965\pi\)
0.929431 + 0.368997i \(0.120299\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 2.59808 + 6.50000i 0.371154 + 0.928571i
\(50\) 0 0
\(51\) −1.13397 + 1.96410i −0.158788 + 0.275029i
\(52\) 0.378937 1.41421i 0.0525492 0.196116i
\(53\) −1.36345 + 5.08845i −0.187284 + 0.698952i 0.806846 + 0.590761i \(0.201172\pi\)
−0.994130 + 0.108191i \(0.965494\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 2.96713 2.96713i 0.393006 0.393006i
\(58\) 7.91688 2.12132i 1.03954 0.278543i
\(59\) −0.267949 0.464102i −0.0348840 0.0604209i 0.848056 0.529906i \(-0.177773\pi\)
−0.882940 + 0.469485i \(0.844440\pi\)
\(60\) 0 0
\(61\) 10.5622 + 6.09808i 1.35235 + 0.780779i 0.988578 0.150710i \(-0.0481560\pi\)
0.363770 + 0.931489i \(0.381489\pi\)
\(62\) −5.60609 5.60609i −0.711974 0.711974i
\(63\) −1.15539 2.38014i −0.145566 0.299869i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −0.633975 + 0.366025i −0.0780369 + 0.0450546i
\(67\) 3.86370 + 1.03528i 0.472026 + 0.126479i 0.486987 0.873409i \(-0.338096\pi\)
−0.0149610 + 0.999888i \(0.504762\pi\)
\(68\) 0.586988 + 2.19067i 0.0711828 + 0.265658i
\(69\) 3.73205 0.449286
\(70\) 0 0
\(71\) −12.8564 −1.52577 −0.762887 0.646531i \(-0.776219\pi\)
−0.762887 + 0.646531i \(0.776219\pi\)
\(72\) 0.258819 + 0.965926i 0.0305021 + 0.113835i
\(73\) 7.72741 + 2.07055i 0.904425 + 0.242340i 0.680915 0.732362i \(-0.261582\pi\)
0.223509 + 0.974702i \(0.428249\pi\)
\(74\) 4.09808 2.36603i 0.476392 0.275045i
\(75\) 0 0
\(76\) 4.19615i 0.481332i
\(77\) 0.138701 1.93185i 0.0158064 0.220155i
\(78\) −1.03528 1.03528i −0.117222 0.117222i
\(79\) 7.03590 + 4.06218i 0.791600 + 0.457031i 0.840526 0.541772i \(-0.182246\pi\)
−0.0489252 + 0.998802i \(0.515580\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 2.38014 0.637756i 0.262842 0.0704284i
\(83\) −8.24504 + 8.24504i −0.905011 + 0.905011i −0.995864 0.0908531i \(-0.971041\pi\)
0.0908531 + 0.995864i \(0.471041\pi\)
\(84\) −2.50000 0.866025i −0.272772 0.0944911i
\(85\) 0 0
\(86\) 0.0980762 0.169873i 0.0105758 0.0183179i
\(87\) 2.12132 7.91688i 0.227429 0.848778i
\(88\) −0.189469 + 0.707107i −0.0201974 + 0.0753778i
\(89\) −3.23205 + 5.59808i −0.342597 + 0.593395i −0.984914 0.173044i \(-0.944640\pi\)
0.642317 + 0.766439i \(0.277973\pi\)
\(90\) 0 0
\(91\) 3.80385 0.732051i 0.398752 0.0767398i
\(92\) 2.63896 2.63896i 0.275130 0.275130i
\(93\) −7.65806 + 2.05197i −0.794103 + 0.212779i
\(94\) −5.50000 9.52628i −0.567282 0.982561i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 4.94975 + 4.94975i 0.502571 + 0.502571i 0.912236 0.409665i \(-0.134354\pi\)
−0.409665 + 0.912236i \(0.634354\pi\)
\(98\) 5.60609 4.19187i 0.566300 0.423443i
\(99\) 0.732051i 0.0735739i
\(100\) 0 0
\(101\) −0.169873 + 0.0980762i −0.0169030 + 0.00975895i −0.508428 0.861105i \(-0.669773\pi\)
0.491525 + 0.870864i \(0.336440\pi\)
\(102\) 2.19067 + 0.586988i 0.216909 + 0.0581205i
\(103\) −1.72380 6.43331i −0.169851 0.633893i −0.997372 0.0724573i \(-0.976916\pi\)
0.827520 0.561436i \(-0.189751\pi\)
\(104\) −1.46410 −0.143567
\(105\) 0 0
\(106\) 5.26795 0.511668
\(107\) 2.58819 + 9.65926i 0.250210 + 0.933796i 0.970693 + 0.240323i \(0.0772534\pi\)
−0.720483 + 0.693472i \(0.756080\pi\)
\(108\) 0.965926 + 0.258819i 0.0929463 + 0.0249049i
\(109\) 11.8301 6.83013i 1.13312 0.654208i 0.188403 0.982092i \(-0.439669\pi\)
0.944718 + 0.327884i \(0.106336\pi\)
\(110\) 0 0
\(111\) 4.73205i 0.449146i
\(112\) −2.38014 + 1.15539i −0.224902 + 0.109175i
\(113\) −2.12132 2.12132i −0.199557 0.199557i 0.600253 0.799810i \(-0.295067\pi\)
−0.799810 + 0.600253i \(0.795067\pi\)
\(114\) −3.63397 2.09808i −0.340353 0.196503i
\(115\) 0 0
\(116\) −4.09808 7.09808i −0.380497 0.659040i
\(117\) −1.41421 + 0.378937i −0.130744 + 0.0350328i
\(118\) −0.378937 + 0.378937i −0.0348840 + 0.0348840i
\(119\) −4.53590 + 3.92820i −0.415805 + 0.360098i
\(120\) 0 0
\(121\) 5.23205 9.06218i 0.475641 0.823834i
\(122\) 3.15660 11.7806i 0.285785 1.06656i
\(123\) 0.637756 2.38014i 0.0575046 0.214610i
\(124\) −3.96410 + 6.86603i −0.355987 + 0.616587i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) −11.2122 + 11.2122i −0.994919 + 0.994919i −0.999987 0.00506773i \(-0.998387\pi\)
0.00506773 + 0.999987i \(0.498387\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −0.0980762 0.169873i −0.00863513 0.0149565i
\(130\) 0 0
\(131\) −11.8301 6.83013i −1.03360 0.596751i −0.115588 0.993297i \(-0.536875\pi\)
−0.918015 + 0.396546i \(0.870209\pi\)
\(132\) 0.517638 + 0.517638i 0.0450546 + 0.0450546i
\(133\) 9.98743 4.84821i 0.866020 0.420393i
\(134\) 4.00000i 0.345547i
\(135\) 0 0
\(136\) 1.96410 1.13397i 0.168420 0.0972375i
\(137\) 7.79676 + 2.08913i 0.666122 + 0.178487i 0.576007 0.817445i \(-0.304610\pi\)
