Properties

Label 605.2.g.d.81.1
Level $605$
Weight $2$
Character 605.81
Analytic conductor $4.831$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 605.81
Dual form 605.2.g.d.366.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.42705 + 1.76336i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-4.85410 - 3.52671i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.42705 + 1.76336i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-4.85410 - 3.52671i) q^{9} -1.00000 q^{10} +3.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{14} +(-0.927051 - 2.85317i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.85410 - 5.70634i) q^{18} +(1.23607 - 3.80423i) q^{19} +(0.809017 + 0.587785i) q^{20} +9.00000 q^{21} -8.00000 q^{23} +(7.28115 + 5.29007i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.23607 - 3.80423i) q^{26} +(7.28115 - 5.29007i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(1.85410 + 5.70634i) q^{29} +(0.927051 - 2.85317i) q^{30} +(1.61803 + 1.17557i) q^{31} -5.00000 q^{32} +(2.42705 + 1.76336i) q^{35} +(-1.85410 + 5.70634i) q^{36} +(-2.47214 - 7.60845i) q^{37} +(3.23607 - 2.35114i) q^{38} +(9.70820 - 7.05342i) q^{39} +(0.927051 + 2.85317i) q^{40} +(-1.54508 + 4.75528i) q^{41} +(7.28115 + 5.29007i) q^{42} +5.00000 q^{43} +6.00000 q^{45} +(-6.47214 - 4.70228i) q^{46} +(-0.927051 + 2.85317i) q^{47} +(0.927051 + 2.85317i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-1.23607 + 3.80423i) q^{52} +(-3.23607 - 2.35114i) q^{53} +9.00000 q^{54} -9.00000 q^{56} +(9.70820 + 7.05342i) q^{57} +(-1.85410 + 5.70634i) q^{58} +(-0.618034 - 1.90211i) q^{59} +(-2.42705 + 1.76336i) q^{60} +(8.89919 - 6.46564i) q^{61} +(0.618034 + 1.90211i) q^{62} +(-5.56231 + 17.1190i) q^{63} +(-5.66312 - 4.11450i) q^{64} +4.00000 q^{65} -13.0000 q^{67} +(7.41641 - 22.8254i) q^{69} +(0.927051 + 2.85317i) q^{70} +(-1.61803 + 1.17557i) q^{71} +(-14.5623 + 10.5801i) q^{72} +(-2.47214 - 7.60845i) q^{73} +(2.47214 - 7.60845i) q^{74} +(2.42705 + 1.76336i) q^{75} -4.00000 q^{76} +12.0000 q^{78} +(-8.09017 - 5.87785i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-4.04508 + 2.93893i) q^{82} +(-3.23607 + 2.35114i) q^{83} +(-2.78115 - 8.55951i) q^{84} +(4.04508 + 2.93893i) q^{86} -18.0000 q^{87} +1.00000 q^{89} +(4.85410 + 3.52671i) q^{90} +(-3.70820 + 11.4127i) q^{91} +(2.47214 + 7.60845i) q^{92} +(-4.85410 + 3.52671i) q^{93} +(-2.42705 + 1.76336i) q^{94} +(1.23607 + 3.80423i) q^{95} +(4.63525 - 14.2658i) q^{96} +(6.47214 + 4.70228i) q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + 3q^{3} + q^{4} - q^{5} - 3q^{6} + 3q^{7} - 3q^{8} - 6q^{9} + O(q^{10}) \) \( 4q + q^{2} + 3q^{3} + q^{4} - q^{5} - 3q^{6} + 3q^{7} - 3q^{8} - 6q^{9} - 4q^{10} + 12q^{12} - 4q^{13} - 3q^{14} + 3q^{15} + q^{16} + 6q^{18} - 4q^{19} + q^{20} + 36q^{21} - 32q^{23} + 9q^{24} - q^{25} + 4q^{26} + 9q^{27} - 3q^{28} - 6q^{29} - 3q^{30} + 2q^{31} - 20q^{32} + 3q^{35} + 6q^{36} + 8q^{37} + 4q^{38} + 12q^{39} - 3q^{40} + 5q^{41} + 9q^{42} + 20q^{43} + 24q^{45} - 8q^{46} + 3q^{47} - 3q^{48} - 2q^{49} + q^{50} + 4q^{52} - 4q^{53} + 36q^{54} - 36q^{56} + 12q^{57} + 6q^{58} + 2q^{59} - 3q^{60} + 11q^{61} - 2q^{62} + 18q^{63} - 7q^{64} + 16q^{65} - 52q^{67} - 24q^{69} - 3q^{70} - 2q^{71} - 18q^{72} + 8q^{73} - 8q^{74} + 3q^{75} - 16q^{76} + 48q^{78} - 10q^{79} + q^{80} - 9q^{81} - 5q^{82} - 4q^{83} + 9q^{84} + 5q^{86} - 72q^{87} + 4q^{89} + 6q^{90} + 12q^{91} - 8q^{92} - 6q^{93} - 3q^{94} - 4q^{95} - 15q^{96} + 8q^{97} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i 0.835853 0.548953i \(-0.184973\pi\)
−0.263792 + 0.964580i \(0.584973\pi\)
\(3\) −0.927051 + 2.85317i −0.535233 + 1.64728i 0.207912 + 0.978148i \(0.433333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) −2.42705 + 1.76336i −0.990839 + 0.719887i
\(7\) −0.927051 2.85317i −0.350392 1.07840i −0.958633 0.284644i \(-0.908125\pi\)
0.608241 0.793752i \(-0.291875\pi\)
\(8\) 0.927051 2.85317i 0.327762 1.00875i
\(9\) −4.85410 3.52671i −1.61803 1.17557i
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) 3.00000 0.866025
\(13\) −3.23607 2.35114i −0.897524 0.652089i 0.0403050 0.999187i \(-0.487167\pi\)
−0.937829 + 0.347098i \(0.887167\pi\)
\(14\) 0.927051 2.85317i 0.247765 0.762542i
\(15\) −0.927051 2.85317i −0.239364 0.736685i
\(16\) 0.809017 0.587785i 0.202254 0.146946i
\(17\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(18\) −1.85410 5.70634i −0.437016 1.34500i
\(19\) 1.23607 3.80423i 0.283573 0.872749i −0.703249 0.710943i \(-0.748268\pi\)
0.986823 0.161806i \(-0.0517318\pi\)
\(20\) 0.809017 + 0.587785i 0.180902 + 0.131433i
\(21\) 9.00000 1.96396
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 7.28115 + 5.29007i 1.48626 + 1.07983i
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) −1.23607 3.80423i −0.242413 0.746070i
\(27\) 7.28115 5.29007i 1.40126 1.01807i
\(28\) −2.42705 + 1.76336i −0.458670 + 0.333243i
\(29\) 1.85410 + 5.70634i 0.344298 + 1.05964i 0.961958 + 0.273196i \(0.0880806\pi\)
−0.617660 + 0.786445i \(0.711919\pi\)
\(30\) 0.927051 2.85317i 0.169256 0.520915i
\(31\) 1.61803 + 1.17557i 0.290607 + 0.211139i 0.723531 0.690292i \(-0.242518\pi\)
−0.432923 + 0.901431i \(0.642518\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 0 0
\(35\) 2.42705 + 1.76336i 0.410246 + 0.298062i
