Properties

Label 507.2.j.i.316.5
Level $507$
Weight $2$
Character 507.316
Analytic conductor $4.048$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
Defining polynomial: \(x^{12} - 5 x^{10} + 19 x^{8} - 28 x^{6} + 31 x^{4} - 6 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.5
Root \(1.07992 - 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.i.361.5

$q$-expansion

\(f(q)\) \(=\) \(q+(2.04113 + 1.17845i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.77748 + 3.07868i) q^{4} -3.69202i q^{5} +(2.04113 - 1.17845i) q^{6} +(-0.694498 + 0.400969i) q^{7} +3.66487i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(2.04113 + 1.17845i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.77748 + 3.07868i) q^{4} -3.69202i q^{5} +(2.04113 - 1.17845i) q^{6} +(-0.694498 + 0.400969i) q^{7} +3.66487i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.35086 - 7.53590i) q^{10} +(2.46891 + 1.42543i) q^{11} +3.55496 q^{12} -1.89008 q^{14} +(-3.19738 - 1.84601i) q^{15} +(-0.763906 + 1.32312i) q^{16} +(1.46950 + 2.54525i) q^{17} -2.35690i q^{18} +(2.11747 - 1.22252i) q^{19} +(11.3666 - 6.56249i) q^{20} +0.801938i q^{21} +(3.35958 + 5.81897i) q^{22} +(-3.89493 + 6.74621i) q^{23} +(3.17387 + 1.83244i) q^{24} -8.63102 q^{25} -1.00000 q^{27} +(-2.46891 - 1.42543i) q^{28} +(-1.92543 + 3.33494i) q^{29} +(-4.35086 - 7.53590i) q^{30} -2.34481i q^{31} +(3.22929 - 1.86443i) q^{32} +(2.46891 - 1.42543i) q^{33} +6.92692i q^{34} +(1.48039 + 2.56410i) q^{35} +(1.77748 - 3.07868i) q^{36} +(-6.44760 - 3.72252i) q^{37} +5.76271 q^{38} +13.5308 q^{40} +(-0.736862 - 0.425428i) q^{41} +(-0.945042 + 1.63686i) q^{42} +(-0.807979 - 1.39946i) q^{43} +10.1347i q^{44} +(-3.19738 + 1.84601i) q^{45} +(-15.9001 + 9.17994i) q^{46} +2.44504i q^{47} +(0.763906 + 1.32312i) q^{48} +(-3.17845 + 5.50523i) q^{49} +(-17.6171 - 10.1712i) q^{50} +2.93900 q^{51} -9.96077 q^{53} +(-2.04113 - 1.17845i) q^{54} +(5.26271 - 9.11528i) q^{55} +(-1.46950 - 2.54525i) q^{56} -2.44504i q^{57} +(-7.86010 + 4.53803i) q^{58} +(-4.66272 + 2.69202i) q^{59} -13.1250i q^{60} +(6.62833 + 11.4806i) q^{61} +(2.76324 - 4.78607i) q^{62} +(0.694498 + 0.400969i) q^{63} +11.8442 q^{64} +6.71917 q^{66} +(12.4653 + 7.19687i) q^{67} +(-5.22401 + 9.04826i) q^{68} +(3.89493 + 6.74621i) q^{69} +6.97823i q^{70} +(-7.03644 + 4.06249i) q^{71} +(3.17387 - 1.83244i) q^{72} -11.8877i q^{73} +(-8.77359 - 15.1963i) q^{74} +(-4.31551 + 7.47468i) q^{75} +(7.52751 + 4.34601i) q^{76} -2.28621 q^{77} +5.40581 q^{79} +(4.88500 + 2.82036i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00269 - 1.73671i) q^{82} -7.04892i q^{83} +(-2.46891 + 1.42543i) q^{84} +(9.39712 - 5.42543i) q^{85} -3.80864i q^{86} +(1.92543 + 3.33494i) q^{87} +(-5.22401 + 9.04826i) q^{88} +(-0.980069 - 0.565843i) q^{89} -8.70171 q^{90} -27.6926 q^{92} +(-2.03067 - 1.17241i) q^{93} +(-2.88135 + 4.99065i) q^{94} +(-4.51357 - 7.81774i) q^{95} -3.72886i q^{96} +(5.14798 - 2.97219i) q^{97} +(-12.9753 + 7.49127i) q^{98} -2.85086i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} + 22q^{4} - 6q^{9} + O(q^{10}) \) \( 12q + 6q^{3} + 22q^{4} - 6q^{9} - 2q^{10} + 44q^{12} - 20q^{14} - 22q^{16} - 2q^{17} + 18q^{22} - 44q^{25} - 12q^{27} + 4q^{29} + 2q^{30} - 8q^{35} + 22q^{36} + 12q^{40} - 10q^{42} - 30q^{43} + 22q^{48} - 30q^{49} - 4q^{51} - 68q^{53} - 6q^{55} + 2q^{56} + 26q^{61} - 4q^{62} + 36q^{66} + 26q^{68} - 30q^{74} - 22q^{75} - 60q^{77} + 12q^{79} - 6q^{81} - 6q^{82} - 4q^{87} + 26q^{88} + 4q^{90} + 28q^{92} - 42q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.04113 + 1.17845i 1.44330 + 0.833289i 0.998068 0.0621278i \(-0.0197886\pi\)
0.445230 + 0.895416i \(0.353122\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 1.77748 + 3.07868i 0.888740 + 1.53934i
\(5\) 3.69202i 1.65112i −0.564313 0.825561i \(-0.690859\pi\)
0.564313 0.825561i \(-0.309141\pi\)
\(6\) 2.04113 1.17845i 0.833289 0.481099i
\(7\) −0.694498 + 0.400969i −0.262496 + 0.151552i −0.625473 0.780246i \(-0.715094\pi\)
0.362977 + 0.931798i \(0.381760\pi\)
\(8\) 3.66487i 1.29573i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 4.35086 7.53590i 1.37586 2.38306i
\(11\) 2.46891 + 1.42543i 0.744405 + 0.429783i 0.823669 0.567071i \(-0.191924\pi\)
−0.0792636 + 0.996854i \(0.525257\pi\)
\(12\) 3.55496 1.02623
\(13\) 0 0
\(14\) −1.89008 −0.505146
\(15\) −3.19738 1.84601i −0.825561 0.476638i
\(16\) −0.763906 + 1.32312i −0.190976 + 0.330781i
\(17\) 1.46950 + 2.54525i 0.356406 + 0.617314i 0.987358 0.158509i \(-0.0506686\pi\)
−0.630951 + 0.775822i \(0.717335\pi\)
\(18\) 2.35690i 0.555526i
\(19\) 2.11747 1.22252i 0.485781 0.280466i −0.237042 0.971499i \(-0.576178\pi\)
0.722822 + 0.691034i \(0.242844\pi\)
\(20\) 11.3666 6.56249i 2.54164 1.46742i
\(21\) 0.801938i 0.174997i
\(22\) 3.35958 + 5.81897i 0.716266 + 1.24061i
\(23\) −3.89493 + 6.74621i −0.812149 + 1.40668i 0.0992087 + 0.995067i \(0.468369\pi\)
−0.911357 + 0.411616i \(0.864964\pi\)
\(24\) 3.17387 + 1.83244i 0.647864 + 0.374045i
\(25\) −8.63102 −1.72620
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −2.46891 1.42543i −0.466581 0.269380i
\(29\) −1.92543 + 3.33494i −0.357543 + 0.619282i −0.987550 0.157307i \(-0.949719\pi\)
0.630007 + 0.776590i \(0.283052\pi\)
\(30\) −4.35086 7.53590i −0.794354 1.37586i
\(31\) 2.34481i 0.421141i −0.977579 0.210571i \(-0.932468\pi\)
0.977579 0.210571i \(-0.0675322\pi\)
\(32\) 3.22929 1.86443i 0.570862 0.329588i