0.0901146 + 0.995931i \(0.471277\pi\)
\(138\) −0.965926 3.60488i −0.0822251 0.306868i
\(139\) 12.9282 1.09656 0.548278 0.836296i \(-0.315284\pi\)
0.548278 + 0.836296i \(0.315284\pi\)
\(140\) 0 0
\(141\) −11.0000 −0.926367
\(142\) 3.32748 + 12.4183i 0.279236 + 1.04212i
\(143\) −1.03528 0.277401i −0.0865741 0.0231975i
\(144\) 0.866025 0.500000i 0.0721688 0.0416667i
\(145\) 0 0
\(146\) 8.00000i 0.662085i
\(147\) −0.827225 6.95095i −0.0682284 0.573305i
\(148\) −3.34607 3.34607i −0.275045 0.275045i
\(149\) −15.5885 9.00000i −1.27706 0.737309i −0.300750 0.953703i \(-0.597237\pi\)
−0.976306 + 0.216394i \(0.930570\pi\)
\(150\) 0 0
\(151\) −5.46410 9.46410i −0.444662 0.770178i 0.553366 0.832938i \(-0.313343\pi\)
−0.998029 + 0.0627603i \(0.980010\pi\)
\(152\) −4.05317 + 1.08604i −0.328756 + 0.0880898i
\(153\) 1.60368 1.60368i 0.129650 0.129650i
\(154\) −1.90192 + 0.366025i −0.153261 + 0.0294952i
\(155\) 0 0
\(156\) −0.732051 + 1.26795i −0.0586110 + 0.101517i
\(157\) −5.36585 + 20.0256i −0.428241 + 1.59822i 0.328500 + 0.944504i \(0.393457\pi\)
−0.756741 + 0.653715i \(0.773210\pi\)
\(158\) 2.10274 7.84752i 0.167285 0.624316i
\(159\) 2.63397 4.56218i 0.208888 0.361804i
\(160\) 0 0
\(161\) 9.33013 + 3.23205i 0.735317 + 0.254721i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −11.5911 + 3.10583i −0.907886 + 0.243267i −0.682400 0.730979i \(-0.739064\pi\)
−0.225486 + 0.974246i \(0.572397\pi\)
\(164\) −1.23205 2.13397i −0.0962070 0.166635i
\(165\) 0 0
\(166\) 10.0981 + 5.83013i 0.783763 + 0.452506i
\(167\) −3.58630 3.58630i −0.277516 0.277516i 0.554600 0.832117i \(-0.312871\pi\)
−0.832117 + 0.554600i \(0.812871\pi\)
\(168\) −0.189469 + 2.63896i −0.0146178 + 0.203600i
\(169\) 10.8564i 0.835108i
\(170\) 0 0
\(171\) −3.63397 + 2.09808i −0.277897 + 0.160444i
\(172\) −0.189469 0.0507680i −0.0144469 0.00387102i
\(173\) −1.93185 7.20977i −0.146876 0.548149i −0.999665 0.0258926i \(-0.991757\pi\)
0.852789 0.522256i \(-0.174909\pi\)
\(174\) −8.19615 −0.621349
\(175\) 0 0
\(176\) 0.732051 0.0551804
\(177\) 0.138701 + 0.517638i 0.0104254 + 0.0389081i
\(178\) 6.24384 + 1.67303i 0.467996 + 0.125399i
\(179\) 17.1962 9.92820i 1.28530 0.742069i 0.307488 0.951552i \(-0.400511\pi\)
0.977812 + 0.209483i \(0.0671781\pi\)
\(180\) 0 0
\(181\) 0.196152i 0.0145799i −0.999973 0.00728995i \(-0.997680\pi\)
0.999973 0.00728995i \(-0.00232048\pi\)
\(182\) −1.69161 3.48477i −0.125391 0.258308i
\(183\) −8.62398 8.62398i −0.637503 0.637503i
\(184\) −3.23205 1.86603i −0.238270 0.137565i
\(185\) 0 0
\(186\) 3.96410 + 6.86603i 0.290662 + 0.503441i
\(187\) 1.60368 0.429705i 0.117273 0.0314232i
\(188\) −7.77817 + 7.77817i −0.567282 + 0.567282i
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −12.4282 + 21.5263i −0.899273 + 1.55759i −0.0708481 + 0.997487i \(0.522571\pi\)
−0.828425 + 0.560100i \(0.810763\pi\)
\(192\) 0.258819 0.965926i 0.0186787 0.0697097i
\(193\) −6.14231 + 22.9234i −0.442133 + 1.65006i 0.281264 + 0.959630i \(0.409246\pi\)
−0.723397 + 0.690432i \(0.757420\pi\)
\(194\) 3.50000 6.06218i 0.251285 0.435239i
\(195\) 0 0
\(196\) −5.50000 4.33013i −0.392857 0.309295i
\(197\) −18.2832 + 18.2832i −1.30263 + 1.30263i −0.376012 + 0.926615i \(0.622705\pi\)
−0.926615 + 0.376012i \(0.877295\pi\)
\(198\) 0.707107 0.189469i 0.0502519 0.0134650i
\(199\) −13.2321 22.9186i −0.937995 1.62466i −0.769204 0.639004i \(-0.779347\pi\)
−0.168791 0.985652i \(-0.553986\pi\)
\(200\) 0 0
\(201\) −3.46410 2.00000i −0.244339 0.141069i
\(202\) 0.138701 + 0.138701i 0.00975895 + 0.00975895i
\(203\) 12.1595 17.9551i 0.853431 1.26020i
\(204\) 2.26795i 0.158788i
\(205\) 0 0
\(206\) −5.76795 + 3.33013i −0.401872 + 0.232021i
\(207\) −3.60488 0.965926i −0.250557 0.0671365i
\(208\) 0.378937 + 1.41421i 0.0262746 + 0.0980581i
\(209\) −3.07180 −0.212481
\(210\) 0 0
\(211\) −19.6603 −1.35347 −0.676734 0.736228i \(-0.736605\pi\)
−0.676734 + 0.736228i \(0.736605\pi\)
\(212\) −1.36345 5.08845i −0.0936418 0.349476i
\(213\) 12.4183 + 3.32748i 0.850890 + 0.227995i
\(214\) 8.66025 5.00000i 0.592003 0.341793i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −20.9222 1.50215i −1.42029 0.101972i
\(218\) −9.65926 9.65926i −0.654208 0.654208i
\(219\) −6.92820 4.00000i −0.468165 0.270295i
\(220\) 0 0
\(221\) 1.66025 + 2.87564i 0.111681 + 0.193437i
\(222\) −4.57081 + 1.22474i −0.306773 + 0.0821995i
\(223\) 8.67475 8.67475i 0.580904 0.580904i −0.354247 0.935152i \(-0.615263\pi\)
0.935152 + 0.354247i \(0.115263\pi\)
\(224\) 1.73205 + 2.00000i 0.115728 + 0.133631i
\(225\) 0 0
\(226\) −1.50000 + 2.59808i −0.0997785 + 0.172821i
\(227\) 1.37705 5.13922i 0.0913979 0.341102i −0.905051 0.425304i \(-0.860167\pi\)
