Properties

Label 950.2.u.g.149.4
Level $950$
Weight $2$
Character 950.149
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 149.4
Character \(\chi\) \(=\) 950.149
Dual form 950.2.u.g.899.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.642788 - 0.766044i) q^{2} +(-0.811037 - 2.22831i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.22831 - 0.811037i) q^{6} +(2.73267 - 1.57771i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.00943 + 1.68611i) q^{9} +O(q^{10})\) \(q+(0.642788 - 0.766044i) q^{2} +(-0.811037 - 2.22831i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.22831 - 0.811037i) q^{6} +(2.73267 - 1.57771i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.00943 + 1.68611i) q^{9} +(-0.688886 + 1.19319i) q^{11} +(-2.05362 + 1.18566i) q^{12} +(1.47931 - 4.06437i) q^{13} +(0.547933 - 3.10748i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(0.833438 - 0.993253i) q^{17} +2.62313i q^{18} +(-1.08907 - 4.22066i) q^{19} +(-5.73192 - 4.80965i) q^{21} +(0.471226 + 1.29468i) q^{22} +(-2.09271 + 0.369001i) q^{23} +(-0.411774 + 2.33529i) q^{24} +(-2.16260 - 3.74574i) q^{26} +(-0.773953 - 0.446842i) q^{27} +(-2.02826 - 2.41719i) q^{28} +(0.0998515 - 0.0837854i) q^{29} +(-0.173355 - 0.300259i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(3.21749 + 0.567331i) q^{33} +(-0.225152 - 1.27690i) q^{34} +(2.00943 + 1.68611i) q^{36} +10.3150i q^{37} +(-3.93325 - 1.87871i) q^{38} -10.2564 q^{39} +(-10.3451 + 3.76531i) q^{41} +(-7.36881 + 1.29932i) q^{42} +(11.3501 + 2.00132i) q^{43} +(1.29468 + 0.471226i) q^{44} +(-1.06250 + 1.84030i) q^{46} +(0.0491361 + 0.0585581i) q^{47} +(1.52425 + 1.81653i) q^{48} +(1.47834 - 2.56055i) q^{49} +(-2.88922 - 1.05159i) q^{51} +(-4.25950 - 0.751065i) q^{52} +(6.12511 - 1.08002i) q^{53} +(-0.839788 + 0.305658i) q^{54} -3.15542 q^{56} +(-8.52164 + 5.84988i) q^{57} -0.130347i q^{58} +(6.27104 + 5.26202i) q^{59} +(1.36244 + 7.72680i) q^{61} +(-0.341442 - 0.0602055i) q^{62} +(-2.83092 + 7.77790i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.50277 - 2.10007i) q^{66} +(-0.662508 - 0.789546i) q^{67} +(-1.12289 - 0.648300i) q^{68} +(2.51951 + 4.36392i) q^{69} +(2.02349 - 11.4758i) q^{71} +(2.58328 - 0.455501i) q^{72} +(-4.18756 - 11.5052i) q^{73} +(7.90176 + 6.63036i) q^{74} +(-3.96742 + 1.80543i) q^{76} +4.34745i q^{77} +(-6.59270 + 7.85688i) q^{78} +(13.1650 - 4.79168i) q^{79} +(-1.73450 + 9.83684i) q^{81} +(-3.76531 + 10.3451i) q^{82} +(-9.85443 + 5.68946i) q^{83} +(-3.74124 + 6.48003i) q^{84} +(8.82879 - 7.40823i) q^{86} +(-0.267683 - 0.154547i) q^{87} +(1.19319 - 0.688886i) q^{88} +(-17.1195 - 6.23099i) q^{89} +(-2.36992 - 13.4405i) q^{91} +(0.726790 + 1.99684i) q^{92} +(-0.528473 + 0.629809i) q^{93} +0.0764422 q^{94} +2.37131 q^{96} +(10.4271 - 12.4265i) q^{97} +(-1.01124 - 2.77836i) q^{98} +(-0.627577 - 3.55916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 36q^{9} + O(q^{10}) \) \( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.642788 0.766044i 0.454519 0.541675i
\(3\) −0.811037 2.22831i −0.468252 1.28651i −0.919140 0.393932i \(-0.871115\pi\)
0.450887 0.892581i \(-0.351108\pi\)
\(4\) −0.173648 0.984808i −0.0868241 0.492404i
\(5\) 0 0
\(6\) −2.22831 0.811037i −0.909702 0.331104i
\(7\) 2.73267 1.57771i 1.03285 0.596318i 0.115053 0.993359i \(-0.463296\pi\)
0.917801 + 0.397041i \(0.129963\pi\)
\(8\) −0.866025 0.500000i −0.306186 0.176777i
\(9\) −2.00943 + 1.68611i −0.669811 + 0.562038i
\(10\) 0 0
\(11\) −0.688886 + 1.19319i −0.207707 + 0.359759i −0.950992 0.309216i \(-0.899933\pi\)
0.743285 + 0.668975i \(0.233267\pi\)
\(12\) −2.05362 + 1.18566i −0.592828 + 0.342270i
\(13\) 1.47931 4.06437i 0.410286 1.12725i −0.546753 0.837294i \(-0.684136\pi\)
0.957039 0.289958i \(-0.0936415\pi\)
\(14\) 0.547933 3.10748i 0.146441 0.830509i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 0.833438 0.993253i 0.202138 0.240899i −0.655446 0.755242i \(-0.727520\pi\)
0.857585 + 0.514342i \(0.171964\pi\)
\(18\) 2.62313i 0.618277i
\(19\) −1.08907 4.22066i −0.249849 0.968285i
\(20\) 0 0
\(21\) −5.73192 4.80965i −1.25081 1.04955i
\(22\) 0.471226 + 1.29468i 0.100466 + 0.276027i
\(23\) −2.09271 + 0.369001i −0.436360 + 0.0769420i −0.387513 0.921864i \(-0.626666\pi\)
−0.0488468 + 0.998806i \(0.515555\pi\)
\(24\) −0.411774 + 2.33529i −0.0840531 + 0.476689i
\(25\) 0 0
\(26\) −2.16260 3.74574i −0.424122 0.734600i
\(27\) −0.773953 0.446842i −0.148947 0.0859948i
\(28\) −2.02826 2.41719i −0.383306 0.456806i
\(29\) 0.0998515 0.0837854i 0.0185420 0.0155586i −0.633470 0.773768i \(-0.718370\pi\)
0.652012 + 0.758209i \(0.273925\pi\)
\(30\) 0 0
\(31\) −0.173355 0.300259i −0.0311355 0.0539282i 0.850038 0.526722i \(-0.176579\pi\)
−0.881173 + 0.472793i \(0.843246\pi\)
\(32\) −0.342020 + 0.939693i −0.0604612 + 0.166116i
\(33\) 3.21749 + 0.567331i 0.560094 + 0.0987596i
\(34\) −0.225152 1.27690i −0.0386133 0.218987i
\(35\) 0 0
\(36\) 2.00943 + 1.68611i 0.334905 + 0.281019i
\(37\) 10.3150i 1.69578i 0.530174 + 0.847889i \(0.322127\pi\)
−0.530174 + 0.847889i \(0.677873\pi\)
\(38\) −3.93325 1.87871i −0.638057 0.304768i
\(39\) −10.2564 −1.64234
\(40\) 0 0
\(41\) −10.3451 + 3.76531i −1.61563 + 0.588042i −0.982543 0.186037i \(-0.940436\pi\)
−0.633089 + 0.774079i \(0.718213\pi\)
\(42\) −7.36881 + 1.29932i −1.13703 + 0.200490i
\(43\) 11.3501 + 2.00132i 1.73087 + 0.305199i 0.948303 0.317367i \(-0.102799\pi\)
0.782567 + 0.622566i \(0.213910\pi\)
\(44\) 1.29468 + 0.471226i 0.195181 + 0.0710400i