\(36\) −1.85410 + 5.70634i −0.309017 + 0.951057i
\(37\) −2.47214 7.60845i −0.406417 1.25082i −0.919707 0.392607i \(-0.871573\pi\)
0.513290 0.858215i \(-0.328427\pi\)
\(38\) 3.23607 2.35114i 0.524960 0.381405i
\(39\) 9.70820 7.05342i 1.55456 1.12945i
\(40\) 0.927051 + 2.85317i 0.146580 + 0.451126i
\(41\) −1.54508 + 4.75528i −0.241302 + 0.742650i 0.754921 + 0.655816i \(0.227675\pi\)
−0.996223 + 0.0868346i \(0.972325\pi\)
\(42\) 7.28115 + 5.29007i 1.12351 + 0.816275i
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 0 0
\(45\) 6.00000 0.894427
\(46\) −6.47214 4.70228i −0.954264 0.693314i
\(47\) −0.927051 + 2.85317i −0.135224 + 0.416178i −0.995625 0.0934408i \(-0.970213\pi\)
0.860401 + 0.509618i \(0.170213\pi\)
\(48\) 0.927051 + 2.85317i 0.133808 + 0.411820i
\(49\) −1.61803 + 1.17557i −0.231148 + 0.167939i
\(50\) 0.809017 0.587785i 0.114412 0.0831254i
\(51\) 0 0
\(52\) −1.23607 + 3.80423i −0.171412 + 0.527551i
\(53\) −3.23607 2.35114i −0.444508 0.322954i 0.342916 0.939366i \(-0.388586\pi\)
−0.787424 + 0.616412i \(0.788586\pi\)
\(54\) 9.00000 1.22474
\(55\) 0 0
\(56\) −9.00000 −1.20268
\(57\) 9.70820 + 7.05342i 1.28588 + 0.934249i
\(58\) −1.85410 + 5.70634i −0.243456 + 0.749279i
\(59\) −0.618034 1.90211i −0.0804612 0.247634i 0.902732 0.430204i \(-0.141558\pi\)
−0.983193 + 0.182570i \(0.941558\pi\)
\(60\) −2.42705 + 1.76336i −0.313331 + 0.227648i
\(61\) 8.89919 6.46564i 1.13942 0.827840i 0.152385 0.988321i \(-0.451305\pi\)
0.987039 + 0.160481i \(0.0513046\pi\)
\(62\) 0.618034 + 1.90211i 0.0784904 + 0.241569i
\(63\) −5.56231 + 17.1190i −0.700785 + 2.15679i
\(64\) −5.66312 4.11450i −0.707890 0.514312i
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) −13.0000 −1.58820 −0.794101 0.607785i \(-0.792058\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) 0 0
\(69\) 7.41641 22.8254i 0.892831 2.74785i
\(70\) 0.927051 + 2.85317i 0.110804 + 0.341019i
\(71\) −1.61803 + 1.17557i −0.192025 + 0.139515i −0.679644 0.733542i \(-0.737866\pi\)
0.487619 + 0.873057i \(0.337866\pi\)
\(72\) −14.5623 + 10.5801i −1.71618 + 1.24688i
\(73\) −2.47214 7.60845i −0.289342 0.890502i −0.985064 0.172191i \(-0.944915\pi\)
0.695722 0.718311i \(-0.255085\pi\)
\(74\) 2.47214 7.60845i 0.287380 0.884465i
\(75\) 2.42705 + 1.76336i 0.280252 + 0.203615i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 12.0000 1.35873
\(79\) −8.09017 5.87785i −0.910215 0.661310i 0.0308541 0.999524i \(-0.490177\pi\)
−0.941069 + 0.338214i \(0.890177\pi\)
\(80\) −0.309017 + 0.951057i −0.0345492 + 0.106331i
\(81\) 2.78115 + 8.55951i 0.309017 + 0.951057i
\(82\) −4.04508 + 2.93893i −0.446705 + 0.324550i
\(83\) −3.23607 + 2.35114i −0.355205 + 0.258071i −0.751049 0.660246i \(-0.770452\pi\)
0.395845 + 0.918318i \(0.370452\pi\)
\(84\) −2.78115 8.55951i −0.303449 0.933919i
\(85\) 0 0
\(86\) 4.04508 + 2.93893i 0.436193 + 0.316913i
\(87\) −18.0000 −1.92980
\(88\) 0 0
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) 4.85410 + 3.52671i 0.511667 + 0.371748i
\(91\) −3.70820 + 11.4127i −0.388725 + 1.19637i
\(92\) 2.47214 + 7.60845i 0.257738 + 0.793236i
\(93\) −4.85410 + 3.52671i −0.503347 + 0.365703i
\(94\) −2.42705 + 1.76336i −0.250331 + 0.181876i
\(95\) 1.23607 + 3.80423i 0.126818 + 0.390305i
\(96\) 4.63525 14.2658i 0.473084 1.45600i
\(97\) 6.47214 + 4.70228i 0.657146 + 0.477444i 0.865698 0.500567i \(-0.166875\pi\)
−0.208552 + 0.978011i \(0.566875\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) 4.04508 + 2.93893i 0.402501 + 0.292434i 0.770559 0.637369i \(-0.219977\pi\)
−0.368058 + 0.929803i \(0.619977\pi\)
\(102\) 0 0
\(103\) 2.47214 + 7.60845i 0.243587 + 0.749683i 0.995866 + 0.0908382i \(0.0289546\pi\)
−0.752279 + 0.658845i \(0.771045\pi\)
\(104\) −9.70820 + 7.05342i −0.951968 + 0.691645i
\(105\) −7.28115 + 5.29007i −0.710568 + 0.516258i
\(106\) −1.23607 3.80423i −0.120058 0.369499i
\(107\) 2.78115 8.55951i 0.268864 0.827479i −0.721914 0.691983i \(-0.756737\pi\)
0.990778 0.135496i \(-0.0432627\pi\)
\(108\) −7.28115 5.29007i −0.700629 0.509037i
\(109\) −9.00000 −0.862044 −0.431022 0.902342i \(-0.641847\pi\)
−0.431022 + 0.902342i \(0.641847\pi\)
\(110\) 0 0
\(111\) 24.0000 2.27798
\(112\) −2.42705 1.76336i −0.229335 0.166621i
\(113\) 1.85410 5.70634i 0.174419 0.536807i −0.825187 0.564859i \(-0.808930\pi\)
0.999606 + 0.0280521i \(0.00893043\pi\)
\(114\) 3.70820 + 11.4127i 0.347305 + 1.06890i
\(115\) 6.47214 4.70228i 0.603530 0.438490i
\(116\) 4.85410 3.52671i 0.450692 0.327447i
\(117\) 7.41641 + 22.8254i 0.685647 + 2.11020i
\(118\) 0.618034 1.90211i 0.0568946 0.175104i
\(119\) 0 0
\(120\) −9.00000 −0.821584
\(121\) 0 0
\(122\) 11.0000 0.995893
\(123\) −12.1353 8.81678i −1.09420 0.794982i
\(124\) 0.618034 1.90211i 0.0555011 0.170815i
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) −14.5623 + 10.5801i −1.29731 + 0.942553i
\(127\) −8.89919 + 6.46564i −0.789675 + 0.573733i −0.907867 0.419258i \(-0.862290\pi\)
0.118192 + 0.992991i \(0.462290\pi\)
\(128\) 0.927051 + 2.85317i 0.0819405 + 0.252187i
\(129\) −4.63525 + 14.2658i −0.408111 + 1.25604i
\(130\) 3.23607 + 2.35114i 0.283822 + 0.206209i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −12.0000 −1.04053
\(134\) −10.5172 7.64121i −0.908550 0.660100i
\(135\) −2.78115 + 8.55951i −0.239364 + 0.736685i
\(136\) 0 0