0.996449 + 0.0842018i \(0.0268340\pi\)
\(228\) −1.08604 + 4.05317i −0.0719250 + 0.268428i
\(229\) −5.90192 + 10.2224i −0.390010 + 0.675517i −0.992450 0.122647i \(-0.960862\pi\)
0.602440 + 0.798164i \(0.294195\pi\)
\(230\) 0 0
\(231\) −0.633975 + 1.83013i −0.0417125 + 0.120414i
\(232\) −5.79555 + 5.79555i −0.380497 + 0.380497i
\(233\) −18.2832 + 4.89898i −1.19777 + 0.320943i −0.801954 0.597385i \(-0.796206\pi\)
−0.395820 + 0.918328i \(0.629540\pi\)
\(234\) 0.732051 + 1.26795i 0.0478557 + 0.0828884i
\(235\) 0 0
\(236\) 0.464102 + 0.267949i 0.0302104 + 0.0174420i
\(237\) −5.74479 5.74479i −0.373164 0.373164i
\(238\) 4.96833 + 3.36465i 0.322049 + 0.218098i
\(239\) 4.85641i 0.314135i 0.987588 + 0.157067i \(0.0502040\pi\)
−0.987588 + 0.157067i \(0.949796\pi\)
\(240\) 0 0
\(241\) 11.1962 6.46410i 0.721208 0.416389i −0.0939894 0.995573i \(-0.529962\pi\)
0.815197 + 0.579184i \(0.196629\pi\)
\(242\) −10.1075 2.70831i −0.649738 0.174097i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) −12.1962 −0.780779
\(245\) 0 0
\(246\) −2.46410 −0.157105
\(247\) −1.59008 5.93426i −0.101174 0.377588i
\(248\) 7.65806 + 2.05197i 0.486287 + 0.130300i
\(249\) 10.0981 5.83013i 0.639940 0.369469i
\(250\) 0 0
\(251\) 17.8564i 1.12709i 0.826087 + 0.563543i \(0.190562\pi\)
−0.826087 + 0.563543i \(0.809438\pi\)
\(252\) 2.19067 + 1.48356i 0.137999 + 0.0934557i
\(253\) −1.93185 1.93185i −0.121454 0.121454i
\(254\) 13.7321 + 7.92820i 0.861625 + 0.497460i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.72500 + 0.998111i −0.232359 + 0.0622605i −0.373120 0.927783i \(-0.621712\pi\)
0.140760 + 0.990044i \(0.455045\pi\)
\(258\) −0.138701 + 0.138701i −0.00863513 + 0.00863513i
\(259\) 4.09808 11.8301i 0.254642 0.735088i
\(260\) 0 0
\(261\) −4.09808 + 7.09808i −0.253665 + 0.439360i
\(262\) −3.53553 + 13.1948i −0.218426 + 0.815177i
\(263\) −4.79246 + 17.8857i −0.295516 + 1.10288i 0.645291 + 0.763937i \(0.276736\pi\)
−0.940807 + 0.338944i \(0.889930\pi\)
\(264\) 0.366025 0.633975i 0.0225273 0.0390184i
\(265\) 0 0
\(266\) −7.26795 8.39230i −0.445627 0.514565i
\(267\) 4.57081 4.57081i 0.279729 0.279729i
\(268\) −3.86370 + 1.03528i −0.236013 + 0.0632396i
\(269\) −12.8301 22.2224i −0.782267 1.35493i −0.930618 0.365991i \(-0.880730\pi\)
0.148352 0.988935i \(-0.452603\pi\)
\(270\) 0 0
\(271\) 2.13397 + 1.23205i 0.129630 + 0.0748418i 0.563413 0.826176i \(-0.309488\pi\)
−0.433783 + 0.901017i \(0.642821\pi\)
\(272\) −1.60368 1.60368i −0.0972375 0.0972375i
\(273\) −3.86370 0.277401i −0.233842 0.0167891i
\(274\) 8.07180i 0.487635i
\(275\) 0 0
\(276\) −3.23205 + 1.86603i −0.194547 + 0.112322i
\(277\) −16.0232 4.29341i −0.962742 0.257966i −0.256981 0.966416i \(-0.582728\pi\)
−0.705761 + 0.708450i \(0.749395\pi\)
\(278\) −3.34607 12.4877i −0.200684 0.748962i
\(279\) 7.92820 0.474649
\(280\) 0 0
\(281\) 19.9808 1.19195 0.595976 0.803002i \(-0.296765\pi\)
0.595976 + 0.803002i \(0.296765\pi\)
\(282\) 2.84701 + 10.6252i 0.169537 + 0.632721i
\(283\) 6.88160 + 1.84392i 0.409069 + 0.109610i 0.457484 0.889218i \(-0.348751\pi\)
−0.0484158 + 0.998827i \(0.515417\pi\)
\(284\) 11.1340 6.42820i 0.660680 0.381444i
\(285\) 0 0
\(286\) 1.07180i 0.0633767i
\(287\) 3.65565 5.39804i 0.215786 0.318636i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 10.2679 + 5.92820i 0.603997 + 0.348718i
\(290\) 0 0
\(291\) −3.50000 6.06218i −0.205174 0.355371i
\(292\) −7.72741 + 2.07055i −0.452212 + 0.121170i
\(293\) 9.38186 9.38186i 0.548094 0.548094i −0.377795 0.925889i \(-0.623318\pi\)
0.925889 + 0.377795i \(0.123318\pi\)
\(294\) −6.50000 + 2.59808i −0.379088 + 0.151523i
\(295\) 0 0
\(296\) −2.36603 + 4.09808i −0.137522 + 0.238196i
\(297\) 0.189469 0.707107i 0.0109941 0.0410305i
\(298\) −4.65874 + 17.3867i −0.269874 + 1.00718i
\(299\) 2.73205 4.73205i 0.157999 0.273662i
\(300\) 0 0
\(301\) −0.0980762 0.509619i −0.00565302 0.0293739i
\(302\) −7.72741 + 7.72741i −0.444662 + 0.444662i
\(303\) 0.189469 0.0507680i 0.0108847 0.00291654i
\(304\) 2.09808 + 3.63397i 0.120333 + 0.208423i
\(305\) 0 0
\(306\) −1.96410 1.13397i −0.112280 0.0648250i
\(307\) 13.3843 + 13.3843i 0.763880 + 0.763880i 0.977021 0.213141i \(-0.0683695\pi\)
−0.213141 + 0.977021i \(0.568369\pi\)
\(308\) 0.845807 + 1.74238i 0.0481944 + 0.0992815i
\(309\) 6.66025i 0.378889i
\(310\) 0 0
\(311\) −11.8923 + 6.86603i −0.674351 + 0.389337i −0.797723 0.603024i \(-0.793962\pi\)
0.123372 + 0.992360i \(0.460629\pi\)
\(312\) 1.41421 + 0.378937i 0.0800641 + 0.0214531i
\(313\) 4.77886 + 17.8350i 0.270117 + 1.00809i 0.959043 + 0.283260i \(0.0914158\pi\)
−0.688926 + 0.724832i \(0.741918\pi\)
\(314\) 20.7321 1.16998
\(315\) 0 0
\(316\) −8.12436 −0.457031