\(45\) 0 0
\(46\) −1.06250 + 1.84030i −0.156656 + 0.271337i
\(47\) 0.0491361 + 0.0585581i 0.00716723 + 0.00854158i 0.769616 0.638507i \(-0.220448\pi\)
−0.762449 + 0.647048i \(0.776003\pi\)
\(48\) 1.52425 + 1.81653i 0.220007 + 0.262194i
\(49\) 1.47834 2.56055i 0.211191 0.365793i
\(50\) 0 0
\(51\) −2.88922 1.05159i −0.404572 0.147252i
\(52\) −4.25950 0.751065i −0.590686 0.104154i
\(53\) 6.12511 1.08002i 0.841348 0.148352i 0.263666 0.964614i \(-0.415068\pi\)
0.577682 + 0.816262i \(0.303957\pi\)
\(54\) −0.839788 + 0.305658i −0.114281 + 0.0415948i
\(55\) 0 0
\(56\) −3.15542 −0.421661
\(57\) −8.52164 + 5.84988i −1.12872 + 0.774835i
\(58\) 0.130347i 0.0171154i
\(59\) 6.27104 + 5.26202i 0.816419 + 0.685057i 0.952131 0.305691i \(-0.0988875\pi\)
−0.135711 + 0.990748i \(0.543332\pi\)
\(60\) 0 0
\(61\) 1.36244 + 7.72680i 0.174443 + 0.989315i 0.938785 + 0.344504i \(0.111953\pi\)
−0.764342 + 0.644811i \(0.776936\pi\)
\(62\) −0.341442 0.0602055i −0.0433632 0.00764611i
\(63\) −2.83092 + 7.77790i −0.356663 + 0.979923i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0 0
\(66\) 2.50277 2.10007i 0.308069 0.258501i
\(67\) −0.662508 0.789546i −0.0809382 0.0964584i 0.724056 0.689742i \(-0.242276\pi\)
−0.804994 + 0.593283i \(0.797831\pi\)
\(68\) −1.12289 0.648300i −0.136170 0.0786179i
\(69\) 2.51951 + 4.36392i 0.303313 + 0.525354i
\(70\) 0 0
\(71\) 2.02349 11.4758i 0.240144 1.36192i −0.591361 0.806407i \(-0.701409\pi\)
0.831505 0.555517i \(-0.187480\pi\)
\(72\) 2.58328 0.455501i 0.304442 0.0536813i
\(73\) −4.18756 11.5052i −0.490117 1.34659i −0.900573 0.434705i \(-0.856853\pi\)
0.410456 0.911881i \(-0.365370\pi\)
\(74\) 7.90176 + 6.63036i 0.918561 + 0.770764i
\(75\) 0 0
\(76\) −3.96742 + 1.80543i −0.455094 + 0.207097i
\(77\) 4.34745i 0.495438i
\(78\) −6.59270 + 7.85688i −0.746477 + 0.889616i
\(79\) 13.1650 4.79168i 1.48118 0.539106i 0.530070 0.847954i \(-0.322166\pi\)
0.951111 + 0.308848i \(0.0999436\pi\)
\(80\) 0 0
\(81\) −1.73450 + 9.83684i −0.192722 + 1.09298i
\(82\) −3.76531 + 10.3451i −0.415808 + 1.14242i
\(83\) −9.85443 + 5.68946i −1.08166 + 0.624499i −0.931345 0.364138i \(-0.881364\pi\)
−0.150319 + 0.988637i \(0.548030\pi\)
\(84\) −3.74124 + 6.48003i −0.408203 + 0.707029i
\(85\) 0 0
\(86\) 8.82879 7.40823i 0.952033 0.798850i
\(87\) −0.267683 0.154547i −0.0286986 0.0165691i
\(88\) 1.19319 0.688886i 0.127194 0.0734355i
\(89\) −17.1195 6.23099i −1.81466 0.660484i −0.996316 0.0857608i \(-0.972668\pi\)
−0.818348 0.574723i \(-0.805110\pi\)
\(90\) 0 0
\(91\) −2.36992 13.4405i −0.248436 1.40895i
\(92\) 0.726790 + 1.99684i 0.0757731 + 0.208185i
\(93\) −0.528473 + 0.629809i −0.0548000 + 0.0653082i
\(94\) 0.0764422 0.00788441
\(95\) 0 0
\(96\) 2.37131 0.242021
\(97\) 10.4271 12.4265i 1.05871 1.26172i 0.0948014 0.995496i \(-0.469778\pi\)
0.963910 0.266227i \(-0.0857771\pi\)
\(98\) −1.01124 2.77836i −0.102151 0.280657i
\(99\) −0.627577 3.55916i −0.0630738 0.357710i
\(100\) 0 0
\(101\) −6.22381 2.26528i −0.619293 0.225404i 0.0132716 0.999912i \(-0.495775\pi\)
−0.632564 + 0.774508i \(0.717998\pi\)
\(102\) −2.66272 + 1.53732i −0.263649 + 0.152218i
\(103\) −10.7020 6.17880i −1.05450 0.608815i −0.130594 0.991436i \(-0.541688\pi\)
−0.923906 + 0.382621i \(0.875022\pi\)
\(104\) −3.31330 + 2.78019i −0.324896 + 0.272620i
\(105\) 0 0
\(106\) 3.10980 5.38633i 0.302050 0.523167i
\(107\) 9.48714 5.47740i 0.917156 0.529521i 0.0344297 0.999407i \(-0.489039\pi\)
0.882727 + 0.469887i \(0.155705\pi\)
\(108\) −0.305658 + 0.839788i −0.0294120 + 0.0808087i
\(109\) −1.29211 + 7.32792i −0.123762 + 0.701887i 0.858274 + 0.513192i \(0.171537\pi\)
−0.982036 + 0.188695i \(0.939574\pi\)
\(110\) 0 0
\(111\) 22.9850 8.36586i 2.18164 0.794052i
\(112\) −2.02826 + 2.41719i −0.191653 + 0.228403i
\(113\) 11.6014i 1.09137i 0.837990 + 0.545686i \(0.183731\pi\)
−0.837990 + 0.545686i \(0.816269\pi\)
\(114\) −0.996338 + 10.2882i −0.0933156 + 0.963577i
\(115\) 0 0
\(116\) −0.0998515 0.0837854i −0.00927098 0.00777928i
\(117\) 3.88041 + 10.6613i 0.358744 + 0.985642i
\(118\) 8.06189 1.42153i 0.742157 0.130862i
\(119\) 0.710449 4.02916i 0.0651268 0.369352i
\(120\) 0 0
\(121\) 4.55087 + 7.88234i 0.413716 + 0.716577i
\(122\) 6.79483 + 3.92300i 0.615175 + 0.355172i
\(123\) 16.7805 + 19.9982i 1.51305 + 1.80318i
\(124\) −0.265595 + 0.222861i −0.0238511 + 0.0200135i
\(125\) 0 0
\(126\) 4.13853 + 7.16815i 0.368690 + 0.638589i
\(127\) 5.60862 15.4096i 0.497685 1.36738i −0.395822 0.918327i \(-0.629540\pi\)
0.893507 0.449050i \(-0.148237\pi\)
\(128\) 0.984808 + 0.173648i 0.0870455 + 0.0153485i
\(129\) −4.74577 26.9146i −0.417841 2.36970i
\(130\) 0 0
\(131\) 8.53118 + 7.15851i 0.745373 + 0.625442i 0.934275 0.356554i \(-0.116048\pi\)
−0.188902 + 0.981996i \(0.560493\pi\)
\(132\) 3.26713i 0.284367i
\(133\) −9.63503 9.81545i −0.835463 0.851107i
\(134\) −1.03068 −0.0890371
\(135\) 0 0
\(136\) −1.21840 + 0.443463i −0.104477 + 0.0380266i
\(137\) −7.23011 + 1.27486i −0.617710 + 0.108919i −0.473743 0.880663i \(-0.657097\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(138\) 4.96247 + 0.875017i 0.422433 + 0.0744864i
\(139\) 11.0992 + 4.03978i 0.941422 + 0.342650i 0.766727 0.641973i \(-0.221884\pi\)
0.174695 + 0.984623i \(0.444106\pi\)
\(140\) 0 0
\(141\) 0.0906342 0.156983i 0.00763277 0.0132203i
\(142\) −7.49028 8.92657i −0.628570 0.749101i
\(143\) 3.83047 + 4.56497i 0.320320 + 0.381742i
\(144\) 1.31156 2.27169i 0.109297 0.189308i
\(145\) 0 0
