Properties

Label 637.2.h.m.471.7
Level $637$
Weight $2$
Character 637.471
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 8 x^{14} + 45 x^{12} + 124 x^{10} + 248 x^{8} + 250 x^{6} + 177 x^{4} + 14 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 471.7
Root \(-0.756863 + 1.31093i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.m.165.7

$q$-expansion

\(f(q)\) \(=\) \(q+2.43210 q^{2} +(-0.376796 + 0.652630i) q^{3} +3.91511 q^{4} +(-0.170769 + 0.295780i) q^{5} +(-0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 + 2.10626i) q^{9} +O(q^{10})\) \(q+2.43210 q^{2} +(-0.376796 + 0.652630i) q^{3} +3.91511 q^{4} +(-0.170769 + 0.295780i) q^{5} +(-0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 + 2.10626i) q^{9} +(-0.415326 + 0.719366i) q^{10} +(1.21605 - 2.10626i) q^{11} +(-1.47520 + 2.55511i) q^{12} +(2.50139 - 2.59674i) q^{13} +(-0.128690 - 0.222897i) q^{15} +3.49784 q^{16} -1.94823 q^{17} +(2.95755 + 5.12263i) q^{18} +(3.14519 + 5.44764i) q^{19} +(-0.668577 + 1.15801i) q^{20} +(2.95755 - 5.12263i) q^{22} -3.68948 q^{23} +(-1.75501 + 3.03977i) q^{24} +(2.44168 + 4.22911i) q^{25} +(6.08362 - 6.31553i) q^{26} -4.09359 q^{27} +(-2.22068 - 3.84632i) q^{29} +(-0.312986 - 0.542108i) q^{30} +(0.987661 + 1.71068i) q^{31} -0.808361 q^{32} +(0.916405 + 1.58726i) q^{33} -4.73830 q^{34} +(4.76096 + 8.24623i) q^{36} -9.62867 q^{37} +(7.64942 + 13.2492i) q^{38} +(0.752198 + 2.61092i) q^{39} +(-0.795393 + 1.37766i) q^{40} +(-6.26793 - 10.8564i) q^{41} +(4.20368 - 7.28099i) q^{43} +(4.76096 - 8.24623i) q^{44} -0.830652 q^{45} -8.97318 q^{46} +(4.50265 - 7.79882i) q^{47} +(-1.31797 + 2.28279i) q^{48} +(5.93840 + 10.2856i) q^{50} +(0.734087 - 1.27148i) q^{51} +(9.79320 - 10.1665i) q^{52} +(-0.746129 - 1.29233i) q^{53} -9.95601 q^{54} +(0.415326 + 0.719366i) q^{55} -4.74039 q^{57} +(-5.40090 - 9.35464i) q^{58} +0.626991 q^{59} +(-0.503834 - 0.872666i) q^{60} +(0.571597 + 0.990035i) q^{61} +(2.40209 + 4.16054i) q^{62} -8.96169 q^{64} +(0.340905 + 1.18330i) q^{65} +(2.22879 + 3.86037i) q^{66} +(2.79599 - 4.84280i) q^{67} -7.62754 q^{68} +(1.39018 - 2.40786i) q^{69} +(-4.74859 + 8.22481i) q^{71} +(5.66402 + 9.81038i) q^{72} +(-5.95934 - 10.3219i) q^{73} -23.4179 q^{74} -3.68006 q^{75} +(12.3138 + 21.3281i) q^{76} +(1.82942 + 6.35002i) q^{78} +(-2.23583 + 3.87258i) q^{79} +(-0.597321 + 1.03459i) q^{80} +(-2.10570 + 3.64718i) q^{81} +(-15.2442 - 26.4038i) q^{82} +1.41231 q^{83} +(0.332697 - 0.576248i) q^{85} +(10.2238 - 17.7081i) q^{86} +3.34697 q^{87} +(5.66402 - 9.81038i) q^{88} +12.4444 q^{89} -2.02023 q^{90} -14.4447 q^{92} -1.48859 q^{93} +(10.9509 - 18.9675i) q^{94} -2.14840 q^{95} +(0.304587 - 0.527560i) q^{96} +(-5.13850 + 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} + O(q^{10}) \) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} - 4q^{11} - 8q^{15} + 8q^{16} + 28q^{18} + 28q^{22} - 24q^{23} + 12q^{25} + 8q^{29} + 28q^{30} + 4q^{36} + 16q^{37} + 20q^{39} + 32q^{43} + 4q^{44} + 8q^{46} + 36q^{50} + 44q^{51} + 4q^{53} - 96q^{57} - 48q^{58} - 64q^{60} - 64q^{64} - 68q^{65} + 20q^{67} + 8q^{71} + 28q^{72} - 152q^{74} + 28q^{78} + 4q^{79} + 56q^{81} + 36q^{85} - 4q^{86} + 28q^{88} - 160q^{92} - 16q^{93} - 104q^{95} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.43210 1.71975 0.859877 0.510502i \(-0.170540\pi\)
0.859877 + 0.510502i \(0.170540\pi\)
\(3\) −0.376796 + 0.652630i −0.217543 + 0.376796i −0.954056 0.299627i \(-0.903138\pi\)
0.736513 + 0.676423i \(0.236471\pi\)
\(4\) 3.91511 1.95755
\(5\) −0.170769 + 0.295780i −0.0763700 + 0.132277i −0.901681 0.432401i \(-0.857666\pi\)
0.825311 + 0.564678i \(0.191000\pi\)
\(6\) −0.916405 + 1.58726i −0.374121 + 0.647996i
\(7\) 0 0
\(8\) 4.65773 1.64675
\(9\) 1.21605 + 2.10626i 0.405350 + 0.702086i
\(10\) −0.415326 + 0.719366i −0.131338 + 0.227483i
\(11\) 1.21605 2.10626i 0.366653 0.635061i −0.622387 0.782710i \(-0.713837\pi\)
0.989040 + 0.147648i \(0.0471704\pi\)
\(12\) −1.47520 + 2.55511i −0.425852 + 0.737598i
\(13\) 2.50139 2.59674i 0.693760 0.720206i
\(14\) 0 0
\(15\) −0.128690 0.222897i −0.0332276 0.0575518i
\(16\) 3.49784 0.874460
\(17\) −1.94823 −0.472516 −0.236258 0.971690i \(-0.575921\pi\)
−0.236258 + 0.971690i \(0.575921\pi\)
\(18\) 2.95755 + 5.12263i 0.697102 + 1.20742i
\(19\) 3.14519 + 5.44764i 0.721557 + 1.24977i 0.960376 + 0.278709i \(0.0899065\pi\)
−0.238819 + 0.971064i \(0.576760\pi\)
\(20\) −0.668577 + 1.15801i −0.149498 + 0.258939i
\(21\) 0 0
\(22\) 2.95755 5.12263i 0.630552 1.09215i
\(23\) −3.68948 −0.769309 −0.384655 0.923061i \(-0.625679\pi\)
−0.384655 + 0.923061i \(0.625679\pi\)
\(24\) −1.75501 + 3.03977i −0.358240 + 0.620491i
\(25\) 2.44168 + 4.22911i 0.488335 + 0.845821i
\(26\) 6.08362 6.31553i 1.19310 1.23858i
\(27\) −4.09359 −0.787811
\(28\) 0 0
\(29\) −2.22068 3.84632i −0.412369 0.714244i 0.582779 0.812631i \(-0.301965\pi\)
−0.995148 + 0.0983864i \(0.968632\pi\)
\(30\) −0.312986 0.542108i −0.0571432 0.0989750i
\(31\) 0.987661 + 1.71068i 0.177389 + 0.307247i 0.940986 0.338447i \(-0.109902\pi\)
−0.763596 + 0.645694i \(0.776568\pi\)
\(32\) −0.808361 −0.142899
\(33\) 0.916405 + 1.58726i 0.159526 + 0.276307i
\(34\) −4.73830 −0.812611
\(35\) 0 0
\(36\) 4.76096 + 8.24623i 0.793494 + 1.37437i
\(37\) −9.62867 −1.58294 −0.791472 0.611206i \(-0.790685\pi\)