\(33\) 2.46891 1.42543i 0.429783 0.248135i
\(34\) 6.92692i 1.18796i
\(35\) 1.48039 + 2.56410i 0.250231 + 0.433413i
\(36\) 1.77748 3.07868i 0.296247 0.513114i
\(37\) −6.44760 3.72252i −1.05998 0.611979i −0.134552 0.990907i \(-0.542960\pi\)
−0.925426 + 0.378928i \(0.876293\pi\)
\(38\) 5.76271 0.934835
\(39\) 0 0
\(40\) 13.5308 2.13941
\(41\) −0.736862 0.425428i −0.115079 0.0664406i 0.441356 0.897332i \(-0.354498\pi\)
−0.556434 + 0.830892i \(0.687831\pi\)
\(42\) −0.945042 + 1.63686i −0.145823 + 0.252573i
\(43\) −0.807979 1.39946i −0.123216 0.213416i 0.797818 0.602898i \(-0.205987\pi\)
−0.921034 + 0.389482i \(0.872654\pi\)
\(44\) 10.1347i 1.52786i
\(45\) −3.19738 + 1.84601i −0.476638 + 0.275187i
\(46\) −15.9001 + 9.17994i −2.34435 + 1.35351i
\(47\) 2.44504i 0.356646i 0.983972 + 0.178323i \(0.0570672\pi\)
−0.983972 + 0.178323i \(0.942933\pi\)
\(48\) 0.763906 + 1.32312i 0.110260 + 0.190976i
\(49\) −3.17845 + 5.50523i −0.454064 + 0.786462i
\(50\) −17.6171 10.1712i −2.49143 1.43843i
\(51\) 2.93900 0.411542
\(52\) 0 0
\(53\) −9.96077 −1.36822 −0.684109 0.729380i \(-0.739809\pi\)
−0.684109 + 0.729380i \(0.739809\pi\)
\(54\) −2.04113 1.17845i −0.277763 0.160366i
\(55\) 5.26271 9.11528i 0.709624 1.22910i
\(56\) −1.46950 2.54525i −0.196370 0.340123i
\(57\) 2.44504i 0.323854i
\(58\) −7.86010 + 4.53803i −1.03208 + 0.595873i
\(59\) −4.66272 + 2.69202i −0.607034 + 0.350471i −0.771804 0.635861i \(-0.780645\pi\)
0.164770 + 0.986332i \(0.447312\pi\)
\(60\) 13.1250i 1.69443i
\(61\) 6.62833 + 11.4806i 0.848671 + 1.46994i 0.882394 + 0.470510i \(0.155930\pi\)
−0.0337232 + 0.999431i \(0.510736\pi\)
\(62\) 2.76324 4.78607i 0.350932 0.607832i
\(63\) 0.694498 + 0.400969i 0.0874986 + 0.0505173i
\(64\) 11.8442 1.48052
\(65\) 0 0
\(66\) 6.71917 0.827072
\(67\) 12.4653 + 7.19687i 1.52288 + 0.879237i 0.999634 + 0.0270575i \(0.00861373\pi\)
0.523249 + 0.852180i \(0.324720\pi\)
\(68\) −5.22401 + 9.04826i −0.633505 + 1.09726i
\(69\) 3.89493 + 6.74621i 0.468894 + 0.812149i
\(70\) 6.97823i 0.834058i
\(71\) −7.03644 + 4.06249i −0.835072 + 0.482129i −0.855586 0.517661i \(-0.826803\pi\)
0.0205142 + 0.999790i \(0.493470\pi\)
\(72\) 3.17387 1.83244i 0.374045 0.215955i
\(73\) 11.8877i 1.39135i −0.718357 0.695674i \(-0.755106\pi\)
0.718357 0.695674i \(-0.244894\pi\)
\(74\) −8.77359 15.1963i −1.01991 1.76654i
\(75\) −4.31551 + 7.47468i −0.498312 + 0.863102i
\(76\) 7.52751 + 4.34601i 0.863465 + 0.498522i
\(77\) −2.28621 −0.260538
\(78\) 0 0
\(79\) 5.40581 0.608202 0.304101 0.952640i \(-0.401644\pi\)
0.304101 + 0.952640i \(0.401644\pi\)
\(80\) 4.88500 + 2.82036i 0.546160 + 0.315325i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.00269 1.73671i −0.110728 0.191787i
\(83\) 7.04892i 0.773719i −0.922139 0.386860i \(-0.873560\pi\)
0.922139 0.386860i \(-0.126440\pi\)
\(84\) −2.46891 + 1.42543i −0.269380 + 0.155527i
\(85\) 9.39712 5.42543i 1.01926 0.588470i
\(86\) 3.80864i 0.410696i
\(87\) 1.92543 + 3.33494i 0.206427 + 0.357543i
\(88\) −5.22401 + 9.04826i −0.556882 + 0.964547i
\(89\) −0.980069 0.565843i −0.103887 0.0599793i 0.447156 0.894456i \(-0.352437\pi\)
−0.551043 + 0.834477i \(0.685770\pi\)
\(90\) −8.70171 −0.917241
\(91\) 0 0
\(92\) −27.6926 −2.88715
\(93\) −2.03067 1.17241i −0.210571 0.121573i
\(94\) −2.88135 + 4.99065i −0.297189 + 0.514746i
\(95\) −4.51357 7.81774i −0.463083 0.802083i
\(96\) 3.72886i 0.380575i
\(97\) 5.14798 2.97219i 0.522698 0.301780i −0.215340 0.976539i \(-0.569086\pi\)
0.738038 + 0.674759i \(0.235753\pi\)
\(98\) −12.9753 + 7.49127i −1.31070 + 0.756733i
\(99\) 2.85086i 0.286522i
\(100\) −15.3415 26.5722i −1.53415 2.65722i
\(101\) 2.31282 4.00593i 0.230134 0.398605i −0.727713 0.685882i \(-0.759417\pi\)
0.957848 + 0.287277i \(0.0927501\pi\)
\(102\) 5.99889 + 3.46346i 0.593978 + 0.342934i
\(103\) −1.20775 −0.119003 −0.0595016 0.998228i \(-0.518951\pi\)
−0.0595016 + 0.998228i \(0.518951\pi\)
\(104\) 0 0
\(105\) 2.96077 0.288942
\(106\) −20.3312 11.7383i −1.97475 1.14012i
\(107\) 4.76055 8.24552i 0.460220 0.797124i −0.538752 0.842465i \(-0.681104\pi\)
0.998972 + 0.0453402i \(0.0144372\pi\)
\(108\) −1.77748 3.07868i −0.171038 0.296247i
\(109\) 1.78448i 0.170922i 0.996342 + 0.0854611i \(0.0272363\pi\)
−0.996342 + 0.0854611i \(0.972764\pi\)
\(110\) 21.4838 12.4037i 2.04840 1.18264i
\(111\) −6.44760 + 3.72252i −0.611979 + 0.353326i
\(112\) 1.22521i 0.115771i
\(113\) −2.47554 4.28776i −0.232879 0.403359i 0.725775 0.687932i \(-0.241481\pi\)
−0.958654 + 0.284573i \(0.908148\pi\)
\(114\) 2.88135 4.99065i 0.269864 0.467417i
\(115\) 24.9072 + 14.3802i 2.32261 + 1.34096i
\(116\) −13.6896 −1.27105
\(117\) 0 0
\(118\) −12.6896 −1.16817
\(119\) −2.04113 1.17845i −0.187110 0.108028i
\(120\) 6.76540 11.7180i 0.617593 1.06970i
\(121\) −1.43631 2.48777i −0.130574 0.226161i
\(122\) 31.2446i 2.82875i
\(123\) −0.736862 + 0.425428i −0.0664406 + 0.0383595i
\(124\) 7.21894 4.16786i 0.648280 0.374285i
\(125\) 13.4058i 1.19905i
\(126\) 0.945042 + 1.63686i 0.0841910 + 0.145823i
\(127\) 2.83513 4.91058i 0.251577 0.435744i −0.712383 0.701791i \(-0.752384\pi\)
0.963960 + 0.266047i \(0.0857176\pi\)
\(128\) 17.7169 + 10.2289i 1.56597 + 0.904112i
\(129\) −1.61596 −0.142277
\(130\) 0 0
\(131\) 18.2228 1.59213 0.796067 0.605208i \(-0.206910\pi\)
0.796067 + 0.605208i \(0.206910\pi\)
\(132\) 8.77688 + 5.06734i 0.763930 + 0.441055i
\(133\) −0.980386 + 1.69808i −0.0850102 + 0.147242i
\(134\) 16.9623 + 29.3795i 1.46532 + 2.53800i
\(135\) 3.69202i 0.317759i