\(317\) 3.05506 + 11.4016i 0.171589 + 0.640380i 0.997107 + 0.0760044i \(0.0242163\pi\)
−0.825518 + 0.564376i \(0.809117\pi\)
\(318\) −5.08845 1.36345i −0.285346 0.0764582i
\(319\) −5.19615 + 3.00000i −0.290929 + 0.167968i
\(320\) 0 0
\(321\) 10.0000i 0.558146i
\(322\) 0.707107 9.84873i 0.0394055 0.548848i
\(323\) 6.72930 + 6.72930i 0.374428 + 0.374428i
\(324\) −0.866025 0.500000i −0.0481125 0.0277778i
\(325\) 0 0
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) −13.1948 + 3.53553i −0.729674 + 0.195515i
\(328\) −1.74238 + 1.74238i −0.0962070 + 0.0962070i
\(329\) −27.5000 9.52628i −1.51612 0.525201i
\(330\) 0 0
\(331\) 5.92820 10.2679i 0.325844 0.564378i −0.655839 0.754901i \(-0.727685\pi\)
0.981683 + 0.190523i \(0.0610184\pi\)
\(332\) 3.01790 11.2629i 0.165629 0.618134i
\(333\) −1.22474 + 4.57081i −0.0671156 + 0.250479i
\(334\) −2.53590 + 4.39230i −0.138758 + 0.240336i
\(335\) 0 0
\(336\) 2.59808 0.500000i 0.141737 0.0272772i
\(337\) −13.2963 + 13.2963i −0.724297 + 0.724297i −0.969477 0.245180i \(-0.921153\pi\)
0.245180 + 0.969477i \(0.421153\pi\)
\(338\) 10.4865 2.80984i 0.570390 0.152835i
\(339\) 1.50000 + 2.59808i 0.0814688 + 0.141108i
\(340\) 0 0
\(341\) 5.02628 + 2.90192i 0.272188 + 0.157148i
\(342\) 2.96713 + 2.96713i 0.160444 + 0.160444i
\(343\) 3.95164 18.0938i 0.213368 0.976972i
\(344\) 0.196152i 0.0105758i
\(345\) 0 0
\(346\) −6.46410 + 3.73205i −0.347512 + 0.200636i
\(347\) 27.6143 + 7.39924i 1.48241 + 0.397212i 0.907168 0.420768i \(-0.138239\pi\)
0.575247 + 0.817980i \(0.304906\pi\)
\(348\) 2.12132 + 7.91688i 0.113715 + 0.424389i
\(349\) 7.26795 0.389044 0.194522 0.980898i \(-0.437684\pi\)
0.194522 + 0.980898i \(0.437684\pi\)
\(350\) 0 0
\(351\) 1.46410 0.0781480
\(352\) −0.189469 0.707107i −0.0100987 0.0376889i
\(353\) 3.46618 + 0.928761i 0.184486 + 0.0494330i 0.349879 0.936795i \(-0.386223\pi\)
−0.165393 + 0.986228i \(0.552889\pi\)
\(354\) 0.464102 0.267949i 0.0246667 0.0142413i
\(355\) 0 0
\(356\) 6.46410i 0.342597i
\(357\) 5.39804 2.62038i 0.285694 0.138685i
\(358\) −14.0406 14.0406i −0.742069 0.742069i
\(359\) −18.0000 10.3923i −0.950004 0.548485i −0.0569216 0.998379i \(-0.518129\pi\)
−0.893082 + 0.449894i \(0.851462\pi\)
\(360\) 0 0
\(361\) 0.696152 + 1.20577i 0.0366396 + 0.0634617i
\(362\) −0.189469 + 0.0507680i −0.00995825 + 0.00266831i
\(363\) −7.39924 + 7.39924i −0.388359 + 0.388359i
\(364\) −2.92820 + 2.53590i −0.153480 + 0.132917i
\(365\) 0 0
\(366\) −6.09808 + 10.5622i −0.318752 + 0.552094i
\(367\) 8.10634 30.2533i 0.423148 1.57921i −0.344787 0.938681i \(-0.612049\pi\)
0.767935 0.640528i \(-0.221284\pi\)
\(368\) −0.965926 + 3.60488i −0.0503524 + 0.187918i
\(369\) −1.23205 + 2.13397i −0.0641380 + 0.111090i
\(370\) 0 0
\(371\) 10.5359 9.12436i 0.546997 0.473713i
\(372\) 5.60609 5.60609i 0.290662 0.290662i
\(373\) 5.93426 1.59008i 0.307264 0.0823312i −0.101892 0.994795i \(-0.532490\pi\)
0.409156 + 0.912464i \(0.365823\pi\)
\(374\) −0.830127 1.43782i −0.0429248 0.0743480i
\(375\) 0 0
\(376\) 9.52628 + 5.50000i 0.491280 + 0.283641i
\(377\) −8.48528 8.48528i −0.437014 0.437014i
\(378\) 2.38014 1.15539i 0.122421 0.0594271i
\(379\) 10.0526i 0.516365i −0.966096 0.258183i \(-0.916876\pi\)
0.966096 0.258183i \(-0.0831236\pi\)
\(380\) 0 0
\(381\) 13.7321 7.92820i 0.703514 0.406174i
\(382\) 24.0094 + 6.43331i 1.22843 + 0.329157i
\(383\) −6.84941 25.5624i −0.349989 1.30618i −0.886675 0.462394i \(-0.846991\pi\)
0.536686 0.843782i \(-0.319676\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 23.7321 1.20793
\(387\) 0.0507680 + 0.189469i 0.00258068 + 0.00963123i
\(388\) −6.76148 1.81173i −0.343262 0.0919768i
\(389\) 23.9545 13.8301i 1.21454 0.701215i 0.250795 0.968040i \(-0.419308\pi\)
0.963745 + 0.266825i \(0.0859745\pi\)
\(390\) 0 0
\(391\) 8.46410i 0.428048i
\(392\) −2.75908 + 6.43331i −0.139354 + 0.324931i
\(393\) 9.65926 + 9.65926i 0.487245 + 0.487245i
\(394\) 22.3923 + 12.9282i 1.12811 + 0.651313i
\(395\) 0 0
\(396\) −0.366025 0.633975i −0.0183935 0.0318584i
\(397\) 18.8009 5.03768i 0.943589 0.252834i 0.245949 0.969283i \(-0.420900\pi\)
0.697640 + 0.716449i \(0.254234\pi\)
\(398\) −18.7129 + 18.7129i −0.937995 + 0.937995i
\(399\) −10.9019 + 2.09808i −0.545779 + 0.105035i
\(400\) 0 0
\(401\) 10.4641 18.1244i 0.522552 0.905087i −0.477103 0.878847i \(-0.658313\pi\)
0.999656 0.0262399i \(-0.00835339\pi\)
\(402\) −1.03528 + 3.86370i −0.0516349 + 0.192704i
\(403\) −3.00429 + 11.2122i −0.149654 + 0.558518i
\(404\) 0.0980762 0.169873i 0.00487947 0.00845150i
\(405\) 0 0
\(406\) −20.4904 7.09808i −1.01692 0.352272i
\(407\) −2.44949 + 2.44949i −0.121417 + 0.121417i
\(408\) −2.19067 + 0.586988i −0.108454 + 0.0290603i