\(137\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(138\) 19.4164 14.1068i 1.65283 1.20085i
\(139\) −5.56231 17.1190i −0.471789 1.45202i −0.850240 0.526395i \(-0.823543\pi\)
0.378452 0.925621i \(-0.376457\pi\)
\(140\) 0.927051 2.85317i 0.0783501 0.241137i
\(141\) −7.28115 5.29007i −0.613184 0.445504i
\(142\) −2.00000 −0.167836
\(143\) 0 0
\(144\) −6.00000 −0.500000
\(145\) −4.85410 3.52671i −0.403111 0.292877i
\(146\) 2.47214 7.60845i 0.204595 0.629680i
\(147\) −1.85410 5.70634i −0.152924 0.470651i
\(148\) −6.47214 + 4.70228i −0.532006 + 0.386525i
\(149\) 13.7533 9.99235i 1.12671 0.818605i 0.141500 0.989938i \(-0.454807\pi\)
0.985213 + 0.171333i \(0.0548074\pi\)
\(150\) 0.927051 + 2.85317i 0.0756934 + 0.232960i
\(151\) −4.32624 + 13.3148i −0.352064 + 1.08354i 0.605628 + 0.795748i \(0.292922\pi\)
−0.957692 + 0.287794i \(0.907078\pi\)
\(152\) −9.70820 7.05342i −0.787439 0.572108i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) −9.70820 7.05342i −0.777278 0.564726i
\(157\) −2.47214 + 7.60845i −0.197298 + 0.607221i 0.802644 + 0.596458i \(0.203426\pi\)
−0.999942 + 0.0107624i \(0.996574\pi\)
\(158\) −3.09017 9.51057i −0.245841 0.756620i
\(159\) 9.70820 7.05342i 0.769911 0.559373i
\(160\) 4.04508 2.93893i 0.319792 0.232343i
\(161\) 7.41641 + 22.8254i 0.584495 + 1.79889i
\(162\) −2.78115 + 8.55951i −0.218508 + 0.672499i
\(163\) 13.7533 + 9.99235i 1.07724 + 0.782661i 0.977200 0.212322i \(-0.0681026\pi\)
0.100041 + 0.994983i \(0.468103\pi\)
\(164\) 5.00000 0.390434
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 5.66312 + 4.11450i 0.438225 + 0.318389i 0.784929 0.619585i \(-0.212699\pi\)
−0.346704 + 0.937975i \(0.612699\pi\)
\(168\) 8.34346 25.6785i 0.643712 1.98114i
\(169\) 0.927051 + 2.85317i 0.0713116 + 0.219475i
\(170\) 0 0
\(171\) −19.4164 + 14.1068i −1.48481 + 1.07878i
\(172\) −1.54508 4.75528i −0.117812 0.362587i
\(173\) 7.41641 22.8254i 0.563859 1.73538i −0.107458 0.994210i \(-0.534271\pi\)
0.671317 0.741170i \(-0.265729\pi\)
\(174\) −14.5623 10.5801i −1.10397 0.802078i
\(175\) −3.00000 −0.226779
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) 0.809017 + 0.587785i 0.0606384 + 0.0440564i
\(179\) −8.03444 + 24.7275i −0.600522 + 1.84822i −0.0754697 + 0.997148i \(0.524046\pi\)
−0.525053 + 0.851070i \(0.675954\pi\)
\(180\) −1.85410 5.70634i −0.138197 0.425325i
\(181\) 15.3713 11.1679i 1.14254 0.830105i 0.155070 0.987903i \(-0.450440\pi\)
0.987471 + 0.157799i \(0.0504397\pi\)
\(182\) −9.70820 + 7.05342i −0.719620 + 0.522834i
\(183\) 10.1976 + 31.3849i 0.753825 + 2.32004i
\(184\) −7.41641 + 22.8254i −0.546745 + 1.68271i
\(185\) 6.47214 + 4.70228i 0.475841 + 0.345719i
\(186\) −6.00000 −0.439941
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) −21.8435 15.8702i −1.58888 1.15439i
\(190\) −1.23607 + 3.80423i −0.0896738 + 0.275988i
\(191\) 2.47214 + 7.60845i 0.178877 + 0.550528i 0.999789 0.0205267i \(-0.00653431\pi\)
−0.820912 + 0.571055i \(0.806534\pi\)
\(192\) 16.9894 12.3435i 1.22610 0.890815i
\(193\) 8.09017 5.87785i 0.582343 0.423097i −0.257225 0.966352i \(-0.582808\pi\)
0.839568 + 0.543254i \(0.182808\pi\)
\(194\) 2.47214 + 7.60845i 0.177489 + 0.546255i
\(195\) −3.70820 + 11.4127i −0.265550 + 0.817279i
\(196\) 1.61803 + 1.17557i 0.115574 + 0.0839693i
\(197\) −14.0000 −0.997459 −0.498729 0.866758i \(-0.666200\pi\)
−0.498729 + 0.866758i \(0.666200\pi\)
\(198\) 0 0
\(199\) −6.00000 −0.425329 −0.212664 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(200\) −2.42705 1.76336i −0.171618 0.124688i
\(201\) 12.0517 37.0912i 0.850059 2.61621i
\(202\) 1.54508 + 4.75528i 0.108712 + 0.334581i
\(203\) 14.5623 10.5801i 1.02207 0.742580i
\(204\) 0 0
\(205\) −1.54508 4.75528i −0.107913 0.332123i
\(206\) −2.47214 + 7.60845i −0.172242 + 0.530106i
\(207\) 38.8328 + 28.2137i 2.69907 + 1.96099i
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) −9.00000 −0.621059
\(211\) 17.7984 + 12.9313i 1.22529 + 0.890226i 0.996528 0.0832566i \(-0.0265321\pi\)
0.228762 + 0.973482i \(0.426532\pi\)
\(212\) −1.23607 + 3.80423i −0.0848935 + 0.261275i
\(213\) −1.85410 5.70634i −0.127041 0.390992i
\(214\) 7.28115 5.29007i 0.497729 0.361622i
\(215\) −4.04508 + 2.93893i −0.275873 + 0.200433i
\(216\) −8.34346 25.6785i −0.567700 1.74720i
\(217\) 1.85410 5.70634i 0.125865 0.387372i
\(218\) −7.28115 5.29007i −0.493142 0.358289i
\(219\) 24.0000 1.62177
\(220\) 0 0
\(221\) 0 0
\(222\) 19.4164 + 14.1068i 1.30314 + 0.946790i
\(223\) 1.54508 4.75528i 0.103467 0.318437i −0.885901 0.463874i \(-0.846459\pi\)
0.989367 + 0.145437i \(0.0464589\pi\)
\(224\) 4.63525 + 14.2658i 0.309706 + 0.953177i
\(225\) −4.85410 + 3.52671i −0.323607 + 0.235114i
\(226\) 4.85410 3.52671i 0.322890 0.234593i
\(227\) −0.309017 0.951057i −0.0205102 0.0631238i 0.940278 0.340409i \(-0.110565\pi\)
−0.960788 + 0.277285i \(0.910565\pi\)
\(228\) 3.70820 11.4127i 0.245582 0.755823i
\(229\) 0.809017 + 0.587785i 0.0534613 + 0.0388419i 0.614195 0.789154i \(-0.289481\pi\)
−0.560734 + 0.827996i \(0.689481\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) 18.0000 1.18176
\(233\) 19.4164 + 14.1068i 1.27201 + 0.924170i 0.999281 0.0379203i \(-0.0120733\pi\)
0.272730 + 0.962090i \(0.412073\pi\)
\(234\) −7.41641 + 22.8254i −0.484826 + 1.49214i
\(235\) −0.927051 2.85317i −0.0604741 0.186120i
\(236\) −1.61803 + 1.17557i −0.105325 + 0.0765231i