−0.791472 + 0.611206i \(0.790685\pi\)
\(38\) 7.64942 + 13.2492i 1.24090 + 2.14930i
\(39\) 0.752198 + 2.61092i 0.120448 + 0.418082i
\(40\) −0.795393 + 1.37766i −0.125763 + 0.217827i
\(41\) −6.26793 10.8564i −0.978887 1.69548i −0.666461 0.745540i \(-0.732192\pi\)
−0.312426 0.949942i \(-0.601141\pi\)
\(42\) 0 0
\(43\) 4.20368 7.28099i 0.641055 1.11034i −0.344142 0.938918i \(-0.611830\pi\)
0.985198 0.171423i \(-0.0548365\pi\)
\(44\) 4.76096 8.24623i 0.717742 1.24317i
\(45\) −0.830652 −0.123826
\(46\) −8.97318 −1.32302
\(47\) 4.50265 7.79882i 0.656779 1.13757i −0.324666 0.945829i \(-0.605252\pi\)
0.981445 0.191745i \(-0.0614148\pi\)
\(48\) −1.31797 + 2.28279i −0.190233 + 0.329493i
\(49\) 0 0
\(50\) 5.93840 + 10.2856i 0.839816 + 1.45460i
\(51\) 0.734087 1.27148i 0.102793 0.178042i
\(52\) 9.79320 10.1665i 1.35807 1.40984i
\(53\) −0.746129 1.29233i −0.102489 0.177516i 0.810221 0.586125i \(-0.199347\pi\)
−0.912709 + 0.408609i \(0.866014\pi\)
\(54\) −9.95601 −1.35484
\(55\) 0.415326 + 0.719366i 0.0560025 + 0.0969993i
\(56\) 0 0
\(57\) −4.74039 −0.627879
\(58\) −5.40090 9.35464i −0.709173 1.22832i
\(59\) 0.626991 0.0816273 0.0408136 0.999167i \(-0.487005\pi\)
0.0408136 + 0.999167i \(0.487005\pi\)
\(60\) −0.503834 0.872666i −0.0650447 0.112661i
\(61\) 0.571597 + 0.990035i 0.0731855 + 0.126761i 0.900296 0.435279i \(-0.143350\pi\)
−0.827110 + 0.562040i \(0.810017\pi\)
\(62\) 2.40209 + 4.16054i 0.305066 + 0.528389i
\(63\) 0 0
\(64\) −8.96169 −1.12021
\(65\) 0.340905 + 1.18330i 0.0422841 + 0.146770i
\(66\) 2.22879 + 3.86037i 0.274345 + 0.475179i
\(67\) 2.79599 4.84280i 0.341585 0.591642i −0.643142 0.765747i \(-0.722370\pi\)
0.984727 + 0.174104i \(0.0557030\pi\)
\(68\) −7.62754 −0.924975
\(69\) 1.39018 2.40786i 0.167358 0.289873i
\(70\) 0 0
\(71\) −4.74859 + 8.22481i −0.563554 + 0.976105i 0.433628 + 0.901092i \(0.357233\pi\)
−0.997183 + 0.0750130i \(0.976100\pi\)
\(72\) 5.66402 + 9.81038i 0.667512 + 1.15616i
\(73\) −5.95934 10.3219i −0.697488 1.20808i −0.969335 0.245744i \(-0.920968\pi\)
0.271847 0.962340i \(-0.412366\pi\)
\(74\) −23.4179 −2.72227
\(75\) −3.68006 −0.424936
\(76\) 12.3138 + 21.3281i 1.41249 + 2.44650i
\(77\) 0 0
\(78\) 1.82942 + 6.35002i 0.207141 + 0.718998i
\(79\) −2.23583 + 3.87258i −0.251551 + 0.435699i −0.963953 0.266073i \(-0.914274\pi\)
0.712402 + 0.701772i \(0.247607\pi\)
\(80\) −0.597321 + 1.03459i −0.0667825 + 0.115671i
\(81\) −2.10570 + 3.64718i −0.233967 + 0.405242i
\(82\) −15.2442 26.4038i −1.68344 2.91581i
\(83\) 1.41231 0.155021 0.0775104 0.996992i \(-0.475303\pi\)
0.0775104 + 0.996992i \(0.475303\pi\)
\(84\) 0 0
\(85\) 0.332697 0.576248i 0.0360861 0.0625029i
\(86\) 10.2238 17.7081i 1.10246 1.90951i
\(87\) 3.34697 0.358833
\(88\) 5.66402 9.81038i 0.603787 1.04579i
\(89\) 12.4444 1.31910 0.659551 0.751660i \(-0.270747\pi\)
0.659551 + 0.751660i \(0.270747\pi\)
\(90\) −2.02023 −0.212951
\(91\) 0 0
\(92\) −14.4447 −1.50596
\(93\) −1.48859 −0.154359
\(94\) 10.9509 18.9675i 1.12950 1.95635i
\(95\) −2.14840 −0.220421
\(96\) 0.304587 0.527560i 0.0310868 0.0538439i
\(97\) −5.13850 + 8.90014i −0.521736 + 0.903673i 0.477945 + 0.878390i \(0.341382\pi\)
−0.999680 + 0.0252826i \(0.991951\pi\)
\(98\) 0 0
\(99\) 5.91511 0.594490
\(100\) 9.55942 + 16.5574i 0.955942 + 1.65574i
\(101\) −7.52683 + 13.0369i −0.748948 + 1.29722i 0.199380 + 0.979922i \(0.436107\pi\)
−0.948328 + 0.317293i \(0.897226\pi\)
\(102\) 1.78537 3.09235i 0.176778 0.306189i
\(103\) −8.80880 + 15.2573i −0.867957 + 1.50335i −0.00387687 + 0.999992i \(0.501234\pi\)
−0.864080 + 0.503354i \(0.832099\pi\)
\(104\) 11.6508 12.0949i 1.14245 1.18600i
\(105\) 0 0
\(106\) −1.81466 3.14308i −0.176255 0.305283i
\(107\) 6.38454 0.617217 0.308608 0.951189i \(-0.400137\pi\)
0.308608 + 0.951189i \(0.400137\pi\)
\(108\) −16.0268 −1.54218
\(109\) 4.08736 + 7.07951i 0.391498 + 0.678095i 0.992647 0.121042i \(-0.0386236\pi\)
−0.601149 + 0.799137i \(0.705290\pi\)
\(110\) 1.01011 + 1.74957i 0.0963106 + 0.166815i
\(111\) 3.62804 6.28396i 0.344359 0.596447i
\(112\) 0 0
\(113\) 4.81083 8.33259i 0.452564 0.783865i −0.545980 0.837798i \(-0.683843\pi\)
0.998545 + 0.0539336i \(0.0171759\pi\)
\(114\) −11.5291 −1.07980
\(115\) 0.630047 1.09127i 0.0587522 0.101762i
\(116\) −8.69418 15.0588i −0.807234 1.39817i
\(117\) 8.51122 + 2.11081i 0.786863 + 0.195144i
\(118\) 1.52490 0.140379
\(119\) 0 0
\(120\) −0.599402 1.03819i −0.0547177 0.0947738i
\(121\) 2.54245 + 4.40365i 0.231132 + 0.400332i
\(122\) 1.39018 + 2.40786i 0.125861 + 0.217998i
\(123\) 9.44693 0.851801
\(124\) 3.86680 + 6.69749i 0.347249 + 0.601452i
\(125\) −3.37553 −0.301917
\(126\) 0 0
\(127\) −4.50988 7.81134i −0.400187 0.693145i 0.593561 0.804789i \(-0.297722\pi\)
−0.993748 + 0.111644i \(0.964388\pi\)
\(128\) −20.1790 −1.78359
\(129\) 3.16786 + 5.48690i 0.278915 + 0.483094i
\(130\) 0.829115 + 2.87791i 0.0727182 + 0.252409i
\(131\) 0.0962416 0.166695i 0.00840867 0.0145642i −0.861790 0.507264i \(-0.830657\pi\)
0.870199 + 0.492700i \(0.163990\pi\)
\(132\) 3.58782 + 6.21429i 0.312280 + 0.540885i
\(133\) 0 0
\(134\) 6.80013 11.7782i 0.587442 1.01748i
\(135\) 0.699056 1.21080i 0.0601651 0.104209i
\(136\) −9.07434 −0.778118
\(137\) 4.87680 0.416653 0.208326 0.978059i \(-0.433198\pi\)
0.208326 + 0.978059i \(0.433198\pi\)
\(138\) 3.38106 5.85616i 0.287815 0.498510i