\(409\) −16.5981 28.7487i −0.820722 1.42153i −0.905145 0.425102i \(-0.860238\pi\)
0.0844233 0.996430i \(-0.473095\pi\)
\(410\) 0 0
\(411\) −6.99038 4.03590i −0.344810 0.199076i
\(412\) 4.70951 + 4.70951i 0.232021 + 0.232021i
\(413\) −0.101536 + 1.41421i −0.00499626 + 0.0695889i
\(414\) 3.73205i 0.183420i
\(415\) 0 0
\(416\) 1.26795 0.732051i 0.0621663 0.0358917i
\(417\) −12.4877 3.34607i −0.611525 0.163858i
\(418\) 0.795040 + 2.96713i 0.0388867 + 0.145127i
\(419\) −10.5885 −0.517280 −0.258640 0.965974i \(-0.583274\pi\)
−0.258640 + 0.965974i \(0.583274\pi\)
\(420\) 0 0
\(421\) −2.53590 −0.123592 −0.0617961 0.998089i \(-0.519683\pi\)
−0.0617961 + 0.998089i \(0.519683\pi\)
\(422\) 5.08845 + 18.9903i 0.247702 + 0.924436i
\(423\) 10.6252 + 2.84701i 0.516614 + 0.138426i
\(424\) −4.56218 + 2.63397i −0.221559 + 0.127917i
\(425\) 0 0
\(426\) 12.8564i 0.622895i
\(427\) −14.0914 29.0285i −0.681929 1.40479i
\(428\) −7.07107 7.07107i −0.341793 0.341793i
\(429\) 0.928203 + 0.535898i 0.0448141 + 0.0258734i
\(430\) 0 0
\(431\) −0.232051 0.401924i −0.0111775 0.0193600i 0.860383 0.509649i \(-0.170225\pi\)
−0.871560 + 0.490289i \(0.836891\pi\)
\(432\) −0.965926 + 0.258819i −0.0464731 + 0.0124524i
\(433\) 20.0256 20.0256i 0.962370 0.962370i −0.0369472 0.999317i \(-0.511763\pi\)
0.999317 + 0.0369472i \(0.0117633\pi\)
\(434\) 3.96410 + 20.5981i 0.190283 + 0.988739i
\(435\) 0 0
\(436\) −6.83013 + 11.8301i −0.327104 + 0.566560i
\(437\) 4.05317 15.1266i 0.193890 0.723606i
\(438\) −2.07055 + 7.72741i −0.0989348 + 0.369230i
\(439\) −19.6962 + 34.1147i −0.940046 + 1.62821i −0.174667 + 0.984628i \(0.555885\pi\)
−0.765379 + 0.643580i \(0.777448\pi\)
\(440\) 0 0
\(441\) −1.00000 + 6.92820i −0.0476190 + 0.329914i
\(442\) 2.34795 2.34795i 0.111681 0.111681i
\(443\) −20.7835 + 5.56892i −0.987454 + 0.264587i −0.716181 0.697915i \(-0.754111\pi\)
−0.271273 + 0.962502i \(0.587445\pi\)
\(444\) 2.36603 + 4.09808i 0.112287 + 0.194486i
\(445\) 0 0
\(446\) −10.6244 6.13397i −0.503078 0.290452i
\(447\) 12.7279 + 12.7279i 0.602010 + 0.602010i
\(448\) 1.48356 2.19067i 0.0700918 0.103499i
\(449\) 29.7321i 1.40314i 0.712599 + 0.701571i \(0.247518\pi\)
−0.712599 + 0.701571i \(0.752482\pi\)
\(450\) 0 0
\(451\) −1.56218 + 0.901924i −0.0735601 + 0.0424699i
\(452\) 2.89778 + 0.776457i 0.136300 + 0.0365215i
\(453\) 2.82843 + 10.5558i 0.132891 + 0.495956i
\(454\) −5.32051 −0.249704
\(455\) 0 0
\(456\) 4.19615 0.196503
\(457\) −8.76268 32.7028i −0.409901 1.52977i −0.794834 0.606827i \(-0.792442\pi\)
0.384933 0.922945i \(-0.374225\pi\)
\(458\) 11.4016 + 3.05506i 0.532764 + 0.142754i
\(459\) −1.96410 + 1.13397i −0.0916764 + 0.0529294i
\(460\) 0 0
\(461\) 19.3205i 0.899846i 0.893067 + 0.449923i \(0.148549\pi\)
−0.893067 + 0.449923i \(0.851451\pi\)
\(462\) 1.93185 + 0.138701i 0.0898779 + 0.00645294i
\(463\) −10.3292 10.3292i −0.480039 0.480039i 0.425105 0.905144i \(-0.360237\pi\)
−0.905144 + 0.425105i \(0.860237\pi\)
\(464\) 7.09808 + 4.09808i 0.329520 + 0.190248i
\(465\) 0 0
\(466\) 9.46410 + 16.3923i 0.438416 + 0.759359i
\(467\) 7.77817 2.08416i 0.359931 0.0964432i −0.0743217 0.997234i \(-0.523679\pi\)
0.434253 + 0.900791i \(0.357012\pi\)
\(468\) 1.03528 1.03528i 0.0478557 0.0478557i
\(469\) −6.92820 8.00000i −0.319915 0.369406i
\(470\) 0 0
\(471\) 10.3660 17.9545i 0.477641 0.827299i
\(472\) 0.138701 0.517638i 0.00638422 0.0238262i
\(473\) −0.0371647 + 0.138701i −0.00170884 + 0.00637747i
\(474\) −4.06218 + 7.03590i −0.186582 + 0.323170i
\(475\) 0 0
\(476\) 1.96410 5.66987i 0.0900244 0.259878i
\(477\) −3.72500 + 3.72500i −0.170556 + 0.170556i
\(478\) 4.69093 1.25693i 0.214558 0.0574907i
\(479\) 9.99038 + 17.3038i 0.456472 + 0.790633i 0.998772 0.0495524i \(-0.0157795\pi\)
−0.542299 + 0.840185i \(0.682446\pi\)
\(480\) 0 0
\(481\) −6.00000 3.46410i −0.273576 0.157949i
\(482\) −9.14162 9.14162i −0.416389 0.416389i
\(483\) −8.17569 5.53674i −0.372007 0.251930i
\(484\) 10.4641i 0.475641i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 13.0747 + 3.50335i 0.592470 + 0.158752i 0.542582 0.840003i \(-0.317447\pi\)
0.0498882 + 0.998755i \(0.484114\pi\)
\(488\) 3.15660 + 11.7806i 0.142892 + 0.533282i
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −1.66025 −0.0749262 −0.0374631 0.999298i \(-0.511928\pi\)
−0.0374631 + 0.999298i \(0.511928\pi\)
\(492\) 0.637756 + 2.38014i 0.0287523 + 0.107305i
\(493\) 17.9551 + 4.81105i 0.808656 + 0.216679i
\(494\) −5.32051 + 3.07180i −0.239381 + 0.138207i
\(495\) 0 0
\(496\) 7.92820i 0.355987i
\(497\) 28.1642 + 19.0733i 1.26333 + 0.855554i
\(498\) −8.24504 8.24504i −0.369469 0.369469i
\(499\) 18.1699 + 10.4904i 0.813395 + 0.469614i 0.848134 0.529782i \(-0.177726\pi\)
−0.0347383 + 0.999396i \(0.511060\pi\)