\(136\) −9.32802 + 5.38553i −0.799871 + 0.461806i
\(137\) 8.18430 4.72521i 0.699232 0.403702i −0.107829 0.994169i \(-0.534390\pi\)
0.807061 + 0.590468i \(0.201057\pi\)
\(138\) 18.3599i 1.56290i
\(139\) −2.00753 3.47715i −0.170277 0.294928i 0.768240 0.640162i \(-0.221133\pi\)
−0.938517 + 0.345234i \(0.887799\pi\)
\(140\) −5.26271 + 9.11528i −0.444780 + 0.770382i
\(141\) 2.11747 + 1.22252i 0.178323 + 0.102955i
\(142\) −19.1497 −1.60701
\(143\) 0 0
\(144\) 1.52781 0.127318
\(145\) 12.3127 + 7.10872i 1.02251 + 0.590347i
\(146\) 14.0090 24.2643i 1.15940 2.00813i
\(147\) 3.17845 + 5.50523i 0.262154 + 0.454064i
\(148\) 26.4668i 2.17556i
\(149\) −16.8059 + 9.70291i −1.37680 + 0.794893i −0.991772 0.128014i \(-0.959140\pi\)
−0.385023 + 0.922907i \(0.625806\pi\)
\(150\) −17.6171 + 10.1712i −1.43843 + 0.830476i
\(151\) 12.3623i 1.00603i −0.864278 0.503014i \(-0.832225\pi\)
0.864278 0.503014i \(-0.167775\pi\)
\(152\) 4.48039 + 7.76026i 0.363407 + 0.629440i
\(153\) 1.46950 2.54525i 0.118802 0.205771i
\(154\) −4.66645 2.69418i −0.376033 0.217103i
\(155\) −8.65710 −0.695355
\(156\) 0 0
\(157\) −18.6775 −1.49063 −0.745315 0.666712i \(-0.767701\pi\)
−0.745315 + 0.666712i \(0.767701\pi\)
\(158\) 11.0340 + 6.37047i 0.877816 + 0.506807i
\(159\) −4.98039 + 8.62628i −0.394970 + 0.684109i
\(160\) −6.88351 11.9226i −0.544189 0.942563i
\(161\) 6.24698i 0.492331i
\(162\) −2.04113 + 1.17845i −0.160366 + 0.0925876i
\(163\) 10.6863 6.16972i 0.837013 0.483250i −0.0192348 0.999815i \(-0.506123\pi\)
0.856248 + 0.516565i \(0.172790\pi\)
\(164\) 3.02475i 0.236194i
\(165\) −5.26271 9.11528i −0.409701 0.709624i
\(166\) 8.30678 14.3878i 0.644731 1.11671i
\(167\) −9.95406 5.74698i −0.770268 0.444715i 0.0627020 0.998032i \(-0.480028\pi\)
−0.832970 + 0.553318i \(0.813362\pi\)
\(168\) −2.93900 −0.226749
\(169\) 0 0
\(170\) 25.5743 1.96146
\(171\) −2.11747 1.22252i −0.161927 0.0934885i
\(172\) 2.87233 4.97502i 0.219013 0.379342i
\(173\) 6.05711 + 10.4912i 0.460514 + 0.797633i 0.998987 0.0450096i \(-0.0143318\pi\)
−0.538473 + 0.842643i \(0.680998\pi\)
\(174\) 9.07606i 0.688055i
\(175\) 5.99423 3.46077i 0.453121 0.261610i
\(176\) −3.77203 + 2.17778i −0.284328 + 0.164157i
\(177\) 5.38404i 0.404689i
\(178\) −1.33363 2.30992i −0.0999601 0.173136i
\(179\) −0.269282 + 0.466411i −0.0201271 + 0.0348612i −0.875914 0.482468i \(-0.839740\pi\)
0.855786 + 0.517329i \(0.173074\pi\)
\(180\) −11.3666 6.56249i −0.847214 0.489139i
\(181\) 23.2838 1.73067 0.865336 0.501192i \(-0.167105\pi\)
0.865336 + 0.501192i \(0.167105\pi\)
\(182\) 0 0
\(183\) 13.2567 0.979961
\(184\) −24.7240 14.2744i −1.82268 1.05232i
\(185\) −13.7436 + 23.8047i −1.01045 + 1.75015i
\(186\) −2.76324 4.78607i −0.202611 0.350932i
\(187\) 8.37867i 0.612709i
\(188\) −7.52751 + 4.34601i −0.549000 + 0.316965i
\(189\) 0.694498 0.400969i 0.0505173 0.0291662i
\(190\) 21.2760i 1.54353i
\(191\) −8.38285 14.5195i −0.606561 1.05060i −0.991803 0.127779i \(-0.959215\pi\)
0.385241 0.922816i \(-0.374118\pi\)
\(192\) 5.92208 10.2573i 0.427389 0.740259i
\(193\) −22.2949 12.8720i −1.60482 0.926544i −0.990504 0.137485i \(-0.956098\pi\)
−0.614318 0.789059i \(-0.710569\pi\)
\(194\) 14.0103 1.00588
\(195\) 0 0
\(196\) −22.5985 −1.61418
\(197\) 18.5510 + 10.7104i 1.32171 + 0.763087i 0.984001 0.178165i \(-0.0570160\pi\)
0.337705 + 0.941252i \(0.390349\pi\)
\(198\) 3.35958 5.81897i 0.238755 0.413536i
\(199\) 1.76391 + 3.05517i 0.125040 + 0.216576i 0.921749 0.387788i \(-0.126761\pi\)
−0.796709 + 0.604364i \(0.793427\pi\)
\(200\) 31.6316i 2.23669i
\(201\) 12.4653 7.19687i 0.879237 0.507628i
\(202\) 9.44155 5.45108i 0.664305 0.383537i
\(203\) 3.08815i 0.216745i
\(204\) 5.22401 + 9.04826i 0.365754 + 0.633505i
\(205\) −1.57069 + 2.72051i −0.109702 + 0.190009i
\(206\) −2.46518 1.42327i −0.171757 0.0991640i
\(207\) 7.78986 0.541432
\(208\) 0 0
\(209\) 6.97046 0.482157
\(210\) 6.04332 + 3.48911i 0.417029 + 0.240772i
\(211\) −0.607760 + 1.05267i −0.0418399 + 0.0724689i −0.886187 0.463328i \(-0.846655\pi\)
0.844347 + 0.535797i \(0.179989\pi\)
\(212\) −17.7051 30.6661i −1.21599 2.10615i
\(213\) 8.12498i 0.556715i
\(214\) 19.4338 11.2201i 1.32847 0.766992i
\(215\) −5.16684 + 2.98307i −0.352375 + 0.203444i
\(216\) 3.66487i 0.249363i
\(217\) 0.940198 + 1.62847i 0.0638248 + 0.110548i
\(218\) −2.10292 + 3.64236i −0.142427 + 0.246692i
\(219\) −10.2950 5.94385i −0.695674 0.401648i
\(220\) 37.4174 2.52268
\(221\) 0 0
\(222\) −17.5472 −1.17769
\(223\) −15.0588 8.69418i −1.00841 0.582205i −0.0976835 0.995218i \(-0.531143\pi\)
−0.910725 + 0.413012i \(0.864477\pi\)
\(224\) −1.49516 + 2.58969i −0.0998993 + 0.173031i
\(225\) 4.31551 + 7.47468i 0.287701 + 0.498312i
\(226\) 11.6692i 0.776223i
\(227\) −15.0823 + 8.70775i −1.00105 + 0.577954i −0.908557 0.417760i \(-0.862815\pi\)
−0.0924878 + 0.995714i \(0.529482\pi\)
\(228\) 7.52751 4.34601i 0.498522 0.287822i
\(229\) 18.7603i 1.23972i 0.784714 + 0.619858i \(0.212810\pi\)
−0.784714 + 0.619858i \(0.787190\pi\)
\(230\) 33.8925 + 58.7036i 2.23481 + 3.87080i
\(231\) −1.14310 + 1.97991i −0.0752107 + 0.130269i
\(232\) −12.2221 7.05645i −0.802422 0.463279i
\(233\) −3.95108 −0.258844 −0.129422 0.991590i \(-0.541312\pi\)
−0.129422 + 0.991590i \(0.541312\pi\)
\(234\) 0 0
\(235\) 9.02715 0.588866
\(236\) −16.5758 9.57002i −1.07899 0.622955i
\(237\) 2.70291 4.68157i 0.175573 0.304101i
\(238\) −2.77748 4.81073i −0.180037 0.311834i
\(239\) 0.818331i 0.0529334i −0.999650 0.0264667i \(-0.991574\pi\)