\(237\) 24.2705 17.6336i 1.57654 1.14542i
\(238\) 0 0
\(239\) 1.23607 3.80423i 0.0799546 0.246075i −0.903087 0.429458i \(-0.858705\pi\)
0.983042 + 0.183383i \(0.0587048\pi\)
\(240\) −2.42705 1.76336i −0.156665 0.113824i
\(241\) 23.0000 1.48156 0.740780 0.671748i \(-0.234456\pi\)
0.740780 + 0.671748i \(0.234456\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −8.89919 6.46564i −0.569712 0.413920i
\(245\) 0.618034 1.90211i 0.0394847 0.121522i
\(246\) −4.63525 14.2658i −0.295533 0.909557i
\(247\) −12.9443 + 9.40456i −0.823624 + 0.598398i
\(248\) 4.85410 3.52671i 0.308236 0.223946i
\(249\) −3.70820 11.4127i −0.234998 0.723249i
\(250\) −0.309017 + 0.951057i −0.0195440 + 0.0601501i
\(251\) −14.5623 10.5801i −0.919165 0.667812i 0.0241513 0.999708i \(-0.492312\pi\)
−0.943316 + 0.331896i \(0.892312\pi\)
\(252\) 18.0000 1.13389
\(253\) 0 0
\(254\) −11.0000 −0.690201
\(255\) 0 0
\(256\) −5.25329 + 16.1680i −0.328331 + 1.01050i
\(257\) −1.85410 5.70634i −0.115656 0.355952i 0.876428 0.481534i \(-0.159920\pi\)
−0.992083 + 0.125582i \(0.959920\pi\)
\(258\) −12.1353 + 8.81678i −0.755508 + 0.548909i
\(259\) −19.4164 + 14.1068i −1.20648 + 0.876557i
\(260\) −1.23607 3.80423i −0.0766577 0.235928i
\(261\) 11.1246 34.2380i 0.688596 2.11928i
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) −9.70820 7.05342i −0.595248 0.432473i
\(267\) −0.927051 + 2.85317i −0.0567346 + 0.174611i
\(268\) 4.01722 + 12.3637i 0.245391 + 0.755235i
\(269\) −16.9894 + 12.3435i −1.03586 + 0.752596i −0.969473 0.245198i \(-0.921147\pi\)
−0.0663864 + 0.997794i \(0.521147\pi\)
\(270\) −7.28115 + 5.29007i −0.443117 + 0.321943i
\(271\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(272\) 0 0
\(273\) −29.1246 21.1603i −1.76270 1.28068i
\(274\) 0 0
\(275\) 0 0
\(276\) −24.0000 −1.44463
\(277\) −11.3262 8.22899i −0.680528 0.494432i 0.193005 0.981198i \(-0.438177\pi\)
−0.873533 + 0.486765i \(0.838177\pi\)
\(278\) 5.56231 17.1190i 0.333605 1.02673i
\(279\) −3.70820 11.4127i −0.222004 0.683259i
\(280\) 7.28115 5.29007i 0.435132 0.316142i
\(281\) 4.85410 3.52671i 0.289571 0.210386i −0.433510 0.901149i \(-0.642725\pi\)
0.723081 + 0.690763i \(0.242725\pi\)
\(282\) −2.78115 8.55951i −0.165615 0.509711i
\(283\) −4.01722 + 12.3637i −0.238799 + 0.734948i 0.757796 + 0.652492i \(0.226276\pi\)
−0.996595 + 0.0824559i \(0.973724\pi\)
\(284\) 1.61803 + 1.17557i 0.0960127 + 0.0697573i
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 15.0000 0.885422
\(288\) 24.2705 + 17.6336i 1.43015 + 1.03907i
\(289\) −5.25329 + 16.1680i −0.309017 + 0.951057i
\(290\) −1.85410 5.70634i −0.108877 0.335088i
\(291\) −19.4164 + 14.1068i −1.13821 + 0.826958i
\(292\) −6.47214 + 4.70228i −0.378753 + 0.275180i
\(293\) −10.5066 32.3359i −0.613801 1.88908i −0.418023 0.908436i \(-0.637277\pi\)
−0.195778 0.980648i \(-0.562723\pi\)
\(294\) 1.85410 5.70634i 0.108133 0.332800i
\(295\) 1.61803 + 1.17557i 0.0942056 + 0.0684444i
\(296\) −24.0000 −1.39497
\(297\) 0 0
\(298\) 17.0000 0.984784
\(299\) 25.8885 + 18.8091i 1.49717 + 1.08776i
\(300\) 0.927051 2.85317i 0.0535233 0.164728i
\(301\) −4.63525 14.2658i −0.267172 0.822270i
\(302\) −11.3262 + 8.22899i −0.651752 + 0.473525i
\(303\) −12.1353 + 8.81678i −0.697152 + 0.506511i
\(304\) −1.23607 3.80423i −0.0708934 0.218187i
\(305\) −3.39919 + 10.4616i −0.194637 + 0.599031i
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) −24.0000 −1.36531
\(310\) −1.61803 1.17557i −0.0918982 0.0667679i
\(311\) 7.41641 22.8254i 0.420546 1.29431i −0.486649 0.873597i \(-0.661781\pi\)
0.907195 0.420710i \(-0.138219\pi\)
\(312\) −11.1246 34.2380i −0.629807 1.93835i
\(313\) −6.47214 + 4.70228i −0.365827 + 0.265789i −0.755478 0.655174i \(-0.772595\pi\)
0.389652 + 0.920962i \(0.372595\pi\)
\(314\) −6.47214 + 4.70228i −0.365244 + 0.265365i
\(315\) −5.56231 17.1190i −0.313400 0.964547i
\(316\) −3.09017 + 9.51057i −0.173836 + 0.535011i
\(317\) −14.5623 10.5801i −0.817901 0.594240i 0.0982098 0.995166i \(-0.468688\pi\)
−0.916110 + 0.400926i \(0.868688\pi\)
\(318\) 12.0000 0.672927
\(319\) 0 0
\(320\) 7.00000 0.391312
\(321\) 21.8435 + 15.8702i 1.21918 + 0.885788i
\(322\) −7.41641 + 22.8254i −0.413300 + 1.27201i
\(323\) 0 0
\(324\) 7.28115 5.29007i 0.404508 0.293893i
\(325\) −3.23607 + 2.35114i −0.179505 + 0.130418i
\(326\) 5.25329 + 16.1680i 0.290953 + 0.895461i
\(327\) 8.34346 25.6785i 0.461394 1.42003i
\(328\) 12.1353 + 8.81678i 0.670057 + 0.486825i
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 3.23607 + 2.35114i 0.177602 + 0.129036i
\(333\) −14.8328 + 45.6507i −0.812833 + 2.50164i
\(334\) 2.16312 + 6.65740i 0.118361 + 0.364276i
\(335\) 10.5172 7.64121i 0.574617 0.417484i
\(336\) 7.28115 5.29007i 0.397219 0.288597i
\(337\) −3.70820 11.4127i −0.201999 0.621688i −0.999823 0.0187985i \(-0.994016\pi\)
0.797825 0.602890i \(-0.205984\pi\)
\(338\) −0.927051 + 2.85317i −0.0504249 + 0.155192i
\(339\) 14.5623 + 10.5801i 0.790916 + 0.574634i
\(340\) 0 0
\(341\) 0 0
\(342\) −24.0000 −1.29777
\(343\) −12.1353 8.81678i −0.655242 0.476061i
\(344\) 4.63525 14.2658i 0.249916 0.769163i
\(345\) 7.41641 + 22.8254i 0.399286 + 1.22888i
\(346\) 19.4164 14.1068i 1.04383 0.758389i
\(347\) −5.66312 + 4.11450i −0.304012 + 0.220878i −0.729323 0.684170i \(-0.760165\pi\)
0.425311 + 0.905047i \(0.360165\pi\)