\(139\) 5.53701 9.59038i 0.469643 0.813446i −0.529755 0.848151i \(-0.677716\pi\)
0.999398 + 0.0347054i \(0.0110493\pi\)
\(140\) 0 0
\(141\) 3.39316 + 5.87713i 0.285756 + 0.494943i
\(142\) −11.5491 + 20.0035i −0.969175 + 1.67866i
\(143\) −2.42760 8.42634i −0.203006 0.704646i
\(144\) 4.25355 + 7.36736i 0.354462 + 0.613946i
\(145\) 1.51689 0.125971
\(146\) −14.4937 25.1038i −1.19951 2.07761i
\(147\) 0 0
\(148\) −37.6973 −3.09869
\(149\) −7.95435 13.7773i −0.651646 1.12868i −0.982723 0.185080i \(-0.940746\pi\)
0.331078 0.943603i \(-0.392588\pi\)
\(150\) −8.95026 −0.730786
\(151\) 5.29518 + 9.17152i 0.430916 + 0.746368i 0.996952 0.0780122i \(-0.0248573\pi\)
−0.566037 + 0.824380i \(0.691524\pi\)
\(152\) 14.6494 + 25.3736i 1.18823 + 2.05807i
\(153\) −2.36915 4.10349i −0.191534 0.331747i
\(154\) 0 0
\(155\) −0.674646 −0.0541889
\(156\) 2.94493 + 10.2220i 0.235783 + 0.818418i
\(157\) −4.56194 7.90151i −0.364082 0.630609i 0.624546 0.780988i \(-0.285284\pi\)
−0.988628 + 0.150379i \(0.951951\pi\)
\(158\) −5.43777 + 9.41849i −0.432606 + 0.749295i
\(159\) 1.12455 0.0891829
\(160\) 0.138043 0.239097i 0.0109132 0.0189023i
\(161\) 0 0
\(162\) −5.12127 + 8.87031i −0.402365 + 0.696917i
\(163\) 5.48196 + 9.49504i 0.429380 + 0.743709i 0.996818 0.0797075i \(-0.0253986\pi\)
−0.567438 + 0.823416i \(0.692065\pi\)
\(164\) −24.5396 42.5039i −1.91622 3.31900i
\(165\) −0.625973 −0.0487319
\(166\) 3.43487 0.266598
\(167\) 9.13884 + 15.8289i 0.707185 + 1.22488i 0.965897 + 0.258925i \(0.0833683\pi\)
−0.258713 + 0.965954i \(0.583298\pi\)
\(168\) 0 0
\(169\) −0.486122 12.9909i −0.0373940 0.999301i
\(170\) 0.809152 1.40149i 0.0620591 0.107490i
\(171\) −7.64942 + 13.2492i −0.584966 + 1.01319i
\(172\) 16.4579 28.5058i 1.25490 2.17355i
\(173\) 4.09918 + 7.09998i 0.311655 + 0.539802i 0.978721 0.205197i \(-0.0657835\pi\)
−0.667066 + 0.744999i \(0.732450\pi\)
\(174\) 8.14015 0.617104
\(175\) 0 0
\(176\) 4.25355 7.36736i 0.320623 0.555335i
\(177\) −0.236248 + 0.409193i −0.0177575 + 0.0307568i
\(178\) 30.2659 2.26853
\(179\) 7.77684 13.4699i 0.581268 1.00679i −0.414061 0.910249i \(-0.635890\pi\)
0.995329 0.0965370i \(-0.0307766\pi\)
\(180\) −3.25209 −0.242396
\(181\) −6.67302 −0.496001 −0.248001 0.968760i \(-0.579774\pi\)
−0.248001 + 0.968760i \(0.579774\pi\)
\(182\) 0 0
\(183\) −0.861502 −0.0636841
\(184\) −17.1846 −1.26686
\(185\) 1.64427 2.84797i 0.120889 0.209387i
\(186\) −3.62039 −0.265460
\(187\) −2.36915 + 4.10349i −0.173249 + 0.300077i
\(188\) 17.6283 30.5332i 1.28568 2.22686i
\(189\) 0 0
\(190\) −5.22512 −0.379070
\(191\) 9.37296 + 16.2344i 0.678204 + 1.17468i 0.975521 + 0.219905i \(0.0705746\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(192\) 3.37673 5.84867i 0.243694 0.422091i
\(193\) 4.08655 7.07811i 0.294156 0.509493i −0.680632 0.732625i \(-0.738295\pi\)
0.974788 + 0.223132i \(0.0716281\pi\)
\(194\) −12.4973 + 21.6460i −0.897257 + 1.55409i
\(195\) −0.900710 0.223378i −0.0645012 0.0159965i
\(196\) 0 0
\(197\) −4.36006 7.55184i −0.310641 0.538047i 0.667860 0.744287i \(-0.267210\pi\)
−0.978501 + 0.206240i \(0.933877\pi\)
\(198\) 14.3861 1.02238
\(199\) −17.4666 −1.23818 −0.619089 0.785321i \(-0.712498\pi\)
−0.619089 + 0.785321i \(0.712498\pi\)
\(200\) 11.3727 + 19.6980i 0.804168 + 1.39286i
\(201\) 2.10704 + 3.64950i 0.148619 + 0.257416i
\(202\) −18.3060 + 31.7069i −1.28801 + 2.23089i
\(203\) 0 0
\(204\) 2.87403 4.97796i 0.201222 0.348527i
\(205\) 4.28146 0.299030
\(206\) −21.4239 + 37.1073i −1.49267 + 2.58539i
\(207\) −4.48659 7.77100i −0.311839 0.540122i
\(208\) 8.74945 9.08298i 0.606665 0.629791i
\(209\) 15.2988 1.05824
\(210\) 0 0
\(211\) 11.6284 + 20.1410i 0.800535 + 1.38657i 0.919265 + 0.393640i \(0.128784\pi\)
−0.118730 + 0.992927i \(0.537882\pi\)
\(212\) −2.92117 5.05962i −0.200627 0.347496i
\(213\) −3.57850 6.19815i −0.245195 0.424690i
\(214\) 15.5278 1.06146
\(215\) 1.43571 + 2.48673i 0.0979148 + 0.169593i
\(216\) −19.0668 −1.29733
\(217\) 0 0
\(218\) 9.94086 + 17.2181i 0.673280 + 1.16616i
\(219\) 8.98182 0.606935
\(220\) 1.62605 + 2.81639i 0.109628 + 0.189881i
\(221\) −4.87329 + 5.05906i −0.327813 + 0.340309i
\(222\) 8.82376 15.2832i 0.592212 1.02574i
\(223\) 14.6364 + 25.3510i 0.980128 + 1.69763i 0.661855 + 0.749632i \(0.269769\pi\)
0.318272 + 0.947999i \(0.396897\pi\)
\(224\) 0 0
\(225\) −5.93840 + 10.2856i −0.395893 + 0.685707i
\(226\) 11.7004 20.2657i 0.778299 1.34805i
\(227\) 19.8110 1.31490 0.657452 0.753496i \(-0.271634\pi\)
0.657452 + 0.753496i \(0.271634\pi\)
\(228\) −18.5591 −1.22911
\(229\) 0.664107 1.15027i 0.0438855 0.0760118i −0.843248 0.537524i \(-0.819360\pi\)
0.887134 + 0.461512i \(0.152693\pi\)
\(230\) 1.53234 2.65408i 0.101039 0.175005i
\(231\) 0 0
\(232\) −10.3433 17.9151i −0.679071 1.17618i
\(233\) −0.758171 + 1.31319i −0.0496695 + 0.0860300i −0.889791 0.456368i \(-0.849150\pi\)
0.840122 + 0.542398i \(0.182483\pi\)
\(234\) 20.7001 + 5.13369i 1.35321 + 0.335600i
\(235\) 1.53782 + 2.66358i 0.100316 + 0.173753i
\(236\) 2.45474 0.159790
\(237\) −1.68491 2.91834i −0.109446 0.189567i
\(238\) 0 0
\(239\) 22.4793 1.45406 0.727032 0.686603i \(-0.240899\pi\)
0.727032 + 0.686603i \(0.240899\pi\)
\(240\) −0.450136 0.779659i −0.0290562 0.0503268i
\(241\) 13.3106 0.857409 0.428704 0.903445i \(-0.358970\pi\)