0.999650 0.0264667i \(-0.00842560\pi\)
\(240\) 4.88500 2.82036i 0.315325 0.182053i
\(241\) 5.22432 3.01626i 0.336528 0.194295i −0.322208 0.946669i \(-0.604425\pi\)
0.658736 + 0.752375i \(0.271092\pi\)
\(242\) 6.77048i 0.435223i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −23.5635 + 40.8131i −1.50850 + 2.61279i
\(245\) 20.3254 + 11.7349i 1.29854 + 0.749715i
\(246\) −2.00538 −0.127858
\(247\) 0 0
\(248\) 8.59345 0.545685
\(249\) −6.10454 3.52446i −0.386860 0.223353i
\(250\) −15.7981 + 27.3630i −0.999157 + 1.73059i
\(251\) −13.4400 23.2787i −0.848323 1.46934i −0.882704 0.469929i \(-0.844279\pi\)
0.0343812 0.999409i \(-0.489054\pi\)
\(252\) 2.85086i 0.179587i
\(253\) −19.2325 + 11.1039i −1.20914 + 0.698095i
\(254\) 11.5737 6.68210i 0.726200 0.419272i
\(255\) 10.8509i 0.679507i
\(256\) 12.2642 + 21.2422i 0.766513 + 1.32764i
\(257\) −4.52661 + 7.84033i −0.282362 + 0.489066i −0.971966 0.235121i \(-0.924451\pi\)
0.689604 + 0.724187i \(0.257785\pi\)
\(258\) −3.29838 1.90432i −0.205348 0.118558i
\(259\) 5.97046 0.370986
\(260\) 0 0
\(261\) 3.85086 0.238362
\(262\) 37.1952 + 21.4746i 2.29793 + 1.32671i
\(263\) −11.5755 + 20.0494i −0.713778 + 1.23630i 0.249651 + 0.968336i \(0.419684\pi\)
−0.963429 + 0.267964i \(0.913649\pi\)
\(264\) 5.22401 + 9.04826i 0.321516 + 0.556882i
\(265\) 36.7754i 2.25909i
\(266\) −4.00219 + 2.31067i −0.245390 + 0.141676i
\(267\) −0.980069 + 0.565843i −0.0599793 + 0.0346290i
\(268\) 51.1691i 3.12565i
\(269\) 1.21044 + 2.09654i 0.0738018 + 0.127828i 0.900565 0.434722i \(-0.143153\pi\)
−0.826763 + 0.562551i \(0.809820\pi\)
\(270\) −4.35086 + 7.53590i −0.264785 + 0.458620i
\(271\) 18.5720 + 10.7225i 1.12817 + 0.651347i 0.943473 0.331450i \(-0.107538\pi\)
0.184693 + 0.982796i \(0.440871\pi\)
\(272\) −4.49024 −0.272261
\(273\) 0 0
\(274\) 22.2737 1.34560
\(275\) −21.3092 12.3029i −1.28500 0.741893i
\(276\) −13.8463 + 23.9825i −0.833450 + 1.44358i
\(277\) −7.40366 12.8235i −0.444843 0.770490i 0.553199 0.833049i \(-0.313407\pi\)
−0.998041 + 0.0625593i \(0.980074\pi\)
\(278\) 9.46309i 0.567558i
\(279\) −2.03067 + 1.17241i −0.121573 + 0.0701902i
\(280\) −9.39712 + 5.42543i −0.561585 + 0.324231i
\(281\) 14.5036i 0.865215i 0.901582 + 0.432608i \(0.142406\pi\)
−0.901582 + 0.432608i \(0.857594\pi\)
\(282\) 2.88135 + 4.99065i 0.171582 + 0.297189i
\(283\) 12.8361 22.2328i 0.763026 1.32160i −0.178258 0.983984i \(-0.557046\pi\)
0.941284 0.337616i \(-0.109621\pi\)
\(284\) −25.0143 14.4420i −1.48432 0.856974i
\(285\) −9.02715 −0.534722
\(286\) 0 0
\(287\) 0.682333 0.0402768
\(288\) −3.22929 1.86443i −0.190287 0.109863i
\(289\) 4.18114 7.24194i 0.245949 0.425997i
\(290\) 16.7545 + 29.0197i 0.983859 + 1.70409i
\(291\) 5.94438i 0.348466i
\(292\) 36.5984 21.1301i 2.14176 1.23655i
\(293\) −22.9696 + 13.2615i −1.34190 + 0.774746i −0.987086 0.160191i \(-0.948789\pi\)
−0.354813 + 0.934937i \(0.615456\pi\)
\(294\) 14.9825i 0.873800i
\(295\) 9.93900 + 17.2149i 0.578671 + 1.00229i
\(296\) 13.6426 23.6296i 0.792958 1.37344i
\(297\) −2.46891 1.42543i −0.143261 0.0827117i
\(298\) −45.7375 −2.64950
\(299\) 0 0
\(300\) −30.6829 −1.77148
\(301\) 1.12228 + 0.647948i 0.0646871 + 0.0373471i
\(302\) 14.5683 25.2330i 0.838311 1.45200i
\(303\) −2.31282 4.00593i −0.132868 0.230134i
\(304\) 3.73556i 0.214249i
\(305\) 42.3867 24.4720i 2.42705 1.40126i
\(306\) 5.99889 3.46346i 0.342934 0.197993i
\(307\) 8.24698i 0.470680i −0.971913 0.235340i \(-0.924380\pi\)
0.971913 0.235340i \(-0.0756204\pi\)
\(308\) −4.06369 7.03851i −0.231550 0.401056i
\(309\) −0.603875 + 1.04594i −0.0343533 + 0.0595016i
\(310\) −17.6703 10.2019i −1.00361 0.579432i
\(311\) 14.4179 0.817564 0.408782 0.912632i \(-0.365954\pi\)
0.408782 + 0.912632i \(0.365954\pi\)
\(312\) 0 0
\(313\) 14.2338 0.804544 0.402272 0.915520i \(-0.368221\pi\)
0.402272 + 0.915520i \(0.368221\pi\)
\(314\) −38.1233 22.0105i −2.15142 1.24213i
\(315\) 1.48039 2.56410i 0.0834103 0.144471i
\(316\) 9.60872 + 16.6428i 0.540533 + 0.936230i
\(317\) 6.84415i 0.384406i 0.981355 + 0.192203i \(0.0615632\pi\)
−0.981355 + 0.192203i \(0.938437\pi\)
\(318\) −20.3312 + 11.7383i −1.14012 + 0.658248i
\(319\) −9.50743 + 5.48911i −0.532314 + 0.307331i
\(320\) 43.7289i 2.44452i
\(321\) −4.76055 8.24552i −0.265708 0.460220i
\(322\) 7.36174 12.7509i 0.410254 0.710580i
\(323\) 6.22324 + 3.59299i 0.346270 + 0.199919i
\(324\) −3.55496 −0.197498
\(325\) 0 0
\(326\) 29.0828 1.61075
\(327\) 1.54540 + 0.892240i 0.0854611 + 0.0493410i
\(328\) 1.55914 2.70051i 0.0860890 0.149111i
\(329\) −0.980386 1.69808i −0.0540504 0.0936181i
\(330\) 24.8073i 1.36560i
\(331\) −8.17757 + 4.72132i −0.449480 + 0.259507i −0.707611 0.706603i \(-0.750227\pi\)
0.258130 + 0.966110i \(0.416894\pi\)
\(332\) 21.7014 12.5293i 1.19102 0.687635i
\(333\) 7.44504i 0.407986i
\(334\) −13.5450 23.4607i −0.741151 1.28371i
\(335\) 26.5710 46.0223i 1.45173 2.51447i
\(336\) −1.06106 0.612605i −0.0578857 0.0334203i
\(337\) −2.64310 −0.143979 −0.0719895 0.997405i \(-0.522935\pi\)
−0.0719895 + 0.997405i \(0.522935\pi\)
\(338\) 0 0
\(339\) −4.95108 −0.268906
\(340\) 33.4064 + 19.2872i 1.81171 + 1.04599i
\(341\) 3.34236 5.78914i 0.180999 0.313500i
\(342\) −2.88135 4.99065i −0.155806 0.269864i
\(343\) 10.7114i 0.578361i
\(344\) 5.12884 2.96114i 0.276529 0.159654i
\(345\) 24.9072 14.3802i 1.34096 0.774202i
\(346\) 28.5520i 1.53496i
\(347\) 5.07942 + 8.79781i 0.272677 + 0.472291i 0.969547 0.244907i \(-0.0787575\pi\)