\(146\) −11.5052 4.18756i −0.952180 0.346565i
\(147\) −6.90468 1.21748i −0.569488 0.100416i
\(148\) 10.1583 1.79118i 0.835007 0.147234i
\(149\) 3.30256 1.20203i 0.270556 0.0984745i −0.203179 0.979142i \(-0.565127\pi\)
0.473736 + 0.880667i \(0.342905\pi\)
\(150\) 0 0
\(151\) −0.212620 −0.0173028 −0.00865139 0.999963i \(-0.502754\pi\)
−0.00865139 + 0.999963i \(0.502754\pi\)
\(152\) −1.16717 + 4.19973i −0.0946700 + 0.340643i
\(153\) 3.40114i 0.274966i
\(154\) 3.33034 + 2.79449i 0.268366 + 0.225186i
\(155\) 0 0
\(156\) 1.78101 + 10.1006i 0.142595 + 0.808696i
\(157\) 7.57072 + 1.33492i 0.604210 + 0.106538i 0.467381 0.884056i \(-0.345198\pi\)
0.136829 + 0.990595i \(0.456309\pi\)
\(158\) 4.79168 13.1650i 0.381205 1.04735i
\(159\) −7.37431 12.7727i −0.584821 1.01294i
\(160\) 0 0
\(161\) −5.13651 + 4.31004i −0.404814 + 0.339679i
\(162\) 6.42054 + 7.65170i 0.504445 + 0.601174i
\(163\) −6.34537 3.66350i −0.497008 0.286948i 0.230469 0.973080i \(-0.425974\pi\)
−0.727477 + 0.686132i \(0.759307\pi\)
\(164\) 5.50451 + 9.53409i 0.429830 + 0.744487i
\(165\) 0 0
\(166\) −1.97593 + 11.2060i −0.153362 + 0.869758i
\(167\) 15.6032 2.75126i 1.20741 0.212899i 0.466511 0.884515i \(-0.345511\pi\)
0.740899 + 0.671617i \(0.234400\pi\)
\(168\) 2.55916 + 7.03124i 0.197444 + 0.542472i
\(169\) −4.37215 3.66867i −0.336319 0.282205i
\(170\) 0 0
\(171\) 9.30491 + 6.64483i 0.711564 + 0.508143i
\(172\) 11.5252i 0.878786i
\(173\) 10.6961 12.7471i 0.813211 0.969147i −0.186701 0.982417i \(-0.559780\pi\)
0.999912 + 0.0132697i \(0.00422402\pi\)
\(174\) −0.290453 + 0.105716i −0.0220192 + 0.00801432i
\(175\) 0 0
\(176\) 0.239248 1.35684i 0.0180340 0.102276i
\(177\) 6.63936 18.2415i 0.499045 1.37111i
\(178\) −15.7774 + 9.10910i −1.18257 + 0.682756i
\(179\) −2.28553 + 3.95866i −0.170829 + 0.295884i −0.938710 0.344708i \(-0.887978\pi\)
0.767881 + 0.640592i \(0.221311\pi\)
\(180\) 0 0
\(181\) 1.29338 1.08527i 0.0961360 0.0806677i −0.593453 0.804869i \(-0.702236\pi\)
0.689589 + 0.724201i \(0.257791\pi\)
\(182\) −11.8194 6.82392i −0.876111 0.505823i
\(183\) 16.1127 9.30266i 1.19108 0.687673i
\(184\) 1.99684 + 0.726790i 0.147209 + 0.0535796i
\(185\) 0 0
\(186\) 0.142766 + 0.809667i 0.0104681 + 0.0593677i
\(187\) 0.610991 + 1.67868i 0.0446801 + 0.122758i
\(188\) 0.0491361 0.0585581i 0.00358362 0.00427079i
\(189\) −2.81995 −0.205121
\(190\) 0 0
\(191\) 11.2207 0.811901 0.405951 0.913895i \(-0.366941\pi\)
0.405951 + 0.913895i \(0.366941\pi\)
\(192\) 1.52425 1.81653i 0.110003 0.131097i
\(193\) −7.34927 20.1920i −0.529012 1.45345i −0.860236 0.509897i \(-0.829684\pi\)
0.331223 0.943552i \(-0.392539\pi\)
\(194\) −2.81687 15.9752i −0.202239 1.14696i
\(195\) 0 0
\(196\) −2.77836 1.01124i −0.198455 0.0722315i
\(197\) 13.2315 7.63921i 0.942705 0.544271i 0.0518981 0.998652i \(-0.483473\pi\)
0.890807 + 0.454381i \(0.150140\pi\)
\(198\) −3.12988 1.80704i −0.222431 0.128420i
\(199\) −0.542940 + 0.455581i −0.0384880 + 0.0322953i −0.661829 0.749655i \(-0.730219\pi\)
0.623341 + 0.781950i \(0.285775\pi\)
\(200\) 0 0
\(201\) −1.22203 + 2.11662i −0.0861955 + 0.149295i
\(202\) −5.73590 + 3.31162i −0.403576 + 0.233005i
\(203\) 0.140673 0.386495i 0.00987328 0.0271266i
\(204\) −0.533906 + 3.02793i −0.0373809 + 0.211998i
\(205\) 0 0
\(206\) −11.6123 + 4.22655i −0.809071 + 0.294478i
\(207\) 3.58298 4.27002i 0.249034 0.296787i
\(208\) 4.32521i 0.299899i
\(209\) 5.78627 + 1.60809i 0.400244 + 0.111234i
\(210\) 0 0
\(211\) 10.7852 + 9.04988i 0.742486 + 0.623020i 0.933504 0.358567i \(-0.116735\pi\)
−0.191018 + 0.981586i \(0.561179\pi\)
\(212\) −2.12723 5.84451i −0.146099 0.401403i
\(213\) −27.2126 + 4.79832i −1.86458 + 0.328776i
\(214\) 1.90228 10.7884i 0.130037 0.737478i
\(215\) 0 0
\(216\) 0.446842 + 0.773953i 0.0304038 + 0.0526608i
\(217\) −0.947444 0.547007i −0.0643167 0.0371333i
\(218\) 4.78296 + 5.70011i 0.323943 + 0.386060i
\(219\) −22.2409 + 18.6623i −1.50290 + 1.26108i
\(220\) 0 0
\(221\) −2.80403 4.85673i −0.188620 0.326699i
\(222\) 8.36586 22.9850i 0.561479 1.54265i
\(223\) −11.5389 2.03461i −0.772699 0.136248i −0.226622 0.973983i \(-0.572768\pi\)
−0.546077 + 0.837735i \(0.683879\pi\)
\(224\) 0.547933 + 3.10748i 0.0366103 + 0.207627i
\(225\) 0 0
\(226\) 8.88722 + 7.45727i 0.591169 + 0.496050i
\(227\) 10.2265i 0.678758i −0.940650 0.339379i \(-0.889783\pi\)
0.940650 0.339379i \(-0.110217\pi\)
\(228\) 7.24077 + 7.37636i 0.479532 + 0.488511i
\(229\) 5.05689 0.334169 0.167084 0.985943i \(-0.446565\pi\)
0.167084 + 0.985943i \(0.446565\pi\)
\(230\) 0 0
\(231\) 9.68744 3.52594i 0.637387 0.231990i
\(232\) −0.128367 + 0.0226345i −0.00842768 + 0.00148603i
\(233\) 7.14818 + 1.26042i 0.468293 + 0.0825727i 0.402815 0.915281i \(-0.368032\pi\)
0.0654778 + 0.997854i \(0.479143\pi\)
\(234\) 10.6613 + 3.88041i 0.696954 + 0.253671i
\(235\) 0 0
\(236\) 4.09313 7.08951i 0.266440 0.461488i
\(237\) −21.3546 25.4495i −1.38713 1.65312i
\(238\) −2.62985 3.13413i −0.170468 0.203155i
\(239\) 7.98657 13.8331i 0.516608 0.894792i −0.483206 0.875507i \(-0.660528\pi\)
0.999814 0.0192850i \(-0.00613899\pi\)
\(240\) 0 0
\(241\) −20.8564 7.59111i −1.34348 0.488986i −0.432572 0.901599i \(-0.642394\pi\)
−0.910906 + 0.412613i \(0.864616\pi\)
\(242\) 8.96347 + 1.58050i 0.576194 + 0.101598i
\(243\) 20.6859 3.64748i 1.32700 0.233986i
\(244\) 7.37283 2.68349i 0.471997 0.171793i
\(245\) 0 0
\(246\) 26.1058 1.66445
\(247\) −18.7654 1.81729i −1.19401 0.115632i
\(248\) 0.346710i 0.0220161i
\(249\) 20.6702 + 17.3443i 1.30992 + 1.09915i