0.428704 + 0.903445i \(0.358970\pi\)
\(242\) 6.18348 + 10.7101i 0.397489 + 0.688472i
\(243\) −7.72722 13.3839i −0.495701 0.858580i
\(244\) 2.23786 + 3.87609i 0.143265 + 0.248141i
\(245\) 0 0
\(246\) 22.9759 1.46489
\(247\) 22.0134 + 5.45939i 1.40068 + 0.347373i
\(248\) 4.60026 + 7.96788i 0.292116 + 0.505961i
\(249\) −0.532152 + 0.921714i −0.0337238 + 0.0584113i
\(250\) −8.20963 −0.519222
\(251\) −7.95169 + 13.7727i −0.501906 + 0.869327i 0.498091 + 0.867125i \(0.334034\pi\)
−0.999998 + 0.00220260i \(0.999299\pi\)
\(252\) 0 0
\(253\) −4.48659 + 7.77100i −0.282069 + 0.488559i
\(254\) −10.9685 18.9980i −0.688224 1.19204i
\(255\) 0.250718 + 0.434256i 0.0157006 + 0.0271942i
\(256\) −31.1539 −1.94712
\(257\) −29.2397 −1.82392 −0.911960 0.410280i \(-0.865431\pi\)
−0.911960 + 0.410280i \(0.865431\pi\)
\(258\) 7.70455 + 13.3447i 0.479664 + 0.830803i
\(259\) 0 0
\(260\) 1.33468 + 4.63275i 0.0827733 + 0.287311i
\(261\) 5.40090 9.35464i 0.334307 0.579037i
\(262\) 0.234069 0.405420i 0.0144608 0.0250469i
\(263\) 0.852177 1.47601i 0.0525475 0.0910149i −0.838555 0.544817i \(-0.816599\pi\)
0.891103 + 0.453802i \(0.149933\pi\)
\(264\) 4.26836 + 7.39302i 0.262700 + 0.455009i
\(265\) 0.509661 0.0313083
\(266\) 0 0
\(267\) −4.68899 + 8.12157i −0.286962 + 0.497032i
\(268\) 10.9466 18.9601i 0.668670 1.15817i
\(269\) 8.37874 0.510861 0.255430 0.966827i \(-0.417783\pi\)
0.255430 + 0.966827i \(0.417783\pi\)
\(270\) 1.70017 2.94479i 0.103469 0.179214i
\(271\) −12.1575 −0.738518 −0.369259 0.929327i \(-0.620388\pi\)
−0.369259 + 0.929327i \(0.620388\pi\)
\(272\) −6.81461 −0.413196
\(273\) 0 0
\(274\) 11.8609 0.716540
\(275\) 11.8768 0.716198
\(276\) 5.44270 9.42704i 0.327612 0.567441i
\(277\) 10.3181 0.619957 0.309979 0.950744i \(-0.399678\pi\)
0.309979 + 0.950744i \(0.399678\pi\)
\(278\) 13.4666 23.3248i 0.807670 1.39893i
\(279\) −2.40209 + 4.16054i −0.143809 + 0.249085i
\(280\) 0 0
\(281\) −2.59677 −0.154910 −0.0774551 0.996996i \(-0.524679\pi\)
−0.0774551 + 0.996996i \(0.524679\pi\)
\(282\) 8.25250 + 14.2938i 0.491429 + 0.851181i
\(283\) −2.30184 + 3.98690i −0.136830 + 0.236997i −0.926295 0.376799i \(-0.877025\pi\)
0.789465 + 0.613796i \(0.210358\pi\)
\(284\) −18.5912 + 32.2010i −1.10319 + 1.91078i
\(285\) 0.809509 1.40211i 0.0479512 0.0830539i
\(286\) −5.90416 20.4937i −0.349120 1.21182i
\(287\) 0 0
\(288\) −0.983006 1.70262i −0.0579242 0.100328i
\(289\) −13.2044 −0.776729
\(290\) 3.68922 0.216638
\(291\) −3.87233 6.70708i −0.227000 0.393176i
\(292\) −23.3314 40.4112i −1.36537 2.36489i
\(293\) 0.980596 1.69844i 0.0572870 0.0992241i −0.835960 0.548791i \(-0.815088\pi\)
0.893247 + 0.449567i \(0.148422\pi\)
\(294\) 0 0
\(295\) −0.107070 + 0.185451i −0.00623388 + 0.0107974i
\(296\) −44.8477 −2.60672
\(297\) −4.97800 + 8.62216i −0.288853 + 0.500308i
\(298\) −19.3458 33.5078i −1.12067 1.94106i
\(299\) −9.22882 + 9.58062i −0.533716 + 0.554061i
\(300\) −14.4078 −0.831835
\(301\) 0 0
\(302\) 12.8784 + 22.3060i 0.741069 + 1.28357i
\(303\) −5.67216 9.82447i −0.325857 0.564401i
\(304\) 11.0014 + 19.0550i 0.630972 + 1.09288i
\(305\) −0.390443 −0.0223567
\(306\) −5.76200 9.98008i −0.329392 0.570523i
\(307\) 7.37658 0.421004 0.210502 0.977593i \(-0.432490\pi\)
0.210502 + 0.977593i \(0.432490\pi\)
\(308\) 0 0
\(309\) −6.63825 11.4978i −0.377637 0.654086i
\(310\) −1.64081 −0.0931915
\(311\) −7.08088 12.2644i −0.401520 0.695453i 0.592390 0.805652i \(-0.298185\pi\)
−0.993910 + 0.110199i \(0.964851\pi\)
\(312\) 3.50353 + 12.1610i 0.198348 + 0.688479i
\(313\) 13.3576 23.1361i 0.755017 1.30773i −0.190349 0.981716i \(-0.560962\pi\)
0.945366 0.326011i \(-0.105705\pi\)
\(314\) −11.0951 19.2173i −0.626132 1.08449i
\(315\) 0 0
\(316\) −8.75352 + 15.1615i −0.492424 + 0.852904i
\(317\) −10.7181 + 18.5643i −0.601989 + 1.04268i 0.390530 + 0.920590i \(0.372292\pi\)
−0.992520 + 0.122086i \(0.961042\pi\)
\(318\) 2.73503 0.153373
\(319\) −10.8018 −0.604785
\(320\) 1.53037 2.65069i 0.0855506 0.148178i
\(321\) −2.40567 + 4.16674i −0.134271 + 0.232565i
\(322\) 0 0
\(323\) −6.12757 10.6133i −0.340947 0.590538i
\(324\) −8.24404 + 14.2791i −0.458002 + 0.793283i
\(325\) 17.0895 + 4.23824i 0.947953 + 0.235095i
\(326\) 13.3327 + 23.0929i 0.738429 + 1.27900i
\(327\) −6.16040 −0.340671
\(328\) −29.1943 50.5660i −1.61199 2.79204i
\(329\) 0 0
\(330\) −1.52243 −0.0838069
\(331\) −5.30692 9.19185i −0.291695 0.505230i 0.682516 0.730871i \(-0.260886\pi\)
−0.974211 + 0.225641i \(0.927552\pi\)
\(332\) 5.52933 0.303462
\(333\) −11.7089 20.2805i −0.641646 1.11136i
\(334\) 22.2266 + 38.4975i 1.21618 + 2.10649i
\(335\) 0.954935 + 1.65400i 0.0521737 + 0.0903675i
\(336\) 0 0
\(337\) 6.75587 0.368016 0.184008 0.982925i \(-0.441093\pi\)
0.184008 + 0.982925i \(0.441093\pi\)
\(338\) −1.18230 31.5952i −0.0643085 1.71855i
\(339\) 3.62540 + 6.27938i 0.196905 + 0.341049i
\(340\) 1.30254 2.25607i 0.0706404 0.122353i
\(341\) 4.80418 0.260161
\(342\) −18.6042 + 32.2233i −1.00600 + 1.74244i
\(343\) 0 0
\(344\) 19.5796 33.9129i 1.05566 1.82846i
\(345\) 0.474798 + 0.822375i 0.0255623 + 0.0442752i
\(346\) 9.96960 + 17.2679i 0.535969 + 0.928326i
\(347\) −16.0204 −0.860021 −0.430010 0.902824i \(-0.641490\pi\)
−0.430010 + 0.902824i \(0.641490\pi\)
\(348\) 13.1037 0.702434
\(349\) −8.01922 13.8897i −0.429259 0.743498i 0.567549 0.823340i \(-0.307892\pi\)