\(500\) 0 0
\(501\) 2.53590 + 4.39230i 0.113296 + 0.196234i
\(502\) 17.2480 4.62158i 0.769814 0.206271i
\(503\) 30.5307 30.5307i 1.36130 1.36130i 0.489028 0.872268i \(-0.337352\pi\)
0.872268 0.489028i \(-0.162648\pi\)
\(504\) 0.866025 2.50000i 0.0385758 0.111359i
\(505\) 0 0
\(506\) −1.36603 + 2.36603i −0.0607272 + 0.105183i
\(507\) 2.80984 10.4865i 0.124790 0.465721i
\(508\) 4.10394 15.3161i 0.182083 0.679543i
\(509\) −2.02628 + 3.50962i −0.0898133 + 0.155561i −0.907432 0.420199i \(-0.861960\pi\)
0.817619 + 0.575760i \(0.195294\pi\)
\(510\) 0 0
\(511\) −13.8564 16.0000i −0.612971 0.707798i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 4.05317 1.08604i 0.178952 0.0479500i
\(514\) 1.92820 + 3.33975i 0.0850494 + 0.147310i
\(515\) 0 0
\(516\) 0.169873 + 0.0980762i 0.00747824 + 0.00431756i
\(517\) 5.69402 + 5.69402i 0.250423 + 0.250423i
\(518\) −12.4877 0.896575i −0.548677 0.0393933i
\(519\) 7.46410i 0.327638i
\(520\) 0 0
\(521\) 27.3109 15.7679i 1.19651 0.690806i 0.236736 0.971574i \(-0.423922\pi\)
0.959776 + 0.280768i \(0.0905890\pi\)
\(522\) 7.91688 + 2.12132i 0.346512 + 0.0928477i
\(523\) −1.74238 6.50266i −0.0761891 0.284342i 0.917311 0.398171i \(-0.130355\pi\)
−0.993500 + 0.113829i \(0.963688\pi\)
\(524\) 13.6603 0.596751
\(525\) 0 0
\(526\) 18.5167 0.807365
\(527\) −4.65376 17.3681i −0.202721 0.756566i
\(528\) −0.707107 0.189469i −0.0307729 0.00824557i
\(529\) −7.85641 + 4.53590i −0.341583 + 0.197213i
\(530\) 0 0
\(531\) 0.535898i 0.0232560i
\(532\) −6.22526 + 9.19239i −0.269899 + 0.398541i
\(533\) −2.55103 2.55103i −0.110497 0.110497i
\(534\) −5.59808 3.23205i −0.242252 0.139865i
\(535\) 0 0
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) −19.1798 + 5.13922i −0.827670 + 0.221774i
\(538\) −18.1445 + 18.1445i −0.782267 + 0.782267i
\(539\) −3.16987 + 4.02628i −0.136536 + 0.173424i
\(540\) 0 0
\(541\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(542\) 0.637756 2.38014i 0.0273940 0.102236i
\(543\) −0.0507680 + 0.189469i −0.00217866 + 0.00813088i
\(544\) −1.13397 + 1.96410i −0.0486188 + 0.0842102i
\(545\) 0 0
\(546\) 0.732051 + 3.80385i 0.0313289 + 0.162790i
\(547\) 31.0483 31.0483i 1.32753 1.32753i 0.420012 0.907519i \(-0.362026\pi\)
0.907519 0.420012i \(-0.137974\pi\)
\(548\) −7.79676 + 2.08913i −0.333061 + 0.0892434i
\(549\) 6.09808 + 10.5622i 0.260260 + 0.450783i
\(550\) 0 0
\(551\) −29.7846 17.1962i −1.26887 0.732581i
\(552\) 2.63896 + 2.63896i 0.112322 + 0.112322i
\(553\) −9.38684 19.3371i −0.399169 0.822297i
\(554\) 16.5885i 0.704776i
\(555\) 0 0
\(556\) −11.1962 + 6.46410i −0.474823 + 0.274139i
\(557\) 11.8313 + 3.17020i 0.501310 + 0.134326i 0.500608 0.865674i \(-0.333110\pi\)
0.000702224 1.00000i \(0.499776\pi\)
\(558\) −2.05197 7.65806i −0.0868668 0.324191i
\(559\) −0.287187 −0.0121467
\(560\) 0 0
\(561\) −1.66025 −0.0700960
\(562\) −5.17140 19.2999i −0.218142 0.814119i
\(563\) 38.5491 + 10.3292i 1.62465 + 0.435324i 0.952363 0.304966i \(-0.0986451\pi\)
0.672288 + 0.740290i \(0.265312\pi\)
\(564\) 9.52628 5.50000i 0.401129 0.231592i
\(565\) 0 0
\(566\) 7.12436i 0.299459i
\(567\) 0.189469 2.63896i 0.00795694 0.110826i
\(568\) −9.09085 9.09085i −0.381444 0.381444i
\(569\) 5.55256 + 3.20577i 0.232775 + 0.134393i 0.611852 0.790972i \(-0.290425\pi\)
−0.379076 + 0.925365i \(0.623758\pi\)
\(570\) 0 0
\(571\) 3.80385 + 6.58846i 0.159186 + 0.275718i 0.934575 0.355765i \(-0.115780\pi\)
−0.775389 + 0.631483i \(0.782446\pi\)
\(572\) 1.03528 0.277401i 0.0432871 0.0115987i
\(573\) 17.5761 17.5761i 0.734254 0.734254i
\(574\) −6.16025 2.13397i −0.257124 0.0890704i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −0.582009 + 2.17209i −0.0242294 + 0.0904252i −0.976982 0.213323i \(-0.931571\pi\)
0.952752 + 0.303748i \(0.0982381\pi\)
\(578\) 3.06866 11.4524i 0.127640 0.476357i
\(579\) 11.8660 20.5526i 0.493135 0.854135i
\(580\) 0 0
\(581\) 30.2942 5.83013i 1.25682 0.241874i
\(582\) −4.94975 + 4.94975i −0.205174 + 0.205174i
\(583\) −3.72500 + 0.998111i −0.154274 + 0.0413376i
\(584\) 4.00000 + 6.92820i 0.165521 + 0.286691i
\(585\) 0 0
\(586\) −11.4904 6.63397i −0.474663 0.274047i
\(587\) 13.0053 + 13.0053i 0.536787 + 0.536787i 0.922584 0.385797i \(-0.126073\pi\)
−0.385797 + 0.922584i \(0.626073\pi\)
\(588\) 4.19187 + 5.60609i 0.172870 + 0.231191i
\(589\) 33.2679i 1.37078i
\(590\) 0 0
\(591\) 22.3923 12.9282i 0.921096 0.531795i
\(592\) 4.57081 + 1.22474i 0.187859 + 0.0503367i
\(593\) 4.34916 + 16.2313i 0.178598 + 0.666538i 0.995911 + 0.0903434i \(0.0287965\pi\)
−0.817312 + 0.576195i \(0.804537\pi\)
\(594\) −0.732051 −0.0300364
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) 6.84941 + 25.5624i 0.280328 + 1.04620i