−0.696869 + 0.717198i \(0.745424\pi\)
\(348\) −6.84481 + 11.8556i −0.366921 + 0.635525i
\(349\) −9.04102 5.21983i −0.483954 0.279411i 0.238109 0.971239i \(-0.423473\pi\)
−0.722063 + 0.691827i \(0.756806\pi\)
\(350\) 16.3134 0.871986
\(351\) 0 0
\(352\) 10.6304 0.566604
\(353\) 15.8406 + 9.14556i 0.843108 + 0.486769i 0.858320 0.513115i \(-0.171509\pi\)
−0.0152113 + 0.999884i \(0.504842\pi\)
\(354\) −6.34481 + 10.9895i −0.337223 + 0.584087i
\(355\) 14.9988 + 25.9787i 0.796054 + 1.37881i
\(356\) 4.02310i 0.213224i
\(357\) −2.04113 + 1.17845i −0.108028 + 0.0623701i
\(358\) −1.09928 + 0.634670i −0.0580988 + 0.0335434i
\(359\) 15.2731i 0.806081i −0.915182 0.403041i \(-0.867953\pi\)
0.915182 0.403041i \(-0.132047\pi\)
\(360\) −6.76540 11.7180i −0.356568 0.617593i
\(361\) −6.51089 + 11.2772i −0.342678 + 0.593536i
\(362\) 47.5253 + 27.4388i 2.49788 + 1.44215i
\(363\) −2.87263 −0.150774
\(364\) 0 0
\(365\) −43.8896 −2.29729
\(366\) 27.0586 + 15.6223i 1.41438 + 0.816590i
\(367\) 11.1359 19.2879i 0.581288 1.00682i −0.414040 0.910259i \(-0.635882\pi\)
0.995327 0.0965606i \(-0.0307842\pi\)
\(368\) −5.95071 10.3069i −0.310202 0.537286i
\(369\) 0.850855i 0.0442937i
\(370\) −56.1051 + 32.3923i −2.91677 + 1.68400i
\(371\) 6.91774 3.99396i 0.359151 0.207356i
\(372\) 8.33572i 0.432187i
\(373\) −2.06315 3.57349i −0.106826 0.185028i 0.807657 0.589653i \(-0.200735\pi\)
−0.914483 + 0.404625i \(0.867402\pi\)
\(374\) −9.87382 + 17.1020i −0.510563 + 0.884321i
\(375\) 11.6098 + 6.70291i 0.599526 + 0.346137i
\(376\) −8.96077 −0.462116
\(377\) 0 0
\(378\) 1.89008 0.0972154
\(379\) −9.27261 5.35354i −0.476302 0.274993i 0.242572 0.970133i \(-0.422009\pi\)
−0.718874 + 0.695140i \(0.755342\pi\)
\(380\) 16.0456 27.7917i 0.823120 1.42569i
\(381\) −2.83513 4.91058i −0.145248 0.251577i
\(382\) 39.5150i 2.02176i
\(383\) −5.65210 + 3.26324i −0.288809 + 0.166744i −0.637405 0.770529i \(-0.719992\pi\)
0.348596 + 0.937273i \(0.386659\pi\)
\(384\) 17.7169 10.2289i 0.904112 0.521989i
\(385\) 8.44073i 0.430179i
\(386\) −30.3379 52.5467i −1.54416 2.67456i
\(387\) −0.807979 + 1.39946i −0.0410719 + 0.0711385i
\(388\) 18.3009 + 10.5660i 0.929085 + 0.536408i
\(389\) 11.7922 0.597891 0.298945 0.954270i \(-0.403365\pi\)
0.298945 + 0.954270i \(0.403365\pi\)
\(390\) 0 0
\(391\) −22.8944 −1.15782
\(392\) −20.1760 11.6486i −1.01904 0.588344i
\(393\) 9.11141 15.7814i 0.459610 0.796067i
\(394\) 25.2434 + 43.7228i 1.27174 + 2.20272i
\(395\) 19.9584i 1.00422i
\(396\) 8.77688 5.06734i 0.441055 0.254643i
\(397\) −10.8624 + 6.27144i −0.545171 + 0.314754i −0.747172 0.664631i \(-0.768589\pi\)
0.202001 + 0.979385i \(0.435256\pi\)
\(398\) 8.31468i 0.416777i
\(399\) 0.980386 + 1.69808i 0.0490807 + 0.0850102i
\(400\) 6.59329 11.4199i 0.329664 0.570995i
\(401\) −15.4761 8.93512i −0.772838 0.446198i 0.0610479 0.998135i \(-0.480556\pi\)
−0.833886 + 0.551936i \(0.813889\pi\)
\(402\) 33.9245 1.69200
\(403\) 0 0
\(404\) 16.4440 0.818118
\(405\) 3.19738 + 1.84601i 0.158879 + 0.0917290i
\(406\) 3.63922 6.30331i 0.180611 0.312828i
\(407\) −10.6124 18.3812i −0.526036 0.911120i
\(408\) 10.7711i 0.533247i
\(409\) 24.1724 13.9559i 1.19525 0.690076i 0.235755 0.971812i \(-0.424244\pi\)
0.959492 + 0.281736i \(0.0909103\pi\)
\(410\) −6.41196 + 3.70195i −0.316664 + 0.182826i
\(411\) 9.45042i 0.466155i
\(412\) −2.14675 3.71828i −0.105763 0.183187i
\(413\) 2.15883 3.73921i 0.106229 0.183994i
\(414\) 15.9001 + 9.17994i 0.781448 + 0.451169i
\(415\) −26.0248 −1.27750
\(416\) 0 0
\(417\) −4.01507 −0.196619
\(418\) 14.2276 + 8.21432i 0.695896 + 0.401776i
\(419\) 8.20171 14.2058i 0.400680 0.693998i −0.593128 0.805108i \(-0.702107\pi\)
0.993808 + 0.111110i \(0.0354407\pi\)
\(420\) 5.26271 + 9.11528i 0.256794 + 0.444780i
\(421\) 3.03684i 0.148006i 0.997258 + 0.0740032i \(0.0235775\pi\)
−0.997258 + 0.0740032i \(0.976423\pi\)
\(422\) −2.48104 + 1.43243i −0.120775 + 0.0697295i
\(423\) 2.11747 1.22252i 0.102955 0.0594410i
\(424\) 36.5050i 1.77284i
\(425\) −12.6833 21.9681i −0.615230 1.06561i
\(426\) −9.57487 + 16.5842i −0.463904 + 0.803505i
\(427\) −9.20674 5.31551i −0.445545 0.257236i
\(428\) 33.8471 1.63606
\(429\) 0 0
\(430\) −14.0616 −0.678110
\(431\) −2.89089 1.66905i −0.139249 0.0803955i 0.428757 0.903420i \(-0.358952\pi\)
−0.568006 + 0.823024i \(0.692285\pi\)
\(432\) 0.763906 1.32312i 0.0367534 0.0636588i
\(433\) 5.95138 + 10.3081i 0.286005 + 0.495375i 0.972852 0.231426i \(-0.0743393\pi\)
−0.686847 + 0.726802i \(0.741006\pi\)
\(434\) 4.43190i 0.212738i
\(435\) 12.3127 7.10872i 0.590347 0.340837i
\(436\) −5.49385 + 3.17187i −0.263108 + 0.151905i
\(437\) 19.0465i 0.911119i
\(438\) −14.0090 24.2643i −0.669377 1.15940i
\(439\) 1.85905 3.21997i 0.0887277 0.153681i −0.818246 0.574868i \(-0.805053\pi\)
0.906974 + 0.421188i \(0.138387\pi\)
\(440\) 33.4064 + 19.2872i 1.59259 + 0.919480i
\(441\) 6.35690 0.302709
\(442\) 0 0
\(443\) 1.45712 0.0692300 0.0346150 0.999401i \(-0.488979\pi\)
0.0346150 + 0.999401i \(0.488979\pi\)
\(444\) −22.9209 13.2334i −1.08778 0.628030i
\(445\) −2.08911 + 3.61844i −0.0990331 + 0.171530i
\(446\) −20.4913 35.4919i −0.970290 1.68059i
\(447\) 19.4058i 0.917863i
\(448\) −8.22574 + 4.74914i −0.388630 + 0.224376i
\(449\) −10.5026 + 6.06369i −0.495649 + 0.286163i −0.726915 0.686727i \(-0.759047\pi\)
0.231266 + 0.972891i \(0.425713\pi\)
\(450\) 20.3424i 0.958951i
\(451\) −1.21283 2.10069i −0.0571100 0.0989175i
\(452\) 8.80045 15.2428i 0.413938 0.716962i