−0.996808 + 0.0798418i \(0.974558\pi\)
\(350\) 0 0
\(351\) −10.2396 + 10.6300i −0.546552 + 0.567386i
\(352\) −0.983006 + 1.70262i −0.0523944 + 0.0907498i
\(353\) −1.92156 + 3.32823i −0.102274 + 0.177144i −0.912621 0.408806i \(-0.865945\pi\)
0.810347 + 0.585950i \(0.199279\pi\)
\(354\) −0.574578 + 0.995198i −0.0305385 + 0.0528942i
\(355\) −1.62182 2.80908i −0.0860773 0.149090i
\(356\) 48.7210 2.58221
\(357\) 0 0
\(358\) 18.9140 32.7601i 0.999638 1.73142i
\(359\) 10.5668 18.3022i 0.557692 0.965952i −0.439996 0.898000i \(-0.645020\pi\)
0.997689 0.0679519i \(-0.0216465\pi\)
\(360\) −3.86895 −0.203912
\(361\) −10.2845 + 17.8133i −0.541289 + 0.937540i
\(362\) −16.2294 −0.853000
\(363\) −3.83194 −0.201125
\(364\) 0 0
\(365\) 4.07067 0.213069
\(366\) −2.09526 −0.109521
\(367\) 7.36961 12.7645i 0.384690 0.666303i −0.607036 0.794674i \(-0.707642\pi\)
0.991726 + 0.128371i \(0.0409749\pi\)
\(368\) −12.9052 −0.672730
\(369\) 15.2442 26.4038i 0.793583 1.37453i
\(370\) 3.99904 6.92653i 0.207900 0.360093i
\(371\) 0 0
\(372\) −5.82798 −0.302166
\(373\) −6.46330 11.1948i −0.334657 0.579643i 0.648762 0.760991i \(-0.275287\pi\)
−0.983419 + 0.181349i \(0.941954\pi\)
\(374\) −5.76200 + 9.98008i −0.297946 + 0.516058i
\(375\) 1.27189 2.20297i 0.0656800 0.113761i
\(376\) 20.9721 36.3247i 1.08155 1.87331i
\(377\) −15.5427 3.85463i −0.800488 0.198523i
\(378\) 0 0
\(379\) 13.4179 + 23.2405i 0.689231 + 1.19378i 0.972087 + 0.234621i \(0.0753848\pi\)
−0.282856 + 0.959162i \(0.591282\pi\)
\(380\) −8.41121 −0.431486
\(381\) 6.79722 0.348232
\(382\) 22.7960 + 39.4838i 1.16634 + 2.02017i
\(383\) 1.45391 + 2.51825i 0.0742914 + 0.128677i 0.900778 0.434280i \(-0.142997\pi\)
−0.826487 + 0.562957i \(0.809664\pi\)
\(384\) 7.60337 13.1694i 0.388008 0.672049i
\(385\) 0 0
\(386\) 9.93889 17.2147i 0.505876 0.876203i
\(387\) 20.4475 1.03941
\(388\) −20.1178 + 34.8450i −1.02132 + 1.76899i
\(389\) 8.35048 + 14.4635i 0.423386 + 0.733327i 0.996268 0.0863114i \(-0.0275080\pi\)
−0.572882 + 0.819638i \(0.694175\pi\)
\(390\) −2.19061 0.543278i −0.110926 0.0275100i
\(391\) 7.18797 0.363511
\(392\) 0 0
\(393\) 0.0725269 + 0.125620i 0.00365850 + 0.00633671i
\(394\) −10.6041 18.3668i −0.534227 0.925308i
\(395\) −0.763620 1.32263i −0.0384219 0.0665487i
\(396\) 23.1583 1.16375
\(397\) 12.0492 + 20.8699i 0.604733 + 1.04743i 0.992094 + 0.125500i \(0.0400536\pi\)
−0.387360 + 0.921928i \(0.626613\pi\)
\(398\) −42.4806 −2.12936
\(399\) 0 0
\(400\) 8.54059 + 14.7927i 0.427030 + 0.739637i
\(401\) 1.84490 0.0921297 0.0460649 0.998938i \(-0.485332\pi\)
0.0460649 + 0.998938i \(0.485332\pi\)
\(402\) 5.12453 + 8.87594i 0.255588 + 0.442692i
\(403\) 6.91271 + 1.71437i 0.344347 + 0.0853990i
\(404\) −29.4683 + 51.0406i −1.46610 + 2.53937i
\(405\) −0.719175 1.24565i −0.0357361 0.0618967i
\(406\) 0 0
\(407\) −11.7089 + 20.2805i −0.580390 + 1.00527i
\(408\) 3.41918 5.92218i 0.169274 0.293192i
\(409\) −25.6703 −1.26931 −0.634657 0.772794i \(-0.718859\pi\)
−0.634657 + 0.772794i \(0.718859\pi\)
\(410\) 10.4129 0.514259
\(411\) −1.83756 + 3.18274i −0.0906400 + 0.156993i
\(412\) −34.4874 + 59.7339i −1.69907 + 2.94288i
\(413\) 0 0
\(414\) −10.9118 18.8998i −0.536287 0.928876i
\(415\) −0.241178 + 0.417732i −0.0118389 + 0.0205057i
\(416\) −2.02202 + 2.09910i −0.0991378 + 0.102917i
\(417\) 4.17265 + 7.22724i 0.204335 + 0.353919i
\(418\) 37.2083 1.81992
\(419\) 13.1199 + 22.7244i 0.640950 + 1.11016i 0.985221 + 0.171288i \(0.0547928\pi\)
−0.344271 + 0.938870i \(0.611874\pi\)
\(420\) 0 0
\(421\) 23.6637 1.15330 0.576650 0.816992i \(-0.304360\pi\)
0.576650 + 0.816992i \(0.304360\pi\)
\(422\) 28.2815 + 48.9850i 1.37672 + 2.38455i
\(423\) 21.9018 1.06490
\(424\) −3.47526 6.01933i −0.168774 0.292325i
\(425\) −4.75696 8.23929i −0.230746 0.399664i
\(426\) −8.70327 15.0745i −0.421675 0.730362i
\(427\) 0 0
\(428\) 24.9961 1.20823
\(429\) 6.41399 + 1.59069i 0.309670 + 0.0767991i
\(430\) 3.49180 + 6.04797i 0.168389 + 0.291659i
\(431\) 11.5088 19.9339i 0.554361 0.960182i −0.443592 0.896229i \(-0.646296\pi\)
0.997953 0.0639528i \(-0.0203707\pi\)
\(432\) −14.3187 −0.688909
\(433\) 12.9304 22.3961i 0.621394 1.07629i −0.367832 0.929892i \(-0.619900\pi\)
0.989226 0.146394i \(-0.0467667\pi\)
\(434\) 0 0
\(435\) −0.571557 + 0.989965i −0.0274040 + 0.0474652i
\(436\) 16.0024 + 27.7170i 0.766378 + 1.32741i
\(437\) −11.6041 20.0989i −0.555101 0.961462i
\(438\) 21.8447 1.04378
\(439\) −35.6771 −1.70277 −0.851387 0.524537i \(-0.824238\pi\)
−0.851387 + 0.524537i \(0.824238\pi\)
\(440\) 1.93447 + 3.35061i 0.0922225 + 0.159734i
\(441\) 0 0
\(442\) −11.8523 + 12.3041i −0.563757 + 0.585248i
\(443\) 3.42940 5.93990i 0.162936 0.282213i −0.772984 0.634425i \(-0.781237\pi\)
0.935920 + 0.352212i \(0.114570\pi\)
\(444\) 14.2042 24.6024i 0.674100 1.16758i
\(445\) −2.12511 + 3.68079i −0.100740 + 0.174486i
\(446\) 35.5972 + 61.6562i 1.68558 + 2.91951i
\(447\) 11.9887 0.567045
\(448\) 0 0
\(449\) 4.99075 8.64423i 0.235528 0.407946i −0.723898 0.689907i \(-0.757651\pi\)
0.959426 + 0.281961i \(0.0909847\pi\)
\(450\) −14.4428 + 25.0156i −0.680839 + 1.17925i
\(451\) −30.4885 −1.43565
\(452\) 18.8349 32.6230i 0.885919 1.53446i
\(453\) −7.98081 −0.374971
\(454\) 48.1824 2.26131
\(455\) 0 0
\(456\) −22.0794 −1.03396
\(457\) −8.77311 −0.410389 −0.205194 0.978721i \(-0.565783\pi\)