\(348\) 5.56231 + 17.1190i 0.298171 + 0.917676i
\(349\) 6.79837 20.9232i 0.363909 1.12000i −0.586753 0.809766i \(-0.699594\pi\)
0.950662 0.310230i \(-0.100406\pi\)
\(350\) −2.42705 1.76336i −0.129731 0.0942553i
\(351\) −36.0000 −1.92154
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 4.85410 + 3.52671i 0.257993 + 0.187443i
\(355\) 0.618034 1.90211i 0.0328018 0.100954i
\(356\) −0.309017 0.951057i −0.0163779 0.0504059i
\(357\) 0 0
\(358\) −21.0344 + 15.2824i −1.11170 + 0.807701i
\(359\) −8.65248 26.6296i −0.456660 1.40546i −0.869175 0.494505i \(-0.835349\pi\)
0.412515 0.910951i \(-0.364651\pi\)
\(360\) 5.56231 17.1190i 0.293159 0.902251i
\(361\) 2.42705 + 1.76336i 0.127740 + 0.0928082i
\(362\) 19.0000 0.998618
\(363\) 0 0
\(364\) 12.0000 0.628971
\(365\) 6.47214 + 4.70228i 0.338767 + 0.246129i
\(366\) −10.1976 + 31.3849i −0.533035 + 1.64051i
\(367\) 0.309017 + 0.951057i 0.0161306 + 0.0496447i 0.958798 0.284089i \(-0.0916912\pi\)
−0.942667 + 0.333734i \(0.891691\pi\)
\(368\) −6.47214 + 4.70228i −0.337383 + 0.245123i
\(369\) 24.2705 17.6336i 1.26347 0.917966i
\(370\) 2.47214 + 7.60845i 0.128520 + 0.395545i
\(371\) −3.70820 + 11.4127i −0.192520 + 0.592517i
\(372\) 4.85410 + 3.52671i 0.251673 + 0.182851i
\(373\) 18.0000 0.932005 0.466002 0.884783i \(-0.345694\pi\)
0.466002 + 0.884783i \(0.345694\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 7.28115 + 5.29007i 0.375497 + 0.272814i
\(377\) 7.41641 22.8254i 0.381964 1.17557i
\(378\) −8.34346 25.6785i −0.429141 1.32076i
\(379\) 17.7984 12.9313i 0.914241 0.664235i −0.0278428 0.999612i \(-0.508864\pi\)
0.942084 + 0.335377i \(0.108864\pi\)
\(380\) 3.23607 2.35114i 0.166007 0.120611i
\(381\) −10.1976 31.3849i −0.522437 1.60790i
\(382\) −2.47214 + 7.60845i −0.126485 + 0.389282i
\(383\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(384\) −9.00000 −0.459279
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −24.2705 17.6336i −1.23374 0.896364i
\(388\) 2.47214 7.60845i 0.125504 0.386261i
\(389\) −0.927051 2.85317i −0.0470034 0.144661i 0.924800 0.380453i \(-0.124232\pi\)
−0.971804 + 0.235791i \(0.924232\pi\)
\(390\) −9.70820 + 7.05342i −0.491594 + 0.357164i
\(391\) 0 0
\(392\) 1.85410 + 5.70634i 0.0936463 + 0.288214i
\(393\) 0 0
\(394\) −11.3262 8.22899i −0.570608 0.414571i
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) −12.0000 −0.602263 −0.301131 0.953583i \(-0.597364\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) −4.85410 3.52671i −0.243314 0.176778i
\(399\) 11.1246 34.2380i 0.556927 1.71405i
\(400\) −0.309017 0.951057i −0.0154508 0.0475528i
\(401\) 29.9336 21.7481i 1.49481 1.08605i 0.522424 0.852686i \(-0.325028\pi\)
0.972390 0.233360i \(-0.0749720\pi\)
\(402\) 31.5517 22.9236i 1.57365 1.14333i
\(403\) −2.47214 7.60845i −0.123146 0.379004i
\(404\) 1.54508 4.75528i 0.0768709 0.236584i
\(405\) −7.28115 5.29007i −0.361803 0.262866i
\(406\) 18.0000 0.893325
\(407\) 0 0
\(408\) 0 0
\(409\) −16.9894 12.3435i −0.840070 0.610346i 0.0823205 0.996606i \(-0.473767\pi\)
−0.922390 + 0.386260i \(0.873767\pi\)
\(410\) 1.54508 4.75528i 0.0763063 0.234847i
\(411\) 0 0
\(412\) 6.47214 4.70228i 0.318859 0.231665i
\(413\) −4.85410 + 3.52671i −0.238855 + 0.173538i
\(414\) 14.8328 + 45.6507i 0.728993 + 2.24361i
\(415\) 1.23607 3.80423i 0.0606762 0.186742i
\(416\) 16.1803 + 11.7557i 0.793306 + 0.576371i
\(417\) 54.0000 2.64439
\(418\) 0 0
\(419\) 32.0000 1.56330 0.781651 0.623716i \(-0.214378\pi\)
0.781651 + 0.623716i \(0.214378\pi\)
\(420\) 7.28115 + 5.29007i 0.355284 + 0.258129i
\(421\) 0.927051 2.85317i 0.0451817 0.139055i −0.925921 0.377718i \(-0.876709\pi\)
0.971103 + 0.238663i \(0.0767090\pi\)
\(422\) 6.79837 + 20.9232i 0.330940 + 1.01853i
\(423\) 14.5623 10.5801i 0.708044 0.514424i
\(424\) −9.70820 + 7.05342i −0.471472 + 0.342545i
\(425\) 0 0
\(426\) 1.85410 5.70634i 0.0898315 0.276473i
\(427\) −26.6976 19.3969i −1.29199 0.938682i
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) −5.00000 −0.241121
\(431\) −14.5623 10.5801i −0.701442 0.509627i 0.178960 0.983856i \(-0.442727\pi\)
−0.880401 + 0.474229i \(0.842727\pi\)
\(432\) 2.78115 8.55951i 0.133808 0.411820i
\(433\) 4.32624 + 13.3148i 0.207906 + 0.639868i 0.999582 + 0.0289266i \(0.00920891\pi\)
−0.791676 + 0.610941i \(0.790791\pi\)
\(434\) 4.85410 3.52671i 0.233004 0.169288i
\(435\) 14.5623 10.5801i 0.698209 0.507279i
\(436\) 2.78115 + 8.55951i 0.133193 + 0.409926i
\(437\) −9.88854 + 30.4338i −0.473033 + 1.45585i
\(438\) 19.4164 + 14.1068i 0.927752 + 0.674051i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) −7.72542 + 23.7764i −0.367046 + 1.12965i 0.581644 + 0.813444i \(0.302410\pi\)
−0.948690 + 0.316208i \(0.897590\pi\)
\(444\) −7.41641 22.8254i −0.351967 1.08324i
\(445\) −0.809017 + 0.587785i −0.0383511 + 0.0278637i
\(446\) 4.04508 2.93893i 0.191540 0.139162i
\(447\) 15.7599 + 48.5039i 0.745416 + 2.29415i
\(448\) −6.48936 + 19.9722i −0.306593 + 0.943597i
\(449\) 10.5172 + 7.64121i 0.496338 + 0.360611i 0.807617 0.589708i \(-0.200757\pi\)
−0.311278 + 0.950319i \(0.600757\pi\)
\(450\) −6.00000 −0.282843
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) −33.9787 24.6870i −1.59646 1.15990i
\(454\) 0.309017 0.951057i 0.0145029 0.0446353i
\(455\) −3.70820 11.4127i −0.173843 0.535035i
\(456\) 29.1246 21.1603i 1.36388 0.990920i