\(250\) 0 0
\(251\) 3.91622 + 22.2100i 0.247190 + 1.40188i 0.815352 + 0.578966i \(0.196544\pi\)
−0.568162 + 0.822917i \(0.692345\pi\)
\(252\) 8.15132 + 1.43730i 0.513485 + 0.0905412i
\(253\) 1.00135 2.75119i 0.0629544 0.172966i
\(254\) −8.19925 14.2015i −0.514467 0.891083i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) 6.88718 + 8.20783i 0.429611 + 0.511990i 0.936810 0.349839i \(-0.113764\pi\)
−0.507199 + 0.861829i \(0.669319\pi\)
\(258\) −23.6683 13.6649i −1.47352 0.850739i
\(259\) 16.2741 + 28.1876i 1.01122 + 1.75149i
\(260\) 0 0
\(261\) −0.0593732 + 0.336722i −0.00367511 + 0.0208426i
\(262\) 10.9675 1.93386i 0.677573 0.119474i
\(263\) 9.12051 + 25.0584i 0.562395 + 1.54517i 0.816115 + 0.577890i \(0.196124\pi\)
−0.253720 + 0.967278i \(0.581654\pi\)
\(264\) −2.50277 2.10007i −0.154035 0.129250i
\(265\) 0 0
\(266\) −13.7123 + 1.07161i −0.840758 + 0.0657049i
\(267\) 43.2011i 2.64386i
\(268\) −0.662508 + 0.789546i −0.0404691 + 0.0482292i
\(269\) 1.34180 0.488375i 0.0818110 0.0297768i −0.300790 0.953690i \(-0.597250\pi\)
0.382601 + 0.923913i \(0.375028\pi\)
\(270\) 0 0
\(271\) 1.27969 7.25749i 0.0777357 0.440861i −0.920953 0.389673i \(-0.872588\pi\)
0.998689 0.0511882i \(-0.0163008\pi\)
\(272\) −0.443463 + 1.21840i −0.0268889 + 0.0738766i
\(273\) −28.0275 + 16.1817i −1.69630 + 0.979359i
\(274\) −3.67083 + 6.35806i −0.221763 + 0.384104i
\(275\) 0 0
\(276\) 3.86011 3.23902i 0.232351 0.194966i
\(277\) 2.18698 + 1.26266i 0.131403 + 0.0758656i 0.564261 0.825597i \(-0.309161\pi\)
−0.432857 + 0.901462i \(0.642495\pi\)
\(278\) 10.2291 5.90576i 0.613500 0.354204i
\(279\) 0.854616 + 0.311055i 0.0511645 + 0.0186224i
\(280\) 0 0
\(281\) 2.99175 + 16.9671i 0.178473 + 1.01217i 0.934058 + 0.357120i \(0.116241\pi\)
−0.755586 + 0.655050i \(0.772648\pi\)
\(282\) −0.0619974 0.170336i −0.00369189 0.0101434i
\(283\) 18.1400 21.6184i 1.07831 1.28508i 0.122061 0.992523i \(-0.461050\pi\)
0.956248 0.292556i \(-0.0945058\pi\)
\(284\) −11.6528 −0.691467
\(285\) 0 0
\(286\) 5.95915 0.352372
\(287\) −22.3292 + 26.6109i −1.31805 + 1.57079i
\(288\) −0.897162 2.46493i −0.0528658 0.145248i
\(289\) 2.66009 + 15.0861i 0.156476 + 0.887418i
\(290\) 0 0
\(291\) −36.1469 13.1564i −2.11897 0.771241i
\(292\) −10.6033 + 6.12181i −0.620510 + 0.358252i
\(293\) −10.9276 6.30904i −0.638396 0.368578i 0.145601 0.989343i \(-0.453489\pi\)
−0.783996 + 0.620766i \(0.786822\pi\)
\(294\) −5.37089 + 4.50671i −0.313237 + 0.262837i
\(295\) 0 0
\(296\) 5.15751 8.93306i 0.299774 0.519224i
\(297\) 1.06633 0.615647i 0.0618748 0.0357234i
\(298\) 1.20203 3.30256i 0.0696320 0.191312i
\(299\) −1.59601 + 9.05140i −0.0922994 + 0.523456i
\(300\) 0 0
\(301\) 34.1735 12.4382i 1.96973 0.716923i
\(302\) −0.136670 + 0.162877i −0.00786445 + 0.00937249i
\(303\) 15.7058i 0.902274i
\(304\) 2.46694 + 3.59364i 0.141488 + 0.206109i
\(305\) 0 0
\(306\) 2.60543 + 2.18621i 0.148942 + 0.124978i
\(307\) −3.10031 8.51802i −0.176944 0.486149i 0.819238 0.573454i \(-0.194397\pi\)
−0.996182 + 0.0873047i \(0.972175\pi\)
\(308\) 4.28140 0.754926i 0.243955 0.0430159i
\(309\) −5.08854 + 28.8586i −0.289477 + 1.64171i
\(310\) 0 0
\(311\) 10.8562 + 18.8035i 0.615599 + 1.06625i 0.990279 + 0.139095i \(0.0444192\pi\)
−0.374680 + 0.927154i \(0.622247\pi\)
\(312\) 8.88232 + 5.12821i 0.502863 + 0.290328i
\(313\) 6.45746 + 7.69570i 0.364997 + 0.434987i 0.917019 0.398843i \(-0.130588\pi\)
−0.552022 + 0.833829i \(0.686144\pi\)
\(314\) 5.88898 4.94144i 0.332334 0.278862i
\(315\) 0 0
\(316\) −7.00496 12.1330i −0.394060 0.682532i
\(317\) −0.721135 + 1.98130i −0.0405030 + 0.111281i −0.958295 0.285780i \(-0.907747\pi\)
0.917792 + 0.397061i \(0.129970\pi\)
\(318\) −14.5245 2.56107i −0.814496 0.143618i
\(319\) 0.0311852 + 0.176860i 0.00174604 + 0.00990226i
\(320\) 0 0
\(321\) −19.8997 16.6979i −1.11070 0.931984i
\(322\) 6.70524i 0.373668i
\(323\) −5.09985 2.43594i −0.283763 0.135539i
\(324\) 9.98859 0.554921
\(325\) 0 0
\(326\) −6.88513 + 2.50598i −0.381332 + 0.138794i
\(327\) 17.3768 3.06400i 0.960939 0.169439i
\(328\) 10.8418 + 1.91170i 0.598636 + 0.105556i
\(329\) 0.226661 + 0.0824977i 0.0124962 + 0.00454824i
\(330\) 0 0
\(331\) 1.72204 2.98267i 0.0946521 0.163942i −0.814811 0.579726i \(-0.803159\pi\)
0.909463 + 0.415784i \(0.136493\pi\)
\(332\) 7.31423 + 8.71676i 0.401420 + 0.478394i
\(333\) −17.3923 20.7273i −0.953091 1.13585i
\(334\) 7.92194 13.7212i 0.433469 0.750791i
\(335\) 0 0
\(336\) 7.03124 + 2.55916i 0.383586 + 0.139614i
\(337\) −25.4658 4.49031i −1.38721 0.244603i −0.570332 0.821414i \(-0.693186\pi\)
−0.816877 + 0.576811i \(0.804297\pi\)
\(338\) −5.62072 + 0.991085i −0.305727 + 0.0539079i
\(339\) 25.8516 9.40920i 1.40406 0.511038i
\(340\) 0 0
\(341\) 0.477687 0.0258682
\(342\) 11.0713 2.85676i 0.598668 0.154476i
\(343\) 12.7584i 0.688889i
\(344\) −8.82879 7.40823i −0.476016 0.399425i
\(345\) 0 0
\(346\) −2.88954 16.3874i −0.155343 0.880992i
\(347\) 2.48488 + 0.438152i 0.133395 + 0.0235212i 0.239947 0.970786i \(-0.422870\pi\)
−0.106552 + 0.994307i \(0.533981\pi\)
\(348\) −0.105716 + 0.290453i −0.00566698 + 0.0155699i
\(349\) 1.83973 + 3.18650i 0.0984782 + 0.170569i 0.911055 0.412285i \(-0.135269\pi\)
−0.812577 + 0.582854i \(0.801936\pi\)
\(350\) 0 0
\(351\) −2.96105 + 2.48461i −0.158049 + 0.132619i
\(352\) −0.885615 1.05543i −0.0472034 0.0562548i
\(353\) 2.42172 + 1.39818i 0.128895 + 0.0744175i 0.563061 0.826415i \(-0.309624\pi\)
−0.434166 + 0.900833i \(0.642957\pi\)