−0.205194 + 0.978721i \(0.565783\pi\)
\(458\) 1.61518 2.79757i 0.0754722 0.130722i
\(459\) 7.97526 0.372253
\(460\) 2.46670 4.27245i 0.115010 0.199204i
\(461\) −3.44272 + 5.96296i −0.160343 + 0.277723i −0.934992 0.354669i \(-0.884593\pi\)
0.774649 + 0.632392i \(0.217927\pi\)
\(462\) 0 0
\(463\) −13.9526 −0.648432 −0.324216 0.945983i \(-0.605100\pi\)
−0.324216 + 0.945983i \(0.605100\pi\)
\(464\) −7.76757 13.4538i −0.360600 0.624578i
\(465\) 0.254204 0.440294i 0.0117884 0.0204181i
\(466\) −1.84395 + 3.19381i −0.0854192 + 0.147950i
\(467\) 14.4056 24.9513i 0.666613 1.15461i −0.312232 0.950006i \(-0.601077\pi\)
0.978845 0.204602i \(-0.0655900\pi\)
\(468\) 33.3223 + 8.26403i 1.54032 + 0.382005i
\(469\) 0 0
\(470\) 3.74013 + 6.47810i 0.172520 + 0.298813i
\(471\) 6.87568 0.316815
\(472\) 2.92035 0.134420
\(473\) −10.2238 17.7081i −0.470089 0.814219i
\(474\) −4.09786 7.09770i −0.188221 0.326008i
\(475\) −15.3591 + 26.6027i −0.704723 + 1.22062i
\(476\) 0 0
\(477\) 1.81466 3.14308i 0.0830876 0.143912i
\(478\) 54.6719 2.50063
\(479\) 12.2936 21.2931i 0.561707 0.972906i −0.435640 0.900121i \(-0.643478\pi\)
0.997348 0.0727849i \(-0.0231887\pi\)
\(480\) 0.104028 + 0.180181i 0.00474820 + 0.00822412i
\(481\) −24.0850 + 25.0032i −1.09818 + 1.14005i
\(482\) 32.3726 1.47453
\(483\) 0 0
\(484\) 9.95395 + 17.2407i 0.452452 + 0.783670i
\(485\) −1.75499 3.03973i −0.0796899 0.138027i
\(486\) −18.7934 32.5511i −0.852484 1.47655i
\(487\) −2.57316 −0.116601 −0.0583004 0.998299i \(-0.518568\pi\)
−0.0583004 + 0.998299i \(0.518568\pi\)
\(488\) 2.66234 + 4.61131i 0.120519 + 0.208744i
\(489\) −8.26233 −0.373635
\(490\) 0 0
\(491\) −7.01897 12.1572i −0.316762 0.548647i 0.663049 0.748576i \(-0.269262\pi\)
−0.979810 + 0.199929i \(0.935929\pi\)
\(492\) 36.9857 1.66745
\(493\) 4.32639 + 7.49354i 0.194851 + 0.337492i
\(494\) 53.5389 + 13.2778i 2.40883 + 0.597396i
\(495\) −1.01011 + 1.74957i −0.0454012 + 0.0786373i
\(496\) 3.45468 + 5.98368i 0.155120 + 0.268675i
\(497\) 0 0
\(498\) −1.29425 + 2.24170i −0.0579965 + 0.100453i
\(499\) −6.76726 + 11.7212i −0.302944 + 0.524715i −0.976801 0.214147i \(-0.931303\pi\)
0.673857 + 0.738862i \(0.264636\pi\)
\(500\) −13.2156 −0.591018
\(501\) −13.7739 −0.615373
\(502\) −19.3393 + 33.4966i −0.863155 + 1.49503i
\(503\) 4.13877 7.16856i 0.184539 0.319630i −0.758882 0.651228i \(-0.774254\pi\)
0.943421 + 0.331597i \(0.107588\pi\)
\(504\) 0 0
\(505\) −2.57069 4.45257i −0.114394 0.198137i
\(506\) −10.9118 + 18.8998i −0.485090 + 0.840200i
\(507\) 8.66142 + 4.57766i 0.384667 + 0.203301i
\(508\) −17.6567 30.5822i −0.783388 1.35687i
\(509\) −0.166218 −0.00736750 −0.00368375 0.999993i \(-0.501173\pi\)
−0.00368375 + 0.999993i \(0.501173\pi\)
\(510\) 0.609771 + 1.05615i 0.0270011 + 0.0467673i
\(511\) 0 0
\(512\) −35.4115 −1.56498
\(513\) −12.8751 22.3004i −0.568451 0.984585i
\(514\) −71.1137 −3.13669
\(515\) −3.00853 5.21093i −0.132572 0.229621i
\(516\) 12.4025 + 21.4818i 0.545990 + 0.945683i
\(517\) −10.9509 18.9675i −0.481619 0.834189i
\(518\) 0 0
\(519\) −6.17821 −0.271193
\(520\) 1.58784 + 5.51149i 0.0696315 + 0.241695i
\(521\) 3.53090 + 6.11569i 0.154691 + 0.267933i 0.932947 0.360015i \(-0.117228\pi\)
−0.778255 + 0.627948i \(0.783895\pi\)
\(522\) 13.1355 22.7514i 0.574926 0.995802i
\(523\) 23.3912 1.02283 0.511414 0.859335i \(-0.329122\pi\)
0.511414 + 0.859335i \(0.329122\pi\)
\(524\) 0.376796 0.652630i 0.0164604 0.0285103i
\(525\) 0 0
\(526\) 2.07258 3.58981i 0.0903687 0.156523i
\(527\) −1.92420 3.33280i −0.0838193 0.145179i
\(528\) 3.20544 + 5.55198i 0.139499 + 0.241619i
\(529\) −9.38775 −0.408163
\(530\) 1.23955 0.0538425
\(531\) 0.762452 + 1.32061i 0.0330876 + 0.0573094i
\(532\) 0 0
\(533\) −43.8697 10.8798i −1.90021 0.471257i
\(534\) −11.4041 + 19.7525i −0.493503 + 0.854773i
\(535\) −1.09028 + 1.88842i −0.0471368 + 0.0816434i
\(536\) 13.0230 22.5564i 0.562507 0.974290i
\(537\) 5.86056 + 10.1508i 0.252902 + 0.438039i
\(538\) 20.3779 0.878554
\(539\) 0 0
\(540\) 2.73688 4.74041i 0.117776 0.203995i
\(541\) −13.1540 + 22.7833i −0.565533 + 0.979532i 0.431467 + 0.902129i \(0.357996\pi\)
−0.997000 + 0.0774030i \(0.975337\pi\)
\(542\) −29.5683 −1.27007
\(543\) 2.51437 4.35501i 0.107902 0.186891i
\(544\) 1.57488 0.0675222
\(545\) −2.79197 −0.119595
\(546\) 0 0
\(547\) 41.7636 1.78568 0.892841 0.450371i \(-0.148708\pi\)
0.892841 + 0.450371i \(0.148708\pi\)
\(548\) 19.0932 0.815620
\(549\) −1.39018 + 2.40786i −0.0593315 + 0.102765i
\(550\) 28.8855 1.23168
\(551\) 13.9689 24.1949i 0.595095 1.03074i
\(552\) 6.47508 11.2152i 0.275598 0.477349i
\(553\) 0 0
\(554\) 25.0948 1.06617
\(555\) 1.23911 + 2.14620i 0.0525974 + 0.0911013i
\(556\) 21.6780 37.5474i 0.919351 1.59236i
\(557\) −3.65494 + 6.33053i −0.154865 + 0.268233i −0.933010 0.359851i \(-0.882827\pi\)
0.778145 + 0.628085i \(0.216161\pi\)
\(558\) −5.84212 + 10.1188i −0.247317 + 0.428365i
\(559\) −8.39181 29.1284i −0.354936 1.23200i
\(560\) 0 0
\(561\) −1.78537 3.09235i −0.0753785 0.130559i
\(562\) −6.31560 −0.266407
\(563\) 44.7737 1.88699 0.943493 0.331393i \(-0.107519\pi\)
0.943493 + 0.331393i \(0.107519\pi\)
\(564\) 13.2846 + 23.0096i 0.559382 + 0.968878i
\(565\) 1.64308 + 2.84589i 0.0691247 + 0.119727i
\(566\) −5.59830 + 9.69654i −0.235314 + 0.407576i
\(567\) 0 0