\(457\) −21.0344 + 15.2824i −0.983950 + 0.714881i −0.958588 0.284797i \(-0.908074\pi\)
−0.0253618 + 0.999678i \(0.508074\pi\)
\(458\) 0.309017 + 0.951057i 0.0144394 + 0.0444400i
\(459\) 0 0
\(460\) −6.47214 4.70228i −0.301765 0.219245i
\(461\) 7.00000 0.326023 0.163011 0.986624i \(-0.447879\pi\)
0.163011 + 0.986624i \(0.447879\pi\)
\(462\) 0 0
\(463\) −15.0000 −0.697109 −0.348555 0.937288i \(-0.613327\pi\)
−0.348555 + 0.937288i \(0.613327\pi\)
\(464\) 4.85410 + 3.52671i 0.225346 + 0.163723i
\(465\) 1.85410 5.70634i 0.0859819 0.264625i
\(466\) 7.41641 + 22.8254i 0.343558 + 1.05736i
\(467\) −21.8435 + 15.8702i −1.01079 + 0.734385i −0.964376 0.264537i \(-0.914781\pi\)
−0.0464191 + 0.998922i \(0.514781\pi\)
\(468\) 19.4164 14.1068i 0.897524 0.652089i
\(469\) 12.0517 + 37.0912i 0.556494 + 1.71271i
\(470\) 0.927051 2.85317i 0.0427617 0.131607i
\(471\) −19.4164 14.1068i −0.894661 0.650009i
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) 30.0000 1.37795
\(475\) −3.23607 2.35114i −0.148481 0.107878i
\(476\) 0 0
\(477\) 7.41641 + 22.8254i 0.339574 + 1.04510i
\(478\) 3.23607 2.35114i 0.148014 0.107539i
\(479\) −4.85410 + 3.52671i −0.221790 + 0.161140i −0.693132 0.720811i \(-0.743770\pi\)
0.471342 + 0.881950i \(0.343770\pi\)
\(480\) 4.63525 + 14.2658i 0.211569 + 0.651144i
\(481\) −9.88854 + 30.4338i −0.450879 + 1.38766i
\(482\) 18.6074 + 13.5191i 0.847543 + 0.615776i
\(483\) −72.0000 −3.27611
\(484\) 0 0
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) −2.47214 + 7.60845i −0.112023 + 0.344772i −0.991315 0.131512i \(-0.958017\pi\)
0.879291 + 0.476284i \(0.158017\pi\)
\(488\) −10.1976 31.3849i −0.461622 1.42073i
\(489\) −41.2599 + 29.9770i −1.86584 + 1.35561i
\(490\) 1.61803 1.17557i 0.0730953 0.0531069i
\(491\) 6.79837 + 20.9232i 0.306806 + 0.944253i 0.978997 + 0.203875i \(0.0653535\pi\)
−0.672191 + 0.740378i \(0.734646\pi\)
\(492\) −4.63525 + 14.2658i −0.208973 + 0.643154i
\(493\) 0 0
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 4.85410 + 3.52671i 0.217736 + 0.158195i
\(498\) 3.70820 11.4127i 0.166169 0.511414i
\(499\) −12.9787 39.9444i −0.581007 1.78816i −0.614746 0.788725i \(-0.710742\pi\)
0.0337391 0.999431i \(-0.489258\pi\)
\(500\) 0.809017 0.587785i 0.0361803 0.0262866i
\(501\) −16.9894 + 12.3435i −0.759028 + 0.551466i
\(502\) −5.56231 17.1190i −0.248258 0.764059i
\(503\) 4.01722 12.3637i 0.179119 0.551272i −0.820679 0.571390i \(-0.806404\pi\)
0.999798 + 0.0201184i \(0.00640433\pi\)
\(504\) 43.6869 + 31.7404i 1.94597 + 1.41383i
\(505\) −5.00000 −0.222497
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) 8.89919 + 6.46564i 0.394838 + 0.286866i
\(509\) 7.10739 21.8743i 0.315030 0.969561i −0.660713 0.750639i \(-0.729746\pi\)
0.975742 0.218922i \(-0.0702542\pi\)
\(510\) 0 0
\(511\) −19.4164 + 14.1068i −0.858931 + 0.624050i
\(512\) −8.89919 + 6.46564i −0.393292 + 0.285744i
\(513\) −11.1246 34.2380i −0.491164 1.51165i
\(514\) 1.85410 5.70634i 0.0817809 0.251696i
\(515\) −6.47214 4.70228i −0.285196 0.207207i
\(516\) 15.0000 0.660338
\(517\) 0 0
\(518\) −24.0000 −1.05450
\(519\) 58.2492 + 42.3205i 2.55686 + 1.85767i
\(520\) 3.70820 11.4127i 0.162615 0.500479i
\(521\) 4.63525 + 14.2658i 0.203074 + 0.624998i 0.999787 + 0.0206400i \(0.00657038\pi\)
−0.796713 + 0.604358i \(0.793430\pi\)
\(522\) 29.1246 21.1603i 1.27475 0.926160i
\(523\) 3.23607 2.35114i 0.141503 0.102808i −0.514782 0.857321i \(-0.672127\pi\)
0.656285 + 0.754513i \(0.272127\pi\)
\(524\) 0 0
\(525\) 2.78115 8.55951i 0.121379 0.373568i
\(526\) 9.70820 + 7.05342i 0.423298 + 0.307544i
\(527\) 0 0
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 3.23607 + 2.35114i 0.140566 + 0.102127i
\(531\) −3.70820 + 11.4127i −0.160922 + 0.495268i
\(532\) 3.70820 + 11.4127i 0.160771 + 0.494802i
\(533\) 16.1803 11.7557i 0.700848 0.509196i
\(534\) −2.42705 + 1.76336i −0.105029 + 0.0763079i
\(535\) 2.78115 + 8.55951i 0.120240 + 0.370060i
\(536\) −12.0517 + 37.0912i −0.520553 + 1.60210i
\(537\) −63.1033 45.8472i −2.72311 1.97845i
\(538\) −21.0000 −0.905374
\(539\) 0 0
\(540\) 9.00000 0.387298
\(541\) −25.0795 18.2213i −1.07825 0.783397i −0.100876 0.994899i \(-0.532164\pi\)
−0.977377 + 0.211502i \(0.932164\pi\)
\(542\) 0 0
\(543\) 17.6140 + 54.2102i 0.755888 + 2.32638i
\(544\) 0 0
\(545\) 7.28115 5.29007i 0.311890 0.226602i
\(546\) −11.1246 34.2380i −0.476089 1.46525i
\(547\) 11.1246 34.2380i 0.475654 1.46391i −0.369420 0.929263i \(-0.620443\pi\)
0.845074 0.534650i \(-0.179557\pi\)
\(548\) 0 0
\(549\) −66.0000 −2.81681
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) −58.2492 42.3205i −2.47925 1.80128i
\(553\) −9.27051 + 28.5317i −0.394222 + 1.21329i
\(554\) −4.32624 13.3148i −0.183804 0.565691i
\(555\) −19.4164 + 14.1068i −0.824181 + 0.598802i
\(556\) −14.5623 + 10.5801i −0.617579 + 0.448698i
\(557\) −8.65248 26.6296i −0.366617 1.12833i −0.948962 0.315390i \(-0.897865\pi\)
0.582345 0.812942i \(-0.302135\pi\)
\(558\) 3.70820 11.4127i 0.156981 0.483137i
\(559\) −16.1803 11.7557i −0.684355 0.497213i
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −16.9894 12.3435i −0.716016 0.520216i 0.169093 0.985600i \(-0.445916\pi\)
−0.885109 + 0.465384i \(0.845916\pi\)
\(564\) −2.78115 + 8.55951i −0.117108 + 0.360420i
\(565\) 1.85410 + 5.70634i 0.0780027 + 0.240067i