\(354\) −9.70609 16.8114i −0.515873 0.893518i
\(355\) 0 0
\(356\) −3.16356 + 17.9414i −0.167668 + 0.950893i
\(357\) −9.55440 + 1.68470i −0.505672 + 0.0891637i
\(358\) 1.56340 + 4.29540i 0.0826281 + 0.227019i
\(359\) −15.4284 12.9460i −0.814280 0.683262i 0.137345 0.990523i \(-0.456143\pi\)
−0.951625 + 0.307261i \(0.900587\pi\)
\(360\) 0 0
\(361\) −16.6279 + 9.19314i −0.875151 + 0.483849i
\(362\) 1.68838i 0.0887395i
\(363\) 13.8733 16.5336i 0.728162 0.867789i
\(364\) −12.8248 + 4.66784i −0.672201 + 0.244661i
\(365\) 0 0
\(366\) 3.23078 18.3227i 0.168876 0.957741i
\(367\) −1.54639 + 4.24866i −0.0807207 + 0.221778i −0.973487 0.228741i \(-0.926539\pi\)
0.892767 + 0.450520i \(0.148761\pi\)
\(368\) 1.84030 1.06250i 0.0959321 0.0553864i
\(369\) 14.4390 25.0091i 0.751666 1.30192i
\(370\) 0 0
\(371\) 15.0340 12.6150i 0.780524 0.654938i
\(372\) 0.712009 + 0.411079i 0.0369160 + 0.0213134i
\(373\) −20.1528 + 11.6352i −1.04347 + 0.602449i −0.920815 0.390000i \(-0.872475\pi\)
−0.122657 + 0.992449i \(0.539142\pi\)
\(374\) 1.67868 + 0.610991i 0.0868027 + 0.0315936i
\(375\) 0 0
\(376\) −0.0132740 0.0752808i −0.000684556 0.00388231i
\(377\) −0.192823 0.529778i −0.00993091 0.0272849i
\(378\) −1.81263 + 2.16021i −0.0932315 + 0.111109i
\(379\) −9.34667 −0.480106 −0.240053 0.970760i \(-0.577165\pi\)
−0.240053 + 0.970760i \(0.577165\pi\)
\(380\) 0 0
\(381\) −38.8860 −1.99219
\(382\) 7.21252 8.59555i 0.369025 0.439787i
\(383\) 11.2306 + 30.8559i 0.573858 + 1.57666i 0.798355 + 0.602187i \(0.205704\pi\)
−0.224497 + 0.974475i \(0.572074\pi\)
\(384\) −0.411774 2.33529i −0.0210133 0.119172i
\(385\) 0 0
\(386\) −20.1920 7.34927i −1.02774 0.374068i
\(387\) −26.1817 + 15.1160i −1.33089 + 0.768389i
\(388\) −14.0484 8.11084i −0.713199 0.411766i
\(389\) −8.17650 + 6.86090i −0.414565 + 0.347862i −0.826091 0.563537i \(-0.809440\pi\)
0.411526 + 0.911398i \(0.364996\pi\)
\(390\) 0 0
\(391\) −1.37763 + 2.38613i −0.0696698 + 0.120672i
\(392\) −2.56055 + 1.47834i −0.129327 + 0.0746673i
\(393\) 9.03225 24.8159i 0.455617 1.25180i
\(394\) 2.65307 15.0463i 0.133660 0.758022i
\(395\) 0 0
\(396\) −3.39612 + 1.23608i −0.170661 + 0.0621156i
\(397\) −6.46404 + 7.70354i −0.324421 + 0.386630i −0.903462 0.428669i \(-0.858983\pi\)
0.579041 + 0.815299i \(0.303427\pi\)
\(398\) 0.708758i 0.0355268i
\(399\) −14.0574 + 29.4305i −0.703753 + 1.47337i
\(400\) 0 0
\(401\) 9.25312 + 7.76429i 0.462079 + 0.387730i 0.843895 0.536508i \(-0.180257\pi\)
−0.381817 + 0.924238i \(0.624701\pi\)
\(402\) 0.835919 + 2.29667i 0.0416918 + 0.114547i
\(403\) −1.47681 + 0.260401i −0.0735651 + 0.0129715i
\(404\) −1.15011 + 6.52262i −0.0572203 + 0.324513i
\(405\) 0 0
\(406\) −0.205650 0.356196i −0.0102062 0.0176777i
\(407\) −12.3077 7.10587i −0.610071 0.352225i
\(408\) 1.97634 + 2.35531i 0.0978435 + 0.116605i
\(409\) 30.2942 25.4198i 1.49795 1.25693i 0.614040 0.789275i \(-0.289543\pi\)
0.883911 0.467655i \(-0.154901\pi\)
\(410\) 0 0
\(411\) 8.70468 + 15.0769i 0.429370 + 0.743691i
\(412\) −4.22655 + 11.6123i −0.208227 + 0.572099i
\(413\) 25.4386 + 4.48552i 1.25175 + 0.220718i
\(414\) −0.967936 5.48944i −0.0475715 0.269791i
\(415\) 0 0
\(416\) 3.31330 + 2.78019i 0.162448 + 0.136310i
\(417\) 28.0088i 1.37160i
\(418\) 4.95121 3.39887i 0.242172 0.166244i
\(419\) −28.5326 −1.39391 −0.696954 0.717116i \(-0.745462\pi\)
−0.696954 + 0.717116i \(0.745462\pi\)
\(420\) 0 0
\(421\) −1.91607 + 0.697393i −0.0933836 + 0.0339888i −0.388289 0.921537i \(-0.626934\pi\)
0.294906 + 0.955526i \(0.404712\pi\)
\(422\) 13.8652 2.44481i 0.674949 0.119012i
\(423\) −0.197471 0.0348195i −0.00960138 0.00169298i
\(424\) −5.84451 2.12723i −0.283834 0.103307i
\(425\) 0 0
\(426\) −13.8162 + 23.9304i −0.669398 + 1.15943i
\(427\) 15.9138 + 18.9653i 0.770121 + 0.917794i
\(428\) −7.04161 8.39187i −0.340369 0.405636i
\(429\) 7.06551 12.2378i 0.341126 0.590847i
\(430\) 0 0
\(431\) −12.7523 4.64147i −0.614258 0.223572i 0.0161074 0.999870i \(-0.494873\pi\)
−0.630365 + 0.776299i \(0.717095\pi\)
\(432\) 0.880107 + 0.155187i 0.0423442 + 0.00746642i
\(433\) 28.5238 5.02952i 1.37077 0.241703i 0.560690 0.828026i \(-0.310536\pi\)
0.810078 + 0.586323i \(0.199425\pi\)
\(434\) −1.02804 + 0.374175i −0.0493474 + 0.0179610i
\(435\) 0 0
\(436\) 7.44096 0.356357
\(437\) 3.83652 + 8.43073i 0.183526 + 0.403297i
\(438\) 29.0334i 1.38727i
\(439\) 8.59028 + 7.20810i 0.409992 + 0.344024i 0.824341 0.566094i \(-0.191546\pi\)
−0.414349 + 0.910118i \(0.635991\pi\)
\(440\) 0 0
\(441\) 1.34677 + 7.63790i 0.0641318 + 0.363710i
\(442\) −5.52286 0.973830i −0.262696 0.0463204i
\(443\) −2.54804 + 7.00068i −0.121061 + 0.332612i −0.985390 0.170315i \(-0.945521\pi\)
0.864329 + 0.502927i \(0.167744\pi\)
\(444\) −12.2301 21.1831i −0.580413 1.00530i
\(445\) 0 0
\(446\) −8.97564 + 7.53146i −0.425009 + 0.356625i
\(447\) −5.35700 6.38422i −0.253377 0.301963i
\(448\) 2.73267 + 1.57771i 0.129107 + 0.0745398i
\(449\) 2.65192 + 4.59326i 0.125152 + 0.216769i 0.921792 0.387684i \(-0.126725\pi\)
−0.796640 + 0.604453i \(0.793392\pi\)
\(450\) 0 0
\(451\) 2.63388 14.9375i 0.124025 0.703378i
\(452\) 11.4252 2.01457i 0.537396 0.0947574i
\(453\) 0.172443 + 0.473783i 0.00810207 + 0.0222603i
\(454\) −7.83397 6.57348i −0.367667 0.308509i
\(455\) 0 0
\(456\) 10.3049 0.805323i 0.482571 0.0377127i
\(457\) 14.9890i 0.701154i 0.936534 + 0.350577i \(0.114014\pi\)
−0.936534 + 0.350577i \(0.885986\pi\)
\(458\) 3.25051 3.87381i 0.151886 0.181011i
\(459\) −1.08887 + 0.396316i −0.0508241 + 0.0184984i