\(598\) −5.27792 1.41421i −0.215830 0.0578315i
\(599\) −38.0429 + 21.9641i −1.55439 + 0.897429i −0.556617 + 0.830770i \(0.687901\pi\)
−0.997776 + 0.0666594i \(0.978766\pi\)
\(600\) 0 0
\(601\) 20.2487i 0.825962i 0.910740 + 0.412981i \(0.135512\pi\)
−0.910740 + 0.412981i \(0.864488\pi\)
\(602\) −0.466870 + 0.226633i −0.0190282 + 0.00923689i
\(603\) 2.82843 + 2.82843i 0.115182 + 0.115182i
\(604\) 9.46410 + 5.46410i 0.385089 + 0.222331i
\(605\) 0 0
\(606\) −0.0980762 0.169873i −0.00398407 0.00690062i
\(607\) 23.3023 6.24384i 0.945813 0.253430i 0.247228 0.968957i \(-0.420480\pi\)
0.698585 + 0.715528i \(0.253814\pi\)
\(608\) 2.96713 2.96713i 0.120333 0.120333i
\(609\) −16.3923 + 14.1962i −0.664250 + 0.575257i
\(610\) 0 0
\(611\) −8.05256 + 13.9474i −0.325772 + 0.564253i
\(612\) −0.586988 + 2.19067i −0.0237276 + 0.0885526i
\(613\) −1.18758 + 4.43211i −0.0479659 + 0.179011i −0.985753 0.168200i \(-0.946205\pi\)
0.937787 + 0.347211i \(0.112871\pi\)
\(614\) 9.46410 16.3923i 0.381940 0.661540i
\(615\) 0 0
\(616\) 1.46410 1.26795i 0.0589903 0.0510871i
\(617\) −3.05506 + 3.05506i −0.122992 + 0.122992i −0.765924 0.642932i \(-0.777718\pi\)
0.642932 + 0.765924i \(0.277718\pi\)
\(618\) 6.43331 1.72380i 0.258786 0.0693414i
\(619\) −6.90192 11.9545i −0.277412 0.480491i 0.693329 0.720621i \(-0.256143\pi\)
−0.970741 + 0.240130i \(0.922810\pi\)
\(620\) 0 0
\(621\) 3.23205 + 1.86603i 0.129698 + 0.0748810i
\(622\) 9.71003 + 9.71003i 0.389337 + 0.389337i
\(623\) 15.3855 7.46859i 0.616406 0.299223i
\(624\) 1.46410i 0.0586110i
\(625\) 0 0
\(626\) 15.9904 9.23205i 0.639104 0.368987i
\(627\) 2.96713 + 0.795040i 0.118496 + 0.0317508i
\(628\) −5.36585 20.0256i −0.214121 0.799109i
\(629\) 10.7321 0.427915
\(630\) 0 0
\(631\) −16.4115 −0.653333 −0.326667 0.945140i \(-0.605925\pi\)
−0.326667 + 0.945140i \(0.605925\pi\)
\(632\) 2.10274 + 7.84752i 0.0836424 + 0.312158i
\(633\) 18.9903 + 5.08845i 0.754799 + 0.202248i
\(634\) 10.2224 5.90192i 0.405985 0.234395i
\(635\) 0 0
\(636\) 5.26795i 0.208888i
\(637\) −9.41902 4.03957i −0.373195 0.160054i
\(638\) 4.24264 + 4.24264i 0.167968 + 0.167968i
\(639\) −11.1340 6.42820i −0.440453 0.254296i
\(640\) 0 0
\(641\) −0.330127 0.571797i −0.0130392 0.0225846i 0.859432 0.511250i \(-0.170817\pi\)
−0.872471 + 0.488665i \(0.837484\pi\)
\(642\) −9.65926 + 2.58819i −0.381221 + 0.102148i
\(643\) −24.3190 + 24.3190i −0.959049 + 0.959049i −0.999194 0.0401449i \(-0.987218\pi\)
0.0401449 + 0.999194i \(0.487218\pi\)
\(644\) −9.69615 + 1.86603i −0.382082 + 0.0735317i
\(645\) 0 0
\(646\) 4.75833 8.24167i 0.187214 0.324264i
\(647\) 5.03768 18.8009i 0.198052 0.739139i −0.793404 0.608695i \(-0.791693\pi\)
0.991456 0.130444i \(-0.0416401\pi\)
\(648\) −0.258819 + 0.965926i −0.0101674 + 0.0379452i
\(649\) 0.196152 0.339746i 0.00769966 0.0133362i
\(650\) 0 0
\(651\) 19.8205 + 6.86603i 0.776827 + 0.269101i
\(652\) 8.48528 8.48528i 0.332309 0.332309i
\(653\) 21.8695 5.85993i 0.855821 0.229317i 0.195875 0.980629i \(-0.437245\pi\)
0.659947 + 0.751312i \(0.270579\pi\)
\(654\) 6.83013 + 11.8301i 0.267079 + 0.462595i
\(655\) 0 0
\(656\) 2.13397 + 1.23205i 0.0833177 + 0.0481035i
\(657\) 5.65685 + 5.65685i 0.220695 + 0.220695i
\(658\) −2.08416 + 29.0285i −0.0812488 + 1.13165i
\(659\) 14.1962i 0.553004i 0.961013 + 0.276502i \(0.0891752\pi\)
−0.961013 + 0.276502i \(0.910825\pi\)
\(660\) 0 0
\(661\) −34.5167 + 19.9282i −1.34254 + 0.775117i −0.987180 0.159611i \(-0.948976\pi\)
−0.355363 + 0.934729i \(0.615643\pi\)
\(662\) −11.4524 3.06866i −0.445111 0.119267i
\(663\) −0.859411 3.20736i −0.0333767 0.124564i
\(664\) −11.6603 −0.452506
\(665\) 0 0
\(666\) 4.73205 0.183363
\(667\) −7.91688 29.5462i −0.306543 1.14403i
\(668\) 4.89898 + 1.31268i 0.189547 + 0.0507890i
\(669\) −10.6244 + 6.13397i −0.410761 + 0.237153i
\(670\) 0 0
\(671\) 8.92820i 0.344669i
\(672\) −1.15539 2.38014i −0.0445703 0.0918159i
\(673\) 1.60368 + 1.60368i 0.0618174 + 0.0618174i 0.737340 0.675522i \(-0.236082\pi\)
−0.675522 + 0.737340i \(0.736082\pi\)
\(674\) 16.2846 + 9.40192i 0.627260 + 0.362149i
\(675\) 0 0
\(676\) −5.42820 9.40192i −0.208777 0.361612i
\(677\) −41.3775 + 11.0871i −1.59027 + 0.426111i −0.942085 0.335374i \(-0.891137\pi\)
−0.648183 + 0.761485i \(0.724471\pi\)
\(678\) 2.12132 2.12132i 0.0814688 0.0814688i
\(679\) −3.50000 18.1865i −0.134318 0.697935i
\(680\) 0 0
\(681\) −2.66025 + 4.60770i −0.101941 + 0.176567i
\(682\) 1.50215 5.60609i 0.0575202 0.214668i
\(683\) −9.83512 + 36.7052i −0.376331 + 1.40448i 0.475060 + 0.879953i \(0.342426\pi\)
−0.851391 + 0.524532i \(0.824240\pi\)
\(684\) 2.09808 3.63397i 0.0802219 0.138948i
\(685\) 0 0
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 8.34658 8.34658i 0.318442 0.318442i