\(568\) −22.1176 + 38.3089i −0.928036 + 1.60741i
\(569\) −42.5127 −1.78222 −0.891112 0.453784i \(-0.850074\pi\)
−0.891112 + 0.453784i \(0.850074\pi\)
\(570\) 1.96881 3.41007i 0.0824642 0.142832i
\(571\) 20.4324 + 35.3899i 0.855069 + 1.48102i 0.876581 + 0.481254i \(0.159818\pi\)
−0.0215128 + 0.999769i \(0.506848\pi\)
\(572\) −9.50430 32.9900i −0.397395 1.37938i
\(573\) −14.1268 −0.590155
\(574\) 0 0
\(575\) −9.00851 15.6032i −0.375681 0.650698i
\(576\) −10.8979 18.8756i −0.454077 0.786485i
\(577\) 10.8640 + 18.8170i 0.452275 + 0.783363i 0.998527 0.0542578i \(-0.0172793\pi\)
−0.546252 + 0.837621i \(0.683946\pi\)
\(578\) −32.1144 −1.33578
\(579\) 3.07959 + 5.33400i 0.127983 + 0.221674i
\(580\) 5.93877 0.246594
\(581\) 0 0
\(582\) −9.41790 16.3123i −0.390384 0.676166i
\(583\) −3.62932 −0.150311
\(584\) −27.7570 48.0765i −1.14859 1.98942i
\(585\) −2.07778 + 2.15699i −0.0859057 + 0.0891805i
\(586\) 2.38491 4.13078i 0.0985196 0.170641i
\(587\) −10.2408 17.7376i −0.422683 0.732108i 0.573518 0.819193i \(-0.305578\pi\)
−0.996201 + 0.0870851i \(0.972245\pi\)
\(588\) 0 0
\(589\) −6.21277 + 10.7608i −0.255993 + 0.443393i
\(590\) −0.260406 + 0.451036i −0.0107207 + 0.0185688i
\(591\) 6.57141 0.270312
\(592\) −33.6795 −1.38422
\(593\) 2.81930 4.88318i 0.115775 0.200528i −0.802314 0.596902i \(-0.796398\pi\)
0.918089 + 0.396374i \(0.129732\pi\)
\(594\) −12.1070 + 20.9699i −0.496756 + 0.860407i
\(595\) 0 0
\(596\) −31.1421 53.9397i −1.27563 2.20946i
\(597\) 6.58136 11.3993i 0.269357 0.466541i
\(598\) −22.4454 + 23.3010i −0.917860 + 0.952849i
\(599\) −19.8359 34.3568i −0.810474 1.40378i −0.912533 0.409004i \(-0.865876\pi\)
0.102058 0.994778i \(-0.467457\pi\)
\(600\) −17.1407 −0.699766
\(601\) −8.41334 14.5723i −0.343187 0.594418i 0.641836 0.766842i \(-0.278173\pi\)
−0.985023 + 0.172425i \(0.944840\pi\)
\(602\) 0 0
\(603\) 13.6003 0.553845
\(604\) 20.7312 + 35.9075i 0.843540 + 1.46105i
\(605\) −1.73668 −0.0706061
\(606\) −13.7953 23.8941i −0.560394 0.970631i
\(607\) −11.2490 19.4838i −0.456582 0.790823i 0.542196 0.840252i \(-0.317593\pi\)
−0.998778 + 0.0494290i \(0.984260\pi\)
\(608\) −2.54245 4.40365i −0.103110 0.178592i
\(609\) 0 0
\(610\) −0.949597 −0.0384480
\(611\) −8.98863 31.2001i −0.363641 1.26222i
\(612\) −9.27547 16.0656i −0.374939 0.649413i
\(613\) −13.7135 + 23.7524i −0.553882 + 0.959351i 0.444108 + 0.895973i \(0.353521\pi\)
−0.997990 + 0.0633780i \(0.979813\pi\)
\(614\) 17.9406 0.724022
\(615\) −1.61324 + 2.79421i −0.0650521 + 0.112673i
\(616\) 0 0
\(617\) −5.31896 + 9.21271i −0.214133 + 0.370890i −0.953004 0.302957i \(-0.902026\pi\)
0.738871 + 0.673847i \(0.235359\pi\)
\(618\) −16.1449 27.9637i −0.649442 1.12487i
\(619\) 22.7339 + 39.3762i 0.913751 + 1.58266i 0.808719 + 0.588195i \(0.200161\pi\)
0.105032 + 0.994469i \(0.466505\pi\)
\(620\) −2.64131 −0.106078
\(621\) 15.1032 0.606071
\(622\) −17.2214 29.8283i −0.690515 1.19601i
\(623\) 0 0
\(624\) 2.63107 + 9.13258i 0.105327 + 0.365596i
\(625\) −11.6319 + 20.1471i −0.465278 + 0.805885i
\(626\) 32.4870 56.2692i 1.29844 2.24897i
\(627\) −5.76454 + 9.98448i −0.230214 + 0.398742i
\(628\) −17.8605 30.9353i −0.712711 1.23445i
\(629\) 18.7589 0.747966
\(630\) 0 0
\(631\) −14.7992 + 25.6329i −0.589146 + 1.02043i 0.405199 + 0.914229i \(0.367202\pi\)
−0.994345 + 0.106202i \(0.966131\pi\)
\(632\) −10.4139 + 18.0374i −0.414243 + 0.717489i
\(633\) −17.5262 −0.696604
\(634\) −26.0675 + 45.1503i −1.03527 + 1.79315i
\(635\) 3.08058 0.122249
\(636\) 4.40275 0.174580
\(637\) 0 0
\(638\) −26.2711 −1.04008
\(639\) −23.0981 −0.913747
\(640\) 3.44594 5.96854i 0.136213 0.235927i
\(641\) −42.5646 −1.68120 −0.840601 0.541654i \(-0.817798\pi\)
−0.840601 + 0.541654i \(0.817798\pi\)
\(642\) −5.85082 + 10.1339i −0.230914 + 0.399954i
\(643\) −10.9980 + 19.0492i −0.433721 + 0.751226i −0.997190 0.0749106i \(-0.976133\pi\)
0.563470 + 0.826137i \(0.309466\pi\)
\(644\) 0 0
\(645\) −2.16388 −0.0852029
\(646\) −14.9029 25.8125i −0.586345 1.01558i
\(647\) −17.4026 + 30.1421i −0.684166 + 1.18501i 0.289533 + 0.957168i \(0.406500\pi\)
−0.973698 + 0.227841i \(0.926833\pi\)
\(648\) −9.80778 + 16.9876i −0.385286 + 0.667335i
\(649\) 0.762452 1.32061i 0.0299289 0.0518383i
\(650\) 41.5633 + 10.3078i 1.63025 + 0.404306i
\(651\) 0 0
\(652\) 21.4625 + 37.1741i 0.840535 + 1.45585i
\(653\) −50.8167 −1.98861 −0.994306 0.106559i \(-0.966017\pi\)
−0.994306 + 0.106559i \(0.966017\pi\)
\(654\) −14.9827 −0.585870
\(655\) 0.0328701 + 0.0569326i 0.00128434 + 0.00222454i
\(656\) −21.9242 37.9739i −0.855997 1.48263i
\(657\) 14.4937 25.1038i 0.565453 0.979394i
\(658\) 0 0
\(659\) 7.37203 12.7687i 0.287173 0.497399i −0.685960 0.727639i \(-0.740618\pi\)
0.973134 + 0.230240i \(0.0739511\pi\)
\(660\) −2.45075 −0.0953953
\(661\) 9.06227 15.6963i 0.352481 0.610516i −0.634202 0.773167i \(-0.718671\pi\)
0.986684 + 0.162651i \(0.0520046\pi\)
\(662\) −12.9069 22.3555i −0.501643 0.868871i
\(663\) −1.46546 5.08669i −0.0569136 0.197551i
\(664\) 6.57814 0.255281
\(665\) 0 0
\(666\) −28.4773 49.3241i −1.10347 1.91127i
\(667\) 8.19313 + 14.1909i 0.317239 + 0.549475i
\(668\) 35.7795 + 61.9719i 1.38435 + 2.39777i
\(669\) −22.0598 −0.852881
\(670\) 2.32250 + 4.02268i 0.0897259 + 0.155410i
\(671\) 2.78036 0.107335
\(672\) 0 0
\(673\) −10.4574 18.1127i −0.403102 0.698193i 0.590997 0.806674i \(-0.298735\pi\)