\(460\) 0 0
\(461\) −1.19157 + 6.75771i −0.0554968 + 0.314738i −0.999901 0.0140479i \(-0.995528\pi\)
0.944405 + 0.328786i \(0.106639\pi\)
\(462\) 3.52594 9.68744i 0.164042 0.450701i
\(463\) −17.8738 + 10.3194i −0.830665 + 0.479585i −0.854080 0.520141i \(-0.825879\pi\)
0.0234152 + 0.999726i \(0.492546\pi\)
\(464\) −0.0651735 + 0.112884i −0.00302560 + 0.00524050i
\(465\) 0 0
\(466\) 5.56030 4.66564i 0.257576 0.216132i
\(467\) 10.4226 + 6.01750i 0.482301 + 0.278457i 0.721375 0.692545i \(-0.243510\pi\)
−0.239074 + 0.971001i \(0.576844\pi\)
\(468\) 9.82555 5.67279i 0.454186 0.262225i
\(469\) −3.05609 1.11233i −0.141117 0.0513625i
\(470\) 0 0
\(471\) −3.16552 17.9526i −0.145859 0.827210i
\(472\) −2.79986 7.69256i −0.128874 0.354079i
\(473\) −10.2069 + 12.1641i −0.469312 + 0.559304i
\(474\) −33.2219 −1.52593
\(475\) 0 0
\(476\) −4.09132 −0.187525
\(477\) −10.4869 + 12.4979i −0.480164 + 0.572238i
\(478\) −5.46314 15.0098i −0.249878 0.686534i
\(479\) −3.95553 22.4329i −0.180733 1.02499i −0.931316 0.364211i \(-0.881339\pi\)
0.750583 0.660776i \(-0.229773\pi\)
\(480\) 0 0
\(481\) 41.9240 + 15.2591i 1.91157 + 0.695754i
\(482\) −19.2214 + 11.0975i −0.875509 + 0.505475i
\(483\) 13.7700 + 7.95011i 0.626556 + 0.361743i
\(484\) 6.97234 5.85049i 0.316925 0.265931i
\(485\) 0 0
\(486\) 10.5025 18.1909i 0.476403 0.825155i
\(487\) 5.58510 3.22456i 0.253085 0.146119i −0.368091 0.929790i \(-0.619989\pi\)
0.621176 + 0.783671i \(0.286655\pi\)
\(488\) 2.68349 7.37283i 0.121476 0.333752i
\(489\) −3.01707 + 17.1107i −0.136437 + 0.773771i
\(490\) 0 0
\(491\) 22.8944 8.33289i 1.03321 0.376058i 0.230908 0.972975i \(-0.425830\pi\)
0.802303 + 0.596917i \(0.203608\pi\)
\(492\) 16.7805 19.9982i 0.756524 0.901590i
\(493\) 0.169008i 0.00761173i
\(494\) −13.4543 + 13.2070i −0.605336 + 0.594209i
\(495\) 0 0
\(496\) 0.265595 + 0.222861i 0.0119256 + 0.0100067i
\(497\) −12.5759 34.5520i −0.564106 1.54987i
\(498\) 26.5730 4.68554i 1.19077 0.209964i
\(499\) −0.282127 + 1.60002i −0.0126298 + 0.0716269i −0.990471 0.137720i \(-0.956023\pi\)
0.977841 + 0.209347i \(0.0671337\pi\)
\(500\) 0 0
\(501\) −18.7854 32.5373i −0.839270 1.45366i
\(502\) 19.5311 + 11.2763i 0.871717 + 0.503286i
\(503\) −22.6234 26.9615i −1.00873 1.20215i −0.979264 0.202588i \(-0.935065\pi\)
−0.0294632 0.999566i \(-0.509380\pi\)
\(504\) 6.34060 5.32040i 0.282433 0.236989i
\(505\) 0 0
\(506\) −1.46388 2.53551i −0.0650772 0.112717i
\(507\) −4.62894 + 12.7179i −0.205578 + 0.564822i
\(508\) −16.1494 2.84757i −0.716513 0.126341i
\(509\) 4.20711 + 23.8597i 0.186477 + 1.05756i 0.924043 + 0.382288i \(0.124864\pi\)
−0.737567 + 0.675274i \(0.764025\pi\)
\(510\) 0 0
\(511\) −29.5952 24.8333i −1.30921 1.09856i
\(512\) 1.00000i 0.0441942i
\(513\) −1.04308 + 3.75323i −0.0460532 + 0.165709i
\(514\) 10.7146 0.472599
\(515\) 0 0
\(516\) −25.6816 + 9.34733i −1.13057 + 0.411493i
\(517\) −0.103720 + 0.0182886i −0.00456159 + 0.000804332i
\(518\) 32.0537 + 5.65193i 1.40836 + 0.248332i
\(519\) −37.0795 13.4958i −1.62761 0.592401i
\(520\) 0 0
\(521\) 3.95859 6.85648i 0.173429 0.300388i −0.766187 0.642617i \(-0.777849\pi\)
0.939616 + 0.342229i \(0.111182\pi\)
\(522\) 0.219780 + 0.261923i 0.00961950 + 0.0114641i
\(523\) 1.57943 + 1.88229i 0.0690637 + 0.0823069i 0.799470 0.600706i \(-0.205114\pi\)
−0.730406 + 0.683013i \(0.760669\pi\)
\(524\) 5.56833 9.64464i 0.243254 0.421328i
\(525\) 0 0
\(526\) 25.0584 + 9.12051i 1.09260 + 0.397673i
\(527\) −0.442714 0.0780624i −0.0192849 0.00340045i
\(528\) −3.21749 + 0.567331i −0.140023 + 0.0246899i
\(529\) −17.3697 + 6.32204i −0.755203 + 0.274871i
\(530\) 0 0
\(531\) −21.4736 −0.931874
\(532\) −7.99322 + 11.1931i −0.346550 + 0.485282i
\(533\) 47.6163i 2.06249i
\(534\) 33.0939 + 27.7691i 1.43211 + 1.20169i
\(535\) 0 0
\(536\) 0.178976 + 1.01502i 0.00773057 + 0.0438422i
\(537\) 10.6748 + 1.88225i 0.460650 + 0.0812250i
\(538\) 0.488375 1.34180i 0.0210554 0.0578491i
\(539\) 2.03681 + 3.52786i 0.0877316 + 0.151956i
\(540\) 0 0
\(541\) 17.2132 14.4436i 0.740054 0.620979i −0.192798 0.981238i \(-0.561756\pi\)
0.932852 + 0.360260i \(0.117312\pi\)
\(542\) −4.73699 5.64532i −0.203471 0.242487i
\(543\) −3.46730 2.00184i −0.148796 0.0859074i
\(544\) 0.648300 + 1.12289i 0.0277956 + 0.0481434i
\(545\) 0 0
\(546\) −5.61983 + 31.8717i −0.240507 + 1.36398i
\(547\) 26.3908 4.65342i 1.12839 0.198966i 0.421869 0.906657i \(-0.361374\pi\)
0.706522 + 0.707691i \(0.250263\pi\)
\(548\) 2.51099 + 6.89889i 0.107264 + 0.294706i
\(549\) −15.7660 13.2292i −0.672876 0.564610i
\(550\) 0 0
\(551\) −0.462374 0.330191i −0.0196978 0.0140666i
\(552\) 5.03902i 0.214475i
\(553\) 28.4158 33.8647i 1.20836 1.44007i
\(554\) 2.37302 0.863707i 0.100820 0.0366954i
\(555\) 0 0
\(556\) 2.05105 11.6321i 0.0869839 0.493310i
\(557\) −13.3749 + 36.7473i −0.566714 + 1.55704i 0.242887 + 0.970055i \(0.421906\pi\)
−0.809601 + 0.586980i \(0.800317\pi\)
\(558\) 0.787619 0.454732i 0.0333426 0.0192503i
\(559\) 24.9244 43.1703i 1.05419 1.82591i
\(560\) 0 0
\(561\) 3.24508 2.72295i 0.137008 0.114963i
\(562\) 14.9206 + 8.61440i 0.629387 + 0.363377i
\(563\) −7.46645 + 4.31076i −0.314673 + 0.181677i −0.649016 0.760775i \(-0.724819\pi\)
0.334343 + 0.942452i \(0.391486\pi\)
\(564\) −0.170336 0.0619974i −0.00717246 0.00261056i
\(565\) 0 0
\(566\) −4.90049 27.7920i −0.205983 1.16819i
\(567\) 10.7799 + 29.6174i 0.452711 + 1.24381i
\(568\) −7.49028 + 8.92657i −0.314285 + 0.374550i
\(569\) −23.0260 −0.965300 −0.482650 0.875813i \(-0.660326\pi\)