\(453\) −10.7060 6.18114i −0.503014 0.290415i
\(454\) −41.0465 −1.92641
\(455\) 0 0
\(456\) 8.96077 0.419627
\(457\) −2.98608 1.72401i −0.139683 0.0806459i 0.428530 0.903528i \(-0.359032\pi\)
−0.568213 + 0.822882i \(0.692365\pi\)
\(458\) −22.1081 + 38.2923i −1.03304 + 1.78928i
\(459\) −1.46950 2.54525i −0.0685904 0.118802i
\(460\) 102.242i 4.76704i
\(461\) 5.85087 3.37800i 0.272502 0.157329i −0.357522 0.933905i \(-0.616378\pi\)
0.630024 + 0.776575i \(0.283045\pi\)
\(462\) −4.66645 + 2.69418i −0.217103 + 0.125344i
\(463\) 7.45175i 0.346312i −0.984894 0.173156i \(-0.944604\pi\)
0.984894 0.173156i \(-0.0553965\pi\)
\(464\) −2.94169 5.09516i −0.136565 0.236537i
\(465\) −4.32855 + 7.49727i −0.200732 + 0.347678i
\(466\) −8.06468 4.65615i −0.373589 0.215692i
\(467\) −32.6098 −1.50900 −0.754502 0.656298i \(-0.772121\pi\)
−0.754502 + 0.656298i \(0.772121\pi\)
\(468\) 0 0
\(469\) −11.5429 −0.533001
\(470\) 18.4256 + 10.6380i 0.849909 + 0.490695i
\(471\) −9.33877 + 16.1752i −0.430308 + 0.745315i
\(472\) −9.86592 17.0883i −0.454116 0.786552i
\(473\) 4.60686i 0.211824i
\(474\) 11.0340 6.37047i 0.506807 0.292605i
\(475\) −18.2759 + 10.5516i −0.838557 + 0.484141i
\(476\) 8.37867i 0.384036i
\(477\) 4.98039 + 8.62628i 0.228036 + 0.394970i
\(478\) 0.964361 1.67032i 0.0441088 0.0763987i
\(479\) −2.45006 1.41454i −0.111946 0.0646321i 0.442982 0.896531i \(-0.353921\pi\)
−0.554928 + 0.831899i \(0.687254\pi\)
\(480\) −13.7670 −0.628376
\(481\) 0 0
\(482\) 14.2180 0.647614
\(483\) −5.41004 3.12349i −0.246165 0.142124i
\(484\) 5.10603 8.84391i 0.232092 0.401996i
\(485\) −10.9734 19.0065i −0.498276 0.863039i
\(486\) 2.35690i 0.106911i
\(487\) 35.7612 20.6468i 1.62050 0.935594i 0.633709 0.773572i \(-0.281532\pi\)
0.986787 0.162022i \(-0.0518015\pi\)
\(488\) −42.0750 + 24.2920i −1.90465 + 1.09965i
\(489\) 12.3394i 0.558009i
\(490\) 27.6579 + 47.9049i 1.24946 + 2.16412i
\(491\) −17.3349 + 30.0249i −0.782313 + 1.35501i 0.148279 + 0.988946i \(0.452627\pi\)
−0.930591 + 0.366060i \(0.880707\pi\)
\(492\) −2.61951 1.51238i −0.118097 0.0681832i
\(493\) −11.3177 −0.509722
\(494\) 0 0
\(495\) −10.5254 −0.473082
\(496\) 3.10248 + 1.79122i 0.139305 + 0.0804280i
\(497\) 3.25786 5.64279i 0.146135 0.253114i
\(498\) −8.30678 14.3878i −0.372236 0.644731i
\(499\) 17.9409i 0.803146i −0.915827 0.401573i \(-0.868464\pi\)
0.915827 0.401573i \(-0.131536\pi\)
\(500\) −41.2723 + 23.8286i −1.84575 + 1.06565i
\(501\) −9.95406 + 5.74698i −0.444715 + 0.256756i
\(502\) 63.3532i 2.82759i
\(503\) 13.0906 + 22.6736i 0.583681 + 1.01096i 0.995038 + 0.0994909i \(0.0317214\pi\)
−0.411358 + 0.911474i \(0.634945\pi\)
\(504\) −1.46950 + 2.54525i −0.0654568 + 0.113374i
\(505\) −14.7900 8.53899i −0.658145 0.379980i
\(506\) −52.3414 −2.32686
\(507\) 0 0
\(508\) 20.1575 0.894345
\(509\) −4.76837 2.75302i −0.211354 0.122025i 0.390586 0.920566i \(-0.372272\pi\)
−0.601941 + 0.798541i \(0.705606\pi\)
\(510\) 12.7872 22.1480i 0.566225 0.980731i
\(511\) 4.76659 + 8.25598i 0.210862 + 0.365223i
\(512\) 16.8955i 0.746681i
\(513\) −2.11747 + 1.22252i −0.0934885 + 0.0539756i
\(514\) −18.4788 + 10.6688i −0.815066 + 0.470579i
\(515\) 4.45904i 0.196489i
\(516\) −2.87233 4.97502i −0.126447 0.219013i
\(517\) −3.48523 + 6.03660i −0.153280 + 0.265489i
\(518\) 12.1865 + 7.03588i 0.535444 + 0.309139i
\(519\) 12.1142 0.531756
\(520\) 0 0
\(521\) −26.7211 −1.17067 −0.585336 0.810791i \(-0.699037\pi\)
−0.585336 + 0.810791i \(0.699037\pi\)
\(522\) 7.86010 + 4.53803i 0.344027 + 0.198624i
\(523\) −18.2615 + 31.6299i −0.798520 + 1.38308i 0.122060 + 0.992523i \(0.461050\pi\)
−0.920580 + 0.390555i \(0.872283\pi\)
\(524\) 32.3907 + 56.1023i 1.41499 + 2.45084i
\(525\) 6.92154i 0.302081i
\(526\) −47.2544 + 27.2823i −2.06039 + 1.18957i
\(527\) 5.96814 3.44571i 0.259976 0.150097i
\(528\) 4.35557i 0.189552i
\(529\) −18.8409 32.6334i −0.819171 1.41885i
\(530\) −43.3379 + 75.0634i −1.88248 + 3.26055i
\(531\) 4.66272 + 2.69202i 0.202345 + 0.116824i
\(532\) −6.97046 −0.302208
\(533\) 0 0
\(534\) −2.66727 −0.115424
\(535\) −30.4426 17.5761i −1.31615 0.759880i
\(536\) −26.3756 + 45.6839i −1.13925 + 1.97324i
\(537\) 0.269282 + 0.466411i 0.0116204 + 0.0201271i
\(538\) 5.70576i 0.245993i
\(539\) −15.6946 + 9.06129i −0.676015 + 0.390298i
\(540\) −11.3666 + 6.56249i −0.489139 + 0.282405i
\(541\) 18.4655i 0.793893i 0.917842 + 0.396947i \(0.129930\pi\)
−0.917842 + 0.396947i \(0.870070\pi\)
\(542\) 25.2719 + 43.7722i 1.08552 + 1.88018i
\(543\) 11.6419 20.1644i 0.499602 0.865336i
\(544\) 9.49087 + 5.47956i 0.406918 + 0.234934i
\(545\) 6.58834 0.282213
\(546\) 0 0
\(547\) 39.8471 1.70374 0.851870 0.523753i \(-0.175468\pi\)
0.851870 + 0.523753i \(0.175468\pi\)
\(548\) 29.0949 + 16.7979i 1.24287 + 0.717572i
\(549\) 6.62833 11.4806i 0.282890 0.489981i
\(550\) −28.9966 50.2237i −1.23642 2.14154i
\(551\) 9.41550i 0.401114i
\(552\) −24.7240 + 14.2744i −1.05232 + 0.607560i
\(553\) −3.75433 + 2.16756i −0.159650 + 0.0921741i
\(554\) 34.8993i 1.48273i
\(555\) 13.7436 + 23.8047i 0.583384 + 1.01045i
\(556\) 7.13669 12.3611i 0.302663 0.524228i
\(557\) −7.97156 4.60238i −0.337766 0.195009i 0.321518 0.946904i \(-0.395807\pi\)
−0.659284 + 0.751894i \(0.729140\pi\)
\(558\) −5.52648 −0.233955
\(559\) 0 0
\(560\) −4.52350 −0.191153
\(561\) 7.25614 + 4.18933i 0.306354 + 0.176874i
\(562\) −17.0918 + 29.6039i −0.720974 + 1.24876i
\(563\) −0.487623 0.844588i −0.0205509 0.0355951i 0.855567 0.517692i \(-0.173209\pi\)