\(566\) −10.5172 + 7.64121i −0.442072 + 0.321184i
\(567\) 21.8435 15.8702i 0.917339 0.666486i
\(568\) 1.85410 + 5.70634i 0.0777964 + 0.239433i
\(569\) −3.39919 + 10.4616i −0.142501 + 0.438574i −0.996681 0.0814036i \(-0.974060\pi\)
0.854180 + 0.519978i \(0.174060\pi\)
\(570\) −9.70820 7.05342i −0.406632 0.295435i
\(571\) −18.0000 −0.753277 −0.376638 0.926360i \(-0.622920\pi\)
−0.376638 + 0.926360i \(0.622920\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) 12.1353 + 8.81678i 0.506516 + 0.368005i
\(575\) −2.47214 + 7.60845i −0.103095 + 0.317294i
\(576\) 12.9787 + 39.9444i 0.540780 + 1.66435i
\(577\) −11.3262 + 8.22899i −0.471517 + 0.342577i −0.798032 0.602615i \(-0.794126\pi\)
0.326515 + 0.945192i \(0.394126\pi\)
\(578\) −13.7533 + 9.99235i −0.572061 + 0.415627i
\(579\) 9.27051 + 28.5317i 0.385269 + 1.18574i
\(580\) −1.85410 + 5.70634i −0.0769874 + 0.236943i
\(581\) 9.70820 + 7.05342i 0.402764 + 0.292625i
\(582\) −24.0000 −0.994832
\(583\) 0 0
\(584\) −24.0000 −0.993127
\(585\) −19.4164 14.1068i −0.802770 0.583246i
\(586\) 10.5066 32.3359i 0.434023 1.33578i
\(587\) 6.48936 + 19.9722i 0.267844 + 0.824340i 0.991024 + 0.133681i \(0.0426797\pi\)
−0.723180 + 0.690660i \(0.757320\pi\)
\(588\) −4.85410 + 3.52671i −0.200180 + 0.145439i
\(589\) 6.47214 4.70228i 0.266680 0.193754i
\(590\) 0.618034 + 1.90211i 0.0254441 + 0.0783088i
\(591\) 12.9787 39.9444i 0.533873 1.64309i
\(592\) −6.47214 4.70228i −0.266003 0.193263i
\(593\) 44.0000 1.80686 0.903432 0.428732i \(-0.141040\pi\)
0.903432 + 0.428732i \(0.141040\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −13.7533 9.99235i −0.563357 0.409303i
\(597\) 5.56231 17.1190i 0.227650 0.700635i
\(598\) 9.88854 + 30.4338i 0.404373 + 1.24453i
\(599\) −19.4164 + 14.1068i −0.793333 + 0.576390i −0.908951 0.416904i \(-0.863115\pi\)
0.115618 + 0.993294i \(0.463115\pi\)
\(600\) 7.28115 5.29007i 0.297252 0.215966i
\(601\) −0.618034 1.90211i −0.0252101 0.0775888i 0.937660 0.347554i \(-0.112988\pi\)
−0.962870 + 0.269965i \(0.912988\pi\)
\(602\) 4.63525 14.2658i 0.188919 0.581433i
\(603\) 63.1033 + 45.8472i 2.56977 + 1.86704i
\(604\) 14.0000 0.569652
\(605\) 0 0
\(606\) −15.0000 −0.609333
\(607\) 32.3607 + 23.5114i 1.31348 + 0.954299i 0.999989 + 0.00470738i \(0.00149841\pi\)
0.313491 + 0.949591i \(0.398502\pi\)
\(608\) −6.18034 + 19.0211i −0.250646 + 0.771409i
\(609\) 16.6869 + 51.3571i 0.676188 + 2.08109i
\(610\) −8.89919 + 6.46564i −0.360318 + 0.261786i
\(611\) 9.70820 7.05342i 0.392752 0.285351i
\(612\) 0 0
\(613\) −6.79837 + 20.9232i −0.274584 + 0.845082i 0.714745 + 0.699385i \(0.246543\pi\)
−0.989329 + 0.145697i \(0.953457\pi\)
\(614\) −6.47214 4.70228i −0.261194 0.189769i
\(615\) 15.0000 0.604858
\(616\) 0 0
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) −19.4164 14.1068i −0.781042 0.567461i
\(619\) −2.47214 + 7.60845i −0.0993635 + 0.305810i −0.988366 0.152092i \(-0.951399\pi\)
0.889003 + 0.457902i \(0.151399\pi\)
\(620\) 0.618034 + 1.90211i 0.0248208 + 0.0763907i
\(621\) −58.2492 + 42.3205i −2.33746 + 1.69826i
\(622\) 19.4164 14.1068i 0.778527 0.565633i
\(623\) −0.927051 2.85317i −0.0371415 0.114310i
\(624\) 3.70820 11.4127i 0.148447 0.456873i
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) −8.00000 −0.319744
\(627\) 0 0
\(628\) 8.00000 0.319235
\(629\) 0 0
\(630\) 5.56231 17.1190i 0.221608 0.682038i
\(631\) −13.5967 41.8465i −0.541278 1.66588i −0.729679 0.683790i \(-0.760330\pi\)
0.188401 0.982092i \(-0.439670\pi\)
\(632\) −24.2705 + 17.6336i −0.965429 + 0.701425i
\(633\) −53.3951 + 38.7938i −2.12227 + 1.54192i
\(634\) −5.56231 17.1190i −0.220907 0.679883i
\(635\) 3.39919 10.4616i 0.134893 0.415157i
\(636\) −9.70820 7.05342i −0.384955 0.279686i
\(637\) 8.00000 0.316972
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) −2.42705 1.76336i −0.0959376 0.0697028i
\(641\) −4.32624 + 13.3148i −0.170876 + 0.525903i −0.999421 0.0340198i \(-0.989169\pi\)
0.828545 + 0.559922i \(0.189169\pi\)
\(642\) 8.34346 + 25.6785i 0.329290 + 1.01345i
\(643\) −28.3156 + 20.5725i −1.11666 + 0.811300i −0.983699 0.179822i \(-0.942448\pi\)
−0.132959 + 0.991122i \(0.542448\pi\)
\(644\) 19.4164 14.1068i 0.765114 0.555888i
\(645\) −4.63525 14.2658i −0.182513 0.561717i
\(646\) 0 0
\(647\) 20.2254 + 14.6946i 0.795143 + 0.577706i 0.909485 0.415736i \(-0.136476\pi\)
−0.114342 + 0.993441i \(0.536476\pi\)
\(648\) 27.0000 1.06066
\(649\) 0 0
\(650\) −4.00000 −0.156893
\(651\) 14.5623 + 10.5801i 0.570742 + 0.414668i
\(652\) 5.25329 16.1680i 0.205735 0.633186i
\(653\) −10.5066 32.3359i −0.411154 1.26540i −0.915646 0.401986i \(-0.868320\pi\)
0.504492 0.863417i \(-0.331680\pi\)
\(654\) 21.8435 15.8702i 0.854147 0.620574i
\(655\) 0 0
\(656\) 1.54508 + 4.75528i 0.0603254 + 0.185663i
\(657\) −14.8328 + 45.6507i −0.578683 + 1.78100i
\(658\) 7.28115 + 5.29007i 0.283849 + 0.206228i
\(659\) −42.0000 −1.63609 −0.818044 0.575156i \(-0.804941\pi\)
−0.818044 + 0.575156i \(0.804941\pi\)
\(660\) 0 0
\(661\) −37.0000 −1.43913 −0.719567 0.694423i \(-0.755660\pi\)
−0.719567 + 0.694423i \(0.755660\pi\)
\(662\) −16.1803 11.7557i −0.628867 0.456898i
\(663\) 0 0
\(664\) 3.70820 + 11.4127i 0.143906 + 0.442898i
\(665\) 9.70820 7.05342i 0.376468 0.273520i
\(666\) −38.8328 + 28.2137i −1.50474 + 1.09326i
\(667\) −14.8328 45.6507i −0.574329 1.76760i