−0.482650 + 0.875813i \(0.660326\pi\)
\(570\) 0 0
\(571\) −29.9673 −1.25409 −0.627047 0.778981i \(-0.715737\pi\)
−0.627047 + 0.778981i \(0.715737\pi\)
\(572\) 3.83047 4.56497i 0.160160 0.190871i
\(573\) −9.10040 25.0031i −0.380175 1.04452i
\(574\) 6.03220 + 34.2103i 0.251779 + 1.42791i
\(575\) 0 0
\(576\) −2.46493 0.897162i −0.102706 0.0373818i
\(577\) 3.93622 2.27258i 0.163867 0.0946087i −0.415824 0.909445i \(-0.636507\pi\)
0.579691 + 0.814837i \(0.303173\pi\)
\(578\) 13.2665 + 7.65941i 0.551813 + 0.318590i
\(579\) −39.0333 + 32.7529i −1.62217 + 1.36116i
\(580\) 0 0
\(581\) −17.9526 + 31.0949i −0.744800 + 1.29003i
\(582\) −33.3131 + 19.2334i −1.38087 + 0.797248i
\(583\) −2.93083 + 8.05240i −0.121383 + 0.333496i
\(584\) −2.12608 + 12.0576i −0.0879779 + 0.498947i
\(585\) 0 0
\(586\) −11.8571 + 4.31563i −0.489813 + 0.178277i
\(587\) −11.8709 + 14.1471i −0.489963 + 0.583915i −0.953208 0.302315i \(-0.902240\pi\)
0.463245 + 0.886230i \(0.346685\pi\)
\(588\) 7.01120i 0.289137i
\(589\) −1.07850 + 1.05867i −0.0444387 + 0.0436219i
\(590\) 0 0
\(591\) −27.7537 23.2881i −1.14164 0.957946i
\(592\) −3.52794 9.69294i −0.144998 0.398377i
\(593\) −15.7488 + 2.77694i −0.646726 + 0.114035i −0.487384 0.873188i \(-0.662049\pi\)
−0.159343 + 0.987223i \(0.550938\pi\)
\(594\) 0.213812 1.21259i 0.00877280 0.0497530i
\(595\) 0 0
\(596\) −1.75726 3.04366i −0.0719800 0.124673i
\(597\) 1.45552 + 0.840343i 0.0595704 + 0.0343930i
\(598\) 5.90788 + 7.04074i 0.241591 + 0.287917i
\(599\) −3.02967 + 2.54220i −0.123789 + 0.103871i −0.702581 0.711604i \(-0.747969\pi\)
0.578792 + 0.815476i \(0.303524\pi\)
\(600\) 0 0
\(601\) 1.10855 + 1.92006i 0.0452186 + 0.0783209i 0.887749 0.460328i \(-0.152268\pi\)
−0.842530 + 0.538649i \(0.818935\pi\)
\(602\) 12.4382 34.1735i 0.506941 1.39281i
\(603\) 2.66253 + 0.469476i 0.108427 + 0.0191185i
\(604\) 0.0369211 + 0.209390i 0.00150230 + 0.00851996i
\(605\) 0 0
\(606\) 12.0313 + 10.0955i 0.488739 + 0.410101i
\(607\) 17.4964i 0.710155i 0.934837 + 0.355078i \(0.115546\pi\)
−0.934837 + 0.355078i \(0.884454\pi\)
\(608\) 4.33860 + 0.420163i 0.175954 + 0.0170399i
\(609\) −0.975319 −0.0395219
\(610\) 0 0
\(611\) 0.310689 0.113082i 0.0125691 0.00457479i
\(612\) 3.34947 0.590603i 0.135394 0.0238737i
\(613\) −8.98922 1.58504i −0.363071 0.0640193i −0.0108633 0.999941i \(-0.503458\pi\)
−0.352208 + 0.935922i \(0.614569\pi\)
\(614\) −8.51802 3.10031i −0.343759 0.125118i
\(615\) 0 0
\(616\) 2.17372 3.76500i 0.0875818 0.151696i
\(617\) 1.00026 + 1.19206i 0.0402689 + 0.0479906i 0.785803 0.618477i \(-0.212250\pi\)
−0.745534 + 0.666467i \(0.767806\pi\)
\(618\) 18.8361 + 22.4480i 0.757699 + 0.902990i
\(619\) 16.2140 28.0835i 0.651695 1.12877i −0.331016 0.943625i \(-0.607391\pi\)
0.982711 0.185144i \(-0.0592753\pi\)
\(620\) 0 0
\(621\) 1.78454 + 0.649520i 0.0716112 + 0.0260644i
\(622\) 21.3826 + 3.77032i 0.857362 + 0.151176i
\(623\) −56.6127 + 9.98235i −2.26814 + 0.399934i
\(624\) 9.63789 3.50790i 0.385824 0.140429i
\(625\) 0 0
\(626\) 10.0460 0.401520
\(627\) −1.10955 14.1978i −0.0443112 0.567005i
\(628\) 7.68751i 0.306765i
\(629\) 10.2454 + 8.59692i 0.408511 + 0.342782i
\(630\) 0 0
\(631\) −1.67744 9.51323i −0.0667778 0.378716i −0.999820 0.0189499i \(-0.993968\pi\)
0.933043 0.359766i \(-0.117143\pi\)
\(632\) −13.7971 2.43280i −0.548819 0.0967715i
\(633\) 11.4187 31.3726i 0.453852 1.24695i
\(634\) 1.05423 + 1.82598i 0.0418688 + 0.0725189i
\(635\) 0 0
\(636\) −11.2981 + 9.48023i −0.447999 + 0.375915i
\(637\) −8.22011 9.79635i −0.325693 0.388145i
\(638\) 0.155528 + 0.0897942i 0.00615741 + 0.00355498i
\(639\) 15.2834 + 26.4716i 0.604602 + 1.04720i
\(640\) 0 0
\(641\) 7.05763 40.0258i 0.278759 1.58092i −0.448001 0.894033i \(-0.647864\pi\)
0.726761 0.686891i \(-0.241025\pi\)
\(642\) −25.5826 + 4.51091i −1.00967 + 0.178031i
\(643\) −14.3882 39.5312i −0.567414 1.55896i −0.808526 0.588460i \(-0.799734\pi\)
0.241112 0.970497i \(-0.422488\pi\)
\(644\) 5.13651 + 4.31004i 0.202407 + 0.169840i
\(645\) 0 0
\(646\) −5.14416 + 2.34092i −0.202394 + 0.0921022i
\(647\) 18.0072i 0.707936i 0.935258 + 0.353968i \(0.115168\pi\)
−0.935258 + 0.353968i \(0.884832\pi\)
\(648\) 6.42054 7.65170i 0.252223 0.300587i
\(649\) −10.5986 + 3.85757i −0.416031 + 0.151423i
\(650\) 0 0
\(651\) −0.450487 + 2.55484i −0.0176560 + 0.100132i
\(652\) −2.50598 + 6.88513i −0.0981419 + 0.269643i
\(653\) −34.1968 + 19.7435i −1.33822 + 0.772624i −0.986544 0.163496i \(-0.947723\pi\)
−0.351680 + 0.936120i \(0.614390\pi\)
\(654\) 8.82243 15.2809i 0.344984 0.597530i
\(655\) 0 0
\(656\) 8.43340 7.07646i 0.329269 0.276289i
\(657\) 27.8138 + 16.0583i 1.08512 + 0.626493i
\(658\) 0.208891 0.120604i 0.00814344 0.00470162i
\(659\) 33.6395 + 12.2438i 1.31041 + 0.476949i 0.900372 0.435120i \(-0.143294\pi\)
0.410035 + 0.912070i \(0.365516\pi\)
\(660\) 0 0
\(661\) 2.36241 + 13.3979i 0.0918871 + 0.521118i 0.995657 + 0.0930988i \(0.0296772\pi\)
−0.903770 + 0.428019i \(0.859212\pi\)
\(662\) −1.17795 3.23639i −0.0457822 0.125786i
\(663\) −8.54809 + 10.1872i −0.331980 + 0.395639i
\(664\) 11.3789 0.441588
\(665\) 0 0
\(666\) −27.0576 −1.04846
\(667\) −0.178043 + 0.212184i −0.00689386 + 0.00821578i
\(668\) −5.41893 14.8884i −0.209665 0.576049i
\(669\) 4.82470 + 27.3623i 0.186534 + 1.05789i
\(670\) 0 0
\(671\) −10.1581 3.69724i −0.392148 0.142730i
\(672\) 6.48003 3.74124i 0.249972 0.144322i
\(673\) −36.5649 21.1108i −1.40947 0.813760i −0.414136 0.910215i \(-0.635916\pi\)