\(688\) 0.189469 0.0507680i 0.00722343 0.00193551i
\(689\) −3.85641 6.67949i −0.146917 0.254468i
\(690\) 0 0
\(691\) 17.6147 + 10.1699i 0.670096 + 0.386880i 0.796113 0.605148i \(-0.206886\pi\)
−0.126017 + 0.992028i \(0.540219\pi\)
\(692\) 5.27792 + 5.27792i 0.200636 + 0.200636i
\(693\) 1.08604 1.60368i 0.0412554 0.0609189i
\(694\) 28.5885i 1.08520i
\(695\) 0 0
\(696\) 7.09808 4.09808i 0.269052 0.155337i
\(697\) 5.39804 + 1.44640i 0.204465 + 0.0547863i
\(698\) −1.88108 7.02030i −0.0712001 0.265722i
\(699\) 18.9282 0.715930
\(700\) 0 0
\(701\) 21.4641 0.810688 0.405344 0.914164i \(-0.367152\pi\)
0.405344 + 0.914164i \(0.367152\pi\)
\(702\) −0.378937 1.41421i −0.0143021 0.0533761i
\(703\) −19.1798 5.13922i −0.723380 0.193829i
\(704\) −0.633975 + 0.366025i −0.0238938 + 0.0137951i
\(705\) 0 0
\(706\) 3.58846i 0.135053i
\(707\) 0.517638 + 0.0371647i 0.0194678 + 0.00139772i
\(708\) −0.378937 0.378937i −0.0142413 0.0142413i
\(709\) 33.9282 + 19.5885i 1.27420 + 0.735660i 0.975776 0.218773i \(-0.0702055\pi\)
0.298425 + 0.954433i \(0.403539\pi\)
\(710\) 0 0
\(711\) 4.06218 + 7.03590i 0.152344 + 0.263867i
\(712\) −6.24384 + 1.67303i −0.233998 + 0.0626995i
\(713\) −20.9222 + 20.9222i −0.783543 + 0.783543i
\(714\) −3.92820 4.53590i −0.147009 0.169752i
\(715\) 0 0
\(716\) −9.92820 + 17.1962i −0.371034 + 0.642650i
\(717\) 1.25693 4.69093i 0.0469409 0.175186i
\(718\) −5.37945 + 20.0764i −0.200759 + 0.749244i
\(719\) −6.66987 + 11.5526i −0.248744 + 0.430838i −0.963178 0.268866i \(-0.913351\pi\)
0.714433 + 0.699703i \(0.246685\pi\)
\(720\) 0 0
\(721\) −5.76795 + 16.6506i −0.214810 + 0.620102i
\(722\) 0.984508 0.984508i 0.0366396 0.0366396i
\(723\) −12.4877 + 3.34607i −0.464422 + 0.124442i
\(724\) 0.0980762 + 0.169873i 0.00364497 + 0.00631328i
\(725\) 0 0
\(726\) 9.06218 + 5.23205i 0.336329 + 0.194180i
\(727\) −0.0879327 0.0879327i −0.00326124 0.00326124i 0.705474 0.708736i \(-0.250734\pi\)
−0.708736 + 0.705474i \(0.750734\pi\)
\(728\) 3.20736 + 2.17209i 0.118873 + 0.0805029i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 0.385263 0.222432i 0.0142495 0.00822694i
\(732\) 11.7806 + 3.15660i 0.435423 + 0.116671i
\(733\) 7.03390 + 26.2509i 0.259803 + 0.969599i 0.965355 + 0.260940i \(0.0840325\pi\)
−0.705552 + 0.708658i \(0.749301\pi\)
\(734\) −31.3205 −1.15606
\(735\) 0 0
\(736\) 3.73205 0.137565
\(737\) 0.757875 + 2.82843i 0.0279167 + 0.104186i
\(738\) 2.38014 + 0.637756i 0.0876141 + 0.0234761i
\(739\) −11.6147 + 6.70577i −0.427255 + 0.246676i −0.698177 0.715926i \(-0.746005\pi\)
0.270922 + 0.962601i \(0.412672\pi\)
\(740\) 0 0
\(741\) 6.14359i 0.225691i
\(742\) −11.5403 7.81534i −0.423659 0.286910i
\(743\) 27.2354 + 27.2354i 0.999170 + 0.999170i 1.00000 0.000830035i \(-0.000264208\pi\)
−0.000830035 1.00000i \(0.500264\pi\)
\(744\) −6.86603 3.96410i −0.251721 0.145331i
\(745\) 0 0
\(746\) −3.07180 5.32051i −0.112466 0.194798i
\(747\) −11.2629 + 3.01790i −0.412089 + 0.110419i
\(748\) −1.17398 + 1.17398i −0.0429248 + 0.0429248i
\(749\) 8.66025 25.0000i 0.316439 0.913480i
\(750\) 0 0
\(751\) 12.9282 22.3923i 0.471757 0.817107i −0.527721 0.849418i \(-0.676953\pi\)
0.999478 + 0.0323109i \(0.0102867\pi\)
\(752\) 2.84701 10.6252i 0.103820 0.387461i
\(753\) 4.62158 17.2480i 0.168420 0.628551i
\(754\) −6.00000 + 10.3923i −0.218507 + 0.378465i
\(755\) 0 0
\(756\) −1.73205 2.00000i −0.0629941 0.0727393i
\(757\) 14.9743 14.9743i 0.544252 0.544252i −0.380521 0.924772i \(-0.624255\pi\)
0.924772 + 0.380521i \(0.124255\pi\)
\(758\) −9.71003 + 2.60179i −0.352684 + 0.0945014i
\(759\) 1.36603 + 2.36603i 0.0495836 + 0.0858813i
\(760\) 0 0
\(761\) −10.7942 6.23205i −0.391290 0.225912i 0.291429 0.956593i \(-0.405869\pi\)
−0.682719 + 0.730681i \(0.739203\pi\)
\(762\) −11.2122 11.2122i −0.406174 0.406174i
\(763\) −36.0488 2.58819i −1.30506 0.0936988i
\(764\) 24.8564i 0.899273i
\(765\) 0 0
\(766\) −22.9186 + 13.2321i −0.828082 + 0.478093i
\(767\) 0.757875 + 0.203072i 0.0273653 + 0.00733250i
\(768\) 0.258819 + 0.965926i 0.00933933 + 0.0348548i
\(769\) −9.07180 −0.327137 −0.163569 0.986532i \(-0.552301\pi\)
−0.163569 + 0.986532i \(0.552301\pi\)
\(770\) 0 0
\(771\) 3.85641 0.138885
\(772\) −6.14231 22.9234i −0.221066 0.825031i
\(773\) −36.8947 9.88589i −1.32701 0.355571i −0.475409 0.879765i \(-0.657700\pi\)
−0.851599 + 0.524194i \(0.824367\pi\)
\(774\) 0.169873 0.0980762i 0.00610596 0.00352528i
\(775\) 0 0
\(776\) 7.00000i 0.251285i
\(777\) −7.02030 + 10.3664i −0.251852 + 0.371891i
\(778\) −19.5588 19.5588i −0.701215 0.701215i
\(779\) −8.95448 5.16987i −0.320828 0.185230i
\(780\) 0 0
\(781\) −4.70577 8.15064i −0.168386 0.291653i
\(782\) 8.17569 2.19067i