−0.876118 + 0.482097i \(0.839875\pi\)
\(564\) 8.69202i 0.366000i
\(565\) −15.8305 + 9.13975i −0.665995 + 0.384512i
\(566\) 52.4003 30.2533i 2.20255 1.27164i
\(567\) 0.801938i 0.0336782i
\(568\) −14.8885 25.7877i −0.624708 1.08203i
\(569\) −8.44720 + 14.6310i −0.354125 + 0.613362i −0.986968 0.160918i \(-0.948555\pi\)
0.632843 + 0.774280i \(0.281888\pi\)
\(570\) −18.4256 10.6380i −0.771763 0.445578i
\(571\) 44.3226 1.85484 0.927421 0.374019i \(-0.122021\pi\)
0.927421 + 0.374019i \(0.122021\pi\)
\(572\) 0 0
\(573\) −16.7657 −0.700397
\(574\) 1.39273 + 0.804094i 0.0581315 + 0.0335622i
\(575\) 33.6172 58.2267i 1.40193 2.42822i
\(576\) −5.92208 10.2573i −0.246753 0.427389i
\(577\) 3.56704i 0.148498i −0.997240 0.0742489i \(-0.976344\pi\)
0.997240 0.0742489i \(-0.0236559\pi\)
\(578\) 17.0685 9.85450i 0.709956 0.409893i
\(579\) −22.2949 + 12.8720i −0.926544 + 0.534940i
\(580\) 50.5424i 2.09866i
\(581\) 2.82640 + 4.89546i 0.117259 + 0.203098i
\(582\) 7.00514 12.1333i 0.290372 0.502940i
\(583\) −24.5923 14.1984i −1.01851 0.588036i
\(584\) 43.5669 1.80281
\(585\) 0 0
\(586\) −62.5120 −2.58235
\(587\) −13.9579 8.05861i −0.576105 0.332614i 0.183479 0.983024i \(-0.441264\pi\)
−0.759584 + 0.650409i \(0.774597\pi\)
\(588\) −11.2992 + 19.5709i −0.465973 + 0.807089i
\(589\) −2.86658 4.96507i −0.118116 0.204582i
\(590\) 46.8504i 1.92880i
\(591\) 18.5510 10.7104i 0.763087 0.440569i
\(592\) 9.85071 5.68731i 0.404862 0.233747i
\(593\) 42.8611i 1.76010i −0.474885 0.880048i \(-0.657510\pi\)
0.474885 0.880048i \(-0.342490\pi\)
\(594\) −3.35958 5.81897i −0.137845 0.238755i
\(595\) −4.35086 + 7.53590i −0.178368 + 0.308942i
\(596\) −59.7444 34.4934i −2.44722 1.41291i
\(597\) 3.52781 0.144384
\(598\) 0 0
\(599\) 40.9420 1.67284 0.836422 0.548086i \(-0.184643\pi\)
0.836422 + 0.548086i \(0.184643\pi\)
\(600\) −27.3938 15.8158i −1.11835 0.645678i
\(601\) −0.593523 + 1.02801i −0.0242103 + 0.0419335i −0.877877 0.478887i \(-0.841040\pi\)
0.853666 + 0.520820i \(0.174374\pi\)
\(602\) 1.52715 + 2.64510i 0.0622419 + 0.107806i
\(603\) 14.3937i 0.586158i
\(604\) 38.0595 21.9737i 1.54862 0.894096i
\(605\) −9.18489 + 5.30290i −0.373419 + 0.215593i
\(606\) 10.9022i 0.442870i
\(607\) −9.99612 17.3138i −0.405730 0.702745i 0.588676 0.808369i \(-0.299649\pi\)
−0.994406 + 0.105624i \(0.966316\pi\)
\(608\) 4.55861 7.89574i 0.184876 0.320214i
\(609\) −2.67441 1.54407i −0.108373 0.0625690i
\(610\) 115.356 4.67062
\(611\) 0 0
\(612\) 10.4480 0.422336
\(613\) −28.8922 16.6809i −1.16694 0.673735i −0.213985 0.976837i \(-0.568644\pi\)
−0.952958 + 0.303102i \(0.901978\pi\)
\(614\) 9.71864 16.8332i 0.392212 0.679332i
\(615\) 1.57069 + 2.72051i 0.0633362 + 0.109702i
\(616\) 8.37867i 0.337586i
\(617\) −10.0660 + 5.81163i −0.405243 + 0.233967i −0.688744 0.725005i \(-0.741838\pi\)
0.283501 + 0.958972i \(0.408504\pi\)
\(618\) −2.46518 + 1.42327i −0.0991640 + 0.0572524i
\(619\) 16.5381i 0.664722i −0.943152 0.332361i \(-0.892155\pi\)
0.943152 0.332361i \(-0.107845\pi\)
\(620\) −15.3878 26.6525i −0.617990 1.07039i
\(621\) 3.89493 6.74621i 0.156298 0.270716i
\(622\) 29.4288 + 16.9907i 1.17999 + 0.681267i
\(623\) 0.907542 0.0363599
\(624\) 0 0
\(625\) 6.33944 0.253577
\(626\) 29.0531 + 16.7738i 1.16120 + 0.670417i
\(627\) 3.48523 6.03660i 0.139187 0.241078i
\(628\) −33.1989 57.5023i −1.32478 2.29459i
\(629\) 21.8810i 0.872452i
\(630\) 6.04332 3.48911i 0.240772 0.139010i
\(631\) −31.5593 + 18.2208i −1.25636 + 0.725358i −0.972364 0.233468i \(-0.924993\pi\)
−0.283993 + 0.958826i \(0.591659\pi\)
\(632\) 19.8116i 0.788064i
\(633\) 0.607760 + 1.05267i 0.0241563 + 0.0418399i
\(634\) −8.06547 + 13.9698i −0.320321 + 0.554812i
\(635\) −18.1300 10.4673i −0.719466 0.415384i
\(636\) −35.4101 −1.40410
\(637\) 0 0
\(638\) −25.8745 −1.02438
\(639\) 7.03644 + 4.06249i 0.278357 + 0.160710i
\(640\) 37.7652 65.4112i 1.49280 2.58560i
\(641\) 13.6033 + 23.5617i 0.537300 + 0.930630i 0.999048 + 0.0436195i \(0.0138889\pi\)
−0.461748 + 0.887011i \(0.652778\pi\)
\(642\) 22.4403i 0.885646i
\(643\) 4.39042 2.53481i 0.173141 0.0999632i −0.410925 0.911669i \(-0.634794\pi\)
0.584066 + 0.811706i \(0.301461\pi\)
\(644\) 19.2325 11.1039i 0.757866 0.437554i
\(645\) 5.96615i 0.234917i
\(646\) 8.46830 + 14.6675i 0.333181 + 0.577086i
\(647\) 9.66033 16.7322i 0.379787 0.657810i −0.611244 0.791442i \(-0.709331\pi\)
0.991031 + 0.133632i \(0.0426641\pi\)
\(648\) −3.17387 1.83244i −0.124682 0.0719849i
\(649\) −15.3491 −0.602506
\(650\) 0 0
\(651\) 1.88040 0.0736985
\(652\) 37.9892 + 21.9331i 1.48777 + 0.858966i
\(653\) −17.6177 + 30.5148i −0.689436 + 1.19414i 0.282585 + 0.959242i \(0.408808\pi\)
−0.972021 + 0.234895i \(0.924525\pi\)
\(654\) 2.10292 + 3.64236i 0.0822305 + 0.142427i
\(655\) 67.2790i 2.62881i
\(656\) 1.12579 0.649973i 0.0439546 0.0253772i
\(657\) −10.2950 + 5.94385i −0.401648 + 0.231891i
\(658\) 4.62133i 0.180158i
\(659\) 2.18084 + 3.77733i 0.0849535 + 0.147144i 0.905371 0.424621i \(-0.139592\pi\)
−0.820418 + 0.571764i \(0.806259\pi\)
\(660\) 18.7087 32.4044i 0.728236 1.26134i
\(661\) 13.3982 + 7.73543i 0.521128 + 0.300873i 0.737396 0.675461i \(-0.236055\pi\)
−0.216268 + 0.976334i \(0.569389\pi\)
\(662\) −22.2553 −0.864978
\(663\) 0 0
\(664\) 25.8334 1.00253
\(665\) 6.26934 + 3.61960i 0.243115 + 0.140362i
\(666\) −8.77359 + 15.1963i −0.339970 + 0.588845i
\(667\) −14.9988 25.9787i −0.580756 1.00590i
\(668\) 40.8605i 1.58094i
\(669\) −15.0588 + 8.69418i −0.582205 + 0.336136i