−0.995337 + 0.0964549i \(0.969250\pi\)
\(674\) −19.8089 + 16.6216i −0.763009 + 0.640241i
\(675\) 0 0
\(676\) −2.85372 + 4.94278i −0.109758 + 0.190107i
\(677\) −37.8202 + 21.8355i −1.45355 + 0.839207i −0.998681 0.0513514i \(-0.983647\pi\)
−0.454869 + 0.890558i \(0.650314\pi\)
\(678\) 9.40920 25.8516i 0.361358 0.992824i
\(679\) 8.88840 50.4086i 0.341105 1.93450i
\(680\) 0 0
\(681\) −22.7878 + 8.29409i −0.873231 + 0.317830i
\(682\) 0.307051 0.365929i 0.0117576 0.0140122i
\(683\) 9.22100i 0.352832i −0.984316 0.176416i \(-0.943550\pi\)
0.984316 0.176416i \(-0.0564504\pi\)
\(684\) 4.92810 10.3174i 0.188431 0.394496i
\(685\) 0 0
\(686\) 9.77350 + 8.20094i 0.373154 + 0.313113i
\(687\) −4.10133 11.2683i −0.156475 0.429913i
\(688\) −11.3501 + 2.00132i −0.432717 + 0.0762998i
\(689\) 4.67132 26.4924i 0.177963 1.00928i
\(690\) 0 0
\(691\) 20.0044 + 34.6487i 0.761004 + 1.31810i 0.942334 + 0.334675i \(0.108626\pi\)
−0.181330 + 0.983422i \(0.558040\pi\)
\(692\) −14.4108 8.32010i −0.547818 0.316283i
\(693\) −7.33029 8.73590i −0.278455 0.331849i
\(694\) 1.93290 1.62189i 0.0733717 0.0615662i
\(695\) 0 0
\(696\) 0.154547 + 0.267683i 0.00585808 + 0.0101465i
\(697\) −4.88209 + 13.4134i −0.184922 + 0.508070i
\(698\) 3.62355 + 0.638930i 0.137153 + 0.0241839i
\(699\) −2.98884 16.9506i −0.113048 0.641130i
\(700\) 0 0
\(701\) −1.37655 1.15507i −0.0519917 0.0436262i 0.616422 0.787416i \(-0.288582\pi\)
−0.668413 + 0.743790i \(0.733026\pi\)
\(702\) 3.86537i 0.145889i
\(703\) 43.5361 11.2337i 1.64200 0.423688i
\(704\) −1.37777 −0.0519267
\(705\) 0 0
\(706\) 2.62772 0.956410i 0.0988954 0.0359950i
\(707\) −20.5816 + 3.62909i −0.774051 + 0.136486i
\(708\) −19.1173 3.37089i −0.718471 0.126686i
\(709\) 31.8904 + 11.6072i 1.19767 + 0.435916i 0.862410 0.506210i \(-0.168954\pi\)
0.335259 + 0.942126i \(0.391176\pi\)
\(710\) 0 0
\(711\) −18.3749 + 31.8263i −0.689113 + 1.19358i
\(712\) 11.7104 + 13.9559i 0.438867 + 0.523021i
\(713\) 0.473577 + 0.564387i 0.0177356 + 0.0211365i
\(714\) −4.85090 + 8.40200i −0.181540 + 0.314437i
\(715\) 0 0
\(716\) 4.29540 + 1.56340i 0.160527 + 0.0584269i
\(717\) −37.3019 6.57733i −1.39306 0.245635i
\(718\) −19.8344 + 3.49734i −0.740212 + 0.130519i
\(719\) −4.77790 + 1.73901i −0.178186 + 0.0648542i −0.429572 0.903033i \(-0.641336\pi\)
0.251387 + 0.967887i \(0.419113\pi\)
\(720\) 0 0
\(721\) −38.9934 −1.45219
\(722\) −3.64584 + 18.6469i −0.135684 + 0.693967i
\(723\) 52.6311i 1.95737i
\(724\) −1.29338 1.08527i −0.0480680 0.0403338i
\(725\) 0 0
\(726\) −3.74786 21.2552i −0.139096 0.788854i
\(727\) −21.2529 3.74747i −0.788228 0.138986i −0.234977 0.972001i \(-0.575502\pi\)
−0.553250 + 0.833015i \(0.686613\pi\)
\(728\) −4.66784 + 12.8248i −0.173002 + 0.475318i
\(729\) −9.92186 17.1852i −0.367476 0.636487i
\(730\) 0 0
\(731\) 11.4474 9.60551i 0.423397 0.355273i
\(732\) −11.9593 14.2525i −0.442027 0.526788i
\(733\) 8.20601 + 4.73774i 0.303096 + 0.174993i 0.643833 0.765166i \(-0.277343\pi\)
−0.340737 + 0.940159i \(0.610677\pi\)
\(734\) 2.26066 + 3.91559i 0.0834426 + 0.144527i
\(735\) 0 0
\(736\) 0.369001 2.09271i 0.0136015 0.0771382i
\(737\) 1.39847 0.246588i 0.0515132 0.00908317i
\(738\) −9.87687 27.1365i −0.363573 0.998908i
\(739\) 6.02954 + 5.05938i 0.221800 + 0.186112i 0.746916 0.664918i \(-0.231534\pi\)
−0.525116 + 0.851031i \(0.675978\pi\)
\(740\) 0 0
\(741\) 11.1699 + 43.2888i 0.410337 + 1.59026i
\(742\) 19.6254i 0.720473i
\(743\) 31.1013 37.0651i 1.14100 1.35979i 0.217553 0.976049i \(-0.430193\pi\)
0.923442 0.383737i \(-0.125363\pi\)
\(744\) 0.772575 0.281194i 0.0283240 0.0103091i
\(745\) 0 0
\(746\) −4.04087 + 22.9169i −0.147947 + 0.839048i
\(747\) 10.2087 28.0483i 0.373518 1.02623i
\(748\) 1.54708 0.893209i 0.0565670 0.0326590i
\(749\) 17.2835 29.9359i 0.631525 1.09383i
\(750\) 0 0
\(751\) −9.30243 + 7.80567i −0.339451 + 0.284833i −0.796537 0.604589i \(-0.793337\pi\)
0.457087 + 0.889422i \(0.348893\pi\)
\(752\) −0.0662008 0.0382211i −0.00241410 0.00139378i
\(753\) 46.3145 26.7397i 1.68779 0.974447i
\(754\) −0.529778 0.192823i −0.0192934 0.00702221i
\(755\) 0 0
\(756\) 0.489679 + 2.77711i 0.0178095 + 0.101002i
\(757\) −11.9596 32.8586i −0.434677 1.19427i −0.942910 0.333046i \(-0.891923\pi\)
0.508233 0.861220i \(-0.330299\pi\)
\(758\) −6.00792 + 7.15997i −0.218218 + 0.260062i
\(759\) −6.94262 −0.252001
\(760\) 0 0
\(761\) 46.9073 1.70039 0.850194 0.526470i \(-0.176485\pi\)
0.850194 + 0.526470i \(0.176485\pi\)
\(762\) −24.9954 + 29.7884i −0.905489 + 1.07912i
\(763\) 8.03041 + 22.0634i 0.290720 + 0.798748i
\(764\) −1.94845 11.0502i −0.0704926 0.399783i
\(765\) 0 0
\(766\) 30.8559 + 11.2306i 1.11487 + 0.405779i
\(767\) 30.6636 17.7036i 1.10720 0.639241i
\(768\) −2.05362 1.18566i −0.0741035 0.0427837i
\(769\) −1.06182 + 0.890969i −0.0382900 + 0.0321292i −0.661732 0.749741i \(-0.730178\pi\)
0.623442 + 0.781870i \(0.285734\pi\)
\(770\) 0 0
\(771\) 12.7038 22.0036i 0.457516 0.792440i
\(772\) −18.6090 + 10.7439i −0.669753 + 0.386682i
\(773\) −2.20242 + 6.05111i −0.0792157 + 0.217643i −0.972978 0.230897i \(-0.925834\pi\)
0.893762 + 0.448541i \(0.148056\pi\)
\(774\) −5.24973 + 29.7727i −0.188698 + 1.07016i
\(775\) 0 0
\(776\) −15.2434 + 5.54814i −0.547206 + 0.199167i
\(777\) 49.6116 59.1248i 1.77981 2.12109i
\(778\) 10.6737i 0.382670i
\(779\) 27.1585 + 39.5624i 0.973056 + 1.41747i
\(780\) 0 0
\(781\) 12.2988 + 10.3199i 0.440085 + 0.369275i
\(782\) 0.942355 + 2.58910i 0.0336985 + 0.0925860i
\(783\)