−0.994099 + 0.108481i \(0.965401\pi\)
\(674\) 16.4309 0.632896
\(675\) −9.99521 17.3122i −0.384716 0.666348i
\(676\) −1.90322 50.8608i −0.0732008 1.95618i
\(677\) 19.1089 33.0976i 0.734416 1.27205i −0.220563 0.975373i \(-0.570790\pi\)
0.954979 0.296673i \(-0.0958771\pi\)
\(678\) 8.81733 + 15.2721i 0.338628 + 0.586520i
\(679\) 0 0
\(680\) 1.54961 2.68401i 0.0594249 0.102927i
\(681\) −7.46472 + 12.9293i −0.286049 + 0.495451i
\(682\) 11.6842 0.447413
\(683\) −23.8253 −0.911649 −0.455825 0.890070i \(-0.650656\pi\)
−0.455825 + 0.890070i \(0.650656\pi\)
\(684\) −29.9483 + 51.8720i −1.14510 + 1.98337i
\(685\) −0.832803 + 1.44246i −0.0318198 + 0.0551135i
\(686\) 0 0
\(687\) 0.500466 + 0.866833i 0.0190940 + 0.0330717i
\(688\) 14.7038 25.4677i 0.560577 0.970948i
\(689\) −5.22221 1.29512i −0.198950 0.0493403i
\(690\) 1.15476 + 2.00010i 0.0439608 + 0.0761424i
\(691\) −19.1413 −0.728168 −0.364084 0.931366i \(-0.618618\pi\)
−0.364084 + 0.931366i \(0.618618\pi\)
\(692\) 16.0487 + 27.7972i 0.610080 + 1.05669i
\(693\) 0 0
\(694\) −38.9632 −1.47902
\(695\) 1.89109 + 3.27547i 0.0717333 + 0.124246i
\(696\) 15.5893 0.590909
\(697\) 12.2114 + 21.1508i 0.462540 + 0.801143i
\(698\) −19.5035 33.7811i −0.738219 1.27863i
\(699\) −0.571352 0.989611i −0.0216105 0.0374305i
\(700\) 0 0
\(701\) −27.2956 −1.03094 −0.515471 0.856907i \(-0.672383\pi\)
−0.515471 + 0.856907i \(0.672383\pi\)
\(702\) −24.9038 + 25.8532i −0.939935 + 0.975765i
\(703\) −30.2840 52.4535i −1.14218 1.97832i
\(704\) −10.8979 + 18.8756i −0.410729 + 0.711403i
\(705\) −2.31778 −0.0872927
\(706\) −4.67342 + 8.09460i −0.175886 + 0.304644i
\(707\) 0 0
\(708\) −0.924935 + 1.60203i −0.0347612 + 0.0602081i
\(709\) −3.08583 5.34481i −0.115891 0.200729i 0.802245 0.596995i \(-0.203639\pi\)
−0.918135 + 0.396267i \(0.870306\pi\)
\(710\) −3.94443 6.83195i −0.148032 0.256399i
\(711\) −10.8755 −0.407865
\(712\) 57.9625 2.17224
\(713\) −3.64395 6.31152i −0.136467 0.236368i
\(714\) 0 0
\(715\) 2.90690 + 0.720919i 0.108712 + 0.0269608i
\(716\) 30.4471 52.7360i 1.13786 1.97084i
\(717\) −8.47011 + 14.6707i −0.316322 + 0.547886i
\(718\) 25.6994 44.5127i 0.959094 1.66120i
\(719\) −1.36066 2.35674i −0.0507442 0.0878915i 0.839538 0.543302i \(-0.182826\pi\)
−0.890282 + 0.455410i \(0.849493\pi\)
\(720\) −2.90549 −0.108281
\(721\) 0 0
\(722\) −25.0129 + 43.3236i −0.930883 + 1.61234i
\(723\) −5.01537 + 8.68687i −0.186524 + 0.323068i
\(724\) −26.1256 −0.970949
\(725\) 10.8443 18.7829i 0.402749 0.697581i
\(726\) −9.31965 −0.345885
\(727\) −9.47153 −0.351280 −0.175640 0.984455i \(-0.556199\pi\)
−0.175640 + 0.984455i \(0.556199\pi\)
\(728\) 0 0
\(729\) −0.987863 −0.0365875
\(730\) 9.90027 0.366426
\(731\) −8.18976 + 14.1851i −0.302909 + 0.524654i
\(732\) −3.37287 −0.124665
\(733\) −1.74853 + 3.02855i −0.0645836 + 0.111862i −0.896509 0.443025i \(-0.853905\pi\)
0.831926 + 0.554887i \(0.187239\pi\)
\(734\) 17.9236 31.0446i 0.661573 1.14588i
\(735\) 0 0
\(736\) 2.98243 0.109934
\(737\) −6.80013 11.7782i −0.250486 0.433855i
\(738\) 37.0755 64.2166i 1.36477 2.36385i
\(739\) −16.0151 + 27.7390i −0.589126 + 1.02040i 0.405221 + 0.914219i \(0.367195\pi\)
−0.994347 + 0.106178i \(0.966139\pi\)
\(740\) 6.43750 11.1501i 0.236647 0.409885i
\(741\) −11.8575 + 12.3096i −0.435598 + 0.452203i
\(742\) 0 0
\(743\) −17.4593 30.2404i −0.640519 1.10941i −0.985317 0.170734i \(-0.945386\pi\)
0.344798 0.938677i \(-0.387947\pi\)
\(744\) −6.93343 −0.254192
\(745\) 5.43341 0.199065
\(746\) −15.7194 27.2268i −0.575527 0.996842i
\(747\) 1.71744 + 2.97469i 0.0628377 + 0.108838i
\(748\) −9.27547 + 16.0656i −0.339145 + 0.587416i
\(749\) 0 0
\(750\) 3.09335 5.35785i 0.112953 0.195641i
\(751\) 26.9972 0.985143 0.492571 0.870272i \(-0.336057\pi\)
0.492571 + 0.870272i \(0.336057\pi\)
\(752\) 15.7495 27.2790i 0.574327 0.994763i
\(753\) −5.99233 10.3790i −0.218373 0.378233i
\(754\) −37.8013 9.37483i −1.37664 0.341411i
\(755\) −3.61700 −0.131636
\(756\) 0 0
\(757\) 26.2950 + 45.5442i 0.955707 + 1.65533i 0.732742 + 0.680507i \(0.238240\pi\)
0.222965 + 0.974826i \(0.428426\pi\)
\(758\) 32.6337 + 56.5231i 1.18531 + 2.05301i
\(759\) −3.38106 5.85616i −0.122725 0.212565i
\(760\) −10.0067 −0.362980
\(761\) −6.96431 12.0625i −0.252456 0.437267i 0.711745 0.702437i \(-0.247905\pi\)
−0.964201 + 0.265171i \(0.914572\pi\)
\(762\) 16.5315 0.598874
\(763\) 0 0
\(764\) 36.6961 + 63.5596i 1.32762 + 2.29950i
\(765\) 1.61830 0.0585099
\(766\) 3.53606 + 6.12463i 0.127763 + 0.221292i
\(767\) 1.56835 1.62813i 0.0566297 0.0587885i
\(768\) 11.7387 20.3320i 0.423583 0.733668i
\(769\) −6.89545 11.9433i −0.248656 0.430685i 0.714497 0.699639i \(-0.246656\pi\)
−0.963153 + 0.268953i \(0.913322\pi\)
\(770\) 0 0
\(771\) 11.0174 19.0827i 0.396781 0.687246i
\(772\) 15.9993 27.7115i 0.575826 0.997360i
\(773\) 50.4870 1.81589 0.907946 0.419087i \(-0.137650\pi\)
0.907946 + 0.419087i \(0.137650\pi\)
\(774\) 49.7304 1.78752
\(775\) −4.82310 + 8.35385i −0.173251 + 0.300079i
\(776\) −23.9337 + 41.4544i −0.859170 + 1.48813i
\(777\) 0 0
\(778\) 20.3092 + 35.1766i 0.728120 + 1.26114i
\(779\) 39.4277 68.2908i 1.41265 2.44677i
\(780\) −3.52637 0.874550i −0.126264 0.0313139i
\(781\) 11.5491 + 20.0035i 0.413258 + 0.715783i
\(782\) 17.4818 0.625150
\(783\) 9.09053 + 15.7453i 0.324869 +