\(670\) 108.470 62.6250i 4.19055 2.41942i
\(671\) 37.7928i 1.45898i
\(672\) 1.49516 + 2.58969i 0.0576769 + 0.0998993i
\(673\) −5.87047 + 10.1680i −0.226290 + 0.391946i −0.956706 0.291057i \(-0.905993\pi\)
0.730416 + 0.683003i \(0.239326\pi\)
\(674\) −5.39492 3.11476i −0.207805 0.119976i
\(675\) 8.63102 0.332208
\(676\) 0 0
\(677\) 3.44504 0.132404 0.0662019 0.997806i \(-0.478912\pi\)
0.0662019 + 0.997806i \(0.478912\pi\)
\(678\) −10.1058 5.83459i −0.388111 0.224076i
\(679\) −2.38351 + 4.12836i −0.0914707 + 0.158432i
\(680\) 19.8835 + 34.4393i 0.762498 + 1.32068i
\(681\) 17.4155i 0.667363i
\(682\) 13.6444 7.87760i 0.522471 0.301649i
\(683\) 17.6720 10.2029i 0.676198 0.390403i −0.122223 0.992503i \(-0.539002\pi\)
0.798421 + 0.602099i \(0.205669\pi\)
\(684\) 8.69202i 0.332348i
\(685\) −17.4456 30.2166i −0.666561 1.15452i
\(686\) 12.6228 21.8634i 0.481942 0.834748i
\(687\) 16.2469 + 9.38016i 0.619858 + 0.357875i
\(688\) 2.46888 0.0941251
\(689\) 0 0
\(690\) 67.7851 2.58053
\(691\) 24.0788 + 13.9019i 0.916002 + 0.528854i 0.882358 0.470580i \(-0.155955\pi\)
0.0336449 + 0.999434i \(0.489288\pi\)
\(692\) −21.5328 + 37.2959i −0.818554 + 1.41778i
\(693\) 1.14310 + 1.97991i 0.0434229 + 0.0752107i
\(694\) 23.9433i 0.908876i
\(695\) −12.8377 + 7.41185i −0.486962 + 0.281148i
\(696\) −12.2221 + 7.05645i −0.463279 + 0.267474i
\(697\) 2.50066i 0.0947194i
\(698\) −12.3026 21.3087i −0.465660 0.806547i
\(699\) −1.97554 + 3.42174i −0.0747218 + 0.129422i
\(700\) 21.3092 + 12.3029i 0.805414 + 0.465006i
\(701\) −11.9715 −0.452158 −0.226079 0.974109i \(-0.572591\pi\)
−0.226079 + 0.974109i \(0.572591\pi\)
\(702\) 0 0
\(703\) −18.2034 −0.686556
\(704\) 29.2422 + 16.8830i 1.10211 + 0.636301i
\(705\) 4.51357 7.81774i 0.169991 0.294433i
\(706\) 21.5551 + 37.3346i 0.811238 + 1.40510i
\(707\) 3.70948i 0.139509i
\(708\) −16.5758 + 9.57002i −0.622955 + 0.359664i
\(709\) 27.9435 16.1332i 1.04944 0.605894i 0.126947 0.991909i \(-0.459482\pi\)
0.922492 + 0.386015i \(0.126149\pi\)
\(710\) 70.7012i 2.65337i
\(711\) −2.70291 4.68157i −0.101367 0.175573i
\(712\) 2.07374 3.59183i 0.0777169 0.134610i
\(713\) 15.8186 + 9.13288i 0.592412 + 0.342029i
\(714\) −5.55496 −0.207889
\(715\) 0 0
\(716\) −1.91457 −0.0715510
\(717\) −0.708696 0.409166i −0.0264667 0.0152806i
\(718\) 17.9985 31.1743i 0.671698 1.16342i
\(719\) 6.05429 + 10.4863i 0.225787 + 0.391075i 0.956555 0.291551i \(-0.0941713\pi\)
−0.730768 + 0.682626i \(0.760838\pi\)
\(720\) 5.64071i 0.210217i
\(721\) 0.838781 0.484271i 0.0312378 0.0180352i
\(722\) −26.5791 + 15.3455i −0.989173 + 0.571100i
\(723\) 6.03252i 0.224352i
\(724\) 41.3865 + 71.6835i 1.53812 + 2.66410i
\(725\) 16.6184 28.7839i 0.617192 1.06901i
\(726\) −5.86341 3.38524i −0.217611 0.125638i
\(727\) 16.6200 0.616402 0.308201 0.951321i \(-0.400273\pi\)
0.308201 + 0.951321i \(0.400273\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −89.5845 51.7216i −3.31567 1.91430i
\(731\) 2.37465 4.11301i 0.0878296 0.152125i
\(732\) 23.5635 + 40.8131i 0.870930 + 1.50850i
\(733\) 17.7912i 0.657132i −0.944481 0.328566i \(-0.893435\pi\)
0.944481 0.328566i \(-0.106565\pi\)
\(734\) 45.4595 26.2461i 1.67794 0.968760i
\(735\) 20.3254 11.7349i 0.749715 0.432848i
\(736\) 29.0473i 1.07070i
\(737\) 20.5172 + 35.5369i 0.755762 + 1.30902i
\(738\) −1.00269 + 1.73671i −0.0369095 + 0.0639291i
\(739\) 23.6960 + 13.6809i 0.871672 + 0.503260i 0.867903 0.496733i \(-0.165467\pi\)
0.00376844 + 0.999993i \(0.498800\pi\)
\(740\) −97.7160 −3.59211
\(741\) 0 0
\(742\) 18.8267 0.691150
\(743\) 7.26246 + 4.19298i 0.266434 + 0.153826i 0.627266 0.778805i \(-0.284174\pi\)
−0.360832 + 0.932631i \(0.617507\pi\)
\(744\) 4.29672 7.44215i 0.157526 0.272842i
\(745\) 35.8233 + 62.0478i 1.31247 + 2.27326i
\(746\) 9.72528i 0.356068i
\(747\) −6.10454 + 3.52446i −0.223353 + 0.128953i
\(748\) −25.7953 + 14.8929i −0.943168 + 0.544538i
\(749\) 7.63533i 0.278989i
\(750\) 15.7981 + 27.3630i 0.576863 + 0.999157i
\(751\) −19.3889 + 33.5825i −0.707511 + 1.22544i 0.258267 + 0.966073i \(0.416848\pi\)
−0.965778 + 0.259371i \(0.916485\pi\)
\(752\) −3.23509 1.86778i −0.117972 0.0681110i
\(753\) −26.8799 −0.979559
\(754\) 0 0
\(755\) −45.6418 −1.66107
\(756\) 2.46891 + 1.42543i 0.0897935 + 0.0518423i
\(757\) −6.48643 + 11.2348i −0.235753 + 0.408336i −0.959491 0.281738i \(-0.909089\pi\)
0.723738 + 0.690075i \(0.242422\pi\)
\(758\) −12.6177 21.8546i −0.458297 0.793794i
\(759\) 22.2078i 0.806090i
\(760\) 28.6510 16.5417i 1.03928 0.600030i
\(761\) −4.46510 + 2.57792i −0.161860 + 0.0934497i −0.578742 0.815511i \(-0.696456\pi\)
0.416882 + 0.908961i \(0.363123\pi\)
\(762\) 13.3642i 0.484134i
\(763\) −0.715521 1.23932i −0.0259036 0.0448663i
\(764\) 29.8007 51.6163i 1.07815 1.86741i
\(765\) −9.39712 5.42543i −0.339753 0.196157i
\(766\) −15.3822 −0.555783
\(767\) 0 0
\(768\) 24.5284 0.885092
\(769\) −30.7450 17.7506i −1.10869 0.640104i −0.170202 0.985409i \(-0.554442\pi\)
−0.938490 + 0.345305i \(0.887775\pi\)
\(770\) −9.94696 + 17.2286i −0.358464 + 0.620877i
\(771\) 4.52661 + 7.84033i 0.163022 + 0.282362i
\(772\) 91.5186i 3.29383i
\(773\) 5.33112 3.07792i 0.191747 0.110705i −0.401053 0.916055i \(-0.631356\pi\)
0.592800 + 0.805350i \(0.298022\pi\)
\(774\) −3.29838 + 1.90432i −0.118558 + 0.0684494i
\(775\) 20.2381i 0.726976i
\(776\) 10.8927 + 18.8667i 0.391025 + 0.677275i
\(777\) 2.98523 5.17057i 0.107095 0.185493i
\(778\) 24.0695 + 13.8966i 0.862935 + 0.498216i