\(668\) 2.16312 6.65740i 0.0836936 0.257582i
\(669\) 12.1353 + 8.81678i 0.469176 + 0.340876i
\(670\) 13.0000 0.502234
\(671\) 0 0
\(672\) −45.0000 −1.73591
\(673\) 8.09017 + 5.87785i 0.311853 + 0.226575i 0.732691 0.680561i \(-0.238264\pi\)
−0.420838 + 0.907136i \(0.638264\pi\)
\(674\) 3.70820 11.4127i 0.142835 0.439600i
\(675\) −2.78115 8.55951i −0.107047 0.329456i
\(676\) 2.42705 1.76336i 0.0933481 0.0678214i
\(677\) 22.6525 16.4580i 0.870605 0.632532i −0.0601440 0.998190i \(-0.519156\pi\)
0.930749 + 0.365658i \(0.119156\pi\)
\(678\) 5.56231 + 17.1190i 0.213619 + 0.657452i
\(679\) 7.41641 22.8254i 0.284616 0.875957i
\(680\) 0 0
\(681\) 3.00000 0.114960
\(682\) 0 0
\(683\) 47.0000 1.79841 0.899203 0.437533i \(-0.144148\pi\)
0.899203 + 0.437533i \(0.144148\pi\)
\(684\) 19.4164 + 14.1068i 0.742405 + 0.539389i
\(685\) 0 0
\(686\) −4.63525 14.2658i −0.176975 0.544673i
\(687\) −2.42705 + 1.76336i −0.0925978 + 0.0672762i
\(688\) 4.04508 2.93893i 0.154217 0.112046i
\(689\) 4.94427 + 15.2169i 0.188362 + 0.579718i
\(690\) −7.41641 + 22.8254i −0.282338 + 0.868946i
\(691\) 32.3607 + 23.5114i 1.23106 + 0.894416i 0.996969 0.0777989i \(-0.0247892\pi\)
0.234089 + 0.972215i \(0.424789\pi\)
\(692\) −24.0000 −0.912343
\(693\) 0 0
\(694\) −7.00000 −0.265716
\(695\) 14.5623 + 10.5801i 0.552380 + 0.401327i
\(696\) −16.6869 + 51.3571i −0.632516 + 1.94668i
\(697\) 0 0
\(698\) 17.7984 12.9313i 0.673678 0.489456i
\(699\) −58.2492 + 42.3205i −2.20319 + 1.60071i
\(700\) 0.927051 + 2.85317i 0.0350392 + 0.107840i
\(701\) 11.7426 36.1401i 0.443514 1.36499i −0.440592 0.897707i \(-0.645231\pi\)
0.884106 0.467287i \(-0.154769\pi\)
\(702\) −29.1246 21.1603i −1.09924 0.798643i
\(703\) −32.0000 −1.20690
\(704\) 0 0
\(705\) 9.00000 0.338960
\(706\) 4.85410 + 3.52671i 0.182687 + 0.132730i
\(707\) 4.63525 14.2658i 0.174327 0.536522i
\(708\) −1.85410 5.70634i −0.0696814 0.214457i
\(709\) 20.2254 14.6946i 0.759582 0.551868i −0.139200 0.990264i \(-0.544453\pi\)
0.898782 + 0.438396i \(0.144453\pi\)
\(710\) 1.61803 1.17557i 0.0607237 0.0441184i
\(711\) 18.5410 + 57.0634i 0.695343 + 2.14004i
\(712\) 0.927051 2.85317i 0.0347427 0.106927i
\(713\) −12.9443 9.40456i −0.484767 0.352204i
\(714\) 0 0
\(715\) 0 0
\(716\) 26.0000 0.971666
\(717\) 9.70820 + 7.05342i 0.362560 + 0.263415i
\(718\) 8.65248 26.6296i 0.322908 0.993807i
\(719\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(720\) 4.85410 3.52671i 0.180902 0.131433i
\(721\) 19.4164 14.1068i 0.723105 0.525366i
\(722\) 0.927051 + 2.85317i 0.0345013 + 0.106184i
\(723\) −21.3222 + 65.6229i −0.792980 + 2.44054i
\(724\) −15.3713 11.1679i −0.571271 0.415052i
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) 29.1246 + 21.1603i 1.07943 + 0.784252i
\(729\) −8.34346 + 25.6785i −0.309017 + 0.951057i
\(730\) 2.47214 + 7.60845i 0.0914979 + 0.281601i
\(731\) 0 0
\(732\) 26.6976 19.3969i 0.986770 0.716931i
\(733\) 11.1246 + 34.2380i 0.410897 + 1.26461i 0.915870 + 0.401475i \(0.131502\pi\)
−0.504973 + 0.863135i \(0.668498\pi\)
\(734\) −0.309017 + 0.951057i −0.0114060 + 0.0351041i
\(735\) 4.85410 + 3.52671i 0.179046 + 0.130085i
\(736\) 40.0000 1.47442
\(737\) 0 0
\(738\) 30.0000 1.10432
\(739\) 8.09017 + 5.87785i 0.297602 + 0.216220i 0.726558 0.687105i \(-0.241119\pi\)
−0.428957 + 0.903325i \(0.641119\pi\)
\(740\) 2.47214 7.60845i 0.0908775 0.279692i
\(741\) −14.8328 45.6507i −0.544897 1.67702i
\(742\) −9.70820 + 7.05342i −0.356399 + 0.258939i
\(743\) 5.66312 4.11450i 0.207760 0.150946i −0.479040 0.877793i \(-0.659015\pi\)
0.686799 + 0.726847i \(0.259015\pi\)
\(744\) 5.56231 + 17.1190i 0.203924 + 0.627614i
\(745\) −5.25329 + 16.1680i −0.192466 + 0.592348i
\(746\) 14.5623 + 10.5801i 0.533164 + 0.387366i
\(747\) 24.0000 0.878114
\(748\) 0 0
\(749\) −27.0000 −0.986559
\(750\) −2.42705 1.76336i −0.0886234 0.0643886i
\(751\) 3.09017 9.51057i 0.112762 0.347045i −0.878712 0.477353i \(-0.841596\pi\)
0.991474 + 0.130307i \(0.0415964\pi\)
\(752\) 0.927051 + 2.85317i 0.0338061 + 0.104044i
\(753\) 43.6869 31.7404i 1.59204 1.15668i
\(754\) 19.4164 14.1068i 0.707104 0.513741i
\(755\) −4.32624 13.3148i −0.157448 0.484575i
\(756\) −8.34346 + 25.6785i −0.303449 + 0.933919i
\(757\) 9.70820 + 7.05342i 0.352851 + 0.256361i 0.750064 0.661365i \(-0.230023\pi\)
−0.397213 + 0.917726i \(0.630023\pi\)
\(758\) 22.0000 0.799076
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) −21.0344 15.2824i −0.762498 0.553987i 0.137178 0.990546i \(-0.456197\pi\)
−0.899675 + 0.436559i \(0.856197\pi\)
\(762\) 10.1976 31.3849i 0.369419 1.13695i
\(763\) 8.34346 + 25.6785i 0.302053 + 0.929625i
\(764\) 6.47214 4.70228i 0.234154 0.170123i
\(765\) 0 0
\(766\) 0 0
\(767\) −2.47214 + 7.60845i −0.0892637 + 0.274725i
\(768\) −41.2599 29.9770i −1.48884 1.08170i
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −8.09017 5.87785i −0.291172 0.211549i
\(773\) −6.79837 + 20.9232i −0.244521 + 0.752557i 0.751194 + 0.660081i \(0.229478\pi\)
−0.995715 + 0.0924757i \(0.970522\pi\)
\(774\) −9.27051 28.5317i −0.333222 1.02555i
\(775\) 1.61803 1.17557i 0.0581215 0.0422277i
\(776\) 19.4164 14.1068i 0.697008 0.506406i
\(777\) −22.2492 68.4761i −0.798186 2.45657i
\(778\) 0.927051 2.85317i 0.0332364 0.102291i
\(779\) 16.1803 + 11.7557i 0.579721 + 0.421192i
\(780\) 12.0000 0.429669
\(781\) 0 0
\(782\)